id	sid	tid	token	lemma	pos
ejpam-1371	1	1	3_xxx_das.dvi	3_xxx_das.dvi	NUM
ejpam-1371	1	2	european	european	PROPN
ejpam-1371	1	3	journal	journal	PROPN
ejpam-1371	1	4	of	of	ADP
ejpam-1371	1	5	pure	pure	ADJ
ejpam-1371	1	6	and	and	CCONJ
ejpam-1371	1	7	applied	apply	VERB
ejpam-1371	1	8	mathematics	mathematic	NOUN
ejpam-1371	1	9	vol	vol	NOUN
ejpam-1371	1	10	.	.	PROPN
ejpam-1371	1	11	4	4	NUM
ejpam-1371	1	12	,	,	PUNCT
ejpam-1371	1	13	no	no	INTJ
ejpam-1371	1	14	.	.	NOUN
ejpam-1371	1	15	4	4	NUM
ejpam-1371	1	16	,	,	PUNCT
ejpam-1371	1	17	2011	2011	NUM
ejpam-1371	1	18	,	,	PUNCT
ejpam-1371	1	19	340	340	NUM
ejpam-1371	1	20	-	-	SYM
ejpam-1371	1	21	360	360	NUM
ejpam-1371	1	22	issn	issn	PROPN
ejpam-1371	1	23	1307	1307	NUM
ejpam-1371	1	24	-	-	SYM
ejpam-1371	1	25	5543	5543	NUM
ejpam-1371	1	26	–	–	PUNCT
ejpam-1371	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1371	1	28	an	an	DET
ejpam-1371	1	29	iterative	iterative	NOUN
ejpam-1371	1	30	method	method	NOUN
ejpam-1371	1	31	for	for	ADP
ejpam-1371	1	32	(	(	PUNCT
ejpam-1371	1	33	agddv	agddv	NOUN
ejpam-1371	1	34	i	i	PRON
ejpam-1371	1	35	p	p	NOUN
ejpam-1371	1	36	)	)	PUNCT
ejpam-1371	1	37	in	in	ADP
ejpam-1371	1	38	hilbert	hilbert	NOUN
ejpam-1371	1	39	space	space	NOUN
ejpam-1371	1	40	and	and	CCONJ
ejpam-1371	1	41	the	the	DET
ejpam-1371	1	42	homology	homology	NOUN
ejpam-1371	1	43	theory	theory	NOUN
ejpam-1371	1	44	to	to	PART
ejpam-1371	1	45	study	study	VERB
ejpam-1371	1	46	the	the	DET
ejpam-1371	1	47	(	(	PUNCT
ejpam-1371	1	48	gddc	gddc	NOUN
ejpam-1371	1	49	pn	pn	PROPN
ejpam-1371	1	50	)	)	PUNCT
ejpam-1371	1	51	in	in	ADP
ejpam-1371	1	52	riemannian	riemannian	ADJ
ejpam-1371	1	53	n	n	CCONJ
ejpam-1371	1	54	-	-	PUNCT
ejpam-1371	1	55	manifolds	manifold	NOUN
ejpam-1371	1	56	in	in	ADP
ejpam-1371	1	57	the	the	DET
ejpam-1371	1	58	presence	presence	NOUN
ejpam-1371	1	59	of	of	ADP
ejpam-1371	1	60	fixed	fix	VERB
ejpam-1371	1	61	point	point	NOUN
ejpam-1371	1	62	inclusion	inclusion	NOUN
ejpam-1371	1	63	prasanta	prasanta	NOUN
ejpam-1371	1	64	kumar	kumar	PROPN
ejpam-1371	1	65	das	das	PROPN
ejpam-1371	1	66	school	school	NOUN
ejpam-1371	1	67	of	of	ADP
ejpam-1371	1	68	applied	apply	VERB
ejpam-1371	1	69	science	science	NOUN
ejpam-1371	1	70	(	(	PUNCT
ejpam-1371	1	71	mathematics	mathematics	PROPN
ejpam-1371	1	72	)	)	PUNCT
ejpam-1371	1	73	,	,	PUNCT
ejpam-1371	1	74	kiit	kiit	PROPN
ejpam-1371	1	75	university	university	PROPN
ejpam-1371	1	76	,	,	PUNCT
ejpam-1371	1	77	bhubaneswar	bhubaneswar	NOUN
ejpam-1371	1	78	,	,	PUNCT
ejpam-1371	1	79	orissa	orissa	PROPN
ejpam-1371	1	80	,	,	PUNCT
ejpam-1371	1	81	721024	721024	NUM
ejpam-1371	1	82	,	,	PUNCT
ejpam-1371	1	83	india	india	PROPN
ejpam-1371	1	84	abstract	abstract	NOUN
ejpam-1371	1	85	.	.	PUNCT
ejpam-1371	2	1	the	the	DET
ejpam-1371	2	2	main	main	ADJ
ejpam-1371	2	3	purpose	purpose	NOUN
ejpam-1371	2	4	of	of	ADP
ejpam-1371	2	5	this	this	DET
ejpam-1371	2	6	paper	paper	NOUN
ejpam-1371	2	7	is	be	AUX
ejpam-1371	2	8	to	to	PART
ejpam-1371	2	9	study	study	VERB
ejpam-1371	2	10	the	the	DET
ejpam-1371	2	11	convergence	convergence	NOUN
ejpam-1371	2	12	of	of	ADP
ejpam-1371	2	13	variable	variable	ADJ
ejpam-1371	2	14	step	step	NOUN
ejpam-1371	2	15	iterative	iterative	NOUN
ejpam-1371	2	16	methods	method	NOUN
ejpam-1371	2	17	for	for	ADP
ejpam-1371	2	18	the	the	DET
ejpam-1371	2	19	defined	define	VERB
ejpam-1371	2	20	problem	problem	NOUN
ejpam-1371	2	21	absolutely	absolutely	ADV
ejpam-1371	2	22	generalized	generalize	VERB
ejpam-1371	2	23	dominated	dominate	VERB
ejpam-1371	2	24	differential	differential	ADJ
ejpam-1371	2	25	variational	variational	ADJ
ejpam-1371	2	26	inequality	inequality	NOUN
ejpam-1371	2	27	problems	problem	NOUN
ejpam-1371	2	28	(	(	PUNCT
ejpam-1371	2	29	agddv	agddv	NOUN
ejpam-1371	2	30	i	i	PRON
ejpam-1371	2	31	p	p	NOUN
ejpam-1371	2	32	)	)	PUNCT
ejpam-1371	2	33	in	in	ADP
ejpam-1371	2	34	hilbert	hilbert	PROPN
ejpam-1371	2	35	spaces	space	NOUN
ejpam-1371	2	36	.	.	PUNCT
ejpam-1371	3	1	the	the	DET
ejpam-1371	3	2	iterative	iterative	NOUN
ejpam-1371	3	3	process	process	NOUN
ejpam-1371	3	4	considered	consider	VERB
ejpam-1371	3	5	in	in	ADP
ejpam-1371	3	6	the	the	DET
ejpam-1371	3	7	paper	paper	NOUN
ejpam-1371	3	8	admit	admit	VERB
ejpam-1371	3	9	the	the	DET
ejpam-1371	3	10	presence	presence	NOUN
ejpam-1371	3	11	of	of	ADP
ejpam-1371	3	12	variable	variable	ADJ
ejpam-1371	3	13	iteration	iteration	NOUN
ejpam-1371	3	14	parameters	parameter	NOUN
ejpam-1371	3	15	,	,	PUNCT
ejpam-1371	3	16	which	which	PRON
ejpam-1371	3	17	can	can	AUX
ejpam-1371	3	18	be	be	AUX
ejpam-1371	3	19	useful	useful	ADJ
ejpam-1371	3	20	in	in	ADP
ejpam-1371	3	21	numerical	numerical	ADJ
ejpam-1371	3	22	implementation	implementation	NOUN
ejpam-1371	3	23	to	to	PART
ejpam-1371	3	24	find	find	VERB
ejpam-1371	3	25	solution	solution	NOUN
ejpam-1371	3	26	of	of	ADP
ejpam-1371	3	27	the	the	DET
ejpam-1371	3	28	problem	problem	NOUN
ejpam-1371	3	29	(	(	PUNCT
ejpam-1371	3	30	agddv	agddv	NOUN
ejpam-1371	3	31	i	i	PRON
ejpam-1371	3	32	p	p	NOUN
ejpam-1371	3	33	)	)	PUNCT
ejpam-1371	3	34	.	.	PUNCT
ejpam-1371	4	1	finally	finally	ADV
ejpam-1371	4	2	,	,	PUNCT
ejpam-1371	4	3	we	we	PRON
ejpam-1371	4	4	study	study	VERB
ejpam-1371	4	5	the	the	DET
ejpam-1371	4	6	existence	existence	NOUN
ejpam-1371	4	7	theorems	theorem	NOUN
ejpam-1371	4	8	of	of	ADP
ejpam-1371	4	9	the	the	DET
ejpam-1371	4	10	problems	problem	NOUN
ejpam-1371	4	11	(	(	PUNCT
ejpam-1371	4	12	gddv	gddv	NOUN
ejpam-1371	4	13	i	i	PRON
ejpam-1371	4	14	pn	pn	PROPN
ejpam-1371	4	15	)	)	PUNCT
ejpam-1371	4	16	and	and	CCONJ
ejpam-1371	4	17	(	(	PUNCT
ejpam-1371	4	18	gddcpn	gddcpn	NOUN
ejpam-1371	4	19	)	)	PUNCT
ejpam-1371	4	20	in	in	ADP
ejpam-1371	4	21	riemannian	riemannian	ADJ
ejpam-1371	4	22	n	n	CCONJ
ejpam-1371	4	23	-	-	PUNCT
ejpam-1371	4	24	manifolds	manifold	NOUN
ejpam-1371	4	25	modelled	model	VERB
ejpam-1371	4	26	on	on	ADP
ejpam-1371	4	27	the	the	DET
ejpam-1371	4	28	hilbert	hilbert	NOUN
ejpam-1371	4	29	space	space	NOUN
ejpam-1371	4	30	in	in	ADP
ejpam-1371	4	31	the	the	DET
ejpam-1371	4	32	presence	presence	NOUN
ejpam-1371	4	33	of	of	ADP
ejpam-1371	4	34	coincidence	coincidence	NOUN
ejpam-1371	4	35	index	index	NOUN
ejpam-1371	4	36	,	,	PUNCT
ejpam-1371	4	37	fixed	fix	VERB
ejpam-1371	4	38	point	point	NOUN
ejpam-1371	4	39	theorem	theorem	NOUN
ejpam-1371	4	40	of	of	ADP
ejpam-1371	4	41	homology	homology	NOUN
ejpam-1371	4	42	theory	theory	NOUN
ejpam-1371	4	43	and	and	CCONJ
ejpam-1371	4	44	one	one	NUM
ejpam-1371	4	45	-	-	PUNCT
ejpam-1371	4	46	point	point	NOUN
ejpam-1371	4	47	compactification	compactification	NOUN
ejpam-1371	4	48	of	of	ADP
ejpam-1371	4	49	topology	topology	NOUN
ejpam-1371	4	50	theory	theory	NOUN
ejpam-1371	4	51	.	.	PUNCT
ejpam-1371	5	1	2000	2000	NUM
ejpam-1371	5	2	mathematics	mathematic	NOUN
ejpam-1371	5	3	subject	subject	NOUN
ejpam-1371	5	4	classifications	classification	NOUN
ejpam-1371	5	5	:	:	PUNCT
ejpam-1371	5	6	65k10	65k10	NUM
ejpam-1371	5	7	;	;	PUNCT
ejpam-1371	5	8	90c33	90c33	NUM
ejpam-1371	5	9	;	;	PUNCT
ejpam-1371	5	10	47j30	47j30	NUM
ejpam-1371	5	11	key	key	ADJ
ejpam-1371	5	12	words	word	NOUN
ejpam-1371	5	13	and	and	CCONJ
ejpam-1371	5	14	phrases	phrase	NOUN
ejpam-1371	5	15	:	:	PUNCT
ejpam-1371	5	16	quasidomonotone	quasidomonotone	NOUN
ejpam-1371	5	17	and	and	CCONJ
ejpam-1371	5	18	potential	potential	ADJ
ejpam-1371	5	19	operator	operator	NOUN
ejpam-1371	5	20	,	,	PUNCT
ejpam-1371	5	21	weakly	weakly	ADJ
ejpam-1371	5	22	η	η	NOUN
ejpam-1371	5	23	-	-	ADJ
ejpam-1371	5	24	invex	invex	ADJ
ejpam-1371	5	25	set	set	NOUN
ejpam-1371	5	26	,	,	PUNCT
ejpam-1371	5	27	t	t	PROPN
ejpam-1371	5	28	-η	-η	ADJ
ejpam-1371	5	29	-	-	PUNCT
ejpam-1371	5	30	invex	invex	NOUN
ejpam-1371	5	31	function	function	NOUN
ejpam-1371	5	32	,	,	PUNCT
ejpam-1371	5	33	hilbert	hilbert	NOUN
ejpam-1371	5	34	spaces	space	NOUN
ejpam-1371	5	35	,	,	PUNCT
ejpam-1371	5	36	banach	banach	NOUN
ejpam-1371	5	37	space	space	NOUN
ejpam-1371	5	38	,	,	PUNCT
ejpam-1371	5	39	iterative	iterative	NOUN
ejpam-1371	5	40	sequence	sequence	NOUN
ejpam-1371	5	41	,	,	PUNCT
ejpam-1371	5	42	lipschitz	lipschitz	NOUN
ejpam-1371	5	43	function	function	NOUN
ejpam-1371	5	44	,	,	PUNCT
ejpam-1371	5	45	generalized	generalize	VERB
ejpam-1371	5	46	dominated	dominate	VERB
ejpam-1371	5	47	differential	differential	ADJ
ejpam-1371	5	48	variational	variational	ADJ
ejpam-1371	5	49	inequality	inequality	NOUN
ejpam-1371	5	50	problems	problem	NOUN
ejpam-1371	5	51	,	,	PUNCT
ejpam-1371	5	52	absolutely	absolutely	ADV
ejpam-1371	5	53	generalized	generalized	ADJ
ejpam-1371	5	54	dominated	dominate	VERB
ejpam-1371	5	55	differential	differential	ADJ
ejpam-1371	5	56	variational	variational	ADJ
ejpam-1371	5	57	inequality	inequality	NOUN
ejpam-1371	5	58	problems	problem	NOUN
ejpam-1371	5	59	,	,	PUNCT
ejpam-1371	5	60	maximal	maximal	ADJ
ejpam-1371	5	61	fixed	fix	VERB
ejpam-1371	5	62	point	point	NOUN
ejpam-1371	5	63	open	open	ADJ
ejpam-1371	5	64	set	set	NOUN
ejpam-1371	5	65	,	,	PUNCT
ejpam-1371	5	66	one	one	NUM
ejpam-1371	5	67	-	-	PUNCT
ejpam-1371	5	68	point	point	NOUN
ejpam-1371	5	69	compactification	compactification	NOUN
ejpam-1371	5	70	,	,	PUNCT
ejpam-1371	5	71	n	n	CCONJ
ejpam-1371	5	72	-	-	PUNCT
ejpam-1371	5	73	manifold	manifold	ADJ
ejpam-1371	5	74	,	,	PUNCT
ejpam-1371	5	75	riemannian	riemannian	ADJ
ejpam-1371	5	76	n	n	CCONJ
ejpam-1371	5	77	-	-	PUNCT
ejpam-1371	5	78	manifolds	manifold	NOUN
ejpam-1371	5	79	,	,	PUNCT
ejpam-1371	5	80	η	η	NOUN
ejpam-1371	5	81	-	-	ADJ
ejpam-1371	5	82	closed	closed	ADJ
ejpam-1371	5	83	,	,	PUNCT
ejpam-1371	5	84	η	η	NOUN
ejpam-1371	5	85	-	-	ADJ
ejpam-1371	5	86	invex	invex	ADJ
ejpam-1371	5	87	set	set	NOUN
ejpam-1371	5	88	,	,	PUNCT
ejpam-1371	5	89	weakly	weakly	ADJ
ejpam-1371	5	90	η	η	NOUN
ejpam-1371	5	91	-	-	ADJ
ejpam-1371	5	92	invex	invex	ADJ
ejpam-1371	5	93	set	set	PROPN
ejpam-1371	5	94	,	,	PUNCT
ejpam-1371	5	95	η	η	NOUN
ejpam-1371	5	96	-	-	ADJ
ejpam-1371	5	97	invex	invex	ADJ
ejpam-1371	5	98	cone	cone	NOUN
ejpam-1371	5	99	,	,	PUNCT
ejpam-1371	5	100	complete	complete	ADJ
ejpam-1371	5	101	w.r.t	w.r.t	NOUN
ejpam-1371	5	102	.	.	PUNCT
ejpam-1371	6	1	η	η	PROPN
ejpam-1371	6	2	,	,	PUNCT
ejpam-1371	6	3	tangent	tangent	ADJ
ejpam-1371	6	4	bundle	bundle	PROPN
ejpam-1371	6	5	,	,	PUNCT
ejpam-1371	6	6	cotangent	cotangent	NOUN
ejpam-1371	6	7	bundle	bundle	NOUN
ejpam-1371	6	8	,	,	PUNCT
ejpam-1371	6	9	coincidence	coincidence	NOUN
ejpam-1371	6	10	index	index	NOUN
ejpam-1371	6	11	set	set	NOUN
ejpam-1371	6	12	,	,	PUNCT
ejpam-1371	6	13	and	and	CCONJ
ejpam-1371	6	14	fixed	fix	VERB
ejpam-1371	6	15	-	-	PUNCT
ejpam-1371	6	16	point	point	NOUN
ejpam-1371	6	17	index	index	NOUN
ejpam-1371	6	18	.	.	PUNCT
ejpam-1371	7	1	1	1	X
ejpam-1371	7	2	.	.	X
ejpam-1371	7	3	introduction	introduction	NOUN
ejpam-1371	7	4	in	in	ADP
ejpam-1371	7	5	the	the	DET
ejpam-1371	7	6	recent	recent	ADJ
ejpam-1371	7	7	decades	decade	NOUN
ejpam-1371	7	8	,	,	PUNCT
ejpam-1371	7	9	there	there	PRON
ejpam-1371	7	10	has	have	AUX
ejpam-1371	7	11	been	be	AUX
ejpam-1371	7	12	a	a	DET
ejpam-1371	7	13	great	great	ADJ
ejpam-1371	7	14	deal	deal	NOUN
ejpam-1371	7	15	of	of	ADP
ejpam-1371	7	16	development	development	NOUN
ejpam-1371	7	17	in	in	ADP
ejpam-1371	7	18	the	the	DET
ejpam-1371	7	19	theory	theory	NOUN
ejpam-1371	7	20	of	of	ADP
ejpam-1371	7	21	optimization	optimization	NOUN
ejpam-1371	7	22	techniques	technique	NOUN
ejpam-1371	7	23	.	.	PUNCT
ejpam-1371	8	1	the	the	DET
ejpam-1371	8	2	study	study	NOUN
ejpam-1371	8	3	of	of	ADP
ejpam-1371	8	4	variational	variational	ADJ
ejpam-1371	8	5	inequalities	inequality	NOUN
ejpam-1371	8	6	is	be	AUX
ejpam-1371	8	7	a	a	DET
ejpam-1371	8	8	part	part	NOUN
ejpam-1371	8	9	of	of	ADP
ejpam-1371	8	10	development	development	NOUN
ejpam-1371	8	11	in	in	ADP
ejpam-1371	8	12	the	the	DET
ejpam-1371	8	13	theory	theory	NOUN
ejpam-1371	8	14	of	of	ADP
ejpam-1371	8	15	optimization	optimization	NOUN
ejpam-1371	8	16	theory	theory	NOUN
ejpam-1371	8	17	because	because	SCONJ
ejpam-1371	8	18	optimization	optimization	NOUN
ejpam-1371	8	19	problems	problem	NOUN
ejpam-1371	8	20	can	can	AUX
ejpam-1371	8	21	often	often	ADV
ejpam-1371	8	22	be	be	AUX
ejpam-1371	8	23	reduced	reduce	VERB
ejpam-1371	8	24	to	to	ADP
ejpam-1371	8	25	the	the	DET
ejpam-1371	8	26	solution	solution	NOUN
ejpam-1371	8	27	of	of	ADP
ejpam-1371	8	28	variational	variational	ADJ
ejpam-1371	8	29	inequalities	inequality	NOUN
ejpam-1371	8	30	.	.	PUNCT
ejpam-1371	9	1	variational	variational	ADJ
ejpam-1371	9	2	inequality	inequality	NOUN
ejpam-1371	9	3	theory	theory	NOUN
ejpam-1371	9	4	has	have	AUX
ejpam-1371	9	5	emerged	emerge	VERB
ejpam-1371	9	6	as	as	ADP
ejpam-1371	9	7	a	a	DET
ejpam-1371	9	8	powerful	powerful	ADJ
ejpam-1371	9	9	tool	tool	NOUN
ejpam-1371	9	10	for	for	ADP
ejpam-1371	9	11	wide	wide	ADJ
ejpam-1371	9	12	class	class	NOUN
ejpam-1371	9	13	of	of	ADP
ejpam-1371	9	14	unrelated	unrelated	ADJ
ejpam-1371	9	15	problems	problem	NOUN
ejpam-1371	9	16	arising	arise	VERB
ejpam-1371	9	17	in	in	ADP
ejpam-1371	9	18	various	various	ADJ
ejpam-1371	9	19	branches	branch	NOUN
ejpam-1371	9	20	of	of	ADP
ejpam-1371	9	21	physical	physical	ADJ
ejpam-1371	9	22	,	,	PUNCT
ejpam-1371	9	23	engineering	engineering	NOUN
ejpam-1371	9	24	,	,	PUNCT
ejpam-1371	9	25	pure	pure	ADJ
ejpam-1371	9	26	and	and	CCONJ
ejpam-1371	9	27	applied	applied	ADJ
ejpam-1371	9	28	sciences	science	NOUN
ejpam-1371	9	29	in	in	ADP
ejpam-1371	9	30	a	a	DET
ejpam-1371	9	31	unified	unified	ADJ
ejpam-1371	9	32	and	and	CCONJ
ejpam-1371	9	33	general	general	ADJ
ejpam-1371	9	34	frame	frame	NOUN
ejpam-1371	9	35	work	work	NOUN
ejpam-1371	9	36	(	(	PUNCT
ejpam-1371	9	37	see	see	VERB
ejpam-1371	9	38	for	for	ADP
ejpam-1371	9	39	example	example	NOUN
ejpam-1371	9	40	[	[	X
ejpam-1371	9	41	14	14	NUM
ejpam-1371	9	42	]	]	PUNCT
ejpam-1371	9	43	,	,	PUNCT
ejpam-1371	9	44	[	[	X
ejpam-1371	9	45	15	15	NUM
ejpam-1371	9	46	]	]	NUM
ejpam-1371	9	47	)	)	PUNCT
ejpam-1371	9	48	.	.	PUNCT
ejpam-1371	10	1	in	in	ADP
ejpam-1371	10	2	this	this	DET
ejpam-1371	10	3	development	development	NOUN
ejpam-1371	10	4	,	,	PUNCT
ejpam-1371	10	5	computer	computer	NOUN
ejpam-1371	10	6	science	science	NOUN
ejpam-1371	10	7	has	have	AUX
ejpam-1371	10	8	played	play	VERB
ejpam-1371	10	9	a	a	DET
ejpam-1371	10	10	vital	vital	ADJ
ejpam-1371	10	11	role	role	NOUN
ejpam-1371	10	12	for	for	ADP
ejpam-1371	10	13	making	make	VERB
ejpam-1371	10	14	it	it	PRON
ejpam-1371	10	15	possible	possible	ADJ
ejpam-1371	10	16	to	to	PART
ejpam-1371	10	17	implement	implement	VERB
ejpam-1371	10	18	such	such	ADJ
ejpam-1371	10	19	techniques	technique	NOUN
ejpam-1371	10	20	for	for	ADP
ejpam-1371	10	21	everyday	everyday	ADJ
ejpam-1371	10	22	use	use	NOUN
ejpam-1371	10	23	as	as	ADV
ejpam-1371	10	24	well	well	ADV
ejpam-1371	10	25	as	as	ADP
ejpam-1371	10	26	stimulating	stimulate	VERB
ejpam-1371	10	27	new	new	ADJ
ejpam-1371	10	28	effort	effort	NOUN
ejpam-1371	10	29	for	for	ADP
ejpam-1371	10	30	finding	find	VERB
ejpam-1371	10	31	solutions	solution	NOUN
ejpam-1371	10	32	of	of	ADP
ejpam-1371	10	33	much	much	ADV
ejpam-1371	10	34	more	more	ADV
ejpam-1371	10	35	complicated	complicated	ADJ
ejpam-1371	10	36	problems	problem	NOUN
ejpam-1371	10	37	.	.	PUNCT
ejpam-1371	11	1	several	several	ADJ
ejpam-1371	11	2	authors	author	NOUN
ejpam-1371	11	3	have	have	AUX
ejpam-1371	11	4	proved	prove	VERB
ejpam-1371	11	5	many	many	ADJ
ejpam-1371	11	6	fascinating	fascinating	ADJ
ejpam-1371	11	7	results	result	NOUN
ejpam-1371	11	8	on	on	ADP
ejpam-1371	11	9	email	email	NOUN
ejpam-1371	11	10	address	address	NOUN
ejpam-1371	11	11	:	:	PUNCT
ejpam-1371	12	1	dasprasantkumar	dasprasantkumar	PROPN
ejpam-1371	12	2	�	�	PROPN
ejpam-1371	12	3	yahoo	yahoo	PROPN
ejpam-1371	12	4	.	.	PUNCT
ejpam-1371	12	5	o.in	o.in	PROPN
ejpam-1371	12	6	,	,	PUNCT
ejpam-1371	12	7	(	(	PUNCT
ejpam-1371	12	8	p.	p.	NOUN
ejpam-1371	12	9	das	das	PROPN
ejpam-1371	12	10	)	)	PUNCT
ejpam-1371	12	11	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1371	12	12	340	340	NUM
ejpam-1371	13	1	c	c	NOUN
ejpam-1371	13	2	©	©	NOUN
ejpam-1371	13	3	2011	2011	NUM
ejpam-1371	13	4	ejpam	ejpam	VERB
ejpam-1371	13	5	all	all	DET
ejpam-1371	13	6	rights	right	NOUN
ejpam-1371	13	7	reserved	reserve	VERB
ejpam-1371	13	8	.	.	PUNCT
ejpam-1371	14	1	p.	p.	NOUN
ejpam-1371	14	2	das	das	PROPN
ejpam-1371	14	3	/	/	SYM
ejpam-1371	14	4	eur	eur	PROPN
ejpam-1371	14	5	.	.	PUNCT
ejpam-1371	15	1	j.	j.	PROPN
ejpam-1371	15	2	pure	pure	PROPN
ejpam-1371	15	3	appl	appl	PROPN
ejpam-1371	15	4	.	.	PROPN
ejpam-1371	15	5	math	math	PROPN
ejpam-1371	15	6	,	,	PUNCT
ejpam-1371	15	7	4	4	NUM
ejpam-1371	15	8	(	(	PUNCT
ejpam-1371	15	9	2011	2011	NUM
ejpam-1371	15	10	)	)	PUNCT
ejpam-1371	15	11	,	,	PUNCT
ejpam-1371	15	12	340	340	NUM
ejpam-1371	15	13	-	-	SYM
ejpam-1371	15	14	360	360	NUM
ejpam-1371	15	15	341	341	NUM
ejpam-1371	15	16	variational	variational	ADJ
ejpam-1371	15	17	inequality	inequality	NOUN
ejpam-1371	15	18	problems	problem	NOUN
ejpam-1371	15	19	.	.	PUNCT
ejpam-1371	16	1	we	we	PRON
ejpam-1371	16	2	list	list	VERB
ejpam-1371	16	3	some	some	PRON
ejpam-1371	16	4	of	of	ADP
ejpam-1371	16	5	them	they	PRON
ejpam-1371	16	6	,	,	PUNCT
ejpam-1371	16	7	which	which	PRON
ejpam-1371	16	8	are	be	AUX
ejpam-1371	16	9	used	use	VERB
ejpam-1371	16	10	frequently	frequently	ADV
ejpam-1371	16	11	in	in	ADP
ejpam-1371	16	12	this	this	DET
ejpam-1371	16	13	paper	paper	NOUN
ejpam-1371	16	14	.	.	PUNCT
ejpam-1371	17	1	the	the	DET
ejpam-1371	17	2	existence	existence	NOUN
ejpam-1371	17	3	of	of	ADP
ejpam-1371	17	4	the	the	DET
ejpam-1371	17	5	solution	solution	NOUN
ejpam-1371	17	6	to	to	ADP
ejpam-1371	17	7	the	the	DET
ejpam-1371	17	8	problem	problem	NOUN
ejpam-1371	17	9	is	be	AUX
ejpam-1371	17	10	studied	study	VERB
ejpam-1371	17	11	by	by	ADP
ejpam-1371	17	12	many	many	ADJ
ejpam-1371	17	13	authors	author	NOUN
ejpam-1371	17	14	such	such	ADJ
ejpam-1371	17	15	as	as	ADP
ejpam-1371	17	16	,	,	PUNCT
ejpam-1371	17	17	j.l	j.l	PROPN
ejpam-1371	17	18	.	.	PROPN
ejpam-1371	17	19	lions	lion	NOUN
ejpam-1371	17	20	and	and	CCONJ
ejpam-1371	17	21	g.	g.	PROPN
ejpam-1371	17	22	stampacchia	stampacchia	PROPN
ejpam-1371	18	1	[	[	X
ejpam-1371	18	2	21	21	NUM
ejpam-1371	18	3	]	]	X
ejpam-1371	18	4	,	,	PUNCT
ejpam-1371	18	5	r.w	r.w	PROPN
ejpam-1371	18	6	.	.	PROPN
ejpam-1371	18	7	cottle	cottle	PROPN
ejpam-1371	18	8	,	,	PUNCT
ejpam-1371	18	9	f.	f.	PROPN
ejpam-1371	18	10	giannessi	giannessi	PROPN
ejpam-1371	18	11	and	and	CCONJ
ejpam-1371	18	12	j.l	j.l	PROPN
ejpam-1371	18	13	.	.	PROPN
ejpam-1371	18	14	lions	lion	NOUN
ejpam-1371	19	1	[	[	X
ejpam-1371	19	2	24	24	NUM
ejpam-1371	19	3	]	]	PUNCT
ejpam-1371	19	4	to	to	PART
ejpam-1371	19	5	name	name	VERB
ejpam-1371	19	6	only	only	ADV
ejpam-1371	19	7	a	a	DET
ejpam-1371	19	8	few	few	ADJ
ejpam-1371	19	9	.	.	PUNCT
ejpam-1371	20	1	the	the	DET
ejpam-1371	20	2	most	most	ADV
ejpam-1371	20	3	general	general	ADJ
ejpam-1371	20	4	and	and	CCONJ
ejpam-1371	20	5	popular	popular	ADJ
ejpam-1371	20	6	forms	form	NOUN
ejpam-1371	20	7	of	of	ADP
ejpam-1371	20	8	inequality	inequality	NOUN
ejpam-1371	20	9	with	with	ADP
ejpam-1371	20	10	very	very	ADV
ejpam-1371	20	11	reasonable	reasonable	ADJ
ejpam-1371	20	12	conditions	condition	NOUN
ejpam-1371	20	13	are	be	AUX
ejpam-1371	20	14	due	due	ADJ
ejpam-1371	20	15	to	to	ADP
ejpam-1371	20	16	f.	f.	PROPN
ejpam-1371	20	17	e.	e.	PROPN
ejpam-1371	20	18	browder	browder	PROPN
ejpam-1371	21	1	[	[	X
ejpam-1371	21	2	7	7	NUM
ejpam-1371	21	3	]	]	PUNCT
ejpam-1371	21	4	,	,	PUNCT
ejpam-1371	21	5	d.	d.	PROPN
ejpam-1371	21	6	kinderlehrer	kinderlehrer	PROPN
ejpam-1371	21	7	and	and	CCONJ
ejpam-1371	21	8	g.	g.	PROPN
ejpam-1371	21	9	stampacchia	stampacchia	PROPN
ejpam-1371	21	10	[	[	X
ejpam-1371	21	11	20	20	NUM
ejpam-1371	21	12	]	]	PUNCT
ejpam-1371	21	13	,	,	PUNCT
ejpam-1371	21	14	c.	c.	PROPN
ejpam-1371	21	15	bardaro	bardaro	PROPN
ejpam-1371	21	16	and	and	CCONJ
ejpam-1371	21	17	r.	r.	PROPN
ejpam-1371	21	18	ceppitelli	ceppitelli	PROPN
ejpam-1371	22	1	[	[	X
ejpam-1371	22	2	2	2	NUM
ejpam-1371	22	3	]	]	PUNCT
ejpam-1371	22	4	,	,	PUNCT
ejpam-1371	22	5	m.	m.	NOUN
ejpam-1371	22	6	chipot	chipot	NOUN
ejpam-1371	23	1	[	[	X
ejpam-1371	23	2	9	9	NUM
ejpam-1371	23	3	]	]	PUNCT
ejpam-1371	23	4	,	,	PUNCT
ejpam-1371	23	5	a.	a.	PROPN
ejpam-1371	23	6	behera	behera	PROPN
ejpam-1371	23	7	and	and	CCONJ
ejpam-1371	23	8	g.	g.	PROPN
ejpam-1371	23	9	k.	k.	PROPN
ejpam-1371	23	10	panda	panda	PROPN
ejpam-1371	24	1	[	[	X
ejpam-1371	24	2	4	4	NUM
ejpam-1371	24	3	,	,	PUNCT
ejpam-1371	24	4	6	6	NUM
ejpam-1371	24	5	]	]	PUNCT
ejpam-1371	24	6	.	.	PUNCT
ejpam-1371	25	1	in	in	ADP
ejpam-1371	25	2	1994	1994	NUM
ejpam-1371	25	3	,	,	PUNCT
ejpam-1371	25	4	a.	a.	NOUN
ejpam-1371	25	5	hassouni	hassouni	PROPN
ejpam-1371	25	6	and	and	CCONJ
ejpam-1371	25	7	a.	a.	NOUN
ejpam-1371	25	8	moudafi	moudafi	PROPN
ejpam-1371	26	1	[	[	X
ejpam-1371	26	2	17	17	NUM
ejpam-1371	26	3	]	]	PUNCT
ejpam-1371	26	4	introduced	introduce	VERB
ejpam-1371	26	5	and	and	CCONJ
ejpam-1371	26	6	studied	study	VERB
ejpam-1371	26	7	a	a	DET
ejpam-1371	26	8	class	class	NOUN
ejpam-1371	26	9	of	of	ADP
ejpam-1371	26	10	variational	variational	ADJ
ejpam-1371	26	11	inclusions	inclusion	NOUN
ejpam-1371	26	12	and	and	CCONJ
ejpam-1371	26	13	developed	develop	VERB
ejpam-1371	26	14	an	an	DET
ejpam-1371	26	15	iterative	iterative	NOUN
ejpam-1371	26	16	algorithm	algorithm	NOUN
ejpam-1371	26	17	for	for	ADP
ejpam-1371	26	18	the	the	DET
ejpam-1371	26	19	variational	variational	ADJ
ejpam-1371	26	20	inclusions	inclusion	NOUN
ejpam-1371	26	21	.	.	PUNCT
ejpam-1371	27	1	s.	s.	PROPN
ejpam-1371	27	2	adly	adly	PROPN
ejpam-1371	28	1	[	[	X
ejpam-1371	28	2	1	1	NUM
ejpam-1371	28	3	]	]	PUNCT
ejpam-1371	28	4	,	,	PUNCT
ejpam-1371	28	5	n.	n.	PROPN
ejpam-1371	28	6	j.	j.	PROPN
ejpam-1371	28	7	haung	haung	PROPN
ejpam-1371	29	1	[	[	X
ejpam-1371	29	2	18	18	NUM
ejpam-1371	29	3	]	]	PUNCT
ejpam-1371	29	4	,	,	PUNCT
ejpam-1371	30	1	x.	x.	NOUN
ejpam-1371	30	2	p.	p.	NOUN
ejpam-1371	30	3	ding	ding	NOUN
ejpam-1371	31	1	[	[	X
ejpam-1371	31	2	12	12	NUM
ejpam-1371	31	3	,	,	PUNCT
ejpam-1371	31	4	13	13	NUM
ejpam-1371	31	5	]	]	PUNCT
ejpam-1371	31	6	and	and	CCONJ
ejpam-1371	31	7	k.	k.	PROPN
ejpam-1371	31	8	r.	r.	PROPN
ejpam-1371	31	9	kazmi	kazmi	PROPN
ejpam-1371	32	1	[	[	X
ejpam-1371	32	2	19	19	NUM
ejpam-1371	32	3	]	]	PUNCT
ejpam-1371	32	4	,	,	PUNCT
ejpam-1371	32	5	have	have	AUX
ejpam-1371	32	6	obtained	obtain	VERB
ejpam-1371	32	7	some	some	DET
ejpam-1371	32	8	important	important	ADJ
ejpam-1371	32	9	extensions	extension	NOUN
ejpam-1371	32	10	of	of	ADP
ejpam-1371	32	11	the	the	DET
ejpam-1371	32	12	result	result	NOUN
ejpam-1371	32	13	[	[	X
ejpam-1371	32	14	17	17	NUM
ejpam-1371	32	15	]	]	PUNCT
ejpam-1371	32	16	in	in	ADP
ejpam-1371	32	17	hilbert	hilbert	PROPN
ejpam-1371	32	18	spaces	space	NOUN
ejpam-1371	32	19	.	.	PUNCT
ejpam-1371	33	1	the	the	DET
ejpam-1371	33	2	variational	variational	ADJ
ejpam-1371	33	3	inequality	inequality	NOUN
ejpam-1371	33	4	problem(v	problem(v	ADP
ejpam-1371	33	5	ip	ip	NOUN
ejpam-1371	33	6	)	)	PUNCT
ejpam-1371	33	7	is	be	AUX
ejpam-1371	33	8	defined	define	VERB
ejpam-1371	33	9	as	as	SCONJ
ejpam-1371	33	10	follows	follow	VERB
ejpam-1371	33	11	.	.	PUNCT
ejpam-1371	34	1	let	let	VERB
ejpam-1371	34	2	x	x	PRON
ejpam-1371	34	3	be	be	AUX
ejpam-1371	34	4	a	a	DET
ejpam-1371	34	5	reflexive	reflexive	ADJ
ejpam-1371	34	6	real	real	ADJ
ejpam-1371	34	7	banach	banach	NOUN
ejpam-1371	34	8	space	space	NOUN
ejpam-1371	34	9	with	with	ADP
ejpam-1371	34	10	its	its	PRON
ejpam-1371	34	11	dual	dual	ADJ
ejpam-1371	34	12	x	x	NUM
ejpam-1371	34	13	∗.	∗.	NUM
ejpam-1371	34	14	let	let	VERB
ejpam-1371	34	15	k	k	PRON
ejpam-1371	34	16	be	be	AUX
ejpam-1371	34	17	a	a	DET
ejpam-1371	34	18	nonempty	nonempty	ADJ
ejpam-1371	34	19	subset	subset	NOUN
ejpam-1371	34	20	of	of	ADP
ejpam-1371	34	21	x	x	X
ejpam-1371	34	22	.	.	PUNCT
ejpam-1371	35	1	let	let	VERB
ejpam-1371	35	2	t	t	NOUN
ejpam-1371	35	3	:	:	PUNCT
ejpam-1371	35	4	k	k	X
ejpam-1371	35	5	→	→	PUNCT
ejpam-1371	35	6	x	x	PROPN
ejpam-1371	35	7	∗	∗	NOUN
ejpam-1371	35	8	be	be	VERB
ejpam-1371	35	9	a	a	DET
ejpam-1371	35	10	nonlinear	nonlinear	ADJ
ejpam-1371	35	11	mapping	mapping	NOUN
ejpam-1371	35	12	.	.	PUNCT
ejpam-1371	36	1	let	let	VERB
ejpam-1371	36	2	〈	〈	PROPN
ejpam-1371	36	3	f	f	X
ejpam-1371	36	4	,	,	PUNCT
ejpam-1371	36	5	x	x	SYM
ejpam-1371	36	6	〉	〉	NOUN
ejpam-1371	36	7	denote	denote	VERB
ejpam-1371	36	8	the	the	DET
ejpam-1371	36	9	value	value	NOUN
ejpam-1371	36	10	of	of	ADP
ejpam-1371	36	11	f	f	PROPN
ejpam-1371	36	12	∈	∈	PROPN
ejpam-1371	36	13	x	x	PROPN
ejpam-1371	36	14	∗	∗	NOUN
ejpam-1371	36	15	at	at	ADP
ejpam-1371	36	16	x	x	PROPN
ejpam-1371	36	17	∈	∈	PROPN
ejpam-1371	36	18	k	k	X
ejpam-1371	36	19	.	.	PUNCT
ejpam-1371	37	1	then	then	ADV
ejpam-1371	37	2	,	,	PUNCT
ejpam-1371	37	3	the	the	DET
ejpam-1371	37	4	variational	variational	ADJ
ejpam-1371	37	5	inequality	inequality	NOUN
ejpam-1371	37	6	problem	problem	NOUN
ejpam-1371	37	7	is	be	AUX
ejpam-1371	37	8	to	to	PART
ejpam-1371	37	9	:	:	PUNCT
ejpam-1371	37	10	(	(	PUNCT
ejpam-1371	37	11	v	v	NOUN
ejpam-1371	37	12	ip	ip	NOUN
ejpam-1371	37	13	)	)	PUNCT
ejpam-1371	37	14	find	find	VERB
ejpam-1371	37	15	x0	x0	PROPN
ejpam-1371	37	16	∈	∈	PROPN
ejpam-1371	38	1	k	k	X
ejpam-1371	38	2	such	such	ADJ
ejpam-1371	38	3	that	that	SCONJ
ejpam-1371	38	4	〈	〈	PROPN
ejpam-1371	38	5	t	t	PROPN
ejpam-1371	38	6	(	(	PUNCT
ejpam-1371	38	7	x0	x0	PROPN
ejpam-1371	38	8	)	)	PUNCT
ejpam-1371	38	9	,	,	PUNCT
ejpam-1371	38	10	x	x	PUNCT
ejpam-1371	38	11	−	−	NOUN
ejpam-1371	38	12	x0	x0	PROPN
ejpam-1371	38	13	〉	〉	X
ejpam-1371	38	14	≥	≥	NUM
ejpam-1371	38	15	0	0	NUM
ejpam-1371	38	16	∀x	∀x	X
ejpam-1371	38	17	∈	∈	PROPN
ejpam-1371	38	18	k	k	X
ejpam-1371	38	19	.	.	PUNCT
ejpam-1371	39	1	the	the	DET
ejpam-1371	39	2	generalized	generalized	ADJ
ejpam-1371	39	3	variational	variational	ADJ
ejpam-1371	39	4	inequality	inequality	NOUN
ejpam-1371	39	5	problem	problem	NOUN
ejpam-1371	39	6	(	(	PUNCT
ejpam-1371	39	7	gv	gv	ADP
ejpam-1371	39	8	ip	ip	NOUN
ejpam-1371	39	9	)	)	PUNCT
ejpam-1371	39	10	and	and	CCONJ
ejpam-1371	39	11	generalized	generalized	ADJ
ejpam-1371	39	12	complementarity	complementarity	NOUN
ejpam-1371	39	13	problem	problem	NOUN
ejpam-1371	39	14	(	(	PUNCT
ejpam-1371	39	15	gc	gc	PROPN
ejpam-1371	39	16	p	p	X
ejpam-1371	39	17	)	)	PUNCT
ejpam-1371	39	18	are	be	AUX
ejpam-1371	39	19	defined	define	VERB
ejpam-1371	39	20	as	as	SCONJ
ejpam-1371	39	21	follows	follow	VERB
ejpam-1371	39	22	.	.	PUNCT
ejpam-1371	40	1	let	let	VERB
ejpam-1371	40	2	x	x	PRON
ejpam-1371	40	3	be	be	AUX
ejpam-1371	40	4	a	a	DET
ejpam-1371	40	5	reflexive	reflexive	ADJ
ejpam-1371	40	6	real	real	ADJ
ejpam-1371	40	7	banach	banach	NOUN
ejpam-1371	40	8	space	space	NOUN
ejpam-1371	40	9	with	with	ADP
ejpam-1371	40	10	its	its	PRON
ejpam-1371	40	11	dual	dual	ADJ
ejpam-1371	40	12	x	x	NOUN
ejpam-1371	40	13	∗	∗	NOUN
ejpam-1371	40	14	and	and	CCONJ
ejpam-1371	40	15	k	k	PROPN
ejpam-1371	40	16	be	be	VERB
ejpam-1371	40	17	any	any	DET
ejpam-1371	40	18	nonempty	nonempty	NOUN
ejpam-1371	40	19	subset	subset	NOUN
ejpam-1371	40	20	of	of	ADP
ejpam-1371	40	21	x	x	X
ejpam-1371	40	22	.	.	PUNCT
ejpam-1371	41	1	let	let	VERB
ejpam-1371	41	2	η	η	PROPN
ejpam-1371	41	3	:	:	PUNCT
ejpam-1371	41	4	k	k	PROPN
ejpam-1371	41	5	×	×	PROPN
ejpam-1371	41	6	k	k	PROPN
ejpam-1371	41	7	→	→	PUNCT
ejpam-1371	41	8	x	x	PUNCT
ejpam-1371	41	9	be	be	AUX
ejpam-1371	41	10	a	a	DET
ejpam-1371	41	11	vector	vector	NOUN
ejpam-1371	41	12	valued	value	VERB
ejpam-1371	41	13	continuous	continuous	ADJ
ejpam-1371	41	14	mapping	mapping	NOUN
ejpam-1371	41	15	.	.	PUNCT
ejpam-1371	42	1	let	let	VERB
ejpam-1371	42	2	t	t	NOUN
ejpam-1371	42	3	:	:	PUNCT
ejpam-1371	42	4	k	k	X
ejpam-1371	42	5	→	→	PUNCT
ejpam-1371	42	6	x	x	PROPN
ejpam-1371	42	7	∗	∗	NOUN
ejpam-1371	42	8	be	be	VERB
ejpam-1371	42	9	a	a	DET
ejpam-1371	42	10	nonlinear	nonlinear	ADJ
ejpam-1371	42	11	mapping	mapping	NOUN
ejpam-1371	42	12	.	.	PUNCT
ejpam-1371	43	1	then	then	ADV
ejpam-1371	43	2	,	,	PUNCT
ejpam-1371	43	3	the	the	DET
ejpam-1371	43	4	generalized	generalize	VERB
ejpam-1371	43	5	variational	variational	ADJ
ejpam-1371	43	6	inequality	inequality	NOUN
ejpam-1371	43	7	problem	problem	NOUN
ejpam-1371	43	8	is	be	AUX
ejpam-1371	43	9	defined	define	VERB
ejpam-1371	43	10	by	by	ADP
ejpam-1371	43	11	:	:	PUNCT
ejpam-1371	43	12	(	(	PUNCT
ejpam-1371	43	13	gv	gv	ADP
ejpam-1371	43	14	ip	ip	NOUN
ejpam-1371	43	15	)	)	PUNCT
ejpam-1371	43	16	find	find	VERB
ejpam-1371	43	17	x0	x0	PROPN
ejpam-1371	43	18	∈	∈	PROPN
ejpam-1371	44	1	k	k	X
ejpam-1371	44	2	such	such	ADJ
ejpam-1371	44	3	that	that	SCONJ
ejpam-1371	44	4	〈	〈	PROPN
ejpam-1371	44	5	t	t	PROPN
ejpam-1371	44	6	(	(	PUNCT
ejpam-1371	44	7	x0),η(x	x0),η(x	PROPN
ejpam-1371	44	8	,	,	PUNCT
ejpam-1371	44	9	x0	x0	PROPN
ejpam-1371	44	10	)	)	PUNCT
ejpam-1371	44	11	〉	〉	NOUN
ejpam-1371	44	12	≥	≥	NOUN
ejpam-1371	44	13	0	0	NUM
ejpam-1371	44	14	∀x	∀x	NUM
ejpam-1371	44	15	∈	∈	PROPN
ejpam-1371	44	16	k	k	NOUN
ejpam-1371	44	17	,	,	PUNCT
ejpam-1371	44	18	and	and	CCONJ
ejpam-1371	44	19	generalized	generalized	ADJ
ejpam-1371	44	20	complementarity	complementarity	NOUN
ejpam-1371	44	21	problem	problem	NOUN
ejpam-1371	44	22	(	(	PUNCT
ejpam-1371	44	23	gc	gc	PROPN
ejpam-1371	44	24	p	p	X
ejpam-1371	44	25	)	)	PUNCT
ejpam-1371	44	26	is	be	AUX
ejpam-1371	44	27	to	to	PART
ejpam-1371	44	28	:	:	PUNCT
ejpam-1371	44	29	(	(	PUNCT
ejpam-1371	44	30	gc	gc	PROPN
ejpam-1371	44	31	p	p	X
ejpam-1371	44	32	)	)	PUNCT
ejpam-1371	44	33	find	find	VERB
ejpam-1371	44	34	x0	x0	PROPN
ejpam-1371	44	35	∈	∈	PROPN
ejpam-1371	45	1	k	k	X
ejpam-1371	45	2	such	such	ADJ
ejpam-1371	45	3	that	that	SCONJ
ejpam-1371	45	4	〈	〈	PROPN
ejpam-1371	45	5	t	t	PROPN
ejpam-1371	45	6	(	(	PUNCT
ejpam-1371	45	7	x0),η(x	x0),η(x	PROPN
ejpam-1371	45	8	,	,	PUNCT
ejpam-1371	45	9	x0)〉=	x0)〉=	PROPN
ejpam-1371	45	10	0	0	PUNCT
ejpam-1371	46	1	∀x	∀x	X
ejpam-1371	46	2	∈	∈	PROPN
ejpam-1371	46	3	k	k	X
ejpam-1371	46	4	,	,	PUNCT
ejpam-1371	46	5	(	(	PUNCT
ejpam-1371	46	6	1	1	X
ejpam-1371	46	7	)	)	PUNCT
ejpam-1371	46	8	for	for	ADP
ejpam-1371	46	9	our	our	PRON
ejpam-1371	46	10	need	need	NOUN
ejpam-1371	46	11	,	,	PUNCT
ejpam-1371	46	12	we	we	PRON
ejpam-1371	46	13	recall	recall	VERB
ejpam-1371	46	14	some	some	DET
ejpam-1371	46	15	known	known	ADJ
ejpam-1371	46	16	definitions	definition	NOUN
ejpam-1371	46	17	and	and	CCONJ
ejpam-1371	46	18	results	result	NOUN
ejpam-1371	46	19	.	.	PUNCT
ejpam-1371	47	1	definition	definition	NOUN
ejpam-1371	47	2	1	1	NUM
ejpam-1371	47	3	(	(	PUNCT
ejpam-1371	47	4	[	[	X
ejpam-1371	47	5	9	9	NUM
ejpam-1371	47	6	]	]	NUM
ejpam-1371	47	7	)	)	PUNCT
ejpam-1371	47	8	.	.	PUNCT
ejpam-1371	48	1	a	a	DET
ejpam-1371	48	2	mapping	mapping	NOUN
ejpam-1371	48	3	t	t	NOUN
ejpam-1371	48	4	:	:	PUNCT
ejpam-1371	48	5	k	k	X
ejpam-1371	48	6	→	→	PUNCT
ejpam-1371	48	7	r	r	NOUN
ejpam-1371	48	8	is	be	AUX
ejpam-1371	48	9	said	say	VERB
ejpam-1371	48	10	to	to	PART
ejpam-1371	48	11	be	be	AUX
ejpam-1371	48	12	monotone	monotone	ADJ
ejpam-1371	48	13	if	if	SCONJ
ejpam-1371	48	14	〈	〈	PROPN
ejpam-1371	48	15	t	t	PROPN
ejpam-1371	48	16	(	(	PUNCT
ejpam-1371	48	17	u)−	u)−	PROPN
ejpam-1371	48	18	t	t	PROPN
ejpam-1371	48	19	(	(	PUNCT
ejpam-1371	48	20	v),u−	v),u−	PROPN
ejpam-1371	48	21	v	v	SYM
ejpam-1371	48	22	〉	〉	NOUN
ejpam-1371	48	23	≥	≥	NOUN
ejpam-1371	48	24	0	0	NUM
ejpam-1371	48	25	∀u	∀u	NOUN
ejpam-1371	48	26	,	,	PUNCT
ejpam-1371	48	27	v	v	NOUN
ejpam-1371	48	28	∈	∈	X
ejpam-1371	48	29	k	k	NOUN
ejpam-1371	48	30	,	,	PUNCT
ejpam-1371	48	31	and	and	CCONJ
ejpam-1371	48	32	t	t	PROPN
ejpam-1371	48	33	is	be	AUX
ejpam-1371	48	34	strictly	strictly	ADV
ejpam-1371	48	35	monotone	monotone	ADJ
ejpam-1371	48	36	if	if	SCONJ
ejpam-1371	48	37	equality	equality	NOUN
ejpam-1371	48	38	holds	hold	VERB
ejpam-1371	48	39	for	for	ADP
ejpam-1371	48	40	u	u	NOUN
ejpam-1371	48	41	=	=	NOUN
ejpam-1371	48	42	v.	v.	ADP
ejpam-1371	48	43	definition	definition	NOUN
ejpam-1371	48	44	2	2	NUM
ejpam-1371	48	45	(	(	PUNCT
ejpam-1371	48	46	[	[	X
ejpam-1371	48	47	10	10	NUM
ejpam-1371	48	48	]	]	NUM
ejpam-1371	48	49	)	)	PUNCT
ejpam-1371	48	50	.	.	PUNCT
ejpam-1371	49	1	a	a	DET
ejpam-1371	49	2	mapping	mapping	NOUN
ejpam-1371	49	3	f	f	X
ejpam-1371	49	4	:	:	PUNCT
ejpam-1371	50	1	k	k	X
ejpam-1371	50	2	→	→	PUNCT
ejpam-1371	50	3	r	r	NOUN
ejpam-1371	50	4	is	be	AUX
ejpam-1371	50	5	said	say	VERB
ejpam-1371	50	6	to	to	PART
ejpam-1371	50	7	be	be	AUX
ejpam-1371	50	8	lipschitz	lipschitz	NOUN
ejpam-1371	50	9	near	near	ADP
ejpam-1371	50	10	each	each	DET
ejpam-1371	50	11	point	point	NOUN
ejpam-1371	50	12	of	of	ADP
ejpam-1371	50	13	k	k	PROPN
ejpam-1371	50	14	with	with	ADP
ejpam-1371	50	15	rank	rank	PROPN
ejpam-1371	50	16	m	m	PROPN
ejpam-1371	50	17	>	>	X
ejpam-1371	50	18	0	0	PUNCT
ejpam-1371	51	1	if	if	SCONJ
ejpam-1371	51	2	|f(v)−	|f(v)−	ADJ
ejpam-1371	51	3	f(x)|	f(x)|	VERB
ejpam-1371	51	4	≤	≤	NUM
ejpam-1371	51	5	m	m	VERB
ejpam-1371	51	6	|v	|v	NOUN
ejpam-1371	51	7	−	−	PROPN
ejpam-1371	51	8	x	x	SYM
ejpam-1371	52	1	|	|	ADV
ejpam-1371	52	2	∀v	∀v	VERB
ejpam-1371	52	3	,	,	PUNCT
ejpam-1371	52	4	x	x	X
ejpam-1371	52	5	∈	∈	PROPN
ejpam-1371	52	6	k	k	X
ejpam-1371	52	7	.	.	PUNCT
ejpam-1371	53	1	p.	p.	NOUN
ejpam-1371	53	2	das	das	PROPN
ejpam-1371	53	3	/	/	SYM
ejpam-1371	53	4	eur	eur	PROPN
ejpam-1371	53	5	.	.	PUNCT
ejpam-1371	54	1	j.	j.	PROPN
ejpam-1371	54	2	pure	pure	PROPN
ejpam-1371	54	3	appl	appl	PROPN
ejpam-1371	54	4	.	.	PROPN
ejpam-1371	54	5	math	math	PROPN
ejpam-1371	54	6	,	,	PUNCT
ejpam-1371	54	7	4	4	NUM
ejpam-1371	54	8	(	(	PUNCT
ejpam-1371	54	9	2011	2011	NUM
ejpam-1371	54	10	)	)	PUNCT
ejpam-1371	54	11	,	,	PUNCT
ejpam-1371	54	12	340	340	NUM
ejpam-1371	54	13	-	-	SYM
ejpam-1371	54	14	360	360	NUM
ejpam-1371	54	15	342	342	NUM
ejpam-1371	54	16	theorem	theorem	NOUN
ejpam-1371	54	17	1	1	NUM
ejpam-1371	54	18	(	(	PUNCT
ejpam-1371	54	19	[	[	X
ejpam-1371	54	20	9	9	NUM
ejpam-1371	54	21	,	,	PUNCT
ejpam-1371	54	22	theorem	theorem	VERB
ejpam-1371	54	23	1.4	1.4	NUM
ejpam-1371	54	24	,	,	PUNCT
ejpam-1371	54	25	p.3	p.3	NOUN
ejpam-1371	54	26	]	]	PUNCT
ejpam-1371	54	27	)	)	PUNCT
ejpam-1371	54	28	.	.	PUNCT
ejpam-1371	55	1	let	let	VERB
ejpam-1371	55	2	k	k	PRON
ejpam-1371	55	3	be	be	AUX
ejpam-1371	55	4	a	a	DET
ejpam-1371	55	5	compact	compact	ADJ
ejpam-1371	55	6	convex	convex	NOUN
ejpam-1371	55	7	subset	subset	NOUN
ejpam-1371	55	8	of	of	ADP
ejpam-1371	55	9	a	a	DET
ejpam-1371	55	10	finite	finite	ADJ
ejpam-1371	55	11	dimensional	dimensional	ADJ
ejpam-1371	55	12	banach	banach	NOUN
ejpam-1371	55	13	space	space	NOUN
ejpam-1371	55	14	x	x	PUNCT
ejpam-1371	55	15	with	with	ADP
ejpam-1371	55	16	dual	dual	ADJ
ejpam-1371	55	17	x	x	SYM
ejpam-1371	55	18	∗	∗	NOUN
ejpam-1371	55	19	and	and	CCONJ
ejpam-1371	55	20	t	t	X
ejpam-1371	55	21	a	a	DET
ejpam-1371	55	22	continuous	continuous	ADJ
ejpam-1371	55	23	mapping	mapping	NOUN
ejpam-1371	55	24	of	of	ADP
ejpam-1371	55	25	k	k	PROPN
ejpam-1371	55	26	into	into	ADP
ejpam-1371	55	27	x	x	X
ejpam-1371	55	28	∗.	∗.	PROPN
ejpam-1371	55	29	then	then	ADV
ejpam-1371	55	30	there	there	PRON
ejpam-1371	55	31	exists	exist	VERB
ejpam-1371	55	32	x0	x0	PROPN
ejpam-1371	55	33	∈	∈	PROPN
ejpam-1371	56	1	k	k	X
ejpam-1371	56	2	such	such	ADJ
ejpam-1371	56	3	that	that	PRON
ejpam-1371	56	4	for	for	ADP
ejpam-1371	56	5	all	all	DET
ejpam-1371	56	6	y	y	PROPN
ejpam-1371	56	7	∈	∈	PROPN
ejpam-1371	56	8	k	k	PROPN
ejpam-1371	56	9	,	,	PUNCT
ejpam-1371	56	10	〈	〈	PROPN
ejpam-1371	56	11	t	t	PROPN
ejpam-1371	56	12	(	(	PUNCT
ejpam-1371	56	13	x0	x0	PROPN
ejpam-1371	56	14	)	)	PUNCT
ejpam-1371	56	15	,	,	PUNCT
ejpam-1371	56	16	y	y	PROPN
ejpam-1371	56	17	−	−	PROPN
ejpam-1371	56	18	x0	x0	PROPN
ejpam-1371	56	19	〉	〉	PROPN
ejpam-1371	56	20	≥	≥	NUM
ejpam-1371	56	21	0	0	NUM
ejpam-1371	56	22	.	.	PUNCT
ejpam-1371	56	23	theorem	theorem	ADJ
ejpam-1371	56	24	2	2	NUM
ejpam-1371	56	25	(	(	PUNCT
ejpam-1371	56	26	[	[	X
ejpam-1371	56	27	5	5	NUM
ejpam-1371	56	28	,	,	PUNCT
ejpam-1371	56	29	theorem	theorem	VERB
ejpam-1371	56	30	5.1	5.1	NUM
ejpam-1371	56	31	,	,	PUNCT
ejpam-1371	56	32	p.900	p.900	NOUN
ejpam-1371	56	33	]	]	PUNCT
ejpam-1371	56	34	)	)	PUNCT
ejpam-1371	56	35	.	.	PUNCT
ejpam-1371	57	1	let	let	VERB
ejpam-1371	57	2	k	k	PRON
ejpam-1371	57	3	be	be	AUX
ejpam-1371	57	4	a	a	DET
ejpam-1371	57	5	closed	closed	ADJ
ejpam-1371	57	6	,	,	PUNCT
ejpam-1371	57	7	convex	convex	ADJ
ejpam-1371	57	8	and	and	CCONJ
ejpam-1371	57	9	bounded	bound	VERB
ejpam-1371	57	10	subset	subset	NOUN
ejpam-1371	57	11	of	of	ADP
ejpam-1371	57	12	a	a	DET
ejpam-1371	57	13	reflexive	reflexive	ADJ
ejpam-1371	57	14	real	real	ADJ
ejpam-1371	57	15	banach	banach	NOUN
ejpam-1371	57	16	space	space	NOUN
ejpam-1371	57	17	x	x	PUNCT
ejpam-1371	57	18	and	and	CCONJ
ejpam-1371	57	19	x	x	SYM
ejpam-1371	57	20	∗	∗	NOUN
ejpam-1371	57	21	be	be	VERB
ejpam-1371	57	22	the	the	DET
ejpam-1371	57	23	dual	dual	ADJ
ejpam-1371	57	24	of	of	ADP
ejpam-1371	57	25	x	x	X
ejpam-1371	57	26	.	.	PUNCT
ejpam-1371	58	1	let	let	VERB
ejpam-1371	58	2	t	t	NOUN
ejpam-1371	58	3	:	:	PUNCT
ejpam-1371	58	4	k	k	X
ejpam-1371	58	5	→	→	PUNCT
ejpam-1371	58	6	x	x	SYM
ejpam-1371	58	7	∗	∗	NOUN
ejpam-1371	58	8	and	and	CCONJ
ejpam-1371	58	9	η	η	PROPN
ejpam-1371	58	10	:	:	PUNCT
ejpam-1371	59	1	k	k	PROPN
ejpam-1371	59	2	×	×	PROPN
ejpam-1371	59	3	k	k	PROPN
ejpam-1371	59	4	→	→	PUNCT
ejpam-1371	59	5	x	x	PUNCT
ejpam-1371	59	6	be	be	AUX
ejpam-1371	59	7	two	two	NUM
ejpam-1371	59	8	maps	map	NOUN
ejpam-1371	59	9	such	such	ADJ
ejpam-1371	59	10	that	that	SCONJ
ejpam-1371	59	11	(	(	PUNCT
ejpam-1371	59	12	i	i	NOUN
ejpam-1371	59	13	)	)	PUNCT
ejpam-1371	59	14	〈	〈	PROPN
ejpam-1371	59	15	t	t	PROPN
ejpam-1371	59	16	(	(	PUNCT
ejpam-1371	59	17	y),η(y	y),η(y	PROPN
ejpam-1371	59	18	,	,	PUNCT
ejpam-1371	59	19	y	y	NOUN
ejpam-1371	59	20	)	)	PUNCT
ejpam-1371	59	21	〉	〉	NOUN
ejpam-1371	59	22	=	=	SYM
ejpam-1371	59	23	0	0	NUM
ejpam-1371	59	24	for	for	ADP
ejpam-1371	59	25	all	all	DET
ejpam-1371	59	26	y	y	PROPN
ejpam-1371	59	27	∈	∈	PROPN
ejpam-1371	59	28	k.	k.	PROPN
ejpam-1371	59	29	(	(	PUNCT
ejpam-1371	59	30	ii	ii	PROPN
ejpam-1371	59	31	)	)	PUNCT
ejpam-1371	59	32	the	the	DET
ejpam-1371	59	33	map	map	NOUN
ejpam-1371	59	34	x	x	SYM
ejpam-1371	59	35	7→	7→	NUM
ejpam-1371	59	36	〈	〈	PROPN
ejpam-1371	59	37	t	t	NOUN
ejpam-1371	59	38	(	(	PUNCT
ejpam-1371	59	39	x),η(y	x),η(y	PROPN
ejpam-1371	59	40	,	,	PUNCT
ejpam-1371	59	41	x	x	NOUN
ejpam-1371	59	42	)	)	PUNCT
ejpam-1371	59	43	〉	〉	NOUN
ejpam-1371	59	44	of	of	ADP
ejpam-1371	59	45	k	k	PROPN
ejpam-1371	59	46	into	into	ADP
ejpam-1371	59	47	r	r	NOUN
ejpam-1371	59	48	is	be	AUX
ejpam-1371	59	49	continuous	continuous	ADJ
ejpam-1371	59	50	on	on	ADP
ejpam-1371	59	51	finite	finite	ADJ
ejpam-1371	59	52	dimensional	dimensional	ADJ
ejpam-1371	59	53	subspaces	subspace	NOUN
ejpam-1371	59	54	(	(	PUNCT
ejpam-1371	59	55	or	or	CCONJ
ejpam-1371	59	56	at	at	ADP
ejpam-1371	59	57	least	least	ADJ
ejpam-1371	59	58	hemicontinuous	hemicontinuous	ADJ
ejpam-1371	59	59	)	)	PUNCT
ejpam-1371	59	60	,	,	PUNCT
ejpam-1371	59	61	for	for	ADP
ejpam-1371	59	62	each	each	DET
ejpam-1371	59	63	y	y	PROPN
ejpam-1371	59	64	∈	∈	PROPN
ejpam-1371	59	65	k	k	PROPN
ejpam-1371	59	66	,	,	PUNCT
ejpam-1371	59	67	(	(	PUNCT
ejpam-1371	59	68	iii	iii	NOUN
ejpam-1371	59	69	)	)	PUNCT
ejpam-1371	59	70	the	the	DET
ejpam-1371	59	71	map	map	NOUN
ejpam-1371	59	72	y	y	PROPN
ejpam-1371	59	73	7→	7→	PROPN
ejpam-1371	60	1	〈	〈	PROPN
ejpam-1371	60	2	t	t	PROPN
ejpam-1371	60	3	(	(	PUNCT
ejpam-1371	60	4	x),η(y	x),η(y	PROPN
ejpam-1371	60	5	,	,	PUNCT
ejpam-1371	60	6	x	x	NOUN
ejpam-1371	60	7	)	)	PUNCT
ejpam-1371	60	8	〉	〉	NOUN
ejpam-1371	60	9	of	of	ADP
ejpam-1371	60	10	k	k	PROPN
ejpam-1371	60	11	into	into	ADP
ejpam-1371	60	12	r	r	NOUN
ejpam-1371	60	13	is	be	AUX
ejpam-1371	60	14	convex	convex	ADJ
ejpam-1371	60	15	for	for	ADP
ejpam-1371	60	16	each	each	DET
ejpam-1371	60	17	x	x	SYM
ejpam-1371	60	18	∈	∈	PROPN
ejpam-1371	60	19	k	k	NOUN
ejpam-1371	60	20	,	,	PUNCT
ejpam-1371	60	21	(	(	PUNCT
ejpam-1371	60	22	iv	iv	X
ejpam-1371	60	23	)	)	PUNCT
ejpam-1371	60	24	〈	〈	PROPN
ejpam-1371	60	25	t	t	PROPN
ejpam-1371	60	26	(	(	PUNCT
ejpam-1371	60	27	x),η(y	x),η(y	PROPN
ejpam-1371	60	28	,	,	PUNCT
ejpam-1371	60	29	x)〉+	x)〉+	PUNCT
ejpam-1371	60	30	〈	〈	PROPN
ejpam-1371	60	31	t	t	PROPN
ejpam-1371	60	32	(	(	PUNCT
ejpam-1371	60	33	y),η(x	y),η(x	PROPN
ejpam-1371	60	34	,	,	PUNCT
ejpam-1371	60	35	y	y	NOUN
ejpam-1371	60	36	)	)	PUNCT
ejpam-1371	60	37	〉	〉	NOUN
ejpam-1371	60	38	≤	≤	NOUN
ejpam-1371	60	39	0	0	NUM
ejpam-1371	60	40	for	for	ADP
ejpam-1371	60	41	all	all	PRON
ejpam-1371	60	42	x	x	SYM
ejpam-1371	60	43	,	,	PUNCT
ejpam-1371	60	44	y	y	PROPN
ejpam-1371	60	45	∈	∈	PROPN
ejpam-1371	60	46	k.	k.	PROPN
ejpam-1371	61	1	then	then	ADV
ejpam-1371	61	2	there	there	PRON
ejpam-1371	61	3	exists	exist	VERB
ejpam-1371	61	4	x0	x0	PROPN
ejpam-1371	61	5	∈	∈	PROPN
ejpam-1371	62	1	k	k	X
ejpam-1371	62	2	such	such	ADJ
ejpam-1371	62	3	that	that	PRON
ejpam-1371	62	4	for	for	ADP
ejpam-1371	62	5	all	all	DET
ejpam-1371	62	6	y	y	PROPN
ejpam-1371	62	7	∈	∈	PROPN
ejpam-1371	62	8	k	k	PROPN
ejpam-1371	62	9	,	,	PUNCT
ejpam-1371	62	10	〈	〈	PROPN
ejpam-1371	62	11	t	t	PROPN
ejpam-1371	62	12	(	(	PUNCT
ejpam-1371	62	13	x0),η(y	x0),η(y	PROPN
ejpam-1371	62	14	,	,	PUNCT
ejpam-1371	62	15	x0	x0	PROPN
ejpam-1371	62	16	)	)	PUNCT
ejpam-1371	62	17	〉	〉	NOUN
ejpam-1371	62	18	≥	≥	NOUN
ejpam-1371	62	19	0	0	NUM
ejpam-1371	62	20	.	.	PUNCT
ejpam-1371	63	1	in	in	ADP
ejpam-1371	63	2	1981	1981	NUM
ejpam-1371	63	3	,	,	PUNCT
ejpam-1371	63	4	m.	m.	NOUN
ejpam-1371	63	5	a.	a.	PROPN
ejpam-1371	63	6	hanson	hanson	PROPN
ejpam-1371	64	1	[	[	X
ejpam-1371	64	2	16	16	NUM
ejpam-1371	64	3	]	]	PUNCT
ejpam-1371	64	4	introduced	introduce	VERB
ejpam-1371	64	5	the	the	DET
ejpam-1371	64	6	invex	invex	NOUN
ejpam-1371	64	7	function	function	NOUN
ejpam-1371	64	8	which	which	PRON
ejpam-1371	64	9	is	be	AUX
ejpam-1371	64	10	the	the	DET
ejpam-1371	64	11	generalized	generalized	ADJ
ejpam-1371	64	12	concept	concept	NOUN
ejpam-1371	64	13	of	of	ADP
ejpam-1371	64	14	convex	convex	ADJ
ejpam-1371	64	15	function	function	NOUN
ejpam-1371	64	16	and	and	CCONJ
ejpam-1371	64	17	concave	concave	NOUN
ejpam-1371	64	18	function	function	NOUN
ejpam-1371	64	19	.	.	PUNCT
ejpam-1371	65	1	the	the	DET
ejpam-1371	65	2	concept	concept	NOUN
ejpam-1371	65	3	of	of	ADP
ejpam-1371	65	4	invexity	invexity	NOUN
ejpam-1371	65	5	of	of	ADP
ejpam-1371	65	6	a	a	DET
ejpam-1371	65	7	function	function	NOUN
ejpam-1371	65	8	brought	bring	VERB
ejpam-1371	65	9	a	a	DET
ejpam-1371	65	10	new	new	ADJ
ejpam-1371	65	11	edge	edge	NOUN
ejpam-1371	65	12	to	to	PART
ejpam-1371	65	13	generalize	generalize	VERB
ejpam-1371	65	14	the	the	DET
ejpam-1371	65	15	variational	variational	ADJ
ejpam-1371	65	16	inequality	inequality	NOUN
ejpam-1371	65	17	problem	problem	NOUN
ejpam-1371	65	18	,	,	PUNCT
ejpam-1371	65	19	that	that	ADV
ejpam-1371	65	20	is	is	ADV
ejpam-1371	65	21	,	,	PUNCT
ejpam-1371	65	22	in	in	ADP
ejpam-1371	65	23	particular	particular	ADJ
ejpam-1371	65	24	case	case	NOUN
ejpam-1371	65	25	,	,	PUNCT
ejpam-1371	65	26	the	the	DET
ejpam-1371	65	27	generalization	generalization	NOUN
ejpam-1371	65	28	of	of	ADP
ejpam-1371	65	29	optimization	optimization	NOUN
ejpam-1371	65	30	problems	problem	NOUN
ejpam-1371	65	31	,	,	PUNCT
ejpam-1371	65	32	complementarity	complementarity	NOUN
ejpam-1371	65	33	problems	problem	NOUN
ejpam-1371	65	34	and	and	CCONJ
ejpam-1371	65	35	fixed	fix	VERB
ejpam-1371	65	36	point	point	NOUN
ejpam-1371	65	37	problems	problem	NOUN
ejpam-1371	65	38	.	.	PUNCT
ejpam-1371	66	1	in	in	ADP
ejpam-1371	66	2	2006	2006	NUM
ejpam-1371	66	3	,	,	PUNCT
ejpam-1371	66	4	a.	a.	PROPN
ejpam-1371	66	5	behera	behera	PROPN
ejpam-1371	66	6	and	and	CCONJ
ejpam-1371	66	7	p.k	p.k	PROPN
ejpam-1371	66	8	.	.	PUNCT
ejpam-1371	66	9	das	das	PROPN
ejpam-1371	67	1	[	[	X
ejpam-1371	67	2	3	3	NUM
ejpam-1371	67	3	]	]	PUNCT
ejpam-1371	67	4	generalized	generalize	VERB
ejpam-1371	67	5	the	the	DET
ejpam-1371	67	6	concept	concept	NOUN
ejpam-1371	67	7	of	of	ADP
ejpam-1371	67	8	invexity	invexity	NOUN
ejpam-1371	67	9	of	of	ADP
ejpam-1371	67	10	any	any	DET
ejpam-1371	67	11	function	function	NOUN
ejpam-1371	67	12	to	to	ADP
ejpam-1371	67	13	t	t	PROPN
ejpam-1371	67	14	η	η	PROPN
ejpam-1371	67	15	-	-	NOUN
ejpam-1371	67	16	invexity	invexity	NOUN
ejpam-1371	67	17	of	of	ADP
ejpam-1371	67	18	the	the	DET
ejpam-1371	67	19	function	function	NOUN
ejpam-1371	67	20	in	in	ADP
ejpam-1371	67	21	ordered	order	VERB
ejpam-1371	67	22	topological	topological	ADJ
ejpam-1371	67	23	vector	vector	NOUN
ejpam-1371	67	24	spaces	space	NOUN
ejpam-1371	67	25	.	.	PUNCT
ejpam-1371	68	1	for	for	ADP
ejpam-1371	68	2	our	our	PRON
ejpam-1371	68	3	need	need	NOUN
ejpam-1371	68	4	we	we	PRON
ejpam-1371	68	5	recall	recall	VERB
ejpam-1371	68	6	the	the	DET
ejpam-1371	68	7	following	follow	VERB
ejpam-1371	68	8	definitions	definition	NOUN
ejpam-1371	68	9	.	.	PUNCT
ejpam-1371	69	1	definition	definition	NOUN
ejpam-1371	69	2	3	3	NUM
ejpam-1371	69	3	(	(	PUNCT
ejpam-1371	69	4	[	[	X
ejpam-1371	69	5	16	16	NUM
ejpam-1371	69	6	]	]	PUNCT
ejpam-1371	69	7	)	)	PUNCT
ejpam-1371	69	8	.	.	PUNCT
ejpam-1371	70	1	the	the	DET
ejpam-1371	70	2	set	set	NOUN
ejpam-1371	70	3	k	k	PROPN
ejpam-1371	70	4	is	be	AUX
ejpam-1371	70	5	said	say	VERB
ejpam-1371	70	6	to	to	PART
ejpam-1371	70	7	be	be	AUX
ejpam-1371	70	8	η	η	NOUN
ejpam-1371	70	9	-	-	ADJ
ejpam-1371	70	10	invex	invex	NOUN
ejpam-1371	70	11	set	set	VERB
ejpam-1371	70	12	where	where	SCONJ
ejpam-1371	70	13	η	η	PROPN
ejpam-1371	70	14	:	:	PUNCT
ejpam-1371	71	1	k	k	PROPN
ejpam-1371	71	2	×	×	PROPN
ejpam-1371	71	3	k	k	PROPN
ejpam-1371	71	4	→	→	PUNCT
ejpam-1371	71	5	x	x	X
ejpam-1371	71	6	is	be	AUX
ejpam-1371	71	7	a	a	DET
ejpam-1371	71	8	vector	vector	NOUN
ejpam-1371	71	9	valued	value	VERB
ejpam-1371	71	10	continuous	continuous	ADJ
ejpam-1371	71	11	mapping	mapping	NOUN
ejpam-1371	71	12	,	,	PUNCT
ejpam-1371	71	13	if	if	SCONJ
ejpam-1371	71	14	for	for	ADP
ejpam-1371	71	15	all	all	DET
ejpam-1371	71	16	x	x	SYM
ejpam-1371	71	17	,	,	PUNCT
ejpam-1371	71	18	u	u	PROPN
ejpam-1371	71	19	∈	∈	PROPN
ejpam-1371	71	20	k	k	NOUN
ejpam-1371	71	21	,	,	PUNCT
ejpam-1371	71	22	and	and	CCONJ
ejpam-1371	71	23	for	for	ADP
ejpam-1371	71	24	all	all	DET
ejpam-1371	71	25	t	t	NOUN
ejpam-1371	71	26	∈	∈	PROPN
ejpam-1371	71	27	(	(	PUNCT
ejpam-1371	71	28	0	0	NUM
ejpam-1371	71	29	,	,	PUNCT
ejpam-1371	71	30	1	1	NUM
ejpam-1371	71	31	)	)	PUNCT
ejpam-1371	71	32	such	such	ADJ
ejpam-1371	71	33	that	that	SCONJ
ejpam-1371	71	34	u+	u+	NOUN
ejpam-1371	71	35	tη(x	tη(x	NUM
ejpam-1371	71	36	,	,	PUNCT
ejpam-1371	71	37	u	u	NOUN
ejpam-1371	71	38	)	)	PUNCT
ejpam-1371	71	39	∈	∈	PROPN
ejpam-1371	71	40	k	k	PROPN
ejpam-1371	71	41	.	.	PUNCT
ejpam-1371	72	1	definition	definition	NOUN
ejpam-1371	72	2	4	4	NUM
ejpam-1371	72	3	(	(	PUNCT
ejpam-1371	72	4	[	[	NOUN
ejpam-1371	72	5	3	3	NUM
ejpam-1371	72	6	,	,	PUNCT
ejpam-1371	72	7	condition	condition	NOUN
ejpam-1371	72	8	c0	c0	NOUN
ejpam-1371	72	9	]	]	PUNCT
ejpam-1371	72	10	)	)	PUNCT
ejpam-1371	72	11	.	.	PUNCT
ejpam-1371	73	1	a	a	DET
ejpam-1371	73	2	vector	vector	NOUN
ejpam-1371	73	3	function	function	NOUN
ejpam-1371	73	4	η	η	PROPN
ejpam-1371	73	5	:	:	PUNCT
ejpam-1371	73	6	k	k	PROPN
ejpam-1371	73	7	×	×	PROPN
ejpam-1371	73	8	k	k	PROPN
ejpam-1371	73	9	→	→	PUNCT
ejpam-1371	73	10	x	x	X
ejpam-1371	73	11	is	be	AUX
ejpam-1371	73	12	said	say	VERB
ejpam-1371	73	13	to	to	PART
ejpam-1371	73	14	satisfy	satisfy	VERB
ejpam-1371	73	15	condition	condition	NOUN
ejpam-1371	73	16	c0	c0	NOUN
ejpam-1371	73	17	if	if	SCONJ
ejpam-1371	73	18	the	the	DET
ejpam-1371	73	19	following	follow	VERB
ejpam-1371	73	20	hold	hold	NOUN
ejpam-1371	73	21	:	:	PUNCT
ejpam-1371	73	22	(	(	PUNCT
ejpam-1371	73	23	a	a	X
ejpam-1371	73	24	)	)	PUNCT
ejpam-1371	73	25	η(x	η(x	PROPN
ejpam-1371	73	26	′+η(x	′+η(x	NOUN
ejpam-1371	73	27	,	,	PUNCT
ejpam-1371	73	28	x	x	NOUN
ejpam-1371	73	29	′	′	NUM
ejpam-1371	73	30	)	)	PUNCT
ejpam-1371	73	31	,	,	PUNCT
ejpam-1371	73	32	x	x	NOUN
ejpam-1371	73	33	′	′	X
ejpam-1371	73	34	)	)	PUNCT
ejpam-1371	74	1	+	+	ADJ
ejpam-1371	74	2	η(x	η(x	ADJ
ejpam-1371	74	3	′	′	NOUN
ejpam-1371	74	4	,	,	PUNCT
ejpam-1371	74	5	x	x	PRON
ejpam-1371	74	6	′+η(x	′+η(x	NOUN
ejpam-1371	74	7	,	,	PUNCT
ejpam-1371	74	8	x	x	NOUN
ejpam-1371	74	9	′	′	NUM
ejpam-1371	74	10	)	)	PUNCT
ejpam-1371	74	11	)	)	PUNCT
ejpam-1371	75	1	=	=	PUNCT
ejpam-1371	75	2	0	0	NUM
ejpam-1371	75	3	,	,	PUNCT
ejpam-1371	75	4	(	(	PUNCT
ejpam-1371	75	5	b	b	NOUN
ejpam-1371	75	6	)	)	PUNCT
ejpam-1371	75	7	η(x	η(x	X
ejpam-1371	75	8	′+	′+	PUNCT
ejpam-1371	75	9	tη(x	tη(x	NUM
ejpam-1371	75	10	,	,	PUNCT
ejpam-1371	75	11	x	x	NOUN
ejpam-1371	75	12	′	′	NUM
ejpam-1371	75	13	)	)	PUNCT
ejpam-1371	75	14	,	,	PUNCT
ejpam-1371	75	15	x	x	NOUN
ejpam-1371	75	16	′	′	NUM
ejpam-1371	75	17	)	)	PUNCT
ejpam-1371	75	18	+	+	CCONJ
ejpam-1371	75	19	tη(x	tη(x	NUM
ejpam-1371	75	20	,	,	PUNCT
ejpam-1371	75	21	x	x	NOUN
ejpam-1371	75	22	′	′	NUM
ejpam-1371	75	23	)	)	PUNCT
ejpam-1371	75	24	=	=	SYM
ejpam-1371	75	25	0	0	NUM
ejpam-1371	75	26	,	,	PUNCT
ejpam-1371	75	27	for	for	ADP
ejpam-1371	75	28	all	all	DET
ejpam-1371	75	29	x	x	SYM
ejpam-1371	75	30	,	,	PUNCT
ejpam-1371	75	31	x	x	NUM
ejpam-1371	75	32	′	′	NUM
ejpam-1371	75	33	∈	∈	PROPN
ejpam-1371	75	34	k	k	NOUN
ejpam-1371	75	35	and	and	CCONJ
ejpam-1371	75	36	for	for	ADP
ejpam-1371	75	37	all	all	DET
ejpam-1371	75	38	t	t	NOUN
ejpam-1371	75	39	∈	∈	PROPN
ejpam-1371	75	40	(	(	PUNCT
ejpam-1371	75	41	0,1	0,1	NUM
ejpam-1371	75	42	)	)	PUNCT
ejpam-1371	75	43	.	.	PUNCT
ejpam-1371	76	1	for	for	ADP
ejpam-1371	76	2	our	our	PRON
ejpam-1371	76	3	need	need	NOUN
ejpam-1371	76	4	,	,	PUNCT
ejpam-1371	76	5	we	we	PRON
ejpam-1371	76	6	define	define	VERB
ejpam-1371	76	7	the	the	DET
ejpam-1371	76	8	following	follow	VERB
ejpam-1371	76	9	definitions	definition	NOUN
ejpam-1371	76	10	.	.	PUNCT
ejpam-1371	77	1	definition	definition	NOUN
ejpam-1371	77	2	5	5	NUM
ejpam-1371	77	3	.	.	PUNCT
ejpam-1371	78	1	the	the	DET
ejpam-1371	78	2	set	set	NOUN
ejpam-1371	78	3	k	k	PROPN
ejpam-1371	78	4	⊂	⊂	PROPN
ejpam-1371	78	5	x	x	X
ejpam-1371	78	6	is	be	AUX
ejpam-1371	78	7	said	say	VERB
ejpam-1371	78	8	to	to	PART
ejpam-1371	78	9	be	be	AUX
ejpam-1371	78	10	weakly	weakly	ADJ
ejpam-1371	78	11	η	η	NOUN
ejpam-1371	78	12	-	-	ADJ
ejpam-1371	78	13	invex	invex	NOUN
ejpam-1371	78	14	set	set	VERB
ejpam-1371	78	15	where	where	SCONJ
ejpam-1371	78	16	η	η	PROPN
ejpam-1371	78	17	:	:	PUNCT
ejpam-1371	79	1	k	k	PROPN
ejpam-1371	79	2	×	×	PROPN
ejpam-1371	79	3	k	k	PROPN
ejpam-1371	79	4	→	→	PUNCT
ejpam-1371	79	5	x	x	X
ejpam-1371	79	6	is	be	AUX
ejpam-1371	79	7	a	a	DET
ejpam-1371	79	8	vector	vector	NOUN
ejpam-1371	79	9	valued	value	VERB
ejpam-1371	79	10	continuous	continuous	ADJ
ejpam-1371	79	11	mapping	mapping	NOUN
ejpam-1371	79	12	,	,	PUNCT
ejpam-1371	79	13	if	if	SCONJ
ejpam-1371	79	14	for	for	ADP
ejpam-1371	79	15	all	all	PRON
ejpam-1371	79	16	x	x	SYM
ejpam-1371	79	17	,	,	PUNCT
ejpam-1371	79	18	u	u	PROPN
ejpam-1371	79	19	∈	∈	PROPN
ejpam-1371	79	20	k	k	NOUN
ejpam-1371	79	21	,	,	PUNCT
ejpam-1371	79	22	there	there	PRON
ejpam-1371	79	23	exists	exist	VERB
ejpam-1371	79	24	a	a	DET
ejpam-1371	79	25	t	t	NOUN
ejpam-1371	79	26	∈	∈	PROPN
ejpam-1371	79	27	(	(	PUNCT
ejpam-1371	79	28	0	0	NUM
ejpam-1371	79	29	,	,	PUNCT
ejpam-1371	79	30	1	1	NUM
ejpam-1371	79	31	)	)	PUNCT
ejpam-1371	79	32	such	such	ADJ
ejpam-1371	79	33	that	that	SCONJ
ejpam-1371	79	34	z	z	NOUN
ejpam-1371	79	35	+	+	CCONJ
ejpam-1371	79	36	tη(x	tη(x	NUM
ejpam-1371	79	37	,	,	PUNCT
ejpam-1371	79	38	u	u	NOUN
ejpam-1371	79	39	)	)	PUNCT
ejpam-1371	79	40	∈	∈	PROPN
ejpam-1371	79	41	k	k	PROPN
ejpam-1371	79	42	where	where	SCONJ
ejpam-1371	79	43	z	z	PROPN
ejpam-1371	79	44	∈	∈	PROPN
ejpam-1371	79	45	{	{	PUNCT
ejpam-1371	79	46	u	u	NOUN
ejpam-1371	79	47	,	,	PUNCT
ejpam-1371	79	48	x	x	NOUN
ejpam-1371	79	49	}	}	PUNCT
ejpam-1371	79	50	.	.	PUNCT
ejpam-1371	80	1	p.	p.	NOUN
ejpam-1371	80	2	das	das	PROPN
ejpam-1371	80	3	/	/	SYM
ejpam-1371	80	4	eur	eur	PROPN
ejpam-1371	80	5	.	.	PUNCT
ejpam-1371	81	1	j.	j.	PROPN
ejpam-1371	81	2	pure	pure	PROPN
ejpam-1371	81	3	appl	appl	PROPN
ejpam-1371	81	4	.	.	PROPN
ejpam-1371	81	5	math	math	PROPN
ejpam-1371	81	6	,	,	PUNCT
ejpam-1371	81	7	4	4	NUM
ejpam-1371	81	8	(	(	PUNCT
ejpam-1371	81	9	2011	2011	NUM
ejpam-1371	81	10	)	)	PUNCT
ejpam-1371	81	11	,	,	PUNCT
ejpam-1371	81	12	340	340	NUM
ejpam-1371	81	13	-	-	SYM
ejpam-1371	81	14	360	360	NUM
ejpam-1371	81	15	343	343	NUM
ejpam-1371	81	16	definition	definition	NOUN
ejpam-1371	81	17	6	6	NUM
ejpam-1371	81	18	.	.	PUNCT
ejpam-1371	82	1	the	the	DET
ejpam-1371	82	2	set	set	NOUN
ejpam-1371	82	3	k	k	PROPN
ejpam-1371	82	4	⊂	⊂	PROPN
ejpam-1371	82	5	x	x	X
ejpam-1371	82	6	is	be	AUX
ejpam-1371	82	7	said	say	VERB
ejpam-1371	82	8	to	to	PART
ejpam-1371	82	9	be	be	AUX
ejpam-1371	82	10	complete	complete	ADJ
ejpam-1371	82	11	w.r.t	w.r.t	NOUN
ejpam-1371	82	12	.	.	PUNCT
ejpam-1371	83	1	η	η	PROPN
ejpam-1371	83	2	,	,	PUNCT
ejpam-1371	83	3	if	if	SCONJ
ejpam-1371	83	4	there	there	PRON
ejpam-1371	83	5	exists	exist	VERB
ejpam-1371	83	6	a	a	DET
ejpam-1371	83	7	vector	vector	NOUN
ejpam-1371	83	8	valued	value	VERB
ejpam-1371	83	9	continuous	continuous	ADJ
ejpam-1371	83	10	function	function	NOUN
ejpam-1371	83	11	η	η	PROPN
ejpam-1371	83	12	:	:	PUNCT
ejpam-1371	83	13	k	k	PROPN
ejpam-1371	83	14	×	×	PROPN
ejpam-1371	83	15	k	k	X
ejpam-1371	83	16	→	→	PUNCT
ejpam-1371	83	17	x	x	X
ejpam-1371	83	18	such	such	ADJ
ejpam-1371	83	19	that	that	DET
ejpam-1371	83	20	for	for	ADP
ejpam-1371	83	21	each	each	DET
ejpam-1371	83	22	two	two	NUM
ejpam-1371	83	23	points	point	NOUN
ejpam-1371	83	24	x	x	X
ejpam-1371	83	25	,	,	PUNCT
ejpam-1371	83	26	u	u	PROPN
ejpam-1371	83	27	∈	∈	PROPN
ejpam-1371	83	28	k	k	NOUN
ejpam-1371	83	29	,	,	PUNCT
ejpam-1371	83	30	we	we	PRON
ejpam-1371	83	31	have	have	VERB
ejpam-1371	83	32	z	z	NOUN
ejpam-1371	83	33	+	+	CCONJ
ejpam-1371	83	34	tη(x	tη(x	NUM
ejpam-1371	83	35	,	,	PUNCT
ejpam-1371	83	36	u	u	NOUN
ejpam-1371	83	37	)	)	PUNCT
ejpam-1371	83	38	∈	∈	PROPN
ejpam-1371	83	39	k	k	PROPN
ejpam-1371	84	1	where	where	SCONJ
ejpam-1371	84	2	z	z	PROPN
ejpam-1371	84	3	∈	∈	PROPN
ejpam-1371	84	4	{	{	PUNCT
ejpam-1371	84	5	u	u	NOUN
ejpam-1371	84	6	,	,	PUNCT
ejpam-1371	84	7	x	x	X
ejpam-1371	84	8	}	}	PUNCT
ejpam-1371	84	9	,	,	PUNCT
ejpam-1371	84	10	t	t	PROPN
ejpam-1371	84	11	∈	∈	PROPN
ejpam-1371	85	1	[	[	X
ejpam-1371	85	2	0	0	NUM
ejpam-1371	85	3	,	,	PUNCT
ejpam-1371	85	4	1	1	NUM
ejpam-1371	85	5	]	]	PUNCT
ejpam-1371	85	6	.	.	PUNCT
ejpam-1371	86	1	remark	remark	PROPN
ejpam-1371	86	2	1	1	NUM
ejpam-1371	86	3	.	.	PUNCT
ejpam-1371	87	1	in	in	ADP
ejpam-1371	87	2	particular	particular	ADJ
ejpam-1371	87	3	,	,	PUNCT
ejpam-1371	87	4	if	if	SCONJ
ejpam-1371	87	5	η(x	η(x	NOUN
ejpam-1371	87	6	,	,	PUNCT
ejpam-1371	87	7	u	u	NOUN
ejpam-1371	87	8	)	)	PUNCT
ejpam-1371	87	9	=	=	SYM
ejpam-1371	88	1	u−	u−	PROPN
ejpam-1371	88	2	x	x	INTJ
ejpam-1371	89	1	when	when	SCONJ
ejpam-1371	89	2	z	z	NOUN
ejpam-1371	89	3	=	=	SYM
ejpam-1371	89	4	x	x	X
ejpam-1371	89	5	and	and	CCONJ
ejpam-1371	89	6	η(x	η(x	PROPN
ejpam-1371	89	7	,	,	PUNCT
ejpam-1371	89	8	u	u	NOUN
ejpam-1371	89	9	)	)	PUNCT
ejpam-1371	89	10	=	=	PUNCT
ejpam-1371	89	11	x	x	PUNCT
ejpam-1371	89	12	−	−	PUNCT
ejpam-1371	89	13	u	u	NOUN
ejpam-1371	89	14	when	when	SCONJ
ejpam-1371	89	15	z	z	NOUN
ejpam-1371	89	16	=	=	SYM
ejpam-1371	89	17	u	u	NOUN
ejpam-1371	89	18	,	,	PUNCT
ejpam-1371	89	19	then	then	ADV
ejpam-1371	89	20	k	k	PROPN
ejpam-1371	89	21	is	be	AUX
ejpam-1371	89	22	complete	complete	ADJ
ejpam-1371	89	23	.	.	PUNCT
ejpam-1371	90	1	in	in	ADP
ejpam-1371	90	2	this	this	DET
ejpam-1371	90	3	case	case	NOUN
ejpam-1371	90	4	,	,	PUNCT
ejpam-1371	90	5	if	if	SCONJ
ejpam-1371	90	6	we	we	PRON
ejpam-1371	90	7	get	get	VERB
ejpam-1371	90	8	the	the	DET
ejpam-1371	90	9	vector	vector	NOUN
ejpam-1371	90	10	−→	−→	NOUN
ejpam-1371	90	11	ab	ab	PROPN
ejpam-1371	90	12	for	for	ADP
ejpam-1371	90	13	z	z	NOUN
ejpam-1371	90	14	=	=	SYM
ejpam-1371	90	15	x	x	NOUN
ejpam-1371	90	16	,	,	PUNCT
ejpam-1371	90	17	then	then	ADV
ejpam-1371	90	18	for	for	ADP
ejpam-1371	90	19	z	z	NOUN
ejpam-1371	90	20	=	=	SYM
ejpam-1371	90	21	u	u	NOUN
ejpam-1371	90	22	,	,	PUNCT
ejpam-1371	90	23	we	we	PRON
ejpam-1371	90	24	get	get	VERB
ejpam-1371	90	25	the	the	DET
ejpam-1371	90	26	vector	vector	NOUN
ejpam-1371	90	27	−→	−→	NOUN
ejpam-1371	90	28	ba	ba	PROPN
ejpam-1371	90	29	contained	contain	VERB
ejpam-1371	90	30	in	in	ADP
ejpam-1371	90	31	k.	k.	PROPN
ejpam-1371	90	32	remark	remark	PROPN
ejpam-1371	90	33	2	2	NUM
ejpam-1371	90	34	.	.	PUNCT
ejpam-1371	91	1	if	if	SCONJ
ejpam-1371	91	2	k	k	PROPN
ejpam-1371	91	3	is	be	AUX
ejpam-1371	91	4	complete	complete	ADJ
ejpam-1371	91	5	w.r.t	w.r.t	NOUN
ejpam-1371	91	6	.	.	PUNCT
ejpam-1371	92	1	η	η	PROPN
ejpam-1371	92	2	then	then	ADV
ejpam-1371	92	3	k	k	PROPN
ejpam-1371	92	4	is	be	AUX
ejpam-1371	92	5	both	both	PRON
ejpam-1371	92	6	weakly	weakly	ADJ
ejpam-1371	92	7	η	η	NOUN
ejpam-1371	92	8	-	-	ADJ
ejpam-1371	92	9	invex	invex	NOUN
ejpam-1371	92	10	set	set	NOUN
ejpam-1371	92	11	and	and	CCONJ
ejpam-1371	92	12	η	η	NOUN
ejpam-1371	92	13	-	-	ADJ
ejpam-1371	92	14	invex	invex	NOUN
ejpam-1371	92	15	set	set	NOUN
ejpam-1371	92	16	but	but	CCONJ
ejpam-1371	92	17	not	not	PART
ejpam-1371	92	18	conversely	conversely	ADV
ejpam-1371	92	19	.	.	PUNCT
ejpam-1371	93	1	in	in	ADP
ejpam-1371	93	2	section	section	NOUN
ejpam-1371	93	3	2	2	NUM
ejpam-1371	93	4	,	,	PUNCT
ejpam-1371	93	5	we	we	PRON
ejpam-1371	93	6	proposed	propose	VERB
ejpam-1371	93	7	the	the	DET
ejpam-1371	93	8	problem	problem	NOUN
ejpam-1371	93	9	of	of	ADP
ejpam-1371	93	10	absolutely	absolutely	ADV
ejpam-1371	93	11	generalized	generalized	ADJ
ejpam-1371	93	12	differential	differential	NOUN
ejpam-1371	93	13	dominated	dominate	VERB
ejpam-1371	93	14	variational	variational	ADJ
ejpam-1371	93	15	inequality	inequality	NOUN
ejpam-1371	93	16	problem	problem	NOUN
ejpam-1371	93	17	(	(	PUNCT
ejpam-1371	93	18	agddv	agddv	NOUN
ejpam-1371	93	19	ip	ip	NOUN
ejpam-1371	93	20	)	)	PUNCT
ejpam-1371	93	21	and	and	CCONJ
ejpam-1371	93	22	find	find	VERB
ejpam-1371	93	23	the	the	DET
ejpam-1371	93	24	iterative	iterative	NOUN
ejpam-1371	93	25	process	process	NOUN
ejpam-1371	93	26	of	of	ADP
ejpam-1371	93	27	it	it	PRON
ejpam-1371	93	28	in	in	ADP
ejpam-1371	93	29	the	the	DET
ejpam-1371	93	30	hilbert	hilbert	NOUN
ejpam-1371	93	31	space	space	NOUN
ejpam-1371	93	32	.	.	PUNCT
ejpam-1371	94	1	in	in	ADP
ejpam-1371	94	2	section	section	NOUN
ejpam-1371	94	3	3	3	NUM
ejpam-1371	94	4	,	,	PUNCT
ejpam-1371	94	5	we	we	PRON
ejpam-1371	94	6	introduce	introduce	VERB
ejpam-1371	94	7	the	the	DET
ejpam-1371	94	8	maximal	maximal	ADJ
ejpam-1371	94	9	fixed	fix	VERB
ejpam-1371	94	10	open	open	ADJ
ejpam-1371	94	11	set	set	VERB
ejpam-1371	94	12	and	and	CCONJ
ejpam-1371	94	13	defined	define	VERB
ejpam-1371	94	14	the	the	DET
ejpam-1371	94	15	generalized	generalize	VERB
ejpam-1371	94	16	differential	differential	NOUN
ejpam-1371	94	17	dominated	dominate	VERB
ejpam-1371	94	18	variational	variational	ADJ
ejpam-1371	94	19	inequality	inequality	NOUN
ejpam-1371	94	20	problems	problem	NOUN
ejpam-1371	94	21	(	(	PUNCT
ejpam-1371	94	22	gddv	gddv	NOUN
ejpam-1371	94	23	ipn	ipn	PROPN
ejpam-1371	94	24	)	)	PUNCT
ejpam-1371	94	25	and	and	CCONJ
ejpam-1371	94	26	generalized	generalized	ADJ
ejpam-1371	94	27	differential	differential	NOUN
ejpam-1371	94	28	dominated	dominate	VERB
ejpam-1371	94	29	complementarity	complementarity	NOUN
ejpam-1371	94	30	problem	problem	NOUN
ejpam-1371	94	31	(	(	PUNCT
ejpam-1371	94	32	gddc	gddc	NOUN
ejpam-1371	94	33	pn	pn	PROPN
ejpam-1371	94	34	)	)	PUNCT
ejpam-1371	94	35	in	in	ADP
ejpam-1371	94	36	riemannian	riemannian	ADJ
ejpam-1371	94	37	n	n	CCONJ
ejpam-1371	94	38	-	-	PUNCT
ejpam-1371	94	39	manifolds	manifold	NOUN
ejpam-1371	94	40	modelled	model	VERB
ejpam-1371	94	41	on	on	ADP
ejpam-1371	94	42	the	the	DET
ejpam-1371	94	43	hilbert	hilbert	NOUN
ejpam-1371	94	44	spaces	space	NOUN
ejpam-1371	94	45	.	.	PUNCT
ejpam-1371	95	1	further	far	ADV
ejpam-1371	95	2	,	,	PUNCT
ejpam-1371	95	3	we	we	PRON
ejpam-1371	95	4	study	study	VERB
ejpam-1371	95	5	the	the	DET
ejpam-1371	95	6	existence	existence	NOUN
ejpam-1371	95	7	theorems	theorem	NOUN
ejpam-1371	95	8	of	of	ADP
ejpam-1371	95	9	the	the	DET
ejpam-1371	95	10	problems	problem	NOUN
ejpam-1371	95	11	(	(	PUNCT
ejpam-1371	95	12	gddv	gddv	PROPN
ejpam-1371	95	13	ipn	ipn	PROPN
ejpam-1371	95	14	)	)	PUNCT
ejpam-1371	95	15	and	and	CCONJ
ejpam-1371	95	16	(	(	PUNCT
ejpam-1371	95	17	gddc	gddc	NOUN
ejpam-1371	95	18	pn	pn	PROPN
ejpam-1371	95	19	)	)	PUNCT
ejpam-1371	95	20	in	in	ADP
ejpam-1371	95	21	the	the	DET
ejpam-1371	95	22	presence	presence	NOUN
ejpam-1371	95	23	of	of	ADP
ejpam-1371	95	24	coincidence	coincidence	NOUN
ejpam-1371	95	25	index	index	NOUN
ejpam-1371	95	26	,	,	PUNCT
ejpam-1371	95	27	fixed	fix	VERB
ejpam-1371	95	28	point	point	NOUN
ejpam-1371	95	29	inclusion	inclusion	NOUN
ejpam-1371	95	30	of	of	ADP
ejpam-1371	95	31	homology	homology	NOUN
ejpam-1371	95	32	theory	theory	NOUN
ejpam-1371	95	33	and	and	CCONJ
ejpam-1371	95	34	one	one	NUM
ejpam-1371	95	35	-	-	PUNCT
ejpam-1371	95	36	point	point	NOUN
ejpam-1371	95	37	compactification	compactification	NOUN
ejpam-1371	95	38	of	of	ADP
ejpam-1371	95	39	topology	topology	NOUN
ejpam-1371	95	40	theory	theory	NOUN
ejpam-1371	95	41	.	.	PUNCT
ejpam-1371	96	1	2	2	X
ejpam-1371	96	2	.	.	X
ejpam-1371	96	3	the	the	DET
ejpam-1371	96	4	iterative	iterative	NOUN
ejpam-1371	96	5	method	method	NOUN
ejpam-1371	96	6	for	for	ADP
ejpam-1371	96	7	(	(	PUNCT
ejpam-1371	96	8	agddv	agddv	NOUN
ejpam-1371	96	9	i	i	PRON
ejpam-1371	96	10	p	p	NOUN
ejpam-1371	96	11	)	)	PUNCT
ejpam-1371	96	12	in	in	ADP
ejpam-1371	96	13	hilbert	hilbert	NOUN
ejpam-1371	96	14	space	space	NOUN
ejpam-1371	96	15	the	the	DET
ejpam-1371	96	16	notion	notion	NOUN
ejpam-1371	96	17	of	of	ADP
ejpam-1371	96	18	η	η	PROPN
ejpam-1371	96	19	-	-	ADJ
ejpam-1371	96	20	invex	invex	ADJ
ejpam-1371	96	21	function	function	NOUN
ejpam-1371	96	22	was	be	AUX
ejpam-1371	96	23	introduced	introduce	VERB
ejpam-1371	96	24	by	by	ADP
ejpam-1371	96	25	hanson	hanson	PROPN
ejpam-1371	97	1	[	[	X
ejpam-1371	97	2	16	16	NUM
ejpam-1371	97	3	]	]	PUNCT
ejpam-1371	97	4	as	as	ADP
ejpam-1371	97	5	a	a	DET
ejpam-1371	97	6	generalization	generalization	NOUN
ejpam-1371	97	7	of	of	ADP
ejpam-1371	97	8	convex	convex	PROPN
ejpam-1371	97	9	function	function	NOUN
ejpam-1371	97	10	.	.	PUNCT
ejpam-1371	98	1	in	in	ADP
ejpam-1371	98	2	2006	2006	NUM
ejpam-1371	98	3	,	,	PUNCT
ejpam-1371	98	4	a.	a.	PROPN
ejpam-1371	98	5	behera	behera	PROPN
ejpam-1371	98	6	and	and	CCONJ
ejpam-1371	98	7	p.k	p.k	PROPN
ejpam-1371	98	8	.	.	PUNCT
ejpam-1371	98	9	das	das	PROPN
ejpam-1371	99	1	[	[	X
ejpam-1371	99	2	3	3	NUM
ejpam-1371	99	3	]	]	PUNCT
ejpam-1371	99	4	generalized	generalize	VERB
ejpam-1371	99	5	the	the	DET
ejpam-1371	99	6	concept	concept	NOUN
ejpam-1371	99	7	of	of	ADP
ejpam-1371	99	8	invexity	invexity	NOUN
ejpam-1371	99	9	of	of	ADP
ejpam-1371	99	10	any	any	DET
ejpam-1371	99	11	function	function	NOUN
ejpam-1371	99	12	to	to	ADP
ejpam-1371	99	13	t	t	PROPN
ejpam-1371	99	14	-η	-η	NOUN
ejpam-1371	99	15	-	-	PUNCT
ejpam-1371	99	16	invexity	invexity	NOUN
ejpam-1371	99	17	of	of	ADP
ejpam-1371	99	18	the	the	DET
ejpam-1371	99	19	function	function	NOUN
ejpam-1371	99	20	in	in	ADP
ejpam-1371	99	21	ordered	order	VERB
ejpam-1371	99	22	topological	topological	ADJ
ejpam-1371	99	23	vector	vector	NOUN
ejpam-1371	99	24	spaces	space	NOUN
ejpam-1371	99	25	.	.	PUNCT
ejpam-1371	100	1	let	let	VERB
ejpam-1371	100	2	f	f	NOUN
ejpam-1371	100	3	:	:	PUNCT
ejpam-1371	100	4	m	m	VERB
ejpam-1371	100	5	→	→	SYM
ejpam-1371	100	6	r	r	NOUN
ejpam-1371	100	7	be	be	AUX
ejpam-1371	100	8	a	a	DET
ejpam-1371	100	9	differentiable	differentiable	ADJ
ejpam-1371	100	10	function	function	NOUN
ejpam-1371	100	11	where	where	SCONJ
ejpam-1371	100	12	∇f(u	∇f(u	PROPN
ejpam-1371	100	13	)	)	PUNCT
ejpam-1371	100	14	is	be	AUX
ejpam-1371	100	15	the	the	DET
ejpam-1371	100	16	differential	differential	NOUN
ejpam-1371	100	17	of	of	ADP
ejpam-1371	100	18	f	f	PROPN
ejpam-1371	100	19	at	at	ADP
ejpam-1371	100	20	u	u	PROPN
ejpam-1371	100	21	∈	∈	PROPN
ejpam-1371	100	22	m	m	VERB
ejpam-1371	100	23	.	.	PUNCT
ejpam-1371	101	1	then	then	ADV
ejpam-1371	101	2	,	,	PUNCT
ejpam-1371	101	3	t	t	PROPN
ejpam-1371	101	4	-η	-η	ADJ
ejpam-1371	101	5	-	-	PUNCT
ejpam-1371	101	6	invex	invex	NOUN
ejpam-1371	101	7	function	function	NOUN
ejpam-1371	101	8	is	be	AUX
ejpam-1371	101	9	defined	define	VERB
ejpam-1371	101	10	as	as	ADP
ejpam-1371	101	11	follows	follow	VERB
ejpam-1371	101	12	.	.	PUNCT
ejpam-1371	102	1	definition	definition	NOUN
ejpam-1371	102	2	7	7	NUM
ejpam-1371	102	3	(	(	PUNCT
ejpam-1371	102	4	[	[	X
ejpam-1371	102	5	3	3	NUM
ejpam-1371	102	6	]	]	NUM
ejpam-1371	102	7	)	)	PUNCT
ejpam-1371	102	8	.	.	PUNCT
ejpam-1371	103	1	let	let	VERB
ejpam-1371	103	2	f	f	NOUN
ejpam-1371	103	3	:	:	PUNCT
ejpam-1371	103	4	m	m	VERB
ejpam-1371	103	5	→	→	SYM
ejpam-1371	103	6	r	r	NOUN
ejpam-1371	103	7	be	be	AUX
ejpam-1371	103	8	any	any	DET
ejpam-1371	103	9	function	function	NOUN
ejpam-1371	103	10	.	.	PUNCT
ejpam-1371	104	1	then	then	ADV
ejpam-1371	104	2	,	,	PUNCT
ejpam-1371	104	3	(	(	PUNCT
ejpam-1371	104	4	a	a	X
ejpam-1371	104	5	)	)	PUNCT
ejpam-1371	104	6	f	f	PROPN
ejpam-1371	104	7	is	be	AUX
ejpam-1371	104	8	t	t	PROPN
ejpam-1371	104	9	-η	-η	NOUN
ejpam-1371	104	10	-	-	PUNCT
ejpam-1371	104	11	invex	invex	NOUN
ejpam-1371	104	12	on	on	ADP
ejpam-1371	104	13	m	m	PROPN
ejpam-1371	104	14	if	if	SCONJ
ejpam-1371	104	15	f(x)−	f(x)−	PROPN
ejpam-1371	104	16	f(u)−	f(u)−	PROPN
ejpam-1371	104	17	〈	〈	PROPN
ejpam-1371	104	18	t	t	PROPN
ejpam-1371	104	19	(	(	PUNCT
ejpam-1371	104	20	u),η(x	u),η(x	ADJ
ejpam-1371	104	21	,	,	PUNCT
ejpam-1371	104	22	u	u	NOUN
ejpam-1371	104	23	)	)	PUNCT
ejpam-1371	104	24	〉	〉	NOUN
ejpam-1371	104	25	≥	≥	NOUN
ejpam-1371	104	26	0	0	NUM
ejpam-1371	104	27	∀x	∀x	NUM
ejpam-1371	104	28	,	,	PUNCT
ejpam-1371	104	29	u	u	PROPN
ejpam-1371	104	30	∈	∈	PROPN
ejpam-1371	104	31	m	m	PRON
ejpam-1371	104	32	,	,	PUNCT
ejpam-1371	104	33	(	(	PUNCT
ejpam-1371	104	34	2	2	NUM
ejpam-1371	104	35	)	)	PUNCT
ejpam-1371	104	36	(	(	PUNCT
ejpam-1371	104	37	b	b	X
ejpam-1371	104	38	)	)	PUNCT
ejpam-1371	104	39	f	f	PROPN
ejpam-1371	104	40	is	be	AUX
ejpam-1371	104	41	t	t	PROPN
ejpam-1371	104	42	-η	-η	NOUN
ejpam-1371	104	43	-	-	PUNCT
ejpam-1371	104	44	invex	invex	NOUN
ejpam-1371	104	45	at	at	ADP
ejpam-1371	104	46	point	point	NOUN
ejpam-1371	104	47	u	u	NOUN
ejpam-1371	104	48	∈	∈	PROPN
ejpam-1371	104	49	m	m	VERB
ejpam-1371	104	50	if	if	SCONJ
ejpam-1371	104	51	f(x)−	f(x)−	PROPN
ejpam-1371	104	52	f(u)−	f(u)−	PROPN
ejpam-1371	104	53	〈	〈	PROPN
ejpam-1371	104	54	t	t	PROPN
ejpam-1371	104	55	(	(	PUNCT
ejpam-1371	104	56	u),η(x	u),η(x	ADJ
ejpam-1371	104	57	,	,	PUNCT
ejpam-1371	104	58	u	u	NOUN
ejpam-1371	104	59	)	)	PUNCT
ejpam-1371	104	60	〉	〉	NOUN
ejpam-1371	104	61	≥	≥	NOUN
ejpam-1371	104	62	0	0	NUM
ejpam-1371	104	63	∀x	∀x	NUM
ejpam-1371	104	64	∈	∈	PROPN
ejpam-1371	104	65	m	m	NOUN
ejpam-1371	104	66	.	.	PUNCT
ejpam-1371	105	1	(	(	PUNCT
ejpam-1371	105	2	3	3	X
ejpam-1371	105	3	)	)	PUNCT
ejpam-1371	105	4	in	in	ADP
ejpam-1371	105	5	this	this	DET
ejpam-1371	105	6	section	section	NOUN
ejpam-1371	105	7	,	,	PUNCT
ejpam-1371	105	8	we	we	PRON
ejpam-1371	105	9	proposed	propose	VERB
ejpam-1371	105	10	the	the	DET
ejpam-1371	105	11	generalized	generalize	VERB
ejpam-1371	105	12	dominated	dominate	VERB
ejpam-1371	105	13	differential	differential	ADJ
ejpam-1371	105	14	variational	variational	ADJ
ejpam-1371	105	15	inequality	inequality	NOUN
ejpam-1371	105	16	problems	problem	NOUN
ejpam-1371	105	17	(	(	PUNCT
ejpam-1371	105	18	gddv	gddv	NOUN
ejpam-1371	105	19	ip	ip	NOUN
ejpam-1371	105	20	)	)	PUNCT
ejpam-1371	105	21	and	and	CCONJ
ejpam-1371	105	22	generalized	generalize	VERB
ejpam-1371	105	23	dominated	dominate	VERB
ejpam-1371	105	24	differential	differential	NOUN
ejpam-1371	105	25	complementarity	complementarity	NOUN
ejpam-1371	105	26	problems	problem	NOUN
ejpam-1371	105	27	(	(	PUNCT
ejpam-1371	105	28	gddc	gddc	NOUN
ejpam-1371	105	29	p	p	X
ejpam-1371	105	30	)	)	PUNCT
ejpam-1371	105	31	in	in	ADP
ejpam-1371	105	32	reflexive	reflexive	ADJ
ejpam-1371	105	33	real	real	ADJ
ejpam-1371	105	34	banach	banach	NOUN
ejpam-1371	105	35	spaces	space	VERB
ejpam-1371	105	36	.	.	PUNCT
ejpam-1371	106	1	we	we	PRON
ejpam-1371	106	2	prove	prove	VERB
ejpam-1371	106	3	the	the	DET
ejpam-1371	106	4	existence	existence	NOUN
ejpam-1371	106	5	of	of	ADP
ejpam-1371	106	6	the	the	DET
ejpam-1371	106	7	solution	solution	NOUN
ejpam-1371	106	8	of	of	ADP
ejpam-1371	106	9	the	the	DET
ejpam-1371	106	10	absolutely	absolutely	ADV
ejpam-1371	106	11	generalized	generalized	ADJ
ejpam-1371	106	12	dominated	dominate	VERB
ejpam-1371	106	13	differential	differential	ADJ
ejpam-1371	106	14	variational	variational	ADJ
ejpam-1371	106	15	inequality	inequality	NOUN
ejpam-1371	106	16	problems	problem	NOUN
ejpam-1371	106	17	(	(	PUNCT
ejpam-1371	106	18	agddv	agddv	NOUN
ejpam-1371	106	19	ip	ip	ADV
ejpam-1371	106	20	)	)	PUNCT
ejpam-1371	106	21	using	use	VERB
ejpam-1371	106	22	the	the	DET
ejpam-1371	106	23	iterative	iterative	NOUN
ejpam-1371	106	24	process	process	NOUN
ejpam-1371	106	25	in	in	ADP
ejpam-1371	106	26	hilbert	hilbert	PROPN
ejpam-1371	106	27	spaces	space	NOUN
ejpam-1371	106	28	.	.	PUNCT
ejpam-1371	107	1	p.	p.	NOUN
ejpam-1371	107	2	das	das	PROPN
ejpam-1371	107	3	/	/	SYM
ejpam-1371	107	4	eur	eur	PROPN
ejpam-1371	107	5	.	.	PUNCT
ejpam-1371	108	1	j.	j.	PROPN
ejpam-1371	108	2	pure	pure	PROPN
ejpam-1371	108	3	appl	appl	PROPN
ejpam-1371	108	4	.	.	PROPN
ejpam-1371	108	5	math	math	PROPN
ejpam-1371	108	6	,	,	PUNCT
ejpam-1371	108	7	4	4	NUM
ejpam-1371	108	8	(	(	PUNCT
ejpam-1371	108	9	2011	2011	NUM
ejpam-1371	108	10	)	)	PUNCT
ejpam-1371	108	11	,	,	PUNCT
ejpam-1371	108	12	340	340	NUM
ejpam-1371	108	13	-	-	SYM
ejpam-1371	108	14	360	360	NUM
ejpam-1371	108	15	344	344	NUM
ejpam-1371	108	16	let	let	VERB
ejpam-1371	108	17	x	x	PRON
ejpam-1371	108	18	be	be	AUX
ejpam-1371	108	19	a	a	DET
ejpam-1371	108	20	reflexive	reflexive	ADJ
ejpam-1371	108	21	real	real	ADJ
ejpam-1371	108	22	banach	banach	NOUN
ejpam-1371	108	23	space	space	NOUN
ejpam-1371	108	24	and	and	CCONJ
ejpam-1371	108	25	k	k	PROPN
ejpam-1371	108	26	be	be	AUX
ejpam-1371	108	27	any	any	PRON
ejpam-1371	108	28	nonempty	nonempty	ADJ
ejpam-1371	108	29	η	η	ADJ
ejpam-1371	108	30	-	-	ADJ
ejpam-1371	108	31	invex	invex	ADJ
ejpam-1371	108	32	subset	subset	NOUN
ejpam-1371	108	33	of	of	ADP
ejpam-1371	108	34	x	x	X
ejpam-1371	108	35	.	.	PUNCT
ejpam-1371	109	1	let	let	VERB
ejpam-1371	109	2	t	t	NOUN
ejpam-1371	109	3	:	:	PUNCT
ejpam-1371	109	4	k	k	X
ejpam-1371	109	5	→	→	PUNCT
ejpam-1371	109	6	x	x	PROPN
ejpam-1371	109	7	∗	∗	NOUN
ejpam-1371	109	8	be	be	VERB
ejpam-1371	109	9	a	a	DET
ejpam-1371	109	10	nonlinear	nonlinear	ADJ
ejpam-1371	109	11	mapping	mapping	NOUN
ejpam-1371	109	12	and	and	CCONJ
ejpam-1371	109	13	f	f	NOUN
ejpam-1371	109	14	:	:	PUNCT
ejpam-1371	110	1	k	k	X
ejpam-1371	110	2	→	→	PUNCT
ejpam-1371	110	3	r	r	NOUN
ejpam-1371	110	4	be	be	AUX
ejpam-1371	110	5	a	a	DET
ejpam-1371	110	6	differentiable	differentiable	ADJ
ejpam-1371	110	7	map	map	NOUN
ejpam-1371	110	8	where	where	SCONJ
ejpam-1371	110	9	∇f	∇f	PROPN
ejpam-1371	110	10	is	be	AUX
ejpam-1371	110	11	the	the	DET
ejpam-1371	110	12	derivative	derivative	NOUN
ejpam-1371	110	13	of	of	ADP
ejpam-1371	110	14	f	f	PROPN
ejpam-1371	110	15	.	.	PUNCT
ejpam-1371	111	1	let	let	VERB
ejpam-1371	111	2	〈	〈	PROPN
ejpam-1371	111	3	f	f	X
ejpam-1371	111	4	,	,	PUNCT
ejpam-1371	111	5	x	x	SYM
ejpam-1371	111	6	〉	〉	NOUN
ejpam-1371	111	7	denote	denote	VERB
ejpam-1371	111	8	the	the	DET
ejpam-1371	111	9	value	value	NOUN
ejpam-1371	111	10	of	of	ADP
ejpam-1371	111	11	f	f	PROPN
ejpam-1371	111	12	∈	∈	PROPN
ejpam-1371	111	13	x	x	PUNCT
ejpam-1371	111	14	∗	∗	NOUN
ejpam-1371	111	15	at	at	ADP
ejpam-1371	111	16	point	point	NOUN
ejpam-1371	111	17	x	x	SYM
ejpam-1371	111	18	∈	∈	PROPN
ejpam-1371	111	19	x	x	X
ejpam-1371	111	20	.	.	PUNCT
ejpam-1371	112	1	the	the	DET
ejpam-1371	112	2	problem	problem	NOUN
ejpam-1371	112	3	(	(	PUNCT
ejpam-1371	112	4	gddv	gddv	NOUN
ejpam-1371	112	5	ip	ip	NOUN
ejpam-1371	112	6	)	)	PUNCT
ejpam-1371	112	7	is	be	AUX
ejpam-1371	112	8	defined	define	VERB
ejpam-1371	112	9	as	as	ADP
ejpam-1371	112	10	follows	follow	VERB
ejpam-1371	112	11	.	.	PUNCT
ejpam-1371	113	1	(	(	PUNCT
ejpam-1371	113	2	gddv	gddv	NOUN
ejpam-1371	113	3	ip	ip	NOUN
ejpam-1371	113	4	)	)	PUNCT
ejpam-1371	113	5	find	find	VERB
ejpam-1371	113	6	x0	x0	PROPN
ejpam-1371	113	7	∈	∈	PROPN
ejpam-1371	114	1	k	k	X
ejpam-1371	114	2	such	such	ADJ
ejpam-1371	114	3	that	that	SCONJ
ejpam-1371	114	4	〈	〈	PROPN
ejpam-1371	114	5	(	(	PUNCT
ejpam-1371	114	6	∇f	∇f	PROPN
ejpam-1371	114	7	−	−	PROPN
ejpam-1371	114	8	t	t	NOUN
ejpam-1371	114	9	)	)	PUNCT
ejpam-1371	114	10	(	(	PUNCT
ejpam-1371	114	11	x0),η(x	x0),η(x	PROPN
ejpam-1371	114	12	,	,	PUNCT
ejpam-1371	114	13	x0	x0	PROPN
ejpam-1371	114	14	)	)	PUNCT
ejpam-1371	114	15	〉	〉	NOUN
ejpam-1371	114	16	≥	≥	NOUN
ejpam-1371	114	17	0	0	NUM
ejpam-1371	114	18	∀x	∀x	NUM
ejpam-1371	114	19	∈	∈	PROPN
ejpam-1371	114	20	k	k	X
ejpam-1371	114	21	.	.	PUNCT
ejpam-1371	115	1	(	(	PUNCT
ejpam-1371	115	2	4	4	NUM
ejpam-1371	115	3	)	)	PUNCT
ejpam-1371	115	4	and	and	CCONJ
ejpam-1371	115	5	the	the	PRON
ejpam-1371	115	6	(	(	PUNCT
ejpam-1371	115	7	gddc	gddc	NOUN
ejpam-1371	115	8	p	p	NOUN
ejpam-1371	115	9	)	)	PUNCT
ejpam-1371	115	10	is	be	AUX
ejpam-1371	115	11	defined	define	VERB
ejpam-1371	115	12	as	as	ADP
ejpam-1371	115	13	follows	follow	VERB
ejpam-1371	115	14	.	.	PUNCT
ejpam-1371	116	1	(	(	PUNCT
ejpam-1371	116	2	gddc	gddc	NOUN
ejpam-1371	116	3	p	p	X
ejpam-1371	116	4	)	)	PUNCT
ejpam-1371	116	5	find	find	VERB
ejpam-1371	116	6	x0	x0	PROPN
ejpam-1371	116	7	∈	∈	PROPN
ejpam-1371	117	1	k	k	X
ejpam-1371	117	2	such	such	ADJ
ejpam-1371	117	3	that	that	SCONJ
ejpam-1371	117	4	〈	〈	PROPN
ejpam-1371	117	5	(	(	PUNCT
ejpam-1371	117	6	∇f	∇f	PROPN
ejpam-1371	117	7	−	−	PROPN
ejpam-1371	117	8	t	t	NOUN
ejpam-1371	117	9	)	)	PUNCT
ejpam-1371	117	10	(	(	PUNCT
ejpam-1371	117	11	x0),η(x	x0),η(x	PROPN
ejpam-1371	117	12	,	,	PUNCT
ejpam-1371	117	13	x0)〉=	x0)〉=	PROPN
ejpam-1371	117	14	0	0	PUNCT
ejpam-1371	117	15	∀x	∀x	X
ejpam-1371	117	16	∈	∈	PROPN
ejpam-1371	117	17	k	k	X
ejpam-1371	117	18	.	.	PUNCT
ejpam-1371	118	1	(	(	PUNCT
ejpam-1371	118	2	5	5	NUM
ejpam-1371	118	3	)	)	PUNCT
ejpam-1371	118	4	in	in	ADP
ejpam-1371	118	5	this	this	DET
ejpam-1371	118	6	section	section	NOUN
ejpam-1371	118	7	,	,	PUNCT
ejpam-1371	118	8	everywhere	everywhere	ADV
ejpam-1371	118	9	v	v	NOUN
ejpam-1371	118	10	is	be	AUX
ejpam-1371	118	11	considered	consider	VERB
ejpam-1371	118	12	as	as	ADP
ejpam-1371	118	13	an	an	DET
ejpam-1371	118	14	hilbert	hilbert	NOUN
ejpam-1371	118	15	space	space	NOUN
ejpam-1371	118	16	space	space	NOUN
ejpam-1371	118	17	with	with	ADP
ejpam-1371	118	18	the	the	DET
ejpam-1371	118	19	inner	inner	ADJ
ejpam-1371	118	20	product	product	NOUN
ejpam-1371	118	21	〈	〈	NOUN
ejpam-1371	118	22	·	·	SYM
ejpam-1371	118	23	〉	〉	NOUN
ejpam-1371	118	24	satisfies	satisfy	VERB
ejpam-1371	118	25	the	the	DET
ejpam-1371	118	26	euclidean	euclidean	ADJ
ejpam-1371	118	27	norm	norm	NOUN
ejpam-1371	118	28	|	|	ADV
ejpam-1371	118	29	·	·	PUNCT
ejpam-1371	118	30	|	|	ADV
ejpam-1371	118	31	by	by	ADP
ejpam-1371	118	32	the	the	DET
ejpam-1371	118	33	rule	rule	NOUN
ejpam-1371	118	34	|v|=	|v|=	PROPN
ejpam-1371	118	35	p	p	PROPN
ejpam-1371	118	36	〈	〈	PROPN
ejpam-1371	118	37	v	v	PROPN
ejpam-1371	118	38	,	,	PUNCT
ejpam-1371	118	39	v	v	NOUN
ejpam-1371	118	40	〉	〉	NOUN
ejpam-1371	118	41	and	and	CCONJ
ejpam-1371	118	42	m	m	NOUN
ejpam-1371	118	43	is	be	AUX
ejpam-1371	118	44	a	a	DET
ejpam-1371	118	45	nonempty	nonempty	ADJ
ejpam-1371	118	46	subset	subset	NOUN
ejpam-1371	118	47	of	of	ADP
ejpam-1371	118	48	v	v	NOUN
ejpam-1371	118	49	.	.	PUNCT
ejpam-1371	119	1	let	let	VERB
ejpam-1371	119	2	v	v	X
ejpam-1371	119	3	∗	∗	NOUN
ejpam-1371	119	4	be	be	AUX
ejpam-1371	119	5	the	the	DET
ejpam-1371	119	6	dual	dual	ADJ
ejpam-1371	119	7	of	of	ADP
ejpam-1371	119	8	v	v	NOUN
ejpam-1371	119	9	.	.	PUNCT
ejpam-1371	120	1	let	let	VERB
ejpam-1371	120	2	η	η	PROPN
ejpam-1371	120	3	:	:	PUNCT
ejpam-1371	120	4	m	m	PROPN
ejpam-1371	120	5	×m	×m	NOUN
ejpam-1371	120	6	→	→	SYM
ejpam-1371	120	7	v	v	X
ejpam-1371	120	8	be	be	AUX
ejpam-1371	120	9	a	a	DET
ejpam-1371	120	10	vector	vector	NOUN
ejpam-1371	120	11	valued	value	VERB
ejpam-1371	120	12	function	function	NOUN
ejpam-1371	120	13	.	.	PUNCT
ejpam-1371	121	1	definition	definition	NOUN
ejpam-1371	121	2	8	8	NUM
ejpam-1371	121	3	.	.	PUNCT
ejpam-1371	122	1	let	let	VERB
ejpam-1371	122	2	m	m	PROPN
ejpam-1371	122	3	⊂	⊂	PROPN
ejpam-1371	122	4	v	v	ADJ
ejpam-1371	122	5	.	.	PUNCT
ejpam-1371	123	1	an	an	DET
ejpam-1371	123	2	operator	operator	NOUN
ejpam-1371	123	3	a	a	DET
ejpam-1371	123	4	:	:	PUNCT
ejpam-1371	123	5	v	v	NOUN
ejpam-1371	123	6	→	→	SYM
ejpam-1371	123	7	v	v	NOUN
ejpam-1371	123	8	is	be	AUX
ejpam-1371	123	9	said	say	VERB
ejpam-1371	123	10	to	to	PART
ejpam-1371	123	11	be	be	AUX
ejpam-1371	123	12	quasi	quasi	ADJ
ejpam-1371	123	13	-	-	VERB
ejpam-1371	123	14	pseudomonotone	pseudomonotone	ADJ
ejpam-1371	123	15	(	(	PUNCT
ejpam-1371	123	16	in	in	ADP
ejpam-1371	123	17	short	short	ADJ
ejpam-1371	123	18	;	;	PUNCT
ejpam-1371	123	19	quasidomonotone	quasidomonotone	NOUN
ejpam-1371	123	20	)	)	PUNCT
ejpam-1371	123	21	with	with	ADP
ejpam-1371	123	22	respect	respect	NOUN
ejpam-1371	123	23	to	to	ADP
ejpam-1371	123	24	η	η	PROPN
ejpam-1371	123	25	on	on	ADP
ejpam-1371	123	26	m	m	PROPN
ejpam-1371	123	27	if	if	SCONJ
ejpam-1371	123	28	for	for	ADP
ejpam-1371	123	29	all	all	DET
ejpam-1371	123	30	t	t	NOUN
ejpam-1371	123	31	∈	∈	PROPN
ejpam-1371	123	32	(	(	PUNCT
ejpam-1371	123	33	0,1	0,1	NUM
ejpam-1371	123	34	)	)	PUNCT
ejpam-1371	123	35	,	,	PUNCT
ejpam-1371	123	36	there	there	PRON
ejpam-1371	123	37	exists	exist	VERB
ejpam-1371	123	38	a	a	DET
ejpam-1371	123	39	vector	vector	NOUN
ejpam-1371	123	40	function	function	NOUN
ejpam-1371	123	41	η	η	PROPN
ejpam-1371	123	42	:	:	PUNCT
ejpam-1371	123	43	m	m	PROPN
ejpam-1371	123	44	×m	×m	NOUN
ejpam-1371	123	45	→	→	SYM
ejpam-1371	123	46	v	v	ADP
ejpam-1371	123	47	such	such	ADJ
ejpam-1371	123	48	that	that	SCONJ
ejpam-1371	123	49	〈	〈	NOUN
ejpam-1371	123	50	a(tu),η(u	a(tu),η(u	NOUN
ejpam-1371	123	51	,	,	PUNCT
ejpam-1371	123	52	u	u	NOUN
ejpam-1371	123	53	)	)	PUNCT
ejpam-1371	123	54	〉	〉	NOUN
ejpam-1371	123	55	−	−	NOUN
ejpam-1371	123	56	〈	〈	NOUN
ejpam-1371	123	57	a(tv),η(v	a(tv),η(v	NOUN
ejpam-1371	123	58	,	,	PUNCT
ejpam-1371	123	59	v)〉=	v)〉=	NOUN
ejpam-1371	123	60	〈	〈	PROPN
ejpam-1371	123	61	a(v+	a(v+	NOUN
ejpam-1371	123	62	tη(v	tη(v	NOUN
ejpam-1371	123	63	,	,	PUNCT
ejpam-1371	123	64	u)),η(v	u)),η(v	PROPN
ejpam-1371	123	65	,	,	PUNCT
ejpam-1371	123	66	u	u	NOUN
ejpam-1371	123	67	)	)	PUNCT
ejpam-1371	123	68	〉	〉	NOUN
ejpam-1371	123	69	∀	∀	X
ejpam-1371	123	70	u	u	NOUN
ejpam-1371	123	71	,	,	PUNCT
ejpam-1371	123	72	v	v	NOUN
ejpam-1371	123	73	∈	∈	NOUN
ejpam-1371	123	74	m	m	NOUN
ejpam-1371	123	75	.	.	PUNCT
ejpam-1371	124	1	definition	definition	NOUN
ejpam-1371	124	2	9	9	NUM
ejpam-1371	124	3	.	.	PUNCT
ejpam-1371	125	1	let	let	VERB
ejpam-1371	125	2	m	m	PROPN
ejpam-1371	125	3	⊂	⊂	PROPN
ejpam-1371	125	4	v	v	ADJ
ejpam-1371	125	5	.	.	PUNCT
ejpam-1371	126	1	an	an	DET
ejpam-1371	126	2	operator	operator	NOUN
ejpam-1371	126	3	a	a	DET
ejpam-1371	126	4	:	:	PUNCT
ejpam-1371	126	5	v	v	NOUN
ejpam-1371	126	6	→	→	SYM
ejpam-1371	126	7	v	v	NOUN
ejpam-1371	126	8	is	be	AUX
ejpam-1371	126	9	said	say	VERB
ejpam-1371	126	10	to	to	PART
ejpam-1371	126	11	be	be	AUX
ejpam-1371	126	12	quasidomonotone	quasidomonotone	NOUN
ejpam-1371	126	13	and	and	CCONJ
ejpam-1371	126	14	potential	potential	ADJ
ejpam-1371	126	15	with	with	ADP
ejpam-1371	126	16	respect	respect	NOUN
ejpam-1371	126	17	to	to	ADP
ejpam-1371	126	18	η	η	PROPN
ejpam-1371	126	19	on	on	ADP
ejpam-1371	126	20	m	m	PROPN
ejpam-1371	126	21	if	if	SCONJ
ejpam-1371	126	22	for	for	ADP
ejpam-1371	126	23	all	all	DET
ejpam-1371	126	24	t	t	NOUN
ejpam-1371	126	25	∈	∈	PROPN
ejpam-1371	126	26	(	(	PUNCT
ejpam-1371	126	27	0,1	0,1	NUM
ejpam-1371	126	28	)	)	PUNCT
ejpam-1371	126	29	,	,	PUNCT
ejpam-1371	126	30	there	there	PRON
ejpam-1371	126	31	exists	exist	VERB
ejpam-1371	126	32	a	a	DET
ejpam-1371	126	33	vector	vector	NOUN
ejpam-1371	126	34	function	function	NOUN
ejpam-1371	126	35	η	η	PROPN
ejpam-1371	126	36	:	:	PUNCT
ejpam-1371	126	37	m	m	VERB
ejpam-1371	126	38	×	×	NOUN
ejpam-1371	126	39	m	m	NOUN
ejpam-1371	126	40	→	→	SYM
ejpam-1371	126	41	v	v	ADP
ejpam-1371	127	1	such	such	ADJ
ejpam-1371	127	2	that	that	SCONJ
ejpam-1371	127	3	1∫	1∫	NUM
ejpam-1371	127	4	0	0	NUM
ejpam-1371	127	5	〈	〈	NOUN
ejpam-1371	127	6	a(tu),η(u	a(tu),η(u	NOUN
ejpam-1371	127	7	,	,	PUNCT
ejpam-1371	127	8	u	u	NOUN
ejpam-1371	127	9	)	)	PUNCT
ejpam-1371	127	10	〉	〉	NOUN
ejpam-1371	127	11	d	d	NOUN
ejpam-1371	127	12	t	t	NOUN
ejpam-1371	127	13	−	−	PROPN
ejpam-1371	128	1	1∫	1∫	NUM
ejpam-1371	128	2	0	0	NUM
ejpam-1371	128	3	〈	〈	NOUN
ejpam-1371	128	4	a(tv),η(v	a(tv),η(v	NOUN
ejpam-1371	128	5	,	,	PUNCT
ejpam-1371	128	6	v	v	NOUN
ejpam-1371	128	7	)	)	PUNCT
ejpam-1371	128	8	〉	〉	NOUN
ejpam-1371	128	9	d	d	X
ejpam-1371	128	10	t	t	NOUN
ejpam-1371	128	11	=	=	SYM
ejpam-1371	128	12	1∫	1∫	NUM
ejpam-1371	128	13	0	0	NUM
ejpam-1371	128	14	〈	〈	NOUN
ejpam-1371	128	15	a(v+	a(v+	NOUN
ejpam-1371	128	16	tη(v	tη(v	NOUN
ejpam-1371	128	17	,	,	PUNCT
ejpam-1371	128	18	u)),η(v	u)),η(v	PROPN
ejpam-1371	128	19	,	,	PUNCT
ejpam-1371	128	20	u	u	NOUN
ejpam-1371	128	21	)	)	PUNCT
ejpam-1371	128	22	〉	〉	NOUN
ejpam-1371	128	23	d	d	PROPN
ejpam-1371	128	24	t	t	PROPN
ejpam-1371	128	25	∀	∀	X
ejpam-1371	128	26	u	u	NOUN
ejpam-1371	128	27	,	,	PUNCT
ejpam-1371	128	28	v	v	NOUN
ejpam-1371	128	29	∈	∈	NOUN
ejpam-1371	128	30	m	m	NOUN
ejpam-1371	128	31	.	.	PUNCT
ejpam-1371	129	1	(	(	PUNCT
ejpam-1371	129	2	agddv	agddv	NOUN
ejpam-1371	129	3	i	i	PRON
ejpam-1371	129	4	p	p	NOUN
ejpam-1371	129	5	)	)	PUNCT
ejpam-1371	129	6	and	and	CCONJ
ejpam-1371	129	7	the	the	DET
ejpam-1371	129	8	iterative	iterative	NOUN
ejpam-1371	129	9	process	process	NOUN
ejpam-1371	129	10	let	let	VERB
ejpam-1371	129	11	f	f	PRON
ejpam-1371	129	12	:	:	PUNCT
ejpam-1371	129	13	m	m	VERB
ejpam-1371	129	14	→	→	SYM
ejpam-1371	129	15	r	r	NOUN
ejpam-1371	129	16	be	be	AUX
ejpam-1371	129	17	a	a	DET
ejpam-1371	129	18	differentiable	differentiable	ADJ
ejpam-1371	129	19	map	map	NOUN
ejpam-1371	129	20	where	where	SCONJ
ejpam-1371	129	21	∇f	∇f	PROPN
ejpam-1371	129	22	is	be	AUX
ejpam-1371	129	23	the	the	DET
ejpam-1371	129	24	derivative	derivative	NOUN
ejpam-1371	129	25	of	of	ADP
ejpam-1371	129	26	f	f	PROPN
ejpam-1371	129	27	and	and	CCONJ
ejpam-1371	129	28	t	t	PROPN
ejpam-1371	129	29	:	:	PUNCT
ejpam-1371	129	30	m	m	VERB
ejpam-1371	129	31	→	→	SYM
ejpam-1371	129	32	v	v	NUM
ejpam-1371	129	33	∗	∗	NOUN
ejpam-1371	129	34	be	be	VERB
ejpam-1371	129	35	a	a	DET
ejpam-1371	129	36	nonlinear	nonlinear	ADJ
ejpam-1371	129	37	map	map	NOUN
ejpam-1371	129	38	.	.	PUNCT
ejpam-1371	130	1	the	the	DET
ejpam-1371	130	2	absolutely	absolutely	ADV
ejpam-1371	130	3	generalized	generalized	ADJ
ejpam-1371	130	4	dominated	dominate	VERB
ejpam-1371	130	5	differential	differential	ADJ
ejpam-1371	130	6	variational	variational	ADJ
ejpam-1371	130	7	inequality	inequality	NOUN
ejpam-1371	130	8	problems	problem	NOUN
ejpam-1371	130	9	(	(	PUNCT
ejpam-1371	130	10	agddv	agddv	NOUN
ejpam-1371	130	11	ip	ip	NOUN
ejpam-1371	130	12	)	)	PUNCT
ejpam-1371	130	13	is	be	AUX
ejpam-1371	130	14	defined	define	VERB
ejpam-1371	130	15	as	as	SCONJ
ejpam-1371	130	16	follows	follow	VERB
ejpam-1371	130	17	:	:	PUNCT
ejpam-1371	130	18	(	(	PUNCT
ejpam-1371	130	19	agddv	agddv	NOUN
ejpam-1371	130	20	ip	ip	NOUN
ejpam-1371	130	21	)	)	PUNCT
ejpam-1371	130	22	find	find	VERB
ejpam-1371	130	23	u∗	u∗	ADJ
ejpam-1371	130	24	∈	∈	PROPN
ejpam-1371	130	25	m	m	VERB
ejpam-1371	130	26	such	such	ADJ
ejpam-1371	130	27	that	that	SCONJ
ejpam-1371	130	28	〈	〈	PROPN
ejpam-1371	130	29	(	(	PUNCT
ejpam-1371	130	30	∇f	∇f	PROPN
ejpam-1371	130	31	−	−	PROPN
ejpam-1371	130	32	t	t	NOUN
ejpam-1371	130	33	)	)	PUNCT
ejpam-1371	130	34	(	(	PUNCT
ejpam-1371	130	35	u∗),η(v	u∗),η(v	NOUN
ejpam-1371	130	36	,	,	PUNCT
ejpam-1371	130	37	u∗	u∗	NOUN
ejpam-1371	130	38	)	)	PUNCT
ejpam-1371	130	39	〉	〉	NOUN
ejpam-1371	130	40	≥	≥	NOUN
ejpam-1371	130	41	0	0	NUM
ejpam-1371	130	42	∀v	∀v	X
ejpam-1371	130	43	∈	∈	PROPN
ejpam-1371	130	44	m	m	NOUN
ejpam-1371	130	45	,	,	PUNCT
ejpam-1371	130	46	(	(	PUNCT
ejpam-1371	130	47	6	6	NUM
ejpam-1371	130	48	)	)	PUNCT
ejpam-1371	130	49	if	if	SCONJ
ejpam-1371	130	50	there	there	PRON
ejpam-1371	130	51	exists	exist	VERB
ejpam-1371	130	52	a	a	DET
ejpam-1371	130	53	finite	finite	ADJ
ejpam-1371	130	54	subsequence	subsequence	NOUN
ejpam-1371	130	55	{	{	PUNCT
ejpam-1371	130	56	unk	unk	NOUN
ejpam-1371	130	57	}	}	PUNCT
ejpam-1371	130	58	∞	∞	NUM
ejpam-1371	130	59	k=1	k=1	NOUN
ejpam-1371	130	60	such	such	ADJ
ejpam-1371	130	61	that	that	DET
ejpam-1371	130	62	unk	unk	NOUN
ejpam-1371	130	63	w	w	NOUN
ejpam-1371	130	64	−→	−→	NOUN
ejpam-1371	130	65	u∗	u∗	NOUN
ejpam-1371	130	66	as	as	ADP
ejpam-1371	130	67	k→∞	k→∞	NOUN
ejpam-1371	130	68	,	,	PUNCT
ejpam-1371	130	69	and	and	CCONJ
ejpam-1371	130	70	satisfying	satisfy	VERB
ejpam-1371	130	71	lim	lim	PROPN
ejpam-1371	130	72	k→∞	k→∞	PROPN
ejpam-1371	130	73	sup	sup	PROPN
ejpam-1371	130	74	〈	〈	PROPN
ejpam-1371	130	75	t	t	PROPN
ejpam-1371	130	76	(	(	PUNCT
ejpam-1371	130	77	unk	unk	NOUN
ejpam-1371	130	78	)	)	PUNCT
ejpam-1371	130	79	,	,	PUNCT
ejpam-1371	130	80	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	130	81	)	)	PUNCT
ejpam-1371	130	82	〉	〉	NOUN
ejpam-1371	130	83	≤	≤	NUM
ejpam-1371	130	84	lim	lim	PROPN
ejpam-1371	130	85	k→∞	k→∞	PROPN
ejpam-1371	130	86	sup	sup	NUM
ejpam-1371	130	87	〈	〈	PROPN
ejpam-1371	130	88	∇f(unk	∇f(unk	NOUN
ejpam-1371	130	89	)	)	PUNCT
ejpam-1371	130	90	,	,	PUNCT
ejpam-1371	130	91	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	130	92	)	)	PUNCT
ejpam-1371	130	93	〉	〉	NOUN
ejpam-1371	130	94	.	.	PUNCT
ejpam-1371	131	1	let	let	VERB
ejpam-1371	131	2	the	the	DET
ejpam-1371	131	3	following	follow	VERB
ejpam-1371	131	4	properties	property	NOUN
ejpam-1371	131	5	satisfies	satisfie	NOUN
ejpam-1371	131	6	.	.	PUNCT
ejpam-1371	132	1	p.	p.	NOUN
ejpam-1371	132	2	das	das	PROPN
ejpam-1371	132	3	/	/	SYM
ejpam-1371	132	4	eur	eur	PROPN
ejpam-1371	132	5	.	.	PUNCT
ejpam-1371	133	1	j.	j.	PROPN
ejpam-1371	133	2	pure	pure	PROPN
ejpam-1371	133	3	appl	appl	PROPN
ejpam-1371	133	4	.	.	PROPN
ejpam-1371	133	5	math	math	PROPN
ejpam-1371	133	6	,	,	PUNCT
ejpam-1371	133	7	4	4	NUM
ejpam-1371	133	8	(	(	PUNCT
ejpam-1371	133	9	2011	2011	NUM
ejpam-1371	133	10	)	)	PUNCT
ejpam-1371	133	11	,	,	PUNCT
ejpam-1371	133	12	340	340	NUM
ejpam-1371	133	13	-	-	SYM
ejpam-1371	133	14	360	360	NUM
ejpam-1371	133	15	345	345	NUM
ejpam-1371	133	16	(	(	PUNCT
ejpam-1371	133	17	p1	p1	PROPN
ejpam-1371	133	18	)	)	PUNCT
ejpam-1371	133	19	(	(	PUNCT
ejpam-1371	133	20	a	a	X
ejpam-1371	133	21	)	)	PUNCT
ejpam-1371	133	22	∇f	∇f	NOUN
ejpam-1371	133	23	and	and	CCONJ
ejpam-1371	133	24	t	t	PROPN
ejpam-1371	133	25	are	be	AUX
ejpam-1371	133	26	quasidomonotone	quasidomonotone	NOUN
ejpam-1371	133	27	and	and	CCONJ
ejpam-1371	133	28	potential	potential	ADJ
ejpam-1371	133	29	with	with	ADP
ejpam-1371	133	30	respect	respect	NOUN
ejpam-1371	133	31	to	to	ADP
ejpam-1371	133	32	η	η	PROPN
ejpam-1371	133	33	on	on	ADP
ejpam-1371	133	34	m	m	PRON
ejpam-1371	133	35	,	,	PUNCT
ejpam-1371	133	36	(	(	PUNCT
ejpam-1371	133	37	b	b	X
ejpam-1371	133	38	)	)	PUNCT
ejpam-1371	133	39	|t	|t	PROPN
ejpam-1371	133	40	(	(	PUNCT
ejpam-1371	133	41	v+	v+	ADP
ejpam-1371	133	42	tη(v	tη(v	NOUN
ejpam-1371	133	43	,	,	PUNCT
ejpam-1371	133	44	u))|	u))|	PROPN
ejpam-1371	133	45	≤	≤	PROPN
ejpam-1371	133	46	|t	|t	VERB
ejpam-1371	133	47	(	(	PUNCT
ejpam-1371	133	48	u+	u+	NOUN
ejpam-1371	133	49	tη(v	tη(v	NOUN
ejpam-1371	133	50	,	,	PUNCT
ejpam-1371	133	51	u))|	u))|	PROPN
ejpam-1371	133	52	∀u	∀u	PROPN
ejpam-1371	133	53	,	,	PUNCT
ejpam-1371	133	54	v	v	X
ejpam-1371	133	55	∈	∈	NOUN
ejpam-1371	133	56	m	m	NOUN
ejpam-1371	133	57	,	,	PUNCT
ejpam-1371	133	58	(	(	PUNCT
ejpam-1371	133	59	c	c	X
ejpam-1371	133	60	)	)	PUNCT
ejpam-1371	133	61	〈	〈	NOUN
ejpam-1371	133	62	t	t	NOUN
ejpam-1371	133	63	(	(	PUNCT
ejpam-1371	133	64	u),η(v	u),η(v	X
ejpam-1371	133	65	,	,	PUNCT
ejpam-1371	133	66	u	u	NOUN
ejpam-1371	133	67	)	)	PUNCT
ejpam-1371	133	68	〉	〉	NOUN
ejpam-1371	133	69	≤	≤	NUM
ejpam-1371	133	70	〈	〈	PROPN
ejpam-1371	133	71	t	t	PROPN
ejpam-1371	133	72	(	(	PUNCT
ejpam-1371	133	73	u),η(v	u),η(v	X
ejpam-1371	133	74	,	,	PUNCT
ejpam-1371	133	75	z)〉+	z)〉+	X
ejpam-1371	133	76	〈	〈	PROPN
ejpam-1371	133	77	t	t	PROPN
ejpam-1371	133	78	(	(	PUNCT
ejpam-1371	133	79	u),η(u	u),η(u	PROPN
ejpam-1371	133	80	,	,	PUNCT
ejpam-1371	133	81	z	z	NOUN
ejpam-1371	133	82	)	)	PUNCT
ejpam-1371	133	83	〉	〉	NOUN
ejpam-1371	133	84	∀u	∀u	NOUN
ejpam-1371	133	85	,	,	PUNCT
ejpam-1371	133	86	v	v	X
ejpam-1371	133	87	∈	∈	NOUN
ejpam-1371	133	88	m	m	NOUN
ejpam-1371	133	89	,	,	PUNCT
ejpam-1371	134	1	fixed	fix	VERB
ejpam-1371	134	2	z	z	PROPN
ejpam-1371	134	3	∈	∈	PROPN
ejpam-1371	134	4	m	m	VERB
ejpam-1371	134	5	,	,	PUNCT
ejpam-1371	134	6	(	(	PUNCT
ejpam-1371	134	7	d	d	X
ejpam-1371	134	8	)	)	PUNCT
ejpam-1371	134	9	|∇f(u)−	|∇f(u)−	NOUN
ejpam-1371	135	1	t	t	NOUN
ejpam-1371	135	2	(	(	PUNCT
ejpam-1371	135	3	u)|	u)|	NOUN
ejpam-1371	135	4	≤	≤	NOUN
ejpam-1371	136	1	α	α	NOUN
ejpam-1371	136	2	∀	∀	NOUN
ejpam-1371	136	3	u	u	NOUN
ejpam-1371	136	4	∈	∈	NOUN
ejpam-1371	136	5	m	m	VERB
ejpam-1371	136	6	.	.	PUNCT
ejpam-1371	137	1	(	(	PUNCT
ejpam-1371	137	2	p2	p2	PROPN
ejpam-1371	137	3	)	)	PUNCT
ejpam-1371	137	4	let	let	VERB
ejpam-1371	137	5	η	η	X
ejpam-1371	137	6	be	be	AUX
ejpam-1371	137	7	an	an	DET
ejpam-1371	137	8	absolutely	absolutely	ADV
ejpam-1371	137	9	bounded	bounded	ADJ
ejpam-1371	137	10	function	function	NOUN
ejpam-1371	137	11	satisfying	satisfy	VERB
ejpam-1371	137	12	the	the	DET
ejpam-1371	137	13	condition	condition	NOUN
ejpam-1371	137	14	|η(v	|η(v	PROPN
ejpam-1371	137	15	,	,	PUNCT
ejpam-1371	137	16	u)|	u)|	NOUN
ejpam-1371	137	17	≤	≤	ADV
ejpam-1371	137	18	2	2	NUM
ejpam-1371	137	19	α	α	PROPN
ejpam-1371	137	20	δ(ε	δ(ε	NOUN
ejpam-1371	137	21	)	)	PUNCT
ejpam-1371	137	22	∀u	∀u	NOUN
ejpam-1371	137	23	,	,	PUNCT
ejpam-1371	137	24	v	v	X
ejpam-1371	137	25	∈	∈	NOUN
ejpam-1371	137	26	m	m	VERB
ejpam-1371	137	27	,	,	PUNCT
ejpam-1371	137	28	(	(	PUNCT
ejpam-1371	137	29	7	7	X
ejpam-1371	137	30	)	)	PUNCT
ejpam-1371	137	31	where	where	SCONJ
ejpam-1371	137	32	α	α	NOUN
ejpam-1371	137	33	>	>	X
ejpam-1371	137	34	0	0	PUNCT
ejpam-1371	138	1	and	and	CCONJ
ejpam-1371	138	2	for	for	ADP
ejpam-1371	138	3	each	each	DET
ejpam-1371	138	4	ε	ε	PROPN
ejpam-1371	138	5	>	>	X
ejpam-1371	138	6	0	0	PROPN
ejpam-1371	138	7	,	,	PUNCT
ejpam-1371	138	8	δ(ε	δ(ε	PROPN
ejpam-1371	138	9	)	)	PUNCT
ejpam-1371	138	10	be	be	VERB
ejpam-1371	138	11	a	a	DET
ejpam-1371	138	12	bounded	bounded	ADJ
ejpam-1371	138	13	continuous	continuous	ADJ
ejpam-1371	138	14	function	function	NOUN
ejpam-1371	138	15	satisfying	satisfy	VERB
ejpam-1371	138	16	δ(ε	δ(ε	NOUN
ejpam-1371	138	17	)	)	PUNCT
ejpam-1371	138	18	<	<	X
ejpam-1371	138	19	α	α	PROPN
ejpam-1371	138	20	2	2	NUM
ejpam-1371	138	21	.	.	PUNCT
ejpam-1371	139	1	(	(	PUNCT
ejpam-1371	139	2	p3	p3	NOUN
ejpam-1371	139	3	)	)	PUNCT
ejpam-1371	139	4	∇f	∇f	PROPN
ejpam-1371	139	5	and	and	CCONJ
ejpam-1371	139	6	t	t	PROPN
ejpam-1371	139	7	are	be	AUX
ejpam-1371	139	8	lipschitz	lipschitz	NOUN
ejpam-1371	139	9	continuous	continuous	ADJ
ejpam-1371	139	10	with	with	ADP
ejpam-1371	139	11	ranks	rank	NOUN
ejpam-1371	139	12	l1	l1	PROPN
ejpam-1371	139	13	>	>	X
ejpam-1371	139	14	0	0	PUNCT
ejpam-1371	139	15	and	and	CCONJ
ejpam-1371	139	16	l2	l2	VERB
ejpam-1371	139	17	>	>	X
ejpam-1371	139	18	0	0	PUNCT
ejpam-1371	139	19	respectively	respectively	ADV
ejpam-1371	139	20	.	.	PUNCT
ejpam-1371	140	1	we	we	PRON
ejpam-1371	140	2	introduce	introduce	VERB
ejpam-1371	140	3	a	a	DET
ejpam-1371	140	4	functional	functional	ADJ
ejpam-1371	140	5	γ	γ	NOUN
ejpam-1371	140	6	:	:	PUNCT
ejpam-1371	140	7	v	v	NOUN
ejpam-1371	140	8	→	→	SYM
ejpam-1371	140	9	r	r	NOUN
ejpam-1371	140	10	by	by	ADP
ejpam-1371	140	11	the	the	DET
ejpam-1371	140	12	relation	relation	NOUN
ejpam-1371	140	13	γ(u	γ(u	NOUN
ejpam-1371	140	14	)	)	PUNCT
ejpam-1371	140	15	=	=	SYM
ejpam-1371	140	16	aη(u)−	aη(u)−	NOUN
ejpam-1371	140	17	bη(u	bη(u	NUM
ejpam-1371	140	18	)	)	PUNCT
ejpam-1371	140	19	,	,	PUNCT
ejpam-1371	140	20	(	(	PUNCT
ejpam-1371	140	21	8)	8)	NUM
ejpam-1371	140	22	where	where	SCONJ
ejpam-1371	140	23	aη(u	aη(u	VERB
ejpam-1371	140	24	)	)	PUNCT
ejpam-1371	140	25	=	=	PUNCT
ejpam-1371	141	1	1∫	1∫	NUM
ejpam-1371	141	2	0	0	NUM
ejpam-1371	141	3	〈	〈	NOUN
ejpam-1371	141	4	∇f(tu),η(u	∇f(tu),η(u	NOUN
ejpam-1371	141	5	,	,	PUNCT
ejpam-1371	141	6	u)〉d	u)〉d	PROPN
ejpam-1371	141	7	t	t	PROPN
ejpam-1371	141	8	(	(	PUNCT
ejpam-1371	141	9	9	9	NUM
ejpam-1371	141	10	)	)	PUNCT
ejpam-1371	141	11	and	and	CCONJ
ejpam-1371	141	12	bη(u	bη(u	NOUN
ejpam-1371	141	13	)	)	PUNCT
ejpam-1371	141	14	=	=	PUNCT
ejpam-1371	142	1	1∫	1∫	NUM
ejpam-1371	142	2	0	0	NUM
ejpam-1371	142	3	〈	〈	PROPN
ejpam-1371	142	4	t	t	PROPN
ejpam-1371	142	5	(	(	PUNCT
ejpam-1371	142	6	tu),η(u	tu),η(u	NOUN
ejpam-1371	142	7	,	,	PUNCT
ejpam-1371	142	8	u	u	NOUN
ejpam-1371	142	9	)	)	PUNCT
ejpam-1371	142	10	〉	〉	NOUN
ejpam-1371	142	11	d	d	NOUN
ejpam-1371	142	12	t.	t.	NOUN
ejpam-1371	142	13	(	(	PUNCT
ejpam-1371	142	14	10	10	NUM
ejpam-1371	142	15	)	)	PUNCT
ejpam-1371	142	16	by	by	ADP
ejpam-1371	142	17	the	the	DET
ejpam-1371	142	18	quasi	quasi	NOUN
ejpam-1371	142	19	-	-	NOUN
ejpam-1371	142	20	pseudomonotone	pseudomonotone	ADJ
ejpam-1371	142	21	and	and	CCONJ
ejpam-1371	142	22	potential	potential	ADJ
ejpam-1371	142	23	property	property	NOUN
ejpam-1371	142	24	(	(	PUNCT
ejpam-1371	142	25	i.e.	i.e.	X
ejpam-1371	142	26	,	,	PUNCT
ejpam-1371	142	27	p1(a	p1(a	NOUN
ejpam-1371	142	28	)	)	PUNCT
ejpam-1371	142	29	)	)	PUNCT
ejpam-1371	142	30	of	of	ADP
ejpam-1371	142	31	∇f	∇f	PROPN
ejpam-1371	142	32	and	and	CCONJ
ejpam-1371	142	33	t	t	PROPN
ejpam-1371	142	34	,	,	PUNCT
ejpam-1371	142	35	we	we	PRON
ejpam-1371	142	36	have	have	VERB
ejpam-1371	142	37	aη(u)−	aη(u)−	NOUN
ejpam-1371	142	38	aη(v	aη(v	NOUN
ejpam-1371	142	39	)	)	PUNCT
ejpam-1371	142	40	=	=	PUNCT
ejpam-1371	143	1	1∫	1∫	NUM
ejpam-1371	143	2	0	0	NUM
ejpam-1371	143	3	〈	〈	NOUN
ejpam-1371	143	4	∇f(tu),η(u	∇f(tu),η(u	NOUN
ejpam-1371	143	5	,	,	PUNCT
ejpam-1371	143	6	u)〉d	u)〉d	NOUN
ejpam-1371	143	7	t	t	PROPN
ejpam-1371	143	8	−	−	PROPN
ejpam-1371	144	1	1∫	1∫	NUM
ejpam-1371	144	2	0	0	NUM
ejpam-1371	144	3	〈	〈	PROPN
ejpam-1371	144	4	∇f(tv),η(v	∇f(tv),η(v	PROPN
ejpam-1371	144	5	,	,	PUNCT
ejpam-1371	144	6	v	v	NOUN
ejpam-1371	144	7	)	)	PUNCT
ejpam-1371	144	8	〉	〉	NOUN
ejpam-1371	144	9	d	d	X
ejpam-1371	144	10	t	t	NOUN
ejpam-1371	144	11	=	=	SYM
ejpam-1371	145	1	1∫	1∫	NUM
ejpam-1371	145	2	0	0	NUM
ejpam-1371	145	3	〈	〈	NOUN
ejpam-1371	145	4	∇f(v	∇f(v	ADJ
ejpam-1371	145	5	+	+	NUM
ejpam-1371	145	6	tη(v	tη(v	NOUN
ejpam-1371	145	7	,	,	PUNCT
ejpam-1371	145	8	u)),η(v	u)),η(v	PROPN
ejpam-1371	145	9	,	,	PUNCT
ejpam-1371	145	10	u	u	NOUN
ejpam-1371	145	11	)	)	PUNCT
ejpam-1371	145	12	〉	〉	NOUN
ejpam-1371	145	13	d	d	NOUN
ejpam-1371	145	14	t.	t.	NOUN
ejpam-1371	145	15	(	(	PUNCT
ejpam-1371	145	16	11	11	NUM
ejpam-1371	145	17	)	)	PUNCT
ejpam-1371	145	18	and	and	CCONJ
ejpam-1371	145	19	bη(u)−	bη(u)−	PROPN
ejpam-1371	145	20	bη(v	bη(v	NOUN
ejpam-1371	145	21	)	)	PUNCT
ejpam-1371	145	22	=	=	PUNCT
ejpam-1371	146	1	1∫	1∫	NUM
ejpam-1371	146	2	0	0	NUM
ejpam-1371	146	3	〈	〈	PROPN
ejpam-1371	146	4	t	t	PROPN
ejpam-1371	146	5	(	(	PUNCT
ejpam-1371	146	6	tu),η(u	tu),η(u	NOUN
ejpam-1371	146	7	,	,	PUNCT
ejpam-1371	146	8	u)〉d	u)〉d	PROPN
ejpam-1371	146	9	t	t	PROPN
ejpam-1371	146	10	−	−	PROPN
ejpam-1371	147	1	1∫	1∫	NUM
ejpam-1371	147	2	0	0	NUM
ejpam-1371	147	3	〈	〈	PROPN
ejpam-1371	147	4	t	t	PROPN
ejpam-1371	147	5	(	(	PUNCT
ejpam-1371	147	6	tv),η(v	tv),η(v	PROPN
ejpam-1371	147	7	,	,	PUNCT
ejpam-1371	147	8	v	v	NOUN
ejpam-1371	147	9	)	)	PUNCT
ejpam-1371	147	10	〉	〉	NOUN
ejpam-1371	147	11	d	d	X
ejpam-1371	147	12	t	t	NOUN
ejpam-1371	147	13	=	=	SYM
ejpam-1371	148	1	1∫	1∫	NUM
ejpam-1371	148	2	0	0	NUM
ejpam-1371	148	3	〈	〈	PROPN
ejpam-1371	148	4	t	t	PROPN
ejpam-1371	148	5	(	(	PUNCT
ejpam-1371	148	6	v	v	NOUN
ejpam-1371	148	7	+	+	NOUN
ejpam-1371	148	8	tη(v	tη(v	NOUN
ejpam-1371	148	9	,	,	PUNCT
ejpam-1371	148	10	u)),η(v	u)),η(v	PROPN
ejpam-1371	148	11	,	,	PUNCT
ejpam-1371	148	12	u	u	NOUN
ejpam-1371	148	13	)	)	PUNCT
ejpam-1371	148	14	〉	〉	NOUN
ejpam-1371	148	15	d	d	NOUN
ejpam-1371	148	16	t.	t.	NOUN
ejpam-1371	148	17	(	(	PUNCT
ejpam-1371	148	18	12	12	NUM
ejpam-1371	148	19	)	)	PUNCT
ejpam-1371	148	20	p.	p.	NOUN
ejpam-1371	148	21	das	das	PROPN
ejpam-1371	148	22	/	/	SYM
ejpam-1371	148	23	eur	eur	PROPN
ejpam-1371	148	24	.	.	PUNCT
ejpam-1371	149	1	j.	j.	PROPN
ejpam-1371	149	2	pure	pure	PROPN
ejpam-1371	149	3	appl	appl	PROPN
ejpam-1371	149	4	.	.	PROPN
ejpam-1371	149	5	math	math	PROPN
ejpam-1371	149	6	,	,	PUNCT
ejpam-1371	149	7	4	4	NUM
ejpam-1371	149	8	(	(	PUNCT
ejpam-1371	149	9	2011	2011	NUM
ejpam-1371	149	10	)	)	PUNCT
ejpam-1371	149	11	,	,	PUNCT
ejpam-1371	149	12	340	340	NUM
ejpam-1371	149	13	-	-	SYM
ejpam-1371	149	14	360	360	NUM
ejpam-1371	149	15	346	346	NUM
ejpam-1371	149	16	hence	hence	ADV
ejpam-1371	149	17	,	,	PUNCT
ejpam-1371	149	18	we	we	PRON
ejpam-1371	149	19	get	get	VERB
ejpam-1371	149	20	γ(u)−	γ(u)−	NOUN
ejpam-1371	149	21	γ(v	γ(v	NOUN
ejpam-1371	149	22	)	)	PUNCT
ejpam-1371	149	23	=	=	NUM
ejpam-1371	149	24	aη(u)−	aη(u)−	NOUN
ejpam-1371	149	25	bη(u)−	bη(u)−	NOUN
ejpam-1371	149	26	aη(v)+	aη(v)+	PART
ejpam-1371	149	27	bη(v	bη(v	NOUN
ejpam-1371	149	28	)	)	PUNCT
ejpam-1371	149	29	,	,	PUNCT
ejpam-1371	149	30	=	=	SYM
ejpam-1371	149	31	�	�	PROPN
ejpam-1371	149	32	aη(u)−	aη(u)−	PROPN
ejpam-1371	149	33	aη(v	aη(v	NOUN
ejpam-1371	149	34	)	)	PUNCT
ejpam-1371	149	35	�	�	PROPN
ejpam-1371	149	36	−	−	PROPN
ejpam-1371	149	37	�	�	PROPN
ejpam-1371	149	38	bη(u)−	bη(u)−	PROPN
ejpam-1371	149	39	bη(v	bη(v	NOUN
ejpam-1371	149	40	)	)	PUNCT
ejpam-1371	149	41	�	�	PROPN
ejpam-1371	149	42	,	,	PUNCT
ejpam-1371	149	43	=	=	PROPN
ejpam-1371	150	1	1∫	1∫	NUM
ejpam-1371	150	2	0	0	NUM
ejpam-1371	150	3	〈	〈	NOUN
ejpam-1371	150	4	∇f(v	∇f(v	ADJ
ejpam-1371	150	5	+	+	NUM
ejpam-1371	150	6	tη(v	tη(v	NOUN
ejpam-1371	150	7	,	,	PUNCT
ejpam-1371	150	8	u)),η(v	u)),η(v	PROPN
ejpam-1371	150	9	,	,	PUNCT
ejpam-1371	150	10	u)〉d	u)〉d	PROPN
ejpam-1371	150	11	t	t	PROPN
ejpam-1371	150	12	−	−	PROPN
ejpam-1371	151	1	1∫	1∫	NUM
ejpam-1371	151	2	0	0	NUM
ejpam-1371	151	3	〈	〈	PROPN
ejpam-1371	151	4	t	t	PROPN
ejpam-1371	151	5	(	(	PUNCT
ejpam-1371	151	6	v	v	NOUN
ejpam-1371	151	7	+	+	NOUN
ejpam-1371	151	8	tη(v	tη(v	NOUN
ejpam-1371	151	9	,	,	PUNCT
ejpam-1371	151	10	u)),η(v	u)),η(v	PROPN
ejpam-1371	151	11	,	,	PUNCT
ejpam-1371	151	12	u	u	NOUN
ejpam-1371	151	13	)	)	PUNCT
ejpam-1371	151	14	〉	〉	NOUN
ejpam-1371	151	15	d	d	NOUN
ejpam-1371	151	16	t.	t.	NOUN
ejpam-1371	151	17	(	(	PUNCT
ejpam-1371	151	18	13	13	NUM
ejpam-1371	151	19	)	)	PUNCT
ejpam-1371	151	20	to	to	PART
ejpam-1371	151	21	solve	solve	VERB
ejpam-1371	151	22	the	the	DET
ejpam-1371	151	23	problem	problem	NOUN
ejpam-1371	151	24	(	(	PUNCT
ejpam-1371	151	25	agddv	agddv	NOUN
ejpam-1371	151	26	ip	ip	NOUN
ejpam-1371	151	27	)	)	PUNCT
ejpam-1371	151	28	,	,	PUNCT
ejpam-1371	151	29	we	we	PRON
ejpam-1371	151	30	consider	consider	VERB
ejpam-1371	151	31	the	the	DET
ejpam-1371	151	32	following	follow	VERB
ejpam-1371	151	33	iterative	iterative	NOUN
ejpam-1371	151	34	process	process	NOUN
ejpam-1371	151	35	.	.	PUNCT
ejpam-1371	152	1	let	let	VERB
ejpam-1371	152	2	u0	u0	ADJ
ejpam-1371	152	3	be	be	AUX
ejpam-1371	152	4	an	an	DET
ejpam-1371	152	5	arbitrary	arbitrary	ADJ
ejpam-1371	152	6	element	element	NOUN
ejpam-1371	152	7	of	of	ADP
ejpam-1371	152	8	m	m	PROPN
ejpam-1371	152	9	.	.	PUNCT
ejpam-1371	153	1	for	for	ADP
ejpam-1371	153	2	n=	n=	ADJ
ejpam-1371	153	3	0,1,2	0,1,2	NUM
ejpam-1371	153	4	,	,	PUNCT
ejpam-1371	153	5	.	.	PUNCT
ejpam-1371	153	6	.	.	PUNCT
ejpam-1371	153	7	.	.	PUNCT
ejpam-1371	154	1	,	,	PUNCT
ejpam-1371	154	2	we	we	PRON
ejpam-1371	154	3	define	define	VERB
ejpam-1371	154	4	un+1	un+1	PROPN
ejpam-1371	154	5	∈	∈	PROPN
ejpam-1371	154	6	m	m	NOUN
ejpam-1371	154	7	as	as	ADP
ejpam-1371	154	8	the	the	DET
ejpam-1371	154	9	solution	solution	NOUN
ejpam-1371	154	10	of	of	ADP
ejpam-1371	154	11	the	the	DET
ejpam-1371	154	12	variational	variational	ADJ
ejpam-1371	154	13	inequality	inequality	NOUN
ejpam-1371	154	14	problem	problem	NOUN
ejpam-1371	154	15	〈	〈	ADP
ejpam-1371	154	16	η(un	η(un	PROPN
ejpam-1371	154	17	,	,	PUNCT
ejpam-1371	154	18	un+1),η(v	un+1),η(v	ADP
ejpam-1371	154	19	,	,	PUNCT
ejpam-1371	154	20	un+1)〉+ρn〈∇f(un),η(v	un+1)〉+ρn〈∇f(un),η(v	PROPN
ejpam-1371	154	21	,	,	PUNCT
ejpam-1371	154	22	un	un	NOUN
ejpam-1371	154	23	)	)	PUNCT
ejpam-1371	154	24	〉	〉	NOUN
ejpam-1371	154	25	≥	≥	NOUN
ejpam-1371	154	26	0	0	NUM
ejpam-1371	155	1	∀v	∀v	X
ejpam-1371	155	2	∈	∈	PROPN
ejpam-1371	155	3	m	m	NOUN
ejpam-1371	155	4	,	,	PUNCT
ejpam-1371	155	5	(	(	PUNCT
ejpam-1371	155	6	14	14	NUM
ejpam-1371	155	7	)	)	PUNCT
ejpam-1371	155	8	where	where	SCONJ
ejpam-1371	155	9	the	the	DET
ejpam-1371	155	10	sequence	sequence	NOUN
ejpam-1371	155	11	{	{	PUNCT
ejpam-1371	155	12	ρn	ρn	PROPN
ejpam-1371	155	13	}	}	PUNCT
ejpam-1371	155	14	∞	∞	PROPN
ejpam-1371	155	15	n=0	n=0	NUM
ejpam-1371	155	16	of	of	ADP
ejpam-1371	155	17	the	the	DET
ejpam-1371	155	18	iteration	iteration	NOUN
ejpam-1371	155	19	parameters	parameter	NOUN
ejpam-1371	155	20	satisfies	satisfy	VERB
ejpam-1371	155	21	the	the	DET
ejpam-1371	155	22	conditions	condition	NOUN
ejpam-1371	155	23	0≤	0≤	ADP
ejpam-1371	155	24	ρ∗	ρ∗	PROPN
ejpam-1371	155	25	≤	≤	NUM
ejpam-1371	155	26	ρn	ρn	VERB
ejpam-1371	155	27	≤	≤	NUM
ejpam-1371	155	28	ρ	ρ	PROPN
ejpam-1371	155	29	∗	∗	NOUN
ejpam-1371	155	30	≤	≤	NUM
ejpam-1371	155	31	2	2	NUM
ejpam-1371	155	32	l1	l1	NOUN
ejpam-1371	155	33	+	+	CCONJ
ejpam-1371	155	34	l2	l2	NOUN
ejpam-1371	155	35	.	.	PUNCT
ejpam-1371	156	1	(	(	PUNCT
ejpam-1371	156	2	15	15	NUM
ejpam-1371	156	3	)	)	PUNCT
ejpam-1371	156	4	for	for	ADP
ejpam-1371	156	5	the	the	DET
ejpam-1371	156	6	sequence	sequence	NOUN
ejpam-1371	156	7	{	{	PUNCT
ejpam-1371	156	8	εn	εn	ADP
ejpam-1371	156	9	}	}	PUNCT
ejpam-1371	156	10	∞	∞	PROPN
ejpam-1371	156	11	n=1	n=1	PROPN
ejpam-1371	156	12	,	,	PUNCT
ejpam-1371	156	13	we	we	PRON
ejpam-1371	156	14	assume	assume	VERB
ejpam-1371	156	15	that	that	SCONJ
ejpam-1371	156	16	∞∑	∞∑	NUM
ejpam-1371	156	17	n=1	n=1	PROPN
ejpam-1371	156	18	δ(εn	δ(εn	PROPN
ejpam-1371	156	19	)	)	PUNCT
ejpam-1371	156	20	=	=	PUNCT
ejpam-1371	157	1	σ	σ	NOUN
ejpam-1371	157	2	<	<	X
ejpam-1371	157	3	∞.	∞.	PROPN
ejpam-1371	157	4	(	(	PUNCT
ejpam-1371	157	5	16	16	NUM
ejpam-1371	157	6	)	)	PUNCT
ejpam-1371	157	7	since	since	SCONJ
ejpam-1371	157	8	|η(v	|η(v	PROPN
ejpam-1371	157	9	,	,	PUNCT
ejpam-1371	157	10	u)|	u)|	NOUN
ejpam-1371	157	11	≤	≤	ADV
ejpam-1371	157	12	2	2	NUM
ejpam-1371	157	13	α	α	PROPN
ejpam-1371	157	14	δ(ε	δ(ε	NOUN
ejpam-1371	157	15	)	)	PUNCT
ejpam-1371	157	16	for	for	ADP
ejpam-1371	157	17	all	all	DET
ejpam-1371	157	18	u	u	NOUN
ejpam-1371	157	19	,	,	PUNCT
ejpam-1371	157	20	v	v	NOUN
ejpam-1371	157	21	∈	∈	NOUN
ejpam-1371	157	22	m	m	NOUN
ejpam-1371	157	23	and	and	CCONJ
ejpam-1371	157	24	δ(ε	δ(ε	NOUN
ejpam-1371	157	25	)	)	PUNCT
ejpam-1371	157	26	<	<	X
ejpam-1371	157	27	2	2	NUM
ejpam-1371	157	28	α	α	NOUN
ejpam-1371	157	29	,	,	PUNCT
ejpam-1371	157	30	we	we	PRON
ejpam-1371	157	31	have	have	VERB
ejpam-1371	157	32	|η(un	|η(un	PROPN
ejpam-1371	157	33	,	,	PUNCT
ejpam-1371	157	34	un+1)|	un+1)|	PROPN
ejpam-1371	157	35	<	<	X
ejpam-1371	157	36	1⇒	1⇒	PROPN
ejpam-1371	157	37	lim	lim	PROPN
ejpam-1371	157	38	n→∞	n→∞	X
ejpam-1371	158	1	|η(un	|η(un	PROPN
ejpam-1371	158	2	,	,	PUNCT
ejpam-1371	158	3	un+1)|=	un+1)|=	PROPN
ejpam-1371	158	4	0	0	NUM
ejpam-1371	158	5	.	.	PUNCT
ejpam-1371	159	1	hence	hence	ADV
ejpam-1371	159	2	,	,	PUNCT
ejpam-1371	159	3	the	the	DET
ejpam-1371	159	4	series	series	NOUN
ejpam-1371	159	5	∞∑	∞∑	PROPN
ejpam-1371	159	6	n=0	n=0	PROPN
ejpam-1371	159	7	|η(un	|η(un	PROPN
ejpam-1371	159	8	,	,	PUNCT
ejpam-1371	159	9	un+1)|	un+1)|	PROPN
ejpam-1371	159	10	2	2	NUM
ejpam-1371	159	11	is	be	AUX
ejpam-1371	159	12	convergent	convergent	NOUN
ejpam-1371	159	13	.	.	PUNCT
ejpam-1371	160	1	let	let	VERB
ejpam-1371	160	2	the	the	DET
ejpam-1371	160	3	limit	limit	NOUN
ejpam-1371	160	4	point	point	NOUN
ejpam-1371	160	5	of	of	ADP
ejpam-1371	160	6	the	the	DET
ejpam-1371	160	7	series	series	NOUN
ejpam-1371	160	8	∞∑	∞∑	PROPN
ejpam-1371	160	9	∗n=0	∗n=0	NOUN
ejpam-1371	160	10	|η(un	|η(un	PROPN
ejpam-1371	160	11	,	,	PUNCT
ejpam-1371	160	12	un+1)|	un+1)|	PROPN
ejpam-1371	160	13	2	2	NUM
ejpam-1371	160	14	be	be	NOUN
ejpam-1371	160	15	2σ	2σ	X
ejpam-1371	160	16	l1+l2	l1+l2	PROPN
ejpam-1371	160	17	.	.	PUNCT
ejpam-1371	161	1	to	to	PART
ejpam-1371	161	2	analyze	analyze	VERB
ejpam-1371	161	3	the	the	DET
ejpam-1371	161	4	convergence	convergence	NOUN
ejpam-1371	161	5	of	of	ADP
ejpam-1371	161	6	the	the	DET
ejpam-1371	161	7	iterative	iterative	NOUN
ejpam-1371	161	8	process	process	NOUN
ejpam-1371	161	9	,	,	PUNCT
ejpam-1371	161	10	we	we	PRON
ejpam-1371	161	11	need	need	VERB
ejpam-1371	161	12	the	the	DET
ejpam-1371	161	13	following	follow	VERB
ejpam-1371	161	14	assertion	assertion	NOUN
ejpam-1371	161	15	.	.	PUNCT
ejpam-1371	162	1	lemma	lemma	PROPN
ejpam-1371	162	2	1	1	NUM
ejpam-1371	162	3	(	(	PUNCT
ejpam-1371	162	4	[	[	X
ejpam-1371	162	5	26	26	NUM
ejpam-1371	162	6	,	,	PUNCT
ejpam-1371	162	7	p.93	p.93	NOUN
ejpam-1371	162	8	]	]	PUNCT
ejpam-1371	162	9	)	)	PUNCT
ejpam-1371	162	10	.	.	PUNCT
ejpam-1371	163	1	let	let	VERB
ejpam-1371	163	2	{	{	PUNCT
ejpam-1371	163	3	ak	ak	PROPN
ejpam-1371	163	4	}	}	PUNCT
ejpam-1371	163	5	∞	∞	NUM
ejpam-1371	163	6	k=0	k=0	PROPN
ejpam-1371	163	7	be	be	AUX
ejpam-1371	163	8	a	a	DET
ejpam-1371	163	9	numerical	numerical	ADJ
ejpam-1371	163	10	sequence	sequence	NOUN
ejpam-1371	163	11	such	such	ADJ
ejpam-1371	163	12	that	that	SCONJ
ejpam-1371	163	13	ak+1	ak+1	VERB
ejpam-1371	163	14	≤	≤	NUM
ejpam-1371	163	15	ak	ak	PROPN
ejpam-1371	164	1	+	+	X
ejpam-1371	164	2	δk	δk	PROPN
ejpam-1371	164	3	where	where	SCONJ
ejpam-1371	164	4	δk	δk	DET
ejpam-1371	164	5	≥	≥	NOUN
ejpam-1371	164	6	0	0	NUM
ejpam-1371	164	7	,	,	PUNCT
ejpam-1371	164	8	k	k	X
ejpam-1371	165	1	=	=	PUNCT
ejpam-1371	165	2	0,1,2	0,1,2	NUM
ejpam-1371	165	3	,	,	PUNCT
ejpam-1371	165	4	.	.	PUNCT
ejpam-1371	165	5	.	.	PUNCT
ejpam-1371	166	1	.	.	PUNCT
ejpam-1371	167	1	,	,	PUNCT
ejpam-1371	167	2	∞∑	∞∑	DET
ejpam-1371	167	3	k=0	k=0	PROPN
ejpam-1371	167	4	δk	δk	ADP
ejpam-1371	167	5	<	<	X
ejpam-1371	167	6	∞	∞	PROPN
ejpam-1371	167	7	,	,	PUNCT
ejpam-1371	167	8	then	then	ADV
ejpam-1371	167	9	,	,	PUNCT
ejpam-1371	167	10	there	there	PRON
ejpam-1371	167	11	exists	exist	VERB
ejpam-1371	167	12	a	a	DET
ejpam-1371	167	13	limit	limit	NOUN
ejpam-1371	167	14	lim	lim	PROPN
ejpam-1371	167	15	k→∞	k→∞	PROPN
ejpam-1371	167	16	ak	ak	PROPN
ejpam-1371	167	17	<	<	PROPN
ejpam-1371	167	18	∞.	∞.	PROPN
ejpam-1371	167	19	in	in	ADP
ejpam-1371	167	20	addition	addition	NOUN
ejpam-1371	167	21	,	,	PUNCT
ejpam-1371	167	22	the	the	DET
ejpam-1371	167	23	sequence	sequence	NOUN
ejpam-1371	167	24	{	{	PUNCT
ejpam-1371	167	25	ak	ak	PROPN
ejpam-1371	167	26	}	}	PUNCT
ejpam-1371	167	27	∞	∞	NUM
ejpam-1371	167	28	k=0	k=0	PROPN
ejpam-1371	167	29	is	be	AUX
ejpam-1371	167	30	bounded	bound	VERB
ejpam-1371	167	31	below	below	ADP
ejpam-1371	167	32	then	then	ADV
ejpam-1371	167	33	the	the	DET
ejpam-1371	167	34	limit	limit	NOUN
ejpam-1371	167	35	is	be	AUX
ejpam-1371	167	36	finite	finite	ADJ
ejpam-1371	167	37	.	.	PUNCT
ejpam-1371	168	1	p.	p.	NOUN
ejpam-1371	168	2	das	das	PROPN
ejpam-1371	168	3	/	/	SYM
ejpam-1371	168	4	eur	eur	PROPN
ejpam-1371	168	5	.	.	PUNCT
ejpam-1371	169	1	j.	j.	PROPN
ejpam-1371	169	2	pure	pure	PROPN
ejpam-1371	169	3	appl	appl	PROPN
ejpam-1371	169	4	.	.	PROPN
ejpam-1371	169	5	math	math	PROPN
ejpam-1371	169	6	,	,	PUNCT
ejpam-1371	169	7	4	4	NUM
ejpam-1371	169	8	(	(	PUNCT
ejpam-1371	169	9	2011	2011	NUM
ejpam-1371	169	10	)	)	PUNCT
ejpam-1371	169	11	,	,	PUNCT
ejpam-1371	169	12	340	340	NUM
ejpam-1371	169	13	-	-	SYM
ejpam-1371	169	14	360	360	NUM
ejpam-1371	169	15	347	347	NUM
ejpam-1371	169	16	theorem	theorem	NOUN
ejpam-1371	169	17	3	3	X
ejpam-1371	169	18	.	.	PUNCT
ejpam-1371	170	1	let	let	VERB
ejpam-1371	170	2	m	m	VERB
ejpam-1371	170	3	⊂	⊂	PROPN
ejpam-1371	170	4	v	v	PART
ejpam-1371	170	5	be	be	AUX
ejpam-1371	170	6	complete	complete	ADJ
ejpam-1371	170	7	w.r.t	w.r.t	NOUN
ejpam-1371	170	8	.	.	PUNCT
ejpam-1371	171	1	η	η	PROPN
ejpam-1371	171	2	(	(	PUNCT
ejpam-1371	171	3	or	or	CCONJ
ejpam-1371	171	4	at	at	ADP
ejpam-1371	171	5	least	least	ADJ
ejpam-1371	171	6	weakly	weakly	ADJ
ejpam-1371	171	7	η	η	ADJ
ejpam-1371	171	8	-	-	ADJ
ejpam-1371	171	9	invex	invex	ADJ
ejpam-1371	171	10	set	set	NOUN
ejpam-1371	171	11	)	)	PUNCT
ejpam-1371	171	12	where	where	SCONJ
ejpam-1371	171	13	η	η	PROPN
ejpam-1371	171	14	:	:	PUNCT
ejpam-1371	171	15	m	m	VERB
ejpam-1371	171	16	×	×	NOUN
ejpam-1371	171	17	m	m	PROPN
ejpam-1371	171	18	→	→	SYM
ejpam-1371	171	19	v	v	PROPN
ejpam-1371	171	20	is	be	AUX
ejpam-1371	171	21	a	a	DET
ejpam-1371	171	22	continuous	continuous	ADJ
ejpam-1371	171	23	function	function	NOUN
ejpam-1371	171	24	.	.	PUNCT
ejpam-1371	172	1	let	let	VERB
ejpam-1371	172	2	the	the	DET
ejpam-1371	172	3	condition	condition	NOUN
ejpam-1371	172	4	given	give	VERB
ejpam-1371	172	5	in	in	ADP
ejpam-1371	172	6	(	(	PUNCT
ejpam-1371	172	7	15	15	NUM
ejpam-1371	172	8	)	)	PUNCT
ejpam-1371	172	9	be	be	AUX
ejpam-1371	172	10	satisfied	satisfied	ADJ
ejpam-1371	172	11	.	.	PUNCT
ejpam-1371	173	1	then	then	ADV
ejpam-1371	173	2	,	,	PUNCT
ejpam-1371	173	3	the	the	DET
ejpam-1371	173	4	iterative	iterative	NOUN
ejpam-1371	173	5	sequence	sequence	NOUN
ejpam-1371	173	6	{	{	PUNCT
ejpam-1371	173	7	un	un	PROPN
ejpam-1371	173	8	}	}	PUNCT
ejpam-1371	173	9	∞	∞	PRON
ejpam-1371	173	10	n=0	n=0	PUNCT
ejpam-1371	173	11	given	give	VERB
ejpam-1371	173	12	by	by	ADP
ejpam-1371	173	13	(	(	PUNCT
ejpam-1371	173	14	14	14	NUM
ejpam-1371	173	15	)	)	PUNCT
ejpam-1371	173	16	is	be	AUX
ejpam-1371	173	17	bounded	bound	VERB
ejpam-1371	173	18	in	in	ADP
ejpam-1371	173	19	v	v	NOUN
ejpam-1371	173	20	,	,	PUNCT
ejpam-1371	173	21	and	and	CCONJ
ejpam-1371	173	22	all	all	DET
ejpam-1371	173	23	its	its	PRON
ejpam-1371	173	24	weak	weak	ADJ
ejpam-1371	173	25	limit	limit	NOUN
ejpam-1371	173	26	points	point	NOUN
ejpam-1371	173	27	are	be	AUX
ejpam-1371	173	28	solutions	solution	NOUN
ejpam-1371	173	29	of	of	ADP
ejpam-1371	173	30	the	the	DET
ejpam-1371	173	31	problem	problem	NOUN
ejpam-1371	173	32	(	(	PUNCT
ejpam-1371	173	33	agddv	agddv	NOUN
ejpam-1371	173	34	ip	ip	NOUN
ejpam-1371	173	35	)	)	PUNCT
ejpam-1371	173	36	.	.	PUNCT
ejpam-1371	174	1	proof	proof	NOUN
ejpam-1371	174	2	.	.	PUNCT
ejpam-1371	175	1	let	let	VERB
ejpam-1371	175	2	us	we	PRON
ejpam-1371	175	3	assume	assume	VERB
ejpam-1371	175	4	m	m	PRON
ejpam-1371	175	5	⊂	⊂	NOUN
ejpam-1371	175	6	v	v	NOUN
ejpam-1371	175	7	as	as	ADP
ejpam-1371	175	8	weakly	weakly	ADJ
ejpam-1371	175	9	η	η	NOUN
ejpam-1371	175	10	-	-	ADJ
ejpam-1371	175	11	invex	invex	ADJ
ejpam-1371	175	12	set	set	NOUN
ejpam-1371	175	13	.	.	PUNCT
ejpam-1371	176	1	let	let	VERB
ejpam-1371	176	2	s(u0)⊂	s(u0)⊂	PROPN
ejpam-1371	176	3	m	m	AUX
ejpam-1371	176	4	be	be	AUX
ejpam-1371	176	5	a	a	DET
ejpam-1371	176	6	bounded	bounded	ADJ
ejpam-1371	176	7	subset	subset	NOUN
ejpam-1371	176	8	of	of	ADP
ejpam-1371	176	9	m	m	AUX
ejpam-1371	176	10	defined	define	VERB
ejpam-1371	176	11	by	by	ADP
ejpam-1371	176	12	s(u0	s(u0	NOUN
ejpam-1371	176	13	)	)	PUNCT
ejpam-1371	177	1	=	=	PRON
ejpam-1371	177	2	{	{	PUNCT
ejpam-1371	177	3	u	u	NOUN
ejpam-1371	177	4	∈	∈	NOUN
ejpam-1371	177	5	m	m	VERB
ejpam-1371	177	6	:	:	PUNCT
ejpam-1371	177	7	γ(u	γ(u	X
ejpam-1371	177	8	)	)	PUNCT
ejpam-1371	177	9	≤	≤	NOUN
ejpam-1371	177	10	γ(u0	γ(u0	NOUN
ejpam-1371	177	11	)	)	PUNCT
ejpam-1371	177	12	+	+	CCONJ
ejpam-1371	177	13	3σ	3σ	NUM
ejpam-1371	177	14	}	}	PUNCT
ejpam-1371	177	15	.	.	PUNCT
ejpam-1371	178	1	then	then	ADV
ejpam-1371	178	2	,	,	PUNCT
ejpam-1371	178	3	s(u0	s(u0	NOUN
ejpam-1371	178	4	)	)	PUNCT
ejpam-1371	178	5	is	be	AUX
ejpam-1371	178	6	nonempty	nonempty	ADJ
ejpam-1371	178	7	because	because	SCONJ
ejpam-1371	178	8	by	by	ADP
ejpam-1371	178	9	definition	definition	NOUN
ejpam-1371	178	10	of	of	ADP
ejpam-1371	178	11	s(u0	s(u0	NOUN
ejpam-1371	178	12	)	)	PUNCT
ejpam-1371	178	13	,	,	PUNCT
ejpam-1371	178	14	we	we	PRON
ejpam-1371	178	15	have	have	VERB
ejpam-1371	178	16	u0	u0	PROPN
ejpam-1371	178	17	∈	∈	PROPN
ejpam-1371	178	18	s(u0	s(u0	NOUN
ejpam-1371	178	19	)	)	PUNCT
ejpam-1371	178	20	.	.	PUNCT
ejpam-1371	179	1	next	next	ADV
ejpam-1371	179	2	,	,	PUNCT
ejpam-1371	179	3	we	we	PRON
ejpam-1371	179	4	show	show	VERB
ejpam-1371	179	5	that	that	SCONJ
ejpam-1371	179	6	the	the	DET
ejpam-1371	179	7	iterative	iterative	NOUN
ejpam-1371	179	8	sequence	sequence	NOUN
ejpam-1371	179	9	defined	define	VERB
ejpam-1371	179	10	by	by	ADP
ejpam-1371	179	11	{	{	PUNCT
ejpam-1371	179	12	un	un	PROPN
ejpam-1371	179	13	}	}	PUNCT
ejpam-1371	179	14	∞	∞	NUM
ejpam-1371	179	15	n=0	n=0	PUNCT
ejpam-1371	180	1	⊂	⊂	X
ejpam-1371	180	2	s(u0	s(u0	NOUN
ejpam-1371	180	3	)	)	PUNCT
ejpam-1371	180	4	(	(	PUNCT
ejpam-1371	180	5	17	17	NUM
ejpam-1371	180	6	)	)	PUNCT
ejpam-1371	180	7	is	be	AUX
ejpam-1371	180	8	bounded	bound	VERB
ejpam-1371	180	9	,	,	PUNCT
ejpam-1371	180	10	i.e	i.e	X
ejpam-1371	180	11	,	,	PUNCT
ejpam-1371	180	12	to	to	PART
ejpam-1371	180	13	show	show	VERB
ejpam-1371	180	14	if	if	SCONJ
ejpam-1371	180	15	un	un	PROPN
ejpam-1371	180	16	∈	∈	PROPN
ejpam-1371	180	17	s(u0	s(u0	NOUN
ejpam-1371	180	18	)	)	PUNCT
ejpam-1371	180	19	then	then	ADV
ejpam-1371	180	20	un+1	un+1	PROPN
ejpam-1371	180	21	∈	∈	PROPN
ejpam-1371	180	22	s(u0	s(u0	NOUN
ejpam-1371	180	23	)	)	PUNCT
ejpam-1371	180	24	.	.	PUNCT
ejpam-1371	181	1	since	since	SCONJ
ejpam-1371	181	2	∇f	∇f	PROPN
ejpam-1371	181	3	and	and	CCONJ
ejpam-1371	181	4	t	t	PROPN
ejpam-1371	181	5	are	be	AUX
ejpam-1371	181	6	lipschitz	lipschitz	NOUN
ejpam-1371	181	7	continuous	continuous	ADJ
ejpam-1371	181	8	with	with	ADP
ejpam-1371	181	9	rank	rank	PROPN
ejpam-1371	181	10	l1	l1	PROPN
ejpam-1371	181	11	and	and	CCONJ
ejpam-1371	181	12	l2	l2	NOUN
ejpam-1371	181	13	respectively	respectively	ADV
ejpam-1371	181	14	,	,	PUNCT
ejpam-1371	181	15	so	so	SCONJ
ejpam-1371	181	16	that	that	SCONJ
ejpam-1371	181	17	,	,	PUNCT
ejpam-1371	181	18	we	we	PRON
ejpam-1371	181	19	get	get	VERB
ejpam-1371	181	20	|∇f(v)−∇f(x)|	|∇f(v)−∇f(x)|	ADJ
ejpam-1371	181	21	≤	≤	NUM
ejpam-1371	182	1	l1|v−	l1|v−	NOUN
ejpam-1371	182	2	x	x	PUNCT
ejpam-1371	182	3	|	|	ADV
ejpam-1371	182	4	(	(	PUNCT
ejpam-1371	182	5	18	18	NUM
ejpam-1371	182	6	)	)	PUNCT
ejpam-1371	182	7	and	and	CCONJ
ejpam-1371	182	8	|t	|t	PROPN
ejpam-1371	182	9	(	(	PUNCT
ejpam-1371	182	10	v)−	v)−	PROPN
ejpam-1371	182	11	t	t	PROPN
ejpam-1371	182	12	(	(	PUNCT
ejpam-1371	182	13	x)|	x)|	PROPN
ejpam-1371	182	14	≤	≤	PROPN
ejpam-1371	182	15	l2|v−	l2|v−	PROPN
ejpam-1371	183	1	x	x	PUNCT
ejpam-1371	183	2	|	|	ADV
ejpam-1371	183	3	(	(	PUNCT
ejpam-1371	183	4	19	19	NUM
ejpam-1371	183	5	)	)	PUNCT
ejpam-1371	183	6	for	for	ADP
ejpam-1371	183	7	all	all	PRON
ejpam-1371	183	8	x	x	SYM
ejpam-1371	183	9	,	,	PUNCT
ejpam-1371	183	10	u	u	PROPN
ejpam-1371	183	11	∈	∈	PROPN
ejpam-1371	183	12	m	m	VERB
ejpam-1371	183	13	.	.	PUNCT
ejpam-1371	184	1	since	since	SCONJ
ejpam-1371	184	2	m	m	PROPN
ejpam-1371	184	3	is	be	AUX
ejpam-1371	184	4	weakly	weakly	ADJ
ejpam-1371	184	5	η	η	ADJ
ejpam-1371	184	6	-	-	ADJ
ejpam-1371	184	7	invex	invex	ADJ
ejpam-1371	184	8	set	set	NOUN
ejpam-1371	184	9	,	,	PUNCT
ejpam-1371	184	10	for	for	ADP
ejpam-1371	184	11	each	each	DET
ejpam-1371	184	12	x	x	X
ejpam-1371	184	13	,	,	PUNCT
ejpam-1371	184	14	u	u	PROPN
ejpam-1371	184	15	∈	∈	PROPN
ejpam-1371	184	16	m	m	VERB
ejpam-1371	184	17	,	,	PUNCT
ejpam-1371	184	18	there	there	PRON
ejpam-1371	184	19	exists	exist	VERB
ejpam-1371	184	20	a	a	DET
ejpam-1371	184	21	t	t	NOUN
ejpam-1371	184	22	∈	∈	PROPN
ejpam-1371	184	23	(	(	PUNCT
ejpam-1371	184	24	0,1	0,1	NOUN
ejpam-1371	184	25	)	)	PUNCT
ejpam-1371	184	26	such	such	ADJ
ejpam-1371	184	27	that	that	SCONJ
ejpam-1371	184	28	z	z	NOUN
ejpam-1371	184	29	+	+	CCONJ
ejpam-1371	184	30	tη(x	tη(x	NUM
ejpam-1371	184	31	,	,	PUNCT
ejpam-1371	184	32	u	u	NOUN
ejpam-1371	184	33	)	)	PUNCT
ejpam-1371	184	34	∈	∈	PROPN
ejpam-1371	184	35	m	m	VERB
ejpam-1371	184	36	where	where	SCONJ
ejpam-1371	184	37	z	z	PROPN
ejpam-1371	184	38	∈	∈	PROPN
ejpam-1371	184	39	{	{	PUNCT
ejpam-1371	184	40	x	x	NOUN
ejpam-1371	184	41	,	,	PUNCT
ejpam-1371	184	42	u	u	NOUN
ejpam-1371	184	43	}	}	PUNCT
ejpam-1371	184	44	,	,	PUNCT
ejpam-1371	184	45	implies	imply	VERB
ejpam-1371	184	46	that	that	SCONJ
ejpam-1371	184	47	,	,	PUNCT
ejpam-1371	184	48	x	x	X
ejpam-1371	184	49	+	+	CCONJ
ejpam-1371	184	50	tη(x	tη(x	NUM
ejpam-1371	184	51	,	,	PUNCT
ejpam-1371	184	52	u	u	NOUN
ejpam-1371	184	53	)	)	PUNCT
ejpam-1371	184	54	∈	∈	PROPN
ejpam-1371	184	55	m	m	VERB
ejpam-1371	184	56	for	for	ADP
ejpam-1371	184	57	all	all	DET
ejpam-1371	184	58	x	x	SYM
ejpam-1371	184	59	,	,	PUNCT
ejpam-1371	184	60	u	u	PROPN
ejpam-1371	184	61	∈	∈	PROPN
ejpam-1371	184	62	m	m	VERB
ejpam-1371	184	63	.	.	PUNCT
ejpam-1371	185	1	from	from	ADP
ejpam-1371	185	2	property	property	NOUN
ejpam-1371	185	3	p3	p3	NOUN
ejpam-1371	185	4	(	(	PUNCT
ejpam-1371	185	5	i.e.	i.e.	X
ejpam-1371	185	6	lipschitz	lipschitz	VERB
ejpam-1371	185	7	continuity	continuity	NOUN
ejpam-1371	185	8	of	of	ADP
ejpam-1371	185	9	t	t	PROPN
ejpam-1371	185	10	)	)	PUNCT
ejpam-1371	185	11	,	,	PUNCT
ejpam-1371	185	12	we	we	PRON
ejpam-1371	185	13	get	get	VERB
ejpam-1371	185	14	|∇f(x	|∇f(x	X
ejpam-1371	185	15	+	+	X
ejpam-1371	185	16	tη(x	tη(x	NUM
ejpam-1371	185	17	,	,	PUNCT
ejpam-1371	185	18	u))−∇f(x)|	u))−∇f(x)|	ADV
ejpam-1371	185	19	≤	≤	PROPN
ejpam-1371	185	20	l1	l1	PROPN
ejpam-1371	185	21	t|η(x	t|η(x	PROPN
ejpam-1371	185	22	,	,	PUNCT
ejpam-1371	185	23	u)|	u)|	PROPN
ejpam-1371	185	24	(	(	PUNCT
ejpam-1371	185	25	20	20	NUM
ejpam-1371	185	26	)	)	PUNCT
ejpam-1371	185	27	and	and	CCONJ
ejpam-1371	185	28	|t	|t	PRON
ejpam-1371	185	29	(	(	PUNCT
ejpam-1371	185	30	x	x	SYM
ejpam-1371	185	31	+	+	SYM
ejpam-1371	185	32	tη(x	tη(x	NUM
ejpam-1371	185	33	,	,	PUNCT
ejpam-1371	185	34	u))−	u))−	PROPN
ejpam-1371	185	35	t	t	NOUN
ejpam-1371	185	36	(	(	PUNCT
ejpam-1371	185	37	x)|	x)|	PROPN
ejpam-1371	185	38	≤	≤	NOUN
ejpam-1371	185	39	l2	l2	NOUN
ejpam-1371	185	40	t|η(x	t|η(x	PROPN
ejpam-1371	185	41	,	,	PUNCT
ejpam-1371	185	42	u)|	u)|	PROPN
ejpam-1371	185	43	(	(	PUNCT
ejpam-1371	185	44	21	21	NUM
ejpam-1371	185	45	)	)	PUNCT
ejpam-1371	185	46	for	for	ADP
ejpam-1371	185	47	all	all	PRON
ejpam-1371	185	48	x	x	SYM
ejpam-1371	185	49	,	,	PUNCT
ejpam-1371	185	50	u	u	PROPN
ejpam-1371	185	51	∈	∈	NOUN
ejpam-1371	185	52	m	m	VERB
ejpam-1371	185	53	and	and	CCONJ
ejpam-1371	185	54	for	for	ADP
ejpam-1371	185	55	each	each	DET
ejpam-1371	185	56	t	t	NOUN
ejpam-1371	185	57	∈	∈	PROPN
ejpam-1371	185	58	(	(	PUNCT
ejpam-1371	185	59	0,1	0,1	NUM
ejpam-1371	185	60	)	)	PUNCT
ejpam-1371	185	61	.	.	PUNCT
ejpam-1371	186	1	replacing	replace	VERB
ejpam-1371	186	2	x	x	SYM
ejpam-1371	186	3	by	by	ADP
ejpam-1371	186	4	un	un	PROPN
ejpam-1371	186	5	and	and	CCONJ
ejpam-1371	186	6	u	u	NOUN
ejpam-1371	186	7	by	by	ADP
ejpam-1371	186	8	un+1	un+1	PROPN
ejpam-1371	186	9	in	in	ADP
ejpam-1371	186	10	(	(	PUNCT
ejpam-1371	186	11	20	20	NUM
ejpam-1371	186	12	)	)	PUNCT
ejpam-1371	186	13	and	and	CCONJ
ejpam-1371	186	14	(	(	PUNCT
ejpam-1371	186	15	21	21	NUM
ejpam-1371	186	16	)	)	PUNCT
ejpam-1371	186	17	,	,	PUNCT
ejpam-1371	186	18	we	we	PRON
ejpam-1371	186	19	get	get	VERB
ejpam-1371	186	20	|∇f(un	|∇f(un	PROPN
ejpam-1371	186	21	+	+	PROPN
ejpam-1371	186	22	tη(un	tη(un	PROPN
ejpam-1371	186	23	,	,	PUNCT
ejpam-1371	186	24	un+1))−∇f(un)|	un+1))−∇f(un)|	PROPN
ejpam-1371	186	25	≤	≤	PROPN
ejpam-1371	186	26	l1	l1	PROPN
ejpam-1371	186	27	t|η(un	t|η(un	PROPN
ejpam-1371	186	28	,	,	PUNCT
ejpam-1371	186	29	un+1)|	un+1)|	PROPN
ejpam-1371	186	30	(	(	PUNCT
ejpam-1371	186	31	22	22	NUM
ejpam-1371	186	32	)	)	PUNCT
ejpam-1371	186	33	and	and	CCONJ
ejpam-1371	186	34	|t	|t	PROPN
ejpam-1371	186	35	(	(	PUNCT
ejpam-1371	186	36	un+	un+	PROPN
ejpam-1371	186	37	tη(un	tη(un	PROPN
ejpam-1371	186	38	,	,	PUNCT
ejpam-1371	186	39	un+1))−	un+1))−	PROPN
ejpam-1371	186	40	t	t	PROPN
ejpam-1371	186	41	(	(	PUNCT
ejpam-1371	186	42	un)|	un)|	PROPN
ejpam-1371	186	43	≤	≤	PROPN
ejpam-1371	186	44	l2	l2	NOUN
ejpam-1371	186	45	t|η(un	t|η(un	PROPN
ejpam-1371	186	46	,	,	PUNCT
ejpam-1371	186	47	un+1)|	un+1)|	NOUN
ejpam-1371	186	48	.	.	PUNCT
ejpam-1371	187	1	(	(	PUNCT
ejpam-1371	187	2	23	23	NUM
ejpam-1371	187	3	)	)	PUNCT
ejpam-1371	187	4	hence	hence	ADV
ejpam-1371	187	5	from	from	ADP
ejpam-1371	187	6	(	(	PUNCT
ejpam-1371	187	7	22	22	NUM
ejpam-1371	187	8	)	)	PUNCT
ejpam-1371	187	9	,	,	PUNCT
ejpam-1371	187	10	we	we	PRON
ejpam-1371	187	11	have	have	VERB
ejpam-1371	187	12	|〈∇f(un	|〈∇f(un	PROPN
ejpam-1371	187	13	+	+	NUM
ejpam-1371	187	14	tη(un	tη(un	PROPN
ejpam-1371	187	15	,	,	PUNCT
ejpam-1371	187	16	un+1))−∇f(un),η(un	un+1))−∇f(un),η(un	NOUN
ejpam-1371	187	17	,	,	PUNCT
ejpam-1371	187	18	un+1)〉|	un+1)〉|	NOUN
ejpam-1371	187	19	≤	≤	PUNCT
ejpam-1371	188	1	|∇f(un	|∇f(un	PROPN
ejpam-1371	188	2	+	+	NUM
ejpam-1371	188	3	tη(un	tη(un	PROPN
ejpam-1371	188	4	,	,	PUNCT
ejpam-1371	188	5	un+1))−∇f(un)|	un+1))−∇f(un)|	PROPN
ejpam-1371	188	6	|η(un	|η(un	PROPN
ejpam-1371	188	7	,	,	PUNCT
ejpam-1371	188	8	un+1)|	un+1)|	PROPN
ejpam-1371	188	9	=	=	PROPN
ejpam-1371	188	10	l1	l1	PROPN
ejpam-1371	188	11	t|η(un	t|η(un	PROPN
ejpam-1371	188	12	,	,	PUNCT
ejpam-1371	188	13	un+1)|	un+1)|	PROPN
ejpam-1371	188	14	2	2	NUM
ejpam-1371	188	15	(	(	PUNCT
ejpam-1371	188	16	24	24	NUM
ejpam-1371	188	17	)	)	PUNCT
ejpam-1371	188	18	p.	p.	NOUN
ejpam-1371	188	19	das	das	PROPN
ejpam-1371	188	20	/	/	SYM
ejpam-1371	188	21	eur	eur	PROPN
ejpam-1371	188	22	.	.	PUNCT
ejpam-1371	189	1	j.	j.	PROPN
ejpam-1371	189	2	pure	pure	PROPN
ejpam-1371	189	3	appl	appl	PROPN
ejpam-1371	189	4	.	.	PROPN
ejpam-1371	189	5	math	math	PROPN
ejpam-1371	189	6	,	,	PUNCT
ejpam-1371	189	7	4	4	NUM
ejpam-1371	189	8	(	(	PUNCT
ejpam-1371	189	9	2011	2011	NUM
ejpam-1371	189	10	)	)	PUNCT
ejpam-1371	189	11	,	,	PUNCT
ejpam-1371	189	12	340	340	NUM
ejpam-1371	189	13	-	-	SYM
ejpam-1371	189	14	360	360	NUM
ejpam-1371	189	15	348	348	NUM
ejpam-1371	189	16	for	for	ADP
ejpam-1371	189	17	each	each	DET
ejpam-1371	189	18	t	t	NOUN
ejpam-1371	189	19	∈	∈	PROPN
ejpam-1371	189	20	(	(	PUNCT
ejpam-1371	189	21	0,1	0,1	NUM
ejpam-1371	189	22	)	)	PUNCT
ejpam-1371	189	23	and	and	CCONJ
ejpam-1371	189	24	from	from	ADP
ejpam-1371	189	25	(	(	PUNCT
ejpam-1371	189	26	23	23	NUM
ejpam-1371	189	27	)	)	PUNCT
ejpam-1371	189	28	,	,	PUNCT
ejpam-1371	189	29	we	we	PRON
ejpam-1371	189	30	have	have	VERB
ejpam-1371	189	31	|〈t	|〈t	PROPN
ejpam-1371	189	32	(	(	PUNCT
ejpam-1371	189	33	un+	un+	ADJ
ejpam-1371	189	34	tη(un	tη(un	PROPN
ejpam-1371	189	35	,	,	PUNCT
ejpam-1371	189	36	un+1))−t	un+1))−t	X
ejpam-1371	189	37	(	(	PUNCT
ejpam-1371	189	38	un),η(un	un),η(un	ADJ
ejpam-1371	189	39	,	,	PUNCT
ejpam-1371	189	40	un+1)〉|	un+1)〉|	NOUN
ejpam-1371	189	41	≤	≤	NUM
ejpam-1371	189	42	|t	|t	PROPN
ejpam-1371	189	43	(	(	PUNCT
ejpam-1371	189	44	un+	un+	PROPN
ejpam-1371	189	45	tη(un	tη(un	PROPN
ejpam-1371	189	46	,	,	PUNCT
ejpam-1371	189	47	un+1))−	un+1))−	PROPN
ejpam-1371	189	48	t	t	PROPN
ejpam-1371	189	49	(	(	PUNCT
ejpam-1371	189	50	un)|	un)|	PROPN
ejpam-1371	189	51	|η(un	|η(un	PROPN
ejpam-1371	189	52	,	,	PUNCT
ejpam-1371	189	53	un+1)|	un+1)|	PROPN
ejpam-1371	189	54	=	=	PUNCT
ejpam-1371	189	55	l2	l2	NOUN
ejpam-1371	189	56	t|η(un	t|η(un	PROPN
ejpam-1371	189	57	,	,	PUNCT
ejpam-1371	189	58	un+1)|	un+1)|	PROPN
ejpam-1371	189	59	2	2	NUM
ejpam-1371	189	60	(	(	PUNCT
ejpam-1371	189	61	25	25	NUM
ejpam-1371	189	62	)	)	PUNCT
ejpam-1371	189	63	for	for	ADP
ejpam-1371	189	64	each	each	DET
ejpam-1371	189	65	t	t	NOUN
ejpam-1371	189	66	∈	∈	PROPN
ejpam-1371	189	67	(	(	PUNCT
ejpam-1371	189	68	0,1	0,1	NUM
ejpam-1371	189	69	)	)	PUNCT
ejpam-1371	189	70	.	.	PUNCT
ejpam-1371	190	1	therefore	therefore	ADV
ejpam-1371	190	2	,	,	PUNCT
ejpam-1371	190	3	substituting	substitute	VERB
ejpam-1371	190	4	v	v	NOUN
ejpam-1371	190	5	=	=	SYM
ejpam-1371	190	6	un	un	PROPN
ejpam-1371	190	7	and	and	CCONJ
ejpam-1371	190	8	u	u	X
ejpam-1371	190	9	=	=	NOUN
ejpam-1371	190	10	un+1	un+1	ADV
ejpam-1371	190	11	in	in	ADP
ejpam-1371	190	12	(	(	PUNCT
ejpam-1371	190	13	13	13	NUM
ejpam-1371	190	14	)	)	PUNCT
ejpam-1371	190	15	and	and	CCONJ
ejpam-1371	190	16	using	use	VERB
ejpam-1371	190	17	the	the	DET
ejpam-1371	190	18	equations	equation	NOUN
ejpam-1371	190	19	from	from	ADP
ejpam-1371	190	20	(	(	PUNCT
ejpam-1371	190	21	22	22	NUM
ejpam-1371	190	22	)	)	PUNCT
ejpam-1371	190	23	to	to	ADP
ejpam-1371	190	24	(	(	PUNCT
ejpam-1371	190	25	25	25	NUM
ejpam-1371	190	26	)	)	PUNCT
ejpam-1371	190	27	,	,	PUNCT
ejpam-1371	190	28	we	we	PRON
ejpam-1371	190	29	have	have	VERB
ejpam-1371	190	30	γ(un+1)−	γ(un+1)−	PROPN
ejpam-1371	190	31	γ(un	γ(un	PROPN
ejpam-1371	190	32	)	)	PUNCT
ejpam-1371	190	33	=	=	PUNCT
ejpam-1371	191	1	1∫	1∫	NUM
ejpam-1371	191	2	0	0	NUM
ejpam-1371	192	1	〈	〈	NOUN
ejpam-1371	192	2	∇f(un	∇f(un	PROPN
ejpam-1371	192	3	+	+	PROPN
ejpam-1371	192	4	tη(un	tη(un	PROPN
ejpam-1371	192	5	,	,	PUNCT
ejpam-1371	192	6	un+1)),η(un	un+1)),η(un	PROPN
ejpam-1371	192	7	,	,	PUNCT
ejpam-1371	192	8	un+1)〉d	un+1)〉d	NOUN
ejpam-1371	192	9	t	t	NOUN
ejpam-1371	192	10	−	−	PROPN
ejpam-1371	192	11	1∫	1∫	NUM
ejpam-1371	192	12	0	0	NUM
ejpam-1371	192	13	〈	〈	PROPN
ejpam-1371	192	14	t	t	PROPN
ejpam-1371	192	15	(	(	PUNCT
ejpam-1371	192	16	un	un	PROPN
ejpam-1371	192	17	+	+	PROPN
ejpam-1371	192	18	tη(un	tη(un	PROPN
ejpam-1371	192	19	,	,	PUNCT
ejpam-1371	192	20	un+1)),η(un	un+1)),η(un	PROPN
ejpam-1371	192	21	,	,	PUNCT
ejpam-1371	192	22	un+1)〉d	un+1)〉d	NOUN
ejpam-1371	192	23	t	t	NOUN
ejpam-1371	192	24	=	=	SYM
ejpam-1371	192	25	1∫	1∫	NUM
ejpam-1371	192	26	0	0	NUM
ejpam-1371	192	27	�	�	PROPN
ejpam-1371	192	28	〈	〈	PROPN
ejpam-1371	192	29	∇f(un	∇f(un	PROPN
ejpam-1371	192	30	+	+	PROPN
ejpam-1371	192	31	tη(un	tη(un	PROPN
ejpam-1371	192	32	,	,	PUNCT
ejpam-1371	192	33	un+1))−∇f(un	un+1))−∇f(un	PROPN
ejpam-1371	192	34	)	)	PUNCT
ejpam-1371	192	35	�	�	PROPN
ejpam-1371	192	36	,	,	PUNCT
ejpam-1371	192	37	η(un	η(un	PROPN
ejpam-1371	192	38	,	,	PUNCT
ejpam-1371	192	39	un+1)〉d	un+1)〉d	NOUN
ejpam-1371	192	40	t	t	NOUN
ejpam-1371	192	41	−	−	PROPN
ejpam-1371	192	42	1∫	1∫	NUM
ejpam-1371	192	43	0	0	NUM
ejpam-1371	192	44	�	�	PROPN
ejpam-1371	192	45	〈	〈	PROPN
ejpam-1371	192	46	t	t	PROPN
ejpam-1371	192	47	(	(	PUNCT
ejpam-1371	192	48	un	un	PROPN
ejpam-1371	192	49	+	+	PROPN
ejpam-1371	192	50	tη(un	tη(un	PROPN
ejpam-1371	192	51	,	,	PUNCT
ejpam-1371	192	52	un+1))−	un+1))−	PROPN
ejpam-1371	192	53	t	t	PROPN
ejpam-1371	192	54	(	(	PUNCT
ejpam-1371	192	55	un),η(un	un),η(un	PROPN
ejpam-1371	192	56	,	,	PUNCT
ejpam-1371	192	57	un+1	un+1	NOUN
ejpam-1371	192	58	)	)	PUNCT
ejpam-1371	192	59	〉	〉	NOUN
ejpam-1371	192	60	�	�	PROPN
ejpam-1371	192	61	d	d	PROPN
ejpam-1371	192	62	t	t	PROPN
ejpam-1371	193	1	+	+	CCONJ
ejpam-1371	193	2	1∫	1∫	NUM
ejpam-1371	193	3	0	0	NUM
ejpam-1371	193	4	〈	〈	PROPN
ejpam-1371	193	5	(	(	PUNCT
ejpam-1371	193	6	∇f	∇f	PROPN
ejpam-1371	193	7	−	−	PROPN
ejpam-1371	193	8	t	t	NOUN
ejpam-1371	193	9	)	)	PUNCT
ejpam-1371	193	10	(	(	PUNCT
ejpam-1371	193	11	un),η(un	un),η(un	ADJ
ejpam-1371	193	12	,	,	PUNCT
ejpam-1371	193	13	un+1)〉d	un+1)〉d	NOUN
ejpam-1371	193	14	t	t	NOUN
ejpam-1371	193	15	≤	≤	NOUN
ejpam-1371	194	1	1∫	1∫	NUM
ejpam-1371	194	2	0	0	NUM
ejpam-1371	194	3	|∇f(un+	|∇f(un+	PROPN
ejpam-1371	194	4	tη(un	tη(un	PROPN
ejpam-1371	194	5	,	,	PUNCT
ejpam-1371	194	6	un+1))−∇f(un)|	un+1))−∇f(un)|	PROPN
ejpam-1371	194	7	η(un	η(un	PROPN
ejpam-1371	194	8	,	,	PUNCT
ejpam-1371	194	9	un+1)|d	un+1)|d	PROPN
ejpam-1371	194	10	t	t	NOUN
ejpam-1371	194	11	+	+	CCONJ
ejpam-1371	194	12	1∫	1∫	NUM
ejpam-1371	194	13	0	0	NUM
ejpam-1371	195	1	|	|	ADV
ejpam-1371	195	2	t	t	PROPN
ejpam-1371	195	3	(	(	PUNCT
ejpam-1371	195	4	un	un	PROPN
ejpam-1371	195	5	+	+	PROPN
ejpam-1371	195	6	tη(un	tη(un	PROPN
ejpam-1371	195	7	,	,	PUNCT
ejpam-1371	195	8	un+1))−	un+1))−	PROPN
ejpam-1371	195	9	t	t	PROPN
ejpam-1371	195	10	(	(	PUNCT
ejpam-1371	195	11	un)||η(un	un)||η(un	PROPN
ejpam-1371	195	12	,	,	PUNCT
ejpam-1371	195	13	un+1)|d	un+1)|d	PROPN
ejpam-1371	195	14	t	t	NOUN
ejpam-1371	195	15	+	+	CCONJ
ejpam-1371	195	16	1∫	1∫	NUM
ejpam-1371	195	17	0	0	NUM
ejpam-1371	195	18	|(∇f	|(∇f	PUNCT
ejpam-1371	195	19	−	−	PROPN
ejpam-1371	195	20	t	t	NOUN
ejpam-1371	195	21	)	)	PUNCT
ejpam-1371	195	22	(	(	PUNCT
ejpam-1371	195	23	un)|	un)|	PROPN
ejpam-1371	195	24	|η(un	|η(un	PROPN
ejpam-1371	195	25	,	,	PUNCT
ejpam-1371	195	26	un+1|d	un+1|d	PROPN
ejpam-1371	195	27	t	t	PROPN
ejpam-1371	195	28	≤	≤	NOUN
ejpam-1371	196	1	1∫	1∫	NUM
ejpam-1371	196	2	0	0	NUM
ejpam-1371	196	3	l1t|η(un	l1t|η(un	PROPN
ejpam-1371	196	4	,	,	PUNCT
ejpam-1371	196	5	un+1)|	un+1)|	PROPN
ejpam-1371	196	6	2d	2d	NOUN
ejpam-1371	196	7	t	t	NOUN
ejpam-1371	196	8	+	+	CCONJ
ejpam-1371	196	9	1∫	1∫	NUM
ejpam-1371	196	10	0	0	NUM
ejpam-1371	196	11	l2	l2	NOUN
ejpam-1371	196	12	t|η(un	t|η(un	PROPN
ejpam-1371	196	13	,	,	PUNCT
ejpam-1371	196	14	un+1)|	un+1)|	NOUN
ejpam-1371	196	15	2d	2d	NOUN
ejpam-1371	196	16	t	t	PROPN
ejpam-1371	196	17	p.	p.	NOUN
ejpam-1371	196	18	das	das	PROPN
ejpam-1371	196	19	/	/	SYM
ejpam-1371	196	20	eur	eur	PROPN
ejpam-1371	196	21	.	.	PUNCT
ejpam-1371	197	1	j.	j.	PROPN
ejpam-1371	197	2	pure	pure	PROPN
ejpam-1371	197	3	appl	appl	PROPN
ejpam-1371	197	4	.	.	PROPN
ejpam-1371	197	5	math	math	PROPN
ejpam-1371	197	6	,	,	PUNCT
ejpam-1371	197	7	4	4	NUM
ejpam-1371	197	8	(	(	PUNCT
ejpam-1371	197	9	2011	2011	NUM
ejpam-1371	197	10	)	)	PUNCT
ejpam-1371	197	11	,	,	PUNCT
ejpam-1371	197	12	340	340	NUM
ejpam-1371	197	13	-	-	SYM
ejpam-1371	197	14	360	360	NUM
ejpam-1371	197	15	349	349	NUM
ejpam-1371	197	16	+	+	CCONJ
ejpam-1371	198	1	1∫	1∫	NUM
ejpam-1371	198	2	0	0	NUM
ejpam-1371	198	3	α	α	NOUN
ejpam-1371	198	4	·	·	SYM
ejpam-1371	198	5	2	2	NUM
ejpam-1371	198	6	α	α	NUM
ejpam-1371	198	7	δ(ε)d	δ(ε)d	NOUN
ejpam-1371	198	8	t	t	NOUN
ejpam-1371	198	9	by	by	ADP
ejpam-1371	198	10	p1(d	p1(d	PROPN
ejpam-1371	198	11	)	)	PUNCT
ejpam-1371	198	12	,	,	PUNCT
ejpam-1371	198	13	(	(	PUNCT
ejpam-1371	198	14	24	24	NUM
ejpam-1371	198	15	)	)	PUNCT
ejpam-1371	198	16	and	and	CCONJ
ejpam-1371	198	17	(	(	PUNCT
ejpam-1371	198	18	25	25	NUM
ejpam-1371	198	19	)	)	PUNCT
ejpam-1371	198	20	)	)	PUNCT
ejpam-1371	198	21	=(	=(	PROPN
ejpam-1371	198	22	l1	l1	PROPN
ejpam-1371	198	23	+	+	CCONJ
ejpam-1371	198	24	l2)|η(un	l2)|η(un	PROPN
ejpam-1371	198	25	,	,	PUNCT
ejpam-1371	198	26	un+1)|	un+1)|	PROPN
ejpam-1371	198	27	2	2	NUM
ejpam-1371	198	28	1∫	1∫	NUM
ejpam-1371	198	29	0	0	NUM
ejpam-1371	199	1	td	td	NOUN
ejpam-1371	199	2	t	t	PROPN
ejpam-1371	199	3	+	+	CCONJ
ejpam-1371	199	4	2δ(ε	2δ(ε	NUM
ejpam-1371	199	5	)	)	PUNCT
ejpam-1371	200	1	1∫	1∫	NUM
ejpam-1371	200	2	0	0	NUM
ejpam-1371	200	3	d	d	PRON
ejpam-1371	200	4	t	t	NOUN
ejpam-1371	200	5	=	=	SYM
ejpam-1371	200	6	l1	l1	PROPN
ejpam-1371	200	7	+	+	CCONJ
ejpam-1371	200	8	l2	l2	PROPN
ejpam-1371	200	9	2	2	NUM
ejpam-1371	200	10	|η(un	|η(un	PROPN
ejpam-1371	200	11	,	,	PUNCT
ejpam-1371	200	12	un+1)|	un+1)|	PROPN
ejpam-1371	200	13	2	2	NUM
ejpam-1371	200	14	+	+	NUM
ejpam-1371	200	15	2δ(ε	2δ(ε	NUM
ejpam-1371	200	16	)	)	PUNCT
ejpam-1371	201	1	thus	thus	ADV
ejpam-1371	201	2	,	,	PUNCT
ejpam-1371	201	3	we	we	PRON
ejpam-1371	201	4	obtained	obtain	VERB
ejpam-1371	201	5	the	the	DET
ejpam-1371	201	6	relation	relation	NOUN
ejpam-1371	201	7	γ(un+1)≤	γ(un+1)≤	PROPN
ejpam-1371	201	8	γ(un	γ(un	PROPN
ejpam-1371	201	9	)	)	PUNCT
ejpam-1371	201	10	+	+	NUM
ejpam-1371	201	11	l1	l1	PROPN
ejpam-1371	201	12	+	+	CCONJ
ejpam-1371	201	13	l2	l2	PROPN
ejpam-1371	201	14	2	2	NUM
ejpam-1371	201	15	|η(un	|η(un	PROPN
ejpam-1371	201	16	,	,	PUNCT
ejpam-1371	201	17	un+1)|	un+1)|	PROPN
ejpam-1371	201	18	2	2	NUM
ejpam-1371	201	19	+	+	NUM
ejpam-1371	201	20	2δ(ε	2δ(ε	NUM
ejpam-1371	201	21	)	)	PUNCT
ejpam-1371	201	22	(	(	PUNCT
ejpam-1371	201	23	26	26	NUM
ejpam-1371	201	24	)	)	PUNCT
ejpam-1371	201	25	which	which	PRON
ejpam-1371	201	26	is	be	AUX
ejpam-1371	201	27	valid	valid	ADJ
ejpam-1371	201	28	for	for	ADP
ejpam-1371	201	29	all	all	DET
ejpam-1371	201	30	n=	n=	ADJ
ejpam-1371	201	31	0,1,2	0,1,2	NUM
ejpam-1371	201	32	,	,	PUNCT
ejpam-1371	201	33	.	.	PUNCT
ejpam-1371	201	34	.	.	PUNCT
ejpam-1371	202	1	..	..	PUNCT
ejpam-1371	202	2	putting	put	VERB
ejpam-1371	202	3	n=	n=	ADJ
ejpam-1371	202	4	0,1,2	0,1,2	NOUN
ejpam-1371	202	5	,	,	PUNCT
ejpam-1371	202	6	.	.	PUNCT
ejpam-1371	202	7	.	.	PUNCT
ejpam-1371	203	1	.	.	PUNCT
ejpam-1371	204	1	,	,	PUNCT
ejpam-1371	204	2	n	n	CCONJ
ejpam-1371	204	3	in	in	ADP
ejpam-1371	204	4	(	(	PUNCT
ejpam-1371	204	5	26	26	NUM
ejpam-1371	204	6	)	)	PUNCT
ejpam-1371	204	7	,	,	PUNCT
ejpam-1371	204	8	we	we	PRON
ejpam-1371	204	9	get	get	VERB
ejpam-1371	204	10	γ(un+1)≤	γ(un+1)≤	PROPN
ejpam-1371	204	11	γ(u0	γ(u0	NOUN
ejpam-1371	204	12	)	)	PUNCT
ejpam-1371	205	1	+	+	CCONJ
ejpam-1371	205	2	�	�	PROPN
ejpam-1371	205	3	l1	l1	PROPN
ejpam-1371	205	4	+	+	CCONJ
ejpam-1371	205	5	l2	l2	PROPN
ejpam-1371	205	6	2	2	NUM
ejpam-1371	205	7	�	�	PROPN
ejpam-1371	205	8	n∑	n∑	PART
ejpam-1371	205	9	n=0	n=0	PROPN
ejpam-1371	205	10	|η(un	|η(un	PROPN
ejpam-1371	205	11	,	,	PUNCT
ejpam-1371	205	12	un+1)|	un+1)|	PROPN
ejpam-1371	205	13	2	2	NUM
ejpam-1371	205	14	+	+	SYM
ejpam-1371	205	15	2	2	NUM
ejpam-1371	205	16	n∑	n∑	PROPN
ejpam-1371	205	17	n=0	n=0	SYM
ejpam-1371	205	18	δ(εn	δ(εn	NUM
ejpam-1371	205	19	)	)	PUNCT
ejpam-1371	205	20	(	(	PUNCT
ejpam-1371	205	21	27	27	NUM
ejpam-1371	205	22	)	)	PUNCT
ejpam-1371	205	23	≤	≤	NOUN
ejpam-1371	205	24	γ(u0	γ(u0	NOUN
ejpam-1371	205	25	)	)	PUNCT
ejpam-1371	206	1	+	+	CCONJ
ejpam-1371	206	2	�	�	PROPN
ejpam-1371	206	3	l1	l1	PROPN
ejpam-1371	206	4	+	+	CCONJ
ejpam-1371	206	5	l2	l2	PROPN
ejpam-1371	206	6	2	2	NUM
ejpam-1371	206	7	�	�	PROPN
ejpam-1371	206	8	�	�	PROPN
ejpam-1371	206	9	2σ	2σ	PROPN
ejpam-1371	206	10	l1	l1	PROPN
ejpam-1371	206	11	+	+	CCONJ
ejpam-1371	206	12	l2	l2	PROPN
ejpam-1371	206	13	�	�	PROPN
ejpam-1371	206	14	+	+	CCONJ
ejpam-1371	206	15	2σ	2σ	X
ejpam-1371	206	16	≤	≤	NUM
ejpam-1371	206	17	γ(u0	γ(u0	NOUN
ejpam-1371	206	18	)	)	PUNCT
ejpam-1371	207	1	+	+	CCONJ
ejpam-1371	207	2	3σ	3σ	NUM
ejpam-1371	207	3	,	,	PUNCT
ejpam-1371	207	4	thus	thus	ADV
ejpam-1371	207	5	,	,	PUNCT
ejpam-1371	207	6	un+1	un+1	PROPN
ejpam-1371	207	7	∈	∈	PROPN
ejpam-1371	207	8	s(u0	s(u0	NOUN
ejpam-1371	207	9	)	)	PUNCT
ejpam-1371	207	10	=	=	PUNCT
ejpam-1371	208	1	{	{	PUNCT
ejpam-1371	208	2	u	u	NOUN
ejpam-1371	208	3	∈	∈	PROPN
ejpam-1371	208	4	m	m	VERB
ejpam-1371	208	5	:	:	PUNCT
ejpam-1371	208	6	γ(u)≤	γ(u)≤	ADV
ejpam-1371	208	7	γ(u0)+3σ	γ(u0)+3σ	NOUN
ejpam-1371	208	8	}	}	PUNCT
ejpam-1371	208	9	.	.	PUNCT
ejpam-1371	209	1	since	since	SCONJ
ejpam-1371	209	2	n	n	PRON
ejpam-1371	209	3	is	be	AUX
ejpam-1371	209	4	arbitrary	arbitrary	ADJ
ejpam-1371	209	5	,	,	PUNCT
ejpam-1371	209	6	replacing	replace	VERB
ejpam-1371	209	7	n	n	PRON
ejpam-1371	209	8	by	by	ADP
ejpam-1371	209	9	n	n	CCONJ
ejpam-1371	209	10	,	,	PUNCT
ejpam-1371	209	11	we	we	PRON
ejpam-1371	209	12	get	get	VERB
ejpam-1371	209	13	un+1	un+1	PROPN
ejpam-1371	209	14	∈	∈	PROPN
ejpam-1371	209	15	s(u0	s(u0	NOUN
ejpam-1371	209	16	)	)	PUNCT
ejpam-1371	209	17	and	and	CCONJ
ejpam-1371	209	18	hence	hence	ADV
ejpam-1371	209	19	,	,	PUNCT
ejpam-1371	209	20	{	{	PUNCT
ejpam-1371	209	21	un	un	PROPN
ejpam-1371	209	22	}	}	PUNCT
ejpam-1371	209	23	∞	∞	NUM
ejpam-1371	209	24	n=0	n=0	PUNCT
ejpam-1371	209	25	⊂	⊂	X
ejpam-1371	209	26	s(u0	s(u0	NOUN
ejpam-1371	209	27	)	)	PUNCT
ejpam-1371	209	28	.	.	PUNCT
ejpam-1371	210	1	now	now	ADV
ejpam-1371	210	2	by	by	ADP
ejpam-1371	210	3	(	(	PUNCT
ejpam-1371	210	4	16	16	NUM
ejpam-1371	210	5	)	)	PUNCT
ejpam-1371	210	6	,	,	PUNCT
ejpam-1371	210	7	the	the	DET
ejpam-1371	210	8	assumptions	assumption	NOUN
ejpam-1371	210	9	of	of	ADP
ejpam-1371	210	10	lemma	lemma	PROPN
ejpam-1371	210	11	1	1	NUM
ejpam-1371	210	12	are	be	AUX
ejpam-1371	210	13	valid	valid	ADJ
ejpam-1371	210	14	the	the	DET
ejpam-1371	210	15	sequence	sequence	NOUN
ejpam-1371	210	16	{	{	PUNCT
ejpam-1371	210	17	γ(un	γ(un	PROPN
ejpam-1371	210	18	)	)	PUNCT
ejpam-1371	210	19	}	}	PUNCT
ejpam-1371	210	20	∞	∞	PROPN
ejpam-1371	210	21	n=1	n=1	PROPN
ejpam-1371	210	22	.	.	PROPN
ejpam-1371	211	1	next	next	ADJ
ejpam-1371	211	2	to	to	PART
ejpam-1371	211	3	show	show	VERB
ejpam-1371	211	4	,	,	PUNCT
ejpam-1371	211	5	the	the	DET
ejpam-1371	211	6	sequence	sequence	NOUN
ejpam-1371	211	7	{	{	PUNCT
ejpam-1371	211	8	γ(un	γ(un	PROPN
ejpam-1371	211	9	)	)	PUNCT
ejpam-1371	211	10	}	}	PUNCT
ejpam-1371	211	11	∞	∞	NUM
ejpam-1371	211	12	n=1	n=1	PROPN
ejpam-1371	211	13	is	be	AUX
ejpam-1371	211	14	bounded	bound	VERB
ejpam-1371	211	15	above	above	ADV
ejpam-1371	211	16	and	and	CCONJ
ejpam-1371	211	17	has	have	VERB
ejpam-1371	211	18	a	a	DET
ejpam-1371	211	19	finite	finite	ADJ
ejpam-1371	211	20	limit	limit	NOUN
ejpam-1371	211	21	.	.	PUNCT
ejpam-1371	212	1	taking	take	VERB
ejpam-1371	212	2	limit	limit	NOUN
ejpam-1371	212	3	n	n	PRON
ejpam-1371	212	4	→∞	→∞	NOUN
ejpam-1371	212	5	in	in	ADP
ejpam-1371	212	6	(	(	PUNCT
ejpam-1371	212	7	27	27	NUM
ejpam-1371	212	8	)	)	PUNCT
ejpam-1371	212	9	,	,	PUNCT
ejpam-1371	212	10	and	and	CCONJ
ejpam-1371	212	11	using	use	VERB
ejpam-1371	212	12	(	(	PUNCT
ejpam-1371	212	13	16	16	NUM
ejpam-1371	212	14	)	)	PUNCT
ejpam-1371	212	15	we	we	PRON
ejpam-1371	212	16	get	get	VERB
ejpam-1371	212	17	lim	lim	PROPN
ejpam-1371	212	18	n→∞	n→∞	X
ejpam-1371	212	19	γ(un+1)≤	γ(un+1)≤	PROPN
ejpam-1371	212	20	γ(u0	γ(u0	NOUN
ejpam-1371	212	21	)	)	PUNCT
ejpam-1371	213	1	+	+	CCONJ
ejpam-1371	213	2	�	�	PROPN
ejpam-1371	213	3	l1	l1	PROPN
ejpam-1371	213	4	+	+	CCONJ
ejpam-1371	213	5	l2	l2	PROPN
ejpam-1371	213	6	2	2	NUM
ejpam-1371	213	7	�	�	PROPN
ejpam-1371	213	8	∞∑	∞∑	NUM
ejpam-1371	213	9	n=0	n=0	PROPN
ejpam-1371	213	10	|η(un	|η(un	PROPN
ejpam-1371	213	11	,	,	PUNCT
ejpam-1371	213	12	un+1)|	un+1)|	PROPN
ejpam-1371	213	13	2	2	NUM
ejpam-1371	213	14	+	+	NUM
ejpam-1371	213	15	2	2	NUM
ejpam-1371	214	1	∞∑	∞∑	PRON
ejpam-1371	214	2	n=0	n=0	PUNCT
ejpam-1371	214	3	δ(εn)≤	δ(εn)≤	NOUN
ejpam-1371	214	4	γ(u0	γ(u0	NOUN
ejpam-1371	214	5	)	)	PUNCT
ejpam-1371	215	1	+	+	CCONJ
ejpam-1371	215	2	3σ	3σ	NUM
ejpam-1371	215	3	,	,	PUNCT
ejpam-1371	215	4	equivalently	equivalently	ADV
ejpam-1371	215	5	,	,	PUNCT
ejpam-1371	215	6	we	we	PRON
ejpam-1371	215	7	have	have	VERB
ejpam-1371	215	8	lim	lim	PROPN
ejpam-1371	215	9	n→∞	n→∞	X
ejpam-1371	215	10	γ(un+1)≤	γ(un+1)≤	PROPN
ejpam-1371	215	11	γ(u0	γ(u0	NOUN
ejpam-1371	215	12	)	)	PUNCT
ejpam-1371	216	1	+	+	NUM
ejpam-1371	216	2	3σ	3σ	NUM
ejpam-1371	216	3	(	(	PUNCT
ejpam-1371	216	4	28	28	NUM
ejpam-1371	216	5	)	)	PUNCT
ejpam-1371	216	6	hence	hence	ADV
ejpam-1371	216	7	,	,	PUNCT
ejpam-1371	216	8	the	the	DET
ejpam-1371	216	9	sequence	sequence	NOUN
ejpam-1371	216	10	{	{	PUNCT
ejpam-1371	216	11	γ(un	γ(un	PROPN
ejpam-1371	216	12	)	)	PUNCT
ejpam-1371	216	13	}	}	PUNCT
ejpam-1371	216	14	∞	∞	NUM
ejpam-1371	216	15	n=1	n=1	PROPN
ejpam-1371	216	16	is	be	AUX
ejpam-1371	216	17	bounded	bound	VERB
ejpam-1371	216	18	above	above	ADV
ejpam-1371	216	19	.	.	PUNCT
ejpam-1371	217	1	again	again	ADV
ejpam-1371	217	2	,	,	PUNCT
ejpam-1371	217	3	by	by	ADP
ejpam-1371	217	4	the	the	DET
ejpam-1371	217	5	property	property	NOUN
ejpam-1371	217	6	p1(c	p1(c	PROPN
ejpam-1371	217	7	)	)	PUNCT
ejpam-1371	217	8	,	,	PUNCT
ejpam-1371	217	9	for	for	ADP
ejpam-1371	217	10	fixed	fix	VERB
ejpam-1371	217	11	z	z	PROPN
ejpam-1371	217	12	∈	∈	PROPN
ejpam-1371	217	13	m	m	VERB
ejpam-1371	217	14	,	,	PUNCT
ejpam-1371	217	15	we	we	PRON
ejpam-1371	217	16	have	have	VERB
ejpam-1371	217	17	〈	〈	PROPN
ejpam-1371	217	18	t	t	PROPN
ejpam-1371	217	19	(	(	PUNCT
ejpam-1371	217	20	u),η(v	u),η(v	X
ejpam-1371	217	21	,	,	PUNCT
ejpam-1371	217	22	u	u	NOUN
ejpam-1371	217	23	)	)	PUNCT
ejpam-1371	217	24	〉	〉	NOUN
ejpam-1371	217	25	≤	≤	NUM
ejpam-1371	217	26	〈	〈	PROPN
ejpam-1371	217	27	t	t	PROPN
ejpam-1371	217	28	(	(	PUNCT
ejpam-1371	217	29	u),η(v	u),η(v	X
ejpam-1371	217	30	,	,	PUNCT
ejpam-1371	217	31	z)〉+	z)〉+	X
ejpam-1371	217	32	〈	〈	PROPN
ejpam-1371	217	33	t	t	PROPN
ejpam-1371	217	34	(	(	PUNCT
ejpam-1371	217	35	u),η(u	u),η(u	PROPN
ejpam-1371	217	36	,	,	PUNCT
ejpam-1371	217	37	z	z	NOUN
ejpam-1371	217	38	)	)	PUNCT
ejpam-1371	217	39	〉	〉	NOUN
ejpam-1371	217	40	∀u	∀u	NOUN
ejpam-1371	217	41	,	,	PUNCT
ejpam-1371	217	42	v	v	X
ejpam-1371	217	43	∈	∈	NOUN
ejpam-1371	217	44	m	m	VERB
ejpam-1371	217	45	.	.	PUNCT
ejpam-1371	218	1	taking	take	VERB
ejpam-1371	218	2	u	u	NOUN
ejpam-1371	218	3	=	=	NOUN
ejpam-1371	218	4	un	un	PROPN
ejpam-1371	218	5	,	,	PUNCT
ejpam-1371	218	6	z	z	NOUN
ejpam-1371	218	7	=	=	SYM
ejpam-1371	218	8	un+1	un+1	ADJ
ejpam-1371	218	9	in	in	ADP
ejpam-1371	218	10	the	the	DET
ejpam-1371	218	11	above	above	ADJ
ejpam-1371	218	12	inequality	inequality	NOUN
ejpam-1371	218	13	,	,	PUNCT
ejpam-1371	218	14	we	we	PRON
ejpam-1371	218	15	get	get	VERB
ejpam-1371	218	16	〈	〈	PROPN
ejpam-1371	218	17	t	t	PROPN
ejpam-1371	218	18	(	(	PUNCT
ejpam-1371	218	19	un),η(v	un),η(v	NOUN
ejpam-1371	218	20	,	,	PUNCT
ejpam-1371	218	21	un	un	ADJ
ejpam-1371	218	22	)	)	PUNCT
ejpam-1371	218	23	〉	〉	NOUN
ejpam-1371	218	24	≤〈t	≤〈t	PROPN
ejpam-1371	218	25	(	(	PUNCT
ejpam-1371	218	26	un),η(v	un),η(v	NOUN
ejpam-1371	218	27	,	,	PUNCT
ejpam-1371	218	28	un+1)〉+	un+1)〉+	PROPN
ejpam-1371	218	29	〈	〈	PROPN
ejpam-1371	218	30	t	t	PROPN
ejpam-1371	218	31	(	(	PUNCT
ejpam-1371	218	32	un),η(un	un),η(un	PROPN
ejpam-1371	218	33	,	,	PUNCT
ejpam-1371	218	34	un+1	un+1	NOUN
ejpam-1371	218	35	)	)	PUNCT
ejpam-1371	218	36	〉	〉	NOUN
ejpam-1371	218	37	p.	p.	NOUN
ejpam-1371	218	38	das	das	PROPN
ejpam-1371	218	39	/	/	SYM
ejpam-1371	218	40	eur	eur	PROPN
ejpam-1371	218	41	.	.	PUNCT
ejpam-1371	219	1	j.	j.	PROPN
ejpam-1371	219	2	pure	pure	PROPN
ejpam-1371	219	3	appl	appl	PROPN
ejpam-1371	219	4	.	.	PROPN
ejpam-1371	219	5	math	math	PROPN
ejpam-1371	219	6	,	,	PUNCT
ejpam-1371	219	7	4	4	NUM
ejpam-1371	219	8	(	(	PUNCT
ejpam-1371	219	9	2011	2011	NUM
ejpam-1371	219	10	)	)	PUNCT
ejpam-1371	219	11	,	,	PUNCT
ejpam-1371	219	12	340	340	NUM
ejpam-1371	219	13	-	-	SYM
ejpam-1371	219	14	360	360	NUM
ejpam-1371	219	15	350	350	NUM
ejpam-1371	219	16	≤〈t	≤〈t	PROPN
ejpam-1371	219	17	(	(	PUNCT
ejpam-1371	219	18	un),η(un	un),η(un	NOUN
ejpam-1371	219	19	,	,	PUNCT
ejpam-1371	219	20	un+1)〉+	un+1)〉+	PROPN
ejpam-1371	219	21	〈	〈	PROPN
ejpam-1371	219	22	t	t	PROPN
ejpam-1371	219	23	(	(	PUNCT
ejpam-1371	219	24	un),η(v	un),η(v	NOUN
ejpam-1371	219	25	,	,	PUNCT
ejpam-1371	219	26	un+1)〉+	un+1)〉+	PROPN
ejpam-1371	219	27	〈	〈	PROPN
ejpam-1371	219	28	∇f(un),η(v	∇f(un),η(v	PROPN
ejpam-1371	219	29	,	,	PUNCT
ejpam-1371	219	30	un	un	NOUN
ejpam-1371	219	31	)	)	PUNCT
ejpam-1371	219	32	〉	〉	NOUN
ejpam-1371	219	33	+	+	CCONJ
ejpam-1371	219	34	1	1	NUM
ejpam-1371	219	35	ρn	ρn	NOUN
ejpam-1371	219	36	〈	〈	PROPN
ejpam-1371	219	37	η(un	η(un	PROPN
ejpam-1371	219	38	,	,	PUNCT
ejpam-1371	219	39	un+1),η(v	un+1),η(v	ADP
ejpam-1371	219	40	,	,	PUNCT
ejpam-1371	219	41	un+1	un+1	NOUN
ejpam-1371	219	42	)	)	PUNCT
ejpam-1371	219	43	〉	〉	NOUN
ejpam-1371	219	44	∀v	∀v	X
ejpam-1371	219	45	∈	∈	NOUN
ejpam-1371	219	46	m	m	X
ejpam-1371	219	47	(	(	PUNCT
ejpam-1371	219	48	from	from	ADP
ejpam-1371	219	49	equation	equation	NOUN
ejpam-1371	219	50	(	(	PUNCT
ejpam-1371	219	51	14	14	NUM
ejpam-1371	219	52	)	)	PUNCT
ejpam-1371	219	53	)	)	PUNCT
ejpam-1371	220	1	≤|t	≤|t	PROPN
ejpam-1371	220	2	(	(	PUNCT
ejpam-1371	220	3	un)|	un)|	PROPN
ejpam-1371	220	4	|η(v	|η(v	PROPN
ejpam-1371	220	5	,	,	PUNCT
ejpam-1371	220	6	un+1)|+	un+1)|+	NUM
ejpam-1371	220	7	|t	|t	PROPN
ejpam-1371	220	8	(	(	PUNCT
ejpam-1371	220	9	un)|	un)|	PROPN
ejpam-1371	220	10	|η(un	|η(un	PROPN
ejpam-1371	220	11	,	,	PUNCT
ejpam-1371	220	12	un+1)|+	un+1)|+	PROPN
ejpam-1371	220	13	〈	〈	PROPN
ejpam-1371	220	14	∇f(un),η(v	∇f(un),η(v	PROPN
ejpam-1371	220	15	,	,	PUNCT
ejpam-1371	220	16	un	un	NOUN
ejpam-1371	220	17	)	)	PUNCT
ejpam-1371	220	18	〉	〉	NOUN
ejpam-1371	220	19	+	+	CCONJ
ejpam-1371	220	20	1	1	NUM
ejpam-1371	220	21	ρn	ρn	ADP
ejpam-1371	220	22	|η(un	|η(un	PROPN
ejpam-1371	220	23	,	,	PUNCT
ejpam-1371	220	24	un+1)|	un+1)|	PROPN
ejpam-1371	220	25	|η(v	|η(v	PROPN
ejpam-1371	220	26	,	,	PUNCT
ejpam-1371	220	27	un+1)|	un+1)|	PROPN
ejpam-1371	220	28	=(	=(	NOUN
ejpam-1371	220	29	|t	|t	PROPN
ejpam-1371	221	1	(	(	PUNCT
ejpam-1371	221	2	un)|+	un)|+	ADJ
ejpam-1371	221	3	1	1	NUM
ejpam-1371	221	4	ρn	ρn	ADP
ejpam-1371	221	5	|η(v	|η(v	PROPN
ejpam-1371	221	6	,	,	PUNCT
ejpam-1371	221	7	un+1)|	un+1)|	NOUN
ejpam-1371	221	8	)	)	PUNCT
ejpam-1371	221	9	|η(un	|η(un	PROPN
ejpam-1371	221	10	,	,	PUNCT
ejpam-1371	221	11	un+1)|+	un+1)|+	NUM
ejpam-1371	221	12	|t	|t	PROPN
ejpam-1371	221	13	(	(	PUNCT
ejpam-1371	221	14	un)|	un)|	PROPN
ejpam-1371	221	15	|η(v	|η(v	PROPN
ejpam-1371	221	16	,	,	PUNCT
ejpam-1371	221	17	un+1)|	un+1)|	PROPN
ejpam-1371	221	18	+	+	CCONJ
ejpam-1371	221	19	〈	〈	PROPN
ejpam-1371	221	20	∇f(un),η(v	∇f(un),η(v	PROPN
ejpam-1371	221	21	,	,	PUNCT
ejpam-1371	221	22	un	un	NOUN
ejpam-1371	221	23	)	)	PUNCT
ejpam-1371	221	24	〉	〉	NOUN
ejpam-1371	221	25	≤cv	≤cv	NOUN
ejpam-1371	221	26	|η(un	|η(un	PROPN
ejpam-1371	221	27	,	,	PUNCT
ejpam-1371	221	28	un+1)|+	un+1)|+	NUM
ejpam-1371	221	29	sv|t	sv|t	PUNCT
ejpam-1371	221	30	(	(	PUNCT
ejpam-1371	221	31	un)|	un)|	PROPN
ejpam-1371	221	32	+	+	NUM
ejpam-1371	221	33	〈	〈	PROPN
ejpam-1371	221	34	∇f(un),η(v	∇f(un),η(v	PROPN
ejpam-1371	221	35	,	,	PUNCT
ejpam-1371	221	36	un	un	NOUN
ejpam-1371	221	37	)	)	PUNCT
ejpam-1371	221	38	〉	〉	NOUN
ejpam-1371	221	39	(	(	PUNCT
ejpam-1371	221	40	29	29	NUM
ejpam-1371	221	41	)	)	PUNCT
ejpam-1371	221	42	for	for	ADP
ejpam-1371	221	43	all	all	PRON
ejpam-1371	221	44	v	v	ADP
ejpam-1371	221	45	∈	∈	NOUN
ejpam-1371	221	46	m	m	NOUN
ejpam-1371	221	47	,	,	PUNCT
ejpam-1371	221	48	where	where	SCONJ
ejpam-1371	221	49	cv	cv	PROPN
ejpam-1371	221	50	=	=	PRON
ejpam-1371	221	51	|t	|t	PROPN
ejpam-1371	221	52	(	(	PUNCT
ejpam-1371	221	53	un)|+	un)|+	ADJ
ejpam-1371	221	54	1	1	NUM
ejpam-1371	221	55	ρn	ρn	ADP
ejpam-1371	221	56	|η(v	|η(v	PROPN
ejpam-1371	221	57	,	,	PUNCT
ejpam-1371	221	58	un+1)|	un+1)|	PROPN
ejpam-1371	221	59	and	and	CCONJ
ejpam-1371	221	60	sv	sv	NOUN
ejpam-1371	221	61	=	=	SYM
ejpam-1371	221	62	|η(v	|η(v	PROPN
ejpam-1371	221	63	,	,	PUNCT
ejpam-1371	221	64	un+1)|	un+1)|	PROPN
ejpam-1371	221	65	(	(	PUNCT
ejpam-1371	221	66	30	30	NUM
ejpam-1371	221	67	)	)	PUNCT
ejpam-1371	221	68	are	be	AUX
ejpam-1371	221	69	the	the	DET
ejpam-1371	221	70	nonnegative	nonnegative	ADJ
ejpam-1371	221	71	constants	constant	NOUN
ejpam-1371	221	72	limits	limit	NOUN
ejpam-1371	221	73	to	to	ADP
ejpam-1371	221	74	0	0	NUM
ejpam-1371	221	75	as	as	ADP
ejpam-1371	221	76	n→∞	n→∞	NOUN
ejpam-1371	221	77	depending	depend	VERB
ejpam-1371	221	78	on	on	ADP
ejpam-1371	221	79	v	v	NUM
ejpam-1371	221	80	∈	∈	NOUN
ejpam-1371	221	81	m	m	NOUN
ejpam-1371	221	82	.	.	PUNCT
ejpam-1371	222	1	since	since	SCONJ
ejpam-1371	222	2	the	the	DET
ejpam-1371	222	3	iterative	iterative	NOUN
ejpam-1371	222	4	sequence	sequence	NOUN
ejpam-1371	222	5	is	be	AUX
ejpam-1371	222	6	bounded	bound	VERB
ejpam-1371	222	7	,	,	PUNCT
ejpam-1371	222	8	it	it	PRON
ejpam-1371	222	9	has	have	VERB
ejpam-1371	222	10	a	a	DET
ejpam-1371	222	11	subsequence	subsequence	NOUN
ejpam-1371	222	12	which	which	PRON
ejpam-1371	222	13	is	be	AUX
ejpam-1371	222	14	of	of	ADP
ejpam-1371	222	15	finite	finite	ADJ
ejpam-1371	222	16	limit	limit	NOUN
ejpam-1371	222	17	.	.	PUNCT
ejpam-1371	223	1	we	we	PRON
ejpam-1371	223	2	claim	claim	VERB
ejpam-1371	223	3	that	that	SCONJ
ejpam-1371	223	4	,	,	PUNCT
ejpam-1371	223	5	there	there	PRON
ejpam-1371	223	6	exists	exist	VERB
ejpam-1371	223	7	a	a	DET
ejpam-1371	223	8	finite	finite	ADJ
ejpam-1371	223	9	subsequence	subsequence	NOUN
ejpam-1371	223	10	{	{	PUNCT
ejpam-1371	223	11	unk	unk	NOUN
ejpam-1371	223	12	}	}	PUNCT
ejpam-1371	223	13	∞	∞	NUM
ejpam-1371	223	14	k=1	k=1	NOUN
ejpam-1371	223	15	such	such	ADJ
ejpam-1371	223	16	that	that	DET
ejpam-1371	223	17	unk	unk	NOUN
ejpam-1371	223	18	w	w	NOUN
ejpam-1371	223	19	−→	−→	NOUN
ejpam-1371	223	20	u∗	u∗	NOUN
ejpam-1371	223	21	as	as	ADP
ejpam-1371	223	22	k→∞.	k→∞.	NOUN
ejpam-1371	223	23	and	and	CCONJ
ejpam-1371	223	24	satisfying	satisfy	VERB
ejpam-1371	223	25	the	the	DET
ejpam-1371	223	26	inequality	inequality	NOUN
ejpam-1371	223	27	lim	lim	PROPN
ejpam-1371	223	28	k→∞	k→∞	PROPN
ejpam-1371	223	29	sup	sup	PROPN
ejpam-1371	223	30	〈	〈	PROPN
ejpam-1371	223	31	t	t	PROPN
ejpam-1371	223	32	(	(	PUNCT
ejpam-1371	223	33	unk	unk	NOUN
ejpam-1371	223	34	)	)	PUNCT
ejpam-1371	223	35	,	,	PUNCT
ejpam-1371	223	36	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	223	37	)	)	PUNCT
ejpam-1371	223	38	〉	〉	NOUN
ejpam-1371	223	39	≤	≤	NUM
ejpam-1371	223	40	lim	lim	PROPN
ejpam-1371	223	41	k→∞	k→∞	PROPN
ejpam-1371	223	42	sup	sup	NUM
ejpam-1371	223	43	〈	〈	PROPN
ejpam-1371	223	44	∇f(unk	∇f(unk	NOUN
ejpam-1371	223	45	)	)	PUNCT
ejpam-1371	223	46	,	,	PUNCT
ejpam-1371	223	47	η(v	η(v	NOUN
ejpam-1371	223	48	,	,	PUNCT
ejpam-1371	223	49	unk	unk	NOUN
ejpam-1371	223	50	)	)	PUNCT
ejpam-1371	223	51	〉	〉	NOUN
ejpam-1371	223	52	.	.	PUNCT
ejpam-1371	224	1	taking	take	VERB
ejpam-1371	224	2	v	v	NOUN
ejpam-1371	224	3	=	=	SYM
ejpam-1371	224	4	u∗	u∗	ADJ
ejpam-1371	224	5	in	in	ADP
ejpam-1371	224	6	the	the	DET
ejpam-1371	224	7	(	(	PUNCT
ejpam-1371	224	8	29	29	NUM
ejpam-1371	224	9	)	)	PUNCT
ejpam-1371	224	10	and	and	CCONJ
ejpam-1371	224	11	using	use	VERB
ejpam-1371	224	12	(	(	PUNCT
ejpam-1371	224	13	30	30	NUM
ejpam-1371	224	14	)	)	PUNCT
ejpam-1371	224	15	,	,	PUNCT
ejpam-1371	224	16	we	we	PRON
ejpam-1371	224	17	have	have	VERB
ejpam-1371	224	18	lim	lim	PROPN
ejpam-1371	224	19	k→∞	k→∞	PROPN
ejpam-1371	224	20	sup	sup	PROPN
ejpam-1371	224	21	〈	〈	PROPN
ejpam-1371	224	22	t	t	PROPN
ejpam-1371	224	23	(	(	PUNCT
ejpam-1371	224	24	unk	unk	NOUN
ejpam-1371	224	25	)	)	PUNCT
ejpam-1371	224	26	,	,	PUNCT
ejpam-1371	224	27	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	224	28	)	)	PUNCT
ejpam-1371	224	29	〉	〉	NOUN
ejpam-1371	224	30	≤	≤	NUM
ejpam-1371	224	31	lim	lim	PROPN
ejpam-1371	224	32	k→∞	k→∞	NOUN
ejpam-1371	224	33	sup	sup	PROPN
ejpam-1371	224	34	cu∗	cu∗	NOUN
ejpam-1371	224	35	|η(unk	|η(unk	ADJ
ejpam-1371	224	36	,	,	PUNCT
ejpam-1371	224	37	unk+1)|+	unk+1)|+	PROPN
ejpam-1371	224	38	lim	lim	PROPN
ejpam-1371	224	39	k→∞	k→∞	PROPN
ejpam-1371	224	40	sup	sup	PROPN
ejpam-1371	224	41	su∗	su∗	NOUN
ejpam-1371	224	42	|t	|t	PROPN
ejpam-1371	225	1	(	(	PUNCT
ejpam-1371	225	2	unk	unk	NOUN
ejpam-1371	225	3	)	)	PUNCT
ejpam-1371	226	1	|	|	NOUN
ejpam-1371	227	1	+	+	CCONJ
ejpam-1371	227	2	lim	lim	PROPN
ejpam-1371	227	3	k→∞	k→∞	PROPN
ejpam-1371	227	4	sup	sup	NUM
ejpam-1371	227	5	〈	〈	PROPN
ejpam-1371	227	6	∇f(unk	∇f(unk	NOUN
ejpam-1371	227	7	)	)	PUNCT
ejpam-1371	227	8	,	,	PUNCT
ejpam-1371	227	9	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	227	10	)	)	PUNCT
ejpam-1371	227	11	〉	〉	NOUN
ejpam-1371	227	12	≤	≤	NUM
ejpam-1371	227	13	lim	lim	PROPN
ejpam-1371	227	14	k→∞	k→∞	PROPN
ejpam-1371	227	15	sup〈∇f(unk	sup〈∇f(unk	PROPN
ejpam-1371	227	16	)	)	PUNCT
ejpam-1371	227	17	,	,	PUNCT
ejpam-1371	227	18	η(u∗,unk	η(u∗,unk	NOUN
ejpam-1371	227	19	)	)	PUNCT
ejpam-1371	227	20	〉	〉	NOUN
ejpam-1371	227	21	.	.	PUNCT
ejpam-1371	228	1	next	next	ADJ
ejpam-1371	228	2	,	,	PUNCT
ejpam-1371	228	3	we	we	PRON
ejpam-1371	228	4	show	show	VERB
ejpam-1371	228	5	that	that	SCONJ
ejpam-1371	228	6	u∗	u∗	NOUN
ejpam-1371	228	7	solves	solve	VERB
ejpam-1371	228	8	the	the	DET
ejpam-1371	228	9	problem	problem	NOUN
ejpam-1371	228	10	(	(	PUNCT
ejpam-1371	228	11	agddv	agddv	NOUN
ejpam-1371	228	12	ip	ip	NOUN
ejpam-1371	228	13	)	)	PUNCT
ejpam-1371	228	14	.	.	PUNCT
ejpam-1371	229	1	from	from	ADP
ejpam-1371	229	2	(	(	PUNCT
ejpam-1371	229	3	29	29	NUM
ejpam-1371	229	4	)	)	PUNCT
ejpam-1371	229	5	,	,	PUNCT
ejpam-1371	229	6	we	we	PRON
ejpam-1371	229	7	have	have	VERB
ejpam-1371	229	8	cv|η(un	cv|η(un	NOUN
ejpam-1371	229	9	,	,	PUNCT
ejpam-1371	229	10	un+1)|+	un+1)|+	NUM
ejpam-1371	229	11	sv	sv	INTJ
ejpam-1371	229	12	|t	|t	PROPN
ejpam-1371	229	13	(	(	PUNCT
ejpam-1371	229	14	un)|	un)|	PROPN
ejpam-1371	229	15	≥	≥	NOUN
ejpam-1371	229	16	〈	〈	PROPN
ejpam-1371	229	17	t	t	PROPN
ejpam-1371	229	18	(	(	PUNCT
ejpam-1371	229	19	un),η(v	un),η(v	NOUN
ejpam-1371	229	20	,	,	PUNCT
ejpam-1371	229	21	un	un	ADJ
ejpam-1371	229	22	)	)	PUNCT
ejpam-1371	229	23	〉	〉	NOUN
ejpam-1371	229	24	−	−	NOUN
ejpam-1371	229	25	〈	〈	PROPN
ejpam-1371	229	26	∇f(un),η(v	∇f(un),η(v	PROPN
ejpam-1371	229	27	,	,	PUNCT
ejpam-1371	229	28	un	un	NOUN
ejpam-1371	229	29	)	)	PUNCT
ejpam-1371	229	30	〉	〉	NOUN
ejpam-1371	229	31	,	,	PUNCT
ejpam-1371	229	32	i.e.	i.e.	X
ejpam-1371	229	33	,	,	PUNCT
ejpam-1371	229	34	cv|η(unk	cv|η(unk	NOUN
ejpam-1371	229	35	,	,	PUNCT
ejpam-1371	229	36	unk+1)|+	unk+1)|+	PROPN
ejpam-1371	229	37	sv|t	sv|t	PUNCT
ejpam-1371	230	1	(	(	PUNCT
ejpam-1371	230	2	unk	unk	NOUN
ejpam-1371	230	3	)	)	PUNCT
ejpam-1371	230	4	|	|	ADV
ejpam-1371	230	5	≥	≥	NOUN
ejpam-1371	230	6	〈	〈	PROPN
ejpam-1371	230	7	t	t	PROPN
ejpam-1371	230	8	(	(	PUNCT
ejpam-1371	230	9	unk	unk	NOUN
ejpam-1371	230	10	)	)	PUNCT
ejpam-1371	230	11	,	,	PUNCT
ejpam-1371	230	12	η(v	η(v	NOUN
ejpam-1371	230	13	,	,	PUNCT
ejpam-1371	230	14	unk	unk	NOUN
ejpam-1371	230	15	)	)	PUNCT
ejpam-1371	230	16	〉	〉	NOUN
ejpam-1371	230	17	−	−	NOUN
ejpam-1371	230	18	〈	〈	NOUN
ejpam-1371	230	19	∇f(unk	∇f(unk	NOUN
ejpam-1371	230	20	)	)	PUNCT
ejpam-1371	230	21	,	,	PUNCT
ejpam-1371	230	22	η(v	η(v	NOUN
ejpam-1371	230	23	,	,	PUNCT
ejpam-1371	230	24	unk	unk	NOUN
ejpam-1371	230	25	)	)	PUNCT
ejpam-1371	230	26	〉	〉	NOUN
ejpam-1371	230	27	for	for	ADP
ejpam-1371	230	28	all	all	PRON
ejpam-1371	230	29	v	v	NOUN
ejpam-1371	230	30	∈	∈	NOUN
ejpam-1371	230	31	m	m	NOUN
ejpam-1371	230	32	.	.	PUNCT
ejpam-1371	231	1	thus	thus	ADV
ejpam-1371	231	2	lim	lim	PROPN
ejpam-1371	231	3	k→∞	k→∞	PROPN
ejpam-1371	231	4	inf	inf	PROPN
ejpam-1371	231	5	�	�	PROPN
ejpam-1371	231	6	cv	cv	PROPN
ejpam-1371	231	7	|η(unk	|η(unk	X
ejpam-1371	231	8	,	,	PUNCT
ejpam-1371	231	9	unk+1)|+	unk+1)|+	PROPN
ejpam-1371	231	10	sv|t	sv|t	PUNCT
ejpam-1371	231	11	(	(	PUNCT
ejpam-1371	231	12	unk	unk	NOUN
ejpam-1371	231	13	)	)	PUNCT
ejpam-1371	231	14	|	|	ADV
ejpam-1371	231	15	�	�	PROPN
ejpam-1371	231	16	≥	≥	PROPN
ejpam-1371	231	17	lim	lim	PROPN
ejpam-1371	231	18	k→∞	k→∞	PROPN
ejpam-1371	231	19	inf	inf	PROPN
ejpam-1371	231	20	�	�	PROPN
ejpam-1371	231	21	〈	〈	PROPN
ejpam-1371	231	22	t	t	PROPN
ejpam-1371	231	23	(	(	PUNCT
ejpam-1371	231	24	unk	unk	NOUN
ejpam-1371	231	25	)	)	PUNCT
ejpam-1371	231	26	,	,	PUNCT
ejpam-1371	231	27	η(v	η(v	NOUN
ejpam-1371	231	28	,	,	PUNCT
ejpam-1371	231	29	unk	unk	NOUN
ejpam-1371	231	30	〉	〉	NOUN
ejpam-1371	231	31	−	−	NOUN
ejpam-1371	231	32	〈	〈	NOUN
ejpam-1371	231	33	∇f(unk	∇f(unk	NOUN
ejpam-1371	231	34	)	)	PUNCT
ejpam-1371	231	35	,	,	PUNCT
ejpam-1371	231	36	η(v	η(v	NOUN
ejpam-1371	231	37	,	,	PUNCT
ejpam-1371	231	38	unk	unk	NOUN
ejpam-1371	231	39	〉	〉	NOUN
ejpam-1371	231	40	)	)	PUNCT
ejpam-1371	231	41	�	�	PROPN
ejpam-1371	231	42	,	,	PUNCT
ejpam-1371	231	43	p.	p.	PROPN
ejpam-1371	231	44	das	das	PROPN
ejpam-1371	231	45	/	/	SYM
ejpam-1371	231	46	eur	eur	PROPN
ejpam-1371	231	47	.	.	PUNCT
ejpam-1371	232	1	j.	j.	PROPN
ejpam-1371	232	2	pure	pure	PROPN
ejpam-1371	232	3	appl	appl	PROPN
ejpam-1371	232	4	.	.	PROPN
ejpam-1371	232	5	math	math	PROPN
ejpam-1371	232	6	,	,	PUNCT
ejpam-1371	232	7	4	4	NUM
ejpam-1371	232	8	(	(	PUNCT
ejpam-1371	232	9	2011	2011	NUM
ejpam-1371	232	10	)	)	PUNCT
ejpam-1371	232	11	,	,	PUNCT
ejpam-1371	232	12	340	340	NUM
ejpam-1371	232	13	-	-	SYM
ejpam-1371	232	14	360	360	NUM
ejpam-1371	232	15	351	351	NUM
ejpam-1371	232	16	i.e.	i.e.	X
ejpam-1371	232	17	,	,	PUNCT
ejpam-1371	232	18	0≥	0≥	PROPN
ejpam-1371	232	19	lim	lim	PROPN
ejpam-1371	232	20	k→∞	k→∞	PROPN
ejpam-1371	232	21	inf	inf	PROPN
ejpam-1371	232	22	〈	〈	PROPN
ejpam-1371	232	23	t	t	PROPN
ejpam-1371	232	24	(	(	PUNCT
ejpam-1371	232	25	unk	unk	NOUN
ejpam-1371	232	26	)	)	PUNCT
ejpam-1371	232	27	,	,	PUNCT
ejpam-1371	232	28	η(v	η(v	NOUN
ejpam-1371	232	29	,	,	PUNCT
ejpam-1371	232	30	unk	unk	NOUN
ejpam-1371	232	31	)	)	PUNCT
ejpam-1371	232	32	〉	〉	NOUN
ejpam-1371	232	33	+	+	CCONJ
ejpam-1371	232	34	lim	lim	PROPN
ejpam-1371	232	35	k→∞	k→∞	PROPN
ejpam-1371	232	36	inf	inf	PROPN
ejpam-1371	232	37	�	�	PROPN
ejpam-1371	232	38	−〈∇f(unk	−〈∇f(unk	PROPN
ejpam-1371	232	39	)	)	PUNCT
ejpam-1371	232	40	,	,	PUNCT
ejpam-1371	232	41	η(v	η(v	NOUN
ejpam-1371	232	42	,	,	PUNCT
ejpam-1371	232	43	unk	unk	NOUN
ejpam-1371	232	44	)	)	PUNCT
ejpam-1371	232	45	〉	〉	NOUN
ejpam-1371	232	46	�	�	NOUN
ejpam-1371	232	47	for	for	ADP
ejpam-1371	232	48	all	all	PRON
ejpam-1371	232	49	v	v	ADP
ejpam-1371	232	50	∈	∈	NOUN
ejpam-1371	232	51	m	m	NOUN
ejpam-1371	232	52	.	.	PUNCT
ejpam-1371	233	1	thus	thus	ADV
ejpam-1371	233	2	0≥	0≥	PROPN
ejpam-1371	233	3	〈	〈	PROPN
ejpam-1371	233	4	t	t	PROPN
ejpam-1371	233	5	(	(	PUNCT
ejpam-1371	233	6	u∗),η(v	u∗),η(v	NOUN
ejpam-1371	233	7	,	,	PUNCT
ejpam-1371	233	8	u∗	u∗	ADJ
ejpam-1371	233	9	)	)	PUNCT
ejpam-1371	233	10	〉	〉	NOUN
ejpam-1371	233	11	−	−	NOUN
ejpam-1371	233	12	〈	〈	NOUN
ejpam-1371	233	13	∇f(u∗),η(v	∇f(u∗),η(v	NOUN
ejpam-1371	233	14	,	,	PUNCT
ejpam-1371	233	15	u∗	u∗	NOUN
ejpam-1371	233	16	)	)	PUNCT
ejpam-1371	233	17	〉	〉	NOUN
ejpam-1371	233	18	,	,	PUNCT
ejpam-1371	233	19	i.e.	i.e.	X
ejpam-1371	233	20	,	,	PUNCT
ejpam-1371	233	21	〈	〈	NOUN
ejpam-1371	233	22	∇f(u∗),η(v	∇f(u∗),η(v	NOUN
ejpam-1371	233	23	,	,	PUNCT
ejpam-1371	233	24	u∗	u∗	ADJ
ejpam-1371	233	25	)	)	PUNCT
ejpam-1371	233	26	〉	〉	NOUN
ejpam-1371	233	27	−	−	NOUN
ejpam-1371	233	28	〈	〈	PROPN
ejpam-1371	233	29	t	t	PROPN
ejpam-1371	233	30	(	(	PUNCT
ejpam-1371	233	31	u∗),η(v	u∗),η(v	NOUN
ejpam-1371	233	32	,	,	PUNCT
ejpam-1371	233	33	u∗	u∗	NOUN
ejpam-1371	233	34	)	)	PUNCT
ejpam-1371	233	35	〉	〉	NOUN
ejpam-1371	233	36	≥	≥	NOUN
ejpam-1371	233	37	0	0	NUM
ejpam-1371	233	38	for	for	ADP
ejpam-1371	233	39	all	all	PRON
ejpam-1371	233	40	v	v	ADP
ejpam-1371	233	41	∈	∈	NOUN
ejpam-1371	233	42	m	m	NOUN
ejpam-1371	233	43	.	.	PUNCT
ejpam-1371	234	1	thus	thus	ADV
ejpam-1371	234	2	〈	〈	ADP
ejpam-1371	234	3	(	(	PUNCT
ejpam-1371	234	4	∇f	∇f	PROPN
ejpam-1371	234	5	−	−	PROPN
ejpam-1371	234	6	t	t	NOUN
ejpam-1371	234	7	)	)	PUNCT
ejpam-1371	234	8	(	(	PUNCT
ejpam-1371	234	9	u∗),η(v	u∗),η(v	NOUN
ejpam-1371	234	10	,	,	PUNCT
ejpam-1371	234	11	u∗	u∗	NOUN
ejpam-1371	234	12	)	)	PUNCT
ejpam-1371	234	13	〉	〉	NOUN
ejpam-1371	234	14	≥	≥	NOUN
ejpam-1371	234	15	0	0	NUM
ejpam-1371	234	16	for	for	ADP
ejpam-1371	234	17	all	all	PRON
ejpam-1371	234	18	v	v	ADP
ejpam-1371	234	19	∈	∈	NOUN
ejpam-1371	234	20	m	m	NOUN
ejpam-1371	234	21	.	.	PUNCT
ejpam-1371	235	1	hence	hence	ADV
ejpam-1371	235	2	u∗	u∗	ADJ
ejpam-1371	235	3	solves	solve	NOUN
ejpam-1371	235	4	(	(	PUNCT
ejpam-1371	235	5	agddv	agddv	NOUN
ejpam-1371	235	6	ip	ip	NOUN
ejpam-1371	235	7	)	)	PUNCT
ejpam-1371	235	8	.	.	PUNCT
ejpam-1371	236	1	this	this	PRON
ejpam-1371	236	2	is	be	AUX
ejpam-1371	236	3	a	a	DET
ejpam-1371	236	4	proof	proof	NOUN
ejpam-1371	236	5	.	.	PUNCT
ejpam-1371	237	1	3	3	X
ejpam-1371	237	2	.	.	X
ejpam-1371	237	3	gddv	gddv	NOUN
ejpam-1371	238	1	i	i	PRON
ejpam-1371	238	2	p	p	NOUN
ejpam-1371	238	3	in	in	ADP
ejpam-1371	238	4	riemannian	riemannian	ADJ
ejpam-1371	238	5	n	n	CCONJ
ejpam-1371	238	6	-	-	PUNCT
ejpam-1371	238	7	manifolds	manifold	NOUN
ejpam-1371	238	8	in	in	ADP
ejpam-1371	238	9	order	order	NOUN
ejpam-1371	238	10	to	to	PART
ejpam-1371	238	11	make	make	VERB
ejpam-1371	238	12	the	the	DET
ejpam-1371	238	13	paper	paper	NOUN
ejpam-1371	238	14	self	self	NOUN
ejpam-1371	238	15	-	-	PUNCT
ejpam-1371	238	16	contained	contain	VERB
ejpam-1371	238	17	,	,	PUNCT
ejpam-1371	238	18	we	we	PRON
ejpam-1371	238	19	recall	recall	VERB
ejpam-1371	238	20	the	the	DET
ejpam-1371	238	21	necessary	necessary	ADJ
ejpam-1371	238	22	terminologies	terminology	NOUN
ejpam-1371	238	23	of	of	ADP
ejpam-1371	238	24	the	the	DET
ejpam-1371	238	25	coincidence	coincidence	NOUN
ejpam-1371	238	26	index	index	NOUN
ejpam-1371	238	27	,	,	PUNCT
ejpam-1371	238	28	differential	differential	NOUN
ejpam-1371	238	29	of	of	ADP
ejpam-1371	238	30	any	any	DET
ejpam-1371	238	31	function	function	NOUN
ejpam-1371	238	32	on	on	ADP
ejpam-1371	238	33	a	a	DET
ejpam-1371	238	34	differentiable	differentiable	ADJ
ejpam-1371	238	35	manifold	manifold	NOUN
ejpam-1371	238	36	,	,	PUNCT
ejpam-1371	238	37	and	and	CCONJ
ejpam-1371	238	38	the	the	DET
ejpam-1371	238	39	riemannian	riemannian	ADJ
ejpam-1371	238	40	metric	metric	NOUN
ejpam-1371	238	41	.	.	PUNCT
ejpam-1371	239	1	if	if	SCONJ
ejpam-1371	239	2	f	f	PROPN
ejpam-1371	239	3	,	,	PUNCT
ejpam-1371	239	4	g	g	PROPN
ejpam-1371	239	5	:	:	PUNCT
ejpam-1371	239	6	m1→	m1→	NUM
ejpam-1371	239	7	m2	m2	PROPN
ejpam-1371	239	8	are	be	AUX
ejpam-1371	239	9	maps	map	NOUN
ejpam-1371	239	10	between	between	ADP
ejpam-1371	239	11	closed	closed	ADJ
ejpam-1371	239	12	oriented	orient	VERB
ejpam-1371	239	13	n	n	CCONJ
ejpam-1371	239	14	-	-	PUNCT
ejpam-1371	239	15	manifolds	manifold	NOUN
ejpam-1371	239	16	,	,	PUNCT
ejpam-1371	239	17	a	a	DET
ejpam-1371	239	18	coincidence	coincidence	NOUN
ejpam-1371	239	19	of	of	ADP
ejpam-1371	239	20	f	f	PROPN
ejpam-1371	239	21	and	and	CCONJ
ejpam-1371	239	22	g	g	PROPN
ejpam-1371	239	23	is	be	AUX
ejpam-1371	239	24	a	a	DET
ejpam-1371	239	25	point	point	NOUN
ejpam-1371	239	26	x	x	SYM
ejpam-1371	239	27	∈	∈	PROPN
ejpam-1371	239	28	m1	m1	NOUN
ejpam-1371	239	29	such	such	ADJ
ejpam-1371	239	30	that	that	SCONJ
ejpam-1371	239	31	f	f	PROPN
ejpam-1371	239	32	(	(	PUNCT
ejpam-1371	239	33	x	x	X
ejpam-1371	239	34	)	)	PUNCT
ejpam-1371	239	35	=	=	SYM
ejpam-1371	239	36	g(x	g(x	NOUN
ejpam-1371	239	37	)	)	PUNCT
ejpam-1371	239	38	.	.	PUNCT
ejpam-1371	240	1	geometrically	geometrically	ADV
ejpam-1371	240	2	,	,	PUNCT
ejpam-1371	240	3	if	if	SCONJ
ejpam-1371	240	4	g	g	PROPN
ejpam-1371	240	5	(	(	PUNCT
ejpam-1371	240	6	f	f	PROPN
ejpam-1371	240	7	)	)	PUNCT
ejpam-1371	240	8	and	and	CCONJ
ejpam-1371	240	9	g(g	g(g	PROPN
ejpam-1371	240	10	)	)	PUNCT
ejpam-1371	240	11	are	be	AUX
ejpam-1371	240	12	the	the	DET
ejpam-1371	240	13	graphs	graph	NOUN
ejpam-1371	240	14	of	of	ADP
ejpam-1371	240	15	the	the	DET
ejpam-1371	240	16	respective	respective	ADJ
ejpam-1371	240	17	functions	function	NOUN
ejpam-1371	240	18	in	in	ADP
ejpam-1371	240	19	m1×m2	m1×m2	PROPN
ejpam-1371	240	20	,	,	PUNCT
ejpam-1371	240	21	their	their	PRON
ejpam-1371	240	22	points	point	NOUN
ejpam-1371	240	23	of	of	ADP
ejpam-1371	240	24	intersection	intersection	NOUN
ejpam-1371	240	25	correspond	correspond	VERB
ejpam-1371	240	26	to	to	ADP
ejpam-1371	240	27	the	the	DET
ejpam-1371	240	28	coincidences	coincidence	NOUN
ejpam-1371	240	29	[	[	X
ejpam-1371	240	30	27	27	NUM
ejpam-1371	240	31	]	]	PUNCT
ejpam-1371	240	32	.	.	PUNCT
ejpam-1371	241	1	hm(m1;q	hm(m1;q	PROPN
ejpam-1371	241	2	)	)	PUNCT
ejpam-1371	241	3	f∗	f∗	NOUN
ejpam-1371	241	4	−→	−→	ADJ
ejpam-1371	241	5	hm(m1;q	hm(m1;q	PROPN
ejpam-1371	241	6	)	)	PUNCT
ejpam-1371	241	7	∼=↑	∼=↑	NOUN
ejpam-1371	241	8	µ	µ	NOUN
ejpam-1371	241	9	∼=↑	∼=↑	PRON
ejpam-1371	241	10	ν	ν	PRON
ejpam-1371	241	11	hn−m(m1;q	hn−m(m1;q	NOUN
ejpam-1371	241	12	)	)	PUNCT
ejpam-1371	241	13	←−	←−	PROPN
ejpam-1371	241	14	g∗	g∗	PROPN
ejpam-1371	241	15	hn−m(m1;q	hn−m(m1;q	NOUN
ejpam-1371	241	16	)	)	PUNCT
ejpam-1371	241	17	where	where	SCONJ
ejpam-1371	241	18	the	the	DET
ejpam-1371	241	19	vertical	vertical	ADJ
ejpam-1371	241	20	homomorphisms	homomorphism	NOUN
ejpam-1371	241	21	are	be	AUX
ejpam-1371	241	22	poincarė	poincarė	ADV
ejpam-1371	241	23	duality	duality	NOUN
ejpam-1371	241	24	isomorphisms	isomorphism	NOUN
ejpam-1371	241	25	.	.	PUNCT
ejpam-1371	242	1	the	the	DET
ejpam-1371	242	2	homomorphism	homomorphism	NOUN
ejpam-1371	242	3	θm	θm	PROPN
ejpam-1371	242	4	:	:	PUNCT
ejpam-1371	242	5	hm(m1;q)→	hm(m1;q)→	X
ejpam-1371	242	6	hm(m1;q	hm(m1;q	PROPN
ejpam-1371	242	7	)	)	PUNCT
ejpam-1371	242	8	is	be	AUX
ejpam-1371	242	9	defined	define	VERB
ejpam-1371	242	10	by	by	ADP
ejpam-1371	242	11	θm	θm	NOUN
ejpam-1371	242	12	=	=	PUNCT
ejpam-1371	242	13	µg∗ν−1	µg∗ν−1	NOUN
ejpam-1371	242	14	f∗.	f∗.	NOUN
ejpam-1371	242	15	then	then	ADV
ejpam-1371	242	16	the	the	DET
ejpam-1371	242	17	coincidence	coincidence	NOUN
ejpam-1371	242	18	number	number	NOUN
ejpam-1371	242	19	of	of	ADP
ejpam-1371	242	20	f	f	PROPN
ejpam-1371	242	21	and	and	CCONJ
ejpam-1371	242	22	g	g	PROPN
ejpam-1371	242	23	is	be	AUX
ejpam-1371	242	24	given	give	VERB
ejpam-1371	242	25	by	by	ADP
ejpam-1371	242	26	l	l	PROPN
ejpam-1371	242	27	(	(	PUNCT
ejpam-1371	242	28	f	f	PROPN
ejpam-1371	242	29	,	,	PUNCT
ejpam-1371	242	30	g	g	NOUN
ejpam-1371	242	31	)	)	PUNCT
ejpam-1371	242	32	=	=	SYM
ejpam-1371	242	33	n∑	n∑	NOUN
ejpam-1371	242	34	k=0	k=0	PROPN
ejpam-1371	242	35	(	(	PUNCT
ejpam-1371	242	36	−1)k	−1)k	PROPN
ejpam-1371	242	37	t	t	PROPN
ejpam-1371	242	38	r(θm	r(θm	PROPN
ejpam-1371	242	39	)	)	PUNCT
ejpam-1371	242	40	,	,	PUNCT
ejpam-1371	242	41	where	where	SCONJ
ejpam-1371	242	42	l	l	NOUN
ejpam-1371	242	43	(	(	PUNCT
ejpam-1371	242	44	f	f	NOUN
ejpam-1371	242	45	,	,	PUNCT
ejpam-1371	242	46	g	g	PROPN
ejpam-1371	242	47	)	)	PUNCT
ejpam-1371	242	48	is	be	AUX
ejpam-1371	242	49	the	the	DET
ejpam-1371	242	50	intersection	intersection	NOUN
ejpam-1371	242	51	number	number	NOUN
ejpam-1371	242	52	of	of	ADP
ejpam-1371	242	53	g	g	PROPN
ejpam-1371	242	54	(	(	PUNCT
ejpam-1371	242	55	f	f	PROPN
ejpam-1371	242	56	)	)	PUNCT
ejpam-1371	242	57	and	and	CCONJ
ejpam-1371	242	58	g(g	g(g	PROPN
ejpam-1371	242	59	)	)	PUNCT
ejpam-1371	242	60	;	;	PUNCT
ejpam-1371	242	61	hence	hence	ADV
ejpam-1371	242	62	if	if	SCONJ
ejpam-1371	242	63	l	l	PROPN
ejpam-1371	242	64	(	(	PUNCT
ejpam-1371	242	65	f	f	NOUN
ejpam-1371	242	66	,	,	PUNCT
ejpam-1371	242	67	g	g	PROPN
ejpam-1371	242	68	)	)	PUNCT
ejpam-1371	242	69	6=	6=	ADP
ejpam-1371	242	70	0	0	NUM
ejpam-1371	242	71	,	,	PUNCT
ejpam-1371	242	72	then	then	ADV
ejpam-1371	242	73	f	f	PROPN
ejpam-1371	242	74	and	and	CCONJ
ejpam-1371	242	75	g	g	PROPN
ejpam-1371	242	76	have	have	VERB
ejpam-1371	242	77	a	a	DET
ejpam-1371	242	78	coincidence	coincidence	NOUN
ejpam-1371	242	79	[	[	X
ejpam-1371	242	80	27	27	NUM
ejpam-1371	242	81	]	]	PUNCT
ejpam-1371	242	82	.	.	PUNCT
ejpam-1371	243	1	let	let	VERB
ejpam-1371	243	2	m1	m1	PROPN
ejpam-1371	243	3	and	and	CCONJ
ejpam-1371	243	4	m2	m2	PROPN
ejpam-1371	243	5	be	be	AUX
ejpam-1371	243	6	closed	close	VERB
ejpam-1371	243	7	,	,	PUNCT
ejpam-1371	243	8	connected	connect	VERB
ejpam-1371	243	9	,	,	PUNCT
ejpam-1371	243	10	oriented	orient	VERB
ejpam-1371	243	11	n	n	CCONJ
ejpam-1371	243	12	-	-	PUNCT
ejpam-1371	243	13	manifolds	manifold	NOUN
ejpam-1371	243	14	with	with	ADP
ejpam-1371	243	15	fundamental	fundamental	ADJ
ejpam-1371	243	16	classes	class	NOUN
ejpam-1371	243	17	zi	zi	NOUN
ejpam-1371	243	18	∈	∈	PROPN
ejpam-1371	243	19	h∗n(mi	h∗n(mi	PROPN
ejpam-1371	243	20	)	)	PUNCT
ejpam-1371	243	21	and	and	CCONJ
ejpam-1371	243	22	corresponding	corresponding	PROPN
ejpam-1371	243	23	thom	thom	PROPN
ejpam-1371	243	24	classes	class	NOUN
ejpam-1371	243	25	ui	ui	PROPN
ejpam-1371	243	26	∈	∈	PROPN
ejpam-1371	243	27	h∗n(mi	h∗n(mi	PROPN
ejpam-1371	243	28	×mi	×mi	PROPN
ejpam-1371	243	29	,	,	PUNCT
ejpam-1371	243	30	mi	mi	PROPN
ejpam-1371	243	31	×mi	×mi	PROPN
ejpam-1371	243	32	−	−	PROPN
ejpam-1371	243	33	△	△	X
ejpam-1371	243	34	(mi	(mi	X
ejpam-1371	243	35	)	)	PUNCT
ejpam-1371	243	36	)	)	PUNCT
ejpam-1371	243	37	,	,	PUNCT
ejpam-1371	243	38	i	i	PRON
ejpam-1371	243	39	=	=	NOUN
ejpam-1371	243	40	1,2	1,2	X
ejpam-1371	243	41	.	.	PUNCT
ejpam-1371	243	42	suppose	suppose	VERB
ejpam-1371	243	43	that	that	SCONJ
ejpam-1371	243	44	w	w	NOUN
ejpam-1371	243	45	is	be	AUX
ejpam-1371	243	46	an	an	DET
ejpam-1371	243	47	open	open	ADJ
ejpam-1371	243	48	set	set	NOUN
ejpam-1371	243	49	in	in	ADP
ejpam-1371	243	50	m1	m1	PROPN
ejpam-1371	243	51	and	and	CCONJ
ejpam-1371	243	52	f	f	PROPN
ejpam-1371	243	53	,	,	PUNCT
ejpam-1371	243	54	g	g	PROPN
ejpam-1371	243	55	:	:	PUNCT
ejpam-1371	243	56	w	w	PROPN
ejpam-1371	243	57	→	→	SYM
ejpam-1371	243	58	m2	m2	PROPN
ejpam-1371	243	59	are	be	AUX
ejpam-1371	243	60	the	the	DET
ejpam-1371	243	61	maps	map	NOUN
ejpam-1371	243	62	for	for	ADP
ejpam-1371	243	63	which	which	PRON
ejpam-1371	243	64	the	the	DET
ejpam-1371	243	65	coincidence	coincidence	NOUN
ejpam-1371	243	66	set	set	VERB
ejpam-1371	243	67	c	c	NOUN
ejpam-1371	243	68	=	=	PRON
ejpam-1371	243	69	{	{	PUNCT
ejpam-1371	243	70	x	x	SYM
ejpam-1371	243	71	∈	∈	PROPN
ejpam-1371	243	72	w	w	NOUN
ejpam-1371	243	73	:	:	PUNCT
ejpam-1371	243	74	f	f	PROPN
ejpam-1371	243	75	(	(	PUNCT
ejpam-1371	243	76	x	x	X
ejpam-1371	243	77	)	)	PUNCT
ejpam-1371	243	78	=	=	SYM
ejpam-1371	243	79	g(x	g(x	NOUN
ejpam-1371	243	80	)	)	PUNCT
ejpam-1371	243	81	}	}	PUNCT
ejpam-1371	243	82	is	be	AUX
ejpam-1371	243	83	a	a	DET
ejpam-1371	243	84	compact	compact	ADJ
ejpam-1371	243	85	subset	subset	NOUN
ejpam-1371	243	86	of	of	ADP
ejpam-1371	243	87	w	w	PROPN
ejpam-1371	243	88	.	.	PUNCT
ejpam-1371	244	1	by	by	ADP
ejpam-1371	244	2	normality	normality	NOUN
ejpam-1371	244	3	of	of	ADP
ejpam-1371	244	4	m1	m1	PROPN
ejpam-1371	244	5	there	there	ADV
ejpam-1371	244	6	p.	p.	PROPN
ejpam-1371	244	7	das	das	PROPN
ejpam-1371	244	8	/	/	SYM
ejpam-1371	244	9	eur	eur	PROPN
ejpam-1371	244	10	.	.	PUNCT
ejpam-1371	245	1	j.	j.	PROPN
ejpam-1371	245	2	pure	pure	PROPN
ejpam-1371	245	3	appl	appl	PROPN
ejpam-1371	245	4	.	.	PROPN
ejpam-1371	245	5	math	math	PROPN
ejpam-1371	245	6	,	,	PUNCT
ejpam-1371	245	7	4	4	NUM
ejpam-1371	245	8	(	(	PUNCT
ejpam-1371	245	9	2011	2011	NUM
ejpam-1371	245	10	)	)	PUNCT
ejpam-1371	245	11	,	,	PUNCT
ejpam-1371	245	12	340	340	NUM
ejpam-1371	245	13	-	-	SYM
ejpam-1371	245	14	360	360	NUM
ejpam-1371	245	15	352	352	NUM
ejpam-1371	245	16	exists	exist	VERB
ejpam-1371	245	17	an	an	DET
ejpam-1371	245	18	open	open	ADJ
ejpam-1371	245	19	set	set	NOUN
ejpam-1371	245	20	v	v	NOUN
ejpam-1371	245	21	in	in	ADP
ejpam-1371	245	22	m1	m1	PROPN
ejpam-1371	245	23	with	with	ADP
ejpam-1371	245	24	c	c	PROPN
ejpam-1371	245	25	⊆	⊆	NUM
ejpam-1371	245	26	v	v	ADP
ejpam-1371	245	27	⊆	⊆	NUM
ejpam-1371	245	28	v̄	v̄	NUM
ejpam-1371	245	29	⊆w	⊆w	NOUN
ejpam-1371	245	30	.	.	PUNCT
ejpam-1371	246	1	the	the	DET
ejpam-1371	246	2	coincidence	coincidence	NOUN
ejpam-1371	246	3	index	index	NOUN
ejpam-1371	246	4	of	of	ADP
ejpam-1371	246	5	the	the	DET
ejpam-1371	246	6	pair	pair	NOUN
ejpam-1371	246	7	(	(	PUNCT
ejpam-1371	246	8	f	f	NOUN
ejpam-1371	246	9	,	,	PUNCT
ejpam-1371	246	10	g	g	PROPN
ejpam-1371	246	11	)	)	PUNCT
ejpam-1371	246	12	on	on	ADP
ejpam-1371	246	13	w	w	NOUN
ejpam-1371	246	14	is	be	AUX
ejpam-1371	246	15	defined	define	VERB
ejpam-1371	246	16	to	to	PART
ejpam-1371	246	17	be	be	AUX
ejpam-1371	246	18	the	the	DET
ejpam-1371	246	19	integer	integer	NOUN
ejpam-1371	246	20	iw	iw	PROPN
ejpam-1371	246	21	f	f	PROPN
ejpam-1371	246	22	,	,	PUNCT
ejpam-1371	246	23	g	g	PROPN
ejpam-1371	246	24	given	give	VERB
ejpam-1371	246	25	by	by	ADP
ejpam-1371	246	26	the	the	DET
ejpam-1371	246	27	image	image	NOUN
ejpam-1371	246	28	of	of	ADP
ejpam-1371	246	29	the	the	DET
ejpam-1371	246	30	fundamental	fundamental	ADJ
ejpam-1371	246	31	class	class	NOUN
ejpam-1371	246	32	of	of	ADP
ejpam-1371	246	33	z1	z1	NOUN
ejpam-1371	246	34	under	under	ADP
ejpam-1371	246	35	the	the	DET
ejpam-1371	246	36	composition	composition	NOUN
ejpam-1371	246	37	hn(m1)→	hn(m1)→	NOUN
ejpam-1371	246	38	hn(m1	hn(m1	NOUN
ejpam-1371	246	39	,	,	PUNCT
ejpam-1371	246	40	m1	m1	PROPN
ejpam-1371	246	41	−	−	PROPN
ejpam-1371	246	42	v	v	NOUN
ejpam-1371	246	43	)	)	PUNCT
ejpam-1371	246	44	∼=	∼=	PROPN
ejpam-1371	246	45	−−−−→	−−−−→	SYM
ejpam-1371	246	46	excision	excision	NOUN
ejpam-1371	246	47	hn(w	hn(w	PROPN
ejpam-1371	246	48	,	,	PUNCT
ejpam-1371	246	49	w	w	PROPN
ejpam-1371	246	50	−	−	PROPN
ejpam-1371	246	51	v	v	NOUN
ejpam-1371	246	52	)	)	PUNCT
ejpam-1371	246	53	(	(	PUNCT
ejpam-1371	246	54	f	f	X
ejpam-1371	246	55	,	,	PUNCT
ejpam-1371	246	56	g)∗−−−→	g)∗−−−→	VERB
ejpam-1371	246	57	hn(m2	hn(m2	NOUN
ejpam-1371	246	58	×m2	×m2	NOUN
ejpam-1371	246	59	,	,	PUNCT
ejpam-1371	246	60	m2	m2	PROPN
ejpam-1371	246	61	×m2	×m2	PROPN
ejpam-1371	246	62	−	−	NUM
ejpam-1371	246	63	△	△	X
ejpam-1371	246	64	(m2	(m2	X
ejpam-1371	246	65	)	)	PUNCT
ejpam-1371	246	66	)	)	PUNCT
ejpam-1371	247	1	∼=	∼=	PROPN
ejpam-1371	247	2	z	z	NOUN
ejpam-1371	247	3	,	,	PUNCT
ejpam-1371	247	4	where	where	SCONJ
ejpam-1371	247	5	the	the	DET
ejpam-1371	247	6	map	map	NOUN
ejpam-1371	247	7	(	(	PUNCT
ejpam-1371	247	8	f	f	NOUN
ejpam-1371	247	9	,	,	PUNCT
ejpam-1371	247	10	g	g	PROPN
ejpam-1371	247	11	)	)	PUNCT
ejpam-1371	247	12	:	:	PUNCT
ejpam-1371	247	13	w	w	X
ejpam-1371	247	14	→	→	SYM
ejpam-1371	247	15	m2	m2	NOUN
ejpam-1371	247	16	×m2	×m2	PROPN
ejpam-1371	247	17	is	be	AUX
ejpam-1371	247	18	given	give	VERB
ejpam-1371	247	19	by	by	ADP
ejpam-1371	247	20	(	(	PUNCT
ejpam-1371	247	21	f	f	PROPN
ejpam-1371	247	22	,	,	PUNCT
ejpam-1371	247	23	g)(x	g)(x	PROPN
ejpam-1371	247	24	)	)	PUNCT
ejpam-1371	248	1	=	=	PRON
ejpam-1371	249	1	(	(	PUNCT
ejpam-1371	249	2	f	f	X
ejpam-1371	249	3	(	(	PUNCT
ejpam-1371	249	4	x	x	NOUN
ejpam-1371	249	5	)	)	PUNCT
ejpam-1371	249	6	,	,	PUNCT
ejpam-1371	249	7	g(x	g(x	NOUN
ejpam-1371	249	8	)	)	PUNCT
ejpam-1371	249	9	)	)	PUNCT
ejpam-1371	249	10	,	,	PUNCT
ejpam-1371	249	11	and	and	CCONJ
ejpam-1371	249	12	the	the	DET
ejpam-1371	249	13	identification	identification	NOUN
ejpam-1371	249	14	hn(m2	hn(m2	NOUN
ejpam-1371	249	15	×m2	×m2	PROPN
ejpam-1371	249	16	,	,	PUNCT
ejpam-1371	249	17	m2	m2	PROPN
ejpam-1371	249	18	×m2	×m2	PROPN
ejpam-1371	249	19	−	−	NUM
ejpam-1371	249	20	△	△	X
ejpam-1371	249	21	(m2	(m2	X
ejpam-1371	249	22	)	)	PUNCT
ejpam-1371	249	23	)	)	PUNCT
ejpam-1371	250	1	∼=	∼=	NOUN
ejpam-1371	250	2	z	z	NOUN
ejpam-1371	250	3	is	be	AUX
ejpam-1371	250	4	given	give	VERB
ejpam-1371	250	5	by	by	ADP
ejpam-1371	250	6	sending	send	VERB
ejpam-1371	250	7	a	a	DET
ejpam-1371	250	8	class	class	NOUN
ejpam-1371	250	9	α	α	NOUN
ejpam-1371	250	10	into	into	ADP
ejpam-1371	250	11	the	the	DET
ejpam-1371	250	12	integer	integer	NOUN
ejpam-1371	250	13	〈	〈	PROPN
ejpam-1371	250	14	u2	u2	NOUN
ejpam-1371	250	15	,	,	PUNCT
ejpam-1371	250	16	α	α	NOUN
ejpam-1371	250	17	〉	〉	NOUN
ejpam-1371	250	18	.	.	PUNCT
ejpam-1371	251	1	if	if	SCONJ
ejpam-1371	251	2	m1	m1	PROPN
ejpam-1371	251	3	=	=	PROPN
ejpam-1371	251	4	m2	m2	PROPN
ejpam-1371	251	5	(	(	PUNCT
ejpam-1371	251	6	denoted	denote	VERB
ejpam-1371	251	7	by	by	ADP
ejpam-1371	251	8	m	m	PROPN
ejpam-1371	251	9	)	)	PUNCT
ejpam-1371	251	10	and	and	CCONJ
ejpam-1371	251	11	g	g	NOUN
ejpam-1371	251	12	=	=	NOUN
ejpam-1371	251	13	identity	identity	NOUN
ejpam-1371	251	14	on	on	ADP
ejpam-1371	251	15	the	the	DET
ejpam-1371	251	16	open	open	ADJ
ejpam-1371	251	17	set	set	NOUN
ejpam-1371	251	18	w	w	PROPN
ejpam-1371	251	19	,	,	PUNCT
ejpam-1371	251	20	the	the	DET
ejpam-1371	251	21	coincidence	coincidence	NOUN
ejpam-1371	251	22	index	index	NOUN
ejpam-1371	251	23	iw	iw	PROPN
ejpam-1371	251	24	f	f	PROPN
ejpam-1371	251	25	,	,	PUNCT
ejpam-1371	251	26	i	i	PROPN
ejpam-1371	251	27	d	d	PROPN
ejpam-1371	251	28	is	be	AUX
ejpam-1371	251	29	denoted	denote	VERB
ejpam-1371	251	30	by	by	ADP
ejpam-1371	251	31	iw	iw	PROPN
ejpam-1371	251	32	f	f	PROPN
ejpam-1371	251	33	,	,	PUNCT
ejpam-1371	251	34	called	call	VERB
ejpam-1371	251	35	the	the	DET
ejpam-1371	251	36	fixed	fix	VERB
ejpam-1371	251	37	-	-	PUNCT
ejpam-1371	251	38	point	point	NOUN
ejpam-1371	251	39	index	index	NOUN
ejpam-1371	251	40	of	of	ADP
ejpam-1371	251	41	f	f	PROPN
ejpam-1371	251	42	on	on	ADP
ejpam-1371	251	43	w	w	PROPN
ejpam-1371	251	44	[	[	X
ejpam-1371	251	45	27	27	NUM
ejpam-1371	251	46	]	]	PUNCT
ejpam-1371	251	47	and	and	CCONJ
ejpam-1371	251	48	fixed	fix	VERB
ejpam-1371	251	49	-	-	PUNCT
ejpam-1371	251	50	point	point	NOUN
ejpam-1371	251	51	index	index	NOUN
ejpam-1371	251	52	of	of	ADP
ejpam-1371	251	53	f	f	PROPN
ejpam-1371	251	54	on	on	ADP
ejpam-1371	251	55	m	m	PROPN
ejpam-1371	251	56	is	be	AUX
ejpam-1371	251	57	denoted	denote	VERB
ejpam-1371	251	58	by	by	ADP
ejpam-1371	251	59	i	i	PROPN
ejpam-1371	251	60	f	f	PROPN
ejpam-1371	251	61	.	.	PUNCT
ejpam-1371	252	1	theorem	theorem	VERB
ejpam-1371	252	2	4	4	NUM
ejpam-1371	252	3	(	(	PUNCT
ejpam-1371	252	4	[	[	X
ejpam-1371	252	5	27	27	NUM
ejpam-1371	252	6	,	,	PUNCT
ejpam-1371	252	7	lemma	lemma	PROPN
ejpam-1371	252	8	6.7	6.7	NUM
ejpam-1371	252	9	,	,	PUNCT
ejpam-1371	252	10	p.180	p.180	NOUN
ejpam-1371	252	11	]	]	PUNCT
ejpam-1371	252	12	)	)	PUNCT
ejpam-1371	252	13	.	.	PUNCT
ejpam-1371	253	1	let	let	VERB
ejpam-1371	253	2	x	x	PRON
ejpam-1371	253	3	be	be	AUX
ejpam-1371	253	4	a	a	DET
ejpam-1371	253	5	closed	closed	ADJ
ejpam-1371	253	6	,	,	PUNCT
ejpam-1371	253	7	convex	convex	ADJ
ejpam-1371	253	8	and	and	CCONJ
ejpam-1371	253	9	oriented	orient	VERB
ejpam-1371	253	10	riemannian	riemannian	ADJ
ejpam-1371	253	11	n	n	CCONJ
ejpam-1371	253	12	-	-	PUNCT
ejpam-1371	253	13	manifold	manifold	ADJ
ejpam-1371	253	14	.	.	PUNCT
ejpam-1371	254	1	let	let	VERB
ejpam-1371	254	2	w	w	NOUN
ejpam-1371	254	3	be	be	AUX
ejpam-1371	254	4	an	an	DET
ejpam-1371	254	5	open	open	ADJ
ejpam-1371	254	6	set	set	NOUN
ejpam-1371	254	7	in	in	ADP
ejpam-1371	254	8	x.	x.	NOUN
ejpam-1371	254	9	if	if	SCONJ
ejpam-1371	254	10	iw	iw	PROPN
ejpam-1371	254	11	f	f	PROPN
ejpam-1371	254	12	6=	6=	PROPN
ejpam-1371	254	13	0	0	NUM
ejpam-1371	254	14	,	,	PUNCT
ejpam-1371	254	15	then	then	ADV
ejpam-1371	254	16	f	f	PROPN
ejpam-1371	254	17	has	have	VERB
ejpam-1371	254	18	a	a	DET
ejpam-1371	254	19	fixed	fix	VERB
ejpam-1371	254	20	point	point	NOUN
ejpam-1371	254	21	on	on	ADP
ejpam-1371	254	22	w.	w.	PROPN
ejpam-1371	254	23	let	let	VERB
ejpam-1371	254	24	x	x	PRON
ejpam-1371	254	25	be	be	AUX
ejpam-1371	254	26	a	a	DET
ejpam-1371	254	27	differentiable	differentiable	ADJ
ejpam-1371	254	28	manifold	manifold	NOUN
ejpam-1371	254	29	with	with	ADP
ejpam-1371	254	30	tangent	tangent	NOUN
ejpam-1371	254	31	bundle	bundle	NOUN
ejpam-1371	254	32	τx	τx	ADP
ejpam-1371	254	33	where	where	SCONJ
ejpam-1371	254	34	τ(x	τ(x	PUNCT
ejpam-1371	254	35	,	,	PUNCT
ejpam-1371	254	36	u	u	NOUN
ejpam-1371	254	37	)	)	PUNCT
ejpam-1371	254	38	is	be	AUX
ejpam-1371	254	39	the	the	DET
ejpam-1371	254	40	tangent	tangent	ADJ
ejpam-1371	254	41	bundle	bundle	NOUN
ejpam-1371	254	42	at	at	ADP
ejpam-1371	254	43	u	u	PROPN
ejpam-1371	254	44	∈	∈	PROPN
ejpam-1371	254	45	k	k	X
ejpam-1371	254	46	.	.	PUNCT
ejpam-1371	255	1	let	let	VERB
ejpam-1371	255	2	k	k	X
ejpam-1371	255	3	be	be	AUX
ejpam-1371	255	4	a	a	DET
ejpam-1371	255	5	closed	closed	ADJ
ejpam-1371	255	6	convex	convex	NOUN
ejpam-1371	255	7	cone	cone	NOUN
ejpam-1371	255	8	in	in	ADP
ejpam-1371	255	9	the	the	DET
ejpam-1371	255	10	manifold	manifold	ADJ
ejpam-1371	255	11	x	x	NOUN
ejpam-1371	255	12	.	.	PUNCT
ejpam-1371	256	1	mititelu	mititelu	NOUN
ejpam-1371	257	1	[	[	X
ejpam-1371	257	2	22	22	NUM
ejpam-1371	257	3	]	]	PUNCT
ejpam-1371	257	4	introduced	introduce	VERB
ejpam-1371	257	5	the	the	DET
ejpam-1371	257	6	differential	differential	ADJ
ejpam-1371	257	7	application	application	NOUN
ejpam-1371	257	8	of	of	ADP
ejpam-1371	257	9	a	a	DET
ejpam-1371	257	10	differentiable	differentiable	ADJ
ejpam-1371	257	11	vector	vector	NOUN
ejpam-1371	257	12	function	function	NOUN
ejpam-1371	257	13	in	in	ADP
ejpam-1371	257	14	the	the	DET
ejpam-1371	257	15	differentiable	differentiable	ADJ
ejpam-1371	257	16	manifold	manifold	NOUN
ejpam-1371	257	17	for	for	ADP
ejpam-1371	257	18	a	a	DET
ejpam-1371	257	19	development	development	NOUN
ejpam-1371	257	20	of	of	ADP
ejpam-1371	257	21	the	the	DET
ejpam-1371	257	22	η	η	PROPN
ejpam-1371	257	23	-	-	ADJ
ejpam-1371	257	24	invex	invex	ADJ
ejpam-1371	257	25	function	function	NOUN
ejpam-1371	257	26	.	.	PUNCT
ejpam-1371	258	1	this	this	PRON
ejpam-1371	258	2	enhanced	enhance	VERB
ejpam-1371	258	3	to	to	PART
ejpam-1371	258	4	develop	develop	VERB
ejpam-1371	258	5	the	the	DET
ejpam-1371	258	6	the	the	DET
ejpam-1371	258	7	scope	scope	NOUN
ejpam-1371	258	8	of	of	ADP
ejpam-1371	258	9	(	(	PUNCT
ejpam-1371	258	10	gv	gv	PROPN
ejpam-1371	258	11	v	v	NOUN
ejpam-1371	258	12	ip	ip	NOUN
ejpam-1371	258	13	)	)	PUNCT
ejpam-1371	258	14	in	in	ADP
ejpam-1371	258	15	differentiable	differentiable	ADJ
ejpam-1371	258	16	manifold	manifold	NOUN
ejpam-1371	258	17	.	.	PUNCT
ejpam-1371	259	1	definition	definition	NOUN
ejpam-1371	259	2	10	10	NUM
ejpam-1371	259	3	(	(	PUNCT
ejpam-1371	259	4	[	[	X
ejpam-1371	259	5	22	22	NUM
ejpam-1371	259	6	]	]	PUNCT
ejpam-1371	259	7	)	)	PUNCT
ejpam-1371	259	8	.	.	PUNCT
ejpam-1371	260	1	let	let	VERB
ejpam-1371	260	2	x	x	PRON
ejpam-1371	260	3	be	be	AUX
ejpam-1371	260	4	a	a	DET
ejpam-1371	260	5	differentiable	differentiable	ADJ
ejpam-1371	260	6	manifold	manifold	NOUN
ejpam-1371	260	7	with	with	ADP
ejpam-1371	260	8	tangent	tangent	NOUN
ejpam-1371	260	9	bundle	bundle	NOUN
ejpam-1371	260	10	τx	τx	X
ejpam-1371	260	11	.	.	PUNCT
ejpam-1371	261	1	let	let	VERB
ejpam-1371	261	2	φ	φ	NOUN
ejpam-1371	261	3	:	:	PUNCT
ejpam-1371	261	4	x	x	SYM
ejpam-1371	261	5	→	→	SYM
ejpam-1371	261	6	rn	rn	AUX
ejpam-1371	261	7	be	be	AUX
ejpam-1371	261	8	a	a	DET
ejpam-1371	261	9	differentiable	differentiable	ADJ
ejpam-1371	261	10	vector	vector	NOUN
ejpam-1371	261	11	function	function	NOUN
ejpam-1371	261	12	.	.	PUNCT
ejpam-1371	262	1	the	the	DET
ejpam-1371	262	2	application	application	NOUN
ejpam-1371	262	3	dφu	dφu	NOUN
ejpam-1371	262	4	:	:	PUNCT
ejpam-1371	262	5	τ(x	τ(x	NOUN
ejpam-1371	262	6	,	,	PUNCT
ejpam-1371	262	7	u)→	u)→	ADP
ejpam-1371	262	8	τ(rn	τ(rn	PROPN
ejpam-1371	262	9	,	,	PUNCT
ejpam-1371	262	10	φ(u	φ(u	NOUN
ejpam-1371	262	11	)	)	PUNCT
ejpam-1371	262	12	)	)	PUNCT
ejpam-1371	263	1	=	=	SYM
ejpam-1371	263	2	rn	rn	PROPN
ejpam-1371	263	3	is	be	AUX
ejpam-1371	263	4	said	say	VERB
ejpam-1371	263	5	to	to	PART
ejpam-1371	263	6	be	be	AUX
ejpam-1371	263	7	differential	differential	NOUN
ejpam-1371	263	8	of	of	ADP
ejpam-1371	263	9	φ	φ	PROPN
ejpam-1371	263	10	at	at	ADP
ejpam-1371	263	11	u	u	PROPN
ejpam-1371	263	12	∈	∈	PROPN
ejpam-1371	263	13	k	k	NOUN
ejpam-1371	263	14	,	,	PUNCT
ejpam-1371	263	15	if	if	SCONJ
ejpam-1371	263	16	dφu(v	dφu(v	PROPN
ejpam-1371	263	17	)	)	PUNCT
ejpam-1371	263	18	=	=	SYM
ejpam-1371	263	19	dφ(u)(v	dφ(u)(v	NOUN
ejpam-1371	263	20	)	)	PUNCT
ejpam-1371	263	21	for	for	ADP
ejpam-1371	263	22	all	all	PRON
ejpam-1371	263	23	v	v	ADP
ejpam-1371	263	24	∈	∈	PRON
ejpam-1371	263	25	τ(x	τ(x	PUNCT
ejpam-1371	263	26	,	,	PUNCT
ejpam-1371	263	27	u	u	NOUN
ejpam-1371	263	28	)	)	PUNCT
ejpam-1371	263	29	.	.	PUNCT
ejpam-1371	264	1	now	now	ADV
ejpam-1371	264	2	,	,	PUNCT
ejpam-1371	264	3	if	if	SCONJ
ejpam-1371	264	4	x	x	PRON
ejpam-1371	264	5	is	be	AUX
ejpam-1371	264	6	modelled	model	VERB
ejpam-1371	264	7	in	in	ADP
ejpam-1371	264	8	the	the	DET
ejpam-1371	264	9	hilbert	hilbert	PROPN
ejpam-1371	264	10	space	space	NOUN
ejpam-1371	264	11	h	h	NOUN
ejpam-1371	264	12	,	,	PUNCT
ejpam-1371	264	13	then	then	ADV
ejpam-1371	264	14	τx	τx	PROPN
ejpam-1371	264	15	=	=	PUNCT
ejpam-1371	265	1	x	x	X
ejpam-1371	265	2	.	.	PUNCT
ejpam-1371	266	1	in	in	ADP
ejpam-1371	266	2	this	this	DET
ejpam-1371	266	3	section	section	NOUN
ejpam-1371	266	4	,	,	PUNCT
ejpam-1371	266	5	we	we	PRON
ejpam-1371	266	6	obtain	obtain	VERB
ejpam-1371	266	7	the	the	DET
ejpam-1371	266	8	generalized	generalized	ADJ
ejpam-1371	266	9	vector	vector	NOUN
ejpam-1371	266	10	variational	variational	ADJ
ejpam-1371	266	11	inequality	inequality	NOUN
ejpam-1371	266	12	problem	problem	NOUN
ejpam-1371	266	13	and	and	CCONJ
ejpam-1371	266	14	generalized	generalized	ADJ
ejpam-1371	266	15	vector	vector	NOUN
ejpam-1371	266	16	complementarity	complementarity	NOUN
ejpam-1371	266	17	problems	problem	NOUN
ejpam-1371	266	18	in	in	ADP
ejpam-1371	266	19	riemannian	riemannian	ADJ
ejpam-1371	266	20	n	n	CCONJ
ejpam-1371	266	21	-	-	PUNCT
ejpam-1371	266	22	manifolds	manifold	NOUN
ejpam-1371	266	23	.	.	PUNCT
ejpam-1371	267	1	let	let	VERB
ejpam-1371	267	2	x	x	PRON
ejpam-1371	267	3	be	be	AUX
ejpam-1371	267	4	a	a	DET
ejpam-1371	267	5	closed	closed	ADJ
ejpam-1371	267	6	,	,	PUNCT
ejpam-1371	267	7	convex	convex	ADJ
ejpam-1371	267	8	and	and	CCONJ
ejpam-1371	267	9	oriented	orient	VERB
ejpam-1371	267	10	riemannian	riemannian	NOUN
ejpam-1371	267	11	nmanifold	nmanifold	ADJ
ejpam-1371	267	12	,	,	PUNCT
ejpam-1371	267	13	modeled	model	VERB
ejpam-1371	267	14	on	on	ADP
ejpam-1371	267	15	the	the	DET
ejpam-1371	267	16	hilbert	hilbert	PROPN
ejpam-1371	267	17	spaceh	spaceh	NOUN
ejpam-1371	267	18	with	with	ADP
ejpam-1371	267	19	riemannian	riemannian	PROPN
ejpam-1371	267	20	metric	metric	ADJ
ejpam-1371	267	21	g.	g.	PROPN
ejpam-1371	268	1	it	it	PRON
ejpam-1371	268	2	is	be	AUX
ejpam-1371	268	3	well	well	ADV
ejpam-1371	268	4	known	know	VERB
ejpam-1371	268	5	that	that	SCONJ
ejpam-1371	268	6	the	the	DET
ejpam-1371	268	7	tangent	tangent	NOUN
ejpam-1371	268	8	bundle	bundle	PROPN
ejpam-1371	268	9	τ(x	τ(x	PUNCT
ejpam-1371	268	10	)	)	PUNCT
ejpam-1371	268	11	can	can	AUX
ejpam-1371	268	12	be	be	AUX
ejpam-1371	268	13	identified	identify	VERB
ejpam-1371	268	14	with	with	ADP
ejpam-1371	268	15	the	the	DET
ejpam-1371	268	16	cotangent	cotangent	NOUN
ejpam-1371	268	17	bundle	bundle	NOUN
ejpam-1371	268	18	τ∗(x	τ∗(x	PRON
ejpam-1371	268	19	)	)	PUNCT
ejpam-1371	268	20	by	by	ADP
ejpam-1371	268	21	the	the	DET
ejpam-1371	268	22	riemannian	riemannian	ADJ
ejpam-1371	268	23	metric	metric	NOUN
ejpam-1371	268	24	,	,	PUNCT
ejpam-1371	268	25	because	because	SCONJ
ejpam-1371	268	26	h∗	h∗	PROPN
ejpam-1371	268	27	,	,	PUNCT
ejpam-1371	268	28	the	the	DET
ejpam-1371	268	29	dual	dual	ADJ
ejpam-1371	268	30	of	of	ADP
ejpam-1371	268	31	h	h	NOUN
ejpam-1371	268	32	can	can	AUX
ejpam-1371	268	33	be	be	AUX
ejpam-1371	268	34	identified	identify	VERB
ejpam-1371	268	35	with	with	ADP
ejpam-1371	268	36	h	h	NOUN
ejpam-1371	269	1	[	[	X
ejpam-1371	269	2	25	25	NUM
ejpam-1371	269	3	]	]	PUNCT
ejpam-1371	269	4	.	.	PUNCT
ejpam-1371	270	1	if	if	SCONJ
ejpam-1371	270	2	v	v	X
ejpam-1371	270	3	,	,	PUNCT
ejpam-1371	270	4	w	w	PROPN
ejpam-1371	270	5	∈	∈	PROPN
ejpam-1371	270	6	τ(x	τ(x	PUNCT
ejpam-1371	270	7	,	,	PUNCT
ejpam-1371	270	8	x	x	X
ejpam-1371	270	9	)	)	PUNCT
ejpam-1371	270	10	,	,	PUNCT
ejpam-1371	270	11	then	then	ADV
ejpam-1371	270	12	we	we	PRON
ejpam-1371	270	13	write	write	VERB
ejpam-1371	270	14	gx(v	gx(v	NOUN
ejpam-1371	270	15	,	,	PUNCT
ejpam-1371	270	16	w	w	NOUN
ejpam-1371	270	17	)	)	PUNCT
ejpam-1371	270	18	=	=	PUNCT
ejpam-1371	271	1	〈	〈	PROPN
ejpam-1371	271	2	v	v	NOUN
ejpam-1371	271	3	,	,	PUNCT
ejpam-1371	271	4	w〉x	w〉x	X
ejpam-1371	271	5	.	.	PUNCT
ejpam-1371	272	1	definition	definition	NOUN
ejpam-1371	272	2	11	11	NUM
ejpam-1371	272	3	(	(	PUNCT
ejpam-1371	272	4	[	[	X
ejpam-1371	272	5	11	11	NUM
ejpam-1371	272	6	]	]	NUM
ejpam-1371	272	7	)	)	PUNCT
ejpam-1371	272	8	.	.	PUNCT
ejpam-1371	273	1	let	let	VERB
ejpam-1371	273	2	x	x	PRON
ejpam-1371	273	3	be	be	AUX
ejpam-1371	273	4	a	a	DET
ejpam-1371	273	5	riemannian	riemannian	ADJ
ejpam-1371	273	6	n	n	CCONJ
ejpam-1371	273	7	-	-	PUNCT
ejpam-1371	273	8	manifold	manifold	ADJ
ejpam-1371	273	9	.	.	PUNCT
ejpam-1371	274	1	let	let	VERB
ejpam-1371	274	2	η	η	NOUN
ejpam-1371	274	3	:	:	PUNCT
ejpam-1371	274	4	x	x	SYM
ejpam-1371	274	5	×	×	NOUN
ejpam-1371	274	6	x	x	INTJ
ejpam-1371	274	7	→	→	SYM
ejpam-1371	274	8	τx	τx	PROPN
ejpam-1371	274	9	defined	define	VERB
ejpam-1371	274	10	by	by	ADP
ejpam-1371	274	11	,	,	PUNCT
ejpam-1371	274	12	for	for	ADP
ejpam-1371	274	13	each	each	DET
ejpam-1371	274	14	u	u	NOUN
ejpam-1371	274	15	∈	∈	PROPN
ejpam-1371	274	16	x	x	SYM
ejpam-1371	274	17	,	,	PUNCT
ejpam-1371	274	18	η(x	η(x	PROPN
ejpam-1371	274	19	,	,	PUNCT
ejpam-1371	274	20	u	u	NOUN
ejpam-1371	274	21	)	)	PUNCT
ejpam-1371	274	22	∈	∈	PROPN
ejpam-1371	274	23	τ(x	τ(x	PUNCT
ejpam-1371	274	24	,	,	PUNCT
ejpam-1371	274	25	u	u	NOUN
ejpam-1371	274	26	)	)	PUNCT
ejpam-1371	274	27	.	.	PUNCT
ejpam-1371	275	1	then	then	ADV
ejpam-1371	275	2	x	x	X
ejpam-1371	275	3	is	be	AUX
ejpam-1371	275	4	said	say	VERB
ejpam-1371	275	5	to	to	PART
ejpam-1371	275	6	be	be	AUX
ejpam-1371	275	7	η	η	NOUN
ejpam-1371	275	8	-	-	ADJ
ejpam-1371	275	9	closed	closed	ADJ
ejpam-1371	275	10	if	if	SCONJ
ejpam-1371	275	11	for	for	ADP
ejpam-1371	275	12	every	every	DET
ejpam-1371	275	13	p	p	NOUN
ejpam-1371	275	14	∈	∈	PROPN
ejpam-1371	275	15	x	x	X
ejpam-1371	275	16	,	,	PUNCT
ejpam-1371	275	17	there	there	PRON
ejpam-1371	275	18	is	be	VERB
ejpam-1371	275	19	an	an	DET
ejpam-1371	275	20	unique	unique	ADJ
ejpam-1371	275	21	x	x	SYM
ejpam-1371	275	22	∈	∈	NOUN
ejpam-1371	275	23	x	x	SYM
ejpam-1371	275	24	closest	close	ADJ
ejpam-1371	275	25	to	to	ADP
ejpam-1371	275	26	p	p	NOUN
ejpam-1371	275	27	with	with	ADP
ejpam-1371	275	28	respect	respect	NOUN
ejpam-1371	275	29	to	to	ADP
ejpam-1371	275	30	η	η	PROPN
ejpam-1371	275	31	,	,	PUNCT
ejpam-1371	275	32	that	that	ADV
ejpam-1371	275	33	is	is	ADV
ejpam-1371	275	34	,	,	PUNCT
ejpam-1371	275	35	〈	〈	PROPN
ejpam-1371	275	36	x	x	PROPN
ejpam-1371	275	37	,	,	PUNCT
ejpam-1371	275	38	η(z	η(z	PROPN
ejpam-1371	275	39	,	,	PUNCT
ejpam-1371	275	40	x)〉x	x)〉x	PROPN
ejpam-1371	275	41	≥	≥	NUM
ejpam-1371	276	1	〈	〈	PROPN
ejpam-1371	276	2	p	p	PROPN
ejpam-1371	276	3	,	,	PUNCT
ejpam-1371	276	4	η(z	η(z	PROPN
ejpam-1371	276	5	,	,	PUNCT
ejpam-1371	276	6	x)〉x	x)〉x	NOUN
ejpam-1371	276	7	for	for	ADP
ejpam-1371	276	8	all	all	DET
ejpam-1371	276	9	z	z	NOUN
ejpam-1371	276	10	∈	∈	NOUN
ejpam-1371	276	11	x	x	X
ejpam-1371	276	12	.	.	PUNCT
ejpam-1371	277	1	p.	p.	NOUN
ejpam-1371	277	2	das	das	PROPN
ejpam-1371	277	3	/	/	SYM
ejpam-1371	277	4	eur	eur	PROPN
ejpam-1371	277	5	.	.	PUNCT
ejpam-1371	278	1	j.	j.	PROPN
ejpam-1371	278	2	pure	pure	PROPN
ejpam-1371	278	3	appl	appl	PROPN
ejpam-1371	278	4	.	.	PROPN
ejpam-1371	278	5	math	math	PROPN
ejpam-1371	278	6	,	,	PUNCT
ejpam-1371	278	7	4	4	NUM
ejpam-1371	278	8	(	(	PUNCT
ejpam-1371	278	9	2011	2011	NUM
ejpam-1371	278	10	)	)	PUNCT
ejpam-1371	278	11	,	,	PUNCT
ejpam-1371	278	12	340	340	NUM
ejpam-1371	278	13	-	-	SYM
ejpam-1371	278	14	360	360	NUM
ejpam-1371	278	15	353	353	NUM
ejpam-1371	278	16	for	for	ADP
ejpam-1371	278	17	our	our	PRON
ejpam-1371	278	18	need	need	NOUN
ejpam-1371	279	1	,	,	PUNCT
ejpam-1371	279	2	we	we	PRON
ejpam-1371	279	3	define	define	VERB
ejpam-1371	279	4	the	the	DET
ejpam-1371	279	5	differential	differential	ADJ
ejpam-1371	279	6	application	application	NOUN
ejpam-1371	279	7	as	as	SCONJ
ejpam-1371	279	8	follows	follow	VERB
ejpam-1371	279	9	.	.	PUNCT
ejpam-1371	280	1	let	let	VERB
ejpam-1371	280	2	x	x	PRON
ejpam-1371	280	3	and	and	CCONJ
ejpam-1371	280	4	y	y	PROPN
ejpam-1371	280	5	be	be	VERB
ejpam-1371	280	6	two	two	NUM
ejpam-1371	280	7	differentiable	differentiable	ADJ
ejpam-1371	280	8	manifolds	manifold	NOUN
ejpam-1371	280	9	with	with	ADP
ejpam-1371	280	10	tangent	tangent	NOUN
ejpam-1371	280	11	bundles	bundle	NOUN
ejpam-1371	280	12	τx	τx	PUNCT
ejpam-1371	280	13	and	and	CCONJ
ejpam-1371	280	14	τy	τy	ADV
ejpam-1371	280	15	respectively	respectively	ADV
ejpam-1371	280	16	.	.	PUNCT
ejpam-1371	281	1	let	let	VERB
ejpam-1371	281	2	k	k	PRON
ejpam-1371	281	3	be	be	AUX
ejpam-1371	281	4	a	a	DET
ejpam-1371	281	5	closed	closed	ADJ
ejpam-1371	281	6	convex	convex	NOUN
ejpam-1371	281	7	cone	cone	NOUN
ejpam-1371	281	8	in	in	ADP
ejpam-1371	281	9	the	the	DET
ejpam-1371	281	10	manifold	manifold	ADJ
ejpam-1371	281	11	x	x	X
ejpam-1371	281	12	and	and	CCONJ
ejpam-1371	281	13	p	p	NOUN
ejpam-1371	281	14	be	be	AUX
ejpam-1371	281	15	a	a	DET
ejpam-1371	281	16	closed	closed	ADJ
ejpam-1371	281	17	convex	convex	NOUN
ejpam-1371	281	18	ordered	order	VERB
ejpam-1371	281	19	cone	cone	NOUN
ejpam-1371	281	20	in	in	ADP
ejpam-1371	281	21	y	y	PROPN
ejpam-1371	281	22	with	with	ADP
ejpam-1371	281	23	intp	intp	PROPN
ejpam-1371	281	24	6=	6=	AUX
ejpam-1371	281	25	∅.	∅.	AUX
ejpam-1371	281	26	let	let	VERB
ejpam-1371	281	27	f	f	PROPN
ejpam-1371	281	28	:	:	PUNCT
ejpam-1371	281	29	k	k	X
ejpam-1371	281	30	→	→	PUNCT
ejpam-1371	281	31	y	y	PROPN
ejpam-1371	281	32	be	be	AUX
ejpam-1371	281	33	the	the	DET
ejpam-1371	281	34	differentiable	differentiable	ADJ
ejpam-1371	281	35	vector	vector	NOUN
ejpam-1371	281	36	function	function	NOUN
ejpam-1371	281	37	.	.	PUNCT
ejpam-1371	282	1	denote	denote	VERB
ejpam-1371	282	2	the	the	DET
ejpam-1371	282	3	differential	differential	NOUN
ejpam-1371	282	4	of	of	ADP
ejpam-1371	282	5	f	f	PROPN
ejpam-1371	282	6	at	at	ADP
ejpam-1371	282	7	u	u	PROPN
ejpam-1371	282	8	∈	∈	PROPN
ejpam-1371	282	9	k	k	X
ejpam-1371	282	10	as	as	SCONJ
ejpam-1371	282	11	dfu	dfu	PROPN
ejpam-1371	282	12	:	:	PUNCT
ejpam-1371	282	13	τ(x	τ(x	PROPN
ejpam-1371	282	14	,	,	PUNCT
ejpam-1371	282	15	u)→	u)→	ADJ
ejpam-1371	282	16	τ(y	τ(y	PROPN
ejpam-1371	282	17	,	,	PUNCT
ejpam-1371	282	18	f(u	f(u	PROPN
ejpam-1371	282	19	)	)	PUNCT
ejpam-1371	282	20	)	)	PUNCT
ejpam-1371	283	1	where	where	SCONJ
ejpam-1371	283	2	dfu(v	dfu(v	NOUN
ejpam-1371	283	3	)	)	PUNCT
ejpam-1371	283	4	=	=	SYM
ejpam-1371	283	5	df(u)(v	df(u)(v	NOUN
ejpam-1371	283	6	)	)	PUNCT
ejpam-1371	283	7	=	=	SYM
ejpam-1371	283	8	〈	〈	PROPN
ejpam-1371	283	9	∇f(u	∇f(u	PROPN
ejpam-1371	283	10	)	)	PUNCT
ejpam-1371	283	11	,	,	PUNCT
ejpam-1371	283	12	v〉u	v〉u	PROPN
ejpam-1371	283	13	.	.	PUNCT
ejpam-1371	283	14	behera	behera	PROPN
ejpam-1371	283	15	and	and	CCONJ
ejpam-1371	283	16	das	das	PROPN
ejpam-1371	284	1	[	[	X
ejpam-1371	284	2	3	3	NUM
ejpam-1371	284	3	]	]	PUNCT
ejpam-1371	284	4	introduced	introduce	VERB
ejpam-1371	284	5	the	the	DET
ejpam-1371	284	6	variational	variational	ADJ
ejpam-1371	284	7	inequality	inequality	NOUN
ejpam-1371	284	8	problem	problem	NOUN
ejpam-1371	284	9	and	and	CCONJ
ejpam-1371	284	10	complementarity	complementarity	NOUN
ejpam-1371	284	11	problem	problem	NOUN
ejpam-1371	284	12	in	in	ADP
ejpam-1371	284	13	the	the	DET
ejpam-1371	284	14	riemannian	riemannian	ADJ
ejpam-1371	284	15	n	n	CCONJ
ejpam-1371	284	16	-	-	PUNCT
ejpam-1371	284	17	manifold	manifold	ADJ
ejpam-1371	284	18	.	.	PUNCT
ejpam-1371	285	1	for	for	ADP
ejpam-1371	285	2	our	our	PRON
ejpam-1371	285	3	purpose	purpose	NOUN
ejpam-1371	285	4	,	,	PUNCT
ejpam-1371	285	5	we	we	PRON
ejpam-1371	285	6	call	call	VERB
ejpam-1371	285	7	these	these	DET
ejpam-1371	285	8	problems	problem	NOUN
ejpam-1371	285	9	as	as	ADP
ejpam-1371	285	10	differential	differential	ADJ
ejpam-1371	285	11	inequality	inequality	NOUN
ejpam-1371	285	12	problem(dipn	problem(dipn	NOUN
ejpam-1371	285	13	)	)	PUNCT
ejpam-1371	285	14	and	and	CCONJ
ejpam-1371	285	15	differential	differential	ADJ
ejpam-1371	285	16	complementarity	complementarity	NOUN
ejpam-1371	285	17	problem(dc	problem(dc	NOUN
ejpam-1371	285	18	pn	pn	NOUN
ejpam-1371	285	19	)	)	PUNCT
ejpam-1371	285	20	in	in	ADP
ejpam-1371	285	21	riemannian	riemannian	ADJ
ejpam-1371	285	22	nmanifold	nmanifold	ADJ
ejpam-1371	285	23	respectively	respectively	ADV
ejpam-1371	285	24	.	.	PUNCT
ejpam-1371	286	1	we	we	PRON
ejpam-1371	286	2	recall	recall	VERB
ejpam-1371	286	3	the	the	DET
ejpam-1371	286	4	known	know	VERB
ejpam-1371	286	5	results	result	NOUN
ejpam-1371	286	6	for	for	ADP
ejpam-1371	286	7	our	our	PRON
ejpam-1371	286	8	need	need	NOUN
ejpam-1371	286	9	.	.	PUNCT
ejpam-1371	287	1	the	the	DET
ejpam-1371	287	2	differential	differential	ADJ
ejpam-1371	287	3	inequality	inequality	NOUN
ejpam-1371	287	4	problem	problem	NOUN
ejpam-1371	287	5	in	in	ADP
ejpam-1371	287	6	riemannian	riemannian	ADJ
ejpam-1371	287	7	n	n	CCONJ
ejpam-1371	287	8	-	-	PUNCT
ejpam-1371	287	9	manifold	manifold	ADJ
ejpam-1371	287	10	(	(	PUNCT
ejpam-1371	287	11	dipn	dipn	NOUN
ejpam-1371	287	12	)	)	PUNCT
ejpam-1371	287	13	is	be	AUX
ejpam-1371	287	14	defined	define	VERB
ejpam-1371	287	15	as	as	SCONJ
ejpam-1371	287	16	follows	follow	VERB
ejpam-1371	287	17	:	:	PUNCT
ejpam-1371	287	18	(	(	PUNCT
ejpam-1371	287	19	dipn	dipn	NOUN
ejpam-1371	287	20	)	)	PUNCT
ejpam-1371	287	21	find	find	VERB
ejpam-1371	287	22	y0	y0	NOUN
ejpam-1371	287	23	∈	∈	NOUN
ejpam-1371	287	24	x	x	PUNCT
ejpam-1371	288	1	such	such	ADJ
ejpam-1371	288	2	that	that	PRON
ejpam-1371	288	3	∇f(y0	∇f(y0	NOUN
ejpam-1371	288	4	)	)	PUNCT
ejpam-1371	288	5	∈	∈	PROPN
ejpam-1371	288	6	τ	τ	X
ejpam-1371	288	7	∗(x	∗(x	PROPN
ejpam-1371	288	8	)	)	PUNCT
ejpam-1371	288	9	and	and	CCONJ
ejpam-1371	288	10	g	g	PROPN
ejpam-1371	288	11	y0	y0	PROPN
ejpam-1371	288	12	(	(	PUNCT
ejpam-1371	288	13	∇f(y0	∇f(y0	NOUN
ejpam-1371	288	14	)	)	PUNCT
ejpam-1371	288	15	,	,	PUNCT
ejpam-1371	288	16	z	z	NOUN
ejpam-1371	288	17	−	−	NOUN
ejpam-1371	288	18	y0	y0	NUM
ejpam-1371	288	19	)	)	PUNCT
ejpam-1371	288	20	=	=	PUNCT
ejpam-1371	289	1	〈	〈	NOUN
ejpam-1371	289	2	∇f(y0	∇f(y0	NUM
ejpam-1371	289	3	)	)	PUNCT
ejpam-1371	289	4	,	,	PUNCT
ejpam-1371	290	1	z	z	NOUN
ejpam-1371	290	2	−	−	NOUN
ejpam-1371	291	1	y0〉y0	y0〉y0	NOUN
ejpam-1371	291	2	≥	≥	NOUN
ejpam-1371	291	3	0	0	NUM
ejpam-1371	291	4	for	for	ADP
ejpam-1371	291	5	allz	allz	PROPN
ejpam-1371	291	6	∈	∈	PROPN
ejpam-1371	291	7	x	x	X
ejpam-1371	291	8	.	.	PUNCT
ejpam-1371	292	1	and	and	CCONJ
ejpam-1371	292	2	the	the	DET
ejpam-1371	292	3	differential	differential	ADJ
ejpam-1371	292	4	complementarity	complementarity	NOUN
ejpam-1371	292	5	problem	problem	NOUN
ejpam-1371	292	6	in	in	ADP
ejpam-1371	292	7	riemannian	riemannian	ADJ
ejpam-1371	292	8	n	n	CCONJ
ejpam-1371	292	9	-	-	PUNCT
ejpam-1371	292	10	manifold	manifold	ADJ
ejpam-1371	292	11	(	(	PUNCT
ejpam-1371	292	12	dc	dc	PROPN
ejpam-1371	292	13	pn	pn	PROPN
ejpam-1371	292	14	)	)	PUNCT
ejpam-1371	292	15	is	be	AUX
ejpam-1371	292	16	defined	define	VERB
ejpam-1371	292	17	as	as	ADP
ejpam-1371	292	18	:	:	PUNCT
ejpam-1371	292	19	(	(	PUNCT
ejpam-1371	292	20	dc	dc	PROPN
ejpam-1371	292	21	pn	pn	PROPN
ejpam-1371	292	22	)	)	PUNCT
ejpam-1371	292	23	find	find	VERB
ejpam-1371	292	24	y0	y0	NOUN
ejpam-1371	292	25	∈	∈	NOUN
ejpam-1371	292	26	x	x	PUNCT
ejpam-1371	293	1	such	such	ADJ
ejpam-1371	293	2	that	that	PRON
ejpam-1371	293	3	∇f(y0	∇f(y0	NOUN
ejpam-1371	293	4	)	)	PUNCT
ejpam-1371	293	5	∈	∈	PROPN
ejpam-1371	293	6	τ	τ	X
ejpam-1371	293	7	∗(x	∗(x	PROPN
ejpam-1371	293	8	)	)	PUNCT
ejpam-1371	293	9	and	and	CCONJ
ejpam-1371	293	10	g	g	PROPN
ejpam-1371	293	11	y0	y0	PROPN
ejpam-1371	293	12	(	(	PUNCT
ejpam-1371	293	13	∇f(y0	∇f(y0	NOUN
ejpam-1371	293	14	)	)	PUNCT
ejpam-1371	293	15	,	,	PUNCT
ejpam-1371	293	16	y0	y0	NOUN
ejpam-1371	293	17	)	)	PUNCT
ejpam-1371	293	18	=	=	PUNCT
ejpam-1371	294	1	〈	〈	NOUN
ejpam-1371	294	2	∇f(y0	∇f(y0	NUM
ejpam-1371	294	3	)	)	PUNCT
ejpam-1371	294	4	,	,	PUNCT
ejpam-1371	295	1	y0〉y0	y0〉y0	NOUN
ejpam-1371	295	2	=	=	SYM
ejpam-1371	295	3	0	0	X
ejpam-1371	295	4	.	.	PUNCT
ejpam-1371	296	1	theorem	theorem	NOUN
ejpam-1371	296	2	5	5	NUM
ejpam-1371	296	3	(	(	PUNCT
ejpam-1371	296	4	[	[	X
ejpam-1371	296	5	3	3	NUM
ejpam-1371	296	6	,	,	PUNCT
ejpam-1371	296	7	theorem-6.1	theorem-6.1	PROPN
ejpam-1371	296	8	]	]	PUNCT
ejpam-1371	296	9	)	)	PUNCT
ejpam-1371	296	10	.	.	PUNCT
ejpam-1371	297	1	let	let	VERB
ejpam-1371	297	2	x	x	PRON
ejpam-1371	297	3	be	be	AUX
ejpam-1371	297	4	a	a	DET
ejpam-1371	297	5	closed	closed	ADJ
ejpam-1371	297	6	,	,	PUNCT
ejpam-1371	297	7	convex	convex	ADJ
ejpam-1371	297	8	and	and	CCONJ
ejpam-1371	297	9	oriented	orient	VERB
ejpam-1371	297	10	riemannian	riemannian	ADJ
ejpam-1371	297	11	n	n	CCONJ
ejpam-1371	297	12	-	-	PUNCT
ejpam-1371	297	13	manifold	manifold	ADJ
ejpam-1371	297	14	,	,	PUNCT
ejpam-1371	297	15	modelled	model	VERB
ejpam-1371	297	16	on	on	ADP
ejpam-1371	297	17	the	the	DET
ejpam-1371	297	18	hilbert	hilbert	PROPN
ejpam-1371	297	19	space	space	NOUN
ejpam-1371	297	20	h	h	NOUN
ejpam-1371	297	21	with	with	ADP
ejpam-1371	297	22	riemannian	riemannian	ADJ
ejpam-1371	297	23	metric	metric	ADJ
ejpam-1371	297	24	g	g	PROPN
ejpam-1371	297	25	and	and	CCONJ
ejpam-1371	297	26	f	f	NOUN
ejpam-1371	297	27	:	:	PUNCT
ejpam-1371	297	28	x	x	X
ejpam-1371	297	29	→	→	SYM
ejpam-1371	297	30	x	x	PUNCT
ejpam-1371	297	31	with	with	ADP
ejpam-1371	297	32	lipschitz	lipschitz	NOUN
ejpam-1371	297	33	number	number	NOUN
ejpam-1371	297	34	l(f	l(f	PROPN
ejpam-1371	297	35	)	)	PUNCT
ejpam-1371	297	36	.	.	PUNCT
ejpam-1371	298	1	let	let	VERB
ejpam-1371	298	2	f	f	NOUN
ejpam-1371	298	3	:	:	PUNCT
ejpam-1371	298	4	x	x	X
ejpam-1371	298	5	→	→	SYM
ejpam-1371	298	6	h	h	NOUN
ejpam-1371	298	7	be	be	AUX
ejpam-1371	298	8	an	an	DET
ejpam-1371	298	9	operator	operator	NOUN
ejpam-1371	298	10	.	.	PUNCT
ejpam-1371	299	1	then	then	ADV
ejpam-1371	299	2	there	there	PRON
ejpam-1371	299	3	exists	exist	VERB
ejpam-1371	299	4	a	a	DET
ejpam-1371	299	5	unique	unique	ADJ
ejpam-1371	299	6	y0	y0	NOUN
ejpam-1371	299	7	∈	∈	NOUN
ejpam-1371	299	8	x	x	PUNCT
ejpam-1371	299	9	such	such	ADJ
ejpam-1371	299	10	that	that	PRON
ejpam-1371	299	11	∇f(y0	∇f(y0	NOUN
ejpam-1371	299	12	)	)	PUNCT
ejpam-1371	299	13	∈	∈	PROPN
ejpam-1371	299	14	τ	τ	X
ejpam-1371	299	15	∗(x	∗(x	PROPN
ejpam-1371	299	16	)	)	PUNCT
ejpam-1371	299	17	and	and	CCONJ
ejpam-1371	299	18	g	g	PROPN
ejpam-1371	299	19	y0	y0	PROPN
ejpam-1371	299	20	(	(	PUNCT
ejpam-1371	299	21	∇f(y0	∇f(y0	NOUN
ejpam-1371	299	22	)	)	PUNCT
ejpam-1371	299	23	,	,	PUNCT
ejpam-1371	299	24	y0	y0	NOUN
ejpam-1371	299	25	)	)	PUNCT
ejpam-1371	299	26	=	=	PUNCT
ejpam-1371	299	27	〈	〈	NOUN
ejpam-1371	299	28	∇f(y0	∇f(y0	NUM
ejpam-1371	299	29	)	)	PUNCT
ejpam-1371	299	30	,	,	PUNCT
ejpam-1371	299	31	y0〉y0	y0〉y0	NOUN
ejpam-1371	300	1	=	=	NOUN
ejpam-1371	300	2	0	0	X
ejpam-1371	300	3	.	.	PUNCT
ejpam-1371	301	1	in	in	ADP
ejpam-1371	301	2	this	this	DET
ejpam-1371	301	3	section	section	NOUN
ejpam-1371	301	4	,	,	PUNCT
ejpam-1371	301	5	we	we	PRON
ejpam-1371	301	6	extend	extend	VERB
ejpam-1371	301	7	the	the	DET
ejpam-1371	301	8	problems	problem	NOUN
ejpam-1371	301	9	(	(	PUNCT
ejpam-1371	301	10	dipn	dipn	NOUN
ejpam-1371	301	11	)	)	PUNCT
ejpam-1371	301	12	and	and	CCONJ
ejpam-1371	301	13	(	(	PUNCT
ejpam-1371	301	14	dc	dc	PROPN
ejpam-1371	301	15	pn	pn	PROPN
ejpam-1371	301	16	)	)	PUNCT
ejpam-1371	301	17	as	as	SCONJ
ejpam-1371	301	18	the	the	DET
ejpam-1371	301	19	generalized	generalize	VERB
ejpam-1371	301	20	differential	differential	NOUN
ejpam-1371	301	21	dominated	dominate	VERB
ejpam-1371	301	22	variational	variational	ADJ
ejpam-1371	301	23	inequality	inequality	NOUN
ejpam-1371	301	24	problem	problem	NOUN
ejpam-1371	301	25	in	in	ADP
ejpam-1371	301	26	riemannian	riemannian	ADJ
ejpam-1371	301	27	n	n	CCONJ
ejpam-1371	301	28	-	-	PUNCT
ejpam-1371	301	29	manifold	manifold	ADJ
ejpam-1371	301	30	(	(	PUNCT
ejpam-1371	301	31	gddv	gddv	PROPN
ejpam-1371	301	32	ipn	ipn	PROPN
ejpam-1371	301	33	)	)	PUNCT
ejpam-1371	301	34	and	and	CCONJ
ejpam-1371	301	35	the	the	DET
ejpam-1371	301	36	generalized	generalize	VERB
ejpam-1371	301	37	differential	differential	NOUN
ejpam-1371	301	38	dominated	dominate	VERB
ejpam-1371	301	39	complementarity	complementarity	NOUN
ejpam-1371	301	40	problem	problem	NOUN
ejpam-1371	301	41	in	in	ADP
ejpam-1371	301	42	riemannian	riemannian	ADJ
ejpam-1371	301	43	n	n	CCONJ
ejpam-1371	301	44	-	-	PUNCT
ejpam-1371	301	45	manifold	manifold	ADJ
ejpam-1371	301	46	(	(	PUNCT
ejpam-1371	301	47	gddc	gddc	NOUN
ejpam-1371	301	48	pn	pn	PROPN
ejpam-1371	301	49	)	)	PUNCT
ejpam-1371	301	50	respectively	respectively	ADV
ejpam-1371	301	51	.	.	PUNCT
ejpam-1371	302	1	we	we	PRON
ejpam-1371	302	2	also	also	ADV
ejpam-1371	302	3	establish	establish	VERB
ejpam-1371	302	4	the	the	DET
ejpam-1371	302	5	existence	existence	NOUN
ejpam-1371	302	6	of	of	ADP
ejpam-1371	302	7	their	their	PRON
ejpam-1371	302	8	solutions	solution	NOUN
ejpam-1371	302	9	in	in	ADP
ejpam-1371	302	10	the	the	DET
ejpam-1371	302	11	presence	presence	NOUN
ejpam-1371	302	12	of	of	ADP
ejpam-1371	302	13	fixed	fix	VERB
ejpam-1371	302	14	point	point	NOUN
ejpam-1371	302	15	index	index	NOUN
ejpam-1371	302	16	set	set	VERB
ejpam-1371	302	17	and	and	CCONJ
ejpam-1371	302	18	fixed	fix	VERB
ejpam-1371	302	19	point	point	NOUN
ejpam-1371	302	20	theorem	theorem	VERB
ejpam-1371	302	21	.	.	PUNCT
ejpam-1371	303	1	we	we	PRON
ejpam-1371	303	2	use	use	VERB
ejpam-1371	303	3	the	the	DET
ejpam-1371	303	4	following	follow	VERB
ejpam-1371	303	5	notations	notation	NOUN
ejpam-1371	303	6	for	for	ADP
ejpam-1371	303	7	our	our	PRON
ejpam-1371	303	8	need	need	NOUN
ejpam-1371	303	9	.	.	PUNCT
ejpam-1371	304	1	definition	definition	NOUN
ejpam-1371	304	2	12	12	NUM
ejpam-1371	304	3	.	.	PUNCT
ejpam-1371	305	1	let	let	VERB
ejpam-1371	305	2	x	x	PRON
ejpam-1371	305	3	be	be	AUX
ejpam-1371	305	4	a	a	DET
ejpam-1371	305	5	riemannian	riemannian	ADJ
ejpam-1371	305	6	n	n	CCONJ
ejpam-1371	305	7	-	-	PUNCT
ejpam-1371	305	8	manifold	manifold	NOUN
ejpam-1371	305	9	modelled	model	VERB
ejpam-1371	305	10	on	on	ADP
ejpam-1371	305	11	the	the	DET
ejpam-1371	305	12	hilbert	hilbert	PROPN
ejpam-1371	305	13	space	space	NOUN
ejpam-1371	305	14	h	h	NOUN
ejpam-1371	305	15	with	with	ADP
ejpam-1371	305	16	the	the	DET
ejpam-1371	305	17	riemannian	riemannian	ADJ
ejpam-1371	305	18	metric	metric	NOUN
ejpam-1371	305	19	g.	g.	PROPN
ejpam-1371	305	20	let	let	VERB
ejpam-1371	305	21	h	h	NOUN
ejpam-1371	305	22	:	:	PUNCT
ejpam-1371	305	23	x	x	X
ejpam-1371	305	24	→	→	SYM
ejpam-1371	305	25	l(x	l(x	PROPN
ejpam-1371	305	26	,	,	PUNCT
ejpam-1371	305	27	h)≡	h)≡	NOUN
ejpam-1371	305	28	h.	h.	PROPN
ejpam-1371	305	29	then	then	ADV
ejpam-1371	305	30	,	,	PUNCT
ejpam-1371	305	31	the	the	DET
ejpam-1371	305	32	the	the	DET
ejpam-1371	305	33	positive	positive	ADJ
ejpam-1371	305	34	orthant	orthant	NOUN
ejpam-1371	305	35	and	and	CCONJ
ejpam-1371	305	36	the	the	DET
ejpam-1371	305	37	negative	negative	ADJ
ejpam-1371	305	38	orthant	orthant	NOUN
ejpam-1371	305	39	of	of	ADP
ejpam-1371	305	40	x	x	SYM
ejpam-1371	305	41	are	be	AUX
ejpam-1371	305	42	defined	define	VERB
ejpam-1371	305	43	as	as	SCONJ
ejpam-1371	305	44	follows	follow	VERB
ejpam-1371	305	45	.	.	PUNCT
ejpam-1371	306	1	(	(	PUNCT
ejpam-1371	306	2	1	1	X
ejpam-1371	306	3	)	)	PUNCT
ejpam-1371	306	4	for	for	ADP
ejpam-1371	306	5	each	each	DET
ejpam-1371	306	6	x	x	SYM
ejpam-1371	306	7	∈	∈	PROPN
ejpam-1371	306	8	x	x	X
ejpam-1371	306	9	,	,	PUNCT
ejpam-1371	306	10	the	the	DET
ejpam-1371	306	11	positive	positive	ADJ
ejpam-1371	306	12	orthant	orthant	NOUN
ejpam-1371	306	13	of	of	ADP
ejpam-1371	306	14	x	x	PRON
ejpam-1371	306	15	denoted	denote	VERB
ejpam-1371	306	16	by	by	ADP
ejpam-1371	306	17	x⊕η	x⊕η	PROPN
ejpam-1371	306	18	where	where	SCONJ
ejpam-1371	306	19	x⊕η	x⊕η	PROPN
ejpam-1371	306	20	=	=	PRON
ejpam-1371	306	21	{	{	PUNCT
ejpam-1371	306	22	h(x	h(x	PROPN
ejpam-1371	306	23	)	)	PUNCT
ejpam-1371	306	24	∈	∈	PROPN
ejpam-1371	306	25	l(x	l(x	PROPN
ejpam-1371	306	26	,	,	PUNCT
ejpam-1371	306	27	h)≡	h)≡	NOUN
ejpam-1371	306	28	h	h	NOUN
ejpam-1371	306	29	:	:	PUNCT
ejpam-1371	306	30	〈	〈	NOUN
ejpam-1371	306	31	h(x),η(z	h(x),η(z	NOUN
ejpam-1371	306	32	,	,	PUNCT
ejpam-1371	306	33	x)〉x	x)〉x	PROPN
ejpam-1371	306	34	≥	≥	NOUN
ejpam-1371	306	35	0	0	NUM
ejpam-1371	306	36	for	for	ADP
ejpam-1371	306	37	all	all	DET
ejpam-1371	306	38	z	z	NOUN
ejpam-1371	306	39	∈	∈	NOUN
ejpam-1371	306	40	x	x	PUNCT
ejpam-1371	306	41	}	}	PUNCT
ejpam-1371	306	42	,	,	PUNCT
ejpam-1371	306	43	(	(	PUNCT
ejpam-1371	306	44	2	2	X
ejpam-1371	306	45	)	)	PUNCT
ejpam-1371	306	46	for	for	ADP
ejpam-1371	306	47	each	each	DET
ejpam-1371	306	48	x	x	SYM
ejpam-1371	306	49	∈	∈	PROPN
ejpam-1371	306	50	x	x	X
ejpam-1371	306	51	,	,	PUNCT
ejpam-1371	306	52	the	the	DET
ejpam-1371	306	53	negative	negative	ADJ
ejpam-1371	306	54	orthant	orthant	NOUN
ejpam-1371	306	55	of	of	ADP
ejpam-1371	306	56	x	x	PRON
ejpam-1371	306	57	denoted	denote	VERB
ejpam-1371	306	58	by	by	ADP
ejpam-1371	306	59	x⊖η	x⊖η	PROPN
ejpam-1371	306	60	where	where	SCONJ
ejpam-1371	306	61	x⊖η	x⊖η	PROPN
ejpam-1371	307	1	=	=	PRON
ejpam-1371	307	2	{	{	PUNCT
ejpam-1371	307	3	h(x	h(x	PROPN
ejpam-1371	307	4	)	)	PUNCT
ejpam-1371	307	5	∈	∈	PROPN
ejpam-1371	307	6	l(x	l(x	PROPN
ejpam-1371	307	7	,	,	PUNCT
ejpam-1371	307	8	h)≡	h)≡	NOUN
ejpam-1371	307	9	h	h	NOUN
ejpam-1371	307	10	:	:	PUNCT
ejpam-1371	307	11	〈	〈	NOUN
ejpam-1371	307	12	h(x),η(z	h(x),η(z	NOUN
ejpam-1371	307	13	,	,	PUNCT
ejpam-1371	307	14	x)〉x	x)〉x	NOUN
ejpam-1371	307	15	≤	≤	NOUN
ejpam-1371	307	16	0	0	NUM
ejpam-1371	307	17	for	for	ADP
ejpam-1371	307	18	all	all	DET
ejpam-1371	307	19	z	z	NOUN
ejpam-1371	307	20	∈	∈	NOUN
ejpam-1371	307	21	x	x	PUNCT
ejpam-1371	307	22	}	}	PUNCT
ejpam-1371	307	23	.	.	PUNCT
ejpam-1371	308	1	p.	p.	NOUN
ejpam-1371	308	2	das	das	PROPN
ejpam-1371	308	3	/	/	SYM
ejpam-1371	308	4	eur	eur	PROPN
ejpam-1371	308	5	.	.	PUNCT
ejpam-1371	309	1	j.	j.	PROPN
ejpam-1371	309	2	pure	pure	PROPN
ejpam-1371	309	3	appl	appl	PROPN
ejpam-1371	309	4	.	.	PROPN
ejpam-1371	309	5	math	math	PROPN
ejpam-1371	309	6	,	,	PUNCT
ejpam-1371	309	7	4	4	NUM
ejpam-1371	309	8	(	(	PUNCT
ejpam-1371	309	9	2011	2011	NUM
ejpam-1371	309	10	)	)	PUNCT
ejpam-1371	309	11	,	,	PUNCT
ejpam-1371	309	12	340	340	NUM
ejpam-1371	309	13	-	-	SYM
ejpam-1371	309	14	360	360	NUM
ejpam-1371	309	15	354	354	NUM
ejpam-1371	309	16	everywhere	everywhere	ADV
ejpam-1371	309	17	,	,	PUNCT
ejpam-1371	309	18	in	in	ADP
ejpam-1371	309	19	this	this	DET
ejpam-1371	309	20	section	section	NOUN
ejpam-1371	309	21	b(x	b(x	NOUN
ejpam-1371	309	22	,	,	PUNCT
ejpam-1371	309	23	r	r	NOUN
ejpam-1371	309	24	)	)	PUNCT
ejpam-1371	309	25	is	be	AUX
ejpam-1371	309	26	assumed	assume	VERB
ejpam-1371	309	27	to	to	PART
ejpam-1371	309	28	be	be	AUX
ejpam-1371	309	29	the	the	DET
ejpam-1371	309	30	open	open	ADJ
ejpam-1371	309	31	ball	ball	NOUN
ejpam-1371	309	32	of	of	ADP
ejpam-1371	309	33	radius	radius	NOUN
ejpam-1371	309	34	r	r	NOUN
ejpam-1371	309	35	and	and	CCONJ
ejpam-1371	309	36	center	center	NOUN
ejpam-1371	309	37	x	x	INTJ
ejpam-1371	309	38	.	.	PUNCT
ejpam-1371	310	1	we	we	PRON
ejpam-1371	310	2	recall	recall	VERB
ejpam-1371	310	3	the	the	DET
ejpam-1371	310	4	following	follow	VERB
ejpam-1371	310	5	known	know	VERB
ejpam-1371	310	6	definitions	definition	NOUN
ejpam-1371	310	7	.	.	PUNCT
ejpam-1371	311	1	definition	definition	NOUN
ejpam-1371	311	2	13	13	NUM
ejpam-1371	311	3	(	(	PUNCT
ejpam-1371	311	4	accumulation	accumulation	NOUN
ejpam-1371	311	5	point	point	NOUN
ejpam-1371	311	6	,	,	PUNCT
ejpam-1371	311	7	[	[	X
ejpam-1371	311	8	8	8	NUM
ejpam-1371	311	9	]	]	PUNCT
ejpam-1371	311	10	)	)	PUNCT
ejpam-1371	311	11	.	.	PUNCT
ejpam-1371	312	1	let	let	VERB
ejpam-1371	312	2	w	w	VERB
ejpam-1371	312	3	⊂	⊂	PROPN
ejpam-1371	312	4	x	x	X
ejpam-1371	312	5	.	.	PUNCT
ejpam-1371	313	1	an	an	DET
ejpam-1371	313	2	element	element	NOUN
ejpam-1371	313	3	x	x	SYM
ejpam-1371	313	4	∈	∈	PROPN
ejpam-1371	313	5	x	x	PUNCT
ejpam-1371	313	6	is	be	AUX
ejpam-1371	313	7	called	call	VERB
ejpam-1371	313	8	accumulation	accumulation	NOUN
ejpam-1371	313	9	point(or	point(or	PROPN
ejpam-1371	313	10	limit	limit	NOUN
ejpam-1371	313	11	point	point	NOUN
ejpam-1371	313	12	)	)	PUNCT
ejpam-1371	313	13	of	of	ADP
ejpam-1371	313	14	w	w	NOUN
ejpam-1371	313	15	if	if	SCONJ
ejpam-1371	313	16	for	for	ADP
ejpam-1371	313	17	every	every	DET
ejpam-1371	313	18	r	r	NOUN
ejpam-1371	313	19	>	>	X
ejpam-1371	313	20	0	0	NUM
ejpam-1371	313	21	,	,	PUNCT
ejpam-1371	313	22	there	there	PRON
ejpam-1371	313	23	is	be	VERB
ejpam-1371	313	24	some	some	DET
ejpam-1371	313	25	y	y	NOUN
ejpam-1371	313	26	in	in	ADP
ejpam-1371	313	27	b(x	b(x	NOUN
ejpam-1371	313	28	,	,	PUNCT
ejpam-1371	313	29	r)∩w	r)∩w	ADJ
ejpam-1371	313	30	with	with	ADP
ejpam-1371	313	31	y	y	PROPN
ejpam-1371	313	32	6=	6=	PROPN
ejpam-1371	313	33	x.	x.	NOUN
ejpam-1371	313	34	definition	definition	NOUN
ejpam-1371	313	35	14	14	NUM
ejpam-1371	313	36	(	(	PUNCT
ejpam-1371	313	37	closure	closure	NOUN
ejpam-1371	313	38	,	,	PUNCT
ejpam-1371	313	39	[	[	X
ejpam-1371	313	40	8	8	NUM
ejpam-1371	313	41	]	]	PUNCT
ejpam-1371	313	42	)	)	PUNCT
ejpam-1371	313	43	.	.	PUNCT
ejpam-1371	314	1	let	let	VERB
ejpam-1371	314	2	w	w	VERB
ejpam-1371	314	3	⊂	⊂	PROPN
ejpam-1371	314	4	x	x	X
ejpam-1371	314	5	.	.	PUNCT
ejpam-1371	315	1	the	the	DET
ejpam-1371	315	2	closure	closure	NOUN
ejpam-1371	315	3	of	of	ADP
ejpam-1371	315	4	w	w	PROPN
ejpam-1371	315	5	is	be	AUX
ejpam-1371	315	6	the	the	DET
ejpam-1371	315	7	set	set	NOUN
ejpam-1371	315	8	of	of	ADP
ejpam-1371	315	9	all	all	DET
ejpam-1371	315	10	accumulation	accumulation	NOUN
ejpam-1371	315	11	points	point	NOUN
ejpam-1371	315	12	of	of	ADP
ejpam-1371	315	13	w	w	NOUN
ejpam-1371	315	14	and	and	CCONJ
ejpam-1371	315	15	is	be	AUX
ejpam-1371	315	16	denoted	denote	VERB
ejpam-1371	315	17	by	by	ADP
ejpam-1371	315	18	w	w	PROPN
ejpam-1371	315	19	where	where	SCONJ
ejpam-1371	315	20	w	w	NOUN
ejpam-1371	315	21	=	=	PRON
ejpam-1371	315	22	{	{	PUNCT
ejpam-1371	315	23	x	x	PUNCT
ejpam-1371	315	24	∈	∈	NOUN
ejpam-1371	315	25	x	x	X
ejpam-1371	315	26	:	:	PUNCT
ejpam-1371	315	27	b(x	b(x	VERB
ejpam-1371	315	28	,	,	PUNCT
ejpam-1371	315	29	r)∩w	r)∩w	ADJ
ejpam-1371	315	30	6=	6=	NOUN
ejpam-1371	315	31	∅	∅	NOUN
ejpam-1371	315	32	for	for	ADP
ejpam-1371	315	33	every	every	DET
ejpam-1371	315	34	r	r	NOUN
ejpam-1371	315	35	>	>	X
ejpam-1371	315	36	0	0	NUM
ejpam-1371	315	37	}	}	PUNCT
ejpam-1371	315	38	.	.	PUNCT
ejpam-1371	316	1	fixed	fix	VERB
ejpam-1371	316	2	point	point	NOUN
ejpam-1371	316	3	inclusion	inclusion	NOUN
ejpam-1371	316	4	set	set	NOUN
ejpam-1371	316	5	let	let	VERB
ejpam-1371	316	6	φ	φ	NOUN
ejpam-1371	316	7	:	:	PUNCT
ejpam-1371	316	8	x	x	SYM
ejpam-1371	316	9	→	→	PUNCT
ejpam-1371	316	10	x	x	PUNCT
ejpam-1371	316	11	be	be	AUX
ejpam-1371	316	12	an	an	DET
ejpam-1371	316	13	open	open	ADJ
ejpam-1371	316	14	map	map	NOUN
ejpam-1371	316	15	.	.	PUNCT
ejpam-1371	317	1	let	let	VERB
ejpam-1371	317	2	x∗	x∗	PROPN
ejpam-1371	317	3	∈	∈	PROPN
ejpam-1371	317	4	x	x	PUNCT
ejpam-1371	317	5	be	be	AUX
ejpam-1371	317	6	the	the	DET
ejpam-1371	317	7	fixed	fix	VERB
ejpam-1371	317	8	point	point	NOUN
ejpam-1371	317	9	of	of	ADP
ejpam-1371	317	10	φ	φ	PROPN
ejpam-1371	317	11	,	,	PUNCT
ejpam-1371	317	12	then	then	ADV
ejpam-1371	317	13	φ(x∗	φ(x∗	NUM
ejpam-1371	317	14	)	)	PUNCT
ejpam-1371	317	15	=	=	SYM
ejpam-1371	317	16	x∗	x∗	NOUN
ejpam-1371	317	17	,	,	PUNCT
ejpam-1371	317	18	that	that	ADV
ejpam-1371	317	19	is	is	ADV
ejpam-1371	317	20	(	(	PUNCT
ejpam-1371	317	21	φ−	φ−	PROPN
ejpam-1371	317	22	1x	1x	NUM
ejpam-1371	317	23	)	)	PUNCT
ejpam-1371	317	24	(	(	PUNCT
ejpam-1371	317	25	x	x	NOUN
ejpam-1371	317	26	∗	∗	NOUN
ejpam-1371	317	27	)	)	PUNCT
ejpam-1371	317	28	∈	∈	PROPN
ejpam-1371	317	29	0x	0x	NOUN
ejpam-1371	317	30	,	,	PUNCT
ejpam-1371	317	31	implies	imply	VERB
ejpam-1371	317	32	that	that	SCONJ
ejpam-1371	317	33	,	,	PUNCT
ejpam-1371	317	34	x∗	x∗	PROPN
ejpam-1371	317	35	∈	∈	PROPN
ejpam-1371	317	36	(	(	PUNCT
ejpam-1371	317	37	φ−	φ−	PROPN
ejpam-1371	317	38	1x	1x	NUM
ejpam-1371	317	39	)	)	PUNCT
ejpam-1371	318	1	−1(0x	−1(0x	ADP
ejpam-1371	318	2	)	)	PUNCT
ejpam-1371	318	3	⊂	⊂	PROPN
ejpam-1371	318	4	x	x	NOUN
ejpam-1371	318	5	holds	hold	VERB
ejpam-1371	318	6	because	because	SCONJ
ejpam-1371	318	7	φ	φ	PROPN
ejpam-1371	318	8	is	be	AUX
ejpam-1371	318	9	an	an	DET
ejpam-1371	318	10	open	open	ADJ
ejpam-1371	318	11	map	map	NOUN
ejpam-1371	318	12	,	,	PUNCT
ejpam-1371	318	13	implies	imply	VERB
ejpam-1371	318	14	that	that	SCONJ
ejpam-1371	318	15	,	,	PUNCT
ejpam-1371	318	16	(	(	PUNCT
ejpam-1371	318	17	φ−	φ−	PROPN
ejpam-1371	318	18	1x	1x	NUM
ejpam-1371	318	19	)	)	PUNCT
ejpam-1371	318	20	−1	−1	NOUN
ejpam-1371	318	21	is	be	AUX
ejpam-1371	318	22	continuous	continuous	ADJ
ejpam-1371	318	23	in	in	ADP
ejpam-1371	318	24	x	x	X
ejpam-1371	318	25	.	.	PUNCT
ejpam-1371	319	1	hence	hence	ADV
ejpam-1371	319	2	,	,	PUNCT
ejpam-1371	319	3	the	the	DET
ejpam-1371	319	4	concept	concept	NOUN
ejpam-1371	319	5	,	,	PUNCT
ejpam-1371	319	6	fixed	fix	VERB
ejpam-1371	319	7	point	point	NOUN
ejpam-1371	319	8	inclusion	inclusion	NOUN
ejpam-1371	319	9	set	set	NOUN
ejpam-1371	319	10	of	of	ADP
ejpam-1371	319	11	the	the	DET
ejpam-1371	319	12	map	map	NOUN
ejpam-1371	319	13	φ	φ	PROPN
ejpam-1371	319	14	states	state	VERB
ejpam-1371	319	15	that	that	SCONJ
ejpam-1371	319	16	φ	φ	PROPN
ejpam-1371	319	17	has	have	VERB
ejpam-1371	319	18	a	a	DET
ejpam-1371	319	19	fixed	fix	VERB
ejpam-1371	319	20	point	point	NOUN
ejpam-1371	319	21	in	in	ADP
ejpam-1371	319	22	x	x	X
ejpam-1371	319	23	,	,	PUNCT
ejpam-1371	319	24	that	that	ADV
ejpam-1371	319	25	is	is	ADV
ejpam-1371	319	26	,	,	PUNCT
ejpam-1371	319	27	if	if	SCONJ
ejpam-1371	319	28	the	the	DET
ejpam-1371	319	29	restricted	restricted	ADJ
ejpam-1371	319	30	map	map	NOUN
ejpam-1371	319	31	(	(	PUNCT
ejpam-1371	319	32	(	(	PUNCT
ejpam-1371	319	33	φ−	φ−	PROPN
ejpam-1371	319	34	1x	1x	NUM
ejpam-1371	319	35	)	)	PUNCT
ejpam-1371	319	36	\w	\w	PUNCT
ejpam-1371	319	37	)	)	PUNCT
ejpam-1371	319	38	−1	−1	NOUN
ejpam-1371	319	39	is	be	AUX
ejpam-1371	319	40	continuous	continuous	ADJ
ejpam-1371	319	41	on	on	ADP
ejpam-1371	319	42	(	(	PUNCT
ejpam-1371	319	43	φ−	φ−	PROPN
ejpam-1371	319	44	1x	1x	NUM
ejpam-1371	319	45	)	)	PUNCT
ejpam-1371	319	46	(	(	PUNCT
ejpam-1371	319	47	x	x	X
ejpam-1371	319	48	)	)	PUNCT
ejpam-1371	319	49	,	,	PUNCT
ejpam-1371	319	50	then	then	ADV
ejpam-1371	319	51	φ	φ	PROPN
ejpam-1371	319	52	has	have	VERB
ejpam-1371	319	53	a	a	DET
ejpam-1371	319	54	fixed	fix	VERB
ejpam-1371	319	55	point	point	NOUN
ejpam-1371	319	56	on	on	ADP
ejpam-1371	319	57	w	w	NOUN
ejpam-1371	319	58	,	,	PUNCT
ejpam-1371	319	59	i.e.	i.e.	X
ejpam-1371	319	60	,	,	PUNCT
ejpam-1371	319	61	iw	iw	PROPN
ejpam-1371	319	62	φ	φ	NUM
ejpam-1371	319	63	6=	6=	PROPN
ejpam-1371	319	64	0	0	NUM
ejpam-1371	319	65	.	.	PUNCT
ejpam-1371	320	1	for	for	ADP
ejpam-1371	320	2	our	our	PRON
ejpam-1371	320	3	purpose	purpose	NOUN
ejpam-1371	320	4	,	,	PUNCT
ejpam-1371	320	5	we	we	PRON
ejpam-1371	320	6	define	define	VERB
ejpam-1371	320	7	the	the	DET
ejpam-1371	320	8	following	follow	VERB
ejpam-1371	320	9	definitions	definition	NOUN
ejpam-1371	320	10	.	.	PUNCT
ejpam-1371	321	1	definition	definition	NOUN
ejpam-1371	321	2	15	15	NUM
ejpam-1371	321	3	(	(	PUNCT
ejpam-1371	321	4	accumulated	accumulate	VERB
ejpam-1371	321	5	fixed	fix	VERB
ejpam-1371	321	6	point	point	NOUN
ejpam-1371	321	7	w.r.t	w.r.t	NOUN
ejpam-1371	321	8	.	.	PUNCT
ejpam-1371	322	1	φ	φ	NUM
ejpam-1371	322	2	)	)	PUNCT
ejpam-1371	322	3	.	.	PUNCT
ejpam-1371	323	1	let	let	VERB
ejpam-1371	323	2	w	w	VERB
ejpam-1371	323	3	⊂	⊂	PROPN
ejpam-1371	323	4	x	x	X
ejpam-1371	323	5	.	.	PUNCT
ejpam-1371	324	1	let	let	VERB
ejpam-1371	325	1	φ	φ	NOUN
ejpam-1371	325	2	:	:	PUNCT
ejpam-1371	325	3	x	x	SYM
ejpam-1371	325	4	→	→	PUNCT
ejpam-1371	325	5	x	x	PUNCT
ejpam-1371	325	6	be	be	AUX
ejpam-1371	325	7	any	any	DET
ejpam-1371	325	8	map	map	NOUN
ejpam-1371	325	9	.	.	PUNCT
ejpam-1371	326	1	an	an	DET
ejpam-1371	326	2	element	element	NOUN
ejpam-1371	326	3	x	x	SYM
ejpam-1371	326	4	∈	∈	PROPN
ejpam-1371	326	5	x	x	X
ejpam-1371	326	6	lies	lie	VERB
ejpam-1371	326	7	outside	outside	ADV
ejpam-1371	326	8	w	w	PROPN
ejpam-1371	326	9	is	be	AUX
ejpam-1371	326	10	called	call	VERB
ejpam-1371	326	11	accumulated	accumulate	VERB
ejpam-1371	326	12	fixed	fix	VERB
ejpam-1371	326	13	point	point	NOUN
ejpam-1371	326	14	of	of	ADP
ejpam-1371	326	15	w	w	NOUN
ejpam-1371	326	16	with	with	ADP
ejpam-1371	326	17	respect	respect	NOUN
ejpam-1371	326	18	to	to	ADP
ejpam-1371	326	19	φ	φ	PROPN
ejpam-1371	326	20	if	if	SCONJ
ejpam-1371	326	21	(	(	PUNCT
ejpam-1371	326	22	φ−1x	φ−1x	NOUN
ejpam-1371	326	23	)	)	PUNCT
ejpam-1371	326	24	−1	−1	NOUN
ejpam-1371	326	25	is	be	AUX
ejpam-1371	326	26	continuous	continuous	ADJ
ejpam-1371	326	27	on	on	ADP
ejpam-1371	326	28	x	x	X
ejpam-1371	326	29	,	,	PUNCT
ejpam-1371	326	30	(	(	PUNCT
ejpam-1371	326	31	φ−1x	φ−1x	NOUN
ejpam-1371	326	32	)	)	PUNCT
ejpam-1371	326	33	−1(0x	−1(0x	ADJ
ejpam-1371	326	34	)	)	PUNCT
ejpam-1371	326	35	⊂w	⊂w	PROPN
ejpam-1371	326	36	,	,	PUNCT
ejpam-1371	326	37	the	the	DET
ejpam-1371	326	38	closure	closure	NOUN
ejpam-1371	326	39	of	of	ADP
ejpam-1371	326	40	w	w	NOUN
ejpam-1371	326	41	and	and	CCONJ
ejpam-1371	326	42	for	for	ADP
ejpam-1371	326	43	every	every	DET
ejpam-1371	326	44	r	r	NOUN
ejpam-1371	326	45	>	>	X
ejpam-1371	326	46	0	0	NUM
ejpam-1371	326	47	,	,	PUNCT
ejpam-1371	326	48	there	there	PRON
ejpam-1371	326	49	is	be	VERB
ejpam-1371	326	50	some	some	DET
ejpam-1371	326	51	y	y	NOUN
ejpam-1371	326	52	in	in	ADP
ejpam-1371	326	53	b(x	b(x	NOUN
ejpam-1371	326	54	,	,	PUNCT
ejpam-1371	326	55	r)∩w	r)∩w	ADJ
ejpam-1371	326	56	for	for	ADP
ejpam-1371	326	57	y	y	PROPN
ejpam-1371	327	1	6=	6=	PROPN
ejpam-1371	327	2	x.	x.	NOUN
ejpam-1371	327	3	definition	definition	NOUN
ejpam-1371	327	4	16	16	NUM
ejpam-1371	327	5	(	(	PUNCT
ejpam-1371	327	6	fixed	fix	VERB
ejpam-1371	327	7	point	point	NOUN
ejpam-1371	327	8	closure	closure	NOUN
ejpam-1371	327	9	w.r.t	w.r.t	PROPN
ejpam-1371	327	10	.	.	PUNCT
ejpam-1371	328	1	φ	φ	NUM
ejpam-1371	328	2	)	)	PUNCT
ejpam-1371	328	3	.	.	PUNCT
ejpam-1371	329	1	let	let	VERB
ejpam-1371	329	2	w	w	VERB
ejpam-1371	329	3	⊂	⊂	PROPN
ejpam-1371	329	4	x	x	X
ejpam-1371	329	5	.	.	PUNCT
ejpam-1371	330	1	let	let	VERB
ejpam-1371	331	1	φ	φ	NOUN
ejpam-1371	331	2	:	:	PUNCT
ejpam-1371	331	3	x	x	SYM
ejpam-1371	331	4	→	→	PUNCT
ejpam-1371	331	5	x	x	PUNCT
ejpam-1371	331	6	be	be	AUX
ejpam-1371	331	7	any	any	DET
ejpam-1371	331	8	map	map	NOUN
ejpam-1371	331	9	such	such	ADJ
ejpam-1371	331	10	that	that	SCONJ
ejpam-1371	331	11	(	(	PUNCT
ejpam-1371	331	12	φ−	φ−	PROPN
ejpam-1371	331	13	1x	1x	NUM
ejpam-1371	331	14	)	)	PUNCT
ejpam-1371	331	15	−1(0x	−1(0x	CCONJ
ejpam-1371	331	16	)	)	PUNCT
ejpam-1371	332	1	⊂	⊂	PROPN
ejpam-1371	332	2	w.	w.	PROPN
ejpam-1371	332	3	the	the	DET
ejpam-1371	332	4	fixed	fixed	ADJ
ejpam-1371	332	5	point	point	NOUN
ejpam-1371	332	6	closure	closure	NOUN
ejpam-1371	332	7	of	of	ADP
ejpam-1371	332	8	w	w	NOUN
ejpam-1371	332	9	,	,	PUNCT
ejpam-1371	332	10	denoted	denote	VERB
ejpam-1371	332	11	by	by	ADP
ejpam-1371	332	12	cw	cw	NOUN
ejpam-1371	332	13	which	which	PRON
ejpam-1371	332	14	is	be	AUX
ejpam-1371	332	15	the	the	DET
ejpam-1371	332	16	set	set	NOUN
ejpam-1371	332	17	of	of	ADP
ejpam-1371	332	18	all	all	DET
ejpam-1371	332	19	fixed	fix	VERB
ejpam-1371	332	20	accumulated	accumulate	VERB
ejpam-1371	332	21	points	point	NOUN
ejpam-1371	332	22	of	of	ADP
ejpam-1371	332	23	w	w	PROPN
ejpam-1371	332	24	w.r.t	w.r.t	PROPN
ejpam-1371	332	25	.	.	PUNCT
ejpam-1371	333	1	φ	φ	PROPN
ejpam-1371	333	2	and	and	CCONJ
ejpam-1371	333	3	is	be	AUX
ejpam-1371	333	4	defined	define	VERB
ejpam-1371	333	5	by	by	ADP
ejpam-1371	333	6	cw	cw	NOUN
ejpam-1371	333	7	=	=	SYM
ejpam-1371	333	8	{	{	PUNCT
ejpam-1371	333	9	x	x	PUNCT
ejpam-1371	333	10	∈	∈	PROPN
ejpam-1371	333	11	x	x	X
ejpam-1371	333	12	:	:	PUNCT
ejpam-1371	333	13	(	(	PUNCT
ejpam-1371	333	14	φ−	φ−	PROPN
ejpam-1371	333	15	1x	1x	NUM
ejpam-1371	333	16	)	)	PUNCT
ejpam-1371	333	17	−1(0x	−1(0x	ADP
ejpam-1371	333	18	)	)	PUNCT
ejpam-1371	334	1	⋃	⋃	ADV
ejpam-1371	334	2	{	{	PUNCT
ejpam-1371	334	3	b(x	b(x	NOUN
ejpam-1371	334	4	,	,	PUNCT
ejpam-1371	334	5	r)∩w	r)∩w	ADJ
ejpam-1371	334	6	6=	6=	NOUN
ejpam-1371	334	7	∅	∅	NOUN
ejpam-1371	334	8	for	for	ADP
ejpam-1371	334	9	every	every	DET
ejpam-1371	334	10	r	r	NOUN
ejpam-1371	334	11	>	>	X
ejpam-1371	334	12	0	0	NUM
ejpam-1371	334	13	}	}	PUNCT
ejpam-1371	334	14	}	}	PUNCT
ejpam-1371	334	15	.	.	PUNCT
ejpam-1371	335	1	remark	remark	NOUN
ejpam-1371	335	2	3	3	NUM
ejpam-1371	335	3	.	.	PUNCT
ejpam-1371	336	1	the	the	DET
ejpam-1371	336	2	definition	definition	NOUN
ejpam-1371	336	3	of	of	ADP
ejpam-1371	336	4	fixed	fix	VERB
ejpam-1371	336	5	point	point	NOUN
ejpam-1371	336	6	closure	closure	NOUN
ejpam-1371	336	7	w.r.t	w.r.t	PROPN
ejpam-1371	336	8	.	.	PUNCT
ejpam-1371	337	1	φ	φ	PROPN
ejpam-1371	337	2	,	,	PUNCT
ejpam-1371	337	3	that	that	ADV
ejpam-1371	337	4	is	is	ADV
ejpam-1371	337	5	,	,	PUNCT
ejpam-1371	337	6	definition	definition	NOUN
ejpam-1371	337	7	16	16	NUM
ejpam-1371	337	8	coincides	coincide	VERB
ejpam-1371	337	9	with	with	ADP
ejpam-1371	337	10	the	the	DET
ejpam-1371	337	11	definition	definition	NOUN
ejpam-1371	337	12	of	of	ADP
ejpam-1371	337	13	closure	closure	NOUN
ejpam-1371	337	14	,	,	PUNCT
ejpam-1371	337	15	that	that	ADV
ejpam-1371	337	16	is	is	ADV
ejpam-1371	337	17	,	,	PUNCT
ejpam-1371	337	18	definition	definition	NOUN
ejpam-1371	337	19	14	14	NUM
ejpam-1371	337	20	if	if	SCONJ
ejpam-1371	337	21	φ	φ	PROPN
ejpam-1371	337	22	has	have	VERB
ejpam-1371	337	23	no	no	DET
ejpam-1371	337	24	fixed	fix	VERB
ejpam-1371	337	25	point	point	NOUN
ejpam-1371	337	26	.	.	PUNCT
ejpam-1371	338	1	by	by	ADP
ejpam-1371	338	2	the	the	DET
ejpam-1371	338	3	definition	definition	NOUN
ejpam-1371	338	4	,	,	PUNCT
ejpam-1371	338	5	we	we	PRON
ejpam-1371	338	6	have	have	VERB
ejpam-1371	338	7	if	if	SCONJ
ejpam-1371	338	8	w	w	NOUN
ejpam-1371	338	9	is	be	AUX
ejpam-1371	338	10	fixed	fix	VERB
ejpam-1371	338	11	point	point	NOUN
ejpam-1371	338	12	closure	closure	NOUN
ejpam-1371	338	13	w.r.t	w.r.t	PROPN
ejpam-1371	338	14	.	.	PUNCT
ejpam-1371	339	1	φ	φ	PROPN
ejpam-1371	339	2	,	,	PUNCT
ejpam-1371	339	3	then	then	ADV
ejpam-1371	339	4	w	w	PROPN
ejpam-1371	339	5	is	be	AUX
ejpam-1371	339	6	fixed	fix	VERB
ejpam-1371	339	7	point	point	NOUN
ejpam-1371	339	8	closure	closure	NOUN
ejpam-1371	339	9	but	but	CCONJ
ejpam-1371	339	10	not	not	PART
ejpam-1371	339	11	conversely	conversely	ADV
ejpam-1371	339	12	.	.	PUNCT
ejpam-1371	340	1	definition	definition	NOUN
ejpam-1371	340	2	17	17	NUM
ejpam-1371	340	3	(	(	PUNCT
ejpam-1371	340	4	fixed	fix	VERB
ejpam-1371	340	5	point	point	NOUN
ejpam-1371	340	6	dense	dense	ADJ
ejpam-1371	340	7	w.r.t	w.r.t	NOUN
ejpam-1371	340	8	.	.	PUNCT
ejpam-1371	341	1	φ	φ	NUM
ejpam-1371	341	2	)	)	PUNCT
ejpam-1371	341	3	.	.	PUNCT
ejpam-1371	342	1	let	let	VERB
ejpam-1371	342	2	w	w	VERB
ejpam-1371	342	3	⊂	⊂	PROPN
ejpam-1371	342	4	x	x	X
ejpam-1371	342	5	.	.	PUNCT
ejpam-1371	343	1	let	let	VERB
ejpam-1371	344	1	φ	φ	NOUN
ejpam-1371	344	2	:	:	PUNCT
ejpam-1371	344	3	x	x	SYM
ejpam-1371	344	4	→	→	PUNCT
ejpam-1371	344	5	x	x	PUNCT
ejpam-1371	344	6	be	be	AUX
ejpam-1371	344	7	any	any	DET
ejpam-1371	344	8	map	map	NOUN
ejpam-1371	344	9	.	.	PUNCT
ejpam-1371	345	1	then	then	ADV
ejpam-1371	345	2	w	w	PROPN
ejpam-1371	345	3	is	be	AUX
ejpam-1371	345	4	fixed	fix	VERB
ejpam-1371	345	5	point	point	NOUN
ejpam-1371	345	6	dense	dense	ADJ
ejpam-1371	345	7	in	in	ADP
ejpam-1371	345	8	x	x	PUNCT
ejpam-1371	345	9	with	with	ADP
ejpam-1371	345	10	respect	respect	NOUN
ejpam-1371	345	11	to	to	ADP
ejpam-1371	345	12	φ	φ	NUM
ejpam-1371	345	13	if	if	SCONJ
ejpam-1371	345	14	cw	cw	NOUN
ejpam-1371	345	15	=	=	SYM
ejpam-1371	345	16	x	x	X
ejpam-1371	345	17	,	,	PUNCT
ejpam-1371	345	18	which	which	PRON
ejpam-1371	345	19	means	mean	VERB
ejpam-1371	345	20	,	,	PUNCT
ejpam-1371	345	21	w	w	PROPN
ejpam-1371	345	22	=	=	PUNCT
ejpam-1371	345	23	x	x	X
ejpam-1371	345	24	and	and	CCONJ
ejpam-1371	345	25	(	(	PUNCT
ejpam-1371	345	26	φ−	φ−	PROPN
ejpam-1371	345	27	1x	1x	NUM
ejpam-1371	345	28	)	)	PUNCT
ejpam-1371	345	29	−1	−1	NOUN
ejpam-1371	345	30	is	be	AUX
ejpam-1371	345	31	continuous	continuous	ADJ
ejpam-1371	345	32	on	on	ADP
ejpam-1371	345	33	x	x	SYM
ejpam-1371	345	34	,	,	PUNCT
ejpam-1371	345	35	that	that	ADV
ejpam-1371	345	36	is	is	ADV
ejpam-1371	345	37	,	,	PUNCT
ejpam-1371	345	38	if	if	SCONJ
ejpam-1371	345	39	f	f	PROPN
ejpam-1371	345	40	is	be	AUX
ejpam-1371	345	41	the	the	DET
ejpam-1371	345	42	collection	collection	NOUN
ejpam-1371	345	43	of	of	ADP
ejpam-1371	345	44	all	all	DET
ejpam-1371	345	45	fixed	fix	VERB
ejpam-1371	345	46	points	point	NOUN
ejpam-1371	345	47	of	of	ADP
ejpam-1371	345	48	φ	φ	NUM
ejpam-1371	345	49	which	which	PRON
ejpam-1371	345	50	are	be	AUX
ejpam-1371	345	51	also	also	ADV
ejpam-1371	345	52	the	the	DET
ejpam-1371	345	53	cluster	cluster	NOUN
ejpam-1371	345	54	points	point	NOUN
ejpam-1371	345	55	or	or	CCONJ
ejpam-1371	345	56	accumulated	accumulate	VERB
ejpam-1371	345	57	points	point	NOUN
ejpam-1371	345	58	of	of	ADP
ejpam-1371	345	59	φ	φ	PROPN
ejpam-1371	345	60	,	,	PUNCT
ejpam-1371	345	61	then	then	ADV
ejpam-1371	345	62	x	x	PUNCT
ejpam-1371	346	1	=	=	X
ejpam-1371	346	2	w	w	NOUN
ejpam-1371	346	3	∪f	∪f	PROPN
ejpam-1371	346	4	is	be	AUX
ejpam-1371	346	5	the	the	DET
ejpam-1371	346	6	extended	extended	ADJ
ejpam-1371	346	7	set	set	NOUN
ejpam-1371	346	8	of	of	ADP
ejpam-1371	346	9	w.	w.	PROPN
ejpam-1371	346	10	definition	definition	NOUN
ejpam-1371	346	11	18	18	NUM
ejpam-1371	346	12	(	(	PUNCT
ejpam-1371	346	13	maximal	maximal	ADJ
ejpam-1371	346	14	open	open	ADJ
ejpam-1371	346	15	set	set	VERB
ejpam-1371	346	16	w.r.t	w.r.t	NOUN
ejpam-1371	346	17	.	.	PUNCT
ejpam-1371	347	1	φ	φ	NUM
ejpam-1371	347	2	)	)	PUNCT
ejpam-1371	347	3	.	.	PUNCT
ejpam-1371	348	1	let	let	VERB
ejpam-1371	348	2	x	x	PRON
ejpam-1371	348	3	be	be	AUX
ejpam-1371	348	4	any	any	DET
ejpam-1371	348	5	set	set	NOUN
ejpam-1371	348	6	then	then	ADV
ejpam-1371	348	7	the	the	DET
ejpam-1371	348	8	open	open	ADJ
ejpam-1371	348	9	set	set	NOUN
ejpam-1371	348	10	w	w	PROPN
ejpam-1371	348	11	⊂	⊂	PROPN
ejpam-1371	348	12	x	x	X
ejpam-1371	348	13	is	be	AUX
ejpam-1371	348	14	said	say	VERB
ejpam-1371	348	15	to	to	PART
ejpam-1371	348	16	be	be	AUX
ejpam-1371	348	17	maximal	maximal	ADV
ejpam-1371	348	18	open	open	ADJ
ejpam-1371	348	19	set	set	VERB
ejpam-1371	348	20	if	if	SCONJ
ejpam-1371	348	21	w	w	NOUN
ejpam-1371	348	22	is	be	AUX
ejpam-1371	348	23	dense	dense	ADJ
ejpam-1371	348	24	in	in	ADP
ejpam-1371	348	25	x	x	PROPN
ejpam-1371	348	26	w.r.t	w.r.t	NOUN
ejpam-1371	348	27	.	.	PUNCT
ejpam-1371	349	1	φ	φ	PROPN
ejpam-1371	349	2	,	,	PUNCT
ejpam-1371	349	3	that	that	ADV
ejpam-1371	349	4	is	is	ADV
ejpam-1371	349	5	,	,	PUNCT
ejpam-1371	349	6	w	w	PROPN
ejpam-1371	349	7	=	=	PUNCT
ejpam-1371	349	8	x	x	X
ejpam-1371	349	9	and	and	CCONJ
ejpam-1371	349	10	there	there	PRON
ejpam-1371	349	11	exist	exist	VERB
ejpam-1371	349	12	no	no	DET
ejpam-1371	349	13	open	open	ADJ
ejpam-1371	349	14	set	set	NOUN
ejpam-1371	349	15	u	u	PROPN
ejpam-1371	349	16	⊂	⊂	PROPN
ejpam-1371	349	17	x	x	PUNCT
ejpam-1371	349	18	such	such	ADJ
ejpam-1371	349	19	that	that	SCONJ
ejpam-1371	349	20	w	w	PROPN
ejpam-1371	349	21	⊂	⊂	PROPN
ejpam-1371	349	22	u	u	NOUN
ejpam-1371	349	23	and	and	CCONJ
ejpam-1371	349	24	u	u	NOUN
ejpam-1371	349	25	=	=	NOUN
ejpam-1371	349	26	x	x	X
ejpam-1371	349	27	.	.	PUNCT
ejpam-1371	350	1	p.	p.	NOUN
ejpam-1371	350	2	das	das	PROPN
ejpam-1371	350	3	/	/	SYM
ejpam-1371	350	4	eur	eur	PROPN
ejpam-1371	350	5	.	.	PUNCT
ejpam-1371	351	1	j.	j.	PROPN
ejpam-1371	351	2	pure	pure	PROPN
ejpam-1371	351	3	appl	appl	PROPN
ejpam-1371	351	4	.	.	PROPN
ejpam-1371	351	5	math	math	PROPN
ejpam-1371	351	6	,	,	PUNCT
ejpam-1371	351	7	4	4	NUM
ejpam-1371	351	8	(	(	PUNCT
ejpam-1371	351	9	2011	2011	NUM
ejpam-1371	351	10	)	)	PUNCT
ejpam-1371	351	11	,	,	PUNCT
ejpam-1371	351	12	340	340	NUM
ejpam-1371	351	13	-	-	SYM
ejpam-1371	351	14	360	360	NUM
ejpam-1371	351	15	355	355	NUM
ejpam-1371	351	16	definition	definition	NOUN
ejpam-1371	351	17	19	19	NUM
ejpam-1371	351	18	(	(	PUNCT
ejpam-1371	351	19	maximal	maximal	ADJ
ejpam-1371	351	20	fixed	fix	VERB
ejpam-1371	351	21	point	point	NOUN
ejpam-1371	351	22	open	open	ADJ
ejpam-1371	351	23	set	set	VERB
ejpam-1371	351	24	w.r.t	w.r.t	NOUN
ejpam-1371	351	25	.	.	PUNCT
ejpam-1371	352	1	φ	φ	NUM
ejpam-1371	352	2	)	)	PUNCT
ejpam-1371	352	3	.	.	PUNCT
ejpam-1371	353	1	let	let	VERB
ejpam-1371	353	2	x	x	PRON
ejpam-1371	353	3	be	be	AUX
ejpam-1371	353	4	any	any	DET
ejpam-1371	353	5	set	set	NOUN
ejpam-1371	353	6	.	.	PUNCT
ejpam-1371	354	1	let	let	VERB
ejpam-1371	354	2	φ	φ	NOUN
ejpam-1371	354	3	:	:	PUNCT
ejpam-1371	354	4	x	x	SYM
ejpam-1371	354	5	→	→	PUNCT
ejpam-1371	354	6	x	x	PUNCT
ejpam-1371	354	7	be	be	AUX
ejpam-1371	354	8	any	any	DET
ejpam-1371	354	9	map	map	NOUN
ejpam-1371	354	10	.	.	PUNCT
ejpam-1371	355	1	then	then	ADV
ejpam-1371	355	2	,	,	PUNCT
ejpam-1371	355	3	the	the	DET
ejpam-1371	355	4	open	open	ADJ
ejpam-1371	355	5	set	set	NOUN
ejpam-1371	355	6	w	w	PROPN
ejpam-1371	355	7	⊂	⊂	PROPN
ejpam-1371	355	8	x	x	X
ejpam-1371	355	9	is	be	AUX
ejpam-1371	355	10	said	say	VERB
ejpam-1371	355	11	to	to	PART
ejpam-1371	355	12	be	be	AUX
ejpam-1371	355	13	maximal	maximal	ADV
ejpam-1371	355	14	fixed	fix	VERB
ejpam-1371	355	15	point	point	NOUN
ejpam-1371	355	16	open	open	ADJ
ejpam-1371	355	17	set	set	VERB
ejpam-1371	355	18	w.r.t	w.r.t	NOUN
ejpam-1371	355	19	.	.	PUNCT
ejpam-1371	356	1	φ	φ	PROPN
ejpam-1371	356	2	if	if	SCONJ
ejpam-1371	356	3	w	w	PROPN
ejpam-1371	356	4	is	be	AUX
ejpam-1371	356	5	fixed	fix	VERB
ejpam-1371	356	6	point	point	NOUN
ejpam-1371	356	7	dense	dense	ADJ
ejpam-1371	356	8	in	in	ADP
ejpam-1371	356	9	x	x	PUNCT
ejpam-1371	356	10	with	with	ADP
ejpam-1371	356	11	respect	respect	NOUN
ejpam-1371	356	12	to	to	ADP
ejpam-1371	356	13	φ	φ	NUM
ejpam-1371	356	14	,	,	PUNCT
ejpam-1371	356	15	that	that	ADV
ejpam-1371	356	16	is	be	AUX
ejpam-1371	356	17	,	,	PUNCT
ejpam-1371	356	18	cw	cw	NOUN
ejpam-1371	356	19	=	=	SYM
ejpam-1371	356	20	x	x	X
ejpam-1371	356	21	.	.	PUNCT
ejpam-1371	357	1	definition	definition	NOUN
ejpam-1371	357	2	20	20	NUM
ejpam-1371	357	3	(	(	PUNCT
ejpam-1371	357	4	[	[	X
ejpam-1371	357	5	23	23	NUM
ejpam-1371	357	6	]	]	PUNCT
ejpam-1371	357	7	)	)	PUNCT
ejpam-1371	357	8	.	.	PUNCT
ejpam-1371	358	1	let	let	VERB
ejpam-1371	358	2	x	x	PRON
ejpam-1371	358	3	be	be	AUX
ejpam-1371	358	4	a	a	DET
ejpam-1371	358	5	locally	locally	ADV
ejpam-1371	358	6	compact	compact	ADJ
ejpam-1371	358	7	housdorff	housdorff	NOUN
ejpam-1371	358	8	space	space	NOUN
ejpam-1371	358	9	.	.	PUNCT
ejpam-1371	359	1	then	then	ADV
ejpam-1371	359	2	y	y	PROPN
ejpam-1371	359	3	=	=	PUNCT
ejpam-1371	359	4	x	x	SYM
ejpam-1371	359	5	∪	∪	X
ejpam-1371	359	6	{	{	PUNCT
ejpam-1371	359	7	∞	∞	NOUN
ejpam-1371	359	8	}	}	PUNCT
ejpam-1371	359	9	is	be	AUX
ejpam-1371	359	10	onepoint	onepoint	NOUN
ejpam-1371	359	11	compactification	compactification	NOUN
ejpam-1371	359	12	of	of	ADP
ejpam-1371	359	13	x	x	SYM
ejpam-1371	359	14	where	where	SCONJ
ejpam-1371	359	15	the	the	DET
ejpam-1371	359	16	symbol∞	symbol∞	PROPN
ejpam-1371	359	17	is	be	AUX
ejpam-1371	359	18	some	some	DET
ejpam-1371	359	19	object	object	NOUN
ejpam-1371	359	20	lies	lie	VERB
ejpam-1371	359	21	outside	outside	ADP
ejpam-1371	359	22	x	x	X
ejpam-1371	359	23	.	.	PUNCT
ejpam-1371	360	1	theorem	theorem	NOUN
ejpam-1371	360	2	6	6	NUM
ejpam-1371	360	3	(	(	PUNCT
ejpam-1371	360	4	[	[	X
ejpam-1371	360	5	23	23	NUM
ejpam-1371	360	6	,	,	PUNCT
ejpam-1371	360	7	theorem	theorem	VERB
ejpam-1371	360	8	8.1	8.1	NUM
ejpam-1371	360	9	]	]	PUNCT
ejpam-1371	360	10	)	)	PUNCT
ejpam-1371	360	11	.	.	PUNCT
ejpam-1371	361	1	let	let	VERB
ejpam-1371	361	2	x	x	PRON
ejpam-1371	361	3	be	be	AUX
ejpam-1371	361	4	a	a	DET
ejpam-1371	361	5	locally	locally	ADV
ejpam-1371	361	6	compact	compact	ADJ
ejpam-1371	361	7	housdorff	housdorff	NOUN
ejpam-1371	361	8	space	space	NOUN
ejpam-1371	361	9	which	which	PRON
ejpam-1371	361	10	is	be	AUX
ejpam-1371	361	11	not	not	PART
ejpam-1371	361	12	compact	compact	ADJ
ejpam-1371	361	13	;	;	PUNCT
ejpam-1371	361	14	let	let	VERB
ejpam-1371	361	15	y	y	PRON
ejpam-1371	361	16	be	be	AUX
ejpam-1371	361	17	the	the	DET
ejpam-1371	361	18	one	one	NUM
ejpam-1371	361	19	-	-	PUNCT
ejpam-1371	361	20	point	point	NOUN
ejpam-1371	361	21	compactification	compactification	NOUN
ejpam-1371	361	22	of	of	ADP
ejpam-1371	361	23	x	x	X
ejpam-1371	361	24	.	.	PUNCT
ejpam-1371	362	1	then	then	ADV
ejpam-1371	362	2	y	y	PROPN
ejpam-1371	362	3	is	be	AUX
ejpam-1371	362	4	compact	compact	ADJ
ejpam-1371	362	5	housdorff	housdorff	NOUN
ejpam-1371	362	6	space	space	NOUN
ejpam-1371	362	7	;	;	PUNCT
ejpam-1371	362	8	x	x	X
ejpam-1371	362	9	is	be	AUX
ejpam-1371	362	10	a	a	DET
ejpam-1371	362	11	subspace	subspace	NOUN
ejpam-1371	362	12	of	of	ADP
ejpam-1371	362	13	y	y	PROPN
ejpam-1371	362	14	;	;	PUNCT
ejpam-1371	362	15	the	the	DET
ejpam-1371	362	16	set	set	NOUN
ejpam-1371	362	17	y	y	PROPN
ejpam-1371	362	18	−	−	PROPN
ejpam-1371	362	19	x	x	PRON
ejpam-1371	362	20	consists	consist	VERB
ejpam-1371	362	21	of	of	ADP
ejpam-1371	362	22	singleton	singleton	NOUN
ejpam-1371	362	23	point	point	NOUN
ejpam-1371	362	24	;	;	PUNCT
ejpam-1371	362	25	and	and	CCONJ
ejpam-1371	362	26	x	x	X
ejpam-1371	362	27	=	=	SYM
ejpam-1371	362	28	y	y	PROPN
ejpam-1371	362	29	.	.	PUNCT
ejpam-1371	362	30	example	example	NOUN
ejpam-1371	363	1	1	1	NUM
ejpam-1371	363	2	.	.	PUNCT
ejpam-1371	364	1	since	since	SCONJ
ejpam-1371	364	2	the	the	DET
ejpam-1371	364	3	one	one	NUM
ejpam-1371	364	4	point	point	NOUN
ejpam-1371	364	5	compactification	compactification	NOUN
ejpam-1371	364	6	of	of	ADP
ejpam-1371	364	7	the	the	DET
ejpam-1371	364	8	real	real	ADJ
ejpam-1371	364	9	line	line	NOUN
ejpam-1371	364	10	r	r	NOUN
ejpam-1371	364	11	is	be	AUX
ejpam-1371	364	12	isomorphic	isomorphic	ADJ
ejpam-1371	364	13	with	with	ADP
ejpam-1371	364	14	the	the	DET
ejpam-1371	364	15	circle	circle	NOUN
ejpam-1371	364	16	.	.	PUNCT
ejpam-1371	365	1	so	so	ADV
ejpam-1371	365	2	the	the	DET
ejpam-1371	365	3	real	real	ADJ
ejpam-1371	365	4	line	line	NOUN
ejpam-1371	365	5	w	w	NOUN
ejpam-1371	366	1	=	=	NOUN
ejpam-1371	366	2	r	r	NOUN
ejpam-1371	366	3	is	be	AUX
ejpam-1371	366	4	a	a	DET
ejpam-1371	366	5	maximal	maximal	ADJ
ejpam-1371	366	6	fixed	fix	VERB
ejpam-1371	366	7	point	point	NOUN
ejpam-1371	366	8	open	open	ADJ
ejpam-1371	366	9	set	set	NOUN
ejpam-1371	366	10	of	of	ADP
ejpam-1371	366	11	x	x	X
ejpam-1371	366	12	=	=	PUNCT
ejpam-1371	366	13	r∞	r∞	NUM
ejpam-1371	366	14	=	=	SYM
ejpam-1371	366	15	r	r	NOUN
ejpam-1371	366	16	∪	∪	X
ejpam-1371	366	17	{	{	PUNCT
ejpam-1371	366	18	∞	∞	NOUN
ejpam-1371	366	19	}	}	PUNCT
ejpam-1371	366	20	,	,	PUNCT
ejpam-1371	366	21	the	the	DET
ejpam-1371	366	22	extended	extended	ADJ
ejpam-1371	366	23	real	real	ADJ
ejpam-1371	366	24	line	line	NOUN
ejpam-1371	366	25	where	where	SCONJ
ejpam-1371	366	26	φ	φ	PROPN
ejpam-1371	366	27	is	be	AUX
ejpam-1371	366	28	the	the	DET
ejpam-1371	366	29	required	require	VERB
ejpam-1371	366	30	isomorphism	isomorphism	NOUN
ejpam-1371	366	31	.	.	PUNCT
ejpam-1371	366	32	example	example	NOUN
ejpam-1371	367	1	2	2	NUM
ejpam-1371	367	2	.	.	PUNCT
ejpam-1371	367	3	since	since	SCONJ
ejpam-1371	367	4	the	the	DET
ejpam-1371	367	5	one	one	NUM
ejpam-1371	367	6	point	point	NOUN
ejpam-1371	367	7	compactification	compactification	NOUN
ejpam-1371	367	8	of	of	ADP
ejpam-1371	367	9	the	the	DET
ejpam-1371	367	10	plane	plane	NOUN
ejpam-1371	367	11	r2	r2	NOUN
ejpam-1371	367	12	is	be	AUX
ejpam-1371	367	13	homeomorphic	homeomorphic	ADJ
ejpam-1371	367	14	with	with	ADP
ejpam-1371	367	15	the	the	DET
ejpam-1371	367	16	riemannian	riemannian	ADJ
ejpam-1371	367	17	sphere	sphere	NOUN
ejpam-1371	367	18	(	(	PUNCT
ejpam-1371	367	19	s)2	s)2	NOUN
ejpam-1371	367	20	which	which	PRON
ejpam-1371	367	21	is	be	AUX
ejpam-1371	367	22	also	also	ADV
ejpam-1371	367	23	known	know	VERB
ejpam-1371	367	24	as	as	ADP
ejpam-1371	367	25	the	the	DET
ejpam-1371	367	26	extended	extended	ADJ
ejpam-1371	367	27	complex	complex	ADJ
ejpam-1371	367	28	plane	plane	NOUN
ejpam-1371	367	29	c∞	c∞	NOUN
ejpam-1371	367	30	=	=	PUNCT
ejpam-1371	367	31	c	c	NOUN
ejpam-1371	367	32	∪	∪	X
ejpam-1371	367	33	{	{	PUNCT
ejpam-1371	367	34	∞	∞	NOUN
ejpam-1371	367	35	}	}	PUNCT
ejpam-1371	367	36	,	,	PUNCT
ejpam-1371	367	37	so	so	SCONJ
ejpam-1371	367	38	w	w	PROPN
ejpam-1371	367	39	=	=	NOUN
ejpam-1371	367	40	r2	r2	PROPN
ejpam-1371	367	41	is	be	AUX
ejpam-1371	367	42	maximal	maximal	ADJ
ejpam-1371	367	43	fixed	fix	VERB
ejpam-1371	367	44	point	point	NOUN
ejpam-1371	367	45	open	open	ADJ
ejpam-1371	367	46	set	set	NOUN
ejpam-1371	367	47	of	of	ADP
ejpam-1371	367	48	x	x	X
ejpam-1371	367	49	=	=	PRON
ejpam-1371	367	50	(	(	PUNCT
ejpam-1371	367	51	s)2	s)2	NOUN
ejpam-1371	367	52	or	or	CCONJ
ejpam-1371	367	53	c∞	c∞	PROPN
ejpam-1371	367	54	where	where	SCONJ
ejpam-1371	367	55	φ	φ	PROPN
ejpam-1371	367	56	is	be	AUX
ejpam-1371	367	57	the	the	DET
ejpam-1371	367	58	stereographic	stereographic	ADJ
ejpam-1371	367	59	projection	projection	NOUN
ejpam-1371	367	60	.	.	PUNCT
ejpam-1371	368	1	remark	remark	PROPN
ejpam-1371	368	2	4	4	NUM
ejpam-1371	368	3	.	.	PUNCT
ejpam-1371	369	1	let	let	VERB
ejpam-1371	369	2	w	w	NOUN
ejpam-1371	369	3	be	be	AUX
ejpam-1371	369	4	locally	locally	ADV
ejpam-1371	369	5	compact	compact	ADJ
ejpam-1371	369	6	housdorff	housdorff	NOUN
ejpam-1371	369	7	space	space	NOUN
ejpam-1371	369	8	and	and	CCONJ
ejpam-1371	369	9	x	x	ADJ
ejpam-1371	369	10	be	be	AUX
ejpam-1371	369	11	the	the	DET
ejpam-1371	369	12	one	one	NUM
ejpam-1371	369	13	-	-	PUNCT
ejpam-1371	369	14	point	point	NOUN
ejpam-1371	369	15	compactification	compactification	NOUN
ejpam-1371	369	16	of	of	ADP
ejpam-1371	369	17	w.	w.	PROPN
ejpam-1371	369	18	then	then	ADV
ejpam-1371	369	19	w	w	PROPN
ejpam-1371	369	20	is	be	AUX
ejpam-1371	369	21	maximal	maximal	ADJ
ejpam-1371	369	22	fixed	fix	VERB
ejpam-1371	369	23	point	point	NOUN
ejpam-1371	369	24	open	open	ADJ
ejpam-1371	369	25	set	set	NOUN
ejpam-1371	369	26	of	of	ADP
ejpam-1371	369	27	x	x	PRON
ejpam-1371	369	28	,	,	PUNCT
ejpam-1371	369	29	but	but	CCONJ
ejpam-1371	369	30	not	not	PART
ejpam-1371	369	31	conversely	conversely	ADV
ejpam-1371	369	32	because	because	SCONJ
ejpam-1371	369	33	of	of	ADP
ejpam-1371	369	34	the	the	DET
ejpam-1371	369	35	existence	existence	NOUN
ejpam-1371	369	36	of	of	ADP
ejpam-1371	369	37	more	more	ADJ
ejpam-1371	369	38	than	than	ADP
ejpam-1371	369	39	one	one	NUM
ejpam-1371	369	40	fixed	fix	VERB
ejpam-1371	369	41	point	point	NOUN
ejpam-1371	369	42	.	.	PUNCT
ejpam-1371	370	1	a	a	DET
ejpam-1371	370	2	möbius	möbius	PROPN
ejpam-1371	370	3	transformation	transformation	NOUN
ejpam-1371	370	4	has	have	VERB
ejpam-1371	370	5	two	two	NUM
ejpam-1371	370	6	fixed	fix	VERB
ejpam-1371	370	7	points	point	NOUN
ejpam-1371	370	8	in	in	ADP
ejpam-1371	370	9	c.	c.	PROPN
ejpam-1371	370	10	the	the	DET
ejpam-1371	370	11	main	main	ADJ
ejpam-1371	370	12	problems	problem	NOUN
ejpam-1371	370	13	and	and	CCONJ
ejpam-1371	370	14	their	their	PRON
ejpam-1371	370	15	existence	existence	NOUN
ejpam-1371	370	16	theorems	theorem	NOUN
ejpam-1371	370	17	let	let	VERB
ejpam-1371	370	18	x	x	PART
ejpam-1371	370	19	be	be	AUX
ejpam-1371	370	20	a	a	DET
ejpam-1371	370	21	closed	closed	ADJ
ejpam-1371	370	22	,	,	PUNCT
ejpam-1371	370	23	convex	convex	ADJ
ejpam-1371	370	24	and	and	CCONJ
ejpam-1371	370	25	oriented	orient	VERB
ejpam-1371	370	26	riemannian	riemannian	ADJ
ejpam-1371	370	27	n	n	CCONJ
ejpam-1371	370	28	-	-	PUNCT
ejpam-1371	370	29	manifold	manifold	ADJ
ejpam-1371	370	30	,	,	PUNCT
ejpam-1371	370	31	modelled	model	VERB
ejpam-1371	370	32	on	on	ADP
ejpam-1371	370	33	the	the	DET
ejpam-1371	370	34	hilbert	hilbert	PROPN
ejpam-1371	370	35	space	space	NOUN
ejpam-1371	370	36	h	h	NOUN
ejpam-1371	370	37	with	with	ADP
ejpam-1371	370	38	riemannian	riemannian	PROPN
ejpam-1371	370	39	metric	metric	ADJ
ejpam-1371	370	40	g.	g.	PROPN
ejpam-1371	371	1	the	the	DET
ejpam-1371	371	2	tangent	tangent	PROPN
ejpam-1371	371	3	bundle	bundle	PROPN
ejpam-1371	371	4	τ(x	τ(x	PUNCT
ejpam-1371	371	5	)	)	PUNCT
ejpam-1371	371	6	is	be	AUX
ejpam-1371	371	7	identified	identify	VERB
ejpam-1371	371	8	with	with	ADP
ejpam-1371	371	9	the	the	DET
ejpam-1371	371	10	cotangent	cotangent	NOUN
ejpam-1371	371	11	bundle	bundle	NOUN
ejpam-1371	371	12	τ∗(x	τ∗(x	PRON
ejpam-1371	371	13	)	)	PUNCT
ejpam-1371	371	14	by	by	ADP
ejpam-1371	371	15	the	the	DET
ejpam-1371	371	16	riemannian	riemannian	ADJ
ejpam-1371	371	17	metric	metric	PROPN
ejpam-1371	371	18	g.	g.	PROPN
ejpam-1371	371	19	let	let	VERB
ejpam-1371	371	20	t	t	NOUN
ejpam-1371	371	21	:	:	PUNCT
ejpam-1371	371	22	x	x	X
ejpam-1371	371	23	→	→	SYM
ejpam-1371	371	24	l(τ∗(x	l(τ∗(x	NOUN
ejpam-1371	371	25	)	)	PUNCT
ejpam-1371	371	26	,	,	PUNCT
ejpam-1371	371	27	h	h	NOUN
ejpam-1371	371	28	)	)	PUNCT
ejpam-1371	371	29	≡	≡	PROPN
ejpam-1371	371	30	h	h	PROPN
ejpam-1371	371	31	be	be	VERB
ejpam-1371	371	32	any	any	DET
ejpam-1371	371	33	application	application	NOUN
ejpam-1371	371	34	.	.	PUNCT
ejpam-1371	372	1	let	let	VERB
ejpam-1371	372	2	f	f	NOUN
ejpam-1371	372	3	:	:	PUNCT
ejpam-1371	372	4	k	k	X
ejpam-1371	372	5	→h	→h	PUNCT
ejpam-1371	372	6	be	be	AUX
ejpam-1371	372	7	the	the	DET
ejpam-1371	372	8	differentiable	differentiable	ADJ
ejpam-1371	372	9	vector	vector	NOUN
ejpam-1371	372	10	function	function	NOUN
ejpam-1371	372	11	.	.	PUNCT
ejpam-1371	373	1	let	let	VERB
ejpam-1371	373	2	∇f(u	∇f(u	PROPN
ejpam-1371	373	3	)	)	PUNCT
ejpam-1371	374	1	=	=	PRON
ejpam-1371	374	2	dfu	dfu	VERB
ejpam-1371	374	3	:	:	PUNCT
ejpam-1371	374	4	τ(x	τ(x	NOUN
ejpam-1371	374	5	,	,	PUNCT
ejpam-1371	374	6	u)→	u)→	ADP
ejpam-1371	374	7	τ(h	τ(h	PROPN
ejpam-1371	374	8	,	,	PUNCT
ejpam-1371	374	9	f(u))≡	f(u))≡	NOUN
ejpam-1371	374	10	h	h	PROPN
ejpam-1371	374	11	be	be	AUX
ejpam-1371	374	12	the	the	DET
ejpam-1371	374	13	differential	differential	NOUN
ejpam-1371	374	14	of	of	ADP
ejpam-1371	374	15	f	f	PROPN
ejpam-1371	374	16	at	at	ADP
ejpam-1371	374	17	u	u	PROPN
ejpam-1371	374	18	∈	∈	PROPN
ejpam-1371	374	19	k	k	X
ejpam-1371	374	20	.	.	PUNCT
ejpam-1371	375	1	let	let	VERB
ejpam-1371	375	2	η	η	NOUN
ejpam-1371	375	3	:	:	PUNCT
ejpam-1371	375	4	x	x	SYM
ejpam-1371	375	5	×	×	NOUN
ejpam-1371	375	6	x	x	INTJ
ejpam-1371	375	7	→	→	SYM
ejpam-1371	375	8	τ(x	τ(x	NOUN
ejpam-1371	375	9	,	,	PUNCT
ejpam-1371	375	10	u)≡	u)≡	NOUN
ejpam-1371	375	11	x	x	PRON
ejpam-1371	375	12	be	be	AUX
ejpam-1371	375	13	an	an	DET
ejpam-1371	375	14	vector	vector	NOUN
ejpam-1371	375	15	application	application	NOUN
ejpam-1371	375	16	.	.	PUNCT
ejpam-1371	376	1	the	the	DET
ejpam-1371	376	2	generalized	generalize	VERB
ejpam-1371	376	3	differential	differential	NOUN
ejpam-1371	376	4	dominated	dominate	VERB
ejpam-1371	376	5	variational	variational	ADJ
ejpam-1371	376	6	inequality	inequality	NOUN
ejpam-1371	376	7	problem	problem	NOUN
ejpam-1371	376	8	in	in	ADP
ejpam-1371	376	9	riemannian	riemannian	ADJ
ejpam-1371	376	10	nmanifold	nmanifold	ADJ
ejpam-1371	376	11	is	be	AUX
ejpam-1371	376	12	defined	define	VERB
ejpam-1371	376	13	as	as	SCONJ
ejpam-1371	376	14	follows	follow	VERB
ejpam-1371	376	15	:	:	PUNCT
ejpam-1371	376	16	(	(	PUNCT
ejpam-1371	376	17	gddv	gddv	PROPN
ejpam-1371	376	18	ipn	ipn	PROPN
ejpam-1371	376	19	)	)	PUNCT
ejpam-1371	376	20	find	find	VERB
ejpam-1371	376	21	y0	y0	NOUN
ejpam-1371	376	22	∈	∈	NOUN
ejpam-1371	376	23	x	x	PUNCT
ejpam-1371	377	1	such	such	ADJ
ejpam-1371	377	2	that	that	SCONJ
ejpam-1371	377	3	(	(	PUNCT
ejpam-1371	377	4	∇f	∇f	PROPN
ejpam-1371	377	5	−	−	PROPN
ejpam-1371	377	6	t	t	NOUN
ejpam-1371	377	7	)	)	PUNCT
ejpam-1371	377	8	(	(	PUNCT
ejpam-1371	377	9	y0	y0	NOUN
ejpam-1371	377	10	)	)	PUNCT
ejpam-1371	377	11	∈	∈	PROPN
ejpam-1371	377	12	�	�	PROPN
ejpam-1371	377	13	τ∗(x	τ∗(x	PUNCT
ejpam-1371	377	14	)	)	PUNCT
ejpam-1371	377	15	�	�	PROPN
ejpam-1371	377	16	⊕	⊕	PROPN
ejpam-1371	377	17	η	η	PROPN
ejpam-1371	377	18	and	and	CCONJ
ejpam-1371	377	19	g	g	PROPN
ejpam-1371	377	20	y0	y0	PROPN
ejpam-1371	377	21	�	�	PROPN
ejpam-1371	378	1	(	(	PUNCT
ejpam-1371	378	2	∇f	∇f	PROPN
ejpam-1371	378	3	−	−	PROPN
ejpam-1371	378	4	t	t	NOUN
ejpam-1371	378	5	)	)	PUNCT
ejpam-1371	378	6	(	(	PUNCT
ejpam-1371	378	7	y0),η(z	y0),η(z	PROPN
ejpam-1371	378	8	,	,	PUNCT
ejpam-1371	378	9	y0	y0	NOUN
ejpam-1371	378	10	)	)	PUNCT
ejpam-1371	378	11	�	�	PROPN
ejpam-1371	378	12	=	=	SYM
ejpam-1371	378	13	〈	〈	PROPN
ejpam-1371	378	14	(	(	PUNCT
ejpam-1371	378	15	∇f	∇f	PROPN
ejpam-1371	378	16	−	−	PROPN
ejpam-1371	378	17	t	t	NOUN
ejpam-1371	378	18	)	)	PUNCT
ejpam-1371	378	19	(	(	PUNCT
ejpam-1371	378	20	y0),η(z	y0),η(z	PROPN
ejpam-1371	378	21	,	,	PUNCT
ejpam-1371	378	22	y0)〉y0	y0)〉y0	PRON
ejpam-1371	378	23	≥	≥	NOUN
ejpam-1371	378	24	0	0	NUM
ejpam-1371	378	25	for	for	ADP
ejpam-1371	378	26	all	all	DET
ejpam-1371	378	27	z	z	NOUN
ejpam-1371	378	28	∈	∈	PROPN
ejpam-1371	378	29	x	x	X
ejpam-1371	378	30	.	.	PUNCT
ejpam-1371	379	1	the	the	DET
ejpam-1371	379	2	generalized	generalize	VERB
ejpam-1371	379	3	differential	differential	NOUN
ejpam-1371	379	4	dominated	dominate	VERB
ejpam-1371	379	5	complementarity	complementarity	NOUN
ejpam-1371	379	6	problem	problem	NOUN
ejpam-1371	379	7	in	in	ADP
ejpam-1371	379	8	riemannian	riemannian	ADJ
ejpam-1371	379	9	n	n	CCONJ
ejpam-1371	379	10	-	-	PUNCT
ejpam-1371	379	11	manifold	manifold	NOUN
ejpam-1371	379	12	is	be	AUX
ejpam-1371	379	13	defined	define	VERB
ejpam-1371	379	14	as	as	SCONJ
ejpam-1371	379	15	follows	follow	VERB
ejpam-1371	379	16	:	:	PUNCT
ejpam-1371	379	17	(	(	PUNCT
ejpam-1371	379	18	gddc	gddc	NOUN
ejpam-1371	379	19	pn	pn	NOUN
ejpam-1371	379	20	)	)	PUNCT
ejpam-1371	379	21	find	find	VERB
ejpam-1371	379	22	y0	y0	NOUN
ejpam-1371	379	23	∈	∈	NOUN
ejpam-1371	379	24	x	x	PUNCT
ejpam-1371	380	1	such	such	ADJ
ejpam-1371	380	2	that	that	SCONJ
ejpam-1371	380	3	(	(	PUNCT
ejpam-1371	380	4	∇f	∇f	PROPN
ejpam-1371	380	5	−	−	PROPN
ejpam-1371	380	6	t	t	NOUN
ejpam-1371	380	7	)	)	PUNCT
ejpam-1371	380	8	(	(	PUNCT
ejpam-1371	380	9	y0	y0	NOUN
ejpam-1371	380	10	)	)	PUNCT
ejpam-1371	380	11	∈	∈	PROPN
ejpam-1371	380	12	�	�	PROPN
ejpam-1371	380	13	τ∗(x	τ∗(x	PUNCT
ejpam-1371	380	14	)	)	PUNCT
ejpam-1371	380	15	�	�	PROPN
ejpam-1371	380	16	⊕	⊕	PROPN
ejpam-1371	380	17	η	η	PROPN
ejpam-1371	380	18	and	and	CCONJ
ejpam-1371	380	19	g	g	PROPN
ejpam-1371	380	20	y0	y0	PROPN
ejpam-1371	380	21	�	�	PROPN
ejpam-1371	381	1	(	(	PUNCT
ejpam-1371	381	2	∇f	∇f	PROPN
ejpam-1371	381	3	−	−	PROPN
ejpam-1371	381	4	t	t	NOUN
ejpam-1371	381	5	)	)	PUNCT
ejpam-1371	381	6	(	(	PUNCT
ejpam-1371	381	7	y0),η(z	y0),η(z	PROPN
ejpam-1371	381	8	,	,	PUNCT
ejpam-1371	381	9	y0	y0	NOUN
ejpam-1371	381	10	)	)	PUNCT
ejpam-1371	381	11	�	�	PROPN
ejpam-1371	381	12	=	=	SYM
ejpam-1371	381	13	〈	〈	PROPN
ejpam-1371	381	14	(	(	PUNCT
ejpam-1371	381	15	∇f	∇f	PROPN
ejpam-1371	381	16	−	−	PROPN
ejpam-1371	381	17	t	t	NOUN
ejpam-1371	381	18	)	)	PUNCT
ejpam-1371	381	19	(	(	PUNCT
ejpam-1371	381	20	y0),η(z	y0),η(z	PROPN
ejpam-1371	381	21	,	,	PUNCT
ejpam-1371	381	22	y0)〉y0	y0)〉y0	NOUN
ejpam-1371	381	23	=	=	SYM
ejpam-1371	381	24	0	0	NUM
ejpam-1371	381	25	for	for	ADP
ejpam-1371	381	26	all	all	DET
ejpam-1371	381	27	z	z	NOUN
ejpam-1371	381	28	∈	∈	NOUN
ejpam-1371	381	29	x	x	X
ejpam-1371	381	30	.	.	PUNCT
ejpam-1371	382	1	p.	p.	NOUN
ejpam-1371	382	2	das	das	PROPN
ejpam-1371	382	3	/	/	SYM
ejpam-1371	382	4	eur	eur	PROPN
ejpam-1371	382	5	.	.	PUNCT
ejpam-1371	383	1	j.	j.	PROPN
ejpam-1371	383	2	pure	pure	PROPN
ejpam-1371	383	3	appl	appl	PROPN
ejpam-1371	383	4	.	.	PROPN
ejpam-1371	383	5	math	math	PROPN
ejpam-1371	383	6	,	,	PUNCT
ejpam-1371	383	7	4	4	NUM
ejpam-1371	383	8	(	(	PUNCT
ejpam-1371	383	9	2011	2011	NUM
ejpam-1371	383	10	)	)	PUNCT
ejpam-1371	383	11	,	,	PUNCT
ejpam-1371	383	12	340	340	NUM
ejpam-1371	383	13	-	-	SYM
ejpam-1371	383	14	360	360	NUM
ejpam-1371	383	15	356	356	NUM
ejpam-1371	383	16	theorem	theorem	VERB
ejpam-1371	383	17	7	7	NUM
ejpam-1371	383	18	.	.	PUNCT
ejpam-1371	384	1	let	let	VERB
ejpam-1371	384	2	x	x	PRON
ejpam-1371	384	3	be	be	AUX
ejpam-1371	384	4	a	a	DET
ejpam-1371	384	5	η	η	NOUN
ejpam-1371	384	6	-	-	ADJ
ejpam-1371	384	7	closed	closed	ADJ
ejpam-1371	384	8	,	,	PUNCT
ejpam-1371	384	9	η	η	NOUN
ejpam-1371	384	10	-	-	NOUN
ejpam-1371	384	11	invex	invex	NOUN
ejpam-1371	384	12	and	and	CCONJ
ejpam-1371	384	13	oriented	orient	VERB
ejpam-1371	384	14	riemannian	riemannian	ADJ
ejpam-1371	384	15	n	n	CCONJ
ejpam-1371	384	16	-	-	PUNCT
ejpam-1371	384	17	manifold	manifold	ADJ
ejpam-1371	384	18	,	,	PUNCT
ejpam-1371	384	19	modelled	model	VERB
ejpam-1371	384	20	on	on	ADP
ejpam-1371	384	21	the	the	DET
ejpam-1371	384	22	hilbert	hilbert	PROPN
ejpam-1371	384	23	space	space	NOUN
ejpam-1371	384	24	h	h	NOUN
ejpam-1371	384	25	with	with	ADP
ejpam-1371	384	26	riemannian	riemannian	PROPN
ejpam-1371	384	27	metric	metric	PROPN
ejpam-1371	384	28	g.	g.	PROPN
ejpam-1371	384	29	let	let	VERB
ejpam-1371	384	30	f	f	NOUN
ejpam-1371	385	1	:	:	PUNCT
ejpam-1371	385	2	x	x	X
ejpam-1371	385	3	→	→	SYM
ejpam-1371	385	4	h	h	PROPN
ejpam-1371	385	5	,	,	PUNCT
ejpam-1371	385	6	η	η	PROPN
ejpam-1371	385	7	:	:	PUNCT
ejpam-1371	385	8	x	x	SYM
ejpam-1371	385	9	×	×	NOUN
ejpam-1371	385	10	x	x	INTJ
ejpam-1371	385	11	→	→	SYM
ejpam-1371	385	12	τ(x	τ(x	ADJ
ejpam-1371	385	13	,	,	PUNCT
ejpam-1371	385	14	u	u	NOUN
ejpam-1371	385	15	)	)	PUNCT
ejpam-1371	385	16	≡	≡	PROPN
ejpam-1371	385	17	x	x	PUNCT
ejpam-1371	385	18	are	be	AUX
ejpam-1371	385	19	two	two	NUM
ejpam-1371	385	20	continuous	continuous	ADJ
ejpam-1371	385	21	maps	map	NOUN
ejpam-1371	385	22	.	.	PUNCT
ejpam-1371	386	1	let	let	VERB
ejpam-1371	386	2	t	t	NOUN
ejpam-1371	386	3	:	:	PUNCT
ejpam-1371	386	4	x	x	X
ejpam-1371	386	5	→	→	SYM
ejpam-1371	386	6	l(τ∗(x	l(τ∗(x	NOUN
ejpam-1371	386	7	)	)	PUNCT
ejpam-1371	386	8	,	,	PUNCT
ejpam-1371	386	9	h	h	NOUN
ejpam-1371	386	10	)	)	PUNCT
ejpam-1371	386	11	≡	≡	PROPN
ejpam-1371	386	12	h	h	PROPN
ejpam-1371	386	13	be	be	VERB
ejpam-1371	386	14	an	an	DET
ejpam-1371	386	15	operator	operator	NOUN
ejpam-1371	386	16	.	.	PUNCT
ejpam-1371	387	1	let	let	VERB
ejpam-1371	387	2	f	f	NOUN
ejpam-1371	387	3	:	:	PUNCT
ejpam-1371	387	4	x	x	X
ejpam-1371	387	5	→	→	SYM
ejpam-1371	387	6	h	h	NOUN
ejpam-1371	387	7	be	be	AUX
ejpam-1371	387	8	an	an	DET
ejpam-1371	387	9	operator	operator	NOUN
ejpam-1371	387	10	such	such	ADJ
ejpam-1371	387	11	that	that	SCONJ
ejpam-1371	387	12	the	the	DET
ejpam-1371	387	13	differential	differential	ADJ
ejpam-1371	387	14	operator	operator	NOUN
ejpam-1371	387	15	∇f	∇f	NOUN
ejpam-1371	388	1	:	:	PUNCT
ejpam-1371	388	2	x	x	X
ejpam-1371	388	3	→	→	SYM
ejpam-1371	388	4	τ(h	τ(h	PROPN
ejpam-1371	388	5	,	,	PUNCT
ejpam-1371	388	6	f(u	f(u	PROPN
ejpam-1371	388	7	)	)	PUNCT
ejpam-1371	388	8	)	)	PUNCT
ejpam-1371	389	1	≡	≡	PROPN
ejpam-1371	389	2	h.	h.	PROPN
ejpam-1371	389	3	let	let	VERB
ejpam-1371	389	4	w	w	PRON
ejpam-1371	389	5	be	be	AUX
ejpam-1371	389	6	a	a	DET
ejpam-1371	389	7	maximal	maximal	ADJ
ejpam-1371	389	8	fixed	fix	VERB
ejpam-1371	389	9	point	point	NOUN
ejpam-1371	389	10	open	open	ADJ
ejpam-1371	389	11	set	set	VERB
ejpam-1371	389	12	in	in	ADP
ejpam-1371	389	13	x	x	PUNCT
ejpam-1371	389	14	with	with	ADP
ejpam-1371	389	15	respect	respect	NOUN
ejpam-1371	389	16	to	to	ADP
ejpam-1371	389	17	∇f	∇f	PROPN
ejpam-1371	389	18	−	−	PROPN
ejpam-1371	389	19	t.	t.	NOUN
ejpam-1371	389	20	then	then	ADV
ejpam-1371	389	21	,	,	PUNCT
ejpam-1371	389	22	there	there	PRON
ejpam-1371	389	23	exists	exist	VERB
ejpam-1371	389	24	a	a	DET
ejpam-1371	389	25	unique	unique	ADJ
ejpam-1371	389	26	y0	y0	NOUN
ejpam-1371	389	27	such	such	ADJ
ejpam-1371	389	28	that	that	SCONJ
ejpam-1371	389	29	y0	y0	PROPN
ejpam-1371	389	30	∈	∈	NOUN
ejpam-1371	389	31	(	(	PUNCT
ejpam-1371	389	32	∇f	∇f	PROPN
ejpam-1371	389	33	−	−	PROPN
ejpam-1371	389	34	t	t	PROPN
ejpam-1371	389	35	−	−	PROPN
ejpam-1371	389	36	1x	1x	NUM
ejpam-1371	389	37	)	)	PUNCT
ejpam-1371	389	38	−1(0x	−1(0x	CCONJ
ejpam-1371	389	39	)	)	PUNCT
ejpam-1371	389	40	and	and	CCONJ
ejpam-1371	389	41	y0	y0	NOUN
ejpam-1371	389	42	solves	solve	VERB
ejpam-1371	389	43	the	the	DET
ejpam-1371	389	44	problem	problem	NOUN
ejpam-1371	389	45	(	(	PUNCT
ejpam-1371	389	46	gddv	gddv	PROPN
ejpam-1371	389	47	ipn	ipn	PROPN
ejpam-1371	389	48	)	)	PUNCT
ejpam-1371	389	49	,	,	PUNCT
ejpam-1371	389	50	that	that	ADV
ejpam-1371	389	51	is	is	ADV
ejpam-1371	389	52	,	,	PUNCT
ejpam-1371	389	53	(	(	PUNCT
ejpam-1371	389	54	∇f	∇f	PROPN
ejpam-1371	389	55	−	−	PROPN
ejpam-1371	389	56	t	t	NOUN
ejpam-1371	389	57	)	)	PUNCT
ejpam-1371	389	58	(	(	PUNCT
ejpam-1371	389	59	y0	y0	NOUN
ejpam-1371	389	60	)	)	PUNCT
ejpam-1371	389	61	∈	∈	PROPN
ejpam-1371	389	62	(	(	PUNCT
ejpam-1371	389	63	τ	τ	X
ejpam-1371	389	64	∗(x	∗(x	PROPN
ejpam-1371	389	65	)	)	PUNCT
ejpam-1371	389	66	)	)	PUNCT
ejpam-1371	390	1	⊕η	⊕η	PROPN
ejpam-1371	390	2	and	and	CCONJ
ejpam-1371	390	3	g	g	PROPN
ejpam-1371	390	4	y0	y0	PROPN
ejpam-1371	390	5	�	�	PROPN
ejpam-1371	390	6	(	(	PUNCT
ejpam-1371	390	7	∇f	∇f	PROPN
ejpam-1371	390	8	−	−	PROPN
ejpam-1371	390	9	t	t	NOUN
ejpam-1371	390	10	)	)	PUNCT
ejpam-1371	390	11	(	(	PUNCT
ejpam-1371	390	12	y0),η(z	y0),η(z	PROPN
ejpam-1371	390	13	,	,	PUNCT
ejpam-1371	390	14	y0	y0	NOUN
ejpam-1371	390	15	)	)	PUNCT
ejpam-1371	390	16	�	�	PROPN
ejpam-1371	390	17	=	=	SYM
ejpam-1371	390	18	〈	〈	PROPN
ejpam-1371	390	19	(	(	PUNCT
ejpam-1371	390	20	∇f	∇f	PROPN
ejpam-1371	390	21	−	−	PROPN
ejpam-1371	390	22	t	t	NOUN
ejpam-1371	390	23	)	)	PUNCT
ejpam-1371	390	24	(	(	PUNCT
ejpam-1371	390	25	y0),η(z	y0),η(z	PROPN
ejpam-1371	390	26	,	,	PUNCT
ejpam-1371	390	27	y0)〉y0	y0)〉y0	PRON
ejpam-1371	390	28	≥	≥	NOUN
ejpam-1371	390	29	0	0	NUM
ejpam-1371	390	30	for	for	ADP
ejpam-1371	390	31	all	all	DET
ejpam-1371	390	32	z	z	NOUN
ejpam-1371	390	33	∈	∈	NOUN
ejpam-1371	390	34	x	x	X
ejpam-1371	390	35	.	.	PUNCT
ejpam-1371	391	1	proof	proof	NOUN
ejpam-1371	391	2	.	.	PUNCT
ejpam-1371	392	1	since	since	SCONJ
ejpam-1371	392	2	x	x	PRON
ejpam-1371	392	3	is	be	AUX
ejpam-1371	392	4	an	an	DET
ejpam-1371	392	5	n	n	ADV
ejpam-1371	392	6	-	-	PUNCT
ejpam-1371	392	7	manifold	manifold	ADJ
ejpam-1371	392	8	,	,	PUNCT
ejpam-1371	392	9	it	it	PRON
ejpam-1371	392	10	is	be	AUX
ejpam-1371	392	11	a	a	DET
ejpam-1371	392	12	housdorff	housdorff	NOUN
ejpam-1371	392	13	space	space	NOUN
ejpam-1371	392	14	with	with	ADP
ejpam-1371	392	15	a	a	DET
ejpam-1371	392	16	countable	countable	ADJ
ejpam-1371	392	17	basis	basis	NOUN
ejpam-1371	392	18	such	such	ADJ
ejpam-1371	392	19	that	that	SCONJ
ejpam-1371	392	20	each	each	DET
ejpam-1371	392	21	point	point	NOUN
ejpam-1371	392	22	x	x	PUNCT
ejpam-1371	392	23	of	of	ADP
ejpam-1371	392	24	x	x	PUNCT
ejpam-1371	392	25	has	have	VERB
ejpam-1371	392	26	a	a	DET
ejpam-1371	392	27	neighborhood	neighborhood	NOUN
ejpam-1371	392	28	that	that	PRON
ejpam-1371	392	29	is	be	AUX
ejpam-1371	392	30	homeomorphic	homeomorphic	ADJ
ejpam-1371	392	31	with	with	ADP
ejpam-1371	392	32	an	an	DET
ejpam-1371	392	33	open	open	ADJ
ejpam-1371	392	34	set	set	NOUN
ejpam-1371	392	35	of	of	ADP
ejpam-1371	392	36	rn	rn	PROPN
ejpam-1371	392	37	.	.	PROPN
ejpam-1371	392	38	again	again	ADV
ejpam-1371	392	39	,	,	PUNCT
ejpam-1371	392	40	since	since	SCONJ
ejpam-1371	392	41	w	w	PROPN
ejpam-1371	392	42	be	be	AUX
ejpam-1371	392	43	a	a	DET
ejpam-1371	392	44	maximal	maximal	ADJ
ejpam-1371	392	45	fixed	fix	VERB
ejpam-1371	392	46	point	point	NOUN
ejpam-1371	392	47	open	open	ADJ
ejpam-1371	392	48	set	set	VERB
ejpam-1371	392	49	in	in	ADP
ejpam-1371	392	50	x	x	PUNCT
ejpam-1371	392	51	,	,	PUNCT
ejpam-1371	392	52	by	by	ADP
ejpam-1371	392	53	the	the	DET
ejpam-1371	392	54	definition	definition	NOUN
ejpam-1371	392	55	,	,	PUNCT
ejpam-1371	392	56	we	we	PRON
ejpam-1371	392	57	have	have	VERB
ejpam-1371	392	58	w	w	NOUN
ejpam-1371	392	59	=	=	NOUN
ejpam-1371	392	60	x	x	PROPN
ejpam-1371	392	61	.	.	PUNCT
ejpam-1371	393	1	now	now	ADV
ejpam-1371	393	2	,	,	PUNCT
ejpam-1371	393	3	to	to	PART
ejpam-1371	393	4	apply	apply	VERB
ejpam-1371	393	5	theorem	theorem	NOUN
ejpam-1371	393	6	6	6	NUM
ejpam-1371	393	7	,	,	PUNCT
ejpam-1371	393	8	we	we	PRON
ejpam-1371	393	9	show	show	VERB
ejpam-1371	393	10	that	that	SCONJ
ejpam-1371	393	11	x	x	PRON
ejpam-1371	393	12	is	be	AUX
ejpam-1371	393	13	one	one	NUM
ejpam-1371	393	14	-	-	PUNCT
ejpam-1371	393	15	point	point	NOUN
ejpam-1371	393	16	compactification	compactification	NOUN
ejpam-1371	393	17	of	of	ADP
ejpam-1371	393	18	w	w	NOUN
ejpam-1371	393	19	by	by	ADP
ejpam-1371	393	20	proving	prove	VERB
ejpam-1371	393	21	f	f	X
ejpam-1371	393	22	has	have	VERB
ejpam-1371	393	23	only	only	ADV
ejpam-1371	393	24	one	one	NUM
ejpam-1371	393	25	fixed	fix	VERB
ejpam-1371	393	26	point	point	NOUN
ejpam-1371	393	27	in	in	ADP
ejpam-1371	393	28	x	x	PUNCT
ejpam-1371	393	29	which	which	PRON
ejpam-1371	393	30	lies	lie	VERB
ejpam-1371	393	31	outside	outside	ADP
ejpam-1371	393	32	w	w	PROPN
ejpam-1371	393	33	.	.	PUNCT
ejpam-1371	394	1	let	let	VERB
ejpam-1371	394	2	i	i	PRON
ejpam-1371	394	3	f	f	AUX
ejpam-1371	394	4	be	be	AUX
ejpam-1371	394	5	the	the	DET
ejpam-1371	394	6	fixed	fix	VERB
ejpam-1371	394	7	point	point	NOUN
ejpam-1371	394	8	index	index	NOUN
ejpam-1371	394	9	of	of	ADP
ejpam-1371	394	10	f	f	PROPN
ejpam-1371	394	11	.	.	PUNCT
ejpam-1371	395	1	then	then	ADV
ejpam-1371	395	2	at	at	ADP
ejpam-1371	395	3	first	first	ADV
ejpam-1371	395	4	we	we	PRON
ejpam-1371	395	5	show	show	VERB
ejpam-1371	395	6	,	,	PUNCT
ejpam-1371	395	7	f	f	PROPN
ejpam-1371	395	8	has	have	VERB
ejpam-1371	395	9	a	a	DET
ejpam-1371	395	10	fixed	fix	VERB
ejpam-1371	395	11	point	point	NOUN
ejpam-1371	395	12	by	by	ADP
ejpam-1371	395	13	proving	prove	VERB
ejpam-1371	395	14	i	i	PRON
ejpam-1371	395	15	f	f	PROPN
ejpam-1371	395	16	6=	6=	PROPN
ejpam-1371	395	17	0	0	NUM
ejpam-1371	395	18	.	.	PUNCT
ejpam-1371	396	1	since	since	SCONJ
ejpam-1371	396	2	x	x	PROPN
ejpam-1371	396	3	is	be	AUX
ejpam-1371	396	4	η	η	NOUN
ejpam-1371	396	5	-	-	ADJ
ejpam-1371	396	6	closed	closed	ADJ
ejpam-1371	396	7	endowed	endow	VERB
ejpam-1371	396	8	with	with	ADP
ejpam-1371	396	9	the	the	DET
ejpam-1371	396	10	riemannian	riemannian	ADJ
ejpam-1371	396	11	metric	metric	NOUN
ejpam-1371	396	12	g	g	PROPN
ejpam-1371	396	13	,	,	PUNCT
ejpam-1371	396	14	w	w	PROPN
ejpam-1371	396	15	is	be	AUX
ejpam-1371	396	16	η	η	NOUN
ejpam-1371	396	17	-	-	ADJ
ejpam-1371	396	18	closed	closed	ADJ
ejpam-1371	396	19	endowed	endow	VERB
ejpam-1371	396	20	with	with	ADP
ejpam-1371	396	21	the	the	DET
ejpam-1371	396	22	riemannian	riemannian	ADJ
ejpam-1371	396	23	metric	metric	PROPN
ejpam-1371	396	24	g.	g.	PROPN
ejpam-1371	397	1	thus	thus	ADV
ejpam-1371	397	2	,	,	PUNCT
ejpam-1371	397	3	for	for	ADP
ejpam-1371	397	4	every	every	DET
ejpam-1371	397	5	y	y	PROPN
ejpam-1371	397	6	∈	∈	PROPN
ejpam-1371	397	7	w	w	NOUN
ejpam-1371	397	8	,	,	PUNCT
ejpam-1371	397	9	there	there	PRON
ejpam-1371	397	10	is	be	VERB
ejpam-1371	397	11	an	an	DET
ejpam-1371	397	12	unique	unique	ADJ
ejpam-1371	397	13	x	x	SYM
ejpam-1371	397	14	∈	∈	PROPN
ejpam-1371	397	15	w	w	NOUN
ejpam-1371	397	16	which	which	PRON
ejpam-1371	397	17	is	be	AUX
ejpam-1371	397	18	closest	close	ADJ
ejpam-1371	397	19	to	to	ADP
ejpam-1371	397	20	y	y	PROPN
ejpam-1371	397	21	−∇f(y	−∇f(y	PROPN
ejpam-1371	397	22	)	)	PUNCT
ejpam-1371	398	1	+	+	NUM
ejpam-1371	398	2	t	t	PROPN
ejpam-1371	398	3	(	(	PUNCT
ejpam-1371	398	4	y	y	NOUN
ejpam-1371	398	5	)	)	PUNCT
ejpam-1371	398	6	with	with	ADP
ejpam-1371	398	7	respect	respect	NOUN
ejpam-1371	398	8	to	to	ADP
ejpam-1371	398	9	η	η	PROPN
ejpam-1371	398	10	.	.	PROPN
ejpam-1371	398	11	let	let	VERB
ejpam-1371	398	12	the	the	DET
ejpam-1371	398	13	mapping	mapping	NOUN
ejpam-1371	398	14	f	f	X
ejpam-1371	399	1	:	:	PUNCT
ejpam-1371	399	2	w	w	X
ejpam-1371	399	3	→	→	SYM
ejpam-1371	399	4	x	x	NOUN
ejpam-1371	399	5	defined	define	VERB
ejpam-1371	399	6	by	by	ADP
ejpam-1371	399	7	the	the	DET
ejpam-1371	399	8	rule	rule	NOUN
ejpam-1371	399	9	f	f	PROPN
ejpam-1371	399	10	(	(	PUNCT
ejpam-1371	399	11	y	y	NOUN
ejpam-1371	399	12	)	)	PUNCT
ejpam-1371	399	13	=	=	SYM
ejpam-1371	399	14	y	y	PROPN
ejpam-1371	399	15	−∇f(y	−∇f(y	PROPN
ejpam-1371	399	16	)	)	PUNCT
ejpam-1371	400	1	+	+	NUM
ejpam-1371	400	2	t	t	PROPN
ejpam-1371	400	3	(	(	PUNCT
ejpam-1371	400	4	y	y	NOUN
ejpam-1371	400	5	)	)	PUNCT
ejpam-1371	401	1	+	+	CCONJ
ejpam-1371	401	2	x	x	X
ejpam-1371	401	3	for	for	ADP
ejpam-1371	401	4	every	every	DET
ejpam-1371	401	5	y	y	PROPN
ejpam-1371	401	6	∈w	∈w	VERB
ejpam-1371	401	7	where	where	SCONJ
ejpam-1371	401	8	x	x	PRON
ejpam-1371	401	9	is	be	AUX
ejpam-1371	401	10	the	the	DET
ejpam-1371	401	11	unique	unique	ADJ
ejpam-1371	401	12	element	element	NOUN
ejpam-1371	401	13	corresponding	correspond	VERB
ejpam-1371	401	14	to	to	ADP
ejpam-1371	401	15	y.	y.	NOUN
ejpam-1371	401	16	now	now	ADV
ejpam-1371	401	17	for	for	ADP
ejpam-1371	401	18	every	every	DET
ejpam-1371	401	19	y	y	PROPN
ejpam-1371	401	20	∈w	∈w	PROPN
ejpam-1371	401	21	,	,	PUNCT
ejpam-1371	401	22	(	(	PUNCT
ejpam-1371	401	23	1w	1w	NUM
ejpam-1371	401	24	−	−	PROPN
ejpam-1371	401	25	f	f	NOUN
ejpam-1371	401	26	)	)	PUNCT
ejpam-1371	401	27	(	(	PUNCT
ejpam-1371	401	28	y	y	X
ejpam-1371	401	29	)	)	PUNCT
ejpam-1371	401	30	=	=	NOUN
ejpam-1371	402	1	1w	1w	NOUN
ejpam-1371	402	2	(	(	PUNCT
ejpam-1371	402	3	y)−	y)−	PROPN
ejpam-1371	402	4	f	f	PROPN
ejpam-1371	402	5	(	(	PUNCT
ejpam-1371	402	6	y	y	NOUN
ejpam-1371	402	7	)	)	PUNCT
ejpam-1371	402	8	=	=	PROPN
ejpam-1371	402	9	∇f(y)−	∇f(y)−	PROPN
ejpam-1371	402	10	t	t	PROPN
ejpam-1371	402	11	(	(	PUNCT
ejpam-1371	402	12	y)−	y)−	PROPN
ejpam-1371	402	13	x	x	SYM
ejpam-1371	402	14	=	=	SYM
ejpam-1371	402	15	(	(	PUNCT
ejpam-1371	402	16	∇f	∇f	PROPN
ejpam-1371	402	17	−	−	PROPN
ejpam-1371	402	18	t	t	NOUN
ejpam-1371	402	19	)	)	PUNCT
ejpam-1371	402	20	(	(	PUNCT
ejpam-1371	402	21	y)−	y)−	PROPN
ejpam-1371	402	22	x	x	X
ejpam-1371	402	23	.	.	PUNCT
ejpam-1371	403	1	let	let	VERB
ejpam-1371	403	2	a	a	PRON
ejpam-1371	403	3	:	:	PUNCT
ejpam-1371	403	4	w	w	PROPN
ejpam-1371	403	5	→h∗	→h∗	PROPN
ejpam-1371	403	6	=	=	PRON
ejpam-1371	403	7	h	h	NOUN
ejpam-1371	403	8	be	be	AUX
ejpam-1371	403	9	a	a	DET
ejpam-1371	403	10	mapping	mapping	NOUN
ejpam-1371	403	11	defined	define	VERB
ejpam-1371	403	12	by	by	ADP
ejpam-1371	403	13	the	the	DET
ejpam-1371	403	14	rule	rule	NOUN
ejpam-1371	403	15	a(y	a(y	PROPN
ejpam-1371	403	16	)	)	PUNCT
ejpam-1371	404	1	=	=	PUNCT
ejpam-1371	404	2	(	(	PUNCT
ejpam-1371	404	3	∇f	∇f	PROPN
ejpam-1371	404	4	−	−	PROPN
ejpam-1371	404	5	t	t	NOUN
ejpam-1371	404	6	)	)	PUNCT
ejpam-1371	404	7	(	(	PUNCT
ejpam-1371	404	8	y	y	NOUN
ejpam-1371	404	9	)	)	PUNCT
ejpam-1371	404	10	for	for	ADP
ejpam-1371	404	11	all	all	DET
ejpam-1371	404	12	y	y	PROPN
ejpam-1371	404	13	∈w	∈w	NOUN
ejpam-1371	404	14	.	.	PUNCT
ejpam-1371	405	1	then	then	ADV
ejpam-1371	405	2	from	from	ADP
ejpam-1371	405	3	the	the	DET
ejpam-1371	405	4	above	above	ADJ
ejpam-1371	405	5	expression	expression	NOUN
ejpam-1371	405	6	,	,	PUNCT
ejpam-1371	405	7	we	we	PRON
ejpam-1371	405	8	have	have	AUX
ejpam-1371	405	9	(	(	PUNCT
ejpam-1371	405	10	1w	1w	NUM
ejpam-1371	405	11	−	−	PROPN
ejpam-1371	405	12	f	f	NOUN
ejpam-1371	405	13	)	)	PUNCT
ejpam-1371	405	14	(	(	PUNCT
ejpam-1371	405	15	y	y	NOUN
ejpam-1371	405	16	)	)	PUNCT
ejpam-1371	405	17	=	=	SYM
ejpam-1371	406	1	a(y)−	a(y)−	PROPN
ejpam-1371	406	2	x	x	X
ejpam-1371	406	3	and	and	CCONJ
ejpam-1371	406	4	at	at	ADP
ejpam-1371	406	5	y	y	PROPN
ejpam-1371	406	6	=	=	PUNCT
ejpam-1371	406	7	x	x	NOUN
ejpam-1371	406	8	,	,	PUNCT
ejpam-1371	406	9	we	we	PRON
ejpam-1371	406	10	have	have	AUX
ejpam-1371	406	11	(	(	PUNCT
ejpam-1371	406	12	1w	1w	NUM
ejpam-1371	406	13	−	−	PROPN
ejpam-1371	406	14	f	f	NOUN
ejpam-1371	406	15	)	)	PUNCT
ejpam-1371	406	16	(	(	PUNCT
ejpam-1371	406	17	x	x	X
ejpam-1371	406	18	)	)	PUNCT
ejpam-1371	406	19	=	=	PUNCT
ejpam-1371	407	1	a(x)−	a(x)−	NOUN
ejpam-1371	407	2	x	x	X
ejpam-1371	407	3	=	=	SYM
ejpam-1371	407	4	(	(	PUNCT
ejpam-1371	407	5	a−	a−	PROPN
ejpam-1371	407	6	1w	1w	NUM
ejpam-1371	407	7	)	)	PUNCT
ejpam-1371	407	8	(	(	PUNCT
ejpam-1371	407	9	x	x	X
ejpam-1371	407	10	)	)	PUNCT
ejpam-1371	407	11	,	,	PUNCT
ejpam-1371	407	12	that	that	ADV
ejpam-1371	407	13	is	is	ADV
ejpam-1371	407	14	,	,	PUNCT
ejpam-1371	407	15	1w	1w	NUM
ejpam-1371	407	16	−	−	PROPN
ejpam-1371	407	17	f	f	NOUN
ejpam-1371	407	18	=	=	SYM
ejpam-1371	407	19	a−	a−	PROPN
ejpam-1371	407	20	1w	1w	NOUN
ejpam-1371	407	21	at	at	ADP
ejpam-1371	407	22	the	the	DET
ejpam-1371	407	23	unique	unique	ADJ
ejpam-1371	407	24	x	x	NOUN
ejpam-1371	407	25	∈w	∈w	NOUN
ejpam-1371	407	26	,	,	PUNCT
ejpam-1371	407	27	that	that	ADV
ejpam-1371	407	28	is	is	ADV
ejpam-1371	407	29	,	,	PUNCT
ejpam-1371	407	30	1w	1w	NUM
ejpam-1371	407	31	−	−	PROPN
ejpam-1371	407	32	f	f	NOUN
ejpam-1371	407	33	=	=	SYM
ejpam-1371	407	34	a−	a−	PROPN
ejpam-1371	407	35	1w	1w	NOUN
ejpam-1371	407	36	at	at	ADP
ejpam-1371	407	37	the	the	DET
ejpam-1371	407	38	unique	unique	ADJ
ejpam-1371	407	39	x	x	NOUN
ejpam-1371	407	40	∈w	∈w	NOUN
ejpam-1371	407	41	.	.	PUNCT
ejpam-1371	408	1	define	define	VERB
ejpam-1371	408	2	g	g	NOUN
ejpam-1371	408	3	:	:	PUNCT
ejpam-1371	408	4	w	w	PROPN
ejpam-1371	408	5	×	×	NOUN
ejpam-1371	408	6	i	i	NOUN
ejpam-1371	408	7	→w	→w	NUM
ejpam-1371	408	8	by	by	ADP
ejpam-1371	408	9	the	the	DET
ejpam-1371	408	10	rule	rule	NOUN
ejpam-1371	408	11	g(y	g(y	PROPN
ejpam-1371	408	12	,	,	PUNCT
ejpam-1371	408	13	t	t	PROPN
ejpam-1371	408	14	)	)	PUNCT
ejpam-1371	408	15	=	=	SYM
ejpam-1371	409	1	(	(	PUNCT
ejpam-1371	409	2	(	(	PUNCT
ejpam-1371	409	3	1w	1w	NUM
ejpam-1371	409	4	−	−	PROPN
ejpam-1371	409	5	f	f	NOUN
ejpam-1371	409	6	)	)	PUNCT
ejpam-1371	409	7	(	(	PUNCT
ejpam-1371	409	8	2	2	NUM
ejpam-1371	409	9	t	t	NOUN
ejpam-1371	409	10	x	x	NOUN
ejpam-1371	409	11	+	+	CCONJ
ejpam-1371	409	12	(	(	PUNCT
ejpam-1371	409	13	1−	1−	NUM
ejpam-1371	409	14	2t)y	2t)y	NUM
ejpam-1371	409	15	)	)	PUNCT
ejpam-1371	410	1	if	if	SCONJ
ejpam-1371	410	2	0≤	0≤	NUM
ejpam-1371	410	3	t	t	VERB
ejpam-1371	410	4	≤	≤	NUM
ejpam-1371	410	5	1	1	NUM
ejpam-1371	410	6	2	2	NUM
ejpam-1371	410	7	;	;	PUNCT
ejpam-1371	410	8	(	(	PUNCT
ejpam-1371	410	9	a−	a−	PROPN
ejpam-1371	410	10	1w	1w	NUM
ejpam-1371	410	11	)	)	PUNCT
ejpam-1371	410	12	(	(	PUNCT
ejpam-1371	410	13	2(1−	2(1−	NUM
ejpam-1371	410	14	t)x	t)x	X
ejpam-1371	410	15	+	+	CCONJ
ejpam-1371	410	16	(	(	PUNCT
ejpam-1371	410	17	2	2	NUM
ejpam-1371	410	18	t	t	NOUN
ejpam-1371	410	19	−	−	PROPN
ejpam-1371	410	20	1)y	1)y	NUM
ejpam-1371	410	21	)	)	PUNCT
ejpam-1371	410	22	if	if	SCONJ
ejpam-1371	410	23	1	1	NUM
ejpam-1371	410	24	2	2	NUM
ejpam-1371	410	25	≤	≤	NOUN
ejpam-1371	410	26	t	t	NOUN
ejpam-1371	410	27	≤	≤	NUM
ejpam-1371	410	28	1	1	NUM
ejpam-1371	410	29	,	,	PUNCT
ejpam-1371	410	30	p.	p.	NOUN
ejpam-1371	410	31	das	das	PROPN
ejpam-1371	410	32	/	/	SYM
ejpam-1371	410	33	eur	eur	PROPN
ejpam-1371	410	34	.	.	PUNCT
ejpam-1371	411	1	j.	j.	PROPN
ejpam-1371	411	2	pure	pure	PROPN
ejpam-1371	411	3	appl	appl	PROPN
ejpam-1371	411	4	.	.	PROPN
ejpam-1371	411	5	math	math	PROPN
ejpam-1371	411	6	,	,	PUNCT
ejpam-1371	411	7	4	4	NUM
ejpam-1371	411	8	(	(	PUNCT
ejpam-1371	411	9	2011	2011	NUM
ejpam-1371	411	10	)	)	PUNCT
ejpam-1371	411	11	,	,	PUNCT
ejpam-1371	411	12	340	340	NUM
ejpam-1371	411	13	-	-	SYM
ejpam-1371	411	14	360	360	NUM
ejpam-1371	411	15	357	357	NUM
ejpam-1371	411	16	where	where	SCONJ
ejpam-1371	411	17	g(y	g(y	NOUN
ejpam-1371	411	18	,	,	PUNCT
ejpam-1371	411	19	0	0	NUM
ejpam-1371	411	20	)	)	PUNCT
ejpam-1371	411	21	=	=	SYM
ejpam-1371	411	22	�	�	PROPN
ejpam-1371	411	23	1w	1w	VERB
ejpam-1371	411	24	−	−	PROPN
ejpam-1371	411	25	f	f	PROPN
ejpam-1371	411	26	�	�	PROPN
ejpam-1371	411	27	(	(	PUNCT
ejpam-1371	411	28	y	y	NOUN
ejpam-1371	411	29	)	)	PUNCT
ejpam-1371	411	30	,	,	PUNCT
ejpam-1371	411	31	g(y	g(y	PROPN
ejpam-1371	411	32	,	,	PUNCT
ejpam-1371	411	33	1	1	NUM
ejpam-1371	411	34	)	)	PUNCT
ejpam-1371	411	35	=	=	PUNCT
ejpam-1371	411	36	�	�	PROPN
ejpam-1371	411	37	a−	a−	PROPN
ejpam-1371	412	1	1w	1w	VERB
ejpam-1371	413	1	�	�	PROPN
ejpam-1371	413	2	(	(	PUNCT
ejpam-1371	413	3	y	y	NOUN
ejpam-1371	413	4	)	)	PUNCT
ejpam-1371	413	5	for	for	ADP
ejpam-1371	413	6	each	each	DET
ejpam-1371	413	7	y	y	PROPN
ejpam-1371	413	8	∈w	∈w	NOUN
ejpam-1371	413	9	and	and	CCONJ
ejpam-1371	413	10	at	at	ADP
ejpam-1371	413	11	t	t	NOUN
ejpam-1371	413	12	=	=	SYM
ejpam-1371	413	13	1	1	NUM
ejpam-1371	413	14	2	2	NUM
ejpam-1371	413	15	,	,	PUNCT
ejpam-1371	413	16	g(y	g(y	PROPN
ejpam-1371	413	17	,	,	PUNCT
ejpam-1371	413	18	1/2	1/2	NUM
ejpam-1371	413	19	)	)	PUNCT
ejpam-1371	413	20	=	=	SYM
ejpam-1371	413	21	�	�	PROPN
ejpam-1371	413	22	1w	1w	VERB
ejpam-1371	413	23	−	−	PROPN
ejpam-1371	413	24	f	f	PROPN
ejpam-1371	413	25	�	�	PROPN
ejpam-1371	413	26	(	(	PUNCT
ejpam-1371	413	27	x	x	NOUN
ejpam-1371	413	28	)	)	PUNCT
ejpam-1371	413	29	=	=	SYM
ejpam-1371	413	30	�	�	PROPN
ejpam-1371	413	31	a−	a−	PROPN
ejpam-1371	413	32	1w	1w	VERB
ejpam-1371	413	33	�	�	PROPN
ejpam-1371	413	34	(	(	PUNCT
ejpam-1371	413	35	x	x	NOUN
ejpam-1371	413	36	)	)	PUNCT
ejpam-1371	413	37	.	.	PUNCT
ejpam-1371	414	1	thus	thus	ADV
ejpam-1371	414	2	g	g	PROPN
ejpam-1371	414	3	is	be	AUX
ejpam-1371	414	4	continuous	continuous	ADJ
ejpam-1371	414	5	by	by	ADP
ejpam-1371	414	6	pasting	paste	VERB
ejpam-1371	414	7	lemma	lemma	PROPN
ejpam-1371	414	8	and	and	CCONJ
ejpam-1371	414	9	g	g	PROPN
ejpam-1371	414	10	:	:	PUNCT
ejpam-1371	414	11	(	(	PUNCT
ejpam-1371	414	12	1w	1w	NUM
ejpam-1371	414	13	−	−	PROPN
ejpam-1371	414	14	f	f	PROPN
ejpam-1371	414	15	)	)	PUNCT
ejpam-1371	414	16	≃	≃	NOUN
ejpam-1371	414	17	(	(	PUNCT
ejpam-1371	414	18	a−	a−	PROPN
ejpam-1371	414	19	1w	1w	NUM
ejpam-1371	414	20	)	)	PUNCT
ejpam-1371	414	21	where	where	SCONJ
ejpam-1371	414	22	≃	≃	ADJ
ejpam-1371	414	23	denotes	denote	VERB
ejpam-1371	414	24	“	"	PUNCT
ejpam-1371	414	25	homotopically	homotopically	ADV
ejpam-1371	414	26	equivalent	equivalent	ADJ
ejpam-1371	414	27	to	to	ADP
ejpam-1371	414	28	”	"	PUNCT
ejpam-1371	414	29	.	.	PUNCT
ejpam-1371	415	1	hence	hence	ADV
ejpam-1371	415	2	the	the	DET
ejpam-1371	415	3	coincidence	coincidence	NOUN
ejpam-1371	415	4	index	index	NOUN
ejpam-1371	415	5	set	set	NOUN
ejpam-1371	415	6	of	of	ADP
ejpam-1371	415	7	f	f	PROPN
ejpam-1371	415	8	is	be	AUX
ejpam-1371	415	9	given	give	VERB
ejpam-1371	415	10	by	by	ADP
ejpam-1371	415	11	iw	iw	PROPN
ejpam-1371	415	12	f	f	PROPN
ejpam-1371	415	13	=	=	PROPN
ejpam-1371	415	14	�	�	PROPN
ejpam-1371	415	15	1w	1w	VERB
ejpam-1371	415	16	−	−	PROPN
ejpam-1371	415	17	f	f	PROPN
ejpam-1371	415	18	�	�	PROPN
ejpam-1371	415	19	∗	∗	VERB
ejpam-1371	415	20	0w	0w	X
ejpam-1371	416	1	=	=	SYM
ejpam-1371	416	2	�	�	PROPN
ejpam-1371	416	3	a−	a−	PROPN
ejpam-1371	416	4	1w	1w	VERB
ejpam-1371	416	5	�	�	PROPN
ejpam-1371	416	6	∗	∗	NOUN
ejpam-1371	416	7	0w	0w	NUM
ejpam-1371	416	8	.	.	PUNCT
ejpam-1371	417	1	(	(	PUNCT
ejpam-1371	417	2	31	31	NUM
ejpam-1371	417	3	)	)	PUNCT
ejpam-1371	417	4	by	by	ADP
ejpam-1371	417	5	(	(	PUNCT
ejpam-1371	417	6	31	31	NUM
ejpam-1371	417	7	)	)	PUNCT
ejpam-1371	417	8	,	,	PUNCT
ejpam-1371	417	9	we	we	PRON
ejpam-1371	417	10	have	have	VERB
ejpam-1371	417	11	iw	iw	PROPN
ejpam-1371	417	12	f	f	PROPN
ejpam-1371	417	13	6=	6=	PROPN
ejpam-1371	417	14	0	0	NUM
ejpam-1371	417	15	.	.	PUNCT
ejpam-1371	418	1	since	since	SCONJ
ejpam-1371	418	2	invex	invex	PROPN
ejpam-1371	418	3	set	set	NOUN
ejpam-1371	418	4	is	be	AUX
ejpam-1371	418	5	the	the	DET
ejpam-1371	418	6	generalization	generalization	NOUN
ejpam-1371	418	7	of	of	ADP
ejpam-1371	418	8	convex	convex	PROPN
ejpam-1371	418	9	set	set	NOUN
ejpam-1371	418	10	,	,	PUNCT
ejpam-1371	418	11	applying	apply	VERB
ejpam-1371	418	12	theorem	theorem	NOUN
ejpam-1371	418	13	4	4	NUM
ejpam-1371	418	14	,	,	PUNCT
ejpam-1371	418	15	we	we	PRON
ejpam-1371	418	16	have	have	VERB
ejpam-1371	418	17	f	f	PROPN
ejpam-1371	418	18	has	have	VERB
ejpam-1371	418	19	a	a	DET
ejpam-1371	418	20	fixed	fix	VERB
ejpam-1371	418	21	point	point	NOUN
ejpam-1371	418	22	on	on	ADP
ejpam-1371	418	23	w	w	PROPN
ejpam-1371	418	24	.	.	PUNCT
ejpam-1371	419	1	again	again	ADV
ejpam-1371	419	2	,	,	PUNCT
ejpam-1371	419	3	since	since	SCONJ
ejpam-1371	419	4	w	w	NOUN
ejpam-1371	419	5	is	be	AUX
ejpam-1371	419	6	maximal	maximal	ADJ
ejpam-1371	419	7	fixed	fix	VERB
ejpam-1371	419	8	point	point	NOUN
ejpam-1371	419	9	open	open	ADJ
ejpam-1371	419	10	set	set	VERB
ejpam-1371	419	11	in	in	ADP
ejpam-1371	419	12	x	x	PUNCT
ejpam-1371	419	13	with	with	ADP
ejpam-1371	419	14	respect	respect	NOUN
ejpam-1371	419	15	to	to	ADP
ejpam-1371	419	16	a	a	PRON
ejpam-1371	419	17	,	,	PUNCT
ejpam-1371	419	18	by	by	ADP
ejpam-1371	419	19	the	the	DET
ejpam-1371	419	20	definition	definition	NOUN
ejpam-1371	419	21	,	,	PUNCT
ejpam-1371	419	22	we	we	PRON
ejpam-1371	419	23	get	get	VERB
ejpam-1371	419	24	cw	cw	NOUN
ejpam-1371	420	1	=	=	SYM
ejpam-1371	420	2	x	x	NOUN
ejpam-1371	420	3	,	,	PUNCT
ejpam-1371	420	4	implies	imply	VERB
ejpam-1371	420	5	that	that	SCONJ
ejpam-1371	420	6	,	,	PUNCT
ejpam-1371	420	7	w	w	PROPN
ejpam-1371	420	8	=	=	SYM
ejpam-1371	420	9	x	x	X
ejpam-1371	420	10	and	and	CCONJ
ejpam-1371	420	11	(	(	PUNCT
ejpam-1371	420	12	a−	a−	PROPN
ejpam-1371	420	13	1w	1w	NUM
ejpam-1371	420	14	)	)	PUNCT
ejpam-1371	421	1	−1(0w	−1(0w	NOUN
ejpam-1371	421	2	)	)	PUNCT
ejpam-1371	421	3	⊂w	⊂w	PROPN
ejpam-1371	421	4	,	,	PUNCT
ejpam-1371	421	5	that	that	ADV
ejpam-1371	421	6	is	is	ADV
ejpam-1371	421	7	,	,	PUNCT
ejpam-1371	421	8	(	(	PUNCT
ejpam-1371	421	9	a−	a−	PROPN
ejpam-1371	421	10	1x	1x	NUM
ejpam-1371	421	11	)	)	PUNCT
ejpam-1371	421	12	−1(0x	−1(0x	CCONJ
ejpam-1371	421	13	)	)	PUNCT
ejpam-1371	422	1	⊂	⊂	PROPN
ejpam-1371	422	2	x	x	X
ejpam-1371	422	3	,	,	PUNCT
ejpam-1371	422	4	implies	imply	VERB
ejpam-1371	422	5	that	that	SCONJ
ejpam-1371	422	6	,	,	PUNCT
ejpam-1371	422	7	(	(	PUNCT
ejpam-1371	422	8	1x	1x	NUM
ejpam-1371	422	9	−	−	PROPN
ejpam-1371	422	10	f	f	PROPN
ejpam-1371	422	11	)	)	PUNCT
ejpam-1371	422	12	−1(0x	−1(0x	PROPN
ejpam-1371	422	13	)	)	PUNCT
ejpam-1371	423	1	⊂	⊂	PROPN
ejpam-1371	423	2	x	x	X
ejpam-1371	423	3	.	.	PUNCT
ejpam-1371	424	1	hence	hence	ADV
ejpam-1371	424	2	,	,	PUNCT
ejpam-1371	424	3	f	f	PROPN
ejpam-1371	424	4	has	have	VERB
ejpam-1371	424	5	a	a	DET
ejpam-1371	424	6	fixed	fix	VERB
ejpam-1371	424	7	point	point	NOUN
ejpam-1371	424	8	in	in	ADP
ejpam-1371	424	9	x	x	X
ejpam-1371	424	10	.	.	PUNCT
ejpam-1371	425	1	let	let	VERB
ejpam-1371	425	2	the	the	DET
ejpam-1371	425	3	fixed	fix	VERB
ejpam-1371	425	4	point	point	NOUN
ejpam-1371	425	5	be	be	AUX
ejpam-1371	425	6	y0	y0	NOUN
ejpam-1371	425	7	in	in	ADP
ejpam-1371	425	8	x	x	SYM
ejpam-1371	425	9	,	,	PUNCT
ejpam-1371	425	10	that	that	ADV
ejpam-1371	425	11	is	is	ADV
ejpam-1371	425	12	,	,	PUNCT
ejpam-1371	425	13	f	f	PROPN
ejpam-1371	425	14	(	(	PUNCT
ejpam-1371	425	15	y0	y0	NOUN
ejpam-1371	425	16	)	)	PUNCT
ejpam-1371	426	1	=	=	SYM
ejpam-1371	426	2	y0	y0	NOUN
ejpam-1371	426	3	.	.	PUNCT
ejpam-1371	427	1	let	let	VERB
ejpam-1371	427	2	x0	x0	PROPN
ejpam-1371	427	3	be	be	AUX
ejpam-1371	427	4	the	the	DET
ejpam-1371	427	5	unique	unique	ADJ
ejpam-1371	427	6	element	element	NOUN
ejpam-1371	427	7	that	that	PRON
ejpam-1371	427	8	corresponds	correspond	VERB
ejpam-1371	427	9	y0	y0	NOUN
ejpam-1371	427	10	.	.	PUNCT
ejpam-1371	428	1	by	by	ADP
ejpam-1371	428	2	η	η	NOUN
ejpam-1371	428	3	-	-	NOUN
ejpam-1371	428	4	closedness	closedness	NOUN
ejpam-1371	428	5	of	of	ADP
ejpam-1371	428	6	x	x	SYM
ejpam-1371	428	7	,	,	PUNCT
ejpam-1371	428	8	we	we	PRON
ejpam-1371	428	9	have	have	AUX
ejpam-1371	428	10	,	,	PUNCT
ejpam-1371	428	11	for	for	ADP
ejpam-1371	428	12	every	every	DET
ejpam-1371	428	13	y	y	PROPN
ejpam-1371	428	14	∈	∈	PROPN
ejpam-1371	428	15	x	x	X
ejpam-1371	428	16	,	,	PUNCT
ejpam-1371	428	17	there	there	PRON
ejpam-1371	428	18	is	be	VERB
ejpam-1371	428	19	an	an	DET
ejpam-1371	428	20	unique	unique	ADJ
ejpam-1371	428	21	x	x	SYM
ejpam-1371	428	22	∈	∈	PROPN
ejpam-1371	428	23	x	x	X
ejpam-1371	428	24	which	which	PRON
ejpam-1371	428	25	is	be	AUX
ejpam-1371	428	26	closest	close	ADJ
ejpam-1371	428	27	to	to	ADP
ejpam-1371	428	28	y	y	PROPN
ejpam-1371	428	29	−	−	PROPN
ejpam-1371	428	30	a(y	a(y	PROPN
ejpam-1371	428	31	)	)	PUNCT
ejpam-1371	428	32	with	with	ADP
ejpam-1371	428	33	respect	respect	NOUN
ejpam-1371	428	34	to	to	ADP
ejpam-1371	428	35	η	η	PROPN
ejpam-1371	428	36	.	.	PROPN
ejpam-1371	428	37	that	that	ADV
ejpam-1371	428	38	is	be	AUX
ejpam-1371	428	39	,	,	PUNCT
ejpam-1371	428	40	〈	〈	PROPN
ejpam-1371	428	41	x	x	PROPN
ejpam-1371	428	42	,	,	PUNCT
ejpam-1371	428	43	η(z	η(z	PROPN
ejpam-1371	428	44	,	,	PUNCT
ejpam-1371	428	45	x)〉x	x)〉x	PROPN
ejpam-1371	428	46	≥	≥	NUM
ejpam-1371	428	47	〈	〈	PROPN
ejpam-1371	428	48	y	y	PROPN
ejpam-1371	428	49	−	−	PROPN
ejpam-1371	428	50	a(y),η(z	a(y),η(z	PROPN
ejpam-1371	428	51	,	,	PUNCT
ejpam-1371	428	52	x)〉x	x)〉x	NOUN
ejpam-1371	428	53	for	for	ADP
ejpam-1371	428	54	all	all	DET
ejpam-1371	428	55	z	z	NOUN
ejpam-1371	428	56	∈	∈	NOUN
ejpam-1371	428	57	x	x	X
ejpam-1371	428	58	.	.	PUNCT
ejpam-1371	429	1	at	at	ADP
ejpam-1371	429	2	x	x	X
ejpam-1371	429	3	=	=	SYM
ejpam-1371	429	4	x0	x0	PROPN
ejpam-1371	429	5	,	,	PUNCT
ejpam-1371	429	6	we	we	PRON
ejpam-1371	429	7	have	have	VERB
ejpam-1371	429	8	〈	〈	PROPN
ejpam-1371	429	9	x0,η(z	x0,η(z	PROPN
ejpam-1371	429	10	,	,	PUNCT
ejpam-1371	429	11	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	429	12	≥	≥	PROPN
ejpam-1371	430	1	〈	〈	NOUN
ejpam-1371	430	2	y0	y0	PROPN
ejpam-1371	430	3	−	−	NOUN
ejpam-1371	431	1	a(y0),η(z	a(y0),η(z	PROPN
ejpam-1371	431	2	,	,	PUNCT
ejpam-1371	431	3	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	431	4	,	,	PUNCT
ejpam-1371	431	5	i.e.	i.e.	X
ejpam-1371	431	6	,	,	PUNCT
ejpam-1371	431	7	〈	〈	PROPN
ejpam-1371	431	8	x0,η(z	x0,η(z	X
ejpam-1371	431	9	,	,	PUNCT
ejpam-1371	431	10	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	431	11	≥	≥	PROPN
ejpam-1371	432	1	〈	〈	PROPN
ejpam-1371	432	2	f	f	X
ejpam-1371	432	3	(	(	PUNCT
ejpam-1371	432	4	y0)−	y0)−	PROPN
ejpam-1371	432	5	x0,η(z	x0,η(z	PROPN
ejpam-1371	432	6	,	,	PUNCT
ejpam-1371	432	7	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	432	8	for	for	ADP
ejpam-1371	432	9	all	all	DET
ejpam-1371	432	10	z	z	NOUN
ejpam-1371	432	11	∈	∈	PROPN
ejpam-1371	432	12	x	x	X
ejpam-1371	432	13	.	.	PUNCT
ejpam-1371	433	1	thus	thus	ADV
ejpam-1371	433	2	〈	〈	ADP
ejpam-1371	433	3	x0	x0	PROPN
ejpam-1371	433	4	,	,	PUNCT
ejpam-1371	433	5	z	z	PROPN
ejpam-1371	433	6	−	−	PROPN
ejpam-1371	433	7	x0〉x0	x0〉x0	NOUN
ejpam-1371	433	8	≥	≥	NOUN
ejpam-1371	433	9	〈	〈	NOUN
ejpam-1371	433	10	y0	y0	PROPN
ejpam-1371	433	11	−	−	NOUN
ejpam-1371	433	12	x0,η(z	x0,η(z	SYM
ejpam-1371	433	13	,	,	PUNCT
ejpam-1371	433	14	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	433	15	,	,	PUNCT
ejpam-1371	433	16	i.e.	i.e.	X
ejpam-1371	433	17	,	,	PUNCT
ejpam-1371	433	18	〈	〈	PROPN
ejpam-1371	433	19	2x0−	2x0−	NUM
ejpam-1371	433	20	y0,η(z	y0,η(z	NOUN
ejpam-1371	433	21	,	,	PUNCT
ejpam-1371	433	22	x0)〉x0	x0)〉x0	PROPN
ejpam-1371	433	23	≥	≥	PROPN
ejpam-1371	433	24	0	0	NUM
ejpam-1371	433	25	(	(	PUNCT
ejpam-1371	433	26	32	32	NUM
ejpam-1371	433	27	)	)	PUNCT
ejpam-1371	433	28	for	for	ADP
ejpam-1371	433	29	all	all	DET
ejpam-1371	433	30	z	z	NOUN
ejpam-1371	433	31	∈	∈	NOUN
ejpam-1371	433	32	x	x	X
ejpam-1371	433	33	.	.	PUNCT
ejpam-1371	434	1	again	again	ADV
ejpam-1371	434	2	at	at	ADP
ejpam-1371	434	3	y	y	PROPN
ejpam-1371	434	4	=	=	SYM
ejpam-1371	434	5	y0	y0	PROPN
ejpam-1371	434	6	,	,	PUNCT
ejpam-1371	434	7	we	we	PRON
ejpam-1371	434	8	get	get	VERB
ejpam-1371	434	9	f	f	NOUN
ejpam-1371	434	10	(	(	PUNCT
ejpam-1371	434	11	y0	y0	NOUN
ejpam-1371	434	12	)	)	PUNCT
ejpam-1371	434	13	=	=	PUNCT
ejpam-1371	434	14	y0	y0	NOUN
ejpam-1371	434	15	−	−	NOUN
ejpam-1371	434	16	a(y0	a(y0	NOUN
ejpam-1371	434	17	)	)	PUNCT
ejpam-1371	435	1	+	+	CCONJ
ejpam-1371	435	2	x0	x0	PROPN
ejpam-1371	435	3	,	,	PUNCT
ejpam-1371	435	4	that	that	ADV
ejpam-1371	435	5	is	is	ADV
ejpam-1371	435	6	,	,	PUNCT
ejpam-1371	435	7	x0	x0	PROPN
ejpam-1371	435	8	=	=	PUNCT
ejpam-1371	435	9	a(y0	a(y0	NOUN
ejpam-1371	435	10	)	)	PUNCT
ejpam-1371	435	11	.	.	PUNCT
ejpam-1371	436	1	since	since	SCONJ
ejpam-1371	436	2	w	w	PROPN
ejpam-1371	436	3	=	=	NOUN
ejpam-1371	436	4	x	x	NOUN
ejpam-1371	436	5	,	,	PUNCT
ejpam-1371	436	6	we	we	PRON
ejpam-1371	436	7	have	have	VERB
ejpam-1371	436	8	iw	iw	NUM
ejpam-1371	436	9	f	f	NOUN
ejpam-1371	437	1	=	=	PRON
ejpam-1371	437	2	ix	ix	PROPN
ejpam-1371	437	3	f	f	PROPN
ejpam-1371	438	1	=	=	PRON
ejpam-1371	438	2	i	i	PRON
ejpam-1371	438	3	f	f	PROPN
ejpam-1371	438	4	.	.	PUNCT
ejpam-1371	439	1	hence	hence	ADV
ejpam-1371	439	2	,	,	PUNCT
ejpam-1371	439	3	by	by	ADP
ejpam-1371	439	4	definition	definition	NOUN
ejpam-1371	439	5	of	of	ADP
ejpam-1371	439	6	coincidence	coincidence	NOUN
ejpam-1371	439	7	index	index	NOUN
ejpam-1371	439	8	set	set	NOUN
ejpam-1371	439	9	,	,	PUNCT
ejpam-1371	439	10	we	we	PRON
ejpam-1371	439	11	have	have	VERB
ejpam-1371	439	12	i	i	NOUN
ejpam-1371	439	13	f	f	NOUN
ejpam-1371	439	14	=	=	SYM
ejpam-1371	439	15	(	(	PUNCT
ejpam-1371	439	16	1x	1x	NUM
ejpam-1371	439	17	−	−	PROPN
ejpam-1371	439	18	f	f	PROPN
ejpam-1371	439	19	)	)	PUNCT
ejpam-1371	439	20	∗	∗	NOUN
ejpam-1371	439	21	0x	0x	NOUN
ejpam-1371	439	22	=	=	SYM
ejpam-1371	439	23	(	(	PUNCT
ejpam-1371	439	24	a−	a−	PROPN
ejpam-1371	439	25	1x	1x	NUM
ejpam-1371	439	26	)	)	PUNCT
ejpam-1371	439	27	∗	∗	NOUN
ejpam-1371	439	28	0x	0x	NOUN
ejpam-1371	439	29	=	=	SYM
ejpam-1371	439	30	ia	ia	PROPN
ejpam-1371	439	31	,	,	PUNCT
ejpam-1371	439	32	which	which	PRON
ejpam-1371	439	33	means	mean	VERB
ejpam-1371	439	34	f	f	PROPN
ejpam-1371	439	35	and	and	CCONJ
ejpam-1371	439	36	a	a	PRON
ejpam-1371	439	37	has	have	VERB
ejpam-1371	439	38	same	same	ADJ
ejpam-1371	439	39	fixed	fix	VERB
ejpam-1371	439	40	point	point	NOUN
ejpam-1371	439	41	in	in	ADP
ejpam-1371	439	42	x	x	X
ejpam-1371	439	43	,	,	PUNCT
ejpam-1371	439	44	that	that	ADV
ejpam-1371	439	45	is	is	ADV
ejpam-1371	439	46	,	,	PUNCT
ejpam-1371	439	47	f	f	PROPN
ejpam-1371	439	48	(	(	PUNCT
ejpam-1371	439	49	y0	y0	NOUN
ejpam-1371	439	50	)	)	PUNCT
ejpam-1371	439	51	=	=	SYM
ejpam-1371	439	52	y0	y0	NOUN
ejpam-1371	439	53	=	=	SYM
ejpam-1371	439	54	a(y0	a(y0	NOUN
ejpam-1371	439	55	)	)	PUNCT
ejpam-1371	439	56	.	.	PUNCT
ejpam-1371	440	1	therefore	therefore	ADV
ejpam-1371	440	2	,	,	PUNCT
ejpam-1371	440	3	(	(	PUNCT
ejpam-1371	440	4	a−	a−	PROPN
ejpam-1371	440	5	1x	1x	NUM
ejpam-1371	440	6	)	)	PUNCT
ejpam-1371	441	1	−1(0x	−1(0x	CCONJ
ejpam-1371	441	2	)	)	PUNCT
ejpam-1371	441	3	contains	contain	VERB
ejpam-1371	441	4	y0	y0	PRON
ejpam-1371	441	5	only	only	ADV
ejpam-1371	441	6	,	,	PUNCT
ejpam-1371	441	7	that	that	ADV
ejpam-1371	441	8	is	is	ADV
ejpam-1371	441	9	,	,	PUNCT
ejpam-1371	441	10	y0	y0	PROPN
ejpam-1371	441	11	∈	∈	NOUN
ejpam-1371	441	12	(	(	PUNCT
ejpam-1371	441	13	∇f	∇f	PROPN
ejpam-1371	441	14	−	−	PROPN
ejpam-1371	441	15	t	t	PROPN
ejpam-1371	441	16	−	−	PROPN
ejpam-1371	441	17	1x	1x	NUM
ejpam-1371	441	18	)	)	PUNCT
ejpam-1371	441	19	−1(0x	−1(0x	ADP
ejpam-1371	441	20	)	)	PUNCT
ejpam-1371	441	21	.	.	PUNCT
ejpam-1371	442	1	now	now	ADV
ejpam-1371	442	2	,	,	PUNCT
ejpam-1371	442	3	since	since	SCONJ
ejpam-1371	442	4	x0	x0	PROPN
ejpam-1371	442	5	=	=	SYM
ejpam-1371	442	6	a(y0	a(y0	NOUN
ejpam-1371	442	7	)	)	PUNCT
ejpam-1371	442	8	,	,	PUNCT
ejpam-1371	442	9	implies	imply	VERB
ejpam-1371	442	10	that	that	SCONJ
ejpam-1371	442	11	,	,	PUNCT
ejpam-1371	442	12	x0	x0	PROPN
ejpam-1371	442	13	=	=	SYM
ejpam-1371	442	14	y0	y0	NOUN
ejpam-1371	442	15	.	.	PUNCT
ejpam-1371	443	1	substituting	substitute	VERB
ejpam-1371	443	2	x0	x0	PROPN
ejpam-1371	444	1	=	=	PUNCT
ejpam-1371	444	2	y0	y0	NOUN
ejpam-1371	444	3	in	in	ADP
ejpam-1371	444	4	(	(	PUNCT
ejpam-1371	444	5	32	32	NUM
ejpam-1371	444	6	)	)	PUNCT
ejpam-1371	444	7	,	,	PUNCT
ejpam-1371	444	8	we	we	PRON
ejpam-1371	444	9	get	get	VERB
ejpam-1371	444	10	〈	〈	ADP
ejpam-1371	444	11	a(y0),η(z	a(y0),η(z	PROPN
ejpam-1371	444	12	,	,	PUNCT
ejpam-1371	444	13	y0)〉y0	y0)〉y0	PRON
ejpam-1371	444	14	≥	≥	NOUN
ejpam-1371	444	15	0	0	NUM
ejpam-1371	444	16	,	,	PUNCT
ejpam-1371	444	17	i.e.	i.e.	X
ejpam-1371	444	18	,	,	PUNCT
ejpam-1371	444	19	〈	〈	PROPN
ejpam-1371	444	20	(	(	PUNCT
ejpam-1371	444	21	∇f	∇f	PROPN
ejpam-1371	444	22	−	−	PROPN
ejpam-1371	444	23	t	t	NOUN
ejpam-1371	444	24	)	)	PUNCT
ejpam-1371	444	25	(	(	PUNCT
ejpam-1371	444	26	y0),η(z	y0),η(z	PROPN
ejpam-1371	444	27	,	,	PUNCT
ejpam-1371	444	28	y0)〉y0	y0)〉y0	PRON
ejpam-1371	444	29	≥	≥	NOUN
ejpam-1371	444	30	0	0	NUM
ejpam-1371	444	31	for	for	ADP
ejpam-1371	444	32	all	all	DET
ejpam-1371	444	33	z	z	NOUN
ejpam-1371	444	34	∈	∈	NOUN
ejpam-1371	444	35	x	x	X
ejpam-1371	444	36	.	.	PUNCT
ejpam-1371	445	1	thus	thus	ADV
ejpam-1371	445	2	(	(	PUNCT
ejpam-1371	445	3	∇f	∇f	PROPN
ejpam-1371	445	4	−	−	PROPN
ejpam-1371	445	5	t	t	NOUN
ejpam-1371	445	6	)	)	PUNCT
ejpam-1371	445	7	(	(	PUNCT
ejpam-1371	445	8	y0	y0	NOUN
ejpam-1371	445	9	)	)	PUNCT
ejpam-1371	445	10	∈	∈	PROPN
ejpam-1371	445	11	(	(	PUNCT
ejpam-1371	445	12	τ	τ	X
ejpam-1371	445	13	∗(x	∗(x	PROPN
ejpam-1371	445	14	)	)	PUNCT
ejpam-1371	445	15	)	)	PUNCT
ejpam-1371	446	1	⊕η	⊕η	NOUN
ejpam-1371	446	2	and	and	CCONJ
ejpam-1371	446	3	y0	y0	PROPN
ejpam-1371	446	4	∈	∈	NOUN
ejpam-1371	446	5	x	x	SYM
ejpam-1371	446	6	solves	solve	NOUN
ejpam-1371	446	7	(	(	PUNCT
ejpam-1371	446	8	gddv	gddv	PROPN
ejpam-1371	446	9	ipn	ipn	PROPN
ejpam-1371	446	10	)	)	PUNCT
ejpam-1371	446	11	.	.	PUNCT
ejpam-1371	447	1	this	this	PRON
ejpam-1371	447	2	is	be	AUX
ejpam-1371	447	3	a	a	DET
ejpam-1371	447	4	proof	proof	NOUN
ejpam-1371	447	5	.	.	PUNCT
ejpam-1371	448	1	p.	p.	NOUN
ejpam-1371	448	2	das	das	PROPN
ejpam-1371	448	3	/	/	SYM
ejpam-1371	448	4	eur	eur	PROPN
ejpam-1371	448	5	.	.	PUNCT
ejpam-1371	449	1	j.	j.	PROPN
ejpam-1371	449	2	pure	pure	PROPN
ejpam-1371	449	3	appl	appl	PROPN
ejpam-1371	449	4	.	.	PROPN
ejpam-1371	449	5	math	math	PROPN
ejpam-1371	449	6	,	,	PUNCT
ejpam-1371	449	7	4	4	NUM
ejpam-1371	449	8	(	(	PUNCT
ejpam-1371	449	9	2011	2011	NUM
ejpam-1371	449	10	)	)	PUNCT
ejpam-1371	449	11	,	,	PUNCT
ejpam-1371	449	12	340	340	NUM
ejpam-1371	449	13	-	-	SYM
ejpam-1371	449	14	360	360	NUM
ejpam-1371	449	15	358	358	NUM
ejpam-1371	449	16	theorem	theorem	VERB
ejpam-1371	449	17	8	8	NUM
ejpam-1371	449	18	.	.	PUNCT
ejpam-1371	450	1	let	let	VERB
ejpam-1371	450	2	x	x	PRON
ejpam-1371	450	3	be	be	AUX
ejpam-1371	450	4	a	a	DET
ejpam-1371	450	5	η	η	NOUN
ejpam-1371	450	6	-	-	ADJ
ejpam-1371	450	7	closed	closed	ADJ
ejpam-1371	450	8	,	,	PUNCT
ejpam-1371	450	9	η	η	NOUN
ejpam-1371	450	10	-	-	NOUN
ejpam-1371	450	11	invex	invex	NOUN
ejpam-1371	450	12	and	and	CCONJ
ejpam-1371	450	13	oriented	orient	VERB
ejpam-1371	450	14	riemannian	riemannian	ADJ
ejpam-1371	450	15	n	n	CCONJ
ejpam-1371	450	16	-	-	PUNCT
ejpam-1371	450	17	manifold	manifold	ADJ
ejpam-1371	450	18	,	,	PUNCT
ejpam-1371	450	19	modelled	model	VERB
ejpam-1371	450	20	on	on	ADP
ejpam-1371	450	21	the	the	DET
ejpam-1371	450	22	hilbert	hilbert	PROPN
ejpam-1371	450	23	space	space	NOUN
ejpam-1371	450	24	h	h	NOUN
ejpam-1371	450	25	with	with	ADP
ejpam-1371	450	26	riemannian	riemannian	PROPN
ejpam-1371	450	27	metric	metric	PROPN
ejpam-1371	450	28	g.	g.	PROPN
ejpam-1371	450	29	let	let	VERB
ejpam-1371	450	30	f	f	NOUN
ejpam-1371	450	31	:	:	PUNCT
ejpam-1371	450	32	x	x	X
ejpam-1371	450	33	→	→	SYM
ejpam-1371	450	34	h	h	PROPN
ejpam-1371	450	35	,	,	PUNCT
ejpam-1371	450	36	η	η	PROPN
ejpam-1371	450	37	:	:	PUNCT
ejpam-1371	450	38	x	x	SYM
ejpam-1371	450	39	×	×	NOUN
ejpam-1371	450	40	x	x	INTJ
ejpam-1371	450	41	→	→	SYM
ejpam-1371	450	42	τ(x	τ(x	ADJ
ejpam-1371	450	43	,	,	PUNCT
ejpam-1371	450	44	u	u	NOUN
ejpam-1371	450	45	)	)	PUNCT
ejpam-1371	450	46	≡	≡	PROPN
ejpam-1371	450	47	x	x	PUNCT
ejpam-1371	450	48	are	be	AUX
ejpam-1371	450	49	two	two	NUM
ejpam-1371	450	50	continuous	continuous	ADJ
ejpam-1371	450	51	maps	map	NOUN
ejpam-1371	450	52	.	.	PUNCT
ejpam-1371	451	1	let	let	VERB
ejpam-1371	451	2	t	t	NOUN
ejpam-1371	451	3	:	:	PUNCT
ejpam-1371	451	4	x	x	X
ejpam-1371	451	5	→	→	SYM
ejpam-1371	451	6	l(τ∗(x	l(τ∗(x	NOUN
ejpam-1371	451	7	)	)	PUNCT
ejpam-1371	451	8	,	,	PUNCT
ejpam-1371	451	9	h	h	NOUN
ejpam-1371	451	10	)	)	PUNCT
ejpam-1371	451	11	≡	≡	PROPN
ejpam-1371	451	12	h	h	PROPN
ejpam-1371	451	13	be	be	VERB
ejpam-1371	451	14	an	an	DET
ejpam-1371	451	15	operator	operator	NOUN
ejpam-1371	451	16	.	.	PUNCT
ejpam-1371	452	1	let	let	VERB
ejpam-1371	452	2	f	f	NOUN
ejpam-1371	452	3	:	:	PUNCT
ejpam-1371	452	4	x	x	X
ejpam-1371	452	5	→	→	SYM
ejpam-1371	452	6	h	h	NOUN
ejpam-1371	452	7	be	be	AUX
ejpam-1371	452	8	an	an	DET
ejpam-1371	452	9	operator	operator	NOUN
ejpam-1371	452	10	such	such	ADJ
ejpam-1371	452	11	that	that	SCONJ
ejpam-1371	452	12	the	the	DET
ejpam-1371	452	13	differential	differential	ADJ
ejpam-1371	452	14	operator	operator	NOUN
ejpam-1371	452	15	∇f	∇f	NOUN
ejpam-1371	453	1	:	:	PUNCT
ejpam-1371	453	2	x	x	X
ejpam-1371	453	3	→	→	SYM
ejpam-1371	453	4	τ(h	τ(h	PROPN
ejpam-1371	453	5	,	,	PUNCT
ejpam-1371	453	6	f(u	f(u	PROPN
ejpam-1371	453	7	)	)	PUNCT
ejpam-1371	453	8	)	)	PUNCT
ejpam-1371	454	1	≡	≡	PROPN
ejpam-1371	454	2	h.	h.	PROPN
ejpam-1371	454	3	let	let	VERB
ejpam-1371	454	4	w	w	PRON
ejpam-1371	454	5	be	be	AUX
ejpam-1371	454	6	a	a	DET
ejpam-1371	454	7	maximal	maximal	ADJ
ejpam-1371	454	8	fixed	fix	VERB
ejpam-1371	454	9	point	point	NOUN
ejpam-1371	454	10	open	open	ADJ
ejpam-1371	454	11	set	set	VERB
ejpam-1371	454	12	in	in	ADP
ejpam-1371	454	13	x	x	PUNCT
ejpam-1371	454	14	with	with	ADP
ejpam-1371	454	15	respect	respect	NOUN
ejpam-1371	454	16	to	to	ADP
ejpam-1371	454	17	∇f	∇f	PROPN
ejpam-1371	454	18	−	−	PROPN
ejpam-1371	454	19	t.	t.	NOUN
ejpam-1371	454	20	then	then	ADV
ejpam-1371	454	21	,	,	PUNCT
ejpam-1371	454	22	there	there	PRON
ejpam-1371	454	23	exists	exist	VERB
ejpam-1371	454	24	an	an	DET
ejpam-1371	454	25	unique	unique	ADJ
ejpam-1371	454	26	y0	y0	NOUN
ejpam-1371	454	27	such	such	ADJ
ejpam-1371	454	28	that	that	SCONJ
ejpam-1371	454	29	y0	y0	PROPN
ejpam-1371	454	30	∈	∈	NOUN
ejpam-1371	454	31	(	(	PUNCT
ejpam-1371	454	32	∇f	∇f	PROPN
ejpam-1371	454	33	−	−	PROPN
ejpam-1371	454	34	t	t	PROPN
ejpam-1371	454	35	−	−	PROPN
ejpam-1371	454	36	1x	1x	NUM
ejpam-1371	454	37	)	)	PUNCT
ejpam-1371	454	38	−1(0x	−1(0x	CCONJ
ejpam-1371	454	39	)	)	PUNCT
ejpam-1371	455	1	and	and	CCONJ
ejpam-1371	455	2	y0	y0	NOUN
ejpam-1371	455	3	that	that	PRON
ejpam-1371	455	4	solves	solve	VERB
ejpam-1371	455	5	the	the	DET
ejpam-1371	455	6	problem	problem	NOUN
ejpam-1371	455	7	(	(	PUNCT
ejpam-1371	455	8	gddv	gddv	NOUN
ejpam-1371	455	9	c	c	PROPN
ejpam-1371	455	10	pn	pn	PROPN
ejpam-1371	455	11	)	)	PUNCT
ejpam-1371	455	12	,	,	PUNCT
ejpam-1371	455	13	that	that	ADV
ejpam-1371	455	14	is	is	ADV
ejpam-1371	455	15	,	,	PUNCT
ejpam-1371	455	16	(	(	PUNCT
ejpam-1371	455	17	∇f	∇f	PROPN
ejpam-1371	455	18	−	−	PROPN
ejpam-1371	455	19	t	t	NOUN
ejpam-1371	455	20	)	)	PUNCT
ejpam-1371	455	21	(	(	PUNCT
ejpam-1371	455	22	y0	y0	NOUN
ejpam-1371	455	23	)	)	PUNCT
ejpam-1371	455	24	∈	∈	PROPN
ejpam-1371	455	25	(	(	PUNCT
ejpam-1371	455	26	τ	τ	X
ejpam-1371	455	27	∗(x	∗(x	PROPN
ejpam-1371	455	28	)	)	PUNCT
ejpam-1371	455	29	)	)	PUNCT
ejpam-1371	456	1	⊕η	⊕η	PROPN
ejpam-1371	456	2	and	and	CCONJ
ejpam-1371	456	3	g	g	PROPN
ejpam-1371	456	4	y0	y0	PROPN
ejpam-1371	456	5	�	�	PROPN
ejpam-1371	456	6	(	(	PUNCT
ejpam-1371	456	7	∇f	∇f	PROPN
ejpam-1371	456	8	−	−	PROPN
ejpam-1371	456	9	t	t	NOUN
ejpam-1371	456	10	)	)	PUNCT
ejpam-1371	456	11	(	(	PUNCT
ejpam-1371	456	12	y0),η(z	y0),η(z	PROPN
ejpam-1371	456	13	,	,	PUNCT
ejpam-1371	456	14	y0	y0	NOUN
ejpam-1371	456	15	)	)	PUNCT
ejpam-1371	456	16	�	�	PROPN
ejpam-1371	456	17	=	=	SYM
ejpam-1371	456	18	〈	〈	PROPN
ejpam-1371	456	19	(	(	PUNCT
ejpam-1371	456	20	∇f	∇f	PROPN
ejpam-1371	456	21	−	−	PROPN
ejpam-1371	456	22	t	t	NOUN
ejpam-1371	456	23	)	)	PUNCT
ejpam-1371	456	24	(	(	PUNCT
ejpam-1371	456	25	y0),η(z	y0),η(z	PROPN
ejpam-1371	456	26	,	,	PUNCT
ejpam-1371	456	27	y0)〉y0	y0)〉y0	NOUN
ejpam-1371	456	28	=	=	SYM
ejpam-1371	456	29	0	0	NUM
ejpam-1371	456	30	for	for	ADP
ejpam-1371	456	31	all	all	DET
ejpam-1371	456	32	z	z	NOUN
ejpam-1371	456	33	∈	∈	NOUN
ejpam-1371	456	34	x	x	X
ejpam-1371	456	35	.	.	PUNCT
ejpam-1371	457	1	proof	proof	NOUN
ejpam-1371	457	2	.	.	PUNCT
ejpam-1371	458	1	by	by	ADP
ejpam-1371	458	2	theorem	theorem	NOUN
ejpam-1371	458	3	7	7	NUM
ejpam-1371	458	4	,	,	PUNCT
ejpam-1371	458	5	we	we	PRON
ejpam-1371	458	6	get	get	VERB
ejpam-1371	458	7	,	,	PUNCT
ejpam-1371	458	8	there	there	PRON
ejpam-1371	458	9	exists	exist	VERB
ejpam-1371	458	10	an	an	DET
ejpam-1371	458	11	unique	unique	ADJ
ejpam-1371	458	12	y0	y0	NOUN
ejpam-1371	458	13	∈	∈	NOUN
ejpam-1371	458	14	x	x	PUNCT
ejpam-1371	458	15	such	such	ADJ
ejpam-1371	458	16	that	that	SCONJ
ejpam-1371	458	17	y0	y0	PROPN
ejpam-1371	458	18	∈	∈	NOUN
ejpam-1371	458	19	(	(	PUNCT
ejpam-1371	458	20	∇f	∇f	PROPN
ejpam-1371	458	21	−	−	PROPN
ejpam-1371	458	22	t	t	PROPN
ejpam-1371	458	23	−	−	PROPN
ejpam-1371	458	24	1x	1x	NUM
ejpam-1371	458	25	)	)	PUNCT
ejpam-1371	458	26	−1(0x	−1(0x	CCONJ
ejpam-1371	458	27	)	)	PUNCT
ejpam-1371	458	28	and	and	CCONJ
ejpam-1371	458	29	y0	y0	NOUN
ejpam-1371	458	30	solves	solve	VERB
ejpam-1371	458	31	the	the	DET
ejpam-1371	458	32	problem	problem	NOUN
ejpam-1371	458	33	(	(	PUNCT
ejpam-1371	458	34	gddv	gddv	PROPN
ejpam-1371	458	35	ipn	ipn	PROPN
ejpam-1371	458	36	)	)	PUNCT
ejpam-1371	458	37	,	,	PUNCT
ejpam-1371	458	38	that	that	ADV
ejpam-1371	458	39	is	is	ADV
ejpam-1371	458	40	,	,	PUNCT
ejpam-1371	458	41	(	(	PUNCT
ejpam-1371	458	42	∇f	∇f	PROPN
ejpam-1371	458	43	−	−	PROPN
ejpam-1371	458	44	t	t	NOUN
ejpam-1371	458	45	)	)	PUNCT
ejpam-1371	458	46	(	(	PUNCT
ejpam-1371	458	47	y0	y0	NOUN
ejpam-1371	458	48	)	)	PUNCT
ejpam-1371	458	49	∈	∈	PROPN
ejpam-1371	458	50	�	�	PROPN
ejpam-1371	458	51	τ∗(x	τ∗(x	PUNCT
ejpam-1371	458	52	)	)	PUNCT
ejpam-1371	458	53	�	�	PROPN
ejpam-1371	458	54	⊕	⊕	PROPN
ejpam-1371	458	55	η	η	PROPN
ejpam-1371	458	56	and	and	CCONJ
ejpam-1371	458	57	g	g	PROPN
ejpam-1371	458	58	y0	y0	PROPN
ejpam-1371	458	59	�	�	PROPN
ejpam-1371	458	60	(	(	PUNCT
ejpam-1371	458	61	∇f	∇f	PROPN
ejpam-1371	458	62	−	−	PROPN
ejpam-1371	458	63	t	t	NOUN
ejpam-1371	458	64	)	)	PUNCT
ejpam-1371	458	65	(	(	PUNCT
ejpam-1371	458	66	y0),η(z	y0),η(z	PROPN
ejpam-1371	458	67	,	,	PUNCT
ejpam-1371	458	68	y0	y0	NOUN
ejpam-1371	458	69	)	)	PUNCT
ejpam-1371	458	70	�	�	PROPN
ejpam-1371	458	71	=	=	SYM
ejpam-1371	458	72	〈	〈	PROPN
ejpam-1371	458	73	(	(	PUNCT
ejpam-1371	458	74	∇f	∇f	PROPN
ejpam-1371	458	75	−	−	PROPN
ejpam-1371	458	76	t	t	NOUN
ejpam-1371	458	77	)	)	PUNCT
ejpam-1371	458	78	(	(	PUNCT
ejpam-1371	458	79	y0),η(z	y0),η(z	PROPN
ejpam-1371	458	80	,	,	PUNCT
ejpam-1371	458	81	y0)〉y0	y0)〉y0	PRON
ejpam-1371	458	82	≥	≥	NOUN
ejpam-1371	458	83	0	0	NUM
ejpam-1371	458	84	(	(	PUNCT
ejpam-1371	458	85	33	33	NUM
ejpam-1371	458	86	)	)	PUNCT
ejpam-1371	458	87	for	for	ADP
ejpam-1371	458	88	all	all	DET
ejpam-1371	458	89	z	z	NOUN
ejpam-1371	458	90	∈	∈	NOUN
ejpam-1371	458	91	x	x	X
ejpam-1371	458	92	.	.	PUNCT
ejpam-1371	459	1	since	since	SCONJ
ejpam-1371	459	2	x	x	PROPN
ejpam-1371	459	3	is	be	AUX
ejpam-1371	459	4	η	η	NOUN
ejpam-1371	459	5	-	-	ADJ
ejpam-1371	459	6	invex	invex	ADJ
ejpam-1371	459	7	set	set	NOUN
ejpam-1371	459	8	,	,	PUNCT
ejpam-1371	459	9	for	for	ADP
ejpam-1371	459	10	fixed	fix	VERB
ejpam-1371	459	11	y0	y0	PROPN
ejpam-1371	459	12	∈	∈	NOUN
ejpam-1371	459	13	x	x	X
ejpam-1371	459	14	and	and	CCONJ
ejpam-1371	459	15	t	t	PROPN
ejpam-1371	459	16	∈	∈	PROPN
ejpam-1371	459	17	(	(	PUNCT
ejpam-1371	459	18	0,1	0,1	NUM
ejpam-1371	459	19	)	)	PUNCT
ejpam-1371	459	20	,	,	PUNCT
ejpam-1371	459	21	we	we	PRON
ejpam-1371	459	22	have	have	VERB
ejpam-1371	459	23	y0	y0	NOUN
ejpam-1371	459	24	+	+	CCONJ
ejpam-1371	459	25	tη(z	tη(z	NOUN
ejpam-1371	459	26	,	,	PUNCT
ejpam-1371	459	27	y0	y0	NOUN
ejpam-1371	459	28	)	)	PUNCT
ejpam-1371	459	29	∈	∈	PROPN
ejpam-1371	459	30	x	x	PUNCT
ejpam-1371	459	31	for	for	ADP
ejpam-1371	459	32	all	all	DET
ejpam-1371	459	33	z	z	NOUN
ejpam-1371	459	34	∈	∈	NOUN
ejpam-1371	459	35	x	x	X
ejpam-1371	459	36	.	.	PUNCT
ejpam-1371	460	1	replacing	replace	VERB
ejpam-1371	460	2	z	z	NOUN
ejpam-1371	460	3	by	by	ADP
ejpam-1371	460	4	y0	y0	PROPN
ejpam-1371	460	5	+	+	SYM
ejpam-1371	460	6	tη(z	tη(z	NOUN
ejpam-1371	460	7	,	,	PUNCT
ejpam-1371	460	8	y0	y0	NOUN
ejpam-1371	460	9	)	)	PUNCT
ejpam-1371	460	10	in	in	ADP
ejpam-1371	460	11	the	the	DET
ejpam-1371	460	12	above	above	ADJ
ejpam-1371	460	13	inequality	inequality	NOUN
ejpam-1371	460	14	,	,	PUNCT
ejpam-1371	460	15	we	we	PRON
ejpam-1371	460	16	have	have	VERB
ejpam-1371	460	17	g	g	PROPN
ejpam-1371	460	18	y0	y0	PROPN
ejpam-1371	460	19	�	�	NOUN
ejpam-1371	460	20	(	(	PUNCT
ejpam-1371	460	21	∇f	∇f	PROPN
ejpam-1371	460	22	−	−	PROPN
ejpam-1371	460	23	t	t	NOUN
ejpam-1371	460	24	)	)	PUNCT
ejpam-1371	460	25	(	(	PUNCT
ejpam-1371	460	26	y0),η(y0	y0),η(y0	NOUN
ejpam-1371	460	27	+	+	CCONJ
ejpam-1371	460	28	tη(z	tη(z	NOUN
ejpam-1371	460	29	,	,	PUNCT
ejpam-1371	460	30	y0	y0	NOUN
ejpam-1371	460	31	)	)	PUNCT
ejpam-1371	460	32	,	,	PUNCT
ejpam-1371	460	33	y0	y0	NOUN
ejpam-1371	460	34	)	)	PUNCT
ejpam-1371	460	35	�	�	PROPN
ejpam-1371	460	36	=	=	SYM
ejpam-1371	460	37	〈	〈	PROPN
ejpam-1371	460	38	(	(	PUNCT
ejpam-1371	460	39	∇f	∇f	PROPN
ejpam-1371	460	40	−	−	PROPN
ejpam-1371	460	41	t	t	NOUN
ejpam-1371	460	42	)	)	PUNCT
ejpam-1371	460	43	(	(	PUNCT
ejpam-1371	460	44	y0),η(y0	y0),η(y0	NOUN
ejpam-1371	460	45	+	+	CCONJ
ejpam-1371	460	46	tη(z	tη(z	NOUN
ejpam-1371	460	47	,	,	PUNCT
ejpam-1371	460	48	y0	y0	NOUN
ejpam-1371	460	49	)	)	PUNCT
ejpam-1371	460	50	,	,	PUNCT
ejpam-1371	460	51	y0)〉y0	y0)〉y0	PRON
ejpam-1371	460	52	≥	≥	NOUN
ejpam-1371	460	53	0	0	NUM
ejpam-1371	460	54	for	for	ADP
ejpam-1371	460	55	all	all	DET
ejpam-1371	460	56	z	z	NOUN
ejpam-1371	460	57	∈	∈	NOUN
ejpam-1371	460	58	x	x	X
ejpam-1371	460	59	.	.	PUNCT
ejpam-1371	461	1	by	by	ADP
ejpam-1371	461	2	condition	condition	NOUN
ejpam-1371	461	3	c0	c0	NOUN
ejpam-1371	461	4	,	,	PUNCT
ejpam-1371	461	5	we	we	PRON
ejpam-1371	461	6	have	have	VERB
ejpam-1371	461	7	〈	〈	PROPN
ejpam-1371	461	8	(	(	PUNCT
ejpam-1371	461	9	∇f	∇f	PROPN
ejpam-1371	461	10	−	−	PROPN
ejpam-1371	461	11	t	t	NOUN
ejpam-1371	461	12	)	)	PUNCT
ejpam-1371	461	13	(	(	PUNCT
ejpam-1371	461	14	y0	y0	NOUN
ejpam-1371	461	15	)	)	PUNCT
ejpam-1371	461	16	,	,	PUNCT
ejpam-1371	461	17	η(y0	η(y0	NOUN
ejpam-1371	461	18	+	+	CCONJ
ejpam-1371	461	19	tη(z	tη(z	NOUN
ejpam-1371	461	20	,	,	PUNCT
ejpam-1371	461	21	y0	y0	NOUN
ejpam-1371	461	22	)	)	PUNCT
ejpam-1371	461	23	,	,	PUNCT
ejpam-1371	461	24	y0)〉y0	y0)〉y0	PRON
ejpam-1371	461	25	≥	≥	NOUN
ejpam-1371	461	26	0	0	NUM
ejpam-1371	461	27	for	for	ADP
ejpam-1371	461	28	allz	allz	PROPN
ejpam-1371	461	29	∈	∈	PROPN
ejpam-1371	461	30	x	x	X
ejpam-1371	461	31	,	,	PUNCT
ejpam-1371	461	32	i.e.	i.e.	X
ejpam-1371	461	33	,	,	PUNCT
ejpam-1371	461	34	〈	〈	PROPN
ejpam-1371	461	35	(	(	PUNCT
ejpam-1371	461	36	∇f	∇f	PROPN
ejpam-1371	461	37	−	−	PROPN
ejpam-1371	461	38	t	t	NOUN
ejpam-1371	461	39	)	)	PUNCT
ejpam-1371	461	40	(	(	PUNCT
ejpam-1371	461	41	y0	y0	NOUN
ejpam-1371	461	42	)	)	PUNCT
ejpam-1371	461	43	,	,	PUNCT
ejpam-1371	461	44	−tη(z	−tη(z	INTJ
ejpam-1371	461	45	,	,	PUNCT
ejpam-1371	461	46	y0)〉y0	y0)〉y0	PRON
ejpam-1371	461	47	≥	≥	NOUN
ejpam-1371	461	48	0	0	NUM
ejpam-1371	461	49	for	for	ADP
ejpam-1371	461	50	allz	allz	PROPN
ejpam-1371	461	51	∈	∈	PROPN
ejpam-1371	461	52	x	x	X
ejpam-1371	461	53	.	.	PUNCT
ejpam-1371	462	1	thus	thus	ADV
ejpam-1371	462	2	−t〈(∇f	−t〈(∇f	NOUN
ejpam-1371	462	3	−	−	PROPN
ejpam-1371	462	4	t	t	NOUN
ejpam-1371	462	5	)	)	PUNCT
ejpam-1371	462	6	(	(	PUNCT
ejpam-1371	462	7	y0	y0	NOUN
ejpam-1371	462	8	)	)	PUNCT
ejpam-1371	462	9	,	,	PUNCT
ejpam-1371	462	10	η(z	η(z	PROPN
ejpam-1371	462	11	,	,	PUNCT
ejpam-1371	462	12	y0)〉y0	y0)〉y0	PRON
ejpam-1371	462	13	≥	≥	NOUN
ejpam-1371	462	14	0	0	NUM
ejpam-1371	462	15	for	for	ADP
ejpam-1371	462	16	allz	allz	PROPN
ejpam-1371	462	17	∈	∈	PROPN
ejpam-1371	462	18	x	x	SYM
ejpam-1371	462	19	,	,	PUNCT
ejpam-1371	462	20	i.e.	i.e.	X
ejpam-1371	462	21	〈	〈	PROPN
ejpam-1371	462	22	(	(	PUNCT
ejpam-1371	462	23	∇f	∇f	PROPN
ejpam-1371	462	24	−	−	PROPN
ejpam-1371	462	25	t	t	NOUN
ejpam-1371	462	26	)	)	PUNCT
ejpam-1371	462	27	(	(	PUNCT
ejpam-1371	462	28	y0	y0	NOUN
ejpam-1371	462	29	)	)	PUNCT
ejpam-1371	462	30	,	,	PUNCT
ejpam-1371	462	31	η(z	η(z	PROPN
ejpam-1371	462	32	,	,	PUNCT
ejpam-1371	462	33	y0)〉y0	y0)〉y0	ADJ
ejpam-1371	462	34	≤	≤	NOUN
ejpam-1371	462	35	0	0	NUM
ejpam-1371	463	1	(	(	PUNCT
ejpam-1371	463	2	34	34	NUM
ejpam-1371	463	3	)	)	PUNCT
ejpam-1371	463	4	for	for	ADP
ejpam-1371	463	5	all	all	DET
ejpam-1371	463	6	z	z	NOUN
ejpam-1371	463	7	∈	∈	NOUN
ejpam-1371	463	8	x	x	X
ejpam-1371	463	9	.	.	PUNCT
ejpam-1371	464	1	hence	hence	ADV
ejpam-1371	464	2	from	from	ADP
ejpam-1371	464	3	(	(	PUNCT
ejpam-1371	464	4	33	33	NUM
ejpam-1371	464	5	)	)	PUNCT
ejpam-1371	464	6	and	and	CCONJ
ejpam-1371	464	7	(	(	PUNCT
ejpam-1371	464	8	34	34	NUM
ejpam-1371	464	9	)	)	PUNCT
ejpam-1371	464	10	,	,	PUNCT
ejpam-1371	464	11	we	we	PRON
ejpam-1371	464	12	have	have	VERB
ejpam-1371	464	13	〈	〈	PROPN
ejpam-1371	464	14	(	(	PUNCT
ejpam-1371	464	15	∇f	∇f	PROPN
ejpam-1371	464	16	−	−	PROPN
ejpam-1371	464	17	t	t	NOUN
ejpam-1371	464	18	)	)	PUNCT
ejpam-1371	464	19	(	(	PUNCT
ejpam-1371	464	20	y0	y0	NOUN
ejpam-1371	464	21	)	)	PUNCT
ejpam-1371	464	22	,	,	PUNCT
ejpam-1371	464	23	η(z	η(z	PROPN
ejpam-1371	464	24	,	,	PUNCT
ejpam-1371	464	25	y0)〉y0	y0)〉y0	NOUN
ejpam-1371	464	26	=	=	NOUN
ejpam-1371	464	27	0	0	NUM
ejpam-1371	464	28	for	for	ADP
ejpam-1371	464	29	all	all	DET
ejpam-1371	464	30	z	z	NOUN
ejpam-1371	464	31	∈	∈	PROPN
ejpam-1371	464	32	x	x	X
ejpam-1371	464	33	.	.	PUNCT
ejpam-1371	465	1	thus	thus	ADV
ejpam-1371	465	2	,	,	PUNCT
ejpam-1371	465	3	y0	y0	PROPN
ejpam-1371	465	4	∈	∈	NOUN
ejpam-1371	465	5	x	x	PRON
ejpam-1371	465	6	solves	solve	VERB
ejpam-1371	465	7	the	the	DET
ejpam-1371	465	8	problem	problem	NOUN
ejpam-1371	465	9	(	(	PUNCT
ejpam-1371	465	10	gddv	gddv	NOUN
ejpam-1371	465	11	c	c	PROPN
ejpam-1371	465	12	pn	pn	PROPN
ejpam-1371	465	13	)	)	PUNCT
ejpam-1371	465	14	.	.	PUNCT
ejpam-1371	466	1	this	this	PRON
ejpam-1371	466	2	is	be	AUX
ejpam-1371	466	3	a	a	DET
ejpam-1371	466	4	proof	proof	NOUN
ejpam-1371	466	5	.	.	PUNCT
ejpam-1371	467	1	references	reference	NOUN
ejpam-1371	467	2	359	359	NUM
ejpam-1371	467	3	4	4	NUM
ejpam-1371	467	4	.	.	PUNCT
ejpam-1371	467	5	conclusion	conclusion	VERB
ejpam-1371	467	6	the	the	DET
ejpam-1371	467	7	convergence	convergence	NOUN
ejpam-1371	467	8	of	of	ADP
ejpam-1371	467	9	variable	variable	ADJ
ejpam-1371	467	10	step	step	NOUN
ejpam-1371	467	11	iterative	iterative	NOUN
ejpam-1371	467	12	methods	method	NOUN
ejpam-1371	467	13	of	of	ADP
ejpam-1371	467	14	absolutely	absolutely	ADV
ejpam-1371	467	15	generalized	generalized	ADJ
ejpam-1371	467	16	dominated	dominate	VERB
ejpam-1371	467	17	differential	differential	ADJ
ejpam-1371	467	18	variational	variational	ADJ
ejpam-1371	467	19	inequality	inequality	NOUN
ejpam-1371	467	20	problems	problem	NOUN
ejpam-1371	467	21	in	in	ADP
ejpam-1371	467	22	hilbert	hilbert	NOUN
ejpam-1371	467	23	spaces	space	NOUN
ejpam-1371	467	24	deals	deal	NOUN
ejpam-1371	467	25	with	with	ADP
ejpam-1371	467	26	the	the	DET
ejpam-1371	467	27	parameter	parameter	NOUN
ejpam-1371	467	28	that	that	PRON
ejpam-1371	467	29	varies	vary	VERB
ejpam-1371	467	30	from	from	ADP
ejpam-1371	467	31	step	step	NOUN
ejpam-1371	467	32	to	to	PART
ejpam-1371	467	33	step	step	VERB
ejpam-1371	467	34	under	under	ADP
ejpam-1371	467	35	the	the	DET
ejpam-1371	467	36	given	give	VERB
ejpam-1371	467	37	assumptions	assumption	NOUN
ejpam-1371	467	38	.	.	PUNCT
ejpam-1371	468	1	we	we	PRON
ejpam-1371	468	2	believe	believe	VERB
ejpam-1371	468	3	that	that	SCONJ
ejpam-1371	468	4	this	this	DET
ejpam-1371	468	5	iterative	iterative	NOUN
ejpam-1371	468	6	approach	approach	NOUN
ejpam-1371	468	7	is	be	AUX
ejpam-1371	468	8	especially	especially	ADV
ejpam-1371	468	9	fruitful	fruitful	ADJ
ejpam-1371	468	10	to	to	PART
ejpam-1371	468	11	solve	solve	VERB
ejpam-1371	468	12	various	various	ADJ
ejpam-1371	468	13	minimization	minimization	NOUN
ejpam-1371	468	14	problems	problem	NOUN
ejpam-1371	468	15	in	in	ADP
ejpam-1371	468	16	mathematical	mathematical	ADJ
ejpam-1371	468	17	modelling	modelling	NOUN
ejpam-1371	468	18	.	.	PUNCT
ejpam-1371	469	1	furthermore	furthermore	ADV
ejpam-1371	469	2	,	,	PUNCT
ejpam-1371	469	3	with	with	ADP
ejpam-1371	469	4	the	the	DET
ejpam-1371	469	5	concept	concept	NOUN
ejpam-1371	469	6	of	of	ADP
ejpam-1371	469	7	fixed	fix	VERB
ejpam-1371	469	8	point	point	NOUN
ejpam-1371	469	9	inclusion	inclusion	NOUN
ejpam-1371	469	10	set	set	NOUN
ejpam-1371	469	11	,	,	PUNCT
ejpam-1371	469	12	the	the	DET
ejpam-1371	469	13	application	application	NOUN
ejpam-1371	469	14	of	of	ADP
ejpam-1371	469	15	the	the	DET
ejpam-1371	469	16	existence	existence	NOUN
ejpam-1371	469	17	theorem	theorem	NOUN
ejpam-1371	469	18	of	of	ADP
ejpam-1371	469	19	(	(	PUNCT
ejpam-1371	469	20	gddvip	gddvip	NOUN
ejpam-1371	469	21	)	)	PUNCT
ejpam-1371	469	22	in	in	ADP
ejpam-1371	469	23	riemannian	riemannian	ADJ
ejpam-1371	469	24	n	n	CCONJ
ejpam-1371	469	25	-	-	PUNCT
ejpam-1371	469	26	manifolds	manifold	NOUN
ejpam-1371	469	27	can	can	AUX
ejpam-1371	469	28	be	be	AUX
ejpam-1371	469	29	useful	useful	ADJ
ejpam-1371	469	30	to	to	PART
ejpam-1371	469	31	study	study	VERB
ejpam-1371	469	32	the	the	DET
ejpam-1371	469	33	generalized	generalize	VERB
ejpam-1371	469	34	obstacle	obstacle	NOUN
ejpam-1371	469	35	problems	problem	NOUN
ejpam-1371	469	36	,	,	PUNCT
ejpam-1371	469	37	generalized	generalized	ADJ
ejpam-1371	469	38	elastic	elastic	ADJ
ejpam-1371	469	39	plastic	plastic	NOUN
ejpam-1371	469	40	torsion	torsion	NOUN
ejpam-1371	469	41	problems	problem	NOUN
ejpam-1371	469	42	,	,	PUNCT
ejpam-1371	469	43	and	and	CCONJ
ejpam-1371	469	44	so	so	ADV
ejpam-1371	469	45	on	on	ADV
ejpam-1371	469	46	.	.	PUNCT
ejpam-1371	470	1	references	reference	NOUN
ejpam-1371	470	2	[	[	X
ejpam-1371	470	3	1	1	NUM
ejpam-1371	470	4	]	]	PUNCT
ejpam-1371	470	5	s.	s.	PROPN
ejpam-1371	470	6	adly	adly	PROPN
ejpam-1371	470	7	.	.	PUNCT
ejpam-1371	471	1	perturbed	perturb	VERB
ejpam-1371	471	2	algorithms	algorithm	NOUN
ejpam-1371	471	3	and	and	CCONJ
ejpam-1371	471	4	sensitivity	sensitivity	NOUN
ejpam-1371	471	5	analysis	analysis	NOUN
ejpam-1371	471	6	for	for	ADP
ejpam-1371	471	7	a	a	DET
ejpam-1371	471	8	general	general	ADJ
ejpam-1371	471	9	class	class	NOUN
ejpam-1371	471	10	of	of	ADP
ejpam-1371	471	11	variational	variational	ADJ
ejpam-1371	471	12	inclusions	inclusion	NOUN
ejpam-1371	471	13	.	.	PUNCT
ejpam-1371	472	1	j.	j.	PROPN
ejpam-1371	472	2	math	math	PROPN
ejpam-1371	472	3	.	.	PUNCT
ejpam-1371	473	1	anal	anal	PROPN
ejpam-1371	473	2	.	.	PUNCT
ejpam-1371	474	1	appl	appl	PROPN
ejpam-1371	474	2	.	.	PROPN
ejpam-1371	474	3	,	,	PUNCT
ejpam-1371	474	4	201(3):609	201(3):609	NOUN
ejpam-1371	474	5	–	–	PUNCT
ejpam-1371	474	6	630	630	NUM
ejpam-1371	474	7	,	,	PUNCT
ejpam-1371	474	8	1996	1996	NUM
ejpam-1371	474	9	.	.	PUNCT
ejpam-1371	475	1	[	[	X
ejpam-1371	475	2	2	2	NUM
ejpam-1371	475	3	]	]	PUNCT
ejpam-1371	475	4	c.	c.	NOUN
ejpam-1371	475	5	bardaro	bardaro	PROPN
ejpam-1371	475	6	and	and	CCONJ
ejpam-1371	475	7	r.	r.	PROPN
ejpam-1371	475	8	ceppitelli	ceppitelli	PROPN
ejpam-1371	475	9	.	.	PUNCT
ejpam-1371	476	1	some	some	DET
ejpam-1371	476	2	further	further	ADJ
ejpam-1371	476	3	generalizations	generalization	NOUN
ejpam-1371	476	4	of	of	ADP
ejpam-1371	476	5	knaster	knaster	NOUN
ejpam-1371	476	6	-	-	PUNCT
ejpam-1371	476	7	kuratowskimazurkiezicz	kuratowskimazurkiezicz	NOUN
ejpam-1371	476	8	theorem	theorem	NOUN
ejpam-1371	476	9	and	and	CCONJ
ejpam-1371	476	10	minimax	minimax	NOUN
ejpam-1371	476	11	inequalities	inequality	NOUN
ejpam-1371	476	12	.	.	PUNCT
ejpam-1371	477	1	journal	journal	PROPN
ejpam-1371	477	2	of	of	ADP
ejpam-1371	477	3	mathematical	mathematical	ADJ
ejpam-1371	477	4	analysis	analysis	NOUN
ejpam-1371	477	5	and	and	CCONJ
ejpam-1371	477	6	applications	application	NOUN
ejpam-1371	477	7	,	,	PUNCT
ejpam-1371	477	8	132(2):484	132(2):484	NOUN
ejpam-1371	477	9	–	–	PUNCT
ejpam-1371	477	10	490	490	NUM
ejpam-1371	477	11	,	,	PUNCT
ejpam-1371	477	12	1988	1988	NUM
ejpam-1371	477	13	.	.	PUNCT
ejpam-1371	478	1	[	[	X
ejpam-1371	478	2	3	3	NUM
ejpam-1371	478	3	]	]	PUNCT
ejpam-1371	478	4	a.	a.	NOUN
ejpam-1371	478	5	behera	behera	PROPN
ejpam-1371	478	6	and	and	CCONJ
ejpam-1371	478	7	p.k	p.k	PROPN
ejpam-1371	478	8	.	.	PUNCT
ejpam-1371	479	1	das	das	PROPN
ejpam-1371	479	2	.	.	PUNCT
ejpam-1371	480	1	variational	variational	ADJ
ejpam-1371	480	2	inequality	inequality	NOUN
ejpam-1371	480	3	problems	problem	NOUN
ejpam-1371	480	4	in	in	ADP
ejpam-1371	480	5	h	h	NOUN
ejpam-1371	480	6	-	-	PUNCT
ejpam-1371	480	7	spaces	space	NOUN
ejpam-1371	480	8	.	.	PUNCT
ejpam-1371	481	1	international	international	ADJ
ejpam-1371	481	2	journal	journal	PROPN
ejpam-1371	481	3	of	of	ADP
ejpam-1371	481	4	mathematics	mathematics	PROPN
ejpam-1371	481	5	and	and	CCONJ
ejpam-1371	481	6	mathematical	mathematical	ADJ
ejpam-1371	481	7	sciences	science	NOUN
ejpam-1371	481	8	,	,	PUNCT
ejpam-1371	481	9	article	article	NOUN
ejpam-1371	481	10	i	i	PROPN
ejpam-1371	481	11	d	d	PROPN
ejpam-1371	481	12	78545	78545	NUM
ejpam-1371	481	13	,	,	PUNCT
ejpam-1371	481	14	pages	page	NOUN
ejpam-1371	481	15	1	1	NUM
ejpam-1371	481	16	–	–	SYM
ejpam-1371	481	17	18	18	NUM
ejpam-1371	481	18	,	,	PUNCT
ejpam-1371	481	19	2006	2006	NUM
ejpam-1371	481	20	.	.	PUNCT
ejpam-1371	482	1	[	[	X
ejpam-1371	482	2	4	4	NUM
ejpam-1371	482	3	]	]	PUNCT
ejpam-1371	482	4	a.	a.	NOUN
ejpam-1371	482	5	behera	behera	PROPN
ejpam-1371	482	6	and	and	CCONJ
ejpam-1371	482	7	g.	g.	PROPN
ejpam-1371	482	8	k.	k.	PROPN
ejpam-1371	482	9	panda	panda	PROPN
ejpam-1371	482	10	.	.	PUNCT
ejpam-1371	483	1	a	a	DET
ejpam-1371	483	2	generalization	generalization	NOUN
ejpam-1371	483	3	of	of	ADP
ejpam-1371	483	4	browder	browder	PROPN
ejpam-1371	483	5	’s	’s	PART
ejpam-1371	483	6	theorem	theorem	PROPN
ejpam-1371	483	7	.	.	PROPN
ejpam-1371	484	1	bull	bull	PROPN
ejpam-1371	484	2	.	.	PUNCT
ejpam-1371	484	3	inst	inst	PROPN
ejpam-1371	484	4	.	.	PUNCT
ejpam-1371	485	1	math	math	NOUN
ejpam-1371	485	2	.	.	PUNCT
ejpam-1371	485	3	,	,	PUNCT
ejpam-1371	485	4	acad	acad	PROPN
ejpam-1371	485	5	.	.	PUNCT
ejpam-1371	486	1	sin	sin	NOUN
ejpam-1371	486	2	.	.	PUNCT
ejpam-1371	486	3	,	,	PUNCT
ejpam-1371	486	4	21:183	21:183	NUM
ejpam-1371	486	5	–	–	PUNCT
ejpam-1371	486	6	186	186	NUM
ejpam-1371	486	7	,	,	PUNCT
ejpam-1371	486	8	1993	1993	NUM
ejpam-1371	486	9	.	.	PUNCT
ejpam-1371	487	1	[	[	X
ejpam-1371	487	2	5	5	NUM
ejpam-1371	487	3	]	]	PUNCT
ejpam-1371	487	4	a.	a.	NOUN
ejpam-1371	487	5	behera	behera	PROPN
ejpam-1371	487	6	and	and	CCONJ
ejpam-1371	487	7	g.	g.	PROPN
ejpam-1371	487	8	k.	k.	PROPN
ejpam-1371	487	9	panda	panda	PROPN
ejpam-1371	487	10	.	.	PUNCT
ejpam-1371	488	1	a	a	DET
ejpam-1371	488	2	generalization	generalization	NOUN
ejpam-1371	488	3	of	of	ADP
ejpam-1371	488	4	minty	minty	PROPN
ejpam-1371	488	5	’s	’s	PART
ejpam-1371	488	6	lemma	lemma	PROPN
ejpam-1371	488	7	.	.	PUNCT
ejpam-1371	489	1	indian	indian	PROPN
ejpam-1371	489	2	j.	j.	PROPN
ejpam-1371	489	3	pure	pure	PROPN
ejpam-1371	489	4	appl	appl	PROPN
ejpam-1371	489	5	.	.	PUNCT
ejpam-1371	489	6	math	math	PROPN
ejpam-1371	489	7	.	.	PUNCT
ejpam-1371	489	8	,	,	PUNCT
ejpam-1371	489	9	28(7):897	28(7):897	PROPN
ejpam-1371	489	10	–	–	PUNCT
ejpam-1371	489	11	903	903	NUM
ejpam-1371	489	12	,	,	PUNCT
ejpam-1371	489	13	1997	1997	NUM
ejpam-1371	489	14	.	.	PUNCT
ejpam-1371	490	1	[	[	X
ejpam-1371	490	2	6	6	NUM
ejpam-1371	490	3	]	]	PUNCT
ejpam-1371	490	4	a.	a.	NOUN
ejpam-1371	490	5	behera	behera	PROPN
ejpam-1371	490	6	and	and	CCONJ
ejpam-1371	490	7	g.	g.	PROPN
ejpam-1371	490	8	k.	k.	PROPN
ejpam-1371	490	9	panda	panda	PROPN
ejpam-1371	490	10	.	.	PUNCT
ejpam-1371	491	1	generalized	generalize	VERB
ejpam-1371	491	2	variational	variational	ADJ
ejpam-1371	491	3	-	-	PUNCT
ejpam-1371	491	4	type	type	NOUN
ejpam-1371	491	5	inequality	inequality	NOUN
ejpam-1371	491	6	in	in	ADP
ejpam-1371	491	7	hausdorff	hausdorff	PROPN
ejpam-1371	491	8	topological	topological	ADJ
ejpam-1371	491	9	vector	vector	NOUN
ejpam-1371	491	10	space	space	NOUN
ejpam-1371	491	11	.	.	PUNCT
ejpam-1371	492	1	indian	indian	PROPN
ejpam-1371	492	2	j.	j.	PROPN
ejpam-1371	492	3	pure	pure	PROPN
ejpam-1371	492	4	appl	appl	PROPN
ejpam-1371	492	5	.	.	PUNCT
ejpam-1371	492	6	math	math	PROPN
ejpam-1371	492	7	.	.	PUNCT
ejpam-1371	492	8	,	,	PUNCT
ejpam-1371	492	9	28(3):343	28(3):343	PROPN
ejpam-1371	492	10	–	–	PUNCT
ejpam-1371	492	11	349	349	NUM
ejpam-1371	492	12	,	,	PUNCT
ejpam-1371	492	13	1997	1997	NUM
ejpam-1371	492	14	.	.	PUNCT
ejpam-1371	493	1	[	[	X
ejpam-1371	493	2	7	7	X
ejpam-1371	493	3	]	]	X
ejpam-1371	493	4	f.e	f.e	PROPN
ejpam-1371	493	5	.	.	PROPN
ejpam-1371	493	6	browder	browder	PROPN
ejpam-1371	493	7	and	and	CCONJ
ejpam-1371	493	8	j.	j.	PROPN
ejpam-1371	493	9	mond	mond	PROPN
ejpam-1371	493	10	.	.	PUNCT
ejpam-1371	494	1	nonlinear	nonlinear	ADJ
ejpam-1371	494	2	monotone	monotone	ADJ
ejpam-1371	494	3	operators	operator	NOUN
ejpam-1371	494	4	and	and	CCONJ
ejpam-1371	494	5	convex	convex	NOUN
ejpam-1371	494	6	sets	set	NOUN
ejpam-1371	494	7	in	in	ADP
ejpam-1371	494	8	banach	banach	NOUN
ejpam-1371	494	9	spaces	space	NOUN
ejpam-1371	494	10	.	.	PUNCT
ejpam-1371	495	1	bull	bull	NOUN
ejpam-1371	495	2	.	.	PUNCT
ejpam-1371	496	1	amer	amer	PROPN
ejpam-1371	496	2	.	.	PUNCT
ejpam-1371	496	3	math	math	PROPN
ejpam-1371	496	4	.	.	PUNCT
ejpam-1371	497	1	soc	soc	PROPN
ejpam-1371	497	2	.	.	PUNCT
ejpam-1371	497	3	,	,	PUNCT
ejpam-1371	497	4	17:780	17:780	NUM
ejpam-1371	497	5	–	–	PUNCT
ejpam-1371	497	6	785	785	NUM
ejpam-1371	497	7	,	,	PUNCT
ejpam-1371	497	8	1965	1965	NUM
ejpam-1371	497	9	.	.	PUNCT
ejpam-1371	498	1	[	[	X
ejpam-1371	498	2	8	8	NUM
ejpam-1371	498	3	]	]	X
ejpam-1371	498	4	b.v.limaye	b.v.limaye	NOUN
ejpam-1371	498	5	.	.	PUNCT
ejpam-1371	499	1	functional	functional	ADJ
ejpam-1371	499	2	analysis	analysis	NOUN
ejpam-1371	499	3	.	.	PUNCT
ejpam-1371	500	1	new	new	ADJ
ejpam-1371	500	2	age	age	NOUN
ejpam-1371	500	3	international	international	ADJ
ejpam-1371	500	4	(	(	PUNCT
ejpam-1371	500	5	p	p	NOUN
ejpam-1371	500	6	)	)	PUNCT
ejpam-1371	500	7	limited	limited	ADJ
ejpam-1371	500	8	,	,	PUNCT
ejpam-1371	500	9	new	new	ADJ
ejpam-1371	500	10	delhi	delhi	PROPN
ejpam-1371	500	11	,	,	PUNCT
ejpam-1371	500	12	1997	1997	NUM
ejpam-1371	500	13	.	.	PUNCT
ejpam-1371	501	1	[	[	X
ejpam-1371	501	2	9	9	NUM
ejpam-1371	501	3	]	]	PUNCT
ejpam-1371	501	4	m.	m.	NOUN
ejpam-1371	501	5	chipot	chipot	NOUN
ejpam-1371	501	6	.	.	PUNCT
ejpam-1371	502	1	variational	variational	ADJ
ejpam-1371	502	2	inequalities	inequality	NOUN
ejpam-1371	502	3	and	and	CCONJ
ejpam-1371	502	4	flow	flow	NOUN
ejpam-1371	502	5	in	in	ADP
ejpam-1371	502	6	porus	porus	NOUN
ejpam-1371	502	7	media	medium	NOUN
ejpam-1371	502	8	.	.	PUNCT
ejpam-1371	503	1	springer	springer	NOUN
ejpam-1371	503	2	-	-	PUNCT
ejpam-1371	503	3	verlag	verlag	PROPN
ejpam-1371	503	4	,	,	PUNCT
ejpam-1371	503	5	1984	1984	NUM
ejpam-1371	503	6	.	.	PUNCT
ejpam-1371	504	1	[	[	X
ejpam-1371	504	2	10	10	NUM
ejpam-1371	504	3	]	]	X
ejpam-1371	504	4	f.	f.	PROPN
ejpam-1371	504	5	h.	h.	PROPN
ejpam-1371	504	6	clarke	clarke	PROPN
ejpam-1371	504	7	.	.	PUNCT
ejpam-1371	504	8	optimization	optimization	NOUN
ejpam-1371	504	9	and	and	CCONJ
ejpam-1371	504	10	nonsmooth	nonsmooth	ADJ
ejpam-1371	504	11	analysis	analysis	NOUN
ejpam-1371	504	12	.	.	PUNCT
ejpam-1371	505	1	a	a	DET
ejpam-1371	505	2	wiley	wiley	NOUN
ejpam-1371	505	3	-	-	PUNCT
ejpam-1371	505	4	interscience	interscience	NOUN
ejpam-1371	505	5	publication	publication	NOUN
ejpam-1371	505	6	,	,	PUNCT
ejpam-1371	505	7	new	new	PROPN
ejpam-1371	505	8	york	york	PROPN
ejpam-1371	505	9	,	,	PUNCT
ejpam-1371	505	10	1983	1983	NUM
ejpam-1371	505	11	.	.	PUNCT
ejpam-1371	506	1	[	[	X
ejpam-1371	506	2	11	11	NUM
ejpam-1371	506	3	]	]	PUNCT
ejpam-1371	506	4	p.	p.	NOUN
ejpam-1371	506	5	k.	k.	PROPN
ejpam-1371	507	1	das	das	PROPN
ejpam-1371	507	2	and	and	CCONJ
ejpam-1371	507	3	s.	s.	PROPN
ejpam-1371	507	4	k.	k.	PROPN
ejpam-1371	507	5	mohanta	mohanta	PROPN
ejpam-1371	507	6	.	.	PUNCT
ejpam-1371	508	1	generalized	generalize	VERB
ejpam-1371	508	2	vector	vector	NOUN
ejpam-1371	508	3	variational	variational	ADJ
ejpam-1371	508	4	inequality	inequality	NOUN
ejpam-1371	508	5	problem	problem	NOUN
ejpam-1371	508	6	,	,	PUNCT
ejpam-1371	508	7	generalized	generalized	ADJ
ejpam-1371	508	8	vector	vector	NOUN
ejpam-1371	508	9	complementarity	complementarity	NOUN
ejpam-1371	508	10	problem	problem	NOUN
ejpam-1371	508	11	in	in	ADP
ejpam-1371	508	12	hilbert	hilbert	PROPN
ejpam-1371	508	13	spaces	space	NOUN
ejpam-1371	508	14	,	,	PUNCT
ejpam-1371	508	15	riemannian	riemannian	ADJ
ejpam-1371	508	16	n	n	CCONJ
ejpam-1371	508	17	-	-	PUNCT
ejpam-1371	508	18	manifold	manifold	ADJ
ejpam-1371	508	19	,	,	PUNCT
ejpam-1371	508	20	sn	sn	PROPN
ejpam-1371	508	21	and	and	CCONJ
ejpam-1371	508	22	ordered	order	VERB
ejpam-1371	508	23	topological	topological	ADJ
ejpam-1371	508	24	vector	vector	NOUN
ejpam-1371	508	25	spaces	space	NOUN
ejpam-1371	508	26	:	:	PUNCT
ejpam-1371	508	27	a	a	DET
ejpam-1371	508	28	study	study	NOUN
ejpam-1371	508	29	using	use	VERB
ejpam-1371	508	30	fixed	fix	VERB
ejpam-1371	508	31	point	point	NOUN
ejpam-1371	508	32	theorem	theorem	NOUN
ejpam-1371	508	33	and	and	CCONJ
ejpam-1371	508	34	homotopy	homotopy	NOUN
ejpam-1371	508	35	function	function	NOUN
ejpam-1371	508	36	.	.	PUNCT
ejpam-1371	509	1	advances	advance	NOUN
ejpam-1371	509	2	in	in	ADP
ejpam-1371	509	3	nonlinear	nonlinear	ADJ
ejpam-1371	509	4	variational	variational	ADJ
ejpam-1371	509	5	inequalities	inequality	NOUN
ejpam-1371	509	6	,	,	PUNCT
ejpam-1371	509	7	12(2):37	12(2):37	NUM
ejpam-1371	509	8	–	–	PUNCT
ejpam-1371	509	9	47	47	NUM
ejpam-1371	509	10	,	,	PUNCT
ejpam-1371	509	11	2009	2009	NUM
ejpam-1371	509	12	.	.	PUNCT
ejpam-1371	510	1	references	reference	NOUN
ejpam-1371	510	2	360	360	NUM
ejpam-1371	511	1	[	[	X
ejpam-1371	511	2	12	12	NUM
ejpam-1371	511	3	]	]	X
ejpam-1371	511	4	x.p	x.p	PROPN
ejpam-1371	511	5	.	.	PUNCT
ejpam-1371	511	6	ding	ding	PROPN
ejpam-1371	511	7	.	.	PUNCT
ejpam-1371	512	1	perturbed	perturb	VERB
ejpam-1371	512	2	proximal	proximal	ADJ
ejpam-1371	512	3	point	point	NOUN
ejpam-1371	512	4	algorithm	algorithm	NOUN
ejpam-1371	512	5	for	for	ADP
ejpam-1371	512	6	generalized	generalized	ADJ
ejpam-1371	512	7	quasi	quasi	ADJ
ejpam-1371	512	8	-	-	ADJ
ejpam-1371	512	9	variational	variational	ADJ
ejpam-1371	512	10	inclusions	inclusion	NOUN
ejpam-1371	512	11	.	.	PUNCT
ejpam-1371	513	1	j.	j.	PROPN
ejpam-1371	513	2	math	math	PROPN
ejpam-1371	513	3	.	.	PUNCT
ejpam-1371	514	1	anal	anal	PROPN
ejpam-1371	514	2	.	.	PUNCT
ejpam-1371	514	3	appl	appl	PROPN
ejpam-1371	514	4	.	.	PROPN
ejpam-1371	515	1	,	,	PUNCT
ejpam-1371	515	2	210(1):88	210(1):88	NUM
ejpam-1371	515	3	–	–	PUNCT
ejpam-1371	515	4	101	101	NUM
ejpam-1371	515	5	,	,	PUNCT
ejpam-1371	515	6	1997	1997	NUM
ejpam-1371	515	7	.	.	PUNCT
ejpam-1371	516	1	[	[	X
ejpam-1371	516	2	13	13	NUM
ejpam-1371	516	3	]	]	X
ejpam-1371	516	4	x.p	x.p	PROPN
ejpam-1371	516	5	.	.	PUNCT
ejpam-1371	516	6	ding	ding	PROPN
ejpam-1371	516	7	.	.	PUNCT
ejpam-1371	517	1	perturbed	perturb	VERB
ejpam-1371	517	2	proximal	proximal	ADJ
ejpam-1371	517	3	point	point	NOUN
ejpam-1371	517	4	algorithm	algorithm	NOUN
ejpam-1371	517	5	for	for	ADP
ejpam-1371	517	6	generalized	generalized	ADJ
ejpam-1371	517	7	quasi	quasi	ADJ
ejpam-1371	517	8	-	-	ADJ
ejpam-1371	517	9	variational	variational	ADJ
ejpam-1371	517	10	inclusions	inclusion	NOUN
ejpam-1371	517	11	.	.	PUNCT
ejpam-1371	518	1	j.	j.	PROPN
ejpam-1371	518	2	math	math	PROPN
ejpam-1371	518	3	.	.	PUNCT
ejpam-1371	519	1	anal	anal	PROPN
ejpam-1371	519	2	.	.	PUNCT
ejpam-1371	520	1	appl	appl	PROPN
ejpam-1371	520	2	.	.	PROPN
ejpam-1371	520	3	,	,	PUNCT
ejpam-1371	520	4	122:267	122:267	NOUN
ejpam-1371	520	5	–	–	PUNCT
ejpam-1371	520	6	282	282	NUM
ejpam-1371	520	7	,	,	PUNCT
ejpam-1371	520	8	2001	2001	NUM
ejpam-1371	520	9	.	.	PUNCT
ejpam-1371	521	1	[	[	X
ejpam-1371	521	2	14	14	NUM
ejpam-1371	521	3	]	]	X
ejpam-1371	521	4	g.	g.	PROPN
ejpam-1371	521	5	duvaut	duvaut	PROPN
ejpam-1371	521	6	and	and	CCONJ
ejpam-1371	521	7	j.	j.	PROPN
ejpam-1371	521	8	l.	l.	PROPN
ejpam-1371	521	9	lions	lions	PROPN
ejpam-1371	521	10	.	.	PUNCT
ejpam-1371	522	1	inequalities	inequality	NOUN
ejpam-1371	522	2	in	in	ADP
ejpam-1371	522	3	mechanics	mechanic	NOUN
ejpam-1371	522	4	and	and	CCONJ
ejpam-1371	522	5	physics	physics	NOUN
ejpam-1371	522	6	translated	translate	VERB
ejpam-1371	522	7	under	under	ADP
ejpam-1371	522	8	the	the	DET
ejpam-1371	522	9	title	title	NOUN
ejpam-1371	522	10	neravenstva	neravenstva	NOUN
ejpam-1371	522	11	v	v	NUM
ejpam-1371	522	12	mekhanike	mekhanike	NOUN
ejpam-1371	522	13	i	i	PRON
ejpam-1371	522	14	fizike	fizike	VERB
ejpam-1371	522	15	,	,	PUNCT
ejpam-1371	522	16	moscow	moscow	PROPN
ejpam-1371	522	17	,	,	PUNCT
ejpam-1371	522	18	1980	1980	NUM
ejpam-1371	522	19	.	.	PUNCT
ejpam-1371	523	1	berlin	berlin	PROPN
ejpam-1371	523	2	,	,	PUNCT
ejpam-1371	523	3	moscow	moscow	PROPN
ejpam-1371	523	4	,	,	PUNCT
ejpam-1371	523	5	1976	1976	NUM
ejpam-1371	523	6	.	.	PUNCT
ejpam-1371	524	1	[	[	X
ejpam-1371	524	2	15	15	NUM
ejpam-1371	524	3	]	]	X
ejpam-1371	524	4	i.	i.	NOUN
ejpam-1371	524	5	ekeland	ekeland	PROPN
ejpam-1371	524	6	and	and	CCONJ
ejpam-1371	524	7	r.	r.	PROPN
ejpam-1371	524	8	temam	temam	NOUN
ejpam-1371	524	9	.	.	PUNCT
ejpam-1371	525	1	convex	convex	VERB
ejpam-1371	525	2	analysis	analysis	NOUN
ejpam-1371	525	3	and	and	CCONJ
ejpam-1371	525	4	variational	variational	ADJ
ejpam-1371	525	5	problems	problem	NOUN
ejpam-1371	525	6	.	.	PUNCT
ejpam-1371	526	1	amsterdam	amsterdam	PROPN
ejpam-1371	526	2	,	,	PUNCT
ejpam-1371	526	3	northholland	northholland	NOUN
ejpam-1371	526	4	,	,	PUNCT
ejpam-1371	526	5	1976	1976	NUM
ejpam-1371	526	6	.	.	PUNCT
ejpam-1371	527	1	[	[	X
ejpam-1371	527	2	16	16	NUM
ejpam-1371	527	3	]	]	PUNCT
ejpam-1371	527	4	m.	m.	NOUN
ejpam-1371	527	5	a.	a.	PROPN
ejpam-1371	527	6	hanson	hanson	PROPN
ejpam-1371	527	7	.	.	PUNCT
ejpam-1371	528	1	on	on	ADP
ejpam-1371	528	2	sufficiency	sufficiency	NOUN
ejpam-1371	528	3	of	of	ADP
ejpam-1371	528	4	the	the	DET
ejpam-1371	528	5	kuhn	kuhn	PROPN
ejpam-1371	528	6	-	-	PUNCT
ejpam-1371	528	7	tucker	tucker	PROPN
ejpam-1371	528	8	conditions	condition	NOUN
ejpam-1371	528	9	.	.	PUNCT
ejpam-1371	529	1	journal	journal	NOUN
ejpam-1371	529	2	of	of	ADP
ejpam-1371	529	3	mathematical	mathematical	ADJ
ejpam-1371	529	4	analysis	analysis	NOUN
ejpam-1371	529	5	and	and	CCONJ
ejpam-1371	529	6	applications	application	NOUN
ejpam-1371	529	7	,	,	PUNCT
ejpam-1371	529	8	142:305	142:305	NOUN
ejpam-1371	529	9	–	–	PUNCT
ejpam-1371	529	10	310	310	NUM
ejpam-1371	529	11	,	,	PUNCT
ejpam-1371	529	12	1961	1961	NUM
ejpam-1371	529	13	.	.	PUNCT
ejpam-1371	530	1	[	[	X
ejpam-1371	530	2	17	17	NUM
ejpam-1371	530	3	]	]	PUNCT
ejpam-1371	530	4	a.	a.	NOUN
ejpam-1371	530	5	hassouni	hassouni	PROPN
ejpam-1371	530	6	and	and	CCONJ
ejpam-1371	530	7	a.	a.	NOUN
ejpam-1371	530	8	moudafi	moudafi	PROPN
ejpam-1371	530	9	.	.	PUNCT
ejpam-1371	531	1	a	a	DET
ejpam-1371	531	2	perturbed	perturb	VERB
ejpam-1371	531	3	algorithm	algorithm	NOUN
ejpam-1371	531	4	for	for	ADP
ejpam-1371	531	5	variational	variational	ADJ
ejpam-1371	531	6	inequalities	inequality	NOUN
ejpam-1371	531	7	.	.	PUNCT
ejpam-1371	532	1	j.	j.	PROPN
ejpam-1371	532	2	math	math	PROPN
ejpam-1371	532	3	.	.	PUNCT
ejpam-1371	533	1	anal	anal	PROPN
ejpam-1371	533	2	.	.	PUNCT
ejpam-1371	534	1	appl	appl	PROPN
ejpam-1371	534	2	.	.	PROPN
ejpam-1371	534	3	,	,	PUNCT
ejpam-1371	534	4	185:706	185:706	PROPN
ejpam-1371	534	5	–	–	PUNCT
ejpam-1371	534	6	712	712	NUM
ejpam-1371	534	7	,	,	PUNCT
ejpam-1371	534	8	1994	1994	NUM
ejpam-1371	534	9	.	.	PUNCT
ejpam-1371	535	1	[	[	X
ejpam-1371	535	2	18	18	NUM
ejpam-1371	535	3	]	]	X
ejpam-1371	535	4	n.j	n.j	PROPN
ejpam-1371	535	5	.	.	PROPN
ejpam-1371	535	6	haung	haung	PROPN
ejpam-1371	535	7	.	.	PUNCT
ejpam-1371	536	1	generalized	generalize	VERB
ejpam-1371	536	2	nonlinear	nonlinear	ADJ
ejpam-1371	536	3	variational	variational	ADJ
ejpam-1371	536	4	inclusions	inclusion	NOUN
ejpam-1371	536	5	with	with	ADP
ejpam-1371	536	6	noncompact	noncompact	NOUN
ejpam-1371	536	7	valued	value	VERB
ejpam-1371	536	8	mappings	mapping	NOUN
ejpam-1371	536	9	.	.	PUNCT
ejpam-1371	537	1	appl	appl	PROPN
ejpam-1371	537	2	.	.	PROPN
ejpam-1371	537	3	math	math	PROPN
ejpam-1371	537	4	.	.	PUNCT
ejpam-1371	538	1	lett	lett	PROPN
ejpam-1371	538	2	.	.	PROPN
ejpam-1371	538	3	,	,	PUNCT
ejpam-1371	538	4	9(3):25	9(3):25	NUM
ejpam-1371	538	5	–	–	PUNCT
ejpam-1371	538	6	29	29	NUM
ejpam-1371	538	7	,	,	PUNCT
ejpam-1371	538	8	1996	1996	NUM
ejpam-1371	538	9	.	.	PUNCT
ejpam-1371	539	1	[	[	X
ejpam-1371	539	2	19	19	NUM
ejpam-1371	539	3	]	]	PUNCT
ejpam-1371	539	4	k.	k.	PROPN
ejpam-1371	539	5	r.	r.	PROPN
ejpam-1371	539	6	kazmi	kazmi	PROPN
ejpam-1371	539	7	.	.	PUNCT
ejpam-1371	540	1	mann	mann	PROPN
ejpam-1371	540	2	and	and	CCONJ
ejpam-1371	540	3	ishikawa	ishikawa	PROPN
ejpam-1371	540	4	type	type	NOUN
ejpam-1371	540	5	perturbed	perturb	VERB
ejpam-1371	540	6	iterative	iterative	ADJ
ejpam-1371	540	7	algorithms	algorithm	NOUN
ejpam-1371	540	8	for	for	ADP
ejpam-1371	540	9	generalized	generalized	ADJ
ejpam-1371	540	10	quasivariational	quasivariational	ADJ
ejpam-1371	540	11	inclusions	inclusion	NOUN
ejpam-1371	540	12	.	.	PUNCT
ejpam-1371	541	1	j.	j.	PROPN
ejpam-1371	541	2	math	math	PROPN
ejpam-1371	541	3	.	.	PUNCT
ejpam-1371	542	1	anal	anal	PROPN
ejpam-1371	542	2	.	.	PUNCT
ejpam-1371	543	1	appl	appl	PROPN
ejpam-1371	543	2	.	.	PROPN
ejpam-1371	543	3	,	,	PUNCT
ejpam-1371	543	4	209:572	209:572	PROPN
ejpam-1371	543	5	–	–	PUNCT
ejpam-1371	543	6	584	584	NUM
ejpam-1371	543	7	,	,	PUNCT
ejpam-1371	543	8	1997	1997	NUM
ejpam-1371	543	9	.	.	PUNCT
ejpam-1371	544	1	[	[	X
ejpam-1371	544	2	20	20	NUM
ejpam-1371	544	3	]	]	X
ejpam-1371	544	4	d.	d.	PROPN
ejpam-1371	544	5	kinderlehrer	kinderlehrer	PROPN
ejpam-1371	544	6	and	and	CCONJ
ejpam-1371	544	7	g.	g.	PROPN
ejpam-1371	544	8	stampacchia	stampacchia	PROPN
ejpam-1371	544	9	.	.	PUNCT
ejpam-1371	545	1	an	an	DET
ejpam-1371	545	2	introduction	introduction	NOUN
ejpam-1371	545	3	to	to	ADP
ejpam-1371	545	4	variational	variational	ADJ
ejpam-1371	545	5	inequalities	inequality	NOUN
ejpam-1371	545	6	and	and	CCONJ
ejpam-1371	545	7	their	their	PRON
ejpam-1371	545	8	applications	application	NOUN
ejpam-1371	545	9	.	.	PUNCT
ejpam-1371	546	1	acad	acad	PROPN
ejpam-1371	546	2	.	.	PUNCT
ejpam-1371	547	1	press	press	NOUN
ejpam-1371	547	2	,	,	PUNCT
ejpam-1371	547	3	1980	1980	NUM
ejpam-1371	547	4	.	.	PUNCT
ejpam-1371	548	1	[	[	X
ejpam-1371	548	2	21	21	NUM
ejpam-1371	548	3	]	]	X
ejpam-1371	548	4	j.	j.	PROPN
ejpam-1371	548	5	l.	l.	PROPN
ejpam-1371	548	6	lions	lions	PROPN
ejpam-1371	548	7	and	and	CCONJ
ejpam-1371	548	8	g.	g.	PROPN
ejpam-1371	548	9	stampacchia	stampacchia	PROPN
ejpam-1371	548	10	.	.	PUNCT
ejpam-1371	549	1	variational	variational	ADJ
ejpam-1371	549	2	inequality	inequality	NOUN
ejpam-1371	549	3	.	.	PUNCT
ejpam-1371	550	1	comm	comm	NOUN
ejpam-1371	550	2	.	.	PUNCT
ejpam-1371	551	1	pure	pure	ADJ
ejpam-1371	551	2	.	.	PUNCT
ejpam-1371	552	1	appl	appl	PROPN
ejpam-1371	552	2	.	.	PROPN
ejpam-1371	552	3	math	math	PROPN
ejpam-1371	552	4	.	.	PUNCT
ejpam-1371	553	1	,	,	PUNCT
ejpam-1371	553	2	48(1):493	48(1):493	NOUN
ejpam-1371	553	3	–	–	PUNCT
ejpam-1371	553	4	519	519	NUM
ejpam-1371	553	5	,	,	PUNCT
ejpam-1371	553	6	1967	1967	NUM
ejpam-1371	553	7	.	.	PUNCT
ejpam-1371	554	1	[	[	X
ejpam-1371	554	2	22	22	NUM
ejpam-1371	554	3	]	]	PUNCT
ejpam-1371	554	4	s.	s.	PROPN
ejpam-1371	554	5	mititelu	mititelu	PROPN
ejpam-1371	554	6	.	.	PUNCT
ejpam-1371	555	1	generalized	generalize	VERB
ejpam-1371	555	2	invexity	invexity	NOUN
ejpam-1371	555	3	and	and	CCONJ
ejpam-1371	555	4	vector	vector	NOUN
ejpam-1371	555	5	optimization	optimization	NOUN
ejpam-1371	555	6	on	on	ADP
ejpam-1371	555	7	differentiable	differentiable	ADJ
ejpam-1371	555	8	manifolds	manifold	NOUN
ejpam-1371	555	9	.	.	PUNCT
ejpam-1371	556	1	differential	differential	ADJ
ejpam-1371	556	2	geometry	geometry	NOUN
ejpam-1371	556	3	dynamical	dynamical	ADJ
ejpam-1371	556	4	systems	system	NOUN
ejpam-1371	556	5	,	,	PUNCT
ejpam-1371	556	6	3(1):21	3(1):21	NUM
ejpam-1371	556	7	–	–	PUNCT
ejpam-1371	556	8	31	31	NUM
ejpam-1371	556	9	„	„	SYM
ejpam-1371	556	10	2001	2001	NUM
ejpam-1371	556	11	.	.	PUNCT
ejpam-1371	557	1	[	[	X
ejpam-1371	557	2	23	23	NUM
ejpam-1371	557	3	]	]	PUNCT
ejpam-1371	557	4	j.	j.	PROPN
ejpam-1371	557	5	r.	r.	PROPN
ejpam-1371	557	6	munkres	munkres	PROPN
ejpam-1371	557	7	.	.	PUNCT
ejpam-1371	558	1	topology	topology	NOUN
ejpam-1371	558	2	.	.	PUNCT
ejpam-1371	559	1	,	,	PUNCT
ejpam-1371	559	2	volume	volume	NOUN
ejpam-1371	559	3	13	13	NUM
ejpam-1371	559	4	.	.	PUNCT
ejpam-1371	560	1	prentice	prentice	PROPN
ejpam-1371	560	2	hall	hall	PROPN
ejpam-1371	560	3	of	of	ADP
ejpam-1371	560	4	india	india	PROPN
ejpam-1371	560	5	pvt	pvt	PROPN
ejpam-1371	560	6	.	.	PROPN
ejpam-1371	560	7	ltd	ltd	PROPN
ejpam-1371	560	8	,	,	PUNCT
ejpam-1371	560	9	new	new	ADJ
ejpam-1371	560	10	delhi	delhi	PROPN
ejpam-1371	560	11	,	,	PUNCT
ejpam-1371	560	12	1999	1999	NUM
ejpam-1371	560	13	.	.	PUNCT
ejpam-1371	561	1	[	[	X
ejpam-1371	561	2	24	24	NUM
ejpam-1371	561	3	]	]	PUNCT
ejpam-1371	561	4	f.	f.	PROPN
ejpam-1371	561	5	giannessi	giannessi	PROPN
ejpam-1371	561	6	r.	r.	PROPN
ejpam-1371	561	7	w.	w.	PROPN
ejpam-1371	561	8	cottle	cottle	PROPN
ejpam-1371	561	9	and	and	CCONJ
ejpam-1371	561	10	j.	j.	PROPN
ejpam-1371	561	11	l.	l.	PROPN
ejpam-1371	561	12	lions	lions	PROPN
ejpam-1371	561	13	.	.	PUNCT
ejpam-1371	562	1	variational	variational	ADJ
ejpam-1371	562	2	inequality	inequality	NOUN
ejpam-1371	562	3	and	and	CCONJ
ejpam-1371	562	4	complementarity	complementarity	NOUN
ejpam-1371	562	5	problems	problem	NOUN
ejpam-1371	562	6	-	-	PUNCT
ejpam-1371	562	7	theory	theory	NOUN
ejpam-1371	562	8	and	and	CCONJ
ejpam-1371	562	9	application	application	NOUN
ejpam-1371	562	10	.	.	PUNCT
ejpam-1371	563	1	john	john	PROPN
ejpam-1371	563	2	wiley	wiley	PROPN
ejpam-1371	563	3	and	and	CCONJ
ejpam-1371	563	4	sons	son	NOUN
ejpam-1371	563	5	,	,	PUNCT
ejpam-1371	563	6	1980	1980	NUM
ejpam-1371	563	7	.	.	PUNCT
ejpam-1371	564	1	[	[	X
ejpam-1371	564	2	25	25	NUM
ejpam-1371	564	3	]	]	PUNCT
ejpam-1371	564	4	l.	l.	PROPN
ejpam-1371	564	5	serge	serge	PROPN
ejpam-1371	564	6	.	.	PUNCT
ejpam-1371	565	1	introduction	introduction	NOUN
ejpam-1371	565	2	to	to	ADP
ejpam-1371	565	3	differentiable	differentiable	ADJ
ejpam-1371	565	4	manifolds	manifold	NOUN
ejpam-1371	565	5	.	.	PUNCT
ejpam-1371	566	1	interscience	interscience	NOUN
ejpam-1371	566	2	publishers	publisher	NOUN
ejpam-1371	566	3	,	,	PUNCT
ejpam-1371	566	4	john	john	PROPN
ejpam-1371	566	5	wiley	wiley	PROPN
ejpam-1371	566	6	and	and	CCONJ
ejpam-1371	566	7	sons	son	NOUN
ejpam-1371	566	8	,	,	PUNCT
ejpam-1371	566	9	1962	1962	NUM
ejpam-1371	566	10	.	.	PUNCT
ejpam-1371	567	1	[	[	X
ejpam-1371	567	2	26	26	NUM
ejpam-1371	567	3	]	]	PUNCT
ejpam-1371	567	4	f.	f.	PROPN
ejpam-1371	567	5	p.	p.	PROPN
ejpam-1371	567	6	vasil’ev	vasil’ev	PROPN
ejpam-1371	567	7	.	.	PUNCT
ejpam-1371	568	1	chislennye	chislennye	PROPN
ejpam-1371	568	2	metody	metody	PROPN
ejpam-1371	568	3	resheniya	resheniya	PROPN
ejpam-1371	568	4	ekstremal’nykh	ekstremal’nykh	PROPN
ejpam-1371	568	5	zadach	zadach	PROPN
ejpam-1371	568	6	(	(	PUNCT
ejpam-1371	568	7	numerical	numerical	ADJ
ejpam-1371	568	8	methods	method	NOUN
ejpam-1371	568	9	for	for	ADP
ejpam-1371	568	10	solving	solve	VERB
ejpam-1371	568	11	extremal	extremal	ADJ
ejpam-1371	568	12	problems	problem	NOUN
ejpam-1371	568	13	)	)	PUNCT
ejpam-1371	568	14	.	.	PUNCT
ejpam-1371	569	1	moscow	moscow	PROPN
ejpam-1371	569	2	,	,	PUNCT
ejpam-1371	569	3	1988	1988	NUM
ejpam-1371	569	4	.	.	PUNCT
ejpam-1371	570	1	[	[	X
ejpam-1371	570	2	27	27	NUM
ejpam-1371	570	3	]	]	PUNCT
ejpam-1371	570	4	j.	j.	PROPN
ejpam-1371	570	5	w.	w.	PROPN
ejpam-1371	570	6	vick	vick	PROPN
ejpam-1371	570	7	.	.	PUNCT
ejpam-1371	570	8	homology	homology	PROPN
ejpam-1371	570	9	theory	theory	NOUN
ejpam-1371	570	10	,	,	PUNCT
ejpam-1371	570	11	an	an	DET
ejpam-1371	570	12	introduction	introduction	NOUN
ejpam-1371	570	13	to	to	ADP
ejpam-1371	570	14	algebraic	algebraic	ADJ
ejpam-1371	570	15	topology	topology	NOUN
ejpam-1371	570	16	.	.	PUNCT
ejpam-1371	571	1	academic	academic	ADJ
ejpam-1371	571	2	press	press	NOUN
ejpam-1371	571	3	,	,	PUNCT
ejpam-1371	571	4	new	new	PROPN
ejpam-1371	571	5	york	york	PROPN
ejpam-1371	571	6	,	,	PUNCT
ejpam-1371	571	7	1973	1973	NUM
ejpam-1371	571	8	.	.	PUNCT