id	sid	tid	token	lemma	pos
ejpam-2337	1	1	compile	compile	NOUN
ejpam-2337	1	2	/	/	SYM
ejpam-2337	1	3	output.dvi	output.dvi	NOUN
ejpam-2337	1	4	european	european	ADJ
ejpam-2337	1	5	journal	journal	NOUN
ejpam-2337	1	6	of	of	ADP
ejpam-2337	1	7	pure	pure	ADJ
ejpam-2337	1	8	and	and	CCONJ
ejpam-2337	1	9	applied	apply	VERB
ejpam-2337	1	10	mathematics	mathematic	NOUN
ejpam-2337	1	11	vol	vol	NOUN
ejpam-2337	1	12	.	.	PROPN
ejpam-2337	1	13	8	8	NUM
ejpam-2337	1	14	,	,	PUNCT
ejpam-2337	1	15	no	no	INTJ
ejpam-2337	1	16	.	.	NOUN
ejpam-2337	1	17	2	2	NUM
ejpam-2337	1	18	,	,	PUNCT
ejpam-2337	1	19	2015	2015	NUM
ejpam-2337	1	20	,	,	PUNCT
ejpam-2337	1	21	283	283	NUM
ejpam-2337	1	22	-	-	SYM
ejpam-2337	1	23	293	293	NUM
ejpam-2337	1	24	issn	issn	PROPN
ejpam-2337	1	25	1307	1307	NUM
ejpam-2337	1	26	-	-	SYM
ejpam-2337	1	27	5543	5543	NUM
ejpam-2337	1	28	–	–	PUNCT
ejpam-2337	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2337	1	30	generalized	generalize	VERB
ejpam-2337	1	31	hyers	hyer	NOUN
ejpam-2337	1	32	-	-	PUNCT
ejpam-2337	1	33	ulam	ulam	ADJ
ejpam-2337	1	34	-	-	PUNCT
ejpam-2337	1	35	rassias	rassias	PROPN
ejpam-2337	1	36	stability	stability	NOUN
ejpam-2337	1	37	of	of	ADP
ejpam-2337	1	38	a	a	DET
ejpam-2337	1	39	system	system	NOUN
ejpam-2337	1	40	of	of	ADP
ejpam-2337	1	41	bi	bi	ADJ
ejpam-2337	1	42	-	-	ADJ
ejpam-2337	1	43	reciprocal	reciprocal	ADJ
ejpam-2337	1	44	functional	functional	ADJ
ejpam-2337	1	45	equations	equation	NOUN
ejpam-2337	1	46	k.	k.	PROPN
ejpam-2337	2	1	ravi1	ravi1	PROPN
ejpam-2337	2	2	,	,	PUNCT
ejpam-2337	2	3	!	!	PUNCT
ejpam-2337	2	4	,	,	PUNCT
ejpam-2337	3	1	b.v	b.v	PROPN
ejpam-2337	3	2	.	.	PROPN
ejpam-2337	3	3	senthil	senthil	PROPN
ejpam-2337	3	4	kumar2	kumar2	X
ejpam-2337	4	1	1	1	NUM
ejpam-2337	4	2	pg	pg	PROPN
ejpam-2337	4	3	&	&	CCONJ
ejpam-2337	4	4	research	research	PROPN
ejpam-2337	4	5	department	department	PROPN
ejpam-2337	4	6	of	of	ADP
ejpam-2337	4	7	mathematics	mathematic	NOUN
ejpam-2337	4	8	,	,	PUNCT
ejpam-2337	4	9	sacred	sacred	ADJ
ejpam-2337	4	10	heart	heart	NOUN
ejpam-2337	4	11	college	college	NOUN
ejpam-2337	4	12	,	,	PUNCT
ejpam-2337	4	13	tirupattur	tirupattur	VERB
ejpam-2337	4	14	635	635	NUM
ejpam-2337	4	15	601	601	NUM
ejpam-2337	4	16	,	,	PUNCT
ejpam-2337	4	17	tamil	tamil	PROPN
ejpam-2337	4	18	nadu	nadu	PROPN
ejpam-2337	4	19	,	,	PUNCT
ejpam-2337	4	20	india	india	PROPN
ejpam-2337	4	21	2	2	NUM
ejpam-2337	4	22	department	department	NOUN
ejpam-2337	4	23	of	of	ADP
ejpam-2337	4	24	mathematics	mathematic	NOUN
ejpam-2337	4	25	,	,	PUNCT
ejpam-2337	4	26	c.	c.	PROPN
ejpam-2337	4	27	abdul	abdul	PROPN
ejpam-2337	4	28	hakeem	hakeem	PROPN
ejpam-2337	4	29	college	college	PROPN
ejpam-2337	4	30	of	of	ADP
ejpam-2337	4	31	engineering	engineering	PROPN
ejpam-2337	4	32	&	&	CCONJ
ejpam-2337	4	33	technology	technology	PROPN
ejpam-2337	4	34	,	,	PUNCT
ejpam-2337	4	35	melvisharam	melvisharam	NOUN
ejpam-2337	4	36	632	632	NUM
ejpam-2337	4	37	509	509	NUM
ejpam-2337	4	38	,	,	PUNCT
ejpam-2337	4	39	tamil	tamil	PROPN
ejpam-2337	4	40	nadu	nadu	PROPN
ejpam-2337	4	41	,	,	PUNCT
ejpam-2337	4	42	india	india	PROPN
ejpam-2337	4	43	abstract	abstract	NOUN
ejpam-2337	4	44	.	.	PUNCT
ejpam-2337	5	1	in	in	ADP
ejpam-2337	5	2	this	this	DET
ejpam-2337	5	3	paper	paper	NOUN
ejpam-2337	5	4	,	,	PUNCT
ejpam-2337	5	5	we	we	PRON
ejpam-2337	5	6	find	find	VERB
ejpam-2337	5	7	the	the	DET
ejpam-2337	5	8	generalized	generalize	VERB
ejpam-2337	5	9	hyers	hyer	NOUN
ejpam-2337	5	10	-	-	PUNCT
ejpam-2337	5	11	ulam	ulam	ADJ
ejpam-2337	5	12	-	-	PUNCT
ejpam-2337	5	13	rassias	rassias	PROPN
ejpam-2337	5	14	stability	stability	NOUN
ejpam-2337	5	15	of	of	ADP
ejpam-2337	5	16	the	the	DET
ejpam-2337	5	17	system	system	NOUN
ejpam-2337	5	18	of	of	ADP
ejpam-2337	5	19	bi	bi	ADJ
ejpam-2337	5	20	-	-	ADJ
ejpam-2337	5	21	reciprocal	reciprocal	ADJ
ejpam-2337	5	22	functional	functional	ADJ
ejpam-2337	5	23	equations	equation	NOUN
ejpam-2337	5	24	r(x	r(x	PROPN
ejpam-2337	5	25	+	+	CCONJ
ejpam-2337	5	26	u	u	PROPN
ejpam-2337	5	27	,	,	PUNCT
ejpam-2337	5	28	y	y	NOUN
ejpam-2337	5	29	)	)	PUNCT
ejpam-2337	5	30	=	=	SYM
ejpam-2337	5	31	r(x	r(x	PROPN
ejpam-2337	5	32	,	,	PUNCT
ejpam-2337	5	33	y)r(u	y)r(u	PROPN
ejpam-2337	5	34	,	,	PUNCT
ejpam-2337	5	35	y	y	PROPN
ejpam-2337	5	36	)	)	PUNCT
ejpam-2337	5	37	r(x	r(x	PROPN
ejpam-2337	5	38	,	,	PUNCT
ejpam-2337	5	39	y	y	PROPN
ejpam-2337	5	40	)	)	PUNCT
ejpam-2337	6	1	+	+	CCONJ
ejpam-2337	7	1	r(u	r(u	PROPN
ejpam-2337	7	2	,	,	PUNCT
ejpam-2337	7	3	y	y	NOUN
ejpam-2337	7	4	)	)	PUNCT
ejpam-2337	7	5	,	,	PUNCT
ejpam-2337	7	6	r(x	r(x	PROPN
ejpam-2337	7	7	,	,	PUNCT
ejpam-2337	7	8	y	y	PROPN
ejpam-2337	7	9	+	+	CCONJ
ejpam-2337	7	10	v	v	NOUN
ejpam-2337	7	11	)	)	PUNCT
ejpam-2337	7	12	=	=	SYM
ejpam-2337	7	13	r(x	r(x	PROPN
ejpam-2337	7	14	,	,	PUNCT
ejpam-2337	7	15	y)r(x	y)r(x	PROPN
ejpam-2337	7	16	,	,	PUNCT
ejpam-2337	7	17	v	v	NOUN
ejpam-2337	7	18	)	)	PUNCT
ejpam-2337	7	19	r(x	r(x	PROPN
ejpam-2337	7	20	,	,	PUNCT
ejpam-2337	7	21	y	y	PROPN
ejpam-2337	7	22	)	)	PUNCT
ejpam-2337	7	23	+	+	CCONJ
ejpam-2337	7	24	r(x	r(x	PROPN
ejpam-2337	7	25	,	,	PUNCT
ejpam-2337	7	26	v	v	NOUN
ejpam-2337	7	27	)	)	PUNCT
ejpam-2337	7	28	in	in	ADP
ejpam-2337	7	29	the	the	DET
ejpam-2337	7	30	setting	setting	NOUN
ejpam-2337	7	31	of	of	ADP
ejpam-2337	7	32	fréchet	fréchet	NOUN
ejpam-2337	7	33	spaces	space	NOUN
ejpam-2337	7	34	.	.	PUNCT
ejpam-2337	8	1	2010	2010	NUM
ejpam-2337	8	2	mathematics	mathematic	NOUN
ejpam-2337	8	3	subject	subject	NOUN
ejpam-2337	8	4	classifications	classification	NOUN
ejpam-2337	8	5	:	:	PUNCT
ejpam-2337	8	6	39b82	39b82	NUM
ejpam-2337	8	7	,	,	PUNCT
ejpam-2337	8	8	39b72	39b72	DET
ejpam-2337	8	9	key	key	ADJ
ejpam-2337	8	10	words	word	NOUN
ejpam-2337	8	11	and	and	CCONJ
ejpam-2337	8	12	phrases	phrase	NOUN
ejpam-2337	8	13	:	:	PUNCT
ejpam-2337	8	14	reciprocal	reciprocal	ADJ
ejpam-2337	8	15	function	function	NOUN
ejpam-2337	8	16	,	,	PUNCT
ejpam-2337	8	17	bi	bi	ADJ
ejpam-2337	8	18	-	-	ADJ
ejpam-2337	8	19	reciprocal	reciprocal	ADJ
ejpam-2337	8	20	functional	functional	ADJ
ejpam-2337	8	21	equation	equation	NOUN
ejpam-2337	8	22	,	,	PUNCT
ejpam-2337	8	23	generalized	generalize	VERB
ejpam-2337	8	24	hyersulam	hyersulam	PROPN
ejpam-2337	8	25	-	-	PUNCT
ejpam-2337	8	26	rassias	rassias	PROPN
ejpam-2337	8	27	stability	stability	NOUN
ejpam-2337	8	28	.	.	PUNCT
ejpam-2337	9	1	1	1	X
ejpam-2337	9	2	.	.	X
ejpam-2337	9	3	introduction	introduction	NOUN
ejpam-2337	9	4	in	in	ADP
ejpam-2337	9	5	functional	functional	ADJ
ejpam-2337	9	6	analysis	analysis	NOUN
ejpam-2337	9	7	and	and	CCONJ
ejpam-2337	9	8	related	related	ADJ
ejpam-2337	9	9	areas	area	NOUN
ejpam-2337	9	10	of	of	ADP
ejpam-2337	9	11	mathematics	mathematic	NOUN
ejpam-2337	9	12	,	,	PUNCT
ejpam-2337	9	13	fréchet	fréchet	NOUN
ejpam-2337	9	14	spaces	space	NOUN
ejpam-2337	9	15	,	,	PUNCT
ejpam-2337	9	16	named	name	VERB
ejpam-2337	9	17	after	after	ADP
ejpam-2337	9	18	maurice	maurice	PROPN
ejpam-2337	9	19	fréchet	fréchet	PROPN
ejpam-2337	9	20	,	,	PUNCT
ejpam-2337	9	21	are	be	AUX
ejpam-2337	9	22	special	special	ADJ
ejpam-2337	9	23	topological	topological	ADJ
ejpam-2337	9	24	vector	vector	NOUN
ejpam-2337	9	25	spaces	space	NOUN
ejpam-2337	9	26	.	.	PUNCT
ejpam-2337	10	1	they	they	PRON
ejpam-2337	10	2	are	be	AUX
ejpam-2337	10	3	generalizations	generalization	NOUN
ejpam-2337	10	4	of	of	ADP
ejpam-2337	10	5	banach	banach	NOUN
ejpam-2337	10	6	spaces	space	NOUN
ejpam-2337	10	7	(	(	PUNCT
ejpam-2337	10	8	normed	normed	ADJ
ejpam-2337	10	9	vector	vector	NOUN
ejpam-2337	10	10	spaces	space	NOUN
ejpam-2337	10	11	which	which	PRON
ejpam-2337	10	12	are	be	AUX
ejpam-2337	10	13	complete	complete	ADJ
ejpam-2337	10	14	with	with	ADP
ejpam-2337	10	15	respect	respect	NOUN
ejpam-2337	10	16	to	to	ADP
ejpam-2337	10	17	the	the	DET
ejpam-2337	10	18	metric	metric	NOUN
ejpam-2337	10	19	induced	induce	VERB
ejpam-2337	10	20	by	by	ADP
ejpam-2337	10	21	the	the	DET
ejpam-2337	10	22	norm	norm	NOUN
ejpam-2337	10	23	)	)	PUNCT
ejpam-2337	10	24	.	.	PUNCT
ejpam-2337	11	1	many	many	ADJ
ejpam-2337	11	2	vector	vector	NOUN
ejpam-2337	11	3	spaces	space	NOUN
ejpam-2337	11	4	of	of	ADP
ejpam-2337	11	5	holomorphic	holomorphic	ADJ
ejpam-2337	11	6	,	,	PUNCT
ejpam-2337	11	7	differentiable	differentiable	ADJ
ejpam-2337	11	8	or	or	CCONJ
ejpam-2337	11	9	continuous	continuous	ADJ
ejpam-2337	11	10	functions	function	NOUN
ejpam-2337	11	11	which	which	PRON
ejpam-2337	11	12	arise	arise	VERB
ejpam-2337	11	13	in	in	ADP
ejpam-2337	11	14	connection	connection	NOUN
ejpam-2337	11	15	with	with	ADP
ejpam-2337	11	16	various	various	ADJ
ejpam-2337	11	17	problems	problem	NOUN
ejpam-2337	11	18	in	in	ADP
ejpam-2337	11	19	analysis	analysis	NOUN
ejpam-2337	11	20	and	and	CCONJ
ejpam-2337	11	21	its	its	PRON
ejpam-2337	11	22	applications	application	NOUN
ejpam-2337	11	23	are	be	AUX
ejpam-2337	11	24	defined	define	VERB
ejpam-2337	11	25	by	by	ADP
ejpam-2337	11	26	(	(	PUNCT
ejpam-2337	11	27	at	at	ADP
ejpam-2337	11	28	most	most	ADV
ejpam-2337	11	29	)	)	PUNCT
ejpam-2337	11	30	countably	countably	ADV
ejpam-2337	11	31	many	many	ADJ
ejpam-2337	11	32	conditions	condition	NOUN
ejpam-2337	11	33	,	,	PUNCT
ejpam-2337	11	34	whence	whence	SCONJ
ejpam-2337	11	35	they	they	PRON
ejpam-2337	11	36	carry	carry	VERB
ejpam-2337	11	37	a	a	DET
ejpam-2337	11	38	natural	natural	ADJ
ejpam-2337	11	39	fréchet	fréchet	NOUN
ejpam-2337	11	40	topology	topology	NOUN
ejpam-2337	11	41	(	(	PUNCT
ejpam-2337	11	42	if	if	SCONJ
ejpam-2337	11	43	they	they	PRON
ejpam-2337	11	44	are	be	AUX
ejpam-2337	11	45	,	,	PUNCT
ejpam-2337	11	46	in	in	ADP
ejpam-2337	11	47	addition	addition	NOUN
ejpam-2337	11	48	,	,	PUNCT
ejpam-2337	11	49	complete	complete	ADJ
ejpam-2337	11	50	)	)	PUNCT
ejpam-2337	11	51	.	.	PUNCT
ejpam-2337	12	1	in	in	ADP
ejpam-2337	12	2	particular	particular	ADJ
ejpam-2337	12	3	,	,	PUNCT
ejpam-2337	12	4	each	each	DET
ejpam-2337	12	5	banach	banach	NOUN
ejpam-2337	12	6	space	space	NOUN
ejpam-2337	12	7	is	be	AUX
ejpam-2337	12	8	a	a	DET
ejpam-2337	12	9	fréchet	fréchet	NOUN
ejpam-2337	12	10	space	space	NOUN
ejpam-2337	12	11	and	and	CCONJ
ejpam-2337	12	12	so	so	ADV
ejpam-2337	12	13	has	have	VERB
ejpam-2337	12	14	a	a	DET
ejpam-2337	12	15	countable	countable	ADJ
ejpam-2337	12	16	basis	basis	NOUN
ejpam-2337	12	17	of	of	ADP
ejpam-2337	12	18	absolutely	absolutely	ADV
ejpam-2337	12	19	convex	convex	ADJ
ejpam-2337	12	20	zero	zero	NUM
ejpam-2337	12	21	neighborhoods	neighborhood	NOUN
ejpam-2337	12	22	.	.	PUNCT
ejpam-2337	13	1	a	a	DET
ejpam-2337	13	2	topological	topological	ADJ
ejpam-2337	13	3	vector	vector	NOUN
ejpam-2337	13	4	space	space	NOUN
ejpam-2337	13	5	x	x	PUNCT
ejpam-2337	13	6	is	be	AUX
ejpam-2337	13	7	a	a	DET
ejpam-2337	13	8	fréchet	fréchet	NOUN
ejpam-2337	13	9	space	space	NOUN
ejpam-2337	13	10	if	if	SCONJ
ejpam-2337	13	11	and	and	CCONJ
ejpam-2337	13	12	only	only	ADV
ejpam-2337	13	13	if	if	SCONJ
ejpam-2337	13	14	it	it	PRON
ejpam-2337	13	15	satisfies	satisfy	VERB
ejpam-2337	13	16	the	the	DET
ejpam-2337	13	17	following	follow	VERB
ejpam-2337	13	18	three	three	NUM
ejpam-2337	13	19	properties	property	NOUN
ejpam-2337	13	20	:	:	PUNCT
ejpam-2337	13	21	!	!	PUNCT
ejpam-2337	14	1	corresponding	correspond	VERB
ejpam-2337	14	2	author	author	NOUN
ejpam-2337	14	3	.	.	PUNCT
ejpam-2337	15	1	email	email	NOUN
ejpam-2337	15	2	addresses	address	NOUN
ejpam-2337	15	3	:	:	PUNCT
ejpam-2337	15	4	shckravi@yahoo.co.in	shckravi@yahoo.co.in	PROPN
ejpam-2337	15	5	(	(	PUNCT
ejpam-2337	15	6	k.	k.	PROPN
ejpam-2337	15	7	ravi	ravi	PROPN
ejpam-2337	15	8	)	)	PUNCT
ejpam-2337	15	9	,	,	PUNCT
ejpam-2337	15	10	bvssree@yahoo.co.in	bvssree@yahoo.co.in	PROPN
ejpam-2337	15	11	(	(	PUNCT
ejpam-2337	15	12	b.	b.	PROPN
ejpam-2337	15	13	kumar	kumar	PROPN
ejpam-2337	15	14	)	)	PUNCT
ejpam-2337	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2337	15	16	283	283	NUM
ejpam-2337	15	17	c	c	NOUN
ejpam-2337	15	18	"	"	PUNCT
ejpam-2337	15	19	2015	2015	NUM
ejpam-2337	15	20	ejpam	ejpam	VERB
ejpam-2337	15	21	all	all	DET
ejpam-2337	15	22	rights	right	NOUN
ejpam-2337	15	23	reserved	reserve	VERB
ejpam-2337	15	24	.	.	PUNCT
ejpam-2337	16	1	k.	k.	PROPN
ejpam-2337	16	2	ravi	ravi	PROPN
ejpam-2337	16	3	,	,	PUNCT
ejpam-2337	16	4	b.	b.	PROPN
ejpam-2337	16	5	kumar	kumar	PROPN
ejpam-2337	16	6	/	/	SYM
ejpam-2337	16	7	eur	eur	PROPN
ejpam-2337	16	8	.	.	PUNCT
ejpam-2337	17	1	j.	j.	PROPN
ejpam-2337	17	2	pure	pure	PROPN
ejpam-2337	17	3	appl	appl	PROPN
ejpam-2337	17	4	.	.	PROPN
ejpam-2337	17	5	math	math	PROPN
ejpam-2337	17	6	,	,	PUNCT
ejpam-2337	17	7	8	8	NUM
ejpam-2337	17	8	(	(	PUNCT
ejpam-2337	17	9	2015	2015	NUM
ejpam-2337	17	10	)	)	PUNCT
ejpam-2337	17	11	,	,	PUNCT
ejpam-2337	17	12	283	283	NUM
ejpam-2337	17	13	-	-	SYM
ejpam-2337	17	14	293	293	NUM
ejpam-2337	17	15	284	284	NUM
ejpam-2337	17	16	(	(	PUNCT
ejpam-2337	17	17	i	i	NOUN
ejpam-2337	17	18	)	)	PUNCT
ejpam-2337	17	19	it	it	PRON
ejpam-2337	17	20	is	be	AUX
ejpam-2337	17	21	complete	complete	ADJ
ejpam-2337	17	22	as	as	ADP
ejpam-2337	17	23	a	a	DET
ejpam-2337	17	24	uniform	uniform	ADJ
ejpam-2337	17	25	space	space	NOUN
ejpam-2337	17	26	(	(	PUNCT
ejpam-2337	17	27	ii	ii	NOUN
ejpam-2337	17	28	)	)	PUNCT
ejpam-2337	17	29	it	it	PRON
ejpam-2337	17	30	is	be	AUX
ejpam-2337	17	31	locally	locally	ADV
ejpam-2337	17	32	convex	convex	ADJ
ejpam-2337	17	33	(	(	PUNCT
ejpam-2337	17	34	iii	iii	NOUN
ejpam-2337	17	35	)	)	PUNCT
ejpam-2337	17	36	its	its	PRON
ejpam-2337	17	37	topology	topology	NOUN
ejpam-2337	17	38	can	can	AUX
ejpam-2337	17	39	be	be	AUX
ejpam-2337	17	40	induced	induce	VERB
ejpam-2337	17	41	by	by	ADP
ejpam-2337	17	42	a	a	DET
ejpam-2337	17	43	translation	translation	NOUN
ejpam-2337	17	44	invariant	invariant	NOUN
ejpam-2337	17	45	metric	metric	NOUN
ejpam-2337	17	46	,	,	PUNCT
ejpam-2337	17	47	i.e.	i.e.	X
ejpam-2337	17	48	a	a	DET
ejpam-2337	17	49	metric	metric	ADJ
ejpam-2337	17	50	d	d	NOUN
ejpam-2337	17	51	:	:	PUNCT
ejpam-2337	17	52	x	x	PUNCT
ejpam-2337	17	53	#	#	SYM
ejpam-2337	17	54	x	x	SYM
ejpam-2337	17	55	$	$	SYM
ejpam-2337	17	56	!	!	PUNCT
ejpam-2337	18	1	such	such	ADJ
ejpam-2337	18	2	that	that	DET
ejpam-2337	18	3	d(x	d(x	PROPN
ejpam-2337	18	4	,	,	PUNCT
ejpam-2337	18	5	y	y	X
ejpam-2337	18	6	)	)	PUNCT
ejpam-2337	18	7	=	=	SYM
ejpam-2337	19	1	d(x	d(x	PROPN
ejpam-2337	19	2	+	+	CCONJ
ejpam-2337	19	3	a	a	X
ejpam-2337	19	4	,	,	PUNCT
ejpam-2337	19	5	y	y	PROPN
ejpam-2337	19	6	+	+	CCONJ
ejpam-2337	19	7	a	a	X
ejpam-2337	19	8	)	)	PUNCT
ejpam-2337	19	9	for	for	ADP
ejpam-2337	19	10	all	all	DET
ejpam-2337	19	11	a	a	PRON
ejpam-2337	19	12	,	,	PUNCT
ejpam-2337	19	13	x	x	NOUN
ejpam-2337	19	14	,	,	PUNCT
ejpam-2337	19	15	%	%	INTJ
ejpam-2337	19	16	x	x	X
ejpam-2337	19	17	.	.	PUNCT
ejpam-2337	20	1	this	this	PRON
ejpam-2337	20	2	means	mean	VERB
ejpam-2337	20	3	that	that	SCONJ
ejpam-2337	20	4	a	a	DET
ejpam-2337	20	5	subset	subset	ADJ
ejpam-2337	20	6	u	u	NOUN
ejpam-2337	20	7	of	of	ADP
ejpam-2337	20	8	x	x	PUNCT
ejpam-2337	20	9	is	be	AUX
ejpam-2337	20	10	open	open	ADJ
ejpam-2337	20	11	if	if	SCONJ
ejpam-2337	20	12	and	and	CCONJ
ejpam-2337	20	13	only	only	ADV
ejpam-2337	20	14	if	if	SCONJ
ejpam-2337	20	15	for	for	ADP
ejpam-2337	20	16	every	every	DET
ejpam-2337	20	17	u	u	NOUN
ejpam-2337	20	18	in	in	ADP
ejpam-2337	20	19	u	u	NOUN
ejpam-2337	20	20	,	,	PUNCT
ejpam-2337	20	21	there	there	PRON
ejpam-2337	20	22	exists	exist	VERB
ejpam-2337	20	23	an	an	DET
ejpam-2337	20	24	!	!	PUNCT
ejpam-2337	20	25	>	>	X
ejpam-2337	20	26	0	0	NUM
ejpam-2337	21	1	such	such	ADJ
ejpam-2337	21	2	that	that	SCONJ
ejpam-2337	21	3	{	{	PUNCT
ejpam-2337	21	4	v	v	NOUN
ejpam-2337	21	5	:	:	PUNCT
ejpam-2337	21	6	d(u	d(u	PROPN
ejpam-2337	21	7	,	,	PUNCT
ejpam-2337	21	8	v	v	NOUN
ejpam-2337	21	9	)	)	PUNCT
ejpam-2337	21	10	<	<	X
ejpam-2337	21	11	!	!	PUNCT
ejpam-2337	21	12	}	}	PUNCT
ejpam-2337	21	13	is	be	AUX
ejpam-2337	21	14	a	a	DET
ejpam-2337	21	15	subset	subset	NOUN
ejpam-2337	21	16	of	of	ADP
ejpam-2337	21	17	u	u	PROPN
ejpam-2337	21	18	.	.	PUNCT
ejpam-2337	22	1	note	note	VERB
ejpam-2337	22	2	that	that	SCONJ
ejpam-2337	22	3	there	there	PRON
ejpam-2337	22	4	is	be	VERB
ejpam-2337	22	5	no	no	DET
ejpam-2337	22	6	natural	natural	ADJ
ejpam-2337	22	7	notion	notion	NOUN
ejpam-2337	22	8	of	of	ADP
ejpam-2337	22	9	distance	distance	NOUN
ejpam-2337	22	10	between	between	ADP
ejpam-2337	22	11	two	two	NUM
ejpam-2337	22	12	points	point	NOUN
ejpam-2337	22	13	of	of	ADP
ejpam-2337	22	14	a	a	DET
ejpam-2337	22	15	fréchet	fréchet	NOUN
ejpam-2337	22	16	space	space	NOUN
ejpam-2337	22	17	:	:	PUNCT
ejpam-2337	22	18	many	many	ADJ
ejpam-2337	22	19	different	different	ADJ
ejpam-2337	22	20	translation	translation	NOUN
ejpam-2337	22	21	-	-	PUNCT
ejpam-2337	22	22	invariant	invariant	ADJ
ejpam-2337	22	23	metrics	metric	NOUN
ejpam-2337	22	24	may	may	AUX
ejpam-2337	22	25	induce	induce	VERB
ejpam-2337	22	26	the	the	DET
ejpam-2337	22	27	same	same	ADJ
ejpam-2337	22	28	topology	topology	NOUN
ejpam-2337	22	29	.	.	PUNCT
ejpam-2337	23	1	the	the	DET
ejpam-2337	23	2	vector	vector	NOUN
ejpam-2337	23	3	space	space	NOUN
ejpam-2337	23	4	c&([0,1	c&([0,1	NOUN
ejpam-2337	23	5	]	]	PUNCT
ejpam-2337	23	6	)	)	PUNCT
ejpam-2337	23	7	of	of	ADP
ejpam-2337	23	8	all	all	DET
ejpam-2337	23	9	infinitely	infinitely	ADV
ejpam-2337	23	10	often	often	ADV
ejpam-2337	23	11	differentiable	differentiable	ADJ
ejpam-2337	23	12	functions	function	NOUN
ejpam-2337	23	13	f	f	NOUN
ejpam-2337	23	14	:	:	PUNCT
ejpam-2337	24	1	[	[	X
ejpam-2337	24	2	0,1	0,1	NUM
ejpam-2337	24	3	]	]	PUNCT
ejpam-2337	24	4	$	$	X
ejpam-2337	24	5	!	!	PUNCT
ejpam-2337	24	6	becomes	become	VERB
ejpam-2337	24	7	a	a	DET
ejpam-2337	24	8	fréchet	fréchet	NOUN
ejpam-2337	24	9	space	space	NOUN
ejpam-2337	24	10	with	with	ADP
ejpam-2337	24	11	the	the	DET
ejpam-2337	24	12	seminorms	seminorm	NOUN
ejpam-2337	24	13	||	||	PROPN
ejpam-2337	25	1	f	f	X
ejpam-2337	25	2	||k	||k	PROPN
ejpam-2337	25	3	=	=	SYM
ejpam-2337	25	4	sup{|	sup{|	NOUN
ejpam-2337	25	5	f	f	PROPN
ejpam-2337	26	1	(	(	PUNCT
ejpam-2337	26	2	k)(x)|	k)(x)|	NOUN
ejpam-2337	26	3	:	:	PUNCT
ejpam-2337	26	4	x	x	PUNCT
ejpam-2337	26	5	%	%	NOUN
ejpam-2337	27	1	[	[	X
ejpam-2337	27	2	0,1	0,1	NUM
ejpam-2337	27	3	]	]	PUNCT
ejpam-2337	27	4	}	}	PUNCT
ejpam-2337	27	5	for	for	ADP
ejpam-2337	27	6	every	every	DET
ejpam-2337	27	7	integer	integer	NOUN
ejpam-2337	27	8	k	k	PROPN
ejpam-2337	27	9	'	'	PUNCT
ejpam-2337	27	10	0	0	NUM
ejpam-2337	27	11	.	.	PUNCT
ejpam-2337	28	1	here	here	ADV
ejpam-2337	28	2	,	,	PUNCT
ejpam-2337	28	3	f	f	PROPN
ejpam-2337	28	4	(	(	PUNCT
ejpam-2337	28	5	k	k	NOUN
ejpam-2337	28	6	)	)	PUNCT
ejpam-2337	28	7	denotes	denote	VERB
ejpam-2337	28	8	the	the	DET
ejpam-2337	28	9	kth	kth	PROPN
ejpam-2337	28	10	derivative	derivative	NOUN
ejpam-2337	28	11	of	of	ADP
ejpam-2337	28	12	f	f	PROPN
ejpam-2337	28	13	,	,	PUNCT
ejpam-2337	28	14	and	and	CCONJ
ejpam-2337	28	15	f	f	PROPN
ejpam-2337	28	16	(	(	PUNCT
ejpam-2337	28	17	0	0	NUM
ejpam-2337	28	18	)	)	PUNCT
ejpam-2337	29	1	=	=	SYM
ejpam-2337	29	2	f	f	PROPN
ejpam-2337	29	3	.	.	PUNCT
ejpam-2337	30	1	the	the	DET
ejpam-2337	30	2	spaces	space	NOUN
ejpam-2337	30	3	c	c	PROPN
ejpam-2337	30	4	&	&	CCONJ
ejpam-2337	30	5	(	(	PUNCT
ejpam-2337	30	6	!	!	PUNCT
ejpam-2337	30	7	)	)	PUNCT
ejpam-2337	30	8	for	for	ADP
ejpam-2337	30	9	!	!	PUNCT
ejpam-2337	31	1	(	(	PUNCT
ejpam-2337	31	2	!	!	PUNCT
ejpam-2337	31	3	n	n	X
ejpam-2337	31	4	open	open	ADJ
ejpam-2337	31	5	,	,	PUNCT
ejpam-2337	31	6	)	)	PUNCT
ejpam-2337	31	7	(	(	PUNCT
ejpam-2337	31	8	k	k	NOUN
ejpam-2337	31	9	)	)	PUNCT
ejpam-2337	31	10	,	,	PUNCT
ejpam-2337	31	11	c&(k	c&(k	NOUN
ejpam-2337	31	12	)	)	PUNCT
ejpam-2337	31	13	for	for	ADP
ejpam-2337	31	14	k	k	PROPN
ejpam-2337	31	15	(	(	PUNCT
ejpam-2337	31	16	!	!	PUNCT
ejpam-2337	31	17	n	n	CCONJ
ejpam-2337	31	18	,	,	PUNCT
ejpam-2337	31	19	)	)	PUNCT
ejpam-2337	31	20	(	(	PUNCT
ejpam-2337	31	21	!	!	PUNCT
ejpam-2337	31	22	n	n	CCONJ
ejpam-2337	31	23	)	)	PUNCT
ejpam-2337	31	24	,	,	PUNCT
ejpam-2337	31	25	*	*	PUNCT
ejpam-2337	31	26	(	(	PUNCT
ejpam-2337	31	27	!	!	PUNCT
ejpam-2337	31	28	)	)	PUNCT
ejpam-2337	31	29	for	for	ADP
ejpam-2337	31	30	!	!	PUNCT
ejpam-2337	32	1	(	(	PUNCT
ejpam-2337	32	2	"	"	PUNCT
ejpam-2337	32	3	n	n	X
ejpam-2337	32	4	open	open	ADJ
ejpam-2337	32	5	are	be	AUX
ejpam-2337	32	6	other	other	ADJ
ejpam-2337	32	7	examples	example	NOUN
ejpam-2337	32	8	of	of	ADP
ejpam-2337	32	9	fréchet	fréchet	NOUN
ejpam-2337	32	10	spaces	space	NOUN
ejpam-2337	32	11	.	.	PUNCT
ejpam-2337	33	1	more	more	ADV
ejpam-2337	33	2	generally	generally	ADV
ejpam-2337	33	3	,	,	PUNCT
ejpam-2337	33	4	if	if	SCONJ
ejpam-2337	33	5	m	m	NOUN
ejpam-2337	33	6	is	be	AUX
ejpam-2337	33	7	a	a	DET
ejpam-2337	33	8	compact	compact	ADJ
ejpam-2337	33	9	c	c	NOUN
ejpam-2337	33	10	&	&	CCONJ
ejpam-2337	33	11	manifold	manifold	ADJ
ejpam-2337	33	12	and	and	CCONJ
ejpam-2337	33	13	b	b	NOUN
ejpam-2337	33	14	is	be	AUX
ejpam-2337	33	15	a	a	DET
ejpam-2337	33	16	banach	banach	NOUN
ejpam-2337	33	17	space	space	NOUN
ejpam-2337	33	18	,	,	PUNCT
ejpam-2337	33	19	then	then	ADV
ejpam-2337	33	20	the	the	DET
ejpam-2337	33	21	set	set	NOUN
ejpam-2337	33	22	of	of	ADP
ejpam-2337	33	23	all	all	DET
ejpam-2337	33	24	infinitely	infinitely	ADV
ejpam-2337	33	25	often	often	ADV
ejpam-2337	33	26	differentiable	differentiable	ADJ
ejpam-2337	33	27	functions	function	NOUN
ejpam-2337	33	28	f	f	X
ejpam-2337	33	29	:	:	PUNCT
ejpam-2337	33	30	m	m	VERB
ejpam-2337	33	31	$	$	PROPN
ejpam-2337	33	32	b	b	NOUN
ejpam-2337	33	33	can	can	AUX
ejpam-2337	33	34	be	be	AUX
ejpam-2337	33	35	turned	turn	VERB
ejpam-2337	33	36	into	into	ADP
ejpam-2337	33	37	a	a	DET
ejpam-2337	33	38	fréchet	fréchet	NOUN
ejpam-2337	33	39	space	space	NOUN
ejpam-2337	33	40	;	;	PUNCT
ejpam-2337	33	41	the	the	DET
ejpam-2337	33	42	seminorms	seminorm	NOUN
ejpam-2337	33	43	are	be	AUX
ejpam-2337	33	44	given	give	VERB
ejpam-2337	33	45	by	by	ADP
ejpam-2337	33	46	the	the	DET
ejpam-2337	33	47	suprema	suprema	NOUN
ejpam-2337	33	48	of	of	ADP
ejpam-2337	33	49	the	the	DET
ejpam-2337	33	50	norms	norm	NOUN
ejpam-2337	33	51	of	of	ADP
ejpam-2337	33	52	all	all	DET
ejpam-2337	33	53	partial	partial	ADJ
ejpam-2337	33	54	derivatives	derivative	NOUN
ejpam-2337	33	55	.	.	PUNCT
ejpam-2337	34	1	the	the	DET
ejpam-2337	34	2	space	space	NOUN
ejpam-2337	34	3	"	"	PUNCT
ejpam-2337	34	4	of	of	ADP
ejpam-2337	34	5	real	real	ADV
ejpam-2337	34	6	valued	value	VERB
ejpam-2337	34	7	sequences	sequence	NOUN
ejpam-2337	34	8	becomes	become	VERB
ejpam-2337	34	9	a	a	DET
ejpam-2337	34	10	fréchet	fréchet	NOUN
ejpam-2337	34	11	space	space	NOUN
ejpam-2337	34	12	if	if	SCONJ
ejpam-2337	34	13	we	we	PRON
ejpam-2337	34	14	define	define	VERB
ejpam-2337	34	15	the	the	DET
ejpam-2337	34	16	kth	kth	PROPN
ejpam-2337	34	17	seminorm	seminorm	NOUN
ejpam-2337	34	18	of	of	ADP
ejpam-2337	34	19	a	a	DET
ejpam-2337	34	20	sequence	sequence	NOUN
ejpam-2337	34	21	to	to	PART
ejpam-2337	34	22	be	be	AUX
ejpam-2337	34	23	the	the	DET
ejpam-2337	34	24	absolute	absolute	ADJ
ejpam-2337	34	25	value	value	NOUN
ejpam-2337	34	26	of	of	ADP
ejpam-2337	34	27	the	the	DET
ejpam-2337	34	28	kth	kth	PROPN
ejpam-2337	34	29	element	element	NOUN
ejpam-2337	34	30	of	of	ADP
ejpam-2337	34	31	the	the	DET
ejpam-2337	34	32	sequence	sequence	NOUN
ejpam-2337	34	33	.	.	PUNCT
ejpam-2337	35	1	convergence	convergence	NOUN
ejpam-2337	35	2	in	in	ADP
ejpam-2337	35	3	this	this	DET
ejpam-2337	35	4	fréchet	fréchet	NOUN
ejpam-2337	35	5	space	space	NOUN
ejpam-2337	35	6	is	be	AUX
ejpam-2337	35	7	equivalent	equivalent	ADJ
ejpam-2337	35	8	to	to	ADP
ejpam-2337	35	9	element	element	VERB
ejpam-2337	35	10	-	-	ADJ
ejpam-2337	35	11	wise	wise	ADJ
ejpam-2337	35	12	convergence	convergence	NOUN
ejpam-2337	35	13	.	.	PUNCT
ejpam-2337	36	1	not	not	PART
ejpam-2337	36	2	all	all	DET
ejpam-2337	36	3	vector	vector	NOUN
ejpam-2337	36	4	spaces	space	NOUN
ejpam-2337	36	5	with	with	ADP
ejpam-2337	36	6	complete	complete	ADJ
ejpam-2337	36	7	translation	translation	NOUN
ejpam-2337	36	8	-	-	PUNCT
ejpam-2337	36	9	variant	variant	NOUN
ejpam-2337	36	10	metrics	metric	NOUN
ejpam-2337	36	11	are	be	AUX
ejpam-2337	36	12	fréchet	fréchet	NOUN
ejpam-2337	36	13	spaces	space	NOUN
ejpam-2337	36	14	.	.	PUNCT
ejpam-2337	37	1	an	an	DET
ejpam-2337	37	2	example	example	NOUN
ejpam-2337	37	3	is	be	AUX
ejpam-2337	37	4	lp	lp	ADJ
ejpam-2337	37	5	with	with	ADP
ejpam-2337	37	6	p	p	X
ejpam-2337	37	7	<	<	X
ejpam-2337	37	8	1	1	NUM
ejpam-2337	37	9	.	.	PUNCT
ejpam-2337	37	10	of	of	ADP
ejpam-2337	37	11	course	course	NOUN
ejpam-2337	37	12	,	,	PUNCT
ejpam-2337	37	13	such	such	ADJ
ejpam-2337	37	14	spaces	space	NOUN
ejpam-2337	37	15	fail	fail	VERB
ejpam-2337	37	16	to	to	PART
ejpam-2337	37	17	be	be	AUX
ejpam-2337	37	18	locally	locally	ADV
ejpam-2337	37	19	convex	convex	ADJ
ejpam-2337	37	20	.	.	PUNCT
ejpam-2337	38	1	the	the	DET
ejpam-2337	38	2	topology	topology	NOUN
ejpam-2337	38	3	of	of	ADP
ejpam-2337	38	4	a	a	DET
ejpam-2337	38	5	fréchet	fréchet	NOUN
ejpam-2337	38	6	space	space	NOUN
ejpam-2337	38	7	e	e	NOUN
ejpam-2337	38	8	can	can	AUX
ejpam-2337	38	9	be	be	AUX
ejpam-2337	38	10	given	give	VERB
ejpam-2337	38	11	by	by	ADP
ejpam-2337	38	12	a	a	DET
ejpam-2337	38	13	sequence	sequence	NOUN
ejpam-2337	38	14	of	of	ADP
ejpam-2337	38	15	seminorms	seminorm	NOUN
ejpam-2337	38	16	+	+	CCONJ
ejpam-2337	38	17	+1	+1	X
ejpam-2337	38	18	,	,	PUNCT
ejpam-2337	38	19	+	+	CCONJ
ejpam-2337	39	1	+2	+2	PRON
ejpam-2337	40	1	,	,	PUNCT
ejpam-2337	40	2	.	.	PUNCT
ejpam-2337	40	3	.	.	PUNCT
ejpam-2337	41	1	.	.	PUNCT
ejpam-2337	42	1	in	in	ADP
ejpam-2337	42	2	the	the	DET
ejpam-2337	42	3	following	following	ADJ
ejpam-2337	42	4	way	way	NOUN
ejpam-2337	42	5	:	:	PUNCT
ejpam-2337	42	6	a	a	DET
ejpam-2337	42	7	basis	basis	NOUN
ejpam-2337	42	8	of	of	ADP
ejpam-2337	42	9	neighborhoods	neighborhood	NOUN
ejpam-2337	42	10	of	of	ADP
ejpam-2337	42	11	zero	zero	NUM
ejpam-2337	42	12	are	be	AUX
ejpam-2337	42	13	the	the	DET
ejpam-2337	42	14	sets	set	NOUN
ejpam-2337	42	15	uk	uk	PROPN
ejpam-2337	42	16	,	,	PUNCT
ejpam-2337	42	17	!	!	PUNCT
ejpam-2337	43	1	=	=	PRON
ejpam-2337	44	1	{	{	PUNCT
ejpam-2337	44	2	x	x	SYM
ejpam-2337	44	3	%	%	INTJ
ejpam-2337	44	4	e	e	NOUN
ejpam-2337	44	5	:	:	PUNCT
ejpam-2337	44	6	+	+	PROPN
ejpam-2337	44	7	x+k	x+k	NUM
ejpam-2337	44	8	,	,	PUNCT
ejpam-2337	44	9	!	!	PUNCT
ejpam-2337	44	10	}	}	PUNCT
ejpam-2337	44	11	.	.	PUNCT
ejpam-2337	45	1	such	such	DET
ejpam-2337	45	2	a	a	DET
ejpam-2337	45	3	system	system	NOUN
ejpam-2337	45	4	is	be	AUX
ejpam-2337	45	5	called	call	VERB
ejpam-2337	45	6	a	a	DET
ejpam-2337	45	7	fundamental	fundamental	ADJ
ejpam-2337	45	8	system	system	NOUN
ejpam-2337	45	9	of	of	ADP
ejpam-2337	45	10	seminorms	seminorm	NOUN
ejpam-2337	45	11	.	.	PUNCT
ejpam-2337	46	1	it	it	PRON
ejpam-2337	46	2	is	be	AUX
ejpam-2337	46	3	by	by	ADP
ejpam-2337	46	4	no	no	DET
ejpam-2337	46	5	means	mean	NOUN
ejpam-2337	46	6	uniquely	uniquely	ADV
ejpam-2337	46	7	determined	determine	VERB
ejpam-2337	46	8	by	by	ADP
ejpam-2337	46	9	the	the	DET
ejpam-2337	46	10	topology	topology	NOUN
ejpam-2337	46	11	.	.	PUNCT
ejpam-2337	47	1	in	in	ADP
ejpam-2337	47	2	fact	fact	NOUN
ejpam-2337	47	3	,	,	PUNCT
ejpam-2337	47	4	two	two	NUM
ejpam-2337	47	5	systems	system	NOUN
ejpam-2337	47	6	+	+	CCONJ
ejpam-2337	47	7	+1	+1	ADJ
ejpam-2337	47	8	,	,	PUNCT
ejpam-2337	47	9	+	+	CCONJ
ejpam-2337	47	10	+2	+2	PRON
ejpam-2337	47	11	,	,	PUNCT
ejpam-2337	47	12	.	.	PUNCT
ejpam-2337	47	13	.	.	PUNCT
ejpam-2337	47	14	.	.	PUNCT
ejpam-2337	48	1	and	and	CCONJ
ejpam-2337	49	1	+	+	PUNCT
ejpam-2337	49	2	+	+	ADJ
ejpam-2337	49	3	-1	-1	ADJ
ejpam-2337	49	4	,	,	PUNCT
ejpam-2337	50	1	+	+	PUNCT
ejpam-2337	50	2	+	+	CCONJ
ejpam-2337	50	3	2	2	NUM
ejpam-2337	50	4	,	,	PUNCT
ejpam-2337	50	5	.	.	PUNCT
ejpam-2337	50	6	.	.	PUNCT
ejpam-2337	51	1	.	.	PUNCT
ejpam-2337	52	1	give	give	VERB
ejpam-2337	52	2	the	the	DET
ejpam-2337	52	3	same	same	ADJ
ejpam-2337	52	4	topology	topology	NOUN
ejpam-2337	52	5	if	if	SCONJ
ejpam-2337	52	6	and	and	CCONJ
ejpam-2337	52	7	only	only	ADV
ejpam-2337	52	8	if	if	SCONJ
ejpam-2337	52	9	there	there	PRON
ejpam-2337	52	10	exist	exist	VERB
ejpam-2337	52	11	constants	constant	NOUN
ejpam-2337	52	12	ck	ck	ADJ
ejpam-2337	52	13	and	and	CCONJ
ejpam-2337	52	14	n(k	n(k	PROPN
ejpam-2337	52	15	)	)	PUNCT
ejpam-2337	52	16	%	%	NOUN
ejpam-2337	52	17	#	#	NOUN
ejpam-2337	53	1	such	such	ADJ
ejpam-2337	53	2	that	that	SCONJ
ejpam-2337	53	3	+	+	PROPN
ejpam-2337	53	4	+	+	ADJ
ejpam-2337	53	5	k	k	X
ejpam-2337	53	6	,	,	PUNCT
ejpam-2337	53	7	ck	ck	PROPN
ejpam-2337	54	1	+	+	X
ejpam-2337	54	2	+	+	CCONJ
ejpam-2337	54	3	n(k	n(k	ADJ
ejpam-2337	54	4	)	)	PUNCT
ejpam-2337	54	5	and	and	CCONJ
ejpam-2337	54	6	+	+	PUNCT
ejpam-2337	55	1	+	+	ADJ
ejpam-2337	55	2	-k	-k	INTJ
ejpam-2337	55	3	,	,	PUNCT
ejpam-2337	55	4	ck	ck	PROPN
ejpam-2337	56	1	+	+	CCONJ
ejpam-2337	56	2	+	+	ADJ
ejpam-2337	56	3	n(k	n(k	PROPN
ejpam-2337	56	4	)	)	PUNCT
ejpam-2337	56	5	for	for	ADP
ejpam-2337	56	6	all	all	DET
ejpam-2337	56	7	k.	k.	PROPN
ejpam-2337	56	8	in	in	ADP
ejpam-2337	56	9	this	this	DET
ejpam-2337	56	10	case	case	NOUN
ejpam-2337	56	11	the	the	DET
ejpam-2337	56	12	systems	system	NOUN
ejpam-2337	56	13	of	of	ADP
ejpam-2337	56	14	seminorms	seminorm	NOUN
ejpam-2337	56	15	are	be	AUX
ejpam-2337	56	16	called	call	VERB
ejpam-2337	56	17	equivalent	equivalent	ADJ
ejpam-2337	56	18	.	.	PUNCT
ejpam-2337	57	1	a	a	DET
ejpam-2337	57	2	fréchet	fréchet	NOUN
ejpam-2337	57	3	space	space	NOUN
ejpam-2337	57	4	equipped	equip	VERB
ejpam-2337	57	5	with	with	ADP
ejpam-2337	57	6	a	a	DET
ejpam-2337	57	7	fixed	fix	VERB
ejpam-2337	57	8	fundamental	fundamental	ADJ
ejpam-2337	57	9	system	system	NOUN
ejpam-2337	57	10	of	of	ADP
ejpam-2337	57	11	seminorms	seminorm	NOUN
ejpam-2337	57	12	is	be	AUX
ejpam-2337	57	13	called	call	VERB
ejpam-2337	57	14	a	a	DET
ejpam-2337	57	15	graded	grade	VERB
ejpam-2337	57	16	fréchet	fréchet	NOUN
ejpam-2337	57	17	space	space	NOUN
ejpam-2337	57	18	.	.	PUNCT
ejpam-2337	58	1	this	this	DET
ejpam-2337	58	2	concept	concept	NOUN
ejpam-2337	58	3	is	be	AUX
ejpam-2337	58	4	important	important	ADJ
ejpam-2337	58	5	in	in	ADP
ejpam-2337	58	6	connection	connection	NOUN
ejpam-2337	58	7	with	with	ADP
ejpam-2337	58	8	many	many	ADJ
ejpam-2337	58	9	problems	problem	NOUN
ejpam-2337	58	10	in	in	ADP
ejpam-2337	58	11	analysis	analysis	NOUN
ejpam-2337	58	12	,	,	PUNCT
ejpam-2337	58	13	where	where	SCONJ
ejpam-2337	58	14	the	the	DET
ejpam-2337	58	15	index	index	NOUN
ejpam-2337	58	16	of	of	ADP
ejpam-2337	58	17	a	a	DET
ejpam-2337	58	18	norm	norm	NOUN
ejpam-2337	58	19	indicates	indicate	VERB
ejpam-2337	58	20	e.g.	e.g.	ADV
ejpam-2337	58	21	the	the	DET
ejpam-2337	58	22	order	order	NOUN
ejpam-2337	58	23	of	of	ADP
ejpam-2337	58	24	derivatives	derivative	NOUN
ejpam-2337	58	25	involved	involve	VERB
ejpam-2337	58	26	.	.	PUNCT
ejpam-2337	59	1	it	it	PRON
ejpam-2337	59	2	is	be	AUX
ejpam-2337	59	3	a	a	DET
ejpam-2337	59	4	classical	classical	ADJ
ejpam-2337	59	5	fact	fact	NOUN
ejpam-2337	59	6	that	that	SCONJ
ejpam-2337	59	7	the	the	DET
ejpam-2337	59	8	fréchet	fréchet	NOUN
ejpam-2337	59	9	spaces	space	NOUN
ejpam-2337	59	10	are	be	AUX
ejpam-2337	59	11	characterized	characterize	VERB
ejpam-2337	59	12	by	by	ADP
ejpam-2337	59	13	the	the	DET
ejpam-2337	59	14	existence	existence	NOUN
ejpam-2337	59	15	of	of	ADP
ejpam-2337	59	16	a	a	DET
ejpam-2337	59	17	countable	countable	ADJ
ejpam-2337	59	18	,	,	PUNCT
ejpam-2337	59	19	sufficient	sufficient	ADJ
ejpam-2337	59	20	and	and	CCONJ
ejpam-2337	59	21	increasing	increase	VERB
ejpam-2337	59	22	family	family	NOUN
ejpam-2337	59	23	of	of	ADP
ejpam-2337	59	24	semi	semi	NOUN
ejpam-2337	59	25	-	-	NOUN
ejpam-2337	59	26	norms	norm	NOUN
ejpam-2337	59	27	{	{	PUNCT
ejpam-2337	59	28	pi}i%	pi}i%	NOUN
ejpam-2337	59	29	#	#	NOUN
ejpam-2337	59	30	(	(	PUNCT
ejpam-2337	59	31	that	that	PRON
ejpam-2337	59	32	is	be	AUX
ejpam-2337	59	33	pi(x	pi(x	NUM
ejpam-2337	59	34	)	)	PUNCT
ejpam-2337	60	1	=	=	SYM
ejpam-2337	60	2	0	0	NUM
ejpam-2337	60	3	implies	imply	VERB
ejpam-2337	60	4	x	x	PUNCT
ejpam-2337	60	5	=	=	SYM
ejpam-2337	60	6	0	0	NUM
ejpam-2337	60	7	and	and	CCONJ
ejpam-2337	60	8	pi(x	pi(x	NUM
ejpam-2337	60	9	)	)	PUNCT
ejpam-2337	60	10	,	,	PUNCT
ejpam-2337	60	11	pi+1(x	pi+1(x	NOUN
ejpam-2337	60	12	)	)	PUNCT
ejpam-2337	60	13	for	for	ADP
ejpam-2337	60	14	all	all	PRON
ejpam-2337	60	15	x	x	SYM
ejpam-2337	60	16	%	%	NOUN
ejpam-2337	60	17	x	x	PUNCT
ejpam-2337	61	1	and	and	CCONJ
ejpam-2337	61	2	i	i	PRON
ejpam-2337	61	3	%	%	VERB
ejpam-2337	61	4	#	#	NOUN
ejpam-2337	61	5	)	)	PUNCT
ejpam-2337	61	6	,	,	PUNCT
ejpam-2337	61	7	which	which	PRON
ejpam-2337	61	8	define	define	VERB
ejpam-2337	61	9	the	the	DET
ejpam-2337	61	10	pseudo	pseudo	NOUN
ejpam-2337	61	11	-	-	NOUN
ejpam-2337	61	12	norm	norm	NOUN
ejpam-2337	61	13	"	"	PUNCT
ejpam-2337	61	14	(	(	PUNCT
ejpam-2337	61	15	x	x	X
ejpam-2337	61	16	)	)	PUNCT
ejpam-2337	61	17	=	=	SYM
ejpam-2337	61	18	&	&	CCONJ
ejpam-2337	61	19	!	!	PUNCT
ejpam-2337	62	1	i=0	i=0	ADJ
ejpam-2337	62	2	1	1	NUM
ejpam-2337	62	3	2i	2i	NUM
ejpam-2337	62	4	pi(x	pi(x	NOUN
ejpam-2337	62	5	)	)	PUNCT
ejpam-2337	62	6	1	1	NUM
ejpam-2337	62	7	+	+	NUM
ejpam-2337	62	8	pi(x	pi(x	NUM
ejpam-2337	62	9	)	)	PUNCT
ejpam-2337	62	10	and	and	CCONJ
ejpam-2337	62	11	the	the	DET
ejpam-2337	62	12	metric	metric	ADJ
ejpam-2337	62	13	d(x	d(x	PROPN
ejpam-2337	62	14	,	,	PUNCT
ejpam-2337	62	15	y	y	X
ejpam-2337	62	16	)	)	PUNCT
ejpam-2337	62	17	=	=	PRON
ejpam-2337	62	18	"	"	PUNCT
ejpam-2337	62	19	(	(	PUNCT
ejpam-2337	62	20	x.y	x.y	PROPN
ejpam-2337	62	21	)	)	PUNCT
ejpam-2337	62	22	invariant	invariant	VERB
ejpam-2337	62	23	with	with	ADP
ejpam-2337	62	24	respect	respect	NOUN
ejpam-2337	62	25	to	to	ADP
ejpam-2337	62	26	translations	translation	NOUN
ejpam-2337	62	27	,	,	PUNCT
ejpam-2337	62	28	such	such	ADJ
ejpam-2337	62	29	that	that	SCONJ
ejpam-2337	62	30	d	d	PROPN
ejpam-2337	62	31	generates	generate	VERB
ejpam-2337	62	32	a	a	DET
ejpam-2337	62	33	complete	complete	ADJ
ejpam-2337	62	34	topology	topology	NOUN
ejpam-2337	62	35	equivalent	equivalent	ADJ
ejpam-2337	62	36	to	to	ADP
ejpam-2337	62	37	that	that	PRON
ejpam-2337	62	38	of	of	ADP
ejpam-2337	62	39	locally	locally	ADV
ejpam-2337	62	40	convex	convex	ADJ
ejpam-2337	62	41	space	space	NOUN
ejpam-2337	62	42	.	.	PUNCT
ejpam-2337	63	1	also	also	ADV
ejpam-2337	63	2	,	,	PUNCT
ejpam-2337	63	3	notice	notice	VERB
ejpam-2337	63	4	that	that	SCONJ
ejpam-2337	63	5	since	since	SCONJ
ejpam-2337	63	6	pi(x	pi(x	NUM
ejpam-2337	63	7	)	)	PUNCT
ejpam-2337	63	8	1+pi(x	1+pi(x	NUM
ejpam-2337	63	9	)	)	PUNCT
ejpam-2337	63	10	,	,	PUNCT
ejpam-2337	63	11	1	1	NUM
ejpam-2337	63	12	and	and	CCONJ
ejpam-2337	63	13	"	"	PUNCT
ejpam-2337	63	14	&	&	CCONJ
ejpam-2337	63	15	i=0	i=0	PROPN
ejpam-2337	63	16	1	1	NUM
ejpam-2337	63	17	2i	2i	NUM
ejpam-2337	63	18	=	=	SYM
ejpam-2337	63	19	1	1	NUM
ejpam-2337	63	20	,	,	PUNCT
ejpam-2337	63	21	it	it	PRON
ejpam-2337	63	22	follows	follow	VERB
ejpam-2337	63	23	that	that	SCONJ
ejpam-2337	63	24	"	"	PUNCT
ejpam-2337	63	25	(	(	PUNCT
ejpam-2337	63	26	x	x	X
ejpam-2337	63	27	)	)	PUNCT
ejpam-2337	63	28	,	,	PUNCT
ejpam-2337	63	29	1	1	NUM
ejpam-2337	63	30	for	for	ADP
ejpam-2337	63	31	all	all	DET
ejpam-2337	63	32	x	x	SYM
ejpam-2337	63	33	%	%	NOUN
ejpam-2337	63	34	x	x	INTJ
ejpam-2337	63	35	(	(	PUNCT
ejpam-2337	63	36	see	see	VERB
ejpam-2337	63	37	[	[	X
ejpam-2337	63	38	7	7	NUM
ejpam-2337	63	39	]	]	NUM
ejpam-2337	63	40	)	)	PUNCT
ejpam-2337	63	41	.	.	PUNCT
ejpam-2337	64	1	k.	k.	PROPN
ejpam-2337	64	2	ravi	ravi	PROPN
ejpam-2337	64	3	,	,	PUNCT
ejpam-2337	64	4	b.	b.	PROPN
ejpam-2337	64	5	kumar	kumar	PROPN
ejpam-2337	64	6	/	/	SYM
ejpam-2337	64	7	eur	eur	PROPN
ejpam-2337	64	8	.	.	PUNCT
ejpam-2337	65	1	j.	j.	PROPN
ejpam-2337	65	2	pure	pure	PROPN
ejpam-2337	65	3	appl	appl	PROPN
ejpam-2337	65	4	.	.	PROPN
ejpam-2337	65	5	math	math	PROPN
ejpam-2337	65	6	,	,	PUNCT
ejpam-2337	65	7	8	8	NUM
ejpam-2337	65	8	(	(	PUNCT
ejpam-2337	65	9	2015	2015	NUM
ejpam-2337	65	10	)	)	PUNCT
ejpam-2337	65	11	,	,	PUNCT
ejpam-2337	65	12	283	283	NUM
ejpam-2337	65	13	-	-	SYM
ejpam-2337	65	14	293	293	NUM
ejpam-2337	65	15	285	285	NUM
ejpam-2337	65	16	moreover	moreover	ADV
ejpam-2337	65	17	,	,	PUNCT
ejpam-2337	65	18	d	d	PROPN
ejpam-2337	65	19	has	have	AUX
ejpam-2337	65	20	the	the	DET
ejpam-2337	65	21	properties	property	NOUN
ejpam-2337	65	22	given	give	VERB
ejpam-2337	65	23	by	by	ADP
ejpam-2337	65	24	the	the	DET
ejpam-2337	65	25	following	following	NOUN
ejpam-2337	65	26	.	.	PUNCT
ejpam-2337	66	1	theorem	theorem	ADJ
ejpam-2337	66	2	1	1	NUM
ejpam-2337	66	3	(	(	PUNCT
ejpam-2337	66	4	[	[	X
ejpam-2337	66	5	7	7	NUM
ejpam-2337	66	6	]	]	NUM
ejpam-2337	66	7	)	)	PUNCT
ejpam-2337	66	8	.	.	PUNCT
ejpam-2337	67	1	let	let	VERB
ejpam-2337	67	2	(	(	PUNCT
ejpam-2337	67	3	x	x	INTJ
ejpam-2337	67	4	,	,	PUNCT
ejpam-2337	67	5	{	{	PUNCT
ejpam-2337	67	6	pi}i%	pi}i%	NOUN
ejpam-2337	67	7	#	#	NUM
ejpam-2337	67	8	,	,	PUNCT
ejpam-2337	67	9	d	d	X
ejpam-2337	67	10	)	)	PUNCT
ejpam-2337	67	11	be	be	AUX
ejpam-2337	67	12	a	a	DET
ejpam-2337	67	13	fréchet	fréchet	NOUN
ejpam-2337	67	14	space	space	NOUN
ejpam-2337	67	15	,	,	PUNCT
ejpam-2337	67	16	then	then	ADV
ejpam-2337	67	17	(	(	PUNCT
ejpam-2337	67	18	i	i	NOUN
ejpam-2337	67	19	)	)	PUNCT
ejpam-2337	67	20	d(cx	d(cx	PROPN
ejpam-2337	67	21	,	,	PUNCT
ejpam-2337	67	22	c	c	PROPN
ejpam-2337	67	23	y	y	PROPN
ejpam-2337	67	24	)	)	PUNCT
ejpam-2337	67	25	,	,	PUNCT
ejpam-2337	67	26	d(x	d(x	PROPN
ejpam-2337	67	27	,	,	PUNCT
ejpam-2337	67	28	y	y	PROPN
ejpam-2337	67	29	)	)	PUNCT
ejpam-2337	67	30	for	for	ADP
ejpam-2337	67	31	x	x	SYM
ejpam-2337	67	32	,	,	PUNCT
ejpam-2337	67	33	y	y	PROPN
ejpam-2337	67	34	%	%	NOUN
ejpam-2337	67	35	x	x	X
ejpam-2337	67	36	,	,	PUNCT
ejpam-2337	67	37	|c|	|c|	PROPN
ejpam-2337	67	38	<	<	X
ejpam-2337	67	39	1	1	NUM
ejpam-2337	67	40	;	;	PUNCT
ejpam-2337	67	41	(	(	PUNCT
ejpam-2337	67	42	ii	ii	NOUN
ejpam-2337	67	43	)	)	PUNCT
ejpam-2337	67	44	d(x	d(x	PROPN
ejpam-2337	68	1	+	+	CCONJ
ejpam-2337	68	2	u	u	PROPN
ejpam-2337	68	3	,	,	PUNCT
ejpam-2337	68	4	y	y	PROPN
ejpam-2337	68	5	+	+	PROPN
ejpam-2337	68	6	v	v	NOUN
ejpam-2337	68	7	)	)	PUNCT
ejpam-2337	68	8	,	,	PUNCT
ejpam-2337	68	9	d(x	d(x	PROPN
ejpam-2337	68	10	,	,	PUNCT
ejpam-2337	68	11	y	y	PROPN
ejpam-2337	68	12	)	)	PUNCT
ejpam-2337	68	13	+	+	CCONJ
ejpam-2337	68	14	d(u	d(u	PROPN
ejpam-2337	68	15	,	,	PUNCT
ejpam-2337	68	16	v	v	NOUN
ejpam-2337	68	17	)	)	PUNCT
ejpam-2337	68	18	for	for	ADP
ejpam-2337	68	19	x	x	SYM
ejpam-2337	68	20	,	,	PUNCT
ejpam-2337	68	21	y	y	PROPN
ejpam-2337	68	22	,	,	PUNCT
ejpam-2337	68	23	u	u	NOUN
ejpam-2337	68	24	,	,	PUNCT
ejpam-2337	68	25	v	v	DET
ejpam-2337	68	26	%	%	NOUN
ejpam-2337	68	27	x	x	X
ejpam-2337	68	28	;	;	PUNCT
ejpam-2337	68	29	(	(	PUNCT
ejpam-2337	68	30	iii	iii	X
ejpam-2337	68	31	)	)	PUNCT
ejpam-2337	68	32	d(kx	d(kx	NOUN
ejpam-2337	68	33	,	,	PUNCT
ejpam-2337	68	34	k	k	PROPN
ejpam-2337	68	35	y	y	PROPN
ejpam-2337	68	36	)	)	PUNCT
ejpam-2337	68	37	,	,	PUNCT
ejpam-2337	68	38	d(r	d(r	PROPN
ejpam-2337	68	39	x	x	SYM
ejpam-2337	68	40	,	,	PUNCT
ejpam-2337	68	41	r	r	NOUN
ejpam-2337	68	42	y	y	PROPN
ejpam-2337	68	43	)	)	PUNCT
ejpam-2337	68	44	if	if	SCONJ
ejpam-2337	68	45	k	k	X
ejpam-2337	68	46	,	,	PUNCT
ejpam-2337	68	47	r	r	NOUN
ejpam-2337	68	48	%	%	NOUN
ejpam-2337	68	49	!	!	PUNCT
ejpam-2337	68	50	,	,	PUNCT
ejpam-2337	69	1	0	0	PUNCT
ejpam-2337	69	2	<	<	X
ejpam-2337	69	3	k	k	X
ejpam-2337	69	4	,	,	PUNCT
ejpam-2337	69	5	r	r	NOUN
ejpam-2337	69	6	;	;	PUNCT
ejpam-2337	69	7	(	(	PUNCT
ejpam-2337	69	8	iv	iv	X
ejpam-2337	69	9	)	)	PUNCT
ejpam-2337	69	10	d(kx	d(kx	PROPN
ejpam-2337	69	11	,	,	PUNCT
ejpam-2337	69	12	k	k	PROPN
ejpam-2337	69	13	y	y	PROPN
ejpam-2337	69	14	)	)	PUNCT
ejpam-2337	69	15	,	,	PUNCT
ejpam-2337	69	16	kd(x	kd(x	X
ejpam-2337	69	17	,	,	PUNCT
ejpam-2337	69	18	y	y	NOUN
ejpam-2337	69	19	)	)	PUNCT
ejpam-2337	69	20	for	for	ADP
ejpam-2337	69	21	x	x	SYM
ejpam-2337	69	22	,	,	PUNCT
ejpam-2337	69	23	y	y	NOUN
ejpam-2337	69	24	%	%	NOUN
ejpam-2337	69	25	x	x	INTJ
ejpam-2337	69	26	,	,	PUNCT
ejpam-2337	69	27	k	k	NOUN
ejpam-2337	70	1	%	%	INTJ
ejpam-2337	70	2	#	#	ADP
ejpam-2337	70	3	,	,	PUNCT
ejpam-2337	70	4	k	k	PROPN
ejpam-2337	70	5	'	'	PUNCT
ejpam-2337	70	6	2	2	NUM
ejpam-2337	70	7	;	;	PUNCT
ejpam-2337	70	8	(	(	PUNCT
ejpam-2337	70	9	v	v	NOUN
ejpam-2337	70	10	)	)	PUNCT
ejpam-2337	70	11	d(cx	d(cx	PROPN
ejpam-2337	70	12	,	,	PUNCT
ejpam-2337	70	13	c	c	PROPN
ejpam-2337	70	14	y	y	PROPN
ejpam-2337	70	15	)	)	PUNCT
ejpam-2337	70	16	,	,	PUNCT
ejpam-2337	70	17	(	(	PUNCT
ejpam-2337	71	1	|c|+	|c|+	NOUN
ejpam-2337	71	2	1)d(x	1)d(x	NUM
ejpam-2337	71	3	,	,	PUNCT
ejpam-2337	71	4	y	y	NOUN
ejpam-2337	71	5	)	)	PUNCT
ejpam-2337	71	6	for	for	ADP
ejpam-2337	71	7	all	all	PRON
ejpam-2337	71	8	x	x	SYM
ejpam-2337	71	9	,	,	PUNCT
ejpam-2337	71	10	y	y	NOUN
ejpam-2337	71	11	%	%	NOUN
ejpam-2337	71	12	x	x	PUNCT
ejpam-2337	72	1	and	and	CCONJ
ejpam-2337	72	2	c	c	NOUN
ejpam-2337	72	3	%	%	NOUN
ejpam-2337	72	4	!	!	PUNCT
ejpam-2337	72	5	.	.	PUNCT
ejpam-2337	73	1	fréchet	fréchet	PROPN
ejpam-2337	73	2	spaces	space	NOUN
ejpam-2337	73	3	are	be	AUX
ejpam-2337	73	4	studied	study	VERB
ejpam-2337	73	5	because	because	SCONJ
ejpam-2337	73	6	even	even	ADV
ejpam-2337	73	7	though	though	SCONJ
ejpam-2337	73	8	their	their	PRON
ejpam-2337	73	9	topological	topological	ADJ
ejpam-2337	73	10	structure	structure	NOUN
ejpam-2337	73	11	is	be	AUX
ejpam-2337	73	12	more	more	ADV
ejpam-2337	73	13	complicated	complicated	ADJ
ejpam-2337	73	14	due	due	ADP
ejpam-2337	73	15	to	to	ADP
ejpam-2337	73	16	the	the	DET
ejpam-2337	73	17	lack	lack	NOUN
ejpam-2337	73	18	of	of	ADP
ejpam-2337	73	19	a	a	DET
ejpam-2337	73	20	norm	norm	NOUN
ejpam-2337	73	21	,	,	PUNCT
ejpam-2337	73	22	many	many	ADJ
ejpam-2337	73	23	important	important	ADJ
ejpam-2337	73	24	results	result	NOUN
ejpam-2337	73	25	in	in	ADP
ejpam-2337	73	26	functional	functional	ADJ
ejpam-2337	73	27	analysis	analysis	NOUN
ejpam-2337	73	28	,	,	PUNCT
ejpam-2337	73	29	like	like	ADP
ejpam-2337	73	30	the	the	DET
ejpam-2337	73	31	open	open	ADJ
ejpam-2337	73	32	mapping	mapping	NOUN
ejpam-2337	73	33	theorem	theorem	NOUN
ejpam-2337	73	34	and	and	CCONJ
ejpam-2337	73	35	the	the	DET
ejpam-2337	73	36	banach	banach	NOUN
ejpam-2337	73	37	-	-	PUNCT
ejpam-2337	73	38	steinhaus	steinhaus	NOUN
ejpam-2337	73	39	theorem	theorem	NOUN
ejpam-2337	73	40	,	,	PUNCT
ejpam-2337	73	41	still	still	ADV
ejpam-2337	73	42	hold	hold	VERB
ejpam-2337	73	43	.	.	PUNCT
ejpam-2337	74	1	for	for	ADP
ejpam-2337	74	2	further	further	ADJ
ejpam-2337	74	3	concepts	concept	NOUN
ejpam-2337	74	4	on	on	ADP
ejpam-2337	74	5	fréchet	fréchet	PROPN
ejpam-2337	74	6	spaces	space	NOUN
ejpam-2337	74	7	,	,	PUNCT
ejpam-2337	74	8	one	one	PRON
ejpam-2337	74	9	can	can	AUX
ejpam-2337	74	10	refer	refer	VERB
ejpam-2337	74	11	to	to	ADP
ejpam-2337	74	12	(	(	PUNCT
ejpam-2337	74	13	[	[	X
ejpam-2337	74	14	6	6	NUM
ejpam-2337	74	15	,	,	PUNCT
ejpam-2337	74	16	14	14	NUM
ejpam-2337	74	17	,	,	PUNCT
ejpam-2337	74	18	17	17	NUM
ejpam-2337	74	19	]	]	PUNCT
ejpam-2337	74	20	)	)	PUNCT
ejpam-2337	74	21	.	.	PUNCT
ejpam-2337	75	1	the	the	DET
ejpam-2337	75	2	stability	stability	NOUN
ejpam-2337	75	3	theory	theory	NOUN
ejpam-2337	75	4	of	of	ADP
ejpam-2337	75	5	functional	functional	ADJ
ejpam-2337	75	6	equations	equation	NOUN
ejpam-2337	75	7	basically	basically	ADV
ejpam-2337	75	8	deals	deal	VERB
ejpam-2337	75	9	with	with	ADP
ejpam-2337	75	10	the	the	DET
ejpam-2337	75	11	following	follow	VERB
ejpam-2337	75	12	question	question	NOUN
ejpam-2337	75	13	:	:	PUNCT
ejpam-2337	75	14	“	"	PUNCT
ejpam-2337	75	15	given	give	VERB
ejpam-2337	75	16	an	an	DET
ejpam-2337	75	17	approximately	approximately	ADV
ejpam-2337	75	18	linear	linear	ADJ
ejpam-2337	75	19	mapping	mapping	NOUN
ejpam-2337	75	20	f	f	NOUN
ejpam-2337	75	21	,	,	PUNCT
ejpam-2337	75	22	when	when	SCONJ
ejpam-2337	75	23	does	do	AUX
ejpam-2337	75	24	a	a	DET
ejpam-2337	75	25	linear	linear	ADJ
ejpam-2337	75	26	mapping	mapping	NOUN
ejpam-2337	75	27	t	t	NOUN
ejpam-2337	75	28	estimating	estimate	VERB
ejpam-2337	75	29	f	f	PRON
ejpam-2337	75	30	exist	exist	VERB
ejpam-2337	75	31	?	?	PUNCT
ejpam-2337	75	32	”	"	PUNCT
ejpam-2337	76	1	this	this	DET
ejpam-2337	76	2	problem	problem	NOUN
ejpam-2337	76	3	was	be	AUX
ejpam-2337	76	4	raised	raise	VERB
ejpam-2337	76	5	by	by	ADP
ejpam-2337	76	6	s.m	s.m	PROPN
ejpam-2337	76	7	.	.	PROPN
ejpam-2337	76	8	ulam	ulam	PROPN
ejpam-2337	77	1	[	[	X
ejpam-2337	77	2	22	22	NUM
ejpam-2337	77	3	]	]	PUNCT
ejpam-2337	77	4	in	in	ADP
ejpam-2337	77	5	the	the	DET
ejpam-2337	77	6	year	year	NOUN
ejpam-2337	77	7	1940	1940	NUM
ejpam-2337	77	8	and	and	CCONJ
ejpam-2337	77	9	d.h	d.h	PROPN
ejpam-2337	77	10	.	.	PROPN
ejpam-2337	77	11	hyers	hyer	NOUN
ejpam-2337	78	1	[	[	X
ejpam-2337	78	2	11	11	NUM
ejpam-2337	78	3	]	]	PUNCT
ejpam-2337	78	4	in	in	ADP
ejpam-2337	78	5	the	the	DET
ejpam-2337	78	6	year	year	NOUN
ejpam-2337	78	7	1941	1941	NUM
ejpam-2337	78	8	,	,	PUNCT
ejpam-2337	78	9	gave	give	VERB
ejpam-2337	78	10	a	a	DET
ejpam-2337	78	11	first	first	ADJ
ejpam-2337	78	12	affirmative	affirmative	ADJ
ejpam-2337	78	13	partial	partial	ADJ
ejpam-2337	78	14	answer	answer	NOUN
ejpam-2337	78	15	to	to	ADP
ejpam-2337	78	16	the	the	DET
ejpam-2337	78	17	question	question	NOUN
ejpam-2337	78	18	of	of	ADP
ejpam-2337	78	19	ulam	ulam	PROPN
ejpam-2337	78	20	in	in	ADP
ejpam-2337	78	21	the	the	DET
ejpam-2337	78	22	case	case	NOUN
ejpam-2337	78	23	of	of	ADP
ejpam-2337	78	24	banach	banach	NOUN
ejpam-2337	78	25	spaces	space	NOUN
ejpam-2337	78	26	.	.	PUNCT
ejpam-2337	79	1	hyers	hyer	NOUN
ejpam-2337	79	2	’	'	PUNCT
ejpam-2337	79	3	theorem	theorem	NOUN
ejpam-2337	79	4	was	be	AUX
ejpam-2337	79	5	generalized	generalize	VERB
ejpam-2337	79	6	by	by	ADP
ejpam-2337	79	7	t.	t.	PROPN
ejpam-2337	79	8	aoki	aoki	PROPN
ejpam-2337	80	1	[	[	X
ejpam-2337	80	2	2	2	NUM
ejpam-2337	80	3	]	]	PUNCT
ejpam-2337	80	4	for	for	ADP
ejpam-2337	80	5	additive	additive	ADJ
ejpam-2337	80	6	mappings	mapping	NOUN
ejpam-2337	80	7	in	in	ADP
ejpam-2337	80	8	the	the	DET
ejpam-2337	80	9	year	year	NOUN
ejpam-2337	80	10	1950	1950	NUM
ejpam-2337	80	11	and	and	CCONJ
ejpam-2337	80	12	by	by	ADP
ejpam-2337	80	13	th.m	th.m	PROPN
ejpam-2337	80	14	.	.	PUNCT
ejpam-2337	81	1	rassias	rassias	PROPN
ejpam-2337	82	1	[	[	X
ejpam-2337	82	2	18	18	NUM
ejpam-2337	82	3	]	]	PUNCT
ejpam-2337	82	4	for	for	ADP
ejpam-2337	82	5	linear	linear	ADJ
ejpam-2337	82	6	mappings	mapping	NOUN
ejpam-2337	82	7	by	by	ADP
ejpam-2337	82	8	considering	consider	VERB
ejpam-2337	82	9	an	an	DET
ejpam-2337	82	10	unbounded	unbounded	ADJ
ejpam-2337	82	11	cauchy	cauchy	ADJ
ejpam-2337	82	12	difference	difference	NOUN
ejpam-2337	82	13	in	in	ADP
ejpam-2337	82	14	the	the	DET
ejpam-2337	82	15	year	year	NOUN
ejpam-2337	82	16	1978	1978	NUM
ejpam-2337	82	17	.	.	PUNCT
ejpam-2337	83	1	the	the	DET
ejpam-2337	83	2	type	type	NOUN
ejpam-2337	83	3	of	of	ADP
ejpam-2337	83	4	stability	stability	NOUN
ejpam-2337	83	5	investigated	investigate	VERB
ejpam-2337	83	6	by	by	ADP
ejpam-2337	83	7	th.m	th.m	PROPN
ejpam-2337	83	8	.	.	PUNCT
ejpam-2337	84	1	rassias	rassias	PROPN
ejpam-2337	84	2	is	be	AUX
ejpam-2337	84	3	known	know	VERB
ejpam-2337	84	4	as	as	ADP
ejpam-2337	84	5	"	"	PUNCT
ejpam-2337	84	6	hyers	hyer	NOUN
ejpam-2337	84	7	-	-	PUNCT
ejpam-2337	84	8	ulamrassias	ulamrassias	ADJ
ejpam-2337	84	9	stability	stability	NOUN
ejpam-2337	84	10	"	"	PUNCT
ejpam-2337	84	11	of	of	ADP
ejpam-2337	84	12	functional	functional	ADJ
ejpam-2337	84	13	equation	equation	NOUN
ejpam-2337	84	14	.	.	PUNCT
ejpam-2337	85	1	a	a	DET
ejpam-2337	85	2	generalized	generalized	ADJ
ejpam-2337	85	3	form	form	NOUN
ejpam-2337	85	4	of	of	ADP
ejpam-2337	85	5	the	the	DET
ejpam-2337	85	6	theorem	theorem	NOUN
ejpam-2337	85	7	given	give	VERB
ejpam-2337	85	8	by	by	ADP
ejpam-2337	85	9	th.m	th.m	PROPN
ejpam-2337	85	10	.	.	PUNCT
ejpam-2337	86	1	rassias	rassias	PROPN
ejpam-2337	86	2	was	be	AUX
ejpam-2337	86	3	advocated	advocate	VERB
ejpam-2337	86	4	by	by	ADP
ejpam-2337	86	5	p.	p.	PROPN
ejpam-2337	86	6	gavruta	gavruta	NOUN
ejpam-2337	87	1	[	[	X
ejpam-2337	87	2	8	8	X
ejpam-2337	87	3	]	]	PUNCT
ejpam-2337	87	4	who	who	PRON
ejpam-2337	87	5	replaced	replace	VERB
ejpam-2337	87	6	the	the	DET
ejpam-2337	87	7	unbounded	unbounded	ADJ
ejpam-2337	87	8	cauchy	cauchy	ADJ
ejpam-2337	87	9	difference	difference	NOUN
ejpam-2337	87	10	in	in	ADP
ejpam-2337	87	11	rassias	rassias	PROPN
ejpam-2337	87	12	’	'	PUNCT
ejpam-2337	87	13	theorem	theorem	VERB
ejpam-2337	87	14	by	by	ADP
ejpam-2337	87	15	a	a	DET
ejpam-2337	87	16	general	general	ADJ
ejpam-2337	87	17	control	control	NOUN
ejpam-2337	87	18	function	function	NOUN
ejpam-2337	87	19	.	.	PUNCT
ejpam-2337	88	1	this	this	DET
ejpam-2337	88	2	type	type	NOUN
ejpam-2337	88	3	of	of	ADP
ejpam-2337	88	4	stability	stability	NOUN
ejpam-2337	88	5	is	be	AUX
ejpam-2337	88	6	called	call	VERB
ejpam-2337	88	7	"	"	PUNCT
ejpam-2337	88	8	generalized	generalized	ADJ
ejpam-2337	88	9	hyers	hyer	NOUN
ejpam-2337	88	10	-	-	PUNCT
ejpam-2337	88	11	ulam	ulam	ADJ
ejpam-2337	88	12	-	-	PUNCT
ejpam-2337	88	13	rassias	rassias	PROPN
ejpam-2337	88	14	stability	stability	NOUN
ejpam-2337	88	15	"	"	PUNCT
ejpam-2337	88	16	.	.	PUNCT
ejpam-2337	89	1	the	the	DET
ejpam-2337	89	2	stability	stability	NOUN
ejpam-2337	89	3	problems	problem	NOUN
ejpam-2337	89	4	of	of	ADP
ejpam-2337	89	5	several	several	ADJ
ejpam-2337	89	6	functional	functional	ADJ
ejpam-2337	89	7	equations	equation	NOUN
ejpam-2337	89	8	have	have	AUX
ejpam-2337	89	9	been	be	AUX
ejpam-2337	89	10	extensively	extensively	ADV
ejpam-2337	89	11	investigated	investigate	VERB
ejpam-2337	89	12	by	by	ADP
ejpam-2337	89	13	a	a	DET
ejpam-2337	89	14	number	number	NOUN
ejpam-2337	89	15	of	of	ADP
ejpam-2337	89	16	authors	author	NOUN
ejpam-2337	89	17	and	and	CCONJ
ejpam-2337	89	18	there	there	PRON
ejpam-2337	89	19	are	be	VERB
ejpam-2337	89	20	many	many	ADJ
ejpam-2337	89	21	interesting	interesting	ADJ
ejpam-2337	89	22	results	result	NOUN
ejpam-2337	89	23	concerning	concern	VERB
ejpam-2337	89	24	this	this	DET
ejpam-2337	89	25	problem	problem	NOUN
ejpam-2337	89	26	(	(	PUNCT
ejpam-2337	89	27	see	see	VERB
ejpam-2337	89	28	[	[	X
ejpam-2337	89	29	1	1	NUM
ejpam-2337	89	30	,	,	PUNCT
ejpam-2337	89	31	4	4	NUM
ejpam-2337	89	32	,	,	PUNCT
ejpam-2337	89	33	5	5	NUM
ejpam-2337	89	34	,	,	PUNCT
ejpam-2337	89	35	10	10	NUM
ejpam-2337	89	36	,	,	PUNCT
ejpam-2337	89	37	12	12	NUM
ejpam-2337	89	38	,	,	PUNCT
ejpam-2337	89	39	13	13	NUM
ejpam-2337	89	40	,	,	PUNCT
ejpam-2337	89	41	15	15	NUM
ejpam-2337	89	42	,	,	PUNCT
ejpam-2337	89	43	16	16	NUM
ejpam-2337	89	44	,	,	PUNCT
ejpam-2337	89	45	21	21	NUM
ejpam-2337	89	46	]	]	PUNCT
ejpam-2337	89	47	)	)	PUNCT
ejpam-2337	89	48	.	.	PUNCT
ejpam-2337	90	1	let	let	VERB
ejpam-2337	90	2	a	a	PRON
ejpam-2337	90	3	and	and	CCONJ
ejpam-2337	90	4	b	b	NOUN
ejpam-2337	90	5	be	be	AUX
ejpam-2337	90	6	vector	vector	NOUN
ejpam-2337	90	7	spaces	space	NOUN
ejpam-2337	90	8	.	.	PUNCT
ejpam-2337	91	1	a	a	DET
ejpam-2337	91	2	mapping	mapping	NOUN
ejpam-2337	91	3	j	j	NOUN
ejpam-2337	91	4	:	:	PUNCT
ejpam-2337	91	5	a$	a$	ADV
ejpam-2337	91	6	b	b	PROPN
ejpam-2337	91	7	is	be	AUX
ejpam-2337	91	8	called	call	VERB
ejpam-2337	91	9	jensen	jensen	PROPN
ejpam-2337	91	10	mapping	mapping	NOUN
ejpam-2337	91	11	if	if	SCONJ
ejpam-2337	91	12	j	j	PROPN
ejpam-2337	91	13	satisfies	satisfy	VERB
ejpam-2337	91	14	the	the	DET
ejpam-2337	91	15	functional	functional	ADJ
ejpam-2337	91	16	equation	equation	NOUN
ejpam-2337	91	17	2j	2j	NOUN
ejpam-2337	91	18	#	#	NOUN
ejpam-2337	91	19	x	x	NOUN
ejpam-2337	92	1	+	+	CCONJ
ejpam-2337	92	2	y	y	PROPN
ejpam-2337	92	3	2	2	NUM
ejpam-2337	92	4	$	$	NOUN
ejpam-2337	92	5	=	=	SYM
ejpam-2337	92	6	j(x	j(x	PROPN
ejpam-2337	92	7	)	)	PUNCT
ejpam-2337	93	1	+	+	CCONJ
ejpam-2337	94	1	j(y	j(y	PROPN
ejpam-2337	94	2	)	)	PUNCT
ejpam-2337	94	3	.	.	PUNCT
ejpam-2337	95	1	definition	definition	NOUN
ejpam-2337	95	2	1	1	NUM
ejpam-2337	95	3	(	(	PUNCT
ejpam-2337	95	4	[	[	X
ejpam-2337	95	5	3	3	NUM
ejpam-2337	95	6	]	]	PUNCT
ejpam-2337	95	7	)	)	PUNCT
ejpam-2337	95	8	.	.	PUNCT
ejpam-2337	96	1	let	let	VERB
ejpam-2337	96	2	a	a	PRON
ejpam-2337	96	3	and	and	CCONJ
ejpam-2337	96	4	b	b	NOUN
ejpam-2337	96	5	be	be	AUX
ejpam-2337	96	6	vector	vector	NOUN
ejpam-2337	96	7	spaces	space	NOUN
ejpam-2337	96	8	.	.	PUNCT
ejpam-2337	97	1	a	a	DET
ejpam-2337	97	2	mapping	mapping	NOUN
ejpam-2337	97	3	f	f	NOUN
ejpam-2337	97	4	:	:	PUNCT
ejpam-2337	97	5	a	a	DET
ejpam-2337	97	6	#	#	NOUN
ejpam-2337	97	7	a$	a$	ADP
ejpam-2337	97	8	b	b	PROPN
ejpam-2337	97	9	is	be	AUX
ejpam-2337	97	10	called	call	VERB
ejpam-2337	97	11	a	a	DET
ejpam-2337	97	12	bi	bi	ADJ
ejpam-2337	97	13	-	-	ADJ
ejpam-2337	97	14	jensen	jensen	ADJ
ejpam-2337	97	15	mapping	mapping	NOUN
ejpam-2337	97	16	if	if	SCONJ
ejpam-2337	97	17	f	f	PROPN
ejpam-2337	97	18	satisfies	satisfy	VERB
ejpam-2337	97	19	the	the	DET
ejpam-2337	97	20	system	system	NOUN
ejpam-2337	97	21	of	of	ADP
ejpam-2337	97	22	functional	functional	ADJ
ejpam-2337	97	23	equations	equation	NOUN
ejpam-2337	97	24	2	2	NUM
ejpam-2337	97	25	f	f	NOUN
ejpam-2337	97	26	#	#	NOUN
ejpam-2337	97	27	x	x	PROPN
ejpam-2337	98	1	+	+	CCONJ
ejpam-2337	98	2	y	y	PROPN
ejpam-2337	98	3	2	2	NUM
ejpam-2337	98	4	,	,	PUNCT
ejpam-2337	98	5	z	z	NOUN
ejpam-2337	98	6	$	$	SYM
ejpam-2337	98	7	=	=	SYM
ejpam-2337	98	8	f	f	X
ejpam-2337	98	9	(	(	PUNCT
ejpam-2337	98	10	x	x	INTJ
ejpam-2337	98	11	,	,	PUNCT
ejpam-2337	98	12	z	z	NOUN
ejpam-2337	98	13	)	)	PUNCT
ejpam-2337	99	1	+	+	NUM
ejpam-2337	99	2	f	f	X
ejpam-2337	99	3	(	(	PUNCT
ejpam-2337	99	4	y	y	PROPN
ejpam-2337	99	5	,	,	PUNCT
ejpam-2337	99	6	z	z	NOUN
ejpam-2337	99	7	)	)	PUNCT
ejpam-2337	99	8	2	2	NUM
ejpam-2337	99	9	f	f	NOUN
ejpam-2337	99	10	#	#	NOUN
ejpam-2337	99	11	x	x	NOUN
ejpam-2337	99	12	,	,	PUNCT
ejpam-2337	99	13	y	y	PROPN
ejpam-2337	99	14	+	+	CCONJ
ejpam-2337	99	15	z	z	NOUN
ejpam-2337	99	16	2	2	NUM
ejpam-2337	99	17	$	$	SYM
ejpam-2337	99	18	=	=	SYM
ejpam-2337	99	19	f	f	X
ejpam-2337	99	20	(	(	PUNCT
ejpam-2337	99	21	x	x	INTJ
ejpam-2337	99	22	,	,	PUNCT
ejpam-2337	99	23	y	y	PROPN
ejpam-2337	99	24	)	)	PUNCT
ejpam-2337	100	1	+	+	CCONJ
ejpam-2337	100	2	f	f	X
ejpam-2337	100	3	(	(	PUNCT
ejpam-2337	100	4	x	x	INTJ
ejpam-2337	100	5	,	,	PUNCT
ejpam-2337	100	6	z	z	NOUN
ejpam-2337	100	7	)	)	PUNCT
ejpam-2337	100	8	.	.	PUNCT
ejpam-2337	101	1	%	%	NOUN
ejpam-2337	101	2	&	&	CCONJ
ejpam-2337	101	3	'	'	PUNCT
ejpam-2337	101	4	&	&	CCONJ
ejpam-2337	101	5	(	(	PUNCT
ejpam-2337	101	6	(	(	PUNCT
ejpam-2337	101	7	1	1	X
ejpam-2337	101	8	)	)	PUNCT
ejpam-2337	101	9	when	when	SCONJ
ejpam-2337	101	10	a=	a=	PROPN
ejpam-2337	101	11	b	b	X
ejpam-2337	101	12	=	=	PUNCT
ejpam-2337	101	13	!	!	PUNCT
ejpam-2337	101	14	,	,	PUNCT
ejpam-2337	101	15	the	the	DET
ejpam-2337	101	16	function	function	NOUN
ejpam-2337	101	17	f	f	NOUN
ejpam-2337	101	18	:	:	PUNCT
ejpam-2337	101	19	!	!	PUNCT
ejpam-2337	102	1	#	#	X
ejpam-2337	102	2	!	!	PUNCT
ejpam-2337	102	3	$	$	X
ejpam-2337	102	4	!	!	PUNCT
ejpam-2337	103	1	given	give	VERB
ejpam-2337	103	2	by	by	ADP
ejpam-2337	103	3	f	f	PROPN
ejpam-2337	103	4	(	(	PUNCT
ejpam-2337	103	5	x	x	PROPN
ejpam-2337	103	6	,	,	PUNCT
ejpam-2337	103	7	y	y	PROPN
ejpam-2337	103	8	)	)	PUNCT
ejpam-2337	103	9	=	=	NOUN
ejpam-2337	104	1	ax	ax	NOUN
ejpam-2337	104	2	y	y	PROPN
ejpam-2337	104	3	+	+	CCONJ
ejpam-2337	104	4	bx	bx	VERB
ejpam-2337	105	1	+	+	CCONJ
ejpam-2337	106	1	c	c	NOUN
ejpam-2337	106	2	y	y	PROPN
ejpam-2337	107	1	+	+	CCONJ
ejpam-2337	107	2	d	d	NOUN
ejpam-2337	107	3	is	be	AUX
ejpam-2337	107	4	a	a	DET
ejpam-2337	107	5	solution	solution	NOUN
ejpam-2337	107	6	of	of	ADP
ejpam-2337	107	7	(	(	PUNCT
ejpam-2337	107	8	1	1	NUM
ejpam-2337	107	9	)	)	PUNCT
ejpam-2337	107	10	.	.	PUNCT
ejpam-2337	108	1	k.	k.	PROPN
ejpam-2337	108	2	ravi	ravi	PROPN
ejpam-2337	108	3	,	,	PUNCT
ejpam-2337	108	4	b.	b.	PROPN
ejpam-2337	108	5	kumar	kumar	PROPN
ejpam-2337	108	6	/	/	SYM
ejpam-2337	108	7	eur	eur	PROPN
ejpam-2337	108	8	.	.	PUNCT
ejpam-2337	109	1	j.	j.	PROPN
ejpam-2337	109	2	pure	pure	PROPN
ejpam-2337	109	3	appl	appl	PROPN
ejpam-2337	109	4	.	.	PROPN
ejpam-2337	109	5	math	math	PROPN
ejpam-2337	109	6	,	,	PUNCT
ejpam-2337	109	7	8	8	NUM
ejpam-2337	109	8	(	(	PUNCT
ejpam-2337	109	9	2015	2015	NUM
ejpam-2337	109	10	)	)	PUNCT
ejpam-2337	109	11	,	,	PUNCT
ejpam-2337	109	12	283	283	NUM
ejpam-2337	109	13	-	-	SYM
ejpam-2337	109	14	293	293	NUM
ejpam-2337	109	15	286	286	NUM
ejpam-2337	109	16	definition	definition	NOUN
ejpam-2337	109	17	2	2	NUM
ejpam-2337	109	18	(	(	PUNCT
ejpam-2337	109	19	[	[	X
ejpam-2337	109	20	9	9	NUM
ejpam-2337	109	21	]	]	PUNCT
ejpam-2337	109	22	)	)	PUNCT
ejpam-2337	109	23	.	.	PUNCT
ejpam-2337	110	1	let	let	VERB
ejpam-2337	110	2	a	a	PRON
ejpam-2337	110	3	and	and	CCONJ
ejpam-2337	110	4	b	b	NOUN
ejpam-2337	110	5	be	be	AUX
ejpam-2337	110	6	vector	vector	NOUN
ejpam-2337	110	7	spaces	space	NOUN
ejpam-2337	110	8	.	.	PUNCT
ejpam-2337	111	1	a	a	DET
ejpam-2337	111	2	mapping	mapping	NOUN
ejpam-2337	111	3	f	f	NOUN
ejpam-2337	111	4	:	:	PUNCT
ejpam-2337	111	5	a#a$	a#a$	PROPN
ejpam-2337	111	6	b	b	X
ejpam-2337	111	7	is	be	AUX
ejpam-2337	111	8	called	call	VERB
ejpam-2337	111	9	a	a	DET
ejpam-2337	111	10	bi	bi	ADJ
ejpam-2337	111	11	-	-	ADJ
ejpam-2337	111	12	quadratic	quadratic	ADJ
ejpam-2337	111	13	mapping	mapping	NOUN
ejpam-2337	111	14	if	if	SCONJ
ejpam-2337	111	15	f	f	PROPN
ejpam-2337	111	16	satisfies	satisfy	VERB
ejpam-2337	111	17	the	the	DET
ejpam-2337	111	18	system	system	NOUN
ejpam-2337	111	19	of	of	ADP
ejpam-2337	111	20	functional	functional	ADJ
ejpam-2337	111	21	equations	equation	NOUN
ejpam-2337	112	1	f	f	X
ejpam-2337	112	2	(	(	PUNCT
ejpam-2337	112	3	x1	x1	PROPN
ejpam-2337	112	4	+	+	CCONJ
ejpam-2337	112	5	x2	x2	PROPN
ejpam-2337	112	6	,	,	PUNCT
ejpam-2337	112	7	y	y	PROPN
ejpam-2337	112	8	)	)	PUNCT
ejpam-2337	113	1	+	+	CCONJ
ejpam-2337	113	2	f	f	X
ejpam-2337	113	3	(	(	PUNCT
ejpam-2337	113	4	x1	x1	PROPN
ejpam-2337	113	5	.	.	PUNCT
ejpam-2337	114	1	x2	x2	PROPN
ejpam-2337	114	2	,	,	PUNCT
ejpam-2337	114	3	y	y	NOUN
ejpam-2337	114	4	)	)	PUNCT
ejpam-2337	114	5	=	=	SYM
ejpam-2337	114	6	2	2	NUM
ejpam-2337	114	7	f	f	X
ejpam-2337	114	8	(	(	PUNCT
ejpam-2337	114	9	x1	x1	PROPN
ejpam-2337	114	10	,	,	PUNCT
ejpam-2337	114	11	y	y	PROPN
ejpam-2337	114	12	)	)	PUNCT
ejpam-2337	114	13	+	+	CCONJ
ejpam-2337	114	14	2	2	NUM
ejpam-2337	114	15	f	f	NOUN
ejpam-2337	114	16	(	(	PUNCT
ejpam-2337	114	17	x2	x2	PROPN
ejpam-2337	114	18	,	,	PUNCT
ejpam-2337	114	19	y	y	PROPN
ejpam-2337	114	20	)	)	PUNCT
ejpam-2337	114	21	f	f	NOUN
ejpam-2337	114	22	(	(	PUNCT
ejpam-2337	114	23	x	x	INTJ
ejpam-2337	114	24	,	,	PUNCT
ejpam-2337	114	25	y1	y1	INTJ
ejpam-2337	114	26	+	+	CCONJ
ejpam-2337	114	27	y2	y2	NOUN
ejpam-2337	114	28	)	)	PUNCT
ejpam-2337	115	1	+	+	NUM
ejpam-2337	115	2	f	f	X
ejpam-2337	115	3	(	(	PUNCT
ejpam-2337	115	4	x	x	INTJ
ejpam-2337	115	5	,	,	PUNCT
ejpam-2337	115	6	y1	y1	INTJ
ejpam-2337	115	7	.	.	PUNCT
ejpam-2337	116	1	y2	y2	NOUN
ejpam-2337	116	2	)	)	PUNCT
ejpam-2337	117	1	=	=	PUNCT
ejpam-2337	117	2	2	2	NUM
ejpam-2337	117	3	f	f	X
ejpam-2337	117	4	(	(	PUNCT
ejpam-2337	117	5	x	x	PROPN
ejpam-2337	117	6	,	,	PUNCT
ejpam-2337	117	7	y1	y1	PROPN
ejpam-2337	117	8	)	)	PUNCT
ejpam-2337	117	9	+	+	CCONJ
ejpam-2337	117	10	2	2	NUM
ejpam-2337	117	11	f	f	NOUN
ejpam-2337	117	12	(	(	PUNCT
ejpam-2337	117	13	x	x	NOUN
ejpam-2337	117	14	,	,	PUNCT
ejpam-2337	117	15	y2	y2	PROPN
ejpam-2337	117	16	)	)	PUNCT
ejpam-2337	117	17	.	.	PUNCT
ejpam-2337	117	18	)	)	PUNCT
ejpam-2337	118	1	(	(	PUNCT
ejpam-2337	118	2	2	2	X
ejpam-2337	118	3	)	)	PUNCT
ejpam-2337	118	4	when	when	SCONJ
ejpam-2337	118	5	a=	a=	PROPN
ejpam-2337	118	6	b	b	X
ejpam-2337	118	7	=	=	PUNCT
ejpam-2337	118	8	!	!	PUNCT
ejpam-2337	118	9	,	,	PUNCT
ejpam-2337	118	10	the	the	DET
ejpam-2337	118	11	function	function	NOUN
ejpam-2337	118	12	f	f	NOUN
ejpam-2337	118	13	:	:	PUNCT
ejpam-2337	118	14	!	!	PUNCT
ejpam-2337	119	1	#	#	X
ejpam-2337	119	2	!	!	PUNCT
ejpam-2337	119	3	$	$	X
ejpam-2337	119	4	!	!	PUNCT
ejpam-2337	120	1	given	give	VERB
ejpam-2337	120	2	by	by	ADP
ejpam-2337	120	3	f	f	PROPN
ejpam-2337	120	4	(	(	PUNCT
ejpam-2337	120	5	x	x	PROPN
ejpam-2337	120	6	,	,	PUNCT
ejpam-2337	120	7	y	y	PROPN
ejpam-2337	120	8	)	)	PUNCT
ejpam-2337	120	9	=	=	SYM
ejpam-2337	121	1	x2	x2	NOUN
ejpam-2337	121	2	y2	y2	PROPN
ejpam-2337	121	3	is	be	AUX
ejpam-2337	121	4	a	a	DET
ejpam-2337	121	5	solution	solution	NOUN
ejpam-2337	121	6	of	of	ADP
ejpam-2337	121	7	(	(	PUNCT
ejpam-2337	121	8	2	2	NUM
ejpam-2337	121	9	)	)	PUNCT
ejpam-2337	121	10	.	.	PUNCT
ejpam-2337	122	1	in	in	ADP
ejpam-2337	122	2	the	the	DET
ejpam-2337	122	3	year	year	NOUN
ejpam-2337	122	4	2010	2010	NUM
ejpam-2337	122	5	,	,	PUNCT
ejpam-2337	122	6	k.	k.	PROPN
ejpam-2337	122	7	ravi	ravi	PROPN
ejpam-2337	122	8	and	and	CCONJ
ejpam-2337	122	9	b.v	b.v	PROPN
ejpam-2337	122	10	.	.	PROPN
ejpam-2337	122	11	senthil	senthil	PROPN
ejpam-2337	122	12	kumar	kumar	PROPN
ejpam-2337	123	1	[	[	X
ejpam-2337	123	2	19	19	NUM
ejpam-2337	123	3	]	]	PUNCT
ejpam-2337	123	4	investigated	investigate	VERB
ejpam-2337	123	5	the	the	DET
ejpam-2337	123	6	generalized	generalize	VERB
ejpam-2337	123	7	hyersulam	hyersulam	NOUN
ejpam-2337	123	8	-	-	PUNCT
ejpam-2337	123	9	rassias	rassias	PROPN
ejpam-2337	123	10	stability	stability	NOUN
ejpam-2337	123	11	for	for	ADP
ejpam-2337	123	12	the	the	DET
ejpam-2337	123	13	reciprocal	reciprocal	ADJ
ejpam-2337	123	14	functional	functional	ADJ
ejpam-2337	123	15	equation	equation	NOUN
ejpam-2337	123	16	r(x	r(x	PROPN
ejpam-2337	123	17	+	+	CCONJ
ejpam-2337	123	18	y	y	NOUN
ejpam-2337	123	19	)	)	PUNCT
ejpam-2337	123	20	=	=	PUNCT
ejpam-2337	123	21	r(x)r(y	r(x)r(y	VERB
ejpam-2337	123	22	)	)	PUNCT
ejpam-2337	123	23	r(x	r(x	PROPN
ejpam-2337	123	24	)	)	PUNCT
ejpam-2337	123	25	+	+	CCONJ
ejpam-2337	123	26	r(y	r(y	ADJ
ejpam-2337	123	27	)	)	PUNCT
ejpam-2337	123	28	(	(	PUNCT
ejpam-2337	123	29	3	3	X
ejpam-2337	123	30	)	)	PUNCT
ejpam-2337	123	31	where	where	SCONJ
ejpam-2337	123	32	r	r	NOUN
ejpam-2337	123	33	:	:	PUNCT
ejpam-2337	123	34	!	!	PUNCT
ejpam-2337	123	35	!	!	PUNCT
ejpam-2337	124	1	$	$	X
ejpam-2337	124	2	!	!	PUNCT
ejpam-2337	124	3	is	be	AUX
ejpam-2337	124	4	a	a	DET
ejpam-2337	124	5	mapping	mapping	NOUN
ejpam-2337	124	6	with	with	ADP
ejpam-2337	124	7	r	r	NOUN
ejpam-2337	124	8	!	!	PUNCT
ejpam-2337	125	1	as	as	ADP
ejpam-2337	125	2	the	the	DET
ejpam-2337	125	3	space	space	NOUN
ejpam-2337	125	4	of	of	ADP
ejpam-2337	125	5	non	non	ADJ
ejpam-2337	125	6	-	-	ADJ
ejpam-2337	125	7	zero	zero	ADJ
ejpam-2337	125	8	real	real	ADJ
ejpam-2337	125	9	numbers	number	NOUN
ejpam-2337	125	10	and	and	CCONJ
ejpam-2337	125	11	with	with	ADP
ejpam-2337	125	12	the	the	DET
ejpam-2337	125	13	assumptions	assumption	NOUN
ejpam-2337	125	14	x+	x+	PUNCT
ejpam-2337	125	15	y	y	PROPN
ejpam-2337	125	16	/=	/=	NOUN
ejpam-2337	125	17	0	0	NUM
ejpam-2337	125	18	,	,	PUNCT
ejpam-2337	125	19	r(x)+	r(x)+	VERB
ejpam-2337	125	20	r(y	r(y	ADJ
ejpam-2337	125	21	)	)	PUNCT
ejpam-2337	125	22	/=	/=	NOUN
ejpam-2337	125	23	0	0	NUM
ejpam-2337	125	24	and	and	CCONJ
ejpam-2337	125	25	r(x	r(x	PROPN
ejpam-2337	125	26	)	)	PUNCT
ejpam-2337	125	27	/=	/=	NOUN
ejpam-2337	125	28	0	0	NUM
ejpam-2337	125	29	,	,	PUNCT
ejpam-2337	125	30	for	for	ADP
ejpam-2337	125	31	all	all	DET
ejpam-2337	125	32	x	x	SYM
ejpam-2337	125	33	,	,	PUNCT
ejpam-2337	125	34	y	y	NOUN
ejpam-2337	125	35	%	%	INTJ
ejpam-2337	125	36	!	!	PUNCT
ejpam-2337	125	37	!	!	PUNCT
ejpam-2337	125	38	.	.	PUNCT
ejpam-2337	126	1	the	the	DET
ejpam-2337	126	2	reciprocal	reciprocal	ADJ
ejpam-2337	126	3	function	function	NOUN
ejpam-2337	126	4	r(x	r(x	PROPN
ejpam-2337	126	5	)	)	PUNCT
ejpam-2337	126	6	=	=	SYM
ejpam-2337	127	1	1	1	NUM
ejpam-2337	127	2	x	x	NOUN
ejpam-2337	127	3	is	be	AUX
ejpam-2337	127	4	a	a	DET
ejpam-2337	127	5	solution	solution	NOUN
ejpam-2337	127	6	of	of	ADP
ejpam-2337	127	7	the	the	DET
ejpam-2337	127	8	functional	functional	ADJ
ejpam-2337	127	9	equation	equation	NOUN
ejpam-2337	127	10	(	(	PUNCT
ejpam-2337	127	11	3	3	NUM
ejpam-2337	127	12	)	)	PUNCT
ejpam-2337	127	13	.	.	PUNCT
ejpam-2337	128	1	k.ravi	k.ravi	PROPN
ejpam-2337	128	2	,	,	PUNCT
ejpam-2337	128	3	j.m	j.m	PROPN
ejpam-2337	128	4	.	.	PROPN
ejpam-2337	128	5	rassias	rassias	PROPN
ejpam-2337	128	6	and	and	CCONJ
ejpam-2337	128	7	b.v	b.v	PROPN
ejpam-2337	128	8	.	.	PROPN
ejpam-2337	129	1	senthil	senthil	PROPN
ejpam-2337	129	2	kumar	kumar	PROPN
ejpam-2337	130	1	[	[	X
ejpam-2337	130	2	20	20	NUM
ejpam-2337	130	3	]	]	PUNCT
ejpam-2337	130	4	obtained	obtain	VERB
ejpam-2337	130	5	the	the	DET
ejpam-2337	130	6	general	general	ADJ
ejpam-2337	130	7	solution	solution	NOUN
ejpam-2337	130	8	and	and	CCONJ
ejpam-2337	130	9	investigated	investigate	VERB
ejpam-2337	130	10	the	the	DET
ejpam-2337	130	11	generalized	generalize	VERB
ejpam-2337	130	12	hyers	hyer	NOUN
ejpam-2337	130	13	-	-	PUNCT
ejpam-2337	130	14	ulam	ulam	ADJ
ejpam-2337	130	15	-	-	PUNCT
ejpam-2337	130	16	rassias	rassias	PROPN
ejpam-2337	130	17	stability	stability	NOUN
ejpam-2337	130	18	of	of	ADP
ejpam-2337	130	19	a	a	DET
ejpam-2337	130	20	2	2	NUM
ejpam-2337	130	21	-	-	PUNCT
ejpam-2337	130	22	variable	variable	ADJ
ejpam-2337	130	23	reciprocal	reciprocal	ADJ
ejpam-2337	130	24	functional	functional	ADJ
ejpam-2337	130	25	equation	equation	NOUN
ejpam-2337	130	26	f(x	f(x	PROPN
ejpam-2337	130	27	+	+	CCONJ
ejpam-2337	130	28	u	u	PROPN
ejpam-2337	130	29	,	,	PUNCT
ejpam-2337	130	30	y	y	PROPN
ejpam-2337	130	31	+	+	CCONJ
ejpam-2337	130	32	v	v	NOUN
ejpam-2337	130	33	)	)	PUNCT
ejpam-2337	130	34	=	=	SYM
ejpam-2337	130	35	f(x	f(x	PROPN
ejpam-2337	130	36	,	,	PUNCT
ejpam-2337	130	37	y)f(u	y)f(u	ADJ
ejpam-2337	130	38	,	,	PUNCT
ejpam-2337	130	39	v	v	NOUN
ejpam-2337	130	40	)	)	PUNCT
ejpam-2337	130	41	f(x	f(x	PROPN
ejpam-2337	130	42	,	,	PUNCT
ejpam-2337	130	43	y	y	PROPN
ejpam-2337	130	44	)	)	PUNCT
ejpam-2337	130	45	+	+	CCONJ
ejpam-2337	130	46	f(u	f(u	PROPN
ejpam-2337	130	47	,	,	PUNCT
ejpam-2337	130	48	v	v	NOUN
ejpam-2337	130	49	)	)	PUNCT
ejpam-2337	130	50	(	(	PUNCT
ejpam-2337	130	51	4	4	X
ejpam-2337	130	52	)	)	PUNCT
ejpam-2337	130	53	where	where	SCONJ
ejpam-2337	130	54	f	f	X
ejpam-2337	130	55	:	:	PUNCT
ejpam-2337	130	56	!	!	PUNCT
ejpam-2337	130	57	!	!	PUNCT
ejpam-2337	131	1	#	#	X
ejpam-2337	131	2	!	!	PUNCT
ejpam-2337	131	3	!	!	PUNCT
ejpam-2337	132	1	$	$	X
ejpam-2337	132	2	!	!	PUNCT
ejpam-2337	132	3	is	be	AUX
ejpam-2337	132	4	a	a	DET
ejpam-2337	132	5	mapping	mapping	NOUN
ejpam-2337	132	6	with	with	ADP
ejpam-2337	132	7	r	r	NOUN
ejpam-2337	132	8	!	!	PUNCT
ejpam-2337	133	1	as	as	ADP
ejpam-2337	133	2	the	the	DET
ejpam-2337	133	3	space	space	NOUN
ejpam-2337	133	4	of	of	ADP
ejpam-2337	133	5	non	non	ADJ
ejpam-2337	133	6	-	-	ADJ
ejpam-2337	133	7	zero	zero	ADJ
ejpam-2337	133	8	real	real	ADJ
ejpam-2337	133	9	numbers	number	NOUN
ejpam-2337	133	10	and	and	CCONJ
ejpam-2337	133	11	with	with	ADP
ejpam-2337	133	12	the	the	DET
ejpam-2337	133	13	conditions	condition	NOUN
ejpam-2337	133	14	x+	x+	PUNCT
ejpam-2337	133	15	y	y	PROPN
ejpam-2337	133	16	/=	/=	PROPN
ejpam-2337	133	17	0	0	NUM
ejpam-2337	133	18	,	,	PUNCT
ejpam-2337	133	19	u+	u+	NOUN
ejpam-2337	133	20	v	v	ADP
ejpam-2337	133	21	/=	/=	PROPN
ejpam-2337	133	22	0	0	NUM
ejpam-2337	133	23	,	,	PUNCT
ejpam-2337	133	24	x+u	x+u	NUM
ejpam-2337	133	25	/=	/=	NOUN
ejpam-2337	133	26	0	0	NUM
ejpam-2337	133	27	,	,	PUNCT
ejpam-2337	133	28	y+	y+	PROPN
ejpam-2337	133	29	v	v	ADP
ejpam-2337	133	30	/=	/=	PROPN
ejpam-2337	133	31	0	0	NUM
ejpam-2337	133	32	,	,	PUNCT
ejpam-2337	133	33	f(x	f(x	PROPN
ejpam-2337	133	34	,	,	PUNCT
ejpam-2337	133	35	y	y	PROPN
ejpam-2337	133	36	)	)	PUNCT
ejpam-2337	133	37	/=	/=	NOUN
ejpam-2337	133	38	0	0	PUNCT
ejpam-2337	133	39	and	and	CCONJ
ejpam-2337	133	40	f(x	f(x	PROPN
ejpam-2337	133	41	,	,	PUNCT
ejpam-2337	133	42	y)+	y)+	PROPN
ejpam-2337	133	43	f(u	f(u	PROPN
ejpam-2337	133	44	,	,	PUNCT
ejpam-2337	133	45	v	v	NOUN
ejpam-2337	133	46	)	)	PUNCT
ejpam-2337	133	47	/=	/=	NOUN
ejpam-2337	133	48	0	0	PUNCT
ejpam-2337	134	1	for	for	ADP
ejpam-2337	134	2	all	all	DET
ejpam-2337	134	3	x	x	SYM
ejpam-2337	134	4	,	,	PUNCT
ejpam-2337	134	5	u	u	NOUN
ejpam-2337	134	6	,	,	PUNCT
ejpam-2337	134	7	y	y	PROPN
ejpam-2337	134	8	,	,	PUNCT
ejpam-2337	134	9	v	v	NOUN
ejpam-2337	134	10	%	%	NOUN
ejpam-2337	134	11	!	!	PUNCT
ejpam-2337	134	12	!	!	PUNCT
ejpam-2337	134	13	.	.	PUNCT
ejpam-2337	135	1	the	the	DET
ejpam-2337	135	2	2	2	NUM
ejpam-2337	135	3	-	-	PUNCT
ejpam-2337	135	4	variable	variable	ADJ
ejpam-2337	135	5	reciprocal	reciprocal	ADJ
ejpam-2337	135	6	function	function	NOUN
ejpam-2337	135	7	f(x	f(x	PROPN
ejpam-2337	135	8	,	,	PUNCT
ejpam-2337	135	9	y	y	PROPN
ejpam-2337	135	10	)	)	PUNCT
ejpam-2337	135	11	=	=	SYM
ejpam-2337	135	12	1	1	NUM
ejpam-2337	135	13	x+y	x+y	NUM
ejpam-2337	135	14	is	be	AUX
ejpam-2337	135	15	a	a	DET
ejpam-2337	135	16	solution	solution	NOUN
ejpam-2337	135	17	of	of	ADP
ejpam-2337	135	18	the	the	DET
ejpam-2337	135	19	functional	functional	ADJ
ejpam-2337	135	20	equation	equation	NOUN
ejpam-2337	135	21	(	(	PUNCT
ejpam-2337	135	22	4	4	NUM
ejpam-2337	135	23	)	)	PUNCT
ejpam-2337	135	24	.	.	PUNCT
ejpam-2337	136	1	motivated	motivate	VERB
ejpam-2337	136	2	by	by	ADP
ejpam-2337	136	3	the	the	DET
ejpam-2337	136	4	system	system	NOUN
ejpam-2337	136	5	of	of	ADP
ejpam-2337	136	6	functional	functional	ADJ
ejpam-2337	136	7	equations	equation	NOUN
ejpam-2337	136	8	(	(	PUNCT
ejpam-2337	136	9	1	1	NUM
ejpam-2337	136	10	)	)	PUNCT
ejpam-2337	136	11	and	and	CCONJ
ejpam-2337	136	12	(	(	PUNCT
ejpam-2337	136	13	2	2	NUM
ejpam-2337	136	14	)	)	PUNCT
ejpam-2337	136	15	,	,	PUNCT
ejpam-2337	136	16	we	we	PRON
ejpam-2337	136	17	say	say	VERB
ejpam-2337	136	18	that	that	SCONJ
ejpam-2337	136	19	a	a	DET
ejpam-2337	136	20	mapping	mapping	NOUN
ejpam-2337	136	21	r	r	NOUN
ejpam-2337	136	22	:	:	PUNCT
ejpam-2337	136	23	!	!	PUNCT
ejpam-2337	137	1	+	+	CCONJ
ejpam-2337	137	2	#	#	X
ejpam-2337	137	3	!	!	PUNCT
ejpam-2337	138	1	+	+	ADV
ejpam-2337	138	2	$	$	X
ejpam-2337	138	3	!	!	PUNCT
ejpam-2337	139	1	+	+	CCONJ
ejpam-2337	139	2	is	be	AUX
ejpam-2337	139	3	bi	bi	NOUN
ejpam-2337	139	4	-	-	ADJ
ejpam-2337	139	5	reciprocal	reciprocal	ADJ
ejpam-2337	139	6	if	if	SCONJ
ejpam-2337	139	7	r	r	NOUN
ejpam-2337	139	8	satisfies	satisfy	VERB
ejpam-2337	139	9	the	the	DET
ejpam-2337	139	10	system	system	NOUN
ejpam-2337	139	11	of	of	ADP
ejpam-2337	139	12	functional	functional	ADJ
ejpam-2337	139	13	equations	equation	NOUN
ejpam-2337	139	14	r(x	r(x	PROPN
ejpam-2337	139	15	+	+	CCONJ
ejpam-2337	139	16	u	u	PROPN
ejpam-2337	139	17	,	,	PUNCT
ejpam-2337	139	18	y	y	NOUN
ejpam-2337	139	19	)	)	PUNCT
ejpam-2337	139	20	=	=	SYM
ejpam-2337	139	21	r(x	r(x	PROPN
ejpam-2337	139	22	,	,	PUNCT
ejpam-2337	139	23	y)r(u	y)r(u	PROPN
ejpam-2337	139	24	,	,	PUNCT
ejpam-2337	139	25	y	y	PROPN
ejpam-2337	139	26	)	)	PUNCT
ejpam-2337	139	27	r(x	r(x	PROPN
ejpam-2337	139	28	,	,	PUNCT
ejpam-2337	139	29	y	y	PROPN
ejpam-2337	139	30	)	)	PUNCT
ejpam-2337	140	1	+	+	CCONJ
ejpam-2337	141	1	r(u	r(u	PROPN
ejpam-2337	141	2	,	,	PUNCT
ejpam-2337	141	3	y	y	NOUN
ejpam-2337	141	4	)	)	PUNCT
ejpam-2337	141	5	r(x	r(x	PROPN
ejpam-2337	141	6	,	,	PUNCT
ejpam-2337	141	7	y	y	PROPN
ejpam-2337	141	8	+	+	CCONJ
ejpam-2337	141	9	v	v	NOUN
ejpam-2337	141	10	)	)	PUNCT
ejpam-2337	141	11	=	=	SYM
ejpam-2337	141	12	r(x	r(x	PROPN
ejpam-2337	141	13	,	,	PUNCT
ejpam-2337	141	14	y)r(x	y)r(x	PROPN
ejpam-2337	141	15	,	,	PUNCT
ejpam-2337	141	16	v	v	NOUN
ejpam-2337	141	17	)	)	PUNCT
ejpam-2337	141	18	r(x	r(x	PROPN
ejpam-2337	141	19	,	,	PUNCT
ejpam-2337	141	20	y	y	PROPN
ejpam-2337	141	21	)	)	PUNCT
ejpam-2337	141	22	+	+	CCONJ
ejpam-2337	141	23	r(x	r(x	PROPN
ejpam-2337	141	24	,	,	PUNCT
ejpam-2337	141	25	v	v	NOUN
ejpam-2337	141	26	)	)	PUNCT
ejpam-2337	141	27	.	.	PUNCT
ejpam-2337	142	1	%	%	INTJ
ejpam-2337	142	2	&	&	CCONJ
ejpam-2337	142	3	&	&	CCONJ
ejpam-2337	142	4	'	'	PUNCT
ejpam-2337	142	5	&	&	CCONJ
ejpam-2337	142	6	&	&	CCONJ
ejpam-2337	142	7	(	(	PUNCT
ejpam-2337	142	8	(	(	PUNCT
ejpam-2337	142	9	5	5	X
ejpam-2337	142	10	)	)	PUNCT
ejpam-2337	142	11	it	it	PRON
ejpam-2337	142	12	is	be	AUX
ejpam-2337	142	13	easy	easy	ADJ
ejpam-2337	142	14	to	to	PART
ejpam-2337	142	15	see	see	VERB
ejpam-2337	142	16	that	that	SCONJ
ejpam-2337	142	17	r(x	r(x	PROPN
ejpam-2337	142	18	,	,	PUNCT
ejpam-2337	142	19	y	y	PROPN
ejpam-2337	142	20	)	)	PUNCT
ejpam-2337	142	21	=	=	SYM
ejpam-2337	143	1	1	1	NUM
ejpam-2337	143	2	x	x	SYM
ejpam-2337	143	3	y	y	NOUN
ejpam-2337	143	4	is	be	AUX
ejpam-2337	143	5	a	a	DET
ejpam-2337	143	6	solution	solution	NOUN
ejpam-2337	143	7	of	of	ADP
ejpam-2337	143	8	the	the	DET
ejpam-2337	143	9	system	system	NOUN
ejpam-2337	143	10	of	of	ADP
ejpam-2337	143	11	functional	functional	ADJ
ejpam-2337	143	12	equations	equation	NOUN
ejpam-2337	143	13	(	(	PUNCT
ejpam-2337	143	14	5	5	NUM
ejpam-2337	143	15	)	)	PUNCT
ejpam-2337	143	16	.	.	PUNCT
ejpam-2337	144	1	in	in	ADP
ejpam-2337	144	2	this	this	DET
ejpam-2337	144	3	paper	paper	NOUN
ejpam-2337	144	4	,	,	PUNCT
ejpam-2337	144	5	we	we	PRON
ejpam-2337	144	6	investigate	investigate	VERB
ejpam-2337	144	7	the	the	DET
ejpam-2337	144	8	generalized	generalize	VERB
ejpam-2337	144	9	hyers	hyer	NOUN
ejpam-2337	144	10	-	-	PUNCT
ejpam-2337	144	11	ulam	ulam	ADJ
ejpam-2337	144	12	-	-	PUNCT
ejpam-2337	144	13	rassias	rassias	PROPN
ejpam-2337	144	14	stability	stability	NOUN
ejpam-2337	144	15	problem	problem	NOUN
ejpam-2337	144	16	for	for	ADP
ejpam-2337	144	17	the	the	DET
ejpam-2337	144	18	system	system	NOUN
ejpam-2337	144	19	of	of	ADP
ejpam-2337	144	20	functional	functional	ADJ
ejpam-2337	144	21	equations	equation	NOUN
ejpam-2337	144	22	(	(	PUNCT
ejpam-2337	144	23	5	5	NUM
ejpam-2337	144	24	)	)	PUNCT
ejpam-2337	144	25	.	.	PUNCT
ejpam-2337	145	1	throughout	throughout	ADP
ejpam-2337	145	2	this	this	DET
ejpam-2337	145	3	paper	paper	NOUN
ejpam-2337	145	4	,	,	PUNCT
ejpam-2337	145	5	we	we	PRON
ejpam-2337	145	6	assume	assume	VERB
ejpam-2337	145	7	that	that	SCONJ
ejpam-2337	145	8	e	e	PRON
ejpam-2337	145	9	is	be	AUX
ejpam-2337	145	10	a	a	DET
ejpam-2337	145	11	real	real	ADV
ejpam-2337	145	12	normed	normed	ADJ
ejpam-2337	145	13	space	space	NOUN
ejpam-2337	145	14	and	and	CCONJ
ejpam-2337	145	15	f	f	PROPN
ejpam-2337	145	16	is	be	AUX
ejpam-2337	145	17	a	a	DET
ejpam-2337	145	18	real	real	ADJ
ejpam-2337	145	19	banach	banach	NOUN
ejpam-2337	145	20	space	space	NOUN
ejpam-2337	145	21	.	.	PUNCT
ejpam-2337	146	1	we	we	PRON
ejpam-2337	146	2	also	also	ADV
ejpam-2337	146	3	assume	assume	VERB
ejpam-2337	146	4	that	that	SCONJ
ejpam-2337	146	5	x	x	PRON
ejpam-2337	146	6	is	be	AUX
ejpam-2337	146	7	the	the	DET
ejpam-2337	146	8	space	space	NOUN
ejpam-2337	146	9	of	of	ADP
ejpam-2337	146	10	non	non	ADJ
ejpam-2337	146	11	-	-	ADJ
ejpam-2337	146	12	zero	zero	ADJ
ejpam-2337	146	13	real	real	ADJ
ejpam-2337	146	14	numbers	number	NOUN
ejpam-2337	146	15	and	and	CCONJ
ejpam-2337	146	16	y	y	PROPN
ejpam-2337	146	17	is	be	AUX
ejpam-2337	146	18	a	a	DET
ejpam-2337	146	19	real	real	ADJ
ejpam-2337	146	20	fréchet	fréchet	NOUN
ejpam-2337	146	21	space	space	NOUN
ejpam-2337	146	22	with	with	ADP
ejpam-2337	146	23	metric	metric	ADJ
ejpam-2337	146	24	d	d	NOUN
ejpam-2337	146	25	with	with	ADP
ejpam-2337	146	26	the	the	DET
ejpam-2337	146	27	conditions	condition	NOUN
ejpam-2337	146	28	x	x	PUNCT
ejpam-2337	147	1	+	+	PUNCT
ejpam-2337	147	2	u	u	NOUN
ejpam-2337	147	3	/=	/=	NOUN
ejpam-2337	147	4	0	0	NUM
ejpam-2337	147	5	,	,	PUNCT
ejpam-2337	147	6	y	y	PROPN
ejpam-2337	147	7	+	+	PROPN
ejpam-2337	147	8	v	v	ADP
ejpam-2337	147	9	/=	/=	NOUN
ejpam-2337	147	10	0	0	NUM
ejpam-2337	147	11	,	,	PUNCT
ejpam-2337	147	12	r(x	r(x	PROPN
ejpam-2337	147	13	,	,	PUNCT
ejpam-2337	147	14	y	y	PROPN
ejpam-2337	147	15	)	)	PUNCT
ejpam-2337	147	16	/=	/=	NOUN
ejpam-2337	147	17	0	0	NUM
ejpam-2337	147	18	,	,	PUNCT
ejpam-2337	147	19	r(x	r(x	PROPN
ejpam-2337	147	20	,	,	PUNCT
ejpam-2337	147	21	y	y	PROPN
ejpam-2337	147	22	)	)	PUNCT
ejpam-2337	148	1	+	+	CCONJ
ejpam-2337	149	1	r(u	r(u	PROPN
ejpam-2337	149	2	,	,	PUNCT
ejpam-2337	149	3	y	y	NOUN
ejpam-2337	149	4	)	)	PUNCT
ejpam-2337	149	5	/=	/=	NOUN
ejpam-2337	149	6	0	0	PUNCT
ejpam-2337	149	7	and	and	CCONJ
ejpam-2337	149	8	r(x	r(x	PROPN
ejpam-2337	149	9	,	,	PUNCT
ejpam-2337	149	10	y	y	PROPN
ejpam-2337	149	11	)	)	PUNCT
ejpam-2337	149	12	+	+	CCONJ
ejpam-2337	149	13	r(x	r(x	PROPN
ejpam-2337	149	14	,	,	PUNCT
ejpam-2337	149	15	v	v	NOUN
ejpam-2337	149	16	)	)	PUNCT
ejpam-2337	149	17	/=	/=	NOUN
ejpam-2337	149	18	0	0	PUNCT
ejpam-2337	150	1	for	for	ADP
ejpam-2337	150	2	all	all	DET
ejpam-2337	150	3	x	x	SYM
ejpam-2337	150	4	,	,	PUNCT
ejpam-2337	150	5	u	u	NOUN
ejpam-2337	150	6	,	,	PUNCT
ejpam-2337	150	7	y	y	PROPN
ejpam-2337	150	8	,	,	PUNCT
ejpam-2337	150	9	v	v	PRON
ejpam-2337	150	10	%	%	NOUN
ejpam-2337	150	11	x	x	X
ejpam-2337	150	12	.	.	PUNCT
ejpam-2337	151	1	for	for	ADP
ejpam-2337	151	2	notational	notational	ADJ
ejpam-2337	151	3	convenience	convenience	NOUN
ejpam-2337	151	4	,	,	PUNCT
ejpam-2337	151	5	let	let	VERB
ejpam-2337	151	6	us	we	PRON
ejpam-2337	151	7	denote	denote	VERB
ejpam-2337	151	8	for	for	ADP
ejpam-2337	151	9	a	a	DET
ejpam-2337	151	10	given	give	VERB
ejpam-2337	151	11	mapping	mapping	NOUN
ejpam-2337	151	12	r	r	NOUN
ejpam-2337	151	13	:	:	PUNCT
ejpam-2337	151	14	x	x	SYM
ejpam-2337	151	15	$	$	SYM
ejpam-2337	151	16	y	y	PROPN
ejpam-2337	151	17	,	,	PUNCT
ejpam-2337	151	18	the	the	DET
ejpam-2337	151	19	difference	difference	NOUN
ejpam-2337	151	20	operators	operator	NOUN
ejpam-2337	152	1	#	#	SYM
ejpam-2337	152	2	r	r	NOUN
ejpam-2337	152	3	:	:	PUNCT
ejpam-2337	152	4	x	x	SYM
ejpam-2337	152	5	#	#	NOUN
ejpam-2337	152	6	x	x	NOUN
ejpam-2337	152	7	#	#	NOUN
ejpam-2337	152	8	x	x	SYM
ejpam-2337	152	9	$	$	SYM
ejpam-2337	152	10	y	y	PROPN
ejpam-2337	152	11	and	and	CCONJ
ejpam-2337	152	12	"	"	PUNCT
ejpam-2337	152	13	r	r	NOUN
ejpam-2337	152	14	:	:	PUNCT
ejpam-2337	152	15	x	x	SYM
ejpam-2337	152	16	#	#	NOUN
ejpam-2337	152	17	x	x	NOUN
ejpam-2337	152	18	#	#	NOUN
ejpam-2337	152	19	x	x	SYM
ejpam-2337	152	20	$	$	SYM
ejpam-2337	152	21	y	y	NOUN
ejpam-2337	152	22	by	by	ADP
ejpam-2337	152	23	#	#	SYM
ejpam-2337	152	24	r(x	r(x	PROPN
ejpam-2337	152	25	,	,	PUNCT
ejpam-2337	152	26	u	u	NOUN
ejpam-2337	152	27	,	,	PUNCT
ejpam-2337	152	28	y	y	NOUN
ejpam-2337	152	29	)	)	PUNCT
ejpam-2337	152	30	=	=	PUNCT
ejpam-2337	153	1	d	d	X
ejpam-2337	153	2	*	*	PUNCT
ejpam-2337	153	3	r(x	r(x	PROPN
ejpam-2337	153	4	+	+	CCONJ
ejpam-2337	153	5	u	u	PROPN
ejpam-2337	153	6	,	,	PUNCT
ejpam-2337	153	7	y	y	PROPN
ejpam-2337	153	8	)	)	PUNCT
ejpam-2337	153	9	,	,	PUNCT
ejpam-2337	153	10	r(x	r(x	PROPN
ejpam-2337	153	11	,	,	PUNCT
ejpam-2337	153	12	y)r(u	y)r(u	PROPN
ejpam-2337	153	13	,	,	PUNCT
ejpam-2337	153	14	y	y	PROPN
ejpam-2337	153	15	)	)	PUNCT
ejpam-2337	153	16	r(x	r(x	PROPN
ejpam-2337	153	17	,	,	PUNCT
ejpam-2337	153	18	y	y	PROPN
ejpam-2337	153	19	)	)	PUNCT
ejpam-2337	154	1	+	+	CCONJ
ejpam-2337	155	1	r(u	r(u	PROPN
ejpam-2337	155	2	,	,	PUNCT
ejpam-2337	155	3	y	y	NOUN
ejpam-2337	155	4	)	)	PUNCT
ejpam-2337	155	5	+	+	CCONJ
ejpam-2337	155	6	,	,	PUNCT
ejpam-2337	155	7	k.	k.	PROPN
ejpam-2337	155	8	ravi	ravi	PROPN
ejpam-2337	155	9	,	,	PUNCT
ejpam-2337	155	10	b.	b.	PROPN
ejpam-2337	155	11	kumar	kumar	PROPN
ejpam-2337	155	12	/	/	SYM
ejpam-2337	155	13	eur	eur	PROPN
ejpam-2337	155	14	.	.	PUNCT
ejpam-2337	156	1	j.	j.	PROPN
ejpam-2337	156	2	pure	pure	PROPN
ejpam-2337	156	3	appl	appl	PROPN
ejpam-2337	156	4	.	.	PROPN
ejpam-2337	156	5	math	math	PROPN
ejpam-2337	156	6	,	,	PUNCT
ejpam-2337	156	7	8	8	NUM
ejpam-2337	156	8	(	(	PUNCT
ejpam-2337	156	9	2015	2015	NUM
ejpam-2337	156	10	)	)	PUNCT
ejpam-2337	156	11	,	,	PUNCT
ejpam-2337	156	12	283	283	NUM
ejpam-2337	156	13	-	-	SYM
ejpam-2337	156	14	293	293	NUM
ejpam-2337	156	15	287	287	NUM
ejpam-2337	156	16	"	"	PUNCT
ejpam-2337	156	17	r(x	r(x	PROPN
ejpam-2337	156	18	,	,	PUNCT
ejpam-2337	156	19	y	y	PROPN
ejpam-2337	156	20	,	,	PUNCT
ejpam-2337	156	21	v	v	NOUN
ejpam-2337	156	22	)	)	PUNCT
ejpam-2337	156	23	=	=	SYM
ejpam-2337	157	1	d	d	PROPN
ejpam-2337	157	2	*	*	PUNCT
ejpam-2337	157	3	r(x	r(x	PROPN
ejpam-2337	157	4	,	,	PUNCT
ejpam-2337	157	5	y	y	PROPN
ejpam-2337	157	6	+	+	PROPN
ejpam-2337	157	7	v	v	NOUN
ejpam-2337	157	8	)	)	PUNCT
ejpam-2337	157	9	,	,	PUNCT
ejpam-2337	157	10	r(x	r(x	PROPN
ejpam-2337	157	11	,	,	PUNCT
ejpam-2337	157	12	y)r(x	y)r(x	PROPN
ejpam-2337	157	13	,	,	PUNCT
ejpam-2337	157	14	v	v	NOUN
ejpam-2337	157	15	)	)	PUNCT
ejpam-2337	157	16	r(x	r(x	PROPN
ejpam-2337	157	17	,	,	PUNCT
ejpam-2337	157	18	y	y	PROPN
ejpam-2337	157	19	)	)	PUNCT
ejpam-2337	158	1	+	+	CCONJ
ejpam-2337	158	2	r(x	r(x	PROPN
ejpam-2337	158	3	,	,	PUNCT
ejpam-2337	158	4	v	v	NOUN
ejpam-2337	158	5	)	)	PUNCT
ejpam-2337	158	6	+	+	CCONJ
ejpam-2337	158	7	for	for	ADP
ejpam-2337	158	8	all	all	DET
ejpam-2337	158	9	x	x	SYM
ejpam-2337	158	10	,	,	PUNCT
ejpam-2337	158	11	u	u	NOUN
ejpam-2337	158	12	,	,	PUNCT
ejpam-2337	158	13	y	y	PROPN
ejpam-2337	158	14	,	,	PUNCT
ejpam-2337	158	15	v	v	PRON
ejpam-2337	158	16	%	%	NOUN
ejpam-2337	158	17	x	x	X
ejpam-2337	158	18	.	.	PUNCT
ejpam-2337	159	1	2	2	X
ejpam-2337	159	2	.	.	NUM
ejpam-2337	159	3	generalized	generalize	VERB
ejpam-2337	159	4	hyers	hyers	PROPN
ejpam-2337	159	5	-	-	PUNCT
ejpam-2337	159	6	ulam	ulam	ADJ
ejpam-2337	159	7	-	-	PUNCT
ejpam-2337	159	8	rassias	rassias	PROPN
ejpam-2337	159	9	stability	stability	NOUN
ejpam-2337	159	10	of	of	ADP
ejpam-2337	159	11	the	the	DET
ejpam-2337	159	12	system	system	NOUN
ejpam-2337	159	13	of	of	ADP
ejpam-2337	159	14	functional	functional	ADJ
ejpam-2337	159	15	equations	equation	NOUN
ejpam-2337	159	16	(	(	PUNCT
ejpam-2337	159	17	5	5	NUM
ejpam-2337	159	18	)	)	PUNCT
ejpam-2337	159	19	theorem	theorem	NOUN
ejpam-2337	159	20	2	2	NUM
ejpam-2337	159	21	.	.	PUNCT
ejpam-2337	160	1	let	let	VERB
ejpam-2337	160	2	g	g	NOUN
ejpam-2337	160	3	,	,	PUNCT
ejpam-2337	160	4	h	h	NOUN
ejpam-2337	160	5	:	:	PUNCT
ejpam-2337	160	6	x	x	SYM
ejpam-2337	160	7	#	#	NOUN
ejpam-2337	160	8	x	x	NOUN
ejpam-2337	160	9	#	#	NOUN
ejpam-2337	160	10	x	x	SYM
ejpam-2337	160	11	$	$	SYM
ejpam-2337	160	12	[	[	X
ejpam-2337	160	13	0	0	NUM
ejpam-2337	160	14	,	,	PUNCT
ejpam-2337	160	15	&	&	CCONJ
ejpam-2337	160	16	)	)	PUNCT
ejpam-2337	160	17	be	be	AUX
ejpam-2337	160	18	mappings	mapping	NOUN
ejpam-2337	160	19	satisfying	satisfying	ADJ
ejpam-2337	160	20	&	&	CCONJ
ejpam-2337	160	21	!	!	PUNCT
ejpam-2337	161	1	i=0	i=0	PROPN
ejpam-2337	162	1	4ig(2i	4ig(2i	X
ejpam-2337	162	2	x	x	PUNCT
ejpam-2337	162	3	,	,	PUNCT
ejpam-2337	162	4	2i	2i	NUM
ejpam-2337	162	5	x	x	SYM
ejpam-2337	162	6	,	,	PUNCT
ejpam-2337	162	7	2i	2i	PROPN
ejpam-2337	162	8	y	y	NOUN
ejpam-2337	162	9	)	)	PUNCT
ejpam-2337	162	10	<	<	X
ejpam-2337	162	11	&	&	CCONJ
ejpam-2337	162	12	,	,	PUNCT
ejpam-2337	162	13	&	&	CCONJ
ejpam-2337	162	14	!	!	PUNCT
ejpam-2337	163	1	i=0	i=0	PROPN
ejpam-2337	163	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	163	3	x	x	PUNCT
ejpam-2337	163	4	,	,	PUNCT
ejpam-2337	163	5	2i	2i	PROPN
ejpam-2337	163	6	y	y	PROPN
ejpam-2337	163	7	,	,	PUNCT
ejpam-2337	163	8	2i	2i	NOUN
ejpam-2337	163	9	y	y	NOUN
ejpam-2337	163	10	)	)	PUNCT
ejpam-2337	163	11	<	<	PROPN
ejpam-2337	163	12	&	&	CCONJ
ejpam-2337	163	13	%	%	PROPN
ejpam-2337	163	14	&	&	CCONJ
ejpam-2337	163	15	&	&	CCONJ
ejpam-2337	163	16	&	&	CCONJ
ejpam-2337	163	17	'	'	PUNCT
ejpam-2337	163	18	&	&	CCONJ
ejpam-2337	163	19	&	&	CCONJ
ejpam-2337	163	20	&	&	CCONJ
ejpam-2337	163	21	(	(	PUNCT
ejpam-2337	163	22	(	(	PUNCT
ejpam-2337	163	23	6	6	NUM
ejpam-2337	163	24	)	)	PUNCT
ejpam-2337	163	25	for	for	ADP
ejpam-2337	163	26	all	all	DET
ejpam-2337	163	27	x	x	SYM
ejpam-2337	163	28	,	,	PUNCT
ejpam-2337	163	29	y	y	NOUN
ejpam-2337	163	30	%	%	NOUN
ejpam-2337	163	31	x	x	INTJ
ejpam-2337	163	32	.	.	PUNCT
ejpam-2337	164	1	let	let	VERB
ejpam-2337	164	2	r	r	NOUN
ejpam-2337	164	3	:	:	PUNCT
ejpam-2337	164	4	x	x	SYM
ejpam-2337	164	5	#	#	NOUN
ejpam-2337	164	6	x	x	SYM
ejpam-2337	164	7	$	$	SYM
ejpam-2337	164	8	y	y	NOUN
ejpam-2337	164	9	be	be	AUX
ejpam-2337	164	10	a	a	DET
ejpam-2337	164	11	mapping	mapping	NOUN
ejpam-2337	164	12	such	such	ADJ
ejpam-2337	164	13	that	that	SCONJ
ejpam-2337	164	14	#	#	SYM
ejpam-2337	164	15	r(x	r(x	PROPN
ejpam-2337	164	16	,	,	PUNCT
ejpam-2337	164	17	u	u	NOUN
ejpam-2337	164	18	,	,	PUNCT
ejpam-2337	164	19	y	y	PROPN
ejpam-2337	164	20	)	)	PUNCT
ejpam-2337	164	21	,	,	PUNCT
ejpam-2337	164	22	g(x	g(x	PROPN
ejpam-2337	164	23	,	,	PUNCT
ejpam-2337	164	24	u	u	NOUN
ejpam-2337	164	25	,	,	PUNCT
ejpam-2337	164	26	y	y	PROPN
ejpam-2337	164	27	)	)	PUNCT
ejpam-2337	164	28	(	(	PUNCT
ejpam-2337	164	29	7	7	X
ejpam-2337	164	30	)	)	PUNCT
ejpam-2337	164	31	"	"	PUNCT
ejpam-2337	164	32	r(x	r(x	PROPN
ejpam-2337	164	33	,	,	PUNCT
ejpam-2337	164	34	y	y	PROPN
ejpam-2337	164	35	,	,	PUNCT
ejpam-2337	164	36	v	v	NOUN
ejpam-2337	164	37	)	)	PUNCT
ejpam-2337	164	38	,	,	PUNCT
ejpam-2337	164	39	h(x	h(x	PROPN
ejpam-2337	164	40	,	,	PUNCT
ejpam-2337	164	41	y	y	PROPN
ejpam-2337	164	42	,	,	PUNCT
ejpam-2337	164	43	v	v	NOUN
ejpam-2337	164	44	)	)	PUNCT
ejpam-2337	164	45	(	(	PUNCT
ejpam-2337	164	46	8)	8)	NUM
ejpam-2337	164	47	for	for	ADP
ejpam-2337	164	48	all	all	DET
ejpam-2337	164	49	x	x	SYM
ejpam-2337	164	50	,	,	PUNCT
ejpam-2337	164	51	u	u	NOUN
ejpam-2337	164	52	,	,	PUNCT
ejpam-2337	164	53	y	y	PROPN
ejpam-2337	164	54	,	,	PUNCT
ejpam-2337	164	55	v	v	PRON
ejpam-2337	164	56	%	%	NOUN
ejpam-2337	164	57	x	x	INTJ
ejpam-2337	164	58	.	.	PUNCT
ejpam-2337	165	1	then	then	ADV
ejpam-2337	165	2	there	there	PRON
ejpam-2337	165	3	exists	exist	VERB
ejpam-2337	165	4	a	a	DET
ejpam-2337	165	5	unique	unique	ADJ
ejpam-2337	165	6	bi	bi	ADJ
ejpam-2337	165	7	-	-	ADJ
ejpam-2337	165	8	reciprocal	reciprocal	ADJ
ejpam-2337	165	9	mapping	mapping	NOUN
ejpam-2337	165	10	r	r	NOUN
ejpam-2337	165	11	:	:	PUNCT
ejpam-2337	165	12	x	x	SYM
ejpam-2337	165	13	#	#	NOUN
ejpam-2337	165	14	x	x	SYM
ejpam-2337	165	15	$	$	SYM
ejpam-2337	165	16	y	y	NOUN
ejpam-2337	165	17	satisfying	satisfy	VERB
ejpam-2337	165	18	(	(	PUNCT
ejpam-2337	165	19	5	5	NUM
ejpam-2337	165	20	)	)	PUNCT
ejpam-2337	165	21	and	and	CCONJ
ejpam-2337	165	22	d(r(x	d(r(x	PROPN
ejpam-2337	165	23	,	,	PUNCT
ejpam-2337	165	24	y	y	PROPN
ejpam-2337	165	25	)	)	PUNCT
ejpam-2337	165	26	,	,	PUNCT
ejpam-2337	165	27	r(x	r(x	PROPN
ejpam-2337	165	28	,	,	PUNCT
ejpam-2337	165	29	y	y	PROPN
ejpam-2337	165	30	)	)	PUNCT
ejpam-2337	165	31	)	)	PUNCT
ejpam-2337	165	32	,	,	PUNCT
ejpam-2337	165	33	2	2	NUM
ejpam-2337	165	34	&	&	CCONJ
ejpam-2337	165	35	!	!	PUNCT
ejpam-2337	166	1	i=0	i=0	PROPN
ejpam-2337	167	1	4ig(2i	4ig(2i	X
ejpam-2337	167	2	x	x	PUNCT
ejpam-2337	167	3	,	,	PUNCT
ejpam-2337	167	4	2i	2i	NUM
ejpam-2337	167	5	x	x	SYM
ejpam-2337	167	6	,	,	PUNCT
ejpam-2337	167	7	2i	2i	PROPN
ejpam-2337	167	8	y	y	NOUN
ejpam-2337	167	9	)	)	PUNCT
ejpam-2337	167	10	+	+	CCONJ
ejpam-2337	167	11	4	4	NUM
ejpam-2337	167	12	&	&	CCONJ
ejpam-2337	167	13	!	!	PUNCT
ejpam-2337	168	1	i=0	i=0	PROPN
ejpam-2337	168	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	168	3	x	x	PUNCT
ejpam-2337	168	4	,	,	PUNCT
ejpam-2337	168	5	2i	2i	PROPN
ejpam-2337	168	6	y	y	PROPN
ejpam-2337	168	7	,	,	PUNCT
ejpam-2337	168	8	2i	2i	NOUN
ejpam-2337	168	9	y	y	NOUN
ejpam-2337	168	10	)	)	PUNCT
ejpam-2337	168	11	(	(	PUNCT
ejpam-2337	168	12	9	9	NUM
ejpam-2337	168	13	)	)	PUNCT
ejpam-2337	168	14	for	for	ADP
ejpam-2337	168	15	all	all	DET
ejpam-2337	168	16	x	x	SYM
ejpam-2337	168	17	,	,	PUNCT
ejpam-2337	168	18	y	y	NOUN
ejpam-2337	168	19	%	%	NOUN
ejpam-2337	168	20	x	x	X
ejpam-2337	168	21	.	.	PUNCT
ejpam-2337	169	1	the	the	DET
ejpam-2337	169	2	mapping	mapping	NOUN
ejpam-2337	169	3	r(x	r(x	PROPN
ejpam-2337	169	4	,	,	PUNCT
ejpam-2337	169	5	y	y	PROPN
ejpam-2337	169	6	)	)	PUNCT
ejpam-2337	169	7	is	be	AUX
ejpam-2337	169	8	defined	define	VERB
ejpam-2337	169	9	by	by	ADP
ejpam-2337	169	10	r(x	r(x	PROPN
ejpam-2337	169	11	,	,	PUNCT
ejpam-2337	169	12	y	y	PROPN
ejpam-2337	169	13	)	)	PUNCT
ejpam-2337	170	1	=	=	NOUN
ejpam-2337	170	2	lim	lim	PROPN
ejpam-2337	170	3	n$	n$	PROPN
ejpam-2337	170	4	&	&	CCONJ
ejpam-2337	170	5	4nr(2n	4nr(2n	PROPN
ejpam-2337	170	6	x	x	PROPN
ejpam-2337	170	7	,	,	PUNCT
ejpam-2337	170	8	2n	2n	NUM
ejpam-2337	170	9	y	y	NOUN
ejpam-2337	170	10	)	)	PUNCT
ejpam-2337	170	11	,	,	PUNCT
ejpam-2337	170	12	for	for	ADP
ejpam-2337	170	13	all	all	DET
ejpam-2337	170	14	x	x	SYM
ejpam-2337	170	15	,	,	PUNCT
ejpam-2337	170	16	y	y	NOUN
ejpam-2337	170	17	%	%	NOUN
ejpam-2337	170	18	x	x	X
ejpam-2337	170	19	.	.	PUNCT
ejpam-2337	171	1	proof	proof	NOUN
ejpam-2337	171	2	.	.	PUNCT
ejpam-2337	172	1	setting	set	VERB
ejpam-2337	172	2	u=	u=	NOUN
ejpam-2337	172	3	x	x	PUNCT
ejpam-2337	172	4	in	in	ADP
ejpam-2337	172	5	(	(	PUNCT
ejpam-2337	172	6	7	7	NUM
ejpam-2337	172	7	)	)	PUNCT
ejpam-2337	172	8	and	and	CCONJ
ejpam-2337	172	9	then	then	ADV
ejpam-2337	172	10	multiplying	multiply	VERB
ejpam-2337	172	11	by	by	ADP
ejpam-2337	172	12	2	2	NUM
ejpam-2337	172	13	on	on	ADP
ejpam-2337	172	14	both	both	DET
ejpam-2337	172	15	sides	side	NOUN
ejpam-2337	172	16	,	,	PUNCT
ejpam-2337	172	17	we	we	PRON
ejpam-2337	172	18	get	get	VERB
ejpam-2337	172	19	d(2r(2x	d(2r(2x	PROPN
ejpam-2337	172	20	,	,	PUNCT
ejpam-2337	172	21	y	y	PROPN
ejpam-2337	172	22	)	)	PUNCT
ejpam-2337	172	23	,	,	PUNCT
ejpam-2337	172	24	r(x	r(x	PROPN
ejpam-2337	172	25	,	,	PUNCT
ejpam-2337	172	26	y	y	PROPN
ejpam-2337	172	27	)	)	PUNCT
ejpam-2337	172	28	)	)	PUNCT
ejpam-2337	172	29	,	,	PUNCT
ejpam-2337	172	30	2g(x	2g(x	NUM
ejpam-2337	172	31	,	,	PUNCT
ejpam-2337	172	32	x	x	SYM
ejpam-2337	172	33	,	,	PUNCT
ejpam-2337	172	34	y	y	PROPN
ejpam-2337	172	35	)	)	PUNCT
ejpam-2337	172	36	(	(	PUNCT
ejpam-2337	172	37	10	10	NUM
ejpam-2337	172	38	)	)	PUNCT
ejpam-2337	172	39	for	for	ADP
ejpam-2337	172	40	all	all	DET
ejpam-2337	172	41	x	x	SYM
ejpam-2337	172	42	,	,	PUNCT
ejpam-2337	172	43	y	y	NOUN
ejpam-2337	172	44	%	%	NOUN
ejpam-2337	172	45	x	x	INTJ
ejpam-2337	172	46	.	.	PUNCT
ejpam-2337	173	1	putting	put	VERB
ejpam-2337	173	2	v	v	NOUN
ejpam-2337	173	3	=	=	SYM
ejpam-2337	173	4	y	y	PROPN
ejpam-2337	173	5	in	in	ADP
ejpam-2337	173	6	(	(	PUNCT
ejpam-2337	173	7	8)	8)	NUM
ejpam-2337	173	8	and	and	CCONJ
ejpam-2337	173	9	then	then	ADV
ejpam-2337	173	10	multiplying	multiply	VERB
ejpam-2337	173	11	by	by	ADP
ejpam-2337	173	12	2	2	NUM
ejpam-2337	173	13	on	on	ADP
ejpam-2337	173	14	both	both	DET
ejpam-2337	173	15	sides	side	NOUN
ejpam-2337	173	16	,	,	PUNCT
ejpam-2337	173	17	we	we	PRON
ejpam-2337	173	18	obtain	obtain	VERB
ejpam-2337	173	19	d(2r(x	d(2r(x	PROPN
ejpam-2337	173	20	,	,	PUNCT
ejpam-2337	173	21	2y	2y	NUM
ejpam-2337	173	22	)	)	PUNCT
ejpam-2337	173	23	,	,	PUNCT
ejpam-2337	173	24	r(x	r(x	PROPN
ejpam-2337	173	25	,	,	PUNCT
ejpam-2337	173	26	y	y	PROPN
ejpam-2337	173	27	)	)	PUNCT
ejpam-2337	173	28	)	)	PUNCT
ejpam-2337	173	29	,	,	PUNCT
ejpam-2337	173	30	2h(x	2h(x	NUM
ejpam-2337	173	31	,	,	PUNCT
ejpam-2337	173	32	y	y	PROPN
ejpam-2337	173	33	,	,	PUNCT
ejpam-2337	173	34	y	y	PROPN
ejpam-2337	173	35	)	)	PUNCT
ejpam-2337	173	36	(	(	PUNCT
ejpam-2337	173	37	11	11	NUM
ejpam-2337	173	38	)	)	PUNCT
ejpam-2337	173	39	for	for	ADP
ejpam-2337	173	40	all	all	DET
ejpam-2337	173	41	x	x	SYM
ejpam-2337	173	42	,	,	PUNCT
ejpam-2337	173	43	y	y	NOUN
ejpam-2337	173	44	%	%	NOUN
ejpam-2337	173	45	x	x	X
ejpam-2337	173	46	.	.	PUNCT
ejpam-2337	174	1	replacing	replace	VERB
ejpam-2337	174	2	x	x	PUNCT
ejpam-2337	174	3	by	by	ADP
ejpam-2337	174	4	2x	2x	NUM
ejpam-2337	174	5	in	in	ADP
ejpam-2337	174	6	(	(	PUNCT
ejpam-2337	174	7	11	11	NUM
ejpam-2337	174	8	)	)	PUNCT
ejpam-2337	174	9	and	and	CCONJ
ejpam-2337	174	10	then	then	ADV
ejpam-2337	174	11	multiplying	multiply	VERB
ejpam-2337	174	12	by	by	ADP
ejpam-2337	174	13	2	2	NUM
ejpam-2337	174	14	on	on	ADP
ejpam-2337	174	15	both	both	DET
ejpam-2337	174	16	sides	side	NOUN
ejpam-2337	174	17	,	,	PUNCT
ejpam-2337	174	18	yields	yield	NOUN
ejpam-2337	174	19	d(4r(2x	d(4r(2x	PROPN
ejpam-2337	174	20	,	,	PUNCT
ejpam-2337	174	21	2y	2y	NUM
ejpam-2337	174	22	)	)	PUNCT
ejpam-2337	174	23	,	,	PUNCT
ejpam-2337	174	24	2r(2x	2r(2x	NUM
ejpam-2337	174	25	,	,	PUNCT
ejpam-2337	174	26	y	y	NOUN
ejpam-2337	174	27	)	)	PUNCT
ejpam-2337	174	28	)	)	PUNCT
ejpam-2337	174	29	,	,	PUNCT
ejpam-2337	174	30	4h(2x	4h(2x	NUM
ejpam-2337	174	31	,	,	PUNCT
ejpam-2337	174	32	y	y	PROPN
ejpam-2337	174	33	,	,	PUNCT
ejpam-2337	174	34	y	y	PROPN
ejpam-2337	174	35	)	)	PUNCT
ejpam-2337	174	36	(	(	PUNCT
ejpam-2337	174	37	12	12	NUM
ejpam-2337	174	38	)	)	PUNCT
ejpam-2337	174	39	for	for	ADP
ejpam-2337	174	40	all	all	DET
ejpam-2337	174	41	x	x	SYM
ejpam-2337	174	42	,	,	PUNCT
ejpam-2337	174	43	y	y	NOUN
ejpam-2337	174	44	%	%	NOUN
ejpam-2337	174	45	x	x	INTJ
ejpam-2337	174	46	.	.	PUNCT
ejpam-2337	175	1	combining	combine	VERB
ejpam-2337	175	2	(	(	PUNCT
ejpam-2337	175	3	10	10	NUM
ejpam-2337	175	4	)	)	PUNCT
ejpam-2337	175	5	and	and	CCONJ
ejpam-2337	175	6	(	(	PUNCT
ejpam-2337	175	7	12	12	NUM
ejpam-2337	175	8	)	)	PUNCT
ejpam-2337	175	9	and	and	CCONJ
ejpam-2337	175	10	using	use	VERB
ejpam-2337	175	11	triangle	triangle	NOUN
ejpam-2337	175	12	inequality	inequality	NOUN
ejpam-2337	175	13	,	,	PUNCT
ejpam-2337	175	14	we	we	PRON
ejpam-2337	175	15	get	get	VERB
ejpam-2337	175	16	d(4r(2x	d(4r(2x	PROPN
ejpam-2337	175	17	,	,	PUNCT
ejpam-2337	175	18	2y	2y	NUM
ejpam-2337	175	19	)	)	PUNCT
ejpam-2337	175	20	,	,	PUNCT
ejpam-2337	176	1	r(x	r(x	PROPN
ejpam-2337	176	2	,	,	PUNCT
ejpam-2337	176	3	y	y	PROPN
ejpam-2337	176	4	)	)	PUNCT
ejpam-2337	176	5	)	)	PUNCT
ejpam-2337	176	6	,	,	PUNCT
ejpam-2337	176	7	2g(x	2g(x	NUM
ejpam-2337	176	8	,	,	PUNCT
ejpam-2337	176	9	x	x	SYM
ejpam-2337	176	10	,	,	PUNCT
ejpam-2337	176	11	y	y	PROPN
ejpam-2337	176	12	)	)	PUNCT
ejpam-2337	177	1	+	+	CCONJ
ejpam-2337	177	2	4h(2x	4h(2x	NUM
ejpam-2337	177	3	,	,	PUNCT
ejpam-2337	177	4	y	y	PROPN
ejpam-2337	177	5	,	,	PUNCT
ejpam-2337	177	6	y	y	PROPN
ejpam-2337	177	7	)	)	PUNCT
ejpam-2337	177	8	(	(	PUNCT
ejpam-2337	177	9	13	13	NUM
ejpam-2337	177	10	)	)	PUNCT
ejpam-2337	177	11	k.	k.	PROPN
ejpam-2337	177	12	ravi	ravi	PROPN
ejpam-2337	177	13	,	,	PUNCT
ejpam-2337	177	14	b.	b.	PROPN
ejpam-2337	177	15	kumar	kumar	PROPN
ejpam-2337	177	16	/	/	SYM
ejpam-2337	177	17	eur	eur	PROPN
ejpam-2337	177	18	.	.	PUNCT
ejpam-2337	178	1	j.	j.	PROPN
ejpam-2337	178	2	pure	pure	PROPN
ejpam-2337	178	3	appl	appl	PROPN
ejpam-2337	178	4	.	.	PROPN
ejpam-2337	178	5	math	math	PROPN
ejpam-2337	178	6	,	,	PUNCT
ejpam-2337	178	7	8	8	NUM
ejpam-2337	178	8	(	(	PUNCT
ejpam-2337	178	9	2015	2015	NUM
ejpam-2337	178	10	)	)	PUNCT
ejpam-2337	178	11	,	,	PUNCT
ejpam-2337	178	12	283	283	NUM
ejpam-2337	178	13	-	-	SYM
ejpam-2337	178	14	293	293	NUM
ejpam-2337	178	15	288	288	NUM
ejpam-2337	178	16	for	for	ADP
ejpam-2337	178	17	all	all	DET
ejpam-2337	178	18	x	x	SYM
ejpam-2337	178	19	,	,	PUNCT
ejpam-2337	178	20	y	y	NOUN
ejpam-2337	178	21	%	%	INTJ
ejpam-2337	178	22	x	x	INTJ
ejpam-2337	178	23	.	.	PUNCT
ejpam-2337	179	1	now	now	ADV
ejpam-2337	179	2	,	,	PUNCT
ejpam-2337	179	3	substituting	substitute	VERB
ejpam-2337	179	4	(	(	PUNCT
ejpam-2337	179	5	x	x	INTJ
ejpam-2337	179	6	,	,	PUNCT
ejpam-2337	179	7	y	y	PROPN
ejpam-2337	179	8	)	)	PUNCT
ejpam-2337	179	9	by	by	ADP
ejpam-2337	179	10	(	(	PUNCT
ejpam-2337	179	11	2x	2x	NUM
ejpam-2337	179	12	,	,	PUNCT
ejpam-2337	179	13	2y	2y	NUM
ejpam-2337	179	14	)	)	PUNCT
ejpam-2337	179	15	in	in	ADP
ejpam-2337	179	16	(	(	PUNCT
ejpam-2337	179	17	13	13	NUM
ejpam-2337	179	18	)	)	PUNCT
ejpam-2337	179	19	and	and	CCONJ
ejpam-2337	179	20	then	then	ADV
ejpam-2337	179	21	multiplying	multiply	VERB
ejpam-2337	179	22	by	by	ADP
ejpam-2337	179	23	4	4	NUM
ejpam-2337	179	24	on	on	ADP
ejpam-2337	179	25	both	both	DET
ejpam-2337	179	26	sides	side	NOUN
ejpam-2337	179	27	,	,	PUNCT
ejpam-2337	179	28	we	we	PRON
ejpam-2337	179	29	have	have	VERB
ejpam-2337	179	30	d(16r(4x	d(16r(4x	NOUN
ejpam-2337	179	31	,	,	PUNCT
ejpam-2337	179	32	4y	4y	PROPN
ejpam-2337	179	33	)	)	PUNCT
ejpam-2337	179	34	,	,	PUNCT
ejpam-2337	179	35	4r(2x	4r(2x	NUM
ejpam-2337	179	36	,	,	PUNCT
ejpam-2337	179	37	2y	2y	NUM
ejpam-2337	179	38	)	)	PUNCT
ejpam-2337	179	39	)	)	PUNCT
ejpam-2337	179	40	,	,	PUNCT
ejpam-2337	179	41	8g(2x	8g(2x	PROPN
ejpam-2337	179	42	,	,	PUNCT
ejpam-2337	179	43	2x	2x	NUM
ejpam-2337	179	44	,	,	PUNCT
ejpam-2337	179	45	2y	2y	NUM
ejpam-2337	179	46	)	)	PUNCT
ejpam-2337	180	1	+	+	CCONJ
ejpam-2337	180	2	16h(4x	16h(4x	NUM
ejpam-2337	180	3	,	,	PUNCT
ejpam-2337	180	4	2y	2y	NUM
ejpam-2337	180	5	,	,	PUNCT
ejpam-2337	180	6	2y	2y	NUM
ejpam-2337	180	7	)	)	PUNCT
ejpam-2337	180	8	(	(	PUNCT
ejpam-2337	180	9	14	14	NUM
ejpam-2337	180	10	)	)	PUNCT
ejpam-2337	180	11	for	for	ADP
ejpam-2337	180	12	all	all	DET
ejpam-2337	180	13	x	x	SYM
ejpam-2337	180	14	,	,	PUNCT
ejpam-2337	180	15	y	y	NOUN
ejpam-2337	180	16	%	%	NOUN
ejpam-2337	180	17	x	x	INTJ
ejpam-2337	180	18	.	.	PUNCT
ejpam-2337	181	1	combining	combine	VERB
ejpam-2337	181	2	(	(	PUNCT
ejpam-2337	181	3	13	13	NUM
ejpam-2337	181	4	)	)	PUNCT
ejpam-2337	181	5	and	and	CCONJ
ejpam-2337	181	6	(	(	PUNCT
ejpam-2337	181	7	14	14	NUM
ejpam-2337	181	8	)	)	PUNCT
ejpam-2337	181	9	,	,	PUNCT
ejpam-2337	181	10	we	we	PRON
ejpam-2337	181	11	see	see	VERB
ejpam-2337	181	12	that	that	PRON
ejpam-2337	181	13	d	d	PROPN
ejpam-2337	181	14	,	,	PUNCT
ejpam-2337	181	15	42r(22	42r(22	PROPN
ejpam-2337	181	16	x	x	SYM
ejpam-2337	181	17	,	,	PUNCT
ejpam-2337	181	18	22	22	NUM
ejpam-2337	181	19	y	y	NOUN
ejpam-2337	181	20	)	)	PUNCT
ejpam-2337	181	21	,	,	PUNCT
ejpam-2337	181	22	r(x	r(x	PROPN
ejpam-2337	181	23	,	,	PUNCT
ejpam-2337	181	24	y	y	PROPN
ejpam-2337	181	25	)	)	PUNCT
ejpam-2337	181	26	,	,	PUNCT
ejpam-2337	181	27	2	2	NUM
ejpam-2337	181	28	1	1	NUM
ejpam-2337	181	29	!	!	PUNCT
ejpam-2337	182	1	i=0	i=0	PROPN
ejpam-2337	182	2	4ig(2i	4ig(2i	X
ejpam-2337	182	3	x	x	PUNCT
ejpam-2337	182	4	,	,	PUNCT
ejpam-2337	182	5	2i	2i	NUM
ejpam-2337	182	6	x	x	SYM
ejpam-2337	182	7	,	,	PUNCT
ejpam-2337	182	8	2i	2i	PROPN
ejpam-2337	182	9	y	y	NOUN
ejpam-2337	182	10	)	)	PUNCT
ejpam-2337	182	11	+	+	CCONJ
ejpam-2337	182	12	4	4	NUM
ejpam-2337	182	13	1	1	NUM
ejpam-2337	182	14	!	!	PUNCT
ejpam-2337	183	1	i=0	i=0	PROPN
ejpam-2337	183	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	183	3	x	x	PUNCT
ejpam-2337	183	4	,	,	PUNCT
ejpam-2337	183	5	2i	2i	PROPN
ejpam-2337	183	6	y	y	PROPN
ejpam-2337	183	7	,	,	PUNCT
ejpam-2337	183	8	2i	2i	NOUN
ejpam-2337	183	9	y	y	NOUN
ejpam-2337	183	10	)	)	PUNCT
ejpam-2337	183	11	for	for	ADP
ejpam-2337	183	12	all	all	DET
ejpam-2337	183	13	x	x	SYM
ejpam-2337	183	14	,	,	PUNCT
ejpam-2337	183	15	y	y	NOUN
ejpam-2337	183	16	%	%	NOUN
ejpam-2337	183	17	x	x	INTJ
ejpam-2337	183	18	.	.	PUNCT
ejpam-2337	184	1	using	use	VERB
ejpam-2337	184	2	induction	induction	NOUN
ejpam-2337	184	3	arguments	argument	NOUN
ejpam-2337	184	4	,	,	PUNCT
ejpam-2337	184	5	we	we	PRON
ejpam-2337	184	6	conclude	conclude	VERB
ejpam-2337	184	7	that	that	SCONJ
ejpam-2337	184	8	d(4nr(2n	d(4nr(2n	NOUN
ejpam-2337	184	9	x	x	SYM
ejpam-2337	184	10	,	,	PUNCT
ejpam-2337	184	11	2n	2n	NUM
ejpam-2337	184	12	y	y	NOUN
ejpam-2337	184	13	)	)	PUNCT
ejpam-2337	184	14	,	,	PUNCT
ejpam-2337	184	15	r(x	r(x	PROPN
ejpam-2337	184	16	,	,	PUNCT
ejpam-2337	184	17	y	y	PROPN
ejpam-2337	184	18	)	)	PUNCT
ejpam-2337	184	19	)	)	PUNCT
ejpam-2337	184	20	,	,	PUNCT
ejpam-2337	184	21	2	2	NUM
ejpam-2337	184	22	n.1	n.1	NOUN
ejpam-2337	184	23	!	!	PUNCT
ejpam-2337	185	1	i=0	i=0	PROPN
ejpam-2337	186	1	4ig(2i	4ig(2i	X
ejpam-2337	186	2	x	x	PUNCT
ejpam-2337	186	3	,	,	PUNCT
ejpam-2337	186	4	2i	2i	NUM
ejpam-2337	186	5	x	x	SYM
ejpam-2337	186	6	,	,	PUNCT
ejpam-2337	186	7	2i	2i	PROPN
ejpam-2337	186	8	y	y	NOUN
ejpam-2337	186	9	)	)	PUNCT
ejpam-2337	187	1	+	+	CCONJ
ejpam-2337	187	2	4	4	NUM
ejpam-2337	187	3	n.1	n.1	NUM
ejpam-2337	187	4	!	!	PUNCT
ejpam-2337	188	1	i=0	i=0	PROPN
ejpam-2337	188	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	189	1	x	x	PUNCT
ejpam-2337	189	2	,	,	PUNCT
ejpam-2337	189	3	2i	2i	PROPN
ejpam-2337	189	4	y	y	PROPN
ejpam-2337	189	5	,	,	PUNCT
ejpam-2337	189	6	2i	2i	NOUN
ejpam-2337	189	7	y	y	NOUN
ejpam-2337	189	8	)	)	PUNCT
ejpam-2337	189	9	,	,	PUNCT
ejpam-2337	189	10	2	2	NUM
ejpam-2337	189	11	&	&	CCONJ
ejpam-2337	189	12	!	!	PUNCT
ejpam-2337	190	1	i=0	i=0	PROPN
ejpam-2337	191	1	4ig(2i	4ig(2i	X
ejpam-2337	191	2	x	x	PUNCT
ejpam-2337	191	3	,	,	PUNCT
ejpam-2337	191	4	2i	2i	NUM
ejpam-2337	191	5	x	x	SYM
ejpam-2337	191	6	,	,	PUNCT
ejpam-2337	191	7	2i	2i	PROPN
ejpam-2337	191	8	y	y	NOUN
ejpam-2337	191	9	)	)	PUNCT
ejpam-2337	191	10	+	+	CCONJ
ejpam-2337	191	11	4	4	NUM
ejpam-2337	191	12	&	&	CCONJ
ejpam-2337	191	13	!	!	PUNCT
ejpam-2337	192	1	i=0	i=0	PROPN
ejpam-2337	192	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	192	3	x	x	PUNCT
ejpam-2337	192	4	,	,	PUNCT
ejpam-2337	192	5	2i	2i	PROPN
ejpam-2337	192	6	y	y	PROPN
ejpam-2337	192	7	,	,	PUNCT
ejpam-2337	192	8	2i	2i	NOUN
ejpam-2337	192	9	y	y	NOUN
ejpam-2337	192	10	)	)	PUNCT
ejpam-2337	192	11	(	(	PUNCT
ejpam-2337	192	12	15	15	NUM
ejpam-2337	192	13	)	)	PUNCT
ejpam-2337	192	14	for	for	ADP
ejpam-2337	192	15	all	all	DET
ejpam-2337	192	16	x	x	SYM
ejpam-2337	192	17	,	,	PUNCT
ejpam-2337	192	18	y	y	NOUN
ejpam-2337	192	19	%	%	NOUN
ejpam-2337	192	20	x	x	INTJ
ejpam-2337	192	21	.	.	PUNCT
ejpam-2337	193	1	in	in	ADP
ejpam-2337	193	2	order	order	NOUN
ejpam-2337	193	3	to	to	PART
ejpam-2337	193	4	prove	prove	VERB
ejpam-2337	193	5	the	the	DET
ejpam-2337	193	6	convergence	convergence	NOUN
ejpam-2337	193	7	of	of	ADP
ejpam-2337	193	8	the	the	DET
ejpam-2337	193	9	sequence	sequence	NOUN
ejpam-2337	193	10	{	{	PUNCT
ejpam-2337	193	11	4nr(2n	4nr(2n	NOUN
ejpam-2337	193	12	x	x	SYM
ejpam-2337	193	13	,	,	PUNCT
ejpam-2337	193	14	2n	2n	NUM
ejpam-2337	193	15	y	y	NOUN
ejpam-2337	193	16	)	)	PUNCT
ejpam-2337	193	17	}	}	PUNCT
ejpam-2337	193	18	,	,	PUNCT
ejpam-2337	193	19	replace	replace	VERB
ejpam-2337	193	20	(	(	PUNCT
ejpam-2337	193	21	x	x	NOUN
ejpam-2337	193	22	,	,	PUNCT
ejpam-2337	193	23	y	y	PROPN
ejpam-2337	193	24	)	)	PUNCT
ejpam-2337	193	25	by	by	ADP
ejpam-2337	193	26	(	(	PUNCT
ejpam-2337	193	27	2	2	NUM
ejpam-2337	193	28	m	m	NOUN
ejpam-2337	193	29	x	x	NOUN
ejpam-2337	193	30	,	,	PUNCT
ejpam-2337	193	31	2	2	NUM
ejpam-2337	193	32	m	m	NOUN
ejpam-2337	193	33	y	y	NOUN
ejpam-2337	193	34	)	)	PUNCT
ejpam-2337	193	35	in	in	ADP
ejpam-2337	193	36	(	(	PUNCT
ejpam-2337	193	37	15	15	NUM
ejpam-2337	193	38	)	)	PUNCT
ejpam-2337	193	39	and	and	CCONJ
ejpam-2337	193	40	multiply	multiply	ADV
ejpam-2337	193	41	by	by	ADP
ejpam-2337	193	42	4	4	NUM
ejpam-2337	193	43	m	m	NOUN
ejpam-2337	193	44	to	to	PART
ejpam-2337	193	45	get	get	VERB
ejpam-2337	193	46	d(4n+mr(2n+m	d(4n+mr(2n+m	NUM
ejpam-2337	193	47	,	,	PUNCT
ejpam-2337	193	48	2n+m	2n+m	PROPN
ejpam-2337	193	49	y	y	NOUN
ejpam-2337	193	50	)	)	PUNCT
ejpam-2337	193	51	,	,	PUNCT
ejpam-2337	194	1	4mr(2	4mr(2	AUX
ejpam-2337	194	2	m	m	NOUN
ejpam-2337	194	3	x	x	INTJ
ejpam-2337	194	4	,	,	PUNCT
ejpam-2337	194	5	2	2	NUM
ejpam-2337	194	6	m	m	NOUN
ejpam-2337	194	7	y	y	NOUN
ejpam-2337	194	8	)	)	PUNCT
ejpam-2337	194	9	)	)	PUNCT
ejpam-2337	195	1	=	=	SYM
ejpam-2337	195	2	4md(4nr(2n+m	4md(4nr(2n+m	NUM
ejpam-2337	195	3	x	x	SYM
ejpam-2337	195	4	,	,	PUNCT
ejpam-2337	195	5	2n+m	2n+m	PROPN
ejpam-2337	195	6	y	y	NOUN
ejpam-2337	195	7	)	)	PUNCT
ejpam-2337	195	8	,	,	PUNCT
ejpam-2337	195	9	r(2	r(2	PROPN
ejpam-2337	195	10	m	m	PROPN
ejpam-2337	195	11	x	x	NOUN
ejpam-2337	195	12	,	,	PUNCT
ejpam-2337	195	13	2	2	NUM
ejpam-2337	195	14	m	m	NOUN
ejpam-2337	195	15	y	y	NOUN
ejpam-2337	195	16	)	)	PUNCT
ejpam-2337	195	17	)	)	PUNCT
ejpam-2337	195	18	,	,	PUNCT
ejpam-2337	195	19	2	2	NUM
ejpam-2337	195	20	&	&	CCONJ
ejpam-2337	195	21	!	!	PUNCT
ejpam-2337	196	1	i=0	i=0	PROPN
ejpam-2337	197	1	4m+ig(2m+i	4m+ig(2m+i	NUM
ejpam-2337	197	2	x	x	X
ejpam-2337	197	3	,	,	PUNCT
ejpam-2337	197	4	2m+i	2m+i	NUM
ejpam-2337	197	5	x	x	SYM
ejpam-2337	197	6	,	,	PUNCT
ejpam-2337	197	7	2m+i	2m+i	NUM
ejpam-2337	197	8	y	y	NOUN
ejpam-2337	197	9	)	)	PUNCT
ejpam-2337	198	1	+	+	CCONJ
ejpam-2337	198	2	4	4	NUM
ejpam-2337	198	3	&	&	CCONJ
ejpam-2337	198	4	!	!	PUNCT
ejpam-2337	199	1	i=0	i=0	PROPN
ejpam-2337	199	2	4m+ih(2m+i+1	4m+ih(2m+i+1	PUNCT
ejpam-2337	200	1	x	x	X
ejpam-2337	200	2	,	,	PUNCT
ejpam-2337	200	3	2m+i	2m+i	NUM
ejpam-2337	200	4	y	y	PROPN
ejpam-2337	200	5	,	,	PUNCT
ejpam-2337	200	6	2m+i	2m+i	NUM
ejpam-2337	200	7	y	y	NOUN
ejpam-2337	200	8	)	)	PUNCT
ejpam-2337	200	9	.	.	PUNCT
ejpam-2337	201	1	using	use	VERB
ejpam-2337	201	2	(	(	PUNCT
ejpam-2337	201	3	6	6	NUM
ejpam-2337	201	4	)	)	PUNCT
ejpam-2337	201	5	,	,	PUNCT
ejpam-2337	201	6	the	the	DET
ejpam-2337	201	7	right	right	ADJ
ejpam-2337	201	8	-	-	PUNCT
ejpam-2337	201	9	hand	hand	NOUN
ejpam-2337	201	10	side	side	NOUN
ejpam-2337	201	11	of	of	ADP
ejpam-2337	201	12	the	the	DET
ejpam-2337	201	13	above	above	ADJ
ejpam-2337	201	14	inequality	inequality	NOUN
ejpam-2337	201	15	tends	tend	VERB
ejpam-2337	201	16	to	to	ADP
ejpam-2337	201	17	zero	zero	NUM
ejpam-2337	201	18	as	as	ADP
ejpam-2337	201	19	m$	m$	NOUN
ejpam-2337	201	20	&	&	CCONJ
ejpam-2337	201	21	.	.	PUNCT
ejpam-2337	202	1	this	this	PRON
ejpam-2337	202	2	shows	show	VERB
ejpam-2337	202	3	that	that	SCONJ
ejpam-2337	202	4	{	{	PUNCT
ejpam-2337	202	5	4nr(2n	4nr(2n	NOUN
ejpam-2337	202	6	x	x	SYM
ejpam-2337	202	7	,	,	PUNCT
ejpam-2337	202	8	2n	2n	NUM
ejpam-2337	202	9	y	y	NOUN
ejpam-2337	202	10	)	)	PUNCT
ejpam-2337	202	11	}	}	PUNCT
ejpam-2337	202	12	is	be	AUX
ejpam-2337	202	13	a	a	DET
ejpam-2337	202	14	cauchy	cauchy	ADJ
ejpam-2337	202	15	sequence	sequence	NOUN
ejpam-2337	202	16	in	in	ADP
ejpam-2337	202	17	y	y	PROPN
ejpam-2337	202	18	.	.	PUNCT
ejpam-2337	203	1	since	since	SCONJ
ejpam-2337	203	2	y	y	PROPN
ejpam-2337	203	3	is	be	AUX
ejpam-2337	203	4	a	a	DET
ejpam-2337	203	5	fréchet	fréchet	NOUN
ejpam-2337	203	6	space	space	NOUN
ejpam-2337	203	7	,	,	PUNCT
ejpam-2337	203	8	it	it	PRON
ejpam-2337	203	9	follows	follow	VERB
ejpam-2337	203	10	that	that	SCONJ
ejpam-2337	203	11	the	the	DET
ejpam-2337	203	12	sequence	sequence	NOUN
ejpam-2337	203	13	{	{	PUNCT
ejpam-2337	203	14	4nr(2n	4nr(2n	NOUN
ejpam-2337	203	15	x	x	SYM
ejpam-2337	203	16	,	,	PUNCT
ejpam-2337	203	17	2n	2n	NUM
ejpam-2337	203	18	y	y	NOUN
ejpam-2337	203	19	)	)	PUNCT
ejpam-2337	203	20	}	}	PUNCT
ejpam-2337	203	21	converges	converge	VERB
ejpam-2337	203	22	.	.	PUNCT
ejpam-2337	204	1	define	define	VERB
ejpam-2337	204	2	r	r	NOUN
ejpam-2337	204	3	:	:	PUNCT
ejpam-2337	204	4	x	x	SYM
ejpam-2337	204	5	#	#	NOUN
ejpam-2337	204	6	x	x	SYM
ejpam-2337	204	7	$	$	SYM
ejpam-2337	204	8	y	y	NOUN
ejpam-2337	204	9	by	by	ADP
ejpam-2337	204	10	r(x	r(x	PROPN
ejpam-2337	204	11	,	,	PUNCT
ejpam-2337	204	12	y	y	PROPN
ejpam-2337	204	13	)	)	PUNCT
ejpam-2337	205	1	=	=	NOUN
ejpam-2337	205	2	lim	lim	PROPN
ejpam-2337	205	3	n$	n$	PROPN
ejpam-2337	205	4	&	&	CCONJ
ejpam-2337	205	5	4nr(2n	4nr(2n	PROPN
ejpam-2337	205	6	x	x	PROPN
ejpam-2337	205	7	,	,	PUNCT
ejpam-2337	205	8	2n	2n	NUM
ejpam-2337	205	9	y	y	NOUN
ejpam-2337	205	10	)	)	PUNCT
ejpam-2337	205	11	for	for	ADP
ejpam-2337	205	12	all	all	PRON
ejpam-2337	205	13	x	x	SYM
ejpam-2337	205	14	,	,	PUNCT
ejpam-2337	205	15	y	y	NOUN
ejpam-2337	205	16	%	%	INTJ
ejpam-2337	205	17	x	x	INTJ
ejpam-2337	205	18	.	.	PUNCT
ejpam-2337	206	1	it	it	PRON
ejpam-2337	206	2	follows	follow	VERB
ejpam-2337	206	3	from	from	ADP
ejpam-2337	206	4	(	(	PUNCT
ejpam-2337	206	5	7	7	NUM
ejpam-2337	206	6	)	)	PUNCT
ejpam-2337	207	1	that	that	SCONJ
ejpam-2337	207	2	#	#	SYM
ejpam-2337	207	3	r(x	r(x	PROPN
ejpam-2337	207	4	,	,	PUNCT
ejpam-2337	207	5	u	u	NOUN
ejpam-2337	207	6	,	,	PUNCT
ejpam-2337	207	7	y	y	NOUN
ejpam-2337	207	8	)	)	PUNCT
ejpam-2337	207	9	=	=	NOUN
ejpam-2337	207	10	lim	lim	PROPN
ejpam-2337	207	11	n$	n$	NOUN
ejpam-2337	207	12	&	&	CCONJ
ejpam-2337	207	13	4n	4n	X
ejpam-2337	207	14	#	#	SYM
ejpam-2337	207	15	r(2	r(2	PROPN
ejpam-2337	207	16	n	n	NOUN
ejpam-2337	207	17	x	x	NOUN
ejpam-2337	207	18	,	,	PUNCT
ejpam-2337	207	19	2nu	2nu	NOUN
ejpam-2337	207	20	,	,	PUNCT
ejpam-2337	207	21	2n	2n	NUM
ejpam-2337	207	22	y	y	NOUN
ejpam-2337	207	23	)	)	PUNCT
ejpam-2337	207	24	,	,	PUNCT
ejpam-2337	207	25	lim	lim	PROPN
ejpam-2337	207	26	n$	n$	PROPN
ejpam-2337	207	27	&	&	CCONJ
ejpam-2337	207	28	4ng(2n	4ng(2n	PROPN
ejpam-2337	207	29	x	x	SYM
ejpam-2337	207	30	,	,	PUNCT
ejpam-2337	207	31	2nu	2nu	NOUN
ejpam-2337	207	32	,	,	PUNCT
ejpam-2337	207	33	2n	2n	NUM
ejpam-2337	207	34	y	y	NOUN
ejpam-2337	207	35	)	)	PUNCT
ejpam-2337	207	36	=	=	SYM
ejpam-2337	207	37	0	0	NUM
ejpam-2337	207	38	for	for	ADP
ejpam-2337	207	39	all	all	DET
ejpam-2337	207	40	x	x	SYM
ejpam-2337	207	41	,	,	PUNCT
ejpam-2337	207	42	u	u	NOUN
ejpam-2337	207	43	,	,	PUNCT
ejpam-2337	207	44	y	y	PROPN
ejpam-2337	207	45	,	,	PUNCT
ejpam-2337	207	46	v	v	PRON
ejpam-2337	207	47	%	%	NOUN
ejpam-2337	207	48	x	x	INTJ
ejpam-2337	207	49	.	.	PUNCT
ejpam-2337	207	50	also	also	ADV
ejpam-2337	207	51	it	it	PRON
ejpam-2337	207	52	follows	follow	VERB
ejpam-2337	207	53	from	from	ADP
ejpam-2337	207	54	(	(	PUNCT
ejpam-2337	207	55	8)	8)	NUM
ejpam-2337	207	56	that	that	SCONJ
ejpam-2337	207	57	"	"	PUNCT
ejpam-2337	207	58	r(x	r(x	PROPN
ejpam-2337	207	59	,	,	PUNCT
ejpam-2337	207	60	y	y	PROPN
ejpam-2337	207	61	,	,	PUNCT
ejpam-2337	207	62	v	v	NOUN
ejpam-2337	207	63	)	)	PUNCT
ejpam-2337	207	64	=	=	SYM
ejpam-2337	207	65	lim	lim	PROPN
ejpam-2337	207	66	n$	n$	PROPN
ejpam-2337	207	67	&	&	CCONJ
ejpam-2337	207	68	4n"r(2	4n"r(2	PROPN
ejpam-2337	207	69	n	n	CCONJ
ejpam-2337	207	70	x	x	NOUN
ejpam-2337	207	71	,	,	PUNCT
ejpam-2337	207	72	2n	2n	NUM
ejpam-2337	207	73	y	y	NOUN
ejpam-2337	207	74	,	,	PUNCT
ejpam-2337	207	75	2nv	2nv	ADJ
ejpam-2337	207	76	)	)	PUNCT
ejpam-2337	207	77	,	,	PUNCT
ejpam-2337	207	78	lim	lim	PROPN
ejpam-2337	207	79	n$	n$	PROPN
ejpam-2337	207	80	&	&	CCONJ
ejpam-2337	207	81	4nh(2n	4nh(2n	PROPN
ejpam-2337	207	82	x	x	SYM
ejpam-2337	207	83	,	,	PUNCT
ejpam-2337	207	84	2n	2n	NUM
ejpam-2337	207	85	y	y	NOUN
ejpam-2337	207	86	,	,	PUNCT
ejpam-2337	207	87	2nv	2nv	ADJ
ejpam-2337	207	88	)	)	PUNCT
ejpam-2337	207	89	=	=	SYM
ejpam-2337	207	90	0	0	PROPN
ejpam-2337	207	91	k.	k.	PROPN
ejpam-2337	207	92	ravi	ravi	PROPN
ejpam-2337	207	93	,	,	PUNCT
ejpam-2337	207	94	b.	b.	PROPN
ejpam-2337	207	95	kumar	kumar	PROPN
ejpam-2337	207	96	/	/	SYM
ejpam-2337	207	97	eur	eur	PROPN
ejpam-2337	207	98	.	.	PUNCT
ejpam-2337	208	1	j.	j.	PROPN
ejpam-2337	208	2	pure	pure	PROPN
ejpam-2337	208	3	appl	appl	PROPN
ejpam-2337	208	4	.	.	PROPN
ejpam-2337	208	5	math	math	PROPN
ejpam-2337	208	6	,	,	PUNCT
ejpam-2337	208	7	8	8	NUM
ejpam-2337	208	8	(	(	PUNCT
ejpam-2337	208	9	2015	2015	NUM
ejpam-2337	208	10	)	)	PUNCT
ejpam-2337	208	11	,	,	PUNCT
ejpam-2337	208	12	283	283	NUM
ejpam-2337	208	13	-	-	SYM
ejpam-2337	208	14	293	293	NUM
ejpam-2337	208	15	289	289	NUM
ejpam-2337	208	16	for	for	ADP
ejpam-2337	208	17	all	all	DET
ejpam-2337	208	18	x	x	SYM
ejpam-2337	208	19	,	,	PUNCT
ejpam-2337	208	20	y	y	PROPN
ejpam-2337	208	21	,	,	PUNCT
ejpam-2337	208	22	v	v	PRON
ejpam-2337	208	23	%	%	NOUN
ejpam-2337	208	24	x	x	PUNCT
ejpam-2337	208	25	,	,	PUNCT
ejpam-2337	208	26	which	which	PRON
ejpam-2337	208	27	shows	show	VERB
ejpam-2337	208	28	that	that	SCONJ
ejpam-2337	208	29	r	r	NOUN
ejpam-2337	208	30	is	be	AUX
ejpam-2337	208	31	bi	bi	NOUN
ejpam-2337	208	32	-	-	ADJ
ejpam-2337	208	33	reciprocal	reciprocal	ADJ
ejpam-2337	208	34	.	.	PUNCT
ejpam-2337	209	1	to	to	PART
ejpam-2337	209	2	prove	prove	VERB
ejpam-2337	209	3	r	r	NOUN
ejpam-2337	209	4	is	be	AUX
ejpam-2337	209	5	unique	unique	ADJ
ejpam-2337	209	6	bi	bi	ADJ
ejpam-2337	209	7	-	-	ADJ
ejpam-2337	209	8	reciprocal	reciprocal	ADJ
ejpam-2337	209	9	mapping	mapping	NOUN
ejpam-2337	209	10	,	,	PUNCT
ejpam-2337	209	11	let	let	VERB
ejpam-2337	209	12	us	we	PRON
ejpam-2337	209	13	consider	consider	VERB
ejpam-2337	209	14	another	another	DET
ejpam-2337	209	15	bi	bi	ADJ
ejpam-2337	209	16	-	-	ADJ
ejpam-2337	209	17	reciprocal	reciprocal	ADJ
ejpam-2337	209	18	mapping	mapping	NOUN
ejpam-2337	209	19	r0	r0	NOUN
ejpam-2337	209	20	:	:	PUNCT
ejpam-2337	209	21	x	x	PUNCT
ejpam-2337	209	22	#	#	NOUN
ejpam-2337	209	23	x	x	SYM
ejpam-2337	209	24	$	$	SYM
ejpam-2337	209	25	y	y	PROPN
ejpam-2337	209	26	which	which	PRON
ejpam-2337	209	27	satisfies	satisfy	VERB
ejpam-2337	209	28	(	(	PUNCT
ejpam-2337	209	29	5	5	NUM
ejpam-2337	209	30	)	)	PUNCT
ejpam-2337	209	31	and	and	CCONJ
ejpam-2337	209	32	(	(	PUNCT
ejpam-2337	209	33	9	9	NUM
ejpam-2337	209	34	)	)	PUNCT
ejpam-2337	209	35	.	.	PUNCT
ejpam-2337	210	1	since	since	SCONJ
ejpam-2337	210	2	4nr(2n	4nr(2n	PROPN
ejpam-2337	210	3	x	x	SYM
ejpam-2337	210	4	,	,	PUNCT
ejpam-2337	210	5	2n	2n	NUM
ejpam-2337	210	6	y	y	NOUN
ejpam-2337	210	7	)	)	PUNCT
ejpam-2337	210	8	=	=	SYM
ejpam-2337	210	9	r(x	r(x	PROPN
ejpam-2337	210	10	,	,	PUNCT
ejpam-2337	210	11	y	y	PROPN
ejpam-2337	210	12	)	)	PUNCT
ejpam-2337	210	13	and	and	CCONJ
ejpam-2337	210	14	4nr0(2n	4nr0(2n	NOUN
ejpam-2337	210	15	x	x	X
ejpam-2337	210	16	,	,	PUNCT
ejpam-2337	210	17	2n	2n	NUM
ejpam-2337	210	18	y	y	NOUN
ejpam-2337	210	19	)	)	PUNCT
ejpam-2337	211	1	=	=	SYM
ejpam-2337	211	2	r0(x	r0(x	PROPN
ejpam-2337	211	3	,	,	PUNCT
ejpam-2337	211	4	y	y	PROPN
ejpam-2337	211	5	)	)	PUNCT
ejpam-2337	211	6	for	for	ADP
ejpam-2337	211	7	all	all	DET
ejpam-2337	211	8	x	x	SYM
ejpam-2337	211	9	,	,	PUNCT
ejpam-2337	211	10	y	y	NOUN
ejpam-2337	211	11	%	%	NOUN
ejpam-2337	211	12	x	x	INTJ
ejpam-2337	211	13	,	,	PUNCT
ejpam-2337	211	14	we	we	PRON
ejpam-2337	211	15	conclude	conclude	VERB
ejpam-2337	211	16	that	that	SCONJ
ejpam-2337	211	17	d(r(x	d(r(x	PROPN
ejpam-2337	211	18	,	,	PUNCT
ejpam-2337	211	19	y),r0(x	y),r0(x	NOUN
ejpam-2337	211	20	,	,	PUNCT
ejpam-2337	211	21	y	y	NOUN
ejpam-2337	211	22	)	)	PUNCT
ejpam-2337	211	23	)	)	PUNCT
ejpam-2337	212	1	=	=	SYM
ejpam-2337	212	2	4nd(r(2n	4nd(r(2n	NUM
ejpam-2337	212	3	x	x	SYM
ejpam-2337	212	4	,	,	PUNCT
ejpam-2337	212	5	2n	2n	NUM
ejpam-2337	212	6	y),r0(2n	y),r0(2n	NOUN
ejpam-2337	212	7	x	x	X
ejpam-2337	212	8	,	,	PUNCT
ejpam-2337	212	9	2n	2n	NUM
ejpam-2337	212	10	y	y	NOUN
ejpam-2337	212	11	)	)	PUNCT
ejpam-2337	212	12	)	)	PUNCT
ejpam-2337	212	13	,	,	PUNCT
ejpam-2337	212	14	4n	4n	X
ejpam-2337	212	15	.	.	PUNCT
ejpam-2337	212	16	d(r(2n	d(r(2n	PUNCT
ejpam-2337	213	1	x	x	X
ejpam-2337	213	2	,	,	PUNCT
ejpam-2337	213	3	2n	2n	NUM
ejpam-2337	213	4	y	y	NOUN
ejpam-2337	213	5	)	)	PUNCT
ejpam-2337	213	6	,	,	PUNCT
ejpam-2337	213	7	r(2n	r(2n	X
ejpam-2337	213	8	x	x	SYM
ejpam-2337	213	9	,	,	PUNCT
ejpam-2337	213	10	2n	2n	NUM
ejpam-2337	213	11	y	y	NOUN
ejpam-2337	213	12	)	)	PUNCT
ejpam-2337	213	13	)	)	PUNCT
ejpam-2337	214	1	+	+	CCONJ
ejpam-2337	214	2	d(r(2n	d(r(2n	NUM
ejpam-2337	214	3	x	x	SYM
ejpam-2337	214	4	,	,	PUNCT
ejpam-2337	214	5	2n	2n	NUM
ejpam-2337	214	6	y),r0(2n	y),r0(2n	NOUN
ejpam-2337	214	7	x	x	X
ejpam-2337	214	8	,	,	PUNCT
ejpam-2337	214	9	2n	2n	NUM
ejpam-2337	214	10	y	y	NOUN
ejpam-2337	214	11	)	)	PUNCT
ejpam-2337	214	12	)	)	PUNCT
ejpam-2337	214	13	/	/	PUNCT
ejpam-2337	214	14	,	,	PUNCT
ejpam-2337	214	15	4	4	NUM
ejpam-2337	214	16	&	&	CCONJ
ejpam-2337	214	17	!	!	PUNCT
ejpam-2337	215	1	i=0	i=0	PROPN
ejpam-2337	215	2	4n+ig(2n+i	4n+ig(2n+i	NOUN
ejpam-2337	215	3	x	x	X
ejpam-2337	215	4	,	,	PUNCT
ejpam-2337	215	5	2n+i	2n+i	NUM
ejpam-2337	215	6	x	x	SYM
ejpam-2337	215	7	,	,	PUNCT
ejpam-2337	215	8	2n+i	2n+i	NUM
ejpam-2337	215	9	x	x	X
ejpam-2337	215	10	)	)	PUNCT
ejpam-2337	215	11	+	+	CCONJ
ejpam-2337	215	12	8	8	NUM
ejpam-2337	215	13	&	&	CCONJ
ejpam-2337	215	14	!	!	PUNCT
ejpam-2337	216	1	i=0	i=0	ADJ
ejpam-2337	216	2	4n+ih(2n+i+1	4n+ih(2n+i+1	NOUN
ejpam-2337	216	3	x	x	SYM
ejpam-2337	216	4	,	,	PUNCT
ejpam-2337	216	5	2n+i	2n+i	NUM
ejpam-2337	216	6	y	y	NOUN
ejpam-2337	216	7	,	,	PUNCT
ejpam-2337	216	8	2n+i	2n+i	NUM
ejpam-2337	216	9	y	y	NOUN
ejpam-2337	216	10	)	)	PUNCT
ejpam-2337	216	11	for	for	ADP
ejpam-2337	216	12	all	all	DET
ejpam-2337	216	13	x	x	SYM
ejpam-2337	216	14	,	,	PUNCT
ejpam-2337	216	15	y	y	NOUN
ejpam-2337	216	16	%	%	NOUN
ejpam-2337	216	17	x	x	INTJ
ejpam-2337	216	18	.	.	PUNCT
ejpam-2337	217	1	using	use	VERB
ejpam-2337	217	2	(	(	PUNCT
ejpam-2337	217	3	6	6	NUM
ejpam-2337	217	4	)	)	PUNCT
ejpam-2337	217	5	,	,	PUNCT
ejpam-2337	217	6	letting	let	VERB
ejpam-2337	217	7	n	n	PRON
ejpam-2337	217	8	$	$	SYM
ejpam-2337	217	9	&	&	CCONJ
ejpam-2337	217	10	in	in	ADP
ejpam-2337	217	11	the	the	DET
ejpam-2337	217	12	right	right	ADJ
ejpam-2337	217	13	-	-	PUNCT
ejpam-2337	217	14	hand	hand	NOUN
ejpam-2337	217	15	side	side	NOUN
ejpam-2337	217	16	of	of	ADP
ejpam-2337	217	17	the	the	DET
ejpam-2337	217	18	above	above	ADJ
ejpam-2337	217	19	inequality	inequality	NOUN
ejpam-2337	217	20	,	,	PUNCT
ejpam-2337	217	21	it	it	PRON
ejpam-2337	217	22	follows	follow	VERB
ejpam-2337	217	23	that	that	SCONJ
ejpam-2337	217	24	r(x	r(x	PROPN
ejpam-2337	217	25	,	,	PUNCT
ejpam-2337	217	26	y	y	PROPN
ejpam-2337	217	27	)	)	PUNCT
ejpam-2337	218	1	=	=	SYM
ejpam-2337	218	2	r0(x	r0(x	PROPN
ejpam-2337	218	3	,	,	PUNCT
ejpam-2337	218	4	y	y	PROPN
ejpam-2337	218	5	)	)	PUNCT
ejpam-2337	218	6	for	for	ADP
ejpam-2337	218	7	all	all	DET
ejpam-2337	218	8	x	x	SYM
ejpam-2337	218	9	,	,	PUNCT
ejpam-2337	218	10	y	y	NOUN
ejpam-2337	218	11	%	%	NOUN
ejpam-2337	218	12	x	x	X
ejpam-2337	218	13	,	,	PUNCT
ejpam-2337	218	14	which	which	PRON
ejpam-2337	218	15	completes	complete	VERB
ejpam-2337	218	16	the	the	DET
ejpam-2337	218	17	proof	proof	NOUN
ejpam-2337	218	18	of	of	ADP
ejpam-2337	218	19	the	the	DET
ejpam-2337	218	20	theorem	theorem	PROPN
ejpam-2337	218	21	.	.	PUNCT
ejpam-2337	218	22	theorem	theorem	NOUN
ejpam-2337	218	23	3	3	X
ejpam-2337	218	24	.	.	PUNCT
ejpam-2337	218	25	suppose	suppose	VERB
ejpam-2337	218	26	the	the	DET
ejpam-2337	218	27	mapping	mapping	NOUN
ejpam-2337	218	28	g	g	PROPN
ejpam-2337	218	29	,	,	PUNCT
ejpam-2337	218	30	h	h	NOUN
ejpam-2337	218	31	:	:	PUNCT
ejpam-2337	218	32	e	e	X
ejpam-2337	218	33	#	#	NOUN
ejpam-2337	218	34	e	e	NOUN
ejpam-2337	218	35	#	#	NOUN
ejpam-2337	218	36	e	e	NOUN
ejpam-2337	218	37	$	$	SYM
ejpam-2337	218	38	[	[	X
ejpam-2337	218	39	0	0	NUM
ejpam-2337	218	40	,	,	PUNCT
ejpam-2337	218	41	&	&	CCONJ
ejpam-2337	218	42	)	)	PUNCT
ejpam-2337	218	43	satisfy	satisfy	NOUN
ejpam-2337	218	44	(	(	PUNCT
ejpam-2337	218	45	6	6	NUM
ejpam-2337	218	46	)	)	PUNCT
ejpam-2337	218	47	for	for	ADP
ejpam-2337	219	1	all	all	DET
ejpam-2337	219	2	x	x	SYM
ejpam-2337	219	3	,	,	PUNCT
ejpam-2337	219	4	y	y	PROPN
ejpam-2337	219	5	%	%	INTJ
ejpam-2337	219	6	e.	e.	PROPN
ejpam-2337	220	1	if	if	SCONJ
ejpam-2337	220	2	r	r	NOUN
ejpam-2337	220	3	:	:	PUNCT
ejpam-2337	220	4	e	e	X
ejpam-2337	220	5	#	#	NOUN
ejpam-2337	220	6	e$	e$	ADJ
ejpam-2337	220	7	f	f	PROPN
ejpam-2337	220	8	is	be	AUX
ejpam-2337	220	9	a	a	DET
ejpam-2337	220	10	mapping	mapping	NOUN
ejpam-2337	220	11	such	such	ADJ
ejpam-2337	220	12	that	that	DET
ejpam-2337	220	13	0	0	NUM
ejpam-2337	220	14	0	0	NUM
ejpam-2337	220	15	0	0	NUM
ejpam-2337	220	16	0	0	NUM
ejpam-2337	220	17	r(x	r(x	PROPN
ejpam-2337	220	18	+	+	CCONJ
ejpam-2337	220	19	u	u	PROPN
ejpam-2337	220	20	,	,	PUNCT
ejpam-2337	220	21	y	y	PROPN
ejpam-2337	220	22	)	)	PUNCT
ejpam-2337	220	23	.	.	PUNCT
ejpam-2337	221	1	r(x	r(x	PROPN
ejpam-2337	221	2	,	,	PUNCT
ejpam-2337	221	3	y)r(u	y)r(u	PROPN
ejpam-2337	221	4	,	,	PUNCT
ejpam-2337	221	5	y	y	PROPN
ejpam-2337	221	6	)	)	PUNCT
ejpam-2337	221	7	r(x	r(x	PROPN
ejpam-2337	221	8	,	,	PUNCT
ejpam-2337	221	9	y	y	PROPN
ejpam-2337	221	10	)	)	PUNCT
ejpam-2337	221	11	+	+	CCONJ
ejpam-2337	221	12	r(u	r(u	PROPN
ejpam-2337	221	13	,	,	PUNCT
ejpam-2337	221	14	y	y	NOUN
ejpam-2337	221	15	)	)	PUNCT
ejpam-2337	221	16	0	0	NUM
ejpam-2337	221	17	0	0	NUM
ejpam-2337	221	18	0	0	NUM
ejpam-2337	221	19	0	0	NUM
ejpam-2337	221	20	,	,	PUNCT
ejpam-2337	221	21	g(x	g(x	PROPN
ejpam-2337	221	22	,	,	PUNCT
ejpam-2337	221	23	u	u	NOUN
ejpam-2337	221	24	,	,	PUNCT
ejpam-2337	221	25	y	y	PROPN
ejpam-2337	221	26	)	)	PUNCT
ejpam-2337	221	27	,	,	PUNCT
ejpam-2337	221	28	(	(	PUNCT
ejpam-2337	221	29	16	16	NUM
ejpam-2337	221	30	)	)	PUNCT
ejpam-2337	221	31	0	0	NUM
ejpam-2337	221	32	0	0	NUM
ejpam-2337	221	33	0	0	SYM
ejpam-2337	221	34	0	0	NUM
ejpam-2337	221	35	r(x	r(x	PROPN
ejpam-2337	221	36	,	,	PUNCT
ejpam-2337	221	37	y	y	PROPN
ejpam-2337	221	38	+	+	PROPN
ejpam-2337	221	39	v	v	NOUN
ejpam-2337	221	40	)	)	PUNCT
ejpam-2337	221	41	.	.	PUNCT
ejpam-2337	222	1	r(x	r(x	PROPN
ejpam-2337	222	2	,	,	PUNCT
ejpam-2337	222	3	y)r(x	y)r(x	PROPN
ejpam-2337	222	4	,	,	PUNCT
ejpam-2337	222	5	v	v	NOUN
ejpam-2337	222	6	)	)	PUNCT
ejpam-2337	222	7	r(x	r(x	PROPN
ejpam-2337	222	8	,	,	PUNCT
ejpam-2337	222	9	y	y	PROPN
ejpam-2337	222	10	)	)	PUNCT
ejpam-2337	222	11	+	+	CCONJ
ejpam-2337	222	12	r(x	r(x	PROPN
ejpam-2337	222	13	,	,	PUNCT
ejpam-2337	222	14	v	v	NOUN
ejpam-2337	222	15	)	)	PUNCT
ejpam-2337	222	16	0	0	NUM
ejpam-2337	222	17	0	0	NUM
ejpam-2337	222	18	0	0	NUM
ejpam-2337	222	19	0	0	NUM
ejpam-2337	222	20	,	,	PUNCT
ejpam-2337	222	21	h(x	h(x	PROPN
ejpam-2337	222	22	,	,	PUNCT
ejpam-2337	222	23	y	y	PROPN
ejpam-2337	222	24	,	,	PUNCT
ejpam-2337	222	25	v	v	NOUN
ejpam-2337	222	26	)	)	PUNCT
ejpam-2337	222	27	(	(	PUNCT
ejpam-2337	222	28	17	17	NUM
ejpam-2337	222	29	)	)	PUNCT
ejpam-2337	222	30	for	for	ADP
ejpam-2337	222	31	all	all	DET
ejpam-2337	222	32	x	x	SYM
ejpam-2337	222	33	,	,	PUNCT
ejpam-2337	222	34	u	u	NOUN
ejpam-2337	222	35	,	,	PUNCT
ejpam-2337	222	36	y	y	PROPN
ejpam-2337	222	37	,	,	PUNCT
ejpam-2337	222	38	v	v	PRON
ejpam-2337	222	39	%	%	NOUN
ejpam-2337	222	40	e	e	NOUN
ejpam-2337	222	41	,	,	PUNCT
ejpam-2337	222	42	then	then	ADV
ejpam-2337	222	43	there	there	PRON
ejpam-2337	222	44	exists	exist	VERB
ejpam-2337	222	45	a	a	DET
ejpam-2337	222	46	unique	unique	ADJ
ejpam-2337	222	47	bi	bi	ADJ
ejpam-2337	222	48	-	-	ADJ
ejpam-2337	222	49	reciprocal	reciprocal	ADJ
ejpam-2337	222	50	mapping	mapping	NOUN
ejpam-2337	222	51	r	r	NOUN
ejpam-2337	222	52	:	:	PUNCT
ejpam-2337	222	53	e	e	X
ejpam-2337	222	54	#	#	NOUN
ejpam-2337	222	55	e	e	VERB
ejpam-2337	222	56	$	$	SYM
ejpam-2337	222	57	f	f	NOUN
ejpam-2337	222	58	satisfying	satisfying	NOUN
ejpam-2337	222	59	(	(	PUNCT
ejpam-2337	222	60	5	5	NUM
ejpam-2337	222	61	)	)	PUNCT
ejpam-2337	222	62	and	and	CCONJ
ejpam-2337	222	63	0	0	NUM
ejpam-2337	222	64	0r(x	0r(x	NOUN
ejpam-2337	222	65	,	,	PUNCT
ejpam-2337	222	66	y	y	PROPN
ejpam-2337	222	67	)	)	PUNCT
ejpam-2337	222	68	.	.	PUNCT
ejpam-2337	223	1	r(x	r(x	PROPN
ejpam-2337	223	2	,	,	PUNCT
ejpam-2337	223	3	y	y	PROPN
ejpam-2337	223	4	)	)	PUNCT
ejpam-2337	223	5	0	0	NUM
ejpam-2337	223	6	0	0	NUM
ejpam-2337	223	7	,	,	PUNCT
ejpam-2337	223	8	2	2	NUM
ejpam-2337	223	9	&	&	CCONJ
ejpam-2337	223	10	!	!	PUNCT
ejpam-2337	224	1	i=0	i=0	PROPN
ejpam-2337	225	1	4ig(2i	4ig(2i	X
ejpam-2337	225	2	x	x	PUNCT
ejpam-2337	225	3	,	,	PUNCT
ejpam-2337	225	4	2i	2i	NUM
ejpam-2337	225	5	x	x	SYM
ejpam-2337	225	6	,	,	PUNCT
ejpam-2337	225	7	2i	2i	PROPN
ejpam-2337	225	8	y	y	NOUN
ejpam-2337	225	9	)	)	PUNCT
ejpam-2337	225	10	+	+	CCONJ
ejpam-2337	225	11	4	4	NUM
ejpam-2337	225	12	&	&	CCONJ
ejpam-2337	225	13	!	!	PUNCT
ejpam-2337	226	1	i=0	i=0	PROPN
ejpam-2337	226	2	4ih(2i+1	4ih(2i+1	NUM
ejpam-2337	226	3	x	x	PUNCT
ejpam-2337	226	4	,	,	PUNCT
ejpam-2337	226	5	2i	2i	PROPN
ejpam-2337	226	6	y	y	PROPN
ejpam-2337	226	7	,	,	PUNCT
ejpam-2337	226	8	2i	2i	NOUN
ejpam-2337	226	9	y	y	NOUN
ejpam-2337	226	10	)	)	PUNCT
ejpam-2337	226	11	for	for	ADP
ejpam-2337	226	12	all	all	DET
ejpam-2337	226	13	x	x	SYM
ejpam-2337	226	14	,	,	PUNCT
ejpam-2337	226	15	y	y	PROPN
ejpam-2337	226	16	%	%	NOUN
ejpam-2337	226	17	e.	e.	PROPN
ejpam-2337	226	18	proof	proof	PROPN
ejpam-2337	226	19	.	.	PUNCT
ejpam-2337	227	1	putting	put	VERB
ejpam-2337	227	2	d(a	d(a	PROPN
ejpam-2337	227	3	,	,	PUNCT
ejpam-2337	227	4	b	b	NOUN
ejpam-2337	227	5	)	)	PUNCT
ejpam-2337	227	6	=	=	PUNCT
ejpam-2337	228	1	+	+	ADJ
ejpam-2337	228	2	a.	a.	NOUN
ejpam-2337	228	3	b+	b+	NOUN
ejpam-2337	228	4	,	,	PUNCT
ejpam-2337	228	5	for	for	ADP
ejpam-2337	228	6	all	all	DET
ejpam-2337	228	7	a	a	PRON
ejpam-2337	228	8	,	,	PUNCT
ejpam-2337	228	9	b	b	NOUN
ejpam-2337	228	10	%	%	NOUN
ejpam-2337	228	11	e	e	X
ejpam-2337	228	12	in	in	ADP
ejpam-2337	228	13	theorem	theorem	NOUN
ejpam-2337	228	14	2	2	NUM
ejpam-2337	228	15	,	,	PUNCT
ejpam-2337	228	16	the	the	DET
ejpam-2337	228	17	proof	proof	NOUN
ejpam-2337	228	18	follows	follow	VERB
ejpam-2337	228	19	immediately	immediately	ADV
ejpam-2337	228	20	.	.	PUNCT
ejpam-2337	229	1	we	we	PRON
ejpam-2337	229	2	investigate	investigate	VERB
ejpam-2337	229	3	the	the	DET
ejpam-2337	229	4	hyers	hyer	NOUN
ejpam-2337	229	5	-	-	PUNCT
ejpam-2337	229	6	ulam	ulam	ADJ
ejpam-2337	229	7	-	-	PUNCT
ejpam-2337	229	8	rassias	rassias	PROPN
ejpam-2337	229	9	stability	stability	NOUN
ejpam-2337	229	10	of	of	ADP
ejpam-2337	229	11	the	the	DET
ejpam-2337	229	12	system	system	NOUN
ejpam-2337	229	13	of	of	ADP
ejpam-2337	229	14	functional	functional	ADJ
ejpam-2337	229	15	equations	equation	NOUN
ejpam-2337	229	16	(	(	PUNCT
ejpam-2337	229	17	5	5	NUM
ejpam-2337	229	18	)	)	PUNCT
ejpam-2337	229	19	in	in	ADP
ejpam-2337	229	20	the	the	DET
ejpam-2337	229	21	corollary	corollary	NOUN
ejpam-2337	229	22	presented	present	VERB
ejpam-2337	229	23	below	below	ADV
ejpam-2337	229	24	.	.	PUNCT
ejpam-2337	230	1	corollary	corollary	ADJ
ejpam-2337	230	2	1	1	NUM
ejpam-2337	230	3	.	.	PUNCT
ejpam-2337	231	1	let	let	VERB
ejpam-2337	231	2	c1	c1	PROPN
ejpam-2337	231	3	>	>	X
ejpam-2337	231	4	0	0	PUNCT
ejpam-2337	232	1	be	be	AUX
ejpam-2337	232	2	fixed	fix	VERB
ejpam-2337	232	3	and	and	CCONJ
ejpam-2337	232	4	p	p	X
ejpam-2337	232	5	<	<	X
ejpam-2337	232	6	.2	.2	NUM
ejpam-2337	232	7	.	.	PUNCT
ejpam-2337	233	1	if	if	SCONJ
ejpam-2337	233	2	a	a	DET
ejpam-2337	233	3	mapping	mapping	NOUN
ejpam-2337	233	4	r	r	NOUN
ejpam-2337	233	5	:	:	PUNCT
ejpam-2337	233	6	e#e$	e#e$	PRON
ejpam-2337	233	7	f	f	NOUN
ejpam-2337	233	8	satisfies	satisfy	VERB
ejpam-2337	233	9	the	the	DET
ejpam-2337	233	10	inequalities	inequality	NOUN
ejpam-2337	233	11	0	0	NUM
ejpam-2337	233	12	0	0	NUM
ejpam-2337	233	13	0	0	NUM
ejpam-2337	233	14	0	0	NUM
ejpam-2337	234	1	r(x	r(x	PROPN
ejpam-2337	234	2	+	+	CCONJ
ejpam-2337	234	3	u	u	PROPN
ejpam-2337	234	4	,	,	PUNCT
ejpam-2337	234	5	y	y	PROPN
ejpam-2337	234	6	)	)	PUNCT
ejpam-2337	234	7	.	.	PUNCT
ejpam-2337	235	1	r(x	r(x	PROPN
ejpam-2337	235	2	,	,	PUNCT
ejpam-2337	235	3	y)r(u	y)r(u	PROPN
ejpam-2337	235	4	,	,	PUNCT
ejpam-2337	235	5	y	y	PROPN
ejpam-2337	235	6	)	)	PUNCT
ejpam-2337	235	7	r(x	r(x	PROPN
ejpam-2337	235	8	,	,	PUNCT
ejpam-2337	235	9	y	y	PROPN
ejpam-2337	235	10	)	)	PUNCT
ejpam-2337	235	11	+	+	CCONJ
ejpam-2337	235	12	r(u	r(u	PROPN
ejpam-2337	235	13	,	,	PUNCT
ejpam-2337	235	14	y	y	NOUN
ejpam-2337	235	15	)	)	PUNCT
ejpam-2337	235	16	0	0	NUM
ejpam-2337	235	17	0	0	NUM
ejpam-2337	235	18	0	0	NUM
ejpam-2337	235	19	0	0	NUM
ejpam-2337	235	20	,	,	PUNCT
ejpam-2337	235	21	c1	c1	NOUN
ejpam-2337	235	22	1	1	NUM
ejpam-2337	235	23	+	+	PROPN
ejpam-2337	235	24	x+p	x+p	PROPN
ejpam-2337	235	25	+	+	CCONJ
ejpam-2337	235	26	+	+	ADJ
ejpam-2337	235	27	u+p	u+p	NUM
ejpam-2337	235	28	+	+	SYM
ejpam-2337	235	29	0	0	NUM
ejpam-2337	235	30	0y	0y	NUM
ejpam-2337	235	31	0	0	NUM
ejpam-2337	235	32	0	0	NUM
ejpam-2337	235	33	p	p	NOUN
ejpam-2337	235	34	2	2	NUM
ejpam-2337	235	35	,	,	PUNCT
ejpam-2337	235	36	0	0	NUM
ejpam-2337	235	37	0	0	NUM
ejpam-2337	235	38	0	0	SYM
ejpam-2337	235	39	0	0	NUM
ejpam-2337	235	40	r(x	r(x	PROPN
ejpam-2337	235	41	,	,	PUNCT
ejpam-2337	235	42	y	y	PROPN
ejpam-2337	235	43	+	+	PROPN
ejpam-2337	235	44	v	v	NOUN
ejpam-2337	235	45	)	)	PUNCT
ejpam-2337	235	46	.	.	PUNCT
ejpam-2337	236	1	r(x	r(x	PROPN
ejpam-2337	236	2	,	,	PUNCT
ejpam-2337	236	3	y)r(x	y)r(x	PROPN
ejpam-2337	236	4	,	,	PUNCT
ejpam-2337	236	5	v	v	NOUN
ejpam-2337	236	6	)	)	PUNCT
ejpam-2337	236	7	r(x	r(x	PROPN
ejpam-2337	236	8	,	,	PUNCT
ejpam-2337	236	9	y	y	PROPN
ejpam-2337	236	10	)	)	PUNCT
ejpam-2337	236	11	+	+	CCONJ
ejpam-2337	236	12	r(x	r(x	PROPN
ejpam-2337	236	13	,	,	PUNCT
ejpam-2337	236	14	v	v	NOUN
ejpam-2337	236	15	)	)	PUNCT
ejpam-2337	236	16	0	0	NUM
ejpam-2337	236	17	0	0	NUM
ejpam-2337	236	18	0	0	NUM
ejpam-2337	236	19	0	0	NUM
ejpam-2337	236	20	,	,	PUNCT
ejpam-2337	236	21	c1	c1	NOUN
ejpam-2337	236	22	1	1	NUM
ejpam-2337	237	1	+	+	NOUN
ejpam-2337	237	2	x+p	x+p	PROPN
ejpam-2337	238	1	+	+	CCONJ
ejpam-2337	238	2	0	0	NUM
ejpam-2337	238	3	0y	0y	NUM
ejpam-2337	238	4	0	0	NUM
ejpam-2337	238	5	0	0	NUM
ejpam-2337	239	1	p	p	NOUN
ejpam-2337	239	2	+	+	X
ejpam-2337	239	3	+	+	NOUN
ejpam-2337	239	4	v+p	v+p	PROPN
ejpam-2337	239	5	2	2	NUM
ejpam-2337	239	6	%	%	NOUN
ejpam-2337	239	7	&	&	CCONJ
ejpam-2337	239	8	&	&	CCONJ
ejpam-2337	239	9	'	'	PUNCT
ejpam-2337	239	10	&	&	CCONJ
ejpam-2337	239	11	&	&	CCONJ
ejpam-2337	239	12	(	(	PUNCT
ejpam-2337	239	13	(	(	PUNCT
ejpam-2337	239	14	18	18	NUM
ejpam-2337	239	15	)	)	PUNCT
ejpam-2337	239	16	for	for	ADP
ejpam-2337	239	17	all	all	DET
ejpam-2337	239	18	x	x	SYM
ejpam-2337	239	19	,	,	PUNCT
ejpam-2337	239	20	u	u	NOUN
ejpam-2337	239	21	,	,	PUNCT
ejpam-2337	239	22	y	y	PROPN
ejpam-2337	239	23	,	,	PUNCT
ejpam-2337	239	24	v	v	PRON
ejpam-2337	239	25	%	%	NOUN
ejpam-2337	239	26	e	e	NOUN
ejpam-2337	239	27	,	,	PUNCT
ejpam-2337	239	28	then	then	ADV
ejpam-2337	239	29	there	there	PRON
ejpam-2337	239	30	exists	exist	VERB
ejpam-2337	239	31	a	a	DET
ejpam-2337	239	32	unique	unique	ADJ
ejpam-2337	239	33	bi	bi	ADJ
ejpam-2337	239	34	-	-	ADJ
ejpam-2337	239	35	reciprocal	reciprocal	ADJ
ejpam-2337	239	36	mapping	mapping	NOUN
ejpam-2337	239	37	r	r	NOUN
ejpam-2337	239	38	:	:	PUNCT
ejpam-2337	239	39	e	e	X
ejpam-2337	239	40	#	#	NOUN
ejpam-2337	239	41	e	e	VERB
ejpam-2337	239	42	$	$	SYM
ejpam-2337	239	43	f	f	NOUN
ejpam-2337	239	44	satisfying	satisfying	NOUN
ejpam-2337	239	45	(	(	PUNCT
ejpam-2337	239	46	5	5	NUM
ejpam-2337	239	47	)	)	PUNCT
ejpam-2337	239	48	and	and	CCONJ
ejpam-2337	239	49	0	0	NUM
ejpam-2337	239	50	0r(x	0r(x	NOUN
ejpam-2337	239	51	,	,	PUNCT
ejpam-2337	239	52	y	y	PROPN
ejpam-2337	239	53	)	)	PUNCT
ejpam-2337	239	54	.	.	PUNCT
ejpam-2337	240	1	r(x	r(x	PROPN
ejpam-2337	240	2	,	,	PUNCT
ejpam-2337	240	3	y	y	PROPN
ejpam-2337	240	4	)	)	PUNCT
ejpam-2337	240	5	0	0	NUM
ejpam-2337	240	6	0	0	NUM
ejpam-2337	240	7	,	,	PUNCT
ejpam-2337	240	8	#	#	NOUN
ejpam-2337	240	9	2c1	2c1	NUM
ejpam-2337	240	10	1	1	NUM
ejpam-2337	240	11	.	.	PUNCT
ejpam-2337	241	1	2p+2	2p+2	NUM
ejpam-2337	241	2	$	$	NOUN
ejpam-2337	241	3	.	.	NOUN
ejpam-2337	241	4	2	2	NUM
ejpam-2337	241	5	(	(	PUNCT
ejpam-2337	241	6	2p	2p	NUM
ejpam-2337	241	7	+	+	CCONJ
ejpam-2337	241	8	1)+x+p	1)+x+p	NUM
ejpam-2337	241	9	+	+	NUM
ejpam-2337	241	10	0	0	NUM
ejpam-2337	241	11	0y	0y	NUM
ejpam-2337	241	12	0	0	NUM
ejpam-2337	241	13	0	0	NUM
ejpam-2337	242	1	p	p	NOUN
ejpam-2337	242	2	/	/	SYM
ejpam-2337	242	3	(	(	PUNCT
ejpam-2337	242	4	19	19	NUM
ejpam-2337	242	5	)	)	PUNCT
ejpam-2337	242	6	for	for	ADP
ejpam-2337	242	7	all	all	DET
ejpam-2337	242	8	x	x	SYM
ejpam-2337	242	9	,	,	PUNCT
ejpam-2337	242	10	y	y	PROPN
ejpam-2337	242	11	%	%	INTJ
ejpam-2337	242	12	e.	e.	PROPN
ejpam-2337	242	13	k.	k.	PROPN
ejpam-2337	242	14	ravi	ravi	PROPN
ejpam-2337	242	15	,	,	PUNCT
ejpam-2337	242	16	b.	b.	PROPN
ejpam-2337	242	17	kumar	kumar	PROPN
ejpam-2337	242	18	/	/	SYM
ejpam-2337	242	19	eur	eur	PROPN
ejpam-2337	242	20	.	.	PUNCT
ejpam-2337	243	1	j.	j.	PROPN
ejpam-2337	243	2	pure	pure	PROPN
ejpam-2337	243	3	appl	appl	PROPN
ejpam-2337	243	4	.	.	PROPN
ejpam-2337	243	5	math	math	PROPN
ejpam-2337	243	6	,	,	PUNCT
ejpam-2337	243	7	8	8	NUM
ejpam-2337	243	8	(	(	PUNCT
ejpam-2337	243	9	2015	2015	NUM
ejpam-2337	243	10	)	)	PUNCT
ejpam-2337	243	11	,	,	PUNCT
ejpam-2337	243	12	283	283	NUM
ejpam-2337	243	13	-	-	SYM
ejpam-2337	243	14	293	293	NUM
ejpam-2337	243	15	290	290	NUM
ejpam-2337	243	16	proof	proof	NOUN
ejpam-2337	243	17	.	.	PUNCT
ejpam-2337	244	1	considering	consider	VERB
ejpam-2337	244	2	g(x	g(x	PROPN
ejpam-2337	244	3	,	,	PUNCT
ejpam-2337	244	4	y	y	PROPN
ejpam-2337	244	5	,	,	PUNCT
ejpam-2337	244	6	z	z	NOUN
ejpam-2337	244	7	)	)	PUNCT
ejpam-2337	245	1	=	=	SYM
ejpam-2337	245	2	h(x	h(x	PROPN
ejpam-2337	245	3	,	,	PUNCT
ejpam-2337	245	4	y	y	PROPN
ejpam-2337	245	5	,	,	PUNCT
ejpam-2337	245	6	z	z	NOUN
ejpam-2337	245	7	)	)	PUNCT
ejpam-2337	245	8	=	=	SYM
ejpam-2337	245	9	c1	c1	NOUN
ejpam-2337	245	10	1	1	NUM
ejpam-2337	245	11	+	+	NOUN
ejpam-2337	245	12	x+p	x+p	PROPN
ejpam-2337	245	13	+	+	CCONJ
ejpam-2337	245	14	0	0	NUM
ejpam-2337	245	15	0y	0y	NUM
ejpam-2337	245	16	0	0	NUM
ejpam-2337	245	17	0	0	NUM
ejpam-2337	246	1	p	p	NOUN
ejpam-2337	247	1	+	+	X
ejpam-2337	247	2	+	+	PROPN
ejpam-2337	247	3	z+p	z+p	NUM
ejpam-2337	247	4	2	2	NUM
ejpam-2337	247	5	,	,	PUNCT
ejpam-2337	247	6	for	for	ADP
ejpam-2337	247	7	all	all	DET
ejpam-2337	247	8	x	x	SYM
ejpam-2337	247	9	,	,	PUNCT
ejpam-2337	247	10	y	y	PROPN
ejpam-2337	247	11	,	,	PUNCT
ejpam-2337	247	12	z	z	NOUN
ejpam-2337	247	13	%	%	NOUN
ejpam-2337	247	14	e	e	X
ejpam-2337	247	15	in	in	ADP
ejpam-2337	247	16	theorem	theorem	NOUN
ejpam-2337	247	17	3	3	NUM
ejpam-2337	247	18	,	,	PUNCT
ejpam-2337	247	19	we	we	PRON
ejpam-2337	247	20	get	get	VERB
ejpam-2337	247	21	0	0	NUM
ejpam-2337	247	22	0r(x	0r(x	NOUN
ejpam-2337	247	23	,	,	PUNCT
ejpam-2337	247	24	y	y	PROPN
ejpam-2337	247	25	)	)	PUNCT
ejpam-2337	247	26	.	.	PUNCT
ejpam-2337	248	1	r(x	r(x	PROPN
ejpam-2337	248	2	,	,	PUNCT
ejpam-2337	248	3	y	y	PROPN
ejpam-2337	248	4	)	)	PUNCT
ejpam-2337	248	5	0	0	NUM
ejpam-2337	248	6	0	0	NUM
ejpam-2337	248	7	,	,	PUNCT
ejpam-2337	248	8	2c1	2c1	NUM
ejpam-2337	248	9	&	&	CCONJ
ejpam-2337	248	10	!	!	PUNCT
ejpam-2337	249	1	i=0	i=0	ADJ
ejpam-2337	249	2	4i	4i	PROPN
ejpam-2337	249	3	10	10	NUM
ejpam-2337	249	4	02i	02i	NOUN
ejpam-2337	249	5	x	x	X
ejpam-2337	249	6	0	0	NUM
ejpam-2337	249	7	0	0	NUM
ejpam-2337	250	1	p	p	NOUN
ejpam-2337	250	2	+	+	NOUN
ejpam-2337	250	3	0	0	NUM
ejpam-2337	250	4	02i	02i	NOUN
ejpam-2337	250	5	x	x	SYM
ejpam-2337	250	6	0	0	NUM
ejpam-2337	250	7	0	0	NUM
ejpam-2337	251	1	p	p	NOUN
ejpam-2337	251	2	+	+	NOUN
ejpam-2337	251	3	0	0	NUM
ejpam-2337	251	4	02i	02i	NUM
ejpam-2337	252	1	y	y	PROPN
ejpam-2337	252	2	0	0	NUM
ejpam-2337	252	3	0	0	NUM
ejpam-2337	253	1	p	p	NOUN
ejpam-2337	253	2	2	2	NUM
ejpam-2337	253	3	+	+	NUM
ejpam-2337	253	4	4c1	4c1	NUM
ejpam-2337	253	5	&	&	CCONJ
ejpam-2337	253	6	!	!	PUNCT
ejpam-2337	254	1	i=0	i=0	ADJ
ejpam-2337	254	2	4i	4i	NUM
ejpam-2337	254	3	10	10	NUM
ejpam-2337	254	4	02i+1	02i+1	NUM
ejpam-2337	254	5	x	x	SYM
ejpam-2337	254	6	0	0	NUM
ejpam-2337	254	7	0	0	NUM
ejpam-2337	255	1	p	p	NOUN
ejpam-2337	255	2	+	+	NOUN
ejpam-2337	255	3	0	0	NUM
ejpam-2337	255	4	02i	02i	NUM
ejpam-2337	256	1	y	y	PROPN
ejpam-2337	256	2	0	0	NUM
ejpam-2337	256	3	0	0	NUM
ejpam-2337	257	1	p	p	NOUN
ejpam-2337	257	2	+	+	NOUN
ejpam-2337	257	3	0	0	NUM
ejpam-2337	257	4	02i	02i	NUM
ejpam-2337	258	1	y	y	PROPN
ejpam-2337	258	2	0	0	NUM
ejpam-2337	258	3	0	0	NUM
ejpam-2337	259	1	p	p	NOUN
ejpam-2337	259	2	2	2	NUM
ejpam-2337	259	3	,	,	PUNCT
ejpam-2337	259	4	2c1	2c1	NUM
ejpam-2337	259	5	&	&	CCONJ
ejpam-2337	259	6	!	!	PUNCT
ejpam-2337	260	1	i=0	i=0	PROPN
ejpam-2337	260	2	4i2pi	4i2pi	NUM
ejpam-2337	260	3	1	1	NUM
ejpam-2337	260	4	2+x+p	2+x+p	NUM
ejpam-2337	260	5	+	+	CCONJ
ejpam-2337	260	6	0	0	NUM
ejpam-2337	260	7	0y	0y	NUM
ejpam-2337	260	8	0	0	NUM
ejpam-2337	260	9	0	0	PUNCT
ejpam-2337	261	1	p	p	NOUN
ejpam-2337	261	2	2	2	NUM
ejpam-2337	261	3	+	+	NUM
ejpam-2337	261	4	4c1	4c1	NUM
ejpam-2337	261	5	&	&	CCONJ
ejpam-2337	261	6	!	!	PUNCT
ejpam-2337	262	1	i=0	i=0	ADJ
ejpam-2337	262	2	4i2pi	4i2pi	NUM
ejpam-2337	262	3	1	1	NUM
ejpam-2337	262	4	2p	2p	NUM
ejpam-2337	262	5	+	+	PRON
ejpam-2337	262	6	x+p	x+p	NOUN
ejpam-2337	262	7	+	+	CCONJ
ejpam-2337	262	8	2	2	NUM
ejpam-2337	262	9	0	0	NUM
ejpam-2337	262	10	0y	0y	NOUN
ejpam-2337	262	11	0	0	NUM
ejpam-2337	262	12	0	0	NUM
ejpam-2337	262	13	p	p	NOUN
ejpam-2337	262	14	2	2	NUM
ejpam-2337	262	15	,	,	PUNCT
ejpam-2337	262	16	2c1	2c1	NUM
ejpam-2337	262	17	&	&	CCONJ
ejpam-2337	262	18	!	!	PUNCT
ejpam-2337	263	1	i=0	i=0	PROPN
ejpam-2337	263	2	2(p+2)i	2(p+2)i	NOUN
ejpam-2337	263	3	1	1	NUM
ejpam-2337	263	4	2+x+p	2+x+p	NUM
ejpam-2337	263	5	+	+	CCONJ
ejpam-2337	263	6	0	0	NUM
ejpam-2337	263	7	0y	0y	NUM
ejpam-2337	263	8	0	0	NUM
ejpam-2337	263	9	0	0	PUNCT
ejpam-2337	264	1	p	p	NOUN
ejpam-2337	264	2	2	2	NUM
ejpam-2337	264	3	+	+	NUM
ejpam-2337	264	4	4c1	4c1	NUM
ejpam-2337	264	5	&	&	CCONJ
ejpam-2337	264	6	!	!	PUNCT
ejpam-2337	265	1	i=0	i=0	PROPN
ejpam-2337	265	2	2(p+2)i	2(p+2)i	NOUN
ejpam-2337	265	3	1	1	NUM
ejpam-2337	265	4	2p	2p	NUM
ejpam-2337	265	5	+	+	PRON
ejpam-2337	265	6	x+p	x+p	NOUN
ejpam-2337	265	7	+	+	CCONJ
ejpam-2337	265	8	2	2	NUM
ejpam-2337	265	9	0	0	NUM
ejpam-2337	265	10	0y	0y	NOUN
ejpam-2337	265	11	0	0	NUM
ejpam-2337	265	12	0	0	NUM
ejpam-2337	266	1	p	p	NOUN
ejpam-2337	266	2	2	2	NUM
ejpam-2337	266	3	,	,	PUNCT
ejpam-2337	266	4	2c1	2c1	NUM
ejpam-2337	266	5	#	#	NOUN
ejpam-2337	266	6	1	1	NUM
ejpam-2337	266	7	1	1	NUM
ejpam-2337	266	8	.	.	PUNCT
ejpam-2337	267	1	2p+2	2p+2	NUM
ejpam-2337	267	2	$	$	SYM
ejpam-2337	267	3	1	1	NUM
ejpam-2337	267	4	2+x+p	2+x+p	NUM
ejpam-2337	267	5	+	+	CCONJ
ejpam-2337	267	6	0	0	NUM
ejpam-2337	267	7	0y	0y	NUM
ejpam-2337	267	8	0	0	NUM
ejpam-2337	267	9	0	0	PUNCT
ejpam-2337	268	1	p	p	NOUN
ejpam-2337	268	2	2	2	NUM
ejpam-2337	268	3	+	+	NUM
ejpam-2337	268	4	#	#	NOUN
ejpam-2337	268	5	4c1	4c1	NUM
ejpam-2337	269	1	1	1	NUM
ejpam-2337	269	2	.	.	PUNCT
ejpam-2337	270	1	2p+2	2p+2	NUM
ejpam-2337	270	2	$	$	SYM
ejpam-2337	270	3	1	1	NUM
ejpam-2337	270	4	2p	2p	NUM
ejpam-2337	270	5	+	+	NOUN
ejpam-2337	270	6	x+p	x+p	NOUN
ejpam-2337	270	7	+	+	CCONJ
ejpam-2337	270	8	2	2	NUM
ejpam-2337	270	9	0	0	NUM
ejpam-2337	270	10	0y	0y	NOUN
ejpam-2337	270	11	0	0	NUM
ejpam-2337	270	12	0	0	NUM
ejpam-2337	271	1	p	p	NOUN
ejpam-2337	271	2	2	2	NUM
ejpam-2337	271	3	,	,	PUNCT
ejpam-2337	271	4	#	#	NOUN
ejpam-2337	271	5	2c1	2c1	NUM
ejpam-2337	271	6	1	1	NUM
ejpam-2337	271	7	.	.	PUNCT
ejpam-2337	272	1	2p+2	2p+2	NUM
ejpam-2337	272	2	$	$	NOUN
ejpam-2337	272	3	.	.	NOUN
ejpam-2337	272	4	2	2	NUM
ejpam-2337	272	5	(	(	PUNCT
ejpam-2337	272	6	2p	2p	NUM
ejpam-2337	272	7	+	+	CCONJ
ejpam-2337	272	8	1)+x+p	1)+x+p	NUM
ejpam-2337	272	9	+	+	NUM
ejpam-2337	272	10	5	5	NUM
ejpam-2337	272	11	0	0	NUM
ejpam-2337	272	12	0y	0y	NOUN
ejpam-2337	272	13	0	0	NUM
ejpam-2337	272	14	0	0	NUM
ejpam-2337	273	1	p	p	NOUN
ejpam-2337	273	2	/	/	PUNCT
ejpam-2337	273	3	,	,	PUNCT
ejpam-2337	273	4	for	for	ADP
ejpam-2337	273	5	all	all	PRON
ejpam-2337	273	6	x	x	SYM
ejpam-2337	273	7	,	,	PUNCT
ejpam-2337	273	8	y	y	PROPN
ejpam-2337	273	9	%	%	PROPN
ejpam-2337	273	10	e.	e.	PROPN
ejpam-2337	273	11	theorem	theorem	PROPN
ejpam-2337	273	12	4	4	X
ejpam-2337	273	13	.	.	PUNCT
ejpam-2337	274	1	let	let	VERB
ejpam-2337	274	2	g	g	NOUN
ejpam-2337	274	3	,	,	PUNCT
ejpam-2337	274	4	h	h	NOUN
ejpam-2337	274	5	:	:	PUNCT
ejpam-2337	274	6	x	x	SYM
ejpam-2337	274	7	#	#	NOUN
ejpam-2337	274	8	x	x	NOUN
ejpam-2337	274	9	#	#	NOUN
ejpam-2337	274	10	x	x	SYM
ejpam-2337	274	11	$	$	SYM
ejpam-2337	274	12	[	[	X
ejpam-2337	274	13	0	0	NUM
ejpam-2337	274	14	,	,	PUNCT
ejpam-2337	274	15	&	&	CCONJ
ejpam-2337	274	16	)	)	PUNCT
ejpam-2337	274	17	be	be	AUX
ejpam-2337	274	18	mappings	mapping	NOUN
ejpam-2337	274	19	satisfying	satisfying	ADJ
ejpam-2337	274	20	&	&	CCONJ
ejpam-2337	274	21	!	!	PUNCT
ejpam-2337	275	1	i=0	i=0	ADJ
ejpam-2337	275	2	1	1	NUM
ejpam-2337	275	3	4i	4i	NOUN
ejpam-2337	275	4	g	g	NOUN
ejpam-2337	275	5	#	#	NOUN
ejpam-2337	275	6	x	x	NOUN
ejpam-2337	275	7	2i+1	2i+1	NOUN
ejpam-2337	275	8	,	,	PUNCT
ejpam-2337	275	9	x	x	PROPN
ejpam-2337	275	10	2i+1	2i+1	NOUN
ejpam-2337	275	11	,	,	PUNCT
ejpam-2337	276	1	y	y	PROPN
ejpam-2337	276	2	2i+1	2i+1	PROPN
ejpam-2337	276	3	$	$	SYM
ejpam-2337	276	4	<	<	X
ejpam-2337	276	5	&	&	CCONJ
ejpam-2337	276	6	,	,	PUNCT
ejpam-2337	276	7	&	&	CCONJ
ejpam-2337	276	8	!	!	PUNCT
ejpam-2337	277	1	i=0	i=0	ADJ
ejpam-2337	277	2	1	1	NUM
ejpam-2337	277	3	4i	4i	NUM
ejpam-2337	277	4	h	h	NOUN
ejpam-2337	277	5	#	#	NOUN
ejpam-2337	277	6	x	x	SYM
ejpam-2337	277	7	2i	2i	NUM
ejpam-2337	277	8	,	,	PUNCT
ejpam-2337	277	9	y	y	PROPN
ejpam-2337	277	10	2i+1	2i+1	PROPN
ejpam-2337	277	11	,	,	PUNCT
ejpam-2337	277	12	y	y	PROPN
ejpam-2337	277	13	2i+1	2i+1	PROPN
ejpam-2337	277	14	$	$	SYM
ejpam-2337	277	15	<	<	X
ejpam-2337	277	16	&	&	CCONJ
ejpam-2337	277	17	%	%	PROPN
ejpam-2337	277	18	&	&	CCONJ
ejpam-2337	277	19	&	&	CCONJ
ejpam-2337	277	20	&	&	CCONJ
ejpam-2337	277	21	'	'	PUNCT
ejpam-2337	277	22	&	&	CCONJ
ejpam-2337	277	23	&	&	CCONJ
ejpam-2337	277	24	&	&	CCONJ
ejpam-2337	277	25	(	(	PUNCT
ejpam-2337	277	26	(	(	PUNCT
ejpam-2337	277	27	20	20	NUM
ejpam-2337	277	28	)	)	PUNCT
ejpam-2337	277	29	for	for	ADP
ejpam-2337	277	30	all	all	PRON
ejpam-2337	277	31	x	x	SYM
ejpam-2337	277	32	,	,	PUNCT
ejpam-2337	277	33	y	y	NOUN
ejpam-2337	277	34	%	%	NOUN
ejpam-2337	277	35	x	x	INTJ
ejpam-2337	277	36	.	.	PUNCT
ejpam-2337	278	1	let	let	VERB
ejpam-2337	279	1	r	r	NOUN
ejpam-2337	279	2	:	:	PUNCT
ejpam-2337	279	3	x	x	PUNCT
ejpam-2337	279	4	#	#	SYM
ejpam-2337	279	5	x	x	SYM
ejpam-2337	279	6	$	$	SYM
ejpam-2337	279	7	y	y	NOUN
ejpam-2337	279	8	be	be	AUX
ejpam-2337	279	9	a	a	DET
ejpam-2337	279	10	mapping	mapping	NOUN
ejpam-2337	279	11	such	such	ADJ
ejpam-2337	279	12	that	that	SCONJ
ejpam-2337	279	13	(	(	PUNCT
ejpam-2337	279	14	7	7	NUM
ejpam-2337	279	15	)	)	PUNCT
ejpam-2337	279	16	and	and	CCONJ
ejpam-2337	279	17	(	(	PUNCT
ejpam-2337	279	18	8)	8)	NUM
ejpam-2337	279	19	hold	hold	VERB
ejpam-2337	279	20	for	for	ADP
ejpam-2337	279	21	all	all	DET
ejpam-2337	279	22	x	x	SYM
ejpam-2337	279	23	,	,	PUNCT
ejpam-2337	279	24	u	u	NOUN
ejpam-2337	279	25	,	,	PUNCT
ejpam-2337	279	26	y	y	PROPN
ejpam-2337	279	27	,	,	PUNCT
ejpam-2337	279	28	z	z	NOUN
ejpam-2337	279	29	%	%	NOUN
ejpam-2337	279	30	x	x	INTJ
ejpam-2337	279	31	.	.	PUNCT
ejpam-2337	280	1	then	then	ADV
ejpam-2337	280	2	there	there	PRON
ejpam-2337	280	3	exists	exist	VERB
ejpam-2337	280	4	a	a	DET
ejpam-2337	280	5	unique	unique	ADJ
ejpam-2337	280	6	bi	bi	ADJ
ejpam-2337	280	7	-	-	ADJ
ejpam-2337	280	8	reciprocal	reciprocal	ADJ
ejpam-2337	280	9	mapping	mapping	NOUN
ejpam-2337	280	10	r	r	NOUN
ejpam-2337	280	11	:	:	PUNCT
ejpam-2337	280	12	x	x	SYM
ejpam-2337	280	13	#	#	NOUN
ejpam-2337	280	14	x	x	SYM
ejpam-2337	280	15	$	$	SYM
ejpam-2337	280	16	y	y	NOUN
ejpam-2337	280	17	satisfying	satisfy	VERB
ejpam-2337	280	18	(	(	PUNCT
ejpam-2337	280	19	5	5	NUM
ejpam-2337	280	20	)	)	PUNCT
ejpam-2337	280	21	and	and	CCONJ
ejpam-2337	280	22	d(r(x	d(r(x	PROPN
ejpam-2337	280	23	,	,	PUNCT
ejpam-2337	280	24	y),r(x	y),r(x	PRON
ejpam-2337	280	25	,	,	PUNCT
ejpam-2337	280	26	y	y	PROPN
ejpam-2337	280	27	)	)	PUNCT
ejpam-2337	280	28	)	)	PUNCT
ejpam-2337	280	29	,	,	PUNCT
ejpam-2337	280	30	1	1	NUM
ejpam-2337	280	31	2	2	NUM
ejpam-2337	280	32	&	&	CCONJ
ejpam-2337	280	33	!	!	PUNCT
ejpam-2337	281	1	i=0	i=0	ADJ
ejpam-2337	281	2	1	1	NUM
ejpam-2337	281	3	4i	4i	NOUN
ejpam-2337	281	4	g	g	NOUN
ejpam-2337	281	5	#	#	NOUN
ejpam-2337	281	6	x	x	NOUN
ejpam-2337	281	7	2i+1	2i+1	NOUN
ejpam-2337	281	8	,	,	PUNCT
ejpam-2337	281	9	x	x	PROPN
ejpam-2337	281	10	2i+1	2i+1	NOUN
ejpam-2337	281	11	,	,	PUNCT
ejpam-2337	281	12	y	y	PROPN
ejpam-2337	281	13	2i+1	2i+1	PROPN
ejpam-2337	281	14	$	$	PROPN
ejpam-2337	281	15	+	+	NOUN
ejpam-2337	281	16	&	&	CCONJ
ejpam-2337	281	17	!	!	PUNCT
ejpam-2337	282	1	i=0	i=0	ADJ
ejpam-2337	282	2	1	1	NUM
ejpam-2337	282	3	4i	4i	NUM
ejpam-2337	282	4	h	h	NOUN
ejpam-2337	282	5	#	#	NOUN
ejpam-2337	282	6	x	x	SYM
ejpam-2337	282	7	2i	2i	NUM
ejpam-2337	282	8	,	,	PUNCT
ejpam-2337	282	9	y	y	PROPN
ejpam-2337	282	10	2i+1	2i+1	PROPN
ejpam-2337	282	11	,	,	PUNCT
ejpam-2337	282	12	y	y	PROPN
ejpam-2337	282	13	2i+1	2i+1	PROPN
ejpam-2337	282	14	$	$	X
ejpam-2337	282	15	(	(	PUNCT
ejpam-2337	282	16	21	21	NUM
ejpam-2337	282	17	)	)	PUNCT
ejpam-2337	282	18	for	for	ADP
ejpam-2337	282	19	all	all	PRON
ejpam-2337	282	20	x	x	SYM
ejpam-2337	282	21	,	,	PUNCT
ejpam-2337	282	22	y	y	NOUN
ejpam-2337	282	23	%	%	NOUN
ejpam-2337	282	24	x	x	X
ejpam-2337	282	25	.	.	PUNCT
ejpam-2337	283	1	the	the	DET
ejpam-2337	283	2	mapping	mapping	NOUN
ejpam-2337	283	3	r(x	r(x	PROPN
ejpam-2337	283	4	,	,	PUNCT
ejpam-2337	283	5	y	y	PROPN
ejpam-2337	283	6	)	)	PUNCT
ejpam-2337	283	7	is	be	AUX
ejpam-2337	283	8	defined	define	VERB
ejpam-2337	283	9	by	by	ADP
ejpam-2337	283	10	r(x	r(x	PROPN
ejpam-2337	283	11	,	,	PUNCT
ejpam-2337	283	12	y	y	PROPN
ejpam-2337	283	13	)	)	PUNCT
ejpam-2337	284	1	=	=	NOUN
ejpam-2337	284	2	lim	lim	PROPN
ejpam-2337	284	3	n$	n$	NOUN
ejpam-2337	284	4	&	&	CCONJ
ejpam-2337	284	5	1	1	NUM
ejpam-2337	284	6	4n	4n	X
ejpam-2337	284	7	r	r	NOUN
ejpam-2337	284	8	#	#	NOUN
ejpam-2337	284	9	x	x	SYM
ejpam-2337	284	10	2n	2n	NUM
ejpam-2337	284	11	,	,	PUNCT
ejpam-2337	284	12	y	y	PROPN
ejpam-2337	284	13	2n	2n	NUM
ejpam-2337	284	14	$	$	ADP
ejpam-2337	284	15	,	,	PUNCT
ejpam-2337	284	16	for	for	ADP
ejpam-2337	284	17	allx	allx	NOUN
ejpam-2337	284	18	,	,	PUNCT
ejpam-2337	284	19	y	y	PROPN
ejpam-2337	284	20	%	%	NOUN
ejpam-2337	284	21	x	x	X
ejpam-2337	284	22	.	.	PUNCT
ejpam-2337	285	1	proof	proof	NOUN
ejpam-2337	285	2	.	.	PUNCT
ejpam-2337	286	1	replacing	replace	VERB
ejpam-2337	286	2	(	(	PUNCT
ejpam-2337	286	3	x	x	INTJ
ejpam-2337	286	4	,	,	PUNCT
ejpam-2337	286	5	u	u	NOUN
ejpam-2337	286	6	,	,	PUNCT
ejpam-2337	286	7	y	y	PROPN
ejpam-2337	286	8	)	)	PUNCT
ejpam-2337	286	9	by	by	ADP
ejpam-2337	286	10	,	,	PUNCT
ejpam-2337	286	11	x	x	PROPN
ejpam-2337	286	12	2	2	NUM
ejpam-2337	286	13	,	,	PUNCT
ejpam-2337	286	14	x	x	PROPN
ejpam-2337	286	15	2	2	NUM
ejpam-2337	286	16	,	,	PUNCT
ejpam-2337	286	17	y	y	PROPN
ejpam-2337	286	18	2	2	NUM
ejpam-2337	286	19	in	in	ADP
ejpam-2337	286	20	(	(	PUNCT
ejpam-2337	286	21	7	7	NUM
ejpam-2337	286	22	)	)	PUNCT
ejpam-2337	286	23	and	and	CCONJ
ejpam-2337	286	24	then	then	ADV
ejpam-2337	286	25	dividing	divide	VERB
ejpam-2337	286	26	by	by	ADP
ejpam-2337	286	27	2	2	NUM
ejpam-2337	286	28	,	,	PUNCT
ejpam-2337	286	29	we	we	PRON
ejpam-2337	286	30	obtain	obtain	VERB
ejpam-2337	286	31	d	d	NOUN
ejpam-2337	286	32	#	#	NOUN
ejpam-2337	286	33	1	1	NUM
ejpam-2337	286	34	2	2	NUM
ejpam-2337	286	35	r	r	NOUN
ejpam-2337	286	36	#	#	NOUN
ejpam-2337	286	37	x	x	NOUN
ejpam-2337	286	38	,	,	PUNCT
ejpam-2337	286	39	y	y	PROPN
ejpam-2337	286	40	2	2	NUM
ejpam-2337	286	41	$	$	NUM
ejpam-2337	286	42	,	,	PUNCT
ejpam-2337	286	43	1	1	NUM
ejpam-2337	286	44	4	4	NUM
ejpam-2337	286	45	r	r	NOUN
ejpam-2337	286	46	#	#	NOUN
ejpam-2337	286	47	x	x	SYM
ejpam-2337	286	48	2	2	NUM
ejpam-2337	286	49	,	,	PUNCT
ejpam-2337	286	50	y	y	PROPN
ejpam-2337	286	51	2	2	NUM
ejpam-2337	286	52	$	$	SYM
ejpam-2337	286	53	$	$	NUM
ejpam-2337	286	54	,	,	PUNCT
ejpam-2337	286	55	1	1	NUM
ejpam-2337	286	56	2	2	NUM
ejpam-2337	286	57	g	g	NOUN
ejpam-2337	286	58	#	#	NOUN
ejpam-2337	286	59	x	x	SYM
ejpam-2337	286	60	2	2	NUM
ejpam-2337	286	61	,	,	PUNCT
ejpam-2337	286	62	x	x	PROPN
ejpam-2337	286	63	2	2	NUM
ejpam-2337	286	64	,	,	PUNCT
ejpam-2337	286	65	y	y	PROPN
ejpam-2337	286	66	2	2	NUM
ejpam-2337	286	67	$	$	SYM
ejpam-2337	286	68	(	(	PUNCT
ejpam-2337	286	69	22	22	NUM
ejpam-2337	286	70	)	)	PUNCT
ejpam-2337	286	71	for	for	ADP
ejpam-2337	286	72	all	all	DET
ejpam-2337	286	73	x	x	SYM
ejpam-2337	286	74	,	,	PUNCT
ejpam-2337	286	75	y	y	NOUN
ejpam-2337	286	76	%	%	INTJ
ejpam-2337	286	77	x	x	INTJ
ejpam-2337	286	78	.	.	PUNCT
ejpam-2337	287	1	now	now	ADV
ejpam-2337	287	2	,	,	PUNCT
ejpam-2337	287	3	replacing	replace	VERB
ejpam-2337	287	4	(	(	PUNCT
ejpam-2337	287	5	x	x	INTJ
ejpam-2337	287	6	,	,	PUNCT
ejpam-2337	287	7	y	y	PROPN
ejpam-2337	287	8	,	,	PUNCT
ejpam-2337	287	9	v	v	NOUN
ejpam-2337	287	10	)	)	PUNCT
ejpam-2337	287	11	by	by	ADP
ejpam-2337	287	12	,	,	PUNCT
ejpam-2337	287	13	x	x	PROPN
ejpam-2337	287	14	2	2	NUM
ejpam-2337	287	15	,	,	PUNCT
ejpam-2337	287	16	y	y	PROPN
ejpam-2337	287	17	2	2	NUM
ejpam-2337	287	18	,	,	PUNCT
ejpam-2337	287	19	y	y	PROPN
ejpam-2337	287	20	2	2	NUM
ejpam-2337	287	21	in	in	ADP
ejpam-2337	287	22	(	(	PUNCT
ejpam-2337	287	23	8)	8)	NUM
ejpam-2337	287	24	,	,	PUNCT
ejpam-2337	287	25	we	we	PRON
ejpam-2337	287	26	get	get	VERB
ejpam-2337	287	27	d	d	NOUN
ejpam-2337	287	28	#	#	NOUN
ejpam-2337	287	29	r	r	NOUN
ejpam-2337	287	30	#	#	NOUN
ejpam-2337	287	31	x	x	SYM
ejpam-2337	287	32	2	2	NUM
ejpam-2337	287	33	,	,	PUNCT
ejpam-2337	287	34	y	y	PROPN
ejpam-2337	287	35	$	$	SYM
ejpam-2337	287	36	,	,	PUNCT
ejpam-2337	287	37	1	1	NUM
ejpam-2337	287	38	2	2	NUM
ejpam-2337	287	39	r	r	NOUN
ejpam-2337	287	40	#	#	NOUN
ejpam-2337	287	41	x	x	SYM
ejpam-2337	287	42	2	2	NUM
ejpam-2337	287	43	,	,	PUNCT
ejpam-2337	287	44	y	y	PROPN
ejpam-2337	287	45	2	2	NUM
ejpam-2337	287	46	$	$	SYM
ejpam-2337	287	47	$	$	NUM
ejpam-2337	287	48	,	,	PUNCT
ejpam-2337	287	49	h	h	NOUN
ejpam-2337	287	50	#	#	NOUN
ejpam-2337	287	51	x	x	SYM
ejpam-2337	287	52	2	2	NUM
ejpam-2337	287	53	,	,	PUNCT
ejpam-2337	287	54	y	y	PROPN
ejpam-2337	287	55	2	2	NUM
ejpam-2337	287	56	,	,	PUNCT
ejpam-2337	287	57	y	y	PROPN
ejpam-2337	287	58	2	2	NUM
ejpam-2337	287	59	$	$	SYM
ejpam-2337	287	60	(	(	PUNCT
ejpam-2337	287	61	23	23	NUM
ejpam-2337	287	62	)	)	PUNCT
ejpam-2337	287	63	k.	k.	PROPN
ejpam-2337	287	64	ravi	ravi	PROPN
ejpam-2337	287	65	,	,	PUNCT
ejpam-2337	287	66	b.	b.	PROPN
ejpam-2337	287	67	kumar	kumar	PROPN
ejpam-2337	287	68	/	/	SYM
ejpam-2337	287	69	eur	eur	PROPN
ejpam-2337	287	70	.	.	PUNCT
ejpam-2337	288	1	j.	j.	PROPN
ejpam-2337	288	2	pure	pure	PROPN
ejpam-2337	288	3	appl	appl	PROPN
ejpam-2337	288	4	.	.	PROPN
ejpam-2337	288	5	math	math	PROPN
ejpam-2337	288	6	,	,	PUNCT
ejpam-2337	288	7	8	8	NUM
ejpam-2337	288	8	(	(	PUNCT
ejpam-2337	288	9	2015	2015	NUM
ejpam-2337	288	10	)	)	PUNCT
ejpam-2337	288	11	,	,	PUNCT
ejpam-2337	288	12	283	283	NUM
ejpam-2337	288	13	-	-	SYM
ejpam-2337	288	14	293	293	NUM
ejpam-2337	288	15	291	291	NUM
ejpam-2337	288	16	for	for	ADP
ejpam-2337	288	17	all	all	DET
ejpam-2337	288	18	x	x	SYM
ejpam-2337	288	19	,	,	PUNCT
ejpam-2337	288	20	y	y	NOUN
ejpam-2337	288	21	%	%	NOUN
ejpam-2337	288	22	x	x	INTJ
ejpam-2337	288	23	.	.	PUNCT
ejpam-2337	289	1	putting	put	VERB
ejpam-2337	289	2	x	x	PUNCT
ejpam-2337	289	3	=	=	NOUN
ejpam-2337	289	4	2x	2x	NUM
ejpam-2337	289	5	in	in	ADP
ejpam-2337	289	6	(	(	PUNCT
ejpam-2337	289	7	23	23	NUM
ejpam-2337	289	8	)	)	PUNCT
ejpam-2337	289	9	,	,	PUNCT
ejpam-2337	289	10	we	we	PRON
ejpam-2337	289	11	lead	lead	VERB
ejpam-2337	289	12	to	to	ADP
ejpam-2337	289	13	d	d	PROPN
ejpam-2337	289	14	#	#	NOUN
ejpam-2337	289	15	r(x	r(x	PROPN
ejpam-2337	289	16	,	,	PUNCT
ejpam-2337	289	17	y	y	PROPN
ejpam-2337	289	18	)	)	PUNCT
ejpam-2337	289	19	,	,	PUNCT
ejpam-2337	289	20	1	1	NUM
ejpam-2337	289	21	2	2	NUM
ejpam-2337	289	22	r	r	NOUN
ejpam-2337	289	23	#	#	NOUN
ejpam-2337	289	24	x	x	NOUN
ejpam-2337	289	25	,	,	PUNCT
ejpam-2337	289	26	y	y	PROPN
ejpam-2337	289	27	2	2	NUM
ejpam-2337	289	28	$	$	SYM
ejpam-2337	289	29	$	$	NUM
ejpam-2337	289	30	,	,	PUNCT
ejpam-2337	289	31	h	h	NOUN
ejpam-2337	289	32	#	#	NOUN
ejpam-2337	290	1	x	x	NOUN
ejpam-2337	290	2	,	,	PUNCT
ejpam-2337	290	3	y	y	PROPN
ejpam-2337	290	4	2	2	NUM
ejpam-2337	290	5	,	,	PUNCT
ejpam-2337	290	6	y	y	PROPN
ejpam-2337	290	7	2	2	NUM
ejpam-2337	290	8	$	$	SYM
ejpam-2337	290	9	(	(	PUNCT
ejpam-2337	290	10	24	24	NUM
ejpam-2337	290	11	)	)	PUNCT
ejpam-2337	290	12	for	for	ADP
ejpam-2337	290	13	all	all	DET
ejpam-2337	290	14	x	x	SYM
ejpam-2337	290	15	,	,	PUNCT
ejpam-2337	290	16	y	y	NOUN
ejpam-2337	290	17	%	%	NOUN
ejpam-2337	290	18	x	x	INTJ
ejpam-2337	290	19	.	.	PUNCT
ejpam-2337	291	1	combining	combine	VERB
ejpam-2337	291	2	(	(	PUNCT
ejpam-2337	291	3	22	22	NUM
ejpam-2337	291	4	)	)	PUNCT
ejpam-2337	291	5	and	and	CCONJ
ejpam-2337	291	6	(	(	PUNCT
ejpam-2337	291	7	24	24	NUM
ejpam-2337	291	8	)	)	PUNCT
ejpam-2337	291	9	,	,	PUNCT
ejpam-2337	291	10	applying	apply	VERB
ejpam-2337	291	11	triangle	triangle	NOUN
ejpam-2337	291	12	inequality	inequality	NOUN
ejpam-2337	291	13	,	,	PUNCT
ejpam-2337	291	14	yields	yield	NOUN
ejpam-2337	291	15	d	d	NOUN
ejpam-2337	291	16	#	#	NOUN
ejpam-2337	291	17	r(x	r(x	PROPN
ejpam-2337	291	18	,	,	PUNCT
ejpam-2337	291	19	y	y	PROPN
ejpam-2337	291	20	)	)	PUNCT
ejpam-2337	291	21	,	,	PUNCT
ejpam-2337	291	22	1	1	NUM
ejpam-2337	291	23	4	4	NUM
ejpam-2337	291	24	r	r	NOUN
ejpam-2337	291	25	#	#	NOUN
ejpam-2337	291	26	x	x	SYM
ejpam-2337	291	27	2	2	NUM
ejpam-2337	291	28	,	,	PUNCT
ejpam-2337	291	29	y	y	PROPN
ejpam-2337	291	30	2	2	NUM
ejpam-2337	291	31	$	$	SYM
ejpam-2337	291	32	$	$	NUM
ejpam-2337	291	33	,	,	PUNCT
ejpam-2337	291	34	1	1	NUM
ejpam-2337	291	35	2	2	NUM
ejpam-2337	291	36	g	g	NOUN
ejpam-2337	291	37	#	#	NOUN
ejpam-2337	291	38	x	x	SYM
ejpam-2337	291	39	2	2	NUM
ejpam-2337	291	40	,	,	PUNCT
ejpam-2337	291	41	x	x	PROPN
ejpam-2337	291	42	2	2	NUM
ejpam-2337	291	43	,	,	PUNCT
ejpam-2337	291	44	y	y	PROPN
ejpam-2337	291	45	2	2	NUM
ejpam-2337	291	46	$	$	SYM
ejpam-2337	291	47	+	+	NUM
ejpam-2337	291	48	h	h	NOUN
ejpam-2337	291	49	#	#	NOUN
ejpam-2337	291	50	x	x	NOUN
ejpam-2337	291	51	,	,	PUNCT
ejpam-2337	291	52	y	y	PROPN
ejpam-2337	291	53	2	2	NUM
ejpam-2337	291	54	,	,	PUNCT
ejpam-2337	291	55	y	y	PROPN
ejpam-2337	291	56	2	2	NUM
ejpam-2337	291	57	$	$	SYM
ejpam-2337	291	58	for	for	ADP
ejpam-2337	291	59	all	all	PRON
ejpam-2337	291	60	x	x	SYM
ejpam-2337	291	61	,	,	PUNCT
ejpam-2337	291	62	y	y	NOUN
ejpam-2337	291	63	%	%	NOUN
ejpam-2337	291	64	x	x	X
ejpam-2337	291	65	.	.	PUNCT
ejpam-2337	292	1	proceeding	proceed	VERB
ejpam-2337	292	2	further	far	ADV
ejpam-2337	292	3	and	and	CCONJ
ejpam-2337	292	4	using	use	VERB
ejpam-2337	292	5	induction	induction	NOUN
ejpam-2337	292	6	arguments	argument	NOUN
ejpam-2337	292	7	on	on	ADP
ejpam-2337	292	8	a	a	DET
ejpam-2337	292	9	positive	positive	ADJ
ejpam-2337	292	10	integer	integer	NOUN
ejpam-2337	292	11	n	n	CCONJ
ejpam-2337	292	12	,	,	PUNCT
ejpam-2337	292	13	we	we	PRON
ejpam-2337	292	14	have	have	VERB
ejpam-2337	292	15	d	d	NOUN
ejpam-2337	292	16	#	#	NOUN
ejpam-2337	292	17	r(x	r(x	PROPN
ejpam-2337	292	18	,	,	PUNCT
ejpam-2337	292	19	y	y	PROPN
ejpam-2337	292	20	)	)	PUNCT
ejpam-2337	292	21	,	,	PUNCT
ejpam-2337	292	22	1	1	NUM
ejpam-2337	292	23	4n	4n	NOUN
ejpam-2337	292	24	r	r	NOUN
ejpam-2337	292	25	#	#	NOUN
ejpam-2337	292	26	x	x	SYM
ejpam-2337	292	27	2n	2n	NUM
ejpam-2337	292	28	,	,	PUNCT
ejpam-2337	292	29	y	y	PROPN
ejpam-2337	292	30	2n	2n	NUM
ejpam-2337	292	31	$	$	SYM
ejpam-2337	292	32	$	$	NUM
ejpam-2337	292	33	,	,	PUNCT
ejpam-2337	292	34	1	1	NUM
ejpam-2337	292	35	2	2	NUM
ejpam-2337	292	36	n.1	n.1	NOUN
ejpam-2337	292	37	!	!	PUNCT
ejpam-2337	293	1	i=0	i=0	ADJ
ejpam-2337	293	2	1	1	NUM
ejpam-2337	293	3	4i	4i	NOUN
ejpam-2337	293	4	g	g	NOUN
ejpam-2337	293	5	#	#	NOUN
ejpam-2337	293	6	x	x	NOUN
ejpam-2337	293	7	2i+1	2i+1	NOUN
ejpam-2337	293	8	,	,	PUNCT
ejpam-2337	293	9	x	x	PROPN
ejpam-2337	293	10	2i+1	2i+1	NOUN
ejpam-2337	293	11	,	,	PUNCT
ejpam-2337	293	12	y	y	PROPN
ejpam-2337	293	13	2i+1	2i+1	PROPN
ejpam-2337	293	14	$	$	SYM
ejpam-2337	293	15	+	+	NOUN
ejpam-2337	293	16	n.1	n.1	PROPN
ejpam-2337	293	17	!	!	PUNCT
ejpam-2337	294	1	i=0	i=0	ADJ
ejpam-2337	294	2	1	1	NUM
ejpam-2337	294	3	4i	4i	NUM
ejpam-2337	294	4	h	h	NOUN
ejpam-2337	294	5	#	#	NOUN
ejpam-2337	294	6	x	x	SYM
ejpam-2337	294	7	2i	2i	NUM
ejpam-2337	294	8	,	,	PUNCT
ejpam-2337	294	9	y	y	PROPN
ejpam-2337	294	10	2i+1	2i+1	PROPN
ejpam-2337	294	11	,	,	PUNCT
ejpam-2337	294	12	y	y	PROPN
ejpam-2337	294	13	2i+1	2i+1	PROPN
ejpam-2337	294	14	$	$	ADP
ejpam-2337	294	15	,	,	PUNCT
ejpam-2337	294	16	1	1	NUM
ejpam-2337	294	17	2	2	NUM
ejpam-2337	294	18	&	&	CCONJ
ejpam-2337	294	19	!	!	PUNCT
ejpam-2337	295	1	i=0	i=0	ADJ
ejpam-2337	295	2	1	1	NUM
ejpam-2337	295	3	4i	4i	NOUN
ejpam-2337	295	4	g	g	NOUN
ejpam-2337	295	5	#	#	NOUN
ejpam-2337	295	6	x	x	NOUN
ejpam-2337	295	7	2i+1	2i+1	NOUN
ejpam-2337	295	8	,	,	PUNCT
ejpam-2337	295	9	x	x	PROPN
ejpam-2337	295	10	2i+1	2i+1	NOUN
ejpam-2337	295	11	,	,	PUNCT
ejpam-2337	295	12	y	y	PROPN
ejpam-2337	295	13	2i+1	2i+1	PROPN
ejpam-2337	295	14	$	$	PROPN
ejpam-2337	295	15	+	+	NOUN
ejpam-2337	295	16	&	&	CCONJ
ejpam-2337	295	17	!	!	PUNCT
ejpam-2337	296	1	i=0	i=0	ADJ
ejpam-2337	296	2	1	1	NUM
ejpam-2337	296	3	4i	4i	NUM
ejpam-2337	296	4	h	h	NOUN
ejpam-2337	296	5	#	#	NOUN
ejpam-2337	296	6	x	x	SYM
ejpam-2337	296	7	2i	2i	NUM
ejpam-2337	296	8	,	,	PUNCT
ejpam-2337	296	9	y	y	PROPN
ejpam-2337	296	10	2i+1	2i+1	PROPN
ejpam-2337	296	11	,	,	PUNCT
ejpam-2337	296	12	y	y	PROPN
ejpam-2337	296	13	2i+1	2i+1	PROPN
ejpam-2337	296	14	$	$	SYM
ejpam-2337	296	15	for	for	ADP
ejpam-2337	296	16	all	all	PRON
ejpam-2337	296	17	x	x	SYM
ejpam-2337	296	18	,	,	PUNCT
ejpam-2337	296	19	y	y	NOUN
ejpam-2337	296	20	%	%	NOUN
ejpam-2337	296	21	x	x	X
ejpam-2337	296	22	.	.	PUNCT
ejpam-2337	297	1	the	the	DET
ejpam-2337	297	2	rest	rest	NOUN
ejpam-2337	297	3	of	of	ADP
ejpam-2337	297	4	the	the	DET
ejpam-2337	297	5	proof	proof	NOUN
ejpam-2337	297	6	is	be	AUX
ejpam-2337	297	7	obtained	obtain	VERB
ejpam-2337	297	8	by	by	ADP
ejpam-2337	297	9	similar	similar	ADJ
ejpam-2337	297	10	arguments	argument	NOUN
ejpam-2337	297	11	as	as	ADP
ejpam-2337	297	12	in	in	ADP
ejpam-2337	297	13	theorem	theorem	NOUN
ejpam-2337	297	14	2	2	NUM
ejpam-2337	297	15	.	.	PUNCT
ejpam-2337	297	16	theorem	theorem	NOUN
ejpam-2337	297	17	5	5	NUM
ejpam-2337	297	18	.	.	PUNCT
ejpam-2337	297	19	suppose	suppose	VERB
ejpam-2337	297	20	the	the	DET
ejpam-2337	297	21	mappings	mapping	NOUN
ejpam-2337	297	22	g	g	NOUN
ejpam-2337	297	23	,	,	PUNCT
ejpam-2337	297	24	h	h	NOUN
ejpam-2337	297	25	:	:	PUNCT
ejpam-2337	297	26	e	e	X
ejpam-2337	297	27	#	#	NOUN
ejpam-2337	297	28	e	e	NOUN
ejpam-2337	297	29	#	#	NOUN
ejpam-2337	297	30	e	e	NOUN
ejpam-2337	297	31	$	$	SYM
ejpam-2337	297	32	[	[	X
ejpam-2337	297	33	0	0	NUM
ejpam-2337	297	34	,	,	PUNCT
ejpam-2337	297	35	&	&	CCONJ
ejpam-2337	297	36	)	)	PUNCT
ejpam-2337	297	37	satisfy	satisfy	NOUN
ejpam-2337	297	38	(	(	PUNCT
ejpam-2337	297	39	23	23	NUM
ejpam-2337	297	40	)	)	PUNCT
ejpam-2337	297	41	and	and	CCONJ
ejpam-2337	297	42	(	(	PUNCT
ejpam-2337	297	43	24	24	NUM
ejpam-2337	297	44	)	)	PUNCT
ejpam-2337	297	45	for	for	ADP
ejpam-2337	297	46	all	all	DET
ejpam-2337	297	47	x	x	SYM
ejpam-2337	297	48	,	,	PUNCT
ejpam-2337	297	49	y	y	PROPN
ejpam-2337	297	50	%	%	INTJ
ejpam-2337	297	51	e.	e.	PROPN
ejpam-2337	298	1	if	if	SCONJ
ejpam-2337	298	2	r	r	NOUN
ejpam-2337	298	3	:	:	PUNCT
ejpam-2337	298	4	e	e	NOUN
ejpam-2337	298	5	#	#	NOUN
ejpam-2337	298	6	e	e	PROPN
ejpam-2337	298	7	$	$	SYM
ejpam-2337	298	8	f	f	X
ejpam-2337	298	9	is	be	AUX
ejpam-2337	298	10	a	a	DET
ejpam-2337	298	11	mapping	mapping	NOUN
ejpam-2337	298	12	such	such	ADJ
ejpam-2337	298	13	that	that	SCONJ
ejpam-2337	298	14	(	(	PUNCT
ejpam-2337	298	15	16	16	NUM
ejpam-2337	298	16	)	)	PUNCT
ejpam-2337	298	17	and	and	CCONJ
ejpam-2337	298	18	(	(	PUNCT
ejpam-2337	298	19	17	17	NUM
ejpam-2337	298	20	)	)	PUNCT
ejpam-2337	298	21	hold	hold	VERB
ejpam-2337	298	22	for	for	ADP
ejpam-2337	298	23	all	all	DET
ejpam-2337	298	24	x	x	SYM
ejpam-2337	298	25	,	,	PUNCT
ejpam-2337	298	26	u	u	NOUN
ejpam-2337	298	27	,	,	PUNCT
ejpam-2337	298	28	y	y	PROPN
ejpam-2337	298	29	,	,	PUNCT
ejpam-2337	298	30	v	v	PRON
ejpam-2337	298	31	%	%	NOUN
ejpam-2337	298	32	e	e	NOUN
ejpam-2337	298	33	,	,	PUNCT
ejpam-2337	298	34	then	then	ADV
ejpam-2337	298	35	there	there	PRON
ejpam-2337	298	36	exists	exist	VERB
ejpam-2337	298	37	a	a	DET
ejpam-2337	298	38	unique	unique	ADJ
ejpam-2337	298	39	bi	bi	ADJ
ejpam-2337	298	40	-	-	ADJ
ejpam-2337	298	41	reciprocal	reciprocal	ADJ
ejpam-2337	298	42	mapping	mapping	NOUN
ejpam-2337	298	43	r	r	NOUN
ejpam-2337	298	44	:	:	PUNCT
ejpam-2337	298	45	e	e	X
ejpam-2337	298	46	#	#	NOUN
ejpam-2337	298	47	e$	e$	NOUN
ejpam-2337	298	48	f	f	PROPN
ejpam-2337	298	49	satisfying	satisfying	NOUN
ejpam-2337	298	50	(	(	PUNCT
ejpam-2337	298	51	5	5	NUM
ejpam-2337	298	52	)	)	PUNCT
ejpam-2337	298	53	and	and	CCONJ
ejpam-2337	298	54	0	0	NUM
ejpam-2337	298	55	0r(x	0r(x	NOUN
ejpam-2337	298	56	,	,	PUNCT
ejpam-2337	298	57	y	y	PROPN
ejpam-2337	298	58	)	)	PUNCT
ejpam-2337	298	59	.	.	PUNCT
ejpam-2337	299	1	r(x	r(x	PROPN
ejpam-2337	299	2	,	,	PUNCT
ejpam-2337	299	3	y	y	PROPN
ejpam-2337	299	4	)	)	PUNCT
ejpam-2337	299	5	0	0	NUM
ejpam-2337	299	6	0	0	NUM
ejpam-2337	299	7	,	,	PUNCT
ejpam-2337	299	8	1	1	NUM
ejpam-2337	299	9	2	2	NUM
ejpam-2337	299	10	&	&	CCONJ
ejpam-2337	299	11	!	!	PUNCT
ejpam-2337	300	1	i=0	i=0	ADJ
ejpam-2337	300	2	1	1	NUM
ejpam-2337	300	3	4i	4i	NOUN
ejpam-2337	300	4	g	g	NOUN
ejpam-2337	300	5	#	#	NOUN
ejpam-2337	300	6	x	x	NOUN
ejpam-2337	300	7	2i+1	2i+1	NOUN
ejpam-2337	300	8	,	,	PUNCT
ejpam-2337	300	9	x	x	PROPN
ejpam-2337	300	10	2i+1	2i+1	NOUN
ejpam-2337	300	11	,	,	PUNCT
ejpam-2337	300	12	y	y	PROPN
ejpam-2337	300	13	2i+1	2i+1	PROPN
ejpam-2337	300	14	$	$	PROPN
ejpam-2337	300	15	+	+	NOUN
ejpam-2337	300	16	&	&	CCONJ
ejpam-2337	300	17	!	!	PUNCT
ejpam-2337	301	1	i=0	i=0	ADJ
ejpam-2337	301	2	1	1	NUM
ejpam-2337	301	3	4i	4i	NUM
ejpam-2337	301	4	h	h	NOUN
ejpam-2337	301	5	#	#	NOUN
ejpam-2337	301	6	x	x	SYM
ejpam-2337	301	7	2i	2i	NUM
ejpam-2337	301	8	,	,	PUNCT
ejpam-2337	301	9	y	y	PROPN
ejpam-2337	301	10	2i+1	2i+1	PROPN
ejpam-2337	301	11	,	,	PUNCT
ejpam-2337	301	12	y	y	PROPN
ejpam-2337	301	13	2i+1	2i+1	PROPN
ejpam-2337	301	14	$	$	SYM
ejpam-2337	301	15	for	for	ADP
ejpam-2337	301	16	all	all	DET
ejpam-2337	301	17	x	x	SYM
ejpam-2337	301	18	,	,	PUNCT
ejpam-2337	301	19	y	y	PROPN
ejpam-2337	301	20	%	%	NOUN
ejpam-2337	301	21	e.	e.	PROPN
ejpam-2337	301	22	proof	proof	PROPN
ejpam-2337	301	23	.	.	PUNCT
ejpam-2337	302	1	by	by	ADP
ejpam-2337	302	2	taking	take	VERB
ejpam-2337	302	3	d(a	d(a	PROPN
ejpam-2337	302	4	,	,	PUNCT
ejpam-2337	302	5	b	b	NOUN
ejpam-2337	302	6	)	)	PUNCT
ejpam-2337	302	7	=	=	PUNCT
ejpam-2337	303	1	+	+	ADJ
ejpam-2337	303	2	a.	a.	NOUN
ejpam-2337	303	3	b+	b+	NOUN
ejpam-2337	303	4	,	,	PUNCT
ejpam-2337	303	5	for	for	ADP
ejpam-2337	303	6	all	all	DET
ejpam-2337	303	7	a	a	PRON
ejpam-2337	303	8	,	,	PUNCT
ejpam-2337	303	9	b	b	NOUN
ejpam-2337	303	10	%	%	NOUN
ejpam-2337	303	11	e	e	X
ejpam-2337	303	12	in	in	ADP
ejpam-2337	303	13	theorem	theorem	NOUN
ejpam-2337	303	14	4	4	NUM
ejpam-2337	303	15	,	,	PUNCT
ejpam-2337	303	16	we	we	PRON
ejpam-2337	303	17	arrive	arrive	VERB
ejpam-2337	303	18	at	at	ADP
ejpam-2337	303	19	the	the	DET
ejpam-2337	303	20	desired	desire	VERB
ejpam-2337	303	21	result	result	NOUN
ejpam-2337	303	22	.	.	PUNCT
ejpam-2337	304	1	corollary	corollary	ADJ
ejpam-2337	304	2	2	2	NUM
ejpam-2337	304	3	.	.	PUNCT
ejpam-2337	305	1	let	let	VERB
ejpam-2337	305	2	!	!	PUNCT
ejpam-2337	305	3	>	>	X
ejpam-2337	305	4	0	0	PUNCT
ejpam-2337	305	5	be	be	AUX
ejpam-2337	305	6	fixed	fix	VERB
ejpam-2337	305	7	.	.	PUNCT
ejpam-2337	306	1	if	if	SCONJ
ejpam-2337	306	2	r	r	NOUN
ejpam-2337	306	3	:	:	PUNCT
ejpam-2337	306	4	e	e	X
ejpam-2337	306	5	#	#	NOUN
ejpam-2337	306	6	e$	e$	NOUN
ejpam-2337	306	7	f	f	PROPN
ejpam-2337	306	8	satisfies	satisfy	VERB
ejpam-2337	306	9	0	0	NUM
ejpam-2337	306	10	0	0	NUM
ejpam-2337	306	11	0	0	NUM
ejpam-2337	306	12	0	0	NUM
ejpam-2337	307	1	r(x	r(x	PROPN
ejpam-2337	307	2	+	+	CCONJ
ejpam-2337	307	3	u	u	PROPN
ejpam-2337	307	4	,	,	PUNCT
ejpam-2337	307	5	y	y	PROPN
ejpam-2337	307	6	)	)	PUNCT
ejpam-2337	307	7	.	.	PUNCT
ejpam-2337	308	1	r(x	r(x	PROPN
ejpam-2337	308	2	,	,	PUNCT
ejpam-2337	308	3	y)r(u	y)r(u	PROPN
ejpam-2337	308	4	,	,	PUNCT
ejpam-2337	308	5	y	y	PROPN
ejpam-2337	308	6	)	)	PUNCT
ejpam-2337	308	7	r(x	r(x	PROPN
ejpam-2337	308	8	,	,	PUNCT
ejpam-2337	308	9	y	y	PROPN
ejpam-2337	308	10	)	)	PUNCT
ejpam-2337	308	11	+	+	CCONJ
ejpam-2337	308	12	r(u	r(u	PROPN
ejpam-2337	308	13	,	,	PUNCT
ejpam-2337	308	14	y	y	NOUN
ejpam-2337	308	15	)	)	PUNCT
ejpam-2337	308	16	0	0	NUM
ejpam-2337	308	17	0	0	NUM
ejpam-2337	308	18	0	0	NUM
ejpam-2337	308	19	0	0	NUM
ejpam-2337	308	20	,	,	PUNCT
ejpam-2337	308	21	!	!	PUNCT
ejpam-2337	308	22	2	2	NUM
ejpam-2337	308	23	,	,	PUNCT
ejpam-2337	308	24	0	0	NUM
ejpam-2337	308	25	0	0	NUM
ejpam-2337	308	26	0	0	SYM
ejpam-2337	308	27	0	0	NUM
ejpam-2337	309	1	r(x	r(x	PROPN
ejpam-2337	309	2	,	,	PUNCT
ejpam-2337	309	3	y	y	PROPN
ejpam-2337	309	4	+	+	PROPN
ejpam-2337	309	5	v	v	NOUN
ejpam-2337	309	6	)	)	PUNCT
ejpam-2337	309	7	.	.	PUNCT
ejpam-2337	310	1	r(x	r(x	PROPN
ejpam-2337	310	2	,	,	PUNCT
ejpam-2337	310	3	y)r(x	y)r(x	PROPN
ejpam-2337	310	4	,	,	PUNCT
ejpam-2337	310	5	v	v	NOUN
ejpam-2337	310	6	)	)	PUNCT
ejpam-2337	310	7	r(x	r(x	PROPN
ejpam-2337	310	8	,	,	PUNCT
ejpam-2337	310	9	y	y	PROPN
ejpam-2337	310	10	)	)	PUNCT
ejpam-2337	310	11	+	+	CCONJ
ejpam-2337	310	12	r(x	r(x	PROPN
ejpam-2337	310	13	,	,	PUNCT
ejpam-2337	310	14	v	v	NOUN
ejpam-2337	310	15	)	)	PUNCT
ejpam-2337	310	16	0	0	NUM
ejpam-2337	310	17	0	0	NUM
ejpam-2337	310	18	0	0	NUM
ejpam-2337	310	19	0	0	NUM
ejpam-2337	310	20	,	,	PUNCT
ejpam-2337	310	21	!	!	PUNCT
ejpam-2337	310	22	2	2	NUM
ejpam-2337	310	23	for	for	ADP
ejpam-2337	310	24	all	all	DET
ejpam-2337	310	25	x	x	SYM
ejpam-2337	310	26	,	,	PUNCT
ejpam-2337	310	27	u	u	NOUN
ejpam-2337	310	28	,	,	PUNCT
ejpam-2337	310	29	y	y	PROPN
ejpam-2337	310	30	,	,	PUNCT
ejpam-2337	310	31	v	v	PRON
ejpam-2337	310	32	%	%	NOUN
ejpam-2337	310	33	e	e	NOUN
ejpam-2337	310	34	,	,	PUNCT
ejpam-2337	310	35	then	then	ADV
ejpam-2337	310	36	there	there	PRON
ejpam-2337	310	37	exists	exist	VERB
ejpam-2337	310	38	a	a	DET
ejpam-2337	310	39	unique	unique	ADJ
ejpam-2337	310	40	bi	bi	ADJ
ejpam-2337	310	41	-	-	ADJ
ejpam-2337	310	42	reciprocal	reciprocal	ADJ
ejpam-2337	310	43	mapping	mapping	NOUN
ejpam-2337	310	44	r	r	NOUN
ejpam-2337	310	45	:	:	PUNCT
ejpam-2337	310	46	e	e	X
ejpam-2337	310	47	#	#	NOUN
ejpam-2337	310	48	e$	e$	NOUN
ejpam-2337	310	49	f	f	PROPN
ejpam-2337	310	50	such	such	ADJ
ejpam-2337	310	51	that	that	DET
ejpam-2337	310	52	0	0	NUM
ejpam-2337	310	53	0r(x	0r(x	NOUN
ejpam-2337	310	54	,	,	PUNCT
ejpam-2337	310	55	y	y	PROPN
ejpam-2337	310	56	)	)	PUNCT
ejpam-2337	310	57	.	.	PUNCT
ejpam-2337	311	1	r(x	r(x	PROPN
ejpam-2337	311	2	,	,	PUNCT
ejpam-2337	311	3	y	y	PROPN
ejpam-2337	311	4	)	)	PUNCT
ejpam-2337	311	5	0	0	NUM
ejpam-2337	311	6	0	0	NUM
ejpam-2337	311	7	,	,	PUNCT
ejpam-2337	311	8	!	!	PUNCT
ejpam-2337	311	9	,	,	PUNCT
ejpam-2337	311	10	for	for	ADP
ejpam-2337	311	11	all	all	PRON
ejpam-2337	311	12	x	x	SYM
ejpam-2337	311	13	,	,	PUNCT
ejpam-2337	311	14	y	y	PROPN
ejpam-2337	311	15	%	%	NOUN
ejpam-2337	311	16	e.	e.	PROPN
ejpam-2337	311	17	references	reference	VERB
ejpam-2337	311	18	292	292	NUM
ejpam-2337	311	19	proof	proof	NOUN
ejpam-2337	311	20	.	.	PUNCT
ejpam-2337	312	1	letting	let	VERB
ejpam-2337	312	2	g(x	g(x	PROPN
ejpam-2337	312	3	,	,	PUNCT
ejpam-2337	312	4	y	y	PROPN
ejpam-2337	312	5	,	,	PUNCT
ejpam-2337	312	6	z	z	NOUN
ejpam-2337	312	7	)	)	PUNCT
ejpam-2337	313	1	=	=	SYM
ejpam-2337	313	2	h(x	h(x	PROPN
ejpam-2337	313	3	,	,	PUNCT
ejpam-2337	313	4	y	y	PROPN
ejpam-2337	313	5	,	,	PUNCT
ejpam-2337	313	6	z	z	NOUN
ejpam-2337	313	7	)	)	PUNCT
ejpam-2337	313	8	=	=	PUNCT
ejpam-2337	313	9	!	!	PUNCT
ejpam-2337	313	10	2	2	NUM
ejpam-2337	313	11	,	,	PUNCT
ejpam-2337	313	12	for	for	ADP
ejpam-2337	313	13	all	all	DET
ejpam-2337	313	14	x	x	SYM
ejpam-2337	313	15	,	,	PUNCT
ejpam-2337	313	16	y	y	PROPN
ejpam-2337	313	17	,	,	PUNCT
ejpam-2337	313	18	z	z	NOUN
ejpam-2337	313	19	%	%	NOUN
ejpam-2337	313	20	e	e	X
ejpam-2337	313	21	in	in	ADP
ejpam-2337	313	22	theorem	theorem	NOUN
ejpam-2337	313	23	5	5	NUM
ejpam-2337	313	24	,	,	PUNCT
ejpam-2337	313	25	we	we	PRON
ejpam-2337	313	26	lead	lead	VERB
ejpam-2337	313	27	to	to	ADP
ejpam-2337	313	28	0	0	NUM
ejpam-2337	313	29	0r(x	0r(x	NOUN
ejpam-2337	313	30	,	,	PUNCT
ejpam-2337	313	31	y	y	PROPN
ejpam-2337	313	32	)	)	PUNCT
ejpam-2337	313	33	.	.	PUNCT
ejpam-2337	314	1	r(x	r(x	PROPN
ejpam-2337	314	2	,	,	PUNCT
ejpam-2337	314	3	y	y	PROPN
ejpam-2337	314	4	)	)	PUNCT
ejpam-2337	314	5	0	0	NUM
ejpam-2337	314	6	0	0	NUM
ejpam-2337	314	7	,	,	PUNCT
ejpam-2337	314	8	1	1	NUM
ejpam-2337	314	9	2	2	NUM
ejpam-2337	314	10	&	&	CCONJ
ejpam-2337	314	11	!	!	PUNCT
ejpam-2337	315	1	i=0	i=0	ADJ
ejpam-2337	315	2	1	1	NUM
ejpam-2337	315	3	4i	4i	NOUN
ejpam-2337	315	4	!	!	PUNCT
ejpam-2337	316	1	2	2	NUM
ejpam-2337	316	2	+	+	NUM
ejpam-2337	316	3	&	&	CCONJ
ejpam-2337	316	4	!	!	PUNCT
ejpam-2337	317	1	i=0	i=0	ADJ
ejpam-2337	317	2	1	1	NUM
ejpam-2337	317	3	4i	4i	NOUN
ejpam-2337	317	4	!	!	PUNCT
ejpam-2337	318	1	2	2	NUM
ejpam-2337	318	2	,	,	PUNCT
ejpam-2337	318	3	3	3	NUM
ejpam-2337	318	4	!	!	SYM
ejpam-2337	318	5	4	4	NUM
ejpam-2337	318	6	&	&	CCONJ
ejpam-2337	318	7	!	!	PUNCT
ejpam-2337	319	1	i=0	i=0	ADJ
ejpam-2337	319	2	1	1	NUM
ejpam-2337	319	3	4i	4i	NOUN
ejpam-2337	319	4	=	=	SYM
ejpam-2337	319	5	3	3	NUM
ejpam-2337	319	6	!	!	NOUN
ejpam-2337	319	7	4	4	NUM
ejpam-2337	319	8	#	#	NOUN
ejpam-2337	319	9	4	4	NUM
ejpam-2337	319	10	3	3	NUM
ejpam-2337	319	11	$	$	NOUN
ejpam-2337	319	12	=	=	PUNCT
ejpam-2337	319	13	!	!	PUNCT
ejpam-2337	319	14	,	,	PUNCT
ejpam-2337	319	15	for	for	ADP
ejpam-2337	319	16	all	all	DET
ejpam-2337	319	17	x	x	SYM
ejpam-2337	319	18	,	,	PUNCT
ejpam-2337	319	19	y	y	PROPN
ejpam-2337	319	20	%	%	NOUN
ejpam-2337	319	21	e.	e.	PROPN
ejpam-2337	319	22	corollary	corollary	PROPN
ejpam-2337	319	23	3	3	X
ejpam-2337	319	24	.	.	PUNCT
ejpam-2337	320	1	let	let	VERB
ejpam-2337	320	2	c1	c1	PROPN
ejpam-2337	320	3	>	>	X
ejpam-2337	320	4	0	0	PUNCT
ejpam-2337	321	1	be	be	AUX
ejpam-2337	321	2	fixed	fix	VERB
ejpam-2337	321	3	and	and	CCONJ
ejpam-2337	321	4	p	p	X
ejpam-2337	321	5	>	>	X
ejpam-2337	322	1	.2	.2	NUM
ejpam-2337	322	2	.	.	PUNCT
ejpam-2337	323	1	if	if	SCONJ
ejpam-2337	323	2	a	a	DET
ejpam-2337	323	3	mapping	mapping	NOUN
ejpam-2337	323	4	r	r	NOUN
ejpam-2337	323	5	:	:	PUNCT
ejpam-2337	323	6	e#e$	e#e$	PRON
ejpam-2337	323	7	f	f	NOUN
ejpam-2337	323	8	satisfies	satisfy	VERB
ejpam-2337	323	9	the	the	DET
ejpam-2337	323	10	inequalities	inequality	NOUN
ejpam-2337	323	11	(	(	PUNCT
ejpam-2337	323	12	18	18	NUM
ejpam-2337	323	13	)	)	PUNCT
ejpam-2337	323	14	,	,	PUNCT
ejpam-2337	323	15	for	for	ADP
ejpam-2337	323	16	all	all	DET
ejpam-2337	323	17	x	x	SYM
ejpam-2337	323	18	,	,	PUNCT
ejpam-2337	323	19	u	u	NOUN
ejpam-2337	323	20	,	,	PUNCT
ejpam-2337	323	21	y	y	PROPN
ejpam-2337	323	22	,	,	PUNCT
ejpam-2337	323	23	v	v	PRON
ejpam-2337	323	24	%	%	NOUN
ejpam-2337	323	25	e	e	NOUN
ejpam-2337	323	26	,	,	PUNCT
ejpam-2337	323	27	then	then	ADV
ejpam-2337	323	28	there	there	PRON
ejpam-2337	323	29	exists	exist	VERB
ejpam-2337	323	30	a	a	DET
ejpam-2337	323	31	unique	unique	ADJ
ejpam-2337	323	32	bi	bi	ADJ
ejpam-2337	323	33	-	-	ADJ
ejpam-2337	323	34	reciprocal	reciprocal	ADJ
ejpam-2337	323	35	mapping	mapping	NOUN
ejpam-2337	323	36	r	r	NOUN
ejpam-2337	323	37	:	:	PUNCT
ejpam-2337	323	38	e	e	X
ejpam-2337	323	39	#	#	NOUN
ejpam-2337	323	40	e	e	VERB
ejpam-2337	323	41	$	$	SYM
ejpam-2337	323	42	f	f	NOUN
ejpam-2337	323	43	satisfying	satisfying	NOUN
ejpam-2337	323	44	(	(	PUNCT
ejpam-2337	323	45	5	5	NUM
ejpam-2337	323	46	)	)	PUNCT
ejpam-2337	323	47	and	and	CCONJ
ejpam-2337	323	48	0	0	NUM
ejpam-2337	323	49	0r(x	0r(x	NOUN
ejpam-2337	323	50	,	,	PUNCT
ejpam-2337	323	51	y	y	PROPN
ejpam-2337	323	52	)	)	PUNCT
ejpam-2337	323	53	.	.	PUNCT
ejpam-2337	324	1	r(x	r(x	PROPN
ejpam-2337	324	2	,	,	PUNCT
ejpam-2337	324	3	y	y	PROPN
ejpam-2337	324	4	)	)	PUNCT
ejpam-2337	324	5	0	0	NUM
ejpam-2337	324	6	0	0	NUM
ejpam-2337	324	7	,	,	PUNCT
ejpam-2337	324	8	#	#	NOUN
ejpam-2337	324	9	2c1	2c1	NUM
ejpam-2337	324	10	2p+2	2p+2	NUM
ejpam-2337	324	11	.	.	PUNCT
ejpam-2337	325	1	1	1	NUM
ejpam-2337	325	2	$	$	NOUN
ejpam-2337	325	3	.	.	NOUN
ejpam-2337	325	4	2	2	NUM
ejpam-2337	325	5	(	(	PUNCT
ejpam-2337	325	6	2p	2p	NUM
ejpam-2337	325	7	+	+	CCONJ
ejpam-2337	325	8	1)+x+p	1)+x+p	NUM
ejpam-2337	325	9	+	+	NUM
ejpam-2337	325	10	5	5	NUM
ejpam-2337	325	11	0	0	NUM
ejpam-2337	325	12	0y	0y	NOUN
ejpam-2337	325	13	0	0	NUM
ejpam-2337	325	14	0	0	NUM
ejpam-2337	326	1	p	p	NOUN
ejpam-2337	326	2	/	/	PUNCT
ejpam-2337	326	3	,	,	PUNCT
ejpam-2337	326	4	for	for	ADP
ejpam-2337	326	5	all	all	DET
ejpam-2337	326	6	x	x	SYM
ejpam-2337	326	7	,	,	PUNCT
ejpam-2337	326	8	y	y	PROPN
ejpam-2337	326	9	%	%	NOUN
ejpam-2337	326	10	e.	e.	PROPN
ejpam-2337	326	11	proof	proof	PROPN
ejpam-2337	326	12	.	.	PUNCT
ejpam-2337	327	1	the	the	DET
ejpam-2337	327	2	proof	proof	NOUN
ejpam-2337	327	3	is	be	AUX
ejpam-2337	327	4	similar	similar	ADJ
ejpam-2337	327	5	to	to	ADP
ejpam-2337	327	6	that	that	PRON
ejpam-2337	327	7	of	of	ADP
ejpam-2337	327	8	corollary	corollary	ADJ
ejpam-2337	327	9	1	1	NUM
ejpam-2337	327	10	.	.	PUNCT
ejpam-2337	327	11	acknowledgement	acknowledgement	NOUN
ejpam-2337	327	12	.	.	PUNCT
ejpam-2337	328	1	the	the	DET
ejpam-2337	328	2	authors	author	NOUN
ejpam-2337	328	3	thank	thank	VERB
ejpam-2337	328	4	the	the	DET
ejpam-2337	328	5	anonymous	anonymous	ADJ
ejpam-2337	328	6	reviewers	reviewer	NOUN
ejpam-2337	328	7	for	for	ADP
ejpam-2337	328	8	their	their	PRON
ejpam-2337	328	9	valuable	valuable	ADJ
ejpam-2337	328	10	comments	comment	NOUN
ejpam-2337	328	11	and	and	CCONJ
ejpam-2337	328	12	suggestions	suggestion	NOUN
ejpam-2337	328	13	to	to	PART
ejpam-2337	328	14	add	add	VERB
ejpam-2337	328	15	more	more	ADJ
ejpam-2337	328	16	credibility	credibility	NOUN
ejpam-2337	328	17	to	to	ADP
ejpam-2337	328	18	the	the	DET
ejpam-2337	328	19	paper	paper	NOUN
ejpam-2337	328	20	.	.	PUNCT
ejpam-2337	329	1	references	reference	NOUN
ejpam-2337	329	2	[	[	X
ejpam-2337	329	3	1	1	NUM
ejpam-2337	329	4	]	]	PUNCT
ejpam-2337	329	5	c.	c.	PROPN
ejpam-2337	329	6	alsina	alsina	PROPN
ejpam-2337	329	7	.	.	PUNCT
ejpam-2337	330	1	on	on	ADP
ejpam-2337	330	2	the	the	DET
ejpam-2337	330	3	stability	stability	NOUN
ejpam-2337	330	4	of	of	ADP
ejpam-2337	330	5	a	a	DET
ejpam-2337	330	6	functional	functional	ADJ
ejpam-2337	330	7	equation	equation	NOUN
ejpam-2337	330	8	.	.	PUNCT
ejpam-2337	331	1	general	general	ADJ
ejpam-2337	331	2	inequalities	inequality	NOUN
ejpam-2337	331	3	,	,	PUNCT
ejpam-2337	331	4	oberwolfach	oberwolfach	ADV
ejpam-2337	331	5	,	,	PUNCT
ejpam-2337	331	6	birkhauser	birkhauser	PROPN
ejpam-2337	331	7	,	,	PUNCT
ejpam-2337	331	8	basel	basel	PROPN
ejpam-2337	331	9	,	,	PUNCT
ejpam-2337	331	10	5:263–271	5:263–271	NUM
ejpam-2337	331	11	,	,	PUNCT
ejpam-2337	331	12	1987	1987	NUM
ejpam-2337	331	13	.	.	PUNCT
ejpam-2337	332	1	[	[	X
ejpam-2337	332	2	2	2	X
ejpam-2337	332	3	]	]	PUNCT
ejpam-2337	332	4	t.	t.	PROPN
ejpam-2337	332	5	aoki	aoki	PROPN
ejpam-2337	332	6	.	.	PUNCT
ejpam-2337	333	1	on	on	ADP
ejpam-2337	333	2	the	the	DET
ejpam-2337	333	3	stability	stability	NOUN
ejpam-2337	333	4	of	of	ADP
ejpam-2337	333	5	the	the	DET
ejpam-2337	333	6	linear	linear	ADJ
ejpam-2337	333	7	transformation	transformation	NOUN
ejpam-2337	333	8	in	in	ADP
ejpam-2337	333	9	banach	banach	NOUN
ejpam-2337	333	10	spaces	space	NOUN
ejpam-2337	333	11	.	.	PUNCT
ejpam-2337	334	1	journal	journal	PROPN
ejpam-2337	334	2	of	of	ADP
ejpam-2337	334	3	mathematical	mathematical	ADJ
ejpam-2337	334	4	society	society	NOUN
ejpam-2337	334	5	of	of	ADP
ejpam-2337	334	6	japan	japan	PROPN
ejpam-2337	334	7	,	,	PUNCT
ejpam-2337	334	8	2:64–66	2:64–66	NUM
ejpam-2337	334	9	,	,	PUNCT
ejpam-2337	334	10	1950	1950	NUM
ejpam-2337	334	11	.	.	PUNCT
ejpam-2337	335	1	[	[	X
ejpam-2337	335	2	3	3	X
ejpam-2337	335	3	]	]	X
ejpam-2337	335	4	j.h	j.h	PROPN
ejpam-2337	335	5	.	.	PROPN
ejpam-2337	335	6	bae	bae	PROPN
ejpam-2337	335	7	and	and	CCONJ
ejpam-2337	335	8	w.g	w.g	PROPN
ejpam-2337	335	9	.	.	PROPN
ejpam-2337	335	10	park	park	NOUN
ejpam-2337	335	11	.	.	PUNCT
ejpam-2337	336	1	on	on	ADP
ejpam-2337	336	2	the	the	DET
ejpam-2337	336	3	solution	solution	NOUN
ejpam-2337	336	4	of	of	ADP
ejpam-2337	336	5	a	a	DET
ejpam-2337	336	6	bi	bi	ADJ
ejpam-2337	336	7	-	-	ADJ
ejpam-2337	336	8	jensen	jensen	ADJ
ejpam-2337	336	9	functional	functional	ADJ
ejpam-2337	336	10	equation	equation	NOUN
ejpam-2337	336	11	and	and	CCONJ
ejpam-2337	336	12	its	its	PRON
ejpam-2337	336	13	stability	stability	NOUN
ejpam-2337	336	14	.	.	PUNCT
ejpam-2337	337	1	bulletin	bulletin	NOUN
ejpam-2337	337	2	of	of	ADP
ejpam-2337	337	3	the	the	DET
ejpam-2337	337	4	korean	korean	PROPN
ejpam-2337	337	5	mathematical	mathematical	ADJ
ejpam-2337	337	6	society	society	NOUN
ejpam-2337	337	7	3	3	NUM
ejpam-2337	337	8	,	,	PUNCT
ejpam-2337	337	9	43(3):499–507	43(3):499–507	NOUN
ejpam-2337	337	10	,	,	PUNCT
ejpam-2337	337	11	2006	2006	NUM
ejpam-2337	337	12	.	.	PUNCT
ejpam-2337	338	1	[	[	X
ejpam-2337	338	2	4	4	NUM
ejpam-2337	338	3	]	]	X
ejpam-2337	338	4	i.s	i.s	PROPN
ejpam-2337	338	5	.	.	PROPN
ejpam-2337	338	6	chang	chang	PROPN
ejpam-2337	338	7	and	and	CCONJ
ejpam-2337	338	8	y.s	y.s	PROPN
ejpam-2337	338	9	.	.	PROPN
ejpam-2337	338	10	jung	jung	PROPN
ejpam-2337	338	11	.	.	PUNCT
ejpam-2337	339	1	stability	stability	NOUN
ejpam-2337	339	2	of	of	ADP
ejpam-2337	339	3	functional	functional	ADJ
ejpam-2337	339	4	equations	equation	NOUN
ejpam-2337	339	5	deriving	derive	VERB
ejpam-2337	339	6	from	from	ADP
ejpam-2337	339	7	cubic	cubic	ADJ
ejpam-2337	339	8	and	and	CCONJ
ejpam-2337	339	9	quadratic	quadratic	ADJ
ejpam-2337	339	10	functions	function	NOUN
ejpam-2337	339	11	.	.	PUNCT
ejpam-2337	340	1	journal	journal	NOUN
ejpam-2337	340	2	of	of	ADP
ejpam-2337	340	3	mathematical	mathematical	ADJ
ejpam-2337	340	4	analysis	analysis	NOUN
ejpam-2337	340	5	and	and	CCONJ
ejpam-2337	340	6	applications	application	NOUN
ejpam-2337	340	7	,	,	PUNCT
ejpam-2337	340	8	283:491–500	283:491–500	NUM
ejpam-2337	340	9	,	,	PUNCT
ejpam-2337	340	10	2003	2003	NUM
ejpam-2337	340	11	.	.	PUNCT
ejpam-2337	341	1	[	[	X
ejpam-2337	341	2	5	5	NUM
ejpam-2337	341	3	]	]	X
ejpam-2337	341	4	i.s	i.s	PROPN
ejpam-2337	341	5	.	.	PROPN
ejpam-2337	341	6	chang	chang	PROPN
ejpam-2337	341	7	and	and	CCONJ
ejpam-2337	341	8	h.m	h.m	PROPN
ejpam-2337	341	9	.	.	PROPN
ejpam-2337	341	10	kim	kim	PROPN
ejpam-2337	341	11	.	.	PUNCT
ejpam-2337	342	1	on	on	ADP
ejpam-2337	342	2	the	the	DET
ejpam-2337	342	3	hyers	hyers	PROPN
ejpam-2337	342	4	-	-	PUNCT
ejpam-2337	342	5	ulam	ulam	ADJ
ejpam-2337	342	6	stability	stability	NOUN
ejpam-2337	342	7	of	of	ADP
ejpam-2337	342	8	quadratic	quadratic	ADJ
ejpam-2337	342	9	functional	functional	ADJ
ejpam-2337	342	10	equations	equation	NOUN
ejpam-2337	342	11	.	.	PUNCT
ejpam-2337	343	1	journal	journal	PROPN
ejpam-2337	343	2	of	of	ADP
ejpam-2337	343	3	inequalities	inequality	NOUN
ejpam-2337	343	4	in	in	ADP
ejpam-2337	343	5	applied	applied	ADJ
ejpam-2337	343	6	mathematics	mathematic	NOUN
ejpam-2337	343	7	,	,	PUNCT
ejpam-2337	343	8	33:1–12	33:1–12	NUM
ejpam-2337	343	9	,	,	PUNCT
ejpam-2337	343	10	2002	2002	NUM
ejpam-2337	343	11	.	.	PUNCT
ejpam-2337	344	1	[	[	X
ejpam-2337	344	2	6	6	NUM
ejpam-2337	344	3	]	]	PUNCT
ejpam-2337	344	4	e.	e.	PROPN
ejpam-2337	344	5	dubinsky	dubinsky	PROPN
ejpam-2337	344	6	.	.	PUNCT
ejpam-2337	345	1	the	the	DET
ejpam-2337	345	2	structure	structure	NOUN
ejpam-2337	345	3	of	of	ADP
ejpam-2337	345	4	nuclear	nuclear	ADJ
ejpam-2337	345	5	fréchet	fréchet	NOUN
ejpam-2337	345	6	spaces	space	NOUN
ejpam-2337	345	7	,	,	PUNCT
ejpam-2337	345	8	lecture	lecture	NOUN
ejpam-2337	345	9	notes	note	NOUN
ejpam-2337	345	10	in	in	ADP
ejpam-2337	345	11	mathematics	mathematic	NOUN
ejpam-2337	345	12	.	.	PUNCT
ejpam-2337	346	1	springer	springer	NOUN
ejpam-2337	346	2	,	,	PUNCT
ejpam-2337	346	3	1979	1979	NUM
ejpam-2337	346	4	.	.	PUNCT
ejpam-2337	347	1	[	[	X
ejpam-2337	347	2	7	7	X
ejpam-2337	347	3	]	]	X
ejpam-2337	347	4	c.s	c.s	PROPN
ejpam-2337	347	5	.	.	PROPN
ejpam-2337	347	6	gal	gal	PROPN
ejpam-2337	347	7	,	,	PUNCT
ejpam-2337	347	8	s.g	s.g	PROPN
ejpam-2337	347	9	.	.	PROPN
ejpam-2337	347	10	gal	gal	PROPN
ejpam-2337	347	11	,	,	PUNCT
ejpam-2337	347	12	and	and	CCONJ
ejpam-2337	347	13	g.m	g.m	PROPN
ejpam-2337	347	14	.	.	PROPN
ejpam-2337	347	15	n’giérékata	n’giérékata	PROPN
ejpam-2337	347	16	.	.	PUNCT
ejpam-2337	348	1	almost	almost	ADV
ejpam-2337	348	2	automorphic	automorphic	ADJ
ejpam-2337	348	3	functions	function	NOUN
ejpam-2337	348	4	in	in	ADP
ejpam-2337	348	5	fréchet	fréchet	NOUN
ejpam-2337	348	6	spaces	space	NOUN
ejpam-2337	348	7	and	and	CCONJ
ejpam-2337	348	8	applications	application	NOUN
ejpam-2337	348	9	to	to	PART
ejpam-2337	348	10	differential	differential	VERB
ejpam-2337	348	11	equations	equation	NOUN
ejpam-2337	348	12	.	.	PUNCT
ejpam-2337	349	1	semigroup	semigroup	PROPN
ejpam-2337	349	2	form	form	NOUN
ejpam-2337	349	3	,	,	PUNCT
ejpam-2337	349	4	72(10):23–48	72(10):23–48	NUM
ejpam-2337	349	5	,	,	PUNCT
ejpam-2337	349	6	2005	2005	NUM
ejpam-2337	349	7	.	.	PUNCT
ejpam-2337	350	1	references	reference	NOUN
ejpam-2337	350	2	293	293	NUM
ejpam-2337	351	1	[	[	X
ejpam-2337	351	2	8	8	NUM
ejpam-2337	351	3	]	]	PUNCT
ejpam-2337	351	4	p.	p.	NOUN
ejpam-2337	351	5	gavruta	gavruta	PROPN
ejpam-2337	351	6	.	.	PUNCT
ejpam-2337	352	1	a	a	DET
ejpam-2337	352	2	generalization	generalization	NOUN
ejpam-2337	352	3	of	of	ADP
ejpam-2337	352	4	the	the	DET
ejpam-2337	352	5	hyers	hyers	PROPN
ejpam-2337	352	6	-	-	PUNCT
ejpam-2337	352	7	ulam	ulam	ADJ
ejpam-2337	352	8	-	-	PUNCT
ejpam-2337	352	9	rassias	rassias	PROPN
ejpam-2337	352	10	stability	stability	NOUN
ejpam-2337	352	11	of	of	ADP
ejpam-2337	352	12	approximately	approximately	ADV
ejpam-2337	352	13	additive	additive	ADJ
ejpam-2337	352	14	mappings	mapping	NOUN
ejpam-2337	352	15	.	.	PUNCT
ejpam-2337	353	1	journal	journal	PROPN
ejpam-2337	353	2	of	of	ADP
ejpam-2337	353	3	mathematical	mathematical	ADJ
ejpam-2337	353	4	analysis	analysis	NOUN
ejpam-2337	353	5	and	and	CCONJ
ejpam-2337	353	6	applications	application	NOUN
ejpam-2337	353	7	,	,	PUNCT
ejpam-2337	353	8	184:431–436	184:431–436	NUM
ejpam-2337	353	9	,	,	PUNCT
ejpam-2337	353	10	1994	1994	NUM
ejpam-2337	353	11	.	.	PUNCT
ejpam-2337	354	1	[	[	X
ejpam-2337	354	2	9	9	NUM
ejpam-2337	354	3	]	]	X
ejpam-2337	354	4	m.e	m.e	PROPN
ejpam-2337	354	5	.	.	PROPN
ejpam-2337	354	6	gordji	gordji	PROPN
ejpam-2337	354	7	,	,	PUNCT
ejpam-2337	354	8	a.	a.	NOUN
ejpam-2337	354	9	javadian	javadian	PROPN
ejpam-2337	354	10	,	,	PUNCT
ejpam-2337	354	11	and	and	CCONJ
ejpam-2337	354	12	j.m	j.m	PROPN
ejpam-2337	354	13	.	.	PROPN
ejpam-2337	354	14	rassias	rassias	PROPN
ejpam-2337	354	15	.	.	PUNCT
ejpam-2337	355	1	stability	stability	NOUN
ejpam-2337	355	2	of	of	ADP
ejpam-2337	355	3	systems	system	NOUN
ejpam-2337	355	4	of	of	ADP
ejpam-2337	355	5	bi	bi	ADJ
ejpam-2337	355	6	-	-	ADJ
ejpam-2337	355	7	quadratic	quadratic	ADJ
ejpam-2337	355	8	and	and	CCONJ
ejpam-2337	355	9	additive	additive	ADJ
ejpam-2337	355	10	-	-	PUNCT
ejpam-2337	355	11	cubic	cubic	ADJ
ejpam-2337	355	12	functional	functional	ADJ
ejpam-2337	355	13	equations	equation	NOUN
ejpam-2337	355	14	in	in	ADP
ejpam-2337	355	15	fréchet	fréchet	NOUN
ejpam-2337	355	16	spaces	space	NOUN
ejpam-2337	355	17	.	.	PUNCT
ejpam-2337	356	1	functional	functional	ADJ
ejpam-2337	356	2	analysis	analysis	NOUN
ejpam-2337	356	3	,	,	PUNCT
ejpam-2337	356	4	approximation	approximation	NOUN
ejpam-2337	356	5	and	and	CCONJ
ejpam-2337	356	6	computation	computation	NOUN
ejpam-2337	356	7	,	,	PUNCT
ejpam-2337	356	8	3(2):57–68	3(2):57–68	NUM
ejpam-2337	356	9	,	,	PUNCT
ejpam-2337	356	10	2011	2011	NUM
ejpam-2337	356	11	.	.	PUNCT
ejpam-2337	357	1	[	[	X
ejpam-2337	357	2	10	10	NUM
ejpam-2337	357	3	]	]	X
ejpam-2337	357	4	m.e	m.e	PROPN
ejpam-2337	357	5	.	.	PROPN
ejpam-2337	357	6	gordji	gordji	PROPN
ejpam-2337	357	7	,	,	PUNCT
ejpam-2337	357	8	s.	s.	PROPN
ejpam-2337	357	9	zolfaghari	zolfaghari	PROPN
ejpam-2337	357	10	,	,	PUNCT
ejpam-2337	357	11	j.m	j.m	PROPN
ejpam-2337	357	12	.	.	PROPN
ejpam-2337	357	13	rassias	rassias	PROPN
ejpam-2337	357	14	,	,	PUNCT
ejpam-2337	357	15	and	and	CCONJ
ejpam-2337	357	16	m.b	m.b	PROPN
ejpam-2337	357	17	.	.	PROPN
ejpam-2337	357	18	savadkouhi	savadkouhi	PROPN
ejpam-2337	357	19	.	.	PUNCT
ejpam-2337	358	1	solution	solution	NOUN
ejpam-2337	358	2	and	and	CCONJ
ejpam-2337	358	3	stability	stability	NOUN
ejpam-2337	358	4	of	of	ADP
ejpam-2337	358	5	a	a	DET
ejpam-2337	358	6	mixed	mixed	ADJ
ejpam-2337	358	7	type	type	NOUN
ejpam-2337	358	8	cubic	cubic	ADJ
ejpam-2337	358	9	and	and	CCONJ
ejpam-2337	358	10	quartic	quartic	ADJ
ejpam-2337	358	11	functional	functional	ADJ
ejpam-2337	358	12	equation	equation	NOUN
ejpam-2337	358	13	in	in	ADP
ejpam-2337	358	14	quasi	quasi	ADJ
ejpam-2337	358	15	-	-	ADJ
ejpam-2337	358	16	banach	banach	ADJ
ejpam-2337	358	17	spaces	space	NOUN
ejpam-2337	358	18	.	.	PUNCT
ejpam-2337	359	1	abstract	abstract	ADJ
ejpam-2337	359	2	and	and	CCONJ
ejpam-2337	359	3	applied	apply	VERB
ejpam-2337	359	4	analysis	analysis	NOUN
ejpam-2337	359	5	,	,	PUNCT
ejpam-2337	359	6	article	article	NOUN
ejpam-2337	359	7	i	i	PROPN
ejpam-2337	359	8	d	d	PROPN
ejpam-2337	359	9	417473:1–14	417473:1–14	PROPN
ejpam-2337	359	10	,	,	PUNCT
ejpam-2337	359	11	2009	2009	NUM
ejpam-2337	359	12	.	.	PUNCT
ejpam-2337	360	1	[	[	X
ejpam-2337	360	2	11	11	NUM
ejpam-2337	360	3	]	]	X
ejpam-2337	360	4	d.h	d.h	PROPN
ejpam-2337	360	5	.	.	PROPN
ejpam-2337	360	6	hyers	hyer	NOUN
ejpam-2337	360	7	.	.	PUNCT
ejpam-2337	361	1	on	on	ADP
ejpam-2337	361	2	the	the	DET
ejpam-2337	361	3	stability	stability	NOUN
ejpam-2337	361	4	of	of	ADP
ejpam-2337	361	5	the	the	DET
ejpam-2337	361	6	linear	linear	ADJ
ejpam-2337	361	7	functional	functional	ADJ
ejpam-2337	361	8	equation	equation	NOUN
ejpam-2337	361	9	.	.	PUNCT
ejpam-2337	362	1	proceedings	proceeding	NOUN
ejpam-2337	362	2	of	of	ADP
ejpam-2337	362	3	the	the	DET
ejpam-2337	362	4	national	national	PROPN
ejpam-2337	362	5	academy	academy	PROPN
ejpam-2337	362	6	of	of	ADP
ejpam-2337	362	7	sciences	sciences	PROPN
ejpam-2337	362	8	,	,	PUNCT
ejpam-2337	362	9	27:222–224	27:222–224	NUM
ejpam-2337	362	10	,	,	PUNCT
ejpam-2337	362	11	1941	1941	NUM
ejpam-2337	362	12	.	.	PUNCT
ejpam-2337	363	1	[	[	X
ejpam-2337	363	2	12	12	NUM
ejpam-2337	363	3	]	]	X
ejpam-2337	363	4	d.h	d.h	PROPN
ejpam-2337	363	5	.	.	PROPN
ejpam-2337	363	6	hyers	hyers	PROPN
ejpam-2337	363	7	,	,	PUNCT
ejpam-2337	363	8	g.	g.	PROPN
ejpam-2337	363	9	isac	isac	PROPN
ejpam-2337	363	10	,	,	PUNCT
ejpam-2337	363	11	and	and	CCONJ
ejpam-2337	363	12	th.m	th.m	PROPN
ejpam-2337	363	13	.	.	PUNCT
ejpam-2337	364	1	rassias	rassias	PROPN
ejpam-2337	364	2	.	.	PUNCT
ejpam-2337	365	1	stability	stability	NOUN
ejpam-2337	365	2	of	of	ADP
ejpam-2337	365	3	functional	functional	ADJ
ejpam-2337	365	4	equations	equation	NOUN
ejpam-2337	365	5	in	in	ADP
ejpam-2337	365	6	several	several	ADJ
ejpam-2337	365	7	variables	variable	NOUN
ejpam-2337	365	8	.	.	PUNCT
ejpam-2337	366	1	birkhauser	birkhauser	PROPN
ejpam-2337	366	2	,	,	PUNCT
ejpam-2337	366	3	basel	basel	PROPN
ejpam-2337	366	4	,	,	PUNCT
ejpam-2337	366	5	1998	1998	NUM
ejpam-2337	366	6	.	.	PUNCT
ejpam-2337	367	1	[	[	X
ejpam-2337	367	2	13	13	NUM
ejpam-2337	367	3	]	]	SYM
ejpam-2337	367	4	s.m	s.m	PROPN
ejpam-2337	367	5	.	.	PROPN
ejpam-2337	367	6	jung	jung	PROPN
ejpam-2337	367	7	.	.	PUNCT
ejpam-2337	368	1	hyers	hyer	NOUN
ejpam-2337	368	2	-	-	PUNCT
ejpam-2337	368	3	ulam	ulam	NOUN
ejpam-2337	368	4	-	-	PUNCT
ejpam-2337	368	5	rassias	rassias	PROPN
ejpam-2337	368	6	stability	stability	NOUN
ejpam-2337	368	7	of	of	ADP
ejpam-2337	368	8	functional	functional	ADJ
ejpam-2337	368	9	equations	equation	NOUN
ejpam-2337	368	10	in	in	ADP
ejpam-2337	368	11	mathematical	mathematical	ADJ
ejpam-2337	368	12	analysis	analysis	NOUN
ejpam-2337	368	13	.	.	PUNCT
ejpam-2337	369	1	hardonic	hardonic	ADJ
ejpam-2337	369	2	press	press	NOUN
ejpam-2337	369	3	,	,	PUNCT
ejpam-2337	369	4	palm	palm	NOUN
ejpam-2337	369	5	harbor	harbor	NOUN
ejpam-2337	369	6	,	,	PUNCT
ejpam-2337	369	7	2001	2001	NUM
ejpam-2337	369	8	.	.	PUNCT
ejpam-2337	370	1	[	[	X
ejpam-2337	370	2	14	14	NUM
ejpam-2337	370	3	]	]	X
ejpam-2337	370	4	g.	g.	PROPN
ejpam-2337	370	5	köthe	köthe	PROPN
ejpam-2337	370	6	.	.	PUNCT
ejpam-2337	370	7	topologische	topologische	PROPN
ejpam-2337	370	8	lineare	lineare	PROPN
ejpam-2337	370	9	räume	räume	PROPN
ejpam-2337	370	10	.	.	PUNCT
ejpam-2337	370	11	springer	springer	NOUN
ejpam-2337	370	12	,	,	PUNCT
ejpam-2337	370	13	1960	1960	NUM
ejpam-2337	370	14	.	.	PUNCT
ejpam-2337	371	1	[	[	X
ejpam-2337	371	2	15	15	NUM
ejpam-2337	371	3	]	]	X
ejpam-2337	371	4	j.r	j.r	PROPN
ejpam-2337	371	5	.	.	PROPN
ejpam-2337	371	6	lee	lee	PROPN
ejpam-2337	371	7	,	,	PUNCT
ejpam-2337	371	8	d.y	d.y	PROPN
ejpam-2337	371	9	.	.	PROPN
ejpam-2337	371	10	shin	shin	PROPN
ejpam-2337	371	11	,	,	PUNCT
ejpam-2337	371	12	and	and	CCONJ
ejpam-2337	371	13	c.	c.	PROPN
ejpam-2337	371	14	park	park	PROPN
ejpam-2337	371	15	.	.	PUNCT
ejpam-2337	372	1	hyers	hyer	NOUN
ejpam-2337	372	2	-	-	PUNCT
ejpam-2337	372	3	ulam	ulam	PROPN
ejpam-2337	372	4	stability	stability	NOUN
ejpam-2337	372	5	of	of	ADP
ejpam-2337	372	6	functional	functional	ADJ
ejpam-2337	372	7	equations	equation	NOUN
ejpam-2337	372	8	in	in	ADP
ejpam-2337	372	9	matrix	matrix	NOUN
ejpam-2337	372	10	normed	norme	VERB
ejpam-2337	372	11	spaces	space	NOUN
ejpam-2337	372	12	.	.	PUNCT
ejpam-2337	373	1	journal	journal	PROPN
ejpam-2337	373	2	of	of	ADP
ejpam-2337	373	3	inequalities	inequality	NOUN
ejpam-2337	373	4	and	and	CCONJ
ejpam-2337	373	5	applications	application	NOUN
ejpam-2337	373	6	,	,	PUNCT
ejpam-2337	373	7	22	22	NUM
ejpam-2337	373	8	,	,	PUNCT
ejpam-2337	373	9	2013	2013	NUM
ejpam-2337	373	10	.	.	PUNCT
ejpam-2337	374	1	[	[	X
ejpam-2337	374	2	16	16	NUM
ejpam-2337	374	3	]	]	X
ejpam-2337	374	4	e.	e.	PROPN
ejpam-2337	374	5	movahednia	movahednia	PROPN
ejpam-2337	374	6	.	.	PUNCT
ejpam-2337	375	1	fixed	fix	VERB
ejpam-2337	375	2	point	point	NOUN
ejpam-2337	375	3	and	and	CCONJ
ejpam-2337	375	4	generalized	generalized	ADJ
ejpam-2337	375	5	hyers	hyer	NOUN
ejpam-2337	375	6	-	-	PUNCT
ejpam-2337	375	7	ulam	ulam	ADJ
ejpam-2337	375	8	-	-	PUNCT
ejpam-2337	375	9	rassias	rassias	PROPN
ejpam-2337	375	10	stability	stability	NOUN
ejpam-2337	375	11	of	of	ADP
ejpam-2337	375	12	a	a	DET
ejpam-2337	375	13	quadratic	quadratic	ADJ
ejpam-2337	375	14	functional	functional	ADJ
ejpam-2337	375	15	equation	equation	NOUN
ejpam-2337	375	16	.	.	PUNCT
ejpam-2337	376	1	journal	journal	NOUN
ejpam-2337	376	2	of	of	ADP
ejpam-2337	376	3	mathematics	mathematics	PROPN
ejpam-2337	376	4	and	and	CCONJ
ejpam-2337	376	5	computer	computer	NOUN
ejpam-2337	376	6	science	science	NOUN
ejpam-2337	376	7	,	,	PUNCT
ejpam-2337	376	8	6:72–78	6:72–78	NUM
ejpam-2337	376	9	,	,	PUNCT
ejpam-2337	376	10	2013	2013	NUM
ejpam-2337	376	11	.	.	PUNCT
ejpam-2337	377	1	[	[	X
ejpam-2337	377	2	17	17	NUM
ejpam-2337	377	3	]	]	PUNCT
ejpam-2337	377	4	a.	a.	NOUN
ejpam-2337	377	5	pietsch	pietsch	PROPN
ejpam-2337	377	6	.	.	PUNCT
ejpam-2337	378	1	nuclear	nuclear	ADJ
ejpam-2337	378	2	locally	locally	ADV
ejpam-2337	378	3	convex	convex	PROPN
ejpam-2337	378	4	spaces	space	NOUN
ejpam-2337	378	5	.	.	PUNCT
ejpam-2337	379	1	ergebnisse	ergebnisse	PROPN
ejpam-2337	379	2	der	der	PROPN
ejpam-2337	379	3	mathematik	mathematik	PROPN
ejpam-2337	379	4	66	66	NUM
ejpam-2337	379	5	,	,	PUNCT
ejpam-2337	379	6	springer	springer	NOUN
ejpam-2337	379	7	,	,	PUNCT
ejpam-2337	379	8	1972	1972	NUM
ejpam-2337	379	9	.	.	PUNCT
ejpam-2337	380	1	[	[	X
ejpam-2337	380	2	18	18	NUM
ejpam-2337	380	3	]	]	PUNCT
ejpam-2337	380	4	th.m	th.m	PROPN
ejpam-2337	380	5	.	.	PUNCT
ejpam-2337	381	1	rassias	rassias	PROPN
ejpam-2337	381	2	.	.	PUNCT
ejpam-2337	382	1	on	on	ADP
ejpam-2337	382	2	the	the	DET
ejpam-2337	382	3	stability	stability	NOUN
ejpam-2337	382	4	of	of	ADP
ejpam-2337	382	5	the	the	DET
ejpam-2337	382	6	linear	linear	ADJ
ejpam-2337	382	7	mapping	mapping	NOUN
ejpam-2337	382	8	in	in	ADP
ejpam-2337	382	9	banach	banach	NOUN
ejpam-2337	382	10	spaces	space	NOUN
ejpam-2337	382	11	.	.	PUNCT
ejpam-2337	383	1	proceedings	proceeding	NOUN
ejpam-2337	383	2	of	of	ADP
ejpam-2337	383	3	american	american	PROPN
ejpam-2337	383	4	mathematical	mathematical	PROPN
ejpam-2337	383	5	society	society	NOUN
ejpam-2337	383	6	,	,	PUNCT
ejpam-2337	383	7	72:297–300	72:297–300	PROPN
ejpam-2337	383	8	,	,	PUNCT
ejpam-2337	383	9	1978	1978	NUM
ejpam-2337	383	10	.	.	PUNCT
ejpam-2337	384	1	[	[	X
ejpam-2337	384	2	19	19	NUM
ejpam-2337	384	3	]	]	PUNCT
ejpam-2337	384	4	k.	k.	PROPN
ejpam-2337	384	5	ravi	ravi	PROPN
ejpam-2337	384	6	and	and	CCONJ
ejpam-2337	384	7	b.v	b.v	PROPN
ejpam-2337	384	8	.	.	PROPN
ejpam-2337	384	9	senthil	senthil	PROPN
ejpam-2337	384	10	kumar	kumar	PROPN
ejpam-2337	384	11	.	.	PUNCT
ejpam-2337	385	1	ulam	ulam	PROPN
ejpam-2337	385	2	-	-	PUNCT
ejpam-2337	385	3	gavruta	gavruta	NOUN
ejpam-2337	385	4	-	-	PUNCT
ejpam-2337	385	5	rassias	rassias	PROPN
ejpam-2337	385	6	stability	stability	NOUN
ejpam-2337	385	7	of	of	ADP
ejpam-2337	385	8	rassias	rassias	PROPN
ejpam-2337	385	9	reciprocal	reciprocal	ADJ
ejpam-2337	385	10	functional	functional	ADJ
ejpam-2337	385	11	equation	equation	NOUN
ejpam-2337	385	12	.	.	PUNCT
ejpam-2337	386	1	global	global	ADJ
ejpam-2337	386	2	journal	journal	PROPN
ejpam-2337	386	3	of	of	ADP
ejpam-2337	386	4	applied	apply	VERB
ejpam-2337	386	5	mathematics	mathematic	NOUN
ejpam-2337	386	6	and	and	CCONJ
ejpam-2337	386	7	mathematical	mathematical	ADJ
ejpam-2337	386	8	sciences	science	NOUN
ejpam-2337	386	9	,	,	PUNCT
ejpam-2337	386	10	3(1	3(1	NUM
ejpam-2337	386	11	-	-	SYM
ejpam-2337	386	12	2):57–79	2):57–79	NUM
ejpam-2337	386	13	,	,	PUNCT
ejpam-2337	386	14	2010	2010	NUM
ejpam-2337	386	15	.	.	PUNCT
ejpam-2337	387	1	[	[	X
ejpam-2337	387	2	20	20	NUM
ejpam-2337	387	3	]	]	PUNCT
ejpam-2337	387	4	k.	k.	PROPN
ejpam-2337	387	5	ravi	ravi	PROPN
ejpam-2337	387	6	,	,	PUNCT
ejpam-2337	387	7	j.m	j.m	PROPN
ejpam-2337	387	8	.	.	PROPN
ejpam-2337	387	9	rassias	rassias	PROPN
ejpam-2337	387	10	,	,	PUNCT
ejpam-2337	387	11	and	and	CCONJ
ejpam-2337	387	12	b.v	b.v	PROPN
ejpam-2337	387	13	.	.	PROPN
ejpam-2337	387	14	senthil	senthil	PROPN
ejpam-2337	387	15	kumar	kumar	PROPN
ejpam-2337	387	16	.	.	PROPN
ejpam-2337	388	1	generalized	generalized	PROPN
ejpam-2337	388	2	hyers	hyers	PROPN
ejpam-2337	388	3	-	-	PUNCT
ejpam-2337	388	4	ulam	ulam	PROPN
ejpam-2337	388	5	stability	stability	NOUN
ejpam-2337	388	6	of	of	ADP
ejpam-2337	388	7	a	a	DET
ejpam-2337	388	8	2	2	NUM
ejpam-2337	388	9	-	-	PUNCT
ejpam-2337	388	10	variable	variable	ADJ
ejpam-2337	388	11	reciprocal	reciprocal	ADJ
ejpam-2337	388	12	functional	functional	ADJ
ejpam-2337	388	13	equation	equation	NOUN
ejpam-2337	388	14	.	.	PUNCT
ejpam-2337	389	1	bulletin	bulletin	NOUN
ejpam-2337	389	2	of	of	ADP
ejpam-2337	389	3	mathematical	mathematical	ADJ
ejpam-2337	389	4	analysis	analysis	NOUN
ejpam-2337	389	5	and	and	CCONJ
ejpam-2337	389	6	applications	application	NOUN
ejpam-2337	389	7	,	,	PUNCT
ejpam-2337	389	8	2(2):84–92	2(2):84–92	NUM
ejpam-2337	389	9	,	,	PUNCT
ejpam-2337	389	10	2010	2010	NUM
ejpam-2337	389	11	.	.	PUNCT
ejpam-2337	390	1	[	[	X
ejpam-2337	390	2	21	21	NUM
ejpam-2337	390	3	]	]	X
ejpam-2337	390	4	f.	f.	PROPN
ejpam-2337	390	5	skof	skof	PROPN
ejpam-2337	390	6	.	.	PUNCT
ejpam-2337	391	1	proprieta	proprieta	PROPN
ejpam-2337	391	2	locali	locali	PROPN
ejpam-2337	391	3	e	e	PROPN
ejpam-2337	391	4	approssimazione	approssimazione	PROPN
ejpam-2337	391	5	di	di	PROPN
ejpam-2337	391	6	operatori	operatori	PROPN
ejpam-2337	391	7	.	.	PROPN
ejpam-2337	391	8	rendiconti	rendiconti	PROPN
ejpam-2337	391	9	del	del	PROPN
ejpam-2337	391	10	seminario	seminario	NOUN
ejpam-2337	391	11	matematico	matematico	NOUN
ejpam-2337	391	12	e	e	PROPN
ejpam-2337	391	13	fisico	fisico	PROPN
ejpam-2337	391	14	di	di	X
ejpam-2337	391	15	milano	milano	PROPN
ejpam-2337	391	16	,	,	PUNCT
ejpam-2337	391	17	53:113–129	53:113–129	PROPN
ejpam-2337	391	18	,	,	PUNCT
ejpam-2337	391	19	1983	1983	NUM
ejpam-2337	391	20	.	.	PUNCT
ejpam-2337	392	1	[	[	X
ejpam-2337	392	2	22	22	NUM
ejpam-2337	392	3	]	]	X
ejpam-2337	392	4	s.m	s.m	PROPN
ejpam-2337	392	5	.	.	PUNCT
ejpam-2337	392	6	ulam	ulam	PROPN
ejpam-2337	392	7	.	.	PUNCT
ejpam-2337	393	1	problems	problem	NOUN
ejpam-2337	393	2	in	in	ADP
ejpam-2337	393	3	modern	modern	ADJ
ejpam-2337	393	4	mathematics	mathematic	NOUN
ejpam-2337	393	5	,	,	PUNCT
ejpam-2337	393	6	chapter	chapter	NOUN
ejpam-2337	393	7	vi	vi	PROPN
ejpam-2337	393	8	.	.	PUNCT
ejpam-2337	393	9	wiley	wiley	PROPN
ejpam-2337	393	10	-	-	PUNCT
ejpam-2337	393	11	interscience	interscience	PROPN
ejpam-2337	393	12	,	,	PUNCT
ejpam-2337	393	13	new	new	PROPN
ejpam-2337	393	14	york	york	PROPN
ejpam-2337	393	15	,	,	PUNCT
ejpam-2337	393	16	1964	1964	NUM
ejpam-2337	393	17	.	.	PUNCT