id	sid	tid	token	lemma	pos
ejpam-2967	1	1	european	european	PROPN
ejpam-2967	1	2	journal	journal	PROPN
ejpam-2967	1	3	of	of	ADP
ejpam-2967	1	4	pure	pure	ADJ
ejpam-2967	1	5	and	and	CCONJ
ejpam-2967	1	6	applied	apply	VERB
ejpam-2967	1	7	mathematics	mathematic	NOUN
ejpam-2967	1	8	vol	vol	NOUN
ejpam-2967	1	9	.	.	PROPN
ejpam-2967	2	1	10	10	NUM
ejpam-2967	2	2	,	,	PUNCT
ejpam-2967	2	3	no	no	INTJ
ejpam-2967	2	4	.	.	NOUN
ejpam-2967	2	5	3	3	NUM
ejpam-2967	2	6	,	,	PUNCT
ejpam-2967	2	7	2017	2017	NUM
ejpam-2967	2	8	,	,	PUNCT
ejpam-2967	2	9	488	488	NUM
ejpam-2967	2	10	-	-	SYM
ejpam-2967	2	11	494	494	NUM
ejpam-2967	2	12	issn	issn	PROPN
ejpam-2967	2	13	1307	1307	NUM
ejpam-2967	2	14	-	-	SYM
ejpam-2967	2	15	5543	5543	NUM
ejpam-2967	2	16	–	–	PUNCT
ejpam-2967	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2967	2	18	published	publish	VERB
ejpam-2967	2	19	by	by	ADP
ejpam-2967	2	20	new	new	PROPN
ejpam-2967	2	21	york	york	PROPN
ejpam-2967	2	22	business	business	PROPN
ejpam-2967	2	23	global	global	PROPN
ejpam-2967	2	24	some	some	DET
ejpam-2967	2	25	results	result	NOUN
ejpam-2967	2	26	on	on	ADP
ejpam-2967	2	27	real	real	ADV
ejpam-2967	2	28	valued	value	VERB
ejpam-2967	2	29	continuous	continuous	ADJ
ejpam-2967	2	30	functions	function	NOUN
ejpam-2967	2	31	on	on	ADP
ejpam-2967	2	32	an	an	DET
ejpam-2967	2	33	interval	interval	NOUN
ejpam-2967	2	34	prasanna	prasanna	NOUN
ejpam-2967	2	35	kumar1,2	kumar1,2	PROPN
ejpam-2967	2	36	1	1	NUM
ejpam-2967	2	37	department	department	NOUN
ejpam-2967	2	38	of	of	ADP
ejpam-2967	2	39	mathematics	mathematics	PROPN
ejpam-2967	2	40	,	,	PUNCT
ejpam-2967	2	41	birla	birla	PROPN
ejpam-2967	2	42	institute	institute	PROPN
ejpam-2967	2	43	of	of	ADP
ejpam-2967	2	44	technology	technology	PROPN
ejpam-2967	2	45	and	and	CCONJ
ejpam-2967	2	46	science	science	NOUN
ejpam-2967	2	47	pilani	pilani	NOUN
ejpam-2967	2	48	,	,	PUNCT
ejpam-2967	2	49	k	k	PROPN
ejpam-2967	2	50	k	k	PROPN
ejpam-2967	2	51	birla	birla	PROPN
ejpam-2967	2	52	goa	goa	PROPN
ejpam-2967	2	53	campus	campus	PROPN
ejpam-2967	2	54	,	,	PUNCT
ejpam-2967	2	55	india	india	PROPN
ejpam-2967	2	56	2	2	NUM
ejpam-2967	2	57	department	department	NOUN
ejpam-2967	2	58	of	of	ADP
ejpam-2967	2	59	mathematics	mathematic	NOUN
ejpam-2967	2	60	and	and	CCONJ
ejpam-2967	2	61	statistics	statistic	NOUN
ejpam-2967	2	62	,	,	PUNCT
ejpam-2967	2	63	auburn	auburn	PROPN
ejpam-2967	2	64	university	university	PROPN
ejpam-2967	2	65	,	,	PUNCT
ejpam-2967	2	66	usa	usa	PROPN
ejpam-2967	2	67	abstract	abstract	NOUN
ejpam-2967	2	68	.	.	PUNCT
ejpam-2967	3	1	in	in	ADP
ejpam-2967	3	2	this	this	DET
ejpam-2967	3	3	paper	paper	NOUN
ejpam-2967	3	4	,	,	PUNCT
ejpam-2967	3	5	results	result	VERB
ejpam-2967	3	6	mainly	mainly	ADV
ejpam-2967	3	7	on	on	ADP
ejpam-2967	3	8	the	the	DET
ejpam-2967	3	9	structures	structure	NOUN
ejpam-2967	3	10	of	of	ADP
ejpam-2967	3	11	some	some	DET
ejpam-2967	3	12	special	special	ADJ
ejpam-2967	3	13	class	class	NOUN
ejpam-2967	3	14	of	of	ADP
ejpam-2967	3	15	real	real	ADJ
ejpam-2967	3	16	valued	value	VERB
ejpam-2967	3	17	functions	function	NOUN
ejpam-2967	3	18	on	on	ADP
ejpam-2967	3	19	an	an	DET
ejpam-2967	3	20	interval	interval	NOUN
ejpam-2967	3	21	are	be	AUX
ejpam-2967	3	22	discussed	discuss	VERB
ejpam-2967	3	23	.	.	PUNCT
ejpam-2967	4	1	another	another	DET
ejpam-2967	4	2	significant	significant	ADJ
ejpam-2967	4	3	result	result	NOUN
ejpam-2967	4	4	is	be	AUX
ejpam-2967	4	5	also	also	ADV
ejpam-2967	4	6	established	establish	VERB
ejpam-2967	4	7	.	.	PUNCT
ejpam-2967	5	1	these	these	DET
ejpam-2967	5	2	results	result	NOUN
ejpam-2967	5	3	have	have	AUX
ejpam-2967	5	4	been	be	AUX
ejpam-2967	5	5	derived	derive	VERB
ejpam-2967	5	6	and	and	CCONJ
ejpam-2967	5	7	presented	present	VERB
ejpam-2967	5	8	mainly	mainly	ADV
ejpam-2967	5	9	in	in	ADP
ejpam-2967	5	10	the	the	DET
ejpam-2967	5	11	perspective	perspective	NOUN
ejpam-2967	5	12	of	of	ADP
ejpam-2967	5	13	study	study	NOUN
ejpam-2967	5	14	of	of	ADP
ejpam-2967	5	15	relations	relation	NOUN
ejpam-2967	5	16	between	between	ADP
ejpam-2967	5	17	real	real	ADJ
ejpam-2967	5	18	valued	value	VERB
ejpam-2967	5	19	functions	function	NOUN
ejpam-2967	5	20	and	and	CCONJ
ejpam-2967	5	21	their	their	PRON
ejpam-2967	5	22	derivatives	derivative	NOUN
ejpam-2967	5	23	.	.	PUNCT
ejpam-2967	6	1	the	the	DET
ejpam-2967	6	2	results	result	NOUN
ejpam-2967	6	3	are	be	AUX
ejpam-2967	6	4	very	very	ADV
ejpam-2967	6	5	fundamental	fundamental	ADJ
ejpam-2967	6	6	in	in	ADP
ejpam-2967	6	7	nature	nature	NOUN
ejpam-2967	6	8	and	and	CCONJ
ejpam-2967	6	9	may	may	AUX
ejpam-2967	6	10	be	be	AUX
ejpam-2967	6	11	useful	useful	ADJ
ejpam-2967	6	12	in	in	ADP
ejpam-2967	6	13	the	the	DET
ejpam-2967	6	14	next	next	ADJ
ejpam-2967	6	15	course	course	NOUN
ejpam-2967	6	16	of	of	ADP
ejpam-2967	6	17	generalizations	generalization	NOUN
ejpam-2967	6	18	or	or	CCONJ
ejpam-2967	6	19	improvements	improvement	NOUN
ejpam-2967	6	20	in	in	ADP
ejpam-2967	6	21	this	this	DET
ejpam-2967	6	22	direction	direction	NOUN
ejpam-2967	6	23	.	.	PUNCT
ejpam-2967	7	1	2010	2010	NUM
ejpam-2967	7	2	mathematics	mathematic	NOUN
ejpam-2967	7	3	subject	subject	NOUN
ejpam-2967	7	4	classifications	classification	NOUN
ejpam-2967	7	5	:	:	PUNCT
ejpam-2967	7	6	26a24	26a24	NUM
ejpam-2967	7	7	key	key	ADJ
ejpam-2967	7	8	words	word	NOUN
ejpam-2967	7	9	and	and	CCONJ
ejpam-2967	7	10	phrases	phrase	NOUN
ejpam-2967	7	11	:	:	PUNCT
ejpam-2967	7	12	real	real	ADJ
ejpam-2967	7	13	valued	value	VERB
ejpam-2967	7	14	function	function	NOUN
ejpam-2967	7	15	,	,	PUNCT
ejpam-2967	7	16	continuity	continuity	NOUN
ejpam-2967	7	17	,	,	PUNCT
ejpam-2967	7	18	derivative	derivative	ADJ
ejpam-2967	7	19	1	1	NUM
ejpam-2967	7	20	.	.	PUNCT
ejpam-2967	7	21	introduction	introduction	NOUN
ejpam-2967	7	22	the	the	DET
ejpam-2967	7	23	notion	notion	NOUN
ejpam-2967	7	24	of	of	ADP
ejpam-2967	7	25	derivative	derivative	NOUN
ejpam-2967	7	26	of	of	ADP
ejpam-2967	7	27	functions	function	NOUN
ejpam-2967	7	28	is	be	AUX
ejpam-2967	7	29	a	a	DET
ejpam-2967	7	30	supreme	supreme	ADJ
ejpam-2967	7	31	fundamental	fundamental	ADJ
ejpam-2967	7	32	concept	concept	NOUN
ejpam-2967	7	33	in	in	ADP
ejpam-2967	7	34	the	the	DET
ejpam-2967	7	35	differential	differential	ADJ
ejpam-2967	7	36	and	and	CCONJ
ejpam-2967	7	37	integral	integral	ADJ
ejpam-2967	7	38	calculus	calculus	NOUN
ejpam-2967	7	39	and	and	CCONJ
ejpam-2967	7	40	it	it	PRON
ejpam-2967	7	41	is	be	AUX
ejpam-2967	7	42	foundational	foundational	ADJ
ejpam-2967	7	43	for	for	ADP
ejpam-2967	7	44	other	other	ADJ
ejpam-2967	7	45	powerful	powerful	ADJ
ejpam-2967	7	46	branches	branch	NOUN
ejpam-2967	7	47	of	of	ADP
ejpam-2967	7	48	mathematics	mathematic	NOUN
ejpam-2967	7	49	like	like	ADP
ejpam-2967	7	50	ordinary	ordinary	ADJ
ejpam-2967	7	51	and	and	CCONJ
ejpam-2967	7	52	partial	partial	ADJ
ejpam-2967	7	53	differential	differential	NOUN
ejpam-2967	7	54	equations	equation	NOUN
ejpam-2967	7	55	,	,	PUNCT
ejpam-2967	7	56	numerical	numerical	ADJ
ejpam-2967	7	57	analysis	analysis	NOUN
ejpam-2967	7	58	,	,	PUNCT
ejpam-2967	7	59	dynamical	dynamical	ADJ
ejpam-2967	7	60	systems	system	NOUN
ejpam-2967	7	61	,	,	PUNCT
ejpam-2967	7	62	differential	differential	ADJ
ejpam-2967	7	63	geometry	geometry	NOUN
ejpam-2967	7	64	etc	etc	X
ejpam-2967	7	65	.	.	X
ejpam-2967	8	1	that	that	PRON
ejpam-2967	8	2	is	be	AUX
ejpam-2967	8	3	why	why	SCONJ
ejpam-2967	8	4	the	the	DET
ejpam-2967	8	5	area	area	NOUN
ejpam-2967	8	6	of	of	ADP
ejpam-2967	8	7	structural	structural	ADJ
ejpam-2967	8	8	study	study	NOUN
ejpam-2967	8	9	of	of	ADP
ejpam-2967	8	10	real	real	ADJ
ejpam-2967	8	11	valued	value	VERB
ejpam-2967	8	12	functions	function	NOUN
ejpam-2967	8	13	is	be	AUX
ejpam-2967	8	14	an	an	DET
ejpam-2967	8	15	interesting	interesting	ADJ
ejpam-2967	8	16	as	as	ADV
ejpam-2967	8	17	well	well	ADV
ejpam-2967	8	18	as	as	ADP
ejpam-2967	8	19	important	important	ADJ
ejpam-2967	8	20	branch	branch	NOUN
ejpam-2967	8	21	of	of	ADP
ejpam-2967	8	22	real	real	ADJ
ejpam-2967	8	23	analysis	analysis	NOUN
ejpam-2967	8	24	.	.	PUNCT
ejpam-2967	9	1	results	result	NOUN
ejpam-2967	9	2	in	in	ADP
ejpam-2967	9	3	this	this	DET
ejpam-2967	9	4	direction	direction	NOUN
ejpam-2967	9	5	involve	involve	VERB
ejpam-2967	9	6	various	various	ADJ
ejpam-2967	9	7	differentiability	differentiability	NOUN
ejpam-2967	9	8	structures	structure	NOUN
ejpam-2967	9	9	on	on	ADP
ejpam-2967	9	10	corresponding	correspond	VERB
ejpam-2967	9	11	domains	domain	NOUN
ejpam-2967	9	12	,	,	PUNCT
ejpam-2967	9	13	and	and	CCONJ
ejpam-2967	9	14	for	for	ADP
ejpam-2967	9	15	different	different	ADJ
ejpam-2967	9	16	class	class	NOUN
ejpam-2967	9	17	of	of	ADP
ejpam-2967	9	18	real	real	ADJ
ejpam-2967	9	19	valued	value	VERB
ejpam-2967	9	20	functions	function	NOUN
ejpam-2967	9	21	.	.	PUNCT
ejpam-2967	10	1	differentiability	differentiability	NOUN
ejpam-2967	10	2	and	and	CCONJ
ejpam-2967	10	3	continuity	continuity	NOUN
ejpam-2967	10	4	properties	property	NOUN
ejpam-2967	10	5	of	of	ADP
ejpam-2967	10	6	real	real	ADJ
ejpam-2967	10	7	valued	value	VERB
ejpam-2967	10	8	functions	function	NOUN
ejpam-2967	10	9	of	of	ADP
ejpam-2967	10	10	real	real	ADJ
ejpam-2967	10	11	variables	variable	NOUN
ejpam-2967	10	12	have	have	AUX
ejpam-2967	10	13	been	be	AUX
ejpam-2967	10	14	studied	study	VERB
ejpam-2967	10	15	vastly	vastly	ADV
ejpam-2967	10	16	.	.	PUNCT
ejpam-2967	11	1	for	for	ADP
ejpam-2967	11	2	the	the	DET
ejpam-2967	11	3	primary	primary	ADJ
ejpam-2967	11	4	reading	reading	NOUN
ejpam-2967	11	5	,	,	PUNCT
ejpam-2967	11	6	one	one	PRON
ejpam-2967	11	7	can	can	AUX
ejpam-2967	11	8	refer	refer	VERB
ejpam-2967	11	9	[	[	NOUN
ejpam-2967	11	10	2	2	NUM
ejpam-2967	11	11	]	]	PUNCT
ejpam-2967	11	12	,	,	PUNCT
ejpam-2967	11	13	and	and	CCONJ
ejpam-2967	11	14	[	[	X
ejpam-2967	11	15	3	3	NUM
ejpam-2967	11	16	]	]	PUNCT
ejpam-2967	11	17	.	.	PUNCT
ejpam-2967	12	1	further	further	ADJ
ejpam-2967	12	2	reading	reading	NOUN
ejpam-2967	12	3	can	can	AUX
ejpam-2967	12	4	be	be	AUX
ejpam-2967	12	5	done	do	VERB
ejpam-2967	12	6	with	with	ADP
ejpam-2967	12	7	[	[	X
ejpam-2967	12	8	4	4	NUM
ejpam-2967	12	9	]	]	PUNCT
ejpam-2967	12	10	,	,	PUNCT
ejpam-2967	12	11	and	and	CCONJ
ejpam-2967	12	12	[	[	X
ejpam-2967	12	13	1	1	NUM
ejpam-2967	12	14	]	]	PUNCT
ejpam-2967	12	15	.	.	PUNCT
ejpam-2967	13	1	a	a	DET
ejpam-2967	13	2	new	new	ADJ
ejpam-2967	13	3	approaches	approach	NOUN
ejpam-2967	13	4	to	to	ADP
ejpam-2967	13	5	differential	differential	ADJ
ejpam-2967	13	6	calculus	calculus	NOUN
ejpam-2967	13	7	based	base	VERB
ejpam-2967	13	8	on	on	ADP
ejpam-2967	13	9	mathematical	mathematical	ADJ
ejpam-2967	13	10	structures	structure	NOUN
ejpam-2967	13	11	are	be	AUX
ejpam-2967	13	12	always	always	ADV
ejpam-2967	13	13	being	be	AUX
ejpam-2967	13	14	tried	try	VERB
ejpam-2967	13	15	across	across	ADP
ejpam-2967	13	16	the	the	DET
ejpam-2967	13	17	world	world	NOUN
ejpam-2967	13	18	in	in	ADP
ejpam-2967	13	19	different	different	ADJ
ejpam-2967	13	20	directions	direction	NOUN
ejpam-2967	13	21	and	and	CCONJ
ejpam-2967	13	22	methods	method	NOUN
ejpam-2967	13	23	.	.	PUNCT
ejpam-2967	14	1	this	this	PRON
ejpam-2967	14	2	will	will	AUX
ejpam-2967	14	3	lead	lead	VERB
ejpam-2967	14	4	to	to	ADP
ejpam-2967	14	5	presenting	present	VERB
ejpam-2967	14	6	continuous	continuous	ADJ
ejpam-2967	14	7	or	or	CCONJ
ejpam-2967	14	8	differentiable	differentiable	ADJ
ejpam-2967	14	9	functions	function	NOUN
ejpam-2967	14	10	and	and	CCONJ
ejpam-2967	14	11	solving	solve	VERB
ejpam-2967	14	12	differential	differential	NOUN
ejpam-2967	14	13	or	or	CCONJ
ejpam-2967	14	14	integral	integral	ADJ
ejpam-2967	14	15	equations	equation	NOUN
ejpam-2967	14	16	.	.	PUNCT
ejpam-2967	15	1	the	the	DET
ejpam-2967	15	2	concept	concept	NOUN
ejpam-2967	15	3	of	of	ADP
ejpam-2967	15	4	derivative	derivative	NOUN
ejpam-2967	15	5	of	of	ADP
ejpam-2967	15	6	a	a	DET
ejpam-2967	15	7	real	real	ADV
ejpam-2967	15	8	-	-	PUNCT
ejpam-2967	15	9	valued	value	VERB
ejpam-2967	15	10	function	function	NOUN
ejpam-2967	15	11	depends	depend	VERB
ejpam-2967	15	12	on	on	ADP
ejpam-2967	15	13	the	the	DET
ejpam-2967	15	14	choice	choice	NOUN
ejpam-2967	15	15	of	of	ADP
ejpam-2967	15	16	the	the	DET
ejpam-2967	15	17	coordinate	coordinate	NOUN
ejpam-2967	15	18	system	system	NOUN
ejpam-2967	15	19	used	use	VERB
ejpam-2967	15	20	.	.	PUNCT
ejpam-2967	16	1	for	for	ADP
ejpam-2967	16	2	functions	function	NOUN
ejpam-2967	16	3	on	on	ADP
ejpam-2967	16	4	finite	finite	ADJ
ejpam-2967	16	5	euclidean	euclidean	ADJ
ejpam-2967	16	6	spaces	space	NOUN
ejpam-2967	16	7	,	,	PUNCT
ejpam-2967	16	8	the	the	DET
ejpam-2967	16	9	derivative	derivative	NOUN
ejpam-2967	16	10	is	be	AUX
ejpam-2967	16	11	an	an	DET
ejpam-2967	16	12	element	element	NOUN
ejpam-2967	16	13	of	of	ADP
ejpam-2967	16	14	a	a	DET
ejpam-2967	16	15	countably	countably	ADV
ejpam-2967	16	16	based	base	VERB
ejpam-2967	16	17	continuous	continuous	ADJ
ejpam-2967	16	18	domain	domain	NOUN
ejpam-2967	16	19	which	which	PRON
ejpam-2967	16	20	can	can	AUX
ejpam-2967	16	21	be	be	AUX
ejpam-2967	16	22	given	give	VERB
ejpam-2967	16	23	an	an	DET
ejpam-2967	16	24	effective	effective	ADJ
ejpam-2967	16	25	structure	structure	NOUN
ejpam-2967	16	26	that	that	PRON
ejpam-2967	16	27	characterizes	characterize	VERB
ejpam-2967	16	28	various	various	ADJ
ejpam-2967	16	29	other	other	ADJ
ejpam-2967	16	30	properties	property	NOUN
ejpam-2967	16	31	like	like	ADP
ejpam-2967	16	32	fixed	fix	VERB
ejpam-2967	16	33	points	point	NOUN
ejpam-2967	16	34	,	,	PUNCT
ejpam-2967	16	35	additivity	additivity	NOUN
ejpam-2967	16	36	or	or	CCONJ
ejpam-2967	16	37	any	any	DET
ejpam-2967	16	38	other	other	ADJ
ejpam-2967	16	39	special	special	ADJ
ejpam-2967	16	40	properties	property	NOUN
ejpam-2967	16	41	of	of	ADP
ejpam-2967	16	42	functions	function	NOUN
ejpam-2967	16	43	.	.	PUNCT
ejpam-2967	17	1	email	email	NOUN
ejpam-2967	17	2	address	address	NOUN
ejpam-2967	17	3	:	:	PUNCT
ejpam-2967	17	4	prasannakornaya@rediffmail.com	prasannakornaya@rediffmail.com	X
ejpam-2967	17	5	p.kumar	p.kumar	NOUN
ejpam-2967	17	6	)	)	PUNCT
ejpam-2967	17	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2967	18	1	488	488	NUM
ejpam-2967	19	1	c	c	X
ejpam-2967	19	2	©	©	PROPN
ejpam-2967	19	3	2017	2017	NUM
ejpam-2967	19	4	ejpam	ejpam	VERB
ejpam-2967	19	5	all	all	DET
ejpam-2967	19	6	rights	right	NOUN
ejpam-2967	19	7	reserved	reserve	VERB
ejpam-2967	19	8	.	.	PUNCT
ejpam-2967	20	1	prasanna	prasanna	PROPN
ejpam-2967	20	2	kumar	kumar	PROPN
ejpam-2967	20	3	/	/	SYM
ejpam-2967	20	4	eur	eur	PROPN
ejpam-2967	20	5	.	.	PUNCT
ejpam-2967	21	1	j.	j.	PROPN
ejpam-2967	21	2	pure	pure	PROPN
ejpam-2967	21	3	appl	appl	PROPN
ejpam-2967	21	4	.	.	PROPN
ejpam-2967	21	5	math	math	PROPN
ejpam-2967	21	6	,	,	PUNCT
ejpam-2967	21	7	10	10	NUM
ejpam-2967	21	8	(	(	PUNCT
ejpam-2967	21	9	3	3	NUM
ejpam-2967	21	10	)	)	PUNCT
ejpam-2967	21	11	(	(	PUNCT
ejpam-2967	21	12	2017	2017	NUM
ejpam-2967	21	13	)	)	PUNCT
ejpam-2967	21	14	,	,	PUNCT
ejpam-2967	21	15	488	488	NUM
ejpam-2967	21	16	-	-	SYM
ejpam-2967	21	17	494	494	NUM
ejpam-2967	21	18	489	489	NUM
ejpam-2967	21	19	results	result	NOUN
ejpam-2967	21	20	of	of	ADP
ejpam-2967	21	21	the	the	DET
ejpam-2967	21	22	kind	kind	NOUN
ejpam-2967	21	23	to	to	PART
ejpam-2967	21	24	be	be	AUX
ejpam-2967	21	25	discussed	discuss	VERB
ejpam-2967	21	26	in	in	ADP
ejpam-2967	21	27	this	this	DET
ejpam-2967	21	28	article	article	NOUN
ejpam-2967	21	29	are	be	AUX
ejpam-2967	21	30	considered	consider	VERB
ejpam-2967	21	31	to	to	PART
ejpam-2967	21	32	be	be	AUX
ejpam-2967	21	33	very	very	ADV
ejpam-2967	21	34	fundamental	fundamental	ADJ
ejpam-2967	21	35	in	in	ADP
ejpam-2967	21	36	nature	nature	NOUN
ejpam-2967	21	37	and	and	CCONJ
ejpam-2967	21	38	may	may	AUX
ejpam-2967	21	39	be	be	AUX
ejpam-2967	21	40	useful	useful	ADJ
ejpam-2967	21	41	in	in	ADP
ejpam-2967	21	42	pure	pure	ADJ
ejpam-2967	21	43	and	and	CCONJ
ejpam-2967	21	44	applied	applied	ADJ
ejpam-2967	21	45	sciences	science	NOUN
ejpam-2967	21	46	.	.	PUNCT
ejpam-2967	22	1	all	all	DET
ejpam-2967	22	2	the	the	DET
ejpam-2967	22	3	results	result	NOUN
ejpam-2967	22	4	are	be	AUX
ejpam-2967	22	5	principally	principally	ADV
ejpam-2967	22	6	from	from	ADP
ejpam-2967	22	7	the	the	DET
ejpam-2967	22	8	point	point	NOUN
ejpam-2967	22	9	of	of	ADP
ejpam-2967	22	10	view	view	NOUN
ejpam-2967	22	11	of	of	ADP
ejpam-2967	22	12	study	study	NOUN
ejpam-2967	22	13	on	on	ADP
ejpam-2967	22	14	the	the	DET
ejpam-2967	22	15	characteristics	characteristic	NOUN
ejpam-2967	22	16	of	of	ADP
ejpam-2967	22	17	some	some	DET
ejpam-2967	22	18	special	special	ADJ
ejpam-2967	22	19	class	class	NOUN
ejpam-2967	22	20	of	of	ADP
ejpam-2967	22	21	real	real	ADJ
ejpam-2967	22	22	valued	value	VERB
ejpam-2967	22	23	functions	function	NOUN
ejpam-2967	22	24	,	,	PUNCT
ejpam-2967	22	25	and	and	CCONJ
ejpam-2967	22	26	the	the	DET
ejpam-2967	22	27	additional	additional	ADJ
ejpam-2967	22	28	properties	property	NOUN
ejpam-2967	22	29	they	they	PRON
ejpam-2967	22	30	enjoyed	enjoy	VERB
ejpam-2967	22	31	in	in	ADP
ejpam-2967	22	32	.	.	PUNCT
ejpam-2967	23	1	let	let	VERB
ejpam-2967	23	2	us	we	PRON
ejpam-2967	23	3	present	present	VERB
ejpam-2967	23	4	the	the	DET
ejpam-2967	23	5	results	result	NOUN
ejpam-2967	23	6	,	,	PUNCT
ejpam-2967	23	7	which	which	PRON
ejpam-2967	23	8	may	may	AUX
ejpam-2967	23	9	be	be	AUX
ejpam-2967	23	10	given	give	VERB
ejpam-2967	23	11	in	in	ADP
ejpam-2967	23	12	more	more	ADJ
ejpam-2967	23	13	generalized	generalized	ADJ
ejpam-2967	23	14	settings	setting	NOUN
ejpam-2967	23	15	in	in	ADP
ejpam-2967	23	16	the	the	DET
ejpam-2967	23	17	coming	come	VERB
ejpam-2967	23	18	years	year	NOUN
ejpam-2967	23	19	.	.	PUNCT
ejpam-2967	24	1	2	2	X
ejpam-2967	24	2	.	.	NUM
ejpam-2967	24	3	theorems	theorem	NOUN
ejpam-2967	24	4	and	and	CCONJ
ejpam-2967	24	5	proofs	proof	NOUN
ejpam-2967	24	6	based	base	VERB
ejpam-2967	24	7	on	on	ADP
ejpam-2967	24	8	the	the	DET
ejpam-2967	24	9	theoretic	theoretic	ADJ
ejpam-2967	24	10	framework	framework	NOUN
ejpam-2967	24	11	for	for	ADP
ejpam-2967	24	12	differential	differential	ADJ
ejpam-2967	24	13	calculus	calculus	NOUN
ejpam-2967	24	14	,	,	PUNCT
ejpam-2967	24	15	one	one	PRON
ejpam-2967	24	16	can	can	AUX
ejpam-2967	24	17	embark	embark	VERB
ejpam-2967	24	18	on	on	ADP
ejpam-2967	24	19	the	the	DET
ejpam-2967	24	20	task	task	NOUN
ejpam-2967	24	21	of	of	ADP
ejpam-2967	24	22	constructing	construct	VERB
ejpam-2967	24	23	consequences	consequence	NOUN
ejpam-2967	24	24	of	of	ADP
ejpam-2967	24	25	mean	mean	ADJ
ejpam-2967	24	26	value	value	NOUN
ejpam-2967	24	27	theorems	theorem	NOUN
ejpam-2967	24	28	for	for	ADP
ejpam-2967	24	29	subspace	subspace	NOUN
ejpam-2967	24	30	of	of	ADP
ejpam-2967	24	31	euclidean	euclidean	ADJ
ejpam-2967	24	32	spaces	space	NOUN
ejpam-2967	24	33	,	,	PUNCT
ejpam-2967	24	34	which	which	PRON
ejpam-2967	24	35	would	would	AUX
ejpam-2967	24	36	extend	extend	VERB
ejpam-2967	24	37	the	the	DET
ejpam-2967	24	38	set	set	NOUN
ejpam-2967	24	39	-	-	PUNCT
ejpam-2967	24	40	theoretic	theoretic	NOUN
ejpam-2967	24	41	model	model	NOUN
ejpam-2967	24	42	for	for	ADP
ejpam-2967	24	43	computational	computational	ADJ
ejpam-2967	24	44	geometry	geometry	NOUN
ejpam-2967	24	45	in	in	ADP
ejpam-2967	24	46	solving	solving	NOUN
ejpam-2967	24	47	models	model	NOUN
ejpam-2967	24	48	carved	carve	VERB
ejpam-2967	24	49	out	out	ADP
ejpam-2967	24	50	of	of	ADP
ejpam-2967	24	51	the	the	DET
ejpam-2967	24	52	physical	physical	ADJ
ejpam-2967	24	53	problems	problem	NOUN
ejpam-2967	24	54	.	.	PUNCT
ejpam-2967	25	1	in	in	ADP
ejpam-2967	25	2	this	this	DET
ejpam-2967	25	3	context	context	NOUN
ejpam-2967	25	4	,	,	PUNCT
ejpam-2967	25	5	it	it	PRON
ejpam-2967	25	6	is	be	AUX
ejpam-2967	25	7	quite	quite	ADV
ejpam-2967	25	8	natural	natural	ADJ
ejpam-2967	25	9	to	to	PART
ejpam-2967	25	10	have	have	VERB
ejpam-2967	25	11	a	a	DET
ejpam-2967	25	12	class	class	NOUN
ejpam-2967	25	13	of	of	ADP
ejpam-2967	25	14	real	real	ADV
ejpam-2967	25	15	valued	value	VERB
ejpam-2967	25	16	continuous	continuous	ADJ
ejpam-2967	25	17	functions	function	NOUN
ejpam-2967	25	18	defined	define	VERB
ejpam-2967	25	19	on	on	ADP
ejpam-2967	25	20	an	an	DET
ejpam-2967	25	21	interval	interval	NOUN
ejpam-2967	25	22	i	i	PRON
ejpam-2967	25	23	relating	relate	VERB
ejpam-2967	25	24	its	its	PRON
ejpam-2967	25	25	extreme	extreme	ADJ
ejpam-2967	25	26	values	value	NOUN
ejpam-2967	25	27	.	.	PUNCT
ejpam-2967	26	1	it	it	PRON
ejpam-2967	26	2	is	be	AUX
ejpam-2967	26	3	equally	equally	ADV
ejpam-2967	26	4	interesting	interesting	ADJ
ejpam-2967	26	5	to	to	PART
ejpam-2967	26	6	link	link	VERB
ejpam-2967	26	7	this	this	DET
ejpam-2967	26	8	structure	structure	NOUN
ejpam-2967	26	9	with	with	ADP
ejpam-2967	26	10	some	some	DET
ejpam-2967	26	11	restricted	restricted	ADJ
ejpam-2967	26	12	class	class	NOUN
ejpam-2967	26	13	of	of	ADP
ejpam-2967	26	14	continuous	continuous	ADJ
ejpam-2967	26	15	functions	function	NOUN
ejpam-2967	26	16	on	on	ADP
ejpam-2967	26	17	i.	i.	NOUN
ejpam-2967	26	18	we	we	PRON
ejpam-2967	26	19	will	will	AUX
ejpam-2967	26	20	first	first	ADV
ejpam-2967	26	21	derive	derive	VERB
ejpam-2967	26	22	a	a	DET
ejpam-2967	26	23	result	result	NOUN
ejpam-2967	26	24	as	as	ADP
ejpam-2967	26	25	a	a	DET
ejpam-2967	26	26	consequence	consequence	NOUN
ejpam-2967	26	27	of	of	ADP
ejpam-2967	26	28	intermediate	intermediate	ADJ
ejpam-2967	26	29	value	value	NOUN
ejpam-2967	26	30	theorem	theorem	VERB
ejpam-2967	26	31	.	.	PUNCT
ejpam-2967	26	32	theorem	theorem	NOUN
ejpam-2967	26	33	1	1	NUM
ejpam-2967	26	34	.	.	PUNCT
ejpam-2967	27	1	let	let	VERB
ejpam-2967	27	2	f	f	PRON
ejpam-2967	27	3	be	be	AUX
ejpam-2967	27	4	a	a	DET
ejpam-2967	27	5	continuous	continuous	ADJ
ejpam-2967	27	6	real	real	ADJ
ejpam-2967	27	7	valued	value	VERB
ejpam-2967	27	8	function	function	NOUN
ejpam-2967	27	9	on	on	ADP
ejpam-2967	27	10	(	(	PUNCT
ejpam-2967	27	11	0	0	NUM
ejpam-2967	27	12	,	,	PUNCT
ejpam-2967	27	13	1	1	NUM
ejpam-2967	27	14	)	)	PUNCT
ejpam-2967	27	15	such	such	ADJ
ejpam-2967	27	16	that	that	PRON
ejpam-2967	27	17	max	max	PROPN
ejpam-2967	27	18	x∈(0,1	x∈(0,1	ADV
ejpam-2967	27	19	)	)	PUNCT
ejpam-2967	27	20	f(x	f(x	PROPN
ejpam-2967	27	21	)	)	PUNCT
ejpam-2967	27	22	>	>	X
ejpam-2967	27	23	0	0	NUM
ejpam-2967	27	24	,	,	PUNCT
ejpam-2967	28	1	min	min	NOUN
ejpam-2967	28	2	x∈(0,1	x∈(0,1	ADV
ejpam-2967	28	3	)	)	PUNCT
ejpam-2967	28	4	f(x	f(x	PROPN
ejpam-2967	28	5	)	)	PUNCT
ejpam-2967	29	1	<	<	X
ejpam-2967	29	2	0	0	X
ejpam-2967	29	3	.	.	PUNCT
ejpam-2967	30	1	then	then	ADV
ejpam-2967	30	2	there	there	PRON
ejpam-2967	30	3	exists	exist	VERB
ejpam-2967	30	4	c	c	PROPN
ejpam-2967	30	5	∈	∈	PROPN
ejpam-2967	30	6	(	(	PUNCT
ejpam-2967	30	7	0	0	NUM
ejpam-2967	30	8	,	,	PUNCT
ejpam-2967	30	9	1	1	NUM
ejpam-2967	30	10	)	)	PUNCT
ejpam-2967	30	11	such	such	ADJ
ejpam-2967	30	12	that	that	DET
ejpam-2967	30	13	cf(c	cf(c	PUNCT
ejpam-2967	30	14	)	)	PUNCT
ejpam-2967	30	15	=	=	SYM
ejpam-2967	30	16	2	2	NUM
ejpam-2967	30	17	∫	∫	NOUN
ejpam-2967	30	18	c	c	NOUN
ejpam-2967	30	19	0	0	NUM
ejpam-2967	30	20	tf(t)dt	tf(t)dt	NUM
ejpam-2967	30	21	.	.	PUNCT
ejpam-2967	31	1	(	(	PUNCT
ejpam-2967	31	2	1	1	X
ejpam-2967	31	3	)	)	PUNCT
ejpam-2967	31	4	proof	proof	NOUN
ejpam-2967	31	5	.	.	PUNCT
ejpam-2967	32	1	if	if	SCONJ
ejpam-2967	32	2	f	f	PROPN
ejpam-2967	32	3	=	=	SYM
ejpam-2967	32	4	0	0	PROPN
ejpam-2967	32	5	,	,	PUNCT
ejpam-2967	32	6	then	then	ADV
ejpam-2967	32	7	there	there	PRON
ejpam-2967	32	8	is	be	VERB
ejpam-2967	32	9	nothing	nothing	PRON
ejpam-2967	32	10	to	to	PART
ejpam-2967	32	11	prove	prove	VERB
ejpam-2967	32	12	.	.	PUNCT
ejpam-2967	33	1	so	so	ADV
ejpam-2967	33	2	assume	assume	VERB
ejpam-2967	33	3	that	that	SCONJ
ejpam-2967	33	4	f	f	PROPN
ejpam-2967	33	5	is	be	AUX
ejpam-2967	33	6	not	not	PART
ejpam-2967	33	7	a	a	DET
ejpam-2967	33	8	zero	zero	NUM
ejpam-2967	33	9	function	function	NOUN
ejpam-2967	33	10	.	.	PUNCT
ejpam-2967	34	1	by	by	ADP
ejpam-2967	34	2	hypothesis	hypothesis	NOUN
ejpam-2967	34	3	,	,	PUNCT
ejpam-2967	34	4	there	there	PRON
ejpam-2967	34	5	exists	exist	VERB
ejpam-2967	34	6	a	a	DET
ejpam-2967	34	7	,	,	PUNCT
ejpam-2967	34	8	b	b	X
ejpam-2967	34	9	∈	∈	PROPN
ejpam-2967	34	10	(	(	PUNCT
ejpam-2967	34	11	0	0	NUM
ejpam-2967	34	12	,	,	PUNCT
ejpam-2967	34	13	1	1	NUM
ejpam-2967	34	14	)	)	PUNCT
ejpam-2967	34	15	such	such	ADJ
ejpam-2967	34	16	that	that	SCONJ
ejpam-2967	34	17	a	a	DET
ejpam-2967	34	18	6=	6=	PROPN
ejpam-2967	34	19	b	b	NOUN
ejpam-2967	34	20	and	and	CCONJ
ejpam-2967	34	21	f(a	f(a	NOUN
ejpam-2967	34	22	)	)	PUNCT
ejpam-2967	35	1	=	=	SYM
ejpam-2967	35	2	max	max	PROPN
ejpam-2967	35	3	x∈(0,1	x∈(0,1	ADV
ejpam-2967	35	4	)	)	PUNCT
ejpam-2967	36	1	f(x	f(x	PROPN
ejpam-2967	36	2	)	)	PUNCT
ejpam-2967	36	3	>	>	X
ejpam-2967	36	4	0	0	NUM
ejpam-2967	36	5	,	,	PUNCT
ejpam-2967	36	6	f(b	f(b	PROPN
ejpam-2967	36	7	)	)	PUNCT
ejpam-2967	36	8	=	=	SYM
ejpam-2967	36	9	min	min	NOUN
ejpam-2967	36	10	x∈(0,1	x∈(0,1	ADV
ejpam-2967	36	11	)	)	PUNCT
ejpam-2967	36	12	f(x	f(x	PROPN
ejpam-2967	36	13	)	)	PUNCT
ejpam-2967	36	14	<	<	X
ejpam-2967	36	15	0	0	X
ejpam-2967	36	16	.	.	PUNCT
ejpam-2967	36	17	define	define	VERB
ejpam-2967	36	18	g(x	g(x	NOUN
ejpam-2967	36	19	)	)	PUNCT
ejpam-2967	37	1	=	=	SYM
ejpam-2967	37	2	xf(x)−	xf(x)−	PROPN
ejpam-2967	37	3	2	2	NUM
ejpam-2967	37	4	∫	∫	NOUN
ejpam-2967	37	5	x	x	SYM
ejpam-2967	37	6	0	0	NUM
ejpam-2967	37	7	tf(t)dt	tf(t)dt	PROPN
ejpam-2967	37	8	.	.	PUNCT
ejpam-2967	38	1	clearly	clearly	ADV
ejpam-2967	38	2	g(x	g(x	NOUN
ejpam-2967	38	3	)	)	PUNCT
ejpam-2967	38	4	is	be	AUX
ejpam-2967	38	5	continuous	continuous	ADJ
ejpam-2967	38	6	on	on	ADP
ejpam-2967	38	7	(	(	PUNCT
ejpam-2967	38	8	0	0	NUM
ejpam-2967	38	9	,	,	PUNCT
ejpam-2967	38	10	1	1	NUM
ejpam-2967	38	11	)	)	PUNCT
ejpam-2967	38	12	.	.	PUNCT
ejpam-2967	39	1	now	now	ADV
ejpam-2967	39	2	g(a	g(a	PROPN
ejpam-2967	39	3	)	)	PUNCT
ejpam-2967	39	4	≥	≥	NOUN
ejpam-2967	39	5	af(a)−	af(a)−	VERB
ejpam-2967	39	6	2	2	NUM
ejpam-2967	39	7	∫	∫	NOUN
ejpam-2967	39	8	a	a	DET
ejpam-2967	39	9	0	0	NUM
ejpam-2967	39	10	tf(a)dt	tf(a)dt	NOUN
ejpam-2967	39	11	=	=	PUNCT
ejpam-2967	39	12	af(a)−	af(a)−	PROPN
ejpam-2967	39	13	a2f(a	a2f(a	PROPN
ejpam-2967	39	14	)	)	PUNCT
ejpam-2967	39	15	.	.	PUNCT
ejpam-2967	40	1	but	but	CCONJ
ejpam-2967	40	2	then	then	ADV
ejpam-2967	40	3	g(a	g(a	PROPN
ejpam-2967	40	4	)	)	PUNCT
ejpam-2967	40	5	≥	≥	NOUN
ejpam-2967	41	1	af(a)(1−	af(a)(1−	NOUN
ejpam-2967	41	2	a	a	X
ejpam-2967	41	3	)	)	PUNCT
ejpam-2967	41	4	>	>	X
ejpam-2967	42	1	0	0	X
ejpam-2967	42	2	.	.	PUNCT
ejpam-2967	42	3	also	also	ADV
ejpam-2967	42	4	g(b	g(b	ADJ
ejpam-2967	42	5	)	)	PUNCT
ejpam-2967	42	6	≤	≤	PUNCT
ejpam-2967	42	7	bf(b)−	bf(b)−	NOUN
ejpam-2967	42	8	2	2	NUM
ejpam-2967	42	9	∫	∫	NOUN
ejpam-2967	42	10	b	b	SYM
ejpam-2967	42	11	0	0	NUM
ejpam-2967	42	12	tf(b)dt	tf(b)dt	PROPN
ejpam-2967	42	13	,	,	PUNCT
ejpam-2967	42	14	prasanna	prasanna	PROPN
ejpam-2967	42	15	kumar	kumar	PROPN
ejpam-2967	42	16	/	/	SYM
ejpam-2967	42	17	eur	eur	PROPN
ejpam-2967	42	18	.	.	PUNCT
ejpam-2967	43	1	j.	j.	PROPN
ejpam-2967	43	2	pure	pure	PROPN
ejpam-2967	43	3	appl	appl	PROPN
ejpam-2967	43	4	.	.	PROPN
ejpam-2967	43	5	math	math	PROPN
ejpam-2967	43	6	,	,	PUNCT
ejpam-2967	43	7	10	10	NUM
ejpam-2967	43	8	(	(	PUNCT
ejpam-2967	43	9	3	3	NUM
ejpam-2967	43	10	)	)	PUNCT
ejpam-2967	43	11	(	(	PUNCT
ejpam-2967	43	12	2017	2017	NUM
ejpam-2967	43	13	)	)	PUNCT
ejpam-2967	43	14	,	,	PUNCT
ejpam-2967	43	15	488	488	NUM
ejpam-2967	43	16	-	-	SYM
ejpam-2967	43	17	494	494	NUM
ejpam-2967	43	18	490	490	NUM
ejpam-2967	43	19	which	which	PRON
ejpam-2967	43	20	is	be	AUX
ejpam-2967	43	21	equivalent	equivalent	ADJ
ejpam-2967	43	22	g(b	g(b	NOUN
ejpam-2967	43	23	)	)	PUNCT
ejpam-2967	43	24	≤	≤	NOUN
ejpam-2967	43	25	bf(b)(1−	bf(b)(1−	PROPN
ejpam-2967	43	26	b	b	NOUN
ejpam-2967	43	27	)	)	PUNCT
ejpam-2967	43	28	<	<	X
ejpam-2967	43	29	0	0	NUM
ejpam-2967	43	30	,	,	PUNCT
ejpam-2967	43	31	since	since	SCONJ
ejpam-2967	43	32	f(b	f(b	PROPN
ejpam-2967	43	33	)	)	PUNCT
ejpam-2967	43	34	<	<	X
ejpam-2967	43	35	0	0	X
ejpam-2967	43	36	.	.	PUNCT
ejpam-2967	44	1	by	by	ADP
ejpam-2967	44	2	intermediate	intermediate	ADJ
ejpam-2967	44	3	value	value	NOUN
ejpam-2967	44	4	theorem	theorem	NOUN
ejpam-2967	44	5	there	there	PRON
ejpam-2967	44	6	exists	exist	VERB
ejpam-2967	44	7	c	c	PROPN
ejpam-2967	44	8	∈	∈	PROPN
ejpam-2967	44	9	(	(	PUNCT
ejpam-2967	44	10	a	a	DET
ejpam-2967	44	11	,	,	PUNCT
ejpam-2967	44	12	b	b	NOUN
ejpam-2967	44	13	)	)	PUNCT
ejpam-2967	44	14	such	such	ADJ
ejpam-2967	44	15	that	that	DET
ejpam-2967	44	16	g(c	g(c	NOUN
ejpam-2967	44	17	)	)	PUNCT
ejpam-2967	44	18	=	=	PUNCT
ejpam-2967	45	1	0	0	X
ejpam-2967	45	2	.	.	PUNCT
ejpam-2967	46	1	hence	hence	ADV
ejpam-2967	46	2	(	(	PUNCT
ejpam-2967	46	3	1	1	X
ejpam-2967	46	4	)	)	PUNCT
ejpam-2967	46	5	is	be	AUX
ejpam-2967	46	6	proved	prove	VERB
ejpam-2967	46	7	.	.	PUNCT
ejpam-2967	47	1	real	real	ADV
ejpam-2967	47	2	valued	value	VERB
ejpam-2967	47	3	functions	function	NOUN
ejpam-2967	47	4	on	on	ADP
ejpam-2967	47	5	the	the	DET
ejpam-2967	47	6	set	set	NOUN
ejpam-2967	47	7	of	of	ADP
ejpam-2967	47	8	real	real	ADJ
ejpam-2967	47	9	numbers	number	NOUN
ejpam-2967	47	10	with	with	ADP
ejpam-2967	47	11	any	any	DET
ejpam-2967	47	12	classical	classical	ADJ
ejpam-2967	47	13	structure	structure	NOUN
ejpam-2967	47	14	like	like	ADP
ejpam-2967	47	15	continuity	continuity	NOUN
ejpam-2967	47	16	,	,	PUNCT
ejpam-2967	47	17	bijection	bijection	NOUN
ejpam-2967	47	18	etc	etc	X
ejpam-2967	47	19	normally	normally	ADV
ejpam-2967	47	20	enjoy	enjoy	VERB
ejpam-2967	47	21	the	the	DET
ejpam-2967	47	22	properties	property	NOUN
ejpam-2967	47	23	like	like	ADP
ejpam-2967	47	24	’	'	PUNCT
ejpam-2967	47	25	0	0	NUM
ejpam-2967	47	26	going	go	VERB
ejpam-2967	47	27	to	to	ADP
ejpam-2967	47	28	0	0	NUM
ejpam-2967	47	29	’	'	PUNCT
ejpam-2967	47	30	,	,	PUNCT
ejpam-2967	47	31	even	even	ADV
ejpam-2967	47	32	-	-	PUNCT
ejpam-2967	47	33	odd	odd	ADJ
ejpam-2967	47	34	property	property	NOUN
ejpam-2967	47	35	or	or	CCONJ
ejpam-2967	47	36	the	the	DET
ejpam-2967	47	37	additivity	additivity	NOUN
ejpam-2967	47	38	etc	etc	X
ejpam-2967	47	39	.	.	X
ejpam-2967	47	40	but	but	CCONJ
ejpam-2967	47	41	a	a	DET
ejpam-2967	47	42	typical	typical	ADJ
ejpam-2967	47	43	function	function	NOUN
ejpam-2967	47	44	of	of	ADP
ejpam-2967	47	45	the	the	DET
ejpam-2967	47	46	kind	kind	NOUN
ejpam-2967	47	47	given	give	VERB
ejpam-2967	47	48	below	below	ADV
ejpam-2967	47	49	in	in	ADP
ejpam-2967	47	50	the	the	DET
ejpam-2967	47	51	next	next	ADJ
ejpam-2967	47	52	theorem	theorem	NOUN
ejpam-2967	47	53	,	,	PUNCT
ejpam-2967	47	54	being	be	AUX
ejpam-2967	47	55	a	a	DET
ejpam-2967	47	56	’	'	PUNCT
ejpam-2967	47	57	translated	translated	ADJ
ejpam-2967	47	58	’	'	PUNCT
ejpam-2967	47	59	composition	composition	NOUN
ejpam-2967	47	60	of	of	ADP
ejpam-2967	47	61	itself	itself	PRON
ejpam-2967	47	62	exhibits	exhibit	VERB
ejpam-2967	47	63	these	these	DET
ejpam-2967	47	64	properties	property	NOUN
ejpam-2967	47	65	and	and	CCONJ
ejpam-2967	47	66	that	that	PRON
ejpam-2967	47	67	is	be	AUX
ejpam-2967	47	68	why	why	SCONJ
ejpam-2967	47	69	the	the	DET
ejpam-2967	47	70	result	result	NOUN
ejpam-2967	47	71	seems	seem	VERB
ejpam-2967	47	72	to	to	PART
ejpam-2967	47	73	be	be	AUX
ejpam-2967	47	74	some	some	PRON
ejpam-2967	47	75	what	what	PRON
ejpam-2967	47	76	interesting	interesting	ADJ
ejpam-2967	47	77	to	to	PART
ejpam-2967	47	78	present	present	VERB
ejpam-2967	47	79	over	over	ADP
ejpam-2967	47	80	here	here	ADV
ejpam-2967	47	81	.	.	PUNCT
ejpam-2967	48	1	theorem	theorem	VERB
ejpam-2967	48	2	2	2	NUM
ejpam-2967	48	3	.	.	PUNCT
ejpam-2967	49	1	if	if	SCONJ
ejpam-2967	49	2	f	f	PROPN
ejpam-2967	49	3	:	:	PUNCT
ejpam-2967	49	4	<	<	X
ejpam-2967	49	5	→	→	X
ejpam-2967	49	6	<	<	X
ejpam-2967	49	7	defined	define	VERB
ejpam-2967	49	8	by	by	ADP
ejpam-2967	49	9	f(x+	f(x+	NOUN
ejpam-2967	49	10	nf(y	nf(y	NUM
ejpam-2967	49	11	)	)	PUNCT
ejpam-2967	49	12	)	)	PUNCT
ejpam-2967	50	1	=	=	SYM
ejpam-2967	50	2	f(x	f(x	PROPN
ejpam-2967	50	3	)	)	PUNCT
ejpam-2967	51	1	+	+	CCONJ
ejpam-2967	51	2	(	(	PUNCT
ejpam-2967	51	3	n−	n−	NOUN
ejpam-2967	51	4	1)y	1)y	NUM
ejpam-2967	51	5	+	+	CCONJ
ejpam-2967	51	6	f(y	f(y	NOUN
ejpam-2967	51	7	)	)	PUNCT
ejpam-2967	51	8	(	(	PUNCT
ejpam-2967	51	9	2	2	X
ejpam-2967	51	10	)	)	PUNCT
ejpam-2967	51	11	for	for	ADP
ejpam-2967	51	12	n	n	PROPN
ejpam-2967	51	13	>	>	X
ejpam-2967	51	14	1	1	NUM
ejpam-2967	51	15	,	,	PUNCT
ejpam-2967	51	16	then	then	ADV
ejpam-2967	51	17	(	(	PUNCT
ejpam-2967	51	18	a	a	X
ejpam-2967	51	19	)	)	PUNCT
ejpam-2967	51	20	f(0	f(0	NOUN
ejpam-2967	51	21	)	)	PUNCT
ejpam-2967	51	22	=	=	SYM
ejpam-2967	51	23	0	0	PUNCT
ejpam-2967	51	24	(	(	PUNCT
ejpam-2967	51	25	b	b	X
ejpam-2967	51	26	)	)	PUNCT
ejpam-2967	51	27	f	f	PROPN
ejpam-2967	51	28	is	be	AUX
ejpam-2967	51	29	an	an	DET
ejpam-2967	51	30	odd	odd	ADJ
ejpam-2967	51	31	function	function	NOUN
ejpam-2967	51	32	(	(	PUNCT
ejpam-2967	51	33	c	c	NOUN
ejpam-2967	51	34	)	)	PUNCT
ejpam-2967	51	35	f(x+	f(x+	NOUN
ejpam-2967	51	36	y	y	NOUN
ejpam-2967	51	37	)	)	PUNCT
ejpam-2967	51	38	=	=	SYM
ejpam-2967	51	39	f(x	f(x	PROPN
ejpam-2967	51	40	)	)	PUNCT
ejpam-2967	52	1	+	+	SYM
ejpam-2967	52	2	f(y	f(y	NOUN
ejpam-2967	52	3	)	)	PUNCT
ejpam-2967	53	1	,	,	PUNCT
ejpam-2967	53	2	∀x	∀x	X
ejpam-2967	53	3	,	,	PUNCT
ejpam-2967	53	4	y	y	PROPN
ejpam-2967	53	5	∈	∈	PROPN
ejpam-2967	53	6	<	<	X
ejpam-2967	53	7	.	.	PUNCT
ejpam-2967	53	8	proof	proof	NOUN
ejpam-2967	53	9	.	.	PUNCT
ejpam-2967	54	1	let	let	VERB
ejpam-2967	54	2	us	we	PRON
ejpam-2967	54	3	prove	prove	VERB
ejpam-2967	54	4	(	(	PUNCT
ejpam-2967	54	5	a	a	X
ejpam-2967	54	6	)	)	PUNCT
ejpam-2967	54	7	first	first	ADV
ejpam-2967	54	8	.	.	PUNCT
ejpam-2967	55	1	assume	assume	VERB
ejpam-2967	55	2	that	that	SCONJ
ejpam-2967	55	3	f(0	f(0	NOUN
ejpam-2967	55	4	)	)	PUNCT
ejpam-2967	55	5	=	=	PUNCT
ejpam-2967	55	6	a.	a.	NOUN
ejpam-2967	55	7	now	now	ADV
ejpam-2967	55	8	taking	take	VERB
ejpam-2967	55	9	x	x	PUNCT
ejpam-2967	55	10	=	=	SYM
ejpam-2967	55	11	0	0	NUM
ejpam-2967	55	12	,	,	PUNCT
ejpam-2967	55	13	y	y	PROPN
ejpam-2967	55	14	=	=	SYM
ejpam-2967	55	15	0	0	NUM
ejpam-2967	55	16	,	,	PUNCT
ejpam-2967	55	17	in	in	ADP
ejpam-2967	55	18	(	(	PUNCT
ejpam-2967	55	19	2)we	2)we	NOUN
ejpam-2967	55	20	have	have	AUX
ejpam-2967	55	21	f(na	f(na	NUM
ejpam-2967	55	22	)	)	PUNCT
ejpam-2967	55	23	=	=	SYM
ejpam-2967	55	24	2a	2a	NUM
ejpam-2967	55	25	.	.	PUNCT
ejpam-2967	56	1	also	also	ADV
ejpam-2967	56	2	if	if	SCONJ
ejpam-2967	56	3	we	we	PRON
ejpam-2967	56	4	take	take	VERB
ejpam-2967	56	5	x	x	NOUN
ejpam-2967	56	6	=	=	SYM
ejpam-2967	56	7	0	0	NUM
ejpam-2967	56	8	,	,	PUNCT
ejpam-2967	56	9	y	y	NOUN
ejpam-2967	56	10	=	=	PRON
ejpam-2967	56	11	na	na	PART
ejpam-2967	56	12	in	in	ADP
ejpam-2967	56	13	(	(	PUNCT
ejpam-2967	56	14	2	2	X
ejpam-2967	56	15	)	)	PUNCT
ejpam-2967	56	16	we	we	PRON
ejpam-2967	56	17	have	have	VERB
ejpam-2967	56	18	f(2na	f(2na	NOUN
ejpam-2967	56	19	)	)	PUNCT
ejpam-2967	56	20	)	)	PUNCT
ejpam-2967	57	1	=	=	SYM
ejpam-2967	57	2	3a+	3a+	NUM
ejpam-2967	57	3	(	(	PUNCT
ejpam-2967	57	4	n−	n−	NOUN
ejpam-2967	57	5	1)na	1)na	NUM
ejpam-2967	57	6	.	.	PUNCT
ejpam-2967	58	1	(	(	PUNCT
ejpam-2967	58	2	3	3	X
ejpam-2967	58	3	)	)	PUNCT
ejpam-2967	58	4	taking	take	VERB
ejpam-2967	58	5	x	x	PUNCT
ejpam-2967	58	6	=	=	PUNCT
ejpam-2967	58	7	na	na	PROPN
ejpam-2967	58	8	,	,	PUNCT
ejpam-2967	58	9	y	y	PROPN
ejpam-2967	58	10	=	=	SYM
ejpam-2967	58	11	0	0	NUM
ejpam-2967	58	12	,	,	PUNCT
ejpam-2967	58	13	again	again	ADV
ejpam-2967	58	14	in	in	ADP
ejpam-2967	58	15	(	(	PUNCT
ejpam-2967	58	16	2	2	X
ejpam-2967	58	17	)	)	PUNCT
ejpam-2967	58	18	we	we	PRON
ejpam-2967	58	19	have	have	VERB
ejpam-2967	58	20	f(2na	f(2na	NOUN
ejpam-2967	58	21	)	)	PUNCT
ejpam-2967	58	22	=	=	SYM
ejpam-2967	58	23	3a	3a	NUM
ejpam-2967	58	24	.	.	PUNCT
ejpam-2967	59	1	(	(	PUNCT
ejpam-2967	59	2	4	4	NUM
ejpam-2967	59	3	)	)	PUNCT
ejpam-2967	59	4	from	from	ADP
ejpam-2967	59	5	(	(	PUNCT
ejpam-2967	59	6	3	3	NUM
ejpam-2967	59	7	)	)	PUNCT
ejpam-2967	59	8	and	and	CCONJ
ejpam-2967	59	9	(	(	PUNCT
ejpam-2967	59	10	4	4	X
ejpam-2967	59	11	)	)	PUNCT
ejpam-2967	59	12	it	it	PRON
ejpam-2967	59	13	follows	follow	VERB
ejpam-2967	59	14	that	that	SCONJ
ejpam-2967	59	15	a	a	DET
ejpam-2967	59	16	=	=	NOUN
ejpam-2967	59	17	0	0	X
ejpam-2967	59	18	.	.	PUNCT
ejpam-2967	60	1	let	let	VERB
ejpam-2967	60	2	us	we	PRON
ejpam-2967	60	3	prove	prove	VERB
ejpam-2967	60	4	the	the	DET
ejpam-2967	60	5	part	part	NOUN
ejpam-2967	60	6	(	(	PUNCT
ejpam-2967	60	7	b	b	NOUN
ejpam-2967	60	8	)	)	PUNCT
ejpam-2967	60	9	now	now	ADV
ejpam-2967	60	10	.	.	PUNCT
ejpam-2967	61	1	taking	take	VERB
ejpam-2967	61	2	x	x	PUNCT
ejpam-2967	61	3	=	=	SYM
ejpam-2967	61	4	0	0	NUM
ejpam-2967	61	5	,	,	PUNCT
ejpam-2967	61	6	in	in	ADP
ejpam-2967	61	7	(	(	PUNCT
ejpam-2967	61	8	2	2	NUM
ejpam-2967	61	9	)	)	PUNCT
ejpam-2967	61	10	,	,	PUNCT
ejpam-2967	61	11	we	we	PRON
ejpam-2967	61	12	get	get	VERB
ejpam-2967	61	13	f(nf(y	f(nf(y	NOUN
ejpam-2967	61	14	)	)	PUNCT
ejpam-2967	61	15	)	)	PUNCT
ejpam-2967	62	1	=	=	PUNCT
ejpam-2967	62	2	(	(	PUNCT
ejpam-2967	62	3	n−	n−	NOUN
ejpam-2967	62	4	1)y	1)y	NUM
ejpam-2967	62	5	+	+	CCONJ
ejpam-2967	62	6	f(y	f(y	NOUN
ejpam-2967	62	7	)	)	PUNCT
ejpam-2967	62	8	(	(	PUNCT
ejpam-2967	62	9	5	5	X
ejpam-2967	62	10	)	)	PUNCT
ejpam-2967	62	11	now	now	ADV
ejpam-2967	62	12	replacing	replace	VERB
ejpam-2967	62	13	x	x	PUNCT
ejpam-2967	62	14	by	by	ADP
ejpam-2967	62	15	nf(x	nf(x	ADJ
ejpam-2967	62	16	)	)	PUNCT
ejpam-2967	62	17	in	in	ADP
ejpam-2967	62	18	the	the	DET
ejpam-2967	62	19	definition	definition	NOUN
ejpam-2967	62	20	and	and	CCONJ
ejpam-2967	62	21	then	then	ADV
ejpam-2967	62	22	using	use	VERB
ejpam-2967	62	23	(	(	PUNCT
ejpam-2967	62	24	5	5	NUM
ejpam-2967	62	25	)	)	PUNCT
ejpam-2967	62	26	,	,	PUNCT
ejpam-2967	62	27	we	we	PRON
ejpam-2967	62	28	get	get	VERB
ejpam-2967	62	29	f(nf(x	f(nf(x	NOUN
ejpam-2967	62	30	)	)	PUNCT
ejpam-2967	62	31	+	+	NOUN
ejpam-2967	62	32	nf(y	nf(y	NUM
ejpam-2967	62	33	)	)	PUNCT
ejpam-2967	62	34	)	)	PUNCT
ejpam-2967	63	1	=	=	PUNCT
ejpam-2967	63	2	f(nf(x	f(nf(x	NOUN
ejpam-2967	63	3	)	)	PUNCT
ejpam-2967	63	4	)	)	PUNCT
ejpam-2967	64	1	+	+	CCONJ
ejpam-2967	64	2	(	(	PUNCT
ejpam-2967	64	3	n−	n−	NOUN
ejpam-2967	64	4	1)y	1)y	NUM
ejpam-2967	64	5	+	+	CCONJ
ejpam-2967	64	6	f(y	f(y	NOUN
ejpam-2967	64	7	)	)	PUNCT
ejpam-2967	64	8	=	=	PUNCT
ejpam-2967	65	1	(	(	PUNCT
ejpam-2967	65	2	n−	n−	PROPN
ejpam-2967	65	3	1)(x+	1)(x+	NUM
ejpam-2967	65	4	y	y	NOUN
ejpam-2967	65	5	)	)	PUNCT
ejpam-2967	66	1	+	+	CCONJ
ejpam-2967	66	2	f(x	f(x	PROPN
ejpam-2967	66	3	)	)	PUNCT
ejpam-2967	66	4	+	+	SYM
ejpam-2967	67	1	f(y	f(y	NOUN
ejpam-2967	67	2	)	)	PUNCT
ejpam-2967	67	3	.	.	PUNCT
ejpam-2967	68	1	(	(	PUNCT
ejpam-2967	68	2	6	6	X
ejpam-2967	68	3	)	)	PUNCT
ejpam-2967	68	4	let	let	VERB
ejpam-2967	68	5	f(x	f(x	PROPN
ejpam-2967	68	6	)	)	PUNCT
ejpam-2967	69	1	+	+	CCONJ
ejpam-2967	69	2	f(−x	f(−x	X
ejpam-2967	69	3	)	)	PUNCT
ejpam-2967	69	4	=	=	SYM
ejpam-2967	70	1	g.	g.	PROPN
ejpam-2967	70	2	now	now	ADV
ejpam-2967	70	3	again	again	ADV
ejpam-2967	70	4	taking	take	VERB
ejpam-2967	70	5	x	x	PUNCT
ejpam-2967	70	6	as	as	ADP
ejpam-2967	70	7	nf(x	nf(x	NOUN
ejpam-2967	70	8	)	)	PUNCT
ejpam-2967	70	9	and	and	CCONJ
ejpam-2967	70	10	y	y	NOUN
ejpam-2967	70	11	=	=	NOUN
ejpam-2967	70	12	−x	−x	PROPN
ejpam-2967	70	13	in	in	ADP
ejpam-2967	70	14	(	(	PUNCT
ejpam-2967	70	15	2	2	NUM
ejpam-2967	70	16	)	)	PUNCT
ejpam-2967	70	17	and	and	CCONJ
ejpam-2967	70	18	then	then	ADV
ejpam-2967	70	19	using	use	VERB
ejpam-2967	70	20	(	(	PUNCT
ejpam-2967	70	21	6	6	NUM
ejpam-2967	70	22	)	)	PUNCT
ejpam-2967	70	23	we	we	PRON
ejpam-2967	70	24	have	have	VERB
ejpam-2967	70	25	f(nf(x	f(nf(x	NOUN
ejpam-2967	70	26	)	)	PUNCT
ejpam-2967	71	1	+	+	CCONJ
ejpam-2967	71	2	nf(−x	nf(−x	NOUN
ejpam-2967	71	3	)	)	PUNCT
ejpam-2967	71	4	)	)	PUNCT
ejpam-2967	72	1	=	=	SYM
ejpam-2967	72	2	f(x	f(x	PROPN
ejpam-2967	72	3	)	)	PUNCT
ejpam-2967	73	1	+	+	NUM
ejpam-2967	73	2	f(−x	f(−x	NUM
ejpam-2967	73	3	)	)	PUNCT
ejpam-2967	73	4	,	,	PUNCT
ejpam-2967	73	5	which	which	PRON
ejpam-2967	73	6	is	be	AUX
ejpam-2967	73	7	equivalent	equivalent	ADJ
ejpam-2967	73	8	to	to	ADP
ejpam-2967	73	9	f(ng	f(ng	NUM
ejpam-2967	73	10	)	)	PUNCT
ejpam-2967	73	11	=	=	SYM
ejpam-2967	73	12	g.	g.	PROPN
ejpam-2967	73	13	prasanna	prasanna	PROPN
ejpam-2967	73	14	kumar	kumar	PROPN
ejpam-2967	73	15	/	/	SYM
ejpam-2967	73	16	eur	eur	PROPN
ejpam-2967	73	17	.	.	PUNCT
ejpam-2967	74	1	j.	j.	PROPN
ejpam-2967	74	2	pure	pure	PROPN
ejpam-2967	74	3	appl	appl	PROPN
ejpam-2967	74	4	.	.	PROPN
ejpam-2967	74	5	math	math	PROPN
ejpam-2967	74	6	,	,	PUNCT
ejpam-2967	74	7	10	10	NUM
ejpam-2967	74	8	(	(	PUNCT
ejpam-2967	74	9	3	3	NUM
ejpam-2967	74	10	)	)	PUNCT
ejpam-2967	74	11	(	(	PUNCT
ejpam-2967	74	12	2017	2017	NUM
ejpam-2967	74	13	)	)	PUNCT
ejpam-2967	74	14	,	,	PUNCT
ejpam-2967	74	15	488	488	NUM
ejpam-2967	74	16	-	-	SYM
ejpam-2967	74	17	494	494	NUM
ejpam-2967	74	18	491	491	NUM
ejpam-2967	74	19	but	but	CCONJ
ejpam-2967	74	20	then	then	ADV
ejpam-2967	74	21	f(nf(ng	f(nf(ng	NOUN
ejpam-2967	74	22	)	)	PUNCT
ejpam-2967	74	23	)	)	PUNCT
ejpam-2967	75	1	=	=	PUNCT
ejpam-2967	75	2	f(ng	f(ng	PROPN
ejpam-2967	75	3	)	)	PUNCT
ejpam-2967	75	4	.	.	PUNCT
ejpam-2967	76	1	(	(	PUNCT
ejpam-2967	76	2	7	7	X
ejpam-2967	76	3	)	)	PUNCT
ejpam-2967	76	4	also	also	ADV
ejpam-2967	76	5	from	from	ADP
ejpam-2967	76	6	(	(	PUNCT
ejpam-2967	76	7	5	5	NUM
ejpam-2967	76	8	)	)	PUNCT
ejpam-2967	76	9	,	,	PUNCT
ejpam-2967	76	10	f(nf(ng	f(nf(ng	NOUN
ejpam-2967	76	11	)	)	PUNCT
ejpam-2967	76	12	)	)	PUNCT
ejpam-2967	77	1	=	=	PUNCT
ejpam-2967	77	2	(	(	PUNCT
ejpam-2967	77	3	n−	n−	NOUN
ejpam-2967	77	4	1)ng	1)ng	NUM
ejpam-2967	77	5	+	+	CCONJ
ejpam-2967	77	6	f(ng	f(ng	NUM
ejpam-2967	77	7	)	)	PUNCT
ejpam-2967	77	8	.	.	PUNCT
ejpam-2967	78	1	(	(	PUNCT
ejpam-2967	78	2	8)	8)	NUM
ejpam-2967	78	3	from	from	ADP
ejpam-2967	78	4	(	(	PUNCT
ejpam-2967	78	5	7	7	NUM
ejpam-2967	78	6	)	)	PUNCT
ejpam-2967	78	7	and	and	CCONJ
ejpam-2967	78	8	(	(	PUNCT
ejpam-2967	78	9	8)	8)	NUM
ejpam-2967	78	10	it	it	PRON
ejpam-2967	78	11	follows	follow	VERB
ejpam-2967	78	12	that	that	SCONJ
ejpam-2967	78	13	g	g	PROPN
ejpam-2967	78	14	=	=	NOUN
ejpam-2967	78	15	0	0	PROPN
ejpam-2967	78	16	since	since	SCONJ
ejpam-2967	78	17	n	n	PROPN
ejpam-2967	78	18	>	>	X
ejpam-2967	78	19	1	1	X
ejpam-2967	78	20	.	.	PUNCT
ejpam-2967	79	1	lastly	lastly	ADV
ejpam-2967	79	2	,	,	PUNCT
ejpam-2967	79	3	we	we	PRON
ejpam-2967	79	4	prove	prove	VERB
ejpam-2967	79	5	that	that	SCONJ
ejpam-2967	79	6	f	f	PROPN
ejpam-2967	79	7	is	be	AUX
ejpam-2967	79	8	an	an	DET
ejpam-2967	79	9	additive	additive	ADJ
ejpam-2967	79	10	function	function	NOUN
ejpam-2967	79	11	.	.	PUNCT
ejpam-2967	80	1	suppose	suppose	VERB
ejpam-2967	80	2	f(x+	f(x+	AUX
ejpam-2967	80	3	y)−	y)−	PROPN
ejpam-2967	80	4	f(x)−	f(x)−	PROPN
ejpam-2967	80	5	f(y	f(y	NOUN
ejpam-2967	80	6	)	)	PUNCT
ejpam-2967	81	1	=	=	SYM
ejpam-2967	81	2	h(x	h(x	PROPN
ejpam-2967	81	3	,	,	PUNCT
ejpam-2967	81	4	y	y	PROPN
ejpam-2967	81	5	)	)	PUNCT
ejpam-2967	81	6	.	.	PUNCT
ejpam-2967	82	1	now	now	ADV
ejpam-2967	82	2	f(nh	f(nh	NOUN
ejpam-2967	82	3	)	)	PUNCT
ejpam-2967	82	4	=	=	SYM
ejpam-2967	82	5	f(−n(f(x)+f(y))+nf(x+y	f(−n(f(x)+f(y))+nf(x+y	NOUN
ejpam-2967	82	6	)	)	PUNCT
ejpam-2967	82	7	)	)	PUNCT
ejpam-2967	83	1	=	=	SYM
ejpam-2967	83	2	f(−n(f(x)+f(y)))+(n−1)(x+y)+f(x+y	f(−n(f(x)+f(y)))+(n−1)(x+y)+f(x+y	NOUN
ejpam-2967	83	3	)	)	PUNCT
ejpam-2967	83	4	,	,	PUNCT
ejpam-2967	83	5	by	by	ADP
ejpam-2967	83	6	definition	definition	NOUN
ejpam-2967	83	7	given	give	VERB
ejpam-2967	83	8	in	in	ADP
ejpam-2967	83	9	(	(	PUNCT
ejpam-2967	83	10	2	2	NUM
ejpam-2967	83	11	)	)	PUNCT
ejpam-2967	83	12	.	.	PUNCT
ejpam-2967	84	1	since	since	SCONJ
ejpam-2967	84	2	f	f	PROPN
ejpam-2967	84	3	is	be	AUX
ejpam-2967	84	4	an	an	DET
ejpam-2967	84	5	odd	odd	ADJ
ejpam-2967	84	6	function	function	NOUN
ejpam-2967	84	7	,	,	PUNCT
ejpam-2967	84	8	and	and	CCONJ
ejpam-2967	84	9	using	use	VERB
ejpam-2967	84	10	(	(	PUNCT
ejpam-2967	84	11	6	6	NUM
ejpam-2967	84	12	)	)	PUNCT
ejpam-2967	84	13	we	we	PRON
ejpam-2967	84	14	get	get	VERB
ejpam-2967	84	15	f(nh	f(nh	NOUN
ejpam-2967	84	16	)	)	PUNCT
ejpam-2967	84	17	=	=	SYM
ejpam-2967	84	18	−f(n(f(x	−f(n(f(x	PROPN
ejpam-2967	84	19	)	)	PUNCT
ejpam-2967	84	20	+	+	SYM
ejpam-2967	84	21	f(y	f(y	NOUN
ejpam-2967	84	22	)	)	PUNCT
ejpam-2967	84	23	)	)	PUNCT
ejpam-2967	84	24	)	)	PUNCT
ejpam-2967	85	1	+	+	CCONJ
ejpam-2967	85	2	(	(	PUNCT
ejpam-2967	85	3	n−	n−	PROPN
ejpam-2967	85	4	1)(x+	1)(x+	NUM
ejpam-2967	85	5	y	y	NOUN
ejpam-2967	85	6	)	)	PUNCT
ejpam-2967	85	7	+	+	CCONJ
ejpam-2967	85	8	f(x+	f(x+	NUM
ejpam-2967	85	9	y	y	NUM
ejpam-2967	85	10	)	)	PUNCT
ejpam-2967	86	1	=	=	PUNCT
ejpam-2967	87	1	−[(n−	−[(n−	PROPN
ejpam-2967	87	2	1)x+	1)x+	NUM
ejpam-2967	87	3	f(x	f(x	PROPN
ejpam-2967	87	4	)	)	PUNCT
ejpam-2967	88	1	+	+	CCONJ
ejpam-2967	88	2	(	(	PUNCT
ejpam-2967	88	3	n−	n−	NOUN
ejpam-2967	88	4	1)y	1)y	NUM
ejpam-2967	88	5	+	+	CCONJ
ejpam-2967	88	6	f(y	f(y	NOUN
ejpam-2967	88	7	)	)	PUNCT
ejpam-2967	88	8	]	]	PUNCT
ejpam-2967	89	1	+	+	CCONJ
ejpam-2967	89	2	(	(	PUNCT
ejpam-2967	89	3	n−	n−	PROPN
ejpam-2967	89	4	1)(x+	1)(x+	NUM
ejpam-2967	89	5	y	y	NOUN
ejpam-2967	89	6	)	)	PUNCT
ejpam-2967	90	1	+	+	CCONJ
ejpam-2967	90	2	f(x+	f(x+	NUM
ejpam-2967	90	3	y	y	NUM
ejpam-2967	90	4	)	)	PUNCT
ejpam-2967	91	1	=	=	SYM
ejpam-2967	91	2	h(x	h(x	PROPN
ejpam-2967	91	3	,	,	PUNCT
ejpam-2967	91	4	y	y	PROPN
ejpam-2967	91	5	)	)	PUNCT
ejpam-2967	91	6	,	,	PUNCT
ejpam-2967	91	7	and	and	CCONJ
ejpam-2967	91	8	hence	hence	ADV
ejpam-2967	91	9	f(nh	f(nh	NOUN
ejpam-2967	91	10	)	)	PUNCT
ejpam-2967	91	11	=	=	SYM
ejpam-2967	91	12	h.	h.	NOUN
ejpam-2967	91	13	(	(	PUNCT
ejpam-2967	91	14	9	9	NUM
ejpam-2967	91	15	)	)	PUNCT
ejpam-2967	91	16	also	also	ADV
ejpam-2967	91	17	taking	take	VERB
ejpam-2967	91	18	y	y	PROPN
ejpam-2967	91	19	=	=	SYM
ejpam-2967	91	20	nh	nh	PROPN
ejpam-2967	91	21	in	in	ADP
ejpam-2967	91	22	(	(	PUNCT
ejpam-2967	91	23	5	5	X
ejpam-2967	91	24	)	)	PUNCT
ejpam-2967	91	25	we	we	PRON
ejpam-2967	91	26	will	will	AUX
ejpam-2967	91	27	have	have	VERB
ejpam-2967	91	28	f(nf(nh	f(nf(nh	NOUN
ejpam-2967	91	29	)	)	PUNCT
ejpam-2967	91	30	)	)	PUNCT
ejpam-2967	92	1	=	=	PUNCT
ejpam-2967	92	2	(	(	PUNCT
ejpam-2967	92	3	n−	n−	NOUN
ejpam-2967	92	4	1)nh+	1)nh+	NUM
ejpam-2967	92	5	f(nh	f(nh	NOUN
ejpam-2967	92	6	)	)	PUNCT
ejpam-2967	92	7	.	.	PUNCT
ejpam-2967	93	1	by	by	ADP
ejpam-2967	93	2	using	use	VERB
ejpam-2967	93	3	(	(	PUNCT
ejpam-2967	93	4	9	9	NUM
ejpam-2967	93	5	)	)	PUNCT
ejpam-2967	93	6	in	in	ADP
ejpam-2967	93	7	the	the	DET
ejpam-2967	93	8	above	above	ADJ
ejpam-2967	93	9	expression	expression	NOUN
ejpam-2967	93	10	we	we	PRON
ejpam-2967	93	11	get	get	VERB
ejpam-2967	93	12	f(nh	f(nh	NOUN
ejpam-2967	93	13	)	)	PUNCT
ejpam-2967	93	14	=	=	PUNCT
ejpam-2967	93	15	(	(	PUNCT
ejpam-2967	93	16	n−	n−	PROPN
ejpam-2967	93	17	1)nh+	1)nh+	PROPN
ejpam-2967	93	18	h.	h.	PROPN
ejpam-2967	93	19	(	(	PUNCT
ejpam-2967	93	20	10	10	NUM
ejpam-2967	93	21	)	)	PUNCT
ejpam-2967	93	22	the	the	DET
ejpam-2967	93	23	equations	equation	NOUN
ejpam-2967	93	24	(	(	PUNCT
ejpam-2967	93	25	9	9	NUM
ejpam-2967	93	26	)	)	PUNCT
ejpam-2967	93	27	and	and	CCONJ
ejpam-2967	93	28	(	(	PUNCT
ejpam-2967	93	29	10	10	NUM
ejpam-2967	93	30	)	)	PUNCT
ejpam-2967	93	31	make	make	VERB
ejpam-2967	93	32	us	we	PRON
ejpam-2967	93	33	to	to	PART
ejpam-2967	93	34	conclude	conclude	VERB
ejpam-2967	93	35	h	h	NOUN
ejpam-2967	93	36	=	=	NOUN
ejpam-2967	93	37	0	0	PROPN
ejpam-2967	93	38	.	.	PUNCT
ejpam-2967	94	1	thus	thus	ADV
ejpam-2967	94	2	the	the	DET
ejpam-2967	94	3	proof	proof	NOUN
ejpam-2967	94	4	is	be	AUX
ejpam-2967	94	5	complete	complete	ADJ
ejpam-2967	94	6	.	.	PUNCT
ejpam-2967	95	1	in	in	ADP
ejpam-2967	95	2	our	our	PRON
ejpam-2967	95	3	next	next	ADJ
ejpam-2967	95	4	result	result	NOUN
ejpam-2967	95	5	,	,	PUNCT
ejpam-2967	95	6	we	we	PRON
ejpam-2967	95	7	show	show	VERB
ejpam-2967	95	8	that	that	SCONJ
ejpam-2967	95	9	a	a	DET
ejpam-2967	95	10	special	special	ADJ
ejpam-2967	95	11	type	type	NOUN
ejpam-2967	95	12	of	of	ADP
ejpam-2967	95	13	functions	function	NOUN
ejpam-2967	95	14	associated	associate	VERB
ejpam-2967	95	15	with	with	ADP
ejpam-2967	95	16	the	the	DET
ejpam-2967	95	17	continuous	continuous	ADJ
ejpam-2967	95	18	functions	function	NOUN
ejpam-2967	95	19	on	on	ADP
ejpam-2967	95	20	an	an	DET
ejpam-2967	95	21	interval	interval	NOUN
ejpam-2967	95	22	can	can	AUX
ejpam-2967	95	23	take	take	VERB
ejpam-2967	95	24	the	the	DET
ejpam-2967	95	25	shape	shape	NOUN
ejpam-2967	95	26	of	of	ADP
ejpam-2967	95	27	exponential	exponential	ADJ
ejpam-2967	95	28	functions	function	NOUN
ejpam-2967	95	29	of	of	ADP
ejpam-2967	95	30	some	some	DET
ejpam-2967	95	31	continuous	continuous	ADJ
ejpam-2967	95	32	functions	function	NOUN
ejpam-2967	95	33	.	.	PUNCT
ejpam-2967	96	1	as	as	SCONJ
ejpam-2967	96	2	exponential	exponential	ADJ
ejpam-2967	96	3	functions	function	NOUN
ejpam-2967	96	4	are	be	AUX
ejpam-2967	96	5	of	of	ADP
ejpam-2967	96	6	great	great	ADJ
ejpam-2967	96	7	useful	useful	ADJ
ejpam-2967	96	8	while	while	SCONJ
ejpam-2967	96	9	studying	study	VERB
ejpam-2967	96	10	differentiability	differentiability	NOUN
ejpam-2967	96	11	structure	structure	NOUN
ejpam-2967	96	12	and	and	CCONJ
ejpam-2967	96	13	they	they	PRON
ejpam-2967	96	14	in	in	ADP
ejpam-2967	96	15	turn	turn	NOUN
ejpam-2967	96	16	help	help	VERB
ejpam-2967	96	17	us	we	PRON
ejpam-2967	96	18	to	to	PART
ejpam-2967	96	19	get	get	VERB
ejpam-2967	96	20	the	the	DET
ejpam-2967	96	21	corresponding	corresponding	ADJ
ejpam-2967	96	22	flavor	flavor	NOUN
ejpam-2967	96	23	of	of	ADP
ejpam-2967	96	24	uniformly	uniformly	ADV
ejpam-2967	96	25	continuous	continuous	ADJ
ejpam-2967	96	26	functions	function	NOUN
ejpam-2967	96	27	.	.	PUNCT
ejpam-2967	97	1	theorem	theorem	NOUN
ejpam-2967	97	2	3	3	NUM
ejpam-2967	97	3	.	.	PUNCT
ejpam-2967	98	1	if	if	SCONJ
ejpam-2967	98	2	f	f	PROPN
ejpam-2967	98	3	and	and	CCONJ
ejpam-2967	98	4	g	g	PROPN
ejpam-2967	98	5	are	be	AUX
ejpam-2967	98	6	real	real	ADV
ejpam-2967	98	7	valued	value	VERB
ejpam-2967	98	8	continuous	continuous	ADJ
ejpam-2967	98	9	functions	function	NOUN
ejpam-2967	98	10	on	on	ADP
ejpam-2967	98	11	[	[	X
ejpam-2967	98	12	0	0	NUM
ejpam-2967	98	13	,	,	PUNCT
ejpam-2967	98	14	1	1	NUM
ejpam-2967	98	15	]	]	PUNCT
ejpam-2967	98	16	such	such	ADJ
ejpam-2967	98	17	that	that	SCONJ
ejpam-2967	98	18	|g(x)|	|g(x)|	NOUN
ejpam-2967	98	19	<	<	X
ejpam-2967	98	20	|f(x)|	|f(x)|	NOUN
ejpam-2967	98	21	for	for	ADP
ejpam-2967	98	22	all	all	DET
ejpam-2967	98	23	x	x	SYM
ejpam-2967	98	24	∈	∈	PROPN
ejpam-2967	98	25	[	[	X
ejpam-2967	98	26	0	0	NUM
ejpam-2967	98	27	,	,	PUNCT
ejpam-2967	98	28	1	1	NUM
ejpam-2967	98	29	]	]	PUNCT
ejpam-2967	98	30	,	,	PUNCT
ejpam-2967	98	31	then	then	ADV
ejpam-2967	98	32	f	f	PROPN
ejpam-2967	99	1	+	+	CCONJ
ejpam-2967	99	2	g	g	PROPN
ejpam-2967	99	3	can	can	AUX
ejpam-2967	99	4	be	be	AUX
ejpam-2967	99	5	expressed	express	VERB
ejpam-2967	99	6	as	as	ADP
ejpam-2967	99	7	feψ	feψ	NUM
ejpam-2967	99	8	where	where	SCONJ
ejpam-2967	99	9	ψ	ψ	NOUN
ejpam-2967	99	10	is	be	AUX
ejpam-2967	99	11	a	a	DET
ejpam-2967	99	12	real	real	ADV
ejpam-2967	99	13	valued	value	VERB
ejpam-2967	99	14	continuous	continuous	ADJ
ejpam-2967	99	15	function	function	NOUN
ejpam-2967	99	16	on	on	ADP
ejpam-2967	99	17	[	[	X
ejpam-2967	99	18	0	0	NUM
ejpam-2967	99	19	,	,	PUNCT
ejpam-2967	99	20	1	1	NUM
ejpam-2967	99	21	]	]	PUNCT
ejpam-2967	99	22	.	.	PUNCT
ejpam-2967	100	1	proof	proof	NOUN
ejpam-2967	100	2	.	.	PUNCT
ejpam-2967	101	1	since	since	SCONJ
ejpam-2967	101	2	|g(x)|	|g(x)|	NOUN
ejpam-2967	101	3	<	<	X
ejpam-2967	101	4	|f(x)|	|f(x)|	NOUN
ejpam-2967	101	5	for	for	ADP
ejpam-2967	101	6	all	all	DET
ejpam-2967	101	7	x	x	SYM
ejpam-2967	101	8	∈	∈	PROPN
ejpam-2967	101	9	[	[	X
ejpam-2967	101	10	0	0	NUM
ejpam-2967	101	11	,	,	PUNCT
ejpam-2967	101	12	1],then	1],then	ADJ
ejpam-2967	101	13	f	f	NOUN
ejpam-2967	102	1	+	+	CCONJ
ejpam-2967	102	2	g	g	PROPN
ejpam-2967	102	3	is	be	AUX
ejpam-2967	102	4	always	always	ADV
ejpam-2967	102	5	a	a	DET
ejpam-2967	102	6	non	non	ADJ
ejpam-2967	102	7	-	-	ADJ
ejpam-2967	102	8	zero	zero	ADJ
ejpam-2967	102	9	function	function	NOUN
ejpam-2967	102	10	on	on	ADP
ejpam-2967	102	11	[	[	X
ejpam-2967	102	12	0	0	NUM
ejpam-2967	102	13	,	,	PUNCT
ejpam-2967	102	14	1	1	NUM
ejpam-2967	102	15	]	]	PUNCT
ejpam-2967	102	16	.	.	PUNCT
ejpam-2967	103	1	if	if	SCONJ
ejpam-2967	103	2	φ	φ	PROPN
ejpam-2967	103	3	=	=	SYM
ejpam-2967	103	4	g	g	PROPN
ejpam-2967	103	5	/	/	SYM
ejpam-2967	103	6	f	f	PROPN
ejpam-2967	103	7	then	then	ADV
ejpam-2967	103	8	|φ(x)|	|φ(x)|	PROPN
ejpam-2967	103	9	<	<	X
ejpam-2967	103	10	1	1	NUM
ejpam-2967	103	11	,	,	PUNCT
ejpam-2967	103	12	for	for	ADP
ejpam-2967	103	13	all	all	DET
ejpam-2967	103	14	x	x	SYM
ejpam-2967	103	15	∈	∈	PROPN
ejpam-2967	103	16	[	[	X
ejpam-2967	103	17	0	0	NUM
ejpam-2967	103	18	,	,	PUNCT
ejpam-2967	103	19	1	1	NUM
ejpam-2967	103	20	]	]	PUNCT
ejpam-2967	103	21	.	.	PUNCT
ejpam-2967	104	1	therefore	therefore	ADV
ejpam-2967	104	2	the	the	DET
ejpam-2967	104	3	range	range	NOUN
ejpam-2967	104	4	of	of	ADP
ejpam-2967	104	5	1	1	NUM
ejpam-2967	104	6	+	+	NUM
ejpam-2967	104	7	φ	φ	PROPN
ejpam-2967	104	8	lies	lie	VERB
ejpam-2967	104	9	in	in	ADP
ejpam-2967	104	10	the	the	DET
ejpam-2967	104	11	positive	positive	ADJ
ejpam-2967	104	12	x	x	NOUN
ejpam-2967	104	13	-	-	NOUN
ejpam-2967	104	14	axis	axis	ADJ
ejpam-2967	104	15	.	.	PUNCT
ejpam-2967	105	1	hence	hence	ADV
ejpam-2967	105	2	there	there	PRON
ejpam-2967	105	3	exist	exist	VERB
ejpam-2967	105	4	a	a	DET
ejpam-2967	105	5	continuous	continuous	ADJ
ejpam-2967	105	6	function	function	NOUN
ejpam-2967	105	7	on	on	ADP
ejpam-2967	105	8	d	d	NOUN
ejpam-2967	105	9	given	give	VERB
ejpam-2967	105	10	by	by	ADP
ejpam-2967	105	11	ψ	ψ	NOUN
ejpam-2967	105	12	=	=	PUNCT
ejpam-2967	105	13	log(1	log(1	NOUN
ejpam-2967	105	14	+	+	NOUN
ejpam-2967	105	15	φ	φ	NOUN
ejpam-2967	105	16	)	)	PUNCT
ejpam-2967	106	1	such	such	ADJ
ejpam-2967	106	2	that	that	SCONJ
ejpam-2967	106	3	f	f	PROPN
ejpam-2967	106	4	+	+	CCONJ
ejpam-2967	106	5	g	g	NOUN
ejpam-2967	106	6	=	=	PUNCT
ejpam-2967	106	7	f(1	f(1	PROPN
ejpam-2967	107	1	+	+	CCONJ
ejpam-2967	107	2	φ	φ	NUM
ejpam-2967	107	3	)	)	PUNCT
ejpam-2967	107	4	=	=	SYM
ejpam-2967	107	5	feψ	feψ	PROPN
ejpam-2967	107	6	.	.	PUNCT
ejpam-2967	108	1	prasanna	prasanna	PROPN
ejpam-2967	108	2	kumar	kumar	PROPN
ejpam-2967	108	3	/	/	SYM
ejpam-2967	108	4	eur	eur	PROPN
ejpam-2967	108	5	.	.	PUNCT
ejpam-2967	109	1	j.	j.	PROPN
ejpam-2967	109	2	pure	pure	PROPN
ejpam-2967	109	3	appl	appl	PROPN
ejpam-2967	109	4	.	.	PROPN
ejpam-2967	109	5	math	math	PROPN
ejpam-2967	109	6	,	,	PUNCT
ejpam-2967	109	7	10	10	NUM
ejpam-2967	109	8	(	(	PUNCT
ejpam-2967	109	9	3	3	NUM
ejpam-2967	109	10	)	)	PUNCT
ejpam-2967	109	11	(	(	PUNCT
ejpam-2967	109	12	2017	2017	NUM
ejpam-2967	109	13	)	)	PUNCT
ejpam-2967	109	14	,	,	PUNCT
ejpam-2967	109	15	488	488	NUM
ejpam-2967	109	16	-	-	SYM
ejpam-2967	109	17	494	494	NUM
ejpam-2967	109	18	492	492	NUM
ejpam-2967	109	19	theorem	theorem	NOUN
ejpam-2967	109	20	4	4	NUM
ejpam-2967	109	21	.	.	PUNCT
ejpam-2967	110	1	let	let	VERB
ejpam-2967	110	2	g	g	NOUN
ejpam-2967	110	3	:	:	PUNCT
ejpam-2967	110	4	[	[	X
ejpam-2967	110	5	0	0	NUM
ejpam-2967	110	6	,	,	PUNCT
ejpam-2967	110	7	1]→	1]→	NOUN
ejpam-2967	110	8	<	<	AUX
ejpam-2967	110	9	be	be	AUX
ejpam-2967	110	10	a	a	DET
ejpam-2967	110	11	non	non	ADJ
ejpam-2967	110	12	-	-	ADJ
ejpam-2967	110	13	constant	constant	ADJ
ejpam-2967	110	14	continuous	continuous	ADJ
ejpam-2967	110	15	function	function	NOUN
ejpam-2967	110	16	vanishing	vanish	VERB
ejpam-2967	110	17	nowhere	nowhere	ADV
ejpam-2967	110	18	in	in	ADP
ejpam-2967	110	19	its	its	PRON
ejpam-2967	110	20	domain	domain	NOUN
ejpam-2967	110	21	and	and	CCONJ
ejpam-2967	110	22	for	for	ADP
ejpam-2967	110	23	x	x	PROPN
ejpam-2967	110	24	∈	∈	PROPN
ejpam-2967	111	1	[	[	X
ejpam-2967	111	2	0	0	NUM
ejpam-2967	111	3	,	,	PUNCT
ejpam-2967	111	4	1	1	NUM
ejpam-2967	111	5	]	]	PUNCT
ejpam-2967	111	6	define	define	VERB
ejpam-2967	111	7	f(x	f(x	PROPN
ejpam-2967	111	8	)	)	PUNCT
ejpam-2967	112	1	=	=	SYM
ejpam-2967	112	2	max	max	PROPN
ejpam-2967	112	3	{	{	PUNCT
ejpam-2967	112	4	g(y	g(y	PROPN
ejpam-2967	112	5	)	)	PUNCT
ejpam-2967	112	6	;	;	PUNCT
ejpam-2967	112	7	0	0	NUM
ejpam-2967	112	8	≤	≤	NUM
ejpam-2967	112	9	y	y	NOUN
ejpam-2967	112	10	≤	≤	NUM
ejpam-2967	112	11	x	x	X
ejpam-2967	112	12	}	}	PUNCT
ejpam-2967	112	13	.	.	PUNCT
ejpam-2967	113	1	then	then	ADV
ejpam-2967	113	2	f	f	PROPN
ejpam-2967	113	3	is	be	AUX
ejpam-2967	113	4	uniformly	uniformly	ADV
ejpam-2967	113	5	continuous	continuous	ADJ
ejpam-2967	113	6	function	function	NOUN
ejpam-2967	113	7	in	in	ADP
ejpam-2967	113	8	its	its	PRON
ejpam-2967	113	9	domain	domain	NOUN
ejpam-2967	113	10	.	.	PUNCT
ejpam-2967	114	1	proof	proof	NOUN
ejpam-2967	114	2	.	.	PUNCT
ejpam-2967	115	1	take	take	VERB
ejpam-2967	115	2	g(x	g(x	NOUN
ejpam-2967	115	3	)	)	PUNCT
ejpam-2967	116	1	=	=	SYM
ejpam-2967	116	2	g(b	g(b	NOUN
ejpam-2967	116	3	)	)	PUNCT
ejpam-2967	116	4	for	for	ADP
ejpam-2967	116	5	all	all	DET
ejpam-2967	116	6	x	x	PROPN
ejpam-2967	116	7	>	>	X
ejpam-2967	116	8	b.	b.	PROPN
ejpam-2967	117	1	it	it	PRON
ejpam-2967	117	2	can	can	AUX
ejpam-2967	117	3	be	be	AUX
ejpam-2967	117	4	easily	easily	ADV
ejpam-2967	117	5	seen	see	VERB
ejpam-2967	117	6	that	that	SCONJ
ejpam-2967	117	7	|f(x)−	|f(x)−	NOUN
ejpam-2967	117	8	f(y)|	f(y)|	PROPN
ejpam-2967	117	9	≤	≤	PROPN
ejpam-2967	117	10	max	max	PROPN
ejpam-2967	117	11	|g(s)−	|g(s)−	ADP
ejpam-2967	117	12	g(t)|	g(t)|	NOUN
ejpam-2967	117	13	for	for	ADP
ejpam-2967	117	14	all	all	DET
ejpam-2967	117	15	s	s	PROPN
ejpam-2967	117	16	,	,	PUNCT
ejpam-2967	117	17	t	t	PROPN
ejpam-2967	117	18	∈	∈	PROPN
ejpam-2967	118	1	[	[	X
ejpam-2967	118	2	x	x	X
ejpam-2967	118	3	,	,	PUNCT
ejpam-2967	118	4	y	y	PROPN
ejpam-2967	118	5	]	]	PUNCT
ejpam-2967	118	6	.	.	PUNCT
ejpam-2967	119	1	but	but	CCONJ
ejpam-2967	119	2	then	then	ADV
ejpam-2967	119	3	|f(x)−	|f(x)−	NOUN
ejpam-2967	119	4	f(y)|	f(y)|	PROPN
ejpam-2967	119	5	≤	≤	PROPN
ejpam-2967	119	6	max	max	PROPN
ejpam-2967	119	7	|g(s)−	|g(s)−	ADP
ejpam-2967	119	8	g(t)|	g(t)|	NOUN
ejpam-2967	119	9	whenever	whenever	SCONJ
ejpam-2967	119	10	|s−	|s−	VERB
ejpam-2967	119	11	t|	t|	PROPN
ejpam-2967	119	12	≤	≤	NUM
ejpam-2967	119	13	|x−	|x−	PROPN
ejpam-2967	119	14	y|	y|	NOUN
ejpam-2967	119	15	.	.	PUNCT
ejpam-2967	120	1	so	so	ADV
ejpam-2967	120	2	given	give	VERB
ejpam-2967	120	3	any	any	DET
ejpam-2967	120	4	ε	ε	PROPN
ejpam-2967	120	5	>	>	X
ejpam-2967	120	6	0	0	PUNCT
ejpam-2967	121	1	there	there	PRON
ejpam-2967	121	2	is	be	VERB
ejpam-2967	121	3	a	a	DET
ejpam-2967	121	4	δ	δ	PROPN
ejpam-2967	121	5	>	>	X
ejpam-2967	121	6	0	0	NUM
ejpam-2967	121	7	such	such	ADJ
ejpam-2967	121	8	that	that	DET
ejpam-2967	121	9	|s−	|s−	ADJ
ejpam-2967	121	10	t|	t|	NOUN
ejpam-2967	121	11	<	<	X
ejpam-2967	121	12	δ	δ	PROPN
ejpam-2967	121	13	=	=	NOUN
ejpam-2967	121	14	⇒	⇒	NOUN
ejpam-2967	121	15	|g(s)−	|g(s)−	ADP
ejpam-2967	121	16	g(t)|	g(t)|	NOUN
ejpam-2967	121	17	<	<	X
ejpam-2967	121	18	ε	ε	PROPN
ejpam-2967	121	19	since	since	SCONJ
ejpam-2967	121	20	g	g	PROPN
ejpam-2967	121	21	is	be	AUX
ejpam-2967	121	22	a	a	DET
ejpam-2967	121	23	continuous	continuous	ADJ
ejpam-2967	121	24	real	real	ADJ
ejpam-2967	121	25	valued	value	VERB
ejpam-2967	121	26	function	function	NOUN
ejpam-2967	121	27	on	on	ADP
ejpam-2967	121	28	a	a	DET
ejpam-2967	121	29	compact	compact	ADJ
ejpam-2967	121	30	set	set	NOUN
ejpam-2967	121	31	[	[	X
ejpam-2967	121	32	0	0	NUM
ejpam-2967	121	33	,	,	PUNCT
ejpam-2967	121	34	1	1	NUM
ejpam-2967	121	35	]	]	PUNCT
ejpam-2967	121	36	and	and	CCONJ
ejpam-2967	121	37	thereby	thereby	ADV
ejpam-2967	121	38	uniformly	uniformly	ADV
ejpam-2967	121	39	continuous	continuous	ADJ
ejpam-2967	121	40	.	.	PUNCT
ejpam-2967	122	1	so	so	ADV
ejpam-2967	122	2	using	use	VERB
ejpam-2967	122	3	the	the	DET
ejpam-2967	122	4	same	same	ADJ
ejpam-2967	122	5	δ	δ	NOUN
ejpam-2967	122	6	we	we	PRON
ejpam-2967	122	7	have	have	VERB
ejpam-2967	122	8	|f(x)−	|f(x)−	NOUN
ejpam-2967	122	9	f(y)|	f(y)|	PROPN
ejpam-2967	122	10	≤	≤	PROPN
ejpam-2967	122	11	max	max	PROPN
ejpam-2967	122	12	|g(s)−	|g(s)−	ADP
ejpam-2967	122	13	g(t)|	g(t)|	NOUN
ejpam-2967	122	14	<	<	X
ejpam-2967	122	15	ε	ε	PROPN
ejpam-2967	122	16	whenever	whenever	SCONJ
ejpam-2967	122	17	|s−	|s−	ADJ
ejpam-2967	122	18	t|	t|	PROPN
ejpam-2967	122	19	≤	≤	NUM
ejpam-2967	122	20	|x−	|x−	PROPN
ejpam-2967	122	21	y|	y|	NOUN
ejpam-2967	122	22	<	<	X
ejpam-2967	122	23	δ	δ	PROPN
ejpam-2967	122	24	.	.	PUNCT
ejpam-2967	123	1	therefore	therefore	ADV
ejpam-2967	123	2	,	,	PUNCT
ejpam-2967	123	3	f	f	PROPN
ejpam-2967	123	4	is	be	AUX
ejpam-2967	123	5	uniformly	uniformly	ADV
ejpam-2967	123	6	continuous	continuous	ADJ
ejpam-2967	123	7	in	in	ADP
ejpam-2967	123	8	its	its	PRON
ejpam-2967	123	9	domain	domain	NOUN
ejpam-2967	123	10	.	.	PUNCT
ejpam-2967	124	1	our	our	PRON
ejpam-2967	124	2	next	next	ADJ
ejpam-2967	124	3	result	result	NOUN
ejpam-2967	124	4	is	be	AUX
ejpam-2967	124	5	originated	originate	VERB
ejpam-2967	124	6	from	from	ADP
ejpam-2967	124	7	the	the	DET
ejpam-2967	124	8	characterization	characterization	NOUN
ejpam-2967	124	9	of	of	ADP
ejpam-2967	124	10	continuous	continuous	ADJ
ejpam-2967	124	11	functions	function	NOUN
ejpam-2967	124	12	between	between	ADP
ejpam-2967	124	13	metric	metric	ADJ
ejpam-2967	124	14	spaces	space	NOUN
ejpam-2967	124	15	.	.	PUNCT
ejpam-2967	125	1	the	the	DET
ejpam-2967	125	2	necessary	necessary	ADJ
ejpam-2967	125	3	and	and	CCONJ
ejpam-2967	125	4	sufficient	sufficient	ADJ
ejpam-2967	125	5	condition	condition	NOUN
ejpam-2967	125	6	for	for	ADP
ejpam-2967	125	7	a	a	DET
ejpam-2967	125	8	function	function	NOUN
ejpam-2967	125	9	f	f	NOUN
ejpam-2967	125	10	:	:	PUNCT
ejpam-2967	125	11	<	<	X
ejpam-2967	125	12	→	→	X
ejpam-2967	125	13	<	<	X
ejpam-2967	125	14	to	to	PART
ejpam-2967	125	15	be	be	AUX
ejpam-2967	125	16	continuous	continuous	ADJ
ejpam-2967	125	17	is	be	AUX
ejpam-2967	125	18	image	image	NOUN
ejpam-2967	125	19	of	of	ADP
ejpam-2967	125	20	convergent	convergent	ADJ
ejpam-2967	125	21	sequences	sequence	NOUN
ejpam-2967	125	22	in	in	ADP
ejpam-2967	125	23	the	the	DET
ejpam-2967	125	24	domain	domain	NOUN
ejpam-2967	125	25	is	be	AUX
ejpam-2967	125	26	convergent	convergent	NOUN
ejpam-2967	125	27	in	in	ADP
ejpam-2967	125	28	the	the	DET
ejpam-2967	125	29	range	range	NOUN
ejpam-2967	125	30	and	and	CCONJ
ejpam-2967	125	31	limits	limit	NOUN
ejpam-2967	125	32	correspond	correspond	VERB
ejpam-2967	125	33	each	each	DET
ejpam-2967	125	34	other	other	ADJ
ejpam-2967	125	35	can	can	AUX
ejpam-2967	125	36	characterize	characterize	VERB
ejpam-2967	125	37	the	the	DET
ejpam-2967	125	38	continuity	continuity	NOUN
ejpam-2967	125	39	only	only	ADV
ejpam-2967	125	40	if	if	SCONJ
ejpam-2967	125	41	the	the	DET
ejpam-2967	125	42	image	image	NOUN
ejpam-2967	125	43	of	of	ADP
ejpam-2967	125	44	the	the	DET
ejpam-2967	125	45	convergent	convergent	NOUN
ejpam-2967	125	46	sequence	sequence	NOUN
ejpam-2967	125	47	converges	converge	VERB
ejpam-2967	125	48	?	?	PUNCT
ejpam-2967	126	1	the	the	DET
ejpam-2967	126	2	below	below	ADJ
ejpam-2967	126	3	theorem	theorem	NOUN
ejpam-2967	126	4	is	be	AUX
ejpam-2967	126	5	some	some	PRON
ejpam-2967	126	6	what	what	PRON
ejpam-2967	126	7	motivated	motivate	VERB
ejpam-2967	126	8	by	by	ADP
ejpam-2967	126	9	this	this	DET
ejpam-2967	126	10	question	question	NOUN
ejpam-2967	126	11	.	.	PUNCT
ejpam-2967	127	1	theorem	theorem	ADJ
ejpam-2967	127	2	5	5	NUM
ejpam-2967	127	3	.	.	PUNCT
ejpam-2967	128	1	let	let	VERB
ejpam-2967	128	2	f	f	NOUN
ejpam-2967	128	3	:	:	PUNCT
ejpam-2967	128	4	<	<	X
ejpam-2967	128	5	→	→	SYM
ejpam-2967	128	6	<	<	X
ejpam-2967	128	7	,	,	PUNCT
ejpam-2967	128	8	be	be	AUX
ejpam-2967	128	9	a	a	DET
ejpam-2967	128	10	connected	connected	ADJ
ejpam-2967	128	11	map	map	NOUN
ejpam-2967	128	12	such	such	ADJ
ejpam-2967	128	13	that	that	SCONJ
ejpam-2967	128	14	{	{	PUNCT
ejpam-2967	128	15	xn	xn	X
ejpam-2967	128	16	}	}	PUNCT
ejpam-2967	128	17	→	→	SYM
ejpam-2967	128	18	a	a	DET
ejpam-2967	128	19	=	=	NOUN
ejpam-2967	128	20	⇒	⇒	NOUN
ejpam-2967	128	21	{	{	PUNCT
ejpam-2967	128	22	f(xn	f(xn	PROPN
ejpam-2967	128	23	)	)	PUNCT
ejpam-2967	128	24	}	}	PUNCT
ejpam-2967	128	25	→	→	SYM
ejpam-2967	128	26	f(a	f(a	NOUN
ejpam-2967	128	27	)	)	PUNCT
ejpam-2967	128	28	for	for	ADP
ejpam-2967	128	29	any	any	DET
ejpam-2967	128	30	convergent	convergent	NOUN
ejpam-2967	128	31	sequences	sequence	NOUN
ejpam-2967	128	32	{	{	PUNCT
ejpam-2967	128	33	xn	xn	NUM
ejpam-2967	128	34	}	}	PUNCT
ejpam-2967	128	35	,	,	PUNCT
ejpam-2967	128	36	{	{	PUNCT
ejpam-2967	128	37	f(xn	f(xn	NOUN
ejpam-2967	128	38	)	)	PUNCT
ejpam-2967	128	39	}	}	PUNCT
ejpam-2967	128	40	in	in	ADP
ejpam-2967	128	41	<	<	X
ejpam-2967	128	42	.	.	PUNCT
ejpam-2967	129	1	then	then	ADV
ejpam-2967	129	2	f	f	PROPN
ejpam-2967	129	3	must	must	AUX
ejpam-2967	129	4	be	be	AUX
ejpam-2967	129	5	continuous	continuous	ADJ
ejpam-2967	129	6	.	.	PUNCT
ejpam-2967	130	1	proof	proof	NOUN
ejpam-2967	130	2	.	.	PUNCT
ejpam-2967	131	1	by	by	ADP
ejpam-2967	131	2	hypothesis	hypothesis	NOUN
ejpam-2967	131	3	,	,	PUNCT
ejpam-2967	131	4	if	if	SCONJ
ejpam-2967	131	5	{	{	PUNCT
ejpam-2967	131	6	xn	xn	X
ejpam-2967	131	7	}	}	PUNCT
ejpam-2967	131	8	is	be	AUX
ejpam-2967	131	9	a	a	DET
ejpam-2967	131	10	sequence	sequence	NOUN
ejpam-2967	131	11	of	of	ADP
ejpam-2967	131	12	terms	term	NOUN
ejpam-2967	131	13	in	in	ADP
ejpam-2967	131	14	<	<	X
ejpam-2967	131	15	such	such	ADJ
ejpam-2967	131	16	that	that	SCONJ
ejpam-2967	131	17	xn	xn	PROPN
ejpam-2967	132	1	→	→	PUNCT
ejpam-2967	132	2	a	a	DET
ejpam-2967	132	3	then	then	ADV
ejpam-2967	132	4	f(xn	f(xn	NOUN
ejpam-2967	132	5	)	)	PUNCT
ejpam-2967	132	6	→	→	SYM
ejpam-2967	132	7	f(a	f(a	PROPN
ejpam-2967	132	8	)	)	PUNCT
ejpam-2967	132	9	,	,	PUNCT
ejpam-2967	132	10	provided	provide	VERB
ejpam-2967	132	11	f(xn	f(xn	NOUN
ejpam-2967	132	12	)	)	PUNCT
ejpam-2967	132	13	also	also	ADV
ejpam-2967	132	14	converges	converge	VERB
ejpam-2967	132	15	.	.	PUNCT
ejpam-2967	133	1	note	note	VERB
ejpam-2967	133	2	that	that	SCONJ
ejpam-2967	133	3	if	if	SCONJ
ejpam-2967	133	4	xn	xn	PROPN
ejpam-2967	133	5	→	→	SYM
ejpam-2967	133	6	a	a	PRON
ejpam-2967	133	7	but	but	CCONJ
ejpam-2967	133	8	f(xn	f(xn	PROPN
ejpam-2967	133	9	)	)	PUNCT
ejpam-2967	133	10	does	do	AUX
ejpam-2967	133	11	not	not	PART
ejpam-2967	133	12	converge	converge	VERB
ejpam-2967	133	13	then	then	ADV
ejpam-2967	133	14	clearly	clearly	ADV
ejpam-2967	133	15	{	{	PUNCT
ejpam-2967	133	16	f(xn	f(xn	PROPN
ejpam-2967	133	17	)	)	PUNCT
ejpam-2967	133	18	}	}	PUNCT
ejpam-2967	133	19	is	be	AUX
ejpam-2967	133	20	an	an	DET
ejpam-2967	133	21	unbounded	unbounded	ADJ
ejpam-2967	133	22	sequence	sequence	NOUN
ejpam-2967	133	23	.	.	PUNCT
ejpam-2967	134	1	now	now	ADV
ejpam-2967	134	2	we	we	PRON
ejpam-2967	134	3	suppose	suppose	VERB
ejpam-2967	134	4	that	that	SCONJ
ejpam-2967	134	5	f	f	PROPN
ejpam-2967	134	6	fails	fail	VERB
ejpam-2967	134	7	to	to	PART
ejpam-2967	134	8	be	be	AUX
ejpam-2967	134	9	continuous	continuous	ADJ
ejpam-2967	134	10	at	at	ADP
ejpam-2967	134	11	x	x	X
ejpam-2967	134	12	=	=	PUNCT
ejpam-2967	134	13	a.	a.	NOUN
ejpam-2967	134	14	let	let	VERB
ejpam-2967	134	15	δ	δ	PROPN
ejpam-2967	134	16	>	>	X
ejpam-2967	134	17	0	0	NUM
ejpam-2967	135	1	such	such	ADJ
ejpam-2967	135	2	that	that	SCONJ
ejpam-2967	135	3	whenever	whenever	SCONJ
ejpam-2967	135	4	|x−	|x−	PROPN
ejpam-2967	135	5	a|	a|	PROPN
ejpam-2967	135	6	<	<	X
ejpam-2967	135	7	δ	δ	X
ejpam-2967	135	8	we	we	PRON
ejpam-2967	135	9	have	have	VERB
ejpam-2967	135	10	|f(x)−	|f(x)−	NOUN
ejpam-2967	135	11	f(a)|	f(a)|	NOUN
ejpam-2967	135	12	<	<	X
ejpam-2967	135	13	α	α	X
ejpam-2967	135	14	(	(	PUNCT
ejpam-2967	135	15	11	11	NUM
ejpam-2967	135	16	)	)	PUNCT
ejpam-2967	135	17	for	for	ADP
ejpam-2967	135	18	some	some	DET
ejpam-2967	135	19	fixed	fix	VERB
ejpam-2967	135	20	α	α	PROPN
ejpam-2967	135	21	>	>	X
ejpam-2967	135	22	0	0	NUM
ejpam-2967	135	23	or	or	CCONJ
ejpam-2967	135	24	|f(x)−	|f(x)−	PROPN
ejpam-2967	135	25	f(a)|	f(a)|	PROPN
ejpam-2967	135	26	>	>	X
ejpam-2967	135	27	(	(	PUNCT
ejpam-2967	135	28	|f(a)|+	|f(a)|+	NOUN
ejpam-2967	135	29	α	α	NOUN
ejpam-2967	135	30	)	)	PUNCT
ejpam-2967	135	31	.	.	PUNCT
ejpam-2967	136	1	(	(	PUNCT
ejpam-2967	136	2	12	12	NUM
ejpam-2967	136	3	)	)	PUNCT
ejpam-2967	136	4	if	if	SCONJ
ejpam-2967	136	5	such	such	DET
ejpam-2967	136	6	a	a	DET
ejpam-2967	136	7	δ	δ	PROPN
ejpam-2967	136	8	does	do	AUX
ejpam-2967	136	9	not	not	PART
ejpam-2967	136	10	exist	exist	VERB
ejpam-2967	136	11	,	,	PUNCT
ejpam-2967	136	12	then	then	ADV
ejpam-2967	136	13	we	we	PRON
ejpam-2967	136	14	can	can	AUX
ejpam-2967	136	15	find	find	VERB
ejpam-2967	136	16	a	a	DET
ejpam-2967	136	17	sequence	sequence	NOUN
ejpam-2967	136	18	{	{	PUNCT
ejpam-2967	136	19	xn	xn	NOUN
ejpam-2967	136	20	}	}	PUNCT
ejpam-2967	136	21	→	→	ADP
ejpam-2967	136	22	a	a	DET
ejpam-2967	136	23	such	such	ADJ
ejpam-2967	136	24	that	that	SCONJ
ejpam-2967	136	25	|f(xn)−	|f(xn)−	NOUN
ejpam-2967	136	26	f(a)|	f(a)|	PROPN
ejpam-2967	136	27	≥	≥	PROPN
ejpam-2967	136	28	α	α	X
ejpam-2967	136	29	>	>	X
ejpam-2967	136	30	0	0	PROPN
ejpam-2967	136	31	,	,	PUNCT
ejpam-2967	136	32	or|f(xn)|	or|f(xn)|	PROPN
ejpam-2967	136	33	≤	≤	NUM
ejpam-2967	136	34	(	(	PUNCT
ejpam-2967	136	35	|f(a)|+	|f(a)|+	NOUN
ejpam-2967	136	36	α	α	NOUN
ejpam-2967	136	37	)	)	PUNCT
ejpam-2967	136	38	prasanna	prasanna	PROPN
ejpam-2967	136	39	kumar	kumar	PROPN
ejpam-2967	136	40	/	/	SYM
ejpam-2967	136	41	eur	eur	PROPN
ejpam-2967	136	42	.	.	PUNCT
ejpam-2967	137	1	j.	j.	PROPN
ejpam-2967	137	2	pure	pure	PROPN
ejpam-2967	137	3	appl	appl	PROPN
ejpam-2967	137	4	.	.	PROPN
ejpam-2967	137	5	math	math	PROPN
ejpam-2967	137	6	,	,	PUNCT
ejpam-2967	137	7	10	10	NUM
ejpam-2967	137	8	(	(	PUNCT
ejpam-2967	137	9	3	3	NUM
ejpam-2967	137	10	)	)	PUNCT
ejpam-2967	137	11	(	(	PUNCT
ejpam-2967	137	12	2017	2017	NUM
ejpam-2967	137	13	)	)	PUNCT
ejpam-2967	137	14	,	,	PUNCT
ejpam-2967	137	15	488	488	NUM
ejpam-2967	137	16	-	-	SYM
ejpam-2967	137	17	494	494	NUM
ejpam-2967	137	18	493	493	NUM
ejpam-2967	137	19	for	for	ADP
ejpam-2967	137	20	all	all	DET
ejpam-2967	137	21	n.	n.	NOUN
ejpam-2967	137	22	but	but	CCONJ
ejpam-2967	137	23	then	then	ADV
ejpam-2967	137	24	the	the	DET
ejpam-2967	137	25	sequence	sequence	NOUN
ejpam-2967	137	26	{	{	PUNCT
ejpam-2967	137	27	f(xn	f(xn	PROPN
ejpam-2967	137	28	)	)	PUNCT
ejpam-2967	137	29	}	}	PUNCT
ejpam-2967	137	30	is	be	AUX
ejpam-2967	137	31	bounded	bound	VERB
ejpam-2967	138	1	and	and	CCONJ
ejpam-2967	138	2	it	it	PRON
ejpam-2967	138	3	will	will	AUX
ejpam-2967	138	4	have	have	VERB
ejpam-2967	138	5	a	a	DET
ejpam-2967	138	6	subsequence	subsequence	NOUN
ejpam-2967	138	7	converging	converge	VERB
ejpam-2967	138	8	to	to	ADP
ejpam-2967	138	9	a	a	DET
ejpam-2967	138	10	limit	limit	NOUN
ejpam-2967	138	11	other	other	ADJ
ejpam-2967	138	12	than	than	ADP
ejpam-2967	138	13	f(a	f(a	PROPN
ejpam-2967	138	14	)	)	PUNCT
ejpam-2967	138	15	.	.	PUNCT
ejpam-2967	139	1	but	but	CCONJ
ejpam-2967	139	2	this	this	PRON
ejpam-2967	139	3	is	be	AUX
ejpam-2967	139	4	not	not	PART
ejpam-2967	139	5	possible	possible	ADJ
ejpam-2967	139	6	.	.	PUNCT
ejpam-2967	140	1	therefore	therefore	ADV
ejpam-2967	140	2	our	our	PRON
ejpam-2967	140	3	claim	claim	NOUN
ejpam-2967	140	4	of	of	ADP
ejpam-2967	140	5	existence	existence	NOUN
ejpam-2967	140	6	of	of	ADP
ejpam-2967	140	7	(	(	PUNCT
ejpam-2967	140	8	11	11	NUM
ejpam-2967	140	9	)	)	PUNCT
ejpam-2967	140	10	and	and	CCONJ
ejpam-2967	140	11	(	(	PUNCT
ejpam-2967	140	12	12	12	NUM
ejpam-2967	140	13	)	)	PUNCT
ejpam-2967	140	14	is	be	AUX
ejpam-2967	140	15	correct	correct	ADJ
ejpam-2967	140	16	.	.	PUNCT
ejpam-2967	141	1	let	let	VERB
ejpam-2967	141	2	us	we	PRON
ejpam-2967	141	3	define	define	VERB
ejpam-2967	141	4	a	a	DET
ejpam-2967	141	5	function	function	NOUN
ejpam-2967	141	6	g(x	g(x	NOUN
ejpam-2967	141	7	,	,	PUNCT
ejpam-2967	141	8	f(x	f(x	PROPN
ejpam-2967	141	9	)	)	PUNCT
ejpam-2967	141	10	)	)	PUNCT
ejpam-2967	142	1	=	=	PUNCT
ejpam-2967	143	1	|f(x)|	|f(x)|	NOUN
ejpam-2967	143	2	for	for	ADP
ejpam-2967	143	3	|x	|x	NOUN
ejpam-2967	143	4	−	−	PROPN
ejpam-2967	143	5	a|	a|	PROPN
ejpam-2967	143	6	≤	≤	PROPN
ejpam-2967	143	7	δ	δ	PROPN
ejpam-2967	143	8	,	,	PUNCT
ejpam-2967	143	9	where	where	SCONJ
ejpam-2967	143	10	δ	δ	PROPN
ejpam-2967	143	11	is	be	AUX
ejpam-2967	143	12	as	as	SCONJ
ejpam-2967	143	13	given	give	VERB
ejpam-2967	143	14	previously	previously	ADV
ejpam-2967	143	15	.	.	PUNCT
ejpam-2967	144	1	clearly	clearly	ADV
ejpam-2967	144	2	g	g	PROPN
ejpam-2967	144	3	is	be	AUX
ejpam-2967	144	4	a	a	DET
ejpam-2967	144	5	continuous	continuous	ADJ
ejpam-2967	144	6	function	function	NOUN
ejpam-2967	144	7	.	.	PUNCT
ejpam-2967	145	1	then	then	ADV
ejpam-2967	145	2	g	g	PROPN
ejpam-2967	145	3	has	have	VERB
ejpam-2967	145	4	image	image	NOUN
ejpam-2967	145	5	points	point	NOUN
ejpam-2967	145	6	in	in	ADP
ejpam-2967	145	7	the	the	DET
ejpam-2967	145	8	set	set	NOUN
ejpam-2967	145	9	(	(	PUNCT
ejpam-2967	145	10	−∞	−∞	NOUN
ejpam-2967	145	11	,	,	PUNCT
ejpam-2967	145	12	|f(a)|	|f(a)|	PROPN
ejpam-2967	145	13	+	+	NOUN
ejpam-2967	145	14	α	α	NOUN
ejpam-2967	145	15	)	)	PUNCT
ejpam-2967	145	16	⋃	⋃	PROPN
ejpam-2967	145	17	(	(	PUNCT
ejpam-2967	145	18	|f(a)|	|f(a)|	PROPN
ejpam-2967	145	19	+	+	CCONJ
ejpam-2967	145	20	α,∞	α,∞	NOUN
ejpam-2967	145	21	)	)	PUNCT
ejpam-2967	145	22	.	.	PUNCT
ejpam-2967	146	1	the	the	DET
ejpam-2967	146	2	point	point	NOUN
ejpam-2967	146	3	g(a	g(a	PROPN
ejpam-2967	146	4	,	,	PUNCT
ejpam-2967	146	5	f(a	f(a	NOUN
ejpam-2967	146	6	)	)	PUNCT
ejpam-2967	146	7	)	)	PUNCT
ejpam-2967	147	1	=	=	PUNCT
ejpam-2967	147	2	|f(a)|	|f(a)|	NOUN
ejpam-2967	147	3	∈	∈	PROPN
ejpam-2967	147	4	(	(	PUNCT
ejpam-2967	147	5	−∞	−∞	NOUN
ejpam-2967	147	6	,	,	PUNCT
ejpam-2967	147	7	|f(a)|+	|f(a)|+	NOUN
ejpam-2967	147	8	α	α	NOUN
ejpam-2967	147	9	)	)	PUNCT
ejpam-2967	147	10	and	and	CCONJ
ejpam-2967	147	11	the	the	DET
ejpam-2967	147	12	unboundedness	unboundedness	NOUN
ejpam-2967	147	13	of	of	ADP
ejpam-2967	147	14	f	f	PROPN
ejpam-2967	147	15	near	near	ADP
ejpam-2967	147	16	a	a	DET
ejpam-2967	147	17	imply	imply	NOUN
ejpam-2967	147	18	that	that	SCONJ
ejpam-2967	147	19	there	there	PRON
ejpam-2967	147	20	are	be	VERB
ejpam-2967	147	21	points	point	NOUN
ejpam-2967	147	22	of	of	ADP
ejpam-2967	147	23	the	the	DET
ejpam-2967	147	24	image	image	NOUN
ejpam-2967	147	25	of	of	ADP
ejpam-2967	147	26	g	g	NOUN
ejpam-2967	147	27	in	in	ADP
ejpam-2967	147	28	(	(	PUNCT
ejpam-2967	147	29	|f(a)|+	|f(a)|+	NOUN
ejpam-2967	147	30	α,∞	α,∞	NOUN
ejpam-2967	147	31	)	)	PUNCT
ejpam-2967	147	32	.	.	PUNCT
ejpam-2967	148	1	therefore	therefore	ADV
ejpam-2967	148	2	g	g	PROPN
ejpam-2967	148	3	(	(	PUNCT
ejpam-2967	148	4	<	<	X
ejpam-2967	148	5	×	×	NOUN
ejpam-2967	148	6	f	f	X
ejpam-2967	148	7	(	(	PUNCT
ejpam-2967	148	8	<	<	NOUN
ejpam-2967	148	9	)	)	PUNCT
ejpam-2967	148	10	)	)	PUNCT
ejpam-2967	148	11	must	must	AUX
ejpam-2967	148	12	be	be	AUX
ejpam-2967	148	13	disconnected	disconnect	VERB
ejpam-2967	148	14	.	.	PUNCT
ejpam-2967	149	1	since	since	SCONJ
ejpam-2967	149	2	g	g	PROPN
ejpam-2967	149	3	is	be	AUX
ejpam-2967	149	4	continuous	continuous	ADJ
ejpam-2967	149	5	,	,	PUNCT
ejpam-2967	149	6	<	<	X
ejpam-2967	149	7	×	×	PROPN
ejpam-2967	149	8	f	f	X
ejpam-2967	149	9	(	(	PUNCT
ejpam-2967	149	10	<	<	X
ejpam-2967	149	11	)	)	PUNCT
ejpam-2967	149	12	must	must	AUX
ejpam-2967	149	13	also	also	ADV
ejpam-2967	149	14	be	be	AUX
ejpam-2967	149	15	disconnected	disconnect	VERB
ejpam-2967	149	16	.	.	PUNCT
ejpam-2967	150	1	this	this	PRON
ejpam-2967	150	2	is	be	AUX
ejpam-2967	150	3	a	a	DET
ejpam-2967	150	4	contradiction	contradiction	NOUN
ejpam-2967	150	5	to	to	ADP
ejpam-2967	150	6	the	the	DET
ejpam-2967	150	7	fact	fact	NOUN
ejpam-2967	150	8	<	<	X
ejpam-2967	150	9	×	×	PROPN
ejpam-2967	150	10	f	f	X
ejpam-2967	150	11	(	(	PUNCT
ejpam-2967	150	12	<	<	X
ejpam-2967	150	13	)	)	PUNCT
ejpam-2967	150	14	is	be	AUX
ejpam-2967	150	15	connected	connect	VERB
ejpam-2967	150	16	being	be	AUX
ejpam-2967	150	17	a	a	DET
ejpam-2967	150	18	product	product	NOUN
ejpam-2967	150	19	of	of	ADP
ejpam-2967	150	20	two	two	NUM
ejpam-2967	150	21	connected	connected	ADJ
ejpam-2967	150	22	sets	set	NOUN
ejpam-2967	150	23	.	.	PUNCT
ejpam-2967	151	1	hence	hence	ADV
ejpam-2967	151	2	our	our	PRON
ejpam-2967	151	3	assumption	assumption	NOUN
ejpam-2967	151	4	is	be	AUX
ejpam-2967	151	5	wrong	wrong	ADJ
ejpam-2967	151	6	and	and	CCONJ
ejpam-2967	151	7	f	f	PROPN
ejpam-2967	151	8	has	have	VERB
ejpam-2967	151	9	no	no	DET
ejpam-2967	151	10	discontinuity	discontinuity	NOUN
ejpam-2967	151	11	.	.	PUNCT
ejpam-2967	152	1	hence	hence	ADV
ejpam-2967	152	2	the	the	DET
ejpam-2967	152	3	proof	proof	NOUN
ejpam-2967	152	4	.	.	PUNCT
ejpam-2967	153	1	finally	finally	ADV
ejpam-2967	153	2	we	we	PRON
ejpam-2967	153	3	will	will	AUX
ejpam-2967	153	4	present	present	VERB
ejpam-2967	153	5	an	an	DET
ejpam-2967	153	6	inequality	inequality	NOUN
ejpam-2967	153	7	involving	involve	VERB
ejpam-2967	153	8	real	real	ADJ
ejpam-2967	153	9	numbers	number	NOUN
ejpam-2967	153	10	and	and	CCONJ
ejpam-2967	153	11	their	their	PRON
ejpam-2967	153	12	behaviour	behaviour	NOUN
ejpam-2967	153	13	on	on	ADP
ejpam-2967	153	14	the	the	DET
ejpam-2967	153	15	unit	unit	NOUN
ejpam-2967	153	16	circle	circle	NOUN
ejpam-2967	153	17	in	in	ADP
ejpam-2967	153	18	lp	lp	ADJ
ejpam-2967	153	19	settings	setting	NOUN
ejpam-2967	153	20	.	.	PUNCT
ejpam-2967	154	1	it	it	PRON
ejpam-2967	154	2	is	be	AUX
ejpam-2967	154	3	quite	quite	ADV
ejpam-2967	154	4	interesting	interesting	ADJ
ejpam-2967	154	5	to	to	PART
ejpam-2967	154	6	see	see	VERB
ejpam-2967	154	7	such	such	ADJ
ejpam-2967	154	8	results	result	NOUN
ejpam-2967	154	9	with	with	ADP
ejpam-2967	154	10	a	a	DET
ejpam-2967	154	11	‘	'	PUNCT
ejpam-2967	154	12	non	non	ADJ
ejpam-2967	154	13	-	-	ADJ
ejpam-2967	154	14	normed	normed	ADJ
ejpam-2967	154	15	’	'	PUNCT
ejpam-2967	154	16	structure	structure	NOUN
ejpam-2967	154	17	.	.	PUNCT
ejpam-2967	155	1	theorem	theorem	VERB
ejpam-2967	155	2	6	6	NUM
ejpam-2967	155	3	.	.	PUNCT
ejpam-2967	156	1	if	if	SCONJ
ejpam-2967	156	2	0	0	NUM
ejpam-2967	156	3	≤	≤	NOUN
ejpam-2967	156	4	a	a	DET
ejpam-2967	156	5	≤	≤	NUM
ejpam-2967	156	6	1	1	NUM
ejpam-2967	156	7	,	,	PUNCT
ejpam-2967	156	8	0	0	PUNCT
ejpam-2967	156	9	<	<	X
ejpam-2967	156	10	c	c	X
ejpam-2967	156	11	≤	≤	NUM
ejpam-2967	156	12	b	b	X
ejpam-2967	156	13	≤	≤	NUM
ejpam-2967	156	14	1	1	NUM
ejpam-2967	156	15	and	and	CCONJ
ejpam-2967	156	16	p	p	X
ejpam-2967	156	17	>	>	X
ejpam-2967	156	18	0	0	PUNCT
ejpam-2967	157	1	then	then	ADV
ejpam-2967	157	2	a+	a+	PUNCT
ejpam-2967	157	3	b{∫	b{∫	PROPN
ejpam-2967	157	4	2π	2π	PROPN
ejpam-2967	157	5	0	0	PUNCT
ejpam-2967	158	1	|eiθ	|eiθ	PROPN
ejpam-2967	159	1	+	+	NUM
ejpam-2967	159	2	b|pdθ	b|pdθ	NOUN
ejpam-2967	159	3	}	}	PUNCT
ejpam-2967	159	4	1	1	NUM
ejpam-2967	159	5	/	/	SYM
ejpam-2967	159	6	p	p	NOUN
ejpam-2967	159	7	≥	≥	NOUN
ejpam-2967	159	8	a+	a+	PUNCT
ejpam-2967	159	9	c{∫	c{∫	NOUN
ejpam-2967	159	10	2π	2π	NOUN
ejpam-2967	159	11	0	0	NUM
ejpam-2967	160	1	|eiθ	|eiθ	PROPN
ejpam-2967	160	2	+	+	CCONJ
ejpam-2967	160	3	c|pdθ	c|pdθ	NOUN
ejpam-2967	160	4	}	}	PUNCT
ejpam-2967	160	5	1	1	NUM
ejpam-2967	160	6	/	/	SYM
ejpam-2967	160	7	p	p	NOUN
ejpam-2967	160	8	.	.	PUNCT
ejpam-2967	161	1	(	(	PUNCT
ejpam-2967	161	2	13	13	NUM
ejpam-2967	161	3	)	)	PUNCT
ejpam-2967	161	4	proof	proof	NOUN
ejpam-2967	161	5	.	.	PUNCT
ejpam-2967	162	1	to	to	PART
ejpam-2967	162	2	prove	prove	VERB
ejpam-2967	162	3	the	the	DET
ejpam-2967	162	4	inequality	inequality	NOUN
ejpam-2967	162	5	(	(	PUNCT
ejpam-2967	162	6	13	13	NUM
ejpam-2967	162	7	)	)	PUNCT
ejpam-2967	162	8	,	,	PUNCT
ejpam-2967	162	9	it	it	PRON
ejpam-2967	162	10	suffices	suffice	VERB
ejpam-2967	162	11	to	to	PART
ejpam-2967	162	12	show	show	VERB
ejpam-2967	162	13	that∫	that∫	NOUN
ejpam-2967	162	14	2π	2π	NOUN
ejpam-2967	162	15	0	0	PUNCT
ejpam-2967	163	1	(	(	PUNCT
ejpam-2967	163	2	|eiθ	|eiθ	PROPN
ejpam-2967	163	3	+	+	CCONJ
ejpam-2967	163	4	b|	b|	PROPN
ejpam-2967	163	5	a+	a+	PUNCT
ejpam-2967	163	6	b	b	X
ejpam-2967	163	7	)	)	PUNCT
ejpam-2967	163	8	p	p	PROPN
ejpam-2967	163	9	dθ	dθ	PROPN
ejpam-2967	163	10	≤	≤	PROPN
ejpam-2967	163	11	∫	∫	PROPN
ejpam-2967	163	12	2π	2π	PROPN
ejpam-2967	163	13	0	0	PUNCT
ejpam-2967	164	1	(	(	PUNCT
ejpam-2967	164	2	|eiθ	|eiθ	PROPN
ejpam-2967	164	3	+	+	CCONJ
ejpam-2967	164	4	c|	c|	PROPN
ejpam-2967	164	5	a+	a+	PUNCT
ejpam-2967	164	6	c	c	NOUN
ejpam-2967	164	7	)	)	PUNCT
ejpam-2967	165	1	p	p	PROPN
ejpam-2967	165	2	dθ	dθ	PROPN
ejpam-2967	165	3	,	,	PUNCT
ejpam-2967	165	4	for	for	ADP
ejpam-2967	165	5	which	which	PRON
ejpam-2967	165	6	we	we	PRON
ejpam-2967	165	7	will	will	AUX
ejpam-2967	165	8	show	show	VERB
ejpam-2967	165	9	(	(	PUNCT
ejpam-2967	165	10	|eiθ	|eiθ	PROPN
ejpam-2967	165	11	+	+	CCONJ
ejpam-2967	165	12	b|	b|	PROPN
ejpam-2967	165	13	a+	a+	PUNCT
ejpam-2967	165	14	b	b	X
ejpam-2967	165	15	)	)	PUNCT
ejpam-2967	165	16	p	p	NOUN
ejpam-2967	165	17	≤	≤	NOUN
ejpam-2967	165	18	(	(	PUNCT
ejpam-2967	165	19	|eiθ	|eiθ	PROPN
ejpam-2967	166	1	+	+	CCONJ
ejpam-2967	166	2	c|	c|	PROPN
ejpam-2967	166	3	a+	a+	PUNCT
ejpam-2967	166	4	c	c	NOUN
ejpam-2967	166	5	)	)	PUNCT
ejpam-2967	166	6	p	p	NOUN
ejpam-2967	166	7	,	,	PUNCT
ejpam-2967	166	8	(	(	PUNCT
ejpam-2967	166	9	14	14	NUM
ejpam-2967	166	10	)	)	PUNCT
ejpam-2967	166	11	for	for	ADP
ejpam-2967	166	12	any	any	DET
ejpam-2967	166	13	θ	θ	PROPN
ejpam-2967	166	14	∈	∈	PROPN
ejpam-2967	167	1	[	[	X
ejpam-2967	167	2	0	0	NUM
ejpam-2967	167	3	,	,	PUNCT
ejpam-2967	167	4	2π	2π	NOUN
ejpam-2967	167	5	]	]	PUNCT
ejpam-2967	167	6	and	and	CCONJ
ejpam-2967	167	7	0	0	NUM
ejpam-2967	167	8	≤	≤	NOUN
ejpam-2967	167	9	a	a	DET
ejpam-2967	167	10	≤	≤	NUM
ejpam-2967	167	11	1	1	NUM
ejpam-2967	167	12	,	,	PUNCT
ejpam-2967	168	1	c	c	NOUN
ejpam-2967	168	2	≤	≤	NUM
ejpam-2967	168	3	b	b	NOUN
ejpam-2967	168	4	≤	≤	NUM
ejpam-2967	168	5	1	1	NUM
ejpam-2967	168	6	.	.	PUNCT
ejpam-2967	169	1	let	let	VERB
ejpam-2967	169	2	us	we	PRON
ejpam-2967	169	3	consider	consider	VERB
ejpam-2967	169	4	the	the	DET
ejpam-2967	169	5	function	function	NOUN
ejpam-2967	169	6	f	f	NOUN
ejpam-2967	169	7	:	:	PUNCT
ejpam-2967	169	8	(	(	PUNCT
ejpam-2967	169	9	0	0	NUM
ejpam-2967	169	10	,	,	PUNCT
ejpam-2967	169	11	1	1	NUM
ejpam-2967	169	12	]	]	SYM
ejpam-2967	169	13	7→	7→	NUM
ejpam-2967	169	14	r	r	NOUN
ejpam-2967	169	15	defined	define	VERB
ejpam-2967	169	16	by	by	ADP
ejpam-2967	169	17	f(x	f(x	PROPN
ejpam-2967	169	18	)	)	PUNCT
ejpam-2967	170	1	=	=	PUNCT
ejpam-2967	170	2	|eiθ+x|	|eiθ+x|	X
ejpam-2967	170	3	a+x	a+x	CCONJ
ejpam-2967	170	4	defined	define	VERB
ejpam-2967	170	5	on	on	ADP
ejpam-2967	170	6	(	(	PUNCT
ejpam-2967	170	7	0	0	NUM
ejpam-2967	170	8	,	,	PUNCT
ejpam-2967	170	9	1	1	NUM
ejpam-2967	170	10	]	]	PUNCT
ejpam-2967	170	11	,	,	PUNCT
ejpam-2967	170	12	and	and	CCONJ
ejpam-2967	170	13	show	show	VERB
ejpam-2967	170	14	that	that	SCONJ
ejpam-2967	170	15	f	f	PROPN
ejpam-2967	170	16	is	be	AUX
ejpam-2967	170	17	non	non	ADJ
ejpam-2967	170	18	-	-	ADJ
ejpam-2967	170	19	increasing	increase	VERB
ejpam-2967	170	20	.	.	PUNCT
ejpam-2967	171	1	observe	observe	VERB
ejpam-2967	171	2	that	that	SCONJ
ejpam-2967	171	3	f	f	PROPN
ejpam-2967	171	4	′(x	′(x	NOUN
ejpam-2967	171	5	)	)	PUNCT
ejpam-2967	171	6	≤	≤	NOUN
ejpam-2967	171	7	0	0	PUNCT
ejpam-2967	172	1	if	if	SCONJ
ejpam-2967	172	2	and	and	CCONJ
ejpam-2967	172	3	only	only	ADV
ejpam-2967	172	4	if	if	SCONJ
ejpam-2967	172	5	x(a−	x(a−	PROPN
ejpam-2967	172	6	cos	cos	PROPN
ejpam-2967	172	7	θ	θ	PROPN
ejpam-2967	172	8	)	)	PUNCT
ejpam-2967	172	9	+	+	CCONJ
ejpam-2967	172	10	a	a	DET
ejpam-2967	172	11	cos	cos	ADP
ejpam-2967	172	12	θ	θ	NOUN
ejpam-2967	172	13	−	−	PROPN
ejpam-2967	172	14	1	1	NUM
ejpam-2967	172	15	≤	≤	NOUN
ejpam-2967	172	16	0	0	NUM
ejpam-2967	172	17	.	.	PUNCT
ejpam-2967	173	1	a	a	DET
ejpam-2967	173	2	simple	simple	ADJ
ejpam-2967	173	3	exercise	exercise	NOUN
ejpam-2967	173	4	makes	make	VERB
ejpam-2967	173	5	us	we	PRON
ejpam-2967	173	6	conclude	conclude	VERB
ejpam-2967	173	7	for	for	ADP
ejpam-2967	173	8	any	any	DET
ejpam-2967	173	9	real	real	ADJ
ejpam-2967	173	10	values	value	NOUN
ejpam-2967	173	11	of	of	ADP
ejpam-2967	173	12	θ	θ	PROPN
ejpam-2967	173	13	,	,	PUNCT
ejpam-2967	173	14	we	we	PRON
ejpam-2967	173	15	have	have	VERB
ejpam-2967	173	16	x(a−cos	x(a−co	NOUN
ejpam-2967	173	17	θ)+a	θ)+a	PROPN
ejpam-2967	173	18	cos	cos	PROPN
ejpam-2967	173	19	θ−	θ−	PROPN
ejpam-2967	173	20	1	1	NUM
ejpam-2967	173	21	≤	≤	NOUN
ejpam-2967	173	22	0	0	NUM
ejpam-2967	173	23	,	,	PUNCT
ejpam-2967	173	24	implying	imply	VERB
ejpam-2967	173	25	that	that	SCONJ
ejpam-2967	173	26	f	f	PROPN
ejpam-2967	173	27	and	and	CCONJ
ejpam-2967	173	28	fp	fp	PROPN
ejpam-2967	173	29	are	be	AUX
ejpam-2967	173	30	non	non	ADJ
ejpam-2967	173	31	-	-	ADJ
ejpam-2967	173	32	increasing	increase	VERB
ejpam-2967	173	33	.	.	PUNCT
ejpam-2967	174	1	hence	hence	ADV
ejpam-2967	174	2	the	the	DET
ejpam-2967	174	3	inequality	inequality	NOUN
ejpam-2967	174	4	(	(	PUNCT
ejpam-2967	174	5	14	14	NUM
ejpam-2967	174	6	)	)	PUNCT
ejpam-2967	174	7	follows	follow	VERB
ejpam-2967	174	8	and	and	CCONJ
ejpam-2967	174	9	thus	thus	ADV
ejpam-2967	174	10	the	the	DET
ejpam-2967	174	11	proof	proof	NOUN
ejpam-2967	174	12	is	be	AUX
ejpam-2967	174	13	complete	complete	ADJ
ejpam-2967	174	14	.	.	PUNCT
ejpam-2967	175	1	acknowledgement	acknowledgement	NOUN
ejpam-2967	175	2	the	the	DET
ejpam-2967	175	3	author	author	NOUN
ejpam-2967	175	4	would	would	AUX
ejpam-2967	175	5	like	like	VERB
ejpam-2967	175	6	to	to	PART
ejpam-2967	175	7	thank	thank	VERB
ejpam-2967	175	8	the	the	DET
ejpam-2967	175	9	dst	dst	NOUN
ejpam-2967	175	10	-	-	PUNCT
ejpam-2967	175	11	fist	fist	ADJ
ejpam-2967	175	12	scientific	scientific	ADJ
ejpam-2967	175	13	computing	computing	NOUN
ejpam-2967	175	14	lab	lab	NOUN
ejpam-2967	175	15	for	for	ADP
ejpam-2967	175	16	facilitating	facilitate	VERB
ejpam-2967	175	17	this	this	DET
ejpam-2967	175	18	research	research	NOUN
ejpam-2967	175	19	work	work	NOUN
ejpam-2967	175	20	.	.	PUNCT
ejpam-2967	176	1	references	reference	NOUN
ejpam-2967	176	2	494	494	NUM
ejpam-2967	176	3	references	reference	NOUN
ejpam-2967	176	4	[	[	X
ejpam-2967	176	5	1	1	NUM
ejpam-2967	176	6	]	]	PUNCT
ejpam-2967	176	7	a.	a.	NOUN
ejpam-2967	176	8	m.	m.	PROPN
ejpam-2967	176	9	bruckner	bruckner	PROPN
ejpam-2967	176	10	,	,	PUNCT
ejpam-2967	176	11	j.	j.	PROPN
ejpam-2967	176	12	g.	g.	PROPN
ejpam-2967	176	13	ceder	ceder	PROPN
ejpam-2967	176	14	and	and	CCONJ
ejpam-2967	176	15	max	max	PROPN
ejpam-2967	176	16	l.	l.	PROPN
ejpam-2967	176	17	weiss	weiss	PROPN
ejpam-2967	176	18	,	,	PUNCT
ejpam-2967	176	19	on	on	ADP
ejpam-2967	176	20	the	the	DET
ejpam-2967	176	21	differentiability	differentiability	NOUN
ejpam-2967	176	22	structure	structure	NOUN
ejpam-2967	176	23	of	of	ADP
ejpam-2967	176	24	real	real	ADJ
ejpam-2967	176	25	functions	function	NOUN
ejpam-2967	176	26	,	,	PUNCT
ejpam-2967	176	27	trans	trans	PROPN
ejpam-2967	176	28	.	.	PROPN
ejpam-2967	177	1	amer	amer	PROPN
ejpam-2967	177	2	.	.	PUNCT
ejpam-2967	177	3	math	math	PROPN
ejpam-2967	177	4	.	.	PUNCT
ejpam-2967	178	1	soc	soc	PROPN
ejpam-2967	178	2	.	.	PUNCT
ejpam-2967	179	1	142	142	NUM
ejpam-2967	179	2	(	(	PUNCT
ejpam-2967	179	3	1969	1969	NUM
ejpam-2967	179	4	)	)	PUNCT
ejpam-2967	179	5	,	,	PUNCT
ejpam-2967	179	6	1	1	NUM
ejpam-2967	179	7	-	-	SYM
ejpam-2967	179	8	13	13	NUM
ejpam-2967	179	9	[	[	X
ejpam-2967	179	10	2	2	NUM
ejpam-2967	179	11	]	]	PUNCT
ejpam-2967	179	12	g.	g.	PROPN
ejpam-2967	179	13	h.	h.	PROPN
ejpam-2967	179	14	hardy	hardy	PROPN
ejpam-2967	179	15	,	,	PUNCT
ejpam-2967	179	16	j.	j.	PROPN
ejpam-2967	179	17	e.	e.	PROPN
ejpam-2967	179	18	littlewood	littlewood	PROPN
ejpam-2967	179	19	,	,	PUNCT
ejpam-2967	179	20	and	and	CCONJ
ejpam-2967	179	21	g.	g.	PROPN
ejpam-2967	179	22	polya	polya	PROPN
ejpam-2967	179	23	,	,	PUNCT
ejpam-2967	179	24	inequalities	inequality	NOUN
ejpam-2967	179	25	,	,	PUNCT
ejpam-2967	179	26	cambridge	cambridge	PROPN
ejpam-2967	179	27	university	university	PROPN
ejpam-2967	179	28	press	press	PROPN
ejpam-2967	179	29	,	,	PUNCT
ejpam-2967	179	30	london	london	PROPN
ejpam-2967	179	31	,	,	PUNCT
ejpam-2967	179	32	1951	1951	NUM
ejpam-2967	179	33	.	.	PUNCT
ejpam-2967	180	1	[	[	X
ejpam-2967	180	2	3	3	X
ejpam-2967	180	3	]	]	X
ejpam-2967	180	4	w.	w.	PROPN
ejpam-2967	180	5	rudin	rudin	PROPN
ejpam-2967	180	6	,	,	PUNCT
ejpam-2967	180	7	principles	principle	NOUN
ejpam-2967	180	8	of	of	ADP
ejpam-2967	180	9	mathematical	mathematical	ADJ
ejpam-2967	180	10	analysis	analysis	NOUN
ejpam-2967	180	11	,	,	PUNCT
ejpam-2967	180	12	mcgraw	mcgraw	PROPN
ejpam-2967	180	13	-	-	PUNCT
ejpam-2967	180	14	hill	hill	NOUN
ejpam-2967	180	15	higher	high	ADJ
ejpam-2967	180	16	education	education	NOUN
ejpam-2967	180	17	,	,	PUNCT
ejpam-2967	180	18	1976	1976	NUM
ejpam-2967	180	19	.	.	PUNCT
ejpam-2967	181	1	[	[	X
ejpam-2967	181	2	4	4	X
ejpam-2967	181	3	]	]	X
ejpam-2967	181	4	h.	h.	PROPN
ejpam-2967	181	5	whitny	whitny	PROPN
ejpam-2967	181	6	,	,	PUNCT
ejpam-2967	181	7	differentiable	differentiable	ADJ
ejpam-2967	181	8	functions	function	NOUN
ejpam-2967	181	9	defined	define	VERB
ejpam-2967	181	10	in	in	ADP
ejpam-2967	181	11	closed	closed	ADJ
ejpam-2967	181	12	discs	disc	NOUN
ejpam-2967	181	13	,	,	PUNCT
ejpam-2967	181	14	tran	tran	PROPN
ejpam-2967	181	15	.	.	PUNCT
ejpam-2967	182	1	amer	amer	PROPN
ejpam-2967	182	2	.	.	PUNCT
ejpam-2967	182	3	math	math	PROPN
ejpam-2967	182	4	.	.	PUNCT
ejpam-2967	183	1	soc	soc	PROPN
ejpam-2967	183	2	.	.	PUNCT
ejpam-2967	183	3	,	,	PUNCT
ejpam-2967	183	4	36	36	NUM
ejpam-2967	183	5	1934	1934	NUM
ejpam-2967	183	6	,	,	PUNCT
ejpam-2967	183	7	369	369	NUM
ejpam-2967	183	8	-	-	SYM
ejpam-2967	183	9	387	387	NUM
ejpam-2967	183	10	.	.	PUNCT