id	sid	tid	token	lemma	pos
ejpam-3709	1	1	european	european	PROPN
ejpam-3709	1	2	journal	journal	PROPN
ejpam-3709	1	3	of	of	ADP
ejpam-3709	1	4	pure	pure	ADJ
ejpam-3709	1	5	and	and	CCONJ
ejpam-3709	1	6	applied	apply	VERB
ejpam-3709	1	7	mathematics	mathematic	NOUN
ejpam-3709	1	8	vol	vol	NOUN
ejpam-3709	1	9	.	.	PROPN
ejpam-3709	2	1	13	13	NUM
ejpam-3709	2	2	,	,	PUNCT
ejpam-3709	2	3	no	no	INTJ
ejpam-3709	2	4	.	.	NOUN
ejpam-3709	2	5	5	5	NUM
ejpam-3709	2	6	,	,	PUNCT
ejpam-3709	2	7	2020	2020	NUM
ejpam-3709	2	8	,	,	PUNCT
ejpam-3709	2	9	1162	1162	NUM
ejpam-3709	2	10	-	-	SYM
ejpam-3709	2	11	1175	1175	NUM
ejpam-3709	2	12	issn	issn	PROPN
ejpam-3709	2	13	1307	1307	NUM
ejpam-3709	2	14	-	-	SYM
ejpam-3709	2	15	5543	5543	NUM
ejpam-3709	2	16	–	–	PUNCT
ejpam-3709	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3709	2	18	published	publish	VERB
ejpam-3709	2	19	by	by	ADP
ejpam-3709	2	20	new	new	PROPN
ejpam-3709	2	21	york	york	PROPN
ejpam-3709	2	22	business	business	PROPN
ejpam-3709	2	23	global	global	ADJ
ejpam-3709	2	24	special	special	ADJ
ejpam-3709	2	25	issue	issue	NOUN
ejpam-3709	2	26	dedicated	dedicate	VERB
ejpam-3709	2	27	to	to	ADP
ejpam-3709	2	28	professor	professor	NOUN
ejpam-3709	2	29	hari	hari	PROPN
ejpam-3709	2	30	m.	m.	PROPN
ejpam-3709	2	31	srivastava	srivastava	PROPN
ejpam-3709	2	32	on	on	ADP
ejpam-3709	2	33	the	the	DET
ejpam-3709	2	34	occasion	occasion	NOUN
ejpam-3709	2	35	of	of	ADP
ejpam-3709	2	36	his	his	PRON
ejpam-3709	2	37	80th	80th	ADJ
ejpam-3709	2	38	birthday	birthday	NOUN
ejpam-3709	2	39	modular	modular	ADJ
ejpam-3709	2	40	stabilities	stability	NOUN
ejpam-3709	2	41	of	of	ADP
ejpam-3709	2	42	a	a	DET
ejpam-3709	2	43	reciprocal	reciprocal	ADJ
ejpam-3709	2	44	second	second	ADJ
ejpam-3709	2	45	power	power	NOUN
ejpam-3709	2	46	functional	functional	ADJ
ejpam-3709	2	47	equation	equation	NOUN
ejpam-3709	2	48	b.v	b.v	PROPN
ejpam-3709	2	49	.	.	PROPN
ejpam-3709	2	50	senthil	senthil	PROPN
ejpam-3709	2	51	kumar1,∗	kumar1,∗	PROPN
ejpam-3709	2	52	,	,	PUNCT
ejpam-3709	2	53	hemen	hemen	PROPN
ejpam-3709	2	54	dutta2	dutta2	PROPN
ejpam-3709	2	55	,	,	PUNCT
ejpam-3709	2	56	s.	s.	PROPN
ejpam-3709	2	57	sabarinathan3	sabarinathan3	PROPN
ejpam-3709	2	58	1	1	NUM
ejpam-3709	2	59	department	department	NOUN
ejpam-3709	2	60	of	of	ADP
ejpam-3709	2	61	information	information	NOUN
ejpam-3709	2	62	technology	technology	NOUN
ejpam-3709	2	63	,	,	PUNCT
ejpam-3709	2	64	university	university	NOUN
ejpam-3709	2	65	of	of	ADP
ejpam-3709	2	66	technology	technology	NOUN
ejpam-3709	2	67	and	and	CCONJ
ejpam-3709	2	68	applied	apply	VERB
ejpam-3709	2	69	sciencesnizwa	sciencesnizwa	NOUN
ejpam-3709	2	70	,	,	PUNCT
ejpam-3709	2	71	nizwa	nizwa	ADV
ejpam-3709	2	72	611	611	NUM
ejpam-3709	2	73	,	,	PUNCT
ejpam-3709	2	74	oman	oman	NOUN
ejpam-3709	2	75	2	2	NUM
ejpam-3709	2	76	department	department	NOUN
ejpam-3709	2	77	of	of	ADP
ejpam-3709	2	78	mathematics	mathematics	PROPN
ejpam-3709	2	79	,	,	PUNCT
ejpam-3709	2	80	gauhati	gauhati	PROPN
ejpam-3709	2	81	university	university	PROPN
ejpam-3709	2	82	,	,	PUNCT
ejpam-3709	2	83	guwahati	guwahati	NOUN
ejpam-3709	2	84	781	781	NUM
ejpam-3709	2	85	014	014	NUM
ejpam-3709	2	86	,	,	PUNCT
ejpam-3709	2	87	assam	assam	PROPN
ejpam-3709	2	88	,	,	PUNCT
ejpam-3709	2	89	india	india	PROPN
ejpam-3709	2	90	3	3	NUM
ejpam-3709	2	91	department	department	NOUN
ejpam-3709	2	92	of	of	ADP
ejpam-3709	2	93	mathematics	mathematics	PROPN
ejpam-3709	2	94	,	,	PUNCT
ejpam-3709	2	95	srm	srm	PROPN
ejpam-3709	2	96	institute	institute	PROPN
ejpam-3709	2	97	of	of	ADP
ejpam-3709	2	98	science	science	PROPN
ejpam-3709	2	99	&	&	CCONJ
ejpam-3709	2	100	technology	technology	PROPN
ejpam-3709	2	101	,	,	PUNCT
ejpam-3709	2	102	kattankulthur-603	kattankulthur-603	NOUN
ejpam-3709	2	103	203	203	NUM
ejpam-3709	2	104	,	,	PUNCT
ejpam-3709	2	105	tamil	tamil	PROPN
ejpam-3709	2	106	nadu	nadu	PROPN
ejpam-3709	2	107	,	,	PUNCT
ejpam-3709	2	108	india	india	PROPN
ejpam-3709	2	109	abstract	abstract	NOUN
ejpam-3709	2	110	.	.	PUNCT
ejpam-3709	3	1	in	in	ADP
ejpam-3709	3	2	the	the	DET
ejpam-3709	3	3	present	present	ADJ
ejpam-3709	3	4	work	work	NOUN
ejpam-3709	3	5	,	,	PUNCT
ejpam-3709	3	6	we	we	PRON
ejpam-3709	3	7	propose	propose	VERB
ejpam-3709	3	8	a	a	DET
ejpam-3709	3	9	different	different	ADJ
ejpam-3709	3	10	reciprocal	reciprocal	ADJ
ejpam-3709	3	11	second	second	ADJ
ejpam-3709	3	12	power	power	NOUN
ejpam-3709	3	13	functional	functional	ADJ
ejpam-3709	3	14	equation	equation	NOUN
ejpam-3709	3	15	(	(	PUNCT
ejpam-3709	3	16	fe	fe	NOUN
ejpam-3709	3	17	)	)	PUNCT
ejpam-3709	3	18	which	which	PRON
ejpam-3709	3	19	involves	involve	VERB
ejpam-3709	3	20	the	the	DET
ejpam-3709	3	21	arguments	argument	NOUN
ejpam-3709	3	22	of	of	ADP
ejpam-3709	3	23	functions	function	NOUN
ejpam-3709	3	24	in	in	ADP
ejpam-3709	3	25	rational	rational	ADJ
ejpam-3709	3	26	form	form	NOUN
ejpam-3709	3	27	and	and	CCONJ
ejpam-3709	3	28	determine	determine	VERB
ejpam-3709	3	29	its	its	PRON
ejpam-3709	3	30	stabilities	stability	NOUN
ejpam-3709	3	31	in	in	ADP
ejpam-3709	3	32	the	the	DET
ejpam-3709	3	33	setting	setting	NOUN
ejpam-3709	3	34	of	of	ADP
ejpam-3709	3	35	modular	modular	ADJ
ejpam-3709	3	36	spaces	space	NOUN
ejpam-3709	3	37	with	with	ADP
ejpam-3709	3	38	and	and	CCONJ
ejpam-3709	3	39	without	without	ADP
ejpam-3709	3	40	using	use	VERB
ejpam-3709	3	41	fatou	fatou	NOUN
ejpam-3709	3	42	property	property	NOUN
ejpam-3709	3	43	.	.	PUNCT
ejpam-3709	4	1	we	we	PRON
ejpam-3709	4	2	also	also	ADV
ejpam-3709	4	3	prove	prove	VERB
ejpam-3709	4	4	the	the	DET
ejpam-3709	4	5	stabilities	stability	NOUN
ejpam-3709	4	6	in	in	ADP
ejpam-3709	4	7	β	β	ADJ
ejpam-3709	4	8	-	-	ADJ
ejpam-3709	4	9	homogenous	homogenous	ADJ
ejpam-3709	4	10	spaces	space	NOUN
ejpam-3709	4	11	.	.	PUNCT
ejpam-3709	5	1	as	as	ADP
ejpam-3709	5	2	an	an	DET
ejpam-3709	5	3	application	application	NOUN
ejpam-3709	5	4	,	,	PUNCT
ejpam-3709	5	5	we	we	PRON
ejpam-3709	5	6	associate	associate	VERB
ejpam-3709	5	7	this	this	DET
ejpam-3709	5	8	equation	equation	NOUN
ejpam-3709	5	9	with	with	ADP
ejpam-3709	5	10	the	the	DET
ejpam-3709	5	11	electrostatic	electrostatic	ADJ
ejpam-3709	5	12	forces	force	NOUN
ejpam-3709	5	13	of	of	ADP
ejpam-3709	5	14	attraction	attraction	NOUN
ejpam-3709	5	15	between	between	ADP
ejpam-3709	5	16	unit	unit	NOUN
ejpam-3709	5	17	charges	charge	NOUN
ejpam-3709	5	18	in	in	ADP
ejpam-3709	5	19	various	various	ADJ
ejpam-3709	5	20	cases	case	NOUN
ejpam-3709	5	21	using	use	VERB
ejpam-3709	5	22	coloumb	coloumb	NOUN
ejpam-3709	5	23	’s	’s	PART
ejpam-3709	5	24	law	law	NOUN
ejpam-3709	5	25	.	.	PUNCT
ejpam-3709	6	1	2020	2020	NUM
ejpam-3709	6	2	mathematics	mathematic	NOUN
ejpam-3709	6	3	subject	subject	NOUN
ejpam-3709	6	4	classifications	classification	NOUN
ejpam-3709	6	5	:	:	PUNCT
ejpam-3709	6	6	39b52	39b52	NUM
ejpam-3709	6	7	,	,	PUNCT
ejpam-3709	6	8	39b62	39b62	NUM
ejpam-3709	6	9	,	,	PUNCT
ejpam-3709	6	10	39b82	39b82	NUM
ejpam-3709	6	11	key	key	ADJ
ejpam-3709	6	12	words	word	NOUN
ejpam-3709	6	13	and	and	CCONJ
ejpam-3709	6	14	phrases	phrase	NOUN
ejpam-3709	6	15	:	:	PUNCT
ejpam-3709	6	16	reciprocal	reciprocal	ADJ
ejpam-3709	6	17	functional	functional	ADJ
ejpam-3709	6	18	equation	equation	NOUN
ejpam-3709	6	19	,	,	PUNCT
ejpam-3709	6	20	quadratic	quadratic	ADJ
ejpam-3709	6	21	functional	functional	ADJ
ejpam-3709	6	22	equation	equation	NOUN
ejpam-3709	6	23	,	,	PUNCT
ejpam-3709	6	24	hugr	hugr	NOUN
ejpam-3709	6	25	stability	stability	NOUN
ejpam-3709	6	26	,	,	PUNCT
ejpam-3709	6	27	non	non	ADJ
ejpam-3709	6	28	-	-	ADJ
ejpam-3709	6	29	archimedean	archimedean	ADJ
ejpam-3709	6	30	field	field	NOUN
ejpam-3709	6	31	1	1	NUM
ejpam-3709	6	32	.	.	PUNCT
ejpam-3709	6	33	introduction	introduction	NOUN
ejpam-3709	6	34	&	&	CCONJ
ejpam-3709	6	35	preliminaries	preliminary	NOUN
ejpam-3709	6	36	the	the	DET
ejpam-3709	6	37	hypothesis	hypothesis	NOUN
ejpam-3709	6	38	connected	connect	VERB
ejpam-3709	6	39	with	with	ADP
ejpam-3709	6	40	linear	linear	ADJ
ejpam-3709	6	41	spaces	space	NOUN
ejpam-3709	6	42	and	and	CCONJ
ejpam-3709	6	43	the	the	DET
ejpam-3709	6	44	concepts	concept	NOUN
ejpam-3709	6	45	of	of	ADP
ejpam-3709	6	46	modular	modular	ADJ
ejpam-3709	6	47	spaces	space	NOUN
ejpam-3709	6	48	were	be	AUX
ejpam-3709	6	49	dealt	deal	VERB
ejpam-3709	6	50	in	in	ADP
ejpam-3709	6	51	[	[	X
ejpam-3709	6	52	20	20	NUM
ejpam-3709	6	53	]	]	PUNCT
ejpam-3709	6	54	.	.	PUNCT
ejpam-3709	7	1	later	later	ADV
ejpam-3709	7	2	,	,	PUNCT
ejpam-3709	7	3	this	this	DET
ejpam-3709	7	4	theory	theory	NOUN
ejpam-3709	7	5	has	have	AUX
ejpam-3709	7	6	been	be	AUX
ejpam-3709	7	7	employed	employ	VERB
ejpam-3709	7	8	by	by	ADP
ejpam-3709	7	9	many	many	ADJ
ejpam-3709	7	10	authors	author	NOUN
ejpam-3709	7	11	[	[	X
ejpam-3709	7	12	1	1	NUM
ejpam-3709	7	13	,	,	PUNCT
ejpam-3709	7	14	9	9	NUM
ejpam-3709	7	15	,	,	PUNCT
ejpam-3709	7	16	16	16	NUM
ejpam-3709	7	17	,	,	PUNCT
ejpam-3709	7	18	29	29	NUM
ejpam-3709	7	19	,	,	PUNCT
ejpam-3709	7	20	32	32	NUM
ejpam-3709	7	21	]	]	PUNCT
ejpam-3709	7	22	.	.	PUNCT
ejpam-3709	8	1	the	the	DET
ejpam-3709	8	2	significant	significant	ADJ
ejpam-3709	8	3	application	application	NOUN
ejpam-3709	8	4	of	of	ADP
ejpam-3709	8	5	modular	modular	ADJ
ejpam-3709	8	6	theory	theory	NOUN
ejpam-3709	8	7	is	be	AUX
ejpam-3709	8	8	that	that	SCONJ
ejpam-3709	8	9	it	it	PRON
ejpam-3709	8	10	is	be	AUX
ejpam-3709	8	11	useful	useful	ADJ
ejpam-3709	8	12	in	in	ADP
ejpam-3709	8	13	interpolation	interpolation	NOUN
ejpam-3709	8	14	(	(	PUNCT
ejpam-3709	8	15	[	[	X
ejpam-3709	8	16	10	10	NUM
ejpam-3709	8	17	,	,	PUNCT
ejpam-3709	8	18	17	17	NUM
ejpam-3709	8	19	]	]	PUNCT
ejpam-3709	8	20	)	)	PUNCT
ejpam-3709	8	21	and	and	CCONJ
ejpam-3709	8	22	in	in	ADP
ejpam-3709	8	23	numerous	numerous	ADJ
ejpam-3709	8	24	orlicz	orlicz	ADJ
ejpam-3709	8	25	spaces	space	NOUN
ejpam-3709	8	26	[	[	X
ejpam-3709	8	27	21	21	NUM
ejpam-3709	8	28	]	]	PUNCT
ejpam-3709	8	29	.	.	PUNCT
ejpam-3709	9	1	the	the	DET
ejpam-3709	9	2	common	common	ADJ
ejpam-3709	9	3	notions	notion	NOUN
ejpam-3709	9	4	and	and	CCONJ
ejpam-3709	9	5	properties	property	NOUN
ejpam-3709	9	6	related	relate	VERB
ejpam-3709	9	7	to	to	ADP
ejpam-3709	9	8	modular	modular	ADJ
ejpam-3709	9	9	theory	theory	NOUN
ejpam-3709	9	10	are	be	AUX
ejpam-3709	9	11	available	available	ADJ
ejpam-3709	9	12	in	in	ADP
ejpam-3709	9	13	[	[	X
ejpam-3709	9	14	18	18	NUM
ejpam-3709	9	15	,	,	PUNCT
ejpam-3709	9	16	19	19	NUM
ejpam-3709	9	17	,	,	PUNCT
ejpam-3709	9	18	21	21	NUM
ejpam-3709	9	19	]	]	PUNCT
ejpam-3709	9	20	.	.	PUNCT
ejpam-3709	10	1	∗corresponding	∗corresponde	VERB
ejpam-3709	10	2	author	author	NOUN
ejpam-3709	10	3	.	.	PUNCT
ejpam-3709	11	1	doi	doi	NOUN
ejpam-3709	11	2	:	:	PUNCT
ejpam-3709	11	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3709	https://doi.org/10.29020/nybg.ejpam.v13i5.3709	PROPN
ejpam-3709	11	4	email	email	NOUN
ejpam-3709	11	5	addresses	address	NOUN
ejpam-3709	11	6	:	:	PUNCT
ejpam-3709	11	7	senthilkumar@nct.edu.om	senthilkumar@nct.edu.om	NOUN
ejpam-3709	11	8	;	;	PUNCT
ejpam-3709	11	9	bvskumarmaths@gmail.com	bvskumarmaths@gmail.com	X
ejpam-3709	11	10	(	(	PUNCT
ejpam-3709	11	11	b.	b.	PROPN
ejpam-3709	11	12	v.	v.	PROPN
ejpam-3709	11	13	senthil	senthil	PROPN
ejpam-3709	11	14	kumar	kumar	PROPN
ejpam-3709	11	15	)	)	PUNCT
ejpam-3709	11	16	,	,	PUNCT
ejpam-3709	11	17	hemen	hemen	PROPN
ejpam-3709	11	18	dutta08@rediffmail.com	dutta08@rediffmail.com	PROPN
ejpam-3709	11	19	(	(	PUNCT
ejpam-3709	11	20	hemen	hemen	PROPN
ejpam-3709	11	21	dutta	dutta	PROPN
ejpam-3709	11	22	)	)	PUNCT
ejpam-3709	11	23	,	,	PUNCT
ejpam-3709	11	24	ssabarimaths@gmail.com	ssabarimaths@gmail.com	X
ejpam-3709	11	25	(	(	PUNCT
ejpam-3709	11	26	s.	s.	PROPN
ejpam-3709	11	27	sabarinathan	sabarinathan	PROPN
ejpam-3709	11	28	)	)	PUNCT
ejpam-3709	11	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3709	11	30	1162	1162	NUM
ejpam-3709	12	1	c	c	NOUN
ejpam-3709	12	2	©	©	PROPN
ejpam-3709	12	3	2020	2020	NUM
ejpam-3709	12	4	ejpam	ejpam	VERB
ejpam-3709	12	5	all	all	DET
ejpam-3709	12	6	rights	right	NOUN
ejpam-3709	12	7	reserved	reserve	VERB
ejpam-3709	12	8	.	.	PUNCT
ejpam-3709	13	1	b.	b.	PROPN
ejpam-3709	14	1	v.	v.	PROPN
ejpam-3709	14	2	senthil	senthil	PROPN
ejpam-3709	14	3	kumar	kumar	PROPN
ejpam-3709	14	4	,	,	PUNCT
ejpam-3709	14	5	hemen	hemen	PROPN
ejpam-3709	14	6	dutta	dutta	PROPN
ejpam-3709	14	7	,	,	PUNCT
ejpam-3709	14	8	s.	s.	PROPN
ejpam-3709	14	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	14	10	/	/	SYM
ejpam-3709	14	11	eur	eur	PROPN
ejpam-3709	14	12	.	.	PUNCT
ejpam-3709	15	1	j.	j.	PROPN
ejpam-3709	15	2	pure	pure	PROPN
ejpam-3709	15	3	appl	appl	PROPN
ejpam-3709	15	4	.	.	PROPN
ejpam-3709	15	5	math	math	PROPN
ejpam-3709	15	6	,	,	PUNCT
ejpam-3709	15	7	13	13	NUM
ejpam-3709	15	8	(	(	PUNCT
ejpam-3709	15	9	5	5	NUM
ejpam-3709	15	10	)	)	PUNCT
ejpam-3709	15	11	(	(	PUNCT
ejpam-3709	15	12	2020	2020	NUM
ejpam-3709	15	13	)	)	PUNCT
ejpam-3709	15	14	,	,	PUNCT
ejpam-3709	15	15	1162	1162	NUM
ejpam-3709	15	16	-	-	SYM
ejpam-3709	15	17	1175	1175	NUM
ejpam-3709	15	18	1163	1163	NUM
ejpam-3709	15	19	the	the	DET
ejpam-3709	15	20	detailed	detailed	ADJ
ejpam-3709	15	21	information	information	NOUN
ejpam-3709	15	22	about	about	ADP
ejpam-3709	15	23	the	the	DET
ejpam-3709	15	24	evolution	evolution	NOUN
ejpam-3709	15	25	of	of	ADP
ejpam-3709	15	26	theory	theory	NOUN
ejpam-3709	15	27	of	of	ADP
ejpam-3709	15	28	stability	stability	NOUN
ejpam-3709	15	29	of	of	ADP
ejpam-3709	15	30	fes	fes	NOUN
ejpam-3709	15	31	are	be	AUX
ejpam-3709	15	32	available	available	ADJ
ejpam-3709	15	33	in	in	ADP
ejpam-3709	15	34	[	[	X
ejpam-3709	15	35	3	3	NUM
ejpam-3709	15	36	,	,	PUNCT
ejpam-3709	15	37	5	5	NUM
ejpam-3709	15	38	,	,	PUNCT
ejpam-3709	15	39	6	6	NUM
ejpam-3709	15	40	,	,	PUNCT
ejpam-3709	15	41	24	24	NUM
ejpam-3709	15	42	,	,	PUNCT
ejpam-3709	15	43	25	25	NUM
ejpam-3709	15	44	,	,	PUNCT
ejpam-3709	15	45	30	30	NUM
ejpam-3709	15	46	]	]	PUNCT
ejpam-3709	15	47	.	.	PUNCT
ejpam-3709	16	1	there	there	PRON
ejpam-3709	16	2	are	be	VERB
ejpam-3709	16	3	many	many	ADJ
ejpam-3709	16	4	techniques	technique	NOUN
ejpam-3709	16	5	of	of	ADP
ejpam-3709	16	6	solving	solve	VERB
ejpam-3709	16	7	stability	stability	NOUN
ejpam-3709	16	8	problems	problem	NOUN
ejpam-3709	16	9	of	of	ADP
ejpam-3709	16	10	fes	fes	NOUN
ejpam-3709	16	11	,	,	PUNCT
ejpam-3709	16	12	such	such	ADJ
ejpam-3709	16	13	as	as	ADP
ejpam-3709	16	14	the	the	DET
ejpam-3709	16	15	technique	technique	NOUN
ejpam-3709	16	16	through	through	ADP
ejpam-3709	16	17	the	the	DET
ejpam-3709	16	18	attribute	attribute	NOUN
ejpam-3709	16	19	of	of	ADP
ejpam-3709	16	20	shadowing	shadow	VERB
ejpam-3709	16	21	[	[	X
ejpam-3709	16	22	28	28	NUM
ejpam-3709	16	23	]	]	PUNCT
ejpam-3709	16	24	,	,	PUNCT
ejpam-3709	16	25	the	the	DET
ejpam-3709	16	26	technique	technique	NOUN
ejpam-3709	16	27	via	via	ADP
ejpam-3709	16	28	fixed	fix	VERB
ejpam-3709	16	29	averages	average	NOUN
ejpam-3709	16	30	[	[	X
ejpam-3709	16	31	27	27	NUM
ejpam-3709	16	32	]	]	PUNCT
ejpam-3709	16	33	,	,	PUNCT
ejpam-3709	16	34	the	the	DET
ejpam-3709	16	35	technique	technique	NOUN
ejpam-3709	16	36	by	by	ADP
ejpam-3709	16	37	virtue	virtue	NOUN
ejpam-3709	16	38	of	of	ADP
ejpam-3709	16	39	sandwich	sandwich	NOUN
ejpam-3709	16	40	hypothesis	hypothesis	NOUN
ejpam-3709	16	41	[	[	X
ejpam-3709	16	42	22	22	NUM
ejpam-3709	16	43	]	]	PUNCT
ejpam-3709	16	44	.	.	PUNCT
ejpam-3709	17	1	the	the	DET
ejpam-3709	17	2	dominant	dominant	ADJ
ejpam-3709	17	3	tools	tool	NOUN
ejpam-3709	17	4	to	to	PART
ejpam-3709	17	5	determine	determine	VERB
ejpam-3709	17	6	classical	classical	ADJ
ejpam-3709	17	7	stability	stability	NOUN
ejpam-3709	17	8	problems	problem	NOUN
ejpam-3709	17	9	are	be	AUX
ejpam-3709	17	10	the	the	DET
ejpam-3709	17	11	direct	direct	ADJ
ejpam-3709	17	12	method	method	NOUN
ejpam-3709	17	13	and	and	CCONJ
ejpam-3709	17	14	the	the	DET
ejpam-3709	17	15	fixed	fix	VERB
ejpam-3709	17	16	point	point	NOUN
ejpam-3709	17	17	method	method	NOUN
ejpam-3709	17	18	[	[	X
ejpam-3709	17	19	6	6	NUM
ejpam-3709	17	20	,	,	PUNCT
ejpam-3709	17	21	23	23	NUM
ejpam-3709	17	22	]	]	PUNCT
ejpam-3709	17	23	.	.	PUNCT
ejpam-3709	18	1	also	also	ADV
ejpam-3709	18	2	,	,	PUNCT
ejpam-3709	18	3	without	without	ADP
ejpam-3709	18	4	the	the	DET
ejpam-3709	18	5	application	application	NOUN
ejpam-3709	18	6	of	of	ADP
ejpam-3709	18	7	∆2	∆2	NOUN
ejpam-3709	18	8	-	-	PUNCT
ejpam-3709	18	9	condition	condition	NOUN
ejpam-3709	18	10	,	,	PUNCT
ejpam-3709	18	11	proposed	propose	VERB
ejpam-3709	18	12	in	in	ADP
ejpam-3709	18	13	[	[	X
ejpam-3709	18	14	7	7	NUM
ejpam-3709	18	15	]	]	PUNCT
ejpam-3709	18	16	,	,	PUNCT
ejpam-3709	18	17	there	there	PRON
ejpam-3709	18	18	are	be	VERB
ejpam-3709	18	19	many	many	ADJ
ejpam-3709	18	20	stability	stability	NOUN
ejpam-3709	18	21	problems	problem	NOUN
ejpam-3709	18	22	via	via	ADP
ejpam-3709	18	23	fixed	fix	VERB
ejpam-3709	18	24	point	point	NOUN
ejpam-3709	18	25	theorem	theorem	NOUN
ejpam-3709	18	26	of	of	ADP
ejpam-3709	18	27	quasicontracion	quasicontracion	NOUN
ejpam-3709	18	28	functions	function	NOUN
ejpam-3709	18	29	in	in	ADP
ejpam-3709	18	30	the	the	DET
ejpam-3709	18	31	setting	setting	NOUN
ejpam-3709	18	32	of	of	ADP
ejpam-3709	18	33	modular	modular	ADJ
ejpam-3709	18	34	spaces	space	NOUN
ejpam-3709	18	35	.	.	PUNCT
ejpam-3709	19	1	by	by	ADP
ejpam-3709	19	2	employing	employ	VERB
ejpam-3709	19	3	khamis	khamis	PROPN
ejpam-3709	19	4	’s	’s	PART
ejpam-3709	19	5	invariant	invariant	PROPN
ejpam-3709	19	6	point	point	NOUN
ejpam-3709	19	7	theorem	theorem	VERB
ejpam-3709	19	8	,	,	PUNCT
ejpam-3709	19	9	the	the	DET
ejpam-3709	19	10	modular	modular	ADJ
ejpam-3709	19	11	stabilities	stability	NOUN
ejpam-3709	19	12	of	of	ADP
ejpam-3709	19	13	additive	additive	ADJ
ejpam-3709	19	14	fe	fe	X
ejpam-3709	19	15	alongwith	alongwith	NOUN
ejpam-3709	19	16	with	with	ADP
ejpam-3709	19	17	the	the	DET
ejpam-3709	19	18	fatou	fatou	NOUN
ejpam-3709	19	19	property	property	NOUN
ejpam-3709	19	20	and	and	CCONJ
ejpam-3709	19	21	∆2	∆2	NOUN
ejpam-3709	19	22	-	-	PUNCT
ejpam-3709	19	23	condition	condition	NOUN
ejpam-3709	19	24	are	be	AUX
ejpam-3709	19	25	dealt	deal	VERB
ejpam-3709	19	26	in	in	ADP
ejpam-3709	19	27	[	[	X
ejpam-3709	19	28	26	26	NUM
ejpam-3709	19	29	]	]	PUNCT
ejpam-3709	19	30	.	.	PUNCT
ejpam-3709	20	1	moreover	moreover	ADV
ejpam-3709	20	2	,	,	PUNCT
ejpam-3709	20	3	the	the	DET
ejpam-3709	20	4	modular	modular	ADJ
ejpam-3709	20	5	stability	stability	NOUN
ejpam-3709	20	6	problems	problem	NOUN
ejpam-3709	20	7	of	of	ADP
ejpam-3709	20	8	quadratic	quadratic	ADJ
ejpam-3709	20	9	fes	fes	NOUN
ejpam-3709	20	10	were	be	AUX
ejpam-3709	20	11	discussed	discuss	VERB
ejpam-3709	20	12	satisfying	satisfying	ADJ
ejpam-3709	20	13	fatou	fatou	NOUN
ejpam-3709	20	14	property	property	NOUN
ejpam-3709	20	15	without	without	ADP
ejpam-3709	20	16	utilizing	utilize	VERB
ejpam-3709	20	17	∆2	∆2	NOUN
ejpam-3709	20	18	-	-	NOUN
ejpam-3709	20	19	condition	condition	NOUN
ejpam-3709	20	20	in	in	ADP
ejpam-3709	20	21	[	[	X
ejpam-3709	20	22	31	31	NUM
ejpam-3709	20	23	]	]	PUNCT
ejpam-3709	20	24	.	.	PUNCT
ejpam-3709	21	1	one	one	PRON
ejpam-3709	21	2	can	can	AUX
ejpam-3709	21	3	refer	refer	VERB
ejpam-3709	21	4	[	[	NOUN
ejpam-3709	21	5	2	2	NUM
ejpam-3709	21	6	,	,	PUNCT
ejpam-3709	21	7	4	4	NUM
ejpam-3709	21	8	,	,	PUNCT
ejpam-3709	21	9	8	8	NUM
ejpam-3709	21	10	,	,	PUNCT
ejpam-3709	21	11	11–15	11–15	NUM
ejpam-3709	21	12	]	]	PUNCT
ejpam-3709	21	13	for	for	ADP
ejpam-3709	21	14	more	more	ADJ
ejpam-3709	21	15	details	detail	NOUN
ejpam-3709	21	16	about	about	ADP
ejpam-3709	21	17	stabilities	stability	NOUN
ejpam-3709	21	18	of	of	ADP
ejpam-3709	21	19	real	real	ADJ
ejpam-3709	21	20	and	and	CCONJ
ejpam-3709	21	21	complex	complex	ADJ
ejpam-3709	21	22	valued	value	VERB
ejpam-3709	21	23	multiplicative	multiplicative	ADJ
ejpam-3709	21	24	inverse	inverse	NOUN
ejpam-3709	21	25	fes	fes	NOUN
ejpam-3709	21	26	.	.	PUNCT
ejpam-3709	22	1	in	in	ADP
ejpam-3709	22	2	this	this	DET
ejpam-3709	22	3	present	present	ADJ
ejpam-3709	22	4	work	work	NOUN
ejpam-3709	22	5	,	,	PUNCT
ejpam-3709	22	6	we	we	PRON
ejpam-3709	22	7	propose	propose	VERB
ejpam-3709	22	8	a	a	DET
ejpam-3709	22	9	different	different	ADJ
ejpam-3709	22	10	reciprocal	reciprocal	ADJ
ejpam-3709	22	11	second	second	ADJ
ejpam-3709	22	12	power	power	NOUN
ejpam-3709	22	13	fe	fe	NOUN
ejpam-3709	22	14	of	of	ADP
ejpam-3709	22	15	the	the	DET
ejpam-3709	22	16	form	form	NOUN
ejpam-3709	22	17	mq	mq	NOUN
ejpam-3709	22	18	(	(	PUNCT
ejpam-3709	22	19	uv	uv	INTJ
ejpam-3709	22	20	2u+	2u+	NUM
ejpam-3709	22	21	v	v	NOUN
ejpam-3709	22	22	)	)	PUNCT
ejpam-3709	23	1	+	+	NUM
ejpam-3709	23	2	mq	mq	NOUN
ejpam-3709	23	3	(	(	PUNCT
ejpam-3709	23	4	uv	uv	NOUN
ejpam-3709	23	5	2u−	2u−	PROPN
ejpam-3709	23	6	v	v	NOUN
ejpam-3709	23	7	)	)	PUNCT
ejpam-3709	23	8	=	=	SYM
ejpam-3709	24	1	2mq(u	2mq(u	NUM
ejpam-3709	24	2	)	)	PUNCT
ejpam-3709	25	1	+	+	NUM
ejpam-3709	25	2	8mq(v	8mq(v	NUM
ejpam-3709	25	3	)	)	PUNCT
ejpam-3709	25	4	.	.	PUNCT
ejpam-3709	26	1	(	(	PUNCT
ejpam-3709	26	2	1	1	X
ejpam-3709	26	3	)	)	PUNCT
ejpam-3709	26	4	we	we	PRON
ejpam-3709	26	5	solve	solve	VERB
ejpam-3709	26	6	equation	equation	NOUN
ejpam-3709	26	7	(	(	PUNCT
ejpam-3709	26	8	1	1	NUM
ejpam-3709	26	9	)	)	PUNCT
ejpam-3709	26	10	for	for	ADP
ejpam-3709	26	11	its	its	PRON
ejpam-3709	26	12	solution	solution	NOUN
ejpam-3709	26	13	and	and	CCONJ
ejpam-3709	26	14	investigate	investigate	VERB
ejpam-3709	26	15	its	its	PRON
ejpam-3709	26	16	various	various	ADJ
ejpam-3709	26	17	stability	stability	NOUN
ejpam-3709	26	18	results	result	NOUN
ejpam-3709	26	19	in	in	ADP
ejpam-3709	26	20	modular	modular	ADJ
ejpam-3709	26	21	spaces	space	NOUN
ejpam-3709	26	22	with	with	ADP
ejpam-3709	26	23	and	and	CCONJ
ejpam-3709	26	24	without	without	ADP
ejpam-3709	26	25	using	use	VERB
ejpam-3709	26	26	fatou	fatou	NOUN
ejpam-3709	26	27	property	property	NOUN
ejpam-3709	26	28	and	and	CCONJ
ejpam-3709	26	29	in	in	ADP
ejpam-3709	26	30	β	β	ADJ
ejpam-3709	26	31	-	-	ADJ
ejpam-3709	26	32	homogenous	homogenous	ADJ
ejpam-3709	26	33	spaces	space	NOUN
ejpam-3709	26	34	.	.	PUNCT
ejpam-3709	27	1	2	2	X
ejpam-3709	27	2	.	.	X
ejpam-3709	27	3	solution	solution	NOUN
ejpam-3709	27	4	of	of	ADP
ejpam-3709	27	5	equation	equation	NOUN
ejpam-3709	27	6	(	(	PUNCT
ejpam-3709	27	7	1	1	NUM
ejpam-3709	27	8	)	)	PUNCT
ejpam-3709	27	9	in	in	ADP
ejpam-3709	27	10	the	the	DET
ejpam-3709	27	11	domain	domain	NOUN
ejpam-3709	27	12	of	of	ADP
ejpam-3709	27	13	non	non	ADJ
ejpam-3709	27	14	-	-	ADJ
ejpam-3709	27	15	zero	zero	ADJ
ejpam-3709	27	16	real	real	ADJ
ejpam-3709	27	17	numbers	number	NOUN
ejpam-3709	27	18	in	in	ADP
ejpam-3709	27	19	this	this	DET
ejpam-3709	27	20	section	section	NOUN
ejpam-3709	27	21	,	,	PUNCT
ejpam-3709	27	22	we	we	PRON
ejpam-3709	27	23	impose	impose	VERB
ejpam-3709	27	24	the	the	DET
ejpam-3709	27	25	definition	definition	NOUN
ejpam-3709	27	26	of	of	ADP
ejpam-3709	27	27	reciprocal	reciprocal	ADJ
ejpam-3709	27	28	second	second	ADJ
ejpam-3709	27	29	power	power	NOUN
ejpam-3709	27	30	function	function	NOUN
ejpam-3709	27	31	and	and	CCONJ
ejpam-3709	27	32	then	then	ADV
ejpam-3709	27	33	we	we	PRON
ejpam-3709	27	34	solve	solve	VERB
ejpam-3709	27	35	equation	equation	NOUN
ejpam-3709	27	36	(	(	PUNCT
ejpam-3709	27	37	1	1	NUM
ejpam-3709	27	38	)	)	PUNCT
ejpam-3709	27	39	for	for	ADP
ejpam-3709	27	40	its	its	PRON
ejpam-3709	27	41	solution	solution	NOUN
ejpam-3709	27	42	in	in	ADP
ejpam-3709	27	43	the	the	DET
ejpam-3709	27	44	setting	setting	NOUN
ejpam-3709	27	45	of	of	ADP
ejpam-3709	27	46	non	non	ADJ
ejpam-3709	27	47	-	-	ADJ
ejpam-3709	27	48	zero	zero	ADJ
ejpam-3709	27	49	real	real	ADJ
ejpam-3709	27	50	numbers	number	NOUN
ejpam-3709	27	51	.	.	PUNCT
ejpam-3709	28	1	definition	definition	NOUN
ejpam-3709	28	2	1	1	NUM
ejpam-3709	28	3	.	.	PUNCT
ejpam-3709	29	1	a	a	DET
ejpam-3709	29	2	mapping	mapping	NOUN
ejpam-3709	29	3	mq	mq	NOUN
ejpam-3709	29	4	:	:	PUNCT
ejpam-3709	29	5	r	r	X
ejpam-3709	29	6	?	?	PUNCT
ejpam-3709	30	1	−→	−→	ADJ
ejpam-3709	30	2	r	r	NOUN
ejpam-3709	30	3	is	be	AUX
ejpam-3709	30	4	called	call	VERB
ejpam-3709	30	5	a	a	DET
ejpam-3709	30	6	reciprocal	reciprocal	ADJ
ejpam-3709	30	7	second	second	ADJ
ejpam-3709	30	8	power	power	NOUN
ejpam-3709	30	9	function	function	NOUN
ejpam-3709	30	10	if	if	SCONJ
ejpam-3709	30	11	it	it	PRON
ejpam-3709	30	12	satisfies	satisfy	VERB
ejpam-3709	30	13	(	(	PUNCT
ejpam-3709	30	14	1	1	NUM
ejpam-3709	30	15	)	)	PUNCT
ejpam-3709	30	16	.	.	PUNCT
ejpam-3709	31	1	hence	hence	ADV
ejpam-3709	31	2	,	,	PUNCT
ejpam-3709	31	3	(	(	PUNCT
ejpam-3709	31	4	1	1	X
ejpam-3709	31	5	)	)	PUNCT
ejpam-3709	31	6	is	be	AUX
ejpam-3709	31	7	said	say	VERB
ejpam-3709	31	8	to	to	PART
ejpam-3709	31	9	be	be	AUX
ejpam-3709	31	10	a	a	DET
ejpam-3709	31	11	reciprocal	reciprocal	ADJ
ejpam-3709	31	12	second	second	ADJ
ejpam-3709	31	13	power	power	NOUN
ejpam-3709	31	14	fe	fe	X
ejpam-3709	31	15	.	.	PROPN
ejpam-3709	31	16	theorem	theorem	NOUN
ejpam-3709	31	17	1	1	NUM
ejpam-3709	31	18	.	.	PUNCT
ejpam-3709	32	1	let	let	VERB
ejpam-3709	32	2	mq	mq	NOUN
ejpam-3709	32	3	:	:	PUNCT
ejpam-3709	33	1	r	r	X
ejpam-3709	33	2	?	?	PUNCT
ejpam-3709	34	1	−→	−→	NOUN
ejpam-3709	34	2	r	r	NOUN
ejpam-3709	34	3	be	be	VERB
ejpam-3709	34	4	a	a	DET
ejpam-3709	34	5	function	function	NOUN
ejpam-3709	34	6	.	.	PUNCT
ejpam-3709	35	1	then	then	ADV
ejpam-3709	35	2	,	,	PUNCT
ejpam-3709	35	3	mq	mq	PROPN
ejpam-3709	35	4	satisfies	satisfie	NOUN
ejpam-3709	35	5	(	(	PUNCT
ejpam-3709	35	6	1	1	X
ejpam-3709	35	7	)	)	PUNCT
ejpam-3709	35	8	if	if	SCONJ
ejpam-3709	35	9	and	and	CCONJ
ejpam-3709	35	10	only	only	ADV
ejpam-3709	35	11	if	if	SCONJ
ejpam-3709	35	12	there	there	PRON
ejpam-3709	35	13	exists	exist	VERB
ejpam-3709	35	14	an	an	DET
ejpam-3709	35	15	identity	identity	NOUN
ejpam-3709	35	16	function	function	NOUN
ejpam-3709	35	17	i	i	PRON
ejpam-3709	35	18	:	:	PUNCT
ejpam-3709	36	1	r	r	X
ejpam-3709	36	2	?	?	NOUN
ejpam-3709	37	1	−→	−→	ADJ
ejpam-3709	37	2	r	r	NOUN
ejpam-3709	37	3	such	such	ADJ
ejpam-3709	37	4	that	that	DET
ejpam-3709	37	5	mq(u	mq(u	NOUN
ejpam-3709	37	6	)	)	PUNCT
ejpam-3709	38	1	=	=	PUNCT
ejpam-3709	39	1	[	[	X
ejpam-3709	39	2	i(1	i(1	X
ejpam-3709	39	3	/	/	SYM
ejpam-3709	39	4	u)]2	u)]2	NOUN
ejpam-3709	39	5	,	,	PUNCT
ejpam-3709	39	6	for	for	ADP
ejpam-3709	39	7	all	all	DET
ejpam-3709	39	8	u	u	NOUN
ejpam-3709	39	9	∈	∈	NOUN
ejpam-3709	39	10	r	r	NOUN
ejpam-3709	39	11	?	?	PUNCT
ejpam-3709	39	12	.	.	PUNCT
ejpam-3709	40	1	proof	proof	NOUN
ejpam-3709	40	2	.	.	PUNCT
ejpam-3709	41	1	let	let	VERB
ejpam-3709	41	2	mq	mq	NOUN
ejpam-3709	41	3	satisfies	satisfie	NOUN
ejpam-3709	41	4	(	(	PUNCT
ejpam-3709	41	5	1	1	NUM
ejpam-3709	41	6	)	)	PUNCT
ejpam-3709	41	7	.	.	PUNCT
ejpam-3709	42	1	then	then	ADV
ejpam-3709	42	2	mq	mq	PROPN
ejpam-3709	42	3	is	be	AUX
ejpam-3709	42	4	a	a	DET
ejpam-3709	42	5	reciprocal	reciprocal	ADJ
ejpam-3709	42	6	second	second	ADJ
ejpam-3709	42	7	power	power	NOUN
ejpam-3709	42	8	function	function	NOUN
ejpam-3709	42	9	and	and	CCONJ
ejpam-3709	42	10	hence	hence	ADV
ejpam-3709	42	11	we	we	PRON
ejpam-3709	42	12	can	can	AUX
ejpam-3709	42	13	assume	assume	VERB
ejpam-3709	42	14	mq(u	mq(u	NOUN
ejpam-3709	42	15	)	)	PUNCT
ejpam-3709	42	16	=	=	SYM
ejpam-3709	42	17	1	1	NUM
ejpam-3709	42	18	u2	u2	NOUN
ejpam-3709	42	19	for	for	ADP
ejpam-3709	42	20	all	all	DET
ejpam-3709	42	21	u	u	NOUN
ejpam-3709	42	22	∈	∈	NOUN
ejpam-3709	42	23	r	r	NOUN
ejpam-3709	42	24	?	?	PUNCT
ejpam-3709	42	25	.	.	PUNCT
ejpam-3709	43	1	if	if	SCONJ
ejpam-3709	43	2	i	i	PRON
ejpam-3709	43	3	is	be	AUX
ejpam-3709	43	4	an	an	DET
ejpam-3709	43	5	identity	identity	NOUN
ejpam-3709	43	6	mapping	mapping	NOUN
ejpam-3709	43	7	,	,	PUNCT
ejpam-3709	43	8	then	then	ADV
ejpam-3709	43	9	[	[	X
ejpam-3709	43	10	i(1	i(1	PROPN
ejpam-3709	43	11	/	/	SYM
ejpam-3709	43	12	u)]2	u)]2	NOUN
ejpam-3709	43	13	=	=	SYM
ejpam-3709	43	14	1	1	NUM
ejpam-3709	43	15	u2	u2	NOUN
ejpam-3709	43	16	=	=	PUNCT
ejpam-3709	43	17	mq(u	mq(u	NOUN
ejpam-3709	43	18	)	)	PUNCT
ejpam-3709	43	19	for	for	ADP
ejpam-3709	43	20	all	all	DET
ejpam-3709	43	21	u	u	NOUN
ejpam-3709	43	22	∈	∈	NOUN
ejpam-3709	43	23	r	r	NOUN
ejpam-3709	43	24	?	?	PUNCT
ejpam-3709	43	25	.	.	PUNCT
ejpam-3709	44	1	on	on	ADP
ejpam-3709	44	2	the	the	DET
ejpam-3709	44	3	other	other	ADJ
ejpam-3709	44	4	hand	hand	NOUN
ejpam-3709	44	5	,	,	PUNCT
ejpam-3709	44	6	let	let	VERB
ejpam-3709	44	7	there	there	PRON
ejpam-3709	44	8	exists	exist	VERB
ejpam-3709	44	9	an	an	DET
ejpam-3709	44	10	identity	identity	NOUN
ejpam-3709	44	11	function	function	NOUN
ejpam-3709	45	1	i	i	PRON
ejpam-3709	45	2	:	:	PUNCT
ejpam-3709	46	1	r	r	X
ejpam-3709	46	2	?	?	NOUN
ejpam-3709	47	1	−→	−→	ADJ
ejpam-3709	47	2	r	r	NOUN
ejpam-3709	47	3	such	such	ADJ
ejpam-3709	47	4	that	that	DET
ejpam-3709	47	5	mq(u	mq(u	NOUN
ejpam-3709	47	6	)	)	PUNCT
ejpam-3709	48	1	=	=	PUNCT
ejpam-3709	49	1	[	[	X
ejpam-3709	49	2	i(1	i(1	X
ejpam-3709	49	3	/	/	SYM
ejpam-3709	49	4	u)]2	u)]2	NOUN
ejpam-3709	49	5	for	for	ADP
ejpam-3709	49	6	all	all	DET
ejpam-3709	49	7	u	u	NOUN
ejpam-3709	49	8	∈	∈	NOUN
ejpam-3709	49	9	r	r	NOUN
ejpam-3709	49	10	?	?	PUNCT
ejpam-3709	49	11	.	.	PUNCT
ejpam-3709	50	1	thus	thus	ADV
ejpam-3709	50	2	,	,	PUNCT
ejpam-3709	50	3	we	we	PRON
ejpam-3709	50	4	have	have	VERB
ejpam-3709	50	5	mq	mq	NOUN
ejpam-3709	50	6	(	(	PUNCT
ejpam-3709	50	7	uv	uv	INTJ
ejpam-3709	50	8	2u+	2u+	NUM
ejpam-3709	50	9	v	v	NOUN
ejpam-3709	50	10	)	)	PUNCT
ejpam-3709	51	1	+	+	NUM
ejpam-3709	51	2	mq	mq	NOUN
ejpam-3709	51	3	(	(	PUNCT
ejpam-3709	51	4	uv	uv	NOUN
ejpam-3709	51	5	2u−	2u−	PROPN
ejpam-3709	51	6	v	v	NOUN
ejpam-3709	51	7	)	)	PUNCT
ejpam-3709	51	8	=	=	PUNCT
ejpam-3709	52	1	[	[	PUNCT
ejpam-3709	52	2	i	i	PRON
ejpam-3709	52	3	(	(	PUNCT
ejpam-3709	52	4	2u+	2u+	NUM
ejpam-3709	52	5	v	v	INTJ
ejpam-3709	52	6	uv	uv	NOUN
ejpam-3709	52	7	)	)	PUNCT
ejpam-3709	52	8	]	]	PUNCT
ejpam-3709	52	9	2	2	X
ejpam-3709	52	10	+	+	CCONJ
ejpam-3709	52	11	[	[	PUNCT
ejpam-3709	52	12	i	i	PRON
ejpam-3709	52	13	(	(	PUNCT
ejpam-3709	52	14	2u−	2u−	PROPN
ejpam-3709	52	15	v	v	NOUN
ejpam-3709	52	16	uv	uv	NOUN
ejpam-3709	52	17	)	)	PUNCT
ejpam-3709	52	18	]	]	SYM
ejpam-3709	52	19	2	2	X
ejpam-3709	52	20	=	=	SYM
ejpam-3709	52	21	(	(	PUNCT
ejpam-3709	52	22	2u+	2u+	NUM
ejpam-3709	52	23	v)2	v)2	PROPN
ejpam-3709	52	24	u2v2	u2v2	NOUN
ejpam-3709	52	25	+	+	CCONJ
ejpam-3709	52	26	(	(	PUNCT
ejpam-3709	52	27	2u−	2u−	NUM
ejpam-3709	52	28	v)2	v)2	ADJ
ejpam-3709	52	29	u2v2	u2v2	NOUN
ejpam-3709	52	30	=	=	SYM
ejpam-3709	52	31	8	8	NUM
ejpam-3709	52	32	v2	v2	NOUN
ejpam-3709	52	33	+	+	CCONJ
ejpam-3709	52	34	2	2	NUM
ejpam-3709	52	35	u2	u2	PROPN
ejpam-3709	52	36	b.	b.	PROPN
ejpam-3709	52	37	v.	v.	PROPN
ejpam-3709	52	38	senthil	senthil	PROPN
ejpam-3709	52	39	kumar	kumar	PROPN
ejpam-3709	52	40	,	,	PUNCT
ejpam-3709	52	41	hemen	hemen	PROPN
ejpam-3709	52	42	dutta	dutta	PROPN
ejpam-3709	52	43	,	,	PUNCT
ejpam-3709	52	44	s.	s.	PROPN
ejpam-3709	52	45	sabarinathan	sabarinathan	PROPN
ejpam-3709	52	46	/	/	SYM
ejpam-3709	52	47	eur	eur	PROPN
ejpam-3709	52	48	.	.	PUNCT
ejpam-3709	53	1	j.	j.	PROPN
ejpam-3709	53	2	pure	pure	PROPN
ejpam-3709	53	3	appl	appl	PROPN
ejpam-3709	53	4	.	.	PROPN
ejpam-3709	53	5	math	math	PROPN
ejpam-3709	53	6	,	,	PUNCT
ejpam-3709	53	7	13	13	NUM
ejpam-3709	53	8	(	(	PUNCT
ejpam-3709	53	9	5	5	NUM
ejpam-3709	53	10	)	)	PUNCT
ejpam-3709	53	11	(	(	PUNCT
ejpam-3709	53	12	2020	2020	NUM
ejpam-3709	53	13	)	)	PUNCT
ejpam-3709	53	14	,	,	PUNCT
ejpam-3709	53	15	1162	1162	NUM
ejpam-3709	53	16	-	-	SYM
ejpam-3709	53	17	1175	1175	NUM
ejpam-3709	53	18	1164	1164	NUM
ejpam-3709	53	19	=	=	SYM
ejpam-3709	53	20	2mq(u	2mq(u	NUM
ejpam-3709	53	21	)	)	PUNCT
ejpam-3709	54	1	+	+	NUM
ejpam-3709	54	2	8mq(v	8mq(v	NUM
ejpam-3709	54	3	)	)	PUNCT
ejpam-3709	54	4	for	for	ADP
ejpam-3709	54	5	all	all	DET
ejpam-3709	54	6	u	u	NOUN
ejpam-3709	54	7	,	,	PUNCT
ejpam-3709	54	8	v	v	NOUN
ejpam-3709	54	9	∈	∈	NOUN
ejpam-3709	54	10	r	r	NOUN
ejpam-3709	54	11	?	?	PUNCT
ejpam-3709	54	12	,	,	PUNCT
ejpam-3709	54	13	which	which	PRON
ejpam-3709	54	14	indicates	indicate	VERB
ejpam-3709	54	15	mq	mq	NOUN
ejpam-3709	54	16	satisfies	satisfie	NOUN
ejpam-3709	54	17	(	(	PUNCT
ejpam-3709	54	18	1	1	NUM
ejpam-3709	54	19	)	)	PUNCT
ejpam-3709	54	20	.	.	PUNCT
ejpam-3709	55	1	in	in	ADP
ejpam-3709	55	2	the	the	DET
ejpam-3709	55	3	following	follow	VERB
ejpam-3709	55	4	results	result	NOUN
ejpam-3709	55	5	,	,	PUNCT
ejpam-3709	55	6	for	for	ADP
ejpam-3709	55	7	the	the	DET
ejpam-3709	55	8	purpose	purpose	NOUN
ejpam-3709	55	9	of	of	ADP
ejpam-3709	55	10	easy	easy	ADJ
ejpam-3709	55	11	computation	computation	NOUN
ejpam-3709	55	12	,	,	PUNCT
ejpam-3709	55	13	let	let	VERB
ejpam-3709	55	14	us	we	PRON
ejpam-3709	55	15	consider	consider	VERB
ejpam-3709	55	16	the	the	DET
ejpam-3709	55	17	difference	difference	NOUN
ejpam-3709	55	18	operator	operator	NOUN
ejpam-3709	55	19	γmq	γmq	VERB
ejpam-3709	55	20	defined	define	VERB
ejpam-3709	55	21	as	as	SCONJ
ejpam-3709	55	22	follows	follow	VERB
ejpam-3709	55	23	:	:	PUNCT
ejpam-3709	56	1	γmq(u	γmq(u	NOUN
ejpam-3709	56	2	,	,	PUNCT
ejpam-3709	56	3	v	v	NOUN
ejpam-3709	56	4	)	)	PUNCT
ejpam-3709	56	5	=	=	SYM
ejpam-3709	56	6	mq	mq	NOUN
ejpam-3709	56	7	(	(	PUNCT
ejpam-3709	56	8	uv	uv	INTJ
ejpam-3709	56	9	2u+	2u+	NUM
ejpam-3709	56	10	v	v	NOUN
ejpam-3709	56	11	)	)	PUNCT
ejpam-3709	57	1	+	+	NUM
ejpam-3709	57	2	mq	mq	NOUN
ejpam-3709	57	3	(	(	PUNCT
ejpam-3709	57	4	uv	uv	PROPN
ejpam-3709	57	5	2u−	2u−	PROPN
ejpam-3709	57	6	v	v	NOUN
ejpam-3709	57	7	)	)	PUNCT
ejpam-3709	57	8	−	−	PROPN
ejpam-3709	57	9	8mq(u)−	8mq(u)−	PROPN
ejpam-3709	57	10	2mq(v	2mq(v	NUM
ejpam-3709	57	11	)	)	PUNCT
ejpam-3709	57	12	.	.	PUNCT
ejpam-3709	58	1	3	3	X
ejpam-3709	58	2	.	.	X
ejpam-3709	58	3	modular	modular	ADJ
ejpam-3709	58	4	stability	stability	NOUN
ejpam-3709	58	5	of	of	ADP
ejpam-3709	58	6	equation	equation	NOUN
ejpam-3709	58	7	(	(	PUNCT
ejpam-3709	58	8	1	1	NUM
ejpam-3709	58	9	)	)	PUNCT
ejpam-3709	58	10	with	with	ADP
ejpam-3709	58	11	∆	∆	PROPN
ejpam-3709	58	12	1	1	NUM
ejpam-3709	58	13	3	3	NUM
ejpam-3709	58	14	-condition	-condition	NOUN
ejpam-3709	58	15	in	in	ADP
ejpam-3709	58	16	this	this	DET
ejpam-3709	58	17	present	present	ADJ
ejpam-3709	58	18	section	section	NOUN
ejpam-3709	58	19	,	,	PUNCT
ejpam-3709	58	20	we	we	PRON
ejpam-3709	58	21	explore	explore	VERB
ejpam-3709	58	22	the	the	DET
ejpam-3709	58	23	investigate	investigate	ADJ
ejpam-3709	58	24	stability	stability	NOUN
ejpam-3709	58	25	results	result	NOUN
ejpam-3709	58	26	of	of	ADP
ejpam-3709	58	27	equation	equation	NOUN
ejpam-3709	58	28	(	(	PUNCT
ejpam-3709	58	29	1	1	X
ejpam-3709	58	30	)	)	PUNCT
ejpam-3709	58	31	connected	connect	VERB
ejpam-3709	58	32	with	with	ADP
ejpam-3709	58	33	modular	modular	ADJ
ejpam-3709	58	34	theory	theory	NOUN
ejpam-3709	58	35	with	with	ADP
ejpam-3709	58	36	modular	modular	ADJ
ejpam-3709	58	37	space	space	NOUN
ejpam-3709	58	38	uµ	uµ	NOUN
ejpam-3709	58	39	without	without	ADP
ejpam-3709	58	40	applying	apply	VERB
ejpam-3709	58	41	the	the	DET
ejpam-3709	58	42	fatou	fatou	NOUN
ejpam-3709	58	43	property	property	NOUN
ejpam-3709	58	44	.	.	PUNCT
ejpam-3709	59	1	in	in	ADP
ejpam-3709	59	2	this	this	DET
ejpam-3709	59	3	section	section	NOUN
ejpam-3709	59	4	,	,	PUNCT
ejpam-3709	59	5	let	let	VERB
ejpam-3709	59	6	p	p	PRON
ejpam-3709	59	7	denote	denote	VERB
ejpam-3709	59	8	a	a	DET
ejpam-3709	59	9	linear	linear	ADJ
ejpam-3709	59	10	space	space	NOUN
ejpam-3709	59	11	.	.	PUNCT
ejpam-3709	60	1	in	in	ADP
ejpam-3709	60	2	the	the	DET
ejpam-3709	60	3	following	follow	VERB
ejpam-3709	60	4	results	result	NOUN
ejpam-3709	60	5	,	,	PUNCT
ejpam-3709	60	6	suppose	suppose	VERB
ejpam-3709	60	7	there	there	PRON
ejpam-3709	60	8	exists	exist	VERB
ejpam-3709	60	9	`	`	PUNCT
ejpam-3709	60	10	>	>	X
ejpam-3709	60	11	0	0	PUNCT
ejpam-3709	61	1	so	so	SCONJ
ejpam-3709	61	2	that	that	SCONJ
ejpam-3709	61	3	µ(3u	µ(3u	VERB
ejpam-3709	61	4	)	)	PUNCT
ejpam-3709	61	5	≤	≤	NUM
ejpam-3709	61	6	1	1	NUM
ejpam-3709	61	7	`	`	PUNCT
ejpam-3709	61	8	µ(u	µ(u	NOUN
ejpam-3709	61	9	)	)	PUNCT
ejpam-3709	61	10	,	,	PUNCT
ejpam-3709	61	11	for	for	ADP
ejpam-3709	61	12	all	all	DET
ejpam-3709	61	13	u	u	PROPN
ejpam-3709	61	14	∈	∈	PROPN
ejpam-3709	61	15	uµ	uµ	NOUN
ejpam-3709	61	16	,	,	PUNCT
ejpam-3709	61	17	then	then	ADV
ejpam-3709	61	18	the	the	DET
ejpam-3709	61	19	modular	modular	ADJ
ejpam-3709	61	20	µ	µ	NOUN
ejpam-3709	61	21	is	be	AUX
ejpam-3709	61	22	said	say	VERB
ejpam-3709	61	23	to	to	PART
ejpam-3709	61	24	satisfy	satisfy	VERB
ejpam-3709	61	25	the	the	DET
ejpam-3709	61	26	∆	∆	PROPN
ejpam-3709	61	27	1	1	NUM
ejpam-3709	61	28	3	3	NUM
ejpam-3709	61	29	-condition	-condition	NOUN
ejpam-3709	61	30	.	.	PUNCT
ejpam-3709	62	1	also	also	ADV
ejpam-3709	62	2	,	,	PUNCT
ejpam-3709	62	3	we	we	PRON
ejpam-3709	62	4	say	say	VERB
ejpam-3709	62	5	this	this	PRON
ejpam-3709	62	6	constant	constant	ADJ
ejpam-3709	62	7	`	`	PUNCT
ejpam-3709	62	8	is	be	AUX
ejpam-3709	62	9	a	a	DET
ejpam-3709	62	10	∆	∆	PROPN
ejpam-3709	62	11	1	1	NUM
ejpam-3709	62	12	3	3	NUM
ejpam-3709	62	13	-constant	-constant	NOUN
ejpam-3709	62	14	related	relate	VERB
ejpam-3709	62	15	to	to	ADP
ejpam-3709	62	16	∆	∆	PROPN
ejpam-3709	62	17	1	1	NUM
ejpam-3709	62	18	3	3	NUM
ejpam-3709	62	19	-condition	-condition	NOUN
ejpam-3709	62	20	.	.	PUNCT
ejpam-3709	63	1	one	one	PRON
ejpam-3709	63	2	can	can	AUX
ejpam-3709	63	3	notice	notice	VERB
ejpam-3709	63	4	that	that	SCONJ
ejpam-3709	63	5	if	if	SCONJ
ejpam-3709	63	6	µ	µ	NOUN
ejpam-3709	63	7	is	be	AUX
ejpam-3709	63	8	convex	convex	ADJ
ejpam-3709	63	9	and	and	CCONJ
ejpam-3709	63	10	satisfies	satisfie	NOUN
ejpam-3709	63	11	∆	∆	X
ejpam-3709	63	12	1	1	NUM
ejpam-3709	63	13	3	3	NUM
ejpam-3709	63	14	-condition	-condition	NOUN
ejpam-3709	63	15	with	with	ADP
ejpam-3709	63	16	∆	∆	PROPN
ejpam-3709	63	17	1	1	NUM
ejpam-3709	63	18	3	3	NUM
ejpam-3709	63	19	-constant	-constant	NOUN
ejpam-3709	63	20	`	`	PUNCT
ejpam-3709	63	21	>	>	X
ejpam-3709	63	22	0	0	X
ejpam-3709	63	23	.	.	PUNCT
ejpam-3709	64	1	if	if	SCONJ
ejpam-3709	64	2	`	`	PUNCT
ejpam-3709	64	3	<	<	X
ejpam-3709	64	4	1	1	NUM
ejpam-3709	64	5	3	3	NUM
ejpam-3709	64	6	,	,	PUNCT
ejpam-3709	64	7	then	then	ADV
ejpam-3709	64	8	µ(u	µ(u	NOUN
ejpam-3709	64	9	)	)	PUNCT
ejpam-3709	64	10	≤	≤	NUM
ejpam-3709	64	11	1	1	NUM
ejpam-3709	64	12	`	`	PUNCT
ejpam-3709	64	13	µ	µ	X
ejpam-3709	64	14	(	(	PUNCT
ejpam-3709	64	15	u	u	NOUN
ejpam-3709	64	16	3	3	NUM
ejpam-3709	64	17	)	)	PUNCT
ejpam-3709	64	18	≤	≤	NOUN
ejpam-3709	64	19	1	1	NUM
ejpam-3709	64	20	3`µ(u	3`µ(u	NUM
ejpam-3709	64	21	)	)	PUNCT
ejpam-3709	64	22	,	,	PUNCT
ejpam-3709	64	23	which	which	PRON
ejpam-3709	64	24	implies	imply	VERB
ejpam-3709	64	25	µ	µ	X
ejpam-3709	64	26	=	=	SYM
ejpam-3709	64	27	0	0	NUM
ejpam-3709	64	28	.	.	PUNCT
ejpam-3709	65	1	when	when	SCONJ
ejpam-3709	65	2	µ	µ	NOUN
ejpam-3709	65	3	is	be	AUX
ejpam-3709	65	4	convex	convex	NOUN
ejpam-3709	65	5	modular	modular	ADJ
ejpam-3709	65	6	,	,	PUNCT
ejpam-3709	65	7	then	then	ADV
ejpam-3709	65	8	we	we	PRON
ejpam-3709	65	9	have	have	VERB
ejpam-3709	65	10	∆	∆	PROPN
ejpam-3709	65	11	1	1	NUM
ejpam-3709	65	12	3	3	NUM
ejpam-3709	65	13	-constant	-constant	NOUN
ejpam-3709	65	14	`	`	PUNCT
ejpam-3709	65	15	≥	≥	NUM
ejpam-3709	65	16	1	1	NUM
ejpam-3709	65	17	3	3	NUM
ejpam-3709	65	18	.	.	PUNCT
ejpam-3709	66	1	in	in	ADP
ejpam-3709	66	2	the	the	DET
ejpam-3709	66	3	following	follow	VERB
ejpam-3709	66	4	main	main	ADJ
ejpam-3709	66	5	results	result	NOUN
ejpam-3709	66	6	,	,	PUNCT
ejpam-3709	66	7	let	let	VERB
ejpam-3709	66	8	us	we	PRON
ejpam-3709	66	9	consider	consider	VERB
ejpam-3709	66	10	u	u	PRON
ejpam-3709	66	11	to	to	PART
ejpam-3709	66	12	be	be	AUX
ejpam-3709	66	13	a	a	DET
ejpam-3709	66	14	normed	normed	ADJ
ejpam-3709	66	15	linear	linear	ADJ
ejpam-3709	66	16	space	space	NOUN
ejpam-3709	66	17	over	over	ADP
ejpam-3709	66	18	the	the	DET
ejpam-3709	66	19	set	set	NOUN
ejpam-3709	66	20	of	of	ADP
ejpam-3709	66	21	real	real	ADJ
ejpam-3709	66	22	numbers	number	NOUN
ejpam-3709	66	23	.	.	PUNCT
ejpam-3709	67	1	theorem	theorem	NOUN
ejpam-3709	67	2	2	2	NUM
ejpam-3709	67	3	.	.	PUNCT
ejpam-3709	67	4	suppose	suppose	VERB
ejpam-3709	67	5	uµ	uµ	PROPN
ejpam-3709	67	6	satisfies	satisfy	VERB
ejpam-3709	67	7	the	the	DET
ejpam-3709	67	8	∆	∆	PROPN
ejpam-3709	67	9	1	1	NUM
ejpam-3709	67	10	3	3	NUM
ejpam-3709	67	11	-condition	-condition	NOUN
ejpam-3709	67	12	.	.	PUNCT
ejpam-3709	68	1	let	let	VERB
ejpam-3709	68	2	there	there	PRON
ejpam-3709	68	3	exists	exist	VERB
ejpam-3709	68	4	a	a	DET
ejpam-3709	68	5	mapping	mapping	NOUN
ejpam-3709	68	6	φ	φ	NOUN
ejpam-3709	68	7	:	:	PUNCT
ejpam-3709	68	8	p	p	X
ejpam-3709	68	9	×	×	NOUN
ejpam-3709	68	10	p	p	NOUN
ejpam-3709	68	11	−→	−→	NOUN
ejpam-3709	68	12	[	[	X
ejpam-3709	68	13	0,∞	0,∞	NOUN
ejpam-3709	68	14	)	)	PUNCT
ejpam-3709	68	15	such	such	ADJ
ejpam-3709	68	16	that	that	SCONJ
ejpam-3709	68	17	the	the	DET
ejpam-3709	68	18	mapping	mapping	NOUN
ejpam-3709	68	19	mq	mq	NOUN
ejpam-3709	68	20	:	:	PUNCT
ejpam-3709	68	21	p	p	NOUN
ejpam-3709	68	22	−→	−→	NOUN
ejpam-3709	68	23	uµ	uµ	X
ejpam-3709	68	24	satisfies	satisfie	NOUN
ejpam-3709	68	25	µ	µ	X
ejpam-3709	68	26	(	(	PUNCT
ejpam-3709	68	27	γmq(u	γmq(u	PROPN
ejpam-3709	68	28	,	,	PUNCT
ejpam-3709	68	29	v	v	NOUN
ejpam-3709	68	30	)	)	PUNCT
ejpam-3709	68	31	)	)	PUNCT
ejpam-3709	69	1	≤	≤	NUM
ejpam-3709	69	2	φ(u	φ(u	NOUN
ejpam-3709	69	3	,	,	PUNCT
ejpam-3709	69	4	v	v	NOUN
ejpam-3709	69	5	)	)	PUNCT
ejpam-3709	69	6	,	,	PUNCT
ejpam-3709	69	7	(	(	PUNCT
ejpam-3709	69	8	2	2	X
ejpam-3709	69	9	)	)	PUNCT
ejpam-3709	69	10	lim	lim	PROPN
ejpam-3709	69	11	n→∞	n→∞	PRON
ejpam-3709	70	1	`	`	PUNCT
ejpam-3709	70	2	2nφ	2nφ	ADJ
ejpam-3709	70	3	(	(	PUNCT
ejpam-3709	70	4	u	u	NOUN
ejpam-3709	70	5	3n	3n	NUM
ejpam-3709	70	6	,	,	PUNCT
ejpam-3709	70	7	v	v	ADP
ejpam-3709	70	8	3n	3n	NUM
ejpam-3709	70	9	)	)	PUNCT
ejpam-3709	70	10	=	=	SYM
ejpam-3709	70	11	0	0	NUM
ejpam-3709	70	12	and	and	CCONJ
ejpam-3709	70	13	∞∑	∞∑	PRON
ejpam-3709	70	14	i=0	i=0	PROPN
ejpam-3709	70	15	(	(	PUNCT
ejpam-3709	70	16	3`3	3`3	NUM
ejpam-3709	70	17	)	)	PUNCT
ejpam-3709	70	18	i	i	PRON
ejpam-3709	70	19	φ	φ	VERB
ejpam-3709	70	20	(	(	PUNCT
ejpam-3709	70	21	u	u	NOUN
ejpam-3709	70	22	3i	3i	NOUN
ejpam-3709	70	23	,	,	PUNCT
ejpam-3709	70	24	u	u	NOUN
ejpam-3709	70	25	3i	3i	NOUN
ejpam-3709	70	26	)	)	PUNCT
ejpam-3709	70	27	<	<	X
ejpam-3709	70	28	∞	∞	NUM
ejpam-3709	70	29	for	for	ADP
ejpam-3709	70	30	all	all	DET
ejpam-3709	70	31	u	u	NOUN
ejpam-3709	70	32	,	,	PUNCT
ejpam-3709	70	33	v	v	NOUN
ejpam-3709	70	34	∈	∈	NOUN
ejpam-3709	70	35	p	p	NOUN
ejpam-3709	70	36	,	,	PUNCT
ejpam-3709	70	37	then	then	ADV
ejpam-3709	70	38	a	a	DET
ejpam-3709	70	39	unique	unique	ADJ
ejpam-3709	70	40	reciprocal	reciprocal	ADJ
ejpam-3709	70	41	second	second	ADJ
ejpam-3709	70	42	power	power	NOUN
ejpam-3709	70	43	function	function	NOUN
ejpam-3709	71	1	d	d	NOUN
ejpam-3709	71	2	:	:	PUNCT
ejpam-3709	71	3	p	p	NOUN
ejpam-3709	71	4	−→	−→	NOUN
ejpam-3709	71	5	uµ	uµ	PROPN
ejpam-3709	71	6	exists	exist	VERB
ejpam-3709	71	7	and	and	CCONJ
ejpam-3709	71	8	satisfies	satisfie	NOUN
ejpam-3709	71	9	µ	µ	X
ejpam-3709	71	10	(	(	PUNCT
ejpam-3709	71	11	mq(u)−d(u	mq(u)−d(u	PROPN
ejpam-3709	71	12	)	)	PUNCT
ejpam-3709	71	13	)	)	PUNCT
ejpam-3709	71	14	≤	≤	ADV
ejpam-3709	71	15	3	3	NUM
ejpam-3709	71	16	`	`	PUNCT
ejpam-3709	71	17	∞∑	∞∑	PROPN
ejpam-3709	71	18	i=0	i=0	PROPN
ejpam-3709	71	19	(	(	PUNCT
ejpam-3709	71	20	3`3	3`3	NUM
ejpam-3709	71	21	)	)	PUNCT
ejpam-3709	71	22	i	i	PRON
ejpam-3709	71	23	φ	φ	VERB
ejpam-3709	71	24	(	(	PUNCT
ejpam-3709	71	25	u	u	NOUN
ejpam-3709	71	26	3i	3i	NOUN
ejpam-3709	71	27	,	,	PUNCT
ejpam-3709	71	28	u	u	NOUN
ejpam-3709	71	29	3i	3i	NOUN
ejpam-3709	71	30	)	)	PUNCT
ejpam-3709	71	31	(	(	PUNCT
ejpam-3709	71	32	3	3	X
ejpam-3709	71	33	)	)	PUNCT
ejpam-3709	71	34	for	for	ADP
ejpam-3709	71	35	all	all	DET
ejpam-3709	71	36	u	u	PROPN
ejpam-3709	71	37	∈	∈	PROPN
ejpam-3709	71	38	p.	p.	NOUN
ejpam-3709	71	39	proof	proof	NOUN
ejpam-3709	71	40	.	.	PUNCT
ejpam-3709	72	1	by	by	ADP
ejpam-3709	72	2	taking	take	VERB
ejpam-3709	72	3	v	v	NOUN
ejpam-3709	72	4	=	=	SYM
ejpam-3709	72	5	u	u	NOUN
ejpam-3709	72	6	in	in	ADP
ejpam-3709	72	7	(	(	PUNCT
ejpam-3709	72	8	2	2	NUM
ejpam-3709	72	9	)	)	PUNCT
ejpam-3709	72	10	,	,	PUNCT
ejpam-3709	72	11	we	we	PRON
ejpam-3709	72	12	obtain	obtain	VERB
ejpam-3709	72	13	µ	µ	X
ejpam-3709	72	14	(	(	PUNCT
ejpam-3709	72	15	mq	mq	PROPN
ejpam-3709	72	16	(	(	PUNCT
ejpam-3709	72	17	u	u	NOUN
ejpam-3709	72	18	3	3	NUM
ejpam-3709	72	19	)	)	PUNCT
ejpam-3709	72	20	−	−	PROPN
ejpam-3709	73	1	9mq(u	9mq(u	NUM
ejpam-3709	73	2	)	)	PUNCT
ejpam-3709	73	3	)	)	PUNCT
ejpam-3709	74	1	≤	≤	NUM
ejpam-3709	74	2	φ(u	φ(u	NOUN
ejpam-3709	74	3	,	,	PUNCT
ejpam-3709	74	4	u	u	NOUN
ejpam-3709	74	5	)	)	PUNCT
ejpam-3709	74	6	for	for	ADP
ejpam-3709	74	7	all	all	PRON
ejpam-3709	74	8	u	u	NOUN
ejpam-3709	74	9	∈	∈	PROPN
ejpam-3709	74	10	p	p	NOUN
ejpam-3709	74	11	.	.	PUNCT
ejpam-3709	75	1	employing	employ	VERB
ejpam-3709	75	2	∆	∆	PROPN
ejpam-3709	75	3	1	1	NUM
ejpam-3709	75	4	3	3	NUM
ejpam-3709	75	5	-condition	-condition	NOUN
ejpam-3709	75	6	of	of	ADP
ejpam-3709	75	7	µ	µ	NOUN
ejpam-3709	75	8	,	,	PUNCT
ejpam-3709	75	9	one	one	PRON
ejpam-3709	75	10	can	can	AUX
ejpam-3709	75	11	find	find	VERB
ejpam-3709	75	12	µ	µ	X
ejpam-3709	75	13	(	(	PUNCT
ejpam-3709	75	14	mq(u)−	mq(u)−	ADV
ejpam-3709	75	15	1	1	NUM
ejpam-3709	75	16	9n	9n	NUM
ejpam-3709	75	17	mq	mq	NOUN
ejpam-3709	75	18	(	(	PUNCT
ejpam-3709	75	19	u	u	NOUN
ejpam-3709	75	20	3n	3n	NUM
ejpam-3709	75	21	)	)	PUNCT
ejpam-3709	75	22	)	)	PUNCT
ejpam-3709	76	1	=	=	SYM
ejpam-3709	76	2	µ	µ	X
ejpam-3709	76	3	(	(	PUNCT
ejpam-3709	76	4	n∑	n∑	PROPN
ejpam-3709	76	5	i=0	i=0	ADJ
ejpam-3709	76	6	3i	3i	NOUN
ejpam-3709	76	7	(	(	PUNCT
ejpam-3709	76	8	1	1	NUM
ejpam-3709	76	9	33i−2	33i−2	NUM
ejpam-3709	76	10	mq	mq	NOUN
ejpam-3709	76	11	(	(	PUNCT
ejpam-3709	76	12	u	u	PROPN
ejpam-3709	76	13	3i−1	3i−1	PROPN
ejpam-3709	76	14	)	)	PUNCT
ejpam-3709	77	1	−	−	PROPN
ejpam-3709	77	2	1	1	NUM
ejpam-3709	77	3	33i	33i	NUM
ejpam-3709	77	4	mq	mq	PROPN
ejpam-3709	77	5	(	(	PUNCT
ejpam-3709	77	6	u	u	NOUN
ejpam-3709	77	7	3i	3i	NOUN
ejpam-3709	77	8	)	)	PUNCT
ejpam-3709	77	9	)	)	PUNCT
ejpam-3709	77	10	)	)	PUNCT
ejpam-3709	78	1	≤	≤	NUM
ejpam-3709	78	2	1	1	NUM
ejpam-3709	78	3	`	`	SYM
ejpam-3709	78	4	2	2	NUM
ejpam-3709	78	5	n∑	n∑	NOUN
ejpam-3709	78	6	i=0	i=0	PROPN
ejpam-3709	78	7	(	(	PUNCT
ejpam-3709	78	8	3`3)iφ	3`3)iφ	NUM
ejpam-3709	78	9	(	(	PUNCT
ejpam-3709	78	10	u	u	NOUN
ejpam-3709	78	11	3i	3i	NOUN
ejpam-3709	78	12	,	,	PUNCT
ejpam-3709	78	13	u	u	NOUN
ejpam-3709	78	14	3i	3i	NOUN
ejpam-3709	78	15	)	)	PUNCT
ejpam-3709	78	16	(	(	PUNCT
ejpam-3709	78	17	4	4	X
ejpam-3709	78	18	)	)	PUNCT
ejpam-3709	78	19	b.	b.	PROPN
ejpam-3709	79	1	v.	v.	ADP
ejpam-3709	79	2	senthil	senthil	PROPN
ejpam-3709	79	3	kumar	kumar	PROPN
ejpam-3709	79	4	,	,	PUNCT
ejpam-3709	79	5	hemen	hemen	PROPN
ejpam-3709	79	6	dutta	dutta	PROPN
ejpam-3709	79	7	,	,	PUNCT
ejpam-3709	79	8	s.	s.	PROPN
ejpam-3709	79	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	79	10	/	/	SYM
ejpam-3709	79	11	eur	eur	PROPN
ejpam-3709	79	12	.	.	PUNCT
ejpam-3709	80	1	j.	j.	PROPN
ejpam-3709	80	2	pure	pure	PROPN
ejpam-3709	80	3	appl	appl	PROPN
ejpam-3709	80	4	.	.	PROPN
ejpam-3709	80	5	math	math	PROPN
ejpam-3709	80	6	,	,	PUNCT
ejpam-3709	80	7	13	13	NUM
ejpam-3709	80	8	(	(	PUNCT
ejpam-3709	80	9	5	5	NUM
ejpam-3709	80	10	)	)	PUNCT
ejpam-3709	80	11	(	(	PUNCT
ejpam-3709	80	12	2020	2020	NUM
ejpam-3709	80	13	)	)	PUNCT
ejpam-3709	80	14	,	,	PUNCT
ejpam-3709	80	15	1162	1162	NUM
ejpam-3709	80	16	-	-	SYM
ejpam-3709	80	17	1175	1175	NUM
ejpam-3709	80	18	1165	1165	NUM
ejpam-3709	80	19	for	for	ADP
ejpam-3709	80	20	all	all	DET
ejpam-3709	80	21	u	u	NOUN
ejpam-3709	80	22	∈	∈	PROPN
ejpam-3709	80	23	p	p	NOUN
ejpam-3709	80	24	.	.	PUNCT
ejpam-3709	81	1	now	now	ADV
ejpam-3709	81	2	,	,	PUNCT
ejpam-3709	81	3	shifting	shift	VERB
ejpam-3709	81	4	u	u	NOUN
ejpam-3709	81	5	to	to	ADP
ejpam-3709	81	6	3−mu	3−mu	NUM
ejpam-3709	81	7	in	in	ADP
ejpam-3709	81	8	(	(	PUNCT
ejpam-3709	81	9	4	4	NUM
ejpam-3709	81	10	)	)	PUNCT
ejpam-3709	81	11	,	,	PUNCT
ejpam-3709	81	12	we	we	PRON
ejpam-3709	81	13	obtain	obtain	VERB
ejpam-3709	81	14	µ	µ	X
ejpam-3709	81	15	(	(	PUNCT
ejpam-3709	81	16	1	1	NUM
ejpam-3709	81	17	9	9	NUM
ejpam-3709	81	18	m	m	NOUN
ejpam-3709	81	19	mq	mq	NOUN
ejpam-3709	81	20	(	(	PUNCT
ejpam-3709	81	21	u	u	NOUN
ejpam-3709	81	22	3	3	NUM
ejpam-3709	81	23	m	m	NOUN
ejpam-3709	81	24	)	)	PUNCT
ejpam-3709	82	1	−	−	NUM
ejpam-3709	82	2	1	1	NUM
ejpam-3709	82	3	9n+m	9n+m	NUM
ejpam-3709	82	4	mq	mq	NOUN
ejpam-3709	82	5	(	(	PUNCT
ejpam-3709	82	6	u	u	NOUN
ejpam-3709	82	7	3n+m	3n+m	NUM
ejpam-3709	82	8	)	)	PUNCT
ejpam-3709	82	9	)	)	PUNCT
ejpam-3709	82	10	≤	≤	NUM
ejpam-3709	83	1	`	`	PUNCT
ejpam-3709	83	2	−2mµ	−2mµ	PROPN
ejpam-3709	83	3	(	(	PUNCT
ejpam-3709	83	4	mq	mq	PROPN
ejpam-3709	83	5	(	(	PUNCT
ejpam-3709	83	6	u	u	NOUN
ejpam-3709	83	7	3	3	NUM
ejpam-3709	83	8	m	m	NOUN
ejpam-3709	83	9	)	)	PUNCT
ejpam-3709	83	10	−	−	PROPN
ejpam-3709	83	11	1	1	NUM
ejpam-3709	83	12	9n	9n	NUM
ejpam-3709	83	13	mq	mq	NOUN
ejpam-3709	83	14	(	(	PUNCT
ejpam-3709	83	15	u	u	NOUN
ejpam-3709	83	16	3n+m	3n+m	NUM
ejpam-3709	83	17	)	)	PUNCT
ejpam-3709	83	18	)	)	PUNCT
ejpam-3709	83	19	≤	≤	NUM
ejpam-3709	83	20	`	`	PUNCT
ejpam-3709	83	21	−(2m+2	−(2m+2	NUM
ejpam-3709	83	22	)	)	PUNCT
ejpam-3709	83	23	n∑	n∑	NOUN
ejpam-3709	83	24	i=0	i=0	PROPN
ejpam-3709	83	25	(	(	PUNCT
ejpam-3709	83	26	3`3)iφ	3`3)iφ	NUM
ejpam-3709	83	27	(	(	PUNCT
ejpam-3709	83	28	u	u	PROPN
ejpam-3709	83	29	3i+m	3i+m	NUM
ejpam-3709	83	30	,	,	PUNCT
ejpam-3709	83	31	u	u	NOUN
ejpam-3709	83	32	3i+m	3i+m	NUM
ejpam-3709	83	33	)	)	PUNCT
ejpam-3709	83	34	≤	≤	NOUN
ejpam-3709	83	35	3−m	3−m	NUM
ejpam-3709	83	36	`	`	PUNCT
ejpam-3709	83	37	m+2	m+2	X
ejpam-3709	83	38	n+m∑	n+m∑	PROPN
ejpam-3709	83	39	i	i	PRON
ejpam-3709	83	40	=	=	NOUN
ejpam-3709	83	41	m+1	m+1	X
ejpam-3709	83	42	(	(	PUNCT
ejpam-3709	83	43	3`3)iφ	3`3)iφ	NUM
ejpam-3709	83	44	(	(	PUNCT
ejpam-3709	83	45	u	u	NOUN
ejpam-3709	83	46	3i	3i	NOUN
ejpam-3709	83	47	,	,	PUNCT
ejpam-3709	83	48	u	u	NOUN
ejpam-3709	83	49	3i	3i	NOUN
ejpam-3709	83	50	)	)	PUNCT
ejpam-3709	83	51	for	for	ADP
ejpam-3709	83	52	all	all	DET
ejpam-3709	83	53	u	u	NOUN
ejpam-3709	83	54	∈	∈	PROPN
ejpam-3709	83	55	p	p	NOUN
ejpam-3709	83	56	.	.	PUNCT
ejpam-3709	84	1	the	the	DET
ejpam-3709	84	2	right	right	ADJ
ejpam-3709	84	3	-	-	PUNCT
ejpam-3709	84	4	hand	hand	NOUN
ejpam-3709	84	5	side	side	NOUN
ejpam-3709	84	6	of	of	ADP
ejpam-3709	84	7	the	the	DET
ejpam-3709	84	8	above	above	ADJ
ejpam-3709	84	9	inequality	inequality	NOUN
ejpam-3709	84	10	tends	tend	VERB
ejpam-3709	84	11	to	to	ADP
ejpam-3709	84	12	0	0	NUM
ejpam-3709	84	13	when	when	SCONJ
ejpam-3709	84	14	m→∞	m→∞	NOUN
ejpam-3709	84	15	since	since	SCONJ
ejpam-3709	84	16	`	`	PUNCT
ejpam-3709	84	17	≥	≥	NUM
ejpam-3709	84	18	1	1	NUM
ejpam-3709	84	19	3	3	NUM
ejpam-3709	84	20	,	,	PUNCT
ejpam-3709	84	21	which	which	PRON
ejpam-3709	84	22	indicates	indicate	VERB
ejpam-3709	84	23	that	that	SCONJ
ejpam-3709	84	24	the	the	DET
ejpam-3709	84	25	series	series	NOUN
ejpam-3709	84	26	is	be	AUX
ejpam-3709	84	27	convergent	convergent	ADJ
ejpam-3709	84	28	.	.	PUNCT
ejpam-3709	85	1	in	in	ADP
ejpam-3709	85	2	lieu	lieu	NOUN
ejpam-3709	85	3	of	of	ADP
ejpam-3709	85	4	completeness	completeness	NOUN
ejpam-3709	85	5	of	of	ADP
ejpam-3709	85	6	uµ	uµ	NOUN
ejpam-3709	85	7	,	,	PUNCT
ejpam-3709	85	8	this	this	DET
ejpam-3709	85	9	sequence	sequence	NOUN
ejpam-3709	85	10	{	{	PUNCT
ejpam-3709	85	11	1	1	NUM
ejpam-3709	85	12	9n	9n	NUM
ejpam-3709	85	13	mq	mq	NOUN
ejpam-3709	85	14	(	(	PUNCT
ejpam-3709	85	15	u	u	NOUN
ejpam-3709	85	16	3n	3n	NUM
ejpam-3709	85	17	)	)	PUNCT
ejpam-3709	85	18	}	}	PUNCT
ejpam-3709	85	19	turns	turn	VERB
ejpam-3709	85	20	out	out	ADP
ejpam-3709	85	21	to	to	PART
ejpam-3709	85	22	be	be	AUX
ejpam-3709	85	23	cauchy	cauchy	ADJ
ejpam-3709	85	24	for	for	ADP
ejpam-3709	85	25	all	all	DET
ejpam-3709	85	26	u	u	NOUN
ejpam-3709	85	27	∈	∈	PROPN
ejpam-3709	85	28	p	p	NOUN
ejpam-3709	85	29	and	and	CCONJ
ejpam-3709	85	30	hence	hence	ADV
ejpam-3709	85	31	it	it	PRON
ejpam-3709	85	32	is	be	AUX
ejpam-3709	85	33	µ−convergent	µ−convergent	NOUN
ejpam-3709	85	34	in	in	ADP
ejpam-3709	85	35	uµ.	uµ.	NOUN
ejpam-3709	85	36	hence	hence	ADV
ejpam-3709	85	37	,	,	PUNCT
ejpam-3709	85	38	we	we	PRON
ejpam-3709	85	39	have	have	VERB
ejpam-3709	85	40	a	a	DET
ejpam-3709	85	41	mapping	mapping	NOUN
ejpam-3709	85	42	d	d	NOUN
ejpam-3709	85	43	:	:	PUNCT
ejpam-3709	85	44	p	p	X
ejpam-3709	85	45	−→	−→	NOUN
ejpam-3709	85	46	uµ	uµ	NOUN
ejpam-3709	85	47	given	give	VERB
ejpam-3709	85	48	by	by	ADP
ejpam-3709	85	49	d(u	d(u	NOUN
ejpam-3709	85	50	)	)	PUNCT
ejpam-3709	86	1	=	=	SYM
ejpam-3709	86	2	µ−	µ−	PROPN
ejpam-3709	86	3	lim	lim	NOUN
ejpam-3709	86	4	n→∞	n→∞	NUM
ejpam-3709	86	5	1	1	NUM
ejpam-3709	86	6	9n	9n	NUM
ejpam-3709	86	7	mq	mq	NOUN
ejpam-3709	86	8	(	(	PUNCT
ejpam-3709	86	9	u	u	NOUN
ejpam-3709	86	10	3n	3n	NUM
ejpam-3709	86	11	)	)	PUNCT
ejpam-3709	86	12	,	,	PUNCT
ejpam-3709	86	13	that	that	ADV
ejpam-3709	86	14	is	is	ADV
ejpam-3709	86	15	,	,	PUNCT
ejpam-3709	86	16	limn→∞	limn→∞	X
ejpam-3709	86	17	µ	µ	X
ejpam-3709	86	18	(	(	PUNCT
ejpam-3709	86	19	1	1	NUM
ejpam-3709	86	20	9nmq	9nmq	PROPN
ejpam-3709	86	21	(	(	PUNCT
ejpam-3709	86	22	u	u	NOUN
ejpam-3709	86	23	3n	3n	NUM
ejpam-3709	86	24	)	)	PUNCT
ejpam-3709	86	25	−d(u	−d(u	NOUN
ejpam-3709	86	26	)	)	PUNCT
ejpam-3709	86	27	)	)	PUNCT
ejpam-3709	87	1	=	=	SYM
ejpam-3709	87	2	0	0	NUM
ejpam-3709	87	3	for	for	ADP
ejpam-3709	87	4	all	all	DET
ejpam-3709	87	5	u	u	NOUN
ejpam-3709	87	6	∈	∈	PROPN
ejpam-3709	87	7	p	p	NOUN
ejpam-3709	87	8	.	.	PUNCT
ejpam-3709	88	1	so	so	ADV
ejpam-3709	88	2	,	,	PUNCT
ejpam-3709	88	3	without	without	ADP
ejpam-3709	88	4	using	use	VERB
ejpam-3709	88	5	fatou	fatou	NOUN
ejpam-3709	88	6	property	property	NOUN
ejpam-3709	88	7	,	,	PUNCT
ejpam-3709	88	8	we	we	PRON
ejpam-3709	88	9	observe	observe	VERB
ejpam-3709	88	10	from	from	ADP
ejpam-3709	88	11	∆	∆	PROPN
ejpam-3709	88	12	1	1	NUM
ejpam-3709	88	13	3	3	NUM
ejpam-3709	88	14	-condition	-condition	NOUN
ejpam-3709	88	15	that	that	PRON
ejpam-3709	88	16	the	the	DET
ejpam-3709	88	17	inequality	inequality	NOUN
ejpam-3709	88	18	µ	µ	X
ejpam-3709	88	19	(	(	PUNCT
ejpam-3709	88	20	mq(u)−d(u	mq(u)−d(u	PROPN
ejpam-3709	88	21	)	)	PUNCT
ejpam-3709	88	22	)	)	PUNCT
ejpam-3709	88	23	≤	≤	NUM
ejpam-3709	88	24	3µ	3µ	NUM
ejpam-3709	88	25	(	(	PUNCT
ejpam-3709	88	26	1	1	NUM
ejpam-3709	88	27	3	3	NUM
ejpam-3709	88	28	mq(u)−	mq(u)−	NOUN
ejpam-3709	88	29	1	1	NUM
ejpam-3709	88	30	3	3	NUM
ejpam-3709	88	31	·	·	SYM
ejpam-3709	88	32	1	1	NUM
ejpam-3709	88	33	9n	9n	NUM
ejpam-3709	88	34	mq	mq	NOUN
ejpam-3709	88	35	(	(	PUNCT
ejpam-3709	88	36	u	u	NOUN
ejpam-3709	88	37	3n	3n	NUM
ejpam-3709	88	38	)	)	PUNCT
ejpam-3709	88	39	)	)	PUNCT
ejpam-3709	89	1	+	+	CCONJ
ejpam-3709	89	2	3µ	3µ	NUM
ejpam-3709	89	3	(	(	PUNCT
ejpam-3709	89	4	1	1	NUM
ejpam-3709	89	5	3	3	NUM
ejpam-3709	89	6	·	·	SYM
ejpam-3709	89	7	1	1	NUM
ejpam-3709	89	8	9n	9n	NUM
ejpam-3709	89	9	mq	mq	NOUN
ejpam-3709	89	10	(	(	PUNCT
ejpam-3709	89	11	u	u	NOUN
ejpam-3709	89	12	3n	3n	NUM
ejpam-3709	89	13	)	)	PUNCT
ejpam-3709	89	14	−	−	PROPN
ejpam-3709	89	15	1	1	NUM
ejpam-3709	89	16	3	3	NUM
ejpam-3709	89	17	d(u	d(u	PROPN
ejpam-3709	89	18	)	)	PUNCT
ejpam-3709	89	19	)	)	PUNCT
ejpam-3709	89	20	≤	≤	ADV
ejpam-3709	89	21	3	3	NUM
ejpam-3709	89	22	k	k	PROPN
ejpam-3709	89	23	µ	µ	X
ejpam-3709	89	24	(	(	PUNCT
ejpam-3709	89	25	mq(u)−	mq(u)−	ADV
ejpam-3709	89	26	1	1	NUM
ejpam-3709	89	27	9n	9n	NUM
ejpam-3709	89	28	mq	mq	NOUN
ejpam-3709	89	29	(	(	PUNCT
ejpam-3709	89	30	u	u	NOUN
ejpam-3709	89	31	3n	3n	NUM
ejpam-3709	89	32	)	)	PUNCT
ejpam-3709	89	33	)	)	PUNCT
ejpam-3709	90	1	+	+	CCONJ
ejpam-3709	90	2	3kµ	3kµ	NOUN
ejpam-3709	90	3	(	(	PUNCT
ejpam-3709	90	4	1	1	NUM
ejpam-3709	90	5	9n	9n	NUM
ejpam-3709	90	6	mq	mq	NOUN
ejpam-3709	90	7	(	(	PUNCT
ejpam-3709	90	8	u	u	NOUN
ejpam-3709	90	9	3n	3n	NUM
ejpam-3709	90	10	)	)	PUNCT
ejpam-3709	90	11	−d(u	−d(u	NOUN
ejpam-3709	90	12	)	)	PUNCT
ejpam-3709	90	13	)	)	PUNCT
ejpam-3709	90	14	≤	≤	ADV
ejpam-3709	91	1	3	3	NUM
ejpam-3709	91	2	`	`	PUNCT
ejpam-3709	91	3	n∑	n∑	NOUN
ejpam-3709	91	4	i=0	i=0	PROPN
ejpam-3709	91	5	(	(	PUNCT
ejpam-3709	91	6	3`3	3`3	NUM
ejpam-3709	91	7	)	)	PUNCT
ejpam-3709	91	8	i	i	PRON
ejpam-3709	91	9	φ	φ	VERB
ejpam-3709	91	10	(	(	PUNCT
ejpam-3709	91	11	u	u	NOUN
ejpam-3709	91	12	3i	3i	NOUN
ejpam-3709	91	13	,	,	PUNCT
ejpam-3709	91	14	u	u	NOUN
ejpam-3709	91	15	3i	3i	NOUN
ejpam-3709	91	16	)	)	PUNCT
ejpam-3709	92	1	+	+	CCONJ
ejpam-3709	92	2	3`µ	3`µ	NUM
ejpam-3709	92	3	(	(	PUNCT
ejpam-3709	92	4	1	1	NUM
ejpam-3709	92	5	9n	9n	NUM
ejpam-3709	92	6	mq	mq	NOUN
ejpam-3709	92	7	(	(	PUNCT
ejpam-3709	92	8	u	u	NOUN
ejpam-3709	92	9	3n	3n	NUM
ejpam-3709	92	10	)	)	PUNCT
ejpam-3709	92	11	−d(u	−d(u	NOUN
ejpam-3709	92	12	)	)	PUNCT
ejpam-3709	92	13	)	)	PUNCT
ejpam-3709	92	14	is	be	AUX
ejpam-3709	92	15	true	true	ADJ
ejpam-3709	92	16	for	for	ADP
ejpam-3709	92	17	u	u	PROPN
ejpam-3709	92	18	∈	∈	PROPN
ejpam-3709	92	19	p	p	NOUN
ejpam-3709	92	20	and	and	CCONJ
ejpam-3709	92	21	all	all	DET
ejpam-3709	92	22	integers	integer	NOUN
ejpam-3709	92	23	n	n	X
ejpam-3709	92	24	>	>	X
ejpam-3709	92	25	1	1	X
ejpam-3709	92	26	.	.	PUNCT
ejpam-3709	92	27	allowing	allow	VERB
ejpam-3709	92	28	n→∞	n→∞	PRON
ejpam-3709	92	29	in	in	ADP
ejpam-3709	92	30	the	the	DET
ejpam-3709	92	31	above	above	ADJ
ejpam-3709	92	32	inequality	inequality	NOUN
ejpam-3709	92	33	indicates	indicate	VERB
ejpam-3709	92	34	that	that	SCONJ
ejpam-3709	92	35	(	(	PUNCT
ejpam-3709	92	36	4	4	X
ejpam-3709	92	37	)	)	PUNCT
ejpam-3709	92	38	holds	hold	VERB
ejpam-3709	92	39	.	.	PUNCT
ejpam-3709	93	1	plugging	plug	VERB
ejpam-3709	93	2	(	(	PUNCT
ejpam-3709	93	3	u	u	NOUN
ejpam-3709	93	4	,	,	PUNCT
ejpam-3709	93	5	v	v	NOUN
ejpam-3709	93	6	)	)	PUNCT
ejpam-3709	93	7	by	by	ADP
ejpam-3709	93	8	(	(	PUNCT
ejpam-3709	93	9	3−nu	3−nu	NUM
ejpam-3709	93	10	,	,	PUNCT
ejpam-3709	93	11	3−nv	3−nv	NUM
ejpam-3709	93	12	)	)	PUNCT
ejpam-3709	93	13	in	in	ADP
ejpam-3709	93	14	(	(	PUNCT
ejpam-3709	93	15	2	2	NUM
ejpam-3709	93	16	)	)	PUNCT
ejpam-3709	93	17	,	,	PUNCT
ejpam-3709	93	18	we	we	PRON
ejpam-3709	93	19	find	find	VERB
ejpam-3709	93	20	that	that	SCONJ
ejpam-3709	93	21	µ	µ	X
ejpam-3709	93	22	(	(	PUNCT
ejpam-3709	93	23	3−nmq	3−nmq	NUM
ejpam-3709	93	24	(	(	PUNCT
ejpam-3709	93	25	3−2nuv	3−2nuv	NUM
ejpam-3709	93	26	3−n(2u+	3−n(2u+	NUM
ejpam-3709	93	27	v	v	NOUN
ejpam-3709	93	28	)	)	PUNCT
ejpam-3709	93	29	)	)	PUNCT
ejpam-3709	94	1	+	+	CCONJ
ejpam-3709	94	2	3−nmq	3−nmq	NUM
ejpam-3709	94	3	(	(	PUNCT
ejpam-3709	94	4	3−2nuv	3−2nuv	NUM
ejpam-3709	94	5	3−n(2u−	3−n(2u−	NUM
ejpam-3709	94	6	v	v	NOUN
ejpam-3709	94	7	)	)	PUNCT
ejpam-3709	94	8	)	)	PUNCT
ejpam-3709	95	1	−	−	ADP
ejpam-3709	96	1	8	8	NUM
ejpam-3709	96	2	·	·	SYM
ejpam-3709	96	3	3−nmq(3	3−nmq(3	NUM
ejpam-3709	96	4	−nu)−	−nu)−	NOUN
ejpam-3709	96	5	2	2	NUM
ejpam-3709	96	6	·	·	SYM
ejpam-3709	96	7	3−nmq(3	3−nmq(3	NUM
ejpam-3709	96	8	−nv	−nv	NOUN
ejpam-3709	96	9	)	)	PUNCT
ejpam-3709	96	10	)	)	PUNCT
ejpam-3709	96	11	≤	≤	NUM
ejpam-3709	97	1	`	`	PUNCT
ejpam-3709	97	2	2nφ	2nφ	ADJ
ejpam-3709	97	3	(	(	PUNCT
ejpam-3709	97	4	u	u	NOUN
ejpam-3709	97	5	3n	3n	NUM
ejpam-3709	97	6	,	,	PUNCT
ejpam-3709	97	7	v	v	ADP
ejpam-3709	97	8	3n	3n	NUM
ejpam-3709	97	9	)	)	PUNCT
ejpam-3709	97	10	which	which	PRON
ejpam-3709	97	11	approaches	approach	VERB
ejpam-3709	97	12	zero	zero	NUM
ejpam-3709	97	13	as	as	ADP
ejpam-3709	97	14	n→∞	n→∞	NUM
ejpam-3709	97	15	for	for	ADP
ejpam-3709	97	16	all	all	DET
ejpam-3709	97	17	u	u	NOUN
ejpam-3709	97	18	,	,	PUNCT
ejpam-3709	97	19	v	v	NOUN
ejpam-3709	97	20	∈	∈	PROPN
ejpam-3709	97	21	p	p	NOUN
ejpam-3709	97	22	.	.	PUNCT
ejpam-3709	98	1	thus	thus	ADV
ejpam-3709	98	2	,	,	PUNCT
ejpam-3709	98	3	in	in	ADP
ejpam-3709	98	4	liue	liue	NOUN
ejpam-3709	98	5	of	of	ADP
ejpam-3709	98	6	the	the	DET
ejpam-3709	98	7	convexity	convexity	NOUN
ejpam-3709	98	8	of	of	ADP
ejpam-3709	98	9	µ	µ	NUM
ejpam-3709	98	10	,	,	PUNCT
ejpam-3709	98	11	we	we	PRON
ejpam-3709	98	12	have	have	VERB
ejpam-3709	98	13	µ	µ	X
ejpam-3709	98	14	(	(	PUNCT
ejpam-3709	98	15	1	1	NUM
ejpam-3709	98	16	13	13	NUM
ejpam-3709	98	17	d	d	NOUN
ejpam-3709	98	18	(	(	PUNCT
ejpam-3709	98	19	uv	uv	INTJ
ejpam-3709	98	20	2u+	2u+	NUM
ejpam-3709	98	21	v	v	NOUN
ejpam-3709	98	22	)	)	PUNCT
ejpam-3709	99	1	+	+	CCONJ
ejpam-3709	99	2	1	1	NUM
ejpam-3709	99	3	13	13	NUM
ejpam-3709	99	4	d	d	NOUN
ejpam-3709	99	5	(	(	PUNCT
ejpam-3709	99	6	uv	uv	PROPN
ejpam-3709	99	7	2u−	2u−	PROPN
ejpam-3709	99	8	v	v	NOUN
ejpam-3709	99	9	)	)	PUNCT
ejpam-3709	99	10	−	−	PROPN
ejpam-3709	99	11	8	8	NUM
ejpam-3709	99	12	13	13	NUM
ejpam-3709	99	13	d(u)−	d(u)−	PROPN
ejpam-3709	99	14	2	2	NUM
ejpam-3709	99	15	13	13	NUM
ejpam-3709	99	16	d(v	d(v	PROPN
ejpam-3709	99	17	)	)	PUNCT
ejpam-3709	99	18	)	)	PUNCT
ejpam-3709	100	1	b.	b.	PROPN
ejpam-3709	101	1	v.	v.	ADP
ejpam-3709	101	2	senthil	senthil	PROPN
ejpam-3709	101	3	kumar	kumar	PROPN
ejpam-3709	101	4	,	,	PUNCT
ejpam-3709	101	5	hemen	hemen	PROPN
ejpam-3709	101	6	dutta	dutta	PROPN
ejpam-3709	101	7	,	,	PUNCT
ejpam-3709	101	8	s.	s.	PROPN
ejpam-3709	101	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	101	10	/	/	SYM
ejpam-3709	101	11	eur	eur	PROPN
ejpam-3709	101	12	.	.	PUNCT
ejpam-3709	102	1	j.	j.	PROPN
ejpam-3709	102	2	pure	pure	PROPN
ejpam-3709	102	3	appl	appl	PROPN
ejpam-3709	102	4	.	.	PROPN
ejpam-3709	102	5	math	math	PROPN
ejpam-3709	102	6	,	,	PUNCT
ejpam-3709	102	7	13	13	NUM
ejpam-3709	102	8	(	(	PUNCT
ejpam-3709	102	9	5	5	NUM
ejpam-3709	102	10	)	)	PUNCT
ejpam-3709	102	11	(	(	PUNCT
ejpam-3709	102	12	2020	2020	NUM
ejpam-3709	102	13	)	)	PUNCT
ejpam-3709	102	14	,	,	PUNCT
ejpam-3709	102	15	1162	1162	NUM
ejpam-3709	102	16	-	-	SYM
ejpam-3709	102	17	1175	1175	NUM
ejpam-3709	102	18	1166	1166	NUM
ejpam-3709	102	19	≤	≤	NUM
ejpam-3709	102	20	1	1	NUM
ejpam-3709	102	21	13	13	NUM
ejpam-3709	102	22	µ	µ	X
ejpam-3709	102	23	(	(	PUNCT
ejpam-3709	102	24	1	1	NUM
ejpam-3709	102	25	13	13	NUM
ejpam-3709	102	26	d	d	NOUN
ejpam-3709	102	27	(	(	PUNCT
ejpam-3709	102	28	uv	uv	INTJ
ejpam-3709	102	29	2u+	2u+	NUM
ejpam-3709	102	30	v	v	NOUN
ejpam-3709	102	31	)	)	PUNCT
ejpam-3709	103	1	−	−	PROPN
ejpam-3709	104	1	3−nmq	3−nmq	INTJ
ejpam-3709	104	2	(	(	PUNCT
ejpam-3709	104	3	3−nuv	3−nuv	NOUN
ejpam-3709	104	4	2u+	2u+	NUM
ejpam-3709	104	5	v	v	NOUN
ejpam-3709	104	6	)	)	PUNCT
ejpam-3709	104	7	+	+	CCONJ
ejpam-3709	104	8	1	1	NUM
ejpam-3709	104	9	13	13	NUM
ejpam-3709	104	10	d	d	NOUN
ejpam-3709	104	11	(	(	PUNCT
ejpam-3709	104	12	uv	uv	PROPN
ejpam-3709	104	13	2u−	2u−	PROPN
ejpam-3709	104	14	v	v	NOUN
ejpam-3709	104	15	)	)	PUNCT
ejpam-3709	104	16	−	−	PROPN
ejpam-3709	105	1	3−nmq	3−nmq	INTJ
ejpam-3709	105	2	(	(	PUNCT
ejpam-3709	105	3	3−nuv	3−nuv	NOUN
ejpam-3709	105	4	2u−	2u−	NUM
ejpam-3709	105	5	v	v	NOUN
ejpam-3709	105	6	)	)	PUNCT
ejpam-3709	105	7	+	+	CCONJ
ejpam-3709	105	8	8	8	NUM
ejpam-3709	105	9	13	13	NUM
ejpam-3709	105	10	µ	µ	X
ejpam-3709	105	11	(	(	PUNCT
ejpam-3709	105	12	d(u)−	d(u)−	PROPN
ejpam-3709	105	13	3−nmq	3−nmq	NUM
ejpam-3709	105	14	(	(	PUNCT
ejpam-3709	105	15	3−nu	3−nu	NUM
ejpam-3709	105	16	)	)	PUNCT
ejpam-3709	105	17	)	)	PUNCT
ejpam-3709	106	1	+	+	CCONJ
ejpam-3709	106	2	2	2	NUM
ejpam-3709	106	3	13	13	NUM
ejpam-3709	106	4	µ	µ	X
ejpam-3709	106	5	(	(	PUNCT
ejpam-3709	106	6	d(v)−	d(v)−	PROPN
ejpam-3709	106	7	3−nmq	3−nmq	PROPN
ejpam-3709	106	8	(	(	PUNCT
ejpam-3709	106	9	3−nv	3−nv	NUM
ejpam-3709	106	10	)	)	PUNCT
ejpam-3709	106	11	)	)	PUNCT
ejpam-3709	107	1	+	+	CCONJ
ejpam-3709	107	2	1	1	NUM
ejpam-3709	107	3	13	13	NUM
ejpam-3709	107	4	µ	µ	X
ejpam-3709	107	5	(	(	PUNCT
ejpam-3709	107	6	3−nmq	3−nmq	PROPN
ejpam-3709	107	7	(	(	PUNCT
ejpam-3709	107	8	3−nuv	3−nuv	NOUN
ejpam-3709	107	9	2u+	2u+	NUM
ejpam-3709	107	10	v	v	NOUN
ejpam-3709	107	11	)	)	PUNCT
ejpam-3709	108	1	+	+	CCONJ
ejpam-3709	108	2	3−nmq	3−nmq	NUM
ejpam-3709	108	3	(	(	PUNCT
ejpam-3709	108	4	3−nuv	3−nuv	NOUN
ejpam-3709	108	5	2u−	2u−	NUM
ejpam-3709	108	6	v	v	NOUN
ejpam-3709	108	7	)	)	PUNCT
ejpam-3709	108	8	)	)	PUNCT
ejpam-3709	109	1	−	−	PROPN
ejpam-3709	109	2	8	8	NUM
ejpam-3709	109	3	·	·	SYM
ejpam-3709	109	4	3−nmq	3−nmq	NUM
ejpam-3709	109	5	(	(	PUNCT
ejpam-3709	109	6	3−nu	3−nu	NUM
ejpam-3709	109	7	)	)	PUNCT
ejpam-3709	109	8	−	−	PROPN
ejpam-3709	109	9	2	2	NUM
ejpam-3709	109	10	·	·	PUNCT
ejpam-3709	109	11	3−nmq	3−nmq	NUM
ejpam-3709	109	12	(	(	PUNCT
ejpam-3709	109	13	3−nv	3−nv	NUM
ejpam-3709	109	14	)	)	PUNCT
ejpam-3709	109	15	)	)	PUNCT
ejpam-3709	109	16	for	for	ADP
ejpam-3709	109	17	all	all	DET
ejpam-3709	109	18	u	u	NOUN
ejpam-3709	109	19	,	,	PUNCT
ejpam-3709	109	20	v	v	NOUN
ejpam-3709	109	21	∈	∈	PROPN
ejpam-3709	109	22	p	p	NOUN
ejpam-3709	109	23	and	and	CCONJ
ejpam-3709	109	24	all	all	DET
ejpam-3709	109	25	integer	integer	NOUN
ejpam-3709	109	26	n	n	CCONJ
ejpam-3709	109	27	>	>	X
ejpam-3709	109	28	1	1	NUM
ejpam-3709	109	29	.	.	PUNCT
ejpam-3709	109	30	letting	let	VERB
ejpam-3709	109	31	the	the	DET
ejpam-3709	109	32	limit	limit	NOUN
ejpam-3709	109	33	n	n	X
ejpam-3709	109	34	→	→	SYM
ejpam-3709	109	35	∞	∞	PROPN
ejpam-3709	109	36	,	,	PUNCT
ejpam-3709	109	37	one	one	PRON
ejpam-3709	109	38	obtains	obtain	VERB
ejpam-3709	109	39	that	that	SCONJ
ejpam-3709	109	40	d	d	NOUN
ejpam-3709	109	41	is	be	AUX
ejpam-3709	109	42	reciprocal	reciprocal	ADJ
ejpam-3709	109	43	inverse	inverse	NOUN
ejpam-3709	109	44	second	second	ADJ
ejpam-3709	109	45	power	power	NOUN
ejpam-3709	109	46	function	function	NOUN
ejpam-3709	109	47	.	.	PUNCT
ejpam-3709	110	1	to	to	PART
ejpam-3709	110	2	show	show	VERB
ejpam-3709	110	3	the	the	DET
ejpam-3709	110	4	uniqueness	uniqueness	NOUN
ejpam-3709	110	5	of	of	ADP
ejpam-3709	110	6	d	d	PROPN
ejpam-3709	110	7	,	,	PUNCT
ejpam-3709	110	8	let	let	VERB
ejpam-3709	110	9	us	we	PRON
ejpam-3709	110	10	assume	assume	VERB
ejpam-3709	110	11	that	that	SCONJ
ejpam-3709	110	12	there	there	PRON
ejpam-3709	110	13	is	be	VERB
ejpam-3709	110	14	another	another	DET
ejpam-3709	110	15	reciprocal	reciprocal	ADJ
ejpam-3709	110	16	second	second	ADJ
ejpam-3709	110	17	power	power	NOUN
ejpam-3709	110	18	function	function	NOUN
ejpam-3709	110	19	d′	d′	PROPN
ejpam-3709	110	20	:	:	PUNCT
ejpam-3709	111	1	p	p	X
ejpam-3709	111	2	−→	−→	NOUN
ejpam-3709	111	3	uµ	uµ	X
ejpam-3709	111	4	satisfying	satisfy	VERB
ejpam-3709	111	5	µ	µ	X
ejpam-3709	111	6	(	(	PUNCT
ejpam-3709	111	7	mq(u)−d′(u	mq(u)−d′(u	NOUN
ejpam-3709	111	8	)	)	PUNCT
ejpam-3709	111	9	)	)	PUNCT
ejpam-3709	111	10	≤	≤	ADV
ejpam-3709	111	11	3	3	NUM
ejpam-3709	111	12	k	k	PROPN
ejpam-3709	111	13	∞∑	∞∑	PROPN
ejpam-3709	111	14	i=0	i=0	PROPN
ejpam-3709	111	15	(	(	PUNCT
ejpam-3709	111	16	3`3)iφ	3`3)iφ	NUM
ejpam-3709	111	17	(	(	PUNCT
ejpam-3709	111	18	u	u	NOUN
ejpam-3709	111	19	3i	3i	NOUN
ejpam-3709	111	20	,	,	PUNCT
ejpam-3709	111	21	u	u	NOUN
ejpam-3709	111	22	3i	3i	NOUN
ejpam-3709	111	23	)	)	PUNCT
ejpam-3709	111	24	.	.	PUNCT
ejpam-3709	112	1	then	then	ADV
ejpam-3709	112	2	we	we	PRON
ejpam-3709	112	3	see	see	VERB
ejpam-3709	112	4	from	from	ADP
ejpam-3709	112	5	the	the	DET
ejpam-3709	112	6	equalities	equality	NOUN
ejpam-3709	112	7	:	:	PUNCT
ejpam-3709	112	8	d(3−nu	d(3−nu	NOUN
ejpam-3709	112	9	)	)	PUNCT
ejpam-3709	112	10	=	=	SYM
ejpam-3709	113	1	9nd(u	9nd(u	NUM
ejpam-3709	113	2	)	)	PUNCT
ejpam-3709	113	3	and	and	CCONJ
ejpam-3709	113	4	d	d	ADP
ejpam-3709	113	5	′	′	NUM
ejpam-3709	113	6	(	(	PUNCT
ejpam-3709	113	7	3−nu	3−nu	NUM
ejpam-3709	113	8	)	)	PUNCT
ejpam-3709	113	9	=	=	SYM
ejpam-3709	114	1	9nd	9nd	ADJ
ejpam-3709	114	2	′	′	NUM
ejpam-3709	114	3	(	(	PUNCT
ejpam-3709	114	4	u	u	NOUN
ejpam-3709	114	5	)	)	PUNCT
ejpam-3709	115	1	that	that	PRON
ejpam-3709	115	2	µ	µ	X
ejpam-3709	115	3	(	(	PUNCT
ejpam-3709	115	4	d(u)−d′(u	d(u)−d′(u	PROPN
ejpam-3709	115	5	)	)	PUNCT
ejpam-3709	115	6	)	)	PUNCT
ejpam-3709	115	7	≤	≤	ADV
ejpam-3709	115	8	3µ	3µ	NUM
ejpam-3709	115	9	(	(	PUNCT
ejpam-3709	115	10	1	1	NUM
ejpam-3709	115	11	3	3	NUM
ejpam-3709	115	12	·	·	SYM
ejpam-3709	115	13	1	1	NUM
ejpam-3709	116	1	9n	9n	NUM
ejpam-3709	116	2	d	d	NOUN
ejpam-3709	116	3	(	(	PUNCT
ejpam-3709	116	4	u	u	NOUN
ejpam-3709	116	5	3n	3n	NUM
ejpam-3709	116	6	)	)	PUNCT
ejpam-3709	116	7	−	−	PROPN
ejpam-3709	116	8	1	1	NUM
ejpam-3709	116	9	3	3	NUM
ejpam-3709	116	10	·	·	SYM
ejpam-3709	116	11	1	1	NUM
ejpam-3709	116	12	9n	9n	NUM
ejpam-3709	116	13	mq	mq	NOUN
ejpam-3709	116	14	(	(	PUNCT
ejpam-3709	116	15	u	u	NOUN
ejpam-3709	116	16	3n	3n	NUM
ejpam-3709	116	17	)	)	PUNCT
ejpam-3709	116	18	)	)	PUNCT
ejpam-3709	117	1	+	+	CCONJ
ejpam-3709	117	2	3µ	3µ	NUM
ejpam-3709	117	3	(	(	PUNCT
ejpam-3709	117	4	1	1	NUM
ejpam-3709	117	5	3	3	NUM
ejpam-3709	117	6	·	·	SYM
ejpam-3709	117	7	1	1	NUM
ejpam-3709	117	8	9n	9n	NUM
ejpam-3709	117	9	mq	mq	NOUN
ejpam-3709	117	10	(	(	PUNCT
ejpam-3709	117	11	u	u	NOUN
ejpam-3709	117	12	3n	3n	NUM
ejpam-3709	117	13	)	)	PUNCT
ejpam-3709	117	14	−	−	PROPN
ejpam-3709	117	15	1	1	NUM
ejpam-3709	117	16	3	3	NUM
ejpam-3709	117	17	·	·	SYM
ejpam-3709	117	18	1	1	NUM
ejpam-3709	117	19	9n	9n	NOUN
ejpam-3709	117	20	d′	d′	NUM
ejpam-3709	117	21	(	(	PUNCT
ejpam-3709	117	22	u	u	NOUN
ejpam-3709	117	23	3n	3n	NUM
ejpam-3709	117	24	)	)	PUNCT
ejpam-3709	117	25	)	)	PUNCT
ejpam-3709	117	26	≤	≤	NOUN
ejpam-3709	117	27	3`−(2n+1)µ	3`−(2n+1)µ	NUM
ejpam-3709	117	28	(	(	PUNCT
ejpam-3709	117	29	d	d	X
ejpam-3709	117	30	(	(	PUNCT
ejpam-3709	117	31	u	u	NOUN
ejpam-3709	117	32	3n	3n	NOUN
ejpam-3709	117	33	)	)	PUNCT
ejpam-3709	117	34	−mq	−mq	PROPN
ejpam-3709	117	35	(	(	PUNCT
ejpam-3709	117	36	u	u	NOUN
ejpam-3709	117	37	3n	3n	NUM
ejpam-3709	117	38	)	)	PUNCT
ejpam-3709	117	39	)	)	PUNCT
ejpam-3709	118	1	+	+	CCONJ
ejpam-3709	118	2	3`−(2n+1)µ	3`−(2n+1)µ	NUM
ejpam-3709	118	3	(	(	PUNCT
ejpam-3709	118	4	mq	mq	PROPN
ejpam-3709	118	5	(	(	PUNCT
ejpam-3709	118	6	u	u	NOUN
ejpam-3709	118	7	3n	3n	NUM
ejpam-3709	118	8	)	)	PUNCT
ejpam-3709	118	9	−d′	−d′	PROPN
ejpam-3709	118	10	(	(	PUNCT
ejpam-3709	118	11	u	u	NOUN
ejpam-3709	118	12	3n	3n	NUM
ejpam-3709	118	13	)	)	PUNCT
ejpam-3709	118	14	)	)	PUNCT
ejpam-3709	118	15	≤	≤	NOUN
ejpam-3709	118	16	3`−3n	3`−3n	VERB
ejpam-3709	118	17	∞∑	∞∑	ADJ
ejpam-3709	118	18	i=1	i=1	X
ejpam-3709	118	19	(	(	PUNCT
ejpam-3709	118	20	3`3)iφ	3`3)iφ	NUM
ejpam-3709	118	21	(	(	PUNCT
ejpam-3709	118	22	u	u	NOUN
ejpam-3709	118	23	3(n+i	3(n+i	NUM
ejpam-3709	118	24	)	)	PUNCT
ejpam-3709	118	25	,	,	PUNCT
ejpam-3709	118	26	u	u	PROPN
ejpam-3709	118	27	3(n+i	3(n+i	NUM
ejpam-3709	118	28	)	)	PUNCT
ejpam-3709	118	29	)	)	PUNCT
ejpam-3709	118	30	≤	≤	NOUN
ejpam-3709	118	31	31−n	31−n	NUM
ejpam-3709	118	32	`	`	PUNCT
ejpam-3709	118	33	n	n	PRON
ejpam-3709	118	34	∞∑	∞∑	PROPN
ejpam-3709	118	35	i=0	i=0	PROPN
ejpam-3709	118	36	(	(	PUNCT
ejpam-3709	118	37	3`3)iφ	3`3)iφ	NUM
ejpam-3709	118	38	(	(	PUNCT
ejpam-3709	118	39	u	u	NOUN
ejpam-3709	118	40	3i	3i	NOUN
ejpam-3709	118	41	,	,	PUNCT
ejpam-3709	118	42	u	u	NOUN
ejpam-3709	118	43	3i	3i	NOUN
ejpam-3709	118	44	)	)	PUNCT
ejpam-3709	118	45	for	for	ADP
ejpam-3709	118	46	all	all	PRON
ejpam-3709	118	47	u	u	NOUN
ejpam-3709	118	48	∈	∈	PROPN
ejpam-3709	118	49	p	p	NOUN
ejpam-3709	118	50	.	.	PUNCT
ejpam-3709	119	1	it	it	PRON
ejpam-3709	119	2	indicates	indicate	VERB
ejpam-3709	119	3	from	from	ADP
ejpam-3709	119	4	the	the	DET
ejpam-3709	119	5	above	above	ADJ
ejpam-3709	119	6	inequality	inequality	NOUN
ejpam-3709	119	7	that	that	SCONJ
ejpam-3709	119	8	d	d	NOUN
ejpam-3709	119	9	is	be	AUX
ejpam-3709	119	10	distinctive	distinctive	ADJ
ejpam-3709	119	11	by	by	ADP
ejpam-3709	119	12	allowing	allow	VERB
ejpam-3709	119	13	n→∞.	n→∞.	NOUN
ejpam-3709	119	14	hence	hence	ADV
ejpam-3709	119	15	the	the	DET
ejpam-3709	119	16	proof	proof	NOUN
ejpam-3709	119	17	is	be	AUX
ejpam-3709	119	18	complete	complete	ADJ
ejpam-3709	119	19	.	.	PUNCT
ejpam-3709	120	1	4	4	X
ejpam-3709	120	2	.	.	X
ejpam-3709	120	3	modular	modular	ADJ
ejpam-3709	120	4	stability	stability	NOUN
ejpam-3709	120	5	of	of	ADP
ejpam-3709	120	6	equation	equation	NOUN
ejpam-3709	120	7	(	(	PUNCT
ejpam-3709	120	8	1	1	NUM
ejpam-3709	120	9	)	)	PUNCT
ejpam-3709	120	10	without	without	ADP
ejpam-3709	120	11	∆	∆	PROPN
ejpam-3709	120	12	1	1	NUM
ejpam-3709	120	13	3	3	NUM
ejpam-3709	120	14	-condition	-condition	NOUN
ejpam-3709	120	15	in	in	ADP
ejpam-3709	120	16	this	this	DET
ejpam-3709	120	17	present	present	ADJ
ejpam-3709	120	18	section	section	NOUN
ejpam-3709	120	19	,	,	PUNCT
ejpam-3709	120	20	we	we	PRON
ejpam-3709	120	21	provide	provide	VERB
ejpam-3709	120	22	a	a	DET
ejpam-3709	120	23	different	different	ADJ
ejpam-3709	120	24	result	result	NOUN
ejpam-3709	120	25	related	relate	VERB
ejpam-3709	120	26	to	to	ADP
ejpam-3709	120	27	modular	modular	ADJ
ejpam-3709	120	28	stability	stability	NOUN
ejpam-3709	120	29	of	of	ADP
ejpam-3709	120	30	equation	equation	NOUN
ejpam-3709	120	31	(	(	PUNCT
ejpam-3709	120	32	1	1	NUM
ejpam-3709	120	33	)	)	PUNCT
ejpam-3709	120	34	without	without	ADP
ejpam-3709	120	35	∆	∆	PROPN
ejpam-3709	120	36	1	1	NUM
ejpam-3709	120	37	3	3	NUM
ejpam-3709	120	38	-condition	-condition	NOUN
ejpam-3709	120	39	.	.	PUNCT
ejpam-3709	121	1	b.	b.	PROPN
ejpam-3709	122	1	v.	v.	PROPN
ejpam-3709	122	2	senthil	senthil	PROPN
ejpam-3709	122	3	kumar	kumar	PROPN
ejpam-3709	122	4	,	,	PUNCT
ejpam-3709	122	5	hemen	hemen	PROPN
ejpam-3709	122	6	dutta	dutta	PROPN
ejpam-3709	122	7	,	,	PUNCT
ejpam-3709	122	8	s.	s.	PROPN
ejpam-3709	122	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	122	10	/	/	SYM
ejpam-3709	122	11	eur	eur	PROPN
ejpam-3709	122	12	.	.	PUNCT
ejpam-3709	123	1	j.	j.	PROPN
ejpam-3709	123	2	pure	pure	PROPN
ejpam-3709	123	3	appl	appl	PROPN
ejpam-3709	123	4	.	.	PROPN
ejpam-3709	123	5	math	math	PROPN
ejpam-3709	123	6	,	,	PUNCT
ejpam-3709	123	7	13	13	NUM
ejpam-3709	123	8	(	(	PUNCT
ejpam-3709	123	9	5	5	NUM
ejpam-3709	123	10	)	)	PUNCT
ejpam-3709	123	11	(	(	PUNCT
ejpam-3709	123	12	2020	2020	NUM
ejpam-3709	123	13	)	)	PUNCT
ejpam-3709	123	14	,	,	PUNCT
ejpam-3709	123	15	1162	1162	NUM
ejpam-3709	123	16	-	-	SYM
ejpam-3709	123	17	1175	1175	NUM
ejpam-3709	123	18	1167	1167	NUM
ejpam-3709	123	19	theorem	theorem	NOUN
ejpam-3709	123	20	3	3	X
ejpam-3709	123	21	.	.	PUNCT
ejpam-3709	123	22	assume	assume	VERB
ejpam-3709	123	23	that	that	SCONJ
ejpam-3709	123	24	up	up	ADP
ejpam-3709	123	25	is	be	AUX
ejpam-3709	123	26	a	a	DET
ejpam-3709	123	27	p	p	ADJ
ejpam-3709	123	28	-	-	PUNCT
ejpam-3709	123	29	complex	complex	ADJ
ejpam-3709	123	30	modular	modular	ADJ
ejpam-3709	123	31	space	space	NOUN
ejpam-3709	123	32	where	where	SCONJ
ejpam-3709	123	33	p	p	NOUN
ejpam-3709	123	34	is	be	AUX
ejpam-3709	123	35	convex	convex	NOUN
ejpam-3709	123	36	.	.	PUNCT
ejpam-3709	124	1	also	also	ADV
ejpam-3709	124	2	,	,	PUNCT
ejpam-3709	124	3	let	let	VERB
ejpam-3709	124	4	φ	φ	NOUN
ejpam-3709	124	5	:	:	PUNCT
ejpam-3709	124	6	u	u	PRON
ejpam-3709	124	7	×	×	NOUN
ejpam-3709	124	8	u	u	NOUN
ejpam-3709	124	9	−→	−→	NOUN
ejpam-3709	124	10	[	[	X
ejpam-3709	124	11	0,∞	0,∞	NOUN
ejpam-3709	124	12	)	)	PUNCT
ejpam-3709	124	13	be	be	VERB
ejpam-3709	124	14	a	a	DET
ejpam-3709	124	15	function	function	NOUN
ejpam-3709	124	16	with	with	ADP
ejpam-3709	124	17	the	the	DET
ejpam-3709	124	18	condition	condition	NOUN
ejpam-3709	124	19	φ̂(u	φ̂(u	NUM
ejpam-3709	124	20	,	,	PUNCT
ejpam-3709	124	21	v	v	NOUN
ejpam-3709	124	22	)	)	PUNCT
ejpam-3709	124	23	=	=	PUNCT
ejpam-3709	125	1	∞∑	∞∑	NUM
ejpam-3709	125	2	i=0	i=0	PROPN
ejpam-3709	125	3	1	1	NUM
ejpam-3709	125	4	9i+1	9i+1	NOUN
ejpam-3709	125	5	φ(3−iu	φ(3−iu	PROPN
ejpam-3709	125	6	,	,	PUNCT
ejpam-3709	125	7	3−iu	3−iu	NUM
ejpam-3709	125	8	)	)	PUNCT
ejpam-3709	125	9	<	<	X
ejpam-3709	125	10	∞	∞	NUM
ejpam-3709	125	11	(	(	PUNCT
ejpam-3709	125	12	5	5	NUM
ejpam-3709	125	13	)	)	PUNCT
ejpam-3709	125	14	for	for	ADP
ejpam-3709	125	15	all	all	DET
ejpam-3709	125	16	u	u	NOUN
ejpam-3709	125	17	,	,	PUNCT
ejpam-3709	125	18	v	v	NOUN
ejpam-3709	125	19	∈	∈	PROPN
ejpam-3709	125	20	u	u	NOUN
ejpam-3709	125	21	.	.	PUNCT
ejpam-3709	125	22	assume	assume	VERB
ejpam-3709	125	23	that	that	SCONJ
ejpam-3709	125	24	mq	mq	VERB
ejpam-3709	125	25	:	:	PUNCT
ejpam-3709	125	26	u	u	NOUN
ejpam-3709	125	27	−→	−→	NOUN
ejpam-3709	125	28	up	up	ADV
ejpam-3709	125	29	is	be	AUX
ejpam-3709	125	30	a	a	DET
ejpam-3709	125	31	mapping	mapping	NOUN
ejpam-3709	125	32	such	such	ADJ
ejpam-3709	125	33	that	that	SCONJ
ejpam-3709	125	34	p	p	NOUN
ejpam-3709	125	35	(	(	PUNCT
ejpam-3709	125	36	γmq(u	γmq(u	PROPN
ejpam-3709	125	37	,	,	PUNCT
ejpam-3709	125	38	v	v	NOUN
ejpam-3709	125	39	)	)	PUNCT
ejpam-3709	125	40	)	)	PUNCT
ejpam-3709	125	41	≤	≤	NUM
ejpam-3709	125	42	φ(u	φ(u	NOUN
ejpam-3709	125	43	,	,	PUNCT
ejpam-3709	125	44	v	v	NOUN
ejpam-3709	125	45	)	)	PUNCT
ejpam-3709	125	46	(	(	PUNCT
ejpam-3709	125	47	6	6	NUM
ejpam-3709	125	48	)	)	PUNCT
ejpam-3709	125	49	for	for	ADP
ejpam-3709	125	50	all	all	DET
ejpam-3709	125	51	u	u	NOUN
ejpam-3709	125	52	,	,	PUNCT
ejpam-3709	125	53	v	v	NOUN
ejpam-3709	125	54	∈	∈	PROPN
ejpam-3709	125	55	u	u	NOUN
ejpam-3709	125	56	.	.	PUNCT
ejpam-3709	126	1	then	then	ADV
ejpam-3709	126	2	a	a	DET
ejpam-3709	126	3	unique	unique	ADJ
ejpam-3709	126	4	reciprocal	reciprocal	ADJ
ejpam-3709	126	5	second	second	ADJ
ejpam-3709	126	6	power	power	NOUN
ejpam-3709	126	7	function	function	NOUN
ejpam-3709	126	8	t	t	NOUN
ejpam-3709	126	9	:	:	PUNCT
ejpam-3709	126	10	u	u	NOUN
ejpam-3709	126	11	−→	−→	NOUN
ejpam-3709	126	12	up	up	ADP
ejpam-3709	126	13	exists	exist	VERB
ejpam-3709	126	14	and	and	CCONJ
ejpam-3709	126	15	satisfies	satisfie	NOUN
ejpam-3709	126	16	p	p	X
ejpam-3709	126	17	(	(	PUNCT
ejpam-3709	126	18	mq(u)−	mq(u)−	ADJ
ejpam-3709	126	19	t	t	NOUN
ejpam-3709	126	20	(	(	PUNCT
ejpam-3709	126	21	u	u	NOUN
ejpam-3709	126	22	)	)	PUNCT
ejpam-3709	126	23	)	)	PUNCT
ejpam-3709	126	24	≤	≤	NOUN
ejpam-3709	127	1	φ̂(u	φ̂(u	NUM
ejpam-3709	127	2	,	,	PUNCT
ejpam-3709	127	3	v	v	NOUN
ejpam-3709	127	4	)	)	PUNCT
ejpam-3709	127	5	(	(	PUNCT
ejpam-3709	127	6	7	7	X
ejpam-3709	127	7	)	)	PUNCT
ejpam-3709	127	8	for	for	ADP
ejpam-3709	127	9	all	all	DET
ejpam-3709	127	10	u	u	NOUN
ejpam-3709	127	11	,	,	PUNCT
ejpam-3709	127	12	v	v	NOUN
ejpam-3709	127	13	∈	∈	PROPN
ejpam-3709	127	14	u	u	NOUN
ejpam-3709	127	15	.	.	PUNCT
ejpam-3709	128	1	proof	proof	NOUN
ejpam-3709	128	2	.	.	PUNCT
ejpam-3709	129	1	putting	put	VERB
ejpam-3709	129	2	(	(	PUNCT
ejpam-3709	129	3	u	u	NOUN
ejpam-3709	129	4	,	,	PUNCT
ejpam-3709	129	5	v	v	NOUN
ejpam-3709	129	6	)	)	PUNCT
ejpam-3709	129	7	as	as	ADP
ejpam-3709	129	8	(	(	PUNCT
ejpam-3709	129	9	u	u	NOUN
ejpam-3709	129	10	,	,	PUNCT
ejpam-3709	129	11	u	u	NOUN
ejpam-3709	129	12	)	)	PUNCT
ejpam-3709	129	13	in	in	ADP
ejpam-3709	129	14	(	(	PUNCT
ejpam-3709	129	15	6	6	NUM
ejpam-3709	129	16	)	)	PUNCT
ejpam-3709	129	17	and	and	CCONJ
ejpam-3709	129	18	then	then	ADV
ejpam-3709	129	19	dividing	divide	VERB
ejpam-3709	129	20	by	by	ADP
ejpam-3709	129	21	9	9	NUM
ejpam-3709	129	22	on	on	ADP
ejpam-3709	129	23	both	both	DET
ejpam-3709	129	24	sides	side	NOUN
ejpam-3709	129	25	,	,	PUNCT
ejpam-3709	129	26	we	we	PRON
ejpam-3709	129	27	obtain	obtain	VERB
ejpam-3709	129	28	p	p	NOUN
ejpam-3709	129	29	(	(	PUNCT
ejpam-3709	129	30	1	1	NUM
ejpam-3709	129	31	9	9	NUM
ejpam-3709	129	32	mq(3	mq(3	NOUN
ejpam-3709	129	33	−1u)−mq(u	−1u)−mq(u	NOUN
ejpam-3709	129	34	)	)	PUNCT
ejpam-3709	129	35	)	)	PUNCT
ejpam-3709	129	36	≤	≤	NOUN
ejpam-3709	129	37	1	1	NUM
ejpam-3709	129	38	9	9	NUM
ejpam-3709	129	39	mq(u	mq(u	NOUN
ejpam-3709	129	40	,	,	PUNCT
ejpam-3709	129	41	u	u	NOUN
ejpam-3709	129	42	)	)	PUNCT
ejpam-3709	129	43	(	(	PUNCT
ejpam-3709	129	44	8)	8)	NUM
ejpam-3709	129	45	for	for	ADP
ejpam-3709	129	46	all	all	PRON
ejpam-3709	129	47	u	u	PRON
ejpam-3709	129	48	∈	∈	PROPN
ejpam-3709	129	49	u	u	NOUN
ejpam-3709	129	50	.	.	PUNCT
ejpam-3709	130	1	then	then	ADV
ejpam-3709	130	2	by	by	ADP
ejpam-3709	130	3	induction	induction	NOUN
ejpam-3709	130	4	arguments	argument	NOUN
ejpam-3709	130	5	,	,	PUNCT
ejpam-3709	130	6	we	we	PRON
ejpam-3709	130	7	arrive	arrive	VERB
ejpam-3709	130	8	at	at	ADP
ejpam-3709	130	9	p	p	PROPN
ejpam-3709	130	10	(	(	PUNCT
ejpam-3709	130	11	mq(3	mq(3	NOUN
ejpam-3709	130	12	−nu	−nu	NOUN
ejpam-3709	130	13	)	)	PUNCT
ejpam-3709	130	14	9n	9n	NUM
ejpam-3709	130	15	−mq(u	−mq(u	NOUN
ejpam-3709	130	16	)	)	PUNCT
ejpam-3709	130	17	)	)	PUNCT
ejpam-3709	131	1	≤	≤	ADV
ejpam-3709	131	2	1	1	NUM
ejpam-3709	131	3	9	9	NUM
ejpam-3709	131	4	n−1∑	n−1∑	PROPN
ejpam-3709	131	5	i=0	i=0	PROPN
ejpam-3709	131	6	1	1	NUM
ejpam-3709	131	7	9i	9i	NOUN
ejpam-3709	131	8	φ(3−iu	φ(3−iu	PROPN
ejpam-3709	131	9	,	,	PUNCT
ejpam-3709	131	10	3−iu	3−iu	NUM
ejpam-3709	131	11	)	)	PUNCT
ejpam-3709	131	12	(	(	PUNCT
ejpam-3709	131	13	9	9	NUM
ejpam-3709	131	14	)	)	PUNCT
ejpam-3709	131	15	for	for	ADP
ejpam-3709	131	16	all	all	PRON
ejpam-3709	131	17	u	u	PRON
ejpam-3709	131	18	∈	∈	PROPN
ejpam-3709	131	19	u	u	NOUN
ejpam-3709	131	20	.	.	PUNCT
ejpam-3709	132	1	it	it	PRON
ejpam-3709	132	2	is	be	AUX
ejpam-3709	132	3	clear	clear	ADJ
ejpam-3709	132	4	that	that	SCONJ
ejpam-3709	132	5	the	the	DET
ejpam-3709	132	6	case	case	NOUN
ejpam-3709	132	7	n	n	NOUN
ejpam-3709	132	8	=	=	SYM
ejpam-3709	132	9	1	1	NUM
ejpam-3709	132	10	follows	follow	VERB
ejpam-3709	132	11	directly	directly	ADV
ejpam-3709	132	12	from	from	ADP
ejpam-3709	132	13	(	(	PUNCT
ejpam-3709	132	14	8)	8)	NUM
ejpam-3709	132	15	.	.	PUNCT
ejpam-3709	133	1	assume	assume	VERB
ejpam-3709	133	2	that	that	SCONJ
ejpam-3709	133	3	(	(	PUNCT
ejpam-3709	133	4	9	9	X
ejpam-3709	133	5	)	)	PUNCT
ejpam-3709	133	6	is	be	AUX
ejpam-3709	133	7	true	true	ADJ
ejpam-3709	133	8	for	for	ADP
ejpam-3709	133	9	n	n	PROPN
ejpam-3709	133	10	∈	∈	PROPN
ejpam-3709	133	11	n.	n.	NOUN
ejpam-3709	133	12	then	then	ADV
ejpam-3709	133	13	,	,	PUNCT
ejpam-3709	133	14	we	we	PRON
ejpam-3709	133	15	obtain	obtain	VERB
ejpam-3709	133	16	the	the	DET
ejpam-3709	133	17	ensuing	ensue	VERB
ejpam-3709	133	18	inequality	inequality	NOUN
ejpam-3709	133	19	:	:	PUNCT
ejpam-3709	133	20	p	p	X
ejpam-3709	133	21	(	(	PUNCT
ejpam-3709	133	22	mq(3	mq(3	NOUN
ejpam-3709	133	23	−(n+1)u	−(n+1)u	X
ejpam-3709	133	24	)	)	PUNCT
ejpam-3709	133	25	9n+1	9n+1	NOUN
ejpam-3709	133	26	−mq(u	−mq(u	NOUN
ejpam-3709	133	27	)	)	PUNCT
ejpam-3709	133	28	)	)	PUNCT
ejpam-3709	134	1	=	=	PUNCT
ejpam-3709	134	2	p	p	X
ejpam-3709	134	3	(	(	PUNCT
ejpam-3709	134	4	1	1	NUM
ejpam-3709	134	5	9	9	NUM
ejpam-3709	134	6	(	(	PUNCT
ejpam-3709	134	7	mq(3	mq(3	NOUN
ejpam-3709	134	8	−nu	−nu	NOUN
ejpam-3709	134	9	)	)	PUNCT
ejpam-3709	134	10	9n	9n	PROPN
ejpam-3709	134	11	−mq(3	−mq(3	PROPN
ejpam-3709	134	12	−1u	−1u	PROPN
ejpam-3709	134	13	)	)	PUNCT
ejpam-3709	134	14	)	)	PUNCT
ejpam-3709	135	1	+	+	CCONJ
ejpam-3709	135	2	1	1	NUM
ejpam-3709	135	3	9	9	NUM
ejpam-3709	135	4	(	(	PUNCT
ejpam-3709	135	5	mq(3	mq(3	NOUN
ejpam-3709	135	6	−1u)−	−1u)−	PRON
ejpam-3709	135	7	9mq(u	9mq(u	NUM
ejpam-3709	135	8	)	)	PUNCT
ejpam-3709	135	9	)	)	PUNCT
ejpam-3709	135	10	)	)	PUNCT
ejpam-3709	135	11	≤	≤	ADV
ejpam-3709	135	12	1	1	NUM
ejpam-3709	135	13	9	9	NUM
ejpam-3709	135	14	p	p	NOUN
ejpam-3709	135	15	(	(	PUNCT
ejpam-3709	135	16	mq(3	mq(3	NOUN
ejpam-3709	135	17	−nu)−mq(3	−nu)−mq(3	PROPN
ejpam-3709	135	18	−1u	−1u	PROPN
ejpam-3709	135	19	)	)	PUNCT
ejpam-3709	135	20	)	)	PUNCT
ejpam-3709	136	1	+	+	CCONJ
ejpam-3709	136	2	1	1	NUM
ejpam-3709	136	3	9	9	NUM
ejpam-3709	136	4	p	p	NOUN
ejpam-3709	136	5	(	(	PUNCT
ejpam-3709	136	6	mq(3	mq(3	NOUN
ejpam-3709	136	7	−1u)−	−1u)−	PRON
ejpam-3709	136	8	9mq(u	9mq(u	NUM
ejpam-3709	136	9	)	)	PUNCT
ejpam-3709	136	10	)	)	PUNCT
ejpam-3709	137	1	≤	≤	NOUN
ejpam-3709	137	2	1	1	NUM
ejpam-3709	137	3	9	9	NUM
ejpam-3709	137	4	.	.	PUNCT
ejpam-3709	137	5	1	1	NUM
ejpam-3709	137	6	9	9	NUM
ejpam-3709	137	7	n−1∑	n−1∑	PROPN
ejpam-3709	137	8	i=0	i=0	PROPN
ejpam-3709	137	9	φ(3−(i+1)u	φ(3−(i+1)u	PROPN
ejpam-3709	137	10	,	,	PUNCT
ejpam-3709	137	11	3−(i+1)u	3−(i+1)u	NUM
ejpam-3709	137	12	)	)	PUNCT
ejpam-3709	137	13	9i	9i	NOUN
ejpam-3709	138	1	+	+	CCONJ
ejpam-3709	138	2	1	1	NUM
ejpam-3709	138	3	9	9	NUM
ejpam-3709	138	4	φ(u	φ(u	NOUN
ejpam-3709	138	5	,	,	PUNCT
ejpam-3709	138	6	u	u	NOUN
ejpam-3709	138	7	)	)	PUNCT
ejpam-3709	138	8	≤	≤	NUM
ejpam-3709	138	9	1	1	NUM
ejpam-3709	138	10	9	9	NUM
ejpam-3709	138	11	(	(	PUNCT
ejpam-3709	138	12	n−1∑	n−1∑	NUM
ejpam-3709	138	13	i=0	i=0	PROPN
ejpam-3709	138	14	φ(3−(i+1)u	φ(3−(i+1)u	PROPN
ejpam-3709	138	15	,	,	PUNCT
ejpam-3709	138	16	3−(i+1)u	3−(i+1)u	NUM
ejpam-3709	138	17	)	)	PUNCT
ejpam-3709	138	18	9i+1	9i+1	NOUN
ejpam-3709	138	19	)	)	PUNCT
ejpam-3709	139	1	+	+	CCONJ
ejpam-3709	139	2	1	1	NUM
ejpam-3709	139	3	9	9	NUM
ejpam-3709	139	4	φ(u	φ(u	NOUN
ejpam-3709	139	5	,	,	PUNCT
ejpam-3709	139	6	u	u	NOUN
ejpam-3709	139	7	)	)	PUNCT
ejpam-3709	139	8	=	=	SYM
ejpam-3709	139	9	1	1	NUM
ejpam-3709	139	10	9	9	NUM
ejpam-3709	139	11	n∑	n∑	PROPN
ejpam-3709	139	12	i=0	i=0	PROPN
ejpam-3709	139	13	φ	φ	X
ejpam-3709	139	14	(	(	PUNCT
ejpam-3709	139	15	3−iu	3−iu	PROPN
ejpam-3709	139	16	,	,	PUNCT
ejpam-3709	139	17	3−iu	3−iu	NUM
ejpam-3709	139	18	)	)	PUNCT
ejpam-3709	139	19	9n	9n	PROPN
ejpam-3709	139	20	b.	b.	PROPN
ejpam-3709	140	1	v.	v.	PROPN
ejpam-3709	140	2	senthil	senthil	PROPN
ejpam-3709	140	3	kumar	kumar	PROPN
ejpam-3709	140	4	,	,	PUNCT
ejpam-3709	140	5	hemen	hemen	PROPN
ejpam-3709	140	6	dutta	dutta	PROPN
ejpam-3709	140	7	,	,	PUNCT
ejpam-3709	140	8	s.	s.	PROPN
ejpam-3709	140	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	140	10	/	/	SYM
ejpam-3709	140	11	eur	eur	PROPN
ejpam-3709	140	12	.	.	PUNCT
ejpam-3709	141	1	j.	j.	PROPN
ejpam-3709	141	2	pure	pure	PROPN
ejpam-3709	141	3	appl	appl	PROPN
ejpam-3709	141	4	.	.	PROPN
ejpam-3709	141	5	math	math	PROPN
ejpam-3709	141	6	,	,	PUNCT
ejpam-3709	141	7	13	13	NUM
ejpam-3709	141	8	(	(	PUNCT
ejpam-3709	141	9	5	5	NUM
ejpam-3709	141	10	)	)	PUNCT
ejpam-3709	141	11	(	(	PUNCT
ejpam-3709	141	12	2020	2020	NUM
ejpam-3709	141	13	)	)	PUNCT
ejpam-3709	141	14	,	,	PUNCT
ejpam-3709	141	15	1162	1162	NUM
ejpam-3709	141	16	-	-	SYM
ejpam-3709	141	17	1175	1175	NUM
ejpam-3709	141	18	1168	1168	NUM
ejpam-3709	141	19	for	for	ADP
ejpam-3709	141	20	all	all	DET
ejpam-3709	141	21	u	u	PRON
ejpam-3709	141	22	∈	∈	PROPN
ejpam-3709	141	23	u	u	NOUN
ejpam-3709	141	24	.	.	PUNCT
ejpam-3709	142	1	hence	hence	ADV
ejpam-3709	142	2	(	(	PUNCT
ejpam-3709	142	3	9	9	X
ejpam-3709	142	4	)	)	PUNCT
ejpam-3709	142	5	holds	hold	VERB
ejpam-3709	142	6	for	for	SCONJ
ejpam-3709	142	7	every	every	DET
ejpam-3709	142	8	k	k	PROPN
ejpam-3709	142	9	∈	∈	PROPN
ejpam-3709	142	10	n.	n.	NOUN
ejpam-3709	142	11	let	let	VERB
ejpam-3709	142	12	m	m	PRON
ejpam-3709	142	13	and	and	CCONJ
ejpam-3709	142	14	n	n	ADV
ejpam-3709	142	15	be	be	AUX
ejpam-3709	142	16	non	non	ADJ
ejpam-3709	142	17	-	-	ADJ
ejpam-3709	142	18	negative	negative	ADJ
ejpam-3709	142	19	integers	integer	NOUN
ejpam-3709	142	20	with	with	ADP
ejpam-3709	142	21	n	n	NOUN
ejpam-3709	142	22	>	>	X
ejpam-3709	142	23	m.	m.	NOUN
ejpam-3709	142	24	then	then	ADV
ejpam-3709	142	25	(	(	PUNCT
ejpam-3709	142	26	9	9	NUM
ejpam-3709	142	27	)	)	PUNCT
ejpam-3709	142	28	,	,	PUNCT
ejpam-3709	142	29	we	we	PRON
ejpam-3709	142	30	have	have	VERB
ejpam-3709	142	31	p	p	NOUN
ejpam-3709	142	32	(	(	PUNCT
ejpam-3709	142	33	mq(3	mq(3	NOUN
ejpam-3709	142	34	−nu	−nu	NOUN
ejpam-3709	142	35	)	)	PUNCT
ejpam-3709	142	36	9n	9n	NOUN
ejpam-3709	142	37	−	−	PROPN
ejpam-3709	142	38	mq(3	mq(3	SYM
ejpam-3709	142	39	−mu	−mu	PROPN
ejpam-3709	142	40	)	)	PUNCT
ejpam-3709	142	41	9	9	NUM
ejpam-3709	142	42	m	m	NOUN
ejpam-3709	142	43	)	)	PUNCT
ejpam-3709	143	1	=	=	SYM
ejpam-3709	143	2	p	p	X
ejpam-3709	143	3	(	(	PUNCT
ejpam-3709	143	4	1	1	NUM
ejpam-3709	143	5	9	9	NUM
ejpam-3709	143	6	m	m	NOUN
ejpam-3709	143	7	(	(	PUNCT
ejpam-3709	143	8	mq(3	mq(3	NOUN
ejpam-3709	143	9	−nu	−nu	NOUN
ejpam-3709	143	10	)	)	PUNCT
ejpam-3709	144	1	9n−m	9n−m	PRON
ejpam-3709	144	2	−mq(3	−mq(3	PROPN
ejpam-3709	144	3	−mu	−mu	PROPN
ejpam-3709	144	4	)	)	PUNCT
ejpam-3709	144	5	)	)	PUNCT
ejpam-3709	144	6	)	)	PUNCT
ejpam-3709	145	1	≤	≤	ADV
ejpam-3709	145	2	1	1	NUM
ejpam-3709	145	3	9	9	NUM
ejpam-3709	145	4	m	m	NOUN
ejpam-3709	145	5	·	·	PUNCT
ejpam-3709	145	6	1	1	NUM
ejpam-3709	145	7	9	9	NUM
ejpam-3709	145	8	n−m−1∑	n−m−1∑	PROPN
ejpam-3709	145	9	i=0	i=0	PROPN
ejpam-3709	145	10	1	1	NUM
ejpam-3709	145	11	9i	9i	NOUN
ejpam-3709	145	12	φ	φ	X
ejpam-3709	145	13	(	(	PUNCT
ejpam-3709	145	14	3−(m+i)u	3−(m+i)u	NUM
ejpam-3709	145	15	,	,	PUNCT
ejpam-3709	145	16	3−(m+i)u	3−(m+i)u	NUM
ejpam-3709	145	17	)	)	PUNCT
ejpam-3709	145	18	≤	≤	NOUN
ejpam-3709	145	19	1	1	NUM
ejpam-3709	145	20	9	9	NUM
ejpam-3709	145	21	n−m−1∑	n−m−1∑	PROPN
ejpam-3709	145	22	i=0	i=0	PROPN
ejpam-3709	145	23	1	1	NUM
ejpam-3709	145	24	9m+i	9m+i	NUM
ejpam-3709	145	25	φ	φ	PROPN
ejpam-3709	145	26	(	(	PUNCT
ejpam-3709	145	27	3−(m+i)u	3−(m+i)u	NUM
ejpam-3709	145	28	,	,	PUNCT
ejpam-3709	145	29	3−(m+i)u	3−(m+i)u	NUM
ejpam-3709	145	30	)	)	PUNCT
ejpam-3709	145	31	≤	≤	NOUN
ejpam-3709	145	32	1	1	NUM
ejpam-3709	145	33	9	9	NUM
ejpam-3709	145	34	n−1∑	n−1∑	NUM
ejpam-3709	145	35	k	k	NOUN
ejpam-3709	145	36	=	=	NOUN
ejpam-3709	145	37	m	m	VERB
ejpam-3709	145	38	1	1	NUM
ejpam-3709	145	39	9k	9k	NUM
ejpam-3709	145	40	φ	φ	X
ejpam-3709	145	41	(	(	PUNCT
ejpam-3709	145	42	3−ku	3−ku	PROPN
ejpam-3709	145	43	,	,	PUNCT
ejpam-3709	145	44	3−ku	3−ku	NUM
ejpam-3709	145	45	)	)	PUNCT
ejpam-3709	145	46	(	(	PUNCT
ejpam-3709	145	47	10	10	NUM
ejpam-3709	145	48	)	)	PUNCT
ejpam-3709	145	49	for	for	ADP
ejpam-3709	145	50	all	all	PRON
ejpam-3709	145	51	u	u	PRON
ejpam-3709	145	52	∈	∈	PROPN
ejpam-3709	145	53	u	u	NOUN
ejpam-3709	145	54	.	.	PUNCT
ejpam-3709	146	1	by	by	ADP
ejpam-3709	146	2	the	the	DET
ejpam-3709	146	3	application	application	NOUN
ejpam-3709	146	4	of	of	ADP
ejpam-3709	146	5	(	(	PUNCT
ejpam-3709	146	6	5	5	NUM
ejpam-3709	146	7	)	)	PUNCT
ejpam-3709	146	8	and	and	CCONJ
ejpam-3709	146	9	(	(	PUNCT
ejpam-3709	146	10	10	10	NUM
ejpam-3709	146	11	)	)	PUNCT
ejpam-3709	146	12	,	,	PUNCT
ejpam-3709	146	13	we	we	PRON
ejpam-3709	146	14	observe	observe	VERB
ejpam-3709	146	15	that	that	SCONJ
ejpam-3709	146	16	the	the	DET
ejpam-3709	146	17	the	the	DET
ejpam-3709	146	18	sequence	sequence	NOUN
ejpam-3709	146	19	{	{	PUNCT
ejpam-3709	146	20	mq(3	mq(3	NOUN
ejpam-3709	146	21	−nu	−nu	NUM
ejpam-3709	146	22	)	)	PUNCT
ejpam-3709	146	23	9n	9n	NOUN
ejpam-3709	146	24	}	}	PUNCT
ejpam-3709	146	25	turns	turn	VERB
ejpam-3709	146	26	out	out	ADP
ejpam-3709	146	27	to	to	PART
ejpam-3709	146	28	be	be	AUX
ejpam-3709	146	29	cauchy	cauchy	ADJ
ejpam-3709	146	30	in	in	ADP
ejpam-3709	146	31	up	up	ADV
ejpam-3709	146	32	.	.	PUNCT
ejpam-3709	147	1	by	by	ADP
ejpam-3709	147	2	virtue	virtue	NOUN
ejpam-3709	147	3	of	of	ADP
ejpam-3709	147	4	completeness	completeness	NOUN
ejpam-3709	147	5	of	of	ADP
ejpam-3709	147	6	up	up	ADP
ejpam-3709	147	7	,	,	PUNCT
ejpam-3709	147	8	the	the	DET
ejpam-3709	147	9	sequence	sequence	NOUN
ejpam-3709	147	10	is	be	AUX
ejpam-3709	147	11	convergent	convergent	ADJ
ejpam-3709	147	12	.	.	PUNCT
ejpam-3709	148	1	this	this	PRON
ejpam-3709	148	2	formulates	formulate	VERB
ejpam-3709	148	3	that	that	SCONJ
ejpam-3709	148	4	there	there	PRON
ejpam-3709	148	5	exists	exist	VERB
ejpam-3709	148	6	a	a	DET
ejpam-3709	148	7	function	function	NOUN
ejpam-3709	148	8	t	t	NOUN
ejpam-3709	148	9	:	:	PUNCT
ejpam-3709	148	10	u	u	NOUN
ejpam-3709	148	11	−→	−→	NOUN
ejpam-3709	148	12	up	up	ADP
ejpam-3709	148	13	defined	define	VERB
ejpam-3709	148	14	by	by	ADP
ejpam-3709	148	15	t	t	PROPN
ejpam-3709	148	16	(	(	PUNCT
ejpam-3709	148	17	u	u	NOUN
ejpam-3709	148	18	)	)	PUNCT
ejpam-3709	148	19	=	=	PUNCT
ejpam-3709	148	20	p−	p−	NOUN
ejpam-3709	148	21	lim	lim	NOUN
ejpam-3709	148	22	mq(3	mq(3	PROPN
ejpam-3709	148	23	−nu	−nu	PROPN
ejpam-3709	148	24	)	)	PUNCT
ejpam-3709	148	25	9n	9n	NOUN
ejpam-3709	148	26	.	.	PUNCT
ejpam-3709	149	1	(	(	PUNCT
ejpam-3709	149	2	11	11	NUM
ejpam-3709	149	3	)	)	PUNCT
ejpam-3709	149	4	to	to	PART
ejpam-3709	149	5	confirm	confirm	VERB
ejpam-3709	149	6	that	that	SCONJ
ejpam-3709	149	7	t	t	PROPN
ejpam-3709	149	8	satisfies	satisfie	NOUN
ejpam-3709	149	9	(	(	PUNCT
ejpam-3709	149	10	1	1	NUM
ejpam-3709	149	11	)	)	PUNCT
ejpam-3709	149	12	,	,	PUNCT
ejpam-3709	149	13	plugging	plug	VERB
ejpam-3709	149	14	(	(	PUNCT
ejpam-3709	149	15	u	u	NOUN
ejpam-3709	149	16	,	,	PUNCT
ejpam-3709	149	17	v	v	NOUN
ejpam-3709	149	18	)	)	PUNCT
ejpam-3709	149	19	into	into	ADP
ejpam-3709	149	20	(	(	PUNCT
ejpam-3709	149	21	3−nu	3−nu	NUM
ejpam-3709	149	22	,	,	PUNCT
ejpam-3709	149	23	3−nv	3−nv	NUM
ejpam-3709	149	24	)	)	PUNCT
ejpam-3709	149	25	in	in	ADP
ejpam-3709	149	26	(	(	PUNCT
ejpam-3709	149	27	6	6	NUM
ejpam-3709	149	28	)	)	PUNCT
ejpam-3709	149	29	and	and	CCONJ
ejpam-3709	149	30	then	then	ADV
ejpam-3709	149	31	multiplying	multiply	VERB
ejpam-3709	149	32	by	by	ADP
ejpam-3709	149	33	9−n	9−n	NUM
ejpam-3709	149	34	on	on	ADP
ejpam-3709	149	35	both	both	DET
ejpam-3709	149	36	sides	side	NOUN
ejpam-3709	149	37	,	,	PUNCT
ejpam-3709	149	38	we	we	PRON
ejpam-3709	149	39	obtain	obtain	VERB
ejpam-3709	149	40	9−np	9−np	NUM
ejpam-3709	149	41	(	(	PUNCT
ejpam-3709	149	42	mq	mq	PROPN
ejpam-3709	149	43	(	(	PUNCT
ejpam-3709	149	44	3−n	3−n	NUM
ejpam-3709	149	45	(	(	PUNCT
ejpam-3709	149	46	uv	uv	NOUN
ejpam-3709	149	47	2u+	2u+	NUM
ejpam-3709	149	48	v	v	NOUN
ejpam-3709	149	49	)	)	PUNCT
ejpam-3709	149	50	)	)	PUNCT
ejpam-3709	150	1	+	+	NUM
ejpam-3709	150	2	mq	mq	NOUN
ejpam-3709	150	3	(	(	PUNCT
ejpam-3709	150	4	3−n	3−n	NUM
ejpam-3709	150	5	(	(	PUNCT
ejpam-3709	150	6	uv	uv	NOUN
ejpam-3709	150	7	2u−	2u−	PROPN
ejpam-3709	150	8	v	v	NOUN
ejpam-3709	150	9	)	)	PUNCT
ejpam-3709	150	10	)	)	PUNCT
ejpam-3709	151	1	−	−	PROPN
ejpam-3709	151	2	8mq(3	8mq(3	PROPN
ejpam-3709	151	3	−nu)−	−nu)−	NOUN
ejpam-3709	151	4	2mq(3	2mq(3	NUM
ejpam-3709	151	5	−nv	−nv	NOUN
ejpam-3709	151	6	)	)	PUNCT
ejpam-3709	151	7	)	)	PUNCT
ejpam-3709	152	1	≤	≤	NOUN
ejpam-3709	152	2	9−nφ(3−nu	9−nφ(3−nu	NOUN
ejpam-3709	152	3	,	,	PUNCT
ejpam-3709	152	4	3−nu	3−nu	NUM
ejpam-3709	152	5	)	)	PUNCT
ejpam-3709	152	6	(	(	PUNCT
ejpam-3709	152	7	12	12	NUM
ejpam-3709	152	8	)	)	PUNCT
ejpam-3709	152	9	for	for	ADP
ejpam-3709	152	10	all	all	DET
ejpam-3709	152	11	u	u	NOUN
ejpam-3709	152	12	,	,	PUNCT
ejpam-3709	152	13	v	v	NOUN
ejpam-3709	152	14	∈	∈	PROPN
ejpam-3709	152	15	u	u	NOUN
ejpam-3709	152	16	.	.	PUNCT
ejpam-3709	153	1	we	we	PRON
ejpam-3709	153	2	can	can	AUX
ejpam-3709	153	3	find	find	VERB
ejpam-3709	153	4	that	that	SCONJ
ejpam-3709	153	5	t	t	PROPN
ejpam-3709	153	6	satisfies	satisfie	NOUN
ejpam-3709	153	7	(	(	PUNCT
ejpam-3709	153	8	1	1	NUM
ejpam-3709	153	9	)	)	PUNCT
ejpam-3709	153	10	by	by	ADP
ejpam-3709	153	11	letting	let	VERB
ejpam-3709	153	12	n→∞	n→∞	PRON
ejpam-3709	153	13	in	in	ADP
ejpam-3709	153	14	the	the	DET
ejpam-3709	153	15	above	above	ADJ
ejpam-3709	153	16	inequality	inequality	NOUN
ejpam-3709	153	17	.	.	PUNCT
ejpam-3709	154	1	to	to	PART
ejpam-3709	154	2	prove	prove	VERB
ejpam-3709	154	3	that	that	SCONJ
ejpam-3709	154	4	t	t	PROPN
ejpam-3709	154	5	is	be	AUX
ejpam-3709	154	6	unique	unique	ADJ
ejpam-3709	154	7	reciprocal	reciprocal	ADJ
ejpam-3709	154	8	second	second	ADJ
ejpam-3709	154	9	power	power	NOUN
ejpam-3709	154	10	function	function	NOUN
ejpam-3709	154	11	which	which	PRON
ejpam-3709	154	12	satisfies	satisfy	VERB
ejpam-3709	154	13	(	(	PUNCT
ejpam-3709	154	14	1	1	NUM
ejpam-3709	154	15	)	)	PUNCT
ejpam-3709	154	16	and	and	CCONJ
ejpam-3709	154	17	also	also	ADV
ejpam-3709	154	18	(	(	PUNCT
ejpam-3709	154	19	7	7	NUM
ejpam-3709	154	20	)	)	PUNCT
ejpam-3709	154	21	.	.	PUNCT
ejpam-3709	155	1	it	it	PRON
ejpam-3709	155	2	is	be	AUX
ejpam-3709	155	3	clear	clear	ADJ
ejpam-3709	155	4	that	that	SCONJ
ejpam-3709	155	5	both	both	DET
ejpam-3709	155	6	t	t	NOUN
ejpam-3709	155	7	′	′	NUM
ejpam-3709	156	1	and	and	CCONJ
ejpam-3709	156	2	t	t	PROPN
ejpam-3709	156	3	satisfy	satisfy	NOUN
ejpam-3709	156	4	(	(	PUNCT
ejpam-3709	156	5	7	7	NUM
ejpam-3709	156	6	)	)	PUNCT
ejpam-3709	156	7	.	.	PUNCT
ejpam-3709	157	1	hence	hence	ADV
ejpam-3709	157	2	,	,	PUNCT
ejpam-3709	157	3	we	we	PRON
ejpam-3709	157	4	obtain	obtain	VERB
ejpam-3709	157	5	p	p	NOUN
ejpam-3709	157	6	(	(	PUNCT
ejpam-3709	157	7	t	t	NOUN
ejpam-3709	157	8	′	′	NUM
ejpam-3709	157	9	(	(	PUNCT
ejpam-3709	157	10	u)−	u)−	PROPN
ejpam-3709	157	11	t	t	PROPN
ejpam-3709	157	12	(	(	PUNCT
ejpam-3709	157	13	u	u	NOUN
ejpam-3709	157	14	)	)	PUNCT
ejpam-3709	157	15	)	)	PUNCT
ejpam-3709	158	1	=	=	SYM
ejpam-3709	159	1	9−np	9−np	NUM
ejpam-3709	159	2	(	(	PUNCT
ejpam-3709	159	3	t	t	NOUN
ejpam-3709	159	4	′	′	NUM
ejpam-3709	159	5	(	(	PUNCT
ejpam-3709	159	6	3−nu)−	3−nu)−	NUM
ejpam-3709	159	7	t	t	NOUN
ejpam-3709	159	8	(	(	PUNCT
ejpam-3709	159	9	3−nu	3−nu	NUM
ejpam-3709	159	10	)	)	PUNCT
ejpam-3709	159	11	)	)	PUNCT
ejpam-3709	160	1	≤	≤	NUM
ejpam-3709	160	2	9−n	9−n	NUM
ejpam-3709	161	1	(	(	PUNCT
ejpam-3709	161	2	p	p	X
ejpam-3709	161	3	(	(	PUNCT
ejpam-3709	161	4	t	t	PROPN
ejpam-3709	161	5	′	′	NUM
ejpam-3709	161	6	(	(	PUNCT
ejpam-3709	161	7	3−nu)−	3−nu)−	NUM
ejpam-3709	161	8	f(3−nu	f(3−nu	PROPN
ejpam-3709	161	9	)	)	PUNCT
ejpam-3709	161	10	)	)	PUNCT
ejpam-3709	162	1	+	+	CCONJ
ejpam-3709	162	2	p	p	X
ejpam-3709	162	3	(	(	PUNCT
ejpam-3709	162	4	f(3−nu)−	f(3−nu)−	NOUN
ejpam-3709	162	5	t	t	NOUN
ejpam-3709	162	6	(	(	PUNCT
ejpam-3709	162	7	3−nu	3−nu	NUM
ejpam-3709	162	8	)	)	PUNCT
ejpam-3709	162	9	)	)	PUNCT
ejpam-3709	162	10	)	)	PUNCT
ejpam-3709	162	11	≤	≤	NOUN
ejpam-3709	163	1	∞∑	∞∑	NUM
ejpam-3709	163	2	i	i	PROPN
ejpam-3709	163	3	=	=	SYM
ejpam-3709	163	4	n+1	n+1	PROPN
ejpam-3709	163	5	1	1	NUM
ejpam-3709	163	6	9i	9i	NOUN
ejpam-3709	163	7	φ(3−iu	φ(3−iu	PROPN
ejpam-3709	163	8	,	,	PUNCT
ejpam-3709	163	9	3−iu	3−iu	NUM
ejpam-3709	163	10	)	)	PUNCT
ejpam-3709	163	11	(	(	PUNCT
ejpam-3709	163	12	13	13	NUM
ejpam-3709	163	13	)	)	PUNCT
ejpam-3709	163	14	for	for	ADP
ejpam-3709	163	15	all	all	DET
ejpam-3709	163	16	u	u	NOUN
ejpam-3709	163	17	,	,	PUNCT
ejpam-3709	163	18	v	v	NOUN
ejpam-3709	163	19	∈	∈	PROPN
ejpam-3709	163	20	u	u	NOUN
ejpam-3709	163	21	.	.	PUNCT
ejpam-3709	164	1	it	it	PRON
ejpam-3709	164	2	is	be	AUX
ejpam-3709	164	3	easy	easy	ADJ
ejpam-3709	164	4	to	to	PART
ejpam-3709	164	5	find	find	VERB
ejpam-3709	164	6	that	that	SCONJ
ejpam-3709	164	7	t	t	PROPN
ejpam-3709	164	8	is	be	AUX
ejpam-3709	164	9	distinctive	distinctive	ADJ
ejpam-3709	164	10	by	by	ADP
ejpam-3709	164	11	allowing	allow	VERB
ejpam-3709	164	12	n	n	PRON
ejpam-3709	164	13	→	→	SYM
ejpam-3709	164	14	∞	∞	NUM
ejpam-3709	164	15	in	in	ADP
ejpam-3709	164	16	(	(	PUNCT
ejpam-3709	164	17	13	13	NUM
ejpam-3709	164	18	)	)	PUNCT
ejpam-3709	164	19	and	and	CCONJ
ejpam-3709	164	20	employing	employ	VERB
ejpam-3709	164	21	(	(	PUNCT
ejpam-3709	164	22	5	5	NUM
ejpam-3709	164	23	)	)	PUNCT
ejpam-3709	164	24	,	,	PUNCT
ejpam-3709	164	25	which	which	PRON
ejpam-3709	164	26	completes	complete	VERB
ejpam-3709	164	27	the	the	DET
ejpam-3709	164	28	proof	proof	NOUN
ejpam-3709	164	29	.	.	PUNCT
ejpam-3709	165	1	corollary	corollary	ADJ
ejpam-3709	165	2	1	1	NUM
ejpam-3709	165	3	.	.	PUNCT
ejpam-3709	166	1	let	let	VERB
ejpam-3709	166	2	mq	mq	NOUN
ejpam-3709	166	3	:	:	PUNCT
ejpam-3709	166	4	u	u	NOUN
ejpam-3709	166	5	−→	−→	NOUN
ejpam-3709	166	6	up	up	ADP
ejpam-3709	166	7	be	be	AUX
ejpam-3709	166	8	a	a	DET
ejpam-3709	166	9	mapping	mapping	NOUN
ejpam-3709	166	10	with	with	ADP
ejpam-3709	166	11	a	a	DET
ejpam-3709	166	12	constant	constant	ADJ
ejpam-3709	166	13	c	c	NOUN
ejpam-3709	166	14	≥	≥	NOUN
ejpam-3709	166	15	0	0	NUM
ejpam-3709	166	16	,	,	PUNCT
ejpam-3709	166	17	not	not	PART
ejpam-3709	166	18	depending	depend	VERB
ejpam-3709	166	19	on	on	ADP
ejpam-3709	166	20	the	the	DET
ejpam-3709	166	21	values	value	NOUN
ejpam-3709	166	22	of	of	ADP
ejpam-3709	166	23	u	u	NOUN
ejpam-3709	166	24	,	,	PUNCT
ejpam-3709	166	25	v	v	ADP
ejpam-3709	166	26	such	such	ADJ
ejpam-3709	166	27	that	that	SCONJ
ejpam-3709	166	28	the	the	DET
ejpam-3709	166	29	inequality	inequality	NOUN
ejpam-3709	166	30	p	p	NOUN
ejpam-3709	166	31	(	(	PUNCT
ejpam-3709	166	32	γmq(u	γmq(u	PROPN
ejpam-3709	166	33	,	,	PUNCT
ejpam-3709	166	34	v	v	NOUN
ejpam-3709	166	35	)	)	PUNCT
ejpam-3709	166	36	)	)	PUNCT
ejpam-3709	166	37	≤	≤	PROPN
ejpam-3709	167	1	c	c	PROPN
ejpam-3709	167	2	b.	b.	PROPN
ejpam-3709	168	1	v.	v.	PROPN
ejpam-3709	168	2	senthil	senthil	PROPN
ejpam-3709	168	3	kumar	kumar	PROPN
ejpam-3709	168	4	,	,	PUNCT
ejpam-3709	168	5	hemen	hemen	PROPN
ejpam-3709	168	6	dutta	dutta	PROPN
ejpam-3709	168	7	,	,	PUNCT
ejpam-3709	168	8	s.	s.	PROPN
ejpam-3709	168	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	168	10	/	/	SYM
ejpam-3709	168	11	eur	eur	PROPN
ejpam-3709	168	12	.	.	PUNCT
ejpam-3709	169	1	j.	j.	PROPN
ejpam-3709	169	2	pure	pure	PROPN
ejpam-3709	169	3	appl	appl	PROPN
ejpam-3709	169	4	.	.	PROPN
ejpam-3709	169	5	math	math	PROPN
ejpam-3709	169	6	,	,	PUNCT
ejpam-3709	169	7	13	13	NUM
ejpam-3709	169	8	(	(	PUNCT
ejpam-3709	169	9	5	5	NUM
ejpam-3709	169	10	)	)	PUNCT
ejpam-3709	169	11	(	(	PUNCT
ejpam-3709	169	12	2020	2020	NUM
ejpam-3709	169	13	)	)	PUNCT
ejpam-3709	169	14	,	,	PUNCT
ejpam-3709	169	15	1162	1162	NUM
ejpam-3709	169	16	-	-	SYM
ejpam-3709	169	17	1175	1175	NUM
ejpam-3709	169	18	1169	1169	NUM
ejpam-3709	169	19	holds	hold	VERB
ejpam-3709	169	20	for	for	ADP
ejpam-3709	169	21	all	all	DET
ejpam-3709	169	22	u	u	NOUN
ejpam-3709	169	23	,	,	PUNCT
ejpam-3709	169	24	v	v	NOUN
ejpam-3709	169	25	∈	∈	PROPN
ejpam-3709	169	26	u	u	NOUN
ejpam-3709	169	27	.	.	PUNCT
ejpam-3709	170	1	then	then	ADV
ejpam-3709	170	2	,	,	PUNCT
ejpam-3709	170	3	t	t	X
ejpam-3709	170	4	:	:	PUNCT
ejpam-3709	170	5	u	u	NOUN
ejpam-3709	170	6	−→	−→	NOUN
ejpam-3709	170	7	up	up	ADV
ejpam-3709	170	8	is	be	AUX
ejpam-3709	170	9	a	a	DET
ejpam-3709	170	10	unique	unique	ADJ
ejpam-3709	170	11	reciprocal	reciprocal	ADJ
ejpam-3709	170	12	second	second	ADJ
ejpam-3709	170	13	power	power	NOUN
ejpam-3709	170	14	function	function	NOUN
ejpam-3709	170	15	satisfying	satisfying	ADJ
ejpam-3709	170	16	(	(	PUNCT
ejpam-3709	170	17	1	1	NUM
ejpam-3709	170	18	)	)	PUNCT
ejpam-3709	170	19	and	and	CCONJ
ejpam-3709	170	20	p	p	X
ejpam-3709	170	21	(	(	PUNCT
ejpam-3709	170	22	mq(u)−	mq(u)−	ADJ
ejpam-3709	170	23	t	t	NOUN
ejpam-3709	170	24	(	(	PUNCT
ejpam-3709	170	25	u	u	NOUN
ejpam-3709	170	26	)	)	PUNCT
ejpam-3709	170	27	)	)	PUNCT
ejpam-3709	171	1	≤	≤	NUM
ejpam-3709	171	2	c	c	NOUN
ejpam-3709	171	3	8	8	NUM
ejpam-3709	171	4	,	,	PUNCT
ejpam-3709	171	5	for	for	ADP
ejpam-3709	171	6	all	all	PRON
ejpam-3709	171	7	u	u	PRON
ejpam-3709	171	8	∈	∈	PROPN
ejpam-3709	171	9	u	u	NOUN
ejpam-3709	171	10	.	.	PUNCT
ejpam-3709	172	1	proof	proof	NOUN
ejpam-3709	172	2	.	.	PUNCT
ejpam-3709	173	1	it	it	PRON
ejpam-3709	173	2	is	be	AUX
ejpam-3709	173	3	easy	easy	ADJ
ejpam-3709	173	4	to	to	PART
ejpam-3709	173	5	prove	prove	VERB
ejpam-3709	173	6	this	this	DET
ejpam-3709	173	7	corollary	corollary	NOUN
ejpam-3709	173	8	by	by	ADP
ejpam-3709	173	9	taking	take	VERB
ejpam-3709	173	10	φ(u	φ(u	NOUN
ejpam-3709	173	11	,	,	PUNCT
ejpam-3709	173	12	v	v	NOUN
ejpam-3709	173	13	)	)	PUNCT
ejpam-3709	173	14	=	=	SYM
ejpam-3709	174	1	c	c	X
ejpam-3709	174	2	,	,	PUNCT
ejpam-3709	174	3	for	for	ADP
ejpam-3709	174	4	all	all	DET
ejpam-3709	174	5	u	u	NOUN
ejpam-3709	174	6	,	,	PUNCT
ejpam-3709	174	7	v	v	PROPN
ejpam-3709	174	8	∈	∈	PROPN
ejpam-3709	174	9	u	u	NOUN
ejpam-3709	174	10	in	in	ADP
ejpam-3709	174	11	theorem	theorem	NOUN
ejpam-3709	174	12	3	3	NUM
ejpam-3709	174	13	.	.	PUNCT
ejpam-3709	174	14	corollary	corollary	ADJ
ejpam-3709	174	15	2	2	NUM
ejpam-3709	174	16	.	.	PUNCT
ejpam-3709	175	1	let	let	VERB
ejpam-3709	175	2	λ1	λ1	PROPN
ejpam-3709	175	3	≥	≥	NOUN
ejpam-3709	175	4	0	0	NUM
ejpam-3709	175	5	be	be	AUX
ejpam-3709	175	6	fixed	fix	VERB
ejpam-3709	175	7	and	and	CCONJ
ejpam-3709	175	8	s	s	AUX
ejpam-3709	175	9	6=	6=	ADP
ejpam-3709	175	10	−2	−2	NOUN
ejpam-3709	175	11	if	if	SCONJ
ejpam-3709	175	12	a	a	DET
ejpam-3709	175	13	function	function	NOUN
ejpam-3709	175	14	mq	mq	NOUN
ejpam-3709	175	15	:	:	PUNCT
ejpam-3709	175	16	u	u	NOUN
ejpam-3709	175	17	−→	−→	NOUN
ejpam-3709	175	18	up	up	ADP
ejpam-3709	175	19	fulfills	fulfill	VERB
ejpam-3709	175	20	the	the	DET
ejpam-3709	175	21	inequality	inequality	NOUN
ejpam-3709	175	22	p	p	NOUN
ejpam-3709	175	23	(	(	PUNCT
ejpam-3709	175	24	γmq(u	γmq(u	PROPN
ejpam-3709	175	25	,	,	PUNCT
ejpam-3709	175	26	v	v	NOUN
ejpam-3709	175	27	)	)	PUNCT
ejpam-3709	175	28	)	)	PUNCT
ejpam-3709	175	29	≤	≤	NOUN
ejpam-3709	175	30	λ1(|u|s	λ1(|u|s	VERB
ejpam-3709	175	31	+	+	X
ejpam-3709	175	32	|v|s	|v|	NOUN
ejpam-3709	175	33	)	)	PUNCT
ejpam-3709	175	34	holds	hold	VERB
ejpam-3709	175	35	for	for	ADP
ejpam-3709	175	36	all	all	DET
ejpam-3709	175	37	u	u	NOUN
ejpam-3709	175	38	,	,	PUNCT
ejpam-3709	175	39	v	v	NOUN
ejpam-3709	175	40	∈	∈	PROPN
ejpam-3709	175	41	u	u	NOUN
ejpam-3709	175	42	.	.	PUNCT
ejpam-3709	176	1	then	then	ADV
ejpam-3709	176	2	,	,	PUNCT
ejpam-3709	176	3	there	there	PRON
ejpam-3709	176	4	exists	exist	VERB
ejpam-3709	176	5	a	a	DET
ejpam-3709	176	6	unique	unique	ADJ
ejpam-3709	176	7	reciprocal	reciprocal	ADJ
ejpam-3709	176	8	second	second	ADJ
ejpam-3709	176	9	power	power	NOUN
ejpam-3709	176	10	function	function	NOUN
ejpam-3709	176	11	t	t	NOUN
ejpam-3709	176	12	:	:	PUNCT
ejpam-3709	176	13	u	u	NOUN
ejpam-3709	176	14	−→	−→	NOUN
ejpam-3709	176	15	up	up	ADP
ejpam-3709	176	16	satisfying	satisfy	VERB
ejpam-3709	176	17	(	(	PUNCT
ejpam-3709	176	18	1	1	NUM
ejpam-3709	176	19	)	)	PUNCT
ejpam-3709	176	20	and	and	CCONJ
ejpam-3709	176	21	p	p	X
ejpam-3709	176	22	(	(	PUNCT
ejpam-3709	176	23	mq(u)−	mq(u)−	ADJ
ejpam-3709	176	24	t	t	NOUN
ejpam-3709	176	25	(	(	PUNCT
ejpam-3709	176	26	u	u	NOUN
ejpam-3709	176	27	)	)	PUNCT
ejpam-3709	176	28	)	)	PUNCT
ejpam-3709	176	29	≤	≤	NUM
ejpam-3709	176	30	2λ1	2λ1	NUM
ejpam-3709	176	31	(	(	PUNCT
ejpam-3709	176	32	9−	9−	NUM
ejpam-3709	176	33	3−s	3−s	NUM
ejpam-3709	176	34	)	)	PUNCT
ejpam-3709	176	35	|u|s	|u|s	PROPN
ejpam-3709	176	36	for	for	ADP
ejpam-3709	176	37	all	all	PRON
ejpam-3709	176	38	u	u	PRON
ejpam-3709	176	39	∈	∈	PROPN
ejpam-3709	176	40	u	u	NOUN
ejpam-3709	176	41	.	.	PUNCT
ejpam-3709	177	1	proof	proof	NOUN
ejpam-3709	177	2	.	.	PUNCT
ejpam-3709	178	1	the	the	DET
ejpam-3709	178	2	proof	proof	NOUN
ejpam-3709	178	3	is	be	AUX
ejpam-3709	178	4	obtained	obtain	VERB
ejpam-3709	178	5	by	by	ADP
ejpam-3709	178	6	taking	take	VERB
ejpam-3709	178	7	φ(u	φ(u	NOUN
ejpam-3709	178	8	,	,	PUNCT
ejpam-3709	178	9	v	v	NOUN
ejpam-3709	178	10	)	)	PUNCT
ejpam-3709	178	11	=	=	PUNCT
ejpam-3709	178	12	λ1(|u|s	λ1(|u|s	VERB
ejpam-3709	178	13	+	+	X
ejpam-3709	178	14	|v|s	|v|	NOUN
ejpam-3709	178	15	)	)	PUNCT
ejpam-3709	178	16	in	in	ADP
ejpam-3709	178	17	theorem	theorem	ADJ
ejpam-3709	178	18	3	3	NUM
ejpam-3709	178	19	.	.	PUNCT
ejpam-3709	178	20	corollary	corollary	ADJ
ejpam-3709	178	21	3	3	X
ejpam-3709	178	22	.	.	PUNCT
ejpam-3709	179	1	let	let	VERB
ejpam-3709	179	2	mq	mq	NOUN
ejpam-3709	179	3	:	:	PUNCT
ejpam-3709	179	4	u	u	NOUN
ejpam-3709	179	5	−→	−→	NOUN
ejpam-3709	179	6	up	up	ADP
ejpam-3709	179	7	be	be	AUX
ejpam-3709	179	8	a	a	DET
ejpam-3709	179	9	mapping	mapping	NOUN
ejpam-3709	179	10	.	.	PUNCT
ejpam-3709	180	1	if	if	SCONJ
ejpam-3709	180	2	there	there	PRON
ejpam-3709	180	3	exist	exist	VERB
ejpam-3709	180	4	x	x	NOUN
ejpam-3709	180	5	,	,	PUNCT
ejpam-3709	180	6	y	y	PROPN
ejpam-3709	180	7	:	:	PUNCT
ejpam-3709	180	8	s	s	X
ejpam-3709	180	9	=	=	PUNCT
ejpam-3709	180	10	x	x	PROPN
ejpam-3709	181	1	+	+	NUM
ejpam-3709	181	2	y	y	PROPN
ejpam-3709	181	3	6=	6=	ADP
ejpam-3709	181	4	−2	−2	NOUN
ejpam-3709	181	5	and	and	CCONJ
ejpam-3709	181	6	λ2	λ2	NOUN
ejpam-3709	181	7	≥	≥	NOUN
ejpam-3709	181	8	0	0	NUM
ejpam-3709	182	1	such	such	ADJ
ejpam-3709	182	2	that	that	SCONJ
ejpam-3709	182	3	p	p	NOUN
ejpam-3709	182	4	(	(	PUNCT
ejpam-3709	182	5	γmq(u	γmq(u	PROPN
ejpam-3709	182	6	,	,	PUNCT
ejpam-3709	182	7	v	v	NOUN
ejpam-3709	182	8	)	)	PUNCT
ejpam-3709	182	9	)	)	PUNCT
ejpam-3709	182	10	≤	≤	NOUN
ejpam-3709	182	11	λ2(|u|x|v|y	λ2(|u|x|v|y	ADV
ejpam-3709	182	12	)	)	PUNCT
ejpam-3709	182	13	holds	hold	VERB
ejpam-3709	182	14	for	for	ADP
ejpam-3709	182	15	all	all	DET
ejpam-3709	182	16	u	u	NOUN
ejpam-3709	182	17	,	,	PUNCT
ejpam-3709	182	18	v	v	NOUN
ejpam-3709	182	19	∈	∈	PROPN
ejpam-3709	182	20	u	u	NOUN
ejpam-3709	182	21	.	.	PUNCT
ejpam-3709	183	1	then	then	ADV
ejpam-3709	183	2	,	,	PUNCT
ejpam-3709	183	3	there	there	PRON
ejpam-3709	183	4	exists	exist	VERB
ejpam-3709	183	5	a	a	DET
ejpam-3709	183	6	unique	unique	ADJ
ejpam-3709	183	7	reciprocal	reciprocal	ADJ
ejpam-3709	183	8	second	second	ADJ
ejpam-3709	183	9	power	power	NOUN
ejpam-3709	183	10	function	function	NOUN
ejpam-3709	183	11	t	t	NOUN
ejpam-3709	183	12	:	:	PUNCT
ejpam-3709	183	13	u	u	NOUN
ejpam-3709	183	14	−→	−→	NOUN
ejpam-3709	183	15	up	up	ADP
ejpam-3709	183	16	satisfying	satisfy	VERB
ejpam-3709	183	17	(	(	PUNCT
ejpam-3709	183	18	1	1	NUM
ejpam-3709	183	19	)	)	PUNCT
ejpam-3709	183	20	and	and	CCONJ
ejpam-3709	183	21	p	p	X
ejpam-3709	183	22	(	(	PUNCT
ejpam-3709	183	23	mq(u)−	mq(u)−	ADJ
ejpam-3709	183	24	t	t	NOUN
ejpam-3709	183	25	(	(	PUNCT
ejpam-3709	183	26	u	u	NOUN
ejpam-3709	183	27	)	)	PUNCT
ejpam-3709	183	28	)	)	PUNCT
ejpam-3709	183	29	≤	≤	NUM
ejpam-3709	183	30	λ2	λ2	NOUN
ejpam-3709	183	31	(	(	PUNCT
ejpam-3709	183	32	9−	9−	NUM
ejpam-3709	183	33	3−s	3−s	NUM
ejpam-3709	183	34	)	)	PUNCT
ejpam-3709	183	35	|u|s	|u|s	PROPN
ejpam-3709	183	36	for	for	ADP
ejpam-3709	183	37	all	all	PRON
ejpam-3709	183	38	u	u	PRON
ejpam-3709	183	39	∈	∈	PROPN
ejpam-3709	183	40	u	u	NOUN
ejpam-3709	183	41	.	.	PUNCT
ejpam-3709	184	1	proof	proof	NOUN
ejpam-3709	184	2	.	.	PUNCT
ejpam-3709	185	1	the	the	DET
ejpam-3709	185	2	proof	proof	NOUN
ejpam-3709	185	3	directly	directly	ADV
ejpam-3709	185	4	follows	follow	VERB
ejpam-3709	185	5	by	by	ADP
ejpam-3709	185	6	taking	take	VERB
ejpam-3709	185	7	φ(u	φ(u	NOUN
ejpam-3709	185	8	,	,	PUNCT
ejpam-3709	185	9	v	v	NOUN
ejpam-3709	185	10	)	)	PUNCT
ejpam-3709	185	11	=	=	SYM
ejpam-3709	185	12	c2(|u|a|v|b	c2(|u|a|v|b	NOUN
ejpam-3709	185	13	)	)	PUNCT
ejpam-3709	185	14	in	in	ADP
ejpam-3709	185	15	theorem	theorem	ADJ
ejpam-3709	185	16	3	3	NUM
ejpam-3709	185	17	.	.	PUNCT
ejpam-3709	185	18	corollary	corollary	ADJ
ejpam-3709	185	19	4	4	NUM
ejpam-3709	185	20	.	.	PUNCT
ejpam-3709	186	1	let	let	VERB
ejpam-3709	186	2	λ3	λ3	PROPN
ejpam-3709	186	3	≥	≥	PRON
ejpam-3709	186	4	0	0	NUM
ejpam-3709	186	5	be	be	AUX
ejpam-3709	186	6	fixed	fix	VERB
ejpam-3709	186	7	and	and	CCONJ
ejpam-3709	186	8	s	s	PROPN
ejpam-3709	186	9	6=	6=	PROPN
ejpam-3709	186	10	−1	−1	NOUN
ejpam-3709	186	11	.	.	PUNCT
ejpam-3709	187	1	if	if	SCONJ
ejpam-3709	187	2	a	a	DET
ejpam-3709	187	3	function	function	NOUN
ejpam-3709	187	4	mq	mq	NOUN
ejpam-3709	187	5	:	:	PUNCT
ejpam-3709	187	6	u	u	NOUN
ejpam-3709	187	7	−→	−→	NOUN
ejpam-3709	187	8	up	up	ADP
ejpam-3709	187	9	satisfies	satisfy	VERB
ejpam-3709	187	10	the	the	DET
ejpam-3709	187	11	inequality	inequality	NOUN
ejpam-3709	187	12	p	p	NOUN
ejpam-3709	187	13	(	(	PUNCT
ejpam-3709	187	14	γmq(u	γmq(u	PROPN
ejpam-3709	187	15	,	,	PUNCT
ejpam-3709	187	16	v	v	NOUN
ejpam-3709	187	17	)	)	PUNCT
ejpam-3709	187	18	)	)	PUNCT
ejpam-3709	187	19	≤	≤	NOUN
ejpam-3709	188	1	λ3(|u|s|v|s	λ3(|u|s|v|s	X
ejpam-3709	188	2	+	+	CCONJ
ejpam-3709	188	3	(	(	PUNCT
ejpam-3709	188	4	|u|2s	|u|2s	X
ejpam-3709	188	5	+	+	CCONJ
ejpam-3709	188	6	|v|2s	|v|2	NOUN
ejpam-3709	188	7	)	)	PUNCT
ejpam-3709	188	8	)	)	PUNCT
ejpam-3709	188	9	for	for	ADP
ejpam-3709	188	10	all	all	DET
ejpam-3709	188	11	u	u	NOUN
ejpam-3709	188	12	,	,	PUNCT
ejpam-3709	188	13	v	v	NOUN
ejpam-3709	188	14	∈	∈	PROPN
ejpam-3709	188	15	u	u	NOUN
ejpam-3709	188	16	.	.	PUNCT
ejpam-3709	189	1	then	then	ADV
ejpam-3709	189	2	,	,	PUNCT
ejpam-3709	189	3	a	a	DET
ejpam-3709	189	4	unique	unique	ADJ
ejpam-3709	189	5	reciprocal	reciprocal	ADJ
ejpam-3709	189	6	second	second	ADJ
ejpam-3709	189	7	power	power	NOUN
ejpam-3709	189	8	function	function	NOUN
ejpam-3709	189	9	t	t	NOUN
ejpam-3709	189	10	:	:	PUNCT
ejpam-3709	189	11	u	u	NOUN
ejpam-3709	189	12	−→	−→	NOUN
ejpam-3709	189	13	up	up	ADP
ejpam-3709	189	14	exists	exist	NOUN
ejpam-3709	189	15	and	and	CCONJ
ejpam-3709	189	16	satisfies	satisfie	NOUN
ejpam-3709	189	17	(	(	PUNCT
ejpam-3709	189	18	1	1	NUM
ejpam-3709	189	19	)	)	PUNCT
ejpam-3709	189	20	and	and	CCONJ
ejpam-3709	189	21	p	p	X
ejpam-3709	189	22	(	(	PUNCT
ejpam-3709	189	23	mq(u)−mq(v	mq(u)−mq(v	PROPN
ejpam-3709	189	24	)	)	PUNCT
ejpam-3709	189	25	)	)	PUNCT
ejpam-3709	189	26	≤	≤	NUM
ejpam-3709	189	27	3λ3	3λ3	NUM
ejpam-3709	189	28	(	(	PUNCT
ejpam-3709	189	29	9−	9−	NUM
ejpam-3709	189	30	3−2s	3−2s	NUM
ejpam-3709	189	31	)	)	PUNCT
ejpam-3709	189	32	|u|2s	|u|2s	NOUN
ejpam-3709	189	33	for	for	ADP
ejpam-3709	189	34	all	all	PRON
ejpam-3709	189	35	u	u	PRON
ejpam-3709	189	36	∈	∈	PROPN
ejpam-3709	189	37	u	u	NOUN
ejpam-3709	189	38	.	.	PUNCT
ejpam-3709	190	1	proof	proof	NOUN
ejpam-3709	190	2	.	.	PUNCT
ejpam-3709	191	1	the	the	DET
ejpam-3709	191	2	proof	proof	NOUN
ejpam-3709	191	3	is	be	AUX
ejpam-3709	191	4	achieved	achieve	VERB
ejpam-3709	191	5	by	by	ADP
ejpam-3709	191	6	considering	consider	VERB
ejpam-3709	191	7	φ(u	φ(u	NOUN
ejpam-3709	191	8	,	,	PUNCT
ejpam-3709	191	9	v	v	NOUN
ejpam-3709	191	10	)	)	PUNCT
ejpam-3709	191	11	=	=	NOUN
ejpam-3709	192	1	λ3(|u|s|v|s	λ3(|u|s|v|s	X
ejpam-3709	192	2	+	+	CCONJ
ejpam-3709	192	3	(	(	PUNCT
ejpam-3709	192	4	|u|2s	|u|2s	X
ejpam-3709	192	5	+	+	CCONJ
ejpam-3709	192	6	|v|2s	|v|2	NOUN
ejpam-3709	192	7	)	)	PUNCT
ejpam-3709	192	8	)	)	PUNCT
ejpam-3709	192	9	in	in	ADP
ejpam-3709	192	10	theorem	theorem	NOUN
ejpam-3709	192	11	3	3	NUM
ejpam-3709	192	12	.	.	PUNCT
ejpam-3709	192	13	b.	b.	PROPN
ejpam-3709	193	1	v.	v.	PROPN
ejpam-3709	193	2	senthil	senthil	PROPN
ejpam-3709	193	3	kumar	kumar	PROPN
ejpam-3709	193	4	,	,	PUNCT
ejpam-3709	193	5	hemen	hemen	PROPN
ejpam-3709	193	6	dutta	dutta	PROPN
ejpam-3709	193	7	,	,	PUNCT
ejpam-3709	193	8	s.	s.	PROPN
ejpam-3709	193	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	193	10	/	/	SYM
ejpam-3709	193	11	eur	eur	PROPN
ejpam-3709	193	12	.	.	PUNCT
ejpam-3709	194	1	j.	j.	PROPN
ejpam-3709	194	2	pure	pure	PROPN
ejpam-3709	194	3	appl	appl	PROPN
ejpam-3709	194	4	.	.	PROPN
ejpam-3709	194	5	math	math	PROPN
ejpam-3709	194	6	,	,	PUNCT
ejpam-3709	194	7	13	13	NUM
ejpam-3709	194	8	(	(	PUNCT
ejpam-3709	194	9	5	5	NUM
ejpam-3709	194	10	)	)	PUNCT
ejpam-3709	194	11	(	(	PUNCT
ejpam-3709	194	12	2020	2020	NUM
ejpam-3709	194	13	)	)	PUNCT
ejpam-3709	194	14	,	,	PUNCT
ejpam-3709	194	15	1162	1162	NUM
ejpam-3709	194	16	-	-	SYM
ejpam-3709	194	17	1175	1175	NUM
ejpam-3709	194	18	1170	1170	NUM
ejpam-3709	194	19	5	5	NUM
ejpam-3709	194	20	.	.	PUNCT
ejpam-3709	195	1	stability	stability	NOUN
ejpam-3709	195	2	of	of	ADP
ejpam-3709	195	3	equation	equation	NOUN
ejpam-3709	195	4	(	(	PUNCT
ejpam-3709	195	5	1	1	NUM
ejpam-3709	195	6	)	)	PUNCT
ejpam-3709	195	7	in	in	ADP
ejpam-3709	195	8	β	β	ADJ
ejpam-3709	195	9	-	-	ADJ
ejpam-3709	195	10	homogeneous	homogeneous	ADJ
ejpam-3709	195	11	spaces	space	NOUN
ejpam-3709	195	12	in	in	ADP
ejpam-3709	195	13	this	this	DET
ejpam-3709	195	14	section	section	NOUN
ejpam-3709	195	15	,	,	PUNCT
ejpam-3709	195	16	we	we	PRON
ejpam-3709	195	17	obtain	obtain	VERB
ejpam-3709	195	18	the	the	DET
ejpam-3709	195	19	stability	stability	NOUN
ejpam-3709	195	20	results	result	NOUN
ejpam-3709	195	21	of	of	ADP
ejpam-3709	195	22	equation	equation	NOUN
ejpam-3709	195	23	(	(	PUNCT
ejpam-3709	195	24	1	1	NUM
ejpam-3709	195	25	)	)	PUNCT
ejpam-3709	195	26	in	in	ADP
ejpam-3709	195	27	β	β	ADJ
ejpam-3709	195	28	-	-	ADJ
ejpam-3709	195	29	homogenous	homogenous	ADJ
ejpam-3709	195	30	spaces	space	NOUN
ejpam-3709	195	31	.	.	PUNCT
ejpam-3709	196	1	theorem	theorem	ADJ
ejpam-3709	196	2	4	4	NUM
ejpam-3709	196	3	.	.	PUNCT
ejpam-3709	197	1	let	let	VERB
ejpam-3709	197	2	v	v	PART
ejpam-3709	197	3	be	be	AUX
ejpam-3709	197	4	a	a	DET
ejpam-3709	197	5	β	β	ADJ
ejpam-3709	197	6	-	-	ADJ
ejpam-3709	197	7	homogeneous	homogeneous	ADJ
ejpam-3709	197	8	complex	complex	ADJ
ejpam-3709	197	9	banach	banach	NOUN
ejpam-3709	197	10	space	space	NOUN
ejpam-3709	197	11	(	(	PUNCT
ejpam-3709	197	12	0	0	PUNCT
ejpam-3709	197	13	<	<	X
ejpam-3709	197	14	β	β	X
ejpam-3709	197	15	≤	≤	NUM
ejpam-3709	197	16	1	1	NUM
ejpam-3709	197	17	)	)	PUNCT
ejpam-3709	197	18	,	,	PUNCT
ejpam-3709	197	19	and	and	CCONJ
ejpam-3709	197	20	φ	φ	NUM
ejpam-3709	197	21	:	:	PUNCT
ejpam-3709	198	1	u	u	PRON
ejpam-3709	198	2	×	×	NOUN
ejpam-3709	198	3	u	u	NOUN
ejpam-3709	198	4	−→	−→	NOUN
ejpam-3709	198	5	(	(	PUNCT
ejpam-3709	198	6	0,∞	0,∞	NOUN
ejpam-3709	198	7	]	]	PUNCT
ejpam-3709	198	8	be	be	AUX
ejpam-3709	198	9	a	a	DET
ejpam-3709	198	10	function	function	NOUN
ejpam-3709	198	11	with	with	ADP
ejpam-3709	198	12	φ̂(u	φ̂(u	NOUN
ejpam-3709	198	13	,	,	PUNCT
ejpam-3709	198	14	v	v	NOUN
ejpam-3709	198	15	)	)	PUNCT
ejpam-3709	198	16	=	=	SYM
ejpam-3709	198	17	1	1	NUM
ejpam-3709	198	18	9β	9β	NOUN
ejpam-3709	198	19	∞∑	∞∑	NUM
ejpam-3709	198	20	i=0	i=0	PROPN
ejpam-3709	198	21	1	1	NUM
ejpam-3709	198	22	9βi	9βi	NOUN
ejpam-3709	198	23	φ	φ	PROPN
ejpam-3709	198	24	(	(	PUNCT
ejpam-3709	198	25	3−iu	3−iu	NUM
ejpam-3709	198	26	,	,	PUNCT
ejpam-3709	198	27	3−iu	3−iu	NUM
ejpam-3709	198	28	)	)	PUNCT
ejpam-3709	199	1	<	<	X
ejpam-3709	199	2	∞	∞	PROPN
ejpam-3709	199	3	(	(	PUNCT
ejpam-3709	199	4	14	14	NUM
ejpam-3709	199	5	)	)	PUNCT
ejpam-3709	199	6	for	for	ADP
ejpam-3709	199	7	all	all	DET
ejpam-3709	199	8	u	u	NOUN
ejpam-3709	199	9	,	,	PUNCT
ejpam-3709	199	10	v	v	NOUN
ejpam-3709	199	11	∈	∈	PROPN
ejpam-3709	199	12	u	u	NOUN
ejpam-3709	199	13	.	.	PUNCT
ejpam-3709	200	1	assume	assume	VERB
ejpam-3709	200	2	that	that	SCONJ
ejpam-3709	200	3	mq	mq	VERB
ejpam-3709	200	4	:	:	PUNCT
ejpam-3709	200	5	u	u	NOUN
ejpam-3709	200	6	−→	−→	ADJ
ejpam-3709	200	7	v	v	NOUN
ejpam-3709	200	8	is	be	AUX
ejpam-3709	200	9	a	a	DET
ejpam-3709	200	10	mapping	mapping	NOUN
ejpam-3709	200	11	such	such	ADJ
ejpam-3709	200	12	that∥∥γmq(u	that∥∥γmq(u	NOUN
ejpam-3709	200	13	,	,	PUNCT
ejpam-3709	200	14	v	v	NOUN
ejpam-3709	200	15	)	)	PUNCT
ejpam-3709	200	16	∥∥	∥∥	PROPN
ejpam-3709	200	17	≤	≤	NUM
ejpam-3709	200	18	φ(u	φ(u	NOUN
ejpam-3709	200	19	,	,	PUNCT
ejpam-3709	200	20	v	v	NOUN
ejpam-3709	200	21	)	)	PUNCT
ejpam-3709	200	22	(	(	PUNCT
ejpam-3709	200	23	15	15	NUM
ejpam-3709	200	24	)	)	PUNCT
ejpam-3709	200	25	holds	hold	VERB
ejpam-3709	200	26	for	for	ADP
ejpam-3709	200	27	all	all	DET
ejpam-3709	200	28	u	u	NOUN
ejpam-3709	200	29	,	,	PUNCT
ejpam-3709	200	30	v	v	NOUN
ejpam-3709	200	31	∈	∈	PROPN
ejpam-3709	200	32	u	u	NOUN
ejpam-3709	200	33	.	.	PUNCT
ejpam-3709	201	1	then	then	ADV
ejpam-3709	201	2	there	there	PRON
ejpam-3709	201	3	exists	exist	VERB
ejpam-3709	201	4	a	a	DET
ejpam-3709	201	5	unique	unique	ADJ
ejpam-3709	201	6	reciprocal	reciprocal	ADJ
ejpam-3709	201	7	second	second	ADJ
ejpam-3709	201	8	power	power	NOUN
ejpam-3709	201	9	function	function	NOUN
ejpam-3709	201	10	t	t	NOUN
ejpam-3709	201	11	:	:	PUNCT
ejpam-3709	201	12	u	u	NOUN
ejpam-3709	201	13	−→	−→	NOUN
ejpam-3709	201	14	v	v	ADP
ejpam-3709	201	15	such	such	ADJ
ejpam-3709	201	16	that	that	DET
ejpam-3709	201	17	‖mq(u)−	‖mq(u)−	PROPN
ejpam-3709	201	18	t	t	PROPN
ejpam-3709	201	19	(	(	PUNCT
ejpam-3709	201	20	u)‖	u)‖	ADJ
ejpam-3709	201	21	≤	≤	PROPN
ejpam-3709	201	22	φ̂(u	φ̂(u	NUM
ejpam-3709	201	23	,	,	PUNCT
ejpam-3709	201	24	u	u	NOUN
ejpam-3709	201	25	)	)	PUNCT
ejpam-3709	201	26	(	(	PUNCT
ejpam-3709	201	27	16	16	NUM
ejpam-3709	201	28	)	)	PUNCT
ejpam-3709	201	29	for	for	ADP
ejpam-3709	201	30	all	all	PRON
ejpam-3709	201	31	u	u	PRON
ejpam-3709	201	32	∈	∈	PROPN
ejpam-3709	201	33	u	u	NOUN
ejpam-3709	201	34	.	.	PUNCT
ejpam-3709	202	1	proof	proof	NOUN
ejpam-3709	202	2	.	.	PUNCT
ejpam-3709	203	1	firstly	firstly	ADV
ejpam-3709	203	2	,	,	PUNCT
ejpam-3709	203	3	let	let	VERB
ejpam-3709	203	4	us	we	PRON
ejpam-3709	203	5	substitute	substitute	VERB
ejpam-3709	203	6	v	v	NOUN
ejpam-3709	203	7	=	=	SYM
ejpam-3709	203	8	u	u	NOUN
ejpam-3709	203	9	in	in	ADP
ejpam-3709	203	10	(	(	PUNCT
ejpam-3709	203	11	15	15	NUM
ejpam-3709	203	12	)	)	PUNCT
ejpam-3709	203	13	.	.	PUNCT
ejpam-3709	204	1	then	then	ADV
ejpam-3709	204	2	,	,	PUNCT
ejpam-3709	204	3	we	we	PRON
ejpam-3709	204	4	get∥∥mq(3	get∥∥mq(3	PROPN
ejpam-3709	204	5	−1u)−	−1u)−	ADP
ejpam-3709	204	6	9mq(u	9mq(u	NUM
ejpam-3709	204	7	)	)	PUNCT
ejpam-3709	205	1	∥∥	∥∥	PROPN
ejpam-3709	205	2	≤	≤	ADJ
ejpam-3709	205	3	φ(u	φ(u	NOUN
ejpam-3709	205	4	,	,	PUNCT
ejpam-3709	205	5	u	u	NOUN
ejpam-3709	205	6	)	)	PUNCT
ejpam-3709	205	7	(	(	PUNCT
ejpam-3709	205	8	17	17	NUM
ejpam-3709	205	9	)	)	PUNCT
ejpam-3709	205	10	for	for	ADP
ejpam-3709	205	11	all	all	PRON
ejpam-3709	205	12	u	u	PRON
ejpam-3709	205	13	∈	∈	PROPN
ejpam-3709	205	14	u	u	NOUN
ejpam-3709	205	15	.	.	PUNCT
ejpam-3709	206	1	by	by	ADP
ejpam-3709	206	2	employing	employ	VERB
ejpam-3709	206	3	induction	induction	NOUN
ejpam-3709	206	4	technique	technique	NOUN
ejpam-3709	206	5	on	on	ADP
ejpam-3709	206	6	k	k	PROPN
ejpam-3709	206	7	∈	∈	PROPN
ejpam-3709	206	8	n	n	ADV
ejpam-3709	206	9	and	and	CCONJ
ejpam-3709	206	10	using	use	VERB
ejpam-3709	206	11	(	(	PUNCT
ejpam-3709	206	12	17	17	NUM
ejpam-3709	206	13	)	)	PUNCT
ejpam-3709	206	14	,	,	PUNCT
ejpam-3709	206	15	we	we	PRON
ejpam-3709	206	16	acquire∥∥∥∥mq(3	acquire∥∥∥∥mq(3	PROPN
ejpam-3709	206	17	−nu	−nu	PROPN
ejpam-3709	206	18	)	)	PUNCT
ejpam-3709	206	19	9n	9n	NUM
ejpam-3709	206	20	−mq(u	−mq(u	NOUN
ejpam-3709	206	21	)	)	PUNCT
ejpam-3709	206	22	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3709	206	23	≤	≤	NUM
ejpam-3709	206	24	1	1	NUM
ejpam-3709	206	25	9β	9β	NOUN
ejpam-3709	206	26	n−1∑	n−1∑	PRON
ejpam-3709	206	27	i=0	i=0	PROPN
ejpam-3709	206	28	φ(3−iu	φ(3−iu	PROPN
ejpam-3709	206	29	,	,	PUNCT
ejpam-3709	206	30	3−iu	3−iu	NUM
ejpam-3709	206	31	)	)	PUNCT
ejpam-3709	206	32	9iβ	9iβ	NOUN
ejpam-3709	206	33	(	(	PUNCT
ejpam-3709	206	34	18	18	NUM
ejpam-3709	206	35	)	)	PUNCT
ejpam-3709	206	36	for	for	ADP
ejpam-3709	206	37	all	all	PRON
ejpam-3709	206	38	u	u	PRON
ejpam-3709	206	39	∈	∈	PROPN
ejpam-3709	206	40	u	u	NOUN
ejpam-3709	206	41	.	.	PUNCT
ejpam-3709	207	1	let	let	VERB
ejpam-3709	207	2	m	m	PRON
ejpam-3709	207	3	and	and	CCONJ
ejpam-3709	207	4	n	n	ADV
ejpam-3709	207	5	be	be	AUX
ejpam-3709	207	6	non	non	ADJ
ejpam-3709	207	7	-	-	ADJ
ejpam-3709	207	8	negative	negative	ADJ
ejpam-3709	207	9	integers	integer	NOUN
ejpam-3709	207	10	with	with	ADP
ejpam-3709	207	11	n	n	NOUN
ejpam-3709	207	12	>	>	PUNCT
ejpam-3709	207	13	m	m	PROPN
ejpam-3709	207	14	,	,	PUNCT
ejpam-3709	207	15	then	then	ADV
ejpam-3709	207	16	using	use	VERB
ejpam-3709	207	17	(	(	PUNCT
ejpam-3709	207	18	18	18	NUM
ejpam-3709	207	19	)	)	PUNCT
ejpam-3709	207	20	,	,	PUNCT
ejpam-3709	207	21	we	we	PRON
ejpam-3709	207	22	have	have	VERB
ejpam-3709	207	23	∥∥∥∥mq(3	∥∥∥∥mq(3	PROPN
ejpam-3709	207	24	−nu	−nu	NOUN
ejpam-3709	207	25	)	)	PUNCT
ejpam-3709	208	1	9n	9n	NOUN
ejpam-3709	209	1	−	−	PROPN
ejpam-3709	209	2	mq(3	mq(3	NOUN
ejpam-3709	209	3	−nu	−nu	PROPN
ejpam-3709	209	4	)	)	PUNCT
ejpam-3709	209	5	9	9	NUM
ejpam-3709	209	6	m	m	NOUN
ejpam-3709	209	7	∥∥∥∥	∥∥∥∥	NUM
ejpam-3709	210	1	=	=	SYM
ejpam-3709	210	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-3709	210	3	1	1	NUM
ejpam-3709	210	4	9	9	NUM
ejpam-3709	210	5	m	m	NOUN
ejpam-3709	210	6	(	(	PUNCT
ejpam-3709	210	7	mq(3	mq(3	NOUN
ejpam-3709	210	8	−n	−n	NOUN
ejpam-3709	210	9	)	)	PUNCT
ejpam-3709	210	10	9n−m	9n−m	NUM
ejpam-3709	211	1	−mq(3	−mq(3	ADJ
ejpam-3709	211	2	−m	−m	NOUN
ejpam-3709	211	3	)	)	PUNCT
ejpam-3709	211	4	)	)	PUNCT
ejpam-3709	211	5	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-3709	212	1	≤	≤	NUM
ejpam-3709	212	2	1	1	NUM
ejpam-3709	212	3	9mβ	9mβ	NOUN
ejpam-3709	212	4	1	1	NUM
ejpam-3709	212	5	9β	9β	NOUN
ejpam-3709	212	6	n−m−1∑	n−m−1∑	PROPN
ejpam-3709	212	7	i=0	i=0	PROPN
ejpam-3709	212	8	φ(3−(i+m)u	φ(3−(i+m)u	PROPN
ejpam-3709	212	9	,	,	PUNCT
ejpam-3709	212	10	3−(i+m)u	3−(i+m)u	NUM
ejpam-3709	212	11	)	)	PUNCT
ejpam-3709	212	12	9iβ	9iβ	NOUN
ejpam-3709	212	13	=	=	SYM
ejpam-3709	212	14	1	1	NUM
ejpam-3709	212	15	9β	9β	NUM
ejpam-3709	212	16	n−1∑	n−1∑	NUM
ejpam-3709	212	17	i	i	PRON
ejpam-3709	212	18	=	=	NOUN
ejpam-3709	212	19	m	m	VERB
ejpam-3709	212	20	1	1	NUM
ejpam-3709	212	21	9iβ	9iβ	NOUN
ejpam-3709	212	22	φ	φ	PROPN
ejpam-3709	212	23	(	(	PUNCT
ejpam-3709	212	24	3−iu	3−iu	NUM
ejpam-3709	212	25	,	,	PUNCT
ejpam-3709	212	26	3−iu	3−iu	NUM
ejpam-3709	212	27	)	)	PUNCT
ejpam-3709	212	28	(	(	PUNCT
ejpam-3709	212	29	19	19	NUM
ejpam-3709	212	30	)	)	PUNCT
ejpam-3709	212	31	for	for	ADP
ejpam-3709	212	32	all	all	PRON
ejpam-3709	212	33	u	u	PRON
ejpam-3709	212	34	∈	∈	PROPN
ejpam-3709	212	35	u	u	NOUN
ejpam-3709	212	36	.	.	PUNCT
ejpam-3709	213	1	letting	let	VERB
ejpam-3709	213	2	n	n	X
ejpam-3709	213	3	→	→	SYM
ejpam-3709	213	4	∞	∞	NUM
ejpam-3709	213	5	in	in	ADP
ejpam-3709	213	6	the	the	DET
ejpam-3709	213	7	above	above	ADJ
ejpam-3709	213	8	inequality	inequality	NOUN
ejpam-3709	213	9	,	,	PUNCT
ejpam-3709	213	10	we	we	PRON
ejpam-3709	213	11	find	find	VERB
ejpam-3709	213	12	that	that	SCONJ
ejpam-3709	213	13	the	the	DET
ejpam-3709	213	14	sequence	sequence	NOUN
ejpam-3709	213	15	{	{	PUNCT
ejpam-3709	213	16	mq(3	mq(3	NOUN
ejpam-3709	213	17	−nu	−nu	NUM
ejpam-3709	213	18	)	)	PUNCT
ejpam-3709	213	19	9n	9n	NOUN
ejpam-3709	213	20	}	}	PUNCT
ejpam-3709	213	21	becomes	become	VERB
ejpam-3709	213	22	cauchy	cauchy	NOUN
ejpam-3709	213	23	in	in	ADP
ejpam-3709	213	24	u	u	PROPN
ejpam-3709	213	25	.	.	PUNCT
ejpam-3709	214	1	due	due	ADP
ejpam-3709	214	2	to	to	ADP
ejpam-3709	214	3	the	the	DET
ejpam-3709	214	4	completeness	completeness	NOUN
ejpam-3709	214	5	of	of	ADP
ejpam-3709	214	6	u	u	PROPN
ejpam-3709	214	7	,	,	PUNCT
ejpam-3709	214	8	the	the	DET
ejpam-3709	214	9	sequence	sequence	NOUN
ejpam-3709	214	10	is	be	AUX
ejpam-3709	214	11	convergent	convergent	ADJ
ejpam-3709	214	12	.	.	PUNCT
ejpam-3709	215	1	hence	hence	ADV
ejpam-3709	215	2	there	there	PRON
ejpam-3709	215	3	exists	exist	VERB
ejpam-3709	215	4	a	a	DET
ejpam-3709	215	5	mapping	mapping	NOUN
ejpam-3709	215	6	t	t	NOUN
ejpam-3709	215	7	:	:	PUNCT
ejpam-3709	215	8	u	u	NOUN
ejpam-3709	215	9	−→	−→	NOUN
ejpam-3709	215	10	v	v	ADP
ejpam-3709	215	11	defined	define	VERB
ejpam-3709	215	12	by	by	ADP
ejpam-3709	215	13	t	t	PROPN
ejpam-3709	215	14	(	(	PUNCT
ejpam-3709	215	15	u	u	NOUN
ejpam-3709	215	16	)	)	PUNCT
ejpam-3709	215	17	=	=	SYM
ejpam-3709	215	18	lim	lim	PROPN
ejpam-3709	215	19	n→∞	n→∞	X
ejpam-3709	216	1	mq(3	mq(3	NOUN
ejpam-3709	216	2	−nu	−nu	NUM
ejpam-3709	216	3	)	)	PUNCT
ejpam-3709	216	4	9n	9n	NOUN
ejpam-3709	216	5	(	(	PUNCT
ejpam-3709	216	6	20	20	NUM
ejpam-3709	216	7	)	)	PUNCT
ejpam-3709	216	8	b.	b.	PROPN
ejpam-3709	217	1	v.	v.	PROPN
ejpam-3709	217	2	senthil	senthil	PROPN
ejpam-3709	217	3	kumar	kumar	PROPN
ejpam-3709	217	4	,	,	PUNCT
ejpam-3709	217	5	hemen	hemen	PROPN
ejpam-3709	217	6	dutta	dutta	PROPN
ejpam-3709	217	7	,	,	PUNCT
ejpam-3709	217	8	s.	s.	PROPN
ejpam-3709	217	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	217	10	/	/	SYM
ejpam-3709	217	11	eur	eur	PROPN
ejpam-3709	217	12	.	.	PUNCT
ejpam-3709	218	1	j.	j.	PROPN
ejpam-3709	218	2	pure	pure	PROPN
ejpam-3709	218	3	appl	appl	PROPN
ejpam-3709	218	4	.	.	PROPN
ejpam-3709	218	5	math	math	PROPN
ejpam-3709	218	6	,	,	PUNCT
ejpam-3709	218	7	13	13	NUM
ejpam-3709	218	8	(	(	PUNCT
ejpam-3709	218	9	5	5	NUM
ejpam-3709	218	10	)	)	PUNCT
ejpam-3709	218	11	(	(	PUNCT
ejpam-3709	218	12	2020	2020	NUM
ejpam-3709	218	13	)	)	PUNCT
ejpam-3709	218	14	,	,	PUNCT
ejpam-3709	218	15	1162	1162	NUM
ejpam-3709	218	16	-	-	SYM
ejpam-3709	218	17	1175	1175	NUM
ejpam-3709	218	18	1171	1171	NUM
ejpam-3709	218	19	for	for	ADP
ejpam-3709	218	20	all	all	PRON
ejpam-3709	218	21	u	u	PRON
ejpam-3709	218	22	∈	∈	PROPN
ejpam-3709	218	23	u	u	NOUN
ejpam-3709	218	24	.	.	PUNCT
ejpam-3709	219	1	putting	put	VERB
ejpam-3709	219	2	m	m	NOUN
ejpam-3709	219	3	=	=	SYM
ejpam-3709	219	4	0	0	PUNCT
ejpam-3709	219	5	and	and	CCONJ
ejpam-3709	219	6	taking	take	VERB
ejpam-3709	219	7	the	the	DET
ejpam-3709	219	8	limit	limit	NOUN
ejpam-3709	219	9	n	n	NOUN
ejpam-3709	219	10	→	→	SYM
ejpam-3709	219	11	∞	∞	NUM
ejpam-3709	219	12	in	in	ADP
ejpam-3709	219	13	the	the	DET
ejpam-3709	219	14	above	above	ADJ
ejpam-3709	219	15	inequality	inequality	NOUN
ejpam-3709	219	16	,	,	PUNCT
ejpam-3709	219	17	we	we	PRON
ejpam-3709	219	18	obtain	obtain	AUX
ejpam-3709	219	19	(	(	PUNCT
ejpam-3709	219	20	16	16	NUM
ejpam-3709	219	21	)	)	PUNCT
ejpam-3709	219	22	using	use	VERB
ejpam-3709	219	23	(	(	PUNCT
ejpam-3709	219	24	20	20	NUM
ejpam-3709	219	25	)	)	PUNCT
ejpam-3709	219	26	.	.	PUNCT
ejpam-3709	220	1	next	next	ADV
ejpam-3709	220	2	,	,	PUNCT
ejpam-3709	220	3	consider	consider	VERB
ejpam-3709	220	4	an	an	DET
ejpam-3709	220	5	additional	additional	ADJ
ejpam-3709	220	6	function	function	NOUN
ejpam-3709	220	7	s	s	PART
ejpam-3709	220	8	:	:	PUNCT
ejpam-3709	220	9	u	u	NOUN
ejpam-3709	220	10	−→	−→	NOUN
ejpam-3709	220	11	v	v	ADP
ejpam-3709	220	12	satisfying	satisfy	VERB
ejpam-3709	220	13	(	(	PUNCT
ejpam-3709	220	14	16	16	NUM
ejpam-3709	220	15	)	)	PUNCT
ejpam-3709	220	16	and	and	CCONJ
ejpam-3709	220	17	(	(	PUNCT
ejpam-3709	220	18	20	20	NUM
ejpam-3709	220	19	)	)	PUNCT
ejpam-3709	220	20	.	.	PUNCT
ejpam-3709	221	1	then	then	ADV
ejpam-3709	221	2	,	,	PUNCT
ejpam-3709	221	3	we	we	PRON
ejpam-3709	221	4	get	get	VERB
ejpam-3709	221	5	‖t	‖t	NOUN
ejpam-3709	221	6	(	(	PUNCT
ejpam-3709	221	7	u)−	u)−	PROPN
ejpam-3709	221	8	s(u)‖	s(u)‖	PROPN
ejpam-3709	221	9	≤	≤	NUM
ejpam-3709	221	10	∥∥∥∥t	∥∥∥∥t	PUNCT
ejpam-3709	221	11	(	(	PUNCT
ejpam-3709	221	12	3−n)−mq(3	3−n)−mq(3	NUM
ejpam-3709	221	13	−n	−n	ADJ
ejpam-3709	221	14	)	)	PUNCT
ejpam-3709	221	15	9n	9n	NOUN
ejpam-3709	221	16	∥∥∥∥+	∥∥∥∥+	PROPN
ejpam-3709	221	17	∥∥∥∥mq(3	∥∥∥∥mq(3	PRON
ejpam-3709	221	18	−n)−	−n)−	NOUN
ejpam-3709	221	19	s(3−n	s(3−n	VERB
ejpam-3709	221	20	)	)	PUNCT
ejpam-3709	222	1	9n	9n	NOUN
ejpam-3709	222	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-3709	222	3	≤	≤	NUM
ejpam-3709	222	4	1	1	NUM
ejpam-3709	222	5	9β	9β	NOUN
ejpam-3709	222	6	∞∑	∞∑	NUM
ejpam-3709	222	7	i=0	i=0	PROPN
ejpam-3709	222	8	1	1	NUM
ejpam-3709	222	9	9(i+n)β	9(i+n)β	NUM
ejpam-3709	222	10	φ	φ	X
ejpam-3709	222	11	(	(	PUNCT
ejpam-3709	222	12	3−(n+i)u	3−(n+i)u	NUM
ejpam-3709	222	13	,	,	PUNCT
ejpam-3709	222	14	3−(n+i)u	3−(n+i)u	NUM
ejpam-3709	222	15	)	)	PUNCT
ejpam-3709	222	16	=	=	SYM
ejpam-3709	223	1	1	1	NUM
ejpam-3709	223	2	9β	9β	NOUN
ejpam-3709	223	3	∞∑	∞∑	NUM
ejpam-3709	223	4	i	i	PRON
ejpam-3709	223	5	=	=	NOUN
ejpam-3709	223	6	n	n	PROPN
ejpam-3709	223	7	1	1	NUM
ejpam-3709	223	8	9iβ	9iβ	NOUN
ejpam-3709	223	9	φ	φ	PROPN
ejpam-3709	223	10	(	(	PUNCT
ejpam-3709	223	11	3−iu	3−iu	NUM
ejpam-3709	223	12	,	,	PUNCT
ejpam-3709	223	13	3−iu	3−iu	NUM
ejpam-3709	223	14	)	)	PUNCT
ejpam-3709	223	15	.	.	PUNCT
ejpam-3709	224	1	from	from	ADP
ejpam-3709	224	2	the	the	DET
ejpam-3709	224	3	above	above	ADJ
ejpam-3709	224	4	inequality	inequality	NOUN
ejpam-3709	224	5	,	,	PUNCT
ejpam-3709	224	6	weobserve	weobserve	PROPN
ejpam-3709	224	7	t	t	PROPN
ejpam-3709	224	8	is	be	AUX
ejpam-3709	224	9	unique	unique	ADJ
ejpam-3709	224	10	by	by	ADP
ejpam-3709	224	11	letting	let	VERB
ejpam-3709	224	12	n→∞	n→∞	NUM
ejpam-3709	224	13	,	,	PUNCT
ejpam-3709	224	14	which	which	PRON
ejpam-3709	224	15	completes	complete	VERB
ejpam-3709	224	16	the	the	DET
ejpam-3709	224	17	proof	proof	NOUN
ejpam-3709	224	18	.	.	PUNCT
ejpam-3709	225	1	corollary	corollary	ADJ
ejpam-3709	225	2	5	5	NUM
ejpam-3709	225	3	.	.	PUNCT
ejpam-3709	226	1	let	let	VERB
ejpam-3709	226	2	mq	mq	NOUN
ejpam-3709	226	3	:	:	PUNCT
ejpam-3709	226	4	u	u	NOUN
ejpam-3709	226	5	−→	−→	ADJ
ejpam-3709	226	6	v	v	AUX
ejpam-3709	226	7	be	be	AUX
ejpam-3709	226	8	a	a	DET
ejpam-3709	226	9	function	function	NOUN
ejpam-3709	226	10	with	with	ADP
ejpam-3709	226	11	a	a	DET
ejpam-3709	226	12	constant	constant	ADJ
ejpam-3709	226	13	λ4	λ4	NOUN
ejpam-3709	226	14	≥	≥	NOUN
ejpam-3709	226	15	0	0	NUM
ejpam-3709	226	16	,	,	PUNCT
ejpam-3709	226	17	not	not	PART
ejpam-3709	226	18	depending	depend	VERB
ejpam-3709	226	19	on	on	ADP
ejpam-3709	226	20	the	the	DET
ejpam-3709	226	21	values	value	NOUN
ejpam-3709	226	22	of	of	ADP
ejpam-3709	226	23	u	u	NOUN
ejpam-3709	226	24	,	,	PUNCT
ejpam-3709	226	25	v	v	ADP
ejpam-3709	226	26	such	such	ADJ
ejpam-3709	226	27	that	that	SCONJ
ejpam-3709	226	28	the	the	DET
ejpam-3709	226	29	inequality∥∥γmq(u	inequality∥∥γmq(u	PROPN
ejpam-3709	226	30	,	,	PUNCT
ejpam-3709	226	31	v	v	NOUN
ejpam-3709	226	32	)	)	PUNCT
ejpam-3709	227	1	∥∥	∥∥	X
ejpam-3709	227	2	≤	≤	NUM
ejpam-3709	227	3	λ4	λ4	PROPN
ejpam-3709	227	4	holds	hold	VERB
ejpam-3709	227	5	for	for	ADP
ejpam-3709	227	6	all	all	DET
ejpam-3709	227	7	u	u	NOUN
ejpam-3709	227	8	,	,	PUNCT
ejpam-3709	227	9	v	v	NOUN
ejpam-3709	227	10	∈	∈	PROPN
ejpam-3709	227	11	u	u	NOUN
ejpam-3709	227	12	.	.	PUNCT
ejpam-3709	228	1	then	then	ADV
ejpam-3709	228	2	,	,	PUNCT
ejpam-3709	228	3	t	t	X
ejpam-3709	228	4	:	:	PUNCT
ejpam-3709	228	5	u	u	NOUN
ejpam-3709	228	6	−→	−→	ADJ
ejpam-3709	228	7	v	v	NOUN
ejpam-3709	228	8	is	be	AUX
ejpam-3709	228	9	a	a	DET
ejpam-3709	228	10	unique	unique	ADJ
ejpam-3709	228	11	reciprocal	reciprocal	ADJ
ejpam-3709	228	12	second	second	ADJ
ejpam-3709	228	13	power	power	NOUN
ejpam-3709	228	14	function	function	NOUN
ejpam-3709	228	15	satisfying	satisfying	ADJ
ejpam-3709	228	16	(	(	PUNCT
ejpam-3709	228	17	1	1	NUM
ejpam-3709	228	18	)	)	PUNCT
ejpam-3709	228	19	and	and	CCONJ
ejpam-3709	229	1	‖mq(u)−	‖mq(u)−	PROPN
ejpam-3709	229	2	t	t	PROPN
ejpam-3709	229	3	(	(	PUNCT
ejpam-3709	229	4	u)‖	u)‖	ADJ
ejpam-3709	229	5	≤	≤	X
ejpam-3709	229	6	λ4	λ4	PROPN
ejpam-3709	229	7	9β	9β	NOUN
ejpam-3709	229	8	−	−	NOUN
ejpam-3709	229	9	1	1	NUM
ejpam-3709	229	10	for	for	ADP
ejpam-3709	229	11	all	all	PRON
ejpam-3709	229	12	u	u	PRON
ejpam-3709	229	13	∈	∈	PROPN
ejpam-3709	229	14	u	u	NOUN
ejpam-3709	229	15	.	.	PUNCT
ejpam-3709	230	1	proof	proof	NOUN
ejpam-3709	230	2	.	.	PUNCT
ejpam-3709	231	1	taking	take	VERB
ejpam-3709	231	2	φ(u	φ(u	NOUN
ejpam-3709	231	3	,	,	PUNCT
ejpam-3709	231	4	v	v	NOUN
ejpam-3709	231	5	)	)	PUNCT
ejpam-3709	231	6	=	=	VERB
ejpam-3709	232	1	λ4	λ4	ADJ
ejpam-3709	232	2	in	in	ADP
ejpam-3709	232	3	theorem	theorem	NOUN
ejpam-3709	232	4	4	4	NUM
ejpam-3709	232	5	,	,	PUNCT
ejpam-3709	232	6	we	we	PRON
ejpam-3709	232	7	arrive	arrive	VERB
ejpam-3709	232	8	at	at	ADP
ejpam-3709	232	9	the	the	DET
ejpam-3709	232	10	required	require	VERB
ejpam-3709	232	11	result	result	NOUN
ejpam-3709	232	12	.	.	PUNCT
ejpam-3709	233	1	corollary	corollary	ADJ
ejpam-3709	233	2	6	6	NUM
ejpam-3709	233	3	.	.	PUNCT
ejpam-3709	234	1	let	let	VERB
ejpam-3709	234	2	λ5	λ5	NOUN
ejpam-3709	234	3	≥	≥	PRON
ejpam-3709	234	4	0	0	NUM
ejpam-3709	234	5	be	be	AUX
ejpam-3709	234	6	fixed	fix	VERB
ejpam-3709	234	7	and	and	CCONJ
ejpam-3709	234	8	s	s	PROPN
ejpam-3709	234	9	6=	6=	PROPN
ejpam-3709	235	1	−2β	−2β	PROPN
ejpam-3709	235	2	.	.	PUNCT
ejpam-3709	235	3	suppose	suppose	VERB
ejpam-3709	235	4	a	a	DET
ejpam-3709	235	5	function	function	NOUN
ejpam-3709	235	6	mq	mq	NOUN
ejpam-3709	235	7	:	:	PUNCT
ejpam-3709	235	8	u	u	NOUN
ejpam-3709	235	9	−→	−→	ADJ
ejpam-3709	235	10	v	v	X
ejpam-3709	235	11	satisfies	satisfy	VERB
ejpam-3709	235	12	the	the	DET
ejpam-3709	235	13	inequality	inequality	NOUN
ejpam-3709	235	14	∥∥γmq(u	∥∥γmq(u	NOUN
ejpam-3709	235	15	,	,	PUNCT
ejpam-3709	235	16	v	v	NOUN
ejpam-3709	235	17	)	)	PUNCT
ejpam-3709	236	1	∥∥	∥∥	PROPN
ejpam-3709	236	2	≤	≤	NUM
ejpam-3709	237	1	λ5(||u||s	λ5(||u||s	NOUN
ejpam-3709	237	2	+	+	CCONJ
ejpam-3709	237	3	||v||s	||v||s	PROPN
ejpam-3709	237	4	)	)	PUNCT
ejpam-3709	237	5	for	for	ADP
ejpam-3709	237	6	all	all	DET
ejpam-3709	237	7	u	u	NOUN
ejpam-3709	237	8	,	,	PUNCT
ejpam-3709	237	9	v	v	NOUN
ejpam-3709	237	10	∈	∈	PROPN
ejpam-3709	237	11	u	u	NOUN
ejpam-3709	237	12	.	.	PUNCT
ejpam-3709	238	1	then	then	ADV
ejpam-3709	238	2	,	,	PUNCT
ejpam-3709	238	3	a	a	DET
ejpam-3709	238	4	unique	unique	ADJ
ejpam-3709	238	5	reciprocal	reciprocal	ADJ
ejpam-3709	238	6	second	second	ADJ
ejpam-3709	238	7	power	power	NOUN
ejpam-3709	238	8	function	function	NOUN
ejpam-3709	238	9	t	t	NOUN
ejpam-3709	238	10	:	:	PUNCT
ejpam-3709	238	11	u	u	NOUN
ejpam-3709	238	12	−→	−→	NOUN
ejpam-3709	238	13	v	v	NOUN
ejpam-3709	238	14	exists	exist	VERB
ejpam-3709	238	15	and	and	CCONJ
ejpam-3709	238	16	satisfies	satisfie	NOUN
ejpam-3709	238	17	(	(	PUNCT
ejpam-3709	238	18	1	1	NUM
ejpam-3709	238	19	)	)	PUNCT
ejpam-3709	238	20	and	and	CCONJ
ejpam-3709	238	21	‖mq(u)−	‖mq(u)−	PROPN
ejpam-3709	238	22	t	t	PROPN
ejpam-3709	238	23	(	(	PUNCT
ejpam-3709	238	24	u)‖	u)‖	ADJ
ejpam-3709	238	25	≤	≤	NOUN
ejpam-3709	238	26	2λ5	2λ5	NUM
ejpam-3709	238	27	(	(	PUNCT
ejpam-3709	238	28	9β	9β	NOUN
ejpam-3709	238	29	−	−	NOUN
ejpam-3709	238	30	3−s	3−s	NUM
ejpam-3709	238	31	)	)	PUNCT
ejpam-3709	238	32	||u||s	||u||s	ADP
ejpam-3709	238	33	for	for	ADP
ejpam-3709	238	34	all	all	DET
ejpam-3709	238	35	u	u	PRON
ejpam-3709	238	36	∈	∈	PROPN
ejpam-3709	238	37	u	u	NOUN
ejpam-3709	238	38	.	.	PUNCT
ejpam-3709	239	1	proof	proof	NOUN
ejpam-3709	239	2	.	.	PUNCT
ejpam-3709	240	1	replacing	replace	VERB
ejpam-3709	240	2	φ(u	φ(u	NOUN
ejpam-3709	240	3	,	,	PUNCT
ejpam-3709	240	4	v	v	NOUN
ejpam-3709	240	5	)	)	PUNCT
ejpam-3709	240	6	=	=	SYM
ejpam-3709	241	1	λ5(||u||s	λ5(||u||s	NOUN
ejpam-3709	241	2	+	+	CCONJ
ejpam-3709	241	3	||v||s	||v||s	PROPN
ejpam-3709	241	4	)	)	PUNCT
ejpam-3709	241	5	in	in	ADP
ejpam-3709	241	6	theorem	theorem	ADJ
ejpam-3709	241	7	4	4	NUM
ejpam-3709	241	8	and	and	CCONJ
ejpam-3709	241	9	proceeding	proceed	VERB
ejpam-3709	241	10	further	far	ADV
ejpam-3709	241	11	,	,	PUNCT
ejpam-3709	241	12	we	we	PRON
ejpam-3709	241	13	obtain	obtain	VERB
ejpam-3709	241	14	the	the	DET
ejpam-3709	241	15	desired	desire	VERB
ejpam-3709	241	16	result	result	NOUN
ejpam-3709	241	17	.	.	PUNCT
ejpam-3709	242	1	corollary	corollary	ADJ
ejpam-3709	242	2	7	7	NUM
ejpam-3709	242	3	.	.	PUNCT
ejpam-3709	243	1	let	let	VERB
ejpam-3709	243	2	mq	mq	NOUN
ejpam-3709	243	3	:	:	PUNCT
ejpam-3709	243	4	u	u	NOUN
ejpam-3709	243	5	−→	−→	ADJ
ejpam-3709	243	6	v	v	INTJ
ejpam-3709	243	7	be	be	AUX
ejpam-3709	243	8	a	a	DET
ejpam-3709	243	9	function	function	NOUN
ejpam-3709	243	10	.	.	PUNCT
ejpam-3709	244	1	if	if	SCONJ
ejpam-3709	244	2	there	there	PRON
ejpam-3709	244	3	exist	exist	VERB
ejpam-3709	244	4	x	x	NOUN
ejpam-3709	244	5	,	,	PUNCT
ejpam-3709	244	6	y	y	PROPN
ejpam-3709	244	7	:	:	PUNCT
ejpam-3709	244	8	s	s	X
ejpam-3709	244	9	=	=	PUNCT
ejpam-3709	244	10	x	x	PROPN
ejpam-3709	245	1	+	+	NUM
ejpam-3709	245	2	y	y	PROPN
ejpam-3709	245	3	6=	6=	PROPN
ejpam-3709	245	4	−2β	−2β	PROPN
ejpam-3709	245	5	and	and	CCONJ
ejpam-3709	245	6	λ6	λ6	PROPN
ejpam-3709	245	7	≥	≥	NOUN
ejpam-3709	245	8	0	0	NUM
ejpam-3709	245	9	such	such	ADJ
ejpam-3709	245	10	that	that	SCONJ
ejpam-3709	245	11	∥∥γmq(u	∥∥γmq(u	NOUN
ejpam-3709	245	12	,	,	PUNCT
ejpam-3709	245	13	v	v	NOUN
ejpam-3709	245	14	)	)	PUNCT
ejpam-3709	245	15	∥∥	∥∥	PROPN
ejpam-3709	245	16	≤	≤	ADV
ejpam-3709	245	17	λ6(||u||x||v||y	λ6(||u||x||v||y	PROPN
ejpam-3709	245	18	)	)	PUNCT
ejpam-3709	245	19	b.	b.	PROPN
ejpam-3709	246	1	v.	v.	ADP
ejpam-3709	246	2	senthil	senthil	PROPN
ejpam-3709	246	3	kumar	kumar	PROPN
ejpam-3709	246	4	,	,	PUNCT
ejpam-3709	246	5	hemen	hemen	PROPN
ejpam-3709	246	6	dutta	dutta	PROPN
ejpam-3709	246	7	,	,	PUNCT
ejpam-3709	246	8	s.	s.	PROPN
ejpam-3709	246	9	sabarinathan	sabarinathan	PROPN
ejpam-3709	246	10	/	/	SYM
ejpam-3709	246	11	eur	eur	PROPN
ejpam-3709	246	12	.	.	PUNCT
ejpam-3709	247	1	j.	j.	PROPN
ejpam-3709	247	2	pure	pure	PROPN
ejpam-3709	247	3	appl	appl	PROPN
ejpam-3709	247	4	.	.	PROPN
ejpam-3709	247	5	math	math	PROPN
ejpam-3709	247	6	,	,	PUNCT
ejpam-3709	247	7	13	13	NUM
ejpam-3709	247	8	(	(	PUNCT
ejpam-3709	247	9	5	5	NUM
ejpam-3709	247	10	)	)	PUNCT
ejpam-3709	247	11	(	(	PUNCT
ejpam-3709	247	12	2020	2020	NUM
ejpam-3709	247	13	)	)	PUNCT
ejpam-3709	247	14	,	,	PUNCT
ejpam-3709	247	15	1162	1162	NUM
ejpam-3709	247	16	-	-	SYM
ejpam-3709	247	17	1175	1175	NUM
ejpam-3709	247	18	1172	1172	NUM
ejpam-3709	247	19	holds	hold	VERB
ejpam-3709	247	20	for	for	ADP
ejpam-3709	247	21	all	all	DET
ejpam-3709	247	22	u	u	NOUN
ejpam-3709	247	23	,	,	PUNCT
ejpam-3709	247	24	v	v	NOUN
ejpam-3709	247	25	∈	∈	PROPN
ejpam-3709	247	26	u	u	NOUN
ejpam-3709	247	27	.	.	PUNCT
ejpam-3709	248	1	then	then	ADV
ejpam-3709	248	2	,	,	PUNCT
ejpam-3709	248	3	there	there	PRON
ejpam-3709	248	4	exists	exist	VERB
ejpam-3709	248	5	a	a	DET
ejpam-3709	248	6	unique	unique	ADJ
ejpam-3709	248	7	reciprocal	reciprocal	ADJ
ejpam-3709	248	8	second	second	ADJ
ejpam-3709	248	9	power	power	NOUN
ejpam-3709	248	10	function	function	NOUN
ejpam-3709	248	11	t	t	NOUN
ejpam-3709	248	12	:	:	PUNCT
ejpam-3709	248	13	u	u	NOUN
ejpam-3709	248	14	−→	−→	NOUN
ejpam-3709	248	15	v	v	ADP
ejpam-3709	248	16	satisfying	satisfy	VERB
ejpam-3709	248	17	(	(	PUNCT
ejpam-3709	248	18	1	1	NUM
ejpam-3709	248	19	)	)	PUNCT
ejpam-3709	248	20	and	and	CCONJ
ejpam-3709	248	21	‖mq(u)−	‖mq(u)−	PROPN
ejpam-3709	248	22	t	t	PROPN
ejpam-3709	248	23	(	(	PUNCT
ejpam-3709	248	24	u)‖	u)‖	ADJ
ejpam-3709	248	25	≤	≤	PROPN
ejpam-3709	248	26	λ6	λ6	PROPN
ejpam-3709	248	27	(	(	PUNCT
ejpam-3709	248	28	9β	9β	NOUN
ejpam-3709	248	29	−	−	NOUN
ejpam-3709	248	30	3−s	3−s	NUM
ejpam-3709	248	31	)	)	PUNCT
ejpam-3709	248	32	||u||s	||u||s	ADP
ejpam-3709	248	33	for	for	ADP
ejpam-3709	248	34	all	all	DET
ejpam-3709	248	35	u	u	PRON
ejpam-3709	248	36	∈	∈	PROPN
ejpam-3709	248	37	u	u	NOUN
ejpam-3709	248	38	.	.	PUNCT
ejpam-3709	249	1	proof	proof	NOUN
ejpam-3709	249	2	.	.	PUNCT
ejpam-3709	250	1	choosing	choose	VERB
ejpam-3709	250	2	φ(u	φ(u	NOUN
ejpam-3709	250	3	,	,	PUNCT
ejpam-3709	250	4	v	v	NOUN
ejpam-3709	250	5	)	)	PUNCT
ejpam-3709	250	6	=	=	NOUN
ejpam-3709	250	7	λ6(|u|x|v|y	λ6(|u|x|v|y	X
ejpam-3709	250	8	)	)	PUNCT
ejpam-3709	250	9	in	in	ADP
ejpam-3709	250	10	theorem	theorem	NOUN
ejpam-3709	250	11	4	4	NUM
ejpam-3709	250	12	,	,	PUNCT
ejpam-3709	250	13	we	we	PRON
ejpam-3709	250	14	achieve	achieve	VERB
ejpam-3709	250	15	the	the	DET
ejpam-3709	250	16	result	result	NOUN
ejpam-3709	250	17	.	.	PUNCT
ejpam-3709	251	1	corollary	corollary	ADJ
ejpam-3709	251	2	8	8	NUM
ejpam-3709	251	3	.	.	PUNCT
ejpam-3709	252	1	let	let	VERB
ejpam-3709	252	2	λ7	λ7	PROPN
ejpam-3709	252	3	≥	≥	PRON
ejpam-3709	252	4	0	0	NUM
ejpam-3709	252	5	be	be	AUX
ejpam-3709	252	6	fixed	fix	VERB
ejpam-3709	252	7	and	and	CCONJ
ejpam-3709	252	8	s	s	PROPN
ejpam-3709	252	9	6=	6=	PROPN
ejpam-3709	252	10	−β	−β	PROPN
ejpam-3709	252	11	.	.	PUNCT
ejpam-3709	253	1	let	let	VERB
ejpam-3709	253	2	a	a	DET
ejpam-3709	253	3	function	function	NOUN
ejpam-3709	253	4	mq	mq	NOUN
ejpam-3709	253	5	:	:	PUNCT
ejpam-3709	253	6	u	u	NOUN
ejpam-3709	253	7	−→	−→	ADJ
ejpam-3709	253	8	v	v	X
ejpam-3709	253	9	satisfies	satisfy	VERB
ejpam-3709	253	10	the	the	DET
ejpam-3709	253	11	inequality	inequality	NOUN
ejpam-3709	253	12	∥∥γmq(u	∥∥γmq(u	NOUN
ejpam-3709	253	13	,	,	PUNCT
ejpam-3709	253	14	v	v	NOUN
ejpam-3709	253	15	)	)	PUNCT
ejpam-3709	254	1	∥∥	∥∥	X
ejpam-3709	254	2	≤	≤	NOUN
ejpam-3709	254	3	λ7(||u||s||v||s	λ7(||u||s||v||s	PRON
ejpam-3709	254	4	+	+	CCONJ
ejpam-3709	254	5	(	(	PUNCT
ejpam-3709	254	6	||u||2s	||u||2s	NOUN
ejpam-3709	254	7	+	+	CCONJ
ejpam-3709	254	8	||v||2s	||v||2s	NOUN
ejpam-3709	254	9	)	)	PUNCT
ejpam-3709	254	10	)	)	PUNCT
ejpam-3709	254	11	for	for	ADP
ejpam-3709	254	12	all	all	DET
ejpam-3709	254	13	u	u	NOUN
ejpam-3709	254	14	,	,	PUNCT
ejpam-3709	254	15	v	v	NOUN
ejpam-3709	254	16	∈	∈	PROPN
ejpam-3709	254	17	u	u	NOUN
ejpam-3709	254	18	.	.	PUNCT
ejpam-3709	255	1	then	then	ADV
ejpam-3709	255	2	,	,	PUNCT
ejpam-3709	255	3	a	a	DET
ejpam-3709	255	4	unique	unique	ADJ
ejpam-3709	255	5	reciprocal	reciprocal	ADJ
ejpam-3709	255	6	second	second	ADJ
ejpam-3709	255	7	power	power	NOUN
ejpam-3709	255	8	function	function	NOUN
ejpam-3709	255	9	t	t	NOUN
ejpam-3709	255	10	:	:	PUNCT
ejpam-3709	255	11	u	u	NOUN
ejpam-3709	255	12	−→	−→	NOUN
ejpam-3709	255	13	v	v	NOUN
ejpam-3709	255	14	exists	exist	VERB
ejpam-3709	255	15	and	and	CCONJ
ejpam-3709	255	16	satisfies	satisfie	NOUN
ejpam-3709	255	17	(	(	PUNCT
ejpam-3709	255	18	1	1	NUM
ejpam-3709	255	19	)	)	PUNCT
ejpam-3709	255	20	and	and	CCONJ
ejpam-3709	255	21	‖mq(u)−	‖mq(u)−	PROPN
ejpam-3709	255	22	t	t	PROPN
ejpam-3709	255	23	(	(	PUNCT
ejpam-3709	255	24	u)‖	u)‖	ADJ
ejpam-3709	255	25	≤	≤	NOUN
ejpam-3709	255	26	3λ7	3λ7	NUM
ejpam-3709	255	27	(	(	PUNCT
ejpam-3709	255	28	9β	9β	NOUN
ejpam-3709	255	29	−	−	PROPN
ejpam-3709	255	30	3−2s	3−2s	NUM
ejpam-3709	255	31	)	)	PUNCT
ejpam-3709	255	32	||u||2s	||u||2s	NOUN
ejpam-3709	255	33	for	for	ADP
ejpam-3709	255	34	all	all	PRON
ejpam-3709	255	35	u	u	NOUN
ejpam-3709	255	36	∈	∈	PROPN
ejpam-3709	255	37	u	u	NOUN
ejpam-3709	255	38	.	.	PUNCT
ejpam-3709	256	1	proof	proof	NOUN
ejpam-3709	256	2	.	.	PUNCT
ejpam-3709	257	1	selecting	select	VERB
ejpam-3709	257	2	φ(u	φ(u	NOUN
ejpam-3709	257	3	,	,	PUNCT
ejpam-3709	257	4	v	v	NOUN
ejpam-3709	257	5	)	)	PUNCT
ejpam-3709	257	6	=	=	SYM
ejpam-3709	258	1	λ7(||u||s||v||s	λ7(||u||s||v||s	PROPN
ejpam-3709	258	2	+	+	CCONJ
ejpam-3709	258	3	(	(	PUNCT
ejpam-3709	258	4	||u||2s	||u||2s	NOUN
ejpam-3709	258	5	+	+	CCONJ
ejpam-3709	258	6	||v||2s	||v||2s	NOUN
ejpam-3709	258	7	)	)	PUNCT
ejpam-3709	258	8	)	)	PUNCT
ejpam-3709	258	9	in	in	ADP
ejpam-3709	258	10	theorem	theorem	NOUN
ejpam-3709	258	11	4	4	NUM
ejpam-3709	258	12	,	,	PUNCT
ejpam-3709	258	13	we	we	PRON
ejpam-3709	258	14	get	get	VERB
ejpam-3709	258	15	the	the	DET
ejpam-3709	258	16	required	require	VERB
ejpam-3709	258	17	result	result	NOUN
ejpam-3709	258	18	.	.	PUNCT
ejpam-3709	259	1	6	6	X
ejpam-3709	259	2	.	.	X
ejpam-3709	259	3	application	application	NOUN
ejpam-3709	259	4	of	of	ADP
ejpam-3709	259	5	equation	equation	NOUN
ejpam-3709	259	6	(	(	PUNCT
ejpam-3709	259	7	1	1	X
ejpam-3709	259	8	)	)	PUNCT
ejpam-3709	259	9	we	we	PRON
ejpam-3709	259	10	close	close	VERB
ejpam-3709	259	11	our	our	PRON
ejpam-3709	259	12	investigation	investigation	NOUN
ejpam-3709	259	13	with	with	ADP
ejpam-3709	259	14	an	an	DET
ejpam-3709	259	15	application	application	NOUN
ejpam-3709	259	16	of	of	ADP
ejpam-3709	259	17	equation	equation	NOUN
ejpam-3709	259	18	(	(	PUNCT
ejpam-3709	259	19	1	1	X
ejpam-3709	259	20	)	)	PUNCT
ejpam-3709	259	21	using	use	VERB
ejpam-3709	259	22	coloumb	coloumb	NOUN
ejpam-3709	259	23	’s	’s	PART
ejpam-3709	259	24	law	law	NOUN
ejpam-3709	259	25	.	.	PUNCT
ejpam-3709	260	1	according	accord	VERB
ejpam-3709	260	2	to	to	ADP
ejpam-3709	260	3	coloumb	coloumb	NOUN
ejpam-3709	260	4	,	,	PUNCT
ejpam-3709	260	5	the	the	DET
ejpam-3709	260	6	electrostatic	electrostatic	ADJ
ejpam-3709	260	7	force	force	NOUN
ejpam-3709	260	8	of	of	ADP
ejpam-3709	260	9	attraction	attraction	NOUN
ejpam-3709	260	10	between	between	ADP
ejpam-3709	260	11	two	two	NUM
ejpam-3709	260	12	point	point	NOUN
ejpam-3709	260	13	charges	charge	NOUN
ejpam-3709	260	14	is	be	AUX
ejpam-3709	260	15	directly	directly	ADV
ejpam-3709	260	16	proportional	proportional	ADJ
ejpam-3709	260	17	to	to	ADP
ejpam-3709	260	18	the	the	DET
ejpam-3709	260	19	product	product	NOUN
ejpam-3709	260	20	of	of	ADP
ejpam-3709	260	21	the	the	DET
ejpam-3709	260	22	charges	charge	NOUN
ejpam-3709	260	23	and	and	CCONJ
ejpam-3709	260	24	inversely	inversely	ADV
ejpam-3709	260	25	proportional	proportional	ADJ
ejpam-3709	260	26	to	to	ADP
ejpam-3709	260	27	the	the	DET
ejpam-3709	260	28	square	square	NOUN
ejpam-3709	260	29	of	of	ADP
ejpam-3709	260	30	the	the	DET
ejpam-3709	260	31	distance	distance	NOUN
ejpam-3709	260	32	between	between	ADP
ejpam-3709	260	33	them	they	PRON
ejpam-3709	260	34	.	.	PUNCT
ejpam-3709	261	1	figure	figure	VERB
ejpam-3709	261	2	1	1	NUM
ejpam-3709	261	3	:	:	PUNCT
ejpam-3709	261	4	electrostatic	electrostatic	ADJ
ejpam-3709	261	5	force	force	NOUN
ejpam-3709	261	6	of	of	ADP
ejpam-3709	261	7	attraction	attraction	NOUN
ejpam-3709	261	8	f	f	PROPN
ejpam-3709	261	9	between	between	ADP
ejpam-3709	261	10	two	two	NUM
ejpam-3709	261	11	point	point	NOUN
ejpam-3709	261	12	charges	charge	NOUN
ejpam-3709	261	13	q1	q1	PROPN
ejpam-3709	261	14	and	and	CCONJ
ejpam-3709	261	15	q2	q2	NOUN
ejpam-3709	261	16	that	that	PRON
ejpam-3709	261	17	is	be	AUX
ejpam-3709	261	18	,	,	PUNCT
ejpam-3709	261	19	f	f	PROPN
ejpam-3709	261	20	=	=	SYM
ejpam-3709	261	21	1	1	NUM
ejpam-3709	261	22	4πε0	4πε0	NUM
ejpam-3709	262	1	q1q2	q1q2	NOUN
ejpam-3709	262	2	r2	r2	NOUN
ejpam-3709	262	3	where	where	SCONJ
ejpam-3709	262	4	f	f	PROPN
ejpam-3709	262	5	and	and	CCONJ
ejpam-3709	262	6	r	r	PROPN
ejpam-3709	262	7	,	,	PUNCT
ejpam-3709	262	8	respectively	respectively	ADV
ejpam-3709	262	9	,	,	PUNCT
ejpam-3709	262	10	are	be	AUX
ejpam-3709	262	11	the	the	DET
ejpam-3709	262	12	force	force	NOUN
ejpam-3709	262	13	of	of	ADP
ejpam-3709	262	14	attraction	attraction	NOUN
ejpam-3709	262	15	and	and	CCONJ
ejpam-3709	262	16	distance	distance	NOUN
ejpam-3709	262	17	between	between	ADP
ejpam-3709	262	18	the	the	DET
ejpam-3709	262	19	point	point	NOUN
ejpam-3709	262	20	charges	charge	NOUN
ejpam-3709	262	21	q1	q1	PROPN
ejpam-3709	262	22	and	and	CCONJ
ejpam-3709	262	23	q2	q2	PROPN
ejpam-3709	262	24	.	.	PUNCT
ejpam-3709	263	1	suppose	suppose	VERB
ejpam-3709	263	2	the	the	DET
ejpam-3709	263	3	constant	constant	ADJ
ejpam-3709	263	4	1	1	NUM
ejpam-3709	263	5	4πε0	4πε0	NUM
ejpam-3709	263	6	is	be	AUX
ejpam-3709	263	7	taken	take	VERB
ejpam-3709	263	8	as	as	ADP
ejpam-3709	263	9	a	a	DET
ejpam-3709	263	10	constant	constant	ADJ
ejpam-3709	263	11	c	c	NOUN
ejpam-3709	263	12	and	and	CCONJ
ejpam-3709	263	13	unit	unit	NOUN
ejpam-3709	263	14	point	point	NOUN
ejpam-3709	263	15	charges	charge	NOUN
ejpam-3709	263	16	are	be	AUX
ejpam-3709	263	17	assumed	assume	VERB
ejpam-3709	263	18	,	,	PUNCT
ejpam-3709	263	19	then	then	ADV
ejpam-3709	263	20	the	the	DET
ejpam-3709	263	21	electrocstatic	electrocstatic	ADJ
ejpam-3709	263	22	force	force	NOUN
ejpam-3709	263	23	of	of	ADP
ejpam-3709	263	24	attraction	attraction	NOUN
ejpam-3709	263	25	is	be	AUX
ejpam-3709	263	26	given	give	VERB
ejpam-3709	263	27	by	by	ADP
ejpam-3709	263	28	f	f	PROPN
ejpam-3709	263	29	=	=	SYM
ejpam-3709	263	30	c	c	PROPN
ejpam-3709	263	31	r2	r2	PROPN
ejpam-3709	263	32	references	reference	NOUN
ejpam-3709	263	33	1173	1173	NUM
ejpam-3709	263	34	which	which	PRON
ejpam-3709	263	35	is	be	AUX
ejpam-3709	263	36	a	a	DET
ejpam-3709	263	37	reciprocal	reciprocal	ADJ
ejpam-3709	263	38	second	second	ADJ
ejpam-3709	263	39	power	power	NOUN
ejpam-3709	263	40	function	function	NOUN
ejpam-3709	263	41	.	.	PUNCT
ejpam-3709	264	1	suppose	suppose	VERB
ejpam-3709	264	2	the	the	DET
ejpam-3709	264	3	distance	distance	NOUN
ejpam-3709	264	4	between	between	ADP
ejpam-3709	264	5	two	two	NUM
ejpam-3709	264	6	unit	unit	NOUN
ejpam-3709	264	7	point	point	NOUN
ejpam-3709	264	8	charges	charge	NOUN
ejpam-3709	264	9	is	be	AUX
ejpam-3709	264	10	uv	uv	ADP
ejpam-3709	264	11	2u+v	2u+v	NUM
ejpam-3709	264	12	,	,	PUNCT
ejpam-3709	264	13	then	then	ADV
ejpam-3709	264	14	the	the	DET
ejpam-3709	264	15	electrocstatic	electrocstatic	ADJ
ejpam-3709	264	16	force	force	NOUN
ejpam-3709	264	17	of	of	ADP
ejpam-3709	264	18	attraction	attraction	NOUN
ejpam-3709	264	19	is	be	AUX
ejpam-3709	264	20	given	give	VERB
ejpam-3709	264	21	by	by	ADP
ejpam-3709	264	22	mq	mq	PROPN
ejpam-3709	264	23	(	(	PUNCT
ejpam-3709	264	24	uv	uv	INTJ
ejpam-3709	264	25	2u+	2u+	NUM
ejpam-3709	264	26	v	v	NOUN
ejpam-3709	264	27	)	)	PUNCT
ejpam-3709	265	1	=	=	VERB
ejpam-3709	265	2	c(2u+	c(2u+	VERB
ejpam-3709	265	3	v)2	v)2	PROPN
ejpam-3709	265	4	u2v2	u2v2	NOUN
ejpam-3709	265	5	.	.	PUNCT
ejpam-3709	266	1	also	also	ADV
ejpam-3709	266	2	,	,	PUNCT
ejpam-3709	266	3	if	if	SCONJ
ejpam-3709	266	4	the	the	DET
ejpam-3709	266	5	distance	distance	NOUN
ejpam-3709	266	6	is	be	AUX
ejpam-3709	266	7	uv	uv	ADP
ejpam-3709	266	8	2u−v	2u−v	NUM
ejpam-3709	266	9	,	,	PUNCT
ejpam-3709	266	10	then	then	ADV
ejpam-3709	266	11	the	the	DET
ejpam-3709	266	12	electrocstatic	electrocstatic	ADJ
ejpam-3709	266	13	force	force	NOUN
ejpam-3709	266	14	of	of	ADP
ejpam-3709	266	15	attraction	attraction	NOUN
ejpam-3709	266	16	is	be	AUX
ejpam-3709	266	17	given	give	VERB
ejpam-3709	266	18	by	by	ADP
ejpam-3709	266	19	mq	mq	PROPN
ejpam-3709	266	20	(	(	PUNCT
ejpam-3709	266	21	uv	uv	PROPN
ejpam-3709	266	22	2u−	2u−	PROPN
ejpam-3709	266	23	v	v	NOUN
ejpam-3709	266	24	)	)	PUNCT
ejpam-3709	266	25	=	=	PUNCT
ejpam-3709	266	26	c(2u−	c(2u−	PROPN
ejpam-3709	266	27	v)2	v)2	PROPN
ejpam-3709	266	28	u2v2	u2v2	NOUN
ejpam-3709	266	29	.	.	PUNCT
ejpam-3709	267	1	then	then	ADV
ejpam-3709	267	2	using	use	VERB
ejpam-3709	267	3	equation	equation	NOUN
ejpam-3709	267	4	(	(	PUNCT
ejpam-3709	267	5	1	1	NUM
ejpam-3709	267	6	)	)	PUNCT
ejpam-3709	267	7	,	,	PUNCT
ejpam-3709	267	8	we	we	PRON
ejpam-3709	267	9	can	can	AUX
ejpam-3709	267	10	relate	relate	VERB
ejpam-3709	267	11	that	that	SCONJ
ejpam-3709	267	12	the	the	DET
ejpam-3709	267	13	sum	sum	NOUN
ejpam-3709	267	14	of	of	ADP
ejpam-3709	267	15	the	the	DET
ejpam-3709	267	16	above	above	ADJ
ejpam-3709	267	17	electrocstatic	electrocstatic	ADJ
ejpam-3709	267	18	forces	force	NOUN
ejpam-3709	267	19	of	of	ADP
ejpam-3709	267	20	attraction	attraction	NOUN
ejpam-3709	267	21	mq	mq	NOUN
ejpam-3709	267	22	(	(	PUNCT
ejpam-3709	267	23	uv	uv	NOUN
ejpam-3709	267	24	2u+v	2u+v	NUM
ejpam-3709	267	25	)	)	PUNCT
ejpam-3709	267	26	and	and	CCONJ
ejpam-3709	267	27	mq	mq	PROPN
ejpam-3709	267	28	(	(	PUNCT
ejpam-3709	267	29	uv	uv	NOUN
ejpam-3709	267	30	2u−v	2u−v	PROPN
ejpam-3709	267	31	)	)	PUNCT
ejpam-3709	267	32	is	be	AUX
ejpam-3709	267	33	given	give	VERB
ejpam-3709	267	34	by	by	ADP
ejpam-3709	267	35	the	the	DET
ejpam-3709	267	36	sum	sum	NOUN
ejpam-3709	267	37	of	of	ADP
ejpam-3709	267	38	electrocstatic	electrocstatic	ADJ
ejpam-3709	267	39	forces	force	NOUN
ejpam-3709	267	40	of	of	ADP
ejpam-3709	267	41	attraction	attraction	NOUN
ejpam-3709	267	42	2mq(u	2mq(u	NUM
ejpam-3709	267	43	)	)	PUNCT
ejpam-3709	267	44	=	=	SYM
ejpam-3709	267	45	2c	2c	NUM
ejpam-3709	267	46	u2	u2	NOUN
ejpam-3709	267	47	and	and	CCONJ
ejpam-3709	267	48	8mq(v	8mq(v	NUM
ejpam-3709	267	49	)	)	PUNCT
ejpam-3709	268	1	=	=	SYM
ejpam-3709	268	2	8c	8c	NUM
ejpam-3709	268	3	v2	v2	NOUN
ejpam-3709	268	4	.	.	PUNCT
ejpam-3709	269	1	hence	hence	ADV
ejpam-3709	269	2	equation	equation	NOUN
ejpam-3709	269	3	(	(	PUNCT
ejpam-3709	269	4	1	1	X
ejpam-3709	269	5	)	)	PUNCT
ejpam-3709	269	6	dealt	deal	VERB
ejpam-3709	269	7	in	in	ADP
ejpam-3709	269	8	this	this	DET
ejpam-3709	269	9	study	study	NOUN
ejpam-3709	269	10	can	can	AUX
ejpam-3709	269	11	be	be	AUX
ejpam-3709	269	12	associated	associate	VERB
ejpam-3709	269	13	with	with	ADP
ejpam-3709	269	14	the	the	DET
ejpam-3709	269	15	electrocstatic	electrocstatic	ADJ
ejpam-3709	269	16	forces	force	NOUN
ejpam-3709	269	17	of	of	ADP
ejpam-3709	269	18	attraction	attraction	NOUN
ejpam-3709	269	19	between	between	ADP
ejpam-3709	269	20	the	the	DET
ejpam-3709	269	21	charges	charge	NOUN
ejpam-3709	269	22	in	in	ADP
ejpam-3709	269	23	different	different	ADJ
ejpam-3709	269	24	situations	situation	NOUN
ejpam-3709	269	25	.	.	PUNCT
ejpam-3709	270	1	7	7	X
ejpam-3709	270	2	.	.	X
ejpam-3709	270	3	conclusion	conclusion	NOUN
ejpam-3709	270	4	in	in	ADP
ejpam-3709	270	5	this	this	DET
ejpam-3709	270	6	investigation	investigation	NOUN
ejpam-3709	270	7	,	,	PUNCT
ejpam-3709	270	8	we	we	PRON
ejpam-3709	270	9	introduced	introduce	VERB
ejpam-3709	270	10	a	a	DET
ejpam-3709	270	11	new	new	ADJ
ejpam-3709	270	12	reciprocal	reciprocal	ADJ
ejpam-3709	270	13	second	second	ADJ
ejpam-3709	270	14	power	power	NOUN
ejpam-3709	270	15	fe	fe	X
ejpam-3709	270	16	(	(	PUNCT
ejpam-3709	270	17	1	1	NUM
ejpam-3709	270	18	)	)	PUNCT
ejpam-3709	270	19	and	and	CCONJ
ejpam-3709	270	20	investigated	investigate	VERB
ejpam-3709	270	21	its	its	PRON
ejpam-3709	270	22	various	various	ADJ
ejpam-3709	270	23	classical	classical	ADJ
ejpam-3709	270	24	stability	stability	NOUN
ejpam-3709	270	25	results	result	NOUN
ejpam-3709	270	26	in	in	ADP
ejpam-3709	270	27	modular	modular	ADJ
ejpam-3709	270	28	spaces	space	NOUN
ejpam-3709	270	29	and	and	CCONJ
ejpam-3709	270	30	β	β	NOUN
ejpam-3709	270	31	-	-	ADJ
ejpam-3709	270	32	homogenous	homogenous	ADJ
ejpam-3709	270	33	spaces	space	NOUN
ejpam-3709	270	34	.	.	PUNCT
ejpam-3709	271	1	we	we	PRON
ejpam-3709	271	2	solved	solve	VERB
ejpam-3709	271	3	equation	equation	NOUN
ejpam-3709	271	4	(	(	PUNCT
ejpam-3709	271	5	1	1	NUM
ejpam-3709	271	6	)	)	PUNCT
ejpam-3709	271	7	for	for	ADP
ejpam-3709	271	8	its	its	PRON
ejpam-3709	271	9	solution	solution	NOUN
ejpam-3709	271	10	in	in	ADP
ejpam-3709	271	11	the	the	DET
ejpam-3709	271	12	setting	setting	NOUN
ejpam-3709	271	13	of	of	ADP
ejpam-3709	271	14	non	non	ADJ
ejpam-3709	271	15	-	-	ADJ
ejpam-3709	271	16	zero	zero	ADJ
ejpam-3709	271	17	real	real	ADJ
ejpam-3709	271	18	numbers	number	NOUN
ejpam-3709	271	19	.	.	PUNCT
ejpam-3709	272	1	we	we	PRON
ejpam-3709	272	2	associated	associate	VERB
ejpam-3709	272	3	equation	equation	NOUN
ejpam-3709	272	4	(	(	PUNCT
ejpam-3709	272	5	1	1	NUM
ejpam-3709	272	6	)	)	PUNCT
ejpam-3709	272	7	with	with	ADP
ejpam-3709	272	8	coloumb	coloumb	PROPN
ejpam-3709	272	9	’s	’s	PART
ejpam-3709	272	10	law	law	NOUN
ejpam-3709	272	11	to	to	PART
ejpam-3709	272	12	employ	employ	VERB
ejpam-3709	272	13	it	it	PRON
ejpam-3709	272	14	in	in	ADP
ejpam-3709	272	15	various	various	ADJ
ejpam-3709	272	16	situations	situation	NOUN
ejpam-3709	272	17	to	to	PART
ejpam-3709	272	18	connect	connect	VERB
ejpam-3709	272	19	the	the	DET
ejpam-3709	272	20	electrocstatic	electrocstatic	ADJ
ejpam-3709	272	21	forces	force	NOUN
ejpam-3709	272	22	of	of	ADP
ejpam-3709	272	23	attraction	attraction	NOUN
ejpam-3709	272	24	in	in	ADP
ejpam-3709	272	25	different	different	ADJ
ejpam-3709	272	26	assumptions	assumption	NOUN
ejpam-3709	272	27	.	.	PUNCT
ejpam-3709	273	1	acknowledgements	acknowledgement	NOUN
ejpam-3709	273	2	the	the	DET
ejpam-3709	273	3	authors	author	NOUN
ejpam-3709	273	4	are	be	AUX
ejpam-3709	273	5	thankful	thankful	ADJ
ejpam-3709	273	6	to	to	ADP
ejpam-3709	273	7	the	the	DET
ejpam-3709	273	8	referees	referee	NOUN
ejpam-3709	273	9	for	for	ADP
ejpam-3709	273	10	their	their	PRON
ejpam-3709	273	11	fruitful	fruitful	ADJ
ejpam-3709	273	12	comments	comment	NOUN
ejpam-3709	273	13	and	and	CCONJ
ejpam-3709	273	14	suggestions	suggestion	NOUN
ejpam-3709	273	15	.	.	PUNCT
ejpam-3709	274	1	references	reference	NOUN
ejpam-3709	274	2	[	[	X
ejpam-3709	274	3	1	1	X
ejpam-3709	274	4	]	]	PUNCT
ejpam-3709	274	5	i	i	PRON
ejpam-3709	274	6	amemiya	amemiya	NOUN
ejpam-3709	274	7	.	.	PUNCT
ejpam-3709	275	1	on	on	ADP
ejpam-3709	275	2	the	the	DET
ejpam-3709	275	3	representation	representation	NOUN
ejpam-3709	275	4	of	of	ADP
ejpam-3709	275	5	complemented	complemented	ADJ
ejpam-3709	275	6	modular	modular	ADJ
ejpam-3709	275	7	lattices	lattice	NOUN
ejpam-3709	275	8	.	.	PUNCT
ejpam-3709	276	1	j.	j.	PROPN
ejpam-3709	276	2	math	math	PROPN
ejpam-3709	276	3	.	.	PUNCT
ejpam-3709	277	1	soc	soc	PROPN
ejpam-3709	277	2	.	.	PUNCT
ejpam-3709	277	3	,	,	PUNCT
ejpam-3709	277	4	9:263–279	9:263–279	NOUN
ejpam-3709	277	5	,	,	PUNCT
ejpam-3709	277	6	1957	1957	NUM
ejpam-3709	277	7	.	.	PUNCT
ejpam-3709	278	1	[	[	X
ejpam-3709	278	2	2	2	NUM
ejpam-3709	278	3	]	]	PUNCT
ejpam-3709	278	4	a	a	DET
ejpam-3709	278	5	bodaghi	bodaghi	NOUN
ejpam-3709	278	6	and	and	CCONJ
ejpam-3709	278	7	b	b	PROPN
ejpam-3709	278	8	v	v	PROPN
ejpam-3709	278	9	senthil	senthil	PROPN
ejpam-3709	278	10	kumar	kumar	PROPN
ejpam-3709	278	11	.	.	PUNCT
ejpam-3709	278	12	estimation	estimation	NOUN
ejpam-3709	278	13	of	of	ADP
ejpam-3709	278	14	inexact	inexact	ADJ
ejpam-3709	278	15	reciprocal	reciprocal	ADJ
ejpam-3709	278	16	-	-	PUNCT
ejpam-3709	278	17	quintic	quintic	ADJ
ejpam-3709	278	18	and	and	CCONJ
ejpam-3709	278	19	reciprocal	reciprocal	ADJ
ejpam-3709	278	20	-	-	PUNCT
ejpam-3709	278	21	sextic	sextic	ADJ
ejpam-3709	278	22	functional	functional	ADJ
ejpam-3709	278	23	equations	equation	NOUN
ejpam-3709	278	24	.	.	PUNCT
ejpam-3709	279	1	mathematica	mathematica	PROPN
ejpam-3709	279	2	,	,	PUNCT
ejpam-3709	279	3	49(82)1	49(82)1	PROPN
ejpam-3709	279	4	-	-	PUNCT
ejpam-3709	279	5	2:3–14	2:3–14	NUM
ejpam-3709	279	6	,	,	PUNCT
ejpam-3709	279	7	2017	2017	NUM
ejpam-3709	279	8	.	.	PUNCT
ejpam-3709	280	1	[	[	X
ejpam-3709	280	2	3	3	X
ejpam-3709	280	3	]	]	X
ejpam-3709	280	4	k	k	PROPN
ejpam-3709	280	5	cieplinski	cieplinski	PROPN
ejpam-3709	280	6	.	.	PUNCT
ejpam-3709	281	1	applications	application	NOUN
ejpam-3709	281	2	of	of	ADP
ejpam-3709	281	3	fixed	fix	VERB
ejpam-3709	281	4	point	point	NOUN
ejpam-3709	281	5	theorems	theorem	NOUN
ejpam-3709	281	6	to	to	ADP
ejpam-3709	281	7	the	the	DET
ejpam-3709	281	8	hyers	hyers	PROPN
ejpam-3709	281	9	-	-	PUNCT
ejpam-3709	281	10	ulam	ulam	ADJ
ejpam-3709	281	11	stability	stability	NOUN
ejpam-3709	281	12	of	of	ADP
ejpam-3709	281	13	functional	functional	ADJ
ejpam-3709	281	14	equations	equation	NOUN
ejpam-3709	281	15	-	-	PUNCT
ejpam-3709	281	16	a	a	DET
ejpam-3709	281	17	survey	survey	NOUN
ejpam-3709	281	18	.	.	PUNCT
ejpam-3709	282	1	ann	ann	PROPN
ejpam-3709	282	2	.	.	PUNCT
ejpam-3709	282	3	funct	funct	PROPN
ejpam-3709	282	4	.	.	PUNCT
ejpam-3709	283	1	anal	anal	PROPN
ejpam-3709	283	2	.	.	PROPN
ejpam-3709	283	3	,	,	PUNCT
ejpam-3709	283	4	3:151–164	3:151–164	NOUN
ejpam-3709	283	5	,	,	PUNCT
ejpam-3709	283	6	2012	2012	NUM
ejpam-3709	283	7	.	.	PUNCT
ejpam-3709	284	1	[	[	X
ejpam-3709	284	2	4	4	NUM
ejpam-3709	284	3	]	]	X
ejpam-3709	284	4	h	h	NOUN
ejpam-3709	284	5	dutta	dutta	PROPN
ejpam-3709	284	6	and	and	CCONJ
ejpam-3709	284	7	b	b	PROPN
ejpam-3709	284	8	v	v	NUM
ejpam-3709	284	9	senthil	senthil	PROPN
ejpam-3709	284	10	kumar	kumar	PROPN
ejpam-3709	284	11	.	.	PUNCT
ejpam-3709	285	1	geometrical	geometrical	ADJ
ejpam-3709	285	2	elucidations	elucidation	NOUN
ejpam-3709	285	3	and	and	CCONJ
ejpam-3709	285	4	approximation	approximation	NOUN
ejpam-3709	285	5	of	of	ADP
ejpam-3709	285	6	some	some	DET
ejpam-3709	285	7	functional	functional	ADJ
ejpam-3709	285	8	equations	equation	NOUN
ejpam-3709	285	9	in	in	ADP
ejpam-3709	285	10	numerous	numerous	ADJ
ejpam-3709	285	11	variables	variable	NOUN
ejpam-3709	285	12	.	.	PUNCT
ejpam-3709	286	1	proc	proc	NOUN
ejpam-3709	286	2	.	.	PUNCT
ejpam-3709	287	1	indian	indian	PROPN
ejpam-3709	287	2	natn	natn	PROPN
ejpam-3709	287	3	.	.	PUNCT
ejpam-3709	288	1	sc	sc	PROPN
ejpam-3709	288	2	.	.	PUNCT
ejpam-3709	288	3	acad	acad	PROPN
ejpam-3709	288	4	.	.	PROPN
ejpam-3709	288	5	,	,	PUNCT
ejpam-3709	288	6	85(3):603	85(3):603	NOUN
ejpam-3709	288	7	–	–	PUNCT
ejpam-3709	288	8	611	611	NUM
ejpam-3709	288	9	,	,	PUNCT
ejpam-3709	288	10	2019	2019	NUM
ejpam-3709	288	11	.	.	PUNCT
ejpam-3709	289	1	references	reference	NOUN
ejpam-3709	289	2	1174	1174	NUM
ejpam-3709	290	1	[	[	X
ejpam-3709	290	2	5	5	X
ejpam-3709	290	3	]	]	X
ejpam-3709	290	4	p	p	PROPN
ejpam-3709	290	5	găvruta	găvruta	PROPN
ejpam-3709	290	6	.	.	PUNCT
ejpam-3709	291	1	a	a	DET
ejpam-3709	291	2	generalization	generalization	NOUN
ejpam-3709	291	3	of	of	ADP
ejpam-3709	291	4	the	the	DET
ejpam-3709	291	5	hyers	hyers	PROPN
ejpam-3709	291	6	-	-	PUNCT
ejpam-3709	291	7	ulam	ulam	ADJ
ejpam-3709	291	8	-	-	PUNCT
ejpam-3709	291	9	rassias	rassias	PROPN
ejpam-3709	291	10	stability	stability	NOUN
ejpam-3709	291	11	of	of	ADP
ejpam-3709	291	12	approximately	approximately	ADV
ejpam-3709	291	13	additive	additive	ADJ
ejpam-3709	291	14	mapppings	mappping	NOUN
ejpam-3709	291	15	.	.	PUNCT
ejpam-3709	292	1	j.	j.	PROPN
ejpam-3709	292	2	math	math	PROPN
ejpam-3709	292	3	.	.	PUNCT
ejpam-3709	293	1	anal	anal	PROPN
ejpam-3709	293	2	.	.	PUNCT
ejpam-3709	294	1	appl	appl	PROPN
ejpam-3709	294	2	.	.	PROPN
ejpam-3709	294	3	,	,	PUNCT
ejpam-3709	294	4	184:431–436	184:431–436	NUM
ejpam-3709	294	5	,	,	PUNCT
ejpam-3709	294	6	1994	1994	NUM
ejpam-3709	294	7	.	.	PUNCT
ejpam-3709	295	1	[	[	X
ejpam-3709	295	2	6	6	NUM
ejpam-3709	295	3	]	]	PUNCT
ejpam-3709	295	4	d	d	PROPN
ejpam-3709	295	5	h	h	PROPN
ejpam-3709	295	6	hyers	hyer	NOUN
ejpam-3709	295	7	.	.	PUNCT
ejpam-3709	296	1	on	on	ADP
ejpam-3709	296	2	the	the	DET
ejpam-3709	296	3	stability	stability	NOUN
ejpam-3709	296	4	of	of	ADP
ejpam-3709	296	5	the	the	DET
ejpam-3709	296	6	linear	linear	ADJ
ejpam-3709	296	7	functional	functional	ADJ
ejpam-3709	296	8	equation	equation	NOUN
ejpam-3709	296	9	.	.	PUNCT
ejpam-3709	297	1	proc	proc	NOUN
ejpam-3709	297	2	.	.	PUNCT
ejpam-3709	298	1	nat	nat	PROPN
ejpam-3709	298	2	.	.	PUNCT
ejpam-3709	299	1	acad	acad	PROPN
ejpam-3709	299	2	.	.	PUNCT
ejpam-3709	300	1	sci	sci	PROPN
ejpam-3709	300	2	.	.	PUNCT
ejpam-3709	300	3	u.s.a	u.s.a	PROPN
ejpam-3709	300	4	.	.	PROPN
ejpam-3709	300	5	,	,	PUNCT
ejpam-3709	300	6	27:222–224	27:222–224	NUM
ejpam-3709	300	7	,	,	PUNCT
ejpam-3709	300	8	1941	1941	NUM
ejpam-3709	300	9	.	.	PUNCT
ejpam-3709	301	1	[	[	X
ejpam-3709	301	2	7	7	NUM
ejpam-3709	301	3	]	]	X
ejpam-3709	301	4	m	m	VERB
ejpam-3709	301	5	a	a	DET
ejpam-3709	301	6	khamsi	khamsi	NOUN
ejpam-3709	301	7	.	.	PUNCT
ejpam-3709	302	1	quasicontraction	quasicontraction	NOUN
ejpam-3709	302	2	mappings	mapping	NOUN
ejpam-3709	302	3	in	in	ADP
ejpam-3709	302	4	modular	modular	ADJ
ejpam-3709	302	5	spaces	space	NOUN
ejpam-3709	302	6	without	without	ADP
ejpam-3709	302	7	δ2	δ2	VERB
ejpam-3709	302	8	-	-	PUNCT
ejpam-3709	302	9	condition	condition	NOUN
ejpam-3709	302	10	.	.	PUNCT
ejpam-3709	303	1	fixed	fix	VERB
ejpam-3709	303	2	point	point	NOUN
ejpam-3709	303	3	theory	theory	NOUN
ejpam-3709	303	4	appl	appl	PROPN
ejpam-3709	303	5	.	.	PROPN
ejpam-3709	303	6	,	,	PUNCT
ejpam-3709	303	7	art	art	NOUN
ejpam-3709	303	8	.	.	PUNCT
ejpam-3709	304	1	i	i	PRON
ejpam-3709	304	2	d	d	PROPN
ejpam-3709	304	3	916187:1–6	916187:1–6	PROPN
ejpam-3709	304	4	,	,	PUNCT
ejpam-3709	304	5	2008	2008	NUM
ejpam-3709	304	6	.	.	PUNCT
ejpam-3709	305	1	[	[	X
ejpam-3709	305	2	8	8	NUM
ejpam-3709	305	3	]	]	SYM
ejpam-3709	305	4	s	s	PART
ejpam-3709	305	5	o	o	X
ejpam-3709	305	6	kim	kim	PROPN
ejpam-3709	305	7	,	,	PUNCT
ejpam-3709	305	8	b	b	PROPN
ejpam-3709	305	9	v	v	NUM
ejpam-3709	305	10	senthil	senthil	PROPN
ejpam-3709	305	11	kumar	kumar	PROPN
ejpam-3709	305	12	,	,	PUNCT
ejpam-3709	305	13	and	and	CCONJ
ejpam-3709	305	14	a	a	DET
ejpam-3709	305	15	bodaghi	bodaghi	NOUN
ejpam-3709	305	16	.	.	PUNCT
ejpam-3709	306	1	stability	stability	NOUN
ejpam-3709	306	2	and	and	CCONJ
ejpam-3709	306	3	non	non	ADJ
ejpam-3709	306	4	-	-	NOUN
ejpam-3709	306	5	stability	stability	NOUN
ejpam-3709	306	6	of	of	ADP
ejpam-3709	306	7	the	the	DET
ejpam-3709	306	8	reciprocal	reciprocal	ADJ
ejpam-3709	306	9	-	-	PUNCT
ejpam-3709	306	10	cubic	cubic	ADJ
ejpam-3709	306	11	and	and	CCONJ
ejpam-3709	306	12	reciprocal	reciprocal	ADJ
ejpam-3709	306	13	-	-	PUNCT
ejpam-3709	306	14	quartic	quartic	ADJ
ejpam-3709	306	15	functional	functional	ADJ
ejpam-3709	306	16	equations	equation	NOUN
ejpam-3709	306	17	in	in	ADP
ejpam-3709	306	18	non	non	ADJ
ejpam-3709	306	19	-	-	ADJ
ejpam-3709	306	20	archimedean	archimedean	ADJ
ejpam-3709	306	21	fields	field	NOUN
ejpam-3709	306	22	.	.	PUNCT
ejpam-3709	307	1	adv	adv	PROPN
ejpam-3709	307	2	.	.	PUNCT
ejpam-3709	307	3	difference	difference	PROPN
ejpam-3709	307	4	equ	equ	PROPN
ejpam-3709	307	5	.	.	PROPN
ejpam-3709	307	6	,	,	PUNCT
ejpam-3709	307	7	77:1–12	77:1–12	NOUN
ejpam-3709	307	8	,	,	PUNCT
ejpam-3709	307	9	2017	2017	NUM
ejpam-3709	307	10	.	.	PUNCT
ejpam-3709	308	1	[	[	X
ejpam-3709	308	2	9	9	NUM
ejpam-3709	308	3	]	]	X
ejpam-3709	308	4	s	s	PART
ejpam-3709	308	5	koshi	koshi	PROPN
ejpam-3709	308	6	and	and	CCONJ
ejpam-3709	308	7	t	t	PROPN
ejpam-3709	308	8	shimogaki	shimogaki	PROPN
ejpam-3709	308	9	.	.	PUNCT
ejpam-3709	309	1	on	on	ADP
ejpam-3709	309	2	f	f	PROPN
ejpam-3709	309	3	-norms	-norm	NOUN
ejpam-3709	309	4	of	of	ADP
ejpam-3709	309	5	quasi	quasi	ADJ
ejpam-3709	309	6	-	-	ADJ
ejpam-3709	309	7	modular	modular	ADJ
ejpam-3709	309	8	spaces	space	NOUN
ejpam-3709	309	9	.	.	PUNCT
ejpam-3709	310	1	j.	j.	PROPN
ejpam-3709	310	2	fac	fac	PROPN
ejpam-3709	310	3	.	.	PUNCT
ejpam-3709	311	1	sci	sci	PROPN
ejpam-3709	311	2	.	.	PROPN
ejpam-3709	311	3	,	,	PUNCT
ejpam-3709	311	4	hokkaido	hokkaido	PROPN
ejpam-3709	311	5	univ	univ	PROPN
ejpam-3709	311	6	.	.	PROPN
ejpam-3709	311	7	,	,	PUNCT
ejpam-3709	311	8	ser	ser	PROPN
ejpam-3709	311	9	.	.	PROPN
ejpam-3709	311	10	,	,	PUNCT
ejpam-3709	311	11	15:202–218	15:202–218	PROPN
ejpam-3709	311	12	,	,	PUNCT
ejpam-3709	311	13	1961	1961	NUM
ejpam-3709	311	14	.	.	PUNCT
ejpam-3709	312	1	[	[	X
ejpam-3709	312	2	10	10	NUM
ejpam-3709	312	3	]	]	X
ejpam-3709	312	4	m	m	NOUN
ejpam-3709	312	5	krbec	krbec	NOUN
ejpam-3709	312	6	.	.	PUNCT
ejpam-3709	313	1	modular	modular	ADJ
ejpam-3709	313	2	interpolation	interpolation	NOUN
ejpam-3709	313	3	spaces	space	NOUN
ejpam-3709	313	4	.	.	PUNCT
ejpam-3709	314	1	i.	i.	PROPN
ejpam-3709	314	2	z.	z.	PROPN
ejpam-3709	314	3	anal	anal	PROPN
ejpam-3709	314	4	.	.	PUNCT
ejpam-3709	315	1	anwend	anwend	PROPN
ejpam-3709	315	2	.	.	PUNCT
ejpam-3709	315	3	,	,	PUNCT
ejpam-3709	315	4	1:25–40	1:25–40	NUM
ejpam-3709	315	5	,	,	PUNCT
ejpam-3709	315	6	1982	1982	NUM
ejpam-3709	315	7	.	.	PUNCT
ejpam-3709	316	1	[	[	X
ejpam-3709	316	2	11	11	NUM
ejpam-3709	316	3	]	]	SYM
ejpam-3709	316	4	b	b	X
ejpam-3709	316	5	v	v	NUM
ejpam-3709	316	6	senthil	senthil	PROPN
ejpam-3709	316	7	kumar	kumar	PROPN
ejpam-3709	316	8	and	and	CCONJ
ejpam-3709	316	9	h	h	PROPN
ejpam-3709	316	10	dutta	dutta	PROPN
ejpam-3709	316	11	.	.	PUNCT
ejpam-3709	317	1	non	non	ADJ
ejpam-3709	317	2	-	-	ADJ
ejpam-3709	317	3	archimedean	archimedean	ADJ
ejpam-3709	317	4	stability	stability	NOUN
ejpam-3709	317	5	of	of	ADP
ejpam-3709	317	6	a	a	DET
ejpam-3709	317	7	generalized	generalized	ADJ
ejpam-3709	317	8	reciprocal	reciprocal	ADJ
ejpam-3709	317	9	-	-	PUNCT
ejpam-3709	317	10	quadratic	quadratic	ADJ
ejpam-3709	317	11	functional	functional	ADJ
ejpam-3709	317	12	equation	equation	NOUN
ejpam-3709	317	13	in	in	ADP
ejpam-3709	317	14	several	several	ADJ
ejpam-3709	317	15	variables	variable	NOUN
ejpam-3709	317	16	by	by	ADP
ejpam-3709	317	17	direct	direct	ADJ
ejpam-3709	317	18	and	and	CCONJ
ejpam-3709	317	19	fixed	fix	VERB
ejpam-3709	317	20	point	point	NOUN
ejpam-3709	317	21	methods	method	NOUN
ejpam-3709	317	22	.	.	PUNCT
ejpam-3709	318	1	filomat	filomat	PROPN
ejpam-3709	318	2	.	.	PROPN
ejpam-3709	318	3	,	,	PUNCT
ejpam-3709	318	4	32(9):3199–3209	32(9):3199–3209	NUM
ejpam-3709	318	5	,	,	PUNCT
ejpam-3709	318	6	2018	2018	NUM
ejpam-3709	318	7	.	.	PUNCT
ejpam-3709	319	1	[	[	X
ejpam-3709	319	2	12	12	NUM
ejpam-3709	319	3	]	]	X
ejpam-3709	319	4	b	b	X
ejpam-3709	319	5	v	v	NUM
ejpam-3709	319	6	senthil	senthil	PROPN
ejpam-3709	319	7	kumar	kumar	PROPN
ejpam-3709	319	8	and	and	CCONJ
ejpam-3709	319	9	h	h	PROPN
ejpam-3709	319	10	dutta	dutta	PROPN
ejpam-3709	319	11	.	.	PUNCT
ejpam-3709	320	1	approximation	approximation	NOUN
ejpam-3709	320	2	of	of	ADP
ejpam-3709	320	3	multiplicative	multiplicative	ADJ
ejpam-3709	320	4	inverse	inverse	NOUN
ejpam-3709	320	5	undecic	undecic	NOUN
ejpam-3709	320	6	and	and	CCONJ
ejpam-3709	320	7	duodecic	duodecic	VERB
ejpam-3709	320	8	functional	functional	ADJ
ejpam-3709	320	9	equations	equation	NOUN
ejpam-3709	320	10	.	.	PUNCT
ejpam-3709	321	1	math	math	NOUN
ejpam-3709	321	2	.	.	PUNCT
ejpam-3709	322	1	meth	meth	NOUN
ejpam-3709	322	2	.	.	PUNCT
ejpam-3709	323	1	appl	appl	PROPN
ejpam-3709	323	2	.	.	PUNCT
ejpam-3709	324	1	sci	sci	PROPN
ejpam-3709	324	2	.	.	PROPN
ejpam-3709	324	3	,	,	PUNCT
ejpam-3709	324	4	42:1073–1081	42:1073–1081	NUM
ejpam-3709	324	5	,	,	PUNCT
ejpam-3709	324	6	2019	2019	NUM
ejpam-3709	324	7	.	.	PUNCT
ejpam-3709	325	1	[	[	X
ejpam-3709	325	2	13	13	NUM
ejpam-3709	325	3	]	]	SYM
ejpam-3709	325	4	b	b	X
ejpam-3709	325	5	v	v	NUM
ejpam-3709	325	6	senthil	senthil	PROPN
ejpam-3709	325	7	kumar	kumar	PROPN
ejpam-3709	325	8	and	and	CCONJ
ejpam-3709	325	9	h	h	PROPN
ejpam-3709	325	10	dutta	dutta	PROPN
ejpam-3709	325	11	.	.	PUNCT
ejpam-3709	325	12	fuzzy	fuzzy	ADJ
ejpam-3709	325	13	stability	stability	NOUN
ejpam-3709	325	14	of	of	ADP
ejpam-3709	325	15	a	a	DET
ejpam-3709	325	16	rational	rational	ADJ
ejpam-3709	325	17	functional	functional	ADJ
ejpam-3709	325	18	equation	equation	NOUN
ejpam-3709	325	19	and	and	CCONJ
ejpam-3709	325	20	its	its	PRON
ejpam-3709	325	21	relevance	relevance	NOUN
ejpam-3709	325	22	to	to	ADP
ejpam-3709	325	23	system	system	NOUN
ejpam-3709	325	24	design	design	NOUN
ejpam-3709	325	25	.	.	PUNCT
ejpam-3709	326	1	int	int	NOUN
ejpam-3709	326	2	.	.	PUNCT
ejpam-3709	327	1	j.	j.	PROPN
ejpam-3709	327	2	general	general	PROPN
ejpam-3709	327	3	syst	syst	PROPN
ejpam-3709	327	4	.	.	PROPN
ejpam-3709	327	5	,	,	PUNCT
ejpam-3709	327	6	38(2):157–169	38(2):157–169	PROPN
ejpam-3709	327	7	,	,	PUNCT
ejpam-3709	327	8	2019	2019	NUM
ejpam-3709	327	9	.	.	PUNCT
ejpam-3709	328	1	[	[	X
ejpam-3709	328	2	14	14	NUM
ejpam-3709	328	3	]	]	SYM
ejpam-3709	328	4	b	b	X
ejpam-3709	328	5	v	v	NUM
ejpam-3709	328	6	senthil	senthil	PROPN
ejpam-3709	328	7	kumar	kumar	PROPN
ejpam-3709	328	8	and	and	CCONJ
ejpam-3709	328	9	h	h	PROPN
ejpam-3709	328	10	dutta	dutta	PROPN
ejpam-3709	328	11	.	.	PUNCT
ejpam-3709	329	1	fundamental	fundamental	ADJ
ejpam-3709	329	2	stabilities	stability	NOUN
ejpam-3709	329	3	of	of	ADP
ejpam-3709	329	4	various	various	ADJ
ejpam-3709	329	5	forms	form	NOUN
ejpam-3709	329	6	of	of	ADP
ejpam-3709	329	7	complex	complex	ADJ
ejpam-3709	329	8	valued	value	VERB
ejpam-3709	329	9	functional	functional	ADJ
ejpam-3709	329	10	equations	equation	NOUN
ejpam-3709	329	11	.	.	PUNCT
ejpam-3709	330	1	in	in	ADP
ejpam-3709	330	2	h.	h.	PROPN
ejpam-3709	330	3	dutta	dutta	PROPN
ejpam-3709	330	4	and	and	CCONJ
ejpam-3709	330	5	j.	j.	PROPN
ejpam-3709	330	6	peters	peters	PROPN
ejpam-3709	330	7	,	,	PUNCT
ejpam-3709	330	8	editors	editor	NOUN
ejpam-3709	330	9	,	,	PUNCT
ejpam-3709	330	10	applied	apply	VERB
ejpam-3709	330	11	mathematical	mathematical	ADJ
ejpam-3709	330	12	analysis	analysis	NOUN
ejpam-3709	330	13	:	:	PUNCT
ejpam-3709	330	14	theory	theory	NOUN
ejpam-3709	330	15	,	,	PUNCT
ejpam-3709	330	16	methods	method	NOUN
ejpam-3709	330	17	,	,	PUNCT
ejpam-3709	330	18	and	and	CCONJ
ejpam-3709	330	19	applications	application	NOUN
ejpam-3709	330	20	.	.	PUNCT
ejpam-3709	331	1	studies	study	NOUN
ejpam-3709	331	2	in	in	ADP
ejpam-3709	331	3	systems	system	NOUN
ejpam-3709	331	4	,	,	PUNCT
ejpam-3709	331	5	decision	decision	NOUN
ejpam-3709	331	6	and	and	CCONJ
ejpam-3709	331	7	contro	contro	PROPN
ejpam-3709	331	8	.	.	PROPN
ejpam-3709	331	9	,	,	PUNCT
ejpam-3709	331	10	volume	volume	NOUN
ejpam-3709	331	11	177	177	NUM
ejpam-3709	331	12	.	.	PUNCT
ejpam-3709	332	1	springer	springer	NOUN
ejpam-3709	332	2	,	,	PUNCT
ejpam-3709	332	3	cham	cham	PROPN
ejpam-3709	332	4	,	,	PUNCT
ejpam-3709	332	5	2020	2020	NUM
ejpam-3709	332	6	.	.	PUNCT
ejpam-3709	333	1	[	[	X
ejpam-3709	333	2	15	15	NUM
ejpam-3709	333	3	]	]	X
ejpam-3709	333	4	b	b	X
ejpam-3709	333	5	v	v	NUM
ejpam-3709	333	6	senthil	senthil	PROPN
ejpam-3709	333	7	kumar	kumar	PROPN
ejpam-3709	333	8	,	,	PUNCT
ejpam-3709	333	9	h	h	PROPN
ejpam-3709	333	10	dutta	dutta	PROPN
ejpam-3709	333	11	,	,	PUNCT
ejpam-3709	333	12	and	and	CCONJ
ejpam-3709	333	13	s.	s.	PROPN
ejpam-3709	333	14	sabarinathan	sabarinathan	PROPN
ejpam-3709	333	15	.	.	PUNCT
ejpam-3709	334	1	approximation	approximation	NOUN
ejpam-3709	334	2	of	of	ADP
ejpam-3709	334	3	a	a	DET
ejpam-3709	334	4	system	system	NOUN
ejpam-3709	334	5	of	of	ADP
ejpam-3709	334	6	rational	rational	ADJ
ejpam-3709	334	7	functional	functional	ADJ
ejpam-3709	334	8	equations	equation	NOUN
ejpam-3709	334	9	of	of	ADP
ejpam-3709	334	10	three	three	NUM
ejpam-3709	334	11	variables	variable	NOUN
ejpam-3709	334	12	.	.	PUNCT
ejpam-3709	335	1	int	int	NOUN
ejpam-3709	335	2	.	.	PUNCT
ejpam-3709	336	1	j.	j.	PROPN
ejpam-3709	336	2	appl	appl	PROPN
ejpam-3709	336	3	.	.	PUNCT
ejpam-3709	337	1	comput	comput	PROPN
ejpam-3709	337	2	.	.	PUNCT
ejpam-3709	338	1	math	math	NOUN
ejpam-3709	338	2	.	.	PUNCT
ejpam-3709	338	3	,	,	PUNCT
ejpam-3709	338	4	5(3):1	5(3):1	NUM
ejpam-3709	338	5	–	–	PUNCT
ejpam-3709	338	6	16	16	NUM
ejpam-3709	338	7	,	,	PUNCT
ejpam-3709	338	8	2019	2019	NUM
ejpam-3709	338	9	.	.	PUNCT
ejpam-3709	339	1	[	[	X
ejpam-3709	339	2	16	16	NUM
ejpam-3709	339	3	]	]	X
ejpam-3709	339	4	w	w	ADP
ejpam-3709	339	5	a	a	DET
ejpam-3709	339	6	luxemburg	luxemburg	NOUN
ejpam-3709	339	7	.	.	PUNCT
ejpam-3709	340	1	banach	banach	NOUN
ejpam-3709	340	2	function	function	NOUN
ejpam-3709	340	3	spaces	space	VERB
ejpam-3709	340	4	.	.	PUNCT
ejpam-3709	341	1	phd	phd	NOUN
ejpam-3709	341	2	thesis	thesis	PROPN
ejpam-3709	341	3	,	,	PUNCT
ejpam-3709	341	4	delft	delft	PROPN
ejpam-3709	341	5	university	university	PROPN
ejpam-3709	341	6	of	of	ADP
ejpam-3709	341	7	technology	technology	PROPN
ejpam-3709	341	8	,	,	PUNCT
ejpam-3709	341	9	delft	delft	NOUN
ejpam-3709	341	10	,	,	PUNCT
ejpam-3709	341	11	the	the	DET
ejpam-3709	341	12	netherlands	netherlands	PROPN
ejpam-3709	341	13	,	,	PUNCT
ejpam-3709	341	14	1959	1959	NUM
ejpam-3709	341	15	.	.	PUNCT
ejpam-3709	342	1	[	[	X
ejpam-3709	342	2	17	17	NUM
ejpam-3709	342	3	]	]	X
ejpam-3709	342	4	l	l	NOUN
ejpam-3709	342	5	maligranda	maligranda	PROPN
ejpam-3709	342	6	.	.	PUNCT
ejpam-3709	343	1	orlicz	orlicz	PROPN
ejpam-3709	343	2	spaces	space	NOUN
ejpam-3709	343	3	and	and	CCONJ
ejpam-3709	343	4	interpolation	interpolation	NOUN
ejpam-3709	343	5	.	.	PUNCT
ejpam-3709	344	1	seminarios	seminarios	PROPN
ejpam-3709	344	2	de	de	PROPN
ejpam-3709	344	3	mathematica	mathematica	PROPN
ejpam-3709	344	4	,	,	PUNCT
ejpam-3709	344	5	5	5	NUM
ejpam-3709	344	6	,	,	PUNCT
ejpam-3709	344	7	universidade	universidade	PROPN
ejpam-3709	344	8	estadual	estadual	PROPN
ejpam-3709	344	9	de	de	PROPN
ejpam-3709	344	10	campinas	campinas	PROPN
ejpam-3709	344	11	,	,	PUNCT
ejpam-3709	344	12	departamento	departamento	PROPN
ejpam-3709	344	13	de	de	PROPN
ejpam-3709	344	14	matematica	matematica	PROPN
ejpam-3709	344	15	,	,	PUNCT
ejpam-3709	344	16	campinas	campinas	PROPN
ejpam-3709	344	17	,	,	PUNCT
ejpam-3709	344	18	1989	1989	NUM
ejpam-3709	344	19	.	.	PUNCT
ejpam-3709	345	1	[	[	X
ejpam-3709	345	2	18	18	NUM
ejpam-3709	345	3	]	]	SYM
ejpam-3709	345	4	b	b	NOUN
ejpam-3709	345	5	mazur	mazur	PROPN
ejpam-3709	345	6	.	.	PUNCT
ejpam-3709	346	1	modular	modular	ADJ
ejpam-3709	346	2	cuves	cuve	NOUN
ejpam-3709	346	3	and	and	CCONJ
ejpam-3709	346	4	the	the	DET
ejpam-3709	346	5	eisenstein	eisenstein	PROPN
ejpam-3709	346	6	ideal	ideal	NOUN
ejpam-3709	346	7	.	.	PUNCT
ejpam-3709	347	1	publ	publ	PROPN
ejpam-3709	347	2	.	.	PUNCT
ejpam-3709	348	1	math	math	NOUN
ejpam-3709	348	2	.	.	PUNCT
ejpam-3709	349	1	ihes	ihe	NOUN
ejpam-3709	349	2	.	.	PUNCT
ejpam-3709	349	3	,	,	PUNCT
ejpam-3709	349	4	47:33–186	47:33–186	NUM
ejpam-3709	349	5	,	,	PUNCT
ejpam-3709	349	6	1978	1978	NUM
ejpam-3709	349	7	.	.	PUNCT
ejpam-3709	350	1	[	[	X
ejpam-3709	350	2	19	19	NUM
ejpam-3709	350	3	]	]	X
ejpam-3709	350	4	j	j	PROPN
ejpam-3709	350	5	musielak	musielak	PROPN
ejpam-3709	350	6	.	.	PUNCT
ejpam-3709	351	1	orlicz	orlicz	PROPN
ejpam-3709	351	2	spaces	space	NOUN
ejpam-3709	351	3	and	and	CCONJ
ejpam-3709	351	4	modular	modular	ADJ
ejpam-3709	351	5	spaces	space	NOUN
ejpam-3709	351	6	.	.	PUNCT
ejpam-3709	352	1	springer	springer	NOUN
ejpam-3709	352	2	,	,	PUNCT
ejpam-3709	352	3	berlin	berlin	PROPN
ejpam-3709	352	4	,	,	PUNCT
ejpam-3709	352	5	1983	1983	NUM
ejpam-3709	352	6	.	.	PUNCT
ejpam-3709	353	1	references	reference	NOUN
ejpam-3709	353	2	1175	1175	NUM
ejpam-3709	354	1	[	[	X
ejpam-3709	354	2	20	20	NUM
ejpam-3709	354	3	]	]	X
ejpam-3709	354	4	h	h	PROPN
ejpam-3709	354	5	nakano	nakano	PROPN
ejpam-3709	354	6	.	.	PUNCT
ejpam-3709	355	1	modulared	modulare	VERB
ejpam-3709	355	2	semi	semi	ADJ
ejpam-3709	355	3	-	-	ADJ
ejpam-3709	355	4	ordered	ordered	ADJ
ejpam-3709	355	5	linear	linear	ADJ
ejpam-3709	355	6	spaces	space	NOUN
ejpam-3709	355	7	.	.	PUNCT
ejpam-3709	356	1	maruzen	maruzen	PROPN
ejpam-3709	356	2	,	,	PUNCT
ejpam-3709	356	3	tokyo	tokyo	PROPN
ejpam-3709	356	4	,	,	PUNCT
ejpam-3709	356	5	1950	1950	NUM
ejpam-3709	356	6	.	.	PUNCT
ejpam-3709	357	1	[	[	X
ejpam-3709	357	2	21	21	NUM
ejpam-3709	357	3	]	]	X
ejpam-3709	357	4	w	w	NOUN
ejpam-3709	357	5	orlicz	orlicz	NOUN
ejpam-3709	357	6	.	.	PUNCT
ejpam-3709	358	1	collected	collect	VERB
ejpam-3709	358	2	papers	paper	NOUN
ejpam-3709	358	3	.	.	PUNCT
ejpam-3709	359	1	pwn	pwn	PROPN
ejpam-3709	359	2	,	,	PUNCT
ejpam-3709	359	3	warszawa	warszawa	PROPN
ejpam-3709	359	4	,	,	PUNCT
ejpam-3709	359	5	1988	1988	NUM
ejpam-3709	359	6	.	.	PUNCT
ejpam-3709	360	1	[	[	X
ejpam-3709	360	2	22	22	NUM
ejpam-3709	360	3	]	]	PUNCT
ejpam-3709	360	4	z	z	NOUN
ejpam-3709	360	5	pales	pale	NOUN
ejpam-3709	360	6	.	.	PUNCT
ejpam-3709	361	1	generalized	generalized	ADJ
ejpam-3709	361	2	stability	stability	NOUN
ejpam-3709	361	3	of	of	ADP
ejpam-3709	361	4	the	the	DET
ejpam-3709	361	5	cauchy	cauchy	ADJ
ejpam-3709	361	6	functional	functional	ADJ
ejpam-3709	361	7	equation	equation	NOUN
ejpam-3709	361	8	.	.	PUNCT
ejpam-3709	362	1	aequ	aequ	PROPN
ejpam-3709	362	2	.	.	PUNCT
ejpam-3709	363	1	math	math	PROPN
ejpam-3709	363	2	.	.	PUNCT
ejpam-3709	363	3	,	,	PUNCT
ejpam-3709	363	4	56:222	56:222	NUM
ejpam-3709	363	5	–	–	PUNCT
ejpam-3709	363	6	232	232	NUM
ejpam-3709	363	7	,	,	PUNCT
ejpam-3709	363	8	1998	1998	NUM
ejpam-3709	363	9	.	.	PUNCT
ejpam-3709	364	1	[	[	X
ejpam-3709	364	2	23	23	NUM
ejpam-3709	364	3	]	]	SYM
ejpam-3709	364	4	v	v	X
ejpam-3709	364	5	radu	radu	PROPN
ejpam-3709	364	6	.	.	PUNCT
ejpam-3709	365	1	the	the	DET
ejpam-3709	365	2	fixed	fixed	ADJ
ejpam-3709	365	3	point	point	NOUN
ejpam-3709	365	4	alternative	alternative	NOUN
ejpam-3709	365	5	and	and	CCONJ
ejpam-3709	365	6	the	the	DET
ejpam-3709	365	7	stability	stability	NOUN
ejpam-3709	365	8	of	of	ADP
ejpam-3709	365	9	functional	functional	ADJ
ejpam-3709	365	10	equations	equation	NOUN
ejpam-3709	365	11	.	.	PUNCT
ejpam-3709	366	1	fixed	fix	VERB
ejpam-3709	366	2	point	point	NOUN
ejpam-3709	366	3	theory	theory	NOUN
ejpam-3709	366	4	.	.	PUNCT
ejpam-3709	366	5	,	,	PUNCT
ejpam-3709	366	6	4:91–96	4:91–96	NOUN
ejpam-3709	366	7	,	,	PUNCT
ejpam-3709	366	8	2003	2003	NUM
ejpam-3709	366	9	.	.	PUNCT
ejpam-3709	367	1	[	[	X
ejpam-3709	367	2	24	24	NUM
ejpam-3709	367	3	]	]	X
ejpam-3709	367	4	j	j	PROPN
ejpam-3709	367	5	m	m	NOUN
ejpam-3709	367	6	rassias	rassias	PROPN
ejpam-3709	367	7	.	.	PUNCT
ejpam-3709	368	1	on	on	ADP
ejpam-3709	368	2	approximately	approximately	ADV
ejpam-3709	368	3	of	of	ADP
ejpam-3709	368	4	approximately	approximately	ADV
ejpam-3709	368	5	linear	linear	ADJ
ejpam-3709	368	6	mappings	mapping	NOUN
ejpam-3709	368	7	by	by	ADP
ejpam-3709	368	8	linear	linear	ADJ
ejpam-3709	368	9	mappings	mapping	NOUN
ejpam-3709	368	10	.	.	PUNCT
ejpam-3709	369	1	j.	j.	PROPN
ejpam-3709	369	2	funct	funct	PROPN
ejpam-3709	369	3	.	.	PUNCT
ejpam-3709	370	1	anal	anal	PROPN
ejpam-3709	370	2	.	.	PROPN
ejpam-3709	370	3	,	,	PUNCT
ejpam-3709	370	4	46:126–130	46:126–130	PROPN
ejpam-3709	370	5	,	,	PUNCT
ejpam-3709	370	6	1982	1982	NUM
ejpam-3709	370	7	.	.	PUNCT
ejpam-3709	371	1	[	[	X
ejpam-3709	371	2	25	25	NUM
ejpam-3709	371	3	]	]	X
ejpam-3709	371	4	t	t	PROPN
ejpam-3709	371	5	m	m	NOUN
ejpam-3709	371	6	rassias	rassias	PROPN
ejpam-3709	371	7	.	.	PUNCT
ejpam-3709	372	1	on	on	ADP
ejpam-3709	372	2	the	the	DET
ejpam-3709	372	3	stability	stability	NOUN
ejpam-3709	372	4	of	of	ADP
ejpam-3709	372	5	the	the	DET
ejpam-3709	372	6	linear	linear	ADJ
ejpam-3709	372	7	mapping	mapping	NOUN
ejpam-3709	372	8	in	in	ADP
ejpam-3709	372	9	banach	banach	NOUN
ejpam-3709	372	10	spaces	space	NOUN
ejpam-3709	372	11	.	.	PUNCT
ejpam-3709	373	1	proc	proc	NOUN
ejpam-3709	373	2	.	.	PUNCT
ejpam-3709	374	1	amer	amer	PROPN
ejpam-3709	374	2	.	.	PUNCT
ejpam-3709	374	3	math	math	PROPN
ejpam-3709	374	4	.	.	PUNCT
ejpam-3709	375	1	soc	soc	PROPN
ejpam-3709	375	2	.	.	PUNCT
ejpam-3709	375	3	,	,	PUNCT
ejpam-3709	375	4	72:297–300	72:297–300	PROPN
ejpam-3709	375	5	,	,	PUNCT
ejpam-3709	375	6	1978	1978	NUM
ejpam-3709	375	7	.	.	PUNCT
ejpam-3709	376	1	[	[	X
ejpam-3709	376	2	26	26	NUM
ejpam-3709	376	3	]	]	X
ejpam-3709	376	4	g	g	PROPN
ejpam-3709	376	5	sadeghi	sadeghi	PROPN
ejpam-3709	376	6	.	.	PUNCT
ejpam-3709	377	1	a	a	DET
ejpam-3709	377	2	fixed	fix	VERB
ejpam-3709	377	3	point	point	NOUN
ejpam-3709	377	4	approach	approach	NOUN
ejpam-3709	377	5	to	to	ADP
ejpam-3709	377	6	stability	stability	NOUN
ejpam-3709	377	7	of	of	ADP
ejpam-3709	377	8	functional	functional	ADJ
ejpam-3709	377	9	equations	equation	NOUN
ejpam-3709	377	10	in	in	ADP
ejpam-3709	377	11	modular	modular	ADJ
ejpam-3709	377	12	spaces	space	NOUN
ejpam-3709	377	13	.	.	PUNCT
ejpam-3709	378	1	bull	bull	NOUN
ejpam-3709	378	2	.	.	PUNCT
ejpam-3709	379	1	malays	malays	PROPN
ejpam-3709	379	2	.	.	PUNCT
ejpam-3709	380	1	math	math	NOUN
ejpam-3709	380	2	.	.	PUNCT
ejpam-3709	381	1	sci	sci	PROPN
ejpam-3709	381	2	.	.	PROPN
ejpam-3709	381	3	soc	soc	PROPN
ejpam-3709	381	4	.	.	PUNCT
ejpam-3709	381	5	,	,	PUNCT
ejpam-3709	381	6	37(2):333–344	37(2):333–344	PROPN
ejpam-3709	381	7	,	,	PUNCT
ejpam-3709	381	8	2014	2014	NUM
ejpam-3709	381	9	.	.	PUNCT
ejpam-3709	382	1	[	[	X
ejpam-3709	382	2	27	27	NUM
ejpam-3709	382	3	]	]	SYM
ejpam-3709	382	4	l	l	NOUN
ejpam-3709	382	5	szekelyhidi	szekelyhidi	NOUN
ejpam-3709	382	6	.	.	PUNCT
ejpam-3709	383	1	note	note	NOUN
ejpam-3709	383	2	on	on	ADP
ejpam-3709	383	3	a	a	DET
ejpam-3709	383	4	stability	stability	NOUN
ejpam-3709	383	5	theorem	theorem	VERB
ejpam-3709	383	6	.	.	PUNCT
ejpam-3709	384	1	can	can	AUX
ejpam-3709	384	2	.	.	PUNCT
ejpam-3709	385	1	math	math	NOUN
ejpam-3709	385	2	.	.	PUNCT
ejpam-3709	386	1	bull	bull	PROPN
ejpam-3709	386	2	.	.	PUNCT
ejpam-3709	386	3	,	,	PUNCT
ejpam-3709	387	1	25:500–501	25:500–501	NUM
ejpam-3709	387	2	,	,	PUNCT
ejpam-3709	387	3	1982	1982	NUM
ejpam-3709	387	4	.	.	PUNCT
ejpam-3709	388	1	[	[	X
ejpam-3709	388	2	28	28	NUM
ejpam-3709	388	3	]	]	X
ejpam-3709	388	4	j	j	PROPN
ejpam-3709	388	5	tabor	tabor	PROPN
ejpam-3709	388	6	.	.	PUNCT
ejpam-3709	389	1	general	general	ADJ
ejpam-3709	389	2	stability	stability	NOUN
ejpam-3709	389	3	of	of	ADP
ejpam-3709	389	4	functional	functional	ADJ
ejpam-3709	389	5	equations	equation	NOUN
ejpam-3709	389	6	of	of	ADP
ejpam-3709	389	7	linear	linear	PROPN
ejpam-3709	389	8	type	type	NOUN
ejpam-3709	389	9	.	.	PUNCT
ejpam-3709	390	1	j.	j.	PROPN
ejpam-3709	390	2	math	math	PROPN
ejpam-3709	390	3	.	.	PUNCT
ejpam-3709	391	1	anal	anal	PROPN
ejpam-3709	391	2	.	.	PUNCT
ejpam-3709	392	1	appl	appl	PROPN
ejpam-3709	392	2	.	.	PROPN
ejpam-3709	392	3	,	,	PUNCT
ejpam-3709	392	4	328:192–200	328:192–200	NUM
ejpam-3709	392	5	,	,	PUNCT
ejpam-3709	392	6	2007	2007	NUM
ejpam-3709	392	7	.	.	PUNCT
ejpam-3709	393	1	[	[	X
ejpam-3709	393	2	29	29	NUM
ejpam-3709	393	3	]	]	X
ejpam-3709	393	4	p	p	X
ejpam-3709	393	5	turpin	turpin	NOUN
ejpam-3709	393	6	.	.	PUNCT
ejpam-3709	394	1	fubini	fubini	ADJ
ejpam-3709	394	2	inequalities	inequality	NOUN
ejpam-3709	394	3	and	and	CCONJ
ejpam-3709	394	4	bounded	bound	VERB
ejpam-3709	394	5	multiplier	multipli	ADJ
ejpam-3709	394	6	property	property	NOUN
ejpam-3709	394	7	in	in	ADP
ejpam-3709	394	8	generalized	generalized	ADJ
ejpam-3709	394	9	modular	modular	ADJ
ejpam-3709	394	10	spaces	space	NOUN
ejpam-3709	394	11	.	.	PUNCT
ejpam-3709	395	1	comment	comment	NOUN
ejpam-3709	395	2	.	.	PUNCT
ejpam-3709	396	1	math	math	NOUN
ejpam-3709	396	2	.	.	PUNCT
ejpam-3709	396	3	,	,	PUNCT
ejpam-3709	396	4	1:331–353	1:331–353	PROPN
ejpam-3709	396	5	,	,	PUNCT
ejpam-3709	396	6	1978	1978	NUM
ejpam-3709	396	7	.	.	PUNCT
ejpam-3709	397	1	[	[	X
ejpam-3709	397	2	30	30	NUM
ejpam-3709	397	3	]	]	SYM
ejpam-3709	397	4	s	s	NOUN
ejpam-3709	397	5	m	m	NOUN
ejpam-3709	397	6	ulam	ulam	PROPN
ejpam-3709	397	7	.	.	PUNCT
ejpam-3709	397	8	problems	problem	NOUN
ejpam-3709	397	9	in	in	ADP
ejpam-3709	397	10	modern	modern	ADJ
ejpam-3709	397	11	mathematics	mathematic	NOUN
ejpam-3709	397	12	.	.	PUNCT
ejpam-3709	398	1	wiley	wiley	PROPN
ejpam-3709	398	2	-	-	PUNCT
ejpam-3709	398	3	interscience	interscience	PROPN
ejpam-3709	398	4	,	,	PUNCT
ejpam-3709	398	5	new	new	PROPN
ejpam-3709	398	6	york	york	PROPN
ejpam-3709	398	7	,	,	PUNCT
ejpam-3709	398	8	1964	1964	NUM
ejpam-3709	398	9	.	.	PUNCT
ejpam-3709	399	1	[	[	X
ejpam-3709	399	2	31	31	NUM
ejpam-3709	399	3	]	]	X
ejpam-3709	399	4	k	k	PROPN
ejpam-3709	399	5	wongkum	wongkum	NOUN
ejpam-3709	399	6	,	,	PUNCT
ejpam-3709	399	7	p	p	NOUN
ejpam-3709	399	8	chaipunya	chaipunya	NOUN
ejpam-3709	399	9	,	,	PUNCT
ejpam-3709	399	10	and	and	CCONJ
ejpam-3709	399	11	p	p	NOUN
ejpam-3709	399	12	kumam	kumam	NOUN
ejpam-3709	399	13	.	.	PUNCT
ejpam-3709	400	1	on	on	ADP
ejpam-3709	400	2	the	the	DET
ejpam-3709	400	3	generalized	generalize	VERB
ejpam-3709	400	4	ulam	ulam	PROPN
ejpam-3709	400	5	-	-	PUNCT
ejpam-3709	400	6	hyers	hyer	NOUN
ejpam-3709	400	7	-	-	PUNCT
ejpam-3709	400	8	rassias	rassias	PROPN
ejpam-3709	400	9	stability	stability	NOUN
ejpam-3709	400	10	of	of	ADP
ejpam-3709	400	11	quadratic	quadratic	ADJ
ejpam-3709	400	12	mappings	mapping	NOUN
ejpam-3709	400	13	in	in	ADP
ejpam-3709	400	14	modular	modular	ADJ
ejpam-3709	400	15	spaces	space	NOUN
ejpam-3709	400	16	without	without	ADP
ejpam-3709	400	17	δ2	δ2	VERB
ejpam-3709	400	18	-	-	PUNCT
ejpam-3709	400	19	conditions	condition	NOUN
ejpam-3709	400	20	.	.	PUNCT
ejpam-3709	401	1	j.	j.	PROPN
ejpam-3709	401	2	funct	funct	PROPN
ejpam-3709	401	3	.	.	PUNCT
ejpam-3709	402	1	spaces	space	NOUN
ejpam-3709	402	2	.	.	PUNCT
ejpam-3709	402	3	,	,	PUNCT
ejpam-3709	402	4	art	art	NOUN
ejpam-3709	402	5	.	.	PUNCT
ejpam-3709	403	1	i	i	PRON
ejpam-3709	403	2	d	d	PROPN
ejpam-3709	403	3	461719:1–6	461719:1–6	PROPN
ejpam-3709	403	4	,	,	PUNCT
ejpam-3709	403	5	2015	2015	NUM
ejpam-3709	403	6	.	.	PUNCT
ejpam-3709	404	1	[	[	X
ejpam-3709	404	2	32	32	NUM
ejpam-3709	404	3	]	]	PUNCT
ejpam-3709	404	4	s	s	VERB
ejpam-3709	404	5	yamamuro	yamamuro	NOUN
ejpam-3709	404	6	.	.	PUNCT
ejpam-3709	405	1	on	on	ADP
ejpam-3709	405	2	conjugate	conjugate	ADJ
ejpam-3709	405	3	spaces	space	NOUN
ejpam-3709	405	4	of	of	ADP
ejpam-3709	405	5	nakano	nakano	PROPN
ejpam-3709	405	6	spaces	space	NOUN
ejpam-3709	405	7	.	.	PUNCT
ejpam-3709	406	1	trans	trans	PROPN
ejpam-3709	406	2	am	be	AUX
ejpam-3709	406	3	.	.	PUNCT
ejpam-3709	407	1	math	math	NOUN
ejpam-3709	407	2	.	.	PUNCT
ejpam-3709	408	1	soc	soc	PROPN
ejpam-3709	408	2	.	.	PUNCT
ejpam-3709	408	3	,	,	PUNCT
ejpam-3709	408	4	90:291	90:291	NUM
ejpam-3709	408	5	–	–	PUNCT
ejpam-3709	408	6	311	311	NUM
ejpam-3709	408	7	,	,	PUNCT
ejpam-3709	408	8	1959	1959	NUM
ejpam-3709	408	9	.	.	PUNCT