id	sid	tid	token	lemma	pos
ejpam-5761	1	1	european	european	PROPN
ejpam-5761	1	2	journal	journal	PROPN
ejpam-5761	1	3	of	of	ADP
ejpam-5761	1	4	pure	pure	ADJ
ejpam-5761	1	5	and	and	CCONJ
ejpam-5761	1	6	applied	applied	ADJ
ejpam-5761	1	7	mathematics	mathematic	NOUN
ejpam-5761	1	8	2025	2025	NUM
ejpam-5761	1	9	,	,	PUNCT
ejpam-5761	1	10	vol	vol	NOUN
ejpam-5761	1	11	.	.	PROPN
ejpam-5761	1	12	18	18	NUM
ejpam-5761	1	13	,	,	PUNCT
ejpam-5761	1	14	issue	issue	NOUN
ejpam-5761	1	15	1	1	NUM
ejpam-5761	1	16	,	,	PUNCT
ejpam-5761	1	17	article	article	NOUN
ejpam-5761	1	18	number	number	NOUN
ejpam-5761	1	19	5761	5761	NUM
ejpam-5761	1	20	issn	issn	PROPN
ejpam-5761	1	21	1307	1307	NUM
ejpam-5761	1	22	-	-	SYM
ejpam-5761	1	23	5543	5543	NUM
ejpam-5761	1	24	–	–	PUNCT
ejpam-5761	1	25	ejpam.com	ejpam.com	X
ejpam-5761	1	26	published	publish	VERB
ejpam-5761	1	27	by	by	ADP
ejpam-5761	1	28	new	new	PROPN
ejpam-5761	1	29	york	york	PROPN
ejpam-5761	1	30	business	business	PROPN
ejpam-5761	1	31	global	global	PROPN
ejpam-5761	1	32	subordinate	subordinate	ADJ
ejpam-5761	1	33	average	average	ADJ
ejpam-5761	1	34	structures	structure	NOUN
ejpam-5761	1	35	on	on	ADP
ejpam-5761	1	36	random	random	ADJ
ejpam-5761	1	37	walks	walk	NOUN
ejpam-5761	1	38	m.	m.	NOUN
ejpam-5761	1	39	surya	surya	PROPN
ejpam-5761	2	1	priya1	priya1	PROPN
ejpam-5761	2	2	,	,	PUNCT
ejpam-5761	2	3	n.	n.	PROPN
ejpam-5761	2	4	nathiya1,∗	nathiya1,∗	PROPN
ejpam-5761	2	5	1	1	NUM
ejpam-5761	2	6	department	department	NOUN
ejpam-5761	2	7	of	of	ADP
ejpam-5761	2	8	mathematics	mathematic	NOUN
ejpam-5761	2	9	,	,	PUNCT
ejpam-5761	2	10	vellore	vellore	PROPN
ejpam-5761	2	11	institute	institute	PROPN
ejpam-5761	2	12	of	of	ADP
ejpam-5761	2	13	technology	technology	PROPN
ejpam-5761	2	14	chennai	chennai	PROPN
ejpam-5761	2	15	,	,	PUNCT
ejpam-5761	2	16	tamilnadu	tamilnadu	NOUN
ejpam-5761	2	17	,	,	PUNCT
ejpam-5761	2	18	india	india	PROPN
ejpam-5761	2	19	abstract	abstract	NOUN
ejpam-5761	2	20	.	.	PUNCT
ejpam-5761	3	1	in	in	ADP
ejpam-5761	3	2	a	a	DET
ejpam-5761	3	3	random	random	ADJ
ejpam-5761	3	4	walk	walk	NOUN
ejpam-5761	3	5	{	{	PUNCT
ejpam-5761	3	6	n	n	CCONJ
ejpam-5761	3	7	,	,	PUNCT
ejpam-5761	3	8	p(x	p(x	PROPN
ejpam-5761	3	9	,	,	PUNCT
ejpam-5761	3	10	y	y	NOUN
ejpam-5761	3	11	)	)	PUNCT
ejpam-5761	3	12	}	}	PUNCT
ejpam-5761	3	13	where	where	SCONJ
ejpam-5761	3	14	n	n	PRON
ejpam-5761	3	15	is	be	AUX
ejpam-5761	3	16	an	an	DET
ejpam-5761	3	17	infinite	infinite	ADJ
ejpam-5761	3	18	graph	graph	NOUN
ejpam-5761	3	19	and	and	CCONJ
ejpam-5761	3	20	{	{	PUNCT
ejpam-5761	3	21	p(x	p(x	PROPN
ejpam-5761	3	22	,	,	PUNCT
ejpam-5761	3	23	y	y	NOUN
ejpam-5761	3	24	)	)	PUNCT
ejpam-5761	3	25	}	}	PUNCT
ejpam-5761	3	26	is	be	AUX
ejpam-5761	3	27	a	a	DET
ejpam-5761	3	28	set	set	NOUN
ejpam-5761	3	29	of	of	ADP
ejpam-5761	3	30	transition	transition	NOUN
ejpam-5761	3	31	probabilities	probability	NOUN
ejpam-5761	3	32	,	,	PUNCT
ejpam-5761	3	33	if	if	SCONJ
ejpam-5761	3	34	{	{	PUNCT
ejpam-5761	3	35	p′	p′	NOUN
ejpam-5761	3	36	(	(	PUNCT
ejpam-5761	3	37	x	x	NOUN
ejpam-5761	3	38	,	,	PUNCT
ejpam-5761	3	39	y	y	NOUN
ejpam-5761	3	40	)	)	PUNCT
ejpam-5761	3	41	}	}	PUNCT
ejpam-5761	3	42	is	be	AUX
ejpam-5761	3	43	another	another	DET
ejpam-5761	3	44	set	set	VERB
ejpam-5761	3	45	subordinate	subordinate	NOUN
ejpam-5761	3	46	to	to	ADP
ejpam-5761	3	47	the	the	DET
ejpam-5761	3	48	set	set	NOUN
ejpam-5761	3	49	{	{	PUNCT
ejpam-5761	3	50	p(x	p(x	PROPN
ejpam-5761	3	51	,	,	PUNCT
ejpam-5761	3	52	y	y	NOUN
ejpam-5761	3	53	)	)	PUNCT
ejpam-5761	3	54	}	}	PUNCT
ejpam-5761	3	55	such	such	ADJ
ejpam-5761	3	56	that	that	SCONJ
ejpam-5761	3	57	p	p	NOUN
ejpam-5761	3	58	′	′	X
ejpam-5761	3	59	(	(	PUNCT
ejpam-5761	3	60	x	x	NOUN
ejpam-5761	3	61	,	,	PUNCT
ejpam-5761	3	62	y	y	NOUN
ejpam-5761	3	63	)	)	PUNCT
ejpam-5761	3	64	≤	≤	NOUN
ejpam-5761	3	65	p(x	p(x	PROPN
ejpam-5761	3	66	,	,	PUNCT
ejpam-5761	3	67	y	y	NOUN
ejpam-5761	3	68	)	)	PUNCT
ejpam-5761	3	69	for	for	ADP
ejpam-5761	3	70	all	all	DET
ejpam-5761	3	71	pairs	pair	NOUN
ejpam-5761	3	72	(	(	PUNCT
ejpam-5761	3	73	x	x	NOUN
ejpam-5761	3	74	,	,	PUNCT
ejpam-5761	3	75	y	y	PROPN
ejpam-5761	3	76	)	)	PUNCT
ejpam-5761	3	77	and	and	CCONJ
ejpam-5761	4	1	p	p	NOUN
ejpam-5761	4	2	′	′	NOUN
ejpam-5761	4	3	(	(	PUNCT
ejpam-5761	4	4	x	x	NOUN
ejpam-5761	4	5	,	,	PUNCT
ejpam-5761	4	6	y	y	NOUN
ejpam-5761	4	7	)	)	PUNCT
ejpam-5761	4	8	<	<	X
ejpam-5761	4	9	p(x	p(x	PROPN
ejpam-5761	4	10	,	,	PUNCT
ejpam-5761	4	11	y	y	NOUN
ejpam-5761	4	12	)	)	PUNCT
ejpam-5761	4	13	for	for	ADP
ejpam-5761	4	14	atleast	atleast	ADJ
ejpam-5761	4	15	one	one	NUM
ejpam-5761	4	16	pair	pair	NOUN
ejpam-5761	4	17	(	(	PUNCT
ejpam-5761	4	18	x	x	NOUN
ejpam-5761	4	19	,	,	PUNCT
ejpam-5761	4	20	y	y	PROPN
ejpam-5761	4	21	)	)	PUNCT
ejpam-5761	4	22	,	,	PUNCT
ejpam-5761	4	23	then	then	ADV
ejpam-5761	4	24	{	{	PUNCT
ejpam-5761	4	25	n	n	X
ejpam-5761	4	26	,	,	PUNCT
ejpam-5761	4	27	p	p	NOUN
ejpam-5761	4	28	′	′	NOUN
ejpam-5761	4	29	(	(	PUNCT
ejpam-5761	4	30	x	x	NOUN
ejpam-5761	4	31	,	,	PUNCT
ejpam-5761	4	32	y	y	NOUN
ejpam-5761	4	33	)	)	PUNCT
ejpam-5761	4	34	}	}	PUNCT
ejpam-5761	4	35	can	can	AUX
ejpam-5761	4	36	be	be	AUX
ejpam-5761	4	37	identified	identify	VERB
ejpam-5761	4	38	as	as	ADP
ejpam-5761	4	39	a	a	DET
ejpam-5761	4	40	schrödinger	schrödinger	NOUN
ejpam-5761	4	41	network	network	NOUN
ejpam-5761	4	42	.	.	PUNCT
ejpam-5761	5	1	in	in	ADP
ejpam-5761	5	2	general	general	ADJ
ejpam-5761	5	3	,	,	PUNCT
ejpam-5761	5	4	we	we	PRON
ejpam-5761	5	5	consider	consider	VERB
ejpam-5761	5	6	the	the	DET
ejpam-5761	5	7	random	random	ADJ
ejpam-5761	5	8	walk	walk	NOUN
ejpam-5761	5	9	{	{	PUNCT
ejpam-5761	5	10	n	n	CCONJ
ejpam-5761	5	11	,	,	PUNCT
ejpam-5761	5	12	p	p	NOUN
ejpam-5761	5	13	′	′	NOUN
ejpam-5761	5	14	}	}	PUNCT
ejpam-5761	5	15	which	which	PRON
ejpam-5761	5	16	is	be	AUX
ejpam-5761	5	17	subordinate	subordinate	ADJ
ejpam-5761	5	18	to	to	ADP
ejpam-5761	5	19	{	{	PUNCT
ejpam-5761	5	20	n	n	CCONJ
ejpam-5761	5	21	,	,	PUNCT
ejpam-5761	5	22	p	p	X
ejpam-5761	5	23	}	}	PUNCT
ejpam-5761	5	24	and	and	CCONJ
ejpam-5761	5	25	discuss	discuss	VERB
ejpam-5761	5	26	the	the	DET
ejpam-5761	5	27	relation	relation	NOUN
ejpam-5761	5	28	between	between	ADP
ejpam-5761	5	29	the	the	DET
ejpam-5761	5	30	classes	class	NOUN
ejpam-5761	5	31	of	of	ADP
ejpam-5761	5	32	superaverage	superaverage	NOUN
ejpam-5761	5	33	functions	function	NOUN
ejpam-5761	5	34	defined	define	VERB
ejpam-5761	5	35	by	by	ADP
ejpam-5761	5	36	the	the	DET
ejpam-5761	5	37	transition	transition	NOUN
ejpam-5761	5	38	probabilities	probability	NOUN
ejpam-5761	5	39	sets	set	VERB
ejpam-5761	5	40	{	{	PUNCT
ejpam-5761	5	41	p(x	p(x	PROPN
ejpam-5761	5	42	,	,	PUNCT
ejpam-5761	5	43	y	y	NOUN
ejpam-5761	5	44	)	)	PUNCT
ejpam-5761	5	45	}	}	PUNCT
ejpam-5761	5	46	and	and	CCONJ
ejpam-5761	5	47	{	{	PUNCT
ejpam-5761	5	48	p′	p′	NOUN
ejpam-5761	5	49	(	(	PUNCT
ejpam-5761	5	50	x	x	NOUN
ejpam-5761	5	51	,	,	PUNCT
ejpam-5761	5	52	y	y	PROPN
ejpam-5761	5	53	)	)	PUNCT
ejpam-5761	5	54	}	}	PUNCT
ejpam-5761	5	55	.	.	PUNCT
ejpam-5761	6	1	moreover	moreover	ADV
ejpam-5761	6	2	,	,	PUNCT
ejpam-5761	6	3	we	we	PRON
ejpam-5761	6	4	define	define	VERB
ejpam-5761	6	5	{	{	PUNCT
ejpam-5761	6	6	n	n	CCONJ
ejpam-5761	6	7	,	,	PUNCT
ejpam-5761	6	8	p	p	NOUN
ejpam-5761	6	9	′	′	NOUN
ejpam-5761	6	10	}	}	PUNCT
ejpam-5761	6	11	as	as	ADP
ejpam-5761	6	12	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	6	13	if	if	SCONJ
ejpam-5761	6	14	0	0	NUM
ejpam-5761	6	15	is	be	AUX
ejpam-5761	6	16	the	the	DET
ejpam-5761	6	17	only	only	ADJ
ejpam-5761	6	18	bounded	bound	VERB
ejpam-5761	6	19	p	p	NOUN
ejpam-5761	6	20	′	′	NUM
ejpam-5761	6	21	-average	-average	NOUN
ejpam-5761	6	22	function	function	NOUN
ejpam-5761	6	23	on	on	ADP
ejpam-5761	6	24	n	n	PRON
ejpam-5761	6	25	and	and	CCONJ
ejpam-5761	6	26	study	study	VERB
ejpam-5761	6	27	various	various	ADJ
ejpam-5761	6	28	potential	potential	ADJ
ejpam-5761	6	29	-	-	PUNCT
ejpam-5761	6	30	theoretic	theoretic	ADJ
ejpam-5761	6	31	properties	property	NOUN
ejpam-5761	6	32	of	of	ADP
ejpam-5761	6	33	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	6	34	networks	network	NOUN
ejpam-5761	6	35	.	.	PUNCT
ejpam-5761	7	1	we	we	PRON
ejpam-5761	7	2	also	also	ADV
ejpam-5761	7	3	give	give	VERB
ejpam-5761	7	4	equivalent	equivalent	ADJ
ejpam-5761	7	5	conditions	condition	NOUN
ejpam-5761	7	6	for	for	ADP
ejpam-5761	7	7	a	a	DET
ejpam-5761	7	8	random	random	ADJ
ejpam-5761	7	9	walk	walk	NOUN
ejpam-5761	7	10	to	to	PART
ejpam-5761	7	11	be	be	AUX
ejpam-5761	7	12	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	7	13	.	.	PUNCT
ejpam-5761	8	1	finally	finally	ADV
ejpam-5761	8	2	,	,	PUNCT
ejpam-5761	8	3	we	we	PRON
ejpam-5761	8	4	discuss	discuss	VERB
ejpam-5761	8	5	the	the	DET
ejpam-5761	8	6	relation	relation	NOUN
ejpam-5761	8	7	between	between	ADP
ejpam-5761	8	8	bounded	bounded	PROPN
ejpam-5761	8	9	p	p	X
ejpam-5761	8	10	′	′	NOUN
ejpam-5761	8	11	and	and	CCONJ
ejpam-5761	8	12	p	p	NOUN
ejpam-5761	8	13	-average	-average	NOUN
ejpam-5761	8	14	functions	function	NOUN
ejpam-5761	8	15	.	.	PUNCT
ejpam-5761	9	1	2020	2020	NUM
ejpam-5761	9	2	mathematics	mathematic	NOUN
ejpam-5761	9	3	subject	subject	NOUN
ejpam-5761	9	4	classifications	classification	NOUN
ejpam-5761	9	5	:	:	PUNCT
ejpam-5761	9	6	31c20	31c20	NUM
ejpam-5761	9	7	,	,	PUNCT
ejpam-5761	9	8	31c05	31c05	NUM
ejpam-5761	9	9	,	,	PUNCT
ejpam-5761	9	10	60j45	60j45	NUM
ejpam-5761	9	11	key	key	ADJ
ejpam-5761	9	12	words	word	NOUN
ejpam-5761	9	13	and	and	CCONJ
ejpam-5761	9	14	phrases	phrase	NOUN
ejpam-5761	9	15	:	:	PUNCT
ejpam-5761	9	16	superaverage	superaverage	NOUN
ejpam-5761	9	17	functions	function	NOUN
ejpam-5761	9	18	,	,	PUNCT
ejpam-5761	9	19	subordinate	subordinate	ADJ
ejpam-5761	9	20	structure	structure	NOUN
ejpam-5761	9	21	,	,	PUNCT
ejpam-5761	9	22	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	9	23	,	,	PUNCT
ejpam-5761	9	24	p	p	NOUN
ejpam-5761	9	25	′	′	NUM
ejpam-5761	9	26	green	green	PROPN
ejpam-5761	9	27	’s	’s	PART
ejpam-5761	9	28	potential	potential	NOUN
ejpam-5761	9	29	,	,	PUNCT
ejpam-5761	9	30	bounded	bound	VERB
ejpam-5761	9	31	p	p	NOUN
ejpam-5761	9	32	and	and	CCONJ
ejpam-5761	9	33	p	p	NOUN
ejpam-5761	9	34	′	′	NOUN
ejpam-5761	9	35	functions	function	NOUN
ejpam-5761	9	36	1	1	NUM
ejpam-5761	9	37	.	.	PUNCT
ejpam-5761	10	1	introduction	introduction	NOUN
ejpam-5761	10	2	in	in	ADP
ejpam-5761	10	3	the	the	DET
ejpam-5761	10	4	state	state	NOUN
ejpam-5761	10	5	space	space	NOUN
ejpam-5761	10	6	n	n	NOUN
ejpam-5761	10	7	=	=	PUNCT
ejpam-5761	10	8	{	{	PUNCT
ejpam-5761	10	9	0	0	NUM
ejpam-5761	10	10	,	,	PUNCT
ejpam-5761	10	11	1	1	NUM
ejpam-5761	10	12	,	,	PUNCT
ejpam-5761	10	13	2	2	NUM
ejpam-5761	10	14	,	,	PUNCT
ejpam-5761	10	15	....	....	PUNCT
ejpam-5761	10	16	}	}	PUNCT
ejpam-5761	10	17	with	with	ADP
ejpam-5761	10	18	the	the	DET
ejpam-5761	10	19	set	set	NOUN
ejpam-5761	10	20	p	p	X
ejpam-5761	10	21	=	=	X
ejpam-5761	10	22	{	{	PUNCT
ejpam-5761	10	23	p(x	p(x	PROPN
ejpam-5761	10	24	,	,	PUNCT
ejpam-5761	10	25	y	y	NOUN
ejpam-5761	10	26	)	)	PUNCT
ejpam-5761	10	27	}	}	PUNCT
ejpam-5761	10	28	of	of	ADP
ejpam-5761	10	29	transition	transition	NOUN
ejpam-5761	10	30	probabilities	probability	NOUN
ejpam-5761	10	31	given	give	VERB
ejpam-5761	10	32	by	by	ADP
ejpam-5761	10	33	p(n	p(n	PROPN
ejpam-5761	10	34	,	,	PUNCT
ejpam-5761	10	35	n	n	NOUN
ejpam-5761	10	36	+	+	NOUN
ejpam-5761	10	37	1	1	NUM
ejpam-5761	10	38	)	)	PUNCT
ejpam-5761	10	39	=	=	SYM
ejpam-5761	10	40	αn	αn	NOUN
ejpam-5761	10	41	,	,	PUNCT
ejpam-5761	10	42	p(n	p(n	PROPN
ejpam-5761	10	43	,	,	PUNCT
ejpam-5761	10	44	n	n	CCONJ
ejpam-5761	10	45	−	−	PROPN
ejpam-5761	10	46	1	1	NUM
ejpam-5761	10	47	)	)	PUNCT
ejpam-5761	10	48	=	=	SYM
ejpam-5761	10	49	βn	βn	NOUN
ejpam-5761	10	50	,	,	PUNCT
ejpam-5761	10	51	for	for	ADP
ejpam-5761	10	52	n	n	PRON
ejpam-5761	10	53	≥	≥	NUM
ejpam-5761	10	54	1	1	NUM
ejpam-5761	10	55	,	,	PUNCT
ejpam-5761	10	56	αn	αn	VERB
ejpam-5761	10	57	,	,	PUNCT
ejpam-5761	10	58	βn	βn	X
ejpam-5761	10	59	>	>	X
ejpam-5761	10	60	0	0	NUM
ejpam-5761	10	61	,	,	PUNCT
ejpam-5761	10	62	αn	αn	NOUN
ejpam-5761	11	1	+	+	CCONJ
ejpam-5761	11	2	βn	βn	ADJ
ejpam-5761	11	3	≤	≤	NUM
ejpam-5761	11	4	1	1	NUM
ejpam-5761	11	5	and	and	CCONJ
ejpam-5761	11	6	0	0	NUM
ejpam-5761	11	7	≤	≤	NUM
ejpam-5761	11	8	p(0	p(0	NOUN
ejpam-5761	11	9	,	,	PUNCT
ejpam-5761	11	10	1	1	X
ejpam-5761	11	11	)	)	PUNCT
ejpam-5761	11	12	≤	≤	NUM
ejpam-5761	11	13	1	1	NUM
ejpam-5761	11	14	,	,	PUNCT
ejpam-5761	11	15	the	the	DET
ejpam-5761	11	16	transience	transience	NOUN
ejpam-5761	11	17	,	,	PUNCT
ejpam-5761	11	18	the	the	DET
ejpam-5761	11	19	recurrence	recurrence	NOUN
ejpam-5761	11	20	,	,	PUNCT
ejpam-5761	11	21	the	the	DET
ejpam-5761	11	22	hitting	hit	VERB
ejpam-5761	11	23	time	time	NOUN
ejpam-5761	11	24	etc	etc	X
ejpam-5761	11	25	.	.	X
ejpam-5761	11	26	of	of	ADP
ejpam-5761	11	27	the	the	DET
ejpam-5761	11	28	random	random	ADJ
ejpam-5761	11	29	walk	walk	NOUN
ejpam-5761	11	30	{	{	PUNCT
ejpam-5761	11	31	n	n	CCONJ
ejpam-5761	11	32	,	,	PUNCT
ejpam-5761	11	33	p	p	X
ejpam-5761	11	34	}	}	PUNCT
ejpam-5761	11	35	depend	depend	VERB
ejpam-5761	11	36	on	on	ADP
ejpam-5761	11	37	p	p	PROPN
ejpam-5761	11	38	.	.	PUNCT
ejpam-5761	12	1	for	for	ADP
ejpam-5761	12	2	example	example	NOUN
ejpam-5761	12	3	if	if	SCONJ
ejpam-5761	12	4	p(n	p(n	PROPN
ejpam-5761	12	5	,	,	PUNCT
ejpam-5761	12	6	n+1	n+1	NOUN
ejpam-5761	12	7	)	)	PUNCT
ejpam-5761	12	8	=	=	SYM
ejpam-5761	12	9	p(n	p(n	PROPN
ejpam-5761	12	10	,	,	PUNCT
ejpam-5761	12	11	n−1	n−1	PROPN
ejpam-5761	12	12	)	)	PUNCT
ejpam-5761	12	13	=	=	SYM
ejpam-5761	12	14	1	1	NUM
ejpam-5761	12	15	2	2	NUM
ejpam-5761	12	16	for	for	ADP
ejpam-5761	12	17	n	n	X
ejpam-5761	12	18	≥	≥	NOUN
ejpam-5761	12	19	1	1	NUM
ejpam-5761	12	20	and	and	CCONJ
ejpam-5761	12	21	p(0	p(0	PROPN
ejpam-5761	12	22	,	,	PUNCT
ejpam-5761	12	23	1	1	X
ejpam-5761	12	24	)	)	PUNCT
ejpam-5761	12	25	=	=	SYM
ejpam-5761	12	26	1	1	NUM
ejpam-5761	12	27	then	then	ADV
ejpam-5761	12	28	{	{	PUNCT
ejpam-5761	12	29	n	n	CCONJ
ejpam-5761	12	30	,	,	PUNCT
ejpam-5761	12	31	p	p	PRON
ejpam-5761	12	32	}	}	PUNCT
ejpam-5761	12	33	is	be	AUX
ejpam-5761	12	34	recurrent	recurrent	ADJ
ejpam-5761	12	35	and	and	CCONJ
ejpam-5761	12	36	any	any	DET
ejpam-5761	12	37	function	function	NOUN
ejpam-5761	12	38	u(x	u(x	VERB
ejpam-5761	12	39	)	)	PUNCT
ejpam-5761	12	40	on	on	ADP
ejpam-5761	12	41	n	n	CCONJ
ejpam-5761	12	42	such	such	ADJ
ejpam-5761	12	43	that	that	SCONJ
ejpam-5761	12	44	u(n	u(n	NOUN
ejpam-5761	12	45	)	)	PUNCT
ejpam-5761	12	46	=	=	SYM
ejpam-5761	13	1	1	1	NUM
ejpam-5761	13	2	2u(n+1)+	2u(n+1)+	NUM
ejpam-5761	13	3	1	1	NUM
ejpam-5761	13	4	2u(n−1	2u(n−1	NUM
ejpam-5761	13	5	)	)	PUNCT
ejpam-5761	13	6	for	for	ADP
ejpam-5761	13	7	n	n	NUM
ejpam-5761	13	8	≥	≥	NUM
ejpam-5761	13	9	1	1	NUM
ejpam-5761	13	10	and	and	CCONJ
ejpam-5761	13	11	u(0	u(0	PROPN
ejpam-5761	13	12	)	)	PUNCT
ejpam-5761	13	13	=	=	SYM
ejpam-5761	13	14	u(1	u(1	PROPN
ejpam-5761	13	15	)	)	PUNCT
ejpam-5761	13	16	is	be	AUX
ejpam-5761	13	17	constant	constant	ADJ
ejpam-5761	13	18	.	.	PUNCT
ejpam-5761	14	1	this	this	DET
ejpam-5761	14	2	example	example	NOUN
ejpam-5761	14	3	is	be	AUX
ejpam-5761	14	4	the	the	DET
ejpam-5761	14	5	motivation	motivation	NOUN
ejpam-5761	14	6	for	for	ADP
ejpam-5761	14	7	the	the	DET
ejpam-5761	14	8	consideration	consideration	NOUN
ejpam-5761	14	9	of	of	ADP
ejpam-5761	14	10	the	the	DET
ejpam-5761	14	11	following	following	ADJ
ejpam-5761	14	12	problem	problem	NOUN
ejpam-5761	14	13	:	:	PUNCT
ejpam-5761	14	14	let	let	VERB
ejpam-5761	14	15	{	{	PUNCT
ejpam-5761	14	16	n	n	CCONJ
ejpam-5761	14	17	,	,	PUNCT
ejpam-5761	14	18	p	p	PRON
ejpam-5761	14	19	}	}	PUNCT
ejpam-5761	14	20	be	be	AUX
ejpam-5761	14	21	a	a	DET
ejpam-5761	14	22	random	random	ADJ
ejpam-5761	14	23	walk	walk	NOUN
ejpam-5761	14	24	(	(	PUNCT
ejpam-5761	14	25	[	[	X
ejpam-5761	14	26	2	2	NUM
ejpam-5761	14	27	]	]	PUNCT
ejpam-5761	14	28	and	and	CCONJ
ejpam-5761	14	29	[	[	X
ejpam-5761	14	30	12	12	NUM
ejpam-5761	14	31	]	]	PUNCT
ejpam-5761	14	32	)	)	PUNCT
ejpam-5761	14	33	where	where	SCONJ
ejpam-5761	14	34	n	n	PRON
ejpam-5761	14	35	is	be	AUX
ejpam-5761	14	36	an	an	DET
ejpam-5761	14	37	infinite	infinite	ADJ
ejpam-5761	14	38	graph	graph	NOUN
ejpam-5761	14	39	which	which	PRON
ejpam-5761	14	40	is	be	AUX
ejpam-5761	14	41	connected	connect	VERB
ejpam-5761	14	42	and	and	CCONJ
ejpam-5761	14	43	p	p	NOUN
ejpam-5761	14	44	=	=	PUNCT
ejpam-5761	14	45	{	{	PUNCT
ejpam-5761	14	46	p(x	p(x	PROPN
ejpam-5761	14	47	,	,	PUNCT
ejpam-5761	14	48	y	y	NOUN
ejpam-5761	14	49	)	)	PUNCT
ejpam-5761	14	50	}	}	PUNCT
ejpam-5761	14	51	is	be	AUX
ejpam-5761	14	52	a	a	DET
ejpam-5761	14	53	set	set	NOUN
ejpam-5761	14	54	of	of	ADP
ejpam-5761	14	55	transition	transition	NOUN
ejpam-5761	14	56	probabilities	probability	NOUN
ejpam-5761	14	57	,	,	PUNCT
ejpam-5761	14	58	p(x	p(x	PROPN
ejpam-5761	14	59	,	,	PUNCT
ejpam-5761	14	60	y	y	PROPN
ejpam-5761	14	61	)	)	PUNCT
ejpam-5761	14	62	>	>	X
ejpam-5761	14	63	0	0	PUNCT
ejpam-5761	15	1	if	if	SCONJ
ejpam-5761	15	2	and	and	CCONJ
ejpam-5761	15	3	only	only	ADV
ejpam-5761	15	4	if	if	SCONJ
ejpam-5761	15	5	x	x	PRON
ejpam-5761	15	6	and	and	CCONJ
ejpam-5761	15	7	y	y	PROPN
ejpam-5761	15	8	are	be	AUX
ejpam-5761	15	9	neighbours	neighbour	NOUN
ejpam-5761	15	10	;	;	PUNCT
ejpam-5761	15	11	p(x	p(x	PROPN
ejpam-5761	15	12	,	,	PUNCT
ejpam-5761	15	13	y	y	NOUN
ejpam-5761	15	14	)	)	PUNCT
ejpam-5761	15	15	and	and	CCONJ
ejpam-5761	15	16	p(y	p(y	NOUN
ejpam-5761	15	17	,	,	PUNCT
ejpam-5761	15	18	x	x	PRON
ejpam-5761	15	19	)	)	PUNCT
ejpam-5761	15	20	may	may	AUX
ejpam-5761	15	21	have	have	VERB
ejpam-5761	15	22	different	different	ADJ
ejpam-5761	15	23	values	value	NOUN
ejpam-5761	15	24	.	.	PUNCT
ejpam-5761	16	1	suppose	suppose	VERB
ejpam-5761	16	2	p	p	X
ejpam-5761	16	3	′	′	NOUN
ejpam-5761	16	4	=	=	SYM
ejpam-5761	16	5	{	{	PUNCT
ejpam-5761	16	6	p′	p′	NOUN
ejpam-5761	16	7	(	(	PUNCT
ejpam-5761	16	8	x	x	NOUN
ejpam-5761	16	9	,	,	PUNCT
ejpam-5761	16	10	y	y	NOUN
ejpam-5761	16	11	)	)	PUNCT
ejpam-5761	16	12	}	}	PUNCT
ejpam-5761	16	13	is	be	AUX
ejpam-5761	16	14	another	another	DET
ejpam-5761	16	15	set	set	NOUN
ejpam-5761	16	16	of	of	ADP
ejpam-5761	16	17	transition	transition	NOUN
ejpam-5761	16	18	probabilities	probability	NOUN
ejpam-5761	16	19	on	on	ADP
ejpam-5761	16	20	n	n	PRON
ejpam-5761	17	1	such	such	ADJ
ejpam-5761	17	2	that	that	SCONJ
ejpam-5761	17	3	p	p	NOUN
ejpam-5761	18	1	′	′	X
ejpam-5761	18	2	(	(	PUNCT
ejpam-5761	18	3	x	x	NOUN
ejpam-5761	18	4	,	,	PUNCT
ejpam-5761	18	5	y	y	NOUN
ejpam-5761	18	6	)	)	PUNCT
ejpam-5761	18	7	≤	≤	NOUN
ejpam-5761	18	8	p(x	p(x	PROPN
ejpam-5761	18	9	,	,	PUNCT
ejpam-5761	18	10	y	y	NOUN
ejpam-5761	18	11	)	)	PUNCT
ejpam-5761	18	12	for	for	ADP
ejpam-5761	18	13	every	every	DET
ejpam-5761	18	14	pair	pair	NOUN
ejpam-5761	18	15	x	x	NOUN
ejpam-5761	18	16	,	,	PUNCT
ejpam-5761	18	17	y.	y.	NOUN
ejpam-5761	18	18	the	the	DET
ejpam-5761	18	19	problem	problem	NOUN
ejpam-5761	18	20	is	be	AUX
ejpam-5761	18	21	to	to	PART
ejpam-5761	18	22	study	study	VERB
ejpam-5761	18	23	how	how	SCONJ
ejpam-5761	18	24	the	the	DET
ejpam-5761	18	25	properties	property	NOUN
ejpam-5761	18	26	of	of	ADP
ejpam-5761	18	27	transience	transience	NOUN
ejpam-5761	18	28	,	,	PUNCT
ejpam-5761	18	29	recurrence	recurrence	NOUN
ejpam-5761	18	30	and	and	CCONJ
ejpam-5761	18	31	other	other	ADJ
ejpam-5761	18	32	probabilistic	probabilistic	ADJ
ejpam-5761	18	33	results	result	NOUN
ejpam-5761	18	34	in	in	ADP
ejpam-5761	18	35	{	{	PUNCT
ejpam-5761	18	36	n	n	CCONJ
ejpam-5761	18	37	,	,	PUNCT
ejpam-5761	18	38	p	p	AUX
ejpam-5761	18	39	}	}	PUNCT
ejpam-5761	18	40	get	get	AUX
ejpam-5761	18	41	transformed	transform	VERB
ejpam-5761	18	42	in	in	ADP
ejpam-5761	18	43	the	the	DET
ejpam-5761	18	44	random	random	ADJ
ejpam-5761	18	45	walk	walk	NOUN
ejpam-5761	18	46	{	{	PUNCT
ejpam-5761	18	47	n	n	CCONJ
ejpam-5761	18	48	,	,	PUNCT
ejpam-5761	18	49	p	p	NOUN
ejpam-5761	18	50	′	′	NOUN
ejpam-5761	18	51	}	}	PUNCT
ejpam-5761	18	52	.	.	PUNCT
ejpam-5761	19	1	we	we	PRON
ejpam-5761	19	2	refer	refer	VERB
ejpam-5761	19	3	to	to	ADP
ejpam-5761	19	4	p	p	NOUN
ejpam-5761	19	5	′	′	NOUN
ejpam-5761	19	6	as	as	ADP
ejpam-5761	19	7	a	a	DET
ejpam-5761	19	8	transition	transition	NOUN
ejpam-5761	19	9	probability	probability	NOUN
ejpam-5761	19	10	structure	structure	NOUN
ejpam-5761	19	11	on	on	ADP
ejpam-5761	19	12	n	n	X
ejpam-5761	19	13	subordinate	subordinate	VERB
ejpam-5761	19	14	to	to	ADP
ejpam-5761	19	15	p	p	NOUN
ejpam-5761	19	16	.	.	PUNCT
ejpam-5761	20	1	∗corresponding	∗corresponde	VERB
ejpam-5761	20	2	author	author	NOUN
ejpam-5761	20	3	.	.	PUNCT
ejpam-5761	21	1	doi	doi	NOUN
ejpam-5761	21	2	:	:	PUNCT
ejpam-5761	21	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5761	https://doi.org/10.29020/nybg.ejpam.v18i1.5761	NOUN
ejpam-5761	21	4	email	email	NOUN
ejpam-5761	21	5	addresses	address	NOUN
ejpam-5761	21	6	:	:	PUNCT
ejpam-5761	21	7	surya.smiley20@gmail.com	surya.smiley20@gmail.com	X
ejpam-5761	21	8	(	(	PUNCT
ejpam-5761	21	9	m.	m.	PROPN
ejpam-5761	21	10	surya	surya	PROPN
ejpam-5761	21	11	priya	priya	PROPN
ejpam-5761	21	12	)	)	PUNCT
ejpam-5761	21	13	,	,	PUNCT
ejpam-5761	21	14	nadhiyan@gmail.com	nadhiyan@gmail.com	X
ejpam-5761	21	15	(	(	PUNCT
ejpam-5761	21	16	n.	n.	PROPN
ejpam-5761	21	17	nathiya	nathiya	PROPN
ejpam-5761	21	18	)	)	PUNCT
ejpam-5761	21	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5761	22	1	1	1	NUM
ejpam-5761	22	2	copyright	copyright	NOUN
ejpam-5761	22	3	:	:	PUNCT
ejpam-5761	22	4	©	©	PROPN
ejpam-5761	22	5	2025	2025	NUM
ejpam-5761	22	6	the	the	DET
ejpam-5761	22	7	author(s	author(s	NOUN
ejpam-5761	22	8	)	)	PUNCT
ejpam-5761	22	9	.	.	PUNCT
ejpam-5761	23	1	(	(	PUNCT
ejpam-5761	23	2	cc	cc	NOUN
ejpam-5761	23	3	by	by	ADP
ejpam-5761	23	4	-	-	PUNCT
ejpam-5761	23	5	nc	nc	PROPN
ejpam-5761	23	6	4.0	4.0	NUM
ejpam-5761	23	7	)	)	PUNCT
ejpam-5761	23	8	m.	m.	NOUN
ejpam-5761	23	9	surya	surya	PROPN
ejpam-5761	23	10	priya	priya	PROPN
ejpam-5761	23	11	,	,	PUNCT
ejpam-5761	23	12	n.	n.	PROPN
ejpam-5761	23	13	nathiya	nathiya	PROPN
ejpam-5761	23	14	/	/	SYM
ejpam-5761	23	15	eur	eur	PROPN
ejpam-5761	23	16	.	.	PUNCT
ejpam-5761	24	1	j.	j.	PROPN
ejpam-5761	24	2	pure	pure	PROPN
ejpam-5761	24	3	appl	appl	PROPN
ejpam-5761	24	4	.	.	PROPN
ejpam-5761	24	5	math	math	PROPN
ejpam-5761	24	6	,	,	PUNCT
ejpam-5761	24	7	18	18	NUM
ejpam-5761	24	8	(	(	PUNCT
ejpam-5761	24	9	1	1	NUM
ejpam-5761	24	10	)	)	PUNCT
ejpam-5761	24	11	(	(	PUNCT
ejpam-5761	24	12	2025	2025	NUM
ejpam-5761	24	13	)	)	PUNCT
ejpam-5761	24	14	,	,	PUNCT
ejpam-5761	24	15	5761	5761	NUM
ejpam-5761	24	16	2	2	NUM
ejpam-5761	24	17	of	of	ADP
ejpam-5761	24	18	11	11	NUM
ejpam-5761	24	19	there	there	PRON
ejpam-5761	24	20	is	be	VERB
ejpam-5761	24	21	an	an	DET
ejpam-5761	24	22	analogy	analogy	NOUN
ejpam-5761	24	23	in	in	ADP
ejpam-5761	24	24	the	the	DET
ejpam-5761	24	25	context	context	NOUN
ejpam-5761	24	26	of	of	ADP
ejpam-5761	24	27	general	general	ADJ
ejpam-5761	24	28	infinite	infinite	ADJ
ejpam-5761	24	29	networks	network	NOUN
ejpam-5761	24	30	(	(	PUNCT
ejpam-5761	24	31	[	[	X
ejpam-5761	24	32	1	1	NUM
ejpam-5761	24	33	]	]	PUNCT
ejpam-5761	24	34	and	and	CCONJ
ejpam-5761	24	35	[	[	X
ejpam-5761	24	36	10	10	NUM
ejpam-5761	24	37	]	]	SYM
ejpam-5761	24	38	)	)	PUNCT
ejpam-5761	24	39	{	{	PUNCT
ejpam-5761	24	40	x	x	NOUN
ejpam-5761	24	41	,	,	PUNCT
ejpam-5761	24	42	t(x	t(x	PROPN
ejpam-5761	24	43	,	,	PUNCT
ejpam-5761	24	44	y	y	NOUN
ejpam-5761	24	45	)	)	PUNCT
ejpam-5761	24	46	}	}	PUNCT
ejpam-5761	24	47	.	.	PUNCT
ejpam-5761	25	1	here	here	ADV
ejpam-5761	25	2	potential	potential	ADJ
ejpam-5761	25	3	-	-	PUNCT
ejpam-5761	25	4	theoretic	theoretic	ADJ
ejpam-5761	25	5	properties	property	NOUN
ejpam-5761	25	6	of	of	ADP
ejpam-5761	25	7	functions	function	NOUN
ejpam-5761	25	8	on	on	ADP
ejpam-5761	25	9	x	x	SYM
ejpam-5761	25	10	are	be	AUX
ejpam-5761	25	11	studied	study	VERB
ejpam-5761	25	12	using	use	VERB
ejpam-5761	25	13	the	the	DET
ejpam-5761	25	14	laplace	laplace	NOUN
ejpam-5761	25	15	operator	operator	NOUN
ejpam-5761	25	16	∆u(x	∆u(x	VERB
ejpam-5761	25	17	)	)	PUNCT
ejpam-5761	25	18	=	=	SYM
ejpam-5761	25	19	∑	∑	PUNCT
ejpam-5761	25	20	t(x	t(x	PROPN
ejpam-5761	25	21	,	,	PUNCT
ejpam-5761	25	22	y)[u(y	y)[u(y	NOUN
ejpam-5761	25	23	)	)	PUNCT
ejpam-5761	25	24	−	−	NOUN
ejpam-5761	25	25	u(x	u(x	NOUN
ejpam-5761	25	26	)	)	PUNCT
ejpam-5761	25	27	]	]	PUNCT
ejpam-5761	25	28	.	.	PUNCT
ejpam-5761	26	1	if	if	SCONJ
ejpam-5761	26	2	q	q	PROPN
ejpam-5761	26	3	≥	≥	X
ejpam-5761	26	4	0	0	NUM
ejpam-5761	26	5	is	be	AUX
ejpam-5761	26	6	a	a	DET
ejpam-5761	26	7	function	function	NOUN
ejpam-5761	26	8	on	on	ADP
ejpam-5761	26	9	x	x	NOUN
ejpam-5761	26	10	,	,	PUNCT
ejpam-5761	26	11	there	there	PRON
ejpam-5761	26	12	is	be	VERB
ejpam-5761	26	13	another	another	DET
ejpam-5761	26	14	interesting	interesting	ADJ
ejpam-5761	26	15	schrödinger	schrödinger	NOUN
ejpam-5761	26	16	operator	operator	NOUN
ejpam-5761	26	17	(	(	PUNCT
ejpam-5761	26	18	[	[	X
ejpam-5761	26	19	4	4	X
ejpam-5761	26	20	]	]	PUNCT
ejpam-5761	26	21	and	and	CCONJ
ejpam-5761	26	22	[	[	X
ejpam-5761	26	23	7	7	NUM
ejpam-5761	26	24	]	]	SYM
ejpam-5761	26	25	)	)	PUNCT
ejpam-5761	26	26	∆qu(x	∆qu(x	VERB
ejpam-5761	26	27	)	)	PUNCT
ejpam-5761	27	1	=	=	VERB
ejpam-5761	27	2	∆u(x	∆u(x	ADV
ejpam-5761	27	3	)	)	PUNCT
ejpam-5761	27	4	−	−	PROPN
ejpam-5761	27	5	q(x)u(x	q(x)u(x	NOUN
ejpam-5761	27	6	)	)	PUNCT
ejpam-5761	27	7	.	.	PUNCT
ejpam-5761	28	1	if	if	SCONJ
ejpam-5761	28	2	we	we	PRON
ejpam-5761	28	3	write	write	VERB
ejpam-5761	28	4	t	t	PROPN
ejpam-5761	28	5	′	′	NUM
ejpam-5761	28	6	(	(	PUNCT
ejpam-5761	28	7	x	x	NOUN
ejpam-5761	28	8	,	,	PUNCT
ejpam-5761	28	9	y	y	NOUN
ejpam-5761	28	10	)	)	PUNCT
ejpam-5761	29	1	=	=	SYM
ejpam-5761	29	2	t(x	t(x	PROPN
ejpam-5761	29	3	,	,	PUNCT
ejpam-5761	29	4	y	y	NOUN
ejpam-5761	29	5	)	)	PUNCT
ejpam-5761	29	6	q(x)+	q(x)+	NOUN
ejpam-5761	29	7	∑	∑	PUNCT
ejpam-5761	29	8	t(x	t(x	PROPN
ejpam-5761	29	9	,	,	PUNCT
ejpam-5761	29	10	y	y	NOUN
ejpam-5761	29	11	)	)	PUNCT
ejpam-5761	29	12	than	than	ADP
ejpam-5761	29	13	{	{	PUNCT
ejpam-5761	29	14	x	x	NOUN
ejpam-5761	29	15	,	,	PUNCT
ejpam-5761	29	16	t	t	NOUN
ejpam-5761	29	17	′	′	NUM
ejpam-5761	29	18	(	(	PUNCT
ejpam-5761	29	19	x	x	X
ejpam-5761	29	20	,	,	PUNCT
ejpam-5761	29	21	y	y	NOUN
ejpam-5761	29	22	)	)	PUNCT
ejpam-5761	29	23	}	}	PUNCT
ejpam-5761	29	24	is	be	AUX
ejpam-5761	29	25	another	another	DET
ejpam-5761	29	26	network	network	NOUN
ejpam-5761	29	27	where	where	SCONJ
ejpam-5761	29	28	t	t	PROPN
ejpam-5761	29	29	′	′	NUM
ejpam-5761	29	30	(	(	PUNCT
ejpam-5761	29	31	x	x	NOUN
ejpam-5761	29	32	,	,	PUNCT
ejpam-5761	29	33	y	y	NOUN
ejpam-5761	29	34	)	)	PUNCT
ejpam-5761	29	35	≤	≤	NOUN
ejpam-5761	30	1	t(x	t(x	PROPN
ejpam-5761	30	2	,	,	PUNCT
ejpam-5761	30	3	y	y	PROPN
ejpam-5761	30	4	)	)	PUNCT
ejpam-5761	30	5	which	which	PRON
ejpam-5761	30	6	provides	provide	VERB
ejpam-5761	30	7	a	a	DET
ejpam-5761	30	8	convenient	convenient	ADJ
ejpam-5761	30	9	base	base	NOUN
ejpam-5761	30	10	for	for	ADP
ejpam-5761	30	11	the	the	DET
ejpam-5761	30	12	study	study	NOUN
ejpam-5761	30	13	of	of	ADP
ejpam-5761	30	14	schrödinger	schrödinger	NOUN
ejpam-5761	30	15	potentials	potential	VERB
ejpam-5761	30	16	with	with	ADP
ejpam-5761	30	17	a	a	DET
ejpam-5761	30	18	comparable	comparable	ADJ
ejpam-5761	30	19	study	study	NOUN
ejpam-5761	30	20	of	of	ADP
ejpam-5761	30	21	laplace	laplace	NOUN
ejpam-5761	30	22	potentials	potential	NOUN
ejpam-5761	30	23	.	.	PUNCT
ejpam-5761	31	1	in	in	ADP
ejpam-5761	31	2	this	this	DET
ejpam-5761	31	3	article	article	NOUN
ejpam-5761	31	4	,	,	PUNCT
ejpam-5761	31	5	we	we	PRON
ejpam-5761	31	6	discuss	discuss	VERB
ejpam-5761	31	7	the	the	DET
ejpam-5761	31	8	potential	potential	ADJ
ejpam-5761	31	9	-	-	PUNCT
ejpam-5761	31	10	theoretic	theoretic	ADJ
ejpam-5761	31	11	aspects	aspect	NOUN
ejpam-5761	31	12	of	of	ADP
ejpam-5761	31	13	functions	function	NOUN
ejpam-5761	31	14	on	on	ADP
ejpam-5761	31	15	n	n	CCONJ
ejpam-5761	31	16	determined	determine	VERB
ejpam-5761	31	17	by	by	ADP
ejpam-5761	31	18	the	the	DET
ejpam-5761	31	19	original	original	ADJ
ejpam-5761	31	20	structure	structure	NOUN
ejpam-5761	31	21	p	p	NOUN
ejpam-5761	31	22	and	and	CCONJ
ejpam-5761	31	23	another	another	DET
ejpam-5761	31	24	structure	structure	NOUN
ejpam-5761	31	25	p	p	NOUN
ejpam-5761	31	26	′	′	NOUN
ejpam-5761	32	1	that	that	PRON
ejpam-5761	32	2	is	be	AUX
ejpam-5761	32	3	subordinate	subordinate	ADJ
ejpam-5761	32	4	to	to	ADP
ejpam-5761	32	5	p	p	PROPN
ejpam-5761	32	6	.	.	PUNCT
ejpam-5761	33	1	for	for	ADP
ejpam-5761	33	2	related	related	ADJ
ejpam-5761	33	3	results	result	NOUN
ejpam-5761	33	4	,	,	PUNCT
ejpam-5761	33	5	we	we	PRON
ejpam-5761	33	6	have	have	AUX
ejpam-5761	33	7	referred	refer	VERB
ejpam-5761	33	8	[	[	X
ejpam-5761	33	9	6	6	NUM
ejpam-5761	33	10	]	]	PUNCT
ejpam-5761	33	11	and	and	CCONJ
ejpam-5761	33	12	[	[	X
ejpam-5761	33	13	11	11	NUM
ejpam-5761	33	14	]	]	PUNCT
ejpam-5761	33	15	.	.	PUNCT
ejpam-5761	34	1	the	the	DET
ejpam-5761	34	2	classification	classification	NOUN
ejpam-5761	34	3	of	of	ADP
ejpam-5761	34	4	connected	connected	ADJ
ejpam-5761	34	5	and	and	CCONJ
ejpam-5761	34	6	locally	locally	ADV
ejpam-5761	34	7	finite	finite	VERB
ejpam-5761	34	8	infinite	infinite	ADJ
ejpam-5761	34	9	network	network	NOUN
ejpam-5761	34	10	into	into	ADP
ejpam-5761	34	11	parabolic	parabolic	NOUN
ejpam-5761	34	12	and	and	CCONJ
ejpam-5761	34	13	hyperbolic	hyperbolic	ADJ
ejpam-5761	34	14	of	of	ADP
ejpam-5761	34	15	order	order	NOUN
ejpam-5761	34	16	p	p	NOUN
ejpam-5761	34	17	is	be	AUX
ejpam-5761	34	18	investigated	investigate	VERB
ejpam-5761	34	19	in	in	ADP
ejpam-5761	34	20	[	[	X
ejpam-5761	34	21	13	13	NUM
ejpam-5761	34	22	]	]	PUNCT
ejpam-5761	34	23	,	,	PUNCT
ejpam-5761	34	24	where	where	SCONJ
ejpam-5761	34	25	as	as	SCONJ
ejpam-5761	34	26	the	the	DET
ejpam-5761	34	27	same	same	ADJ
ejpam-5761	34	28	is	be	AUX
ejpam-5761	34	29	done	do	VERB
ejpam-5761	34	30	for	for	ADP
ejpam-5761	34	31	non	non	ADJ
ejpam-5761	34	32	-	-	ADJ
ejpam-5761	34	33	locally	locally	ADV
ejpam-5761	34	34	finite	finite	ADJ
ejpam-5761	34	35	networks	network	NOUN
ejpam-5761	34	36	in	in	ADP
ejpam-5761	34	37	[	[	X
ejpam-5761	34	38	3	3	NUM
ejpam-5761	34	39	]	]	PUNCT
ejpam-5761	34	40	.	.	PUNCT
ejpam-5761	35	1	the	the	DET
ejpam-5761	35	2	concept	concept	NOUN
ejpam-5761	35	3	of	of	ADP
ejpam-5761	35	4	recurrent	recurrent	ADJ
ejpam-5761	35	5	random	random	ADJ
ejpam-5761	35	6	walks	walk	NOUN
ejpam-5761	35	7	on	on	ADP
ejpam-5761	35	8	countable	countable	ADJ
ejpam-5761	35	9	infinite	infinite	ADJ
ejpam-5761	35	10	state	state	NOUN
ejpam-5761	35	11	spaces	space	NOUN
ejpam-5761	35	12	is	be	AUX
ejpam-5761	35	13	explored	explore	VERB
ejpam-5761	35	14	by	by	ADP
ejpam-5761	35	15	v.	v.	PROPN
ejpam-5761	35	16	r.	r.	PROPN
ejpam-5761	35	17	manivannan	manivannan	PROPN
ejpam-5761	35	18	and	and	CCONJ
ejpam-5761	35	19	m.	m.	PROPN
ejpam-5761	35	20	venkataraman	venkataraman	NOUN
ejpam-5761	35	21	[	[	X
ejpam-5761	35	22	5	5	NUM
ejpam-5761	35	23	]	]	PUNCT
ejpam-5761	35	24	.	.	PUNCT
ejpam-5761	36	1	in	in	ADP
ejpam-5761	36	2	[	[	X
ejpam-5761	36	3	8	8	NUM
ejpam-5761	36	4	]	]	PUNCT
ejpam-5761	36	5	m.	m.	NOUN
ejpam-5761	36	6	surya	surya	PROPN
ejpam-5761	36	7	priya	priya	PROPN
ejpam-5761	36	8	and	and	CCONJ
ejpam-5761	36	9	n.	n.	PROPN
ejpam-5761	36	10	nathiya	nathiya	PROPN
ejpam-5761	36	11	establishes	establish	VERB
ejpam-5761	36	12	the	the	DET
ejpam-5761	36	13	existence	existence	NOUN
ejpam-5761	36	14	of	of	ADP
ejpam-5761	36	15	green	green	PROPN
ejpam-5761	36	16	’s	’s	PART
ejpam-5761	36	17	function	function	NOUN
ejpam-5761	36	18	on	on	ADP
ejpam-5761	36	19	non	non	ADJ
ejpam-5761	36	20	-	-	ADJ
ejpam-5761	36	21	reversible	reversible	ADJ
ejpam-5761	36	22	random	random	ADJ
ejpam-5761	36	23	walks	walk	NOUN
ejpam-5761	36	24	through	through	ADP
ejpam-5761	36	25	the	the	DET
ejpam-5761	36	26	application	application	NOUN
ejpam-5761	36	27	of	of	ADP
ejpam-5761	36	28	potential	potential	ADJ
ejpam-5761	36	29	theoretic	theoretic	ADJ
ejpam-5761	36	30	techniques	technique	NOUN
ejpam-5761	36	31	.	.	PUNCT
ejpam-5761	37	1	with	with	ADP
ejpam-5761	37	2	reference	reference	NOUN
ejpam-5761	37	3	to	to	ADP
ejpam-5761	37	4	the	the	DET
ejpam-5761	37	5	aforementioned	aforementioned	ADJ
ejpam-5761	37	6	,	,	PUNCT
ejpam-5761	37	7	we	we	PRON
ejpam-5761	37	8	have	have	AUX
ejpam-5761	37	9	looked	look	VERB
ejpam-5761	37	10	into	into	ADP
ejpam-5761	37	11	the	the	DET
ejpam-5761	37	12	concepts	concept	NOUN
ejpam-5761	37	13	of	of	ADP
ejpam-5761	37	14	p	p	NOUN
ejpam-5761	37	15	′	′	NUM
ejpam-5761	37	16	-green	-green	PROPN
ejpam-5761	37	17	’s	’s	PART
ejpam-5761	37	18	function	function	NOUN
ejpam-5761	37	19	as	as	ADV
ejpam-5761	37	20	well	well	ADV
ejpam-5761	37	21	as	as	ADP
ejpam-5761	37	22	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	37	23	and	and	CCONJ
ejpam-5761	37	24	bounded	bound	VERB
ejpam-5761	37	25	hyperbolic	hyperbolic	ADJ
ejpam-5761	37	26	subordinate	subordinate	ADJ
ejpam-5761	37	27	structures	structure	NOUN
ejpam-5761	37	28	.	.	PUNCT
ejpam-5761	38	1	s.	s.	PROPN
ejpam-5761	38	2	sivan	sivan	PROPN
ejpam-5761	38	3	and	and	CCONJ
ejpam-5761	38	4	m.	m.	PROPN
ejpam-5761	38	5	venkataraman	venkataraman	NOUN
ejpam-5761	38	6	[	[	X
ejpam-5761	38	7	9	9	NUM
ejpam-5761	38	8	]	]	PUNCT
ejpam-5761	38	9	,	,	PUNCT
ejpam-5761	38	10	says	say	VERB
ejpam-5761	38	11	that	that	SCONJ
ejpam-5761	38	12	an	an	DET
ejpam-5761	38	13	infinite	infinite	ADJ
ejpam-5761	38	14	network	network	NOUN
ejpam-5761	38	15	is	be	AUX
ejpam-5761	38	16	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	38	17	if	if	SCONJ
ejpam-5761	38	18	and	and	CCONJ
ejpam-5761	38	19	only	only	ADV
ejpam-5761	38	20	if	if	SCONJ
ejpam-5761	38	21	constant	constant	ADJ
ejpam-5761	38	22	1	1	NUM
ejpam-5761	38	23	is	be	AUX
ejpam-5761	38	24	a	a	DET
ejpam-5761	38	25	potential	potential	NOUN
ejpam-5761	38	26	.	.	PUNCT
ejpam-5761	39	1	they	they	PRON
ejpam-5761	39	2	have	have	AUX
ejpam-5761	39	3	given	give	VERB
ejpam-5761	39	4	neccessary	neccessary	ADJ
ejpam-5761	39	5	and	and	CCONJ
ejpam-5761	39	6	sufficient	sufficient	ADJ
ejpam-5761	39	7	condition	condition	NOUN
ejpam-5761	39	8	for	for	SCONJ
ejpam-5761	39	9	a	a	DET
ejpam-5761	39	10	network	network	NOUN
ejpam-5761	39	11	to	to	PART
ejpam-5761	39	12	be	be	AUX
ejpam-5761	39	13	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	39	14	.	.	PUNCT
ejpam-5761	40	1	v.	v.	ADP
ejpam-5761	40	2	anandam	anandam	PROPN
ejpam-5761	41	1	[	[	X
ejpam-5761	41	2	1	1	NUM
ejpam-5761	41	3	]	]	PUNCT
ejpam-5761	41	4	has	have	AUX
ejpam-5761	41	5	studied	study	VERB
ejpam-5761	41	6	the	the	DET
ejpam-5761	41	7	schrödinger	schrödinger	NOUN
ejpam-5761	41	8	operators	operator	NOUN
ejpam-5761	41	9	and	and	CCONJ
ejpam-5761	41	10	subordinate	subordinate	ADJ
ejpam-5761	41	11	structures	structure	NOUN
ejpam-5761	41	12	on	on	ADP
ejpam-5761	41	13	infinite	infinite	ADJ
ejpam-5761	41	14	networks	network	NOUN
ejpam-5761	41	15	.	.	PUNCT
ejpam-5761	42	1	where	where	SCONJ
ejpam-5761	42	2	as	as	SCONJ
ejpam-5761	42	3	in	in	ADP
ejpam-5761	42	4	the	the	DET
ejpam-5761	42	5	present	present	ADJ
ejpam-5761	42	6	article	article	NOUN
ejpam-5761	42	7	,	,	PUNCT
ejpam-5761	42	8	we	we	PRON
ejpam-5761	42	9	delve	delve	VERB
ejpam-5761	42	10	into	into	ADP
ejpam-5761	42	11	the	the	DET
ejpam-5761	42	12	potential	potential	ADJ
ejpam-5761	42	13	theory	theory	NOUN
ejpam-5761	42	14	associated	associate	VERB
ejpam-5761	42	15	to	to	ADP
ejpam-5761	42	16	a	a	DET
ejpam-5761	42	17	structure	structure	NOUN
ejpam-5761	42	18	subordinate	subordinate	NOUN
ejpam-5761	42	19	to	to	ADP
ejpam-5761	42	20	a	a	DET
ejpam-5761	42	21	non	non	ADJ
ejpam-5761	42	22	-	-	ADJ
ejpam-5761	42	23	locally	locally	ADV
ejpam-5761	42	24	finite	finite	ADJ
ejpam-5761	42	25	random	random	ADJ
ejpam-5761	42	26	walk	walk	NOUN
ejpam-5761	42	27	.	.	PUNCT
ejpam-5761	43	1	we	we	PRON
ejpam-5761	43	2	define	define	VERB
ejpam-5761	43	3	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	43	4	random	random	ADJ
ejpam-5761	43	5	walk	walk	NOUN
ejpam-5761	43	6	and	and	CCONJ
ejpam-5761	43	7	its	its	PRON
ejpam-5761	43	8	subordinate	subordinate	ADJ
ejpam-5761	43	9	structure	structure	NOUN
ejpam-5761	43	10	.	.	PUNCT
ejpam-5761	44	1	finally	finally	ADV
ejpam-5761	44	2	a	a	DET
ejpam-5761	44	3	section	section	NOUN
ejpam-5761	44	4	is	be	AUX
ejpam-5761	44	5	devoted	devote	VERB
ejpam-5761	44	6	to	to	PART
ejpam-5761	44	7	investigate	investigate	VERB
ejpam-5761	44	8	the	the	DET
ejpam-5761	44	9	relation	relation	NOUN
ejpam-5761	44	10	between	between	ADP
ejpam-5761	44	11	bounded	bound	VERB
ejpam-5761	44	12	p	p	NOUN
ejpam-5761	44	13	-average	-average	NOUN
ejpam-5761	44	14	functions	function	NOUN
ejpam-5761	44	15	and	and	CCONJ
ejpam-5761	44	16	bounded	bound	VERB
ejpam-5761	44	17	p	p	X
ejpam-5761	44	18	′	′	NUM
ejpam-5761	44	19	-average	-average	NOUN
ejpam-5761	44	20	functions	function	NOUN
ejpam-5761	44	21	.	.	PUNCT
ejpam-5761	45	1	2	2	X
ejpam-5761	45	2	.	.	X
ejpam-5761	45	3	preliminaries	preliminary	NOUN
ejpam-5761	45	4	definition	definition	NOUN
ejpam-5761	45	5	1	1	NUM
ejpam-5761	45	6	.	.	PUNCT
ejpam-5761	45	7	random	random	ADJ
ejpam-5761	45	8	walk	walk	NOUN
ejpam-5761	45	9	:	:	PUNCT
ejpam-5761	45	10	let	let	AUX
ejpam-5761	45	11	{	{	PUNCT
ejpam-5761	45	12	n	n	CCONJ
ejpam-5761	45	13	,	,	PUNCT
ejpam-5761	45	14	p	p	PRON
ejpam-5761	45	15	}	}	PUNCT
ejpam-5761	45	16	be	be	AUX
ejpam-5761	45	17	a	a	DET
ejpam-5761	45	18	random	random	ADJ
ejpam-5761	45	19	walk	walk	NOUN
ejpam-5761	45	20	with	with	ADP
ejpam-5761	45	21	a	a	DET
ejpam-5761	45	22	countable	countable	ADJ
ejpam-5761	45	23	infinite	infinite	ADJ
ejpam-5761	45	24	number	number	NOUN
ejpam-5761	45	25	of	of	ADP
ejpam-5761	45	26	states	state	NOUN
ejpam-5761	45	27	n	n	CCONJ
ejpam-5761	45	28	and	and	CCONJ
ejpam-5761	45	29	p	p	NOUN
ejpam-5761	45	30	=	=	NOUN
ejpam-5761	45	31	{	{	PUNCT
ejpam-5761	45	32	p(x	p(x	PROPN
ejpam-5761	45	33	,	,	PUNCT
ejpam-5761	45	34	y	y	NOUN
ejpam-5761	45	35	)	)	PUNCT
ejpam-5761	45	36	}	}	PUNCT
ejpam-5761	45	37	is	be	AUX
ejpam-5761	45	38	the	the	DET
ejpam-5761	45	39	probability	probability	NOUN
ejpam-5761	45	40	transition	transition	NOUN
ejpam-5761	45	41	matrix	matrix	NOUN
ejpam-5761	45	42	,	,	PUNCT
ejpam-5761	45	43	where	where	SCONJ
ejpam-5761	45	44	p(x	p(x	PROPN
ejpam-5761	45	45	,	,	PUNCT
ejpam-5761	45	46	y	y	NOUN
ejpam-5761	45	47	)	)	PUNCT
ejpam-5761	45	48	denotes	denote	VERB
ejpam-5761	45	49	the	the	DET
ejpam-5761	45	50	transition	transition	NOUN
ejpam-5761	45	51	probability	probability	NOUN
ejpam-5761	45	52	from	from	ADP
ejpam-5761	45	53	state	state	NOUN
ejpam-5761	45	54	x	x	INTJ
ejpam-5761	45	55	to	to	ADP
ejpam-5761	45	56	state	state	NOUN
ejpam-5761	45	57	y.	y.	NOUN
ejpam-5761	45	58	we	we	PRON
ejpam-5761	45	59	assume	assume	VERB
ejpam-5761	45	60	{	{	PUNCT
ejpam-5761	45	61	n	n	CCONJ
ejpam-5761	45	62	,	,	PUNCT
ejpam-5761	45	63	p	p	PRON
ejpam-5761	45	64	}	}	PUNCT
ejpam-5761	45	65	is	be	AUX
ejpam-5761	45	66	connected	connect	VERB
ejpam-5761	45	67	(	(	PUNCT
ejpam-5761	45	68	i.e	i.e	NOUN
ejpam-5761	45	69	,	,	PUNCT
ejpam-5761	45	70	for	for	ADP
ejpam-5761	45	71	any	any	DET
ejpam-5761	45	72	two	two	NUM
ejpam-5761	45	73	distinct	distinct	ADJ
ejpam-5761	45	74	states	state	NOUN
ejpam-5761	45	75	there	there	PRON
ejpam-5761	45	76	exists	exist	VERB
ejpam-5761	45	77	a	a	DET
ejpam-5761	45	78	path	path	NOUN
ejpam-5761	45	79	connecting	connect	VERB
ejpam-5761	45	80	them	they	PRON
ejpam-5761	45	81	)	)	PUNCT
ejpam-5761	45	82	and	and	CCONJ
ejpam-5761	45	83	without	without	ADP
ejpam-5761	45	84	self	self	NOUN
ejpam-5761	45	85	loops	loop	NOUN
ejpam-5761	45	86	.	.	PUNCT
ejpam-5761	46	1	as	as	ADP
ejpam-5761	46	2	usual	usual	ADJ
ejpam-5761	46	3	,	,	PUNCT
ejpam-5761	46	4	we	we	PRON
ejpam-5761	46	5	shall	shall	AUX
ejpam-5761	46	6	take	take	VERB
ejpam-5761	46	7	n	n	PRON
ejpam-5761	46	8	as	as	ADP
ejpam-5761	46	9	an	an	DET
ejpam-5761	46	10	infinite	infinite	ADJ
ejpam-5761	46	11	graph	graph	NOUN
ejpam-5761	46	12	by	by	ADP
ejpam-5761	46	13	defining	define	VERB
ejpam-5761	46	14	[	[	X
ejpam-5761	46	15	x	x	NOUN
ejpam-5761	46	16	,	,	PUNCT
ejpam-5761	46	17	y	y	PROPN
ejpam-5761	46	18	]	]	PUNCT
ejpam-5761	46	19	as	as	ADP
ejpam-5761	46	20	an	an	DET
ejpam-5761	46	21	edge	edge	NOUN
ejpam-5761	46	22	if	if	SCONJ
ejpam-5761	46	23	and	and	CCONJ
ejpam-5761	46	24	only	only	ADV
ejpam-5761	46	25	if	if	SCONJ
ejpam-5761	46	26	p(x	p(x	PROPN
ejpam-5761	46	27	,	,	PUNCT
ejpam-5761	46	28	y	y	PROPN
ejpam-5761	46	29	)	)	PUNCT
ejpam-5761	46	30	>	>	X
ejpam-5761	47	1	0	0	X
ejpam-5761	47	2	.	.	PUNCT
ejpam-5761	48	1	we	we	PRON
ejpam-5761	48	2	say	say	VERB
ejpam-5761	48	3	two	two	NUM
ejpam-5761	48	4	states	state	NOUN
ejpam-5761	48	5	x	x	PUNCT
ejpam-5761	48	6	and	and	CCONJ
ejpam-5761	48	7	y	y	PROPN
ejpam-5761	48	8	are	be	AUX
ejpam-5761	48	9	neighbours	neighbour	NOUN
ejpam-5761	48	10	if	if	SCONJ
ejpam-5761	48	11	there	there	PRON
ejpam-5761	48	12	exists	exist	VERB
ejpam-5761	48	13	an	an	DET
ejpam-5761	48	14	edge	edge	NOUN
ejpam-5761	48	15	between	between	ADP
ejpam-5761	48	16	them	they	PRON
ejpam-5761	48	17	and	and	CCONJ
ejpam-5761	48	18	it	it	PRON
ejpam-5761	48	19	is	be	AUX
ejpam-5761	48	20	denoted	denote	VERB
ejpam-5761	48	21	by	by	ADP
ejpam-5761	48	22	x	x	SYM
ejpam-5761	48	23	∼	∼	NOUN
ejpam-5761	48	24	y	y	NOUN
ejpam-5761	48	25	and	and	CCONJ
ejpam-5761	48	26	p(x	p(x	PROPN
ejpam-5761	48	27	)	)	PUNCT
ejpam-5761	48	28	=	=	PUNCT
ejpam-5761	48	29	∑	∑	PUNCT
ejpam-5761	48	30	y∼x	y∼x	PROPN
ejpam-5761	48	31	p(x	p(x	PROPN
ejpam-5761	48	32	,	,	PUNCT
ejpam-5761	48	33	y	y	NOUN
ejpam-5761	48	34	)	)	PUNCT
ejpam-5761	48	35	=	=	SYM
ejpam-5761	48	36	1	1	NUM
ejpam-5761	48	37	for	for	ADP
ejpam-5761	48	38	every	every	DET
ejpam-5761	48	39	x	x	SYM
ejpam-5761	48	40	∈	∈	PROPN
ejpam-5761	48	41	n	n	X
ejpam-5761	48	42	.	.	PUNCT
ejpam-5761	49	1	note	note	NOUN
ejpam-5761	49	2	:	:	PUNCT
ejpam-5761	49	3	we	we	PRON
ejpam-5761	49	4	do	do	AUX
ejpam-5761	49	5	not	not	PART
ejpam-5761	49	6	place	place	VERB
ejpam-5761	49	7	the	the	DET
ejpam-5761	49	8	condition	condition	NOUN
ejpam-5761	49	9	that	that	SCONJ
ejpam-5761	49	10	the	the	DET
ejpam-5761	49	11	number	number	NOUN
ejpam-5761	49	12	of	of	ADP
ejpam-5761	49	13	neighbours	neighbour	NOUN
ejpam-5761	49	14	of	of	ADP
ejpam-5761	49	15	any	any	DET
ejpam-5761	49	16	state	state	NOUN
ejpam-5761	49	17	is	be	AUX
ejpam-5761	49	18	finite	finite	ADJ
ejpam-5761	49	19	.	.	PUNCT
ejpam-5761	50	1	hence	hence	ADV
ejpam-5761	50	2	we	we	PRON
ejpam-5761	50	3	consider	consider	VERB
ejpam-5761	50	4	only	only	ADV
ejpam-5761	50	5	those	those	DET
ejpam-5761	50	6	real	real	ADV
ejpam-5761	50	7	-	-	PUNCT
ejpam-5761	50	8	valued	value	VERB
ejpam-5761	50	9	functions	function	NOUN
ejpam-5761	50	10	s	s	PART
ejpam-5761	50	11	on	on	ADP
ejpam-5761	50	12	n	n	X
ejpam-5761	50	13	for	for	ADP
ejpam-5761	50	14	which	which	PRON
ejpam-5761	50	15	∑	∑	PUNCT
ejpam-5761	50	16	y∼x	y∼x	PROPN
ejpam-5761	50	17	p(x	p(x	PROPN
ejpam-5761	50	18	,	,	PUNCT
ejpam-5761	50	19	y)|s(y)|	y)|s(y)|	X
ejpam-5761	50	20	<	<	X
ejpam-5761	50	21	∞	∞	PROPN
ejpam-5761	50	22	for	for	ADP
ejpam-5761	50	23	any	any	DET
ejpam-5761	50	24	x	x	SYM
ejpam-5761	50	25	∈	∈	PROPN
ejpam-5761	50	26	n	n	X
ejpam-5761	50	27	.	.	PUNCT
ejpam-5761	51	1	write	write	VERB
ejpam-5761	51	2	as(x	as(x	NOUN
ejpam-5761	51	3	)	)	PUNCT
ejpam-5761	52	1	=	=	PUNCT
ejpam-5761	52	2	∑	∑	PUNCT
ejpam-5761	52	3	y	y	PROPN
ejpam-5761	52	4	p(x	p(x	PROPN
ejpam-5761	52	5	,	,	PUNCT
ejpam-5761	52	6	y)s(y	y)s(y	NOUN
ejpam-5761	52	7	)	)	PUNCT
ejpam-5761	52	8	.	.	PUNCT
ejpam-5761	53	1	definition	definition	NOUN
ejpam-5761	53	2	2	2	NUM
ejpam-5761	53	3	.	.	PUNCT
ejpam-5761	53	4	interior	interior	ADJ
ejpam-5761	53	5	and	and	CCONJ
ejpam-5761	53	6	boundary	boundary	ADJ
ejpam-5761	53	7	of	of	ADP
ejpam-5761	53	8	a	a	DET
ejpam-5761	53	9	set	set	NOUN
ejpam-5761	53	10	:	:	PUNCT
ejpam-5761	53	11	we	we	PRON
ejpam-5761	53	12	say	say	VERB
ejpam-5761	53	13	a	a	DET
ejpam-5761	53	14	state	state	NOUN
ejpam-5761	53	15	x	x	PUNCT
ejpam-5761	53	16	is	be	AUX
ejpam-5761	53	17	an	an	DET
ejpam-5761	53	18	interior	interior	ADJ
ejpam-5761	53	19	state	state	NOUN
ejpam-5761	53	20	of	of	ADP
ejpam-5761	53	21	m.	m.	PROPN
ejpam-5761	53	22	surya	surya	PROPN
ejpam-5761	53	23	priya	priya	PROPN
ejpam-5761	53	24	,	,	PUNCT
ejpam-5761	53	25	n.	n.	PROPN
ejpam-5761	53	26	nathiya	nathiya	PROPN
ejpam-5761	53	27	/	/	SYM
ejpam-5761	53	28	eur	eur	PROPN
ejpam-5761	53	29	.	.	PUNCT
ejpam-5761	54	1	j.	j.	PROPN
ejpam-5761	54	2	pure	pure	PROPN
ejpam-5761	54	3	appl	appl	PROPN
ejpam-5761	54	4	.	.	PROPN
ejpam-5761	54	5	math	math	PROPN
ejpam-5761	54	6	,	,	PUNCT
ejpam-5761	54	7	18	18	NUM
ejpam-5761	54	8	(	(	PUNCT
ejpam-5761	54	9	1	1	NUM
ejpam-5761	54	10	)	)	PUNCT
ejpam-5761	54	11	(	(	PUNCT
ejpam-5761	54	12	2025	2025	NUM
ejpam-5761	54	13	)	)	PUNCT
ejpam-5761	54	14	,	,	PUNCT
ejpam-5761	54	15	5761	5761	NUM
ejpam-5761	54	16	3	3	NUM
ejpam-5761	54	17	of	of	ADP
ejpam-5761	54	18	11	11	NUM
ejpam-5761	54	19	a	a	DET
ejpam-5761	54	20	subset	subset	NOUN
ejpam-5761	55	1	k	k	PROPN
ejpam-5761	55	2	if	if	SCONJ
ejpam-5761	55	3	and	and	CCONJ
ejpam-5761	55	4	only	only	ADV
ejpam-5761	55	5	if	if	SCONJ
ejpam-5761	55	6	x	x	PROPN
ejpam-5761	55	7	and	and	CCONJ
ejpam-5761	55	8	all	all	PRON
ejpam-5761	55	9	its	its	PRON
ejpam-5761	55	10	neighbours	neighbour	NOUN
ejpam-5761	55	11	are	be	AUX
ejpam-5761	55	12	in	in	ADP
ejpam-5761	55	13	a	a	DET
ejpam-5761	55	14	subset	subset	NOUN
ejpam-5761	55	15	k	k	PROPN
ejpam-5761	55	16	of	of	ADP
ejpam-5761	55	17	n	n	PROPN
ejpam-5761	55	18	.	.	PUNCT
ejpam-5761	56	1	the	the	DET
ejpam-5761	56	2	set	set	NOUN
ejpam-5761	56	3	of	of	ADP
ejpam-5761	56	4	all	all	DET
ejpam-5761	56	5	interior	interior	ADJ
ejpam-5761	56	6	states	state	NOUN
ejpam-5761	56	7	of	of	ADP
ejpam-5761	56	8	k	k	PROPN
ejpam-5761	56	9	is	be	AUX
ejpam-5761	56	10	denoted	denote	VERB
ejpam-5761	56	11	by	by	ADP
ejpam-5761	56	12	k̊	k̊	PROPN
ejpam-5761	56	13	and	and	CCONJ
ejpam-5761	56	14	the	the	DET
ejpam-5761	56	15	boundary	boundary	NOUN
ejpam-5761	56	16	of	of	ADP
ejpam-5761	56	17	k	k	X
ejpam-5761	56	18	by	by	ADP
ejpam-5761	56	19	∂k	∂k	PROPN
ejpam-5761	56	20	=	=	PUNCT
ejpam-5761	56	21	k\k̊.	k\k̊.	NOUN
ejpam-5761	56	22	definition	definition	NOUN
ejpam-5761	56	23	3	3	NUM
ejpam-5761	56	24	.	.	PUNCT
ejpam-5761	57	1	laplacian(∆	laplacian(∆	NOUN
ejpam-5761	57	2	):	):	PUNCT
ejpam-5761	57	3	let	let	VERB
ejpam-5761	57	4	s(x	s(x	PROPN
ejpam-5761	57	5	)	)	PUNCT
ejpam-5761	57	6	be	be	AUX
ejpam-5761	57	7	a	a	DET
ejpam-5761	57	8	real	real	ADV
ejpam-5761	57	9	valued	value	VERB
ejpam-5761	57	10	function	function	NOUN
ejpam-5761	57	11	defined	define	VERB
ejpam-5761	57	12	on	on	ADP
ejpam-5761	57	13	n	n	X
ejpam-5761	57	14	.	.	PUNCT
ejpam-5761	58	1	for	for	ADP
ejpam-5761	58	2	x	x	PROPN
ejpam-5761	58	3	∈	∈	PROPN
ejpam-5761	58	4	k̊	k̊	PROPN
ejpam-5761	58	5	,	,	PUNCT
ejpam-5761	58	6	k	k	PROPN
ejpam-5761	58	7	⊂	⊂	PROPN
ejpam-5761	58	8	n	n	PROPN
ejpam-5761	58	9	,	,	PUNCT
ejpam-5761	58	10	the	the	DET
ejpam-5761	58	11	laplacian	laplacian	X
ejpam-5761	58	12	(	(	PUNCT
ejpam-5761	58	13	∆	∆	PROPN
ejpam-5761	58	14	)	)	PUNCT
ejpam-5761	58	15	of	of	ADP
ejpam-5761	58	16	s	s	PRON
ejpam-5761	58	17	at	at	ADP
ejpam-5761	58	18	x	x	PROPN
ejpam-5761	58	19	is	be	AUX
ejpam-5761	58	20	defined	define	VERB
ejpam-5761	58	21	as	as	ADP
ejpam-5761	58	22	∆s(x	∆s(x	PROPN
ejpam-5761	58	23	)	)	PUNCT
ejpam-5761	59	1	=	=	PUNCT
ejpam-5761	59	2	∑	∑	PUNCT
ejpam-5761	59	3	y∼x	y∼x	PROPN
ejpam-5761	59	4	p(x	p(x	PROPN
ejpam-5761	59	5	,	,	PUNCT
ejpam-5761	59	6	y)[s(y)−	y)[s(y)−	NOUN
ejpam-5761	59	7	s(x	s(x	PROPN
ejpam-5761	59	8	)	)	PUNCT
ejpam-5761	59	9	]	]	PUNCT
ejpam-5761	60	1	=	=	SYM
ejpam-5761	60	2	(	(	PUNCT
ejpam-5761	60	3	a−	a−	PROPN
ejpam-5761	60	4	i)s(x	i)s(x	PROPN
ejpam-5761	60	5	)	)	PUNCT
ejpam-5761	60	6	definition	definition	NOUN
ejpam-5761	60	7	4	4	NUM
ejpam-5761	60	8	.	.	PUNCT
ejpam-5761	61	1	a	a	DET
ejpam-5761	61	2	function	function	NOUN
ejpam-5761	61	3	u	u	NOUN
ejpam-5761	61	4	defined	define	VERB
ejpam-5761	61	5	on	on	ADP
ejpam-5761	61	6	a	a	DET
ejpam-5761	61	7	subset	subset	NOUN
ejpam-5761	61	8	k	k	PROPN
ejpam-5761	61	9	is	be	AUX
ejpam-5761	61	10	said	say	VERB
ejpam-5761	61	11	to	to	PART
ejpam-5761	61	12	be	be	AUX
ejpam-5761	61	13	p	p	ADJ
ejpam-5761	61	14	-superaverage	-superaverage	NOUN
ejpam-5761	61	15	(	(	PUNCT
ejpam-5761	61	16	respectively	respectively	ADV
ejpam-5761	61	17	,	,	PUNCT
ejpam-5761	61	18	p	p	NOUN
ejpam-5761	61	19	-subaverage	-subaverage	NOUN
ejpam-5761	61	20	and	and	CCONJ
ejpam-5761	61	21	p	p	NOUN
ejpam-5761	61	22	-average	-average	NOUN
ejpam-5761	61	23	)	)	PUNCT
ejpam-5761	61	24	on	on	ADP
ejpam-5761	61	25	k	k	PROPN
ejpam-5761	61	26	if	if	SCONJ
ejpam-5761	62	1	and	and	CCONJ
ejpam-5761	62	2	only	only	ADV
ejpam-5761	62	3	if	if	SCONJ
ejpam-5761	62	4	s(x	s(x	NOUN
ejpam-5761	62	5	)	)	PUNCT
ejpam-5761	62	6	≥	≥	NOUN
ejpam-5761	62	7	as(x	as(x	NOUN
ejpam-5761	62	8	)	)	PUNCT
ejpam-5761	62	9	(	(	PUNCT
ejpam-5761	62	10	respectively	respectively	ADV
ejpam-5761	62	11	s(x	s(x	ADJ
ejpam-5761	62	12	)	)	PUNCT
ejpam-5761	62	13	≤	≤	NOUN
ejpam-5761	62	14	as(x	as(x	NOUN
ejpam-5761	62	15	)	)	PUNCT
ejpam-5761	62	16	and	and	CCONJ
ejpam-5761	62	17	s(x	s(x	NOUN
ejpam-5761	62	18	)	)	PUNCT
ejpam-5761	62	19	=	=	SYM
ejpam-5761	62	20	as(x	as(x	NOUN
ejpam-5761	62	21	)	)	PUNCT
ejpam-5761	62	22	)	)	PUNCT
ejpam-5761	62	23	for	for	ADP
ejpam-5761	62	24	every	every	DET
ejpam-5761	62	25	x	x	SYM
ejpam-5761	62	26	∈	∈	PROPN
ejpam-5761	62	27	k̊.	k̊.	PROPN
ejpam-5761	62	28	definition	definition	NOUN
ejpam-5761	62	29	5	5	NUM
ejpam-5761	62	30	.	.	PUNCT
ejpam-5761	63	1	if	if	SCONJ
ejpam-5761	63	2	p	p	PRON
ejpam-5761	63	3	≥	≥	NOUN
ejpam-5761	63	4	0	0	NUM
ejpam-5761	63	5	is	be	AUX
ejpam-5761	63	6	a	a	DET
ejpam-5761	63	7	p	p	ADJ
ejpam-5761	63	8	-superaverage	-superaverage	NOUN
ejpam-5761	63	9	function	function	NOUN
ejpam-5761	63	10	such	such	ADJ
ejpam-5761	63	11	that	that	SCONJ
ejpam-5761	63	12	any	any	DET
ejpam-5761	63	13	p	p	NOUN
ejpam-5761	63	14	-subaverage	-subaverage	NOUN
ejpam-5761	63	15	function	function	NOUN
ejpam-5761	63	16	majorized	majorize	VERB
ejpam-5761	63	17	by	by	ADP
ejpam-5761	63	18	p	p	PROPN
ejpam-5761	63	19	is	be	AUX
ejpam-5761	63	20	non	non	ADJ
ejpam-5761	63	21	-	-	ADJ
ejpam-5761	63	22	positive	positive	ADJ
ejpam-5761	63	23	,	,	PUNCT
ejpam-5761	63	24	then	then	ADV
ejpam-5761	63	25	p	p	PROPN
ejpam-5761	63	26	is	be	AUX
ejpam-5761	63	27	called	call	VERB
ejpam-5761	63	28	a	a	DET
ejpam-5761	63	29	p	p	NOUN
ejpam-5761	63	30	-potential	-potential	PROPN
ejpam-5761	63	31	.	.	PUNCT
ejpam-5761	64	1	definition	definition	NOUN
ejpam-5761	64	2	6	6	NUM
ejpam-5761	64	3	.	.	PUNCT
ejpam-5761	65	1	if	if	SCONJ
ejpam-5761	65	2	s	s	PROPN
ejpam-5761	65	3	is	be	AUX
ejpam-5761	65	4	a	a	DET
ejpam-5761	65	5	p	p	ADJ
ejpam-5761	65	6	-superaverage	-superaverage	NOUN
ejpam-5761	65	7	function	function	NOUN
ejpam-5761	65	8	on	on	ADP
ejpam-5761	65	9	n	n	NOUN
ejpam-5761	65	10	and	and	CCONJ
ejpam-5761	65	11	if	if	SCONJ
ejpam-5761	65	12	k	k	PROPN
ejpam-5761	65	13	is	be	AUX
ejpam-5761	65	14	a	a	DET
ejpam-5761	65	15	subset	subset	NOUN
ejpam-5761	65	16	of	of	ADP
ejpam-5761	65	17	n	n	CCONJ
ejpam-5761	65	18	such	such	ADJ
ejpam-5761	65	19	that	that	SCONJ
ejpam-5761	65	20	∆s(x	∆s(x	NOUN
ejpam-5761	65	21	)	)	PUNCT
ejpam-5761	66	1	=	=	SYM
ejpam-5761	66	2	0	0	NUM
ejpam-5761	66	3	for	for	ADP
ejpam-5761	66	4	each	each	DET
ejpam-5761	66	5	x	x	PUNCT
ejpam-5761	66	6	in	in	ADP
ejpam-5761	66	7	n\k	n\k	PROPN
ejpam-5761	66	8	,	,	PUNCT
ejpam-5761	66	9	then	then	ADV
ejpam-5761	66	10	k	k	PROPN
ejpam-5761	66	11	is	be	AUX
ejpam-5761	66	12	said	say	VERB
ejpam-5761	66	13	to	to	PART
ejpam-5761	66	14	be	be	AUX
ejpam-5761	66	15	the	the	DET
ejpam-5761	66	16	p	p	NOUN
ejpam-5761	66	17	-average	-average	NOUN
ejpam-5761	66	18	support	support	NOUN
ejpam-5761	66	19	of	of	ADP
ejpam-5761	66	20	s	s	PRON
ejpam-5761	66	21	in	in	ADP
ejpam-5761	66	22	n	n	PROPN
ejpam-5761	66	23	.	.	PUNCT
ejpam-5761	67	1	if	if	SCONJ
ejpam-5761	67	2	there	there	PRON
ejpam-5761	67	3	is	be	VERB
ejpam-5761	67	4	a	a	DET
ejpam-5761	67	5	perturbation	perturbation	NOUN
ejpam-5761	67	6	on	on	ADP
ejpam-5761	67	7	laplace	laplace	NOUN
ejpam-5761	67	8	operator	operator	NOUN
ejpam-5761	67	9	indicated	indicate	VERB
ejpam-5761	67	10	by	by	ADP
ejpam-5761	67	11	the	the	DET
ejpam-5761	67	12	operator	operator	NOUN
ejpam-5761	67	13	∆qu(x	∆qu(x	VERB
ejpam-5761	67	14	)	)	PUNCT
ejpam-5761	68	1	=	=	VERB
ejpam-5761	68	2	∆u(x	∆u(x	ADV
ejpam-5761	68	3	)	)	PUNCT
ejpam-5761	68	4	−	−	PROPN
ejpam-5761	68	5	q(x)u(x	q(x)u(x	PROPN
ejpam-5761	68	6	)	)	PUNCT
ejpam-5761	68	7	,	,	PUNCT
ejpam-5761	68	8	q	q	X
ejpam-5761	68	9	≥	≥	NOUN
ejpam-5761	68	10	0	0	NUM
ejpam-5761	68	11	,	,	PUNCT
ejpam-5761	68	12	(	(	PUNCT
ejpam-5761	68	13	the	the	DET
ejpam-5761	68	14	operator	operator	NOUN
ejpam-5761	68	15	∆q	∆q	PROPN
ejpam-5761	68	16	is	be	AUX
ejpam-5761	68	17	commonly	commonly	ADV
ejpam-5761	68	18	referred	refer	VERB
ejpam-5761	68	19	to	to	ADP
ejpam-5761	68	20	as	as	ADP
ejpam-5761	68	21	a	a	DET
ejpam-5761	68	22	schrödinger	schrödinger	NOUN
ejpam-5761	68	23	operator	operator	NOUN
ejpam-5761	68	24	on	on	ADP
ejpam-5761	68	25	n	n	CCONJ
ejpam-5761	68	26	)	)	PUNCT
ejpam-5761	68	27	we	we	PRON
ejpam-5761	68	28	have	have	VERB
ejpam-5761	68	29	∆qu(x	∆qu(x	NOUN
ejpam-5761	68	30	)	)	PUNCT
ejpam-5761	69	1	=	=	SYM
ejpam-5761	69	2	∑	∑	PUNCT
ejpam-5761	69	3	y	y	PROPN
ejpam-5761	69	4	p(x	p(x	PROPN
ejpam-5761	69	5	,	,	PUNCT
ejpam-5761	69	6	y)u(y)−	y)u(y)−	PROPN
ejpam-5761	69	7	[	[	X
ejpam-5761	69	8	1	1	NUM
ejpam-5761	69	9	+	+	NUM
ejpam-5761	69	10	q(x)]u(x	q(x)]u(x	NOUN
ejpam-5761	69	11	)	)	PUNCT
ejpam-5761	70	1	=[	=[	NOUN
ejpam-5761	70	2	1	1	NUM
ejpam-5761	70	3	+	+	X
ejpam-5761	70	4	q(x)][a	q(x)][a	PROPN
ejpam-5761	70	5	′	′	NOUN
ejpam-5761	71	1	−	−	PROPN
ejpam-5761	71	2	i]u(x	i]u(x	NOUN
ejpam-5761	71	3	)	)	PUNCT
ejpam-5761	71	4	where	where	SCONJ
ejpam-5761	71	5	a	a	DET
ejpam-5761	71	6	′	′	NOUN
ejpam-5761	71	7	u(x	u(x	NOUN
ejpam-5761	71	8	)	)	PUNCT
ejpam-5761	72	1	=	=	PUNCT
ejpam-5761	72	2	∑	∑	PUNCT
ejpam-5761	73	1	p	p	NOUN
ejpam-5761	74	1	′	′	NUM
ejpam-5761	74	2	(	(	PUNCT
ejpam-5761	74	3	x	x	NOUN
ejpam-5761	74	4	,	,	PUNCT
ejpam-5761	74	5	y)u(y	y)u(y	NOUN
ejpam-5761	74	6	)	)	PUNCT
ejpam-5761	74	7	,	,	PUNCT
ejpam-5761	74	8	p	p	NOUN
ejpam-5761	74	9	′	′	X
ejpam-5761	74	10	(	(	PUNCT
ejpam-5761	74	11	x	x	NOUN
ejpam-5761	74	12	,	,	PUNCT
ejpam-5761	74	13	y	y	NOUN
ejpam-5761	74	14	)	)	PUNCT
ejpam-5761	74	15	=	=	SYM
ejpam-5761	74	16	p(x	p(x	PROPN
ejpam-5761	74	17	,	,	PUNCT
ejpam-5761	74	18	y	y	NOUN
ejpam-5761	74	19	)	)	PUNCT
ejpam-5761	74	20	1+q(x	1+q(x	NUM
ejpam-5761	74	21	)	)	PUNCT
ejpam-5761	74	22	≤	≤	NUM
ejpam-5761	74	23	p(x	p(x	PROPN
ejpam-5761	74	24	,	,	PUNCT
ejpam-5761	74	25	y	y	PROPN
ejpam-5761	74	26	)	)	PUNCT
ejpam-5761	74	27	.	.	PUNCT
ejpam-5761	75	1	then	then	ADV
ejpam-5761	75	2	the	the	DET
ejpam-5761	75	3	potential	potential	ADJ
ejpam-5761	75	4	theory	theory	NOUN
ejpam-5761	75	5	associated	associate	VERB
ejpam-5761	75	6	with	with	ADP
ejpam-5761	75	7	the	the	DET
ejpam-5761	75	8	schrödinger	schrödinger	NOUN
ejpam-5761	75	9	operator	operator	NOUN
ejpam-5761	75	10	∆q	∆q	PROPN
ejpam-5761	75	11	depends	depend	VERB
ejpam-5761	75	12	on	on	ADP
ejpam-5761	75	13	a	a	DET
ejpam-5761	75	14	′	′	NOUN
ejpam-5761	75	15	,	,	PUNCT
ejpam-5761	75	16	just	just	ADV
ejpam-5761	75	17	as	as	SCONJ
ejpam-5761	75	18	the	the	DET
ejpam-5761	75	19	potential	potential	ADJ
ejpam-5761	75	20	theory	theory	NOUN
ejpam-5761	75	21	associated	associate	VERB
ejpam-5761	75	22	with	with	ADP
ejpam-5761	75	23	the	the	DET
ejpam-5761	75	24	laplace	laplace	NOUN
ejpam-5761	75	25	operator	operator	NOUN
ejpam-5761	75	26	∆	∆	PROPN
ejpam-5761	75	27	depends	depend	VERB
ejpam-5761	75	28	on	on	ADP
ejpam-5761	75	29	the	the	DET
ejpam-5761	75	30	operator	operator	NOUN
ejpam-5761	75	31	a.	a.	NOUN
ejpam-5761	75	32	since	since	SCONJ
ejpam-5761	75	33	a	a	DET
ejpam-5761	75	34	′	′	NUM
ejpam-5761	75	35	φ(x	φ(x	NOUN
ejpam-5761	75	36	)	)	PUNCT
ejpam-5761	75	37	≤	≤	NOUN
ejpam-5761	75	38	aφ(x	aφ(x	NOUN
ejpam-5761	75	39	)	)	PUNCT
ejpam-5761	75	40	for	for	ADP
ejpam-5761	75	41	any	any	DET
ejpam-5761	75	42	functions	function	NOUN
ejpam-5761	75	43	φ	φ	X
ejpam-5761	75	44	≥	≥	NOUN
ejpam-5761	75	45	0	0	NUM
ejpam-5761	75	46	on	on	ADP
ejpam-5761	75	47	n	n	PRON
ejpam-5761	75	48	,	,	PUNCT
ejpam-5761	75	49	the	the	DET
ejpam-5761	75	50	relation	relation	NOUN
ejpam-5761	75	51	between	between	ADP
ejpam-5761	75	52	the	the	DET
ejpam-5761	75	53	schrödinger	schrödinger	NOUN
ejpam-5761	75	54	potentials	potential	VERB
ejpam-5761	75	55	and	and	CCONJ
ejpam-5761	75	56	the	the	DET
ejpam-5761	75	57	laplace	laplace	NOUN
ejpam-5761	75	58	potentials	potential	NOUN
ejpam-5761	75	59	is	be	AUX
ejpam-5761	75	60	exhibited	exhibit	VERB
ejpam-5761	75	61	by	by	ADP
ejpam-5761	75	62	the	the	DET
ejpam-5761	75	63	relation	relation	NOUN
ejpam-5761	75	64	between	between	ADP
ejpam-5761	75	65	p	p	NOUN
ejpam-5761	75	66	′	′	NOUN
ejpam-5761	75	67	=	=	SYM
ejpam-5761	75	68	{	{	PUNCT
ejpam-5761	75	69	p′	p′	NOUN
ejpam-5761	75	70	(	(	PUNCT
ejpam-5761	75	71	x	x	NOUN
ejpam-5761	75	72	,	,	PUNCT
ejpam-5761	75	73	y	y	NOUN
ejpam-5761	75	74	)	)	PUNCT
ejpam-5761	75	75	}	}	PUNCT
ejpam-5761	75	76	and	and	CCONJ
ejpam-5761	75	77	p	p	NOUN
ejpam-5761	75	78	=	=	NOUN
ejpam-5761	75	79	{	{	PUNCT
ejpam-5761	75	80	p(x	p(x	PROPN
ejpam-5761	75	81	,	,	PUNCT
ejpam-5761	75	82	y	y	NOUN
ejpam-5761	75	83	)	)	PUNCT
ejpam-5761	75	84	}	}	PUNCT
ejpam-5761	75	85	.	.	PUNCT
ejpam-5761	76	1	here	here	ADV
ejpam-5761	76	2	p	p	X
ejpam-5761	76	3	′	′	NOUN
ejpam-5761	76	4	(	(	PUNCT
ejpam-5761	76	5	x	x	NOUN
ejpam-5761	76	6	,	,	PUNCT
ejpam-5761	76	7	y	y	NOUN
ejpam-5761	76	8	)	)	PUNCT
ejpam-5761	76	9	≤	≤	NOUN
ejpam-5761	76	10	p(x	p(x	PROPN
ejpam-5761	76	11	,	,	PUNCT
ejpam-5761	76	12	y	y	NOUN
ejpam-5761	76	13	)	)	PUNCT
ejpam-5761	76	14	for	for	ADP
ejpam-5761	76	15	any	any	DET
ejpam-5761	76	16	pair	pair	NOUN
ejpam-5761	76	17	x	x	NOUN
ejpam-5761	76	18	,	,	PUNCT
ejpam-5761	76	19	y	y	PROPN
ejpam-5761	76	20	and	and	CCONJ
ejpam-5761	76	21	we	we	PRON
ejpam-5761	76	22	say	say	VERB
ejpam-5761	76	23	that	that	SCONJ
ejpam-5761	76	24	p	p	ADJ
ejpam-5761	76	25	′	′	NOUN
ejpam-5761	76	26	is	be	AUX
ejpam-5761	76	27	subordinate	subordinate	ADJ
ejpam-5761	76	28	to	to	ADP
ejpam-5761	76	29	p	p	PROPN
ejpam-5761	76	30	.	.	PUNCT
ejpam-5761	77	1	in	in	ADP
ejpam-5761	77	2	the	the	DET
ejpam-5761	77	3	following	follow	VERB
ejpam-5761	77	4	sections	section	NOUN
ejpam-5761	77	5	we	we	PRON
ejpam-5761	77	6	investigate	investigate	VERB
ejpam-5761	77	7	this	this	DET
ejpam-5761	77	8	subordinate	subordinate	ADJ
ejpam-5761	77	9	structure	structure	NOUN
ejpam-5761	77	10	in	in	ADP
ejpam-5761	77	11	an	an	DET
ejpam-5761	77	12	abstract	abstract	ADJ
ejpam-5761	77	13	setting	setting	NOUN
ejpam-5761	77	14	.	.	PUNCT
ejpam-5761	78	1	3	3	X
ejpam-5761	78	2	.	.	X
ejpam-5761	78	3	subordinate	subordinate	ADJ
ejpam-5761	78	4	structure	structure	NOUN
ejpam-5761	78	5	definition	definition	NOUN
ejpam-5761	78	6	7	7	NUM
ejpam-5761	78	7	.	.	PUNCT
ejpam-5761	79	1	let	let	VERB
ejpam-5761	79	2	{	{	PUNCT
ejpam-5761	79	3	p′	p′	NOUN
ejpam-5761	79	4	(	(	PUNCT
ejpam-5761	79	5	x	x	NOUN
ejpam-5761	79	6	,	,	PUNCT
ejpam-5761	79	7	y	y	NOUN
ejpam-5761	79	8	)	)	PUNCT
ejpam-5761	79	9	}	}	PUNCT
ejpam-5761	79	10	be	be	AUX
ejpam-5761	79	11	a	a	DET
ejpam-5761	79	12	set	set	NOUN
ejpam-5761	79	13	of	of	ADP
ejpam-5761	79	14	transition	transition	NOUN
ejpam-5761	79	15	indices	index	NOUN
ejpam-5761	79	16	on	on	ADP
ejpam-5761	79	17	n	n	CCONJ
ejpam-5761	79	18	such	such	ADJ
ejpam-5761	79	19	that	that	DET
ejpam-5761	79	20	p(x	p(x	PROPN
ejpam-5761	79	21	,	,	PUNCT
ejpam-5761	79	22	y	y	PROPN
ejpam-5761	79	23	)	)	PUNCT
ejpam-5761	80	1	≥	≥	NOUN
ejpam-5761	81	1	p	p	NOUN
ejpam-5761	81	2	′	′	NOUN
ejpam-5761	81	3	(	(	PUNCT
ejpam-5761	81	4	x	x	NOUN
ejpam-5761	81	5	,	,	PUNCT
ejpam-5761	81	6	y	y	PROPN
ejpam-5761	81	7	)	)	PUNCT
ejpam-5761	81	8	≥	≥	NOUN
ejpam-5761	81	9	0	0	NUM
ejpam-5761	81	10	for	for	ADP
ejpam-5761	81	11	any	any	DET
ejpam-5761	81	12	pair	pair	NOUN
ejpam-5761	81	13	of	of	ADP
ejpam-5761	81	14	states	state	NOUN
ejpam-5761	81	15	x	x	PUNCT
ejpam-5761	81	16	and	and	CCONJ
ejpam-5761	81	17	y	y	PROPN
ejpam-5761	81	18	and	and	CCONJ
ejpam-5761	81	19	p	p	NOUN
ejpam-5761	82	1	′	′	NOUN
ejpam-5761	82	2	(	(	PUNCT
ejpam-5761	82	3	x	x	NOUN
ejpam-5761	82	4	,	,	PUNCT
ejpam-5761	82	5	y	y	NOUN
ejpam-5761	82	6	)	)	PUNCT
ejpam-5761	82	7	<	<	X
ejpam-5761	83	1	p(x	p(x	PROPN
ejpam-5761	83	2	,	,	PUNCT
ejpam-5761	83	3	y	y	NOUN
ejpam-5761	83	4	)	)	PUNCT
ejpam-5761	83	5	for	for	ADP
ejpam-5761	83	6	atleast	atleast	ADJ
ejpam-5761	83	7	one	one	NUM
ejpam-5761	83	8	pair	pair	NOUN
ejpam-5761	83	9	of	of	ADP
ejpam-5761	83	10	x	x	PUNCT
ejpam-5761	83	11	and	and	CCONJ
ejpam-5761	83	12	y.	y.	PROPN
ejpam-5761	84	1	then	then	ADV
ejpam-5761	84	2	we	we	PRON
ejpam-5761	84	3	say	say	VERB
ejpam-5761	84	4	that	that	SCONJ
ejpam-5761	84	5	p	p	NOUN
ejpam-5761	85	1	′	′	NOUN
ejpam-5761	85	2	=	=	SYM
ejpam-5761	85	3	{	{	PUNCT
ejpam-5761	85	4	p′	p′	NOUN
ejpam-5761	85	5	(	(	PUNCT
ejpam-5761	85	6	x	x	NOUN
ejpam-5761	85	7	,	,	PUNCT
ejpam-5761	85	8	y	y	NOUN
ejpam-5761	85	9	)	)	PUNCT
ejpam-5761	85	10	}	}	PUNCT
ejpam-5761	85	11	defines	define	VERB
ejpam-5761	85	12	a	a	DET
ejpam-5761	85	13	submarkov	submarkov	ADJ
ejpam-5761	85	14	average	average	ADJ
ejpam-5761	85	15	structure	structure	NOUN
ejpam-5761	85	16	on	on	ADP
ejpam-5761	85	17	n	n	PROPN
ejpam-5761	85	18	that	that	PRON
ejpam-5761	85	19	is	be	AUX
ejpam-5761	85	20	subordinate	subordinate	ADJ
ejpam-5761	85	21	to	to	ADP
ejpam-5761	85	22	the	the	DET
ejpam-5761	85	23	average	average	ADJ
ejpam-5761	85	24	structure	structure	NOUN
ejpam-5761	85	25	defined	define	VERB
ejpam-5761	85	26	by	by	ADP
ejpam-5761	85	27	p	p	PROPN
ejpam-5761	85	28	=	=	PUNCT
ejpam-5761	85	29	{	{	PUNCT
ejpam-5761	85	30	p(x	p(x	PROPN
ejpam-5761	85	31	,	,	PUNCT
ejpam-5761	85	32	y	y	NOUN
ejpam-5761	85	33	)	)	PUNCT
ejpam-5761	85	34	}	}	PUNCT
ejpam-5761	85	35	;	;	PUNCT
ejpam-5761	85	36	or	or	CCONJ
ejpam-5761	85	37	simply	simply	ADV
ejpam-5761	85	38	that	that	DET
ejpam-5761	85	39	p	p	ADJ
ejpam-5761	85	40	′	′	NOUN
ejpam-5761	85	41	is	be	AUX
ejpam-5761	85	42	subordinate	subordinate	ADJ
ejpam-5761	85	43	to	to	ADP
ejpam-5761	85	44	p	p	NOUN
ejpam-5761	85	45	on	on	ADP
ejpam-5761	85	46	n	n	PROPN
ejpam-5761	85	47	.	.	PUNCT
ejpam-5761	86	1	m.	m.	PROPN
ejpam-5761	86	2	surya	surya	PROPN
ejpam-5761	86	3	priya	priya	PROPN
ejpam-5761	86	4	,	,	PUNCT
ejpam-5761	86	5	n.	n.	PROPN
ejpam-5761	86	6	nathiya	nathiya	PROPN
ejpam-5761	86	7	/	/	SYM
ejpam-5761	86	8	eur	eur	PROPN
ejpam-5761	86	9	.	.	PUNCT
ejpam-5761	87	1	j.	j.	PROPN
ejpam-5761	87	2	pure	pure	PROPN
ejpam-5761	87	3	appl	appl	PROPN
ejpam-5761	87	4	.	.	PROPN
ejpam-5761	87	5	math	math	PROPN
ejpam-5761	87	6	,	,	PUNCT
ejpam-5761	87	7	18	18	NUM
ejpam-5761	87	8	(	(	PUNCT
ejpam-5761	87	9	1	1	NUM
ejpam-5761	87	10	)	)	PUNCT
ejpam-5761	87	11	(	(	PUNCT
ejpam-5761	87	12	2025	2025	NUM
ejpam-5761	87	13	)	)	PUNCT
ejpam-5761	87	14	,	,	PUNCT
ejpam-5761	87	15	5761	5761	NUM
ejpam-5761	87	16	4	4	NUM
ejpam-5761	87	17	of	of	ADP
ejpam-5761	87	18	11	11	NUM
ejpam-5761	87	19	remark	remark	NOUN
ejpam-5761	87	20	1	1	NUM
ejpam-5761	87	21	.	.	PUNCT
ejpam-5761	88	1	a	a	DET
ejpam-5761	88	2	schrödinger	schrödinger	NOUN
ejpam-5761	88	3	operator	operator	NOUN
ejpam-5761	88	4	∆q	∆q	PROPN
ejpam-5761	88	5	defines	define	VERB
ejpam-5761	88	6	a	a	DET
ejpam-5761	88	7	subordinate	subordinate	ADJ
ejpam-5761	88	8	structure	structure	NOUN
ejpam-5761	88	9	on	on	ADP
ejpam-5761	88	10	n	n	PROPN
ejpam-5761	88	11	,	,	PUNCT
ejpam-5761	88	12	when	when	SCONJ
ejpam-5761	88	13	q	q	X
ejpam-5761	88	14	>	>	X
ejpam-5761	88	15	0	0	PUNCT
ejpam-5761	88	16	and	and	CCONJ
ejpam-5761	88	17	p	p	NOUN
ejpam-5761	88	18	′	′	NOUN
ejpam-5761	88	19	(	(	PUNCT
ejpam-5761	88	20	x	x	NOUN
ejpam-5761	88	21	,	,	PUNCT
ejpam-5761	88	22	y	y	NOUN
ejpam-5761	88	23	)	)	PUNCT
ejpam-5761	88	24	=	=	SYM
ejpam-5761	88	25	p(x	p(x	PROPN
ejpam-5761	88	26	,	,	PUNCT
ejpam-5761	88	27	y	y	NOUN
ejpam-5761	88	28	)	)	PUNCT
ejpam-5761	88	29	1+q(x	1+q(x	NUM
ejpam-5761	88	30	)	)	PUNCT
ejpam-5761	88	31	.	.	PUNCT
ejpam-5761	89	1	but	but	CCONJ
ejpam-5761	89	2	for	for	ADP
ejpam-5761	89	3	a	a	DET
ejpam-5761	89	4	subordinate	subordinate	ADJ
ejpam-5761	89	5	structure	structure	NOUN
ejpam-5761	89	6	{	{	PUNCT
ejpam-5761	89	7	n	n	CCONJ
ejpam-5761	89	8	,	,	PUNCT
ejpam-5761	89	9	p	p	NOUN
ejpam-5761	89	10	′	′	NOUN
ejpam-5761	89	11	}	}	PUNCT
ejpam-5761	89	12	to	to	PART
ejpam-5761	89	13	define	define	VERB
ejpam-5761	89	14	a	a	DET
ejpam-5761	89	15	schrödinger	schrödinger	NOUN
ejpam-5761	89	16	operator	operator	NOUN
ejpam-5761	89	17	on	on	ADP
ejpam-5761	89	18	n	n	PROPN
ejpam-5761	89	19	,	,	PUNCT
ejpam-5761	89	20	it	it	PRON
ejpam-5761	89	21	is	be	AUX
ejpam-5761	89	22	necessary	necessary	ADJ
ejpam-5761	89	23	that	that	SCONJ
ejpam-5761	89	24	for	for	ADP
ejpam-5761	89	25	every	every	DET
ejpam-5761	89	26	x	x	SYM
ejpam-5761	89	27	∈	∈	PROPN
ejpam-5761	89	28	n	n	X
ejpam-5761	89	29	,	,	PUNCT
ejpam-5761	89	30	the	the	DET
ejpam-5761	89	31	quantity	quantity	NOUN
ejpam-5761	89	32	p(x	p(x	PROPN
ejpam-5761	89	33	,	,	PUNCT
ejpam-5761	89	34	y	y	PROPN
ejpam-5761	89	35	)	)	PUNCT
ejpam-5761	89	36	p′	p′	NOUN
ejpam-5761	89	37	(	(	PUNCT
ejpam-5761	89	38	x	x	NOUN
ejpam-5761	89	39	,	,	PUNCT
ejpam-5761	89	40	y	y	NOUN
ejpam-5761	89	41	)	)	PUNCT
ejpam-5761	89	42	is	be	AUX
ejpam-5761	89	43	independent	independent	ADJ
ejpam-5761	89	44	of	of	ADP
ejpam-5761	89	45	y	y	PROPN
ejpam-5761	89	46	,	,	PUNCT
ejpam-5761	89	47	for	for	ADP
ejpam-5761	89	48	any	any	DET
ejpam-5761	89	49	y	y	PROPN
ejpam-5761	89	50	∼	∼	NOUN
ejpam-5761	89	51	x.	x.	NOUN
ejpam-5761	89	52	definition	definition	NOUN
ejpam-5761	89	53	8	8	NUM
ejpam-5761	89	54	.	.	PUNCT
ejpam-5761	90	1	a	a	DET
ejpam-5761	90	2	real	real	ADV
ejpam-5761	90	3	valued	value	VERB
ejpam-5761	90	4	function	function	NOUN
ejpam-5761	90	5	u	u	NOUN
ejpam-5761	90	6	on	on	ADP
ejpam-5761	90	7	a	a	DET
ejpam-5761	90	8	subset	subset	NOUN
ejpam-5761	90	9	k	k	PROPN
ejpam-5761	90	10	of	of	ADP
ejpam-5761	90	11	n	n	PROPN
ejpam-5761	90	12	is	be	AUX
ejpam-5761	90	13	said	say	VERB
ejpam-5761	90	14	to	to	PART
ejpam-5761	90	15	be	be	AUX
ejpam-5761	90	16	p	p	NOUN
ejpam-5761	90	17	′	′	ADJ
ejpam-5761	90	18	-superaverage	-superaverage	NOUN
ejpam-5761	90	19	(	(	PUNCT
ejpam-5761	90	20	respectively	respectively	ADV
ejpam-5761	90	21	p	p	ADJ
ejpam-5761	90	22	′	′	NUM
ejpam-5761	90	23	-subaverage	-subaverage	NOUN
ejpam-5761	90	24	)	)	PUNCT
ejpam-5761	90	25	on	on	ADP
ejpam-5761	90	26	k	k	X
ejpam-5761	90	27	if	if	SCONJ
ejpam-5761	90	28	and	and	CCONJ
ejpam-5761	90	29	only	only	ADV
ejpam-5761	90	30	if	if	SCONJ
ejpam-5761	90	31	∆	∆	PROPN
ejpam-5761	90	32	′	′	NUM
ejpam-5761	90	33	u(x	u(x	PROPN
ejpam-5761	90	34	)	)	PUNCT
ejpam-5761	90	35	≤	≤	NUM
ejpam-5761	90	36	0	0	NUM
ejpam-5761	90	37	(	(	PUNCT
ejpam-5761	90	38	∆	∆	PROPN
ejpam-5761	90	39	′	′	NUM
ejpam-5761	90	40	u(x	u(x	PROPN
ejpam-5761	90	41	)	)	PUNCT
ejpam-5761	90	42	≥	≥	NOUN
ejpam-5761	90	43	0	0	NUM
ejpam-5761	90	44	respectively	respectively	ADV
ejpam-5761	90	45	)	)	PUNCT
ejpam-5761	90	46	or	or	CCONJ
ejpam-5761	90	47	u(x	u(x	PROPN
ejpam-5761	90	48	)	)	PUNCT
ejpam-5761	90	49	≥	≥	NOUN
ejpam-5761	90	50	∑	∑	PUNCT
ejpam-5761	90	51	y	y	PROPN
ejpam-5761	90	52	p	p	NOUN
ejpam-5761	91	1	′	′	NUM
ejpam-5761	91	2	(	(	PUNCT
ejpam-5761	91	3	x	x	NOUN
ejpam-5761	91	4	,	,	PUNCT
ejpam-5761	91	5	y)u(y	y)u(y	NOUN
ejpam-5761	91	6	)	)	PUNCT
ejpam-5761	91	7	for	for	ADP
ejpam-5761	91	8	every	every	DET
ejpam-5761	91	9	x	x	NOUN
ejpam-5761	91	10	in	in	ADP
ejpam-5761	91	11	k̊.	k̊.	PROPN
ejpam-5761	91	12	(	(	PUNCT
ejpam-5761	91	13	here	here	ADV
ejpam-5761	91	14	∆	∆	PROPN
ejpam-5761	91	15	′	′	NUM
ejpam-5761	91	16	u(x	u(x	PROPN
ejpam-5761	91	17	)	)	PUNCT
ejpam-5761	92	1	=	=	PUNCT
ejpam-5761	93	1	[	[	PUNCT
ejpam-5761	93	2	∑	∑	PUNCT
ejpam-5761	93	3	y	y	PROPN
ejpam-5761	93	4	p	p	NOUN
ejpam-5761	93	5	′	′	NOUN
ejpam-5761	93	6	(	(	PUNCT
ejpam-5761	93	7	x	x	NOUN
ejpam-5761	93	8	,	,	PUNCT
ejpam-5761	93	9	y)u(y	y)u(y	NOUN
ejpam-5761	93	10	)	)	PUNCT
ejpam-5761	93	11	]	]	PUNCT
ejpam-5761	93	12	−	−	PROPN
ejpam-5761	93	13	u(x	u(x	PROPN
ejpam-5761	93	14	)	)	PUNCT
ejpam-5761	93	15	=	=	SYM
ejpam-5761	93	16	(	(	PUNCT
ejpam-5761	93	17	a	a	DET
ejpam-5761	93	18	′	′	NOUN
ejpam-5761	93	19	−	−	NOUN
ejpam-5761	93	20	i)u(x	i)u(x	VERB
ejpam-5761	93	21	)	)	PUNCT
ejpam-5761	93	22	)	)	PUNCT
ejpam-5761	93	23	.	.	PUNCT
ejpam-5761	94	1	definition	definition	NOUN
ejpam-5761	94	2	9	9	NUM
ejpam-5761	94	3	.	.	PUNCT
ejpam-5761	95	1	a	a	DET
ejpam-5761	95	2	real	real	ADV
ejpam-5761	95	3	valued	value	VERB
ejpam-5761	95	4	function	function	NOUN
ejpam-5761	95	5	u	u	NOUN
ejpam-5761	95	6	on	on	ADP
ejpam-5761	95	7	a	a	DET
ejpam-5761	95	8	subset	subset	NOUN
ejpam-5761	95	9	k	k	PROPN
ejpam-5761	95	10	of	of	ADP
ejpam-5761	95	11	n	n	PROPN
ejpam-5761	95	12	is	be	AUX
ejpam-5761	95	13	said	say	VERB
ejpam-5761	95	14	to	to	PART
ejpam-5761	95	15	be	be	AUX
ejpam-5761	95	16	p	p	NOUN
ejpam-5761	95	17	′	′	NUM
ejpam-5761	95	18	-average	-average	NOUN
ejpam-5761	95	19	on	on	ADP
ejpam-5761	95	20	k	k	NOUN
ejpam-5761	95	21	if	if	SCONJ
ejpam-5761	95	22	and	and	CCONJ
ejpam-5761	95	23	only	only	ADV
ejpam-5761	95	24	if	if	SCONJ
ejpam-5761	95	25	∆	∆	PROPN
ejpam-5761	95	26	′	′	NUM
ejpam-5761	95	27	u(x	u(x	PROPN
ejpam-5761	95	28	)	)	PUNCT
ejpam-5761	95	29	=	=	SYM
ejpam-5761	95	30	0	0	NUM
ejpam-5761	95	31	for	for	ADP
ejpam-5761	95	32	every	every	DET
ejpam-5761	95	33	x	x	NOUN
ejpam-5761	95	34	in	in	ADP
ejpam-5761	95	35	k̊.	k̊.	PROPN
ejpam-5761	95	36	proposition	proposition	NOUN
ejpam-5761	95	37	1	1	X
ejpam-5761	95	38	.	.	PUNCT
ejpam-5761	96	1	if	if	SCONJ
ejpam-5761	96	2	p	p	NOUN
ejpam-5761	96	3	′	′	NOUN
ejpam-5761	96	4	is	be	AUX
ejpam-5761	96	5	subordinate	subordinate	ADJ
ejpam-5761	96	6	to	to	ADP
ejpam-5761	96	7	p	p	NOUN
ejpam-5761	96	8	then	then	ADV
ejpam-5761	96	9	for	for	ADP
ejpam-5761	96	10	any	any	DET
ejpam-5761	96	11	u	u	NOUN
ejpam-5761	96	12	≥	≥	NOUN
ejpam-5761	96	13	0	0	NUM
ejpam-5761	96	14	on	on	ADP
ejpam-5761	96	15	a	a	DET
ejpam-5761	96	16	subset	subset	NOUN
ejpam-5761	96	17	k	k	PROPN
ejpam-5761	96	18	of	of	ADP
ejpam-5761	96	19	n	n	PROPN
ejpam-5761	96	20	,	,	PUNCT
ejpam-5761	96	21	∑	∑	ADV
ejpam-5761	96	22	p(x	p(x	PROPN
ejpam-5761	96	23	,	,	PUNCT
ejpam-5761	96	24	y)u(y	y)u(y	NOUN
ejpam-5761	96	25	)	)	PUNCT
ejpam-5761	96	26	≥	≥	NOUN
ejpam-5761	97	1	∑	∑	PUNCT
ejpam-5761	97	2	p	p	NOUN
ejpam-5761	97	3	′	′	NUM
ejpam-5761	97	4	(	(	PUNCT
ejpam-5761	97	5	x	x	NOUN
ejpam-5761	97	6	,	,	PUNCT
ejpam-5761	97	7	y)u(y	y)u(y	NOUN
ejpam-5761	97	8	)	)	PUNCT
ejpam-5761	97	9	,	,	PUNCT
ejpam-5761	97	10	for	for	ADP
ejpam-5761	97	11	every	every	DET
ejpam-5761	97	12	x	x	PROPN
ejpam-5761	97	13	∈	∈	PROPN
ejpam-5761	97	14	k̊.	k̊.	PROPN
ejpam-5761	97	15	hence	hence	ADV
ejpam-5761	97	16	(	(	PUNCT
ejpam-5761	97	17	i	i	NOUN
ejpam-5761	97	18	)	)	PUNCT
ejpam-5761	97	19	if	if	SCONJ
ejpam-5761	97	20	u	u	PRON
ejpam-5761	97	21	≥	≥	NOUN
ejpam-5761	97	22	0	0	NUM
ejpam-5761	97	23	is	be	AUX
ejpam-5761	97	24	p	p	ADJ
ejpam-5761	97	25	-superaverage	-superaverage	NOUN
ejpam-5761	97	26	on	on	ADP
ejpam-5761	97	27	k	k	PROPN
ejpam-5761	97	28	then	then	ADV
ejpam-5761	97	29	u	u	PROPN
ejpam-5761	97	30	is	be	AUX
ejpam-5761	97	31	p	p	NOUN
ejpam-5761	97	32	′	′	ADJ
ejpam-5761	97	33	-superaverage	-superaverage	NOUN
ejpam-5761	97	34	on	on	ADP
ejpam-5761	97	35	k.	k.	PROPN
ejpam-5761	97	36	(	(	PUNCT
ejpam-5761	97	37	ii	ii	PROPN
ejpam-5761	97	38	)	)	PUNCT
ejpam-5761	97	39	if	if	SCONJ
ejpam-5761	97	40	u	u	PRON
ejpam-5761	97	41	≥	≥	NOUN
ejpam-5761	97	42	0	0	NUM
ejpam-5761	97	43	is	be	AUX
ejpam-5761	97	44	p	p	NOUN
ejpam-5761	97	45	′	′	NUM
ejpam-5761	97	46	-subaverage	-subaverage	NOUN
ejpam-5761	97	47	on	on	ADP
ejpam-5761	97	48	k	k	PROPN
ejpam-5761	97	49	then	then	ADV
ejpam-5761	97	50	u	u	PROPN
ejpam-5761	97	51	is	be	AUX
ejpam-5761	97	52	p	p	NOUN
ejpam-5761	97	53	-subaverage	-subaverage	NOUN
ejpam-5761	97	54	on	on	ADP
ejpam-5761	97	55	k.	k.	PROPN
ejpam-5761	97	56	(	(	PUNCT
ejpam-5761	97	57	iii	iii	X
ejpam-5761	97	58	)	)	PUNCT
ejpam-5761	97	59	if	if	SCONJ
ejpam-5761	97	60	u	u	NOUN
ejpam-5761	97	61	=	=	NOUN
ejpam-5761	97	62	0	0	NUM
ejpam-5761	97	63	is	be	AUX
ejpam-5761	97	64	p	p	NOUN
ejpam-5761	97	65	′	′	NUM
ejpam-5761	97	66	-average	-average	NOUN
ejpam-5761	97	67	on	on	ADP
ejpam-5761	97	68	k	k	PROPN
ejpam-5761	97	69	then	then	ADV
ejpam-5761	97	70	u	u	PROPN
ejpam-5761	97	71	is	be	AUX
ejpam-5761	97	72	p	p	NOUN
ejpam-5761	97	73	′	′	ADJ
ejpam-5761	97	74	-superaverage	-superaverage	NOUN
ejpam-5761	97	75	on	on	ADP
ejpam-5761	97	76	k.	k.	NOUN
ejpam-5761	97	77	proof	proof	PROPN
ejpam-5761	97	78	.	.	PUNCT
ejpam-5761	98	1	for	for	ADP
ejpam-5761	98	2	a	a	DET
ejpam-5761	98	3	p	p	ADJ
ejpam-5761	98	4	-superaverage	-superaverage	NOUN
ejpam-5761	98	5	function	function	NOUN
ejpam-5761	98	6	u	u	NOUN
ejpam-5761	98	7	on	on	ADP
ejpam-5761	98	8	k	k	PROPN
ejpam-5761	98	9	⊂	⊂	PROPN
ejpam-5761	98	10	n	n	CCONJ
ejpam-5761	98	11	,	,	PUNCT
ejpam-5761	98	12	we	we	PRON
ejpam-5761	98	13	have	have	AUX
ejpam-5761	98	14	∑	∑	ADV
ejpam-5761	98	15	p(x	p(x	VERB
ejpam-5761	98	16	,	,	PUNCT
ejpam-5761	98	17	y)u(y	y)u(y	NOUN
ejpam-5761	98	18	)	)	PUNCT
ejpam-5761	98	19	≤	≤	NUM
ejpam-5761	98	20	u(x	u(x	NOUN
ejpam-5761	98	21	)	)	PUNCT
ejpam-5761	98	22	.	.	PUNCT
ejpam-5761	99	1	since	since	SCONJ
ejpam-5761	99	2	p	p	NOUN
ejpam-5761	99	3	′	′	NOUN
ejpam-5761	99	4	is	be	AUX
ejpam-5761	99	5	subordinate	subordinate	ADJ
ejpam-5761	99	6	to	to	ADP
ejpam-5761	99	7	p	p	PROPN
ejpam-5761	99	8	,	,	PUNCT
ejpam-5761	99	9	∑	∑	PUNCT
ejpam-5761	99	10	p(x	p(x	PROPN
ejpam-5761	99	11	,	,	PUNCT
ejpam-5761	99	12	y)u(y	y)u(y	NOUN
ejpam-5761	99	13	)	)	PUNCT
ejpam-5761	99	14	≥	≥	NOUN
ejpam-5761	100	1	∑	∑	PUNCT
ejpam-5761	100	2	p	p	NOUN
ejpam-5761	100	3	′	′	NUM
ejpam-5761	100	4	(	(	PUNCT
ejpam-5761	100	5	x	x	NOUN
ejpam-5761	100	6	,	,	PUNCT
ejpam-5761	100	7	y)u(y	y)u(y	NOUN
ejpam-5761	100	8	)	)	PUNCT
ejpam-5761	100	9	u(x	u(x	PROPN
ejpam-5761	100	10	)	)	PUNCT
ejpam-5761	100	11	≥	≥	AUX
ejpam-5761	100	12	∑	∑	PUNCT
ejpam-5761	100	13	p(x	p(x	PROPN
ejpam-5761	100	14	,	,	PUNCT
ejpam-5761	100	15	y)u(y	y)u(y	NOUN
ejpam-5761	100	16	)	)	PUNCT
ejpam-5761	100	17	≥	≥	NOUN
ejpam-5761	101	1	∑	∑	PUNCT
ejpam-5761	101	2	p	p	NOUN
ejpam-5761	101	3	′	′	NUM
ejpam-5761	101	4	(	(	PUNCT
ejpam-5761	101	5	x	x	NOUN
ejpam-5761	101	6	,	,	PUNCT
ejpam-5761	101	7	y)u(y	y)u(y	NOUN
ejpam-5761	101	8	)	)	PUNCT
ejpam-5761	101	9	u(x	u(x	PROPN
ejpam-5761	101	10	)	)	PUNCT
ejpam-5761	101	11	≥	≥	AUX
ejpam-5761	101	12	∑	∑	PUNCT
ejpam-5761	101	13	p(x	p(x	PROPN
ejpam-5761	101	14	,	,	PUNCT
ejpam-5761	101	15	y	y	NOUN
ejpam-5761	101	16	)	)	PUNCT
ejpam-5761	101	17	′	′	NUM
ejpam-5761	102	1	u(y	u(y	NOUN
ejpam-5761	102	2	)	)	PUNCT
ejpam-5761	102	3	thus	thus	ADV
ejpam-5761	102	4	,	,	PUNCT
ejpam-5761	102	5	if	if	SCONJ
ejpam-5761	102	6	u	u	NOUN
ejpam-5761	102	7	is	be	AUX
ejpam-5761	102	8	p	p	ADJ
ejpam-5761	102	9	-superaverage	-superaverage	NOUN
ejpam-5761	102	10	on	on	ADP
ejpam-5761	102	11	a	a	DET
ejpam-5761	102	12	subset	subset	NOUN
ejpam-5761	102	13	k	k	PROPN
ejpam-5761	102	14	of	of	ADP
ejpam-5761	102	15	n	n	PROPN
ejpam-5761	102	16	then	then	ADV
ejpam-5761	102	17	u	u	NOUN
ejpam-5761	102	18	is	be	AUX
ejpam-5761	102	19	p	p	NOUN
ejpam-5761	102	20	′	′	ADJ
ejpam-5761	102	21	-superaverage	-superaverage	NOUN
ejpam-5761	102	22	on	on	ADP
ejpam-5761	102	23	k	k	PROPN
ejpam-5761	102	24	⊂	⊂	PROPN
ejpam-5761	102	25	n	n	PROPN
ejpam-5761	102	26	.	.	PUNCT
ejpam-5761	103	1	similarly	similarly	ADV
ejpam-5761	103	2	the	the	DET
ejpam-5761	103	3	proof	proof	NOUN
ejpam-5761	103	4	follows	follow	VERB
ejpam-5761	103	5	for	for	ADP
ejpam-5761	103	6	(	(	PUNCT
ejpam-5761	103	7	ii	ii	NOUN
ejpam-5761	103	8	)	)	PUNCT
ejpam-5761	103	9	and	and	CCONJ
ejpam-5761	103	10	(	(	PUNCT
ejpam-5761	103	11	iii	iii	NOUN
ejpam-5761	103	12	)	)	PUNCT
ejpam-5761	103	13	.	.	PUNCT
ejpam-5761	104	1	3.1	3.1	NUM
ejpam-5761	104	2	.	.	PUNCT
ejpam-5761	104	3	properties	property	NOUN
ejpam-5761	104	4	of	of	ADP
ejpam-5761	104	5	p	p	NOUN
ejpam-5761	104	6	′	′	ADJ
ejpam-5761	104	7	-superaverage	-superaverage	NOUN
ejpam-5761	104	8	functions	function	NOUN
ejpam-5761	104	9	(	(	PUNCT
ejpam-5761	104	10	i	i	NOUN
ejpam-5761	104	11	)	)	PUNCT
ejpam-5761	104	12	if	if	SCONJ
ejpam-5761	104	13	s1	s1	PROPN
ejpam-5761	104	14	and	and	CCONJ
ejpam-5761	104	15	s2	s2	PROPN
ejpam-5761	104	16	are	be	AUX
ejpam-5761	104	17	p	p	ADJ
ejpam-5761	104	18	′	′	ADJ
ejpam-5761	104	19	-superaverage	-superaverage	NOUN
ejpam-5761	104	20	on	on	ADP
ejpam-5761	104	21	a	a	DET
ejpam-5761	104	22	subset	subset	NOUN
ejpam-5761	104	23	k	k	NOUN
ejpam-5761	104	24	and	and	CCONJ
ejpam-5761	104	25	if	if	SCONJ
ejpam-5761	104	26	α1	α1	PROPN
ejpam-5761	104	27	,	,	PUNCT
ejpam-5761	104	28	α2	α2	PROPN
ejpam-5761	104	29	are	be	AUX
ejpam-5761	104	30	two	two	NUM
ejpam-5761	104	31	non	non	ADJ
ejpam-5761	104	32	-	-	ADJ
ejpam-5761	104	33	negative	negative	ADJ
ejpam-5761	104	34	numbers	number	NOUN
ejpam-5761	104	35	,	,	PUNCT
ejpam-5761	104	36	then	then	ADV
ejpam-5761	104	37	α1s1	α1s1	ADP
ejpam-5761	104	38	+	+	X
ejpam-5761	104	39	α2s2	α2s2	NOUN
ejpam-5761	104	40	and	and	CCONJ
ejpam-5761	104	41	inf(s1	inf(s1	ADJ
ejpam-5761	104	42	,	,	PUNCT
ejpam-5761	104	43	s2	s2	PROPN
ejpam-5761	104	44	)	)	PUNCT
ejpam-5761	104	45	are	be	AUX
ejpam-5761	104	46	p	p	NOUN
ejpam-5761	104	47	′	′	ADJ
ejpam-5761	104	48	-superaverage	-superaverage	NOUN
ejpam-5761	104	49	on	on	ADP
ejpam-5761	104	50	k.	k.	PROPN
ejpam-5761	104	51	(	(	PUNCT
ejpam-5761	104	52	ii	ii	PROPN
ejpam-5761	104	53	)	)	PUNCT
ejpam-5761	104	54	if	if	SCONJ
ejpam-5761	104	55	{	{	PUNCT
ejpam-5761	104	56	si	si	AUX
ejpam-5761	104	57	}	}	PUNCT
ejpam-5761	104	58	is	be	AUX
ejpam-5761	104	59	a	a	DET
ejpam-5761	104	60	lower	low	ADJ
ejpam-5761	104	61	directed	direct	VERB
ejpam-5761	104	62	family	family	NOUN
ejpam-5761	104	63	of	of	ADP
ejpam-5761	104	64	p	p	NOUN
ejpam-5761	104	65	′	′	ADJ
ejpam-5761	104	66	-superaverage	-superaverage	NOUN
ejpam-5761	104	67	functions	function	NOUN
ejpam-5761	104	68	on	on	ADP
ejpam-5761	104	69	k	k	NOUN
ejpam-5761	104	70	,	,	PUNCT
ejpam-5761	104	71	then	then	ADV
ejpam-5761	104	72	s(x	s(x	PROPN
ejpam-5761	104	73	)	)	PUNCT
ejpam-5761	105	1	=	=	SYM
ejpam-5761	105	2	infi	infi	NOUN
ejpam-5761	105	3	ui(x	ui(x	PUNCT
ejpam-5761	105	4	)	)	PUNCT
ejpam-5761	105	5	and	and	CCONJ
ejpam-5761	105	6	then	then	ADV
ejpam-5761	105	7	s	s	AUX
ejpam-5761	105	8	is	be	AUX
ejpam-5761	105	9	p	p	ADJ
ejpam-5761	105	10	′	′	ADJ
ejpam-5761	105	11	-superaverage	-superaverage	NOUN
ejpam-5761	105	12	onk	onk	PROPN
ejpam-5761	105	13	.	.	PUNCT
ejpam-5761	106	1	(	(	PUNCT
ejpam-5761	106	2	a	a	DET
ejpam-5761	106	3	lower	lower	ADV
ejpam-5761	106	4	directed	direct	VERB
ejpam-5761	106	5	family	family	NOUN
ejpam-5761	106	6	f	f	PROPN
ejpam-5761	106	7	of	of	ADP
ejpam-5761	106	8	functions	function	NOUN
ejpam-5761	106	9	means	mean	VERB
ejpam-5761	106	10	that	that	SCONJ
ejpam-5761	106	11	if	if	SCONJ
ejpam-5761	106	12	f	f	X
ejpam-5761	106	13	,	,	PUNCT
ejpam-5761	106	14	g	g	PROPN
ejpam-5761	106	15	∈	∈	PROPN
ejpam-5761	106	16	f	f	X
ejpam-5761	106	17	then	then	ADV
ejpam-5761	106	18	inf(f	inf(f	PROPN
ejpam-5761	106	19	,	,	PUNCT
ejpam-5761	106	20	g	g	NOUN
ejpam-5761	106	21	)	)	PUNCT
ejpam-5761	106	22	is	be	AUX
ejpam-5761	106	23	also	also	ADV
ejpam-5761	106	24	in	in	ADP
ejpam-5761	106	25	f	f	PROPN
ejpam-5761	106	26	)	)	PUNCT
ejpam-5761	106	27	(	(	PUNCT
ejpam-5761	106	28	iii	iii	NOUN
ejpam-5761	106	29	)	)	PUNCT
ejpam-5761	106	30	greatest	great	ADJ
ejpam-5761	106	31	p	p	NOUN
ejpam-5761	106	32	′	′	NUM
ejpam-5761	106	33	-average	-average	NOUN
ejpam-5761	106	34	minorant	minorant	NOUN
ejpam-5761	106	35	(	(	PUNCT
ejpam-5761	106	36	g.p	g.p	NOUN
ejpam-5761	106	37	′	′	NUM
ejpam-5761	106	38	-a.m	-a.m	PUNCT
ejpam-5761	106	39	):	):	PUNCT
ejpam-5761	106	40	suppose	suppose	VERB
ejpam-5761	106	41	u(x	u(x	NOUN
ejpam-5761	106	42	)	)	PUNCT
ejpam-5761	106	43	≥	≥	NOUN
ejpam-5761	106	44	v(x	v(x	NOUN
ejpam-5761	106	45	)	)	PUNCT
ejpam-5761	106	46	on	on	ADP
ejpam-5761	106	47	n	n	PRON
ejpam-5761	106	48	where	where	SCONJ
ejpam-5761	106	49	u(x	u(x	NOUN
ejpam-5761	106	50	)	)	PUNCT
ejpam-5761	106	51	is	be	AUX
ejpam-5761	106	52	p	p	NOUN
ejpam-5761	106	53	′	′	ADJ
ejpam-5761	106	54	-superaverage	-superaverage	NOUN
ejpam-5761	106	55	and	and	CCONJ
ejpam-5761	106	56	v(x	v(x	PROPN
ejpam-5761	106	57	)	)	PUNCT
ejpam-5761	106	58	is	be	AUX
ejpam-5761	106	59	p	p	NOUN
ejpam-5761	106	60	′	′	NUM
ejpam-5761	106	61	-subaverage	-subaverage	NOUN
ejpam-5761	106	62	on	on	ADP
ejpam-5761	106	63	n	n	PROPN
ejpam-5761	106	64	.	.	PUNCT
ejpam-5761	107	1	then	then	ADV
ejpam-5761	107	2	there	there	PRON
ejpam-5761	107	3	exists	exist	VERB
ejpam-5761	107	4	a	a	DET
ejpam-5761	107	5	p	p	NOUN
ejpam-5761	107	6	′	′	NUM
ejpam-5761	107	7	average	average	ADJ
ejpam-5761	107	8	function	function	NOUN
ejpam-5761	107	9	h(x	h(x	PROPN
ejpam-5761	107	10	)	)	PUNCT
ejpam-5761	107	11	on	on	ADP
ejpam-5761	107	12	n	n	PROPN
ejpam-5761	107	13	,	,	PUNCT
ejpam-5761	107	14	u(x	u(x	PROPN
ejpam-5761	107	15	)	)	PUNCT
ejpam-5761	107	16	≥	≥	NOUN
ejpam-5761	107	17	h(x	h(x	PROPN
ejpam-5761	107	18	)	)	PUNCT
ejpam-5761	107	19	≥	≥	NOUN
ejpam-5761	107	20	v(x	v(x	PROPN
ejpam-5761	107	21	)	)	PUNCT
ejpam-5761	107	22	and	and	CCONJ
ejpam-5761	107	23	if	if	SCONJ
ejpam-5761	107	24	h1	h1	NOUN
ejpam-5761	107	25	is	be	AUX
ejpam-5761	107	26	any	any	DET
ejpam-5761	107	27	other	other	ADJ
ejpam-5761	107	28	p	p	NOUN
ejpam-5761	107	29	′	′	NUM
ejpam-5761	107	30	-average	-average	NOUN
ejpam-5761	107	31	function	function	NOUN
ejpam-5761	107	32	on	on	ADP
ejpam-5761	107	33	n	n	X
ejpam-5761	107	34	between	between	ADP
ejpam-5761	107	35	u(x	u(x	NOUN
ejpam-5761	107	36	)	)	PUNCT
ejpam-5761	107	37	and	and	CCONJ
ejpam-5761	107	38	v(x	v(x	PROPN
ejpam-5761	107	39	)	)	PUNCT
ejpam-5761	107	40	,	,	PUNCT
ejpam-5761	107	41	then	then	ADV
ejpam-5761	107	42	h(x	h(x	PROPN
ejpam-5761	107	43	)	)	PUNCT
ejpam-5761	107	44	≥	≥	NOUN
ejpam-5761	107	45	h1(x	h1(x	NOUN
ejpam-5761	107	46	)	)	PUNCT
ejpam-5761	107	47	on	on	ADP
ejpam-5761	107	48	n	n	PROPN
ejpam-5761	107	49	(	(	PUNCT
ejpam-5761	107	50	section	section	NOUN
ejpam-5761	107	51	3.1	3.1	NUM
ejpam-5761	107	52	,	,	PUNCT
ejpam-5761	107	53	[	[	X
ejpam-5761	107	54	1	1	NUM
ejpam-5761	107	55	]	]	NUM
ejpam-5761	107	56	)	)	PUNCT
ejpam-5761	107	57	.	.	PUNCT
ejpam-5761	108	1	m.	m.	PROPN
ejpam-5761	108	2	surya	surya	PROPN
ejpam-5761	108	3	priya	priya	PROPN
ejpam-5761	108	4	,	,	PUNCT
ejpam-5761	108	5	n.	n.	PROPN
ejpam-5761	108	6	nathiya	nathiya	PROPN
ejpam-5761	108	7	/	/	SYM
ejpam-5761	108	8	eur	eur	PROPN
ejpam-5761	108	9	.	.	PUNCT
ejpam-5761	109	1	j.	j.	PROPN
ejpam-5761	109	2	pure	pure	PROPN
ejpam-5761	109	3	appl	appl	PROPN
ejpam-5761	109	4	.	.	PROPN
ejpam-5761	109	5	math	math	PROPN
ejpam-5761	109	6	,	,	PUNCT
ejpam-5761	109	7	18	18	NUM
ejpam-5761	109	8	(	(	PUNCT
ejpam-5761	109	9	1	1	NUM
ejpam-5761	109	10	)	)	PUNCT
ejpam-5761	109	11	(	(	PUNCT
ejpam-5761	109	12	2025	2025	NUM
ejpam-5761	109	13	)	)	PUNCT
ejpam-5761	109	14	,	,	PUNCT
ejpam-5761	109	15	5761	5761	NUM
ejpam-5761	109	16	5	5	NUM
ejpam-5761	109	17	of	of	ADP
ejpam-5761	109	18	11	11	NUM
ejpam-5761	109	19	proof	proof	NOUN
ejpam-5761	109	20	.	.	PUNCT
ejpam-5761	110	1	let	let	VERB
ejpam-5761	110	2	{	{	PUNCT
ejpam-5761	110	3	kn	kn	NOUN
ejpam-5761	110	4	}	}	PUNCT
ejpam-5761	110	5	be	be	AUX
ejpam-5761	110	6	an	an	DET
ejpam-5761	110	7	exhaustion	exhaustion	NOUN
ejpam-5761	110	8	of	of	ADP
ejpam-5761	110	9	n	n	NUM
ejpam-5761	110	10	by	by	ADP
ejpam-5761	110	11	finite	finite	ADJ
ejpam-5761	110	12	sets	set	NOUN
ejpam-5761	110	13	;	;	PUNCT
ejpam-5761	110	14	that	that	PRON
ejpam-5761	110	15	is	is	ADV
ejpam-5761	111	1	kn	kn	PROPN
ejpam-5761	111	2	⊂	⊂	PROPN
ejpam-5761	111	3	k̊n+1	k̊n+1	PROPN
ejpam-5761	111	4	⊂	⊂	PROPN
ejpam-5761	111	5	kn+1	kn+1	PROPN
ejpam-5761	111	6	and	and	CCONJ
ejpam-5761	111	7	x	x	X
ejpam-5761	111	8	=	=	PROPN
ejpam-5761	111	9	∪kn	∪kn	PROPN
ejpam-5761	111	10	.	.	PUNCT
ejpam-5761	112	1	let	let	VERB
ejpam-5761	112	2	dnu	dnu	PROPN
ejpam-5761	112	3	denote	denote	VERB
ejpam-5761	112	4	the	the	DET
ejpam-5761	112	5	p	p	NOUN
ejpam-5761	112	6	′	′	ADJ
ejpam-5761	112	7	-superaverage	-superaverage	NOUN
ejpam-5761	112	8	function	function	NOUN
ejpam-5761	112	9	on	on	ADP
ejpam-5761	112	10	n	n	PROPN
ejpam-5761	112	11	,	,	PUNCT
ejpam-5761	112	12	equal	equal	ADJ
ejpam-5761	112	13	to	to	ADP
ejpam-5761	112	14	the	the	DET
ejpam-5761	112	15	dirichlet	dirichlet	NOUN
ejpam-5761	112	16	solution	solution	NOUN
ejpam-5761	112	17	on	on	ADP
ejpam-5761	112	18	kn	kn	PROPN
ejpam-5761	112	19	with	with	ADP
ejpam-5761	112	20	boundary	boundary	ADJ
ejpam-5761	112	21	values	value	NOUN
ejpam-5761	112	22	u	u	NOUN
ejpam-5761	112	23	and	and	CCONJ
ejpam-5761	112	24	extended	extend	VERB
ejpam-5761	112	25	by	by	ADP
ejpam-5761	112	26	u	u	PROPN
ejpam-5761	112	27	outside	outside	ADP
ejpam-5761	112	28	kn	kn	PROPN
ejpam-5761	112	29	.	.	PUNCT
ejpam-5761	113	1	then	then	ADV
ejpam-5761	113	2	{	{	PUNCT
ejpam-5761	113	3	dnu	dnu	PROPN
ejpam-5761	113	4	}	}	PUNCT
ejpam-5761	113	5	is	be	AUX
ejpam-5761	113	6	a	a	DET
ejpam-5761	113	7	decreasing	decrease	VERB
ejpam-5761	113	8	sequence	sequence	NOUN
ejpam-5761	113	9	of	of	ADP
ejpam-5761	113	10	p	p	NOUN
ejpam-5761	113	11	′	′	ADJ
ejpam-5761	113	12	-superaverage	-superaverage	NOUN
ejpam-5761	113	13	functions	function	NOUN
ejpam-5761	113	14	,	,	PUNCT
ejpam-5761	113	15	each	each	DET
ejpam-5761	113	16	dnu	dnu	PROPN
ejpam-5761	113	17	≥	≥	NUM
ejpam-5761	113	18	v	v	NOUN
ejpam-5761	113	19	on	on	ADP
ejpam-5761	113	20	n	n	PROPN
ejpam-5761	113	21	.	.	PUNCT
ejpam-5761	114	1	hence	hence	ADV
ejpam-5761	114	2	d[u	d[u	PROPN
ejpam-5761	114	3	]	]	X
ejpam-5761	114	4	=	=	SYM
ejpam-5761	114	5	limndnu	limndnu	NOUN
ejpam-5761	114	6	is	be	AUX
ejpam-5761	114	7	p	p	NOUN
ejpam-5761	114	8	′	′	ADJ
ejpam-5761	114	9	-superaverage	-superaverage	NOUN
ejpam-5761	114	10	function	function	NOUN
ejpam-5761	114	11	.	.	PUNCT
ejpam-5761	115	1	now	now	ADV
ejpam-5761	115	2	for	for	ADP
ejpam-5761	115	3	any	any	DET
ejpam-5761	115	4	z	z	NOUN
ejpam-5761	115	5	in	in	ADP
ejpam-5761	115	6	n	n	PROPN
ejpam-5761	115	7	,	,	PUNCT
ejpam-5761	115	8	z	z	NOUN
ejpam-5761	115	9	∈	∈	NOUN
ejpam-5761	115	10	k̊m	k̊m	NOUN
ejpam-5761	115	11	for	for	ADP
ejpam-5761	115	12	some	some	DET
ejpam-5761	115	13	m.	m.	NOUN
ejpam-5761	115	14	hence	hence	ADV
ejpam-5761	115	15	dn(x	dn(x	PUNCT
ejpam-5761	115	16	)	)	PUNCT
ejpam-5761	115	17	is	be	AUX
ejpam-5761	115	18	p	p	NOUN
ejpam-5761	115	19	′	′	NUM
ejpam-5761	115	20	-average	-average	NOUN
ejpam-5761	115	21	at	at	ADP
ejpam-5761	115	22	x	x	X
ejpam-5761	115	23	=	=	PUNCT
ejpam-5761	115	24	z	z	NOUN
ejpam-5761	115	25	for	for	ADP
ejpam-5761	115	26	all	all	PRON
ejpam-5761	115	27	n	n	DET
ejpam-5761	115	28	≥	≥	NOUN
ejpam-5761	115	29	m.	m.	NOUN
ejpam-5761	115	30	consequently	consequently	ADV
ejpam-5761	115	31	,	,	PUNCT
ejpam-5761	115	32	d[u](x	d[u](x	X
ejpam-5761	115	33	)	)	PUNCT
ejpam-5761	115	34	is	be	AUX
ejpam-5761	115	35	p	p	NOUN
ejpam-5761	115	36	′	′	NUM
ejpam-5761	115	37	-average	-average	NOUN
ejpam-5761	115	38	at	at	ADP
ejpam-5761	115	39	x	x	X
ejpam-5761	115	40	=	=	PUNCT
ejpam-5761	115	41	z.	z.	PROPN
ejpam-5761	116	1	this	this	PRON
ejpam-5761	116	2	shows	show	VERB
ejpam-5761	116	3	that	that	SCONJ
ejpam-5761	116	4	d[u	d[u	PROPN
ejpam-5761	116	5	]	]	X
ejpam-5761	116	6	is	be	AUX
ejpam-5761	116	7	p	p	ADJ
ejpam-5761	116	8	′	′	NUM
ejpam-5761	116	9	-average	-average	NOUN
ejpam-5761	116	10	on	on	ADP
ejpam-5761	116	11	n	n	PROPN
ejpam-5761	116	12	.	.	PUNCT
ejpam-5761	117	1	thus	thus	ADV
ejpam-5761	117	2	u	u	PROPN
ejpam-5761	117	3	≥	≥	PROPN
ejpam-5761	117	4	d[u	d[u	PROPN
ejpam-5761	117	5	]	]	X
ejpam-5761	117	6	≥	≥	X
ejpam-5761	117	7	v.	v.	ADP
ejpam-5761	117	8	moreover	moreover	ADV
ejpam-5761	117	9	if	if	SCONJ
ejpam-5761	117	10	h1	h1	PROPN
ejpam-5761	117	11	is	be	AUX
ejpam-5761	117	12	p	p	ADJ
ejpam-5761	117	13	-average	-average	NOUN
ejpam-5761	117	14	,	,	PUNCT
ejpam-5761	117	15	u	u	PROPN
ejpam-5761	117	16	≥	≥	NOUN
ejpam-5761	117	17	h1	h1	VERB
ejpam-5761	117	18	≥	≥	PROPN
ejpam-5761	117	19	v	v	NOUN
ejpam-5761	117	20	,	,	PUNCT
ejpam-5761	117	21	then	then	ADV
ejpam-5761	117	22	dnu	dnu	PROPN
ejpam-5761	117	23	≥	≥	PROPN
ejpam-5761	117	24	h1	h1	PROPN
ejpam-5761	117	25	for	for	ADP
ejpam-5761	117	26	any	any	DET
ejpam-5761	117	27	n	n	NOUN
ejpam-5761	117	28	so	so	SCONJ
ejpam-5761	117	29	that	that	SCONJ
ejpam-5761	117	30	d[u	d[u	PROPN
ejpam-5761	117	31	]	]	X
ejpam-5761	117	32	≥	≥	X
ejpam-5761	117	33	h1	h1	PROPN
ejpam-5761	117	34	.	.	PUNCT
ejpam-5761	118	1	we	we	PRON
ejpam-5761	118	2	term	term	PROPN
ejpam-5761	118	3	d[u	d[u	PROPN
ejpam-5761	118	4	]	]	PUNCT
ejpam-5761	118	5	as	as	ADP
ejpam-5761	118	6	the	the	DET
ejpam-5761	118	7	greatest	great	ADJ
ejpam-5761	118	8	p	p	ADJ
ejpam-5761	118	9	′	′	NUM
ejpam-5761	118	10	-average	-average	NOUN
ejpam-5761	118	11	minorant	minorant	NOUN
ejpam-5761	118	12	of	of	ADP
ejpam-5761	118	13	u	u	NOUN
ejpam-5761	118	14	on	on	ADP
ejpam-5761	118	15	n	n	PROPN
ejpam-5761	118	16	.	.	PUNCT
ejpam-5761	119	1	(	(	PUNCT
ejpam-5761	119	2	iv	iv	X
ejpam-5761	119	3	)	)	PUNCT
ejpam-5761	119	4	riesz	riesz	NOUN
ejpam-5761	119	5	representation	representation	NOUN
ejpam-5761	119	6	theorem	theorem	VERB
ejpam-5761	119	7	:	:	PUNCT
ejpam-5761	119	8	any	any	DET
ejpam-5761	119	9	non	non	ADJ
ejpam-5761	119	10	-	-	ADJ
ejpam-5761	119	11	negative	negative	ADJ
ejpam-5761	119	12	p	p	ADJ
ejpam-5761	119	13	′	′	ADJ
ejpam-5761	119	14	-superaverage	-superaverage	NOUN
ejpam-5761	119	15	function	function	NOUN
ejpam-5761	119	16	s	s	NOUN
ejpam-5761	119	17	on	on	ADP
ejpam-5761	119	18	a	a	DET
ejpam-5761	119	19	subsetk	subsetk	NOUN
ejpam-5761	119	20	can	can	AUX
ejpam-5761	119	21	be	be	AUX
ejpam-5761	119	22	written	write	VERB
ejpam-5761	119	23	as	as	ADP
ejpam-5761	119	24	the	the	DET
ejpam-5761	119	25	sum	sum	NOUN
ejpam-5761	119	26	of	of	ADP
ejpam-5761	119	27	a	a	DET
ejpam-5761	119	28	p	p	NOUN
ejpam-5761	119	29	′	′	NUM
ejpam-5761	119	30	-potential	-potential	NOUN
ejpam-5761	119	31	and	and	CCONJ
ejpam-5761	119	32	a	a	DET
ejpam-5761	119	33	non	non	ADJ
ejpam-5761	119	34	-	-	ADJ
ejpam-5761	119	35	negative	negative	ADJ
ejpam-5761	119	36	p	p	ADJ
ejpam-5761	119	37	′	′	NUM
ejpam-5761	119	38	-average	-average	NOUN
ejpam-5761	119	39	function	function	NOUN
ejpam-5761	119	40	on	on	ADP
ejpam-5761	119	41	k	k	PROPN
ejpam-5761	119	42	and	and	CCONJ
ejpam-5761	119	43	this	this	DET
ejpam-5761	119	44	representation	representation	NOUN
ejpam-5761	119	45	is	be	AUX
ejpam-5761	119	46	unique	unique	ADJ
ejpam-5761	119	47	.	.	PUNCT
ejpam-5761	120	1	proposition	proposition	NOUN
ejpam-5761	120	2	2	2	NUM
ejpam-5761	120	3	.	.	PUNCT
ejpam-5761	121	1	if	if	SCONJ
ejpam-5761	121	2	s	s	PROPN
ejpam-5761	121	3	is	be	AUX
ejpam-5761	121	4	a	a	DET
ejpam-5761	121	5	p	p	NOUN
ejpam-5761	121	6	-potential	-potential	NOUN
ejpam-5761	121	7	then	then	ADV
ejpam-5761	121	8	it	it	PRON
ejpam-5761	121	9	is	be	AUX
ejpam-5761	121	10	a	a	DET
ejpam-5761	121	11	p	p	NOUN
ejpam-5761	121	12	′	′	NUM
ejpam-5761	121	13	-potential	-potential	ADJ
ejpam-5761	121	14	.	.	PUNCT
ejpam-5761	122	1	proof	proof	NOUN
ejpam-5761	122	2	.	.	PUNCT
ejpam-5761	123	1	first	first	ADV
ejpam-5761	123	2	note	note	VERB
ejpam-5761	123	3	that	that	SCONJ
ejpam-5761	123	4	s	s	VERB
ejpam-5761	123	5	is	be	AUX
ejpam-5761	123	6	p	p	ADJ
ejpam-5761	123	7	′	′	ADJ
ejpam-5761	123	8	-superaverage	-superaverage	NOUN
ejpam-5761	123	9	on	on	ADP
ejpam-5761	123	10	n	n	NOUN
ejpam-5761	123	11	.	.	PUNCT
ejpam-5761	124	1	let	let	VERB
ejpam-5761	124	2	u	u	PRON
ejpam-5761	124	3	≥	≥	X
ejpam-5761	124	4	0	0	NUM
ejpam-5761	124	5	be	be	AUX
ejpam-5761	124	6	a	a	DET
ejpam-5761	124	7	p	p	NOUN
ejpam-5761	124	8	′	′	NUM
ejpam-5761	124	9	-subaverage	-subaverage	NOUN
ejpam-5761	124	10	function	function	NOUN
ejpam-5761	124	11	such	such	ADJ
ejpam-5761	124	12	that	that	SCONJ
ejpam-5761	124	13	u	u	PROPN
ejpam-5761	124	14	≤	≤	X
ejpam-5761	124	15	s	s	VERB
ejpam-5761	124	16	on	on	ADP
ejpam-5761	124	17	n	n	PROPN
ejpam-5761	124	18	.	.	PUNCT
ejpam-5761	125	1	note	note	VERB
ejpam-5761	125	2	that	that	SCONJ
ejpam-5761	125	3	u	u	PRON
ejpam-5761	125	4	is	be	AUX
ejpam-5761	125	5	p	p	NOUN
ejpam-5761	125	6	-subaverage	-subaverage	NOUN
ejpam-5761	125	7	function	function	NOUN
ejpam-5761	125	8	on	on	ADP
ejpam-5761	125	9	n	n	NOUN
ejpam-5761	125	10	and	and	CCONJ
ejpam-5761	125	11	s	s	VERB
ejpam-5761	125	12	is	be	AUX
ejpam-5761	125	13	a	a	DET
ejpam-5761	125	14	p	p	NOUN
ejpam-5761	125	15	-	-	PUNCT
ejpam-5761	125	16	potential	potential	NOUN
ejpam-5761	125	17	,	,	PUNCT
ejpam-5761	125	18	therefore	therefore	ADV
ejpam-5761	125	19	u	u	X
ejpam-5761	125	20	=	=	NOUN
ejpam-5761	125	21	0	0	NUM
ejpam-5761	125	22	.	.	PUNCT
ejpam-5761	126	1	consequently	consequently	ADV
ejpam-5761	126	2	s	s	VERB
ejpam-5761	126	3	is	be	AUX
ejpam-5761	126	4	a	a	DET
ejpam-5761	126	5	p	p	NOUN
ejpam-5761	126	6	′	′	ADJ
ejpam-5761	126	7	-potential	-potential	NOUN
ejpam-5761	126	8	on	on	ADP
ejpam-5761	126	9	n	n	PROPN
ejpam-5761	126	10	.	.	PUNCT
ejpam-5761	127	1	3.2	3.2	NUM
ejpam-5761	127	2	.	.	PUNCT
ejpam-5761	128	1	p	p	NOUN
ejpam-5761	128	2	′	′	NUM
ejpam-5761	128	3	-green	-green	PROPN
ejpam-5761	128	4	’s	’s	PART
ejpam-5761	128	5	potential	potential	NOUN
ejpam-5761	128	6	though	though	SCONJ
ejpam-5761	128	7	positive	positive	ADJ
ejpam-5761	128	8	p	p	NOUN
ejpam-5761	128	9	′	′	NUM
ejpam-5761	128	10	-potentials	-potential	NOUN
ejpam-5761	128	11	always	always	ADV
ejpam-5761	128	12	exist	exist	VERB
ejpam-5761	128	13	on	on	ADP
ejpam-5761	128	14	n	n	PROPN
ejpam-5761	128	15	,	,	PUNCT
ejpam-5761	128	16	positive	positive	ADJ
ejpam-5761	128	17	p	p	ADJ
ejpam-5761	128	18	-potentials	-potential	NOUN
ejpam-5761	128	19	may	may	AUX
ejpam-5761	128	20	exist	exist	VERB
ejpam-5761	128	21	(	(	PUNCT
ejpam-5761	128	22	hyperbolic	hyperbolic	ADJ
ejpam-5761	128	23	random	random	ADJ
ejpam-5761	128	24	walk	walk	NOUN
ejpam-5761	128	25	)	)	PUNCT
ejpam-5761	128	26	or	or	CCONJ
ejpam-5761	128	27	may	may	AUX
ejpam-5761	128	28	not	not	PART
ejpam-5761	128	29	exist	exist	VERB
ejpam-5761	128	30	(	(	PUNCT
ejpam-5761	128	31	parabolic	parabolic	ADV
ejpam-5761	128	32	random	random	ADJ
ejpam-5761	128	33	walk	walk	NOUN
ejpam-5761	128	34	)	)	PUNCT
ejpam-5761	128	35	on	on	ADP
ejpam-5761	128	36	n	n	PROPN
ejpam-5761	128	37	.	.	PUNCT
ejpam-5761	129	1	thus	thus	ADV
ejpam-5761	129	2	on	on	ADP
ejpam-5761	129	3	a	a	DET
ejpam-5761	129	4	hyperbolic	hyperbolic	ADJ
ejpam-5761	129	5	random	random	ADJ
ejpam-5761	129	6	walk	walk	NOUN
ejpam-5761	129	7	n	n	X
ejpam-5761	129	8	,	,	PUNCT
ejpam-5761	129	9	for	for	ADP
ejpam-5761	129	10	a	a	DET
ejpam-5761	129	11	fixed	fix	VERB
ejpam-5761	129	12	state	state	NOUN
ejpam-5761	129	13	e	e	NOUN
ejpam-5761	129	14	,	,	PUNCT
ejpam-5761	129	15	we	we	PRON
ejpam-5761	129	16	have	have	VERB
ejpam-5761	129	17	the	the	DET
ejpam-5761	129	18	p	p	PROPN
ejpam-5761	129	19	-green	-green	PROPN
ejpam-5761	129	20	’s	’s	PART
ejpam-5761	129	21	potential	potential	ADJ
ejpam-5761	129	22	ge(x	ge(x	NOUN
ejpam-5761	129	23	)	)	PUNCT
ejpam-5761	129	24	,	,	PUNCT
ejpam-5761	129	25	−∆[ge(x	−∆[ge(x	NUM
ejpam-5761	129	26	)	)	PUNCT
ejpam-5761	129	27	]	]	PUNCT
ejpam-5761	130	1	=	=	PUNCT
ejpam-5761	130	2	δe(x	δe(x	X
ejpam-5761	130	3	)	)	PUNCT
ejpam-5761	130	4	and	and	CCONJ
ejpam-5761	130	5	p	p	NOUN
ejpam-5761	130	6	′	′	NUM
ejpam-5761	130	7	-green	-green	PROPN
ejpam-5761	130	8	’s	’s	PART
ejpam-5761	130	9	potential	potential	NOUN
ejpam-5761	130	10	g	g	NOUN
ejpam-5761	130	11	′	′	NOUN
ejpam-5761	130	12	e(x	e(x	NUM
ejpam-5761	130	13	)	)	PUNCT
ejpam-5761	131	1	=	=	SYM
ejpam-5761	131	2	−∆	−∆	NOUN
ejpam-5761	131	3	′	′	NUM
ejpam-5761	132	1	[	[	X
ejpam-5761	132	2	g	g	X
ejpam-5761	132	3	′	′	NOUN
ejpam-5761	132	4	e(x	e(x	NUM
ejpam-5761	132	5	)	)	PUNCT
ejpam-5761	132	6	]	]	PUNCT
ejpam-5761	133	1	=	=	PUNCT
ejpam-5761	133	2	δe(x	δe(x	X
ejpam-5761	133	3	)	)	PUNCT
ejpam-5761	133	4	.	.	PUNCT
ejpam-5761	134	1	the	the	DET
ejpam-5761	134	2	following	follow	VERB
ejpam-5761	134	3	theorem	theorem	NOUN
ejpam-5761	134	4	indicates	indicate	VERB
ejpam-5761	134	5	a	a	DET
ejpam-5761	134	6	relation	relation	NOUN
ejpam-5761	134	7	between	between	ADP
ejpam-5761	134	8	them	they	PRON
ejpam-5761	134	9	.	.	PUNCT
ejpam-5761	135	1	lemma	lemma	PROPN
ejpam-5761	135	2	1	1	X
ejpam-5761	135	3	.	.	PUNCT
ejpam-5761	136	1	let	let	VERB
ejpam-5761	136	2	s	s	PRON
ejpam-5761	136	3	≥	≥	X
ejpam-5761	136	4	0	0	NUM
ejpam-5761	136	5	be	be	AUX
ejpam-5761	136	6	a	a	DET
ejpam-5761	136	7	p	p	NOUN
ejpam-5761	136	8	′	′	NUM
ejpam-5761	136	9	-superaverage	-superaverage	NOUN
ejpam-5761	136	10	function	function	NOUN
ejpam-5761	136	11	and	and	CCONJ
ejpam-5761	136	12	p	p	NOUN
ejpam-5761	136	13	be	be	AUX
ejpam-5761	136	14	a	a	DET
ejpam-5761	136	15	p	p	NOUN
ejpam-5761	136	16	′	′	ADJ
ejpam-5761	136	17	-potential	-potential	NOUN
ejpam-5761	136	18	on	on	ADP
ejpam-5761	136	19	n	n	PROPN
ejpam-5761	136	20	.	.	PUNCT
ejpam-5761	137	1	if	if	SCONJ
ejpam-5761	137	2	(	(	PUNCT
ejpam-5761	137	3	−∆	−∆	NOUN
ejpam-5761	137	4	′	′	NUM
ejpam-5761	137	5	)	)	PUNCT
ejpam-5761	137	6	s	s	PART
ejpam-5761	137	7	≥	≥	NOUN
ejpam-5761	137	8	(	(	PUNCT
ejpam-5761	137	9	−∆	−∆	NOUN
ejpam-5761	137	10	′	′	NUM
ejpam-5761	137	11	)	)	PUNCT
ejpam-5761	138	1	p	p	X
ejpam-5761	138	2	,	,	PUNCT
ejpam-5761	138	3	then	then	ADV
ejpam-5761	138	4	s	s	VERB
ejpam-5761	138	5	≥	≥	NOUN
ejpam-5761	138	6	p	p	NOUN
ejpam-5761	138	7	on	on	ADP
ejpam-5761	138	8	n	n	PROPN
ejpam-5761	138	9	.	.	PUNCT
ejpam-5761	139	1	proof	proof	NOUN
ejpam-5761	139	2	.	.	PUNCT
ejpam-5761	140	1	by	by	ADP
ejpam-5761	140	2	hypothesis	hypothesis	NOUN
ejpam-5761	140	3	,	,	PUNCT
ejpam-5761	140	4	s	s	PART
ejpam-5761	140	5	=	=	NOUN
ejpam-5761	140	6	p+u	p+u	X
ejpam-5761	140	7	where	where	SCONJ
ejpam-5761	140	8	u	u	NOUN
ejpam-5761	140	9	is	be	AUX
ejpam-5761	140	10	p	p	NOUN
ejpam-5761	140	11	′	′	ADJ
ejpam-5761	140	12	-superaverage	-superaverage	NOUN
ejpam-5761	140	13	on	on	ADP
ejpam-5761	140	14	n	n	NOUN
ejpam-5761	140	15	.	.	PUNCT
ejpam-5761	141	1	since	since	SCONJ
ejpam-5761	141	2	s	s	PRON
ejpam-5761	141	3	≥	≥	NOUN
ejpam-5761	141	4	0,−u	0,−u	NUM
ejpam-5761	141	5	≤	≤	NUM
ejpam-5761	141	6	p	p	NOUN
ejpam-5761	141	7	on	on	ADP
ejpam-5761	141	8	n	n	PROPN
ejpam-5761	141	9	.	.	PUNCT
ejpam-5761	142	1	hence	hence	ADV
ejpam-5761	142	2	−u	−u	PROPN
ejpam-5761	142	3	≤	≤	NOUN
ejpam-5761	142	4	0	0	PUNCT
ejpam-5761	143	1	so	so	SCONJ
ejpam-5761	143	2	that	that	PRON
ejpam-5761	143	3	s	s	VERB
ejpam-5761	143	4	≥	≥	NOUN
ejpam-5761	143	5	p	p	NOUN
ejpam-5761	143	6	on	on	ADP
ejpam-5761	143	7	n	n	PROPN
ejpam-5761	143	8	.	.	PUNCT
ejpam-5761	144	1	theorem	theorem	NOUN
ejpam-5761	144	2	1	1	X
ejpam-5761	144	3	.	.	PUNCT
ejpam-5761	145	1	let	let	AUX
ejpam-5761	145	2	(	(	PUNCT
ejpam-5761	145	3	n	n	X
ejpam-5761	145	4	,	,	PUNCT
ejpam-5761	145	5	p	p	NOUN
ejpam-5761	145	6	)	)	PUNCT
ejpam-5761	145	7	be	be	AUX
ejpam-5761	145	8	a	a	DET
ejpam-5761	145	9	hyperbolic	hyperbolic	ADJ
ejpam-5761	145	10	network	network	NOUN
ejpam-5761	145	11	.	.	PUNCT
ejpam-5761	146	1	let	let	AUX
ejpam-5761	146	2	ge(x	ge(x	VERB
ejpam-5761	146	3	)	)	PUNCT
ejpam-5761	146	4	be	be	AUX
ejpam-5761	146	5	the	the	DET
ejpam-5761	146	6	p	p	PROPN
ejpam-5761	146	7	-green	-green	PROPN
ejpam-5761	146	8	’s	’s	PART
ejpam-5761	146	9	function	function	NOUN
ejpam-5761	146	10	on	on	ADP
ejpam-5761	146	11	n	n	CCONJ
ejpam-5761	146	12	with	with	ADP
ejpam-5761	146	13	average	average	ADJ
ejpam-5761	146	14	support	support	NOUN
ejpam-5761	146	15	{	{	PUNCT
ejpam-5761	146	16	e	e	NOUN
ejpam-5761	146	17	}	}	PUNCT
ejpam-5761	146	18	.	.	PUNCT
ejpam-5761	147	1	then	then	ADV
ejpam-5761	147	2	ge	ge	PROPN
ejpam-5761	148	1	′	′	PROPN
ejpam-5761	148	2	(	(	PUNCT
ejpam-5761	148	3	x	x	X
ejpam-5761	148	4	)	)	PUNCT
ejpam-5761	148	5	≤	≤	NOUN
ejpam-5761	148	6	ge(x	ge(x	NOUN
ejpam-5761	148	7	)	)	PUNCT
ejpam-5761	148	8	for	for	ADP
ejpam-5761	148	9	every	every	DET
ejpam-5761	148	10	x	x	SYM
ejpam-5761	148	11	∈	∈	PROPN
ejpam-5761	148	12	n	n	X
ejpam-5761	148	13	.	.	PUNCT
ejpam-5761	149	1	proof	proof	NOUN
ejpam-5761	149	2	.	.	PUNCT
ejpam-5761	150	1	since	since	SCONJ
ejpam-5761	150	2	any	any	DET
ejpam-5761	150	3	positive	positive	ADJ
ejpam-5761	150	4	p	p	ADJ
ejpam-5761	150	5	-superaverage	-superaverage	NOUN
ejpam-5761	150	6	function	function	NOUN
ejpam-5761	150	7	on	on	ADP
ejpam-5761	150	8	n	n	X
ejpam-5761	150	9	is	be	AUX
ejpam-5761	150	10	a	a	DET
ejpam-5761	150	11	p	p	NOUN
ejpam-5761	150	12	′	′	NUM
ejpam-5761	150	13	-superaverage	-superaverage	NOUN
ejpam-5761	150	14	function	function	NOUN
ejpam-5761	150	15	on	on	ADP
ejpam-5761	150	16	n	n	PRON
ejpam-5761	150	17	,	,	PUNCT
ejpam-5761	150	18	ge(x	ge(x	X
ejpam-5761	150	19	)	)	PUNCT
ejpam-5761	150	20	is	be	AUX
ejpam-5761	150	21	a	a	DET
ejpam-5761	150	22	p	p	NOUN
ejpam-5761	150	23	′	′	NUM
ejpam-5761	150	24	-superaverage	-superaverage	NOUN
ejpam-5761	150	25	function	function	NOUN
ejpam-5761	150	26	on	on	ADP
ejpam-5761	150	27	n	n	NOUN
ejpam-5761	150	28	.	.	PUNCT
ejpam-5761	151	1	if	if	SCONJ
ejpam-5761	151	2	x	x	PROPN
ejpam-5761	151	3	̸=	̸=	PROPN
ejpam-5761	151	4	e	e	NOUN
ejpam-5761	151	5	,	,	PUNCT
ejpam-5761	151	6	(	(	PUNCT
ejpam-5761	151	7	−∆	−∆	NOUN
ejpam-5761	151	8	′	′	NUM
ejpam-5761	151	9	)	)	PUNCT
ejpam-5761	151	10	ge(x	ge(x	X
ejpam-5761	151	11	)	)	PUNCT
ejpam-5761	151	12	≥	≥	NOUN
ejpam-5761	151	13	0	0	NUM
ejpam-5761	152	1	and	and	CCONJ
ejpam-5761	152	2	(	(	PUNCT
ejpam-5761	152	3	−∆	−∆	NOUN
ejpam-5761	152	4	′	′	NUM
ejpam-5761	152	5	)	)	PUNCT
ejpam-5761	153	1	g	g	NOUN
ejpam-5761	153	2	′	′	NOUN
ejpam-5761	153	3	e(x	e(x	NUM
ejpam-5761	153	4	)	)	PUNCT
ejpam-5761	154	1	=	=	SYM
ejpam-5761	154	2	0	0	PUNCT
ejpam-5761	155	1	when	when	SCONJ
ejpam-5761	155	2	x	x	X
ejpam-5761	155	3	=	=	SYM
ejpam-5761	155	4	e	e	NOUN
ejpam-5761	155	5	,	,	PUNCT
ejpam-5761	155	6	(	(	PUNCT
ejpam-5761	155	7	−∆	−∆	NOUN
ejpam-5761	155	8	′	′	NUM
ejpam-5761	155	9	)	)	PUNCT
ejpam-5761	155	10	ge(e	ge(e	X
ejpam-5761	155	11	)	)	PUNCT
ejpam-5761	156	1	=	=	NOUN
ejpam-5761	156	2	ge(e)−	ge(e)−	X
ejpam-5761	156	3	∑	∑	PUNCT
ejpam-5761	156	4	y	y	PROPN
ejpam-5761	156	5	p	p	NOUN
ejpam-5761	156	6	′	′	NOUN
ejpam-5761	156	7	(	(	PUNCT
ejpam-5761	156	8	e	e	NOUN
ejpam-5761	156	9	,	,	PUNCT
ejpam-5761	156	10	y)ge(y	y)ge(y	NUM
ejpam-5761	156	11	)	)	PUNCT
ejpam-5761	156	12	m.	m.	NOUN
ejpam-5761	156	13	surya	surya	PROPN
ejpam-5761	156	14	priya	priya	PROPN
ejpam-5761	156	15	,	,	PUNCT
ejpam-5761	156	16	n.	n.	PROPN
ejpam-5761	156	17	nathiya	nathiya	PROPN
ejpam-5761	156	18	/	/	SYM
ejpam-5761	156	19	eur	eur	PROPN
ejpam-5761	156	20	.	.	PUNCT
ejpam-5761	157	1	j.	j.	PROPN
ejpam-5761	157	2	pure	pure	PROPN
ejpam-5761	157	3	appl	appl	PROPN
ejpam-5761	157	4	.	.	PROPN
ejpam-5761	157	5	math	math	PROPN
ejpam-5761	157	6	,	,	PUNCT
ejpam-5761	157	7	18	18	NUM
ejpam-5761	157	8	(	(	PUNCT
ejpam-5761	157	9	1	1	NUM
ejpam-5761	157	10	)	)	PUNCT
ejpam-5761	157	11	(	(	PUNCT
ejpam-5761	157	12	2025	2025	NUM
ejpam-5761	157	13	)	)	PUNCT
ejpam-5761	157	14	,	,	PUNCT
ejpam-5761	157	15	5761	5761	NUM
ejpam-5761	157	16	6	6	NUM
ejpam-5761	157	17	of	of	ADP
ejpam-5761	157	18	11	11	NUM
ejpam-5761	157	19	≥ge(e)−	≥ge(e)−	NOUN
ejpam-5761	157	20	∑	∑	PUNCT
ejpam-5761	157	21	y	y	PROPN
ejpam-5761	157	22	p(e	p(e	PROPN
ejpam-5761	157	23	,	,	PUNCT
ejpam-5761	157	24	y)ge(y	y)ge(y	NOUN
ejpam-5761	157	25	)	)	PUNCT
ejpam-5761	157	26	=(	=(	NOUN
ejpam-5761	157	27	−∆)ge(e	−∆)ge(e	NOUN
ejpam-5761	157	28	)	)	PUNCT
ejpam-5761	157	29	=	=	SYM
ejpam-5761	157	30	1	1	NUM
ejpam-5761	157	31	=(	=(	ADJ
ejpam-5761	157	32	−∆	−∆	NOUN
ejpam-5761	157	33	′	′	NUM
ejpam-5761	157	34	)	)	PUNCT
ejpam-5761	158	1	g	g	NOUN
ejpam-5761	158	2	′	′	NUM
ejpam-5761	158	3	e(e	e(e	NOUN
ejpam-5761	158	4	)	)	PUNCT
ejpam-5761	158	5	since	since	SCONJ
ejpam-5761	158	6	for	for	ADP
ejpam-5761	158	7	all	all	DET
ejpam-5761	158	8	x	x	SYM
ejpam-5761	158	9	∈	∈	PROPN
ejpam-5761	158	10	n	n	NOUN
ejpam-5761	158	11	,	,	PUNCT
ejpam-5761	158	12	(	(	PUNCT
ejpam-5761	158	13	−∆	−∆	NOUN
ejpam-5761	158	14	′	′	NUM
ejpam-5761	158	15	)	)	PUNCT
ejpam-5761	158	16	ge(x	ge(x	X
ejpam-5761	158	17	)	)	PUNCT
ejpam-5761	158	18	≥	≥	PROPN
ejpam-5761	158	19	(	(	PUNCT
ejpam-5761	158	20	−∆	−∆	NOUN
ejpam-5761	158	21	′	′	NUM
ejpam-5761	158	22	)	)	PUNCT
ejpam-5761	159	1	g	g	NOUN
ejpam-5761	159	2	′	′	NOUN
ejpam-5761	159	3	e(x	e(x	NUM
ejpam-5761	159	4	)	)	PUNCT
ejpam-5761	159	5	by	by	ADP
ejpam-5761	159	6	the	the	DET
ejpam-5761	159	7	above	above	ADJ
ejpam-5761	159	8	lemma	lemma	PROPN
ejpam-5761	159	9	1	1	NUM
ejpam-5761	159	10	,	,	PUNCT
ejpam-5761	159	11	ge	ge	PROPN
ejpam-5761	159	12	′	′	X
ejpam-5761	159	13	(	(	PUNCT
ejpam-5761	159	14	x	x	X
ejpam-5761	159	15	)	)	PUNCT
ejpam-5761	159	16	≤	≤	NOUN
ejpam-5761	160	1	ge(x	ge(x	NOUN
ejpam-5761	160	2	)	)	PUNCT
ejpam-5761	161	1	for	for	ADP
ejpam-5761	161	2	every	every	DET
ejpam-5761	161	3	x	x	SYM
ejpam-5761	161	4	∈	∈	PROPN
ejpam-5761	161	5	n	n	ADV
ejpam-5761	161	6	.	.	PUNCT
ejpam-5761	162	1	lemma	lemma	PROPN
ejpam-5761	162	2	2	2	X
ejpam-5761	162	3	.	.	PUNCT
ejpam-5761	163	1	if	if	SCONJ
ejpam-5761	163	2	pn	pn	PROPN
ejpam-5761	163	3	is	be	AUX
ejpam-5761	163	4	a	a	DET
ejpam-5761	163	5	sequence	sequence	NOUN
ejpam-5761	163	6	of	of	ADP
ejpam-5761	163	7	p	p	NOUN
ejpam-5761	163	8	′	′	NUM
ejpam-5761	163	9	-potentials	-potential	NOUN
ejpam-5761	163	10	and	and	CCONJ
ejpam-5761	163	11	if	if	SCONJ
ejpam-5761	163	12	p(x	p(x	PROPN
ejpam-5761	163	13	)	)	PUNCT
ejpam-5761	163	14	=	=	PUNCT
ejpam-5761	163	15	∑	∑	PROPN
ejpam-5761	163	16	n	n	X
ejpam-5761	163	17	pn(x	pn(x	X
ejpam-5761	163	18	)	)	PUNCT
ejpam-5761	163	19	is	be	AUX
ejpam-5761	163	20	finite	finite	ADJ
ejpam-5761	163	21	at	at	ADP
ejpam-5761	163	22	one	one	NUM
ejpam-5761	163	23	state	state	NOUN
ejpam-5761	163	24	,	,	PUNCT
ejpam-5761	163	25	then	then	ADV
ejpam-5761	163	26	p	p	NOUN
ejpam-5761	163	27	is	be	AUX
ejpam-5761	163	28	a	a	DET
ejpam-5761	163	29	p	p	NOUN
ejpam-5761	163	30	′	′	NUM
ejpam-5761	163	31	-potential	-potential	ADJ
ejpam-5761	163	32	.	.	PUNCT
ejpam-5761	164	1	proof	proof	NOUN
ejpam-5761	164	2	.	.	PUNCT
ejpam-5761	165	1	the	the	DET
ejpam-5761	165	2	p	p	ADJ
ejpam-5761	165	3	′	′	ADJ
ejpam-5761	165	4	-superaverage	-superaverage	NOUN
ejpam-5761	165	5	function	function	NOUN
ejpam-5761	165	6	(	(	PUNCT
ejpam-5761	165	7	actually	actually	ADV
ejpam-5761	165	8	a	a	DET
ejpam-5761	165	9	p	p	NOUN
ejpam-5761	165	10	′	′	ADJ
ejpam-5761	165	11	-potential	-potential	NOUN
ejpam-5761	165	12	)	)	PUNCT
ejpam-5761	165	13	sm	sm	PROPN
ejpam-5761	165	14	=	=	SYM
ejpam-5761	165	15	∑m	∑m	PROPN
ejpam-5761	165	16	1	1	NUM
ejpam-5761	165	17	pn	pn	NOUN
ejpam-5761	165	18	introduces	introduce	VERB
ejpam-5761	165	19	a	a	DET
ejpam-5761	165	20	sequence	sequence	NOUN
ejpam-5761	165	21	{	{	PUNCT
ejpam-5761	165	22	sm	sm	NOUN
ejpam-5761	165	23	}	}	PUNCT
ejpam-5761	165	24	of	of	ADP
ejpam-5761	165	25	increasing	increase	VERB
ejpam-5761	165	26	p	p	NOUN
ejpam-5761	165	27	′	′	ADJ
ejpam-5761	165	28	-superaverage	-superaverage	NOUN
ejpam-5761	165	29	functions	function	NOUN
ejpam-5761	165	30	so	so	SCONJ
ejpam-5761	165	31	that	that	PRON
ejpam-5761	165	32	s	s	VERB
ejpam-5761	165	33	=	=	X
ejpam-5761	165	34	lim	lim	PROPN
ejpam-5761	165	35	m	m	VERB
ejpam-5761	165	36	sm	sm	PROPN
ejpam-5761	165	37	is	be	AUX
ejpam-5761	165	38	a	a	DET
ejpam-5761	165	39	p	p	NOUN
ejpam-5761	165	40	′	′	NUM
ejpam-5761	165	41	-superaverage	-superaverage	NOUN
ejpam-5761	165	42	function	function	NOUN
ejpam-5761	165	43	if	if	SCONJ
ejpam-5761	165	44	s	s	VERB
ejpam-5761	165	45	is	be	AUX
ejpam-5761	165	46	finite	finite	ADJ
ejpam-5761	165	47	at	at	ADP
ejpam-5761	165	48	one	one	NUM
ejpam-5761	165	49	state	state	NOUN
ejpam-5761	165	50	.	.	PUNCT
ejpam-5761	166	1	hence	hence	ADV
ejpam-5761	166	2	p(x	p(x	VERB
ejpam-5761	166	3	)	)	PUNCT
ejpam-5761	166	4	=	=	PUNCT
ejpam-5761	166	5	∑	∑	PROPN
ejpam-5761	166	6	n	n	X
ejpam-5761	166	7	pn(x	pn(x	X
ejpam-5761	166	8	)	)	PUNCT
ejpam-5761	166	9	is	be	AUX
ejpam-5761	166	10	a	a	DET
ejpam-5761	166	11	p	p	NOUN
ejpam-5761	166	12	′	′	NUM
ejpam-5761	166	13	superaverage	superaverage	NOUN
ejpam-5761	166	14	function	function	NOUN
ejpam-5761	166	15	.	.	PUNCT
ejpam-5761	167	1	to	to	PART
ejpam-5761	167	2	show	show	VERB
ejpam-5761	167	3	p(x	p(x	PROPN
ejpam-5761	167	4	)	)	PUNCT
ejpam-5761	167	5	is	be	AUX
ejpam-5761	167	6	a	a	DET
ejpam-5761	167	7	p	p	NOUN
ejpam-5761	167	8	′	′	NUM
ejpam-5761	167	9	-potential	-potential	NOUN
ejpam-5761	167	10	:	:	PUNCT
ejpam-5761	167	11	let	let	VERB
ejpam-5761	167	12	h(x	h(x	PROPN
ejpam-5761	167	13	)	)	PUNCT
ejpam-5761	167	14	be	be	AUX
ejpam-5761	167	15	a	a	DET
ejpam-5761	167	16	non	non	ADJ
ejpam-5761	167	17	-	-	ADJ
ejpam-5761	167	18	negative	negative	ADJ
ejpam-5761	167	19	p	p	ADJ
ejpam-5761	167	20	′	′	NUM
ejpam-5761	167	21	-average	-average	NOUN
ejpam-5761	167	22	and	and	CCONJ
ejpam-5761	167	23	h	h	NOUN
ejpam-5761	167	24	≤	≤	PROPN
ejpam-5761	168	1	p.	p.	NOUN
ejpam-5761	169	1	then	then	ADV
ejpam-5761	169	2	h	h	NOUN
ejpam-5761	170	1	−	−	PROPN
ejpam-5761	170	2	∞∑	∞∑	NUM
ejpam-5761	170	3	2	2	NUM
ejpam-5761	170	4	pn	pn	PROPN
ejpam-5761	170	5	≤	≤	PROPN
ejpam-5761	170	6	p1	p1	NOUN
ejpam-5761	170	7	.	.	PUNCT
ejpam-5761	171	1	here	here	ADV
ejpam-5761	171	2	the	the	DET
ejpam-5761	171	3	left	left	ADJ
ejpam-5761	171	4	side	side	NOUN
ejpam-5761	171	5	is	be	AUX
ejpam-5761	171	6	p	p	NOUN
ejpam-5761	171	7	′	′	NUM
ejpam-5761	171	8	-subaverage	-subaverage	NOUN
ejpam-5761	171	9	and	and	CCONJ
ejpam-5761	171	10	the	the	DET
ejpam-5761	171	11	right	right	ADJ
ejpam-5761	171	12	side	side	NOUN
ejpam-5761	171	13	a	a	DET
ejpam-5761	171	14	p	p	NOUN
ejpam-5761	171	15	′	′	NUM
ejpam-5761	171	16	-potential	-potential	ADJ
ejpam-5761	171	17	,	,	PUNCT
ejpam-5761	171	18	so	so	SCONJ
ejpam-5761	171	19	that	that	SCONJ
ejpam-5761	171	20	h−	h−	VERB
ejpam-5761	171	21	∞∑	∞∑	NOUN
ejpam-5761	171	22	2	2	NUM
ejpam-5761	171	23	pn	pn	NOUN
ejpam-5761	171	24	≤	≤	NUM
ejpam-5761	171	25	0	0	NUM
ejpam-5761	171	26	.	.	PUNCT
ejpam-5761	172	1	continuing	continue	VERB
ejpam-5761	172	2	this	this	DET
ejpam-5761	172	3	process	process	NOUN
ejpam-5761	172	4	we	we	PRON
ejpam-5761	172	5	find	find	VERB
ejpam-5761	172	6	h(x	h(x	PROPN
ejpam-5761	172	7	)	)	PUNCT
ejpam-5761	172	8	≤	≤	NOUN
ejpam-5761	173	1	∞∑	∞∑	NUM
ejpam-5761	173	2	m	m	NOUN
ejpam-5761	173	3	pn(x	pn(x	NOUN
ejpam-5761	173	4	)	)	PUNCT
ejpam-5761	173	5	for	for	ADP
ejpam-5761	173	6	any	any	DET
ejpam-5761	173	7	m.	m.	NOUN
ejpam-5761	173	8	for	for	ADP
ejpam-5761	173	9	any	any	DET
ejpam-5761	173	10	z	z	NOUN
ejpam-5761	173	11	in	in	ADP
ejpam-5761	173	12	n	n	PROPN
ejpam-5761	173	13	,	,	PUNCT
ejpam-5761	173	14	since	since	SCONJ
ejpam-5761	173	15	∞∑	∞∑	NUM
ejpam-5761	173	16	1	1	NUM
ejpam-5761	173	17	pn(z	pn(z	NOUN
ejpam-5761	173	18	)	)	PUNCT
ejpam-5761	173	19	is	be	AUX
ejpam-5761	173	20	convergent	convergent	ADJ
ejpam-5761	173	21	h(z	h(z	NOUN
ejpam-5761	173	22	)	)	PUNCT
ejpam-5761	173	23	≤	≤	NOUN
ejpam-5761	174	1	∞∑	∞∑	NUM
ejpam-5761	174	2	m	m	NOUN
ejpam-5761	174	3	pn(z	pn(z	PUNCT
ejpam-5761	174	4	)	)	PUNCT
ejpam-5761	174	5	≤	≤	NUM
ejpam-5761	175	1	ϵ	ϵ	X
ejpam-5761	175	2	for	for	ADP
ejpam-5761	175	3	sufficiently	sufficiently	ADV
ejpam-5761	175	4	large	large	ADJ
ejpam-5761	175	5	m.	m.	NOUN
ejpam-5761	175	6	this	this	PRON
ejpam-5761	175	7	leads	lead	VERB
ejpam-5761	175	8	to	to	ADP
ejpam-5761	175	9	h(z	h(z	NOUN
ejpam-5761	175	10	)	)	PUNCT
ejpam-5761	175	11	=	=	SYM
ejpam-5761	176	1	0	0	NUM
ejpam-5761	176	2	,	,	PUNCT
ejpam-5761	176	3	hence	hence	ADV
ejpam-5761	176	4	h	h	NOUN
ejpam-5761	177	1	=	=	NOUN
ejpam-5761	177	2	0	0	NUM
ejpam-5761	178	1	and	and	CCONJ
ejpam-5761	178	2	consequently	consequently	ADV
ejpam-5761	178	3	p	p	X
ejpam-5761	178	4	=	=	PUNCT
ejpam-5761	178	5	∞∑	∞∑	NUM
ejpam-5761	178	6	1	1	NUM
ejpam-5761	178	7	pn	pn	NOUN
ejpam-5761	178	8	is	be	AUX
ejpam-5761	178	9	a	a	DET
ejpam-5761	178	10	p	p	NOUN
ejpam-5761	178	11	′	′	ADJ
ejpam-5761	178	12	-potential	-potential	NOUN
ejpam-5761	178	13	on	on	ADP
ejpam-5761	178	14	n	n	PROPN
ejpam-5761	178	15	.	.	PUNCT
ejpam-5761	179	1	recall	recall	VERB
ejpam-5761	179	2	that	that	PRON
ejpam-5761	179	3	for	for	ADP
ejpam-5761	179	4	any	any	DET
ejpam-5761	179	5	p	p	NOUN
ejpam-5761	179	6	′	′	ADJ
ejpam-5761	179	7	-superaverage	-superaverage	NOUN
ejpam-5761	179	8	function	function	NOUN
ejpam-5761	179	9	s	s	PART
ejpam-5761	179	10	≥	≥	NOUN
ejpam-5761	179	11	0	0	NUM
ejpam-5761	179	12	we	we	PRON
ejpam-5761	179	13	write	write	VERB
ejpam-5761	179	14	by	by	ADP
ejpam-5761	179	15	riesz	riesz	PROPN
ejpam-5761	179	16	representation	representation	NOUN
ejpam-5761	179	17	,	,	PUNCT
ejpam-5761	179	18	s	s	PART
ejpam-5761	179	19	=	=	PUNCT
ejpam-5761	179	20	p+d[s	p+d[s	PROPN
ejpam-5761	179	21	]	]	X
ejpam-5761	179	22	,	,	PUNCT
ejpam-5761	179	23	where	where	SCONJ
ejpam-5761	179	24	d[s	d[s	NOUN
ejpam-5761	179	25	]	]	PUNCT
ejpam-5761	179	26	is	be	AUX
ejpam-5761	179	27	the	the	DET
ejpam-5761	179	28	greatest	great	ADJ
ejpam-5761	179	29	p	p	NOUN
ejpam-5761	179	30	′	′	NUM
ejpam-5761	179	31	-verage	-verage	NOUN
ejpam-5761	179	32	minorant	minorant	NOUN
ejpam-5761	179	33	of	of	ADP
ejpam-5761	179	34	s.	s.	PROPN
ejpam-5761	179	35	theorem	theorem	VERB
ejpam-5761	179	36	2	2	NUM
ejpam-5761	179	37	.	.	PUNCT
ejpam-5761	180	1	any	any	DET
ejpam-5761	180	2	p	p	NOUN
ejpam-5761	180	3	′	′	ADJ
ejpam-5761	180	4	-superaverage	-superaverage	NOUN
ejpam-5761	180	5	function	function	NOUN
ejpam-5761	180	6	s	s	PART
ejpam-5761	180	7	≥	≥	NOUN
ejpam-5761	180	8	0	0	NUM
ejpam-5761	180	9	has	have	VERB
ejpam-5761	180	10	a	a	DET
ejpam-5761	180	11	unique	unique	ADJ
ejpam-5761	180	12	representation	representation	NOUN
ejpam-5761	180	13	s(x	s(x	NOUN
ejpam-5761	180	14	)	)	PUNCT
ejpam-5761	181	1	=	=	X
ejpam-5761	181	2	∑	∑	PUNCT
ejpam-5761	181	3	y	y	PROPN
ejpam-5761	182	1	[	[	X
ejpam-5761	182	2	−∆	−∆	NOUN
ejpam-5761	182	3	′	′	NUM
ejpam-5761	182	4	s(y)]g	s(y)]g	INTJ
ejpam-5761	182	5	′	′	NUM
ejpam-5761	182	6	y(x	y(x	PROPN
ejpam-5761	182	7	)	)	PUNCT
ejpam-5761	183	1	+	+	NOUN
ejpam-5761	183	2	d[s](x	d[s](x	NOUN
ejpam-5761	183	3	)	)	PUNCT
ejpam-5761	183	4	.	.	PUNCT
ejpam-5761	184	1	proof	proof	NOUN
ejpam-5761	184	2	.	.	PUNCT
ejpam-5761	185	1	letk	letk	PROPN
ejpam-5761	185	2	be	be	VERB
ejpam-5761	185	3	a	a	DET
ejpam-5761	185	4	finite	finite	NOUN
ejpam-5761	185	5	set	set	NOUN
ejpam-5761	185	6	and	and	CCONJ
ejpam-5761	185	7	uk(x	uk(x	PUNCT
ejpam-5761	185	8	)	)	PUNCT
ejpam-5761	186	1	=	=	VERB
ejpam-5761	186	2	s(x)−	s(x)−	PROPN
ejpam-5761	186	3	∑	∑	PUNCT
ejpam-5761	186	4	y∈k	y∈k	PROPN
ejpam-5761	186	5	[	[	X
ejpam-5761	186	6	−∆	−∆	NOUN
ejpam-5761	186	7	′	′	NUM
ejpam-5761	187	1	s(y)]g	s(y)]g	INTJ
ejpam-5761	187	2	′	′	NUM
ejpam-5761	187	3	y(x	y(x	NOUN
ejpam-5761	187	4	)	)	PUNCT
ejpam-5761	187	5	.	.	PUNCT
ejpam-5761	188	1	then	then	ADV
ejpam-5761	188	2	−∆	−∆	NOUN
ejpam-5761	188	3	′	′	NUM
ejpam-5761	189	1	[	[	X
ejpam-5761	189	2	uk(x	uk(x	NOUN
ejpam-5761	189	3	)	)	PUNCT
ejpam-5761	189	4	]	]	PUNCT
ejpam-5761	190	1	=	=	PUNCT
ejpam-5761	190	2	0	0	PUNCT
ejpam-5761	191	1	if	if	SCONJ
ejpam-5761	191	2	x	x	PROPN
ejpam-5761	191	3	∈	∈	PROPN
ejpam-5761	191	4	k	k	NOUN
ejpam-5761	191	5	and	and	CCONJ
ejpam-5761	191	6	−∆	−∆	NOUN
ejpam-5761	191	7	′	′	NUM
ejpam-5761	192	1	[	[	X
ejpam-5761	192	2	uk(x	uk(x	NOUN
ejpam-5761	192	3	)	)	PUNCT
ejpam-5761	192	4	]	]	PUNCT
ejpam-5761	193	1	≥	≥	NOUN
ejpam-5761	193	2	0	0	PUNCT
ejpam-5761	194	1	if	if	SCONJ
ejpam-5761	194	2	x	x	X
ejpam-5761	194	3	∈	∈	PROPN
ejpam-5761	194	4	n\k	n\k	PROPN
ejpam-5761	194	5	.	.	PUNCT
ejpam-5761	194	6	then	then	ADV
ejpam-5761	194	7	uk(x	uk(x	PUNCT
ejpam-5761	194	8	)	)	PUNCT
ejpam-5761	194	9	is	be	AUX
ejpam-5761	194	10	a	a	DET
ejpam-5761	194	11	p	p	NOUN
ejpam-5761	194	12	′	′	NUM
ejpam-5761	194	13	-superaverage	-superaverage	NOUN
ejpam-5761	194	14	function	function	NOUN
ejpam-5761	194	15	on	on	ADP
ejpam-5761	194	16	n	n	PRON
ejpam-5761	194	17	and	and	CCONJ
ejpam-5761	194	18	−uk(x	−uk(x	NOUN
ejpam-5761	194	19	)	)	PUNCT
ejpam-5761	194	20	≤	≤	NOUN
ejpam-5761	194	21	∑	∑	PUNCT
ejpam-5761	194	22	y∈k	y∈k	NOUN
ejpam-5761	195	1	[	[	X
ejpam-5761	195	2	−∆	−∆	NOUN
ejpam-5761	195	3	′	′	NUM
ejpam-5761	196	1	s(y)]g	s(y)]g	INTJ
ejpam-5761	196	2	′	′	NUM
ejpam-5761	196	3	y(x	y(x	NOUN
ejpam-5761	196	4	)	)	PUNCT
ejpam-5761	196	5	.	.	PUNCT
ejpam-5761	197	1	since	since	SCONJ
ejpam-5761	197	2	the	the	DET
ejpam-5761	197	3	left	left	ADJ
ejpam-5761	197	4	side	side	NOUN
ejpam-5761	197	5	is	be	AUX
ejpam-5761	197	6	p	p	NOUN
ejpam-5761	197	7	′	′	NUM
ejpam-5761	197	8	-subaverage	-subaverage	NOUN
ejpam-5761	197	9	and	and	CCONJ
ejpam-5761	197	10	the	the	DET
ejpam-5761	197	11	right	right	ADJ
ejpam-5761	197	12	side	side	NOUN
ejpam-5761	197	13	is	be	AUX
ejpam-5761	197	14	a	a	DET
ejpam-5761	197	15	p	p	NOUN
ejpam-5761	197	16	′	′	NUM
ejpam-5761	197	17	-potential	-potential	ADJ
ejpam-5761	197	18	;	;	PUNCT
ejpam-5761	197	19	−uk(x	−uk(x	X
ejpam-5761	197	20	)	)	PUNCT
ejpam-5761	197	21	≤	≤	NOUN
ejpam-5761	197	22	0	0	NUM
ejpam-5761	197	23	on	on	ADP
ejpam-5761	197	24	n	n	PROPN
ejpam-5761	197	25	.	.	PUNCT
ejpam-5761	198	1	that	that	PRON
ejpam-5761	198	2	is	be	AUX
ejpam-5761	198	3	∑	∑	PUNCT
ejpam-5761	198	4	y∈k	y∈k	ADJ
ejpam-5761	198	5	[	[	X
ejpam-5761	198	6	−∆	−∆	NOUN
ejpam-5761	198	7	′	′	NUM
ejpam-5761	199	1	s(y)]g	s(y)]g	INTJ
ejpam-5761	199	2	′	′	NUM
ejpam-5761	199	3	y(x	y(x	PROPN
ejpam-5761	199	4	)	)	PUNCT
ejpam-5761	199	5	≤	≤	NUM
ejpam-5761	199	6	s(x	s(x	NOUN
ejpam-5761	199	7	)	)	PUNCT
ejpam-5761	199	8	.	.	PUNCT
ejpam-5761	200	1	allowing	allow	VERB
ejpam-5761	200	2	k	k	PROPN
ejpam-5761	200	3	to	to	PART
ejpam-5761	200	4	grow	grow	VERB
ejpam-5761	200	5	into	into	ADP
ejpam-5761	200	6	n	n	PROPN
ejpam-5761	200	7	,	,	PUNCT
ejpam-5761	200	8	s(x	s(x	PROPN
ejpam-5761	200	9	)	)	PUNCT
ejpam-5761	200	10	≥	≥	NOUN
ejpam-5761	200	11	∑	∑	PUNCT
ejpam-5761	200	12	y∈n	y∈n	NOUN
ejpam-5761	201	1	[	[	X
ejpam-5761	201	2	−∆	−∆	NOUN
ejpam-5761	201	3	′	′	NUM
ejpam-5761	201	4	s(y)]g	s(y)]g	INTJ
ejpam-5761	201	5	′	′	NUM
ejpam-5761	201	6	y(x	y(x	NOUN
ejpam-5761	201	7	)	)	PUNCT
ejpam-5761	201	8	.	.	PUNCT
ejpam-5761	202	1	note	note	VERB
ejpam-5761	202	2	that	that	SCONJ
ejpam-5761	202	3	the	the	DET
ejpam-5761	202	4	right	right	ADJ
ejpam-5761	202	5	side	side	NOUN
ejpam-5761	202	6	is	be	AUX
ejpam-5761	202	7	a	a	DET
ejpam-5761	202	8	p	p	NOUN
ejpam-5761	202	9	′	′	ADJ
ejpam-5761	202	10	-potential	-potential	NOUN
ejpam-5761	202	11	by	by	ADP
ejpam-5761	202	12	lemma	lemma	PROPN
ejpam-5761	202	13	2	2	NUM
ejpam-5761	202	14	.	.	X
ejpam-5761	202	15	write	write	VERB
ejpam-5761	202	16	h(x	h(x	PROPN
ejpam-5761	202	17	)	)	PUNCT
ejpam-5761	203	1	=	=	PUNCT
ejpam-5761	203	2	s(x)−	s(x)−	PROPN
ejpam-5761	203	3	∑	∑	PUNCT
ejpam-5761	203	4	y∈n	y∈n	NOUN
ejpam-5761	204	1	[	[	X
ejpam-5761	204	2	−∆	−∆	NOUN
ejpam-5761	204	3	′	′	NUM
ejpam-5761	204	4	s(y)]g	s(y)]g	INTJ
ejpam-5761	204	5	′	′	NUM
ejpam-5761	204	6	y(x	y(x	NOUN
ejpam-5761	204	7	)	)	PUNCT
ejpam-5761	204	8	.	.	PUNCT
ejpam-5761	205	1	note	note	VERB
ejpam-5761	205	2	−∆	−∆	NOUN
ejpam-5761	205	3	′	′	NUM
ejpam-5761	206	1	h	h	NOUN
ejpam-5761	207	1	=	=	NOUN
ejpam-5761	208	1	0	0	NUM
ejpam-5761	209	1	so	so	SCONJ
ejpam-5761	209	2	that	that	SCONJ
ejpam-5761	209	3	h	h	NOUN
ejpam-5761	209	4	is	be	AUX
ejpam-5761	209	5	a	a	DET
ejpam-5761	209	6	p	p	NOUN
ejpam-5761	209	7	′	′	NUM
ejpam-5761	209	8	-average	-average	NOUN
ejpam-5761	209	9	function	function	NOUN
ejpam-5761	209	10	on	on	ADP
ejpam-5761	209	11	n	n	PROPN
ejpam-5761	209	12	.	.	PUNCT
ejpam-5761	210	1	by	by	ADP
ejpam-5761	210	2	the	the	DET
ejpam-5761	210	3	uniqueness	uniqueness	NOUN
ejpam-5761	210	4	of	of	ADP
ejpam-5761	210	5	riesz	riesz	PROPN
ejpam-5761	210	6	representation	representation	NOUN
ejpam-5761	210	7	,	,	PUNCT
ejpam-5761	210	8	h(x	h(x	PROPN
ejpam-5761	210	9	)	)	PUNCT
ejpam-5761	210	10	=	=	SYM
ejpam-5761	210	11	d[s](x	d[s](x	PROPN
ejpam-5761	210	12	)	)	PUNCT
ejpam-5761	210	13	.	.	PUNCT
ejpam-5761	211	1	m.	m.	PROPN
ejpam-5761	211	2	surya	surya	PROPN
ejpam-5761	211	3	priya	priya	PROPN
ejpam-5761	211	4	,	,	PUNCT
ejpam-5761	211	5	n.	n.	PROPN
ejpam-5761	211	6	nathiya	nathiya	PROPN
ejpam-5761	211	7	/	/	SYM
ejpam-5761	211	8	eur	eur	PROPN
ejpam-5761	211	9	.	.	PUNCT
ejpam-5761	212	1	j.	j.	PROPN
ejpam-5761	212	2	pure	pure	PROPN
ejpam-5761	212	3	appl	appl	PROPN
ejpam-5761	212	4	.	.	PROPN
ejpam-5761	212	5	math	math	PROPN
ejpam-5761	212	6	,	,	PUNCT
ejpam-5761	212	7	18	18	NUM
ejpam-5761	212	8	(	(	PUNCT
ejpam-5761	212	9	1	1	NUM
ejpam-5761	212	10	)	)	PUNCT
ejpam-5761	212	11	(	(	PUNCT
ejpam-5761	212	12	2025	2025	NUM
ejpam-5761	212	13	)	)	PUNCT
ejpam-5761	212	14	,	,	PUNCT
ejpam-5761	212	15	5761	5761	NUM
ejpam-5761	212	16	7	7	NUM
ejpam-5761	212	17	of	of	ADP
ejpam-5761	212	18	11	11	NUM
ejpam-5761	212	19	in	in	ADP
ejpam-5761	212	20	the	the	DET
ejpam-5761	212	21	particular	particular	ADJ
ejpam-5761	212	22	case	case	NOUN
ejpam-5761	212	23	,	,	PUNCT
ejpam-5761	212	24	when	when	SCONJ
ejpam-5761	212	25	s	s	VERB
ejpam-5761	212	26	=	=	SYM
ejpam-5761	212	27	1	1	NUM
ejpam-5761	212	28	is	be	AUX
ejpam-5761	212	29	the	the	DET
ejpam-5761	212	30	constant	constant	ADJ
ejpam-5761	212	31	function	function	NOUN
ejpam-5761	212	32	then	then	ADV
ejpam-5761	212	33	−∆	−∆	VERB
ejpam-5761	212	34	′	′	NUM
ejpam-5761	212	35	s(x	s(x	PROPN
ejpam-5761	212	36	)	)	PUNCT
ejpam-5761	212	37	=	=	SYM
ejpam-5761	212	38	s(x	s(x	PROPN
ejpam-5761	212	39	)	)	PUNCT
ejpam-5761	213	1	−∑	−∑	PROPN
ejpam-5761	214	1	y	y	NOUN
ejpam-5761	214	2	p	p	NOUN
ejpam-5761	214	3	′	′	NUM
ejpam-5761	214	4	(	(	PUNCT
ejpam-5761	214	5	x	x	NOUN
ejpam-5761	214	6	,	,	PUNCT
ejpam-5761	214	7	y)s(y	y)s(y	NOUN
ejpam-5761	214	8	)	)	PUNCT
ejpam-5761	214	9	=	=	SYM
ejpam-5761	215	1	1−	1−	NUM
ejpam-5761	215	2	p	p	NOUN
ejpam-5761	215	3	′	′	NOUN
ejpam-5761	215	4	(	(	PUNCT
ejpam-5761	215	5	x	x	X
ejpam-5761	215	6	)	)	PUNCT
ejpam-5761	215	7	when	when	SCONJ
ejpam-5761	215	8	p	p	PRON
ejpam-5761	215	9	′	′	X
ejpam-5761	215	10	(	(	PUNCT
ejpam-5761	215	11	x	x	X
ejpam-5761	215	12	)	)	PUNCT
ejpam-5761	215	13	=	=	PUNCT
ejpam-5761	215	14	∑	∑	PUNCT
ejpam-5761	215	15	y	y	PROPN
ejpam-5761	215	16	p	p	NOUN
ejpam-5761	215	17	′	′	NUM
ejpam-5761	215	18	(	(	PUNCT
ejpam-5761	215	19	x	x	NOUN
ejpam-5761	215	20	,	,	PUNCT
ejpam-5761	215	21	y	y	PROPN
ejpam-5761	215	22	)	)	PUNCT
ejpam-5761	215	23	.	.	PUNCT
ejpam-5761	216	1	hence	hence	ADV
ejpam-5761	216	2	obtain	obtain	VERB
ejpam-5761	216	3	the	the	DET
ejpam-5761	216	4	following	follow	VERB
ejpam-5761	216	5	result	result	NOUN
ejpam-5761	216	6	.	.	PUNCT
ejpam-5761	217	1	corollary	corollary	ADJ
ejpam-5761	217	2	1	1	NUM
ejpam-5761	217	3	.	.	PUNCT
ejpam-5761	218	1	for	for	ADP
ejpam-5761	218	2	any	any	DET
ejpam-5761	218	3	x	x	SYM
ejpam-5761	218	4	∈	∈	PROPN
ejpam-5761	218	5	n	n	NOUN
ejpam-5761	218	6	,	,	PUNCT
ejpam-5761	218	7	1	1	X
ejpam-5761	218	8	=	=	SYM
ejpam-5761	218	9	∑	∑	PUNCT
ejpam-5761	218	10	y[1−	y[1−	PROPN
ejpam-5761	218	11	p	p	NOUN
ejpam-5761	218	12	′	′	NOUN
ejpam-5761	218	13	(	(	PUNCT
ejpam-5761	218	14	y)]g	y)]g	INTJ
ejpam-5761	218	15	′	′	NUM
ejpam-5761	218	16	y(x	y(x	NOUN
ejpam-5761	218	17	)	)	PUNCT
ejpam-5761	219	1	+	+	SYM
ejpam-5761	219	2	d[1](x	d[1](x	NOUN
ejpam-5761	219	3	)	)	PUNCT
ejpam-5761	219	4	.	.	PUNCT
ejpam-5761	220	1	4	4	X
ejpam-5761	220	2	.	.	X
ejpam-5761	220	3	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	220	4	subordinate	subordinate	ADJ
ejpam-5761	220	5	structures	structure	NOUN
ejpam-5761	220	6	since	since	SCONJ
ejpam-5761	220	7	a	a	DET
ejpam-5761	220	8	′	′	NUM
ejpam-5761	220	9	u(x	u(x	NOUN
ejpam-5761	220	10	)	)	PUNCT
ejpam-5761	220	11	≤	≤	NOUN
ejpam-5761	220	12	au(x	au(x	NOUN
ejpam-5761	220	13	)	)	PUNCT
ejpam-5761	220	14	for	for	ADP
ejpam-5761	220	15	any	any	DET
ejpam-5761	220	16	non	non	ADJ
ejpam-5761	220	17	-	-	ADJ
ejpam-5761	220	18	negative	negative	ADJ
ejpam-5761	220	19	functions	function	NOUN
ejpam-5761	220	20	u(x	u(x	NOUN
ejpam-5761	220	21	)	)	PUNCT
ejpam-5761	220	22	,	,	PUNCT
ejpam-5761	220	23	then	then	ADV
ejpam-5761	220	24	any	any	DET
ejpam-5761	220	25	non	non	ADJ
ejpam-5761	220	26	-	-	ADJ
ejpam-5761	220	27	negative	negative	ADJ
ejpam-5761	220	28	p	p	NOUN
ejpam-5761	220	29	superaverage	superaverage	NOUN
ejpam-5761	220	30	functions	function	NOUN
ejpam-5761	220	31	is	be	AUX
ejpam-5761	220	32	a	a	DET
ejpam-5761	220	33	p	p	NOUN
ejpam-5761	220	34	′	′	NUM
ejpam-5761	220	35	-superaverage	-superaverage	NOUN
ejpam-5761	220	36	function	function	NOUN
ejpam-5761	220	37	.	.	PUNCT
ejpam-5761	221	1	in	in	ADP
ejpam-5761	221	2	particular	particular	ADJ
ejpam-5761	221	3	,	,	PUNCT
ejpam-5761	221	4	the	the	DET
ejpam-5761	221	5	constant	constant	ADJ
ejpam-5761	221	6	function	function	NOUN
ejpam-5761	221	7	1	1	NUM
ejpam-5761	221	8	is	be	AUX
ejpam-5761	221	9	a	a	DET
ejpam-5761	221	10	p	p	NOUN
ejpam-5761	221	11	′	′	NUM
ejpam-5761	221	12	-superaverage	-superaverage	NOUN
ejpam-5761	221	13	function	function	NOUN
ejpam-5761	221	14	so	so	SCONJ
ejpam-5761	221	15	that	that	SCONJ
ejpam-5761	221	16	1	1	NUM
ejpam-5761	221	17	=	=	SYM
ejpam-5761	221	18	s	s	PART
ejpam-5761	222	1	+	+	NUM
ejpam-5761	222	2	h	h	NOUN
ejpam-5761	222	3	where	where	SCONJ
ejpam-5761	222	4	s	s	VERB
ejpam-5761	222	5	>	>	X
ejpam-5761	222	6	0	0	NUM
ejpam-5761	222	7	is	be	AUX
ejpam-5761	222	8	p	p	NOUN
ejpam-5761	222	9	′	′	ADJ
ejpam-5761	222	10	-superaverage	-superaverage	NOUN
ejpam-5761	222	11	and	and	CCONJ
ejpam-5761	222	12	h	h	NOUN
ejpam-5761	222	13	≥	≥	NOUN
ejpam-5761	222	14	0	0	NUM
ejpam-5761	222	15	is	be	AUX
ejpam-5761	222	16	a	a	DET
ejpam-5761	222	17	p	p	NOUN
ejpam-5761	222	18	′	′	NUM
ejpam-5761	222	19	-average	-average	NOUN
ejpam-5761	222	20	function	function	NOUN
ejpam-5761	222	21	.	.	PUNCT
ejpam-5761	223	1	since	since	SCONJ
ejpam-5761	223	2	h	h	PROPN
ejpam-5761	223	3	>	>	X
ejpam-5761	223	4	0	0	PUNCT
ejpam-5761	223	5	or	or	CCONJ
ejpam-5761	223	6	h	h	NOUN
ejpam-5761	223	7	≡	≡	PROPN
ejpam-5761	223	8	0	0	NUM
ejpam-5761	223	9	,	,	PUNCT
ejpam-5761	223	10	the	the	DET
ejpam-5761	223	11	constant	constant	ADJ
ejpam-5761	223	12	1	1	NUM
ejpam-5761	223	13	is	be	AUX
ejpam-5761	223	14	a	a	DET
ejpam-5761	223	15	p	p	NOUN
ejpam-5761	223	16	′	′	NUM
ejpam-5761	223	17	-potential	-potential	NOUN
ejpam-5761	223	18	or	or	CCONJ
ejpam-5761	223	19	just	just	ADV
ejpam-5761	223	20	a	a	DET
ejpam-5761	223	21	positive	positive	ADJ
ejpam-5761	223	22	p	p	NOUN
ejpam-5761	223	23	′	′	ADJ
ejpam-5761	223	24	-superaverage	-superaverage	NOUN
ejpam-5761	223	25	function	function	NOUN
ejpam-5761	223	26	that	that	PRON
ejpam-5761	223	27	is	be	AUX
ejpam-5761	223	28	not	not	PART
ejpam-5761	223	29	a	a	DET
ejpam-5761	223	30	p	p	NOUN
ejpam-5761	223	31	′	′	NUM
ejpam-5761	223	32	-potential	-potential	PROPN
ejpam-5761	223	33	.	.	PUNCT
ejpam-5761	224	1	this	this	PRON
ejpam-5761	224	2	opens	open	VERB
ejpam-5761	224	3	up	up	ADP
ejpam-5761	224	4	two	two	NUM
ejpam-5761	224	5	possibilities	possibility	NOUN
ejpam-5761	224	6	in	in	ADP
ejpam-5761	224	7	the	the	DET
ejpam-5761	224	8	study	study	NOUN
ejpam-5761	224	9	of	of	ADP
ejpam-5761	224	10	p	p	NOUN
ejpam-5761	224	11	′	′	ADJ
ejpam-5761	224	12	-superaverage	-superaverage	NOUN
ejpam-5761	224	13	functions	function	NOUN
ejpam-5761	224	14	on	on	ADP
ejpam-5761	224	15	n	n	PROPN
ejpam-5761	224	16	,	,	PUNCT
ejpam-5761	224	17	as	as	SCONJ
ejpam-5761	224	18	shown	show	VERB
ejpam-5761	224	19	in	in	ADP
ejpam-5761	224	20	this	this	DET
ejpam-5761	224	21	section	section	NOUN
ejpam-5761	224	22	.	.	PUNCT
ejpam-5761	225	1	in	in	ADP
ejpam-5761	225	2	a	a	DET
ejpam-5761	225	3	random	random	ADJ
ejpam-5761	225	4	walk	walk	NOUN
ejpam-5761	225	5	(	(	PUNCT
ejpam-5761	225	6	n	n	X
ejpam-5761	225	7	,	,	PUNCT
ejpam-5761	225	8	p	p	NOUN
ejpam-5761	225	9	)	)	PUNCT
ejpam-5761	225	10	the	the	DET
ejpam-5761	225	11	constant	constant	ADJ
ejpam-5761	225	12	1	1	NUM
ejpam-5761	225	13	is	be	AUX
ejpam-5761	225	14	p	p	NOUN
ejpam-5761	225	15	-average	-average	NOUN
ejpam-5761	225	16	.	.	PUNCT
ejpam-5761	226	1	it	it	PRON
ejpam-5761	226	2	is	be	AUX
ejpam-5761	226	3	possible	possible	ADJ
ejpam-5761	226	4	that	that	SCONJ
ejpam-5761	226	5	any	any	DET
ejpam-5761	226	6	positive	positive	ADJ
ejpam-5761	226	7	p	p	ADJ
ejpam-5761	226	8	-superaverage	-superaverage	NOUN
ejpam-5761	226	9	function	function	NOUN
ejpam-5761	226	10	is	be	AUX
ejpam-5761	226	11	constant	constant	ADJ
ejpam-5761	226	12	,	,	PUNCT
ejpam-5761	226	13	hence	hence	ADV
ejpam-5761	226	14	there	there	PRON
ejpam-5761	226	15	may	may	AUX
ejpam-5761	226	16	not	not	PART
ejpam-5761	226	17	be	be	AUX
ejpam-5761	226	18	any	any	DET
ejpam-5761	226	19	positive	positive	ADJ
ejpam-5761	226	20	p	p	NOUN
ejpam-5761	226	21	-potential	-potential	NOUN
ejpam-5761	226	22	on	on	ADP
ejpam-5761	226	23	n	n	PROPN
ejpam-5761	226	24	.	.	PUNCT
ejpam-5761	227	1	on	on	ADP
ejpam-5761	227	2	the	the	DET
ejpam-5761	227	3	other	other	ADJ
ejpam-5761	227	4	hand	hand	NOUN
ejpam-5761	227	5	,	,	PUNCT
ejpam-5761	227	6	the	the	DET
ejpam-5761	227	7	constant	constant	ADJ
ejpam-5761	227	8	1	1	NUM
ejpam-5761	227	9	is	be	AUX
ejpam-5761	227	10	p	p	NOUN
ejpam-5761	227	11	′	′	ADJ
ejpam-5761	227	12	-superaverage	-superaverage	NOUN
ejpam-5761	227	13	but	but	CCONJ
ejpam-5761	227	14	not	not	PART
ejpam-5761	227	15	p	p	ADJ
ejpam-5761	227	16	′	′	ADJ
ejpam-5761	227	17	-average	-average	NOUN
ejpam-5761	227	18	.	.	PUNCT
ejpam-5761	228	1	hence	hence	ADV
ejpam-5761	228	2	there	there	PRON
ejpam-5761	228	3	are	be	VERB
ejpam-5761	228	4	always	always	ADV
ejpam-5761	228	5	p	p	ADJ
ejpam-5761	228	6	′	′	NUM
ejpam-5761	228	7	-potentials	-potential	NOUN
ejpam-5761	228	8	on	on	ADP
ejpam-5761	228	9	n	n	PROPN
ejpam-5761	228	10	.	.	PUNCT
ejpam-5761	229	1	let	let	VERB
ejpam-5761	229	2	p	p	PRON
ejpam-5761	229	3	′	′	NOUN
ejpam-5761	229	4	be	be	AUX
ejpam-5761	229	5	a	a	DET
ejpam-5761	229	6	subordinate	subordinate	ADJ
ejpam-5761	229	7	structure	structure	NOUN
ejpam-5761	229	8	to	to	ADP
ejpam-5761	229	9	p	p	PROPN
ejpam-5761	229	10	.	.	PUNCT
ejpam-5761	230	1	then	then	ADV
ejpam-5761	230	2	the	the	DET
ejpam-5761	230	3	constant	constant	ADJ
ejpam-5761	230	4	1	1	NUM
ejpam-5761	230	5	is	be	AUX
ejpam-5761	230	6	a	a	DET
ejpam-5761	230	7	p	p	NOUN
ejpam-5761	230	8	′	′	NUM
ejpam-5761	230	9	-superaverage	-superaverage	NOUN
ejpam-5761	230	10	function	function	NOUN
ejpam-5761	230	11	,	,	PUNCT
ejpam-5761	230	12	write	write	VERB
ejpam-5761	230	13	1	1	NUM
ejpam-5761	230	14	=	=	SYM
ejpam-5761	230	15	v	v	PROPN
ejpam-5761	230	16	+	+	CCONJ
ejpam-5761	230	17	h	h	NOUN
ejpam-5761	230	18	where	where	SCONJ
ejpam-5761	230	19	v	v	NOUN
ejpam-5761	230	20	is	be	AUX
ejpam-5761	230	21	a	a	DET
ejpam-5761	230	22	p	p	NOUN
ejpam-5761	231	1	′	′	NUM
ejpam-5761	231	2	-potential	-potential	NOUN
ejpam-5761	231	3	and	and	CCONJ
ejpam-5761	231	4	h	h	NOUN
ejpam-5761	231	5	≥	≥	NOUN
ejpam-5761	231	6	0	0	NUM
ejpam-5761	231	7	is	be	AUX
ejpam-5761	231	8	a	a	DET
ejpam-5761	231	9	p	p	NOUN
ejpam-5761	231	10	′	′	NUM
ejpam-5761	231	11	-average	-average	NOUN
ejpam-5761	231	12	function	function	NOUN
ejpam-5761	231	13	.	.	PUNCT
ejpam-5761	232	1	(	(	PUNCT
ejpam-5761	232	2	i	i	NOUN
ejpam-5761	232	3	)	)	PUNCT
ejpam-5761	232	4	it	it	PRON
ejpam-5761	232	5	is	be	AUX
ejpam-5761	232	6	possible	possible	ADJ
ejpam-5761	232	7	that	that	SCONJ
ejpam-5761	232	8	h	h	NOUN
ejpam-5761	232	9	̸=	̸=	PROPN
ejpam-5761	232	10	0	0	NUM
ejpam-5761	232	11	.	.	PUNCT
ejpam-5761	233	1	it	it	PRON
ejpam-5761	233	2	means	mean	VERB
ejpam-5761	233	3	that	that	SCONJ
ejpam-5761	233	4	there	there	PRON
ejpam-5761	233	5	are	be	VERB
ejpam-5761	233	6	bounded	bound	VERB
ejpam-5761	233	7	positive	positive	ADJ
ejpam-5761	233	8	p	p	NOUN
ejpam-5761	233	9	′	′	NUM
ejpam-5761	233	10	-average	-average	NOUN
ejpam-5761	233	11	functions	function	NOUN
ejpam-5761	233	12	n	n	X
ejpam-5761	233	13	.	.	PUNCT
ejpam-5761	234	1	(	(	PUNCT
ejpam-5761	234	2	ii	ii	NOUN
ejpam-5761	234	3	)	)	PUNCT
ejpam-5761	234	4	if	if	SCONJ
ejpam-5761	234	5	h	h	NOUN
ejpam-5761	234	6	=	=	NOUN
ejpam-5761	234	7	0	0	NUM
ejpam-5761	234	8	,	,	PUNCT
ejpam-5761	234	9	then	then	ADV
ejpam-5761	234	10	1	1	NUM
ejpam-5761	234	11	is	be	AUX
ejpam-5761	234	12	a	a	DET
ejpam-5761	234	13	p	p	NOUN
ejpam-5761	234	14	′	′	NUM
ejpam-5761	234	15	-potential	-potential	ADJ
ejpam-5761	234	16	,	,	PUNCT
ejpam-5761	234	17	hence	hence	ADV
ejpam-5761	234	18	there	there	PRON
ejpam-5761	234	19	is	be	VERB
ejpam-5761	234	20	no	no	DET
ejpam-5761	234	21	bounded	bounded	ADJ
ejpam-5761	234	22	positive	positive	ADJ
ejpam-5761	234	23	p	p	NOUN
ejpam-5761	234	24	′	′	NUM
ejpam-5761	234	25	-average	-average	NOUN
ejpam-5761	234	26	functions	function	NOUN
ejpam-5761	234	27	on	on	ADP
ejpam-5761	234	28	n	n	PROPN
ejpam-5761	234	29	.	.	PUNCT
ejpam-5761	235	1	definition	definition	NOUN
ejpam-5761	235	2	10	10	NUM
ejpam-5761	235	3	.	.	PUNCT
ejpam-5761	236	1	if	if	SCONJ
ejpam-5761	236	2	the	the	DET
ejpam-5761	236	3	constant	constant	ADJ
ejpam-5761	236	4	1	1	NUM
ejpam-5761	236	5	is	be	AUX
ejpam-5761	236	6	a	a	DET
ejpam-5761	236	7	p	p	NOUN
ejpam-5761	236	8	′	′	NUM
ejpam-5761	236	9	-potential	-potential	NOUN
ejpam-5761	236	10	,	,	PUNCT
ejpam-5761	236	11	then	then	ADV
ejpam-5761	236	12	(	(	PUNCT
ejpam-5761	236	13	n	n	CCONJ
ejpam-5761	236	14	,	,	PUNCT
ejpam-5761	236	15	p	p	NOUN
ejpam-5761	236	16	′	′	NOUN
ejpam-5761	236	17	)	)	PUNCT
ejpam-5761	236	18	is	be	AUX
ejpam-5761	236	19	referred	refer	VERB
ejpam-5761	236	20	to	to	ADP
ejpam-5761	236	21	as	as	ADP
ejpam-5761	236	22	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	236	23	.	.	PUNCT
ejpam-5761	237	1	otherwise	otherwise	ADV
ejpam-5761	237	2	(	(	PUNCT
ejpam-5761	237	3	n	n	X
ejpam-5761	237	4	,	,	PUNCT
ejpam-5761	237	5	p	p	NOUN
ejpam-5761	237	6	′	′	NOUN
ejpam-5761	237	7	)	)	PUNCT
ejpam-5761	237	8	is	be	AUX
ejpam-5761	237	9	termed	term	VERB
ejpam-5761	237	10	bounded	bounded	ADJ
ejpam-5761	237	11	hyperbolic	hyperbolic	ADJ
ejpam-5761	237	12	.	.	PUNCT
ejpam-5761	238	1	proposition	proposition	NOUN
ejpam-5761	238	2	3	3	NUM
ejpam-5761	238	3	.	.	PUNCT
ejpam-5761	239	1	(	(	PUNCT
ejpam-5761	239	2	maximum	maximum	INTJ
ejpam-5761	239	3	principle	principle	NOUN
ejpam-5761	239	4	:)	:)	INTJ
ejpam-5761	239	5	the	the	DET
ejpam-5761	239	6	following	follow	VERB
ejpam-5761	239	7	are	be	AUX
ejpam-5761	239	8	equivalent	equivalent	ADJ
ejpam-5761	239	9	(	(	PUNCT
ejpam-5761	239	10	theorem	theorem	VERB
ejpam-5761	239	11	4.3.7	4.3.7	NOUN
ejpam-5761	239	12	,	,	PUNCT
ejpam-5761	239	13	[	[	X
ejpam-5761	239	14	1	1	NUM
ejpam-5761	239	15	]	]	PUNCT
ejpam-5761	239	16	):	):	PUNCT
ejpam-5761	239	17	(	(	PUNCT
ejpam-5761	239	18	i	i	NOUN
ejpam-5761	239	19	)	)	PUNCT
ejpam-5761	239	20	(	(	PUNCT
ejpam-5761	239	21	n	n	CCONJ
ejpam-5761	239	22	,	,	PUNCT
ejpam-5761	239	23	p	p	NOUN
ejpam-5761	239	24	′	′	NOUN
ejpam-5761	239	25	)	)	PUNCT
ejpam-5761	239	26	is	be	AUX
ejpam-5761	239	27	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	239	28	.	.	PUNCT
ejpam-5761	240	1	(	(	PUNCT
ejpam-5761	240	2	ii	ii	NOUN
ejpam-5761	240	3	)	)	PUNCT
ejpam-5761	240	4	in	in	ADP
ejpam-5761	240	5	an	an	DET
ejpam-5761	240	6	arbitrary	arbitrary	ADJ
ejpam-5761	240	7	subset	subset	NOUN
ejpam-5761	240	8	f	f	PROPN
ejpam-5761	240	9	of	of	ADP
ejpam-5761	240	10	n	n	PROPN
ejpam-5761	240	11	,	,	PUNCT
ejpam-5761	240	12	if	if	SCONJ
ejpam-5761	240	13	u	u	NOUN
ejpam-5761	240	14	is	be	AUX
ejpam-5761	240	15	an	an	DET
ejpam-5761	240	16	upper	upper	ADJ
ejpam-5761	240	17	bounded	bounded	ADJ
ejpam-5761	240	18	subaverage	subaverage	NOUN
ejpam-5761	240	19	function	function	VERB
ejpam-5761	240	20	such	such	ADJ
ejpam-5761	240	21	that	that	SCONJ
ejpam-5761	240	22	u	u	PROPN
ejpam-5761	240	23	≤	≤	ADV
ejpam-5761	240	24	0	0	NUM
ejpam-5761	240	25	on	on	ADP
ejpam-5761	240	26	∂f	∂f	PROPN
ejpam-5761	240	27	,	,	PUNCT
ejpam-5761	240	28	then	then	ADV
ejpam-5761	240	29	u	u	NOUN
ejpam-5761	240	30	≤	≤	ADJ
ejpam-5761	240	31	0	0	NUM
ejpam-5761	240	32	on	on	ADP
ejpam-5761	240	33	f	f	PROPN
ejpam-5761	240	34	.	.	PUNCT
ejpam-5761	241	1	definition	definition	NOUN
ejpam-5761	241	2	11	11	NUM
ejpam-5761	241	3	.	.	PUNCT
ejpam-5761	242	1	(	(	PUNCT
ejpam-5761	242	2	perron	perron	PROPN
ejpam-5761	242	3	family	family	NOUN
ejpam-5761	242	4	:)	:)	INTJ
ejpam-5761	242	5	let	let	VERB
ejpam-5761	242	6	f	f	PRON
ejpam-5761	242	7	be	be	AUX
ejpam-5761	242	8	the	the	DET
ejpam-5761	242	9	family	family	NOUN
ejpam-5761	242	10	of	of	ADP
ejpam-5761	242	11	all	all	DET
ejpam-5761	242	12	p	p	DET
ejpam-5761	242	13	′	′	NUM
ejpam-5761	242	14	-subaverage	-subaverage	NOUN
ejpam-5761	242	15	functions	function	NOUN
ejpam-5761	242	16	u	u	NOUN
ejpam-5761	242	17	on	on	ADP
ejpam-5761	242	18	n	n	CCONJ
ejpam-5761	242	19	such	such	ADJ
ejpam-5761	242	20	that	that	PRON
ejpam-5761	242	21	for	for	ADP
ejpam-5761	242	22	a	a	DET
ejpam-5761	242	23	p	p	NOUN
ejpam-5761	242	24	′	′	ADJ
ejpam-5761	242	25	-superaverage	-superaverage	NOUN
ejpam-5761	242	26	function	function	NOUN
ejpam-5761	242	27	v	v	NOUN
ejpam-5761	242	28	on	on	ADP
ejpam-5761	242	29	n	n	PROPN
ejpam-5761	242	30	,	,	PUNCT
ejpam-5761	242	31	u	u	NOUN
ejpam-5761	242	32	≤	≤	X
ejpam-5761	242	33	v	v	NOUN
ejpam-5761	242	34	on	on	ADP
ejpam-5761	242	35	n	n	PROPN
ejpam-5761	242	36	.	.	PUNCT
ejpam-5761	243	1	if	if	SCONJ
ejpam-5761	243	2	u1	u1	PROPN
ejpam-5761	243	3	,	,	PUNCT
ejpam-5761	243	4	u2	u2	PROPN
ejpam-5761	243	5	∈	∈	PROPN
ejpam-5761	243	6	f	f	X
ejpam-5761	243	7	,	,	PUNCT
ejpam-5761	243	8	then	then	ADV
ejpam-5761	243	9	sup(u1	sup(u1	NOUN
ejpam-5761	243	10	,	,	PUNCT
ejpam-5761	243	11	u2	u2	PROPN
ejpam-5761	243	12	)	)	PUNCT
ejpam-5761	243	13	∈	∈	PROPN
ejpam-5761	244	1	f	f	X
ejpam-5761	244	2	,	,	PUNCT
ejpam-5761	244	3	hence	hence	ADV
ejpam-5761	244	4	is	be	AUX
ejpam-5761	244	5	an	an	DET
ejpam-5761	244	6	upper	upper	ADJ
ejpam-5761	244	7	directed	direct	VERB
ejpam-5761	244	8	family	family	NOUN
ejpam-5761	244	9	of	of	ADP
ejpam-5761	244	10	p	p	NOUN
ejpam-5761	244	11	′	′	NUM
ejpam-5761	244	12	-subaverage	-subaverage	NOUN
ejpam-5761	244	13	functions	function	NOUN
ejpam-5761	244	14	.	.	PUNCT
ejpam-5761	245	1	fix	fix	VERB
ejpam-5761	245	2	a	a	DET
ejpam-5761	245	3	state	state	NOUN
ejpam-5761	245	4	z	z	NOUN
ejpam-5761	245	5	and	and	CCONJ
ejpam-5761	245	6	choose	choose	VERB
ejpam-5761	245	7	any	any	DET
ejpam-5761	245	8	u	u	PROPN
ejpam-5761	245	9	∈	∈	PROPN
ejpam-5761	245	10	f.	f.	NOUN
ejpam-5761	245	11	then	then	ADV
ejpam-5761	245	12	the	the	DET
ejpam-5761	245	13	function	function	NOUN
ejpam-5761	245	14	uz(x	uz(x	NOUN
ejpam-5761	245	15	)	)	PUNCT
ejpam-5761	245	16	=	=	PRON
ejpam-5761	245	17	{	{	PUNCT
ejpam-5761	245	18	u(x	u(x	PROPN
ejpam-5761	245	19	)	)	PUNCT
ejpam-5761	245	20	,	,	PUNCT
ejpam-5761	245	21	if	if	SCONJ
ejpam-5761	245	22	x	x	PROPN
ejpam-5761	245	23	̸=	̸=	PROPN
ejpam-5761	245	24	z∑	z∑	NOUN
ejpam-5761	245	25	p	p	NOUN
ejpam-5761	246	1	′	′	NOUN
ejpam-5761	246	2	(	(	PUNCT
ejpam-5761	246	3	z	z	NOUN
ejpam-5761	246	4	,	,	PUNCT
ejpam-5761	246	5	y)u(y	y)u(y	NOUN
ejpam-5761	246	6	)	)	PUNCT
ejpam-5761	246	7	,	,	PUNCT
ejpam-5761	246	8	if	if	SCONJ
ejpam-5761	246	9	x	x	X
ejpam-5761	246	10	=	=	SYM
ejpam-5761	246	11	z	z	NOUN
ejpam-5761	246	12	(	(	PUNCT
ejpam-5761	246	13	known	know	VERB
ejpam-5761	246	14	as	as	ADP
ejpam-5761	246	15	the	the	DET
ejpam-5761	246	16	poisson	poisson	NOUN
ejpam-5761	246	17	modification	modification	NOUN
ejpam-5761	246	18	of	of	ADP
ejpam-5761	246	19	u(x	u(x	NOUN
ejpam-5761	246	20	)	)	PUNCT
ejpam-5761	246	21	at	at	ADP
ejpam-5761	246	22	x	x	X
ejpam-5761	246	23	=	=	SYM
ejpam-5761	246	24	z	z	NOUN
ejpam-5761	246	25	)	)	PUNCT
ejpam-5761	246	26	also	also	ADV
ejpam-5761	246	27	is	be	AUX
ejpam-5761	246	28	in	in	ADP
ejpam-5761	246	29	f.	f.	PROPN
ejpam-5761	246	30	note	note	PROPN
ejpam-5761	246	31	uz	uz	PROPN
ejpam-5761	246	32	≥	≥	PROPN
ejpam-5761	246	33	u	u	NOUN
ejpam-5761	246	34	and	and	CCONJ
ejpam-5761	246	35	uz(x	uz(x	NUM
ejpam-5761	246	36	)	)	PUNCT
ejpam-5761	246	37	is	be	AUX
ejpam-5761	246	38	p	p	NOUN
ejpam-5761	246	39	′	′	NUM
ejpam-5761	246	40	-average	-average	NOUN
ejpam-5761	246	41	at	at	ADP
ejpam-5761	246	42	x	x	X
ejpam-5761	246	43	=	=	PUNCT
ejpam-5761	246	44	z.	z.	PROPN
ejpam-5761	246	45	consequently	consequently	ADV
ejpam-5761	246	46	,	,	PUNCT
ejpam-5761	246	47	h(x	h(x	PROPN
ejpam-5761	246	48	)	)	PUNCT
ejpam-5761	246	49	=	=	SYM
ejpam-5761	246	50	sup	sup	NUM
ejpam-5761	246	51	u∈f	u∈f	NOUN
ejpam-5761	246	52	u(x	u(x	NOUN
ejpam-5761	246	53	)	)	PUNCT
ejpam-5761	246	54	is	be	AUX
ejpam-5761	246	55	p	p	NOUN
ejpam-5761	246	56	′	′	NUM
ejpam-5761	246	57	-subaverage	-subaverage	NOUN
ejpam-5761	246	58	on	on	ADP
ejpam-5761	246	59	m.	m.	PROPN
ejpam-5761	246	60	surya	surya	PROPN
ejpam-5761	246	61	priya	priya	PROPN
ejpam-5761	246	62	,	,	PUNCT
ejpam-5761	246	63	n.	n.	PROPN
ejpam-5761	246	64	nathiya	nathiya	PROPN
ejpam-5761	246	65	/	/	SYM
ejpam-5761	246	66	eur	eur	PROPN
ejpam-5761	246	67	.	.	PUNCT
ejpam-5761	247	1	j.	j.	PROPN
ejpam-5761	247	2	pure	pure	PROPN
ejpam-5761	247	3	appl	appl	PROPN
ejpam-5761	247	4	.	.	PROPN
ejpam-5761	247	5	math	math	PROPN
ejpam-5761	247	6	,	,	PUNCT
ejpam-5761	247	7	18	18	NUM
ejpam-5761	247	8	(	(	PUNCT
ejpam-5761	247	9	1	1	NUM
ejpam-5761	247	10	)	)	PUNCT
ejpam-5761	247	11	(	(	PUNCT
ejpam-5761	247	12	2025	2025	NUM
ejpam-5761	247	13	)	)	PUNCT
ejpam-5761	247	14	,	,	PUNCT
ejpam-5761	247	15	5761	5761	NUM
ejpam-5761	247	16	8	8	NUM
ejpam-5761	247	17	of	of	ADP
ejpam-5761	247	18	11	11	NUM
ejpam-5761	247	19	n	n	CCONJ
ejpam-5761	247	20	and	and	CCONJ
ejpam-5761	247	21	at	at	ADP
ejpam-5761	247	22	x	x	X
ejpam-5761	247	23	=	=	SYM
ejpam-5761	247	24	z	z	PROPN
ejpam-5761	247	25	,	,	PUNCT
ejpam-5761	247	26	h(z	h(z	NOUN
ejpam-5761	247	27	)	)	PUNCT
ejpam-5761	247	28	=	=	SYM
ejpam-5761	248	1	sup	sup	NUM
ejpam-5761	248	2	u∈f	u∈f	NOUN
ejpam-5761	248	3	uz(z	uz(z	NOUN
ejpam-5761	248	4	)	)	PUNCT
ejpam-5761	248	5	is	be	AUX
ejpam-5761	248	6	p	p	NOUN
ejpam-5761	248	7	′	′	NUM
ejpam-5761	248	8	-average	-average	NOUN
ejpam-5761	248	9	.	.	PUNCT
ejpam-5761	249	1	since	since	SCONJ
ejpam-5761	249	2	z	z	PROPN
ejpam-5761	249	3	is	be	AUX
ejpam-5761	249	4	arbitrary	arbitrary	ADJ
ejpam-5761	249	5	,	,	PUNCT
ejpam-5761	249	6	we	we	PRON
ejpam-5761	249	7	conclude	conclude	VERB
ejpam-5761	249	8	that	that	SCONJ
ejpam-5761	249	9	h(x	h(x	PROPN
ejpam-5761	249	10	)	)	PUNCT
ejpam-5761	249	11	=	=	SYM
ejpam-5761	249	12	sup	sup	NUM
ejpam-5761	249	13	u∈f	u∈f	NOUN
ejpam-5761	249	14	u(x	u(x	NOUN
ejpam-5761	249	15	)	)	PUNCT
ejpam-5761	249	16	is	be	AUX
ejpam-5761	249	17	p	p	NOUN
ejpam-5761	249	18	′	′	NUM
ejpam-5761	249	19	-harmonic	-harmonic	ADJ
ejpam-5761	249	20	on	on	ADP
ejpam-5761	249	21	n	n	PROPN
ejpam-5761	249	22	.	.	PUNCT
ejpam-5761	250	1	we	we	PRON
ejpam-5761	250	2	refer	refer	VERB
ejpam-5761	250	3	to	to	ADP
ejpam-5761	250	4	f	f	PROPN
ejpam-5761	250	5	as	as	ADP
ejpam-5761	250	6	the	the	DET
ejpam-5761	250	7	perron	perron	PROPN
ejpam-5761	250	8	family	family	NOUN
ejpam-5761	250	9	of	of	ADP
ejpam-5761	250	10	p	p	NOUN
ejpam-5761	250	11	′	′	NUM
ejpam-5761	250	12	-subaverage	-subaverage	NOUN
ejpam-5761	250	13	functions	function	NOUN
ejpam-5761	250	14	.	.	PUNCT
ejpam-5761	251	1	theorem	theorem	NOUN
ejpam-5761	251	2	3	3	NUM
ejpam-5761	251	3	.	.	PUNCT
ejpam-5761	252	1	the	the	DET
ejpam-5761	252	2	following	follow	VERB
ejpam-5761	252	3	are	be	AUX
ejpam-5761	252	4	equivalent	equivalent	ADJ
ejpam-5761	252	5	:	:	PUNCT
ejpam-5761	252	6	(	(	PUNCT
ejpam-5761	252	7	i	i	NOUN
ejpam-5761	252	8	)	)	PUNCT
ejpam-5761	252	9	any	any	DET
ejpam-5761	252	10	bounded	bound	VERB
ejpam-5761	252	11	p	p	NOUN
ejpam-5761	252	12	′	′	ADJ
ejpam-5761	252	13	-superaverage	-superaverage	NOUN
ejpam-5761	252	14	function	function	NOUN
ejpam-5761	252	15	u	u	NOUN
ejpam-5761	252	16	defined	define	VERB
ejpam-5761	252	17	outside	outside	ADP
ejpam-5761	252	18	a	a	DET
ejpam-5761	252	19	finite	finite	NOUN
ejpam-5761	252	20	set	set	NOUN
ejpam-5761	252	21	is	be	AUX
ejpam-5761	252	22	of	of	ADP
ejpam-5761	252	23	the	the	DET
ejpam-5761	252	24	form	form	NOUN
ejpam-5761	252	25	u	u	NOUN
ejpam-5761	252	26	=	=	NOUN
ejpam-5761	252	27	p−	p−	X
ejpam-5761	252	28	q	q	NOUN
ejpam-5761	252	29	where	where	SCONJ
ejpam-5761	252	30	p	p	NOUN
ejpam-5761	252	31	and	and	CCONJ
ejpam-5761	252	32	q	q	NOUN
ejpam-5761	252	33	are	be	AUX
ejpam-5761	252	34	bounded	bound	VERB
ejpam-5761	252	35	p	p	X
ejpam-5761	252	36	′	′	NUM
ejpam-5761	252	37	-potentials	-potential	NOUN
ejpam-5761	252	38	on	on	ADP
ejpam-5761	252	39	n	n	PRON
ejpam-5761	252	40	.	.	PUNCT
ejpam-5761	253	1	(	(	PUNCT
ejpam-5761	253	2	ii	ii	NOUN
ejpam-5761	253	3	)	)	PUNCT
ejpam-5761	253	4	any	any	DET
ejpam-5761	253	5	bounded	bounded	ADJ
ejpam-5761	253	6	p	p	X
ejpam-5761	253	7	′	′	ADJ
ejpam-5761	253	8	-superaverage	-superaverage	NOUN
ejpam-5761	253	9	function	function	NOUN
ejpam-5761	253	10	in	in	ADP
ejpam-5761	253	11	n	n	PROPN
ejpam-5761	253	12	is	be	AUX
ejpam-5761	253	13	a	a	DET
ejpam-5761	253	14	p	p	NOUN
ejpam-5761	253	15	′	′	NUM
ejpam-5761	253	16	-potential	-potential	NOUN
ejpam-5761	253	17	.	.	PUNCT
ejpam-5761	254	1	(	(	PUNCT
ejpam-5761	254	2	iii	iii	NOUN
ejpam-5761	254	3	)	)	PUNCT
ejpam-5761	254	4	0	0	NUM
ejpam-5761	254	5	is	be	AUX
ejpam-5761	254	6	the	the	DET
ejpam-5761	254	7	only	only	ADJ
ejpam-5761	254	8	bounded	bound	VERB
ejpam-5761	254	9	p	p	NOUN
ejpam-5761	254	10	′	′	NUM
ejpam-5761	254	11	-average	-average	NOUN
ejpam-5761	254	12	function	function	NOUN
ejpam-5761	254	13	in	in	ADP
ejpam-5761	254	14	n	n	PROPN
ejpam-5761	254	15	.	.	PUNCT
ejpam-5761	255	1	(	(	PUNCT
ejpam-5761	255	2	iv	iv	X
ejpam-5761	255	3	)	)	PUNCT
ejpam-5761	255	4	the	the	DET
ejpam-5761	255	5	constant	constant	ADJ
ejpam-5761	255	6	function	function	NOUN
ejpam-5761	255	7	1	1	NUM
ejpam-5761	255	8	is	be	AUX
ejpam-5761	255	9	a	a	DET
ejpam-5761	255	10	p	p	NOUN
ejpam-5761	255	11	′	′	ADJ
ejpam-5761	255	12	-potential	-potential	NOUN
ejpam-5761	255	13	on	on	ADP
ejpam-5761	255	14	n	n	PROPN
ejpam-5761	255	15	,	,	PUNCT
ejpam-5761	255	16	that	that	PRON
ejpam-5761	255	17	is	be	AUX
ejpam-5761	255	18	n	n	PRON
ejpam-5761	255	19	is	be	AUX
ejpam-5761	255	20	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	255	21	.	.	PUNCT
ejpam-5761	256	1	proof	proof	NOUN
ejpam-5761	256	2	.	.	PUNCT
ejpam-5761	257	1	(	(	PUNCT
ejpam-5761	257	2	i	i	NOUN
ejpam-5761	257	3	)	)	PUNCT
ejpam-5761	257	4	implies	imply	VERB
ejpam-5761	257	5	(	(	PUNCT
ejpam-5761	257	6	ii	ii	NOUN
ejpam-5761	257	7	)	)	PUNCT
ejpam-5761	257	8	.	.	PUNCT
ejpam-5761	258	1	let	let	VERB
ejpam-5761	258	2	s	s	PRON
ejpam-5761	258	3	be	be	AUX
ejpam-5761	258	4	a	a	DET
ejpam-5761	258	5	bounded	bounded	ADJ
ejpam-5761	258	6	p	p	X
ejpam-5761	258	7	′	′	ADJ
ejpam-5761	258	8	-superaverage	-superaverage	NOUN
ejpam-5761	258	9	function	function	NOUN
ejpam-5761	258	10	in	in	ADP
ejpam-5761	258	11	n	n	PROPN
ejpam-5761	258	12	.	.	PUNCT
ejpam-5761	259	1	then	then	ADV
ejpam-5761	259	2	by	by	ADP
ejpam-5761	259	3	(	(	PUNCT
ejpam-5761	259	4	i	i	NOUN
ejpam-5761	259	5	)	)	PUNCT
ejpam-5761	259	6	,	,	PUNCT
ejpam-5761	259	7	s	s	VERB
ejpam-5761	259	8	=	=	NOUN
ejpam-5761	259	9	p	p	NOUN
ejpam-5761	259	10	−	−	PROPN
ejpam-5761	259	11	q	q	PROPN
ejpam-5761	259	12	outside	outside	ADP
ejpam-5761	259	13	a	a	DET
ejpam-5761	259	14	finite	finite	NOUN
ejpam-5761	259	15	set	set	VERB
ejpam-5761	259	16	a.	a.	NOUN
ejpam-5761	259	17	hence	hence	ADV
ejpam-5761	259	18	|s|	|s|	VERB
ejpam-5761	259	19	≤	≤	NOUN
ejpam-5761	259	20	p	p	NOUN
ejpam-5761	259	21	+	+	CCONJ
ejpam-5761	259	22	q	q	NOUN
ejpam-5761	259	23	on	on	ADP
ejpam-5761	259	24	n	n	CCONJ
ejpam-5761	259	25	/	/	SYM
ejpam-5761	259	26	a.	a.	NOUN
ejpam-5761	259	27	since	since	SCONJ
ejpam-5761	259	28	a	a	PRON
ejpam-5761	259	29	is	be	AUX
ejpam-5761	259	30	a	a	DET
ejpam-5761	259	31	finite	finite	ADJ
ejpam-5761	259	32	set	set	NOUN
ejpam-5761	259	33	,	,	PUNCT
ejpam-5761	259	34	s	s	VERB
ejpam-5761	259	35	is	be	AUX
ejpam-5761	259	36	bounded	bound	VERB
ejpam-5761	259	37	on	on	ADP
ejpam-5761	259	38	a	a	PRON
ejpam-5761	259	39	and	and	CCONJ
ejpam-5761	259	40	we	we	PRON
ejpam-5761	259	41	select	select	VERB
ejpam-5761	259	42	a	a	DET
ejpam-5761	259	43	large	large	ADJ
ejpam-5761	259	44	constant	constant	ADJ
ejpam-5761	259	45	α	α	NOUN
ejpam-5761	259	46	>	>	X
ejpam-5761	259	47	1	1	NUM
ejpam-5761	259	48	such	such	ADJ
ejpam-5761	259	49	that	that	SCONJ
ejpam-5761	259	50	|s|	|s|	NOUN
ejpam-5761	259	51	≤	≤	PROPN
ejpam-5761	259	52	α(p	α(p	PROPN
ejpam-5761	259	53	+	+	CCONJ
ejpam-5761	259	54	q	q	X
ejpam-5761	259	55	)	)	PUNCT
ejpam-5761	259	56	on	on	ADP
ejpam-5761	259	57	a.	a.	NOUN
ejpam-5761	259	58	consequently	consequently	ADV
ejpam-5761	259	59	,	,	PUNCT
ejpam-5761	259	60	|s|	|s|	PROPN
ejpam-5761	259	61	≤	≤	PROPN
ejpam-5761	259	62	α(p	α(p	PROPN
ejpam-5761	260	1	+	+	CCONJ
ejpam-5761	260	2	q	q	X
ejpam-5761	260	3	)	)	PUNCT
ejpam-5761	260	4	on	on	ADP
ejpam-5761	260	5	n	n	PROPN
ejpam-5761	260	6	.	.	PUNCT
ejpam-5761	261	1	since	since	SCONJ
ejpam-5761	261	2	−s	−s	NOUN
ejpam-5761	261	3	≤	≤	NOUN
ejpam-5761	261	4	α(p	α(p	PROPN
ejpam-5761	261	5	+	+	CCONJ
ejpam-5761	261	6	q	q	X
ejpam-5761	261	7	)	)	PUNCT
ejpam-5761	261	8	,	,	PUNCT
ejpam-5761	261	9	we	we	PRON
ejpam-5761	261	10	see	see	VERB
ejpam-5761	261	11	that	that	DET
ejpam-5761	261	12	−s	−s	NOUN
ejpam-5761	261	13	≤	≤	ADV
ejpam-5761	261	14	0	0	NUM
ejpam-5761	261	15	,	,	PUNCT
ejpam-5761	261	16	then	then	ADV
ejpam-5761	261	17	0	0	NUM
ejpam-5761	261	18	≤	≤	NUM
ejpam-5761	261	19	s	s	PART
ejpam-5761	261	20	≤	≤	NUM
ejpam-5761	261	21	α(p+	α(p+	PROPN
ejpam-5761	261	22	q	q	X
ejpam-5761	261	23	)	)	PUNCT
ejpam-5761	261	24	so	so	SCONJ
ejpam-5761	261	25	that	that	PRON
ejpam-5761	261	26	s	s	VERB
ejpam-5761	261	27	is	be	AUX
ejpam-5761	261	28	a	a	DET
ejpam-5761	261	29	p	p	NOUN
ejpam-5761	261	30	′	′	ADJ
ejpam-5761	261	31	-potential	-potential	NOUN
ejpam-5761	261	32	on	on	ADP
ejpam-5761	261	33	n	n	PROPN
ejpam-5761	261	34	.	.	PUNCT
ejpam-5761	262	1	(	(	PUNCT
ejpam-5761	262	2	ii	ii	NOUN
ejpam-5761	262	3	)	)	PUNCT
ejpam-5761	262	4	implies	imply	VERB
ejpam-5761	262	5	(	(	PUNCT
ejpam-5761	262	6	iii	iii	X
ejpam-5761	262	7	)	)	PUNCT
ejpam-5761	262	8	if	if	SCONJ
ejpam-5761	262	9	h	h	NOUN
ejpam-5761	262	10	̸=	̸=	PROPN
ejpam-5761	262	11	0	0	NUM
ejpam-5761	262	12	is	be	AUX
ejpam-5761	262	13	a	a	DET
ejpam-5761	262	14	bounded	bounded	ADJ
ejpam-5761	262	15	p	p	NOUN
ejpam-5761	262	16	′	′	NUM
ejpam-5761	262	17	-average	-average	NOUN
ejpam-5761	262	18	function	function	NOUN
ejpam-5761	262	19	on	on	ADP
ejpam-5761	262	20	n	n	PROPN
ejpam-5761	262	21	,	,	PUNCT
ejpam-5761	262	22	then	then	ADV
ejpam-5761	262	23	by	by	ADP
ejpam-5761	262	24	(	(	PUNCT
ejpam-5761	262	25	ii	ii	NOUN
ejpam-5761	262	26	)	)	PUNCT
ejpam-5761	262	27	it	it	PRON
ejpam-5761	262	28	is	be	AUX
ejpam-5761	262	29	a	a	DET
ejpam-5761	262	30	p	p	NOUN
ejpam-5761	262	31	′	′	NUM
ejpam-5761	262	32	-potential	-potential	NOUN
ejpam-5761	262	33	.	.	PUNCT
ejpam-5761	263	1	(	(	PUNCT
ejpam-5761	263	2	iii	iii	NOUN
ejpam-5761	263	3	)	)	PUNCT
ejpam-5761	263	4	implies	imply	VERB
ejpam-5761	263	5	(	(	PUNCT
ejpam-5761	263	6	iv	iv	X
ejpam-5761	263	7	)	)	PUNCT
ejpam-5761	263	8	since	since	SCONJ
ejpam-5761	263	9	1	1	NUM
ejpam-5761	263	10	is	be	AUX
ejpam-5761	263	11	p	p	NOUN
ejpam-5761	263	12	′	′	ADJ
ejpam-5761	263	13	-superaverage	-superaverage	NOUN
ejpam-5761	263	14	on	on	ADP
ejpam-5761	263	15	n	n	PRON
ejpam-5761	263	16	,	,	PUNCT
ejpam-5761	263	17	the	the	DET
ejpam-5761	263	18	greatest	great	ADJ
ejpam-5761	263	19	p	p	ADJ
ejpam-5761	263	20	′	′	NUM
ejpam-5761	263	21	-average	-average	NOUN
ejpam-5761	263	22	minorant	minorant	NOUN
ejpam-5761	263	23	of	of	ADP
ejpam-5761	263	24	1	1	NUM
ejpam-5761	263	25	is	be	AUX
ejpam-5761	263	26	0	0	NUM
ejpam-5761	263	27	.	.	PUNCT
ejpam-5761	264	1	hence	hence	ADV
ejpam-5761	264	2	1	1	NUM
ejpam-5761	264	3	is	be	AUX
ejpam-5761	264	4	a	a	DET
ejpam-5761	264	5	p	p	NOUN
ejpam-5761	264	6	′	′	NUM
ejpam-5761	264	7	-potential	-potential	ADJ
ejpam-5761	264	8	,	,	PUNCT
ejpam-5761	264	9	thus	thus	ADV
ejpam-5761	264	10	{	{	PUNCT
ejpam-5761	264	11	n	n	X
ejpam-5761	264	12	,	,	PUNCT
ejpam-5761	264	13	p	p	NOUN
ejpam-5761	264	14	′	′	NOUN
ejpam-5761	264	15	}	}	PUNCT
ejpam-5761	264	16	is	be	AUX
ejpam-5761	264	17	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	264	18	.	.	PUNCT
ejpam-5761	265	1	(	(	PUNCT
ejpam-5761	265	2	iv	iv	X
ejpam-5761	265	3	)	)	PUNCT
ejpam-5761	265	4	implies	imply	VERB
ejpam-5761	265	5	i	i	PRON
ejpam-5761	265	6	)	)	PUNCT
ejpam-5761	265	7	let	let	VERB
ejpam-5761	265	8	u	u	NOUN
ejpam-5761	266	1	=	=	NOUN
ejpam-5761	266	2	p	p	PROPN
ejpam-5761	266	3	−	−	PROPN
ejpam-5761	266	4	q	q	PROPN
ejpam-5761	266	5	outside	outside	ADP
ejpam-5761	266	6	a	a	DET
ejpam-5761	266	7	finite	finite	NOUN
ejpam-5761	266	8	set	set	VERB
ejpam-5761	266	9	in	in	ADP
ejpam-5761	266	10	n	n	PROPN
ejpam-5761	266	11	.	.	PUNCT
ejpam-5761	267	1	since	since	SCONJ
ejpam-5761	267	2	u	u	NOUN
ejpam-5761	267	3	is	be	AUX
ejpam-5761	267	4	bounded	bound	VERB
ejpam-5761	267	5	by	by	ADP
ejpam-5761	267	6	hypothesis	hypothesis	NOUN
ejpam-5761	267	7	and	and	CCONJ
ejpam-5761	267	8	q	q	NOUN
ejpam-5761	267	9	is	be	AUX
ejpam-5761	267	10	bounded	bound	VERB
ejpam-5761	267	11	,	,	PUNCT
ejpam-5761	267	12	it	it	PRON
ejpam-5761	267	13	is	be	AUX
ejpam-5761	267	14	clear	clear	ADJ
ejpam-5761	267	15	that	that	SCONJ
ejpam-5761	267	16	p	p	NOUN
ejpam-5761	267	17	is	be	AUX
ejpam-5761	267	18	bounded	bound	VERB
ejpam-5761	267	19	on	on	ADP
ejpam-5761	267	20	n	n	PROPN
ejpam-5761	267	21	.	.	PUNCT
ejpam-5761	268	1	since	since	SCONJ
ejpam-5761	268	2	1	1	NUM
ejpam-5761	268	3	is	be	AUX
ejpam-5761	268	4	a	a	DET
ejpam-5761	268	5	p	p	NOUN
ejpam-5761	268	6	′	′	ADJ
ejpam-5761	268	7	-potential	-potential	NOUN
ejpam-5761	268	8	by	by	ADP
ejpam-5761	268	9	(	(	PUNCT
ejpam-5761	268	10	iv	iv	X
ejpam-5761	268	11	)	)	PUNCT
ejpam-5761	268	12	the	the	DET
ejpam-5761	268	13	bounded	bounded	ADJ
ejpam-5761	268	14	p	p	X
ejpam-5761	268	15	′	′	ADJ
ejpam-5761	268	16	-superaverage	-superaverage	NOUN
ejpam-5761	268	17	function	function	NOUN
ejpam-5761	268	18	p	p	NOUN
ejpam-5761	268	19	is	be	AUX
ejpam-5761	268	20	a	a	DET
ejpam-5761	268	21	p	p	NOUN
ejpam-5761	268	22	′	′	NUM
ejpam-5761	268	23	-potential	-potential	PROPN
ejpam-5761	268	24	.	.	PUNCT
ejpam-5761	269	1	theorem	theorem	NOUN
ejpam-5761	269	2	4	4	NUM
ejpam-5761	269	3	.	.	PUNCT
ejpam-5761	270	1	if	if	SCONJ
ejpam-5761	270	2	(	(	PUNCT
ejpam-5761	270	3	n	n	X
ejpam-5761	270	4	,	,	PUNCT
ejpam-5761	270	5	p	p	NOUN
ejpam-5761	270	6	)	)	PUNCT
ejpam-5761	270	7	is	be	AUX
ejpam-5761	270	8	parabolic	parabolic	ADJ
ejpam-5761	270	9	,	,	PUNCT
ejpam-5761	270	10	then	then	ADV
ejpam-5761	270	11	(	(	PUNCT
ejpam-5761	270	12	n	n	CCONJ
ejpam-5761	270	13	,	,	PUNCT
ejpam-5761	270	14	p	p	NOUN
ejpam-5761	270	15	′	′	NOUN
ejpam-5761	270	16	)	)	PUNCT
ejpam-5761	270	17	is	be	AUX
ejpam-5761	270	18	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	270	19	.	.	PUNCT
ejpam-5761	271	1	proof	proof	NOUN
ejpam-5761	271	2	.	.	PUNCT
ejpam-5761	272	1	for	for	ADP
ejpam-5761	272	2	let	let	VERB
ejpam-5761	272	3	h	h	PRON
ejpam-5761	272	4	′	′	VERB
ejpam-5761	272	5	be	be	AUX
ejpam-5761	272	6	a	a	DET
ejpam-5761	272	7	p	p	NOUN
ejpam-5761	272	8	′	′	NUM
ejpam-5761	272	9	-average	-average	NOUN
ejpam-5761	272	10	function	function	NOUN
ejpam-5761	272	11	on	on	ADP
ejpam-5761	272	12	n	n	CCONJ
ejpam-5761	272	13	such	such	ADJ
ejpam-5761	272	14	that	that	SCONJ
ejpam-5761	272	15	|h′	|h′	PROPN
ejpam-5761	272	16	|	|	NOUN
ejpam-5761	272	17	≤	≤	ADV
ejpam-5761	272	18	m	m	VERB
ejpam-5761	272	19	,	,	PUNCT
ejpam-5761	272	20	where	where	SCONJ
ejpam-5761	272	21	m	m	NOUN
ejpam-5761	272	22	is	be	AUX
ejpam-5761	272	23	a	a	DET
ejpam-5761	272	24	constant	constant	ADJ
ejpam-5761	272	25	.	.	PUNCT
ejpam-5761	273	1	then	then	ADV
ejpam-5761	273	2	,	,	PUNCT
ejpam-5761	273	3	|h′	|h′	PROPN
ejpam-5761	273	4	|	|	ADV
ejpam-5761	273	5	is	be	AUX
ejpam-5761	273	6	p	p	NOUN
ejpam-5761	273	7	′	′	NUM
ejpam-5761	273	8	-subaverage	-subaverage	NOUN
ejpam-5761	273	9	on	on	ADP
ejpam-5761	273	10	n	n	CCONJ
ejpam-5761	273	11	and	and	CCONJ
ejpam-5761	273	12	hence	hence	ADV
ejpam-5761	273	13	p	p	NOUN
ejpam-5761	273	14	-subaverage	-subaverage	NOUN
ejpam-5761	273	15	.	.	PUNCT
ejpam-5761	274	1	since	since	SCONJ
ejpam-5761	274	2	,	,	PUNCT
ejpam-5761	274	3	by	by	ADP
ejpam-5761	274	4	assumption	assumption	NOUN
ejpam-5761	274	5	there	there	PRON
ejpam-5761	274	6	is	be	VERB
ejpam-5761	274	7	no	no	DET
ejpam-5761	274	8	positive	positive	ADJ
ejpam-5761	274	9	p	p	X
ejpam-5761	274	10	-potential	-potential	NOUN
ejpam-5761	274	11	on	on	ADP
ejpam-5761	274	12	n	n	PROPN
ejpam-5761	274	13	,	,	PUNCT
ejpam-5761	274	14	|h|	|h|	PROPN
ejpam-5761	274	15	must	must	AUX
ejpam-5761	274	16	be	be	AUX
ejpam-5761	274	17	a	a	DET
ejpam-5761	274	18	constant	constant	ADJ
ejpam-5761	274	19	thus	thus	ADV
ejpam-5761	274	20	|h|	|h|	PROPN
ejpam-5761	274	21	=	=	SYM
ejpam-5761	274	22	c.	c.	NOUN
ejpam-5761	274	23	if	if	SCONJ
ejpam-5761	274	24	c	c	PROPN
ejpam-5761	274	25	̸=	̸=	PROPN
ejpam-5761	274	26	0	0	NUM
ejpam-5761	274	27	,	,	PUNCT
ejpam-5761	274	28	in	in	ADP
ejpam-5761	274	29	|h|	|h|	PROPN
ejpam-5761	274	30	=	=	SYM
ejpam-5761	274	31	c	c	X
ejpam-5761	274	32	,	,	PUNCT
ejpam-5761	274	33	|h|	|h|	PROPN
ejpam-5761	274	34	is	be	AUX
ejpam-5761	274	35	p	p	NOUN
ejpam-5761	274	36	′	′	NUM
ejpam-5761	274	37	-subaverage	-subaverage	NOUN
ejpam-5761	274	38	and	and	CCONJ
ejpam-5761	274	39	c	c	NOUN
ejpam-5761	274	40	is	be	AUX
ejpam-5761	274	41	p	p	NOUN
ejpam-5761	274	42	′	′	ADJ
ejpam-5761	274	43	-superaverage	-superaverage	NOUN
ejpam-5761	274	44	which	which	PRON
ejpam-5761	274	45	is	be	AUX
ejpam-5761	274	46	a	a	DET
ejpam-5761	274	47	contradiction	contradiction	NOUN
ejpam-5761	274	48	.	.	PUNCT
ejpam-5761	275	1	hence	hence	ADV
ejpam-5761	275	2	c	c	X
ejpam-5761	276	1	=	=	PUNCT
ejpam-5761	276	2	0	0	PROPN
ejpam-5761	277	1	that	that	PRON
ejpam-5761	277	2	is	be	AUX
ejpam-5761	277	3	h	h	NOUN
ejpam-5761	277	4	=	=	NOUN
ejpam-5761	277	5	0	0	NUM
ejpam-5761	277	6	.	.	PUNCT
ejpam-5761	278	1	thus	thus	ADV
ejpam-5761	278	2	0	0	NUM
ejpam-5761	278	3	is	be	AUX
ejpam-5761	278	4	the	the	DET
ejpam-5761	278	5	only	only	ADJ
ejpam-5761	278	6	bounded	bound	VERB
ejpam-5761	278	7	p	p	NOUN
ejpam-5761	278	8	′	′	NUM
ejpam-5761	278	9	-average	-average	NOUN
ejpam-5761	278	10	function	function	NOUN
ejpam-5761	278	11	on	on	ADP
ejpam-5761	278	12	n	n	PROPN
ejpam-5761	278	13	.	.	PUNCT
ejpam-5761	279	1	hence	hence	ADV
ejpam-5761	279	2	the	the	DET
ejpam-5761	279	3	constant	constant	ADJ
ejpam-5761	279	4	function	function	NOUN
ejpam-5761	279	5	1	1	NUM
ejpam-5761	279	6	is	be	AUX
ejpam-5761	279	7	a	a	DET
ejpam-5761	279	8	p	p	NOUN
ejpam-5761	279	9	′	′	ADJ
ejpam-5761	279	10	-potential	-potential	NOUN
ejpam-5761	279	11	on	on	ADP
ejpam-5761	279	12	n	n	PART
ejpam-5761	279	13	by	by	ADP
ejpam-5761	279	14	the	the	DET
ejpam-5761	279	15	theorem	theorem	ADJ
ejpam-5761	279	16	3	3	X
ejpam-5761	279	17	.	.	PUNCT
ejpam-5761	279	18	theorem	theorem	NOUN
ejpam-5761	279	19	5	5	NUM
ejpam-5761	279	20	.	.	PUNCT
ejpam-5761	280	1	if	if	SCONJ
ejpam-5761	280	2	(	(	PUNCT
ejpam-5761	280	3	n	n	X
ejpam-5761	280	4	,	,	PUNCT
ejpam-5761	280	5	p	p	NOUN
ejpam-5761	280	6	′	′	NOUN
ejpam-5761	280	7	)	)	PUNCT
ejpam-5761	280	8	is	be	AUX
ejpam-5761	280	9	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	280	10	,	,	PUNCT
ejpam-5761	280	11	then	then	ADV
ejpam-5761	280	12	any	any	DET
ejpam-5761	280	13	lower	lower	ADV
ejpam-5761	280	14	bounded	bounded	ADJ
ejpam-5761	280	15	p	p	X
ejpam-5761	280	16	′	′	ADJ
ejpam-5761	280	17	-superaverage	-superaverage	NOUN
ejpam-5761	280	18	function	function	NOUN
ejpam-5761	280	19	is	be	AUX
ejpam-5761	280	20	non	non	ADJ
ejpam-5761	280	21	-	-	ADJ
ejpam-5761	280	22	negative	negative	ADJ
ejpam-5761	280	23	.	.	PUNCT
ejpam-5761	281	1	conversely	conversely	ADV
ejpam-5761	281	2	,	,	PUNCT
ejpam-5761	281	3	if	if	SCONJ
ejpam-5761	281	4	any	any	PRON
ejpam-5761	281	5	lower	low	ADJ
ejpam-5761	281	6	bounded	bounded	ADJ
ejpam-5761	281	7	p	p	NOUN
ejpam-5761	281	8	′	′	NUM
ejpam-5761	281	9	-average	-average	NOUN
ejpam-5761	281	10	function	function	NOUN
ejpam-5761	281	11	is	be	AUX
ejpam-5761	281	12	non	non	ADJ
ejpam-5761	281	13	-	-	ADJ
ejpam-5761	281	14	negative	negative	ADJ
ejpam-5761	281	15	,	,	PUNCT
ejpam-5761	281	16	then	then	ADV
ejpam-5761	281	17	(	(	PUNCT
ejpam-5761	281	18	n	n	CCONJ
ejpam-5761	281	19	,	,	PUNCT
ejpam-5761	281	20	p	p	NOUN
ejpam-5761	281	21	′	′	NOUN
ejpam-5761	281	22	)	)	PUNCT
ejpam-5761	281	23	is	be	AUX
ejpam-5761	281	24	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	281	25	.	.	PUNCT
ejpam-5761	282	1	proof	proof	NOUN
ejpam-5761	282	2	.	.	PUNCT
ejpam-5761	283	1	let	let	VERB
ejpam-5761	283	2	(	(	PUNCT
ejpam-5761	283	3	n	n	X
ejpam-5761	283	4	,	,	PUNCT
ejpam-5761	283	5	p	p	NOUN
ejpam-5761	283	6	′	′	NOUN
ejpam-5761	283	7	)	)	PUNCT
ejpam-5761	283	8	be	be	AUX
ejpam-5761	283	9	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	283	10	.	.	PUNCT
ejpam-5761	284	1	suppose	suppose	VERB
ejpam-5761	284	2	s	s	PRON
ejpam-5761	284	3	is	be	AUX
ejpam-5761	284	4	a	a	DET
ejpam-5761	284	5	p	p	NOUN
ejpam-5761	284	6	′	′	NUM
ejpam-5761	284	7	-superaverage	-superaverage	NOUN
ejpam-5761	284	8	function	function	NOUN
ejpam-5761	284	9	on	on	ADP
ejpam-5761	284	10	n	n	PRON
ejpam-5761	284	11	such	such	ADJ
ejpam-5761	284	12	that	that	PRON
ejpam-5761	284	13	s	s	VERB
ejpam-5761	284	14	≥	≥	NOUN
ejpam-5761	284	15	−m	−m	NOUN
ejpam-5761	284	16	for	for	ADP
ejpam-5761	284	17	some	some	DET
ejpam-5761	284	18	m	m	NOUN
ejpam-5761	284	19	>	>	X
ejpam-5761	284	20	0	0	NUM
ejpam-5761	284	21	.	.	PUNCT
ejpam-5761	285	1	since	since	SCONJ
ejpam-5761	285	2	m	m	PROPN
ejpam-5761	285	3	is	be	AUX
ejpam-5761	285	4	p	p	ADJ
ejpam-5761	285	5	′	′	ADJ
ejpam-5761	285	6	-potential	-potential	NOUN
ejpam-5761	285	7	by	by	ADP
ejpam-5761	285	8	assumption	assumption	NOUN
ejpam-5761	285	9	,	,	PUNCT
ejpam-5761	285	10	−s	−s	NOUN
ejpam-5761	285	11	≤	≤	NOUN
ejpam-5761	285	12	m	m	VERB
ejpam-5761	285	13	implies	imply	VERB
ejpam-5761	285	14	that	that	SCONJ
ejpam-5761	285	15	s	s	VERB
ejpam-5761	285	16	≥	≥	NOUN
ejpam-5761	285	17	0	0	NUM
ejpam-5761	285	18	.	.	PUNCT
ejpam-5761	286	1	conversely	conversely	ADV
ejpam-5761	286	2	,	,	PUNCT
ejpam-5761	286	3	suppose	suppose	VERB
ejpam-5761	286	4	any	any	DET
ejpam-5761	286	5	lower	low	ADJ
ejpam-5761	286	6	bounded	bounded	ADJ
ejpam-5761	286	7	p	p	NOUN
ejpam-5761	286	8	′	′	NUM
ejpam-5761	286	9	-average	-average	NOUN
ejpam-5761	286	10	function	function	NOUN
ejpam-5761	286	11	on	on	ADP
ejpam-5761	286	12	n	n	X
ejpam-5761	286	13	is	be	AUX
ejpam-5761	286	14	non	non	ADJ
ejpam-5761	286	15	-	-	ADJ
ejpam-5761	286	16	negative	negative	ADJ
ejpam-5761	286	17	.	.	PUNCT
ejpam-5761	287	1	if	if	SCONJ
ejpam-5761	287	2	(	(	PUNCT
ejpam-5761	287	3	n	n	X
ejpam-5761	287	4	,	,	PUNCT
ejpam-5761	287	5	p	p	NOUN
ejpam-5761	287	6	′	′	NOUN
ejpam-5761	287	7	)	)	PUNCT
ejpam-5761	287	8	is	be	AUX
ejpam-5761	287	9	not	not	PART
ejpam-5761	287	10	parahyperbolic	parahyperbolic	ADJ
ejpam-5761	287	11	,	,	PUNCT
ejpam-5761	287	12	then	then	ADV
ejpam-5761	287	13	by	by	ADP
ejpam-5761	287	14	theorem	theorem	NOUN
ejpam-5761	287	15	4	4	NUM
ejpam-5761	287	16	there	there	ADV
ejpam-5761	287	17	exists	exist	VERB
ejpam-5761	287	18	a	a	DET
ejpam-5761	287	19	p	p	NOUN
ejpam-5761	287	20	′	′	NUM
ejpam-5761	287	21	-average	-average	NOUN
ejpam-5761	287	22	function	function	NOUN
ejpam-5761	287	23	h	h	NOUN
ejpam-5761	287	24	on	on	ADP
ejpam-5761	287	25	n	n	PROPN
ejpam-5761	287	26	,	,	PUNCT
ejpam-5761	287	27	0	0	PUNCT
ejpam-5761	287	28	<	<	X
ejpam-5761	287	29	h	h	X
ejpam-5761	287	30	<	<	X
ejpam-5761	287	31	1	1	NUM
ejpam-5761	287	32	.	.	PUNCT
ejpam-5761	288	1	since	since	SCONJ
ejpam-5761	288	2	−h	−h	ADJ
ejpam-5761	288	3	is	be	AUX
ejpam-5761	288	4	lower	low	ADJ
ejpam-5761	288	5	bounded	bounded	ADJ
ejpam-5761	288	6	,	,	PUNCT
ejpam-5761	288	7	−h	−h	ADJ
ejpam-5761	288	8	≥	≥	NOUN
ejpam-5761	288	9	0	0	NUM
ejpam-5761	288	10	a	a	DET
ejpam-5761	288	11	contradiction	contradiction	NOUN
ejpam-5761	288	12	.	.	PUNCT
ejpam-5761	289	1	m.	m.	NOUN
ejpam-5761	289	2	surya	surya	PROPN
ejpam-5761	289	3	priya	priya	PROPN
ejpam-5761	289	4	,	,	PUNCT
ejpam-5761	289	5	n.	n.	PROPN
ejpam-5761	289	6	nathiya	nathiya	PROPN
ejpam-5761	289	7	/	/	SYM
ejpam-5761	289	8	eur	eur	PROPN
ejpam-5761	289	9	.	.	PUNCT
ejpam-5761	290	1	j.	j.	PROPN
ejpam-5761	290	2	pure	pure	PROPN
ejpam-5761	290	3	appl	appl	PROPN
ejpam-5761	290	4	.	.	PROPN
ejpam-5761	290	5	math	math	PROPN
ejpam-5761	290	6	,	,	PUNCT
ejpam-5761	290	7	18	18	NUM
ejpam-5761	290	8	(	(	PUNCT
ejpam-5761	290	9	1	1	NUM
ejpam-5761	290	10	)	)	PUNCT
ejpam-5761	290	11	(	(	PUNCT
ejpam-5761	290	12	2025	2025	NUM
ejpam-5761	290	13	)	)	PUNCT
ejpam-5761	290	14	,	,	PUNCT
ejpam-5761	290	15	5761	5761	NUM
ejpam-5761	290	16	9	9	NUM
ejpam-5761	290	17	of	of	ADP
ejpam-5761	290	18	11	11	NUM
ejpam-5761	290	19	corollary	corollary	ADJ
ejpam-5761	290	20	2	2	NUM
ejpam-5761	290	21	.	.	PUNCT
ejpam-5761	290	22	suppose	suppose	VERB
ejpam-5761	290	23	h	h	NOUN
ejpam-5761	290	24	is	be	AUX
ejpam-5761	290	25	a	a	DET
ejpam-5761	290	26	p	p	NOUN
ejpam-5761	290	27	′	′	NUM
ejpam-5761	290	28	-average	-average	NOUN
ejpam-5761	290	29	function	function	NOUN
ejpam-5761	290	30	bounded	bound	VERB
ejpam-5761	290	31	on	on	ADP
ejpam-5761	290	32	one	one	NUM
ejpam-5761	290	33	side	side	NOUN
ejpam-5761	290	34	in	in	ADP
ejpam-5761	290	35	n	n	PROPN
ejpam-5761	290	36	.	.	PUNCT
ejpam-5761	291	1	if	if	SCONJ
ejpam-5761	291	2	h	h	NOUN
ejpam-5761	291	3	takes	take	VERB
ejpam-5761	291	4	both	both	CCONJ
ejpam-5761	291	5	positive	positive	ADJ
ejpam-5761	291	6	and	and	CCONJ
ejpam-5761	291	7	negative	negative	ADJ
ejpam-5761	291	8	values	value	NOUN
ejpam-5761	291	9	in	in	ADP
ejpam-5761	291	10	n	n	PROPN
ejpam-5761	291	11	,	,	PUNCT
ejpam-5761	291	12	then	then	ADV
ejpam-5761	291	13	there	there	PRON
ejpam-5761	291	14	exists	exist	VERB
ejpam-5761	291	15	a	a	DET
ejpam-5761	291	16	bounded	bounded	ADJ
ejpam-5761	291	17	p	p	NOUN
ejpam-5761	291	18	′	′	NUM
ejpam-5761	291	19	-average	-average	NOUN
ejpam-5761	291	20	function	function	NOUN
ejpam-5761	291	21	h	h	NOUN
ejpam-5761	291	22	,	,	PUNCT
ejpam-5761	291	23	0	0	PUNCT
ejpam-5761	291	24	<	<	X
ejpam-5761	291	25	h	h	X
ejpam-5761	291	26	<	<	X
ejpam-5761	291	27	1	1	NUM
ejpam-5761	291	28	,	,	PUNCT
ejpam-5761	291	29	on	on	ADP
ejpam-5761	291	30	n	n	PRON
ejpam-5761	291	31	,	,	PUNCT
ejpam-5761	291	32	hence	hence	ADV
ejpam-5761	291	33	n	n	ADV
ejpam-5761	291	34	is	be	AUX
ejpam-5761	291	35	bounded	bound	VERB
ejpam-5761	291	36	hyperbolic	hyperbolic	ADJ
ejpam-5761	291	37	.	.	PUNCT
ejpam-5761	292	1	5	5	X
ejpam-5761	292	2	.	.	X
ejpam-5761	292	3	relation	relation	NOUN
ejpam-5761	292	4	between	between	ADP
ejpam-5761	292	5	bounded	bounded	PROPN
ejpam-5761	292	6	p	p	X
ejpam-5761	292	7	′	′	NOUN
ejpam-5761	293	1	and	and	CCONJ
ejpam-5761	293	2	p	p	NOUN
ejpam-5761	293	3	-average	-average	NOUN
ejpam-5761	293	4	functions	function	NOUN
ejpam-5761	293	5	in	in	ADP
ejpam-5761	293	6	a	a	DET
ejpam-5761	293	7	random	random	ADJ
ejpam-5761	293	8	walk	walk	NOUN
ejpam-5761	293	9	the	the	DET
ejpam-5761	293	10	constant	constant	ADJ
ejpam-5761	293	11	function	function	NOUN
ejpam-5761	293	12	1	1	NUM
ejpam-5761	293	13	is	be	AUX
ejpam-5761	293	14	p	p	NOUN
ejpam-5761	293	15	-average	-average	NOUN
ejpam-5761	293	16	on	on	ADP
ejpam-5761	293	17	n	n	NOUN
ejpam-5761	293	18	.	.	PUNCT
ejpam-5761	294	1	the	the	DET
ejpam-5761	294	2	question	question	NOUN
ejpam-5761	294	3	is	be	AUX
ejpam-5761	294	4	:	:	PUNCT
ejpam-5761	294	5	what	what	PRON
ejpam-5761	294	6	can	can	AUX
ejpam-5761	294	7	we	we	PRON
ejpam-5761	294	8	say	say	VERB
ejpam-5761	294	9	about	about	ADP
ejpam-5761	294	10	the	the	DET
ejpam-5761	294	11	existence	existence	NOUN
ejpam-5761	294	12	of	of	ADP
ejpam-5761	294	13	bounded	bounded	ADJ
ejpam-5761	294	14	or	or	CCONJ
ejpam-5761	294	15	just	just	ADV
ejpam-5761	294	16	positive	positive	ADJ
ejpam-5761	294	17	p	p	ADJ
ejpam-5761	294	18	-average	-average	NOUN
ejpam-5761	294	19	functions	function	NOUN
ejpam-5761	294	20	on	on	ADP
ejpam-5761	294	21	n	n	PRON
ejpam-5761	294	22	that	that	PRON
ejpam-5761	294	23	are	be	AUX
ejpam-5761	294	24	not	not	PART
ejpam-5761	294	25	constants	constant	NOUN
ejpam-5761	294	26	?	?	PUNCT
ejpam-5761	295	1	we	we	PRON
ejpam-5761	295	2	have	have	VERB
ejpam-5761	295	3	examples	example	NOUN
ejpam-5761	295	4	of	of	ADP
ejpam-5761	295	5	{	{	PUNCT
ejpam-5761	295	6	n	n	X
ejpam-5761	295	7	,	,	PUNCT
ejpam-5761	295	8	p	p	X
ejpam-5761	295	9	}	}	PUNCT
ejpam-5761	295	10	on	on	ADP
ejpam-5761	295	11	which	which	PRON
ejpam-5761	295	12	there	there	PRON
ejpam-5761	295	13	are	be	VERB
ejpam-5761	295	14	no	no	DET
ejpam-5761	295	15	non	non	ADJ
ejpam-5761	295	16	-	-	ADJ
ejpam-5761	295	17	constant	constant	ADJ
ejpam-5761	295	18	bounded	bounded	ADJ
ejpam-5761	295	19	or	or	CCONJ
ejpam-5761	295	20	just	just	ADV
ejpam-5761	295	21	positive	positive	ADJ
ejpam-5761	295	22	p	p	ADJ
ejpam-5761	295	23	-average	-average	NOUN
ejpam-5761	295	24	functions	function	NOUN
ejpam-5761	295	25	.	.	PUNCT
ejpam-5761	296	1	in	in	ADP
ejpam-5761	296	2	this	this	DET
ejpam-5761	296	3	section	section	NOUN
ejpam-5761	296	4	we	we	PRON
ejpam-5761	296	5	try	try	VERB
ejpam-5761	296	6	to	to	PART
ejpam-5761	296	7	assert	assert	VERB
ejpam-5761	296	8	the	the	DET
ejpam-5761	296	9	existence	existence	NOUN
ejpam-5761	296	10	of	of	ADP
ejpam-5761	296	11	such	such	ADJ
ejpam-5761	296	12	functions	function	NOUN
ejpam-5761	296	13	on	on	ADP
ejpam-5761	296	14	{	{	PUNCT
ejpam-5761	296	15	x	x	NOUN
ejpam-5761	296	16	,	,	PUNCT
ejpam-5761	296	17	p	p	X
ejpam-5761	296	18	}	}	PUNCT
ejpam-5761	296	19	if	if	SCONJ
ejpam-5761	296	20	similar	similar	ADJ
ejpam-5761	296	21	functions	function	NOUN
ejpam-5761	296	22	exist	exist	VERB
ejpam-5761	296	23	on	on	ADP
ejpam-5761	296	24	{	{	PUNCT
ejpam-5761	296	25	x	x	NOUN
ejpam-5761	296	26	,	,	PUNCT
ejpam-5761	296	27	p	p	NOUN
ejpam-5761	296	28	′	′	NOUN
ejpam-5761	296	29	}	}	PUNCT
ejpam-5761	296	30	where	where	SCONJ
ejpam-5761	296	31	p	p	NOUN
ejpam-5761	296	32	′	′	NOUN
ejpam-5761	296	33	is	be	AUX
ejpam-5761	296	34	subordinate	subordinate	ADJ
ejpam-5761	296	35	to	to	ADP
ejpam-5761	296	36	p	p	PROPN
ejpam-5761	296	37	.	.	PUNCT
ejpam-5761	297	1	if	if	SCONJ
ejpam-5761	297	2	there	there	PRON
ejpam-5761	297	3	are	be	VERB
ejpam-5761	297	4	non	non	ADJ
ejpam-5761	297	5	-	-	ADJ
ejpam-5761	297	6	zero	zero	NUM
ejpam-5761	297	7	bounded	bound	VERB
ejpam-5761	297	8	p	p	NOUN
ejpam-5761	297	9	′	′	NUM
ejpam-5761	297	10	-average	-average	NOUN
ejpam-5761	297	11	functions	function	NOUN
ejpam-5761	297	12	on	on	ADP
ejpam-5761	297	13	n	n	PROPN
ejpam-5761	297	14	,	,	PUNCT
ejpam-5761	297	15	then	then	ADV
ejpam-5761	297	16	the	the	DET
ejpam-5761	297	17	constant	constant	ADJ
ejpam-5761	297	18	1	1	NUM
ejpam-5761	297	19	is	be	AUX
ejpam-5761	297	20	not	not	PART
ejpam-5761	297	21	a	a	DET
ejpam-5761	297	22	p	p	NOUN
ejpam-5761	297	23	′	′	NUM
ejpam-5761	297	24	-potential	-potential	ADJ
ejpam-5761	297	25	,	,	PUNCT
ejpam-5761	297	26	hence	hence	ADV
ejpam-5761	297	27	there	there	PRON
ejpam-5761	297	28	are	be	VERB
ejpam-5761	297	29	bounded	bound	VERB
ejpam-5761	297	30	positive	positive	ADJ
ejpam-5761	297	31	p	p	NOUN
ejpam-5761	297	32	′	′	NUM
ejpam-5761	297	33	-average	-average	NOUN
ejpam-5761	297	34	functions	function	NOUN
ejpam-5761	297	35	on	on	ADP
ejpam-5761	297	36	n	n	NOUN
ejpam-5761	297	37	.	.	PUNCT
ejpam-5761	298	1	in	in	ADP
ejpam-5761	298	2	this	this	DET
ejpam-5761	298	3	section	section	NOUN
ejpam-5761	298	4	we	we	PRON
ejpam-5761	298	5	investigate	investigate	VERB
ejpam-5761	298	6	the	the	DET
ejpam-5761	298	7	relation	relation	NOUN
ejpam-5761	298	8	between	between	ADP
ejpam-5761	298	9	bounded	bound	VERB
ejpam-5761	298	10	p	p	NOUN
ejpam-5761	298	11	′	′	NUM
ejpam-5761	298	12	-average	-average	NOUN
ejpam-5761	298	13	functions	function	NOUN
ejpam-5761	298	14	and	and	CCONJ
ejpam-5761	298	15	bounded	bound	VERB
ejpam-5761	298	16	p	p	NOUN
ejpam-5761	298	17	-average	-average	NOUN
ejpam-5761	298	18	functions	function	NOUN
ejpam-5761	298	19	on	on	ADP
ejpam-5761	298	20	n	n	PROPN
ejpam-5761	298	21	.	.	PUNCT
ejpam-5761	299	1	theorem	theorem	ADJ
ejpam-5761	299	2	6	6	NUM
ejpam-5761	299	3	.	.	PUNCT
ejpam-5761	300	1	let	let	AUX
ejpam-5761	300	2	(	(	PUNCT
ejpam-5761	300	3	n	n	X
ejpam-5761	300	4	,	,	PUNCT
ejpam-5761	300	5	p	p	NOUN
ejpam-5761	300	6	)	)	PUNCT
ejpam-5761	300	7	be	be	AUX
ejpam-5761	300	8	hyperbolic	hyperbolic	ADJ
ejpam-5761	300	9	with	with	ADP
ejpam-5761	300	10	its	its	PRON
ejpam-5761	300	11	green	green	NOUN
ejpam-5761	300	12	’s	’s	PART
ejpam-5761	300	13	potential	potential	ADJ
ejpam-5761	300	14	gy(x	gy(x	NOUN
ejpam-5761	300	15	)	)	PUNCT
ejpam-5761	300	16	satisfying	satisfy	VERB
ejpam-5761	300	17	the	the	DET
ejpam-5761	300	18	condition	condition	NOUN
ejpam-5761	300	19	supz∈ngz(z	supz∈ngz(z	ADJ
ejpam-5761	300	20	)	)	PUNCT
ejpam-5761	300	21	≤	≤	NUM
ejpam-5761	300	22	m	m	NOUN
ejpam-5761	300	23	.	.	PUNCT
ejpam-5761	301	1	if	if	SCONJ
ejpam-5761	301	2	∑	∑	PUNCT
ejpam-5761	301	3	x	x	PUNCT
ejpam-5761	302	1	[	[	X
ejpam-5761	302	2	1	1	NUM
ejpam-5761	302	3	−	−	PROPN
ejpam-5761	302	4	p	p	NOUN
ejpam-5761	302	5	′	′	X
ejpam-5761	302	6	(	(	PUNCT
ejpam-5761	302	7	x	x	NOUN
ejpam-5761	302	8	)	)	PUNCT
ejpam-5761	302	9	]	]	PUNCT
ejpam-5761	302	10	<	<	X
ejpam-5761	302	11	∞	∞	PROPN
ejpam-5761	302	12	,	,	PUNCT
ejpam-5761	302	13	then	then	ADV
ejpam-5761	302	14	n	n	PRON
ejpam-5761	302	15	has	have	AUX
ejpam-5761	302	16	bounded	bound	VERB
ejpam-5761	302	17	positive	positive	ADJ
ejpam-5761	302	18	p	p	NOUN
ejpam-5761	302	19	′	′	NUM
ejpam-5761	302	20	-average	-average	NOUN
ejpam-5761	302	21	functions	function	NOUN
ejpam-5761	302	22	on	on	ADP
ejpam-5761	302	23	n	n	PROPN
ejpam-5761	302	24	.	.	PUNCT
ejpam-5761	303	1	proof	proof	NOUN
ejpam-5761	303	2	.	.	PUNCT
ejpam-5761	304	1	if	if	SCONJ
ejpam-5761	304	2	0	0	NUM
ejpam-5761	304	3	is	be	AUX
ejpam-5761	304	4	the	the	DET
ejpam-5761	304	5	only	only	ADJ
ejpam-5761	304	6	bounded	bound	VERB
ejpam-5761	304	7	positive	positive	ADJ
ejpam-5761	304	8	p	p	NOUN
ejpam-5761	304	9	′	′	NUM
ejpam-5761	304	10	-average	-average	NOUN
ejpam-5761	304	11	function	function	NOUN
ejpam-5761	304	12	on	on	ADP
ejpam-5761	304	13	n	n	PROPN
ejpam-5761	304	14	,	,	PUNCT
ejpam-5761	304	15	then	then	ADV
ejpam-5761	304	16	constant	constant	ADJ
ejpam-5761	304	17	1	1	NUM
ejpam-5761	304	18	is	be	AUX
ejpam-5761	304	19	a	a	DET
ejpam-5761	304	20	p	p	NOUN
ejpam-5761	304	21	′	′	ADJ
ejpam-5761	304	22	-potential	-potential	NOUN
ejpam-5761	304	23	in	in	ADP
ejpam-5761	304	24	n	n	NOUN
ejpam-5761	304	25	and	and	CCONJ
ejpam-5761	304	26	1	1	NUM
ejpam-5761	304	27	=	=	SYM
ejpam-5761	304	28	∑	∑	PUNCT
ejpam-5761	304	29	y	y	PROPN
ejpam-5761	305	1	[	[	X
ejpam-5761	305	2	1−	1−	NUM
ejpam-5761	305	3	p	p	NOUN
ejpam-5761	305	4	′	′	NOUN
ejpam-5761	305	5	(	(	PUNCT
ejpam-5761	305	6	y)]g	y)]g	INTJ
ejpam-5761	305	7	′	′	NUM
ejpam-5761	305	8	y(x	y(x	NOUN
ejpam-5761	305	9	)	)	PUNCT
ejpam-5761	305	10	for	for	ADP
ejpam-5761	305	11	x	x	PROPN
ejpam-5761	305	12	∈	∈	PROPN
ejpam-5761	305	13	n	n	PRON
ejpam-5761	305	14	≤	≤	NUM
ejpam-5761	305	15	∑	∑	PUNCT
ejpam-5761	305	16	y	y	PROPN
ejpam-5761	306	1	[	[	X
ejpam-5761	306	2	1−	1−	NUM
ejpam-5761	306	3	p	p	NOUN
ejpam-5761	306	4	′	′	NUM
ejpam-5761	306	5	(	(	PUNCT
ejpam-5761	306	6	y)]gy(x	y)]gy(x	NOUN
ejpam-5761	306	7	)	)	PUNCT
ejpam-5761	306	8	≤	≤	NOUN
ejpam-5761	306	9	∑	∑	PUNCT
ejpam-5761	306	10	y	y	PROPN
ejpam-5761	307	1	[	[	X
ejpam-5761	307	2	1−	1−	NUM
ejpam-5761	307	3	p	p	NOUN
ejpam-5761	307	4	′	′	NUM
ejpam-5761	307	5	(	(	PUNCT
ejpam-5761	307	6	y)]gy(y	y)]gy(y	NOUN
ejpam-5761	307	7	)	)	PUNCT
ejpam-5761	307	8	≤m	≤m	NOUN
ejpam-5761	307	9	∑	∑	PUNCT
ejpam-5761	307	10	y	y	PROPN
ejpam-5761	308	1	[	[	X
ejpam-5761	308	2	1−	1−	NUM
ejpam-5761	308	3	p	p	NOUN
ejpam-5761	308	4	′	′	NUM
ejpam-5761	308	5	(	(	PUNCT
ejpam-5761	308	6	y	y	NOUN
ejpam-5761	308	7	)	)	PUNCT
ejpam-5761	308	8	]	]	PUNCT
ejpam-5761	309	1	<	<	X
ejpam-5761	309	2	∞.	∞.	PROPN
ejpam-5761	309	3	hence	hence	ADV
ejpam-5761	309	4	u(x	u(x	VERB
ejpam-5761	309	5	)	)	PUNCT
ejpam-5761	309	6	=	=	PUNCT
ejpam-5761	310	1	∑	∑	PUNCT
ejpam-5761	310	2	y[1−	y[1−	PROPN
ejpam-5761	310	3	p	p	NOUN
ejpam-5761	310	4	′	′	NUM
ejpam-5761	310	5	(	(	PUNCT
ejpam-5761	310	6	y)]gy(x	y)]gy(x	NOUN
ejpam-5761	310	7	)	)	PUNCT
ejpam-5761	310	8	should	should	AUX
ejpam-5761	310	9	be	be	AUX
ejpam-5761	310	10	a	a	DET
ejpam-5761	310	11	p	p	NOUN
ejpam-5761	310	12	-potential	-potential	NOUN
ejpam-5761	310	13	.	.	PUNCT
ejpam-5761	311	1	but	but	CCONJ
ejpam-5761	311	2	this	this	PRON
ejpam-5761	311	3	is	be	AUX
ejpam-5761	311	4	not	not	PART
ejpam-5761	311	5	possible	possible	ADJ
ejpam-5761	311	6	since	since	SCONJ
ejpam-5761	311	7	u(x	u(x	NOUN
ejpam-5761	311	8	)	)	PUNCT
ejpam-5761	311	9	maximizes	maximize	VERB
ejpam-5761	311	10	the	the	DET
ejpam-5761	311	11	p	p	NOUN
ejpam-5761	311	12	-average	-average	NOUN
ejpam-5761	311	13	function	function	NOUN
ejpam-5761	311	14	1	1	NUM
ejpam-5761	311	15	.	.	PUNCT
ejpam-5761	311	16	theorem	theorem	VERB
ejpam-5761	311	17	7	7	NUM
ejpam-5761	311	18	.	.	PUNCT
ejpam-5761	312	1	let	let	VERB
ejpam-5761	312	2	b	b	NOUN
ejpam-5761	312	3	(	(	PUNCT
ejpam-5761	312	4	respectively	respectively	ADV
ejpam-5761	312	5	b	b	NOUN
ejpam-5761	312	6	′	′	NUM
ejpam-5761	312	7	)	)	PUNCT
ejpam-5761	312	8	be	be	AUX
ejpam-5761	312	9	the	the	DET
ejpam-5761	312	10	set	set	NOUN
ejpam-5761	312	11	of	of	ADP
ejpam-5761	312	12	all	all	DET
ejpam-5761	312	13	bounded	bounded	ADJ
ejpam-5761	312	14	non	non	ADJ
ejpam-5761	312	15	-	-	ADJ
ejpam-5761	312	16	negative	negative	ADJ
ejpam-5761	312	17	p	p	NOUN
ejpam-5761	312	18	-(respectively	-(respectively	ADV
ejpam-5761	312	19	p	p	NOUN
ejpam-5761	312	20	′	′	NUM
ejpam-5761	312	21	-	-	PUNCT
ejpam-5761	312	22	)	)	PUNCT
ejpam-5761	312	23	average	average	ADJ
ejpam-5761	312	24	functions	function	NOUN
ejpam-5761	312	25	in	in	ADP
ejpam-5761	312	26	n	n	PROPN
ejpam-5761	312	27	.	.	PUNCT
ejpam-5761	313	1	then	then	ADV
ejpam-5761	313	2	there	there	PRON
ejpam-5761	313	3	is	be	VERB
ejpam-5761	313	4	an	an	DET
ejpam-5761	313	5	injective	injective	ADJ
ejpam-5761	313	6	map	map	NOUN
ejpam-5761	313	7	s	s	PART
ejpam-5761	313	8	:	:	PUNCT
ejpam-5761	313	9	b	b	NOUN
ejpam-5761	313	10	′	′	NUM
ejpam-5761	313	11	→	→	SYM
ejpam-5761	313	12	b	b	X
ejpam-5761	313	13	such	such	ADJ
ejpam-5761	313	14	that	that	SCONJ
ejpam-5761	313	15	s(α1h1	s(α1h1	PROPN
ejpam-5761	313	16	+	+	CCONJ
ejpam-5761	313	17	α2h2	α2h2	NOUN
ejpam-5761	313	18	)	)	PUNCT
ejpam-5761	313	19	=	=	SYM
ejpam-5761	313	20	α1s(h1	α1s(h1	PROPN
ejpam-5761	313	21	)	)	PUNCT
ejpam-5761	314	1	+	+	NUM
ejpam-5761	314	2	α2s(h2	α2s(h2	X
ejpam-5761	314	3	)	)	PUNCT
ejpam-5761	314	4	where	where	SCONJ
ejpam-5761	314	5	α1	α1	PROPN
ejpam-5761	314	6	,	,	PUNCT
ejpam-5761	314	7	α2	α2	PROPN
ejpam-5761	314	8	are	be	AUX
ejpam-5761	314	9	non	non	ADJ
ejpam-5761	314	10	-	-	ADJ
ejpam-5761	314	11	negative	negative	ADJ
ejpam-5761	314	12	constants	constant	NOUN
ejpam-5761	314	13	and	and	CCONJ
ejpam-5761	314	14	h1	h1	PROPN
ejpam-5761	314	15	,	,	PUNCT
ejpam-5761	314	16	h2	h2	PROPN
ejpam-5761	314	17	are	be	AUX
ejpam-5761	314	18	in	in	ADP
ejpam-5761	314	19	b	b	NOUN
ejpam-5761	314	20	′	′	NUM
ejpam-5761	314	21	.	.	PUNCT
ejpam-5761	315	1	m.	m.	PROPN
ejpam-5761	315	2	surya	surya	PROPN
ejpam-5761	315	3	priya	priya	PROPN
ejpam-5761	315	4	,	,	PUNCT
ejpam-5761	315	5	n.	n.	PROPN
ejpam-5761	315	6	nathiya	nathiya	PROPN
ejpam-5761	315	7	/	/	SYM
ejpam-5761	315	8	eur	eur	PROPN
ejpam-5761	315	9	.	.	PUNCT
ejpam-5761	316	1	j.	j.	PROPN
ejpam-5761	316	2	pure	pure	PROPN
ejpam-5761	316	3	appl	appl	PROPN
ejpam-5761	316	4	.	.	PROPN
ejpam-5761	316	5	math	math	PROPN
ejpam-5761	316	6	,	,	PUNCT
ejpam-5761	316	7	18	18	NUM
ejpam-5761	316	8	(	(	PUNCT
ejpam-5761	316	9	1	1	NUM
ejpam-5761	316	10	)	)	PUNCT
ejpam-5761	316	11	(	(	PUNCT
ejpam-5761	316	12	2025	2025	NUM
ejpam-5761	316	13	)	)	PUNCT
ejpam-5761	316	14	,	,	PUNCT
ejpam-5761	316	15	5761	5761	NUM
ejpam-5761	316	16	10	10	NUM
ejpam-5761	316	17	of	of	ADP
ejpam-5761	316	18	11	11	NUM
ejpam-5761	316	19	proof	proof	NOUN
ejpam-5761	316	20	.	.	PUNCT
ejpam-5761	317	1	let	let	VERB
ejpam-5761	317	2	h	h	NOUN
ejpam-5761	317	3	∈	∈	PROPN
ejpam-5761	317	4	b	b	PROPN
ejpam-5761	317	5	′	′	NOUN
ejpam-5761	317	6	.	.	PUNCT
ejpam-5761	318	1	then	then	ADV
ejpam-5761	318	2	h	h	PROPN
ejpam-5761	318	3	is	be	AUX
ejpam-5761	318	4	a	a	DET
ejpam-5761	318	5	bounded	bounded	ADJ
ejpam-5761	318	6	p	p	NOUN
ejpam-5761	318	7	-subaverage	-subaverage	NOUN
ejpam-5761	318	8	function	function	NOUN
ejpam-5761	318	9	.	.	PUNCT
ejpam-5761	319	1	let	let	VERB
ejpam-5761	319	2	s(h	s(h	PROPN
ejpam-5761	319	3	)	)	PUNCT
ejpam-5761	319	4	be	be	VERB
ejpam-5761	319	5	the	the	DET
ejpam-5761	319	6	least	least	ADJ
ejpam-5761	319	7	p	p	NOUN
ejpam-5761	319	8	-average	-average	NOUN
ejpam-5761	319	9	majorant	majorant	NOUN
ejpam-5761	319	10	of	of	ADP
ejpam-5761	319	11	h.	h.	PROPN
ejpam-5761	319	12	then	then	ADV
ejpam-5761	319	13	s(α1h1+α2h2	s(α1h1+α2h2	PROPN
ejpam-5761	319	14	)	)	PUNCT
ejpam-5761	319	15	=	=	SYM
ejpam-5761	319	16	α1sh1+α2sh2	α1sh1+α2sh2	VERB
ejpam-5761	319	17	.	.	PUNCT
ejpam-5761	320	1	suppose	suppose	VERB
ejpam-5761	320	2	s(h1	s(h1	ADJ
ejpam-5761	320	3	)	)	PUNCT
ejpam-5761	320	4	=	=	SYM
ejpam-5761	320	5	s(h2	s(h2	NOUN
ejpam-5761	320	6	)	)	PUNCT
ejpam-5761	320	7	.	.	PUNCT
ejpam-5761	321	1	note	note	VERB
ejpam-5761	321	2	that	that	SCONJ
ejpam-5761	321	3	for	for	ADP
ejpam-5761	321	4	h	h	PROPN
ejpam-5761	321	5	∈	∈	PROPN
ejpam-5761	321	6	b	b	PROPN
ejpam-5761	321	7	′	′	NOUN
ejpam-5761	321	8	,	,	PUNCT
ejpam-5761	321	9	s(h	s(h	PROPN
ejpam-5761	321	10	)	)	PUNCT
ejpam-5761	321	11	−	−	PROPN
ejpam-5761	321	12	h	h	NOUN
ejpam-5761	321	13	is	be	AUX
ejpam-5761	321	14	a	a	DET
ejpam-5761	321	15	p	p	NOUN
ejpam-5761	321	16	-potential	-potential	NOUN
ejpam-5761	321	17	and	and	CCONJ
ejpam-5761	321	18	hence	hence	ADV
ejpam-5761	321	19	a	a	DET
ejpam-5761	321	20	p	p	NOUN
ejpam-5761	321	21	′	′	NUM
ejpam-5761	321	22	-potential	-potential	NOUN
ejpam-5761	321	23	.	.	PUNCT
ejpam-5761	322	1	consequently	consequently	ADV
ejpam-5761	322	2	,	,	PUNCT
ejpam-5761	322	3	if	if	SCONJ
ejpam-5761	322	4	s(h1	s(h1	ADJ
ejpam-5761	322	5	)	)	PUNCT
ejpam-5761	322	6	=	=	SYM
ejpam-5761	322	7	s(h2	s(h2	NOUN
ejpam-5761	322	8	)	)	PUNCT
ejpam-5761	322	9	,	,	PUNCT
ejpam-5761	322	10	then	then	ADV
ejpam-5761	322	11	|h1	|h1	CCONJ
ejpam-5761	322	12	−	−	PROPN
ejpam-5761	323	1	h2|	h2|	NOUN
ejpam-5761	323	2	=	=	SYM
ejpam-5761	323	3	|[s(h1)−	|[s(h1)−	NOUN
ejpam-5761	323	4	h1]−	h1]−	NOUN
ejpam-5761	323	5	[	[	X
ejpam-5761	323	6	s(h2)−	s(h2)−	VERB
ejpam-5761	323	7	h2]|	h2]|	PROPN
ejpam-5761	323	8	≤	≤	PROPN
ejpam-5761	323	9	p1	p1	NOUN
ejpam-5761	323	10	+	+	CCONJ
ejpam-5761	323	11	p2	p2	PROPN
ejpam-5761	323	12	where	where	SCONJ
ejpam-5761	323	13	p1	p1	NOUN
ejpam-5761	323	14	and	and	CCONJ
ejpam-5761	323	15	p2	p2	PROPN
ejpam-5761	323	16	are	be	AUX
ejpam-5761	323	17	p	p	ADJ
ejpam-5761	323	18	′	′	ADJ
ejpam-5761	323	19	-potential	-potential	NOUN
ejpam-5761	323	20	on	on	ADP
ejpam-5761	323	21	n	n	PROPN
ejpam-5761	323	22	.	.	PUNCT
ejpam-5761	324	1	since	since	SCONJ
ejpam-5761	324	2	|h1	|h1	PRON
ejpam-5761	324	3	−	−	PROPN
ejpam-5761	324	4	h2|	h2|	PROPN
ejpam-5761	324	5	is	be	AUX
ejpam-5761	324	6	p	p	NOUN
ejpam-5761	324	7	′	′	NUM
ejpam-5761	324	8	-subaverage	-subaverage	NOUN
ejpam-5761	324	9	function	function	NOUN
ejpam-5761	324	10	on	on	ADP
ejpam-5761	324	11	n	n	PROPN
ejpam-5761	324	12	,	,	PUNCT
ejpam-5761	324	13	h1	h1	PROPN
ejpam-5761	324	14	=	=	PUNCT
ejpam-5761	324	15	h2	h2	PROPN
ejpam-5761	324	16	.	.	PUNCT
ejpam-5761	325	1	corollary	corollary	ADJ
ejpam-5761	325	2	3	3	NUM
ejpam-5761	325	3	.	.	PUNCT
ejpam-5761	326	1	if	if	SCONJ
ejpam-5761	326	2	there	there	PRON
ejpam-5761	326	3	are	be	VERB
ejpam-5761	326	4	non	non	ADJ
ejpam-5761	326	5	-	-	ADJ
ejpam-5761	326	6	proportional	proportional	ADJ
ejpam-5761	326	7	bounded	bounded	ADJ
ejpam-5761	326	8	non	non	ADJ
ejpam-5761	326	9	-	-	ADJ
ejpam-5761	326	10	negative	negative	ADJ
ejpam-5761	326	11	p	p	ADJ
ejpam-5761	326	12	′	′	NUM
ejpam-5761	326	13	-average	-average	NOUN
ejpam-5761	326	14	functions	function	NOUN
ejpam-5761	326	15	in	in	ADP
ejpam-5761	326	16	n	n	PROPN
ejpam-5761	326	17	,	,	PUNCT
ejpam-5761	326	18	then	then	ADV
ejpam-5761	326	19	there	there	PRON
ejpam-5761	326	20	is	be	VERB
ejpam-5761	326	21	atleast	atleast	ADJ
ejpam-5761	326	22	one	one	NUM
ejpam-5761	326	23	non	non	ADJ
ejpam-5761	326	24	-	-	ADJ
ejpam-5761	326	25	constant	constant	ADJ
ejpam-5761	326	26	bounded	bounded	ADJ
ejpam-5761	326	27	p	p	NOUN
ejpam-5761	326	28	-average	-average	NOUN
ejpam-5761	326	29	function	function	NOUN
ejpam-5761	326	30	in	in	ADP
ejpam-5761	326	31	n	n	PROPN
ejpam-5761	326	32	.	.	PUNCT
ejpam-5761	327	1	proof	proof	NOUN
ejpam-5761	327	2	.	.	PUNCT
ejpam-5761	328	1	if	if	SCONJ
ejpam-5761	328	2	h1	h1	PROPN
ejpam-5761	328	3	and	and	CCONJ
ejpam-5761	328	4	h2	h2	PROPN
ejpam-5761	328	5	are	be	AUX
ejpam-5761	328	6	non	non	ADJ
ejpam-5761	328	7	-	-	ADJ
ejpam-5761	328	8	proportional	proportional	ADJ
ejpam-5761	328	9	in	in	ADP
ejpam-5761	328	10	b	b	NOUN
ejpam-5761	328	11	′	′	NUM
ejpam-5761	328	12	,	,	PUNCT
ejpam-5761	328	13	then	then	ADV
ejpam-5761	328	14	s(h1	s(h1	PROPN
ejpam-5761	328	15	)	)	PUNCT
ejpam-5761	328	16	and	and	CCONJ
ejpam-5761	328	17	s(h2	s(h2	NOUN
ejpam-5761	328	18	)	)	PUNCT
ejpam-5761	328	19	are	be	AUX
ejpam-5761	328	20	nonproportional	nonproportional	ADJ
ejpam-5761	328	21	bounded	bounded	ADJ
ejpam-5761	328	22	p	p	NOUN
ejpam-5761	328	23	-average	-average	NOUN
ejpam-5761	328	24	functions	function	NOUN
ejpam-5761	328	25	in	in	ADP
ejpam-5761	328	26	n	n	PROPN
ejpam-5761	328	27	.	.	PUNCT
ejpam-5761	329	1	hence	hence	ADV
ejpam-5761	329	2	atleast	atleast	ADV
ejpam-5761	329	3	one	one	NUM
ejpam-5761	329	4	of	of	ADP
ejpam-5761	329	5	them	they	PRON
ejpam-5761	329	6	is	be	AUX
ejpam-5761	329	7	nonconstant	nonconstant	ADJ
ejpam-5761	329	8	.	.	PUNCT
ejpam-5761	330	1	lemma	lemma	PROPN
ejpam-5761	330	2	3	3	X
ejpam-5761	330	3	.	.	PUNCT
ejpam-5761	331	1	let	let	VERB
ejpam-5761	331	2	h	h	PRON
ejpam-5761	331	3	be	be	AUX
ejpam-5761	331	4	a	a	DET
ejpam-5761	331	5	p	p	NOUN
ejpam-5761	331	6	′	′	NUM
ejpam-5761	331	7	-average	-average	NOUN
ejpam-5761	331	8	function	function	NOUN
ejpam-5761	331	9	in	in	ADP
ejpam-5761	331	10	n	n	PROPN
ejpam-5761	331	11	,	,	PUNCT
ejpam-5761	331	12	such	such	ADJ
ejpam-5761	331	13	that	that	SCONJ
ejpam-5761	331	14	|h|	|h|	PROPN
ejpam-5761	331	15	≤	≤	X
ejpam-5761	331	16	s	s	VERB
ejpam-5761	331	17	where	where	SCONJ
ejpam-5761	331	18	s	s	VERB
ejpam-5761	331	19	is	be	AUX
ejpam-5761	331	20	p	p	NOUN
ejpam-5761	331	21	′	′	NUM
ejpam-5761	331	22	superaverage	superaverage	NOUN
ejpam-5761	331	23	on	on	ADP
ejpam-5761	331	24	n	n	PROPN
ejpam-5761	331	25	.	.	PUNCT
ejpam-5761	332	1	then	then	ADV
ejpam-5761	332	2	h	h	NOUN
ejpam-5761	332	3	=	=	PRON
ejpam-5761	332	4	h1	h1	PROPN
ejpam-5761	332	5	−	−	PROPN
ejpam-5761	332	6	h2	h2	NOUN
ejpam-5761	332	7	where	where	SCONJ
ejpam-5761	332	8	h1	h1	PROPN
ejpam-5761	332	9	and	and	CCONJ
ejpam-5761	332	10	h2	h2	PROPN
ejpam-5761	332	11	are	be	AUX
ejpam-5761	332	12	non	non	ADJ
ejpam-5761	332	13	-	-	ADJ
ejpam-5761	332	14	negative	negative	ADJ
ejpam-5761	332	15	p	p	ADJ
ejpam-5761	332	16	′	′	NUM
ejpam-5761	332	17	-average	-average	NOUN
ejpam-5761	332	18	functions	function	NOUN
ejpam-5761	332	19	such	such	ADJ
ejpam-5761	332	20	that	that	DET
ejpam-5761	332	21	h1	h1	PROPN
ejpam-5761	332	22	−	−	PROPN
ejpam-5761	332	23	h+	h+	X
ejpam-5761	332	24	and	and	CCONJ
ejpam-5761	332	25	h2	h2	PROPN
ejpam-5761	332	26	−	−	PROPN
ejpam-5761	333	1	h−	h−	PROPN
ejpam-5761	333	2	are	be	AUX
ejpam-5761	333	3	p	p	NOUN
ejpam-5761	333	4	′	′	NUM
ejpam-5761	333	5	-potentials	-potential	NOUN
ejpam-5761	333	6	.	.	PUNCT
ejpam-5761	334	1	this	this	DET
ejpam-5761	334	2	decomposition	decomposition	NOUN
ejpam-5761	334	3	is	be	AUX
ejpam-5761	334	4	unique	unique	ADJ
ejpam-5761	334	5	.	.	PUNCT
ejpam-5761	335	1	proof	proof	NOUN
ejpam-5761	335	2	.	.	PUNCT
ejpam-5761	336	1	let	let	VERB
ejpam-5761	336	2	h1	h1	PROPN
ejpam-5761	336	3	be	be	AUX
ejpam-5761	336	4	the	the	DET
ejpam-5761	336	5	least	least	ADJ
ejpam-5761	336	6	p	p	ADJ
ejpam-5761	336	7	′	′	NUM
ejpam-5761	336	8	-average	-average	NOUN
ejpam-5761	336	9	majorant	majorant	NOUN
ejpam-5761	336	10	of	of	ADP
ejpam-5761	336	11	h+	h+	X
ejpam-5761	336	12	and	and	CCONJ
ejpam-5761	336	13	h2	h2	PROPN
ejpam-5761	336	14	be	be	AUX
ejpam-5761	336	15	the	the	DET
ejpam-5761	336	16	least	least	ADJ
ejpam-5761	336	17	p	p	ADJ
ejpam-5761	336	18	′	′	NUM
ejpam-5761	336	19	-average	-average	NOUN
ejpam-5761	336	20	majorant	majorant	NOUN
ejpam-5761	336	21	of	of	ADP
ejpam-5761	336	22	h−.	h−.	PROPN
ejpam-5761	336	23	then	then	ADV
ejpam-5761	336	24	p1	p1	PROPN
ejpam-5761	336	25	=	=	PUNCT
ejpam-5761	336	26	h1	h1	PROPN
ejpam-5761	336	27	−	−	NOUN
ejpam-5761	336	28	h+	h+	PUNCT
ejpam-5761	336	29	and	and	CCONJ
ejpam-5761	336	30	p2	p2	PROPN
ejpam-5761	336	31	=	=	SYM
ejpam-5761	336	32	h2	h2	PROPN
ejpam-5761	337	1	−	−	PROPN
ejpam-5761	337	2	h−	h−	PROPN
ejpam-5761	337	3	are	be	AUX
ejpam-5761	337	4	p	p	ADJ
ejpam-5761	337	5	′	′	NUM
ejpam-5761	337	6	-potentials	-potential	NOUN
ejpam-5761	337	7	on	on	ADP
ejpam-5761	337	8	n	n	PROPN
ejpam-5761	337	9	.	.	PUNCT
ejpam-5761	338	1	hence	hence	ADV
ejpam-5761	338	2	h	h	NOUN
ejpam-5761	339	1	=	=	PRON
ejpam-5761	339	2	h+	h+	X
ejpam-5761	340	1	−	−	X
ejpam-5761	340	2	h−	h−	PROPN
ejpam-5761	340	3	=	=	SYM
ejpam-5761	340	4	(	(	PUNCT
ejpam-5761	340	5	h1	h1	PROPN
ejpam-5761	340	6	−	−	PROPN
ejpam-5761	340	7	h2	h2	NOUN
ejpam-5761	340	8	)	)	PUNCT
ejpam-5761	340	9	−	−	PROPN
ejpam-5761	341	1	(	(	PUNCT
ejpam-5761	341	2	p1	p1	NOUN
ejpam-5761	341	3	−	−	PROPN
ejpam-5761	341	4	p2	p2	PROPN
ejpam-5761	341	5	)	)	PUNCT
ejpam-5761	341	6	.	.	PUNCT
ejpam-5761	342	1	then	then	ADV
ejpam-5761	342	2	by	by	ADP
ejpam-5761	342	3	the	the	DET
ejpam-5761	342	4	uniqueness	uniqueness	NOUN
ejpam-5761	342	5	of	of	ADP
ejpam-5761	342	6	riesz	riesz	PROPN
ejpam-5761	342	7	decomposition	decomposition	NOUN
ejpam-5761	342	8	,	,	PUNCT
ejpam-5761	342	9	h	h	NOUN
ejpam-5761	342	10	=	=	NOUN
ejpam-5761	342	11	h1	h1	PROPN
ejpam-5761	342	12	−	−	PROPN
ejpam-5761	342	13	h2	h2	PROPN
ejpam-5761	342	14	on	on	ADP
ejpam-5761	342	15	n	n	PROPN
ejpam-5761	342	16	.	.	PUNCT
ejpam-5761	343	1	suppose	suppose	VERB
ejpam-5761	343	2	h	h	NOUN
ejpam-5761	343	3	=	=	NOUN
ejpam-5761	343	4	u1	u1	PROPN
ejpam-5761	343	5	−	−	PROPN
ejpam-5761	343	6	u2	u2	PROPN
ejpam-5761	343	7	is	be	AUX
ejpam-5761	343	8	another	another	DET
ejpam-5761	343	9	such	such	ADJ
ejpam-5761	343	10	decomposition	decomposition	NOUN
ejpam-5761	343	11	.	.	PUNCT
ejpam-5761	344	1	since	since	SCONJ
ejpam-5761	344	2	u1	u1	PROPN
ejpam-5761	344	3	−	−	PROPN
ejpam-5761	344	4	h+	h+	PUNCT
ejpam-5761	344	5	and	and	CCONJ
ejpam-5761	344	6	h1	h1	VERB
ejpam-5761	344	7	−	−	PROPN
ejpam-5761	344	8	h+	h+	X
ejpam-5761	344	9	are	be	AUX
ejpam-5761	344	10	potentials	potential	NOUN
ejpam-5761	344	11	,	,	PUNCT
ejpam-5761	344	12	so	so	ADV
ejpam-5761	344	13	u1	u1	NOUN
ejpam-5761	344	14	=	=	PUNCT
ejpam-5761	344	15	h1	h1	PROPN
ejpam-5761	344	16	and	and	CCONJ
ejpam-5761	344	17	then	then	ADV
ejpam-5761	344	18	u2	u2	PROPN
ejpam-5761	344	19	=	=	PUNCT
ejpam-5761	344	20	h2	h2	PROPN
ejpam-5761	344	21	.	.	PUNCT
ejpam-5761	345	1	theorem	theorem	VERB
ejpam-5761	345	2	8	8	NUM
ejpam-5761	345	3	.	.	PUNCT
ejpam-5761	346	1	if	if	SCONJ
ejpam-5761	346	2	there	there	PRON
ejpam-5761	346	3	exists	exist	VERB
ejpam-5761	346	4	a	a	DET
ejpam-5761	346	5	bounded	bounded	ADJ
ejpam-5761	346	6	p	p	NOUN
ejpam-5761	346	7	′	′	NUM
ejpam-5761	346	8	-average	-average	NOUN
ejpam-5761	346	9	function	function	NOUN
ejpam-5761	346	10	on	on	ADP
ejpam-5761	346	11	n	n	PROPN
ejpam-5761	346	12	that	that	PRON
ejpam-5761	346	13	takes	take	VERB
ejpam-5761	346	14	both	both	DET
ejpam-5761	346	15	positive	positive	ADJ
ejpam-5761	346	16	and	and	CCONJ
ejpam-5761	346	17	negative	negative	ADJ
ejpam-5761	346	18	values	value	NOUN
ejpam-5761	346	19	,	,	PUNCT
ejpam-5761	346	20	then	then	ADV
ejpam-5761	346	21	there	there	PRON
ejpam-5761	346	22	is	be	VERB
ejpam-5761	346	23	atleast	atleast	ADJ
ejpam-5761	346	24	one	one	NUM
ejpam-5761	346	25	bounded	bound	VERB
ejpam-5761	346	26	non	non	ADJ
ejpam-5761	346	27	-	-	ADJ
ejpam-5761	346	28	constant	constant	ADJ
ejpam-5761	346	29	p	p	ADJ
ejpam-5761	346	30	-average	-average	NOUN
ejpam-5761	346	31	function	function	NOUN
ejpam-5761	346	32	on	on	ADP
ejpam-5761	346	33	n	n	PROPN
ejpam-5761	346	34	.	.	PUNCT
ejpam-5761	347	1	proof	proof	NOUN
ejpam-5761	347	2	.	.	PUNCT
ejpam-5761	348	1	let	let	VERB
ejpam-5761	348	2	h	h	PRON
ejpam-5761	348	3	be	be	AUX
ejpam-5761	348	4	a	a	DET
ejpam-5761	348	5	bounded	bounded	ADJ
ejpam-5761	348	6	p	p	NOUN
ejpam-5761	348	7	′	′	NUM
ejpam-5761	348	8	-average	-average	NOUN
ejpam-5761	348	9	function	function	NOUN
ejpam-5761	348	10	,	,	PUNCT
ejpam-5761	348	11	write	write	VERB
ejpam-5761	348	12	h	h	NOUN
ejpam-5761	348	13	=	=	PUNCT
ejpam-5761	348	14	h1	h1	PROPN
ejpam-5761	348	15	−	−	PROPN
ejpam-5761	348	16	h2	h2	NOUN
ejpam-5761	348	17	as	as	ADP
ejpam-5761	348	18	in	in	ADP
ejpam-5761	348	19	lemma	lemma	PROPN
ejpam-5761	348	20	3	3	NUM
ejpam-5761	348	21	,	,	PUNCT
ejpam-5761	348	22	since	since	SCONJ
ejpam-5761	348	23	h	h	NOUN
ejpam-5761	348	24	takes	take	VERB
ejpam-5761	348	25	both	both	CCONJ
ejpam-5761	348	26	positive	positive	ADJ
ejpam-5761	348	27	and	and	CCONJ
ejpam-5761	348	28	negative	negative	ADJ
ejpam-5761	348	29	values	value	NOUN
ejpam-5761	348	30	by	by	ADP
ejpam-5761	348	31	the	the	DET
ejpam-5761	348	32	assumption	assumption	NOUN
ejpam-5761	348	33	,	,	PUNCT
ejpam-5761	348	34	h1	h1	PROPN
ejpam-5761	348	35	and	and	CCONJ
ejpam-5761	348	36	h2	h2	NOUN
ejpam-5761	348	37	are	be	AUX
ejpam-5761	348	38	positive	positive	ADJ
ejpam-5761	348	39	.	.	PUNCT
ejpam-5761	349	1	suppose	suppose	VERB
ejpam-5761	349	2	h1	h1	PROPN
ejpam-5761	349	3	=	=	PUNCT
ejpam-5761	349	4	λh2	λh2	PROPN
ejpam-5761	349	5	.	.	PUNCT
ejpam-5761	350	1	then	then	ADV
ejpam-5761	350	2	h	h	NOUN
ejpam-5761	350	3	=	=	PUNCT
ejpam-5761	350	4	(	(	PUNCT
ejpam-5761	350	5	λ	λ	X
ejpam-5761	350	6	−	−	NOUN
ejpam-5761	350	7	1)h2	1)h2	NUM
ejpam-5761	350	8	,	,	PUNCT
ejpam-5761	350	9	contradicting	contradict	VERB
ejpam-5761	350	10	the	the	DET
ejpam-5761	350	11	assumption	assumption	NOUN
ejpam-5761	350	12	that	that	SCONJ
ejpam-5761	350	13	h	h	NOUN
ejpam-5761	350	14	takes	take	VERB
ejpam-5761	350	15	both	both	CCONJ
ejpam-5761	350	16	positive	positive	ADJ
ejpam-5761	350	17	and	and	CCONJ
ejpam-5761	350	18	negative	negative	ADJ
ejpam-5761	350	19	values	value	NOUN
ejpam-5761	350	20	on	on	ADP
ejpam-5761	350	21	n	n	PROPN
ejpam-5761	350	22	.	.	PUNCT
ejpam-5761	351	1	since	since	SCONJ
ejpam-5761	351	2	h1	h1	PROPN
ejpam-5761	351	3	and	and	CCONJ
ejpam-5761	351	4	h2	h2	PROPN
ejpam-5761	351	5	are	be	AUX
ejpam-5761	351	6	non	non	ADJ
ejpam-5761	351	7	-	-	ADJ
ejpam-5761	351	8	proportional	proportional	ADJ
ejpam-5761	351	9	,	,	PUNCT
ejpam-5761	351	10	by	by	ADP
ejpam-5761	351	11	corollary	corollary	ADJ
ejpam-5761	351	12	3	3	NUM
ejpam-5761	351	13	,	,	PUNCT
ejpam-5761	351	14	there	there	PRON
ejpam-5761	351	15	is	be	VERB
ejpam-5761	351	16	atleast	atleast	ADJ
ejpam-5761	351	17	one	one	NUM
ejpam-5761	351	18	non	non	ADJ
ejpam-5761	351	19	-	-	ADJ
ejpam-5761	351	20	constant	constant	ADJ
ejpam-5761	351	21	bounded	bounded	ADJ
ejpam-5761	351	22	p	p	NOUN
ejpam-5761	351	23	-average	-average	NOUN
ejpam-5761	351	24	function	function	NOUN
ejpam-5761	351	25	on	on	ADP
ejpam-5761	351	26	n	n	PROPN
ejpam-5761	351	27	.	.	PUNCT
ejpam-5761	352	1	statements	statement	NOUN
ejpam-5761	352	2	and	and	CCONJ
ejpam-5761	352	3	declarations	declaration	NOUN
ejpam-5761	352	4	•	•	PRON
ejpam-5761	352	5	availability	availability	NOUN
ejpam-5761	352	6	of	of	ADP
ejpam-5761	352	7	data	datum	NOUN
ejpam-5761	352	8	and	and	CCONJ
ejpam-5761	352	9	materials	material	NOUN
ejpam-5761	352	10	not	not	PART
ejpam-5761	352	11	applicable	applicable	ADJ
ejpam-5761	352	12	•	•	NOUN
ejpam-5761	352	13	competing	compete	VERB
ejpam-5761	352	14	interests	interest	NOUN
ejpam-5761	352	15	the	the	DET
ejpam-5761	352	16	authors	author	NOUN
ejpam-5761	352	17	disclose	disclose	VERB
ejpam-5761	352	18	no	no	DET
ejpam-5761	352	19	potential	potential	ADJ
ejpam-5761	352	20	conflicts	conflict	NOUN
ejpam-5761	352	21	of	of	ADP
ejpam-5761	352	22	interest	interest	NOUN
ejpam-5761	352	23	.	.	PUNCT
ejpam-5761	353	1	•	•	NUM
ejpam-5761	353	2	funding	fund	VERB
ejpam-5761	353	3	this	this	DET
ejpam-5761	353	4	research	research	NOUN
ejpam-5761	353	5	received	receive	VERB
ejpam-5761	353	6	no	no	DET
ejpam-5761	353	7	external	external	ADJ
ejpam-5761	353	8	funding	funding	NOUN
ejpam-5761	353	9	.	.	PUNCT
ejpam-5761	354	1	•	•	NUM
ejpam-5761	354	2	authors	author	NOUN
ejpam-5761	354	3	’	'	PUNCT
ejpam-5761	354	4	contributions	contribution	NOUN
ejpam-5761	354	5	all	all	DET
ejpam-5761	354	6	authors	author	NOUN
ejpam-5761	354	7	equally	equally	ADV
ejpam-5761	354	8	contributed	contribute	VERB
ejpam-5761	354	9	in	in	ADP
ejpam-5761	354	10	this	this	DET
ejpam-5761	354	11	paper	paper	NOUN
ejpam-5761	354	12	.	.	PUNCT
ejpam-5761	355	1	m.	m.	NOUN
ejpam-5761	355	2	surya	surya	PROPN
ejpam-5761	355	3	priya	priya	PROPN
ejpam-5761	355	4	,	,	PUNCT
ejpam-5761	355	5	n.	n.	PROPN
ejpam-5761	355	6	nathiya	nathiya	PROPN
ejpam-5761	355	7	/	/	SYM
ejpam-5761	355	8	eur	eur	PROPN
ejpam-5761	355	9	.	.	PUNCT
ejpam-5761	356	1	j.	j.	PROPN
ejpam-5761	356	2	pure	pure	PROPN
ejpam-5761	356	3	appl	appl	PROPN
ejpam-5761	356	4	.	.	PROPN
ejpam-5761	356	5	math	math	PROPN
ejpam-5761	356	6	,	,	PUNCT
ejpam-5761	356	7	18	18	NUM
ejpam-5761	356	8	(	(	PUNCT
ejpam-5761	356	9	1	1	NUM
ejpam-5761	356	10	)	)	PUNCT
ejpam-5761	356	11	(	(	PUNCT
ejpam-5761	356	12	2025	2025	NUM
ejpam-5761	356	13	)	)	PUNCT
ejpam-5761	356	14	,	,	PUNCT
ejpam-5761	356	15	5761	5761	NUM
ejpam-5761	356	16	11	11	NUM
ejpam-5761	356	17	of	of	ADP
ejpam-5761	356	18	11	11	NUM
ejpam-5761	356	19	references	reference	NOUN
ejpam-5761	356	20	[	[	X
ejpam-5761	356	21	1	1	NUM
ejpam-5761	356	22	]	]	X
ejpam-5761	356	23	victor	victor	PROPN
ejpam-5761	356	24	anandam	anandam	PROPN
ejpam-5761	356	25	.	.	PUNCT
ejpam-5761	357	1	harmonic	harmonic	ADJ
ejpam-5761	357	2	functions	function	NOUN
ejpam-5761	357	3	and	and	CCONJ
ejpam-5761	357	4	potentials	potential	NOUN
ejpam-5761	357	5	on	on	ADP
ejpam-5761	357	6	finite	finite	NOUN
ejpam-5761	357	7	or	or	CCONJ
ejpam-5761	357	8	infinite	infinite	ADJ
ejpam-5761	357	9	networks	network	NOUN
ejpam-5761	357	10	.	.	PUNCT
ejpam-5761	358	1	springer	springer	NOUN
ejpam-5761	358	2	science	science	PROPN
ejpam-5761	358	3	&	&	CCONJ
ejpam-5761	358	4	business	business	NOUN
ejpam-5761	358	5	media	medium	NOUN
ejpam-5761	358	6	,	,	PUNCT
ejpam-5761	358	7	germany	germany	PROPN
ejpam-5761	358	8	,	,	PUNCT
ejpam-5761	358	9	2011	2011	NUM
ejpam-5761	358	10	.	.	PUNCT
ejpam-5761	359	1	[	[	X
ejpam-5761	359	2	2	2	NUM
ejpam-5761	359	3	]	]	X
ejpam-5761	359	4	victor	victor	NOUN
ejpam-5761	359	5	anandam	anandam	PROPN
ejpam-5761	359	6	.	.	PUNCT
ejpam-5761	360	1	random	random	ADJ
ejpam-5761	360	2	walks	walk	NOUN
ejpam-5761	360	3	on	on	ADP
ejpam-5761	360	4	infinite	infinite	ADJ
ejpam-5761	360	5	trees	tree	NOUN
ejpam-5761	360	6	.	.	PUNCT
ejpam-5761	361	1	revue	revue	PROPN
ejpam-5761	361	2	roumaine	roumaine	NOUN
ejpam-5761	361	3	de	de	X
ejpam-5761	361	4	mathematiques	mathematique	NOUN
ejpam-5761	361	5	pures	pure	NOUN
ejpam-5761	361	6	et	et	PROPN
ejpam-5761	361	7	appliquees	appliquee	NOUN
ejpam-5761	361	8	,	,	PUNCT
ejpam-5761	361	9	65:75–82	65:75–82	NUM
ejpam-5761	361	10	,	,	PUNCT
ejpam-5761	361	11	2020	2020	NUM
ejpam-5761	361	12	.	.	PUNCT
ejpam-5761	362	1	[	[	X
ejpam-5761	362	2	3	3	X
ejpam-5761	362	3	]	]	X
ejpam-5761	362	4	victor	victor	NOUN
ejpam-5761	362	5	anandam	anandam	PROPN
ejpam-5761	362	6	and	and	CCONJ
ejpam-5761	362	7	kamaleldin	kamaleldin	NOUN
ejpam-5761	362	8	abodayeh	abodayeh	NOUN
ejpam-5761	362	9	.	.	PUNCT
ejpam-5761	363	1	non	non	ADJ
ejpam-5761	363	2	-	-	ADJ
ejpam-5761	363	3	locally	locally	ADV
ejpam-5761	363	4	-	-	PUNCT
ejpam-5761	363	5	finite	finite	ADJ
ejpam-5761	363	6	parahyperbolic	parahyperbolic	NOUN
ejpam-5761	363	7	networks	network	NOUN
ejpam-5761	363	8	.	.	PUNCT
ejpam-5761	364	1	memoirs	memoir	NOUN
ejpam-5761	364	2	of	of	ADP
ejpam-5761	364	3	the	the	DET
ejpam-5761	364	4	graduate	graduate	ADJ
ejpam-5761	364	5	school	school	NOUN
ejpam-5761	364	6	of	of	ADP
ejpam-5761	364	7	science	science	NOUN
ejpam-5761	364	8	and	and	CCONJ
ejpam-5761	364	9	engineering	engineering	NOUN
ejpam-5761	364	10	,	,	PUNCT
ejpam-5761	364	11	shimane	shimane	PROPN
ejpam-5761	364	12	university	university	PROPN
ejpam-5761	364	13	.	.	PUNCT
ejpam-5761	365	1	series	series	PROPN
ejpam-5761	365	2	b	b	PROPN
ejpam-5761	365	3	:	:	PUNCT
ejpam-5761	365	4	mathematics	mathematic	NOUN
ejpam-5761	365	5	,	,	PUNCT
ejpam-5761	365	6	47:19–35	47:19–35	NUM
ejpam-5761	365	7	,	,	PUNCT
ejpam-5761	365	8	2014	2014	NUM
ejpam-5761	365	9	.	.	PUNCT
ejpam-5761	366	1	[	[	X
ejpam-5761	366	2	4	4	NUM
ejpam-5761	366	3	]	]	X
ejpam-5761	366	4	enrique	enrique	PROPN
ejpam-5761	366	5	bendito	bendito	PROPN
ejpam-5761	366	6	,	,	PUNCT
ejpam-5761	366	7	angeles	angeles	PROPN
ejpam-5761	366	8	carmona	carmona	PROPN
ejpam-5761	366	9	,	,	PUNCT
ejpam-5761	366	10	and	and	CCONJ
ejpam-5761	366	11	andrés	andré	NOUN
ejpam-5761	366	12	m	m	VERB
ejpam-5761	366	13	encinas	encina	NOUN
ejpam-5761	366	14	.	.	PUNCT
ejpam-5761	367	1	potential	potential	ADJ
ejpam-5761	367	2	theory	theory	NOUN
ejpam-5761	367	3	for	for	ADP
ejpam-5761	367	4	schrödinger	schrödinger	NOUN
ejpam-5761	367	5	operators	operator	NOUN
ejpam-5761	367	6	on	on	ADP
ejpam-5761	367	7	finite	finite	ADJ
ejpam-5761	367	8	networks	network	NOUN
ejpam-5761	367	9	.	.	PUNCT
ejpam-5761	368	1	revista	revista	PROPN
ejpam-5761	368	2	matemática	matemática	PROPN
ejpam-5761	368	3	iberoamericana	iberoamericana	PROPN
ejpam-5761	368	4	,	,	PUNCT
ejpam-5761	368	5	21(3):771–818	21(3):771–818	PROPN
ejpam-5761	368	6	]	]	PUNCT
ejpam-5761	368	7	,	,	PUNCT
ejpam-5761	368	8	doi	doi	X
ejpam-5761	368	9	=	=	NOUN
ejpam-5761	368	10	10.4171	10.4171	NUM
ejpam-5761	368	11	/	/	SYM
ejpam-5761	368	12	rmi/435	rmi/435	ADJ
ejpam-5761	368	13	,	,	PUNCT
ejpam-5761	368	14	,	,	PUNCT
ejpam-5761	368	15	2005	2005	NUM
ejpam-5761	368	16	.	.	PUNCT
ejpam-5761	369	1	[	[	X
ejpam-5761	369	2	5	5	NUM
ejpam-5761	369	3	]	]	PUNCT
ejpam-5761	369	4	varadha	varadha	NOUN
ejpam-5761	369	5	raj	raj	PROPN
ejpam-5761	369	6	manivannan	manivannan	PROPN
ejpam-5761	369	7	and	and	CCONJ
ejpam-5761	369	8	madhu	madhu	PROPN
ejpam-5761	369	9	venkataraman	venkataraman	PROPN
ejpam-5761	369	10	.	.	PUNCT
ejpam-5761	370	1	∆-functions	∆-function	NOUN
ejpam-5761	370	2	on	on	ADP
ejpam-5761	370	3	recurrent	recurrent	ADJ
ejpam-5761	370	4	random	random	ADJ
ejpam-5761	370	5	walks	walk	NOUN
ejpam-5761	370	6	.	.	PUNCT
ejpam-5761	371	1	vestnik	vestnik	PROPN
ejpam-5761	371	2	udmurtskogo	udmurtskogo	PROPN
ejpam-5761	371	3	universiteta	universiteta	PROPN
ejpam-5761	371	4	.	.	PROPN
ejpam-5761	371	5	matematika	matematika	PROPN
ejpam-5761	371	6	.	.	PUNCT
ejpam-5761	371	7	mekhanika	mekhanika	PROPN
ejpam-5761	371	8	.	.	PUNCT
ejpam-5761	372	1	komp’yuternye	komp’yuternye	NOUN
ejpam-5761	372	2	nauki	nauki	PROPN
ejpam-5761	372	3	,	,	PUNCT
ejpam-5761	372	4	33:119–129	33:119–129	NUM
ejpam-5761	372	5	,	,	PUNCT
ejpam-5761	372	6	2023	2023	NUM
ejpam-5761	372	7	.	.	PUNCT
ejpam-5761	373	1	[	[	X
ejpam-5761	373	2	6	6	NUM
ejpam-5761	373	3	]	]	PUNCT
ejpam-5761	373	4	minoru	minoru	PROPN
ejpam-5761	373	5	murata	murata	PROPN
ejpam-5761	373	6	.	.	PUNCT
ejpam-5761	374	1	structure	structure	NOUN
ejpam-5761	374	2	of	of	ADP
ejpam-5761	374	3	positive	positive	ADJ
ejpam-5761	374	4	solutions	solution	NOUN
ejpam-5761	374	5	to	to	ADP
ejpam-5761	374	6	(	(	PUNCT
ejpam-5761	374	7	∆+	∆+	NUM
ejpam-5761	374	8	v	v	NOUN
ejpam-5761	374	9	)	)	PUNCT
ejpam-5761	374	10	u=	u=	ADV
ejpam-5761	374	11	0	0	NUM
ejpam-5761	375	1	in	in	ADP
ejpam-5761	375	2	r	r	NOUN
ejpam-5761	375	3	n.	n.	NOUN
ejpam-5761	375	4	duke	duke	PROPN
ejpam-5761	375	5	mathematical	mathematical	PROPN
ejpam-5761	375	6	journal	journal	PROPN
ejpam-5761	375	7	.	.	PUNCT
ejpam-5761	376	1	[	[	X
ejpam-5761	376	2	7	7	NUM
ejpam-5761	376	3	]	]	SYM
ejpam-5761	376	4	narayanaraju	narayanaraju	ADJ
ejpam-5761	376	5	nathiya	nathiya	NOUN
ejpam-5761	376	6	and	and	CCONJ
ejpam-5761	376	7	chinnathambi	chinnathambi	PROPN
ejpam-5761	376	8	amulya	amulya	PROPN
ejpam-5761	376	9	smyrna	smyrna	PROPN
ejpam-5761	376	10	.	.	PUNCT
ejpam-5761	377	1	infinite	infinite	PROPN
ejpam-5761	377	2	schrodinger	schrodinger	PROPN
ejpam-5761	377	3	networks	network	NOUN
ejpam-5761	377	4	.	.	PUNCT
ejpam-5761	378	1	vestnik	vestnik	PROPN
ejpam-5761	378	2	udmurtskogo	udmurtskogo	PROPN
ejpam-5761	378	3	universiteta	universiteta	PROPN
ejpam-5761	378	4	.	.	PROPN
ejpam-5761	378	5	matematika	matematika	PROPN
ejpam-5761	378	6	.	.	PUNCT
ejpam-5761	378	7	mekhanika	mekhanika	PROPN
ejpam-5761	378	8	.	.	PUNCT
ejpam-5761	379	1	komp’yuternye	komp’yuternye	NOUN
ejpam-5761	379	2	nauki	nauki	PROPN
ejpam-5761	379	3	,	,	PUNCT
ejpam-5761	379	4	31(4):640–650	31(4):640–650	PROPN
ejpam-5761	379	5	,	,	PUNCT
ejpam-5761	379	6	2021	2021	NUM
ejpam-5761	379	7	.	.	PUNCT
ejpam-5761	380	1	[	[	X
ejpam-5761	380	2	8	8	NUM
ejpam-5761	380	3	]	]	SYM
ejpam-5761	380	4	m	m	VERB
ejpam-5761	380	5	surya	surya	PROPN
ejpam-5761	380	6	priya	priya	PROPN
ejpam-5761	380	7	and	and	CCONJ
ejpam-5761	380	8	n	n	PRON
ejpam-5761	380	9	nathiya	nathiya	NOUN
ejpam-5761	380	10	.	.	PUNCT
ejpam-5761	381	1	green	green	PROPN
ejpam-5761	381	2	’s	’s	PART
ejpam-5761	381	3	function	function	NOUN
ejpam-5761	381	4	on	on	ADP
ejpam-5761	381	5	infinite	infinite	ADJ
ejpam-5761	381	6	random	random	ADJ
ejpam-5761	381	7	walks	walk	NOUN
ejpam-5761	381	8	.	.	PUNCT
ejpam-5761	382	1	in	in	ADP
ejpam-5761	382	2	aip	aip	PROPN
ejpam-5761	382	3	conference	conference	NOUN
ejpam-5761	382	4	proceedings	proceeding	NOUN
ejpam-5761	382	5	,	,	PUNCT
ejpam-5761	382	6	volume	volume	NOUN
ejpam-5761	382	7	2852	2852	NUM
ejpam-5761	382	8	,	,	PUNCT
ejpam-5761	382	9	2023	2023	NUM
ejpam-5761	382	10	.	.	PUNCT
ejpam-5761	383	1	[	[	X
ejpam-5761	383	2	9	9	NUM
ejpam-5761	383	3	]	]	PUNCT
ejpam-5761	383	4	sujith	sujith	NOUN
ejpam-5761	383	5	sivan	sivan	PROPN
ejpam-5761	383	6	,	,	PUNCT
ejpam-5761	383	7	madhu	madhu	PROPN
ejpam-5761	383	8	venkataraman	venkataraman	PROPN
ejpam-5761	383	9	,	,	PUNCT
ejpam-5761	383	10	et	et	PROPN
ejpam-5761	383	11	al	al	PROPN
ejpam-5761	383	12	.	.	PROPN
ejpam-5761	383	13	parahyperbolic	parahyperbolic	PROPN
ejpam-5761	383	14	networks	network	NOUN
ejpam-5761	383	15	.	.	PUNCT
ejpam-5761	384	1	mem	mem	PROPN
ejpam-5761	384	2	.	.	PUNCT
ejpam-5761	384	3	fac	fac	PROPN
ejpam-5761	384	4	.	.	PUNCT
ejpam-5761	385	1	sci	sci	PROPN
ejpam-5761	385	2	.	.	PUNCT
ejpam-5761	386	1	eng	eng	PROPN
ejpam-5761	386	2	.	.	PROPN
ejpam-5761	387	1	shimane	shimane	PROPN
ejpam-5761	387	2	university	university	PROPN
ejpam-5761	387	3	,	,	PUNCT
ejpam-5761	387	4	44:1–16	44:1–16	NUM
ejpam-5761	387	5	,	,	PUNCT
ejpam-5761	387	6	2011	2011	NUM
ejpam-5761	387	7	.	.	PUNCT
ejpam-5761	388	1	[	[	X
ejpam-5761	388	2	10	10	NUM
ejpam-5761	388	3	]	]	X
ejpam-5761	388	4	paolo	paolo	PROPN
ejpam-5761	388	5	m	m	PROPN
ejpam-5761	388	6	soardi	soardi	PROPN
ejpam-5761	388	7	.	.	PUNCT
ejpam-5761	389	1	potential	potential	ADJ
ejpam-5761	389	2	theory	theory	NOUN
ejpam-5761	389	3	on	on	ADP
ejpam-5761	389	4	infinite	infinite	ADJ
ejpam-5761	389	5	networks	network	NOUN
ejpam-5761	389	6	.	.	PUNCT
ejpam-5761	390	1	springer	springer	NOUN
ejpam-5761	390	2	,	,	PUNCT
ejpam-5761	390	3	2006	2006	NUM
ejpam-5761	390	4	.	.	PUNCT
ejpam-5761	391	1	[	[	X
ejpam-5761	391	2	11	11	NUM
ejpam-5761	391	3	]	]	X
ejpam-5761	391	4	masayoshi	masayoshi	PROPN
ejpam-5761	391	5	takeda	takeda	PROPN
ejpam-5761	391	6	.	.	PUNCT
ejpam-5761	392	1	criticality	criticality	NOUN
ejpam-5761	392	2	and	and	CCONJ
ejpam-5761	392	3	subcriticality	subcriticality	NOUN
ejpam-5761	392	4	of	of	ADP
ejpam-5761	392	5	generalized	generalized	ADJ
ejpam-5761	392	6	schrödinger	schrödinger	NOUN
ejpam-5761	392	7	forms	form	NOUN
ejpam-5761	392	8	.	.	PUNCT
ejpam-5761	393	1	illinois	illinois	PROPN
ejpam-5761	393	2	journal	journal	PROPN
ejpam-5761	393	3	of	of	ADP
ejpam-5761	393	4	mathematics	mathematics	PROPN
ejpam-5761	393	5	,	,	PUNCT
ejpam-5761	393	6	58(1):251–277	58(1):251–277	NOUN
ejpam-5761	393	7	,	,	PUNCT
ejpam-5761	393	8	2014	2014	NUM
ejpam-5761	393	9	.	.	PUNCT
ejpam-5761	394	1	[	[	X
ejpam-5761	394	2	12	12	NUM
ejpam-5761	394	3	]	]	X
ejpam-5761	394	4	wolfgang	wolfgang	PROPN
ejpam-5761	394	5	woess	woess	PROPN
ejpam-5761	394	6	.	.	PUNCT
ejpam-5761	395	1	random	random	ADJ
ejpam-5761	395	2	walks	walk	VERB
ejpam-5761	395	3	on	on	ADP
ejpam-5761	395	4	infinite	infinite	ADJ
ejpam-5761	395	5	graphs	graph	NOUN
ejpam-5761	395	6	and	and	CCONJ
ejpam-5761	395	7	groups	group	NOUN
ejpam-5761	395	8	.	.	PUNCT
ejpam-5761	396	1	number	number	NOUN
ejpam-5761	396	2	138	138	NUM
ejpam-5761	396	3	.	.	PUNCT
ejpam-5761	396	4	2000	2000	NUM
ejpam-5761	396	5	.	.	PUNCT
ejpam-5761	397	1	[	[	X
ejpam-5761	397	2	13	13	NUM
ejpam-5761	397	3	]	]	PUNCT
ejpam-5761	397	4	maretsugu	maretsugu	ADJ
ejpam-5761	397	5	yamasaki	yamasaki	PROPN
ejpam-5761	397	6	.	.	PUNCT
ejpam-5761	398	1	parabolic	parabolic	PROPN
ejpam-5761	398	2	and	and	CCONJ
ejpam-5761	398	3	hyperbolic	hyperbolic	ADJ
ejpam-5761	398	4	infinite	infinite	ADJ
ejpam-5761	398	5	networks	network	NOUN
ejpam-5761	398	6	.	.	PUNCT
ejpam-5761	399	1	hiroshima	hiroshima	PROPN
ejpam-5761	399	2	mathematical	mathematical	PROPN
ejpam-5761	399	3	journal	journal	PROPN
ejpam-5761	399	4	,	,	PUNCT
ejpam-5761	399	5	7(1):135–146	7(1):135–146	NOUN
ejpam-5761	399	6	,	,	PUNCT
ejpam-5761	399	7	1977	1977	NUM
ejpam-5761	399	8	.	.	PUNCT