id	sid	tid	token	lemma	pos
ejpam-4425	1	1	european	european	PROPN
ejpam-4425	1	2	journal	journal	PROPN
ejpam-4425	1	3	of	of	ADP
ejpam-4425	1	4	pure	pure	ADJ
ejpam-4425	1	5	and	and	CCONJ
ejpam-4425	1	6	applied	apply	VERB
ejpam-4425	1	7	mathematics	mathematic	NOUN
ejpam-4425	1	8	vol	vol	NOUN
ejpam-4425	1	9	.	.	PROPN
ejpam-4425	2	1	15	15	NUM
ejpam-4425	2	2	,	,	PUNCT
ejpam-4425	2	3	no	no	INTJ
ejpam-4425	2	4	.	.	NOUN
ejpam-4425	2	5	3	3	NUM
ejpam-4425	2	6	,	,	PUNCT
ejpam-4425	2	7	2022	2022	NUM
ejpam-4425	2	8	,	,	PUNCT
ejpam-4425	2	9	1189	1189	NUM
ejpam-4425	2	10	-	-	SYM
ejpam-4425	2	11	1200	1200	NUM
ejpam-4425	2	12	issn	issn	PROPN
ejpam-4425	2	13	1307	1307	NUM
ejpam-4425	2	14	-	-	SYM
ejpam-4425	2	15	5543	5543	NUM
ejpam-4425	2	16	–	–	PUNCT
ejpam-4425	3	1	ejpam.com	ejpam.com	X
ejpam-4425	3	2	published	publish	VERB
ejpam-4425	3	3	by	by	ADP
ejpam-4425	3	4	new	new	PROPN
ejpam-4425	3	5	york	york	PROPN
ejpam-4425	3	6	business	business	PROPN
ejpam-4425	3	7	global	global	ADJ
ejpam-4425	3	8	neural	neural	ADJ
ejpam-4425	3	9	network	network	NOUN
ejpam-4425	3	10	of	of	ADP
ejpam-4425	3	11	multivariate	multivariate	PROPN
ejpam-4425	3	12	square	square	ADJ
ejpam-4425	3	13	rational	rational	ADJ
ejpam-4425	3	14	bernstein	bernstein	PROPN
ejpam-4425	3	15	operators	operators	PROPN
ejpam-4425	3	16	with	with	ADP
ejpam-4425	3	17	positive	positive	ADJ
ejpam-4425	3	18	integer	integer	NOUN
ejpam-4425	3	19	parameter	parameter	PROPN
ejpam-4425	3	20	ibtihal	ibtihal	PROPN
ejpam-4425	3	21	j.	j.	PROPN
ejpam-4425	3	22	mohammad1,∗	mohammad1,∗	PROPN
ejpam-4425	3	23	,	,	PUNCT
ejpam-4425	3	24	ali	ali	PROPN
ejpam-4425	3	25	j.	j.	PROPN
ejpam-4425	3	26	mohammad1	mohammad1	PROPN
ejpam-4425	3	27	1	1	NUM
ejpam-4425	3	28	department	department	NOUN
ejpam-4425	3	29	of	of	ADP
ejpam-4425	3	30	mathematics	mathematic	NOUN
ejpam-4425	3	31	,	,	PUNCT
ejpam-4425	3	32	college	college	NOUN
ejpam-4425	3	33	of	of	ADP
ejpam-4425	3	34	education	education	NOUN
ejpam-4425	3	35	for	for	ADP
ejpam-4425	3	36	pure	pure	ADJ
ejpam-4425	3	37	science	science	NOUN
ejpam-4425	3	38	,	,	PUNCT
ejpam-4425	3	39	university	university	NOUN
ejpam-4425	3	40	of	of	ADP
ejpam-4425	3	41	basrah	basrah	PROPN
ejpam-4425	3	42	,	,	PUNCT
ejpam-4425	3	43	basrah	basrah	PROPN
ejpam-4425	3	44	,	,	PUNCT
ejpam-4425	3	45	iraq	iraq	PROPN
ejpam-4425	3	46	abstract	abstract	NOUN
ejpam-4425	3	47	.	.	PUNCT
ejpam-4425	4	1	this	this	DET
ejpam-4425	4	2	research	research	NOUN
ejpam-4425	4	3	is	be	AUX
ejpam-4425	4	4	defined	define	VERB
ejpam-4425	4	5	a	a	DET
ejpam-4425	4	6	new	new	ADJ
ejpam-4425	4	7	neural	neural	ADJ
ejpam-4425	4	8	network(nn	network(nn	NOUN
ejpam-4425	4	9	)	)	PUNCT
ejpam-4425	4	10	that	that	PRON
ejpam-4425	4	11	depends	depend	VERB
ejpam-4425	4	12	upon	upon	SCONJ
ejpam-4425	4	13	a	a	DET
ejpam-4425	4	14	positive	positive	ADJ
ejpam-4425	4	15	integer	integer	NOUN
ejpam-4425	4	16	parameter	parameter	NOUN
ejpam-4425	4	17	using	use	VERB
ejpam-4425	4	18	the	the	DET
ejpam-4425	4	19	multivariate	multivariate	NOUN
ejpam-4425	4	20	square	square	ADJ
ejpam-4425	4	21	rational	rational	ADJ
ejpam-4425	4	22	bernstein	bernstein	PROPN
ejpam-4425	4	23	polynomials	polynomial	NOUN
ejpam-4425	4	24	.	.	PUNCT
ejpam-4425	5	1	some	some	DET
ejpam-4425	5	2	theorems	theorem	NOUN
ejpam-4425	5	3	for	for	ADP
ejpam-4425	5	4	this	this	DET
ejpam-4425	5	5	network	network	NOUN
ejpam-4425	5	6	are	be	AUX
ejpam-4425	5	7	proved	prove	VERB
ejpam-4425	5	8	,	,	PUNCT
ejpam-4425	5	9	such	such	ADJ
ejpam-4425	5	10	as	as	ADP
ejpam-4425	5	11	the	the	DET
ejpam-4425	5	12	pointwise	pointwise	NOUN
ejpam-4425	5	13	and	and	CCONJ
ejpam-4425	5	14	the	the	DET
ejpam-4425	5	15	uniform	uniform	ADJ
ejpam-4425	5	16	approximation	approximation	NOUN
ejpam-4425	5	17	theorems	theorem	NOUN
ejpam-4425	5	18	.	.	PUNCT
ejpam-4425	6	1	firstly	firstly	ADV
ejpam-4425	6	2	,	,	PUNCT
ejpam-4425	6	3	the	the	DET
ejpam-4425	6	4	absolute	absolute	ADJ
ejpam-4425	6	5	moment	moment	NOUN
ejpam-4425	6	6	for	for	ADP
ejpam-4425	6	7	a	a	DET
ejpam-4425	6	8	function	function	NOUN
ejpam-4425	6	9	that	that	PRON
ejpam-4425	6	10	belongs	belong	VERB
ejpam-4425	6	11	to	to	PART
ejpam-4425	6	12	lipschitz	lipschitz	VERB
ejpam-4425	6	13	space	space	NOUN
ejpam-4425	6	14	is	be	AUX
ejpam-4425	6	15	defined	define	VERB
ejpam-4425	6	16	to	to	PART
ejpam-4425	6	17	estimate	estimate	VERB
ejpam-4425	6	18	the	the	DET
ejpam-4425	6	19	order	order	NOUN
ejpam-4425	6	20	of	of	ADP
ejpam-4425	6	21	the	the	DET
ejpam-4425	6	22	nn	nn	PROPN
ejpam-4425	6	23	.	.	PROPN
ejpam-4425	6	24	secondly	secondly	ADV
ejpam-4425	6	25	,	,	PUNCT
ejpam-4425	6	26	some	some	DET
ejpam-4425	6	27	numerical	numerical	ADJ
ejpam-4425	6	28	applications	application	NOUN
ejpam-4425	6	29	for	for	ADP
ejpam-4425	6	30	this	this	PRON
ejpam-4425	6	31	nn	nn	PROPN
ejpam-4425	6	32	are	be	AUX
ejpam-4425	6	33	given	give	VERB
ejpam-4425	6	34	by	by	ADP
ejpam-4425	6	35	taking	take	VERB
ejpam-4425	6	36	two	two	NUM
ejpam-4425	6	37	test	test	NOUN
ejpam-4425	6	38	functions	function	NOUN
ejpam-4425	6	39	.	.	PUNCT
ejpam-4425	7	1	finally	finally	ADV
ejpam-4425	7	2	,	,	PUNCT
ejpam-4425	7	3	the	the	DET
ejpam-4425	7	4	numerical	numerical	ADJ
ejpam-4425	7	5	results	result	NOUN
ejpam-4425	7	6	for	for	ADP
ejpam-4425	7	7	this	this	DET
ejpam-4425	7	8	network	network	NOUN
ejpam-4425	7	9	are	be	AUX
ejpam-4425	7	10	compared	compare	VERB
ejpam-4425	7	11	with	with	ADP
ejpam-4425	7	12	the	the	DET
ejpam-4425	7	13	classical	classical	ADJ
ejpam-4425	7	14	neural	neural	ADJ
ejpam-4425	7	15	networks(nns	networks(nn	NOUN
ejpam-4425	7	16	)	)	PUNCT
ejpam-4425	7	17	.	.	PUNCT
ejpam-4425	8	1	the	the	DET
ejpam-4425	8	2	results	result	NOUN
ejpam-4425	8	3	turn	turn	VERB
ejpam-4425	8	4	out	out	ADP
ejpam-4425	8	5	that	that	SCONJ
ejpam-4425	8	6	the	the	DET
ejpam-4425	8	7	new	new	ADJ
ejpam-4425	8	8	network	network	NOUN
ejpam-4425	8	9	is	be	AUX
ejpam-4425	8	10	better	well	ADJ
ejpam-4425	8	11	than	than	ADP
ejpam-4425	8	12	the	the	DET
ejpam-4425	8	13	classical	classical	ADJ
ejpam-4425	8	14	one	one	NUM
ejpam-4425	8	15	.	.	PUNCT
ejpam-4425	9	1	2020	2020	NUM
ejpam-4425	9	2	mathematics	mathematic	NOUN
ejpam-4425	9	3	subject	subject	NOUN
ejpam-4425	9	4	classifications	classification	NOUN
ejpam-4425	9	5	:	:	PUNCT
ejpam-4425	9	6	41a25	41a25	NUM
ejpam-4425	9	7	,	,	PUNCT
ejpam-4425	9	8	41a30	41a30	NUM
ejpam-4425	9	9	,	,	PUNCT
ejpam-4425	9	10	47a58	47a58	NOUN
ejpam-4425	9	11	key	key	ADJ
ejpam-4425	9	12	words	word	NOUN
ejpam-4425	9	13	and	and	CCONJ
ejpam-4425	9	14	phrases	phrase	NOUN
ejpam-4425	9	15	:	:	PUNCT
ejpam-4425	9	16	multivariate	multivariate	VERB
ejpam-4425	9	17	neural	neural	ADJ
ejpam-4425	9	18	network	network	NOUN
ejpam-4425	9	19	,	,	PUNCT
ejpam-4425	9	20	multivariate	multivariate	NOUN
ejpam-4425	9	21	square	square	ADJ
ejpam-4425	9	22	rational	rational	ADJ
ejpam-4425	9	23	bernstein	bernstein	PROPN
ejpam-4425	9	24	polynomials	polynomials	PROPN
ejpam-4425	9	25	,	,	PUNCT
ejpam-4425	9	26	activation	activation	NOUN
ejpam-4425	9	27	functions	function	NOUN
ejpam-4425	9	28	,	,	PUNCT
ejpam-4425	9	29	lipschitz	lipschitz	VERB
ejpam-4425	9	30	space	space	NOUN
ejpam-4425	9	31	1	1	NUM
ejpam-4425	9	32	.	.	PUNCT
ejpam-4425	9	33	introduction	introduction	NOUN
ejpam-4425	9	34	in	in	ADP
ejpam-4425	9	35	2013	2013	NUM
ejpam-4425	9	36	,	,	PUNCT
ejpam-4425	9	37	costarelli	costarelli	NOUN
ejpam-4425	9	38	and	and	CCONJ
ejpam-4425	9	39	spigler	spigler	NOUN
ejpam-4425	9	40	[	[	X
ejpam-4425	9	41	3	3	NUM
ejpam-4425	9	42	]	]	PUNCT
ejpam-4425	9	43	introduced	introduce	VERB
ejpam-4425	9	44	the	the	DET
ejpam-4425	9	45	artificial	artificial	ADJ
ejpam-4425	9	46	nn	nn	PROPN
ejpam-4425	9	47	operators	operator	NOUN
ejpam-4425	9	48	and	and	CCONJ
ejpam-4425	9	49	studied	study	VERB
ejpam-4425	9	50	the	the	DET
ejpam-4425	9	51	behavior	behavior	NOUN
ejpam-4425	9	52	of	of	ADP
ejpam-4425	9	53	this	this	DET
ejpam-4425	9	54	neural	neural	ADJ
ejpam-4425	9	55	network	network	NOUN
ejpam-4425	9	56	in	in	ADP
ejpam-4425	9	57	univariate	univariate	ADJ
ejpam-4425	9	58	bernstein	bernstein	PROPN
ejpam-4425	9	59	polynomials	polynomial	NOUN
ejpam-4425	9	60	as	as	ADP
ejpam-4425	9	61	:	:	PUNCT
ejpam-4425	9	62	for	for	ADP
ejpam-4425	9	63	a	a	DET
ejpam-4425	9	64	bounded	bounded	ADJ
ejpam-4425	9	65	function	function	NOUN
ejpam-4425	9	66	f	f	NOUN
ejpam-4425	9	67	:	:	PUNCT
ejpam-4425	10	1	[	[	X
ejpam-4425	10	2	a	a	X
ejpam-4425	10	3	,	,	PUNCT
ejpam-4425	10	4	b	b	NOUN
ejpam-4425	10	5	]	]	X
ejpam-4425	10	6	−→	−→	ADJ
ejpam-4425	10	7	r	r	NOUN
ejpam-4425	10	8	,	,	PUNCT
ejpam-4425	10	9	the	the	DET
ejpam-4425	10	10	artificial	artificial	ADJ
ejpam-4425	10	11	neural	neural	ADJ
ejpam-4425	10	12	networks	network	NOUN
ejpam-4425	10	13	fn(f	fn(f	ADP
ejpam-4425	10	14	;	;	PUNCT
ejpam-4425	10	15	x	x	X
ejpam-4425	10	16	)	)	PUNCT
ejpam-4425	10	17	,	,	PUNCT
ejpam-4425	10	18	activated	activate	VERB
ejpam-4425	10	19	by	by	ADP
ejpam-4425	10	20	the	the	DET
ejpam-4425	10	21	sigmoidal	sigmoidal	NOUN
ejpam-4425	10	22	function	function	NOUN
ejpam-4425	10	23	σ	σ	PROPN
ejpam-4425	10	24	and	and	CCONJ
ejpam-4425	10	25	its	its	PRON
ejpam-4425	10	26	acting	acting	NOUN
ejpam-4425	10	27	on	on	ADP
ejpam-4425	10	28	f	f	PROPN
ejpam-4425	10	29	,	,	PUNCT
ejpam-4425	10	30	is	be	AUX
ejpam-4425	10	31	defined	define	VERB
ejpam-4425	10	32	as	as	ADP
ejpam-4425	10	33	:	:	PUNCT
ejpam-4425	10	34	fn(f	fn(f	NUM
ejpam-4425	10	35	;	;	PUNCT
ejpam-4425	10	36	x	x	X
ejpam-4425	10	37	)	)	PUNCT
ejpam-4425	11	1	=	=	SYM
ejpam-4425	11	2	⌊nb⌋∑	⌊nb⌋∑	NOUN
ejpam-4425	11	3	k=⌈na⌉	k=⌈na⌉	VERB
ejpam-4425	11	4	f	f	PROPN
ejpam-4425	11	5	(	(	PUNCT
ejpam-4425	11	6	k	k	PROPN
ejpam-4425	11	7	n	n	PROPN
ejpam-4425	11	8	)	)	PUNCT
ejpam-4425	11	9	φσ(x−	φσ(x−	NOUN
ejpam-4425	11	10	k	k	NOUN
ejpam-4425	11	11	)	)	PUNCT
ejpam-4425	11	12	⌊nb⌋∑	⌊nb⌋∑	NOUN
ejpam-4425	11	13	k=⌈na⌉	k=⌈na⌉	VERB
ejpam-4425	11	14	φσ(x−	φσ(x−	NOUN
ejpam-4425	11	15	k	k	NOUN
ejpam-4425	11	16	)	)	PUNCT
ejpam-4425	11	17	,	,	PUNCT
ejpam-4425	11	18	x	x	PUNCT
ejpam-4425	11	19	∈	∈	PROPN
ejpam-4425	12	1	[	[	X
ejpam-4425	12	2	a	a	X
ejpam-4425	12	3	,	,	PUNCT
ejpam-4425	12	4	b	b	NOUN
ejpam-4425	12	5	]	]	X
ejpam-4425	12	6	,	,	PUNCT
ejpam-4425	12	7	∗corresponding	∗corresponde	VERB
ejpam-4425	12	8	author	author	NOUN
ejpam-4425	12	9	.	.	PUNCT
ejpam-4425	13	1	doi	doi	NOUN
ejpam-4425	13	2	:	:	PUNCT
ejpam-4425	13	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4425	https://doi.org/10.29020/nybg.ejpam.v15i3.4425	NOUN
ejpam-4425	13	4	email	email	NOUN
ejpam-4425	13	5	addresses	address	NOUN
ejpam-4425	13	6	:	:	PUNCT
ejpam-4425	13	7	pgs2206@uobasrah.edu.iq	pgs2206@uobasrah.edu.iq	PROPN
ejpam-4425	13	8	,	,	PUNCT
ejpam-4425	13	9	ibtihaljas.moh@gmail.com	ibtihaljas.moh@gmail.com	PROPN
ejpam-4425	13	10	(	(	PUNCT
ejpam-4425	13	11	i.j	i.j	PROPN
ejpam-4425	13	12	.	.	PROPN
ejpam-4425	13	13	mohammad	mohammad	PROPN
ejpam-4425	13	14	)	)	PUNCT
ejpam-4425	13	15	,	,	PUNCT
ejpam-4425	13	16	ali.mohammad@uobasrah.edu.iq	ali.mohammad@uobasrah.edu.iq	PROPN
ejpam-4425	13	17	,	,	PUNCT
ejpam-4425	13	18	alijasmoh@gmail.com	alijasmoh@gmail.com	X
ejpam-4425	13	19	(	(	PUNCT
ejpam-4425	13	20	a.j	a.j	PROPN
ejpam-4425	13	21	.	.	PROPN
ejpam-4425	13	22	mohammad	mohammad	PROPN
ejpam-4425	13	23	)	)	PUNCT
ejpam-4425	13	24	.	.	PUNCT
ejpam-4425	14	1	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4425	14	2	1189	1189	NUM
ejpam-4425	15	1	©	©	ADP
ejpam-4425	15	2	2022	2022	NUM
ejpam-4425	15	3	ejpam	ejpam	VERB
ejpam-4425	15	4	all	all	DET
ejpam-4425	15	5	rights	right	NOUN
ejpam-4425	15	6	reserved	reserve	VERB
ejpam-4425	15	7	.	.	PUNCT
ejpam-4425	16	1	i.j	i.j	PROPN
ejpam-4425	16	2	.	.	PROPN
ejpam-4425	16	3	mohammad	mohammad	PROPN
ejpam-4425	16	4	,	,	PUNCT
ejpam-4425	16	5	a.j	a.j	PROPN
ejpam-4425	16	6	.	.	PROPN
ejpam-4425	16	7	mohammad	mohammad	PROPN
ejpam-4425	16	8	/	/	SYM
ejpam-4425	16	9	eur	eur	PROPN
ejpam-4425	16	10	.	.	PUNCT
ejpam-4425	17	1	j.	j.	PROPN
ejpam-4425	17	2	pure	pure	PROPN
ejpam-4425	17	3	appl	appl	PROPN
ejpam-4425	17	4	.	.	PROPN
ejpam-4425	17	5	math	math	PROPN
ejpam-4425	17	6	,	,	PUNCT
ejpam-4425	17	7	15	15	NUM
ejpam-4425	17	8	(	(	PUNCT
ejpam-4425	17	9	3	3	NUM
ejpam-4425	17	10	)	)	PUNCT
ejpam-4425	17	11	(	(	PUNCT
ejpam-4425	17	12	2022	2022	NUM
ejpam-4425	17	13	)	)	PUNCT
ejpam-4425	17	14	,	,	PUNCT
ejpam-4425	17	15	1189	1189	NUM
ejpam-4425	17	16	-	-	SYM
ejpam-4425	17	17	1200	1200	NUM
ejpam-4425	17	18	1190	1190	NUM
ejpam-4425	17	19	where	where	SCONJ
ejpam-4425	17	20	the	the	DET
ejpam-4425	17	21	symbols	symbols	PROPN
ejpam-4425	17	22	⌊.⌋	⌊.⌋	PROPN
ejpam-4425	17	23	,	,	PUNCT
ejpam-4425	17	24	⌈.⌉	⌈.⌉	VERB
ejpam-4425	17	25	denote	denote	NOUN
ejpam-4425	17	26	taking	take	VERB
ejpam-4425	17	27	the	the	DET
ejpam-4425	17	28	”	"	PUNCT
ejpam-4425	17	29	floor	floor	NOUN
ejpam-4425	17	30	”	"	PUNCT
ejpam-4425	17	31	and	and	CCONJ
ejpam-4425	17	32	the	the	DET
ejpam-4425	17	33	”	"	PUNCT
ejpam-4425	17	34	ceiling	ceiling	NOUN
ejpam-4425	17	35	”	"	PUNCT
ejpam-4425	17	36	of	of	ADP
ejpam-4425	17	37	a	a	DET
ejpam-4425	17	38	given	give	VERB
ejpam-4425	17	39	number	number	NOUN
ejpam-4425	17	40	,	,	PUNCT
ejpam-4425	17	41	respectively	respectively	ADV
ejpam-4425	17	42	.	.	PUNCT
ejpam-4425	18	1	and	and	CCONJ
ejpam-4425	18	2	the	the	DET
ejpam-4425	18	3	case	case	NOUN
ejpam-4425	18	4	of	of	ADP
ejpam-4425	18	5	multivariate	multivariate	NOUN
ejpam-4425	18	6	in	in	ADP
ejpam-4425	18	7	[	[	X
ejpam-4425	18	8	4	4	X
ejpam-4425	18	9	]	]	PUNCT
ejpam-4425	18	10	it	it	PRON
ejpam-4425	18	11	is	be	AUX
ejpam-4425	18	12	given	give	VERB
ejpam-4425	18	13	by	by	ADP
ejpam-4425	18	14	the	the	DET
ejpam-4425	18	15	formula	formula	NOUN
ejpam-4425	18	16	:	:	PUNCT
ejpam-4425	18	17	the	the	DET
ejpam-4425	18	18	bounded	bounded	ADJ
ejpam-4425	18	19	function	function	NOUN
ejpam-4425	18	20	:	:	PUNCT
ejpam-4425	18	21	f	f	X
ejpam-4425	18	22	:	:	PUNCT
ejpam-4425	18	23	r	r	AUX
ejpam-4425	18	24	−→	−→	NOUN
ejpam-4425	18	25	r	r	NOUN
ejpam-4425	18	26	,	,	PUNCT
ejpam-4425	18	27	activated	activate	VERB
ejpam-4425	18	28	by	by	ADP
ejpam-4425	18	29	the	the	DET
ejpam-4425	18	30	sigmoidal	sigmoidal	NOUN
ejpam-4425	18	31	function	function	NOUN
ejpam-4425	18	32	σ	σ	PROPN
ejpam-4425	18	33	and	and	CCONJ
ejpam-4425	18	34	acting	act	VERB
ejpam-4425	18	35	on	on	ADP
ejpam-4425	18	36	f	f	PROPN
ejpam-4425	18	37	,	,	PUNCT
ejpam-4425	18	38	is	be	AUX
ejpam-4425	18	39	defined	define	VERB
ejpam-4425	18	40	as	as	ADP
ejpam-4425	18	41	:	:	PUNCT
ejpam-4425	18	42	f	f	PROPN
ejpam-4425	18	43	s	s	VERB
ejpam-4425	18	44	n(f	n(f	PROPN
ejpam-4425	18	45	;	;	PUNCT
ejpam-4425	18	46	x	x	X
ejpam-4425	18	47	)	)	PUNCT
ejpam-4425	18	48	=	=	SYM
ejpam-4425	18	49	⌊nb1⌋∑	⌊nb1⌋∑	X
ejpam-4425	18	50	k1=⌈na1⌉	k1=⌈na1⌉	PROPN
ejpam-4425	18	51	...	...	PUNCT
ejpam-4425	18	52	⌊nbs⌋∑	⌊nbs⌋∑	PROPN
ejpam-4425	19	1	ks=⌈nas⌉	ks=⌈nas⌉	NOUN
ejpam-4425	19	2	f	f	PROPN
ejpam-4425	19	3	(	(	PUNCT
ejpam-4425	19	4	k	k	PROPN
ejpam-4425	19	5	n	n	PROPN
ejpam-4425	19	6	)	)	PUNCT
ejpam-4425	19	7	ψσ(nx−	ψσ(nx−	PUNCT
ejpam-4425	20	1	k	k	X
ejpam-4425	20	2	)	)	PUNCT
ejpam-4425	20	3	⌊nb1⌋∑	⌊nb1⌋∑	X
ejpam-4425	21	1	k1=⌈na1⌉	k1=⌈na1⌉	PROPN
ejpam-4425	21	2	...	...	PUNCT
ejpam-4425	21	3	⌊nbs⌋∑	⌊nbs⌋∑	PROPN
ejpam-4425	22	1	ks=⌈nas⌉	ks=⌈nas⌉	PROPN
ejpam-4425	22	2	ψσ(nx−	ψσ(nx−	PROPN
ejpam-4425	22	3	k	k	NOUN
ejpam-4425	22	4	)	)	PUNCT
ejpam-4425	22	5	,	,	PUNCT
ejpam-4425	22	6	(	(	PUNCT
ejpam-4425	22	7	1	1	X
ejpam-4425	22	8	)	)	PUNCT
ejpam-4425	22	9	where	where	SCONJ
ejpam-4425	22	10	x	x	SYM
ejpam-4425	22	11	∈	∈	NOUN
ejpam-4425	22	12	r	r	NOUN
ejpam-4425	22	13	=	=	PUNCT
ejpam-4425	23	1	[	[	X
ejpam-4425	23	2	a1	a1	NOUN
ejpam-4425	23	3	,	,	PUNCT
ejpam-4425	23	4	b1	b1	NOUN
ejpam-4425	23	5	]	]	X
ejpam-4425	23	6	×	×	NOUN
ejpam-4425	23	7	.	.	PUNCT
ejpam-4425	23	8	.	.	PUNCT
ejpam-4425	24	1	.	.	PUNCT
ejpam-4425	25	1	×	×	NOUN
ejpam-4425	26	1	[	[	X
ejpam-4425	26	2	as	as	SCONJ
ejpam-4425	26	3	,	,	PUNCT
ejpam-4425	26	4	bs	bs	NOUN
ejpam-4425	26	5	]	]	X
ejpam-4425	26	6	,	,	PUNCT
ejpam-4425	26	7	ψσ	ψσ	ADP
ejpam-4425	26	8	is	be	AUX
ejpam-4425	26	9	a	a	DET
ejpam-4425	26	10	density	density	NOUN
ejpam-4425	26	11	function	function	NOUN
ejpam-4425	26	12	that	that	PRON
ejpam-4425	26	13	is	be	AUX
ejpam-4425	26	14	built	build	VERB
ejpam-4425	26	15	from	from	ADP
ejpam-4425	26	16	a	a	DET
ejpam-4425	26	17	sigmoidal	sigmoidal	NOUN
ejpam-4425	26	18	function	function	NOUN
ejpam-4425	26	19	σ	σ	PROPN
ejpam-4425	26	20	and	and	CCONJ
ejpam-4425	26	21	k	k	PROPN
ejpam-4425	26	22	=	=	SYM
ejpam-4425	26	23	(	(	PUNCT
ejpam-4425	26	24	k1	k1	PROPN
ejpam-4425	26	25	,	,	PUNCT
ejpam-4425	26	26	.	.	PUNCT
ejpam-4425	26	27	.	.	PUNCT
ejpam-4425	27	1	.	.	PUNCT
ejpam-4425	28	1	,	,	PUNCT
ejpam-4425	28	2	ks	ks	NOUN
ejpam-4425	28	3	)	)	PUNCT
ejpam-4425	28	4	∈	∈	PROPN
ejpam-4425	28	5	z+	z+	PROPN
ejpam-4425	28	6	.	.	PUNCT
ejpam-4425	29	1	in	in	ADP
ejpam-4425	29	2	2014	2014	NUM
ejpam-4425	29	3	,	,	PUNCT
ejpam-4425	29	4	costarelli	costarelli	NOUN
ejpam-4425	29	5	and	and	CCONJ
ejpam-4425	29	6	spigler	spigler	NOUN
ejpam-4425	29	7	[	[	X
ejpam-4425	29	8	5	5	NUM
ejpam-4425	29	9	]	]	PUNCT
ejpam-4425	29	10	extended	extended	ADJ
ejpam-4425	29	11	formula	formula	NOUN
ejpam-4425	29	12	(	(	PUNCT
ejpam-4425	29	13	1	1	NUM
ejpam-4425	29	14	)	)	PUNCT
ejpam-4425	29	15	through	through	ADP
ejpam-4425	29	16	the	the	DET
ejpam-4425	29	17	use	use	NOUN
ejpam-4425	29	18	of	of	ADP
ejpam-4425	29	19	the	the	DET
ejpam-4425	29	20	kantorovich	kantorovich	PROPN
ejpam-4425	29	21	operator	operator	NOUN
ejpam-4425	29	22	type	type	NOUN
ejpam-4425	29	23	to	to	PART
ejpam-4425	29	24	introduce	introduce	VERB
ejpam-4425	29	25	and	and	CCONJ
ejpam-4425	29	26	studied	study	VERB
ejpam-4425	29	27	approximation	approximation	NOUN
ejpam-4425	29	28	theorems	theorem	NOUN
ejpam-4425	29	29	to	to	ADP
ejpam-4425	29	30	this	this	DET
ejpam-4425	29	31	multivariate	multivariate	NOUN
ejpam-4425	29	32	nn	nn	PROPN
ejpam-4425	29	33	operators	operator	NOUN
ejpam-4425	29	34	.	.	PUNCT
ejpam-4425	30	1	in	in	ADP
ejpam-4425	30	2	2016	2016	NUM
ejpam-4425	30	3	,	,	PUNCT
ejpam-4425	30	4	costarelli	costarelli	NOUN
ejpam-4425	30	5	and	and	CCONJ
ejpam-4425	30	6	vinti	vinti	NOUN
ejpam-4425	30	7	[	[	X
ejpam-4425	30	8	6	6	NUM
ejpam-4425	30	9	]	]	PUNCT
ejpam-4425	30	10	introduced	introduce	VERB
ejpam-4425	30	11	the	the	DET
ejpam-4425	30	12	structure	structure	NOUN
ejpam-4425	30	13	of	of	ADP
ejpam-4425	30	14	a	a	DET
ejpam-4425	30	15	nn	nn	X
ejpam-4425	30	16	operators	operator	NOUN
ejpam-4425	30	17	of	of	ADP
ejpam-4425	30	18	type	type	NOUN
ejpam-4425	30	19	multivariate	multivariate	NOUN
ejpam-4425	30	20	max	max	PROPN
ejpam-4425	30	21	-	-	PUNCT
ejpam-4425	30	22	product	product	NOUN
ejpam-4425	30	23	then	then	ADV
ejpam-4425	30	24	studied	study	VERB
ejpam-4425	30	25	the	the	DET
ejpam-4425	30	26	approximation	approximation	NOUN
ejpam-4425	30	27	theoremed	theoreme	VERB
ejpam-4425	30	28	and	and	CCONJ
ejpam-4425	30	29	estimates	estimate	VERB
ejpam-4425	30	30	the	the	DET
ejpam-4425	30	31	rate	rate	NOUN
ejpam-4425	30	32	of	of	ADP
ejpam-4425	30	33	convergence	convergence	NOUN
ejpam-4425	30	34	to	to	ADP
ejpam-4425	30	35	this	this	DET
ejpam-4425	30	36	nn	nn	PROPN
ejpam-4425	30	37	operators	operator	NOUN
ejpam-4425	30	38	.	.	PUNCT
ejpam-4425	31	1	in	in	ADP
ejpam-4425	31	2	2017	2017	NUM
ejpam-4425	31	3	,	,	PUNCT
ejpam-4425	31	4	gavrea	gavrea	VERB
ejpam-4425	31	5	and	and	CCONJ
ejpam-4425	31	6	ivan	ivan	PROPN
ejpam-4425	32	1	[	[	X
ejpam-4425	32	2	7	7	X
ejpam-4425	32	3	]	]	PUNCT
ejpam-4425	32	4	introduced	introduce	VERB
ejpam-4425	32	5	definition	definition	NOUN
ejpam-4425	32	6	to	to	ADP
ejpam-4425	32	7	square	square	PROPN
ejpam-4425	32	8	bernstein	bernstein	PROPN
ejpam-4425	32	9	polynomials	polynomial	NOUN
ejpam-4425	32	10	it	it	PRON
ejpam-4425	32	11	is	be	AUX
ejpam-4425	32	12	given	give	VERB
ejpam-4425	32	13	by	by	ADP
ejpam-4425	32	14	the	the	DET
ejpam-4425	32	15	formula	formula	NOUN
ejpam-4425	32	16	:	:	PUNCT
ejpam-4425	32	17	for	for	ADP
ejpam-4425	32	18	x	x	PROPN
ejpam-4425	32	19	∈	∈	PROPN
ejpam-4425	33	1	[	[	X
ejpam-4425	33	2	0	0	NUM
ejpam-4425	33	3	,	,	PUNCT
ejpam-4425	33	4	1	1	NUM
ejpam-4425	33	5	]	]	PUNCT
ejpam-4425	33	6	,	,	PUNCT
ejpam-4425	33	7	f	f	PROPN
ejpam-4425	33	8	∈	∈	PROPN
ejpam-4425	33	9	c[0	c[0	PROPN
ejpam-4425	33	10	,	,	PUNCT
ejpam-4425	33	11	1	1	NUM
ejpam-4425	33	12	]	]	PUNCT
ejpam-4425	33	13	,	,	PUNCT
ejpam-4425	33	14	bn,2(f	bn,2(f	PROPN
ejpam-4425	33	15	;	;	PUNCT
ejpam-4425	33	16	x	x	X
ejpam-4425	33	17	)	)	PUNCT
ejpam-4425	33	18	=	=	SYM
ejpam-4425	34	1	n∑	n∑	PROPN
ejpam-4425	34	2	k=0	k=0	PROPN
ejpam-4425	34	3	b2n	b2n	PROPN
ejpam-4425	34	4	,	,	PUNCT
ejpam-4425	34	5	k(x)f	k(x)f	PROPN
ejpam-4425	34	6	(	(	PUNCT
ejpam-4425	34	7	k	k	NOUN
ejpam-4425	34	8	n	n	PROPN
ejpam-4425	34	9	)	)	PUNCT
ejpam-4425	35	1	n∑	n∑	DET
ejpam-4425	35	2	k=0	k=0	PROPN
ejpam-4425	35	3	b2n	b2n	PROPN
ejpam-4425	35	4	,	,	PUNCT
ejpam-4425	35	5	k(x	k(x	PROPN
ejpam-4425	35	6	)	)	PUNCT
ejpam-4425	35	7	,	,	PUNCT
ejpam-4425	35	8	n	n	NOUN
ejpam-4425	35	9	=	=	SYM
ejpam-4425	35	10	1	1	NUM
ejpam-4425	35	11	,	,	PUNCT
ejpam-4425	35	12	2	2	NUM
ejpam-4425	35	13	,	,	PUNCT
ejpam-4425	35	14	...	...	PUNCT
ejpam-4425	35	15	,	,	PUNCT
ejpam-4425	35	16	(	(	PUNCT
ejpam-4425	35	17	2	2	X
ejpam-4425	35	18	)	)	PUNCT
ejpam-4425	35	19	where	where	SCONJ
ejpam-4425	35	20	b2n	b2n	NOUN
ejpam-4425	35	21	,	,	PUNCT
ejpam-4425	35	22	k(x	k(x	PROPN
ejpam-4425	35	23	)	)	PUNCT
ejpam-4425	35	24	=	=	PUNCT
ejpam-4425	35	25	(	(	PUNCT
ejpam-4425	35	26	bn	bn	X
ejpam-4425	35	27	,	,	PUNCT
ejpam-4425	35	28	k(x	k(x	PROPN
ejpam-4425	35	29	)	)	PUNCT
ejpam-4425	35	30	)	)	PUNCT
ejpam-4425	36	1	2	2	X
ejpam-4425	36	2	.	.	X
ejpam-4425	36	3	in	in	ADP
ejpam-4425	36	4	2017	2017	NUM
ejpam-4425	36	5	,	,	PUNCT
ejpam-4425	36	6	mohammad	mohammad	PROPN
ejpam-4425	36	7	and	and	CCONJ
ejpam-4425	36	8	mohammad	mohammad	PROPN
ejpam-4425	36	9	[	[	X
ejpam-4425	36	10	9	9	NUM
ejpam-4425	36	11	]	]	PUNCT
ejpam-4425	36	12	introduced	introduce	VERB
ejpam-4425	36	13	a	a	DET
ejpam-4425	36	14	definition	definition	NOUN
ejpam-4425	36	15	of	of	ADP
ejpam-4425	36	16	the	the	DET
ejpam-4425	36	17	nn	nn	PROPN
ejpam-4425	36	18	operators	operator	NOUN
ejpam-4425	36	19	by	by	ADP
ejpam-4425	36	20	using	use	VERB
ejpam-4425	36	21	the	the	DET
ejpam-4425	36	22	type	type	NOUN
ejpam-4425	36	23	of	of	ADP
ejpam-4425	36	24	summation	summation	NOUN
ejpam-4425	36	25	-	-	PUNCT
ejpam-4425	36	26	integral	integral	ADJ
ejpam-4425	36	27	bernstein	bernstein	NOUN
ejpam-4425	36	28	,	,	PUNCT
ejpam-4425	36	29	and	and	CCONJ
ejpam-4425	36	30	then	then	ADV
ejpam-4425	36	31	studied	study	VERB
ejpam-4425	36	32	approximation	approximation	NOUN
ejpam-4425	36	33	theorems	theorem	NOUN
ejpam-4425	36	34	for	for	ADP
ejpam-4425	36	35	this	this	DET
ejpam-4425	36	36	nn	nn	PROPN
ejpam-4425	36	37	operators	operator	NOUN
ejpam-4425	36	38	.	.	PUNCT
ejpam-4425	37	1	in	in	ADP
ejpam-4425	37	2	2018	2018	NUM
ejpam-4425	37	3	,	,	PUNCT
ejpam-4425	37	4	hassan	hassan	PROPN
ejpam-4425	37	5	[	[	X
ejpam-4425	37	6	8	8	NUM
ejpam-4425	37	7	]	]	X
ejpam-4425	37	8	introduce	introduce	NOUN
ejpam-4425	37	9	and	and	CCONJ
ejpam-4425	37	10	define	define	VERB
ejpam-4425	37	11	the	the	DET
ejpam-4425	37	12	new	new	ADJ
ejpam-4425	37	13	modified	modified	NOUN
ejpam-4425	37	14	of	of	ADP
ejpam-4425	37	15	bernstein	bernstein	PROPN
ejpam-4425	37	16	operators	operators	PROPN
ejpam-4425	37	17	that	that	PRON
ejpam-4425	37	18	can	can	AUX
ejpam-4425	37	19	use	use	VERB
ejpam-4425	37	20	to	to	PART
ejpam-4425	37	21	build	build	VERB
ejpam-4425	37	22	nns	nn	NOUN
ejpam-4425	37	23	.	.	PUNCT
ejpam-4425	38	1	in	in	ADP
ejpam-4425	38	2	2019	2019	NUM
ejpam-4425	38	3	,	,	PUNCT
ejpam-4425	38	4	bajpeyi	bajpeyi	NOUN
ejpam-4425	38	5	and	and	CCONJ
ejpam-4425	38	6	kumar	kumar	PROPN
ejpam-4425	38	7	[	[	X
ejpam-4425	38	8	1	1	NUM
ejpam-4425	38	9	]	]	PUNCT
ejpam-4425	38	10	introduced	introduce	VERB
ejpam-4425	38	11	definition	definition	NOUN
ejpam-4425	38	12	to	to	ADP
ejpam-4425	38	13	the	the	DET
ejpam-4425	38	14	neural	neural	ADJ
ejpam-4425	38	15	network	network	NOUN
ejpam-4425	38	16	of	of	ADP
ejpam-4425	38	17	exponential	exponential	ADJ
ejpam-4425	38	18	type	type	NOUN
ejpam-4425	38	19	and	and	CCONJ
ejpam-4425	38	20	studied	study	VERB
ejpam-4425	38	21	behavior	behavior	NOUN
ejpam-4425	38	22	in	in	ADP
ejpam-4425	38	23	two	two	NUM
ejpam-4425	38	24	case	case	NOUN
ejpam-4425	38	25	onedimensional	onedimensional	ADJ
ejpam-4425	38	26	and	and	CCONJ
ejpam-4425	38	27	multi-dimensional.in	multi-dimensional.in	X
ejpam-4425	38	28	2019	2019	NUM
ejpam-4425	38	29	,	,	PUNCT
ejpam-4425	38	30	costarelli	costarelli	NOUN
ejpam-4425	38	31	and	and	CCONJ
ejpam-4425	38	32	others	other	NOUN
ejpam-4425	39	1	[	[	X
ejpam-4425	39	2	2	2	NUM
ejpam-4425	39	3	]	]	PUNCT
ejpam-4425	39	4	introduced	introduce	VERB
ejpam-4425	39	5	definition	definition	NOUN
ejpam-4425	39	6	to	to	ADP
ejpam-4425	39	7	the	the	DET
ejpam-4425	39	8	neural	neural	ADJ
ejpam-4425	39	9	network	network	NOUN
ejpam-4425	39	10	of	of	ADP
ejpam-4425	39	11	multivariate	multivariate	NOUN
ejpam-4425	39	12	max	max	PROPN
ejpam-4425	39	13	-	-	PUNCT
ejpam-4425	39	14	product	product	NOUN
ejpam-4425	39	15	nn	nn	PROPN
ejpam-4425	39	16	of	of	ADP
ejpam-4425	39	17	kantorovich	kantorovich	PROPN
ejpam-4425	39	18	type	type	NOUN
ejpam-4425	39	19	.	.	PUNCT
ejpam-4425	40	1	in	in	ADP
ejpam-4425	40	2	2021	2021	NUM
ejpam-4425	40	3	,	,	PUNCT
ejpam-4425	40	4	mohammad	mohammad	PROPN
ejpam-4425	40	5	and	and	CCONJ
ejpam-4425	40	6	mohammad	mohammad	PROPN
ejpam-4425	41	1	[	[	X
ejpam-4425	41	2	10	10	NUM
ejpam-4425	41	3	]	]	PUNCT
ejpam-4425	41	4	give	give	VERB
ejpam-4425	41	5	a	a	DET
ejpam-4425	41	6	new	new	ADJ
ejpam-4425	41	7	modification	modification	NOUN
ejpam-4425	41	8	to	to	ADP
ejpam-4425	41	9	the	the	DET
ejpam-4425	41	10	formula	formula	NOUN
ejpam-4425	41	11	(	(	PUNCT
ejpam-4425	41	12	1	1	NUM
ejpam-4425	41	13	)	)	PUNCT
ejpam-4425	41	14	and	and	CCONJ
ejpam-4425	41	15	studied	study	VERB
ejpam-4425	41	16	approximation	approximation	NOUN
ejpam-4425	41	17	theorems	theorem	NOUN
ejpam-4425	41	18	for	for	ADP
ejpam-4425	41	19	this	this	DET
ejpam-4425	41	20	nn	nn	PROPN
ejpam-4425	41	21	operators	operator	NOUN
ejpam-4425	41	22	,	,	PUNCT
ejpam-4425	41	23	activated	activate	VERB
ejpam-4425	41	24	by	by	ADP
ejpam-4425	41	25	the	the	DET
ejpam-4425	41	26	sigmoidal	sigmoidal	NOUN
ejpam-4425	41	27	function	function	NOUN
ejpam-4425	41	28	σ	σ	PROPN
ejpam-4425	41	29	and	and	CCONJ
ejpam-4425	41	30	acting	act	VERB
ejpam-4425	41	31	on	on	ADP
ejpam-4425	41	32	f	f	PROPN
ejpam-4425	41	33	,	,	PUNCT
ejpam-4425	41	34	it	it	PRON
ejpam-4425	41	35	is	be	AUX
ejpam-4425	41	36	given	give	VERB
ejpam-4425	41	37	by	by	ADP
ejpam-4425	41	38	the	the	DET
ejpam-4425	41	39	formula	formula	NOUN
ejpam-4425	41	40	:	:	PUNCT
ejpam-4425	41	41	i.j	i.j	PROPN
ejpam-4425	41	42	.	.	PROPN
ejpam-4425	41	43	mohammad	mohammad	PROPN
ejpam-4425	41	44	,	,	PUNCT
ejpam-4425	41	45	a.j	a.j	PROPN
ejpam-4425	41	46	.	.	PROPN
ejpam-4425	41	47	mohammad	mohammad	PROPN
ejpam-4425	41	48	/	/	SYM
ejpam-4425	41	49	eur	eur	PROPN
ejpam-4425	41	50	.	.	PUNCT
ejpam-4425	42	1	j.	j.	PROPN
ejpam-4425	42	2	pure	pure	PROPN
ejpam-4425	42	3	appl	appl	PROPN
ejpam-4425	42	4	.	.	PROPN
ejpam-4425	42	5	math	math	PROPN
ejpam-4425	42	6	,	,	PUNCT
ejpam-4425	42	7	15	15	NUM
ejpam-4425	42	8	(	(	PUNCT
ejpam-4425	42	9	3	3	NUM
ejpam-4425	42	10	)	)	PUNCT
ejpam-4425	42	11	(	(	PUNCT
ejpam-4425	42	12	2022	2022	NUM
ejpam-4425	42	13	)	)	PUNCT
ejpam-4425	42	14	,	,	PUNCT
ejpam-4425	42	15	1189	1189	NUM
ejpam-4425	42	16	-	-	SYM
ejpam-4425	42	17	1200	1200	NUM
ejpam-4425	42	18	1191	1191	NUM
ejpam-4425	42	19	gn	gn	PROPN
ejpam-4425	42	20	,	,	PUNCT
ejpam-4425	42	21	m(f	m(f	PROPN
ejpam-4425	42	22	;	;	PUNCT
ejpam-4425	42	23	x	x	X
ejpam-4425	42	24	)	)	PUNCT
ejpam-4425	42	25	=	=	PUNCT
ejpam-4425	42	26	∑	∑	PUNCT
ejpam-4425	42	27	k	k	PROPN
ejpam-4425	42	28	ψσ(nx−	ψσ(nx−	X
ejpam-4425	42	29	k)f	k)f	PUNCT
ejpam-4425	42	30	(	(	PUNCT
ejpam-4425	42	31	(	(	PUNCT
ejpam-4425	42	32	n−1k−	n−1k−	NOUN
ejpam-4425	42	33	x	x	SYM
ejpam-4425	42	34	)	)	PUNCT
ejpam-4425	42	35	m	m	NOUN
ejpam-4425	42	36	−	−	NOUN
ejpam-4425	42	37	x	x	SYM
ejpam-4425	42	38	)	)	PUNCT
ejpam-4425	42	39	∑	∑	PROPN
ejpam-4425	42	40	k	k	PROPN
ejpam-4425	42	41	ψσ(nx−	ψσ(nx−	PROPN
ejpam-4425	42	42	k	k	PROPN
ejpam-4425	42	43	)	)	PUNCT
ejpam-4425	42	44	,	,	PUNCT
ejpam-4425	42	45	(	(	PUNCT
ejpam-4425	42	46	3	3	X
ejpam-4425	42	47	)	)	PUNCT
ejpam-4425	42	48	this	this	DET
ejpam-4425	42	49	paper	paper	NOUN
ejpam-4425	42	50	gives	gives	AUX
ejpam-4425	42	51	extended	extend	VERB
ejpam-4425	42	52	to	to	ADP
ejpam-4425	42	53	the	the	DET
ejpam-4425	42	54	nn	nn	PROPN
ejpam-4425	42	55	operators	operator	NOUN
ejpam-4425	42	56	in	in	ADP
ejpam-4425	42	57	formula	formula	NOUN
ejpam-4425	42	58	(	(	PUNCT
ejpam-4425	42	59	3	3	NUM
ejpam-4425	42	60	)	)	PUNCT
ejpam-4425	42	61	by	by	ADP
ejpam-4425	42	62	using	use	VERB
ejpam-4425	42	63	formula	formula	NOUN
ejpam-4425	42	64	of	of	ADP
ejpam-4425	42	65	square	square	PROPN
ejpam-4425	42	66	bernstein	bernstein	PROPN
ejpam-4425	42	67	polynomials	polynomial	NOUN
ejpam-4425	42	68	in	in	ADP
ejpam-4425	42	69	formula	formula	NOUN
ejpam-4425	42	70	(	(	PUNCT
ejpam-4425	42	71	2	2	NUM
ejpam-4425	42	72	)	)	PUNCT
ejpam-4425	42	73	and	and	CCONJ
ejpam-4425	42	74	studied	study	VERB
ejpam-4425	42	75	approximation	approximation	NOUN
ejpam-4425	42	76	theorems	theorem	NOUN
ejpam-4425	42	77	for	for	ADP
ejpam-4425	42	78	this	this	DET
ejpam-4425	42	79	neural	neural	ADJ
ejpam-4425	42	80	network	network	NOUN
ejpam-4425	42	81	.	.	PUNCT
ejpam-4425	43	1	in	in	ADP
ejpam-4425	43	2	the	the	DET
ejpam-4425	43	3	end	end	NOUN
ejpam-4425	43	4	,	,	PUNCT
ejpam-4425	43	5	we	we	PRON
ejpam-4425	43	6	give	give	VERB
ejpam-4425	43	7	some	some	DET
ejpam-4425	43	8	numerical	numerical	ADJ
ejpam-4425	43	9	examples	example	NOUN
ejpam-4425	43	10	for	for	ADP
ejpam-4425	43	11	this	this	DET
ejpam-4425	43	12	nns	nn	NOUN
ejpam-4425	43	13	.	.	PUNCT
ejpam-4425	44	1	2	2	NUM
ejpam-4425	44	2	.	.	X
ejpam-4425	44	3	preliminary	preliminary	ADJ
ejpam-4425	44	4	results	result	NOUN
ejpam-4425	44	5	in	in	ADP
ejpam-4425	44	6	this	this	DET
ejpam-4425	44	7	part	part	NOUN
ejpam-4425	44	8	recall	recall	VERB
ejpam-4425	44	9	some	some	DET
ejpam-4425	44	10	preliminary	preliminary	ADJ
ejpam-4425	44	11	results	result	NOUN
ejpam-4425	44	12	.	.	PUNCT
ejpam-4425	45	1	a	a	DET
ejpam-4425	45	2	sigmoidal	sigmoidal	NOUN
ejpam-4425	45	3	function	function	NOUN
ejpam-4425	45	4	is	be	AUX
ejpam-4425	45	5	measurable	measurable	ADJ
ejpam-4425	45	6	functions	function	NOUN
ejpam-4425	45	7	satisfying	satisfy	VERB
ejpam-4425	45	8	limx→−∞	limx→−∞	NOUN
ejpam-4425	45	9	σ(x	σ(x	PROPN
ejpam-4425	45	10	)	)	PUNCT
ejpam-4425	45	11	=	=	SYM
ejpam-4425	45	12	0	0	NUM
ejpam-4425	45	13	and	and	CCONJ
ejpam-4425	45	14	limx→+∞	limx→+∞	PROPN
ejpam-4425	45	15	σ(x	σ(x	PROPN
ejpam-4425	45	16	)	)	PUNCT
ejpam-4425	46	1	=	=	SYM
ejpam-4425	46	2	1	1	NUM
ejpam-4425	46	3	,	,	PUNCT
ejpam-4425	46	4	for	for	ADP
ejpam-4425	46	5	example	example	NOUN
ejpam-4425	46	6	logistic	logistic	ADJ
ejpam-4425	46	7	function	function	NOUN
ejpam-4425	46	8	σl(x	σl(x	X
ejpam-4425	46	9	)	)	PUNCT
ejpam-4425	46	10	=	=	PUNCT
ejpam-4425	47	1	(	(	PUNCT
ejpam-4425	47	2	1	1	NUM
ejpam-4425	47	3	+	+	CCONJ
ejpam-4425	47	4	e−x)−1	e−x)−1	PROPN
ejpam-4425	47	5	,	,	PUNCT
ejpam-4425	47	6	hyperbolic	hyperbolic	ADJ
ejpam-4425	47	7	tangent	tangent	NOUN
ejpam-4425	47	8	function	function	NOUN
ejpam-4425	47	9	σh(x	σh(x	X
ejpam-4425	47	10	)	)	PUNCT
ejpam-4425	47	11	=	=	SYM
ejpam-4425	47	12	1	1	NUM
ejpam-4425	47	13	2	2	NUM
ejpam-4425	47	14	[	[	X
ejpam-4425	47	15	tanh(x	tanh(x	PROPN
ejpam-4425	47	16	)	)	PUNCT
ejpam-4425	47	17	+	+	CCONJ
ejpam-4425	47	18	1	1	NUM
ejpam-4425	47	19	]	]	PUNCT
ejpam-4425	47	20	.	.	PUNCT
ejpam-4425	48	1	for	for	ADP
ejpam-4425	48	2	every	every	DET
ejpam-4425	48	3	non	non	ADJ
ejpam-4425	48	4	-	-	ADJ
ejpam-4425	48	5	decreasing	decrease	VERB
ejpam-4425	48	6	function	function	NOUN
ejpam-4425	48	7	σ	σ	NOUN
ejpam-4425	48	8	satisfying	satisfy	VERB
ejpam-4425	48	9	assumptions	assumption	NOUN
ejpam-4425	48	10	:	:	PUNCT
ejpam-4425	48	11	(	(	PUNCT
ejpam-4425	48	12	i	i	NOUN
ejpam-4425	48	13	)	)	PUNCT
ejpam-4425	48	14	the	the	DET
ejpam-4425	48	15	function	function	NOUN
ejpam-4425	48	16	such	such	ADJ
ejpam-4425	48	17	that	that	PRON
ejpam-4425	48	18	gσ(x	gσ(x	PUNCT
ejpam-4425	48	19	)	)	PUNCT
ejpam-4425	48	20	=	=	SYM
ejpam-4425	48	21	σ(x)−	σ(x)−	PROPN
ejpam-4425	48	22	1/2	1/2	NUM
ejpam-4425	48	23	,	,	PUNCT
ejpam-4425	48	24	is	be	AUX
ejpam-4425	48	25	odd	odd	ADJ
ejpam-4425	48	26	;	;	PUNCT
ejpam-4425	48	27	(	(	PUNCT
ejpam-4425	48	28	ii	ii	NOUN
ejpam-4425	48	29	)	)	PUNCT
ejpam-4425	48	30	function	function	NOUN
ejpam-4425	48	31	σ	σ	PROPN
ejpam-4425	48	32	∈	∈	PROPN
ejpam-4425	48	33	c2(r	c2(r	PROPN
ejpam-4425	48	34	)	)	PUNCT
ejpam-4425	48	35	is	be	AUX
ejpam-4425	48	36	concave	concave	VERB
ejpam-4425	48	37	for	for	ADP
ejpam-4425	48	38	x	x	X
ejpam-4425	48	39	≥	≥	NOUN
ejpam-4425	48	40	0	0	NUM
ejpam-4425	48	41	;	;	PUNCT
ejpam-4425	48	42	(	(	PUNCT
ejpam-4425	48	43	iii	iii	X
ejpam-4425	48	44	)	)	PUNCT
ejpam-4425	48	45	function	function	NOUN
ejpam-4425	48	46	σ	σ	NOUN
ejpam-4425	48	47	satisfying	satisfy	VERB
ejpam-4425	48	48	σ(x	σ(x	PROPN
ejpam-4425	48	49	)	)	PUNCT
ejpam-4425	48	50	=	=	SYM
ejpam-4425	48	51	o(|x|−1−α	o(|x|−1−α	PROPN
ejpam-4425	48	52	)	)	PUNCT
ejpam-4425	48	53	as	as	ADP
ejpam-4425	48	54	x	x	PUNCT
ejpam-4425	48	55	−→	−→	NOUN
ejpam-4425	48	56	−∞	−∞	NOUN
ejpam-4425	48	57	,	,	PUNCT
ejpam-4425	48	58	for	for	ADP
ejpam-4425	48	59	some	some	DET
ejpam-4425	48	60	α>0	α>0	NOUN
ejpam-4425	48	61	.	.	PUNCT
ejpam-4425	49	1	defined	define	VERB
ejpam-4425	49	2	the	the	DET
ejpam-4425	49	3	function	function	NOUN
ejpam-4425	49	4	as	as	ADP
ejpam-4425	49	5	:	:	PUNCT
ejpam-4425	49	6	φσ(x	φσ(x	NUM
ejpam-4425	49	7	)	)	PUNCT
ejpam-4425	49	8	=	=	SYM
ejpam-4425	49	9	1	1	NUM
ejpam-4425	49	10	2	2	NUM
ejpam-4425	50	1	[	[	X
ejpam-4425	50	2	σ(x+	σ(x+	X
ejpam-4425	50	3	1)−	1)−	NUM
ejpam-4425	50	4	σ(x−	σ(x−	NOUN
ejpam-4425	50	5	1	1	NUM
ejpam-4425	50	6	)	)	PUNCT
ejpam-4425	50	7	]	]	PUNCT
ejpam-4425	50	8	,	,	PUNCT
ejpam-4425	50	9	x	x	PROPN
ejpam-4425	50	10	∈	∈	PROPN
ejpam-4425	50	11	r.	r.	PROPN
ejpam-4425	50	12	now	now	ADV
ejpam-4425	50	13	,	,	PUNCT
ejpam-4425	50	14	gives	give	VERB
ejpam-4425	50	15	some	some	DET
ejpam-4425	50	16	definitions	definition	NOUN
ejpam-4425	50	17	that	that	SCONJ
ejpam-4425	50	18	we	we	PRON
ejpam-4425	50	19	will	will	AUX
ejpam-4425	50	20	use	use	VERB
ejpam-4425	50	21	:	:	PUNCT
ejpam-4425	50	22	definition	definition	NOUN
ejpam-4425	50	23	1	1	NUM
ejpam-4425	50	24	.	.	PUNCT
ejpam-4425	51	1	[	[	X
ejpam-4425	51	2	4	4	X
ejpam-4425	51	3	]	]	X
ejpam-4425	51	4	a	a	DET
ejpam-4425	51	5	sigmoidal	sigmoidal	NOUN
ejpam-4425	51	6	function	function	NOUN
ejpam-4425	51	7	is	be	AUX
ejpam-4425	51	8	a	a	DET
ejpam-4425	51	9	measurable	measurable	ADJ
ejpam-4425	51	10	function	function	NOUN
ejpam-4425	51	11	satisfying	satisfy	VERB
ejpam-4425	51	12	the	the	DET
ejpam-4425	51	13	following	follow	VERB
ejpam-4425	51	14	two	two	NUM
ejpam-4425	51	15	conditions	condition	NOUN
ejpam-4425	51	16	:	:	PUNCT
ejpam-4425	51	17	limx→−∞	limx→−∞	PROPN
ejpam-4425	51	18	ζ(x	ζ(x	NOUN
ejpam-4425	51	19	)	)	PUNCT
ejpam-4425	51	20	=	=	SYM
ejpam-4425	51	21	0	0	NUM
ejpam-4425	51	22	;	;	PUNCT
ejpam-4425	51	23	limx→+∞	limx→+∞	X
ejpam-4425	51	24	ζ(x	ζ(x	NOUN
ejpam-4425	51	25	)	)	PUNCT
ejpam-4425	51	26	=	=	SYM
ejpam-4425	51	27	1	1	X
ejpam-4425	51	28	.	.	X
ejpam-4425	51	29	definition	definition	NOUN
ejpam-4425	51	30	2	2	NUM
ejpam-4425	51	31	.	.	PUNCT
ejpam-4425	52	1	[	[	X
ejpam-4425	52	2	4	4	X
ejpam-4425	52	3	]	]	PUNCT
ejpam-4425	52	4	the	the	DET
ejpam-4425	52	5	lipschitz	lipschitz	NOUN
ejpam-4425	52	6	classes	class	NOUN
ejpam-4425	52	7	are	be	AUX
ejpam-4425	52	8	defined	define	VERB
ejpam-4425	52	9	as	as	SCONJ
ejpam-4425	52	10	follows	follow	VERB
ejpam-4425	52	11	:	:	PUNCT
ejpam-4425	52	12	lip(v	lip(v	PROPN
ejpam-4425	52	13	)	)	PUNCT
ejpam-4425	52	14	=	=	PRON
ejpam-4425	53	1	{	{	PUNCT
ejpam-4425	53	2	f	f	PROPN
ejpam-4425	53	3	∈	∈	PROPN
ejpam-4425	53	4	c0(r	c0(r	PROPN
ejpam-4425	53	5	)	)	PUNCT
ejpam-4425	53	6	such	such	ADJ
ejpam-4425	53	7	that	that	SCONJ
ejpam-4425	53	8	there	there	PRON
ejpam-4425	53	9	exist	exist	VERB
ejpam-4425	53	10	γ>0	γ>0	NOUN
ejpam-4425	53	11	,	,	PUNCT
ejpam-4425	53	12	c>0	c>0	VERB
ejpam-4425	53	13	so	so	SCONJ
ejpam-4425	53	14	that	that	SCONJ
ejpam-4425	53	15	,	,	PUNCT
ejpam-4425	53	16	for	for	ADP
ejpam-4425	53	17	each	each	DET
ejpam-4425	53	18	x	x	SYM
ejpam-4425	53	19	∈	∈	PROPN
ejpam-4425	53	20	r	r	NOUN
ejpam-4425	53	21	,	,	PUNCT
ejpam-4425	53	22	|f(x+	|f(x+	ADJ
ejpam-4425	53	23	t)−	t)−	PROPN
ejpam-4425	53	24	f(x)|	f(x)|	VERB
ejpam-4425	54	1	≤	≤	NUM
ejpam-4425	54	2	c∥t∥v2	c∥t∥v2	NOUN
ejpam-4425	54	3	for	for	ADP
ejpam-4425	54	4	every	every	DET
ejpam-4425	54	5	∥t∥2	∥t∥2	NOUN
ejpam-4425	54	6	≤	≤	NOUN
ejpam-4425	54	7	γ	γ	NOUN
ejpam-4425	54	8	with	with	ADP
ejpam-4425	54	9	(	(	PUNCT
ejpam-4425	54	10	x+	x+	PROPN
ejpam-4425	54	11	t	t	PROPN
ejpam-4425	54	12	)	)	PUNCT
ejpam-4425	54	13	∈	∈	PROPN
ejpam-4425	54	14	r	r	NOUN
ejpam-4425	54	15	}	}	PUNCT
ejpam-4425	54	16	.	.	PUNCT
ejpam-4425	55	1	definition	definition	NOUN
ejpam-4425	55	2	3	3	NUM
ejpam-4425	55	3	.	.	PUNCT
ejpam-4425	56	1	[	[	X
ejpam-4425	56	2	5	5	X
ejpam-4425	56	3	]	]	PUNCT
ejpam-4425	56	4	the	the	DET
ejpam-4425	56	5	multivariate	multivariate	NOUN
ejpam-4425	56	6	for	for	ADP
ejpam-4425	56	7	the	the	DET
ejpam-4425	56	8	φσ(x	φσ(x	NOUN
ejpam-4425	56	9	)	)	PUNCT
ejpam-4425	56	10	define	define	NOUN
ejpam-4425	56	11	as	as	SCONJ
ejpam-4425	56	12	follows	follow	VERB
ejpam-4425	56	13	:	:	PUNCT
ejpam-4425	56	14	ψσ(x	ψσ(x	X
ejpam-4425	56	15	)	)	PUNCT
ejpam-4425	56	16	=	=	SYM
ejpam-4425	56	17	φσ(x1	φσ(x1	PROPN
ejpam-4425	56	18	)	)	PUNCT
ejpam-4425	56	19	·	·	SYM
ejpam-4425	56	20	φσ(x2	φσ(x2	NOUN
ejpam-4425	56	21	)	)	PUNCT
ejpam-4425	56	22	·	·	PUNCT
ejpam-4425	56	23	...	...	PUNCT
ejpam-4425	56	24	·	·	PUNCT
ejpam-4425	56	25	φσ(xs	φσ(x	NOUN
ejpam-4425	56	26	)	)	PUNCT
ejpam-4425	56	27	,	,	PUNCT
ejpam-4425	56	28	for	for	ADP
ejpam-4425	56	29	every	every	DET
ejpam-4425	56	30	x	x	PROPN
ejpam-4425	56	31	∈	∈	PROPN
ejpam-4425	56	32	rs	rs	NOUN
ejpam-4425	56	33	.	.	PUNCT
ejpam-4425	57	1	now	now	ADV
ejpam-4425	57	2	,	,	PUNCT
ejpam-4425	57	3	in	in	ADP
ejpam-4425	57	4	the	the	DET
ejpam-4425	57	5	following	follow	VERB
ejpam-4425	57	6	lemmas	lemmas	PROPN
ejpam-4425	57	7	set	set	NOUN
ejpam-4425	57	8	of	of	ADP
ejpam-4425	57	9	properties	property	NOUN
ejpam-4425	57	10	for	for	ADP
ejpam-4425	57	11	the	the	DET
ejpam-4425	57	12	functions	function	NOUN
ejpam-4425	57	13	φσ(x	φσ(x	PUNCT
ejpam-4425	57	14	)	)	PUNCT
ejpam-4425	57	15	will	will	AUX
ejpam-4425	57	16	be	be	AUX
ejpam-4425	57	17	studied	study	VERB
ejpam-4425	57	18	.	.	PUNCT
ejpam-4425	58	1	lemma	lemma	PROPN
ejpam-4425	58	2	1	1	NUM
ejpam-4425	58	3	.	.	PUNCT
ejpam-4425	59	1	[	[	X
ejpam-4425	59	2	5	5	NUM
ejpam-4425	59	3	]	]	PUNCT
ejpam-4425	59	4	to	to	ADP
ejpam-4425	59	5	the	the	DET
ejpam-4425	59	6	function	function	NOUN
ejpam-4425	59	7	φσ(x	φσ(x	PUNCT
ejpam-4425	59	8	)	)	PUNCT
ejpam-4425	59	9	for	for	ADP
ejpam-4425	59	10	x	x	PROPN
ejpam-4425	59	11	∈	∈	PROPN
ejpam-4425	59	12	r	r	NOUN
ejpam-4425	59	13	,	,	PUNCT
ejpam-4425	59	14	then	then	ADV
ejpam-4425	59	15	:	:	PUNCT
ejpam-4425	59	16	i.j	i.j	PROPN
ejpam-4425	59	17	.	.	PROPN
ejpam-4425	59	18	mohammad	mohammad	PROPN
ejpam-4425	59	19	,	,	PUNCT
ejpam-4425	59	20	a.j	a.j	PROPN
ejpam-4425	59	21	.	.	PROPN
ejpam-4425	59	22	mohammad	mohammad	PROPN
ejpam-4425	59	23	/	/	SYM
ejpam-4425	59	24	eur	eur	PROPN
ejpam-4425	59	25	.	.	PUNCT
ejpam-4425	60	1	j.	j.	PROPN
ejpam-4425	60	2	pure	pure	PROPN
ejpam-4425	60	3	appl	appl	PROPN
ejpam-4425	60	4	.	.	PROPN
ejpam-4425	60	5	math	math	PROPN
ejpam-4425	60	6	,	,	PUNCT
ejpam-4425	60	7	15	15	NUM
ejpam-4425	60	8	(	(	PUNCT
ejpam-4425	60	9	3	3	NUM
ejpam-4425	60	10	)	)	PUNCT
ejpam-4425	60	11	(	(	PUNCT
ejpam-4425	60	12	2022	2022	NUM
ejpam-4425	60	13	)	)	PUNCT
ejpam-4425	60	14	,	,	PUNCT
ejpam-4425	60	15	1189	1189	NUM
ejpam-4425	60	16	-	-	SYM
ejpam-4425	60	17	1200	1200	NUM
ejpam-4425	60	18	1192	1192	NUM
ejpam-4425	60	19	(	(	PUNCT
ejpam-4425	60	20	i	i	NOUN
ejpam-4425	60	21	)	)	PUNCT
ejpam-4425	60	22	φσ(x	φσ(x	NUM
ejpam-4425	60	23	)	)	PUNCT
ejpam-4425	60	24	≥	≥	NOUN
ejpam-4425	60	25	0	0	NUM
ejpam-4425	60	26	for	for	ADP
ejpam-4425	60	27	every	every	DET
ejpam-4425	60	28	x	x	SYM
ejpam-4425	60	29	∈	∈	PROPN
ejpam-4425	60	30	r	r	NOUN
ejpam-4425	60	31	and	and	CCONJ
ejpam-4425	60	32	limx→±∞	limx→±∞	PROPN
ejpam-4425	60	33	φσ(x	φσ(x	PUNCT
ejpam-4425	60	34	)	)	PUNCT
ejpam-4425	60	35	=	=	SYM
ejpam-4425	60	36	0	0	NUM
ejpam-4425	60	37	;	;	PUNCT
ejpam-4425	60	38	(	(	PUNCT
ejpam-4425	60	39	ii	ii	NOUN
ejpam-4425	60	40	)	)	PUNCT
ejpam-4425	60	41	φσ(x	φσ(x	PUNCT
ejpam-4425	60	42	)	)	PUNCT
ejpam-4425	60	43	is	be	AUX
ejpam-4425	60	44	a	a	DET
ejpam-4425	60	45	symmetrical	symmetrical	ADJ
ejpam-4425	60	46	function	function	NOUN
ejpam-4425	60	47	about	about	ADP
ejpam-4425	60	48	the	the	DET
ejpam-4425	60	49	y	y	NOUN
ejpam-4425	60	50	-	-	PUNCT
ejpam-4425	60	51	axis	axis	NOUN
ejpam-4425	60	52	;	;	PUNCT
ejpam-4425	60	53	(	(	PUNCT
ejpam-4425	60	54	iii	iii	NOUN
ejpam-4425	60	55	)	)	PUNCT
ejpam-4425	60	56	∑	∑	ADP
ejpam-4425	60	57	k∈z	k∈z	PROPN
ejpam-4425	60	58	φσ(x−	φσ(x−	PROPN
ejpam-4425	60	59	k	k	NOUN
ejpam-4425	60	60	)	)	PUNCT
ejpam-4425	60	61	=	=	SYM
ejpam-4425	60	62	1	1	NUM
ejpam-4425	60	63	,	,	PUNCT
ejpam-4425	60	64	for	for	ADP
ejpam-4425	60	65	every	every	DET
ejpam-4425	60	66	x	x	SYM
ejpam-4425	60	67	∈	∈	PROPN
ejpam-4425	60	68	r	r	NOUN
ejpam-4425	60	69	;	;	PUNCT
ejpam-4425	60	70	(	(	PUNCT
ejpam-4425	60	71	iv	iv	X
ejpam-4425	60	72	)	)	PUNCT
ejpam-4425	60	73	for	for	ADP
ejpam-4425	60	74	x<0	x<0	NOUN
ejpam-4425	60	75	the	the	DET
ejpam-4425	60	76	function	function	NOUN
ejpam-4425	60	77	φσ(x	φσ(x	PUNCT
ejpam-4425	60	78	)	)	PUNCT
ejpam-4425	60	79	is	be	AUX
ejpam-4425	60	80	non	non	ADJ
ejpam-4425	60	81	-	-	ADJ
ejpam-4425	60	82	decreasing	decrease	VERB
ejpam-4425	60	83	and	and	CCONJ
ejpam-4425	60	84	for	for	ADP
ejpam-4425	60	85	x	x	X
ejpam-4425	60	86	≥	≥	NOUN
ejpam-4425	60	87	0	0	NUM
ejpam-4425	61	1	it	it	PRON
ejpam-4425	61	2	is	be	AUX
ejpam-4425	61	3	non	non	ADJ
ejpam-4425	61	4	-	-	ADJ
ejpam-4425	61	5	increasing	increasing	ADJ
ejpam-4425	61	6	;	;	PUNCT
ejpam-4425	61	7	(	(	PUNCT
ejpam-4425	61	8	v	v	NOUN
ejpam-4425	61	9	)	)	PUNCT
ejpam-4425	61	10	φσ(x	φσ(x	NUM
ejpam-4425	61	11	)	)	PUNCT
ejpam-4425	61	12	=	=	SYM
ejpam-4425	61	13	o(|x|−1−α	o(|x|−1−α	PROPN
ejpam-4425	61	14	)	)	PUNCT
ejpam-4425	61	15	as	as	ADP
ejpam-4425	61	16	x	x	SYM
ejpam-4425	61	17	−→	−→	NOUN
ejpam-4425	61	18	±∞	±∞	PROPN
ejpam-4425	61	19	;	;	PUNCT
ejpam-4425	61	20	(	(	PUNCT
ejpam-4425	61	21	vi	vi	X
ejpam-4425	61	22	)	)	PUNCT
ejpam-4425	61	23	the	the	DET
ejpam-4425	61	24	sum	sum	NOUN
ejpam-4425	61	25	∑	∑	ADV
ejpam-4425	61	26	k∈z	k∈z	PROPN
ejpam-4425	61	27	φσ(x−	φσ(x−	PROPN
ejpam-4425	61	28	k	k	X
ejpam-4425	61	29	)	)	PUNCT
ejpam-4425	61	30	converges	converge	VERB
ejpam-4425	61	31	uniformly	uniformly	ADV
ejpam-4425	61	32	on	on	ADP
ejpam-4425	61	33	subsets	subset	NOUN
ejpam-4425	61	34	compact	compact	ADJ
ejpam-4425	61	35	of	of	ADP
ejpam-4425	61	36	r.	r.	PROPN
ejpam-4425	61	37	the	the	DET
ejpam-4425	61	38	following	follow	VERB
ejpam-4425	61	39	lemmas	lemmas	PROPN
ejpam-4425	61	40	set	set	NOUN
ejpam-4425	61	41	of	of	ADP
ejpam-4425	61	42	properties	property	NOUN
ejpam-4425	61	43	for	for	ADP
ejpam-4425	61	44	the	the	DET
ejpam-4425	61	45	functions	function	NOUN
ejpam-4425	61	46	ψσ(x−	ψσ(x−	PART
ejpam-4425	61	47	k	k	X
ejpam-4425	61	48	)	)	PUNCT
ejpam-4425	61	49	will	will	AUX
ejpam-4425	61	50	be	be	AUX
ejpam-4425	61	51	studied	study	VERB
ejpam-4425	61	52	.	.	PUNCT
ejpam-4425	62	1	lemma	lemma	PROPN
ejpam-4425	62	2	2	2	NUM
ejpam-4425	62	3	.	.	PUNCT
ejpam-4425	63	1	[	[	X
ejpam-4425	63	2	4	4	X
ejpam-4425	63	3	]	]	PUNCT
ejpam-4425	63	4	to	to	ADP
ejpam-4425	63	5	the	the	DET
ejpam-4425	63	6	function	function	NOUN
ejpam-4425	63	7	ψσ(x−	ψσ(x−	PROPN
ejpam-4425	63	8	k	k	X
ejpam-4425	63	9	)	)	PUNCT
ejpam-4425	63	10	for	for	ADP
ejpam-4425	63	11	x	x	PROPN
ejpam-4425	63	12	∈	∈	PROPN
ejpam-4425	63	13	rs	rs	NOUN
ejpam-4425	63	14	,	,	PUNCT
ejpam-4425	63	15	then	then	ADV
ejpam-4425	63	16	:	:	PUNCT
ejpam-4425	63	17	(	(	PUNCT
ejpam-4425	63	18	i	i	NOUN
ejpam-4425	63	19	)	)	PUNCT
ejpam-4425	63	20	∑	∑	PROPN
ejpam-4425	63	21	k	k	PROPN
ejpam-4425	63	22	ψσ(x−	ψσ(x−	PROPN
ejpam-4425	63	23	k	k	X
ejpam-4425	63	24	)	)	PUNCT
ejpam-4425	63	25	=	=	PUNCT
ejpam-4425	64	1	1,for	1,for	NUM
ejpam-4425	64	2	every	every	DET
ejpam-4425	64	3	x	x	PROPN
ejpam-4425	64	4	∈	∈	NOUN
ejpam-4425	64	5	rs	rs	NOUN
ejpam-4425	64	6	;	;	PUNCT
ejpam-4425	64	7	(	(	PUNCT
ejpam-4425	64	8	ii	ii	NOUN
ejpam-4425	64	9	)	)	PUNCT
ejpam-4425	64	10	on	on	ADP
ejpam-4425	64	11	compact	compact	ADJ
ejpam-4425	64	12	subsets	subset	NOUN
ejpam-4425	64	13	of	of	ADP
ejpam-4425	64	14	rs	rs	PROPN
ejpam-4425	64	15	the	the	DET
ejpam-4425	64	16	series	series	NOUN
ejpam-4425	64	17	∑	∑	PROPN
ejpam-4425	64	18	k	k	PROPN
ejpam-4425	64	19	ψσ(x−	ψσ(x−	PROPN
ejpam-4425	64	20	k	k	PROPN
ejpam-4425	64	21	)	)	PUNCT
ejpam-4425	64	22	converges	converge	VERB
ejpam-4425	64	23	uniformly	uniformly	ADV
ejpam-4425	64	24	on	on	ADP
ejpam-4425	64	25	compact	compact	ADJ
ejpam-4425	64	26	subsets	subset	NOUN
ejpam-4425	64	27	of	of	ADP
ejpam-4425	64	28	rs	rs	NOUN
ejpam-4425	64	29	;	;	PUNCT
ejpam-4425	64	30	(	(	PUNCT
ejpam-4425	64	31	iii	iii	NOUN
ejpam-4425	64	32	)	)	PUNCT
ejpam-4425	64	33	for	for	ADP
ejpam-4425	64	34	every	every	DET
ejpam-4425	64	35	γ>0	γ>0	NOUN
ejpam-4425	64	36	,	,	PUNCT
ejpam-4425	64	37	we	we	PRON
ejpam-4425	64	38	get	get	VERB
ejpam-4425	64	39	lim	lim	PROPN
ejpam-4425	64	40	x→∞	x→∞	PUNCT
ejpam-4425	64	41	∑	∑	PUNCT
ejpam-4425	64	42	∥x−k∥>γn	∥x−k∥>γn	PROPN
ejpam-4425	64	43	ψσ(x−	ψσ(x−	X
ejpam-4425	64	44	k	k	X
ejpam-4425	64	45	)	)	PUNCT
ejpam-4425	64	46	=	=	SYM
ejpam-4425	64	47	0	0	NUM
ejpam-4425	64	48	,	,	PUNCT
ejpam-4425	64	49	uniformly	uniformly	ADV
ejpam-4425	64	50	respect	respect	VERB
ejpam-4425	64	51	to	to	ADP
ejpam-4425	64	52	x	x	SYM
ejpam-4425	64	53	∈	∈	PROPN
ejpam-4425	65	1	rs.in	rs.in	ADP
ejpam-4425	65	2	a	a	DET
ejpam-4425	65	3	special	special	ADJ
ejpam-4425	65	4	case	case	NOUN
ejpam-4425	65	5	,	,	PUNCT
ejpam-4425	65	6	for	for	ADP
ejpam-4425	65	7	every	every	DET
ejpam-4425	65	8	γ>0	γ>0	NOUN
ejpam-4425	65	9	and	and	CCONJ
ejpam-4425	65	10	0	0	NUM
ejpam-4425	65	11	<	<	X
ejpam-4425	65	12	v	v	X
ejpam-4425	65	13	<	<	X
ejpam-4425	65	14	α	α	X
ejpam-4425	65	15	,	,	PUNCT
ejpam-4425	65	16	∑	∑	PROPN
ejpam-4425	65	17	∥x−k∥>γn	∥x−k∥>γn	PROPN
ejpam-4425	65	18	ψσ(x−	ψσ(x−	X
ejpam-4425	65	19	k	k	X
ejpam-4425	65	20	)	)	PUNCT
ejpam-4425	65	21	=	=	SYM
ejpam-4425	65	22	o(n−v	o(n−v	PROPN
ejpam-4425	65	23	)	)	PUNCT
ejpam-4425	65	24	,	,	PUNCT
ejpam-4425	65	25	n	n	CCONJ
ejpam-4425	66	1	−→	−→	ADJ
ejpam-4425	66	2	+	+	NOUN
ejpam-4425	66	3	∞	∞	PROPN
ejpam-4425	66	4	,	,	PUNCT
ejpam-4425	66	5	where	where	SCONJ
ejpam-4425	66	6	the	the	DET
ejpam-4425	66	7	constant	constant	ADJ
ejpam-4425	66	8	α>0	α>0	NOUN
ejpam-4425	66	9	as	as	ADP
ejpam-4425	66	10	in	in	ADP
ejpam-4425	66	11	condition	condition	NOUN
ejpam-4425	66	12	(	(	PUNCT
ejpam-4425	66	13	iii	iii	NOUN
ejpam-4425	66	14	)	)	PUNCT
ejpam-4425	66	15	.	.	PUNCT
ejpam-4425	67	1	lemma	lemma	PROPN
ejpam-4425	67	2	3	3	X
ejpam-4425	67	3	.	.	PUNCT
ejpam-4425	68	1	[	[	X
ejpam-4425	68	2	3	3	NUM
ejpam-4425	68	3	]	]	PUNCT
ejpam-4425	68	4	,	,	PUNCT
ejpam-4425	68	5	[	[	X
ejpam-4425	68	6	4	4	X
ejpam-4425	68	7	]	]	PUNCT
ejpam-4425	68	8	(	(	PUNCT
ejpam-4425	68	9	i	i	NOUN
ejpam-4425	68	10	)	)	PUNCT
ejpam-4425	68	11	for	for	ADP
ejpam-4425	68	12	x	x	PROPN
ejpam-4425	68	13	∈	∈	PROPN
ejpam-4425	68	14	[	[	X
ejpam-4425	68	15	a	a	X
ejpam-4425	68	16	,	,	PUNCT
ejpam-4425	68	17	b	b	NOUN
ejpam-4425	68	18	]	]	X
ejpam-4425	68	19	⊂	⊂	PROPN
ejpam-4425	68	20	r	r	X
ejpam-4425	68	21	,	,	PUNCT
ejpam-4425	68	22	n	n	PRON
ejpam-4425	68	23	∈	∈	PROPN
ejpam-4425	68	24	n+	n+	PROPN
ejpam-4425	68	25	,	,	PUNCT
ejpam-4425	68	26	⌈na⌉	⌈na⌉	VERB
ejpam-4425	68	27	≤	≤	NOUN
ejpam-4425	68	28	⌊nb⌋	⌊nb⌋	NOUN
ejpam-4425	68	29	,	,	PUNCT
ejpam-4425	68	30	then	then	ADV
ejpam-4425	68	31	:	:	PUNCT
ejpam-4425	68	32	1	1	NUM
ejpam-4425	68	33	⌊nb⌋∑	⌊nb⌋∑	NOUN
ejpam-4425	68	34	k=⌈na⌉	k=⌈na⌉	VERB
ejpam-4425	68	35	φσ(nx−	φσ(nx−	PROPN
ejpam-4425	68	36	k	k	NOUN
ejpam-4425	68	37	)	)	PUNCT
ejpam-4425	68	38	≤	≤	NOUN
ejpam-4425	68	39	1	1	NUM
ejpam-4425	68	40	φσ(1	φσ(1	PROPN
ejpam-4425	68	41	)	)	PUNCT
ejpam-4425	68	42	;	;	PUNCT
ejpam-4425	68	43	(	(	PUNCT
ejpam-4425	68	44	ii	ii	NOUN
ejpam-4425	68	45	)	)	PUNCT
ejpam-4425	68	46	for	for	ADP
ejpam-4425	68	47	x	x	PROPN
ejpam-4425	68	48	∈	∈	PROPN
ejpam-4425	68	49	[	[	X
ejpam-4425	68	50	a1	a1	NOUN
ejpam-4425	68	51	,	,	PUNCT
ejpam-4425	68	52	b1]×	b1]×	NOUN
ejpam-4425	68	53	...	...	SYM
ejpam-4425	68	54	×	×	NOUN
ejpam-4425	69	1	[	[	X
ejpam-4425	69	2	as	as	ADP
ejpam-4425	69	3	,	,	PUNCT
ejpam-4425	69	4	bs	bs	X
ejpam-4425	69	5	]	]	X
ejpam-4425	69	6	⊂	⊂	PROPN
ejpam-4425	69	7	rs	rs	PROPN
ejpam-4425	69	8	,	,	PUNCT
ejpam-4425	69	9	n	n	PRON
ejpam-4425	69	10	∈	∈	NOUN
ejpam-4425	69	11	n+	n+	PUNCT
ejpam-4425	69	12	so	so	SCONJ
ejpam-4425	69	13	that	that	PRON
ejpam-4425	69	14	⌈na⌉	⌈na⌉	VERB
ejpam-4425	69	15	≤	≤	ADJ
ejpam-4425	69	16	⌊nb⌋	⌊nb⌋	NOUN
ejpam-4425	69	17	for	for	ADP
ejpam-4425	69	18	every	every	DET
ejpam-4425	69	19	i	i	NOUN
ejpam-4425	69	20	=	=	NOUN
ejpam-4425	69	21	1	1	NUM
ejpam-4425	69	22	,	,	PUNCT
ejpam-4425	69	23	...	...	PUNCT
ejpam-4425	69	24	,	,	PUNCT
ejpam-4425	69	25	s	s	X
ejpam-4425	69	26	,	,	PUNCT
ejpam-4425	69	27	then	then	ADV
ejpam-4425	69	28	:	:	PUNCT
ejpam-4425	69	29	1	1	NUM
ejpam-4425	69	30	s∏	s∏	PROPN
ejpam-4425	69	31	i=1	i=1	X
ejpam-4425	69	32	⌊nbi⌋∑	⌊nbi⌋∑	PROPN
ejpam-4425	69	33	ki=⌈nai⌉	ki=⌈nai⌉	PROPN
ejpam-4425	69	34	φσ(nxi	φσ(nxi	PROPN
ejpam-4425	69	35	−	−	PROPN
ejpam-4425	69	36	ki	ki	PROPN
ejpam-4425	69	37	)	)	PUNCT
ejpam-4425	69	38	≤	≤	NOUN
ejpam-4425	69	39	1	1	NUM
ejpam-4425	70	1	[	[	X
ejpam-4425	70	2	φσ(1	φσ(1	NOUN
ejpam-4425	70	3	)	)	PUNCT
ejpam-4425	70	4	]	]	PUNCT
ejpam-4425	71	1	s	s	X
ejpam-4425	71	2	.	.	PUNCT
ejpam-4425	72	1	i.j	i.j	PROPN
ejpam-4425	72	2	.	.	PROPN
ejpam-4425	72	3	mohammad	mohammad	PROPN
ejpam-4425	72	4	,	,	PUNCT
ejpam-4425	72	5	a.j	a.j	PROPN
ejpam-4425	72	6	.	.	PROPN
ejpam-4425	72	7	mohammad	mohammad	PROPN
ejpam-4425	72	8	/	/	SYM
ejpam-4425	72	9	eur	eur	PROPN
ejpam-4425	72	10	.	.	PUNCT
ejpam-4425	73	1	j.	j.	PROPN
ejpam-4425	73	2	pure	pure	PROPN
ejpam-4425	73	3	appl	appl	PROPN
ejpam-4425	73	4	.	.	PROPN
ejpam-4425	73	5	math	math	PROPN
ejpam-4425	73	6	,	,	PUNCT
ejpam-4425	73	7	15	15	NUM
ejpam-4425	73	8	(	(	PUNCT
ejpam-4425	73	9	3	3	NUM
ejpam-4425	73	10	)	)	PUNCT
ejpam-4425	73	11	(	(	PUNCT
ejpam-4425	73	12	2022	2022	NUM
ejpam-4425	73	13	)	)	PUNCT
ejpam-4425	73	14	,	,	PUNCT
ejpam-4425	73	15	1189	1189	NUM
ejpam-4425	73	16	-	-	SYM
ejpam-4425	73	17	1200	1200	NUM
ejpam-4425	73	18	1193	1193	NUM
ejpam-4425	73	19	3	3	NUM
ejpam-4425	73	20	.	.	PUNCT
ejpam-4425	73	21	auxiliary	auxiliary	ADJ
ejpam-4425	73	22	results	result	NOUN
ejpam-4425	73	23	we	we	PRON
ejpam-4425	73	24	will	will	AUX
ejpam-4425	73	25	define	define	VERB
ejpam-4425	73	26	and	and	CCONJ
ejpam-4425	73	27	discuss	discuss	VERB
ejpam-4425	73	28	multivariate	multivariate	NOUN
ejpam-4425	73	29	nn	nn	PROPN
ejpam-4425	73	30	operators	operators	PROPN
ejpam-4425	73	31	qm(f	qm(f	VERB
ejpam-4425	73	32	;	;	PUNCT
ejpam-4425	73	33	x	x	X
ejpam-4425	73	34	)	)	PUNCT
ejpam-4425	73	35	as	as	SCONJ
ejpam-4425	73	36	follows	follow	VERB
ejpam-4425	73	37	:	:	PUNCT
ejpam-4425	73	38	definition	definition	NOUN
ejpam-4425	73	39	4	4	NUM
ejpam-4425	73	40	.	.	PUNCT
ejpam-4425	74	1	for	for	ADP
ejpam-4425	74	2	a	a	DET
ejpam-4425	74	3	continuous	continuous	ADJ
ejpam-4425	74	4	bounded	bounded	ADJ
ejpam-4425	74	5	function	function	NOUN
ejpam-4425	74	6	f	f	NOUN
ejpam-4425	74	7	:	:	PUNCT
ejpam-4425	74	8	r	r	VERB
ejpam-4425	74	9	−→	−→	NOUN
ejpam-4425	74	10	r	r	NOUN
ejpam-4425	74	11	,	,	PUNCT
ejpam-4425	74	12	the	the	DET
ejpam-4425	74	13	nn	nn	PROPN
ejpam-4425	74	14	operators	operator	NOUN
ejpam-4425	74	15	of	of	ADP
ejpam-4425	74	16	multivariate	multivariate	PROPN
ejpam-4425	74	17	square	square	ADJ
ejpam-4425	74	18	rational	rational	ADJ
ejpam-4425	74	19	bernstein	bernstein	PROPN
ejpam-4425	74	20	operators	operators	PROPN
ejpam-4425	74	21	with	with	ADP
ejpam-4425	74	22	positive	positive	ADJ
ejpam-4425	74	23	integer	integer	NOUN
ejpam-4425	74	24	parameter	parameter	PROPN
ejpam-4425	74	25	m	m	PROPN
ejpam-4425	74	26	,	,	PUNCT
ejpam-4425	74	27	qm(f	qm(f	PUNCT
ejpam-4425	74	28	;	;	PUNCT
ejpam-4425	74	29	x	x	X
ejpam-4425	74	30	)	)	PUNCT
ejpam-4425	74	31	activated	activate	VERB
ejpam-4425	74	32	by	by	ADP
ejpam-4425	74	33	the	the	DET
ejpam-4425	74	34	sigmoidal	sigmoidal	NOUN
ejpam-4425	74	35	function	function	NOUN
ejpam-4425	74	36	σ	σ	NOUN
ejpam-4425	74	37	acting	act	VERB
ejpam-4425	74	38	on	on	ADP
ejpam-4425	74	39	f	f	PROPN
ejpam-4425	74	40	,	,	PUNCT
ejpam-4425	74	41	defined	define	VERB
ejpam-4425	74	42	as	as	ADP
ejpam-4425	74	43	the	the	DET
ejpam-4425	74	44	following	following	NOUN
ejpam-4425	74	45	:	:	PUNCT
ejpam-4425	74	46	qm(f	qm(f	NOUN
ejpam-4425	74	47	;	;	PUNCT
ejpam-4425	74	48	x	x	X
ejpam-4425	74	49	)	)	PUNCT
ejpam-4425	74	50	=	=	PUNCT
ejpam-4425	74	51	∑	∑	PUNCT
ejpam-4425	74	52	k	k	PROPN
ejpam-4425	74	53	ψ2	ψ2	NOUN
ejpam-4425	74	54	σ(nx−	σ(nx−	X
ejpam-4425	74	55	k)f	k)f	X
ejpam-4425	74	56	(	(	PUNCT
ejpam-4425	74	57	(	(	PUNCT
ejpam-4425	74	58	n−1k−	n−1k−	NOUN
ejpam-4425	74	59	x	x	SYM
ejpam-4425	74	60	)	)	PUNCT
ejpam-4425	74	61	m	m	NOUN
ejpam-4425	74	62	−	−	NOUN
ejpam-4425	74	63	x	x	SYM
ejpam-4425	74	64	)	)	PUNCT
ejpam-4425	74	65	∑	∑	PUNCT
ejpam-4425	74	66	k	k	PROPN
ejpam-4425	74	67	ψ2	ψ2	NOUN
ejpam-4425	74	68	σ(nx−	σ(nx−	SYM
ejpam-4425	74	69	k	k	NOUN
ejpam-4425	74	70	)	)	PUNCT
ejpam-4425	74	71	,	,	PUNCT
ejpam-4425	74	72	m	m	VERB
ejpam-4425	74	73	∈	∈	ADJ
ejpam-4425	74	74	n+	n+	PUNCT
ejpam-4425	74	75	∑	∑	PUNCT
ejpam-4425	74	76	k	k	X
ejpam-4425	74	77	=	=	PUNCT
ejpam-4425	74	78	⌊nb1⌋∑	⌊nb1⌋∑	X
ejpam-4425	74	79	k1=⌈na1⌉	k1=⌈na1⌉	PROPN
ejpam-4425	74	80	...	...	PUNCT
ejpam-4425	74	81	⌊nbs⌋∑	⌊nbs⌋∑	PROPN
ejpam-4425	75	1	ks=⌈nas⌉	ks=⌈nas⌉	PROPN
ejpam-4425	75	2	.	.	PUNCT
ejpam-4425	76	1	for	for	ADP
ejpam-4425	76	2	sufficiently	sufficiently	ADV
ejpam-4425	76	3	large	large	ADJ
ejpam-4425	76	4	n	n	CCONJ
ejpam-4425	76	5	∈	∈	PROPN
ejpam-4425	76	6	n	n	CCONJ
ejpam-4425	76	7	,	,	PUNCT
ejpam-4425	76	8	x	x	PUNCT
ejpam-4425	76	9	∈	∈	PROPN
ejpam-4425	76	10	r	r	NOUN
ejpam-4425	76	11	,	,	PUNCT
ejpam-4425	76	12	qm(1;x	qm(1;x	PROPN
ejpam-4425	76	13	)	)	PUNCT
ejpam-4425	76	14	=	=	SYM
ejpam-4425	77	1	1	1	X
ejpam-4425	77	2	.	.	X
ejpam-4425	77	3	definition	definition	NOUN
ejpam-4425	77	4	5	5	NUM
ejpam-4425	77	5	.	.	PUNCT
ejpam-4425	78	1	for	for	ADP
ejpam-4425	78	2	v	v	NOUN
ejpam-4425	78	3	>	>	SYM
ejpam-4425	78	4	0	0	NUM
ejpam-4425	78	5	,	,	PUNCT
ejpam-4425	78	6	the	the	DET
ejpam-4425	78	7	discrete	discrete	NOUN
ejpam-4425	78	8	absolutely	absolutely	ADV
ejpam-4425	78	9	moment	moment	NOUN
ejpam-4425	78	10	of	of	ADP
ejpam-4425	78	11	the	the	DET
ejpam-4425	78	12	function	function	NOUN
ejpam-4425	78	13	φ2	φ2	PROPN
ejpam-4425	78	14	σ(x	σ(x	PROPN
ejpam-4425	78	15	)	)	PUNCT
ejpam-4425	78	16	of	of	ADP
ejpam-4425	78	17	order	order	NOUN
ejpam-4425	78	18	v	v	NOUN
ejpam-4425	78	19	is	be	AUX
ejpam-4425	78	20	defined	define	VERB
ejpam-4425	78	21	as	as	ADP
ejpam-4425	78	22	mv(φ	mv(φ	X
ejpam-4425	78	23	2	2	NUM
ejpam-4425	78	24	σ	σ	NOUN
ejpam-4425	78	25	)	)	PUNCT
ejpam-4425	79	1	=	=	SYM
ejpam-4425	79	2	sup	sup	NOUN
ejpam-4425	79	3	x∈r	x∈r	PROPN
ejpam-4425	79	4	∑	∑	ADV
ejpam-4425	79	5	k∈z	k∈z	PROPN
ejpam-4425	79	6	φ2	φ2	PROPN
ejpam-4425	79	7	σ(x−	σ(x−	PROPN
ejpam-4425	79	8	k)|x−	k)|x−	PROPN
ejpam-4425	79	9	k|v	k|v	PROPN
ejpam-4425	79	10	.	.	PUNCT
ejpam-4425	80	1	we	we	PRON
ejpam-4425	80	2	will	will	AUX
ejpam-4425	80	3	need	need	VERB
ejpam-4425	80	4	to	to	PART
ejpam-4425	80	5	give	give	VERB
ejpam-4425	80	6	some	some	DET
ejpam-4425	80	7	properties	property	NOUN
ejpam-4425	80	8	of	of	ADP
ejpam-4425	80	9	the	the	DET
ejpam-4425	80	10	functions	function	NOUN
ejpam-4425	80	11	φ2	φ2	PROPN
ejpam-4425	80	12	σ(x	σ(x	PROPN
ejpam-4425	80	13	)	)	PUNCT
ejpam-4425	80	14	and	and	CCONJ
ejpam-4425	80	15	ψ2	ψ2	NOUN
ejpam-4425	80	16	σ(x	σ(x	NOUN
ejpam-4425	80	17	)	)	PUNCT
ejpam-4425	80	18	in	in	ADP
ejpam-4425	80	19	the	the	DET
ejpam-4425	80	20	following	following	ADJ
ejpam-4425	80	21	lemmas	lemmas	PROPN
ejpam-4425	80	22	:	:	PUNCT
ejpam-4425	80	23	lemma	lemma	PROPN
ejpam-4425	80	24	4	4	NUM
ejpam-4425	80	25	.	.	PUNCT
ejpam-4425	81	1	some	some	DET
ejpam-4425	81	2	properties	property	NOUN
ejpam-4425	81	3	to	to	ADP
ejpam-4425	81	4	the	the	DET
ejpam-4425	81	5	function	function	NOUN
ejpam-4425	81	6	φ2	φ2	PROPN
ejpam-4425	81	7	σ(x	σ(x	PROPN
ejpam-4425	81	8	)	)	PUNCT
ejpam-4425	81	9	defined	define	VERB
ejpam-4425	81	10	on	on	ADP
ejpam-4425	81	11	x	x	PUNCT
ejpam-4425	81	12	∈	∈	PROPN
ejpam-4425	81	13	r	r	NOUN
ejpam-4425	81	14	,	,	PUNCT
ejpam-4425	81	15	then	then	ADV
ejpam-4425	81	16	:	:	PUNCT
ejpam-4425	81	17	(	(	PUNCT
ejpam-4425	81	18	i	i	NOUN
ejpam-4425	81	19	)	)	PUNCT
ejpam-4425	81	20	φ2	φ2	PROPN
ejpam-4425	81	21	σ(x	σ(x	PROPN
ejpam-4425	81	22	)	)	PUNCT
ejpam-4425	81	23	≥	≥	NOUN
ejpam-4425	81	24	0	0	NUM
ejpam-4425	81	25	for	for	ADP
ejpam-4425	81	26	every	every	DET
ejpam-4425	81	27	x	x	SYM
ejpam-4425	81	28	∈	∈	PROPN
ejpam-4425	81	29	r	r	NOUN
ejpam-4425	81	30	and	and	CCONJ
ejpam-4425	81	31	limx→±∞	limx→±∞	PROPN
ejpam-4425	81	32	φ2	φ2	PROPN
ejpam-4425	81	33	σ(x	σ(x	PROPN
ejpam-4425	81	34	)	)	PUNCT
ejpam-4425	81	35	=	=	SYM
ejpam-4425	81	36	0	0	NUM
ejpam-4425	81	37	;	;	PUNCT
ejpam-4425	81	38	(	(	PUNCT
ejpam-4425	81	39	ii	ii	NOUN
ejpam-4425	81	40	)	)	PUNCT
ejpam-4425	81	41	φ2	φ2	PROPN
ejpam-4425	81	42	σ(x	σ(x	PROPN
ejpam-4425	81	43	)	)	PUNCT
ejpam-4425	81	44	is	be	AUX
ejpam-4425	81	45	a	a	DET
ejpam-4425	81	46	symmetrical	symmetrical	ADJ
ejpam-4425	81	47	function	function	NOUN
ejpam-4425	81	48	about	about	ADP
ejpam-4425	81	49	the	the	DET
ejpam-4425	81	50	y	y	NOUN
ejpam-4425	81	51	-	-	PUNCT
ejpam-4425	81	52	axis	axis	NOUN
ejpam-4425	81	53	;	;	PUNCT
ejpam-4425	81	54	(	(	PUNCT
ejpam-4425	81	55	iii	iii	NOUN
ejpam-4425	81	56	)	)	PUNCT
ejpam-4425	81	57	∑	∑	ADV
ejpam-4425	81	58	k∈z	k∈z	PROPN
ejpam-4425	81	59	φ	φ	PROPN
ejpam-4425	81	60	2	2	NUM
ejpam-4425	81	61	σ(x−	σ(x−	PROPN
ejpam-4425	81	62	k	k	NOUN
ejpam-4425	81	63	)	)	PUNCT
ejpam-4425	81	64	≈	≈	PROPN
ejpam-4425	81	65	0.156517	0.156517	NUM
ejpam-4425	81	66	,	,	PUNCT
ejpam-4425	81	67	for	for	ADP
ejpam-4425	81	68	every	every	DET
ejpam-4425	81	69	x	x	SYM
ejpam-4425	81	70	∈	∈	PROPN
ejpam-4425	81	71	r	r	NOUN
ejpam-4425	81	72	;	;	PUNCT
ejpam-4425	81	73	(	(	PUNCT
ejpam-4425	81	74	iv	iv	X
ejpam-4425	81	75	)	)	PUNCT
ejpam-4425	81	76	for	for	ADP
ejpam-4425	81	77	x<0	x<0	NOUN
ejpam-4425	81	78	the	the	DET
ejpam-4425	81	79	function	function	NOUN
ejpam-4425	81	80	φ2	φ2	PROPN
ejpam-4425	81	81	σ(x	σ(x	PROPN
ejpam-4425	81	82	)	)	PUNCT
ejpam-4425	81	83	is	be	AUX
ejpam-4425	81	84	non	non	ADJ
ejpam-4425	81	85	-	-	ADJ
ejpam-4425	81	86	decreasing	decrease	VERB
ejpam-4425	81	87	and	and	CCONJ
ejpam-4425	81	88	for	for	ADP
ejpam-4425	81	89	x	x	X
ejpam-4425	81	90	≥	≥	NOUN
ejpam-4425	81	91	0	0	NUM
ejpam-4425	82	1	it	it	PRON
ejpam-4425	82	2	is	be	AUX
ejpam-4425	82	3	non	non	ADJ
ejpam-4425	82	4	-	-	ADJ
ejpam-4425	82	5	increasing	increasing	ADJ
ejpam-4425	82	6	;	;	PUNCT
ejpam-4425	82	7	(	(	PUNCT
ejpam-4425	82	8	v	v	NOUN
ejpam-4425	82	9	)	)	PUNCT
ejpam-4425	82	10	φ2	φ2	PROPN
ejpam-4425	82	11	σ(x	σ(x	PROPN
ejpam-4425	82	12	)	)	PUNCT
ejpam-4425	83	1	=	=	SYM
ejpam-4425	83	2	o(|x|2(−1−α	o(|x|2(−1−α	PROPN
ejpam-4425	83	3	)	)	PUNCT
ejpam-4425	83	4	)	)	PUNCT
ejpam-4425	84	1	as	as	ADP
ejpam-4425	84	2	x	x	SYM
ejpam-4425	84	3	−→	−→	NOUN
ejpam-4425	84	4	±∞	±∞	PROPN
ejpam-4425	84	5	;	;	PUNCT
ejpam-4425	84	6	(	(	PUNCT
ejpam-4425	84	7	vi	vi	X
ejpam-4425	84	8	)	)	PUNCT
ejpam-4425	84	9	the	the	DET
ejpam-4425	84	10	sum	sum	NOUN
ejpam-4425	84	11	∑	∑	ADV
ejpam-4425	84	12	k∈z	k∈z	PROPN
ejpam-4425	84	13	φ	φ	PROPN
ejpam-4425	84	14	2	2	NUM
ejpam-4425	84	15	σ(x−	σ(x−	PROPN
ejpam-4425	84	16	k	k	NOUN
ejpam-4425	84	17	)	)	PUNCT
ejpam-4425	84	18	converges	converge	VERB
ejpam-4425	84	19	uniformly	uniformly	ADV
ejpam-4425	84	20	on	on	ADP
ejpam-4425	84	21	subsets	subset	NOUN
ejpam-4425	84	22	compact	compact	ADJ
ejpam-4425	84	23	of	of	ADP
ejpam-4425	84	24	r.	r.	PROPN
ejpam-4425	84	25	proof	proof	NOUN
ejpam-4425	84	26	.	.	PUNCT
ejpam-4425	85	1	by	by	ADP
ejpam-4425	85	2	applying	apply	VERB
ejpam-4425	85	3	lemma	lemma	PROPN
ejpam-4425	85	4	1	1	NUM
ejpam-4425	85	5	,	,	PUNCT
ejpam-4425	85	6	we	we	PRON
ejpam-4425	85	7	can	can	AUX
ejpam-4425	85	8	prove	prove	VERB
ejpam-4425	85	9	(	(	PUNCT
ejpam-4425	85	10	i	i	NOUN
ejpam-4425	85	11	)	)	PUNCT
ejpam-4425	85	12	,	,	PUNCT
ejpam-4425	85	13	(	(	PUNCT
ejpam-4425	85	14	ii	ii	NOUN
ejpam-4425	85	15	)	)	PUNCT
ejpam-4425	85	16	,	,	PUNCT
ejpam-4425	85	17	(	(	PUNCT
ejpam-4425	85	18	iv),(v	iv),(v	X
ejpam-4425	85	19	)	)	PUNCT
ejpam-4425	85	20	and	and	CCONJ
ejpam-4425	85	21	(	(	PUNCT
ejpam-4425	85	22	vi	vi	X
ejpam-4425	85	23	)	)	PUNCT
ejpam-4425	85	24	immediately	immediately	ADV
ejpam-4425	85	25	,	,	PUNCT
ejpam-4425	85	26	the	the	DET
ejpam-4425	85	27	consequence	consequence	NOUN
ejpam-4425	85	28	(	(	PUNCT
ejpam-4425	85	29	iii	iii	NOUN
ejpam-4425	85	30	)	)	PUNCT
ejpam-4425	85	31	can	can	AUX
ejpam-4425	85	32	be	be	AUX
ejpam-4425	85	33	claimed	claim	VERB
ejpam-4425	85	34	by	by	ADP
ejpam-4425	85	35	using	use	VERB
ejpam-4425	85	36	maple	maple	NOUN
ejpam-4425	85	37	software	software	NOUN
ejpam-4425	85	38	.	.	PUNCT
ejpam-4425	86	1	□	□	PUNCT
ejpam-4425	86	2	the	the	DET
ejpam-4425	86	3	next	next	ADJ
ejpam-4425	86	4	lemma	lemma	PROPN
ejpam-4425	86	5	gives	give	VERB
ejpam-4425	86	6	some	some	DET
ejpam-4425	86	7	properties	property	NOUN
ejpam-4425	86	8	for	for	ADP
ejpam-4425	86	9	the	the	DET
ejpam-4425	86	10	function	function	NOUN
ejpam-4425	86	11	ψ2	ψ2	VERB
ejpam-4425	86	12	σ(nx−	σ(nx−	PUNCT
ejpam-4425	86	13	k	k	NOUN
ejpam-4425	86	14	)	)	PUNCT
ejpam-4425	86	15	.	.	PUNCT
ejpam-4425	87	1	lemma	lemma	PROPN
ejpam-4425	87	2	5	5	NUM
ejpam-4425	87	3	.	.	PUNCT
ejpam-4425	87	4	to	to	ADP
ejpam-4425	87	5	the	the	DET
ejpam-4425	87	6	function	function	NOUN
ejpam-4425	87	7	ψ2	ψ2	VERB
ejpam-4425	87	8	σ(x−	σ(x−	PROPN
ejpam-4425	87	9	k	k	NOUN
ejpam-4425	87	10	)	)	PUNCT
ejpam-4425	87	11	for	for	ADP
ejpam-4425	87	12	x	x	PROPN
ejpam-4425	87	13	∈	∈	PROPN
ejpam-4425	87	14	rs	rs	NOUN
ejpam-4425	87	15	,	,	PUNCT
ejpam-4425	87	16	then	then	ADV
ejpam-4425	87	17	:	:	PUNCT
ejpam-4425	87	18	i.j	i.j	PROPN
ejpam-4425	87	19	.	.	PROPN
ejpam-4425	87	20	mohammad	mohammad	PROPN
ejpam-4425	87	21	,	,	PUNCT
ejpam-4425	87	22	a.j	a.j	PROPN
ejpam-4425	87	23	.	.	PROPN
ejpam-4425	87	24	mohammad	mohammad	PROPN
ejpam-4425	87	25	/	/	SYM
ejpam-4425	87	26	eur	eur	PROPN
ejpam-4425	87	27	.	.	PUNCT
ejpam-4425	88	1	j.	j.	PROPN
ejpam-4425	88	2	pure	pure	PROPN
ejpam-4425	88	3	appl	appl	PROPN
ejpam-4425	88	4	.	.	PROPN
ejpam-4425	88	5	math	math	PROPN
ejpam-4425	88	6	,	,	PUNCT
ejpam-4425	88	7	15	15	NUM
ejpam-4425	88	8	(	(	PUNCT
ejpam-4425	88	9	3	3	NUM
ejpam-4425	88	10	)	)	PUNCT
ejpam-4425	88	11	(	(	PUNCT
ejpam-4425	88	12	2022	2022	NUM
ejpam-4425	88	13	)	)	PUNCT
ejpam-4425	88	14	,	,	PUNCT
ejpam-4425	88	15	1189	1189	NUM
ejpam-4425	88	16	-	-	SYM
ejpam-4425	88	17	1200	1200	NUM
ejpam-4425	88	18	1194	1194	NUM
ejpam-4425	88	19	(	(	PUNCT
ejpam-4425	88	20	i	i	NOUN
ejpam-4425	88	21	)	)	PUNCT
ejpam-4425	88	22	∑	∑	PUNCT
ejpam-4425	89	1	k	k	PROPN
ejpam-4425	89	2	ψ	ψ	PROPN
ejpam-4425	89	3	2	2	NUM
ejpam-4425	89	4	σ(x−	σ(x−	PROPN
ejpam-4425	89	5	k	k	NOUN
ejpam-4425	89	6	)	)	PUNCT
ejpam-4425	90	1	≈	≈	PROPN
ejpam-4425	90	2	(	(	PUNCT
ejpam-4425	90	3	0.156517)s	0.156517)s	PROPN
ejpam-4425	90	4	,	,	PUNCT
ejpam-4425	90	5	for	for	ADP
ejpam-4425	90	6	every	every	DET
ejpam-4425	90	7	x	x	PROPN
ejpam-4425	90	8	∈	∈	NOUN
ejpam-4425	90	9	rs	rs	NOUN
ejpam-4425	90	10	;	;	PUNCT
ejpam-4425	90	11	(	(	PUNCT
ejpam-4425	90	12	ii	ii	NOUN
ejpam-4425	90	13	)	)	PUNCT
ejpam-4425	90	14	on	on	ADP
ejpam-4425	90	15	compact	compact	ADJ
ejpam-4425	90	16	subsets	subset	NOUN
ejpam-4425	90	17	of	of	ADP
ejpam-4425	90	18	rs	rs	PROPN
ejpam-4425	90	19	the	the	DET
ejpam-4425	90	20	series	series	NOUN
ejpam-4425	90	21	∑	∑	PROPN
ejpam-4425	90	22	k	k	PROPN
ejpam-4425	90	23	ψ	ψ	PROPN
ejpam-4425	90	24	2	2	NUM
ejpam-4425	90	25	σ(x−	σ(x−	PROPN
ejpam-4425	90	26	k	k	NOUN
ejpam-4425	90	27	)	)	PUNCT
ejpam-4425	90	28	converges	converge	VERB
ejpam-4425	90	29	uniformly	uniformly	ADV
ejpam-4425	90	30	on	on	ADP
ejpam-4425	90	31	compact	compact	ADJ
ejpam-4425	90	32	subsets	subset	NOUN
ejpam-4425	90	33	of	of	ADP
ejpam-4425	90	34	rs	rs	NOUN
ejpam-4425	90	35	;	;	PUNCT
ejpam-4425	90	36	(	(	PUNCT
ejpam-4425	90	37	iii	iii	NOUN
ejpam-4425	90	38	)	)	PUNCT
ejpam-4425	90	39	for	for	ADP
ejpam-4425	90	40	every	every	DET
ejpam-4425	90	41	γ>0	γ>0	NOUN
ejpam-4425	90	42	,	,	PUNCT
ejpam-4425	90	43	we	we	PRON
ejpam-4425	90	44	get	get	VERB
ejpam-4425	90	45	lim	lim	PROPN
ejpam-4425	90	46	x→∞	x→∞	NUM
ejpam-4425	90	47	∑	∑	PUNCT
ejpam-4425	90	48	∥x−k∥>γn	∥x−k∥>γn	PROPN
ejpam-4425	90	49	ψ2	ψ2	NOUN
ejpam-4425	90	50	σ(x−	σ(x−	PROPN
ejpam-4425	90	51	k	k	NOUN
ejpam-4425	90	52	)	)	PUNCT
ejpam-4425	90	53	=	=	SYM
ejpam-4425	90	54	0	0	NUM
ejpam-4425	90	55	,	,	PUNCT
ejpam-4425	90	56	uniformly	uniformly	ADV
ejpam-4425	90	57	respect	respect	VERB
ejpam-4425	90	58	to	to	ADP
ejpam-4425	90	59	x	x	SYM
ejpam-4425	90	60	∈	∈	PROPN
ejpam-4425	91	1	rs.in	rs.in	ADP
ejpam-4425	91	2	a	a	DET
ejpam-4425	91	3	special	special	ADJ
ejpam-4425	91	4	case	case	NOUN
ejpam-4425	91	5	,	,	PUNCT
ejpam-4425	91	6	for	for	ADP
ejpam-4425	91	7	every	every	DET
ejpam-4425	91	8	γ>0	γ>0	NOUN
ejpam-4425	91	9	and	and	CCONJ
ejpam-4425	91	10	0	0	NUM
ejpam-4425	91	11	<	<	X
ejpam-4425	91	12	v	v	NOUN
ejpam-4425	91	13	<	<	X
ejpam-4425	91	14	α,∑	α,∑	PRON
ejpam-4425	91	15	∥x−k∥>γn	∥x−k∥>γn	NOUN
ejpam-4425	91	16	ψ2	ψ2	VERB
ejpam-4425	91	17	σ(x−	σ(x−	PROPN
ejpam-4425	91	18	k	k	NOUN
ejpam-4425	91	19	)	)	PUNCT
ejpam-4425	91	20	=	=	SYM
ejpam-4425	91	21	o(n−v	o(n−v	PROPN
ejpam-4425	91	22	)	)	PUNCT
ejpam-4425	91	23	,	,	PUNCT
ejpam-4425	91	24	as	as	ADP
ejpam-4425	91	25	n	n	PRON
ejpam-4425	91	26	−→	−→	NOUN
ejpam-4425	91	27	+	+	NOUN
ejpam-4425	91	28	∞	∞	PROPN
ejpam-4425	91	29	where	where	SCONJ
ejpam-4425	91	30	the	the	DET
ejpam-4425	91	31	constant	constant	ADJ
ejpam-4425	91	32	α>0	α>0	NOUN
ejpam-4425	91	33	as	as	ADP
ejpam-4425	91	34	in	in	ADP
ejpam-4425	91	35	condition	condition	NOUN
ejpam-4425	91	36	(	(	PUNCT
ejpam-4425	91	37	iii	iii	NOUN
ejpam-4425	91	38	)	)	PUNCT
ejpam-4425	91	39	.	.	PUNCT
ejpam-4425	92	1	proof.using	proof.use	VERB
ejpam-4425	92	2	the	the	DET
ejpam-4425	92	3	definition	definition	NOUN
ejpam-4425	92	4	3	3	NUM
ejpam-4425	92	5	and	and	CCONJ
ejpam-4425	92	6	lemma	lemma	PROPN
ejpam-4425	92	7	2	2	NUM
ejpam-4425	92	8	,	,	PUNCT
ejpam-4425	92	9	the	the	DET
ejpam-4425	92	10	consequence	consequence	NOUN
ejpam-4425	92	11	(	(	PUNCT
ejpam-4425	92	12	i),(ii),(iii	i),(ii),(iii	X
ejpam-4425	92	13	)	)	PUNCT
ejpam-4425	92	14	gets	get	VERB
ejpam-4425	92	15	immediate	immediate	ADJ
ejpam-4425	92	16	.	.	PUNCT
ejpam-4425	93	1	□	□	PUNCT
ejpam-4425	93	2	lemma	lemma	PROPN
ejpam-4425	93	3	6	6	NUM
ejpam-4425	93	4	.	.	PUNCT
ejpam-4425	94	1	(	(	PUNCT
ejpam-4425	94	2	i	i	NOUN
ejpam-4425	94	3	)	)	PUNCT
ejpam-4425	94	4	for	for	ADP
ejpam-4425	94	5	x	x	PROPN
ejpam-4425	94	6	∈	∈	PROPN
ejpam-4425	95	1	[	[	X
ejpam-4425	95	2	a	a	X
ejpam-4425	95	3	,	,	PUNCT
ejpam-4425	95	4	b	b	NOUN
ejpam-4425	95	5	]	]	X
ejpam-4425	95	6	⊂	⊂	PROPN
ejpam-4425	95	7	r	r	X
ejpam-4425	95	8	,	,	PUNCT
ejpam-4425	95	9	n	n	PRON
ejpam-4425	95	10	∈	∈	PROPN
ejpam-4425	95	11	n+	n+	PROPN
ejpam-4425	95	12	,	,	PUNCT
ejpam-4425	95	13	⌈na⌉	⌈na⌉	VERB
ejpam-4425	95	14	≤	≤	NOUN
ejpam-4425	95	15	⌊nb⌋	⌊nb⌋	NOUN
ejpam-4425	95	16	,	,	PUNCT
ejpam-4425	95	17	then	then	ADV
ejpam-4425	95	18	:	:	PUNCT
ejpam-4425	95	19	1	1	NUM
ejpam-4425	95	20	⌊nb⌋∑	⌊nb⌋∑	NOUN
ejpam-4425	95	21	k=⌈na⌉	k=⌈na⌉	VERB
ejpam-4425	95	22	φ2	φ2	PROPN
ejpam-4425	95	23	σ(nx−	σ(nx−	PROPN
ejpam-4425	95	24	k	k	X
ejpam-4425	95	25	)	)	PUNCT
ejpam-4425	95	26	≤	≤	NUM
ejpam-4425	95	27	1	1	NUM
ejpam-4425	95	28	φ2	φ2	NOUN
ejpam-4425	95	29	σ(1	σ(1	PROPN
ejpam-4425	95	30	)	)	PUNCT
ejpam-4425	95	31	;	;	PUNCT
ejpam-4425	95	32	(	(	PUNCT
ejpam-4425	95	33	ii	ii	NOUN
ejpam-4425	95	34	)	)	PUNCT
ejpam-4425	95	35	for	for	ADP
ejpam-4425	95	36	x	x	PROPN
ejpam-4425	95	37	∈	∈	PROPN
ejpam-4425	95	38	[	[	X
ejpam-4425	95	39	a1	a1	NOUN
ejpam-4425	95	40	,	,	PUNCT
ejpam-4425	95	41	b1]×	b1]×	NOUN
ejpam-4425	95	42	...	...	SYM
ejpam-4425	95	43	×	×	NOUN
ejpam-4425	95	44	[	[	X
ejpam-4425	95	45	as	as	ADP
ejpam-4425	95	46	,	,	PUNCT
ejpam-4425	95	47	bs	bs	X
ejpam-4425	95	48	]	]	X
ejpam-4425	95	49	⊂	⊂	PROPN
ejpam-4425	95	50	rs	rs	PROPN
ejpam-4425	95	51	,	,	PUNCT
ejpam-4425	95	52	n	n	PRON
ejpam-4425	95	53	∈	∈	NOUN
ejpam-4425	95	54	n+	n+	PUNCT
ejpam-4425	95	55	so	so	SCONJ
ejpam-4425	95	56	that	that	PRON
ejpam-4425	95	57	⌈na⌉	⌈na⌉	VERB
ejpam-4425	95	58	≤	≤	ADJ
ejpam-4425	95	59	⌊nb⌋	⌊nb⌋	NOUN
ejpam-4425	95	60	for	for	ADP
ejpam-4425	95	61	every	every	DET
ejpam-4425	95	62	i	i	NOUN
ejpam-4425	95	63	=	=	NOUN
ejpam-4425	95	64	1	1	NUM
ejpam-4425	95	65	,	,	PUNCT
ejpam-4425	95	66	...	...	PUNCT
ejpam-4425	95	67	,	,	PUNCT
ejpam-4425	95	68	s	s	X
ejpam-4425	95	69	,	,	PUNCT
ejpam-4425	95	70	then	then	ADV
ejpam-4425	95	71	:	:	PUNCT
ejpam-4425	95	72	1	1	NUM
ejpam-4425	95	73	s∏	s∏	PROPN
ejpam-4425	95	74	i=1	i=1	X
ejpam-4425	96	1	⌊nbi⌋∑	⌊nbi⌋∑	PROPN
ejpam-4425	96	2	ki=⌈nai⌉	ki=⌈nai⌉	PROPN
ejpam-4425	96	3	φ2	φ2	PROPN
ejpam-4425	96	4	σ(nxi	σ(nxi	PROPN
ejpam-4425	96	5	−	−	PROPN
ejpam-4425	96	6	ki	ki	PROPN
ejpam-4425	96	7	)	)	PUNCT
ejpam-4425	96	8	≤	≤	NOUN
ejpam-4425	96	9	1	1	NUM
ejpam-4425	97	1	[	[	X
ejpam-4425	97	2	φ2	φ2	PROPN
ejpam-4425	97	3	σ(1	σ(1	PROPN
ejpam-4425	97	4	)	)	PUNCT
ejpam-4425	97	5	]	]	PUNCT
ejpam-4425	97	6	s	s	X
ejpam-4425	97	7	.	.	PUNCT
ejpam-4425	98	1	proof	proof	NOUN
ejpam-4425	98	2	.	.	PUNCT
ejpam-4425	99	1	using	use	VERB
ejpam-4425	99	2	the	the	DET
ejpam-4425	99	3	properties	property	NOUN
ejpam-4425	99	4	of	of	ADP
ejpam-4425	99	5	lemma	lemma	PROPN
ejpam-4425	99	6	3	3	NUM
ejpam-4425	99	7	the	the	DET
ejpam-4425	99	8	proof	proof	NOUN
ejpam-4425	99	9	of	of	ADP
ejpam-4425	99	10	this	this	DET
ejpam-4425	99	11	lemma	lemma	PROPN
ejpam-4425	99	12	follows	follow	VERB
ejpam-4425	99	13	immediately	immediately	ADV
ejpam-4425	99	14	.	.	PUNCT
ejpam-4425	100	1	□	□	PUNCT
ejpam-4425	100	2	the	the	DET
ejpam-4425	100	3	following	follow	VERB
ejpam-4425	100	4	theorem	theorem	VERB
ejpam-4425	100	5	studies	study	NOUN
ejpam-4425	100	6	the	the	DET
ejpam-4425	100	7	pointwise	pointwise	NOUN
ejpam-4425	100	8	and	and	CCONJ
ejpam-4425	100	9	the	the	DET
ejpam-4425	100	10	uniform	uniform	ADJ
ejpam-4425	100	11	convergence	convergence	NOUN
ejpam-4425	100	12	for	for	ADP
ejpam-4425	100	13	the	the	DET
ejpam-4425	100	14	nn	nn	PROPN
ejpam-4425	100	15	operators	operator	NOUN
ejpam-4425	100	16	,	,	PUNCT
ejpam-4425	100	17	qm(f	qm(f	PROPN
ejpam-4425	100	18	;	;	PUNCT
ejpam-4425	100	19	x	x	X
ejpam-4425	100	20	)	)	PUNCT
ejpam-4425	100	21	.	.	PUNCT
ejpam-4425	101	1	theorem	theorem	NOUN
ejpam-4425	101	2	1	1	NUM
ejpam-4425	101	3	.	.	X
ejpam-4425	101	4	for	for	ADP
ejpam-4425	101	5	a	a	DET
ejpam-4425	101	6	bounded	bounded	ADJ
ejpam-4425	101	7	function	function	NOUN
ejpam-4425	102	1	f	f	NOUN
ejpam-4425	102	2	:	:	PUNCT
ejpam-4425	102	3	r	r	VERB
ejpam-4425	102	4	−→	−→	NOUN
ejpam-4425	102	5	r	r	NOUN
ejpam-4425	102	6	,	,	PUNCT
ejpam-4425	102	7	and	and	CCONJ
ejpam-4425	102	8	continuous	continuous	ADJ
ejpam-4425	102	9	at	at	ADP
ejpam-4425	102	10	each	each	DET
ejpam-4425	102	11	point	point	NOUN
ejpam-4425	102	12	x	x	X
ejpam-4425	102	13	∈	∈	NOUN
ejpam-4425	102	14	r	r	NOUN
ejpam-4425	102	15	,	,	PUNCT
ejpam-4425	102	16	then	then	ADV
ejpam-4425	102	17	lim	lim	PROPN
ejpam-4425	102	18	n→∞	n→∞	NUM
ejpam-4425	102	19	qm(f	qm(f	PROPN
ejpam-4425	102	20	;	;	PUNCT
ejpam-4425	102	21	x	x	X
ejpam-4425	102	22	)	)	PUNCT
ejpam-4425	102	23	=	=	SYM
ejpam-4425	102	24	f(x	f(x	PROPN
ejpam-4425	102	25	)	)	PUNCT
ejpam-4425	102	26	if	if	SCONJ
ejpam-4425	102	27	f	f	PROPN
ejpam-4425	102	28	∈	∈	PROPN
ejpam-4425	102	29	c0(r	c0(r	PROPN
ejpam-4425	102	30	)	)	PUNCT
ejpam-4425	102	31	,	,	PUNCT
ejpam-4425	102	32	then	then	ADV
ejpam-4425	102	33	lim	lim	PROPN
ejpam-4425	102	34	n→∞	n→∞	NUM
ejpam-4425	102	35	sup	sup	NOUN
ejpam-4425	102	36	x∈r	x∈r	PROPN
ejpam-4425	102	37	|qm(f	|qm(f	PROPN
ejpam-4425	102	38	;	;	PUNCT
ejpam-4425	102	39	x)−	x)−	PROPN
ejpam-4425	102	40	f(x)|	f(x)|	VERB
ejpam-4425	102	41	=	=	SYM
ejpam-4425	102	42	lim	lim	PROPN
ejpam-4425	102	43	n−→∞	n−→∞	PROPN
ejpam-4425	102	44	∥qm(f	∥qm(f	PROPN
ejpam-4425	102	45	;	;	PUNCT
ejpam-4425	102	46	.)−	.)−	PROPN
ejpam-4425	102	47	f(.)∥∞	f(.)∥∞	PROPN
ejpam-4425	102	48	=	=	NOUN
ejpam-4425	102	49	0	0	X
ejpam-4425	102	50	.	.	PUNCT
ejpam-4425	103	1	i.j	i.j	PROPN
ejpam-4425	103	2	.	.	PROPN
ejpam-4425	103	3	mohammad	mohammad	PROPN
ejpam-4425	103	4	,	,	PUNCT
ejpam-4425	103	5	a.j	a.j	PROPN
ejpam-4425	103	6	.	.	PROPN
ejpam-4425	103	7	mohammad	mohammad	PROPN
ejpam-4425	103	8	/	/	SYM
ejpam-4425	103	9	eur	eur	PROPN
ejpam-4425	103	10	.	.	PUNCT
ejpam-4425	104	1	j.	j.	PROPN
ejpam-4425	104	2	pure	pure	PROPN
ejpam-4425	104	3	appl	appl	PROPN
ejpam-4425	104	4	.	.	PROPN
ejpam-4425	104	5	math	math	PROPN
ejpam-4425	104	6	,	,	PUNCT
ejpam-4425	104	7	15	15	NUM
ejpam-4425	104	8	(	(	PUNCT
ejpam-4425	104	9	3	3	NUM
ejpam-4425	104	10	)	)	PUNCT
ejpam-4425	104	11	(	(	PUNCT
ejpam-4425	104	12	2022	2022	NUM
ejpam-4425	104	13	)	)	PUNCT
ejpam-4425	104	14	,	,	PUNCT
ejpam-4425	104	15	1189	1189	NUM
ejpam-4425	104	16	-	-	SYM
ejpam-4425	104	17	1200	1200	NUM
ejpam-4425	104	18	1195	1195	NUM
ejpam-4425	104	19	proof	proof	NOUN
ejpam-4425	104	20	.	.	PUNCT
ejpam-4425	104	21	suppose	suppose	VERB
ejpam-4425	104	22	x	x	SYM
ejpam-4425	104	23	∈	∈	NOUN
ejpam-4425	104	24	r	r	NOUN
ejpam-4425	104	25	is	be	AUX
ejpam-4425	104	26	a	a	DET
ejpam-4425	104	27	point	point	NOUN
ejpam-4425	104	28	of	of	ADP
ejpam-4425	104	29	continuity	continuity	NOUN
ejpam-4425	104	30	of	of	ADP
ejpam-4425	104	31	fwe	fwe	NOUN
ejpam-4425	104	32	have	have	VERB
ejpam-4425	104	33	|qm(f	|qm(f	PROPN
ejpam-4425	104	34	;	;	PUNCT
ejpam-4425	104	35	x)−	x)−	PROPN
ejpam-4425	104	36	f(x)|	f(x)|	VERB
ejpam-4425	104	37	=	=	SYM
ejpam-4425	105	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4425	105	2	∑	∑	PUNCT
ejpam-4425	105	3	k	k	PROPN
ejpam-4425	105	4	ψ2	ψ2	NOUN
ejpam-4425	105	5	σ(nx−	σ(nx−	X
ejpam-4425	105	6	k)f	k)f	X
ejpam-4425	105	7	(	(	PUNCT
ejpam-4425	105	8	(	(	PUNCT
ejpam-4425	105	9	n−1k−	n−1k−	NOUN
ejpam-4425	105	10	x	x	SYM
ejpam-4425	105	11	)	)	PUNCT
ejpam-4425	105	12	m	m	NOUN
ejpam-4425	105	13	−	−	NOUN
ejpam-4425	105	14	x	x	SYM
ejpam-4425	105	15	)	)	PUNCT
ejpam-4425	105	16	∑	∑	PUNCT
ejpam-4425	105	17	k	k	PROPN
ejpam-4425	105	18	ψ2	ψ2	NOUN
ejpam-4425	105	19	σ(nx−	σ(nx−	SYM
ejpam-4425	105	20	k	k	NOUN
ejpam-4425	105	21	)	)	PUNCT
ejpam-4425	105	22	−	−	PROPN
ejpam-4425	105	23	f(x	f(x	PROPN
ejpam-4425	105	24	)	)	PUNCT
ejpam-4425	105	25	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4425	106	1	=	=	PUNCT
ejpam-4425	106	2	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-4425	106	3	∑	∑	PUNCT
ejpam-4425	106	4	k	k	PROPN
ejpam-4425	106	5	ψ2	ψ2	NOUN
ejpam-4425	106	6	σ(nx−	σ(nx−	SYM
ejpam-4425	106	7	k	k	NOUN
ejpam-4425	106	8	)	)	PUNCT
ejpam-4425	106	9	[	[	PUNCT
ejpam-4425	106	10	f	f	X
ejpam-4425	106	11	(	(	PUNCT
ejpam-4425	106	12	(	(	PUNCT
ejpam-4425	106	13	n−1k−	n−1k−	NOUN
ejpam-4425	106	14	x	x	SYM
ejpam-4425	106	15	)	)	PUNCT
ejpam-4425	106	16	m	m	NOUN
ejpam-4425	106	17	−	−	NOUN
ejpam-4425	106	18	x	x	SYM
ejpam-4425	106	19	)	)	PUNCT
ejpam-4425	106	20	−	−	PROPN
ejpam-4425	106	21	f(x	f(x	PROPN
ejpam-4425	106	22	)	)	PUNCT
ejpam-4425	106	23	]	]	PUNCT
ejpam-4425	107	1	∑	∑	PUNCT
ejpam-4425	107	2	k	k	PROPN
ejpam-4425	107	3	ψ2	ψ2	NOUN
ejpam-4425	107	4	σ(nx−	σ(nx−	SYM
ejpam-4425	107	5	k	k	NOUN
ejpam-4425	107	6	)	)	PUNCT
ejpam-4425	107	7	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	VERB
ejpam-4425	107	8	by	by	ADP
ejpam-4425	107	9	using	use	VERB
ejpam-4425	107	10	lemma	lemma	PROPN
ejpam-4425	107	11	6(ii),we	6(ii),we	NOUN
ejpam-4425	107	12	get	get	VERB
ejpam-4425	107	13	:	:	PUNCT
ejpam-4425	107	14	|qm(f	|qm(f	PROPN
ejpam-4425	107	15	;	;	PUNCT
ejpam-4425	107	16	x)−	x)−	PROPN
ejpam-4425	107	17	f(x)|	f(x)|	VERB
ejpam-4425	107	18	≤	≤	NUM
ejpam-4425	107	19	1	1	NUM
ejpam-4425	108	1	[	[	X
ejpam-4425	108	2	φ2	φ2	PROPN
ejpam-4425	108	3	σ(1	σ(1	PROPN
ejpam-4425	108	4	)	)	PUNCT
ejpam-4425	108	5	]	]	PUNCT
ejpam-4425	108	6	s	s	VERB
ejpam-4425	108	7	∑	∑	PUNCT
ejpam-4425	108	8	k	k	PROPN
ejpam-4425	108	9	ψ2	ψ2	NOUN
ejpam-4425	108	10	σ(nx−	σ(nx−	SYM
ejpam-4425	108	11	k	k	NOUN
ejpam-4425	108	12	)	)	PUNCT
ejpam-4425	108	13	∣∣f	∣∣f	NOUN
ejpam-4425	108	14	(	(	PUNCT
ejpam-4425	108	15	(	(	PUNCT
ejpam-4425	108	16	n−1k−	n−1k−	NOUN
ejpam-4425	108	17	x	x	SYM
ejpam-4425	108	18	)	)	PUNCT
ejpam-4425	108	19	m	m	NOUN
ejpam-4425	108	20	−	−	NOUN
ejpam-4425	108	21	x	x	SYM
ejpam-4425	108	22	)	)	PUNCT
ejpam-4425	108	23	−	−	PROPN
ejpam-4425	108	24	f(x	f(x	PROPN
ejpam-4425	108	25	)	)	PUNCT
ejpam-4425	108	26	∣∣	∣∣	X
ejpam-4425	108	27	for	for	SCONJ
ejpam-4425	108	28	every	every	DET
ejpam-4425	108	29	n	n	PRON
ejpam-4425	108	30	−→	−→	ADJ
ejpam-4425	108	31	∞,n	∞,n	PROPN
ejpam-4425	108	32	∈	∈	PROPN
ejpam-4425	108	33	n+,x	n+,x	PROPN
ejpam-4425	108	34	∈	∈	PROPN
ejpam-4425	108	35	rs	r	NOUN
ejpam-4425	108	36	are	be	AUX
ejpam-4425	108	37	arbitrary	arbitrary	ADJ
ejpam-4425	108	38	but	but	CCONJ
ejpam-4425	108	39	fixed	fix	VERB
ejpam-4425	108	40	.	.	PUNCT
ejpam-4425	109	1	suppose	suppose	VERB
ejpam-4425	109	2	for	for	ADP
ejpam-4425	109	3	a	a	DET
ejpam-4425	109	4	fixed	fix	VERB
ejpam-4425	109	5	ε>0	ε>0	PROPN
ejpam-4425	109	6	,	,	PUNCT
ejpam-4425	109	7	and	and	CCONJ
ejpam-4425	109	8	from	from	ADP
ejpam-4425	109	9	the	the	DET
ejpam-4425	109	10	continuity	continuity	NOUN
ejpam-4425	109	11	of	of	ADP
ejpam-4425	109	12	f	f	PROPN
ejpam-4425	109	13	at	at	ADP
ejpam-4425	109	14	x	x	PROPN
ejpam-4425	109	15	,	,	PUNCT
ejpam-4425	109	16	∃γ>0	∃γ>0	PROPN
ejpam-4425	109	17	:	:	PUNCT
ejpam-4425	109	18	|f(y)−	|f(y)−	NOUN
ejpam-4425	109	19	f(x)|<ε	f(x)|<ε	PROPN
ejpam-4425	109	20	,	,	PUNCT
ejpam-4425	109	21	∀y	∀y	NUM
ejpam-4425	109	22	∈	∈	NOUN
ejpam-4425	109	23	r	r	NOUN
ejpam-4425	109	24	with	with	ADP
ejpam-4425	109	25	∥y	∥y	PROPN
ejpam-4425	109	26	−	−	PROPN
ejpam-4425	109	27	x∥<ε	x∥<ε	PROPN
ejpam-4425	109	28	,	,	PUNCT
ejpam-4425	109	29	the	the	DET
ejpam-4425	109	30	symbol	symbol	NOUN
ejpam-4425	109	31	∥.∥2	∥.∥2	PROPN
ejpam-4425	109	32	denote	denote	VERB
ejpam-4425	109	33	to	to	ADP
ejpam-4425	109	34	euclidean	euclidean	ADJ
ejpam-4425	109	35	norm	norm	NOUN
ejpam-4425	109	36	.	.	PUNCT
ejpam-4425	110	1	now	now	ADV
ejpam-4425	110	2	we	we	PRON
ejpam-4425	110	3	get	get	VERB
ejpam-4425	110	4	|qm(f	|qm(f	NOUN
ejpam-4425	110	5	;	;	PUNCT
ejpam-4425	110	6	x)−	x)−	PROPN
ejpam-4425	110	7	f(x)|	f(x)|	VERB
ejpam-4425	110	8	≤	≤	NUM
ejpam-4425	110	9	1	1	NUM
ejpam-4425	111	1	[	[	X
ejpam-4425	111	2	φ2	φ2	PROPN
ejpam-4425	111	3	σ(1	σ(1	PROPN
ejpam-4425	111	4	)	)	PUNCT
ejpam-4425	112	1	]	]	PUNCT
ejpam-4425	112	2	s	s	X
ejpam-4425	112	3	∑	∑	PUNCT
ejpam-4425	112	4	∥(n−1k−x)m∥	∥(n−1k−x)m∥	X
ejpam-4425	112	5	<	<	X
ejpam-4425	112	6	γ√	γ√	PROPN
ejpam-4425	112	7	s	s	PART
ejpam-4425	112	8	ψ2	ψ2	NOUN
ejpam-4425	112	9	σ(nx−	σ(nx−	SYM
ejpam-4425	112	10	k	k	X
ejpam-4425	112	11	)	)	PUNCT
ejpam-4425	112	12	∣∣f	∣∣f	NOUN
ejpam-4425	112	13	(	(	PUNCT
ejpam-4425	112	14	(	(	PUNCT
ejpam-4425	112	15	n−1k−	n−1k−	NOUN
ejpam-4425	112	16	x)m	x)m	PUNCT
ejpam-4425	112	17	−	−	PROPN
ejpam-4425	112	18	x	x	SYM
ejpam-4425	112	19	)	)	PUNCT
ejpam-4425	112	20	−	−	PROPN
ejpam-4425	112	21	f(x	f(x	PROPN
ejpam-4425	112	22	)	)	PUNCT
ejpam-4425	112	23	∣∣+	∣∣+	PROPN
ejpam-4425	113	1	1	1	NUM
ejpam-4425	114	1	[	[	X
ejpam-4425	114	2	φ2	φ2	PROPN
ejpam-4425	114	3	σ(1	σ(1	PROPN
ejpam-4425	114	4	)	)	PUNCT
ejpam-4425	114	5	]	]	PUNCT
ejpam-4425	114	6	s	s	VERB
ejpam-4425	114	7	∑	∑	X
ejpam-4425	114	8	∥(n−1k−x)m∥≥	∥(n−1k−x)m∥≥	ADJ
ejpam-4425	114	9	γ√	γ√	PROPN
ejpam-4425	114	10	s	s	PART
ejpam-4425	114	11	ψ2	ψ2	NOUN
ejpam-4425	114	12	σ(nx−	σ(nx−	SYM
ejpam-4425	114	13	k	k	X
ejpam-4425	114	14	)	)	PUNCT
ejpam-4425	114	15	∣∣f	∣∣f	NOUN
ejpam-4425	114	16	(	(	PUNCT
ejpam-4425	114	17	(	(	PUNCT
ejpam-4425	114	18	n−1k−	n−1k−	NOUN
ejpam-4425	114	19	x)m	x)m	PUNCT
ejpam-4425	114	20	−	−	PROPN
ejpam-4425	114	21	x	x	SYM
ejpam-4425	114	22	)	)	PUNCT
ejpam-4425	114	23	−	−	PROPN
ejpam-4425	114	24	f(x	f(x	PROPN
ejpam-4425	114	25	)	)	PUNCT
ejpam-4425	114	26	∣∣	∣∣	NUM
ejpam-4425	114	27	:	:	PUNCT
ejpam-4425	114	28	=	=	SYM
ejpam-4425	114	29	1	1	NUM
ejpam-4425	115	1	[	[	X
ejpam-4425	115	2	φ2	φ2	PROPN
ejpam-4425	115	3	σ(1	σ(1	PROPN
ejpam-4425	115	4	)	)	PUNCT
ejpam-4425	115	5	]	]	PUNCT
ejpam-4425	116	1	s	s	X
ejpam-4425	116	2	(	(	PUNCT
ejpam-4425	116	3	i1	i1	PROPN
ejpam-4425	116	4	+	+	CCONJ
ejpam-4425	116	5	i2	i2	PROPN
ejpam-4425	116	6	)	)	PUNCT
ejpam-4425	116	7	now	now	ADV
ejpam-4425	116	8	using	use	VERB
ejpam-4425	116	9	the	the	DET
ejpam-4425	116	10	continuity	continuity	NOUN
ejpam-4425	116	11	of	of	ADP
ejpam-4425	116	12	f	f	PROPN
ejpam-4425	116	13	and	and	CCONJ
ejpam-4425	116	14	lemma	lemma	PROPN
ejpam-4425	116	15	5	5	NUM
ejpam-4425	116	16	we	we	PRON
ejpam-4425	116	17	get	get	VERB
ejpam-4425	116	18	that∥∥(n−1k−	that∥∥(n−1k−	NOUN
ejpam-4425	116	19	x	x	SYM
ejpam-4425	116	20	)	)	PUNCT
ejpam-4425	116	21	m	m	VERB
ejpam-4425	116	22	−	−	NOUN
ejpam-4425	116	23	x	x	SYM
ejpam-4425	116	24	∥∥	∥∥	PROPN
ejpam-4425	116	25	2	2	NUM
ejpam-4425	116	26	≤	≤	NUM
ejpam-4425	116	27	√	√	NUM
ejpam-4425	116	28	s	s	NOUN
ejpam-4425	116	29	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	116	30	x	x	SYM
ejpam-4425	116	31	)	)	PUNCT
ejpam-4425	116	32	m	m	VERB
ejpam-4425	116	33	−	−	NOUN
ejpam-4425	116	34	x	x	X
ejpam-4425	116	35	∥∥	∥∥	PUNCT
ejpam-4425	116	36	≤	≤	ADV
ejpam-4425	116	37	γ	γ	PROPN
ejpam-4425	116	38	so	so	PROPN
ejpam-4425	116	39	estimation	estimation	PROPN
ejpam-4425	116	40	i1	i1	PROPN
ejpam-4425	116	41	is	be	AUX
ejpam-4425	116	42	,	,	PUNCT
ejpam-4425	116	43	i1	i1	PROPN
ejpam-4425	116	44	<	<	X
ejpam-4425	116	45	ε	ε	PROPN
ejpam-4425	116	46	∑	∑	PUNCT
ejpam-4425	116	47	∥(nx−k)m∥	∥(nx−k)m∥	X
ejpam-4425	116	48	<	<	X
ejpam-4425	116	49	γn√	γn√	PUNCT
ejpam-4425	116	50	s	s	PART
ejpam-4425	116	51	ψ2	ψ2	NOUN
ejpam-4425	116	52	σ(nx−	σ(nx−	SYM
ejpam-4425	116	53	k	k	X
ejpam-4425	116	54	)	)	PUNCT
ejpam-4425	116	55	≤	≤	NUM
ejpam-4425	116	56	ε	ε	PROPN
ejpam-4425	116	57	.	.	PUNCT
ejpam-4425	116	58	i2	i2	PROPN
ejpam-4425	116	59	≤	≤	NUM
ejpam-4425	116	60	2	2	NUM
ejpam-4425	116	61	∥f∥∞	∥f∥∞	ADP
ejpam-4425	116	62	∑	∑	PUNCT
ejpam-4425	116	63	∥(nx−k)m∥≥	∥(nx−k)m∥≥	ADJ
ejpam-4425	116	64	γn√	γn√	NUM
ejpam-4425	116	65	s	s	PART
ejpam-4425	116	66	ψ2	ψ2	NOUN
ejpam-4425	116	67	σ(nx−	σ(nx−	SYM
ejpam-4425	116	68	k	k	X
ejpam-4425	116	69	)	)	PUNCT
ejpam-4425	116	70	≤	≤	NUM
ejpam-4425	116	71	ε	ε	PROPN
ejpam-4425	116	72	.	.	PUNCT
ejpam-4425	117	1	i.j	i.j	PROPN
ejpam-4425	117	2	.	.	PROPN
ejpam-4425	117	3	mohammad	mohammad	PROPN
ejpam-4425	117	4	,	,	PUNCT
ejpam-4425	117	5	a.j	a.j	PROPN
ejpam-4425	117	6	.	.	PROPN
ejpam-4425	117	7	mohammad	mohammad	PROPN
ejpam-4425	117	8	/	/	SYM
ejpam-4425	117	9	eur	eur	PROPN
ejpam-4425	117	10	.	.	PUNCT
ejpam-4425	118	1	j.	j.	PROPN
ejpam-4425	118	2	pure	pure	PROPN
ejpam-4425	118	3	appl	appl	PROPN
ejpam-4425	118	4	.	.	PROPN
ejpam-4425	118	5	math	math	PROPN
ejpam-4425	118	6	,	,	PUNCT
ejpam-4425	118	7	15	15	NUM
ejpam-4425	118	8	(	(	PUNCT
ejpam-4425	118	9	3	3	NUM
ejpam-4425	118	10	)	)	PUNCT
ejpam-4425	118	11	(	(	PUNCT
ejpam-4425	118	12	2022	2022	NUM
ejpam-4425	118	13	)	)	PUNCT
ejpam-4425	118	14	,	,	PUNCT
ejpam-4425	118	15	1189	1189	NUM
ejpam-4425	118	16	-	-	SYM
ejpam-4425	118	17	1200	1200	NUM
ejpam-4425	118	18	1196	1196	NUM
ejpam-4425	118	19	uniformly	uniformly	ADV
ejpam-4425	118	20	∀x	∀x	X
ejpam-4425	118	21	∈	∈	PROPN
ejpam-4425	118	22	rs.the	rs.the	DET
ejpam-4425	118	23	first	first	ADJ
ejpam-4425	118	24	direction	direction	NOUN
ejpam-4425	118	25	of	of	ADP
ejpam-4425	118	26	the	the	DET
ejpam-4425	118	27	theorem	theorem	NOUN
ejpam-4425	118	28	holds	hold	VERB
ejpam-4425	118	29	because	because	SCONJ
ejpam-4425	118	30	ε	ε	PROPN
ejpam-4425	118	31	arbitrarily	arbitrarily	ADV
ejpam-4425	118	32	.	.	PUNCT
ejpam-4425	119	1	when	when	SCONJ
ejpam-4425	119	2	f	f	PROPN
ejpam-4425	119	3	∈	∈	PROPN
ejpam-4425	119	4	c0(r	c0(r	PROPN
ejpam-4425	119	5	)	)	PUNCT
ejpam-4425	119	6	,	,	PUNCT
ejpam-4425	119	7	the	the	DET
ejpam-4425	119	8	prove	prove	NOUN
ejpam-4425	119	9	of	of	ADP
ejpam-4425	119	10	other	other	ADJ
ejpam-4425	119	11	direction	direction	NOUN
ejpam-4425	119	12	is	be	AUX
ejpam-4425	119	13	readily	readily	ADV
ejpam-4425	119	14	followed	follow	VERB
ejpam-4425	119	15	in	in	ADP
ejpam-4425	119	16	the	the	DET
ejpam-4425	119	17	same	same	ADJ
ejpam-4425	119	18	way	way	NOUN
ejpam-4425	119	19	by	by	ADP
ejpam-4425	119	20	exchange	exchange	NOUN
ejpam-4425	119	21	γ>0	γ>0	NOUN
ejpam-4425	119	22	with	with	ADP
ejpam-4425	119	23	the	the	DET
ejpam-4425	119	24	parameter	parameter	NOUN
ejpam-4425	119	25	of	of	ADP
ejpam-4425	119	26	the	the	DET
ejpam-4425	119	27	uniform	uniform	ADJ
ejpam-4425	119	28	continuity	continuity	NOUN
ejpam-4425	119	29	of	of	ADP
ejpam-4425	119	30	f	f	PROPN
ejpam-4425	119	31	on	on	ADP
ejpam-4425	119	32	r.	r.	PROPN
ejpam-4425	119	33	□	□	PUNCT
ejpam-4425	119	34	now	now	ADV
ejpam-4425	119	35	,	,	PUNCT
ejpam-4425	119	36	in	in	ADP
ejpam-4425	119	37	the	the	DET
ejpam-4425	119	38	following	following	NOUN
ejpam-4425	119	39	,	,	PUNCT
ejpam-4425	119	40	study	study	VERB
ejpam-4425	119	41	the	the	DET
ejpam-4425	119	42	order	order	NOUN
ejpam-4425	119	43	of	of	ADP
ejpam-4425	119	44	approximation	approximation	NOUN
ejpam-4425	119	45	of	of	ADP
ejpam-4425	119	46	nn	nn	PROPN
ejpam-4425	119	47	operators	operator	NOUN
ejpam-4425	119	48	in	in	ADP
ejpam-4425	119	49	f	f	PROPN
ejpam-4425	119	50	∈	∈	PROPN
ejpam-4425	119	51	lip(v	lip(v	PROPN
ejpam-4425	119	52	)	)	PUNCT
ejpam-4425	119	53	.	.	PUNCT
ejpam-4425	120	1	theorem	theorem	NOUN
ejpam-4425	120	2	2	2	NUM
ejpam-4425	120	3	.	.	PUNCT
ejpam-4425	120	4	suppose	suppose	VERB
ejpam-4425	120	5	f	f	PROPN
ejpam-4425	120	6	∈	∈	PROPN
ejpam-4425	120	7	lip(v	lip(v	PROPN
ejpam-4425	120	8	)	)	PUNCT
ejpam-4425	120	9	for	for	ADP
ejpam-4425	120	10	some	some	DET
ejpam-4425	120	11	v	v	NOUN
ejpam-4425	120	12	,	,	PUNCT
ejpam-4425	120	13	at	at	ADP
ejpam-4425	120	14	0	0	NUM
ejpam-4425	120	15	<	<	X
ejpam-4425	120	16	v	v	NOUN
ejpam-4425	120	17	≤	≤	NUM
ejpam-4425	120	18	1	1	NUM
ejpam-4425	120	19	,	,	PUNCT
ejpam-4425	120	20	and	and	CCONJ
ejpam-4425	120	21	let	let	VERB
ejpam-4425	120	22	sigmoidal	sigmoidal	NOUN
ejpam-4425	120	23	function	function	NOUN
ejpam-4425	120	24	σ	σ	PROPN
ejpam-4425	120	25	satisfies	satisfy	VERB
ejpam-4425	120	26	the	the	DET
ejpam-4425	120	27	condition	condition	NOUN
ejpam-4425	120	28	(	(	PUNCT
ejpam-4425	120	29	iii	iii	NOUN
ejpam-4425	120	30	)	)	PUNCT
ejpam-4425	120	31	for	for	ADP
ejpam-4425	120	32	∥qm(f	∥qm(f	NOUN
ejpam-4425	120	33	;	;	PUNCT
ejpam-4425	120	34	x)−	x)−	PROPN
ejpam-4425	120	35	f(x)∥∞	f(x)∥∞	PROPN
ejpam-4425	120	36	=	=	SYM
ejpam-4425	120	37	o(n−vm	o(n−vm	PROPN
ejpam-4425	120	38	)	)	PUNCT
ejpam-4425	120	39	,	,	PUNCT
ejpam-4425	120	40	as	as	ADP
ejpam-4425	120	41	n	n	NUM
ejpam-4425	120	42	−→	−→	ADJ
ejpam-4425	120	43	∞.	∞.	PROPN
ejpam-4425	120	44	proof	proof	NOUN
ejpam-4425	120	45	.	.	PUNCT
ejpam-4425	121	1	let	let	VERB
ejpam-4425	121	2	f	f	PROPN
ejpam-4425	121	3	∈	∈	PROPN
ejpam-4425	121	4	lip(v	lip(v	PROPN
ejpam-4425	121	5	)	)	PUNCT
ejpam-4425	121	6	,	,	PUNCT
ejpam-4425	121	7	for	for	ADP
ejpam-4425	121	8	every	every	DET
ejpam-4425	121	9	x	x	SYM
ejpam-4425	121	10	∈	∈	PROPN
ejpam-4425	121	11	r	r	NOUN
ejpam-4425	121	12	,	,	PUNCT
ejpam-4425	121	13	for	for	ADP
ejpam-4425	121	14	some	some	DET
ejpam-4425	121	15	v	v	NOUN
ejpam-4425	121	16	,	,	PUNCT
ejpam-4425	121	17	with	with	ADP
ejpam-4425	121	18	v	v	ADP
ejpam-4425	121	19	∈	∈	NOUN
ejpam-4425	121	20	(	(	PUNCT
ejpam-4425	121	21	0	0	NUM
ejpam-4425	121	22	,	,	PUNCT
ejpam-4425	121	23	1	1	NUM
ejpam-4425	121	24	]	]	PUNCT
ejpam-4425	121	25	,	,	PUNCT
ejpam-4425	121	26	and	and	CCONJ
ejpam-4425	121	27	lemma	lemma	PROPN
ejpam-4425	121	28	6	6	NUM
ejpam-4425	121	29	one	one	NOUN
ejpam-4425	121	30	can	can	AUX
ejpam-4425	121	31	write	write	VERB
ejpam-4425	121	32	as	as	ADP
ejpam-4425	121	33	in	in	ADP
ejpam-4425	121	34	the	the	DET
ejpam-4425	121	35	theorem	theorem	NOUN
ejpam-4425	121	36	1	1	NUM
ejpam-4425	121	37	|qm(f	|qm(f	NOUN
ejpam-4425	121	38	;	;	PUNCT
ejpam-4425	121	39	x)−	x)−	PROPN
ejpam-4425	121	40	f(x)|	f(x)|	VERB
ejpam-4425	122	1	≤	≤	NUM
ejpam-4425	122	2	1	1	NUM
ejpam-4425	123	1	[	[	X
ejpam-4425	123	2	φ2	φ2	PROPN
ejpam-4425	123	3	σ(1	σ(1	PROPN
ejpam-4425	123	4	)	)	PUNCT
ejpam-4425	123	5	]	]	PUNCT
ejpam-4425	123	6	s	s	VERB
ejpam-4425	123	7	∑	∑	PUNCT
ejpam-4425	123	8	k	k	PROPN
ejpam-4425	123	9	ψ2	ψ2	NOUN
ejpam-4425	123	10	σ(nx−	σ(nx−	SYM
ejpam-4425	123	11	k	k	NOUN
ejpam-4425	123	12	)	)	PUNCT
ejpam-4425	123	13	∣∣f	∣∣f	NOUN
ejpam-4425	123	14	(	(	PUNCT
ejpam-4425	123	15	(	(	PUNCT
ejpam-4425	123	16	n−1k−	n−1k−	NOUN
ejpam-4425	123	17	x	x	SYM
ejpam-4425	123	18	)	)	PUNCT
ejpam-4425	123	19	m	m	NOUN
ejpam-4425	123	20	−	−	NOUN
ejpam-4425	123	21	x	x	SYM
ejpam-4425	123	22	)	)	PUNCT
ejpam-4425	124	1	−	−	PROPN
ejpam-4425	124	2	f(x	f(x	PROPN
ejpam-4425	124	3	)	)	PUNCT
ejpam-4425	124	4	∣∣	∣∣	NUM
ejpam-4425	124	5	now	now	ADV
ejpam-4425	124	6	by	by	ADP
ejpam-4425	124	7	using	use	VERB
ejpam-4425	124	8	the	the	DET
ejpam-4425	124	9	definition	definition	NOUN
ejpam-4425	124	10	of	of	ADP
ejpam-4425	124	11	lip(v	lip(v	NOUN
ejpam-4425	124	12	)	)	PUNCT
ejpam-4425	124	13	,	,	PUNCT
ejpam-4425	124	14	where	where	SCONJ
ejpam-4425	124	15	γ>0	γ>0	NOUN
ejpam-4425	124	16	,	,	PUNCT
ejpam-4425	124	17	c>0	c>0	PROPN
ejpam-4425	124	18	are	be	AUX
ejpam-4425	124	19	constants	constant	NOUN
ejpam-4425	124	20	relative	relative	ADJ
ejpam-4425	124	21	to	to	ADP
ejpam-4425	124	22	f	f	PROPN
ejpam-4425	124	23	we	we	PRON
ejpam-4425	124	24	obtain	obtain	VERB
ejpam-4425	124	25	let	let	VERB
ejpam-4425	124	26	x	x	PUNCT
ejpam-4425	124	27	∈	∈	NOUN
ejpam-4425	124	28	r	r	NOUN
ejpam-4425	124	29	the	the	DET
ejpam-4425	124	30	point	point	NOUN
ejpam-4425	124	31	of	of	ADP
ejpam-4425	124	32	continuity	continuity	NOUN
ejpam-4425	124	33	of	of	ADP
ejpam-4425	124	34	f	f	PROPN
ejpam-4425	124	35	|qm(f	|qm(f	PROPN
ejpam-4425	124	36	;	;	PUNCT
ejpam-4425	124	37	x)−	x)−	PROPN
ejpam-4425	124	38	f(x)|	f(x)|	VERB
ejpam-4425	125	1	≤	≤	NUM
ejpam-4425	125	2	1	1	NUM
ejpam-4425	125	3	[	[	X
ejpam-4425	125	4	φ2	φ2	PROPN
ejpam-4425	125	5	σ(1	σ(1	PROPN
ejpam-4425	125	6	)	)	PUNCT
ejpam-4425	125	7	]	]	PUNCT
ejpam-4425	125	8	s	s	X
ejpam-4425	125	9	∑	∑	PUNCT
ejpam-4425	125	10	∥(n−1k−x)m∥	∥(n−1k−x)m∥	X
ejpam-4425	125	11	<	<	X
ejpam-4425	125	12	γ√	γ√	PROPN
ejpam-4425	125	13	s	s	PART
ejpam-4425	125	14	ψ2	ψ2	NOUN
ejpam-4425	125	15	σ(n	σ(n	PROPN
ejpam-4425	125	16	−1k−	−1k−	NOUN
ejpam-4425	125	17	x	x	NOUN
ejpam-4425	125	18	)	)	PUNCT
ejpam-4425	125	19	∣∣f	∣∣f	NOUN
ejpam-4425	125	20	(	(	PUNCT
ejpam-4425	125	21	(	(	PUNCT
ejpam-4425	125	22	n−1k−	n−1k−	NOUN
ejpam-4425	125	23	x)m	x)m	PUNCT
ejpam-4425	125	24	−	−	PROPN
ejpam-4425	125	25	x	x	SYM
ejpam-4425	125	26	)	)	PUNCT
ejpam-4425	125	27	−	−	PROPN
ejpam-4425	125	28	f(x	f(x	PROPN
ejpam-4425	125	29	)	)	PUNCT
ejpam-4425	125	30	∣∣	∣∣	X
ejpam-4425	126	1	+	+	CCONJ
ejpam-4425	126	2	1	1	NUM
ejpam-4425	126	3	[	[	X
ejpam-4425	126	4	φ2	φ2	PROPN
ejpam-4425	126	5	σ(1	σ(1	PROPN
ejpam-4425	126	6	)	)	PUNCT
ejpam-4425	126	7	]	]	PUNCT
ejpam-4425	126	8	s	s	VERB
ejpam-4425	126	9	∑	∑	X
ejpam-4425	126	10	∥(n−1k−x)m∥≥	∥(n−1k−x)m∥≥	ADJ
ejpam-4425	126	11	γ√	γ√	PROPN
ejpam-4425	126	12	s	s	PART
ejpam-4425	126	13	ψ2	ψ2	NOUN
ejpam-4425	126	14	σ(nx−	σ(nx−	SYM
ejpam-4425	126	15	k	k	X
ejpam-4425	126	16	)	)	PUNCT
ejpam-4425	126	17	∣∣f	∣∣f	NOUN
ejpam-4425	126	18	(	(	PUNCT
ejpam-4425	126	19	(	(	PUNCT
ejpam-4425	126	20	n−1k−	n−1k−	NOUN
ejpam-4425	126	21	x)m	x)m	PUNCT
ejpam-4425	126	22	−	−	PROPN
ejpam-4425	126	23	x	x	SYM
ejpam-4425	126	24	)	)	PUNCT
ejpam-4425	126	25	−	−	PROPN
ejpam-4425	126	26	f(x	f(x	PROPN
ejpam-4425	126	27	)	)	PUNCT
ejpam-4425	126	28	∣∣	∣∣	NUM
ejpam-4425	126	29	:	:	PUNCT
ejpam-4425	126	30	=	=	SYM
ejpam-4425	126	31	1	1	NUM
ejpam-4425	127	1	[	[	X
ejpam-4425	127	2	φ2	φ2	PROPN
ejpam-4425	127	3	σ(1	σ(1	PROPN
ejpam-4425	127	4	)	)	PUNCT
ejpam-4425	127	5	]	]	PUNCT
ejpam-4425	128	1	s	s	X
ejpam-4425	128	2	(	(	PUNCT
ejpam-4425	128	3	j1	j1	PROPN
ejpam-4425	128	4	+	+	CCONJ
ejpam-4425	128	5	j2	j2	PROPN
ejpam-4425	128	6	)	)	PUNCT
ejpam-4425	128	7	since	since	SCONJ
ejpam-4425	128	8	f	f	PROPN
ejpam-4425	128	9	∈	∈	PROPN
ejpam-4425	128	10	lip(v	lip(v	PROPN
ejpam-4425	128	11	)	)	PUNCT
ejpam-4425	128	12	,	,	PUNCT
ejpam-4425	128	13	we	we	PRON
ejpam-4425	128	14	get	get	VERB
ejpam-4425	128	15	for	for	ADP
ejpam-4425	128	16	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	128	17	x	x	SYM
ejpam-4425	128	18	)	)	PUNCT
ejpam-4425	128	19	m	m	VERB
ejpam-4425	128	20	−	−	NOUN
ejpam-4425	128	21	x	x	SYM
ejpam-4425	128	22	∥∥	∥∥	PROPN
ejpam-4425	128	23	2	2	NUM
ejpam-4425	128	24	≤	≤	NUM
ejpam-4425	128	25	√	√	NUM
ejpam-4425	128	26	s	s	NOUN
ejpam-4425	128	27	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	128	28	x	x	SYM
ejpam-4425	128	29	)	)	PUNCT
ejpam-4425	128	30	m	m	VERB
ejpam-4425	128	31	−	−	NOUN
ejpam-4425	128	32	x	x	X
ejpam-4425	128	33	∥∥	∥∥	PUNCT
ejpam-4425	128	34	≤	≤	ADV
ejpam-4425	128	35	γ	γ	NOUN
ejpam-4425	128	36	and	and	CCONJ
ejpam-4425	128	37	hence	hence	ADV
ejpam-4425	128	38	|f	|f	PROPN
ejpam-4425	128	39	(	(	PUNCT
ejpam-4425	128	40	(	(	PUNCT
ejpam-4425	128	41	nx−	nx−	X
ejpam-4425	128	42	k)m	k)m	PROPN
ejpam-4425	129	1	−	−	PROPN
ejpam-4425	129	2	x)−	x)−	PROPN
ejpam-4425	129	3	f(x)|<c	f(x)|<c	VERB
ejpam-4425	129	4	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	129	5	x	x	SYM
ejpam-4425	129	6	)	)	PUNCT
ejpam-4425	129	7	m∥∥v	m∥∥v	NOUN
ejpam-4425	129	8	2	2	NUM
ejpam-4425	129	9	≤	≤	NUM
ejpam-4425	129	10	cs	cs	PROPN
ejpam-4425	129	11	v	v	ADP
ejpam-4425	129	12	2	2	NUM
ejpam-4425	129	13	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	129	14	x	x	X
ejpam-4425	129	15	)	)	PUNCT
ejpam-4425	129	16	m∥∥v	m∥∥v	NOUN
ejpam-4425	129	17	j1	j1	PROPN
ejpam-4425	129	18	<	<	X
ejpam-4425	129	19	n−vmcs	n−vmcs	PROPN
ejpam-4425	129	20	v	v	ADP
ejpam-4425	129	21	2	2	NUM
ejpam-4425	129	22	∑	∑	SYM
ejpam-4425	129	23	∥(nx−k)m∥	∥(nx−k)m∥	NOUN
ejpam-4425	129	24	<	<	X
ejpam-4425	129	25	γn√	γn√	PUNCT
ejpam-4425	129	26	s	s	PART
ejpam-4425	129	27	ψ2	ψ2	NOUN
ejpam-4425	129	28	σ(nx−	σ(nx−	SYM
ejpam-4425	129	29	k	k	X
ejpam-4425	129	30	)	)	PUNCT
ejpam-4425	129	31	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	129	32	x	x	X
ejpam-4425	129	33	)	)	PUNCT
ejpam-4425	129	34	m∥∥v	m∥∥v	NOUN
ejpam-4425	129	35	for	for	SCONJ
ejpam-4425	129	36	fixed	fix	VERB
ejpam-4425	129	37	0	0	NUM
ejpam-4425	129	38	<	<	X
ejpam-4425	129	39	vi	vi	X
ejpam-4425	129	40	<	<	X
ejpam-4425	129	41	α	α	NOUN
ejpam-4425	129	42	,	,	PUNCT
ejpam-4425	129	43	by	by	ADP
ejpam-4425	129	44	using	use	VERB
ejpam-4425	129	45	lemma	lemma	PROPN
ejpam-4425	129	46	5	5	NUM
ejpam-4425	129	47	,	,	PUNCT
ejpam-4425	129	48	for	for	ADP
ejpam-4425	129	49	a	a	DET
ejpam-4425	129	50	compact	compact	ADJ
ejpam-4425	129	51	subset	subset	NOUN
ejpam-4425	130	1	k	k	PROPN
ejpam-4425	130	2	⊂	⊂	PROPN
ejpam-4425	130	3	rs	rs	PROPN
ejpam-4425	130	4	,	,	PUNCT
ejpam-4425	130	5	for	for	ADP
ejpam-4425	130	6	every	every	DET
ejpam-4425	130	7	x	x	PROPN
ejpam-4425	130	8	∈	∈	PROPN
ejpam-4425	130	9	rs	rs	NOUN
ejpam-4425	130	10	,	,	PUNCT
ejpam-4425	130	11	if	if	SCONJ
ejpam-4425	130	12	n	n	CCONJ
ejpam-4425	130	13	−→	−→	NOUN
ejpam-4425	130	14	∞	∞	PROPN
ejpam-4425	130	15	can	can	AUX
ejpam-4425	130	16	write	write	VERB
ejpam-4425	130	17	the	the	DET
ejpam-4425	130	18	following	following	NOUN
ejpam-4425	130	19	:	:	PUNCT
ejpam-4425	130	20	j1	j1	PROPN
ejpam-4425	130	21	≤	≤	PUNCT
ejpam-4425	130	22	n−vmcs	n−vmcs	PROPN
ejpam-4425	130	23	v	v	ADP
ejpam-4425	130	24	2	2	NUM
ejpam-4425	130	25	∑	∑	SYM
ejpam-4425	130	26	∥(nx−k)m∥	∥(nx−k)m∥	NOUN
ejpam-4425	130	27	<	<	X
ejpam-4425	130	28	γn√	γn√	PUNCT
ejpam-4425	130	29	s	s	PART
ejpam-4425	130	30	ψ2	ψ2	NOUN
ejpam-4425	130	31	σ(nx−	σ(nx−	SYM
ejpam-4425	130	32	k	k	X
ejpam-4425	130	33	)	)	PUNCT
ejpam-4425	130	34	∥∥(n−1k−	∥∥(n−1k−	NOUN
ejpam-4425	130	35	x	x	X
ejpam-4425	130	36	)	)	PUNCT
ejpam-4425	130	37	m∥∥v	m∥∥v	PROPN
ejpam-4425	130	38	i.j	i.j	PROPN
ejpam-4425	130	39	.	.	PROPN
ejpam-4425	130	40	mohammad	mohammad	PROPN
ejpam-4425	130	41	,	,	PUNCT
ejpam-4425	130	42	a.j	a.j	PROPN
ejpam-4425	130	43	.	.	PROPN
ejpam-4425	130	44	mohammad	mohammad	PROPN
ejpam-4425	130	45	/	/	SYM
ejpam-4425	130	46	eur	eur	PROPN
ejpam-4425	130	47	.	.	PUNCT
ejpam-4425	131	1	j.	j.	PROPN
ejpam-4425	131	2	pure	pure	PROPN
ejpam-4425	131	3	appl	appl	PROPN
ejpam-4425	131	4	.	.	PROPN
ejpam-4425	131	5	math	math	PROPN
ejpam-4425	131	6	,	,	PUNCT
ejpam-4425	131	7	15	15	NUM
ejpam-4425	131	8	(	(	PUNCT
ejpam-4425	131	9	3	3	NUM
ejpam-4425	131	10	)	)	PUNCT
ejpam-4425	131	11	(	(	PUNCT
ejpam-4425	131	12	2022	2022	NUM
ejpam-4425	131	13	)	)	PUNCT
ejpam-4425	131	14	,	,	PUNCT
ejpam-4425	131	15	1189	1189	NUM
ejpam-4425	131	16	-	-	SYM
ejpam-4425	131	17	1200	1200	NUM
ejpam-4425	131	18	1197	1197	NUM
ejpam-4425	131	19	≤	≤	NOUN
ejpam-4425	131	20	n−vmcs	n−vmcs	PROPN
ejpam-4425	131	21	v	v	ADP
ejpam-4425	131	22	2	2	NUM
ejpam-4425	131	23	s∑	s∑	PROPN
ejpam-4425	131	24	j=1	j=1	PROPN
ejpam-4425	131	25	∑	∑	PROPN
ejpam-4425	131	26	kj∈z	kj∈z	PROPN
ejpam-4425	131	27	φ2	φ2	PROPN
ejpam-4425	131	28	σ(nxj	σ(nxj	PROPN
ejpam-4425	131	29	−	−	ADP
ejpam-4425	131	30	kj	kj	PROPN
ejpam-4425	131	31	)	)	PUNCT
ejpam-4425	131	32	|nxj	|nxj	VERB
ejpam-4425	131	33	−	−	PROPN
ejpam-4425	131	34	kj	kj	PROPN
ejpam-4425	131	35	|vm	|vm	X
ejpam-4425	131	36			PROPN
ejpam-4425	131	37	∑	∑	PROPN
ejpam-4425	131	38	k[j]∈zs−1	k[j]∈zs−1	PROPN
ejpam-4425	131	39	ψ2[j	ψ2[j	PROPN
ejpam-4425	131	40	]	]	X
ejpam-4425	132	1	σ	σ	PROPN
ejpam-4425	132	2	(	(	PUNCT
ejpam-4425	132	3	nx[j	nx[j	PROPN
ejpam-4425	132	4	]	]	X
ejpam-4425	132	5	−	−	PROPN
ejpam-4425	132	6	k[j	k[j	PROPN
ejpam-4425	132	7	]	]	PUNCT
ejpam-4425	132	8	)	)	PUNCT
ejpam-4425	132	9			X
ejpam-4425	132	10	where	where	SCONJ
ejpam-4425	132	11	ψ2[j	ψ2[j	NOUN
ejpam-4425	132	12	]	]	X
ejpam-4425	132	13	σ	σ	PROPN
ejpam-4425	132	14	(	(	PUNCT
ejpam-4425	132	15	nx[j	nx[j	PROPN
ejpam-4425	132	16	]	]	X
ejpam-4425	132	17	−	−	PROPN
ejpam-4425	132	18	k[j	k[j	NOUN
ejpam-4425	132	19	]	]	PUNCT
ejpam-4425	132	20	)	)	PUNCT
ejpam-4425	132	21	=	=	SYM
ejpam-4425	132	22	φ2	φ2	NOUN
ejpam-4425	132	23	σ(nx1	σ(nx1	PROPN
ejpam-4425	132	24	−	−	PROPN
ejpam-4425	132	25	k1	k1	PROPN
ejpam-4425	132	26	)	)	PUNCT
ejpam-4425	132	27	·	·	PUNCT
ejpam-4425	132	28	...	...	PUNCT
ejpam-4425	132	29	·	·	PUNCT
ejpam-4425	132	30	φ2	φ2	ADJ
ejpam-4425	132	31	σ(nxj−1	σ(nxj−1	NOUN
ejpam-4425	132	32	−	−	PROPN
ejpam-4425	132	33	kj−1	kj−1	PROPN
ejpam-4425	132	34	)	)	PUNCT
ejpam-4425	132	35	·	·	PUNCT
ejpam-4425	132	36	φ2	φ2	NOUN
ejpam-4425	132	37	σ(nxj+1	σ(nxj+1	VERB
ejpam-4425	132	38	−	−	PROPN
ejpam-4425	132	39	kj+1	kj+1	X
ejpam-4425	132	40	)	)	PUNCT
ejpam-4425	132	41	·	·	PUNCT
ejpam-4425	132	42	...	...	PUNCT
ejpam-4425	133	1	·	·	PUNCT
ejpam-4425	133	2	φ2	φ2	NOUN
ejpam-4425	133	3	σ(nxs	σ(nxs	PROPN
ejpam-4425	134	1	−	−	PROPN
ejpam-4425	134	2	ks	ks	PROPN
ejpam-4425	134	3	)	)	PUNCT
ejpam-4425	134	4	,	,	PUNCT
ejpam-4425	134	5	notice	notice	VERB
ejpam-4425	134	6	for	for	ADP
ejpam-4425	134	7	every	every	DET
ejpam-4425	134	8	j	j	PROPN
ejpam-4425	134	9	=	=	SYM
ejpam-4425	134	10	1	1	NUM
ejpam-4425	134	11	,	,	PUNCT
ejpam-4425	134	12	...	...	PUNCT
ejpam-4425	134	13	,	,	PUNCT
ejpam-4425	134	14	s	s	VERB
ejpam-4425	134	15	x[j	x[j	X
ejpam-4425	134	16	]	]	X
ejpam-4425	134	17	=	=	SYM
ejpam-4425	134	18	(	(	PUNCT
ejpam-4425	134	19	x1	x1	PROPN
ejpam-4425	134	20	,	,	PUNCT
ejpam-4425	134	21	...	...	PUNCT
ejpam-4425	134	22	,	,	PUNCT
ejpam-4425	134	23	xj−1	xj−1	PROPN
ejpam-4425	134	24	,	,	PUNCT
ejpam-4425	134	25	xj+1	xj+1	NUM
ejpam-4425	134	26	,	,	PUNCT
ejpam-4425	134	27	...	...	PUNCT
ejpam-4425	134	28	,	,	PUNCT
ejpam-4425	134	29	xs	xs	PROPN
ejpam-4425	134	30	)	)	PUNCT
ejpam-4425	134	31	∈	∈	PROPN
ejpam-4425	134	32	rs−1	rs−1	PROPN
ejpam-4425	134	33	,	,	PUNCT
ejpam-4425	134	34	k[j	k[j	NOUN
ejpam-4425	134	35	]	]	X
ejpam-4425	134	36	=	=	SYM
ejpam-4425	134	37	(	(	PUNCT
ejpam-4425	134	38	k1	k1	PROPN
ejpam-4425	134	39	,	,	PUNCT
ejpam-4425	134	40	...	...	PUNCT
ejpam-4425	134	41	,	,	PUNCT
ejpam-4425	134	42	kj−1	kj−1	PROPN
ejpam-4425	134	43	,	,	PUNCT
ejpam-4425	134	44	kj+1	kj+1	PROPN
ejpam-4425	134	45	,	,	PUNCT
ejpam-4425	134	46	...	...	PUNCT
ejpam-4425	134	47	,	,	PUNCT
ejpam-4425	134	48	ks	ks	NOUN
ejpam-4425	134	49	)	)	PUNCT
ejpam-4425	134	50	∈	∈	PROPN
ejpam-4425	134	51	zs−1	zs−1	PROPN
ejpam-4425	134	52	.	.	PUNCT
ejpam-4425	135	1	now	now	ADV
ejpam-4425	135	2	k[j	k[j	X
ejpam-4425	135	3	]	]	X
ejpam-4425	136	1	⊂	⊂	X
ejpam-4425	136	2	r	r	VERB
ejpam-4425	136	3	the	the	DET
ejpam-4425	136	4	set	set	NOUN
ejpam-4425	136	5	of	of	ADP
ejpam-4425	136	6	the	the	DET
ejpam-4425	136	7	j	j	PROPN
ejpam-4425	136	8	-	-	PUNCT
ejpam-4425	136	9	th	th	PROPN
ejpam-4425	136	10	projection	projection	NOUN
ejpam-4425	136	11	of	of	ADP
ejpam-4425	136	12	a	a	DET
ejpam-4425	136	13	compact	compact	ADJ
ejpam-4425	136	14	set	set	NOUN
ejpam-4425	136	15	of	of	ADP
ejpam-4425	136	16	all	all	DET
ejpam-4425	136	17	elements	element	NOUN
ejpam-4425	136	18	.	.	PUNCT
ejpam-4425	137	1	by	by	ADP
ejpam-4425	137	2	using	use	VERB
ejpam-4425	137	3	lemma	lemma	PROPN
ejpam-4425	137	4	5	5	NUM
ejpam-4425	137	5	and	and	CCONJ
ejpam-4425	137	6	for	for	ADP
ejpam-4425	137	7	all	all	DET
ejpam-4425	137	8	sufficiently	sufficiently	ADV
ejpam-4425	137	9	large	large	ADJ
ejpam-4425	137	10	n	n	PRON
ejpam-4425	137	11	∈	∈	NOUN
ejpam-4425	137	12	n+	n+	PUNCT
ejpam-4425	137	13	one	one	PRON
ejpam-4425	137	14	can	can	AUX
ejpam-4425	137	15	obtain	obtain	VERB
ejpam-4425	137	16	≤	≤	NOUN
ejpam-4425	137	17	(	(	PUNCT
ejpam-4425	137	18	0.156517)s−1n−vmcs	0.156517)s−1n−vmcs	NUM
ejpam-4425	137	19	v	v	NOUN
ejpam-4425	137	20	2	2	NUM
ejpam-4425	137	21	s∑	s∑	PROPN
ejpam-4425	137	22	j=1	j=1	PROPN
ejpam-4425	137	23	∑	∑	PROPN
ejpam-4425	137	24	kj∈z	kj∈z	PROPN
ejpam-4425	137	25	φ2	φ2	PROPN
ejpam-4425	137	26	σ(nxj	σ(nxj	PROPN
ejpam-4425	137	27	−	−	ADP
ejpam-4425	137	28	kj	kj	PROPN
ejpam-4425	137	29	)	)	PUNCT
ejpam-4425	137	30	|nxj	|nxj	VERB
ejpam-4425	137	31	−	−	PROPN
ejpam-4425	137	32	kj	kj	NOUN
ejpam-4425	137	33	|vm	|vm	X
ejpam-4425	138	1			PROPN
ejpam-4425	138	2	≤	≤	PROPN
ejpam-4425	138	3	(	(	PUNCT
ejpam-4425	138	4	0.156517)s−1n−vmcs1	0.156517)s−1n−vmcs1	NOUN
ejpam-4425	138	5	+	+	NOUN
ejpam-4425	138	6	v	v	ADP
ejpam-4425	138	7	2mvm(φ2	2mvm(φ2	NUM
ejpam-4425	138	8	σ	σ	NOUN
ejpam-4425	138	9	)	)	PUNCT
ejpam-4425	138	10	note	note	NOUN
ejpam-4425	138	11	that	that	SCONJ
ejpam-4425	138	12	mvm(φ2	mvm(φ2	PROPN
ejpam-4425	138	13	σ	σ	PROPN
ejpam-4425	138	14	)	)	PUNCT
ejpam-4425	138	15	≤	≤	NOUN
ejpam-4425	138	16	∞	∞	PROPN
ejpam-4425	138	17	,	,	PUNCT
ejpam-4425	138	18	where	where	SCONJ
ejpam-4425	138	19	mvm(φ2	mvm(φ2	PROPN
ejpam-4425	138	20	σ	σ	PROPN
ejpam-4425	138	21	)	)	PUNCT
ejpam-4425	138	22	give	give	VERB
ejpam-4425	138	23	in	in	ADP
ejpam-4425	138	24	definition	definition	NOUN
ejpam-4425	138	25	5	5	NUM
ejpam-4425	138	26	,	,	PUNCT
ejpam-4425	138	27	since	since	SCONJ
ejpam-4425	138	28	v	v	ADP
ejpam-4425	138	29	<	<	X
ejpam-4425	138	30	α	α	DET
ejpam-4425	138	31	one	one	NOUN
ejpam-4425	138	32	can	can	AUX
ejpam-4425	138	33	obtain	obtain	VERB
ejpam-4425	138	34	:	:	PUNCT
ejpam-4425	138	35	j1	j1	PROPN
ejpam-4425	138	36	=	=	SYM
ejpam-4425	138	37	o(n−vm	o(n−vm	PROPN
ejpam-4425	138	38	)	)	PUNCT
ejpam-4425	138	39	,	,	PUNCT
ejpam-4425	138	40	as	as	ADP
ejpam-4425	138	41	n	n	PRON
ejpam-4425	138	42	−→	−→	NOUN
ejpam-4425	138	43	∞	∞	PROPN
ejpam-4425	138	44	,	,	PUNCT
ejpam-4425	138	45	now	now	ADV
ejpam-4425	138	46	,	,	PUNCT
ejpam-4425	138	47	we	we	PRON
ejpam-4425	138	48	estimate	estimate	VERB
ejpam-4425	138	49	j2	j2	PROPN
ejpam-4425	138	50	by	by	ADP
ejpam-4425	138	51	using	use	VERB
ejpam-4425	138	52	the	the	DET
ejpam-4425	138	53	other	other	ADJ
ejpam-4425	138	54	direction	direction	NOUN
ejpam-4425	138	55	of	of	ADP
ejpam-4425	138	56	lemma	lemma	PROPN
ejpam-4425	138	57	5	5	NUM
ejpam-4425	138	58	,	,	PUNCT
ejpam-4425	138	59	i2	i2	PROPN
ejpam-4425	138	60	≤	≤	ADV
ejpam-4425	138	61	2	2	NUM
ejpam-4425	138	62	∥f∥∞	∥f∥∞	ADP
ejpam-4425	138	63	∑	∑	PUNCT
ejpam-4425	138	64	∥(nx−k)m∥≥	∥(nx−k)m∥≥	ADJ
ejpam-4425	138	65	γn√	γn√	NUM
ejpam-4425	139	1	s	s	PART
ejpam-4425	139	2	ψ2	ψ2	NOUN
ejpam-4425	139	3	σ(nx−	σ(nx−	SYM
ejpam-4425	139	4	k	k	X
ejpam-4425	139	5	)	)	PUNCT
ejpam-4425	139	6	=	=	SYM
ejpam-4425	139	7	o(n−vm	o(n−vm	PROPN
ejpam-4425	139	8	)	)	PUNCT
ejpam-4425	139	9	,	,	PUNCT
ejpam-4425	139	10	as	as	SCONJ
ejpam-4425	139	11	n	n	NUM
ejpam-4425	139	12	−→	−→	ADJ
ejpam-4425	139	13	∞.	∞.	PROPN
ejpam-4425	139	14	□	□	PUNCT
ejpam-4425	139	15	theorem	theorem	ADJ
ejpam-4425	139	16	3	3	X
ejpam-4425	139	17	.	.	PUNCT
ejpam-4425	140	1	let	let	VERB
ejpam-4425	140	2	the	the	DET
ejpam-4425	140	3	function	function	NOUN
ejpam-4425	140	4	σ	σ	NOUN
ejpam-4425	140	5	for	for	ADP
ejpam-4425	140	6	some	some	DET
ejpam-4425	140	7	α	α	NOUN
ejpam-4425	140	8	∈	∈	PROPN
ejpam-4425	140	9	(	(	PUNCT
ejpam-4425	140	10	0	0	NUM
ejpam-4425	140	11	,	,	PUNCT
ejpam-4425	140	12	1	1	NUM
ejpam-4425	140	13	]	]	PUNCT
ejpam-4425	140	14	satisfy	satisfy	VERB
ejpam-4425	140	15	the	the	DET
ejpam-4425	140	16	condition	condition	NOUN
ejpam-4425	140	17	(	(	PUNCT
ejpam-4425	140	18	iii	iii	NOUN
ejpam-4425	140	19	)	)	PUNCT
ejpam-4425	140	20	,	,	PUNCT
ejpam-4425	140	21	and	and	CCONJ
ejpam-4425	140	22	let	let	VERB
ejpam-4425	140	23	f	f	PROPN
ejpam-4425	140	24	∈	∈	PROPN
ejpam-4425	140	25	lip(v	lip(v	PROPN
ejpam-4425	140	26	)	)	PUNCT
ejpam-4425	140	27	for	for	ADP
ejpam-4425	140	28	some	some	DET
ejpam-4425	140	29	v	v	NOUN
ejpam-4425	140	30	∈	∈	NOUN
ejpam-4425	140	31	(	(	PUNCT
ejpam-4425	140	32	0	0	NUM
ejpam-4425	140	33	,	,	PUNCT
ejpam-4425	140	34	1	1	NUM
ejpam-4425	140	35	]	]	PUNCT
ejpam-4425	140	36	,	,	PUNCT
ejpam-4425	140	37	then	then	ADV
ejpam-4425	140	38	we	we	PRON
ejpam-4425	140	39	have	have	VERB
ejpam-4425	140	40	,	,	PUNCT
ejpam-4425	140	41	(	(	PUNCT
ejpam-4425	140	42	i	i	NOUN
ejpam-4425	140	43	)	)	PUNCT
ejpam-4425	140	44	∥qm(f	∥qm(f	NOUN
ejpam-4425	140	45	;	;	PUNCT
ejpam-4425	140	46	.)−	.)−	PROPN
ejpam-4425	140	47	f(.)∥∞	f(.)∥∞	PROPN
ejpam-4425	140	48	=	=	SYM
ejpam-4425	140	49	o(n−vm	o(n−vm	PROPN
ejpam-4425	140	50	)	)	PUNCT
ejpam-4425	140	51	,	,	PUNCT
ejpam-4425	140	52	as	as	ADP
ejpam-4425	140	53	n	n	PRON
ejpam-4425	140	54	−→	−→	NOUN
ejpam-4425	140	55	∞	∞	NUM
ejpam-4425	140	56	if	if	SCONJ
ejpam-4425	140	57	v	v	ADP
ejpam-4425	140	58	<	<	X
ejpam-4425	140	59	α	α	X
ejpam-4425	140	60	;	;	PUNCT
ejpam-4425	140	61	(	(	PUNCT
ejpam-4425	140	62	ii	ii	NOUN
ejpam-4425	140	63	)	)	PUNCT
ejpam-4425	140	64	∥qm(f	∥qm(f	NOUN
ejpam-4425	140	65	;	;	PUNCT
ejpam-4425	140	66	.)−	.)−	PROPN
ejpam-4425	140	67	f(.)∥∞	f(.)∥∞	PROPN
ejpam-4425	140	68	=	=	SYM
ejpam-4425	140	69	o(n−(α−ε)m	o(n−(α−ε)m	PROPN
ejpam-4425	140	70	)	)	PUNCT
ejpam-4425	140	71	,	,	PUNCT
ejpam-4425	140	72	as	as	ADP
ejpam-4425	140	73	n	n	PRON
ejpam-4425	140	74	−→	−→	NOUN
ejpam-4425	140	75	∞	∞	PROPN
ejpam-4425	140	76	,	,	PUNCT
ejpam-4425	140	77	for	for	ADP
ejpam-4425	140	78	every	every	DET
ejpam-4425	140	79	0	0	NUM
ejpam-4425	140	80	<	<	X
ejpam-4425	140	81	ε	ε	X
ejpam-4425	140	82	<	<	X
ejpam-4425	140	83	α	α	X
ejpam-4425	140	84	,	,	PUNCT
ejpam-4425	140	85	if	if	SCONJ
ejpam-4425	140	86	α	α	DET
ejpam-4425	140	87	≤	≤	NUM
ejpam-4425	140	88	v<1	v<1	NOUN
ejpam-4425	140	89	.	.	PUNCT
ejpam-4425	141	1	proof	proof	NOUN
ejpam-4425	141	2	.	.	PUNCT
ejpam-4425	142	1	(	(	PUNCT
ejpam-4425	142	2	i	i	NOUN
ejpam-4425	142	3	)	)	PUNCT
ejpam-4425	142	4	using	use	VERB
ejpam-4425	142	5	the	the	DET
ejpam-4425	142	6	same	same	ADJ
ejpam-4425	142	7	step	step	NOUN
ejpam-4425	142	8	of	of	ADP
ejpam-4425	142	9	the	the	DET
ejpam-4425	142	10	”	"	PUNCT
ejpam-4425	142	11	theorm	theorm	NOUN
ejpam-4425	142	12	2	2	NUM
ejpam-4425	142	13	”	"	PUNCT
ejpam-4425	142	14	we	we	PRON
ejpam-4425	142	15	can	can	AUX
ejpam-4425	142	16	obtain	obtain	VERB
ejpam-4425	142	17	proving	prove	VERB
ejpam-4425	142	18	∥qm(f	∥qm(f	NOUN
ejpam-4425	142	19	;	;	PUNCT
ejpam-4425	142	20	.)−	.)−	PROPN
ejpam-4425	142	21	f(.)∥∞	f(.)∥∞	PROPN
ejpam-4425	142	22	=	=	SYM
ejpam-4425	142	23	o(n−vm	o(n−vm	PROPN
ejpam-4425	142	24	)	)	PUNCT
ejpam-4425	142	25	,	,	PUNCT
ejpam-4425	142	26	as	as	ADP
ejpam-4425	142	27	n	n	PRON
ejpam-4425	142	28	−→	−→	NOUN
ejpam-4425	142	29	∞	∞	PROPN
ejpam-4425	142	30	(	(	PUNCT
ejpam-4425	142	31	ii	ii	NOUN
ejpam-4425	142	32	)	)	PUNCT
ejpam-4425	142	33	as	as	ADP
ejpam-4425	142	34	a	a	DET
ejpam-4425	142	35	special	special	ADJ
ejpam-4425	142	36	case	case	NOUN
ejpam-4425	142	37	for	for	ADP
ejpam-4425	142	38	all	all	DET
ejpam-4425	142	39	f	f	PROPN
ejpam-4425	142	40	∈	∈	PROPN
ejpam-4425	142	41	lip(v	lip(v	PROPN
ejpam-4425	142	42	)	)	PUNCT
ejpam-4425	142	43	with	with	ADP
ejpam-4425	142	44	α	α	PROPN
ejpam-4425	142	45	≤	≤	NUM
ejpam-4425	142	46	v	v	ADP
ejpam-4425	142	47	≤	≤	NUM
ejpam-4425	142	48	1	1	NUM
ejpam-4425	142	49	,	,	PUNCT
ejpam-4425	142	50	with	with	ADP
ejpam-4425	142	51	ε	ε	PROPN
ejpam-4425	142	52	is	be	AUX
ejpam-4425	142	53	fixed	fix	VERB
ejpam-4425	142	54	but	but	CCONJ
ejpam-4425	142	55	arbitrary	arbitrary	ADJ
ejpam-4425	142	56	choose	choose	VERB
ejpam-4425	142	57	β	β	X
ejpam-4425	142	58	:	:	PUNCT
ejpam-4425	142	59	=	=	SYM
ejpam-4425	142	60	α−	α−	ADP
ejpam-4425	142	61	ε	ε	PROPN
ejpam-4425	142	62	,	,	PUNCT
ejpam-4425	142	63	and	and	CCONJ
ejpam-4425	142	64	get	get	VERB
ejpam-4425	142	65	0	0	NUM
ejpam-4425	142	66	<	<	X
ejpam-4425	142	67	β	β	X
ejpam-4425	142	68	<	<	X
ejpam-4425	142	69	α	α	X
ejpam-4425	142	70	,	,	PUNCT
ejpam-4425	142	71	by	by	ADP
ejpam-4425	142	72	based	base	VERB
ejpam-4425	142	73	on	on	ADP
ejpam-4425	142	74	part	part	NOUN
ejpam-4425	142	75	(	(	PUNCT
ejpam-4425	142	76	i	i	NOUN
ejpam-4425	142	77	)	)	PUNCT
ejpam-4425	142	78	we	we	PRON
ejpam-4425	142	79	obtain	obtain	VERB
ejpam-4425	142	80	,	,	PUNCT
ejpam-4425	142	81	∥qm(f	∥qm(f	NOUN
ejpam-4425	142	82	;	;	PUNCT
ejpam-4425	143	1	.)−	.)−	PROPN
ejpam-4425	143	2	f(.)∥∞	f(.)∥∞	PROPN
ejpam-4425	143	3	=	=	SYM
ejpam-4425	143	4	o(n−βm	o(n−βm	NOUN
ejpam-4425	143	5	)	)	PUNCT
ejpam-4425	143	6	=	=	SYM
ejpam-4425	143	7	o(n−(α−ε)m	o(n−(α−ε)m	PROPN
ejpam-4425	143	8	)	)	PUNCT
ejpam-4425	143	9	,	,	PUNCT
ejpam-4425	143	10	as	as	ADP
ejpam-4425	143	11	n	n	PRON
ejpam-4425	143	12	−→	−→	NOUN
ejpam-4425	143	13	∞	∞	NUM
ejpam-4425	143	14	for	for	ADP
ejpam-4425	143	15	function	function	NOUN
ejpam-4425	143	16	f	f	PROPN
ejpam-4425	143	17	∈	∈	PROPN
ejpam-4425	143	18	lip(β	lip(β	PROPN
ejpam-4425	143	19	)	)	PUNCT
ejpam-4425	143	20	,	,	PUNCT
ejpam-4425	143	21	0	0	NUM
ejpam-4425	143	22	<	<	X
ejpam-4425	143	23	ε	ε	X
ejpam-4425	143	24	<	<	X
ejpam-4425	143	25	α	α	X
ejpam-4425	143	26	.	.	PUNCT
ejpam-4425	144	1	□	□	PUNCT
ejpam-4425	144	2	i.j	i.j	PROPN
ejpam-4425	144	3	.	.	PROPN
ejpam-4425	144	4	mohammad	mohammad	PROPN
ejpam-4425	144	5	,	,	PUNCT
ejpam-4425	144	6	a.j	a.j	PROPN
ejpam-4425	144	7	.	.	PROPN
ejpam-4425	144	8	mohammad	mohammad	PROPN
ejpam-4425	144	9	/	/	SYM
ejpam-4425	144	10	eur	eur	PROPN
ejpam-4425	144	11	.	.	PUNCT
ejpam-4425	145	1	j.	j.	PROPN
ejpam-4425	145	2	pure	pure	PROPN
ejpam-4425	145	3	appl	appl	PROPN
ejpam-4425	145	4	.	.	PROPN
ejpam-4425	145	5	math	math	PROPN
ejpam-4425	145	6	,	,	PUNCT
ejpam-4425	145	7	15	15	NUM
ejpam-4425	145	8	(	(	PUNCT
ejpam-4425	145	9	3	3	NUM
ejpam-4425	145	10	)	)	PUNCT
ejpam-4425	145	11	(	(	PUNCT
ejpam-4425	145	12	2022	2022	NUM
ejpam-4425	145	13	)	)	PUNCT
ejpam-4425	145	14	,	,	PUNCT
ejpam-4425	145	15	1189	1189	NUM
ejpam-4425	145	16	-	-	SYM
ejpam-4425	145	17	1200	1200	NUM
ejpam-4425	145	18	1198	1198	NUM
ejpam-4425	145	19	4	4	NUM
ejpam-4425	145	20	.	.	PUNCT
ejpam-4425	145	21	numerical	numerical	ADJ
ejpam-4425	145	22	examples	example	NOUN
ejpam-4425	145	23	this	this	DET
ejpam-4425	145	24	section	section	NOUN
ejpam-4425	145	25	gives	give	VERB
ejpam-4425	145	26	numerical	numerical	ADJ
ejpam-4425	145	27	examples	example	NOUN
ejpam-4425	145	28	for	for	ADP
ejpam-4425	145	29	the	the	DET
ejpam-4425	145	30	real	real	ADJ
ejpam-4425	145	31	value	value	NOUN
ejpam-4425	145	32	of	of	ADP
ejpam-4425	145	33	n	n	NOUN
ejpam-4425	145	34	=	=	SYM
ejpam-4425	145	35	10	10	NUM
ejpam-4425	145	36	,	,	PUNCT
ejpam-4425	145	37	30	30	NUM
ejpam-4425	145	38	,	,	PUNCT
ejpam-4425	145	39	m	m	VERB
ejpam-4425	145	40	=	=	NOUN
ejpam-4425	145	41	1	1	NUM
ejpam-4425	145	42	,	,	PUNCT
ejpam-4425	145	43	2	2	NUM
ejpam-4425	145	44	,	,	PUNCT
ejpam-4425	145	45	3	3	NUM
ejpam-4425	145	46	and	and	CCONJ
ejpam-4425	145	47	the	the	DET
ejpam-4425	145	48	functions	function	NOUN
ejpam-4425	145	49	of	of	ADP
ejpam-4425	145	50	testing	test	VERB
ejpam-4425	145	51	f(x	f(x	PROPN
ejpam-4425	145	52	,	,	PUNCT
ejpam-4425	145	53	y	y	NOUN
ejpam-4425	145	54	)	)	PUNCT
ejpam-4425	145	55	=	=	SYM
ejpam-4425	145	56	cos	cos	X
ejpam-4425	145	57	(	(	PUNCT
ejpam-4425	145	58	9xy	9xy	NOUN
ejpam-4425	145	59	)	)	PUNCT
ejpam-4425	146	1	+	+	CCONJ
ejpam-4425	146	2	2	2	NUM
ejpam-4425	146	3	sin	sin	NOUN
ejpam-4425	146	4	(	(	PUNCT
ejpam-4425	146	5	x+	x+	X
ejpam-4425	146	6	y	y	NOUN
ejpam-4425	146	7	)	)	PUNCT
ejpam-4425	146	8	and	and	CCONJ
ejpam-4425	146	9	g(x	g(x	PROPN
ejpam-4425	146	10	,	,	PUNCT
ejpam-4425	146	11	y	y	NOUN
ejpam-4425	146	12	)	)	PUNCT
ejpam-4425	146	13	=	=	PUNCT
ejpam-4425	146	14	(	(	PUNCT
ejpam-4425	146	15	2x−	2x−	NUM
ejpam-4425	146	16	1)2	1)2	NUM
ejpam-4425	146	17	−	−	PROPN
ejpam-4425	146	18	(	(	PUNCT
ejpam-4425	146	19	2y	2y	PROPN
ejpam-4425	146	20	−	−	PROPN
ejpam-4425	146	21	1)2	1)2	NUM
ejpam-4425	146	22	,	,	PUNCT
ejpam-4425	146	23	(	(	PUNCT
ejpam-4425	146	24	x	x	X
ejpam-4425	146	25	,	,	PUNCT
ejpam-4425	146	26	y	y	NOUN
ejpam-4425	146	27	)	)	PUNCT
ejpam-4425	146	28	∈	∈	PROPN
ejpam-4425	147	1	[	[	X
ejpam-4425	147	2	0	0	NUM
ejpam-4425	147	3	,	,	PUNCT
ejpam-4425	147	4	1]2	1]2	NUM
ejpam-4425	147	5	.	.	PUNCT
ejpam-4425	148	1	for	for	ADP
ejpam-4425	148	2	the	the	DET
ejpam-4425	148	3	nn	nn	PROPN
ejpam-4425	148	4	operators	operators	PROPN
ejpam-4425	148	5	qm(.;x	qm(.;x	PROPN
ejpam-4425	148	6	,	,	PUNCT
ejpam-4425	148	7	y	y	NOUN
ejpam-4425	148	8	)	)	PUNCT
ejpam-4425	148	9	with	with	ADP
ejpam-4425	148	10	the	the	DET
ejpam-4425	148	11	nn	nn	PROPN
ejpam-4425	148	12	operators	operators	PROPN
ejpam-4425	148	13	fn(.;x	fn(.;x	PROPN
ejpam-4425	148	14	,	,	PUNCT
ejpam-4425	148	15	y	y	NOUN
ejpam-4425	148	16	)	)	PUNCT
ejpam-4425	148	17	.	.	PUNCT
ejpam-4425	149	1	we	we	PRON
ejpam-4425	149	2	analyze	analyze	VERB
ejpam-4425	149	3	the	the	DET
ejpam-4425	149	4	results	result	NOUN
ejpam-4425	149	5	in	in	ADP
ejpam-4425	149	6	the	the	DET
ejpam-4425	149	7	figures	figure	NOUN
ejpam-4425	149	8	as	as	ADP
ejpam-4425	149	9	examples	example	NOUN
ejpam-4425	149	10	of	of	ADP
ejpam-4425	149	11	the	the	DET
ejpam-4425	149	12	convergence	convergence	NOUN
ejpam-4425	149	13	of	of	ADP
ejpam-4425	149	14	nn	nn	PROPN
ejpam-4425	149	15	operators	operators	PROPN
ejpam-4425	149	16	qm(.;x	qm(.;x	PROPN
ejpam-4425	149	17	,	,	PUNCT
ejpam-4425	149	18	y	y	NOUN
ejpam-4425	149	19	)	)	PUNCT
ejpam-4425	149	20	,	,	PUNCT
ejpam-4425	149	21	fn(.;x	fn(.;x	PROPN
ejpam-4425	149	22	,	,	PUNCT
ejpam-4425	149	23	y	y	NOUN
ejpam-4425	149	24	)	)	PUNCT
ejpam-4425	149	25	with	with	ADP
ejpam-4425	149	26	test	test	NOUN
ejpam-4425	149	27	the	the	DET
ejpam-4425	149	28	functions	function	NOUN
ejpam-4425	149	29	f(x	f(x	PROPN
ejpam-4425	149	30	,	,	PUNCT
ejpam-4425	149	31	y	y	PROPN
ejpam-4425	149	32	)	)	PUNCT
ejpam-4425	149	33	,	,	PUNCT
ejpam-4425	149	34	g(x	g(x	PROPN
ejpam-4425	149	35	,	,	PUNCT
ejpam-4425	149	36	y	y	NOUN
ejpam-4425	149	37	)	)	PUNCT
ejpam-4425	149	38	.	.	PUNCT
ejpam-4425	150	1	also	also	ADV
ejpam-4425	150	2	,	,	PUNCT
ejpam-4425	150	3	we	we	PRON
ejpam-4425	150	4	give	give	VERB
ejpam-4425	150	5	the	the	DET
ejpam-4425	150	6	table	table	NOUN
ejpam-4425	150	7	to	to	ADP
ejpam-4425	150	8	maximum	maximum	ADJ
ejpam-4425	150	9	error	error	NOUN
ejpam-4425	150	10	function	function	NOUN
ejpam-4425	150	11	for	for	ADP
ejpam-4425	150	12	qm(.;x	qm(.;x	PROPN
ejpam-4425	150	13	,	,	PUNCT
ejpam-4425	150	14	y),fn(.;x	y),fn(.;x	X
ejpam-4425	150	15	,	,	PUNCT
ejpam-4425	150	16	y	y	PROPN
ejpam-4425	150	17	)	)	PUNCT
ejpam-4425	150	18	as	as	SCONJ
ejpam-4425	150	19	follows	follow	VERB
ejpam-4425	150	20	:	:	PUNCT
ejpam-4425	150	21	example	example	NOUN
ejpam-4425	151	1	1	1	NUM
ejpam-4425	151	2	.	.	X
ejpam-4425	151	3	for	for	ADP
ejpam-4425	151	4	n	n	NOUN
ejpam-4425	151	5	=	=	SYM
ejpam-4425	151	6	10	10	NUM
ejpam-4425	151	7	,	,	PUNCT
ejpam-4425	151	8	30,m	30,m	NUM
ejpam-4425	151	9	=	=	SYM
ejpam-4425	151	10	1	1	NUM
ejpam-4425	151	11	,	,	PUNCT
ejpam-4425	151	12	2	2	NUM
ejpam-4425	151	13	,	,	PUNCT
ejpam-4425	151	14	3	3	NUM
ejpam-4425	151	15	,	,	PUNCT
ejpam-4425	151	16	the	the	DET
ejpam-4425	151	17	convergence	convergence	NOUN
ejpam-4425	151	18	of	of	ADP
ejpam-4425	151	19	nn	nn	PROPN
ejpam-4425	151	20	operators	operator	NOUN
ejpam-4425	151	21	qm(f	qm(f	NUM
ejpam-4425	151	22	;	;	PUNCT
ejpam-4425	151	23	x	x	X
ejpam-4425	151	24	,	,	PUNCT
ejpam-4425	151	25	y	y	PROPN
ejpam-4425	151	26	)	)	PUNCT
ejpam-4425	151	27	,	,	PUNCT
ejpam-4425	151	28	fn(f	fn(f	ADP
ejpam-4425	151	29	;	;	PUNCT
ejpam-4425	151	30	x	x	X
ejpam-4425	151	31	,	,	PUNCT
ejpam-4425	151	32	y	y	PROPN
ejpam-4425	151	33	)	)	PUNCT
ejpam-4425	151	34	to	to	PART
ejpam-4425	151	35	test	test	VERB
ejpam-4425	151	36	function	function	VERB
ejpam-4425	151	37	f(x	f(x	PROPN
ejpam-4425	151	38	,	,	PUNCT
ejpam-4425	151	39	y	y	NOUN
ejpam-4425	151	40	)	)	PUNCT
ejpam-4425	151	41	can	can	AUX
ejpam-4425	151	42	be	be	AUX
ejpam-4425	151	43	descripted	descripte	VERB
ejpam-4425	151	44	in	in	ADP
ejpam-4425	151	45	the	the	DET
ejpam-4425	151	46	figure	figure	NOUN
ejpam-4425	151	47	1	1	NUM
ejpam-4425	151	48	.	.	PUNCT
ejpam-4425	152	1	𝑛	𝑛	NOUN
ejpam-4425	152	2	=	=	SYM
ejpam-4425	152	3	10	10	NUM
ejpam-4425	152	4	,	,	PUNCT
ejpam-4425	152	5	𝑚	𝑚	NOUN
ejpam-4425	152	6	=	=	SYM
ejpam-4425	152	7	1	1	NUM
ejpam-4425	152	8	𝑛	𝑛	NOUN
ejpam-4425	152	9	=	=	SYM
ejpam-4425	152	10	10	10	NUM
ejpam-4425	152	11	,	,	PUNCT
ejpam-4425	152	12	𝑚	𝑚	NOUN
ejpam-4425	152	13	=	=	SYM
ejpam-4425	152	14	2	2	NUM
ejpam-4425	152	15	𝑛	𝑛	NOUN
ejpam-4425	152	16	=	=	SYM
ejpam-4425	152	17	10	10	NUM
ejpam-4425	152	18	,	,	PUNCT
ejpam-4425	152	19	𝑚	𝑚	NOUN
ejpam-4425	152	20	=	=	SYM
ejpam-4425	152	21	3	3	NUM
ejpam-4425	152	22	𝑛	𝑛	NOUN
ejpam-4425	152	23	=	=	SYM
ejpam-4425	152	24	30	30	NUM
ejpam-4425	152	25	,	,	PUNCT
ejpam-4425	152	26	𝑚	𝑚	X
ejpam-4425	152	27	=	=	SYM
ejpam-4425	152	28	1	1	NUM
ejpam-4425	152	29	𝑛	𝑛	NOUN
ejpam-4425	152	30	=	=	SYM
ejpam-4425	152	31	30	30	NUM
ejpam-4425	152	32	,	,	PUNCT
ejpam-4425	152	33	𝑚	𝑚	X
ejpam-4425	152	34	=	=	SYM
ejpam-4425	152	35	2	2	NUM
ejpam-4425	152	36	𝑛	𝑛	NOUN
ejpam-4425	152	37	=	=	SYM
ejpam-4425	152	38	30	30	NUM
ejpam-4425	152	39	,	,	PUNCT
ejpam-4425	152	40	𝑚	𝑚	NOUN
ejpam-4425	152	41	=	=	SYM
ejpam-4425	152	42	3	3	NUM
ejpam-4425	152	43	figure	figure	NOUN
ejpam-4425	152	44	1	1	NUM
ejpam-4425	152	45	:	:	PUNCT
ejpam-4425	152	46	the	the	DET
ejpam-4425	152	47	numerical	numerical	ADJ
ejpam-4425	152	48	convergence	convergence	NOUN
ejpam-4425	152	49	of	of	ADP
ejpam-4425	152	50	nn	nn	X
ejpam-4425	152	51	operators	operator	NOUN
ejpam-4425	152	52	fn(f	fn(f	ADP
ejpam-4425	152	53	;	;	PUNCT
ejpam-4425	152	54	x	x	X
ejpam-4425	152	55	,	,	PUNCT
ejpam-4425	152	56	y	y	PROPN
ejpam-4425	152	57	)	)	PUNCT
ejpam-4425	152	58	(	(	PUNCT
ejpam-4425	152	59	red	red	ADJ
ejpam-4425	152	60	)	)	PUNCT
ejpam-4425	152	61	and	and	CCONJ
ejpam-4425	152	62	qm(f	qm(f	PROPN
ejpam-4425	152	63	;	;	PUNCT
ejpam-4425	153	1	x	x	X
ejpam-4425	153	2	,	,	PUNCT
ejpam-4425	153	3	y	y	PROPN
ejpam-4425	153	4	)	)	PUNCT
ejpam-4425	153	5	(	(	PUNCT
ejpam-4425	153	6	lime	lime	NOUN
ejpam-4425	153	7	)	)	PUNCT
ejpam-4425	153	8	to	to	ADP
ejpam-4425	153	9	f(x	f(x	PROPN
ejpam-4425	153	10	,	,	PUNCT
ejpam-4425	153	11	y	y	PROPN
ejpam-4425	153	12	)	)	PUNCT
ejpam-4425	153	13	(	(	PUNCT
ejpam-4425	153	14	blue	blue	ADJ
ejpam-4425	153	15	)	)	PUNCT
ejpam-4425	153	16	.	.	PUNCT
ejpam-4425	154	1	example	example	NOUN
ejpam-4425	155	1	2	2	NUM
ejpam-4425	155	2	.	.	PUNCT
ejpam-4425	155	3	forn	forn	PROPN
ejpam-4425	155	4	=	=	SYM
ejpam-4425	155	5	10	10	NUM
ejpam-4425	155	6	,	,	PUNCT
ejpam-4425	155	7	30,m	30,m	NUM
ejpam-4425	155	8	=	=	SYM
ejpam-4425	155	9	1	1	NUM
ejpam-4425	155	10	,	,	PUNCT
ejpam-4425	155	11	2	2	NUM
ejpam-4425	155	12	,	,	PUNCT
ejpam-4425	155	13	3	3	NUM
ejpam-4425	155	14	,	,	PUNCT
ejpam-4425	155	15	the	the	DET
ejpam-4425	155	16	convergence	convergence	NOUN
ejpam-4425	155	17	of	of	ADP
ejpam-4425	155	18	nn	nn	PROPN
ejpam-4425	155	19	operators	operator	NOUN
ejpam-4425	155	20	qm(g;x	qm(g;x	VERB
ejpam-4425	155	21	,	,	PUNCT
ejpam-4425	155	22	y	y	PROPN
ejpam-4425	155	23	)	)	PUNCT
ejpam-4425	155	24	,	,	PUNCT
ejpam-4425	155	25	fn(g;x	fn(g;x	PROPN
ejpam-4425	155	26	,	,	PUNCT
ejpam-4425	155	27	y)to	y)to	PROPN
ejpam-4425	155	28	test	test	NOUN
ejpam-4425	155	29	function	function	NOUN
ejpam-4425	155	30	g(x	g(x	PROPN
ejpam-4425	155	31	,	,	PUNCT
ejpam-4425	155	32	y	y	NOUN
ejpam-4425	155	33	)	)	PUNCT
ejpam-4425	155	34	can	can	AUX
ejpam-4425	155	35	be	be	AUX
ejpam-4425	155	36	descripted	descripte	VERB
ejpam-4425	155	37	in	in	ADP
ejpam-4425	155	38	the	the	DET
ejpam-4425	155	39	figure	figure	NOUN
ejpam-4425	155	40	2	2	NUM
ejpam-4425	155	41	.	.	PUNCT
ejpam-4425	156	1	i.j	i.j	PROPN
ejpam-4425	156	2	.	.	PROPN
ejpam-4425	156	3	mohammad	mohammad	PROPN
ejpam-4425	156	4	,	,	PUNCT
ejpam-4425	156	5	a.j	a.j	PROPN
ejpam-4425	156	6	.	.	PROPN
ejpam-4425	156	7	mohammad	mohammad	PROPN
ejpam-4425	156	8	/	/	SYM
ejpam-4425	156	9	eur	eur	PROPN
ejpam-4425	156	10	.	.	PUNCT
ejpam-4425	157	1	j.	j.	PROPN
ejpam-4425	157	2	pure	pure	PROPN
ejpam-4425	157	3	appl	appl	PROPN
ejpam-4425	157	4	.	.	PROPN
ejpam-4425	157	5	math	math	PROPN
ejpam-4425	157	6	,	,	PUNCT
ejpam-4425	157	7	15	15	NUM
ejpam-4425	157	8	(	(	PUNCT
ejpam-4425	157	9	3	3	NUM
ejpam-4425	157	10	)	)	PUNCT
ejpam-4425	157	11	(	(	PUNCT
ejpam-4425	157	12	2022	2022	NUM
ejpam-4425	157	13	)	)	PUNCT
ejpam-4425	157	14	,	,	PUNCT
ejpam-4425	157	15	1189	1189	NUM
ejpam-4425	157	16	-	-	SYM
ejpam-4425	157	17	1200	1200	NUM
ejpam-4425	157	18	1199	1199	NUM
ejpam-4425	157	19	𝑛	𝑛	NOUN
ejpam-4425	157	20	=	=	SYM
ejpam-4425	157	21	10	10	NUM
ejpam-4425	157	22	,	,	PUNCT
ejpam-4425	157	23	𝑚	𝑚	NOUN
ejpam-4425	157	24	=	=	SYM
ejpam-4425	157	25	1	1	NUM
ejpam-4425	157	26	𝑛	𝑛	NOUN
ejpam-4425	157	27	=	=	SYM
ejpam-4425	157	28	10	10	NUM
ejpam-4425	157	29	,	,	PUNCT
ejpam-4425	157	30	𝑚	𝑚	NOUN
ejpam-4425	157	31	=	=	SYM
ejpam-4425	157	32	2	2	NUM
ejpam-4425	157	33	𝑛	𝑛	NOUN
ejpam-4425	157	34	=	=	SYM
ejpam-4425	157	35	10	10	NUM
ejpam-4425	157	36	,	,	PUNCT
ejpam-4425	157	37	𝑚	𝑚	NOUN
ejpam-4425	157	38	=	=	SYM
ejpam-4425	157	39	3	3	NUM
ejpam-4425	157	40	𝑛	𝑛	NOUN
ejpam-4425	157	41	=	=	SYM
ejpam-4425	157	42	30	30	NUM
ejpam-4425	157	43	,	,	PUNCT
ejpam-4425	157	44	𝑚	𝑚	X
ejpam-4425	157	45	=	=	SYM
ejpam-4425	157	46	1	1	NUM
ejpam-4425	157	47	𝑛	𝑛	NOUN
ejpam-4425	157	48	=	=	SYM
ejpam-4425	157	49	30	30	NUM
ejpam-4425	157	50	,	,	PUNCT
ejpam-4425	157	51	𝑚	𝑚	X
ejpam-4425	157	52	=	=	SYM
ejpam-4425	157	53	2	2	NUM
ejpam-4425	157	54	𝑛	𝑛	NOUN
ejpam-4425	157	55	=	=	SYM
ejpam-4425	157	56	30	30	NUM
ejpam-4425	157	57	,	,	PUNCT
ejpam-4425	157	58	𝑚	𝑚	NOUN
ejpam-4425	157	59	=	=	SYM
ejpam-4425	157	60	3	3	NUM
ejpam-4425	157	61	figure	figure	NOUN
ejpam-4425	157	62	2	2	NUM
ejpam-4425	157	63	:	:	PUNCT
ejpam-4425	157	64	the	the	DET
ejpam-4425	157	65	numerical	numerical	ADJ
ejpam-4425	157	66	convergence	convergence	NOUN
ejpam-4425	157	67	of	of	ADP
ejpam-4425	157	68	nn	nn	PROPN
ejpam-4425	157	69	operators	operators	PROPN
ejpam-4425	157	70	fn(g;x	fn(g;x	PROPN
ejpam-4425	157	71	,	,	PUNCT
ejpam-4425	157	72	y	y	PROPN
ejpam-4425	157	73	)	)	PUNCT
ejpam-4425	157	74	(	(	PUNCT
ejpam-4425	157	75	red	red	ADJ
ejpam-4425	157	76	)	)	PUNCT
ejpam-4425	157	77	and	and	CCONJ
ejpam-4425	157	78	qm(g;x	qm(g;x	VERB
ejpam-4425	157	79	,	,	PUNCT
ejpam-4425	157	80	y	y	PROPN
ejpam-4425	157	81	)	)	PUNCT
ejpam-4425	157	82	(	(	PUNCT
ejpam-4425	157	83	lime	lime	NOUN
ejpam-4425	157	84	)	)	PUNCT
ejpam-4425	157	85	to	to	ADP
ejpam-4425	157	86	g(x	g(x	PROPN
ejpam-4425	157	87	,	,	PUNCT
ejpam-4425	157	88	y	y	NOUN
ejpam-4425	157	89	)	)	PUNCT
ejpam-4425	157	90	(	(	PUNCT
ejpam-4425	157	91	blue	blue	ADJ
ejpam-4425	157	92	)	)	PUNCT
ejpam-4425	157	93	.	.	PUNCT
ejpam-4425	158	1	now	now	ADV
ejpam-4425	158	2	,	,	PUNCT
ejpam-4425	158	3	the	the	DET
ejpam-4425	158	4	maximum	maximum	ADJ
ejpam-4425	158	5	error	error	NOUN
ejpam-4425	158	6	values	value	NOUN
ejpam-4425	158	7	calculated	calculate	VERB
ejpam-4425	158	8	by	by	ADP
ejpam-4425	158	9	the	the	DET
ejpam-4425	158	10	flowing	flow	VERB
ejpam-4425	158	11	table	table	NOUN
ejpam-4425	158	12	between	between	ADP
ejpam-4425	158	13	the	the	DET
ejpam-4425	158	14	test	test	NOUN
ejpam-4425	158	15	function	function	NOUN
ejpam-4425	158	16	f(x	f(x	PROPN
ejpam-4425	158	17	,	,	PUNCT
ejpam-4425	158	18	y	y	NOUN
ejpam-4425	158	19	)	)	PUNCT
ejpam-4425	158	20	,	,	PUNCT
ejpam-4425	158	21	g(x	g(x	PROPN
ejpam-4425	158	22	,	,	PUNCT
ejpam-4425	158	23	y	y	PROPN
ejpam-4425	158	24	)	)	PUNCT
ejpam-4425	158	25	and	and	CCONJ
ejpam-4425	158	26	nn	nn	X
ejpam-4425	158	27	operators	operator	NOUN
ejpam-4425	158	28	in	in	ADP
ejpam-4425	158	29	r2	r2	PROPN
ejpam-4425	158	30	:	:	PUNCT
ejpam-4425	158	31	table	table	NOUN
ejpam-4425	158	32	1	1	NUM
ejpam-4425	158	33	:	:	PUNCT
ejpam-4425	158	34	maximum	maximum	ADJ
ejpam-4425	158	35	error	error	NOUN
ejpam-4425	158	36	.	.	PUNCT
ejpam-4425	159	1	nn	nn	PROPN
ejpam-4425	159	2	n	n	ADV
ejpam-4425	159	3	m	m	PROPN
ejpam-4425	159	4	=	=	ADJ
ejpam-4425	159	5	1	1	NUM
ejpam-4425	159	6	m	m	NOUN
ejpam-4425	159	7	=	=	SYM
ejpam-4425	159	8	2	2	NUM
ejpam-4425	159	9	m	m	NOUN
ejpam-4425	159	10	=	=	NOUN
ejpam-4425	159	11	3	3	NUM
ejpam-4425	159	12	fn(f	fn(f	X
ejpam-4425	159	13	;	;	PUNCT
ejpam-4425	159	14	x	x	X
ejpam-4425	159	15	,	,	PUNCT
ejpam-4425	159	16	y	y	PROPN
ejpam-4425	159	17	)	)	PUNCT
ejpam-4425	159	18	10	10	NUM
ejpam-4425	159	19	0.757395453	0.757395453	NUM
ejpam-4425	159	20	0.757395451	0.757395451	NUM
ejpam-4425	159	21	0.757395451	0.757395451	NUM
ejpam-4425	159	22	qm(f	qm(f	NOUN
ejpam-4425	159	23	;	;	PUNCT
ejpam-4425	159	24	x	x	X
ejpam-4425	159	25	,	,	PUNCT
ejpam-4425	159	26	y	y	PROPN
ejpam-4425	159	27	)	)	PUNCT
ejpam-4425	159	28	0.490870074	0.490870074	PROPN
ejpam-4425	159	29	0.187277077	0.187277077	NUM
ejpam-4425	159	30	0.019435682	0.019435682	NUM
ejpam-4425	159	31	fn(g;x	fn(g;x	NOUN
ejpam-4425	159	32	,	,	PUNCT
ejpam-4425	159	33	y	y	PROPN
ejpam-4425	159	34	)	)	PUNCT
ejpam-4425	159	35	0.4733567674	0.4733567674	NUM
ejpam-4425	159	36	0.4733567674	0.4733567674	NUM
ejpam-4425	159	37	0.4733567674	0.4733567674	NUM
ejpam-4425	159	38	qm(g;x	qm(g;x	NOUN
ejpam-4425	159	39	,	,	PUNCT
ejpam-4425	159	40	y	y	PROPN
ejpam-4425	159	41	)	)	PUNCT
ejpam-4425	159	42	0.2810197385	0.2810197385	NUM
ejpam-4425	159	43	0.0785342121	0.0785342121	NUM
ejpam-4425	159	44	0.0091303333	0.0091303333	NUM
ejpam-4425	159	45	fn(f	fn(f	ADP
ejpam-4425	159	46	;	;	PUNCT
ejpam-4425	159	47	x	x	X
ejpam-4425	159	48	,	,	PUNCT
ejpam-4425	159	49	y	y	PROPN
ejpam-4425	159	50	)	)	PUNCT
ejpam-4425	159	51	30	30	NUM
ejpam-4425	159	52	0.185638151	0.185638151	NUM
ejpam-4425	159	53	0.185638151	0.185638151	NUM
ejpam-4425	159	54	0.185638151	0.185638151	NUM
ejpam-4425	159	55	qm(f	qm(f	NOUN
ejpam-4425	159	56	;	;	PUNCT
ejpam-4425	159	57	x	x	X
ejpam-4425	159	58	,	,	PUNCT
ejpam-4425	159	59	y	y	PROPN
ejpam-4425	159	60	)	)	PUNCT
ejpam-4425	159	61	0.091746328	0.091746328	NUM
ejpam-4425	159	62	0.024034970	0.024034970	NUM
ejpam-4425	159	63	0.000333905	0.000333905	NUM
ejpam-4425	159	64	fn(g;x	fn(g;x	PROPN
ejpam-4425	159	65	,	,	PUNCT
ejpam-4425	159	66	y	y	NOUN
ejpam-4425	159	67	)	)	PUNCT
ejpam-4425	159	68	0.1551244367	0.1551244367	NUM
ejpam-4425	159	69	0.1551244367	0.1551244367	NUM
ejpam-4425	159	70	0.1551244367	0.1551244367	NUM
ejpam-4425	159	71	qm(g;x	qm(g;x	NOUN
ejpam-4425	159	72	,	,	PUNCT
ejpam-4425	159	73	y	y	PROPN
ejpam-4425	159	74	)	)	PUNCT
ejpam-4425	159	75	0.0888466026	0.0888466026	NUM
ejpam-4425	159	76	0.01026517101	0.01026517101	NUM
ejpam-4425	159	77	0.0003333514	0.0003333514	NUM
ejpam-4425	159	78	5	5	NUM
ejpam-4425	159	79	.	.	PUNCT
ejpam-4425	160	1	conclusions	conclusion	NOUN
ejpam-4425	160	2	from	from	ADP
ejpam-4425	160	3	table	table	NOUN
ejpam-4425	160	4	1	1	NUM
ejpam-4425	160	5	above	above	ADV
ejpam-4425	160	6	and	and	CCONJ
ejpam-4425	160	7	the	the	DET
ejpam-4425	160	8	two	two	NUM
ejpam-4425	160	9	numerical	numerical	ADJ
ejpam-4425	160	10	examples	example	NOUN
ejpam-4425	160	11	,	,	PUNCT
ejpam-4425	160	12	the	the	DET
ejpam-4425	160	13	nn	nn	PROPN
ejpam-4425	160	14	operators	operators	PROPN
ejpam-4425	160	15	qm(.;x	qm(.;x	PROPN
ejpam-4425	160	16	,	,	PUNCT
ejpam-4425	160	17	y	y	NOUN
ejpam-4425	160	18	)	)	PUNCT
ejpam-4425	160	19	better	well	ADV
ejpam-4425	160	20	the	the	DET
ejpam-4425	160	21	classical	classical	ADJ
ejpam-4425	160	22	nn	nn	PROPN
ejpam-4425	160	23	operators	operator	NOUN
ejpam-4425	160	24	fn(.;x	fn(.;x	PROPN
ejpam-4425	160	25	,	,	PUNCT
ejpam-4425	160	26	y	y	NOUN
ejpam-4425	160	27	)	)	PUNCT
ejpam-4425	160	28	in	in	ADP
ejpam-4425	160	29	terms	term	NOUN
ejpam-4425	160	30	of	of	ADP
ejpam-4425	160	31	numerical	numerical	ADJ
ejpam-4425	160	32	results	result	NOUN
ejpam-4425	160	33	for	for	ADP
ejpam-4425	160	34	the	the	DET
ejpam-4425	160	35	two	two	NUM
ejpam-4425	160	36	test	test	NOUN
ejpam-4425	160	37	functions	function	NOUN
ejpam-4425	160	38	f	f	PROPN
ejpam-4425	160	39	and	and	CCONJ
ejpam-4425	160	40	g.	g.	PROPN
ejpam-4425	160	41	references	reference	NOUN
ejpam-4425	160	42	1200	1200	NUM
ejpam-4425	160	43	references	reference	NOUN
ejpam-4425	160	44	[	[	X
ejpam-4425	160	45	1	1	NUM
ejpam-4425	160	46	]	]	X
ejpam-4425	160	47	s	s	VERB
ejpam-4425	160	48	bajpeyi	bajpeyi	NOUN
ejpam-4425	160	49	and	and	CCONJ
ejpam-4425	160	50	a	a	DET
ejpam-4425	160	51	sathish	sathish	NOUN
ejpam-4425	160	52	kumar	kumar	PROPN
ejpam-4425	160	53	.	.	PROPN
ejpam-4425	161	1	approximation	approximation	NOUN
ejpam-4425	161	2	by	by	ADP
ejpam-4425	161	3	exponential	exponential	ADJ
ejpam-4425	161	4	type	type	NOUN
ejpam-4425	161	5	neural	neural	ADJ
ejpam-4425	161	6	network	network	NOUN
ejpam-4425	161	7	operators	operator	NOUN
ejpam-4425	161	8	.	.	PUNCT
ejpam-4425	162	1	arxiv	arxiv	PROPN
ejpam-4425	162	2	preprint	preprint	PROPN
ejpam-4425	162	3	arxiv:1911.05587	arxiv:1911.05587	PROPN
ejpam-4425	162	4	,	,	PUNCT
ejpam-4425	162	5	2019	2019	NUM
ejpam-4425	162	6	.	.	PUNCT
ejpam-4425	163	1	[	[	X
ejpam-4425	163	2	2	2	NUM
ejpam-4425	163	3	]	]	X
ejpam-4425	163	4	danilo	danilo	PROPN
ejpam-4425	163	5	costarelli	costarelli	PROPN
ejpam-4425	163	6	,	,	PUNCT
ejpam-4425	163	7	anna	anna	PROPN
ejpam-4425	163	8	rita	rita	PROPN
ejpam-4425	163	9	sambucini	sambucini	PROPN
ejpam-4425	163	10	,	,	PUNCT
ejpam-4425	163	11	and	and	CCONJ
ejpam-4425	163	12	gianluca	gianluca	PROPN
ejpam-4425	163	13	vinti	vinti	PROPN
ejpam-4425	163	14	.	.	PUNCT
ejpam-4425	164	1	convergence	convergence	NOUN
ejpam-4425	164	2	in	in	ADP
ejpam-4425	164	3	orlicz	orlicz	ADJ
ejpam-4425	164	4	spaces	space	NOUN
ejpam-4425	164	5	by	by	ADP
ejpam-4425	164	6	means	mean	NOUN
ejpam-4425	164	7	of	of	ADP
ejpam-4425	164	8	the	the	DET
ejpam-4425	164	9	multivariate	multivariate	NOUN
ejpam-4425	164	10	max	max	NOUN
ejpam-4425	164	11	-	-	PUNCT
ejpam-4425	164	12	product	product	NOUN
ejpam-4425	164	13	neural	neural	ADJ
ejpam-4425	164	14	network	network	NOUN
ejpam-4425	164	15	operators	operator	NOUN
ejpam-4425	164	16	of	of	ADP
ejpam-4425	164	17	the	the	DET
ejpam-4425	164	18	kantorovich	kantorovich	PROPN
ejpam-4425	164	19	type	type	NOUN
ejpam-4425	164	20	and	and	CCONJ
ejpam-4425	164	21	applications	application	NOUN
ejpam-4425	164	22	.	.	PUNCT
ejpam-4425	165	1	neural	neural	ADJ
ejpam-4425	165	2	computing	computing	NOUN
ejpam-4425	165	3	and	and	CCONJ
ejpam-4425	165	4	applications	application	NOUN
ejpam-4425	165	5	,	,	PUNCT
ejpam-4425	165	6	31(9):5069	31(9):5069	NUM
ejpam-4425	165	7	–	–	PUNCT
ejpam-4425	165	8	5078	5078	NUM
ejpam-4425	165	9	,	,	PUNCT
ejpam-4425	165	10	2019	2019	NUM
ejpam-4425	165	11	.	.	PUNCT
ejpam-4425	166	1	[	[	X
ejpam-4425	166	2	3	3	X
ejpam-4425	166	3	]	]	X
ejpam-4425	166	4	danilo	danilo	PROPN
ejpam-4425	166	5	costarelli	costarelli	PROPN
ejpam-4425	166	6	and	and	CCONJ
ejpam-4425	166	7	renato	renato	PROPN
ejpam-4425	166	8	spigler	spigler	NOUN
ejpam-4425	166	9	.	.	PUNCT
ejpam-4425	167	1	approximation	approximation	NOUN
ejpam-4425	167	2	results	result	NOUN
ejpam-4425	167	3	for	for	ADP
ejpam-4425	167	4	neural	neural	ADJ
ejpam-4425	167	5	network	network	NOUN
ejpam-4425	167	6	operators	operator	NOUN
ejpam-4425	167	7	activated	activate	VERB
ejpam-4425	167	8	by	by	ADP
ejpam-4425	167	9	sigmoidal	sigmoidal	NOUN
ejpam-4425	167	10	functions	function	NOUN
ejpam-4425	167	11	.	.	PUNCT
ejpam-4425	168	1	neural	neural	ADJ
ejpam-4425	168	2	networks	network	NOUN
ejpam-4425	168	3	,	,	PUNCT
ejpam-4425	168	4	44:101–106	44:101–106	PROPN
ejpam-4425	168	5	,	,	PUNCT
ejpam-4425	168	6	2013	2013	NUM
ejpam-4425	168	7	.	.	PUNCT
ejpam-4425	169	1	[	[	X
ejpam-4425	169	2	4	4	NUM
ejpam-4425	169	3	]	]	X
ejpam-4425	169	4	danilo	danilo	PROPN
ejpam-4425	169	5	costarelli	costarelli	PROPN
ejpam-4425	169	6	and	and	CCONJ
ejpam-4425	169	7	renato	renato	PROPN
ejpam-4425	169	8	spigler	spigler	NOUN
ejpam-4425	169	9	.	.	PUNCT
ejpam-4425	170	1	multivariate	multivariate	NOUN
ejpam-4425	170	2	neural	neural	ADJ
ejpam-4425	170	3	network	network	NOUN
ejpam-4425	170	4	operators	operator	NOUN
ejpam-4425	170	5	with	with	ADP
ejpam-4425	170	6	sigmoidal	sigmoidal	NOUN
ejpam-4425	170	7	activation	activation	NOUN
ejpam-4425	170	8	functions	function	NOUN
ejpam-4425	170	9	.	.	PUNCT
ejpam-4425	171	1	neural	neural	ADJ
ejpam-4425	171	2	networks	network	NOUN
ejpam-4425	171	3	,	,	PUNCT
ejpam-4425	171	4	48:72–77	48:72–77	NUM
ejpam-4425	171	5	,	,	PUNCT
ejpam-4425	171	6	2013	2013	NUM
ejpam-4425	171	7	.	.	PUNCT
ejpam-4425	172	1	[	[	X
ejpam-4425	172	2	5	5	NUM
ejpam-4425	172	3	]	]	X
ejpam-4425	172	4	danilo	danilo	PROPN
ejpam-4425	172	5	costarelli	costarelli	PROPN
ejpam-4425	172	6	and	and	CCONJ
ejpam-4425	172	7	renato	renato	PROPN
ejpam-4425	172	8	spigler	spigler	NOUN
ejpam-4425	172	9	.	.	PUNCT
ejpam-4425	173	1	convergence	convergence	NOUN
ejpam-4425	173	2	of	of	ADP
ejpam-4425	173	3	a	a	DET
ejpam-4425	173	4	family	family	NOUN
ejpam-4425	173	5	of	of	ADP
ejpam-4425	173	6	neural	neural	ADJ
ejpam-4425	173	7	network	network	NOUN
ejpam-4425	173	8	operators	operator	NOUN
ejpam-4425	173	9	of	of	ADP
ejpam-4425	173	10	the	the	DET
ejpam-4425	173	11	kantorovich	kantorovich	PROPN
ejpam-4425	173	12	type	type	NOUN
ejpam-4425	173	13	.	.	PUNCT
ejpam-4425	174	1	journal	journal	PROPN
ejpam-4425	174	2	of	of	ADP
ejpam-4425	174	3	approximation	approximation	NOUN
ejpam-4425	174	4	theory	theory	NOUN
ejpam-4425	174	5	,	,	PUNCT
ejpam-4425	174	6	185:80–90	185:80–90	NUM
ejpam-4425	174	7	,	,	PUNCT
ejpam-4425	174	8	2014	2014	NUM
ejpam-4425	174	9	.	.	PUNCT
ejpam-4425	175	1	[	[	X
ejpam-4425	175	2	6	6	NUM
ejpam-4425	175	3	]	]	X
ejpam-4425	175	4	danilo	danilo	PROPN
ejpam-4425	175	5	costarelli	costarelli	PROPN
ejpam-4425	175	6	and	and	CCONJ
ejpam-4425	175	7	gianluca	gianluca	PROPN
ejpam-4425	175	8	vinti	vinti	PROPN
ejpam-4425	175	9	.	.	PUNCT
ejpam-4425	176	1	pointwise	pointwise	PROPN
ejpam-4425	176	2	and	and	CCONJ
ejpam-4425	176	3	uniform	uniform	ADJ
ejpam-4425	176	4	approximation	approximation	NOUN
ejpam-4425	176	5	by	by	ADP
ejpam-4425	176	6	multivariate	multivariate	NOUN
ejpam-4425	176	7	neural	neural	ADJ
ejpam-4425	176	8	network	network	NOUN
ejpam-4425	176	9	operators	operator	NOUN
ejpam-4425	176	10	of	of	ADP
ejpam-4425	176	11	the	the	DET
ejpam-4425	176	12	max	max	PROPN
ejpam-4425	176	13	-	-	PUNCT
ejpam-4425	176	14	product	product	NOUN
ejpam-4425	176	15	type	type	NOUN
ejpam-4425	176	16	.	.	PUNCT
ejpam-4425	177	1	neural	neural	ADJ
ejpam-4425	177	2	networks	network	NOUN
ejpam-4425	177	3	,	,	PUNCT
ejpam-4425	177	4	81:81–90	81:81–90	NUM
ejpam-4425	177	5	,	,	PUNCT
ejpam-4425	177	6	2016	2016	NUM
ejpam-4425	177	7	.	.	PUNCT
ejpam-4425	178	1	[	[	X
ejpam-4425	178	2	7	7	X
ejpam-4425	178	3	]	]	PUNCT
ejpam-4425	178	4	ioan	ioan	NOUN
ejpam-4425	178	5	gavrea	gavrea	PROPN
ejpam-4425	178	6	and	and	CCONJ
ejpam-4425	178	7	mircea	mircea	PROPN
ejpam-4425	178	8	ivan	ivan	PROPN
ejpam-4425	178	9	.	.	PUNCT
ejpam-4425	179	1	on	on	ADP
ejpam-4425	179	2	a	a	DET
ejpam-4425	179	3	new	new	ADJ
ejpam-4425	179	4	sequence	sequence	NOUN
ejpam-4425	179	5	of	of	ADP
ejpam-4425	179	6	positive	positive	ADJ
ejpam-4425	179	7	linear	linear	NOUN
ejpam-4425	179	8	operators	operator	NOUN
ejpam-4425	179	9	related	relate	VERB
ejpam-4425	179	10	to	to	ADP
ejpam-4425	179	11	squared	square	VERB
ejpam-4425	179	12	bernstein	bernstein	PROPN
ejpam-4425	179	13	polynomials	polynomials	PROPN
ejpam-4425	179	14	.	.	PUNCT
ejpam-4425	180	1	positivity	positivity	NOUN
ejpam-4425	180	2	,	,	PUNCT
ejpam-4425	180	3	21(3):911–917	21(3):911–917	NUM
ejpam-4425	180	4	,	,	PUNCT
ejpam-4425	180	5	2017	2017	NUM
ejpam-4425	180	6	.	.	PUNCT
ejpam-4425	181	1	[	[	X
ejpam-4425	181	2	8	8	NUM
ejpam-4425	181	3	]	]	X
ejpam-4425	181	4	amal	amal	PROPN
ejpam-4425	181	5	k	k	PROPN
ejpam-4425	181	6	hassan	hassan	PROPN
ejpam-4425	181	7	.	.	PUNCT
ejpam-4425	182	1	on	on	ADP
ejpam-4425	182	2	generalized	generalized	ADJ
ejpam-4425	182	3	szasz	szasz	NOUN
ejpam-4425	182	4	-	-	PUNCT
ejpam-4425	182	5	bernstein	bernstein	NOUN
ejpam-4425	182	6	–	–	PUNCT
ejpam-4425	182	7	type	type	NOUN
ejpam-4425	182	8	operators	operator	NOUN
ejpam-4425	182	9	.	.	PUNCT
ejpam-4425	183	1	journal	journal	PROPN
ejpam-4425	183	2	of	of	ADP
ejpam-4425	183	3	university	university	PROPN
ejpam-4425	183	4	of	of	ADP
ejpam-4425	183	5	babylon	babylon	PROPN
ejpam-4425	183	6	for	for	ADP
ejpam-4425	183	7	pure	pure	ADJ
ejpam-4425	183	8	and	and	CCONJ
ejpam-4425	183	9	applied	applied	ADJ
ejpam-4425	183	10	sciences	science	NOUN
ejpam-4425	183	11	,	,	PUNCT
ejpam-4425	183	12	26(4):36–44	26(4):36–44	NUM
ejpam-4425	183	13	,	,	PUNCT
ejpam-4425	183	14	2018	2018	NUM
ejpam-4425	183	15	.	.	PUNCT
ejpam-4425	184	1	[	[	X
ejpam-4425	184	2	9	9	NUM
ejpam-4425	184	3	]	]	PUNCT
ejpam-4425	184	4	ali	ali	PROPN
ejpam-4425	184	5	j	j	PROPN
ejpam-4425	184	6	mohammad	mohammad	PROPN
ejpam-4425	184	7	and	and	CCONJ
ejpam-4425	184	8	ibtihal	ibtihal	PROPN
ejpam-4425	184	9	jassim	jassim	PROPN
ejpam-4425	184	10	mohammad	mohammad	PROPN
ejpam-4425	184	11	.	.	PUNCT
ejpam-4425	184	12	summationintegral	summationintegral	PROPN
ejpam-4425	184	13	bernstein	bernstein	PROPN
ejpam-4425	184	14	type	type	PROPN
ejpam-4425	184	15	of	of	ADP
ejpam-4425	184	16	neural	neural	ADJ
ejpam-4425	184	17	network	network	NOUN
ejpam-4425	184	18	operators	operator	NOUN
ejpam-4425	184	19	.	.	PUNCT
ejpam-4425	185	1	asian	asian	ADJ
ejpam-4425	185	2	journal	journal	PROPN
ejpam-4425	185	3	of	of	ADP
ejpam-4425	185	4	mathematics	mathematics	PROPN
ejpam-4425	185	5	and	and	CCONJ
ejpam-4425	185	6	computer	computer	NOUN
ejpam-4425	185	7	research	research	NOUN
ejpam-4425	185	8	,	,	PUNCT
ejpam-4425	185	9	pages	page	NOUN
ejpam-4425	185	10	74–86	74–86	NUM
ejpam-4425	185	11	,	,	PUNCT
ejpam-4425	185	12	2017	2017	NUM
ejpam-4425	185	13	.	.	PUNCT
ejpam-4425	186	1	[	[	X
ejpam-4425	186	2	10	10	NUM
ejpam-4425	186	3	]	]	X
ejpam-4425	186	4	ibtihal	ibtihal	NOUN
ejpam-4425	186	5	j	j	PROPN
ejpam-4425	186	6	mohammad	mohammad	PROPN
ejpam-4425	186	7	and	and	CCONJ
ejpam-4425	186	8	ali	ali	PROPN
ejpam-4425	186	9	j	j	PROPN
ejpam-4425	186	10	mohammad	mohammad	PROPN
ejpam-4425	186	11	.	.	PUNCT
ejpam-4425	186	12	neural	neural	ADJ
ejpam-4425	186	13	network	network	NOUN
ejpam-4425	186	14	of	of	ADP
ejpam-4425	186	15	multivariate	multivariate	PROPN
ejpam-4425	186	16	bernstein	bernstein	PROPN
ejpam-4425	186	17	operators	operators	PROPN
ejpam-4425	186	18	with	with	ADP
ejpam-4425	186	19	positive	positive	ADJ
ejpam-4425	186	20	integer	integer	NOUN
ejpam-4425	186	21	parameter	parameter	PROPN
ejpam-4425	186	22	m.	m.	PROPN
ejpam-4425	186	23	journal	journal	PROPN
ejpam-4425	186	24	of	of	ADP
ejpam-4425	186	25	interdisciplinary	interdisciplinary	ADJ
ejpam-4425	186	26	mathematics	mathematic	NOUN
ejpam-4425	186	27	,	,	PUNCT
ejpam-4425	186	28	pages	page	NOUN
ejpam-4425	186	29	1–10	1–10	NOUN
ejpam-4425	186	30	,	,	PUNCT
ejpam-4425	186	31	2022	2022	NUM
ejpam-4425	186	32	.	.	PUNCT