id	sid	tid	token	lemma	pos
ejpam-6147	1	1	european	european	PROPN
ejpam-6147	1	2	journal	journal	PROPN
ejpam-6147	1	3	of	of	ADP
ejpam-6147	1	4	pure	pure	ADJ
ejpam-6147	1	5	and	and	CCONJ
ejpam-6147	1	6	applied	applied	ADJ
ejpam-6147	1	7	mathematics	mathematic	NOUN
ejpam-6147	1	8	2025	2025	NUM
ejpam-6147	1	9	,	,	PUNCT
ejpam-6147	1	10	vol	vol	NOUN
ejpam-6147	1	11	.	.	PROPN
ejpam-6147	1	12	18	18	NUM
ejpam-6147	1	13	,	,	PUNCT
ejpam-6147	1	14	issue	issue	NOUN
ejpam-6147	1	15	3	3	NUM
ejpam-6147	1	16	,	,	PUNCT
ejpam-6147	1	17	article	article	NOUN
ejpam-6147	1	18	number	number	NOUN
ejpam-6147	1	19	6147	6147	NUM
ejpam-6147	1	20	issn	issn	PROPN
ejpam-6147	1	21	1307	1307	NUM
ejpam-6147	1	22	-	-	SYM
ejpam-6147	1	23	5543	5543	NUM
ejpam-6147	1	24	–	–	PUNCT
ejpam-6147	1	25	ejpam.com	ejpam.com	X
ejpam-6147	1	26	published	publish	VERB
ejpam-6147	1	27	by	by	ADP
ejpam-6147	1	28	new	new	PROPN
ejpam-6147	1	29	york	york	PROPN
ejpam-6147	1	30	business	business	PROPN
ejpam-6147	1	31	global	global	ADJ
ejpam-6147	1	32	fixed	fix	VERB
ejpam-6147	1	33	point	point	NOUN
ejpam-6147	1	34	theorems	theorem	NOUN
ejpam-6147	1	35	for	for	ADP
ejpam-6147	1	36	a	a	DET
ejpam-6147	1	37	subfamily	subfamily	NOUN
ejpam-6147	1	38	of	of	ADP
ejpam-6147	1	39	non	non	ADJ
ejpam-6147	1	40	-	-	ADJ
ejpam-6147	1	41	expansive	expansive	ADJ
ejpam-6147	1	42	evolution	evolution	NOUN
ejpam-6147	1	43	operators	operator	NOUN
ejpam-6147	1	44	muhammad	muhammad	PROPN
ejpam-6147	1	45	sarwar1,3,∗	sarwar1,3,∗	PROPN
ejpam-6147	1	46	,	,	PUNCT
ejpam-6147	1	47	gul	gul	PROPN
ejpam-6147	1	48	rahmat2	rahmat2	PROPN
ejpam-6147	1	49	,	,	PUNCT
ejpam-6147	1	50	sadam	sadam	PROPN
ejpam-6147	1	51	hussain1	hussain1	PROPN
ejpam-6147	1	52	,	,	PUNCT
ejpam-6147	1	53	mohammad	mohammad	PROPN
ejpam-6147	1	54	yousef	yousef	PROPN
ejpam-6147	1	55	bani	bani	PROPN
ejpam-6147	1	56	mufarrej3	mufarrej3	PROPN
ejpam-6147	1	57	,	,	PUNCT
ejpam-6147	1	58	kamaleldin	kamaleldin	NOUN
ejpam-6147	1	59	abodayeh3	abodayeh3	PROPN
ejpam-6147	1	60	1	1	NUM
ejpam-6147	1	61	department	department	NOUN
ejpam-6147	1	62	of	of	ADP
ejpam-6147	1	63	mathematics	mathematic	NOUN
ejpam-6147	1	64	,	,	PUNCT
ejpam-6147	1	65	university	university	NOUN
ejpam-6147	1	66	of	of	ADP
ejpam-6147	1	67	malakand	malakand	PROPN
ejpam-6147	1	68	,	,	PUNCT
ejpam-6147	1	69	chakdara	chakdara	NOUN
ejpam-6147	1	70	,	,	PUNCT
ejpam-6147	1	71	18800	18800	NUM
ejpam-6147	1	72	,	,	PUNCT
ejpam-6147	1	73	khyber	khyber	PROPN
ejpam-6147	1	74	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6147	1	75	,	,	PUNCT
ejpam-6147	1	76	pakistan	pakistan	PROPN
ejpam-6147	1	77	2	2	NUM
ejpam-6147	1	78	department	department	NOUN
ejpam-6147	1	79	of	of	ADP
ejpam-6147	1	80	mathematics	mathematics	PROPN
ejpam-6147	1	81	,	,	PUNCT
ejpam-6147	1	82	islamia	islamia	PROPN
ejpam-6147	1	83	college	college	PROPN
ejpam-6147	1	84	peshawar	peshawar	PROPN
ejpam-6147	1	85	,	,	PUNCT
ejpam-6147	1	86	khyber	khyber	PROPN
ejpam-6147	1	87	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-6147	1	88	,	,	PUNCT
ejpam-6147	1	89	peshawar	peshawar	PROPN
ejpam-6147	1	90	,	,	PUNCT
ejpam-6147	1	91	pakistan	pakistan	PROPN
ejpam-6147	1	92	3	3	NUM
ejpam-6147	1	93	department	department	NOUN
ejpam-6147	1	94	of	of	ADP
ejpam-6147	1	95	mathematics	mathematic	NOUN
ejpam-6147	1	96	and	and	CCONJ
ejpam-6147	1	97	sciences	science	NOUN
ejpam-6147	1	98	,	,	PUNCT
ejpam-6147	1	99	prince	prince	PROPN
ejpam-6147	1	100	sultan	sultan	PROPN
ejpam-6147	1	101	university	university	PROPN
ejpam-6147	1	102	,	,	PUNCT
ejpam-6147	1	103	riyadh	riyadh	PROPN
ejpam-6147	1	104	11586	11586	NUM
ejpam-6147	1	105	,	,	PUNCT
ejpam-6147	1	106	saudi	saudi	PROPN
ejpam-6147	1	107	arabia	arabia	PROPN
ejpam-6147	1	108	abstract	abstract	NOUN
ejpam-6147	1	109	.	.	PUNCT
ejpam-6147	2	1	in	in	ADP
ejpam-6147	2	2	this	this	DET
ejpam-6147	2	3	manuscript	manuscript	NOUN
ejpam-6147	2	4	,	,	PUNCT
ejpam-6147	2	5	we	we	PRON
ejpam-6147	2	6	study	study	VERB
ejpam-6147	2	7	the	the	DET
ejpam-6147	2	8	fixed	fix	VERB
ejpam-6147	2	9	points	point	NOUN
ejpam-6147	2	10	of	of	ADP
ejpam-6147	2	11	a	a	DET
ejpam-6147	2	12	specific	specific	ADJ
ejpam-6147	2	13	subfamily	subfamily	ADV
ejpam-6147	2	14	within	within	ADP
ejpam-6147	2	15	a	a	DET
ejpam-6147	2	16	nonexpansive	nonexpansive	ADJ
ejpam-6147	2	17	evolution	evolution	NOUN
ejpam-6147	2	18	family	family	NOUN
ejpam-6147	2	19	of	of	ADP
ejpam-6147	2	20	bounded	bounded	ADJ
ejpam-6147	2	21	linear	linear	PROPN
ejpam-6147	2	22	operators	operator	NOUN
ejpam-6147	2	23	on	on	ADP
ejpam-6147	2	24	a	a	DET
ejpam-6147	2	25	hilbert	hilbert	NOUN
ejpam-6147	2	26	space	space	NOUN
ejpam-6147	2	27	h.	h.	NOUN
ejpam-6147	2	28	employing	employ	VERB
ejpam-6147	2	29	the	the	DET
ejpam-6147	2	30	framework	framework	NOUN
ejpam-6147	2	31	of	of	ADP
ejpam-6147	2	32	nets	net	NOUN
ejpam-6147	2	33	and	and	CCONJ
ejpam-6147	2	34	a	a	DET
ejpam-6147	2	35	progression	progression	NOUN
ejpam-6147	2	36	algorithm	algorithm	NOUN
ejpam-6147	2	37	,	,	PUNCT
ejpam-6147	2	38	we	we	PRON
ejpam-6147	2	39	establish	establish	VERB
ejpam-6147	2	40	several	several	ADJ
ejpam-6147	2	41	theorems	theorem	NOUN
ejpam-6147	2	42	concerning	concern	VERB
ejpam-6147	2	43	the	the	DET
ejpam-6147	2	44	strong	strong	ADJ
ejpam-6147	2	45	convergence	convergence	NOUN
ejpam-6147	2	46	of	of	ADP
ejpam-6147	2	47	sequences	sequence	NOUN
ejpam-6147	2	48	to	to	ADP
ejpam-6147	2	49	a	a	DET
ejpam-6147	2	50	common	common	ADJ
ejpam-6147	2	51	fixed	fix	VERB
ejpam-6147	2	52	point	point	NOUN
ejpam-6147	2	53	of	of	ADP
ejpam-6147	2	54	the	the	DET
ejpam-6147	2	55	considered	consider	VERB
ejpam-6147	2	56	subfamily	subfamily	ADV
ejpam-6147	2	57	.	.	PUNCT
ejpam-6147	3	1	to	to	PART
ejpam-6147	3	2	illustrate	illustrate	VERB
ejpam-6147	3	3	the	the	DET
ejpam-6147	3	4	applicability	applicability	NOUN
ejpam-6147	3	5	of	of	ADP
ejpam-6147	3	6	our	our	PRON
ejpam-6147	3	7	results	result	NOUN
ejpam-6147	3	8	,	,	PUNCT
ejpam-6147	3	9	we	we	PRON
ejpam-6147	3	10	provide	provide	VERB
ejpam-6147	3	11	a	a	DET
ejpam-6147	3	12	concrete	concrete	ADJ
ejpam-6147	3	13	example	example	NOUN
ejpam-6147	3	14	that	that	PRON
ejpam-6147	3	15	supports	support	VERB
ejpam-6147	3	16	the	the	DET
ejpam-6147	3	17	theoretical	theoretical	ADJ
ejpam-6147	3	18	findings	finding	NOUN
ejpam-6147	3	19	.	.	PUNCT
ejpam-6147	4	1	the	the	DET
ejpam-6147	4	2	manuscript	manuscript	NOUN
ejpam-6147	4	3	concludes	conclude	VERB
ejpam-6147	4	4	with	with	ADP
ejpam-6147	4	5	an	an	DET
ejpam-6147	4	6	open	open	ADJ
ejpam-6147	4	7	problem	problem	NOUN
ejpam-6147	4	8	to	to	PART
ejpam-6147	4	9	encourage	encourage	VERB
ejpam-6147	4	10	further	further	ADJ
ejpam-6147	4	11	research	research	NOUN
ejpam-6147	4	12	.	.	PUNCT
ejpam-6147	5	1	2020	2020	NUM
ejpam-6147	5	2	mathematics	mathematic	NOUN
ejpam-6147	5	3	subject	subject	NOUN
ejpam-6147	5	4	classifications	classification	NOUN
ejpam-6147	5	5	:	:	PUNCT
ejpam-6147	5	6	46a32	46a32	NUM
ejpam-6147	5	7	,	,	PUNCT
ejpam-6147	5	8	46e20	46e20	NUM
ejpam-6147	5	9	,	,	PUNCT
ejpam-6147	5	10	47b02	47b02	NUM
ejpam-6147	5	11	,	,	PUNCT
ejpam-6147	5	12	47h10	47h10	DET
ejpam-6147	5	13	key	key	ADJ
ejpam-6147	5	14	words	word	NOUN
ejpam-6147	5	15	and	and	CCONJ
ejpam-6147	5	16	phrases	phrase	NOUN
ejpam-6147	5	17	:	:	PUNCT
ejpam-6147	5	18	fixed	fix	VERB
ejpam-6147	5	19	point	point	NOUN
ejpam-6147	5	20	,	,	PUNCT
ejpam-6147	5	21	hilbert	hilbert	NOUN
ejpam-6147	5	22	space	space	NOUN
ejpam-6147	5	23	,	,	PUNCT
ejpam-6147	5	24	nonexpansive	nonexpansive	ADJ
ejpam-6147	5	25	mapping	mapping	NOUN
ejpam-6147	5	26	,	,	PUNCT
ejpam-6147	5	27	evolution	evolution	NOUN
ejpam-6147	5	28	family	family	NOUN
ejpam-6147	5	29	,	,	PUNCT
ejpam-6147	5	30	linear	linear	ADJ
ejpam-6147	5	31	operator	operator	NOUN
ejpam-6147	5	32	1	1	NUM
ejpam-6147	5	33	.	.	PUNCT
ejpam-6147	6	1	introduction	introduction	NOUN
ejpam-6147	6	2	our	our	PRON
ejpam-6147	6	3	primary	primary	ADJ
ejpam-6147	6	4	objective	objective	NOUN
ejpam-6147	6	5	in	in	ADP
ejpam-6147	6	6	this	this	DET
ejpam-6147	6	7	paper	paper	NOUN
ejpam-6147	6	8	is	be	AUX
ejpam-6147	6	9	to	to	PART
ejpam-6147	6	10	demonstrate	demonstrate	VERB
ejpam-6147	6	11	the	the	DET
ejpam-6147	6	12	convergence	convergence	NOUN
ejpam-6147	6	13	of	of	ADP
ejpam-6147	6	14	an	an	DET
ejpam-6147	6	15	algorithm	algorithm	NOUN
ejpam-6147	6	16	to	to	ADP
ejpam-6147	6	17	a	a	DET
ejpam-6147	6	18	shared	share	VERB
ejpam-6147	6	19	fixed	fix	VERB
ejpam-6147	6	20	point(fp	point(fp	NOUN
ejpam-6147	6	21	)	)	PUNCT
ejpam-6147	6	22	of	of	ADP
ejpam-6147	6	23	a	a	DET
ejpam-6147	6	24	subfamily	subfamily	ADV
ejpam-6147	6	25	within	within	ADP
ejpam-6147	6	26	a	a	DET
ejpam-6147	6	27	nee	nee	NOUN
ejpam-6147	6	28	family	family	NOUN
ejpam-6147	6	29	in	in	ADP
ejpam-6147	6	30	hilbert	hilbert	PROPN
ejpam-6147	6	31	spaces	space	NOUN
ejpam-6147	6	32	.	.	PUNCT
ejpam-6147	7	1	initially	initially	ADV
ejpam-6147	7	2	,	,	PUNCT
ejpam-6147	7	3	we	we	PRON
ejpam-6147	7	4	delve	delve	VERB
ejpam-6147	7	5	into	into	ADP
ejpam-6147	7	6	the	the	DET
ejpam-6147	7	7	significance	significance	NOUN
ejpam-6147	7	8	and	and	CCONJ
ejpam-6147	7	9	concept	concept	NOUN
ejpam-6147	7	10	of	of	ADP
ejpam-6147	7	11	semigroups	semigroup	NOUN
ejpam-6147	7	12	and	and	CCONJ
ejpam-6147	7	13	evolution	evolution	NOUN
ejpam-6147	7	14	families	family	NOUN
ejpam-6147	7	15	of	of	ADP
ejpam-6147	7	16	bounded	bounded	ADJ
ejpam-6147	7	17	linear	linear	PROPN
ejpam-6147	7	18	operators	operator	NOUN
ejpam-6147	7	19	.	.	PUNCT
ejpam-6147	8	1	let	let	VERB
ejpam-6147	8	2	’s	’s	NOUN
ejpam-6147	8	3	consider	consider	VERB
ejpam-6147	8	4	the	the	DET
ejpam-6147	8	5	autonomous	autonomous	ADJ
ejpam-6147	8	6	system	system	NOUN
ejpam-6147	8	7	{	{	PUNCT
ejpam-6147	8	8	℧	℧	NOUN
ejpam-6147	8	9	̇(t	̇(t	NUM
ejpam-6147	8	10	)	)	PUNCT
ejpam-6147	8	11	=	=	SYM
ejpam-6147	9	1	a	a	DET
ejpam-6147	9	2	℧	℧	NOUN
ejpam-6147	9	3	(t	(t	NOUN
ejpam-6147	9	4	)	)	PUNCT
ejpam-6147	9	5	,	,	PUNCT
ejpam-6147	9	6	t	t	PROPN
ejpam-6147	9	7	≥	≥	NOUN
ejpam-6147	9	8	0	0	NUM
ejpam-6147	9	9	℧	℧	PROPN
ejpam-6147	9	10	(	(	PUNCT
ejpam-6147	9	11	0	0	NUM
ejpam-6147	9	12	)	)	PUNCT
ejpam-6147	9	13	=	=	PUNCT
ejpam-6147	9	14	℧	℧	NOUN
ejpam-6147	9	15	0	0	NUM
ejpam-6147	9	16	,	,	PUNCT
ejpam-6147	9	17	∗corresponding	∗corresponde	VERB
ejpam-6147	9	18	author	author	NOUN
ejpam-6147	9	19	.	.	PUNCT
ejpam-6147	10	1	doi	doi	NOUN
ejpam-6147	10	2	:	:	PUNCT
ejpam-6147	10	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6147	https://doi.org/10.29020/nybg.ejpam.v18i3.6147	ADJ
ejpam-6147	10	4	email	email	NOUN
ejpam-6147	10	5	addresses	address	NOUN
ejpam-6147	10	6	:	:	PUNCT
ejpam-6147	10	7	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-6147	10	8	(	(	PUNCT
ejpam-6147	10	9	m.	m.	NOUN
ejpam-6147	10	10	sarwar	sarwar	PROPN
ejpam-6147	10	11	)	)	PUNCT
ejpam-6147	10	12	,	,	PUNCT
ejpam-6147	10	13	gulrahmat@icp.edu	gulrahmat@icp.edu	PROPN
ejpam-6147	10	14	(	(	PUNCT
ejpam-6147	10	15	g.	g.	PROPN
ejpam-6147	10	16	rahmat	rahmat	PROPN
ejpam-6147	10	17	)	)	PUNCT
ejpam-6147	10	18	,	,	PUNCT
ejpam-6147	10	19	sadamgaloch@gmail.com	sadamgaloch@gmail.com	X
ejpam-6147	10	20	(	(	PUNCT
ejpam-6147	10	21	s.	s.	PROPN
ejpam-6147	10	22	hussain	hussain	PROPN
ejpam-6147	10	23	)	)	PUNCT
ejpam-6147	10	24	,	,	PUNCT
ejpam-6147	10	25	mfarrej@psu.edu.sa	mfarrej@psu.edu.sa	PROPN
ejpam-6147	10	26	(	(	PUNCT
ejpam-6147	10	27	m.y.b	m.y.b	PROPN
ejpam-6147	10	28	.	.	PUNCT
ejpam-6147	10	29	mufarrej	mufarrej	PROPN
ejpam-6147	10	30	)	)	PUNCT
ejpam-6147	10	31	,	,	PUNCT
ejpam-6147	10	32	kamal@psu.edu.pk	kamal@psu.edu.pk	PROPN
ejpam-6147	10	33	(	(	PUNCT
ejpam-6147	10	34	k.	k.	PROPN
ejpam-6147	10	35	abodayeh	abodayeh	PROPN
ejpam-6147	10	36	)	)	PUNCT
ejpam-6147	10	37	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6147	10	38	1	1	NUM
ejpam-6147	10	39	copyright	copyright	NOUN
ejpam-6147	10	40	:	:	PUNCT
ejpam-6147	10	41	©	©	PROPN
ejpam-6147	10	42	2025	2025	NUM
ejpam-6147	10	43	the	the	DET
ejpam-6147	10	44	author(s	author(s	NOUN
ejpam-6147	10	45	)	)	PUNCT
ejpam-6147	10	46	.	.	PUNCT
ejpam-6147	11	1	(	(	PUNCT
ejpam-6147	11	2	cc	cc	NOUN
ejpam-6147	11	3	by	by	ADP
ejpam-6147	11	4	-	-	PUNCT
ejpam-6147	11	5	nc	nc	PROPN
ejpam-6147	11	6	4.0	4.0	NUM
ejpam-6147	11	7	)	)	PUNCT
ejpam-6147	11	8	m.	m.	NOUN
ejpam-6147	11	9	sarwar	sarwar	PROPN
ejpam-6147	11	10	et	et	PROPN
ejpam-6147	11	11	al	al	PROPN
ejpam-6147	11	12	.	.	PUNCT
ejpam-6147	11	13	/	/	SYM
ejpam-6147	11	14	eur	eur	PROPN
ejpam-6147	11	15	.	.	PUNCT
ejpam-6147	12	1	j.	j.	PROPN
ejpam-6147	12	2	pure	pure	PROPN
ejpam-6147	12	3	appl	appl	PROPN
ejpam-6147	12	4	.	.	PROPN
ejpam-6147	12	5	math	math	PROPN
ejpam-6147	12	6	,	,	PUNCT
ejpam-6147	12	7	18	18	NUM
ejpam-6147	12	8	(	(	PUNCT
ejpam-6147	12	9	3	3	NUM
ejpam-6147	12	10	)	)	PUNCT
ejpam-6147	12	11	(	(	PUNCT
ejpam-6147	12	12	2025	2025	NUM
ejpam-6147	12	13	)	)	PUNCT
ejpam-6147	12	14	,	,	PUNCT
ejpam-6147	12	15	6147	6147	NUM
ejpam-6147	12	16	2	2	NUM
ejpam-6147	12	17	of	of	ADP
ejpam-6147	12	18	18	18	NUM
ejpam-6147	12	19	where	where	SCONJ
ejpam-6147	12	20	a	a	PRON
ejpam-6147	12	21	is	be	AUX
ejpam-6147	12	22	a	a	DET
ejpam-6147	12	23	matrix	matrix	NOUN
ejpam-6147	12	24	of	of	ADP
ejpam-6147	12	25	order	order	NOUN
ejpam-6147	12	26	m	m	VERB
ejpam-6147	12	27	with	with	ADP
ejpam-6147	12	28	complex	complex	ADJ
ejpam-6147	12	29	entries	entry	NOUN
ejpam-6147	12	30	.	.	PUNCT
ejpam-6147	13	1	the	the	DET
ejpam-6147	13	2	solution	solution	NOUN
ejpam-6147	13	3	of	of	ADP
ejpam-6147	13	4	such	such	DET
ejpam-6147	13	5	a	a	DET
ejpam-6147	13	6	system	system	NOUN
ejpam-6147	13	7	leads	lead	VERB
ejpam-6147	13	8	to	to	ADP
ejpam-6147	13	9	the	the	DET
ejpam-6147	13	10	idea	idea	NOUN
ejpam-6147	13	11	of	of	ADP
ejpam-6147	13	12	a	a	DET
ejpam-6147	13	13	semigroup	semigroup	NOUN
ejpam-6147	13	14	.	.	PUNCT
ejpam-6147	14	1	we	we	PRON
ejpam-6147	14	2	recall	recall	VERB
ejpam-6147	14	3	that	that	SCONJ
ejpam-6147	14	4	a	a	DET
ejpam-6147	14	5	family	family	NOUN
ejpam-6147	14	6	s	s	PART
ejpam-6147	14	7	=	=	PUNCT
ejpam-6147	14	8	{	{	PUNCT
ejpam-6147	14	9	s(a	s(a	PROPN
ejpam-6147	14	10	)	)	PUNCT
ejpam-6147	14	11	,	,	PUNCT
ejpam-6147	14	12	a	a	DET
ejpam-6147	14	13	≥	≥	NOUN
ejpam-6147	14	14	0	0	NUM
ejpam-6147	14	15	}	}	PUNCT
ejpam-6147	14	16	,	,	PUNCT
ejpam-6147	14	17	of	of	ADP
ejpam-6147	14	18	bounded	bounded	ADJ
ejpam-6147	14	19	linear	linear	PROPN
ejpam-6147	14	20	operators	operator	NOUN
ejpam-6147	14	21	on	on	ADP
ejpam-6147	14	22	a	a	DET
ejpam-6147	14	23	hilbert	hilbert	NOUN
ejpam-6147	14	24	space	space	NOUN
ejpam-6147	14	25	h	h	NOUN
ejpam-6147	14	26	is	be	AUX
ejpam-6147	14	27	said	say	VERB
ejpam-6147	14	28	to	to	PART
ejpam-6147	14	29	be	be	AUX
ejpam-6147	14	30	a	a	DET
ejpam-6147	14	31	semigroup	semigroup	NOUN
ejpam-6147	14	32	if	if	SCONJ
ejpam-6147	14	33	it	it	PRON
ejpam-6147	14	34	satisfies	satisfy	VERB
ejpam-6147	14	35	the	the	DET
ejpam-6147	14	36	following	follow	VERB
ejpam-6147	14	37	two	two	NUM
ejpam-6147	14	38	conditions	condition	NOUN
ejpam-6147	14	39	,	,	PUNCT
ejpam-6147	14	40	s(a	s(a	PROPN
ejpam-6147	14	41	+	+	PROPN
ejpam-6147	14	42	b	b	X
ejpam-6147	14	43	)	)	PUNCT
ejpam-6147	14	44	=	=	SYM
ejpam-6147	14	45	s(a	s(a	PROPN
ejpam-6147	14	46	)	)	PUNCT
ejpam-6147	14	47	+	+	NUM
ejpam-6147	15	1	s(b	s(b	NOUN
ejpam-6147	15	2	)	)	PUNCT
ejpam-6147	15	3	and	and	CCONJ
ejpam-6147	15	4	s(0	s(0	PROPN
ejpam-6147	15	5	)	)	PUNCT
ejpam-6147	15	6	=	=	NOUN
ejpam-6147	16	1	i	i	PRON
ejpam-6147	16	2	for	for	ADP
ejpam-6147	16	3	all	all	DET
ejpam-6147	16	4	a	a	DET
ejpam-6147	16	5	,	,	PUNCT
ejpam-6147	16	6	b	b	PROPN
ejpam-6147	16	7	≥	≥	NOUN
ejpam-6147	16	8	0	0	NUM
ejpam-6147	16	9	,	,	PUNCT
ejpam-6147	16	10	where	where	SCONJ
ejpam-6147	16	11	i	i	PRON
ejpam-6147	16	12	is	be	AUX
ejpam-6147	16	13	the	the	DET
ejpam-6147	16	14	identity	identity	NOUN
ejpam-6147	16	15	operator	operator	NOUN
ejpam-6147	16	16	on	on	ADP
ejpam-6147	16	17	h.	h.	PROPN
ejpam-6147	16	18	similarly	similarly	ADV
ejpam-6147	16	19	the	the	DET
ejpam-6147	16	20	solution	solution	NOUN
ejpam-6147	16	21	of	of	ADP
ejpam-6147	16	22	the	the	DET
ejpam-6147	16	23	following	follow	VERB
ejpam-6147	16	24	non	non	ADJ
ejpam-6147	16	25	-	-	ADJ
ejpam-6147	16	26	autonomous	autonomous	ADJ
ejpam-6147	16	27	system	system	NOUN
ejpam-6147	16	28	{	{	PUNCT
ejpam-6147	16	29	℧	℧	NOUN
ejpam-6147	16	30	̇(t	̇(t	NUM
ejpam-6147	16	31	)	)	PUNCT
ejpam-6147	16	32	=	=	PUNCT
ejpam-6147	17	1	a(t)	a(t)	PROPN
ejpam-6147	17	2	℧	℧	NOUN
ejpam-6147	17	3	(t	(t	NOUN
ejpam-6147	17	4	)	)	PUNCT
ejpam-6147	18	1	+	+	NUM
ejpam-6147	18	2	eiνti	eiνti	PROPN
ejpam-6147	18	3	t	t	PROPN
ejpam-6147	18	4	≥	≥	PROPN
ejpam-6147	18	5	0	0	NUM
ejpam-6147	18	6	℧	℧	PROPN
ejpam-6147	18	7	(	(	PUNCT
ejpam-6147	18	8	0	0	NUM
ejpam-6147	18	9	)	)	PUNCT
ejpam-6147	18	10	=	=	PUNCT
ejpam-6147	18	11	℧	℧	PROPN
ejpam-6147	18	12	0	0	NUM
ejpam-6147	18	13	,	,	PUNCT
ejpam-6147	18	14	where	where	SCONJ
ejpam-6147	18	15	a(t	a(t	NOUN
ejpam-6147	18	16	)	)	PUNCT
ejpam-6147	18	17	is	be	AUX
ejpam-6147	18	18	a	a	DET
ejpam-6147	18	19	matrix	matrix	NOUN
ejpam-6147	18	20	of	of	ADP
ejpam-6147	18	21	order	order	NOUN
ejpam-6147	18	22	m	m	ADP
ejpam-6147	18	23	,	,	PUNCT
ejpam-6147	18	24	leads	lead	VERB
ejpam-6147	18	25	to	to	ADP
ejpam-6147	18	26	the	the	DET
ejpam-6147	18	27	idea	idea	NOUN
ejpam-6147	18	28	of	of	ADP
ejpam-6147	18	29	an	an	DET
ejpam-6147	18	30	evolution	evolution	NOUN
ejpam-6147	18	31	family	family	NOUN
ejpam-6147	18	32	.	.	PUNCT
ejpam-6147	19	1	a	a	DET
ejpam-6147	19	2	family	family	NOUN
ejpam-6147	19	3	of	of	ADP
ejpam-6147	19	4	bounded	bounded	ADJ
ejpam-6147	19	5	linear	linear	PROPN
ejpam-6147	19	6	operators	operator	NOUN
ejpam-6147	19	7	e	e	X
ejpam-6147	19	8	=	=	PUNCT
ejpam-6147	19	9	{	{	PUNCT
ejpam-6147	19	10	e(a	e(a	PROPN
ejpam-6147	19	11	,	,	PUNCT
ejpam-6147	19	12	b	b	NOUN
ejpam-6147	19	13	)	)	PUNCT
ejpam-6147	19	14	,	,	PUNCT
ejpam-6147	19	15	a	a	DET
ejpam-6147	19	16	≥	≥	NOUN
ejpam-6147	19	17	b	b	NOUN
ejpam-6147	19	18	≥	≥	NOUN
ejpam-6147	19	19	0	0	NUM
ejpam-6147	19	20	}	}	PUNCT
ejpam-6147	19	21	,	,	PUNCT
ejpam-6147	19	22	is	be	AUX
ejpam-6147	19	23	said	say	VERB
ejpam-6147	19	24	to	to	PART
ejpam-6147	19	25	be	be	AUX
ejpam-6147	19	26	an	an	DET
ejpam-6147	19	27	evolution	evolution	NOUN
ejpam-6147	19	28	family	family	NOUN
ejpam-6147	19	29	if	if	SCONJ
ejpam-6147	19	30	it	it	PRON
ejpam-6147	19	31	satisfies	satisfy	VERB
ejpam-6147	19	32	e(a	e(a	NOUN
ejpam-6147	19	33	,	,	PUNCT
ejpam-6147	19	34	b)e(b	b)e(b	ADJ
ejpam-6147	19	35	,	,	PUNCT
ejpam-6147	19	36	c	c	NOUN
ejpam-6147	19	37	)	)	PUNCT
ejpam-6147	19	38	=	=	SYM
ejpam-6147	19	39	e(a	e(a	NOUN
ejpam-6147	19	40	,	,	PUNCT
ejpam-6147	19	41	c	c	NOUN
ejpam-6147	19	42	)	)	PUNCT
ejpam-6147	19	43	and	and	CCONJ
ejpam-6147	19	44	e(a	e(a	PROPN
ejpam-6147	19	45	,	,	PUNCT
ejpam-6147	19	46	a	a	PRON
ejpam-6147	19	47	)	)	PUNCT
ejpam-6147	20	1	=	=	VERB
ejpam-6147	20	2	i	i	PRON
ejpam-6147	20	3	for	for	ADP
ejpam-6147	20	4	all	all	DET
ejpam-6147	20	5	a	a	DET
ejpam-6147	20	6	≥	≥	NOUN
ejpam-6147	20	7	b	b	NOUN
ejpam-6147	20	8	≥	≥	NOUN
ejpam-6147	20	9	c	c	PROPN
ejpam-6147	20	10	≥	≥	PROPN
ejpam-6147	20	11	0	0	NUM
ejpam-6147	20	12	.	.	PUNCT
ejpam-6147	21	1	the	the	DET
ejpam-6147	21	2	theory	theory	NOUN
ejpam-6147	21	3	of	of	ADP
ejpam-6147	21	4	fixed	fix	VERB
ejpam-6147	21	5	points	point	NOUN
ejpam-6147	21	6	finds	find	VERB
ejpam-6147	21	7	myriad	myriad	ADJ
ejpam-6147	21	8	applications	application	NOUN
ejpam-6147	21	9	in	in	ADP
ejpam-6147	21	10	mathematics	mathematic	NOUN
ejpam-6147	21	11	,	,	PUNCT
ejpam-6147	21	12	engineering	engineering	NOUN
ejpam-6147	21	13	sciences	science	NOUN
ejpam-6147	21	14	,	,	PUNCT
ejpam-6147	21	15	economics	economic	NOUN
ejpam-6147	21	16	,	,	PUNCT
ejpam-6147	21	17	and	and	CCONJ
ejpam-6147	21	18	statistics	statistic	NOUN
ejpam-6147	21	19	,	,	PUNCT
ejpam-6147	21	20	among	among	ADP
ejpam-6147	21	21	other	other	ADJ
ejpam-6147	21	22	fields	field	NOUN
ejpam-6147	21	23	(	(	PUNCT
ejpam-6147	21	24	see	see	VERB
ejpam-6147	21	25	,	,	PUNCT
ejpam-6147	21	26	for	for	ADP
ejpam-6147	21	27	example	example	NOUN
ejpam-6147	21	28	,	,	PUNCT
ejpam-6147	21	29	[	[	X
ejpam-6147	21	30	1–5	1–5	X
ejpam-6147	21	31	]	]	X
ejpam-6147	21	32	)	)	PUNCT
ejpam-6147	21	33	.	.	PUNCT
ejpam-6147	22	1	motivated	motivate	VERB
ejpam-6147	22	2	by	by	ADP
ejpam-6147	22	3	baillon	baillon	NOUN
ejpam-6147	22	4	’s	’s	PART
ejpam-6147	22	5	work	work	NOUN
ejpam-6147	23	1	[	[	X
ejpam-6147	23	2	6	6	NUM
ejpam-6147	23	3	]	]	PUNCT
ejpam-6147	23	4	,	,	PUNCT
ejpam-6147	23	5	various	various	ADJ
ejpam-6147	23	6	authors	author	NOUN
ejpam-6147	23	7	have	have	AUX
ejpam-6147	23	8	explored	explore	VERB
ejpam-6147	23	9	fp	fp	NOUN
ejpam-6147	23	10	approximations	approximation	NOUN
ejpam-6147	23	11	for	for	ADP
ejpam-6147	23	12	non	non	ADJ
ejpam-6147	23	13	-	-	ADJ
ejpam-6147	23	14	expansive	expansive	ADJ
ejpam-6147	23	15	families	family	NOUN
ejpam-6147	23	16	using	use	VERB
ejpam-6147	23	17	different	different	ADJ
ejpam-6147	23	18	progressions	progression	NOUN
ejpam-6147	23	19	and	and	CCONJ
ejpam-6147	23	20	algorithms	algorithm	NOUN
ejpam-6147	23	21	.	.	PUNCT
ejpam-6147	24	1	for	for	ADP
ejpam-6147	24	2	instance	instance	NOUN
ejpam-6147	24	3	,	,	PUNCT
ejpam-6147	24	4	in	in	ADP
ejpam-6147	24	5	[	[	PUNCT
ejpam-6147	24	6	7	7	NUM
ejpam-6147	24	7	]	]	PUNCT
ejpam-6147	24	8	,	,	PUNCT
ejpam-6147	24	9	it	it	PRON
ejpam-6147	24	10	is	be	AUX
ejpam-6147	24	11	demonstrated	demonstrate	VERB
ejpam-6147	24	12	that	that	SCONJ
ejpam-6147	24	13	a	a	DET
ejpam-6147	24	14	sequence	sequence	NOUN
ejpam-6147	24	15	of	of	ADP
ejpam-6147	24	16	approximations	approximation	NOUN
ejpam-6147	24	17	converges	converge	VERB
ejpam-6147	24	18	to	to	ADP
ejpam-6147	24	19	a	a	DET
ejpam-6147	24	20	fp	fp	NOUN
ejpam-6147	24	21	of	of	ADP
ejpam-6147	24	22	a	a	DET
ejpam-6147	24	23	non	non	ADJ
ejpam-6147	24	24	-	-	ADJ
ejpam-6147	24	25	expansive	expansive	ADJ
ejpam-6147	24	26	and	and	CCONJ
ejpam-6147	24	27	non	non	ADJ
ejpam-6147	24	28	-	-	ADJ
ejpam-6147	24	29	linear	linear	ADJ
ejpam-6147	24	30	mapping	mapping	NOUN
ejpam-6147	24	31	in	in	ADP
ejpam-6147	24	32	hilbert	hilbert	PROPN
ejpam-6147	24	33	spaces	space	NOUN
ejpam-6147	24	34	.	.	PUNCT
ejpam-6147	25	1	halpern	halpern	PROPN
ejpam-6147	25	2	,	,	PUNCT
ejpam-6147	25	3	in	in	ADP
ejpam-6147	25	4	[	[	X
ejpam-6147	25	5	8	8	NUM
ejpam-6147	25	6	]	]	PUNCT
ejpam-6147	25	7	,	,	PUNCT
ejpam-6147	25	8	provides	provide	VERB
ejpam-6147	25	9	an	an	DET
ejpam-6147	25	10	approximation	approximation	NOUN
ejpam-6147	25	11	of	of	ADP
ejpam-6147	25	12	a	a	DET
ejpam-6147	25	13	fp	fp	PROPN
ejpam-6147	25	14	of	of	ADP
ejpam-6147	25	15	nonexpansive	nonexpansive	ADJ
ejpam-6147	25	16	maps	map	NOUN
ejpam-6147	25	17	.	.	PUNCT
ejpam-6147	26	1	indeed	indeed	ADV
ejpam-6147	26	2	,	,	PUNCT
ejpam-6147	26	3	all	all	DET
ejpam-6147	26	4	the	the	DET
ejpam-6147	26	5	aforementioned	aforementioned	ADJ
ejpam-6147	26	6	references	reference	NOUN
ejpam-6147	26	7	focus	focus	VERB
ejpam-6147	26	8	on	on	ADP
ejpam-6147	26	9	the	the	DET
ejpam-6147	26	10	convergence	convergence	NOUN
ejpam-6147	26	11	of	of	ADP
ejpam-6147	26	12	algorithms	algorithm	NOUN
ejpam-6147	26	13	or	or	CCONJ
ejpam-6147	26	14	progressions	progression	NOUN
ejpam-6147	26	15	to	to	ADP
ejpam-6147	26	16	fixed	fix	VERB
ejpam-6147	26	17	points	point	NOUN
ejpam-6147	26	18	of	of	ADP
ejpam-6147	26	19	non	non	ADJ
ejpam-6147	26	20	-	-	ADJ
ejpam-6147	26	21	expansive	expansive	ADJ
ejpam-6147	26	22	maps	map	NOUN
ejpam-6147	26	23	in	in	ADP
ejpam-6147	26	24	hilbert	hilbert	PROPN
ejpam-6147	26	25	spaces	space	NOUN
ejpam-6147	26	26	.	.	PUNCT
ejpam-6147	27	1	these	these	DET
ejpam-6147	27	2	results	result	NOUN
ejpam-6147	27	3	are	be	AUX
ejpam-6147	27	4	then	then	ADV
ejpam-6147	27	5	utilized	utilize	VERB
ejpam-6147	27	6	to	to	PART
ejpam-6147	27	7	prove	prove	VERB
ejpam-6147	27	8	the	the	DET
ejpam-6147	27	9	convergence	convergence	NOUN
ejpam-6147	27	10	of	of	ADP
ejpam-6147	27	11	algorithms	algorithm	NOUN
ejpam-6147	27	12	to	to	ADP
ejpam-6147	27	13	fixed	fix	VERB
ejpam-6147	27	14	points	point	NOUN
ejpam-6147	27	15	of	of	ADP
ejpam-6147	27	16	semigroups	semigroup	NOUN
ejpam-6147	27	17	in	in	ADP
ejpam-6147	27	18	hilbert	hilbert	NOUN
ejpam-6147	27	19	spaces	space	NOUN
ejpam-6147	27	20	,	,	PUNCT
ejpam-6147	27	21	as	as	SCONJ
ejpam-6147	27	22	seen	see	VERB
ejpam-6147	27	23	in	in	ADP
ejpam-6147	27	24	[	[	X
ejpam-6147	27	25	9	9	NUM
ejpam-6147	27	26	]	]	PUNCT
ejpam-6147	27	27	.	.	PUNCT
ejpam-6147	28	1	baillon	baillon	NOUN
ejpam-6147	29	1	[	[	X
ejpam-6147	29	2	6	6	NUM
ejpam-6147	29	3	]	]	PUNCT
ejpam-6147	29	4	states	state	VERB
ejpam-6147	29	5	that	that	SCONJ
ejpam-6147	29	6	if	if	SCONJ
ejpam-6147	29	7	z	z	NOUN
ejpam-6147	29	8	is	be	AUX
ejpam-6147	29	9	a	a	DET
ejpam-6147	29	10	convex	convex	NOUN
ejpam-6147	29	11	and	and	CCONJ
ejpam-6147	29	12	closed	closed	ADJ
ejpam-6147	29	13	subset	subset	NOUN
ejpam-6147	29	14	of	of	ADP
ejpam-6147	29	15	a	a	DET
ejpam-6147	29	16	hilbert	hilbert	NOUN
ejpam-6147	29	17	space	space	NOUN
ejpam-6147	29	18	h	h	NOUN
ejpam-6147	29	19	,	,	PUNCT
ejpam-6147	29	20	and	and	CCONJ
ejpam-6147	29	21	g	g	NOUN
ejpam-6147	29	22	:	:	PUNCT
ejpam-6147	29	23	z	z	PROPN
ejpam-6147	29	24	→	→	SYM
ejpam-6147	29	25	z	z	NOUN
ejpam-6147	29	26	is	be	AUX
ejpam-6147	29	27	a	a	DET
ejpam-6147	29	28	non	non	ADJ
ejpam-6147	29	29	-	-	ADJ
ejpam-6147	29	30	expansive	expansive	ADJ
ejpam-6147	29	31	mapping	mapping	NOUN
ejpam-6147	29	32	such	such	ADJ
ejpam-6147	29	33	that	that	DET
ejpam-6147	29	34	fg(z	fg(z	ADJ
ejpam-6147	29	35	)	)	PUNCT
ejpam-6147	29	36	̸=	̸=	NOUN
ejpam-6147	29	37	∅	∅	NOUN
ejpam-6147	29	38	,	,	PUNCT
ejpam-6147	29	39	where	where	SCONJ
ejpam-6147	29	40	fg(z	fg(z	NUM
ejpam-6147	29	41	)	)	PUNCT
ejpam-6147	29	42	represents	represent	VERB
ejpam-6147	29	43	the	the	DET
ejpam-6147	29	44	set	set	NOUN
ejpam-6147	29	45	of	of	ADP
ejpam-6147	29	46	all	all	DET
ejpam-6147	29	47	fixed	fix	VERB
ejpam-6147	29	48	points	point	NOUN
ejpam-6147	29	49	of	of	ADP
ejpam-6147	29	50	g	g	NOUN
ejpam-6147	29	51	,	,	PUNCT
ejpam-6147	29	52	then	then	ADV
ejpam-6147	29	53	for	for	ADP
ejpam-6147	29	54	every	every	DET
ejpam-6147	29	55	element	element	NOUN
ejpam-6147	29	56	z	z	PROPN
ejpam-6147	29	57	∈	∈	PROPN
ejpam-6147	30	1	z	z	PROPN
ejpam-6147	30	2	,	,	PUNCT
ejpam-6147	30	3	the	the	DET
ejpam-6147	30	4	cesaro	cesaro	NOUN
ejpam-6147	30	5	mean	mean	NOUN
ejpam-6147	30	6	(	(	PUNCT
ejpam-6147	30	7	1	1	NUM
ejpam-6147	30	8	m	m	NOUN
ejpam-6147	30	9	)	)	PUNCT
ejpam-6147	30	10	∑m	∑m	PROPN
ejpam-6147	31	1	q=1	q=1	PROPN
ejpam-6147	31	2	g	g	PROPN
ejpam-6147	31	3	qz	qz	PROPN
ejpam-6147	31	4	converges	converge	VERB
ejpam-6147	31	5	weakly	weakly	ADV
ejpam-6147	31	6	to	to	ADP
ejpam-6147	31	7	some	some	DET
ejpam-6147	31	8	z	z	NOUN
ejpam-6147	31	9	∈	∈	PROPN
ejpam-6147	31	10	fg(z	fg(z	PROPN
ejpam-6147	31	11	)	)	PUNCT
ejpam-6147	31	12	.	.	PUNCT
ejpam-6147	32	1	here	here	ADV
ejpam-6147	32	2	,	,	PUNCT
ejpam-6147	32	3	if	if	SCONJ
ejpam-6147	32	4	we	we	PRON
ejpam-6147	32	5	set	set	VERB
ejpam-6147	32	6	z	z	NOUN
ejpam-6147	32	7	=	=	SYM
ejpam-6147	32	8	pfg(z	pfg(z	PROPN
ejpam-6147	32	9	)	)	PUNCT
ejpam-6147	32	10	z	z	NOUN
ejpam-6147	32	11	for	for	ADP
ejpam-6147	32	12	any	any	DET
ejpam-6147	32	13	element	element	NOUN
ejpam-6147	32	14	z	z	PROPN
ejpam-6147	32	15	∈	∈	PROPN
ejpam-6147	33	1	z	z	PROPN
ejpam-6147	33	2	,	,	PUNCT
ejpam-6147	33	3	then	then	ADV
ejpam-6147	33	4	pfg(z	pfg(z	PROPN
ejpam-6147	33	5	)	)	PUNCT
ejpam-6147	33	6	from	from	ADP
ejpam-6147	33	7	z	z	PROPN
ejpam-6147	33	8	onto	onto	ADP
ejpam-6147	33	9	fg(z	fg(z	NUM
ejpam-6147	33	10	)	)	PUNCT
ejpam-6147	33	11	is	be	AUX
ejpam-6147	33	12	a	a	DET
ejpam-6147	33	13	non	non	ADJ
ejpam-6147	33	14	-	-	ADJ
ejpam-6147	33	15	expansive	expansive	ADJ
ejpam-6147	33	16	retraction	retraction	NOUN
ejpam-6147	33	17	.	.	PUNCT
ejpam-6147	34	1	in	in	ADP
ejpam-6147	34	2	1976	1976	NUM
ejpam-6147	34	3	,	,	PUNCT
ejpam-6147	34	4	brezis	brezis	NOUN
ejpam-6147	34	5	and	and	CCONJ
ejpam-6147	34	6	baillon	baillon	NOUN
ejpam-6147	35	1	[	[	X
ejpam-6147	35	2	8	8	NUM
ejpam-6147	35	3	]	]	PUNCT
ejpam-6147	35	4	proved	prove	VERB
ejpam-6147	35	5	that	that	SCONJ
ejpam-6147	35	6	if	if	SCONJ
ejpam-6147	35	7	g	g	PROPN
ejpam-6147	35	8	=	=	VERB
ejpam-6147	35	9	g(s)s	g(s)s	X
ejpam-6147	35	10	≥	≥	NOUN
ejpam-6147	35	11	0	0	NUM
ejpam-6147	35	12	:	:	PUNCT
ejpam-6147	35	13	z	z	X
ejpam-6147	35	14	→	→	SYM
ejpam-6147	35	15	z	z	NOUN
ejpam-6147	35	16	is	be	AUX
ejpam-6147	35	17	a	a	DET
ejpam-6147	35	18	non	non	ADJ
ejpam-6147	35	19	-	-	ADJ
ejpam-6147	35	20	expansive	expansive	ADJ
ejpam-6147	35	21	semigroup	semigroup	NOUN
ejpam-6147	35	22	,	,	PUNCT
ejpam-6147	35	23	then	then	ADV
ejpam-6147	35	24	{	{	PUNCT
ejpam-6147	35	25	(	(	PUNCT
ejpam-6147	35	26	1	1	NUM
ejpam-6147	35	27	a	a	PRON
ejpam-6147	35	28	)	)	PUNCT
ejpam-6147	35	29	∫	∫	PROPN
ejpam-6147	35	30	a	a	DET
ejpam-6147	35	31	0	0	NUM
ejpam-6147	35	32	g(s)uds	g(s)uds	PROPN
ejpam-6147	35	33	}	}	PUNCT
ejpam-6147	35	34	s≥0	s≥0	VERB
ejpam-6147	35	35	converges	converge	VERB
ejpam-6147	35	36	weakly	weakly	ADV
ejpam-6147	35	37	to	to	ADP
ejpam-6147	35	38	a	a	DET
ejpam-6147	35	39	common	common	ADJ
ejpam-6147	35	40	fp	fp	NOUN
ejpam-6147	35	41	of	of	ADP
ejpam-6147	35	42	g.	g.	PROPN
ejpam-6147	35	43	these	these	DET
ejpam-6147	35	44	results	result	NOUN
ejpam-6147	35	45	have	have	AUX
ejpam-6147	35	46	been	be	AUX
ejpam-6147	35	47	generalized	generalize	VERB
ejpam-6147	35	48	by	by	ADP
ejpam-6147	35	49	several	several	ADJ
ejpam-6147	35	50	authors	author	NOUN
ejpam-6147	35	51	,	,	PUNCT
ejpam-6147	35	52	first	first	ADV
ejpam-6147	35	53	by	by	ADP
ejpam-6147	35	54	halpern	halpern	PROPN
ejpam-6147	35	55	in	in	ADP
ejpam-6147	35	56	[	[	X
ejpam-6147	35	57	10	10	NUM
ejpam-6147	35	58	]	]	PUNCT
ejpam-6147	35	59	and	and	CCONJ
ejpam-6147	35	60	then	then	ADV
ejpam-6147	35	61	by	by	ADP
ejpam-6147	35	62	wittmann	wittmann	PROPN
ejpam-6147	35	63	in	in	ADP
ejpam-6147	35	64	[	[	X
ejpam-6147	35	65	11	11	NUM
ejpam-6147	35	66	]	]	PUNCT
ejpam-6147	35	67	.	.	PUNCT
ejpam-6147	36	1	they	they	PRON
ejpam-6147	36	2	considered	consider	VERB
ejpam-6147	36	3	the	the	DET
ejpam-6147	36	4	following	follow	VERB
ejpam-6147	36	5	algorithm	algorithm	NOUN
ejpam-6147	36	6	ς0	ς0	NOUN
ejpam-6147	36	7	=	=	PUNCT
ejpam-6147	37	1	ς	ς	PROPN
ejpam-6147	37	2	∈	∈	PROPN
ejpam-6147	37	3	z	z	NOUN
ejpam-6147	37	4	;	;	PUNCT
ejpam-6147	37	5	ςm+1	ςm+1	PROPN
ejpam-6147	37	6	=	=	SYM
ejpam-6147	37	7	µm+1ς	µm+1ς	PROPN
ejpam-6147	37	8	+	+	CCONJ
ejpam-6147	37	9	(	(	PUNCT
ejpam-6147	37	10	1−	1−	NUM
ejpam-6147	37	11	µm+1)twm	µm+1)twm	NOUN
ejpam-6147	37	12	,	,	PUNCT
ejpam-6147	37	13	m	m	VERB
ejpam-6147	37	14	≥	≥	NOUN
ejpam-6147	37	15	0	0	NUM
ejpam-6147	37	16	.	.	PUNCT
ejpam-6147	38	1	where	where	SCONJ
ejpam-6147	38	2	{	{	PUNCT
ejpam-6147	38	3	ςm	ςm	NOUN
ejpam-6147	38	4	}	}	PUNCT
ejpam-6147	38	5	is	be	AUX
ejpam-6147	38	6	a	a	DET
ejpam-6147	38	7	progression	progression	NOUN
ejpam-6147	38	8	whose	whose	DET
ejpam-6147	38	9	terms	term	NOUN
ejpam-6147	38	10	are	be	AUX
ejpam-6147	38	11	between	between	ADP
ejpam-6147	38	12	0	0	NUM
ejpam-6147	38	13	and	and	CCONJ
ejpam-6147	38	14	1	1	NUM
ejpam-6147	38	15	and	and	CCONJ
ejpam-6147	38	16	satisfying	satisfy	VERB
ejpam-6147	38	17	the	the	DET
ejpam-6147	38	18	following	follow	VERB
ejpam-6147	38	19	three	three	NUM
ejpam-6147	38	20	conditions	condition	NOUN
ejpam-6147	38	21	,	,	PUNCT
ejpam-6147	38	22	•	•	NUM
ejpam-6147	38	23	limm→+∞	limm→+∞	X
ejpam-6147	38	24	ςm	ςm	ADJ
ejpam-6147	39	1	=	=	SYM
ejpam-6147	39	2	0	0	NUM
ejpam-6147	39	3	;	;	PUNCT
ejpam-6147	39	4	•	•	X
ejpam-6147	39	5	∑+∞	∑+∞	PUNCT
ejpam-6147	40	1	m=1	m=1	X
ejpam-6147	40	2	ςm	ςm	NOUN
ejpam-6147	40	3	=	=	SYM
ejpam-6147	40	4	+	+	NOUN
ejpam-6147	40	5	∞	∞	NOUN
ejpam-6147	40	6	;	;	PUNCT
ejpam-6147	40	7	•	•	NUM
ejpam-6147	40	8	∑+∞	∑+∞	NOUN
ejpam-6147	40	9	m=1	m=1	PART
ejpam-6147	40	10	|ςm+1	|ςm+1	PUNCT
ejpam-6147	40	11	−	−	NOUN
ejpam-6147	41	1	ςm|	ςm|	NOUN
ejpam-6147	41	2	<	<	X
ejpam-6147	41	3	+	+	NOUN
ejpam-6147	41	4	∞.	∞.	PROPN
ejpam-6147	41	5	in	in	ADP
ejpam-6147	41	6	[	[	X
ejpam-6147	41	7	11	11	NUM
ejpam-6147	41	8	]	]	PUNCT
ejpam-6147	41	9	,	,	PUNCT
ejpam-6147	41	10	wittmann	wittmann	PROPN
ejpam-6147	41	11	proved	prove	VERB
ejpam-6147	41	12	that	that	SCONJ
ejpam-6147	41	13	for	for	ADP
ejpam-6147	41	14	every	every	DET
ejpam-6147	41	15	ς	ς	PROPN
ejpam-6147	41	16	∈	∈	PROPN
ejpam-6147	41	17	z	z	PROPN
ejpam-6147	41	18	,	,	PUNCT
ejpam-6147	41	19	the	the	DET
ejpam-6147	41	20	progression	progression	NOUN
ejpam-6147	41	21	ςm	ςm	NOUN
ejpam-6147	41	22	strongly	strongly	ADV
ejpam-6147	41	23	converges	converge	VERB
ejpam-6147	41	24	to	to	ADP
ejpam-6147	41	25	a	a	DET
ejpam-6147	41	26	unique	unique	ADJ
ejpam-6147	41	27	fp	fp	X
ejpam-6147	41	28	p	p	X
ejpam-6147	41	29	(	(	PUNCT
ejpam-6147	41	30	ς	ς	PROPN
ejpam-6147	41	31	)	)	PUNCT
ejpam-6147	41	32	∈	∈	PROPN
ejpam-6147	41	33	fg	fg	NOUN
ejpam-6147	41	34	,	,	PUNCT
ejpam-6147	41	35	where	where	SCONJ
ejpam-6147	41	36	p	p	NOUN
ejpam-6147	41	37	:	:	PUNCT
ejpam-6147	41	38	h	h	PROPN
ejpam-6147	41	39	→	→	SYM
ejpam-6147	41	40	fg	fg	PROPN
ejpam-6147	41	41	is	be	AUX
ejpam-6147	41	42	a	a	DET
ejpam-6147	41	43	metric	metric	ADJ
ejpam-6147	41	44	projection	projection	NOUN
ejpam-6147	41	45	.	.	PUNCT
ejpam-6147	42	1	recently	recently	ADV
ejpam-6147	42	2	,	,	PUNCT
ejpam-6147	42	3	in	in	ADP
ejpam-6147	42	4	[	[	X
ejpam-6147	42	5	12	12	NUM
ejpam-6147	42	6	]	]	PUNCT
ejpam-6147	42	7	,	,	PUNCT
ejpam-6147	42	8	m.	m.	NOUN
ejpam-6147	42	9	sarwar	sarwar	PROPN
ejpam-6147	42	10	et	et	PROPN
ejpam-6147	42	11	al	al	PROPN
ejpam-6147	42	12	.	.	PUNCT
ejpam-6147	42	13	/	/	SYM
ejpam-6147	42	14	eur	eur	PROPN
ejpam-6147	42	15	.	.	PUNCT
ejpam-6147	43	1	j.	j.	PROPN
ejpam-6147	43	2	pure	pure	PROPN
ejpam-6147	43	3	appl	appl	PROPN
ejpam-6147	43	4	.	.	PROPN
ejpam-6147	43	5	math	math	PROPN
ejpam-6147	43	6	,	,	PUNCT
ejpam-6147	43	7	18	18	NUM
ejpam-6147	43	8	(	(	PUNCT
ejpam-6147	43	9	3	3	NUM
ejpam-6147	43	10	)	)	PUNCT
ejpam-6147	43	11	(	(	PUNCT
ejpam-6147	43	12	2025	2025	NUM
ejpam-6147	43	13	)	)	PUNCT
ejpam-6147	43	14	,	,	PUNCT
ejpam-6147	43	15	6147	6147	NUM
ejpam-6147	43	16	3	3	NUM
ejpam-6147	43	17	of	of	ADP
ejpam-6147	43	18	18	18	NUM
ejpam-6147	43	19	kimure	kimure	NOUN
ejpam-6147	43	20	et	et	PROPN
ejpam-6147	43	21	al	al	PROPN
ejpam-6147	43	22	.	.	PROPN
ejpam-6147	44	1	generalized	generalized	PROPN
ejpam-6147	44	2	wittmann	wittmann	PROPN
ejpam-6147	44	3	’s	’s	PART
ejpam-6147	44	4	result	result	NOUN
ejpam-6147	44	5	by	by	ADP
ejpam-6147	44	6	proving	prove	VERB
ejpam-6147	44	7	that	that	SCONJ
ejpam-6147	44	8	if	if	SCONJ
ejpam-6147	44	9	ς1	ς1	NOUN
ejpam-6147	44	10	∈	∈	PROPN
ejpam-6147	44	11	z	z	NOUN
ejpam-6147	44	12	,	,	PUNCT
ejpam-6147	44	13	where	where	SCONJ
ejpam-6147	44	14	z	z	NOUN
ejpam-6147	44	15	is	be	AUX
ejpam-6147	44	16	a	a	DET
ejpam-6147	44	17	convex	convex	NOUN
ejpam-6147	44	18	and	and	CCONJ
ejpam-6147	44	19	closed	closed	ADJ
ejpam-6147	44	20	subset	subset	NOUN
ejpam-6147	44	21	of	of	ADP
ejpam-6147	44	22	a	a	DET
ejpam-6147	44	23	hilbert	hilbert	NOUN
ejpam-6147	44	24	space	space	NOUN
ejpam-6147	44	25	,	,	PUNCT
ejpam-6147	44	26	then	then	ADV
ejpam-6147	44	27	the	the	DET
ejpam-6147	44	28	following	follow	VERB
ejpam-6147	44	29	iterative	iterative	NOUN
ejpam-6147	44	30	scheme	scheme	NOUN
ejpam-6147	44	31	converges	converge	NOUN
ejpam-6147	44	32	strongly	strongly	ADV
ejpam-6147	44	33	to	to	PART
ejpam-6147	44	34	pς	pς	VERB
ejpam-6147	44	35	,	,	PUNCT
ejpam-6147	44	36	where	where	SCONJ
ejpam-6147	44	37	p	p	NOUN
ejpam-6147	44	38	:	:	PUNCT
ejpam-6147	44	39	z	z	PROPN
ejpam-6147	44	40	→	→	SYM
ejpam-6147	44	41	f	f	PROPN
ejpam-6147	44	42	is	be	AUX
ejpam-6147	44	43	a	a	DET
ejpam-6147	44	44	non	non	ADJ
ejpam-6147	44	45	-	-	ADJ
ejpam-6147	44	46	expansive	expansive	ADJ
ejpam-6147	44	47	retraction	retraction	NOUN
ejpam-6147	44	48	and	and	CCONJ
ejpam-6147	44	49	f	f	NOUN
ejpam-6147	44	50	=	=	NOUN
ejpam-6147	44	51	⋂q	⋂q	PROPN
ejpam-6147	44	52	k=1	k=1	NOUN
ejpam-6147	44	53	fgk	fgk	NOUN
ejpam-6147	44	54	̸=	̸=	PROPN
ejpam-6147	44	55	∅.	∅.	ADP
ejpam-6147	44	56	takahashi	takahashi	PROPN
ejpam-6147	44	57	and	and	CCONJ
ejpam-6147	44	58	shimizu	shimizu	PROPN
ejpam-6147	44	59	,	,	PUNCT
ejpam-6147	44	60	in	in	ADP
ejpam-6147	44	61	[	[	X
ejpam-6147	44	62	13	13	NUM
ejpam-6147	44	63	]	]	PUNCT
ejpam-6147	44	64	,	,	PUNCT
ejpam-6147	44	65	studied	study	VERB
ejpam-6147	44	66	the	the	DET
ejpam-6147	44	67	strong	strong	ADJ
ejpam-6147	44	68	convergence	convergence	NOUN
ejpam-6147	44	69	of	of	ADP
ejpam-6147	44	70	the	the	DET
ejpam-6147	44	71	progression	progression	NOUN
ejpam-6147	44	72	℧	℧	VERB
ejpam-6147	44	73	m	m	AUX
ejpam-6147	44	74	defined	define	VERB
ejpam-6147	44	75	by	by	ADP
ejpam-6147	44	76	the	the	DET
ejpam-6147	44	77	equation	equation	NOUN
ejpam-6147	44	78	℧	℧	NOUN
ejpam-6147	44	79	m+1	m+1	NOUN
ejpam-6147	44	80	=	=	SYM
ejpam-6147	44	81	δm	δm	PROPN
ejpam-6147	44	82	℧	℧	PROPN
ejpam-6147	44	83	+	+	CCONJ
ejpam-6147	44	84	(	(	PUNCT
ejpam-6147	44	85	1−	1−	NUM
ejpam-6147	44	86	δ	δ	NOUN
ejpam-6147	44	87	)	)	PUNCT
ejpam-6147	44	88	1	1	NUM
ejpam-6147	45	1	αm	αm	NOUN
ejpam-6147	45	2	∫	∫	PROPN
ejpam-6147	45	3	αm	αm	NOUN
ejpam-6147	45	4	1	1	NUM
ejpam-6147	45	5	g(s)	g(s)	PROPN
ejpam-6147	45	6	℧	℧	PROPN
ejpam-6147	45	7	mds	mds	PROPN
ejpam-6147	45	8	,	,	PUNCT
ejpam-6147	45	9	m	m	PROPN
ejpam-6147	45	10	≥	≥	NOUN
ejpam-6147	45	11	0	0	NUM
ejpam-6147	45	12	,	,	PUNCT
ejpam-6147	45	13	where	where	SCONJ
ejpam-6147	45	14	δm	δm	ADV
ejpam-6147	45	15	is	be	AUX
ejpam-6147	45	16	a	a	DET
ejpam-6147	45	17	progression	progression	NOUN
ejpam-6147	45	18	in	in	ADP
ejpam-6147	45	19	(	(	PUNCT
ejpam-6147	45	20	0	0	NUM
ejpam-6147	45	21	,	,	PUNCT
ejpam-6147	45	22	1	1	NUM
ejpam-6147	45	23	)	)	PUNCT
ejpam-6147	45	24	and	and	CCONJ
ejpam-6147	45	25	αm	αm	NOUN
ejpam-6147	45	26	is	be	AUX
ejpam-6147	45	27	a	a	DET
ejpam-6147	45	28	progression	progression	NOUN
ejpam-6147	45	29	in	in	ADP
ejpam-6147	45	30	(	(	PUNCT
ejpam-6147	45	31	0,+∞	0,+∞	NUM
ejpam-6147	45	32	)	)	PUNCT
ejpam-6147	45	33	that	that	PRON
ejpam-6147	45	34	diverges	diverge	VERB
ejpam-6147	45	35	to	to	ADP
ejpam-6147	45	36	+	+	PROPN
ejpam-6147	45	37	∞.	∞.	PROPN
ejpam-6147	45	38	for	for	ADP
ejpam-6147	45	39	other	other	ADJ
ejpam-6147	45	40	recent	recent	ADJ
ejpam-6147	45	41	work	work	NOUN
ejpam-6147	45	42	in	in	ADP
ejpam-6147	45	43	the	the	DET
ejpam-6147	45	44	field	field	NOUN
ejpam-6147	45	45	of	of	ADP
ejpam-6147	45	46	fixed	fix	VERB
ejpam-6147	45	47	point	point	NOUN
ejpam-6147	45	48	theory	theory	NOUN
ejpam-6147	45	49	we	we	PRON
ejpam-6147	45	50	refer	refer	VERB
ejpam-6147	45	51	to	to	ADP
ejpam-6147	45	52	[	[	X
ejpam-6147	45	53	12	12	NUM
ejpam-6147	45	54	,	,	PUNCT
ejpam-6147	45	55	14–19	14–19	NUM
ejpam-6147	45	56	]	]	PUNCT
ejpam-6147	45	57	.	.	PUNCT
ejpam-6147	46	1	in	in	ADP
ejpam-6147	46	2	this	this	DET
ejpam-6147	46	3	paper	paper	NOUN
ejpam-6147	46	4	,	,	PUNCT
ejpam-6147	46	5	we	we	PRON
ejpam-6147	46	6	aim	aim	VERB
ejpam-6147	46	7	to	to	PART
ejpam-6147	46	8	generalize	generalize	VERB
ejpam-6147	46	9	the	the	DET
ejpam-6147	46	10	results	result	NOUN
ejpam-6147	46	11	provided	provide	VERB
ejpam-6147	46	12	in	in	ADP
ejpam-6147	46	13	[	[	NOUN
ejpam-6147	46	14	9	9	NUM
ejpam-6147	46	15	]	]	PUNCT
ejpam-6147	46	16	from	from	ADP
ejpam-6147	46	17	a	a	DET
ejpam-6147	46	18	semigroup	semigroup	NOUN
ejpam-6147	46	19	to	to	ADP
ejpam-6147	46	20	a	a	DET
ejpam-6147	46	21	subfamily	subfamily	NOUN
ejpam-6147	46	22	of	of	ADP
ejpam-6147	46	23	a	a	DET
ejpam-6147	46	24	nee	nee	NOUN
ejpam-6147	46	25	equation	equation	NOUN
ejpam-6147	46	26	in	in	ADP
ejpam-6147	46	27	a	a	DET
ejpam-6147	46	28	hilbert	hilbert	NOUN
ejpam-6147	46	29	space	space	NOUN
ejpam-6147	46	30	.	.	PUNCT
ejpam-6147	47	1	for	for	ADP
ejpam-6147	47	2	same	same	ADJ
ejpam-6147	47	3	generalization	generalization	NOUN
ejpam-6147	47	4	we	we	PRON
ejpam-6147	47	5	refer	refer	VERB
ejpam-6147	47	6	to	to	ADP
ejpam-6147	47	7	[	[	X
ejpam-6147	47	8	20	20	NUM
ejpam-6147	47	9	,	,	PUNCT
ejpam-6147	47	10	21	21	NUM
ejpam-6147	47	11	]	]	PUNCT
ejpam-6147	47	12	.	.	PUNCT
ejpam-6147	48	1	2	2	X
ejpam-6147	48	2	.	.	X
ejpam-6147	48	3	preliminaries	preliminary	NOUN
ejpam-6147	48	4	in	in	ADP
ejpam-6147	48	5	this	this	DET
ejpam-6147	48	6	section	section	NOUN
ejpam-6147	48	7	,	,	PUNCT
ejpam-6147	48	8	we	we	PRON
ejpam-6147	48	9	present	present	VERB
ejpam-6147	48	10	basic	basic	ADJ
ejpam-6147	48	11	definitions	definition	NOUN
ejpam-6147	48	12	and	and	CCONJ
ejpam-6147	48	13	results	result	NOUN
ejpam-6147	48	14	that	that	PRON
ejpam-6147	48	15	are	be	AUX
ejpam-6147	48	16	instrumental	instrumental	ADJ
ejpam-6147	48	17	in	in	ADP
ejpam-6147	48	18	proving	prove	VERB
ejpam-6147	48	19	our	our	PRON
ejpam-6147	48	20	main	main	ADJ
ejpam-6147	48	21	results	result	NOUN
ejpam-6147	48	22	.	.	PUNCT
ejpam-6147	49	1	let	let	VERB
ejpam-6147	49	2	z	z	NOUN
ejpam-6147	49	3	̸=	̸=	PROPN
ejpam-6147	49	4	∅	∅	NOUN
ejpam-6147	49	5	be	be	AUX
ejpam-6147	49	6	a	a	DET
ejpam-6147	49	7	closed	closed	ADJ
ejpam-6147	49	8	and	and	CCONJ
ejpam-6147	49	9	convex	convex	NOUN
ejpam-6147	49	10	subset	subset	NOUN
ejpam-6147	49	11	of	of	ADP
ejpam-6147	49	12	a	a	DET
ejpam-6147	49	13	real	real	ADJ
ejpam-6147	49	14	hilbert	hilbert	NOUN
ejpam-6147	49	15	space	space	NOUN
ejpam-6147	49	16	h.	h.	PROPN
ejpam-6147	49	17	an	an	DET
ejpam-6147	49	18	operator	operator	NOUN
ejpam-6147	49	19	g	g	NOUN
ejpam-6147	49	20	:	:	PUNCT
ejpam-6147	49	21	z	z	PROPN
ejpam-6147	49	22	→	→	SYM
ejpam-6147	49	23	z	z	NOUN
ejpam-6147	49	24	is	be	AUX
ejpam-6147	49	25	considered	consider	VERB
ejpam-6147	49	26	non	non	ADJ
ejpam-6147	49	27	-	-	ADJ
ejpam-6147	49	28	expansive	expansive	ADJ
ejpam-6147	49	29	if	if	SCONJ
ejpam-6147	49	30	∥gd−gb∥	∥gd−gb∥	ADJ
ejpam-6147	49	31	≤	≤	PUNCT
ejpam-6147	50	1	∥d−	∥d−	PRON
ejpam-6147	50	2	b∥	b∥	NOUN
ejpam-6147	50	3	for	for	ADP
ejpam-6147	50	4	all	all	DET
ejpam-6147	50	5	d	d	PROPN
ejpam-6147	50	6	,	,	PUNCT
ejpam-6147	50	7	b	b	PROPN
ejpam-6147	50	8	∈	∈	PROPN
ejpam-6147	50	9	z.	z.	X
ejpam-6147	51	1	an	an	DET
ejpam-6147	51	2	operator	operator	NOUN
ejpam-6147	51	3	pz	pz	NOUN
ejpam-6147	51	4	:	:	PUNCT
ejpam-6147	51	5	h	h	PROPN
ejpam-6147	51	6	→	→	SYM
ejpam-6147	51	7	z	z	NOUN
ejpam-6147	51	8	is	be	AUX
ejpam-6147	51	9	is	be	AUX
ejpam-6147	51	10	said	say	VERB
ejpam-6147	51	11	to	to	PART
ejpam-6147	51	12	be	be	AUX
ejpam-6147	51	13	a	a	DET
ejpam-6147	51	14	projection	projection	NOUN
ejpam-6147	51	15	from	from	ADP
ejpam-6147	51	16	h	h	NOUN
ejpam-6147	51	17	onto	onto	ADP
ejpam-6147	51	18	z	z	NOUN
ejpam-6147	51	19	if	if	SCONJ
ejpam-6147	51	20	for	for	ADP
ejpam-6147	51	21	each	each	DET
ejpam-6147	51	22	element	element	NOUN
ejpam-6147	51	23	ς	ς	PROPN
ejpam-6147	51	24	∈	∈	PROPN
ejpam-6147	51	25	h	h	NOUN
ejpam-6147	51	26	and	and	CCONJ
ejpam-6147	51	27	pzς	pzς	NOUN
ejpam-6147	51	28	∈	∈	PROPN
ejpam-6147	51	29	z	z	NOUN
ejpam-6147	51	30	the	the	DET
ejpam-6147	51	31	following	follow	VERB
ejpam-6147	51	32	hold	hold	NOUN
ejpam-6147	51	33	,	,	PUNCT
ejpam-6147	51	34	∥ς	∥ς	NOUN
ejpam-6147	51	35	−	−	NOUN
ejpam-6147	51	36	pzς∥	pzς∥	PROPN
ejpam-6147	51	37	=	=	X
ejpam-6147	51	38	inf	inf	ADJ
ejpam-6147	51	39	℧	℧	PROPN
ejpam-6147	51	40	∈z	∈z	PROPN
ejpam-6147	51	41	∥ς	∥ς	PROPN
ejpam-6147	51	42	−	−	NOUN
ejpam-6147	51	43	℧	℧	NOUN
ejpam-6147	51	44	∥	∥	NUM
ejpam-6147	51	45	:	:	PUNCT
ejpam-6147	51	46	=	=	SYM
ejpam-6147	51	47	d(ς	d(ς	NOUN
ejpam-6147	51	48	,	,	PUNCT
ejpam-6147	51	49	z	z	NOUN
ejpam-6147	51	50	)	)	PUNCT
ejpam-6147	51	51	,	,	PUNCT
ejpam-6147	51	52	and	and	CCONJ
ejpam-6147	51	53	∥pzς	∥pzς	NOUN
ejpam-6147	51	54	−	−	PROPN
ejpam-6147	51	55	pz	pz	PROPN
ejpam-6147	51	56	℧	℧	NOUN
ejpam-6147	51	57	∥	∥	PUNCT
ejpam-6147	51	58	≤	≤	NUM
ejpam-6147	51	59	∥ς	∥ς	PROPN
ejpam-6147	51	60	−	−	NOUN
ejpam-6147	51	61	℧	℧	NOUN
ejpam-6147	51	62	∥.	∥.	NOUN
ejpam-6147	51	63	the	the	DET
ejpam-6147	51	64	above	above	ADJ
ejpam-6147	51	65	inequality	inequality	NOUN
ejpam-6147	51	66	illustrates	illustrate	VERB
ejpam-6147	51	67	that	that	SCONJ
ejpam-6147	51	68	pz	pz	NOUN
ejpam-6147	51	69	is	be	AUX
ejpam-6147	51	70	non	non	ADJ
ejpam-6147	51	71	-	-	ADJ
ejpam-6147	51	72	expansive	expansive	ADJ
ejpam-6147	51	73	,	,	PUNCT
ejpam-6147	51	74	and	and	CCONJ
ejpam-6147	51	75	furthermore	furthermore	ADV
ejpam-6147	51	76	∥pzς	∥pzς	PROPN
ejpam-6147	51	77	−	−	PROPN
ejpam-6147	51	78	pz	pz	PROPN
ejpam-6147	51	79	℧	℧	PROPN
ejpam-6147	51	80	∥2	∥2	NOUN
ejpam-6147	51	81	≤	≤	NOUN
ejpam-6147	51	82	⟨ς	⟨ς	PRON
ejpam-6147	51	83	−	−	PROPN
ejpam-6147	51	84	℧	℧	PROPN
ejpam-6147	51	85	,	,	PUNCT
ejpam-6147	51	86	pzς	pzς	NOUN
ejpam-6147	51	87	−	−	PROPN
ejpam-6147	51	88	pz	pz	PROPN
ejpam-6147	51	89	℧	℧	PROPN
ejpam-6147	51	90	⟩	⟩	NOUN
ejpam-6147	51	91	,	,	PUNCT
ejpam-6147	51	92	for	for	ADP
ejpam-6147	51	93	all	all	DET
ejpam-6147	51	94	ς	ς	PROPN
ejpam-6147	51	95	,	,	PUNCT
ejpam-6147	51	96	℧	℧	PROPN
ejpam-6147	51	97	∈	∈	PROPN
ejpam-6147	51	98	h.	h.	PROPN
ejpam-6147	51	99	moreover	moreover	ADV
ejpam-6147	51	100	,	,	PUNCT
ejpam-6147	51	101	we	we	PRON
ejpam-6147	51	102	have	have	VERB
ejpam-6147	51	103	⟨ς	⟨ς	PUNCT
ejpam-6147	51	104	−	−	NOUN
ejpam-6147	51	105	℧	℧	PROPN
ejpam-6147	51	106	,	,	PUNCT
ejpam-6147	51	107	pzς	pzς	NOUN
ejpam-6147	51	108	−	−	PROPN
ejpam-6147	51	109	pz	pz	PROPN
ejpam-6147	51	110	℧	℧	PROPN
ejpam-6147	51	111	⟩	⟩	NOUN
ejpam-6147	51	112	≤	≤	NOUN
ejpam-6147	51	113	0	0	NUM
ejpam-6147	51	114	,	,	PUNCT
ejpam-6147	51	115	(	(	PUNCT
ejpam-6147	51	116	1	1	X
ejpam-6147	51	117	)	)	PUNCT
ejpam-6147	51	118	and	and	CCONJ
ejpam-6147	51	119	∥ς	∥ς	PROPN
ejpam-6147	51	120	−	−	PROPN
ejpam-6147	51	121	pzς∥2	pzς∥2	NOUN
ejpam-6147	51	122	+	+	CCONJ
ejpam-6147	51	123	∥	∥	NUM
ejpam-6147	51	124	℧	℧	NOUN
ejpam-6147	51	125	−	−	NOUN
ejpam-6147	51	126	pz	pz	PROPN
ejpam-6147	51	127	℧	℧	PROPN
ejpam-6147	51	128	∥2	∥2	NOUN
ejpam-6147	51	129	≤	≤	PROPN
ejpam-6147	51	130	∥ς	∥ς	PROPN
ejpam-6147	51	131	−	−	NOUN
ejpam-6147	51	132	℧	℧	NOUN
ejpam-6147	51	133	∥2	∥2	NOUN
ejpam-6147	51	134	,	,	PUNCT
ejpam-6147	51	135	for	for	ADP
ejpam-6147	51	136	all	all	DET
ejpam-6147	51	137	ς	ς	PROPN
ejpam-6147	51	138	∈	∈	PROPN
ejpam-6147	51	139	h	h	NOUN
ejpam-6147	51	140	and	and	CCONJ
ejpam-6147	51	141	℧	℧	PROPN
ejpam-6147	51	142	∈	∈	PROPN
ejpam-6147	51	143	z.	z.	NOUN
ejpam-6147	52	1	the	the	DET
ejpam-6147	52	2	evolution	evolution	PROPN
ejpam-6147	52	3	family	family	NOUN
ejpam-6147	52	4	e	e	NOUN
ejpam-6147	52	5	=	=	PRON
ejpam-6147	52	6	{	{	PUNCT
ejpam-6147	52	7	e(d	e(d	PROPN
ejpam-6147	52	8	,	,	PUNCT
ejpam-6147	52	9	b)}d≥b≥0	b)}d≥b≥0	NOUN
ejpam-6147	52	10	is	be	AUX
ejpam-6147	52	11	called	call	VERB
ejpam-6147	52	12	non	non	ADJ
ejpam-6147	52	13	-	-	ADJ
ejpam-6147	52	14	expansive	expansive	ADJ
ejpam-6147	52	15	,	,	PUNCT
ejpam-6147	52	16	continuous	continuous	ADJ
ejpam-6147	52	17	and	and	CCONJ
ejpam-6147	52	18	periodic	periodic	ADJ
ejpam-6147	52	19	with	with	ADP
ejpam-6147	52	20	period	period	NOUN
ejpam-6147	52	21	q	q	X
ejpam-6147	52	22	≥	≥	NOUN
ejpam-6147	52	23	0	0	NUM
ejpam-6147	52	24	if	if	SCONJ
ejpam-6147	52	25	it	it	PRON
ejpam-6147	52	26	satisfy	satisfy	VERB
ejpam-6147	52	27	the	the	DET
ejpam-6147	52	28	following	follow	VERB
ejpam-6147	52	29	conditions	condition	NOUN
ejpam-6147	52	30	:	:	PUNCT
ejpam-6147	52	31	•	•	NUM
ejpam-6147	52	32	∥e(d	∥e(d	PROPN
ejpam-6147	52	33	,	,	PUNCT
ejpam-6147	52	34	b)y	b)y	PUNCT
ejpam-6147	53	1	−	−	PROPN
ejpam-6147	53	2	e(d	e(d	PROPN
ejpam-6147	53	3	,	,	PUNCT
ejpam-6147	53	4	b)z∥	b)z∥	NOUN
ejpam-6147	53	5	≤	≤	ADJ
ejpam-6147	53	6	∥y	∥y	PROPN
ejpam-6147	53	7	−	−	PROPN
ejpam-6147	53	8	z∥	z∥	NUM
ejpam-6147	53	9	∀	∀	X
ejpam-6147	53	10	y	y	NOUN
ejpam-6147	53	11	,	,	PUNCT
ejpam-6147	53	12	z	z	NOUN
ejpam-6147	53	13	∈	∈	PROPN
ejpam-6147	53	14	h	h	NOUN
ejpam-6147	53	15	and	and	CCONJ
ejpam-6147	54	1	d	d	DET
ejpam-6147	54	2	≥	≥	PROPN
ejpam-6147	54	3	b	b	NOUN
ejpam-6147	54	4	≥	≥	NOUN
ejpam-6147	54	5	0	0	NUM
ejpam-6147	54	6	;	;	PUNCT
ejpam-6147	54	7	•	•	NUM
ejpam-6147	54	8	for	for	ADP
ejpam-6147	54	9	each	each	DET
ejpam-6147	54	10	z	z	PROPN
ejpam-6147	54	11	∈	∈	PROPN
ejpam-6147	54	12	h	h	NOUN
ejpam-6147	54	13	,	,	PUNCT
ejpam-6147	54	14	(	(	PUNCT
ejpam-6147	54	15	d	d	X
ejpam-6147	54	16	,	,	PUNCT
ejpam-6147	54	17	b	b	NOUN
ejpam-6147	54	18	)	)	PUNCT
ejpam-6147	54	19	→	→	SYM
ejpam-6147	54	20	e(d	e(d	PROPN
ejpam-6147	54	21	,	,	PUNCT
ejpam-6147	54	22	b)z	b)z	ADJ
ejpam-6147	54	23	is	be	AUX
ejpam-6147	54	24	continuous	continuous	ADJ
ejpam-6147	54	25	.	.	PUNCT
ejpam-6147	55	1	•	•	NUM
ejpam-6147	55	2	e(a+	e(a+	PROPN
ejpam-6147	55	3	q	q	ADJ
ejpam-6147	55	4	,	,	PUNCT
ejpam-6147	55	5	b+	b+	X
ejpam-6147	55	6	q	q	X
ejpam-6147	55	7	)	)	PUNCT
ejpam-6147	55	8	=	=	SYM
ejpam-6147	55	9	e(a	e(a	X
ejpam-6147	55	10	,	,	PUNCT
ejpam-6147	55	11	b	b	NOUN
ejpam-6147	55	12	)	)	PUNCT
ejpam-6147	55	13	for	for	ADP
ejpam-6147	55	14	all	all	DET
ejpam-6147	55	15	a	a	DET
ejpam-6147	55	16	≥	≥	NOUN
ejpam-6147	55	17	b	b	NOUN
ejpam-6147	55	18	≥	≥	NOUN
ejpam-6147	55	19	0	0	NUM
ejpam-6147	55	20	.	.	PUNCT
ejpam-6147	56	1	evolution	evolution	PROPN
ejpam-6147	56	2	family	family	PROPN
ejpam-6147	56	3	is	be	AUX
ejpam-6147	56	4	a	a	DET
ejpam-6147	56	5	generalized	generalized	ADJ
ejpam-6147	56	6	form	form	NOUN
ejpam-6147	56	7	of	of	ADP
ejpam-6147	56	8	a	a	DET
ejpam-6147	56	9	semigroup	semigroup	NOUN
ejpam-6147	56	10	,	,	PUNCT
ejpam-6147	56	11	see	see	VERB
ejpam-6147	56	12	the	the	DET
ejpam-6147	56	13	following	follow	VERB
ejpam-6147	56	14	remarks	remark	NOUN
ejpam-6147	56	15	.	.	PUNCT
ejpam-6147	57	1	m.	m.	NOUN
ejpam-6147	57	2	sarwar	sarwar	PROPN
ejpam-6147	57	3	et	et	PROPN
ejpam-6147	57	4	al	al	PROPN
ejpam-6147	57	5	.	.	PUNCT
ejpam-6147	57	6	/	/	SYM
ejpam-6147	57	7	eur	eur	PROPN
ejpam-6147	57	8	.	.	PUNCT
ejpam-6147	58	1	j.	j.	PROPN
ejpam-6147	58	2	pure	pure	PROPN
ejpam-6147	58	3	appl	appl	PROPN
ejpam-6147	58	4	.	.	PROPN
ejpam-6147	58	5	math	math	PROPN
ejpam-6147	58	6	,	,	PUNCT
ejpam-6147	58	7	18	18	NUM
ejpam-6147	58	8	(	(	PUNCT
ejpam-6147	58	9	3	3	NUM
ejpam-6147	58	10	)	)	PUNCT
ejpam-6147	58	11	(	(	PUNCT
ejpam-6147	58	12	2025	2025	NUM
ejpam-6147	58	13	)	)	PUNCT
ejpam-6147	58	14	,	,	PUNCT
ejpam-6147	58	15	6147	6147	NUM
ejpam-6147	58	16	4	4	NUM
ejpam-6147	58	17	of	of	ADP
ejpam-6147	58	18	18	18	NUM
ejpam-6147	58	19	remark	remark	NOUN
ejpam-6147	58	20	1	1	NUM
ejpam-6147	58	21	.	.	PUNCT
ejpam-6147	59	1	[	[	X
ejpam-6147	59	2	22	22	NUM
ejpam-6147	59	3	]	]	PUNCT
ejpam-6147	59	4	every	every	DET
ejpam-6147	59	5	semigroup	semigroup	NOUN
ejpam-6147	59	6	can	can	AUX
ejpam-6147	59	7	be	be	AUX
ejpam-6147	59	8	viewed	view	VERB
ejpam-6147	59	9	as	as	ADP
ejpam-6147	59	10	a	a	DET
ejpam-6147	59	11	special	special	ADJ
ejpam-6147	59	12	case	case	NOUN
ejpam-6147	59	13	of	of	ADP
ejpam-6147	59	14	an	an	DET
ejpam-6147	59	15	evolution	evolution	NOUN
ejpam-6147	59	16	family	family	NOUN
ejpam-6147	59	17	,	,	PUNCT
ejpam-6147	59	18	not	not	PART
ejpam-6147	59	19	every	every	DET
ejpam-6147	59	20	evolution	evolution	NOUN
ejpam-6147	59	21	family	family	NOUN
ejpam-6147	59	22	is	be	AUX
ejpam-6147	59	23	a	a	DET
ejpam-6147	59	24	semigroup	semigroup	NOUN
ejpam-6147	59	25	,	,	PUNCT
ejpam-6147	59	26	particularly	particularly	ADV
ejpam-6147	59	27	if	if	SCONJ
ejpam-6147	59	28	it	it	PRON
ejpam-6147	59	29	does	do	AUX
ejpam-6147	59	30	n’t	not	PART
ejpam-6147	59	31	satisfy	satisfy	VERB
ejpam-6147	59	32	the	the	DET
ejpam-6147	59	33	semigroup	semigroup	ADJ
ejpam-6147	59	34	property	property	NOUN
ejpam-6147	59	35	.	.	PUNCT
ejpam-6147	60	1	remark	remark	NOUN
ejpam-6147	60	2	2	2	NUM
ejpam-6147	60	3	.	.	PUNCT
ejpam-6147	61	1	[	[	X
ejpam-6147	61	2	22	22	NUM
ejpam-6147	61	3	]	]	X
ejpam-6147	61	4	if	if	SCONJ
ejpam-6147	61	5	an	an	DET
ejpam-6147	61	6	evolution	evolution	NOUN
ejpam-6147	61	7	family	family	NOUN
ejpam-6147	61	8	repeats	repeat	VERB
ejpam-6147	61	9	periodically	periodically	ADV
ejpam-6147	61	10	for	for	ADP
ejpam-6147	61	11	every	every	DET
ejpam-6147	61	12	positive	positive	ADJ
ejpam-6147	61	13	number	number	NOUN
ejpam-6147	61	14	,	,	PUNCT
ejpam-6147	61	15	then	then	ADV
ejpam-6147	61	16	it	it	PRON
ejpam-6147	61	17	transforms	transform	VERB
ejpam-6147	61	18	into	into	ADP
ejpam-6147	61	19	a	a	DET
ejpam-6147	61	20	semigroup	semigroup	NOUN
ejpam-6147	61	21	.	.	PUNCT
ejpam-6147	62	1	in	in	ADP
ejpam-6147	62	2	this	this	DET
ejpam-6147	62	3	paper	paper	NOUN
ejpam-6147	62	4	,	,	PUNCT
ejpam-6147	62	5	we	we	PRON
ejpam-6147	62	6	aim	aim	VERB
ejpam-6147	62	7	to	to	PART
ejpam-6147	62	8	establish	establish	VERB
ejpam-6147	62	9	a	a	DET
ejpam-6147	62	10	convergence	convergence	NOUN
ejpam-6147	62	11	theorem	theorem	VERB
ejpam-6147	62	12	to	to	ADP
ejpam-6147	62	13	a	a	DET
ejpam-6147	62	14	fp	fp	NOUN
ejpam-6147	62	15	of	of	ADP
ejpam-6147	62	16	a	a	DET
ejpam-6147	62	17	subfamily	subfamily	ADV
ejpam-6147	62	18	ls	ls	ADJ
ejpam-6147	62	19	of	of	ADP
ejpam-6147	62	20	a	a	DET
ejpam-6147	62	21	nee	nee	NOUN
ejpam-6147	62	22	family	family	NOUN
ejpam-6147	62	23	on	on	ADP
ejpam-6147	62	24	a	a	DET
ejpam-6147	62	25	hilbert	hilbert	NOUN
ejpam-6147	62	26	space	space	NOUN
ejpam-6147	62	27	h.	h.	PROPN
ejpam-6147	63	1	it	it	PRON
ejpam-6147	63	2	’s	’	VERB
ejpam-6147	63	3	important	important	ADJ
ejpam-6147	63	4	to	to	PART
ejpam-6147	63	5	note	note	VERB
ejpam-6147	63	6	that	that	SCONJ
ejpam-6147	63	7	such	such	DET
ejpam-6147	63	8	a	a	DET
ejpam-6147	63	9	family	family	NOUN
ejpam-6147	63	10	need	need	AUX
ejpam-6147	63	11	not	not	PART
ejpam-6147	63	12	be	be	AUX
ejpam-6147	63	13	a	a	DET
ejpam-6147	63	14	semigroup	semigroup	NOUN
ejpam-6147	63	15	.	.	PUNCT
ejpam-6147	64	1	the	the	DET
ejpam-6147	64	2	following	follow	VERB
ejpam-6147	64	3	example	example	NOUN
ejpam-6147	64	4	will	will	AUX
ejpam-6147	64	5	illustrate	illustrate	VERB
ejpam-6147	64	6	this	this	DET
ejpam-6147	64	7	fact	fact	NOUN
ejpam-6147	64	8	.	.	PUNCT
ejpam-6147	65	1	example	example	NOUN
ejpam-6147	66	1	1	1	NUM
ejpam-6147	66	2	.	.	PUNCT
ejpam-6147	67	1	the	the	DET
ejpam-6147	67	2	family	family	NOUN
ejpam-6147	67	3	defined	define	VERB
ejpam-6147	67	4	by	by	ADP
ejpam-6147	67	5	l	l	NOUN
ejpam-6147	67	6	=	=	SYM
ejpam-6147	67	7	l(s	l(s	PROPN
ejpam-6147	67	8	,	,	PUNCT
ejpam-6147	67	9	r	r	NOUN
ejpam-6147	67	10	)	)	PUNCT
ejpam-6147	67	11	=	=	SYM
ejpam-6147	68	1	s+1	s+1	PROPN
ejpam-6147	68	2	r+1	r+1	PROPN
ejpam-6147	68	3	:	:	PUNCT
ejpam-6147	68	4	s	s	X
ejpam-6147	68	5	≥	≥	PROPN
ejpam-6147	68	6	r	r	NOUN
ejpam-6147	68	7	≥	≥	NOUN
ejpam-6147	68	8	0	0	NUM
ejpam-6147	68	9	is	be	AUX
ejpam-6147	68	10	evidently	evidently	ADV
ejpam-6147	68	11	an	an	DET
ejpam-6147	68	12	evolution	evolution	NOUN
ejpam-6147	68	13	family	family	NOUN
ejpam-6147	68	14	acting	act	VERB
ejpam-6147	68	15	on	on	ADP
ejpam-6147	68	16	r+	r+	X
ejpam-6147	68	17	.	.	PUNCT
ejpam-6147	69	1	since	since	SCONJ
ejpam-6147	69	2	l(s	l(s	PROPN
ejpam-6147	69	3	,	,	PUNCT
ejpam-6147	69	4	s	s	PART
ejpam-6147	69	5	)	)	PUNCT
ejpam-6147	69	6	=	=	SYM
ejpam-6147	69	7	1	1	NUM
ejpam-6147	69	8	(	(	PUNCT
ejpam-6147	69	9	the	the	DET
ejpam-6147	69	10	identity	identity	NOUN
ejpam-6147	69	11	on	on	ADP
ejpam-6147	69	12	r+	r+	X
ejpam-6147	69	13	)	)	PUNCT
ejpam-6147	69	14	and	and	CCONJ
ejpam-6147	69	15	l(s	l(s	PROPN
ejpam-6147	69	16	,	,	PUNCT
ejpam-6147	69	17	t)l(t	t)l(t	NOUN
ejpam-6147	69	18	,	,	PUNCT
ejpam-6147	69	19	r	r	NOUN
ejpam-6147	69	20	)	)	PUNCT
ejpam-6147	69	21	=	=	SYM
ejpam-6147	69	22	(	(	PUNCT
ejpam-6147	69	23	s+	s+	NUM
ejpam-6147	69	24	1	1	NUM
ejpam-6147	69	25	t+	t+	NUM
ejpam-6147	69	26	1	1	NUM
ejpam-6147	69	27	)	)	PUNCT
ejpam-6147	69	28	(	(	PUNCT
ejpam-6147	69	29	t+	t+	X
ejpam-6147	69	30	1	1	NUM
ejpam-6147	69	31	r+	r+	NOUN
ejpam-6147	69	32	1	1	NUM
ejpam-6147	69	33	)	)	PUNCT
ejpam-6147	70	1	=	=	PUNCT
ejpam-6147	70	2	s+	s+	PUNCT
ejpam-6147	70	3	1	1	NUM
ejpam-6147	70	4	r+	r+	VERB
ejpam-6147	70	5	1	1	NUM
ejpam-6147	70	6	=	=	SYM
ejpam-6147	70	7	l(s	l(s	PROPN
ejpam-6147	70	8	,	,	PUNCT
ejpam-6147	70	9	r	r	NOUN
ejpam-6147	70	10	)	)	PUNCT
ejpam-6147	70	11	.	.	PUNCT
ejpam-6147	71	1	setting	set	VERB
ejpam-6147	71	2	r	r	NOUN
ejpam-6147	71	3	=	=	SYM
ejpam-6147	71	4	0	0	NUM
ejpam-6147	71	5	,	,	PUNCT
ejpam-6147	71	6	we	we	PRON
ejpam-6147	71	7	obtain	obtain	VERB
ejpam-6147	71	8	ls	ls	ADJ
ejpam-6147	71	9	=	=	SYM
ejpam-6147	71	10	l(s	l(s	PROPN
ejpam-6147	71	11	,	,	PUNCT
ejpam-6147	71	12	0	0	NUM
ejpam-6147	71	13	)	)	PUNCT
ejpam-6147	71	14	=	=	PUNCT
ejpam-6147	71	15	s+	s+	PUNCT
ejpam-6147	71	16	1	1	NUM
ejpam-6147	71	17	,	,	PUNCT
ejpam-6147	71	18	which	which	PRON
ejpam-6147	71	19	is	be	AUX
ejpam-6147	71	20	indeed	indeed	ADV
ejpam-6147	71	21	a	a	DET
ejpam-6147	71	22	sub	sub	NOUN
ejpam-6147	71	23	-	-	NOUN
ejpam-6147	71	24	family	family	NOUN
ejpam-6147	71	25	of	of	ADP
ejpam-6147	71	26	l.	l.	PROPN
ejpam-6147	71	27	however	however	ADV
ejpam-6147	71	28	,	,	PUNCT
ejpam-6147	71	29	it	it	PRON
ejpam-6147	71	30	is	be	AUX
ejpam-6147	71	31	not	not	PART
ejpam-6147	71	32	a	a	DET
ejpam-6147	71	33	semigroup	semigroup	NOUN
ejpam-6147	71	34	.	.	PUNCT
ejpam-6147	72	1	definition	definition	NOUN
ejpam-6147	72	2	1	1	NUM
ejpam-6147	72	3	.	.	PUNCT
ejpam-6147	73	1	let	let	VERB
ejpam-6147	73	2	z	z	NOUN
ejpam-6147	73	3	̸=	̸=	PROPN
ejpam-6147	73	4	∅	∅	NOUN
ejpam-6147	73	5	and	and	CCONJ
ejpam-6147	73	6	g	g	NOUN
ejpam-6147	73	7	:	:	PUNCT
ejpam-6147	73	8	z	z	PROPN
ejpam-6147	73	9	→	→	SYM
ejpam-6147	73	10	z	z	X
ejpam-6147	73	11	,	,	PUNCT
ejpam-6147	73	12	be	be	AUX
ejpam-6147	73	13	an	an	DET
ejpam-6147	73	14	operator	operator	NOUN
ejpam-6147	73	15	,	,	PUNCT
ejpam-6147	73	16	then	then	ADV
ejpam-6147	73	17	the	the	DET
ejpam-6147	73	18	set	set	NOUN
ejpam-6147	73	19	of	of	ADP
ejpam-6147	73	20	all	all	DET
ejpam-6147	73	21	fixed	fix	VERB
ejpam-6147	73	22	points	point	NOUN
ejpam-6147	73	23	of	of	ADP
ejpam-6147	73	24	g	g	PROPN
ejpam-6147	73	25	is	be	AUX
ejpam-6147	73	26	denoted	denote	VERB
ejpam-6147	73	27	by	by	ADP
ejpam-6147	73	28	fg(z	fg(z	PROPN
ejpam-6147	73	29	)	)	PUNCT
ejpam-6147	73	30	and	and	CCONJ
ejpam-6147	73	31	is	be	AUX
ejpam-6147	73	32	defined	define	VERB
ejpam-6147	73	33	as	as	ADP
ejpam-6147	73	34	fg(z	fg(z	ADJ
ejpam-6147	73	35	)	)	PUNCT
ejpam-6147	73	36	=	=	SYM
ejpam-6147	74	1	{	{	PUNCT
ejpam-6147	74	2	z	z	NOUN
ejpam-6147	74	3	∈	∈	PROPN
ejpam-6147	74	4	z	z	NOUN
ejpam-6147	74	5	:	:	PUNCT
ejpam-6147	75	1	g(z	g(z	ADJ
ejpam-6147	75	2	)	)	PUNCT
ejpam-6147	75	3	=	=	PUNCT
ejpam-6147	76	1	z	z	X
ejpam-6147	76	2	}	}	PUNCT
ejpam-6147	76	3	.	.	PUNCT
ejpam-6147	77	1	definition	definition	NOUN
ejpam-6147	77	2	2	2	NUM
ejpam-6147	77	3	.	.	PUNCT
ejpam-6147	78	1	a	a	DET
ejpam-6147	78	2	mapping	mapping	NOUN
ejpam-6147	78	3	that	that	PRON
ejpam-6147	78	4	is	be	AUX
ejpam-6147	78	5	continuous	continuous	ADJ
ejpam-6147	78	6	from	from	ADP
ejpam-6147	78	7	a	a	DET
ejpam-6147	78	8	topological	topological	ADJ
ejpam-6147	78	9	space	space	NOUN
ejpam-6147	78	10	into	into	ADP
ejpam-6147	78	11	one	one	NUM
ejpam-6147	78	12	of	of	ADP
ejpam-6147	78	13	its	its	PRON
ejpam-6147	78	14	subspaces	subspace	NOUN
ejpam-6147	78	15	and	and	CCONJ
ejpam-6147	78	16	maintains	maintain	VERB
ejpam-6147	78	17	the	the	DET
ejpam-6147	78	18	positions	position	NOUN
ejpam-6147	78	19	of	of	ADP
ejpam-6147	78	20	all	all	DET
ejpam-6147	78	21	points	point	NOUN
ejpam-6147	78	22	in	in	ADP
ejpam-6147	78	23	that	that	DET
ejpam-6147	78	24	subspace	subspace	NOUN
ejpam-6147	78	25	is	be	AUX
ejpam-6147	78	26	referred	refer	VERB
ejpam-6147	78	27	to	to	ADP
ejpam-6147	78	28	as	as	ADP
ejpam-6147	78	29	a	a	DET
ejpam-6147	78	30	retraction	retraction	NOUN
ejpam-6147	78	31	.	.	PUNCT
ejpam-6147	79	1	definition	definition	NOUN
ejpam-6147	79	2	3	3	NUM
ejpam-6147	79	3	.	.	PUNCT
ejpam-6147	79	4	open	open	ADJ
ejpam-6147	79	5	ball	ball	PROPN
ejpam-6147	79	6	and	and	CCONJ
ejpam-6147	79	7	closed	closed	ADJ
ejpam-6147	79	8	ball	ball	NOUN
ejpam-6147	79	9	:	:	PUNCT
ejpam-6147	79	10	an	an	DET
ejpam-6147	79	11	open	open	ADJ
ejpam-6147	79	12	ball	ball	NOUN
ejpam-6147	79	13	is	be	AUX
ejpam-6147	79	14	denoted	denote	VERB
ejpam-6147	79	15	by	by	ADP
ejpam-6147	79	16	b(υ;k	b(υ;k	PROPN
ejpam-6147	79	17	)	)	PUNCT
ejpam-6147	79	18	and	and	CCONJ
ejpam-6147	79	19	define	define	VERB
ejpam-6147	79	20	as	as	ADP
ejpam-6147	79	21	b(υ;k	b(υ;k	PROPN
ejpam-6147	79	22	)	)	PUNCT
ejpam-6147	80	1	=	=	PRON
ejpam-6147	80	2	{	{	PUNCT
ejpam-6147	80	3	ζ	ζ	NOUN
ejpam-6147	80	4	∈	∈	NOUN
ejpam-6147	80	5	h	h	NOUN
ejpam-6147	80	6	:	:	PUNCT
ejpam-6147	80	7	∥ζ	∥ζ	PROPN
ejpam-6147	80	8	−υ∥	−υ∥	PROPN
ejpam-6147	80	9	<	<	X
ejpam-6147	80	10	k	k	X
ejpam-6147	80	11	}	}	PUNCT
ejpam-6147	80	12	,	,	PUNCT
ejpam-6147	80	13	while	while	SCONJ
ejpam-6147	80	14	closed	closed	ADJ
ejpam-6147	80	15	ball	ball	NOUN
ejpam-6147	80	16	is	be	AUX
ejpam-6147	80	17	denoted	denote	VERB
ejpam-6147	80	18	by	by	ADP
ejpam-6147	80	19	b(υ;k	b(υ;k	PROPN
ejpam-6147	80	20	)	)	PUNCT
ejpam-6147	80	21	and	and	CCONJ
ejpam-6147	80	22	define	define	VERB
ejpam-6147	80	23	as	as	ADP
ejpam-6147	80	24	b(υ;k	b(υ;k	PROPN
ejpam-6147	80	25	)	)	PUNCT
ejpam-6147	80	26	=	=	PRON
ejpam-6147	80	27	{	{	PUNCT
ejpam-6147	80	28	ζ	ζ	NOUN
ejpam-6147	80	29	∈	∈	NOUN
ejpam-6147	80	30	h	h	NOUN
ejpam-6147	80	31	:	:	PUNCT
ejpam-6147	81	1	∥ζ	∥ζ	PROPN
ejpam-6147	81	2	−υ∥	−υ∥	PROPN
ejpam-6147	81	3	≤	≤	NUM
ejpam-6147	81	4	k	k	NOUN
ejpam-6147	81	5	}	}	PUNCT
ejpam-6147	81	6	.	.	PUNCT
ejpam-6147	82	1	throughout	throughout	ADP
ejpam-6147	82	2	this	this	DET
ejpam-6147	82	3	paper	paper	NOUN
ejpam-6147	82	4	we	we	PRON
ejpam-6147	82	5	will	will	AUX
ejpam-6147	82	6	denote	denote	VERB
ejpam-6147	82	7	by	by	ADP
ejpam-6147	82	8	fe(d	fe(d	PROPN
ejpam-6147	82	9	,	,	PUNCT
ejpam-6147	82	10	b	b	NOUN
ejpam-6147	82	11	)	)	PUNCT
ejpam-6147	82	12	and	and	CCONJ
ejpam-6147	82	13	fe	fe	X
ejpam-6147	82	14	the	the	DET
ejpam-6147	82	15	set	set	NOUN
ejpam-6147	82	16	of	of	ADP
ejpam-6147	82	17	all	all	DET
ejpam-6147	82	18	fixed	fix	VERB
ejpam-6147	82	19	points	point	NOUN
ejpam-6147	82	20	of	of	ADP
ejpam-6147	82	21	the	the	DET
ejpam-6147	82	22	operator	operator	NOUN
ejpam-6147	82	23	e(d	e(d	PROPN
ejpam-6147	82	24	,	,	PUNCT
ejpam-6147	82	25	b	b	NOUN
ejpam-6147	82	26	)	)	PUNCT
ejpam-6147	82	27	and	and	CCONJ
ejpam-6147	82	28	the	the	DET
ejpam-6147	82	29	family	family	NOUN
ejpam-6147	82	30	e	e	NOUN
ejpam-6147	82	31	respectively	respectively	ADV
ejpam-6147	82	32	,	,	PUNCT
ejpam-6147	82	33	i.e.	i.e.	X
ejpam-6147	82	34	fe	fe	X
ejpam-6147	82	35	=	=	SYM
ejpam-6147	82	36	∩	∩	PROPN
ejpam-6147	82	37	d≥b≥0	d≥b≥0	PROPN
ejpam-6147	82	38	fe(d	fe(d	PROPN
ejpam-6147	82	39	,	,	PUNCT
ejpam-6147	82	40	b	b	NOUN
ejpam-6147	82	41	)	)	PUNCT
ejpam-6147	82	42	.	.	PUNCT
ejpam-6147	83	1	the	the	DET
ejpam-6147	83	2	following	follow	VERB
ejpam-6147	83	3	lemmas	lemmas	PROPN
ejpam-6147	83	4	will	will	AUX
ejpam-6147	83	5	be	be	AUX
ejpam-6147	83	6	useful	useful	ADJ
ejpam-6147	83	7	in	in	ADP
ejpam-6147	83	8	the	the	DET
ejpam-6147	83	9	proof	proof	NOUN
ejpam-6147	83	10	of	of	ADP
ejpam-6147	83	11	our	our	PRON
ejpam-6147	83	12	main	main	ADJ
ejpam-6147	83	13	results	result	NOUN
ejpam-6147	83	14	.	.	PUNCT
ejpam-6147	84	1	lemma	lemma	PROPN
ejpam-6147	84	2	1	1	NUM
ejpam-6147	84	3	.	.	PUNCT
ejpam-6147	85	1	[	[	X
ejpam-6147	85	2	7	7	X
ejpam-6147	85	3	]	]	PUNCT
ejpam-6147	85	4	consider	consider	VERB
ejpam-6147	85	5	z	z	NOUN
ejpam-6147	85	6	as	as	ADP
ejpam-6147	85	7	a	a	DET
ejpam-6147	85	8	closed	closed	ADJ
ejpam-6147	85	9	and	and	CCONJ
ejpam-6147	85	10	convex	convex	NOUN
ejpam-6147	85	11	subset	subset	NOUN
ejpam-6147	85	12	of	of	ADP
ejpam-6147	85	13	h	h	NOUN
ejpam-6147	85	14	,	,	PUNCT
ejpam-6147	85	15	and	and	CCONJ
ejpam-6147	85	16	let	let	VERB
ejpam-6147	85	17	g	g	NOUN
ejpam-6147	85	18	:	:	PUNCT
ejpam-6147	85	19	z	z	PROPN
ejpam-6147	85	20	→	→	SYM
ejpam-6147	85	21	z	z	AUX
ejpam-6147	85	22	be	be	AUX
ejpam-6147	85	23	a	a	DET
ejpam-6147	85	24	non	non	ADJ
ejpam-6147	85	25	-	-	ADJ
ejpam-6147	85	26	expansive	expansive	ADJ
ejpam-6147	85	27	map	map	NOUN
ejpam-6147	85	28	.	.	PUNCT
ejpam-6147	86	1	then	then	ADV
ejpam-6147	86	2	,	,	PUNCT
ejpam-6147	86	3	i	i	PRON
ejpam-6147	86	4	−g	−g	VERB
ejpam-6147	86	5	is	be	AUX
ejpam-6147	86	6	demiclosed	demiclose	VERB
ejpam-6147	86	7	.	.	PUNCT
ejpam-6147	87	1	specifically	specifically	ADV
ejpam-6147	87	2	,	,	PUNCT
ejpam-6147	87	3	if	if	SCONJ
ejpam-6147	87	4	ςm	ςm	NOUN
ejpam-6147	87	5	is	be	AUX
ejpam-6147	87	6	a	a	DET
ejpam-6147	87	7	sequence	sequence	NOUN
ejpam-6147	87	8	in	in	ADP
ejpam-6147	87	9	z	z	NOUN
ejpam-6147	87	10	such	such	ADJ
ejpam-6147	87	11	that	that	DET
ejpam-6147	87	12	ςm	ςm	NOUN
ejpam-6147	88	1	⇀	⇀	NUM
ejpam-6147	88	2	ς	ς	PROPN
ejpam-6147	89	1	and	and	CCONJ
ejpam-6147	89	2	(	(	PUNCT
ejpam-6147	89	3	i	i	NOUN
ejpam-6147	89	4	−g)ςm	−g)ςm	PUNCT
ejpam-6147	89	5	→	→	SYM
ejpam-6147	89	6	℧	℧	PROPN
ejpam-6147	89	7	,	,	PUNCT
ejpam-6147	89	8	then	then	ADV
ejpam-6147	89	9	(	(	PUNCT
ejpam-6147	89	10	i	i	PRON
ejpam-6147	89	11	−g)ς	−g)ς	VERB
ejpam-6147	89	12	=	=	SYM
ejpam-6147	89	13	℧	℧	PROPN
ejpam-6147	89	14	.	.	PUNCT
ejpam-6147	89	15	lemma	lemma	PROPN
ejpam-6147	89	16	2	2	NUM
ejpam-6147	89	17	.	.	PUNCT
ejpam-6147	90	1	[	[	X
ejpam-6147	90	2	23	23	NUM
ejpam-6147	90	3	]	]	PUNCT
ejpam-6147	90	4	let	let	VERB
ejpam-6147	90	5	ςn	ςn	NOUN
ejpam-6147	90	6	and	and	CCONJ
ejpam-6147	90	7	℧	℧	PROPN
ejpam-6147	90	8	n	n	ADV
ejpam-6147	90	9	be	be	AUX
ejpam-6147	90	10	bounded	bound	VERB
ejpam-6147	90	11	sequences	sequence	NOUN
ejpam-6147	90	12	in	in	ADP
ejpam-6147	90	13	a	a	DET
ejpam-6147	90	14	banach	banach	NOUN
ejpam-6147	90	15	space	space	NOUN
ejpam-6147	90	16	y	y	NOUN
ejpam-6147	90	17	,	,	PUNCT
ejpam-6147	90	18	and	and	CCONJ
ejpam-6147	90	19	λn	λn	PROPN
ejpam-6147	90	20	be	be	AUX
ejpam-6147	90	21	a	a	DET
ejpam-6147	90	22	sequence	sequence	NOUN
ejpam-6147	90	23	in	in	ADP
ejpam-6147	90	24	the	the	DET
ejpam-6147	90	25	closed	closed	ADJ
ejpam-6147	90	26	interval	interval	NOUN
ejpam-6147	90	27	[	[	X
ejpam-6147	90	28	0	0	NUM
ejpam-6147	90	29	,	,	PUNCT
ejpam-6147	90	30	1	1	NUM
ejpam-6147	90	31	]	]	PUNCT
ejpam-6147	90	32	satisfying	satisfy	VERB
ejpam-6147	90	33	the	the	DET
ejpam-6147	90	34	condition	condition	NOUN
ejpam-6147	90	35	0	0	PUNCT
ejpam-6147	90	36	<	<	X
ejpam-6147	90	37	lim	lim	PROPN
ejpam-6147	90	38	inf	inf	PROPN
ejpam-6147	90	39	n→+∞	n→+∞	VERB
ejpam-6147	90	40	λn	λn	PROPN
ejpam-6147	90	41	≤	≤	ADJ
ejpam-6147	91	1	lim	lim	PROPN
ejpam-6147	91	2	sup	sup	PROPN
ejpam-6147	91	3	n→+∞	n→+∞	VERB
ejpam-6147	91	4	λn	λn	NOUN
ejpam-6147	91	5	<	<	X
ejpam-6147	91	6	1	1	NUM
ejpam-6147	91	7	.	.	PUNCT
ejpam-6147	92	1	if	if	SCONJ
ejpam-6147	92	2	the	the	DET
ejpam-6147	92	3	sequence	sequence	NOUN
ejpam-6147	92	4	ςn+1	ςn+1	NUM
ejpam-6147	92	5	=	=	SYM
ejpam-6147	92	6	(	(	PUNCT
ejpam-6147	92	7	1−	1−	NUM
ejpam-6147	92	8	λn)ςn	λn)ςn	PUNCT
ejpam-6147	92	9	+	+	CCONJ
ejpam-6147	92	10	λn	λn	NOUN
ejpam-6147	92	11	℧	℧	NOUN
ejpam-6147	92	12	n	n	CCONJ
ejpam-6147	92	13	∀n	∀n	NUM
ejpam-6147	92	14	≥	≥	NOUN
ejpam-6147	92	15	0	0	NUM
ejpam-6147	92	16	,	,	PUNCT
ejpam-6147	92	17	m.	m.	NOUN
ejpam-6147	92	18	sarwar	sarwar	PROPN
ejpam-6147	92	19	et	et	PROPN
ejpam-6147	92	20	al	al	PROPN
ejpam-6147	92	21	.	.	PUNCT
ejpam-6147	92	22	/	/	SYM
ejpam-6147	92	23	eur	eur	PROPN
ejpam-6147	92	24	.	.	PUNCT
ejpam-6147	92	25	j.	j.	PROPN
ejpam-6147	92	26	pure	pure	PROPN
ejpam-6147	92	27	appl	appl	PROPN
ejpam-6147	92	28	.	.	PROPN
ejpam-6147	92	29	math	math	PROPN
ejpam-6147	92	30	,	,	PUNCT
ejpam-6147	92	31	18	18	NUM
ejpam-6147	92	32	(	(	PUNCT
ejpam-6147	92	33	3	3	NUM
ejpam-6147	92	34	)	)	PUNCT
ejpam-6147	92	35	(	(	PUNCT
ejpam-6147	92	36	2025	2025	NUM
ejpam-6147	92	37	)	)	PUNCT
ejpam-6147	92	38	,	,	PUNCT
ejpam-6147	92	39	6147	6147	NUM
ejpam-6147	92	40	5	5	NUM
ejpam-6147	92	41	of	of	ADP
ejpam-6147	92	42	18	18	NUM
ejpam-6147	92	43	satisfy	satisfy	NOUN
ejpam-6147	92	44	lim	lim	PROPN
ejpam-6147	92	45	sup	sup	PROPN
ejpam-6147	92	46	n→+∞	n→+∞	PROPN
ejpam-6147	92	47	(	(	PUNCT
ejpam-6147	92	48	∥ςn	∥ςn	NOUN
ejpam-6147	92	49	−	−	NOUN
ejpam-6147	92	50	℧	℧	NOUN
ejpam-6147	92	51	n−1∥	n−1∥	NOUN
ejpam-6147	92	52	−	−	PROPN
ejpam-6147	92	53	∥ςn	∥ςn	PROPN
ejpam-6147	92	54	−	−	PROPN
ejpam-6147	92	55	ςn−1∥	ςn−1∥	NOUN
ejpam-6147	92	56	)	)	PUNCT
ejpam-6147	92	57	≤	≤	NUM
ejpam-6147	92	58	0	0	NUM
ejpam-6147	92	59	.	.	PUNCT
ejpam-6147	93	1	then	then	ADV
ejpam-6147	93	2	lim	lim	PROPN
ejpam-6147	93	3	n→+∞	n→+∞	PROPN
ejpam-6147	93	4	∥ςn	∥ςn	PROPN
ejpam-6147	94	1	−	−	NOUN
ejpam-6147	94	2	℧	℧	NOUN
ejpam-6147	94	3	n∥	n∥	NOUN
ejpam-6147	94	4	=	=	NOUN
ejpam-6147	94	5	0	0	X
ejpam-6147	94	6	.	.	PUNCT
ejpam-6147	95	1	lemma	lemma	PROPN
ejpam-6147	95	2	3	3	X
ejpam-6147	95	3	.	.	PUNCT
ejpam-6147	96	1	[	[	X
ejpam-6147	96	2	24	24	NUM
ejpam-6147	96	3	]	]	PUNCT
ejpam-6147	96	4	consider	consider	VERB
ejpam-6147	96	5	that	that	SCONJ
ejpam-6147	96	6	{	{	PUNCT
ejpam-6147	96	7	bn	bn	NOUN
ejpam-6147	96	8	}	}	PUNCT
ejpam-6147	96	9	is	be	AUX
ejpam-6147	96	10	a	a	DET
ejpam-6147	96	11	sequence	sequence	NOUN
ejpam-6147	96	12	in	in	ADP
ejpam-6147	96	13	[	[	X
ejpam-6147	96	14	0,+∞	0,+∞	NUM
ejpam-6147	96	15	)	)	PUNCT
ejpam-6147	96	16	such	such	ADJ
ejpam-6147	96	17	that	that	DET
ejpam-6147	96	18	bn+1	bn+1	PROPN
ejpam-6147	96	19	≤	≤	NOUN
ejpam-6147	96	20	(	(	PUNCT
ejpam-6147	96	21	1−λn)bn+	1−λn)bn+	NUM
ejpam-6147	96	22	δnλn	δnλn	NOUN
ejpam-6147	96	23	for	for	ADP
ejpam-6147	96	24	all	all	DET
ejpam-6147	96	25	n	n	CCONJ
ejpam-6147	96	26	,	,	PUNCT
ejpam-6147	96	27	where	where	SCONJ
ejpam-6147	96	28	{	{	PUNCT
ejpam-6147	96	29	λn	λn	NOUN
ejpam-6147	96	30	}	}	PUNCT
ejpam-6147	96	31	∈]0	∈]0	X
ejpam-6147	96	32	,	,	PUNCT
ejpam-6147	96	33	1	1	NUM
ejpam-6147	96	34	[	[	PUNCT
ejpam-6147	96	35	and	and	CCONJ
ejpam-6147	96	36	{	{	PUNCT
ejpam-6147	96	37	δn	δn	NOUN
ejpam-6147	96	38	}	}	PUNCT
ejpam-6147	96	39	are	be	AUX
ejpam-6147	96	40	sequences	sequence	NOUN
ejpam-6147	96	41	satisfiyng	satisfiyng	X
ejpam-6147	96	42	(	(	PUNCT
ejpam-6147	96	43	a	a	NOUN
ejpam-6147	96	44	)	)	PUNCT
ejpam-6147	96	45	∑+∞	∑+∞	ADJ
ejpam-6147	96	46	n=1	n=1	PROPN
ejpam-6147	96	47	λn	λn	NOUN
ejpam-6147	96	48	=	=	PUNCT
ejpam-6147	97	1	+	+	PROPN
ejpam-6147	97	2	∞	∞	PROPN
ejpam-6147	97	3	,	,	PUNCT
ejpam-6147	97	4	and	and	CCONJ
ejpam-6147	97	5	(	(	PUNCT
ejpam-6147	97	6	b	b	X
ejpam-6147	97	7	)	)	PUNCT
ejpam-6147	97	8	lim	lim	NOUN
ejpam-6147	97	9	supn→∞	supn→∞	PROPN
ejpam-6147	97	10	λn	λn	VERB
ejpam-6147	97	11	≤	≤	NUM
ejpam-6147	97	12	0	0	NUM
ejpam-6147	97	13	or	or	CCONJ
ejpam-6147	97	14	∑+∞	∑+∞	ADJ
ejpam-6147	97	15	n=1	n=1	PROPN
ejpam-6147	97	16	|δnλn|	|δnλn|	ADP
ejpam-6147	97	17	<	<	X
ejpam-6147	98	1	+	+	NOUN
ejpam-6147	98	2	∞.	∞.	PROPN
ejpam-6147	98	3	then	then	ADV
ejpam-6147	98	4	limn→+∞	limn→+∞	VERB
ejpam-6147	98	5	bn	bn	NOUN
ejpam-6147	98	6	=	=	SYM
ejpam-6147	98	7	0	0	NUM
ejpam-6147	98	8	.	.	NOUN
ejpam-6147	99	1	3	3	X
ejpam-6147	99	2	.	.	X
ejpam-6147	99	3	main	main	ADJ
ejpam-6147	99	4	results	result	NOUN
ejpam-6147	99	5	this	this	DET
ejpam-6147	99	6	section	section	NOUN
ejpam-6147	99	7	is	be	AUX
ejpam-6147	99	8	devoted	devote	VERB
ejpam-6147	99	9	to	to	ADP
ejpam-6147	99	10	our	our	PRON
ejpam-6147	99	11	main	main	ADJ
ejpam-6147	99	12	results	result	NOUN
ejpam-6147	99	13	.	.	PUNCT
ejpam-6147	100	1	throughout	throughout	ADP
ejpam-6147	100	2	the	the	DET
ejpam-6147	100	3	paper	paper	NOUN
ejpam-6147	100	4	z	z	NOUN
ejpam-6147	100	5	will	will	AUX
ejpam-6147	100	6	be	be	AUX
ejpam-6147	100	7	a	a	DET
ejpam-6147	100	8	nonempty	nonempty	ADJ
ejpam-6147	100	9	,	,	PUNCT
ejpam-6147	100	10	closed	closed	ADJ
ejpam-6147	100	11	,	,	PUNCT
ejpam-6147	100	12	bounded	bound	VERB
ejpam-6147	100	13	and	and	CCONJ
ejpam-6147	100	14	convex	convex	PROPN
ejpam-6147	100	15	subset	subset	NOUN
ejpam-6147	100	16	of	of	ADP
ejpam-6147	100	17	hilbert	hilbert	PROPN
ejpam-6147	100	18	space	space	PROPN
ejpam-6147	100	19	h.	h.	PROPN
ejpam-6147	100	20	lemma	lemma	PROPN
ejpam-6147	101	1	4	4	X
ejpam-6147	101	2	.	.	PUNCT
ejpam-6147	101	3	let	let	VERB
ejpam-6147	101	4	e	e	NOUN
ejpam-6147	101	5	=	=	PRON
ejpam-6147	101	6	{	{	PUNCT
ejpam-6147	101	7	e(z	e(z	PROPN
ejpam-6147	101	8	,	,	PUNCT
ejpam-6147	101	9	0)z≥0	0)z≥0	PROPN
ejpam-6147	101	10	}	}	PUNCT
ejpam-6147	101	11	be	be	AUX
ejpam-6147	101	12	a	a	DET
ejpam-6147	101	13	subfamily	subfamily	NOUN
ejpam-6147	101	14	of	of	ADP
ejpam-6147	101	15	a	a	DET
ejpam-6147	101	16	nee	nee	NOUN
ejpam-6147	101	17	family	family	NOUN
ejpam-6147	101	18	on	on	ADP
ejpam-6147	101	19	z	z	PROPN
ejpam-6147	101	20	with	with	ADP
ejpam-6147	101	21	condition	condition	NOUN
ejpam-6147	101	22	∥	∥	PUNCT
ejpam-6147	101	23	℧	℧	NOUN
ejpam-6147	101	24	r	r	NOUN
ejpam-6147	101	25	−	−	NOUN
ejpam-6147	101	26	e	e	NOUN
ejpam-6147	101	27	(	(	PUNCT
ejpam-6147	101	28	(	(	PUNCT
ejpam-6147	101	29	sr	sr	PROPN
ejpam-6147	101	30	)	)	PUNCT
ejpam-6147	101	31	jr	jr	PROPN
ejpam-6147	101	32	,	,	PUNCT
ejpam-6147	101	33	0)	0)	PART
ejpam-6147	101	34	℧	℧	PROPN
ejpam-6147	101	35	r∥2	r∥2	ADJ
ejpam-6147	101	36	≤	≤	PUNCT
ejpam-6147	101	37	jr	jr	PROPN
ejpam-6147	101	38	r	r	NOUN
ejpam-6147	101	39	diam(z	diam(z	NOUN
ejpam-6147	101	40	)	)	PUNCT
ejpam-6147	101	41	,	,	PUNCT
ejpam-6147	101	42	where	where	SCONJ
ejpam-6147	101	43	℧	℧	NOUN
ejpam-6147	101	44	r	r	NOUN
ejpam-6147	101	45	=	=	SYM
ejpam-6147	101	46	(	(	PUNCT
ejpam-6147	101	47	1r	1r	NUM
ejpam-6147	101	48	)	)	PUNCT
ejpam-6147	102	1	∑r	∑r	PROPN
ejpam-6147	102	2	j=1	j=1	NOUN
ejpam-6147	102	3	ςj	ςj	VERB
ejpam-6147	102	4	,	,	PUNCT
ejpam-6147	102	5	r	r	NOUN
ejpam-6147	102	6	∈	∈	PROPN
ejpam-6147	102	7	z	z	PROPN
ejpam-6147	102	8	and	and	CCONJ
ejpam-6147	102	9	jr	jr	PROPN
ejpam-6147	102	10	≥	≥	X
ejpam-6147	102	11	0	0	NUM
ejpam-6147	102	12	is	be	AUX
ejpam-6147	102	13	an	an	DET
ejpam-6147	102	14	integer	integer	NOUN
ejpam-6147	102	15	.	.	PUNCT
ejpam-6147	103	1	for	for	ADP
ejpam-6147	103	2	ς	ς	PROPN
ejpam-6147	103	3	∈	∈	PROPN
ejpam-6147	103	4	d	d	PROPN
ejpam-6147	103	5	and	and	CCONJ
ejpam-6147	103	6	s	s	PROPN
ejpam-6147	103	7	>	>	X
ejpam-6147	103	8	0	0	PROPN
ejpam-6147	103	9	,	,	PUNCT
ejpam-6147	103	10	set	set	VERB
ejpam-6147	103	11	ft(ς	ft(ς	NOUN
ejpam-6147	103	12	)	)	PUNCT
ejpam-6147	103	13	=	=	SYM
ejpam-6147	104	1	1	1	NUM
ejpam-6147	104	2	s	s	X
ejpam-6147	104	3	∫	∫	PROPN
ejpam-6147	104	4	s	s	PART
ejpam-6147	104	5	0	0	NUM
ejpam-6147	104	6	e(z	e(z	PROPN
ejpam-6147	104	7	,	,	PUNCT
ejpam-6147	104	8	0)wdz	0)wdz	PROPN
ejpam-6147	104	9	.	.	PUNCT
ejpam-6147	105	1	then	then	ADV
ejpam-6147	105	2	,	,	PUNCT
ejpam-6147	105	3	for	for	ADP
ejpam-6147	105	4	each	each	DET
ejpam-6147	105	5	t	t	PROPN
ejpam-6147	105	6	≥	≥	NOUN
ejpam-6147	105	7	0	0	NUM
ejpam-6147	105	8	,	,	PUNCT
ejpam-6147	105	9	lim	lim	PROPN
ejpam-6147	105	10	s→+∞	s→+∞	PROPN
ejpam-6147	105	11	sup	sup	PROPN
ejpam-6147	105	12	ς∈z	ς∈z	PROPN
ejpam-6147	105	13	∥∥e(t	∥∥e(t	NOUN
ejpam-6147	105	14	,	,	PUNCT
ejpam-6147	105	15	0)fs(ς)−	0)fs(ς)−	NOUN
ejpam-6147	105	16	fs(ς	fs(ς	NOUN
ejpam-6147	105	17	)	)	PUNCT
ejpam-6147	105	18	∥∥	∥∥	X
ejpam-6147	106	1	=	=	NOUN
ejpam-6147	106	2	0	0	X
ejpam-6147	106	3	.	.	PUNCT
ejpam-6147	106	4	proof	proof	NOUN
ejpam-6147	106	5	.	.	PUNCT
ejpam-6147	107	1	assume	assume	VERB
ejpam-6147	107	2	that	that	SCONJ
ejpam-6147	107	3	s	s	VERB
ejpam-6147	107	4	>	>	X
ejpam-6147	107	5	t	t	PROPN
ejpam-6147	107	6	where	where	SCONJ
ejpam-6147	107	7	t	t	PROPN
ejpam-6147	107	8	∈	∈	PROPN
ejpam-6147	107	9	r+	r+	NOUN
ejpam-6147	107	10	is	be	AUX
ejpam-6147	107	11	fix	fix	NOUN
ejpam-6147	107	12	.	.	PUNCT
ejpam-6147	108	1	then	then	ADV
ejpam-6147	108	2	,	,	PUNCT
ejpam-6147	108	3	for	for	ADP
ejpam-6147	108	4	r	r	PROPN
ejpam-6147	108	5	∈	∈	PROPN
ejpam-6147	108	6	n	n	CCONJ
ejpam-6147	108	7	,	,	PUNCT
ejpam-6147	108	8	there	there	PRON
ejpam-6147	108	9	exist	exist	VERB
ejpam-6147	108	10	jr	jr	PROPN
ejpam-6147	108	11	∈	∈	PROPN
ejpam-6147	108	12	n	n	PRON
ejpam-6147	108	13	such	such	ADJ
ejpam-6147	108	14	that	that	SCONJ
ejpam-6147	108	15	(	(	PUNCT
ejpam-6147	108	16	s	s	NOUN
ejpam-6147	108	17	r	r	NOUN
ejpam-6147	108	18	)	)	PUNCT
ejpam-6147	108	19	jr	jr	PROPN
ejpam-6147	108	20	≤	≤	PROPN
ejpam-6147	108	21	s	s	PART
ejpam-6147	108	22	≤	≤	NUM
ejpam-6147	108	23	(	(	PUNCT
ejpam-6147	108	24	s	s	NOUN
ejpam-6147	108	25	r	r	NOUN
ejpam-6147	108	26	)	)	PUNCT
ejpam-6147	108	27	jr	jr	PROPN
ejpam-6147	109	1	+	+	NOUN
ejpam-6147	109	2	1	1	X
ejpam-6147	109	3	.	.	PUNCT
ejpam-6147	109	4	therefore	therefore	ADV
ejpam-6147	109	5	,	,	PUNCT
ejpam-6147	109	6	we	we	PRON
ejpam-6147	109	7	have	have	VERB
ejpam-6147	109	8	limr→+∞	limr→+∞	NOUN
ejpam-6147	109	9	(	(	PUNCT
ejpam-6147	109	10	sr	sr	PROPN
ejpam-6147	109	11	)	)	PUNCT
ejpam-6147	109	12	jr	jr	PROPN
ejpam-6147	110	1	=	=	PUNCT
ejpam-6147	110	2	t.	t.	NOUN
ejpam-6147	110	3	by	by	ADP
ejpam-6147	110	4	using	use	VERB
ejpam-6147	110	5	the	the	DET
ejpam-6147	110	6	idea	idea	NOUN
ejpam-6147	110	7	in	in	ADP
ejpam-6147	110	8	[	[	X
ejpam-6147	110	9	3	3	X
ejpam-6147	110	10	]	]	PUNCT
ejpam-6147	110	11	for	for	ADP
ejpam-6147	110	12	{	{	PUNCT
ejpam-6147	110	13	ςj	ςj	NOUN
ejpam-6147	110	14	,	,	PUNCT
ejpam-6147	110	15	r}∞j	r}∞j	NOUN
ejpam-6147	110	16	,	,	PUNCT
ejpam-6147	110	17	r=1	r=1	NOUN
ejpam-6147	110	18	⊆	⊆	NUM
ejpam-6147	110	19	z	z	NOUN
ejpam-6147	110	20	and	and	CCONJ
ejpam-6147	110	21	℧	℧	NOUN
ejpam-6147	110	22	r	r	NOUN
ejpam-6147	110	23	=	=	SYM
ejpam-6147	110	24	(	(	PUNCT
ejpam-6147	110	25	1r	1r	NUM
ejpam-6147	110	26	)	)	PUNCT
ejpam-6147	110	27	∑r	∑r	PROPN
ejpam-6147	110	28	j=1	j=1	NOUN
ejpam-6147	110	29	ςj	ςj	VERB
ejpam-6147	110	30	,	,	PUNCT
ejpam-6147	110	31	r	r	NOUN
ejpam-6147	110	32	∈	∈	PROPN
ejpam-6147	110	33	z	z	NOUN
ejpam-6147	110	34	,	,	PUNCT
ejpam-6147	110	35	we	we	PRON
ejpam-6147	110	36	have	have	VERB
ejpam-6147	110	37	∥	∥	NUM
ejpam-6147	110	38	℧	℧	NOUN
ejpam-6147	110	39	r	r	NOUN
ejpam-6147	110	40	−	−	NOUN
ejpam-6147	110	41	η∥2	η∥2	ADJ
ejpam-6147	110	42	=	=	SYM
ejpam-6147	110	43	1	1	NUM
ejpam-6147	110	44	r	r	NOUN
ejpam-6147	110	45	r∑	r∑	NOUN
ejpam-6147	110	46	j=1	j=1	NOUN
ejpam-6147	110	47	∥ςj	∥ςj	PROPN
ejpam-6147	110	48	,	,	PUNCT
ejpam-6147	110	49	r	r	NOUN
ejpam-6147	110	50	−	−	NOUN
ejpam-6147	110	51	η∥2	η∥2	ADJ
ejpam-6147	110	52	−	−	NOUN
ejpam-6147	110	53	1	1	NUM
ejpam-6147	110	54	r	r	NOUN
ejpam-6147	110	55	r∑	r∑	NOUN
ejpam-6147	110	56	j=1	j=1	NOUN
ejpam-6147	110	57	∥ςj	∥ςj	PROPN
ejpam-6147	110	58	,	,	PUNCT
ejpam-6147	110	59	r	r	NOUN
ejpam-6147	110	60	−	−	PROPN
ejpam-6147	110	61	℧	℧	PROPN
ejpam-6147	110	62	r∥2	r∥2	ADJ
ejpam-6147	110	63	∀η	∀η	PROPN
ejpam-6147	110	64	∈	∈	PROPN
ejpam-6147	110	65	h.	h.	PROPN
ejpam-6147	110	66	set	set	VERB
ejpam-6147	110	67	η	η	PROPN
ejpam-6147	110	68	=	=	PROPN
ejpam-6147	110	69	e	e	PROPN
ejpam-6147	110	70	(	(	PUNCT
ejpam-6147	110	71	(	(	PUNCT
ejpam-6147	110	72	tr	tr	NOUN
ejpam-6147	110	73	)	)	PUNCT
ejpam-6147	110	74	jr	jr	PROPN
ejpam-6147	110	75	,	,	PUNCT
ejpam-6147	110	76	0)	0)	PUNCT
ejpam-6147	110	77	℧	℧	NOUN
ejpam-6147	110	78	r	r	NOUN
ejpam-6147	110	79	and	and	CCONJ
ejpam-6147	110	80	ςj	ςj	ADP
ejpam-6147	110	81	,	,	PUNCT
ejpam-6147	110	82	r	r	NOUN
ejpam-6147	110	83	=	=	SYM
ejpam-6147	110	84	e	e	NOUN
ejpam-6147	110	85	(	(	PUNCT
ejpam-6147	110	86	(	(	PUNCT
ejpam-6147	110	87	tr	tr	PROPN
ejpam-6147	110	88	)	)	PUNCT
ejpam-6147	110	89	j	j	PROPN
ejpam-6147	110	90	,	,	PUNCT
ejpam-6147	110	91	0)ς	0)ς	NOUN
ejpam-6147	110	92	,	,	PUNCT
ejpam-6147	110	93	for	for	ADP
ejpam-6147	110	94	ς	ς	PROPN
ejpam-6147	110	95	∈	∈	PROPN
ejpam-6147	110	96	z.	z.	PROPN
ejpam-6147	110	97	therefore	therefore	ADV
ejpam-6147	110	98	from	from	ADP
ejpam-6147	110	99	the	the	DET
ejpam-6147	110	100	given	give	VERB
ejpam-6147	110	101	condition	condition	NOUN
ejpam-6147	110	102	we	we	PRON
ejpam-6147	110	103	have	have	VERB
ejpam-6147	110	104	∥∥∥∥	∥∥∥∥	NOUN
ejpam-6147	110	105	℧	℧	NOUN
ejpam-6147	110	106	r	r	NOUN
ejpam-6147	110	107	−	−	NOUN
ejpam-6147	110	108	e	e	NOUN
ejpam-6147	110	109	(	(	PUNCT
ejpam-6147	110	110	(	(	PUNCT
ejpam-6147	110	111	s	s	NOUN
ejpam-6147	110	112	r	r	NOUN
ejpam-6147	110	113	)	)	PUNCT
ejpam-6147	110	114	jr	jr	PROPN
ejpam-6147	110	115	,	,	PUNCT
ejpam-6147	110	116	0)	0)	PUNCT
ejpam-6147	110	117	℧	℧	NOUN
ejpam-6147	110	118	r	r	NOUN
ejpam-6147	110	119	∥∥∥∥2	∥∥∥∥2	NOUN
ejpam-6147	110	120	≤	≤	PUNCT
ejpam-6147	110	121	jr	jr	PROPN
ejpam-6147	110	122	r	r	NOUN
ejpam-6147	110	123	diam(z	diam(z	NOUN
ejpam-6147	110	124	)	)	PUNCT
ejpam-6147	110	125	.	.	PUNCT
ejpam-6147	111	1	for	for	ADP
ejpam-6147	111	2	ϵ	ϵ	PROPN
ejpam-6147	111	3	>	>	X
ejpam-6147	111	4	0	0	NUM
ejpam-6147	111	5	,	,	PUNCT
ejpam-6147	111	6	and	and	CCONJ
ejpam-6147	111	7	from	from	ADP
ejpam-6147	111	8	jr	jr	PROPN
ejpam-6147	111	9	r	r	NOUN
ejpam-6147	111	10	≤	≤	PUNCT
ejpam-6147	111	11	t	t	PROPN
ejpam-6147	111	12	s	s	PART
ejpam-6147	111	13	,	,	PUNCT
ejpam-6147	111	14	there	there	PRON
ejpam-6147	111	15	exists	exist	VERB
ejpam-6147	111	16	a	a	DET
ejpam-6147	111	17	number	number	NOUN
ejpam-6147	111	18	s1	s1	NOUN
ejpam-6147	111	19	>	>	X
ejpam-6147	111	20	0	0	NUM
ejpam-6147	111	21	such	such	ADJ
ejpam-6147	111	22	that	that	SCONJ
ejpam-6147	111	23	0	0	NUM
ejpam-6147	111	24	<	<	X
ejpam-6147	111	25	jr	jr	PROPN
ejpam-6147	111	26	r	r	NOUN
ejpam-6147	111	27	diam(z	diam(z	NOUN
ejpam-6147	111	28	)	)	PUNCT
ejpam-6147	111	29	≤	≤	NOUN
ejpam-6147	111	30	t	t	PROPN
ejpam-6147	111	31	s	s	PART
ejpam-6147	111	32	diam(z	diam(z	NOUN
ejpam-6147	111	33	)	)	PUNCT
ejpam-6147	111	34	<	<	X
ejpam-6147	111	35	ϵ2	ϵ2	PROPN
ejpam-6147	111	36	,	,	PUNCT
ejpam-6147	111	37	∀s	∀s	PROPN
ejpam-6147	111	38	≥	≥	NUM
ejpam-6147	111	39	s1	s1	PROPN
ejpam-6147	111	40	.	.	PUNCT
ejpam-6147	112	1	from	from	ADP
ejpam-6147	112	2	the	the	DET
ejpam-6147	112	3	above	above	ADJ
ejpam-6147	112	4	estimation	estimation	NOUN
ejpam-6147	112	5	we	we	PRON
ejpam-6147	112	6	have∥∥∥∥	have∥∥∥∥	VERB
ejpam-6147	112	7	℧	℧	NOUN
ejpam-6147	112	8	r	r	NOUN
ejpam-6147	112	9	−	−	NOUN
ejpam-6147	112	10	e	e	NOUN
ejpam-6147	112	11	(	(	PUNCT
ejpam-6147	112	12	(	(	PUNCT
ejpam-6147	112	13	s	s	NOUN
ejpam-6147	112	14	r	r	NOUN
ejpam-6147	112	15	)	)	PUNCT
ejpam-6147	112	16	jr	jr	PROPN
ejpam-6147	112	17	,	,	PUNCT
ejpam-6147	112	18	0)	0)	PUNCT
ejpam-6147	112	19	℧	℧	NOUN
ejpam-6147	112	20	r	r	NOUN
ejpam-6147	112	21	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	112	22	<	<	X
ejpam-6147	112	23	ϵ	ϵ	X
ejpam-6147	112	24	,	,	PUNCT
ejpam-6147	112	25	∀r	∀r	PROPN
ejpam-6147	112	26	∈	∈	NOUN
ejpam-6147	112	27	n	n	CCONJ
ejpam-6147	112	28	,	,	PUNCT
ejpam-6147	112	29	ς	ς	PROPN
ejpam-6147	112	30	∈	∈	PROPN
ejpam-6147	112	31	z.	z.	PROPN
ejpam-6147	112	32	m.	m.	PROPN
ejpam-6147	112	33	sarwar	sarwar	PROPN
ejpam-6147	112	34	et	et	PROPN
ejpam-6147	112	35	al	al	PROPN
ejpam-6147	112	36	.	.	PUNCT
ejpam-6147	112	37	/	/	SYM
ejpam-6147	112	38	eur	eur	PROPN
ejpam-6147	112	39	.	.	PUNCT
ejpam-6147	113	1	j.	j.	PROPN
ejpam-6147	113	2	pure	pure	PROPN
ejpam-6147	113	3	appl	appl	PROPN
ejpam-6147	113	4	.	.	PROPN
ejpam-6147	113	5	math	math	PROPN
ejpam-6147	113	6	,	,	PUNCT
ejpam-6147	113	7	18	18	NUM
ejpam-6147	113	8	(	(	PUNCT
ejpam-6147	113	9	3	3	NUM
ejpam-6147	113	10	)	)	PUNCT
ejpam-6147	113	11	(	(	PUNCT
ejpam-6147	113	12	2025	2025	NUM
ejpam-6147	113	13	)	)	PUNCT
ejpam-6147	113	14	,	,	PUNCT
ejpam-6147	113	15	6147	6147	NUM
ejpam-6147	113	16	6	6	NUM
ejpam-6147	113	17	of	of	ADP
ejpam-6147	113	18	18	18	NUM
ejpam-6147	113	19	one	one	NUM
ejpam-6147	113	20	can	can	AUX
ejpam-6147	113	21	write	write	VERB
ejpam-6147	113	22	lim	lim	PROPN
ejpam-6147	113	23	r→+∞	r→+∞	PROPN
ejpam-6147	113	24	℧	℧	PROPN
ejpam-6147	113	25	r	r	NOUN
ejpam-6147	113	26	=	=	SYM
ejpam-6147	113	27	lim	lim	PROPN
ejpam-6147	113	28	r→+∞	r→+∞	PROPN
ejpam-6147	113	29	1	1	NUM
ejpam-6147	113	30	r	r	NOUN
ejpam-6147	113	31	r∑	r∑	NOUN
ejpam-6147	113	32	j=1	j=1	ADJ
ejpam-6147	113	33	e	e	X
ejpam-6147	113	34	(	(	PUNCT
ejpam-6147	113	35	(	(	PUNCT
ejpam-6147	113	36	s	s	PROPN
ejpam-6147	113	37	r	r	NOUN
ejpam-6147	113	38	j	j	PROPN
ejpam-6147	113	39	)	)	PUNCT
ejpam-6147	113	40	,	,	PUNCT
ejpam-6147	113	41	0)ς	0)ς	NOUN
ejpam-6147	113	42	=	=	SYM
ejpam-6147	113	43	lim	lim	PROPN
ejpam-6147	113	44	r→∞	r→∞	PUNCT
ejpam-6147	113	45	1	1	NUM
ejpam-6147	113	46	s	s	NOUN
ejpam-6147	113	47	r∑	r∑	NOUN
ejpam-6147	113	48	j=1	j=1	NOUN
ejpam-6147	113	49	s	s	PART
ejpam-6147	113	50	r	r	NOUN
ejpam-6147	113	51	e	e	NOUN
ejpam-6147	113	52	(	(	PUNCT
ejpam-6147	113	53	(	(	PUNCT
ejpam-6147	113	54	s	s	PROPN
ejpam-6147	113	55	r	r	NOUN
ejpam-6147	113	56	j	j	PROPN
ejpam-6147	113	57	)	)	PUNCT
ejpam-6147	113	58	,	,	PUNCT
ejpam-6147	113	59	0)ς	0)ς	NOUN
ejpam-6147	113	60	=	=	SYM
ejpam-6147	114	1	1	1	NUM
ejpam-6147	114	2	s	s	NOUN
ejpam-6147	114	3	∫	∫	PROPN
ejpam-6147	114	4	s	s	PART
ejpam-6147	114	5	0	0	NUM
ejpam-6147	114	6	e(z	e(z	PROPN
ejpam-6147	114	7	,	,	PUNCT
ejpam-6147	114	8	0)wdz	0)wdz	X
ejpam-6147	114	9	=	=	SYM
ejpam-6147	114	10	fs(ς	fs(ς	NOUN
ejpam-6147	114	11	)	)	PUNCT
ejpam-6147	114	12	,	,	PUNCT
ejpam-6147	114	13	∀	∀	PUNCT
ejpam-6147	114	14	ς	ς	PROPN
ejpam-6147	114	15	∈	∈	PROPN
ejpam-6147	114	16	z.	z.	PROPN
ejpam-6147	114	17	therefore	therefore	ADV
ejpam-6147	114	18	,	,	PUNCT
ejpam-6147	114	19	for	for	ADP
ejpam-6147	114	20	each	each	DET
ejpam-6147	114	21	ς	ς	PROPN
ejpam-6147	114	22	∈	∈	PROPN
ejpam-6147	114	23	z	z	PROPN
ejpam-6147	114	24	,	,	PUNCT
ejpam-6147	114	25	lim	lim	PROPN
ejpam-6147	114	26	r→+∞	r→+∞	PROPN
ejpam-6147	114	27	∥	∥	PRON
ejpam-6147	114	28	℧	℧	NOUN
ejpam-6147	114	29	r	r	NOUN
ejpam-6147	114	30	−	−	NOUN
ejpam-6147	114	31	fs(ς)∥	fs(ς)∥	NOUN
ejpam-6147	114	32	=	=	NOUN
ejpam-6147	114	33	0	0	PROPN
ejpam-6147	114	34	.	.	PUNCT
ejpam-6147	114	35	(	(	PUNCT
ejpam-6147	114	36	2	2	X
ejpam-6147	114	37	)	)	PUNCT
ejpam-6147	114	38	also	also	ADV
ejpam-6147	114	39	we	we	PRON
ejpam-6147	114	40	have	have	VERB
ejpam-6147	114	41	∥fs(ς)−	∥fs(ς)−	NOUN
ejpam-6147	114	42	e(t	e(t	NOUN
ejpam-6147	114	43	,	,	PUNCT
ejpam-6147	114	44	0)fs(ς)∥	0)fs(ς)∥	NUM
ejpam-6147	114	45	≤	≤	NUM
ejpam-6147	114	46	∥fs(ς)−	∥fs(ς)−	NOUN
ejpam-6147	114	47	℧	℧	PROPN
ejpam-6147	114	48	r∥+	r∥+	NOUN
ejpam-6147	114	49	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	114	50	℧	℧	NOUN
ejpam-6147	114	51	r	r	NOUN
ejpam-6147	114	52	−	−	NOUN
ejpam-6147	114	53	e	e	NOUN
ejpam-6147	114	54	(	(	PUNCT
ejpam-6147	114	55	(	(	PUNCT
ejpam-6147	114	56	s	s	NOUN
ejpam-6147	114	57	r	r	NOUN
ejpam-6147	114	58	jr	jr	PROPN
ejpam-6147	114	59	)	)	PUNCT
ejpam-6147	114	60	,	,	PUNCT
ejpam-6147	114	61	0)	0)	PUNCT
ejpam-6147	114	62	℧	℧	NOUN
ejpam-6147	114	63	r	r	NOUN
ejpam-6147	114	64	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	114	65	+	+	CCONJ
ejpam-6147	114	66	∥∥∥∥e	∥∥∥∥e	PROPN
ejpam-6147	114	67	(	(	PUNCT
ejpam-6147	114	68	(	(	PUNCT
ejpam-6147	114	69	s	s	NOUN
ejpam-6147	114	70	r	r	NOUN
ejpam-6147	114	71	jr	jr	PROPN
ejpam-6147	114	72	)	)	PUNCT
ejpam-6147	114	73	,	,	PUNCT
ejpam-6147	114	74	0)	0)	PUNCT
ejpam-6147	114	75	℧	℧	NOUN
ejpam-6147	114	76	r	r	NOUN
ejpam-6147	114	77	−	−	NOUN
ejpam-6147	115	1	e	e	NOUN
ejpam-6147	115	2	(	(	PUNCT
ejpam-6147	115	3	(	(	PUNCT
ejpam-6147	115	4	s	s	NOUN
ejpam-6147	115	5	r	r	NOUN
ejpam-6147	115	6	jr	jr	PROPN
ejpam-6147	115	7	)	)	PUNCT
ejpam-6147	115	8	,	,	PUNCT
ejpam-6147	115	9	0)fs(ς	0)fs(ς	NOUN
ejpam-6147	115	10	)	)	PUNCT
ejpam-6147	115	11	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	116	1	+	+	CCONJ
ejpam-6147	116	2	∥∥∥∥e	∥∥∥∥e	X
ejpam-6147	116	3	(	(	PUNCT
ejpam-6147	116	4	(	(	PUNCT
ejpam-6147	116	5	s	s	NOUN
ejpam-6147	116	6	r	r	NOUN
ejpam-6147	116	7	jr	jr	PROPN
ejpam-6147	116	8	)	)	PUNCT
ejpam-6147	116	9	,	,	PUNCT
ejpam-6147	116	10	0)fs(ς)−	0)fs(ς)−	NOUN
ejpam-6147	116	11	e(t	e(t	NOUN
ejpam-6147	116	12	,	,	PUNCT
ejpam-6147	116	13	0)fs(ς	0)fs(ς	NOUN
ejpam-6147	116	14	)	)	PUNCT
ejpam-6147	116	15	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	117	1	≤	≤	NOUN
ejpam-6147	118	1	2∥	2∥	NUM
ejpam-6147	118	2	℧	℧	NOUN
ejpam-6147	118	3	r	r	NOUN
ejpam-6147	118	4	−	−	NOUN
ejpam-6147	118	5	fs(ς)∥+	fs(ς)∥+	NOUN
ejpam-6147	118	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	118	7	℧	℧	SYM
ejpam-6147	118	8	r	r	NOUN
ejpam-6147	118	9	−	−	NOUN
ejpam-6147	118	10	e	e	NOUN
ejpam-6147	118	11	(	(	PUNCT
ejpam-6147	118	12	(	(	PUNCT
ejpam-6147	118	13	s	s	NOUN
ejpam-6147	118	14	r	r	NOUN
ejpam-6147	118	15	jr	jr	PROPN
ejpam-6147	118	16	)	)	PUNCT
ejpam-6147	118	17	,	,	PUNCT
ejpam-6147	118	18	0)	0)	PUNCT
ejpam-6147	118	19	℧	℧	NOUN
ejpam-6147	118	20	r	r	NOUN
ejpam-6147	118	21	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	118	22	+	+	CCONJ
ejpam-6147	118	23	∥∥∥∥e	∥∥∥∥e	PROPN
ejpam-6147	118	24	(	(	PUNCT
ejpam-6147	118	25	(	(	PUNCT
ejpam-6147	118	26	s	s	NOUN
ejpam-6147	118	27	r	r	NOUN
ejpam-6147	118	28	jr	jr	PROPN
ejpam-6147	118	29	)	)	PUNCT
ejpam-6147	118	30	,	,	PUNCT
ejpam-6147	118	31	0)fs(ς)−	0)fs(ς)−	NOUN
ejpam-6147	118	32	e(t	e(t	NOUN
ejpam-6147	118	33	,	,	PUNCT
ejpam-6147	118	34	0)fs(ς	0)fs(ς	NOUN
ejpam-6147	118	35	)	)	PUNCT
ejpam-6147	118	36	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	118	37	<	<	X
ejpam-6147	118	38	2∥	2∥	NUM
ejpam-6147	118	39	℧	℧	NOUN
ejpam-6147	118	40	r	r	NOUN
ejpam-6147	118	41	−	−	NOUN
ejpam-6147	118	42	fs(ς)∥	fs(ς)∥	NOUN
ejpam-6147	118	43	+	+	CCONJ
ejpam-6147	118	44	∥∥∥∥e	∥∥∥∥e	PROPN
ejpam-6147	118	45	(	(	PUNCT
ejpam-6147	118	46	(	(	PUNCT
ejpam-6147	118	47	s	s	NOUN
ejpam-6147	118	48	r	r	NOUN
ejpam-6147	118	49	jr	jr	PROPN
ejpam-6147	118	50	)	)	PUNCT
ejpam-6147	118	51	,	,	PUNCT
ejpam-6147	118	52	0)fs(ς)−	0)fs(ς)−	NOUN
ejpam-6147	118	53	e(t	e(t	NOUN
ejpam-6147	118	54	,	,	PUNCT
ejpam-6147	118	55	0)fs(ς	0)fs(ς	NOUN
ejpam-6147	118	56	)	)	PUNCT
ejpam-6147	118	57	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-6147	118	58	ϵ	ϵ	X
ejpam-6147	118	59	∀s	∀s	PROPN
ejpam-6147	118	60	≥	≥	NOUN
ejpam-6147	118	61	s1	s1	NOUN
ejpam-6147	118	62	,	,	PUNCT
ejpam-6147	118	63	r	r	NOUN
ejpam-6147	118	64	∈	∈	PROPN
ejpam-6147	118	65	n	n	CCONJ
ejpam-6147	118	66	,	,	PUNCT
ejpam-6147	118	67	ς	ς	PROPN
ejpam-6147	118	68	∈	∈	PROPN
ejpam-6147	118	69	z.	z.	PROPN
ejpam-6147	118	70	from	from	ADP
ejpam-6147	118	71	limr→+∞	limr→+∞	PROPN
ejpam-6147	118	72	(	(	PUNCT
ejpam-6147	118	73	sr	sr	PROPN
ejpam-6147	118	74	)	)	PUNCT
ejpam-6147	118	75	jr	jr	PROPN
ejpam-6147	118	76	=	=	PROPN
ejpam-6147	118	77	t	t	PROPN
ejpam-6147	118	78	,	,	PUNCT
ejpam-6147	118	79	and	and	CCONJ
ejpam-6147	118	80	(	(	PUNCT
ejpam-6147	118	81	2	2	X
ejpam-6147	118	82	)	)	PUNCT
ejpam-6147	118	83	we	we	PRON
ejpam-6147	118	84	have	have	VERB
ejpam-6147	118	85	∥fs(ς)−	∥fs(ς)−	NOUN
ejpam-6147	118	86	e(t	e(t	NOUN
ejpam-6147	118	87	,	,	PUNCT
ejpam-6147	118	88	0)fs(ς)∥	0)fs(ς)∥	X
ejpam-6147	118	89	<	<	X
ejpam-6147	118	90	ϵ	ϵ	X
ejpam-6147	118	91	∀s	∀s	PROPN
ejpam-6147	118	92	≥	≥	NUM
ejpam-6147	118	93	s1	s1	NOUN
ejpam-6147	118	94	,	,	PUNCT
ejpam-6147	118	95	r	r	NOUN
ejpam-6147	118	96	∈	∈	PROPN
ejpam-6147	118	97	n	n	CCONJ
ejpam-6147	118	98	,	,	PUNCT
ejpam-6147	118	99	ς	ς	PROPN
ejpam-6147	118	100	∈	∈	PROPN
ejpam-6147	118	101	z.	z.	PROPN
ejpam-6147	118	102	therefore	therefore	ADV
ejpam-6147	118	103	,	,	PUNCT
ejpam-6147	118	104	for	for	ADP
ejpam-6147	118	105	each	each	DET
ejpam-6147	118	106	t	t	PROPN
ejpam-6147	118	107	∈	∈	PROPN
ejpam-6147	118	108	r+	r+	PUNCT
ejpam-6147	118	109	we	we	PRON
ejpam-6147	118	110	have	have	VERB
ejpam-6147	118	111	lim	lim	PROPN
ejpam-6147	118	112	s→+∞	s→+∞	PROPN
ejpam-6147	118	113	sup	sup	PROPN
ejpam-6147	118	114	ς∈z	ς∈z	NOUN
ejpam-6147	118	115	∥∥fs(ς)−	∥∥fs(ς)−	PROPN
ejpam-6147	118	116	e(t	e(t	NOUN
ejpam-6147	118	117	,	,	PUNCT
ejpam-6147	118	118	0)fs(ς	0)fs(ς	NOUN
ejpam-6147	118	119	)	)	PUNCT
ejpam-6147	118	120	∥∥	∥∥	X
ejpam-6147	119	1	=	=	SYM
ejpam-6147	119	2	0	0	X
ejpam-6147	119	3	.	.	PUNCT
ejpam-6147	119	4	theorem	theorem	NOUN
ejpam-6147	119	5	1	1	NUM
ejpam-6147	119	6	.	.	PUNCT
ejpam-6147	120	1	let	let	VERB
ejpam-6147	120	2	e	e	NOUN
ejpam-6147	120	3	=	=	PRON
ejpam-6147	120	4	{	{	PUNCT
ejpam-6147	120	5	e(s	e(s	PROPN
ejpam-6147	120	6	,	,	PUNCT
ejpam-6147	120	7	0)}s≥0	0)}s≥0	X
ejpam-6147	120	8	:	:	PUNCT
ejpam-6147	120	9	z	z	X
ejpam-6147	120	10	→	→	SYM
ejpam-6147	120	11	z	z	AUX
ejpam-6147	120	12	be	be	AUX
ejpam-6147	120	13	a	a	DET
ejpam-6147	120	14	subfamily	subfamily	NOUN
ejpam-6147	120	15	of	of	ADP
ejpam-6147	120	16	a	a	DET
ejpam-6147	120	17	nee	nee	NOUN
ejpam-6147	120	18	family	family	NOUN
ejpam-6147	120	19	such	such	ADJ
ejpam-6147	120	20	that	that	SCONJ
ejpam-6147	120	21	∥	∥	PUNCT
ejpam-6147	120	22	℧	℧	NOUN
ejpam-6147	120	23	m	m	NOUN
ejpam-6147	120	24	−	−	NOUN
ejpam-6147	120	25	e	e	NOUN
ejpam-6147	120	26	(	(	PUNCT
ejpam-6147	120	27	(	(	PUNCT
ejpam-6147	120	28	t	t	PROPN
ejpam-6147	120	29	m)im	m)im	PROPN
ejpam-6147	120	30	,	,	PUNCT
ejpam-6147	120	31	0)	0)	NOUN
ejpam-6147	120	32	℧	℧	NOUN
ejpam-6147	120	33	m∥2	m∥2	PROPN
ejpam-6147	120	34	≤	≤	PROPN
ejpam-6147	121	1	i	i	PRON
ejpam-6147	121	2	m	m	VERB
ejpam-6147	121	3	m	m	VERB
ejpam-6147	121	4	diam(z	diam(z	NOUN
ejpam-6147	121	5	)	)	PUNCT
ejpam-6147	121	6	where	where	SCONJ
ejpam-6147	121	7	ς	ς	PROPN
ejpam-6147	121	8	∈	∈	PROPN
ejpam-6147	121	9	z	z	PROPN
ejpam-6147	121	10	,	,	PUNCT
ejpam-6147	121	11	t	t	PROPN
ejpam-6147	121	12	>	>	X
ejpam-6147	121	13	0	0	PUNCT
ejpam-6147	122	1	and	and	CCONJ
ejpam-6147	122	2	fe	fe	X
ejpam-6147	122	3	̸=	̸=	PROPN
ejpam-6147	122	4	∅.	∅.	ADV
ejpam-6147	122	5	let	let	VERB
ejpam-6147	122	6	{	{	PUNCT
ejpam-6147	122	7	λt	λt	PART
ejpam-6147	122	8	}	}	PUNCT
ejpam-6147	122	9	and	and	CCONJ
ejpam-6147	122	10	{	{	PUNCT
ejpam-6147	122	11	γt}0	γt}0	X
ejpam-6147	122	12	<	<	X
ejpam-6147	122	13	t<1	t<1	ADJ
ejpam-6147	122	14	be	be	VERB
ejpam-6147	122	15	nets	net	NOUN
ejpam-6147	122	16	of	of	ADP
ejpam-6147	122	17	positive	positive	ADJ
ejpam-6147	122	18	real	real	ADJ
ejpam-6147	122	19	numbers	number	NOUN
ejpam-6147	122	20	such	such	ADJ
ejpam-6147	122	21	that	that	SCONJ
ejpam-6147	122	22	λt	λt	ADP
ejpam-6147	122	23	∈	∈	PROPN
ejpam-6147	122	24	(	(	PUNCT
ejpam-6147	122	25	0	0	NUM
ejpam-6147	122	26	,	,	PUNCT
ejpam-6147	122	27	1	1	NUM
ejpam-6147	122	28	)	)	PUNCT
ejpam-6147	122	29	,	,	PUNCT
ejpam-6147	122	30	limt→0	limt→0	NOUN
ejpam-6147	122	31	λt	λt	ADP
ejpam-6147	122	32	=	=	SYM
ejpam-6147	122	33	1	1	NUM
ejpam-6147	122	34	,	,	PUNCT
ejpam-6147	122	35	limt→0	limt→0	NOUN
ejpam-6147	122	36	γt	γt	NOUN
ejpam-6147	122	37	=	=	PUNCT
ejpam-6147	122	38	+	+	PROPN
ejpam-6147	122	39	∞	∞	NUM
ejpam-6147	122	40	and	and	CCONJ
ejpam-6147	122	41	{	{	PUNCT
ejpam-6147	122	42	ςt	ςt	AUX
ejpam-6147	122	43	}	}	PUNCT
ejpam-6147	122	44	be	be	AUX
ejpam-6147	122	45	the	the	DET
ejpam-6147	122	46	net	net	ADJ
ejpam-6147	122	47	ςt	ςt	NOUN
ejpam-6147	122	48	=	=	SYM
ejpam-6147	122	49	pz	pz	NOUN
ejpam-6147	122	50	[	[	PUNCT
ejpam-6147	122	51	t(λtςt	t(λtςt	ADJ
ejpam-6147	122	52	)	)	PUNCT
ejpam-6147	123	1	+	+	CCONJ
ejpam-6147	123	2	(	(	PUNCT
ejpam-6147	123	3	1−	1−	NUM
ejpam-6147	123	4	t	t	NOUN
ejpam-6147	123	5	)	)	PUNCT
ejpam-6147	123	6	1	1	NUM
ejpam-6147	123	7	γt	γt	NOUN
ejpam-6147	123	8	∫	∫	PROPN
ejpam-6147	123	9	γt	γt	NOUN
ejpam-6147	123	10	0	0	PROPN
ejpam-6147	123	11	e(s	e(s	PROPN
ejpam-6147	123	12	,	,	PUNCT
ejpam-6147	123	13	0)ςtds	0)ςtds	NUM
ejpam-6147	123	14	]	]	PUNCT
ejpam-6147	123	15	,	,	PUNCT
ejpam-6147	123	16	∀	∀	X
ejpam-6147	123	17	t	t	NOUN
ejpam-6147	123	18	∈	∈	PROPN
ejpam-6147	123	19	(	(	PUNCT
ejpam-6147	123	20	0	0	NUM
ejpam-6147	123	21	,	,	PUNCT
ejpam-6147	123	22	1	1	NUM
ejpam-6147	123	23	)	)	PUNCT
ejpam-6147	123	24	.	.	PUNCT
ejpam-6147	124	1	(	(	PUNCT
ejpam-6147	124	2	3	3	X
ejpam-6147	124	3	)	)	PUNCT
ejpam-6147	124	4	then	then	ADV
ejpam-6147	124	5	ςt	ςt	X
ejpam-6147	124	6	→	→	PUNCT
ejpam-6147	124	7	ς∗	ς∗	PROPN
ejpam-6147	124	8	∈	∈	PROPN
ejpam-6147	124	9	fe	fe	NOUN
ejpam-6147	124	10	,	,	PUNCT
ejpam-6147	124	11	strongly	strongly	ADV
ejpam-6147	124	12	as	as	ADP
ejpam-6147	124	13	t	t	PROPN
ejpam-6147	124	14	→	→	SYM
ejpam-6147	124	15	0	0	NUM
ejpam-6147	124	16	+	+	NOUN
ejpam-6147	124	17	.	.	PUNCT
ejpam-6147	124	18	m.	m.	NOUN
ejpam-6147	124	19	sarwar	sarwar	PROPN
ejpam-6147	124	20	et	et	PROPN
ejpam-6147	125	1	al	al	PROPN
ejpam-6147	125	2	.	.	PUNCT
ejpam-6147	125	3	/	/	SYM
ejpam-6147	125	4	eur	eur	PROPN
ejpam-6147	125	5	.	.	PUNCT
ejpam-6147	126	1	j.	j.	PROPN
ejpam-6147	126	2	pure	pure	PROPN
ejpam-6147	126	3	appl	appl	PROPN
ejpam-6147	126	4	.	.	PROPN
ejpam-6147	126	5	math	math	PROPN
ejpam-6147	126	6	,	,	PUNCT
ejpam-6147	126	7	18	18	NUM
ejpam-6147	126	8	(	(	PUNCT
ejpam-6147	126	9	3	3	NUM
ejpam-6147	126	10	)	)	PUNCT
ejpam-6147	126	11	(	(	PUNCT
ejpam-6147	126	12	2025	2025	NUM
ejpam-6147	126	13	)	)	PUNCT
ejpam-6147	126	14	,	,	PUNCT
ejpam-6147	126	15	6147	6147	NUM
ejpam-6147	126	16	7	7	NUM
ejpam-6147	126	17	of	of	ADP
ejpam-6147	126	18	18	18	NUM
ejpam-6147	126	19	proof	proof	NOUN
ejpam-6147	126	20	.	.	PUNCT
ejpam-6147	127	1	first	first	ADV
ejpam-6147	127	2	of	of	ADP
ejpam-6147	127	3	all	all	PRON
ejpam-6147	127	4	we	we	PRON
ejpam-6147	127	5	will	will	AUX
ejpam-6147	127	6	show	show	VERB
ejpam-6147	127	7	that	that	SCONJ
ejpam-6147	127	8	ςt	ςt	NOUN
ejpam-6147	127	9	is	be	AUX
ejpam-6147	127	10	well	well	ADV
ejpam-6147	127	11	defined	define	VERB
ejpam-6147	127	12	.	.	PUNCT
ejpam-6147	128	1	for	for	ADP
ejpam-6147	128	2	this	this	PRON
ejpam-6147	128	3	let	let	VERB
ejpam-6147	128	4	wς	wς	VERB
ejpam-6147	128	5	=	=	PROPN
ejpam-6147	128	6	pz	pz	PROPN
ejpam-6147	128	7	[	[	PUNCT
ejpam-6147	128	8	t(λtς	t(λtς	PROPN
ejpam-6147	128	9	)	)	PUNCT
ejpam-6147	128	10	+	+	CCONJ
ejpam-6147	128	11	(	(	PUNCT
ejpam-6147	128	12	1−	1−	NUM
ejpam-6147	128	13	t	t	NOUN
ejpam-6147	128	14	)	)	PUNCT
ejpam-6147	128	15	1	1	NUM
ejpam-6147	128	16	γt	γt	NOUN
ejpam-6147	128	17	∫	∫	PROPN
ejpam-6147	128	18	γt	γt	NOUN
ejpam-6147	128	19	0	0	PROPN
ejpam-6147	128	20	e(s	e(s	PROPN
ejpam-6147	128	21	,	,	PUNCT
ejpam-6147	128	22	0)wds	0)wds	NUM
ejpam-6147	128	23	]	]	PUNCT
ejpam-6147	128	24	,	,	PUNCT
ejpam-6147	128	25	∀	∀	X
ejpam-6147	128	26	t	t	NOUN
ejpam-6147	128	27	∈	∈	PROPN
ejpam-6147	128	28	(	(	PUNCT
ejpam-6147	128	29	0	0	NUM
ejpam-6147	128	30	,	,	PUNCT
ejpam-6147	128	31	1	1	NUM
ejpam-6147	128	32	)	)	PUNCT
ejpam-6147	128	33	.	.	PUNCT
ejpam-6147	129	1	it	it	PRON
ejpam-6147	129	2	gives	give	VERB
ejpam-6147	129	3	∥wς	∥wς	PROPN
ejpam-6147	129	4	−w	−w	ADV
ejpam-6147	129	5	℧	℧	NOUN
ejpam-6147	129	6	∥	∥	PUNCT
ejpam-6147	129	7	≤	≤	NUM
ejpam-6147	129	8	∥∥∥∥pz	∥∥∥∥pz	PUNCT
ejpam-6147	130	1	(	(	PUNCT
ejpam-6147	130	2	t(λtς	t(λtς	PROPN
ejpam-6147	130	3	)	)	PUNCT
ejpam-6147	130	4	+	+	CCONJ
ejpam-6147	130	5	(	(	PUNCT
ejpam-6147	130	6	1−	1−	NUM
ejpam-6147	130	7	t	t	NOUN
ejpam-6147	130	8	)	)	PUNCT
ejpam-6147	130	9	1	1	NUM
ejpam-6147	130	10	γt	γt	NOUN
ejpam-6147	130	11	∫	∫	PROPN
ejpam-6147	130	12	γt	γt	NOUN
ejpam-6147	130	13	0	0	PROPN
ejpam-6147	130	14	e(s	e(s	PROPN
ejpam-6147	130	15	,	,	PUNCT
ejpam-6147	130	16	0)wds	0)wds	NUM
ejpam-6147	130	17	)	)	PUNCT
ejpam-6147	130	18	−pz	−pz	PROPN
ejpam-6147	130	19	(	(	PUNCT
ejpam-6147	130	20	t(λt	t(λt	NOUN
ejpam-6147	130	21	℧	℧	NOUN
ejpam-6147	130	22	)	)	PUNCT
ejpam-6147	131	1	+	+	CCONJ
ejpam-6147	131	2	(	(	PUNCT
ejpam-6147	131	3	1−	1−	NUM
ejpam-6147	131	4	t	t	NOUN
ejpam-6147	131	5	)	)	PUNCT
ejpam-6147	131	6	1	1	NUM
ejpam-6147	131	7	γt	γt	NOUN
ejpam-6147	131	8	∫	∫	PROPN
ejpam-6147	131	9	γt	γt	NOUN
ejpam-6147	131	10	0	0	PROPN
ejpam-6147	131	11	e(s	e(s	PROPN
ejpam-6147	131	12	,	,	PUNCT
ejpam-6147	131	13	0)uds	0)ud	NOUN
ejpam-6147	131	14	)	)	PUNCT
ejpam-6147	131	15	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	131	16	≤	≤	PUNCT
ejpam-6147	131	17	tλt∥ς	tλt∥ς	NOUN
ejpam-6147	131	18	−	−	ADP
ejpam-6147	131	19	℧	℧	PUNCT
ejpam-6147	131	20	∥+	∥+	PROPN
ejpam-6147	131	21	(	(	PUNCT
ejpam-6147	131	22	1−	1−	NUM
ejpam-6147	131	23	t	t	PROPN
ejpam-6147	131	24	)	)	PUNCT
ejpam-6147	131	25	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	131	26	1	1	NUM
ejpam-6147	131	27	γt	γt	NOUN
ejpam-6147	131	28	∫	∫	PROPN
ejpam-6147	131	29	γt	γt	NOUN
ejpam-6147	131	30	0	0	PROPN
ejpam-6147	131	31	(	(	PUNCT
ejpam-6147	131	32	e(s	e(s	PROPN
ejpam-6147	131	33	,	,	PUNCT
ejpam-6147	131	34	0)ς	0)ς	NOUN
ejpam-6147	131	35	−	−	NOUN
ejpam-6147	131	36	e(s	e(s	PROPN
ejpam-6147	131	37	,	,	PUNCT
ejpam-6147	131	38	0	0	NUM
ejpam-6147	131	39	)	)	PUNCT
ejpam-6147	131	40	℧	℧	PUNCT
ejpam-6147	131	41	)	)	PUNCT
ejpam-6147	131	42	ds	ds	ADP
ejpam-6147	131	43	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	131	44	≤	≤	PUNCT
ejpam-6147	131	45	tλt∥ς	tλt∥ς	NOUN
ejpam-6147	131	46	−	−	ADP
ejpam-6147	131	47	℧	℧	PUNCT
ejpam-6147	131	48	∥+	∥+	PROPN
ejpam-6147	131	49	(	(	PUNCT
ejpam-6147	131	50	1−	1−	NUM
ejpam-6147	131	51	t)∥ς	t)∥ς	NOUN
ejpam-6147	131	52	−	−	ADP
ejpam-6147	131	53	℧	℧	NOUN
ejpam-6147	131	54	∥	∥	X
ejpam-6147	131	55	=	=	PUNCT
ejpam-6147	132	1	[	[	X
ejpam-6147	132	2	1−	1−	NUM
ejpam-6147	132	3	(	(	PUNCT
ejpam-6147	132	4	1−	1−	NUM
ejpam-6147	132	5	λt)t]∥ς	λt)t]∥ς	NOUN
ejpam-6147	132	6	−	−	PROPN
ejpam-6147	132	7	℧	℧	NOUN
ejpam-6147	132	8	∥.	∥.	X
ejpam-6147	132	9	which	which	PRON
ejpam-6147	132	10	implies	imply	VERB
ejpam-6147	132	11	that	that	SCONJ
ejpam-6147	132	12	∥wς	∥wς	PROPN
ejpam-6147	132	13	−w	−w	ADV
ejpam-6147	132	14	℧	℧	ADP
ejpam-6147	132	15	∥	∥	PUNCT
ejpam-6147	132	16	≤	≤	NOUN
ejpam-6147	133	1	[	[	X
ejpam-6147	133	2	1−	1−	NUM
ejpam-6147	133	3	(	(	PUNCT
ejpam-6147	133	4	1−	1−	NUM
ejpam-6147	133	5	λt)t]∥ς	λt)t]∥ς	NOUN
ejpam-6147	133	6	−	−	PROPN
ejpam-6147	133	7	℧	℧	NUM
ejpam-6147	133	8	∥.	∥.	NOUN
ejpam-6147	133	9	this	this	PRON
ejpam-6147	133	10	shows	show	VERB
ejpam-6147	133	11	that	that	SCONJ
ejpam-6147	133	12	ςt	ςt	NOUN
ejpam-6147	133	13	is	be	AUX
ejpam-6147	133	14	a	a	DET
ejpam-6147	133	15	contraction	contraction	NOUN
ejpam-6147	133	16	,	,	PUNCT
ejpam-6147	133	17	so	so	ADV
ejpam-6147	133	18	by	by	ADP
ejpam-6147	133	19	banach	banach	NOUN
ejpam-6147	133	20	contraction	contraction	NOUN
ejpam-6147	133	21	principle	principle	NOUN
ejpam-6147	133	22	it	it	PRON
ejpam-6147	133	23	has	have	VERB
ejpam-6147	133	24	a	a	DET
ejpam-6147	133	25	unique	unique	ADJ
ejpam-6147	133	26	fp	fp	NOUN
ejpam-6147	133	27	,	,	PUNCT
ejpam-6147	133	28	and	and	CCONJ
ejpam-6147	133	29	hence	hence	ADV
ejpam-6147	133	30	the	the	DET
ejpam-6147	133	31	net	net	ADJ
ejpam-6147	133	32	ςt	ςt	NOUN
ejpam-6147	133	33	is	be	AUX
ejpam-6147	133	34	well	well	ADV
ejpam-6147	133	35	defined	define	VERB
ejpam-6147	133	36	.	.	PUNCT
ejpam-6147	134	1	now	now	ADV
ejpam-6147	134	2	for	for	ADP
ejpam-6147	134	3	any	any	DET
ejpam-6147	134	4	υ	υ	PROPN
ejpam-6147	134	5	∈	∈	PROPN
ejpam-6147	134	6	fe	fe	X
ejpam-6147	134	7	,	,	PUNCT
ejpam-6147	134	8	we	we	PRON
ejpam-6147	134	9	have	have	VERB
ejpam-6147	134	10	∥ςt	∥ςt	NOUN
ejpam-6147	134	11	−υ∥	−υ∥	NOUN
ejpam-6147	134	12	=	=	SYM
ejpam-6147	134	13	∥∥∥∥pz	∥∥∥∥pz	PUNCT
ejpam-6147	135	1	[	[	PUNCT
ejpam-6147	135	2	t(λtςt	t(λtςt	ADJ
ejpam-6147	135	3	)	)	PUNCT
ejpam-6147	136	1	+	+	CCONJ
ejpam-6147	136	2	(	(	PUNCT
ejpam-6147	136	3	1−	1−	NUM
ejpam-6147	136	4	t	t	NOUN
ejpam-6147	136	5	)	)	PUNCT
ejpam-6147	136	6	1	1	NUM
ejpam-6147	137	1	γt	γt	NOUN
ejpam-6147	137	2	∫	∫	PROPN
ejpam-6147	137	3	γt	γt	NOUN
ejpam-6147	137	4	0	0	PROPN
ejpam-6147	137	5	e(s	e(s	PROPN
ejpam-6147	137	6	,	,	PUNCT
ejpam-6147	137	7	0)ςtds	0)ςtds	NUM
ejpam-6147	137	8	]	]	PUNCT
ejpam-6147	137	9	−	−	NOUN
ejpam-6147	137	10	pz(υ	pz(υ	NUM
ejpam-6147	137	11	)	)	PUNCT
ejpam-6147	137	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	137	13	=	=	SYM
ejpam-6147	137	14	∥∥∥∥t(λtςt	∥∥∥∥t(λtςt	PROPN
ejpam-6147	137	15	)	)	PUNCT
ejpam-6147	138	1	+	+	CCONJ
ejpam-6147	138	2	(	(	PUNCT
ejpam-6147	138	3	1−	1−	NUM
ejpam-6147	138	4	t	t	NOUN
ejpam-6147	138	5	)	)	PUNCT
ejpam-6147	138	6	1	1	NUM
ejpam-6147	138	7	γt	γt	NOUN
ejpam-6147	138	8	∫	∫	PROPN
ejpam-6147	138	9	γt	γt	NOUN
ejpam-6147	138	10	0	0	PROPN
ejpam-6147	138	11	e(s	e(s	PROPN
ejpam-6147	138	12	,	,	PUNCT
ejpam-6147	138	13	0)ςtds−υ	0)ςtds−υ	NUM
ejpam-6147	138	14	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	139	1	=	=	SYM
ejpam-6147	139	2	∥∥∥∥tλtςt	∥∥∥∥tλtςt	PUNCT
ejpam-6147	139	3	−	−	NUM
ejpam-6147	139	4	tλtυ−	tλtυ−	NOUN
ejpam-6147	139	5	tυ+	tυ+	NOUN
ejpam-6147	139	6	tλtυ+	tλtυ+	X
ejpam-6147	139	7	tυ+	tυ+	NOUN
ejpam-6147	139	8	(	(	PUNCT
ejpam-6147	139	9	1−	1−	NUM
ejpam-6147	139	10	t	t	NOUN
ejpam-6147	139	11	)	)	PUNCT
ejpam-6147	139	12	1	1	NUM
ejpam-6147	139	13	γt	γt	NOUN
ejpam-6147	139	14	∫	∫	PROPN
ejpam-6147	139	15	γt	γt	NOUN
ejpam-6147	139	16	0	0	PROPN
ejpam-6147	139	17	e(s	e(s	PROPN
ejpam-6147	139	18	,	,	PUNCT
ejpam-6147	139	19	0)ςtds−υ	0)ςtds−υ	NUM
ejpam-6147	139	20	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	139	21	≤	≤	NOUN
ejpam-6147	139	22	tλt∥ςt	tλt∥ςt	NOUN
ejpam-6147	139	23	−υ∥+	−υ∥+	PUNCT
ejpam-6147	139	24	t(1−	t(1−	PROPN
ejpam-6147	139	25	λt)∥υ∥+	λt)∥υ∥+	PROPN
ejpam-6147	139	26	(	(	PUNCT
ejpam-6147	139	27	1−	1−	NUM
ejpam-6147	139	28	t)∥ςt	t)∥ςt	VERB
ejpam-6147	139	29	−υ∥	−υ∥	NOUN
ejpam-6147	139	30	=	=	PUNCT
ejpam-6147	140	1	[	[	X
ejpam-6147	140	2	1−	1−	NUM
ejpam-6147	140	3	(	(	PUNCT
ejpam-6147	140	4	1−	1−	NUM
ejpam-6147	140	5	λt)t]∥ςt	λt)t]∥ςt	NOUN
ejpam-6147	140	6	−υ∥+	−υ∥+	ADV
ejpam-6147	140	7	t(1−	t(1−	PROPN
ejpam-6147	140	8	λt)∥υ∥.	λt)∥υ∥.	X
ejpam-6147	140	9	from	from	ADP
ejpam-6147	140	10	this	this	PRON
ejpam-6147	140	11	we	we	PRON
ejpam-6147	140	12	have	have	VERB
ejpam-6147	140	13	∥ςt	∥ςt	PROPN
ejpam-6147	140	14	−υ∥	−υ∥	PROPN
ejpam-6147	140	15	≤	≤	NOUN
ejpam-6147	141	1	[	[	X
ejpam-6147	141	2	1−	1−	NUM
ejpam-6147	141	3	(	(	PUNCT
ejpam-6147	141	4	1−	1−	NUM
ejpam-6147	141	5	λt)t]∥ςt	λt)t]∥ςt	NOUN
ejpam-6147	141	6	−υ∥+	−υ∥+	PUNCT
ejpam-6147	141	7	t(1−	t(1−	PROPN
ejpam-6147	141	8	λt)∥υ∥	λt)∥υ∥	NOUN
ejpam-6147	141	9	≤	≤	NOUN
ejpam-6147	141	10	∥ςt	∥ςt	ADP
ejpam-6147	141	11	−υ∥	−υ∥	PROPN
ejpam-6147	141	12	−	−	PROPN
ejpam-6147	141	13	(	(	PUNCT
ejpam-6147	141	14	1−	1−	NUM
ejpam-6147	141	15	λt)t∥ςt	λt)t∥ςt	PROPN
ejpam-6147	141	16	−υ∥+	−υ∥+	ADV
ejpam-6147	141	17	(	(	PUNCT
ejpam-6147	141	18	1−	1−	NUM
ejpam-6147	141	19	λt)t∥υ∥.	λt)t∥υ∥.	PROPN
ejpam-6147	141	20	it	it	PRON
ejpam-6147	141	21	follows	follow	VERB
ejpam-6147	141	22	that	that	SCONJ
ejpam-6147	141	23	∥ςt−υ∥	∥ςt−υ∥	ADP
ejpam-6147	141	24	≤	≤	ADJ
ejpam-6147	141	25	∥υ∥	∥υ∥	ADJ
ejpam-6147	141	26	,	,	PUNCT
ejpam-6147	141	27	therefore	therefore	ADV
ejpam-6147	141	28	the	the	DET
ejpam-6147	141	29	net	net	NOUN
ejpam-6147	141	30	ςt	ςt	NOUN
ejpam-6147	141	31	is	be	AUX
ejpam-6147	141	32	bounded	bound	VERB
ejpam-6147	141	33	.	.	PUNCT
ejpam-6147	142	1	let	let	VERB
ejpam-6147	142	2	k	k	NOUN
ejpam-6147	142	3	:	:	PUNCT
ejpam-6147	142	4	=	=	NOUN
ejpam-6147	142	5	∥υ∥	∥υ∥	ADJ
ejpam-6147	142	6	,	,	PUNCT
ejpam-6147	142	7	then	then	ADV
ejpam-6147	142	8	clearly	clearly	ADV
ejpam-6147	142	9	{	{	PUNCT
ejpam-6147	142	10	ςt	ςt	X
ejpam-6147	142	11	}	}	PUNCT
ejpam-6147	142	12	⊂	⊂	PROPN
ejpam-6147	142	13	b(υ	b(υ	PROPN
ejpam-6147	142	14	,	,	PUNCT
ejpam-6147	142	15	k	k	NOUN
ejpam-6147	142	16	)	)	PUNCT
ejpam-6147	142	17	.	.	PUNCT
ejpam-6147	143	1	note	note	VERB
ejpam-6147	143	2	that	that	SCONJ
ejpam-6147	143	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	143	4	1	1	NUM
ejpam-6147	143	5	γt	γt	NOUN
ejpam-6147	143	6	∫	∫	PROPN
ejpam-6147	143	7	γt	γt	NOUN
ejpam-6147	143	8	0	0	PROPN
ejpam-6147	143	9	e(s	e(s	PROPN
ejpam-6147	143	10	,	,	PUNCT
ejpam-6147	143	11	0)ςtds−υ	0)ςtds−υ	NUM
ejpam-6147	143	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	144	1	=	=	SYM
ejpam-6147	144	2	∥∥∥∥	∥∥∥∥	SYM
ejpam-6147	144	3	1	1	NUM
ejpam-6147	144	4	γt	γt	NOUN
ejpam-6147	144	5	∫	∫	PROPN
ejpam-6147	144	6	γt	γt	NOUN
ejpam-6147	144	7	0	0	PROPN
ejpam-6147	144	8	e(s	e(s	PROPN
ejpam-6147	144	9	,	,	PUNCT
ejpam-6147	144	10	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	144	11	1	1	NUM
ejpam-6147	144	12	γt	γt	NOUN
ejpam-6147	144	13	∫	∫	PROPN
ejpam-6147	144	14	γt	γt	NOUN
ejpam-6147	144	15	0	0	NUM
ejpam-6147	144	16	υds	υds	X
ejpam-6147	144	17	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	144	18	=	=	SYM
ejpam-6147	144	19	∥∥∥∥	∥∥∥∥	SYM
ejpam-6147	144	20	1	1	NUM
ejpam-6147	144	21	γt	γt	NOUN
ejpam-6147	144	22	∫	∫	PROPN
ejpam-6147	144	23	γt	γt	NOUN
ejpam-6147	144	24	0	0	PROPN
ejpam-6147	144	25	(	(	PUNCT
ejpam-6147	144	26	e(s	e(s	PROPN
ejpam-6147	144	27	,	,	PUNCT
ejpam-6147	144	28	0)ςt	0)ςt	NUM
ejpam-6147	144	29	−	−	PROPN
ejpam-6147	144	30	e(s	e(s	PROPN
ejpam-6147	144	31	,	,	PUNCT
ejpam-6147	144	32	0)υ	0)υ	NOUN
ejpam-6147	144	33	)	)	PUNCT
ejpam-6147	144	34	ds	ds	ADP
ejpam-6147	144	35	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	144	36	m.	m.	NOUN
ejpam-6147	144	37	sarwar	sarwar	PROPN
ejpam-6147	144	38	et	et	PROPN
ejpam-6147	144	39	al	al	PROPN
ejpam-6147	144	40	.	.	PUNCT
ejpam-6147	144	41	/	/	SYM
ejpam-6147	144	42	eur	eur	PROPN
ejpam-6147	144	43	.	.	PUNCT
ejpam-6147	145	1	j.	j.	PROPN
ejpam-6147	145	2	pure	pure	PROPN
ejpam-6147	145	3	appl	appl	PROPN
ejpam-6147	145	4	.	.	PROPN
ejpam-6147	145	5	math	math	PROPN
ejpam-6147	145	6	,	,	PUNCT
ejpam-6147	145	7	18	18	NUM
ejpam-6147	145	8	(	(	PUNCT
ejpam-6147	145	9	3	3	NUM
ejpam-6147	145	10	)	)	PUNCT
ejpam-6147	145	11	(	(	PUNCT
ejpam-6147	145	12	2025	2025	NUM
ejpam-6147	145	13	)	)	PUNCT
ejpam-6147	145	14	,	,	PUNCT
ejpam-6147	145	15	6147	6147	NUM
ejpam-6147	145	16	8	8	NUM
ejpam-6147	145	17	of	of	ADP
ejpam-6147	145	18	18	18	NUM
ejpam-6147	145	19	≤	≤	NUM
ejpam-6147	145	20	1	1	NUM
ejpam-6147	145	21	γt	γt	NOUN
ejpam-6147	145	22	∫	∫	PROPN
ejpam-6147	145	23	γt	γt	NOUN
ejpam-6147	145	24	0	0	NUM
ejpam-6147	145	25	∥∥∥∥(e(s	∥∥∥∥(e(s	NOUN
ejpam-6147	145	26	,	,	PUNCT
ejpam-6147	145	27	0)ςt	0)ςt	NUM
ejpam-6147	145	28	−	−	PROPN
ejpam-6147	145	29	e(s	e(s	PROPN
ejpam-6147	145	30	,	,	PUNCT
ejpam-6147	145	31	0)υ	0)υ	NOUN
ejpam-6147	145	32	)	)	PUNCT
ejpam-6147	145	33	∥∥∥∥ds	∥∥∥∥ds	SYM
ejpam-6147	145	34	≤	≤	NUM
ejpam-6147	145	35	1	1	NUM
ejpam-6147	145	36	γt	γt	NOUN
ejpam-6147	145	37	∫	∫	PROPN
ejpam-6147	145	38	γt	γt	NOUN
ejpam-6147	145	39	0	0	NUM
ejpam-6147	145	40	∥ςt	∥ςt	PART
ejpam-6147	145	41	−υ∥ds	−υ∥ds	NOUN
ejpam-6147	145	42	=	=	PUNCT
ejpam-6147	145	43	∥ςt	∥ςt	NUM
ejpam-6147	145	44	−υ∥	−υ∥	PROPN
ejpam-6147	145	45	≤	≤	PROPN
ejpam-6147	145	46	k.	k.	NOUN
ejpam-6147	146	1	also	also	ADV
ejpam-6147	146	2	we	we	PRON
ejpam-6147	146	3	note	note	VERB
ejpam-6147	146	4	that	that	SCONJ
ejpam-6147	146	5	,	,	PUNCT
ejpam-6147	146	6	if	if	SCONJ
ejpam-6147	146	7	ς	ς	PROPN
ejpam-6147	146	8	∈	∈	PROPN
ejpam-6147	146	9	b(υ	b(υ	PROPN
ejpam-6147	146	10	,	,	PUNCT
ejpam-6147	146	11	k	k	NOUN
ejpam-6147	146	12	)	)	PUNCT
ejpam-6147	146	13	,	,	PUNCT
ejpam-6147	146	14	then	then	ADV
ejpam-6147	146	15	∥e(s	∥e(s	ADJ
ejpam-6147	146	16	,	,	PUNCT
ejpam-6147	146	17	0)ς	0)ς	NUM
ejpam-6147	146	18	−υ∥	−υ∥	PROPN
ejpam-6147	146	19	≤	≤	NOUN
ejpam-6147	146	20	∥e(s	∥e(s	NOUN
ejpam-6147	146	21	,	,	PUNCT
ejpam-6147	146	22	0)ς	0)ς	NOUN
ejpam-6147	146	23	−	−	PROPN
ejpam-6147	147	1	e(s	e(s	PROPN
ejpam-6147	147	2	,	,	PUNCT
ejpam-6147	147	3	0)υ∥	0)υ∥	NUM
ejpam-6147	147	4	≤	≤	NUM
ejpam-6147	147	5	∥ς	∥ς	PROPN
ejpam-6147	147	6	−υ∥	−υ∥	VERB
ejpam-6147	147	7	≤	≤	NUM
ejpam-6147	147	8	k	k	NOUN
ejpam-6147	147	9	,	,	PUNCT
ejpam-6147	147	10	that	that	PRON
ejpam-6147	147	11	is	be	AUX
ejpam-6147	147	12	b(υ	b(υ	PROPN
ejpam-6147	147	13	,	,	PUNCT
ejpam-6147	147	14	k	k	NOUN
ejpam-6147	147	15	)	)	PUNCT
ejpam-6147	147	16	is	be	AUX
ejpam-6147	147	17	e(s	e(s	PROPN
ejpam-6147	147	18	,	,	PUNCT
ejpam-6147	147	19	0)-invariant	0)-invariant	NUM
ejpam-6147	147	20	∀	∀	X
ejpam-6147	147	21	s	s	PART
ejpam-6147	147	22	≥	≥	NOUN
ejpam-6147	147	23	0	0	NUM
ejpam-6147	147	24	.	.	PUNCT
ejpam-6147	148	1	set	set	VERB
ejpam-6147	148	2	℧	℧	PROPN
ejpam-6147	148	3	t	t	NOUN
ejpam-6147	148	4	=	=	PUNCT
ejpam-6147	148	5	t(λtςt	t(λtςt	ADJ
ejpam-6147	148	6	)	)	PUNCT
ejpam-6147	149	1	+	+	CCONJ
ejpam-6147	149	2	(	(	PUNCT
ejpam-6147	149	3	1−	1−	NUM
ejpam-6147	149	4	t	t	NOUN
ejpam-6147	149	5	)	)	PUNCT
ejpam-6147	149	6	1	1	NUM
ejpam-6147	149	7	γt	γt	NOUN
ejpam-6147	149	8	∫	∫	PROPN
ejpam-6147	149	9	γt	γt	NOUN
ejpam-6147	149	10	0	0	PROPN
ejpam-6147	149	11	e(s	e(s	PROPN
ejpam-6147	149	12	,	,	PUNCT
ejpam-6147	149	13	0)ςtds	0)ςtds	PROPN
ejpam-6147	149	14	.	.	PUNCT
ejpam-6147	150	1	then	then	ADV
ejpam-6147	150	2	ςt	ςt	VERB
ejpam-6147	150	3	=	=	SYM
ejpam-6147	150	4	pz	pz	NOUN
ejpam-6147	151	1	[	[	X
ejpam-6147	151	2	℧	℧	PROPN
ejpam-6147	151	3	t	t	X
ejpam-6147	151	4	]	]	PUNCT
ejpam-6147	151	5	,	,	PUNCT
ejpam-6147	151	6	therefore	therefore	ADV
ejpam-6147	151	7	we	we	PRON
ejpam-6147	151	8	have	have	VERB
ejpam-6147	151	9	∥e(τ	∥e(τ	NOUN
ejpam-6147	151	10	,	,	PUNCT
ejpam-6147	151	11	0)ςt	0)ςt	NUM
ejpam-6147	151	12	−	−	NOUN
ejpam-6147	151	13	ςt∥	ςt∥	PROPN
ejpam-6147	151	14	=	=	SYM
ejpam-6147	151	15	∥pz	∥pz	PROPN
ejpam-6147	152	1	[	[	X
ejpam-6147	152	2	e(τ	e(τ	PROPN
ejpam-6147	152	3	,	,	PUNCT
ejpam-6147	152	4	0)ςt]−	0)ςt]−	NOUN
ejpam-6147	152	5	pz	pz	NOUN
ejpam-6147	153	1	[	[	X
ejpam-6147	153	2	℧	℧	ADP
ejpam-6147	153	3	t]∥	t]∥	NOUN
ejpam-6147	153	4	≤	≤	NOUN
ejpam-6147	153	5	∥e(τ	∥e(τ	NOUN
ejpam-6147	153	6	,	,	PUNCT
ejpam-6147	153	7	0)ςt	0)ςt	NOUN
ejpam-6147	153	8	−	−	NOUN
ejpam-6147	153	9	℧	℧	NOUN
ejpam-6147	153	10	t∥	t∥	NUM
ejpam-6147	153	11	≤	≤	NUM
ejpam-6147	153	12	∥∥∥∥e(τ	∥∥∥∥e(τ	NOUN
ejpam-6147	153	13	,	,	PUNCT
ejpam-6147	153	14	0)ςt	0)ςt	PROPN
ejpam-6147	153	15	−	−	PROPN
ejpam-6147	153	16	e(τ	e(τ	PROPN
ejpam-6147	153	17	,	,	PUNCT
ejpam-6147	153	18	0	0	NUM
ejpam-6147	153	19	)	)	PUNCT
ejpam-6147	153	20	1	1	NUM
ejpam-6147	153	21	γt	γt	NOUN
ejpam-6147	153	22	∫	∫	PROPN
ejpam-6147	153	23	γt	γt	NOUN
ejpam-6147	153	24	0	0	PROPN
ejpam-6147	153	25	e(s	e(s	PROPN
ejpam-6147	153	26	,	,	PUNCT
ejpam-6147	153	27	0)ςtds	0)ςtds	NUM
ejpam-6147	153	28	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	153	29	+	+	CCONJ
ejpam-6147	153	30	∥∥∥∥e(τ	∥∥∥∥e(τ	NOUN
ejpam-6147	153	31	,	,	PUNCT
ejpam-6147	153	32	0	0	NUM
ejpam-6147	153	33	)	)	PUNCT
ejpam-6147	153	34	1	1	NUM
ejpam-6147	153	35	γt	γt	NOUN
ejpam-6147	153	36	∫	∫	PROPN
ejpam-6147	153	37	γt	γt	NOUN
ejpam-6147	153	38	0	0	PROPN
ejpam-6147	153	39	e(s	e(s	PROPN
ejpam-6147	153	40	,	,	PUNCT
ejpam-6147	153	41	0)ςtds	0)ςtds	PUNCT
ejpam-6147	153	42	−	−	PROPN
ejpam-6147	153	43	1	1	NUM
ejpam-6147	153	44	γt	γt	NOUN
ejpam-6147	153	45	∫	∫	PROPN
ejpam-6147	153	46	γt	γt	NOUN
ejpam-6147	153	47	0	0	PROPN
ejpam-6147	153	48	e(s	e(s	PROPN
ejpam-6147	153	49	,	,	PUNCT
ejpam-6147	153	50	0)ςtds	0)ςtds	NUM
ejpam-6147	153	51	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-6147	153	52	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	153	53	1	1	NUM
ejpam-6147	153	54	γt	γt	NOUN
ejpam-6147	153	55	∫	∫	PROPN
ejpam-6147	153	56	γt	γt	NOUN
ejpam-6147	153	57	0	0	PROPN
ejpam-6147	153	58	e(s	e(s	PROPN
ejpam-6147	153	59	,	,	PUNCT
ejpam-6147	153	60	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	153	61	℧	℧	PROPN
ejpam-6147	153	62	t	t	NOUN
ejpam-6147	153	63	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	153	64	≤	≤	NUM
ejpam-6147	153	65	∥∥∥∥e(τ	∥∥∥∥e(τ	NOUN
ejpam-6147	153	66	,	,	PUNCT
ejpam-6147	153	67	0	0	NUM
ejpam-6147	153	68	)	)	PUNCT
ejpam-6147	153	69	1	1	NUM
ejpam-6147	153	70	γt	γt	NOUN
ejpam-6147	153	71	∫	∫	PROPN
ejpam-6147	153	72	γt	γt	NOUN
ejpam-6147	153	73	0	0	PROPN
ejpam-6147	153	74	e(s	e(s	PROPN
ejpam-6147	153	75	,	,	PUNCT
ejpam-6147	153	76	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	153	77	1	1	NUM
ejpam-6147	153	78	γt	γt	NOUN
ejpam-6147	153	79	∫	∫	PROPN
ejpam-6147	153	80	γt	γt	NOUN
ejpam-6147	153	81	0	0	PROPN
ejpam-6147	153	82	e(s	e(s	PROPN
ejpam-6147	153	83	,	,	PUNCT
ejpam-6147	153	84	0)ςtds	0)ςtds	NUM
ejpam-6147	153	85	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	154	1	+	+	CCONJ
ejpam-6147	154	2	∥∥∥∥ςt	∥∥∥∥ςt	PUNCT
ejpam-6147	154	3	−	−	PROPN
ejpam-6147	154	4	1	1	NUM
ejpam-6147	154	5	γt	γt	PROPN
ejpam-6147	154	6	∫	∫	PROPN
ejpam-6147	154	7	γt	γt	NOUN
ejpam-6147	154	8	0	0	PROPN
ejpam-6147	154	9	e(s	e(s	PROPN
ejpam-6147	154	10	,	,	PUNCT
ejpam-6147	154	11	0)ςtds	0)ςtds	NUM
ejpam-6147	154	12	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	155	1	+	+	CCONJ
ejpam-6147	155	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6147	155	3	1	1	NUM
ejpam-6147	155	4	γt	γt	NOUN
ejpam-6147	155	5	∫	∫	PROPN
ejpam-6147	155	6	γt	γt	NOUN
ejpam-6147	155	7	0	0	PROPN
ejpam-6147	155	8	e(s	e(s	PROPN
ejpam-6147	155	9	,	,	PUNCT
ejpam-6147	155	10	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	155	11	(	(	PUNCT
ejpam-6147	155	12	t(λtςt	t(λtςt	ADJ
ejpam-6147	155	13	)	)	PUNCT
ejpam-6147	155	14	+	+	CCONJ
ejpam-6147	155	15	(	(	PUNCT
ejpam-6147	155	16	1−	1−	NUM
ejpam-6147	155	17	t	t	NOUN
ejpam-6147	155	18	)	)	PUNCT
ejpam-6147	155	19	1	1	NUM
ejpam-6147	155	20	γt	γt	NOUN
ejpam-6147	155	21	∫	∫	PROPN
ejpam-6147	155	22	γt	γt	NOUN
ejpam-6147	155	23	0	0	PROPN
ejpam-6147	155	24	e(s	e(s	PROPN
ejpam-6147	155	25	,	,	PUNCT
ejpam-6147	155	26	0)ςtds	0)ςtds	NUM
ejpam-6147	155	27	)	)	PUNCT
ejpam-6147	155	28	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	155	29	≤	≤	NUM
ejpam-6147	155	30	∥∥∥∥e((τ	∥∥∥∥e((τ	X
ejpam-6147	155	31	)	)	PUNCT
ejpam-6147	155	32	,	,	PUNCT
ejpam-6147	155	33	0	0	X
ejpam-6147	155	34	)	)	PUNCT
ejpam-6147	155	35	1	1	NUM
ejpam-6147	155	36	γt	γt	NOUN
ejpam-6147	155	37	∫	∫	PROPN
ejpam-6147	155	38	γt	γt	NOUN
ejpam-6147	155	39	0	0	PROPN
ejpam-6147	155	40	e(s	e(s	PROPN
ejpam-6147	155	41	,	,	PUNCT
ejpam-6147	155	42	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	155	43	1	1	NUM
ejpam-6147	155	44	γt	γt	NOUN
ejpam-6147	155	45	∫	∫	PROPN
ejpam-6147	155	46	γt	γt	NOUN
ejpam-6147	155	47	0	0	PROPN
ejpam-6147	155	48	e(s	e(s	PROPN
ejpam-6147	155	49	,	,	PUNCT
ejpam-6147	155	50	0)ςtds	0)ςtds	NUM
ejpam-6147	155	51	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	156	1	+	+	CCONJ
ejpam-6147	156	2	∥∥∥∥ςt	∥∥∥∥ςt	PUNCT
ejpam-6147	156	3	−	−	PROPN
ejpam-6147	156	4	1	1	NUM
ejpam-6147	156	5	γt	γt	PROPN
ejpam-6147	156	6	∫	∫	PROPN
ejpam-6147	156	7	γt	γt	NOUN
ejpam-6147	156	8	0	0	PROPN
ejpam-6147	156	9	e(s	e(s	PROPN
ejpam-6147	156	10	,	,	PUNCT
ejpam-6147	156	11	0)ςtds	0)ςtds	PUNCT
ejpam-6147	156	12	∥∥∥∥+	∥∥∥∥+	NOUN
ejpam-6147	156	13	t	t	NOUN
ejpam-6147	156	14	∥∥∥∥λtςt	∥∥∥∥λtςt	NOUN
ejpam-6147	156	15	−	−	PROPN
ejpam-6147	156	16	1	1	NUM
ejpam-6147	156	17	γt	γt	NOUN
ejpam-6147	156	18	∫	∫	PROPN
ejpam-6147	156	19	γt	γt	NOUN
ejpam-6147	156	20	0	0	PROPN
ejpam-6147	156	21	e(s	e(s	PROPN
ejpam-6147	156	22	,	,	PUNCT
ejpam-6147	156	23	0)ςtds	0)ςtds	NUM
ejpam-6147	156	24	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	156	25	≤	≤	NUM
ejpam-6147	156	26	∥∥∥∥e((τ	∥∥∥∥e((τ	X
ejpam-6147	156	27	)	)	PUNCT
ejpam-6147	156	28	,	,	PUNCT
ejpam-6147	156	29	0	0	X
ejpam-6147	156	30	)	)	PUNCT
ejpam-6147	156	31	1	1	NUM
ejpam-6147	156	32	γt	γt	NOUN
ejpam-6147	156	33	∫	∫	PROPN
ejpam-6147	156	34	γt	γt	NOUN
ejpam-6147	156	35	0	0	PROPN
ejpam-6147	156	36	e(s	e(s	PROPN
ejpam-6147	156	37	,	,	PUNCT
ejpam-6147	156	38	0)ςtds−	0)ςtds−	NOUN
ejpam-6147	156	39	1	1	NUM
ejpam-6147	156	40	γt	γt	NOUN
ejpam-6147	156	41	∫	∫	PROPN
ejpam-6147	156	42	γt	γt	NOUN
ejpam-6147	156	43	0	0	PROPN
ejpam-6147	156	44	e(s	e(s	PROPN
ejpam-6147	156	45	,	,	PUNCT
ejpam-6147	156	46	0)ςtds	0)ςtds	NUM
ejpam-6147	156	47	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	156	48	+2	+2	ADP
ejpam-6147	156	49	t	t	NOUN
ejpam-6147	156	50	∥∥∥∥λtςt	∥∥∥∥λtςt	VERB
ejpam-6147	156	51	−	−	PROPN
ejpam-6147	156	52	1	1	NUM
ejpam-6147	156	53	γt	γt	NOUN
ejpam-6147	156	54	∫	∫	PROPN
ejpam-6147	156	55	γt	γt	NOUN
ejpam-6147	156	56	0	0	PROPN
ejpam-6147	156	57	e(s	e(s	PROPN
ejpam-6147	156	58	,	,	PUNCT
ejpam-6147	156	59	0)ςtds	0)ςtds	NUM
ejpam-6147	156	60	∥∥∥∥.	∥∥∥∥.	PROPN
ejpam-6147	156	61	using	use	VERB
ejpam-6147	156	62	lemma	lemma	PROPN
ejpam-6147	156	63	(	(	PUNCT
ejpam-6147	156	64	4	4	NUM
ejpam-6147	156	65	)	)	PUNCT
ejpam-6147	156	66	,	,	PUNCT
ejpam-6147	156	67	we	we	PRON
ejpam-6147	156	68	get	get	VERB
ejpam-6147	156	69	that	that	DET
ejpam-6147	156	70	lim	lim	PROPN
ejpam-6147	156	71	t→0	t→0	PROPN
ejpam-6147	156	72	∥e(τ	∥e(τ	PROPN
ejpam-6147	156	73	,	,	PUNCT
ejpam-6147	156	74	0)ςt	0)ςt	PROPN
ejpam-6147	157	1	−	−	NOUN
ejpam-6147	158	1	ςt∥	ςt∥	PROPN
ejpam-6147	159	1	=	=	SYM
ejpam-6147	160	1	0	0	PROPN
ejpam-6147	160	2	,	,	PUNCT
ejpam-6147	160	3	(	(	PUNCT
ejpam-6147	160	4	4	4	NUM
ejpam-6147	160	5	)	)	PUNCT
ejpam-6147	160	6	for	for	ADP
ejpam-6147	160	7	all	all	DET
ejpam-6147	160	8	τ	τ	PRON
ejpam-6147	160	9	∈	∈	PROPN
ejpam-6147	161	1	[	[	X
ejpam-6147	161	2	0,∞	0,∞	NOUN
ejpam-6147	161	3	)	)	PUNCT
ejpam-6147	161	4	.	.	PUNCT
ejpam-6147	162	1	note	note	VERB
ejpam-6147	162	2	that	that	SCONJ
ejpam-6147	162	3	we	we	PRON
ejpam-6147	162	4	have	have	VERB
ejpam-6147	162	5	ςt	ςt	NOUN
ejpam-6147	162	6	=	=	PUNCT
ejpam-6147	162	7	pz	pz	NOUN
ejpam-6147	163	1	[	[	X
ejpam-6147	163	2	℧	℧	PROPN
ejpam-6147	163	3	t	t	X
ejpam-6147	163	4	]	]	PUNCT
ejpam-6147	163	5	.	.	PUNCT
ejpam-6147	164	1	by	by	ADP
ejpam-6147	164	2	using	use	VERB
ejpam-6147	164	3	metric	metric	ADJ
ejpam-6147	164	4	projection	projection	NOUN
ejpam-6147	164	5	property	property	NOUN
ejpam-6147	164	6	(	(	PUNCT
ejpam-6147	164	7	1	1	NUM
ejpam-6147	164	8	)	)	PUNCT
ejpam-6147	164	9	,	,	PUNCT
ejpam-6147	164	10	we	we	PRON
ejpam-6147	164	11	have	have	VERB
ejpam-6147	164	12	∥ςt	∥ςt	NOUN
ejpam-6147	164	13	−υ∥2	−υ∥2	NOUN
ejpam-6147	164	14	=	=	PUNCT
ejpam-6147	165	1	⟨ςt	⟨ςt	PROPN
ejpam-6147	166	1	−	−	NOUN
ejpam-6147	166	2	ςt	ςt	NOUN
ejpam-6147	167	1	+	+	CCONJ
ejpam-6147	167	2	ςt	ςt	NOUN
ejpam-6147	167	3	−υ	−υ	NOUN
ejpam-6147	167	4	,	,	PUNCT
ejpam-6147	167	5	ςt	ςt	PART
ejpam-6147	168	1	−υ⟩	−υ⟩	PROPN
ejpam-6147	168	2	m.	m.	NOUN
ejpam-6147	168	3	sarwar	sarwar	PROPN
ejpam-6147	168	4	et	et	PROPN
ejpam-6147	168	5	al	al	PROPN
ejpam-6147	168	6	.	.	PUNCT
ejpam-6147	168	7	/	/	SYM
ejpam-6147	168	8	eur	eur	PROPN
ejpam-6147	168	9	.	.	PUNCT
ejpam-6147	169	1	j.	j.	PROPN
ejpam-6147	169	2	pure	pure	PROPN
ejpam-6147	169	3	appl	appl	PROPN
ejpam-6147	169	4	.	.	PROPN
ejpam-6147	169	5	math	math	PROPN
ejpam-6147	169	6	,	,	PUNCT
ejpam-6147	169	7	18	18	NUM
ejpam-6147	169	8	(	(	PUNCT
ejpam-6147	169	9	3	3	NUM
ejpam-6147	169	10	)	)	PUNCT
ejpam-6147	169	11	(	(	PUNCT
ejpam-6147	169	12	2025	2025	NUM
ejpam-6147	169	13	)	)	PUNCT
ejpam-6147	169	14	,	,	PUNCT
ejpam-6147	169	15	6147	6147	NUM
ejpam-6147	169	16	9	9	NUM
ejpam-6147	169	17	of	of	ADP
ejpam-6147	169	18	18	18	NUM
ejpam-6147	169	19	≤	≤	NUM
ejpam-6147	169	20	⟨	⟨	NOUN
ejpam-6147	169	21	℧	℧	NOUN
ejpam-6147	169	22	t	t	NOUN
ejpam-6147	169	23	−υ	−υ	NOUN
ejpam-6147	169	24	,	,	PUNCT
ejpam-6147	169	25	ςt	ςt	VERB
ejpam-6147	169	26	−υ⟩	−υ⟩	PROPN
ejpam-6147	169	27	=	=	SYM
ejpam-6147	169	28	⟨t(λtςt)−	⟨t(λtςt)−	PROPN
ejpam-6147	169	29	tλtυ+	tλtυ+	X
ejpam-6147	169	30	tλtυ	tλtυ	NOUN
ejpam-6147	169	31	+	+	PROPN
ejpam-6147	169	32	(	(	PUNCT
ejpam-6147	169	33	1−	1−	NUM
ejpam-6147	169	34	t	t	NOUN
ejpam-6147	169	35	)	)	PUNCT
ejpam-6147	169	36	1	1	NUM
ejpam-6147	169	37	γt	γt	NOUN
ejpam-6147	169	38	∫	∫	PROPN
ejpam-6147	169	39	γt	γt	NOUN
ejpam-6147	169	40	0	0	PROPN
ejpam-6147	169	41	e(s	e(s	PROPN
ejpam-6147	169	42	,	,	PUNCT
ejpam-6147	169	43	0)ςtds+	0)ςtds+	PROPN
ejpam-6147	169	44	(	(	PUNCT
ejpam-6147	169	45	1−	1−	NUM
ejpam-6147	169	46	t)υ−	t)υ−	PROPN
ejpam-6147	169	47	(	(	PUNCT
ejpam-6147	169	48	1−	1−	NUM
ejpam-6147	169	49	t)υ	t)υ	PUNCT
ejpam-6147	169	50	,	,	PUNCT
ejpam-6147	169	51	υ−	υ−	PROPN
ejpam-6147	169	52	ςt⟩	ςt⟩	PROPN
ejpam-6147	169	53	−	−	PROPN
ejpam-6147	170	1	⟨υ	⟨υ	PROPN
ejpam-6147	170	2	,	,	PUNCT
ejpam-6147	170	3	ςt	ςt	VERB
ejpam-6147	170	4	−υ⟩	−υ⟩	PROPN
ejpam-6147	170	5	=	=	PUNCT
ejpam-6147	170	6	tλt⟨ςt	tλt⟨ςt	NUM
ejpam-6147	170	7	−υ	−υ	NOUN
ejpam-6147	170	8	,	,	PUNCT
ejpam-6147	170	9	ςt	ςt	NOUN
ejpam-6147	170	10	−υ⟩+	−υ⟩+	X
ejpam-6147	170	11	(	(	PUNCT
ejpam-6147	170	12	1−	1−	NUM
ejpam-6147	170	13	t	t	NOUN
ejpam-6147	170	14	)	)	PUNCT
ejpam-6147	170	15	〈	〈	PROPN
ejpam-6147	170	16	1	1	NUM
ejpam-6147	170	17	γt	γt	NOUN
ejpam-6147	170	18	∫	∫	PROPN
ejpam-6147	170	19	γt	γt	NOUN
ejpam-6147	170	20	0	0	PROPN
ejpam-6147	170	21	e(s	e(s	PROPN
ejpam-6147	170	22	,	,	PUNCT
ejpam-6147	170	23	0)ςtds−υ	0)ςtds−υ	NUM
ejpam-6147	170	24	,	,	PUNCT
ejpam-6147	171	1	ςt	ςt	VERB
ejpam-6147	171	2	−υ	−υ	NOUN
ejpam-6147	171	3	〉	〉	NOUN
ejpam-6147	172	1	+	+	NOUN
ejpam-6147	172	2	⟨tλtυ+υ−	⟨tλtυ+υ−	NOUN
ejpam-6147	172	3	tυ	tυ	ADP
ejpam-6147	172	4	,	,	PUNCT
ejpam-6147	172	5	ςt	ςt	PART
ejpam-6147	172	6	−υ⟩	−υ⟩	PROPN
ejpam-6147	172	7	−	−	PROPN
ejpam-6147	172	8	⟨υ	⟨υ	NOUN
ejpam-6147	172	9	,	,	PUNCT
ejpam-6147	172	10	ςt	ςt	VERB
ejpam-6147	172	11	−υ⟩	−υ⟩	PROPN
ejpam-6147	172	12	=	=	PUNCT
ejpam-6147	172	13	tλt⟨ςt	tλt⟨ςt	NUM
ejpam-6147	172	14	−υ	−υ	NOUN
ejpam-6147	172	15	,	,	PUNCT
ejpam-6147	172	16	ςt	ςt	NOUN
ejpam-6147	172	17	−υ⟩+	−υ⟩+	X
ejpam-6147	172	18	(	(	PUNCT
ejpam-6147	172	19	1−	1−	NUM
ejpam-6147	172	20	t	t	NOUN
ejpam-6147	172	21	)	)	PUNCT
ejpam-6147	172	22	〈	〈	PROPN
ejpam-6147	172	23	1	1	NUM
ejpam-6147	172	24	γt	γt	NOUN
ejpam-6147	172	25	∫	∫	PROPN
ejpam-6147	172	26	γt	γt	NOUN
ejpam-6147	172	27	0	0	PROPN
ejpam-6147	172	28	e(s	e(s	PROPN
ejpam-6147	172	29	,	,	PUNCT
ejpam-6147	172	30	0)ςtds−υ	0)ςtds−υ	NUM
ejpam-6147	172	31	,	,	PUNCT
ejpam-6147	172	32	ςt	ςt	VERB
ejpam-6147	172	33	−υ	−υ	NOUN
ejpam-6147	172	34	〉	〉	NOUN
ejpam-6147	173	1	+	+	ADP
ejpam-6147	173	2	⟨t(λt	⟨t(λt	X
ejpam-6147	173	3	−	−	PROPN
ejpam-6147	173	4	1)υ	1)υ	NUM
ejpam-6147	174	1	+	+	SYM
ejpam-6147	174	2	υ−υ	υ−υ	ADJ
ejpam-6147	174	3	,	,	PUNCT
ejpam-6147	174	4	ςt	ςt	VERB
ejpam-6147	174	5	−υ⟩	−υ⟩	PROPN
ejpam-6147	174	6	=	=	PUNCT
ejpam-6147	174	7	tλt⟨ςt	tλt⟨ςt	NUM
ejpam-6147	174	8	−υ	−υ	NOUN
ejpam-6147	174	9	,	,	PUNCT
ejpam-6147	174	10	ςt	ςt	NOUN
ejpam-6147	174	11	−υ⟩+	−υ⟩+	X
ejpam-6147	174	12	(	(	PUNCT
ejpam-6147	174	13	1−	1−	NUM
ejpam-6147	174	14	t	t	NOUN
ejpam-6147	174	15	)	)	PUNCT
ejpam-6147	174	16	〈	〈	PROPN
ejpam-6147	174	17	1	1	NUM
ejpam-6147	174	18	γt	γt	NOUN
ejpam-6147	174	19	∫	∫	PROPN
ejpam-6147	174	20	γt	γt	NOUN
ejpam-6147	174	21	0	0	PROPN
ejpam-6147	175	1	(	(	PUNCT
ejpam-6147	175	2	e(s	e(s	PROPN
ejpam-6147	175	3	,	,	PUNCT
ejpam-6147	175	4	0)ςt	0)ςt	PRON
ejpam-6147	175	5	−υ)ds	−υ)ds	NUM
ejpam-6147	175	6	,	,	PUNCT
ejpam-6147	175	7	ςt	ςt	NOUN
ejpam-6147	175	8	−υ	−υ	NOUN
ejpam-6147	175	9	〉	〉	NOUN
ejpam-6147	175	10	−(1−	−(1−	NOUN
ejpam-6147	175	11	λt)t⟨υ	λt)t⟨υ	NOUN
ejpam-6147	175	12	,	,	PUNCT
ejpam-6147	175	13	ςt	ςt	PART
ejpam-6147	175	14	−υ⟩	−υ⟩	PROPN
ejpam-6147	175	15	≤	≤	PROPN
ejpam-6147	175	16	tλt⟨ςt	tλt⟨ςt	NUM
ejpam-6147	175	17	−υ	−υ	NOUN
ejpam-6147	175	18	,	,	PUNCT
ejpam-6147	175	19	ςt	ςt	NOUN
ejpam-6147	175	20	−υ⟩+	−υ⟩+	X
ejpam-6147	175	21	(	(	PUNCT
ejpam-6147	175	22	1−	1−	NUM
ejpam-6147	175	23	t	t	NOUN
ejpam-6147	175	24	)	)	PUNCT
ejpam-6147	175	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6147	175	26	〈	〈	PROPN
ejpam-6147	175	27	1	1	NUM
ejpam-6147	175	28	γt	γt	NOUN
ejpam-6147	175	29	∫	∫	PROPN
ejpam-6147	175	30	γt	γt	NOUN
ejpam-6147	175	31	0	0	PROPN
ejpam-6147	175	32	(	(	PUNCT
ejpam-6147	175	33	e(s	e(s	PROPN
ejpam-6147	175	34	,	,	PUNCT
ejpam-6147	175	35	0)ςt	0)ςt	PRON
ejpam-6147	175	36	−υ)ds	−υ)ds	NUM
ejpam-6147	175	37	,	,	PUNCT
ejpam-6147	175	38	ςt	ςt	NOUN
ejpam-6147	175	39	−υ	−υ	NOUN
ejpam-6147	175	40	〉	〉	NOUN
ejpam-6147	175	41	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6147	175	42	−(1−	−(1−	NOUN
ejpam-6147	175	43	λt)t⟨υ	λt)t⟨υ	NUM
ejpam-6147	175	44	,	,	PUNCT
ejpam-6147	175	45	ςt	ςt	VERB
ejpam-6147	175	46	−υ⟩	−υ⟩	PROPN
ejpam-6147	175	47	≤	≤	NUM
ejpam-6147	175	48	tλt∥ςt	tλt∥ςt	NOUN
ejpam-6147	175	49	−υ∥2	−υ∥2	NOUN
ejpam-6147	175	50	+	+	CCONJ
ejpam-6147	175	51	(	(	PUNCT
ejpam-6147	175	52	1−	1−	NUM
ejpam-6147	175	53	t	t	NOUN
ejpam-6147	175	54	)	)	PUNCT
ejpam-6147	175	55	[	[	PUNCT
ejpam-6147	175	56	1	1	NUM
ejpam-6147	175	57	γt	γt	NOUN
ejpam-6147	175	58	∫	∫	PROPN
ejpam-6147	175	59	γt	γt	NOUN
ejpam-6147	175	60	0	0	NUM
ejpam-6147	175	61	∥e(s	∥e(s	PROPN
ejpam-6147	175	62	,	,	PUNCT
ejpam-6147	175	63	0)ςt	0)ςt	PROPN
ejpam-6147	175	64	−υ∥ds	−υ∥ds	NOUN
ejpam-6147	175	65	]	]	PUNCT
ejpam-6147	175	66	∥ςt	∥ςt	X
ejpam-6147	175	67	−υ∥	−υ∥	PROPN
ejpam-6147	175	68	−(1−	−(1−	NOUN
ejpam-6147	175	69	λt)t⟨υ	λt)t⟨υ	NOUN
ejpam-6147	175	70	,	,	PUNCT
ejpam-6147	175	71	ςt	ςt	VERB
ejpam-6147	175	72	−υ⟩	−υ⟩	NOUN
ejpam-6147	176	1	=	=	PUNCT
ejpam-6147	177	1	[	[	X
ejpam-6147	177	2	1−	1−	NUM
ejpam-6147	177	3	(	(	PUNCT
ejpam-6147	177	4	1−	1−	NUM
ejpam-6147	177	5	λt)t]∥ςt	λt)t]∥ςt	NOUN
ejpam-6147	177	6	−υ∥2	−υ∥2	NOUN
ejpam-6147	177	7	−	−	PROPN
ejpam-6147	177	8	(	(	PUNCT
ejpam-6147	177	9	1−	1−	NUM
ejpam-6147	177	10	λt)t⟨υ	λt)t⟨υ	NUM
ejpam-6147	177	11	,	,	PUNCT
ejpam-6147	177	12	ςt	ςt	NOUN
ejpam-6147	177	13	−υ⟩.	−υ⟩.	NOUN
ejpam-6147	177	14	from	from	ADP
ejpam-6147	177	15	above	above	ADP
ejpam-6147	177	16	we	we	PRON
ejpam-6147	177	17	have	have	VERB
ejpam-6147	177	18	∥ςt	∥ςt	NOUN
ejpam-6147	177	19	−υ∥2	−υ∥2	NOUN
ejpam-6147	177	20	≤	≤	NOUN
ejpam-6147	177	21	∥ςt	∥ςt	PART
ejpam-6147	177	22	−υ∥2	−υ∥2	NOUN
ejpam-6147	177	23	−	−	PROPN
ejpam-6147	177	24	(	(	PUNCT
ejpam-6147	177	25	1−	1−	NUM
ejpam-6147	177	26	λt)t∥ςt	λt)t∥ςt	PROPN
ejpam-6147	177	27	−υ∥2	−υ∥2	NOUN
ejpam-6147	178	1	−	−	PROPN
ejpam-6147	179	1	(	(	PUNCT
ejpam-6147	179	2	1−	1−	NUM
ejpam-6147	179	3	λt)t⟨υ	λt)t⟨υ	NUM
ejpam-6147	179	4	,	,	PUNCT
ejpam-6147	179	5	ςt	ςt	NOUN
ejpam-6147	179	6	−υ⟩.	−υ⟩.	NOUN
ejpam-6147	179	7	which	which	PRON
ejpam-6147	179	8	implies	imply	VERB
ejpam-6147	179	9	that	that	SCONJ
ejpam-6147	180	1	∥ςt	∥ςt	PROPN
ejpam-6147	180	2	−υ∥2	−υ∥2	NOUN
ejpam-6147	180	3	≤	≤	PROPN
ejpam-6147	180	4	⟨υ	⟨υ	PROPN
ejpam-6147	180	5	,	,	PUNCT
ejpam-6147	180	6	υ−	υ−	PROPN
ejpam-6147	180	7	ςt⟩	ςt⟩	NUM
ejpam-6147	180	8	,	,	PUNCT
ejpam-6147	180	9	∀υ	∀υ	PROPN
ejpam-6147	180	10	∈	∈	PROPN
ejpam-6147	180	11	fe	fe	X
ejpam-6147	180	12	.	.	PUNCT
ejpam-6147	180	13	(	(	PUNCT
ejpam-6147	180	14	5	5	X
ejpam-6147	180	15	)	)	PUNCT
ejpam-6147	180	16	the	the	DET
ejpam-6147	180	17	last	last	ADJ
ejpam-6147	180	18	inequality	inequality	NOUN
ejpam-6147	180	19	(	(	PUNCT
ejpam-6147	180	20	5	5	NUM
ejpam-6147	180	21	)	)	PUNCT
ejpam-6147	180	22	,	,	PUNCT
ejpam-6147	180	23	shows	show	VERB
ejpam-6147	180	24	that	that	SCONJ
ejpam-6147	180	25	ωs(ςt	ωs(ςt	NOUN
ejpam-6147	180	26	)	)	PUNCT
ejpam-6147	180	27	=	=	SYM
ejpam-6147	180	28	ως(ςt	ως(ςt	NOUN
ejpam-6147	180	29	)	)	PUNCT
ejpam-6147	180	30	,	,	PUNCT
ejpam-6147	180	31	where	where	SCONJ
ejpam-6147	180	32	ωs(ςt	ωs(ςt	NOUN
ejpam-6147	180	33	)	)	PUNCT
ejpam-6147	180	34	and	and	CCONJ
ejpam-6147	180	35	ως(ςt	ως(ςt	NOUN
ejpam-6147	180	36	)	)	PUNCT
ejpam-6147	180	37	denoting	denote	VERB
ejpam-6147	180	38	the	the	DET
ejpam-6147	180	39	strong	strong	ADJ
ejpam-6147	180	40	and	and	CCONJ
ejpam-6147	180	41	weak	weak	ADJ
ejpam-6147	180	42	limit	limit	NOUN
ejpam-6147	180	43	points	point	NOUN
ejpam-6147	180	44	sets	set	NOUN
ejpam-6147	180	45	of	of	ADP
ejpam-6147	180	46	ςt	ςt	NOUN
ejpam-6147	180	47	respectively	respectively	ADV
ejpam-6147	180	48	.	.	PUNCT
ejpam-6147	181	1	let	let	AUX
ejpam-6147	181	2	{	{	PUNCT
ejpam-6147	181	3	tn	tn	NOUN
ejpam-6147	181	4	}	}	PUNCT
ejpam-6147	181	5	be	be	AUX
ejpam-6147	181	6	a	a	DET
ejpam-6147	181	7	progression	progression	NOUN
ejpam-6147	181	8	in	in	ADP
ejpam-6147	181	9	(	(	PUNCT
ejpam-6147	181	10	0	0	NUM
ejpam-6147	181	11	,	,	PUNCT
ejpam-6147	181	12	1	1	NUM
ejpam-6147	181	13	)	)	PUNCT
ejpam-6147	181	14	such	such	ADJ
ejpam-6147	181	15	that	that	SCONJ
ejpam-6147	181	16	tn	tn	PROPN
ejpam-6147	181	17	→	→	SYM
ejpam-6147	181	18	0	0	NUM
ejpam-6147	181	19	,	,	PUNCT
ejpam-6147	181	20	as	as	SCONJ
ejpam-6147	181	21	n	n	PROPN
ejpam-6147	181	22	→	→	ADP
ejpam-6147	181	23	∞.	∞.	PROPN
ejpam-6147	181	24	put	put	VERB
ejpam-6147	181	25	ςn	ςn	NOUN
ejpam-6147	181	26	:	:	PUNCT
ejpam-6147	181	27	=	=	NUM
ejpam-6147	181	28	ςtn	ςtn	NOUN
ejpam-6147	181	29	,	,	PUNCT
ejpam-6147	181	30	ςn	ςn	PROPN
ejpam-6147	181	31	:	:	PUNCT
ejpam-6147	181	32	=	=	SYM
ejpam-6147	182	1	℧	℧	PROPN
ejpam-6147	182	2	tn	tn	PROPN
ejpam-6147	182	3	and	and	CCONJ
ejpam-6147	182	4	γn	γn	X
ejpam-6147	182	5	:	:	PUNCT
ejpam-6147	182	6	=	=	SYM
ejpam-6147	182	7	βtn	βtn	PROPN
ejpam-6147	182	8	.	.	PUNCT
ejpam-6147	183	1	so	so	ADV
ejpam-6147	183	2	ςn	ςn	PROPN
ejpam-6147	183	3	become	become	VERB
ejpam-6147	183	4	bounded	bounded	ADJ
ejpam-6147	183	5	,	,	PUNCT
ejpam-6147	183	6	hence	hence	ADV
ejpam-6147	183	7	we	we	PRON
ejpam-6147	183	8	may	may	AUX
ejpam-6147	183	9	assume	assume	VERB
ejpam-6147	183	10	that	that	SCONJ
ejpam-6147	183	11	the	the	DET
ejpam-6147	183	12	sequence	sequence	NOUN
ejpam-6147	183	13	{	{	PUNCT
ejpam-6147	183	14	ςn	ςn	NOUN
ejpam-6147	183	15	}	}	PUNCT
ejpam-6147	183	16	converge	converge	VERB
ejpam-6147	183	17	to	to	ADP
ejpam-6147	183	18	a	a	DET
ejpam-6147	183	19	point	point	NOUN
ejpam-6147	183	20	ς∗	ς∗	NOUN
ejpam-6147	183	21	∈	∈	PROPN
ejpam-6147	183	22	z	z	PROPN
ejpam-6147	183	23	,	,	PUNCT
ejpam-6147	183	24	in	in	ADP
ejpam-6147	183	25	a	a	DET
ejpam-6147	183	26	weak	weak	ADJ
ejpam-6147	183	27	sense	sense	NOUN
ejpam-6147	183	28	.	.	PUNCT
ejpam-6147	184	1	also	also	ADV
ejpam-6147	184	2	,	,	PUNCT
ejpam-6147	184	3	℧	℧	NOUN
ejpam-6147	184	4	n	n	X
ejpam-6147	184	5	→	→	SYM
ejpam-6147	184	6	ς∗.	ς∗.	NUM
ejpam-6147	184	7	from	from	ADP
ejpam-6147	184	8	equation(4	equation(4	PROPN
ejpam-6147	184	9	)	)	PUNCT
ejpam-6147	184	10	and	and	CCONJ
ejpam-6147	184	11	lemma	lemma	PROPN
ejpam-6147	184	12	(	(	PUNCT
ejpam-6147	184	13	1	1	X
ejpam-6147	184	14	)	)	PUNCT
ejpam-6147	184	15	we	we	PRON
ejpam-6147	184	16	obtain	obtain	VERB
ejpam-6147	184	17	that	that	DET
ejpam-6147	184	18	ς∗	ς∗	PROPN
ejpam-6147	184	19	∈	∈	PROPN
ejpam-6147	184	20	fe	fe	PROPN
ejpam-6147	184	21	.	.	PROPN
ejpam-6147	185	1	from	from	ADP
ejpam-6147	185	2	(	(	PUNCT
ejpam-6147	185	3	5	5	X
ejpam-6147	185	4	)	)	PUNCT
ejpam-6147	185	5	we	we	PRON
ejpam-6147	185	6	have	have	VERB
ejpam-6147	185	7	∥ςn	∥ςn	PROPN
ejpam-6147	185	8	−υ∥2	−υ∥2	NOUN
ejpam-6147	185	9	≤	≤	PUNCT
ejpam-6147	185	10	⟨υ	⟨υ	NOUN
ejpam-6147	185	11	,	,	PUNCT
ejpam-6147	185	12	υ−	υ−	PROPN
ejpam-6147	185	13	ςn⟩	ςn⟩	NUM
ejpam-6147	185	14	∀υ	∀υ	VERB
ejpam-6147	185	15	∈	∈	PROPN
ejpam-6147	185	16	fe	fe	X
ejpam-6147	185	17	.	.	PUNCT
ejpam-6147	186	1	(	(	PUNCT
ejpam-6147	186	2	6	6	NUM
ejpam-6147	186	3	)	)	PUNCT
ejpam-6147	186	4	in	in	ADP
ejpam-6147	186	5	particular	particular	ADJ
ejpam-6147	186	6	,	,	PUNCT
ejpam-6147	186	7	if	if	SCONJ
ejpam-6147	186	8	we	we	PRON
ejpam-6147	186	9	replace	replace	VERB
ejpam-6147	186	10	υ	υ	NOUN
ejpam-6147	186	11	by	by	ADP
ejpam-6147	186	12	ς∗	ς∗	NOUN
ejpam-6147	186	13	in	in	ADP
ejpam-6147	186	14	(	(	PUNCT
ejpam-6147	186	15	6	6	NUM
ejpam-6147	186	16	)	)	PUNCT
ejpam-6147	186	17	,	,	PUNCT
ejpam-6147	186	18	then	then	ADV
ejpam-6147	186	19	we	we	PRON
ejpam-6147	186	20	have	have	VERB
ejpam-6147	186	21	∥ςn	∥ςn	NUM
ejpam-6147	186	22	−	−	NUM
ejpam-6147	186	23	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	186	24	≤	≤	PROPN
ejpam-6147	186	25	⟨ς∗	⟨ς∗	PROPN
ejpam-6147	186	26	,	,	PUNCT
ejpam-6147	186	27	ς∗	ς∗	NOUN
ejpam-6147	186	28	−	−	PROPN
ejpam-6147	186	29	ςn⟩.	ςn⟩.	NOUN
ejpam-6147	186	30	(	(	PUNCT
ejpam-6147	186	31	7	7	NUM
ejpam-6147	186	32	)	)	PUNCT
ejpam-6147	186	33	however	however	ADV
ejpam-6147	186	34	,	,	PUNCT
ejpam-6147	186	35	ςn	ςn	PROPN
ejpam-6147	186	36	→	→	SYM
ejpam-6147	186	37	ς∗.	ς∗.	NUM
ejpam-6147	187	1	this	this	PRON
ejpam-6147	187	2	and	and	CCONJ
ejpam-6147	187	3	(	(	PUNCT
ejpam-6147	187	4	7	7	X
ejpam-6147	187	5	)	)	PUNCT
ejpam-6147	187	6	guarantees	guarantee	VERB
ejpam-6147	187	7	that	that	SCONJ
ejpam-6147	187	8	ςn	ςn	PROPN
ejpam-6147	187	9	→	→	SYM
ejpam-6147	187	10	ς∗	ς∗	PROPN
ejpam-6147	188	1	and	and	CCONJ
ejpam-6147	188	2	so	so	ADV
ejpam-6147	188	3	if	if	SCONJ
ejpam-6147	188	4	t	t	PROPN
ejpam-6147	188	5	goes	go	VERB
ejpam-6147	188	6	to	to	ADP
ejpam-6147	188	7	0	0	NUM
ejpam-6147	188	8	,	,	PUNCT
ejpam-6147	188	9	from	from	ADP
ejpam-6147	188	10	the	the	DET
ejpam-6147	188	11	right	right	ADJ
ejpam-6147	188	12	side	side	NOUN
ejpam-6147	188	13	then	then	ADV
ejpam-6147	188	14	{	{	PUNCT
ejpam-6147	188	15	ςt	ςt	PRON
ejpam-6147	188	16	}	}	PUNCT
ejpam-6147	188	17	become	become	VERB
ejpam-6147	188	18	relatively	relatively	ADV
ejpam-6147	188	19	compact	compact	ADJ
ejpam-6147	188	20	,	,	PUNCT
ejpam-6147	188	21	in	in	ADP
ejpam-6147	188	22	the	the	DET
ejpam-6147	188	23	norm	norm	NOUN
ejpam-6147	188	24	topology	topology	NOUN
ejpam-6147	188	25	.	.	PUNCT
ejpam-6147	189	1	taking	take	VERB
ejpam-6147	189	2	limit	limit	NOUN
ejpam-6147	190	1	n	n	PRON
ejpam-6147	190	2	goes	go	VERB
ejpam-6147	190	3	to	to	ADP
ejpam-6147	190	4	∞	∞	PROPN
ejpam-6147	190	5	in	in	ADP
ejpam-6147	190	6	(	(	PUNCT
ejpam-6147	190	7	6	6	NUM
ejpam-6147	190	8	)	)	PUNCT
ejpam-6147	190	9	,	,	PUNCT
ejpam-6147	190	10	we	we	PRON
ejpam-6147	190	11	have	have	VERB
ejpam-6147	190	12	∥ς∗	∥ς∗	PROPN
ejpam-6147	190	13	−υ∥2	−υ∥2	VERB
ejpam-6147	190	14	≤	≤	ADJ
ejpam-6147	190	15	⟨υ	⟨υ	NOUN
ejpam-6147	190	16	,	,	PUNCT
ejpam-6147	190	17	υ−	υ−	PROPN
ejpam-6147	190	18	ς∗⟩	ς∗⟩	NUM
ejpam-6147	190	19	∀υ	∀υ	NUM
ejpam-6147	190	20	∈	∈	PROPN
ejpam-6147	190	21	fe	fe	X
ejpam-6147	190	22	.	.	PUNCT
ejpam-6147	191	1	m.	m.	PROPN
ejpam-6147	191	2	sarwar	sarwar	PROPN
ejpam-6147	191	3	et	et	PROPN
ejpam-6147	191	4	al	al	PROPN
ejpam-6147	191	5	.	.	PUNCT
ejpam-6147	191	6	/	/	SYM
ejpam-6147	191	7	eur	eur	PROPN
ejpam-6147	191	8	.	.	PUNCT
ejpam-6147	192	1	j.	j.	PROPN
ejpam-6147	192	2	pure	pure	PROPN
ejpam-6147	192	3	appl	appl	PROPN
ejpam-6147	192	4	.	.	PROPN
ejpam-6147	192	5	math	math	PROPN
ejpam-6147	192	6	,	,	PUNCT
ejpam-6147	192	7	18	18	NUM
ejpam-6147	192	8	(	(	PUNCT
ejpam-6147	192	9	3	3	NUM
ejpam-6147	192	10	)	)	PUNCT
ejpam-6147	192	11	(	(	PUNCT
ejpam-6147	192	12	2025	2025	NUM
ejpam-6147	192	13	)	)	PUNCT
ejpam-6147	192	14	,	,	PUNCT
ejpam-6147	192	15	6147	6147	NUM
ejpam-6147	192	16	10	10	NUM
ejpam-6147	192	17	of	of	ADP
ejpam-6147	192	18	18	18	NUM
ejpam-6147	192	19	which	which	PRON
ejpam-6147	192	20	implies	imply	VERB
ejpam-6147	192	21	that	that	SCONJ
ejpam-6147	192	22	0	0	NUM
ejpam-6147	192	23	≤	≤	NUM
ejpam-6147	192	24	⟨υ	⟨υ	NOUN
ejpam-6147	192	25	,	,	PUNCT
ejpam-6147	192	26	υ−	υ−	PROPN
ejpam-6147	192	27	ς∗⟩	ς∗⟩	NUM
ejpam-6147	192	28	∀υ	∀υ	NUM
ejpam-6147	192	29	∈	∈	PROPN
ejpam-6147	192	30	fe	fe	NOUN
ejpam-6147	192	31	.	.	PUNCT
ejpam-6147	193	1	hence	hence	ADV
ejpam-6147	193	2	,	,	PUNCT
ejpam-6147	193	3	ς∗	ς∗	NOUN
ejpam-6147	193	4	=	=	SYM
ejpam-6147	193	5	pfe(0	pfe(0	NOUN
ejpam-6147	193	6	)	)	PUNCT
ejpam-6147	193	7	,	,	PUNCT
ejpam-6147	193	8	which	which	PRON
ejpam-6147	193	9	is	be	AUX
ejpam-6147	193	10	obviously	obviously	ADV
ejpam-6147	193	11	unique	unique	ADJ
ejpam-6147	193	12	and	and	CCONJ
ejpam-6147	193	13	this	this	PRON
ejpam-6147	193	14	shows	show	VERB
ejpam-6147	193	15	that	that	SCONJ
ejpam-6147	193	16	the	the	DET
ejpam-6147	193	17	net	net	NOUN
ejpam-6147	193	18	ςt	ςt	NOUN
ejpam-6147	193	19	converge	converge	VERB
ejpam-6147	193	20	strongly	strongly	ADV
ejpam-6147	193	21	to	to	ADP
ejpam-6147	193	22	ς∗.	ς∗.	PROPN
ejpam-6147	193	23	remark	remark	VERB
ejpam-6147	193	24	3	3	NUM
ejpam-6147	193	25	.	.	PUNCT
ejpam-6147	194	1	clearly	clearly	ADV
ejpam-6147	194	2	the	the	DET
ejpam-6147	194	3	net	net	NOUN
ejpam-6147	194	4	ςt	ςt	X
ejpam-6147	194	5	=	=	SYM
ejpam-6147	194	6	pz	pz	NOUN
ejpam-6147	194	7	[	[	PUNCT
ejpam-6147	194	8	twt	twt	NOUN
ejpam-6147	194	9	+	+	X
ejpam-6147	194	10	(	(	PUNCT
ejpam-6147	194	11	1−	1−	NUM
ejpam-6147	194	12	t	t	NOUN
ejpam-6147	194	13	)	)	PUNCT
ejpam-6147	194	14	1	1	NUM
ejpam-6147	194	15	γt	γt	NOUN
ejpam-6147	194	16	∫	∫	PROPN
ejpam-6147	194	17	γt	γt	NOUN
ejpam-6147	194	18	0	0	PROPN
ejpam-6147	194	19	e(s	e(s	PROPN
ejpam-6147	194	20	,	,	PUNCT
ejpam-6147	194	21	0)ςtds	0)ςtds	NUM
ejpam-6147	194	22	]	]	PUNCT
ejpam-6147	194	23	,	,	PUNCT
ejpam-6147	194	24	∀	∀	X
ejpam-6147	194	25	0	0	PUNCT
ejpam-6147	194	26	<	<	X
ejpam-6147	194	27	t	t	PROPN
ejpam-6147	194	28	1	1	NUM
ejpam-6147	194	29	,	,	PUNCT
ejpam-6147	194	30	has	have	VERB
ejpam-6147	194	31	only	only	ADV
ejpam-6147	194	32	weak	weak	ADJ
ejpam-6147	194	33	convergence	convergence	NOUN
ejpam-6147	194	34	.	.	PUNCT
ejpam-6147	195	1	but	but	CCONJ
ejpam-6147	195	2	,	,	PUNCT
ejpam-6147	195	3	the	the	DET
ejpam-6147	195	4	similar	similar	ADJ
ejpam-6147	195	5	net	net	NOUN
ejpam-6147	195	6	(	(	PUNCT
ejpam-6147	195	7	3	3	NUM
ejpam-6147	195	8	)	)	PUNCT
ejpam-6147	195	9	has	have	VERB
ejpam-6147	195	10	strong	strong	ADJ
ejpam-6147	195	11	convergence	convergence	NOUN
ejpam-6147	195	12	(	(	PUNCT
ejpam-6147	195	13	withλt	withλt	NOUN
ejpam-6147	195	14	→	→	SYM
ejpam-6147	195	15	1	1	NUM
ejpam-6147	195	16	)	)	PUNCT
ejpam-6147	195	17	.	.	PUNCT
ejpam-6147	196	1	now	now	ADV
ejpam-6147	196	2	we	we	PRON
ejpam-6147	196	3	define	define	VERB
ejpam-6147	196	4	a	a	DET
ejpam-6147	196	5	sequence	sequence	NOUN
ejpam-6147	196	6	ςn	ςn	NOUN
ejpam-6147	196	7	for	for	ADP
ejpam-6147	196	8	the	the	DET
ejpam-6147	196	9	non	non	ADJ
ejpam-6147	196	10	-	-	ADJ
ejpam-6147	196	11	expansive	expansive	ADJ
ejpam-6147	196	12	family	family	NOUN
ejpam-6147	196	13	e	e	NOUN
ejpam-6147	196	14	=	=	PUNCT
ejpam-6147	196	15	{	{	PUNCT
ejpam-6147	196	16	e(s	e(s	PROPN
ejpam-6147	196	17	,	,	PUNCT
ejpam-6147	196	18	0)}s≥0	0)}s≥0	X
ejpam-6147	196	19	:	:	PUNCT
ejpam-6147	196	20	z	z	X
ejpam-6147	196	21	→	→	SYM
ejpam-6147	196	22	z	z	NOUN
ejpam-6147	197	1	and	and	CCONJ
ejpam-6147	197	2	we	we	PRON
ejpam-6147	197	3	will	will	AUX
ejpam-6147	197	4	prove	prove	VERB
ejpam-6147	197	5	that	that	SCONJ
ejpam-6147	197	6	the	the	DET
ejpam-6147	197	7	sequence	sequence	NOUN
ejpam-6147	197	8	ςn	ςn	PRON
ejpam-6147	197	9	converge	converge	VERB
ejpam-6147	197	10	strongly	strongly	ADV
ejpam-6147	197	11	to	to	ADP
ejpam-6147	197	12	x	x	SYM
ejpam-6147	197	13	∈	∈	PROPN
ejpam-6147	197	14	fe	fe	X
ejpam-6147	197	15	theorem	theorem	NOUN
ejpam-6147	197	16	2	2	X
ejpam-6147	197	17	.	.	PUNCT
ejpam-6147	198	1	let	let	VERB
ejpam-6147	198	2	e	e	NOUN
ejpam-6147	198	3	=	=	PRON
ejpam-6147	198	4	{	{	PUNCT
ejpam-6147	198	5	e(s	e(s	PROPN
ejpam-6147	198	6	,	,	PUNCT
ejpam-6147	198	7	0)}s≥0	0)}s≥0	X
ejpam-6147	198	8	:	:	PUNCT
ejpam-6147	198	9	z	z	X
ejpam-6147	198	10	→	→	SYM
ejpam-6147	198	11	z	z	NOUN
ejpam-6147	198	12	is	be	AUX
ejpam-6147	198	13	non	non	ADJ
ejpam-6147	198	14	-	-	ADJ
ejpam-6147	198	15	expansive	expansive	ADJ
ejpam-6147	198	16	family	family	NOUN
ejpam-6147	198	17	with	with	ADP
ejpam-6147	198	18	conditions	condition	NOUN
ejpam-6147	198	19	∥	∥	NUM
ejpam-6147	198	20	℧	℧	NOUN
ejpam-6147	198	21	m	m	NOUN
ejpam-6147	198	22	−	−	NOUN
ejpam-6147	198	23	e	e	NOUN
ejpam-6147	198	24	(	(	PUNCT
ejpam-6147	198	25	(	(	PUNCT
ejpam-6147	198	26	t	t	PROPN
ejpam-6147	198	27	m)im	m)im	PROPN
ejpam-6147	198	28	,	,	PUNCT
ejpam-6147	198	29	0)	0)	NOUN
ejpam-6147	198	30	℧	℧	NOUN
ejpam-6147	198	31	m∥2	m∥2	PROPN
ejpam-6147	198	32	≤	≤	PROPN
ejpam-6147	199	1	i	i	PRON
ejpam-6147	199	2	m	m	VERB
ejpam-6147	199	3	m	m	VERB
ejpam-6147	199	4	diam(z	diam(z	ADJ
ejpam-6147	199	5	)	)	PUNCT
ejpam-6147	199	6	and	and	CCONJ
ejpam-6147	199	7	fe	fe	X
ejpam-6147	199	8	̸=	̸=	PROPN
ejpam-6147	199	9	∅.	∅.	ADV
ejpam-6147	199	10	consider	consider	VERB
ejpam-6147	199	11	{	{	PUNCT
ejpam-6147	199	12	ςn	ςn	AUX
ejpam-6147	199	13	}	}	PUNCT
ejpam-6147	199	14	be	be	AUX
ejpam-6147	199	15	the	the	DET
ejpam-6147	199	16	sequence	sequence	NOUN
ejpam-6147	199	17	ςn+1	ςn+1	NUM
ejpam-6147	199	18	=	=	SYM
ejpam-6147	199	19	(	(	PUNCT
ejpam-6147	199	20	1−	1−	NUM
ejpam-6147	199	21	µn)ςn	µn)ςn	PUNCT
ejpam-6147	200	1	+	+	X
ejpam-6147	200	2	µnpz	µnpz	ADV
ejpam-6147	200	3	[	[	PUNCT
ejpam-6147	200	4	ηn(λnςn	ηn(λnςn	NOUN
ejpam-6147	200	5	)	)	PUNCT
ejpam-6147	200	6	+	+	CCONJ
ejpam-6147	201	1	(	(	PUNCT
ejpam-6147	201	2	1−	1−	NUM
ejpam-6147	201	3	ηn	ηn	ADJ
ejpam-6147	201	4	)	)	PUNCT
ejpam-6147	201	5	1	1	NUM
ejpam-6147	201	6	γn	γn	ADP
ejpam-6147	201	7	∫	∫	PROPN
ejpam-6147	201	8	γn	γn	ADP
ejpam-6147	201	9	0	0	PUNCT
ejpam-6147	201	10	e(s	e(s	PROPN
ejpam-6147	201	11	,	,	PUNCT
ejpam-6147	201	12	0)ςnds	0)ςnds	NUM
ejpam-6147	201	13	]	]	PUNCT
ejpam-6147	201	14	,	,	PUNCT
ejpam-6147	201	15	∀n	∀n	NUM
ejpam-6147	201	16	≥	≥	NOUN
ejpam-6147	201	17	0	0	NUM
ejpam-6147	201	18	.	.	PUNCT
ejpam-6147	202	1	(	(	PUNCT
ejpam-6147	202	2	8)	8)	NUM
ejpam-6147	202	3	where	where	SCONJ
ejpam-6147	202	4	{	{	PUNCT
ejpam-6147	202	5	ηn	ηn	ADJ
ejpam-6147	202	6	}	}	PUNCT
ejpam-6147	202	7	,	,	PUNCT
ejpam-6147	202	8	{	{	PUNCT
ejpam-6147	202	9	µn	µn	NOUN
ejpam-6147	202	10	}	}	PUNCT
ejpam-6147	202	11	and	and	CCONJ
ejpam-6147	202	12	{	{	PUNCT
ejpam-6147	202	13	λn	λn	NOUN
ejpam-6147	202	14	}	}	PUNCT
ejpam-6147	202	15	are	be	AUX
ejpam-6147	202	16	sequences	sequence	NOUN
ejpam-6147	202	17	in	in	ADP
ejpam-6147	202	18	[	[	X
ejpam-6147	202	19	0	0	NUM
ejpam-6147	202	20	,	,	PUNCT
ejpam-6147	202	21	1	1	NUM
ejpam-6147	202	22	]	]	PUNCT
ejpam-6147	202	23	and	and	CCONJ
ejpam-6147	202	24	{	{	PUNCT
ejpam-6147	202	25	γn	γn	NOUN
ejpam-6147	202	26	}	}	PUNCT
ejpam-6147	202	27	is	be	AUX
ejpam-6147	202	28	a	a	DET
ejpam-6147	202	29	sequence	sequence	NOUN
ejpam-6147	202	30	in	in	ADP
ejpam-6147	202	31	(	(	PUNCT
ejpam-6147	202	32	0,+∞	0,+∞	NUM
ejpam-6147	202	33	)	)	PUNCT
ejpam-6147	202	34	,	,	PUNCT
ejpam-6147	202	35	with	with	ADP
ejpam-6147	202	36	the	the	DET
ejpam-6147	202	37	following	follow	VERB
ejpam-6147	202	38	conditions	condition	NOUN
ejpam-6147	202	39	:	:	PUNCT
ejpam-6147	202	40	•	•	NUM
ejpam-6147	202	41	(	(	PUNCT
ejpam-6147	202	42	a	a	NOUN
ejpam-6147	202	43	)	)	PUNCT
ejpam-6147	202	44	limn→+∞	limn→+∞	VERB
ejpam-6147	202	45	ηn	ηn	PROPN
ejpam-6147	202	46	=	=	PUNCT
ejpam-6147	202	47	0,σ+∞	0,σ+∞	NUM
ejpam-6147	202	48	n=0ηn	n=0ηn	X
ejpam-6147	202	49	=	=	PUNCT
ejpam-6147	203	1	+	+	ADV
ejpam-6147	203	2	∞and	∞and	ADJ
ejpam-6147	203	3	limn→+∞	limn→+∞	ADP
ejpam-6147	203	4	λn	λn	NOUN
ejpam-6147	203	5	=	=	SYM
ejpam-6147	203	6	1	1	NUM
ejpam-6147	203	7	;	;	PUNCT
ejpam-6147	203	8	•	•	PRON
ejpam-6147	203	9	(	(	PUNCT
ejpam-6147	203	10	b	b	NOUN
ejpam-6147	203	11	)	)	PUNCT
ejpam-6147	203	12	0	0	PUNCT
ejpam-6147	204	1	<	<	X
ejpam-6147	204	2	lim	lim	PROPN
ejpam-6147	204	3	infn→+∞	infn→+∞	VERB
ejpam-6147	204	4	µn	µn	PROPN
ejpam-6147	204	5	≤	≤	NUM
ejpam-6147	204	6	lim	lim	PROPN
ejpam-6147	204	7	supn→+∞	supn→+∞	PROPN
ejpam-6147	204	8	µn	µn	PROPN
ejpam-6147	204	9	<	<	X
ejpam-6147	204	10	1	1	NUM
ejpam-6147	204	11	;	;	PUNCT
ejpam-6147	204	12	•	•	NUM
ejpam-6147	204	13	(	(	PUNCT
ejpam-6147	204	14	c	c	X
ejpam-6147	204	15	)	)	PUNCT
ejpam-6147	204	16	limn→+∞	limn→+∞	VERB
ejpam-6147	204	17	γn	γn	NOUN
ejpam-6147	204	18	=	=	PUNCT
ejpam-6147	205	1	+	+	NOUN
ejpam-6147	205	2	∞	∞	NUM
ejpam-6147	205	3	and	and	CCONJ
ejpam-6147	205	4	limn→+∞	limn→+∞	ADP
ejpam-6147	205	5	γn−1	γn−1	PROPN
ejpam-6147	205	6	γn	γn	NOUN
ejpam-6147	206	1	=	=	NOUN
ejpam-6147	206	2	1	1	X
ejpam-6147	206	3	.	.	PUNCT
ejpam-6147	207	1	then	then	ADV
ejpam-6147	207	2	ςn	ςn	PROPN
ejpam-6147	207	3	→	→	PUNCT
ejpam-6147	207	4	ς∗	ς∗	PROPN
ejpam-6147	207	5	∈	∈	PROPN
ejpam-6147	207	6	fe	fe	NOUN
ejpam-6147	207	7	,	,	PUNCT
ejpam-6147	207	8	in	in	ADP
ejpam-6147	207	9	a	a	DET
ejpam-6147	207	10	strong	strong	ADJ
ejpam-6147	207	11	sense	sense	NOUN
ejpam-6147	207	12	.	.	PUNCT
ejpam-6147	208	1	proof	proof	NOUN
ejpam-6147	208	2	.	.	PUNCT
ejpam-6147	209	1	let	let	VERB
ejpam-6147	209	2	p	p	PROPN
ejpam-6147	209	3	∈	∈	PROPN
ejpam-6147	209	4	fe	fe	X
ejpam-6147	209	5	,	,	PUNCT
ejpam-6147	209	6	then	then	ADV
ejpam-6147	209	7	we	we	PRON
ejpam-6147	209	8	have	have	VERB
ejpam-6147	209	9	∥ςn+1	∥ςn+1	NOUN
ejpam-6147	210	1	−	−	NOUN
ejpam-6147	210	2	p∥	p∥	NOUN
ejpam-6147	210	3	=	=	SYM
ejpam-6147	210	4	∥∥∥∥(1−	∥∥∥∥(1−	PROPN
ejpam-6147	210	5	µn)ςn	µn)ςn	PUNCT
ejpam-6147	210	6	+	+	NUM
ejpam-6147	210	7	µnpz	µnpz	ADV
ejpam-6147	210	8	[	[	PUNCT
ejpam-6147	210	9	ηn(λnςn	ηn(λnςn	NOUN
ejpam-6147	210	10	)	)	PUNCT
ejpam-6147	210	11	+	+	CCONJ
ejpam-6147	211	1	(	(	PUNCT
ejpam-6147	211	2	1−	1−	NUM
ejpam-6147	211	3	ηn	ηn	ADJ
ejpam-6147	211	4	)	)	PUNCT
ejpam-6147	211	5	1	1	NUM
ejpam-6147	211	6	γn	γn	ADP
ejpam-6147	211	7	∫	∫	PROPN
ejpam-6147	211	8	γn	γn	ADP
ejpam-6147	211	9	0	0	PUNCT
ejpam-6147	211	10	e(s	e(s	PROPN
ejpam-6147	211	11	,	,	PUNCT
ejpam-6147	211	12	0)ςnds	0)ςnds	X
ejpam-6147	211	13	]	]	PUNCT
ejpam-6147	211	14	−	−	PROPN
ejpam-6147	212	1	p	p	NOUN
ejpam-6147	212	2	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6147	212	3	=	=	SYM
ejpam-6147	212	4	∥∥∥∥(1−	∥∥∥∥(1−	PROPN
ejpam-6147	212	5	µn)ςn	µn)ςn	SYM
ejpam-6147	212	6	−	−	PROPN
ejpam-6147	212	7	p+	p+	ADV
ejpam-6147	212	8	µnp+	µnp+	ADJ
ejpam-6147	212	9	µn	µn	PROPN
ejpam-6147	212	10	(	(	PUNCT
ejpam-6147	212	11	pz	pz	X
ejpam-6147	212	12	[	[	PUNCT
ejpam-6147	212	13	ηn(λnςn	ηn(λnςn	PROPN
ejpam-6147	212	14	)	)	PUNCT
ejpam-6147	212	15	+	+	CCONJ
ejpam-6147	212	16	(	(	PUNCT
ejpam-6147	212	17	1−	1−	NUM
ejpam-6147	212	18	ηn	ηn	ADJ
ejpam-6147	212	19	)	)	PUNCT
ejpam-6147	212	20	1	1	NUM
ejpam-6147	212	21	γn	γn	ADP
ejpam-6147	212	22	∫	∫	PROPN
ejpam-6147	212	23	γn	γn	ADP
ejpam-6147	212	24	0	0	PUNCT
ejpam-6147	212	25	e(s	e(s	PROPN
ejpam-6147	212	26	,	,	PUNCT
ejpam-6147	212	27	0)ςnds	0)ςnds	X
ejpam-6147	212	28	]	]	PUNCT
ejpam-6147	212	29	−	−	PROPN
ejpam-6147	212	30	p	p	NOUN
ejpam-6147	212	31	)	)	PUNCT
ejpam-6147	212	32	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6147	212	33	≤	≤	NUM
ejpam-6147	212	34	(	(	PUNCT
ejpam-6147	212	35	1−	1−	NUM
ejpam-6147	212	36	µn)∥ςn	µn)∥ςn	NOUN
ejpam-6147	212	37	−	−	NOUN
ejpam-6147	213	1	p∥+	p∥+	NOUN
ejpam-6147	213	2	µn	µn	INTJ
ejpam-6147	213	3	∥∥∥∥pz	∥∥∥∥pz	PROPN
ejpam-6147	213	4	[	[	PUNCT
ejpam-6147	213	5	ηn(λnςn	ηn(λnςn	PROPN
ejpam-6147	213	6	)	)	PUNCT
ejpam-6147	213	7	+	+	CCONJ
ejpam-6147	213	8	(	(	PUNCT
ejpam-6147	213	9	1−	1−	NUM
ejpam-6147	213	10	ηn	ηn	ADJ
ejpam-6147	213	11	)	)	PUNCT
ejpam-6147	213	12	1	1	NUM
ejpam-6147	213	13	γn	γn	ADP
ejpam-6147	213	14	∫	∫	PROPN
ejpam-6147	214	1	γn	γn	ADP
ejpam-6147	214	2	0	0	PUNCT
ejpam-6147	214	3	e(s	e(s	ADJ
ejpam-6147	214	4	,	,	PUNCT
ejpam-6147	214	5	0)ςnds−	0)ςnds−	NOUN
ejpam-6147	214	6	pz(p	pz(p	PUNCT
ejpam-6147	214	7	)	)	PUNCT
ejpam-6147	214	8	]	]	PUNCT
ejpam-6147	214	9	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	214	10	=	=	SYM
ejpam-6147	214	11	(	(	PUNCT
ejpam-6147	214	12	1−	1−	NUM
ejpam-6147	214	13	µn)∥ςn	µn)∥ςn	NOUN
ejpam-6147	214	14	−	−	NOUN
ejpam-6147	214	15	p∥+	p∥+	NOUN
ejpam-6147	214	16	µn	µn	NOUN
ejpam-6147	214	17	∥∥∥∥ηn(λnςn	∥∥∥∥ηn(λnςn	NOUN
ejpam-6147	214	18	)	)	PUNCT
ejpam-6147	215	1	+	+	CCONJ
ejpam-6147	215	2	(	(	PUNCT
ejpam-6147	215	3	1−	1−	NUM
ejpam-6147	215	4	ηn	ηn	ADJ
ejpam-6147	215	5	)	)	PUNCT
ejpam-6147	215	6	1	1	NUM
ejpam-6147	215	7	γn	γn	ADP
ejpam-6147	215	8	∫	∫	PROPN
ejpam-6147	215	9	γn	γn	ADP
ejpam-6147	215	10	0	0	PUNCT
ejpam-6147	215	11	e(s	e(s	ADJ
ejpam-6147	215	12	,	,	PUNCT
ejpam-6147	215	13	0)ςnds−	0)ςnds−	NOUN
ejpam-6147	215	14	p	p	X
ejpam-6147	215	15	∥∥∥∥	∥∥∥∥	PROPN
ejpam-6147	215	16	=	=	SYM
ejpam-6147	215	17	(	(	PUNCT
ejpam-6147	215	18	1−	1−	NUM
ejpam-6147	215	19	µn)∥ςn	µn)∥ςn	NOUN
ejpam-6147	215	20	−	−	NOUN
ejpam-6147	215	21	p∥+	p∥+	NOUN
ejpam-6147	215	22	µn	µn	NOUN
ejpam-6147	215	23	∥∥∥∥ηnλn(ςn	∥∥∥∥ηnλn(ςn	PROPN
ejpam-6147	215	24	−	−	PROPN
ejpam-6147	215	25	p)−	p)−	NOUN
ejpam-6147	215	26	ηn(1−	ηn(1−	PROPN
ejpam-6147	215	27	λn)p	λn)p	PROPN
ejpam-6147	215	28	m.	m.	NOUN
ejpam-6147	215	29	sarwar	sarwar	PROPN
ejpam-6147	215	30	et	et	PROPN
ejpam-6147	215	31	al	al	PROPN
ejpam-6147	215	32	.	.	PUNCT
ejpam-6147	215	33	/	/	SYM
ejpam-6147	215	34	eur	eur	PROPN
ejpam-6147	215	35	.	.	PUNCT
ejpam-6147	216	1	j.	j.	PROPN
ejpam-6147	216	2	pure	pure	PROPN
ejpam-6147	216	3	appl	appl	PROPN
ejpam-6147	216	4	.	.	PROPN
ejpam-6147	216	5	math	math	PROPN
ejpam-6147	216	6	,	,	PUNCT
ejpam-6147	216	7	18	18	NUM
ejpam-6147	216	8	(	(	PUNCT
ejpam-6147	216	9	3	3	NUM
ejpam-6147	216	10	)	)	PUNCT
ejpam-6147	216	11	(	(	PUNCT
ejpam-6147	216	12	2025	2025	NUM
ejpam-6147	216	13	)	)	PUNCT
ejpam-6147	216	14	,	,	PUNCT
ejpam-6147	216	15	6147	6147	NUM
ejpam-6147	216	16	11	11	NUM
ejpam-6147	216	17	of	of	ADP
ejpam-6147	216	18	18	18	NUM
ejpam-6147	216	19	+	+	ADJ
ejpam-6147	216	20	(	(	PUNCT
ejpam-6147	216	21	1−	1−	NUM
ejpam-6147	216	22	ηn	ηn	ADJ
ejpam-6147	216	23	)	)	PUNCT
ejpam-6147	216	24	(	(	PUNCT
ejpam-6147	216	25	1	1	NUM
ejpam-6147	216	26	γn	γn	ADP
ejpam-6147	216	27	∫	∫	PROPN
ejpam-6147	216	28	γn	γn	ADP
ejpam-6147	216	29	0	0	PUNCT
ejpam-6147	216	30	e(s	e(s	ADJ
ejpam-6147	216	31	,	,	PUNCT
ejpam-6147	216	32	0)ςnds−	0)ςnds−	NUM
ejpam-6147	216	33	1	1	NUM
ejpam-6147	216	34	γn	γn	ADP
ejpam-6147	216	35	∫	∫	PROPN
ejpam-6147	216	36	γn	γn	ADP
ejpam-6147	216	37	0	0	NUM
ejpam-6147	216	38	pds	pds	NOUN
ejpam-6147	216	39	)	)	PUNCT
ejpam-6147	216	40	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	216	41	≤	≤	NUM
ejpam-6147	216	42	(	(	PUNCT
ejpam-6147	216	43	1−	1−	NUM
ejpam-6147	216	44	µn)∥ςn	µn)∥ςn	NOUN
ejpam-6147	216	45	−	−	NOUN
ejpam-6147	216	46	p∥+	p∥+	NOUN
ejpam-6147	216	47	µn	µn	NOUN
ejpam-6147	216	48	(	(	PUNCT
ejpam-6147	216	49	ηnλn∥ςn	ηnλn∥ςn	NOUN
ejpam-6147	216	50	−	−	PROPN
ejpam-6147	216	51	p∥+	p∥+	NOUN
ejpam-6147	216	52	ηn(1−	ηn(1−	PROPN
ejpam-6147	217	1	λn)∥p∥	λn)∥p∥	ADJ
ejpam-6147	217	2	+	+	PROPN
ejpam-6147	217	3	(	(	PUNCT
ejpam-6147	217	4	1−	1−	NUM
ejpam-6147	217	5	ηn	ηn	ADJ
ejpam-6147	217	6	)	)	PUNCT
ejpam-6147	217	7	1	1	NUM
ejpam-6147	217	8	γn	γn	ADP
ejpam-6147	217	9	∫	∫	PROPN
ejpam-6147	217	10	γn	γn	ADP
ejpam-6147	217	11	0	0	NUM
ejpam-6147	217	12	∥ςn	∥ςn	NOUN
ejpam-6147	217	13	−	−	NOUN
ejpam-6147	217	14	p∥ds	p∥ds	PROPN
ejpam-6147	217	15	)	)	PUNCT
ejpam-6147	217	16	=	=	PUNCT
ejpam-6147	218	1	[	[	X
ejpam-6147	218	2	1−	1−	NUM
ejpam-6147	218	3	(	(	PUNCT
ejpam-6147	218	4	1−	1−	NUM
ejpam-6147	218	5	λn)ηnµn]∥ςn	λn)ηnµn]∥ςn	NOUN
ejpam-6147	218	6	−	−	NOUN
ejpam-6147	218	7	p∥+	p∥+	NOUN
ejpam-6147	218	8	(	(	PUNCT
ejpam-6147	218	9	1−	1−	NUM
ejpam-6147	218	10	λn)ηnµn∥p∥.	λn)ηnµn∥p∥.	NOUN
ejpam-6147	218	11	from	from	ADP
ejpam-6147	218	12	the	the	DET
ejpam-6147	218	13	above	above	ADJ
ejpam-6147	218	14	∥ςn+1	∥ςn+1	NOUN
ejpam-6147	218	15	−	−	PROPN
ejpam-6147	218	16	p∥	p∥	NOUN
ejpam-6147	218	17	≤	≤	NOUN
ejpam-6147	219	1	[	[	X
ejpam-6147	219	2	1−	1−	NUM
ejpam-6147	219	3	(	(	PUNCT
ejpam-6147	219	4	1−	1−	NUM
ejpam-6147	219	5	λn)ηnµn]∥ςn	λn)ηnµn]∥ςn	NOUN
ejpam-6147	219	6	−	−	NOUN
ejpam-6147	219	7	p∥+	p∥+	NOUN
ejpam-6147	219	8	(	(	PUNCT
ejpam-6147	219	9	1−	1−	NUM
ejpam-6147	219	10	λn)ηnµn∥p∥.	λn)ηnµn∥p∥.	NOUN
ejpam-6147	219	11	≤	≤	PUNCT
ejpam-6147	220	1	[	[	X
ejpam-6147	220	2	1−	1−	NUM
ejpam-6147	220	3	ηnµn	ηnµn	ADJ
ejpam-6147	220	4	+	+	CCONJ
ejpam-6147	220	5	ηnµnλn	ηnµnλn	NOUN
ejpam-6147	220	6	+	+	CCONJ
ejpam-6147	220	7	ηnµn	ηnµn	ADJ
ejpam-6147	220	8	−	−	NUM
ejpam-6147	220	9	ηnµnλn]max{∥ςn	ηnµnλn]max{∥ςn	NOUN
ejpam-6147	220	10	−	−	PROPN
ejpam-6147	220	11	p∥	p∥	PROPN
ejpam-6147	220	12	,	,	PUNCT
ejpam-6147	220	13	∥p∥	∥p∥	NUM
ejpam-6147	220	14	}	}	PUNCT
ejpam-6147	220	15	.	.	PUNCT
ejpam-6147	221	1	which	which	PRON
ejpam-6147	221	2	imply	imply	VERB
ejpam-6147	221	3	that	that	DET
ejpam-6147	221	4	∥ςn+1	∥ςn+1	VERB
ejpam-6147	222	1	−	−	NOUN
ejpam-6147	222	2	p∥	p∥	NOUN
ejpam-6147	222	3	≤	≤	NUM
ejpam-6147	222	4	max{∥ςn	max{∥ςn	NOUN
ejpam-6147	222	5	−	−	PROPN
ejpam-6147	222	6	p∥	p∥	NOUN
ejpam-6147	222	7	,	,	PUNCT
ejpam-6147	222	8	∥p∥	∥p∥	NUM
ejpam-6147	222	9	}	}	PUNCT
ejpam-6147	222	10	.	.	PUNCT
ejpam-6147	223	1	by	by	ADP
ejpam-6147	223	2	induction	induction	NOUN
ejpam-6147	223	3	,	,	PUNCT
ejpam-6147	223	4	we	we	PRON
ejpam-6147	223	5	have	have	VERB
ejpam-6147	223	6	,	,	PUNCT
ejpam-6147	223	7	∥ςn	∥ςn	AUX
ejpam-6147	223	8	−	−	NOUN
ejpam-6147	223	9	p∥	p∥	NOUN
ejpam-6147	223	10	≤	≤	NOUN
ejpam-6147	223	11	max{∥ς0	max{∥ς0	PROPN
ejpam-6147	223	12	−	−	PROPN
ejpam-6147	223	13	p∥	p∥	NOUN
ejpam-6147	223	14	,	,	PUNCT
ejpam-6147	223	15	∥p∥	∥p∥	NUM
ejpam-6147	223	16	}	}	PUNCT
ejpam-6147	223	17	.	.	PUNCT
ejpam-6147	224	1	set	set	VERB
ejpam-6147	224	2	℧	℧	PROPN
ejpam-6147	224	3	n	n	NOUN
ejpam-6147	224	4	=	=	SYM
ejpam-6147	224	5	pz	pz	PROPN
ejpam-6147	225	1	[	[	X
ejpam-6147	225	2	ηn(λnςn	ηn(λnςn	PROPN
ejpam-6147	225	3	)	)	PUNCT
ejpam-6147	225	4	+	+	CCONJ
ejpam-6147	225	5	(	(	PUNCT
ejpam-6147	225	6	1	1	NUM
ejpam-6147	225	7	−	−	NOUN
ejpam-6147	225	8	ηn)vn	ηn)vn	ADP
ejpam-6147	225	9	]	]	PUNCT
ejpam-6147	225	10	for	for	ADP
ejpam-6147	225	11	all	all	DET
ejpam-6147	225	12	n	n	PRON
ejpam-6147	225	13	≥	≥	NOUN
ejpam-6147	225	14	0	0	NUM
ejpam-6147	225	15	,	,	PUNCT
ejpam-6147	225	16	where	where	SCONJ
ejpam-6147	225	17	vn	vn	PROPN
ejpam-6147	225	18	=	=	SYM
ejpam-6147	225	19	1	1	NUM
ejpam-6147	225	20	γn	γn	ADP
ejpam-6147	225	21	∫	∫	PROPN
ejpam-6147	225	22	γn	γn	ADP
ejpam-6147	225	23	0	0	NUM
ejpam-6147	225	24	e(s	e(s	PROPN
ejpam-6147	225	25	,	,	PUNCT
ejpam-6147	225	26	0)ςnds	0)ςnds	NUM
ejpam-6147	225	27	.	.	PUNCT
ejpam-6147	226	1	so	so	ADV
ejpam-6147	226	2	we	we	PRON
ejpam-6147	226	3	have	have	VERB
ejpam-6147	226	4	∥	∥	NUM
ejpam-6147	226	5	℧	℧	NOUN
ejpam-6147	226	6	n	n	NOUN
ejpam-6147	226	7	−	−	PROPN
ejpam-6147	226	8	℧	℧	NOUN
ejpam-6147	226	9	n−1∥	n−1∥	NOUN
ejpam-6147	226	10	≤	≤	NUM
ejpam-6147	226	11	∥ηn(λnςn	∥ηn(λnςn	PUNCT
ejpam-6147	226	12	)	)	PUNCT
ejpam-6147	227	1	+	+	CCONJ
ejpam-6147	227	2	(	(	PUNCT
ejpam-6147	227	3	1−	1−	NUM
ejpam-6147	227	4	ηn)vn	ηn)vn	X
ejpam-6147	227	5	−	−	PROPN
ejpam-6147	227	6	µn−1(αn−1ςn−1)−	µn−1(αn−1ςn−1)−	PROPN
ejpam-6147	227	7	(	(	PUNCT
ejpam-6147	227	8	1−	1−	NUM
ejpam-6147	227	9	µn−1)vn−1∥	µn−1)vn−1∥	PROPN
ejpam-6147	227	10	=	=	SYM
ejpam-6147	227	11	∥ηnλn(ςn	∥ηnλn(ςn	PROPN
ejpam-6147	227	12	−	−	PROPN
ejpam-6147	227	13	ςn−1	ςn−1	NOUN
ejpam-6147	227	14	)	)	PUNCT
ejpam-6147	228	1	+	+	CCONJ
ejpam-6147	228	2	(	(	PUNCT
ejpam-6147	228	3	ηnλn	ηnλn	NOUN
ejpam-6147	228	4	−	−	NOUN
ejpam-6147	228	5	µn−1αn−1)ςn−1	µn−1αn−1)ςn−1	PROPN
ejpam-6147	228	6	+	+	PROPN
ejpam-6147	228	7	(	(	PUNCT
ejpam-6147	228	8	ηn−1	ηn−1	ADJ
ejpam-6147	228	9	−	−	PROPN
ejpam-6147	228	10	ηn)vn−1	ηn)vn−1	ADJ
ejpam-6147	228	11	+	+	CCONJ
ejpam-6147	228	12	(	(	PUNCT
ejpam-6147	228	13	1−	1−	NUM
ejpam-6147	228	14	ηn)(vn	ηn)(vn	PRON
ejpam-6147	228	15	−	−	NOUN
ejpam-6147	228	16	vn−1)∥	vn−1)∥	PROPN
ejpam-6147	228	17	=	=	PUNCT
ejpam-6147	228	18	ηnλn∥ςn	ηnλn∥ςn	NOUN
ejpam-6147	228	19	−	−	NOUN
ejpam-6147	229	1	℧	℧	NOUN
ejpam-6147	229	2	n−1∥+	n−1∥+	NOUN
ejpam-6147	229	3	|ηnλn	|ηnλn	VERB
ejpam-6147	229	4	−	−	PROPN
ejpam-6147	229	5	ηn−1αn−1|∥ςn−1∥+	ηn−1αn−1|∥ςn−1∥+	NOUN
ejpam-6147	229	6	|ηn−1	|ηn−1	ADP
ejpam-6147	229	7	−	−	NOUN
ejpam-6147	229	8	ηn|∥vn−1∥	ηn|∥vn−1∥	NOUN
ejpam-6147	229	9	+	+	NOUN
ejpam-6147	229	10	(	(	PUNCT
ejpam-6147	229	11	1−	1−	NUM
ejpam-6147	229	12	ηn)∥vn	ηn)∥vn	NUM
ejpam-6147	229	13	−	−	PROPN
ejpam-6147	229	14	vn−1∥.	vn−1∥.	PROPN
ejpam-6147	229	15	and	and	CCONJ
ejpam-6147	229	16	∥vn	∥vn	NOUN
ejpam-6147	229	17	−	−	NOUN
ejpam-6147	229	18	vn−1∥	vn−1∥	NOUN
ejpam-6147	229	19	=	=	PUNCT
ejpam-6147	229	20	∥∥	∥∥	X
ejpam-6147	229	21	1	1	NUM
ejpam-6147	229	22	γn	γn	ADP
ejpam-6147	229	23	∫	∫	PROPN
ejpam-6147	229	24	γn	γn	ADP
ejpam-6147	229	25	0	0	NUM
ejpam-6147	230	1	[	[	X
ejpam-6147	230	2	e(s	e(s	X
ejpam-6147	230	3	,	,	PUNCT
ejpam-6147	230	4	0)ςn	0)ςn	PROPN
ejpam-6147	230	5	−	−	PROPN
ejpam-6147	231	1	e(s	e(s	PROPN
ejpam-6147	231	2	,	,	PUNCT
ejpam-6147	231	3	0)ςn−1]ds	0)ςn−1]ds	PUNCT
ejpam-6147	232	1	+	+	CCONJ
ejpam-6147	232	2	(	(	PUNCT
ejpam-6147	232	3	1	1	NUM
ejpam-6147	232	4	γn	γn	ADP
ejpam-6147	232	5	−	−	PROPN
ejpam-6147	232	6	1	1	NUM
ejpam-6147	232	7	γn−1	γn−1	PROPN
ejpam-6147	232	8	)	)	PUNCT
ejpam-6147	232	9	∫	∫	PROPN
ejpam-6147	233	1	γn−1	γn−1	PROPN
ejpam-6147	233	2	0	0	PUNCT
ejpam-6147	234	1	[	[	X
ejpam-6147	234	2	e(s	e(s	X
ejpam-6147	234	3	,	,	PUNCT
ejpam-6147	234	4	0)ςn−1	0)ςn−1	PROPN
ejpam-6147	234	5	−	−	PROPN
ejpam-6147	234	6	e(s	e(s	PROPN
ejpam-6147	234	7	,	,	PUNCT
ejpam-6147	234	8	0)p]ds	0)p]ds	PUNCT
ejpam-6147	235	1	−	−	PROPN
ejpam-6147	235	2	1	1	NUM
ejpam-6147	235	3	γn−1	γn−1	PROPN
ejpam-6147	235	4	∫	∫	PROPN
ejpam-6147	235	5	γn	γn	ADV
ejpam-6147	235	6	0	0	NUM
ejpam-6147	236	1	[	[	X
ejpam-6147	236	2	e(s	e(s	X
ejpam-6147	236	3	,	,	PUNCT
ejpam-6147	236	4	0)ςn−1	0)ςn−1	PROPN
ejpam-6147	236	5	−	−	PROPN
ejpam-6147	236	6	e(s	e(s	PROPN
ejpam-6147	236	7	,	,	PUNCT
ejpam-6147	236	8	0)p]ds	0)p]ds	NUM
ejpam-6147	237	1	∥∥	∥∥	X
ejpam-6147	237	2	≤	≤	ADV
ejpam-6147	237	3	1	1	NUM
ejpam-6147	237	4	γn	γn	ADP
ejpam-6147	237	5	∫	∫	PROPN
ejpam-6147	237	6	γn	γn	ADP
ejpam-6147	237	7	0	0	NUM
ejpam-6147	237	8	∥ςn	∥ςn	NOUN
ejpam-6147	237	9	−	−	NOUN
ejpam-6147	237	10	ςn−1∥ds+	ςn−1∥ds+	NUM
ejpam-6147	237	11	(	(	PUNCT
ejpam-6147	237	12	γn−1	γn−1	PROPN
ejpam-6147	237	13	)	)	PUNCT
ejpam-6147	237	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6147	237	15	1γn	1γn	ADJ
ejpam-6147	237	16	−	−	PROPN
ejpam-6147	237	17	1	1	NUM
ejpam-6147	237	18	γn−1	γn−1	PROPN
ejpam-6147	237	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6147	237	20	1	1	NUM
ejpam-6147	237	21	γn−1	γn−1	PROPN
ejpam-6147	237	22	∫	∫	PROPN
ejpam-6147	238	1	γn−1	γn−1	PROPN
ejpam-6147	238	2	0	0	NUM
ejpam-6147	239	1	∥ςn−1	∥ςn−1	ADJ
ejpam-6147	239	2	−	−	PUNCT
ejpam-6147	240	1	p∥ds	p∥ds	PROPN
ejpam-6147	240	2	+	+	CCONJ
ejpam-6147	240	3	1	1	NUM
ejpam-6147	240	4	γn−1	γn−1	PROPN
ejpam-6147	240	5	∫	∫	PROPN
ejpam-6147	240	6	γn	γn	ADP
ejpam-6147	240	7	0	0	NUM
ejpam-6147	240	8	∥ςn−1	∥ςn−1	PROPN
ejpam-6147	240	9	−	−	PROPN
ejpam-6147	240	10	p∥ds	p∥ds	PROPN
ejpam-6147	240	11	≤	≤	NUM
ejpam-6147	240	12	∥ςn	∥ςn	PROPN
ejpam-6147	240	13	−	−	NOUN
ejpam-6147	240	14	ςn−1∥+	ςn−1∥+	NOUN
ejpam-6147	240	15	2	2	NUM
ejpam-6147	240	16	|γn	|γn	NUM
ejpam-6147	240	17	−	−	NOUN
ejpam-6147	240	18	γn−1|	γn−1|	PUNCT
ejpam-6147	240	19	γn	γn	NOUN
ejpam-6147	240	20	∥ςn−1	∥ςn−1	PROPN
ejpam-6147	240	21	−	−	PROPN
ejpam-6147	240	22	p∥.	p∥.	PROPN
ejpam-6147	240	23	therefore	therefore	ADV
ejpam-6147	240	24	,	,	PUNCT
ejpam-6147	240	25	we	we	PRON
ejpam-6147	240	26	have	have	VERB
ejpam-6147	240	27	∥	∥	NUM
ejpam-6147	240	28	℧	℧	NOUN
ejpam-6147	240	29	n	n	NOUN
ejpam-6147	240	30	−	−	ADP
ejpam-6147	240	31	℧	℧	NOUN
ejpam-6147	240	32	n−1∥	n−1∥	NOUN
ejpam-6147	240	33	≤	≤	ADJ
ejpam-6147	240	34	ηnλn∥ςn	ηnλn∥ςn	PROPN
ejpam-6147	240	35	−	−	PROPN
ejpam-6147	240	36	ςn−1∥+	ςn−1∥+	NOUN
ejpam-6147	240	37	|ηnλn	|ηnλn	NOUN
ejpam-6147	240	38	−	−	NOUN
ejpam-6147	240	39	ηn−1αn−1|∥ςn−1∥+	ηn−1αn−1|∥ςn−1∥+	NOUN
ejpam-6147	240	40	|ηn−1	|ηn−1	ADP
ejpam-6147	240	41	−	−	PROPN
ejpam-6147	240	42	ηn|∥vn−1∥	ηn|∥vn−1∥	NOUN
ejpam-6147	240	43	m.	m.	NOUN
ejpam-6147	240	44	sarwar	sarwar	PROPN
ejpam-6147	240	45	et	et	PROPN
ejpam-6147	241	1	al	al	PROPN
ejpam-6147	241	2	.	.	PUNCT
ejpam-6147	241	3	/	/	SYM
ejpam-6147	241	4	eur	eur	PROPN
ejpam-6147	241	5	.	.	PUNCT
ejpam-6147	242	1	j.	j.	PROPN
ejpam-6147	242	2	pure	pure	PROPN
ejpam-6147	242	3	appl	appl	PROPN
ejpam-6147	242	4	.	.	PROPN
ejpam-6147	242	5	math	math	PROPN
ejpam-6147	242	6	,	,	PUNCT
ejpam-6147	242	7	18	18	NUM
ejpam-6147	242	8	(	(	PUNCT
ejpam-6147	242	9	3	3	NUM
ejpam-6147	242	10	)	)	PUNCT
ejpam-6147	242	11	(	(	PUNCT
ejpam-6147	242	12	2025	2025	NUM
ejpam-6147	242	13	)	)	PUNCT
ejpam-6147	242	14	,	,	PUNCT
ejpam-6147	242	15	6147	6147	NUM
ejpam-6147	242	16	12	12	NUM
ejpam-6147	242	17	of	of	ADP
ejpam-6147	242	18	18	18	NUM
ejpam-6147	242	19	+	+	ADJ
ejpam-6147	242	20	(	(	PUNCT
ejpam-6147	242	21	1−	1−	NUM
ejpam-6147	242	22	ηn	ηn	ADJ
ejpam-6147	242	23	)	)	PUNCT
ejpam-6147	242	24	(	(	PUNCT
ejpam-6147	242	25	∥ςn	∥ςn	NOUN
ejpam-6147	242	26	−	−	NOUN
ejpam-6147	242	27	ςn−1∥+	ςn−1∥+	NOUN
ejpam-6147	242	28	2	2	NUM
ejpam-6147	242	29	|γn	|γn	NUM
ejpam-6147	242	30	−	−	NOUN
ejpam-6147	242	31	γn−1|	γn−1|	PUNCT
ejpam-6147	242	32	γn	γn	NOUN
ejpam-6147	242	33	∥ςn−1	∥ςn−1	ADJ
ejpam-6147	242	34	−	−	NOUN
ejpam-6147	242	35	p∥	p∥	NOUN
ejpam-6147	242	36	)	)	PUNCT
ejpam-6147	242	37	≤	≤	NOUN
ejpam-6147	243	1	[	[	X
ejpam-6147	243	2	1−	1−	NUM
ejpam-6147	243	3	(	(	PUNCT
ejpam-6147	243	4	1−	1−	NUM
ejpam-6147	243	5	λn)ηn]∥ςn	λn)ηn]∥ςn	NOUN
ejpam-6147	243	6	−	−	NOUN
ejpam-6147	243	7	ςn−1∥+	ςn−1∥+	NOUN
ejpam-6147	243	8	|ηnλn	|ηnλn	NOUN
ejpam-6147	243	9	−	−	NOUN
ejpam-6147	243	10	ηn−1αn−1|∥ςn−1∥	ηn−1αn−1|∥ςn−1∥	NOUN
ejpam-6147	243	11	+	+	VERB
ejpam-6147	243	12	|ηn−1	|ηn−1	ADJ
ejpam-6147	243	13	−	−	NOUN
ejpam-6147	243	14	ηn|∥vn−1∥+	ηn|∥vn−1∥+	NOUN
ejpam-6147	243	15	|γn	|γn	X
ejpam-6147	243	16	−	−	NOUN
ejpam-6147	244	1	γn−1|	γn−1|	X
ejpam-6147	244	2	γn	γn	ADP
ejpam-6147	244	3	2∥ςn−1	2∥ςn−1	PROPN
ejpam-6147	244	4	−	−	PROPN
ejpam-6147	244	5	p∥.	p∥.	PROPN
ejpam-6147	244	6	≤	≤	NOUN
ejpam-6147	245	1	[	[	X
ejpam-6147	245	2	1−	1−	NUM
ejpam-6147	245	3	(	(	PUNCT
ejpam-6147	245	4	1−	1−	NUM
ejpam-6147	245	5	λn)ηn]∥ςn	λn)ηn]∥ςn	NOUN
ejpam-6147	245	6	−	−	PROPN
ejpam-6147	245	7	ςn−1∥	ςn−1∥	NOUN
ejpam-6147	246	1	+	+	NOUN
ejpam-6147	246	2	m	m	PART
ejpam-6147	246	3	(	(	PUNCT
ejpam-6147	246	4	|ηnλn	|ηnλn	ADV
ejpam-6147	246	5	−	−	NOUN
ejpam-6147	246	6	ηn−1αn−1|+	ηn−1αn−1|+	NOUN
ejpam-6147	246	7	|ηn−1	|ηn−1	ADP
ejpam-6147	246	8	−	−	NOUN
ejpam-6147	246	9	ηn|+	ηn|+	NOUN
ejpam-6147	246	10	|γn	|γn	NUM
ejpam-6147	246	11	−	−	NOUN
ejpam-6147	246	12	γn−1|	γn−1|	X
ejpam-6147	246	13	γn	γn	NOUN
ejpam-6147	246	14	)	)	PUNCT
ejpam-6147	246	15	.	.	PUNCT
ejpam-6147	247	1	where	where	SCONJ
ejpam-6147	247	2	m	m	VERB
ejpam-6147	247	3	>	>	X
ejpam-6147	247	4	0	0	NUM
ejpam-6147	247	5	,	,	PUNCT
ejpam-6147	247	6	and	and	CCONJ
ejpam-6147	247	7	sup	sup	NOUN
ejpam-6147	247	8	n≥1	n≥1	NOUN
ejpam-6147	247	9	{	{	PUNCT
ejpam-6147	247	10	∥ςn−1∥	∥ςn−1∥	NOUN
ejpam-6147	247	11	,	,	PUNCT
ejpam-6147	247	12	∥vn−1∥	∥vn−1∥	NOUN
ejpam-6147	247	13	,	,	PUNCT
ejpam-6147	247	14	2∥ςn−1	2∥ςn−1	PROPN
ejpam-6147	247	15	−	−	NOUN
ejpam-6147	247	16	p∥	p∥	NOUN
ejpam-6147	247	17	}	}	PUNCT
ejpam-6147	247	18	≤	≤	NUM
ejpam-6147	247	19	m.	m.	NOUN
ejpam-6147	247	20	hence	hence	ADV
ejpam-6147	247	21	lim	lim	PROPN
ejpam-6147	247	22	sup	sup	PROPN
ejpam-6147	247	23	n→+∞	n→+∞	PROPN
ejpam-6147	247	24	(	(	PUNCT
ejpam-6147	247	25	∥	∥	X
ejpam-6147	247	26	℧	℧	NOUN
ejpam-6147	247	27	n	n	CCONJ
ejpam-6147	247	28	−	−	PROPN
ejpam-6147	247	29	℧	℧	PROPN
ejpam-6147	247	30	n−1∥	n−1∥	NOUN
ejpam-6147	247	31	−	−	PROPN
ejpam-6147	247	32	∥ςn	∥ςn	PROPN
ejpam-6147	248	1	−	−	PROPN
ejpam-6147	248	2	ςn−1∥	ςn−1∥	NOUN
ejpam-6147	248	3	)	)	PUNCT
ejpam-6147	248	4	≤	≤	NUM
ejpam-6147	248	5	0	0	NUM
ejpam-6147	248	6	.	.	PUNCT
ejpam-6147	249	1	using	use	VERB
ejpam-6147	249	2	lemma	lemma	PROPN
ejpam-6147	249	3	(	(	PUNCT
ejpam-6147	249	4	2	2	X
ejpam-6147	249	5	)	)	PUNCT
ejpam-6147	249	6	we	we	PRON
ejpam-6147	249	7	have	have	VERB
ejpam-6147	249	8	lim	lim	PROPN
ejpam-6147	249	9	n→+∞	n→+∞	VERB
ejpam-6147	249	10	∥	∥	PRON
ejpam-6147	249	11	℧	℧	PROPN
ejpam-6147	249	12	n	n	NUM
ejpam-6147	249	13	−	−	PROPN
ejpam-6147	249	14	ςn∥	ςn∥	PROPN
ejpam-6147	249	15	=	=	NOUN
ejpam-6147	249	16	0	0	PROPN
ejpam-6147	249	17	.	.	PUNCT
ejpam-6147	250	1	so	so	ADV
ejpam-6147	250	2	,	,	PUNCT
ejpam-6147	250	3	it	it	PRON
ejpam-6147	250	4	follows	follow	VERB
ejpam-6147	250	5	that	that	SCONJ
ejpam-6147	250	6	lim	lim	PROPN
ejpam-6147	250	7	n→+∞	n→+∞	PROPN
ejpam-6147	250	8	∥ςn+1	∥ςn+1	PROPN
ejpam-6147	250	9	−	−	PROPN
ejpam-6147	251	1	ςn∥	ςn∥	PROPN
ejpam-6147	251	2	=	=	PROPN
ejpam-6147	251	3	lim	lim	PROPN
ejpam-6147	251	4	n→+∞	n→+∞	VERB
ejpam-6147	251	5	µn∥	µn∥	PROPN
ejpam-6147	251	6	℧	℧	PROPN
ejpam-6147	251	7	n	n	NUM
ejpam-6147	251	8	−	−	PROPN
ejpam-6147	251	9	ςn∥.	ςn∥.	PRON
ejpam-6147	251	10	note	note	VERB
ejpam-6147	251	11	that	that	SCONJ
ejpam-6147	251	12	∥e(τ	∥e(τ	NOUN
ejpam-6147	251	13	,	,	PUNCT
ejpam-6147	251	14	0)ςn	0)ςn	PROPN
ejpam-6147	251	15	−	−	PROPN
ejpam-6147	252	1	ςn∥	ςn∥	PROPN
ejpam-6147	252	2	≤	≤	NUM
ejpam-6147	252	3	∥∥e(τ	∥∥e(τ	NOUN
ejpam-6147	252	4	,	,	PUNCT
ejpam-6147	252	5	0)ςn	0)ςn	PROPN
ejpam-6147	252	6	−	−	PROPN
ejpam-6147	252	7	e(τ	e(τ	PROPN
ejpam-6147	252	8	,	,	PUNCT
ejpam-6147	252	9	0	0	NUM
ejpam-6147	252	10	)	)	PUNCT
ejpam-6147	252	11	1	1	NUM
ejpam-6147	253	1	γn	γn	ADP
ejpam-6147	253	2	∫	∫	PROPN
ejpam-6147	253	3	γn	γn	ADP
ejpam-6147	253	4	0	0	PUNCT
ejpam-6147	253	5	e(s	e(s	PROPN
ejpam-6147	253	6	,	,	PUNCT
ejpam-6147	253	7	0)ςnds	0)ςnds	X
ejpam-6147	253	8	∥∥	∥∥	X
ejpam-6147	253	9	+	+	NUM
ejpam-6147	253	10	∥∥e(τ	∥∥e(τ	ADJ
ejpam-6147	253	11	,	,	PUNCT
ejpam-6147	253	12	0	0	NUM
ejpam-6147	253	13	)	)	PUNCT
ejpam-6147	253	14	1	1	NUM
ejpam-6147	253	15	γn	γn	ADP
ejpam-6147	253	16	∫	∫	PROPN
ejpam-6147	253	17	γn	γn	ADP
ejpam-6147	253	18	0	0	PUNCT
ejpam-6147	253	19	e(s	e(s	ADJ
ejpam-6147	253	20	,	,	PUNCT
ejpam-6147	253	21	0)ςnds−	0)ςnds−	NUM
ejpam-6147	253	22	1	1	NUM
ejpam-6147	253	23	γn	γn	ADP
ejpam-6147	253	24	∫	∫	PROPN
ejpam-6147	253	25	γn	γn	ADP
ejpam-6147	253	26	0	0	PUNCT
ejpam-6147	253	27	e(s	e(s	PROPN
ejpam-6147	253	28	,	,	PUNCT
ejpam-6147	253	29	0)ςnds	0)ςnds	X
ejpam-6147	253	30	∥∥	∥∥	X
ejpam-6147	254	1	+	+	CCONJ
ejpam-6147	254	2	∥∥	∥∥	PUNCT
ejpam-6147	254	3	1	1	NUM
ejpam-6147	254	4	γn	γn	ADP
ejpam-6147	254	5	∫	∫	PROPN
ejpam-6147	254	6	γn	γn	ADP
ejpam-6147	254	7	0	0	PUNCT
ejpam-6147	254	8	e(s	e(s	PROPN
ejpam-6147	254	9	,	,	PUNCT
ejpam-6147	254	10	0)ςnds−	0)ςnds−	NUM
ejpam-6147	254	11	ςn	ςn	NOUN
ejpam-6147	254	12	∥∥	∥∥	PUNCT
ejpam-6147	254	13	≤	≤	NUM
ejpam-6147	254	14	∥∥e(τ	∥∥e(τ	NOUN
ejpam-6147	254	15	,	,	PUNCT
ejpam-6147	254	16	0	0	NUM
ejpam-6147	254	17	)	)	PUNCT
ejpam-6147	254	18	1	1	NUM
ejpam-6147	254	19	γn	γn	ADP
ejpam-6147	254	20	∫	∫	PROPN
ejpam-6147	254	21	γn	γn	ADP
ejpam-6147	254	22	0	0	PUNCT
ejpam-6147	254	23	e(s	e(s	ADJ
ejpam-6147	254	24	,	,	PUNCT
ejpam-6147	254	25	0)ςnds−	0)ςnds−	NUM
ejpam-6147	254	26	1	1	NUM
ejpam-6147	254	27	γn	γn	ADP
ejpam-6147	254	28	∫	∫	PROPN
ejpam-6147	254	29	γn	γn	ADP
ejpam-6147	254	30	0	0	PUNCT
ejpam-6147	254	31	e(s	e(s	PROPN
ejpam-6147	254	32	,	,	PUNCT
ejpam-6147	254	33	0)ςnds	0)ςnds	X
ejpam-6147	254	34	∥∥	∥∥	X
ejpam-6147	254	35	+2	+2	NOUN
ejpam-6147	255	1	∥∥ςn	∥∥ςn	NOUN
ejpam-6147	255	2	−	−	NUM
ejpam-6147	255	3	1	1	NUM
ejpam-6147	256	1	γn	γn	ADP
ejpam-6147	256	2	∫	∫	PROPN
ejpam-6147	256	3	γn	γn	ADP
ejpam-6147	256	4	0	0	PUNCT
ejpam-6147	256	5	e(s	e(s	PROPN
ejpam-6147	256	6	,	,	PUNCT
ejpam-6147	256	7	0)ςnds	0)ςnds	X
ejpam-6147	256	8	∥∥.	∥∥.	NUM
ejpam-6147	256	9	(	(	PUNCT
ejpam-6147	256	10	9	9	NUM
ejpam-6147	256	11	)	)	PUNCT
ejpam-6147	256	12	from	from	ADP
ejpam-6147	256	13	(	(	PUNCT
ejpam-6147	256	14	8)	8)	NUM
ejpam-6147	256	15	,	,	PUNCT
ejpam-6147	256	16	we	we	PRON
ejpam-6147	256	17	have∥∥∥∥ςn	have∥∥∥∥ςn	NOUN
ejpam-6147	257	1	−	−	NUM
ejpam-6147	257	2	1	1	NUM
ejpam-6147	257	3	γn	γn	ADP
ejpam-6147	257	4	∫	∫	PROPN
ejpam-6147	257	5	γn	γn	ADP
ejpam-6147	257	6	0	0	NUM
ejpam-6147	257	7	e(s	e(s	PROPN
ejpam-6147	257	8	,	,	PUNCT
ejpam-6147	257	9	0)ςnds	0)ςnds	NUM
ejpam-6147	257	10	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	257	11	≤	≤	NUM
ejpam-6147	258	1	∥∥ςn	∥∥ςn	NOUN
ejpam-6147	259	1	−	−	NUM
ejpam-6147	259	2	ςn+1	ςn+1	NUM
ejpam-6147	259	3	∥∥+	∥∥+	SYM
ejpam-6147	259	4	∥∥∥∥ςn+1	∥∥∥∥ςn+1	NOUN
ejpam-6147	259	5	−	−	PROPN
ejpam-6147	259	6	1	1	NUM
ejpam-6147	259	7	γn	γn	ADP
ejpam-6147	259	8	∫	∫	PROPN
ejpam-6147	259	9	γn	γn	ADP
ejpam-6147	259	10	0	0	NUM
ejpam-6147	259	11	e(s	e(s	PROPN
ejpam-6147	259	12	,	,	PUNCT
ejpam-6147	259	13	0)ςnds	0)ςnds	NUM
ejpam-6147	259	14	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	259	15	≤	≤	NUM
ejpam-6147	260	1	∥∥ςn	∥∥ςn	NOUN
ejpam-6147	261	1	−	−	NUM
ejpam-6147	261	2	ςn+1	ςn+1	NUM
ejpam-6147	261	3	∥∥+	∥∥+	SYM
ejpam-6147	261	4	(	(	PUNCT
ejpam-6147	261	5	1−	1−	NUM
ejpam-6147	261	6	µn	µn	NOUN
ejpam-6147	261	7	)	)	PUNCT
ejpam-6147	261	8	∥∥∥∥ςn	∥∥∥∥ςn	NUM
ejpam-6147	261	9	−	−	ADP
ejpam-6147	261	10	1	1	NUM
ejpam-6147	262	1	γn	γn	ADP
ejpam-6147	262	2	∫	∫	PROPN
ejpam-6147	262	3	γn	γn	ADP
ejpam-6147	262	4	0	0	NUM
ejpam-6147	262	5	e(s	e(s	PROPN
ejpam-6147	262	6	,	,	PUNCT
ejpam-6147	262	7	0)ςnds	0)ςnds	NUM
ejpam-6147	262	8	∥∥∥∥	∥∥∥∥	VERB
ejpam-6147	262	9	m.	m.	NOUN
ejpam-6147	262	10	sarwar	sarwar	PROPN
ejpam-6147	262	11	et	et	PROPN
ejpam-6147	262	12	al	al	PROPN
ejpam-6147	262	13	.	.	PUNCT
ejpam-6147	262	14	/	/	SYM
ejpam-6147	262	15	eur	eur	PROPN
ejpam-6147	262	16	.	.	PUNCT
ejpam-6147	263	1	j.	j.	PROPN
ejpam-6147	263	2	pure	pure	PROPN
ejpam-6147	263	3	appl	appl	PROPN
ejpam-6147	263	4	.	.	PROPN
ejpam-6147	263	5	math	math	PROPN
ejpam-6147	263	6	,	,	PUNCT
ejpam-6147	263	7	18	18	NUM
ejpam-6147	263	8	(	(	PUNCT
ejpam-6147	263	9	3	3	NUM
ejpam-6147	263	10	)	)	PUNCT
ejpam-6147	263	11	(	(	PUNCT
ejpam-6147	263	12	2025	2025	NUM
ejpam-6147	263	13	)	)	PUNCT
ejpam-6147	263	14	,	,	PUNCT
ejpam-6147	263	15	6147	6147	NUM
ejpam-6147	263	16	13	13	NUM
ejpam-6147	263	17	of	of	ADP
ejpam-6147	263	18	18	18	NUM
ejpam-6147	263	19	+	+	NOUN
ejpam-6147	263	20	ηnλn	ηnλn	NOUN
ejpam-6147	263	21	∥∥∥∥ςn	∥∥∥∥ςn	NUM
ejpam-6147	263	22	−	−	ADP
ejpam-6147	263	23	1	1	NUM
ejpam-6147	263	24	γn	γn	ADP
ejpam-6147	263	25	∫	∫	PROPN
ejpam-6147	263	26	γn	γn	ADP
ejpam-6147	263	27	0	0	PUNCT
ejpam-6147	263	28	e(s	e(s	PROPN
ejpam-6147	263	29	,	,	PUNCT
ejpam-6147	263	30	0)ςnds	0)ςnds	X
ejpam-6147	263	31	∥∥∥∥+	∥∥∥∥+	PROPN
ejpam-6147	263	32	ηn(1−	ηn(1−	PROPN
ejpam-6147	263	33	λn	λn	NOUN
ejpam-6147	263	34	)	)	PUNCT
ejpam-6147	263	35	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	263	36	1	1	NUM
ejpam-6147	264	1	γn	γn	ADP
ejpam-6147	264	2	∫	∫	PROPN
ejpam-6147	264	3	γn	γn	ADP
ejpam-6147	264	4	0	0	PUNCT
ejpam-6147	264	5	e(s	e(s	PROPN
ejpam-6147	264	6	,	,	PUNCT
ejpam-6147	264	7	0)ςnds	0)ςnds	NUM
ejpam-6147	264	8	∥∥∥∥.	∥∥∥∥.	VERB
ejpam-6147	264	9	now	now	ADV
ejpam-6147	264	10	(	(	PUNCT
ejpam-6147	264	11	1−	1−	NUM
ejpam-6147	264	12	1	1	NUM
ejpam-6147	264	13	+	+	NUM
ejpam-6147	264	14	µn	µn	PROPN
ejpam-6147	264	15	−	−	NOUN
ejpam-6147	264	16	ηnλn	ηnλn	NOUN
ejpam-6147	264	17	)	)	PUNCT
ejpam-6147	264	18	∥∥∥∥ςn	∥∥∥∥ςn	PUNCT
ejpam-6147	264	19	−	−	ADP
ejpam-6147	264	20	1	1	NUM
ejpam-6147	264	21	γn	γn	ADP
ejpam-6147	264	22	∫	∫	PROPN
ejpam-6147	264	23	γn	γn	ADP
ejpam-6147	264	24	0	0	NUM
ejpam-6147	264	25	e(s	e(s	PROPN
ejpam-6147	264	26	,	,	PUNCT
ejpam-6147	264	27	0)ςnds	0)ςnds	NUM
ejpam-6147	264	28	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6147	264	29	≤	≤	NUM
ejpam-6147	265	1	∥∥ςn	∥∥ςn	NOUN
ejpam-6147	265	2	−	−	NUM
ejpam-6147	266	1	ςn+1	ςn+1	NUM
ejpam-6147	266	2	∥∥+	∥∥+	SYM
ejpam-6147	266	3	ηn(1−	ηn(1−	PROPN
ejpam-6147	266	4	λn	λn	NOUN
ejpam-6147	266	5	)	)	PUNCT
ejpam-6147	266	6	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	266	7	1	1	NUM
ejpam-6147	267	1	γn	γn	ADP
ejpam-6147	267	2	∫	∫	PROPN
ejpam-6147	267	3	γn	γn	ADP
ejpam-6147	267	4	0	0	PUNCT
ejpam-6147	267	5	e(s	e(s	PROPN
ejpam-6147	267	6	,	,	PUNCT
ejpam-6147	267	7	0)ςnds	0)ςnds	NUM
ejpam-6147	267	8	∥∥∥∥.	∥∥∥∥.	VERB
ejpam-6147	267	9	it	it	PRON
ejpam-6147	267	10	gives	give	VERB
ejpam-6147	267	11	that∥∥∥∥ςn	that∥∥∥∥ςn	NOUN
ejpam-6147	267	12	−	−	PROPN
ejpam-6147	267	13	1	1	NUM
ejpam-6147	267	14	γn	γn	ADP
ejpam-6147	267	15	∫	∫	PROPN
ejpam-6147	267	16	γn	γn	ADP
ejpam-6147	267	17	0	0	NUM
ejpam-6147	267	18	e(s	e(s	PROPN
ejpam-6147	267	19	,	,	PUNCT
ejpam-6147	267	20	0)ςnds	0)ςnds	NUM
ejpam-6147	267	21	∥∥∥∥	∥∥∥∥	SYM
ejpam-6147	267	22	≤	≤	NUM
ejpam-6147	267	23	1	1	NUM
ejpam-6147	267	24	µn	µn	PROPN
ejpam-6147	267	25	−	−	PROPN
ejpam-6147	267	26	ηnλn	ηnλn	NOUN
ejpam-6147	267	27	[	[	PUNCT
ejpam-6147	267	28	∥ςn	∥ςn	NOUN
ejpam-6147	267	29	−	−	PROPN
ejpam-6147	267	30	ςn+1∥+	ςn+1∥+	NUM
ejpam-6147	267	31	ηn(1−	ηn(1−	PROPN
ejpam-6147	267	32	λn	λn	NOUN
ejpam-6147	267	33	)	)	PUNCT
ejpam-6147	267	34	∥∥∥∥	∥∥∥∥	NUM
ejpam-6147	267	35	1	1	NUM
ejpam-6147	267	36	γn	γn	ADP
ejpam-6147	267	37	∫	∫	PROPN
ejpam-6147	267	38	γn	γn	ADP
ejpam-6147	267	39	0	0	PUNCT
ejpam-6147	267	40	e(s	e(s	PROPN
ejpam-6147	267	41	,	,	PUNCT
ejpam-6147	267	42	0)ςnds	0)ςnds	X
ejpam-6147	267	43	∥∥∥∥	∥∥∥∥	NOUN
ejpam-6147	267	44	]	]	PUNCT
ejpam-6147	267	45	.	.	PUNCT
ejpam-6147	268	1	(	(	PUNCT
ejpam-6147	268	2	10	10	NUM
ejpam-6147	268	3	)	)	PUNCT
ejpam-6147	268	4	from	from	ADP
ejpam-6147	268	5	(	(	PUNCT
ejpam-6147	268	6	9	9	NUM
ejpam-6147	268	7	)	)	PUNCT
ejpam-6147	268	8	,	,	PUNCT
ejpam-6147	268	9	(	(	PUNCT
ejpam-6147	268	10	10	10	NUM
ejpam-6147	268	11	)	)	PUNCT
ejpam-6147	268	12	and	and	CCONJ
ejpam-6147	268	13	lemma	lemma	PROPN
ejpam-6147	268	14	(	(	PUNCT
ejpam-6147	268	15	4	4	NUM
ejpam-6147	268	16	)	)	PUNCT
ejpam-6147	268	17	,	,	PUNCT
ejpam-6147	268	18	we	we	PRON
ejpam-6147	268	19	have	have	VERB
ejpam-6147	268	20	lim	lim	PROPN
ejpam-6147	268	21	n→+∞	n→+∞	PROPN
ejpam-6147	268	22	∥e(τ	∥e(τ	PROPN
ejpam-6147	268	23	,	,	PUNCT
ejpam-6147	268	24	0)ςn	0)ςn	PROPN
ejpam-6147	268	25	−	−	PROPN
ejpam-6147	269	1	ςn∥	ςn∥	PROPN
ejpam-6147	269	2	=	=	SYM
ejpam-6147	269	3	0	0	PROPN
ejpam-6147	269	4	,	,	PUNCT
ejpam-6147	269	5	∀τ	∀τ	NOUN
ejpam-6147	269	6	≥	≥	NOUN
ejpam-6147	269	7	0	0	NUM
ejpam-6147	269	8	.	.	PUNCT
ejpam-6147	270	1	(	(	PUNCT
ejpam-6147	270	2	11	11	NUM
ejpam-6147	270	3	)	)	PUNCT
ejpam-6147	270	4	note	note	NOUN
ejpam-6147	270	5	that	that	SCONJ
ejpam-6147	270	6	the	the	DET
ejpam-6147	270	7	sequence	sequence	NOUN
ejpam-6147	270	8	{	{	PUNCT
ejpam-6147	270	9	ςn	ςn	NOUN
ejpam-6147	270	10	}	}	PUNCT
ejpam-6147	270	11	is	be	AUX
ejpam-6147	270	12	bounded	bound	VERB
ejpam-6147	270	13	and	and	CCONJ
ejpam-6147	270	14	{	{	PUNCT
ejpam-6147	270	15	ςn	ςn	NOUN
ejpam-6147	270	16	}	}	PUNCT
ejpam-6147	270	17	→	→	SYM
ejpam-6147	270	18	ς̃	ς̃	PRON
ejpam-6147	270	19	weakly	weakly	ADV
ejpam-6147	270	20	.	.	PUNCT
ejpam-6147	271	1	let	let	VERB
ejpam-6147	271	2	ς∗	ς∗	NOUN
ejpam-6147	271	3	=	=	SYM
ejpam-6147	271	4	pfe(0	pfe(0	PROPN
ejpam-6147	271	5	)	)	PUNCT
ejpam-6147	271	6	,	,	PUNCT
ejpam-6147	271	7	then	then	ADV
ejpam-6147	271	8	there	there	PRON
ejpam-6147	271	9	exists	exist	VERB
ejpam-6147	271	10	m	m	VERB
ejpam-6147	271	11	>	>	X
ejpam-6147	271	12	0	0	NUM
ejpam-6147	272	1	such	such	ADJ
ejpam-6147	272	2	that	that	DET
ejpam-6147	272	3	b(ς∗,m	b(ς∗,m	PROPN
ejpam-6147	272	4	)	)	PUNCT
ejpam-6147	272	5	contains	contain	VERB
ejpam-6147	272	6	{	{	PUNCT
ejpam-6147	272	7	ςn	ςn	NOUN
ejpam-6147	272	8	}	}	PUNCT
ejpam-6147	272	9	.	.	PUNCT
ejpam-6147	273	1	also	also	ADV
ejpam-6147	273	2	,	,	PUNCT
ejpam-6147	273	3	b(ς∗,k	b(ς∗,k	NOUN
ejpam-6147	273	4	)	)	PUNCT
ejpam-6147	273	5	is	be	AUX
ejpam-6147	273	6	e(s)-invariant	e(s)-invariant	ADJ
ejpam-6147	273	7	for	for	ADP
ejpam-6147	273	8	all	all	PRON
ejpam-6147	273	9	s	s	PART
ejpam-6147	273	10	≥	≥	NOUN
ejpam-6147	273	11	0	0	NUM
ejpam-6147	273	12	and	and	CCONJ
ejpam-6147	273	13	so	so	ADV
ejpam-6147	273	14	,	,	PUNCT
ejpam-6147	273	15	we	we	PRON
ejpam-6147	273	16	can	can	AUX
ejpam-6147	273	17	assume	assume	VERB
ejpam-6147	273	18	that	that	SCONJ
ejpam-6147	273	19	{	{	PUNCT
ejpam-6147	273	20	e(s	e(s	PROPN
ejpam-6147	273	21	,	,	PUNCT
ejpam-6147	273	22	0)}s≥0	0)}s≥0	NUM
ejpam-6147	273	23	is	be	AUX
ejpam-6147	273	24	a	a	DET
ejpam-6147	273	25	nonexpansive	nonexpansive	ADJ
ejpam-6147	273	26	family	family	NOUN
ejpam-6147	273	27	on	on	ADP
ejpam-6147	273	28	b(ς∗,k	b(ς∗,k	NOUN
ejpam-6147	273	29	)	)	PUNCT
ejpam-6147	273	30	.	.	PUNCT
ejpam-6147	274	1	by	by	ADP
ejpam-6147	274	2	making	make	VERB
ejpam-6147	274	3	use	use	NOUN
ejpam-6147	274	4	of	of	ADP
ejpam-6147	274	5	(	(	PUNCT
ejpam-6147	274	6	11	11	NUM
ejpam-6147	274	7	)	)	PUNCT
ejpam-6147	274	8	and	and	CCONJ
ejpam-6147	274	9	lemma	lemma	PROPN
ejpam-6147	274	10	1(demiclosedness	1(demiclosedness	PROPN
ejpam-6147	274	11	principle	principle	NOUN
ejpam-6147	274	12	)	)	PUNCT
ejpam-6147	274	13	,	,	PUNCT
ejpam-6147	274	14	we	we	PRON
ejpam-6147	274	15	have	have	VERB
ejpam-6147	274	16	ς̃	ς̃	PROPN
ejpam-6147	274	17	∈	∈	PROPN
ejpam-6147	274	18	fe	fe	NOUN
ejpam-6147	274	19	and	and	CCONJ
ejpam-6147	274	20	therefore	therefore	ADV
ejpam-6147	274	21	lim	lim	PROPN
ejpam-6147	274	22	sup	sup	PROPN
ejpam-6147	274	23	n→+∞	n→+∞	PROPN
ejpam-6147	274	24	⟨ς∗	⟨ς∗	PROPN
ejpam-6147	274	25	,	,	PUNCT
ejpam-6147	274	26	ςn+1	ςn+1	NUM
ejpam-6147	274	27	−	−	PROPN
ejpam-6147	274	28	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	274	29	=	=	SYM
ejpam-6147	274	30	lim	lim	PROPN
ejpam-6147	274	31	n→+∞	n→+∞	PROPN
ejpam-6147	274	32	⟨ς∗	⟨ς∗	PROPN
ejpam-6147	274	33	,	,	PUNCT
ejpam-6147	274	34	ς̃	ς̃	PROPN
ejpam-6147	274	35	−	−	NUM
ejpam-6147	274	36	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	274	37	≤	≤	NOUN
ejpam-6147	274	38	0	0	NUM
ejpam-6147	274	39	.	.	PUNCT
ejpam-6147	275	1	in	in	ADP
ejpam-6147	275	2	the	the	DET
ejpam-6147	275	3	end	end	NOUN
ejpam-6147	275	4	,	,	PUNCT
ejpam-6147	275	5	we	we	PRON
ejpam-6147	275	6	prove	prove	VERB
ejpam-6147	275	7	that	that	SCONJ
ejpam-6147	275	8	ςn	ςn	PROPN
ejpam-6147	275	9	→	→	SYM
ejpam-6147	275	10	ς∗.	ς∗.	NOUN
ejpam-6147	275	11	set	set	VERB
ejpam-6147	275	12	ς́n	ς́n	NOUN
ejpam-6147	275	13	=	=	SYM
ejpam-6147	275	14	ηn(λnςn	ηn(λnςn	PROPN
ejpam-6147	275	15	)	)	PUNCT
ejpam-6147	275	16	+	+	CCONJ
ejpam-6147	276	1	(	(	PUNCT
ejpam-6147	276	2	1−	1−	NUM
ejpam-6147	276	3	ηn	ηn	ADJ
ejpam-6147	276	4	)	)	PUNCT
ejpam-6147	276	5	1	1	NUM
ejpam-6147	276	6	γn	γn	ADP
ejpam-6147	276	7	∫	∫	PROPN
ejpam-6147	276	8	γn	γn	ADP
ejpam-6147	276	9	0	0	PUNCT
ejpam-6147	276	10	e(s	e(s	PROPN
ejpam-6147	276	11	,	,	PUNCT
ejpam-6147	276	12	0)ςnds	0)ςnd	NOUN
ejpam-6147	276	13	,	,	PUNCT
ejpam-6147	276	14	which	which	PRON
ejpam-6147	276	15	gives	give	VERB
ejpam-6147	276	16	that	that	PRON
ejpam-6147	276	17	℧	℧	PROPN
ejpam-6147	276	18	n	n	NOUN
ejpam-6147	276	19	=	=	SYM
ejpam-6147	276	20	pz	pz	NOUN
ejpam-6147	277	1	[	[	X
ejpam-6147	277	2	ς́n	ς́n	NOUN
ejpam-6147	277	3	]	]	X
ejpam-6147	277	4	∀n	∀n	NUM
ejpam-6147	277	5	≥	≥	NOUN
ejpam-6147	277	6	0	0	NUM
ejpam-6147	277	7	.	.	PUNCT
ejpam-6147	278	1	by	by	ADP
ejpam-6147	278	2	making	make	VERB
ejpam-6147	278	3	use	use	NOUN
ejpam-6147	278	4	of	of	ADP
ejpam-6147	278	5	metric	metric	ADJ
ejpam-6147	278	6	projection	projection	NOUN
ejpam-6147	278	7	property	property	NOUN
ejpam-6147	278	8	1	1	NUM
ejpam-6147	278	9	,	,	PUNCT
ejpam-6147	278	10	we	we	PRON
ejpam-6147	278	11	have	have	AUX
ejpam-6147	278	12	⟨	⟨	NOUN
ejpam-6147	278	13	℧	℧	NOUN
ejpam-6147	278	14	n	n	NOUN
ejpam-6147	278	15	−	−	PROPN
ejpam-6147	278	16	ς́n,	ς́n,	NUM
ejpam-6147	278	17	℧	℧	PROPN
ejpam-6147	278	18	n	n	CCONJ
ejpam-6147	278	19	−	−	PROPN
ejpam-6147	278	20	ς∗⟩	ς∗⟩	NUM
ejpam-6147	278	21	=	=	SYM
ejpam-6147	278	22	⟨ς́n	⟨ς́n	NOUN
ejpam-6147	278	23	−	−	PROPN
ejpam-6147	278	24	℧	℧	NOUN
ejpam-6147	278	25	n	n	CCONJ
ejpam-6147	278	26	,	,	PUNCT
ejpam-6147	278	27	ς	ς	PROPN
ejpam-6147	278	28	∗	∗	NOUN
ejpam-6147	278	29	−	−	PROPN
ejpam-6147	278	30	℧	℧	NOUN
ejpam-6147	278	31	n⟩	n⟩	PROPN
ejpam-6147	278	32	≤	≤	NUM
ejpam-6147	278	33	0	0	NUM
ejpam-6147	278	34	.	.	PUNCT
ejpam-6147	279	1	therefore	therefore	ADV
ejpam-6147	279	2	∥	∥	X
ejpam-6147	279	3	℧	℧	SYM
ejpam-6147	279	4	n	n	CCONJ
ejpam-6147	279	5	−	−	PROPN
ejpam-6147	279	6	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	279	7	=	=	PUNCT
ejpam-6147	279	8	⟨	⟨	VERB
ejpam-6147	279	9	℧	℧	NOUN
ejpam-6147	279	10	n	n	NUM
ejpam-6147	279	11	−	−	PROPN
ejpam-6147	279	12	ς∗,	ς∗,	NUM
ejpam-6147	279	13	℧	℧	PROPN
ejpam-6147	279	14	n	n	NUM
ejpam-6147	279	15	−	−	PROPN
ejpam-6147	279	16	ς∗⟩	ς∗⟩	NUM
ejpam-6147	279	17	=	=	PUNCT
ejpam-6147	279	18	⟨	⟨	NOUN
ejpam-6147	279	19	℧	℧	NOUN
ejpam-6147	279	20	n	n	NOUN
ejpam-6147	279	21	−	−	PROPN
ejpam-6147	279	22	ς́n,	ς́n,	NUM
ejpam-6147	279	23	℧	℧	PROPN
ejpam-6147	279	24	n	n	NUM
ejpam-6147	279	25	−	−	NOUN
ejpam-6147	279	26	ς∗⟩+	ς∗⟩+	PROPN
ejpam-6147	280	1	⟨ς́n	⟨ς́n	VERB
ejpam-6147	280	2	−	−	PROPN
ejpam-6147	280	3	ς∗,	ς∗,	NUM
ejpam-6147	280	4	℧	℧	PROPN
ejpam-6147	280	5	n	n	NUM
ejpam-6147	280	6	−	−	PROPN
ejpam-6147	280	7	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	280	8	≤	≤	NUM
ejpam-6147	280	9	⟨ς́n	⟨ς́n	NOUN
ejpam-6147	280	10	−	−	PROPN
ejpam-6147	280	11	ς∗,	ς∗,	NUM
ejpam-6147	280	12	℧	℧	PROPN
ejpam-6147	280	13	n	n	NUM
ejpam-6147	280	14	−	−	PROPN
ejpam-6147	280	15	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	280	16	=	=	SYM
ejpam-6147	280	17	⟨ηn(λnςn	⟨ηn(λnςn	PROPN
ejpam-6147	280	18	)	)	PUNCT
ejpam-6147	280	19	+	+	CCONJ
ejpam-6147	280	20	(	(	PUNCT
ejpam-6147	280	21	1−	1−	NUM
ejpam-6147	280	22	ηn	ηn	ADJ
ejpam-6147	280	23	)	)	PUNCT
ejpam-6147	280	24	1	1	NUM
ejpam-6147	280	25	γn	γn	ADP
ejpam-6147	280	26	∫	∫	PROPN
ejpam-6147	280	27	γn	γn	ADP
ejpam-6147	280	28	0	0	PUNCT
ejpam-6147	280	29	e(s	e(s	PROPN
ejpam-6147	280	30	,	,	PUNCT
ejpam-6147	280	31	0)ςnds−	0)ςnds−	PROPN
ejpam-6147	280	32	ς∗,	ς∗,	NUM
ejpam-6147	280	33	℧	℧	PROPN
ejpam-6147	280	34	n	n	NUM
ejpam-6147	280	35	−	−	PROPN
ejpam-6147	280	36	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	280	37	=	=	SYM
ejpam-6147	280	38	⟨ηn(λnςn	⟨ηn(λnςn	PROPN
ejpam-6147	280	39	)	)	PUNCT
ejpam-6147	281	1	+	+	NUM
ejpam-6147	281	2	ηnλnς	ηnλnς	NOUN
ejpam-6147	281	3	∗	∗	NOUN
ejpam-6147	281	4	−	−	PROPN
ejpam-6147	281	5	ηnλnς	ηnλnς	NOUN
ejpam-6147	281	6	∗	∗	NOUN
ejpam-6147	281	7	−	−	PROPN
ejpam-6147	281	8	ηnς	ηnς	PROPN
ejpam-6147	281	9	∗	∗	NOUN
ejpam-6147	281	10	+	+	CCONJ
ejpam-6147	281	11	ηnς	ηnς	PROPN
ejpam-6147	281	12	∗	∗	NOUN
ejpam-6147	281	13	+	+	PROPN
ejpam-6147	281	14	(	(	PUNCT
ejpam-6147	281	15	1−	1−	NUM
ejpam-6147	281	16	ηn	ηn	ADJ
ejpam-6147	281	17	)	)	PUNCT
ejpam-6147	281	18	1	1	NUM
ejpam-6147	281	19	γn	γn	ADP
ejpam-6147	281	20	∫	∫	PROPN
ejpam-6147	282	1	γn	γn	ADP
ejpam-6147	282	2	0	0	PUNCT
ejpam-6147	282	3	e(s	e(s	PROPN
ejpam-6147	282	4	,	,	PUNCT
ejpam-6147	282	5	0)ςnds−	0)ςnds−	PROPN
ejpam-6147	282	6	ς∗,	ς∗,	NUM
ejpam-6147	282	7	℧	℧	PROPN
ejpam-6147	282	8	n	n	NUM
ejpam-6147	282	9	−	−	PROPN
ejpam-6147	282	10	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	282	11	m.	m.	NOUN
ejpam-6147	282	12	sarwar	sarwar	NOUN
ejpam-6147	282	13	et	et	PROPN
ejpam-6147	282	14	al	al	PROPN
ejpam-6147	282	15	.	.	PUNCT
ejpam-6147	282	16	/	/	SYM
ejpam-6147	282	17	eur	eur	PROPN
ejpam-6147	282	18	.	.	PUNCT
ejpam-6147	283	1	j.	j.	PROPN
ejpam-6147	283	2	pure	pure	PROPN
ejpam-6147	283	3	appl	appl	PROPN
ejpam-6147	283	4	.	.	PROPN
ejpam-6147	283	5	math	math	PROPN
ejpam-6147	283	6	,	,	PUNCT
ejpam-6147	283	7	18	18	NUM
ejpam-6147	283	8	(	(	PUNCT
ejpam-6147	283	9	3	3	NUM
ejpam-6147	283	10	)	)	PUNCT
ejpam-6147	283	11	(	(	PUNCT
ejpam-6147	283	12	2025	2025	NUM
ejpam-6147	283	13	)	)	PUNCT
ejpam-6147	283	14	,	,	PUNCT
ejpam-6147	283	15	6147	6147	NUM
ejpam-6147	283	16	14	14	NUM
ejpam-6147	283	17	of	of	ADP
ejpam-6147	283	18	18	18	NUM
ejpam-6147	283	19	=	=	SYM
ejpam-6147	283	20	⟨ηnλn(ςn	⟨ηnλn(ςn	NOUN
ejpam-6147	283	21	−	−	NOUN
ejpam-6147	283	22	ς∗)−	ς∗)−	NOUN
ejpam-6147	283	23	ηn(1−	ηn(1−	PRON
ejpam-6147	284	1	λn)ς	λn)ς	ADP
ejpam-6147	284	2	∗	∗	NOUN
ejpam-6147	284	3	+	+	CCONJ
ejpam-6147	284	4	(	(	PUNCT
ejpam-6147	284	5	1−	1−	NUM
ejpam-6147	284	6	ηn)(vn	ηn)(vn	X
ejpam-6147	284	7	−	−	PROPN
ejpam-6147	284	8	ς∗),	ς∗),	X
ejpam-6147	284	9	℧	℧	NOUN
ejpam-6147	284	10	n	n	NUM
ejpam-6147	284	11	−	−	PROPN
ejpam-6147	284	12	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	284	13	=	=	SYM
ejpam-6147	284	14	ηnλn⟨ςn	ηnλn⟨ςn	PROPN
ejpam-6147	285	1	−	−	PROPN
ejpam-6147	285	2	ς∗,	ς∗,	NUM
ejpam-6147	285	3	℧	℧	PROPN
ejpam-6147	285	4	n	n	NUM
ejpam-6147	285	5	−	−	PROPN
ejpam-6147	285	6	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	285	7	−	−	PUNCT
ejpam-6147	285	8	ηn(1−	ηn(1−	PROPN
ejpam-6147	285	9	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	285	10	℧	℧	PROPN
ejpam-6147	285	11	n	n	PRON
ejpam-6147	285	12	−	−	PROPN
ejpam-6147	285	13	ς∗⟩	ς∗⟩	NUM
ejpam-6147	285	14	+	+	NOUN
ejpam-6147	285	15	(	(	PUNCT
ejpam-6147	285	16	1−	1−	NUM
ejpam-6147	285	17	ηn)⟨vn	ηn)⟨vn	PROPN
ejpam-6147	286	1	−	−	PROPN
ejpam-6147	286	2	ς∗,	ς∗,	NUM
ejpam-6147	286	3	℧	℧	PROPN
ejpam-6147	286	4	n	n	NUM
ejpam-6147	286	5	−	−	PROPN
ejpam-6147	286	6	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	286	7	=	=	SYM
ejpam-6147	286	8	ηnλn∥ςn	ηnλn∥ςn	PROPN
ejpam-6147	286	9	−	−	PROPN
ejpam-6147	286	10	ς∗∥∥	ς∗∥∥	NOUN
ejpam-6147	286	11	℧	℧	PROPN
ejpam-6147	286	12	n	n	ADP
ejpam-6147	286	13	−	−	PROPN
ejpam-6147	286	14	ς∗∥	ς∗∥	NOUN
ejpam-6147	286	15	−	−	ADP
ejpam-6147	286	16	ηn(1−	ηn(1−	PROPN
ejpam-6147	286	17	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	286	18	℧	℧	PROPN
ejpam-6147	286	19	n	n	PRON
ejpam-6147	286	20	−	−	PROPN
ejpam-6147	286	21	ς∗⟩	ς∗⟩	NUM
ejpam-6147	286	22	+	+	NOUN
ejpam-6147	286	23	(	(	PUNCT
ejpam-6147	286	24	1−	1−	NUM
ejpam-6147	286	25	ηn)∥vn	ηn)∥vn	PROPN
ejpam-6147	286	26	−	−	PROPN
ejpam-6147	286	27	ς∗∥∥	ς∗∥∥	PROPN
ejpam-6147	286	28	℧	℧	PROPN
ejpam-6147	286	29	n	n	ADP
ejpam-6147	286	30	−	−	PROPN
ejpam-6147	286	31	ς∗∥	ς∗∥	PROPN
ejpam-6147	286	32	≤	≤	PROPN
ejpam-6147	286	33	ηnλn∥ςn	ηnλn∥ςn	PROPN
ejpam-6147	286	34	−	−	PROPN
ejpam-6147	286	35	ς∗∥∥	ς∗∥∥	NOUN
ejpam-6147	286	36	℧	℧	PROPN
ejpam-6147	286	37	n	n	ADP
ejpam-6147	286	38	−	−	PROPN
ejpam-6147	286	39	ς∗∥	ς∗∥	NOUN
ejpam-6147	286	40	−	−	ADP
ejpam-6147	286	41	ηn(1−	ηn(1−	PROPN
ejpam-6147	286	42	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	286	43	℧	℧	PROPN
ejpam-6147	286	44	n	n	PRON
ejpam-6147	286	45	−	−	PROPN
ejpam-6147	286	46	ς∗⟩	ς∗⟩	NUM
ejpam-6147	286	47	+	+	NOUN
ejpam-6147	286	48	(	(	PUNCT
ejpam-6147	286	49	1−	1−	NUM
ejpam-6147	286	50	ηn)∥ςn	ηn)∥ςn	NOUN
ejpam-6147	286	51	−	−	NOUN
ejpam-6147	286	52	ς∗∥∥	ς∗∥∥	NOUN
ejpam-6147	286	53	℧	℧	NOUN
ejpam-6147	286	54	n	n	ADP
ejpam-6147	286	55	−	−	PROPN
ejpam-6147	286	56	ς∗∥	ς∗∥	NOUN
ejpam-6147	286	57	=	=	SYM
ejpam-6147	287	1	[	[	X
ejpam-6147	287	2	1−	1−	NUM
ejpam-6147	287	3	(	(	PUNCT
ejpam-6147	287	4	1−	1−	NUM
ejpam-6147	287	5	λn)ηn]∥ςn	λn)ηn]∥ςn	NOUN
ejpam-6147	287	6	−	−	PROPN
ejpam-6147	287	7	ς∗∥∥	ς∗∥∥	PROPN
ejpam-6147	287	8	℧	℧	PROPN
ejpam-6147	287	9	n	n	ADP
ejpam-6147	287	10	−	−	PROPN
ejpam-6147	287	11	ς∗∥	ς∗∥	NOUN
ejpam-6147	287	12	−	−	ADP
ejpam-6147	287	13	ηn(1−	ηn(1−	PROPN
ejpam-6147	287	14	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	287	15	℧	℧	PROPN
ejpam-6147	287	16	n	n	PRON
ejpam-6147	287	17	−	−	PROPN
ejpam-6147	287	18	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	287	19	≤	≤	NOUN
ejpam-6147	288	1	[	[	X
ejpam-6147	288	2	1−	1−	NUM
ejpam-6147	288	3	(	(	PUNCT
ejpam-6147	288	4	1−	1−	NUM
ejpam-6147	288	5	λn)ηn	λn)ηn	X
ejpam-6147	288	6	]	]	X
ejpam-6147	288	7	2	2	NUM
ejpam-6147	288	8	∥ςn	∥ςn	NOUN
ejpam-6147	288	9	−	−	NOUN
ejpam-6147	288	10	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	288	11	+	+	CCONJ
ejpam-6147	288	12	1	1	NUM
ejpam-6147	288	13	2	2	NUM
ejpam-6147	288	14	∥	∥	NUM
ejpam-6147	288	15	℧	℧	NOUN
ejpam-6147	288	16	n	n	ADP
ejpam-6147	288	17	−	−	PROPN
ejpam-6147	288	18	ς∗∥	ς∗∥	NOUN
ejpam-6147	288	19	−	−	ADP
ejpam-6147	288	20	ηn(1−	ηn(1−	PROPN
ejpam-6147	288	21	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	288	22	℧	℧	PROPN
ejpam-6147	288	23	n	n	PRON
ejpam-6147	288	24	−	−	PROPN
ejpam-6147	288	25	ς∗⟩	ς∗⟩	NUM
ejpam-6147	288	26	,	,	PUNCT
ejpam-6147	288	27	that	that	ADV
ejpam-6147	288	28	is	is	ADV
ejpam-6147	288	29	,	,	PUNCT
ejpam-6147	288	30	∥ςn	∥ςn	PROPN
ejpam-6147	288	31	−	−	NOUN
ejpam-6147	288	32	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	288	33	≤	≤	NOUN
ejpam-6147	289	1	[	[	X
ejpam-6147	289	2	1−	1−	NUM
ejpam-6147	289	3	(	(	PUNCT
ejpam-6147	289	4	1−	1−	NUM
ejpam-6147	289	5	λn)ηn]∥ςn	λn)ηn]∥ςn	NOUN
ejpam-6147	289	6	−	−	PROPN
ejpam-6147	289	7	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	8	−	−	PROPN
ejpam-6147	289	9	2ηn(1−	2ηn(1−	NUM
ejpam-6147	289	10	λn)⟨ς∗,	λn)⟨ς∗,	PROPN
ejpam-6147	289	11	℧	℧	PROPN
ejpam-6147	289	12	n	n	PRON
ejpam-6147	289	13	−	−	NOUN
ejpam-6147	289	14	ς∗⟩.	ς∗⟩.	PUNCT
ejpam-6147	289	15	by	by	ADP
ejpam-6147	289	16	the	the	DET
ejpam-6147	289	17	convexity	convexity	NOUN
ejpam-6147	289	18	of	of	ADP
ejpam-6147	289	19	norm	norm	NOUN
ejpam-6147	289	20	,	,	PUNCT
ejpam-6147	289	21	we	we	PRON
ejpam-6147	289	22	have	have	VERB
ejpam-6147	289	23	∥ςn+1	∥ςn+1	NOUN
ejpam-6147	289	24	−	−	PROPN
ejpam-6147	289	25	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	26	≤	≤	NUM
ejpam-6147	289	27	(	(	PUNCT
ejpam-6147	289	28	1−	1−	NUM
ejpam-6147	289	29	η)∥ςn	η)∥ςn	NOUN
ejpam-6147	289	30	−	−	NOUN
ejpam-6147	289	31	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	32	+	+	CCONJ
ejpam-6147	289	33	η∥	η∥	PROPN
ejpam-6147	289	34	℧	℧	PROPN
ejpam-6147	289	35	n	n	CCONJ
ejpam-6147	289	36	−	−	PROPN
ejpam-6147	289	37	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	38	≤	≤	NUM
ejpam-6147	289	39	(	(	PUNCT
ejpam-6147	289	40	1−	1−	NUM
ejpam-6147	289	41	η)∥ςn	η)∥ςn	NOUN
ejpam-6147	289	42	−	−	NOUN
ejpam-6147	289	43	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	44	+	+	PROPN
ejpam-6147	289	45	η	η	X
ejpam-6147	289	46	(	(	PUNCT
ejpam-6147	289	47	[	[	X
ejpam-6147	289	48	1−	1−	NUM
ejpam-6147	289	49	(	(	PUNCT
ejpam-6147	289	50	1−	1−	NUM
ejpam-6147	289	51	λn)ηn]∥ςn	λn)ηn]∥ςn	NOUN
ejpam-6147	289	52	−	−	PROPN
ejpam-6147	289	53	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	289	54	−	−	NOUN
ejpam-6147	289	55	2ηn(1−	2ηn(1−	NUM
ejpam-6147	289	56	λn)⟨ς∗	λn)⟨ς∗	NOUN
ejpam-6147	289	57	,	,	PUNCT
ejpam-6147	289	58	ςn	ςn	NOUN
ejpam-6147	289	59	−	−	PROPN
ejpam-6147	289	60	ς∗⟩	ς∗⟩	PROPN
ejpam-6147	289	61	)	)	PUNCT
ejpam-6147	289	62	=	=	PUNCT
ejpam-6147	290	1	[	[	X
ejpam-6147	290	2	1−	1−	NUM
ejpam-6147	290	3	(	(	PUNCT
ejpam-6147	290	4	1−	1−	NUM
ejpam-6147	290	5	λn)ηnη]∥ςn	λn)ηnη]∥ςn	NOUN
ejpam-6147	290	6	−	−	PROPN
ejpam-6147	290	7	ς∗∥2	ς∗∥2	NOUN
ejpam-6147	290	8	−	−	PROPN
ejpam-6147	290	9	2(1−	2(1−	NUM
ejpam-6147	290	10	λn)ηnη⟨ς∗,	λn)ηnη⟨ς∗,	PROPN
ejpam-6147	290	11	℧	℧	PROPN
ejpam-6147	290	12	n	n	NUM
ejpam-6147	290	13	−	−	NOUN
ejpam-6147	290	14	ς∗⟩.	ς∗⟩.	PUNCT
ejpam-6147	291	1	so	so	ADV
ejpam-6147	291	2	all	all	DET
ejpam-6147	291	3	the	the	DET
ejpam-6147	291	4	conditions	condition	NOUN
ejpam-6147	291	5	of	of	ADP
ejpam-6147	291	6	lemma	lemma	PROPN
ejpam-6147	291	7	1	1	NUM
ejpam-6147	291	8	are	be	AUX
ejpam-6147	291	9	satisfied	satisfied	ADJ
ejpam-6147	291	10	.	.	PUNCT
ejpam-6147	292	1	therefore	therefore	ADV
ejpam-6147	292	2	,	,	PUNCT
ejpam-6147	292	3	we	we	PRON
ejpam-6147	292	4	obtain	obtain	VERB
ejpam-6147	292	5	that	that	SCONJ
ejpam-6147	292	6	ςn	ςn	PROPN
ejpam-6147	292	7	→	→	SYM
ejpam-6147	292	8	ς∗.	ς∗.	PROPN
ejpam-6147	292	9	if	if	SCONJ
ejpam-6147	292	10	we	we	PRON
ejpam-6147	292	11	put	put	VERB
ejpam-6147	292	12	1	1	NUM
ejpam-6147	292	13	instead	instead	ADV
ejpam-6147	292	14	of	of	ADP
ejpam-6147	292	15	µn	µn	NOUN
ejpam-6147	292	16	,	,	PUNCT
ejpam-6147	292	17	∀	∀	X
ejpam-6147	292	18	n	n	PRON
ejpam-6147	292	19	≥	≥	NOUN
ejpam-6147	292	20	0	0	NUM
ejpam-6147	292	21	,	,	PUNCT
ejpam-6147	292	22	in	in	ADP
ejpam-6147	292	23	theorem	theorem	NOUN
ejpam-6147	292	24	2	2	NUM
ejpam-6147	292	25	,	,	PUNCT
ejpam-6147	292	26	then	then	ADV
ejpam-6147	292	27	we	we	PRON
ejpam-6147	292	28	have	have	VERB
ejpam-6147	292	29	the	the	DET
ejpam-6147	292	30	following	follow	VERB
ejpam-6147	292	31	result	result	NOUN
ejpam-6147	292	32	.	.	PUNCT
ejpam-6147	293	1	corollary	corollary	ADJ
ejpam-6147	293	2	1	1	NUM
ejpam-6147	293	3	.	.	PUNCT
ejpam-6147	294	1	let	let	VERB
ejpam-6147	294	2	e	e	NOUN
ejpam-6147	294	3	=	=	PRON
ejpam-6147	294	4	{	{	PUNCT
ejpam-6147	294	5	e(s	e(s	PROPN
ejpam-6147	294	6	,	,	PUNCT
ejpam-6147	294	7	0)}s≥0	0)}s≥0	X
ejpam-6147	294	8	:	:	PUNCT
ejpam-6147	294	9	z	z	X
ejpam-6147	294	10	→	→	SYM
ejpam-6147	294	11	z	z	AUX
ejpam-6147	294	12	be	be	AUX
ejpam-6147	294	13	nonexpansive	nonexpansive	ADJ
ejpam-6147	294	14	family	family	NOUN
ejpam-6147	294	15	with	with	ADP
ejpam-6147	294	16	condition	condition	NOUN
ejpam-6147	294	17	fe	fe	NOUN
ejpam-6147	294	18	̸=	̸=	PROPN
ejpam-6147	294	19	∅.	∅.	ADV
ejpam-6147	294	20	let	let	VERB
ejpam-6147	294	21	{	{	PUNCT
ejpam-6147	294	22	ςn	ςn	AUX
ejpam-6147	294	23	}	}	PUNCT
ejpam-6147	294	24	be	be	AUX
ejpam-6147	294	25	the	the	DET
ejpam-6147	294	26	sequence	sequence	NOUN
ejpam-6147	294	27	ςn+1	ςn+1	NUM
ejpam-6147	294	28	=	=	SYM
ejpam-6147	294	29	(	(	PUNCT
ejpam-6147	294	30	1−	1−	NUM
ejpam-6147	294	31	µn)ςn	µn)ςn	PUNCT
ejpam-6147	295	1	+	+	X
ejpam-6147	295	2	µnpz	µnpz	ADJ
ejpam-6147	295	3	[	[	X
ejpam-6147	295	4	(	(	PUNCT
ejpam-6147	295	5	1−	1−	NUM
ejpam-6147	295	6	ηn	ηn	ADJ
ejpam-6147	295	7	)	)	PUNCT
ejpam-6147	295	8	γn	γn	NOUN
ejpam-6147	295	9	∫	∫	PROPN
ejpam-6147	296	1	γn	γn	ADP
ejpam-6147	296	2	0	0	NUM
ejpam-6147	296	3	e(s	e(s	PROPN
ejpam-6147	296	4	,	,	PUNCT
ejpam-6147	296	5	0)ςnds+	0)ςnds+	PROPN
ejpam-6147	296	6	ηn(λnςn	ηn(λnςn	PROPN
ejpam-6147	296	7	)	)	PUNCT
ejpam-6147	296	8	]	]	PUNCT
ejpam-6147	296	9	,	,	PUNCT
ejpam-6147	296	10	∀n	∀n	NUM
ejpam-6147	296	11	≥	≥	NOUN
ejpam-6147	296	12	0	0	NUM
ejpam-6147	296	13	.	.	PUNCT
ejpam-6147	297	1	(	(	PUNCT
ejpam-6147	297	2	12	12	NUM
ejpam-6147	297	3	)	)	PUNCT
ejpam-6147	297	4	where	where	SCONJ
ejpam-6147	297	5	{	{	PUNCT
ejpam-6147	297	6	ηn	ηn	ADJ
ejpam-6147	297	7	}	}	PUNCT
ejpam-6147	297	8	,	,	PUNCT
ejpam-6147	297	9	{	{	PUNCT
ejpam-6147	297	10	µn	µn	NOUN
ejpam-6147	297	11	}	}	PUNCT
ejpam-6147	297	12	and	and	CCONJ
ejpam-6147	297	13	{	{	PUNCT
ejpam-6147	297	14	λn	λn	NOUN
ejpam-6147	297	15	}	}	PUNCT
ejpam-6147	297	16	are	be	AUX
ejpam-6147	297	17	sequences	sequence	NOUN
ejpam-6147	297	18	in	in	ADP
ejpam-6147	297	19	[	[	X
ejpam-6147	297	20	0	0	NUM
ejpam-6147	297	21	,	,	PUNCT
ejpam-6147	297	22	1	1	NUM
ejpam-6147	297	23	]	]	PUNCT
ejpam-6147	297	24	and	and	CCONJ
ejpam-6147	297	25	{	{	PUNCT
ejpam-6147	297	26	γn	γn	NOUN
ejpam-6147	297	27	}	}	PUNCT
ejpam-6147	297	28	is	be	AUX
ejpam-6147	297	29	a	a	DET
ejpam-6147	297	30	sequence	sequence	NOUN
ejpam-6147	297	31	in	in	ADP
ejpam-6147	297	32	(	(	PUNCT
ejpam-6147	297	33	0,∞	0,∞	NOUN
ejpam-6147	297	34	)	)	PUNCT
ejpam-6147	297	35	.	.	PUNCT
ejpam-6147	298	1	suppose	suppose	VERB
ejpam-6147	298	2	the	the	DET
ejpam-6147	298	3	following	follow	VERB
ejpam-6147	298	4	axioms	axiom	NOUN
ejpam-6147	298	5	holds	hold	VERB
ejpam-6147	298	6	:	:	PUNCT
ejpam-6147	298	7	(	(	PUNCT
ejpam-6147	298	8	i	i	NOUN
ejpam-6147	298	9	)	)	PUNCT
ejpam-6147	298	10	limn→+∞	limn→+∞	VERB
ejpam-6147	298	11	ηn	ηn	PROPN
ejpam-6147	298	12	=	=	PUNCT
ejpam-6147	298	13	0,σ+∞	0,σ+∞	NUM
ejpam-6147	298	14	n=0ηn	n=0ηn	X
ejpam-6147	298	15	=	=	PUNCT
ejpam-6147	299	1	+	+	PUNCT
ejpam-6147	299	2	∞	∞	NUM
ejpam-6147	299	3	and	and	CCONJ
ejpam-6147	299	4	limn→∞	limn→∞	PROPN
ejpam-6147	299	5	λn	λn	X
ejpam-6147	299	6	=	=	SYM
ejpam-6147	299	7	1	1	NUM
ejpam-6147	299	8	;	;	PUNCT
ejpam-6147	299	9	(	(	PUNCT
ejpam-6147	299	10	ii	ii	NOUN
ejpam-6147	299	11	)	)	PUNCT
ejpam-6147	299	12	limn→+∞	limn→+∞	VERB
ejpam-6147	299	13	γn	γn	NOUN
ejpam-6147	299	14	=	=	SYM
ejpam-6147	299	15	∞	∞	PROPN
ejpam-6147	299	16	and	and	CCONJ
ejpam-6147	299	17	limn→+∞	limn→+∞	ADP
ejpam-6147	299	18	γn−1	γn−1	PROPN
ejpam-6147	299	19	γn	γn	NOUN
ejpam-6147	299	20	=	=	SYM
ejpam-6147	299	21	1	1	X
ejpam-6147	299	22	.	.	PUNCT
ejpam-6147	300	1	then	then	ADV
ejpam-6147	300	2	the	the	DET
ejpam-6147	300	3	sequence	sequence	NOUN
ejpam-6147	300	4	{	{	PUNCT
ejpam-6147	300	5	ςn	ςn	NOUN
ejpam-6147	300	6	}	}	PUNCT
ejpam-6147	300	7	strongly	strongly	ADV
ejpam-6147	300	8	converge	converge	VERB
ejpam-6147	300	9	to	to	ADP
ejpam-6147	300	10	a	a	DET
ejpam-6147	300	11	point	point	NOUN
ejpam-6147	300	12	ς∗	ς∗	NOUN
ejpam-6147	300	13	∈	∈	PROPN
ejpam-6147	300	14	fe	fe	PROPN
ejpam-6147	300	15	.	.	PROPN
ejpam-6147	300	16	remark	remark	PROPN
ejpam-6147	300	17	4	4	NUM
ejpam-6147	300	18	.	.	PUNCT
ejpam-6147	301	1	the	the	DET
ejpam-6147	301	2	algorithm	algorithm	NOUN
ejpam-6147	301	3	ςn+1	ςn+1	NUM
ejpam-6147	301	4	=	=	SYM
ejpam-6147	301	5	(	(	PUNCT
ejpam-6147	301	6	1−	1−	NUM
ejpam-6147	301	7	µn)ςn	µn)ςn	PUNCT
ejpam-6147	301	8	+	+	X
ejpam-6147	301	9	µnpz	µnpz	ADV
ejpam-6147	301	10	[	[	PUNCT
ejpam-6147	301	11	ηn(λnςn	ηn(λnςn	NOUN
ejpam-6147	301	12	)	)	PUNCT
ejpam-6147	301	13	+	+	CCONJ
ejpam-6147	301	14	(	(	PUNCT
ejpam-6147	301	15	1−	1−	NUM
ejpam-6147	301	16	ηn	ηn	ADJ
ejpam-6147	301	17	)	)	PUNCT
ejpam-6147	301	18	1	1	NUM
ejpam-6147	301	19	γn	γn	ADP
ejpam-6147	301	20	∫	∫	PROPN
ejpam-6147	301	21	γn	γn	ADP
ejpam-6147	301	22	0	0	PUNCT
ejpam-6147	301	23	e(s	e(s	PROPN
ejpam-6147	301	24	,	,	PUNCT
ejpam-6147	301	25	0)ςnds	0)ςnds	NUM
ejpam-6147	301	26	]	]	PUNCT
ejpam-6147	301	27	,	,	PUNCT
ejpam-6147	301	28	∀n	∀n	NUM
ejpam-6147	301	29	≥	≥	NOUN
ejpam-6147	301	30	0	0	NUM
ejpam-6147	301	31	,	,	PUNCT
ejpam-6147	301	32	has	have	VERB
ejpam-6147	301	33	just	just	ADV
ejpam-6147	301	34	weak	weak	ADJ
ejpam-6147	301	35	convergence	convergence	NOUN
ejpam-6147	301	36	.	.	PUNCT
ejpam-6147	302	1	but	but	CCONJ
ejpam-6147	302	2	,	,	PUNCT
ejpam-6147	302	3	the	the	DET
ejpam-6147	302	4	sequence	sequence	NOUN
ejpam-6147	302	5	(	(	PUNCT
ejpam-6147	302	6	8)	8)	NUM
ejpam-6147	302	7	(	(	PUNCT
ejpam-6147	302	8	with	with	ADP
ejpam-6147	302	9	λn	λn	PROPN
ejpam-6147	302	10	→	→	SYM
ejpam-6147	302	11	1	1	NUM
ejpam-6147	302	12	)	)	PUNCT
ejpam-6147	302	13	has	have	VERB
ejpam-6147	302	14	strong	strong	ADJ
ejpam-6147	302	15	convergence	convergence	NOUN
ejpam-6147	302	16	.	.	PUNCT
ejpam-6147	303	1	m.	m.	NOUN
ejpam-6147	303	2	sarwar	sarwar	PROPN
ejpam-6147	303	3	et	et	PROPN
ejpam-6147	303	4	al	al	PROPN
ejpam-6147	303	5	.	.	PUNCT
ejpam-6147	303	6	/	/	SYM
ejpam-6147	303	7	eur	eur	PROPN
ejpam-6147	303	8	.	.	PUNCT
ejpam-6147	304	1	j.	j.	PROPN
ejpam-6147	304	2	pure	pure	PROPN
ejpam-6147	304	3	appl	appl	PROPN
ejpam-6147	304	4	.	.	PROPN
ejpam-6147	304	5	math	math	PROPN
ejpam-6147	304	6	,	,	PUNCT
ejpam-6147	304	7	18	18	NUM
ejpam-6147	304	8	(	(	PUNCT
ejpam-6147	304	9	3	3	NUM
ejpam-6147	304	10	)	)	PUNCT
ejpam-6147	304	11	(	(	PUNCT
ejpam-6147	304	12	2025	2025	NUM
ejpam-6147	304	13	)	)	PUNCT
ejpam-6147	304	14	,	,	PUNCT
ejpam-6147	304	15	6147	6147	NUM
ejpam-6147	304	16	15	15	NUM
ejpam-6147	304	17	of	of	ADP
ejpam-6147	304	18	18	18	NUM
ejpam-6147	304	19	using	use	VERB
ejpam-6147	304	20	remark	remark	NOUN
ejpam-6147	304	21	2	2	NUM
ejpam-6147	304	22	,	,	PUNCT
ejpam-6147	304	23	we	we	PRON
ejpam-6147	304	24	have	have	VERB
ejpam-6147	304	25	the	the	DET
ejpam-6147	304	26	following	follow	VERB
ejpam-6147	304	27	remark	remark	NOUN
ejpam-6147	304	28	.	.	PUNCT
ejpam-6147	305	1	remark	remark	PROPN
ejpam-6147	305	2	5	5	NUM
ejpam-6147	305	3	.	.	PUNCT
ejpam-6147	306	1	the	the	DET
ejpam-6147	306	2	results	result	NOUN
ejpam-6147	306	3	given	give	VERB
ejpam-6147	306	4	in	in	ADP
ejpam-6147	306	5	[	[	PUNCT
ejpam-6147	306	6	9	9	NUM
ejpam-6147	306	7	]	]	PUNCT
ejpam-6147	306	8	,	,	PUNCT
ejpam-6147	306	9	become	become	VERB
ejpam-6147	306	10	special	special	ADJ
ejpam-6147	306	11	case	case	NOUN
ejpam-6147	306	12	of	of	ADP
ejpam-6147	306	13	our	our	PRON
ejpam-6147	306	14	work	work	NOUN
ejpam-6147	306	15	,	,	PUNCT
ejpam-6147	306	16	if	if	SCONJ
ejpam-6147	306	17	an	an	DET
ejpam-6147	306	18	evolution	evolution	NOUN
ejpam-6147	306	19	family	family	NOUN
ejpam-6147	306	20	is	be	AUX
ejpam-6147	306	21	periodic	periodic	ADJ
ejpam-6147	306	22	of	of	ADP
ejpam-6147	306	23	every	every	DET
ejpam-6147	306	24	positive	positive	ADJ
ejpam-6147	306	25	real	real	ADJ
ejpam-6147	306	26	number	number	NOUN
ejpam-6147	306	27	.	.	PUNCT
ejpam-6147	307	1	4	4	NUM
ejpam-6147	307	2	.	.	NOUN
ejpam-6147	307	3	example	example	NOUN
ejpam-6147	307	4	and	and	CCONJ
ejpam-6147	307	5	open	open	ADJ
ejpam-6147	307	6	problem	problem	NOUN
ejpam-6147	307	7	example	example	NOUN
ejpam-6147	307	8	2	2	X
ejpam-6147	307	9	.	.	PUNCT
ejpam-6147	308	1	let	let	VERB
ejpam-6147	308	2	h	h	NOUN
ejpam-6147	308	3	:	:	PUNCT
ejpam-6147	308	4	=	=	SYM
ejpam-6147	308	5	l2([0	l2([0	X
ejpam-6147	308	6	,	,	PUNCT
ejpam-6147	308	7	π	π	NOUN
ejpam-6147	308	8	]	]	X
ejpam-6147	308	9	,	,	PUNCT
ejpam-6147	308	10	c	c	X
ejpam-6147	308	11	)	)	PUNCT
ejpam-6147	308	12	be	be	VERB
ejpam-6147	308	13	the	the	DET
ejpam-6147	308	14	hilbert	hilbert	NOUN
ejpam-6147	308	15	space	space	NOUN
ejpam-6147	308	16	of	of	ADP
ejpam-6147	308	17	all	all	DET
ejpam-6147	308	18	square	square	ADJ
ejpam-6147	308	19	integrable	integrable	ADJ
ejpam-6147	308	20	functions	function	NOUN
ejpam-6147	308	21	on	on	ADP
ejpam-6147	308	22	[	[	X
ejpam-6147	308	23	0	0	NUM
ejpam-6147	308	24	,	,	PUNCT
ejpam-6147	308	25	π	π	X
ejpam-6147	308	26	]	]	X
ejpam-6147	308	27	and	and	CCONJ
ejpam-6147	308	28	s	s	NOUN
ejpam-6147	308	29	=	=	SYM
ejpam-6147	308	30	{	{	PUNCT
ejpam-6147	308	31	s(a	s(a	PROPN
ejpam-6147	308	32	)	)	PUNCT
ejpam-6147	308	33	:	:	PUNCT
ejpam-6147	308	34	a	a	DET
ejpam-6147	308	35	≥	≥	NOUN
ejpam-6147	308	36	0	0	NUM
ejpam-6147	308	37	}	}	PUNCT
ejpam-6147	308	38	be	be	AUX
ejpam-6147	308	39	a	a	DET
ejpam-6147	308	40	semigroup	semigroup	NOUN
ejpam-6147	308	41	defined	define	VERB
ejpam-6147	308	42	by	by	ADP
ejpam-6147	308	43	(	(	PUNCT
ejpam-6147	308	44	s(a)ϑ)(t	s(a)ϑ)(t	PROPN
ejpam-6147	308	45	)	)	PUNCT
ejpam-6147	308	46	=	=	SYM
ejpam-6147	308	47	2	2	NUM
ejpam-6147	308	48	π	π	PROPN
ejpam-6147	308	49	∞∑	∞∑	PROPN
ejpam-6147	308	50	m=1	m=1	AUX
ejpam-6147	308	51	e−am2	e−am2	NOUN
ejpam-6147	308	52	cm(ϑ	cm(ϑ	NOUN
ejpam-6147	308	53	)	)	PUNCT
ejpam-6147	308	54	sinmυ	sinmυ	NOUN
ejpam-6147	308	55	,	,	PUNCT
ejpam-6147	308	56	υ	υ	PROPN
ejpam-6147	308	57	∈	∈	PROPN
ejpam-6147	309	1	[	[	X
ejpam-6147	309	2	0	0	NUM
ejpam-6147	309	3	,	,	PUNCT
ejpam-6147	309	4	π	π	PROPN
ejpam-6147	309	5	]	]	X
ejpam-6147	309	6	,	,	PUNCT
ejpam-6147	309	7	a	a	DET
ejpam-6147	309	8	≥	≥	NOUN
ejpam-6147	309	9	0	0	NUM
ejpam-6147	309	10	,	,	PUNCT
ejpam-6147	309	11	(	(	PUNCT
ejpam-6147	309	12	13	13	NUM
ejpam-6147	309	13	)	)	PUNCT
ejpam-6147	309	14	where	where	SCONJ
ejpam-6147	309	15	cm(ϑ	cm(ϑ	NOUN
ejpam-6147	309	16	)	)	PUNCT
ejpam-6147	309	17	:	:	PUNCT
ejpam-6147	310	1	=	=	SYM
ejpam-6147	310	2	∫	∫	PROPN
ejpam-6147	310	3	π	π	PROPN
ejpam-6147	310	4	0	0	NUM
ejpam-6147	310	5	y(s	y(s	PROPN
ejpam-6147	310	6	)	)	PUNCT
ejpam-6147	310	7	sin(ms)ds	sin(ms)ds	PROPN
ejpam-6147	310	8	.	.	PUNCT
ejpam-6147	311	1	obviously	obviously	ADV
ejpam-6147	311	2	,	,	PUNCT
ejpam-6147	311	3	s	s	VERB
ejpam-6147	311	4	is	be	AUX
ejpam-6147	311	5	a	a	DET
ejpam-6147	311	6	strongly	strongly	ADV
ejpam-6147	311	7	continuous	continuous	ADJ
ejpam-6147	311	8	and	and	CCONJ
ejpam-6147	311	9	non	non	ADJ
ejpam-6147	311	10	-	-	ADJ
ejpam-6147	311	11	expansive	expansive	ADJ
ejpam-6147	311	12	semigroup	semigroup	NOUN
ejpam-6147	311	13	on	on	ADP
ejpam-6147	311	14	h	h	NOUN
ejpam-6147	311	15	and	and	CCONJ
ejpam-6147	311	16	it	it	PRON
ejpam-6147	311	17	is	be	AUX
ejpam-6147	311	18	generated	generate	VERB
ejpam-6147	311	19	by	by	ADP
ejpam-6147	311	20	the	the	DET
ejpam-6147	311	21	linear	linear	ADJ
ejpam-6147	311	22	operator	operator	NOUN
ejpam-6147	311	23	a	a	DET
ejpam-6147	311	24	given	give	VERB
ejpam-6147	311	25	by	by	ADP
ejpam-6147	311	26	ϑ̈	ϑ̈	NOUN
ejpam-6147	311	27	=	=	SYM
ejpam-6147	311	28	aϑ.	aϑ.	PROPN
ejpam-6147	311	29	now	now	ADV
ejpam-6147	311	30	consider	consider	VERB
ejpam-6147	311	31	the	the	PRON
ejpam-6147	311	32	following	follow	VERB
ejpam-6147	311	33	non	non	ADJ
ejpam-6147	311	34	-	-	ADJ
ejpam-6147	311	35	autonomous	autonomous	ADJ
ejpam-6147	311	36	cauchy	cauchy	NOUN
ejpam-6147	311	37	problem	problem	PUNCT
ejpam-6147	311	38	∂	∂	NUM
ejpam-6147	311	39	℧	℧	NOUN
ejpam-6147	311	40	(υ	(υ	NOUN
ejpam-6147	311	41	,	,	PUNCT
ejpam-6147	311	42	ζ	ζ	NOUN
ejpam-6147	311	43	)	)	PUNCT
ejpam-6147	311	44	∂υ	∂υ	NOUN
ejpam-6147	311	45	=	=	PUNCT
ejpam-6147	312	1	k(υ)∂	k(υ)∂	PROPN
ejpam-6147	312	2	2	2	NUM
ejpam-6147	312	3	℧	℧	NOUN
ejpam-6147	312	4	(υ	(υ	PROPN
ejpam-6147	312	5	,	,	PUNCT
ejpam-6147	312	6	ζ	ζ	NOUN
ejpam-6147	312	7	)	)	PUNCT
ejpam-6147	312	8	∂2ζ	∂2ζ	NOUN
ejpam-6147	312	9	,	,	PUNCT
ejpam-6147	312	10	υ	υ	PROPN
ejpam-6147	312	11	>	>	X
ejpam-6147	312	12	0	0	NUM
ejpam-6147	312	13	,	,	PUNCT
ejpam-6147	312	14	ζ	ζ	PROPN
ejpam-6147	312	15	∈	∈	NOUN
ejpam-6147	313	1	[	[	X
ejpam-6147	313	2	0	0	NUM
ejpam-6147	313	3	,	,	PUNCT
ejpam-6147	313	4	π	π	NOUN
ejpam-6147	313	5	]	]	X
ejpam-6147	313	6	,	,	PUNCT
ejpam-6147	313	7	℧	℧	PROPN
ejpam-6147	313	8	(	(	PUNCT
ejpam-6147	313	9	υ	υ	NOUN
ejpam-6147	313	10	,	,	PUNCT
ejpam-6147	313	11	0	0	NUM
ejpam-6147	313	12	)	)	PUNCT
ejpam-6147	313	13	=	=	SYM
ejpam-6147	313	14	℧	℧	PROPN
ejpam-6147	313	15	(	(	PUNCT
ejpam-6147	313	16	υ	υ	PROPN
ejpam-6147	313	17	,	,	PUNCT
ejpam-6147	313	18	π	π	NOUN
ejpam-6147	313	19	)	)	PUNCT
ejpam-6147	313	20	=	=	SYM
ejpam-6147	313	21	0	0	NUM
ejpam-6147	313	22	,	,	PUNCT
ejpam-6147	313	23	υ	υ	PRON
ejpam-6147	313	24	≥	≥	NOUN
ejpam-6147	313	25	0	0	NUM
ejpam-6147	313	26	,	,	PUNCT
ejpam-6147	313	27	℧	℧	PROPN
ejpam-6147	313	28	(	(	PUNCT
ejpam-6147	313	29	0	0	NUM
ejpam-6147	313	30	,	,	PUNCT
ejpam-6147	313	31	ζ	ζ	NOUN
ejpam-6147	313	32	)	)	PUNCT
ejpam-6147	313	33	=	=	PUNCT
ejpam-6147	313	34	q(ζ	q(ζ	NOUN
ejpam-6147	313	35	)	)	PUNCT
ejpam-6147	313	36	,	,	PUNCT
ejpam-6147	313	37	where	where	SCONJ
ejpam-6147	313	38	q(υ	q(υ	NOUN
ejpam-6147	313	39	)	)	PUNCT
ejpam-6147	313	40	∈	∈	PROPN
ejpam-6147	313	41	h	h	NOUN
ejpam-6147	313	42	,	,	PUNCT
ejpam-6147	313	43	and	and	CCONJ
ejpam-6147	313	44	k	k	NOUN
ejpam-6147	313	45	:	:	PUNCT
ejpam-6147	313	46	r+	r+	X
ejpam-6147	313	47	→	→	PUNCT
ejpam-6147	313	48	[	[	X
ejpam-6147	313	49	1,∞	1,∞	NUM
ejpam-6147	313	50	)	)	PUNCT
ejpam-6147	313	51	is	be	AUX
ejpam-6147	313	52	a	a	DET
ejpam-6147	313	53	non	non	ADJ
ejpam-6147	313	54	-	-	ADJ
ejpam-6147	313	55	expansive	expansive	ADJ
ejpam-6147	313	56	and	and	CCONJ
ejpam-6147	313	57	periodic	periodic	ADJ
ejpam-6147	313	58	function	function	NOUN
ejpam-6147	313	59	,	,	PUNCT
ejpam-6147	313	60	i.e.	i.e.	X
ejpam-6147	313	61	,	,	PUNCT
ejpam-6147	313	62	k(υ	k(υ	PROPN
ejpam-6147	313	63	+	+	CCONJ
ejpam-6147	313	64	p	p	X
ejpam-6147	313	65	)	)	PUNCT
ejpam-6147	313	66	=	=	SYM
ejpam-6147	313	67	k(υ	k(υ	PROPN
ejpam-6147	313	68	)	)	PUNCT
ejpam-6147	313	69	for	for	ADP
ejpam-6147	313	70	all	all	PRON
ejpam-6147	313	71	υ	υ	PRON
ejpam-6147	313	72	∈	∈	PROPN
ejpam-6147	313	73	r+	r+	NOUN
ejpam-6147	313	74	for	for	ADP
ejpam-6147	313	75	some	some	DET
ejpam-6147	313	76	p	p	NOUN
ejpam-6147	313	77	≥	≥	NUM
ejpam-6147	313	78	1	1	NUM
ejpam-6147	313	79	.	.	X
ejpam-6147	313	80	letk(υ	letk(υ	PROPN
ejpam-6147	313	81	)	)	PUNCT
ejpam-6147	314	1	=	=	SYM
ejpam-6147	314	2	∫	∫	PUNCT
ejpam-6147	315	1	υ	υ	PROPN
ejpam-6147	315	2	0	0	PROPN
ejpam-6147	315	3	k(υ)dυ	k(υ)dυ	PROPN
ejpam-6147	315	4	.	.	NOUN
ejpam-6147	316	1	clearly	clearly	ADV
ejpam-6147	316	2	the	the	DET
ejpam-6147	316	3	solution	solution	NOUN
ejpam-6147	316	4	y	y	PROPN
ejpam-6147	316	5	(	(	PUNCT
ejpam-6147	316	6	.	.	PUNCT
ejpam-6147	316	7	)	)	PUNCT
ejpam-6147	316	8	of	of	ADP
ejpam-6147	316	9	the	the	DET
ejpam-6147	316	10	above	above	PROPN
ejpam-6147	316	11	cauchy	cauchy	PROPN
ejpam-6147	316	12	problem	problem	NOUN
ejpam-6147	316	13	satisfies	satisfy	VERB
ejpam-6147	316	14	the	the	DET
ejpam-6147	316	15	evolution	evolution	NOUN
ejpam-6147	316	16	property	property	NOUN
ejpam-6147	316	17	:	:	PUNCT
ejpam-6147	316	18	y(υ	y(υ	PROPN
ejpam-6147	316	19	)	)	PUNCT
ejpam-6147	317	1	=	=	SYM
ejpam-6147	317	2	e(υ	e(υ	NOUN
ejpam-6147	317	3	,	,	PUNCT
ejpam-6147	317	4	ξ)y(ξ	ξ)y(ξ	NOUN
ejpam-6147	317	5	)	)	PUNCT
ejpam-6147	317	6	,	,	PUNCT
ejpam-6147	317	7	(	(	PUNCT
ejpam-6147	317	8	14	14	NUM
ejpam-6147	317	9	)	)	PUNCT
ejpam-6147	317	10	where	where	SCONJ
ejpam-6147	317	11	e(υ	e(υ	NOUN
ejpam-6147	317	12	,	,	PUNCT
ejpam-6147	317	13	ξ	ξ	NOUN
ejpam-6147	317	14	)	)	PUNCT
ejpam-6147	317	15	=	=	SYM
ejpam-6147	317	16	s(k(υ)−k(ξ	s(k(υ)−k(ξ	NOUN
ejpam-6147	317	17	)	)	PUNCT
ejpam-6147	317	18	)	)	PUNCT
ejpam-6147	317	19	.	.	PUNCT
ejpam-6147	318	1	see	see	VERB
ejpam-6147	319	1	[	[	X
ejpam-6147	319	2	[	[	X
ejpam-6147	319	3	25	25	NUM
ejpam-6147	319	4	]	]	PUNCT
ejpam-6147	319	5	,	,	PUNCT
ejpam-6147	319	6	example	example	NOUN
ejpam-6147	319	7	2.9b	2.9b	NUM
ejpam-6147	319	8	]	]	X
ejpam-6147	319	9	.	.	PUNCT
ejpam-6147	320	1	we	we	PRON
ejpam-6147	320	2	can	can	AUX
ejpam-6147	320	3	find	find	VERB
ejpam-6147	320	4	ϑ	ϑ	PRON
ejpam-6147	320	5	≥	≥	NOUN
ejpam-6147	320	6	0	0	NUM
ejpam-6147	320	7	such	such	ADJ
ejpam-6147	320	8	that	that	SCONJ
ejpam-6147	320	9	the	the	DET
ejpam-6147	320	10	function	function	NOUN
ejpam-6147	320	11	υ	υ	PROPN
ejpam-6147	320	12	7→	7→	NUM
ejpam-6147	320	13	eϑυ∥	eϑυ∥	PROPN
ejpam-6147	320	14	℧	℧	PROPN
ejpam-6147	320	15	(υ)∥	(υ)∥	PROPN
ejpam-6147	320	16	is	be	AUX
ejpam-6147	320	17	bounded	bound	VERB
ejpam-6147	320	18	on	on	ADP
ejpam-6147	320	19	r+	r+	X
ejpam-6147	320	20	.	.	PUNCT
ejpam-6147	321	1	in	in	ADP
ejpam-6147	321	2	fact	fact	NOUN
ejpam-6147	321	3	,	,	PUNCT
ejpam-6147	321	4	we	we	PRON
ejpam-6147	321	5	have∫	have∫	VERB
ejpam-6147	321	6	+	+	NOUN
ejpam-6147	321	7	∞	∞	NOUN
ejpam-6147	321	8	0	0	NUM
ejpam-6147	321	9	∥e(υ	∥e(υ	NOUN
ejpam-6147	321	10	,	,	PUNCT
ejpam-6147	321	11	0)ϑ∥2dυ	0)ϑ∥2dυ	NOUN
ejpam-6147	321	12	=	=	SYM
ejpam-6147	321	13	2	2	NUM
ejpam-6147	321	14	π	π	NOUN
ejpam-6147	321	15	∫	∫	PROPN
ejpam-6147	322	1	+	+	ADJ
ejpam-6147	322	2	∞	∞	NOUN
ejpam-6147	322	3	0	0	PUNCT
ejpam-6147	323	1	+	+	ADJ
ejpam-6147	323	2	∞∑	∞∑	ADJ
ejpam-6147	323	3	ϑ=1	ϑ=1	DET
ejpam-6147	323	4	c2ϑ(ϑ)e	c2ϑ(ϑ)e	ADJ
ejpam-6147	323	5	−2ϑ2k(υ)dυ	−2ϑ2k(υ)dυ	NOUN
ejpam-6147	323	6	=	=	SYM
ejpam-6147	323	7	2	2	NUM
ejpam-6147	323	8	π	π	X
ejpam-6147	323	9	+	+	ADP
ejpam-6147	323	10	∞∑	∞∑	ADJ
ejpam-6147	323	11	ϑ=1	ϑ=1	NUM
ejpam-6147	323	12	c2ϑ(ϑ	c2ϑ(ϑ	PROPN
ejpam-6147	323	13	)	)	PUNCT
ejpam-6147	323	14	∫	∫	PROPN
ejpam-6147	324	1	+	+	PROPN
ejpam-6147	324	2	∞	∞	NOUN
ejpam-6147	324	3	0	0	PUNCT
ejpam-6147	325	1	e−2ϑ2k(υ)dυ	e−2ϑ2k(υ)dυ	PROPN
ejpam-6147	325	2	=	=	SYM
ejpam-6147	325	3	∥ϑ∥22	∥ϑ∥22	PROPN
ejpam-6147	325	4	∫	∫	PROPN
ejpam-6147	326	1	+	+	NUM
ejpam-6147	326	2	∞	∞	NOUN
ejpam-6147	326	3	0	0	PUNCT
ejpam-6147	326	4	e−2ϑ2k(υ)dυ	e−2ϑ2k(υ)dυ	PROPN
ejpam-6147	326	5	=	=	SYM
ejpam-6147	326	6	∥ϑ∥22	∥ϑ∥22	PROPN
ejpam-6147	326	7	∫	∫	PROPN
ejpam-6147	327	1	+	+	NUM
ejpam-6147	327	2	∞	∞	PROPN
ejpam-6147	327	3	0	0	NUM
ejpam-6147	327	4	e−2k(υ)dυ	e−2k(υ)dυ	PROPN
ejpam-6147	327	5	.	.	PUNCT
ejpam-6147	328	1	(	(	PUNCT
ejpam-6147	328	2	15	15	NUM
ejpam-6147	328	3	)	)	PUNCT
ejpam-6147	328	4	now	now	ADV
ejpam-6147	328	5	consider	consider	VERB
ejpam-6147	328	6	∫	∫	PROPN
ejpam-6147	329	1	+	+	ADJ
ejpam-6147	329	2	∞	∞	NOUN
ejpam-6147	329	3	0	0	NUM
ejpam-6147	329	4	e−2k(υ)dυ	e−2k(υ)dυ	NOUN
ejpam-6147	329	5	=	=	PUNCT
ejpam-6147	330	1	+	+	PROPN
ejpam-6147	330	2	∞∑	∞∑	PROPN
ejpam-6147	330	3	j=0	j=0	PROPN
ejpam-6147	330	4	∫	∫	PROPN
ejpam-6147	330	5	(	(	PUNCT
ejpam-6147	330	6	j+1)z	j+1)z	PROPN
ejpam-6147	330	7	jz	jz	PROPN
ejpam-6147	330	8	e−2k(υ)dυ	e−2k(υ)dυ	PROPN
ejpam-6147	330	9	m.	m.	PROPN
ejpam-6147	330	10	sarwar	sarwar	PROPN
ejpam-6147	330	11	et	et	PROPN
ejpam-6147	330	12	al	al	PROPN
ejpam-6147	330	13	.	.	PUNCT
ejpam-6147	330	14	/	/	SYM
ejpam-6147	330	15	eur	eur	PROPN
ejpam-6147	330	16	.	.	PUNCT
ejpam-6147	331	1	j.	j.	PROPN
ejpam-6147	331	2	pure	pure	PROPN
ejpam-6147	331	3	appl	appl	PROPN
ejpam-6147	331	4	.	.	PROPN
ejpam-6147	331	5	math	math	PROPN
ejpam-6147	331	6	,	,	PUNCT
ejpam-6147	331	7	18	18	NUM
ejpam-6147	331	8	(	(	PUNCT
ejpam-6147	331	9	3	3	NUM
ejpam-6147	331	10	)	)	PUNCT
ejpam-6147	331	11	(	(	PUNCT
ejpam-6147	331	12	2025	2025	NUM
ejpam-6147	331	13	)	)	PUNCT
ejpam-6147	331	14	,	,	PUNCT
ejpam-6147	331	15	6147	6147	NUM
ejpam-6147	331	16	16	16	NUM
ejpam-6147	331	17	of	of	ADP
ejpam-6147	331	18	18	18	NUM
ejpam-6147	331	19	=	=	SYM
ejpam-6147	332	1	+	+	PROPN
ejpam-6147	332	2	∞∑	∞∑	NUM
ejpam-6147	332	3	j=0	j=0	PROPN
ejpam-6147	332	4	∫	∫	PROPN
ejpam-6147	332	5	z	z	PROPN
ejpam-6147	332	6	0	0	NUM
ejpam-6147	333	1	e−2k(jz+υ)dυ	e−2k(jz+υ)dυ	NOUN
ejpam-6147	333	2	=	=	PUNCT
ejpam-6147	334	1	+	+	ADJ
ejpam-6147	334	2	∞∑	∞∑	NUM
ejpam-6147	334	3	j=0	j=0	ADJ
ejpam-6147	334	4	e−2jk(z	e−2jk(z	PROPN
ejpam-6147	334	5	)	)	PUNCT
ejpam-6147	335	1	∫	∫	PROPN
ejpam-6147	335	2	z	z	NOUN
ejpam-6147	335	3	0	0	NUM
ejpam-6147	335	4	e−2k(υ)dυ	e−2k(υ)dυ	PROPN
ejpam-6147	335	5	≤	≤	NOUN
ejpam-6147	335	6	z	z	NOUN
ejpam-6147	336	1	+	+	ADP
ejpam-6147	336	2	∞∑	∞∑	NUM
ejpam-6147	336	3	j=0	j=0	ADJ
ejpam-6147	336	4	e−2jk(z	e−2jk(z	PROPN
ejpam-6147	336	5	)	)	PUNCT
ejpam-6147	337	1	=	=	SYM
ejpam-6147	337	2	ze2k(z	ze2k(z	X
ejpam-6147	337	3	)	)	PUNCT
ejpam-6147	337	4	e2k(z	e2k(z	PROPN
ejpam-6147	337	5	)	)	PUNCT
ejpam-6147	338	1	−	−	NOUN
ejpam-6147	338	2	1	1	NUM
ejpam-6147	338	3	:	:	PUNCT
ejpam-6147	338	4	=	=	SYM
ejpam-6147	338	5	c.	c.	PROPN
ejpam-6147	338	6	(	(	PUNCT
ejpam-6147	338	7	16	16	NUM
ejpam-6147	338	8	)	)	PUNCT
ejpam-6147	338	9	hence	hence	ADV
ejpam-6147	338	10	,	,	PUNCT
ejpam-6147	338	11	∫	∫	PROPN
ejpam-6147	339	1	+	+	ADJ
ejpam-6147	339	2	∞	∞	NOUN
ejpam-6147	339	3	0	0	NUM
ejpam-6147	339	4	∥e(υ	∥e(υ	NOUN
ejpam-6147	339	5	,	,	PUNCT
ejpam-6147	339	6	0)ϑ∥2dυ	0)ϑ∥2dυ	ADJ
ejpam-6147	339	7	≤	≤	NUM
ejpam-6147	339	8	c∥ϑ∥22	c∥ϑ∥22	PROPN
ejpam-6147	339	9	.	.	PUNCT
ejpam-6147	340	1	(	(	PUNCT
ejpam-6147	340	2	17	17	NUM
ejpam-6147	340	3	)	)	PUNCT
ejpam-6147	340	4	now	now	ADV
ejpam-6147	340	5	,	,	PUNCT
ejpam-6147	340	6	by	by	ADP
ejpam-6147	340	7	theorem	theorem	NOUN
ejpam-6147	340	8	8	8	NUM
ejpam-6147	340	9	in	in	ADP
ejpam-6147	340	10	[	[	X
ejpam-6147	340	11	26	26	NUM
ejpam-6147	340	12	]	]	PUNCT
ejpam-6147	340	13	,	,	PUNCT
ejpam-6147	340	14	for	for	ADP
ejpam-6147	340	15	m	m	PROPN
ejpam-6147	340	16	≥	≥	NOUN
ejpam-6147	340	17	1	1	NUM
ejpam-6147	340	18	the	the	DET
ejpam-6147	340	19	growth	growth	NOUN
ejpam-6147	340	20	bound	bind	VERB
ejpam-6147	340	21	ω0	ω0	NOUN
ejpam-6147	340	22	of	of	ADP
ejpam-6147	340	23	the	the	DET
ejpam-6147	340	24	family	family	NOUN
ejpam-6147	340	25	e	e	NOUN
ejpam-6147	340	26	satisfy	satisfy	NOUN
ejpam-6147	340	27	ω0	ω0	PROPN
ejpam-6147	340	28	≤	≤	NUM
ejpam-6147	340	29	−1	−1	NOUN
ejpam-6147	340	30	2	2	NUM
ejpam-6147	340	31	m	m	NOUN
ejpam-6147	340	32	,	,	PUNCT
ejpam-6147	340	33	for	for	SCONJ
ejpam-6147	340	34	further	further	ADJ
ejpam-6147	340	35	details	detail	NOUN
ejpam-6147	340	36	see	see	VERB
ejpam-6147	340	37	[	[	X
ejpam-6147	340	38	26	26	NUM
ejpam-6147	340	39	]	]	PUNCT
ejpam-6147	340	40	,	,	PUNCT
ejpam-6147	340	41	obviously	obviously	ADV
ejpam-6147	340	42	this	this	PRON
ejpam-6147	340	43	shows	show	VERB
ejpam-6147	340	44	that	that	SCONJ
ejpam-6147	340	45	the	the	DET
ejpam-6147	340	46	evolution	evolution	NOUN
ejpam-6147	340	47	family	family	NOUN
ejpam-6147	340	48	is	be	AUX
ejpam-6147	340	49	non	non	ADJ
ejpam-6147	340	50	-	-	ADJ
ejpam-6147	340	51	expansive	expansive	ADJ
ejpam-6147	340	52	on	on	ADP
ejpam-6147	340	53	the	the	DET
ejpam-6147	340	54	hilbert	hilbert	PROPN
ejpam-6147	340	55	space	space	PROPN
ejpam-6147	340	56	h.	h.	PROPN
ejpam-6147	340	57	therefore	therefore	ADV
ejpam-6147	340	58	both	both	CCONJ
ejpam-6147	340	59	the	the	DET
ejpam-6147	340	60	net	net	NOUN
ejpam-6147	340	61	ςt	ςt	NOUN
ejpam-6147	340	62	in	in	ADP
ejpam-6147	340	63	theorem	theorem	NOUN
ejpam-6147	340	64	?	?	PUNCT
ejpam-6147	340	65	?	?	PUNCT
ejpam-6147	341	1	and	and	CCONJ
ejpam-6147	341	2	the	the	DET
ejpam-6147	341	3	sequence	sequence	NOUN
ejpam-6147	341	4	ςm	ςm	NOUN
ejpam-6147	341	5	in	in	ADP
ejpam-6147	341	6	theorem	theorem	ADJ
ejpam-6147	341	7	2	2	NUM
ejpam-6147	341	8	strongly	strongly	ADV
ejpam-6147	341	9	converges	converge	VERB
ejpam-6147	341	10	to	to	ADP
ejpam-6147	341	11	a	a	DET
ejpam-6147	341	12	fp	fp	NOUN
ejpam-6147	341	13	of	of	ADP
ejpam-6147	341	14	a	a	DET
ejpam-6147	341	15	subfamily	subfamily	NOUN
ejpam-6147	341	16	of	of	ADP
ejpam-6147	341	17	the	the	DET
ejpam-6147	341	18	above	above	ADJ
ejpam-6147	341	19	nee	nee	NOUN
ejpam-6147	341	20	family	family	NOUN
ejpam-6147	341	21	.	.	PUNCT
ejpam-6147	342	1	open	open	ADJ
ejpam-6147	342	2	problem	problem	NOUN
ejpam-6147	342	3	:	:	PUNCT
ejpam-6147	342	4	we	we	PRON
ejpam-6147	342	5	leave	leave	VERB
ejpam-6147	342	6	open	open	ADJ
ejpam-6147	342	7	the	the	DET
ejpam-6147	342	8	question	question	NOUN
ejpam-6147	342	9	whether	whether	SCONJ
ejpam-6147	342	10	all	all	DET
ejpam-6147	342	11	the	the	DET
ejpam-6147	342	12	main	main	ADJ
ejpam-6147	342	13	results	result	NOUN
ejpam-6147	342	14	could	could	AUX
ejpam-6147	342	15	be	be	AUX
ejpam-6147	342	16	generalized	generalize	VERB
ejpam-6147	342	17	for	for	ADP
ejpam-6147	342	18	the	the	DET
ejpam-6147	342	19	whole	whole	ADJ
ejpam-6147	342	20	periodic	periodic	NOUN
ejpam-6147	342	21	and	and	CCONJ
ejpam-6147	342	22	then	then	ADV
ejpam-6147	342	23	for	for	ADP
ejpam-6147	342	24	the	the	DET
ejpam-6147	342	25	general	general	ADJ
ejpam-6147	342	26	non	non	ADJ
ejpam-6147	342	27	-	-	ADJ
ejpam-6147	342	28	periodic	periodic	ADJ
ejpam-6147	342	29	evolution	evolution	NOUN
ejpam-6147	342	30	families	family	NOUN
ejpam-6147	342	31	in	in	ADP
ejpam-6147	342	32	hilbert	hilbert	PROPN
ejpam-6147	342	33	spaces	space	NOUN
ejpam-6147	342	34	?	?	PUNCT
ejpam-6147	343	1	5	5	X
ejpam-6147	343	2	.	.	X
ejpam-6147	343	3	conclusion	conclusion	NOUN
ejpam-6147	343	4	in	in	ADP
ejpam-6147	343	5	this	this	DET
ejpam-6147	343	6	work	work	NOUN
ejpam-6147	343	7	,	,	PUNCT
ejpam-6147	343	8	we	we	PRON
ejpam-6147	343	9	investigated	investigate	VERB
ejpam-6147	343	10	the	the	DET
ejpam-6147	343	11	fixed	fix	VERB
ejpam-6147	343	12	point	point	NOUN
ejpam-6147	343	13	properties	property	NOUN
ejpam-6147	343	14	of	of	ADP
ejpam-6147	343	15	a	a	DET
ejpam-6147	343	16	specific	specific	ADJ
ejpam-6147	343	17	subfamily	subfamily	ADV
ejpam-6147	343	18	within	within	ADP
ejpam-6147	343	19	a	a	DET
ejpam-6147	343	20	non	non	ADJ
ejpam-6147	343	21	-	-	ADJ
ejpam-6147	343	22	expansive	expansive	ADJ
ejpam-6147	343	23	evolution	evolution	NOUN
ejpam-6147	343	24	family	family	NOUN
ejpam-6147	343	25	of	of	ADP
ejpam-6147	343	26	bounded	bounded	ADJ
ejpam-6147	343	27	linear	linear	PROPN
ejpam-6147	343	28	operators	operator	NOUN
ejpam-6147	343	29	on	on	ADP
ejpam-6147	343	30	a	a	DET
ejpam-6147	343	31	hilbert	hilbert	NOUN
ejpam-6147	343	32	space	space	NOUN
ejpam-6147	343	33	h.	h.	NOUN
ejpam-6147	343	34	by	by	ADP
ejpam-6147	343	35	utilizing	utilize	VERB
ejpam-6147	343	36	the	the	DET
ejpam-6147	343	37	framework	framework	NOUN
ejpam-6147	343	38	of	of	ADP
ejpam-6147	343	39	nets	net	NOUN
ejpam-6147	343	40	and	and	CCONJ
ejpam-6147	343	41	a	a	DET
ejpam-6147	343	42	progression	progression	NOUN
ejpam-6147	343	43	algorithm	algorithm	NOUN
ejpam-6147	343	44	,	,	PUNCT
ejpam-6147	343	45	we	we	PRON
ejpam-6147	343	46	established	establish	VERB
ejpam-6147	343	47	several	several	ADJ
ejpam-6147	343	48	results	result	NOUN
ejpam-6147	343	49	concerning	concern	VERB
ejpam-6147	343	50	the	the	DET
ejpam-6147	343	51	strong	strong	ADJ
ejpam-6147	343	52	convergence	convergence	NOUN
ejpam-6147	343	53	of	of	ADP
ejpam-6147	343	54	sequences	sequence	NOUN
ejpam-6147	343	55	to	to	ADP
ejpam-6147	343	56	a	a	DET
ejpam-6147	343	57	common	common	ADJ
ejpam-6147	343	58	fixed	fix	VERB
ejpam-6147	343	59	point	point	NOUN
ejpam-6147	343	60	of	of	ADP
ejpam-6147	343	61	the	the	DET
ejpam-6147	343	62	considered	consider	VERB
ejpam-6147	343	63	subfamily	subfamily	ADV
ejpam-6147	343	64	.	.	PUNCT
ejpam-6147	344	1	the	the	DET
ejpam-6147	344	2	theoretical	theoretical	ADJ
ejpam-6147	344	3	findings	finding	NOUN
ejpam-6147	344	4	were	be	AUX
ejpam-6147	344	5	further	far	ADV
ejpam-6147	344	6	supported	support	VERB
ejpam-6147	344	7	by	by	ADP
ejpam-6147	344	8	a	a	DET
ejpam-6147	344	9	concrete	concrete	ADJ
ejpam-6147	344	10	example	example	NOUN
ejpam-6147	344	11	,	,	PUNCT
ejpam-6147	344	12	demonstrating	demonstrate	VERB
ejpam-6147	344	13	the	the	DET
ejpam-6147	344	14	applicability	applicability	NOUN
ejpam-6147	344	15	of	of	ADP
ejpam-6147	344	16	the	the	DET
ejpam-6147	344	17	developed	develop	VERB
ejpam-6147	344	18	framework	framework	NOUN
ejpam-6147	344	19	.	.	PUNCT
ejpam-6147	345	1	we	we	PRON
ejpam-6147	345	2	conclude	conclude	VERB
ejpam-6147	345	3	by	by	ADP
ejpam-6147	345	4	posing	pose	VERB
ejpam-6147	345	5	an	an	DET
ejpam-6147	345	6	open	open	ADJ
ejpam-6147	345	7	problem	problem	NOUN
ejpam-6147	345	8	to	to	PART
ejpam-6147	345	9	inspire	inspire	VERB
ejpam-6147	345	10	future	future	ADJ
ejpam-6147	345	11	research	research	NOUN
ejpam-6147	345	12	in	in	ADP
ejpam-6147	345	13	this	this	DET
ejpam-6147	345	14	direction	direction	NOUN
ejpam-6147	345	15	.	.	PUNCT
ejpam-6147	346	1	acknowledgements	acknowledgement	VERB
ejpam-6147	346	2	the	the	DET
ejpam-6147	346	3	authors	author	NOUN
ejpam-6147	346	4	m.	m.	NOUN
ejpam-6147	346	5	sarwar	sarwar	PROPN
ejpam-6147	346	6	,	,	PUNCT
ejpam-6147	346	7	m.y.b.mufarrej	m.y.b.mufarrej	PROPN
ejpam-6147	346	8	and	and	CCONJ
ejpam-6147	346	9	k.	k.	PROPN
ejpam-6147	346	10	abodayeh	abodayeh	PROPN
ejpam-6147	346	11	would	would	AUX
ejpam-6147	346	12	like	like	VERB
ejpam-6147	346	13	to	to	PART
ejpam-6147	346	14	thank	thank	VERB
ejpam-6147	346	15	prince	prince	PROPN
ejpam-6147	346	16	sultan	sultan	PROPN
ejpam-6147	346	17	university	university	PROPN
ejpam-6147	346	18	for	for	ADP
ejpam-6147	346	19	paying	pay	VERB
ejpam-6147	346	20	the	the	DET
ejpam-6147	346	21	apc	apc	NOUN
ejpam-6147	346	22	and	and	CCONJ
ejpam-6147	346	23	for	for	ADP
ejpam-6147	346	24	the	the	DET
ejpam-6147	346	25	support	support	NOUN
ejpam-6147	346	26	through	through	ADP
ejpam-6147	346	27	the	the	DET
ejpam-6147	346	28	tas	tas	PROPN
ejpam-6147	346	29	research	research	NOUN
ejpam-6147	346	30	lab	lab	NOUN
ejpam-6147	346	31	.	.	PUNCT
ejpam-6147	347	1	m.	m.	NOUN
ejpam-6147	347	2	sarwar	sarwar	PROPN
ejpam-6147	347	3	et	et	PROPN
ejpam-6147	347	4	al	al	PROPN
ejpam-6147	347	5	.	.	PUNCT
ejpam-6147	347	6	/	/	SYM
ejpam-6147	347	7	eur	eur	PROPN
ejpam-6147	347	8	.	.	PUNCT
ejpam-6147	348	1	j.	j.	PROPN
ejpam-6147	348	2	pure	pure	PROPN
ejpam-6147	348	3	appl	appl	PROPN
ejpam-6147	348	4	.	.	PROPN
ejpam-6147	348	5	math	math	PROPN
ejpam-6147	348	6	,	,	PUNCT
ejpam-6147	348	7	18	18	NUM
ejpam-6147	348	8	(	(	PUNCT
ejpam-6147	348	9	3	3	NUM
ejpam-6147	348	10	)	)	PUNCT
ejpam-6147	348	11	(	(	PUNCT
ejpam-6147	348	12	2025	2025	NUM
ejpam-6147	348	13	)	)	PUNCT
ejpam-6147	348	14	,	,	PUNCT
ejpam-6147	348	15	6147	6147	NUM
ejpam-6147	348	16	17	17	NUM
ejpam-6147	348	17	of	of	ADP
ejpam-6147	348	18	18	18	NUM
ejpam-6147	348	19	competing	compete	VERB
ejpam-6147	348	20	interest	interest	NOUN
ejpam-6147	348	21	the	the	DET
ejpam-6147	348	22	authors	author	NOUN
ejpam-6147	348	23	declare	declare	VERB
ejpam-6147	348	24	that	that	SCONJ
ejpam-6147	348	25	they	they	PRON
ejpam-6147	348	26	have	have	VERB
ejpam-6147	348	27	no	no	DET
ejpam-6147	348	28	competing	compete	VERB
ejpam-6147	348	29	interests	interest	NOUN
ejpam-6147	348	30	concerning	concern	VERB
ejpam-6147	348	31	the	the	DET
ejpam-6147	348	32	publication	publication	NOUN
ejpam-6147	348	33	of	of	ADP
ejpam-6147	348	34	this	this	DET
ejpam-6147	348	35	article	article	NOUN
ejpam-6147	348	36	.	.	PUNCT
ejpam-6147	349	1	author	author	PROPN
ejpam-6147	349	2	’s	’s	PART
ejpam-6147	349	3	contributions	contribution	NOUN
ejpam-6147	349	4	all	all	DET
ejpam-6147	349	5	authors	author	NOUN
ejpam-6147	349	6	contribute	contribute	VERB
ejpam-6147	349	7	equally	equally	ADV
ejpam-6147	349	8	to	to	ADP
ejpam-6147	349	9	the	the	DET
ejpam-6147	349	10	writing	writing	NOUN
ejpam-6147	349	11	of	of	ADP
ejpam-6147	349	12	this	this	DET
ejpam-6147	349	13	manuscript	manuscript	NOUN
ejpam-6147	349	14	.	.	PUNCT
ejpam-6147	350	1	all	all	DET
ejpam-6147	350	2	authours	authour	NOUN
ejpam-6147	350	3	reads	read	VERB
ejpam-6147	350	4	and	and	CCONJ
ejpam-6147	350	5	approved	approve	VERB
ejpam-6147	350	6	the	the	DET
ejpam-6147	350	7	final	final	ADJ
ejpam-6147	350	8	version	version	NOUN
ejpam-6147	350	9	.	.	PUNCT
ejpam-6147	351	1	references	reference	NOUN
ejpam-6147	351	2	[	[	X
ejpam-6147	351	3	1	1	NUM
ejpam-6147	351	4	]	]	PUNCT
ejpam-6147	351	5	f.	f.	PROPN
ejpam-6147	351	6	e.	e.	PROPN
ejpam-6147	351	7	browder	browder	PROPN
ejpam-6147	351	8	.	.	PUNCT
ejpam-6147	352	1	convergence	convergence	NOUN
ejpam-6147	352	2	of	of	ADP
ejpam-6147	352	3	approximation	approximation	NOUN
ejpam-6147	352	4	to	to	ADP
ejpam-6147	352	5	fixed	fix	VERB
ejpam-6147	352	6	points	point	NOUN
ejpam-6147	352	7	of	of	ADP
ejpam-6147	352	8	nonexpansive	nonexpansive	ADJ
ejpam-6147	352	9	nonlinear	nonlinear	ADJ
ejpam-6147	352	10	mappings	mapping	NOUN
ejpam-6147	352	11	in	in	ADP
ejpam-6147	352	12	hilbert	hilbert	PROPN
ejpam-6147	352	13	spaces	space	NOUN
ejpam-6147	352	14	.	.	PUNCT
ejpam-6147	353	1	archive	archive	NOUN
ejpam-6147	353	2	for	for	ADP
ejpam-6147	353	3	rational	rational	ADJ
ejpam-6147	353	4	mechanics	mechanic	NOUN
ejpam-6147	353	5	and	and	CCONJ
ejpam-6147	353	6	analysis	analysis	NOUN
ejpam-6147	353	7	,	,	PUNCT
ejpam-6147	353	8	24:82–90	24:82–90	NUM
ejpam-6147	353	9	,	,	PUNCT
ejpam-6147	353	10	1967	1967	NUM
ejpam-6147	353	11	.	.	PUNCT
ejpam-6147	354	1	[	[	X
ejpam-6147	354	2	2	2	X
ejpam-6147	354	3	]	]	PUNCT
ejpam-6147	354	4	h.	h.	PROPN
ejpam-6147	354	5	brezis	brezis	PROPN
ejpam-6147	354	6	and	and	CCONJ
ejpam-6147	354	7	f.	f.	PROPN
ejpam-6147	354	8	e.	e.	PROPN
ejpam-6147	354	9	browder	browder	PROPN
ejpam-6147	354	10	.	.	PUNCT
ejpam-6147	355	1	nonlinear	nonlinear	ADJ
ejpam-6147	355	2	ergodic	ergodic	ADJ
ejpam-6147	355	3	theorems	theorem	NOUN
ejpam-6147	355	4	.	.	PUNCT
ejpam-6147	356	1	bulletin	bulletin	NOUN
ejpam-6147	356	2	of	of	ADP
ejpam-6147	356	3	the	the	DET
ejpam-6147	356	4	american	american	PROPN
ejpam-6147	356	5	mathematical	mathematical	PROPN
ejpam-6147	356	6	society	society	NOUN
ejpam-6147	356	7	,	,	PUNCT
ejpam-6147	356	8	82(6):959–961	82(6):959–961	PROPN
ejpam-6147	356	9	,	,	PUNCT
ejpam-6147	356	10	1976	1976	NUM
ejpam-6147	356	11	.	.	PUNCT
ejpam-6147	357	1	[	[	X
ejpam-6147	357	2	3	3	X
ejpam-6147	357	3	]	]	PUNCT
ejpam-6147	357	4	k.	k.	PROPN
ejpam-6147	357	5	goebel	goebel	PROPN
ejpam-6147	357	6	and	and	CCONJ
ejpam-6147	357	7	w.	w.	PROPN
ejpam-6147	357	8	a.	a.	PROPN
ejpam-6147	357	9	kirk	kirk	PROPN
ejpam-6147	357	10	.	.	PUNCT
ejpam-6147	358	1	topics	topic	NOUN
ejpam-6147	358	2	in	in	ADP
ejpam-6147	358	3	metric	metric	ADJ
ejpam-6147	358	4	fixed	fix	VERB
ejpam-6147	358	5	point	point	NOUN
ejpam-6147	358	6	theory	theory	NOUN
ejpam-6147	358	7	,	,	PUNCT
ejpam-6147	358	8	volume	volume	NOUN
ejpam-6147	358	9	28	28	NUM
ejpam-6147	358	10	of	of	ADP
ejpam-6147	358	11	cambridge	cambridge	PROPN
ejpam-6147	358	12	studies	study	NOUN
ejpam-6147	358	13	in	in	ADP
ejpam-6147	358	14	advanced	advanced	ADJ
ejpam-6147	358	15	mathematics	mathematic	NOUN
ejpam-6147	358	16	.	.	PUNCT
ejpam-6147	359	1	cambridge	cambridge	PROPN
ejpam-6147	359	2	university	university	PROPN
ejpam-6147	359	3	press	press	PROPN
ejpam-6147	359	4	,	,	PUNCT
ejpam-6147	359	5	cambridge	cambridge	PROPN
ejpam-6147	359	6	,	,	PUNCT
ejpam-6147	359	7	1990	1990	NUM
ejpam-6147	359	8	.	.	PUNCT
ejpam-6147	360	1	[	[	X
ejpam-6147	360	2	4	4	X
ejpam-6147	360	3	]	]	X
ejpam-6147	360	4	t.	t.	NOUN
ejpam-6147	360	5	abdeljawad	abdeljawad	PROPN
ejpam-6147	360	6	,	,	PUNCT
ejpam-6147	360	7	r.	r.	PROPN
ejpam-6147	360	8	p.	p.	PROPN
ejpam-6147	360	9	agarwal	agarwal	PROPN
ejpam-6147	360	10	,	,	PUNCT
ejpam-6147	360	11	e.	e.	PROPN
ejpam-6147	360	12	karapınar	karapınar	PROPN
ejpam-6147	360	13	,	,	PUNCT
ejpam-6147	360	14	and	and	CCONJ
ejpam-6147	360	15	p.	p.	NOUN
ejpam-6147	360	16	s.	s.	PROPN
ejpam-6147	360	17	kumari	kumari	PROPN
ejpam-6147	360	18	.	.	PUNCT
ejpam-6147	361	1	solutions	solution	NOUN
ejpam-6147	361	2	of	of	ADP
ejpam-6147	361	3	the	the	DET
ejpam-6147	361	4	nonlinear	nonlinear	ADJ
ejpam-6147	361	5	integral	integral	ADJ
ejpam-6147	361	6	equation	equation	NOUN
ejpam-6147	361	7	and	and	CCONJ
ejpam-6147	361	8	fractional	fractional	ADJ
ejpam-6147	361	9	differential	differential	NOUN
ejpam-6147	361	10	equation	equation	NOUN
ejpam-6147	361	11	using	use	VERB
ejpam-6147	361	12	the	the	DET
ejpam-6147	361	13	technique	technique	NOUN
ejpam-6147	361	14	of	of	ADP
ejpam-6147	361	15	a	a	DET
ejpam-6147	361	16	fixed	fix	VERB
ejpam-6147	361	17	point	point	NOUN
ejpam-6147	361	18	with	with	ADP
ejpam-6147	361	19	a	a	DET
ejpam-6147	361	20	numerical	numerical	ADJ
ejpam-6147	361	21	experiment	experiment	NOUN
ejpam-6147	361	22	in	in	ADP
ejpam-6147	361	23	extended	extended	ADJ
ejpam-6147	361	24	b	b	X
ejpam-6147	361	25	-	-	PUNCT
ejpam-6147	361	26	metric	metric	ADJ
ejpam-6147	361	27	space	space	NOUN
ejpam-6147	361	28	.	.	PUNCT
ejpam-6147	362	1	symmetry	symmetry	NOUN
ejpam-6147	362	2	,	,	PUNCT
ejpam-6147	362	3	11(5):686	11(5):686	NUM
ejpam-6147	362	4	,	,	PUNCT
ejpam-6147	362	5	2019	2019	NUM
ejpam-6147	362	6	.	.	PUNCT
ejpam-6147	363	1	[	[	X
ejpam-6147	363	2	5	5	X
ejpam-6147	363	3	]	]	PUNCT
ejpam-6147	363	4	h.	h.	PROPN
ejpam-6147	363	5	qawaqneh	qawaqneh	PROPN
ejpam-6147	363	6	,	,	PUNCT
ejpam-6147	363	7	m.	m.	PROPN
ejpam-6147	363	8	s.	s.	PROPN
ejpam-6147	363	9	m.	m.	PROPN
ejpam-6147	363	10	noorani	noorani	PROPN
ejpam-6147	363	11	,	,	PUNCT
ejpam-6147	363	12	w.	w.	PROPN
ejpam-6147	363	13	shatanawi	shatanawi	PROPN
ejpam-6147	363	14	,	,	PUNCT
ejpam-6147	363	15	h.	h.	PROPN
ejpam-6147	363	16	aydi	aydi	PROPN
ejpam-6147	363	17	,	,	PUNCT
ejpam-6147	363	18	and	and	CCONJ
ejpam-6147	363	19	h.	h.	PROPN
ejpam-6147	363	20	alsamir	alsamir	PROPN
ejpam-6147	363	21	.	.	PUNCT
ejpam-6147	364	1	fixed	fix	VERB
ejpam-6147	364	2	point	point	NOUN
ejpam-6147	364	3	results	result	NOUN
ejpam-6147	364	4	for	for	ADP
ejpam-6147	364	5	multi	multi	ADJ
ejpam-6147	364	6	-	-	ADJ
ejpam-6147	364	7	valued	value	VERB
ejpam-6147	364	8	contractions	contraction	NOUN
ejpam-6147	364	9	in	in	ADP
ejpam-6147	364	10	b	b	NOUN
ejpam-6147	364	11	-	-	ADJ
ejpam-6147	364	12	metric	metric	ADJ
ejpam-6147	364	13	spaces	space	NOUN
ejpam-6147	364	14	and	and	CCONJ
ejpam-6147	364	15	an	an	DET
ejpam-6147	364	16	application	application	NOUN
ejpam-6147	364	17	.	.	PUNCT
ejpam-6147	365	1	mathematics	mathematic	NOUN
ejpam-6147	365	2	,	,	PUNCT
ejpam-6147	365	3	7(2):132	7(2):132	NUM
ejpam-6147	365	4	,	,	PUNCT
ejpam-6147	365	5	2019	2019	NUM
ejpam-6147	365	6	.	.	PUNCT
ejpam-6147	366	1	[	[	X
ejpam-6147	366	2	6	6	NUM
ejpam-6147	366	3	]	]	PUNCT
ejpam-6147	366	4	j.	j.	PROPN
ejpam-6147	366	5	b.	b.	PROPN
ejpam-6147	366	6	baillon	baillon	PROPN
ejpam-6147	366	7	and	and	CCONJ
ejpam-6147	366	8	h.	h.	PROPN
ejpam-6147	366	9	brezis	brezis	PROPN
ejpam-6147	366	10	.	.	PUNCT
ejpam-6147	367	1	une	une	PROPN
ejpam-6147	367	2	remarque	remarque	PROPN
ejpam-6147	367	3	sur	sur	PROPN
ejpam-6147	367	4	le	le	X
ejpam-6147	367	5	comportement	comportement	PROPN
ejpam-6147	367	6	asymptotique	asymptotique	PROPN
ejpam-6147	367	7	des	des	PROPN
ejpam-6147	367	8	semigroup	semigroup	PROPN
ejpam-6147	367	9	non	non	PROPN
ejpam-6147	367	10	linéaires	linéaire	NOUN
ejpam-6147	367	11	.	.	PUNCT
ejpam-6147	368	1	monatshefte	monatshefte	PROPN
ejpam-6147	368	2	für	für	PROPN
ejpam-6147	368	3	mathematik	mathematik	PROPN
ejpam-6147	368	4	,	,	PUNCT
ejpam-6147	368	5	2:5–7	2:5–7	NUM
ejpam-6147	368	6	,	,	PUNCT
ejpam-6147	368	7	1976	1976	NUM
ejpam-6147	368	8	.	.	PUNCT
ejpam-6147	369	1	[	[	X
ejpam-6147	369	2	7	7	X
ejpam-6147	369	3	]	]	X
ejpam-6147	369	4	y.	y.	PROPN
ejpam-6147	369	5	kimurta	kimurta	PROPN
ejpam-6147	369	6	,	,	PUNCT
ejpam-6147	369	7	w.	w.	PROPN
ejpam-6147	369	8	takahashi	takahashi	PROPN
ejpam-6147	369	9	,	,	PUNCT
ejpam-6147	369	10	and	and	CCONJ
ejpam-6147	369	11	m.	m.	PROPN
ejpam-6147	369	12	toyoda	toyoda	PROPN
ejpam-6147	369	13	.	.	PUNCT
ejpam-6147	370	1	convergence	convergence	NOUN
ejpam-6147	370	2	to	to	ADP
ejpam-6147	370	3	common	common	ADJ
ejpam-6147	370	4	fixed	fix	VERB
ejpam-6147	370	5	points	point	NOUN
ejpam-6147	370	6	of	of	ADP
ejpam-6147	370	7	a	a	DET
ejpam-6147	370	8	finite	finite	ADJ
ejpam-6147	370	9	family	family	NOUN
ejpam-6147	370	10	of	of	ADP
ejpam-6147	370	11	nonexpansive	nonexpansive	ADJ
ejpam-6147	370	12	mappings	mapping	NOUN
ejpam-6147	370	13	.	.	PUNCT
ejpam-6147	371	1	archiv	archiv	PROPN
ejpam-6147	371	2	der	der	PROPN
ejpam-6147	371	3	mathematik	mathematik	PROPN
ejpam-6147	371	4	,	,	PUNCT
ejpam-6147	371	5	84:350–363	84:350–363	NUM
ejpam-6147	371	6	,	,	PUNCT
ejpam-6147	371	7	2005	2005	NUM
ejpam-6147	371	8	.	.	PUNCT
ejpam-6147	372	1	[	[	X
ejpam-6147	372	2	8	8	NUM
ejpam-6147	372	3	]	]	X
ejpam-6147	372	4	b.	b.	PROPN
ejpam-6147	372	5	halpern	halpern	PROPN
ejpam-6147	372	6	.	.	PUNCT
ejpam-6147	373	1	fixed	fix	VERB
ejpam-6147	373	2	points	point	NOUN
ejpam-6147	373	3	of	of	ADP
ejpam-6147	373	4	nonexpansive	nonexpansive	ADJ
ejpam-6147	373	5	maps	map	NOUN
ejpam-6147	373	6	.	.	PUNCT
ejpam-6147	374	1	bulletin	bulletin	NOUN
ejpam-6147	374	2	of	of	ADP
ejpam-6147	374	3	the	the	DET
ejpam-6147	374	4	american	american	PROPN
ejpam-6147	374	5	mathematical	mathematical	PROPN
ejpam-6147	374	6	society	society	NOUN
ejpam-6147	374	7	,	,	PUNCT
ejpam-6147	374	8	73:957–961	73:957–961	PROPN
ejpam-6147	374	9	,	,	PUNCT
ejpam-6147	374	10	1967	1967	NUM
ejpam-6147	374	11	.	.	PUNCT
ejpam-6147	375	1	[	[	X
ejpam-6147	375	2	9	9	X
ejpam-6147	375	3	]	]	X
ejpam-6147	375	4	y.	y.	PROPN
ejpam-6147	375	5	yao	yao	PROPN
ejpam-6147	375	6	,	,	PUNCT
ejpam-6147	375	7	j.	j.	PROPN
ejpam-6147	375	8	i.	i.	PROPN
ejpam-6147	375	9	kang	kang	PROPN
ejpam-6147	375	10	,	,	PUNCT
ejpam-6147	375	11	y.	y.	PROPN
ejpam-6147	375	12	cho	cho	PROPN
ejpam-6147	375	13	,	,	PUNCT
ejpam-6147	375	14	and	and	CCONJ
ejpam-6147	375	15	y.	y.	PROPN
ejpam-6147	375	16	c.	c.	PROPN
ejpam-6147	375	17	liou	liou	PROPN
ejpam-6147	375	18	.	.	PUNCT
ejpam-6147	376	1	approximation	approximation	NOUN
ejpam-6147	376	2	of	of	ADP
ejpam-6147	376	3	fixed	fix	VERB
ejpam-6147	376	4	points	point	NOUN
ejpam-6147	376	5	for	for	ADP
ejpam-6147	376	6	non	non	ADJ
ejpam-6147	376	7	-	-	ADJ
ejpam-6147	376	8	expansive	expansive	ADJ
ejpam-6147	376	9	semigroups	semigroup	NOUN
ejpam-6147	376	10	in	in	ADP
ejpam-6147	376	11	hilbert	hilbert	NOUN
ejpam-6147	376	12	spaces	space	NOUN
ejpam-6147	376	13	.	.	PUNCT
ejpam-6147	377	1	fixed	fix	VERB
ejpam-6147	377	2	point	point	NOUN
ejpam-6147	377	3	theory	theory	NOUN
ejpam-6147	377	4	and	and	CCONJ
ejpam-6147	377	5	applications	application	NOUN
ejpam-6147	377	6	,	,	PUNCT
ejpam-6147	377	7	31:1–11	31:1–11	NUM
ejpam-6147	377	8	,	,	PUNCT
ejpam-6147	377	9	2013	2013	NUM
ejpam-6147	377	10	.	.	PUNCT
ejpam-6147	378	1	[	[	X
ejpam-6147	378	2	10	10	NUM
ejpam-6147	378	3	]	]	X
ejpam-6147	378	4	p.	p.	PROPN
ejpam-6147	378	5	e.	e.	PROPN
ejpam-6147	378	6	mainge	mainge	PROPN
ejpam-6147	378	7	.	.	PUNCT
ejpam-6147	379	1	approximation	approximation	NOUN
ejpam-6147	379	2	methods	method	NOUN
ejpam-6147	379	3	for	for	ADP
ejpam-6147	379	4	common	common	ADJ
ejpam-6147	379	5	fixed	fix	VERB
ejpam-6147	379	6	points	point	NOUN
ejpam-6147	379	7	of	of	ADP
ejpam-6147	379	8	nonexpansive	nonexpansive	ADJ
ejpam-6147	379	9	mappings	mapping	NOUN
ejpam-6147	379	10	in	in	ADP
ejpam-6147	379	11	hilbert	hilbert	PROPN
ejpam-6147	379	12	spaces	space	NOUN
ejpam-6147	379	13	.	.	PUNCT
ejpam-6147	380	1	journal	journal	PROPN
ejpam-6147	380	2	of	of	ADP
ejpam-6147	380	3	mathematical	mathematical	ADJ
ejpam-6147	380	4	analysis	analysis	NOUN
ejpam-6147	380	5	and	and	CCONJ
ejpam-6147	380	6	applications	application	NOUN
ejpam-6147	380	7	,	,	PUNCT
ejpam-6147	380	8	325:469	325:469	NOUN
ejpam-6147	380	9	–	–	PUNCT
ejpam-6147	380	10	479	479	NUM
ejpam-6147	380	11	,	,	PUNCT
ejpam-6147	380	12	2007	2007	NUM
ejpam-6147	380	13	.	.	PUNCT
ejpam-6147	381	1	[	[	X
ejpam-6147	381	2	11	11	NUM
ejpam-6147	381	3	]	]	X
ejpam-6147	381	4	r.	r.	PROPN
ejpam-6147	381	5	wittmann	wittmann	PROPN
ejpam-6147	381	6	.	.	PUNCT
ejpam-6147	382	1	approximation	approximation	NOUN
ejpam-6147	382	2	of	of	ADP
ejpam-6147	382	3	fixed	fix	VERB
ejpam-6147	382	4	points	point	NOUN
ejpam-6147	382	5	of	of	ADP
ejpam-6147	382	6	nonexpansive	nonexpansive	ADJ
ejpam-6147	382	7	mappings	mapping	NOUN
ejpam-6147	382	8	.	.	PUNCT
ejpam-6147	383	1	archiv	archiv	PROPN
ejpam-6147	383	2	der	der	PROPN
ejpam-6147	383	3	mathematik	mathematik	PROPN
ejpam-6147	383	4	,	,	PUNCT
ejpam-6147	383	5	58:486–491	58:486–491	PROPN
ejpam-6147	383	6	,	,	PUNCT
ejpam-6147	383	7	1992	1992	NUM
ejpam-6147	383	8	.	.	PUNCT
ejpam-6147	384	1	[	[	X
ejpam-6147	384	2	12	12	NUM
ejpam-6147	384	3	]	]	PUNCT
ejpam-6147	384	4	a.	a.	NOUN
ejpam-6147	384	5	petrusel	petrusel	NOUN
ejpam-6147	384	6	and	and	CCONJ
ejpam-6147	384	7	j.	j.	PROPN
ejpam-6147	384	8	c.	c.	PROPN
ejpam-6147	384	9	yao	yao	PROPN
ejpam-6147	384	10	.	.	PUNCT
ejpam-6147	385	1	viscosity	viscosity	NOUN
ejpam-6147	385	2	approximation	approximation	NOUN
ejpam-6147	385	3	to	to	ADP
ejpam-6147	385	4	common	common	ADJ
ejpam-6147	385	5	fixed	fix	VERB
ejpam-6147	385	6	points	point	NOUN
ejpam-6147	385	7	of	of	ADP
ejpam-6147	385	8	famm	famm	PROPN
ejpam-6147	385	9	.	.	PUNCT
ejpam-6147	386	1	sarwar	sarwar	PROPN
ejpam-6147	386	2	et	et	PROPN
ejpam-6147	386	3	al	al	PROPN
ejpam-6147	386	4	.	.	PUNCT
ejpam-6147	386	5	/	/	SYM
ejpam-6147	386	6	eur	eur	PROPN
ejpam-6147	386	7	.	.	PUNCT
ejpam-6147	387	1	j.	j.	PROPN
ejpam-6147	387	2	pure	pure	PROPN
ejpam-6147	387	3	appl	appl	PROPN
ejpam-6147	387	4	.	.	PROPN
ejpam-6147	387	5	math	math	PROPN
ejpam-6147	387	6	,	,	PUNCT
ejpam-6147	387	7	18	18	NUM
ejpam-6147	387	8	(	(	PUNCT
ejpam-6147	387	9	3	3	NUM
ejpam-6147	387	10	)	)	PUNCT
ejpam-6147	387	11	(	(	PUNCT
ejpam-6147	387	12	2025	2025	NUM
ejpam-6147	387	13	)	)	PUNCT
ejpam-6147	387	14	,	,	PUNCT
ejpam-6147	387	15	6147	6147	NUM
ejpam-6147	387	16	18	18	NUM
ejpam-6147	387	17	of	of	ADP
ejpam-6147	387	18	18	18	NUM
ejpam-6147	387	19	ilies	ilie	NOUN
ejpam-6147	387	20	of	of	ADP
ejpam-6147	387	21	nonexpansive	nonexpansive	ADJ
ejpam-6147	387	22	mappings	mapping	NOUN
ejpam-6147	387	23	with	with	ADP
ejpam-6147	387	24	generalized	generalized	ADJ
ejpam-6147	387	25	contractions	contraction	NOUN
ejpam-6147	387	26	mappings	mapping	NOUN
ejpam-6147	387	27	.	.	PUNCT
ejpam-6147	388	1	nonlinear	nonlinear	ADJ
ejpam-6147	388	2	analysis	analysis	NOUN
ejpam-6147	388	3	:	:	PUNCT
ejpam-6147	388	4	theory	theory	NOUN
ejpam-6147	388	5	,	,	PUNCT
ejpam-6147	388	6	methods	method	NOUN
ejpam-6147	388	7	and	and	CCONJ
ejpam-6147	388	8	applications	application	NOUN
ejpam-6147	388	9	,	,	PUNCT
ejpam-6147	388	10	69:1100–1111	69:1100–1111	NUM
ejpam-6147	388	11	,	,	PUNCT
ejpam-6147	388	12	2008	2008	NUM
ejpam-6147	388	13	.	.	PUNCT
ejpam-6147	389	1	[	[	X
ejpam-6147	389	2	13	13	NUM
ejpam-6147	389	3	]	]	PUNCT
ejpam-6147	389	4	t.	t.	PROPN
ejpam-6147	389	5	shimizu	shimizu	PROPN
ejpam-6147	389	6	and	and	CCONJ
ejpam-6147	389	7	w.	w.	PROPN
ejpam-6147	389	8	takahashi	takahashi	PROPN
ejpam-6147	389	9	.	.	PUNCT
ejpam-6147	390	1	strong	strong	ADJ
ejpam-6147	390	2	convergence	convergence	NOUN
ejpam-6147	390	3	to	to	ADP
ejpam-6147	390	4	common	common	ADJ
ejpam-6147	390	5	fixed	fix	VERB
ejpam-6147	390	6	points	point	NOUN
ejpam-6147	390	7	of	of	ADP
ejpam-6147	390	8	families	family	NOUN
ejpam-6147	390	9	of	of	ADP
ejpam-6147	390	10	nonexpansive	nonexpansive	ADJ
ejpam-6147	390	11	mappings	mapping	NOUN
ejpam-6147	390	12	.	.	PUNCT
ejpam-6147	391	1	journal	journal	PROPN
ejpam-6147	391	2	of	of	ADP
ejpam-6147	391	3	mathematical	mathematical	ADJ
ejpam-6147	391	4	analysis	analysis	NOUN
ejpam-6147	391	5	and	and	CCONJ
ejpam-6147	391	6	applications	application	NOUN
ejpam-6147	391	7	,	,	PUNCT
ejpam-6147	391	8	211:71–83	211:71–83	NUM
ejpam-6147	391	9	,	,	PUNCT
ejpam-6147	391	10	1997	1997	NUM
ejpam-6147	391	11	.	.	PUNCT
ejpam-6147	392	1	[	[	X
ejpam-6147	392	2	14	14	NUM
ejpam-6147	392	3	]	]	X
ejpam-6147	392	4	n.	n.	PROPN
ejpam-6147	392	5	shioji	shioji	PROPN
ejpam-6147	392	6	and	and	CCONJ
ejpam-6147	392	7	w.	w.	PROPN
ejpam-6147	392	8	takahashi	takahashi	PROPN
ejpam-6147	392	9	.	.	PUNCT
ejpam-6147	393	1	strong	strong	ADJ
ejpam-6147	393	2	convergence	convergence	NOUN
ejpam-6147	393	3	of	of	ADP
ejpam-6147	393	4	approximated	approximate	VERB
ejpam-6147	393	5	sequences	sequence	NOUN
ejpam-6147	393	6	for	for	ADP
ejpam-6147	393	7	nonexpansive	nonexpansive	ADJ
ejpam-6147	393	8	mappings	mapping	NOUN
ejpam-6147	393	9	in	in	ADP
ejpam-6147	393	10	banach	banach	NOUN
ejpam-6147	393	11	spaces	space	NOUN
ejpam-6147	393	12	.	.	PUNCT
ejpam-6147	394	1	proceedings	proceeding	NOUN
ejpam-6147	394	2	of	of	ADP
ejpam-6147	394	3	the	the	DET
ejpam-6147	394	4	american	american	PROPN
ejpam-6147	394	5	mathematical	mathematical	PROPN
ejpam-6147	394	6	society	society	NOUN
ejpam-6147	394	7	,	,	PUNCT
ejpam-6147	394	8	125:3641–3645	125:3641–3645	NOUN
ejpam-6147	394	9	,	,	PUNCT
ejpam-6147	394	10	1997	1997	NUM
ejpam-6147	394	11	.	.	PUNCT
ejpam-6147	395	1	[	[	X
ejpam-6147	395	2	15	15	NUM
ejpam-6147	395	3	]	]	X
ejpam-6147	395	4	y.	y.	PROPN
ejpam-6147	395	5	yao	yao	PROPN
ejpam-6147	395	6	,	,	PUNCT
ejpam-6147	395	7	y.	y.	PROPN
ejpam-6147	395	8	j.	j.	PROPN
ejpam-6147	395	9	cho	cho	PROPN
ejpam-6147	395	10	,	,	PUNCT
ejpam-6147	395	11	and	and	CCONJ
ejpam-6147	395	12	y.	y.	PROPN
ejpam-6147	395	13	c.	c.	PROPN
ejpam-6147	395	14	liou	liou	PROPN
ejpam-6147	395	15	.	.	PUNCT
ejpam-6147	396	1	hierarchical	hierarchical	ADJ
ejpam-6147	396	2	convergence	convergence	NOUN
ejpam-6147	396	3	of	of	ADP
ejpam-6147	396	4	an	an	DET
ejpam-6147	396	5	implicit	implicit	ADJ
ejpam-6147	396	6	doublenet	doublenet	NOUN
ejpam-6147	396	7	algorithm	algorithm	NOUN
ejpam-6147	396	8	for	for	ADP
ejpam-6147	396	9	nonexpansive	nonexpansive	ADJ
ejpam-6147	396	10	semigroups	semigroup	NOUN
ejpam-6147	396	11	and	and	CCONJ
ejpam-6147	396	12	variational	variational	ADJ
ejpam-6147	396	13	inequality	inequality	NOUN
ejpam-6147	396	14	problems	problem	NOUN
ejpam-6147	396	15	.	.	PUNCT
ejpam-6147	397	1	fixed	fix	VERB
ejpam-6147	397	2	point	point	NOUN
ejpam-6147	397	3	theory	theory	NOUN
ejpam-6147	397	4	and	and	CCONJ
ejpam-6147	397	5	applications	application	NOUN
ejpam-6147	397	6	,	,	PUNCT
ejpam-6147	397	7	101	101	NUM
ejpam-6147	397	8	,	,	PUNCT
ejpam-6147	397	9	2011	2011	NUM
ejpam-6147	397	10	.	.	PUNCT
ejpam-6147	398	1	[	[	X
ejpam-6147	398	2	16	16	NUM
ejpam-6147	398	3	]	]	X
ejpam-6147	398	4	g.	g.	PROPN
ejpam-6147	398	5	rahmat	rahmat	PROPN
ejpam-6147	398	6	,	,	PUNCT
ejpam-6147	398	7	m.	m.	NOUN
ejpam-6147	398	8	sarwar	sarwar	PROPN
ejpam-6147	398	9	,	,	PUNCT
ejpam-6147	398	10	and	and	CCONJ
ejpam-6147	398	11	c.	c.	PROPN
ejpam-6147	398	12	tune	tune	NOUN
ejpam-6147	398	13	.	.	PUNCT
ejpam-6147	399	1	strong	strong	ADJ
ejpam-6147	399	2	convergence	convergence	NOUN
ejpam-6147	399	3	to	to	ADP
ejpam-6147	399	4	a	a	DET
ejpam-6147	399	5	fixed	fix	VERB
ejpam-6147	399	6	point	point	NOUN
ejpam-6147	399	7	of	of	ADP
ejpam-6147	399	8	nonexpansive	nonexpansive	ADJ
ejpam-6147	399	9	discrete	discrete	ADJ
ejpam-6147	399	10	semigroup	semigroup	NOUN
ejpam-6147	399	11	in	in	ADP
ejpam-6147	399	12	strictly	strictly	ADV
ejpam-6147	399	13	convex	convex	VERB
ejpam-6147	399	14	banach	banach	NOUN
ejpam-6147	399	15	spaces	space	NOUN
ejpam-6147	399	16	.	.	PUNCT
ejpam-6147	400	1	journal	journal	NOUN
ejpam-6147	400	2	of	of	ADP
ejpam-6147	400	3	mathematical	mathematical	ADJ
ejpam-6147	400	4	analysis	analysis	NOUN
ejpam-6147	400	5	,	,	PUNCT
ejpam-6147	400	6	12(4):26–37	12(4):26–37	NUM
ejpam-6147	400	7	,	,	PUNCT
ejpam-6147	400	8	2021	2021	NUM
ejpam-6147	400	9	.	.	PUNCT
ejpam-6147	401	1	[	[	X
ejpam-6147	401	2	17	17	NUM
ejpam-6147	401	3	]	]	X
ejpam-6147	401	4	e.	e.	PROPN
ejpam-6147	401	5	karapınar	karapınar	PROPN
ejpam-6147	401	6	,	,	PUNCT
ejpam-6147	401	7	t.	t.	NOUN
ejpam-6147	401	8	abdeljawad	abdeljawad	NOUN
ejpam-6147	401	9	,	,	PUNCT
ejpam-6147	401	10	and	and	CCONJ
ejpam-6147	401	11	f.	f.	PROPN
ejpam-6147	401	12	jarad	jarad	PROPN
ejpam-6147	401	13	.	.	PUNCT
ejpam-6147	402	1	applying	apply	VERB
ejpam-6147	402	2	new	new	ADJ
ejpam-6147	402	3	fixed	fix	VERB
ejpam-6147	402	4	point	point	NOUN
ejpam-6147	402	5	theorems	theorem	NOUN
ejpam-6147	402	6	on	on	ADP
ejpam-6147	402	7	fractional	fractional	ADJ
ejpam-6147	402	8	and	and	CCONJ
ejpam-6147	402	9	ordinary	ordinary	ADJ
ejpam-6147	402	10	differential	differential	ADJ
ejpam-6147	402	11	equations	equation	NOUN
ejpam-6147	402	12	.	.	PUNCT
ejpam-6147	403	1	advances	advance	NOUN
ejpam-6147	403	2	in	in	ADP
ejpam-6147	403	3	continuous	continuous	ADJ
ejpam-6147	403	4	and	and	CCONJ
ejpam-6147	403	5	discrete	discrete	ADJ
ejpam-6147	403	6	models	model	NOUN
ejpam-6147	403	7	,	,	PUNCT
ejpam-6147	403	8	421	421	NUM
ejpam-6147	403	9	,	,	PUNCT
ejpam-6147	403	10	2019	2019	NUM
ejpam-6147	403	11	.	.	PUNCT
ejpam-6147	404	1	[	[	X
ejpam-6147	404	2	18	18	NUM
ejpam-6147	404	3	]	]	PUNCT
ejpam-6147	404	4	s.	s.	PROPN
ejpam-6147	404	5	f.	f.	PROPN
ejpam-6147	404	6	aldosary	aldosary	PROPN
ejpam-6147	404	7	,	,	PUNCT
ejpam-6147	404	8	mohamed	mohamed	PROPN
ejpam-6147	404	9	m.	m.	PROPN
ejpam-6147	404	10	a.	a.	PROPN
ejpam-6147	404	11	metwali	metwali	PROPN
ejpam-6147	404	12	,	,	PUNCT
ejpam-6147	404	13	m.	m.	NOUN
ejpam-6147	404	14	kazemi	kazemi	PROPN
ejpam-6147	404	15	,	,	PUNCT
ejpam-6147	404	16	and	and	CCONJ
ejpam-6147	404	17	a.	a.	NOUN
ejpam-6147	404	18	alsaadi	alsaadi	NOUN
ejpam-6147	404	19	.	.	PUNCT
ejpam-6147	405	1	on	on	ADP
ejpam-6147	405	2	integrable	integrable	ADJ
ejpam-6147	405	3	and	and	CCONJ
ejpam-6147	405	4	approximate	approximate	ADJ
ejpam-6147	405	5	solutions	solution	NOUN
ejpam-6147	405	6	for	for	ADP
ejpam-6147	405	7	hadamard	hadamard	ADJ
ejpam-6147	405	8	fractional	fractional	ADJ
ejpam-6147	405	9	quadratic	quadratic	ADJ
ejpam-6147	405	10	integral	integral	ADJ
ejpam-6147	405	11	equations	equation	NOUN
ejpam-6147	405	12	.	.	PUNCT
ejpam-6147	406	1	aims	aim	VERB
ejpam-6147	406	2	mathematics	mathematic	NOUN
ejpam-6147	406	3	,	,	PUNCT
ejpam-6147	406	4	9(3):5746–5762	9(3):5746–5762	NUM
ejpam-6147	406	5	,	,	PUNCT
ejpam-6147	406	6	2020	2020	NUM
ejpam-6147	406	7	.	.	PUNCT
ejpam-6147	407	1	[	[	X
ejpam-6147	407	2	19	19	NUM
ejpam-6147	407	3	]	]	X
ejpam-6147	407	4	mohamed	mohamed	PROPN
ejpam-6147	407	5	m.	m.	PROPN
ejpam-6147	407	6	a.	a.	PROPN
ejpam-6147	407	7	metwali	metwali	PROPN
ejpam-6147	407	8	,	,	PUNCT
ejpam-6147	407	9	k.	k.	PROPN
ejpam-6147	407	10	cichon	cichon	PROPN
ejpam-6147	407	11	,	,	PUNCT
ejpam-6147	407	12	and	and	CCONJ
ejpam-6147	407	13	m.	m.	NOUN
ejpam-6147	407	14	cichon	cichon	PROPN
ejpam-6147	407	15	.	.	PUNCT
ejpam-6147	408	1	on	on	ADP
ejpam-6147	408	2	some	some	DET
ejpam-6147	408	3	fixed	fix	VERB
ejpam-6147	408	4	point	point	NOUN
ejpam-6147	408	5	theorems	theorem	NOUN
ejpam-6147	408	6	in	in	ADP
ejpam-6147	408	7	abstract	abstract	ADJ
ejpam-6147	408	8	duality	duality	NOUN
ejpam-6147	408	9	pairs	pair	NOUN
ejpam-6147	408	10	.	.	PUNCT
ejpam-6147	409	1	revista	revista	PROPN
ejpam-6147	409	2	de	de	X
ejpam-6147	409	3	la	la	PROPN
ejpam-6147	409	4	union	union	PROPN
ejpam-6147	409	5	matematica	matematica	PROPN
ejpam-6147	409	6	argentina	argentina	PROPN
ejpam-6147	409	7	,	,	PUNCT
ejpam-6147	409	8	61(2):249–266	61(2):249–266	PROPN
ejpam-6147	409	9	,	,	PUNCT
ejpam-6147	409	10	2020	2020	NUM
ejpam-6147	409	11	.	.	PUNCT
ejpam-6147	410	1	[	[	X
ejpam-6147	410	2	20	20	NUM
ejpam-6147	410	3	]	]	X
ejpam-6147	410	4	l.	l.	PROPN
ejpam-6147	410	5	luo	luo	PROPN
ejpam-6147	410	6	,	,	PUNCT
ejpam-6147	410	7	r.	r.	PROPN
ejpam-6147	410	8	ullah	ullah	PROPN
ejpam-6147	410	9	,	,	PUNCT
ejpam-6147	410	10	g.	g.	PROPN
ejpam-6147	410	11	rahmat	rahmat	PROPN
ejpam-6147	410	12	,	,	PUNCT
ejpam-6147	410	13	s.	s.	PROPN
ejpam-6147	410	14	i.	i.	PROPN
ejpam-6147	410	15	butt	butt	PROPN
ejpam-6147	410	16	,	,	PUNCT
ejpam-6147	410	17	and	and	CCONJ
ejpam-6147	410	18	m.	m.	PROPN
ejpam-6147	410	19	numan	numan	PROPN
ejpam-6147	410	20	.	.	PUNCT
ejpam-6147	410	21	approximate	approximate	ADJ
ejpam-6147	410	22	common	common	ADJ
ejpam-6147	410	23	fixed	fix	VERB
ejpam-6147	410	24	points	point	NOUN
ejpam-6147	410	25	of	of	ADP
ejpam-6147	410	26	an	an	DET
ejpam-6147	410	27	evolution	evolution	NOUN
ejpam-6147	410	28	family	family	NOUN
ejpam-6147	410	29	on	on	ADP
ejpam-6147	410	30	a	a	DET
ejpam-6147	410	31	metric	metric	ADJ
ejpam-6147	410	32	space	space	NOUN
ejpam-6147	410	33	.	.	PUNCT
ejpam-6147	411	1	journal	journal	NOUN
ejpam-6147	411	2	of	of	ADP
ejpam-6147	411	3	mathematics	mathematic	NOUN
ejpam-6147	411	4	,	,	PUNCT
ejpam-6147	411	5	6764280	6764280	NUM
ejpam-6147	411	6	,	,	PUNCT
ejpam-6147	411	7	2021	2021	NUM
ejpam-6147	411	8	.	.	PUNCT
ejpam-6147	412	1	[	[	X
ejpam-6147	412	2	21	21	NUM
ejpam-6147	412	3	]	]	X
ejpam-6147	412	4	g.	g.	PROPN
ejpam-6147	412	5	rahmat	rahmat	PROPN
ejpam-6147	412	6	,	,	PUNCT
ejpam-6147	412	7	m.	m.	PROPN
ejpam-6147	412	8	khan	khan	PROPN
ejpam-6147	412	9	,	,	PUNCT
ejpam-6147	412	10	m.	m.	NOUN
ejpam-6147	412	11	sarwar	sarwar	PROPN
ejpam-6147	412	12	,	,	PUNCT
ejpam-6147	412	13	h.	h.	PROPN
ejpam-6147	412	14	aydi	aydi	PROPN
ejpam-6147	412	15	,	,	PUNCT
ejpam-6147	412	16	and	and	CCONJ
ejpam-6147	412	17	e.	e.	PROPN
ejpam-6147	412	18	ameer	ameer	PROPN
ejpam-6147	412	19	.	.	PUNCT
ejpam-6147	413	1	a	a	DET
ejpam-6147	413	2	strong	strong	ADJ
ejpam-6147	413	3	convergence	convergence	NOUN
ejpam-6147	413	4	to	to	ADP
ejpam-6147	413	5	a	a	DET
ejpam-6147	413	6	common	common	ADJ
ejpam-6147	413	7	fixed	fix	VERB
ejpam-6147	413	8	point	point	NOUN
ejpam-6147	413	9	of	of	ADP
ejpam-6147	413	10	a	a	DET
ejpam-6147	413	11	subfamily	subfamily	NOUN
ejpam-6147	413	12	of	of	ADP
ejpam-6147	413	13	a	a	DET
ejpam-6147	413	14	non	non	ADJ
ejpam-6147	413	15	-	-	ADJ
ejpam-6147	413	16	expansive	expansive	ADJ
ejpam-6147	413	17	evolution	evolution	NOUN
ejpam-6147	413	18	family	family	NOUN
ejpam-6147	413	19	of	of	ADP
ejpam-6147	413	20	bounded	bounded	ADJ
ejpam-6147	413	21	linear	linear	PROPN
ejpam-6147	413	22	operators	operator	NOUN
ejpam-6147	413	23	on	on	ADP
ejpam-6147	413	24	a	a	DET
ejpam-6147	413	25	hilbert	hilbert	NOUN
ejpam-6147	413	26	space	space	NOUN
ejpam-6147	413	27	.	.	PUNCT
ejpam-6147	414	1	journal	journal	PROPN
ejpam-6147	414	2	of	of	ADP
ejpam-6147	414	3	mathematics	mathematic	NOUN
ejpam-6147	414	4	,	,	PUNCT
ejpam-6147	414	5	2021:2392088	2021:2392088	NUM
ejpam-6147	414	6	,	,	PUNCT
ejpam-6147	414	7	2021	2021	NUM
ejpam-6147	414	8	.	.	PUNCT
ejpam-6147	415	1	[	[	X
ejpam-6147	415	2	22	22	NUM
ejpam-6147	415	3	]	]	PUNCT
ejpam-6147	415	4	s.	s.	PROPN
ejpam-6147	415	5	fuan	fuan	PROPN
ejpam-6147	415	6	,	,	PUNCT
ejpam-6147	415	7	r.	r.	PROPN
ejpam-6147	415	8	ullah	ullah	PROPN
ejpam-6147	415	9	,	,	PUNCT
ejpam-6147	415	10	g.	g.	PROPN
ejpam-6147	415	11	rahmat	rahmat	PROPN
ejpam-6147	415	12	,	,	PUNCT
ejpam-6147	415	13	m.	m.	PROPN
ejpam-6147	415	14	numan	numan	PROPN
ejpam-6147	415	15	,	,	PUNCT
ejpam-6147	415	16	s.	s.	PROPN
ejpam-6147	415	17	i.	i.	PROPN
ejpam-6147	415	18	butt	butt	PROPN
ejpam-6147	415	19	,	,	PUNCT
ejpam-6147	415	20	and	and	CCONJ
ejpam-6147	415	21	x.	x.	NOUN
ejpam-6147	415	22	ge	ge	PROPN
ejpam-6147	415	23	.	.	PROPN
ejpam-6147	415	24	approximate	approximate	PROPN
ejpam-6147	415	25	fixed	fix	VERB
ejpam-6147	415	26	point	point	NOUN
ejpam-6147	415	27	sequences	sequence	NOUN
ejpam-6147	415	28	of	of	ADP
ejpam-6147	415	29	an	an	DET
ejpam-6147	415	30	evolution	evolution	NOUN
ejpam-6147	415	31	family	family	NOUN
ejpam-6147	415	32	on	on	ADP
ejpam-6147	415	33	a	a	DET
ejpam-6147	415	34	metric	metric	ADJ
ejpam-6147	415	35	space	space	NOUN
ejpam-6147	415	36	.	.	PUNCT
ejpam-6147	416	1	journal	journal	NOUN
ejpam-6147	416	2	of	of	ADP
ejpam-6147	416	3	mathematics	mathematic	NOUN
ejpam-6147	416	4	,	,	PUNCT
ejpam-6147	416	5	2020:1647193	2020:1647193	NUM
ejpam-6147	416	6	,	,	PUNCT
ejpam-6147	416	7	2020	2020	NUM
ejpam-6147	416	8	.	.	PUNCT
ejpam-6147	417	1	[	[	X
ejpam-6147	417	2	23	23	NUM
ejpam-6147	417	3	]	]	PUNCT
ejpam-6147	417	4	t.	t.	PROPN
ejpam-6147	417	5	suzuki	suzuki	PROPN
ejpam-6147	417	6	.	.	PUNCT
ejpam-6147	418	1	strong	strong	ADJ
ejpam-6147	418	2	convergence	convergence	NOUN
ejpam-6147	418	3	theorems	theorem	NOUN
ejpam-6147	418	4	for	for	ADP
ejpam-6147	418	5	infinite	infinite	ADJ
ejpam-6147	418	6	families	family	NOUN
ejpam-6147	418	7	of	of	ADP
ejpam-6147	418	8	nonexpansive	nonexpansive	ADJ
ejpam-6147	418	9	mappings	mapping	NOUN
ejpam-6147	418	10	in	in	ADP
ejpam-6147	418	11	general	general	ADJ
ejpam-6147	418	12	banach	banach	NOUN
ejpam-6147	418	13	spaces	space	VERB
ejpam-6147	418	14	.	.	PUNCT
ejpam-6147	419	1	fixed	fix	VERB
ejpam-6147	419	2	point	point	NOUN
ejpam-6147	419	3	theory	theory	NOUN
ejpam-6147	419	4	and	and	CCONJ
ejpam-6147	419	5	applications	application	NOUN
ejpam-6147	419	6	,	,	PUNCT
ejpam-6147	419	7	685918:103–123	685918:103–123	NOUN
ejpam-6147	419	8	,	,	PUNCT
ejpam-6147	419	9	2005	2005	NUM
ejpam-6147	419	10	.	.	PUNCT
ejpam-6147	420	1	[	[	X
ejpam-6147	420	2	24	24	NUM
ejpam-6147	420	3	]	]	PUNCT
ejpam-6147	420	4	h.	h.	PROPN
ejpam-6147	420	5	k.	k.	PROPN
ejpam-6147	421	1	xu	xu	PROPN
ejpam-6147	421	2	.	.	PUNCT
ejpam-6147	422	1	iterative	iterative	NOUN
ejpam-6147	422	2	algorithms	algorithm	NOUN
ejpam-6147	422	3	for	for	ADP
ejpam-6147	422	4	nonlinear	nonlinear	ADJ
ejpam-6147	422	5	operators	operator	NOUN
ejpam-6147	422	6	.	.	PUNCT
ejpam-6147	423	1	journal	journal	NOUN
ejpam-6147	423	2	of	of	ADP
ejpam-6147	423	3	the	the	DET
ejpam-6147	423	4	london	london	PROPN
ejpam-6147	423	5	mathematical	mathematical	ADJ
ejpam-6147	423	6	society	society	NOUN
ejpam-6147	423	7	,	,	PUNCT
ejpam-6147	423	8	66:240–256	66:240–256	NUM
ejpam-6147	423	9	,	,	PUNCT
ejpam-6147	423	10	2002	2002	NUM
ejpam-6147	423	11	.	.	PUNCT
ejpam-6147	424	1	[	[	X
ejpam-6147	424	2	25	25	NUM
ejpam-6147	424	3	]	]	PUNCT
ejpam-6147	424	4	t.	t.	PROPN
ejpam-6147	424	5	suzuki	suzuki	PROPN
ejpam-6147	424	6	.	.	PUNCT
ejpam-6147	425	1	the	the	DET
ejpam-6147	425	2	set	set	NOUN
ejpam-6147	425	3	of	of	ADP
ejpam-6147	425	4	common	common	ADJ
ejpam-6147	425	5	fixed	fix	VERB
ejpam-6147	425	6	points	point	NOUN
ejpam-6147	425	7	of	of	ADP
ejpam-6147	425	8	one	one	NUM
ejpam-6147	425	9	-	-	PUNCT
ejpam-6147	425	10	parameter	parameter	NOUN
ejpam-6147	425	11	continuous	continuous	ADJ
ejpam-6147	425	12	semigroup	semigroup	NOUN
ejpam-6147	425	13	of	of	ADP
ejpam-6147	425	14	mappings	mapping	NOUN
ejpam-6147	425	15	is	be	AUX
ejpam-6147	425	16	f(t(1	f(t(1	PROPN
ejpam-6147	425	17	)	)	PUNCT
ejpam-6147	425	18	)	)	PUNCT
ejpam-6147	425	19	∩	∩	NOUN
ejpam-6147	425	20	f(t	f(t	NOUN
ejpam-6147	425	21	(	(	PUNCT
ejpam-6147	425	22	√	√	ADP
ejpam-6147	425	23	2	2	NUM
ejpam-6147	425	24	)	)	PUNCT
ejpam-6147	425	25	)	)	PUNCT
ejpam-6147	425	26	.	.	PUNCT
ejpam-6147	426	1	proceedings	proceeding	NOUN
ejpam-6147	426	2	of	of	ADP
ejpam-6147	426	3	the	the	DET
ejpam-6147	426	4	american	american	PROPN
ejpam-6147	426	5	mathematical	mathematical	PROPN
ejpam-6147	426	6	society	society	NOUN
ejpam-6147	426	7	,	,	PUNCT
ejpam-6147	426	8	134(3):673–681	134(3):673–681	NUM
ejpam-6147	426	9	,	,	PUNCT
ejpam-6147	426	10	2006	2006	NUM
ejpam-6147	426	11	.	.	PUNCT
ejpam-6147	427	1	[	[	X
ejpam-6147	427	2	26	26	NUM
ejpam-6147	427	3	]	]	X
ejpam-6147	427	4	c.	c.	NOUN
ejpam-6147	427	5	buse	buse	PROPN
ejpam-6147	427	6	,	,	PUNCT
ejpam-6147	427	7	a.	a.	PROPN
ejpam-6147	427	8	khan	khan	PROPN
ejpam-6147	427	9	,	,	PUNCT
ejpam-6147	427	10	g.	g.	PROPN
ejpam-6147	427	11	rahmat	rahmat	PROPN
ejpam-6147	427	12	,	,	PUNCT
ejpam-6147	427	13	and	and	CCONJ
ejpam-6147	427	14	a.	a.	NOUN
ejpam-6147	427	15	tabassum	tabassum	NOUN
ejpam-6147	427	16	.	.	PUNCT
ejpam-6147	428	1	a	a	DET
ejpam-6147	428	2	new	new	ADJ
ejpam-6147	428	3	estimation	estimation	NOUN
ejpam-6147	428	4	of	of	ADP
ejpam-6147	428	5	the	the	DET
ejpam-6147	428	6	growth	growth	NOUN
ejpam-6147	428	7	bound	bind	VERB
ejpam-6147	428	8	of	of	ADP
ejpam-6147	428	9	a	a	DET
ejpam-6147	428	10	periodic	periodic	ADJ
ejpam-6147	428	11	evolution	evolution	NOUN
ejpam-6147	428	12	family	family	NOUN
ejpam-6147	428	13	on	on	ADP
ejpam-6147	428	14	banach	banach	NOUN
ejpam-6147	428	15	spaces	space	NOUN
ejpam-6147	428	16	.	.	PUNCT
ejpam-6147	429	1	journal	journal	NOUN
ejpam-6147	429	2	of	of	ADP
ejpam-6147	429	3	function	function	NOUN
ejpam-6147	429	4	spaces	space	NOUN
ejpam-6147	429	5	,	,	PUNCT
ejpam-6147	429	6	2013:260920	2013:260920	NUM
ejpam-6147	429	7	,	,	PUNCT
ejpam-6147	429	8	2013	2013	NUM
ejpam-6147	429	9	.	.	PUNCT