id	sid	tid	token	lemma	pos
ejpam-6133	1	1	european	european	PROPN
ejpam-6133	1	2	journal	journal	PROPN
ejpam-6133	1	3	of	of	ADP
ejpam-6133	1	4	pure	pure	ADJ
ejpam-6133	1	5	and	and	CCONJ
ejpam-6133	1	6	applied	applied	ADJ
ejpam-6133	1	7	mathematics	mathematic	NOUN
ejpam-6133	1	8	2025	2025	NUM
ejpam-6133	1	9	,	,	PUNCT
ejpam-6133	1	10	vol	vol	NOUN
ejpam-6133	1	11	.	.	PROPN
ejpam-6133	1	12	18	18	NUM
ejpam-6133	1	13	,	,	PUNCT
ejpam-6133	1	14	issue	issue	NOUN
ejpam-6133	1	15	3	3	NUM
ejpam-6133	1	16	,	,	PUNCT
ejpam-6133	1	17	article	article	NOUN
ejpam-6133	1	18	number	number	NOUN
ejpam-6133	1	19	6133	6133	NUM
ejpam-6133	1	20	issn	issn	VERB
ejpam-6133	1	21	1307	1307	NUM
ejpam-6133	1	22	-	-	SYM
ejpam-6133	1	23	5543	5543	NUM
ejpam-6133	1	24	–	–	PUNCT
ejpam-6133	1	25	ejpam.com	ejpam.com	X
ejpam-6133	1	26	published	publish	VERB
ejpam-6133	1	27	by	by	ADP
ejpam-6133	1	28	new	new	PROPN
ejpam-6133	1	29	york	york	PROPN
ejpam-6133	1	30	business	business	PROPN
ejpam-6133	1	31	global	global	PROPN
ejpam-6133	1	32	a	a	DET
ejpam-6133	1	33	fixed	fix	VERB
ejpam-6133	1	34	point	point	NOUN
ejpam-6133	1	35	result	result	NOUN
ejpam-6133	1	36	in	in	ADP
ejpam-6133	1	37	a	a	DET
ejpam-6133	1	38	dcms	dcms	NOUN
ejpam-6133	1	39	setting	setting	NOUN
ejpam-6133	1	40	and	and	CCONJ
ejpam-6133	1	41	a	a	DET
ejpam-6133	1	42	fredholm	fredholm	ADJ
ejpam-6133	1	43	integral	integral	ADJ
ejpam-6133	1	44	equation	equation	NOUN
ejpam-6133	1	45	hassen	hassen	NOUN
ejpam-6133	1	46	aydi1,2,∗	aydi1,2,∗	PROPN
ejpam-6133	1	47	,	,	PUNCT
ejpam-6133	1	48	hamdi	hamdi	PROPN
ejpam-6133	1	49	hammouda3	hammouda3	PROPN
ejpam-6133	1	50	,	,	PUNCT
ejpam-6133	1	51	saber	saber	NOUN
ejpam-6133	1	52	mansour4	mansour4	PROPN
ejpam-6133	1	53	1	1	NUM
ejpam-6133	2	1	institut	institut	PROPN
ejpam-6133	2	2	supérieur	supérieur	PROPN
ejpam-6133	2	3	d’informatique	d’informatique	PROPN
ejpam-6133	2	4	et	et	NOUN
ejpam-6133	2	5	des	des	X
ejpam-6133	2	6	techniques	techniques	X
ejpam-6133	2	7	de	de	X
ejpam-6133	2	8	communication	communication	NOUN
ejpam-6133	2	9	,	,	PUNCT
ejpam-6133	2	10	université	université	ADJ
ejpam-6133	2	11	de	de	X
ejpam-6133	2	12	sousse	sousse	PROPN
ejpam-6133	2	13	,	,	PUNCT
ejpam-6133	2	14	h.	h.	PROPN
ejpam-6133	2	15	sousse	sousse	PROPN
ejpam-6133	2	16	4000	4000	NUM
ejpam-6133	2	17	,	,	PUNCT
ejpam-6133	2	18	tunisia	tunisia	PROPN
ejpam-6133	2	19	2	2	NUM
ejpam-6133	2	20	department	department	NOUN
ejpam-6133	2	21	of	of	ADP
ejpam-6133	2	22	mathematics	mathematic	NOUN
ejpam-6133	2	23	and	and	CCONJ
ejpam-6133	2	24	applied	apply	VERB
ejpam-6133	2	25	mathematics	mathematic	NOUN
ejpam-6133	2	26	,	,	PUNCT
ejpam-6133	2	27	sefako	sefako	VERB
ejpam-6133	2	28	makgatho	makgatho	PROPN
ejpam-6133	2	29	health	health	PROPN
ejpam-6133	2	30	sciences	sciences	PROPN
ejpam-6133	2	31	university	university	PROPN
ejpam-6133	2	32	,	,	PUNCT
ejpam-6133	2	33	ga	ga	PROPN
ejpam-6133	2	34	-	-	NOUN
ejpam-6133	2	35	rankuwa	rankuwa	ADJ
ejpam-6133	2	36	,	,	PUNCT
ejpam-6133	2	37	south	south	PROPN
ejpam-6133	2	38	africa	africa	PROPN
ejpam-6133	2	39	.	.	PUNCT
ejpam-6133	3	1	3	3	NUM
ejpam-6133	3	2	université	université	NOUN
ejpam-6133	3	3	de	de	X
ejpam-6133	3	4	monastir	monastir	PROPN
ejpam-6133	3	5	,	,	PUNCT
ejpam-6133	3	6	institut	institut	PROPN
ejpam-6133	3	7	préparatoire	préparatoire	PROPN
ejpam-6133	3	8	des	des	PROPN
ejpam-6133	3	9	études	études	PROPN
ejpam-6133	3	10	d’ingénieurs	d’ingénieurs	PROPN
ejpam-6133	3	11	de	de	PROPN
ejpam-6133	3	12	monastir	monastir	PROPN
ejpam-6133	3	13	,	,	PUNCT
ejpam-6133	3	14	monastir	monastir	PROPN
ejpam-6133	3	15	,	,	PUNCT
ejpam-6133	3	16	tunisia	tunisia	PROPN
ejpam-6133	3	17	4	4	NUM
ejpam-6133	3	18	department	department	NOUN
ejpam-6133	3	19	of	of	ADP
ejpam-6133	3	20	mathematics	mathematic	NOUN
ejpam-6133	3	21	,	,	PUNCT
ejpam-6133	3	22	umm	umm	INTJ
ejpam-6133	3	23	al	al	PROPN
ejpam-6133	3	24	-	-	PUNCT
ejpam-6133	3	25	qura	qura	PROPN
ejpam-6133	3	26	university	university	NOUN
ejpam-6133	3	27	,	,	PUNCT
ejpam-6133	3	28	faculty	faculty	NOUN
ejpam-6133	3	29	of	of	ADP
ejpam-6133	3	30	sciences	sciences	PROPN
ejpam-6133	3	31	,	,	PUNCT
ejpam-6133	3	32	p.o	p.o	PROPN
ejpam-6133	3	33	.	.	PROPN
ejpam-6133	3	34	box	box	PROPN
ejpam-6133	3	35	14035	14035	NUM
ejpam-6133	3	36	,	,	PUNCT
ejpam-6133	3	37	holy	holy	PROPN
ejpam-6133	3	38	makkah	makkah	PROPN
ejpam-6133	3	39	21955	21955	NUM
ejpam-6133	3	40	,	,	PUNCT
ejpam-6133	3	41	saudi	saudi	PROPN
ejpam-6133	3	42	arabia	arabia	PROPN
ejpam-6133	3	43	abstract	abstract	NOUN
ejpam-6133	3	44	.	.	PUNCT
ejpam-6133	4	1	in	in	ADP
ejpam-6133	4	2	this	this	DET
ejpam-6133	4	3	present	present	ADJ
ejpam-6133	4	4	work	work	NOUN
ejpam-6133	4	5	,	,	PUNCT
ejpam-6133	4	6	we	we	PRON
ejpam-6133	4	7	prove	prove	VERB
ejpam-6133	4	8	a	a	DET
ejpam-6133	4	9	fixed	fix	VERB
ejpam-6133	4	10	point	point	NOUN
ejpam-6133	4	11	result	result	NOUN
ejpam-6133	4	12	for	for	ADP
ejpam-6133	4	13	generalized	generalized	ADJ
ejpam-6133	4	14	contraction	contraction	NOUN
ejpam-6133	4	15	mappings	mapping	NOUN
ejpam-6133	4	16	in	in	ADP
ejpam-6133	4	17	the	the	DET
ejpam-6133	4	18	setting	setting	NOUN
ejpam-6133	4	19	of	of	ADP
ejpam-6133	4	20	a	a	DET
ejpam-6133	4	21	double	double	ADJ
ejpam-6133	4	22	control	control	NOUN
ejpam-6133	4	23	metric	metric	ADJ
ejpam-6133	4	24	space	space	NOUN
ejpam-6133	4	25	(	(	PUNCT
ejpam-6133	4	26	dcms	dcms	NOUN
ejpam-6133	4	27	)	)	PUNCT
ejpam-6133	4	28	by	by	ADP
ejpam-6133	4	29	using	use	VERB
ejpam-6133	4	30	α	α	NUM
ejpam-6133	4	31	-	-	ADJ
ejpam-6133	4	32	orbital	orbital	ADJ
ejpam-6133	4	33	admissibility	admissibility	NOUN
ejpam-6133	4	34	.	.	PUNCT
ejpam-6133	5	1	the	the	DET
ejpam-6133	5	2	uniqueness	uniqueness	NOUN
ejpam-6133	5	3	of	of	ADP
ejpam-6133	5	4	the	the	DET
ejpam-6133	5	5	fixed	fix	VERB
ejpam-6133	5	6	point	point	NOUN
ejpam-6133	5	7	is	be	AUX
ejpam-6133	5	8	established	establish	VERB
ejpam-6133	5	9	by	by	ADP
ejpam-6133	5	10	adding	add	VERB
ejpam-6133	5	11	further	further	ADJ
ejpam-6133	5	12	hypotheses	hypothesis	NOUN
ejpam-6133	5	13	.	.	PUNCT
ejpam-6133	6	1	the	the	DET
ejpam-6133	6	2	presented	present	VERB
ejpam-6133	6	3	result	result	NOUN
ejpam-6133	6	4	is	be	AUX
ejpam-6133	6	5	supported	support	VERB
ejpam-6133	6	6	by	by	ADP
ejpam-6133	6	7	a	a	DET
ejpam-6133	6	8	concrete	concrete	ADJ
ejpam-6133	6	9	example	example	NOUN
ejpam-6133	6	10	.	.	PUNCT
ejpam-6133	7	1	moreover	moreover	ADV
ejpam-6133	7	2	,	,	PUNCT
ejpam-6133	7	3	we	we	PRON
ejpam-6133	7	4	ensure	ensure	VERB
ejpam-6133	7	5	the	the	DET
ejpam-6133	7	6	existence	existence	NOUN
ejpam-6133	7	7	of	of	ADP
ejpam-6133	7	8	a	a	DET
ejpam-6133	7	9	solution	solution	NOUN
ejpam-6133	7	10	of	of	ADP
ejpam-6133	7	11	a	a	DET
ejpam-6133	7	12	fredholm	fredholm	NOUN
ejpam-6133	7	13	type	type	NOUN
ejpam-6133	7	14	integral	integral	ADJ
ejpam-6133	7	15	equation	equation	NOUN
ejpam-6133	7	16	via	via	ADP
ejpam-6133	7	17	a	a	DET
ejpam-6133	7	18	fixed	fix	VERB
ejpam-6133	7	19	point	point	NOUN
ejpam-6133	7	20	technique	technique	NOUN
ejpam-6133	7	21	.	.	PUNCT
ejpam-6133	8	1	some	some	DET
ejpam-6133	8	2	consequences	consequence	NOUN
ejpam-6133	8	3	are	be	AUX
ejpam-6133	8	4	also	also	ADV
ejpam-6133	8	5	presented	present	VERB
ejpam-6133	8	6	to	to	PART
ejpam-6133	8	7	make	make	VERB
ejpam-6133	8	8	effective	effective	ADJ
ejpam-6133	8	9	the	the	DET
ejpam-6133	8	10	obtained	obtain	VERB
ejpam-6133	8	11	results	result	NOUN
ejpam-6133	8	12	.	.	PUNCT
ejpam-6133	9	1	2020	2020	NUM
ejpam-6133	9	2	mathematics	mathematic	NOUN
ejpam-6133	9	3	subject	subject	NOUN
ejpam-6133	9	4	classifications	classification	NOUN
ejpam-6133	9	5	:	:	PUNCT
ejpam-6133	9	6	74h10	74h10	NUM
ejpam-6133	9	7	,	,	PUNCT
ejpam-6133	9	8	34a08	34a08	NUM
ejpam-6133	9	9	,	,	PUNCT
ejpam-6133	9	10	26a33	26a33	NUM
ejpam-6133	9	11	,	,	PUNCT
ejpam-6133	9	12	34b15	34b15	NUM
ejpam-6133	9	13	key	key	ADJ
ejpam-6133	9	14	words	word	NOUN
ejpam-6133	9	15	and	and	CCONJ
ejpam-6133	9	16	phrases	phrase	NOUN
ejpam-6133	9	17	:	:	PUNCT
ejpam-6133	9	18	contraction	contraction	NOUN
ejpam-6133	9	19	,	,	PUNCT
ejpam-6133	9	20	fixed	fix	VERB
ejpam-6133	9	21	point	point	NOUN
ejpam-6133	9	22	,	,	PUNCT
ejpam-6133	9	23	double	double	ADJ
ejpam-6133	9	24	controlled	control	VERB
ejpam-6133	9	25	metric	metric	ADJ
ejpam-6133	9	26	space	space	NOUN
ejpam-6133	9	27	,	,	PUNCT
ejpam-6133	9	28	α	α	NOUN
ejpam-6133	9	29	-	-	ADJ
ejpam-6133	9	30	admissible	admissible	ADJ
ejpam-6133	9	31	,	,	PUNCT
ejpam-6133	9	32	fredholm	fredholm	ADJ
ejpam-6133	9	33	integral	integral	ADJ
ejpam-6133	9	34	equation	equation	NOUN
ejpam-6133	9	35	1	1	NUM
ejpam-6133	9	36	.	.	PUNCT
ejpam-6133	10	1	introduction	introduction	NOUN
ejpam-6133	10	2	the	the	DET
ejpam-6133	10	3	fixed	fix	VERB
ejpam-6133	10	4	point	point	NOUN
ejpam-6133	10	5	result	result	VERB
ejpam-6133	10	6	due	due	ADP
ejpam-6133	10	7	to	to	ADP
ejpam-6133	10	8	banach	banach	NOUN
ejpam-6133	10	9	[	[	X
ejpam-6133	10	10	1	1	NUM
ejpam-6133	10	11	]	]	PUNCT
ejpam-6133	10	12	is	be	AUX
ejpam-6133	10	13	considered	consider	VERB
ejpam-6133	10	14	as	as	ADP
ejpam-6133	10	15	the	the	DET
ejpam-6133	10	16	most	most	ADV
ejpam-6133	10	17	essential	essential	ADJ
ejpam-6133	10	18	theorem	theorem	NOUN
ejpam-6133	10	19	in	in	ADP
ejpam-6133	10	20	fixed	fix	VERB
ejpam-6133	10	21	point	point	NOUN
ejpam-6133	10	22	theory	theory	NOUN
ejpam-6133	10	23	.	.	PUNCT
ejpam-6133	11	1	it	it	PRON
ejpam-6133	11	2	asserts	assert	VERB
ejpam-6133	11	3	that	that	SCONJ
ejpam-6133	11	4	a	a	DET
ejpam-6133	11	5	contraction	contraction	NOUN
ejpam-6133	11	6	mapping	mapping	NOUN
ejpam-6133	11	7	on	on	ADP
ejpam-6133	11	8	a	a	DET
ejpam-6133	11	9	complete	complete	ADJ
ejpam-6133	11	10	metric	metric	ADJ
ejpam-6133	11	11	space	space	NOUN
ejpam-6133	11	12	admits	admit	VERB
ejpam-6133	11	13	a	a	DET
ejpam-6133	11	14	unique	unique	ADJ
ejpam-6133	11	15	fixed	fix	VERB
ejpam-6133	11	16	point	point	NOUN
ejpam-6133	11	17	.	.	PUNCT
ejpam-6133	12	1	in	in	ADP
ejpam-6133	12	2	1989	1989	NUM
ejpam-6133	12	3	,	,	PUNCT
ejpam-6133	12	4	an	an	DET
ejpam-6133	12	5	interesting	interesting	ADJ
ejpam-6133	12	6	extension	extension	NOUN
ejpam-6133	12	7	of	of	ADP
ejpam-6133	12	8	the	the	DET
ejpam-6133	12	9	metric	metric	ADJ
ejpam-6133	12	10	space	space	NOUN
ejpam-6133	12	11	was	be	AUX
ejpam-6133	12	12	explored	explore	VERB
ejpam-6133	12	13	by	by	ADP
ejpam-6133	12	14	bakhtin	bakhtin	NOUN
ejpam-6133	12	15	[	[	X
ejpam-6133	12	16	2	2	NUM
ejpam-6133	12	17	]	]	PUNCT
ejpam-6133	12	18	and	and	CCONJ
ejpam-6133	12	19	czerwik	czerwik	PROPN
ejpam-6133	13	1	[	[	X
ejpam-6133	13	2	3	3	X
ejpam-6133	13	3	]	]	PUNCT
ejpam-6133	13	4	by	by	ADP
ejpam-6133	13	5	initiating	initiate	VERB
ejpam-6133	13	6	the	the	DET
ejpam-6133	13	7	concept	concept	NOUN
ejpam-6133	13	8	of	of	ADP
ejpam-6133	13	9	b	b	NOUN
ejpam-6133	13	10	-	-	PUNCT
ejpam-6133	13	11	metric	metric	ADJ
ejpam-6133	13	12	spaces	space	NOUN
ejpam-6133	13	13	.	.	PUNCT
ejpam-6133	14	1	later	later	ADV
ejpam-6133	14	2	,	,	PUNCT
ejpam-6133	14	3	in	in	ADP
ejpam-6133	14	4	2017	2017	NUM
ejpam-6133	14	5	,	,	PUNCT
ejpam-6133	14	6	this	this	DET
ejpam-6133	14	7	setting	setting	NOUN
ejpam-6133	14	8	was	be	AUX
ejpam-6133	14	9	generalized	generalize	VERB
ejpam-6133	14	10	to	to	ADP
ejpam-6133	14	11	extended	extend	VERB
ejpam-6133	14	12	b	b	X
ejpam-6133	14	13	-	-	ADJ
ejpam-6133	14	14	metric	metric	ADJ
ejpam-6133	14	15	spaces	space	NOUN
ejpam-6133	14	16	initiated	initiate	VERB
ejpam-6133	14	17	by	by	ADP
ejpam-6133	14	18	kiran	kiran	PROPN
ejpam-6133	14	19	et	et	PROPN
ejpam-6133	14	20	al	al	PROPN
ejpam-6133	14	21	.	.	PUNCT
ejpam-6133	15	1	[	[	X
ejpam-6133	15	2	4	4	NUM
ejpam-6133	15	3	]	]	PUNCT
ejpam-6133	15	4	,	,	PUNCT
ejpam-6133	15	5	where	where	SCONJ
ejpam-6133	15	6	the	the	DET
ejpam-6133	15	7	triangular	triangular	NOUN
ejpam-6133	15	8	inequality	inequality	NOUN
ejpam-6133	15	9	is	be	AUX
ejpam-6133	15	10	extended	extend	VERB
ejpam-6133	15	11	via	via	ADP
ejpam-6133	15	12	a	a	DET
ejpam-6133	15	13	controlled	control	VERB
ejpam-6133	15	14	function	function	NOUN
ejpam-6133	15	15	.	.	PUNCT
ejpam-6133	16	1	on	on	ADP
ejpam-6133	16	2	the	the	DET
ejpam-6133	16	3	other	other	ADJ
ejpam-6133	16	4	hand	hand	NOUN
ejpam-6133	16	5	,	,	PUNCT
ejpam-6133	16	6	using	use	VERB
ejpam-6133	16	7	two	two	NUM
ejpam-6133	16	8	control	control	NOUN
ejpam-6133	16	9	functions	function	NOUN
ejpam-6133	16	10	ϖ	ϖ	NOUN
ejpam-6133	16	11	,	,	PUNCT
ejpam-6133	16	12	ϵ	ϵ	X
ejpam-6133	16	13	:	:	PUNCT
ejpam-6133	16	14	℧	℧	PROPN
ejpam-6133	16	15	×	×	NOUN
ejpam-6133	16	16	℧	℧	X
ejpam-6133	16	17	−→	−→	NOUN
ejpam-6133	16	18	[	[	X
ejpam-6133	16	19	1,∞	1,∞	NUM
ejpam-6133	16	20	)	)	PUNCT
ejpam-6133	16	21	,	,	PUNCT
ejpam-6133	16	22	the	the	DET
ejpam-6133	16	23	notion	notion	NOUN
ejpam-6133	16	24	of	of	ADP
ejpam-6133	16	25	a	a	DET
ejpam-6133	16	26	double	double	ADJ
ejpam-6133	16	27	controlled	control	VERB
ejpam-6133	16	28	metric	metric	ADJ
ejpam-6133	16	29	space	space	NOUN
ejpam-6133	16	30	[	[	X
ejpam-6133	16	31	5	5	NUM
ejpam-6133	16	32	]	]	PUNCT
ejpam-6133	16	33	(	(	PUNCT
ejpam-6133	16	34	dcms	dcms	NOUN
ejpam-6133	16	35	)	)	PUNCT
ejpam-6133	16	36	was	be	AUX
ejpam-6133	16	37	considred	considre	VERB
ejpam-6133	16	38	by	by	ADP
ejpam-6133	16	39	abdeljawad	abdeljawad	PROPN
ejpam-6133	16	40	et	et	PROPN
ejpam-6133	16	41	al	al	PROPN
ejpam-6133	16	42	.	.	PUNCT
ejpam-6133	17	1	[	[	X
ejpam-6133	17	2	5	5	NUM
ejpam-6133	17	3	]	]	PUNCT
ejpam-6133	17	4	.	.	PUNCT
ejpam-6133	18	1	many	many	ADJ
ejpam-6133	18	2	related	related	ADJ
ejpam-6133	18	3	∗corresponding	∗corresponde	VERB
ejpam-6133	18	4	author	author	NOUN
ejpam-6133	18	5	.	.	PUNCT
ejpam-6133	19	1	doi	doi	NOUN
ejpam-6133	19	2	:	:	PUNCT
ejpam-6133	19	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6133	https://doi.org/10.29020/nybg.ejpam.v18i3.6133	NUM
ejpam-6133	19	4	email	email	NOUN
ejpam-6133	19	5	addresses	address	VERB
ejpam-6133	19	6	:	:	PUNCT
ejpam-6133	19	7	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	INTJ
ejpam-6133	19	8	(	(	PUNCT
ejpam-6133	19	9	h.	h.	PROPN
ejpam-6133	19	10	aydi	aydi	ADV
ejpam-6133	19	11	)	)	PUNCT
ejpam-6133	19	12	,	,	PUNCT
ejpam-6133	19	13	7amdi7ammouda@gmail.com	7amdi7ammouda@gmail.com	NUM
ejpam-6133	19	14	(	(	PUNCT
ejpam-6133	19	15	h.	h.	PROPN
ejpam-6133	19	16	hammouda	hammouda	PROPN
ejpam-6133	19	17	)	)	PUNCT
ejpam-6133	19	18	,	,	PUNCT
ejpam-6133	19	19	samansour@uqu.edu.sa	samansour@uqu.edu.sa	PROPN
ejpam-6133	19	20	(	(	PUNCT
ejpam-6133	19	21	s.	s.	PROPN
ejpam-6133	19	22	mansour	mansour	PROPN
ejpam-6133	19	23	)	)	PUNCT
ejpam-6133	19	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6133	19	25	1	1	NUM
ejpam-6133	19	26	copyright	copyright	NOUN
ejpam-6133	19	27	:	:	PUNCT
ejpam-6133	20	1	©	©	PROPN
ejpam-6133	20	2	2025	2025	NUM
ejpam-6133	20	3	the	the	DET
ejpam-6133	20	4	author(s	author(s	NOUN
ejpam-6133	20	5	)	)	PUNCT
ejpam-6133	20	6	.	.	PUNCT
ejpam-6133	21	1	(	(	PUNCT
ejpam-6133	21	2	cc	cc	NOUN
ejpam-6133	21	3	by	by	ADP
ejpam-6133	21	4	-	-	PUNCT
ejpam-6133	21	5	nc	nc	PROPN
ejpam-6133	21	6	4.0	4.0	NUM
ejpam-6133	21	7	)	)	PUNCT
ejpam-6133	21	8	h.	h.	NOUN
ejpam-6133	21	9	aydi	aydi	PROPN
ejpam-6133	21	10	,	,	PUNCT
ejpam-6133	21	11	h.	h.	PROPN
ejpam-6133	21	12	hammouda	hammouda	PROPN
ejpam-6133	21	13	,	,	PUNCT
ejpam-6133	21	14	s.	s.	PROPN
ejpam-6133	21	15	mansour	mansour	PROPN
ejpam-6133	21	16	/	/	SYM
ejpam-6133	21	17	eur	eur	PROPN
ejpam-6133	21	18	.	.	PUNCT
ejpam-6133	22	1	j.	j.	PROPN
ejpam-6133	22	2	pure	pure	PROPN
ejpam-6133	22	3	appl	appl	PROPN
ejpam-6133	22	4	.	.	PROPN
ejpam-6133	22	5	math	math	PROPN
ejpam-6133	22	6	,	,	PUNCT
ejpam-6133	22	7	18	18	NUM
ejpam-6133	22	8	(	(	PUNCT
ejpam-6133	22	9	3	3	NUM
ejpam-6133	22	10	)	)	PUNCT
ejpam-6133	22	11	(	(	PUNCT
ejpam-6133	22	12	2025	2025	NUM
ejpam-6133	22	13	)	)	PUNCT
ejpam-6133	22	14	,	,	PUNCT
ejpam-6133	22	15	6133	6133	NUM
ejpam-6133	22	16	2	2	NUM
ejpam-6133	22	17	of	of	ADP
ejpam-6133	22	18	18	18	NUM
ejpam-6133	22	19	works	work	NOUN
ejpam-6133	22	20	in	in	ADP
ejpam-6133	22	21	this	this	DET
ejpam-6133	22	22	direction	direction	NOUN
ejpam-6133	22	23	appeared	appear	VERB
ejpam-6133	22	24	,	,	PUNCT
ejpam-6133	22	25	see	see	VERB
ejpam-6133	22	26	as	as	ADP
ejpam-6133	22	27	examples	example	NOUN
ejpam-6133	22	28	[	[	X
ejpam-6133	22	29	6–9	6–9	NOUN
ejpam-6133	22	30	]	]	PUNCT
ejpam-6133	22	31	.	.	PUNCT
ejpam-6133	23	1	these	these	DET
ejpam-6133	23	2	generalizations	generalization	NOUN
ejpam-6133	23	3	led	lead	VERB
ejpam-6133	23	4	to	to	PART
ejpam-6133	23	5	study	study	VERB
ejpam-6133	23	6	several	several	ADJ
ejpam-6133	23	7	fixed	fix	VERB
ejpam-6133	23	8	point	point	NOUN
ejpam-6133	23	9	results	result	NOUN
ejpam-6133	23	10	for	for	ADP
ejpam-6133	23	11	contractions	contraction	NOUN
ejpam-6133	23	12	arising	arise	VERB
ejpam-6133	23	13	in	in	ADP
ejpam-6133	23	14	many	many	ADJ
ejpam-6133	23	15	real	real	ADJ
ejpam-6133	23	16	applications	application	NOUN
ejpam-6133	23	17	for	for	ADP
ejpam-6133	23	18	several	several	ADJ
ejpam-6133	23	19	problems	problem	NOUN
ejpam-6133	23	20	in	in	ADP
ejpam-6133	23	21	nonlinear	nonlinear	ADJ
ejpam-6133	23	22	analysis	analysis	NOUN
ejpam-6133	23	23	.	.	PUNCT
ejpam-6133	24	1	integral	integral	ADJ
ejpam-6133	24	2	equations	equation	NOUN
ejpam-6133	24	3	appear	appear	VERB
ejpam-6133	24	4	naturally	naturally	ADV
ejpam-6133	24	5	in	in	ADP
ejpam-6133	24	6	several	several	ADJ
ejpam-6133	24	7	branches	branch	NOUN
ejpam-6133	24	8	of	of	ADP
ejpam-6133	24	9	and	and	CCONJ
ejpam-6133	24	10	engineering	engineering	NOUN
ejpam-6133	24	11	and	and	CCONJ
ejpam-6133	24	12	science	science	NOUN
ejpam-6133	24	13	.	.	PUNCT
ejpam-6133	25	1	particularly	particularly	ADV
ejpam-6133	25	2	,	,	PUNCT
ejpam-6133	25	3	fredholm	fredholm	ADJ
ejpam-6133	25	4	integral	integral	ADJ
ejpam-6133	25	5	equations	equation	NOUN
ejpam-6133	25	6	appeared	appear	VERB
ejpam-6133	25	7	widely	widely	ADV
ejpam-6133	25	8	in	in	ADP
ejpam-6133	25	9	various	various	ADJ
ejpam-6133	25	10	scientific	scientific	ADJ
ejpam-6133	25	11	areas	area	NOUN
ejpam-6133	25	12	,	,	PUNCT
ejpam-6133	25	13	like	like	ADP
ejpam-6133	25	14	computational	computational	ADJ
ejpam-6133	25	15	mathematics	mathematic	NOUN
ejpam-6133	25	16	,	,	PUNCT
ejpam-6133	25	17	physics	physic	NOUN
ejpam-6133	25	18	,	,	PUNCT
ejpam-6133	25	19	continuum	continuum	ADJ
ejpam-6133	25	20	mechanics	mechanic	NOUN
ejpam-6133	25	21	,	,	PUNCT
ejpam-6133	25	22	medicine	medicine	NOUN
ejpam-6133	25	23	,	,	PUNCT
ejpam-6133	25	24	acoustics	acoustic	NOUN
ejpam-6133	25	25	and	and	CCONJ
ejpam-6133	25	26	approximation	approximation	NOUN
ejpam-6133	25	27	theory	theory	NOUN
ejpam-6133	25	28	.	.	PUNCT
ejpam-6133	26	1	there	there	PRON
ejpam-6133	26	2	are	be	VERB
ejpam-6133	26	3	several	several	ADJ
ejpam-6133	26	4	analytical	analytical	ADJ
ejpam-6133	26	5	and	and	CCONJ
ejpam-6133	26	6	numerical	numerical	ADJ
ejpam-6133	26	7	methods	method	NOUN
ejpam-6133	26	8	to	to	PART
ejpam-6133	26	9	solve	solve	VERB
ejpam-6133	26	10	fredholm	fredholm	ADJ
ejpam-6133	26	11	integral	integral	ADJ
ejpam-6133	26	12	equations	equation	NOUN
ejpam-6133	26	13	.	.	PUNCT
ejpam-6133	27	1	in	in	ADP
ejpam-6133	27	2	2018	2018	NUM
ejpam-6133	27	3	,	,	PUNCT
ejpam-6133	27	4	karapinar	karapinar	VERB
ejpam-6133	27	5	et	et	PROPN
ejpam-6133	27	6	al	al	PROPN
ejpam-6133	27	7	.	.	PUNCT
ejpam-6133	28	1	[	[	X
ejpam-6133	28	2	10	10	NUM
ejpam-6133	28	3	]	]	PUNCT
ejpam-6133	28	4	solved	solve	VERB
ejpam-6133	28	5	a	a	DET
ejpam-6133	28	6	fredholm	fredholm	ADJ
ejpam-6133	28	7	integral	integral	ADJ
ejpam-6133	28	8	equation	equation	NOUN
ejpam-6133	28	9	given	give	VERB
ejpam-6133	28	10	as	as	SCONJ
ejpam-6133	28	11	follows	follow	VERB
ejpam-6133	28	12	:	:	PUNCT
ejpam-6133	28	13	ℏ(ς	ℏ(ς	PROPN
ejpam-6133	28	14	)	)	PUNCT
ejpam-6133	29	1	=	=	SYM
ejpam-6133	29	2	∫	∫	PROPN
ejpam-6133	29	3	b	b	PROPN
ejpam-6133	29	4	a	a	DET
ejpam-6133	29	5	ℵ(ς	ℵ(ς	PROPN
ejpam-6133	29	6	,	,	PUNCT
ejpam-6133	29	7	υ	υ	NOUN
ejpam-6133	29	8	,	,	PUNCT
ejpam-6133	29	9	ℏ(υ))dυ	ℏ(υ))dυ	PROPN
ejpam-6133	29	10	+	+	ADJ
ejpam-6133	29	11	ζ(ς	ζ(ς	PROPN
ejpam-6133	29	12	)	)	PUNCT
ejpam-6133	29	13	,	,	PUNCT
ejpam-6133	29	14	(	(	PUNCT
ejpam-6133	29	15	1	1	X
ejpam-6133	29	16	)	)	PUNCT
ejpam-6133	29	17	by	by	ADP
ejpam-6133	29	18	using	use	VERB
ejpam-6133	29	19	a	a	DET
ejpam-6133	29	20	fixed	fix	VERB
ejpam-6133	29	21	point	point	NOUN
ejpam-6133	29	22	method	method	NOUN
ejpam-6133	29	23	in	in	ADP
ejpam-6133	29	24	the	the	DET
ejpam-6133	29	25	context	context	NOUN
ejpam-6133	29	26	of	of	ADP
ejpam-6133	29	27	extended	extended	ADJ
ejpam-6133	29	28	b	b	X
ejpam-6133	29	29	-	-	ADJ
ejpam-6133	29	30	metric	metric	ADJ
ejpam-6133	29	31	spaces	space	NOUN
ejpam-6133	29	32	.	.	PUNCT
ejpam-6133	30	1	several	several	ADJ
ejpam-6133	30	2	works	work	NOUN
ejpam-6133	30	3	in	in	ADP
ejpam-6133	30	4	literature	literature	NOUN
ejpam-6133	30	5	dealing	deal	VERB
ejpam-6133	30	6	with	with	ADP
ejpam-6133	30	7	the	the	DET
ejpam-6133	30	8	existence	existence	NOUN
ejpam-6133	30	9	of	of	ADP
ejpam-6133	30	10	a	a	DET
ejpam-6133	30	11	solution	solution	NOUN
ejpam-6133	30	12	of	of	ADP
ejpam-6133	30	13	a	a	DET
ejpam-6133	30	14	fredholm	fredholm	NOUN
ejpam-6133	30	15	type	type	NOUN
ejpam-6133	30	16	integhral	integhral	ADJ
ejpam-6133	30	17	equations	equation	NOUN
ejpam-6133	30	18	arise	arise	VERB
ejpam-6133	30	19	.	.	PUNCT
ejpam-6133	31	1	for	for	ADP
ejpam-6133	31	2	more	more	ADJ
ejpam-6133	31	3	details	detail	NOUN
ejpam-6133	31	4	,	,	PUNCT
ejpam-6133	31	5	see	see	VERB
ejpam-6133	31	6	the	the	DET
ejpam-6133	31	7	papers	paper	NOUN
ejpam-6133	31	8	[	[	X
ejpam-6133	31	9	11–14	11–14	NUM
ejpam-6133	31	10	]	]	PUNCT
ejpam-6133	31	11	.	.	PUNCT
ejpam-6133	32	1	in	in	ADP
ejpam-6133	32	2	this	this	DET
ejpam-6133	32	3	work	work	NOUN
ejpam-6133	32	4	,	,	PUNCT
ejpam-6133	32	5	by	by	ADP
ejpam-6133	32	6	generalizing	generalize	VERB
ejpam-6133	32	7	the	the	DET
ejpam-6133	32	8	equation	equation	NOUN
ejpam-6133	32	9	(	(	PUNCT
ejpam-6133	32	10	1	1	NUM
ejpam-6133	32	11	)	)	PUNCT
ejpam-6133	32	12	,	,	PUNCT
ejpam-6133	32	13	the	the	DET
ejpam-6133	32	14	following	follow	VERB
ejpam-6133	32	15	fredholm	fredholm	ADJ
ejpam-6133	32	16	functional	functional	ADJ
ejpam-6133	32	17	integral	integral	ADJ
ejpam-6133	32	18	equation	equation	NOUN
ejpam-6133	32	19	is	be	AUX
ejpam-6133	32	20	studied	study	VERB
ejpam-6133	32	21	:	:	PUNCT
ejpam-6133	32	22	ℏ(t	ℏ(t	NUM
ejpam-6133	32	23	)	)	PUNCT
ejpam-6133	33	1	=	=	SYM
ejpam-6133	34	1	∫	∫	PROPN
ejpam-6133	34	2	b	b	PROPN
ejpam-6133	34	3	a	a	DET
ejpam-6133	34	4	k(t	k(t	PROPN
ejpam-6133	34	5	,	,	PUNCT
ejpam-6133	34	6	r	r	NOUN
ejpam-6133	34	7	,	,	PUNCT
ejpam-6133	34	8	ℏ(r	ℏ(r	PROPN
ejpam-6133	34	9	)	)	PUNCT
ejpam-6133	34	10	,	,	PUNCT
ejpam-6133	34	11	ℏ(g(r	ℏ(g(r	PROPN
ejpam-6133	34	12	)	)	PUNCT
ejpam-6133	34	13	)	)	PUNCT
ejpam-6133	34	14	,	,	PUNCT
ejpam-6133	34	15	ℏ(a	ℏ(a	NOUN
ejpam-6133	34	16	)	)	PUNCT
ejpam-6133	34	17	,	,	PUNCT
ejpam-6133	34	18	ℏ(b))dr	ℏ(b))dr	NOUN
ejpam-6133	34	19	+	+	CCONJ
ejpam-6133	34	20	f(t	f(t	NOUN
ejpam-6133	34	21	)	)	PUNCT
ejpam-6133	34	22	.	.	PUNCT
ejpam-6133	35	1	(	(	PUNCT
ejpam-6133	35	2	2	2	X
ejpam-6133	35	3	)	)	PUNCT
ejpam-6133	35	4	under	under	ADP
ejpam-6133	35	5	appropriate	appropriate	ADJ
ejpam-6133	35	6	conditions	condition	NOUN
ejpam-6133	35	7	on	on	ADP
ejpam-6133	35	8	functions	function	NOUN
ejpam-6133	35	9	k	k	PROPN
ejpam-6133	35	10	,	,	PUNCT
ejpam-6133	35	11	g	g	PROPN
ejpam-6133	35	12	and	and	CCONJ
ejpam-6133	35	13	f	f	PROPN
ejpam-6133	35	14	,	,	PUNCT
ejpam-6133	35	15	we	we	PRON
ejpam-6133	35	16	aim	aim	VERB
ejpam-6133	35	17	to	to	PART
ejpam-6133	35	18	resolve	resolve	VERB
ejpam-6133	35	19	the	the	DET
ejpam-6133	35	20	equation	equation	NOUN
ejpam-6133	35	21	(	(	PUNCT
ejpam-6133	35	22	2	2	NUM
ejpam-6133	35	23	)	)	PUNCT
ejpam-6133	35	24	via	via	ADP
ejpam-6133	35	25	a	a	DET
ejpam-6133	35	26	fixed	fix	VERB
ejpam-6133	35	27	point	point	NOUN
ejpam-6133	35	28	technique	technique	NOUN
ejpam-6133	35	29	.	.	PUNCT
ejpam-6133	36	1	namely	namely	ADV
ejpam-6133	36	2	,	,	PUNCT
ejpam-6133	36	3	we	we	PRON
ejpam-6133	36	4	give	give	VERB
ejpam-6133	36	5	some	some	DET
ejpam-6133	36	6	fixed	fix	VERB
ejpam-6133	36	7	point	point	NOUN
ejpam-6133	36	8	results	result	NOUN
ejpam-6133	36	9	in	in	ADP
ejpam-6133	36	10	a	a	DET
ejpam-6133	36	11	dcms	dcms	NOUN
ejpam-6133	36	12	via	via	ADP
ejpam-6133	36	13	orbital	orbital	ADJ
ejpam-6133	36	14	α	α	NOUN
ejpam-6133	36	15	-	-	NOUN
ejpam-6133	36	16	admissibility	admissibility	NOUN
ejpam-6133	36	17	.	.	PUNCT
ejpam-6133	37	1	we	we	PRON
ejpam-6133	37	2	also	also	ADV
ejpam-6133	37	3	present	present	VERB
ejpam-6133	37	4	some	some	DET
ejpam-6133	37	5	illustrated	illustrated	ADJ
ejpam-6133	37	6	concrete	concrete	ADJ
ejpam-6133	37	7	examples	example	NOUN
ejpam-6133	37	8	.	.	PUNCT
ejpam-6133	38	1	at	at	ADP
ejpam-6133	38	2	the	the	DET
ejpam-6133	38	3	end	end	NOUN
ejpam-6133	38	4	,	,	PUNCT
ejpam-6133	38	5	we	we	PRON
ejpam-6133	38	6	solve	solve	VERB
ejpam-6133	38	7	a	a	DET
ejpam-6133	38	8	fredhom	fredhom	ADJ
ejpam-6133	38	9	type	type	NOUN
ejpam-6133	38	10	integral	integral	ADJ
ejpam-6133	38	11	equation	equation	NOUN
ejpam-6133	38	12	in	in	ADP
ejpam-6133	38	13	order	order	NOUN
ejpam-6133	38	14	to	to	PART
ejpam-6133	38	15	show	show	VERB
ejpam-6133	38	16	that	that	SCONJ
ejpam-6133	38	17	our	our	PRON
ejpam-6133	38	18	required	require	VERB
ejpam-6133	38	19	conditions	condition	NOUN
ejpam-6133	38	20	are	be	AUX
ejpam-6133	38	21	applicable	applicable	ADJ
ejpam-6133	38	22	.	.	PUNCT
ejpam-6133	39	1	2	2	X
ejpam-6133	39	2	.	.	X
ejpam-6133	39	3	preliminaries	preliminary	NOUN
ejpam-6133	39	4	definition	definition	NOUN
ejpam-6133	39	5	1	1	NUM
ejpam-6133	39	6	.	.	PUNCT
ejpam-6133	40	1	[	[	X
ejpam-6133	40	2	5	5	NUM
ejpam-6133	40	3	]	]	PUNCT
ejpam-6133	40	4	consider	consider	VERB
ejpam-6133	40	5	a	a	DET
ejpam-6133	40	6	nonempty	nonempty	ADJ
ejpam-6133	40	7	set	set	VERB
ejpam-6133	40	8	℧	℧	PROPN
ejpam-6133	40	9	.	.	PUNCT
ejpam-6133	41	1	a	a	DET
ejpam-6133	41	2	function	function	NOUN
ejpam-6133	41	3	ζ	ζ	NOUN
ejpam-6133	41	4	:	:	PUNCT
ejpam-6133	41	5	℧	℧	VERB
ejpam-6133	41	6	×	×	NOUN
ejpam-6133	41	7	℧	℧	X
ejpam-6133	41	8	−→	−→	NOUN
ejpam-6133	41	9	[	[	X
ejpam-6133	41	10	0,∞	0,∞	NOUN
ejpam-6133	41	11	)	)	PUNCT
ejpam-6133	41	12	is	be	AUX
ejpam-6133	41	13	termed	term	VERB
ejpam-6133	41	14	as	as	ADP
ejpam-6133	41	15	a	a	DET
ejpam-6133	41	16	dcm	dcm	NOUN
ejpam-6133	41	17	with	with	ADP
ejpam-6133	41	18	controlled	control	VERB
ejpam-6133	41	19	functions	function	NOUN
ejpam-6133	41	20	ϖ	ϖ	NOUN
ejpam-6133	41	21	,	,	PUNCT
ejpam-6133	41	22	ϵ	ϵ	X
ejpam-6133	41	23	:	:	PUNCT
ejpam-6133	41	24	℧	℧	VERB
ejpam-6133	41	25	×	×	NOUN
ejpam-6133	41	26	℧	℧	X
ejpam-6133	41	27	−→	−→	NOUN
ejpam-6133	41	28	[	[	X
ejpam-6133	41	29	1,∞	1,∞	NUM
ejpam-6133	41	30	)	)	PUNCT
ejpam-6133	41	31	if	if	SCONJ
ejpam-6133	41	32	for	for	ADP
ejpam-6133	41	33	all	all	DET
ejpam-6133	41	34	η	η	PROPN
ejpam-6133	41	35	,	,	PUNCT
ejpam-6133	41	36	y	y	PROPN
ejpam-6133	41	37	,	,	PUNCT
ejpam-6133	41	38	ג	ג	PROPN
ejpam-6133	41	39	∈	∈	PROPN
ejpam-6133	41	40	℧	℧	PROPN
ejpam-6133	41	41	,	,	PUNCT
ejpam-6133	41	42	we	we	PRON
ejpam-6133	41	43	have	have	VERB
ejpam-6133	41	44	(	(	PUNCT
ejpam-6133	41	45	µ1	µ1	ADJ
ejpam-6133	41	46	):	):	PUNCT
ejpam-6133	41	47	ζ	ζ	PROPN
ejpam-6133	41	48	(	(	PUNCT
ejpam-6133	41	49	η	η	PROPN
ejpam-6133	41	50	,	,	PUNCT
ejpam-6133	41	51	y	y	NOUN
ejpam-6133	41	52	)	)	PUNCT
ejpam-6133	41	53	=	=	SYM
ejpam-6133	41	54	0	0	NUM
ejpam-6133	41	55	⇐	⇐	PROPN
ejpam-6133	41	56	⇒	⇒	PROPN
ejpam-6133	41	57	η	η	PROPN
ejpam-6133	41	58	=	=	PROPN
ejpam-6133	41	59	y	y	PROPN
ejpam-6133	41	60	;	;	PUNCT
ejpam-6133	41	61	(	(	PUNCT
ejpam-6133	41	62	µ2	µ2	PROPN
ejpam-6133	41	63	):	):	PUNCT
ejpam-6133	41	64	ζ(η	ζ(η	PROPN
ejpam-6133	41	65	,	,	PUNCT
ejpam-6133	41	66	y	y	PROPN
ejpam-6133	41	67	)	)	PUNCT
ejpam-6133	41	68	=	=	SYM
ejpam-6133	41	69	ζ(y	ζ(y	PROPN
ejpam-6133	41	70	,	,	PUNCT
ejpam-6133	41	71	η	η	PROPN
ejpam-6133	41	72	)	)	PUNCT
ejpam-6133	41	73	;	;	PUNCT
ejpam-6133	41	74	(	(	PUNCT
ejpam-6133	41	75	µ3	µ3	NUM
ejpam-6133	41	76	):	):	PUNCT
ejpam-6133	41	77	ζ(η	ζ(η	PROPN
ejpam-6133	41	78	,	,	PUNCT
ejpam-6133	41	79	y	y	NOUN
ejpam-6133	41	80	)	)	PUNCT
ejpam-6133	41	81	≤	≤	NOUN
ejpam-6133	41	82	ϖ(η	ϖ(η	PROPN
ejpam-6133	41	83	,	,	PUNCT
ejpam-6133	41	84	,	,	PUNCT
ejpam-6133	41	85	ζ(η(ג	ζ(η(ג	PROPN
ejpam-6133	41	86	(	(	PUNCT
ejpam-6133	41	87	ג	ג	PROPN
ejpam-6133	41	88	+	+	CCONJ
ejpam-6133	41	89	ϵ(ג	ϵ(ג	PROPN
ejpam-6133	41	90	,	,	PUNCT
ejpam-6133	41	91	y)ζ(ג	y)ζ(ג	PROPN
ejpam-6133	41	92	,	,	PUNCT
ejpam-6133	41	93	y	y	PROPN
ejpam-6133	41	94	)	)	PUNCT
ejpam-6133	41	95	.	.	PUNCT
ejpam-6133	42	1	here	here	ADV
ejpam-6133	42	2	,	,	PUNCT
ejpam-6133	42	3	(	(	PUNCT
ejpam-6133	42	4	℧	℧	PROPN
ejpam-6133	42	5	,	,	PUNCT
ejpam-6133	42	6	ζ	ζ	NOUN
ejpam-6133	42	7	)	)	PUNCT
ejpam-6133	42	8	is	be	AUX
ejpam-6133	42	9	termed	term	VERB
ejpam-6133	42	10	as	as	ADP
ejpam-6133	42	11	a	a	DET
ejpam-6133	42	12	dcms	dcms	NOUN
ejpam-6133	42	13	.	.	PUNCT
ejpam-6133	43	1	example	example	NOUN
ejpam-6133	44	1	1	1	NUM
ejpam-6133	44	2	.	.	PUNCT
ejpam-6133	44	3	let	let	VERB
ejpam-6133	44	4	℧	℧	PROPN
ejpam-6133	44	5	=	=	PUNCT
ejpam-6133	45	1	[	[	X
ejpam-6133	45	2	0,∞	0,∞	X
ejpam-6133	45	3	]	]	PUNCT
ejpam-6133	45	4	.	.	PUNCT
ejpam-6133	46	1	given	give	VERB
ejpam-6133	46	2	ζ	ζ	NOUN
ejpam-6133	46	3	:	:	PUNCT
ejpam-6133	46	4	℧	℧	PROPN
ejpam-6133	46	5	×	×	NOUN
ejpam-6133	46	6	℧	℧	X
ejpam-6133	46	7	−→	−→	NOUN
ejpam-6133	46	8	[	[	X
ejpam-6133	46	9	0,∞	0,∞	NOUN
ejpam-6133	46	10	)	)	PUNCT
ejpam-6133	46	11	as	as	ADP
ejpam-6133	46	12	ζ(η	ζ(η	PROPN
ejpam-6133	46	13	,	,	PUNCT
ejpam-6133	46	14	ι	ι	PROPN
ejpam-6133	46	15	)	)	PUNCT
ejpam-6133	46	16	=	=	PUNCT
ejpam-6133	46	17			NOUN
ejpam-6133	46	18	0	0	PUNCT
ejpam-6133	47	1	if	if	SCONJ
ejpam-6133	47	2	η	η	PROPN
ejpam-6133	47	3	=	=	PROPN
ejpam-6133	47	4	ι	ι	PROPN
ejpam-6133	47	5	η	η	PROPN
ejpam-6133	47	6	η+1	η+1	PROPN
ejpam-6133	47	7	if	if	SCONJ
ejpam-6133	47	8	η	η	PROPN
ejpam-6133	47	9	̸=	̸=	PROPN
ejpam-6133	47	10	0	0	NUM
ejpam-6133	47	11	and	and	CCONJ
ejpam-6133	47	12	ι	ι	X
ejpam-6133	48	1	=	=	NOUN
ejpam-6133	48	2	0	0	PUNCT
ejpam-6133	48	3	ι	ι	NOUN
ejpam-6133	48	4	ι+1	ι+1	PUNCT
ejpam-6133	48	5	if	if	SCONJ
ejpam-6133	48	6	ι	ι	PRON
ejpam-6133	48	7	̸=	̸=	PROPN
ejpam-6133	48	8	0	0	NUM
ejpam-6133	48	9	and	and	CCONJ
ejpam-6133	48	10	η	η	PROPN
ejpam-6133	48	11	=	=	SYM
ejpam-6133	48	12	0	0	NUM
ejpam-6133	48	13	η	η	PROPN
ejpam-6133	48	14	+	+	PROPN
ejpam-6133	48	15	ι	ι	X
ejpam-6133	48	16	if	if	SCONJ
ejpam-6133	48	17	0	0	NUM
ejpam-6133	48	18	̸=	̸=	PROPN
ejpam-6133	48	19	η	η	PROPN
ejpam-6133	48	20	̸=	̸=	PROPN
ejpam-6133	48	21	ι	ι	ADP
ejpam-6133	48	22	̸=	̸=	PROPN
ejpam-6133	48	23	0	0	NUM
ejpam-6133	48	24	.	.	PUNCT
ejpam-6133	49	1	take	take	VERB
ejpam-6133	49	2	ϖ	ϖ	NOUN
ejpam-6133	49	3	,	,	PUNCT
ejpam-6133	49	4	ϵ	ϵ	X
ejpam-6133	49	5	:	:	PUNCT
ejpam-6133	49	6	℧	℧	VERB
ejpam-6133	49	7	×	×	NOUN
ejpam-6133	49	8	℧	℧	X
ejpam-6133	49	9	−→	−→	NOUN
ejpam-6133	49	10	[	[	X
ejpam-6133	49	11	1,∞	1,∞	NUM
ejpam-6133	49	12	)	)	PUNCT
ejpam-6133	49	13	as	as	ADP
ejpam-6133	49	14	ϖ(η	ϖ(η	PROPN
ejpam-6133	49	15	,	,	PUNCT
ejpam-6133	49	16	ι	ι	PROPN
ejpam-6133	49	17	)	)	PUNCT
ejpam-6133	49	18	=	=	SYM
ejpam-6133	49	19	ϵ(η	ϵ(η	PROPN
ejpam-6133	49	20	,	,	PUNCT
ejpam-6133	49	21	ι	ι	PROPN
ejpam-6133	49	22	)	)	PUNCT
ejpam-6133	49	23	=	=	SYM
ejpam-6133	49	24	2η	2η	PROPN
ejpam-6133	49	25	+	+	CCONJ
ejpam-6133	49	26	2ι+	2ι+	NUM
ejpam-6133	49	27	2	2	NUM
ejpam-6133	49	28	.	.	PUNCT
ejpam-6133	50	1	here	here	ADV
ejpam-6133	50	2	,	,	PUNCT
ejpam-6133	50	3	(	(	PUNCT
ejpam-6133	50	4	℧	℧	PROPN
ejpam-6133	50	5	,	,	PUNCT
ejpam-6133	50	6	ζ	ζ	NOUN
ejpam-6133	50	7	)	)	PUNCT
ejpam-6133	50	8	is	be	AUX
ejpam-6133	50	9	a	a	DET
ejpam-6133	50	10	dcms	dcms	NOUN
ejpam-6133	50	11	.	.	PUNCT
ejpam-6133	51	1	h.	h.	PROPN
ejpam-6133	51	2	aydi	aydi	PROPN
ejpam-6133	51	3	,	,	PUNCT
ejpam-6133	51	4	h.	h.	PROPN
ejpam-6133	51	5	hammouda	hammouda	PROPN
ejpam-6133	51	6	,	,	PUNCT
ejpam-6133	51	7	s.	s.	PROPN
ejpam-6133	51	8	mansour	mansour	PROPN
ejpam-6133	51	9	/	/	SYM
ejpam-6133	51	10	eur	eur	PROPN
ejpam-6133	51	11	.	.	PUNCT
ejpam-6133	52	1	j.	j.	PROPN
ejpam-6133	52	2	pure	pure	PROPN
ejpam-6133	52	3	appl	appl	PROPN
ejpam-6133	52	4	.	.	PROPN
ejpam-6133	52	5	math	math	PROPN
ejpam-6133	52	6	,	,	PUNCT
ejpam-6133	52	7	18	18	NUM
ejpam-6133	52	8	(	(	PUNCT
ejpam-6133	52	9	3	3	NUM
ejpam-6133	52	10	)	)	PUNCT
ejpam-6133	52	11	(	(	PUNCT
ejpam-6133	52	12	2025	2025	NUM
ejpam-6133	52	13	)	)	PUNCT
ejpam-6133	52	14	,	,	PUNCT
ejpam-6133	52	15	6133	6133	NUM
ejpam-6133	52	16	3	3	NUM
ejpam-6133	52	17	of	of	ADP
ejpam-6133	52	18	18	18	NUM
ejpam-6133	52	19	definition	definition	NOUN
ejpam-6133	52	20	2	2	NUM
ejpam-6133	52	21	.	.	PUNCT
ejpam-6133	53	1	[	[	X
ejpam-6133	53	2	5	5	NUM
ejpam-6133	53	3	]	]	PUNCT
ejpam-6133	53	4	let	let	AUX
ejpam-6133	53	5	{	{	PUNCT
ejpam-6133	53	6	s̃n	s̃n	VERB
ejpam-6133	53	7	}	}	PUNCT
ejpam-6133	53	8	be	be	AUX
ejpam-6133	53	9	a	a	DET
ejpam-6133	53	10	sequence	sequence	NOUN
ejpam-6133	53	11	in	in	ADP
ejpam-6133	53	12	a	a	DET
ejpam-6133	53	13	dcms	dcms	NOUN
ejpam-6133	53	14	(	(	PUNCT
ejpam-6133	53	15	℧	℧	PROPN
ejpam-6133	53	16	,	,	PUNCT
ejpam-6133	53	17	ζ	ζ	NOUN
ejpam-6133	53	18	)	)	PUNCT
ejpam-6133	53	19	.	.	PUNCT
ejpam-6133	54	1	then	then	ADV
ejpam-6133	54	2	,	,	PUNCT
ejpam-6133	54	3	(	(	PUNCT
ejpam-6133	54	4	i	i	NOUN
ejpam-6133	54	5	)	)	PUNCT
ejpam-6133	54	6	{	{	PUNCT
ejpam-6133	54	7	s̃ȷ	s̃ȷ	NOUN
ejpam-6133	54	8	}	}	PUNCT
ejpam-6133	54	9	is	be	AUX
ejpam-6133	54	10	called	call	VERB
ejpam-6133	54	11	a	a	DET
ejpam-6133	54	12	convergent	convergent	NOUN
ejpam-6133	54	13	sequence	sequence	NOUN
ejpam-6133	54	14	,	,	PUNCT
ejpam-6133	54	15	if	if	SCONJ
ejpam-6133	54	16	,	,	PUNCT
ejpam-6133	54	17	for	for	ADP
ejpam-6133	54	18	any	any	DET
ejpam-6133	54	19	ϵ	ϵ	X
ejpam-6133	54	20	>	>	X
ejpam-6133	54	21	0	0	NUM
ejpam-6133	54	22	,	,	PUNCT
ejpam-6133	54	23	there	there	PRON
ejpam-6133	54	24	is	be	VERB
ejpam-6133	54	25	an	an	DET
ejpam-6133	54	26	integer	integer	NOUN
ejpam-6133	54	27	ȷ0	ȷ0	NOUN
ejpam-6133	54	28	=	=	SYM
ejpam-6133	54	29	ȷ0(ϵ	ȷ0(ϵ	PROPN
ejpam-6133	54	30	)	)	PUNCT
ejpam-6133	54	31	so	so	SCONJ
ejpam-6133	54	32	that	that	SCONJ
ejpam-6133	54	33	ζ(s̃ȷ	ζ(s̃ȷ	NOUN
ejpam-6133	54	34	,	,	PUNCT
ejpam-6133	54	35	η	η	NOUN
ejpam-6133	54	36	)	)	PUNCT
ejpam-6133	54	37	<	<	X
ejpam-6133	54	38	ϵ	ϵ	X
ejpam-6133	54	39	,	,	PUNCT
ejpam-6133	54	40	for	for	ADP
ejpam-6133	54	41	all	all	DET
ejpam-6133	54	42	ȷ	ȷ	PRON
ejpam-6133	54	43	≥	≥	NOUN
ejpam-6133	54	44	ȷ0	ȷ0	NOUN
ejpam-6133	54	45	.	.	PUNCT
ejpam-6133	55	1	one	one	NUM
ejpam-6133	55	2	writes	write	VERB
ejpam-6133	55	3	lim	lim	PROPN
ejpam-6133	55	4	n→∞	n→∞	PRON
ejpam-6133	55	5	s̃ȷ	s̃ȷ	PROPN
ejpam-6133	55	6	=	=	SYM
ejpam-6133	55	7	η	η	PROPN
ejpam-6133	55	8	;	;	PUNCT
ejpam-6133	55	9	(	(	PUNCT
ejpam-6133	55	10	ii	ii	NOUN
ejpam-6133	55	11	)	)	PUNCT
ejpam-6133	55	12	{	{	PUNCT
ejpam-6133	55	13	s̃ȷ	s̃ȷ	NOUN
ejpam-6133	55	14	}	}	PUNCT
ejpam-6133	55	15	is	be	AUX
ejpam-6133	55	16	named	name	VERB
ejpam-6133	55	17	cauchy	cauchy	ADJ
ejpam-6133	55	18	if	if	SCONJ
ejpam-6133	55	19	lim	lim	PROPN
ejpam-6133	55	20	ȷ	ȷ	NOUN
ejpam-6133	55	21	,	,	PUNCT
ejpam-6133	55	22	m→∞	m→∞	NOUN
ejpam-6133	55	23	ζ(s̃ȷ	ζ(s̃ȷ	NOUN
ejpam-6133	55	24	,	,	PUNCT
ejpam-6133	55	25	s̃m	s̃m	NOUN
ejpam-6133	55	26	)	)	PUNCT
ejpam-6133	55	27	=	=	SYM
ejpam-6133	55	28	0	0	NUM
ejpam-6133	55	29	;	;	PUNCT
ejpam-6133	55	30	(	(	PUNCT
ejpam-6133	55	31	iii	iii	X
ejpam-6133	55	32	)	)	PUNCT
ejpam-6133	55	33	(	(	PUNCT
ejpam-6133	55	34	℧	℧	PROPN
ejpam-6133	55	35	,	,	PUNCT
ejpam-6133	55	36	ζ	ζ	NOUN
ejpam-6133	55	37	)	)	PUNCT
ejpam-6133	55	38	is	be	AUX
ejpam-6133	55	39	called	call	VERB
ejpam-6133	55	40	complete	complete	ADJ
ejpam-6133	55	41	if	if	SCONJ
ejpam-6133	55	42	each	each	DET
ejpam-6133	55	43	cauchy	cauchy	ADJ
ejpam-6133	55	44	sequence	sequence	NOUN
ejpam-6133	55	45	converges	converge	VERB
ejpam-6133	55	46	in	in	ADP
ejpam-6133	55	47	℧	℧	PROPN
ejpam-6133	55	48	.	.	PUNCT
ejpam-6133	55	49	definition	definition	NOUN
ejpam-6133	56	1	3	3	NUM
ejpam-6133	56	2	.	.	PUNCT
ejpam-6133	57	1	let	let	VERB
ejpam-6133	57	2	⊤	⊤	NOUN
ejpam-6133	57	3	be	be	AUX
ejpam-6133	57	4	a	a	DET
ejpam-6133	57	5	self	self	NOUN
ejpam-6133	57	6	-	-	PUNCT
ejpam-6133	57	7	mapping	mapping	NOUN
ejpam-6133	57	8	on	on	ADP
ejpam-6133	57	9	a	a	DET
ejpam-6133	57	10	dcms	dcms	NOUN
ejpam-6133	57	11	(	(	PUNCT
ejpam-6133	57	12	℧	℧	PROPN
ejpam-6133	57	13	,	,	PUNCT
ejpam-6133	57	14	ζ	ζ	NOUN
ejpam-6133	57	15	)	)	PUNCT
ejpam-6133	57	16	.	.	PUNCT
ejpam-6133	58	1	for	for	ADP
ejpam-6133	58	2	s̃0	s̃0	PROPN
ejpam-6133	58	3	∈	∈	PROPN
ejpam-6133	58	4	℧	℧	PROPN
ejpam-6133	58	5	,	,	PUNCT
ejpam-6133	58	6	the	the	DET
ejpam-6133	58	7	set	set	NOUN
ejpam-6133	58	8	o(s̃0,⊤	o(s̃0,⊤	NOUN
ejpam-6133	58	9	)	)	PUNCT
ejpam-6133	59	1	=	=	PRON
ejpam-6133	59	2	{	{	PUNCT
ejpam-6133	59	3	s̃0,⊤s̃0,⊤2s̃0,⊤3s̃0	s̃0,⊤s̃0,⊤2s̃0,⊤3s̃0	PROPN
ejpam-6133	59	4	,	,	PUNCT
ejpam-6133	59	5	·	·	PUNCT
ejpam-6133	59	6	·	·	PUNCT
ejpam-6133	59	7	·	·	PUNCT
ejpam-6133	59	8	}	}	PUNCT
ejpam-6133	59	9	is	be	AUX
ejpam-6133	59	10	named	name	VERB
ejpam-6133	59	11	as	as	ADP
ejpam-6133	59	12	an	an	DET
ejpam-6133	59	13	orbit	orbit	NOUN
ejpam-6133	59	14	of	of	ADP
ejpam-6133	59	15	⊤	⊤	NOUN
ejpam-6133	59	16	at	at	ADP
ejpam-6133	59	17	s̃0	s̃0	PROPN
ejpam-6133	59	18	.	.	PUNCT
ejpam-6133	60	1	⊤	⊤	NOUN
ejpam-6133	60	2	is	be	AUX
ejpam-6133	60	3	said	say	VERB
ejpam-6133	60	4	to	to	PART
ejpam-6133	60	5	be	be	AUX
ejpam-6133	60	6	orbitally	orbitally	ADV
ejpam-6133	60	7	continuous	continuous	ADJ
ejpam-6133	60	8	at	at	ADP
ejpam-6133	60	9	℘	℘	NOUN
ejpam-6133	60	10	∈	∈	NOUN
ejpam-6133	60	11	℧	℧	PROPN
ejpam-6133	60	12	if	if	SCONJ
ejpam-6133	60	13	lim	lim	PROPN
ejpam-6133	60	14	k→∞	k→∞	PROPN
ejpam-6133	60	15	⊤ks̃0	⊤ks̃0	PROPN
ejpam-6133	60	16	=	=	PUNCT
ejpam-6133	60	17	℘	℘	PROPN
ejpam-6133	60	18	yields	yield	NOUN
ejpam-6133	60	19	that	that	SCONJ
ejpam-6133	60	20	lim	lim	PROPN
ejpam-6133	60	21	k→∞	k→∞	NOUN
ejpam-6133	60	22	⊤⊤ks̃0	⊤⊤ks̃0	PUNCT
ejpam-6133	60	23	=	=	SYM
ejpam-6133	60	24	⊤℘.	⊤℘.	PUNCT
ejpam-6133	60	25	also	also	ADV
ejpam-6133	60	26	,	,	PUNCT
ejpam-6133	60	27	when	when	SCONJ
ejpam-6133	60	28	each	each	DET
ejpam-6133	60	29	cauchy	cauchy	ADJ
ejpam-6133	60	30	sequence	sequence	NOUN
ejpam-6133	60	31	having	have	VERB
ejpam-6133	60	32	the	the	DET
ejpam-6133	60	33	form	form	NOUN
ejpam-6133	60	34	{	{	PUNCT
ejpam-6133	60	35	⊤ks̃0}k	⊤ks̃0}k	PROPN
ejpam-6133	60	36	converges	converge	VERB
ejpam-6133	60	37	in	in	ADP
ejpam-6133	60	38	℧	℧	PROPN
ejpam-6133	60	39	,	,	PUNCT
ejpam-6133	60	40	then	then	ADV
ejpam-6133	60	41	(	(	PUNCT
ejpam-6133	60	42	℧	℧	PROPN
ejpam-6133	60	43	,	,	PUNCT
ejpam-6133	60	44	ζ	ζ	NOUN
ejpam-6133	60	45	)	)	PUNCT
ejpam-6133	60	46	is	be	AUX
ejpam-6133	60	47	orbitally	orbitally	ADV
ejpam-6133	60	48	complete	complete	ADJ
ejpam-6133	60	49	.	.	PUNCT
ejpam-6133	61	1	in	in	ADP
ejpam-6133	61	2	the	the	DET
ejpam-6133	61	3	sequel	sequel	NOUN
ejpam-6133	61	4	,	,	PUNCT
ejpam-6133	61	5	fix(⊤	fix(⊤	ADJ
ejpam-6133	61	6	)	)	PUNCT
ejpam-6133	61	7	=	=	SYM
ejpam-6133	61	8	{	{	PUNCT
ejpam-6133	61	9	℘	℘	NOUN
ejpam-6133	61	10	∈	∈	NOUN
ejpam-6133	61	11	℧	℧	X
ejpam-6133	61	12	/⊤℘	/⊤℘	PUNCT
ejpam-6133	61	13	=	=	PUNCT
ejpam-6133	61	14	℘	℘	PROPN
ejpam-6133	61	15	}	}	PUNCT
ejpam-6133	61	16	.	.	PUNCT
ejpam-6133	62	1	remark	remark	NOUN
ejpam-6133	62	2	1	1	NUM
ejpam-6133	62	3	.	.	PUNCT
ejpam-6133	63	1	the	the	DET
ejpam-6133	63	2	continuity	continuity	NOUN
ejpam-6133	63	3	yields	yield	VERB
ejpam-6133	63	4	the	the	DET
ejpam-6133	63	5	orbital	orbital	ADJ
ejpam-6133	63	6	continuity	continuity	NOUN
ejpam-6133	63	7	.	.	PUNCT
ejpam-6133	64	1	definition	definition	NOUN
ejpam-6133	64	2	4	4	NUM
ejpam-6133	64	3	.	.	PUNCT
ejpam-6133	65	1	[	[	X
ejpam-6133	65	2	15	15	NUM
ejpam-6133	65	3	]	]	PUNCT
ejpam-6133	65	4	let	let	VERB
ejpam-6133	65	5	α	α	NOUN
ejpam-6133	65	6	:	:	PUNCT
ejpam-6133	65	7	℧	℧	VERB
ejpam-6133	65	8	×	×	NOUN
ejpam-6133	65	9	℧	℧	X
ejpam-6133	65	10	−→	−→	NOUN
ejpam-6133	65	11	r	r	NOUN
ejpam-6133	65	12	be	be	VERB
ejpam-6133	65	13	a	a	DET
ejpam-6133	65	14	function	function	NOUN
ejpam-6133	65	15	(	(	PUNCT
ejpam-6133	65	16	℧	℧	PROPN
ejpam-6133	65	17	is	be	AUX
ejpam-6133	65	18	a	a	DET
ejpam-6133	65	19	nonempty	nonempty	ADJ
ejpam-6133	65	20	set	set	NOUN
ejpam-6133	65	21	)	)	PUNCT
ejpam-6133	65	22	.	.	PUNCT
ejpam-6133	66	1	⊤	⊤	NOUN
ejpam-6133	66	2	:	:	PUNCT
ejpam-6133	66	3	℧	℧	PUNCT
ejpam-6133	66	4	−→	−→	NOUN
ejpam-6133	66	5	℧	℧	PROPN
ejpam-6133	66	6	is	be	AUX
ejpam-6133	66	7	termed	term	VERB
ejpam-6133	66	8	an	an	DET
ejpam-6133	66	9	α	α	NUM
ejpam-6133	66	10	-	-	PUNCT
ejpam-6133	66	11	admissible	admissible	ADJ
ejpam-6133	66	12	mapping	mapping	NOUN
ejpam-6133	66	13	,	,	PUNCT
ejpam-6133	66	14	if	if	SCONJ
ejpam-6133	66	15	for	for	ADP
ejpam-6133	66	16	every	every	DET
ejpam-6133	66	17	ı	ı	PROPN
ejpam-6133	66	18	,	,	PUNCT
ejpam-6133	66	19	ℓ	ℓ	PROPN
ejpam-6133	66	20	∈	∈	PROPN
ejpam-6133	66	21	℧	℧	PROPN
ejpam-6133	66	22	,	,	PUNCT
ejpam-6133	66	23	α(ı	α(ı	NUM
ejpam-6133	66	24	,	,	PUNCT
ejpam-6133	66	25	ℓ	ℓ	NUM
ejpam-6133	66	26	)	)	PUNCT
ejpam-6133	66	27	≥	≥	NOUN
ejpam-6133	66	28	1	1	NUM
ejpam-6133	66	29	implies	imply	VERB
ejpam-6133	66	30	α(⊤ı,⊤ℓ	α(⊤ı,⊤ℓ	NOUN
ejpam-6133	66	31	)	)	PUNCT
ejpam-6133	66	32	≥	≥	NOUN
ejpam-6133	66	33	1	1	NUM
ejpam-6133	66	34	.	.	PUNCT
ejpam-6133	67	1	⊤	⊤	NOUN
ejpam-6133	67	2	is	be	AUX
ejpam-6133	67	3	called	call	VERB
ejpam-6133	67	4	α	α	DET
ejpam-6133	67	5	-	-	ADJ
ejpam-6133	67	6	orbitally	orbitally	ADV
ejpam-6133	67	7	admissible	admissible	ADJ
ejpam-6133	67	8	if	if	SCONJ
ejpam-6133	67	9	,	,	PUNCT
ejpam-6133	67	10	for	for	ADP
ejpam-6133	67	11	each	each	DET
ejpam-6133	67	12	ı	ı	PROPN
ejpam-6133	67	13	∈	∈	PROPN
ejpam-6133	67	14	℧	℧	PROPN
ejpam-6133	67	15	,	,	PUNCT
ejpam-6133	67	16	α(ı,⊤ı	α(ı,⊤ı	PROPN
ejpam-6133	67	17	)	)	PUNCT
ejpam-6133	67	18	≥	≥	NOUN
ejpam-6133	67	19	1	1	NUM
ejpam-6133	67	20	leads	lead	VERB
ejpam-6133	67	21	to	to	ADP
ejpam-6133	67	22	α(⊤ı,⊤2ı	α(⊤ı,⊤2ı	NUM
ejpam-6133	67	23	)	)	PUNCT
ejpam-6133	67	24	≥	≥	NOUN
ejpam-6133	68	1	1	1	NUM
ejpam-6133	68	2	.	.	PUNCT
ejpam-6133	68	3	definition	definition	NOUN
ejpam-6133	68	4	5	5	NUM
ejpam-6133	68	5	.	.	PUNCT
ejpam-6133	69	1	ψ	ψ	X
ejpam-6133	69	2	:	:	PUNCT
ejpam-6133	70	1	[	[	X
ejpam-6133	70	2	0,+∞	0,+∞	NUM
ejpam-6133	70	3	)	)	PUNCT
ejpam-6133	70	4	−→	−→	NOUN
ejpam-6133	70	5	[	[	X
ejpam-6133	70	6	0,+∞	0,+∞	NUM
ejpam-6133	70	7	)	)	PUNCT
ejpam-6133	70	8	is	be	AUX
ejpam-6133	70	9	termed	term	VERB
ejpam-6133	70	10	as	as	ADP
ejpam-6133	70	11	a	a	DET
ejpam-6133	70	12	comparison	comparison	NOUN
ejpam-6133	70	13	function	function	NOUN
ejpam-6133	70	14	,	,	PUNCT
ejpam-6133	70	15	if	if	SCONJ
ejpam-6133	70	16	it	it	PRON
ejpam-6133	70	17	is	be	AUX
ejpam-6133	70	18	nondecreasing	nondecrease	VERB
ejpam-6133	70	19	and	and	CCONJ
ejpam-6133	70	20	lim	lim	PROPN
ejpam-6133	70	21	ȷ→∞	ȷ→∞	NUM
ejpam-6133	70	22	ψȷ(τ	ψȷ(τ	PUNCT
ejpam-6133	70	23	)	)	PUNCT
ejpam-6133	71	1	=	=	SYM
ejpam-6133	71	2	0	0	NUM
ejpam-6133	71	3	for	for	ADP
ejpam-6133	71	4	each	each	PRON
ejpam-6133	71	5	τ	τ	PROPN
ejpam-6133	71	6	>	>	X
ejpam-6133	71	7	0	0	PROPN
ejpam-6133	71	8	.	.	PUNCT
ejpam-6133	72	1	here	here	ADV
ejpam-6133	72	2	,	,	PUNCT
ejpam-6133	72	3	ψȷ	ψȷ	PROPN
ejpam-6133	72	4	is	be	AUX
ejpam-6133	72	5	the	the	DET
ejpam-6133	72	6	nth	nth	ADJ
ejpam-6133	72	7	iteration	iteration	NOUN
ejpam-6133	72	8	of	of	ADP
ejpam-6133	72	9	ψ	ψ	PROPN
ejpam-6133	72	10	.	.	PUNCT
ejpam-6133	73	1	ψ	ψ	NOUN
ejpam-6133	73	2	is	be	AUX
ejpam-6133	73	3	denoted	denote	VERB
ejpam-6133	73	4	the	the	DET
ejpam-6133	73	5	set	set	NOUN
ejpam-6133	73	6	of	of	ADP
ejpam-6133	73	7	all	all	DET
ejpam-6133	73	8	comparison	comparison	NOUN
ejpam-6133	73	9	functions	function	NOUN
ejpam-6133	73	10	.	.	PUNCT
ejpam-6133	74	1	fp	fp	X
ejpam-6133	74	2	is	be	AUX
ejpam-6133	74	3	the	the	DET
ejpam-6133	74	4	abbreviation	abbreviation	NOUN
ejpam-6133	74	5	of	of	ADP
ejpam-6133	74	6	a	a	DET
ejpam-6133	74	7	fixed	fix	VERB
ejpam-6133	74	8	point	point	NOUN
ejpam-6133	74	9	.	.	PUNCT
ejpam-6133	75	1	lemma	lemma	PROPN
ejpam-6133	75	2	1	1	NUM
ejpam-6133	75	3	.	.	PUNCT
ejpam-6133	76	1	for	for	ADP
ejpam-6133	76	2	each	each	DET
ejpam-6133	76	3	ψ	ψ	X
ejpam-6133	76	4	∈	∈	PROPN
ejpam-6133	76	5	ψ	ψ	NOUN
ejpam-6133	76	6	,	,	PUNCT
ejpam-6133	76	7	we	we	PRON
ejpam-6133	76	8	have	have	VERB
ejpam-6133	76	9	ψ(0	ψ(0	NOUN
ejpam-6133	76	10	)	)	PUNCT
ejpam-6133	76	11	=	=	SYM
ejpam-6133	76	12	0	0	NUM
ejpam-6133	76	13	and	and	CCONJ
ejpam-6133	76	14	ψ(θ	ψ(θ	PROPN
ejpam-6133	76	15	)	)	PUNCT
ejpam-6133	76	16	<	<	X
ejpam-6133	76	17	θ	θ	NOUN
ejpam-6133	76	18	for	for	ADP
ejpam-6133	76	19	any	any	DET
ejpam-6133	76	20	θ	θ	PROPN
ejpam-6133	76	21	>	>	X
ejpam-6133	76	22	0	0	X
ejpam-6133	76	23	.	.	PUNCT
ejpam-6133	77	1	the	the	DET
ejpam-6133	77	2	next	next	ADJ
ejpam-6133	77	3	result	result	NOUN
ejpam-6133	77	4	is	be	AUX
ejpam-6133	77	5	needful	needful	ADJ
ejpam-6133	77	6	in	in	ADP
ejpam-6133	77	7	the	the	DET
ejpam-6133	77	8	sequel	sequel	NOUN
ejpam-6133	77	9	.	.	PUNCT
ejpam-6133	78	1	proposition	proposition	NOUN
ejpam-6133	78	2	1	1	NUM
ejpam-6133	78	3	.	.	PUNCT
ejpam-6133	79	1	let	let	AUX
ejpam-6133	79	2	(	(	PUNCT
ejpam-6133	79	3	℧	℧	NOUN
ejpam-6133	79	4	,	,	PUNCT
ejpam-6133	79	5	ζ	ζ	NOUN
ejpam-6133	79	6	)	)	PUNCT
ejpam-6133	79	7	be	be	VERB
ejpam-6133	79	8	a	a	DET
ejpam-6133	79	9	dcms	dcms	NOUN
ejpam-6133	79	10	with	with	ADP
ejpam-6133	79	11	two	two	NUM
ejpam-6133	79	12	controlled	control	VERB
ejpam-6133	79	13	functions	function	NOUN
ejpam-6133	79	14	ϖ	ϖ	NOUN
ejpam-6133	79	15	,	,	PUNCT
ejpam-6133	79	16	ϵ.	ϵ.	NOUN
ejpam-6133	80	1	let	let	VERB
ejpam-6133	80	2	{	{	PUNCT
ejpam-6133	80	3	s̃n	s̃n	AUX
ejpam-6133	80	4	}	}	PUNCT
ejpam-6133	80	5	be	be	AUX
ejpam-6133	80	6	a	a	DET
ejpam-6133	80	7	convergent	convergent	NOUN
ejpam-6133	80	8	sequence	sequence	NOUN
ejpam-6133	80	9	in	in	ADP
ejpam-6133	80	10	℧	℧	PROPN
ejpam-6133	80	11	so	so	SCONJ
ejpam-6133	80	12	that	that	SCONJ
ejpam-6133	80	13	lim	lim	PROPN
ejpam-6133	80	14	n→∞	n→∞	PRON
ejpam-6133	80	15	ϵ(γ	ϵ(γ	PROPN
ejpam-6133	80	16	,	,	PUNCT
ejpam-6133	80	17	s̃n	s̃n	PROPN
ejpam-6133	80	18	)	)	PUNCT
ejpam-6133	80	19	and	and	CCONJ
ejpam-6133	80	20	lim	lim	PROPN
ejpam-6133	80	21	n→∞	n→∞	X
ejpam-6133	80	22	ϖ(s̃n	ϖ(s̃n	PROPN
ejpam-6133	80	23	,	,	PUNCT
ejpam-6133	80	24	β	β	NOUN
ejpam-6133	80	25	)	)	PUNCT
ejpam-6133	80	26	exist	exist	VERB
ejpam-6133	80	27	and	and	CCONJ
ejpam-6133	80	28	are	be	AUX
ejpam-6133	80	29	finite	finite	ADJ
ejpam-6133	80	30	for	for	ADP
ejpam-6133	80	31	any	any	DET
ejpam-6133	80	32	γ	γ	NOUN
ejpam-6133	80	33	,	,	PUNCT
ejpam-6133	80	34	β	β	X
ejpam-6133	80	35	∈	∈	PROPN
ejpam-6133	80	36	℧	℧	PROPN
ejpam-6133	80	37	,	,	PUNCT
ejpam-6133	80	38	then	then	ADV
ejpam-6133	80	39	such	such	DET
ejpam-6133	80	40	a	a	DET
ejpam-6133	80	41	convergent	convergent	NOUN
ejpam-6133	80	42	sequence	sequence	NOUN
ejpam-6133	80	43	possesses	possess	VERB
ejpam-6133	80	44	a	a	DET
ejpam-6133	80	45	unique	unique	ADJ
ejpam-6133	80	46	limit	limit	NOUN
ejpam-6133	80	47	.	.	PUNCT
ejpam-6133	81	1	proof	proof	NOUN
ejpam-6133	81	2	.	.	PUNCT
ejpam-6133	82	1	suppose	suppose	VERB
ejpam-6133	82	2	{	{	PUNCT
ejpam-6133	82	3	s̃ℓ	s̃ℓ	ADV
ejpam-6133	82	4	}	}	PUNCT
ejpam-6133	82	5	∈	∈	PROPN
ejpam-6133	82	6	℧	℧	NOUN
ejpam-6133	82	7	converges	converge	NOUN
ejpam-6133	82	8	to	to	ADP
ejpam-6133	82	9	σ	σ	PROPN
ejpam-6133	82	10	and	and	CCONJ
ejpam-6133	82	11	ς	ς	PROPN
ejpam-6133	82	12	in	in	ADP
ejpam-6133	82	13	℧	℧	PROPN
ejpam-6133	82	14	.	.	PUNCT
ejpam-6133	83	1	we	we	PRON
ejpam-6133	83	2	have	have	VERB
ejpam-6133	83	3	lim	lim	PROPN
ejpam-6133	83	4	ℓ→∞	ℓ→∞	NUM
ejpam-6133	83	5	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	83	6	,	,	PUNCT
ejpam-6133	83	7	σ	σ	PROPN
ejpam-6133	83	8	)	)	PUNCT
ejpam-6133	83	9	=	=	SYM
ejpam-6133	83	10	0	0	NUM
ejpam-6133	83	11	and	and	CCONJ
ejpam-6133	83	12	lim	lim	PROPN
ejpam-6133	83	13	ℓ→∞	ℓ→∞	NUM
ejpam-6133	83	14	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	83	15	,	,	PUNCT
ejpam-6133	83	16	ς	ς	NOUN
ejpam-6133	83	17	)	)	PUNCT
ejpam-6133	83	18	=	=	SYM
ejpam-6133	83	19	0	0	X
ejpam-6133	83	20	.	.	PUNCT
ejpam-6133	84	1	by	by	ADP
ejpam-6133	84	2	the	the	DET
ejpam-6133	84	3	triangle	triangle	NOUN
ejpam-6133	84	4	inequality	inequality	NOUN
ejpam-6133	84	5	in	in	ADP
ejpam-6133	84	6	the	the	DET
ejpam-6133	84	7	dcms	dcms	NOUN
ejpam-6133	84	8	,	,	PUNCT
ejpam-6133	84	9	we	we	PRON
ejpam-6133	84	10	obtain	obtain	VERB
ejpam-6133	84	11	ζ(σ	ζ(σ	ADJ
ejpam-6133	84	12	,	,	PUNCT
ejpam-6133	84	13	ς	ς	NOUN
ejpam-6133	84	14	)	)	PUNCT
ejpam-6133	84	15	≤	≤	NOUN
ejpam-6133	84	16	ϖ(σ	ϖ(σ	PROPN
ejpam-6133	84	17	,	,	PUNCT
ejpam-6133	84	18	s̃ℓ)ζ(σ	s̃ℓ)ζ(σ	NOUN
ejpam-6133	84	19	,	,	PUNCT
ejpam-6133	84	20	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	84	21	)	)	PUNCT
ejpam-6133	85	1	+	+	NUM
ejpam-6133	86	1	ϵ(s̃ℓ	ϵ(s̃ℓ	NOUN
ejpam-6133	86	2	,	,	PUNCT
ejpam-6133	86	3	ς)ζ(s̃ℓ	ς)ζ(s̃ℓ	X
ejpam-6133	86	4	,	,	PUNCT
ejpam-6133	86	5	ς	ς	NOUN
ejpam-6133	86	6	)	)	PUNCT
ejpam-6133	86	7	.	.	PUNCT
ejpam-6133	87	1	taking	take	VERB
ejpam-6133	87	2	ℓ	ℓ	PROPN
ejpam-6133	87	3	−→	−→	NOUN
ejpam-6133	87	4	0	0	NUM
ejpam-6133	87	5	,	,	PUNCT
ejpam-6133	87	6	we	we	PRON
ejpam-6133	87	7	get	get	VERB
ejpam-6133	87	8	ζ(σ	ζ(σ	ADJ
ejpam-6133	87	9	,	,	PUNCT
ejpam-6133	87	10	ς	ς	NOUN
ejpam-6133	87	11	)	)	PUNCT
ejpam-6133	87	12	≤	≤	NOUN
ejpam-6133	87	13	0	0	NUM
ejpam-6133	87	14	.	.	PUNCT
ejpam-6133	88	1	thus	thus	ADV
ejpam-6133	88	2	,	,	PUNCT
ejpam-6133	88	3	ζ(σ	ζ(σ	X
ejpam-6133	88	4	,	,	PUNCT
ejpam-6133	88	5	ς	ς	NOUN
ejpam-6133	88	6	)	)	PUNCT
ejpam-6133	88	7	=	=	SYM
ejpam-6133	88	8	0	0	NUM
ejpam-6133	88	9	,	,	PUNCT
ejpam-6133	88	10	which	which	PRON
ejpam-6133	88	11	further	far	ADV
ejpam-6133	88	12	implies	imply	VERB
ejpam-6133	88	13	that	that	SCONJ
ejpam-6133	88	14	σ	σ	PROPN
ejpam-6133	88	15	=	=	SYM
ejpam-6133	88	16	ς	ς	PROPN
ejpam-6133	88	17	.	.	PUNCT
ejpam-6133	88	18	h.	h.	PROPN
ejpam-6133	88	19	aydi	aydi	PROPN
ejpam-6133	88	20	,	,	PUNCT
ejpam-6133	88	21	h.	h.	PROPN
ejpam-6133	88	22	hammouda	hammouda	PROPN
ejpam-6133	88	23	,	,	PUNCT
ejpam-6133	88	24	s.	s.	PROPN
ejpam-6133	88	25	mansour	mansour	PROPN
ejpam-6133	88	26	/	/	SYM
ejpam-6133	88	27	eur	eur	PROPN
ejpam-6133	88	28	.	.	PUNCT
ejpam-6133	89	1	j.	j.	PROPN
ejpam-6133	89	2	pure	pure	PROPN
ejpam-6133	89	3	appl	appl	PROPN
ejpam-6133	89	4	.	.	PROPN
ejpam-6133	89	5	math	math	PROPN
ejpam-6133	89	6	,	,	PUNCT
ejpam-6133	89	7	18	18	NUM
ejpam-6133	89	8	(	(	PUNCT
ejpam-6133	89	9	3	3	NUM
ejpam-6133	89	10	)	)	PUNCT
ejpam-6133	89	11	(	(	PUNCT
ejpam-6133	89	12	2025	2025	NUM
ejpam-6133	89	13	)	)	PUNCT
ejpam-6133	89	14	,	,	PUNCT
ejpam-6133	89	15	6133	6133	NUM
ejpam-6133	89	16	4	4	NUM
ejpam-6133	89	17	of	of	ADP
ejpam-6133	89	18	18	18	NUM
ejpam-6133	89	19	3	3	NUM
ejpam-6133	89	20	.	.	PUNCT
ejpam-6133	89	21	main	main	ADJ
ejpam-6133	89	22	results	result	NOUN
ejpam-6133	89	23	our	our	PRON
ejpam-6133	89	24	first	first	ADJ
ejpam-6133	89	25	theorem	theorem	NOUN
ejpam-6133	89	26	is	be	AUX
ejpam-6133	89	27	stated	state	VERB
ejpam-6133	89	28	as	as	SCONJ
ejpam-6133	89	29	follows	follow	VERB
ejpam-6133	89	30	:	:	PUNCT
ejpam-6133	89	31	theorem	theorem	NOUN
ejpam-6133	89	32	1	1	X
ejpam-6133	89	33	.	.	PUNCT
ejpam-6133	90	1	let	let	VERB
ejpam-6133	90	2	⊤	⊤	NOUN
ejpam-6133	90	3	be	be	AUX
ejpam-6133	90	4	a	a	DET
ejpam-6133	90	5	self	self	NOUN
ejpam-6133	90	6	-	-	PUNCT
ejpam-6133	90	7	mapping	mapping	NOUN
ejpam-6133	90	8	on	on	ADP
ejpam-6133	90	9	a	a	DET
ejpam-6133	90	10	orbitally	orbitally	ADV
ejpam-6133	90	11	complete	complete	ADJ
ejpam-6133	90	12	dcms	dcms	NOUN
ejpam-6133	90	13	(	(	PUNCT
ejpam-6133	90	14	℧	℧	PROPN
ejpam-6133	90	15	,	,	PUNCT
ejpam-6133	90	16	ζ	ζ	NOUN
ejpam-6133	90	17	)	)	PUNCT
ejpam-6133	90	18	with	with	ADP
ejpam-6133	90	19	controlled	control	VERB
ejpam-6133	90	20	functions	function	NOUN
ejpam-6133	90	21	ϖ	ϖ	NOUN
ejpam-6133	90	22	,	,	PUNCT
ejpam-6133	90	23	ϵ	ϵ	X
ejpam-6133	90	24	:	:	PUNCT
ejpam-6133	90	25	℧	℧	VERB
ejpam-6133	90	26	×	×	NOUN
ejpam-6133	90	27	℧	℧	X
ejpam-6133	90	28	−→	−→	NOUN
ejpam-6133	90	29	[	[	X
ejpam-6133	90	30	1,+∞	1,+∞	NUM
ejpam-6133	90	31	[	[	X
ejpam-6133	90	32	.	.	PUNCT
ejpam-6133	90	33	suppose	suppose	VERB
ejpam-6133	90	34	there	there	PRON
ejpam-6133	90	35	are	be	VERB
ejpam-6133	90	36	two	two	NUM
ejpam-6133	90	37	functions	function	NOUN
ejpam-6133	90	38	α	α	NOUN
ejpam-6133	90	39	:	:	PUNCT
ejpam-6133	90	40	℧	℧	VERB
ejpam-6133	90	41	×	×	NOUN
ejpam-6133	90	42	℧	℧	X
ejpam-6133	90	43	−→	−→	NOUN
ejpam-6133	90	44	[	[	X
ejpam-6133	90	45	0,+∞	0,+∞	NUM
ejpam-6133	90	46	)	)	PUNCT
ejpam-6133	90	47	,	,	PUNCT
ejpam-6133	90	48	and	and	CCONJ
ejpam-6133	90	49	ψ	ψ	AUX
ejpam-6133	90	50	∈	∈	NOUN
ejpam-6133	90	51	ψ	ψ	NOUN
ejpam-6133	90	52	so	so	SCONJ
ejpam-6133	91	1	that	that	SCONJ
ejpam-6133	91	2	α(x	α(x	NOUN
ejpam-6133	91	3	,	,	PUNCT
ejpam-6133	91	4	y)ϖ(x	y)ϖ(x	PROPN
ejpam-6133	91	5	,	,	PUNCT
ejpam-6133	91	6	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	91	7	,	,	PUNCT
ejpam-6133	91	8	y)ζ(⊤x,⊤y	y)ζ(⊤x,⊤y	PROPN
ejpam-6133	91	9	)	)	PUNCT
ejpam-6133	91	10	≤	≤	NUM
ejpam-6133	91	11	ψ(r(x	ψ(r(x	PROPN
ejpam-6133	91	12	,	,	PUNCT
ejpam-6133	91	13	y	y	NOUN
ejpam-6133	91	14	)	)	PUNCT
ejpam-6133	91	15	)	)	PUNCT
ejpam-6133	92	1	∀x	∀x	NUM
ejpam-6133	92	2	,	,	PUNCT
ejpam-6133	92	3	y	y	PROPN
ejpam-6133	92	4	∈	∈	PROPN
ejpam-6133	92	5	℧	℧	PROPN
ejpam-6133	92	6	,	,	PUNCT
ejpam-6133	92	7	(	(	PUNCT
ejpam-6133	92	8	3	3	X
ejpam-6133	92	9	)	)	PUNCT
ejpam-6133	92	10	where	where	SCONJ
ejpam-6133	92	11	r(x	r(x	PROPN
ejpam-6133	92	12	,	,	PUNCT
ejpam-6133	92	13	y	y	NOUN
ejpam-6133	92	14	)	)	PUNCT
ejpam-6133	92	15	=	=	SYM
ejpam-6133	92	16	max	max	X
ejpam-6133	92	17	{	{	PUNCT
ejpam-6133	92	18	ζ(x	ζ(x	PROPN
ejpam-6133	92	19	,	,	PUNCT
ejpam-6133	92	20	y	y	PROPN
ejpam-6133	92	21	)	)	PUNCT
ejpam-6133	92	22	,	,	PUNCT
ejpam-6133	92	23	ζ(x,⊤x	ζ(x,⊤x	NOUN
ejpam-6133	92	24	)	)	PUNCT
ejpam-6133	92	25	,	,	PUNCT
ejpam-6133	92	26	ζ(y,⊤y	ζ(y,⊤y	NOUN
ejpam-6133	92	27	)	)	PUNCT
ejpam-6133	92	28	,	,	PUNCT
ejpam-6133	92	29	ζ(x,⊤x)[ϖ(x	ζ(x,⊤x)[ϖ(x	NOUN
ejpam-6133	92	30	,	,	PUNCT
ejpam-6133	92	31	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	92	32	,	,	PUNCT
ejpam-6133	92	33	y	y	PROPN
ejpam-6133	92	34	)	)	PUNCT
ejpam-6133	92	35	+	+	PUNCT
ejpam-6133	92	36	ζ(y,⊤y	ζ(y,⊤y	NOUN
ejpam-6133	92	37	)	)	PUNCT
ejpam-6133	92	38	]	]	PUNCT
ejpam-6133	92	39	ϖ(x	ϖ(x	PROPN
ejpam-6133	92	40	,	,	PUNCT
ejpam-6133	92	41	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	92	42	,	,	PUNCT
ejpam-6133	92	43	y	y	PROPN
ejpam-6133	92	44	)	)	PUNCT
ejpam-6133	92	45	+	+	CCONJ
ejpam-6133	92	46	ζ(x	ζ(x	PROPN
ejpam-6133	92	47	,	,	PUNCT
ejpam-6133	92	48	y	y	NOUN
ejpam-6133	92	49	)	)	PUNCT
ejpam-6133	92	50	,	,	PUNCT
ejpam-6133	92	51	ζ(y,⊤y)[ϖ(x	ζ(y,⊤y)[ϖ(x	PROPN
ejpam-6133	92	52	,	,	PUNCT
ejpam-6133	92	53	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	92	54	,	,	PUNCT
ejpam-6133	92	55	y	y	PROPN
ejpam-6133	92	56	)	)	PUNCT
ejpam-6133	92	57	+	+	NUM
ejpam-6133	92	58	ζ(x,⊤x	ζ(x,⊤x	NOUN
ejpam-6133	92	59	)	)	PUNCT
ejpam-6133	92	60	]	]	PUNCT
ejpam-6133	93	1	ϖ(x	ϖ(x	PROPN
ejpam-6133	93	2	,	,	PUNCT
ejpam-6133	93	3	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	93	4	,	,	PUNCT
ejpam-6133	93	5	y	y	PROPN
ejpam-6133	93	6	)	)	PUNCT
ejpam-6133	93	7	+	+	CCONJ
ejpam-6133	93	8	ζ(x	ζ(x	PROPN
ejpam-6133	93	9	,	,	PUNCT
ejpam-6133	93	10	y	y	NOUN
ejpam-6133	93	11	)	)	PUNCT
ejpam-6133	93	12	}	}	PUNCT
ejpam-6133	93	13	.	.	PUNCT
ejpam-6133	94	1	assume	assume	VERB
ejpam-6133	94	2	that	that	SCONJ
ejpam-6133	94	3	:	:	PUNCT
ejpam-6133	94	4	(	(	PUNCT
ejpam-6133	94	5	i	i	NOUN
ejpam-6133	94	6	)	)	PUNCT
ejpam-6133	94	7	⊤	⊤	PROPN
ejpam-6133	94	8	is	be	AUX
ejpam-6133	94	9	α	α	PRON
ejpam-6133	94	10	-	-	ADJ
ejpam-6133	94	11	orbitally	orbitally	ADV
ejpam-6133	94	12	admissible	admissible	NOUN
ejpam-6133	94	13	;	;	PUNCT
ejpam-6133	94	14	(	(	PUNCT
ejpam-6133	94	15	ii	ii	NOUN
ejpam-6133	94	16	)	)	PUNCT
ejpam-6133	94	17	there	there	PRON
ejpam-6133	94	18	is	be	VERB
ejpam-6133	94	19	s̃0	s̃0	PROPN
ejpam-6133	94	20	∈	∈	PROPN
ejpam-6133	94	21	℧	℧	NOUN
ejpam-6133	94	22	satisfying	satisfy	VERB
ejpam-6133	94	23	α(s̃0,⊤s̃0	α(s̃0,⊤s̃0	PROPN
ejpam-6133	94	24	)	)	PUNCT
ejpam-6133	94	25	≥	≥	NOUN
ejpam-6133	94	26	1	1	NUM
ejpam-6133	94	27	;	;	PUNCT
ejpam-6133	94	28	(	(	PUNCT
ejpam-6133	94	29	iii	iii	NOUN
ejpam-6133	94	30	)	)	PUNCT
ejpam-6133	94	31	supm≥1	supm≥1	PROPN
ejpam-6133	94	32	lim	lim	PROPN
ejpam-6133	94	33	i→∞	i→∞	VERB
ejpam-6133	94	34	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	94	35	,	,	PUNCT
ejpam-6133	94	36	s̃m)ϖ(s̃i+1	s̃m)ϖ(s̃i+1	PROPN
ejpam-6133	94	37	,	,	PUNCT
ejpam-6133	95	1	s̃i+2)ψ	s̃i+2)ψ	PRON
ejpam-6133	95	2	i+1(ζ(s̃0	i+1(ζ(s̃0	ADJ
ejpam-6133	95	3	,	,	PUNCT
ejpam-6133	95	4	s̃1	s̃1	PROPN
ejpam-6133	95	5	)	)	PUNCT
ejpam-6133	95	6	)	)	PUNCT
ejpam-6133	96	1	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	96	2	,	,	PUNCT
ejpam-6133	96	3	s̃i+1)ψi(ζ(s̃0	s̃i+1)ψi(ζ(s̃0	PROPN
ejpam-6133	96	4	,	,	PUNCT
ejpam-6133	96	5	s̃1	s̃1	PROPN
ejpam-6133	96	6	)	)	PUNCT
ejpam-6133	96	7	)	)	PUNCT
ejpam-6133	97	1	<	<	X
ejpam-6133	97	2	1	1	NUM
ejpam-6133	97	3	,	,	PUNCT
ejpam-6133	97	4	where	where	SCONJ
ejpam-6133	97	5	s̃i	s̃i	PROPN
ejpam-6133	97	6	=	=	SYM
ejpam-6133	97	7	⊤i(s̃0	⊤i(s̃0	PROPN
ejpam-6133	97	8	)	)	PUNCT
ejpam-6133	97	9	;	;	PUNCT
ejpam-6133	97	10	(	(	PUNCT
ejpam-6133	97	11	iv	iv	X
ejpam-6133	97	12	)	)	PUNCT
ejpam-6133	97	13	⊤	⊤	NOUN
ejpam-6133	97	14	is	be	AUX
ejpam-6133	97	15	orbitally	orbitally	ADV
ejpam-6133	97	16	continuous	continuous	ADJ
ejpam-6133	97	17	on	on	ADP
ejpam-6133	97	18	℧	℧	PROPN
ejpam-6133	97	19	;	;	PUNCT
ejpam-6133	97	20	(	(	PUNCT
ejpam-6133	97	21	v	v	NOUN
ejpam-6133	97	22	)	)	PUNCT
ejpam-6133	97	23	lim	lim	PROPN
ejpam-6133	97	24	n→∞	n→∞	NUM
ejpam-6133	97	25	ϵ(s̃n	ϵ(s̃n	PROPN
ejpam-6133	97	26	,	,	PUNCT
ejpam-6133	97	27	x	x	NOUN
ejpam-6133	97	28	)	)	PUNCT
ejpam-6133	97	29	and	and	CCONJ
ejpam-6133	97	30	lim	lim	PROPN
ejpam-6133	97	31	n→∞	n→∞	X
ejpam-6133	98	1	ϖ(s̃n	ϖ(s̃n	PROPN
ejpam-6133	98	2	,	,	PUNCT
ejpam-6133	98	3	x	x	X
ejpam-6133	98	4	)	)	PUNCT
ejpam-6133	98	5	exist	exist	VERB
ejpam-6133	98	6	and	and	CCONJ
ejpam-6133	98	7	are	be	AUX
ejpam-6133	98	8	finite	finite	ADJ
ejpam-6133	98	9	.	.	PUNCT
ejpam-6133	99	1	therefore	therefore	ADV
ejpam-6133	99	2	,	,	PUNCT
ejpam-6133	99	3	⊤	⊤	PROPN
ejpam-6133	99	4	possesses	possess	VERB
ejpam-6133	99	5	a	a	DET
ejpam-6133	99	6	fp	fp	NOUN
ejpam-6133	99	7	in	in	ADP
ejpam-6133	99	8	℧	℧	PROPN
ejpam-6133	99	9	.	.	PUNCT
ejpam-6133	100	1	if	if	SCONJ
ejpam-6133	100	2	in	in	ADP
ejpam-6133	100	3	addition	addition	NOUN
ejpam-6133	100	4	,	,	PUNCT
ejpam-6133	100	5	we	we	PRON
ejpam-6133	100	6	have	have	VERB
ejpam-6133	100	7	(	(	PUNCT
ejpam-6133	100	8	u	u	NOUN
ejpam-6133	100	9	)	)	PUNCT
ejpam-6133	100	10	:	:	PUNCT
ejpam-6133	101	1	x	x	X
ejpam-6133	101	2	,	,	PUNCT
ejpam-6133	101	3	x∗	x∗	PROPN
ejpam-6133	101	4	∈	∈	PROPN
ejpam-6133	101	5	fix(⊤	fix(⊤	NOUN
ejpam-6133	101	6	)	)	PUNCT
ejpam-6133	101	7	implies	imply	VERB
ejpam-6133	101	8	α(x	α(x	NOUN
ejpam-6133	101	9	,	,	PUNCT
ejpam-6133	101	10	x∗	x∗	PROPN
ejpam-6133	101	11	)	)	PUNCT
ejpam-6133	101	12	≥	≥	NOUN
ejpam-6133	101	13	1	1	NUM
ejpam-6133	101	14	,	,	PUNCT
ejpam-6133	101	15	then	then	ADV
ejpam-6133	101	16	such	such	DET
ejpam-6133	101	17	a	a	DET
ejpam-6133	101	18	fp	fp	PROPN
ejpam-6133	101	19	is	be	AUX
ejpam-6133	101	20	unique	unique	ADJ
ejpam-6133	101	21	.	.	PUNCT
ejpam-6133	102	1	proof	proof	NOUN
ejpam-6133	102	2	.	.	PUNCT
ejpam-6133	103	1	by	by	ADP
ejpam-6133	103	2	(	(	PUNCT
ejpam-6133	103	3	ii	ii	NOUN
ejpam-6133	103	4	)	)	PUNCT
ejpam-6133	103	5	,	,	PUNCT
ejpam-6133	103	6	define	define	VERB
ejpam-6133	103	7	a	a	DET
ejpam-6133	103	8	sequence	sequence	NOUN
ejpam-6133	103	9	{	{	PUNCT
ejpam-6133	103	10	s̃ℓ	s̃ℓ	ADV
ejpam-6133	103	11	}	}	PUNCT
ejpam-6133	103	12	in	in	ADP
ejpam-6133	103	13	℧	℧	ADP
ejpam-6133	103	14	such	such	ADJ
ejpam-6133	103	15	that	that	DET
ejpam-6133	103	16	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	103	17	=	=	PUNCT
ejpam-6133	103	18	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	103	19	=	=	SYM
ejpam-6133	103	20	⊤n+1s̃0	⊤n+1s̃0	PROPN
ejpam-6133	103	21	,	,	PUNCT
ejpam-6133	103	22	for	for	ADP
ejpam-6133	103	23	all	all	DET
ejpam-6133	103	24	ℓ	ℓ	PROPN
ejpam-6133	103	25	∈	∈	PROPN
ejpam-6133	103	26	n.	n.	NOUN
ejpam-6133	103	27	when	when	SCONJ
ejpam-6133	103	28	s̃ℓ	s̃ℓ	ADV
ejpam-6133	103	29	=	=	SYM
ejpam-6133	103	30	s̃ℓ+1	s̃ℓ+1	NOUN
ejpam-6133	103	31	for	for	ADP
ejpam-6133	103	32	some	some	DET
ejpam-6133	103	33	ℓ	ℓ	PROPN
ejpam-6133	103	34	∈	∈	PROPN
ejpam-6133	103	35	n	n	CCONJ
ejpam-6133	103	36	,	,	PUNCT
ejpam-6133	103	37	then	then	ADV
ejpam-6133	103	38	s̃ℓ	s̃ℓ	PRON
ejpam-6133	103	39	is	be	AUX
ejpam-6133	103	40	a	a	DET
ejpam-6133	103	41	fp	fp	NOUN
ejpam-6133	103	42	of	of	ADP
ejpam-6133	103	43	⊤.	⊤.	PROPN
ejpam-6133	103	44	now	now	ADV
ejpam-6133	103	45	,	,	PUNCT
ejpam-6133	103	46	suppose	suppose	VERB
ejpam-6133	103	47	that	that	SCONJ
ejpam-6133	103	48	s̃ℓ	s̃ℓ	VERB
ejpam-6133	103	49	̸=	̸=	PROPN
ejpam-6133	103	50	s̃ℓ+1	s̃ℓ+1	NOUN
ejpam-6133	103	51	,	,	PUNCT
ejpam-6133	103	52	for	for	ADP
ejpam-6133	103	53	any	any	DET
ejpam-6133	103	54	ℓ	ℓ	PROPN
ejpam-6133	103	55	∈	∈	PROPN
ejpam-6133	103	56	n.	n.	NOUN
ejpam-6133	103	57	due	due	ADP
ejpam-6133	103	58	to	to	ADP
ejpam-6133	103	59	(	(	PUNCT
ejpam-6133	103	60	i	i	NOUN
ejpam-6133	103	61	)	)	PUNCT
ejpam-6133	103	62	,	,	PUNCT
ejpam-6133	103	63	α(s̃0	α(s̃0	PROPN
ejpam-6133	103	64	,	,	PUNCT
ejpam-6133	103	65	s̃1	s̃1	PROPN
ejpam-6133	103	66	)	)	PUNCT
ejpam-6133	103	67	=	=	SYM
ejpam-6133	103	68	α(s̃0,⊤s̃0	α(s̃0,⊤s̃0	PROPN
ejpam-6133	103	69	)	)	PUNCT
ejpam-6133	103	70	≥	≥	NOUN
ejpam-6133	103	71	1	1	NUM
ejpam-6133	103	72	implies	imply	VERB
ejpam-6133	103	73	that	that	DET
ejpam-6133	103	74	α(s̃1	α(s̃1	NOUN
ejpam-6133	103	75	,	,	PUNCT
ejpam-6133	103	76	s̃2	s̃2	X
ejpam-6133	103	77	)	)	PUNCT
ejpam-6133	103	78	=	=	SYM
ejpam-6133	103	79	α(⊤s̃0,⊤s̃1	α(⊤s̃0,⊤s̃1	NOUN
ejpam-6133	103	80	)	)	PUNCT
ejpam-6133	103	81	≥	≥	NOUN
ejpam-6133	103	82	1	1	NUM
ejpam-6133	103	83	.	.	PUNCT
ejpam-6133	104	1	then	then	ADV
ejpam-6133	104	2	,	,	PUNCT
ejpam-6133	104	3	α(s̃2	α(s̃2	X
ejpam-6133	104	4	,	,	PUNCT
ejpam-6133	104	5	s̃3	s̃3	NOUN
ejpam-6133	104	6	)	)	PUNCT
ejpam-6133	104	7	=	=	SYM
ejpam-6133	104	8	α(⊤s̃1,⊤s̃2	α(⊤s̃1,⊤s̃2	X
ejpam-6133	104	9	)	)	PUNCT
ejpam-6133	104	10	≥	≥	NOUN
ejpam-6133	104	11	1	1	NUM
ejpam-6133	104	12	.	.	PUNCT
ejpam-6133	105	1	continuing	continue	VERB
ejpam-6133	105	2	this	this	DET
ejpam-6133	105	3	process	process	NOUN
ejpam-6133	105	4	,	,	PUNCT
ejpam-6133	105	5	one	one	PRON
ejpam-6133	105	6	gets	get	VERB
ejpam-6133	105	7	α(s̃ℓ	α(s̃ℓ	NOUN
ejpam-6133	105	8	,	,	PUNCT
ejpam-6133	105	9	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	105	10	)	)	PUNCT
ejpam-6133	105	11	≥	≥	NOUN
ejpam-6133	105	12	1	1	NUM
ejpam-6133	105	13	,	,	PUNCT
ejpam-6133	105	14	for	for	ADP
ejpam-6133	105	15	any	any	DET
ejpam-6133	105	16	ℓ	ℓ	PROPN
ejpam-6133	105	17	∈	∈	PROPN
ejpam-6133	105	18	n.	n.	NOUN
ejpam-6133	105	19	letting	let	VERB
ejpam-6133	105	20	x	x	SYM
ejpam-6133	105	21	=	=	SYM
ejpam-6133	105	22	s̃ℓ−1	s̃ℓ−1	X
ejpam-6133	105	23	and	and	CCONJ
ejpam-6133	105	24	y	y	NOUN
ejpam-6133	105	25	=	=	PUNCT
ejpam-6133	105	26	s̃ℓ	s̃ℓ	PROPN
ejpam-6133	105	27	in	in	ADP
ejpam-6133	105	28	(	(	PUNCT
ejpam-6133	105	29	3	3	NUM
ejpam-6133	105	30	)	)	PUNCT
ejpam-6133	105	31	,	,	PUNCT
ejpam-6133	105	32	we	we	PRON
ejpam-6133	105	33	have	have	VERB
ejpam-6133	105	34	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	105	35	,	,	PUNCT
ejpam-6133	105	36	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	105	37	)	)	PUNCT
ejpam-6133	105	38	=	=	SYM
ejpam-6133	105	39	ζ(⊤s̃ℓ−1,⊤s̃ℓ	ζ(⊤s̃ℓ−1,⊤s̃ℓ	X
ejpam-6133	105	40	)	)	PUNCT
ejpam-6133	105	41	≤	≤	NUM
ejpam-6133	105	42	α(s̃ℓ−1	α(s̃ℓ−1	NOUN
ejpam-6133	105	43	,	,	PUNCT
ejpam-6133	105	44	s̃ℓ)ϖ(s̃ℓ−1	s̃ℓ)ϖ(s̃ℓ−1	NOUN
ejpam-6133	105	45	,	,	PUNCT
ejpam-6133	105	46	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	105	47	,	,	PUNCT
ejpam-6133	105	48	s̃ℓ)ζ(⊤s̃ℓ−1,⊤s̃ℓ	s̃ℓ)ζ(⊤s̃ℓ−1,⊤s̃ℓ	NOUN
ejpam-6133	105	49	)	)	PUNCT
ejpam-6133	105	50	≤	≤	NOUN
ejpam-6133	106	1	ψ(r(s̃ℓ−1	ψ(r(s̃ℓ−1	PROPN
ejpam-6133	106	2	,	,	PUNCT
ejpam-6133	106	3	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	106	4	)	)	PUNCT
ejpam-6133	106	5	)	)	PUNCT
ejpam-6133	106	6	,	,	PUNCT
ejpam-6133	106	7	(	(	PUNCT
ejpam-6133	106	8	4	4	X
ejpam-6133	106	9	)	)	PUNCT
ejpam-6133	106	10	h.	h.	NOUN
ejpam-6133	106	11	aydi	aydi	PROPN
ejpam-6133	106	12	,	,	PUNCT
ejpam-6133	106	13	h.	h.	PROPN
ejpam-6133	106	14	hammouda	hammouda	PROPN
ejpam-6133	106	15	,	,	PUNCT
ejpam-6133	106	16	s.	s.	PROPN
ejpam-6133	106	17	mansour	mansour	PROPN
ejpam-6133	106	18	/	/	SYM
ejpam-6133	106	19	eur	eur	PROPN
ejpam-6133	106	20	.	.	PUNCT
ejpam-6133	107	1	j.	j.	PROPN
ejpam-6133	107	2	pure	pure	PROPN
ejpam-6133	107	3	appl	appl	PROPN
ejpam-6133	107	4	.	.	PROPN
ejpam-6133	107	5	math	math	PROPN
ejpam-6133	107	6	,	,	PUNCT
ejpam-6133	107	7	18	18	NUM
ejpam-6133	107	8	(	(	PUNCT
ejpam-6133	107	9	3	3	NUM
ejpam-6133	107	10	)	)	PUNCT
ejpam-6133	107	11	(	(	PUNCT
ejpam-6133	107	12	2025	2025	NUM
ejpam-6133	107	13	)	)	PUNCT
ejpam-6133	107	14	,	,	PUNCT
ejpam-6133	107	15	6133	6133	NUM
ejpam-6133	107	16	5	5	NUM
ejpam-6133	107	17	of	of	ADP
ejpam-6133	107	18	18	18	NUM
ejpam-6133	107	19	where	where	SCONJ
ejpam-6133	107	20	r(s̃ℓ−1	r(s̃ℓ−1	NOUN
ejpam-6133	107	21	,	,	PUNCT
ejpam-6133	107	22	s̃ℓ	s̃ℓ	NUM
ejpam-6133	107	23	)	)	PUNCT
ejpam-6133	107	24	=	=	SYM
ejpam-6133	107	25	max{ζ(s̃ℓ−1	max{ζ(s̃ℓ−1	NOUN
ejpam-6133	107	26	,	,	PUNCT
ejpam-6133	107	27	s̃ℓ	s̃ℓ	NUM
ejpam-6133	107	28	)	)	PUNCT
ejpam-6133	107	29	,	,	PUNCT
ejpam-6133	107	30	ζ(s̃ℓ−1,⊤s̃ℓ−1	ζ(s̃ℓ−1,⊤s̃ℓ−1	NOUN
ejpam-6133	107	31	)	)	PUNCT
ejpam-6133	107	32	,	,	PUNCT
ejpam-6133	107	33	ζ(s̃ℓ,⊤s̃ℓ	ζ(s̃ℓ,⊤s̃ℓ	NOUN
ejpam-6133	107	34	)	)	PUNCT
ejpam-6133	107	35	;	;	PUNCT
ejpam-6133	107	36	ζ(s̃ℓ−1,⊤s̃ℓ−1)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,⊤s̃ℓ	ζ(s̃ℓ−1,⊤s̃ℓ−1)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,⊤s̃ℓ	NOUN
ejpam-6133	107	37	)	)	PUNCT
ejpam-6133	107	38	]	]	PUNCT
ejpam-6133	108	1	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	108	2	)	)	PUNCT
ejpam-6133	108	3	,	,	PUNCT
ejpam-6133	108	4	ζ(s̃ℓ,⊤s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,⊤s̃ℓ−1	ζ(s̃ℓ,⊤s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,⊤s̃ℓ−1	NUM
ejpam-6133	108	5	)	)	PUNCT
ejpam-6133	108	6	]	]	PUNCT
ejpam-6133	108	7	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	108	8	)	)	PUNCT
ejpam-6133	108	9	}	}	PUNCT
ejpam-6133	108	10	=	=	SYM
ejpam-6133	108	11	max{ζ(s̃ℓ−1	max{ζ(s̃ℓ−1	NOUN
ejpam-6133	108	12	,	,	PUNCT
ejpam-6133	108	13	s̃ℓ	s̃ℓ	NUM
ejpam-6133	108	14	)	)	PUNCT
ejpam-6133	108	15	,	,	PUNCT
ejpam-6133	108	16	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	108	17	,	,	PUNCT
ejpam-6133	108	18	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	108	19	)	)	PUNCT
ejpam-6133	108	20	,	,	PUNCT
ejpam-6133	108	21	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	108	22	,	,	PUNCT
ejpam-6133	108	23	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	108	24	)	)	PUNCT
ejpam-6133	108	25	;	;	PUNCT
ejpam-6133	108	26	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	NUM
ejpam-6133	108	27	)	)	PUNCT
ejpam-6133	108	28	]	]	PUNCT
ejpam-6133	108	29	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	108	30	)	)	PUNCT
ejpam-6133	108	31	;	;	PUNCT
ejpam-6133	108	32	ζ(s̃ℓ,s̃ℓ+1)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ζ(s̃ℓ,s̃ℓ+1)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	PROPN
ejpam-6133	108	33	)	)	PUNCT
ejpam-6133	108	34	]	]	PUNCT
ejpam-6133	108	35	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	108	36	)	)	PUNCT
ejpam-6133	108	37	}	}	PUNCT
ejpam-6133	108	38	=	=	SYM
ejpam-6133	108	39	max{ζ(s̃ℓ−1	max{ζ(s̃ℓ−1	NOUN
ejpam-6133	108	40	,	,	PUNCT
ejpam-6133	108	41	s̃ℓ	s̃ℓ	NUM
ejpam-6133	108	42	)	)	PUNCT
ejpam-6133	108	43	,	,	PUNCT
ejpam-6133	108	44	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	108	45	,	,	PUNCT
ejpam-6133	108	46	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	108	47	)	)	PUNCT
ejpam-6133	108	48	,	,	PUNCT
ejpam-6133	108	49	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	NOUN
ejpam-6133	108	50	)	)	PUNCT
ejpam-6133	108	51	]	]	PUNCT
ejpam-6133	108	52	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	108	53	)	)	PUNCT
ejpam-6133	108	54	}	}	PUNCT
ejpam-6133	108	55	.	.	PUNCT
ejpam-6133	109	1	(	(	PUNCT
ejpam-6133	109	2	5	5	X
ejpam-6133	109	3	)	)	PUNCT
ejpam-6133	109	4	we	we	PRON
ejpam-6133	109	5	should	should	AUX
ejpam-6133	109	6	take	take	VERB
ejpam-6133	109	7	the	the	DET
ejpam-6133	109	8	following	following	NOUN
ejpam-6133	109	9	:	:	PUNCT
ejpam-6133	109	10	case	case	NOUN
ejpam-6133	109	11	1	1	NUM
ejpam-6133	109	12	if	if	SCONJ
ejpam-6133	109	13	r(s̃ℓ−1	r(s̃ℓ−1	NOUN
ejpam-6133	109	14	,	,	PUNCT
ejpam-6133	109	15	s̃ℓ	s̃ℓ	NUM
ejpam-6133	109	16	)	)	PUNCT
ejpam-6133	109	17	=	=	SYM
ejpam-6133	109	18	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	109	19	,	,	PUNCT
ejpam-6133	109	20	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	109	21	)	)	PUNCT
ejpam-6133	109	22	,	,	PUNCT
ejpam-6133	109	23	so	so	ADV
ejpam-6133	109	24	using	use	VERB
ejpam-6133	109	25	(	(	PUNCT
ejpam-6133	109	26	4	4	NUM
ejpam-6133	109	27	)	)	PUNCT
ejpam-6133	109	28	,	,	PUNCT
ejpam-6133	109	29	one	one	NUM
ejpam-6133	109	30	writes	write	VERB
ejpam-6133	109	31	0	0	NUM
ejpam-6133	109	32	<	<	X
ejpam-6133	109	33	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	109	34	,	,	PUNCT
ejpam-6133	109	35	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	109	36	)	)	PUNCT
ejpam-6133	109	37	≤	≤	NUM
ejpam-6133	109	38	ψ(ζ(s̃ℓ	ψ(ζ(s̃ℓ	NOUN
ejpam-6133	109	39	,	,	PUNCT
ejpam-6133	109	40	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	109	41	)	)	PUNCT
ejpam-6133	109	42	)	)	PUNCT
ejpam-6133	109	43	<	<	X
ejpam-6133	110	1	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	110	2	,	,	PUNCT
ejpam-6133	110	3	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	110	4	)	)	PUNCT
ejpam-6133	110	5	.	.	PUNCT
ejpam-6133	111	1	it	it	PRON
ejpam-6133	111	2	is	be	AUX
ejpam-6133	111	3	a	a	DET
ejpam-6133	111	4	contradiction	contradiction	NOUN
ejpam-6133	111	5	.	.	PUNCT
ejpam-6133	112	1	case	case	NOUN
ejpam-6133	112	2	2	2	NUM
ejpam-6133	113	1	if	if	SCONJ
ejpam-6133	113	2	r(s̃ℓ−1	r(s̃ℓ−1	NOUN
ejpam-6133	113	3	,	,	PUNCT
ejpam-6133	113	4	s̃ℓ	s̃ℓ	NUM
ejpam-6133	113	5	)	)	PUNCT
ejpam-6133	113	6	=	=	SYM
ejpam-6133	113	7	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	ζ(s̃ℓ−1,s̃ℓ)[ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ,s̃ℓ+1	NOUN
ejpam-6133	113	8	)	)	PUNCT
ejpam-6133	113	9	]	]	PUNCT
ejpam-6133	114	1	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	ϖ(s̃ℓ−1,s̃ℓ)ϵ(s̃ℓ−1,s̃ℓ)+ζ(s̃ℓ−1,s̃ℓ	NOUN
ejpam-6133	114	2	)	)	PUNCT
ejpam-6133	114	3	,	,	PUNCT
ejpam-6133	114	4	then	then	ADV
ejpam-6133	114	5	by	by	ADP
ejpam-6133	114	6	(	(	PUNCT
ejpam-6133	114	7	5	5	NUM
ejpam-6133	114	8	)	)	PUNCT
ejpam-6133	114	9	,	,	PUNCT
ejpam-6133	114	10	we	we	PRON
ejpam-6133	114	11	have	have	VERB
ejpam-6133	114	12	max	max	PROPN
ejpam-6133	114	13	{	{	PUNCT
ejpam-6133	114	14	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	114	15	,	,	PUNCT
ejpam-6133	114	16	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	114	17	)	)	PUNCT
ejpam-6133	114	18	;	;	PUNCT
ejpam-6133	114	19	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	114	20	,	,	PUNCT
ejpam-6133	114	21	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	114	22	)	)	PUNCT
ejpam-6133	114	23	}	}	PUNCT
ejpam-6133	114	24	≤	≤	NUM
ejpam-6133	114	25	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	114	26	,	,	PUNCT
ejpam-6133	114	27	s̃ℓ)[ϖ(s̃ℓ−1	s̃ℓ)[ϖ(s̃ℓ−1	PROPN
ejpam-6133	114	28	,	,	PUNCT
ejpam-6133	114	29	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	114	30	,	,	PUNCT
ejpam-6133	114	31	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	114	32	)	)	PUNCT
ejpam-6133	114	33	+	+	NUM
ejpam-6133	114	34	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	114	35	,	,	PUNCT
ejpam-6133	114	36	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	114	37	)	)	PUNCT
ejpam-6133	114	38	]	]	PUNCT
ejpam-6133	114	39	ϖ(s̃ℓ−1	ϖ(s̃ℓ−1	NOUN
ejpam-6133	114	40	,	,	PUNCT
ejpam-6133	114	41	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	114	42	,	,	PUNCT
ejpam-6133	114	43	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	114	44	)	)	PUNCT
ejpam-6133	114	45	+	+	NUM
ejpam-6133	114	46	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	114	47	,	,	PUNCT
ejpam-6133	114	48	s̃ℓ	s̃ℓ	NUM
ejpam-6133	114	49	)	)	PUNCT
ejpam-6133	114	50	.	.	PUNCT
ejpam-6133	115	1	we	we	PRON
ejpam-6133	115	2	study	study	VERB
ejpam-6133	115	3	two	two	NUM
ejpam-6133	115	4	subcases	subcase	NOUN
ejpam-6133	115	5	:	:	PUNCT
ejpam-6133	115	6	subcase	subcase	NOUN
ejpam-6133	115	7	1	1	NUM
ejpam-6133	115	8	:	:	PUNCT
ejpam-6133	115	9	if	if	SCONJ
ejpam-6133	115	10	max	max	PROPN
ejpam-6133	115	11	{	{	PUNCT
ejpam-6133	115	12	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	115	13	,	,	PUNCT
ejpam-6133	115	14	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	15	)	)	PUNCT
ejpam-6133	115	16	;	;	PUNCT
ejpam-6133	115	17	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	115	18	,	,	PUNCT
ejpam-6133	115	19	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	115	20	)	)	PUNCT
ejpam-6133	115	21	}	}	PUNCT
ejpam-6133	115	22	=	=	SYM
ejpam-6133	115	23	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	115	24	,	,	PUNCT
ejpam-6133	115	25	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	26	)	)	PUNCT
ejpam-6133	115	27	,	,	PUNCT
ejpam-6133	115	28	then	then	ADV
ejpam-6133	115	29	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	115	30	,	,	PUNCT
ejpam-6133	115	31	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	115	32	)	)	PUNCT
ejpam-6133	115	33	<	<	X
ejpam-6133	115	34	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	115	35	,	,	PUNCT
ejpam-6133	115	36	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	37	)	)	PUNCT
ejpam-6133	115	38	and	and	CCONJ
ejpam-6133	115	39	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	115	40	,	,	PUNCT
ejpam-6133	115	41	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	42	)	)	PUNCT
ejpam-6133	115	43	≤	≤	NOUN
ejpam-6133	115	44	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	115	45	,	,	PUNCT
ejpam-6133	115	46	s̃ℓ)[ϖ(s̃ℓ−1	s̃ℓ)[ϖ(s̃ℓ−1	PROPN
ejpam-6133	115	47	,	,	PUNCT
ejpam-6133	115	48	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	115	49	,	,	PUNCT
ejpam-6133	115	50	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	51	)	)	PUNCT
ejpam-6133	115	52	+	+	NUM
ejpam-6133	115	53	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	115	54	,	,	PUNCT
ejpam-6133	115	55	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	115	56	)	)	PUNCT
ejpam-6133	115	57	]	]	PUNCT
ejpam-6133	115	58	ϖ(s̃ℓ−1	ϖ(s̃ℓ−1	NOUN
ejpam-6133	115	59	,	,	PUNCT
ejpam-6133	115	60	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	115	61	,	,	PUNCT
ejpam-6133	115	62	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	115	63	)	)	PUNCT
ejpam-6133	116	1	+	+	NUM
ejpam-6133	116	2	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	116	3	,	,	PUNCT
ejpam-6133	116	4	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	116	5	)	)	PUNCT
ejpam-6133	116	6	.	.	PUNCT
ejpam-6133	117	1	that	that	PRON
ejpam-6133	117	2	is	be	AUX
ejpam-6133	117	3	,	,	PUNCT
ejpam-6133	117	4	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	117	5	,	,	PUNCT
ejpam-6133	117	6	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	117	7	)	)	PUNCT
ejpam-6133	117	8	≤	≤	NOUN
ejpam-6133	118	1	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	118	2	,	,	PUNCT
ejpam-6133	118	3	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	118	4	)	)	PUNCT
ejpam-6133	118	5	,	,	PUNCT
ejpam-6133	118	6	which	which	PRON
ejpam-6133	118	7	is	be	AUX
ejpam-6133	118	8	a	a	DET
ejpam-6133	118	9	contradiction	contradiction	NOUN
ejpam-6133	118	10	.	.	PUNCT
ejpam-6133	119	1	subcase	subcase	NOUN
ejpam-6133	119	2	2	2	NUM
ejpam-6133	119	3	:	:	PUNCT
ejpam-6133	119	4	if	if	SCONJ
ejpam-6133	119	5	max	max	PROPN
ejpam-6133	119	6	{	{	PUNCT
ejpam-6133	119	7	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	119	8	,	,	PUNCT
ejpam-6133	119	9	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	119	10	)	)	PUNCT
ejpam-6133	119	11	,	,	PUNCT
ejpam-6133	119	12	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	119	13	,	,	PUNCT
ejpam-6133	119	14	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	119	15	)	)	PUNCT
ejpam-6133	119	16	}	}	PUNCT
ejpam-6133	119	17	=	=	SYM
ejpam-6133	119	18	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	119	19	,	,	PUNCT
ejpam-6133	119	20	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	119	21	)	)	PUNCT
ejpam-6133	119	22	,	,	PUNCT
ejpam-6133	119	23	then	then	ADV
ejpam-6133	119	24	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	119	25	,	,	PUNCT
ejpam-6133	119	26	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	119	27	)	)	PUNCT
ejpam-6133	119	28	>	>	X
ejpam-6133	119	29	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	119	30	,	,	PUNCT
ejpam-6133	119	31	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	119	32	)	)	PUNCT
ejpam-6133	119	33	and	and	CCONJ
ejpam-6133	119	34	h.	h.	PROPN
ejpam-6133	119	35	aydi	aydi	PROPN
ejpam-6133	119	36	,	,	PUNCT
ejpam-6133	119	37	h.	h.	PROPN
ejpam-6133	119	38	hammouda	hammouda	PROPN
ejpam-6133	119	39	,	,	PUNCT
ejpam-6133	119	40	s.	s.	PROPN
ejpam-6133	119	41	mansour	mansour	PROPN
ejpam-6133	119	42	/	/	SYM
ejpam-6133	119	43	eur	eur	PROPN
ejpam-6133	119	44	.	.	PUNCT
ejpam-6133	120	1	j.	j.	PROPN
ejpam-6133	120	2	pure	pure	PROPN
ejpam-6133	120	3	appl	appl	PROPN
ejpam-6133	120	4	.	.	PROPN
ejpam-6133	120	5	math	math	PROPN
ejpam-6133	120	6	,	,	PUNCT
ejpam-6133	120	7	18	18	NUM
ejpam-6133	120	8	(	(	PUNCT
ejpam-6133	120	9	3	3	NUM
ejpam-6133	120	10	)	)	PUNCT
ejpam-6133	120	11	(	(	PUNCT
ejpam-6133	120	12	2025	2025	NUM
ejpam-6133	120	13	)	)	PUNCT
ejpam-6133	120	14	,	,	PUNCT
ejpam-6133	120	15	6133	6133	NUM
ejpam-6133	120	16	6	6	NUM
ejpam-6133	120	17	of	of	ADP
ejpam-6133	120	18	18	18	NUM
ejpam-6133	120	19	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	120	20	,	,	PUNCT
ejpam-6133	120	21	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	120	22	)	)	PUNCT
ejpam-6133	120	23	≤	≤	NUM
ejpam-6133	120	24	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	120	25	,	,	PUNCT
ejpam-6133	120	26	s̃ℓ)[ϖ(s̃ℓ−1	s̃ℓ)[ϖ(s̃ℓ−1	PROPN
ejpam-6133	120	27	,	,	PUNCT
ejpam-6133	120	28	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	120	29	,	,	PUNCT
ejpam-6133	120	30	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	120	31	)	)	PUNCT
ejpam-6133	120	32	+	+	NUM
ejpam-6133	120	33	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	120	34	,	,	PUNCT
ejpam-6133	120	35	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	120	36	)	)	PUNCT
ejpam-6133	120	37	]	]	PUNCT
ejpam-6133	121	1	ϖ(s̃ℓ−1	ϖ(s̃ℓ−1	NOUN
ejpam-6133	121	2	,	,	PUNCT
ejpam-6133	121	3	s̃ℓ)ϵ(s̃ℓ−1	s̃ℓ)ϵ(s̃ℓ−1	NOUN
ejpam-6133	121	4	,	,	PUNCT
ejpam-6133	121	5	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	121	6	)	)	PUNCT
ejpam-6133	121	7	+	+	NUM
ejpam-6133	121	8	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	121	9	,	,	PUNCT
ejpam-6133	121	10	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	121	11	)	)	PUNCT
ejpam-6133	121	12	.	.	PUNCT
ejpam-6133	122	1	that	that	PRON
ejpam-6133	122	2	is	be	AUX
ejpam-6133	122	3	,	,	PUNCT
ejpam-6133	122	4	ζ(s̃ℓ−1	ζ(s̃ℓ−1	PROPN
ejpam-6133	122	5	,	,	PUNCT
ejpam-6133	122	6	s̃ℓ	s̃ℓ	NUM
ejpam-6133	122	7	)	)	PUNCT
ejpam-6133	122	8	≥	≥	NOUN
ejpam-6133	122	9	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	122	10	,	,	PUNCT
ejpam-6133	122	11	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	122	12	)	)	PUNCT
ejpam-6133	122	13	,	,	PUNCT
ejpam-6133	122	14	which	which	PRON
ejpam-6133	122	15	is	be	AUX
ejpam-6133	122	16	a	a	DET
ejpam-6133	122	17	contradiction	contradiction	NOUN
ejpam-6133	122	18	.	.	PUNCT
ejpam-6133	123	1	thus	thus	ADV
ejpam-6133	123	2	,	,	PUNCT
ejpam-6133	123	3	r(s̃ℓ−1	r(s̃ℓ−1	NOUN
ejpam-6133	123	4	,	,	PUNCT
ejpam-6133	123	5	s̃ℓ	s̃ℓ	NUM
ejpam-6133	123	6	)	)	PUNCT
ejpam-6133	123	7	=	=	SYM
ejpam-6133	123	8	ζ(s̃ℓ−1	ζ(s̃ℓ−1	NOUN
ejpam-6133	123	9	,	,	PUNCT
ejpam-6133	123	10	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	123	11	)	)	PUNCT
ejpam-6133	123	12	and	and	CCONJ
ejpam-6133	123	13	by	by	ADP
ejpam-6133	123	14	(	(	PUNCT
ejpam-6133	123	15	4	4	NUM
ejpam-6133	123	16	)	)	PUNCT
ejpam-6133	123	17	,	,	PUNCT
ejpam-6133	123	18	we	we	PRON
ejpam-6133	123	19	get	get	VERB
ejpam-6133	123	20	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	123	21	,	,	PUNCT
ejpam-6133	123	22	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	123	23	)	)	PUNCT
ejpam-6133	123	24	≤	≤	NOUN
ejpam-6133	123	25	ψ(ζ(s̃ℓ−1	ψ(ζ(s̃ℓ−1	NOUN
ejpam-6133	123	26	,	,	PUNCT
ejpam-6133	123	27	s̃ℓ	s̃ℓ	NUM
ejpam-6133	123	28	)	)	PUNCT
ejpam-6133	123	29	)	)	PUNCT
ejpam-6133	124	1	≤	≤	NUM
ejpam-6133	124	2	...	...	PUNCT
ejpam-6133	125	1	≤	≤	NUM
ejpam-6133	125	2	ψℓ(ζ(s̃0	ψℓ(ζ(s̃0	PROPN
ejpam-6133	125	3	,	,	PUNCT
ejpam-6133	125	4	s̃1	s̃1	PROPN
ejpam-6133	125	5	)	)	PUNCT
ejpam-6133	125	6	)	)	PUNCT
ejpam-6133	125	7	.	.	PUNCT
ejpam-6133	126	1	when	when	SCONJ
ejpam-6133	126	2	ℓ	ℓ	PROPN
ejpam-6133	126	3	−→	−→	NOUN
ejpam-6133	126	4	∞	∞	PROPN
ejpam-6133	126	5	,	,	PUNCT
ejpam-6133	126	6	we	we	PRON
ejpam-6133	126	7	find	find	VERB
ejpam-6133	126	8	lim	lim	PROPN
ejpam-6133	126	9	ℓ→∞	ℓ→∞	NUM
ejpam-6133	126	10	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	126	11	,	,	PUNCT
ejpam-6133	126	12	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	126	13	)	)	PUNCT
ejpam-6133	126	14	=	=	SYM
ejpam-6133	127	1	0	0	X
ejpam-6133	127	2	.	.	PUNCT
ejpam-6133	128	1	now	now	ADV
ejpam-6133	128	2	,	,	PUNCT
ejpam-6133	128	3	we	we	PRON
ejpam-6133	128	4	show	show	VERB
ejpam-6133	128	5	that	that	SCONJ
ejpam-6133	128	6	{	{	PUNCT
ejpam-6133	128	7	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	128	8	}	}	PUNCT
ejpam-6133	128	9	is	be	AUX
ejpam-6133	128	10	a	a	DET
ejpam-6133	128	11	cauchy	cauchy	ADJ
ejpam-6133	128	12	sequence	sequence	NOUN
ejpam-6133	128	13	in	in	ADP
ejpam-6133	128	14	℧	℧	PROPN
ejpam-6133	128	15	.	.	PROPN
ejpam-6133	129	1	for	for	ADP
ejpam-6133	129	2	m	m	PROPN
ejpam-6133	129	3	,	,	PUNCT
ejpam-6133	129	4	ℓ	ℓ	PROPN
ejpam-6133	129	5	∈	∈	PROPN
ejpam-6133	129	6	n	n	X
ejpam-6133	129	7	with	with	ADP
ejpam-6133	129	8	m	m	PROPN
ejpam-6133	129	9	>	>	X
ejpam-6133	129	10	ℓ	ℓ	PROPN
ejpam-6133	129	11	,	,	PUNCT
ejpam-6133	129	12	we	we	PRON
ejpam-6133	129	13	have	have	VERB
ejpam-6133	129	14	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	129	15	,	,	PUNCT
ejpam-6133	129	16	s̃m	s̃m	NOUN
ejpam-6133	129	17	)	)	PUNCT
ejpam-6133	129	18	≤	≤	NUM
ejpam-6133	129	19	ϖ(s̃ℓ	ϖ(s̃ℓ	NOUN
ejpam-6133	129	20	,	,	PUNCT
ejpam-6133	129	21	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	129	22	,	,	PUNCT
ejpam-6133	129	23	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	129	24	)	)	PUNCT
ejpam-6133	129	25	+	+	CCONJ
ejpam-6133	130	1	ϵ(s̃ℓ+1	ϵ(s̃ℓ+1	PROPN
ejpam-6133	130	2	,	,	PUNCT
ejpam-6133	130	3	s̃m)ζ(s̃ℓ+1	s̃m)ζ(s̃ℓ+1	PROPN
ejpam-6133	130	4	,	,	PUNCT
ejpam-6133	130	5	s̃m	s̃m	NOUN
ejpam-6133	130	6	)	)	PUNCT
ejpam-6133	130	7	≤	≤	NUM
ejpam-6133	130	8	ϖ(s̃ℓ	ϖ(s̃ℓ	NOUN
ejpam-6133	130	9	,	,	PUNCT
ejpam-6133	130	10	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	130	11	,	,	PUNCT
ejpam-6133	130	12	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	130	13	)	)	PUNCT
ejpam-6133	130	14	+	+	CCONJ
ejpam-6133	130	15	ϵ(s̃ℓ+1	ϵ(s̃ℓ+1	PROPN
ejpam-6133	130	16	,	,	PUNCT
ejpam-6133	130	17	s̃m)[ϖ(s̃ℓ+1	s̃m)[ϖ(s̃ℓ+1	PROPN
ejpam-6133	130	18	,	,	PUNCT
ejpam-6133	130	19	s̃ℓ+2)ζ(s̃ℓ+1	s̃ℓ+2)ζ(s̃ℓ+1	NOUN
ejpam-6133	130	20	,	,	PUNCT
ejpam-6133	130	21	s̃ℓ+2)+	s̃ℓ+2)+	PROPN
ejpam-6133	130	22	ϵ(s̃ℓ+2	ϵ(s̃ℓ+2	PROPN
ejpam-6133	130	23	,	,	PUNCT
ejpam-6133	130	24	s̃m)ζ(s̃ℓ+2	s̃m)ζ(s̃ℓ+2	PROPN
ejpam-6133	130	25	,	,	PUNCT
ejpam-6133	130	26	s̃m	s̃m	NOUN
ejpam-6133	130	27	)	)	PUNCT
ejpam-6133	130	28	]	]	PUNCT
ejpam-6133	131	1	=	=	PUNCT
ejpam-6133	131	2	ϖ(s̃ℓ	ϖ(s̃ℓ	PROPN
ejpam-6133	131	3	,	,	PUNCT
ejpam-6133	131	4	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	131	5	,	,	PUNCT
ejpam-6133	131	6	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	131	7	)	)	PUNCT
ejpam-6133	131	8	+	+	CCONJ
ejpam-6133	131	9	ϵ(s̃ℓ+1	ϵ(s̃ℓ+1	PROPN
ejpam-6133	131	10	,	,	PUNCT
ejpam-6133	131	11	s̃m)ϖ(s̃ℓ+1	s̃m)ϖ(s̃ℓ+1	NUM
ejpam-6133	131	12	,	,	PUNCT
ejpam-6133	131	13	s̃ℓ+2)ζ(s̃ℓ+1	s̃ℓ+2)ζ(s̃ℓ+1	NOUN
ejpam-6133	131	14	,	,	PUNCT
ejpam-6133	131	15	s̃ℓ+2	s̃ℓ+2	NOUN
ejpam-6133	131	16	)	)	PUNCT
ejpam-6133	131	17	+	+	PUNCT
ejpam-6133	132	1	ϵ(s̃ℓ+1	ϵ(s̃ℓ+1	PROPN
ejpam-6133	132	2	,	,	PUNCT
ejpam-6133	132	3	s̃m)ϵ(s̃ℓ+2	s̃m)ϵ(s̃ℓ+2	PROPN
ejpam-6133	132	4	,	,	PUNCT
ejpam-6133	132	5	s̃m)ζ(s̃ℓ+2	s̃m)ζ(s̃ℓ+2	PROPN
ejpam-6133	132	6	,	,	PUNCT
ejpam-6133	132	7	s̃m	s̃m	NOUN
ejpam-6133	132	8	)	)	PUNCT
ejpam-6133	132	9	.	.	PUNCT
ejpam-6133	132	10	.	.	PUNCT
ejpam-6133	132	11	.	.	PUNCT
ejpam-6133	133	1	≤	≤	NUM
ejpam-6133	133	2	ϖ(s̃ℓ	ϖ(s̃ℓ	PROPN
ejpam-6133	133	3	,	,	PUNCT
ejpam-6133	133	4	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	133	5	,	,	PUNCT
ejpam-6133	133	6	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	133	7	)	)	PUNCT
ejpam-6133	133	8	+	+	CCONJ
ejpam-6133	133	9	m−2∑	m−2∑	ADV
ejpam-6133	133	10	i=ℓ+1	i=ℓ+1	ADJ
ejpam-6133	133	11			PROPN
ejpam-6133	133	12	i∏	i∏	PROPN
ejpam-6133	133	13	j=ℓ+1	j=ℓ+1	ADJ
ejpam-6133	133	14	ϵ(s̃j	ϵ(s̃j	ADJ
ejpam-6133	133	15	,	,	PUNCT
ejpam-6133	133	16	s̃m	s̃m	PROPN
ejpam-6133	133	17	)	)	PUNCT
ejpam-6133	133	18	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	133	19	,	,	PUNCT
ejpam-6133	133	20	s̃i+1)ζ(s̃i	s̃i+1)ζ(s̃i	NOUN
ejpam-6133	133	21	,	,	PUNCT
ejpam-6133	133	22	s̃i+1	s̃i+1	NOUN
ejpam-6133	133	23	)	)	PUNCT
ejpam-6133	133	24	+	+	CCONJ
ejpam-6133	134	1			PROPN
ejpam-6133	134	2	m−1∏	m−1∏	PROPN
ejpam-6133	134	3	j=ℓ+1	j=ℓ+1	NOUN
ejpam-6133	134	4	ϵ(s̃j	ϵ(s̃j	PROPN
ejpam-6133	134	5	,	,	PUNCT
ejpam-6133	134	6	s̃m	s̃m	PROPN
ejpam-6133	134	7	)	)	PUNCT
ejpam-6133	134	8			PROPN
ejpam-6133	134	9	ζ(s̃m−1	ζ(s̃m−1	PROPN
ejpam-6133	134	10	,	,	PUNCT
ejpam-6133	134	11	s̃m	s̃m	NOUN
ejpam-6133	134	12	)	)	PUNCT
ejpam-6133	134	13	.	.	PUNCT
ejpam-6133	135	1	by	by	ADP
ejpam-6133	135	2	using	use	VERB
ejpam-6133	135	3	the	the	DET
ejpam-6133	135	4	fact	fact	NOUN
ejpam-6133	136	1	that	that	SCONJ
ejpam-6133	136	2	ϖ(σ	ϖ(σ	NOUN
ejpam-6133	136	3	,	,	PUNCT
ejpam-6133	136	4	ς	ς	PROPN
ejpam-6133	136	5	)	)	PUNCT
ejpam-6133	136	6	≥	≥	NOUN
ejpam-6133	136	7	1	1	NUM
ejpam-6133	136	8	and	and	CCONJ
ejpam-6133	136	9	ϵ(σ	ϵ(σ	PROPN
ejpam-6133	136	10	,	,	PUNCT
ejpam-6133	136	11	ς	ς	PROPN
ejpam-6133	136	12	)	)	PUNCT
ejpam-6133	136	13	≥	≥	NOUN
ejpam-6133	136	14	1	1	NUM
ejpam-6133	136	15	for	for	ADP
ejpam-6133	136	16	all	all	DET
ejpam-6133	136	17	σ	σ	NOUN
ejpam-6133	136	18	,	,	PUNCT
ejpam-6133	136	19	ς	ς	PROPN
ejpam-6133	136	20	∈	∈	PROPN
ejpam-6133	136	21	x	x	NOUN
ejpam-6133	136	22	,	,	PUNCT
ejpam-6133	136	23	we	we	PRON
ejpam-6133	136	24	deduce	deduce	VERB
ejpam-6133	136	25	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	136	26	,	,	PUNCT
ejpam-6133	136	27	s̃m	s̃m	NOUN
ejpam-6133	136	28	)	)	PUNCT
ejpam-6133	136	29	≤	≤	NUM
ejpam-6133	136	30	ϖ(s̃ℓ	ϖ(s̃ℓ	NOUN
ejpam-6133	136	31	,	,	PUNCT
ejpam-6133	136	32	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	136	33	,	,	PUNCT
ejpam-6133	136	34	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	136	35	)	)	PUNCT
ejpam-6133	136	36	+	+	CCONJ
ejpam-6133	137	1	m−1∑	m−1∑	NUM
ejpam-6133	137	2	i	i	NOUN
ejpam-6133	137	3	=	=	NOUN
ejpam-6133	137	4	n+1	n+1	PROPN
ejpam-6133	137	5			PROPN
ejpam-6133	137	6	i∏	i∏	PROPN
ejpam-6133	137	7	j	j	NOUN
ejpam-6133	137	8	=	=	NOUN
ejpam-6133	137	9	n+1	n+1	PROPN
ejpam-6133	137	10	ϵ(s̃j	ϵ(s̃j	PROPN
ejpam-6133	137	11	,	,	PUNCT
ejpam-6133	137	12	s̃m	s̃m	PROPN
ejpam-6133	137	13	)	)	PUNCT
ejpam-6133	137	14	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	137	15	,	,	PUNCT
ejpam-6133	137	16	s̃i+1)ζ(s̃i	s̃i+1)ζ(s̃i	NOUN
ejpam-6133	137	17	,	,	PUNCT
ejpam-6133	137	18	s̃i+1	s̃i+1	NOUN
ejpam-6133	137	19	)	)	PUNCT
ejpam-6133	137	20	≤	≤	NOUN
ejpam-6133	137	21	m−1∑	m−1∑	NUM
ejpam-6133	137	22	i	i	NOUN
ejpam-6133	137	23	=	=	PROPN
ejpam-6133	137	24	n	n	PRON
ejpam-6133	137	25			PROPN
ejpam-6133	137	26	i∏	i∏	PROPN
ejpam-6133	137	27	j	j	NOUN
ejpam-6133	137	28	=	=	NOUN
ejpam-6133	137	29	n+1	n+1	PROPN
ejpam-6133	137	30	ϵ(s̃j	ϵ(s̃j	PROPN
ejpam-6133	137	31	,	,	PUNCT
ejpam-6133	137	32	s̃m	s̃m	PROPN
ejpam-6133	137	33	)	)	PUNCT
ejpam-6133	137	34	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	137	35	,	,	PUNCT
ejpam-6133	137	36	s̃i+1)ζ(s̃i	s̃i+1)ζ(s̃i	NOUN
ejpam-6133	137	37	,	,	PUNCT
ejpam-6133	137	38	s̃i+1	s̃i+1	NOUN
ejpam-6133	137	39	)	)	PUNCT
ejpam-6133	137	40	≤	≤	NOUN
ejpam-6133	137	41	m−1∑	m−1∑	NUM
ejpam-6133	137	42	i	i	NOUN
ejpam-6133	137	43	=	=	PROPN
ejpam-6133	137	44	n	n	PRON
ejpam-6133	137	45			PROPN
ejpam-6133	137	46	i∏	i∏	PROPN
ejpam-6133	137	47	j	j	NOUN
ejpam-6133	137	48	=	=	NOUN
ejpam-6133	137	49	n+1	n+1	PROPN
ejpam-6133	137	50	ϵ(s̃j	ϵ(s̃j	PROPN
ejpam-6133	137	51	,	,	PUNCT
ejpam-6133	137	52	s̃m	s̃m	PROPN
ejpam-6133	137	53	)	)	PUNCT
ejpam-6133	137	54	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	137	55	,	,	PUNCT
ejpam-6133	137	56	s̃i+1)ψ	s̃i+1)ψ	PROPN
ejpam-6133	137	57	i(ζ(s̃0	i(ζ(s̃0	PROPN
ejpam-6133	137	58	,	,	PUNCT
ejpam-6133	137	59	s̃1	s̃1	PROPN
ejpam-6133	137	60	)	)	PUNCT
ejpam-6133	137	61	)	)	PUNCT
ejpam-6133	137	62	.	.	PUNCT
ejpam-6133	138	1	h.	h.	PROPN
ejpam-6133	138	2	aydi	aydi	PROPN
ejpam-6133	138	3	,	,	PUNCT
ejpam-6133	138	4	h.	h.	PROPN
ejpam-6133	138	5	hammouda	hammouda	PROPN
ejpam-6133	138	6	,	,	PUNCT
ejpam-6133	138	7	s.	s.	PROPN
ejpam-6133	138	8	mansour	mansour	PROPN
ejpam-6133	138	9	/	/	SYM
ejpam-6133	138	10	eur	eur	PROPN
ejpam-6133	138	11	.	.	PUNCT
ejpam-6133	139	1	j.	j.	PROPN
ejpam-6133	139	2	pure	pure	PROPN
ejpam-6133	139	3	appl	appl	PROPN
ejpam-6133	139	4	.	.	PROPN
ejpam-6133	139	5	math	math	PROPN
ejpam-6133	139	6	,	,	PUNCT
ejpam-6133	139	7	18	18	NUM
ejpam-6133	139	8	(	(	PUNCT
ejpam-6133	139	9	3	3	NUM
ejpam-6133	139	10	)	)	PUNCT
ejpam-6133	139	11	(	(	PUNCT
ejpam-6133	139	12	2025	2025	NUM
ejpam-6133	139	13	)	)	PUNCT
ejpam-6133	139	14	,	,	PUNCT
ejpam-6133	139	15	6133	6133	NUM
ejpam-6133	139	16	7	7	NUM
ejpam-6133	139	17	of	of	ADP
ejpam-6133	139	18	18	18	NUM
ejpam-6133	139	19	choose	choose	NOUN
ejpam-6133	139	20	ai	ai	NOUN
ejpam-6133	139	21	=	=	PUNCT
ejpam-6133	139	22			PROPN
ejpam-6133	139	23	i∏	i∏	PROPN
ejpam-6133	139	24	j	j	NOUN
ejpam-6133	139	25	=	=	NOUN
ejpam-6133	139	26	n+1	n+1	PROPN
ejpam-6133	139	27	ϵ(s̃j	ϵ(s̃j	PROPN
ejpam-6133	139	28	,	,	PUNCT
ejpam-6133	139	29	s̃m	s̃m	PROPN
ejpam-6133	139	30	)	)	PUNCT
ejpam-6133	139	31	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	139	32	,	,	PUNCT
ejpam-6133	139	33	s̃i+1)ψ	s̃i+1)ψ	PROPN
ejpam-6133	139	34	i(ζ(s̃0	i(ζ(s̃0	PROPN
ejpam-6133	139	35	,	,	PUNCT
ejpam-6133	139	36	s̃1	s̃1	PROPN
ejpam-6133	139	37	)	)	PUNCT
ejpam-6133	139	38	)	)	PUNCT
ejpam-6133	139	39	,	,	PUNCT
ejpam-6133	139	40	and	and	CCONJ
ejpam-6133	139	41	ωp	ωp	NOUN
ejpam-6133	139	42	=	=	SYM
ejpam-6133	140	1	∑p	∑p	PROPN
ejpam-6133	140	2	i=1	i=1	X
ejpam-6133	140	3	ai	ai	VERB
ejpam-6133	140	4	.	.	PUNCT
ejpam-6133	141	1	then	then	ADV
ejpam-6133	141	2	we	we	PRON
ejpam-6133	141	3	have	have	VERB
ejpam-6133	141	4	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	141	5	,	,	PUNCT
ejpam-6133	141	6	s̃m	s̃m	NOUN
ejpam-6133	141	7	)	)	PUNCT
ejpam-6133	141	8	≤	≤	NOUN
ejpam-6133	141	9	ωm−1	ωm−1	PROPN
ejpam-6133	141	10	−	−	PROPN
ejpam-6133	141	11	ωn−1	ωn−1	PROPN
ejpam-6133	141	12	.	.	PUNCT
ejpam-6133	142	1	(	(	PUNCT
ejpam-6133	142	2	6	6	NUM
ejpam-6133	142	3	)	)	PUNCT
ejpam-6133	142	4	since	since	SCONJ
ejpam-6133	142	5	lim	lim	PROPN
ejpam-6133	142	6	i→∞	i→∞	VERB
ejpam-6133	142	7	ai+1	ai+1	INTJ
ejpam-6133	142	8	ai	ai	VERB
ejpam-6133	142	9	≤	≤	NUM
ejpam-6133	142	10	sup	sup	NOUN
ejpam-6133	142	11	m≥1	m≥1	PROPN
ejpam-6133	142	12	lim	lim	PROPN
ejpam-6133	142	13	i→∞	i→∞	VERB
ejpam-6133	142	14	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	142	15	,	,	PUNCT
ejpam-6133	142	16	s̃m)ϖ(s̃i+1	s̃m)ϖ(s̃i+1	PROPN
ejpam-6133	142	17	,	,	PUNCT
ejpam-6133	142	18	s̃i+2)ψ	s̃i+2)ψ	PRON
ejpam-6133	142	19	i+1(ζ(s̃0	i+1(ζ(s̃0	ADJ
ejpam-6133	142	20	,	,	PUNCT
ejpam-6133	142	21	s̃1	s̃1	PROPN
ejpam-6133	142	22	)	)	PUNCT
ejpam-6133	142	23	)	)	PUNCT
ejpam-6133	143	1	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	143	2	,	,	PUNCT
ejpam-6133	143	3	s̃i+1)ψi(ζ(s̃0	s̃i+1)ψi(ζ(s̃0	PROPN
ejpam-6133	143	4	,	,	PUNCT
ejpam-6133	143	5	s̃1	s̃1	PROPN
ejpam-6133	143	6	)	)	PUNCT
ejpam-6133	143	7	)	)	PUNCT
ejpam-6133	143	8	,	,	PUNCT
ejpam-6133	143	9	by	by	ADP
ejpam-6133	143	10	condition	condition	NOUN
ejpam-6133	143	11	(	(	PUNCT
ejpam-6133	143	12	iii	iii	NOUN
ejpam-6133	143	13	)	)	PUNCT
ejpam-6133	143	14	one	one	NOUN
ejpam-6133	143	15	gets	get	VERB
ejpam-6133	143	16	lim	lim	PROPN
ejpam-6133	143	17	i→∞	i→∞	NOUN
ejpam-6133	143	18	ai+1	ai+1	INTJ
ejpam-6133	143	19	ai	ai	INTJ
ejpam-6133	143	20	<	<	X
ejpam-6133	143	21	1	1	NUM
ejpam-6133	143	22	,	,	PUNCT
ejpam-6133	143	23	so	so	SCONJ
ejpam-6133	143	24	we	we	PRON
ejpam-6133	143	25	conclude	conclude	VERB
ejpam-6133	143	26	that	that	SCONJ
ejpam-6133	143	27	the	the	DET
ejpam-6133	143	28	real	real	ADJ
ejpam-6133	143	29	sequence	sequence	NOUN
ejpam-6133	143	30	{	{	PUNCT
ejpam-6133	143	31	ωp	ωp	NOUN
ejpam-6133	143	32	}	}	PUNCT
ejpam-6133	143	33	converges	converge	NOUN
ejpam-6133	143	34	,	,	PUNCT
ejpam-6133	143	35	then	then	ADV
ejpam-6133	143	36	it	it	PRON
ejpam-6133	143	37	is	be	AUX
ejpam-6133	143	38	a	a	DET
ejpam-6133	143	39	cauchy	cauchy	ADJ
ejpam-6133	143	40	sequence	sequence	NOUN
ejpam-6133	143	41	in	in	ADP
ejpam-6133	143	42	r.	r.	PROPN
ejpam-6133	143	43	by	by	ADP
ejpam-6133	143	44	(	(	PUNCT
ejpam-6133	143	45	6	6	NUM
ejpam-6133	143	46	)	)	PUNCT
ejpam-6133	143	47	,	,	PUNCT
ejpam-6133	143	48	{	{	PUNCT
ejpam-6133	143	49	s̃ℓ	s̃ℓ	ADV
ejpam-6133	143	50	}	}	PUNCT
ejpam-6133	143	51	is	be	AUX
ejpam-6133	143	52	a	a	DET
ejpam-6133	143	53	cauchy	cauchy	ADJ
ejpam-6133	143	54	sequence	sequence	NOUN
ejpam-6133	143	55	in	in	ADP
ejpam-6133	143	56	℧	℧	PROPN
ejpam-6133	143	57	.	.	PUNCT
ejpam-6133	144	1	since	since	SCONJ
ejpam-6133	144	2	(	(	PUNCT
ejpam-6133	144	3	℧	℧	PROPN
ejpam-6133	144	4	,	,	PUNCT
ejpam-6133	144	5	ζ	ζ	NOUN
ejpam-6133	144	6	)	)	PUNCT
ejpam-6133	144	7	is	be	AUX
ejpam-6133	144	8	orbitally	orbitally	ADV
ejpam-6133	144	9	complete	complete	ADJ
ejpam-6133	144	10	,	,	PUNCT
ejpam-6133	144	11	{	{	PUNCT
ejpam-6133	144	12	s̃ℓ	s̃ℓ	ADJ
ejpam-6133	144	13	}	}	PUNCT
ejpam-6133	144	14	converges	converge	NOUN
ejpam-6133	144	15	to	to	ADP
ejpam-6133	144	16	x∗	x∗	PROPN
ejpam-6133	144	17	∈	∈	PROPN
ejpam-6133	144	18	℧	℧	PROPN
ejpam-6133	144	19	.	.	PUNCT
ejpam-6133	145	1	next	next	ADV
ejpam-6133	145	2	,	,	PUNCT
ejpam-6133	145	3	we	we	PRON
ejpam-6133	145	4	show	show	VERB
ejpam-6133	145	5	that	that	SCONJ
ejpam-6133	145	6	⊤x∗	⊤x∗	ADV
ejpam-6133	145	7	=	=	SYM
ejpam-6133	145	8	x∗.	x∗.	PROPN
ejpam-6133	146	1	the	the	DET
ejpam-6133	146	2	orbital	orbital	ADJ
ejpam-6133	146	3	continuity	continuity	NOUN
ejpam-6133	146	4	of	of	ADP
ejpam-6133	146	5	⊤	⊤	NOUN
ejpam-6133	146	6	on	on	ADP
ejpam-6133	146	7	℧	℧	PROPN
ejpam-6133	146	8	leads	lead	VERB
ejpam-6133	146	9	to	to	ADP
ejpam-6133	146	10	s̃ℓ+1	s̃ℓ+1	NOUN
ejpam-6133	146	11	=	=	PUNCT
ejpam-6133	146	12	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	146	13	=	=	SYM
ejpam-6133	146	14	⊤(⊤ℓs̃0	⊤(⊤ℓs̃0	ADJ
ejpam-6133	146	15	)	)	PUNCT
ejpam-6133	146	16	−→	−→	NOUN
ejpam-6133	146	17	⊤x∗	⊤x∗	ADV
ejpam-6133	146	18	as	as	ADP
ejpam-6133	146	19	ℓ→	ℓ→	PROPN
ejpam-6133	146	20	+	+	PROPN
ejpam-6133	146	21	∞	∞	PROPN
ejpam-6133	146	22	and	and	CCONJ
ejpam-6133	146	23	ζ(s̃ℓ+1,⊤x∗	ζ(s̃ℓ+1,⊤x∗	PROPN
ejpam-6133	146	24	)	)	PUNCT
ejpam-6133	147	1	−→	−→	NOUN
ejpam-6133	147	2	0	0	PUNCT
ejpam-6133	147	3	as	as	SCONJ
ejpam-6133	147	4	ℓ→	ℓ→	PROPN
ejpam-6133	147	5	+	+	PROPN
ejpam-6133	147	6	∞.	∞.	PROPN
ejpam-6133	147	7	the	the	DET
ejpam-6133	147	8	triangle	triangle	NOUN
ejpam-6133	147	9	inequality	inequality	NOUN
ejpam-6133	147	10	of	of	ADP
ejpam-6133	147	11	dcms	dcms	NOUN
ejpam-6133	147	12	implies	imply	VERB
ejpam-6133	147	13	ζ(x∗	ζ(x∗	ADV
ejpam-6133	147	14	,	,	PUNCT
ejpam-6133	147	15	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	147	16	)	)	PUNCT
ejpam-6133	147	17	≤	≤	NOUN
ejpam-6133	147	18	ϖ(x∗	ϖ(x∗	NOUN
ejpam-6133	147	19	,	,	PUNCT
ejpam-6133	147	20	s̃ℓ)ζ(x	s̃ℓ)ζ(x	NOUN
ejpam-6133	147	21	∗	∗	NOUN
ejpam-6133	147	22	,	,	PUNCT
ejpam-6133	147	23	s̃ℓ	s̃ℓ	NUM
ejpam-6133	147	24	)	)	PUNCT
ejpam-6133	147	25	+	+	NUM
ejpam-6133	147	26	ϵ(s̃ℓ	ϵ(s̃ℓ	NOUN
ejpam-6133	147	27	,	,	PUNCT
ejpam-6133	147	28	s̃ℓ+1)ζ(s̃ℓ	s̃ℓ+1)ζ(s̃ℓ	NOUN
ejpam-6133	147	29	,	,	PUNCT
ejpam-6133	147	30	s̃ℓ+1	s̃ℓ+1	NOUN
ejpam-6133	147	31	)	)	PUNCT
ejpam-6133	147	32	.	.	PUNCT
ejpam-6133	148	1	using	use	VERB
ejpam-6133	148	2	the	the	DET
ejpam-6133	148	3	condition	condition	NOUN
ejpam-6133	148	4	(	(	PUNCT
ejpam-6133	148	5	v	v	NOUN
ejpam-6133	148	6	)	)	PUNCT
ejpam-6133	148	7	and	and	CCONJ
ejpam-6133	148	8	the	the	DET
ejpam-6133	148	9	fact	fact	NOUN
ejpam-6133	148	10	that	that	SCONJ
ejpam-6133	148	11	lim	lim	PROPN
ejpam-6133	148	12	ℓ→∞	ℓ→∞	NUM
ejpam-6133	148	13	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	148	14	,	,	PUNCT
ejpam-6133	148	15	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	148	16	)	)	PUNCT
ejpam-6133	148	17	=	=	SYM
ejpam-6133	148	18	0	0	NUM
ejpam-6133	148	19	,	,	PUNCT
ejpam-6133	148	20	one	one	NUM
ejpam-6133	148	21	writes	write	VERB
ejpam-6133	148	22	ζ(x∗	ζ(x∗	NOUN
ejpam-6133	148	23	,	,	PUNCT
ejpam-6133	148	24	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	148	25	)	)	PUNCT
ejpam-6133	148	26	−→ℓ→∞	−→ℓ→∞	NOUN
ejpam-6133	148	27	0	0	NUM
ejpam-6133	148	28	.	.	PUNCT
ejpam-6133	149	1	since	since	SCONJ
ejpam-6133	149	2	we	we	PRON
ejpam-6133	149	3	have	have	VERB
ejpam-6133	149	4	a	a	DET
ejpam-6133	149	5	unique	unique	ADJ
ejpam-6133	149	6	limit	limit	NOUN
ejpam-6133	149	7	of	of	ADP
ejpam-6133	149	8	a	a	DET
ejpam-6133	149	9	convergent	convergent	NOUN
ejpam-6133	149	10	sequence	sequence	NOUN
ejpam-6133	149	11	in	in	ADP
ejpam-6133	149	12	the	the	DET
ejpam-6133	149	13	dcms	dcms	NOUN
ejpam-6133	149	14	,	,	PUNCT
ejpam-6133	149	15	one	one	PRON
ejpam-6133	149	16	has	have	VERB
ejpam-6133	149	17	x∗	x∗	PROPN
ejpam-6133	149	18	=	=	PUNCT
ejpam-6133	150	1	⊤x∗.	⊤x∗.	PRON
ejpam-6133	150	2	thus	thus	ADV
ejpam-6133	150	3	,	,	PUNCT
ejpam-6133	150	4	⊤	⊤	PROPN
ejpam-6133	150	5	admits	admit	VERB
ejpam-6133	150	6	a	a	DET
ejpam-6133	150	7	fp	fp	X
ejpam-6133	150	8	x∗	x∗	PROPN
ejpam-6133	150	9	∈	∈	PROPN
ejpam-6133	150	10	℧	℧	PROPN
ejpam-6133	150	11	,	,	PUNCT
ejpam-6133	150	12	i.e.	i.e.	X
ejpam-6133	150	13	,	,	PUNCT
ejpam-6133	150	14	fix(⊤	fix(⊤	ADJ
ejpam-6133	150	15	)	)	PUNCT
ejpam-6133	150	16	is	be	AUX
ejpam-6133	150	17	nonempty	nonempty	ADJ
ejpam-6133	150	18	.	.	PUNCT
ejpam-6133	151	1	now	now	ADV
ejpam-6133	151	2	,	,	PUNCT
ejpam-6133	151	3	we	we	PRON
ejpam-6133	151	4	show	show	VERB
ejpam-6133	151	5	its	its	PRON
ejpam-6133	151	6	uniqueness	uniqueness	NOUN
ejpam-6133	151	7	.	.	PUNCT
ejpam-6133	152	1	let	let	VERB
ejpam-6133	152	2	ϑ	ϑ	X
ejpam-6133	152	3	and	and	CCONJ
ejpam-6133	152	4	θ	θ	PROPN
ejpam-6133	152	5	be	be	VERB
ejpam-6133	152	6	two	two	NUM
ejpam-6133	152	7	distinct	distinct	ADJ
ejpam-6133	152	8	fps	fps	NOUN
ejpam-6133	152	9	of	of	ADP
ejpam-6133	152	10	⊤.	⊤.	PROPN
ejpam-6133	152	11	due	due	ADP
ejpam-6133	152	12	to	to	ADP
ejpam-6133	152	13	condition	condition	NOUN
ejpam-6133	152	14	(	(	PUNCT
ejpam-6133	152	15	u	u	NOUN
ejpam-6133	152	16	)	)	PUNCT
ejpam-6133	152	17	,	,	PUNCT
ejpam-6133	152	18	we	we	PRON
ejpam-6133	152	19	have	have	AUX
ejpam-6133	152	20	α(ϑ	α(ϑ	VERB
ejpam-6133	152	21	,	,	PUNCT
ejpam-6133	152	22	θ	θ	NOUN
ejpam-6133	152	23	)	)	PUNCT
ejpam-6133	152	24	=	=	SYM
ejpam-6133	152	25	α(⊤ϑ,⊤θ	α(⊤ϑ,⊤θ	NOUN
ejpam-6133	152	26	)	)	PUNCT
ejpam-6133	152	27	≥	≥	NOUN
ejpam-6133	152	28	1	1	NUM
ejpam-6133	152	29	.	.	PUNCT
ejpam-6133	153	1	taking	take	VERB
ejpam-6133	153	2	x	x	PUNCT
ejpam-6133	153	3	=	=	SYM
ejpam-6133	153	4	ϑ	ϑ	X
ejpam-6133	153	5	and	and	CCONJ
ejpam-6133	153	6	y	y	PROPN
ejpam-6133	153	7	=	=	SYM
ejpam-6133	153	8	θ	θ	PROPN
ejpam-6133	153	9	in	in	ADP
ejpam-6133	153	10	(	(	PUNCT
ejpam-6133	153	11	3	3	NUM
ejpam-6133	153	12	)	)	PUNCT
ejpam-6133	153	13	,	,	PUNCT
ejpam-6133	153	14	we	we	PRON
ejpam-6133	153	15	obtain	obtain	VERB
ejpam-6133	153	16	ζ(ϑ	ζ(ϑ	PROPN
ejpam-6133	153	17	,	,	PUNCT
ejpam-6133	153	18	θ	θ	NOUN
ejpam-6133	153	19	)	)	PUNCT
ejpam-6133	153	20	=	=	SYM
ejpam-6133	153	21	ζ(⊤ϑ,⊤θ	ζ(⊤ϑ,⊤θ	NOUN
ejpam-6133	153	22	)	)	PUNCT
ejpam-6133	153	23	≤	≤	NOUN
ejpam-6133	153	24	α(ϑ	α(ϑ	PROPN
ejpam-6133	153	25	,	,	PUNCT
ejpam-6133	153	26	θ)ϖ(ϑ	θ)ϖ(ϑ	NOUN
ejpam-6133	153	27	,	,	PUNCT
ejpam-6133	153	28	θ)ϵ(ϑ	θ)ϵ(ϑ	ADJ
ejpam-6133	153	29	,	,	PUNCT
ejpam-6133	153	30	θ)ζ(⊤ϑ,⊤θ	θ)ζ(⊤ϑ,⊤θ	ADJ
ejpam-6133	153	31	)	)	PUNCT
ejpam-6133	153	32	≤	≤	NUM
ejpam-6133	153	33	ψ(ℜ(ϑ	ψ(ℜ(ϑ	NUM
ejpam-6133	153	34	,	,	PUNCT
ejpam-6133	153	35	θ	θ	NOUN
ejpam-6133	153	36	)	)	PUNCT
ejpam-6133	153	37	)	)	PUNCT
ejpam-6133	154	1	=	=	PUNCT
ejpam-6133	154	2	max{ζ(ϑ	max{ζ(ϑ	PROPN
ejpam-6133	154	3	,	,	PUNCT
ejpam-6133	154	4	θ	θ	PROPN
ejpam-6133	154	5	)	)	PUNCT
ejpam-6133	154	6	;	;	PUNCT
ejpam-6133	154	7	ζ(ϑ,⊤ϑ	ζ(ϑ,⊤ϑ	NUM
ejpam-6133	154	8	)	)	PUNCT
ejpam-6133	154	9	;	;	PUNCT
ejpam-6133	154	10	ζ(θ,⊤θ	ζ(θ,⊤θ	NOUN
ejpam-6133	154	11	)	)	PUNCT
ejpam-6133	154	12	;	;	PUNCT
ejpam-6133	154	13	ζ(ϑ,⊤ϑ)[ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(θ,⊤θ	ζ(ϑ,⊤ϑ)[ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(θ,⊤θ	NUM
ejpam-6133	154	14	)	)	PUNCT
ejpam-6133	154	15	]	]	PUNCT
ejpam-6133	155	1	ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,θ	ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,θ	ADJ
ejpam-6133	155	2	)	)	PUNCT
ejpam-6133	155	3	;	;	PUNCT
ejpam-6133	155	4	ζ(θ,⊤θ)[ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,⊤ϑ	ζ(θ,⊤θ)[ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,⊤ϑ	ADJ
ejpam-6133	155	5	)	)	PUNCT
ejpam-6133	155	6	]	]	PUNCT
ejpam-6133	156	1	ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,θ	ϖ(ϑ,θ)ϵ(ϑ,θ)+ζ(ϑ,θ	ADJ
ejpam-6133	156	2	)	)	PUNCT
ejpam-6133	156	3	}	}	PUNCT
ejpam-6133	156	4	=	=	SYM
ejpam-6133	156	5	ψ(ζ(ϑ	ψ(ζ(ϑ	PROPN
ejpam-6133	156	6	,	,	PUNCT
ejpam-6133	156	7	θ	θ	NOUN
ejpam-6133	156	8	)	)	PUNCT
ejpam-6133	156	9	)	)	PUNCT
ejpam-6133	156	10	<	<	X
ejpam-6133	156	11	ζ(ϑ	ζ(ϑ	PROPN
ejpam-6133	156	12	,	,	PUNCT
ejpam-6133	156	13	θ	θ	PROPN
ejpam-6133	156	14	)	)	PUNCT
ejpam-6133	156	15	,	,	PUNCT
ejpam-6133	156	16	which	which	PRON
ejpam-6133	156	17	is	be	AUX
ejpam-6133	156	18	a	a	DET
ejpam-6133	156	19	contradiction	contradiction	NOUN
ejpam-6133	156	20	.	.	PUNCT
ejpam-6133	157	1	therefore	therefore	ADV
ejpam-6133	157	2	,	,	PUNCT
ejpam-6133	157	3	⊤	⊤	PROPN
ejpam-6133	157	4	possesses	possess	VERB
ejpam-6133	157	5	a	a	DET
ejpam-6133	157	6	unique	unique	ADJ
ejpam-6133	157	7	fp	fp	NOUN
ejpam-6133	157	8	in	in	ADP
ejpam-6133	157	9	℧	℧	PROPN
ejpam-6133	157	10	.	.	PROPN
ejpam-6133	157	11	example	example	NOUN
ejpam-6133	157	12	2	2	NUM
ejpam-6133	157	13	.	.	PUNCT
ejpam-6133	157	14	given	give	VERB
ejpam-6133	157	15	the	the	DET
ejpam-6133	157	16	dcms	dcms	NOUN
ejpam-6133	157	17	as	as	ADP
ejpam-6133	157	18	in	in	ADP
ejpam-6133	157	19	example	example	NOUN
ejpam-6133	157	20	1	1	NUM
ejpam-6133	157	21	.	.	X
ejpam-6133	157	22	consider	consider	VERB
ejpam-6133	157	23	⊤	⊤	NOUN
ejpam-6133	157	24	:	:	PUNCT
ejpam-6133	157	25	℧	℧	PUNCT
ejpam-6133	157	26	−→	−→	NOUN
ejpam-6133	157	27	℧	℧	PROPN
ejpam-6133	157	28	as	as	ADP
ejpam-6133	157	29	⊤x	⊤x	PUNCT
ejpam-6133	157	30	=	=	X
ejpam-6133	157	31	{	{	PUNCT
ejpam-6133	157	32	x	x	INTJ
ejpam-6133	157	33	β+βx	β+βx	NOUN
ejpam-6133	157	34	if	if	SCONJ
ejpam-6133	157	35	x	x	PUNCT
ejpam-6133	157	36	∈	∈	PROPN
ejpam-6133	157	37	[	[	X
ejpam-6133	157	38	0	0	NUM
ejpam-6133	157	39	,	,	PUNCT
ejpam-6133	157	40	1	1	NUM
ejpam-6133	157	41	]	]	PUNCT
ejpam-6133	157	42	0	0	PUNCT
ejpam-6133	158	1	otherwise	otherwise	ADV
ejpam-6133	158	2	,	,	PUNCT
ejpam-6133	158	3	where	where	SCONJ
ejpam-6133	158	4	β	β	X
ejpam-6133	158	5	>	>	X
ejpam-6133	158	6	108	108	NUM
ejpam-6133	158	7	.	.	PUNCT
ejpam-6133	159	1	to	to	PART
ejpam-6133	159	2	prove	prove	VERB
ejpam-6133	159	3	that	that	SCONJ
ejpam-6133	159	4	the	the	DET
ejpam-6133	159	5	mapping	mapping	NOUN
ejpam-6133	159	6	⊤	⊤	NOUN
ejpam-6133	159	7	is	be	AUX
ejpam-6133	159	8	continuous	continuous	ADJ
ejpam-6133	159	9	,	,	PUNCT
ejpam-6133	159	10	let	let	VERB
ejpam-6133	159	11	{	{	PUNCT
ejpam-6133	159	12	s̃ℓ	s̃ℓ	ADV
ejpam-6133	159	13	}	}	PUNCT
ejpam-6133	159	14	be	be	AUX
ejpam-6133	159	15	a	a	DET
ejpam-6133	159	16	convergent	convergent	NOUN
ejpam-6133	159	17	sequence	sequence	NOUN
ejpam-6133	159	18	in	in	ADP
ejpam-6133	159	19	℧	℧	PROPN
ejpam-6133	159	20	to	to	PART
ejpam-6133	159	21	x.	x.	PROPN
ejpam-6133	159	22	h.	h.	PROPN
ejpam-6133	159	23	aydi	aydi	PROPN
ejpam-6133	159	24	,	,	PUNCT
ejpam-6133	159	25	h.	h.	PROPN
ejpam-6133	159	26	hammouda	hammouda	PROPN
ejpam-6133	159	27	,	,	PUNCT
ejpam-6133	159	28	s.	s.	PROPN
ejpam-6133	159	29	mansour	mansour	PROPN
ejpam-6133	159	30	/	/	SYM
ejpam-6133	159	31	eur	eur	PROPN
ejpam-6133	159	32	.	.	PUNCT
ejpam-6133	160	1	j.	j.	PROPN
ejpam-6133	160	2	pure	pure	PROPN
ejpam-6133	160	3	appl	appl	PROPN
ejpam-6133	160	4	.	.	PROPN
ejpam-6133	160	5	math	math	PROPN
ejpam-6133	160	6	,	,	PUNCT
ejpam-6133	160	7	18	18	NUM
ejpam-6133	160	8	(	(	PUNCT
ejpam-6133	160	9	3	3	NUM
ejpam-6133	160	10	)	)	PUNCT
ejpam-6133	160	11	(	(	PUNCT
ejpam-6133	160	12	2025	2025	NUM
ejpam-6133	160	13	)	)	PUNCT
ejpam-6133	160	14	,	,	PUNCT
ejpam-6133	160	15	6133	6133	NUM
ejpam-6133	160	16	8	8	NUM
ejpam-6133	160	17	of	of	ADP
ejpam-6133	160	18	18	18	NUM
ejpam-6133	160	19	then	then	ADV
ejpam-6133	160	20	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	160	21	,	,	PUNCT
ejpam-6133	160	22	x	x	X
ejpam-6133	160	23	)	)	PUNCT
ejpam-6133	160	24	−→	−→	NOUN
ejpam-6133	160	25	0	0	PUNCT
ejpam-6133	160	26	as	as	SCONJ
ejpam-6133	160	27	ℓ→	ℓ→	PROPN
ejpam-6133	160	28	∞.	∞.	PROPN
ejpam-6133	160	29	we	we	PRON
ejpam-6133	160	30	require	require	VERB
ejpam-6133	160	31	the	the	DET
ejpam-6133	160	32	following	follow	VERB
ejpam-6133	160	33	cases	case	NOUN
ejpam-6133	160	34	:	:	PUNCT
ejpam-6133	160	35	case	case	NOUN
ejpam-6133	160	36	1	1	NUM
ejpam-6133	160	37	:	:	PUNCT
ejpam-6133	160	38	s̃ℓ	s̃ℓ	ADP
ejpam-6133	160	39	=	=	PUNCT
ejpam-6133	160	40	x	x	PUNCT
ejpam-6133	160	41	for	for	ADP
ejpam-6133	160	42	all	all	PRON
ejpam-6133	160	43	but	but	ADV
ejpam-6133	160	44	finitely	finitely	ADV
ejpam-6133	160	45	many	many	ADJ
ejpam-6133	160	46	ℓ	ℓ	NOUN
ejpam-6133	160	47	,	,	PUNCT
ejpam-6133	160	48	then	then	ADV
ejpam-6133	160	49	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	160	50	=	=	PUNCT
ejpam-6133	160	51	⊤x	⊤x	PROPN
ejpam-6133	160	52	.	.	PUNCT
ejpam-6133	161	1	here	here	ADV
ejpam-6133	162	1	,	,	PUNCT
ejpam-6133	162	2	ζ(s̃ℓ	ζ(s̃ℓ	PROPN
ejpam-6133	162	3	,	,	PUNCT
ejpam-6133	162	4	x	x	NOUN
ejpam-6133	162	5	)	)	PUNCT
ejpam-6133	162	6	=	=	SYM
ejpam-6133	162	7	0	0	NUM
ejpam-6133	162	8	and	and	CCONJ
ejpam-6133	162	9	ζ(⊤s̃ℓ,⊤x	ζ(⊤s̃ℓ,⊤x	NOUN
ejpam-6133	162	10	)	)	PUNCT
ejpam-6133	162	11	=	=	SYM
ejpam-6133	162	12	0	0	NUM
ejpam-6133	162	13	for	for	ADP
ejpam-6133	162	14	all	all	PRON
ejpam-6133	162	15	but	but	ADV
ejpam-6133	162	16	finitely	finitely	ADV
ejpam-6133	162	17	many	many	ADJ
ejpam-6133	162	18	.	.	PUNCT
ejpam-6133	163	1	so	so	ADV
ejpam-6133	163	2	ζ(⊤s̃ℓ,⊤x	ζ(⊤s̃ℓ,⊤x	NOUN
ejpam-6133	163	3	)	)	PUNCT
ejpam-6133	164	1	−→	−→	NOUN
ejpam-6133	164	2	0	0	PUNCT
ejpam-6133	164	3	as	as	ADP
ejpam-6133	164	4	ℓ→	ℓ→	PROPN
ejpam-6133	164	5	∞.	∞.	PROPN
ejpam-6133	164	6	case	case	NOUN
ejpam-6133	164	7	2	2	NUM
ejpam-6133	164	8	:	:	PUNCT
ejpam-6133	164	9	s̃ℓ	s̃ℓ	X
ejpam-6133	164	10	̸=	̸=	PROPN
ejpam-6133	164	11	0	0	NUM
ejpam-6133	165	1	and	and	CCONJ
ejpam-6133	165	2	x	x	SYM
ejpam-6133	165	3	̸=	̸=	PROPN
ejpam-6133	165	4	0	0	NUM
ejpam-6133	165	5	for	for	ADP
ejpam-6133	165	6	all	all	DET
ejpam-6133	165	7	but	but	CCONJ
ejpam-6133	165	8	finitely	finitely	ADV
ejpam-6133	165	9	many	many	ADJ
ejpam-6133	165	10	ℓ	ℓ	NOUN
ejpam-6133	165	11	,	,	PUNCT
ejpam-6133	165	12	then	then	ADV
ejpam-6133	165	13	⊤s̃ℓ	⊤s̃ℓ	X
ejpam-6133	165	14	̸=	̸=	PROPN
ejpam-6133	165	15	0	0	NUM
ejpam-6133	166	1	and	and	CCONJ
ejpam-6133	166	2	⊤x	⊤x	PUNCT
ejpam-6133	166	3	̸=	̸=	PROPN
ejpam-6133	166	4	0	0	NUM
ejpam-6133	166	5	.	.	PUNCT
ejpam-6133	167	1	we	we	PRON
ejpam-6133	167	2	have	have	VERB
ejpam-6133	167	3	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	167	4	,	,	PUNCT
ejpam-6133	167	5	x	x	NOUN
ejpam-6133	167	6	)	)	PUNCT
ejpam-6133	167	7	=	=	PUNCT
ejpam-6133	167	8	s̃ℓ	s̃ℓ	PRON
ejpam-6133	168	1	+	+	NUM
ejpam-6133	168	2	x→	x→	SYM
ejpam-6133	168	3	0	0	NUM
ejpam-6133	168	4	and	and	CCONJ
ejpam-6133	168	5	ζ(⊤s̃ℓ,⊤x	ζ(⊤s̃ℓ,⊤x	NOUN
ejpam-6133	168	6	)	)	PUNCT
ejpam-6133	169	1	=	=	PUNCT
ejpam-6133	170	1	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	171	1	+	+	NOUN
ejpam-6133	171	2	⊤x	⊤x	X
ejpam-6133	171	3	=	=	X
ejpam-6133	171	4	s̃ℓ	s̃ℓ	ADJ
ejpam-6133	171	5	β	β	NOUN
ejpam-6133	171	6	+	+	NUM
ejpam-6133	171	7	βs̃ℓ	βs̃ℓ	PUNCT
ejpam-6133	172	1	+	+	CCONJ
ejpam-6133	172	2	x	x	SYM
ejpam-6133	172	3	β	β	X
ejpam-6133	172	4	+	+	NOUN
ejpam-6133	172	5	βx	βx	X
ejpam-6133	172	6	=	=	SYM
ejpam-6133	172	7	1	1	NUM
ejpam-6133	172	8	β	β	NOUN
ejpam-6133	172	9	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	173	1	+	+	CCONJ
ejpam-6133	174	1	x+	x+	ADJ
ejpam-6133	174	2	2s̃ℓx	2s̃ℓx	X
ejpam-6133	174	3	(	(	PUNCT
ejpam-6133	174	4	x+	x+	PROPN
ejpam-6133	174	5	1)(s̃ℓ	1)(s̃ℓ	NUM
ejpam-6133	174	6	+	+	CCONJ
ejpam-6133	174	7	1	1	X
ejpam-6133	174	8	)	)	PUNCT
ejpam-6133	174	9	≤	≤	NOUN
ejpam-6133	174	10	(	(	PUNCT
ejpam-6133	174	11	s̃ℓ	s̃ℓ	ADV
ejpam-6133	174	12	+	+	NOUN
ejpam-6133	174	13	x	x	X
ejpam-6133	174	14	)	)	PUNCT
ejpam-6133	175	1	+	+	CCONJ
ejpam-6133	175	2	(	(	PUNCT
ejpam-6133	175	3	s̃ℓ	s̃ℓ	ADV
ejpam-6133	175	4	+	+	NUM
ejpam-6133	175	5	x)2	x)2	NOUN
ejpam-6133	175	6	β(x+	β(x+	X
ejpam-6133	175	7	1)(s̃ℓ	1)(s̃ℓ	NUM
ejpam-6133	176	1	+	+	CCONJ
ejpam-6133	176	2	1	1	X
ejpam-6133	176	3	)	)	PUNCT
ejpam-6133	176	4	−→	−→	NOUN
ejpam-6133	176	5	0	0	NUM
ejpam-6133	176	6	.	.	PUNCT
ejpam-6133	177	1	thus	thus	ADV
ejpam-6133	177	2	,	,	PUNCT
ejpam-6133	177	3	{	{	PUNCT
ejpam-6133	177	4	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	177	5	}	}	PUNCT
ejpam-6133	177	6	converges	converge	NOUN
ejpam-6133	177	7	to	to	ADP
ejpam-6133	177	8	⊤x	⊤x	VERB
ejpam-6133	177	9	in	in	ADP
ejpam-6133	177	10	(	(	PUNCT
ejpam-6133	177	11	℧	℧	PROPN
ejpam-6133	177	12	,	,	PUNCT
ejpam-6133	177	13	ζ	ζ	NOUN
ejpam-6133	177	14	)	)	PUNCT
ejpam-6133	177	15	.	.	PUNCT
ejpam-6133	178	1	case	case	NOUN
ejpam-6133	178	2	3	3	NUM
ejpam-6133	178	3	:	:	PUNCT
ejpam-6133	178	4	if	if	SCONJ
ejpam-6133	178	5	s̃ℓ	s̃ℓ	VERB
ejpam-6133	178	6	̸=	̸=	PROPN
ejpam-6133	178	7	0	0	NUM
ejpam-6133	178	8	for	for	ADP
ejpam-6133	178	9	all	all	DET
ejpam-6133	178	10	but	but	CCONJ
ejpam-6133	178	11	finitely	finitely	ADV
ejpam-6133	178	12	many	many	ADJ
ejpam-6133	178	13	ℓ	ℓ	NOUN
ejpam-6133	178	14	and	and	CCONJ
ejpam-6133	178	15	x	x	SYM
ejpam-6133	178	16	=	=	SYM
ejpam-6133	178	17	0	0	NUM
ejpam-6133	178	18	,	,	PUNCT
ejpam-6133	178	19	we	we	PRON
ejpam-6133	178	20	have	have	VERB
ejpam-6133	178	21	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	178	22	,	,	PUNCT
ejpam-6133	178	23	0	0	NUM
ejpam-6133	178	24	)	)	PUNCT
ejpam-6133	178	25	=	=	VERB
ejpam-6133	179	1	s̃ℓ	s̃ℓ	ADV
ejpam-6133	179	2	1	1	NUM
ejpam-6133	179	3	+	+	NOUN
ejpam-6133	179	4	s̃ℓ	s̃ℓ	ADV
ejpam-6133	179	5	−→	−→	NOUN
ejpam-6133	179	6	0	0	NUM
ejpam-6133	180	1	=	=	NOUN
ejpam-6133	180	2	⇒	⇒	NOUN
ejpam-6133	180	3	s̃ℓ	s̃ℓ	ADV
ejpam-6133	180	4	−→	−→	NOUN
ejpam-6133	180	5	0	0	NUM
ejpam-6133	180	6	,	,	PUNCT
ejpam-6133	180	7	then	then	ADV
ejpam-6133	180	8	ζ(⊤s̃ℓ,⊤0	ζ(⊤s̃ℓ,⊤0	PROPN
ejpam-6133	180	9	)	)	PUNCT
ejpam-6133	180	10	=	=	PUNCT
ejpam-6133	181	1	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	181	2	1	1	NUM
ejpam-6133	182	1	+	+	NOUN
ejpam-6133	182	2	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	182	3	=	=	SYM
ejpam-6133	182	4	s̃ℓ	s̃ℓ	PUNCT
ejpam-6133	182	5	β	β	NOUN
ejpam-6133	182	6	+	+	X
ejpam-6133	182	7	(	(	PUNCT
ejpam-6133	182	8	β	β	X
ejpam-6133	182	9	+	+	NOUN
ejpam-6133	182	10	1)s̃ℓ	1)s̃ℓ	NUM
ejpam-6133	182	11	−→	−→	NOUN
ejpam-6133	182	12	0	0	NUM
ejpam-6133	182	13	.	.	PUNCT
ejpam-6133	183	1	thus	thus	ADV
ejpam-6133	183	2	,	,	PUNCT
ejpam-6133	183	3	{	{	PUNCT
ejpam-6133	183	4	⊤s̃ℓ	⊤s̃ℓ	NOUN
ejpam-6133	183	5	}	}	PUNCT
ejpam-6133	183	6	converges	converge	NOUN
ejpam-6133	183	7	to	to	ADP
ejpam-6133	183	8	⊤x	⊤x	VERB
ejpam-6133	183	9	in	in	ADP
ejpam-6133	183	10	(	(	PUNCT
ejpam-6133	183	11	℧	℧	PROPN
ejpam-6133	183	12	,	,	PUNCT
ejpam-6133	183	13	ζ	ζ	NOUN
ejpam-6133	183	14	)	)	PUNCT
ejpam-6133	183	15	.	.	PUNCT
ejpam-6133	184	1	case	case	NOUN
ejpam-6133	184	2	4	4	NUM
ejpam-6133	184	3	:	:	PUNCT
ejpam-6133	184	4	if	if	SCONJ
ejpam-6133	184	5	s̃ℓ	s̃ℓ	ADV
ejpam-6133	184	6	=	=	NOUN
ejpam-6133	184	7	0	0	NUM
ejpam-6133	184	8	for	for	ADP
ejpam-6133	184	9	all	all	PRON
ejpam-6133	184	10	but	but	CCONJ
ejpam-6133	184	11	finitely	finitely	ADV
ejpam-6133	184	12	many	many	ADJ
ejpam-6133	184	13	ℓ	ℓ	NOUN
ejpam-6133	184	14	,	,	PUNCT
ejpam-6133	184	15	then	then	ADV
ejpam-6133	184	16	,	,	PUNCT
ejpam-6133	184	17	when	when	SCONJ
ejpam-6133	184	18	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	184	19	,	,	PUNCT
ejpam-6133	184	20	x	x	X
ejpam-6133	184	21	)	)	PUNCT
ejpam-6133	184	22	−→	−→	NOUN
ejpam-6133	184	23	0	0	NUM
ejpam-6133	184	24	we	we	PRON
ejpam-6133	184	25	necessarily	necessarily	ADV
ejpam-6133	184	26	have	have	VERB
ejpam-6133	184	27	x	x	X
ejpam-6133	184	28	=	=	SYM
ejpam-6133	184	29	0	0	NUM
ejpam-6133	184	30	,	,	PUNCT
ejpam-6133	184	31	consequently	consequently	ADV
ejpam-6133	184	32	ζ(⊤s̃ℓ,⊤x	ζ(⊤s̃ℓ,⊤x	NOUN
ejpam-6133	184	33	)	)	PUNCT
ejpam-6133	185	1	−→	−→	NOUN
ejpam-6133	185	2	0	0	NUM
ejpam-6133	185	3	.	.	PUNCT
ejpam-6133	186	1	in	in	ADP
ejpam-6133	186	2	all	all	DET
ejpam-6133	186	3	the	the	DET
ejpam-6133	186	4	cases	case	NOUN
ejpam-6133	186	5	,	,	PUNCT
ejpam-6133	186	6	if	if	SCONJ
ejpam-6133	186	7	ζ(s̃ℓ	ζ(s̃ℓ	NOUN
ejpam-6133	186	8	,	,	PUNCT
ejpam-6133	186	9	x	x	X
ejpam-6133	186	10	)	)	PUNCT
ejpam-6133	186	11	−→	−→	ADJ
ejpam-6133	186	12	0	0	NUM
ejpam-6133	186	13	=	=	NOUN
ejpam-6133	186	14	⇒	⇒	NOUN
ejpam-6133	186	15	ζ(⊤s̃ℓ,⊤x	ζ(⊤s̃ℓ,⊤x	NOUN
ejpam-6133	186	16	)	)	PUNCT
ejpam-6133	186	17	−→	−→	NOUN
ejpam-6133	186	18	0	0	NUM
ejpam-6133	186	19	,	,	PUNCT
ejpam-6133	186	20	so	so	ADV
ejpam-6133	186	21	⊤	⊤	PROPN
ejpam-6133	186	22	is	be	AUX
ejpam-6133	186	23	continuous	continuous	ADJ
ejpam-6133	186	24	.	.	PUNCT
ejpam-6133	187	1	we	we	PRON
ejpam-6133	187	2	have	have	VERB
ejpam-6133	187	3	⊤ℓx	⊤ℓx	NOUN
ejpam-6133	187	4	=	=	PUNCT
ejpam-6133	187	5	x	x	SYM
ejpam-6133	187	6	βℓ	βℓ	X
ejpam-6133	187	7	+	+	X
ejpam-6133	187	8	(	(	PUNCT
ejpam-6133	187	9	∑ℓ	∑ℓ	ADJ
ejpam-6133	187	10	k=1	k=1	X
ejpam-6133	187	11	β	β	X
ejpam-6133	187	12	k	k	X
ejpam-6133	187	13	)	)	PUNCT
ejpam-6133	188	1	x	x	X
ejpam-6133	188	2	.	.	PUNCT
ejpam-6133	189	1	it	it	PRON
ejpam-6133	189	2	is	be	AUX
ejpam-6133	189	3	obvious	obvious	ADJ
ejpam-6133	189	4	that	that	SCONJ
ejpam-6133	189	5	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	189	6	=	=	PUNCT
ejpam-6133	189	7	⊤ℓx	⊤ℓx	NOUN
ejpam-6133	189	8	−→	−→	NOUN
ejpam-6133	189	9	0	0	NUM
ejpam-6133	189	10	as	as	ADP
ejpam-6133	189	11	ℓ	ℓ	PROPN
ejpam-6133	189	12	−→	−→	NOUN
ejpam-6133	189	13	∞	∞	PROPN
ejpam-6133	189	14	and	and	CCONJ
ejpam-6133	189	15	so	so	ADV
ejpam-6133	189	16	for	for	ADP
ejpam-6133	189	17	each	each	DET
ejpam-6133	189	18	x	x	SYM
ejpam-6133	189	19	∈	∈	PROPN
ejpam-6133	189	20	x	x	NOUN
ejpam-6133	189	21	,	,	PUNCT
ejpam-6133	189	22	lim	lim	PROPN
ejpam-6133	189	23	ℓ→∞	ℓ→∞	PROPN
ejpam-6133	189	24	ϖ(s̃ℓ	ϖ(s̃ℓ	PROPN
ejpam-6133	189	25	,	,	PUNCT
ejpam-6133	189	26	x	x	X
ejpam-6133	189	27	)	)	PUNCT
ejpam-6133	189	28	=	=	SYM
ejpam-6133	189	29	lim	lim	PROPN
ejpam-6133	189	30	ℓ→∞	ℓ→∞	NOUN
ejpam-6133	189	31	ϵ(s̃ℓ	ϵ(s̃ℓ	PROPN
ejpam-6133	189	32	,	,	PUNCT
ejpam-6133	189	33	x	x	X
ejpam-6133	189	34	)	)	PUNCT
ejpam-6133	189	35	=	=	SYM
ejpam-6133	189	36	2	2	NUM
ejpam-6133	189	37	+	+	NUM
ejpam-6133	189	38	2x	2x	NUM
ejpam-6133	190	1	<	<	X
ejpam-6133	190	2	∞.	∞.	PROPN
ejpam-6133	190	3	in	in	ADP
ejpam-6133	190	4	addition	addition	NOUN
ejpam-6133	190	5	,	,	PUNCT
ejpam-6133	190	6	we	we	PRON
ejpam-6133	190	7	define	define	VERB
ejpam-6133	190	8	a	a	DET
ejpam-6133	190	9	mapping	mapping	NOUN
ejpam-6133	190	10	⊤	⊤	NOUN
ejpam-6133	190	11	:	:	PUNCT
ejpam-6133	190	12	℧	℧	PROPN
ejpam-6133	190	13	×	×	NOUN
ejpam-6133	190	14	℧	℧	X
ejpam-6133	190	15	−→	−→	NOUN
ejpam-6133	190	16	[	[	X
ejpam-6133	190	17	0,+∞	0,+∞	NUM
ejpam-6133	190	18	[	[	PUNCT
ejpam-6133	190	19	as	as	ADP
ejpam-6133	190	20	α(x	α(x	PROPN
ejpam-6133	190	21	,	,	PUNCT
ejpam-6133	190	22	y	y	PROPN
ejpam-6133	190	23	)	)	PUNCT
ejpam-6133	190	24	=	=	PRON
ejpam-6133	190	25	{	{	PUNCT
ejpam-6133	190	26	1	1	NUM
ejpam-6133	190	27	if	if	SCONJ
ejpam-6133	190	28	x	x	X
ejpam-6133	190	29	,	,	PUNCT
ejpam-6133	190	30	y	y	PROPN
ejpam-6133	190	31	∈	∈	PROPN
ejpam-6133	191	1	[	[	X
ejpam-6133	191	2	0	0	NUM
ejpam-6133	191	3	,	,	PUNCT
ejpam-6133	191	4	1	1	NUM
ejpam-6133	191	5	]	]	PUNCT
ejpam-6133	191	6	0	0	PUNCT
ejpam-6133	192	1	otherwise	otherwise	ADV
ejpam-6133	192	2	.	.	PUNCT
ejpam-6133	193	1	let	let	VERB
ejpam-6133	193	2	s̃0	s̃0	PROPN
ejpam-6133	193	3	∈	∈	PROPN
ejpam-6133	193	4	℧	℧	AUX
ejpam-6133	193	5	be	be	AUX
ejpam-6133	193	6	a	a	DET
ejpam-6133	193	7	point	point	NOUN
ejpam-6133	193	8	with	with	ADP
ejpam-6133	193	9	α(s̃0,⊤s̃0	α(s̃0,⊤s̃0	PROPN
ejpam-6133	193	10	)	)	PUNCT
ejpam-6133	193	11	≥	≥	NOUN
ejpam-6133	193	12	1	1	NUM
ejpam-6133	193	13	,	,	PUNCT
ejpam-6133	194	1	then	then	ADV
ejpam-6133	194	2	s̃0	s̃0	PROPN
ejpam-6133	194	3	∈	∈	PROPN
ejpam-6133	195	1	[	[	X
ejpam-6133	195	2	0	0	NUM
ejpam-6133	195	3	,	,	PUNCT
ejpam-6133	195	4	1	1	NUM
ejpam-6133	195	5	]	]	PUNCT
ejpam-6133	195	6	and	and	CCONJ
ejpam-6133	195	7	α(⊤s̃0,⊤2s̃0	α(⊤s̃0,⊤2s̃0	NOUN
ejpam-6133	195	8	)	)	PUNCT
ejpam-6133	195	9	=	=	SYM
ejpam-6133	195	10	α	α	PROPN
ejpam-6133	195	11	(	(	PUNCT
ejpam-6133	195	12	s̃0	s̃0	PROPN
ejpam-6133	195	13	β+βs̃0	β+βs̃0	PROPN
ejpam-6133	195	14	,	,	PUNCT
ejpam-6133	195	15	s̃0	s̃0	PROPN
ejpam-6133	195	16	β2+(β+β2)s̃0	β2+(β+β2)s̃0	PROPN
ejpam-6133	195	17	)	)	PUNCT
ejpam-6133	195	18	≥	≥	NOUN
ejpam-6133	195	19	1	1	NUM
ejpam-6133	195	20	.	.	PUNCT
ejpam-6133	196	1	therefore	therefore	ADV
ejpam-6133	196	2	,	,	PUNCT
ejpam-6133	196	3	⊤	⊤	PROPN
ejpam-6133	196	4	is	be	AUX
ejpam-6133	196	5	α	α	NOUN
ejpam-6133	196	6	-	-	ADJ
ejpam-6133	196	7	orbitally	orbitally	ADV
ejpam-6133	196	8	admissible	admissible	NOUN
ejpam-6133	196	9	.	.	PUNCT
ejpam-6133	197	1	h.	h.	PROPN
ejpam-6133	197	2	aydi	aydi	PROPN
ejpam-6133	197	3	,	,	PUNCT
ejpam-6133	197	4	h.	h.	PROPN
ejpam-6133	197	5	hammouda	hammouda	PROPN
ejpam-6133	197	6	,	,	PUNCT
ejpam-6133	197	7	s.	s.	PROPN
ejpam-6133	197	8	mansour	mansour	PROPN
ejpam-6133	197	9	/	/	SYM
ejpam-6133	197	10	eur	eur	PROPN
ejpam-6133	197	11	.	.	PUNCT
ejpam-6133	198	1	j.	j.	PROPN
ejpam-6133	198	2	pure	pure	PROPN
ejpam-6133	198	3	appl	appl	PROPN
ejpam-6133	198	4	.	.	PROPN
ejpam-6133	198	5	math	math	PROPN
ejpam-6133	198	6	,	,	PUNCT
ejpam-6133	198	7	18	18	NUM
ejpam-6133	198	8	(	(	PUNCT
ejpam-6133	198	9	3	3	NUM
ejpam-6133	198	10	)	)	PUNCT
ejpam-6133	198	11	(	(	PUNCT
ejpam-6133	198	12	2025	2025	NUM
ejpam-6133	198	13	)	)	PUNCT
ejpam-6133	198	14	,	,	PUNCT
ejpam-6133	198	15	6133	6133	NUM
ejpam-6133	198	16	9	9	NUM
ejpam-6133	198	17	of	of	ADP
ejpam-6133	198	18	18	18	NUM
ejpam-6133	198	19	let	let	VERB
ejpam-6133	198	20	ψ(χ	ψ(χ	NOUN
ejpam-6133	198	21	)	)	PUNCT
ejpam-6133	198	22	=	=	SYM
ejpam-6133	198	23	kχ	kχ	NOUN
ejpam-6133	198	24	,	,	PUNCT
ejpam-6133	198	25	for	for	ADP
ejpam-6133	198	26	χ	χ	X
ejpam-6133	198	27	>	>	X
ejpam-6133	198	28	0	0	PROPN
ejpam-6133	198	29	,	,	PUNCT
ejpam-6133	198	30	where	where	SCONJ
ejpam-6133	198	31	k	k	PROPN
ejpam-6133	198	32	=	=	PUNCT
ejpam-6133	198	33	36	36	NUM
ejpam-6133	198	34	β	β	NOUN
ejpam-6133	198	35	.	.	PUNCT
ejpam-6133	199	1	here	here	ADV
ejpam-6133	199	2	,	,	PUNCT
ejpam-6133	199	3	ψℓ(χ	ψℓ(χ	PUNCT
ejpam-6133	199	4	)	)	PUNCT
ejpam-6133	199	5	=	=	SYM
ejpam-6133	199	6	kℓχ	kℓχ	NOUN
ejpam-6133	199	7	.	.	PUNCT
ejpam-6133	200	1	for	for	ADP
ejpam-6133	200	2	all	all	DET
ejpam-6133	200	3	x	x	NOUN
ejpam-6133	200	4	,	,	PUNCT
ejpam-6133	200	5	y	y	PROPN
ejpam-6133	200	6	∈	∈	PROPN
ejpam-6133	200	7	℧	℧	PROPN
ejpam-6133	200	8	,	,	PUNCT
ejpam-6133	200	9	we	we	PRON
ejpam-6133	200	10	will	will	AUX
ejpam-6133	200	11	show	show	VERB
ejpam-6133	200	12	that	that	SCONJ
ejpam-6133	200	13	α(x	α(x	NOUN
ejpam-6133	200	14	,	,	PUNCT
ejpam-6133	200	15	y)ϖ(x	y)ϖ(x	PROPN
ejpam-6133	200	16	,	,	PUNCT
ejpam-6133	200	17	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	200	18	,	,	PUNCT
ejpam-6133	200	19	y)ζ(⊤x,⊤y	y)ζ(⊤x,⊤y	PROPN
ejpam-6133	200	20	)	)	PUNCT
ejpam-6133	200	21	≤	≤	NOUN
ejpam-6133	200	22	ψ(ζ(x	ψ(ζ(x	PROPN
ejpam-6133	200	23	,	,	PUNCT
ejpam-6133	200	24	y	y	NOUN
ejpam-6133	200	25	)	)	PUNCT
ejpam-6133	200	26	.	.	PUNCT
ejpam-6133	201	1	for	for	ADP
ejpam-6133	201	2	this	this	PRON
ejpam-6133	201	3	,	,	PUNCT
ejpam-6133	201	4	we	we	PRON
ejpam-6133	201	5	consider	consider	VERB
ejpam-6133	201	6	the	the	DET
ejpam-6133	201	7	following	follow	VERB
ejpam-6133	201	8	cases	case	NOUN
ejpam-6133	201	9	:	:	PUNCT
ejpam-6133	201	10	case	case	NOUN
ejpam-6133	201	11	1	1	NUM
ejpam-6133	201	12	:	:	PUNCT
ejpam-6133	201	13	x	x	SYM
ejpam-6133	201	14	=	=	PUNCT
ejpam-6133	201	15	y.	y.	NOUN
ejpam-6133	201	16	we	we	PRON
ejpam-6133	201	17	have	have	VERB
ejpam-6133	201	18	0	0	NUM
ejpam-6133	201	19	=	=	SYM
ejpam-6133	201	20	α(x	α(x	NOUN
ejpam-6133	201	21	,	,	PUNCT
ejpam-6133	201	22	y)ϖ(x	y)ϖ(x	PROPN
ejpam-6133	201	23	,	,	PUNCT
ejpam-6133	201	24	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	201	25	,	,	PUNCT
ejpam-6133	201	26	y)ζ(⊤x,⊤y	y)ζ(⊤x,⊤y	PROPN
ejpam-6133	201	27	)	)	PUNCT
ejpam-6133	201	28	≤	≤	NOUN
ejpam-6133	202	1	ψ(ζ(x	ψ(ζ(x	PROPN
ejpam-6133	202	2	,	,	PUNCT
ejpam-6133	202	3	y	y	NOUN
ejpam-6133	202	4	)	)	PUNCT
ejpam-6133	202	5	.	.	PUNCT
ejpam-6133	203	1	case	case	NOUN
ejpam-6133	203	2	2	2	NUM
ejpam-6133	203	3	:	:	PUNCT
ejpam-6133	203	4	(	(	PUNCT
ejpam-6133	203	5	x	x	SYM
ejpam-6133	203	6	̸=	̸=	PROPN
ejpam-6133	203	7	0	0	NUM
ejpam-6133	203	8	and	and	CCONJ
ejpam-6133	203	9	y	y	PROPN
ejpam-6133	203	10	=	=	NOUN
ejpam-6133	203	11	0	0	NUM
ejpam-6133	203	12	)	)	PUNCT
ejpam-6133	203	13	or	or	CCONJ
ejpam-6133	203	14	(	(	PUNCT
ejpam-6133	203	15	y	y	PROPN
ejpam-6133	203	16	̸=	̸=	PROPN
ejpam-6133	203	17	0	0	PUNCT
ejpam-6133	203	18	and	and	CCONJ
ejpam-6133	203	19	x	x	SYM
ejpam-6133	203	20	=	=	NOUN
ejpam-6133	203	21	0	0	NUM
ejpam-6133	203	22	)	)	PUNCT
ejpam-6133	203	23	.	.	PUNCT
ejpam-6133	204	1	without	without	ADP
ejpam-6133	204	2	generality	generality	NOUN
ejpam-6133	204	3	,	,	PUNCT
ejpam-6133	204	4	suppose	suppose	VERB
ejpam-6133	204	5	that	that	SCONJ
ejpam-6133	204	6	x	x	PROPN
ejpam-6133	204	7	̸=	̸=	PROPN
ejpam-6133	204	8	0	0	NUM
ejpam-6133	204	9	and	and	CCONJ
ejpam-6133	204	10	y	y	PROPN
ejpam-6133	204	11	=	=	SYM
ejpam-6133	204	12	0	0	PROPN
ejpam-6133	204	13	.	.	PUNCT
ejpam-6133	205	1	here	here	ADV
ejpam-6133	205	2	,	,	PUNCT
ejpam-6133	205	3	we	we	PRON
ejpam-6133	205	4	have	have	VERB
ejpam-6133	205	5	α(x	α(x	NOUN
ejpam-6133	205	6	,	,	PUNCT
ejpam-6133	205	7	0)ϖ(x	0)ϖ(x	PROPN
ejpam-6133	205	8	,	,	PUNCT
ejpam-6133	205	9	0)ϵ(x	0)ϵ(x	PROPN
ejpam-6133	205	10	,	,	PUNCT
ejpam-6133	205	11	0)ζ(⊤x,⊤0	0)ζ(⊤x,⊤0	NUM
ejpam-6133	205	12	)	)	PUNCT
ejpam-6133	205	13	=	=	NOUN
ejpam-6133	206	1	(	(	PUNCT
ejpam-6133	206	2	2	2	NUM
ejpam-6133	206	3	+	+	CCONJ
ejpam-6133	206	4	2x)2ζ	2x)2ζ	NUM
ejpam-6133	206	5	(	(	PUNCT
ejpam-6133	206	6	x	x	X
ejpam-6133	206	7	β	β	X
ejpam-6133	206	8	+	+	NOUN
ejpam-6133	206	9	βx	βx	PROPN
ejpam-6133	206	10	,	,	PUNCT
ejpam-6133	206	11	0	0	X
ejpam-6133	206	12	)	)	PUNCT
ejpam-6133	206	13	=	=	NOUN
ejpam-6133	207	1	(	(	PUNCT
ejpam-6133	207	2	2	2	NUM
ejpam-6133	207	3	+	+	NUM
ejpam-6133	207	4	2x)2	2x)2	NUM
ejpam-6133	207	5	x	x	SYM
ejpam-6133	207	6	β+βx	β+βx	PUNCT
ejpam-6133	207	7	x	x	PUNCT
ejpam-6133	207	8	β+βx	β+βx	PROPN
ejpam-6133	208	1	+	+	CCONJ
ejpam-6133	208	2	1	1	X
ejpam-6133	208	3	=	=	SYM
ejpam-6133	208	4	(	(	PUNCT
ejpam-6133	208	5	2	2	NUM
ejpam-6133	208	6	+	+	NUM
ejpam-6133	208	7	2x)2	2x)2	NUM
ejpam-6133	208	8	x	x	SYM
ejpam-6133	208	9	β	β	X
ejpam-6133	208	10	+	+	X
ejpam-6133	208	11	(	(	PUNCT
ejpam-6133	208	12	β	β	X
ejpam-6133	208	13	+	+	NOUN
ejpam-6133	208	14	1)x	1)x	NUM
ejpam-6133	208	15	≤	≤	NUM
ejpam-6133	208	16	1	1	NUM
ejpam-6133	208	17	β	β	X
ejpam-6133	208	18	(	(	PUNCT
ejpam-6133	208	19	2	2	NUM
ejpam-6133	208	20	+	+	NUM
ejpam-6133	208	21	2x)2	2x)2	NUM
ejpam-6133	208	22	x	x	SYM
ejpam-6133	208	23	x+	x+	PROPN
ejpam-6133	208	24	1	1	NUM
ejpam-6133	208	25	≤	≤	NUM
ejpam-6133	208	26	16	16	NUM
ejpam-6133	208	27	β	β	NOUN
ejpam-6133	208	28	x	x	SYM
ejpam-6133	208	29	x+	x+	PROPN
ejpam-6133	208	30	1	1	NUM
ejpam-6133	208	31	≤	≤	NUM
ejpam-6133	208	32	k.ζ(x	k.ζ(x	NOUN
ejpam-6133	208	33	,	,	PUNCT
ejpam-6133	208	34	y	y	NOUN
ejpam-6133	208	35	)	)	PUNCT
ejpam-6133	209	1	=	=	PUNCT
ejpam-6133	209	2	ψ(ζ(x	ψ(ζ(x	PROPN
ejpam-6133	209	3	,	,	PUNCT
ejpam-6133	209	4	y	y	NOUN
ejpam-6133	209	5	)	)	PUNCT
ejpam-6133	209	6	)	)	PUNCT
ejpam-6133	209	7	.	.	PUNCT
ejpam-6133	210	1	case	case	NOUN
ejpam-6133	210	2	3	3	NUM
ejpam-6133	210	3	:	:	SYM
ejpam-6133	210	4	0	0	NUM
ejpam-6133	210	5	̸=	̸=	PROPN
ejpam-6133	210	6	x	x	SYM
ejpam-6133	210	7	̸=	̸=	PROPN
ejpam-6133	210	8	y	y	PROPN
ejpam-6133	210	9	̸=	̸=	PROPN
ejpam-6133	210	10	0	0	NUM
ejpam-6133	210	11	.	.	PUNCT
ejpam-6133	211	1	here	here	ADV
ejpam-6133	211	2	,	,	PUNCT
ejpam-6133	211	3	we	we	PRON
ejpam-6133	211	4	have	have	VERB
ejpam-6133	211	5	0	0	NUM
ejpam-6133	211	6	̸=	̸=	NOUN
ejpam-6133	211	7	x	x	SYM
ejpam-6133	211	8	β+βx	β+βx	PROPN
ejpam-6133	212	1	̸=	̸=	PROPN
ejpam-6133	212	2	y	y	PROPN
ejpam-6133	212	3	β+βy	β+βy	INTJ
ejpam-6133	212	4	̸=	̸=	PROPN
ejpam-6133	212	5	0	0	NUM
ejpam-6133	212	6	.	.	PUNCT
ejpam-6133	213	1	one	one	NUM
ejpam-6133	213	2	writes	write	VERB
ejpam-6133	213	3	α(x	α(x	PROPN
ejpam-6133	213	4	,	,	PUNCT
ejpam-6133	213	5	y)ϖ(x	y)ϖ(x	PROPN
ejpam-6133	213	6	,	,	PUNCT
ejpam-6133	213	7	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	213	8	,	,	PUNCT
ejpam-6133	213	9	y)ζ(⊤x,⊤y	y)ζ(⊤x,⊤y	PROPN
ejpam-6133	213	10	)	)	PUNCT
ejpam-6133	213	11	=	=	NOUN
ejpam-6133	214	1	(	(	PUNCT
ejpam-6133	214	2	2	2	NUM
ejpam-6133	214	3	+	+	NUM
ejpam-6133	214	4	2x+	2x+	NUM
ejpam-6133	214	5	2y)2ζ	2y)2ζ	NUM
ejpam-6133	214	6	(	(	PUNCT
ejpam-6133	214	7	x	x	X
ejpam-6133	214	8	β	β	X
ejpam-6133	214	9	+	+	X
ejpam-6133	214	10	βx	βx	PROPN
ejpam-6133	214	11	,	,	PUNCT
ejpam-6133	214	12	y	y	PROPN
ejpam-6133	214	13	β	β	X
ejpam-6133	214	14	+	+	ADJ
ejpam-6133	214	15	βy	βy	ADJ
ejpam-6133	214	16	)	)	PUNCT
ejpam-6133	214	17	=	=	PUNCT
ejpam-6133	215	1	(	(	PUNCT
ejpam-6133	215	2	2	2	NUM
ejpam-6133	215	3	+	+	NUM
ejpam-6133	215	4	2x+	2x+	NUM
ejpam-6133	215	5	2y)2	2y)2	NUM
ejpam-6133	215	6	[	[	PUNCT
ejpam-6133	215	7	x	x	X
ejpam-6133	215	8	β	β	X
ejpam-6133	215	9	+	+	NOUN
ejpam-6133	215	10	βx	βx	PROPN
ejpam-6133	216	1	+	+	CCONJ
ejpam-6133	216	2	y	y	PROPN
ejpam-6133	216	3	β	β	NOUN
ejpam-6133	217	1	+	+	X
ejpam-6133	217	2	βy	βy	X
ejpam-6133	217	3	]	]	PUNCT
ejpam-6133	217	4	≤	≤	NUM
ejpam-6133	217	5	1	1	NUM
ejpam-6133	217	6	β	β	X
ejpam-6133	217	7	(	(	PUNCT
ejpam-6133	217	8	2x+	2x+	NUM
ejpam-6133	217	9	2y	2y	NUM
ejpam-6133	217	10	+	+	CCONJ
ejpam-6133	217	11	2)2(x+	2)2(x+	NUM
ejpam-6133	217	12	y	y	NOUN
ejpam-6133	217	13	)	)	PUNCT
ejpam-6133	217	14	≤	≤	NOUN
ejpam-6133	217	15	36	36	NUM
ejpam-6133	217	16	β	β	NOUN
ejpam-6133	218	1	[	[	X
ejpam-6133	218	2	x+	x+	ADJ
ejpam-6133	218	3	y	y	X
ejpam-6133	218	4	]	]	X
ejpam-6133	218	5	=	=	PUNCT
ejpam-6133	218	6	k.ζ(x	k.ζ(x	NOUN
ejpam-6133	218	7	,	,	PUNCT
ejpam-6133	218	8	y	y	NOUN
ejpam-6133	218	9	)	)	PUNCT
ejpam-6133	218	10	=	=	PUNCT
ejpam-6133	219	1	ψ(ζ(x	ψ(ζ(x	PROPN
ejpam-6133	219	2	,	,	PUNCT
ejpam-6133	219	3	y	y	NOUN
ejpam-6133	219	4	)	)	PUNCT
ejpam-6133	219	5	)	)	PUNCT
ejpam-6133	219	6	.	.	PUNCT
ejpam-6133	220	1	moreover	moreover	ADV
ejpam-6133	220	2	,	,	PUNCT
ejpam-6133	220	3	there	there	PRON
ejpam-6133	220	4	is	be	VERB
ejpam-6133	220	5	s̃0	s̃0	PROPN
ejpam-6133	220	6	∈	∈	PROPN
ejpam-6133	220	7	℧	℧	PROPN
ejpam-6133	220	8	with	with	ADP
ejpam-6133	220	9	α(s̃0,⊤s̃0	α(s̃0,⊤s̃0	PROPN
ejpam-6133	220	10	)	)	PUNCT
ejpam-6133	220	11	≥	≥	NOUN
ejpam-6133	220	12	1	1	NUM
ejpam-6133	220	13	,	,	PUNCT
ejpam-6133	220	14	then	then	ADV
ejpam-6133	220	15	α(⊤s̃0,⊤2s̃0	α(⊤s̃0,⊤2s̃0	NOUN
ejpam-6133	220	16	)	)	PUNCT
ejpam-6133	220	17	≥	≥	NOUN
ejpam-6133	220	18	1	1	NUM
ejpam-6133	220	19	.	.	PUNCT
ejpam-6133	221	1	by	by	ADP
ejpam-6133	221	2	induction	induction	NOUN
ejpam-6133	221	3	,	,	PUNCT
ejpam-6133	221	4	we	we	PRON
ejpam-6133	221	5	obtain	obtain	VERB
ejpam-6133	221	6	α(s̃ℓ	α(s̃ℓ	NOUN
ejpam-6133	221	7	,	,	PUNCT
ejpam-6133	221	8	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	221	9	)	)	PUNCT
ejpam-6133	221	10	≥	≥	NOUN
ejpam-6133	221	11	1	1	NUM
ejpam-6133	221	12	,	,	PUNCT
ejpam-6133	221	13	where	where	SCONJ
ejpam-6133	221	14	s̃ℓ	s̃ℓ	ADV
ejpam-6133	221	15	=	=	SYM
ejpam-6133	221	16	⊤ℓs̃0	⊤ℓs̃0	NUM
ejpam-6133	221	17	=	=	SYM
ejpam-6133	221	18	s̃0	s̃0	ADJ
ejpam-6133	221	19	βℓ+	βℓ+	NOUN
ejpam-6133	221	20	(	(	PUNCT
ejpam-6133	221	21	∑ℓ	∑ℓ	ADJ
ejpam-6133	221	22	k=1	k=1	X
ejpam-6133	221	23	β	β	X
ejpam-6133	221	24	k)s̃0	k)s̃0	PROPN
ejpam-6133	221	25	=	=	SYM
ejpam-6133	221	26	s̃0	s̃0	PROPN
ejpam-6133	221	27	βℓ+β	βℓ+β	PROPN
ejpam-6133	222	1	βℓ−1	βℓ−1	PROPN
ejpam-6133	222	2	β−1	β−1	PUNCT
ejpam-6133	222	3	s̃0	s̃0	PROPN
ejpam-6133	222	4	,	,	PUNCT
ejpam-6133	222	5	for	for	ADP
ejpam-6133	222	6	each	each	DET
ejpam-6133	222	7	ℓ	ℓ	PROPN
ejpam-6133	222	8	∈	∈	PROPN
ejpam-6133	222	9	n.	n.	NOUN
ejpam-6133	222	10	it	it	PRON
ejpam-6133	222	11	is	be	AUX
ejpam-6133	222	12	easy	easy	ADJ
ejpam-6133	222	13	that	that	SCONJ
ejpam-6133	222	14	s̃ℓ	s̃ℓ	ADV
ejpam-6133	222	15	−→	−→	NOUN
ejpam-6133	222	16	0	0	NUM
ejpam-6133	222	17	as	as	ADP
ejpam-6133	222	18	ℓ	ℓ	PROPN
ejpam-6133	222	19	−→	−→	NOUN
ejpam-6133	222	20	+	+	PROPN
ejpam-6133	222	21	∞.	∞.	PROPN
ejpam-6133	222	22	thus	thus	ADV
ejpam-6133	222	23	,	,	PUNCT
ejpam-6133	222	24	(	(	PUNCT
ejpam-6133	222	25	℧	℧	PROPN
ejpam-6133	222	26	,	,	PUNCT
ejpam-6133	222	27	ζ	ζ	NOUN
ejpam-6133	222	28	)	)	PUNCT
ejpam-6133	222	29	is	be	AUX
ejpam-6133	222	30	an	an	DET
ejpam-6133	222	31	orbitally	orbitally	ADV
ejpam-6133	222	32	complete	complete	ADJ
ejpam-6133	222	33	dcms	dcms	NOUN
ejpam-6133	222	34	.	.	PUNCT
ejpam-6133	223	1	recall	recall	VERB
ejpam-6133	223	2	that	that	SCONJ
ejpam-6133	223	3	lim	lim	PROPN
ejpam-6133	223	4	i	i	PRON
ejpam-6133	223	5	,	,	PUNCT
ejpam-6133	223	6	m→+∞	m→+∞	PROPN
ejpam-6133	223	7	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	223	8	,	,	PUNCT
ejpam-6133	223	9	s̃m	s̃m	PROPN
ejpam-6133	223	10	)	)	PUNCT
ejpam-6133	224	1	=	=	SYM
ejpam-6133	224	2	lim	lim	PROPN
ejpam-6133	224	3	i	i	PRON
ejpam-6133	224	4	,	,	PUNCT
ejpam-6133	224	5	m→+∞	m→+∞	PROPN
ejpam-6133	224	6	ϵ(s̃i	ϵ(s̃i	PROPN
ejpam-6133	224	7	,	,	PUNCT
ejpam-6133	224	8	s̃m	s̃m	NOUN
ejpam-6133	224	9	)	)	PUNCT
ejpam-6133	224	10	=	=	SYM
ejpam-6133	224	11	2	2	NUM
ejpam-6133	224	12	then	then	ADV
ejpam-6133	224	13	we	we	PRON
ejpam-6133	224	14	have	have	AUX
ejpam-6133	224	15	sup	sup	NOUN
ejpam-6133	224	16	m≥1	m≥1	PROPN
ejpam-6133	224	17	lim	lim	PROPN
ejpam-6133	224	18	i→∞	i→∞	VERB
ejpam-6133	224	19	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	224	20	,	,	PUNCT
ejpam-6133	224	21	s̃m)ϖ(s̃i+1	s̃m)ϖ(s̃i+1	PROPN
ejpam-6133	224	22	,	,	PUNCT
ejpam-6133	224	23	s̃i+2)ψ	s̃i+2)ψ	PRON
ejpam-6133	224	24	i+1(ζ(s̃0	i+1(ζ(s̃0	ADJ
ejpam-6133	224	25	,	,	PUNCT
ejpam-6133	224	26	s̃1	s̃1	PROPN
ejpam-6133	224	27	)	)	PUNCT
ejpam-6133	224	28	)	)	PUNCT
ejpam-6133	225	1	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	225	2	,	,	PUNCT
ejpam-6133	225	3	s̃i+1)ψi(ζ(s̃0	s̃i+1)ψi(ζ(s̃0	PROPN
ejpam-6133	225	4	,	,	PUNCT
ejpam-6133	225	5	s̃1	s̃1	PROPN
ejpam-6133	225	6	)	)	PUNCT
ejpam-6133	225	7	)	)	PUNCT
ejpam-6133	226	1	=	=	PUNCT
ejpam-6133	226	2	2(2	2(2	NUM
ejpam-6133	227	1	+	+	CCONJ
ejpam-6133	227	2	s̃0)k	s̃0)k	PROPN
ejpam-6133	227	3	i+1ζ(s̃0	i+1ζ(s̃0	PROPN
ejpam-6133	227	4	,	,	PUNCT
ejpam-6133	227	5	s̃1	s̃1	PROPN
ejpam-6133	227	6	)	)	PUNCT
ejpam-6133	227	7	2.kiζ(s̃0	2.kiζ(s̃0	NUM
ejpam-6133	227	8	,	,	PUNCT
ejpam-6133	227	9	s̃1	s̃1	PROPN
ejpam-6133	227	10	)	)	PUNCT
ejpam-6133	227	11	≤	≤	NOUN
ejpam-6133	227	12	3k	3k	X
ejpam-6133	227	13	<	<	X
ejpam-6133	227	14	1	1	NUM
ejpam-6133	227	15	,	,	PUNCT
ejpam-6133	227	16	where	where	SCONJ
ejpam-6133	227	17	s̃i	s̃i	PROPN
ejpam-6133	227	18	=	=	SYM
ejpam-6133	227	19	⊤i(s̃0	⊤i(s̃0	PROPN
ejpam-6133	227	20	)	)	PUNCT
ejpam-6133	227	21	and	and	CCONJ
ejpam-6133	227	22	ψi(ζ(s̃0	ψi(ζ(s̃0	PROPN
ejpam-6133	227	23	,	,	PUNCT
ejpam-6133	227	24	s̃1	s̃1	PROPN
ejpam-6133	227	25	)	)	PUNCT
ejpam-6133	227	26	)	)	PUNCT
ejpam-6133	228	1	=	=	SYM
ejpam-6133	228	2	kiζ(s̃0	kiζ(s̃0	PROPN
ejpam-6133	228	3	,	,	PUNCT
ejpam-6133	228	4	s̃1	s̃1	PROPN
ejpam-6133	228	5	)	)	PUNCT
ejpam-6133	228	6	.	.	PUNCT
ejpam-6133	229	1	h.	h.	PROPN
ejpam-6133	229	2	aydi	aydi	PROPN
ejpam-6133	229	3	,	,	PUNCT
ejpam-6133	229	4	h.	h.	PROPN
ejpam-6133	229	5	hammouda	hammouda	PROPN
ejpam-6133	229	6	,	,	PUNCT
ejpam-6133	229	7	s.	s.	PROPN
ejpam-6133	229	8	mansour	mansour	PROPN
ejpam-6133	229	9	/	/	SYM
ejpam-6133	229	10	eur	eur	PROPN
ejpam-6133	229	11	.	.	PUNCT
ejpam-6133	230	1	j.	j.	PROPN
ejpam-6133	230	2	pure	pure	PROPN
ejpam-6133	230	3	appl	appl	PROPN
ejpam-6133	230	4	.	.	PROPN
ejpam-6133	230	5	math	math	PROPN
ejpam-6133	230	6	,	,	PUNCT
ejpam-6133	230	7	18	18	NUM
ejpam-6133	230	8	(	(	PUNCT
ejpam-6133	230	9	3	3	NUM
ejpam-6133	230	10	)	)	PUNCT
ejpam-6133	230	11	(	(	PUNCT
ejpam-6133	230	12	2025	2025	NUM
ejpam-6133	230	13	)	)	PUNCT
ejpam-6133	230	14	,	,	PUNCT
ejpam-6133	230	15	6133	6133	NUM
ejpam-6133	230	16	10	10	NUM
ejpam-6133	230	17	of	of	ADP
ejpam-6133	230	18	18	18	NUM
ejpam-6133	230	19	proposition	proposition	NOUN
ejpam-6133	230	20	2	2	NUM
ejpam-6133	230	21	.	.	PUNCT
ejpam-6133	231	1	if	if	SCONJ
ejpam-6133	231	2	we	we	PRON
ejpam-6133	231	3	replace	replace	VERB
ejpam-6133	231	4	the	the	DET
ejpam-6133	231	5	condition	condition	NOUN
ejpam-6133	231	6	(	(	PUNCT
ejpam-6133	231	7	u	u	NOUN
ejpam-6133	231	8	)	)	PUNCT
ejpam-6133	231	9	by	by	ADP
ejpam-6133	231	10	(	(	PUNCT
ejpam-6133	231	11	w	w	NOUN
ejpam-6133	231	12	)	)	PUNCT
ejpam-6133	231	13	:	:	PUNCT
ejpam-6133	231	14	∀µ	∀µ	PROPN
ejpam-6133	231	15	,	,	PUNCT
ejpam-6133	231	16	ν	ν	PROPN
ejpam-6133	231	17	∈	∈	PROPN
ejpam-6133	231	18	fix(⊤	fix(⊤	NOUN
ejpam-6133	231	19	)	)	PUNCT
ejpam-6133	231	20	,	,	PUNCT
ejpam-6133	231	21	there	there	PRON
ejpam-6133	231	22	is	be	VERB
ejpam-6133	231	23	δ	δ	PROPN
ejpam-6133	231	24	∈	∈	NOUN
ejpam-6133	231	25	℧	℧	PROPN
ejpam-6133	231	26	so	so	SCONJ
ejpam-6133	231	27	that	that	SCONJ
ejpam-6133	231	28	α(µ	α(µ	PROPN
ejpam-6133	231	29	,	,	PUNCT
ejpam-6133	231	30	δ	δ	PROPN
ejpam-6133	231	31	)	)	PUNCT
ejpam-6133	231	32	≥	≥	NOUN
ejpam-6133	231	33	1	1	NUM
ejpam-6133	231	34	and	and	CCONJ
ejpam-6133	231	35	α(ν	α(ν	PROPN
ejpam-6133	231	36	,	,	PUNCT
ejpam-6133	231	37	δ	δ	PROPN
ejpam-6133	231	38	)	)	PUNCT
ejpam-6133	231	39	≥	≥	NOUN
ejpam-6133	231	40	1	1	NUM
ejpam-6133	231	41	,	,	PUNCT
ejpam-6133	231	42	then	then	ADV
ejpam-6133	231	43	the	the	DET
ejpam-6133	231	44	map	map	NOUN
ejpam-6133	231	45	⊤	⊤	PROPN
ejpam-6133	231	46	has	have	VERB
ejpam-6133	231	47	a	a	DET
ejpam-6133	231	48	unique	unique	ADJ
ejpam-6133	231	49	fp	fp	NOUN
ejpam-6133	231	50	in	in	ADP
ejpam-6133	231	51	℧	℧	PROPN
ejpam-6133	231	52	.	.	PUNCT
ejpam-6133	231	53	proof	proof	NOUN
ejpam-6133	231	54	.	.	PUNCT
ejpam-6133	232	1	assume	assume	VERB
ejpam-6133	232	2	there	there	PRON
ejpam-6133	232	3	are	be	VERB
ejpam-6133	232	4	two	two	NUM
ejpam-6133	232	5	distinct	distinct	ADJ
ejpam-6133	232	6	fps	fps	NOUN
ejpam-6133	232	7	,	,	PUNCT
ejpam-6133	232	8	say	say	VERB
ejpam-6133	232	9	x	x	X
ejpam-6133	232	10	̸=	̸=	PROPN
ejpam-6133	232	11	y	y	PROPN
ejpam-6133	232	12	∈	∈	PROPN
ejpam-6133	232	13	℧	℧	PROPN
ejpam-6133	232	14	.	.	PUNCT
ejpam-6133	233	1	according	accord	VERB
ejpam-6133	233	2	to	to	ADP
ejpam-6133	233	3	(	(	PUNCT
ejpam-6133	233	4	w	w	PROPN
ejpam-6133	233	5	)	)	PUNCT
ejpam-6133	233	6	,	,	PUNCT
ejpam-6133	233	7	there	there	PRON
ejpam-6133	233	8	is	be	VERB
ejpam-6133	233	9	z	z	PROPN
ejpam-6133	233	10	∈	∈	PROPN
ejpam-6133	233	11	℧	℧	PROPN
ejpam-6133	233	12	,	,	PUNCT
ejpam-6133	233	13	so	so	SCONJ
ejpam-6133	233	14	that	that	SCONJ
ejpam-6133	233	15	α(x	α(x	NOUN
ejpam-6133	233	16	,	,	PUNCT
ejpam-6133	233	17	z	z	NOUN
ejpam-6133	233	18	)	)	PUNCT
ejpam-6133	233	19	≥	≥	NOUN
ejpam-6133	233	20	1	1	NUM
ejpam-6133	233	21	,	,	PUNCT
ejpam-6133	233	22	α(y	α(y	NOUN
ejpam-6133	233	23	,	,	PUNCT
ejpam-6133	233	24	z	z	NOUN
ejpam-6133	233	25	)	)	PUNCT
ejpam-6133	233	26	≥	≥	NOUN
ejpam-6133	233	27	1	1	NUM
ejpam-6133	233	28	.	.	PUNCT
ejpam-6133	234	1	the	the	DET
ejpam-6133	234	2	α	α	NOUN
ejpam-6133	234	3	-	-	PUNCT
ejpam-6133	234	4	admissibility	admissibility	NOUN
ejpam-6133	234	5	of	of	ADP
ejpam-6133	234	6	⊤	⊤	PROPN
ejpam-6133	234	7	yields	yield	NOUN
ejpam-6133	234	8	that	that	PRON
ejpam-6133	234	9	α(x,⊤ℓz	α(x,⊤ℓz	PROPN
ejpam-6133	234	10	)	)	PUNCT
ejpam-6133	234	11	≥	≥	NOUN
ejpam-6133	234	12	1	1	NUM
ejpam-6133	234	13	;	;	PUNCT
ejpam-6133	234	14	;	;	PUNCT
ejpam-6133	234	15	α(y,⊤ℓz	α(y,⊤ℓz	NUM
ejpam-6133	234	16	)	)	PUNCT
ejpam-6133	234	17	≥	≥	NOUN
ejpam-6133	234	18	1	1	NUM
ejpam-6133	234	19	;	;	PUNCT
ejpam-6133	234	20	∀ℓ	∀ℓ	PROPN
ejpam-6133	234	21	∈	∈	PROPN
ejpam-6133	234	22	n.	n.	NOUN
ejpam-6133	234	23	consider	consider	VERB
ejpam-6133	234	24	the	the	DET
ejpam-6133	234	25	sequence	sequence	NOUN
ejpam-6133	234	26	{	{	PUNCT
ejpam-6133	234	27	zℓ	zℓ	NOUN
ejpam-6133	234	28	}	}	PUNCT
ejpam-6133	234	29	∈	∈	PROPN
ejpam-6133	234	30	℧	℧	PROPN
ejpam-6133	234	31	defined	define	VERB
ejpam-6133	234	32	as	as	ADP
ejpam-6133	234	33	zℓ	zℓ	NOUN
ejpam-6133	234	34	=	=	SYM
ejpam-6133	234	35	⊤ℓz	⊤ℓz	NOUN
ejpam-6133	234	36	.	.	PUNCT
ejpam-6133	235	1	we	we	PRON
ejpam-6133	235	2	have	have	VERB
ejpam-6133	235	3	ζ(x	ζ(x	NOUN
ejpam-6133	235	4	,	,	PUNCT
ejpam-6133	235	5	zℓ+1	zℓ+1	NUM
ejpam-6133	235	6	)	)	PUNCT
ejpam-6133	235	7	=	=	SYM
ejpam-6133	235	8	ζ(⊤x,⊤zℓ	ζ(⊤x,⊤zℓ	PROPN
ejpam-6133	235	9	)	)	PUNCT
ejpam-6133	235	10	≤	≤	NOUN
ejpam-6133	235	11	α(x	α(x	NOUN
ejpam-6133	235	12	,	,	PUNCT
ejpam-6133	235	13	zℓ)ζ(⊤x,⊤zℓ	zℓ)ζ(⊤x,⊤zℓ	NUM
ejpam-6133	235	14	)	)	PUNCT
ejpam-6133	235	15	≤	≤	PUNCT
ejpam-6133	236	1	ψ(r(x	ψ(r(x	PROPN
ejpam-6133	236	2	,	,	PUNCT
ejpam-6133	236	3	zℓ	zℓ	NOUN
ejpam-6133	236	4	)	)	PUNCT
ejpam-6133	236	5	)	)	PUNCT
ejpam-6133	236	6	,	,	PUNCT
ejpam-6133	236	7	where	where	SCONJ
ejpam-6133	236	8	r(x	r(x	NOUN
ejpam-6133	236	9	,	,	PUNCT
ejpam-6133	236	10	zℓ	zℓ	NOUN
ejpam-6133	236	11	)	)	PUNCT
ejpam-6133	236	12	=	=	SYM
ejpam-6133	236	13	max{ζ(x	max{ζ(x	PROPN
ejpam-6133	236	14	,	,	PUNCT
ejpam-6133	236	15	zℓ	zℓ	NOUN
ejpam-6133	236	16	)	)	PUNCT
ejpam-6133	236	17	,	,	PUNCT
ejpam-6133	236	18	ζ(x,⊤x	ζ(x,⊤x	NOUN
ejpam-6133	236	19	)	)	PUNCT
ejpam-6133	236	20	,	,	PUNCT
ejpam-6133	236	21	ζ(zℓ,⊤zℓ	ζ(zℓ,⊤zℓ	NOUN
ejpam-6133	236	22	)	)	PUNCT
ejpam-6133	236	23	,	,	PUNCT
ejpam-6133	236	24	ζ(x,⊤x)[ϖ(x	ζ(x,⊤x)[ϖ(x	NOUN
ejpam-6133	236	25	,	,	PUNCT
ejpam-6133	236	26	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	27	,	,	PUNCT
ejpam-6133	236	28	zℓ)+ζ(zℓ,⊤zℓ	zℓ)+ζ(zℓ,⊤zℓ	NOUN
ejpam-6133	236	29	)	)	PUNCT
ejpam-6133	236	30	]	]	PUNCT
ejpam-6133	236	31	ϖ(x	ϖ(x	PROPN
ejpam-6133	236	32	,	,	PUNCT
ejpam-6133	236	33	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	34	,	,	PUNCT
ejpam-6133	236	35	zℓ)+ζ(x	zℓ)+ζ(x	NOUN
ejpam-6133	236	36	,	,	PUNCT
ejpam-6133	236	37	zℓ	zℓ	NUM
ejpam-6133	236	38	)	)	PUNCT
ejpam-6133	236	39	,	,	PUNCT
ejpam-6133	236	40	ζ(zℓ,⊤zℓ)[ϖ(x	ζ(zℓ,⊤zℓ)[ϖ(x	ADP
ejpam-6133	236	41	,	,	PUNCT
ejpam-6133	236	42	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	43	,	,	PUNCT
ejpam-6133	236	44	zℓ)+ζ(x,⊤x	zℓ)+ζ(x,⊤x	X
ejpam-6133	236	45	)	)	PUNCT
ejpam-6133	236	46	]	]	PUNCT
ejpam-6133	236	47	ϖ(x	ϖ(x	PROPN
ejpam-6133	236	48	,	,	PUNCT
ejpam-6133	236	49	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	50	,	,	PUNCT
ejpam-6133	236	51	zℓ)+ζ(x	zℓ)+ζ(x	NOUN
ejpam-6133	236	52	,	,	PUNCT
ejpam-6133	236	53	zℓ	zℓ	NOUN
ejpam-6133	236	54	)	)	PUNCT
ejpam-6133	236	55	}	}	PUNCT
ejpam-6133	236	56	=	=	SYM
ejpam-6133	236	57	max	max	X
ejpam-6133	236	58	{	{	PUNCT
ejpam-6133	236	59	ζ(x	ζ(x	NOUN
ejpam-6133	236	60	,	,	PUNCT
ejpam-6133	236	61	zℓ	zℓ	NOUN
ejpam-6133	236	62	)	)	PUNCT
ejpam-6133	236	63	,	,	PUNCT
ejpam-6133	236	64	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	236	65	,	,	PUNCT
ejpam-6133	236	66	zℓ+1	zℓ+1	NUM
ejpam-6133	236	67	)	)	PUNCT
ejpam-6133	236	68	,	,	PUNCT
ejpam-6133	236	69	ζ(zℓ,zℓ+1)ϖ(x	ζ(zℓ,zℓ+1)ϖ(x	PROPN
ejpam-6133	236	70	,	,	PUNCT
ejpam-6133	236	71	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	72	,	,	PUNCT
ejpam-6133	236	73	zℓ	zℓ	NUM
ejpam-6133	236	74	)	)	PUNCT
ejpam-6133	236	75	ϖ(x	ϖ(x	PROPN
ejpam-6133	236	76	,	,	PUNCT
ejpam-6133	236	77	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	236	78	,	,	PUNCT
ejpam-6133	236	79	zℓ)+ζ(x	zℓ)+ζ(x	NOUN
ejpam-6133	236	80	,	,	PUNCT
ejpam-6133	236	81	zℓ	zℓ	ADV
ejpam-6133	236	82	)	)	PUNCT
ejpam-6133	236	83	}	}	PUNCT
ejpam-6133	236	84	.	.	PUNCT
ejpam-6133	237	1	if	if	SCONJ
ejpam-6133	237	2	r(x	r(x	PROPN
ejpam-6133	237	3	,	,	PUNCT
ejpam-6133	237	4	zℓ	zℓ	VERB
ejpam-6133	237	5	)	)	PUNCT
ejpam-6133	237	6	=	=	SYM
ejpam-6133	237	7	ζ(zℓ,zℓ+1)ϖ(x	ζ(zℓ,zℓ+1)ϖ(x	PROPN
ejpam-6133	237	8	,	,	PUNCT
ejpam-6133	237	9	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	237	10	,	,	PUNCT
ejpam-6133	237	11	zℓ	zℓ	NUM
ejpam-6133	237	12	)	)	PUNCT
ejpam-6133	237	13	ϖ(x	ϖ(x	PROPN
ejpam-6133	237	14	,	,	PUNCT
ejpam-6133	237	15	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	237	16	,	,	PUNCT
ejpam-6133	237	17	zℓ)+ζ(x	zℓ)+ζ(x	NOUN
ejpam-6133	237	18	,	,	PUNCT
ejpam-6133	237	19	zℓ	zℓ	NOUN
ejpam-6133	237	20	)	)	PUNCT
ejpam-6133	237	21	for	for	ADP
ejpam-6133	237	22	some	some	DET
ejpam-6133	237	23	ℓ	ℓ	NOUN
ejpam-6133	237	24	,	,	PUNCT
ejpam-6133	237	25	then	then	ADV
ejpam-6133	237	26	ζ(x	ζ(x	NOUN
ejpam-6133	237	27	,	,	PUNCT
ejpam-6133	237	28	zℓ+1	zℓ+1	NUM
ejpam-6133	237	29	)	)	PUNCT
ejpam-6133	237	30	=	=	SYM
ejpam-6133	237	31	ζ(⊤x,⊤zℓ	ζ(⊤x,⊤zℓ	PROPN
ejpam-6133	237	32	)	)	PUNCT
ejpam-6133	237	33	≤	≤	NOUN
ejpam-6133	237	34	α(x	α(x	NOUN
ejpam-6133	237	35	,	,	PUNCT
ejpam-6133	237	36	zℓ)ζ(⊤x,⊤zℓ	zℓ)ζ(⊤x,⊤zℓ	NUM
ejpam-6133	237	37	)	)	PUNCT
ejpam-6133	237	38	≤	≤	PUNCT
ejpam-6133	237	39	ψ(r(x	ψ(r(x	PROPN
ejpam-6133	237	40	,	,	PUNCT
ejpam-6133	237	41	zℓ	zℓ	NOUN
ejpam-6133	237	42	)	)	PUNCT
ejpam-6133	237	43	)	)	PUNCT
ejpam-6133	238	1	<	<	X
ejpam-6133	238	2	r(x	r(x	PROPN
ejpam-6133	238	3	,	,	PUNCT
ejpam-6133	238	4	zℓ	zℓ	X
ejpam-6133	238	5	)	)	PUNCT
ejpam-6133	238	6	=	=	SYM
ejpam-6133	238	7	ζ(zℓ,zℓ+1)ϖ(x	ζ(zℓ,zℓ+1)ϖ(x	PROPN
ejpam-6133	238	8	,	,	PUNCT
ejpam-6133	238	9	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	238	10	,	,	PUNCT
ejpam-6133	238	11	zℓ	zℓ	NUM
ejpam-6133	238	12	)	)	PUNCT
ejpam-6133	238	13	ϖ(x	ϖ(x	PROPN
ejpam-6133	238	14	,	,	PUNCT
ejpam-6133	238	15	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	238	16	,	,	PUNCT
ejpam-6133	238	17	zℓ)+ζ(x	zℓ)+ζ(x	NOUN
ejpam-6133	238	18	,	,	PUNCT
ejpam-6133	238	19	zℓ	zℓ	NOUN
ejpam-6133	238	20	)	)	PUNCT
ejpam-6133	238	21	.	.	PUNCT
ejpam-6133	239	1	therefore	therefore	ADV
ejpam-6133	239	2	,	,	PUNCT
ejpam-6133	239	3	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	239	4	,	,	PUNCT
ejpam-6133	239	5	zℓ+1	zℓ+1	NUM
ejpam-6133	239	6	)	)	PUNCT
ejpam-6133	239	7	<	<	X
ejpam-6133	239	8	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	239	9	,	,	PUNCT
ejpam-6133	239	10	zℓ+1)ϖ(x	zℓ+1)ϖ(x	NUM
ejpam-6133	239	11	,	,	PUNCT
ejpam-6133	239	12	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	239	13	,	,	PUNCT
ejpam-6133	239	14	zℓ	zℓ	NUM
ejpam-6133	239	15	)	)	PUNCT
ejpam-6133	239	16	ϖ(x	ϖ(x	PROPN
ejpam-6133	239	17	,	,	PUNCT
ejpam-6133	239	18	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	239	19	,	,	PUNCT
ejpam-6133	239	20	zℓ	zℓ	X
ejpam-6133	239	21	)	)	PUNCT
ejpam-6133	239	22	+	+	CCONJ
ejpam-6133	239	23	ζ(x	ζ(x	NOUN
ejpam-6133	239	24	,	,	PUNCT
ejpam-6133	239	25	zℓ	zℓ	NOUN
ejpam-6133	239	26	)	)	PUNCT
ejpam-6133	239	27	.	.	PUNCT
ejpam-6133	240	1	that	that	PRON
ejpam-6133	240	2	is	be	AUX
ejpam-6133	240	3	,	,	PUNCT
ejpam-6133	240	4	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	240	5	,	,	PUNCT
ejpam-6133	240	6	zℓ+1)ϖ(x	zℓ+1)ϖ(x	NUM
ejpam-6133	240	7	,	,	PUNCT
ejpam-6133	240	8	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	240	9	,	,	PUNCT
ejpam-6133	240	10	zℓ	zℓ	X
ejpam-6133	240	11	)	)	PUNCT
ejpam-6133	241	1	+	+	CCONJ
ejpam-6133	241	2	ζ(zℓ	ζ(zℓ	NOUN
ejpam-6133	241	3	,	,	PUNCT
ejpam-6133	241	4	zℓ+1)ζ(x	zℓ+1)ζ(x	NUM
ejpam-6133	241	5	,	,	PUNCT
ejpam-6133	241	6	zℓ	zℓ	NUM
ejpam-6133	241	7	)	)	PUNCT
ejpam-6133	241	8	<	<	X
ejpam-6133	241	9	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	241	10	,	,	PUNCT
ejpam-6133	241	11	zℓ+1)ϖ(x	zℓ+1)ϖ(x	NUM
ejpam-6133	241	12	,	,	PUNCT
ejpam-6133	241	13	zℓ)ϵ(x	zℓ)ϵ(x	NOUN
ejpam-6133	241	14	,	,	PUNCT
ejpam-6133	241	15	zℓ	zℓ	NUM
ejpam-6133	241	16	)	)	PUNCT
ejpam-6133	241	17	.	.	PUNCT
ejpam-6133	242	1	thus	thus	ADV
ejpam-6133	242	2	,	,	PUNCT
ejpam-6133	242	3	ζ(zℓ	ζ(zℓ	PRON
ejpam-6133	242	4	,	,	PUNCT
ejpam-6133	242	5	zℓ+1)ζ(x	zℓ+1)ζ(x	NUM
ejpam-6133	242	6	,	,	PUNCT
ejpam-6133	242	7	zℓ	zℓ	X
ejpam-6133	242	8	)	)	PUNCT
ejpam-6133	242	9	<	<	X
ejpam-6133	242	10	0	0	NUM
ejpam-6133	242	11	,	,	PUNCT
ejpam-6133	242	12	witch	witch	NOUN
ejpam-6133	242	13	is	be	AUX
ejpam-6133	242	14	a	a	DET
ejpam-6133	242	15	contradiction	contradiction	NOUN
ejpam-6133	242	16	.	.	PUNCT
ejpam-6133	243	1	we	we	PRON
ejpam-6133	243	2	have	have	VERB
ejpam-6133	243	3	r(x	r(x	PROPN
ejpam-6133	243	4	,	,	PUNCT
ejpam-6133	243	5	zℓ	zℓ	X
ejpam-6133	243	6	)	)	PUNCT
ejpam-6133	243	7	=	=	SYM
ejpam-6133	243	8	max{ζ(x	max{ζ(x	PROPN
ejpam-6133	243	9	,	,	PUNCT
ejpam-6133	243	10	zℓ	zℓ	NOUN
ejpam-6133	243	11	)	)	PUNCT
ejpam-6133	243	12	,	,	PUNCT
ejpam-6133	243	13	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	243	14	,	,	PUNCT
ejpam-6133	243	15	zℓ+1	zℓ+1	NOUN
ejpam-6133	243	16	)	)	PUNCT
ejpam-6133	243	17	}	}	PUNCT
ejpam-6133	243	18	.	.	PUNCT
ejpam-6133	244	1	h.	h.	PROPN
ejpam-6133	244	2	aydi	aydi	PROPN
ejpam-6133	244	3	,	,	PUNCT
ejpam-6133	244	4	h.	h.	PROPN
ejpam-6133	244	5	hammouda	hammouda	PROPN
ejpam-6133	244	6	,	,	PUNCT
ejpam-6133	244	7	s.	s.	PROPN
ejpam-6133	244	8	mansour	mansour	PROPN
ejpam-6133	244	9	/	/	SYM
ejpam-6133	244	10	eur	eur	PROPN
ejpam-6133	244	11	.	.	PUNCT
ejpam-6133	245	1	j.	j.	PROPN
ejpam-6133	245	2	pure	pure	PROPN
ejpam-6133	245	3	appl	appl	PROPN
ejpam-6133	245	4	.	.	PROPN
ejpam-6133	245	5	math	math	PROPN
ejpam-6133	245	6	,	,	PUNCT
ejpam-6133	245	7	18	18	NUM
ejpam-6133	245	8	(	(	PUNCT
ejpam-6133	245	9	3	3	NUM
ejpam-6133	245	10	)	)	PUNCT
ejpam-6133	245	11	(	(	PUNCT
ejpam-6133	245	12	2025	2025	NUM
ejpam-6133	245	13	)	)	PUNCT
ejpam-6133	245	14	,	,	PUNCT
ejpam-6133	245	15	6133	6133	NUM
ejpam-6133	245	16	11	11	NUM
ejpam-6133	245	17	of	of	ADP
ejpam-6133	245	18	18	18	NUM
ejpam-6133	245	19	that	that	PRON
ejpam-6133	245	20	is	be	AUX
ejpam-6133	245	21	,	,	PUNCT
ejpam-6133	245	22	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	245	23	,	,	PUNCT
ejpam-6133	245	24	zℓ+1	zℓ+1	NOUN
ejpam-6133	245	25	)	)	PUNCT
ejpam-6133	245	26	≤	≤	NUM
ejpam-6133	245	27	ψℓ(ζ(z,⊤z	ψℓ(ζ(z,⊤z	NOUN
ejpam-6133	245	28	)	)	PUNCT
ejpam-6133	245	29	)	)	PUNCT
ejpam-6133	245	30	.	.	PUNCT
ejpam-6133	246	1	then	then	ADV
ejpam-6133	246	2	lim	lim	PROPN
ejpam-6133	246	3	ℓ→+∞	ℓ→+∞	PROPN
ejpam-6133	246	4	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	246	5	,	,	PUNCT
ejpam-6133	246	6	zℓ+1	zℓ+1	NUM
ejpam-6133	246	7	)	)	PUNCT
ejpam-6133	246	8	=	=	SYM
ejpam-6133	247	1	0	0	X
ejpam-6133	247	2	.	.	PUNCT
ejpam-6133	248	1	so	so	ADV
ejpam-6133	248	2	for	for	ADP
ejpam-6133	248	3	all	all	DET
ejpam-6133	248	4	δ	δ	PROPN
ejpam-6133	248	5	>	>	X
ejpam-6133	248	6	0	0	PROPN
ejpam-6133	248	7	,	,	PUNCT
ejpam-6133	248	8	there	there	PRON
ejpam-6133	248	9	is	be	VERB
ejpam-6133	248	10	ℓ0	ℓ0	PROPN
ejpam-6133	248	11	∈	∈	PROPN
ejpam-6133	248	12	n	n	PRON
ejpam-6133	248	13	such	such	ADJ
ejpam-6133	248	14	that	that	PRON
ejpam-6133	248	15	for	for	ADP
ejpam-6133	248	16	all	all	DET
ejpam-6133	248	17	ℓ	ℓ	PROPN
ejpam-6133	248	18	≥	≥	NUM
ejpam-6133	248	19	ℓ0	ℓ0	ADV
ejpam-6133	248	20	,	,	PUNCT
ejpam-6133	248	21	ζ(zℓ	ζ(zℓ	PROPN
ejpam-6133	248	22	,	,	PUNCT
ejpam-6133	248	23	zℓ+1	zℓ+1	NUM
ejpam-6133	248	24	)	)	PUNCT
ejpam-6133	248	25	<	<	X
ejpam-6133	248	26	δ	δ	PROPN
ejpam-6133	248	27	.	.	PUNCT
ejpam-6133	249	1	now	now	ADV
ejpam-6133	249	2	,	,	PUNCT
ejpam-6133	249	3	we	we	PRON
ejpam-6133	249	4	show	show	VERB
ejpam-6133	249	5	that	that	SCONJ
ejpam-6133	249	6	lim	lim	PROPN
ejpam-6133	249	7	ℓ→+∞	ℓ→+∞	ADP
ejpam-6133	249	8	ζ(x	ζ(x	NOUN
ejpam-6133	249	9	,	,	PUNCT
ejpam-6133	249	10	zℓ	zℓ	X
ejpam-6133	249	11	)	)	PUNCT
ejpam-6133	249	12	=	=	SYM
ejpam-6133	249	13	0	0	X
ejpam-6133	249	14	.	.	PUNCT
ejpam-6133	249	15	suppose	suppose	VERB
ejpam-6133	249	16	on	on	ADP
ejpam-6133	249	17	the	the	DET
ejpam-6133	249	18	contrary	contrary	NOUN
ejpam-6133	249	19	that	that	PRON
ejpam-6133	249	20	lim	lim	PROPN
ejpam-6133	249	21	ℓ→+∞	ℓ→+∞	ADP
ejpam-6133	249	22	ζ(x	ζ(x	NOUN
ejpam-6133	249	23	,	,	PUNCT
ejpam-6133	249	24	zℓ	zℓ	X
ejpam-6133	249	25	)	)	PUNCT
ejpam-6133	249	26	̸=	̸=	PROPN
ejpam-6133	249	27	0	0	NUM
ejpam-6133	249	28	,	,	PUNCT
ejpam-6133	249	29	then	then	ADV
ejpam-6133	249	30	there	there	PRON
ejpam-6133	249	31	exists	exist	VERB
ejpam-6133	249	32	a	a	DET
ejpam-6133	249	33	subsequence	subsequence	NOUN
ejpam-6133	249	34	{	{	PUNCT
ejpam-6133	249	35	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	249	36	)	)	PUNCT
ejpam-6133	249	37	}	}	PUNCT
ejpam-6133	249	38	of	of	ADP
ejpam-6133	249	39	{	{	PUNCT
ejpam-6133	249	40	zℓ	zℓ	NOUN
ejpam-6133	249	41	}	}	PUNCT
ejpam-6133	249	42	such	such	ADJ
ejpam-6133	249	43	that	that	SCONJ
ejpam-6133	249	44	φ(ℓ	φ(ℓ	PROPN
ejpam-6133	249	45	)	)	PUNCT
ejpam-6133	249	46	>	>	X
ejpam-6133	249	47	n	n	CCONJ
ejpam-6133	249	48	;	;	PUNCT
ejpam-6133	249	49	ζ(x	ζ(x	NOUN
ejpam-6133	249	50	,	,	PUNCT
ejpam-6133	249	51	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	249	52	)	)	PUNCT
ejpam-6133	249	53	)	)	PUNCT
ejpam-6133	249	54	≥	≥	PROPN
ejpam-6133	250	1	δ	δ	PROPN
ejpam-6133	250	2	.	.	PUNCT
ejpam-6133	251	1	so	so	ADV
ejpam-6133	251	2	for	for	ADP
ejpam-6133	251	3	all	all	DET
ejpam-6133	251	4	ℓ	ℓ	NOUN
ejpam-6133	251	5	≥	≥	NOUN
ejpam-6133	251	6	ℓ0	ℓ0	INTJ
ejpam-6133	251	7	we	we	PRON
ejpam-6133	251	8	have	have	VERB
ejpam-6133	251	9	φ(ℓ	φ(ℓ	PROPN
ejpam-6133	251	10	)	)	PUNCT
ejpam-6133	252	1	>	>	PUNCT
ejpam-6133	252	2	ℓ	ℓ	PROPN
ejpam-6133	252	3	≥	≥	NUM
ejpam-6133	253	1	ℓ0	ℓ0	ADV
ejpam-6133	253	2	and	and	CCONJ
ejpam-6133	253	3	then	then	ADV
ejpam-6133	253	4	{	{	PUNCT
ejpam-6133	253	5	ζ(zφ(ℓ	ζ(zφ(ℓ	NOUN
ejpam-6133	253	6	)	)	PUNCT
ejpam-6133	253	7	,	,	PUNCT
ejpam-6133	253	8	zφ(ℓ)+1	zφ(ℓ)+1	NUM
ejpam-6133	253	9	)	)	PUNCT
ejpam-6133	253	10	<	<	X
ejpam-6133	253	11	δ	δ	PROPN
ejpam-6133	253	12	ζ(x	ζ(x	NOUN
ejpam-6133	253	13	,	,	PUNCT
ejpam-6133	253	14	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	253	15	)	)	PUNCT
ejpam-6133	253	16	)	)	PUNCT
ejpam-6133	254	1	≥	≥	PROPN
ejpam-6133	255	1	δ	δ	X
ejpam-6133	255	2	.	.	PUNCT
ejpam-6133	256	1	hence	hence	ADV
ejpam-6133	256	2	,	,	PUNCT
ejpam-6133	256	3	for	for	ADP
ejpam-6133	256	4	all	all	DET
ejpam-6133	256	5	ℓ	ℓ	PROPN
ejpam-6133	256	6	≥	≥	NUM
ejpam-6133	256	7	ℓ0	ℓ0	PROPN
ejpam-6133	256	8	,	,	PUNCT
ejpam-6133	256	9	r(x	r(x	PROPN
ejpam-6133	256	10	,	,	PUNCT
ejpam-6133	256	11	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	256	12	)	)	PUNCT
ejpam-6133	256	13	)	)	PUNCT
ejpam-6133	257	1	=	=	PUNCT
ejpam-6133	257	2	ζ(x	ζ(x	NOUN
ejpam-6133	257	3	,	,	PUNCT
ejpam-6133	257	4	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	257	5	)	)	PUNCT
ejpam-6133	257	6	)	)	PUNCT
ejpam-6133	257	7	.	.	PUNCT
ejpam-6133	258	1	also	also	ADV
ejpam-6133	258	2	,	,	PUNCT
ejpam-6133	258	3	we	we	PRON
ejpam-6133	258	4	have	have	VERB
ejpam-6133	258	5	for	for	ADP
ejpam-6133	258	6	all	all	DET
ejpam-6133	258	7	ℓ	ℓ	PROPN
ejpam-6133	258	8	≥	≥	NOUN
ejpam-6133	258	9	ℓ0	ℓ0	ADV
ejpam-6133	258	10	,	,	PUNCT
ejpam-6133	258	11	ζ(x	ζ(x	NOUN
ejpam-6133	258	12	,	,	PUNCT
ejpam-6133	258	13	zφ(ℓ)+1	zφ(ℓ)+1	NOUN
ejpam-6133	258	14	)	)	PUNCT
ejpam-6133	258	15	=	=	PUNCT
ejpam-6133	258	16	ζ(⊤x,⊤zφ(ℓ	ζ(⊤x,⊤zφ(ℓ	NUM
ejpam-6133	258	17	)	)	PUNCT
ejpam-6133	258	18	)	)	PUNCT
ejpam-6133	258	19	≤	≤	NUM
ejpam-6133	258	20	α(x	α(x	NOUN
ejpam-6133	258	21	,	,	PUNCT
ejpam-6133	258	22	zφ(ℓ))ζ(⊤x,⊤zφ(ℓ	zφ(ℓ))ζ(⊤x,⊤zφ(ℓ	PROPN
ejpam-6133	258	23	)	)	PUNCT
ejpam-6133	258	24	)	)	PUNCT
ejpam-6133	258	25	≤	≤	PROPN
ejpam-6133	259	1	ψ(ζ(x	ψ(ζ(x	PROPN
ejpam-6133	259	2	,	,	PUNCT
ejpam-6133	259	3	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	259	4	)	)	PUNCT
ejpam-6133	259	5	)	)	PUNCT
ejpam-6133	259	6	)	)	PUNCT
ejpam-6133	259	7	.	.	PUNCT
ejpam-6133	259	8	.	.	PUNCT
ejpam-6133	259	9	.	.	PUNCT
ejpam-6133	260	1	≤	≤	NOUN
ejpam-6133	260	2	ψφ(ℓ)−ℓ0(ζ(x	ψφ(ℓ)−ℓ0(ζ(x	NOUN
ejpam-6133	260	3	,	,	PUNCT
ejpam-6133	260	4	zℓ0	zℓ0	NOUN
ejpam-6133	260	5	)	)	PUNCT
ejpam-6133	260	6	)	)	PUNCT
ejpam-6133	260	7	.	.	PUNCT
ejpam-6133	261	1	letting	let	VERB
ejpam-6133	261	2	ℓ	ℓ	NOUN
ejpam-6133	261	3	−→	−→	NOUN
ejpam-6133	261	4	+	+	NOUN
ejpam-6133	261	5	∞	∞	NOUN
ejpam-6133	261	6	we	we	PRON
ejpam-6133	261	7	deduce	deduce	VERB
ejpam-6133	261	8	that	that	SCONJ
ejpam-6133	261	9	lim	lim	PROPN
ejpam-6133	261	10	ℓ→+∞	ℓ→+∞	ADP
ejpam-6133	261	11	ζ(x	ζ(x	NOUN
ejpam-6133	261	12	,	,	PUNCT
ejpam-6133	261	13	zφ(ℓ)+1	zφ(ℓ)+1	NUM
ejpam-6133	261	14	)	)	PUNCT
ejpam-6133	261	15	=	=	PUNCT
ejpam-6133	262	1	0	0	X
ejpam-6133	262	2	.	.	PUNCT
ejpam-6133	263	1	so	so	ADV
ejpam-6133	263	2	for	for	ADP
ejpam-6133	263	3	all	all	DET
ejpam-6133	263	4	ℓ	ℓ	NOUN
ejpam-6133	263	5	≥	≥	NOUN
ejpam-6133	263	6	ℓ0	ℓ0	ADV
ejpam-6133	263	7	and	and	CCONJ
ejpam-6133	263	8	by	by	ADP
ejpam-6133	263	9	triangle	triangle	NOUN
ejpam-6133	263	10	inequality	inequality	NOUN
ejpam-6133	263	11	,	,	PUNCT
ejpam-6133	263	12	we	we	PRON
ejpam-6133	263	13	obtain	obtain	VERB
ejpam-6133	263	14	δ	δ	NOUN
ejpam-6133	263	15	≤	≤	ADJ
ejpam-6133	263	16	ζ(x	ζ(x	NOUN
ejpam-6133	263	17	,	,	PUNCT
ejpam-6133	263	18	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	263	19	)	)	PUNCT
ejpam-6133	263	20	)	)	PUNCT
ejpam-6133	264	1	≤	≤	NUM
ejpam-6133	264	2	ϖ(x	ϖ(x	PUNCT
ejpam-6133	264	3	,	,	PUNCT
ejpam-6133	264	4	zφ(ℓ)+1)ζ(x	zφ(ℓ)+1)ζ(x	NOUN
ejpam-6133	264	5	,	,	PUNCT
ejpam-6133	264	6	zφ(ℓ)+1	zφ(ℓ)+1	NOUN
ejpam-6133	264	7	)	)	PUNCT
ejpam-6133	265	1	+	+	CCONJ
ejpam-6133	265	2	ϵ(zφ(ℓ)+1	ϵ(zφ(ℓ)+1	NOUN
ejpam-6133	265	3	,	,	PUNCT
ejpam-6133	265	4	zφ(ℓ))ζ(zφ(ℓ)+1	zφ(ℓ))ζ(zφ(ℓ)+1	NOUN
ejpam-6133	265	5	,	,	PUNCT
ejpam-6133	265	6	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	265	7	)	)	PUNCT
ejpam-6133	265	8	)	)	PUNCT
ejpam-6133	265	9	.	.	PUNCT
ejpam-6133	266	1	when	when	SCONJ
ejpam-6133	266	2	ℓ	ℓ	X
ejpam-6133	266	3	−→	−→	NOUN
ejpam-6133	266	4	+	+	PROPN
ejpam-6133	266	5	∞	∞	PROPN
ejpam-6133	266	6	,	,	PUNCT
ejpam-6133	266	7	one	one	PRON
ejpam-6133	266	8	finds	find	VERB
ejpam-6133	266	9	δ	δ	PROPN
ejpam-6133	266	10	≤	≤	PROPN
ejpam-6133	266	11	lim	lim	PROPN
ejpam-6133	266	12	ℓ→+∞	ℓ→+∞	ADP
ejpam-6133	266	13	ζ(x	ζ(x	NOUN
ejpam-6133	266	14	,	,	PUNCT
ejpam-6133	266	15	zφ(ℓ	zφ(ℓ	NUM
ejpam-6133	266	16	)	)	PUNCT
ejpam-6133	266	17	)	)	PUNCT
ejpam-6133	267	1	=	=	PUNCT
ejpam-6133	267	2	0	0	X
ejpam-6133	267	3	.	.	PUNCT
ejpam-6133	268	1	it	it	PRON
ejpam-6133	268	2	is	be	AUX
ejpam-6133	268	3	a	a	DET
ejpam-6133	268	4	contradiction	contradiction	NOUN
ejpam-6133	268	5	.	.	PUNCT
ejpam-6133	269	1	therefore	therefore	ADV
ejpam-6133	269	2	,	,	PUNCT
ejpam-6133	269	3	lim	lim	PROPN
ejpam-6133	269	4	ℓ→+∞	ℓ→+∞	VERB
ejpam-6133	269	5	ζ(x	ζ(x	NOUN
ejpam-6133	269	6	,	,	PUNCT
ejpam-6133	269	7	zℓ	zℓ	X
ejpam-6133	269	8	)	)	PUNCT
ejpam-6133	269	9	=	=	SYM
ejpam-6133	269	10	0	0	X
ejpam-6133	269	11	.	.	PUNCT
ejpam-6133	270	1	similarly	similarly	ADV
ejpam-6133	270	2	,	,	PUNCT
ejpam-6133	270	3	lim	lim	PROPN
ejpam-6133	270	4	ℓ→+∞	ℓ→+∞	VERB
ejpam-6133	270	5	ζ(y	ζ(y	PRON
ejpam-6133	270	6	,	,	PUNCT
ejpam-6133	270	7	zℓ	zℓ	X
ejpam-6133	270	8	)	)	PUNCT
ejpam-6133	270	9	=	=	SYM
ejpam-6133	271	1	0	0	X
ejpam-6133	271	2	.	.	PUNCT
ejpam-6133	272	1	by	by	ADP
ejpam-6133	272	2	uniqueness	uniqueness	NOUN
ejpam-6133	272	3	of	of	ADP
ejpam-6133	272	4	the	the	DET
ejpam-6133	272	5	limit	limit	NOUN
ejpam-6133	272	6	,	,	PUNCT
ejpam-6133	272	7	we	we	PRON
ejpam-6133	272	8	have	have	VERB
ejpam-6133	272	9	x	x	X
ejpam-6133	272	10	=	=	SYM
ejpam-6133	272	11	y.	y.	NOUN
ejpam-6133	272	12	4	4	NUM
ejpam-6133	272	13	.	.	PUNCT
ejpam-6133	273	1	applications	application	NOUN
ejpam-6133	273	2	using	use	VERB
ejpam-6133	273	3	theorem	theorem	NOUN
ejpam-6133	273	4	1	1	NUM
ejpam-6133	273	5	,	,	PUNCT
ejpam-6133	273	6	we	we	PRON
ejpam-6133	273	7	will	will	AUX
ejpam-6133	273	8	establish	establish	VERB
ejpam-6133	273	9	in	in	ADP
ejpam-6133	273	10	this	this	DET
ejpam-6133	273	11	section	section	NOUN
ejpam-6133	273	12	an	an	DET
ejpam-6133	273	13	existence	existence	NOUN
ejpam-6133	273	14	result	result	NOUN
ejpam-6133	273	15	of	of	ADP
ejpam-6133	273	16	a	a	DET
ejpam-6133	273	17	solution	solution	NOUN
ejpam-6133	273	18	of	of	ADP
ejpam-6133	273	19	the	the	DET
ejpam-6133	273	20	following	following	ADJ
ejpam-6133	273	21	nonlinear	nonlinear	ADJ
ejpam-6133	273	22	fredholm	fredholm	NOUN
ejpam-6133	273	23	type	type	NOUN
ejpam-6133	273	24	functional	functional	ADJ
ejpam-6133	273	25	integral	integral	ADJ
ejpam-6133	273	26	equation	equation	NOUN
ejpam-6133	273	27	x(t	x(t	PROPN
ejpam-6133	273	28	)	)	PUNCT
ejpam-6133	274	1	=	=	SYM
ejpam-6133	274	2	f(t	f(t	NOUN
ejpam-6133	274	3	)	)	PUNCT
ejpam-6133	275	1	+	+	NUM
ejpam-6133	275	2	λ	λ	PROPN
ejpam-6133	275	3	∫	∫	PROPN
ejpam-6133	275	4	τ2	τ2	PROPN
ejpam-6133	275	5	τ1	τ1	PROPN
ejpam-6133	275	6	k	k	PROPN
ejpam-6133	275	7	(	(	PUNCT
ejpam-6133	275	8	t	t	PROPN
ejpam-6133	275	9	,	,	PUNCT
ejpam-6133	275	10	r	r	NOUN
ejpam-6133	275	11	,	,	PUNCT
ejpam-6133	275	12	x(r	x(r	PROPN
ejpam-6133	275	13	)	)	PUNCT
ejpam-6133	275	14	,	,	PUNCT
ejpam-6133	275	15	x(g(r	x(g(r	PROPN
ejpam-6133	275	16	)	)	PUNCT
ejpam-6133	275	17	)	)	PUNCT
ejpam-6133	275	18	,	,	PUNCT
ejpam-6133	275	19	x(τ1	x(τ1	PROPN
ejpam-6133	275	20	)	)	PUNCT
ejpam-6133	275	21	,	,	PUNCT
ejpam-6133	275	22	x(τ2	x(τ2	NUM
ejpam-6133	275	23	)	)	PUNCT
ejpam-6133	275	24	)	)	PUNCT
ejpam-6133	276	1	dr	dr	PROPN
ejpam-6133	276	2	,	,	PUNCT
ejpam-6133	276	3	(	(	PUNCT
ejpam-6133	276	4	7	7	X
ejpam-6133	276	5	)	)	PUNCT
ejpam-6133	276	6	h.	h.	NOUN
ejpam-6133	276	7	aydi	aydi	PROPN
ejpam-6133	276	8	,	,	PUNCT
ejpam-6133	276	9	h.	h.	PROPN
ejpam-6133	276	10	hammouda	hammouda	PROPN
ejpam-6133	276	11	,	,	PUNCT
ejpam-6133	276	12	s.	s.	PROPN
ejpam-6133	276	13	mansour	mansour	PROPN
ejpam-6133	276	14	/	/	SYM
ejpam-6133	276	15	eur	eur	PROPN
ejpam-6133	276	16	.	.	PUNCT
ejpam-6133	277	1	j.	j.	PROPN
ejpam-6133	277	2	pure	pure	PROPN
ejpam-6133	277	3	appl	appl	PROPN
ejpam-6133	277	4	.	.	PROPN
ejpam-6133	277	5	math	math	PROPN
ejpam-6133	277	6	,	,	PUNCT
ejpam-6133	277	7	18	18	NUM
ejpam-6133	277	8	(	(	PUNCT
ejpam-6133	277	9	3	3	NUM
ejpam-6133	277	10	)	)	PUNCT
ejpam-6133	277	11	(	(	PUNCT
ejpam-6133	277	12	2025	2025	NUM
ejpam-6133	277	13	)	)	PUNCT
ejpam-6133	277	14	,	,	PUNCT
ejpam-6133	277	15	6133	6133	NUM
ejpam-6133	277	16	12	12	NUM
ejpam-6133	277	17	of	of	ADP
ejpam-6133	277	18	18	18	NUM
ejpam-6133	277	19	where	where	SCONJ
ejpam-6133	277	20	τ1	τ1	NOUN
ejpam-6133	277	21	,	,	PUNCT
ejpam-6133	277	22	τ2	τ2	NOUN
ejpam-6133	277	23	∈	∈	NOUN
ejpam-6133	277	24	r	r	NOUN
ejpam-6133	277	25	with	with	ADP
ejpam-6133	277	26	τ1	τ1	NOUN
ejpam-6133	277	27	<	<	X
ejpam-6133	277	28	τ2	τ2	PROPN
ejpam-6133	277	29	,	,	PUNCT
ejpam-6133	277	30	k	k	PROPN
ejpam-6133	277	31	∈	∈	PROPN
ejpam-6133	277	32	c([τ1	c([τ1	PROPN
ejpam-6133	277	33	,	,	PUNCT
ejpam-6133	277	34	τ2	τ2	PROPN
ejpam-6133	277	35	]	]	PUNCT
ejpam-6133	277	36	×	×	NOUN
ejpam-6133	278	1	[	[	X
ejpam-6133	278	2	τ1	τ1	NOUN
ejpam-6133	278	3	,	,	PUNCT
ejpam-6133	278	4	τ2	τ2	PROPN
ejpam-6133	278	5	]	]	PUNCT
ejpam-6133	278	6	×	×	NOUN
ejpam-6133	278	7	r4	r4	NOUN
ejpam-6133	278	8	)	)	PUNCT
ejpam-6133	278	9	,	,	PUNCT
ejpam-6133	278	10	g	g	PROPN
ejpam-6133	278	11	∈	∈	PROPN
ejpam-6133	278	12	c([τ1	c([τ1	NOUN
ejpam-6133	278	13	,	,	PUNCT
ejpam-6133	278	14	τ2	τ2	PROPN
ejpam-6133	278	15	]	]	PUNCT
ejpam-6133	278	16	×	×	NOUN
ejpam-6133	279	1	[	[	X
ejpam-6133	279	2	τ1	τ1	NOUN
ejpam-6133	279	3	,	,	PUNCT
ejpam-6133	279	4	τ2	τ2	PROPN
ejpam-6133	279	5	]	]	PUNCT
ejpam-6133	279	6	)	)	PUNCT
ejpam-6133	279	7	and	and	CCONJ
ejpam-6133	279	8	f	f	PROPN
ejpam-6133	279	9	∈	∈	PROPN
ejpam-6133	279	10	c([τ1	c([τ1	PROPN
ejpam-6133	279	11	,	,	PUNCT
ejpam-6133	279	12	τ2	τ2	PROPN
ejpam-6133	279	13	]	]	PUNCT
ejpam-6133	279	14	)	)	PUNCT
ejpam-6133	279	15	are	be	AUX
ejpam-6133	279	16	given	give	VERB
ejpam-6133	279	17	functions	function	NOUN
ejpam-6133	279	18	and	and	CCONJ
ejpam-6133	279	19	x	x	PUNCT
ejpam-6133	279	20	∈	∈	PROPN
ejpam-6133	279	21	c[τ1	c[τ1	NOUN
ejpam-6133	279	22	,	,	PUNCT
ejpam-6133	279	23	τ2	τ2	PROPN
ejpam-6133	279	24	]	]	PUNCT
ejpam-6133	279	25	is	be	AUX
ejpam-6133	279	26	an	an	DET
ejpam-6133	279	27	unknown	unknown	ADJ
ejpam-6133	279	28	function	function	NOUN
ejpam-6133	279	29	.	.	PUNCT
ejpam-6133	280	1	take	take	VERB
ejpam-6133	280	2	℧	℧	NOUN
ejpam-6133	280	3	=	=	SYM
ejpam-6133	280	4	c([τ1	c([τ1	PROPN
ejpam-6133	280	5	,	,	PUNCT
ejpam-6133	280	6	τ2	τ2	PROPN
ejpam-6133	280	7	]	]	PUNCT
ejpam-6133	280	8	)	)	PUNCT
ejpam-6133	280	9	.	.	PUNCT
ejpam-6133	281	1	given	give	VERB
ejpam-6133	281	2	ζ	ζ	NOUN
ejpam-6133	281	3	:	:	PUNCT
ejpam-6133	281	4	℧	℧	PROPN
ejpam-6133	281	5	×	×	NOUN
ejpam-6133	281	6	℧	℧	X
ejpam-6133	281	7	−→	−→	NOUN
ejpam-6133	281	8	[	[	X
ejpam-6133	281	9	0,+∞	0,+∞	NUM
ejpam-6133	281	10	)	)	PUNCT
ejpam-6133	281	11	as	as	ADP
ejpam-6133	281	12	ζ(µ	ζ(µ	PROPN
ejpam-6133	281	13	,	,	PUNCT
ejpam-6133	281	14	ν	ν	X
ejpam-6133	281	15	)	)	PUNCT
ejpam-6133	281	16	=	=	SYM
ejpam-6133	281	17	sup	sup	NOUN
ejpam-6133	281	18	t∈[τ1,τ2	t∈[τ1,τ2	PROPN
ejpam-6133	281	19	]	]	PUNCT
ejpam-6133	281	20	|µ(t)−	|µ(t)−	PROPN
ejpam-6133	281	21	ν(t)|p	ν(t)|p	PROPN
ejpam-6133	281	22	,	,	PUNCT
ejpam-6133	281	23	∀µ	∀µ	PROPN
ejpam-6133	281	24	,	,	PUNCT
ejpam-6133	281	25	ν	ν	X
ejpam-6133	281	26	∈	∈	PROPN
ejpam-6133	281	27	℧	℧	PROPN
ejpam-6133	281	28	.	.	PUNCT
ejpam-6133	282	1	then	then	ADV
ejpam-6133	282	2	(	(	PUNCT
ejpam-6133	282	3	℧	℧	PROPN
ejpam-6133	282	4	,	,	PUNCT
ejpam-6133	282	5	ζ	ζ	NOUN
ejpam-6133	282	6	)	)	PUNCT
ejpam-6133	282	7	is	be	AUX
ejpam-6133	282	8	a	a	DET
ejpam-6133	282	9	complete	complete	ADJ
ejpam-6133	282	10	dcms	dcms	NOUN
ejpam-6133	282	11	with	with	ADP
ejpam-6133	282	12	the	the	DET
ejpam-6133	282	13	controlled	control	VERB
ejpam-6133	282	14	functions	function	NOUN
ejpam-6133	282	15	ϖ(µ	ϖ(µ	NOUN
ejpam-6133	282	16	,	,	PUNCT
ejpam-6133	282	17	ν	ν	NOUN
ejpam-6133	282	18	)	)	PUNCT
ejpam-6133	282	19	=	=	SYM
ejpam-6133	282	20	2p−1	2p−1	NUM
ejpam-6133	282	21	,	,	PUNCT
ejpam-6133	282	22	ϵ(µ	ϵ(µ	PROPN
ejpam-6133	282	23	,	,	PUNCT
ejpam-6133	282	24	ν	ν	NOUN
ejpam-6133	282	25	)	)	PUNCT
ejpam-6133	282	26	=	=	SYM
ejpam-6133	283	1	2p−1	2p−1	NUM
ejpam-6133	284	1	+	+	CCONJ
ejpam-6133	284	2	1	1	NUM
ejpam-6133	284	3	1	1	NUM
ejpam-6133	284	4	+	+	SYM
ejpam-6133	284	5	1	1	NUM
ejpam-6133	284	6	1+∥µ∥∞	1+∥µ∥∞	NOUN
ejpam-6133	284	7	+	+	CCONJ
ejpam-6133	284	8	1	1	NUM
ejpam-6133	284	9	1	1	NUM
ejpam-6133	284	10	+	+	NUM
ejpam-6133	284	11	1	1	NUM
ejpam-6133	284	12	1+∥ν∥∞	1+∥ν∥∞	NOUN
ejpam-6133	284	13	,	,	PUNCT
ejpam-6133	284	14	where	where	SCONJ
ejpam-6133	284	15	p	p	X
ejpam-6133	284	16	>	>	X
ejpam-6133	284	17	1	1	NUM
ejpam-6133	284	18	where	where	SCONJ
ejpam-6133	284	19	,	,	PUNCT
ejpam-6133	284	20	∥u∥∞	∥u∥∞	PRON
ejpam-6133	284	21	=	=	SYM
ejpam-6133	284	22	sup	sup	NOUN
ejpam-6133	284	23	t∈[τ1,τ2	t∈[τ1,τ2	PROPN
ejpam-6133	284	24	]	]	X
ejpam-6133	285	1	|u(t)|	|u(t)|	NOUN
ejpam-6133	285	2	.	.	PUNCT
ejpam-6133	285	3	define	define	VERB
ejpam-6133	285	4	the	the	DET
ejpam-6133	285	5	operator	operator	NOUN
ejpam-6133	285	6	⊤	⊤	NOUN
ejpam-6133	285	7	:	:	PUNCT
ejpam-6133	285	8	℧	℧	PUNCT
ejpam-6133	285	9	−→	−→	NOUN
ejpam-6133	285	10	℧	℧	PROPN
ejpam-6133	285	11	by	by	ADP
ejpam-6133	285	12	⊤(x)(t	⊤(x)(t	PROPN
ejpam-6133	285	13	)	)	PUNCT
ejpam-6133	285	14	:	:	PUNCT
ejpam-6133	285	15	=	=	SYM
ejpam-6133	285	16	f(t	f(t	NOUN
ejpam-6133	285	17	)	)	PUNCT
ejpam-6133	286	1	+	+	NUM
ejpam-6133	286	2	λ	λ	PROPN
ejpam-6133	286	3	∫	∫	PROPN
ejpam-6133	286	4	τ2	τ2	PROPN
ejpam-6133	286	5	τ1	τ1	PROPN
ejpam-6133	286	6	k	k	PROPN
ejpam-6133	286	7	(	(	PUNCT
ejpam-6133	286	8	t	t	PROPN
ejpam-6133	286	9	,	,	PUNCT
ejpam-6133	286	10	r	r	NOUN
ejpam-6133	286	11	,	,	PUNCT
ejpam-6133	286	12	x(r	x(r	PROPN
ejpam-6133	286	13	)	)	PUNCT
ejpam-6133	286	14	,	,	PUNCT
ejpam-6133	286	15	x(g(r	x(g(r	PROPN
ejpam-6133	286	16	)	)	PUNCT
ejpam-6133	286	17	)	)	PUNCT
ejpam-6133	286	18	,	,	PUNCT
ejpam-6133	286	19	x(τ1	x(τ1	PROPN
ejpam-6133	286	20	)	)	PUNCT
ejpam-6133	286	21	,	,	PUNCT
ejpam-6133	286	22	x(τ2	x(τ2	NUM
ejpam-6133	286	23	)	)	PUNCT
ejpam-6133	286	24	)	)	PUNCT
ejpam-6133	286	25	dr	dr	PROPN
ejpam-6133	286	26	;	;	PUNCT
ejpam-6133	286	27	∀x	∀x	X
ejpam-6133	286	28	∈	∈	PROPN
ejpam-6133	286	29	℧	℧	PROPN
ejpam-6133	286	30	,	,	PUNCT
ejpam-6133	286	31	t	t	PROPN
ejpam-6133	286	32	∈	∈	PROPN
ejpam-6133	287	1	[	[	X
ejpam-6133	287	2	τ1	τ1	NOUN
ejpam-6133	287	3	,	,	PUNCT
ejpam-6133	287	4	τ2	τ2	PROPN
ejpam-6133	287	5	]	]	PUNCT
ejpam-6133	287	6	.	.	PUNCT
ejpam-6133	288	1	in	in	ADP
ejpam-6133	288	2	what	what	PRON
ejpam-6133	288	3	follows	follow	VERB
ejpam-6133	288	4	,	,	PUNCT
ejpam-6133	288	5	we	we	PRON
ejpam-6133	288	6	will	will	AUX
ejpam-6133	288	7	establish	establish	VERB
ejpam-6133	288	8	the	the	DET
ejpam-6133	288	9	conditions	condition	NOUN
ejpam-6133	288	10	so	so	SCONJ
ejpam-6133	288	11	that	that	SCONJ
ejpam-6133	288	12	the	the	DET
ejpam-6133	288	13	operator	operator	NOUN
ejpam-6133	288	14	⊤	⊤	NOUN
ejpam-6133	288	15	has	have	VERB
ejpam-6133	288	16	at	at	ADV
ejpam-6133	288	17	least	least	ADV
ejpam-6133	288	18	one	one	NUM
ejpam-6133	288	19	fp	fp	NOUN
ejpam-6133	288	20	.	.	PROPN
ejpam-6133	289	1	for	for	ADP
ejpam-6133	289	2	this	this	PRON
ejpam-6133	289	3	,	,	PUNCT
ejpam-6133	289	4	define	define	VERB
ejpam-6133	289	5	α	α	NOUN
ejpam-6133	289	6	:	:	PUNCT
ejpam-6133	289	7	℧	℧	VERB
ejpam-6133	289	8	×	×	NOUN
ejpam-6133	289	9	℧	℧	X
ejpam-6133	289	10	−→	−→	NOUN
ejpam-6133	289	11	[	[	X
ejpam-6133	289	12	0,+∞	0,+∞	NUM
ejpam-6133	289	13	)	)	PUNCT
ejpam-6133	289	14	by	by	ADP
ejpam-6133	289	15	α(µ	α(µ	ADP
ejpam-6133	289	16	,	,	PUNCT
ejpam-6133	289	17	ν	ν	X
ejpam-6133	289	18	)	)	PUNCT
ejpam-6133	289	19	=	=	SYM
ejpam-6133	289	20	{	{	PUNCT
ejpam-6133	289	21	1	1	NUM
ejpam-6133	289	22	if	if	SCONJ
ejpam-6133	289	23	µ(t	µ(t	ADJ
ejpam-6133	289	24	)	)	PUNCT
ejpam-6133	289	25	≤	≤	NOUN
ejpam-6133	289	26	ν(t	ν(t	NOUN
ejpam-6133	289	27	)	)	PUNCT
ejpam-6133	289	28	0	0	PUNCT
ejpam-6133	290	1	otherwise	otherwise	ADV
ejpam-6133	290	2	.	.	PUNCT
ejpam-6133	291	1	theorem	theorem	NOUN
ejpam-6133	291	2	2	2	NUM
ejpam-6133	291	3	.	.	PUNCT
ejpam-6133	291	4	assume	assume	VERB
ejpam-6133	291	5	the	the	DET
ejpam-6133	291	6	following	follow	VERB
ejpam-6133	291	7	conditions	condition	NOUN
ejpam-6133	291	8	hold	hold	VERB
ejpam-6133	291	9	:	:	PUNCT
ejpam-6133	291	10	(	(	PUNCT
ejpam-6133	291	11	i	i	NOUN
ejpam-6133	291	12	)	)	PUNCT
ejpam-6133	291	13	s̃0(t	s̃0(t	PROPN
ejpam-6133	291	14	)	)	PUNCT
ejpam-6133	291	15	≤	≤	NOUN
ejpam-6133	291	16	f(t	f(t	NOUN
ejpam-6133	291	17	)	)	PUNCT
ejpam-6133	292	1	+	+	NUM
ejpam-6133	292	2	λ	λ	X
ejpam-6133	292	3	∫	∫	PROPN
ejpam-6133	292	4	τ2	τ2	PROPN
ejpam-6133	292	5	τ1	τ1	PROPN
ejpam-6133	292	6	k	k	PROPN
ejpam-6133	292	7	(	(	PUNCT
ejpam-6133	292	8	t	t	PROPN
ejpam-6133	292	9	,	,	PUNCT
ejpam-6133	292	10	r	r	NOUN
ejpam-6133	292	11	,	,	PUNCT
ejpam-6133	292	12	s̃0(r	s̃0(r	NOUN
ejpam-6133	292	13	)	)	PUNCT
ejpam-6133	292	14	,	,	PUNCT
ejpam-6133	292	15	s̃0(g(r	s̃0(g(r	NOUN
ejpam-6133	292	16	)	)	PUNCT
ejpam-6133	292	17	)	)	PUNCT
ejpam-6133	292	18	,	,	PUNCT
ejpam-6133	292	19	s̃0(τ1	s̃0(τ1	NOUN
ejpam-6133	292	20	)	)	PUNCT
ejpam-6133	292	21	,	,	PUNCT
ejpam-6133	292	22	s̃0(τ2	s̃0(τ2	NOUN
ejpam-6133	292	23	)	)	PUNCT
ejpam-6133	292	24	)	)	PUNCT
ejpam-6133	292	25	dr	dr	PROPN
ejpam-6133	292	26	,	,	PUNCT
ejpam-6133	292	27	∀t	∀t	PROPN
ejpam-6133	292	28	∈	∈	PROPN
ejpam-6133	293	1	[	[	X
ejpam-6133	293	2	τ1	τ1	NOUN
ejpam-6133	293	3	,	,	PUNCT
ejpam-6133	293	4	τ2	τ2	PROPN
ejpam-6133	293	5	]	]	PUNCT
ejpam-6133	293	6	;	;	PUNCT
ejpam-6133	293	7	(	(	PUNCT
ejpam-6133	293	8	ii	ii	NOUN
ejpam-6133	293	9	)	)	PUNCT
ejpam-6133	293	10	for	for	ADP
ejpam-6133	293	11	any	any	DET
ejpam-6133	293	12	x	x	NOUN
ejpam-6133	293	13	,	,	PUNCT
ejpam-6133	293	14	y	y	PROPN
ejpam-6133	293	15	∈	∈	PROPN
ejpam-6133	293	16	℧	℧	PROPN
ejpam-6133	293	17	with	with	ADP
ejpam-6133	293	18	x(r	x(r	PROPN
ejpam-6133	293	19	)	)	PUNCT
ejpam-6133	293	20	≤	≤	NUM
ejpam-6133	293	21	y(r	y(r	NOUN
ejpam-6133	293	22	)	)	PUNCT
ejpam-6133	293	23	for	for	ADP
ejpam-6133	293	24	each	each	DET
ejpam-6133	293	25	r	r	NOUN
ejpam-6133	293	26	∈	∈	PROPN
ejpam-6133	294	1	[	[	X
ejpam-6133	294	2	τ1	τ1	NOUN
ejpam-6133	294	3	,	,	PUNCT
ejpam-6133	294	4	τ2	τ2	PROPN
ejpam-6133	294	5	]	]	PUNCT
ejpam-6133	294	6	,	,	PUNCT
ejpam-6133	294	7	|k	|k	NOUN
ejpam-6133	294	8	(	(	PUNCT
ejpam-6133	294	9	t	t	PROPN
ejpam-6133	294	10	,	,	PUNCT
ejpam-6133	294	11	r	r	NOUN
ejpam-6133	294	12	,	,	PUNCT
ejpam-6133	294	13	x(r	x(r	PROPN
ejpam-6133	294	14	)	)	PUNCT
ejpam-6133	294	15	,	,	PUNCT
ejpam-6133	294	16	x(g(r	x(g(r	PROPN
ejpam-6133	294	17	)	)	PUNCT
ejpam-6133	294	18	)	)	PUNCT
ejpam-6133	294	19	,	,	PUNCT
ejpam-6133	294	20	x(τ1	x(τ1	PROPN
ejpam-6133	294	21	)	)	PUNCT
ejpam-6133	294	22	,	,	PUNCT
ejpam-6133	294	23	x(τ2))−k	x(τ2))−k	X
ejpam-6133	294	24	(	(	PUNCT
ejpam-6133	294	25	t	t	PROPN
ejpam-6133	294	26	,	,	PUNCT
ejpam-6133	294	27	r	r	NOUN
ejpam-6133	294	28	,	,	PUNCT
ejpam-6133	294	29	y(r	y(r	PROPN
ejpam-6133	294	30	)	)	PUNCT
ejpam-6133	294	31	,	,	PUNCT
ejpam-6133	294	32	y(g(r	y(g(r	PROPN
ejpam-6133	294	33	)	)	PUNCT
ejpam-6133	294	34	)	)	PUNCT
ejpam-6133	294	35	,	,	PUNCT
ejpam-6133	294	36	y(τ1	y(τ1	PROPN
ejpam-6133	294	37	)	)	PUNCT
ejpam-6133	294	38	,	,	PUNCT
ejpam-6133	294	39	y(τ2))|	y(τ2))|	NOUN
ejpam-6133	294	40	≤	≤	PUNCT
ejpam-6133	294	41	γ(t	γ(t	PROPN
ejpam-6133	294	42	,	,	PUNCT
ejpam-6133	294	43	r	r	NOUN
ejpam-6133	294	44	)	)	PUNCT
ejpam-6133	294	45	2	2	NUM
ejpam-6133	294	46	1−	1−	NUM
ejpam-6133	294	47	1	1	NUM
ejpam-6133	294	48	p	p	NOUN
ejpam-6133	294	49	(	(	PUNCT
ejpam-6133	294	50	2p−1	2p−1	NUM
ejpam-6133	294	51	+	+	SYM
ejpam-6133	294	52	1	1	NUM
ejpam-6133	294	53	1	1	NUM
ejpam-6133	294	54	+	+	NUM
ejpam-6133	294	55	1	1	NUM
ejpam-6133	294	56	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	294	57	+	+	CCONJ
ejpam-6133	294	58	1	1	NUM
ejpam-6133	294	59	1	1	NUM
ejpam-6133	294	60	+	+	NUM
ejpam-6133	294	61	1	1	NUM
ejpam-6133	294	62	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	294	63	)	)	PUNCT
ejpam-6133	294	64	1	1	NUM
ejpam-6133	294	65	p	p	NOUN
ejpam-6133	295	1	[	[	X
ejpam-6133	295	2	|x(r)−	|x(r)−	NOUN
ejpam-6133	295	3	y(r)|p	y(r)|p	NOUN
ejpam-6133	295	4	+	+	CCONJ
ejpam-6133	295	5	|x(g(r))−	|x(g(r))−	PROPN
ejpam-6133	295	6	y(g(r))|p	y(g(r))|p	PROPN
ejpam-6133	296	1	+	+	CCONJ
ejpam-6133	297	1	|x(τ1)−	|x(τ1)−	VERB
ejpam-6133	297	2	y(τ1)|p	y(τ1)|p	PROPN
ejpam-6133	298	1	+	+	CCONJ
ejpam-6133	298	2	|x(τ2)−	|x(τ2)−	PROPN
ejpam-6133	298	3	y(τ2)|p	y(τ2)|p	X
ejpam-6133	298	4	]	]	X
ejpam-6133	298	5	1	1	NUM
ejpam-6133	298	6	p	p	NOUN
ejpam-6133	298	7	;	;	PUNCT
ejpam-6133	298	8	p	p	X
ejpam-6133	298	9	>	>	X
ejpam-6133	298	10	1	1	NUM
ejpam-6133	298	11	(	(	PUNCT
ejpam-6133	298	12	8)	8)	NUM
ejpam-6133	298	13	where	where	SCONJ
ejpam-6133	298	14	t	t	NOUN
ejpam-6133	298	15	,	,	PUNCT
ejpam-6133	298	16	r	r	NOUN
ejpam-6133	298	17	∈	∈	PROPN
ejpam-6133	299	1	[	[	X
ejpam-6133	299	2	τ1	τ1	NOUN
ejpam-6133	299	3	,	,	PUNCT
ejpam-6133	299	4	τ2	τ2	PROPN
ejpam-6133	299	5	]	]	PUNCT
ejpam-6133	299	6	and	and	CCONJ
ejpam-6133	299	7	γ	γ	X
ejpam-6133	299	8	:	:	PUNCT
ejpam-6133	300	1	[	[	X
ejpam-6133	300	2	τ1	τ1	NOUN
ejpam-6133	300	3	,	,	PUNCT
ejpam-6133	300	4	τ2]×	τ2]×	PROPN
ejpam-6133	301	1	[	[	X
ejpam-6133	301	2	τ1	τ1	NOUN
ejpam-6133	301	3	,	,	PUNCT
ejpam-6133	301	4	τ2	τ2	PROPN
ejpam-6133	301	5	]	]	X
ejpam-6133	301	6	−→	−→	NOUN
ejpam-6133	301	7	r	r	NOUN
ejpam-6133	301	8	is	be	AUX
ejpam-6133	301	9	continuous	continuous	ADJ
ejpam-6133	301	10	so	so	SCONJ
ejpam-6133	301	11	that	that	SCONJ
ejpam-6133	301	12	sup	sup	NOUN
ejpam-6133	301	13	t∈[τ1,τ2	t∈[τ1,τ2	PROPN
ejpam-6133	301	14	]	]	X
ejpam-6133	301	15	∫	∫	PROPN
ejpam-6133	301	16	τ2	τ2	PROPN
ejpam-6133	301	17	τ1	τ1	PROPN
ejpam-6133	301	18	γp(t	γp(t	PUNCT
ejpam-6133	301	19	,	,	PUNCT
ejpam-6133	301	20	r)dr	r)dr	ADP
ejpam-6133	301	21	<	<	X
ejpam-6133	301	22	1	1	NUM
ejpam-6133	301	23	2p+2	2p+2	NUM
ejpam-6133	301	24	|λ|p	|λ|p	NUM
ejpam-6133	301	25	(	(	PUNCT
ejpam-6133	301	26	τ2	τ2	NOUN
ejpam-6133	301	27	−	−	PROPN
ejpam-6133	301	28	1)p−1	1)p−1	NUM
ejpam-6133	301	29	;	;	PUNCT
ejpam-6133	301	30	(	(	PUNCT
ejpam-6133	301	31	9	9	X
ejpam-6133	301	32	)	)	PUNCT
ejpam-6133	301	33	(	(	PUNCT
ejpam-6133	301	34	iii	iii	NOUN
ejpam-6133	301	35	)	)	PUNCT
ejpam-6133	301	36	for	for	ADP
ejpam-6133	301	37	any	any	DET
ejpam-6133	301	38	s̃0	s̃0	PROPN
ejpam-6133	301	39	∈	∈	PROPN
ejpam-6133	301	40	℧	℧	PROPN
ejpam-6133	301	41	,	,	PUNCT
ejpam-6133	301	42	lim	lim	PROPN
ejpam-6133	301	43	i	i	PRON
ejpam-6133	301	44	,	,	PUNCT
ejpam-6133	301	45	m→∞	m→∞	NOUN
ejpam-6133	301	46	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	301	47	,	,	PUNCT
ejpam-6133	301	48	s̃m	s̃m	NOUN
ejpam-6133	301	49	)	)	PUNCT
ejpam-6133	301	50	<	<	X
ejpam-6133	301	51	2p	2p	NUM
ejpam-6133	301	52	;	;	PUNCT
ejpam-6133	301	53	(	(	PUNCT
ejpam-6133	301	54	iv	iv	X
ejpam-6133	301	55	)	)	PUNCT
ejpam-6133	301	56	k	k	PROPN
ejpam-6133	301	57	is	be	AUX
ejpam-6133	301	58	non	non	ADJ
ejpam-6133	301	59	-	-	ADJ
ejpam-6133	301	60	decreasing	decrease	VERB
ejpam-6133	301	61	.	.	PUNCT
ejpam-6133	302	1	then	then	ADV
ejpam-6133	302	2	(	(	PUNCT
ejpam-6133	302	3	7	7	X
ejpam-6133	302	4	)	)	PUNCT
ejpam-6133	302	5	has	have	VERB
ejpam-6133	302	6	a	a	DET
ejpam-6133	302	7	unique	unique	ADJ
ejpam-6133	302	8	solution	solution	NOUN
ejpam-6133	302	9	in	in	ADP
ejpam-6133	302	10	℧	℧	PROPN
ejpam-6133	302	11	.	.	PUNCT
ejpam-6133	303	1	h.	h.	PROPN
ejpam-6133	303	2	aydi	aydi	PROPN
ejpam-6133	303	3	,	,	PUNCT
ejpam-6133	303	4	h.	h.	PROPN
ejpam-6133	303	5	hammouda	hammouda	PROPN
ejpam-6133	303	6	,	,	PUNCT
ejpam-6133	303	7	s.	s.	PROPN
ejpam-6133	303	8	mansour	mansour	PROPN
ejpam-6133	303	9	/	/	SYM
ejpam-6133	303	10	eur	eur	PROPN
ejpam-6133	303	11	.	.	PUNCT
ejpam-6133	304	1	j.	j.	PROPN
ejpam-6133	304	2	pure	pure	PROPN
ejpam-6133	304	3	appl	appl	PROPN
ejpam-6133	304	4	.	.	PROPN
ejpam-6133	304	5	math	math	PROPN
ejpam-6133	304	6	,	,	PUNCT
ejpam-6133	304	7	18	18	NUM
ejpam-6133	304	8	(	(	PUNCT
ejpam-6133	304	9	3	3	NUM
ejpam-6133	304	10	)	)	PUNCT
ejpam-6133	304	11	(	(	PUNCT
ejpam-6133	304	12	2025	2025	NUM
ejpam-6133	304	13	)	)	PUNCT
ejpam-6133	304	14	,	,	PUNCT
ejpam-6133	304	15	6133	6133	NUM
ejpam-6133	304	16	13	13	NUM
ejpam-6133	304	17	of	of	ADP
ejpam-6133	304	18	18	18	NUM
ejpam-6133	304	19	proof	proof	NOUN
ejpam-6133	304	20	.	.	PUNCT
ejpam-6133	305	1	for	for	ADP
ejpam-6133	305	2	s̃0	s̃0	PROPN
ejpam-6133	305	3	∈	∈	PROPN
ejpam-6133	305	4	℧	℧	PROPN
ejpam-6133	305	5	,	,	PUNCT
ejpam-6133	305	6	choose	choose	VERB
ejpam-6133	305	7	{	{	PUNCT
ejpam-6133	305	8	s̃ℓ	s̃ℓ	ADV
ejpam-6133	305	9	}	}	PUNCT
ejpam-6133	305	10	in	in	ADP
ejpam-6133	305	11	℧	℧	NUM
ejpam-6133	305	12	by	by	ADP
ejpam-6133	305	13	s̃ℓ	s̃ℓ	NOUN
ejpam-6133	305	14	=	=	SYM
ejpam-6133	305	15	⊤ℓs̃0	⊤ℓs̃0	PROPN
ejpam-6133	305	16	,	,	PUNCT
ejpam-6133	305	17	ℓ	ℓ	PROPN
ejpam-6133	305	18	≥	≥	NUM
ejpam-6133	305	19	1	1	NUM
ejpam-6133	305	20	.	.	PUNCT
ejpam-6133	305	21	consider	consider	VERB
ejpam-6133	305	22	s̃ℓ+1(t	s̃ℓ+1(t	NUM
ejpam-6133	305	23	)	)	PUNCT
ejpam-6133	305	24	=	=	SYM
ejpam-6133	305	25	⊤s̃ℓ(t	⊤s̃ℓ(t	NUM
ejpam-6133	305	26	)	)	PUNCT
ejpam-6133	305	27	=	=	NOUN
ejpam-6133	305	28	f(t	f(t	NOUN
ejpam-6133	305	29	)	)	PUNCT
ejpam-6133	306	1	+	+	NUM
ejpam-6133	306	2	λ	λ	PROPN
ejpam-6133	306	3	∫	∫	PROPN
ejpam-6133	306	4	τ2	τ2	PROPN
ejpam-6133	306	5	τ1	τ1	PROPN
ejpam-6133	306	6	k	k	PROPN
ejpam-6133	306	7	(	(	PUNCT
ejpam-6133	306	8	t	t	PROPN
ejpam-6133	306	9	,	,	PUNCT
ejpam-6133	306	10	r	r	NOUN
ejpam-6133	306	11	,	,	PUNCT
ejpam-6133	306	12	s̃ℓ(r	s̃ℓ(r	PROPN
ejpam-6133	306	13	)	)	PUNCT
ejpam-6133	306	14	,	,	PUNCT
ejpam-6133	306	15	s̃ℓ(g(r	s̃ℓ(g(r	NUM
ejpam-6133	306	16	)	)	PUNCT
ejpam-6133	306	17	)	)	PUNCT
ejpam-6133	306	18	,	,	PUNCT
ejpam-6133	306	19	s̃ℓ(τ1	s̃ℓ(τ1	NOUN
ejpam-6133	306	20	)	)	PUNCT
ejpam-6133	306	21	,	,	PUNCT
ejpam-6133	306	22	s̃ℓ(τ2	s̃ℓ(τ2	NUM
ejpam-6133	306	23	)	)	PUNCT
ejpam-6133	306	24	)	)	PUNCT
ejpam-6133	307	1	dr	dr	PROPN
ejpam-6133	307	2	.	.	PUNCT
ejpam-6133	308	1	the	the	DET
ejpam-6133	308	2	function	function	NOUN
ejpam-6133	308	3	k	k	PROPN
ejpam-6133	308	4	is	be	AUX
ejpam-6133	308	5	non	non	ADJ
ejpam-6133	308	6	-	-	ADJ
ejpam-6133	308	7	decreasing	decrease	VERB
ejpam-6133	308	8	in	in	ADP
ejpam-6133	308	9	the	the	DET
ejpam-6133	308	10	last	last	ADJ
ejpam-6133	308	11	four	four	NUM
ejpam-6133	308	12	arguments	argument	NOUN
ejpam-6133	308	13	,	,	PUNCT
ejpam-6133	308	14	and	and	CCONJ
ejpam-6133	308	15	so	so	ADV
ejpam-6133	308	16	α(ν	α(ν	PROPN
ejpam-6133	308	17	,	,	PUNCT
ejpam-6133	308	18	ς	ς	PROPN
ejpam-6133	308	19	)	)	PUNCT
ejpam-6133	308	20	≥	≥	NOUN
ejpam-6133	308	21	1	1	NUM
ejpam-6133	308	22	=	=	NOUN
ejpam-6133	308	23	⇒	⇒	X
ejpam-6133	308	24	α(⊤ν,⊤ς	α(⊤ν,⊤ς	NOUN
ejpam-6133	308	25	)	)	PUNCT
ejpam-6133	308	26	≥	≥	NOUN
ejpam-6133	308	27	1	1	NUM
ejpam-6133	308	28	.	.	PUNCT
ejpam-6133	309	1	hence	hence	ADV
ejpam-6133	309	2	⊤	⊤	PROPN
ejpam-6133	309	3	is	be	AUX
ejpam-6133	309	4	α	α	PRON
ejpam-6133	309	5	-	-	ADJ
ejpam-6133	309	6	admissible	admissible	ADJ
ejpam-6133	309	7	,	,	PUNCT
ejpam-6133	309	8	and	and	CCONJ
ejpam-6133	309	9	therefore	therefore	ADV
ejpam-6133	309	10	⊤	⊤	PROPN
ejpam-6133	309	11	is	be	AUX
ejpam-6133	309	12	α	α	PRON
ejpam-6133	309	13	-	-	ADJ
ejpam-6133	309	14	orbitally	orbitally	ADV
ejpam-6133	309	15	admissible	admissible	NOUN
ejpam-6133	309	16	.	.	PUNCT
ejpam-6133	310	1	next	next	ADV
ejpam-6133	310	2	,	,	PUNCT
ejpam-6133	310	3	by	by	ADP
ejpam-6133	310	4	condition	condition	NOUN
ejpam-6133	310	5	(	(	PUNCT
ejpam-6133	310	6	i	i	NOUN
ejpam-6133	310	7	)	)	PUNCT
ejpam-6133	310	8	,	,	PUNCT
ejpam-6133	310	9	α(s̃0,⊤s̃0	α(s̃0,⊤s̃0	PROPN
ejpam-6133	310	10	)	)	PUNCT
ejpam-6133	310	11	≥	≥	NOUN
ejpam-6133	310	12	1	1	NUM
ejpam-6133	310	13	.	.	PUNCT
ejpam-6133	311	1	consequently	consequently	ADV
ejpam-6133	311	2	,	,	PUNCT
ejpam-6133	311	3	it	it	PRON
ejpam-6133	311	4	follows	follow	VERB
ejpam-6133	311	5	that	that	SCONJ
ejpam-6133	311	6	α(s̃ℓ	α(s̃ℓ	NOUN
ejpam-6133	311	7	,	,	PUNCT
ejpam-6133	311	8	s̃ℓ+1	s̃ℓ+1	ADJ
ejpam-6133	311	9	)	)	PUNCT
ejpam-6133	311	10	≥	≥	NOUN
ejpam-6133	311	11	1	1	NUM
ejpam-6133	311	12	for	for	ADP
ejpam-6133	311	13	each	each	DET
ejpam-6133	311	14	ℓ	ℓ	PROPN
ejpam-6133	311	15	∈	∈	PROPN
ejpam-6133	311	16	n.	n.	NOUN
ejpam-6133	311	17	let	let	VERB
ejpam-6133	311	18	q	q	PRON
ejpam-6133	311	19	>	>	X
ejpam-6133	311	20	1	1	NUM
ejpam-6133	312	1	so	so	SCONJ
ejpam-6133	312	2	that	that	SCONJ
ejpam-6133	312	3	1	1	NUM
ejpam-6133	312	4	p	p	NOUN
ejpam-6133	312	5	+	+	NOUN
ejpam-6133	312	6	1	1	NUM
ejpam-6133	312	7	q	q	NOUN
ejpam-6133	312	8	=	=	NOUN
ejpam-6133	312	9	1	1	X
ejpam-6133	312	10	.	.	X
ejpam-6133	313	1	using	use	VERB
ejpam-6133	313	2	(	(	PUNCT
ejpam-6133	313	3	8)	8)	NUM
ejpam-6133	313	4	and	and	CCONJ
ejpam-6133	313	5	the	the	DET
ejpam-6133	313	6	holder	holder	NOUN
ejpam-6133	313	7	’s	’s	PART
ejpam-6133	313	8	inequality	inequality	NOUN
ejpam-6133	313	9	,	,	PUNCT
ejpam-6133	313	10	one	one	PRON
ejpam-6133	313	11	has	have	VERB
ejpam-6133	313	12	|⊤x(t)−⊤y(t)|p	|⊤x(t)−⊤y(t)|p	NOUN
ejpam-6133	313	13	=	=	SYM
ejpam-6133	313	14	∣∣∣λ	∣∣∣λ	PROPN
ejpam-6133	313	15	∫	∫	PROPN
ejpam-6133	313	16	τ2	τ2	PROPN
ejpam-6133	313	17	τ1	τ1	PROPN
ejpam-6133	313	18	k	k	PROPN
ejpam-6133	313	19	(	(	PUNCT
ejpam-6133	313	20	t	t	PROPN
ejpam-6133	313	21	,	,	PUNCT
ejpam-6133	313	22	r	r	NOUN
ejpam-6133	313	23	,	,	PUNCT
ejpam-6133	313	24	x(r	x(r	PROPN
ejpam-6133	313	25	)	)	PUNCT
ejpam-6133	313	26	,	,	PUNCT
ejpam-6133	313	27	x(g(r	x(g(r	PROPN
ejpam-6133	313	28	)	)	PUNCT
ejpam-6133	313	29	)	)	PUNCT
ejpam-6133	313	30	,	,	PUNCT
ejpam-6133	313	31	x(τ1	x(τ1	PROPN
ejpam-6133	313	32	)	)	PUNCT
ejpam-6133	313	33	,	,	PUNCT
ejpam-6133	313	34	x(τ2	x(τ2	NUM
ejpam-6133	313	35	)	)	PUNCT
ejpam-6133	313	36	)	)	PUNCT
ejpam-6133	314	1	dr	dr	PROPN
ejpam-6133	314	2	−	−	PROPN
ejpam-6133	314	3	λ	λ	PROPN
ejpam-6133	314	4	∫	∫	PROPN
ejpam-6133	314	5	τ2	τ2	PROPN
ejpam-6133	314	6	τ1	τ1	PROPN
ejpam-6133	314	7	k	k	PROPN
ejpam-6133	314	8	(	(	PUNCT
ejpam-6133	314	9	t	t	PROPN
ejpam-6133	314	10	,	,	PUNCT
ejpam-6133	314	11	r	r	NOUN
ejpam-6133	314	12	,	,	PUNCT
ejpam-6133	314	13	y(r	y(r	PROPN
ejpam-6133	314	14	)	)	PUNCT
ejpam-6133	314	15	,	,	PUNCT
ejpam-6133	314	16	y(g(r	y(g(r	PROPN
ejpam-6133	314	17	)	)	PUNCT
ejpam-6133	314	18	)	)	PUNCT
ejpam-6133	314	19	,	,	PUNCT
ejpam-6133	314	20	y(τ1	y(τ1	NOUN
ejpam-6133	314	21	)	)	PUNCT
ejpam-6133	314	22	,	,	PUNCT
ejpam-6133	314	23	y(τ2	y(τ2	VERB
ejpam-6133	314	24	)	)	PUNCT
ejpam-6133	314	25	)	)	PUNCT
ejpam-6133	315	1	dr	dr	PROPN
ejpam-6133	315	2	∣∣∣p	∣∣∣p	NOUN
ejpam-6133	315	3	≤	≤	PROPN
ejpam-6133	315	4	(	(	PUNCT
ejpam-6133	315	5	∫	∫	PROPN
ejpam-6133	315	6	τ2	τ2	PROPN
ejpam-6133	315	7	τ1	τ1	PROPN
ejpam-6133	315	8	|λ|	|λ|	NOUN
ejpam-6133	315	9	|k	|k	NOUN
ejpam-6133	315	10	(	(	PUNCT
ejpam-6133	315	11	t	t	PROPN
ejpam-6133	315	12	,	,	PUNCT
ejpam-6133	315	13	r	r	NOUN
ejpam-6133	315	14	,	,	PUNCT
ejpam-6133	315	15	x(r	x(r	PROPN
ejpam-6133	315	16	)	)	PUNCT
ejpam-6133	315	17	,	,	PUNCT
ejpam-6133	315	18	x(g(r	x(g(r	PROPN
ejpam-6133	315	19	)	)	PUNCT
ejpam-6133	315	20	)	)	PUNCT
ejpam-6133	315	21	,	,	PUNCT
ejpam-6133	315	22	x(τ1	x(τ1	PROPN
ejpam-6133	315	23	)	)	PUNCT
ejpam-6133	315	24	,	,	PUNCT
ejpam-6133	315	25	x(τ2))−k	x(τ2))−k	X
ejpam-6133	315	26	(	(	PUNCT
ejpam-6133	315	27	t	t	PROPN
ejpam-6133	315	28	,	,	PUNCT
ejpam-6133	315	29	r	r	NOUN
ejpam-6133	315	30	,	,	PUNCT
ejpam-6133	315	31	y(r	y(r	PROPN
ejpam-6133	315	32	)	)	PUNCT
ejpam-6133	315	33	,	,	PUNCT
ejpam-6133	315	34	y(g(r	y(g(r	PROPN
ejpam-6133	315	35	)	)	PUNCT
ejpam-6133	315	36	)	)	PUNCT
ejpam-6133	315	37	,	,	PUNCT
ejpam-6133	315	38	y(τ1	y(τ1	PROPN
ejpam-6133	315	39	)	)	PUNCT
ejpam-6133	315	40	,	,	PUNCT
ejpam-6133	315	41	y(τ2))|	y(τ2))|	PROPN
ejpam-6133	315	42	dr	dr	PROPN
ejpam-6133	315	43	)	)	PUNCT
ejpam-6133	315	44	p	p	NOUN
ejpam-6133	315	45	≤	≤	PROPN
ejpam-6133	315	46	(	(	PUNCT
ejpam-6133	315	47	∫	∫	PROPN
ejpam-6133	315	48	τ2	τ2	PROPN
ejpam-6133	315	49	τ1	τ1	PROPN
ejpam-6133	315	50	|λ|q	|λ|q	NUM
ejpam-6133	315	51	)	)	PUNCT
ejpam-6133	316	1	p	p	X
ejpam-6133	316	2	q((∫	q((∫	ADJ
ejpam-6133	316	3	τ2	τ2	NOUN
ejpam-6133	316	4	τ1	τ1	NOUN
ejpam-6133	316	5	|k	|k	NOUN
ejpam-6133	316	6	(	(	PUNCT
ejpam-6133	316	7	t	t	PROPN
ejpam-6133	316	8	,	,	PUNCT
ejpam-6133	316	9	r	r	NOUN
ejpam-6133	316	10	,	,	PUNCT
ejpam-6133	316	11	x(r	x(r	PROPN
ejpam-6133	316	12	)	)	PUNCT
ejpam-6133	316	13	,	,	PUNCT
ejpam-6133	316	14	x(g(r	x(g(r	PROPN
ejpam-6133	316	15	)	)	PUNCT
ejpam-6133	316	16	)	)	PUNCT
ejpam-6133	316	17	,	,	PUNCT
ejpam-6133	316	18	x(τ1	x(τ1	PROPN
ejpam-6133	316	19	)	)	PUNCT
ejpam-6133	316	20	,	,	PUNCT
ejpam-6133	316	21	x(τ2))−k	x(τ2))−k	X
ejpam-6133	316	22	(	(	PUNCT
ejpam-6133	316	23	t	t	PROPN
ejpam-6133	316	24	,	,	PUNCT
ejpam-6133	316	25	r	r	NOUN
ejpam-6133	316	26	,	,	PUNCT
ejpam-6133	316	27	y(r	y(r	PROPN
ejpam-6133	316	28	)	)	PUNCT
ejpam-6133	316	29	,	,	PUNCT
ejpam-6133	316	30	y(g(r	y(g(r	PROPN
ejpam-6133	316	31	)	)	PUNCT
ejpam-6133	316	32	)	)	PUNCT
ejpam-6133	316	33	,	,	PUNCT
ejpam-6133	316	34	y(τ1	y(τ1	PROPN
ejpam-6133	316	35	)	)	PUNCT
ejpam-6133	316	36	,	,	PUNCT
ejpam-6133	316	37	y(τ2))|p	y(τ2))|p	PROPN
ejpam-6133	316	38	dr	dr	PROPN
ejpam-6133	316	39	)	)	PUNCT
ejpam-6133	316	40	1	1	NUM
ejpam-6133	316	41	p	p	NOUN
ejpam-6133	316	42	)	)	PUNCT
ejpam-6133	316	43	p	p	X
ejpam-6133	316	44	=	=	PUNCT
ejpam-6133	316	45	|λ|p	|λ|p	PROPN
ejpam-6133	316	46	(	(	PUNCT
ejpam-6133	316	47	τ2	τ2	ADJ
ejpam-6133	316	48	−	−	NOUN
ejpam-6133	316	49	τ1	τ1	NOUN
ejpam-6133	316	50	)	)	PUNCT
ejpam-6133	316	51	p−1(∫	p−1(∫	PROPN
ejpam-6133	316	52	τ2	τ2	NOUN
ejpam-6133	316	53	τ1	τ1	PROPN
ejpam-6133	316	54	|k	|k	NOUN
ejpam-6133	316	55	(	(	PUNCT
ejpam-6133	316	56	t	t	PROPN
ejpam-6133	316	57	,	,	PUNCT
ejpam-6133	316	58	r	r	NOUN
ejpam-6133	316	59	,	,	PUNCT
ejpam-6133	316	60	x(r	x(r	PROPN
ejpam-6133	316	61	)	)	PUNCT
ejpam-6133	316	62	,	,	PUNCT
ejpam-6133	316	63	x(g(r	x(g(r	PROPN
ejpam-6133	316	64	)	)	PUNCT
ejpam-6133	316	65	)	)	PUNCT
ejpam-6133	316	66	,	,	PUNCT
ejpam-6133	316	67	x(τ1	x(τ1	PROPN
ejpam-6133	316	68	)	)	PUNCT
ejpam-6133	316	69	,	,	PUNCT
ejpam-6133	316	70	x(τ2))−k	x(τ2))−k	X
ejpam-6133	316	71	(	(	PUNCT
ejpam-6133	316	72	t	t	PROPN
ejpam-6133	316	73	,	,	PUNCT
ejpam-6133	316	74	r	r	NOUN
ejpam-6133	316	75	,	,	PUNCT
ejpam-6133	316	76	y(r	y(r	PROPN
ejpam-6133	316	77	)	)	PUNCT
ejpam-6133	316	78	,	,	PUNCT
ejpam-6133	316	79	y(g(r	y(g(r	PROPN
ejpam-6133	316	80	)	)	PUNCT
ejpam-6133	316	81	)	)	PUNCT
ejpam-6133	316	82	,	,	PUNCT
ejpam-6133	316	83	y(τ1	y(τ1	PROPN
ejpam-6133	316	84	)	)	PUNCT
ejpam-6133	316	85	,	,	PUNCT
ejpam-6133	316	86	y(τ2))|p	y(τ2))|p	PROPN
ejpam-6133	316	87	dr	dr	PROPN
ejpam-6133	316	88	)	)	PUNCT
ejpam-6133	316	89	≤	≤	PUNCT
ejpam-6133	316	90	|λ|p	|λ|p	PROPN
ejpam-6133	316	91	(	(	PUNCT
ejpam-6133	316	92	τ2	τ2	NOUN
ejpam-6133	316	93	−	−	NOUN
ejpam-6133	316	94	τ1	τ1	NOUN
ejpam-6133	316	95	)	)	PUNCT
ejpam-6133	316	96	p−1	p−1	PROPN
ejpam-6133	316	97	∫	∫	PROPN
ejpam-6133	316	98	τ2	τ2	PROPN
ejpam-6133	316	99	τ1	τ1	PROPN
ejpam-6133	316	100	γp(t	γp(t	PUNCT
ejpam-6133	316	101	,	,	PUNCT
ejpam-6133	316	102	r	r	NOUN
ejpam-6133	316	103	)	)	PUNCT
ejpam-6133	316	104	2p−1(2p−1	2p−1(2p−1	NUM
ejpam-6133	317	1	+	+	CCONJ
ejpam-6133	317	2	1	1	NUM
ejpam-6133	317	3	1	1	NUM
ejpam-6133	317	4	+	+	NUM
ejpam-6133	317	5	1	1	NUM
ejpam-6133	317	6	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	317	7	+	+	CCONJ
ejpam-6133	317	8	1	1	NUM
ejpam-6133	317	9	1	1	NUM
ejpam-6133	317	10	+	+	NUM
ejpam-6133	317	11	1	1	NUM
ejpam-6133	317	12	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	317	13	)	)	PUNCT
ejpam-6133	318	1	[	[	X
ejpam-6133	318	2	|x(r)−	|x(r)−	NOUN
ejpam-6133	318	3	y(r)|p	y(r)|p	NOUN
ejpam-6133	318	4	+	+	CCONJ
ejpam-6133	318	5	|x(g(r))−	|x(g(r))−	PROPN
ejpam-6133	318	6	y(g(r))|p	y(g(r))|p	PROPN
ejpam-6133	319	1	+	+	CCONJ
ejpam-6133	320	1	|x(τ1)−	|x(τ1)−	VERB
ejpam-6133	320	2	y(τ1)|p	y(τ1)|p	PROPN
ejpam-6133	321	1	+	+	CCONJ
ejpam-6133	321	2	|x(τ2)−	|x(τ2)−	PROPN
ejpam-6133	321	3	y(τ2)|p	y(τ2)|p	PROPN
ejpam-6133	321	4	]	]	X
ejpam-6133	321	5	dr	dr	PROPN
ejpam-6133	321	6	≤	≤	PROPN
ejpam-6133	321	7	|λ|p	|λ|p	PROPN
ejpam-6133	321	8	(	(	PUNCT
ejpam-6133	321	9	τ2	τ2	NOUN
ejpam-6133	321	10	−	−	NOUN
ejpam-6133	321	11	τ1	τ1	NOUN
ejpam-6133	321	12	)	)	PUNCT
ejpam-6133	321	13	p−1	p−1	PROPN
ejpam-6133	321	14	∫	∫	PROPN
ejpam-6133	321	15	τ2	τ2	PROPN
ejpam-6133	321	16	τ1	τ1	PROPN
ejpam-6133	321	17	γp(t	γp(t	PUNCT
ejpam-6133	321	18	,	,	PUNCT
ejpam-6133	321	19	r	r	NOUN
ejpam-6133	321	20	)	)	PUNCT
ejpam-6133	321	21	2p−1(2p−1	2p−1(2p−1	NUM
ejpam-6133	322	1	+	+	CCONJ
ejpam-6133	322	2	1	1	NUM
ejpam-6133	322	3	1	1	NUM
ejpam-6133	322	4	+	+	NUM
ejpam-6133	322	5	1	1	NUM
ejpam-6133	322	6	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	322	7	+	+	CCONJ
ejpam-6133	322	8	1	1	NUM
ejpam-6133	322	9	1	1	NUM
ejpam-6133	322	10	+	+	NUM
ejpam-6133	322	11	1	1	NUM
ejpam-6133	322	12	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	322	13	)	)	PUNCT
ejpam-6133	323	1	[	[	X
ejpam-6133	323	2	4ζ(x	4ζ(x	NOUN
ejpam-6133	323	3	,	,	PUNCT
ejpam-6133	323	4	y	y	PROPN
ejpam-6133	323	5	)	)	PUNCT
ejpam-6133	323	6	]	]	PUNCT
ejpam-6133	323	7	dr	dr	PROPN
ejpam-6133	323	8	≤	≤	PROPN
ejpam-6133	323	9	4	4	NUM
ejpam-6133	323	10	|λ|p	|λ|p	NUM
ejpam-6133	323	11	(	(	PUNCT
ejpam-6133	323	12	τ2	τ2	NOUN
ejpam-6133	323	13	−	−	NOUN
ejpam-6133	323	14	τ1	τ1	NOUN
ejpam-6133	323	15	)	)	PUNCT
ejpam-6133	323	16	p−1	p−1	PROPN
ejpam-6133	323	17	∫	∫	PROPN
ejpam-6133	323	18	τ2	τ2	PROPN
ejpam-6133	323	19	τ1	τ1	PROPN
ejpam-6133	323	20	γp(t	γp(t	PUNCT
ejpam-6133	323	21	,	,	PUNCT
ejpam-6133	323	22	r	r	NOUN
ejpam-6133	323	23	)	)	PUNCT
ejpam-6133	323	24	2p−1(2p−1	2p−1(2p−1	NUM
ejpam-6133	324	1	+	+	CCONJ
ejpam-6133	324	2	1	1	NUM
ejpam-6133	324	3	1	1	NUM
ejpam-6133	324	4	+	+	NUM
ejpam-6133	324	5	1	1	NUM
ejpam-6133	324	6	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	324	7	+	+	CCONJ
ejpam-6133	324	8	1	1	NUM
ejpam-6133	324	9	1	1	NUM
ejpam-6133	324	10	+	+	NUM
ejpam-6133	324	11	1	1	NUM
ejpam-6133	324	12	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	324	13	)	)	PUNCT
ejpam-6133	325	1	[	[	X
ejpam-6133	325	2	r(x	r(x	PROPN
ejpam-6133	325	3	,	,	PUNCT
ejpam-6133	325	4	y	y	PROPN
ejpam-6133	325	5	)	)	PUNCT
ejpam-6133	325	6	]	]	PUNCT
ejpam-6133	325	7	dr	dr	PROPN
ejpam-6133	325	8	≤	≤	PROPN
ejpam-6133	325	9	4|λ|p(τ2−τ1)p−1[r(x	4|λ|p(τ2−τ1)p−1[r(x	PROPN
ejpam-6133	325	10	,	,	PUNCT
ejpam-6133	325	11	y	y	PROPN
ejpam-6133	325	12	)	)	PUNCT
ejpam-6133	325	13	]	]	PUNCT
ejpam-6133	326	1	2p−1(2p−1	2p−1(2p−1	NUM
ejpam-6133	326	2	+	+	CCONJ
ejpam-6133	326	3	1	1	NUM
ejpam-6133	326	4	1	1	NUM
ejpam-6133	326	5	+	+	NUM
ejpam-6133	326	6	1	1	NUM
ejpam-6133	326	7	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	326	8	+	+	CCONJ
ejpam-6133	326	9	1	1	NUM
ejpam-6133	326	10	1	1	NUM
ejpam-6133	326	11	+	+	NUM
ejpam-6133	326	12	1	1	NUM
ejpam-6133	326	13	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	326	14	)	)	PUNCT
ejpam-6133	326	15	sup	sup	NOUN
ejpam-6133	326	16	t∈[τ1,τ2	t∈[τ1,τ2	PROPN
ejpam-6133	326	17	]	]	X
ejpam-6133	326	18	(	(	PUNCT
ejpam-6133	326	19	∫	∫	PROPN
ejpam-6133	326	20	τ2	τ2	PROPN
ejpam-6133	326	21	τ1	τ1	PROPN
ejpam-6133	326	22	γp(t	γp(t	NOUN
ejpam-6133	326	23	,	,	PUNCT
ejpam-6133	326	24	r)dr	r)dr	PROPN
ejpam-6133	326	25	)	)	PUNCT
ejpam-6133	326	26	.	.	PUNCT
ejpam-6133	327	1	from	from	ADP
ejpam-6133	327	2	(	(	PUNCT
ejpam-6133	327	3	9	9	NUM
ejpam-6133	327	4	)	)	PUNCT
ejpam-6133	327	5	,	,	PUNCT
ejpam-6133	327	6	it	it	PRON
ejpam-6133	327	7	results	result	VERB
ejpam-6133	327	8	that	that	SCONJ
ejpam-6133	328	1	2p−1	2p−1	NUM
ejpam-6133	328	2	(	(	PUNCT
ejpam-6133	328	3	2p−1	2p−1	NUM
ejpam-6133	329	1	+	+	CCONJ
ejpam-6133	329	2	1	1	NUM
ejpam-6133	329	3	1	1	NUM
ejpam-6133	329	4	+	+	SYM
ejpam-6133	329	5	1	1	NUM
ejpam-6133	329	6	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	329	7	+	+	CCONJ
ejpam-6133	329	8	1	1	NUM
ejpam-6133	329	9	1	1	NUM
ejpam-6133	329	10	+	+	CCONJ
ejpam-6133	329	11	1	1	NUM
ejpam-6133	329	12	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	329	13	)	)	PUNCT
ejpam-6133	329	14	|⊤x(t)−⊤y(t)|p	|⊤x(t)−⊤y(t)|p	PROPN
ejpam-6133	329	15	≤	≤	NUM
ejpam-6133	329	16	1	1	NUM
ejpam-6133	329	17	2p	2p	NUM
ejpam-6133	329	18	(	(	PUNCT
ejpam-6133	329	19	ℜ(x	ℜ(x	PROPN
ejpam-6133	329	20	,	,	PUNCT
ejpam-6133	329	21	y	y	NOUN
ejpam-6133	329	22	)	)	PUNCT
ejpam-6133	329	23	)	)	PUNCT
ejpam-6133	329	24	.	.	PUNCT
ejpam-6133	330	1	setting	set	VERB
ejpam-6133	330	2	ψ(t	ψ(t	PROPN
ejpam-6133	330	3	)	)	PUNCT
ejpam-6133	330	4	=	=	SYM
ejpam-6133	330	5	1	1	NUM
ejpam-6133	330	6	2p	2p	NUM
ejpam-6133	330	7	t	t	NOUN
ejpam-6133	330	8	,	,	PUNCT
ejpam-6133	330	9	we	we	PRON
ejpam-6133	330	10	obtain	obtain	VERB
ejpam-6133	330	11	that	that	DET
ejpam-6133	330	12	α(x	α(x	NOUN
ejpam-6133	330	13	,	,	PUNCT
ejpam-6133	330	14	y)ϖ(x	y)ϖ(x	PROPN
ejpam-6133	330	15	,	,	PUNCT
ejpam-6133	330	16	y)ϵ(x	y)ϵ(x	PROPN
ejpam-6133	330	17	,	,	PUNCT
ejpam-6133	330	18	y)ζ(⊤x,⊤y	y)ζ(⊤x,⊤y	PROPN
ejpam-6133	330	19	)	)	PUNCT
ejpam-6133	330	20	≤	≤	NUM
ejpam-6133	330	21	ψ(ℜ(x	ψ(ℜ(x	NOUN
ejpam-6133	330	22	,	,	PUNCT
ejpam-6133	330	23	y	y	NOUN
ejpam-6133	330	24	)	)	PUNCT
ejpam-6133	330	25	)	)	PUNCT
ejpam-6133	330	26	.	.	PUNCT
ejpam-6133	331	1	next	next	ADV
ejpam-6133	331	2	,	,	PUNCT
ejpam-6133	331	3	using	use	VERB
ejpam-6133	331	4	the	the	DET
ejpam-6133	331	5	condition	condition	NOUN
ejpam-6133	331	6	lim	lim	PROPN
ejpam-6133	331	7	i	i	PRON
ejpam-6133	331	8	,	,	PUNCT
ejpam-6133	331	9	m→∞	m→∞	NOUN
ejpam-6133	331	10	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	331	11	,	,	PUNCT
ejpam-6133	331	12	s̃m	s̃m	NOUN
ejpam-6133	331	13	)	)	PUNCT
ejpam-6133	331	14	<	<	X
ejpam-6133	331	15	2p	2p	NUM
ejpam-6133	331	16	,	,	PUNCT
ejpam-6133	331	17	h.	h.	PROPN
ejpam-6133	331	18	aydi	aydi	PROPN
ejpam-6133	331	19	,	,	PUNCT
ejpam-6133	331	20	h.	h.	PROPN
ejpam-6133	331	21	hammouda	hammouda	PROPN
ejpam-6133	331	22	,	,	PUNCT
ejpam-6133	331	23	s.	s.	PROPN
ejpam-6133	331	24	mansour	mansour	PROPN
ejpam-6133	331	25	/	/	SYM
ejpam-6133	331	26	eur	eur	PROPN
ejpam-6133	331	27	.	.	PUNCT
ejpam-6133	332	1	j.	j.	PROPN
ejpam-6133	332	2	pure	pure	PROPN
ejpam-6133	332	3	appl	appl	PROPN
ejpam-6133	332	4	.	.	PROPN
ejpam-6133	332	5	math	math	PROPN
ejpam-6133	332	6	,	,	PUNCT
ejpam-6133	332	7	18	18	NUM
ejpam-6133	332	8	(	(	PUNCT
ejpam-6133	332	9	3	3	NUM
ejpam-6133	332	10	)	)	PUNCT
ejpam-6133	332	11	(	(	PUNCT
ejpam-6133	332	12	2025	2025	NUM
ejpam-6133	332	13	)	)	PUNCT
ejpam-6133	332	14	,	,	PUNCT
ejpam-6133	332	15	6133	6133	NUM
ejpam-6133	332	16	14	14	NUM
ejpam-6133	332	17	of	of	ADP
ejpam-6133	332	18	18	18	NUM
ejpam-6133	332	19	we	we	PRON
ejpam-6133	332	20	deduce	deduce	VERB
ejpam-6133	332	21	supm	supm	PROPN
ejpam-6133	332	22	lim	lim	PROPN
ejpam-6133	332	23	i→∞	i→∞	VERB
ejpam-6133	332	24	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	332	25	,	,	PUNCT
ejpam-6133	332	26	s̃m)ϖ(s̃i+1	s̃m)ϖ(s̃i+1	PROPN
ejpam-6133	332	27	,	,	PUNCT
ejpam-6133	332	28	s̃i+2)ψ	s̃i+2)ψ	PRON
ejpam-6133	332	29	i+1(ζ(s̃0	i+1(ζ(s̃0	ADJ
ejpam-6133	332	30	,	,	PUNCT
ejpam-6133	332	31	s̃1	s̃1	PROPN
ejpam-6133	332	32	)	)	PUNCT
ejpam-6133	332	33	)	)	PUNCT
ejpam-6133	333	1	ϖ(s̃i	ϖ(s̃i	PROPN
ejpam-6133	333	2	,	,	PUNCT
ejpam-6133	333	3	s̃i+1)ψi(ζ(s̃0	s̃i+1)ψi(ζ(s̃0	PROPN
ejpam-6133	333	4	,	,	PUNCT
ejpam-6133	333	5	s̃1	s̃1	PROPN
ejpam-6133	333	6	)	)	PUNCT
ejpam-6133	333	7	)	)	PUNCT
ejpam-6133	334	1	=	=	SYM
ejpam-6133	334	2	supm	supm	PROPN
ejpam-6133	334	3	lim	lim	PROPN
ejpam-6133	334	4	i→∞	i→∞	VERB
ejpam-6133	334	5	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	334	6	,	,	PUNCT
ejpam-6133	334	7	s̃m	s̃m	PROPN
ejpam-6133	334	8	)	)	PUNCT
ejpam-6133	334	9	1	1	NUM
ejpam-6133	334	10	2p(i+1	2p(i+1	NUM
ejpam-6133	334	11	)	)	PUNCT
ejpam-6133	334	12	(	(	PUNCT
ejpam-6133	334	13	ζ(s̃0	ζ(s̃0	PROPN
ejpam-6133	334	14	,	,	PUNCT
ejpam-6133	334	15	s̃1	s̃1	PROPN
ejpam-6133	334	16	)	)	PUNCT
ejpam-6133	334	17	)	)	PUNCT
ejpam-6133	334	18	1	1	NUM
ejpam-6133	334	19	2pi	2pi	NOUN
ejpam-6133	334	20	(	(	PUNCT
ejpam-6133	334	21	ζ(s̃0	ζ(s̃0	PROPN
ejpam-6133	334	22	,	,	PUNCT
ejpam-6133	334	23	s̃1	s̃1	PROPN
ejpam-6133	334	24	)	)	PUNCT
ejpam-6133	334	25	)	)	PUNCT
ejpam-6133	335	1	=	=	SYM
ejpam-6133	335	2	supm	supm	PROPN
ejpam-6133	335	3	lim	lim	PROPN
ejpam-6133	335	4	i→∞	i→∞	VERB
ejpam-6133	335	5	1	1	NUM
ejpam-6133	335	6	2p	2p	NUM
ejpam-6133	335	7	ϵ(s̃i+1	ϵ(s̃i+1	PROPN
ejpam-6133	335	8	,	,	PUNCT
ejpam-6133	335	9	s̃m	s̃m	NOUN
ejpam-6133	335	10	)	)	PUNCT
ejpam-6133	335	11	<	<	X
ejpam-6133	336	1	1	1	X
ejpam-6133	336	2	.	.	PUNCT
ejpam-6133	336	3	thus	thus	ADV
ejpam-6133	336	4	,	,	PUNCT
ejpam-6133	336	5	the	the	DET
ejpam-6133	336	6	condition	condition	NOUN
ejpam-6133	336	7	(	(	PUNCT
ejpam-6133	336	8	iii	iii	NOUN
ejpam-6133	336	9	)	)	PUNCT
ejpam-6133	336	10	in	in	ADP
ejpam-6133	336	11	theorem	theorem	ADJ
ejpam-6133	336	12	1	1	NUM
ejpam-6133	336	13	holds	hold	NOUN
ejpam-6133	336	14	.	.	PUNCT
ejpam-6133	337	1	since	since	SCONJ
ejpam-6133	337	2	f	f	PROPN
ejpam-6133	337	3	,	,	PUNCT
ejpam-6133	337	4	g	g	PROPN
ejpam-6133	337	5	andk	andk	NOUN
ejpam-6133	337	6	are	be	AUX
ejpam-6133	337	7	continuous	continuous	ADJ
ejpam-6133	337	8	,	,	PUNCT
ejpam-6133	337	9	the	the	DET
ejpam-6133	337	10	operator	operator	NOUN
ejpam-6133	337	11	⊤	⊤	NOUN
ejpam-6133	337	12	is	be	AUX
ejpam-6133	337	13	continuous	continuous	ADJ
ejpam-6133	337	14	on	on	ADP
ejpam-6133	337	15	℧	℧	PROPN
ejpam-6133	337	16	and	and	CCONJ
ejpam-6133	337	17	so	so	ADV
ejpam-6133	337	18	⊤	⊤	PROPN
ejpam-6133	337	19	is	be	AUX
ejpam-6133	337	20	orbitally	orbitally	ADV
ejpam-6133	337	21	continuous	continuous	ADJ
ejpam-6133	337	22	on	on	ADP
ejpam-6133	337	23	℧	℧	PROPN
ejpam-6133	337	24	.	.	PUNCT
ejpam-6133	338	1	the	the	DET
ejpam-6133	338	2	controlled	control	VERB
ejpam-6133	338	3	functions	function	NOUN
ejpam-6133	338	4	ϖ	ϖ	NOUN
ejpam-6133	338	5	;	;	PUNCT
ejpam-6133	338	6	ϵ	ϵ	NOUN
ejpam-6133	338	7	are	be	AUX
ejpam-6133	338	8	defined	define	VERB
ejpam-6133	338	9	by	by	ADP
ejpam-6133	338	10	ϖ(µ	ϖ(µ	NOUN
ejpam-6133	338	11	,	,	PUNCT
ejpam-6133	338	12	ν	ν	NOUN
ejpam-6133	338	13	)	)	PUNCT
ejpam-6133	338	14	=	=	SYM
ejpam-6133	338	15	2p−1	2p−1	NUM
ejpam-6133	338	16	;	;	PUNCT
ejpam-6133	338	17	ϵ(µ	ϵ(µ	NOUN
ejpam-6133	338	18	,	,	PUNCT
ejpam-6133	338	19	ν	ν	NOUN
ejpam-6133	338	20	)	)	PUNCT
ejpam-6133	338	21	=	=	SYM
ejpam-6133	339	1	2p−1	2p−1	NUM
ejpam-6133	340	1	+	+	CCONJ
ejpam-6133	340	2	1	1	NUM
ejpam-6133	340	3	1	1	NUM
ejpam-6133	340	4	+	+	SYM
ejpam-6133	340	5	1	1	NUM
ejpam-6133	340	6	1+∥µ∥∞	1+∥µ∥∞	NOUN
ejpam-6133	340	7	+	+	CCONJ
ejpam-6133	340	8	1	1	NUM
ejpam-6133	340	9	1	1	NUM
ejpam-6133	340	10	+	+	NUM
ejpam-6133	340	11	1	1	NUM
ejpam-6133	340	12	1+∥ν∥∞	1+∥ν∥∞	NOUN
ejpam-6133	340	13	,	,	PUNCT
ejpam-6133	341	1	where	where	SCONJ
ejpam-6133	341	2	p	p	X
ejpam-6133	341	3	>	>	X
ejpam-6133	341	4	1	1	NUM
ejpam-6133	341	5	.	.	PUNCT
ejpam-6133	341	6	then	then	ADV
ejpam-6133	341	7	lim	lim	PROPN
ejpam-6133	341	8	ℓ→∞	ℓ→∞	PROPN
ejpam-6133	341	9	ϖ(s̃ℓ	ϖ(s̃ℓ	PROPN
ejpam-6133	341	10	,	,	PUNCT
ejpam-6133	341	11	x	x	X
ejpam-6133	341	12	)	)	PUNCT
ejpam-6133	341	13	=	=	SYM
ejpam-6133	341	14	2p−1	2p−1	NUM
ejpam-6133	341	15	.	.	PUNCT
ejpam-6133	342	1	on	on	ADP
ejpam-6133	342	2	the	the	DET
ejpam-6133	342	3	other	other	ADJ
ejpam-6133	342	4	hand	hand	NOUN
ejpam-6133	342	5	,	,	PUNCT
ejpam-6133	342	6	{	{	PUNCT
ejpam-6133	342	7	⊤ℓx(t	⊤ℓx(t	NOUN
ejpam-6133	342	8	)	)	PUNCT
ejpam-6133	342	9	}	}	PUNCT
ejpam-6133	342	10	n	n	PRON
ejpam-6133	342	11	converges	converge	NOUN
ejpam-6133	342	12	because	because	SCONJ
ejpam-6133	342	13	{	{	PUNCT
ejpam-6133	342	14	⊤ℓ	⊤ℓ	NOUN
ejpam-6133	342	15	}	}	PUNCT
ejpam-6133	342	16	ℓ	ℓ	PROPN
ejpam-6133	342	17	is	be	AUX
ejpam-6133	342	18	a	a	DET
ejpam-6133	342	19	monotonic	monotonic	ADJ
ejpam-6133	342	20	sequence	sequence	NOUN
ejpam-6133	342	21	and	and	CCONJ
ejpam-6133	342	22	so	so	ADV
ejpam-6133	342	23	it	it	PRON
ejpam-6133	342	24	follows	follow	VERB
ejpam-6133	342	25	from	from	ADP
ejpam-6133	342	26	dini	dini	NOUN
ejpam-6133	342	27	theorem	theorem	NOUN
ejpam-6133	342	28	that	that	PRON
ejpam-6133	342	29	sup	sup	NOUN
ejpam-6133	342	30	t∈[τ1,τ2	t∈[τ1,τ2	PROPN
ejpam-6133	342	31	]	]	X
ejpam-6133	342	32	∣∣∣⊤ℓx(t	∣∣∣⊤ℓx(t	PROPN
ejpam-6133	342	33	)	)	PUNCT
ejpam-6133	342	34	∣∣∣	∣∣∣	NOUN
ejpam-6133	342	35	converges	converge	NOUN
ejpam-6133	342	36	and	and	CCONJ
ejpam-6133	342	37	hence	hence	ADV
ejpam-6133	342	38	lim	lim	PROPN
ejpam-6133	342	39	ℓ→∞	ℓ→∞	NUM
ejpam-6133	342	40	ϵ(s̃ℓ	ϵ(s̃ℓ	PROPN
ejpam-6133	342	41	,	,	PUNCT
ejpam-6133	342	42	x	x	PRON
ejpam-6133	342	43	)	)	PUNCT
ejpam-6133	342	44	exists	exist	VERB
ejpam-6133	342	45	and	and	CCONJ
ejpam-6133	342	46	is	be	AUX
ejpam-6133	342	47	finite	finite	ADJ
ejpam-6133	342	48	.	.	PUNCT
ejpam-6133	343	1	in	in	ADP
ejpam-6133	343	2	℧	℧	PROPN
ejpam-6133	343	3	=	=	SYM
ejpam-6133	343	4	c([τ1	c([τ1	PROPN
ejpam-6133	343	5	,	,	PUNCT
ejpam-6133	343	6	τ2	τ2	PROPN
ejpam-6133	343	7	]	]	PUNCT
ejpam-6133	343	8	)	)	PUNCT
ejpam-6133	343	9	,	,	PUNCT
ejpam-6133	343	10	if	if	SCONJ
ejpam-6133	343	11	x	x	ADP
ejpam-6133	343	12	≤	≤	NOUN
ejpam-6133	343	13	y	y	NOUN
ejpam-6133	343	14	,	,	PUNCT
ejpam-6133	343	15	then	then	ADV
ejpam-6133	343	16	there	there	PRON
ejpam-6133	343	17	is	be	VERB
ejpam-6133	343	18	z	z	PROPN
ejpam-6133	343	19	∈	∈	PROPN
ejpam-6133	343	20	℧	℧	PROPN
ejpam-6133	343	21	so	so	SCONJ
ejpam-6133	343	22	that	that	SCONJ
ejpam-6133	343	23	x	x	X
ejpam-6133	343	24	≤	≤	NUM
ejpam-6133	343	25	z	z	NOUN
ejpam-6133	343	26	and	and	CCONJ
ejpam-6133	343	27	y	y	PROPN
ejpam-6133	343	28	≤	≤	PROPN
ejpam-6133	343	29	z	z	NOUN
ejpam-6133	343	30	,	,	PUNCT
ejpam-6133	343	31	and	and	CCONJ
ejpam-6133	343	32	so	so	ADV
ejpam-6133	343	33	(	(	PUNCT
ejpam-6133	343	34	w	w	NOUN
ejpam-6133	343	35	)	)	PUNCT
ejpam-6133	343	36	is	be	AUX
ejpam-6133	343	37	satisfied	satisfied	ADJ
ejpam-6133	343	38	.	.	PUNCT
ejpam-6133	344	1	thus	thus	ADV
ejpam-6133	344	2	,	,	PUNCT
ejpam-6133	344	3	all	all	DET
ejpam-6133	344	4	the	the	DET
ejpam-6133	344	5	conditions	condition	NOUN
ejpam-6133	344	6	of	of	ADP
ejpam-6133	344	7	theorem	theorem	ADJ
ejpam-6133	344	8	1	1	NUM
ejpam-6133	344	9	are	be	AUX
ejpam-6133	344	10	satisfied	satisfied	ADJ
ejpam-6133	344	11	,	,	PUNCT
ejpam-6133	344	12	and	and	CCONJ
ejpam-6133	344	13	hence	hence	ADV
ejpam-6133	344	14	⊤	⊤	PROPN
ejpam-6133	344	15	possesses	possess	VERB
ejpam-6133	344	16	a	a	DET
ejpam-6133	344	17	unique	unique	ADJ
ejpam-6133	344	18	fp	fp	NOUN
ejpam-6133	344	19	in	in	ADP
ejpam-6133	344	20	℧	℧	PROPN
ejpam-6133	344	21	.	.	PUNCT
ejpam-6133	345	1	that	that	PRON
ejpam-6133	345	2	is	be	AUX
ejpam-6133	345	3	,	,	PUNCT
ejpam-6133	345	4	the	the	DET
ejpam-6133	345	5	nonlinear	nonlinear	ADJ
ejpam-6133	345	6	fredholm	fredholm	ADJ
ejpam-6133	345	7	functional	functional	ADJ
ejpam-6133	345	8	integral	integral	ADJ
ejpam-6133	345	9	equation	equation	NOUN
ejpam-6133	345	10	(	(	PUNCT
ejpam-6133	345	11	7	7	X
ejpam-6133	345	12	)	)	PUNCT
ejpam-6133	345	13	has	have	VERB
ejpam-6133	345	14	a	a	DET
ejpam-6133	345	15	unique	unique	ADJ
ejpam-6133	345	16	solution	solution	NOUN
ejpam-6133	345	17	.	.	PUNCT
ejpam-6133	346	1	example	example	NOUN
ejpam-6133	347	1	3	3	X
ejpam-6133	347	2	.	.	X
ejpam-6133	347	3	take	take	VERB
ejpam-6133	347	4	the	the	DET
ejpam-6133	347	5	following	following	ADJ
ejpam-6133	347	6	nonlinear	nonlinear	ADJ
ejpam-6133	347	7	fredholm	fredholm	ADJ
ejpam-6133	347	8	functional	functional	ADJ
ejpam-6133	347	9	integral	integral	ADJ
ejpam-6133	347	10	equation	equation	NOUN
ejpam-6133	347	11	:	:	PUNCT
ejpam-6133	347	12	for	for	ADP
ejpam-6133	347	13	t	t	PROPN
ejpam-6133	347	14	∈	∈	PROPN
ejpam-6133	348	1	[	[	X
ejpam-6133	348	2	0	0	NUM
ejpam-6133	348	3	,	,	PUNCT
ejpam-6133	348	4	1	1	NUM
ejpam-6133	348	5	]	]	PUNCT
ejpam-6133	348	6	and	and	CCONJ
ejpam-6133	348	7	λ	λ	X
ejpam-6133	348	8	=	=	NOUN
ejpam-6133	348	9	1	1	NUM
ejpam-6133	348	10	,	,	PUNCT
ejpam-6133	348	11	x(t	x(t	PROPN
ejpam-6133	348	12	)	)	PUNCT
ejpam-6133	348	13	=	=	SYM
ejpam-6133	349	1	1	1	NUM
ejpam-6133	349	2	+	+	NUM
ejpam-6133	349	3	∫	∫	PROPN
ejpam-6133	349	4	1	1	NUM
ejpam-6133	349	5	0	0	NUM
ejpam-6133	349	6	1	1	NUM
ejpam-6133	349	7	256	256	NUM
ejpam-6133	349	8	(	(	PUNCT
ejpam-6133	349	9	|x(r)|	|x(r)|	PROPN
ejpam-6133	349	10	(	(	PUNCT
ejpam-6133	349	11	1	1	NUM
ejpam-6133	349	12	+	+	CCONJ
ejpam-6133	349	13	|x(r)|	|x(r)|	NOUN
ejpam-6133	349	14	)	)	PUNCT
ejpam-6133	349	15	2	2	NUM
ejpam-6133	350	1	+	+	CCONJ
ejpam-6133	350	2	|x(r)|	|x(r)|	PROPN
ejpam-6133	350	3	+	+	CCONJ
ejpam-6133	350	4	∣∣x	∣∣x	PROPN
ejpam-6133	350	5	(	(	PUNCT
ejpam-6133	350	6	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	350	7	(	(	PUNCT
ejpam-6133	350	8	1	1	NUM
ejpam-6133	350	9	+	+	NUM
ejpam-6133	350	10	∣∣x	∣∣x	PROPN
ejpam-6133	350	11	(	(	PUNCT
ejpam-6133	350	12	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	350	13	)	)	PUNCT
ejpam-6133	350	14	2	2	NUM
ejpam-6133	350	15	+	+	X
ejpam-6133	350	16	∣∣x	∣∣x	NOUN
ejpam-6133	350	17	(	(	PUNCT
ejpam-6133	350	18	r2)∣∣	r2)∣∣	VERB
ejpam-6133	350	19	+	+	CCONJ
ejpam-6133	350	20	tr	tr	NOUN
ejpam-6133	350	21	|x(0)|	|x(0)|	NOUN
ejpam-6133	350	22	(	(	PUNCT
ejpam-6133	350	23	1	1	NUM
ejpam-6133	350	24	+	+	CCONJ
ejpam-6133	350	25	|x(0)|	|x(0)|	NOUN
ejpam-6133	350	26	)	)	PUNCT
ejpam-6133	350	27	2	2	NUM
ejpam-6133	351	1	+	+	NUM
ejpam-6133	351	2	|x(0)|	|x(0)|	NOUN
ejpam-6133	351	3	+	+	CCONJ
ejpam-6133	351	4	tr	tr	VERB
ejpam-6133	351	5	|x(1)|	|x(1)|	ADJ
ejpam-6133	351	6	(	(	PUNCT
ejpam-6133	351	7	1	1	NUM
ejpam-6133	351	8	+	+	CCONJ
ejpam-6133	351	9	|x(1)|	|x(1)|	ADJ
ejpam-6133	351	10	)	)	PUNCT
ejpam-6133	351	11	2	2	NUM
ejpam-6133	351	12	+	+	CCONJ
ejpam-6133	351	13	|x(1)|	|x(1)|	ADJ
ejpam-6133	351	14	)	)	PUNCT
ejpam-6133	351	15	dr	dr	PROPN
ejpam-6133	351	16	,	,	PUNCT
ejpam-6133	351	17	(	(	PUNCT
ejpam-6133	351	18	10	10	NUM
ejpam-6133	351	19	)	)	PUNCT
ejpam-6133	351	20	where	where	SCONJ
ejpam-6133	351	21	k	k	NOUN
ejpam-6133	352	1	:	:	PUNCT
ejpam-6133	353	1	[	[	X
ejpam-6133	353	2	0	0	NUM
ejpam-6133	353	3	,	,	PUNCT
ejpam-6133	353	4	1]×	1]×	NUM
ejpam-6133	353	5	[	[	X
ejpam-6133	353	6	0	0	NUM
ejpam-6133	353	7	,	,	PUNCT
ejpam-6133	353	8	1]×	1]×	NUM
ejpam-6133	353	9	r4	r4	NOUN
ejpam-6133	353	10	−→	−→	NOUN
ejpam-6133	353	11	r	r	NOUN
ejpam-6133	353	12	is	be	AUX
ejpam-6133	353	13	defined	define	VERB
ejpam-6133	353	14	by	by	ADP
ejpam-6133	353	15	k(t	k(t	PROPN
ejpam-6133	353	16	,	,	PUNCT
ejpam-6133	353	17	r	r	NOUN
ejpam-6133	353	18	,	,	PUNCT
ejpam-6133	353	19	x(r	x(r	PROPN
ejpam-6133	353	20	)	)	PUNCT
ejpam-6133	353	21	,	,	PUNCT
ejpam-6133	353	22	x	x	X
ejpam-6133	353	23	(	(	PUNCT
ejpam-6133	353	24	r	r	NOUN
ejpam-6133	353	25	2	2	NUM
ejpam-6133	353	26	)	)	PUNCT
ejpam-6133	353	27	,	,	PUNCT
ejpam-6133	353	28	x(0	x(0	PROPN
ejpam-6133	353	29	)	)	PUNCT
ejpam-6133	353	30	,	,	PUNCT
ejpam-6133	353	31	x(1	x(1	PROPN
ejpam-6133	353	32	)	)	PUNCT
ejpam-6133	353	33	)	)	PUNCT
ejpam-6133	354	1	=	=	PUNCT
ejpam-6133	355	1	1	1	NUM
ejpam-6133	355	2	256	256	NUM
ejpam-6133	355	3	(	(	PUNCT
ejpam-6133	355	4	|x(r)|	|x(r)|	PROPN
ejpam-6133	355	5	(	(	PUNCT
ejpam-6133	355	6	1	1	NUM
ejpam-6133	355	7	+	+	CCONJ
ejpam-6133	355	8	|x(r)|	|x(r)|	NOUN
ejpam-6133	355	9	)	)	PUNCT
ejpam-6133	355	10	2	2	NUM
ejpam-6133	355	11	+	+	CCONJ
ejpam-6133	355	12	|x(r)|	|x(r)|	PROPN
ejpam-6133	355	13	+	+	CCONJ
ejpam-6133	355	14	∣∣x	∣∣x	PROPN
ejpam-6133	355	15	(	(	PUNCT
ejpam-6133	355	16	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	355	17	(	(	PUNCT
ejpam-6133	355	18	1	1	NUM
ejpam-6133	355	19	+	+	NUM
ejpam-6133	355	20	∣∣x	∣∣x	PROPN
ejpam-6133	355	21	(	(	PUNCT
ejpam-6133	355	22	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	355	23	)	)	PUNCT
ejpam-6133	355	24	2	2	NUM
ejpam-6133	355	25	+	+	X
ejpam-6133	355	26	∣∣x	∣∣x	NOUN
ejpam-6133	355	27	(	(	PUNCT
ejpam-6133	355	28	r2)∣∣	r2)∣∣	VERB
ejpam-6133	355	29	+	+	CCONJ
ejpam-6133	355	30	tr	tr	NOUN
ejpam-6133	355	31	|x(0)|	|x(0)|	NOUN
ejpam-6133	355	32	(	(	PUNCT
ejpam-6133	355	33	1	1	NUM
ejpam-6133	355	34	+	+	CCONJ
ejpam-6133	355	35	|x(0)|	|x(0)|	NOUN
ejpam-6133	355	36	)	)	PUNCT
ejpam-6133	355	37	2	2	NUM
ejpam-6133	356	1	+	+	NUM
ejpam-6133	357	1	|x(0)|	|x(0)|	NOUN
ejpam-6133	357	2	+	+	CCONJ
ejpam-6133	357	3	tr	tr	VERB
ejpam-6133	357	4	|x(1)|	|x(1)|	ADJ
ejpam-6133	357	5	(	(	PUNCT
ejpam-6133	357	6	1	1	NUM
ejpam-6133	357	7	+	+	CCONJ
ejpam-6133	357	8	|x(1)|	|x(1)|	ADJ
ejpam-6133	357	9	)	)	PUNCT
ejpam-6133	357	10	2	2	NUM
ejpam-6133	358	1	+	+	CCONJ
ejpam-6133	358	2	|x(1)|	|x(1)|	NOUN
ejpam-6133	358	3	)	)	PUNCT
ejpam-6133	358	4	.	.	PUNCT
ejpam-6133	359	1	let	let	VERB
ejpam-6133	359	2	g	g	NOUN
ejpam-6133	359	3	:	:	PUNCT
ejpam-6133	360	1	[	[	X
ejpam-6133	360	2	0	0	NUM
ejpam-6133	360	3	,	,	PUNCT
ejpam-6133	360	4	1	1	NUM
ejpam-6133	360	5	]	]	X
ejpam-6133	360	6	−→	−→	NOUN
ejpam-6133	360	7	[	[	X
ejpam-6133	360	8	0	0	NUM
ejpam-6133	360	9	,	,	PUNCT
ejpam-6133	360	10	1	1	NUM
ejpam-6133	360	11	]	]	PUNCT
ejpam-6133	360	12	be	be	AUX
ejpam-6133	360	13	given	give	VERB
ejpam-6133	360	14	as	as	ADP
ejpam-6133	360	15	g(r	g(r	NOUN
ejpam-6133	360	16	)	)	PUNCT
ejpam-6133	360	17	=	=	SYM
ejpam-6133	361	1	r	r	NOUN
ejpam-6133	361	2	2	2	NUM
ejpam-6133	361	3	and	and	CCONJ
ejpam-6133	361	4	f	f	NOUN
ejpam-6133	361	5	:	:	PUNCT
ejpam-6133	362	1	[	[	X
ejpam-6133	362	2	0	0	NUM
ejpam-6133	362	3	,	,	PUNCT
ejpam-6133	362	4	1	1	NUM
ejpam-6133	362	5	]	]	X
ejpam-6133	362	6	−→	−→	NOUN
ejpam-6133	362	7	r	r	NOUN
ejpam-6133	362	8	be	be	AUX
ejpam-6133	362	9	defined	define	VERB
ejpam-6133	362	10	by	by	ADP
ejpam-6133	362	11	f(t	f(t	NOUN
ejpam-6133	362	12	)	)	PUNCT
ejpam-6133	362	13	=	=	SYM
ejpam-6133	363	1	1	1	X
ejpam-6133	363	2	.	.	PUNCT
ejpam-6133	363	3	these	these	DET
ejpam-6133	363	4	functions	function	NOUN
ejpam-6133	363	5	are	be	AUX
ejpam-6133	363	6	continuous	continuous	ADJ
ejpam-6133	363	7	and	and	CCONJ
ejpam-6133	363	8	x	x	SYM
ejpam-6133	363	9	∈	∈	PROPN
ejpam-6133	363	10	c([0	c([0	NOUN
ejpam-6133	363	11	,	,	PUNCT
ejpam-6133	363	12	1	1	NUM
ejpam-6133	363	13	]	]	PUNCT
ejpam-6133	363	14	)	)	PUNCT
ejpam-6133	363	15	is	be	AUX
ejpam-6133	363	16	the	the	DET
ejpam-6133	363	17	unknown	unknown	ADJ
ejpam-6133	363	18	function	function	NOUN
ejpam-6133	363	19	.	.	PUNCT
ejpam-6133	364	1	in	in	ADP
ejpam-6133	364	2	this	this	DET
ejpam-6133	364	3	case	case	NOUN
ejpam-6133	364	4	,	,	PUNCT
ejpam-6133	364	5	we	we	PRON
ejpam-6133	364	6	will	will	AUX
ejpam-6133	364	7	use	use	VERB
ejpam-6133	364	8	the	the	DET
ejpam-6133	364	9	space	space	NOUN
ejpam-6133	364	10	℧	℧	PROPN
ejpam-6133	364	11	=	=	SYM
ejpam-6133	364	12	c([0	c([0	PROPN
ejpam-6133	364	13	,	,	PUNCT
ejpam-6133	364	14	1	1	NUM
ejpam-6133	364	15	]	]	PUNCT
ejpam-6133	364	16	)	)	PUNCT
ejpam-6133	364	17	endowed	endow	VERB
ejpam-6133	364	18	with	with	ADP
ejpam-6133	364	19	the	the	DET
ejpam-6133	364	20	double	double	ADJ
ejpam-6133	364	21	controlled	control	VERB
ejpam-6133	364	22	metric	metric	ADJ
ejpam-6133	364	23	ζ	ζ	NOUN
ejpam-6133	364	24	:	:	PUNCT
ejpam-6133	364	25	℧	℧	PROPN
ejpam-6133	364	26	×	×	NOUN
ejpam-6133	364	27	℧	℧	X
ejpam-6133	364	28	−→	−→	NOUN
ejpam-6133	364	29	[	[	X
ejpam-6133	364	30	0,+∞	0,+∞	NUM
ejpam-6133	364	31	[	[	PUNCT
ejpam-6133	364	32	defined	define	VERB
ejpam-6133	364	33	by	by	ADP
ejpam-6133	364	34	ζ(µ	ζ(µ	PROPN
ejpam-6133	364	35	,	,	PUNCT
ejpam-6133	364	36	ν	ν	X
ejpam-6133	364	37	)	)	PUNCT
ejpam-6133	364	38	=	=	SYM
ejpam-6133	364	39	sup	sup	NOUN
ejpam-6133	364	40	t∈[0,1	t∈[0,1	NUM
ejpam-6133	364	41	]	]	PUNCT
ejpam-6133	364	42	|µ(t)−	|µ(t)−	X
ejpam-6133	364	43	ν(t)|2	ν(t)|2	PROPN
ejpam-6133	364	44	,	,	PUNCT
ejpam-6133	364	45	∀µ	∀µ	PROPN
ejpam-6133	364	46	,	,	PUNCT
ejpam-6133	364	47	ν	ν	PROPN
ejpam-6133	364	48	∈	∈	PROPN
ejpam-6133	364	49	℧	℧	PROPN
ejpam-6133	364	50	h.	h.	PROPN
ejpam-6133	364	51	aydi	aydi	PROPN
ejpam-6133	364	52	,	,	PUNCT
ejpam-6133	364	53	h.	h.	PROPN
ejpam-6133	364	54	hammouda	hammouda	PROPN
ejpam-6133	364	55	,	,	PUNCT
ejpam-6133	364	56	s.	s.	PROPN
ejpam-6133	364	57	mansour	mansour	PROPN
ejpam-6133	364	58	/	/	SYM
ejpam-6133	364	59	eur	eur	PROPN
ejpam-6133	364	60	.	.	PUNCT
ejpam-6133	365	1	j.	j.	PROPN
ejpam-6133	365	2	pure	pure	PROPN
ejpam-6133	365	3	appl	appl	PROPN
ejpam-6133	365	4	.	.	PROPN
ejpam-6133	365	5	math	math	PROPN
ejpam-6133	365	6	,	,	PUNCT
ejpam-6133	365	7	18	18	NUM
ejpam-6133	365	8	(	(	PUNCT
ejpam-6133	365	9	3	3	NUM
ejpam-6133	365	10	)	)	PUNCT
ejpam-6133	365	11	(	(	PUNCT
ejpam-6133	365	12	2025	2025	NUM
ejpam-6133	365	13	)	)	PUNCT
ejpam-6133	365	14	,	,	PUNCT
ejpam-6133	365	15	6133	6133	NUM
ejpam-6133	365	16	15	15	NUM
ejpam-6133	365	17	of	of	ADP
ejpam-6133	365	18	18	18	NUM
ejpam-6133	365	19	the	the	DET
ejpam-6133	365	20	space	space	NOUN
ejpam-6133	365	21	(	(	PUNCT
ejpam-6133	365	22	℧	℧	PROPN
ejpam-6133	365	23	,	,	PUNCT
ejpam-6133	365	24	ζ	ζ	NOUN
ejpam-6133	365	25	)	)	PUNCT
ejpam-6133	365	26	is	be	AUX
ejpam-6133	365	27	a	a	DET
ejpam-6133	365	28	dcms	dcms	NOUN
ejpam-6133	365	29	with	with	ADP
ejpam-6133	365	30	controlled	control	VERB
ejpam-6133	365	31	functions	function	NOUN
ejpam-6133	365	32	ϖ(µ	ϖ(µ	NOUN
ejpam-6133	365	33	,	,	PUNCT
ejpam-6133	365	34	ν	ν	X
ejpam-6133	365	35	)	)	PUNCT
ejpam-6133	365	36	=	=	SYM
ejpam-6133	365	37	2	2	NUM
ejpam-6133	365	38	;	;	PUNCT
ejpam-6133	365	39	ϵ(µ	ϵ(µ	NOUN
ejpam-6133	365	40	,	,	PUNCT
ejpam-6133	365	41	ν	ν	NOUN
ejpam-6133	365	42	)	)	PUNCT
ejpam-6133	365	43	=	=	SYM
ejpam-6133	365	44	2	2	NUM
ejpam-6133	365	45	+	+	CCONJ
ejpam-6133	365	46	1	1	NUM
ejpam-6133	365	47	1	1	NUM
ejpam-6133	365	48	+	+	SYM
ejpam-6133	365	49	1	1	NUM
ejpam-6133	365	50	1+∥µ∥∞	1+∥µ∥∞	NOUN
ejpam-6133	365	51	+	+	CCONJ
ejpam-6133	365	52	1	1	NUM
ejpam-6133	365	53	1	1	NUM
ejpam-6133	365	54	+	+	CCONJ
ejpam-6133	365	55	1	1	NUM
ejpam-6133	365	56	1+∥ν∥∞	1+∥ν∥∞	NOUN
ejpam-6133	365	57	.	.	PUNCT
ejpam-6133	366	1	take	take	VERB
ejpam-6133	366	2	the	the	DET
ejpam-6133	366	3	operator	operator	NOUN
ejpam-6133	366	4	⊤	⊤	NOUN
ejpam-6133	366	5	:	:	PUNCT
ejpam-6133	366	6	℧	℧	PUNCT
ejpam-6133	366	7	−→	−→	NOUN
ejpam-6133	366	8	℧	℧	PROPN
ejpam-6133	366	9	defined	define	VERB
ejpam-6133	366	10	for	for	ADP
ejpam-6133	366	11	t	t	PROPN
ejpam-6133	366	12	∈	∈	PROPN
ejpam-6133	367	1	[	[	X
ejpam-6133	367	2	0	0	NUM
ejpam-6133	367	3	,	,	PUNCT
ejpam-6133	367	4	1	1	NUM
ejpam-6133	367	5	]	]	PUNCT
ejpam-6133	367	6	and	and	CCONJ
ejpam-6133	367	7	x	x	SYM
ejpam-6133	367	8	∈	∈	PROPN
ejpam-6133	367	9	℧	℧	PROPN
ejpam-6133	367	10	as	as	SCONJ
ejpam-6133	367	11	follows	follow	VERB
ejpam-6133	367	12	:	:	PUNCT
ejpam-6133	367	13	⊤x(t	⊤x(t	PROPN
ejpam-6133	367	14	)	)	PUNCT
ejpam-6133	367	15	=	=	SYM
ejpam-6133	368	1	1	1	NUM
ejpam-6133	368	2	+	+	NUM
ejpam-6133	368	3	∫	∫	PROPN
ejpam-6133	368	4	1	1	NUM
ejpam-6133	368	5	0	0	NUM
ejpam-6133	368	6	1	1	NUM
ejpam-6133	368	7	256	256	NUM
ejpam-6133	368	8	(	(	PUNCT
ejpam-6133	368	9	|x(r)|	|x(r)|	PROPN
ejpam-6133	368	10	(	(	PUNCT
ejpam-6133	368	11	1	1	NUM
ejpam-6133	368	12	+	+	CCONJ
ejpam-6133	368	13	|x(r)|	|x(r)|	NOUN
ejpam-6133	368	14	)	)	PUNCT
ejpam-6133	368	15	2	2	NUM
ejpam-6133	369	1	+	+	CCONJ
ejpam-6133	369	2	|x(r)|	|x(r)|	PROPN
ejpam-6133	369	3	+	+	CCONJ
ejpam-6133	369	4	∣∣x	∣∣x	PROPN
ejpam-6133	369	5	(	(	PUNCT
ejpam-6133	369	6	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	369	7	(	(	PUNCT
ejpam-6133	369	8	1	1	NUM
ejpam-6133	369	9	+	+	NUM
ejpam-6133	369	10	∣∣x	∣∣x	PROPN
ejpam-6133	369	11	(	(	PUNCT
ejpam-6133	369	12	r2)∣∣	r2)∣∣	NOUN
ejpam-6133	369	13	)	)	PUNCT
ejpam-6133	369	14	2	2	NUM
ejpam-6133	369	15	+	+	X
ejpam-6133	369	16	∣∣x	∣∣x	NOUN
ejpam-6133	369	17	(	(	PUNCT
ejpam-6133	369	18	r2)∣∣	r2)∣∣	VERB
ejpam-6133	369	19	+	+	CCONJ
ejpam-6133	369	20	tr	tr	NOUN
ejpam-6133	369	21	|x(0)|	|x(0)|	NOUN
ejpam-6133	369	22	(	(	PUNCT
ejpam-6133	369	23	1	1	NUM
ejpam-6133	369	24	+	+	CCONJ
ejpam-6133	369	25	|x(0)|	|x(0)|	NOUN
ejpam-6133	369	26	)	)	PUNCT
ejpam-6133	369	27	2	2	NUM
ejpam-6133	370	1	+	+	NUM
ejpam-6133	370	2	|x(0)|	|x(0)|	NOUN
ejpam-6133	370	3	+	+	CCONJ
ejpam-6133	370	4	tr	tr	VERB
ejpam-6133	370	5	|x(1)|	|x(1)|	ADJ
ejpam-6133	370	6	(	(	PUNCT
ejpam-6133	370	7	1	1	NUM
ejpam-6133	370	8	+	+	CCONJ
ejpam-6133	370	9	|x(1)|	|x(1)|	ADJ
ejpam-6133	370	10	)	)	PUNCT
ejpam-6133	370	11	2	2	NUM
ejpam-6133	370	12	+	+	CCONJ
ejpam-6133	370	13	|x(1)|	|x(1)|	ADJ
ejpam-6133	370	14	)	)	PUNCT
ejpam-6133	370	15	dr	dr	PROPN
ejpam-6133	370	16	.	.	PROPN
ejpam-6133	371	1	in	in	ADP
ejpam-6133	371	2	what	what	PRON
ejpam-6133	371	3	follows	follow	VERB
ejpam-6133	371	4	,	,	PUNCT
ejpam-6133	371	5	the	the	DET
ejpam-6133	371	6	conditions	condition	NOUN
ejpam-6133	371	7	of	of	ADP
ejpam-6133	371	8	theorem	theorem	NOUN
ejpam-6133	371	9	1	1	NUM
ejpam-6133	371	10	are	be	AUX
ejpam-6133	371	11	checked	check	VERB
ejpam-6133	371	12	.	.	PUNCT
ejpam-6133	372	1	it	it	PRON
ejpam-6133	372	2	is	be	AUX
ejpam-6133	372	3	observed	observe	VERB
ejpam-6133	372	4	that	that	SCONJ
ejpam-6133	372	5	the	the	DET
ejpam-6133	372	6	function	function	NOUN
ejpam-6133	372	7	k	k	PROPN
ejpam-6133	372	8	is	be	AUX
ejpam-6133	372	9	non	non	ADJ
ejpam-6133	372	10	-	-	ADJ
ejpam-6133	372	11	decreasing	decrease	VERB
ejpam-6133	372	12	.	.	PUNCT
ejpam-6133	373	1	thereafter	thereafter	ADV
ejpam-6133	373	2	,	,	PUNCT
ejpam-6133	373	3	we	we	PRON
ejpam-6133	373	4	will	will	AUX
ejpam-6133	373	5	quote	quote	VERB
ejpam-6133	373	6	the	the	DET
ejpam-6133	373	7	following	follow	VERB
ejpam-6133	373	8	lemma	lemma	PROPN
ejpam-6133	373	9	that	that	SCONJ
ejpam-6133	373	10	we	we	PRON
ejpam-6133	373	11	will	will	AUX
ejpam-6133	373	12	use	use	VERB
ejpam-6133	373	13	in	in	ADP
ejpam-6133	373	14	the	the	DET
ejpam-6133	373	15	sequel	sequel	NOUN
ejpam-6133	373	16	.	.	PUNCT
ejpam-6133	374	1	lemma	lemma	PROPN
ejpam-6133	374	2	2	2	NUM
ejpam-6133	374	3	.	.	PUNCT
ejpam-6133	375	1	for	for	ADP
ejpam-6133	375	2	all	all	DET
ejpam-6133	375	3	τ1	τ1	NOUN
ejpam-6133	375	4	,	,	PUNCT
ejpam-6133	375	5	τ2	τ2	ADJ
ejpam-6133	375	6	≥	≥	NOUN
ejpam-6133	375	7	0	0	NUM
ejpam-6133	375	8	,	,	PUNCT
ejpam-6133	375	9	we	we	PRON
ejpam-6133	375	10	have	have	VERB
ejpam-6133	375	11	the	the	DET
ejpam-6133	375	12	a+	a+	PRON
ejpam-6133	375	13	b	b	NOUN
ejpam-6133	375	14	≤	≤	ADV
ejpam-6133	375	15	2	2	NUM
ejpam-6133	375	16	(	(	PUNCT
ejpam-6133	375	17	a2	a2	NOUN
ejpam-6133	375	18	+	+	CCONJ
ejpam-6133	375	19	b2	b2	NOUN
ejpam-6133	375	20	)	)	PUNCT
ejpam-6133	375	21	1	1	NUM
ejpam-6133	375	22	2	2	NUM
ejpam-6133	375	23	.	.	PUNCT
ejpam-6133	376	1	at	at	ADP
ejpam-6133	376	2	this	this	DET
ejpam-6133	376	3	moment	moment	NOUN
ejpam-6133	376	4	,	,	PUNCT
ejpam-6133	376	5	for	for	ADP
ejpam-6133	376	6	t	t	PROPN
ejpam-6133	376	7	,	,	PUNCT
ejpam-6133	376	8	r	r	NOUN
ejpam-6133	376	9	∈	∈	PROPN
ejpam-6133	377	1	[	[	X
ejpam-6133	377	2	0	0	NUM
ejpam-6133	377	3	,	,	PUNCT
ejpam-6133	377	4	1	1	NUM
ejpam-6133	377	5	]	]	PUNCT
ejpam-6133	377	6	,	,	PUNCT
ejpam-6133	377	7	x	x	X
ejpam-6133	377	8	,	,	PUNCT
ejpam-6133	377	9	y	y	PROPN
ejpam-6133	377	10	∈	∈	PROPN
ejpam-6133	377	11	℧	℧	PROPN
ejpam-6133	377	12	=	=	SYM
ejpam-6133	377	13	c([0	c([0	PROPN
ejpam-6133	377	14	,	,	PUNCT
ejpam-6133	377	15	1	1	NUM
ejpam-6133	377	16	]	]	PUNCT
ejpam-6133	377	17	)	)	PUNCT
ejpam-6133	377	18	with	with	ADP
ejpam-6133	377	19	x(r	x(r	NOUN
ejpam-6133	377	20	)	)	PUNCT
ejpam-6133	377	21	≤	≤	NUM
ejpam-6133	377	22	y(r	y(r	NOUN
ejpam-6133	377	23	)	)	PUNCT
ejpam-6133	377	24	for	for	ADP
ejpam-6133	377	25	all	all	DET
ejpam-6133	377	26	r	r	NOUN
ejpam-6133	377	27	∈	∈	PROPN
ejpam-6133	378	1	[	[	X
ejpam-6133	378	2	0	0	NUM
ejpam-6133	378	3	,	,	PUNCT
ejpam-6133	378	4	1	1	NUM
ejpam-6133	378	5	]	]	PUNCT
ejpam-6133	378	6	,	,	PUNCT
ejpam-6133	378	7	we	we	PRON
ejpam-6133	378	8	estimate	estimate	VERB
ejpam-6133	378	9	the	the	DET
ejpam-6133	378	10	difference	difference	NOUN
ejpam-6133	378	11	|k	|k	NOUN
ejpam-6133	378	12	(	(	PUNCT
ejpam-6133	378	13	t	t	PROPN
ejpam-6133	378	14	,	,	PUNCT
ejpam-6133	378	15	r	r	NOUN
ejpam-6133	378	16	,	,	PUNCT
ejpam-6133	378	17	x(r	x(r	PROPN
ejpam-6133	378	18	)	)	PUNCT
ejpam-6133	378	19	,	,	PUNCT
ejpam-6133	378	20	x(g(r	x(g(r	PROPN
ejpam-6133	378	21	)	)	PUNCT
ejpam-6133	378	22	)	)	PUNCT
ejpam-6133	378	23	,	,	PUNCT
ejpam-6133	378	24	x(τ1	x(τ1	PROPN
ejpam-6133	378	25	)	)	PUNCT
ejpam-6133	378	26	,	,	PUNCT
ejpam-6133	378	27	x(τ2))−k	x(τ2))−k	X
ejpam-6133	378	28	(	(	PUNCT
ejpam-6133	378	29	t	t	PROPN
ejpam-6133	378	30	,	,	PUNCT
ejpam-6133	378	31	r	r	NOUN
ejpam-6133	378	32	,	,	PUNCT
ejpam-6133	378	33	y(r	y(r	PROPN
ejpam-6133	378	34	)	)	PUNCT
ejpam-6133	378	35	,	,	PUNCT
ejpam-6133	378	36	y(g(r	y(g(r	PROPN
ejpam-6133	378	37	)	)	PUNCT
ejpam-6133	378	38	)	)	PUNCT
ejpam-6133	378	39	,	,	PUNCT
ejpam-6133	378	40	y(τ1	y(τ1	PROPN
ejpam-6133	378	41	)	)	PUNCT
ejpam-6133	378	42	,	,	PUNCT
ejpam-6133	378	43	y(τ2))|	y(τ2))|	NOUN
ejpam-6133	378	44	≤	≤	NOUN
ejpam-6133	378	45	1	1	NUM
ejpam-6133	378	46	256	256	NUM
ejpam-6133	378	47	∣∣∣	∣∣∣	ADJ
ejpam-6133	378	48	|x(r)|(1+|x(r)|	|x(r)|(1+|x(r)|	PROPN
ejpam-6133	378	49	)	)	PUNCT
ejpam-6133	379	1	2+|x(r)|	2+|x(r)|	NUM
ejpam-6133	379	2	−	−	PROPN
ejpam-6133	379	3	|y(r)|(1+|y(r)|	|y(r)|(1+|y(r)|	PROPN
ejpam-6133	379	4	)	)	PUNCT
ejpam-6133	379	5	2+|y(r)|	2+|y(r)|	NUM
ejpam-6133	379	6	∣∣∣+	∣∣∣+	NUM
ejpam-6133	379	7	1	1	NUM
ejpam-6133	379	8	256	256	NUM
ejpam-6133	379	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6133	379	10	|x	|x	NOUN
ejpam-6133	379	11	(	(	PUNCT
ejpam-6133	379	12	r2	r2	PROPN
ejpam-6133	379	13	)	)	PUNCT
ejpam-6133	379	14	|(1+|x	|(1+|x	NOUN
ejpam-6133	379	15	(	(	PUNCT
ejpam-6133	379	16	r2	r2	PROPN
ejpam-6133	379	17	)	)	PUNCT
ejpam-6133	379	18	|)2+|x	|)2+|x	PROPN
ejpam-6133	379	19	(	(	PUNCT
ejpam-6133	379	20	r2	r2	PROPN
ejpam-6133	379	21	)	)	PUNCT
ejpam-6133	379	22	|	|	ADV
ejpam-6133	379	23	−	−	PROPN
ejpam-6133	379	24	|y	|y	NOUN
ejpam-6133	379	25	(	(	PUNCT
ejpam-6133	379	26	r2	r2	PROPN
ejpam-6133	379	27	)	)	PUNCT
ejpam-6133	379	28	|(1+|y	|(1+|y	PROPN
ejpam-6133	379	29	(	(	PUNCT
ejpam-6133	379	30	r2	r2	PROPN
ejpam-6133	379	31	)	)	PUNCT
ejpam-6133	379	32	|	|	ADV
ejpam-6133	379	33	)	)	PUNCT
ejpam-6133	379	34	2+|y	2+|y	PROPN
ejpam-6133	379	35	(	(	PUNCT
ejpam-6133	379	36	r2	r2	PROPN
ejpam-6133	379	37	)	)	PUNCT
ejpam-6133	379	38	|	|	ADV
ejpam-6133	379	39	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6133	379	40	+	+	CCONJ
ejpam-6133	379	41	1	1	NUM
ejpam-6133	379	42	256	256	NUM
ejpam-6133	379	43	∣∣∣	∣∣∣	NOUN
ejpam-6133	379	44	tr|x(0)|(1+|x(0)|	tr|x(0)|(1+|x(0)|	NOUN
ejpam-6133	379	45	)	)	PUNCT
ejpam-6133	379	46	2+|x(0)|	2+|x(0)|	NUM
ejpam-6133	379	47	−	−	PROPN
ejpam-6133	379	48	tr|y(0)|(1+|y(0)|	tr|y(0)|(1+|y(0)|	NOUN
ejpam-6133	379	49	)	)	PUNCT
ejpam-6133	379	50	2+|y(0)|	2+|y(0)|	NOUN
ejpam-6133	379	51	∣∣∣+	∣∣∣+	PROPN
ejpam-6133	379	52	1	1	NUM
ejpam-6133	379	53	256	256	NUM
ejpam-6133	379	54	∣∣∣	∣∣∣	ADJ
ejpam-6133	379	55	tr|x(1)|(1+|x(1)|	tr|x(1)|(1+|x(1)|	NOUN
ejpam-6133	379	56	)	)	PUNCT
ejpam-6133	379	57	2+|x(1)|	2+|x(1)|	PROPN
ejpam-6133	380	1	−	−	PROPN
ejpam-6133	381	1	tr|y(1)|(1+|y(1)|	tr|y(1)|(1+|y(1)|	NOUN
ejpam-6133	381	2	)	)	PUNCT
ejpam-6133	381	3	2+|y(1)|	2+|y(1)|	NUM
ejpam-6133	381	4	∣∣∣	∣∣∣	ADJ
ejpam-6133	381	5	=	=	SYM
ejpam-6133	381	6	1	1	NUM
ejpam-6133	381	7	256	256	NUM
ejpam-6133	381	8	(	(	PUNCT
ejpam-6133	381	9	2	2	NUM
ejpam-6133	381	10	+	+	NOUN
ejpam-6133	381	11	2|x(r)|+2|y(r)|+|x(r)||y(r)|)||x(r)|−|y(r)||	2|x(r)|+2|y(r)|+|x(r)||y(r)|)||x(r)|−|y(r)||	NUM
ejpam-6133	381	12	(	(	PUNCT
ejpam-6133	381	13	2+|x(r)|)(2+|y(r)|	2+|x(r)|)(2+|y(r)|	NOUN
ejpam-6133	381	14	)	)	PUNCT
ejpam-6133	382	1	+	+	CCONJ
ejpam-6133	382	2	1	1	NUM
ejpam-6133	382	3	256	256	NUM
ejpam-6133	382	4	(	(	PUNCT
ejpam-6133	382	5	2	2	NUM
ejpam-6133	382	6	+	+	NOUN
ejpam-6133	382	7	2|x	2|x	NUM
ejpam-6133	382	8	(	(	PUNCT
ejpam-6133	382	9	r2	r2	PROPN
ejpam-6133	382	10	)	)	PUNCT
ejpam-6133	382	11	|+2|y	|+2|y	PROPN
ejpam-6133	382	12	(	(	PUNCT
ejpam-6133	382	13	r2	r2	PROPN
ejpam-6133	382	14	)	)	PUNCT
ejpam-6133	382	15	|+|x	|+|x	NOUN
ejpam-6133	382	16	(	(	PUNCT
ejpam-6133	382	17	r2	r2	PROPN
ejpam-6133	382	18	)	)	PUNCT
ejpam-6133	382	19	||y	||y	PROPN
ejpam-6133	382	20	(	(	PUNCT
ejpam-6133	382	21	r2	r2	PROPN
ejpam-6133	382	22	)	)	PUNCT
ejpam-6133	382	23	|)||x	|)||x	NOUN
ejpam-6133	382	24	(	(	PUNCT
ejpam-6133	382	25	r2	r2	PROPN
ejpam-6133	382	26	)	)	PUNCT
ejpam-6133	382	27	|−|y	|−|y	PROPN
ejpam-6133	382	28	(	(	PUNCT
ejpam-6133	382	29	r2	r2	PROPN
ejpam-6133	382	30	)	)	PUNCT
ejpam-6133	382	31	||	||	NOUN
ejpam-6133	383	1	(	(	PUNCT
ejpam-6133	383	2	2+|x	2+|x	NOUN
ejpam-6133	383	3	(	(	PUNCT
ejpam-6133	383	4	r2	r2	PROPN
ejpam-6133	383	5	)	)	PUNCT
ejpam-6133	383	6	|)(2+|y	|)(2+|y	NOUN
ejpam-6133	383	7	(	(	PUNCT
ejpam-6133	383	8	r2	r2	PROPN
ejpam-6133	383	9	)	)	PUNCT
ejpam-6133	383	10	|	|	ADV
ejpam-6133	383	11	)	)	PUNCT
ejpam-6133	384	1	+	+	CCONJ
ejpam-6133	384	2	1	1	NUM
ejpam-6133	384	3	256	256	NUM
ejpam-6133	384	4	(	(	PUNCT
ejpam-6133	384	5	2	2	NUM
ejpam-6133	384	6	+	+	NOUN
ejpam-6133	384	7	2|x(0)|+2|y(0)|+|x(0)||y(0)|)||x(0)|−|y(0)||	2|x(0)|+2|y(0)|+|x(0)||y(0)|)||x(0)|−|y(0)||	NUM
ejpam-6133	384	8	(	(	PUNCT
ejpam-6133	384	9	2+|x(0)|)(2+|y(0)|	2+|x(0)|)(2+|y(0)|	NUM
ejpam-6133	384	10	)	)	PUNCT
ejpam-6133	384	11	+	+	CCONJ
ejpam-6133	384	12	1	1	NUM
ejpam-6133	384	13	256	256	NUM
ejpam-6133	384	14	(	(	PUNCT
ejpam-6133	384	15	2	2	NUM
ejpam-6133	384	16	+	+	NOUN
ejpam-6133	384	17	2|x(1)|+2|y(1)|+|x(1)||y(1)|)||x(1)|−|y(1)||	2|x(1)|+2|y(1)|+|x(1)||y(1)|)||x(1)|−|y(1)||	NUM
ejpam-6133	384	18	(	(	PUNCT
ejpam-6133	384	19	2+|x(1)|)(2+|y(1)|	2+|x(1)|)(2+|y(1)|	NUM
ejpam-6133	384	20	)	)	PUNCT
ejpam-6133	384	21	≤	≤	NOUN
ejpam-6133	384	22	1	1	NUM
ejpam-6133	384	23	256	256	NUM
ejpam-6133	384	24	2(1+|x(r)|)(1+|y(r)|)|x(r)−y(r)|	2(1+|x(r)|)(1+|y(r)|)|x(r)−y(r)|	NUM
ejpam-6133	384	25	(	(	PUNCT
ejpam-6133	384	26	2+|x(r)|)(2+|y(r)|	2+|x(r)|)(2+|y(r)|	NOUN
ejpam-6133	384	27	)	)	PUNCT
ejpam-6133	385	1	+	+	CCONJ
ejpam-6133	385	2	1	1	NUM
ejpam-6133	385	3	256	256	NUM
ejpam-6133	385	4	2(1+|x	2(1+|x	NUM
ejpam-6133	385	5	(	(	PUNCT
ejpam-6133	385	6	r2	r2	PROPN
ejpam-6133	385	7	)	)	PUNCT
ejpam-6133	385	8	|)(1+|y	|)(1+|y	PROPN
ejpam-6133	385	9	(	(	PUNCT
ejpam-6133	385	10	r2	r2	PROPN
ejpam-6133	385	11	)	)	PUNCT
ejpam-6133	385	12	|)|x	|)|x	NOUN
ejpam-6133	385	13	(	(	PUNCT
ejpam-6133	385	14	r2	r2	PROPN
ejpam-6133	385	15	)	)	PUNCT
ejpam-6133	385	16	−y	−y	PROPN
ejpam-6133	385	17	(	(	PUNCT
ejpam-6133	385	18	r	r	NOUN
ejpam-6133	385	19	2	2	NUM
ejpam-6133	385	20	)	)	PUNCT
ejpam-6133	385	21	|	|	CCONJ
ejpam-6133	385	22	(	(	PUNCT
ejpam-6133	385	23	2+|x	2+|x	NOUN
ejpam-6133	385	24	(	(	PUNCT
ejpam-6133	385	25	r2	r2	PROPN
ejpam-6133	385	26	)	)	PUNCT
ejpam-6133	385	27	|)(2+|y	|)(2+|y	NOUN
ejpam-6133	385	28	(	(	PUNCT
ejpam-6133	385	29	r2	r2	PROPN
ejpam-6133	385	30	)	)	PUNCT
ejpam-6133	385	31	|	|	ADV
ejpam-6133	385	32	)	)	PUNCT
ejpam-6133	386	1	+	+	CCONJ
ejpam-6133	386	2	1	1	NUM
ejpam-6133	386	3	256	256	NUM
ejpam-6133	386	4	2(1+|x(0)|)(1+|y(0)|)|x(0)−y(0)|	2(1+|x(0)|)(1+|y(0)|)|x(0)−y(0)|	NUM
ejpam-6133	386	5	(	(	PUNCT
ejpam-6133	386	6	2+|x(0)|)(2+|y(0)|	2+|x(0)|)(2+|y(0)|	NUM
ejpam-6133	386	7	)	)	PUNCT
ejpam-6133	386	8	+	+	CCONJ
ejpam-6133	386	9	1	1	NUM
ejpam-6133	386	10	256	256	NUM
ejpam-6133	386	11	2(1+|x(1)|)(1+|y(1)|)|x(1)−y(1)|	2(1+|x(1)|)(1+|y(1)|)|x(1)−y(1)|	NUM
ejpam-6133	386	12	(	(	PUNCT
ejpam-6133	386	13	2+|x(1)|)(2+|y(1)|	2+|x(1)|)(2+|y(1)|	NUM
ejpam-6133	386	14	)	)	PUNCT
ejpam-6133	386	15	=	=	SYM
ejpam-6133	386	16	1	1	NUM
ejpam-6133	386	17	128	128	NUM
ejpam-6133	386	18	(	(	PUNCT
ejpam-6133	386	19	1+|x(r)|)(1+|y(r)|)|x(r)−y(r)|	1+|x(r)|)(1+|y(r)|)|x(r)−y(r)|	NUM
ejpam-6133	386	20	(	(	PUNCT
ejpam-6133	386	21	2+|x(r)|)(2+|y(r)|	2+|x(r)|)(2+|y(r)|	NOUN
ejpam-6133	386	22	)	)	PUNCT
ejpam-6133	386	23	+	+	CCONJ
ejpam-6133	386	24	1	1	NUM
ejpam-6133	386	25	128	128	NUM
ejpam-6133	386	26	(	(	PUNCT
ejpam-6133	386	27	1+|x	1+|x	NOUN
ejpam-6133	386	28	(	(	PUNCT
ejpam-6133	386	29	r2	r2	PROPN
ejpam-6133	386	30	)	)	PUNCT
ejpam-6133	386	31	|)(1+|y	|)(1+|y	PROPN
ejpam-6133	386	32	(	(	PUNCT
ejpam-6133	386	33	r2	r2	PROPN
ejpam-6133	386	34	)	)	PUNCT
ejpam-6133	386	35	|)|x	|)|x	NOUN
ejpam-6133	386	36	(	(	PUNCT
ejpam-6133	386	37	r2	r2	PROPN
ejpam-6133	386	38	)	)	PUNCT
ejpam-6133	386	39	−y	−y	PROPN
ejpam-6133	386	40	(	(	PUNCT
ejpam-6133	386	41	r	r	NOUN
ejpam-6133	386	42	2	2	NUM
ejpam-6133	386	43	)	)	PUNCT
ejpam-6133	386	44	|	|	CCONJ
ejpam-6133	386	45	(	(	PUNCT
ejpam-6133	386	46	2+|x	2+|x	NOUN
ejpam-6133	386	47	(	(	PUNCT
ejpam-6133	386	48	r2	r2	PROPN
ejpam-6133	386	49	)	)	PUNCT
ejpam-6133	386	50	|)(2+|y	|)(2+|y	NOUN
ejpam-6133	386	51	(	(	PUNCT
ejpam-6133	386	52	r2	r2	PROPN
ejpam-6133	386	53	)	)	PUNCT
ejpam-6133	386	54	|	|	ADV
ejpam-6133	386	55	)	)	PUNCT
ejpam-6133	387	1	+	+	CCONJ
ejpam-6133	387	2	1	1	NUM
ejpam-6133	387	3	128	128	NUM
ejpam-6133	387	4	(	(	PUNCT
ejpam-6133	387	5	1+|x(0)|)(1+|y(0)|)|x(0)−y(0)|	1+|x(0)|)(1+|y(0)|)|x(0)−y(0)|	NUM
ejpam-6133	387	6	(	(	PUNCT
ejpam-6133	387	7	2+|x(0)|)(2+|y(0)|	2+|x(0)|)(2+|y(0)|	NUM
ejpam-6133	387	8	)	)	PUNCT
ejpam-6133	387	9	+	+	CCONJ
ejpam-6133	387	10	1	1	NUM
ejpam-6133	387	11	128	128	NUM
ejpam-6133	387	12	(	(	PUNCT
ejpam-6133	387	13	1+|x(1)|)(1+|y(1)|)|x(1)−y(1)|	1+|x(1)|)(1+|y(1)|)|x(1)−y(1)|	NUM
ejpam-6133	387	14	(	(	PUNCT
ejpam-6133	387	15	2+|x(1)|)(2+|y(1)|	2+|x(1)|)(2+|y(1)|	NUM
ejpam-6133	387	16	)	)	PUNCT
ejpam-6133	387	17	=	=	SYM
ejpam-6133	387	18	1	1	NUM
ejpam-6133	387	19	64	64	NUM
ejpam-6133	387	20	1	1	NUM
ejpam-6133	387	21	2	2	NUM
ejpam-6133	387	22	(	(	PUNCT
ejpam-6133	387	23	1	1	NUM
ejpam-6133	387	24	+	+	NUM
ejpam-6133	387	25	1	1	NUM
ejpam-6133	387	26	1+|x(r)|	1+|x(r)|	NUM
ejpam-6133	387	27	)	)	PUNCT
ejpam-6133	387	28	(	(	PUNCT
ejpam-6133	387	29	1	1	NUM
ejpam-6133	387	30	+	+	NUM
ejpam-6133	387	31	1	1	NUM
ejpam-6133	387	32	1+|y(r)|	1+|y(r)|	NUM
ejpam-6133	387	33	)	)	PUNCT
ejpam-6133	387	34	|x(r)−	|x(r)−	NOUN
ejpam-6133	387	35	y(r)|+	y(r)|+	PROPN
ejpam-6133	387	36	1	1	NUM
ejpam-6133	387	37	64	64	NUM
ejpam-6133	387	38	1	1	NUM
ejpam-6133	387	39	2	2	NUM
ejpam-6133	387	40	(	(	PUNCT
ejpam-6133	387	41	1	1	NUM
ejpam-6133	387	42	+	+	NUM
ejpam-6133	387	43	1	1	NUM
ejpam-6133	387	44	1+|x	1+|x	NUM
ejpam-6133	387	45	(	(	PUNCT
ejpam-6133	387	46	r2	r2	PROPN
ejpam-6133	387	47	)	)	PUNCT
ejpam-6133	387	48	|	|	ADV
ejpam-6133	387	49	)	)	PUNCT
ejpam-6133	387	50	(	(	PUNCT
ejpam-6133	387	51	1	1	NUM
ejpam-6133	387	52	+	+	NUM
ejpam-6133	387	53	1	1	NUM
ejpam-6133	387	54	1+|y	1+|y	NUM
ejpam-6133	387	55	(	(	PUNCT
ejpam-6133	387	56	r2	r2	PROPN
ejpam-6133	387	57	)	)	PUNCT
ejpam-6133	387	58	|	|	ADV
ejpam-6133	387	59	)	)	PUNCT
ejpam-6133	388	1	∣∣x	∣∣x	NOUN
ejpam-6133	388	2	(	(	PUNCT
ejpam-6133	388	3	r2)−	r2)−	VERB
ejpam-6133	388	4	y	y	PROPN
ejpam-6133	388	5	(	(	PUNCT
ejpam-6133	388	6	r2	r2	PROPN
ejpam-6133	388	7	)	)	PUNCT
ejpam-6133	388	8	∣∣	∣∣	NUM
ejpam-6133	388	9	1	1	NUM
ejpam-6133	388	10	64	64	NUM
ejpam-6133	388	11	1	1	NUM
ejpam-6133	388	12	2	2	NUM
ejpam-6133	388	13	(	(	PUNCT
ejpam-6133	388	14	1	1	NUM
ejpam-6133	388	15	+	+	NUM
ejpam-6133	388	16	1	1	NUM
ejpam-6133	388	17	1+|x(0)|	1+|x(0)|	NUM
ejpam-6133	388	18	)	)	PUNCT
ejpam-6133	388	19	(	(	PUNCT
ejpam-6133	388	20	1	1	NUM
ejpam-6133	388	21	+	+	SYM
ejpam-6133	388	22	1	1	NUM
ejpam-6133	388	23	1+|y(0)|	1+|y(0)|	NUM
ejpam-6133	388	24	)	)	PUNCT
ejpam-6133	388	25	|x(0)−	|x(0)−	NOUN
ejpam-6133	388	26	y(0)|+	y(0)|+	VERB
ejpam-6133	388	27	1	1	NUM
ejpam-6133	388	28	64	64	NUM
ejpam-6133	388	29	1	1	NUM
ejpam-6133	388	30	2	2	NUM
ejpam-6133	388	31	(	(	PUNCT
ejpam-6133	388	32	1	1	NUM
ejpam-6133	388	33	+	+	NUM
ejpam-6133	388	34	1	1	NUM
ejpam-6133	388	35	1+|x(1)|	1+|x(1)|	NUM
ejpam-6133	388	36	)	)	PUNCT
ejpam-6133	388	37	(	(	PUNCT
ejpam-6133	388	38	1	1	NUM
ejpam-6133	388	39	+	+	SYM
ejpam-6133	388	40	1	1	NUM
ejpam-6133	388	41	1+|y(1)|	1+|y(1)|	NUM
ejpam-6133	388	42	)	)	PUNCT
ejpam-6133	389	1	|x(1)−	|x(1)−	PROPN
ejpam-6133	389	2	y(1)|	y(1)|	PROPN
ejpam-6133	389	3	≤	≤	NOUN
ejpam-6133	389	4	1	1	NUM
ejpam-6133	389	5	64	64	NUM
ejpam-6133	389	6	1	1	NUM
ejpam-6133	389	7	2	2	NUM
ejpam-6133	389	8	+	+	NUM
ejpam-6133	389	9	1	1	NUM
ejpam-6133	389	10	1+|x(r)|+	1+|x(r)|+	NUM
ejpam-6133	389	11	1	1	NUM
ejpam-6133	389	12	1+|y(r)|	1+|y(r)|	NUM
ejpam-6133	389	13	|x(r)−	|x(r)−	NOUN
ejpam-6133	389	14	y(r)|+	y(r)|+	PROPN
ejpam-6133	389	15	1	1	NUM
ejpam-6133	389	16	64	64	NUM
ejpam-6133	389	17	1	1	NUM
ejpam-6133	389	18	2	2	NUM
ejpam-6133	389	19	+	+	NUM
ejpam-6133	389	20	1	1	NUM
ejpam-6133	389	21	1+|x	1+|x	NUM
ejpam-6133	389	22	(	(	PUNCT
ejpam-6133	389	23	r2	r2	PROPN
ejpam-6133	389	24	)	)	PUNCT
ejpam-6133	389	25	|+	|+	NOUN
ejpam-6133	390	1	1	1	NUM
ejpam-6133	390	2	1+|y	1+|y	NUM
ejpam-6133	390	3	(	(	PUNCT
ejpam-6133	390	4	r2	r2	PROPN
ejpam-6133	390	5	)	)	PUNCT
ejpam-6133	391	1	|	|	ADV
ejpam-6133	391	2	∣∣x	∣∣x	ADV
ejpam-6133	391	3	(	(	PUNCT
ejpam-6133	391	4	r2)−	r2)−	VERB
ejpam-6133	391	5	y	y	PROPN
ejpam-6133	391	6	(	(	PUNCT
ejpam-6133	391	7	r2	r2	PROPN
ejpam-6133	391	8	)	)	PUNCT
ejpam-6133	391	9	∣∣	∣∣	NUM
ejpam-6133	391	10	1	1	NUM
ejpam-6133	391	11	64	64	NUM
ejpam-6133	391	12	1	1	NUM
ejpam-6133	391	13	2	2	NUM
ejpam-6133	391	14	+	+	NUM
ejpam-6133	391	15	1	1	NUM
ejpam-6133	391	16	1+|x(0)|+	1+|x(0)|+	NUM
ejpam-6133	391	17	1	1	NUM
ejpam-6133	391	18	1+|y(0)|	1+|y(0)|	NUM
ejpam-6133	391	19	|x(0)−	|x(0)−	NOUN
ejpam-6133	391	20	y(0)|+	y(0)|+	DET
ejpam-6133	391	21	1	1	NUM
ejpam-6133	391	22	64	64	NUM
ejpam-6133	391	23	1	1	NUM
ejpam-6133	391	24	2	2	NUM
ejpam-6133	391	25	+	+	NUM
ejpam-6133	391	26	1	1	NUM
ejpam-6133	391	27	1+|x(1)|+	1+|x(1)|+	NUM
ejpam-6133	391	28	1	1	NUM
ejpam-6133	391	29	1+|y(1)|	1+|y(1)|	NUM
ejpam-6133	391	30	|x(1)−	|x(1)−	PROPN
ejpam-6133	391	31	y(1)|	y(1)|	PROPN
ejpam-6133	391	32	≤	≤	NOUN
ejpam-6133	391	33	1	1	NUM
ejpam-6133	391	34	64	64	NUM
ejpam-6133	391	35	1	1	NUM
ejpam-6133	391	36	2	2	NUM
ejpam-6133	391	37	+	+	NUM
ejpam-6133	391	38	1	1	NUM
ejpam-6133	391	39	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	391	40	+	+	CCONJ
ejpam-6133	391	41	1	1	NUM
ejpam-6133	391	42	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	391	43	|x(r)−	|x(r)−	NOUN
ejpam-6133	391	44	y(r)|+	y(r)|+	PROPN
ejpam-6133	391	45	1	1	NUM
ejpam-6133	391	46	64	64	NUM
ejpam-6133	391	47	1	1	NUM
ejpam-6133	391	48	2	2	NUM
ejpam-6133	391	49	+	+	NUM
ejpam-6133	391	50	1	1	NUM
ejpam-6133	391	51	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	392	1	+	+	CCONJ
ejpam-6133	392	2	1	1	NUM
ejpam-6133	392	3	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	392	4	∣∣x	∣∣x	NOUN
ejpam-6133	392	5	(	(	PUNCT
ejpam-6133	392	6	r2)−	r2)−	VERB
ejpam-6133	392	7	y	y	PROPN
ejpam-6133	392	8	(	(	PUNCT
ejpam-6133	392	9	r2	r2	PROPN
ejpam-6133	392	10	)	)	PUNCT
ejpam-6133	392	11	∣∣	∣∣	NUM
ejpam-6133	392	12	1	1	NUM
ejpam-6133	392	13	64	64	NUM
ejpam-6133	392	14	1	1	NUM
ejpam-6133	392	15	2	2	NUM
ejpam-6133	392	16	+	+	NUM
ejpam-6133	392	17	1	1	NUM
ejpam-6133	392	18	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	392	19	+	+	CCONJ
ejpam-6133	392	20	1	1	NUM
ejpam-6133	392	21	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	392	22	|x(0)−	|x(0)−	PROPN
ejpam-6133	392	23	y(0)|+	y(0)|+	DET
ejpam-6133	392	24	1	1	NUM
ejpam-6133	392	25	64	64	NUM
ejpam-6133	392	26	1	1	NUM
ejpam-6133	392	27	2	2	NUM
ejpam-6133	392	28	+	+	NUM
ejpam-6133	392	29	1	1	NUM
ejpam-6133	392	30	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	392	31	+	+	CCONJ
ejpam-6133	392	32	1	1	NUM
ejpam-6133	392	33	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	392	34	|x(1)−	|x(1)−	VERB
ejpam-6133	392	35	y(1)|	y(1)|	NOUN
ejpam-6133	392	36	=	=	NOUN
ejpam-6133	392	37	1	1	NUM
ejpam-6133	392	38	64	64	NUM
ejpam-6133	392	39	1	1	NUM
ejpam-6133	392	40	2	2	NUM
ejpam-6133	392	41	+	+	NUM
ejpam-6133	392	42	1	1	NUM
ejpam-6133	392	43	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	392	44	+	+	CCONJ
ejpam-6133	392	45	1	1	NUM
ejpam-6133	392	46	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	392	47	[	[	PUNCT
ejpam-6133	392	48	|x(r)−	|x(r)−	NOUN
ejpam-6133	392	49	y(r)|+	y(r)|+	PROPN
ejpam-6133	392	50	∣∣x	∣∣x	PROPN
ejpam-6133	392	51	(	(	PUNCT
ejpam-6133	392	52	r2)−	r2)−	VERB
ejpam-6133	392	53	y	y	PROPN
ejpam-6133	392	54	(	(	PUNCT
ejpam-6133	392	55	r2	r2	PROPN
ejpam-6133	392	56	)	)	PUNCT
ejpam-6133	392	57	∣∣+	∣∣+	PROPN
ejpam-6133	392	58	|x(0)−	|x(0)−	PROPN
ejpam-6133	392	59	y(0)|+	y(0)|+	PRON
ejpam-6133	392	60	|x(1)−	|x(1)−	PROPN
ejpam-6133	392	61	y(1)|	y(1)|	PROPN
ejpam-6133	392	62	]	]	PUNCT
ejpam-6133	392	63	.	.	PUNCT
ejpam-6133	393	1	h.	h.	PROPN
ejpam-6133	393	2	aydi	aydi	PROPN
ejpam-6133	393	3	,	,	PUNCT
ejpam-6133	393	4	h.	h.	PROPN
ejpam-6133	393	5	hammouda	hammouda	PROPN
ejpam-6133	393	6	,	,	PUNCT
ejpam-6133	393	7	s.	s.	PROPN
ejpam-6133	393	8	mansour	mansour	PROPN
ejpam-6133	393	9	/	/	SYM
ejpam-6133	393	10	eur	eur	PROPN
ejpam-6133	393	11	.	.	PUNCT
ejpam-6133	394	1	j.	j.	PROPN
ejpam-6133	394	2	pure	pure	PROPN
ejpam-6133	394	3	appl	appl	PROPN
ejpam-6133	394	4	.	.	PROPN
ejpam-6133	394	5	math	math	PROPN
ejpam-6133	394	6	,	,	PUNCT
ejpam-6133	394	7	18	18	NUM
ejpam-6133	394	8	(	(	PUNCT
ejpam-6133	394	9	3	3	NUM
ejpam-6133	394	10	)	)	PUNCT
ejpam-6133	394	11	(	(	PUNCT
ejpam-6133	394	12	2025	2025	NUM
ejpam-6133	394	13	)	)	PUNCT
ejpam-6133	394	14	,	,	PUNCT
ejpam-6133	394	15	6133	6133	NUM
ejpam-6133	394	16	16	16	NUM
ejpam-6133	394	17	of	of	ADP
ejpam-6133	394	18	18	18	NUM
ejpam-6133	394	19	so	so	ADV
ejpam-6133	394	20	by	by	ADP
ejpam-6133	394	21	lemma	lemma	PROPN
ejpam-6133	394	22	2	2	NUM
ejpam-6133	394	23	,	,	PUNCT
ejpam-6133	394	24	one	one	NUM
ejpam-6133	394	25	writes|x(r)−	writes|x(r)−	NOUN
ejpam-6133	394	26	y(r)|+	y(r)|+	PROPN
ejpam-6133	395	1	∣∣x	∣∣x	PROPN
ejpam-6133	395	2	(	(	PUNCT
ejpam-6133	395	3	r2)−	r2)−	VERB
ejpam-6133	395	4	y	y	PROPN
ejpam-6133	395	5	(	(	PUNCT
ejpam-6133	395	6	r2	r2	PROPN
ejpam-6133	395	7	)	)	PUNCT
ejpam-6133	395	8	∣∣	∣∣	NUM
ejpam-6133	395	9	≤	≤	ADV
ejpam-6133	395	10	2	2	NUM
ejpam-6133	395	11	(	(	PUNCT
ejpam-6133	395	12	|x(r)−	|x(r)−	VERB
ejpam-6133	395	13	y(r)|2	y(r)|2	PROPN
ejpam-6133	395	14	+	+	CCONJ
ejpam-6133	395	15	∣∣x	∣∣x	PROPN
ejpam-6133	395	16	(	(	PUNCT
ejpam-6133	395	17	r2)−	r2)−	VERB
ejpam-6133	395	18	y	y	PROPN
ejpam-6133	395	19	(	(	PUNCT
ejpam-6133	395	20	r2	r2	PROPN
ejpam-6133	395	21	)	)	PUNCT
ejpam-6133	395	22	∣∣2	∣∣2	PROPN
ejpam-6133	395	23	)	)	PUNCT
ejpam-6133	395	24	1	1	NUM
ejpam-6133	395	25	2	2	NUM
ejpam-6133	395	26	|x(0)−	|x(0)−	NOUN
ejpam-6133	395	27	y(0)|+	y(0)|+	VERB
ejpam-6133	395	28	|x(1)−	|x(1)−	VERB
ejpam-6133	395	29	y(1)|	y(1)|	PROPN
ejpam-6133	395	30	≤	≤	NUM
ejpam-6133	395	31	2	2	NUM
ejpam-6133	395	32	(	(	PUNCT
ejpam-6133	395	33	|x(0)−	|x(0)−	NOUN
ejpam-6133	395	34	y(0)|2	y(0)|2	X
ejpam-6133	395	35	+	+	CCONJ
ejpam-6133	395	36	|x(1)−	|x(1)−	VERB
ejpam-6133	395	37	y(1)|2	y(1)|2	NOUN
ejpam-6133	395	38	)	)	PUNCT
ejpam-6133	395	39	1	1	NUM
ejpam-6133	395	40	2	2	NUM
ejpam-6133	395	41	.	.	PUNCT
ejpam-6133	396	1	thus	thus	ADV
ejpam-6133	396	2	,	,	PUNCT
ejpam-6133	396	3	we	we	PRON
ejpam-6133	396	4	have	have	VERB
ejpam-6133	396	5	|k(t	|k(t	NOUN
ejpam-6133	396	6	,	,	PUNCT
ejpam-6133	396	7	r	r	NOUN
ejpam-6133	396	8	,	,	PUNCT
ejpam-6133	396	9	x(r	x(r	PROPN
ejpam-6133	396	10	)	)	PUNCT
ejpam-6133	396	11	,	,	PUNCT
ejpam-6133	396	12	x(g(r	x(g(r	PROPN
ejpam-6133	396	13	)	)	PUNCT
ejpam-6133	396	14	)	)	PUNCT
ejpam-6133	396	15	,	,	PUNCT
ejpam-6133	396	16	x(τ1	x(τ1	PROPN
ejpam-6133	396	17	)	)	PUNCT
ejpam-6133	396	18	,	,	PUNCT
ejpam-6133	396	19	x(τ2))−k(t	x(τ2))−k(t	PROPN
ejpam-6133	396	20	,	,	PUNCT
ejpam-6133	396	21	r	r	NOUN
ejpam-6133	396	22	,	,	PUNCT
ejpam-6133	396	23	y(r	y(r	PROPN
ejpam-6133	396	24	)	)	PUNCT
ejpam-6133	396	25	,	,	PUNCT
ejpam-6133	396	26	y(g(r	y(g(r	PROPN
ejpam-6133	396	27	)	)	PUNCT
ejpam-6133	396	28	)	)	PUNCT
ejpam-6133	396	29	,	,	PUNCT
ejpam-6133	396	30	y(τ1	y(τ1	PROPN
ejpam-6133	396	31	)	)	PUNCT
ejpam-6133	396	32	,	,	PUNCT
ejpam-6133	396	33	y(τ2))|	y(τ2))|	NOUN
ejpam-6133	396	34	≤	≤	NOUN
ejpam-6133	396	35	1	1	NUM
ejpam-6133	396	36	64	64	NUM
ejpam-6133	396	37	1	1	NUM
ejpam-6133	396	38	2	2	NUM
ejpam-6133	396	39	+	+	SYM
ejpam-6133	396	40	1	1	NUM
ejpam-6133	396	41	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	396	42	+	+	CCONJ
ejpam-6133	396	43	1	1	NUM
ejpam-6133	396	44	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	396	45	(	(	PUNCT
ejpam-6133	396	46	2(|x(r)−	2(|x(r)−	NUM
ejpam-6133	396	47	y(r)|2	y(r)|2	PROPN
ejpam-6133	396	48	+	+	CCONJ
ejpam-6133	396	49	∣∣∣x(r	∣∣∣x(r	NUM
ejpam-6133	396	50	2	2	NUM
ejpam-6133	396	51	)	)	PUNCT
ejpam-6133	396	52	−	−	PROPN
ejpam-6133	397	1	y	y	PROPN
ejpam-6133	397	2	(	(	PUNCT
ejpam-6133	397	3	r	r	NOUN
ejpam-6133	397	4	2	2	NUM
ejpam-6133	397	5	)	)	PUNCT
ejpam-6133	397	6	∣∣∣2	∣∣∣2	NOUN
ejpam-6133	397	7	)	)	PUNCT
ejpam-6133	397	8	1	1	NUM
ejpam-6133	397	9	2	2	NUM
ejpam-6133	397	10	+	+	NUM
ejpam-6133	397	11	2(|x(0)−	2(|x(0)−	NUM
ejpam-6133	397	12	y(0)|2	y(0)|2	NOUN
ejpam-6133	397	13	+	+	CCONJ
ejpam-6133	397	14	|x(1)−	|x(1)−	VERB
ejpam-6133	397	15	y(1)|2	y(1)|2	NOUN
ejpam-6133	397	16	)	)	PUNCT
ejpam-6133	397	17	1	1	NUM
ejpam-6133	397	18	2	2	NUM
ejpam-6133	397	19	)	)	PUNCT
ejpam-6133	397	20	=	=	SYM
ejpam-6133	398	1	1	1	NUM
ejpam-6133	398	2	16	16	NUM
ejpam-6133	398	3	1	1	NUM
ejpam-6133	398	4	2(2	2(2	NUM
ejpam-6133	398	5	+	+	SYM
ejpam-6133	398	6	1	1	NUM
ejpam-6133	398	7	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	398	8	+	+	CCONJ
ejpam-6133	398	9	1	1	NUM
ejpam-6133	398	10	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	398	11	)	)	PUNCT
ejpam-6133	398	12	(	(	PUNCT
ejpam-6133	398	13	(	(	PUNCT
ejpam-6133	398	14	|x(r)−	|x(r)−	VERB
ejpam-6133	398	15	y(r)|2	y(r)|2	PROPN
ejpam-6133	398	16	+	+	CCONJ
ejpam-6133	398	17	∣∣∣x(r	∣∣∣x(r	NUM
ejpam-6133	398	18	2	2	NUM
ejpam-6133	398	19	)	)	PUNCT
ejpam-6133	398	20	−	−	PROPN
ejpam-6133	399	1	y	y	PROPN
ejpam-6133	399	2	(	(	PUNCT
ejpam-6133	399	3	r	r	NOUN
ejpam-6133	399	4	2	2	NUM
ejpam-6133	399	5	)	)	PUNCT
ejpam-6133	399	6	∣∣∣2	∣∣∣2	NOUN
ejpam-6133	399	7	)	)	PUNCT
ejpam-6133	399	8	1	1	NUM
ejpam-6133	399	9	2	2	NUM
ejpam-6133	399	10	+	+	CCONJ
ejpam-6133	399	11	(	(	PUNCT
ejpam-6133	399	12	|x(0)−	|x(0)−	PROPN
ejpam-6133	399	13	y(0)|2	y(0)|2	X
ejpam-6133	399	14	+	+	CCONJ
ejpam-6133	399	15	|x(1)−	|x(1)−	VERB
ejpam-6133	399	16	y(1)|2	y(1)|2	NOUN
ejpam-6133	399	17	)	)	PUNCT
ejpam-6133	399	18	1	1	NUM
ejpam-6133	399	19	2	2	NUM
ejpam-6133	399	20	)	)	PUNCT
ejpam-6133	399	21	.	.	PUNCT
ejpam-6133	400	1	we	we	PRON
ejpam-6133	400	2	apply	apply	VERB
ejpam-6133	400	3	another	another	DET
ejpam-6133	400	4	time	time	NOUN
ejpam-6133	400	5	lemma	lemma	PROPN
ejpam-6133	400	6	2	2	NUM
ejpam-6133	400	7	to	to	PART
ejpam-6133	400	8	have	have	VERB
ejpam-6133	400	9	a	a	PRON
ejpam-6133	400	10	=	=	PUNCT
ejpam-6133	400	11	(	(	PUNCT
ejpam-6133	400	12	|x(r)−	|x(r)−	NOUN
ejpam-6133	400	13	y(r)|2	y(r)|2	PROPN
ejpam-6133	400	14	+	+	CCONJ
ejpam-6133	400	15	∣∣∣x(r	∣∣∣x(r	NUM
ejpam-6133	400	16	2	2	NUM
ejpam-6133	400	17	)	)	PUNCT
ejpam-6133	400	18	−	−	PROPN
ejpam-6133	401	1	y	y	PROPN
ejpam-6133	401	2	(	(	PUNCT
ejpam-6133	401	3	r	r	NOUN
ejpam-6133	401	4	2	2	NUM
ejpam-6133	401	5	)	)	PUNCT
ejpam-6133	401	6	∣∣∣2	∣∣∣2	NOUN
ejpam-6133	401	7	)	)	PUNCT
ejpam-6133	401	8	1	1	NUM
ejpam-6133	401	9	2	2	NUM
ejpam-6133	401	10	b	b	X
ejpam-6133	401	11	=	=	PUNCT
ejpam-6133	401	12	(	(	PUNCT
ejpam-6133	401	13	|x(0)−	|x(0)−	PROPN
ejpam-6133	401	14	y(0)|2	y(0)|2	X
ejpam-6133	401	15	+	+	CCONJ
ejpam-6133	401	16	|x(1)−	|x(1)−	VERB
ejpam-6133	401	17	y(1)|2	y(1)|2	NOUN
ejpam-6133	401	18	)	)	PUNCT
ejpam-6133	401	19	1	1	NUM
ejpam-6133	401	20	2	2	NUM
ejpam-6133	401	21	.	.	PUNCT
ejpam-6133	402	1	that	that	PRON
ejpam-6133	402	2	is	be	AUX
ejpam-6133	402	3	,	,	PUNCT
ejpam-6133	402	4	|k	|k	NOUN
ejpam-6133	402	5	(	(	PUNCT
ejpam-6133	402	6	t	t	PROPN
ejpam-6133	402	7	,	,	PUNCT
ejpam-6133	402	8	r	r	NOUN
ejpam-6133	402	9	,	,	PUNCT
ejpam-6133	402	10	x(r	x(r	PROPN
ejpam-6133	402	11	)	)	PUNCT
ejpam-6133	402	12	,	,	PUNCT
ejpam-6133	402	13	x(g(r	x(g(r	PROPN
ejpam-6133	402	14	)	)	PUNCT
ejpam-6133	402	15	)	)	PUNCT
ejpam-6133	402	16	,	,	PUNCT
ejpam-6133	402	17	x(τ1	x(τ1	PROPN
ejpam-6133	402	18	)	)	PUNCT
ejpam-6133	402	19	,	,	PUNCT
ejpam-6133	402	20	x(τ2))−k	x(τ2))−k	X
ejpam-6133	402	21	(	(	PUNCT
ejpam-6133	402	22	t	t	PROPN
ejpam-6133	402	23	,	,	PUNCT
ejpam-6133	402	24	r	r	NOUN
ejpam-6133	402	25	,	,	PUNCT
ejpam-6133	402	26	y(r	y(r	PROPN
ejpam-6133	402	27	)	)	PUNCT
ejpam-6133	402	28	,	,	PUNCT
ejpam-6133	402	29	y(g(r	y(g(r	PROPN
ejpam-6133	402	30	)	)	PUNCT
ejpam-6133	402	31	)	)	PUNCT
ejpam-6133	402	32	,	,	PUNCT
ejpam-6133	402	33	y(τ1	y(τ1	PROPN
ejpam-6133	402	34	)	)	PUNCT
ejpam-6133	402	35	,	,	PUNCT
ejpam-6133	403	1	y(τ2))|	y(τ2))|	NOUN
ejpam-6133	403	2	≤	≤	NOUN
ejpam-6133	403	3	1	1	NUM
ejpam-6133	403	4	8	8	NUM
ejpam-6133	403	5	1	1	NUM
ejpam-6133	403	6	2(2	2(2	NUM
ejpam-6133	403	7	+	+	SYM
ejpam-6133	403	8	1	1	NUM
ejpam-6133	403	9	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	403	10	+	+	CCONJ
ejpam-6133	403	11	1	1	NUM
ejpam-6133	403	12	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	403	13	)	)	PUNCT
ejpam-6133	403	14	(	(	PUNCT
ejpam-6133	403	15	|x(r)−	|x(r)−	VERB
ejpam-6133	403	16	y(r)|2	y(r)|2	PROPN
ejpam-6133	403	17	+	+	CCONJ
ejpam-6133	403	18	∣∣∣x(r	∣∣∣x(r	NUM
ejpam-6133	403	19	2	2	NUM
ejpam-6133	403	20	)	)	PUNCT
ejpam-6133	403	21	−	−	PROPN
ejpam-6133	404	1	y	y	PROPN
ejpam-6133	404	2	(	(	PUNCT
ejpam-6133	404	3	r	r	NOUN
ejpam-6133	404	4	2	2	NUM
ejpam-6133	404	5	)	)	PUNCT
ejpam-6133	404	6	∣∣∣2	∣∣∣2	NOUN
ejpam-6133	405	1	+	+	CCONJ
ejpam-6133	405	2	|x(0)−	|x(0)−	PROPN
ejpam-6133	405	3	y(0)|2	y(0)|2	NOUN
ejpam-6133	405	4	+	+	CCONJ
ejpam-6133	405	5	|x(1)−	|x(1)−	VERB
ejpam-6133	405	6	y(1)|2	y(1)|2	NOUN
ejpam-6133	405	7	)	)	PUNCT
ejpam-6133	405	8	1	1	NUM
ejpam-6133	405	9	2	2	NUM
ejpam-6133	405	10	≤	≤	NUM
ejpam-6133	405	11	1	1	NUM
ejpam-6133	405	12	8	8	NUM
ejpam-6133	405	13	1	1	NUM
ejpam-6133	405	14	√	√	NUM
ejpam-6133	405	15	2	2	NUM
ejpam-6133	405	16	√	√	NUM
ejpam-6133	405	17	2	2	NUM
ejpam-6133	405	18	+	+	SYM
ejpam-6133	405	19	1	1	NUM
ejpam-6133	405	20	1+∥x∥∞	1+∥x∥∞	NOUN
ejpam-6133	405	21	+	+	CCONJ
ejpam-6133	405	22	1	1	NUM
ejpam-6133	405	23	1+∥y∥∞	1+∥y∥∞	NUM
ejpam-6133	405	24	(	(	PUNCT
ejpam-6133	405	25	|x(r)−	|x(r)−	VERB
ejpam-6133	405	26	y(r)|2	y(r)|2	PROPN
ejpam-6133	405	27	+	+	CCONJ
ejpam-6133	405	28	∣∣∣x(r	∣∣∣x(r	NUM
ejpam-6133	405	29	2	2	NUM
ejpam-6133	405	30	)	)	PUNCT
ejpam-6133	405	31	−	−	PROPN
ejpam-6133	406	1	y	y	PROPN
ejpam-6133	406	2	(	(	PUNCT
ejpam-6133	406	3	r	r	NOUN
ejpam-6133	406	4	2	2	NUM
ejpam-6133	406	5	)	)	PUNCT
ejpam-6133	406	6	∣∣∣2	∣∣∣2	NOUN
ejpam-6133	407	1	+	+	CCONJ
ejpam-6133	407	2	|x(0)−	|x(0)−	PROPN
ejpam-6133	407	3	y(0)|2	y(0)|2	NOUN
ejpam-6133	407	4	+	+	CCONJ
ejpam-6133	407	5	|x(1)−	|x(1)−	VERB
ejpam-6133	407	6	y(1)|2	y(1)|2	NOUN
ejpam-6133	407	7	)	)	PUNCT
ejpam-6133	407	8	1	1	NUM
ejpam-6133	407	9	2	2	NUM
ejpam-6133	407	10	.	.	PUNCT
ejpam-6133	408	1	thus	thus	ADV
ejpam-6133	408	2	,	,	PUNCT
ejpam-6133	408	3	the	the	DET
ejpam-6133	408	4	second	second	ADJ
ejpam-6133	408	5	condition	condition	NOUN
ejpam-6133	408	6	(	(	PUNCT
ejpam-6133	408	7	ii	ii	NOUN
ejpam-6133	408	8	)	)	PUNCT
ejpam-6133	408	9	of	of	ADP
ejpam-6133	408	10	theorem	theorem	ADJ
ejpam-6133	408	11	2	2	NUM
ejpam-6133	408	12	is	be	AUX
ejpam-6133	408	13	satisfied	satisfied	ADJ
ejpam-6133	408	14	with	with	ADP
ejpam-6133	408	15	γ(t	γ(t	NOUN
ejpam-6133	408	16	,	,	PUNCT
ejpam-6133	408	17	r	r	NOUN
ejpam-6133	408	18	)	)	PUNCT
ejpam-6133	408	19	=	=	SYM
ejpam-6133	408	20	1	1	NUM
ejpam-6133	408	21	8	8	NUM
ejpam-6133	408	22	.	.	PUNCT
ejpam-6133	409	1	that	that	PRON
ejpam-6133	409	2	is	be	AUX
ejpam-6133	409	3	,	,	PUNCT
ejpam-6133	409	4	sup	sup	PROPN
ejpam-6133	409	5	t∈[0,1	t∈[0,1	NOUN
ejpam-6133	409	6	]	]	PUNCT
ejpam-6133	409	7	∫	∫	PROPN
ejpam-6133	410	1	1	1	NUM
ejpam-6133	410	2	0	0	NUM
ejpam-6133	410	3	γ2(t	γ2(t	PROPN
ejpam-6133	410	4	,	,	PUNCT
ejpam-6133	410	5	r)dr	r)dr	PROPN
ejpam-6133	410	6	=	=	SYM
ejpam-6133	410	7	1	1	NUM
ejpam-6133	410	8	64	64	NUM
ejpam-6133	410	9	<	<	SYM
ejpam-6133	410	10	1	1	NUM
ejpam-6133	410	11	16	16	NUM
ejpam-6133	410	12	=	=	SYM
ejpam-6133	410	13	1	1	NUM
ejpam-6133	410	14	22	22	NUM
ejpam-6133	410	15	+	+	SYM
ejpam-6133	410	16	2	2	NUM
ejpam-6133	410	17	|1|p	|1|p	VERB
ejpam-6133	410	18	(	(	PUNCT
ejpam-6133	410	19	1−	1−	NUM
ejpam-6133	410	20	0)2−1	0)2−1	NUM
ejpam-6133	410	21	.	.	PUNCT
ejpam-6133	411	1	next	next	ADV
ejpam-6133	411	2	,	,	PUNCT
ejpam-6133	411	3	using	use	VERB
ejpam-6133	411	4	the	the	DET
ejpam-6133	411	5	properties	property	NOUN
ejpam-6133	411	6	of	of	ADP
ejpam-6133	411	7	the	the	DET
ejpam-6133	411	8	functions	function	NOUN
ejpam-6133	411	9	k	k	NOUN
ejpam-6133	411	10	,	,	PUNCT
ejpam-6133	411	11	g	g	PROPN
ejpam-6133	411	12	and	and	CCONJ
ejpam-6133	411	13	f	f	PROPN
ejpam-6133	411	14	,	,	PUNCT
ejpam-6133	411	15	it	it	PRON
ejpam-6133	411	16	is	be	AUX
ejpam-6133	411	17	observed	observe	VERB
ejpam-6133	411	18	that	that	SCONJ
ejpam-6133	411	19	the	the	DET
ejpam-6133	411	20	hypothesis	hypothesis	NOUN
ejpam-6133	411	21	(	(	PUNCT
ejpam-6133	411	22	i	i	NOUN
ejpam-6133	411	23	)	)	PUNCT
ejpam-6133	411	24	is	be	AUX
ejpam-6133	411	25	satisfied	satisfied	ADJ
ejpam-6133	411	26	for	for	ADP
ejpam-6133	411	27	s̃0	s̃0	PROPN
ejpam-6133	411	28	=	=	SYM
ejpam-6133	411	29	f	f	PROPN
ejpam-6133	411	30	∈	∈	PROPN
ejpam-6133	411	31	℧	℧	PROPN
ejpam-6133	411	32	=	=	SYM
ejpam-6133	411	33	c([0	c([0	PROPN
ejpam-6133	411	34	,	,	PUNCT
ejpam-6133	411	35	1	1	NUM
ejpam-6133	411	36	]	]	PUNCT
ejpam-6133	411	37	)	)	PUNCT
ejpam-6133	411	38	.	.	PUNCT
ejpam-6133	412	1	on	on	ADP
ejpam-6133	412	2	the	the	DET
ejpam-6133	412	3	other	other	ADJ
ejpam-6133	412	4	hand	hand	NOUN
ejpam-6133	412	5	,	,	PUNCT
ejpam-6133	412	6	by	by	ADP
ejpam-6133	412	7	definition	definition	NOUN
ejpam-6133	412	8	of	of	ADP
ejpam-6133	412	9	the	the	DET
ejpam-6133	412	10	function	function	NOUN
ejpam-6133	412	11	ϵ	ϵ	ADP
ejpam-6133	412	12	the	the	DET
ejpam-6133	412	13	condition	condition	NOUN
ejpam-6133	412	14	(	(	PUNCT
ejpam-6133	412	15	iii	iii	NOUN
ejpam-6133	412	16	)	)	PUNCT
ejpam-6133	412	17	is	be	AUX
ejpam-6133	412	18	satisfied	satisfied	ADJ
ejpam-6133	412	19	.	.	PUNCT
ejpam-6133	413	1	it	it	PRON
ejpam-6133	413	2	remains	remain	VERB
ejpam-6133	413	3	to	to	PART
ejpam-6133	413	4	check	check	VERB
ejpam-6133	413	5	that	that	SCONJ
ejpam-6133	413	6	the	the	DET
ejpam-6133	413	7	operator	operator	NOUN
ejpam-6133	413	8	k	k	PROPN
ejpam-6133	413	9	is	be	AUX
ejpam-6133	413	10	non	non	ADJ
ejpam-6133	413	11	-	-	ADJ
ejpam-6133	413	12	decreasing	decrease	VERB
ejpam-6133	413	13	.	.	PUNCT
ejpam-6133	414	1	it	it	PRON
ejpam-6133	414	2	is	be	AUX
ejpam-6133	414	3	clear	clear	ADJ
ejpam-6133	414	4	that	that	SCONJ
ejpam-6133	414	5	the	the	DET
ejpam-6133	414	6	function	function	NOUN
ejpam-6133	414	7	σ	σ	X
ejpam-6133	414	8	:	:	PUNCT
ejpam-6133	414	9	s	s	VERB
ejpam-6133	414	10	7−→	7−→	NOUN
ejpam-6133	414	11	s(1+s	s(1+s	NOUN
ejpam-6133	414	12	)	)	PUNCT
ejpam-6133	414	13	2+s	2+s	NUM
ejpam-6133	414	14	;	;	PUNCT
ejpam-6133	414	15	s	s	X
ejpam-6133	414	16	≥	≥	NOUN
ejpam-6133	414	17	0	0	NUM
ejpam-6133	414	18	is	be	AUX
ejpam-6133	414	19	increasing	increase	VERB
ejpam-6133	414	20	,	,	PUNCT
ejpam-6133	414	21	so	so	ADV
ejpam-6133	414	22	on	on	ADP
ejpam-6133	414	23	the	the	DET
ejpam-6133	414	24	space	space	NOUN
ejpam-6133	414	25	of	of	ADP
ejpam-6133	414	26	continuous	continuous	ADJ
ejpam-6133	414	27	functions	function	NOUN
ejpam-6133	414	28	on	on	ADP
ejpam-6133	414	29	[	[	X
ejpam-6133	414	30	0	0	NUM
ejpam-6133	414	31	,	,	PUNCT
ejpam-6133	414	32	1	1	NUM
ejpam-6133	414	33	]	]	PUNCT
ejpam-6133	414	34	with	with	ADP
ejpam-6133	414	35	value	value	NOUN
ejpam-6133	414	36	in	in	ADP
ejpam-6133	414	37	[	[	X
ejpam-6133	414	38	0,+∞	0,+∞	PROPN
ejpam-6133	415	1	[	[	X
ejpam-6133	415	2	,	,	PUNCT
ejpam-6133	415	3	we	we	PRON
ejpam-6133	415	4	easily	easily	ADV
ejpam-6133	415	5	see	see	VERB
ejpam-6133	415	6	that	that	SCONJ
ejpam-6133	415	7	the	the	DET
ejpam-6133	415	8	operator	operator	NOUN
ejpam-6133	415	9	is	be	AUX
ejpam-6133	415	10	indeed	indeed	ADV
ejpam-6133	415	11	non	non	ADJ
ejpam-6133	415	12	-	-	ADJ
ejpam-6133	415	13	decreasing	decrease	VERB
ejpam-6133	415	14	with	with	ADP
ejpam-6133	415	15	respect	respect	NOUN
ejpam-6133	415	16	to	to	ADP
ejpam-6133	415	17	the	the	DET
ejpam-6133	415	18	variable	variable	NOUN
ejpam-6133	415	19	x.	x.	NOUN
ejpam-6133	416	1	the	the	DET
ejpam-6133	416	2	conditions	condition	NOUN
ejpam-6133	416	3	of	of	ADP
ejpam-6133	416	4	theorem	theorem	ADJ
ejpam-6133	416	5	2	2	NUM
ejpam-6133	416	6	are	be	AUX
ejpam-6133	416	7	fulfilled	fulfil	VERB
ejpam-6133	416	8	and	and	CCONJ
ejpam-6133	416	9	it	it	PRON
ejpam-6133	416	10	results	result	VERB
ejpam-6133	416	11	that	that	SCONJ
ejpam-6133	416	12	the	the	DET
ejpam-6133	416	13	integral	integral	ADJ
ejpam-6133	416	14	equation	equation	NOUN
ejpam-6133	416	15	(	(	PUNCT
ejpam-6133	416	16	10	10	NUM
ejpam-6133	416	17	)	)	PUNCT
ejpam-6133	416	18	has	have	VERB
ejpam-6133	416	19	a	a	DET
ejpam-6133	416	20	unique	unique	ADJ
ejpam-6133	416	21	solution	solution	NOUN
ejpam-6133	416	22	.	.	PUNCT
ejpam-6133	417	1	h.	h.	PROPN
ejpam-6133	417	2	aydi	aydi	PROPN
ejpam-6133	417	3	,	,	PUNCT
ejpam-6133	417	4	h.	h.	PROPN
ejpam-6133	417	5	hammouda	hammouda	PROPN
ejpam-6133	417	6	,	,	PUNCT
ejpam-6133	417	7	s.	s.	PROPN
ejpam-6133	417	8	mansour	mansour	PROPN
ejpam-6133	417	9	/	/	SYM
ejpam-6133	417	10	eur	eur	PROPN
ejpam-6133	417	11	.	.	PUNCT
ejpam-6133	418	1	j.	j.	PROPN
ejpam-6133	418	2	pure	pure	PROPN
ejpam-6133	418	3	appl	appl	PROPN
ejpam-6133	418	4	.	.	PROPN
ejpam-6133	418	5	math	math	PROPN
ejpam-6133	418	6	,	,	PUNCT
ejpam-6133	418	7	18	18	NUM
ejpam-6133	418	8	(	(	PUNCT
ejpam-6133	418	9	3	3	NUM
ejpam-6133	418	10	)	)	PUNCT
ejpam-6133	418	11	(	(	PUNCT
ejpam-6133	418	12	2025	2025	NUM
ejpam-6133	418	13	)	)	PUNCT
ejpam-6133	418	14	,	,	PUNCT
ejpam-6133	418	15	6133	6133	NUM
ejpam-6133	418	16	17	17	NUM
ejpam-6133	418	17	of	of	ADP
ejpam-6133	418	18	18	18	NUM
ejpam-6133	418	19	acknowledgements	acknowledgement	NOUN
ejpam-6133	418	20	the	the	DET
ejpam-6133	418	21	authors	author	NOUN
ejpam-6133	418	22	extend	extend	VERB
ejpam-6133	418	23	their	their	PRON
ejpam-6133	418	24	appreciation	appreciation	NOUN
ejpam-6133	418	25	to	to	ADP
ejpam-6133	418	26	umm	umm	INTJ
ejpam-6133	418	27	al	al	PROPN
ejpam-6133	418	28	-	-	PUNCT
ejpam-6133	418	29	qura	qura	PROPN
ejpam-6133	418	30	university	university	PROPN
ejpam-6133	418	31	,	,	PUNCT
ejpam-6133	418	32	saudi	saudi	PROPN
ejpam-6133	418	33	arabia	arabia	PROPN
ejpam-6133	418	34	for	for	ADP
ejpam-6133	418	35	funding	fund	VERB
ejpam-6133	418	36	this	this	DET
ejpam-6133	418	37	research	research	NOUN
ejpam-6133	418	38	work	work	NOUN
ejpam-6133	418	39	through	through	ADP
ejpam-6133	418	40	grant	grant	NOUN
ejpam-6133	418	41	number	number	NOUN
ejpam-6133	418	42	:	:	PUNCT
ejpam-6133	418	43	25uqu4331214gssr07	25uqu4331214gssr07	NUM
ejpam-6133	418	44	.	.	PUNCT
ejpam-6133	419	1	funding	fund	VERB
ejpam-6133	419	2	this	this	DET
ejpam-6133	419	3	research	research	NOUN
ejpam-6133	419	4	work	work	NOUN
ejpam-6133	419	5	was	be	AUX
ejpam-6133	419	6	funded	fund	VERB
ejpam-6133	419	7	by	by	ADP
ejpam-6133	419	8	umm	umm	INTJ
ejpam-6133	419	9	al	al	PROPN
ejpam-6133	419	10	-	-	PUNCT
ejpam-6133	419	11	qura	qura	PROPN
ejpam-6133	419	12	university	university	NOUN
ejpam-6133	419	13	,	,	PUNCT
ejpam-6133	419	14	saudi	saudi	PROPN
ejpam-6133	419	15	arabia	arabia	PROPN
ejpam-6133	419	16	under	under	ADP
ejpam-6133	419	17	grant	grant	NOUN
ejpam-6133	419	18	number	number	NOUN
ejpam-6133	419	19	:	:	PUNCT
ejpam-6133	419	20	25uqu4331214gssr07	25uqu4331214gssr07	NUM
ejpam-6133	419	21	.	.	PUNCT
ejpam-6133	420	1	references	reference	NOUN
ejpam-6133	420	2	[	[	X
ejpam-6133	420	3	1	1	X
ejpam-6133	420	4	]	]	PUNCT
ejpam-6133	420	5	s.	s.	PROPN
ejpam-6133	420	6	banach	banach	PROPN
ejpam-6133	420	7	.	.	PUNCT
ejpam-6133	421	1	sur	sur	PROPN
ejpam-6133	421	2	les	les	X
ejpam-6133	421	3	opérations	opération	NOUN
ejpam-6133	421	4	dans	dan	NOUN
ejpam-6133	421	5	les	les	X
ejpam-6133	421	6	ensembles	ensemble	NOUN
ejpam-6133	421	7	abstraits	abstrait	NOUN
ejpam-6133	421	8	et	et	PROPN
ejpam-6133	421	9	leur	leur	X
ejpam-6133	421	10	application	application	PROPN
ejpam-6133	421	11	aux	aux	PROPN
ejpam-6133	421	12	équations	équations	PROPN
ejpam-6133	421	13	intégrales	intégrale	NOUN
ejpam-6133	421	14	.	.	PUNCT
ejpam-6133	422	1	fundamenta	fundamenta	PROPN
ejpam-6133	422	2	mathematicae	mathematicae	PROPN
ejpam-6133	422	3	,	,	PUNCT
ejpam-6133	422	4	3:133–181	3:133–181	NUM
ejpam-6133	422	5	,	,	PUNCT
ejpam-6133	422	6	1922	1922	NUM
ejpam-6133	422	7	.	.	PUNCT
ejpam-6133	423	1	[	[	X
ejpam-6133	423	2	2	2	NUM
ejpam-6133	423	3	]	]	PUNCT
ejpam-6133	423	4	i.	i.	PROPN
ejpam-6133	423	5	a.	a.	PROPN
ejpam-6133	423	6	bakhtin	bakhtin	PROPN
ejpam-6133	423	7	.	.	PUNCT
ejpam-6133	424	1	the	the	DET
ejpam-6133	424	2	contraction	contraction	NOUN
ejpam-6133	424	3	mapping	map	VERB
ejpam-6133	424	4	principle	principle	NOUN
ejpam-6133	424	5	in	in	ADP
ejpam-6133	424	6	quasi	quasi	ADJ
ejpam-6133	424	7	-	-	ADJ
ejpam-6133	424	8	metric	metric	ADJ
ejpam-6133	424	9	spaces	space	NOUN
ejpam-6133	424	10	.	.	PUNCT
ejpam-6133	425	1	functional	functional	ADJ
ejpam-6133	425	2	analysis	analysis	NOUN
ejpam-6133	425	3	,	,	PUNCT
ejpam-6133	425	4	ulyanovsk	ulyanovsk	VERB
ejpam-6133	425	5	state	state	PROPN
ejpam-6133	425	6	pedagogical	pedagogical	PROPN
ejpam-6133	425	7	institute	institute	PROPN
ejpam-6133	425	8	,	,	PUNCT
ejpam-6133	425	9	298:26–37	298:26–37	NUM
ejpam-6133	425	10	,	,	PUNCT
ejpam-6133	425	11	1989	1989	NUM
ejpam-6133	425	12	.	.	PUNCT
ejpam-6133	426	1	[	[	X
ejpam-6133	426	2	3	3	X
ejpam-6133	426	3	]	]	X
ejpam-6133	426	4	s.	s.	PROPN
ejpam-6133	426	5	czerwik	czerwik	PROPN
ejpam-6133	426	6	.	.	PUNCT
ejpam-6133	427	1	contraction	contraction	NOUN
ejpam-6133	427	2	mappings	mapping	NOUN
ejpam-6133	427	3	in	in	ADP
ejpam-6133	427	4	b	b	NOUN
ejpam-6133	427	5	-	-	ADJ
ejpam-6133	427	6	metric	metric	ADJ
ejpam-6133	427	7	spaces	space	NOUN
ejpam-6133	427	8	.	.	PUNCT
ejpam-6133	428	1	acta	acta	PROPN
ejpam-6133	428	2	mathematica	mathematica	PROPN
ejpam-6133	428	3	et	et	PROPN
ejpam-6133	428	4	informatica	informatica	PROPN
ejpam-6133	428	5	universitatis	universitatis	PROPN
ejpam-6133	428	6	ostraviensis	ostraviensis	PROPN
ejpam-6133	428	7	,	,	PUNCT
ejpam-6133	428	8	1:5–11	1:5–11	NUM
ejpam-6133	428	9	,	,	PUNCT
ejpam-6133	428	10	1983	1983	NUM
ejpam-6133	428	11	.	.	PUNCT
ejpam-6133	429	1	[	[	X
ejpam-6133	429	2	4	4	X
ejpam-6133	429	3	]	]	PUNCT
ejpam-6133	429	4	t.	t.	PROPN
ejpam-6133	429	5	kamran	kamran	PROPN
ejpam-6133	429	6	,	,	PUNCT
ejpam-6133	429	7	m.	m.	NOUN
ejpam-6133	429	8	samreen	samreen	PROPN
ejpam-6133	429	9	,	,	PUNCT
ejpam-6133	429	10	and	and	CCONJ
ejpam-6133	429	11	q.	q.	PROPN
ejpam-6133	429	12	ul	ul	PROPN
ejpam-6133	429	13	ain	ain	PROPN
ejpam-6133	429	14	.	.	PUNCT
ejpam-6133	429	15	generalization	generalization	NOUN
ejpam-6133	429	16	of	of	ADP
ejpam-6133	429	17	b	b	NOUN
ejpam-6133	429	18	-	-	PUNCT
ejpam-6133	429	19	metric	metric	ADJ
ejpam-6133	429	20	space	space	NOUN
ejpam-6133	429	21	and	and	CCONJ
ejpam-6133	429	22	some	some	DET
ejpam-6133	429	23	fixed	fix	VERB
ejpam-6133	429	24	point	point	NOUN
ejpam-6133	429	25	theorems	theorem	NOUN
ejpam-6133	429	26	.	.	PUNCT
ejpam-6133	430	1	mathematics	mathematic	NOUN
ejpam-6133	430	2	,	,	PUNCT
ejpam-6133	430	3	5(2):19	5(2):19	NUM
ejpam-6133	430	4	,	,	PUNCT
ejpam-6133	430	5	2017	2017	NUM
ejpam-6133	430	6	.	.	PUNCT
ejpam-6133	431	1	[	[	X
ejpam-6133	431	2	5	5	X
ejpam-6133	431	3	]	]	PUNCT
ejpam-6133	431	4	t.	t.	NOUN
ejpam-6133	431	5	abdeljawad	abdeljawad	PROPN
ejpam-6133	431	6	,	,	PUNCT
ejpam-6133	431	7	n.	n.	PROPN
ejpam-6133	431	8	mlaiki	mlaiki	PROPN
ejpam-6133	431	9	,	,	PUNCT
ejpam-6133	431	10	h.	h.	PROPN
ejpam-6133	431	11	aydi	aydi	PROPN
ejpam-6133	431	12	,	,	PUNCT
ejpam-6133	431	13	and	and	CCONJ
ejpam-6133	431	14	n.	n.	NOUN
ejpam-6133	431	15	souayah	souayah	NOUN
ejpam-6133	431	16	.	.	PUNCT
ejpam-6133	432	1	double	double	PROPN
ejpam-6133	432	2	controlled	control	VERB
ejpam-6133	432	3	metric	metric	ADJ
ejpam-6133	432	4	type	type	NOUN
ejpam-6133	432	5	spaces	space	NOUN
ejpam-6133	432	6	and	and	CCONJ
ejpam-6133	432	7	some	some	DET
ejpam-6133	432	8	fixed	fix	VERB
ejpam-6133	432	9	point	point	NOUN
ejpam-6133	432	10	results	result	NOUN
ejpam-6133	432	11	.	.	PUNCT
ejpam-6133	433	1	mathematics	mathematic	NOUN
ejpam-6133	433	2	,	,	PUNCT
ejpam-6133	433	3	6(12):320	6(12):320	PROPN
ejpam-6133	433	4	,	,	PUNCT
ejpam-6133	433	5	2018	2018	NUM
ejpam-6133	433	6	.	.	PUNCT
ejpam-6133	434	1	[	[	X
ejpam-6133	434	2	6	6	NUM
ejpam-6133	434	3	]	]	X
ejpam-6133	434	4	n.	n.	PROPN
ejpam-6133	434	5	mlaiki	mlaiki	PROPN
ejpam-6133	434	6	.	.	PUNCT
ejpam-6133	434	7	double	double	PROPN
ejpam-6133	434	8	controlled	control	VERB
ejpam-6133	434	9	metric	metric	ADJ
ejpam-6133	434	10	-	-	PUNCT
ejpam-6133	434	11	like	like	ADJ
ejpam-6133	434	12	spaces	space	NOUN
ejpam-6133	434	13	.	.	PUNCT
ejpam-6133	435	1	journal	journal	PROPN
ejpam-6133	435	2	of	of	ADP
ejpam-6133	435	3	inequalities	inequality	NOUN
ejpam-6133	435	4	and	and	CCONJ
ejpam-6133	435	5	applications	application	NOUN
ejpam-6133	435	6	,	,	PUNCT
ejpam-6133	435	7	2020:189	2020:189	NUM
ejpam-6133	435	8	,	,	PUNCT
ejpam-6133	435	9	2020	2020	NUM
ejpam-6133	435	10	.	.	PUNCT
ejpam-6133	436	1	[	[	X
ejpam-6133	436	2	7	7	X
ejpam-6133	436	3	]	]	PUNCT
ejpam-6133	436	4	a.	a.	NOUN
ejpam-6133	436	5	tas	tas	PROPN
ejpam-6133	436	6	.	.	PUNCT
ejpam-6133	437	1	on	on	ADP
ejpam-6133	437	2	double	double	ADJ
ejpam-6133	437	3	controlled	control	VERB
ejpam-6133	437	4	metric	metric	NOUN
ejpam-6133	437	5	like	like	ADP
ejpam-6133	437	6	spaces	space	NOUN
ejpam-6133	437	7	and	and	CCONJ
ejpam-6133	437	8	related	relate	VERB
ejpam-6133	437	9	fixed	fix	VERB
ejpam-6133	437	10	point	point	NOUN
ejpam-6133	437	11	theorems	theorem	NOUN
ejpam-6133	437	12	.	.	PUNCT
ejpam-6133	438	1	advances	advance	NOUN
ejpam-6133	438	2	in	in	ADP
ejpam-6133	438	3	theory	theory	NOUN
ejpam-6133	438	4	of	of	ADP
ejpam-6133	438	5	nonlinear	nonlinear	ADJ
ejpam-6133	438	6	analysis	analysis	NOUN
ejpam-6133	438	7	and	and	CCONJ
ejpam-6133	438	8	its	its	PRON
ejpam-6133	438	9	applications	application	NOUN
ejpam-6133	438	10	,	,	PUNCT
ejpam-6133	438	11	5(2):167–172	5(2):167–172	NUM
ejpam-6133	438	12	,	,	PUNCT
ejpam-6133	438	13	2021	2021	NUM
ejpam-6133	438	14	.	.	PUNCT
ejpam-6133	439	1	[	[	X
ejpam-6133	439	2	8	8	NUM
ejpam-6133	439	3	]	]	X
ejpam-6133	439	4	h.	h.	PROPN
ejpam-6133	439	5	ahmad	ahmad	PROPN
ejpam-6133	439	6	,	,	PUNCT
ejpam-6133	439	7	m.	m.	NOUN
ejpam-6133	439	8	younis	younis	PROPN
ejpam-6133	439	9	,	,	PUNCT
ejpam-6133	439	10	and	and	CCONJ
ejpam-6133	439	11	m.	m.	PROPN
ejpam-6133	439	12	k.	k.	PROPN
ejpam-6133	439	13	kosal	kosal	PROPN
ejpam-6133	439	14	.	.	PUNCT
ejpam-6133	440	1	double	double	PROPN
ejpam-6133	440	2	controlled	control	VERB
ejpam-6133	440	3	partial	partial	ADJ
ejpam-6133	440	4	metric	metric	ADJ
ejpam-6133	440	5	type	type	NOUN
ejpam-6133	440	6	spaces	space	NOUN
ejpam-6133	440	7	and	and	CCONJ
ejpam-6133	440	8	convergence	convergence	NOUN
ejpam-6133	440	9	results	result	NOUN
ejpam-6133	440	10	.	.	PUNCT
ejpam-6133	441	1	journal	journal	NOUN
ejpam-6133	441	2	of	of	ADP
ejpam-6133	441	3	mathematics	mathematic	NOUN
ejpam-6133	441	4	,	,	PUNCT
ejpam-6133	441	5	2021:7008737	2021:7008737	NUM
ejpam-6133	441	6	,	,	PUNCT
ejpam-6133	441	7	2021	2021	NUM
ejpam-6133	441	8	.	.	PUNCT
ejpam-6133	442	1	[	[	X
ejpam-6133	442	2	9	9	NUM
ejpam-6133	442	3	]	]	PUNCT
ejpam-6133	442	4	s.	s.	PROPN
ejpam-6133	442	5	haque	haque	PROPN
ejpam-6133	442	6	,	,	PUNCT
ejpam-6133	442	7	a.	a.	NOUN
ejpam-6133	442	8	souayah	souayah	NOUN
ejpam-6133	442	9	,	,	PUNCT
ejpam-6133	442	10	n.	n.	PROPN
ejpam-6133	442	11	mlaiki	mlaiki	PROPN
ejpam-6133	442	12	,	,	PUNCT
ejpam-6133	442	13	and	and	CCONJ
ejpam-6133	442	14	d.	d.	PROPN
ejpam-6133	442	15	rizk	rizk	PROPN
ejpam-6133	442	16	.	.	PROPN
ejpam-6133	442	17	double	double	PROPN
ejpam-6133	442	18	controlled	control	VERB
ejpam-6133	442	19	quasi	quasi	NOUN
ejpam-6133	442	20	metric	metric	ADJ
ejpam-6133	442	21	like	like	ADP
ejpam-6133	442	22	spaces	space	NOUN
ejpam-6133	442	23	.	.	PUNCT
ejpam-6133	443	1	symmetry	symmetry	NOUN
ejpam-6133	443	2	,	,	PUNCT
ejpam-6133	443	3	14(618	14(618	NOUN
ejpam-6133	443	4	)	)	PUNCT
ejpam-6133	443	5	,	,	PUNCT
ejpam-6133	443	6	2022	2022	NUM
ejpam-6133	443	7	.	.	PUNCT
ejpam-6133	444	1	[	[	X
ejpam-6133	444	2	10	10	NUM
ejpam-6133	444	3	]	]	X
ejpam-6133	444	4	e.	e.	PROPN
ejpam-6133	444	5	karapinar	karapinar	PROPN
ejpam-6133	444	6	,	,	PUNCT
ejpam-6133	444	7	p.	p.	PROPN
ejpam-6133	444	8	s.	s.	PROPN
ejpam-6133	444	9	kumari	kumari	PROPN
ejpam-6133	444	10	,	,	PUNCT
ejpam-6133	444	11	and	and	CCONJ
ejpam-6133	444	12	d.	d.	PROPN
ejpam-6133	444	13	lateef	lateef	PROPN
ejpam-6133	444	14	.	.	PUNCT
ejpam-6133	445	1	a	a	DET
ejpam-6133	445	2	new	new	ADJ
ejpam-6133	445	3	approach	approach	NOUN
ejpam-6133	445	4	to	to	ADP
ejpam-6133	445	5	the	the	DET
ejpam-6133	445	6	solution	solution	NOUN
ejpam-6133	445	7	of	of	ADP
ejpam-6133	445	8	the	the	DET
ejpam-6133	445	9	fredholm	fredholm	ADJ
ejpam-6133	445	10	integral	integral	ADJ
ejpam-6133	445	11	equation	equation	NOUN
ejpam-6133	445	12	via	via	ADP
ejpam-6133	445	13	a	a	DET
ejpam-6133	445	14	fixed	fix	VERB
ejpam-6133	445	15	point	point	NOUN
ejpam-6133	445	16	on	on	ADP
ejpam-6133	445	17	extended	extended	ADJ
ejpam-6133	445	18	b	b	NOUN
ejpam-6133	445	19	-	-	ADJ
ejpam-6133	445	20	metric	metric	ADJ
ejpam-6133	445	21	spaces	space	NOUN
ejpam-6133	445	22	.	.	PUNCT
ejpam-6133	446	1	symmetry	symmetry	NOUN
ejpam-6133	446	2	,	,	PUNCT
ejpam-6133	446	3	10(512	10(512	NOUN
ejpam-6133	446	4	)	)	PUNCT
ejpam-6133	446	5	,	,	PUNCT
ejpam-6133	446	6	2018	2018	NUM
ejpam-6133	446	7	.	.	PUNCT
ejpam-6133	447	1	[	[	X
ejpam-6133	447	2	11	11	NUM
ejpam-6133	447	3	]	]	PUNCT
ejpam-6133	447	4	m.	m.	PROPN
ejpam-6133	447	5	d.	d.	PROPN
ejpam-6133	447	6	rus	rus	PROPN
ejpam-6133	447	7	.	.	PUNCT
ejpam-6133	448	1	a	a	DET
ejpam-6133	448	2	note	note	NOUN
ejpam-6133	448	3	on	on	ADP
ejpam-6133	448	4	the	the	DET
ejpam-6133	448	5	existence	existence	NOUN
ejpam-6133	448	6	of	of	ADP
ejpam-6133	448	7	positive	positive	ADJ
ejpam-6133	448	8	solution	solution	NOUN
ejpam-6133	448	9	of	of	ADP
ejpam-6133	448	10	fredholm	fredholm	ADJ
ejpam-6133	448	11	integral	integral	ADJ
ejpam-6133	448	12	equations	equation	NOUN
ejpam-6133	448	13	.	.	PUNCT
ejpam-6133	449	1	fixed	fix	VERB
ejpam-6133	449	2	point	point	NOUN
ejpam-6133	449	3	theory	theory	NOUN
ejpam-6133	449	4	,	,	PUNCT
ejpam-6133	449	5	5:369–377	5:369–377	NOUN
ejpam-6133	449	6	,	,	PUNCT
ejpam-6133	449	7	2004	2004	NUM
ejpam-6133	449	8	.	.	PUNCT
ejpam-6133	450	1	[	[	X
ejpam-6133	450	2	12	12	NUM
ejpam-6133	450	3	]	]	PUNCT
ejpam-6133	450	4	m.	m.	NOUN
ejpam-6133	450	5	i.	i.	PROPN
ejpam-6133	450	6	berenguer	berenguer	PROPN
ejpam-6133	450	7	,	,	PUNCT
ejpam-6133	450	8	m.	m.	NOUN
ejpam-6133	450	9	v.	v.	ADP
ejpam-6133	450	10	f.	f.	PROPN
ejpam-6133	450	11	muñoz	muñoz	PROPN
ejpam-6133	450	12	,	,	PUNCT
ejpam-6133	450	13	a.	a.	NOUN
ejpam-6133	450	14	i.	i.	PROPN
ejpam-6133	450	15	g.	g.	PROPN
ejpam-6133	450	16	guillem	guillem	PROPN
ejpam-6133	450	17	,	,	PUNCT
ejpam-6133	450	18	and	and	CCONJ
ejpam-6133	450	19	m.	m.	PROPN
ejpam-6133	450	20	r.	r.	PROPN
ejpam-6133	450	21	galan	galan	PROPN
ejpam-6133	450	22	.	.	PUNCT
ejpam-6133	451	1	numerical	numerical	PROPN
ejpam-6133	451	2	treatment	treatment	NOUN
ejpam-6133	451	3	of	of	ADP
ejpam-6133	451	4	fixed	fix	VERB
ejpam-6133	451	5	point	point	NOUN
ejpam-6133	451	6	applied	apply	VERB
ejpam-6133	451	7	to	to	ADP
ejpam-6133	451	8	the	the	DET
ejpam-6133	451	9	nonlinear	nonlinear	ADJ
ejpam-6133	451	10	fredholm	fredholm	ADJ
ejpam-6133	451	11	integral	integral	ADJ
ejpam-6133	451	12	equation	equation	NOUN
ejpam-6133	451	13	.	.	PUNCT
ejpam-6133	452	1	fixed	fix	VERB
ejpam-6133	452	2	point	point	NOUN
ejpam-6133	452	3	theory	theory	NOUN
ejpam-6133	452	4	and	and	CCONJ
ejpam-6133	452	5	applications	application	NOUN
ejpam-6133	452	6	,	,	PUNCT
ejpam-6133	452	7	pages	page	NOUN
ejpam-6133	452	8	1–8	1–8	NUM
ejpam-6133	452	9	,	,	PUNCT
ejpam-6133	452	10	2009	2009	NUM
ejpam-6133	452	11	.	.	PUNCT
ejpam-6133	453	1	[	[	X
ejpam-6133	453	2	13	13	NUM
ejpam-6133	453	3	]	]	PUNCT
ejpam-6133	453	4	h.	h.	PROPN
ejpam-6133	453	5	k.	k.	PROPN
ejpam-6133	453	6	pathak	pathak	PROPN
ejpam-6133	453	7	,	,	PUNCT
ejpam-6133	453	8	m.	m.	PROPN
ejpam-6133	453	9	s.	s.	PROPN
ejpam-6133	453	10	khan	khan	PROPN
ejpam-6133	453	11	,	,	PUNCT
ejpam-6133	453	12	and	and	CCONJ
ejpam-6133	453	13	r.	r.	PROPN
ejpam-6133	453	14	tiwari	tiwari	PROPN
ejpam-6133	453	15	.	.	PUNCT
ejpam-6133	454	1	common	common	ADJ
ejpam-6133	454	2	fixed	fix	VERB
ejpam-6133	454	3	point	point	NOUN
ejpam-6133	454	4	theorem	theorem	NOUN
ejpam-6133	454	5	and	and	CCONJ
ejpam-6133	454	6	its	its	PRON
ejpam-6133	454	7	application	application	NOUN
ejpam-6133	454	8	to	to	ADP
ejpam-6133	454	9	nonlinear	nonlinear	ADJ
ejpam-6133	454	10	integral	integral	ADJ
ejpam-6133	454	11	equations	equation	NOUN
ejpam-6133	454	12	.	.	PUNCT
ejpam-6133	455	1	computers	computer	NOUN
ejpam-6133	455	2	and	and	CCONJ
ejpam-6133	455	3	mathematics	mathematic	NOUN
ejpam-6133	455	4	with	with	ADP
ejpam-6133	455	5	applications	application	NOUN
ejpam-6133	455	6	,	,	PUNCT
ejpam-6133	455	7	53:961–971	53:961–971	PROPN
ejpam-6133	455	8	,	,	PUNCT
ejpam-6133	455	9	2007	2007	NUM
ejpam-6133	455	10	.	.	PUNCT
ejpam-6133	456	1	[	[	X
ejpam-6133	456	2	14	14	NUM
ejpam-6133	456	3	]	]	PUNCT
ejpam-6133	456	4	a.	a.	NOUN
ejpam-6133	456	5	felhi	felhi	PROPN
ejpam-6133	456	6	and	and	CCONJ
ejpam-6133	456	7	h.	h.	PROPN
ejpam-6133	456	8	aydi	aydi	VERB
ejpam-6133	456	9	.	.	PUNCT
ejpam-6133	457	1	new	new	ADJ
ejpam-6133	457	2	fixed	fix	VERB
ejpam-6133	457	3	point	point	NOUN
ejpam-6133	457	4	results	result	NOUN
ejpam-6133	457	5	for	for	ADP
ejpam-6133	457	6	multi	multi	ADJ
ejpam-6133	457	7	-	-	ADJ
ejpam-6133	457	8	valued	value	VERB
ejpam-6133	457	9	maps	map	NOUN
ejpam-6133	457	10	via	via	ADP
ejpam-6133	457	11	manageable	manageable	ADJ
ejpam-6133	457	12	h.	h.	PROPN
ejpam-6133	457	13	aydi	aydi	PROPN
ejpam-6133	457	14	,	,	PUNCT
ejpam-6133	457	15	h.	h.	PROPN
ejpam-6133	457	16	hammouda	hammouda	PROPN
ejpam-6133	457	17	,	,	PUNCT
ejpam-6133	457	18	s.	s.	PROPN
ejpam-6133	457	19	mansour	mansour	PROPN
ejpam-6133	457	20	/	/	SYM
ejpam-6133	457	21	eur	eur	PROPN
ejpam-6133	457	22	.	.	PUNCT
ejpam-6133	458	1	j.	j.	PROPN
ejpam-6133	458	2	pure	pure	PROPN
ejpam-6133	458	3	appl	appl	PROPN
ejpam-6133	458	4	.	.	PROPN
ejpam-6133	458	5	math	math	PROPN
ejpam-6133	458	6	,	,	PUNCT
ejpam-6133	458	7	18	18	NUM
ejpam-6133	458	8	(	(	PUNCT
ejpam-6133	458	9	3	3	NUM
ejpam-6133	458	10	)	)	PUNCT
ejpam-6133	458	11	(	(	PUNCT
ejpam-6133	458	12	2025	2025	NUM
ejpam-6133	458	13	)	)	PUNCT
ejpam-6133	458	14	,	,	PUNCT
ejpam-6133	458	15	6133	6133	NUM
ejpam-6133	458	16	18	18	NUM
ejpam-6133	458	17	of	of	ADP
ejpam-6133	458	18	18	18	NUM
ejpam-6133	458	19	functions	function	NOUN
ejpam-6133	458	20	and	and	CCONJ
ejpam-6133	458	21	an	an	DET
ejpam-6133	458	22	application	application	NOUN
ejpam-6133	458	23	on	on	ADP
ejpam-6133	458	24	a	a	DET
ejpam-6133	458	25	boundary	boundary	ADJ
ejpam-6133	458	26	value	value	NOUN
ejpam-6133	458	27	problem	problem	NOUN
ejpam-6133	458	28	.	.	PUNCT
ejpam-6133	459	1	u.p.b	u.p.b	ADJ
ejpam-6133	459	2	.	.	PUNCT
ejpam-6133	460	1	scientific	scientific	ADJ
ejpam-6133	460	2	bulletin	bulletin	NOUN
ejpam-6133	460	3	,	,	PUNCT
ejpam-6133	460	4	series	series	NOUN
ejpam-6133	460	5	a	a	NOUN
ejpam-6133	460	6	,	,	PUNCT
ejpam-6133	460	7	80(1):1–12	80(1):1–12	NUM
ejpam-6133	460	8	,	,	PUNCT
ejpam-6133	460	9	2018	2018	NUM
ejpam-6133	460	10	.	.	PUNCT
ejpam-6133	461	1	[	[	X
ejpam-6133	461	2	15	15	NUM
ejpam-6133	461	3	]	]	X
ejpam-6133	461	4	b.	b.	PROPN
ejpam-6133	461	5	samet	samet	PROPN
ejpam-6133	461	6	,	,	PUNCT
ejpam-6133	461	7	c.	c.	PROPN
ejpam-6133	461	8	vetro	vetro	PROPN
ejpam-6133	461	9	,	,	PUNCT
ejpam-6133	461	10	and	and	CCONJ
ejpam-6133	461	11	p.	p.	PROPN
ejpam-6133	461	12	vetro	vetro	PROPN
ejpam-6133	461	13	.	.	PUNCT
ejpam-6133	462	1	fixed	fix	VERB
ejpam-6133	462	2	point	point	NOUN
ejpam-6133	462	3	theorems	theorem	NOUN
ejpam-6133	462	4	for	for	ADP
ejpam-6133	462	5	α	α	PRON
ejpam-6133	462	6	−	−	ADP
ejpam-6133	462	7	ψ	ψ	NOUN
ejpam-6133	462	8	-	-	ADJ
ejpam-6133	462	9	contractive	contractive	ADJ
ejpam-6133	462	10	type	type	NOUN
ejpam-6133	462	11	mappings	mapping	NOUN
ejpam-6133	462	12	.	.	PUNCT
ejpam-6133	463	1	nonlinear	nonlinear	ADJ
ejpam-6133	463	2	analysis	analysis	NOUN
ejpam-6133	463	3	:	:	PUNCT
ejpam-6133	463	4	theory	theory	NOUN
ejpam-6133	463	5	,	,	PUNCT
ejpam-6133	463	6	methods	method	NOUN
ejpam-6133	463	7	and	and	CCONJ
ejpam-6133	463	8	applications	application	NOUN
ejpam-6133	463	9	,	,	PUNCT
ejpam-6133	463	10	75:2154–2165	75:2154–2165	NUM
ejpam-6133	463	11	,	,	PUNCT
ejpam-6133	463	12	2012	2012	NUM
ejpam-6133	463	13	.	.	PUNCT