id	sid	tid	token	lemma	pos
ejpam-5605	1	1	european	european	PROPN
ejpam-5605	1	2	journal	journal	PROPN
ejpam-5605	1	3	of	of	ADP
ejpam-5605	1	4	pure	pure	ADJ
ejpam-5605	1	5	and	and	CCONJ
ejpam-5605	1	6	applied	applied	ADJ
ejpam-5605	1	7	mathematics	mathematic	NOUN
ejpam-5605	1	8	2025	2025	NUM
ejpam-5605	1	9	,	,	PUNCT
ejpam-5605	1	10	vol	vol	NOUN
ejpam-5605	1	11	.	.	PROPN
ejpam-5605	1	12	18	18	NUM
ejpam-5605	1	13	,	,	PUNCT
ejpam-5605	1	14	issue	issue	NOUN
ejpam-5605	1	15	1	1	NUM
ejpam-5605	1	16	,	,	PUNCT
ejpam-5605	1	17	article	article	NOUN
ejpam-5605	1	18	number	number	NOUN
ejpam-5605	1	19	5605	5605	NUM
ejpam-5605	1	20	issn	issn	VERB
ejpam-5605	1	21	1307	1307	NUM
ejpam-5605	1	22	-	-	SYM
ejpam-5605	1	23	5543	5543	NUM
ejpam-5605	1	24	–	–	PUNCT
ejpam-5605	1	25	ejpam.com	ejpam.com	X
ejpam-5605	1	26	published	publish	VERB
ejpam-5605	1	27	by	by	ADP
ejpam-5605	1	28	new	new	PROPN
ejpam-5605	1	29	york	york	PROPN
ejpam-5605	1	30	business	business	PROPN
ejpam-5605	1	31	global	global	PROPN
ejpam-5605	1	32	langevin	langevin	PROPN
ejpam-5605	1	33	fractional	fractional	ADJ
ejpam-5605	1	34	system	system	NOUN
ejpam-5605	1	35	driven	drive	VERB
ejpam-5605	1	36	by	by	ADP
ejpam-5605	1	37	two	two	NUM
ejpam-5605	1	38	ψ	ψ	NOUN
ejpam-5605	1	39	-	-	PUNCT
ejpam-5605	1	40	caputo	caputo	ADJ
ejpam-5605	1	41	derivatives	derivative	NOUN
ejpam-5605	1	42	with	with	ADP
ejpam-5605	1	43	random	random	ADJ
ejpam-5605	1	44	effects	effect	NOUN
ejpam-5605	1	45	mohamed	mohamed	PROPN
ejpam-5605	1	46	ziane1	ziane1	PROPN
ejpam-5605	1	47	,	,	PUNCT
ejpam-5605	1	48	hussein	hussein	PROPN
ejpam-5605	1	49	al	al	PROPN
ejpam-5605	1	50	-	-	PUNCT
ejpam-5605	1	51	taani2	taani2	PROPN
ejpam-5605	1	52	,	,	PUNCT
ejpam-5605	1	53	mohammad	mohammad	PROPN
ejpam-5605	1	54	abudayah2,∗	abudayah2,∗	PROPN
ejpam-5605	1	55	,	,	PUNCT
ejpam-5605	1	56	oualid	oualid	ADJ
ejpam-5605	1	57	zentar3	zentar3	NOUN
ejpam-5605	1	58	,	,	PUNCT
ejpam-5605	1	59	ma’mon	ma’mon	PROPN
ejpam-5605	1	60	abu	abu	PROPN
ejpam-5605	1	61	hammad4	hammad4	PROPN
ejpam-5605	1	62	1	1	NUM
ejpam-5605	1	63	department	department	NOUN
ejpam-5605	1	64	of	of	ADP
ejpam-5605	1	65	mathematics	mathematic	NOUN
ejpam-5605	1	66	,	,	PUNCT
ejpam-5605	1	67	university	university	NOUN
ejpam-5605	1	68	of	of	ADP
ejpam-5605	1	69	tiaret	tiaret	NOUN
ejpam-5605	1	70	,	,	PUNCT
ejpam-5605	1	71	tiaret	tiaret	NOUN
ejpam-5605	1	72	,	,	PUNCT
ejpam-5605	1	73	algeria	algeria	PROPN
ejpam-5605	1	74	and	and	CCONJ
ejpam-5605	1	75	laboratory	laboratory	NOUN
ejpam-5605	1	76	of	of	ADP
ejpam-5605	1	77	research	research	NOUN
ejpam-5605	1	78	in	in	ADP
ejpam-5605	1	79	artificial	artificial	ADJ
ejpam-5605	1	80	intelligence	intelligence	NOUN
ejpam-5605	1	81	and	and	CCONJ
ejpam-5605	1	82	systems	system	NOUN
ejpam-5605	1	83	(	(	PUNCT
ejpam-5605	1	84	lrais	lrais	PROPN
ejpam-5605	1	85	)	)	PUNCT
ejpam-5605	1	86	,	,	PUNCT
ejpam-5605	1	87	university	university	NOUN
ejpam-5605	1	88	of	of	ADP
ejpam-5605	1	89	tiaret	tiaret	NOUN
ejpam-5605	1	90	,	,	PUNCT
ejpam-5605	1	91	algeria	algeria	PROPN
ejpam-5605	1	92	2	2	NUM
ejpam-5605	1	93	school	school	NOUN
ejpam-5605	1	94	of	of	ADP
ejpam-5605	1	95	electrical	electrical	ADJ
ejpam-5605	1	96	engineering	engineering	NOUN
ejpam-5605	1	97	and	and	CCONJ
ejpam-5605	1	98	information	information	NOUN
ejpam-5605	1	99	technology	technology	NOUN
ejpam-5605	1	100	,	,	PUNCT
ejpam-5605	1	101	german	german	ADJ
ejpam-5605	1	102	jordanian	jordanian	ADJ
ejpam-5605	1	103	university	university	NOUN
ejpam-5605	1	104	,	,	PUNCT
ejpam-5605	1	105	amman	amman	PROPN
ejpam-5605	1	106	11180	11180	NUM
ejpam-5605	1	107	,	,	PUNCT
ejpam-5605	1	108	jordan	jordan	PROPN
ejpam-5605	1	109	3	3	NUM
ejpam-5605	1	110	department	department	PROPN
ejpam-5605	1	111	of	of	ADP
ejpam-5605	1	112	computer	computer	NOUN
ejpam-5605	1	113	science	science	NOUN
ejpam-5605	1	114	,	,	PUNCT
ejpam-5605	1	115	university	university	NOUN
ejpam-5605	1	116	of	of	ADP
ejpam-5605	1	117	tiaret	tiaret	NOUN
ejpam-5605	1	118	,	,	PUNCT
ejpam-5605	1	119	tiaret	tiaret	NOUN
ejpam-5605	1	120	,	,	PUNCT
ejpam-5605	1	121	algeria	algeria	PROPN
ejpam-5605	1	122	and	and	CCONJ
ejpam-5605	1	123	laboratory	laboratory	NOUN
ejpam-5605	1	124	of	of	ADP
ejpam-5605	1	125	research	research	NOUN
ejpam-5605	1	126	in	in	ADP
ejpam-5605	1	127	artificial	artificial	ADJ
ejpam-5605	1	128	intelligence	intelligence	NOUN
ejpam-5605	1	129	and	and	CCONJ
ejpam-5605	1	130	systems	system	NOUN
ejpam-5605	1	131	(	(	PUNCT
ejpam-5605	1	132	lrais	lrais	PROPN
ejpam-5605	1	133	)	)	PUNCT
ejpam-5605	1	134	,	,	PUNCT
ejpam-5605	1	135	university	university	NOUN
ejpam-5605	1	136	of	of	ADP
ejpam-5605	1	137	tiaret	tiaret	NOUN
ejpam-5605	1	138	,	,	PUNCT
ejpam-5605	1	139	algeria	algeria	PROPN
ejpam-5605	1	140	.	.	PUNCT
ejpam-5605	2	1	4	4	NUM
ejpam-5605	2	2	department	department	NOUN
ejpam-5605	2	3	of	of	ADP
ejpam-5605	2	4	mathematics	mathematics	PROPN
ejpam-5605	2	5	,	,	PUNCT
ejpam-5605	2	6	al	al	PROPN
ejpam-5605	2	7	-	-	PROPN
ejpam-5605	2	8	zaytoonah	zaytoonah	PROPN
ejpam-5605	2	9	university	university	PROPN
ejpam-5605	2	10	of	of	ADP
ejpam-5605	2	11	jordan	jordan	PROPN
ejpam-5605	2	12	,	,	PUNCT
ejpam-5605	2	13	amman	amman	PROPN
ejpam-5605	2	14	11733	11733	NUM
ejpam-5605	2	15	,	,	PUNCT
ejpam-5605	2	16	jordan	jordan	PROPN
ejpam-5605	2	17	abstract	abstract	PROPN
ejpam-5605	2	18	.	.	PUNCT
ejpam-5605	3	1	a	a	DET
ejpam-5605	3	2	nonlinear	nonlinear	ADJ
ejpam-5605	3	3	langevin	langevin	ADJ
ejpam-5605	3	4	fractional	fractional	ADJ
ejpam-5605	3	5	system	system	NOUN
ejpam-5605	3	6	involving	involve	VERB
ejpam-5605	3	7	two	two	NUM
ejpam-5605	3	8	ψ	ψ	NOUN
ejpam-5605	3	9	-	-	PUNCT
ejpam-5605	3	10	caputo	caputo	ADJ
ejpam-5605	3	11	derivatives	derivative	NOUN
ejpam-5605	3	12	with	with	ADP
ejpam-5605	3	13	random	random	ADJ
ejpam-5605	3	14	effects	effect	NOUN
ejpam-5605	3	15	is	be	AUX
ejpam-5605	3	16	investigated	investigate	VERB
ejpam-5605	3	17	.	.	PUNCT
ejpam-5605	4	1	first	first	ADV
ejpam-5605	4	2	,	,	PUNCT
ejpam-5605	4	3	a	a	DET
ejpam-5605	4	4	random	random	ADJ
ejpam-5605	4	5	version	version	NOUN
ejpam-5605	4	6	of	of	ADP
ejpam-5605	4	7	perov	perov	PROPN
ejpam-5605	4	8	’s	’s	PART
ejpam-5605	4	9	fixed	fix	VERB
ejpam-5605	4	10	-	-	PUNCT
ejpam-5605	4	11	point	point	NOUN
ejpam-5605	4	12	theorem	theorem	NOUN
ejpam-5605	4	13	in	in	ADP
ejpam-5605	4	14	generalized	generalized	ADJ
ejpam-5605	4	15	banach	banach	NOUN
ejpam-5605	4	16	space	space	NOUN
ejpam-5605	4	17	endowed	endow	VERB
ejpam-5605	4	18	with	with	ADP
ejpam-5605	4	19	the	the	DET
ejpam-5605	4	20	bielecki	bielecki	ADJ
ejpam-5605	4	21	-	-	PUNCT
ejpam-5605	4	22	type	type	NOUN
ejpam-5605	4	23	vector	vector	NOUN
ejpam-5605	4	24	-	-	PUNCT
ejpam-5605	4	25	valued	value	VERB
ejpam-5605	4	26	norm	norm	NOUN
ejpam-5605	4	27	is	be	AUX
ejpam-5605	4	28	employed	employ	VERB
ejpam-5605	4	29	to	to	PART
ejpam-5605	4	30	achieve	achieve	VERB
ejpam-5605	4	31	a	a	DET
ejpam-5605	4	32	uniqueness	uniqueness	NOUN
ejpam-5605	4	33	result	result	NOUN
ejpam-5605	4	34	.	.	PUNCT
ejpam-5605	5	1	second	second	ADJ
ejpam-5605	5	2	,	,	PUNCT
ejpam-5605	5	3	the	the	DET
ejpam-5605	5	4	existence	existence	NOUN
ejpam-5605	5	5	result	result	NOUN
ejpam-5605	5	6	is	be	AUX
ejpam-5605	5	7	established	establish	VERB
ejpam-5605	5	8	using	use	VERB
ejpam-5605	5	9	sadovskii	sadovskii	PROPN
ejpam-5605	5	10	’s	’s	PART
ejpam-5605	5	11	fixed	fix	VERB
ejpam-5605	5	12	point	point	NOUN
ejpam-5605	5	13	principle	principle	NOUN
ejpam-5605	5	14	under	under	ADP
ejpam-5605	5	15	fairly	fairly	ADV
ejpam-5605	5	16	general	general	ADJ
ejpam-5605	5	17	conditions	condition	NOUN
ejpam-5605	5	18	on	on	ADP
ejpam-5605	5	19	the	the	DET
ejpam-5605	5	20	nonlinear	nonlinear	ADJ
ejpam-5605	5	21	forcing	force	VERB
ejpam-5605	5	22	terms	term	NOUN
ejpam-5605	5	23	.	.	PUNCT
ejpam-5605	6	1	finally	finally	ADV
ejpam-5605	6	2	,	,	PUNCT
ejpam-5605	6	3	our	our	PRON
ejpam-5605	6	4	findings	finding	NOUN
ejpam-5605	6	5	are	be	AUX
ejpam-5605	6	6	justified	justify	VERB
ejpam-5605	6	7	through	through	ADP
ejpam-5605	6	8	illustrative	illustrative	ADJ
ejpam-5605	6	9	examples	example	NOUN
ejpam-5605	6	10	.	.	PUNCT
ejpam-5605	7	1	2020	2020	NUM
ejpam-5605	7	2	mathematics	mathematic	NOUN
ejpam-5605	7	3	subject	subject	NOUN
ejpam-5605	7	4	classifications	classification	NOUN
ejpam-5605	7	5	:	:	PUNCT
ejpam-5605	7	6	ams	am	NOUN
ejpam-5605	7	7	34a08	34a08	NUM
ejpam-5605	7	8	,	,	PUNCT
ejpam-5605	7	9	47h08	47h08	NUM
ejpam-5605	7	10	,	,	PUNCT
ejpam-5605	7	11	60h25	60h25	NUM
ejpam-5605	7	12	key	key	ADJ
ejpam-5605	7	13	words	word	NOUN
ejpam-5605	7	14	and	and	CCONJ
ejpam-5605	7	15	phrases	phrase	NOUN
ejpam-5605	7	16	:	:	PUNCT
ejpam-5605	7	17	langevin	langevin	ADJ
ejpam-5605	7	18	equation	equation	NOUN
ejpam-5605	7	19	,	,	PUNCT
ejpam-5605	7	20	ψ	ψ	PROPN
ejpam-5605	7	21	-	-	PUNCT
ejpam-5605	7	22	caputo	caputo	ADJ
ejpam-5605	7	23	derivative	derivative	NOUN
ejpam-5605	7	24	,	,	PUNCT
ejpam-5605	7	25	random	random	ADJ
ejpam-5605	7	26	variable	variable	NOUN
ejpam-5605	7	27	,	,	PUNCT
ejpam-5605	7	28	vectorvalued	vectorvalue	VERB
ejpam-5605	7	29	norm	norm	NOUN
ejpam-5605	7	30	,	,	PUNCT
ejpam-5605	7	31	measure	measure	NOUN
ejpam-5605	7	32	of	of	ADP
ejpam-5605	7	33	noncompactness	noncompactness	ADJ
ejpam-5605	7	34	1	1	NUM
ejpam-5605	7	35	.	.	PUNCT
ejpam-5605	7	36	introduction	introduction	NOUN
ejpam-5605	7	37	fractional	fractional	ADJ
ejpam-5605	7	38	calculus	calculus	NOUN
ejpam-5605	7	39	and	and	CCONJ
ejpam-5605	7	40	its	its	PRON
ejpam-5605	7	41	applications	application	NOUN
ejpam-5605	7	42	have	have	AUX
ejpam-5605	7	43	garnered	garner	VERB
ejpam-5605	7	44	significant	significant	ADJ
ejpam-5605	7	45	attention	attention	NOUN
ejpam-5605	7	46	from	from	ADP
ejpam-5605	7	47	scientists	scientist	NOUN
ejpam-5605	7	48	and	and	CCONJ
ejpam-5605	7	49	researchers	researcher	NOUN
ejpam-5605	7	50	in	in	ADP
ejpam-5605	7	51	recent	recent	ADJ
ejpam-5605	7	52	years	year	NOUN
ejpam-5605	7	53	,	,	PUNCT
ejpam-5605	7	54	not	not	PART
ejpam-5605	7	55	only	only	ADV
ejpam-5605	7	56	in	in	ADP
ejpam-5605	7	57	mathematics	mathematic	NOUN
ejpam-5605	7	58	but	but	CCONJ
ejpam-5605	7	59	also	also	ADV
ejpam-5605	7	60	across	across	ADP
ejpam-5605	7	61	various	various	ADJ
ejpam-5605	7	62	scientific	scientific	ADJ
ejpam-5605	7	63	disciplines	discipline	NOUN
ejpam-5605	7	64	,	,	PUNCT
ejpam-5605	7	65	including	include	VERB
ejpam-5605	7	66	physics	physics	NOUN
ejpam-5605	7	67	[	[	X
ejpam-5605	7	68	20	20	NUM
ejpam-5605	7	69	]	]	PUNCT
ejpam-5605	7	70	,	,	PUNCT
ejpam-5605	7	71	chemical	chemical	ADJ
ejpam-5605	7	72	kinetics	kinetic	NOUN
ejpam-5605	8	1	[	[	X
ejpam-5605	8	2	26	26	NUM
ejpam-5605	8	3	]	]	PUNCT
ejpam-5605	8	4	,	,	PUNCT
ejpam-5605	8	5	fluid	fluid	ADJ
ejpam-5605	8	6	dynamics	dynamic	NOUN
ejpam-5605	8	7	[	[	X
ejpam-5605	8	8	21	21	NUM
ejpam-5605	8	9	]	]	PUNCT
ejpam-5605	8	10	,	,	PUNCT
ejpam-5605	8	11	viscoelastic	viscoelastic	ADJ
ejpam-5605	9	1	[	[	X
ejpam-5605	9	2	11	11	NUM
ejpam-5605	9	3	]	]	PUNCT
ejpam-5605	9	4	,	,	PUNCT
ejpam-5605	9	5	electrochemistry	electrochemistry	NOUN
ejpam-5605	9	6	[	[	X
ejpam-5605	9	7	19	19	NUM
ejpam-5605	9	8	]	]	PUNCT
ejpam-5605	9	9	,	,	PUNCT
ejpam-5605	9	10	elasticity	elasticity	NOUN
ejpam-5605	9	11	[	[	X
ejpam-5605	9	12	4	4	NUM
ejpam-5605	9	13	]	]	PUNCT
ejpam-5605	9	14	,	,	PUNCT
ejpam-5605	9	15	engineering	engineer	VERB
ejpam-5605	10	1	[	[	X
ejpam-5605	10	2	29],economics	29],economics	NUM
ejpam-5605	11	1	[	[	X
ejpam-5605	11	2	28	28	NUM
ejpam-5605	11	3	]	]	PUNCT
ejpam-5605	11	4	,	,	PUNCT
ejpam-5605	11	5	financial	financial	ADJ
ejpam-5605	11	6	systems	system	NOUN
ejpam-5605	11	7	[	[	X
ejpam-5605	11	8	22	22	NUM
ejpam-5605	11	9	]	]	PUNCT
ejpam-5605	11	10	,	,	PUNCT
ejpam-5605	11	11	biology	biology	NOUN
ejpam-5605	11	12	[	[	X
ejpam-5605	11	13	14	14	NUM
ejpam-5605	11	14	]	]	PUNCT
ejpam-5605	11	15	,	,	PUNCT
ejpam-5605	11	16	medicine	medicine	NOUN
ejpam-5605	11	17	[	[	X
ejpam-5605	11	18	24	24	NUM
ejpam-5605	11	19	]	]	PUNCT
ejpam-5605	11	20	,	,	PUNCT
ejpam-5605	11	21	statistics	statistic	NOUN
ejpam-5605	12	1	[	[	X
ejpam-5605	12	2	2	2	NUM
ejpam-5605	12	3	]	]	PUNCT
ejpam-5605	12	4	,	,	PUNCT
ejpam-5605	12	5	computing	compute	VERB
ejpam-5605	12	6	image	image	NOUN
ejpam-5605	12	7	[	[	X
ejpam-5605	12	8	31	31	NUM
ejpam-5605	12	9	]	]	PUNCT
ejpam-5605	12	10	,	,	PUNCT
ejpam-5605	12	11	nonlinear	nonlinear	ADJ
ejpam-5605	12	12	heat	heat	NOUN
ejpam-5605	12	13	conduction	conduction	NOUN
ejpam-5605	12	14	[	[	X
ejpam-5605	12	15	8	8	NUM
ejpam-5605	12	16	]	]	PUNCT
ejpam-5605	12	17	,	,	PUNCT
ejpam-5605	12	18	optimal	optimal	ADJ
ejpam-5605	12	19	control	control	NOUN
ejpam-5605	13	1	[	[	X
ejpam-5605	13	2	9	9	NUM
ejpam-5605	13	3	]	]	PUNCT
ejpam-5605	13	4	,	,	PUNCT
ejpam-5605	13	5	etc	etc	X
ejpam-5605	13	6	.	.	X
ejpam-5605	13	7	moreover	moreover	ADV
ejpam-5605	13	8	,	,	PUNCT
ejpam-5605	13	9	many	many	ADJ
ejpam-5605	13	10	cosmic	cosmic	ADJ
ejpam-5605	13	11	events	event	NOUN
ejpam-5605	13	12	that	that	PRON
ejpam-5605	13	13	classical	classical	ADJ
ejpam-5605	13	14	differential	differential	ADJ
ejpam-5605	13	15	equations	equation	NOUN
ejpam-5605	13	16	can	can	AUX
ejpam-5605	13	17	not	not	PART
ejpam-5605	13	18	describe	describe	VERB
ejpam-5605	13	19	can	can	AUX
ejpam-5605	13	20	be	be	AUX
ejpam-5605	13	21	described	describe	VERB
ejpam-5605	13	22	by	by	ADP
ejpam-5605	13	23	fractional	fractional	ADJ
ejpam-5605	13	24	differential	differential	ADJ
ejpam-5605	13	25	equations	equation	NOUN
ejpam-5605	13	26	.	.	PUNCT
ejpam-5605	14	1	∗corresponding	∗corresponde	VERB
ejpam-5605	14	2	author	author	NOUN
ejpam-5605	14	3	.	.	PUNCT
ejpam-5605	15	1	doi	doi	NOUN
ejpam-5605	15	2	:	:	PUNCT
ejpam-5605	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5605	https://doi.org/10.29020/nybg.ejpam.v18i1.5605	X
ejpam-5605	15	4	email	email	NOUN
ejpam-5605	15	5	addresses	address	VERB
ejpam-5605	15	6	:	:	PUNCT
ejpam-5605	15	7	mohamed.ziane@univ-tiaret.dz	mohamed.ziane@univ-tiaret.dz	PROPN
ejpam-5605	15	8	(	(	PUNCT
ejpam-5605	15	9	m.	m.	NOUN
ejpam-5605	15	10	ziane	ziane	PROPN
ejpam-5605	15	11	)	)	PUNCT
ejpam-5605	15	12	,	,	PUNCT
ejpam-5605	15	13	hussein.taani@gju.edu.jo	hussein.taani@gju.edu.jo	PROPN
ejpam-5605	15	14	(	(	PUNCT
ejpam-5605	15	15	h.	h.	PROPN
ejpam-5605	15	16	al	al	PROPN
ejpam-5605	15	17	-	-	PUNCT
ejpam-5605	15	18	taani	taani	ADJ
ejpam-5605	15	19	)	)	PUNCT
ejpam-5605	15	20	,	,	PUNCT
ejpam-5605	15	21	mohammad.abudayah@gju.edu.jo	mohammad.abudayah@gju.edu.jo	PROPN
ejpam-5605	15	22	(	(	PUNCT
ejpam-5605	15	23	m.	m.	NOUN
ejpam-5605	15	24	abudayah	abudayah	PROPN
ejpam-5605	15	25	)	)	PUNCT
ejpam-5605	15	26	,	,	PUNCT
ejpam-5605	15	27	oualid.zentar@univ-tiaret.dz	oualid.zentar@univ-tiaret.dz	PROPN
ejpam-5605	15	28	(	(	PUNCT
ejpam-5605	15	29	o.	o.	NOUN
ejpam-5605	15	30	zentar),m.abuhammad@zuj.edu.jo	zentar),m.abuhammad@zuj.edu.jo	PROPN
ejpam-5605	15	31	(	(	PUNCT
ejpam-5605	15	32	m.	m.	PROPN
ejpam-5605	15	33	abu	abu	PROPN
ejpam-5605	15	34	hammad	hammad	PROPN
ejpam-5605	15	35	)	)	PUNCT
ejpam-5605	15	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5605	15	37	1	1	NUM
ejpam-5605	15	38	copyright	copyright	NOUN
ejpam-5605	15	39	:	:	PUNCT
ejpam-5605	16	1	©	©	PROPN
ejpam-5605	16	2	2025	2025	NUM
ejpam-5605	16	3	the	the	DET
ejpam-5605	16	4	author(s	author(s	NOUN
ejpam-5605	16	5	)	)	PUNCT
ejpam-5605	16	6	.	.	PUNCT
ejpam-5605	17	1	(	(	PUNCT
ejpam-5605	17	2	cc	cc	NOUN
ejpam-5605	17	3	by	by	ADP
ejpam-5605	17	4	-	-	PUNCT
ejpam-5605	17	5	nc	nc	PROPN
ejpam-5605	17	6	4.0	4.0	NUM
ejpam-5605	17	7	)	)	PUNCT
ejpam-5605	17	8	m.	m.	NOUN
ejpam-5605	17	9	ziane	ziane	NOUN
ejpam-5605	17	10	et	et	PROPN
ejpam-5605	17	11	al	al	PROPN
ejpam-5605	17	12	.	.	PUNCT
ejpam-5605	17	13	/	/	SYM
ejpam-5605	17	14	eur	eur	PROPN
ejpam-5605	17	15	.	.	PUNCT
ejpam-5605	18	1	j.	j.	PROPN
ejpam-5605	18	2	pure	pure	PROPN
ejpam-5605	18	3	appl	appl	PROPN
ejpam-5605	18	4	.	.	PROPN
ejpam-5605	18	5	math	math	PROPN
ejpam-5605	18	6	,	,	PUNCT
ejpam-5605	18	7	18	18	NUM
ejpam-5605	18	8	(	(	PUNCT
ejpam-5605	18	9	1	1	NUM
ejpam-5605	18	10	)	)	PUNCT
ejpam-5605	18	11	(	(	PUNCT
ejpam-5605	18	12	2025	2025	NUM
ejpam-5605	18	13	)	)	PUNCT
ejpam-5605	18	14	,	,	PUNCT
ejpam-5605	18	15	5605	5605	NUM
ejpam-5605	18	16	2	2	NUM
ejpam-5605	18	17	of	of	ADP
ejpam-5605	18	18	21	21	NUM
ejpam-5605	18	19	on	on	ADP
ejpam-5605	18	20	the	the	DET
ejpam-5605	18	21	other	other	ADJ
ejpam-5605	18	22	side	side	NOUN
ejpam-5605	18	23	,	,	PUNCT
ejpam-5605	18	24	almeida	almeida	PROPN
ejpam-5605	19	1	[	[	X
ejpam-5605	19	2	3	3	X
ejpam-5605	19	3	]	]	PUNCT
ejpam-5605	19	4	proposed	propose	VERB
ejpam-5605	19	5	a	a	DET
ejpam-5605	19	6	general	general	ADJ
ejpam-5605	19	7	definition	definition	NOUN
ejpam-5605	19	8	of	of	ADP
ejpam-5605	19	9	caputo	caputo	PROPN
ejpam-5605	19	10	fd	fd	PROPN
ejpam-5605	19	11	with	with	ADP
ejpam-5605	19	12	respect	respect	NOUN
ejpam-5605	19	13	to	to	ADP
ejpam-5605	19	14	functions	function	NOUN
ejpam-5605	19	15	which	which	PRON
ejpam-5605	19	16	is	be	AUX
ejpam-5605	19	17	more	more	ADV
ejpam-5605	19	18	flexible	flexible	ADJ
ejpam-5605	19	19	,	,	PUNCT
ejpam-5605	19	20	beneficial	beneficial	ADJ
ejpam-5605	19	21	and	and	CCONJ
ejpam-5605	19	22	play	play	VERB
ejpam-5605	19	23	an	an	DET
ejpam-5605	19	24	important	important	ADJ
ejpam-5605	19	25	role	role	NOUN
ejpam-5605	19	26	in	in	ADP
ejpam-5605	19	27	modeling	model	VERB
ejpam-5605	19	28	practical	practical	ADJ
ejpam-5605	19	29	applications	application	NOUN
ejpam-5605	19	30	,	,	PUNCT
ejpam-5605	19	31	see	see	VERB
ejpam-5605	19	32	for	for	ADP
ejpam-5605	19	33	instance	instance	NOUN
ejpam-5605	19	34	[	[	X
ejpam-5605	19	35	10	10	NUM
ejpam-5605	19	36	]	]	PUNCT
ejpam-5605	19	37	.	.	PUNCT
ejpam-5605	20	1	multitude	multitude	PROPN
ejpam-5605	20	2	scholars	scholar	NOUN
ejpam-5605	20	3	investigate	investigate	VERB
ejpam-5605	20	4	several	several	ADJ
ejpam-5605	20	5	aspect	aspect	NOUN
ejpam-5605	20	6	of	of	ADP
ejpam-5605	20	7	the	the	DET
ejpam-5605	20	8	theory	theory	NOUN
ejpam-5605	20	9	[	[	X
ejpam-5605	20	10	6	6	NUM
ejpam-5605	20	11	,	,	PUNCT
ejpam-5605	20	12	32	32	NUM
ejpam-5605	20	13	,	,	PUNCT
ejpam-5605	20	14	33	33	NUM
ejpam-5605	20	15	]	]	PUNCT
ejpam-5605	20	16	.	.	PUNCT
ejpam-5605	21	1	the	the	DET
ejpam-5605	21	2	classical	classical	ADJ
ejpam-5605	21	3	langevin	langevin	NOUN
ejpam-5605	21	4	equation	equation	NOUN
ejpam-5605	21	5	,	,	PUNCT
ejpam-5605	21	6	as	as	SCONJ
ejpam-5605	21	7	proposed	propose	VERB
ejpam-5605	21	8	in	in	ADP
ejpam-5605	21	9	[	[	X
ejpam-5605	21	10	18	18	NUM
ejpam-5605	21	11	]	]	PUNCT
ejpam-5605	21	12	,	,	PUNCT
ejpam-5605	21	13	is	be	AUX
ejpam-5605	21	14	crucial	crucial	ADJ
ejpam-5605	21	15	for	for	ADP
ejpam-5605	21	16	demonstrating	demonstrate	VERB
ejpam-5605	21	17	how	how	SCONJ
ejpam-5605	21	18	particles	particle	NOUN
ejpam-5605	21	19	interact	interact	VERB
ejpam-5605	21	20	with	with	ADP
ejpam-5605	21	21	their	their	PRON
ejpam-5605	21	22	surrounding	surround	VERB
ejpam-5605	21	23	medium	medium	NOUN
ejpam-5605	21	24	and	and	CCONJ
ejpam-5605	21	25	the	the	DET
ejpam-5605	21	26	random	random	ADJ
ejpam-5605	21	27	forces	force	NOUN
ejpam-5605	21	28	or	or	CCONJ
ejpam-5605	21	29	fluctuations	fluctuation	NOUN
ejpam-5605	21	30	that	that	PRON
ejpam-5605	21	31	lead	lead	VERB
ejpam-5605	21	32	to	to	ADP
ejpam-5605	21	33	their	their	PRON
ejpam-5605	21	34	unpredictable	unpredictable	ADJ
ejpam-5605	21	35	motion	motion	NOUN
ejpam-5605	21	36	.	.	PUNCT
ejpam-5605	22	1	nevertheless	nevertheless	ADV
ejpam-5605	22	2	,	,	PUNCT
ejpam-5605	22	3	the	the	DET
ejpam-5605	22	4	reliance	reliance	NOUN
ejpam-5605	22	5	on	on	ADP
ejpam-5605	22	6	the	the	DET
ejpam-5605	22	7	specific	specific	ADJ
ejpam-5605	22	8	relationship	relationship	NOUN
ejpam-5605	22	9	between	between	ADP
ejpam-5605	22	10	a	a	DET
ejpam-5605	22	11	particle	particle	NOUN
ejpam-5605	22	12	’s	’s	PART
ejpam-5605	22	13	position	position	NOUN
ejpam-5605	22	14	and	and	CCONJ
ejpam-5605	22	15	velocity	velocity	NOUN
ejpam-5605	22	16	has	have	AUX
ejpam-5605	22	17	prompted	prompt	VERB
ejpam-5605	22	18	the	the	DET
ejpam-5605	22	19	development	development	NOUN
ejpam-5605	22	20	of	of	ADP
ejpam-5605	22	21	the	the	DET
ejpam-5605	22	22	fractional	fractional	ADJ
ejpam-5605	22	23	langevin	langevin	PROPN
ejpam-5605	22	24	model	model	PROPN
ejpam-5605	22	25	,	,	PUNCT
ejpam-5605	22	26	aimed	aim	VERB
ejpam-5605	22	27	at	at	ADP
ejpam-5605	22	28	describing	describe	VERB
ejpam-5605	22	29	anomalous	anomalous	ADJ
ejpam-5605	22	30	diffusion	diffusion	NOUN
ejpam-5605	22	31	phenomena	phenomena	NOUN
ejpam-5605	22	32	[	[	X
ejpam-5605	22	33	17	17	NUM
ejpam-5605	22	34	]	]	PUNCT
ejpam-5605	22	35	.	.	PUNCT
ejpam-5605	23	1	also	also	ADV
ejpam-5605	23	2	,	,	PUNCT
ejpam-5605	23	3	it	it	PRON
ejpam-5605	23	4	’s	’	VERB
ejpam-5605	23	5	important	important	ADJ
ejpam-5605	23	6	to	to	PART
ejpam-5605	23	7	highlight	highlight	VERB
ejpam-5605	23	8	that	that	SCONJ
ejpam-5605	23	9	certain	certain	ADJ
ejpam-5605	23	10	phenomena	phenomenon	NOUN
ejpam-5605	23	11	are	be	AUX
ejpam-5605	23	12	more	more	ADV
ejpam-5605	23	13	accurately	accurately	ADV
ejpam-5605	23	14	described	describe	VERB
ejpam-5605	23	15	by	by	ADP
ejpam-5605	23	16	coupled	couple	VERB
ejpam-5605	23	17	random	random	ADJ
ejpam-5605	23	18	systems	system	NOUN
ejpam-5605	23	19	.	.	PUNCT
ejpam-5605	24	1	for	for	ADP
ejpam-5605	24	2	example	example	NOUN
ejpam-5605	24	3	,	,	PUNCT
ejpam-5605	24	4	in	in	ADP
ejpam-5605	24	5	epidemiology	epidemiology	NOUN
ejpam-5605	24	6	,	,	PUNCT
ejpam-5605	24	7	the	the	DET
ejpam-5605	24	8	migration	migration	NOUN
ejpam-5605	24	9	of	of	ADP
ejpam-5605	24	10	birds	bird	NOUN
ejpam-5605	24	11	from	from	ADP
ejpam-5605	24	12	various	various	ADJ
ejpam-5605	24	13	regions	region	NOUN
ejpam-5605	24	14	worldwide	worldwide	ADV
ejpam-5605	24	15	can	can	AUX
ejpam-5605	24	16	introduce	introduce	VERB
ejpam-5605	24	17	infectious	infectious	ADJ
ejpam-5605	24	18	diseases	disease	NOUN
ejpam-5605	24	19	.	.	PUNCT
ejpam-5605	25	1	therefore	therefore	ADV
ejpam-5605	25	2	,	,	PUNCT
ejpam-5605	25	3	the	the	DET
ejpam-5605	25	4	transmission	transmission	NOUN
ejpam-5605	25	5	rate	rate	NOUN
ejpam-5605	25	6	of	of	ADP
ejpam-5605	25	7	these	these	DET
ejpam-5605	25	8	diseases	disease	NOUN
ejpam-5605	25	9	increases	increase	VERB
ejpam-5605	25	10	as	as	SCONJ
ejpam-5605	25	11	migratory	migratory	ADJ
ejpam-5605	25	12	birds	bird	NOUN
ejpam-5605	25	13	flock	flock	VERB
ejpam-5605	25	14	together	together	ADV
ejpam-5605	25	15	.	.	PUNCT
ejpam-5605	26	1	moreover	moreover	ADV
ejpam-5605	26	2	,	,	PUNCT
ejpam-5605	26	3	this	this	DET
ejpam-5605	26	4	scenario	scenario	NOUN
ejpam-5605	26	5	warrants	warrant	VERB
ejpam-5605	26	6	consideration	consideration	NOUN
ejpam-5605	26	7	of	of	ADP
ejpam-5605	26	8	the	the	DET
ejpam-5605	26	9	presence	presence	NOUN
ejpam-5605	26	10	of	of	ADP
ejpam-5605	26	11	random	random	ADJ
ejpam-5605	26	12	disturbances	disturbance	NOUN
ejpam-5605	26	13	.	.	PUNCT
ejpam-5605	27	1	while	while	SCONJ
ejpam-5605	27	2	the	the	DET
ejpam-5605	27	3	above	above	ADV
ejpam-5605	27	4	-	-	PUNCT
ejpam-5605	27	5	mentioned	mention	VERB
ejpam-5605	27	6	motivational	motivational	NOUN
ejpam-5605	27	7	models	model	NOUN
ejpam-5605	27	8	have	have	VERB
ejpam-5605	27	9	a	a	DET
ejpam-5605	27	10	great	great	ADJ
ejpam-5605	27	11	advantage	advantage	NOUN
ejpam-5605	27	12	,	,	PUNCT
ejpam-5605	27	13	the	the	DET
ejpam-5605	27	14	difficulty	difficulty	NOUN
ejpam-5605	27	15	of	of	ADP
ejpam-5605	27	16	the	the	DET
ejpam-5605	27	17	corresponding	corresponding	ADJ
ejpam-5605	27	18	mathematical	mathematical	ADJ
ejpam-5605	27	19	model	model	NOUN
ejpam-5605	27	20	may	may	AUX
ejpam-5605	27	21	significantly	significantly	ADV
ejpam-5605	27	22	increase	increase	VERB
ejpam-5605	27	23	,	,	PUNCT
ejpam-5605	27	24	complicating	complicate	VERB
ejpam-5605	27	25	the	the	DET
ejpam-5605	27	26	study	study	NOUN
ejpam-5605	27	27	of	of	ADP
ejpam-5605	27	28	the	the	DET
ejpam-5605	27	29	existence	existence	NOUN
ejpam-5605	27	30	of	of	ADP
ejpam-5605	27	31	solutions	solution	NOUN
ejpam-5605	27	32	.	.	PUNCT
ejpam-5605	28	1	accordingly	accordingly	ADV
ejpam-5605	28	2	,	,	PUNCT
ejpam-5605	28	3	exploring	explore	VERB
ejpam-5605	28	4	the	the	DET
ejpam-5605	28	5	qualitative	qualitative	ADJ
ejpam-5605	28	6	aspects	aspect	NOUN
ejpam-5605	28	7	of	of	ADP
ejpam-5605	28	8	ψ	ψ	PROPN
ejpam-5605	28	9	-	-	PROPN
ejpam-5605	28	10	caputo	caputo	PROPN
ejpam-5605	28	11	nonlinear	nonlinear	PROPN
ejpam-5605	28	12	langevin	langevin	PROPN
ejpam-5605	28	13	coupled	couple	VERB
ejpam-5605	28	14	systems	system	NOUN
ejpam-5605	28	15	with	with	ADP
ejpam-5605	28	16	random	random	ADJ
ejpam-5605	28	17	effects	effect	NOUN
ejpam-5605	28	18	has	have	AUX
ejpam-5605	28	19	become	become	VERB
ejpam-5605	28	20	increasingly	increasingly	ADV
ejpam-5605	28	21	important	important	ADJ
ejpam-5605	28	22	.	.	PUNCT
ejpam-5605	29	1	recently	recently	ADV
ejpam-5605	29	2	,	,	PUNCT
ejpam-5605	29	3	the	the	DET
ejpam-5605	29	4	authors	author	NOUN
ejpam-5605	29	5	in	in	ADP
ejpam-5605	29	6	[	[	X
ejpam-5605	29	7	13	13	NUM
ejpam-5605	29	8	,	,	PUNCT
ejpam-5605	29	9	33	33	NUM
ejpam-5605	29	10	]	]	PUNCT
ejpam-5605	29	11	studied	study	VERB
ejpam-5605	29	12	theoretically	theoretically	ADV
ejpam-5605	29	13	some	some	DET
ejpam-5605	29	14	quantitative	quantitative	ADJ
ejpam-5605	29	15	aspects	aspect	NOUN
ejpam-5605	29	16	for	for	ADP
ejpam-5605	29	17	the	the	DET
ejpam-5605	29	18	following	follow	VERB
ejpam-5605	29	19	problem:	problem:	PROPN
ejpam-5605	29	20	(	(	PUNCT
ejpam-5605	29	21	cd	cd	PROPN
ejpam-5605	29	22	ϑ;ψ	ϑ;ψ	NOUN
ejpam-5605	29	23	a+	a+	PUNCT
ejpam-5605	30	1	+	+	ADJ
ejpam-5605	30	2	ϖcd	ϖcd	ADJ
ejpam-5605	30	3	ϑ−1;ψ	ϑ−1;ψ	NOUN
ejpam-5605	30	4	a+	a+	PRON
ejpam-5605	30	5	)	)	PUNCT
ejpam-5605	30	6	z(ξ	z(ξ	NOUN
ejpam-5605	30	7	)	)	PUNCT
ejpam-5605	30	8	=	=	SYM
ejpam-5605	30	9	f(ξ	f(ξ	NOUN
ejpam-5605	30	10	,	,	PUNCT
ejpam-5605	30	11	z(ξ	z(ξ	NOUN
ejpam-5605	30	12	)	)	PUNCT
ejpam-5605	30	13	)	)	PUNCT
ejpam-5605	30	14	,	,	PUNCT
ejpam-5605	30	15	ξ	ξ	X
ejpam-5605	30	16	∈	∈	PROPN
ejpam-5605	30	17	[	[	X
ejpam-5605	30	18	a	a	X
ejpam-5605	30	19	,	,	PUNCT
ejpam-5605	30	20	b	b	NOUN
ejpam-5605	30	21	]	]	X
ejpam-5605	30	22	,	,	PUNCT
ejpam-5605	30	23	z(a	z(a	NOUN
ejpam-5605	30	24	)	)	PUNCT
ejpam-5605	30	25	=	=	PUNCT
ejpam-5605	30	26	z′(a	z′(a	X
ejpam-5605	30	27	)	)	PUNCT
ejpam-5605	30	28	=	=	SYM
ejpam-5605	30	29	0	0	NUM
ejpam-5605	30	30	,	,	PUNCT
ejpam-5605	30	31	where	where	SCONJ
ejpam-5605	30	32	1	1	X
ejpam-5605	30	33	<	<	X
ejpam-5605	30	34	ϑ	ϑ	X
ejpam-5605	30	35	<	<	X
ejpam-5605	30	36	2	2	NUM
ejpam-5605	30	37	,	,	PUNCT
ejpam-5605	30	38	ϖ	ϖ	PROPN
ejpam-5605	30	39	∈	∈	NOUN
ejpam-5605	30	40	r	r	NOUN
ejpam-5605	30	41	,	,	PUNCT
ejpam-5605	30	42	cdθ;ψ	cdθ;ψ	ADJ
ejpam-5605	30	43	a+	a+	PUNCT
ejpam-5605	30	44	represents	represent	VERB
ejpam-5605	30	45	the	the	DET
ejpam-5605	30	46	caputo	caputo	PROPN
ejpam-5605	30	47	fractional	fractional	PROPN
ejpam-5605	30	48	derivative	derivative	PROPN
ejpam-5605	30	49	fd	fd	PROPN
ejpam-5605	30	50	with	with	ADP
ejpam-5605	30	51	respect	respect	NOUN
ejpam-5605	30	52	to	to	ADP
ejpam-5605	30	53	ψ	ψ	NOUN
ejpam-5605	30	54	of	of	ADP
ejpam-5605	30	55	order	order	NOUN
ejpam-5605	30	56	θ	θ	PROPN
ejpam-5605	30	57	∈	∈	PROPN
ejpam-5605	30	58	{	{	PUNCT
ejpam-5605	30	59	ϑ	ϑ	NOUN
ejpam-5605	30	60	,	,	PUNCT
ejpam-5605	30	61	ϑ	ϑ	X
ejpam-5605	30	62	−	−	PROPN
ejpam-5605	30	63	1	1	NUM
ejpam-5605	30	64	}	}	PUNCT
ejpam-5605	30	65	,	,	PUNCT
ejpam-5605	30	66	f	f	X
ejpam-5605	30	67	:	:	PUNCT
ejpam-5605	31	1	[	[	X
ejpam-5605	31	2	a	a	X
ejpam-5605	31	3	,	,	PUNCT
ejpam-5605	31	4	b	b	NOUN
ejpam-5605	31	5	]	]	X
ejpam-5605	31	6	×	×	NOUN
ejpam-5605	31	7	g	g	NOUN
ejpam-5605	31	8	→	→	SYM
ejpam-5605	31	9	g	g	PROPN
ejpam-5605	31	10	is	be	AUX
ejpam-5605	31	11	a	a	DET
ejpam-5605	31	12	given	give	VERB
ejpam-5605	31	13	function	function	NOUN
ejpam-5605	31	14	and	and	CCONJ
ejpam-5605	31	15	x	x	X
ejpam-5605	31	16	is	be	AUX
ejpam-5605	31	17	a	a	DET
ejpam-5605	31	18	banach	banach	NOUN
ejpam-5605	31	19	space	space	NOUN
ejpam-5605	31	20	.	.	PUNCT
ejpam-5605	32	1	o.	o.	PROPN
ejpam-5605	32	2	zentar	zentar	PROPN
ejpam-5605	32	3	et	et	PROPN
ejpam-5605	32	4	al	al	PROPN
ejpam-5605	32	5	.	.	PUNCT
ejpam-5605	33	1	in	in	ADP
ejpam-5605	33	2	[	[	X
ejpam-5605	33	3	34	34	NUM
ejpam-5605	33	4	]	]	PUNCT
ejpam-5605	33	5	investigated	investigate	VERB
ejpam-5605	33	6	the	the	DET
ejpam-5605	33	7	existence	existence	NOUN
ejpam-5605	33	8	of	of	ADP
ejpam-5605	33	9	solutions	solution	NOUN
ejpam-5605	33	10	for	for	ADP
ejpam-5605	33	11	the	the	DET
ejpam-5605	33	12	following	follow	VERB
ejpam-5605	33	13	system:	system:	NUM
ejpam-5605	33	14	dϑ1	dϑ1	NOUN
ejpam-5605	33	15	0	0	NUM
ejpam-5605	34	1	+	+	NUM
ejpam-5605	34	2	z1(ξ	z1(ξ	NUM
ejpam-5605	34	3	,	,	PUNCT
ejpam-5605	34	4	ω	ω	NOUN
ejpam-5605	34	5	)	)	PUNCT
ejpam-5605	34	6	=	=	SYM
ejpam-5605	34	7	f1(ξ	f1(ξ	PROPN
ejpam-5605	34	8	,	,	PUNCT
ejpam-5605	34	9	z1(ξ	z1(ξ	PROPN
ejpam-5605	34	10	,	,	PUNCT
ejpam-5605	34	11	ω	ω	NOUN
ejpam-5605	34	12	)	)	PUNCT
ejpam-5605	34	13	,	,	PUNCT
ejpam-5605	34	14	z2(ξ	z2(ξ	PROPN
ejpam-5605	34	15	,	,	PUNCT
ejpam-5605	34	16	ω	ω	NOUN
ejpam-5605	34	17	)	)	PUNCT
ejpam-5605	34	18	,	,	PUNCT
ejpam-5605	34	19	ω	ω	NOUN
ejpam-5605	34	20	)	)	PUNCT
ejpam-5605	34	21	,	,	PUNCT
ejpam-5605	34	22	ξ	ξ	PROPN
ejpam-5605	34	23	∈	∈	PROPN
ejpam-5605	34	24	(	(	PUNCT
ejpam-5605	34	25	0	0	NUM
ejpam-5605	34	26	,	,	PUNCT
ejpam-5605	34	27	b	b	NOUN
ejpam-5605	34	28	]	]	X
ejpam-5605	34	29	,	,	PUNCT
ejpam-5605	34	30	dϑ2	dϑ2	PROPN
ejpam-5605	34	31	0	0	NUM
ejpam-5605	34	32	+	+	NUM
ejpam-5605	34	33	z2(ξ	z2(ξ	NUM
ejpam-5605	34	34	,	,	PUNCT
ejpam-5605	34	35	ω	ω	NOUN
ejpam-5605	34	36	)	)	PUNCT
ejpam-5605	34	37	=	=	SYM
ejpam-5605	35	1	f2(ξ	f2(ξ	PROPN
ejpam-5605	35	2	,	,	PUNCT
ejpam-5605	35	3	z1(ξ	z1(ξ	PROPN
ejpam-5605	35	4	,	,	PUNCT
ejpam-5605	35	5	ω	ω	NOUN
ejpam-5605	35	6	)	)	PUNCT
ejpam-5605	35	7	,	,	PUNCT
ejpam-5605	35	8	z2(ξ	z2(ξ	PROPN
ejpam-5605	35	9	,	,	PUNCT
ejpam-5605	35	10	ω	ω	NOUN
ejpam-5605	35	11	)	)	PUNCT
ejpam-5605	35	12	,	,	PUNCT
ejpam-5605	35	13	ω	ω	NOUN
ejpam-5605	35	14	)	)	PUNCT
ejpam-5605	35	15	,	,	PUNCT
ejpam-5605	35	16	ξ	ξ	PROPN
ejpam-5605	35	17	∈	∈	PROPN
ejpam-5605	35	18	(	(	PUNCT
ejpam-5605	35	19	0	0	NUM
ejpam-5605	35	20	,	,	PUNCT
ejpam-5605	35	21	b	b	NOUN
ejpam-5605	35	22	]	]	X
ejpam-5605	35	23	,	,	PUNCT
ejpam-5605	35	24	lim	lim	PROPN
ejpam-5605	35	25	ξ→0	ξ→0	PROPN
ejpam-5605	35	26	+	+	PROPN
ejpam-5605	35	27	ξ1−ϑ1z1(ξ	ξ1−ϑ1z1(ξ	PROPN
ejpam-5605	35	28	,	,	PUNCT
ejpam-5605	35	29	ω	ω	NOUN
ejpam-5605	35	30	)	)	PUNCT
ejpam-5605	35	31	=	=	SYM
ejpam-5605	35	32	z3(ω	z3(ω	NOUN
ejpam-5605	35	33	)	)	PUNCT
ejpam-5605	35	34	,	,	PUNCT
ejpam-5605	35	35	ω	ω	PROPN
ejpam-5605	35	36	∈	∈	PROPN
ejpam-5605	35	37	ω	ω	PROPN
ejpam-5605	35	38	,	,	PUNCT
ejpam-5605	35	39	lim	lim	PROPN
ejpam-5605	35	40	ξ→0	ξ→0	PROPN
ejpam-5605	35	41	+	+	PROPN
ejpam-5605	35	42	ξ1−ϑ2z2(ξ	ξ1−ϑ2z2(ξ	PROPN
ejpam-5605	35	43	,	,	PUNCT
ejpam-5605	35	44	ω	ω	NUM
ejpam-5605	35	45	)	)	PUNCT
ejpam-5605	35	46	=	=	SYM
ejpam-5605	35	47	z4(ω	z4(ω	PROPN
ejpam-5605	35	48	)	)	PUNCT
ejpam-5605	35	49	,	,	PUNCT
ejpam-5605	35	50	ω	ω	PROPN
ejpam-5605	35	51	∈	∈	PROPN
ejpam-5605	35	52	ω	ω	NOUN
ejpam-5605	35	53	,	,	PUNCT
ejpam-5605	35	54	where	where	SCONJ
ejpam-5605	35	55	z3,z4	z3,z4	PROPN
ejpam-5605	35	56	:	:	PUNCT
ejpam-5605	35	57	ω	ω	X
ejpam-5605	35	58	→	→	SYM
ejpam-5605	35	59	g	g	PROPN
ejpam-5605	35	60	are	be	AUX
ejpam-5605	35	61	random	random	ADJ
ejpam-5605	35	62	variables	variable	NOUN
ejpam-5605	35	63	,	,	PUNCT
ejpam-5605	35	64	dϑi	dϑi	NOUN
ejpam-5605	35	65	0	0	NUM
ejpam-5605	35	66	+	+	NUM
ejpam-5605	35	67	represents	represent	VERB
ejpam-5605	35	68	the	the	DET
ejpam-5605	35	69	standard	standard	ADJ
ejpam-5605	35	70	riemannliouville	riemannliouville	NOUN
ejpam-5605	35	71	fd	fd	VERB
ejpam-5605	35	72	of	of	ADP
ejpam-5605	35	73	order	order	NOUN
ejpam-5605	35	74	ϑi	ϑi	PROPN
ejpam-5605	35	75	∈	∈	PROPN
ejpam-5605	35	76	(	(	PUNCT
ejpam-5605	35	77	0	0	NUM
ejpam-5605	35	78	,	,	PUNCT
ejpam-5605	35	79	1	1	NUM
ejpam-5605	35	80	]	]	PUNCT
ejpam-5605	35	81	for	for	ADP
ejpam-5605	35	82	each	each	DET
ejpam-5605	35	83	i	i	NOUN
ejpam-5605	35	84	=	=	NOUN
ejpam-5605	35	85	1	1	NUM
ejpam-5605	35	86	,	,	PUNCT
ejpam-5605	35	87	2	2	NUM
ejpam-5605	35	88	and	and	CCONJ
ejpam-5605	35	89	fi	fi	NOUN
ejpam-5605	35	90	:	:	PUNCT
ejpam-5605	36	1	[	[	X
ejpam-5605	36	2	0	0	NUM
ejpam-5605	36	3	,	,	PUNCT
ejpam-5605	36	4	b	b	NOUN
ejpam-5605	36	5	]	]	X
ejpam-5605	36	6	×	×	NOUN
ejpam-5605	36	7	g	g	PROPN
ejpam-5605	36	8	×	×	NOUN
ejpam-5605	36	9	g	g	PROPN
ejpam-5605	36	10	×	×	PROPN
ejpam-5605	36	11	ω	ω	PROPN
ejpam-5605	36	12	→	→	SYM
ejpam-5605	36	13	g	g	PROPN
ejpam-5605	36	14	are	be	AUX
ejpam-5605	36	15	funcions	funcion	NOUN
ejpam-5605	36	16	and	and	CCONJ
ejpam-5605	36	17	(	(	PUNCT
ejpam-5605	36	18	g	g	NOUN
ejpam-5605	36	19	,	,	PUNCT
ejpam-5605	36	20	∥	∥	X
ejpam-5605	36	21	·	·	PUNCT
ejpam-5605	36	22	∥	∥	X
ejpam-5605	36	23	)	)	PUNCT
ejpam-5605	36	24	is	be	AUX
ejpam-5605	36	25	a	a	DET
ejpam-5605	36	26	real	real	ADJ
ejpam-5605	36	27	separable	separable	ADJ
ejpam-5605	36	28	banach	banach	NOUN
ejpam-5605	36	29	space	space	NOUN
ejpam-5605	36	30	.	.	PUNCT
ejpam-5605	37	1	motivated	motivate	VERB
ejpam-5605	37	2	by	by	ADP
ejpam-5605	37	3	the	the	DET
ejpam-5605	37	4	preceding	precede	VERB
ejpam-5605	37	5	discussions	discussion	NOUN
ejpam-5605	37	6	,	,	PUNCT
ejpam-5605	37	7	this	this	DET
ejpam-5605	37	8	paper	paper	NOUN
ejpam-5605	37	9	presents	present	VERB
ejpam-5605	37	10	new	new	ADJ
ejpam-5605	37	11	qualitative	qualitative	NOUN
ejpam-5605	37	12	results	result	NOUN
ejpam-5605	37	13	for	for	ADP
ejpam-5605	37	14	m.	m.	NOUN
ejpam-5605	37	15	ziane	ziane	PROPN
ejpam-5605	37	16	et	et	PROPN
ejpam-5605	37	17	al	al	PROPN
ejpam-5605	37	18	.	.	PUNCT
ejpam-5605	37	19	/	/	SYM
ejpam-5605	37	20	eur	eur	PROPN
ejpam-5605	37	21	.	.	PUNCT
ejpam-5605	38	1	j.	j.	PROPN
ejpam-5605	38	2	pure	pure	PROPN
ejpam-5605	38	3	appl	appl	PROPN
ejpam-5605	38	4	.	.	PROPN
ejpam-5605	38	5	math	math	PROPN
ejpam-5605	38	6	,	,	PUNCT
ejpam-5605	38	7	18	18	NUM
ejpam-5605	38	8	(	(	PUNCT
ejpam-5605	38	9	1	1	NUM
ejpam-5605	38	10	)	)	PUNCT
ejpam-5605	38	11	(	(	PUNCT
ejpam-5605	38	12	2025	2025	NUM
ejpam-5605	38	13	)	)	PUNCT
ejpam-5605	38	14	,	,	PUNCT
ejpam-5605	38	15	5605	5605	NUM
ejpam-5605	38	16	3	3	NUM
ejpam-5605	38	17	of	of	ADP
ejpam-5605	38	18	21	21	NUM
ejpam-5605	38	19	the	the	DET
ejpam-5605	38	20	following	follow	VERB
ejpam-5605	38	21	random	random	ADJ
ejpam-5605	38	22	coupled	couple	VERB
ejpam-5605	38	23	langevin	langevin	NOUN
ejpam-5605	38	24	system	system	NOUN
ejpam-5605	38	25	involving	involve	VERB
ejpam-5605	38	26	ψ	ψ	NOUN
ejpam-5605	38	27	-	-	ADJ
ejpam-5605	38	28	caputo	caputo	ADJ
ejpam-5605	38	29	fd:	fd:	PROPN
ejpam-5605	38	30	(	(	PUNCT
ejpam-5605	38	31	cd	cd	PROPN
ejpam-5605	38	32	ϑ1;ψ	ϑ1;ψ	PROPN
ejpam-5605	38	33	a+	a+	PUNCT
ejpam-5605	39	1	+	+	ADJ
ejpam-5605	39	2	ϖ1	ϖ1	ADJ
ejpam-5605	39	3	cd	cd	NOUN
ejpam-5605	39	4	ϑ1−1;ψ	ϑ1−1;ψ	X
ejpam-5605	39	5	a+	a+	PUNCT
ejpam-5605	39	6	)	)	PUNCT
ejpam-5605	39	7	z1(ξ	z1(ξ	PROPN
ejpam-5605	39	8	,	,	PUNCT
ejpam-5605	39	9	ω	ω	NUM
ejpam-5605	39	10	)	)	PUNCT
ejpam-5605	39	11	=	=	SYM
ejpam-5605	39	12	f1(ξ	f1(ξ	PROPN
ejpam-5605	39	13	,	,	PUNCT
ejpam-5605	39	14	z1(ξ	z1(ξ	PROPN
ejpam-5605	39	15	,	,	PUNCT
ejpam-5605	39	16	ω	ω	NOUN
ejpam-5605	39	17	)	)	PUNCT
ejpam-5605	39	18	,	,	PUNCT
ejpam-5605	39	19	z2(ξ	z2(ξ	PROPN
ejpam-5605	39	20	,	,	PUNCT
ejpam-5605	39	21	ω	ω	NOUN
ejpam-5605	39	22	)	)	PUNCT
ejpam-5605	39	23	,	,	PUNCT
ejpam-5605	39	24	ω	ω	NOUN
ejpam-5605	39	25	)	)	PUNCT
ejpam-5605	39	26	,	,	PUNCT
ejpam-5605	39	27	ξ	ξ	PROPN
ejpam-5605	39	28	∈	∈	PROPN
ejpam-5605	40	1	i	i	PRON
ejpam-5605	40	2	:	:	PUNCT
ejpam-5605	40	3	=	=	PUNCT
ejpam-5605	41	1	[	[	X
ejpam-5605	41	2	a	a	X
ejpam-5605	41	3	,	,	PUNCT
ejpam-5605	41	4	b	b	NOUN
ejpam-5605	41	5	]	]	X
ejpam-5605	41	6	,	,	PUNCT
ejpam-5605	41	7	(	(	PUNCT
ejpam-5605	41	8	cd	cd	PROPN
ejpam-5605	41	9	ϑ2;ψ	ϑ2;ψ	PROPN
ejpam-5605	41	10	a+	a+	PUNCT
ejpam-5605	42	1	+	+	ADJ
ejpam-5605	42	2	ϖ2	ϖ2	ADJ
ejpam-5605	42	3	cd	cd	PROPN
ejpam-5605	42	4	ϑ2−1;ψ	ϑ2−1;ψ	PROPN
ejpam-5605	42	5	a+	a+	PUNCT
ejpam-5605	42	6	)	)	PUNCT
ejpam-5605	42	7	z2(ξ	z2(ξ	NUM
ejpam-5605	42	8	,	,	PUNCT
ejpam-5605	42	9	ω	ω	NOUN
ejpam-5605	42	10	)	)	PUNCT
ejpam-5605	42	11	=	=	SYM
ejpam-5605	43	1	f2(ξ	f2(ξ	PROPN
ejpam-5605	43	2	,	,	PUNCT
ejpam-5605	43	3	z1(ξ	z1(ξ	PROPN
ejpam-5605	43	4	,	,	PUNCT
ejpam-5605	43	5	ω	ω	NOUN
ejpam-5605	43	6	)	)	PUNCT
ejpam-5605	43	7	,	,	PUNCT
ejpam-5605	43	8	z2(ξ	z2(ξ	PROPN
ejpam-5605	43	9	,	,	PUNCT
ejpam-5605	43	10	ω	ω	NOUN
ejpam-5605	43	11	)	)	PUNCT
ejpam-5605	43	12	,	,	PUNCT
ejpam-5605	43	13	ω	ω	NOUN
ejpam-5605	43	14	)	)	PUNCT
ejpam-5605	43	15	,	,	PUNCT
ejpam-5605	43	16	ξ	ξ	PROPN
ejpam-5605	43	17	∈	∈	PROPN
ejpam-5605	44	1	i	i	PRON
ejpam-5605	44	2	:	:	PUNCT
ejpam-5605	44	3	=	=	PUNCT
ejpam-5605	45	1	[	[	X
ejpam-5605	45	2	a	a	X
ejpam-5605	45	3	,	,	PUNCT
ejpam-5605	45	4	b	b	NOUN
ejpam-5605	45	5	]	]	X
ejpam-5605	45	6	,	,	PUNCT
ejpam-5605	45	7	z1(a	z1(a	NUM
ejpam-5605	45	8	,	,	PUNCT
ejpam-5605	45	9	ω	ω	NUM
ejpam-5605	45	10	)	)	PUNCT
ejpam-5605	45	11	=	=	SYM
ejpam-5605	45	12	z′1(a	z′1(a	PROPN
ejpam-5605	45	13	,	,	PUNCT
ejpam-5605	45	14	ω	ω	NOUN
ejpam-5605	45	15	)	)	PUNCT
ejpam-5605	45	16	=	=	SYM
ejpam-5605	45	17	0	0	NUM
ejpam-5605	45	18	,	,	PUNCT
ejpam-5605	45	19	z2(a	z2(a	NOUN
ejpam-5605	45	20	,	,	PUNCT
ejpam-5605	45	21	ω	ω	NOUN
ejpam-5605	45	22	)	)	PUNCT
ejpam-5605	45	23	=	=	SYM
ejpam-5605	45	24	z′2(a	z′2(a	NOUN
ejpam-5605	45	25	,	,	PUNCT
ejpam-5605	45	26	ω	ω	NOUN
ejpam-5605	45	27	)	)	PUNCT
ejpam-5605	45	28	=	=	SYM
ejpam-5605	45	29	0	0	NUM
ejpam-5605	45	30	,	,	PUNCT
ejpam-5605	45	31	(	(	PUNCT
ejpam-5605	45	32	1	1	X
ejpam-5605	45	33	)	)	PUNCT
ejpam-5605	45	34	where	where	SCONJ
ejpam-5605	45	35	1	1	NUM
ejpam-5605	45	36	<	<	X
ejpam-5605	45	37	ϑi	ϑi	X
ejpam-5605	45	38	<	<	X
ejpam-5605	45	39	2	2	NUM
ejpam-5605	45	40	,	,	PUNCT
ejpam-5605	45	41	ϖi	ϖi	VERB
ejpam-5605	45	42	>	>	X
ejpam-5605	45	43	0	0	X
ejpam-5605	45	44	.	.	PUNCT
ejpam-5605	45	45	cd	cd	PROPN
ejpam-5605	45	46	θi;ψ	θi;ψ	PROPN
ejpam-5605	45	47	a+	a+	PUNCT
ejpam-5605	45	48	(	(	PUNCT
ejpam-5605	45	49	for	for	ADP
ejpam-5605	45	50	i	i	PRON
ejpam-5605	45	51	=	=	SYM
ejpam-5605	45	52	1	1	NUM
ejpam-5605	45	53	,	,	PUNCT
ejpam-5605	45	54	2	2	NUM
ejpam-5605	45	55	)	)	PUNCT
ejpam-5605	45	56	is	be	AUX
ejpam-5605	45	57	the	the	DET
ejpam-5605	45	58	fd	fd	PROPN
ejpam-5605	45	59	with	with	ADP
ejpam-5605	45	60	respect	respect	NOUN
ejpam-5605	45	61	to	to	ADP
ejpam-5605	45	62	ψ	ψ	NOUN
ejpam-5605	45	63	of	of	ADP
ejpam-5605	45	64	order	order	NOUN
ejpam-5605	45	65	θi	θi	ADP
ejpam-5605	45	66	∈	∈	PROPN
ejpam-5605	45	67	{	{	PUNCT
ejpam-5605	45	68	ϑi	ϑi	PROPN
ejpam-5605	45	69	,	,	PUNCT
ejpam-5605	45	70	ϑi	ϑi	NOUN
ejpam-5605	45	71	−	−	PROPN
ejpam-5605	45	72	1	1	NUM
ejpam-5605	45	73	}	}	PUNCT
ejpam-5605	45	74	,	,	PUNCT
ejpam-5605	45	75	fi	fi	NOUN
ejpam-5605	45	76	:	:	PUNCT
ejpam-5605	46	1	i	i	PRON
ejpam-5605	46	2	×	×	VERB
ejpam-5605	46	3	g	g	ADP
ejpam-5605	46	4	×	×	NOUN
ejpam-5605	46	5	g	g	PROPN
ejpam-5605	46	6	→	→	SYM
ejpam-5605	46	7	g	g	PROPN
ejpam-5605	46	8	,	,	PUNCT
ejpam-5605	46	9	(	(	PUNCT
ejpam-5605	46	10	i	i	NOUN
ejpam-5605	46	11	=	=	NOUN
ejpam-5605	46	12	1	1	NUM
ejpam-5605	46	13	,	,	PUNCT
ejpam-5605	46	14	2	2	X
ejpam-5605	46	15	)	)	PUNCT
ejpam-5605	46	16	verifying	verify	VERB
ejpam-5605	46	17	some	some	DET
ejpam-5605	46	18	conditions	condition	NOUN
ejpam-5605	46	19	that	that	PRON
ejpam-5605	46	20	will	will	AUX
ejpam-5605	46	21	be	be	AUX
ejpam-5605	46	22	precised	precis	VERB
ejpam-5605	46	23	later	later	ADV
ejpam-5605	46	24	.	.	PUNCT
ejpam-5605	47	1	a	a	DET
ejpam-5605	47	2	notable	notable	ADJ
ejpam-5605	47	3	feature	feature	NOUN
ejpam-5605	47	4	of	of	ADP
ejpam-5605	47	5	our	our	PRON
ejpam-5605	47	6	research	research	NOUN
ejpam-5605	47	7	is	be	AUX
ejpam-5605	47	8	the	the	DET
ejpam-5605	47	9	following	following	NOUN
ejpam-5605	47	10	:	:	PUNCT
ejpam-5605	47	11	•	•	ADP
ejpam-5605	47	12	we	we	PRON
ejpam-5605	47	13	utilize	utilize	VERB
ejpam-5605	47	14	perov	perov	PROPN
ejpam-5605	47	15	’s	’s	PART
ejpam-5605	47	16	fixed	fix	VERB
ejpam-5605	47	17	-	-	PUNCT
ejpam-5605	47	18	point	point	NOUN
ejpam-5605	47	19	theorem	theorem	NOUN
ejpam-5605	47	20	with	with	ADP
ejpam-5605	47	21	the	the	DET
ejpam-5605	47	22	bielecki	bielecki	ADJ
ejpam-5605	47	23	-	-	PUNCT
ejpam-5605	47	24	type	type	NOUN
ejpam-5605	47	25	vector	vector	NOUN
ejpam-5605	47	26	-	-	PUNCT
ejpam-5605	47	27	valued	value	VERB
ejpam-5605	47	28	norm	norm	NOUN
ejpam-5605	47	29	to	to	PART
ejpam-5605	47	30	establish	establish	VERB
ejpam-5605	47	31	a	a	DET
ejpam-5605	47	32	new	new	ADJ
ejpam-5605	47	33	uniqueness	uniqueness	NOUN
ejpam-5605	47	34	criterion	criterion	NOUN
ejpam-5605	47	35	.	.	PUNCT
ejpam-5605	48	1	•	•	NOUN
ejpam-5605	48	2	we	we	PRON
ejpam-5605	48	3	established	establish	VERB
ejpam-5605	48	4	existence	existence	NOUN
ejpam-5605	48	5	results	result	NOUN
ejpam-5605	48	6	by	by	ADP
ejpam-5605	48	7	applying	apply	VERB
ejpam-5605	48	8	sadovskii	sadovskii	PROPN
ejpam-5605	48	9	’s	’s	PART
ejpam-5605	48	10	fixed	fix	VERB
ejpam-5605	48	11	-	-	PUNCT
ejpam-5605	48	12	point	point	NOUN
ejpam-5605	48	13	principle	principle	NOUN
ejpam-5605	48	14	in	in	ADP
ejpam-5605	48	15	a	a	DET
ejpam-5605	48	16	random	random	ADJ
ejpam-5605	48	17	setting	setting	NOUN
ejpam-5605	48	18	,	,	PUNCT
ejpam-5605	48	19	utilizing	utilize	VERB
ejpam-5605	48	20	the	the	DET
ejpam-5605	48	21	measure	measure	NOUN
ejpam-5605	48	22	of	of	ADP
ejpam-5605	48	23	noncompactness	noncompactness	ADJ
ejpam-5605	48	24	(	(	PUNCT
ejpam-5605	48	25	mnc	mnc	PROPN
ejpam-5605	48	26	)	)	PUNCT
ejpam-5605	48	27	procedure	procedure	NOUN
ejpam-5605	48	28	and	and	CCONJ
ejpam-5605	48	29	the	the	DET
ejpam-5605	48	30	a	a	DET
ejpam-5605	48	31	priori	priori	ADJ
ejpam-5605	48	32	estimate	estimate	NOUN
ejpam-5605	48	33	technique	technique	NOUN
ejpam-5605	48	34	.	.	PUNCT
ejpam-5605	49	1	•	•	NUM
ejpam-5605	49	2	the	the	DET
ejpam-5605	49	3	obtained	obtain	VERB
ejpam-5605	49	4	findings	finding	NOUN
ejpam-5605	49	5	generalize	generalize	VERB
ejpam-5605	49	6	the	the	DET
ejpam-5605	49	7	results	result	NOUN
ejpam-5605	49	8	appearing	appear	VERB
ejpam-5605	49	9	in	in	ADP
ejpam-5605	49	10	the	the	DET
ejpam-5605	49	11	existing	exist	VERB
ejpam-5605	49	12	research	research	NOUN
ejpam-5605	49	13	,	,	PUNCT
ejpam-5605	49	14	such	such	ADJ
ejpam-5605	49	15	as	as	ADP
ejpam-5605	49	16	in	in	ADP
ejpam-5605	49	17	[	[	X
ejpam-5605	49	18	6	6	NUM
ejpam-5605	49	19	,	,	PUNCT
ejpam-5605	49	20	13	13	NUM
ejpam-5605	49	21	,	,	PUNCT
ejpam-5605	49	22	33	33	NUM
ejpam-5605	49	23	]	]	PUNCT
ejpam-5605	49	24	.	.	PUNCT
ejpam-5605	50	1	this	this	DET
ejpam-5605	50	2	research	research	NOUN
ejpam-5605	50	3	is	be	AUX
ejpam-5605	50	4	structured	structure	VERB
ejpam-5605	50	5	as	as	SCONJ
ejpam-5605	50	6	follows	follow	VERB
ejpam-5605	50	7	.	.	PUNCT
ejpam-5605	51	1	section	section	NOUN
ejpam-5605	51	2	2	2	NUM
ejpam-5605	51	3	presents	present	VERB
ejpam-5605	51	4	some	some	DET
ejpam-5605	51	5	preliminary	preliminary	ADJ
ejpam-5605	51	6	facts	fact	NOUN
ejpam-5605	51	7	that	that	PRON
ejpam-5605	51	8	will	will	AUX
ejpam-5605	51	9	be	be	AUX
ejpam-5605	51	10	utilized	utilize	VERB
ejpam-5605	51	11	in	in	ADP
ejpam-5605	51	12	subsequent	subsequent	ADJ
ejpam-5605	51	13	sections	section	NOUN
ejpam-5605	51	14	.	.	PUNCT
ejpam-5605	52	1	the	the	DET
ejpam-5605	52	2	main	main	ADJ
ejpam-5605	52	3	results	result	NOUN
ejpam-5605	52	4	are	be	AUX
ejpam-5605	52	5	provided	provide	VERB
ejpam-5605	52	6	in	in	ADP
ejpam-5605	52	7	section	section	NOUN
ejpam-5605	52	8	3	3	NUM
ejpam-5605	52	9	.	.	PUNCT
ejpam-5605	53	1	finally	finally	ADV
ejpam-5605	53	2	,	,	PUNCT
ejpam-5605	53	3	illustrative	illustrative	ADJ
ejpam-5605	53	4	examples	example	NOUN
ejpam-5605	53	5	are	be	AUX
ejpam-5605	53	6	presented	present	VERB
ejpam-5605	53	7	in	in	ADP
ejpam-5605	53	8	section	section	NOUN
ejpam-5605	53	9	4	4	NUM
ejpam-5605	53	10	.	.	NOUN
ejpam-5605	54	1	2	2	NUM
ejpam-5605	54	2	.	.	X
ejpam-5605	54	3	preliminary	preliminary	ADJ
ejpam-5605	54	4	results	result	NOUN
ejpam-5605	54	5	throughout	throughout	ADP
ejpam-5605	54	6	the	the	DET
ejpam-5605	54	7	paper	paper	NOUN
ejpam-5605	54	8	,	,	PUNCT
ejpam-5605	54	9	let	let	VERB
ejpam-5605	54	10	(	(	PUNCT
ejpam-5605	54	11	g	g	NOUN
ejpam-5605	54	12	,	,	PUNCT
ejpam-5605	54	13	∥	∥	X
ejpam-5605	54	14	·	·	PUNCT
ejpam-5605	54	15	∥	∥	X
ejpam-5605	54	16	)	)	PUNCT
ejpam-5605	54	17	be	be	VERB
ejpam-5605	54	18	a	a	DET
ejpam-5605	54	19	separable	separable	ADJ
ejpam-5605	54	20	banach	banach	NOUN
ejpam-5605	54	21	space	space	NOUN
ejpam-5605	55	1	,	,	PUNCT
ejpam-5605	55	2	we	we	PRON
ejpam-5605	55	3	endow	endow	VERB
ejpam-5605	55	4	the	the	DET
ejpam-5605	55	5	space	space	NOUN
ejpam-5605	55	6	c(i	c(i	NOUN
ejpam-5605	55	7	,	,	PUNCT
ejpam-5605	55	8	g	g	NOUN
ejpam-5605	55	9	)	)	PUNCT
ejpam-5605	55	10	of	of	ADP
ejpam-5605	55	11	g	g	NOUN
ejpam-5605	55	12	-	-	PUNCT
ejpam-5605	55	13	valued	value	VERB
ejpam-5605	55	14	continuous	continuous	ADJ
ejpam-5605	55	15	functions	function	NOUN
ejpam-5605	55	16	on	on	ADP
ejpam-5605	55	17	i	i	PRON
ejpam-5605	55	18	with	with	ADP
ejpam-5605	55	19	the	the	DET
ejpam-5605	55	20	supnorm	supnorm	NOUN
ejpam-5605	55	21	∥u∥∞	∥u∥∞	PUNCT
ejpam-5605	55	22	=	=	SYM
ejpam-5605	55	23	sup	sup	NOUN
ejpam-5605	55	24	ξ∈i	ξ∈i	VERB
ejpam-5605	55	25	∥u(ξ)∥.	∥u(ξ)∥.	PROPN
ejpam-5605	55	26	(	(	PUNCT
ejpam-5605	55	27	2	2	NUM
ejpam-5605	55	28	)	)	PUNCT
ejpam-5605	55	29	l1(i	l1(i	PROPN
ejpam-5605	55	30	,	,	PUNCT
ejpam-5605	55	31	g	g	NOUN
ejpam-5605	55	32	)	)	PUNCT
ejpam-5605	55	33	denotes	denote	VERB
ejpam-5605	55	34	the	the	DET
ejpam-5605	55	35	space	space	NOUN
ejpam-5605	55	36	of	of	ADP
ejpam-5605	55	37	bochner	bochner	NOUN
ejpam-5605	55	38	integrable	integrable	ADJ
ejpam-5605	55	39	functions	function	NOUN
ejpam-5605	55	40	u	u	NOUN
ejpam-5605	55	41	:	:	PUNCT
ejpam-5605	55	42	i	i	PRON
ejpam-5605	55	43	→	→	PUNCT
ejpam-5605	55	44	g	g	PROPN
ejpam-5605	55	45	normed	norme	VERB
ejpam-5605	55	46	by	by	ADP
ejpam-5605	55	47	∥u∥l1	∥u∥l1	PROPN
ejpam-5605	55	48	=	=	SYM
ejpam-5605	55	49	∫	∫	PROPN
ejpam-5605	56	1	b	b	PROPN
ejpam-5605	57	1	a	a	DET
ejpam-5605	57	2	∥u(s)∥ds	∥u(s)∥ds	PROPN
ejpam-5605	57	3	,	,	PUNCT
ejpam-5605	57	4	for	for	ADP
ejpam-5605	57	5	all	all	DET
ejpam-5605	57	6	u	u	PROPN
ejpam-5605	57	7	∈	∈	PROPN
ejpam-5605	57	8	l1(i	l1(i	PROPN
ejpam-5605	57	9	,	,	PUNCT
ejpam-5605	57	10	g	g	NOUN
ejpam-5605	57	11	)	)	PUNCT
ejpam-5605	57	12	.	.	PUNCT
ejpam-5605	58	1	l∞(i	l∞(i	ADJ
ejpam-5605	58	2	,	,	PUNCT
ejpam-5605	58	3	r+	r+	X
ejpam-5605	58	4	)	)	PUNCT
ejpam-5605	58	5	stands	stand	VERB
ejpam-5605	58	6	for	for	ADP
ejpam-5605	58	7	the	the	DET
ejpam-5605	58	8	space	space	NOUN
ejpam-5605	58	9	all	all	PRON
ejpam-5605	58	10	essentially	essentially	ADV
ejpam-5605	58	11	bounded	bound	VERB
ejpam-5605	58	12	functions	function	NOUN
ejpam-5605	58	13	normed	norme	VERB
ejpam-5605	58	14	by	by	ADP
ejpam-5605	58	15	∥u∥l∞	∥u∥l∞	NOUN
ejpam-5605	58	16	=	=	PUNCT
ejpam-5605	59	1	ess	ess	PROPN
ejpam-5605	59	2	sup	sup	PROPN
ejpam-5605	59	3	ξ∈i	ξ∈i	PROPN
ejpam-5605	59	4	∥u(ξ)∥	∥u(ξ)∥	PROPN
ejpam-5605	59	5	=	=	SYM
ejpam-5605	59	6	inf{m	inf{m	PROPN
ejpam-5605	59	7	>	>	X
ejpam-5605	59	8	0	0	NUM
ejpam-5605	59	9	;	;	PUNCT
ejpam-5605	59	10	∥u(ξ)∥	∥u(ξ)∥	PROPN
ejpam-5605	59	11	≤m	≤m	NOUN
ejpam-5605	59	12	for	for	ADP
ejpam-5605	59	13	almost	almost	ADV
ejpam-5605	59	14	every	every	DET
ejpam-5605	59	15	ξ	ξ	PROPN
ejpam-5605	59	16	∈	∈	PROPN
ejpam-5605	59	17	i	i	X
ejpam-5605	59	18	}	}	PUNCT
ejpam-5605	59	19	.	.	PUNCT
ejpam-5605	60	1	m.	m.	NOUN
ejpam-5605	60	2	ziane	ziane	PROPN
ejpam-5605	60	3	et	et	PROPN
ejpam-5605	60	4	al	al	PROPN
ejpam-5605	60	5	.	.	PUNCT
ejpam-5605	60	6	/	/	SYM
ejpam-5605	60	7	eur	eur	PROPN
ejpam-5605	60	8	.	.	PUNCT
ejpam-5605	61	1	j.	j.	PROPN
ejpam-5605	61	2	pure	pure	PROPN
ejpam-5605	61	3	appl	appl	PROPN
ejpam-5605	61	4	.	.	PROPN
ejpam-5605	61	5	math	math	PROPN
ejpam-5605	61	6	,	,	PUNCT
ejpam-5605	61	7	18	18	NUM
ejpam-5605	61	8	(	(	PUNCT
ejpam-5605	61	9	1	1	NUM
ejpam-5605	61	10	)	)	PUNCT
ejpam-5605	61	11	(	(	PUNCT
ejpam-5605	61	12	2025	2025	NUM
ejpam-5605	61	13	)	)	PUNCT
ejpam-5605	61	14	,	,	PUNCT
ejpam-5605	61	15	5605	5605	NUM
ejpam-5605	61	16	4	4	NUM
ejpam-5605	61	17	of	of	ADP
ejpam-5605	61	18	21	21	NUM
ejpam-5605	61	19	set	set	VERB
ejpam-5605	61	20	s1+(i	s1+(i	PROPN
ejpam-5605	61	21	,	,	PUNCT
ejpam-5605	61	22	r	r	NOUN
ejpam-5605	61	23	)	)	PUNCT
ejpam-5605	61	24	=	=	SYM
ejpam-5605	61	25	{	{	PUNCT
ejpam-5605	61	26	ψ	ψ	X
ejpam-5605	61	27	:	:	PUNCT
ejpam-5605	61	28	ψ	ψ	X
ejpam-5605	61	29	∈	∈	PROPN
ejpam-5605	61	30	c1(i	c1(i	NOUN
ejpam-5605	61	31	,	,	PUNCT
ejpam-5605	61	32	r	r	NOUN
ejpam-5605	61	33	)	)	PUNCT
ejpam-5605	61	34	and	and	CCONJ
ejpam-5605	61	35	ψ′(ξ	ψ′(ξ	PUNCT
ejpam-5605	61	36	)	)	PUNCT
ejpam-5605	61	37	>	>	X
ejpam-5605	61	38	0	0	PUNCT
ejpam-5605	62	1	for	for	ADP
ejpam-5605	62	2	all	all	DET
ejpam-5605	62	3	ξ	ξ	PROPN
ejpam-5605	62	4	∈	∈	PROPN
ejpam-5605	62	5	i	i	X
ejpam-5605	62	6	}	}	PUNCT
ejpam-5605	62	7	.	.	PUNCT
ejpam-5605	63	1	let	let	VERB
ejpam-5605	63	2	ψ	ψ	PRON
ejpam-5605	63	3	∈	∈	PROPN
ejpam-5605	63	4	s1+(i	s1+(i	PROPN
ejpam-5605	63	5	,	,	PUNCT
ejpam-5605	63	6	r	r	NOUN
ejpam-5605	63	7	)	)	PUNCT
ejpam-5605	63	8	for	for	ADP
ejpam-5605	63	9	ξ	ξ	X
ejpam-5605	63	10	,	,	PUNCT
ejpam-5605	63	11	s	s	VERB
ejpam-5605	63	12	∈	∈	PROPN
ejpam-5605	64	1	i	i	PRON
ejpam-5605	64	2	,	,	PUNCT
ejpam-5605	64	3	(	(	PUNCT
ejpam-5605	64	4	s	s	X
ejpam-5605	64	5	<	<	X
ejpam-5605	64	6	ξ	ξ	PROPN
ejpam-5605	64	7	)	)	PUNCT
ejpam-5605	64	8	,	,	PUNCT
ejpam-5605	64	9	we	we	PRON
ejpam-5605	64	10	define	define	VERB
ejpam-5605	64	11	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	64	12	,	,	PUNCT
ejpam-5605	64	13	s	s	X
ejpam-5605	64	14	)	)	PUNCT
ejpam-5605	64	15	=	=	SYM
ejpam-5605	65	1	ψ(ξ)−	ψ(ξ)−	PROPN
ejpam-5605	65	2	ψ(s	ψ(s	NUM
ejpam-5605	65	3	)	)	PUNCT
ejpam-5605	65	4	and	and	CCONJ
ejpam-5605	65	5	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	65	6	,	,	PUNCT
ejpam-5605	65	7	s)ϑ	s)ϑ	X
ejpam-5605	65	8	=	=	SYM
ejpam-5605	65	9	(	(	PUNCT
ejpam-5605	65	10	ψ(ξ)−	ψ(ξ)−	PROPN
ejpam-5605	65	11	ψ(s))ϑ	ψ(s))ϑ	PROPN
ejpam-5605	65	12	.	.	PUNCT
ejpam-5605	66	1	definition	definition	NOUN
ejpam-5605	66	2	1	1	NUM
ejpam-5605	66	3	.	.	PUNCT
ejpam-5605	67	1	the	the	DET
ejpam-5605	67	2	mittag	mittag	ADJ
ejpam-5605	67	3	-	-	PUNCT
ejpam-5605	67	4	leffler	leffler	NOUN
ejpam-5605	67	5	function	function	NOUN
ejpam-5605	67	6	is	be	AUX
ejpam-5605	67	7	defined	define	VERB
ejpam-5605	67	8	as	as	SCONJ
ejpam-5605	67	9	follows	follow	VERB
ejpam-5605	67	10	:	:	PUNCT
ejpam-5605	67	11	eϑ(u	eϑ(u	X
ejpam-5605	67	12	)	)	PUNCT
ejpam-5605	68	1	=	=	SYM
ejpam-5605	68	2	∞∑	∞∑	NUM
ejpam-5605	68	3	j=0	j=0	PROPN
ejpam-5605	68	4	uj	uj	VERB
ejpam-5605	68	5	γ(jϑ+	γ(jϑ+	NOUN
ejpam-5605	68	6	1	1	NUM
ejpam-5605	68	7	)	)	PUNCT
ejpam-5605	68	8	,	,	PUNCT
ejpam-5605	68	9	ϑ	ϑ	X
ejpam-5605	68	10	>	>	X
ejpam-5605	68	11	0	0	NUM
ejpam-5605	68	12	.	.	PUNCT
ejpam-5605	68	13	where	where	SCONJ
ejpam-5605	68	14	γ	γ	X
ejpam-5605	68	15	(	(	PUNCT
ejpam-5605	68	16	·	·	PUNCT
ejpam-5605	68	17	)	)	PUNCT
ejpam-5605	68	18	is	be	AUX
ejpam-5605	68	19	the	the	DET
ejpam-5605	68	20	gamma	gamma	PROPN
ejpam-5605	68	21	function	function	NOUN
ejpam-5605	68	22	.	.	PUNCT
ejpam-5605	69	1	definition	definition	NOUN
ejpam-5605	69	2	2	2	NUM
ejpam-5605	69	3	.	.	PUNCT
ejpam-5605	70	1	[	[	X
ejpam-5605	70	2	3	3	NUM
ejpam-5605	70	3	,	,	PUNCT
ejpam-5605	70	4	16	16	NUM
ejpam-5605	70	5	]	]	PUNCT
ejpam-5605	70	6	let	let	VERB
ejpam-5605	70	7	ψ	ψ	ADP
ejpam-5605	70	8	∈	∈	PROPN
ejpam-5605	70	9	s1+(i	s1+(i	PROPN
ejpam-5605	70	10	,	,	PUNCT
ejpam-5605	70	11	r	r	NOUN
ejpam-5605	70	12	)	)	PUNCT
ejpam-5605	70	13	and	and	CCONJ
ejpam-5605	70	14	ϑ	ϑ	X
ejpam-5605	70	15	>	>	X
ejpam-5605	70	16	0	0	NUM
ejpam-5605	70	17	.	.	PUNCT
ejpam-5605	71	1	the	the	DET
ejpam-5605	71	2	ψ	ψ	ADJ
ejpam-5605	71	3	-	-	ADJ
ejpam-5605	71	4	fractional	fractional	ADJ
ejpam-5605	71	5	integral	integral	ADJ
ejpam-5605	71	6	(	(	PUNCT
ejpam-5605	71	7	fi	fi	NOUN
ejpam-5605	71	8	)	)	PUNCT
ejpam-5605	71	9	of	of	ADP
ejpam-5605	71	10	a	a	DET
ejpam-5605	71	11	function	function	NOUN
ejpam-5605	71	12	f	f	NOUN
ejpam-5605	71	13	of	of	ADP
ejpam-5605	71	14	order	order	NOUN
ejpam-5605	71	15	ϑ	ϑ	NOUN
ejpam-5605	71	16	is	be	AUX
ejpam-5605	71	17	defined	define	VERB
ejpam-5605	71	18	by	by	ADP
ejpam-5605	71	19	i	i	PRON
ejpam-5605	71	20	ϑ,ψ	ϑ,ψ	ADP
ejpam-5605	71	21	a+	a+	PRON
ejpam-5605	71	22	f(ξ	f(ξ	X
ejpam-5605	71	23	)	)	PUNCT
ejpam-5605	71	24	=	=	SYM
ejpam-5605	71	25	1	1	NUM
ejpam-5605	71	26	γ(ϑ	γ(ϑ	PROPN
ejpam-5605	71	27	)	)	PUNCT
ejpam-5605	71	28	∫	∫	PROPN
ejpam-5605	72	1	ξ	ξ	PRON
ejpam-5605	72	2	a	a	DET
ejpam-5605	72	3	ϕ(t	ϕ(t	PROPN
ejpam-5605	72	4	,	,	PUNCT
ejpam-5605	72	5	s)ϑ−1ψ′(s)f(s)ds	s)ϑ−1ψ′(s)f(s)ds	PROPN
ejpam-5605	72	6	,	,	PUNCT
ejpam-5605	72	7	t	t	X
ejpam-5605	72	8	>	>	X
ejpam-5605	72	9	a	a	PROPN
ejpam-5605	72	10	,	,	PUNCT
ejpam-5605	72	11	lemma	lemma	PROPN
ejpam-5605	72	12	1	1	NUM
ejpam-5605	72	13	.	.	PUNCT
ejpam-5605	73	1	[	[	X
ejpam-5605	73	2	3	3	NUM
ejpam-5605	73	3	,	,	PUNCT
ejpam-5605	73	4	16	16	NUM
ejpam-5605	73	5	]	]	PUNCT
ejpam-5605	73	6	let	let	VERB
ejpam-5605	73	7	ϑ	ϑ	X
ejpam-5605	73	8	,	,	PUNCT
ejpam-5605	73	9	γ	γ	X
ejpam-5605	73	10	>	>	X
ejpam-5605	73	11	0	0	PROPN
ejpam-5605	73	12	,	,	PUNCT
ejpam-5605	73	13	then	then	ADV
ejpam-5605	73	14	i	i	PRON
ejpam-5605	73	15	ϑ;ψ	ϑ;ψ	VERB
ejpam-5605	73	16	a+	a+	PUNCT
ejpam-5605	74	1	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	74	2	,	,	PUNCT
ejpam-5605	74	3	a)γ−1	a)γ−1	PUNCT
ejpam-5605	74	4	=	=	SYM
ejpam-5605	74	5	γ(γ	γ(γ	PROPN
ejpam-5605	74	6	)	)	PUNCT
ejpam-5605	75	1	γ(ϑ+	γ(ϑ+	VERB
ejpam-5605	75	2	γ	γ	X
ejpam-5605	75	3	)	)	PUNCT
ejpam-5605	75	4	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	75	5	,	,	PUNCT
ejpam-5605	75	6	a)ϑ+γ−1	a)ϑ+γ−1	PROPN
ejpam-5605	75	7	.	.	PROPN
ejpam-5605	75	8	definition	definition	NOUN
ejpam-5605	75	9	3	3	NUM
ejpam-5605	75	10	.	.	PUNCT
ejpam-5605	76	1	[	[	X
ejpam-5605	76	2	3	3	X
ejpam-5605	76	3	]	]	PUNCT
ejpam-5605	76	4	let	let	VERB
ejpam-5605	76	5	n−	n−	NOUN
ejpam-5605	76	6	1	1	NUM
ejpam-5605	76	7	<	<	X
ejpam-5605	76	8	ϑ	ϑ	X
ejpam-5605	76	9	≤	≤	NUM
ejpam-5605	76	10	n	n	NOUN
ejpam-5605	76	11	with	with	ADP
ejpam-5605	76	12	n	n	PRON
ejpam-5605	76	13	∈	∈	PROPN
ejpam-5605	76	14	n	n	CCONJ
ejpam-5605	76	15	,	,	PUNCT
ejpam-5605	76	16	ψ	ψ	ADP
ejpam-5605	76	17	∈	∈	PROPN
ejpam-5605	76	18	s1+(i	s1+(i	PROPN
ejpam-5605	76	19	,	,	PUNCT
ejpam-5605	76	20	r	r	NOUN
ejpam-5605	76	21	)	)	PUNCT
ejpam-5605	76	22	.	.	PUNCT
ejpam-5605	77	1	the	the	DET
ejpam-5605	77	2	ψ	ψ	PROPN
ejpam-5605	77	3	-	-	PROPN
ejpam-5605	77	4	caputo	caputo	ADJ
ejpam-5605	77	5	fds	fds	NOUN
ejpam-5605	77	6	of	of	ADP
ejpam-5605	77	7	a	a	DET
ejpam-5605	77	8	function	function	NOUN
ejpam-5605	77	9	f	f	NOUN
ejpam-5605	77	10	of	of	ADP
ejpam-5605	77	11	order	order	NOUN
ejpam-5605	77	12	ϑ	ϑ	NOUN
ejpam-5605	77	13	is	be	AUX
ejpam-5605	77	14	defined	define	VERB
ejpam-5605	77	15	as	as	ADP
ejpam-5605	77	16	(	(	PUNCT
ejpam-5605	77	17	cd	cd	PROPN
ejpam-5605	77	18	ϑ;ψ	ϑ;ψ	NOUN
ejpam-5605	77	19	a+	a+	PUNCT
ejpam-5605	77	20	f	f	PROPN
ejpam-5605	77	21	)	)	PUNCT
ejpam-5605	77	22	(	(	PUNCT
ejpam-5605	77	23	ξ	ξ	X
ejpam-5605	77	24	)	)	PUNCT
ejpam-5605	78	1	=	=	VERB
ejpam-5605	78	2	i	i	PRON
ejpam-5605	78	3	n−ϑ;ψ	n−ϑ;ψ	VERB
ejpam-5605	78	4	a+	a+	PUNCT
ejpam-5605	78	5	(	(	PUNCT
ejpam-5605	78	6	1	1	NUM
ejpam-5605	78	7	ψ′(ξ	ψ′(ξ	NOUN
ejpam-5605	78	8	)	)	PUNCT
ejpam-5605	78	9	d	d	PROPN
ejpam-5605	78	10	dξ	dξ	PROPN
ejpam-5605	78	11	)	)	PUNCT
ejpam-5605	78	12	n	n	CCONJ
ejpam-5605	78	13	f(ξ	f(ξ	NOUN
ejpam-5605	78	14	)	)	PUNCT
ejpam-5605	78	15	.	.	PUNCT
ejpam-5605	79	1	now	now	ADV
ejpam-5605	79	2	,	,	PUNCT
ejpam-5605	79	3	for	for	ADP
ejpam-5605	79	4	ζ	ζ	NOUN
ejpam-5605	79	5	>	>	SYM
ejpam-5605	79	6	0	0	NUM
ejpam-5605	79	7	,	,	PUNCT
ejpam-5605	79	8	we	we	PRON
ejpam-5605	79	9	endow	endow	VERB
ejpam-5605	79	10	the	the	DET
ejpam-5605	79	11	space	space	NOUN
ejpam-5605	79	12	c(i	c(i	NOUN
ejpam-5605	79	13	,	,	PUNCT
ejpam-5605	79	14	g	g	NOUN
ejpam-5605	79	15	)	)	PUNCT
ejpam-5605	79	16	by	by	ADP
ejpam-5605	79	17	the	the	DET
ejpam-5605	79	18	bielecky	bielecky	PROPN
ejpam-5605	79	19	norm	norm	NOUN
ejpam-5605	79	20	∥f∥b	∥f∥b	NOUN
ejpam-5605	79	21	=	=	PUNCT
ejpam-5605	79	22	sup	sup	NUM
ejpam-5605	79	23	ξ∈i	ξ∈i	PROPN
ejpam-5605	79	24	e−ζϕ(ξ	e−ζϕ(ξ	PROPN
ejpam-5605	79	25	,	,	PUNCT
ejpam-5605	79	26	a)∥f(ξ)∥.	a)∥f(ξ)∥.	ADJ
ejpam-5605	79	27	(	(	PUNCT
ejpam-5605	79	28	3	3	NUM
ejpam-5605	79	29	)	)	PUNCT
ejpam-5605	79	30	lemma	lemma	PROPN
ejpam-5605	79	31	2	2	NUM
ejpam-5605	79	32	.	.	PUNCT
ejpam-5605	80	1	[	[	X
ejpam-5605	80	2	27	27	NUM
ejpam-5605	80	3	,	,	PUNCT
ejpam-5605	80	4	30	30	NUM
ejpam-5605	80	5	]	]	PUNCT
ejpam-5605	80	6	the	the	DET
ejpam-5605	80	7	norms	norm	NOUN
ejpam-5605	80	8	∥	∥	X
ejpam-5605	80	9	·	·	PUNCT
ejpam-5605	81	1	∥b	∥b	NOUN
ejpam-5605	81	2	defined	define	VERB
ejpam-5605	81	3	by	by	ADP
ejpam-5605	81	4	(	(	PUNCT
ejpam-5605	81	5	3	3	NUM
ejpam-5605	81	6	)	)	PUNCT
ejpam-5605	81	7	and	and	CCONJ
ejpam-5605	81	8	∥	∥	X
ejpam-5605	81	9	·	·	PUNCT
ejpam-5605	81	10	∥∞	∥∞	ADJ
ejpam-5605	81	11	are	be	AUX
ejpam-5605	81	12	equivalent	equivalent	ADJ
ejpam-5605	81	13	,	,	PUNCT
ejpam-5605	81	14	i.e	i.e	X
ejpam-5605	81	15	;	;	PUNCT
ejpam-5605	81	16	there	there	PRON
ejpam-5605	81	17	exist	exist	VERB
ejpam-5605	81	18	c0	c0	PROPN
ejpam-5605	81	19	∈	∈	PROPN
ejpam-5605	81	20	(	(	PUNCT
ejpam-5605	81	21	0,∞	0,∞	NOUN
ejpam-5605	81	22	)	)	PUNCT
ejpam-5605	82	1	such	such	ADJ
ejpam-5605	82	2	that	that	SCONJ
ejpam-5605	82	3	∥	∥	NOUN
ejpam-5605	82	4	·	·	PUNCT
ejpam-5605	82	5	∥b	∥b	NOUN
ejpam-5605	82	6	≤	≤	ADV
ejpam-5605	82	7	∥	∥	PUNCT
ejpam-5605	82	8	·	·	PUNCT
ejpam-5605	82	9	∥∞	∥∞	ADJ
ejpam-5605	82	10	≤	≤	ADJ
ejpam-5605	82	11	c0∥	c0∥	NOUN
ejpam-5605	82	12	·	·	PUNCT
ejpam-5605	83	1	∥b	∥b	NOUN
ejpam-5605	83	2	.	.	PUNCT
ejpam-5605	84	1	lemma	lemma	PROPN
ejpam-5605	84	2	3	3	NUM
ejpam-5605	84	3	.	.	PUNCT
ejpam-5605	85	1	[	[	X
ejpam-5605	85	2	6	6	NUM
ejpam-5605	85	3	]	]	PUNCT
ejpam-5605	85	4	let	let	VERB
ejpam-5605	85	5	ϑ	ϑ	PRON
ejpam-5605	85	6	>	>	ADP
ejpam-5605	85	7	1	1	NUM
ejpam-5605	85	8	and	and	CCONJ
ejpam-5605	85	9	ζ	ζ	NOUN
ejpam-5605	85	10	>	>	X
ejpam-5605	85	11	0	0	NUM
ejpam-5605	85	12	.	.	PUNCT
ejpam-5605	86	1	then	then	ADV
ejpam-5605	86	2	for	for	ADP
ejpam-5605	86	3	all	all	DET
ejpam-5605	86	4	ξ	ξ	X
ejpam-5605	86	5	∈	∈	PROPN
ejpam-5605	86	6	i	i	PRON
ejpam-5605	86	7	,	,	PUNCT
ejpam-5605	86	8	one	one	PRON
ejpam-5605	86	9	has	have	VERB
ejpam-5605	86	10	i	i	PRON
ejpam-5605	86	11	ϑ−1;ψ	ϑ−1;ψ	VERB
ejpam-5605	86	12	a+	a+	PUNCT
ejpam-5605	86	13	eζϕ(ξ	eζϕ(ξ	PROPN
ejpam-5605	86	14	,	,	PUNCT
ejpam-5605	86	15	a	a	PRON
ejpam-5605	86	16	)	)	PUNCT
ejpam-5605	86	17	≤	≤	NOUN
ejpam-5605	87	1	eζϕ(ξ	eζϕ(ξ	PROPN
ejpam-5605	87	2	,	,	PUNCT
ejpam-5605	87	3	a	a	PRON
ejpam-5605	87	4	)	)	PUNCT
ejpam-5605	87	5	ζϑ−1	ζϑ−1	NOUN
ejpam-5605	87	6	.	.	PUNCT
ejpam-5605	88	1	if	if	SCONJ
ejpam-5605	88	2	,	,	PUNCT
ejpam-5605	88	3	y	y	PROPN
ejpam-5605	88	4	,	,	PUNCT
ejpam-5605	88	5	v	v	PROPN
ejpam-5605	88	6	∈	∈	PROPN
ejpam-5605	88	7	rn	rn	PROPN
ejpam-5605	88	8	,	,	PUNCT
ejpam-5605	88	9	y	y	PROPN
ejpam-5605	88	10	=	=	SYM
ejpam-5605	88	11	(	(	PUNCT
ejpam-5605	88	12	y1	y1	INTJ
ejpam-5605	88	13	,	,	PUNCT
ejpam-5605	88	14	.	.	PUNCT
ejpam-5605	88	15	.	.	PUNCT
ejpam-5605	89	1	.	.	PUNCT
ejpam-5605	90	1	,	,	PUNCT
ejpam-5605	90	2	yn	yn	PROPN
ejpam-5605	90	3	)	)	PUNCT
ejpam-5605	90	4	,	,	PUNCT
ejpam-5605	90	5	v	v	X
ejpam-5605	90	6	=	=	SYM
ejpam-5605	90	7	(	(	PUNCT
ejpam-5605	90	8	v1	v1	NOUN
ejpam-5605	90	9	,	,	PUNCT
ejpam-5605	90	10	.	.	PUNCT
ejpam-5605	90	11	.	.	PUNCT
ejpam-5605	91	1	.	.	PUNCT
ejpam-5605	92	1	,	,	PUNCT
ejpam-5605	92	2	vn	vn	PROPN
ejpam-5605	92	3	)	)	PUNCT
ejpam-5605	92	4	,	,	PUNCT
ejpam-5605	92	5	by	by	ADP
ejpam-5605	92	6	y	y	PROPN
ejpam-5605	92	7	≤	≤	NUM
ejpam-5605	92	8	v	v	NOUN
ejpam-5605	92	9	we	we	PRON
ejpam-5605	92	10	mean	mean	VERB
ejpam-5605	92	11	yi	yi	PROPN
ejpam-5605	92	12	≤	≤	PROPN
ejpam-5605	92	13	vi	vi	PROPN
ejpam-5605	92	14	for	for	ADP
ejpam-5605	92	15	all	all	DET
ejpam-5605	92	16	i	i	PRON
ejpam-5605	92	17	=	=	NOUN
ejpam-5605	92	18	1	1	NUM
ejpam-5605	92	19	,	,	PUNCT
ejpam-5605	92	20	.	.	PUNCT
ejpam-5605	92	21	.	.	PUNCT
ejpam-5605	93	1	.	.	PUNCT
ejpam-5605	94	1	,	,	PUNCT
ejpam-5605	94	2	n.	n.	PROPN
ejpam-5605	94	3	also	also	ADV
ejpam-5605	94	4	|y|	|y|	PROPN
ejpam-5605	94	5	=	=	SYM
ejpam-5605	94	6	(	(	PUNCT
ejpam-5605	94	7	|y1|	|y1|	NOUN
ejpam-5605	94	8	,	,	PUNCT
ejpam-5605	94	9	.	.	PUNCT
ejpam-5605	94	10	.	.	PUNCT
ejpam-5605	95	1	.	.	PUNCT
ejpam-5605	96	1	,	,	PUNCT
ejpam-5605	96	2	|yn|	|yn|	PROPN
ejpam-5605	96	3	)	)	PUNCT
ejpam-5605	96	4	,	,	PUNCT
ejpam-5605	96	5	max(y	max(y	PROPN
ejpam-5605	96	6	,	,	PUNCT
ejpam-5605	96	7	v	v	NOUN
ejpam-5605	96	8	)	)	PUNCT
ejpam-5605	96	9	=	=	SYM
ejpam-5605	96	10	(	(	PUNCT
ejpam-5605	96	11	max(y1	max(y1	ADJ
ejpam-5605	96	12	,	,	PUNCT
ejpam-5605	96	13	v1	v1	NOUN
ejpam-5605	96	14	)	)	PUNCT
ejpam-5605	96	15	,	,	PUNCT
ejpam-5605	96	16	.	.	PUNCT
ejpam-5605	96	17	.	.	PUNCT
ejpam-5605	96	18	.	.	PUNCT
ejpam-5605	97	1	,	,	PUNCT
ejpam-5605	97	2	max(yn	max(yn	NOUN
ejpam-5605	97	3	,	,	PUNCT
ejpam-5605	97	4	vn	vn	NOUN
ejpam-5605	97	5	)	)	PUNCT
ejpam-5605	97	6	)	)	PUNCT
ejpam-5605	97	7	and	and	CCONJ
ejpam-5605	97	8	rn+	rn+	NOUN
ejpam-5605	97	9	=	=	PUNCT
ejpam-5605	97	10	{	{	PUNCT
ejpam-5605	97	11	y	y	PROPN
ejpam-5605	97	12	∈	∈	PROPN
ejpam-5605	97	13	rn	rn	PROPN
ejpam-5605	97	14	:	:	PUNCT
ejpam-5605	97	15	yi	yi	PROPN
ejpam-5605	97	16	>	>	X
ejpam-5605	97	17	0	0	NUM
ejpam-5605	97	18	}	}	PUNCT
ejpam-5605	97	19	.	.	PUNCT
ejpam-5605	98	1	if	if	SCONJ
ejpam-5605	98	2	c	c	PROPN
ejpam-5605	98	3	∈	∈	PROPN
ejpam-5605	98	4	r	r	NOUN
ejpam-5605	98	5	,	,	PUNCT
ejpam-5605	98	6	then	then	ADV
ejpam-5605	98	7	y	y	PROPN
ejpam-5605	98	8	≤	≤	PROPN
ejpam-5605	98	9	c	c	PROPN
ejpam-5605	98	10	means	mean	VERB
ejpam-5605	98	11	yi	yi	PROPN
ejpam-5605	98	12	≤	≤	PROPN
ejpam-5605	98	13	c	c	NOUN
ejpam-5605	98	14	for	for	ADP
ejpam-5605	98	15	each	each	DET
ejpam-5605	98	16	i	i	NOUN
ejpam-5605	98	17	=	=	NOUN
ejpam-5605	98	18	1	1	NUM
ejpam-5605	98	19	,	,	PUNCT
ejpam-5605	98	20	.	.	PUNCT
ejpam-5605	98	21	.	.	PUNCT
ejpam-5605	99	1	.	.	PUNCT
ejpam-5605	100	1	,	,	PUNCT
ejpam-5605	100	2	n.	n.	PROPN
ejpam-5605	100	3	m.	m.	PROPN
ejpam-5605	100	4	ziane	ziane	PROPN
ejpam-5605	100	5	et	et	PROPN
ejpam-5605	100	6	al	al	PROPN
ejpam-5605	100	7	.	.	PUNCT
ejpam-5605	100	8	/	/	SYM
ejpam-5605	100	9	eur	eur	PROPN
ejpam-5605	100	10	.	.	PUNCT
ejpam-5605	101	1	j.	j.	PROPN
ejpam-5605	101	2	pure	pure	PROPN
ejpam-5605	101	3	appl	appl	PROPN
ejpam-5605	101	4	.	.	PROPN
ejpam-5605	101	5	math	math	PROPN
ejpam-5605	101	6	,	,	PUNCT
ejpam-5605	101	7	18	18	NUM
ejpam-5605	101	8	(	(	PUNCT
ejpam-5605	101	9	1	1	NUM
ejpam-5605	101	10	)	)	PUNCT
ejpam-5605	101	11	(	(	PUNCT
ejpam-5605	101	12	2025	2025	NUM
ejpam-5605	101	13	)	)	PUNCT
ejpam-5605	101	14	,	,	PUNCT
ejpam-5605	101	15	5605	5605	NUM
ejpam-5605	101	16	5	5	NUM
ejpam-5605	101	17	of	of	ADP
ejpam-5605	101	18	21	21	NUM
ejpam-5605	101	19	definition	definition	NOUN
ejpam-5605	101	20	4	4	NUM
ejpam-5605	101	21	.	.	PUNCT
ejpam-5605	102	1	let	let	VERB
ejpam-5605	102	2	f	f	PRON
ejpam-5605	102	3	be	be	AUX
ejpam-5605	102	4	a	a	DET
ejpam-5605	102	5	nonempty	nonempty	ADJ
ejpam-5605	102	6	set	set	VERB
ejpam-5605	102	7	.	.	PUNCT
ejpam-5605	103	1	by	by	ADP
ejpam-5605	103	2	a	a	DET
ejpam-5605	103	3	vector	vector	NOUN
ejpam-5605	103	4	-	-	PUNCT
ejpam-5605	103	5	valued	value	VERB
ejpam-5605	103	6	metric	metric	NOUN
ejpam-5605	103	7	on	on	ADP
ejpam-5605	103	8	f	f	PROPN
ejpam-5605	103	9	we	we	PRON
ejpam-5605	103	10	mean	mean	VERB
ejpam-5605	103	11	a	a	DET
ejpam-5605	103	12	map	map	NOUN
ejpam-5605	103	13	d	d	X
ejpam-5605	103	14	:	:	PUNCT
ejpam-5605	103	15	f×	f×	VERB
ejpam-5605	103	16	f	f	X
ejpam-5605	103	17	→	→	PUNCT
ejpam-5605	103	18	rn+	rn+	NOUN
ejpam-5605	103	19	with	with	ADP
ejpam-5605	103	20	the	the	DET
ejpam-5605	103	21	following	follow	VERB
ejpam-5605	103	22	properties	property	NOUN
ejpam-5605	103	23	:	:	PUNCT
ejpam-5605	103	24	(	(	PUNCT
ejpam-5605	103	25	i	i	NOUN
ejpam-5605	103	26	)	)	PUNCT
ejpam-5605	103	27	d(y	d(y	PROPN
ejpam-5605	103	28	,	,	PUNCT
ejpam-5605	103	29	v	v	NOUN
ejpam-5605	103	30	)	)	PUNCT
ejpam-5605	103	31	≥	≥	NOUN
ejpam-5605	103	32	0	0	NUM
ejpam-5605	103	33	for	for	ADP
ejpam-5605	103	34	all	all	DET
ejpam-5605	103	35	y	y	PROPN
ejpam-5605	103	36	,	,	PUNCT
ejpam-5605	103	37	v	v	NOUN
ejpam-5605	103	38	∈	∈	NOUN
ejpam-5605	104	1	f	f	X
ejpam-5605	104	2	;	;	PUNCT
ejpam-5605	104	3	if	if	SCONJ
ejpam-5605	104	4	d(y	d(y	PROPN
ejpam-5605	104	5	,	,	PUNCT
ejpam-5605	104	6	v	v	NOUN
ejpam-5605	104	7	)	)	PUNCT
ejpam-5605	104	8	=	=	SYM
ejpam-5605	105	1	0	0	PUNCT
ejpam-5605	105	2	then	then	ADV
ejpam-5605	105	3	y	y	PROPN
ejpam-5605	105	4	=	=	PUNCT
ejpam-5605	105	5	v	v	PROPN
ejpam-5605	105	6	;	;	PUNCT
ejpam-5605	105	7	(	(	PUNCT
ejpam-5605	105	8	ii	ii	NOUN
ejpam-5605	105	9	)	)	PUNCT
ejpam-5605	105	10	d(y	d(y	PROPN
ejpam-5605	105	11	,	,	PUNCT
ejpam-5605	105	12	v	v	NOUN
ejpam-5605	105	13	)	)	PUNCT
ejpam-5605	105	14	=	=	SYM
ejpam-5605	106	1	d(v	d(v	PROPN
ejpam-5605	106	2	,	,	PUNCT
ejpam-5605	106	3	u	u	NOUN
ejpam-5605	106	4	)	)	PUNCT
ejpam-5605	106	5	for	for	ADP
ejpam-5605	106	6	all	all	DET
ejpam-5605	106	7	y	y	PROPN
ejpam-5605	106	8	,	,	PUNCT
ejpam-5605	106	9	v	v	ADP
ejpam-5605	106	10	∈	∈	NOUN
ejpam-5605	106	11	f	f	X
ejpam-5605	106	12	;	;	PUNCT
ejpam-5605	106	13	(	(	PUNCT
ejpam-5605	106	14	iii	iii	X
ejpam-5605	106	15	)	)	PUNCT
ejpam-5605	106	16	d(y	d(y	NOUN
ejpam-5605	106	17	,	,	PUNCT
ejpam-5605	106	18	v	v	NOUN
ejpam-5605	106	19	)	)	PUNCT
ejpam-5605	106	20	≤	≤	NOUN
ejpam-5605	106	21	d(y	d(y	NOUN
ejpam-5605	106	22	,	,	PUNCT
ejpam-5605	106	23	u	u	NOUN
ejpam-5605	106	24	)	)	PUNCT
ejpam-5605	106	25	+	+	CCONJ
ejpam-5605	106	26	d(u	d(u	PROPN
ejpam-5605	106	27	,	,	PUNCT
ejpam-5605	106	28	v	v	NOUN
ejpam-5605	106	29	)	)	PUNCT
ejpam-5605	106	30	for	for	ADP
ejpam-5605	106	31	all	all	DET
ejpam-5605	106	32	u	u	NOUN
ejpam-5605	106	33	,	,	PUNCT
ejpam-5605	106	34	v	v	PROPN
ejpam-5605	106	35	,	,	PUNCT
ejpam-5605	106	36	y	y	PROPN
ejpam-5605	106	37	∈	∈	PROPN
ejpam-5605	106	38	f.	f.	PROPN
ejpam-5605	106	39	for	for	ADP
ejpam-5605	106	40	di	di	PROPN
ejpam-5605	106	41	,	,	PUNCT
ejpam-5605	106	42	i	i	PROPN
ejpam-5605	106	43	=	=	NOUN
ejpam-5605	106	44	1	1	NUM
ejpam-5605	106	45	,	,	PUNCT
ejpam-5605	106	46	.	.	PUNCT
ejpam-5605	106	47	.	.	PUNCT
ejpam-5605	106	48	.	.	PUNCT
ejpam-5605	107	1	,	,	PUNCT
ejpam-5605	107	2	n	n	PRON
ejpam-5605	107	3	are	be	AUX
ejpam-5605	107	4	metrics	metric	NOUN
ejpam-5605	107	5	on	on	ADP
ejpam-5605	107	6	f	f	PROPN
ejpam-5605	107	7	,	,	PUNCT
ejpam-5605	107	8	the	the	DET
ejpam-5605	107	9	pair	pair	NOUN
ejpam-5605	107	10	(	(	PUNCT
ejpam-5605	107	11	f	f	X
ejpam-5605	107	12	,	,	PUNCT
ejpam-5605	107	13	d	d	X
ejpam-5605	107	14	)	)	PUNCT
ejpam-5605	107	15	is	be	AUX
ejpam-5605	107	16	called	call	VERB
ejpam-5605	107	17	a	a	DET
ejpam-5605	107	18	generalized	generalize	VERB
ejpam-5605	107	19	metric	metric	ADJ
ejpam-5605	107	20	space	space	NOUN
ejpam-5605	107	21	(	(	PUNCT
ejpam-5605	107	22	shortly	shortly	ADV
ejpam-5605	107	23	,	,	PUNCT
ejpam-5605	107	24	gms	gms	NOUN
ejpam-5605	107	25	)	)	PUNCT
ejpam-5605	107	26	(	(	PUNCT
ejpam-5605	107	27	or	or	CCONJ
ejpam-5605	107	28	a	a	DET
ejpam-5605	107	29	vector	vector	NOUN
ejpam-5605	107	30	-	-	PUNCT
ejpam-5605	107	31	valued	value	VERB
ejpam-5605	107	32	metric	metric	ADJ
ejpam-5605	107	33	space	space	NOUN
ejpam-5605	107	34	)	)	PUNCT
ejpam-5605	107	35	with	with	ADP
ejpam-5605	107	36	d(y	d(y	PROPN
ejpam-5605	107	37	,	,	PUNCT
ejpam-5605	107	38	v	v	NOUN
ejpam-5605	107	39	)	)	PUNCT
ejpam-5605	107	40	:	:	PUNCT
ejpam-5605	107	41	=	=	SYM
ejpam-5605	107	42	d1(y	d1(y	NUM
ejpam-5605	107	43	,	,	PUNCT
ejpam-5605	107	44	v	v	NOUN
ejpam-5605	107	45	)	)	PUNCT
ejpam-5605	107	46	...	...	PUNCT
ejpam-5605	108	1	dn(y	dn(y	X
ejpam-5605	108	2	,	,	PUNCT
ejpam-5605	108	3	v	v	NOUN
ejpam-5605	108	4	)	)	PUNCT
ejpam-5605	108	5	.	.	PROPN
ejpam-5605	108	6	definition	definition	NOUN
ejpam-5605	108	7	5	5	NUM
ejpam-5605	108	8	.	.	PUNCT
ejpam-5605	109	1	we	we	PRON
ejpam-5605	109	2	call	call	VERB
ejpam-5605	109	3	a	a	DET
ejpam-5605	109	4	matrix	matrix	NOUN
ejpam-5605	109	5	m	m	NOUN
ejpam-5605	109	6	∈	∈	NOUN
ejpam-5605	109	7	mn×n(r	mn×n(r	NOUN
ejpam-5605	109	8	)	)	PUNCT
ejpam-5605	109	9	of	of	ADP
ejpam-5605	109	10	real	real	ADJ
ejpam-5605	109	11	numbers	number	NOUN
ejpam-5605	109	12	convergent	convergent	ADJ
ejpam-5605	109	13	to	to	ADP
ejpam-5605	109	14	zero	zero	NUM
ejpam-5605	109	15	if	if	SCONJ
ejpam-5605	109	16	its	its	PRON
ejpam-5605	109	17	spectral	spectral	ADJ
ejpam-5605	109	18	radius	radius	NOUN
ejpam-5605	109	19	ρ(m	ρ(m	NUM
ejpam-5605	109	20	)	)	PUNCT
ejpam-5605	109	21	<	<	X
ejpam-5605	109	22	1	1	X
ejpam-5605	109	23	.	.	PUNCT
ejpam-5605	110	1	in	in	ADP
ejpam-5605	110	2	other	other	ADJ
ejpam-5605	110	3	words	word	NOUN
ejpam-5605	110	4	,	,	PUNCT
ejpam-5605	110	5	this	this	PRON
ejpam-5605	110	6	means	mean	VERB
ejpam-5605	110	7	that	that	SCONJ
ejpam-5605	110	8	all	all	DET
ejpam-5605	110	9	the	the	DET
ejpam-5605	110	10	eigenvalues	eigenvalue	NOUN
ejpam-5605	110	11	of	of	ADP
ejpam-5605	110	12	m	m	NOUN
ejpam-5605	110	13	are	be	AUX
ejpam-5605	110	14	in	in	ADP
ejpam-5605	110	15	the	the	DET
ejpam-5605	110	16	open	open	ADJ
ejpam-5605	110	17	unit	unit	NOUN
ejpam-5605	110	18	disc	disc	VERB
ejpam-5605	110	19	i.e.	i.e.	X
ejpam-5605	110	20	|λ|	|λ|	X
ejpam-5605	110	21	<	<	X
ejpam-5605	110	22	1	1	NUM
ejpam-5605	110	23	,	,	PUNCT
ejpam-5605	110	24	for	for	ADP
ejpam-5605	110	25	every	every	DET
ejpam-5605	110	26	λ	λ	PROPN
ejpam-5605	110	27	∈	∈	PROPN
ejpam-5605	110	28	c	c	NOUN
ejpam-5605	110	29	with	with	ADP
ejpam-5605	110	30	det(m−	det(m−	NOUN
ejpam-5605	110	31	λi	λi	NOUN
ejpam-5605	110	32	)	)	PUNCT
ejpam-5605	110	33	=	=	SYM
ejpam-5605	110	34	0	0	NUM
ejpam-5605	110	35	,	,	PUNCT
ejpam-5605	110	36	where	where	SCONJ
ejpam-5605	110	37	i	i	PRON
ejpam-5605	110	38	denote	denote	VERB
ejpam-5605	110	39	the	the	DET
ejpam-5605	110	40	unit	unit	NOUN
ejpam-5605	110	41	matrix	matrix	NOUN
ejpam-5605	110	42	.	.	PUNCT
ejpam-5605	111	1	proposition	proposition	NOUN
ejpam-5605	111	2	1	1	NUM
ejpam-5605	111	3	.	.	PUNCT
ejpam-5605	112	1	[	[	X
ejpam-5605	112	2	23	23	NUM
ejpam-5605	112	3	]	]	PUNCT
ejpam-5605	112	4	let	let	VERB
ejpam-5605	112	5	m	m	PRON
ejpam-5605	112	6	∈	∈	NOUN
ejpam-5605	112	7	mn×n(r+	mn×n(r+	NOUN
ejpam-5605	112	8	)	)	PUNCT
ejpam-5605	112	9	.	.	PUNCT
ejpam-5605	113	1	the	the	DET
ejpam-5605	113	2	following	follow	VERB
ejpam-5605	113	3	statements	statement	NOUN
ejpam-5605	113	4	are	be	AUX
ejpam-5605	113	5	equivalent	equivalent	ADJ
ejpam-5605	113	6	:	:	PUNCT
ejpam-5605	113	7	(	(	PUNCT
ejpam-5605	113	8	i	i	NOUN
ejpam-5605	113	9	)	)	PUNCT
ejpam-5605	113	10	mr	mr	PROPN
ejpam-5605	113	11	→	→	SYM
ejpam-5605	113	12	0	0	NUM
ejpam-5605	113	13	when	when	SCONJ
ejpam-5605	113	14	r	r	NOUN
ejpam-5605	113	15	→	→	SYM
ejpam-5605	113	16	∞.	∞.	PROPN
ejpam-5605	113	17	(	(	PUNCT
ejpam-5605	113	18	ii	ii	NOUN
ejpam-5605	113	19	)	)	PUNCT
ejpam-5605	113	20	m	m	VERB
ejpam-5605	113	21	is	be	AUX
ejpam-5605	113	22	convergent	convergent	ADJ
ejpam-5605	113	23	to	to	ADP
ejpam-5605	113	24	zero	zero	NUM
ejpam-5605	113	25	.	.	PUNCT
ejpam-5605	114	1	(	(	PUNCT
ejpam-5605	114	2	iii	iii	X
ejpam-5605	114	3	)	)	PUNCT
ejpam-5605	114	4	the	the	DET
ejpam-5605	114	5	matrix	matrix	NOUN
ejpam-5605	114	6	(	(	PUNCT
ejpam-5605	114	7	i	i	PRON
ejpam-5605	114	8	−m	−m	NOUN
ejpam-5605	114	9	)	)	PUNCT
ejpam-5605	114	10	is	be	AUX
ejpam-5605	114	11	nonsingular	nonsingular	ADJ
ejpam-5605	114	12	and	and	CCONJ
ejpam-5605	114	13	(	(	PUNCT
ejpam-5605	114	14	i	i	PRON
ejpam-5605	114	15	−m)−1	−m)−1	VERB
ejpam-5605	114	16	=	=	PUNCT
ejpam-5605	115	1	i	i	PRON
ejpam-5605	115	2	+	+	VERB
ejpam-5605	115	3	m+m2	m+m2	PROPN
ejpam-5605	115	4	+	+	X
ejpam-5605	115	5	.	.	PUNCT
ejpam-5605	115	6	.	.	PUNCT
ejpam-5605	115	7	.+mk	.+mk	PUNCT
ejpam-5605	116	1	+	+	CCONJ
ejpam-5605	116	2	.	.	PUNCT
ejpam-5605	116	3	.	.	PUNCT
ejpam-5605	116	4	.	.	PUNCT
ejpam-5605	117	1	.	.	PUNCT
ejpam-5605	118	1	(	(	PUNCT
ejpam-5605	118	2	iv	iv	X
ejpam-5605	118	3	)	)	PUNCT
ejpam-5605	118	4	(	(	PUNCT
ejpam-5605	118	5	i	i	PRON
ejpam-5605	118	6	−m	−m	NOUN
ejpam-5605	118	7	)	)	PUNCT
ejpam-5605	118	8	is	be	AUX
ejpam-5605	118	9	nonsingular	nonsingular	ADJ
ejpam-5605	118	10	matrix	matrix	NOUN
ejpam-5605	118	11	and	and	CCONJ
ejpam-5605	118	12	(	(	PUNCT
ejpam-5605	118	13	i	i	PRON
ejpam-5605	118	14	−m)−1	−m)−1	VERB
ejpam-5605	118	15	has	have	VERB
ejpam-5605	118	16	positive	positive	ADJ
ejpam-5605	118	17	elements	element	NOUN
ejpam-5605	118	18	.	.	PUNCT
ejpam-5605	119	1	let	let	VERB
ejpam-5605	119	2	g	g	PRON
ejpam-5605	119	3	be	be	AUX
ejpam-5605	119	4	a	a	DET
ejpam-5605	119	5	separable	separable	ADJ
ejpam-5605	119	6	gms	gms	NOUN
ejpam-5605	119	7	and	and	CCONJ
ejpam-5605	119	8	(	(	PUNCT
ejpam-5605	119	9	ω	ω	PROPN
ejpam-5605	119	10	,	,	PUNCT
ejpam-5605	119	11	f	f	AUX
ejpam-5605	119	12	)	)	PUNCT
ejpam-5605	119	13	be	be	AUX
ejpam-5605	119	14	a	a	DET
ejpam-5605	119	15	measurable	measurable	ADJ
ejpam-5605	119	16	space	space	NOUN
ejpam-5605	119	17	.	.	PUNCT
ejpam-5605	120	1	we	we	PRON
ejpam-5605	120	2	denote	denote	VERB
ejpam-5605	120	3	b(g	b(g	PROPN
ejpam-5605	120	4	)	)	PUNCT
ejpam-5605	120	5	the	the	DET
ejpam-5605	120	6	borel	borel	PROPN
ejpam-5605	120	7	σ	σ	PROPN
ejpam-5605	120	8	-	-	PROPN
ejpam-5605	120	9	algebra	algebra	PROPN
ejpam-5605	120	10	on	on	ADP
ejpam-5605	120	11	ω×g	ω×g	PROPN
ejpam-5605	120	12	.	.	PUNCT
ejpam-5605	121	1	therefore	therefore	ADV
ejpam-5605	121	2	,	,	PUNCT
ejpam-5605	121	3	f×b(g	f×b(g	PROPN
ejpam-5605	121	4	)	)	PUNCT
ejpam-5605	121	5	is	be	AUX
ejpam-5605	121	6	the	the	DET
ejpam-5605	121	7	smallest	small	ADJ
ejpam-5605	121	8	σ	σ	NOUN
ejpam-5605	121	9	-	-	NOUN
ejpam-5605	121	10	algebra	algebra	PROPN
ejpam-5605	121	11	on	on	ADP
ejpam-5605	121	12	ω×g	ω×g	PROPN
ejpam-5605	121	13	which	which	PRON
ejpam-5605	121	14	contains	contain	VERB
ejpam-5605	121	15	all	all	DET
ejpam-5605	121	16	the	the	DET
ejpam-5605	121	17	sets	set	NOUN
ejpam-5605	121	18	f	f	X
ejpam-5605	121	19	×	×	PROPN
ejpam-5605	121	20	s	s	PROPN
ejpam-5605	121	21	,	,	PUNCT
ejpam-5605	121	22	where	where	SCONJ
ejpam-5605	121	23	f	f	PROPN
ejpam-5605	121	24	∈	∈	PROPN
ejpam-5605	121	25	f	f	PROPN
ejpam-5605	121	26	and	and	CCONJ
ejpam-5605	121	27	s	s	PROPN
ejpam-5605	121	28	∈	∈	PROPN
ejpam-5605	121	29	b(g	b(g	PROPN
ejpam-5605	121	30	)	)	PUNCT
ejpam-5605	121	31	.	.	PUNCT
ejpam-5605	122	1	definition	definition	NOUN
ejpam-5605	122	2	6	6	NUM
ejpam-5605	122	3	.	.	PUNCT
ejpam-5605	123	1	given	give	VERB
ejpam-5605	123	2	two	two	NUM
ejpam-5605	123	3	separable	separable	ADJ
ejpam-5605	123	4	gmss	gmss	NOUN
ejpam-5605	123	5	g	g	PROPN
ejpam-5605	123	6	and	and	CCONJ
ejpam-5605	123	7	x	x	NOUN
ejpam-5605	123	8	,	,	PUNCT
ejpam-5605	123	9	a	a	DET
ejpam-5605	123	10	mapping	mapping	NOUN
ejpam-5605	123	11	q	q	NOUN
ejpam-5605	123	12	:	:	PUNCT
ejpam-5605	123	13	ω	ω	NUM
ejpam-5605	123	14	×	×	NOUN
ejpam-5605	123	15	g	g	PROPN
ejpam-5605	123	16	→	→	PUNCT
ejpam-5605	123	17	x	x	X
ejpam-5605	123	18	is	be	AUX
ejpam-5605	123	19	called	call	VERB
ejpam-5605	123	20	a	a	DET
ejpam-5605	123	21	random	random	ADJ
ejpam-5605	123	22	operator	operator	NOUN
ejpam-5605	123	23	if	if	SCONJ
ejpam-5605	123	24	ω	ω	PROPN
ejpam-5605	123	25	7−→	7−→	PROPN
ejpam-5605	123	26	q(ω	q(ω	NOUN
ejpam-5605	123	27	,	,	PUNCT
ejpam-5605	123	28	u	u	NOUN
ejpam-5605	123	29	)	)	PUNCT
ejpam-5605	123	30	is	be	AUX
ejpam-5605	123	31	measurable	measurable	ADJ
ejpam-5605	123	32	for	for	ADP
ejpam-5605	123	33	all	all	DET
ejpam-5605	123	34	u	u	PROPN
ejpam-5605	123	35	∈	∈	PROPN
ejpam-5605	123	36	g.	g.	NOUN
ejpam-5605	123	37	the	the	DET
ejpam-5605	123	38	random	random	ADJ
ejpam-5605	123	39	operator	operator	NOUN
ejpam-5605	123	40	l	l	NOUN
ejpam-5605	123	41	on	on	ADP
ejpam-5605	123	42	g	g	PROPN
ejpam-5605	123	43	will	will	AUX
ejpam-5605	123	44	be	be	AUX
ejpam-5605	123	45	denoted	denote	VERB
ejpam-5605	123	46	by	by	ADP
ejpam-5605	123	47	q(u)(ω	q(u)(ω	NOUN
ejpam-5605	123	48	)	)	PUNCT
ejpam-5605	123	49	=	=	SYM
ejpam-5605	123	50	q(ω	q(ω	PROPN
ejpam-5605	123	51	,	,	PUNCT
ejpam-5605	123	52	u	u	NOUN
ejpam-5605	123	53	)	)	PUNCT
ejpam-5605	123	54	,	,	PUNCT
ejpam-5605	123	55	ω	ω	PROPN
ejpam-5605	123	56	∈	∈	PROPN
ejpam-5605	123	57	ω	ω	PROPN
ejpam-5605	123	58	,	,	PUNCT
ejpam-5605	123	59	u	u	PROPN
ejpam-5605	123	60	∈	∈	PROPN
ejpam-5605	123	61	g.	g.	NOUN
ejpam-5605	123	62	definition	definition	NOUN
ejpam-5605	123	63	7	7	NUM
ejpam-5605	123	64	.	.	PUNCT
ejpam-5605	124	1	the	the	DET
ejpam-5605	124	2	fixed	fixed	ADJ
ejpam-5605	124	3	point	point	NOUN
ejpam-5605	124	4	of	of	ADP
ejpam-5605	124	5	a	a	DET
ejpam-5605	124	6	random	random	ADJ
ejpam-5605	124	7	operator	operator	NOUN
ejpam-5605	124	8	q	q	PUNCT
ejpam-5605	124	9	is	be	AUX
ejpam-5605	124	10	a	a	DET
ejpam-5605	124	11	measurable	measurable	ADJ
ejpam-5605	124	12	function	function	NOUN
ejpam-5605	124	13	u	u	NOUN
ejpam-5605	124	14	:	:	PUNCT
ejpam-5605	124	15	ω	ω	PROPN
ejpam-5605	124	16	→	→	SYM
ejpam-5605	124	17	g	g	PROPN
ejpam-5605	124	18	such	such	ADJ
ejpam-5605	124	19	that	that	SCONJ
ejpam-5605	124	20	u(ω	u(ω	PROPN
ejpam-5605	124	21	)	)	PUNCT
ejpam-5605	124	22	=	=	SYM
ejpam-5605	124	23	q(ω	q(ω	NOUN
ejpam-5605	124	24	,	,	PUNCT
ejpam-5605	124	25	u(ω	u(ω	PROPN
ejpam-5605	124	26	)	)	PUNCT
ejpam-5605	124	27	)	)	PUNCT
ejpam-5605	124	28	for	for	ADP
ejpam-5605	124	29	all	all	DET
ejpam-5605	124	30	ω	ω	PROPN
ejpam-5605	124	31	∈	∈	PROPN
ejpam-5605	124	32	ω	ω	PROPN
ejpam-5605	124	33	.	.	PUNCT
ejpam-5605	124	34	definition	definition	NOUN
ejpam-5605	124	35	8	8	NUM
ejpam-5605	124	36	.	.	PUNCT
ejpam-5605	125	1	let	let	VERB
ejpam-5605	125	2	f	f	NOUN
ejpam-5605	125	3	:	:	PUNCT
ejpam-5605	126	1	i	i	PRON
ejpam-5605	126	2	×	×	VERB
ejpam-5605	126	3	g	g	PROPN
ejpam-5605	126	4	×	×	PROPN
ejpam-5605	126	5	ω	ω	PROPN
ejpam-5605	126	6	→	→	PUNCT
ejpam-5605	126	7	x	x	X
ejpam-5605	126	8	is	be	AUX
ejpam-5605	126	9	called	call	VERB
ejpam-5605	126	10	random	random	ADJ
ejpam-5605	126	11	carathéodory	carathéodory	NOUN
ejpam-5605	126	12	if	if	SCONJ
ejpam-5605	126	13	the	the	DET
ejpam-5605	126	14	following	follow	VERB
ejpam-5605	126	15	statements	statement	NOUN
ejpam-5605	126	16	are	be	AUX
ejpam-5605	126	17	verified	verify	VERB
ejpam-5605	126	18	:	:	PUNCT
ejpam-5605	126	19	m.	m.	NOUN
ejpam-5605	126	20	ziane	ziane	PROPN
ejpam-5605	126	21	et	et	PROPN
ejpam-5605	126	22	al	al	PROPN
ejpam-5605	126	23	.	.	PUNCT
ejpam-5605	126	24	/	/	SYM
ejpam-5605	126	25	eur	eur	PROPN
ejpam-5605	126	26	.	.	PUNCT
ejpam-5605	127	1	j.	j.	PROPN
ejpam-5605	127	2	pure	pure	PROPN
ejpam-5605	127	3	appl	appl	PROPN
ejpam-5605	127	4	.	.	PROPN
ejpam-5605	127	5	math	math	PROPN
ejpam-5605	127	6	,	,	PUNCT
ejpam-5605	127	7	18	18	NUM
ejpam-5605	127	8	(	(	PUNCT
ejpam-5605	127	9	1	1	NUM
ejpam-5605	127	10	)	)	PUNCT
ejpam-5605	127	11	(	(	PUNCT
ejpam-5605	127	12	2025	2025	NUM
ejpam-5605	127	13	)	)	PUNCT
ejpam-5605	127	14	,	,	PUNCT
ejpam-5605	127	15	5605	5605	NUM
ejpam-5605	127	16	6	6	NUM
ejpam-5605	127	17	of	of	ADP
ejpam-5605	127	18	21	21	NUM
ejpam-5605	127	19	(	(	PUNCT
ejpam-5605	127	20	i	i	NOUN
ejpam-5605	127	21	)	)	PUNCT
ejpam-5605	127	22	the	the	DET
ejpam-5605	127	23	map	map	NOUN
ejpam-5605	127	24	u	u	NOUN
ejpam-5605	127	25	7−→	7−→	PROPN
ejpam-5605	127	26	f(ξ	f(ξ	PROPN
ejpam-5605	127	27	,	,	PUNCT
ejpam-5605	127	28	u	u	NOUN
ejpam-5605	127	29	,	,	PUNCT
ejpam-5605	127	30	ω	ω	NOUN
ejpam-5605	127	31	)	)	PUNCT
ejpam-5605	127	32	is	be	AUX
ejpam-5605	127	33	continuous	continuous	ADJ
ejpam-5605	127	34	for	for	ADP
ejpam-5605	127	35	all	all	PRON
ejpam-5605	127	36	ξ	ξ	X
ejpam-5605	127	37	∈	∈	PRON
ejpam-5605	128	1	i	i	PRON
ejpam-5605	128	2	and	and	CCONJ
ejpam-5605	128	3	ω	ω	NUM
ejpam-5605	128	4	∈	∈	PROPN
ejpam-5605	128	5	ω	ω	PROPN
ejpam-5605	128	6	.	.	PUNCT
ejpam-5605	128	7	(	(	PUNCT
ejpam-5605	128	8	ii	ii	NOUN
ejpam-5605	128	9	)	)	PUNCT
ejpam-5605	128	10	the	the	DET
ejpam-5605	128	11	map	map	NOUN
ejpam-5605	128	12	(	(	PUNCT
ejpam-5605	128	13	ξ	ξ	PROPN
ejpam-5605	128	14	,	,	PUNCT
ejpam-5605	128	15	ω	ω	NOUN
ejpam-5605	128	16	)	)	PUNCT
ejpam-5605	128	17	7−→	7−→	NOUN
ejpam-5605	128	18	f(ξ	f(ξ	NOUN
ejpam-5605	128	19	,	,	PUNCT
ejpam-5605	128	20	u	u	NOUN
ejpam-5605	128	21	,	,	PUNCT
ejpam-5605	128	22	ω	ω	NOUN
ejpam-5605	128	23	)	)	PUNCT
ejpam-5605	128	24	is	be	AUX
ejpam-5605	128	25	jointly	jointly	ADV
ejpam-5605	128	26	measurable	measurable	ADJ
ejpam-5605	128	27	for	for	ADP
ejpam-5605	128	28	all	all	DET
ejpam-5605	128	29	u	u	PROPN
ejpam-5605	128	30	∈	∈	PROPN
ejpam-5605	128	31	g.	g.	NOUN
ejpam-5605	128	32	lemma	lemma	PROPN
ejpam-5605	128	33	4	4	X
ejpam-5605	128	34	.	.	PUNCT
ejpam-5605	129	1	[	[	X
ejpam-5605	129	2	25	25	NUM
ejpam-5605	129	3	]	]	PUNCT
ejpam-5605	129	4	let	let	VERB
ejpam-5605	129	5	g	g	PRON
ejpam-5605	129	6	be	be	AUX
ejpam-5605	129	7	a	a	DET
ejpam-5605	129	8	separable	separable	ADJ
ejpam-5605	129	9	metric	metric	ADJ
ejpam-5605	129	10	space	space	NOUN
ejpam-5605	129	11	and	and	CCONJ
ejpam-5605	129	12	q	q	NOUN
ejpam-5605	129	13	:	:	PUNCT
ejpam-5605	129	14	ω×g	ω×g	PROPN
ejpam-5605	129	15	→	→	SYM
ejpam-5605	129	16	g	g	NOUN
ejpam-5605	129	17	be	be	AUX
ejpam-5605	129	18	a	a	DET
ejpam-5605	129	19	mapping	mapping	NOUN
ejpam-5605	129	20	such	such	ADJ
ejpam-5605	129	21	that	that	SCONJ
ejpam-5605	129	22	q(ω	q(ω	NOUN
ejpam-5605	129	23	,	,	PUNCT
ejpam-5605	129	24	·	·	PUNCT
ejpam-5605	129	25	)	)	PUNCT
ejpam-5605	129	26	is	be	AUX
ejpam-5605	129	27	continuous	continuous	ADJ
ejpam-5605	129	28	for	for	ADP
ejpam-5605	129	29	all	all	DET
ejpam-5605	129	30	ω	ω	NUM
ejpam-5605	129	31	∈	∈	PROPN
ejpam-5605	129	32	ω	ω	NOUN
ejpam-5605	129	33	and	and	CCONJ
ejpam-5605	129	34	q	q	ADJ
ejpam-5605	129	35	(	(	PUNCT
ejpam-5605	129	36	·	·	PUNCT
ejpam-5605	129	37	,	,	PUNCT
ejpam-5605	129	38	u	u	NOUN
ejpam-5605	129	39	)	)	PUNCT
ejpam-5605	129	40	is	be	AUX
ejpam-5605	129	41	measurable	measurable	ADJ
ejpam-5605	129	42	for	for	ADP
ejpam-5605	129	43	all	all	PRON
ejpam-5605	129	44	u	u	NOUN
ejpam-5605	129	45	∈	∈	PROPN
ejpam-5605	129	46	g	g	NOUN
ejpam-5605	129	47	.	.	PUNCT
ejpam-5605	130	1	then	then	ADV
ejpam-5605	130	2	the	the	DET
ejpam-5605	130	3	map	map	NOUN
ejpam-5605	130	4	(	(	PUNCT
ejpam-5605	130	5	ω	ω	NOUN
ejpam-5605	130	6	,	,	PUNCT
ejpam-5605	130	7	u	u	NOUN
ejpam-5605	130	8	)	)	PUNCT
ejpam-5605	130	9	→	→	SYM
ejpam-5605	130	10	q(ω	q(ω	PROPN
ejpam-5605	130	11	,	,	PUNCT
ejpam-5605	130	12	u	u	NOUN
ejpam-5605	130	13	)	)	PUNCT
ejpam-5605	130	14	is	be	AUX
ejpam-5605	130	15	jointly	jointly	ADV
ejpam-5605	130	16	measurable	measurable	ADJ
ejpam-5605	130	17	.	.	PUNCT
ejpam-5605	131	1	definition	definition	NOUN
ejpam-5605	131	2	9	9	NUM
ejpam-5605	131	3	.	.	PUNCT
ejpam-5605	132	1	[	[	X
ejpam-5605	132	2	12	12	NUM
ejpam-5605	132	3	]	]	PUNCT
ejpam-5605	132	4	let	let	VERB
ejpam-5605	132	5	g	g	PRON
ejpam-5605	132	6	be	be	AUX
ejpam-5605	132	7	a	a	DET
ejpam-5605	132	8	generalized	generalized	ADJ
ejpam-5605	132	9	banach	banach	NOUN
ejpam-5605	132	10	space	space	NOUN
ejpam-5605	132	11	and	and	CCONJ
ejpam-5605	132	12	(	(	PUNCT
ejpam-5605	132	13	o,≤	o,≤	X
ejpam-5605	132	14	)	)	PUNCT
ejpam-5605	132	15	be	be	VERB
ejpam-5605	132	16	a	a	DET
ejpam-5605	132	17	partially	partially	ADV
ejpam-5605	132	18	ordered	order	VERB
ejpam-5605	132	19	set	set	NOUN
ejpam-5605	132	20	.	.	PUNCT
ejpam-5605	133	1	a	a	DET
ejpam-5605	133	2	map	map	NOUN
ejpam-5605	133	3	λ	λ	X
ejpam-5605	133	4	:	:	PUNCT
ejpam-5605	133	5	p(g	p(g	NOUN
ejpam-5605	133	6	)	)	PUNCT
ejpam-5605	133	7	→	→	PUNCT
ejpam-5605	133	8	o×	o×	PROPN
ejpam-5605	133	9	o×	o×	PROPN
ejpam-5605	133	10	.	.	PUNCT
ejpam-5605	133	11	.	.	PUNCT
ejpam-5605	134	1	.×	.×	PROPN
ejpam-5605	134	2	o	o	PROPN
ejpam-5605	134	3	is	be	AUX
ejpam-5605	134	4	called	call	VERB
ejpam-5605	134	5	a	a	DET
ejpam-5605	134	6	generalized	generalized	ADJ
ejpam-5605	134	7	mnc	mnc	NOUN
ejpam-5605	134	8	on	on	ADP
ejpam-5605	134	9	g	g	PROPN
ejpam-5605	134	10	,	,	PUNCT
ejpam-5605	134	11	if	if	SCONJ
ejpam-5605	134	12	λ(co	λ(co	PROPN
ejpam-5605	134	13	o	o	NOUN
ejpam-5605	134	14	)	)	PUNCT
ejpam-5605	134	15	=	=	SYM
ejpam-5605	134	16	λ(o	λ(o	X
ejpam-5605	134	17	)	)	PUNCT
ejpam-5605	134	18	for	for	ADP
ejpam-5605	134	19	every	every	DET
ejpam-5605	134	20	o	o	PROPN
ejpam-5605	134	21	∈	∈	PROPN
ejpam-5605	134	22	p(g	p(g	PROPN
ejpam-5605	134	23	)	)	PUNCT
ejpam-5605	134	24	,	,	PUNCT
ejpam-5605	134	25	where	where	SCONJ
ejpam-5605	134	26	λ(o	λ(o	PROPN
ejpam-5605	134	27	)	)	PUNCT
ejpam-5605	135	1	:	:	PUNCT
ejpam-5605	135	2	=	=	SYM
ejpam-5605	135	3			X
ejpam-5605	135	4	λ1(o	λ1(o	X
ejpam-5605	135	5	)	)	PUNCT
ejpam-5605	135	6	...	...	PUNCT
ejpam-5605	135	7	λn(o	λn(o	X
ejpam-5605	135	8	)	)	PUNCT
ejpam-5605	135	9			PROPN
ejpam-5605	135	10	,	,	PUNCT
ejpam-5605	135	11	p(g	p(g	NOUN
ejpam-5605	135	12	)	)	PUNCT
ejpam-5605	135	13	denotes	denote	VERB
ejpam-5605	135	14	the	the	DET
ejpam-5605	135	15	family	family	NOUN
ejpam-5605	135	16	of	of	ADP
ejpam-5605	135	17	all	all	DET
ejpam-5605	135	18	bounded	bound	VERB
ejpam-5605	135	19	subsets	subset	NOUN
ejpam-5605	135	20	of	of	ADP
ejpam-5605	135	21	g	g	PROPN
ejpam-5605	135	22	and	and	CCONJ
ejpam-5605	135	23	coo	coo	NOUN
ejpam-5605	135	24	is	be	AUX
ejpam-5605	135	25	the	the	DET
ejpam-5605	135	26	closed	closed	ADJ
ejpam-5605	135	27	convex	convex	NOUN
ejpam-5605	135	28	hull	hull	NOUN
ejpam-5605	135	29	of	of	ADP
ejpam-5605	135	30	o.	o.	ADJ
ejpam-5605	135	31	definition	definition	NOUN
ejpam-5605	135	32	10	10	NUM
ejpam-5605	135	33	.	.	PUNCT
ejpam-5605	136	1	the	the	DET
ejpam-5605	136	2	application	application	NOUN
ejpam-5605	136	3	λ	λ	PROPN
ejpam-5605	136	4	is	be	AUX
ejpam-5605	136	5	called	call	VERB
ejpam-5605	136	6	:	:	PUNCT
ejpam-5605	136	7	(	(	PUNCT
ejpam-5605	136	8	i	i	NOUN
ejpam-5605	136	9	)	)	PUNCT
ejpam-5605	136	10	monotone	monotone	ADJ
ejpam-5605	136	11	if	if	SCONJ
ejpam-5605	136	12	o0,o1	o0,o1	PROPN
ejpam-5605	136	13	∈	∈	PROPN
ejpam-5605	136	14	p(g),o0	p(g),o0	PROPN
ejpam-5605	136	15	⊂	⊂	PROPN
ejpam-5605	136	16	o1	o1	PROPN
ejpam-5605	136	17	implies	imply	VERB
ejpam-5605	136	18	λ	λ	PROPN
ejpam-5605	136	19	(	(	PUNCT
ejpam-5605	136	20	o0	o0	NOUN
ejpam-5605	136	21	)	)	PUNCT
ejpam-5605	137	1	≤	≤	NUM
ejpam-5605	137	2	λ	λ	PROPN
ejpam-5605	137	3	(	(	PUNCT
ejpam-5605	137	4	o1	o1	PROPN
ejpam-5605	137	5	)	)	PUNCT
ejpam-5605	137	6	.	.	PUNCT
ejpam-5605	138	1	(	(	PUNCT
ejpam-5605	138	2	ii	ii	NOUN
ejpam-5605	138	3	)	)	PUNCT
ejpam-5605	138	4	nonsingular	nonsingular	ADJ
ejpam-5605	138	5	if	if	SCONJ
ejpam-5605	138	6	λ({a	λ({a	PROPN
ejpam-5605	138	7	}	}	PUNCT
ejpam-5605	138	8	∪	∪	ADP
ejpam-5605	138	9	o	o	NOUN
ejpam-5605	138	10	)	)	PUNCT
ejpam-5605	138	11	=	=	SYM
ejpam-5605	138	12	λ(o	λ(o	X
ejpam-5605	138	13	)	)	PUNCT
ejpam-5605	138	14	for	for	ADP
ejpam-5605	138	15	every	every	DET
ejpam-5605	138	16	a	a	DET
ejpam-5605	138	17	∈	∈	PROPN
ejpam-5605	138	18	g	g	NOUN
ejpam-5605	138	19	and	and	CCONJ
ejpam-5605	138	20	o	o	PROPN
ejpam-5605	138	21	∈	∈	PROPN
ejpam-5605	138	22	p(g	p(g	PROPN
ejpam-5605	138	23	)	)	PUNCT
ejpam-5605	138	24	.	.	PUNCT
ejpam-5605	139	1	if	if	SCONJ
ejpam-5605	139	2	o	o	NOUN
ejpam-5605	139	3	is	be	AUX
ejpam-5605	139	4	a	a	DET
ejpam-5605	139	5	cone	cone	NOUN
ejpam-5605	139	6	in	in	ADP
ejpam-5605	139	7	a	a	DET
ejpam-5605	139	8	normed	normed	ADJ
ejpam-5605	139	9	space	space	NOUN
ejpam-5605	139	10	,	,	PUNCT
ejpam-5605	139	11	we	we	PRON
ejpam-5605	139	12	say	say	VERB
ejpam-5605	139	13	that	that	SCONJ
ejpam-5605	139	14	the	the	DET
ejpam-5605	139	15	mnc	mnc	PROPN
ejpam-5605	139	16	is	be	AUX
ejpam-5605	139	17	(	(	PUNCT
ejpam-5605	139	18	iii	iii	NOUN
ejpam-5605	139	19	)	)	PUNCT
ejpam-5605	139	20	regular	regular	ADJ
ejpam-5605	139	21	if	if	SCONJ
ejpam-5605	139	22	the	the	DET
ejpam-5605	139	23	condition	condition	NOUN
ejpam-5605	139	24	λ(o	λ(o	X
ejpam-5605	139	25	)	)	PUNCT
ejpam-5605	140	1	=	=	SYM
ejpam-5605	140	2	0	0	PUNCT
ejpam-5605	140	3	is	be	AUX
ejpam-5605	140	4	equivalent	equivalent	ADJ
ejpam-5605	140	5	to	to	ADP
ejpam-5605	140	6	the	the	DET
ejpam-5605	140	7	compactness	compactness	NOUN
ejpam-5605	140	8	of	of	ADP
ejpam-5605	140	9	o.	o.	NOUN
ejpam-5605	140	10	the	the	DET
ejpam-5605	140	11	most	most	ADV
ejpam-5605	140	12	well	well	ADV
ejpam-5605	140	13	-	-	PUNCT
ejpam-5605	140	14	known	know	VERB
ejpam-5605	140	15	example	example	NOUN
ejpam-5605	140	16	of	of	ADP
ejpam-5605	140	17	a	a	DET
ejpam-5605	140	18	mnc	mnc	PROPN
ejpam-5605	140	19	possessing	possess	VERB
ejpam-5605	140	20	all	all	DET
ejpam-5605	140	21	previous	previous	ADJ
ejpam-5605	140	22	properties	property	NOUN
ejpam-5605	140	23	is	be	AUX
ejpam-5605	140	24	the	the	DET
ejpam-5605	140	25	hausdorff	hausdorff	NOUN
ejpam-5605	140	26	mnc	mnc	PROPN
ejpam-5605	140	27	defined	define	VERB
ejpam-5605	140	28	by	by	ADP
ejpam-5605	140	29	:	:	PUNCT
ejpam-5605	140	30	η(o	η(o	NUM
ejpam-5605	140	31	)	)	PUNCT
ejpam-5605	140	32	=	=	SYM
ejpam-5605	140	33	inf	inf	NOUN
ejpam-5605	140	34	{	{	PUNCT
ejpam-5605	140	35	ϵ	ϵ	X
ejpam-5605	140	36	>	>	X
ejpam-5605	140	37	0	0	NUM
ejpam-5605	140	38	:	:	PUNCT
ejpam-5605	140	39	o	o	X
ejpam-5605	140	40	has	have	VERB
ejpam-5605	140	41	a	a	DET
ejpam-5605	140	42	finite	finite	ADJ
ejpam-5605	140	43	ϵ−	ϵ−	NOUN
ejpam-5605	140	44	net	net	NOUN
ejpam-5605	140	45	}	}	PUNCT
ejpam-5605	140	46	.	.	PUNCT
ejpam-5605	141	1	definition	definition	NOUN
ejpam-5605	141	2	11	11	NUM
ejpam-5605	141	3	.	.	PUNCT
ejpam-5605	142	1	[	[	X
ejpam-5605	142	2	12	12	NUM
ejpam-5605	142	3	]	]	X
ejpam-5605	142	4	let	let	VERB
ejpam-5605	142	5	x	x	PRON
ejpam-5605	142	6	,	,	PUNCT
ejpam-5605	142	7	y	y	PROPN
ejpam-5605	142	8	be	be	VERB
ejpam-5605	142	9	two	two	NUM
ejpam-5605	142	10	generalized	generalized	ADJ
ejpam-5605	142	11	normed	normed	ADJ
ejpam-5605	142	12	spaces	space	NOUN
ejpam-5605	142	13	.	.	PUNCT
ejpam-5605	143	1	a	a	DET
ejpam-5605	143	2	continuous	continuous	ADJ
ejpam-5605	143	3	map	map	NOUN
ejpam-5605	143	4	g	g	NOUN
ejpam-5605	143	5	:	:	PUNCT
ejpam-5605	143	6	x	x	SYM
ejpam-5605	143	7	→	→	SYM
ejpam-5605	143	8	y	y	PROPN
ejpam-5605	143	9	is	be	AUX
ejpam-5605	143	10	called	call	VERB
ejpam-5605	143	11	a	a	DET
ejpam-5605	143	12	m	m	NOUN
ejpam-5605	143	13	-	-	NOUN
ejpam-5605	143	14	contraction	contraction	NOUN
ejpam-5605	143	15	(	(	PUNCT
ejpam-5605	143	16	with	with	ADP
ejpam-5605	143	17	respect	respect	NOUN
ejpam-5605	143	18	to	to	ADP
ejpam-5605	143	19	the	the	DET
ejpam-5605	143	20	generalized	generalized	ADJ
ejpam-5605	143	21	mnc	mnc	PROPN
ejpam-5605	143	22	λ	λ	PROPN
ejpam-5605	143	23	)	)	PUNCT
ejpam-5605	143	24	if	if	SCONJ
ejpam-5605	143	25	there	there	PRON
ejpam-5605	143	26	exists	exist	VERB
ejpam-5605	143	27	a	a	DET
ejpam-5605	143	28	matrix	matrix	NOUN
ejpam-5605	143	29	m	m	NOUN
ejpam-5605	143	30	∈	∈	PROPN
ejpam-5605	143	31	mn×n(r	mn×n(r	NOUN
ejpam-5605	143	32	)	)	PUNCT
ejpam-5605	143	33	converges	converge	NOUN
ejpam-5605	143	34	to	to	ADP
ejpam-5605	143	35	zero	zero	NUM
ejpam-5605	143	36	such	such	ADJ
ejpam-5605	143	37	that	that	PRON
ejpam-5605	143	38	for	for	ADP
ejpam-5605	143	39	every	every	DET
ejpam-5605	143	40	d	d	PROPN
ejpam-5605	143	41	∈	∈	PROPN
ejpam-5605	143	42	p(x	p(x	PROPN
ejpam-5605	143	43	)	)	PUNCT
ejpam-5605	143	44	,	,	PUNCT
ejpam-5605	143	45	one	one	PRON
ejpam-5605	143	46	has	have	VERB
ejpam-5605	143	47	λ(g(d	λ(g(d	PROPN
ejpam-5605	143	48	)	)	PUNCT
ejpam-5605	143	49	)	)	PUNCT
ejpam-5605	143	50	≤	≤	NUM
ejpam-5605	143	51	mλ(d	mλ(d	NUM
ejpam-5605	143	52	)	)	PUNCT
ejpam-5605	143	53	.	.	PUNCT
ejpam-5605	144	1	lemma	lemma	PROPN
ejpam-5605	144	2	5	5	NUM
ejpam-5605	144	3	.	.	PUNCT
ejpam-5605	145	1	[	[	X
ejpam-5605	145	2	15	15	NUM
ejpam-5605	145	3	]	]	X
ejpam-5605	145	4	if	if	SCONJ
ejpam-5605	145	5	{	{	PUNCT
ejpam-5605	145	6	xn}+∞	xn}+∞	PROPN
ejpam-5605	145	7	n=1	n=1	PROPN
ejpam-5605	145	8	⊂	⊂	PROPN
ejpam-5605	145	9	l1(i	l1(i	PROPN
ejpam-5605	145	10	,	,	PUNCT
ejpam-5605	145	11	g	g	NOUN
ejpam-5605	145	12	)	)	PUNCT
ejpam-5605	145	13	satisfies	satisfie	NOUN
ejpam-5605	145	14	∥xn(ξ)∥	∥xn(ξ)∥	PROPN
ejpam-5605	145	15	≤	≤	PROPN
ejpam-5605	145	16	ι(ξ	ι(ξ	NOUN
ejpam-5605	145	17	)	)	PUNCT
ejpam-5605	146	1	a.e	a.e	PROPN
ejpam-5605	146	2	.	.	PROPN
ejpam-5605	147	1	on	on	ADP
ejpam-5605	147	2	i	i	PRON
ejpam-5605	147	3	for	for	ADP
ejpam-5605	147	4	all	all	DET
ejpam-5605	147	5	n	n	PRON
ejpam-5605	147	6	≥	≥	NOUN
ejpam-5605	147	7	1	1	NUM
ejpam-5605	147	8	with	with	ADP
ejpam-5605	147	9	some	some	PRON
ejpam-5605	147	10	ι	ι	ADP
ejpam-5605	147	11	∈	∈	PROPN
ejpam-5605	147	12	l1(i	l1(i	PROPN
ejpam-5605	147	13	,	,	PUNCT
ejpam-5605	147	14	r+	r+	X
ejpam-5605	147	15	)	)	PUNCT
ejpam-5605	147	16	.	.	PUNCT
ejpam-5605	148	1	then	then	ADV
ejpam-5605	148	2	,	,	PUNCT
ejpam-5605	148	3	the	the	DET
ejpam-5605	148	4	function	function	NOUN
ejpam-5605	148	5	η({xn(ξ)}+∞	η({xn(ξ)}+∞	PROPN
ejpam-5605	148	6	n=1	n=1	PROPN
ejpam-5605	148	7	)	)	PUNCT
ejpam-5605	148	8	is	be	AUX
ejpam-5605	148	9	integrable	integrable	ADJ
ejpam-5605	148	10	and	and	CCONJ
ejpam-5605	148	11	η	η	PROPN
ejpam-5605	148	12	(	(	PUNCT
ejpam-5605	148	13	{	{	PUNCT
ejpam-5605	148	14	∫	∫	PROPN
ejpam-5605	148	15	ξ	ξ	SYM
ejpam-5605	148	16	0	0	NUM
ejpam-5605	148	17	xn(s)ds	xn(s)d	NOUN
ejpam-5605	148	18	:	:	PUNCT
ejpam-5605	148	19	n	n	PRON
ejpam-5605	148	20	≥	≥	NOUN
ejpam-5605	148	21	1	1	NUM
ejpam-5605	148	22	}	}	PUNCT
ejpam-5605	148	23	)	)	PUNCT
ejpam-5605	148	24	≤	≤	NUM
ejpam-5605	148	25	∫	∫	PROPN
ejpam-5605	149	1	ξ	ξ	X
ejpam-5605	149	2	0	0	PUNCT
ejpam-5605	149	3	η(xn(s	η(xn(s	PROPN
ejpam-5605	149	4	)	)	PUNCT
ejpam-5605	149	5	:	:	PUNCT
ejpam-5605	150	1	n	n	PRON
ejpam-5605	150	2	≥	≥	NOUN
ejpam-5605	150	3	1)ds	1)ds	NUM
ejpam-5605	150	4	.	.	PUNCT
ejpam-5605	151	1	(	(	PUNCT
ejpam-5605	151	2	4	4	X
ejpam-5605	151	3	)	)	PUNCT
ejpam-5605	151	4	theorem	theorem	NOUN
ejpam-5605	151	5	1	1	NUM
ejpam-5605	151	6	.	.	PUNCT
ejpam-5605	152	1	[	[	X
ejpam-5605	152	2	7	7	NUM
ejpam-5605	152	3	,	,	PUNCT
ejpam-5605	152	4	25	25	NUM
ejpam-5605	152	5	]	]	PUNCT
ejpam-5605	152	6	let	let	VERB
ejpam-5605	152	7	x	x	PRON
ejpam-5605	152	8	be	be	AUX
ejpam-5605	152	9	a	a	DET
ejpam-5605	152	10	real	real	ADJ
ejpam-5605	152	11	separable	separable	ADJ
ejpam-5605	152	12	generalized	generalize	VERB
ejpam-5605	152	13	banach	banach	NOUN
ejpam-5605	152	14	space	space	NOUN
ejpam-5605	152	15	and	and	CCONJ
ejpam-5605	152	16	(	(	PUNCT
ejpam-5605	152	17	ω	ω	NOUN
ejpam-5605	152	18	,	,	PUNCT
ejpam-5605	152	19	g	g	NOUN
ejpam-5605	152	20	)	)	PUNCT
ejpam-5605	152	21	be	be	AUX
ejpam-5605	152	22	a	a	DET
ejpam-5605	152	23	measurable	measurable	ADJ
ejpam-5605	152	24	space	space	NOUN
ejpam-5605	152	25	and	and	CCONJ
ejpam-5605	152	26	q	q	NOUN
ejpam-5605	152	27	:	:	PUNCT
ejpam-5605	152	28	ω	ω	NUM
ejpam-5605	152	29	×	×	NOUN
ejpam-5605	152	30	x	x	INTJ
ejpam-5605	152	31	→	→	SYM
ejpam-5605	152	32	x	x	X
ejpam-5605	152	33	a	a	DET
ejpam-5605	152	34	continuous	continuous	ADJ
ejpam-5605	152	35	random	random	ADJ
ejpam-5605	152	36	operator	operator	NOUN
ejpam-5605	152	37	,	,	PUNCT
ejpam-5605	152	38	and	and	CCONJ
ejpam-5605	152	39	let	let	VERB
ejpam-5605	152	40	m(ω	m(ω	NOUN
ejpam-5605	152	41	)	)	PUNCT
ejpam-5605	152	42	∈	∈	PROPN
ejpam-5605	152	43	mn×n(r+	mn×n(r+	AUX
ejpam-5605	152	44	)	)	PUNCT
ejpam-5605	152	45	be	be	AUX
ejpam-5605	152	46	a	a	DET
ejpam-5605	152	47	random	random	ADJ
ejpam-5605	152	48	variable	variable	ADJ
ejpam-5605	152	49	matrix	matrix	NOUN
ejpam-5605	152	50	such	such	ADJ
ejpam-5605	152	51	that	that	PRON
ejpam-5605	152	52	for	for	SCONJ
ejpam-5605	152	53	every	every	DET
ejpam-5605	152	54	ω	ω	PROPN
ejpam-5605	152	55	∈	∈	PROPN
ejpam-5605	152	56	ω	ω	PROPN
ejpam-5605	152	57	,	,	PUNCT
ejpam-5605	152	58	the	the	DET
ejpam-5605	152	59	matrix	matrix	NOUN
ejpam-5605	152	60	m(ω	m(ω	PROPN
ejpam-5605	152	61	)	)	PUNCT
ejpam-5605	152	62	converges	converge	VERB
ejpam-5605	152	63	to	to	ADP
ejpam-5605	152	64	zero	zero	NUM
ejpam-5605	152	65	and	and	CCONJ
ejpam-5605	152	66	:	:	PUNCT
ejpam-5605	152	67	d(q(ω	d(q(ω	PROPN
ejpam-5605	152	68	,	,	PUNCT
ejpam-5605	152	69	z1),q(ω	z1),q(ω	NUM
ejpam-5605	152	70	,	,	PUNCT
ejpam-5605	152	71	z2	z2	NOUN
ejpam-5605	152	72	)	)	PUNCT
ejpam-5605	152	73	)	)	PUNCT
ejpam-5605	153	1	≤	≤	NUM
ejpam-5605	153	2	m(ω)d(z1	m(ω)d(z1	PROPN
ejpam-5605	153	3	,	,	PUNCT
ejpam-5605	153	4	z2	z2	PROPN
ejpam-5605	153	5	)	)	PUNCT
ejpam-5605	153	6	,	,	PUNCT
ejpam-5605	153	7	for	for	ADP
ejpam-5605	153	8	each	each	DET
ejpam-5605	153	9	z1	z1	VERB
ejpam-5605	153	10	,	,	PUNCT
ejpam-5605	153	11	z2	z2	PROPN
ejpam-5605	153	12	∈	∈	PROPN
ejpam-5605	153	13	x	x	X
ejpam-5605	153	14	and	and	CCONJ
ejpam-5605	153	15	ω	ω	NUM
ejpam-5605	153	16	∈	∈	PROPN
ejpam-5605	153	17	ω	ω	X
ejpam-5605	153	18	.	.	PUNCT
ejpam-5605	154	1	then	then	ADV
ejpam-5605	154	2	,	,	PUNCT
ejpam-5605	154	3	there	there	PRON
ejpam-5605	154	4	exists	exist	VERB
ejpam-5605	154	5	a	a	DET
ejpam-5605	154	6	unique	unique	ADJ
ejpam-5605	154	7	random	random	ADJ
ejpam-5605	154	8	fixed	fix	VERB
ejpam-5605	154	9	point	point	NOUN
ejpam-5605	154	10	of	of	ADP
ejpam-5605	154	11	q.	q.	PROPN
ejpam-5605	154	12	m.	m.	PROPN
ejpam-5605	154	13	ziane	ziane	PROPN
ejpam-5605	154	14	et	et	PROPN
ejpam-5605	154	15	al	al	PROPN
ejpam-5605	154	16	.	.	PUNCT
ejpam-5605	154	17	/	/	SYM
ejpam-5605	154	18	eur	eur	PROPN
ejpam-5605	154	19	.	.	PUNCT
ejpam-5605	155	1	j.	j.	PROPN
ejpam-5605	155	2	pure	pure	PROPN
ejpam-5605	155	3	appl	appl	PROPN
ejpam-5605	155	4	.	.	PROPN
ejpam-5605	155	5	math	math	PROPN
ejpam-5605	155	6	,	,	PUNCT
ejpam-5605	155	7	18	18	NUM
ejpam-5605	155	8	(	(	PUNCT
ejpam-5605	155	9	1	1	NUM
ejpam-5605	155	10	)	)	PUNCT
ejpam-5605	155	11	(	(	PUNCT
ejpam-5605	155	12	2025	2025	NUM
ejpam-5605	155	13	)	)	PUNCT
ejpam-5605	155	14	,	,	PUNCT
ejpam-5605	155	15	5605	5605	NUM
ejpam-5605	155	16	7	7	NUM
ejpam-5605	155	17	of	of	ADP
ejpam-5605	155	18	21	21	NUM
ejpam-5605	155	19	theorem	theorem	NOUN
ejpam-5605	155	20	2	2	NUM
ejpam-5605	155	21	.	.	PUNCT
ejpam-5605	156	1	[	[	X
ejpam-5605	156	2	7	7	NUM
ejpam-5605	156	3	,	,	PUNCT
ejpam-5605	156	4	25	25	NUM
ejpam-5605	156	5	]	]	PUNCT
ejpam-5605	156	6	let	let	VERB
ejpam-5605	156	7	g	g	PRON
ejpam-5605	156	8	be	be	AUX
ejpam-5605	156	9	a	a	DET
ejpam-5605	156	10	separable	separable	ADJ
ejpam-5605	156	11	generalized	generalize	VERB
ejpam-5605	156	12	banach	banach	NOUN
ejpam-5605	156	13	space	space	NOUN
ejpam-5605	156	14	,	,	PUNCT
ejpam-5605	156	15	and	and	CCONJ
ejpam-5605	156	16	let	let	VERB
ejpam-5605	156	17	q	q	NOUN
ejpam-5605	156	18	:	:	PUNCT
ejpam-5605	156	19	ω×g	ω×g	PROPN
ejpam-5605	156	20	→	→	SYM
ejpam-5605	156	21	g	g	NOUN
ejpam-5605	156	22	be	be	AUX
ejpam-5605	156	23	a	a	DET
ejpam-5605	156	24	condensing	condense	VERB
ejpam-5605	156	25	continuous	continuous	ADJ
ejpam-5605	156	26	random	random	ADJ
ejpam-5605	156	27	operator	operator	NOUN
ejpam-5605	156	28	.	.	PUNCT
ejpam-5605	157	1	then	then	ADV
ejpam-5605	157	2	either	either	PRON
ejpam-5605	157	3	of	of	ADP
ejpam-5605	157	4	the	the	DET
ejpam-5605	157	5	following	follow	VERB
ejpam-5605	157	6	holds	hold	VERB
ejpam-5605	157	7	:	:	PUNCT
ejpam-5605	157	8	(	(	PUNCT
ejpam-5605	157	9	i	i	NOUN
ejpam-5605	157	10	)	)	PUNCT
ejpam-5605	157	11	the	the	DET
ejpam-5605	157	12	random	random	ADJ
ejpam-5605	157	13	equation	equation	NOUN
ejpam-5605	157	14	q(ω	q(ω	NOUN
ejpam-5605	157	15	,	,	PUNCT
ejpam-5605	157	16	z	z	NOUN
ejpam-5605	157	17	)	)	PUNCT
ejpam-5605	157	18	=	=	NOUN
ejpam-5605	158	1	z	z	NOUN
ejpam-5605	158	2	has	have	VERB
ejpam-5605	158	3	a	a	DET
ejpam-5605	158	4	random	random	ADJ
ejpam-5605	158	5	solution	solution	NOUN
ejpam-5605	158	6	,	,	PUNCT
ejpam-5605	158	7	i.e.	i.e.	X
ejpam-5605	158	8	,	,	PUNCT
ejpam-5605	158	9	there	there	PRON
ejpam-5605	158	10	is	be	VERB
ejpam-5605	158	11	a	a	DET
ejpam-5605	158	12	measurable	measurable	ADJ
ejpam-5605	158	13	function	function	NOUN
ejpam-5605	158	14	z	z	NOUN
ejpam-5605	158	15	:	:	PUNCT
ejpam-5605	159	1	ω	ω	X
ejpam-5605	159	2	→	→	SYM
ejpam-5605	159	3	g	g	PROPN
ejpam-5605	159	4	such	such	ADJ
ejpam-5605	159	5	that	that	SCONJ
ejpam-5605	159	6	q(ω	q(ω	NOUN
ejpam-5605	159	7	,	,	PUNCT
ejpam-5605	159	8	z(ω	z(ω	NUM
ejpam-5605	159	9	)	)	PUNCT
ejpam-5605	159	10	)	)	PUNCT
ejpam-5605	160	1	=	=	SYM
ejpam-5605	160	2	z(ω	z(ω	PROPN
ejpam-5605	160	3	)	)	PUNCT
ejpam-5605	160	4	for	for	ADP
ejpam-5605	160	5	all	all	DET
ejpam-5605	160	6	ω	ω	PROPN
ejpam-5605	160	7	∈	∈	PROPN
ejpam-5605	160	8	ω	ω	PROPN
ejpam-5605	160	9	,	,	PUNCT
ejpam-5605	160	10	or	or	CCONJ
ejpam-5605	160	11	(	(	PUNCT
ejpam-5605	160	12	ii	ii	NOUN
ejpam-5605	160	13	)	)	PUNCT
ejpam-5605	161	1	the	the	DET
ejpam-5605	161	2	set	set	NOUN
ejpam-5605	161	3	w	w	PROPN
ejpam-5605	161	4	=	=	PUNCT
ejpam-5605	161	5	{	{	PUNCT
ejpam-5605	161	6	z	z	NOUN
ejpam-5605	161	7	:	:	PUNCT
ejpam-5605	161	8	ω	ω	X
ejpam-5605	161	9	→	→	SYM
ejpam-5605	161	10	g	g	PROPN
ejpam-5605	161	11	is	be	AUX
ejpam-5605	161	12	measurable	measurable	ADJ
ejpam-5605	161	13	κ(ω)q(ω	κ(ω)q(ω	NOUN
ejpam-5605	161	14	,	,	PUNCT
ejpam-5605	161	15	z	z	NOUN
ejpam-5605	161	16	)	)	PUNCT
ejpam-5605	161	17	=	=	SYM
ejpam-5605	162	1	z	z	X
ejpam-5605	162	2	}	}	PUNCT
ejpam-5605	162	3	is	be	AUX
ejpam-5605	162	4	unbounded	unbounded	ADJ
ejpam-5605	162	5	for	for	ADP
ejpam-5605	162	6	some	some	DET
ejpam-5605	162	7	measurable	measurable	ADJ
ejpam-5605	162	8	function	function	NOUN
ejpam-5605	162	9	κ	κ	PROPN
ejpam-5605	162	10	:	:	PUNCT
ejpam-5605	162	11	ω	ω	PROPN
ejpam-5605	162	12	→	→	SYM
ejpam-5605	162	13	g	g	NOUN
ejpam-5605	162	14	with	with	ADP
ejpam-5605	162	15	µ(ω	µ(ω	NOUN
ejpam-5605	162	16	)	)	PUNCT
ejpam-5605	162	17	∈	∈	PROPN
ejpam-5605	162	18	(	(	PUNCT
ejpam-5605	162	19	0	0	NUM
ejpam-5605	162	20	,	,	PUNCT
ejpam-5605	162	21	1	1	NUM
ejpam-5605	162	22	)	)	PUNCT
ejpam-5605	162	23	on	on	ADP
ejpam-5605	162	24	ω	ω	PROPN
ejpam-5605	162	25	.	.	PUNCT
ejpam-5605	163	1	lemma	lemma	PROPN
ejpam-5605	163	2	6	6	NUM
ejpam-5605	163	3	.	.	PUNCT
ejpam-5605	164	1	[	[	X
ejpam-5605	164	2	5	5	NUM
ejpam-5605	164	3	,	,	PUNCT
ejpam-5605	164	4	corollary	corollary	ADJ
ejpam-5605	164	5	2.1	2.1	NUM
ejpam-5605	164	6	.	.	PUNCT
ejpam-5605	164	7	]	]	PUNCT
ejpam-5605	165	1	let	let	VERB
ejpam-5605	165	2	αl	αl	ADP
ejpam-5605	165	3	>	>	X
ejpam-5605	165	4	0	0	PROPN
ejpam-5605	165	5	,	,	PUNCT
ejpam-5605	165	6	l	l	NOUN
ejpam-5605	165	7	=	=	SYM
ejpam-5605	165	8	1	1	NUM
ejpam-5605	165	9	,	,	PUNCT
ejpam-5605	165	10	n	n	CCONJ
ejpam-5605	165	11	,	,	PUNCT
ejpam-5605	165	12	n	n	CCONJ
ejpam-5605	165	13	∈	∈	PROPN
ejpam-5605	165	14	n	n	NOUN
ejpam-5605	165	15	and	and	CCONJ
ejpam-5605	165	16	ψ	ψ	X
ejpam-5605	166	1	∈	∈	PROPN
ejpam-5605	166	2	s1+(i	s1+(i	PROPN
ejpam-5605	166	3	,	,	PUNCT
ejpam-5605	166	4	r	r	NOUN
ejpam-5605	166	5	)	)	PUNCT
ejpam-5605	166	6	.	.	PUNCT
ejpam-5605	167	1	assume	assume	VERB
ejpam-5605	167	2	that	that	SCONJ
ejpam-5605	167	3	(	(	PUNCT
ejpam-5605	167	4	i	i	NOUN
ejpam-5605	167	5	)	)	PUNCT
ejpam-5605	167	6	the	the	DET
ejpam-5605	167	7	functions	function	NOUN
ejpam-5605	167	8	gl	gl	X
ejpam-5605	167	9	are	be	AUX
ejpam-5605	167	10	the	the	DET
ejpam-5605	167	11	bounded	bounded	ADJ
ejpam-5605	167	12	and	and	CCONJ
ejpam-5605	167	13	monotonic	monotonic	ADJ
ejpam-5605	167	14	increasing	increase	VERB
ejpam-5605	167	15	functions	function	NOUN
ejpam-5605	167	16	on	on	ADP
ejpam-5605	167	17	[	[	X
ejpam-5605	167	18	a	a	DET
ejpam-5605	167	19	,	,	PUNCT
ejpam-5605	167	20	b	b	NOUN
ejpam-5605	167	21	)	)	PUNCT
ejpam-5605	167	22	,	,	PUNCT
ejpam-5605	167	23	(	(	PUNCT
ejpam-5605	167	24	ii	ii	NOUN
ejpam-5605	167	25	)	)	PUNCT
ejpam-5605	167	26	s	s	PART
ejpam-5605	167	27	and	and	CCONJ
ejpam-5605	167	28	u	u	NOUN
ejpam-5605	167	29	are	be	AUX
ejpam-5605	167	30	nonnegative	nonnegative	ADJ
ejpam-5605	167	31	functions	function	NOUN
ejpam-5605	167	32	locally	locally	ADV
ejpam-5605	167	33	integrable	integrable	ADJ
ejpam-5605	167	34	on	on	ADP
ejpam-5605	167	35	[	[	X
ejpam-5605	167	36	a	a	DET
ejpam-5605	167	37	,	,	PUNCT
ejpam-5605	167	38	b	b	NOUN
ejpam-5605	167	39	)	)	PUNCT
ejpam-5605	167	40	.	.	PUNCT
ejpam-5605	168	1	(	(	PUNCT
ejpam-5605	168	2	iii	iii	X
ejpam-5605	168	3	)	)	PUNCT
ejpam-5605	168	4	u(ξ	u(ξ	NOUN
ejpam-5605	168	5	)	)	PUNCT
ejpam-5605	168	6	is	be	AUX
ejpam-5605	168	7	a	a	DET
ejpam-5605	168	8	nondecreasing	nondecreasing	ADJ
ejpam-5605	168	9	function	function	NOUN
ejpam-5605	168	10	for	for	ADP
ejpam-5605	168	11	ξ	ξ	PROPN
ejpam-5605	168	12	∈	∈	PROPN
ejpam-5605	168	13	[	[	X
ejpam-5605	168	14	a	a	X
ejpam-5605	168	15	,	,	PUNCT
ejpam-5605	168	16	b	b	NOUN
ejpam-5605	168	17	)	)	PUNCT
ejpam-5605	168	18	,	,	PUNCT
ejpam-5605	168	19	if	if	SCONJ
ejpam-5605	168	20	s(ξ	s(ξ	PROPN
ejpam-5605	168	21	)	)	PUNCT
ejpam-5605	168	22	≤	≤	NOUN
ejpam-5605	168	23	u(ξ	u(ξ	NOUN
ejpam-5605	168	24	)	)	PUNCT
ejpam-5605	168	25	+	+	NUM
ejpam-5605	168	26	n∑	n∑	ADJ
ejpam-5605	168	27	l=1	l=1	NOUN
ejpam-5605	168	28	gl(ξ	gl(ξ	NOUN
ejpam-5605	168	29	)	)	PUNCT
ejpam-5605	168	30	∫	∫	PROPN
ejpam-5605	169	1	ξ	ξ	PROPN
ejpam-5605	169	2	a	a	DET
ejpam-5605	169	3	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	169	4	,	,	PUNCT
ejpam-5605	169	5	s)αl−1s(s)ψ′(s)ds	s)αl−1s(s)ψ′(s)ds	PROPN
ejpam-5605	169	6	,	,	PUNCT
ejpam-5605	169	7	(	(	PUNCT
ejpam-5605	169	8	5	5	NUM
ejpam-5605	169	9	)	)	PUNCT
ejpam-5605	169	10	then	then	ADV
ejpam-5605	169	11	s(ξ	s(ξ	NUM
ejpam-5605	169	12	)	)	PUNCT
ejpam-5605	169	13	≤	≤	NOUN
ejpam-5605	169	14	u(ξ	u(ξ	NOUN
ejpam-5605	169	15	)	)	PUNCT
ejpam-5605	169	16	n∑	n∑	NOUN
ejpam-5605	169	17	l=0	l=0	PROPN
ejpam-5605	169	18	eαl	eαl	VERB
ejpam-5605	169	19	(	(	PUNCT
ejpam-5605	169	20	gl(ξ)γ(αl)ϕ(ξ	gl(ξ)γ(αl)ϕ(ξ	PROPN
ejpam-5605	169	21	,	,	PUNCT
ejpam-5605	169	22	a	a	PRON
ejpam-5605	169	23	)	)	PUNCT
ejpam-5605	169	24	αl	αl	ADP
ejpam-5605	169	25	)	)	PUNCT
ejpam-5605	169	26	.	.	PUNCT
ejpam-5605	170	1	lemma	lemma	PROPN
ejpam-5605	170	2	7	7	X
ejpam-5605	170	3	.	.	PUNCT
ejpam-5605	171	1	let	let	VERB
ejpam-5605	171	2	ψ	ψ	PRON
ejpam-5605	171	3	∈	∈	PROPN
ejpam-5605	171	4	s1+(i	s1+(i	PROPN
ejpam-5605	171	5	,	,	PUNCT
ejpam-5605	171	6	r	r	NOUN
ejpam-5605	171	7	)	)	PUNCT
ejpam-5605	171	8	,	,	PUNCT
ejpam-5605	171	9	γ	γ	X
ejpam-5605	171	10	>	>	X
ejpam-5605	171	11	0	0	NUM
ejpam-5605	171	12	,	,	PUNCT
ejpam-5605	171	13	1	1	NUM
ejpam-5605	171	14	<	<	X
ejpam-5605	171	15	ϑi	ϑi	X
ejpam-5605	171	16	<	<	X
ejpam-5605	171	17	2	2	NUM
ejpam-5605	171	18	,	,	PUNCT
ejpam-5605	171	19	ϖi	ϖi	VERB
ejpam-5605	171	20	>	>	X
ejpam-5605	171	21	0	0	PUNCT
ejpam-5605	172	1	and	and	CCONJ
ejpam-5605	172	2	a	a	DET
ejpam-5605	172	3	constant	constant	ADJ
ejpam-5605	172	4	random	random	ADJ
ejpam-5605	172	5	variable	variable	NOUN
ejpam-5605	172	6	ϱi	ϱi	NOUN
ejpam-5605	172	7	,	,	PUNCT
ejpam-5605	172	8	j	j	PROPN
ejpam-5605	172	9	:	:	PUNCT
ejpam-5605	172	10	ω	ω	X
ejpam-5605	172	11	→	→	PUNCT
ejpam-5605	173	1	[	[	X
ejpam-5605	173	2	0,∞	0,∞	NOUN
ejpam-5605	173	3	)	)	PUNCT
ejpam-5605	173	4	,	,	PUNCT
ejpam-5605	173	5	i	i	PRON
ejpam-5605	173	6	,	,	PUNCT
ejpam-5605	173	7	j	j	PROPN
ejpam-5605	173	8	=	=	SYM
ejpam-5605	173	9	1	1	NUM
ejpam-5605	173	10	,	,	PUNCT
ejpam-5605	173	11	2	2	NUM
ejpam-5605	173	12	.	.	PUNCT
ejpam-5605	174	1	then	then	ADV
ejpam-5605	174	2	ℵi	ℵi	PROPN
ejpam-5605	174	3	,	,	PUNCT
ejpam-5605	174	4	j(γ	j(γ	PROPN
ejpam-5605	174	5	,	,	PUNCT
ejpam-5605	174	6	ω	ω	NOUN
ejpam-5605	174	7	)	)	PUNCT
ejpam-5605	174	8	:	:	PUNCT
ejpam-5605	175	1	=	=	SYM
ejpam-5605	175	2	sup	sup	NUM
ejpam-5605	175	3	ξ∈i	ξ∈i	NUM
ejpam-5605	175	4	4eϖiϕ(b	4eϖiϕ(b	NUM
ejpam-5605	175	5	,	,	PUNCT
ejpam-5605	175	6	a)ϱi	a)ϱi	PROPN
ejpam-5605	175	7	,	,	PUNCT
ejpam-5605	175	8	j(ω	j(ω	PROPN
ejpam-5605	175	9	)	)	PUNCT
ejpam-5605	175	10	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	175	11	−	−	NOUN
ejpam-5605	175	12	1	1	NUM
ejpam-5605	175	13	)	)	PUNCT
ejpam-5605	175	14	∫	∫	PROPN
ejpam-5605	176	1	ξ	ξ	PROPN
ejpam-5605	176	2	a	a	DET
ejpam-5605	176	3	ψ′(s)ϕ(s	ψ′(s)ϕ(s	PROPN
ejpam-5605	176	4	,	,	PUNCT
ejpam-5605	176	5	a)ϑi−1e−γ(ξ−s)ds	a)ϑi−1e−γ(ξ−s)ds	ADV
ejpam-5605	176	6	−−−−→	−−−−→	X
ejpam-5605	176	7	0	0	NUM
ejpam-5605	177	1	γ→+∞	γ→+∞	NOUN
ejpam-5605	177	2	,	,	PUNCT
ejpam-5605	177	3	i	i	PRON
ejpam-5605	177	4	,	,	PUNCT
ejpam-5605	177	5	j	j	PROPN
ejpam-5605	177	6	=	=	SYM
ejpam-5605	177	7	1	1	NUM
ejpam-5605	177	8	,	,	PUNCT
ejpam-5605	177	9	2	2	NUM
ejpam-5605	177	10	,	,	PUNCT
ejpam-5605	177	11	(	(	PUNCT
ejpam-5605	177	12	6	6	X
ejpam-5605	177	13	)	)	PUNCT
ejpam-5605	177	14	proof	proof	NOUN
ejpam-5605	177	15	.	.	PUNCT
ejpam-5605	178	1	from	from	ADP
ejpam-5605	178	2	ϕ	ϕ	PROPN
ejpam-5605	178	3	(	(	PUNCT
ejpam-5605	178	4	·	·	PUNCT
ejpam-5605	178	5	,	,	PUNCT
ejpam-5605	178	6	a)ϑi−1ψ′	a)ϑi−1ψ′	PROPN
ejpam-5605	178	7	(	(	PUNCT
ejpam-5605	178	8	·	·	PUNCT
ejpam-5605	178	9	)	)	PUNCT
ejpam-5605	178	10	∈	∈	PROPN
ejpam-5605	178	11	l1(i	l1(i	PROPN
ejpam-5605	178	12	,	,	PUNCT
ejpam-5605	178	13	r	r	NOUN
ejpam-5605	178	14	)	)	PUNCT
ejpam-5605	178	15	,	,	PUNCT
ejpam-5605	178	16	i	i	PRON
ejpam-5605	178	17	=	=	NOUN
ejpam-5605	178	18	1	1	NUM
ejpam-5605	178	19	,	,	PUNCT
ejpam-5605	178	20	2	2	NUM
ejpam-5605	178	21	.	.	PUNCT
ejpam-5605	179	1	so	so	ADV
ejpam-5605	179	2	,	,	PUNCT
ejpam-5605	179	3	there	there	PRON
ejpam-5605	179	4	exists	exist	VERB
ejpam-5605	179	5	ℏ	ℏ	PROPN
ejpam-5605	179	6	∈	∈	PROPN
ejpam-5605	179	7	c(i	c(i	NOUN
ejpam-5605	179	8	,	,	PUNCT
ejpam-5605	179	9	r	r	NOUN
ejpam-5605	179	10	)	)	PUNCT
ejpam-5605	179	11	such	such	ADJ
ejpam-5605	179	12	that∫	that∫	NOUN
ejpam-5605	179	13	ξ	ξ	X
ejpam-5605	179	14	a	a	DET
ejpam-5605	179	15	∣∣∣ϕ(s	∣∣∣ϕ(s	NOUN
ejpam-5605	179	16	,	,	PUNCT
ejpam-5605	179	17	a)ϑi−1ψ′(s)−	a)ϑi−1ψ′(s)−	VERB
ejpam-5605	179	18	ℏ(s	ℏ(s	NOUN
ejpam-5605	179	19	)	)	PUNCT
ejpam-5605	179	20	∣∣∣	∣∣∣	NOUN
ejpam-5605	179	21	ds	ds	X
ejpam-5605	179	22	<	<	X
ejpam-5605	179	23	1	1	NUM
ejpam-5605	179	24	2	2	NUM
ejpam-5605	179	25	ϵ.	ϵ.	NOUN
ejpam-5605	179	26	hence	hence	ADV
ejpam-5605	179	27	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-5605	179	28	ξ	ξ	ADP
ejpam-5605	179	29	a	a	DET
ejpam-5605	179	30	ϕ(s	ϕ(s	PROPN
ejpam-5605	179	31	,	,	PUNCT
ejpam-5605	179	32	a)ϑi−1ψ′(s)e−γ(ξ−s)ds	a)ϑi−1ψ′(s)e−γ(ξ−s)ds	PROPN
ejpam-5605	179	33	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5605	179	34	≤	≤	NUM
ejpam-5605	179	35	∫	∫	PROPN
ejpam-5605	179	36	ξ	ξ	X
ejpam-5605	179	37	a	a	DET
ejpam-5605	179	38	∣∣∣ϕ(s	∣∣∣ϕ(s	NOUN
ejpam-5605	179	39	,	,	PUNCT
ejpam-5605	179	40	a)ϑi−1ψ′(s)−	a)ϑi−1ψ′(s)−	VERB
ejpam-5605	179	41	ℏ(s	ℏ(s	NOUN
ejpam-5605	179	42	)	)	PUNCT
ejpam-5605	179	43	∣∣∣	∣∣∣	ADJ
ejpam-5605	179	44	e−γ(ξ−s)ds+	e−γ(ξ−s)ds+	PROPN
ejpam-5605	179	45	∫	∫	PROPN
ejpam-5605	180	1	ξ	ξ	PROPN
ejpam-5605	180	2	a	a	DET
ejpam-5605	180	3	|ℏ(s)|e−γ(ξ−s)ds	|ℏ(s)|e−γ(ξ−s)ds	PROPN
ejpam-5605	180	4	≤	≤	NOUN
ejpam-5605	180	5	ϵ	ϵ	ADP
ejpam-5605	180	6	2	2	NUM
ejpam-5605	180	7	+	+	SYM
ejpam-5605	180	8	1−	1−	NUM
ejpam-5605	180	9	e−γ(b−a	e−γ(b−a	NUM
ejpam-5605	180	10	)	)	PUNCT
ejpam-5605	180	11	γ	γ	NOUN
ejpam-5605	180	12	∥ℏ∥∞	∥ℏ∥∞	NUM
ejpam-5605	180	13	,	,	PUNCT
ejpam-5605	180	14	i	i	PRON
ejpam-5605	180	15	=	=	NOUN
ejpam-5605	180	16	1	1	NUM
ejpam-5605	180	17	,	,	PUNCT
ejpam-5605	180	18	2	2	NUM
ejpam-5605	180	19	,	,	PUNCT
ejpam-5605	180	20	m.	m.	NOUN
ejpam-5605	180	21	ziane	ziane	PROPN
ejpam-5605	180	22	et	et	PROPN
ejpam-5605	180	23	al	al	PROPN
ejpam-5605	180	24	.	.	PUNCT
ejpam-5605	180	25	/	/	SYM
ejpam-5605	180	26	eur	eur	PROPN
ejpam-5605	180	27	.	.	PUNCT
ejpam-5605	181	1	j.	j.	PROPN
ejpam-5605	181	2	pure	pure	PROPN
ejpam-5605	181	3	appl	appl	PROPN
ejpam-5605	181	4	.	.	PROPN
ejpam-5605	181	5	math	math	PROPN
ejpam-5605	181	6	,	,	PUNCT
ejpam-5605	181	7	18	18	NUM
ejpam-5605	181	8	(	(	PUNCT
ejpam-5605	181	9	1	1	NUM
ejpam-5605	181	10	)	)	PUNCT
ejpam-5605	181	11	(	(	PUNCT
ejpam-5605	181	12	2025	2025	NUM
ejpam-5605	181	13	)	)	PUNCT
ejpam-5605	181	14	,	,	PUNCT
ejpam-5605	181	15	5605	5605	NUM
ejpam-5605	181	16	8	8	NUM
ejpam-5605	181	17	of	of	ADP
ejpam-5605	181	18	21	21	NUM
ejpam-5605	181	19	consequently	consequently	ADV
ejpam-5605	181	20	,	,	PUNCT
ejpam-5605	181	21	∫	∫	PROPN
ejpam-5605	181	22	ξ	ξ	PROPN
ejpam-5605	181	23	a	a	DET
ejpam-5605	181	24	ψ′(s)ϕ(s	ψ′(s)ϕ(s	PROPN
ejpam-5605	181	25	,	,	PUNCT
ejpam-5605	181	26	a)ϑi−1e−γ(ξ−s)ds	a)ϑi−1e−γ(ξ−s)ds	ADV
ejpam-5605	181	27	−→	−→	ADV
ejpam-5605	181	28	0	0	NUM
ejpam-5605	181	29	as	as	ADP
ejpam-5605	181	30	γ	γ	X
ejpam-5605	181	31	−→	−→	NOUN
ejpam-5605	181	32	+	+	PROPN
ejpam-5605	181	33	∞	∞	PROPN
ejpam-5605	181	34	,	,	PUNCT
ejpam-5605	181	35	i	i	PRON
ejpam-5605	181	36	=	=	NOUN
ejpam-5605	181	37	1	1	NUM
ejpam-5605	181	38	,	,	PUNCT
ejpam-5605	181	39	2	2	NUM
ejpam-5605	181	40	.	.	PUNCT
ejpam-5605	182	1	this	this	PRON
ejpam-5605	182	2	completes	complete	VERB
ejpam-5605	182	3	the	the	DET
ejpam-5605	182	4	proof	proof	NOUN
ejpam-5605	182	5	of	of	ADP
ejpam-5605	182	6	the	the	DET
ejpam-5605	182	7	lemma	lemma	PROPN
ejpam-5605	182	8	.	.	PROPN
ejpam-5605	183	1	3	3	X
ejpam-5605	183	2	.	.	X
ejpam-5605	183	3	main	main	ADJ
ejpam-5605	183	4	results	result	NOUN
ejpam-5605	183	5	our	our	PRON
ejpam-5605	183	6	first	first	ADJ
ejpam-5605	183	7	result	result	NOUN
ejpam-5605	183	8	establishes	establish	VERB
ejpam-5605	183	9	the	the	DET
ejpam-5605	183	10	existence	existence	NOUN
ejpam-5605	183	11	and	and	CCONJ
ejpam-5605	183	12	uniqueness	uniqueness	NOUN
ejpam-5605	183	13	result	result	NOUN
ejpam-5605	183	14	for	for	ADP
ejpam-5605	183	15	the	the	DET
ejpam-5605	183	16	system	system	NOUN
ejpam-5605	183	17	(	(	PUNCT
ejpam-5605	183	18	1	1	NUM
ejpam-5605	183	19	)	)	PUNCT
ejpam-5605	183	20	,	,	PUNCT
ejpam-5605	183	21	where	where	SCONJ
ejpam-5605	183	22	perov	perov	PROPN
ejpam-5605	183	23	’s	’s	PART
ejpam-5605	183	24	fixed	fix	VERB
ejpam-5605	183	25	-	-	PUNCT
ejpam-5605	183	26	point	point	NOUN
ejpam-5605	183	27	principle	principle	NOUN
ejpam-5605	183	28	is	be	AUX
ejpam-5605	183	29	applied	apply	VERB
ejpam-5605	183	30	.	.	PUNCT
ejpam-5605	184	1	theorem	theorem	NOUN
ejpam-5605	184	2	3	3	X
ejpam-5605	184	3	.	.	PUNCT
ejpam-5605	184	4	suppose	suppose	VERB
ejpam-5605	184	5	that	that	SCONJ
ejpam-5605	184	6	(	(	PUNCT
ejpam-5605	184	7	a1	a1	PROPN
ejpam-5605	184	8	)	)	PUNCT
ejpam-5605	184	9	the	the	DET
ejpam-5605	184	10	functions	function	NOUN
ejpam-5605	184	11	fi	fi	NOUN
ejpam-5605	184	12	are	be	AUX
ejpam-5605	184	13	random	random	ADJ
ejpam-5605	184	14	carathéodory	carathéodory	NOUN
ejpam-5605	184	15	on	on	ADP
ejpam-5605	184	16	i×g×g×	i×g×g×	PROPN
ejpam-5605	184	17	ω	ω	PROPN
ejpam-5605	184	18	.	.	PUNCT
ejpam-5605	185	1	(	(	PUNCT
ejpam-5605	185	2	a2	a2	PROPN
ejpam-5605	185	3	)	)	PUNCT
ejpam-5605	185	4	there	there	PRON
ejpam-5605	185	5	exists	exist	VERB
ejpam-5605	185	6	random	random	ADJ
ejpam-5605	185	7	variables	variable	NOUN
ejpam-5605	185	8	φi	φi	ADP
ejpam-5605	185	9	,	,	PUNCT
ejpam-5605	185	10	j	j	PROPN
ejpam-5605	185	11	:	:	PUNCT
ejpam-5605	185	12	ω	ω	PROPN
ejpam-5605	185	13	→	→	SYM
ejpam-5605	185	14	(	(	PUNCT
ejpam-5605	185	15	0,∞	0,∞	NUM
ejpam-5605	185	16	)	)	PUNCT
ejpam-5605	185	17	;	;	PUNCT
ejpam-5605	186	1	i	i	PRON
ejpam-5605	186	2	,	,	PUNCT
ejpam-5605	186	3	j	j	PROPN
ejpam-5605	186	4	=	=	SYM
ejpam-5605	186	5	1	1	NUM
ejpam-5605	186	6	,	,	PUNCT
ejpam-5605	186	7	2	2	NUM
ejpam-5605	186	8	such	such	ADJ
ejpam-5605	186	9	that	that	SCONJ
ejpam-5605	186	10	:	:	PUNCT
ejpam-5605	186	11	∥fi(ξ	∥fi(ξ	ADJ
ejpam-5605	186	12	,	,	PUNCT
ejpam-5605	186	13	u1	u1	NOUN
ejpam-5605	186	14	,	,	PUNCT
ejpam-5605	186	15	u2	u2	PROPN
ejpam-5605	186	16	,	,	PUNCT
ejpam-5605	186	17	ω)−	ω)−	PROPN
ejpam-5605	186	18	fi(ξ	fi(ξ	PART
ejpam-5605	186	19	,	,	PUNCT
ejpam-5605	186	20	v1	v1	NOUN
ejpam-5605	186	21	,	,	PUNCT
ejpam-5605	186	22	v2	v2	PROPN
ejpam-5605	186	23	,	,	PUNCT
ejpam-5605	186	24	ω)∥	ω)∥	PUNCT
ejpam-5605	186	25	≤	≤	NUM
ejpam-5605	186	26	φi,1(ω)∥u1	φi,1(ω)∥u1	PROPN
ejpam-5605	186	27	−	−	PROPN
ejpam-5605	186	28	v1∥+φi,2(ω)∥u2	v1∥+φi,2(ω)∥u2	NOUN
ejpam-5605	186	29	−	−	PROPN
ejpam-5605	186	30	v2∥	v2∥	PROPN
ejpam-5605	186	31	,	,	PUNCT
ejpam-5605	186	32	i	i	NOUN
ejpam-5605	186	33	=	=	NOUN
ejpam-5605	186	34	1	1	NUM
ejpam-5605	186	35	,	,	PUNCT
ejpam-5605	186	36	2	2	NUM
ejpam-5605	186	37	,	,	PUNCT
ejpam-5605	186	38	for	for	ADP
ejpam-5605	186	39	u1	u1	NOUN
ejpam-5605	186	40	,	,	PUNCT
ejpam-5605	186	41	u2	u2	NOUN
ejpam-5605	186	42	,	,	PUNCT
ejpam-5605	186	43	v1	v1	NOUN
ejpam-5605	186	44	,	,	PUNCT
ejpam-5605	186	45	v2	v2	PROPN
ejpam-5605	186	46	∈	∈	PROPN
ejpam-5605	186	47	g	g	NOUN
ejpam-5605	186	48	,	,	PUNCT
ejpam-5605	186	49	(	(	PUNCT
ejpam-5605	186	50	ξ	ξ	X
ejpam-5605	186	51	,	,	PUNCT
ejpam-5605	186	52	ω	ω	NOUN
ejpam-5605	186	53	)	)	PUNCT
ejpam-5605	186	54	∈	∈	PROPN
ejpam-5605	186	55	i×	i×	PROPN
ejpam-5605	187	1	ω	ω	PROPN
ejpam-5605	187	2	.	.	PUNCT
ejpam-5605	188	1	then	then	ADV
ejpam-5605	188	2	,	,	PUNCT
ejpam-5605	188	3	system	system	NOUN
ejpam-5605	188	4	(	(	PUNCT
ejpam-5605	188	5	1	1	X
ejpam-5605	188	6	)	)	PUNCT
ejpam-5605	188	7	admits	admit	VERB
ejpam-5605	188	8	a	a	DET
ejpam-5605	188	9	unique	unique	ADJ
ejpam-5605	188	10	random	random	ADJ
ejpam-5605	188	11	solution	solution	NOUN
ejpam-5605	188	12	.	.	PUNCT
ejpam-5605	189	1	proof	proof	NOUN
ejpam-5605	189	2	.	.	PUNCT
ejpam-5605	190	1	firstly	firstly	ADV
ejpam-5605	190	2	,	,	PUNCT
ejpam-5605	190	3	endowing	endow	VERB
ejpam-5605	190	4	the	the	DET
ejpam-5605	190	5	product	product	NOUN
ejpam-5605	190	6	banach	banach	NOUN
ejpam-5605	190	7	space	space	NOUN
ejpam-5605	190	8	j	j	PROPN
ejpam-5605	190	9	=	=	PUNCT
ejpam-5605	190	10	c(i	c(i	PROPN
ejpam-5605	190	11	,	,	PUNCT
ejpam-5605	190	12	g	g	NOUN
ejpam-5605	190	13	)	)	PUNCT
ejpam-5605	190	14	×	×	NOUN
ejpam-5605	190	15	c(i	c(i	NOUN
ejpam-5605	190	16	,	,	PUNCT
ejpam-5605	190	17	g	g	NOUN
ejpam-5605	190	18	)	)	PUNCT
ejpam-5605	190	19	by	by	ADP
ejpam-5605	190	20	the	the	DET
ejpam-5605	190	21	vector	vector	NOUN
ejpam-5605	190	22	-	-	PUNCT
ejpam-5605	190	23	norm	norm	NOUN
ejpam-5605	190	24	∥(z1	∥(z1	NOUN
ejpam-5605	190	25	,	,	PUNCT
ejpam-5605	190	26	z2)∥j	z2)∥j	PROPN
ejpam-5605	190	27	=	=	PUNCT
ejpam-5605	190	28	(	(	PUNCT
ejpam-5605	190	29	∥z1∥∞	∥z1∥∞	X
ejpam-5605	190	30	∥z2∥∞	∥z2∥∞	X
ejpam-5605	190	31	)	)	PUNCT
ejpam-5605	190	32	.	.	PUNCT
ejpam-5605	191	1	(	(	PUNCT
ejpam-5605	191	2	7	7	X
ejpam-5605	191	3	)	)	PUNCT
ejpam-5605	191	4	next	next	ADV
ejpam-5605	191	5	,	,	PUNCT
ejpam-5605	191	6	according	accord	VERB
ejpam-5605	191	7	to	to	ADP
ejpam-5605	191	8	[	[	X
ejpam-5605	191	9	13	13	NUM
ejpam-5605	191	10	,	,	PUNCT
ejpam-5605	191	11	theorem	theorem	VERB
ejpam-5605	191	12	3.1	3.1	NUM
ejpam-5605	191	13	]	]	PUNCT
ejpam-5605	191	14	,	,	PUNCT
ejpam-5605	191	15	system	system	NOUN
ejpam-5605	191	16	(	(	PUNCT
ejpam-5605	191	17	1	1	X
ejpam-5605	191	18	)	)	PUNCT
ejpam-5605	191	19	is	be	AUX
ejpam-5605	191	20	equivalent	equivalent	ADJ
ejpam-5605	191	21	to	to	ADP
ejpam-5605	191	22	the	the	DET
ejpam-5605	191	23	operator	operator	NOUN
ejpam-5605	191	24	equation	equation	NOUN
ejpam-5605	191	25	h(z1	h(z1	NOUN
ejpam-5605	191	26	,	,	PUNCT
ejpam-5605	191	27	z2	z2	PROPN
ejpam-5605	191	28	,	,	PUNCT
ejpam-5605	191	29	ω	ω	NUM
ejpam-5605	191	30	)	)	PUNCT
ejpam-5605	192	1	=	=	SYM
ejpam-5605	192	2	(	(	PUNCT
ejpam-5605	192	3	z1	z1	PROPN
ejpam-5605	192	4	,	,	PUNCT
ejpam-5605	192	5	z2	z2	PROPN
ejpam-5605	192	6	)	)	PUNCT
ejpam-5605	192	7	where	where	SCONJ
ejpam-5605	192	8	h	h	NOUN
ejpam-5605	192	9	:	:	PUNCT
ejpam-5605	192	10	j×	j×	PROPN
ejpam-5605	192	11	ω	ω	PROPN
ejpam-5605	192	12	→	→	SYM
ejpam-5605	192	13	j	j	PROPN
ejpam-5605	192	14	be	be	VERB
ejpam-5605	192	15	the	the	DET
ejpam-5605	192	16	operator	operator	NOUN
ejpam-5605	192	17	given	give	VERB
ejpam-5605	192	18	by	by	ADP
ejpam-5605	192	19	:	:	PUNCT
ejpam-5605	192	20	h(z1(ξ	h(z1(ξ	PROPN
ejpam-5605	192	21	,	,	PUNCT
ejpam-5605	192	22	ω	ω	NOUN
ejpam-5605	192	23	)	)	PUNCT
ejpam-5605	192	24	,	,	PUNCT
ejpam-5605	192	25	z2(ξ	z2(ξ	PROPN
ejpam-5605	192	26	,	,	PUNCT
ejpam-5605	192	27	ω	ω	NOUN
ejpam-5605	192	28	)	)	PUNCT
ejpam-5605	192	29	,	,	PUNCT
ejpam-5605	192	30	ω	ω	X
ejpam-5605	192	31	)	)	PUNCT
ejpam-5605	192	32	=	=	SYM
ejpam-5605	192	33	(	(	PUNCT
ejpam-5605	192	34	h1(z1(ξ	h1(z1(ξ	PROPN
ejpam-5605	192	35	,	,	PUNCT
ejpam-5605	192	36	ω	ω	NOUN
ejpam-5605	192	37	)	)	PUNCT
ejpam-5605	192	38	,	,	PUNCT
ejpam-5605	192	39	z2(ξ	z2(ξ	PROPN
ejpam-5605	192	40	,	,	PUNCT
ejpam-5605	192	41	ω	ω	NOUN
ejpam-5605	192	42	)	)	PUNCT
ejpam-5605	192	43	,	,	PUNCT
ejpam-5605	192	44	ω),h2(z1(ξ	ω),h2(z1(ξ	NOUN
ejpam-5605	192	45	,	,	PUNCT
ejpam-5605	192	46	ω	ω	NOUN
ejpam-5605	192	47	)	)	PUNCT
ejpam-5605	192	48	,	,	PUNCT
ejpam-5605	192	49	z2(ξ	z2(ξ	PROPN
ejpam-5605	192	50	,	,	PUNCT
ejpam-5605	192	51	ω	ω	NOUN
ejpam-5605	192	52	)	)	PUNCT
ejpam-5605	192	53	,	,	PUNCT
ejpam-5605	192	54	ω	ω	NOUN
ejpam-5605	192	55	)	)	PUNCT
ejpam-5605	192	56	)	)	PUNCT
ejpam-5605	192	57	.	.	PUNCT
ejpam-5605	193	1	(	(	PUNCT
ejpam-5605	193	2	8)	8)	NUM
ejpam-5605	193	3	where	where	SCONJ
ejpam-5605	193	4	,	,	PUNCT
ejpam-5605	193	5	hi(z1(ξ	hi(z1(ξ	PROPN
ejpam-5605	193	6	,	,	PUNCT
ejpam-5605	193	7	ω	ω	NOUN
ejpam-5605	193	8	)	)	PUNCT
ejpam-5605	193	9	,	,	PUNCT
ejpam-5605	193	10	z2(ξ	z2(ξ	PROPN
ejpam-5605	193	11	,	,	PUNCT
ejpam-5605	193	12	ω	ω	NOUN
ejpam-5605	193	13	)	)	PUNCT
ejpam-5605	193	14	,	,	PUNCT
ejpam-5605	193	15	ω	ω	X
ejpam-5605	193	16	)	)	PUNCT
ejpam-5605	193	17	=	=	PUNCT
ejpam-5605	194	1	(	(	PUNCT
ejpam-5605	194	2	ϑi	ϑi	NOUN
ejpam-5605	194	3	−	−	PROPN
ejpam-5605	194	4	1	1	NUM
ejpam-5605	194	5	)	)	PUNCT
ejpam-5605	194	6	∫	∫	PROPN
ejpam-5605	195	1	ξ	ξ	PROPN
ejpam-5605	195	2	a	a	DET
ejpam-5605	195	3	e−ϖiϕ(ξ	e−ϖiϕ(ξ	PROPN
ejpam-5605	195	4	,	,	PUNCT
ejpam-5605	195	5	s	s	PART
ejpam-5605	195	6	)	)	PUNCT
ejpam-5605	195	7	(	(	PUNCT
ejpam-5605	195	8	∫	∫	PROPN
ejpam-5605	195	9	s	s	VERB
ejpam-5605	195	10	a	a	DET
ejpam-5605	195	11	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	195	12	,	,	PUNCT
ejpam-5605	195	13	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	195	14	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	195	15	−	−	PROPN
ejpam-5605	195	16	1	1	NUM
ejpam-5605	195	17	)	)	PUNCT
ejpam-5605	195	18	fi(τ	fi(τ	PROPN
ejpam-5605	195	19	,	,	PUNCT
ejpam-5605	195	20	z1(τ	z1(τ	PROPN
ejpam-5605	195	21	,	,	PUNCT
ejpam-5605	195	22	ω	ω	NOUN
ejpam-5605	195	23	)	)	PUNCT
ejpam-5605	195	24	,	,	PUNCT
ejpam-5605	195	25	z2(τ	z2(τ	PROPN
ejpam-5605	195	26	,	,	PUNCT
ejpam-5605	195	27	ω	ω	NOUN
ejpam-5605	195	28	)	)	PUNCT
ejpam-5605	195	29	,	,	PUNCT
ejpam-5605	195	30	ω)dτ	ω)dτ	PROPN
ejpam-5605	195	31	)	)	PUNCT
ejpam-5605	196	1	ψ′(s)ds	ψ′(s)ds	PROPN
ejpam-5605	196	2	,	,	PUNCT
ejpam-5605	196	3	i	i	NOUN
ejpam-5605	196	4	=	=	NOUN
ejpam-5605	196	5	1	1	NUM
ejpam-5605	196	6	,	,	PUNCT
ejpam-5605	196	7	2	2	NUM
ejpam-5605	196	8	.	.	PUNCT
ejpam-5605	196	9	(	(	PUNCT
ejpam-5605	196	10	9	9	NUM
ejpam-5605	196	11	)	)	PUNCT
ejpam-5605	196	12	since	since	SCONJ
ejpam-5605	196	13	the	the	DET
ejpam-5605	196	14	function	function	NOUN
ejpam-5605	196	15	fi	fi	NOUN
ejpam-5605	196	16	,	,	PUNCT
ejpam-5605	196	17	i	i	PRON
ejpam-5605	196	18	=	=	NOUN
ejpam-5605	196	19	1	1	NUM
ejpam-5605	196	20	,	,	PUNCT
ejpam-5605	196	21	2	2	NUM
ejpam-5605	196	22	are	be	AUX
ejpam-5605	196	23	absolutely	absolutely	ADV
ejpam-5605	196	24	continuous	continuous	ADJ
ejpam-5605	196	25	for	for	ADP
ejpam-5605	196	26	all	all	DET
ejpam-5605	196	27	ω	ω	NUM
ejpam-5605	196	28	∈	∈	PROPN
ejpam-5605	196	29	ω	ω	NOUN
ejpam-5605	196	30	and	and	CCONJ
ejpam-5605	196	31	ξ	ξ	PROPN
ejpam-5605	196	32	∈	∈	PROPN
ejpam-5605	197	1	i	i	PRON
ejpam-5605	197	2	,	,	PUNCT
ejpam-5605	197	3	then	then	ADV
ejpam-5605	197	4	(	(	PUNCT
ejpam-5605	197	5	z1	z1	PROPN
ejpam-5605	197	6	,	,	PUNCT
ejpam-5605	197	7	z2	z2	PROPN
ejpam-5605	197	8	)	)	PUNCT
ejpam-5605	197	9	is	be	AUX
ejpam-5605	197	10	a	a	DET
ejpam-5605	197	11	random	random	ADJ
ejpam-5605	197	12	solution	solution	NOUN
ejpam-5605	197	13	for	for	ADP
ejpam-5605	197	14	the	the	DET
ejpam-5605	197	15	problem	problem	NOUN
ejpam-5605	197	16	(	(	PUNCT
ejpam-5605	197	17	1	1	X
ejpam-5605	197	18	)	)	PUNCT
ejpam-5605	197	19	if	if	SCONJ
ejpam-5605	197	20	and	and	CCONJ
ejpam-5605	197	21	only	only	ADV
ejpam-5605	197	22	if	if	SCONJ
ejpam-5605	197	23	(	(	PUNCT
ejpam-5605	197	24	z1	z1	ADJ
ejpam-5605	197	25	,	,	PUNCT
ejpam-5605	197	26	z2	z2	NUM
ejpam-5605	197	27	)	)	PUNCT
ejpam-5605	197	28	=	=	SYM
ejpam-5605	197	29	(	(	PUNCT
ejpam-5605	197	30	h(z1	h(z1	NOUN
ejpam-5605	197	31	,	,	PUNCT
ejpam-5605	197	32	z2))(ξ	z2))(ξ	NOUN
ejpam-5605	197	33	,	,	PUNCT
ejpam-5605	197	34	ω	ω	NUM
ejpam-5605	197	35	)	)	PUNCT
ejpam-5605	197	36	.	.	PUNCT
ejpam-5605	198	1	we	we	PRON
ejpam-5605	198	2	need	need	VERB
ejpam-5605	198	3	to	to	PART
ejpam-5605	198	4	demonstrate	demonstrate	VERB
ejpam-5605	198	5	that	that	SCONJ
ejpam-5605	198	6	the	the	DET
ejpam-5605	198	7	operator	operator	NOUN
ejpam-5605	198	8	h	h	NOUN
ejpam-5605	198	9	is	be	AUX
ejpam-5605	198	10	a	a	DET
ejpam-5605	198	11	contraction	contraction	NOUN
ejpam-5605	198	12	mapping	mapping	NOUN
ejpam-5605	198	13	on	on	ADP
ejpam-5605	198	14	j	j	PROPN
ejpam-5605	198	15	using	use	VERB
ejpam-5605	198	16	bielecki	bielecki	NOUN
ejpam-5605	198	17	’s	’s	PART
ejpam-5605	198	18	vector	vector	NOUN
ejpam-5605	198	19	-	-	PUNCT
ejpam-5605	198	20	norm	norm	NOUN
ejpam-5605	198	21	.	.	PUNCT
ejpam-5605	199	1	m.	m.	NOUN
ejpam-5605	199	2	ziane	ziane	PROPN
ejpam-5605	199	3	et	et	PROPN
ejpam-5605	199	4	al	al	PROPN
ejpam-5605	199	5	.	.	PUNCT
ejpam-5605	199	6	/	/	SYM
ejpam-5605	199	7	eur	eur	PROPN
ejpam-5605	199	8	.	.	PUNCT
ejpam-5605	200	1	j.	j.	PROPN
ejpam-5605	200	2	pure	pure	PROPN
ejpam-5605	200	3	appl	appl	PROPN
ejpam-5605	200	4	.	.	PROPN
ejpam-5605	200	5	math	math	PROPN
ejpam-5605	200	6	,	,	PUNCT
ejpam-5605	200	7	18	18	NUM
ejpam-5605	200	8	(	(	PUNCT
ejpam-5605	200	9	1	1	NUM
ejpam-5605	200	10	)	)	PUNCT
ejpam-5605	200	11	(	(	PUNCT
ejpam-5605	200	12	2025	2025	NUM
ejpam-5605	200	13	)	)	PUNCT
ejpam-5605	200	14	,	,	PUNCT
ejpam-5605	200	15	5605	5605	NUM
ejpam-5605	200	16	9	9	NUM
ejpam-5605	200	17	of	of	ADP
ejpam-5605	200	18	21	21	NUM
ejpam-5605	200	19	step	step	NOUN
ejpam-5605	200	20	1	1	NUM
ejpam-5605	200	21	.	.	PUNCT
ejpam-5605	201	1	h	h	PROPN
ejpam-5605	201	2	is	be	AUX
ejpam-5605	201	3	a	a	DET
ejpam-5605	201	4	random	random	ADJ
ejpam-5605	201	5	operator	operator	NOUN
ejpam-5605	201	6	on	on	ADP
ejpam-5605	201	7	j.	j.	PROPN
ejpam-5605	201	8	using	use	VERB
ejpam-5605	201	9	(	(	PUNCT
ejpam-5605	201	10	a1	a1	PROPN
ejpam-5605	201	11	)	)	PUNCT
ejpam-5605	201	12	,	,	PUNCT
ejpam-5605	201	13	the	the	DET
ejpam-5605	201	14	functions	function	NOUN
ejpam-5605	201	15	ω	ω	X
ejpam-5605	201	16	→	→	SYM
ejpam-5605	201	17	fi(ξ	fi(ξ	PROPN
ejpam-5605	201	18	,	,	PUNCT
ejpam-5605	201	19	z1	z1	NOUN
ejpam-5605	201	20	,	,	PUNCT
ejpam-5605	201	21	z2	z2	PROPN
ejpam-5605	201	22	,	,	PUNCT
ejpam-5605	201	23	ω	ω	NUM
ejpam-5605	201	24	)	)	PUNCT
ejpam-5605	201	25	are	be	AUX
ejpam-5605	201	26	measurable	measurable	ADJ
ejpam-5605	201	27	for	for	ADP
ejpam-5605	201	28	i	i	PROPN
ejpam-5605	201	29	=	=	NOUN
ejpam-5605	201	30	1	1	NUM
ejpam-5605	201	31	,	,	PUNCT
ejpam-5605	201	32	2	2	NUM
ejpam-5605	201	33	.	.	PUNCT
ejpam-5605	202	1	in	in	ADP
ejpam-5605	202	2	view	view	NOUN
ejpam-5605	202	3	of	of	ADP
ejpam-5605	202	4	lemma	lemma	PROPN
ejpam-5605	202	5	4	4	NUM
ejpam-5605	202	6	,	,	PUNCT
ejpam-5605	202	7	the	the	DET
ejpam-5605	202	8	products	product	NOUN
ejpam-5605	202	9	ϕ(s	ϕ(s	PRON
ejpam-5605	202	10	,	,	PUNCT
ejpam-5605	202	11	τ)ϑi−2fi(τ	τ)ϑi−2fi(τ	PROPN
ejpam-5605	202	12	,	,	PUNCT
ejpam-5605	202	13	z1(τ	z1(τ	PROPN
ejpam-5605	202	14	,	,	PUNCT
ejpam-5605	202	15	ω	ω	NOUN
ejpam-5605	202	16	)	)	PUNCT
ejpam-5605	202	17	,	,	PUNCT
ejpam-5605	202	18	z2(τ	z2(τ	PROPN
ejpam-5605	202	19	,	,	PUNCT
ejpam-5605	202	20	ω	ω	NOUN
ejpam-5605	202	21	)	)	PUNCT
ejpam-5605	202	22	,	,	PUNCT
ejpam-5605	202	23	ω	ω	PROPN
ejpam-5605	202	24	)	)	PUNCT
ejpam-5605	202	25	,	,	PUNCT
ejpam-5605	202	26	i	i	PRON
ejpam-5605	202	27	=	=	NOUN
ejpam-5605	202	28	1	1	NUM
ejpam-5605	202	29	,	,	PUNCT
ejpam-5605	202	30	2	2	NUM
ejpam-5605	202	31	,	,	PUNCT
ejpam-5605	202	32	are	be	AUX
ejpam-5605	202	33	again	again	ADV
ejpam-5605	202	34	measurable	measurable	ADJ
ejpam-5605	202	35	.	.	PUNCT
ejpam-5605	203	1	further	far	ADV
ejpam-5605	203	2	,	,	PUNCT
ejpam-5605	203	3	the	the	DET
ejpam-5605	203	4	integral	integral	NOUN
ejpam-5605	203	5	is	be	AUX
ejpam-5605	203	6	a	a	DET
ejpam-5605	203	7	limit	limit	NOUN
ejpam-5605	203	8	of	of	ADP
ejpam-5605	203	9	a	a	DET
ejpam-5605	203	10	finite	finite	ADJ
ejpam-5605	203	11	sum	sum	NOUN
ejpam-5605	203	12	of	of	ADP
ejpam-5605	203	13	measurable	measurable	ADJ
ejpam-5605	203	14	functions	function	NOUN
ejpam-5605	203	15	,	,	PUNCT
ejpam-5605	203	16	therefore	therefore	ADV
ejpam-5605	203	17	,	,	PUNCT
ejpam-5605	203	18	the	the	DET
ejpam-5605	203	19	maps	maps	PROPN
ejpam-5605	203	20	ω	ω	PROPN
ejpam-5605	203	21	→	→	SYM
ejpam-5605	203	22	hi(z1(ξ	hi(z1(ξ	PROPN
ejpam-5605	203	23	,	,	PUNCT
ejpam-5605	203	24	ω	ω	NOUN
ejpam-5605	203	25	)	)	PUNCT
ejpam-5605	203	26	,	,	PUNCT
ejpam-5605	203	27	z2(ξ	z2(ξ	PROPN
ejpam-5605	203	28	,	,	PUNCT
ejpam-5605	203	29	ω	ω	NOUN
ejpam-5605	203	30	)	)	PUNCT
ejpam-5605	203	31	,	,	PUNCT
ejpam-5605	203	32	ω	ω	PROPN
ejpam-5605	203	33	)	)	PUNCT
ejpam-5605	203	34	,	,	PUNCT
ejpam-5605	203	35	i	i	PRON
ejpam-5605	203	36	=	=	NOUN
ejpam-5605	203	37	1	1	NUM
ejpam-5605	203	38	,	,	PUNCT
ejpam-5605	203	39	2	2	NUM
ejpam-5605	203	40	,	,	PUNCT
ejpam-5605	203	41	are	be	AUX
ejpam-5605	203	42	measurable	measurable	ADJ
ejpam-5605	203	43	.	.	PUNCT
ejpam-5605	204	1	accordingly	accordingly	ADV
ejpam-5605	204	2	,	,	PUNCT
ejpam-5605	204	3	h	h	NOUN
ejpam-5605	204	4	is	be	AUX
ejpam-5605	204	5	a	a	DET
ejpam-5605	204	6	random	random	ADJ
ejpam-5605	204	7	operator	operator	NOUN
ejpam-5605	204	8	on	on	ADP
ejpam-5605	204	9	j×	j×	PROPN
ejpam-5605	204	10	ω	ω	PROPN
ejpam-5605	204	11	into	into	ADP
ejpam-5605	204	12	j.	j.	PROPN
ejpam-5605	204	13	step	step	PROPN
ejpam-5605	204	14	2	2	NUM
ejpam-5605	204	15	.	.	PUNCT
ejpam-5605	205	1	h	h	PROPN
ejpam-5605	205	2	is	be	AUX
ejpam-5605	205	3	a	a	DET
ejpam-5605	205	4	contraction	contraction	NOUN
ejpam-5605	205	5	mapping	mapping	NOUN
ejpam-5605	205	6	on	on	ADP
ejpam-5605	205	7	j.	j.	PROPN
ejpam-5605	205	8	for	for	ADP
ejpam-5605	205	9	any	any	DET
ejpam-5605	205	10	ω	ω	PROPN
ejpam-5605	205	11	∈	∈	PROPN
ejpam-5605	205	12	ω	ω	NOUN
ejpam-5605	205	13	and	and	CCONJ
ejpam-5605	205	14	each	each	DET
ejpam-5605	205	15	(	(	PUNCT
ejpam-5605	205	16	z1	z1	PROPN
ejpam-5605	205	17	,	,	PUNCT
ejpam-5605	205	18	z2	z2	PROPN
ejpam-5605	205	19	)	)	PUNCT
ejpam-5605	205	20	,	,	PUNCT
ejpam-5605	205	21	(	(	PUNCT
ejpam-5605	205	22	r1	r1	NOUN
ejpam-5605	205	23	,	,	PUNCT
ejpam-5605	205	24	r2	r2	PROPN
ejpam-5605	205	25	)	)	PUNCT
ejpam-5605	206	1	∈	∈	PROPN
ejpam-5605	206	2	j	j	PROPN
ejpam-5605	206	3	,	,	PUNCT
ejpam-5605	206	4	using	use	VERB
ejpam-5605	206	5	(	(	PUNCT
ejpam-5605	206	6	a2	a2	PROPN
ejpam-5605	206	7	)	)	PUNCT
ejpam-5605	206	8	,	,	PUNCT
ejpam-5605	206	9	we	we	PRON
ejpam-5605	206	10	can	can	AUX
ejpam-5605	206	11	get	get	VERB
ejpam-5605	206	12	∥hi(z1(ξ	∥hi(z1(ξ	ADP
ejpam-5605	206	13	,	,	PUNCT
ejpam-5605	206	14	ω	ω	NOUN
ejpam-5605	206	15	)	)	PUNCT
ejpam-5605	206	16	,	,	PUNCT
ejpam-5605	206	17	z2(ξ	z2(ξ	PROPN
ejpam-5605	206	18	,	,	PUNCT
ejpam-5605	206	19	ω	ω	NOUN
ejpam-5605	206	20	)	)	PUNCT
ejpam-5605	206	21	,	,	PUNCT
ejpam-5605	206	22	ω)−hi(r1(ξ	ω)−hi(r1(ξ	PROPN
ejpam-5605	206	23	,	,	PUNCT
ejpam-5605	206	24	ω	ω	NOUN
ejpam-5605	206	25	)	)	PUNCT
ejpam-5605	206	26	,	,	PUNCT
ejpam-5605	206	27	r2(ξ	r2(ξ	PROPN
ejpam-5605	206	28	,	,	PUNCT
ejpam-5605	206	29	ω	ω	NOUN
ejpam-5605	206	30	)	)	PUNCT
ejpam-5605	206	31	,	,	PUNCT
ejpam-5605	206	32	ω)∥	ω)∥	PUNCT
ejpam-5605	206	33	≤	≤	NOUN
ejpam-5605	206	34	(	(	PUNCT
ejpam-5605	206	35	ϑi	ϑi	NOUN
ejpam-5605	206	36	−	−	PROPN
ejpam-5605	206	37	1	1	NUM
ejpam-5605	206	38	)	)	PUNCT
ejpam-5605	206	39	∫	∫	PROPN
ejpam-5605	207	1	ξ	ξ	PROPN
ejpam-5605	207	2	a	a	DET
ejpam-5605	207	3	ψ′(s)e−ϖiϕ(ξ	ψ′(s)e−ϖiϕ(ξ	ADJ
ejpam-5605	207	4	,	,	PUNCT
ejpam-5605	207	5	s	s	PART
ejpam-5605	207	6	)	)	PUNCT
ejpam-5605	207	7	∫	∫	PROPN
ejpam-5605	207	8	s	s	PROPN
ejpam-5605	207	9	a	a	DET
ejpam-5605	207	10	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	207	11	,	,	PUNCT
ejpam-5605	207	12	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	207	13	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	207	14	−	−	PROPN
ejpam-5605	207	15	1	1	NUM
ejpam-5605	207	16	)	)	PUNCT
ejpam-5605	207	17	∥fi(τ	∥fi(τ	ADJ
ejpam-5605	207	18	,	,	PUNCT
ejpam-5605	207	19	z1(τ	z1(τ	PROPN
ejpam-5605	207	20	,	,	PUNCT
ejpam-5605	207	21	ω	ω	NOUN
ejpam-5605	207	22	)	)	PUNCT
ejpam-5605	207	23	,	,	PUNCT
ejpam-5605	207	24	z2(τ	z2(τ	PROPN
ejpam-5605	207	25	,	,	PUNCT
ejpam-5605	207	26	ω	ω	NOUN
ejpam-5605	207	27	)	)	PUNCT
ejpam-5605	207	28	,	,	PUNCT
ejpam-5605	207	29	ω	ω	X
ejpam-5605	207	30	)	)	PUNCT
ejpam-5605	207	31	−fi(τ	−fi(τ	PROPN
ejpam-5605	207	32	,	,	PUNCT
ejpam-5605	207	33	r1(τ	r1(τ	PROPN
ejpam-5605	207	34	,	,	PUNCT
ejpam-5605	207	35	ω	ω	NOUN
ejpam-5605	207	36	)	)	PUNCT
ejpam-5605	207	37	,	,	PUNCT
ejpam-5605	207	38	r2(τ	r2(τ	PROPN
ejpam-5605	207	39	,	,	PUNCT
ejpam-5605	207	40	ω	ω	NOUN
ejpam-5605	207	41	)	)	PUNCT
ejpam-5605	207	42	,	,	PUNCT
ejpam-5605	208	1	ω)∥dτds	ω)∥dτds	NUM
ejpam-5605	208	2	≤	≤	NUM
ejpam-5605	208	3	2∑	2∑	NUM
ejpam-5605	208	4	j=1	j=1	NOUN
ejpam-5605	208	5	(	(	PUNCT
ejpam-5605	208	6	ϑi	ϑi	NOUN
ejpam-5605	208	7	−	−	PROPN
ejpam-5605	208	8	1	1	NUM
ejpam-5605	208	9	)	)	PUNCT
ejpam-5605	208	10	∫	∫	PROPN
ejpam-5605	209	1	ξ	ξ	PROPN
ejpam-5605	209	2	a	a	DET
ejpam-5605	209	3	ψ′(s)e−ϖiϕ(ξ	ψ′(s)e−ϖiϕ(ξ	ADJ
ejpam-5605	209	4	,	,	PUNCT
ejpam-5605	209	5	s	s	PART
ejpam-5605	209	6	)	)	PUNCT
ejpam-5605	209	7	∫	∫	PROPN
ejpam-5605	209	8	s	s	PROPN
ejpam-5605	209	9	a	a	DET
ejpam-5605	209	10	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	209	11	,	,	PUNCT
ejpam-5605	209	12	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	209	13	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	209	14	−	−	PROPN
ejpam-5605	209	15	1	1	NUM
ejpam-5605	209	16	)	)	PUNCT
ejpam-5605	209	17	φi	φi	ADV
ejpam-5605	209	18	,	,	PUNCT
ejpam-5605	209	19	j(ω)×	j(ω)×	PROPN
ejpam-5605	209	20	∥zj(τ	∥zj(τ	NOUN
ejpam-5605	209	21	,	,	PUNCT
ejpam-5605	209	22	ω)−	ω)−	PROPN
ejpam-5605	209	23	rj(τ	rj(τ	NUM
ejpam-5605	209	24	,	,	PUNCT
ejpam-5605	209	25	ω)∥dτds	ω)∥dτds	NUM
ejpam-5605	209	26	,	,	PUNCT
ejpam-5605	209	27	i	i	PRON
ejpam-5605	209	28	=	=	NOUN
ejpam-5605	209	29	1	1	NUM
ejpam-5605	209	30	,	,	PUNCT
ejpam-5605	209	31	2	2	NUM
ejpam-5605	209	32	.	.	NOUN
ejpam-5605	209	33	which	which	PRON
ejpam-5605	209	34	,	,	PUNCT
ejpam-5605	209	35	by	by	ADP
ejpam-5605	209	36	(	(	PUNCT
ejpam-5605	209	37	3	3	NUM
ejpam-5605	209	38	)	)	PUNCT
ejpam-5605	209	39	,	,	PUNCT
ejpam-5605	209	40	can	can	AUX
ejpam-5605	209	41	be	be	AUX
ejpam-5605	209	42	written	write	VERB
ejpam-5605	209	43	as	as	ADP
ejpam-5605	209	44	∥hi(z1(ξ	∥hi(z1(ξ	PROPN
ejpam-5605	209	45	,	,	PUNCT
ejpam-5605	209	46	ω	ω	NOUN
ejpam-5605	209	47	)	)	PUNCT
ejpam-5605	209	48	,	,	PUNCT
ejpam-5605	209	49	z2(ξ	z2(ξ	PROPN
ejpam-5605	209	50	,	,	PUNCT
ejpam-5605	209	51	ω	ω	NOUN
ejpam-5605	209	52	)	)	PUNCT
ejpam-5605	209	53	,	,	PUNCT
ejpam-5605	209	54	ω)−hi(r1(ξ	ω)−hi(r1(ξ	PROPN
ejpam-5605	209	55	,	,	PUNCT
ejpam-5605	209	56	ω	ω	NOUN
ejpam-5605	209	57	)	)	PUNCT
ejpam-5605	209	58	,	,	PUNCT
ejpam-5605	209	59	r2(ξ	r2(ξ	PROPN
ejpam-5605	209	60	,	,	PUNCT
ejpam-5605	209	61	ω	ω	NOUN
ejpam-5605	209	62	)	)	PUNCT
ejpam-5605	209	63	,	,	PUNCT
ejpam-5605	209	64	ω)∥	ω)∥	PUNCT
ejpam-5605	209	65	≤	≤	NUM
ejpam-5605	210	1	2∑	2∑	NUM
ejpam-5605	210	2	j=1	j=1	NOUN
ejpam-5605	210	3	(	(	PUNCT
ejpam-5605	210	4	ϑi	ϑi	NOUN
ejpam-5605	210	5	−	−	PROPN
ejpam-5605	210	6	1)φi	1)φi	PROPN
ejpam-5605	210	7	,	,	PUNCT
ejpam-5605	210	8	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	210	9	(	(	PUNCT
ejpam-5605	210	10	·	·	PUNCT
ejpam-5605	210	11	,	,	PUNCT
ejpam-5605	210	12	ω)−	ω)−	PROPN
ejpam-5605	210	13	rj	rj	PROPN
ejpam-5605	210	14	(	(	PUNCT
ejpam-5605	210	15	·	·	PUNCT
ejpam-5605	210	16	,	,	PUNCT
ejpam-5605	210	17	ω)∥b×∫	ω)∥b×∫	PROPN
ejpam-5605	210	18	ξ	ξ	PROPN
ejpam-5605	210	19	a	a	DET
ejpam-5605	210	20	ψ′(s)e−ϖiϕ(ξ	ψ′(s)e−ϖiϕ(ξ	ADJ
ejpam-5605	210	21	,	,	PUNCT
ejpam-5605	210	22	s	s	PART
ejpam-5605	210	23	)	)	PUNCT
ejpam-5605	210	24	∫	∫	PROPN
ejpam-5605	210	25	s	s	PROPN
ejpam-5605	210	26	a	a	DET
ejpam-5605	210	27	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	210	28	,	,	PUNCT
ejpam-5605	210	29	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	210	30	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	210	31	−	−	PROPN
ejpam-5605	210	32	1	1	X
ejpam-5605	210	33	)	)	PUNCT
ejpam-5605	210	34	eζϕ(τ	eζϕ(τ	PROPN
ejpam-5605	210	35	,	,	PUNCT
ejpam-5605	210	36	a)dτds	a)dτds	PROPN
ejpam-5605	210	37	,	,	PUNCT
ejpam-5605	210	38	i	i	NOUN
ejpam-5605	210	39	=	=	NOUN
ejpam-5605	210	40	1	1	NUM
ejpam-5605	210	41	,	,	PUNCT
ejpam-5605	210	42	2	2	NUM
ejpam-5605	210	43	.	.	PUNCT
ejpam-5605	210	44	by	by	ADP
ejpam-5605	210	45	lemma	lemma	PROPN
ejpam-5605	210	46	3	3	NUM
ejpam-5605	210	47	,	,	PUNCT
ejpam-5605	210	48	one	one	NOUN
ejpam-5605	210	49	obtains	obtain	VERB
ejpam-5605	210	50	∥hi(z1(ξ	∥hi(z1(ξ	PROPN
ejpam-5605	210	51	,	,	PUNCT
ejpam-5605	210	52	ω	ω	NOUN
ejpam-5605	210	53	)	)	PUNCT
ejpam-5605	210	54	,	,	PUNCT
ejpam-5605	210	55	z2(ξ	z2(ξ	PROPN
ejpam-5605	210	56	,	,	PUNCT
ejpam-5605	210	57	ω	ω	NOUN
ejpam-5605	210	58	)	)	PUNCT
ejpam-5605	210	59	,	,	PUNCT
ejpam-5605	210	60	ω)−hi(r1(ξ	ω)−hi(r1(ξ	PROPN
ejpam-5605	210	61	,	,	PUNCT
ejpam-5605	210	62	ω	ω	NOUN
ejpam-5605	210	63	)	)	PUNCT
ejpam-5605	210	64	,	,	PUNCT
ejpam-5605	210	65	r2(ξ	r2(ξ	PROPN
ejpam-5605	210	66	,	,	PUNCT
ejpam-5605	210	67	ω	ω	NOUN
ejpam-5605	210	68	)	)	PUNCT
ejpam-5605	210	69	,	,	PUNCT
ejpam-5605	210	70	ω)∥	ω)∥	PUNCT
ejpam-5605	210	71	≤	≤	NUM
ejpam-5605	211	1	2∑	2∑	NUM
ejpam-5605	211	2	j=1	j=1	NOUN
ejpam-5605	211	3	(	(	PUNCT
ejpam-5605	211	4	ϑi	ϑi	NOUN
ejpam-5605	211	5	−	−	PROPN
ejpam-5605	211	6	1)φi	1)φi	PROPN
ejpam-5605	211	7	,	,	PUNCT
ejpam-5605	211	8	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	211	9	(	(	PUNCT
ejpam-5605	211	10	·	·	PUNCT
ejpam-5605	211	11	,	,	PUNCT
ejpam-5605	211	12	ω)−	ω)−	PROPN
ejpam-5605	211	13	rj	rj	PROPN
ejpam-5605	211	14	(	(	PUNCT
ejpam-5605	211	15	·	·	PUNCT
ejpam-5605	211	16	,	,	PUNCT
ejpam-5605	211	17	ω)∥b	ω)∥b	NOUN
ejpam-5605	211	18	∫	∫	PROPN
ejpam-5605	211	19	ξ	ξ	PROPN
ejpam-5605	211	20	a	a	DET
ejpam-5605	211	21	ψ′(s	ψ′(s	NOUN
ejpam-5605	211	22	)	)	PUNCT
ejpam-5605	211	23	e−ϖiϕ(ξ	e−ϖiϕ(ξ	PROPN
ejpam-5605	211	24	,	,	PUNCT
ejpam-5605	211	25	s)eζϕ(s	s)eζϕ(s	X
ejpam-5605	211	26	,	,	PUNCT
ejpam-5605	211	27	a	a	PRON
ejpam-5605	211	28	)	)	PUNCT
ejpam-5605	211	29	ζϑi−1	ζϑi−1	PROPN
ejpam-5605	211	30	ds	ds	NOUN
ejpam-5605	211	31	,	,	PUNCT
ejpam-5605	211	32	≤	≤	NUM
ejpam-5605	211	33	2∑	2∑	NUM
ejpam-5605	211	34	j=1	j=1	NOUN
ejpam-5605	211	35	(	(	PUNCT
ejpam-5605	211	36	ϑi	ϑi	NOUN
ejpam-5605	211	37	−	−	PROPN
ejpam-5605	211	38	1)φi	1)φi	PROPN
ejpam-5605	211	39	,	,	PUNCT
ejpam-5605	211	40	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	211	41	(	(	PUNCT
ejpam-5605	211	42	·	·	PUNCT
ejpam-5605	211	43	,	,	PUNCT
ejpam-5605	211	44	ω)−	ω)−	PROPN
ejpam-5605	211	45	rj	rj	PROPN
ejpam-5605	211	46	(	(	PUNCT
ejpam-5605	211	47	·	·	PUNCT
ejpam-5605	211	48	,	,	PUNCT
ejpam-5605	211	49	ω)∥b	ω)∥b	X
ejpam-5605	211	50	e−ϖiψ(ξ)−ζψ(a	e−ϖiψ(ξ)−ζψ(a	PROPN
ejpam-5605	211	51	)	)	PUNCT
ejpam-5605	211	52	(	(	PUNCT
ejpam-5605	212	1	ζ	ζ	PROPN
ejpam-5605	212	2	+	+	PROPN
ejpam-5605	212	3	ϖi)ζϑi−1	ϖi)ζϑi−1	NUM
ejpam-5605	212	4	∫	∫	PROPN
ejpam-5605	212	5	ξ	ξ	PROPN
ejpam-5605	212	6	a	a	DET
ejpam-5605	212	7	ψ′(s)(ζ	ψ′(s)(ζ	ADJ
ejpam-5605	212	8	+	+	NOUN
ejpam-5605	212	9	ϖi)e	ϖi)e	PROPN
ejpam-5605	212	10	(	(	PUNCT
ejpam-5605	212	11	ζ+ϖi)ψ(s)ds	ζ+ϖi)ψ(s)ds	X
ejpam-5605	212	12	=	=	SYM
ejpam-5605	212	13	2∑	2∑	NUM
ejpam-5605	212	14	j=1	j=1	NOUN
ejpam-5605	212	15	(	(	PUNCT
ejpam-5605	212	16	ϑi	ϑi	PROPN
ejpam-5605	212	17	−	−	PROPN
ejpam-5605	212	18	1)e−ϖiψ(ξ)−ζψ(a	1)e−ϖiψ(ξ)−ζψ(a	NUM
ejpam-5605	212	19	)	)	PUNCT
ejpam-5605	212	20	(	(	PUNCT
ejpam-5605	212	21	ζ	ζ	NOUN
ejpam-5605	212	22	+	+	NOUN
ejpam-5605	212	23	ϖi)ζϑi−1	ϖi)ζϑi−1	PUNCT
ejpam-5605	212	24	[	[	PUNCT
ejpam-5605	212	25	e(ζ+ϖi)ψ(ξ	e(ζ+ϖi)ψ(ξ	PROPN
ejpam-5605	212	26	)	)	PUNCT
ejpam-5605	212	27	−	−	PROPN
ejpam-5605	212	28	e(ζ+ϖi)ψ(a	e(ζ+ϖi)ψ(a	PROPN
ejpam-5605	212	29	)	)	PUNCT
ejpam-5605	212	30	]	]	PUNCT
ejpam-5605	213	1	φi	φi	ADP
ejpam-5605	213	2	,	,	PUNCT
ejpam-5605	213	3	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	213	4	(	(	PUNCT
ejpam-5605	213	5	·	·	PUNCT
ejpam-5605	213	6	,	,	PUNCT
ejpam-5605	213	7	ω)−	ω)−	PROPN
ejpam-5605	213	8	rj	rj	PROPN
ejpam-5605	213	9	(	(	PUNCT
ejpam-5605	213	10	·	·	PUNCT
ejpam-5605	213	11	,	,	PUNCT
ejpam-5605	213	12	ω)∥b	ω)∥b	NUM
ejpam-5605	213	13	,	,	PUNCT
ejpam-5605	213	14	i	i	PRON
ejpam-5605	213	15	=	=	NOUN
ejpam-5605	213	16	1	1	NUM
ejpam-5605	213	17	,	,	PUNCT
ejpam-5605	213	18	2	2	NUM
ejpam-5605	213	19	.	.	PUNCT
ejpam-5605	213	20	m.	m.	NOUN
ejpam-5605	213	21	ziane	ziane	PROPN
ejpam-5605	213	22	et	et	PROPN
ejpam-5605	213	23	al	al	PROPN
ejpam-5605	213	24	.	.	PUNCT
ejpam-5605	213	25	/	/	SYM
ejpam-5605	213	26	eur	eur	PROPN
ejpam-5605	213	27	.	.	PUNCT
ejpam-5605	214	1	j.	j.	PROPN
ejpam-5605	214	2	pure	pure	PROPN
ejpam-5605	214	3	appl	appl	PROPN
ejpam-5605	214	4	.	.	PROPN
ejpam-5605	214	5	math	math	PROPN
ejpam-5605	214	6	,	,	PUNCT
ejpam-5605	214	7	18	18	NUM
ejpam-5605	214	8	(	(	PUNCT
ejpam-5605	214	9	1	1	NUM
ejpam-5605	214	10	)	)	PUNCT
ejpam-5605	214	11	(	(	PUNCT
ejpam-5605	214	12	2025	2025	NUM
ejpam-5605	214	13	)	)	PUNCT
ejpam-5605	214	14	,	,	PUNCT
ejpam-5605	214	15	5605	5605	NUM
ejpam-5605	214	16	10	10	NUM
ejpam-5605	214	17	of	of	ADP
ejpam-5605	214	18	21	21	NUM
ejpam-5605	214	19	by	by	ADP
ejpam-5605	214	20	e(ϖi+ζ)ψ(ξ	e(ϖi+ζ)ψ(ξ	PROPN
ejpam-5605	214	21	)	)	PUNCT
ejpam-5605	215	1	−	−	PROPN
ejpam-5605	215	2	e(ϖi+ζ)ψ(a	e(ϖi+ζ)ψ(a	PROPN
ejpam-5605	215	3	)	)	PUNCT
ejpam-5605	215	4	≤	≤	NUM
ejpam-5605	215	5	e(ϖi+ζ)ψ(ξ	e(ϖi+ζ)ψ(ξ	PROPN
ejpam-5605	215	6	)	)	PUNCT
ejpam-5605	215	7	and	and	CCONJ
ejpam-5605	215	8	e−ϖiψ(ξ)−ζψ(a	e−ϖiψ(ξ)−ζψ(a	PROPN
ejpam-5605	215	9	)	)	PUNCT
ejpam-5605	215	10	≤	≤	NOUN
ejpam-5605	215	11	e−(ϖi+ζ)ψ(a	e−(ϖi+ζ)ψ(a	PROPN
ejpam-5605	215	12	)	)	PUNCT
ejpam-5605	215	13	,	,	PUNCT
ejpam-5605	215	14	we	we	PRON
ejpam-5605	215	15	get	get	VERB
ejpam-5605	215	16	∥hi(z1(ξ	∥hi(z1(ξ	ADP
ejpam-5605	215	17	,	,	PUNCT
ejpam-5605	215	18	ω	ω	NOUN
ejpam-5605	215	19	)	)	PUNCT
ejpam-5605	215	20	,	,	PUNCT
ejpam-5605	215	21	z2(ξ	z2(ξ	PROPN
ejpam-5605	215	22	,	,	PUNCT
ejpam-5605	215	23	ω	ω	NOUN
ejpam-5605	215	24	)	)	PUNCT
ejpam-5605	215	25	,	,	PUNCT
ejpam-5605	215	26	ω)−hi(r1(ξ	ω)−hi(r1(ξ	PROPN
ejpam-5605	215	27	,	,	PUNCT
ejpam-5605	215	28	ω	ω	NOUN
ejpam-5605	215	29	)	)	PUNCT
ejpam-5605	215	30	,	,	PUNCT
ejpam-5605	215	31	r2(ξ	r2(ξ	PROPN
ejpam-5605	215	32	,	,	PUNCT
ejpam-5605	215	33	ω	ω	NOUN
ejpam-5605	215	34	)	)	PUNCT
ejpam-5605	215	35	,	,	PUNCT
ejpam-5605	215	36	ω)∥	ω)∥	PUNCT
ejpam-5605	215	37	≤	≤	NUM
ejpam-5605	216	1	2∑	2∑	NUM
ejpam-5605	216	2	j=1	j=1	NOUN
ejpam-5605	216	3	(	(	PUNCT
ejpam-5605	216	4	ϑi	ϑi	NOUN
ejpam-5605	216	5	−	−	PROPN
ejpam-5605	216	6	1)e(ϖi+ζ)ϕ(ξ	1)e(ϖi+ζ)ϕ(ξ	NUM
ejpam-5605	216	7	,	,	PUNCT
ejpam-5605	216	8	a	a	PRON
ejpam-5605	216	9	)	)	PUNCT
ejpam-5605	216	10	(	(	PUNCT
ejpam-5605	216	11	ζ	ζ	PROPN
ejpam-5605	216	12	+	+	PROPN
ejpam-5605	216	13	ϖi)ζϑi−1	ϖi)ζϑi−1	PROPN
ejpam-5605	216	14	φi	φi	PROPN
ejpam-5605	216	15	,	,	PUNCT
ejpam-5605	216	16	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	216	17	(	(	PUNCT
ejpam-5605	216	18	·	·	PUNCT
ejpam-5605	216	19	,	,	PUNCT
ejpam-5605	216	20	ω)−	ω)−	PROPN
ejpam-5605	216	21	rj	rj	PROPN
ejpam-5605	216	22	(	(	PUNCT
ejpam-5605	216	23	·	·	PUNCT
ejpam-5605	216	24	,	,	PUNCT
ejpam-5605	216	25	ω)∥b	ω)∥b	NUM
ejpam-5605	216	26	,	,	PUNCT
ejpam-5605	216	27	i	i	PRON
ejpam-5605	216	28	=	=	NOUN
ejpam-5605	216	29	1	1	NUM
ejpam-5605	216	30	,	,	PUNCT
ejpam-5605	216	31	2	2	NUM
ejpam-5605	216	32	.	.	X
ejpam-5605	216	33	hence	hence	ADV
ejpam-5605	216	34	∥hi(z1	∥hi(z1	X
ejpam-5605	216	35	(	(	PUNCT
ejpam-5605	216	36	·	·	PUNCT
ejpam-5605	216	37	,	,	PUNCT
ejpam-5605	216	38	ω	ω	NOUN
ejpam-5605	216	39	)	)	PUNCT
ejpam-5605	216	40	,	,	PUNCT
ejpam-5605	216	41	z2	z2	PROPN
ejpam-5605	216	42	(	(	PUNCT
ejpam-5605	216	43	·	·	NUM
ejpam-5605	216	44	,	,	PUNCT
ejpam-5605	216	45	ω	ω	NOUN
ejpam-5605	216	46	)	)	PUNCT
ejpam-5605	216	47	,	,	PUNCT
ejpam-5605	216	48	ω)−hi(r1	ω)−hi(r1	NUM
ejpam-5605	216	49	(	(	PUNCT
ejpam-5605	216	50	·	·	NUM
ejpam-5605	216	51	,	,	PUNCT
ejpam-5605	216	52	ω	ω	NOUN
ejpam-5605	216	53	)	)	PUNCT
ejpam-5605	216	54	,	,	PUNCT
ejpam-5605	216	55	r2	r2	PROPN
ejpam-5605	216	56	(	(	PUNCT
ejpam-5605	216	57	·	·	PROPN
ejpam-5605	216	58	,	,	PUNCT
ejpam-5605	216	59	ω	ω	NOUN
ejpam-5605	216	60	)	)	PUNCT
ejpam-5605	216	61	,	,	PUNCT
ejpam-5605	216	62	ω)∥b	ω)∥b	VERB
ejpam-5605	216	63	≤	≤	NUM
ejpam-5605	216	64	2∑	2∑	NUM
ejpam-5605	216	65	j=1	j=1	NOUN
ejpam-5605	216	66	(	(	PUNCT
ejpam-5605	216	67	ϑi	ϑi	PROPN
ejpam-5605	216	68	−	−	PROPN
ejpam-5605	216	69	1)eϖiϕ(ξ	1)eϖiϕ(ξ	PROPN
ejpam-5605	216	70	,	,	PUNCT
ejpam-5605	216	71	a	a	PRON
ejpam-5605	216	72	)	)	PUNCT
ejpam-5605	216	73	(	(	PUNCT
ejpam-5605	216	74	ζ	ζ	PROPN
ejpam-5605	216	75	+	+	PROPN
ejpam-5605	216	76	ϖi)ζϑi−1	ϖi)ζϑi−1	PROPN
ejpam-5605	216	77	φi	φi	PROPN
ejpam-5605	216	78	,	,	PUNCT
ejpam-5605	216	79	j(ω)∥zj	j(ω)∥zj	NOUN
ejpam-5605	216	80	(	(	PUNCT
ejpam-5605	216	81	·	·	PUNCT
ejpam-5605	216	82	,	,	PUNCT
ejpam-5605	216	83	ω)−	ω)−	PROPN
ejpam-5605	216	84	rj	rj	PROPN
ejpam-5605	216	85	(	(	PUNCT
ejpam-5605	216	86	·	·	PUNCT
ejpam-5605	216	87	,	,	PUNCT
ejpam-5605	216	88	ω)∥b	ω)∥b	NUM
ejpam-5605	216	89	,	,	PUNCT
ejpam-5605	216	90	i	i	PRON
ejpam-5605	216	91	=	=	NOUN
ejpam-5605	216	92	1	1	NUM
ejpam-5605	216	93	,	,	PUNCT
ejpam-5605	216	94	2	2	NUM
ejpam-5605	216	95	.	.	X
ejpam-5605	216	96	therefore	therefore	ADV
ejpam-5605	216	97	,	,	PUNCT
ejpam-5605	216	98	we	we	PRON
ejpam-5605	216	99	have	have	VERB
ejpam-5605	216	100	d((h(z1	d((h(z1	ADJ
ejpam-5605	216	101	,	,	PUNCT
ejpam-5605	216	102	z2	z2	NOUN
ejpam-5605	216	103	)	)	PUNCT
ejpam-5605	216	104	)	)	PUNCT
ejpam-5605	216	105	(	(	PUNCT
ejpam-5605	216	106	·	·	PUNCT
ejpam-5605	216	107	,	,	PUNCT
ejpam-5605	216	108	ω	ω	NOUN
ejpam-5605	216	109	)	)	PUNCT
ejpam-5605	216	110	,	,	PUNCT
ejpam-5605	216	111	(	(	PUNCT
ejpam-5605	216	112	h(r1	h(r1	ADV
ejpam-5605	216	113	,	,	PUNCT
ejpam-5605	216	114	r2	r2	PROPN
ejpam-5605	216	115	)	)	PUNCT
ejpam-5605	216	116	)	)	PUNCT
ejpam-5605	216	117	(	(	PUNCT
ejpam-5605	216	118	·	·	PUNCT
ejpam-5605	216	119	,	,	PUNCT
ejpam-5605	216	120	ω	ω	NOUN
ejpam-5605	216	121	)	)	PUNCT
ejpam-5605	216	122	)	)	PUNCT
ejpam-5605	217	1	≤	≤	NOUN
ejpam-5605	217	2	nζ(ω)d	nζ(ω)d	PUNCT
ejpam-5605	217	3	(	(	PUNCT
ejpam-5605	217	4	(	(	PUNCT
ejpam-5605	217	5	z1	z1	PROPN
ejpam-5605	217	6	(	(	PUNCT
ejpam-5605	217	7	·	·	NUM
ejpam-5605	217	8	,	,	PUNCT
ejpam-5605	217	9	ω	ω	NOUN
ejpam-5605	217	10	)	)	PUNCT
ejpam-5605	217	11	,	,	PUNCT
ejpam-5605	217	12	z2	z2	PROPN
ejpam-5605	217	13	(	(	PUNCT
ejpam-5605	217	14	·	·	NUM
ejpam-5605	217	15	,	,	PUNCT
ejpam-5605	217	16	ω	ω	NOUN
ejpam-5605	217	17	)	)	PUNCT
ejpam-5605	217	18	)	)	PUNCT
ejpam-5605	217	19	,	,	PUNCT
ejpam-5605	217	20	(	(	PUNCT
ejpam-5605	217	21	r1	r1	PROPN
ejpam-5605	217	22	(	(	PUNCT
ejpam-5605	217	23	·	·	PROPN
ejpam-5605	217	24	,	,	PUNCT
ejpam-5605	217	25	ω	ω	NOUN
ejpam-5605	217	26	)	)	PUNCT
ejpam-5605	217	27	,	,	PUNCT
ejpam-5605	217	28	r2	r2	PROPN
ejpam-5605	217	29	(	(	PUNCT
ejpam-5605	217	30	·	·	PROPN
ejpam-5605	217	31	,	,	PUNCT
ejpam-5605	217	32	ω	ω	NOUN
ejpam-5605	217	33	)	)	PUNCT
ejpam-5605	217	34	)	)	PUNCT
ejpam-5605	217	35	)	)	PUNCT
ejpam-5605	217	36	,	,	PUNCT
ejpam-5605	217	37	where	where	SCONJ
ejpam-5605	217	38	:	:	PUNCT
ejpam-5605	217	39	nζ(ω	nζ(ω	NUM
ejpam-5605	217	40	)	)	PUNCT
ejpam-5605	217	41	=	=	VERB
ejpam-5605	217	42			NOUN
ejpam-5605	217	43	(	(	PUNCT
ejpam-5605	217	44	ϑ1	ϑ1	NOUN
ejpam-5605	217	45	−	−	PROPN
ejpam-5605	217	46	1)eϖ1ϕ(b	1)eϖ1ϕ(b	PROPN
ejpam-5605	217	47	,	,	PUNCT
ejpam-5605	217	48	a	a	NOUN
ejpam-5605	217	49	)	)	PUNCT
ejpam-5605	217	50	(	(	PUNCT
ejpam-5605	217	51	ζ	ζ	NOUN
ejpam-5605	217	52	+	+	ADJ
ejpam-5605	217	53	ϖ1)ζϑ1−1	ϖ1)ζϑ1−1	NOUN
ejpam-5605	217	54	φ1,1(ω	φ1,1(ω	ADJ
ejpam-5605	217	55	)	)	PUNCT
ejpam-5605	217	56	(	(	PUNCT
ejpam-5605	217	57	ϑ1	ϑ1	NOUN
ejpam-5605	217	58	−	−	PROPN
ejpam-5605	217	59	1)eϖ1ϕ(b	1)eϖ1ϕ(b	PROPN
ejpam-5605	217	60	,	,	PUNCT
ejpam-5605	217	61	a	a	NOUN
ejpam-5605	217	62	)	)	PUNCT
ejpam-5605	217	63	(	(	PUNCT
ejpam-5605	217	64	ζ	ζ	NOUN
ejpam-5605	217	65	+	+	ADJ
ejpam-5605	217	66	ϖ1)ζϑ1−1	ϖ1)ζϑ1−1	NOUN
ejpam-5605	217	67	φ1,2(ω	φ1,2(ω	ADV
ejpam-5605	217	68	)	)	PUNCT
ejpam-5605	217	69	(	(	PUNCT
ejpam-5605	217	70	ϑ2	ϑ2	PROPN
ejpam-5605	217	71	−	−	PROPN
ejpam-5605	217	72	1)eϖ2ϕ(b	1)eϖ2ϕ(b	NOUN
ejpam-5605	217	73	,	,	PUNCT
ejpam-5605	217	74	a	a	NOUN
ejpam-5605	217	75	)	)	PUNCT
ejpam-5605	217	76	(	(	PUNCT
ejpam-5605	217	77	ζ	ζ	NOUN
ejpam-5605	217	78	+	+	NOUN
ejpam-5605	217	79	ϖ2)ζϑ2−1	ϖ2)ζϑ2−1	NOUN
ejpam-5605	217	80	φ2,1(ω	φ2,1(ω	PROPN
ejpam-5605	217	81	)	)	PUNCT
ejpam-5605	217	82	(	(	PUNCT
ejpam-5605	217	83	ϑ2	ϑ2	PROPN
ejpam-5605	217	84	−	−	PROPN
ejpam-5605	217	85	1)eϖ2ϕ(b	1)eϖ2ϕ(b	NOUN
ejpam-5605	217	86	,	,	PUNCT
ejpam-5605	217	87	a	a	NOUN
ejpam-5605	217	88	)	)	PUNCT
ejpam-5605	217	89	(	(	PUNCT
ejpam-5605	217	90	ζ	ζ	NOUN
ejpam-5605	217	91	+	+	NOUN
ejpam-5605	217	92	ϖ2)ζϑ2−1	ϖ2)ζϑ2−1	NOUN
ejpam-5605	217	93	φ2,2(ω	φ2,2(ω	ADJ
ejpam-5605	217	94	)	)	PUNCT
ejpam-5605	217	95			NOUN
ejpam-5605	217	96	,	,	PUNCT
ejpam-5605	217	97	and	and	CCONJ
ejpam-5605	217	98	d	d	X
ejpam-5605	217	99	(	(	PUNCT
ejpam-5605	217	100	(	(	PUNCT
ejpam-5605	217	101	z1	z1	PROPN
ejpam-5605	217	102	(	(	PUNCT
ejpam-5605	217	103	·	·	NUM
ejpam-5605	217	104	,	,	PUNCT
ejpam-5605	217	105	ω	ω	NOUN
ejpam-5605	217	106	)	)	PUNCT
ejpam-5605	217	107	,	,	PUNCT
ejpam-5605	217	108	z2	z2	PROPN
ejpam-5605	217	109	(	(	PUNCT
ejpam-5605	217	110	·	·	NUM
ejpam-5605	217	111	,	,	PUNCT
ejpam-5605	217	112	ω	ω	NOUN
ejpam-5605	217	113	)	)	PUNCT
ejpam-5605	217	114	)	)	PUNCT
ejpam-5605	217	115	,	,	PUNCT
ejpam-5605	217	116	(	(	PUNCT
ejpam-5605	217	117	r1	r1	PROPN
ejpam-5605	217	118	(	(	PUNCT
ejpam-5605	217	119	·	·	PROPN
ejpam-5605	217	120	,	,	PUNCT
ejpam-5605	217	121	ω	ω	NOUN
ejpam-5605	217	122	)	)	PUNCT
ejpam-5605	217	123	,	,	PUNCT
ejpam-5605	217	124	r2	r2	PROPN
ejpam-5605	217	125	(	(	PUNCT
ejpam-5605	217	126	·	·	PROPN
ejpam-5605	217	127	,	,	PUNCT
ejpam-5605	217	128	ω	ω	NOUN
ejpam-5605	217	129	)	)	PUNCT
ejpam-5605	217	130	)	)	PUNCT
ejpam-5605	217	131	)	)	PUNCT
ejpam-5605	218	1	=	=	SYM
ejpam-5605	218	2	(	(	PUNCT
ejpam-5605	218	3	∥z1	∥z1	PROPN
ejpam-5605	218	4	(	(	PUNCT
ejpam-5605	218	5	·	·	PUNCT
ejpam-5605	218	6	,	,	PUNCT
ejpam-5605	218	7	ω)−	ω)−	PROPN
ejpam-5605	218	8	r1	r1	PROPN
ejpam-5605	218	9	(	(	PUNCT
ejpam-5605	218	10	·	·	PUNCT
ejpam-5605	218	11	,	,	PUNCT
ejpam-5605	218	12	ω)∥b	ω)∥b	X
ejpam-5605	218	13	∥z2	∥z2	PROPN
ejpam-5605	218	14	(	(	PUNCT
ejpam-5605	218	15	·	·	PUNCT
ejpam-5605	218	16	,	,	PUNCT
ejpam-5605	218	17	ω)−	ω)−	PROPN
ejpam-5605	218	18	r2	r2	NOUN
ejpam-5605	218	19	(	(	PUNCT
ejpam-5605	218	20	·	·	PUNCT
ejpam-5605	218	21	,	,	PUNCT
ejpam-5605	218	22	ω)∥b	ω)∥b	NUM
ejpam-5605	218	23	)	)	PUNCT
ejpam-5605	218	24	.	.	PUNCT
ejpam-5605	219	1	choosing	choose	VERB
ejpam-5605	219	2	ζ	ζ	NOUN
ejpam-5605	219	3	>	>	SYM
ejpam-5605	219	4	0	0	PUNCT
ejpam-5605	220	1	large	large	ADJ
ejpam-5605	220	2	enough	enough	ADV
ejpam-5605	220	3	,	,	PUNCT
ejpam-5605	220	4	the	the	DET
ejpam-5605	220	5	matrix	matrix	NOUN
ejpam-5605	220	6	nζ(ω	nζ(ω	NUM
ejpam-5605	220	7	)	)	PUNCT
ejpam-5605	220	8	converges	converge	NOUN
ejpam-5605	220	9	to	to	ADP
ejpam-5605	220	10	zero	zero	NUM
ejpam-5605	220	11	.	.	PUNCT
ejpam-5605	221	1	then	then	ADV
ejpam-5605	221	2	,	,	PUNCT
ejpam-5605	221	3	according	accord	VERB
ejpam-5605	221	4	to	to	ADP
ejpam-5605	221	5	theorem	theorem	ADJ
ejpam-5605	221	6	1	1	NUM
ejpam-5605	221	7	,	,	PUNCT
ejpam-5605	221	8	h	h	NOUN
ejpam-5605	221	9	possesses	possess	VERB
ejpam-5605	221	10	a	a	DET
ejpam-5605	221	11	unique	unique	ADJ
ejpam-5605	221	12	random	random	ADJ
ejpam-5605	221	13	fixed	fix	VERB
ejpam-5605	221	14	-	-	PUNCT
ejpam-5605	221	15	point	point	NOUN
ejpam-5605	221	16	,	,	PUNCT
ejpam-5605	221	17	serving	serve	VERB
ejpam-5605	221	18	as	as	ADP
ejpam-5605	221	19	the	the	DET
ejpam-5605	221	20	unique	unique	ADJ
ejpam-5605	221	21	random	random	ADJ
ejpam-5605	221	22	solution	solution	NOUN
ejpam-5605	221	23	to	to	ADP
ejpam-5605	221	24	system	system	NOUN
ejpam-5605	221	25	(	(	PUNCT
ejpam-5605	221	26	1	1	NUM
ejpam-5605	221	27	)	)	PUNCT
ejpam-5605	221	28	.	.	PUNCT
ejpam-5605	222	1	our	our	PRON
ejpam-5605	222	2	second	second	ADJ
ejpam-5605	222	3	result	result	NOUN
ejpam-5605	222	4	investigates	investigate	VERB
ejpam-5605	222	5	the	the	DET
ejpam-5605	222	6	existence	existence	NOUN
ejpam-5605	222	7	result	result	VERB
ejpam-5605	222	8	for	for	ADP
ejpam-5605	222	9	the	the	DET
ejpam-5605	222	10	system	system	NOUN
ejpam-5605	222	11	(	(	PUNCT
ejpam-5605	222	12	1	1	NUM
ejpam-5605	222	13	)	)	PUNCT
ejpam-5605	222	14	,	,	PUNCT
ejpam-5605	222	15	employing	employ	VERB
ejpam-5605	222	16	theorem	theorem	NOUN
ejpam-5605	222	17	2	2	NUM
ejpam-5605	222	18	as	as	ADP
ejpam-5605	222	19	a	a	DET
ejpam-5605	222	20	tool	tool	NOUN
ejpam-5605	222	21	.	.	PUNCT
ejpam-5605	223	1	theorem	theorem	NOUN
ejpam-5605	223	2	4	4	NUM
ejpam-5605	223	3	.	.	PUNCT
ejpam-5605	223	4	suppose	suppose	VERB
ejpam-5605	223	5	that	that	SCONJ
ejpam-5605	223	6	(	(	PUNCT
ejpam-5605	223	7	a1	a1	PROPN
ejpam-5605	223	8	)	)	PUNCT
ejpam-5605	223	9	the	the	DET
ejpam-5605	223	10	functions	function	NOUN
ejpam-5605	223	11	fi	fi	NOUN
ejpam-5605	223	12	are	be	AUX
ejpam-5605	223	13	random	random	ADJ
ejpam-5605	223	14	carathéodory	carathéodory	NOUN
ejpam-5605	223	15	on	on	ADP
ejpam-5605	223	16	i×g×g×	i×g×g×	PROPN
ejpam-5605	223	17	ω	ω	PROPN
ejpam-5605	223	18	.	.	PUNCT
ejpam-5605	224	1	(	(	PUNCT
ejpam-5605	224	2	a3	a3	NOUN
ejpam-5605	224	3	)	)	PUNCT
ejpam-5605	224	4	there	there	PRON
ejpam-5605	224	5	exist	exist	VERB
ejpam-5605	224	6	ψi	ψi	ADP
ejpam-5605	224	7	:	:	PUNCT
ejpam-5605	224	8	i×	i×	PROPN
ejpam-5605	224	9	ω	ω	X
ejpam-5605	224	10	→	→	SYM
ejpam-5605	224	11	l∞(i	l∞(i	PROPN
ejpam-5605	224	12	,	,	PUNCT
ejpam-5605	224	13	r+	r+	X
ejpam-5605	224	14	)	)	PUNCT
ejpam-5605	224	15	,	,	PUNCT
ejpam-5605	225	1	i	i	PRON
ejpam-5605	225	2	=	=	NOUN
ejpam-5605	225	3	1	1	NUM
ejpam-5605	225	4	,	,	PUNCT
ejpam-5605	225	5	2	2	NUM
ejpam-5605	225	6	such	such	ADJ
ejpam-5605	225	7	that	that	SCONJ
ejpam-5605	225	8	∥fi(ξ	∥fi(ξ	PROPN
ejpam-5605	225	9	,	,	PUNCT
ejpam-5605	225	10	u1	u1	NOUN
ejpam-5605	225	11	,	,	PUNCT
ejpam-5605	225	12	u2	u2	NOUN
ejpam-5605	225	13	,	,	PUNCT
ejpam-5605	225	14	ω)∥	ω)∥	PUNCT
ejpam-5605	225	15	≤	≤	PROPN
ejpam-5605	225	16	ψi(ξ	ψi(ξ	PUNCT
ejpam-5605	225	17	,	,	PUNCT
ejpam-5605	225	18	ω)(1	ω)(1	NUM
ejpam-5605	225	19	+	+	CCONJ
ejpam-5605	225	20	∥u1∥+	∥u1∥+	PROPN
ejpam-5605	225	21	∥u2∥	∥u2∥	PROPN
ejpam-5605	225	22	)	)	PUNCT
ejpam-5605	225	23	,	,	PUNCT
ejpam-5605	225	24	i	i	PRON
ejpam-5605	225	25	=	=	NOUN
ejpam-5605	225	26	1	1	NUM
ejpam-5605	225	27	,	,	PUNCT
ejpam-5605	225	28	2	2	NUM
ejpam-5605	225	29	,	,	PUNCT
ejpam-5605	225	30	for	for	ADP
ejpam-5605	225	31	all	all	DET
ejpam-5605	225	32	(	(	PUNCT
ejpam-5605	225	33	ξ	ξ	PROPN
ejpam-5605	225	34	,	,	PUNCT
ejpam-5605	225	35	u1	u1	NOUN
ejpam-5605	225	36	,	,	PUNCT
ejpam-5605	225	37	u2	u2	PROPN
ejpam-5605	225	38	,	,	PUNCT
ejpam-5605	225	39	ω	ω	NOUN
ejpam-5605	225	40	)	)	PUNCT
ejpam-5605	225	41	∈	∈	PROPN
ejpam-5605	226	1	i×g2	i×g2	NOUN
ejpam-5605	226	2	×	×	PROPN
ejpam-5605	226	3	ω	ω	PROPN
ejpam-5605	226	4	.	.	PUNCT
ejpam-5605	226	5	(	(	PUNCT
ejpam-5605	226	6	a4	a4	NUM
ejpam-5605	226	7	)	)	PUNCT
ejpam-5605	226	8	there	there	PRON
ejpam-5605	226	9	exists	exist	VERB
ejpam-5605	226	10	a	a	DET
ejpam-5605	226	11	constant	constant	ADJ
ejpam-5605	226	12	random	random	ADJ
ejpam-5605	226	13	variable	variable	NOUN
ejpam-5605	226	14	ϱi	ϱi	NOUN
ejpam-5605	226	15	,	,	PUNCT
ejpam-5605	226	16	j	j	PROPN
ejpam-5605	226	17	:	:	PUNCT
ejpam-5605	226	18	ω	ω	X
ejpam-5605	226	19	→	→	PUNCT
ejpam-5605	227	1	[	[	X
ejpam-5605	227	2	0,∞	0,∞	NOUN
ejpam-5605	227	3	)	)	PUNCT
ejpam-5605	227	4	,	,	PUNCT
ejpam-5605	227	5	i	i	PRON
ejpam-5605	227	6	,	,	PUNCT
ejpam-5605	227	7	j	j	PROPN
ejpam-5605	227	8	=	=	SYM
ejpam-5605	227	9	1	1	NUM
ejpam-5605	227	10	,	,	PUNCT
ejpam-5605	227	11	2	2	NUM
ejpam-5605	227	12	such	such	ADJ
ejpam-5605	227	13	that	that	PRON
ejpam-5605	227	14	for	for	ADP
ejpam-5605	227	15	each	each	DET
ejpam-5605	227	16	u	u	PROPN
ejpam-5605	227	17	j	j	PROPN
ejpam-5605	227	18	⊂	⊂	PROPN
ejpam-5605	227	19	p(c(i	p(c(i	PROPN
ejpam-5605	227	20	,	,	PUNCT
ejpam-5605	227	21	o	o	NOUN
ejpam-5605	227	22	)	)	PUNCT
ejpam-5605	227	23	)	)	PUNCT
ejpam-5605	227	24	,	,	PUNCT
ejpam-5605	227	25	λ(fi(ξ	λ(fi(ξ	PROPN
ejpam-5605	227	26	,	,	PUNCT
ejpam-5605	227	27	u	u	NOUN
ejpam-5605	227	28	1	1	NUM
ejpam-5605	227	29	,	,	PUNCT
ejpam-5605	227	30	u2	u2	PROPN
ejpam-5605	227	31	,	,	PUNCT
ejpam-5605	227	32	ω	ω	NOUN
ejpam-5605	227	33	)	)	PUNCT
ejpam-5605	227	34	)	)	PUNCT
ejpam-5605	227	35	≤	≤	NUM
ejpam-5605	228	1	2∑	2∑	NUM
ejpam-5605	228	2	j=1	j=1	PROPN
ejpam-5605	228	3	ϱi	ϱi	PROPN
ejpam-5605	228	4	,	,	PUNCT
ejpam-5605	228	5	j(ω)λ(u	j(ω)λ(u	PROPN
ejpam-5605	228	6	j(ξ	j(ξ	PROPN
ejpam-5605	228	7	)	)	PUNCT
ejpam-5605	228	8	)	)	PUNCT
ejpam-5605	228	9	,	,	PUNCT
ejpam-5605	228	10	for	for	ADP
ejpam-5605	228	11	all	all	DET
ejpam-5605	228	12	(	(	PUNCT
ejpam-5605	228	13	ξ	ξ	PROPN
ejpam-5605	228	14	,	,	PUNCT
ejpam-5605	228	15	ω	ω	NOUN
ejpam-5605	228	16	)	)	PUNCT
ejpam-5605	228	17	∈	∈	PROPN
ejpam-5605	228	18	i×	i×	PROPN
ejpam-5605	228	19	ω	ω	PROPN
ejpam-5605	228	20	.	.	PUNCT
ejpam-5605	228	21	m.	m.	PROPN
ejpam-5605	228	22	ziane	ziane	PROPN
ejpam-5605	228	23	et	et	PROPN
ejpam-5605	228	24	al	al	PROPN
ejpam-5605	228	25	.	.	PUNCT
ejpam-5605	228	26	/	/	SYM
ejpam-5605	228	27	eur	eur	PROPN
ejpam-5605	228	28	.	.	PUNCT
ejpam-5605	229	1	j.	j.	PROPN
ejpam-5605	229	2	pure	pure	PROPN
ejpam-5605	229	3	appl	appl	PROPN
ejpam-5605	229	4	.	.	PROPN
ejpam-5605	229	5	math	math	PROPN
ejpam-5605	229	6	,	,	PUNCT
ejpam-5605	229	7	18	18	NUM
ejpam-5605	229	8	(	(	PUNCT
ejpam-5605	229	9	1	1	NUM
ejpam-5605	229	10	)	)	PUNCT
ejpam-5605	229	11	(	(	PUNCT
ejpam-5605	229	12	2025	2025	NUM
ejpam-5605	229	13	)	)	PUNCT
ejpam-5605	229	14	,	,	PUNCT
ejpam-5605	229	15	5605	5605	NUM
ejpam-5605	229	16	11	11	NUM
ejpam-5605	229	17	of	of	ADP
ejpam-5605	229	18	21	21	NUM
ejpam-5605	229	19	then	then	ADV
ejpam-5605	229	20	,	,	PUNCT
ejpam-5605	229	21	the	the	DET
ejpam-5605	229	22	system	system	NOUN
ejpam-5605	229	23	(	(	PUNCT
ejpam-5605	229	24	1	1	X
ejpam-5605	229	25	)	)	PUNCT
ejpam-5605	229	26	possesses	possess	VERB
ejpam-5605	229	27	at	at	ADV
ejpam-5605	229	28	least	least	ADV
ejpam-5605	229	29	one	one	NUM
ejpam-5605	229	30	random	random	ADJ
ejpam-5605	229	31	solution	solution	NOUN
ejpam-5605	229	32	.	.	PUNCT
ejpam-5605	230	1	for	for	ADP
ejpam-5605	230	2	easy	easy	ADJ
ejpam-5605	230	3	computations	computation	NOUN
ejpam-5605	230	4	,	,	PUNCT
ejpam-5605	230	5	let	let	VERB
ejpam-5605	230	6	ψ∗	ψ∗	NOUN
ejpam-5605	230	7	i	i	NOUN
ejpam-5605	230	8	=	=	PUNCT
ejpam-5605	230	9	sup	sup	NUM
ejpam-5605	230	10	ω∈ω	ω∈ω	X
ejpam-5605	230	11	∥ψi	∥ψi	PROPN
ejpam-5605	230	12	(	(	PUNCT
ejpam-5605	230	13	·	·	PUNCT
ejpam-5605	230	14	,	,	PUNCT
ejpam-5605	230	15	ω)∥l∞	ω)∥l∞	NUM
ejpam-5605	230	16	,	,	PUNCT
ejpam-5605	230	17	i	i	PRON
ejpam-5605	230	18	=	=	NOUN
ejpam-5605	230	19	1	1	NUM
ejpam-5605	230	20	,	,	PUNCT
ejpam-5605	230	21	2	2	NUM
ejpam-5605	230	22	.	.	PUNCT
ejpam-5605	230	23	proof	proof	NOUN
ejpam-5605	230	24	.	.	PUNCT
ejpam-5605	231	1	for	for	ADP
ejpam-5605	231	2	r	r	NOUN
ejpam-5605	231	3	>	>	X
ejpam-5605	231	4	0	0	NUM
ejpam-5605	231	5	,	,	PUNCT
ejpam-5605	231	6	consider	consider	VERB
ejpam-5605	231	7	a	a	DET
ejpam-5605	231	8	closed	closed	ADJ
ejpam-5605	231	9	ball	ball	NOUN
ejpam-5605	231	10	br	br	NOUN
ejpam-5605	231	11	=	=	PUNCT
ejpam-5605	232	1	{	{	PUNCT
ejpam-5605	232	2	(	(	PUNCT
ejpam-5605	232	3	z1	z1	PROPN
ejpam-5605	232	4	,	,	PUNCT
ejpam-5605	232	5	z2	z2	PROPN
ejpam-5605	232	6	)	)	PUNCT
ejpam-5605	232	7	∈	∈	PROPN
ejpam-5605	232	8	j	j	PROPN
ejpam-5605	232	9	:	:	PUNCT
ejpam-5605	232	10	∥zi	∥zi	PROPN
ejpam-5605	232	11	(	(	PUNCT
ejpam-5605	232	12	·	·	PUNCT
ejpam-5605	232	13	,	,	PUNCT
ejpam-5605	232	14	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	232	15	<	<	X
ejpam-5605	232	16	r	r	NOUN
ejpam-5605	232	17	,	,	PUNCT
ejpam-5605	232	18	i	i	NOUN
ejpam-5605	232	19	=	=	NOUN
ejpam-5605	232	20	1	1	NUM
ejpam-5605	232	21	,	,	PUNCT
ejpam-5605	232	22	2	2	NUM
ejpam-5605	232	23	}	}	PUNCT
ejpam-5605	232	24	.	.	PUNCT
ejpam-5605	233	1	(	(	PUNCT
ejpam-5605	233	2	10	10	NUM
ejpam-5605	233	3	)	)	PUNCT
ejpam-5605	233	4	the	the	DET
ejpam-5605	233	5	proof	proof	NOUN
ejpam-5605	233	6	of	of	ADP
ejpam-5605	233	7	theorem	theorem	NOUN
ejpam-5605	233	8	4	4	NUM
ejpam-5605	233	9	will	will	AUX
ejpam-5605	233	10	proceed	proceed	VERB
ejpam-5605	233	11	through	through	ADP
ejpam-5605	233	12	several	several	ADJ
ejpam-5605	233	13	steps	step	NOUN
ejpam-5605	233	14	.	.	PUNCT
ejpam-5605	234	1	step	step	NOUN
ejpam-5605	234	2	1	1	NUM
ejpam-5605	234	3	.	.	PUNCT
ejpam-5605	235	1	h	h	PROPN
ejpam-5605	235	2	transforms	transform	VERB
ejpam-5605	235	3	bounded	bounded	ADJ
ejpam-5605	235	4	sets	set	NOUN
ejpam-5605	235	5	into	into	ADP
ejpam-5605	235	6	bounded	bounded	ADJ
ejpam-5605	235	7	sets	set	NOUN
ejpam-5605	235	8	in	in	ADP
ejpam-5605	235	9	j.	j.	PROPN
ejpam-5605	235	10	let	let	PROPN
ejpam-5605	235	11	(	(	PUNCT
ejpam-5605	235	12	z1	z1	ADJ
ejpam-5605	235	13	,	,	PUNCT
ejpam-5605	235	14	z2	z2	NUM
ejpam-5605	235	15	)	)	PUNCT
ejpam-5605	235	16	∈	∈	PROPN
ejpam-5605	235	17	br	br	NOUN
ejpam-5605	235	18	and	and	CCONJ
ejpam-5605	235	19	ξ	ξ	PROPN
ejpam-5605	235	20	∈	∈	PROPN
ejpam-5605	236	1	i	i	PRON
ejpam-5605	236	2	,	,	PUNCT
ejpam-5605	236	3	then	then	ADV
ejpam-5605	236	4	for	for	ADP
ejpam-5605	236	5	i	i	PROPN
ejpam-5605	236	6	=	=	SYM
ejpam-5605	236	7	1	1	NUM
ejpam-5605	236	8	,	,	PUNCT
ejpam-5605	236	9	2	2	NUM
ejpam-5605	236	10	we	we	PRON
ejpam-5605	236	11	have	have	VERB
ejpam-5605	236	12	:	:	PUNCT
ejpam-5605	236	13	∥hi(z1(ξ	∥hi(z1(ξ	ADJ
ejpam-5605	236	14	,	,	PUNCT
ejpam-5605	236	15	ω	ω	NOUN
ejpam-5605	236	16	)	)	PUNCT
ejpam-5605	236	17	,	,	PUNCT
ejpam-5605	236	18	z2(ξ	z2(ξ	PROPN
ejpam-5605	236	19	,	,	PUNCT
ejpam-5605	236	20	ω	ω	NOUN
ejpam-5605	236	21	)	)	PUNCT
ejpam-5605	236	22	,	,	PUNCT
ejpam-5605	236	23	ω)∥	ω)∥	PUNCT
ejpam-5605	236	24	≤	≤	NOUN
ejpam-5605	236	25	(	(	PUNCT
ejpam-5605	236	26	ϑi	ϑi	PROPN
ejpam-5605	236	27	−	−	PROPN
ejpam-5605	236	28	1)e−ϖiϕ(ξ	1)e−ϖiϕ(ξ	PROPN
ejpam-5605	236	29	,	,	PUNCT
ejpam-5605	236	30	a	a	PRON
ejpam-5605	236	31	)	)	PUNCT
ejpam-5605	236	32	∫	∫	PROPN
ejpam-5605	236	33	ξ	ξ	PROPN
ejpam-5605	236	34	a	a	DET
ejpam-5605	236	35	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	236	36	,	,	PUNCT
ejpam-5605	236	37	a	a	PRON
ejpam-5605	236	38	)	)	PUNCT
ejpam-5605	236	39	(	(	PUNCT
ejpam-5605	236	40	∫	∫	PROPN
ejpam-5605	236	41	s	s	VERB
ejpam-5605	236	42	a	a	DET
ejpam-5605	236	43	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	236	44	,	,	PUNCT
ejpam-5605	236	45	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	236	46	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	236	47	−	−	PROPN
ejpam-5605	236	48	1	1	NUM
ejpam-5605	236	49	)	)	PUNCT
ejpam-5605	236	50	∥fi(τ	∥fi(τ	ADJ
ejpam-5605	236	51	,	,	PUNCT
ejpam-5605	236	52	z1(τ	z1(τ	PROPN
ejpam-5605	236	53	,	,	PUNCT
ejpam-5605	236	54	ω	ω	NOUN
ejpam-5605	236	55	)	)	PUNCT
ejpam-5605	236	56	,	,	PUNCT
ejpam-5605	236	57	z2τ	z2τ	NUM
ejpam-5605	236	58	,	,	PUNCT
ejpam-5605	236	59	ω))∥dτ	ω))∥dτ	PROPN
ejpam-5605	236	60	)	)	PUNCT
ejpam-5605	236	61	ψ′(s)ds	ψ′(s)ds	PROPN
ejpam-5605	236	62	by	by	ADP
ejpam-5605	236	63	using	use	VERB
ejpam-5605	236	64	hypothesis	hypothesis	NOUN
ejpam-5605	236	65	(	(	PUNCT
ejpam-5605	236	66	a3	a3	NOUN
ejpam-5605	236	67	)	)	PUNCT
ejpam-5605	236	68	,	,	PUNCT
ejpam-5605	236	69	for	for	ADP
ejpam-5605	236	70	each	each	DET
ejpam-5605	236	71	ξ	ξ	X
ejpam-5605	236	72	∈	∈	PROPN
ejpam-5605	236	73	i	i	PRON
ejpam-5605	236	74	,	,	PUNCT
ejpam-5605	236	75	we	we	PRON
ejpam-5605	236	76	have	have	AUX
ejpam-5605	236	77	∥fi(τ	∥fi(τ	VERB
ejpam-5605	236	78	,	,	PUNCT
ejpam-5605	236	79	z1(τ	z1(τ	PROPN
ejpam-5605	236	80	,	,	PUNCT
ejpam-5605	236	81	ω	ω	NOUN
ejpam-5605	236	82	)	)	PUNCT
ejpam-5605	236	83	,	,	PUNCT
ejpam-5605	236	84	z2τ	z2τ	NUM
ejpam-5605	236	85	,	,	PUNCT
ejpam-5605	236	86	ω))∥	ω))∥	NUM
ejpam-5605	236	87	≤	≤	NOUN
ejpam-5605	236	88	ψi(τ	ψi(τ	PUNCT
ejpam-5605	236	89	,	,	PUNCT
ejpam-5605	236	90	ω)(1	ω)(1	NUM
ejpam-5605	236	91	+	+	CCONJ
ejpam-5605	236	92	∥z1(τ	∥z1(τ	NOUN
ejpam-5605	236	93	,	,	PUNCT
ejpam-5605	236	94	ω)∥+	ω)∥+	ADJ
ejpam-5605	236	95	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	236	96	,	,	PUNCT
ejpam-5605	236	97	ω)∥	ω)∥	NUM
ejpam-5605	236	98	)	)	PUNCT
ejpam-5605	237	1	≤	≤	NUM
ejpam-5605	237	2	∥ψi	∥ψi	PROPN
ejpam-5605	237	3	(	(	PUNCT
ejpam-5605	237	4	·	·	PUNCT
ejpam-5605	237	5	,	,	PUNCT
ejpam-5605	237	6	ω)∥l∞(1	ω)∥l∞(1	PROPN
ejpam-5605	237	7	+	+	CCONJ
ejpam-5605	237	8	∥z1	∥z1	PROPN
ejpam-5605	237	9	(	(	PUNCT
ejpam-5605	237	10	·	·	PUNCT
ejpam-5605	237	11	,	,	PUNCT
ejpam-5605	237	12	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	237	13	+	+	CCONJ
ejpam-5605	237	14	∥z1	∥z1	PROPN
ejpam-5605	237	15	(	(	PUNCT
ejpam-5605	237	16	·	·	PUNCT
ejpam-5605	237	17	,	,	PUNCT
ejpam-5605	237	18	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	237	19	)	)	PUNCT
ejpam-5605	237	20	,	,	PUNCT
ejpam-5605	237	21	i	i	PRON
ejpam-5605	237	22	=	=	NOUN
ejpam-5605	237	23	1	1	NUM
ejpam-5605	237	24	,	,	PUNCT
ejpam-5605	237	25	2	2	NUM
ejpam-5605	237	26	.	.	PUNCT
ejpam-5605	237	27	(	(	PUNCT
ejpam-5605	237	28	11	11	NUM
ejpam-5605	237	29	)	)	PUNCT
ejpam-5605	237	30	so	so	ADV
ejpam-5605	237	31	,	,	PUNCT
ejpam-5605	237	32	by	by	ADP
ejpam-5605	237	33	the	the	DET
ejpam-5605	237	34	fact	fact	NOUN
ejpam-5605	237	35	e−ϖiϕ(ξ	e−ϖiϕ(ξ	NUM
ejpam-5605	237	36	,	,	PUNCT
ejpam-5605	237	37	a	a	PRON
ejpam-5605	237	38	)	)	PUNCT
ejpam-5605	237	39	≤	≤	NOUN
ejpam-5605	237	40	1	1	NUM
ejpam-5605	237	41	for	for	ADP
ejpam-5605	237	42	ξ	ξ	PROPN
ejpam-5605	237	43	∈	∈	PROPN
ejpam-5605	237	44	i	i	PRON
ejpam-5605	237	45	and	and	CCONJ
ejpam-5605	237	46	using	use	VERB
ejpam-5605	237	47	(	(	PUNCT
ejpam-5605	237	48	11	11	NUM
ejpam-5605	237	49	)	)	PUNCT
ejpam-5605	237	50	to	to	PART
ejpam-5605	237	51	gathere	gathere	VERB
ejpam-5605	237	52	lemma	lemma	PROPN
ejpam-5605	237	53	1	1	NUM
ejpam-5605	237	54	,	,	PUNCT
ejpam-5605	237	55	we	we	PRON
ejpam-5605	237	56	get	get	VERB
ejpam-5605	237	57	∥hi(z1(ξ	∥hi(z1(ξ	ADP
ejpam-5605	237	58	,	,	PUNCT
ejpam-5605	237	59	ω	ω	NOUN
ejpam-5605	237	60	)	)	PUNCT
ejpam-5605	237	61	,	,	PUNCT
ejpam-5605	237	62	z2(ξ	z2(ξ	PROPN
ejpam-5605	237	63	,	,	PUNCT
ejpam-5605	237	64	ω	ω	NOUN
ejpam-5605	237	65	)	)	PUNCT
ejpam-5605	237	66	,	,	PUNCT
ejpam-5605	237	67	ω)∥	ω)∥	PUNCT
ejpam-5605	237	68	≤	≤	NOUN
ejpam-5605	237	69	(	(	PUNCT
ejpam-5605	237	70	ϑi	ϑi	NOUN
ejpam-5605	237	71	−	−	PROPN
ejpam-5605	237	72	1)∥ψi	1)∥ψi	PROPN
ejpam-5605	237	73	(	(	PUNCT
ejpam-5605	237	74	·	·	PUNCT
ejpam-5605	237	75	,	,	PUNCT
ejpam-5605	237	76	ω)∥l∞(1	ω)∥l∞(1	PROPN
ejpam-5605	237	77	+	+	CCONJ
ejpam-5605	237	78	∥z1	∥z1	PROPN
ejpam-5605	237	79	(	(	PUNCT
ejpam-5605	237	80	·	·	PUNCT
ejpam-5605	237	81	,	,	PUNCT
ejpam-5605	237	82	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	237	83	+	+	CCONJ
ejpam-5605	237	84	∥z1	∥z1	PROPN
ejpam-5605	237	85	(	(	PUNCT
ejpam-5605	237	86	·	·	PUNCT
ejpam-5605	237	87	,	,	PUNCT
ejpam-5605	237	88	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	237	89	)	)	PUNCT
ejpam-5605	237	90	∫	∫	PROPN
ejpam-5605	238	1	ξ	ξ	PROPN
ejpam-5605	238	2	a	a	DET
ejpam-5605	238	3	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	238	4	,	,	PUNCT
ejpam-5605	238	5	a	a	PRON
ejpam-5605	238	6	)	)	PUNCT
ejpam-5605	238	7	∫	∫	PROPN
ejpam-5605	238	8	s	s	PROPN
ejpam-5605	238	9	a	a	DET
ejpam-5605	238	10	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	238	11	,	,	PUNCT
ejpam-5605	238	12	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	238	13	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	238	14	−	−	PROPN
ejpam-5605	238	15	1	1	NUM
ejpam-5605	238	16	)	)	PUNCT
ejpam-5605	238	17	dτψ′(s)ds	dτψ′(s)ds	X
ejpam-5605	238	18	≤	≤	NUM
ejpam-5605	238	19	(	(	PUNCT
ejpam-5605	238	20	1	1	NUM
ejpam-5605	238	21	+	+	NUM
ejpam-5605	238	22	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	238	23	(	(	PUNCT
ejpam-5605	238	24	·	·	PUNCT
ejpam-5605	238	25	,	,	PUNCT
ejpam-5605	238	26	ω)∥l∞	ω)∥l∞	NUM
ejpam-5605	238	27	∫	∫	PROPN
ejpam-5605	238	28	ξ	ξ	PROPN
ejpam-5605	238	29	a	a	DET
ejpam-5605	238	30	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	238	31	,	,	PUNCT
ejpam-5605	238	32	a	a	PRON
ejpam-5605	238	33	)	)	PUNCT
ejpam-5605	238	34	ϕ(s	ϕ(s	PROPN
ejpam-5605	238	35	,	,	PUNCT
ejpam-5605	238	36	a)ϑi−1	a)ϑi−1	PROPN
ejpam-5605	238	37	γ(ϑi	γ(ϑi	PROPN
ejpam-5605	238	38	−	−	PROPN
ejpam-5605	238	39	1	1	NUM
ejpam-5605	238	40	)	)	PUNCT
ejpam-5605	238	41	ψ′(s)ds	ψ′(s)ds	PROPN
ejpam-5605	238	42	≤	≤	PROPN
ejpam-5605	238	43	(	(	PUNCT
ejpam-5605	238	44	1	1	NUM
ejpam-5605	238	45	+	+	NUM
ejpam-5605	238	46	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	238	47	(	(	PUNCT
ejpam-5605	238	48	·	·	PUNCT
ejpam-5605	238	49	,	,	PUNCT
ejpam-5605	238	50	ω)∥l∞eϖiϕ(b	ω)∥l∞eϖiϕ(b	PROPN
ejpam-5605	238	51	,	,	PUNCT
ejpam-5605	238	52	a	a	PRON
ejpam-5605	238	53	)	)	PUNCT
ejpam-5605	238	54	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	238	55	,	,	PUNCT
ejpam-5605	238	56	a)ϑi	a)ϑi	PROPN
ejpam-5605	238	57	ϑiγ(ϑi	ϑiγ(ϑi	PRON
ejpam-5605	238	58	−	−	PROPN
ejpam-5605	238	59	1	1	NUM
ejpam-5605	238	60	)	)	PUNCT
ejpam-5605	238	61	,	,	PUNCT
ejpam-5605	239	1	i	i	PRON
ejpam-5605	239	2	=	=	NOUN
ejpam-5605	239	3	1	1	NUM
ejpam-5605	239	4	,	,	PUNCT
ejpam-5605	239	5	2	2	NUM
ejpam-5605	239	6	.	.	X
ejpam-5605	239	7	hence	hence	ADV
ejpam-5605	239	8	∥hi(z1	∥hi(z1	X
ejpam-5605	239	9	(	(	PUNCT
ejpam-5605	239	10	·	·	PUNCT
ejpam-5605	239	11	,	,	PUNCT
ejpam-5605	239	12	ω	ω	NOUN
ejpam-5605	239	13	)	)	PUNCT
ejpam-5605	239	14	,	,	PUNCT
ejpam-5605	239	15	z2	z2	PROPN
ejpam-5605	239	16	(	(	PUNCT
ejpam-5605	239	17	·	·	NUM
ejpam-5605	239	18	,	,	PUNCT
ejpam-5605	239	19	ω	ω	NOUN
ejpam-5605	239	20	)	)	PUNCT
ejpam-5605	239	21	,	,	PUNCT
ejpam-5605	239	22	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	239	23	≤	≤	NUM
ejpam-5605	239	24	(	(	PUNCT
ejpam-5605	239	25	1	1	NUM
ejpam-5605	239	26	+	+	NUM
ejpam-5605	239	27	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	239	28	(	(	PUNCT
ejpam-5605	239	29	·	·	PUNCT
ejpam-5605	239	30	,	,	PUNCT
ejpam-5605	239	31	ω)∥l∞eϖiϕ(b	ω)∥l∞eϖiϕ(b	PROPN
ejpam-5605	239	32	,	,	PUNCT
ejpam-5605	239	33	a	a	PRON
ejpam-5605	239	34	)	)	PUNCT
ejpam-5605	239	35	ϕ(b	ϕ(b	PROPN
ejpam-5605	239	36	,	,	PUNCT
ejpam-5605	239	37	a)ϑi	a)ϑi	PROPN
ejpam-5605	239	38	ϑiγ(ϑi	ϑiγ(ϑi	PRON
ejpam-5605	239	39	−	−	PROPN
ejpam-5605	239	40	1	1	NUM
ejpam-5605	239	41	)	)	PUNCT
ejpam-5605	239	42	,	,	PUNCT
ejpam-5605	239	43	i	i	PRON
ejpam-5605	239	44	=	=	NOUN
ejpam-5605	239	45	1	1	NUM
ejpam-5605	239	46	,	,	PUNCT
ejpam-5605	239	47	2	2	NUM
ejpam-5605	239	48	.	.	PUNCT
ejpam-5605	240	1	this	this	PRON
ejpam-5605	240	2	implies	imply	VERB
ejpam-5605	240	3	that	that	SCONJ
ejpam-5605	240	4	:	:	PUNCT
ejpam-5605	240	5	∥h(z1	∥h(z1	NUM
ejpam-5605	240	6	(	(	PUNCT
ejpam-5605	240	7	·	·	PUNCT
ejpam-5605	240	8	,	,	PUNCT
ejpam-5605	240	9	ω	ω	NOUN
ejpam-5605	240	10	)	)	PUNCT
ejpam-5605	240	11	,	,	PUNCT
ejpam-5605	240	12	z2	z2	PROPN
ejpam-5605	240	13	(	(	PUNCT
ejpam-5605	240	14	·	·	NUM
ejpam-5605	240	15	,	,	PUNCT
ejpam-5605	240	16	ω	ω	NOUN
ejpam-5605	240	17	)	)	PUNCT
ejpam-5605	240	18	,	,	PUNCT
ejpam-5605	240	19	ω)∥j	ω)∥j	NOUN
ejpam-5605	240	20	=	=	SYM
ejpam-5605	240	21	∥h1(z1	∥h1(z1	ADJ
ejpam-5605	240	22	(	(	PUNCT
ejpam-5605	240	23	·	·	NUM
ejpam-5605	240	24	,	,	PUNCT
ejpam-5605	240	25	ω	ω	NOUN
ejpam-5605	240	26	)	)	PUNCT
ejpam-5605	240	27	,	,	PUNCT
ejpam-5605	240	28	z2	z2	PROPN
ejpam-5605	240	29	(	(	PUNCT
ejpam-5605	240	30	·	·	NUM
ejpam-5605	240	31	,	,	PUNCT
ejpam-5605	240	32	ω	ω	NOUN
ejpam-5605	240	33	)	)	PUNCT
ejpam-5605	240	34	,	,	PUNCT
ejpam-5605	240	35	ω)∥∞	ω)∥∞	PRON
ejpam-5605	240	36	+	+	CCONJ
ejpam-5605	240	37	∥h2(z1	∥h2(z1	ADJ
ejpam-5605	240	38	(	(	PUNCT
ejpam-5605	240	39	·	·	PUNCT
ejpam-5605	240	40	,	,	PUNCT
ejpam-5605	240	41	ω	ω	NOUN
ejpam-5605	240	42	)	)	PUNCT
ejpam-5605	240	43	,	,	PUNCT
ejpam-5605	240	44	z2	z2	PROPN
ejpam-5605	240	45	(	(	PUNCT
ejpam-5605	240	46	·	·	NUM
ejpam-5605	240	47	,	,	PUNCT
ejpam-5605	240	48	ω	ω	NOUN
ejpam-5605	240	49	)	)	PUNCT
ejpam-5605	240	50	,	,	PUNCT
ejpam-5605	240	51	ω)∥∞	ω)∥∞	NOUN
ejpam-5605	240	52	≤	≤	NUM
ejpam-5605	240	53	2∑	2∑	NUM
ejpam-5605	240	54	i=1	i=1	X
ejpam-5605	240	55	(	(	PUNCT
ejpam-5605	240	56	1	1	NUM
ejpam-5605	240	57	+	+	NUM
ejpam-5605	240	58	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	240	59	(	(	PUNCT
ejpam-5605	240	60	·	·	PUNCT
ejpam-5605	240	61	,	,	PUNCT
ejpam-5605	240	62	ω)∥l∞eϖiϕ(b	ω)∥l∞eϖiϕ(b	PROPN
ejpam-5605	240	63	,	,	PUNCT
ejpam-5605	240	64	a	a	PRON
ejpam-5605	240	65	)	)	PUNCT
ejpam-5605	240	66	ϕ(b	ϕ(b	PROPN
ejpam-5605	240	67	,	,	PUNCT
ejpam-5605	240	68	a)ϑi	a)ϑi	PROPN
ejpam-5605	240	69	ϑiγ(ϑi	ϑiγ(ϑi	PRON
ejpam-5605	240	70	−	−	PROPN
ejpam-5605	240	71	1	1	NUM
ejpam-5605	240	72	)	)	PUNCT
ejpam-5605	240	73	.	.	PUNCT
ejpam-5605	241	1	m.	m.	NOUN
ejpam-5605	241	2	ziane	ziane	PROPN
ejpam-5605	241	3	et	et	PROPN
ejpam-5605	241	4	al	al	PROPN
ejpam-5605	241	5	.	.	PUNCT
ejpam-5605	241	6	/	/	SYM
ejpam-5605	241	7	eur	eur	PROPN
ejpam-5605	241	8	.	.	PUNCT
ejpam-5605	242	1	j.	j.	PROPN
ejpam-5605	242	2	pure	pure	PROPN
ejpam-5605	242	3	appl	appl	PROPN
ejpam-5605	242	4	.	.	PROPN
ejpam-5605	242	5	math	math	PROPN
ejpam-5605	242	6	,	,	PUNCT
ejpam-5605	242	7	18	18	NUM
ejpam-5605	242	8	(	(	PUNCT
ejpam-5605	242	9	1	1	NUM
ejpam-5605	242	10	)	)	PUNCT
ejpam-5605	242	11	(	(	PUNCT
ejpam-5605	242	12	2025	2025	NUM
ejpam-5605	242	13	)	)	PUNCT
ejpam-5605	242	14	,	,	PUNCT
ejpam-5605	242	15	5605	5605	NUM
ejpam-5605	242	16	12	12	NUM
ejpam-5605	242	17	of	of	ADP
ejpam-5605	242	18	21	21	NUM
ejpam-5605	242	19	this	this	PRON
ejpam-5605	242	20	shows	show	VERB
ejpam-5605	242	21	that	that	SCONJ
ejpam-5605	242	22	h	h	NOUN
ejpam-5605	242	23	transforms	transform	VERB
ejpam-5605	242	24	bounded	bounded	ADJ
ejpam-5605	242	25	sets	set	NOUN
ejpam-5605	242	26	into	into	ADP
ejpam-5605	242	27	bounded	bounded	ADJ
ejpam-5605	242	28	sets	set	NOUN
ejpam-5605	242	29	in	in	ADP
ejpam-5605	242	30	j.	j.	PROPN
ejpam-5605	242	31	step	step	PROPN
ejpam-5605	242	32	2	2	NUM
ejpam-5605	242	33	.	.	PUNCT
ejpam-5605	243	1	h	h	PROPN
ejpam-5605	243	2	is	be	AUX
ejpam-5605	243	3	continuous	continuous	ADJ
ejpam-5605	243	4	.	.	PUNCT
ejpam-5605	244	1	let	let	VERB
ejpam-5605	244	2	{	{	PUNCT
ejpam-5605	244	3	z1,n	z1,n	PROPN
ejpam-5605	244	4	,	,	PUNCT
ejpam-5605	244	5	z2,n	z2,n	PROPN
ejpam-5605	244	6	}	}	PUNCT
ejpam-5605	244	7	be	be	AUX
ejpam-5605	244	8	a	a	DET
ejpam-5605	244	9	sequence	sequence	NOUN
ejpam-5605	244	10	satisfying	satisfy	VERB
ejpam-5605	244	11	{	{	PUNCT
ejpam-5605	244	12	z1,n	z1,n	PROPN
ejpam-5605	244	13	,	,	PUNCT
ejpam-5605	244	14	sz	sz	NOUN
ejpam-5605	244	15	,	,	PUNCT
ejpam-5605	244	16	n	n	CCONJ
ejpam-5605	244	17	}	}	PUNCT
ejpam-5605	244	18	→	→	SYM
ejpam-5605	244	19	(	(	PUNCT
ejpam-5605	244	20	z1	z1	PROPN
ejpam-5605	244	21	,	,	PUNCT
ejpam-5605	244	22	z2	z2	PROPN
ejpam-5605	244	23	)	)	PUNCT
ejpam-5605	244	24	in	in	ADP
ejpam-5605	244	25	br	br	NOUN
ejpam-5605	244	26	as	as	ADP
ejpam-5605	244	27	n	n	PROPN
ejpam-5605	244	28	→	→	SYM
ejpam-5605	244	29	∞.	∞.	PROPN
ejpam-5605	244	30	for	for	ADP
ejpam-5605	244	31	each	each	DET
ejpam-5605	244	32	(	(	PUNCT
ejpam-5605	244	33	ξ	ξ	PROPN
ejpam-5605	244	34	,	,	PUNCT
ejpam-5605	244	35	ω	ω	NOUN
ejpam-5605	244	36	)	)	PUNCT
ejpam-5605	244	37	∈	∈	PROPN
ejpam-5605	244	38	i×	i×	PROPN
ejpam-5605	244	39	ω	ω	PROPN
ejpam-5605	244	40	,	,	PUNCT
ejpam-5605	244	41	making	make	VERB
ejpam-5605	244	42	use	use	NOUN
ejpam-5605	244	43	of	of	ADP
ejpam-5605	244	44	(	(	PUNCT
ejpam-5605	244	45	a1	a1	NOUN
ejpam-5605	244	46	)	)	PUNCT
ejpam-5605	244	47	,	,	PUNCT
ejpam-5605	244	48	we	we	PRON
ejpam-5605	244	49	easily	easily	ADV
ejpam-5605	244	50	have	have	AUX
ejpam-5605	244	51	∥fi(τ	∥fi(τ	VERB
ejpam-5605	244	52	,	,	PUNCT
ejpam-5605	244	53	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	244	54	,	,	PUNCT
ejpam-5605	244	55	ω	ω	NOUN
ejpam-5605	244	56	)	)	PUNCT
ejpam-5605	244	57	,	,	PUNCT
ejpam-5605	244	58	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	244	59	,	,	PUNCT
ejpam-5605	244	60	ω	ω	NOUN
ejpam-5605	244	61	)	)	PUNCT
ejpam-5605	244	62	,	,	PUNCT
ejpam-5605	245	1	ω)−	ω)−	PROPN
ejpam-5605	245	2	fi(τ	fi(τ	PROPN
ejpam-5605	245	3	,	,	PUNCT
ejpam-5605	245	4	z1(τ	z1(τ	PROPN
ejpam-5605	245	5	,	,	PUNCT
ejpam-5605	245	6	ω	ω	NOUN
ejpam-5605	245	7	)	)	PUNCT
ejpam-5605	245	8	,	,	PUNCT
ejpam-5605	245	9	z2(τ	z2(τ	PROPN
ejpam-5605	245	10	,	,	PUNCT
ejpam-5605	245	11	ω	ω	NOUN
ejpam-5605	245	12	)	)	PUNCT
ejpam-5605	245	13	,	,	PUNCT
ejpam-5605	245	14	ω)∥	ω)∥	PUNCT
ejpam-5605	245	15	→	→	SYM
ejpam-5605	245	16	0	0	NUM
ejpam-5605	245	17	,	,	PUNCT
ejpam-5605	245	18	as	as	ADP
ejpam-5605	245	19	n	n	PRON
ejpam-5605	245	20	−→	−→	NOUN
ejpam-5605	245	21	∞	∞	NUM
ejpam-5605	245	22	,	,	PUNCT
ejpam-5605	245	23	i	i	PRON
ejpam-5605	245	24	=	=	NOUN
ejpam-5605	245	25	1	1	NUM
ejpam-5605	245	26	,	,	PUNCT
ejpam-5605	245	27	2	2	NUM
ejpam-5605	245	28	.	.	PUNCT
ejpam-5605	245	29	next	next	ADV
ejpam-5605	245	30	,	,	PUNCT
ejpam-5605	245	31	in	in	ADP
ejpam-5605	245	32	view	view	NOUN
ejpam-5605	245	33	of	of	ADP
ejpam-5605	245	34	(	(	PUNCT
ejpam-5605	245	35	a3	a3	NOUN
ejpam-5605	245	36	)	)	PUNCT
ejpam-5605	245	37	,	,	PUNCT
ejpam-5605	245	38	one	one	PRON
ejpam-5605	245	39	gets	get	VERB
ejpam-5605	245	40	∥fi(τ	∥fi(τ	ADJ
ejpam-5605	245	41	,	,	PUNCT
ejpam-5605	245	42	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	245	43	,	,	PUNCT
ejpam-5605	245	44	ω	ω	NOUN
ejpam-5605	245	45	)	)	PUNCT
ejpam-5605	245	46	,	,	PUNCT
ejpam-5605	245	47	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	245	48	,	,	PUNCT
ejpam-5605	245	49	ω	ω	NOUN
ejpam-5605	245	50	)	)	PUNCT
ejpam-5605	245	51	,	,	PUNCT
ejpam-5605	245	52	ω)−	ω)−	PROPN
ejpam-5605	245	53	fi(τ	fi(τ	PROPN
ejpam-5605	245	54	,	,	PUNCT
ejpam-5605	245	55	z1(τ	z1(τ	PROPN
ejpam-5605	245	56	,	,	PUNCT
ejpam-5605	245	57	ω	ω	NOUN
ejpam-5605	245	58	)	)	PUNCT
ejpam-5605	245	59	,	,	PUNCT
ejpam-5605	245	60	z2(τ	z2(τ	PROPN
ejpam-5605	245	61	,	,	PUNCT
ejpam-5605	245	62	ω	ω	NOUN
ejpam-5605	245	63	)	)	PUNCT
ejpam-5605	245	64	,	,	PUNCT
ejpam-5605	245	65	ω)∥	ω)∥	PUNCT
ejpam-5605	245	66	≤	≤	NUM
ejpam-5605	245	67	∥fi(τ	∥fi(τ	NOUN
ejpam-5605	245	68	,	,	PUNCT
ejpam-5605	245	69	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	245	70	,	,	PUNCT
ejpam-5605	245	71	ω	ω	NOUN
ejpam-5605	245	72	)	)	PUNCT
ejpam-5605	245	73	,	,	PUNCT
ejpam-5605	245	74	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	245	75	,	,	PUNCT
ejpam-5605	245	76	ω	ω	NOUN
ejpam-5605	245	77	)	)	PUNCT
ejpam-5605	245	78	,	,	PUNCT
ejpam-5605	245	79	ω)∥+	ω)∥+	ADJ
ejpam-5605	245	80	∥fi(τ	∥fi(τ	VERB
ejpam-5605	245	81	,	,	PUNCT
ejpam-5605	245	82	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	245	83	,	,	PUNCT
ejpam-5605	245	84	ω	ω	NOUN
ejpam-5605	245	85	)	)	PUNCT
ejpam-5605	245	86	,	,	PUNCT
ejpam-5605	245	87	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	245	88	,	,	PUNCT
ejpam-5605	245	89	ω	ω	NOUN
ejpam-5605	245	90	)	)	PUNCT
ejpam-5605	245	91	,	,	PUNCT
ejpam-5605	245	92	ω)∥	ω)∥	PUNCT
ejpam-5605	245	93	≤	≤	NUM
ejpam-5605	245	94	2ψi(τ	2ψi(τ	NUM
ejpam-5605	245	95	,	,	PUNCT
ejpam-5605	245	96	ω	ω	NOUN
ejpam-5605	245	97	)	)	PUNCT
ejpam-5605	245	98	(	(	PUNCT
ejpam-5605	245	99	1	1	NUM
ejpam-5605	245	100	+	+	NUM
ejpam-5605	245	101	∥z1(τ	∥z1(τ	NOUN
ejpam-5605	245	102	,	,	PUNCT
ejpam-5605	245	103	ω)∥+	ω)∥+	ADJ
ejpam-5605	245	104	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	245	105	,	,	PUNCT
ejpam-5605	245	106	ω)∥	ω)∥	NUM
ejpam-5605	245	107	)	)	PUNCT
ejpam-5605	245	108	≤	≤	NOUN
ejpam-5605	245	109	2(1	2(1	NUM
ejpam-5605	246	1	+	+	CCONJ
ejpam-5605	246	2	2r)ψi(τ	2r)ψi(τ	NUM
ejpam-5605	246	3	,	,	PUNCT
ejpam-5605	246	4	ω	ω	NOUN
ejpam-5605	246	5	)	)	PUNCT
ejpam-5605	246	6	,	,	PUNCT
ejpam-5605	246	7	i	i	PRON
ejpam-5605	246	8	=	=	NOUN
ejpam-5605	246	9	1	1	NUM
ejpam-5605	246	10	,	,	PUNCT
ejpam-5605	246	11	2	2	NUM
ejpam-5605	246	12	.	.	PUNCT
ejpam-5605	247	1	since	since	ADV
ejpam-5605	247	2	,	,	PUNCT
ejpam-5605	247	3	the	the	DET
ejpam-5605	247	4	functions	function	NOUN
ejpam-5605	247	5	τ	τ	PROPN
ejpam-5605	247	6	7→	7→	NUM
ejpam-5605	247	7	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	247	8	,	,	PUNCT
ejpam-5605	247	9	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	247	10	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	247	11	−	−	PROPN
ejpam-5605	247	12	1	1	NUM
ejpam-5605	247	13	)	)	PUNCT
ejpam-5605	247	14	ψi(τ	ψi(τ	PUNCT
ejpam-5605	247	15	,	,	PUNCT
ejpam-5605	247	16	ω	ω	NOUN
ejpam-5605	247	17	)	)	PUNCT
ejpam-5605	247	18	and	and	CCONJ
ejpam-5605	247	19	s	s	PROPN
ejpam-5605	247	20	7→	7→	NUM
ejpam-5605	247	21	ψ′(s)ϕ(s	ψ′(s)ϕ(s	PROPN
ejpam-5605	247	22	,	,	PUNCT
ejpam-5605	247	23	a)ϑi−1	a)ϑi−1	PROPN
ejpam-5605	247	24	γ(ϑi	γ(ϑi	PROPN
ejpam-5605	247	25	)	)	PUNCT
ejpam-5605	247	26	ψi(s	ψi(s	NOUN
ejpam-5605	247	27	,	,	PUNCT
ejpam-5605	247	28	ω	ω	NOUN
ejpam-5605	247	29	)	)	PUNCT
ejpam-5605	247	30	,	,	PUNCT
ejpam-5605	247	31	i	i	PRON
ejpam-5605	247	32	=	=	NOUN
ejpam-5605	247	33	1	1	NUM
ejpam-5605	247	34	,	,	PUNCT
ejpam-5605	247	35	2	2	NUM
ejpam-5605	247	36	are	be	AUX
ejpam-5605	247	37	lebesgue	lebesgue	NOUN
ejpam-5605	247	38	integrable	integrable	ADJ
ejpam-5605	247	39	over	over	ADP
ejpam-5605	247	40	[	[	X
ejpam-5605	247	41	a	a	X
ejpam-5605	247	42	,	,	PUNCT
ejpam-5605	247	43	s	s	AUX
ejpam-5605	247	44	]	]	X
ejpam-5605	247	45	(	(	PUNCT
ejpam-5605	247	46	resp	resp	NOUN
ejpam-5605	247	47	.	.	PUNCT
ejpam-5605	248	1	[	[	X
ejpam-5605	248	2	a	a	DET
ejpam-5605	248	3	,	,	PUNCT
ejpam-5605	248	4	ξ	ξ	NOUN
ejpam-5605	248	5	]	]	PUNCT
ejpam-5605	248	6	)	)	PUNCT
ejpam-5605	248	7	.	.	PUNCT
ejpam-5605	249	1	then	then	ADV
ejpam-5605	249	2	it	it	PRON
ejpam-5605	249	3	follows	follow	VERB
ejpam-5605	249	4	from	from	ADP
ejpam-5605	249	5	the	the	DET
ejpam-5605	249	6	lebesgue	lebesgue	NOUN
ejpam-5605	249	7	dominated	dominate	VERB
ejpam-5605	249	8	convergence	convergence	NOUN
ejpam-5605	249	9	theorem	theorem	VERB
ejpam-5605	249	10	that	that	SCONJ
ejpam-5605	249	11	∥hi(z1,n(ξ	∥hi(z1,n(ξ	PROPN
ejpam-5605	249	12	,	,	PUNCT
ejpam-5605	249	13	ω	ω	NOUN
ejpam-5605	249	14	)	)	PUNCT
ejpam-5605	249	15	,	,	PUNCT
ejpam-5605	249	16	z2,n(ξ	z2,n(ξ	NOUN
ejpam-5605	249	17	,	,	PUNCT
ejpam-5605	249	18	ω	ω	NOUN
ejpam-5605	249	19	)	)	PUNCT
ejpam-5605	249	20	,	,	PUNCT
ejpam-5605	249	21	ω)−hi(z1(ξ	ω)−hi(z1(ξ	PROPN
ejpam-5605	249	22	,	,	PUNCT
ejpam-5605	249	23	ω	ω	NOUN
ejpam-5605	249	24	)	)	PUNCT
ejpam-5605	249	25	,	,	PUNCT
ejpam-5605	249	26	z2(ξ	z2(ξ	PROPN
ejpam-5605	249	27	,	,	PUNCT
ejpam-5605	249	28	ω	ω	NOUN
ejpam-5605	249	29	)	)	PUNCT
ejpam-5605	249	30	,	,	PUNCT
ejpam-5605	249	31	ω)∥	ω)∥	PUNCT
ejpam-5605	249	32	≤	≤	NUM
ejpam-5605	249	33	(	(	PUNCT
ejpam-5605	249	34	ϑi	ϑi	PROPN
ejpam-5605	249	35	−	−	PROPN
ejpam-5605	249	36	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	249	37	,	,	PUNCT
ejpam-5605	249	38	a	a	PRON
ejpam-5605	249	39	)	)	PUNCT
ejpam-5605	249	40	∫	∫	PROPN
ejpam-5605	250	1	ξ	ξ	PROPN
ejpam-5605	251	1	a	a	DET
ejpam-5605	251	2	∫	∫	PROPN
ejpam-5605	251	3	s	s	VERB
ejpam-5605	251	4	a	a	DET
ejpam-5605	251	5	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	251	6	,	,	PUNCT
ejpam-5605	251	7	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	251	8	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	251	9	−	−	NOUN
ejpam-5605	251	10	1	1	NUM
ejpam-5605	251	11	)	)	PUNCT
ejpam-5605	251	12	×	×	NOUN
ejpam-5605	251	13	∥fi(τ	∥fi(τ	NOUN
ejpam-5605	251	14	,	,	PUNCT
ejpam-5605	251	15	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	251	16	,	,	PUNCT
ejpam-5605	251	17	ω	ω	NOUN
ejpam-5605	251	18	)	)	PUNCT
ejpam-5605	251	19	,	,	PUNCT
ejpam-5605	251	20	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	251	21	,	,	PUNCT
ejpam-5605	251	22	ω	ω	NOUN
ejpam-5605	251	23	)	)	PUNCT
ejpam-5605	251	24	,	,	PUNCT
ejpam-5605	251	25	ω)−	ω)−	PROPN
ejpam-5605	251	26	fi(τ	fi(τ	PROPN
ejpam-5605	251	27	,	,	PUNCT
ejpam-5605	251	28	z1(τ	z1(τ	PROPN
ejpam-5605	251	29	,	,	PUNCT
ejpam-5605	251	30	ω	ω	NOUN
ejpam-5605	251	31	)	)	PUNCT
ejpam-5605	251	32	,	,	PUNCT
ejpam-5605	251	33	z2(τ	z2(τ	PROPN
ejpam-5605	251	34	,	,	PUNCT
ejpam-5605	251	35	ω	ω	NOUN
ejpam-5605	251	36	)	)	PUNCT
ejpam-5605	251	37	,	,	PUNCT
ejpam-5605	251	38	ω)∥dτψ′(s)ds	ω)∥dτψ′(s)ds	NUM
ejpam-5605	251	39	−−−→	−−−→	VERB
ejpam-5605	251	40	n→∞	n→∞	NUM
ejpam-5605	251	41	0	0	NUM
ejpam-5605	251	42	,	,	PUNCT
ejpam-5605	251	43	for	for	ADP
ejpam-5605	251	44	all	all	DET
ejpam-5605	251	45	ξ	ξ	X
ejpam-5605	251	46	∈	∈	PROPN
ejpam-5605	251	47	i	i	PRON
ejpam-5605	251	48	,	,	PUNCT
ejpam-5605	251	49	i	i	NOUN
ejpam-5605	251	50	=	=	NOUN
ejpam-5605	251	51	1	1	NUM
ejpam-5605	251	52	,	,	PUNCT
ejpam-5605	251	53	2	2	NUM
ejpam-5605	251	54	.	.	X
ejpam-5605	251	55	therefore	therefore	ADV
ejpam-5605	251	56	,	,	PUNCT
ejpam-5605	251	57	∥hi	∥hi	ADV
ejpam-5605	251	58	(	(	PUNCT
ejpam-5605	251	59	·	·	PUNCT
ejpam-5605	251	60	,	,	PUNCT
ejpam-5605	251	61	z1,n	z1,n	PROPN
ejpam-5605	251	62	(	(	PUNCT
ejpam-5605	251	63	·	·	NUM
ejpam-5605	251	64	,	,	PUNCT
ejpam-5605	251	65	ω	ω	NOUN
ejpam-5605	251	66	)	)	PUNCT
ejpam-5605	251	67	,	,	PUNCT
ejpam-5605	251	68	z2,n	z2,n	PROPN
ejpam-5605	251	69	(	(	PUNCT
ejpam-5605	251	70	·	·	NUM
ejpam-5605	251	71	,	,	PUNCT
ejpam-5605	251	72	ω	ω	NOUN
ejpam-5605	251	73	)	)	PUNCT
ejpam-5605	251	74	,	,	PUNCT
ejpam-5605	251	75	ω)−hi	ω)−hi	PROPN
ejpam-5605	251	76	(	(	PUNCT
ejpam-5605	251	77	·	·	PUNCT
ejpam-5605	251	78	,	,	PUNCT
ejpam-5605	251	79	z1	z1	PROPN
ejpam-5605	251	80	(	(	PUNCT
ejpam-5605	251	81	·	·	NUM
ejpam-5605	251	82	,	,	PUNCT
ejpam-5605	251	83	ω	ω	NOUN
ejpam-5605	251	84	)	)	PUNCT
ejpam-5605	251	85	,	,	PUNCT
ejpam-5605	251	86	z2	z2	PROPN
ejpam-5605	251	87	(	(	PUNCT
ejpam-5605	251	88	·	·	NUM
ejpam-5605	251	89	,	,	PUNCT
ejpam-5605	251	90	ω	ω	NOUN
ejpam-5605	251	91	)	)	PUNCT
ejpam-5605	251	92	,	,	PUNCT
ejpam-5605	251	93	ω)∥∞	ω)∥∞	PRON
ejpam-5605	251	94	−−−→	−−−→	VERB
ejpam-5605	251	95	n→∞	n→∞	NUM
ejpam-5605	251	96	0	0	NUM
ejpam-5605	251	97	,	,	PUNCT
ejpam-5605	251	98	i	i	PRON
ejpam-5605	251	99	=	=	NOUN
ejpam-5605	251	100	1	1	NUM
ejpam-5605	251	101	,	,	PUNCT
ejpam-5605	251	102	2	2	NUM
ejpam-5605	251	103	.	.	PUNCT
ejpam-5605	251	104	accordingly	accordingly	ADV
ejpam-5605	251	105	,	,	PUNCT
ejpam-5605	251	106	the	the	DET
ejpam-5605	251	107	operator	operator	NOUN
ejpam-5605	251	108	h	h	NOUN
ejpam-5605	251	109	(	(	PUNCT
ejpam-5605	251	110	·	·	PUNCT
ejpam-5605	251	111	,	,	PUNCT
ejpam-5605	251	112	·	·	PUNCT
ejpam-5605	251	113	)	)	PUNCT
ejpam-5605	251	114	is	be	AUX
ejpam-5605	251	115	continuous	continuous	ADJ
ejpam-5605	251	116	.	.	PUNCT
ejpam-5605	252	1	step	step	NOUN
ejpam-5605	252	2	3	3	NUM
ejpam-5605	252	3	.	.	PUNCT
ejpam-5605	252	4	h(br	h(br	PROPN
ejpam-5605	252	5	)	)	PUNCT
ejpam-5605	252	6	is	be	AUX
ejpam-5605	252	7	equicontinuous	equicontinuous	ADJ
ejpam-5605	252	8	.	.	PUNCT
ejpam-5605	253	1	for	for	ADP
ejpam-5605	253	2	any	any	DET
ejpam-5605	253	3	ξ1	ξ1	NOUN
ejpam-5605	253	4	,	,	PUNCT
ejpam-5605	253	5	ξ2	ξ2	NOUN
ejpam-5605	253	6	∈	∈	PROPN
ejpam-5605	254	1	i	i	PRON
ejpam-5605	254	2	with	with	ADP
ejpam-5605	254	3	ξ1	ξ1	PROPN
ejpam-5605	254	4	<	<	X
ejpam-5605	254	5	ξ2	ξ2	PROPN
ejpam-5605	254	6	and	and	CCONJ
ejpam-5605	254	7	(	(	PUNCT
ejpam-5605	254	8	z1	z1	PROPN
ejpam-5605	254	9	,	,	PUNCT
ejpam-5605	254	10	z2	z2	NUM
ejpam-5605	254	11	)	)	PUNCT
ejpam-5605	254	12	∈	∈	PROPN
ejpam-5605	254	13	br	br	NOUN
ejpam-5605	254	14	,	,	PUNCT
ejpam-5605	254	15	we	we	PRON
ejpam-5605	254	16	obtain	obtain	VERB
ejpam-5605	254	17	∥hi(z1(ξ2	∥hi(z1(ξ2	PROPN
ejpam-5605	254	18	,	,	PUNCT
ejpam-5605	254	19	ω	ω	NOUN
ejpam-5605	254	20	)	)	PUNCT
ejpam-5605	254	21	,	,	PUNCT
ejpam-5605	254	22	z2(ξ2	z2(ξ2	NOUN
ejpam-5605	254	23	,	,	PUNCT
ejpam-5605	254	24	ω	ω	NOUN
ejpam-5605	254	25	)	)	PUNCT
ejpam-5605	254	26	,	,	PUNCT
ejpam-5605	254	27	ω)−hi(z1(ξ1	ω)−hi(z1(ξ1	PROPN
ejpam-5605	254	28	,	,	PUNCT
ejpam-5605	254	29	ω	ω	NOUN
ejpam-5605	254	30	)	)	PUNCT
ejpam-5605	254	31	,	,	PUNCT
ejpam-5605	254	32	z2(ξ1	z2(ξ1	PROPN
ejpam-5605	254	33	,	,	PUNCT
ejpam-5605	254	34	ω	ω	NOUN
ejpam-5605	254	35	)	)	PUNCT
ejpam-5605	254	36	,	,	PUNCT
ejpam-5605	254	37	ω)∥	ω)∥	PUNCT
ejpam-5605	254	38	≤	≤	PROPN
ejpam-5605	255	1	ji,1	ji,1	PROPN
ejpam-5605	255	2	+	+	CCONJ
ejpam-5605	255	3	ji,2	ji,2	PROPN
ejpam-5605	255	4	,	,	PUNCT
ejpam-5605	255	5	i	i	NOUN
ejpam-5605	255	6	=	=	NOUN
ejpam-5605	255	7	1	1	NUM
ejpam-5605	255	8	,	,	PUNCT
ejpam-5605	255	9	2	2	NUM
ejpam-5605	255	10	,	,	PUNCT
ejpam-5605	255	11	where	where	SCONJ
ejpam-5605	255	12	ji,1	ji,1	PROPN
ejpam-5605	255	13	=	=	PRON
ejpam-5605	255	14	(	(	PUNCT
ejpam-5605	255	15	ϑi	ϑi	NOUN
ejpam-5605	255	16	−	−	PROPN
ejpam-5605	255	17	1	1	NUM
ejpam-5605	255	18	)	)	PUNCT
ejpam-5605	255	19	eϖiϕ(ξ2,a	eϖiϕ(ξ2,a	PROPN
ejpam-5605	255	20	)	)	PUNCT
ejpam-5605	255	21	∫	∫	PROPN
ejpam-5605	255	22	ξ2	ξ2	PROPN
ejpam-5605	255	23	ξ1	ξ1	PROPN
ejpam-5605	255	24	ψ′(s)eϖiϕ(s	ψ′(s)eϖiϕ(s	PROPN
ejpam-5605	255	25	,	,	PUNCT
ejpam-5605	255	26	a	a	PRON
ejpam-5605	255	27	)	)	PUNCT
ejpam-5605	255	28	∫	∫	PROPN
ejpam-5605	255	29	s	s	PROPN
ejpam-5605	255	30	a	a	DET
ejpam-5605	255	31	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	255	32	,	,	PUNCT
ejpam-5605	255	33	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	255	34	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	255	35	−	−	PROPN
ejpam-5605	255	36	1	1	NUM
ejpam-5605	255	37	)	)	PUNCT
ejpam-5605	255	38	∥fi(τ	∥fi(τ	ADJ
ejpam-5605	255	39	,	,	PUNCT
ejpam-5605	255	40	z1(τ	z1(τ	PROPN
ejpam-5605	255	41	,	,	PUNCT
ejpam-5605	255	42	ω	ω	NOUN
ejpam-5605	255	43	)	)	PUNCT
ejpam-5605	255	44	,	,	PUNCT
ejpam-5605	255	45	z2(τ	z2(τ	PROPN
ejpam-5605	255	46	,	,	PUNCT
ejpam-5605	255	47	ω	ω	NOUN
ejpam-5605	255	48	)	)	PUNCT
ejpam-5605	255	49	,	,	PUNCT
ejpam-5605	255	50	ω)∥dτds	ω)∥dτd	NOUN
ejpam-5605	255	51	,	,	PUNCT
ejpam-5605	255	52	m.	m.	NOUN
ejpam-5605	255	53	ziane	ziane	PROPN
ejpam-5605	255	54	et	et	PROPN
ejpam-5605	255	55	al	al	PROPN
ejpam-5605	255	56	.	.	PUNCT
ejpam-5605	255	57	/	/	SYM
ejpam-5605	255	58	eur	eur	PROPN
ejpam-5605	255	59	.	.	PUNCT
ejpam-5605	256	1	j.	j.	PROPN
ejpam-5605	256	2	pure	pure	PROPN
ejpam-5605	256	3	appl	appl	PROPN
ejpam-5605	256	4	.	.	PROPN
ejpam-5605	256	5	math	math	PROPN
ejpam-5605	256	6	,	,	PUNCT
ejpam-5605	256	7	18	18	NUM
ejpam-5605	256	8	(	(	PUNCT
ejpam-5605	256	9	1	1	NUM
ejpam-5605	256	10	)	)	PUNCT
ejpam-5605	256	11	(	(	PUNCT
ejpam-5605	256	12	2025	2025	NUM
ejpam-5605	256	13	)	)	PUNCT
ejpam-5605	256	14	,	,	PUNCT
ejpam-5605	256	15	5605	5605	NUM
ejpam-5605	256	16	13	13	NUM
ejpam-5605	256	17	of	of	ADP
ejpam-5605	256	18	21	21	NUM
ejpam-5605	256	19	and	and	CCONJ
ejpam-5605	256	20	ji,2	ji,2	PROPN
ejpam-5605	256	21	=	=	PUNCT
ejpam-5605	256	22	(	(	PUNCT
ejpam-5605	256	23	ϑi−	ϑi−	NUM
ejpam-5605	256	24	1	1	NUM
ejpam-5605	256	25	)	)	PUNCT
ejpam-5605	256	26	∫	∫	PROPN
ejpam-5605	256	27	ξ1	ξ1	PROPN
ejpam-5605	256	28	a	a	DET
ejpam-5605	256	29	ψ′(s	ψ′(s	NOUN
ejpam-5605	256	30	)	)	PUNCT
ejpam-5605	256	31	∣∣∣e−ϖiϕ(ξ2,s)−	∣∣∣e−ϖiϕ(ξ2,s)−	ADP
ejpam-5605	256	32	e−ϖiϕ(ξ1,s	e−ϖiϕ(ξ1,s	NOUN
ejpam-5605	256	33	)	)	PUNCT
ejpam-5605	256	34	∣∣∣∥∥∥(iϑi−1;ψ	∣∣∣∥∥∥(iϑi−1;ψ	PROPN
ejpam-5605	256	35	a+	a+	PUNCT
ejpam-5605	256	36	fi(τ	fi(τ	PROPN
ejpam-5605	256	37	,	,	PUNCT
ejpam-5605	256	38	z1(τ	z1(τ	PROPN
ejpam-5605	256	39	,	,	PUNCT
ejpam-5605	256	40	ω	ω	NOUN
ejpam-5605	256	41	)	)	PUNCT
ejpam-5605	256	42	,	,	PUNCT
ejpam-5605	256	43	z2(τ	z2(τ	PROPN
ejpam-5605	256	44	,	,	PUNCT
ejpam-5605	256	45	ω	ω	NOUN
ejpam-5605	256	46	)	)	PUNCT
ejpam-5605	256	47	,	,	PUNCT
ejpam-5605	256	48	ω	ω	PROPN
ejpam-5605	256	49	)	)	PUNCT
ejpam-5605	256	50	(	(	PUNCT
ejpam-5605	256	51	s	s	X
ejpam-5605	256	52	)	)	PUNCT
ejpam-5605	256	53	∥∥∥ds	∥∥∥ds	PROPN
ejpam-5605	256	54	,	,	PUNCT
ejpam-5605	256	55	from	from	ADP
ejpam-5605	256	56	(	(	PUNCT
ejpam-5605	256	57	a3	a3	NOUN
ejpam-5605	256	58	)	)	PUNCT
ejpam-5605	256	59	and	and	CCONJ
ejpam-5605	256	60	using	use	VERB
ejpam-5605	256	61	(	(	PUNCT
ejpam-5605	256	62	11	11	NUM
ejpam-5605	256	63	)	)	PUNCT
ejpam-5605	256	64	and	and	CCONJ
ejpam-5605	256	65	the	the	DET
ejpam-5605	256	66	fact	fact	NOUN
ejpam-5605	256	67	e−ϖiϕ(ξ2,a	e−ϖiϕ(ξ2,a	NUM
ejpam-5605	256	68	)	)	PUNCT
ejpam-5605	256	69	≤	≤	NOUN
ejpam-5605	256	70	1	1	NUM
ejpam-5605	256	71	and	and	CCONJ
ejpam-5605	256	72	lemma	lemma	PROPN
ejpam-5605	256	73	1	1	NUM
ejpam-5605	256	74	,	,	PUNCT
ejpam-5605	256	75	we	we	PRON
ejpam-5605	256	76	get	get	VERB
ejpam-5605	256	77	ji,1	ji,1	PROPN
ejpam-5605	256	78	≤	≤	NOUN
ejpam-5605	256	79	(	(	PUNCT
ejpam-5605	256	80	1	1	NUM
ejpam-5605	256	81	+	+	NUM
ejpam-5605	256	82	2r)(ϑi	2r)(ϑi	NUM
ejpam-5605	256	83	−	−	NOUN
ejpam-5605	256	84	1)∥ψi	1)∥ψi	NUM
ejpam-5605	256	85	(	(	PUNCT
ejpam-5605	256	86	·	·	PUNCT
ejpam-5605	256	87	,	,	PUNCT
ejpam-5605	256	88	ω)∥l∞	ω)∥l∞	NUM
ejpam-5605	256	89	∫	∫	NOUN
ejpam-5605	256	90	ξ2	ξ2	PROPN
ejpam-5605	256	91	ξ1	ξ1	PROPN
ejpam-5605	256	92	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	256	93	,	,	PUNCT
ejpam-5605	256	94	a	a	PRON
ejpam-5605	256	95	)	)	PUNCT
ejpam-5605	256	96	∫	∫	PROPN
ejpam-5605	256	97	s	s	PROPN
ejpam-5605	256	98	a	a	DET
ejpam-5605	256	99	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	256	100	,	,	PUNCT
ejpam-5605	256	101	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	256	102	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	256	103	−	−	PROPN
ejpam-5605	256	104	1	1	NUM
ejpam-5605	256	105	)	)	PUNCT
ejpam-5605	256	106	dτψ′(s)ds	dτψ′(s)ds	X
ejpam-5605	256	107	≤	≤	NUM
ejpam-5605	256	108	(	(	PUNCT
ejpam-5605	256	109	1	1	NUM
ejpam-5605	257	1	+	+	NUM
ejpam-5605	257	2	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	257	3	(	(	PUNCT
ejpam-5605	257	4	·	·	PUNCT
ejpam-5605	257	5	,	,	PUNCT
ejpam-5605	257	6	ω)∥l∞	ω)∥l∞	NUM
ejpam-5605	257	7	∫	∫	NOUN
ejpam-5605	257	8	ξ2	ξ2	PROPN
ejpam-5605	257	9	ξ1	ξ1	PROPN
ejpam-5605	257	10	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	257	11	,	,	PUNCT
ejpam-5605	257	12	a	a	PRON
ejpam-5605	257	13	)	)	PUNCT
ejpam-5605	257	14	ψ′(s)ϕ(s	ψ′(s)ϕ(s	PROPN
ejpam-5605	257	15	,	,	PUNCT
ejpam-5605	257	16	a)ϑi−1	a)ϑi−1	PROPN
ejpam-5605	257	17	γ(ϑi	γ(ϑi	PROPN
ejpam-5605	257	18	−	−	PROPN
ejpam-5605	257	19	1	1	NUM
ejpam-5605	257	20	)	)	PUNCT
ejpam-5605	257	21	ds	ds	ADJ
ejpam-5605	257	22	≤	≤	NOUN
ejpam-5605	257	23	(	(	PUNCT
ejpam-5605	257	24	1	1	NUM
ejpam-5605	257	25	+	+	NUM
ejpam-5605	257	26	2r)∥ψi	2r)∥ψi	PROPN
ejpam-5605	257	27	(	(	PUNCT
ejpam-5605	257	28	·	·	PUNCT
ejpam-5605	257	29	,	,	PUNCT
ejpam-5605	257	30	ω)∥l∞eϖiϕ(b	ω)∥l∞eϖiϕ(b	PROPN
ejpam-5605	257	31	,	,	PUNCT
ejpam-5605	257	32	a	a	PRON
ejpam-5605	257	33	)	)	PUNCT
ejpam-5605	257	34	[	[	PUNCT
ejpam-5605	257	35	ϕ(ξ2	ϕ(ξ2	NOUN
ejpam-5605	257	36	,	,	PUNCT
ejpam-5605	257	37	a	a	PRON
ejpam-5605	257	38	)	)	PUNCT
ejpam-5605	257	39	ϑi	ϑi	NOUN
ejpam-5605	257	40	−	−	PROPN
ejpam-5605	257	41	ϕ(ξ1	ϕ(ξ1	NOUN
ejpam-5605	257	42	,	,	PUNCT
ejpam-5605	257	43	a	a	PRON
ejpam-5605	257	44	)	)	PUNCT
ejpam-5605	257	45	ϑi	ϑi	NOUN
ejpam-5605	257	46	ϑiγ(ϑi	ϑiγ(ϑi	NOUN
ejpam-5605	257	47	−	−	PROPN
ejpam-5605	257	48	1	1	NUM
ejpam-5605	257	49	)	)	PUNCT
ejpam-5605	257	50	]	]	PUNCT
ejpam-5605	257	51	,	,	PUNCT
ejpam-5605	257	52	i	i	PRON
ejpam-5605	257	53	=	=	NOUN
ejpam-5605	257	54	1	1	NUM
ejpam-5605	257	55	,	,	PUNCT
ejpam-5605	257	56	2	2	NUM
ejpam-5605	257	57	.	.	PUNCT
ejpam-5605	257	58	thus	thus	ADV
ejpam-5605	257	59	,	,	PUNCT
ejpam-5605	257	60	ji,1	ji,1	PROPN
ejpam-5605	257	61	−→	−→	NOUN
ejpam-5605	257	62	0	0	PUNCT
ejpam-5605	257	63	when	when	SCONJ
ejpam-5605	257	64	ξ2	ξ2	ADJ
ejpam-5605	257	65	−→	−→	ADJ
ejpam-5605	257	66	ξ1	ξ1	NOUN
ejpam-5605	257	67	,	,	PUNCT
ejpam-5605	257	68	i	i	PRON
ejpam-5605	257	69	=	=	NOUN
ejpam-5605	257	70	1	1	NUM
ejpam-5605	257	71	,	,	PUNCT
ejpam-5605	257	72	2	2	NUM
ejpam-5605	257	73	.	.	PUNCT
ejpam-5605	257	74	(	(	PUNCT
ejpam-5605	257	75	12	12	NUM
ejpam-5605	257	76	)	)	PUNCT
ejpam-5605	257	77	on	on	ADP
ejpam-5605	257	78	the	the	DET
ejpam-5605	257	79	other	other	ADJ
ejpam-5605	257	80	side	side	NOUN
ejpam-5605	257	81	,	,	PUNCT
ejpam-5605	257	82	ji,2	ji,2	PROPN
ejpam-5605	257	83	=	=	PUNCT
ejpam-5605	257	84	(	(	PUNCT
ejpam-5605	257	85	ϑi	ϑi	NOUN
ejpam-5605	257	86	−	−	PROPN
ejpam-5605	257	87	1	1	NUM
ejpam-5605	257	88	)	)	PUNCT
ejpam-5605	257	89	(	(	PUNCT
ejpam-5605	257	90	e−ϖiϕ(ξ1	e−ϖiϕ(ξ1	PROPN
ejpam-5605	257	91	)	)	PUNCT
ejpam-5605	257	92	−	−	PROPN
ejpam-5605	257	93	e−ϖiϕ(ξ2	e−ϖiϕ(ξ2	PROPN
ejpam-5605	257	94	)	)	PUNCT
ejpam-5605	257	95	)	)	PUNCT
ejpam-5605	257	96	×∫	×∫	VERB
ejpam-5605	257	97	ξ1	ξ1	NOUN
ejpam-5605	257	98	a	a	DET
ejpam-5605	257	99	eϖiϕ(s	eϖiϕ(s	NOUN
ejpam-5605	257	100	)	)	PUNCT
ejpam-5605	257	101	∥∥∥(iϑi−1;ψ	∥∥∥(iϑi−1;ψ	ADV
ejpam-5605	257	102	a+	a+	PUNCT
ejpam-5605	257	103	fi(τ	fi(τ	PROPN
ejpam-5605	257	104	,	,	PUNCT
ejpam-5605	257	105	z1(τ	z1(τ	PROPN
ejpam-5605	257	106	,	,	PUNCT
ejpam-5605	257	107	ω	ω	NOUN
ejpam-5605	257	108	)	)	PUNCT
ejpam-5605	257	109	,	,	PUNCT
ejpam-5605	257	110	z2(τ	z2(τ	PROPN
ejpam-5605	257	111	,	,	PUNCT
ejpam-5605	257	112	ω	ω	NOUN
ejpam-5605	257	113	)	)	PUNCT
ejpam-5605	257	114	,	,	PUNCT
ejpam-5605	257	115	ω	ω	PROPN
ejpam-5605	257	116	)	)	PUNCT
ejpam-5605	257	117	(	(	PUNCT
ejpam-5605	257	118	s	s	NOUN
ejpam-5605	257	119	)	)	PUNCT
ejpam-5605	257	120	∥∥∥ψ′(s)ds	∥∥∥ψ′(s)d	NOUN
ejpam-5605	257	121	,	,	PUNCT
ejpam-5605	257	122	i	i	NOUN
ejpam-5605	257	123	=	=	NOUN
ejpam-5605	257	124	1	1	NUM
ejpam-5605	257	125	,	,	PUNCT
ejpam-5605	257	126	2	2	NUM
ejpam-5605	257	127	.	.	PUNCT
ejpam-5605	258	1	thus	thus	ADV
ejpam-5605	258	2	,	,	PUNCT
ejpam-5605	258	3	ji,2	ji,2	PROPN
ejpam-5605	258	4	−→	−→	NOUN
ejpam-5605	258	5	0	0	NUM
ejpam-5605	258	6	when	when	SCONJ
ejpam-5605	258	7	ξ2	ξ2	ADJ
ejpam-5605	258	8	−→	−→	ADJ
ejpam-5605	258	9	ξ1	ξ1	NOUN
ejpam-5605	258	10	,	,	PUNCT
ejpam-5605	258	11	i	i	PRON
ejpam-5605	258	12	=	=	NOUN
ejpam-5605	258	13	1	1	NUM
ejpam-5605	258	14	,	,	PUNCT
ejpam-5605	258	15	2	2	NUM
ejpam-5605	258	16	.	.	PUNCT
ejpam-5605	258	17	(	(	PUNCT
ejpam-5605	258	18	13	13	NUM
ejpam-5605	258	19	)	)	PUNCT
ejpam-5605	258	20	from	from	ADP
ejpam-5605	258	21	(	(	PUNCT
ejpam-5605	258	22	12	12	NUM
ejpam-5605	258	23	)	)	PUNCT
ejpam-5605	258	24	and	and	CCONJ
ejpam-5605	258	25	(	(	PUNCT
ejpam-5605	258	26	13	13	NUM
ejpam-5605	258	27	)	)	PUNCT
ejpam-5605	258	28	,	,	PUNCT
ejpam-5605	258	29	we	we	PRON
ejpam-5605	258	30	get	get	VERB
ejpam-5605	258	31	∥hi(z1(ξ2	∥hi(z1(ξ2	PROPN
ejpam-5605	258	32	,	,	PUNCT
ejpam-5605	258	33	ω	ω	NOUN
ejpam-5605	258	34	)	)	PUNCT
ejpam-5605	258	35	,	,	PUNCT
ejpam-5605	258	36	z2(ξ2	z2(ξ2	NOUN
ejpam-5605	258	37	,	,	PUNCT
ejpam-5605	258	38	ω	ω	NOUN
ejpam-5605	258	39	)	)	PUNCT
ejpam-5605	258	40	,	,	PUNCT
ejpam-5605	258	41	ω)−hi(z1(ξ1	ω)−hi(z1(ξ1	PROPN
ejpam-5605	258	42	,	,	PUNCT
ejpam-5605	258	43	ω	ω	NOUN
ejpam-5605	258	44	)	)	PUNCT
ejpam-5605	258	45	,	,	PUNCT
ejpam-5605	258	46	z2(ξ1	z2(ξ1	PROPN
ejpam-5605	258	47	,	,	PUNCT
ejpam-5605	258	48	ω	ω	NOUN
ejpam-5605	258	49	)	)	PUNCT
ejpam-5605	258	50	,	,	PUNCT
ejpam-5605	258	51	ω)∥	ω)∥	PUNCT
ejpam-5605	258	52	−−−−→	−−−−→	X
ejpam-5605	259	1	ξ2→ξ1	ξ2→ξ1	NOUN
ejpam-5605	259	2	0	0	NUM
ejpam-5605	259	3	,	,	PUNCT
ejpam-5605	259	4	i	i	PRON
ejpam-5605	259	5	=	=	NOUN
ejpam-5605	259	6	1	1	NUM
ejpam-5605	259	7	,	,	PUNCT
ejpam-5605	259	8	2	2	NUM
ejpam-5605	259	9	.	.	PUNCT
ejpam-5605	260	1	this	this	PRON
ejpam-5605	260	2	proves	prove	VERB
ejpam-5605	260	3	that	that	SCONJ
ejpam-5605	260	4	,	,	PUNCT
ejpam-5605	260	5	h(br	h(br	PROPN
ejpam-5605	260	6	)	)	PUNCT
ejpam-5605	260	7	is	be	AUX
ejpam-5605	260	8	equicontinuous	equicontinuous	ADJ
ejpam-5605	260	9	.	.	PUNCT
ejpam-5605	261	1	step	step	NOUN
ejpam-5605	261	2	4	4	NUM
ejpam-5605	261	3	.	.	PUNCT
ejpam-5605	262	1	h	h	PROPN
ejpam-5605	262	2	is	be	AUX
ejpam-5605	262	3	θj	θj	ADV
ejpam-5605	262	4	-	-	PUNCT
ejpam-5605	262	5	condensing	condense	VERB
ejpam-5605	262	6	.	.	PUNCT
ejpam-5605	263	1	first	first	ADV
ejpam-5605	263	2	,	,	PUNCT
ejpam-5605	263	3	for	for	ADP
ejpam-5605	263	4	every	every	DET
ejpam-5605	263	5	u1	u1	NOUN
ejpam-5605	263	6	×	×	PROPN
ejpam-5605	263	7	u2	u2	PROPN
ejpam-5605	263	8	⊂	⊂	PROPN
ejpam-5605	263	9	p(j	p(j	PROPN
ejpam-5605	263	10	)	)	PUNCT
ejpam-5605	263	11	,	,	PUNCT
ejpam-5605	263	12	we	we	PRON
ejpam-5605	263	13	define	define	VERB
ejpam-5605	263	14	the	the	DET
ejpam-5605	263	15	mnc	mnc	PROPN
ejpam-5605	263	16	as	as	ADP
ejpam-5605	263	17	θj(u	θj(u	X
ejpam-5605	263	18	1	1	NUM
ejpam-5605	263	19	×	×	NOUN
ejpam-5605	263	20	u2	u2	NOUN
ejpam-5605	263	21	)	)	PUNCT
ejpam-5605	263	22	=	=	PRON
ejpam-5605	263	23	(	(	PUNCT
ejpam-5605	263	24	θ(u1	θ(u1	NOUN
ejpam-5605	263	25	)	)	PUNCT
ejpam-5605	263	26	θ(u2	θ(u2	NOUN
ejpam-5605	263	27	)	)	PUNCT
ejpam-5605	263	28	)	)	PUNCT
ejpam-5605	263	29	,	,	PUNCT
ejpam-5605	263	30	(	(	PUNCT
ejpam-5605	263	31	14	14	NUM
ejpam-5605	263	32	)	)	PUNCT
ejpam-5605	263	33	where	where	SCONJ
ejpam-5605	263	34	θ(u	θ(u	PROPN
ejpam-5605	263	35	i	i	PROPN
ejpam-5605	263	36	)	)	PUNCT
ejpam-5605	263	37	=	=	SYM
ejpam-5605	263	38	sup	sup	NUM
ejpam-5605	263	39	ξ∈i	ξ∈i	PROPN
ejpam-5605	263	40	e−γξλ(u	e−γξλ(u	NUM
ejpam-5605	263	41	i(ξ	i(ξ	PROPN
ejpam-5605	263	42	)	)	PUNCT
ejpam-5605	263	43	)	)	PUNCT
ejpam-5605	263	44	;	;	PUNCT
ejpam-5605	263	45	γ	γ	X
ejpam-5605	263	46	>	>	X
ejpam-5605	263	47	0	0	PROPN
ejpam-5605	263	48	,	,	PUNCT
ejpam-5605	263	49	i	i	PRON
ejpam-5605	263	50	=	=	NOUN
ejpam-5605	263	51	1	1	NUM
ejpam-5605	263	52	,	,	PUNCT
ejpam-5605	263	53	2	2	NUM
ejpam-5605	263	54	,	,	PUNCT
ejpam-5605	263	55	(	(	PUNCT
ejpam-5605	263	56	15	15	NUM
ejpam-5605	263	57	)	)	PUNCT
ejpam-5605	263	58	the	the	DET
ejpam-5605	263	59	mnc	mnc	PROPN
ejpam-5605	263	60	θj	θj	NOUN
ejpam-5605	263	61	is	be	AUX
ejpam-5605	263	62	well	well	ADV
ejpam-5605	263	63	defined	define	VERB
ejpam-5605	263	64	and	and	CCONJ
ejpam-5605	263	65	gives	give	VERB
ejpam-5605	263	66	a	a	DET
ejpam-5605	263	67	semiadditive	semiadditive	ADJ
ejpam-5605	263	68	,	,	PUNCT
ejpam-5605	263	69	monotone	monotone	ADJ
ejpam-5605	263	70	,	,	PUNCT
ejpam-5605	263	71	nonsingular	nonsingular	ADJ
ejpam-5605	263	72	and	and	CCONJ
ejpam-5605	263	73	regular	regular	ADJ
ejpam-5605	263	74	mnc	mnc	PROPN
ejpam-5605	263	75	in	in	ADP
ejpam-5605	263	76	j.	j.	PROPN
ejpam-5605	263	77	m.	m.	PROPN
ejpam-5605	263	78	ziane	ziane	PROPN
ejpam-5605	263	79	et	et	PROPN
ejpam-5605	263	80	al	al	PROPN
ejpam-5605	263	81	.	.	PUNCT
ejpam-5605	263	82	/	/	SYM
ejpam-5605	263	83	eur	eur	PROPN
ejpam-5605	263	84	.	.	PUNCT
ejpam-5605	264	1	j.	j.	PROPN
ejpam-5605	264	2	pure	pure	PROPN
ejpam-5605	264	3	appl	appl	PROPN
ejpam-5605	264	4	.	.	PROPN
ejpam-5605	264	5	math	math	PROPN
ejpam-5605	264	6	,	,	PUNCT
ejpam-5605	264	7	18	18	NUM
ejpam-5605	264	8	(	(	PUNCT
ejpam-5605	264	9	1	1	NUM
ejpam-5605	264	10	)	)	PUNCT
ejpam-5605	264	11	(	(	PUNCT
ejpam-5605	264	12	2025	2025	NUM
ejpam-5605	264	13	)	)	PUNCT
ejpam-5605	264	14	,	,	PUNCT
ejpam-5605	264	15	5605	5605	NUM
ejpam-5605	264	16	14	14	NUM
ejpam-5605	264	17	of	of	ADP
ejpam-5605	264	18	21	21	NUM
ejpam-5605	264	19	secondly	secondly	ADV
ejpam-5605	264	20	,	,	PUNCT
ejpam-5605	264	21	let	let	AUX
ejpam-5605	264	22	u1	u1	VERB
ejpam-5605	264	23	×	×	PROPN
ejpam-5605	264	24	u2	u2	PROPN
ejpam-5605	264	25	⊂	⊂	PROPN
ejpam-5605	264	26	p(j	p(j	PROPN
ejpam-5605	264	27	)	)	PUNCT
ejpam-5605	264	28	be	be	VERB
ejpam-5605	264	29	such	such	ADJ
ejpam-5605	264	30	that	that	SCONJ
ejpam-5605	264	31	θj	θj	NOUN
ejpam-5605	264	32	(	(	PUNCT
ejpam-5605	264	33	hi(u	hi(u	NUM
ejpam-5605	264	34	1	1	NUM
ejpam-5605	264	35	×	×	NOUN
ejpam-5605	264	36	u2	u2	NOUN
ejpam-5605	264	37	)	)	PUNCT
ejpam-5605	264	38	)	)	PUNCT
ejpam-5605	265	1	≥	≥	NOUN
ejpam-5605	265	2	θj(u	θj(u	NUM
ejpam-5605	265	3	1	1	NUM
ejpam-5605	265	4	×	×	NOUN
ejpam-5605	265	5	u2	u2	NOUN
ejpam-5605	265	6	)	)	PUNCT
ejpam-5605	265	7	,	,	PUNCT
ejpam-5605	265	8	i	i	PRON
ejpam-5605	265	9	=	=	NOUN
ejpam-5605	265	10	1	1	NUM
ejpam-5605	265	11	,	,	PUNCT
ejpam-5605	265	12	2	2	NUM
ejpam-5605	265	13	.	.	PUNCT
ejpam-5605	266	1	(	(	PUNCT
ejpam-5605	266	2	16	16	NUM
ejpam-5605	266	3	)	)	PUNCT
ejpam-5605	266	4	we	we	PRON
ejpam-5605	266	5	will	will	AUX
ejpam-5605	266	6	show	show	VERB
ejpam-5605	266	7	that	that	SCONJ
ejpam-5605	266	8	(	(	PUNCT
ejpam-5605	266	9	16	16	NUM
ejpam-5605	266	10	)	)	PUNCT
ejpam-5605	266	11	implies	imply	VERB
ejpam-5605	266	12	the	the	DET
ejpam-5605	266	13	relative	relative	ADJ
ejpam-5605	266	14	compactness	compactness	NOUN
ejpam-5605	266	15	of	of	ADP
ejpam-5605	266	16	u1	u1	NOUN
ejpam-5605	266	17	×	×	PROPN
ejpam-5605	266	18	u2	u2	PROPN
ejpam-5605	266	19	.	.	PUNCT
ejpam-5605	267	1	there	there	PRON
ejpam-5605	267	2	exists	exist	VERB
ejpam-5605	267	3	a	a	DET
ejpam-5605	267	4	countable	countable	ADJ
ejpam-5605	267	5	set	set	NOUN
ejpam-5605	267	6	{	{	PUNCT
ejpam-5605	267	7	(	(	PUNCT
ejpam-5605	267	8	z1,n	z1,n	PROPN
ejpam-5605	267	9	,	,	PUNCT
ejpam-5605	267	10	z2,n)}∞n=1	z2,n)}∞n=1	PROPN
ejpam-5605	267	11	such	such	ADJ
ejpam-5605	267	12	that	that	DET
ejpam-5605	267	13	zi	zi	NOUN
ejpam-5605	267	14	,	,	PUNCT
ejpam-5605	267	15	n(ξ	n(ξ	PROPN
ejpam-5605	267	16	,	,	PUNCT
ejpam-5605	267	17	ω	ω	NOUN
ejpam-5605	267	18	)	)	PUNCT
ejpam-5605	267	19	=	=	SYM
ejpam-5605	267	20	hi	hi	INTJ
ejpam-5605	267	21	(	(	PUNCT
ejpam-5605	267	22	{	{	PUNCT
ejpam-5605	267	23	z1,n(ξ	z1,n(ξ	PROPN
ejpam-5605	267	24	,	,	PUNCT
ejpam-5605	267	25	ω	ω	NOUN
ejpam-5605	267	26	)	)	PUNCT
ejpam-5605	267	27	,	,	PUNCT
ejpam-5605	267	28	z2,n(ξ	z2,n(ξ	NOUN
ejpam-5605	267	29	,	,	PUNCT
ejpam-5605	267	30	ω	ω	NOUN
ejpam-5605	267	31	)	)	PUNCT
ejpam-5605	267	32	,	,	PUNCT
ejpam-5605	267	33	ω	ω	PROPN
ejpam-5605	267	34	}	}	PUNCT
ejpam-5605	267	35	)	)	PUNCT
ejpam-5605	267	36	,	,	PUNCT
ejpam-5605	267	37	i	i	PRON
ejpam-5605	267	38	=	=	NOUN
ejpam-5605	267	39	1	1	NUM
ejpam-5605	267	40	,	,	PUNCT
ejpam-5605	267	41	2	2	NUM
ejpam-5605	267	42	,	,	PUNCT
ejpam-5605	267	43	where	where	SCONJ
ejpam-5605	267	44	{	{	PUNCT
ejpam-5605	267	45	(	(	PUNCT
ejpam-5605	267	46	z1,n	z1,n	PROPN
ejpam-5605	267	47	,	,	PUNCT
ejpam-5605	267	48	z2,n)}∞n=1	z2,n)}∞n=1	PROPN
ejpam-5605	267	49	⊂	⊂	PROPN
ejpam-5605	267	50	j.	j.	PROPN
ejpam-5605	267	51	from	from	ADP
ejpam-5605	267	52	the	the	DET
ejpam-5605	267	53	properties	property	NOUN
ejpam-5605	267	54	of	of	ADP
ejpam-5605	267	55	the	the	DET
ejpam-5605	267	56	mnc	mnc	PROPN
ejpam-5605	267	57	,	,	PUNCT
ejpam-5605	267	58	one	one	PRON
ejpam-5605	267	59	gets	get	VERB
ejpam-5605	267	60	(	(	PUNCT
ejpam-5605	267	61	for	for	ADP
ejpam-5605	267	62	i	i	PRON
ejpam-5605	267	63	=	=	SYM
ejpam-5605	267	64	1	1	NUM
ejpam-5605	267	65	,	,	PUNCT
ejpam-5605	267	66	2	2	NUM
ejpam-5605	267	67	)	)	PUNCT
ejpam-5605	267	68	θ({zi	θ({zi	PROPN
ejpam-5605	267	69	,	,	PUNCT
ejpam-5605	267	70	n}∞n=1	n}∞n=1	PROPN
ejpam-5605	267	71	)	)	PUNCT
ejpam-5605	267	72	≤	≤	NUM
ejpam-5605	267	73	θ	θ	NOUN
ejpam-5605	267	74	(	(	PUNCT
ejpam-5605	267	75	{	{	PUNCT
ejpam-5605	267	76	(	(	PUNCT
ejpam-5605	267	77	ϑi	ϑi	PROPN
ejpam-5605	267	78	−	−	PROPN
ejpam-5605	267	79	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	267	80	,	,	PUNCT
ejpam-5605	267	81	a	a	PRON
ejpam-5605	267	82	)	)	PUNCT
ejpam-5605	267	83	∫	∫	PROPN
ejpam-5605	268	1	ξ	ξ	PROPN
ejpam-5605	269	1	a	a	DET
ejpam-5605	269	2	∫	∫	PROPN
ejpam-5605	269	3	s	s	VERB
ejpam-5605	269	4	a	a	DET
ejpam-5605	269	5	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	269	6	,	,	PUNCT
ejpam-5605	269	7	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	269	8	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	269	9	−	−	PROPN
ejpam-5605	269	10	1	1	NUM
ejpam-5605	269	11	)	)	PUNCT
ejpam-5605	269	12	fi(τ	fi(τ	PROPN
ejpam-5605	269	13	,	,	PUNCT
ejpam-5605	269	14	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	269	15	,	,	PUNCT
ejpam-5605	269	16	ω	ω	NOUN
ejpam-5605	269	17	)	)	PUNCT
ejpam-5605	269	18	,	,	PUNCT
ejpam-5605	269	19	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	269	20	,	,	PUNCT
ejpam-5605	269	21	ω))dτψ	ω))dτψ	ADJ
ejpam-5605	269	22	′(s)ds	′(s)ds	PROPN
ejpam-5605	269	23	}	}	PUNCT
ejpam-5605	269	24	+	+	PROPN
ejpam-5605	269	25	∞	∞	NUM
ejpam-5605	269	26	n=1	n=1	PUNCT
ejpam-5605	269	27	)	)	PUNCT
ejpam-5605	269	28	.	.	PUNCT
ejpam-5605	270	1	(	(	PUNCT
ejpam-5605	270	2	17	17	NUM
ejpam-5605	270	3	)	)	PUNCT
ejpam-5605	270	4	now	now	ADV
ejpam-5605	270	5	,	,	PUNCT
ejpam-5605	270	6	we	we	PRON
ejpam-5605	270	7	will	will	AUX
ejpam-5605	270	8	find	find	VERB
ejpam-5605	270	9	an	an	DET
ejpam-5605	270	10	estimate	estimate	NOUN
ejpam-5605	270	11	for	for	ADP
ejpam-5605	270	12	θ({zi	θ({zi	PROPN
ejpam-5605	270	13	,	,	PUNCT
ejpam-5605	270	14	n}∞n=1	n}∞n=1	PROPN
ejpam-5605	270	15	)	)	PUNCT
ejpam-5605	270	16	,	,	PUNCT
ejpam-5605	270	17	i	i	NOUN
ejpam-5605	270	18	=	=	NOUN
ejpam-5605	270	19	1	1	NUM
ejpam-5605	270	20	,	,	PUNCT
ejpam-5605	270	21	2	2	NUM
ejpam-5605	270	22	.	.	PUNCT
ejpam-5605	270	23	by	by	ADP
ejpam-5605	270	24	using	use	VERB
ejpam-5605	270	25	(	(	PUNCT
ejpam-5605	270	26	a4	a4	NOUN
ejpam-5605	270	27	)	)	PUNCT
ejpam-5605	270	28	,	,	PUNCT
ejpam-5605	270	29	for	for	ADP
ejpam-5605	270	30	all	all	PRON
ejpam-5605	270	31	ξ	ξ	X
ejpam-5605	270	32	∈	∈	PRON
ejpam-5605	270	33	i	i	PRON
ejpam-5605	270	34	and	and	CCONJ
ejpam-5605	270	35	τ	τ	PROPN
ejpam-5605	270	36	≤	≤	PROPN
ejpam-5605	270	37	s	s	PART
ejpam-5605	270	38	≤	≤	NOUN
ejpam-5605	270	39	ξ	ξ	NUM
ejpam-5605	270	40	,	,	PUNCT
ejpam-5605	270	41	one	one	NUM
ejpam-5605	270	42	has	have	VERB
ejpam-5605	270	43	λ	λ	X
ejpam-5605	270	44	(	(	PUNCT
ejpam-5605	270	45	{	{	PUNCT
ejpam-5605	270	46	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	270	47	,	,	PUNCT
ejpam-5605	270	48	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	270	49	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	270	50	−	−	PROPN
ejpam-5605	270	51	1	1	NUM
ejpam-5605	270	52	)	)	PUNCT
ejpam-5605	270	53	fi(τ	fi(τ	PROPN
ejpam-5605	270	54	,	,	PUNCT
ejpam-5605	270	55	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	270	56	,	,	PUNCT
ejpam-5605	270	57	ω	ω	NOUN
ejpam-5605	270	58	)	)	PUNCT
ejpam-5605	270	59	,	,	PUNCT
ejpam-5605	270	60	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	270	61	,	,	PUNCT
ejpam-5605	270	62	ω	ω	NOUN
ejpam-5605	270	63	)	)	PUNCT
ejpam-5605	270	64	)	)	PUNCT
ejpam-5605	270	65	}	}	PUNCT
ejpam-5605	271	1	+	+	NUM
ejpam-5605	271	2	∞	∞	NUM
ejpam-5605	271	3	n=1	n=1	PUNCT
ejpam-5605	271	4	)	)	PUNCT
ejpam-5605	271	5	≤	≤	PROPN
ejpam-5605	271	6	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	271	7	,	,	PUNCT
ejpam-5605	271	8	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	271	9	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	271	10	−	−	PROPN
ejpam-5605	271	11	1	1	NUM
ejpam-5605	271	12	)	)	PUNCT
ejpam-5605	271	13	2∑	2∑	NOUN
ejpam-5605	272	1	j=1	j=1	PROPN
ejpam-5605	272	2	ϱi	ϱi	VERB
ejpam-5605	272	3	,	,	PUNCT
ejpam-5605	272	4	j(ω)λ({zj	j(ω)λ({zj	PROPN
ejpam-5605	272	5	,	,	PUNCT
ejpam-5605	272	6	n(τ	n(τ	PROPN
ejpam-5605	272	7	,	,	PUNCT
ejpam-5605	272	8	ω)}+∞	ω)}+∞	NOUN
ejpam-5605	272	9	n=1	n=1	PROPN
ejpam-5605	272	10	)	)	PUNCT
ejpam-5605	272	11	≤	≤	NOUN
ejpam-5605	273	1	2∑	2∑	NUM
ejpam-5605	273	2	j=1	j=1	PROPN
ejpam-5605	273	3	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	273	4	,	,	PUNCT
ejpam-5605	273	5	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	273	6	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	273	7	−	−	PROPN
ejpam-5605	273	8	1	1	NUM
ejpam-5605	273	9	)	)	PUNCT
ejpam-5605	273	10	ϱi	ϱi	PROPN
ejpam-5605	273	11	,	,	PUNCT
ejpam-5605	273	12	j(ω)e	j(ω)e	NOUN
ejpam-5605	273	13	γτ	γτ	NOUN
ejpam-5605	273	14	sup	sup	PROPN
ejpam-5605	273	15	a≤τ≤s	a≤τ≤s	PUNCT
ejpam-5605	273	16	e−γτλ({zj	e−γτλ({zj	NOUN
ejpam-5605	273	17	,	,	PUNCT
ejpam-5605	273	18	n(τ	n(τ	PROPN
ejpam-5605	273	19	,	,	PUNCT
ejpam-5605	273	20	ω)}+∞	ω)}+∞	NOUN
ejpam-5605	273	21	n=1	n=1	PROPN
ejpam-5605	273	22	)	)	PUNCT
ejpam-5605	273	23	≤	≤	NOUN
ejpam-5605	274	1	2∑	2∑	NUM
ejpam-5605	274	2	j=1	j=1	PROPN
ejpam-5605	274	3	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	274	4	,	,	PUNCT
ejpam-5605	274	5	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	274	6	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	274	7	−	−	PROPN
ejpam-5605	274	8	1	1	NUM
ejpam-5605	274	9	)	)	PUNCT
ejpam-5605	274	10	ϱi	ϱi	PROPN
ejpam-5605	274	11	,	,	PUNCT
ejpam-5605	274	12	j(ω)e	j(ω)e	NOUN
ejpam-5605	274	13	γτθ({zj	γτθ({zj	PROPN
ejpam-5605	274	14	,	,	PUNCT
ejpam-5605	274	15	n	n	CCONJ
ejpam-5605	274	16	(	(	PUNCT
ejpam-5605	274	17	·	·	PUNCT
ejpam-5605	274	18	,	,	PUNCT
ejpam-5605	274	19	ω)}+∞	ω)}+∞	NOUN
ejpam-5605	274	20	n=1	n=1	PROPN
ejpam-5605	274	21	)	)	PUNCT
ejpam-5605	274	22	.	.	PUNCT
ejpam-5605	275	1	then	then	ADV
ejpam-5605	275	2	,	,	PUNCT
ejpam-5605	275	3	applying	apply	VERB
ejpam-5605	275	4	lemma	lemma	PROPN
ejpam-5605	275	5	5	5	NUM
ejpam-5605	275	6	,	,	PUNCT
ejpam-5605	275	7	we	we	PRON
ejpam-5605	275	8	get	get	VERB
ejpam-5605	275	9	for	for	ADP
ejpam-5605	275	10	all	all	DET
ejpam-5605	275	11	ξ	ξ	X
ejpam-5605	275	12	∈	∈	PROPN
ejpam-5605	275	13	i	i	PRON
ejpam-5605	275	14	,	,	PUNCT
ejpam-5605	275	15	s	s	VERB
ejpam-5605	275	16	∈	∈	PROPN
ejpam-5605	276	1	[	[	X
ejpam-5605	276	2	a	a	X
ejpam-5605	276	3	,	,	PUNCT
ejpam-5605	276	4	ξ	ξ	X
ejpam-5605	276	5	]	]	PUNCT
ejpam-5605	276	6	and	and	CCONJ
ejpam-5605	276	7	τ	τ	PROPN
ejpam-5605	276	8	≤	≤	PROPN
ejpam-5605	276	9	s	s	PROPN
ejpam-5605	276	10	,	,	PUNCT
ejpam-5605	276	11	λ	λ	X
ejpam-5605	276	12	(	(	PUNCT
ejpam-5605	276	13	{	{	PUNCT
ejpam-5605	276	14	(	(	PUNCT
ejpam-5605	276	15	ϑi	ϑi	PROPN
ejpam-5605	276	16	−	−	PROPN
ejpam-5605	276	17	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	276	18	,	,	PUNCT
ejpam-5605	276	19	a	a	PRON
ejpam-5605	276	20	)	)	PUNCT
ejpam-5605	276	21	∫	∫	PROPN
ejpam-5605	277	1	ξ	ξ	PROPN
ejpam-5605	278	1	a	a	DET
ejpam-5605	278	2	∫	∫	PROPN
ejpam-5605	278	3	s	s	VERB
ejpam-5605	278	4	a	a	DET
ejpam-5605	278	5	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	278	6	,	,	PUNCT
ejpam-5605	278	7	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	278	8	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	278	9	−	−	PROPN
ejpam-5605	278	10	1	1	NUM
ejpam-5605	278	11	)	)	PUNCT
ejpam-5605	278	12	fi(τ	fi(τ	PROPN
ejpam-5605	278	13	,	,	PUNCT
ejpam-5605	278	14	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	278	15	,	,	PUNCT
ejpam-5605	278	16	ω	ω	NOUN
ejpam-5605	278	17	)	)	PUNCT
ejpam-5605	278	18	,	,	PUNCT
ejpam-5605	278	19	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	278	20	,	,	PUNCT
ejpam-5605	278	21	ω))dτψ	ω))dτψ	ADJ
ejpam-5605	278	22	′(s)ds	′(s)ds	PROPN
ejpam-5605	278	23	}	}	PUNCT
ejpam-5605	278	24	+	+	PROPN
ejpam-5605	278	25	∞	∞	NUM
ejpam-5605	278	26	n=1	n=1	PUNCT
ejpam-5605	278	27	)	)	PUNCT
ejpam-5605	278	28	≤	≤	NUM
ejpam-5605	279	1	2∑	2∑	NUM
ejpam-5605	279	2	j=1	j=1	PROPN
ejpam-5605	279	3	θ({zj	θ({zj	PROPN
ejpam-5605	279	4	,	,	PUNCT
ejpam-5605	279	5	n	n	CCONJ
ejpam-5605	279	6	(	(	PUNCT
ejpam-5605	279	7	·	·	PUNCT
ejpam-5605	279	8	,	,	PUNCT
ejpam-5605	279	9	ω)}+∞	ω)}+∞	X
ejpam-5605	279	10	n=1)ϱi	n=1)ϱi	PROPN
ejpam-5605	279	11	,	,	PUNCT
ejpam-5605	279	12	j(ω	j(ω	PROPN
ejpam-5605	279	13	)	)	PUNCT
ejpam-5605	279	14	4(ϑi	4(ϑi	PROPN
ejpam-5605	279	15	−	−	PROPN
ejpam-5605	279	16	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	279	17	,	,	PUNCT
ejpam-5605	279	18	a	a	PRON
ejpam-5605	279	19	)	)	PUNCT
ejpam-5605	279	20	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	279	21	−	−	NOUN
ejpam-5605	279	22	1	1	NUM
ejpam-5605	279	23	)	)	PUNCT
ejpam-5605	279	24	∫	∫	PROPN
ejpam-5605	280	1	ξ	ξ	PROPN
ejpam-5605	280	2	a	a	DET
ejpam-5605	280	3	∫	∫	PROPN
ejpam-5605	280	4	s	s	VERB
ejpam-5605	280	5	a	a	DET
ejpam-5605	280	6	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	280	7	,	,	PUNCT
ejpam-5605	280	8	τ)ϑi−2eγτdτψ′(s)ds	τ)ϑi−2eγτdτψ′(s)ds	PRON
ejpam-5605	280	9	≤	≤	NUM
ejpam-5605	280	10	2∑	2∑	NUM
ejpam-5605	280	11	j=1	j=1	PROPN
ejpam-5605	280	12	θ({zj	θ({zj	PROPN
ejpam-5605	280	13	,	,	PUNCT
ejpam-5605	280	14	n	n	CCONJ
ejpam-5605	280	15	(	(	PUNCT
ejpam-5605	280	16	·	·	PUNCT
ejpam-5605	280	17	,	,	PUNCT
ejpam-5605	280	18	ω)}+∞	ω)}+∞	X
ejpam-5605	280	19	n=1)ϱi	n=1)ϱi	PROPN
ejpam-5605	280	20	,	,	PUNCT
ejpam-5605	280	21	j(ω	j(ω	PROPN
ejpam-5605	280	22	)	)	PUNCT
ejpam-5605	280	23	4(ϑi	4(ϑi	PROPN
ejpam-5605	280	24	−	−	PROPN
ejpam-5605	280	25	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	280	26	,	,	PUNCT
ejpam-5605	280	27	a	a	PRON
ejpam-5605	280	28	)	)	PUNCT
ejpam-5605	280	29	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	280	30	−	−	NOUN
ejpam-5605	280	31	1	1	NUM
ejpam-5605	280	32	)	)	PUNCT
ejpam-5605	280	33	∫	∫	PROPN
ejpam-5605	281	1	ξ	ξ	PROPN
ejpam-5605	281	2	a	a	DET
ejpam-5605	281	3	ψ′(s)eγs	ψ′(s)eγs	ADJ
ejpam-5605	281	4	∫	∫	PROPN
ejpam-5605	281	5	s	s	VERB
ejpam-5605	281	6	a	a	DET
ejpam-5605	281	7	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	281	8	,	,	PUNCT
ejpam-5605	281	9	τ)ϑi−2dτds	τ)ϑi−2dτds	NUM
ejpam-5605	281	10	≤	≤	NUM
ejpam-5605	281	11	2∑	2∑	NUM
ejpam-5605	281	12	j=1	j=1	PROPN
ejpam-5605	281	13	θ({zj	θ({zj	PROPN
ejpam-5605	281	14	,	,	PUNCT
ejpam-5605	281	15	n	n	CCONJ
ejpam-5605	281	16	(	(	PUNCT
ejpam-5605	281	17	·	·	PUNCT
ejpam-5605	281	18	,	,	PUNCT
ejpam-5605	281	19	ω)}+∞	ω)}+∞	X
ejpam-5605	281	20	n=1)ϱi	n=1)ϱi	PROPN
ejpam-5605	281	21	,	,	PUNCT
ejpam-5605	281	22	j(ω	j(ω	PROPN
ejpam-5605	281	23	)	)	PUNCT
ejpam-5605	281	24	4eϖiϕ(b	4eϖiϕ(b	NUM
ejpam-5605	281	25	,	,	PUNCT
ejpam-5605	281	26	a	a	PRON
ejpam-5605	281	27	)	)	PUNCT
ejpam-5605	281	28	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	281	29	−	−	NOUN
ejpam-5605	281	30	1	1	NUM
ejpam-5605	281	31	)	)	PUNCT
ejpam-5605	281	32	∫	∫	PROPN
ejpam-5605	282	1	ξ	ξ	PRON
ejpam-5605	283	1	a	a	DET
ejpam-5605	283	2	ψ′(s)eγsϕ(s	ψ′(s)eγsϕ(s	NOUN
ejpam-5605	283	3	,	,	PUNCT
ejpam-5605	283	4	a)ϑi−1ds	a)ϑi−1ds	PROPN
ejpam-5605	283	5	.	.	PUNCT
ejpam-5605	283	6	m.	m.	PROPN
ejpam-5605	283	7	ziane	ziane	PROPN
ejpam-5605	283	8	et	et	PROPN
ejpam-5605	283	9	al	al	PROPN
ejpam-5605	283	10	.	.	PUNCT
ejpam-5605	283	11	/	/	SYM
ejpam-5605	283	12	eur	eur	PROPN
ejpam-5605	283	13	.	.	PUNCT
ejpam-5605	284	1	j.	j.	PROPN
ejpam-5605	284	2	pure	pure	PROPN
ejpam-5605	284	3	appl	appl	PROPN
ejpam-5605	284	4	.	.	PROPN
ejpam-5605	284	5	math	math	PROPN
ejpam-5605	284	6	,	,	PUNCT
ejpam-5605	284	7	18	18	NUM
ejpam-5605	284	8	(	(	PUNCT
ejpam-5605	284	9	1	1	NUM
ejpam-5605	284	10	)	)	PUNCT
ejpam-5605	284	11	(	(	PUNCT
ejpam-5605	284	12	2025	2025	NUM
ejpam-5605	284	13	)	)	PUNCT
ejpam-5605	284	14	,	,	PUNCT
ejpam-5605	284	15	5605	5605	NUM
ejpam-5605	284	16	15	15	NUM
ejpam-5605	284	17	of	of	ADP
ejpam-5605	284	18	21	21	NUM
ejpam-5605	284	19	multiplying	multiply	VERB
ejpam-5605	284	20	both	both	DET
ejpam-5605	284	21	sides	side	NOUN
ejpam-5605	284	22	by	by	ADP
ejpam-5605	284	23	e−γξ	e−γξ	NOUN
ejpam-5605	284	24	and	and	CCONJ
ejpam-5605	284	25	taking	take	VERB
ejpam-5605	284	26	sup	sup	NOUN
ejpam-5605	284	27	ξ∈i	ξ∈i	NOUN
ejpam-5605	284	28	,	,	PUNCT
ejpam-5605	284	29	one	one	PRON
ejpam-5605	284	30	obtains	obtain	VERB
ejpam-5605	284	31	sup	sup	NOUN
ejpam-5605	284	32	ξ∈i	ξ∈i	VERB
ejpam-5605	284	33	e−γξλ	e−γξλ	NOUN
ejpam-5605	284	34	(	(	PUNCT
ejpam-5605	284	35	{	{	PUNCT
ejpam-5605	284	36	(	(	PUNCT
ejpam-5605	284	37	ϑi	ϑi	PROPN
ejpam-5605	284	38	−	−	PROPN
ejpam-5605	284	39	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	284	40	,	,	PUNCT
ejpam-5605	284	41	a	a	PRON
ejpam-5605	284	42	)	)	PUNCT
ejpam-5605	284	43	∫	∫	PROPN
ejpam-5605	285	1	ξ	ξ	PROPN
ejpam-5605	285	2	a	a	DET
ejpam-5605	285	3	∫	∫	PROPN
ejpam-5605	285	4	s	s	VERB
ejpam-5605	285	5	a	a	DET
ejpam-5605	285	6	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	285	7	,	,	PUNCT
ejpam-5605	285	8	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	285	9	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	285	10	−	−	PROPN
ejpam-5605	285	11	1	1	NUM
ejpam-5605	285	12	)	)	PUNCT
ejpam-5605	285	13	fi(τ	fi(τ	PROPN
ejpam-5605	285	14	,	,	PUNCT
ejpam-5605	285	15	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	285	16	,	,	PUNCT
ejpam-5605	285	17	ω	ω	NOUN
ejpam-5605	285	18	)	)	PUNCT
ejpam-5605	285	19	,	,	PUNCT
ejpam-5605	285	20	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	285	21	,	,	PUNCT
ejpam-5605	285	22	ω))dτψ	ω))dτψ	ADJ
ejpam-5605	285	23	′(s)ds	′(s)ds	PROPN
ejpam-5605	285	24	}	}	PUNCT
ejpam-5605	285	25	+	+	PROPN
ejpam-5605	285	26	∞	∞	NUM
ejpam-5605	285	27	n=1	n=1	PUNCT
ejpam-5605	285	28	)	)	PUNCT
ejpam-5605	285	29	≤	≤	NUM
ejpam-5605	286	1	2∑	2∑	NUM
ejpam-5605	286	2	j=1	j=1	PROPN
ejpam-5605	286	3	θ({zj	θ({zj	PROPN
ejpam-5605	286	4	,	,	PUNCT
ejpam-5605	286	5	n	n	CCONJ
ejpam-5605	286	6	(	(	PUNCT
ejpam-5605	286	7	·	·	PUNCT
ejpam-5605	286	8	,	,	PUNCT
ejpam-5605	286	9	ω)}+∞	ω)}+∞	X
ejpam-5605	286	10	n=1)ℵi	n=1)ℵi	PROPN
ejpam-5605	286	11	,	,	PUNCT
ejpam-5605	286	12	j(γ	j(γ	PROPN
ejpam-5605	286	13	,	,	PUNCT
ejpam-5605	286	14	ω	ω	NOUN
ejpam-5605	286	15	)	)	PUNCT
ejpam-5605	286	16	.	.	PUNCT
ejpam-5605	287	1	where	where	SCONJ
ejpam-5605	287	2	ℵi	ℵi	PROPN
ejpam-5605	287	3	,	,	PUNCT
ejpam-5605	287	4	j(γ	j(γ	PROPN
ejpam-5605	287	5	,	,	PUNCT
ejpam-5605	287	6	ω	ω	NOUN
ejpam-5605	287	7	)	)	PUNCT
ejpam-5605	287	8	,	,	PUNCT
ejpam-5605	287	9	i	i	PRON
ejpam-5605	287	10	,	,	PUNCT
ejpam-5605	287	11	j	j	PROPN
ejpam-5605	287	12	=	=	SYM
ejpam-5605	287	13	1	1	NUM
ejpam-5605	287	14	,	,	PUNCT
ejpam-5605	287	15	2	2	NUM
ejpam-5605	287	16	are	be	AUX
ejpam-5605	287	17	defined	define	VERB
ejpam-5605	287	18	in	in	ADP
ejpam-5605	287	19	(	(	PUNCT
ejpam-5605	287	20	6	6	NUM
ejpam-5605	287	21	)	)	PUNCT
ejpam-5605	287	22	.	.	PUNCT
ejpam-5605	288	1	hence	hence	ADV
ejpam-5605	288	2	,	,	PUNCT
ejpam-5605	288	3	θ	θ	PROPN
ejpam-5605	288	4	(	(	PUNCT
ejpam-5605	288	5	{	{	PUNCT
ejpam-5605	288	6	(	(	PUNCT
ejpam-5605	288	7	ϑi	ϑi	PROPN
ejpam-5605	288	8	−	−	PROPN
ejpam-5605	288	9	1)eϖiϕ(b	1)eϖiϕ(b	PROPN
ejpam-5605	288	10	,	,	PUNCT
ejpam-5605	288	11	a	a	PRON
ejpam-5605	288	12	)	)	PUNCT
ejpam-5605	288	13	∫	∫	PROPN
ejpam-5605	288	14	ξ	ξ	PROPN
ejpam-5605	288	15	a	a	DET
ejpam-5605	288	16	∫	∫	PROPN
ejpam-5605	288	17	s	s	VERB
ejpam-5605	288	18	a	a	DET
ejpam-5605	288	19	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	288	20	,	,	PUNCT
ejpam-5605	288	21	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	288	22	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	288	23	−	−	PROPN
ejpam-5605	288	24	1	1	NUM
ejpam-5605	288	25	)	)	PUNCT
ejpam-5605	288	26	fi(τ	fi(τ	PROPN
ejpam-5605	288	27	,	,	PUNCT
ejpam-5605	288	28	z1,n(τ	z1,n(τ	PROPN
ejpam-5605	288	29	,	,	PUNCT
ejpam-5605	288	30	ω	ω	NOUN
ejpam-5605	288	31	)	)	PUNCT
ejpam-5605	288	32	,	,	PUNCT
ejpam-5605	288	33	z2,n(τ	z2,n(τ	PROPN
ejpam-5605	288	34	,	,	PUNCT
ejpam-5605	288	35	ω))dτψ	ω))dτψ	ADJ
ejpam-5605	288	36	′(s)ds	′(s)ds	PROPN
ejpam-5605	288	37	}	}	PUNCT
ejpam-5605	288	38	+	+	PROPN
ejpam-5605	288	39	∞	∞	NUM
ejpam-5605	288	40	n=1	n=1	PUNCT
ejpam-5605	288	41	)	)	PUNCT
ejpam-5605	288	42	≤	≤	NUM
ejpam-5605	288	43	2∑	2∑	NUM
ejpam-5605	288	44	r=1	r=1	NOUN
ejpam-5605	288	45	θ({zj	θ({zj	PROPN
ejpam-5605	288	46	,	,	PUNCT
ejpam-5605	288	47	n	n	CCONJ
ejpam-5605	288	48	(	(	PUNCT
ejpam-5605	288	49	·	·	PUNCT
ejpam-5605	288	50	,	,	PUNCT
ejpam-5605	288	51	ω)}∞n=1)ℵi	ω)}∞n=1)ℵi	PROPN
ejpam-5605	288	52	,	,	PUNCT
ejpam-5605	288	53	j(γ	j(γ	PROPN
ejpam-5605	288	54	,	,	PUNCT
ejpam-5605	288	55	ω	ω	NOUN
ejpam-5605	288	56	)	)	PUNCT
ejpam-5605	288	57	,	,	PUNCT
ejpam-5605	288	58	i	i	PRON
ejpam-5605	288	59	=	=	NOUN
ejpam-5605	288	60	1	1	NUM
ejpam-5605	288	61	,	,	PUNCT
ejpam-5605	288	62	2	2	NUM
ejpam-5605	288	63	.	.	PUNCT
ejpam-5605	288	64	(	(	PUNCT
ejpam-5605	288	65	18	18	NUM
ejpam-5605	288	66	)	)	PUNCT
ejpam-5605	288	67	next	next	ADV
ejpam-5605	288	68	,	,	PUNCT
ejpam-5605	288	69	by	by	ADP
ejpam-5605	288	70	(	(	PUNCT
ejpam-5605	288	71	17	17	NUM
ejpam-5605	288	72	)	)	PUNCT
ejpam-5605	288	73	and	and	CCONJ
ejpam-5605	288	74	(	(	PUNCT
ejpam-5605	288	75	18	18	NUM
ejpam-5605	288	76	)	)	PUNCT
ejpam-5605	289	1	,	,	PUNCT
ejpam-5605	289	2	we	we	PRON
ejpam-5605	289	3	derive	derive	VERB
ejpam-5605	289	4	θ({zi	θ({zi	PROPN
ejpam-5605	289	5	,	,	PUNCT
ejpam-5605	289	6	n}∞n=1	n}∞n=1	PROPN
ejpam-5605	289	7	)	)	PUNCT
ejpam-5605	289	8	≤	≤	NUM
ejpam-5605	289	9	2∑	2∑	NUM
ejpam-5605	289	10	r=1	r=1	NOUN
ejpam-5605	289	11	θ({zj	θ({zj	PROPN
ejpam-5605	289	12	,	,	PUNCT
ejpam-5605	289	13	n	n	CCONJ
ejpam-5605	289	14	(	(	PUNCT
ejpam-5605	289	15	·	·	PUNCT
ejpam-5605	289	16	,	,	PUNCT
ejpam-5605	289	17	ω)}∞n=1)ℵi	ω)}∞n=1)ℵi	PROPN
ejpam-5605	289	18	,	,	PUNCT
ejpam-5605	289	19	j(γ	j(γ	PROPN
ejpam-5605	289	20	,	,	PUNCT
ejpam-5605	289	21	ω	ω	NOUN
ejpam-5605	289	22	)	)	PUNCT
ejpam-5605	289	23	,	,	PUNCT
ejpam-5605	289	24	i	i	PRON
ejpam-5605	289	25	=	=	NOUN
ejpam-5605	289	26	1	1	NUM
ejpam-5605	289	27	,	,	PUNCT
ejpam-5605	289	28	2	2	NUM
ejpam-5605	289	29	,	,	PUNCT
ejpam-5605	289	30	which	which	PRON
ejpam-5605	289	31	implies	imply	VERB
ejpam-5605	289	32	θj(h({z1,n	θj(h({z1,n	NOUN
ejpam-5605	289	33	(	(	PUNCT
ejpam-5605	289	34	·	·	PUNCT
ejpam-5605	289	35	,	,	PUNCT
ejpam-5605	289	36	ω	ω	NOUN
ejpam-5605	289	37	)	)	PUNCT
ejpam-5605	289	38	,	,	PUNCT
ejpam-5605	289	39	z2,n	z2,n	PROPN
ejpam-5605	289	40	(	(	PUNCT
ejpam-5605	289	41	·	·	NUM
ejpam-5605	289	42	,	,	PUNCT
ejpam-5605	289	43	ω	ω	NOUN
ejpam-5605	289	44	)	)	PUNCT
ejpam-5605	289	45	,	,	PUNCT
ejpam-5605	289	46	ω}+∞	ω}+∞	PROPN
ejpam-5605	289	47	n=1	n=1	PROPN
ejpam-5605	289	48	)	)	PUNCT
ejpam-5605	289	49	=	=	PRON
ejpam-5605	289	50	(	(	PUNCT
ejpam-5605	289	51	θ(h1({z1,n	θ(h1({z1,n	X
ejpam-5605	289	52	(	(	PUNCT
ejpam-5605	289	53	·	·	PUNCT
ejpam-5605	289	54	,	,	PUNCT
ejpam-5605	289	55	ω	ω	NOUN
ejpam-5605	289	56	)	)	PUNCT
ejpam-5605	289	57	,	,	PUNCT
ejpam-5605	289	58	z2,n	z2,n	PROPN
ejpam-5605	289	59	(	(	PUNCT
ejpam-5605	289	60	·	·	NUM
ejpam-5605	289	61	,	,	PUNCT
ejpam-5605	289	62	ω	ω	NOUN
ejpam-5605	289	63	)	)	PUNCT
ejpam-5605	289	64	,	,	PUNCT
ejpam-5605	289	65	ω}+∞	ω}+∞	PROPN
ejpam-5605	289	66	n=1	n=1	PROPN
ejpam-5605	289	67	)	)	PUNCT
ejpam-5605	289	68	θ(h2({z1,n	θ(h2({z1,n	PROPN
ejpam-5605	289	69	(	(	PUNCT
ejpam-5605	289	70	·	·	PROPN
ejpam-5605	289	71	,	,	PUNCT
ejpam-5605	289	72	ω	ω	NOUN
ejpam-5605	289	73	)	)	PUNCT
ejpam-5605	289	74	,	,	PUNCT
ejpam-5605	289	75	z2,n	z2,n	PROPN
ejpam-5605	289	76	(	(	PUNCT
ejpam-5605	289	77	·	·	NUM
ejpam-5605	289	78	,	,	PUNCT
ejpam-5605	289	79	ω	ω	NOUN
ejpam-5605	289	80	)	)	PUNCT
ejpam-5605	289	81	,	,	PUNCT
ejpam-5605	289	82	ω}+∞	ω}+∞	PROPN
ejpam-5605	289	83	n=1	n=1	PROPN
ejpam-5605	289	84	)	)	PUNCT
ejpam-5605	289	85	)	)	PUNCT
ejpam-5605	289	86	≤	≤	NOUN
ejpam-5605	289	87	ξγ(ω	ξγ(ω	NOUN
ejpam-5605	289	88	)	)	PUNCT
ejpam-5605	289	89	(	(	PUNCT
ejpam-5605	289	90	θ({z1,n	θ({z1,n	X
ejpam-5605	289	91	(	(	PUNCT
ejpam-5605	289	92	·	·	PUNCT
ejpam-5605	289	93	,	,	PUNCT
ejpam-5605	289	94	ω)}∞n=1	ω)}∞n=1	NUM
ejpam-5605	289	95	)	)	PUNCT
ejpam-5605	289	96	θ	θ	NOUN
ejpam-5605	289	97	(	(	PUNCT
ejpam-5605	289	98	{	{	PUNCT
ejpam-5605	289	99	z2,n	z2,n	PROPN
ejpam-5605	289	100	(	(	PUNCT
ejpam-5605	289	101	·	·	PUNCT
ejpam-5605	289	102	,	,	PUNCT
ejpam-5605	289	103	ω)}∞n=1	ω)}∞n=1	NUM
ejpam-5605	289	104	)	)	PUNCT
ejpam-5605	289	105	)	)	PUNCT
ejpam-5605	289	106	,	,	PUNCT
ejpam-5605	289	107	where	where	SCONJ
ejpam-5605	289	108	ξγ(ω	ξγ(ω	VERB
ejpam-5605	289	109	)	)	PUNCT
ejpam-5605	289	110	=	=	SYM
ejpam-5605	290	1	ℵ1,1(γ	ℵ1,1(γ	PROPN
ejpam-5605	290	2	,	,	PUNCT
ejpam-5605	290	3	ω	ω	NOUN
ejpam-5605	290	4	)	)	PUNCT
ejpam-5605	290	5	ℵ1,2(γ	ℵ1,2(γ	PROPN
ejpam-5605	290	6	,	,	PUNCT
ejpam-5605	290	7	ω	ω	NOUN
ejpam-5605	290	8	)	)	PUNCT
ejpam-5605	290	9	ℵ2,1(γ	ℵ2,1(γ	PROPN
ejpam-5605	290	10	,	,	PUNCT
ejpam-5605	290	11	ω	ω	NOUN
ejpam-5605	290	12	)	)	PUNCT
ejpam-5605	290	13	ℵ2,2(γ	ℵ2,2(γ	PROPN
ejpam-5605	290	14	,	,	PUNCT
ejpam-5605	290	15	ω	ω	NOUN
ejpam-5605	290	16	)	)	PUNCT
ejpam-5605	290	17			PROPN
ejpam-5605	290	18	.	.	PUNCT
ejpam-5605	291	1	by	by	ADP
ejpam-5605	291	2	lemma	lemma	PROPN
ejpam-5605	291	3	7	7	NUM
ejpam-5605	291	4	,	,	PUNCT
ejpam-5605	291	5	one	one	PRON
ejpam-5605	291	6	can	can	AUX
ejpam-5605	291	7	choose	choose	VERB
ejpam-5605	291	8	γ	γ	PRON
ejpam-5605	291	9	such	such	ADJ
ejpam-5605	291	10	that	that	SCONJ
ejpam-5605	291	11	the	the	DET
ejpam-5605	291	12	spectral	spectral	ADJ
ejpam-5605	291	13	radius	radius	NOUN
ejpam-5605	291	14	ρ(ξγ(ω	ρ(ξγ(ω	PROPN
ejpam-5605	291	15	)	)	PUNCT
ejpam-5605	291	16	)	)	PUNCT
ejpam-5605	292	1	<	<	X
ejpam-5605	292	2	1	1	NUM
ejpam-5605	292	3	,	,	PUNCT
ejpam-5605	292	4	therefore	therefore	ADV
ejpam-5605	292	5	θ(hi({z1,n	θ(hi({z1,n	X
ejpam-5605	292	6	(	(	PUNCT
ejpam-5605	292	7	·	·	PUNCT
ejpam-5605	292	8	,	,	PUNCT
ejpam-5605	292	9	ω	ω	NOUN
ejpam-5605	292	10	)	)	PUNCT
ejpam-5605	292	11	,	,	PUNCT
ejpam-5605	292	12	z2,n	z2,n	PROPN
ejpam-5605	292	13	(	(	PUNCT
ejpam-5605	292	14	·	·	NUM
ejpam-5605	292	15	,	,	PUNCT
ejpam-5605	292	16	ω	ω	NOUN
ejpam-5605	292	17	)	)	PUNCT
ejpam-5605	292	18	,	,	PUNCT
ejpam-5605	292	19	ω}+∞	ω}+∞	PROPN
ejpam-5605	292	20	n=1	n=1	PROPN
ejpam-5605	292	21	)	)	PUNCT
ejpam-5605	292	22	=	=	SYM
ejpam-5605	293	1	0	0	NUM
ejpam-5605	293	2	,	,	PUNCT
ejpam-5605	293	3	i	i	PRON
ejpam-5605	293	4	=	=	NOUN
ejpam-5605	293	5	1	1	NUM
ejpam-5605	293	6	,	,	PUNCT
ejpam-5605	293	7	2	2	NUM
ejpam-5605	293	8	.	.	PUNCT
ejpam-5605	294	1	this	this	PRON
ejpam-5605	294	2	implies	imply	VERB
ejpam-5605	294	3	that	that	SCONJ
ejpam-5605	294	4	θ(hi({z1,n(ξ	θ(hi({z1,n(ξ	PROPN
ejpam-5605	294	5	,	,	PUNCT
ejpam-5605	294	6	ω	ω	NOUN
ejpam-5605	294	7	)	)	PUNCT
ejpam-5605	294	8	,	,	PUNCT
ejpam-5605	294	9	z2,n(ξ	z2,n(ξ	NOUN
ejpam-5605	294	10	,	,	PUNCT
ejpam-5605	294	11	ω	ω	NOUN
ejpam-5605	294	12	)	)	PUNCT
ejpam-5605	294	13	,	,	PUNCT
ejpam-5605	294	14	ω}+∞	ω}+∞	PROPN
ejpam-5605	294	15	n=1	n=1	PROPN
ejpam-5605	294	16	)	)	PUNCT
ejpam-5605	294	17	=	=	SYM
ejpam-5605	294	18	0	0	NUM
ejpam-5605	294	19	,	,	PUNCT
ejpam-5605	294	20	for	for	ADP
ejpam-5605	294	21	ξ	ξ	PROPN
ejpam-5605	294	22	∈	∈	PROPN
ejpam-5605	294	23	i	i	PRON
ejpam-5605	294	24	,	,	PUNCT
ejpam-5605	294	25	i	i	NOUN
ejpam-5605	294	26	=	=	NOUN
ejpam-5605	294	27	1	1	NUM
ejpam-5605	294	28	,	,	PUNCT
ejpam-5605	294	29	2	2	NUM
ejpam-5605	294	30	.	.	PUNCT
ejpam-5605	294	31	m.	m.	NOUN
ejpam-5605	294	32	ziane	ziane	PROPN
ejpam-5605	294	33	et	et	PROPN
ejpam-5605	294	34	al	al	PROPN
ejpam-5605	294	35	.	.	PUNCT
ejpam-5605	294	36	/	/	SYM
ejpam-5605	294	37	eur	eur	PROPN
ejpam-5605	294	38	.	.	PUNCT
ejpam-5605	295	1	j.	j.	PROPN
ejpam-5605	295	2	pure	pure	PROPN
ejpam-5605	295	3	appl	appl	PROPN
ejpam-5605	295	4	.	.	PROPN
ejpam-5605	295	5	math	math	PROPN
ejpam-5605	295	6	,	,	PUNCT
ejpam-5605	295	7	18	18	NUM
ejpam-5605	295	8	(	(	PUNCT
ejpam-5605	295	9	1	1	NUM
ejpam-5605	295	10	)	)	PUNCT
ejpam-5605	295	11	(	(	PUNCT
ejpam-5605	295	12	2025	2025	NUM
ejpam-5605	295	13	)	)	PUNCT
ejpam-5605	295	14	,	,	PUNCT
ejpam-5605	295	15	5605	5605	NUM
ejpam-5605	295	16	16	16	NUM
ejpam-5605	295	17	of	of	ADP
ejpam-5605	295	18	21	21	NUM
ejpam-5605	295	19	finally	finally	ADV
ejpam-5605	295	20	,	,	PUNCT
ejpam-5605	295	21	θj(u	θj(u	PUNCT
ejpam-5605	295	22	1	1	NUM
ejpam-5605	295	23	×	×	NOUN
ejpam-5605	295	24	u2	u2	NOUN
ejpam-5605	295	25	)	)	PUNCT
ejpam-5605	295	26	=	=	PUNCT
ejpam-5605	295	27	(	(	PUNCT
ejpam-5605	295	28	0	0	NUM
ejpam-5605	295	29	,	,	PUNCT
ejpam-5605	295	30	0	0	NUM
ejpam-5605	295	31	)	)	PUNCT
ejpam-5605	295	32	,	,	PUNCT
ejpam-5605	295	33	which	which	PRON
ejpam-5605	295	34	proves	prove	VERB
ejpam-5605	295	35	the	the	DET
ejpam-5605	295	36	compactness	compactness	NOUN
ejpam-5605	295	37	of	of	ADP
ejpam-5605	295	38	the	the	DET
ejpam-5605	295	39	set	set	VERB
ejpam-5605	295	40	u1	u1	NOUN
ejpam-5605	295	41	×	×	PROPN
ejpam-5605	295	42	u2	u2	PROPN
ejpam-5605	295	43	.	.	PUNCT
ejpam-5605	296	1	step	step	NOUN
ejpam-5605	296	2	5	5	NUM
ejpam-5605	296	3	.	.	PUNCT
ejpam-5605	297	1	the	the	DET
ejpam-5605	297	2	set	set	PROPN
ejpam-5605	297	3	w	w	PROPN
ejpam-5605	297	4	(	(	PUNCT
ejpam-5605	297	5	see	see	VERB
ejpam-5605	297	6	theorem	theorem	NOUN
ejpam-5605	297	7	2	2	NUM
ejpam-5605	297	8	(	(	PUNCT
ejpam-5605	297	9	2	2	NUM
ejpam-5605	297	10	)	)	PUNCT
ejpam-5605	297	11	)	)	PUNCT
ejpam-5605	297	12	is	be	AUX
ejpam-5605	297	13	bounded	bound	VERB
ejpam-5605	297	14	.	.	PUNCT
ejpam-5605	298	1	let	let	VERB
ejpam-5605	298	2	(	(	PUNCT
ejpam-5605	298	3	z1	z1	ADJ
ejpam-5605	298	4	,	,	PUNCT
ejpam-5605	298	5	z2	z2	PROPN
ejpam-5605	298	6	)	)	PUNCT
ejpam-5605	298	7	∈	∈	PROPN
ejpam-5605	298	8	j	j	PROPN
ejpam-5605	298	9	and	and	CCONJ
ejpam-5605	298	10	(	(	PUNCT
ejpam-5605	298	11	z1	z1	PROPN
ejpam-5605	298	12	,	,	PUNCT
ejpam-5605	298	13	z2	z2	NUM
ejpam-5605	298	14	)	)	PUNCT
ejpam-5605	298	15	=	=	SYM
ejpam-5605	298	16	κ(ω)h(z1	κ(ω)h(z1	PROPN
ejpam-5605	298	17	,	,	PUNCT
ejpam-5605	298	18	z2	z2	PROPN
ejpam-5605	298	19	)	)	PUNCT
ejpam-5605	298	20	for	for	ADP
ejpam-5605	298	21	some	some	DET
ejpam-5605	298	22	κ(ω	κ(ω	PROPN
ejpam-5605	298	23	)	)	PUNCT
ejpam-5605	298	24	∈	∈	PROPN
ejpam-5605	298	25	(	(	PUNCT
ejpam-5605	298	26	0	0	NUM
ejpam-5605	298	27	,	,	PUNCT
ejpam-5605	298	28	1	1	NUM
ejpam-5605	298	29	)	)	PUNCT
ejpam-5605	298	30	.	.	PUNCT
ejpam-5605	299	1	then	then	ADV
ejpam-5605	299	2	,	,	PUNCT
ejpam-5605	299	3	by	by	ADP
ejpam-5605	299	4	the	the	DET
ejpam-5605	299	5	fact	fact	NOUN
ejpam-5605	299	6	e−ϱχ(ξ	e−ϱχ(ξ	NOUN
ejpam-5605	299	7	,	,	PUNCT
ejpam-5605	299	8	a	a	PRON
ejpam-5605	299	9	)	)	PUNCT
ejpam-5605	299	10	≤	≤	NOUN
ejpam-5605	299	11	1	1	NUM
ejpam-5605	299	12	for	for	ADP
ejpam-5605	299	13	all	all	DET
ejpam-5605	299	14	ξ	ξ	PROPN
ejpam-5605	299	15	∈	∈	PROPN
ejpam-5605	300	1	i	i	PRON
ejpam-5605	300	2	,	,	PUNCT
ejpam-5605	300	3	we	we	PRON
ejpam-5605	300	4	obtain	obtain	VERB
ejpam-5605	300	5	zi(ξ	zi(ξ	NUM
ejpam-5605	300	6	,	,	PUNCT
ejpam-5605	300	7	ω	ω	NUM
ejpam-5605	300	8	)	)	PUNCT
ejpam-5605	300	9	=	=	SYM
ejpam-5605	300	10	κ(ω	κ(ω	NOUN
ejpam-5605	300	11	)	)	PUNCT
ejpam-5605	301	1	[	[	PUNCT
ejpam-5605	301	2	(	(	PUNCT
ejpam-5605	301	3	ϑi	ϑi	PROPN
ejpam-5605	301	4	−	−	PROPN
ejpam-5605	301	5	1)e−ϖiϕ(ξ	1)e−ϖiϕ(ξ	PROPN
ejpam-5605	301	6	,	,	PUNCT
ejpam-5605	301	7	a	a	PRON
ejpam-5605	301	8	)	)	PUNCT
ejpam-5605	301	9	∫	∫	PROPN
ejpam-5605	301	10	ξ	ξ	PROPN
ejpam-5605	301	11	a	a	DET
ejpam-5605	301	12	eϖiϕ(s	eϖiϕ(s	PROPN
ejpam-5605	301	13	,	,	PUNCT
ejpam-5605	301	14	a	a	PRON
ejpam-5605	301	15	)	)	PUNCT
ejpam-5605	301	16	∫	∫	PROPN
ejpam-5605	301	17	s	s	PROPN
ejpam-5605	301	18	a	a	DET
ejpam-5605	301	19	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	301	20	,	,	PUNCT
ejpam-5605	301	21	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	301	22	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	301	23	−	−	PROPN
ejpam-5605	301	24	1	1	NUM
ejpam-5605	301	25	)	)	PUNCT
ejpam-5605	301	26	×	×	NOUN
ejpam-5605	301	27	fi(τ	fi(τ	NOUN
ejpam-5605	301	28	,	,	PUNCT
ejpam-5605	301	29	z1(τ	z1(τ	PROPN
ejpam-5605	301	30	,	,	PUNCT
ejpam-5605	301	31	ω	ω	NOUN
ejpam-5605	301	32	)	)	PUNCT
ejpam-5605	301	33	,	,	PUNCT
ejpam-5605	301	34	z2(τ	z2(τ	PROPN
ejpam-5605	301	35	,	,	PUNCT
ejpam-5605	301	36	ω	ω	NOUN
ejpam-5605	301	37	)	)	PUNCT
ejpam-5605	301	38	,	,	PUNCT
ejpam-5605	301	39	ω)dτψ	ω)dτψ	PROPN
ejpam-5605	301	40	′(s)ds	′(s)ds	PROPN
ejpam-5605	301	41	]	]	PUNCT
ejpam-5605	301	42	≤	≤	X
ejpam-5605	301	43	(	(	PUNCT
ejpam-5605	301	44	ϑi	ϑi	NOUN
ejpam-5605	301	45	−	−	PROPN
ejpam-5605	301	46	1	1	NUM
ejpam-5605	301	47	)	)	PUNCT
ejpam-5605	301	48	e−ϖiϕ(b	e−ϖiϕ(b	PROPN
ejpam-5605	301	49	,	,	PUNCT
ejpam-5605	301	50	a	a	PRON
ejpam-5605	301	51	)	)	PUNCT
ejpam-5605	301	52	∫	∫	PROPN
ejpam-5605	302	1	ξ	ξ	PROPN
ejpam-5605	302	2	a	a	DET
ejpam-5605	302	3	∫	∫	PROPN
ejpam-5605	302	4	s	s	VERB
ejpam-5605	302	5	a	a	DET
ejpam-5605	302	6	ψ′(τ)ϕ(s	ψ′(τ)ϕ(s	PROPN
ejpam-5605	302	7	,	,	PUNCT
ejpam-5605	302	8	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	302	9	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	302	10	−	−	PROPN
ejpam-5605	302	11	1	1	NUM
ejpam-5605	302	12	)	)	PUNCT
ejpam-5605	302	13	fi(τ	fi(τ	PROPN
ejpam-5605	302	14	,	,	PUNCT
ejpam-5605	302	15	z1(τ	z1(τ	PROPN
ejpam-5605	302	16	,	,	PUNCT
ejpam-5605	302	17	ω	ω	NOUN
ejpam-5605	302	18	)	)	PUNCT
ejpam-5605	302	19	,	,	PUNCT
ejpam-5605	302	20	z2(τ	z2(τ	PROPN
ejpam-5605	302	21	,	,	PUNCT
ejpam-5605	302	22	ω	ω	NOUN
ejpam-5605	302	23	)	)	PUNCT
ejpam-5605	302	24	,	,	PUNCT
ejpam-5605	302	25	ω)dτψ	ω)dτψ	PROPN
ejpam-5605	302	26	′(s)ds	′(s)ds	PROPN
ejpam-5605	302	27	,	,	PUNCT
ejpam-5605	302	28	i	i	NOUN
ejpam-5605	302	29	=	=	NOUN
ejpam-5605	302	30	1	1	NUM
ejpam-5605	302	31	,	,	PUNCT
ejpam-5605	302	32	2	2	NUM
ejpam-5605	302	33	.	.	PUNCT
ejpam-5605	302	34	using	use	VERB
ejpam-5605	302	35	fubini	fubini	NOUN
ejpam-5605	302	36	’s	’s	PART
ejpam-5605	302	37	theorem	theorem	NOUN
ejpam-5605	302	38	,	,	PUNCT
ejpam-5605	302	39	we	we	PRON
ejpam-5605	302	40	have	have	AUX
ejpam-5605	302	41	∥zi(ξ	∥zi(ξ	PROPN
ejpam-5605	302	42	,	,	PUNCT
ejpam-5605	302	43	ω)∥	ω)∥	PUNCT
ejpam-5605	302	44	≤	≤	NUM
ejpam-5605	302	45	(	(	PUNCT
ejpam-5605	302	46	ϑi	ϑi	NOUN
ejpam-5605	302	47	−	−	PROPN
ejpam-5605	302	48	1	1	NUM
ejpam-5605	302	49	)	)	PUNCT
ejpam-5605	302	50	e−ϖiϕ(b	e−ϖiϕ(b	PROPN
ejpam-5605	302	51	,	,	PUNCT
ejpam-5605	302	52	a	a	PRON
ejpam-5605	302	53	)	)	PUNCT
ejpam-5605	302	54	∫	∫	PROPN
ejpam-5605	303	1	ξ	ξ	PRON
ejpam-5605	303	2	a	a	DET
ejpam-5605	303	3	∥fi(τ	∥fi(τ	ADJ
ejpam-5605	303	4	,	,	PUNCT
ejpam-5605	303	5	z1(τ	z1(τ	PROPN
ejpam-5605	303	6	,	,	PUNCT
ejpam-5605	303	7	ω	ω	NOUN
ejpam-5605	303	8	)	)	PUNCT
ejpam-5605	303	9	,	,	PUNCT
ejpam-5605	303	10	z2(τ	z2(τ	PROPN
ejpam-5605	303	11	,	,	PUNCT
ejpam-5605	303	12	ω	ω	NOUN
ejpam-5605	303	13	)	)	PUNCT
ejpam-5605	303	14	,	,	PUNCT
ejpam-5605	303	15	ω)∥	ω)∥	PUNCT
ejpam-5605	303	16	∫	∫	PROPN
ejpam-5605	304	1	ξ	ξ	PROPN
ejpam-5605	304	2	τ	τ	PROPN
ejpam-5605	304	3	ψ′(s)ϕ(s	ψ′(s)ϕ(s	PROPN
ejpam-5605	304	4	,	,	PUNCT
ejpam-5605	304	5	τ)ϑi−2	τ)ϑi−2	NOUN
ejpam-5605	304	6	γ(ϑi	γ(ϑi	NOUN
ejpam-5605	304	7	−	−	PROPN
ejpam-5605	304	8	1	1	NUM
ejpam-5605	304	9	)	)	PUNCT
ejpam-5605	304	10	dsψ′(τ)dτ	dsψ′(τ)dτ	NOUN
ejpam-5605	304	11	≤	≤	NOUN
ejpam-5605	304	12	(	(	PUNCT
ejpam-5605	304	13	ϑi	ϑi	NOUN
ejpam-5605	304	14	−	−	PROPN
ejpam-5605	304	15	1	1	NUM
ejpam-5605	304	16	)	)	PUNCT
ejpam-5605	304	17	e−ϖiϕ(b	e−ϖiϕ(b	NUM
ejpam-5605	304	18	,	,	PUNCT
ejpam-5605	304	19	a)γ(ϑi	a)γ(ϑi	PROPN
ejpam-5605	304	20	)	)	PUNCT
ejpam-5605	304	21	∫	∫	PROPN
ejpam-5605	305	1	ξ	ξ	PROPN
ejpam-5605	305	2	a	a	DET
ejpam-5605	305	3	ψ′(τ)ϕ(ξ	ψ′(τ)ϕ(ξ	PROPN
ejpam-5605	305	4	,	,	PUNCT
ejpam-5605	305	5	τ)ϑi−1∥fi(τ	τ)ϑi−1∥fi(τ	ADJ
ejpam-5605	305	6	,	,	PUNCT
ejpam-5605	305	7	z1(τ	z1(τ	PROPN
ejpam-5605	305	8	,	,	PUNCT
ejpam-5605	305	9	ω	ω	NOUN
ejpam-5605	305	10	)	)	PUNCT
ejpam-5605	305	11	,	,	PUNCT
ejpam-5605	305	12	z2(τ	z2(τ	PROPN
ejpam-5605	305	13	,	,	PUNCT
ejpam-5605	305	14	ω	ω	NOUN
ejpam-5605	305	15	)	)	PUNCT
ejpam-5605	305	16	,	,	PUNCT
ejpam-5605	305	17	ω)∥dτ	ω)∥dτ	PROPN
ejpam-5605	305	18	,	,	PUNCT
ejpam-5605	305	19	i	i	NOUN
ejpam-5605	305	20	=	=	NOUN
ejpam-5605	305	21	1	1	NUM
ejpam-5605	305	22	,	,	PUNCT
ejpam-5605	305	23	2	2	NUM
ejpam-5605	305	24	.	.	X
ejpam-5605	306	1	using	use	VERB
ejpam-5605	306	2	(	(	PUNCT
ejpam-5605	306	3	a3	a3	NOUN
ejpam-5605	306	4	)	)	PUNCT
ejpam-5605	306	5	,	,	PUNCT
ejpam-5605	306	6	we	we	PRON
ejpam-5605	306	7	get	get	VERB
ejpam-5605	306	8	∥zi(ξ	∥zi(ξ	PROPN
ejpam-5605	306	9	,	,	PUNCT
ejpam-5605	306	10	ω)∥	ω)∥	PUNCT
ejpam-5605	306	11	≤	≤	NUM
ejpam-5605	306	12	(	(	PUNCT
ejpam-5605	306	13	ϑi	ϑi	NOUN
ejpam-5605	306	14	−	−	PROPN
ejpam-5605	306	15	1	1	NUM
ejpam-5605	306	16	)	)	PUNCT
ejpam-5605	306	17	e−ϖiϕ(b	e−ϖiϕ(b	NUM
ejpam-5605	306	18	,	,	PUNCT
ejpam-5605	306	19	a)γ(ϑi	a)γ(ϑi	PROPN
ejpam-5605	306	20	)	)	PUNCT
ejpam-5605	306	21	∫	∫	PROPN
ejpam-5605	307	1	ξ	ξ	PROPN
ejpam-5605	307	2	a	a	DET
ejpam-5605	307	3	ψ′(τ)ϕ(ξ	ψ′(τ)ϕ(ξ	PROPN
ejpam-5605	307	4	,	,	PUNCT
ejpam-5605	307	5	τ)ϑi−1ψi(τ	τ)ϑi−1ψi(τ	PROPN
ejpam-5605	307	6	,	,	PUNCT
ejpam-5605	307	7	ω)(1	ω)(1	NUM
ejpam-5605	307	8	+	+	CCONJ
ejpam-5605	307	9	∥z1(τ	∥z1(τ	NOUN
ejpam-5605	307	10	,	,	PUNCT
ejpam-5605	307	11	ω)∥+	ω)∥+	ADJ
ejpam-5605	307	12	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	307	13	,	,	PUNCT
ejpam-5605	307	14	ω)∥)dτ	ω)∥)dτ	PROPN
ejpam-5605	307	15	≤	≤	NUM
ejpam-5605	308	1	(	(	PUNCT
ejpam-5605	308	2	ϑi	ϑi	NOUN
ejpam-5605	308	3	−	−	PROPN
ejpam-5605	308	4	1	1	NUM
ejpam-5605	308	5	)	)	PUNCT
ejpam-5605	308	6	e−ϖiϕ(b	e−ϖiϕ(b	NUM
ejpam-5605	308	7	,	,	PUNCT
ejpam-5605	308	8	a)γ(ϑi	a)γ(ϑi	PROPN
ejpam-5605	308	9	)	)	PUNCT
ejpam-5605	308	10	∫	∫	PROPN
ejpam-5605	309	1	ξ	ξ	PROPN
ejpam-5605	309	2	a	a	DET
ejpam-5605	309	3	ψ′(τ)ϕ(ξ	ψ′(τ)ϕ(ξ	PROPN
ejpam-5605	309	4	,	,	PUNCT
ejpam-5605	309	5	τ)ϑi−1ψi(τ	τ)ϑi−1ψi(τ	PROPN
ejpam-5605	309	6	,	,	PUNCT
ejpam-5605	309	7	ω)(∥z1(τ	ω)(∥z1(τ	NOUN
ejpam-5605	309	8	,	,	PUNCT
ejpam-5605	309	9	ω)∥+	ω)∥+	ADJ
ejpam-5605	309	10	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	309	11	,	,	PUNCT
ejpam-5605	309	12	ω)∥)dτ	ω)∥)dτ	PROPN
ejpam-5605	309	13	+	+	CCONJ
ejpam-5605	309	14	(	(	PUNCT
ejpam-5605	309	15	ϑi	ϑi	PROPN
ejpam-5605	309	16	−	−	PROPN
ejpam-5605	309	17	1)ψi(b	1)ψi(b	NUM
ejpam-5605	309	18	,	,	PUNCT
ejpam-5605	309	19	ω	ω	NUM
ejpam-5605	309	20	)	)	PUNCT
ejpam-5605	309	21	e−ϖiϕ(b	e−ϖiϕ(b	PROPN
ejpam-5605	309	22	,	,	PUNCT
ejpam-5605	309	23	a)ϑiγ(ϑi	a)ϑiγ(ϑi	PROPN
ejpam-5605	309	24	)	)	PUNCT
ejpam-5605	309	25	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	309	26	,	,	PUNCT
ejpam-5605	309	27	a)ϑi	a)ϑi	PROPN
ejpam-5605	309	28	,	,	PUNCT
ejpam-5605	309	29	i	i	PRON
ejpam-5605	309	30	=	=	NOUN
ejpam-5605	309	31	1	1	NUM
ejpam-5605	309	32	,	,	PUNCT
ejpam-5605	309	33	2	2	NUM
ejpam-5605	309	34	.	.	X
ejpam-5605	309	35	therefore	therefore	ADV
ejpam-5605	309	36	∥z1(ξ	∥z1(ξ	VERB
ejpam-5605	309	37	,	,	PUNCT
ejpam-5605	309	38	ω)∥+	ω)∥+	ADJ
ejpam-5605	309	39	∥z2(ξ	∥z2(ξ	PROPN
ejpam-5605	309	40	,	,	PUNCT
ejpam-5605	309	41	ω)∥	ω)∥	PUNCT
ejpam-5605	309	42	≤	≤	NUM
ejpam-5605	309	43	ς(ξ	ς(ξ	NOUN
ejpam-5605	309	44	)	)	PUNCT
ejpam-5605	310	1	+	+	CCONJ
ejpam-5605	310	2	(	(	PUNCT
ejpam-5605	310	3	ϑ1	ϑ1	NOUN
ejpam-5605	310	4	−	−	NOUN
ejpam-5605	310	5	1	1	NUM
ejpam-5605	310	6	)	)	PUNCT
ejpam-5605	310	7	e−ϖ1ϕ(b	e−ϖ1ϕ(b	ADV
ejpam-5605	310	8	,	,	PUNCT
ejpam-5605	310	9	a)γ(ϑ1	a)γ(ϑ1	NUM
ejpam-5605	310	10	)	)	PUNCT
ejpam-5605	310	11	∫	∫	PROPN
ejpam-5605	311	1	ξ	ξ	PROPN
ejpam-5605	311	2	a	a	DET
ejpam-5605	311	3	ψ′(τ)ϕ(ξ	ψ′(τ)ϕ(ξ	PROPN
ejpam-5605	311	4	,	,	PUNCT
ejpam-5605	311	5	τ)ϑ1−1ψ1(τ	τ)ϑ1−1ψ1(τ	NOUN
ejpam-5605	311	6	,	,	PUNCT
ejpam-5605	311	7	ω)(∥z1(τ	ω)(∥z1(τ	PROPN
ejpam-5605	311	8	,	,	PUNCT
ejpam-5605	311	9	ω)∥+	ω)∥+	ADJ
ejpam-5605	311	10	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	311	11	,	,	PUNCT
ejpam-5605	311	12	ω)∥)dτ	ω)∥)dτ	PROPN
ejpam-5605	311	13	+	+	CCONJ
ejpam-5605	311	14	(	(	PUNCT
ejpam-5605	311	15	ϑ2	ϑ2	PROPN
ejpam-5605	311	16	−	−	PROPN
ejpam-5605	311	17	1	1	NUM
ejpam-5605	311	18	)	)	PUNCT
ejpam-5605	311	19	e−ϖ2ϕ(b	e−ϖ2ϕ(b	ADJ
ejpam-5605	311	20	,	,	PUNCT
ejpam-5605	311	21	a)γ(ϑ2	a)γ(ϑ2	PROPN
ejpam-5605	311	22	)	)	PUNCT
ejpam-5605	311	23	∫	∫	PROPN
ejpam-5605	312	1	ξ	ξ	PROPN
ejpam-5605	312	2	a	a	DET
ejpam-5605	312	3	ψ′(τ)ϕ(ξ	ψ′(τ)ϕ(ξ	PROPN
ejpam-5605	312	4	,	,	PUNCT
ejpam-5605	312	5	τ)ϑ2−1ψ2(τ	τ)ϑ2−1ψ2(τ	PROPN
ejpam-5605	312	6	,	,	PUNCT
ejpam-5605	312	7	ω)(∥z1(τ	ω)(∥z1(τ	NOUN
ejpam-5605	312	8	,	,	PUNCT
ejpam-5605	312	9	ω)∥+	ω)∥+	ADJ
ejpam-5605	312	10	∥z2(τ	∥z2(τ	PROPN
ejpam-5605	312	11	,	,	PUNCT
ejpam-5605	312	12	ω)∥)dτ	ω)∥)dτ	PROPN
ejpam-5605	312	13	m.	m.	NOUN
ejpam-5605	312	14	ziane	ziane	PROPN
ejpam-5605	312	15	et	et	PROPN
ejpam-5605	312	16	al	al	PROPN
ejpam-5605	312	17	.	.	PUNCT
ejpam-5605	312	18	/	/	SYM
ejpam-5605	312	19	eur	eur	PROPN
ejpam-5605	312	20	.	.	PUNCT
ejpam-5605	313	1	j.	j.	PROPN
ejpam-5605	313	2	pure	pure	PROPN
ejpam-5605	313	3	appl	appl	PROPN
ejpam-5605	313	4	.	.	PROPN
ejpam-5605	313	5	math	math	PROPN
ejpam-5605	313	6	,	,	PUNCT
ejpam-5605	313	7	18	18	NUM
ejpam-5605	313	8	(	(	PUNCT
ejpam-5605	313	9	1	1	NUM
ejpam-5605	313	10	)	)	PUNCT
ejpam-5605	313	11	(	(	PUNCT
ejpam-5605	313	12	2025	2025	NUM
ejpam-5605	313	13	)	)	PUNCT
ejpam-5605	313	14	,	,	PUNCT
ejpam-5605	313	15	5605	5605	NUM
ejpam-5605	313	16	17	17	NUM
ejpam-5605	313	17	of	of	ADP
ejpam-5605	313	18	21	21	NUM
ejpam-5605	313	19	where	where	SCONJ
ejpam-5605	313	20	ς(ξ	ς(ξ	NOUN
ejpam-5605	313	21	)	)	PUNCT
ejpam-5605	313	22	:	:	PUNCT
ejpam-5605	314	1	=	=	SYM
ejpam-5605	314	2	(	(	PUNCT
ejpam-5605	314	3	ϑ1	ϑ1	NOUN
ejpam-5605	314	4	−	−	PROPN
ejpam-5605	314	5	1)ψ1(b	1)ψ1(b	NUM
ejpam-5605	314	6	,	,	PUNCT
ejpam-5605	314	7	ω	ω	NOUN
ejpam-5605	314	8	)	)	PUNCT
ejpam-5605	314	9	e−ϖ1ϕ(b	e−ϖ1ϕ(b	ADV
ejpam-5605	314	10	,	,	PUNCT
ejpam-5605	314	11	a)ϑ1γ(ϑ1	a)ϑ1γ(ϑ1	NOUN
ejpam-5605	314	12	)	)	PUNCT
ejpam-5605	314	13	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	314	14	,	,	PUNCT
ejpam-5605	314	15	a)ϑ1	a)ϑ1	PROPN
ejpam-5605	314	16	+	+	CCONJ
ejpam-5605	314	17	(	(	PUNCT
ejpam-5605	314	18	ϑ2	ϑ2	PROPN
ejpam-5605	314	19	−	−	PROPN
ejpam-5605	314	20	1)ψ2(b	1)ψ2(b	NUM
ejpam-5605	314	21	,	,	PUNCT
ejpam-5605	314	22	ω	ω	NOUN
ejpam-5605	314	23	)	)	PUNCT
ejpam-5605	314	24	e−ϖ2ϕ(b	e−ϖ2ϕ(b	ADJ
ejpam-5605	314	25	,	,	PUNCT
ejpam-5605	314	26	a)ϑ2γ(ϑ2	a)ϑ2γ(ϑ2	NOUN
ejpam-5605	314	27	)	)	PUNCT
ejpam-5605	314	28	ϕ(ξ	ϕ(ξ	PROPN
ejpam-5605	314	29	,	,	PUNCT
ejpam-5605	314	30	a)ϑ2	a)ϑ2	PROPN
ejpam-5605	314	31	applying	apply	VERB
ejpam-5605	314	32	lemma	lemma	PROPN
ejpam-5605	314	33	6	6	NUM
ejpam-5605	314	34	,	,	PUNCT
ejpam-5605	314	35	we	we	PRON
ejpam-5605	314	36	obtain	obtain	VERB
ejpam-5605	314	37	∥z1(ξ	∥z1(ξ	ADV
ejpam-5605	314	38	,	,	PUNCT
ejpam-5605	314	39	ω)∥+	ω)∥+	ADJ
ejpam-5605	314	40	∥z2(ξ	∥z2(ξ	PROPN
ejpam-5605	314	41	,	,	PUNCT
ejpam-5605	314	42	ω)∥	ω)∥	PUNCT
ejpam-5605	314	43	≤	≤	NUM
ejpam-5605	314	44	ς(b	ς(b	PROPN
ejpam-5605	314	45	)	)	PUNCT
ejpam-5605	314	46	2∑	2∑	NUM
ejpam-5605	314	47	j=0	j=0	X
ejpam-5605	314	48	eϑj	eϑj	PROPN
ejpam-5605	314	49	(	(	PUNCT
ejpam-5605	314	50	(	(	PUNCT
ejpam-5605	314	51	ϑj	ϑj	X
ejpam-5605	314	52	−	−	PROPN
ejpam-5605	314	53	1)eϖjϕ(b	1)eϖjϕ(b	PROPN
ejpam-5605	314	54	,	,	PUNCT
ejpam-5605	314	55	a)ϕ(b	a)ϕ(b	NOUN
ejpam-5605	314	56	,	,	PUNCT
ejpam-5605	314	57	a)ϑj	a)ϑj	PROPN
ejpam-5605	314	58	)	)	PUNCT
ejpam-5605	314	59	:	:	PUNCT
ejpam-5605	314	60	=	=	SYM
ejpam-5605	314	61	d.	d.	PROPN
ejpam-5605	314	62	hence	hence	ADV
ejpam-5605	314	63	∥(z1	∥(z1	PROPN
ejpam-5605	314	64	(	(	PUNCT
ejpam-5605	314	65	·	·	PUNCT
ejpam-5605	314	66	,	,	PUNCT
ejpam-5605	314	67	ω	ω	NOUN
ejpam-5605	314	68	)	)	PUNCT
ejpam-5605	314	69	,	,	PUNCT
ejpam-5605	314	70	z2	z2	PROPN
ejpam-5605	314	71	(	(	PUNCT
ejpam-5605	314	72	·	·	PUNCT
ejpam-5605	314	73	,	,	PUNCT
ejpam-5605	314	74	ω))∥j	ω))∥j	NUM
ejpam-5605	314	75	≤	≤	NUM
ejpam-5605	314	76	d̂	d̂	NUM
ejpam-5605	314	77	:	:	PUNCT
ejpam-5605	314	78	=	=	SYM
ejpam-5605	314	79	(	(	PUNCT
ejpam-5605	314	80	d	d	X
ejpam-5605	314	81	d	d	PROPN
ejpam-5605	314	82	)	)	PUNCT
ejpam-5605	314	83	which	which	PRON
ejpam-5605	314	84	achieves	achieve	VERB
ejpam-5605	314	85	the	the	DET
ejpam-5605	314	86	desired	desire	VERB
ejpam-5605	314	87	estimate	estimate	NOUN
ejpam-5605	314	88	.	.	PUNCT
ejpam-5605	315	1	therefore	therefore	ADV
ejpam-5605	315	2	,	,	PUNCT
ejpam-5605	315	3	theorem	theorem	VERB
ejpam-5605	315	4	2	2	NUM
ejpam-5605	315	5	ensures	ensure	VERB
ejpam-5605	315	6	the	the	DET
ejpam-5605	315	7	existence	existence	NOUN
ejpam-5605	315	8	of	of	ADP
ejpam-5605	315	9	a	a	DET
ejpam-5605	315	10	random	random	ADJ
ejpam-5605	315	11	solution	solution	NOUN
ejpam-5605	315	12	for	for	ADP
ejpam-5605	315	13	the	the	DET
ejpam-5605	315	14	system	system	NOUN
ejpam-5605	315	15	(	(	PUNCT
ejpam-5605	315	16	1	1	NUM
ejpam-5605	315	17	)	)	PUNCT
ejpam-5605	315	18	.	.	PUNCT
ejpam-5605	316	1	4	4	X
ejpam-5605	316	2	.	.	X
ejpam-5605	316	3	examples	example	NOUN
ejpam-5605	316	4	let	let	VERB
ejpam-5605	316	5	ω	ω	PROPN
ejpam-5605	316	6	=	=	SYM
ejpam-5605	316	7	(	(	PUNCT
ejpam-5605	316	8	−∞	−∞	NOUN
ejpam-5605	316	9	,	,	PUNCT
ejpam-5605	316	10	0	0	NUM
ejpam-5605	316	11	)	)	PUNCT
ejpam-5605	316	12	be	be	AUX
ejpam-5605	316	13	endowed	endow	VERB
ejpam-5605	316	14	with	with	ADP
ejpam-5605	316	15	the	the	DET
ejpam-5605	316	16	usual	usual	ADJ
ejpam-5605	316	17	σ	σ	PROPN
ejpam-5605	316	18	-	-	PUNCT
ejpam-5605	316	19	algebra	algebra	PROPN
ejpam-5605	316	20	consisting	consist	VERB
ejpam-5605	316	21	of	of	ADP
ejpam-5605	316	22	lebesgue	lebesgue	ADJ
ejpam-5605	316	23	measurable	measurable	ADJ
ejpam-5605	316	24	subsets	subset	NOUN
ejpam-5605	316	25	of	of	ADP
ejpam-5605	316	26	(	(	PUNCT
ejpam-5605	316	27	−∞	−∞	NOUN
ejpam-5605	316	28	,	,	PUNCT
ejpam-5605	316	29	0	0	NUM
ejpam-5605	316	30	)	)	PUNCT
ejpam-5605	316	31	.	.	PUNCT
ejpam-5605	317	1	consider	consider	VERB
ejpam-5605	317	2	the	the	DET
ejpam-5605	317	3	separable	separable	ADJ
ejpam-5605	317	4	banach	banach	NOUN
ejpam-5605	317	5	space	space	NOUN
ejpam-5605	317	6	g	g	PROPN
ejpam-5605	317	7	=	=	SYM
ejpam-5605	317	8	c0	c0	PROPN
ejpam-5605	317	9	=	=	PUNCT
ejpam-5605	317	10	{	{	PUNCT
ejpam-5605	317	11	s	s	NOUN
ejpam-5605	317	12	=	=	PUNCT
ejpam-5605	317	13	(	(	PUNCT
ejpam-5605	317	14	s1	s1	PROPN
ejpam-5605	317	15	,	,	PUNCT
ejpam-5605	317	16	s2	s2	PROPN
ejpam-5605	317	17	,	,	PUNCT
ejpam-5605	317	18	·	·	PUNCT
ejpam-5605	317	19	·	·	PUNCT
ejpam-5605	317	20	·	·	PUNCT
ejpam-5605	317	21	,	,	PUNCT
ejpam-5605	317	22	sn	sn	PROPN
ejpam-5605	317	23	,	,	PUNCT
ejpam-5605	317	24	·	·	PUNCT
ejpam-5605	317	25	·	·	PUNCT
ejpam-5605	317	26	·	·	PUNCT
ejpam-5605	317	27	)	)	PUNCT
ejpam-5605	317	28	:	:	PUNCT
ejpam-5605	318	1	sn	sn	PROPN
ejpam-5605	318	2	→	→	SYM
ejpam-5605	318	3	0	0	PUNCT
ejpam-5605	318	4	as	as	ADP
ejpam-5605	318	5	n→	n→	ADV
ejpam-5605	318	6	∞	∞	PROPN
ejpam-5605	318	7	}	}	PUNCT
ejpam-5605	318	8	endowed	endow	VERB
ejpam-5605	318	9	with	with	ADP
ejpam-5605	318	10	∥s∥g	∥s∥g	NOUN
ejpam-5605	318	11	=	=	NOUN
ejpam-5605	318	12	sup	sup	NOUN
ejpam-5605	318	13	n≥1	n≥1	NOUN
ejpam-5605	318	14	|sn|	|sn|	PROPN
ejpam-5605	318	15	.	.	PUNCT
ejpam-5605	318	16	example	example	NOUN
ejpam-5605	319	1	1	1	NUM
ejpam-5605	319	2	:	:	PUNCT
ejpam-5605	319	3	illustration	illustration	NOUN
ejpam-5605	319	4	of	of	ADP
ejpam-5605	319	5	theorem	theorem	NOUN
ejpam-5605	319	6	3	3	X
ejpam-5605	319	7	.	.	PUNCT
ejpam-5605	319	8	let	let	VERB
ejpam-5605	319	9	us	we	PRON
ejpam-5605	319	10	take	take	VERB
ejpam-5605	319	11	ϖi	ϖi	NOUN
ejpam-5605	319	12	=	=	PUNCT
ejpam-5605	319	13	....	....	PUNCT
ejpam-5605	319	14	,	,	PUNCT
ejpam-5605	319	15	i	i	PRON
ejpam-5605	319	16	=	=	NOUN
ejpam-5605	319	17	1	1	NUM
ejpam-5605	319	18	,	,	PUNCT
ejpam-5605	319	19	2	2	NUM
ejpam-5605	319	20	.	.	X
ejpam-5605	320	1	for	for	ADP
ejpam-5605	320	2	(	(	PUNCT
ejpam-5605	320	3	ξ	ξ	PROPN
ejpam-5605	320	4	,	,	PUNCT
ejpam-5605	320	5	ω	ω	NOUN
ejpam-5605	320	6	)	)	PUNCT
ejpam-5605	320	7	∈	∈	PROPN
ejpam-5605	320	8	i×	i×	PROPN
ejpam-5605	320	9	ω	ω	PROPN
ejpam-5605	320	10	,	,	PUNCT
ejpam-5605	320	11	consider	consider	VERB
ejpam-5605	320	12	the	the	DET
ejpam-5605	320	13	nonlinear	nonlinear	ADJ
ejpam-5605	320	14	functions	function	NOUN
ejpam-5605	320	15	fi	fi	NOUN
ejpam-5605	320	16	,	,	PUNCT
ejpam-5605	320	17	i	i	NOUN
ejpam-5605	320	18	=	=	NOUN
ejpam-5605	320	19	1	1	NUM
ejpam-5605	320	20	,	,	PUNCT
ejpam-5605	320	21	2	2	NUM
ejpam-5605	320	22	be	be	AUX
ejpam-5605	320	23	defined	define	VERB
ejpam-5605	320	24	by	by	PROPN
ejpam-5605	320	25	f1(ξ	f1(ξ	PROPN
ejpam-5605	320	26	,	,	PUNCT
ejpam-5605	320	27	z1(ξ	z1(ξ	PROPN
ejpam-5605	320	28	,	,	PUNCT
ejpam-5605	320	29	ω	ω	NOUN
ejpam-5605	320	30	)	)	PUNCT
ejpam-5605	320	31	,	,	PUNCT
ejpam-5605	320	32	z2(ξ	z2(ξ	PROPN
ejpam-5605	320	33	,	,	PUNCT
ejpam-5605	320	34	ω	ω	NOUN
ejpam-5605	320	35	)	)	PUNCT
ejpam-5605	320	36	,	,	PUNCT
ejpam-5605	320	37	ω	ω	X
ejpam-5605	320	38	)	)	PUNCT
ejpam-5605	321	1	=	=	PRON
ejpam-5605	321	2	{	{	PUNCT
ejpam-5605	321	3	z1,n(ξ	z1,n(ξ	PROPN
ejpam-5605	321	4	,	,	PUNCT
ejpam-5605	321	5	ω	ω	NOUN
ejpam-5605	321	6	)	)	PUNCT
ejpam-5605	321	7	|ω|(1	|ω|(1	PROPN
ejpam-5605	321	8	+	+	CCONJ
ejpam-5605	321	9	|ω|	|ω|	PROPN
ejpam-5605	321	10	)	)	PUNCT
ejpam-5605	321	11	+	+	CCONJ
ejpam-5605	321	12	sin(z2,n(ξ	sin(z2,n(ξ	PROPN
ejpam-5605	321	13	,	,	PUNCT
ejpam-5605	321	14	ω	ω	NOUN
ejpam-5605	321	15	)	)	PUNCT
ejpam-5605	321	16	)	)	PUNCT
ejpam-5605	321	17	1	1	NUM
ejpam-5605	322	1	+	+	NUM
ejpam-5605	322	2	|ω|2	|ω|2	NOUN
ejpam-5605	322	3	}	}	PUNCT
ejpam-5605	322	4	n≥1	n≥1	NOUN
ejpam-5605	322	5	,	,	PUNCT
ejpam-5605	322	6	f2(ξ	f2(ξ	PROPN
ejpam-5605	322	7	,	,	PUNCT
ejpam-5605	322	8	z1(ξ	z1(ξ	PROPN
ejpam-5605	322	9	,	,	PUNCT
ejpam-5605	322	10	ω	ω	NOUN
ejpam-5605	322	11	)	)	PUNCT
ejpam-5605	322	12	,	,	PUNCT
ejpam-5605	322	13	z2(ξ	z2(ξ	PROPN
ejpam-5605	322	14	,	,	PUNCT
ejpam-5605	322	15	ω	ω	NOUN
ejpam-5605	322	16	)	)	PUNCT
ejpam-5605	322	17	,	,	PUNCT
ejpam-5605	322	18	ω	ω	X
ejpam-5605	322	19	)	)	PUNCT
ejpam-5605	322	20	=	=	PRON
ejpam-5605	322	21	{	{	PUNCT
ejpam-5605	322	22	arctan	arctan	PROPN
ejpam-5605	322	23	|s1,n(ξ	|s1,n(ξ	VERB
ejpam-5605	322	24	,	,	PUNCT
ejpam-5605	322	25	ω)|	ω)|	ADJ
ejpam-5605	322	26	1	1	NUM
ejpam-5605	322	27	+	+	NUM
ejpam-5605	322	28	|ω|	|ω|	ADP
ejpam-5605	322	29	+	+	CCONJ
ejpam-5605	322	30	e−|ω|z2,n(ξ	e−|ω|z2,n(ξ	PROPN
ejpam-5605	322	31	,	,	PUNCT
ejpam-5605	322	32	ω	ω	NOUN
ejpam-5605	322	33	)	)	PUNCT
ejpam-5605	322	34	1	1	NUM
ejpam-5605	323	1	+	+	NUM
ejpam-5605	323	2	|z2,n(ξ	|z2,n(ξ	NOUN
ejpam-5605	323	3	,	,	PUNCT
ejpam-5605	323	4	ω)|	ω)|	ADJ
ejpam-5605	323	5	}	}	PUNCT
ejpam-5605	323	6	n≥1	n≥1	NOUN
ejpam-5605	323	7	(	(	PUNCT
ejpam-5605	323	8	19	19	NUM
ejpam-5605	323	9	)	)	PUNCT
ejpam-5605	323	10	firstly	firstly	ADV
ejpam-5605	323	11	,	,	PUNCT
ejpam-5605	323	12	we	we	PRON
ejpam-5605	323	13	easily	easily	ADV
ejpam-5605	323	14	see	see	VERB
ejpam-5605	323	15	that	that	SCONJ
ejpam-5605	323	16	,	,	PUNCT
ejpam-5605	323	17	the	the	DET
ejpam-5605	323	18	functions	function	NOUN
ejpam-5605	323	19	fi	fi	NOUN
ejpam-5605	323	20	,	,	PUNCT
ejpam-5605	323	21	i	i	NOUN
ejpam-5605	323	22	=	=	NOUN
ejpam-5605	323	23	1	1	NUM
ejpam-5605	323	24	,	,	PUNCT
ejpam-5605	323	25	2	2	NUM
ejpam-5605	323	26	,	,	PUNCT
ejpam-5605	323	27	satisfy	satisfy	NOUN
ejpam-5605	323	28	(	(	PUNCT
ejpam-5605	323	29	a1	a1	NOUN
ejpam-5605	323	30	)	)	PUNCT
ejpam-5605	323	31	.	.	PUNCT
ejpam-5605	324	1	secondly	secondly	ADV
ejpam-5605	324	2	,	,	PUNCT
ejpam-5605	324	3	we	we	PRON
ejpam-5605	324	4	can	can	AUX
ejpam-5605	324	5	check	check	VERB
ejpam-5605	324	6	that	that	DET
ejpam-5605	324	7	∥f1(ξ	∥f1(ξ	NOUN
ejpam-5605	324	8	,	,	PUNCT
ejpam-5605	324	9	z1(ξ	z1(ξ	PROPN
ejpam-5605	324	10	,	,	PUNCT
ejpam-5605	324	11	ω	ω	NOUN
ejpam-5605	324	12	)	)	PUNCT
ejpam-5605	324	13	,	,	PUNCT
ejpam-5605	324	14	z2(ξ	z2(ξ	PROPN
ejpam-5605	324	15	,	,	PUNCT
ejpam-5605	324	16	ω	ω	NOUN
ejpam-5605	324	17	)	)	PUNCT
ejpam-5605	324	18	,	,	PUNCT
ejpam-5605	324	19	ω)−	ω)−	PROPN
ejpam-5605	324	20	f1(ξ	f1(ξ	PROPN
ejpam-5605	324	21	,	,	PUNCT
ejpam-5605	324	22	r1(ξ	r1(ξ	PROPN
ejpam-5605	324	23	,	,	PUNCT
ejpam-5605	324	24	ω	ω	NOUN
ejpam-5605	324	25	)	)	PUNCT
ejpam-5605	324	26	,	,	PUNCT
ejpam-5605	324	27	r2(ξ	r2(ξ	PROPN
ejpam-5605	324	28	,	,	PUNCT
ejpam-5605	324	29	ω	ω	NOUN
ejpam-5605	324	30	)	)	PUNCT
ejpam-5605	324	31	,	,	PUNCT
ejpam-5605	324	32	ω)∥	ω)∥	PUNCT
ejpam-5605	324	33	≤	≤	NUM
ejpam-5605	325	1	1	1	NUM
ejpam-5605	325	2	|ω|(1	|ω|(1	PROPN
ejpam-5605	325	3	+	+	CCONJ
ejpam-5605	325	4	|ω|	|ω|	PROPN
ejpam-5605	325	5	)	)	PUNCT
ejpam-5605	325	6	∥z1,n(ξ	∥z1,n(ξ	VERB
ejpam-5605	325	7	,	,	PUNCT
ejpam-5605	325	8	ω)−	ω)−	PROPN
ejpam-5605	325	9	r1,n(ξ	r1,n(ξ	NOUN
ejpam-5605	325	10	,	,	PUNCT
ejpam-5605	325	11	ω)∥+	ω)∥+	ADJ
ejpam-5605	325	12	1	1	NUM
ejpam-5605	325	13	1	1	NUM
ejpam-5605	325	14	+	+	NUM
ejpam-5605	325	15	|ω|2	|ω|2	PROPN
ejpam-5605	325	16	∥z2,n(ξ	∥z2,n(ξ	NOUN
ejpam-5605	325	17	,	,	PUNCT
ejpam-5605	325	18	ω)−	ω)−	PROPN
ejpam-5605	325	19	r2,n(ξ	r2,n(ξ	NOUN
ejpam-5605	325	20	,	,	PUNCT
ejpam-5605	325	21	ω)∥	ω)∥	PUNCT
ejpam-5605	325	22	,	,	PUNCT
ejpam-5605	325	23	and	and	CCONJ
ejpam-5605	325	24	∥f2(ξ	∥f2(ξ	NOUN
ejpam-5605	325	25	,	,	PUNCT
ejpam-5605	325	26	z1(ξ	z1(ξ	PROPN
ejpam-5605	325	27	,	,	PUNCT
ejpam-5605	325	28	ω	ω	NOUN
ejpam-5605	325	29	)	)	PUNCT
ejpam-5605	325	30	,	,	PUNCT
ejpam-5605	325	31	z2(ξ	z2(ξ	PROPN
ejpam-5605	325	32	,	,	PUNCT
ejpam-5605	325	33	ω	ω	NOUN
ejpam-5605	325	34	)	)	PUNCT
ejpam-5605	325	35	,	,	PUNCT
ejpam-5605	325	36	ω)−	ω)−	PROPN
ejpam-5605	325	37	f2(ξ	f2(ξ	PROPN
ejpam-5605	325	38	,	,	PUNCT
ejpam-5605	325	39	r1(ξ	r1(ξ	PROPN
ejpam-5605	325	40	,	,	PUNCT
ejpam-5605	325	41	ω	ω	NOUN
ejpam-5605	325	42	)	)	PUNCT
ejpam-5605	325	43	,	,	PUNCT
ejpam-5605	325	44	r2(ξ	r2(ξ	PROPN
ejpam-5605	325	45	,	,	PUNCT
ejpam-5605	325	46	ω	ω	NOUN
ejpam-5605	325	47	)	)	PUNCT
ejpam-5605	325	48	,	,	PUNCT
ejpam-5605	325	49	ω)∥	ω)∥	PUNCT
ejpam-5605	325	50	≤	≤	NUM
ejpam-5605	325	51	1	1	NUM
ejpam-5605	325	52	1	1	NUM
ejpam-5605	325	53	+	+	NUM
ejpam-5605	325	54	|ω|	|ω|	PROPN
ejpam-5605	325	55	∥z1,n(ξ	∥z1,n(ξ	NOUN
ejpam-5605	325	56	,	,	PUNCT
ejpam-5605	325	57	ω)−	ω)−	PROPN
ejpam-5605	325	58	r1,n(ξ	r1,n(ξ	NOUN
ejpam-5605	325	59	,	,	PUNCT
ejpam-5605	325	60	ω)∥+	ω)∥+	ADJ
ejpam-5605	325	61	1	1	NUM
ejpam-5605	325	62	e|ω|	e|ω|	ADJ
ejpam-5605	325	63	∥z2,n(ξ	∥z2,n(ξ	NOUN
ejpam-5605	325	64	,	,	PUNCT
ejpam-5605	325	65	ω)−	ω)−	PROPN
ejpam-5605	325	66	r2,n(ξ	r2,n(ξ	NOUN
ejpam-5605	325	67	,	,	PUNCT
ejpam-5605	325	68	ω)∥.	ω)∥.	ADP
ejpam-5605	325	69	m.	m.	NOUN
ejpam-5605	325	70	ziane	ziane	PROPN
ejpam-5605	325	71	et	et	PROPN
ejpam-5605	325	72	al	al	PROPN
ejpam-5605	325	73	.	.	PUNCT
ejpam-5605	325	74	/	/	SYM
ejpam-5605	325	75	eur	eur	PROPN
ejpam-5605	325	76	.	.	PUNCT
ejpam-5605	326	1	j.	j.	PROPN
ejpam-5605	326	2	pure	pure	PROPN
ejpam-5605	326	3	appl	appl	PROPN
ejpam-5605	326	4	.	.	PROPN
ejpam-5605	326	5	math	math	PROPN
ejpam-5605	326	6	,	,	PUNCT
ejpam-5605	326	7	18	18	NUM
ejpam-5605	326	8	(	(	PUNCT
ejpam-5605	326	9	1	1	NUM
ejpam-5605	326	10	)	)	PUNCT
ejpam-5605	326	11	(	(	PUNCT
ejpam-5605	326	12	2025	2025	NUM
ejpam-5605	326	13	)	)	PUNCT
ejpam-5605	326	14	,	,	PUNCT
ejpam-5605	326	15	5605	5605	NUM
ejpam-5605	326	16	18	18	NUM
ejpam-5605	326	17	of	of	ADP
ejpam-5605	326	18	21	21	NUM
ejpam-5605	326	19	so	so	ADV
ejpam-5605	326	20	,	,	PUNCT
ejpam-5605	326	21	the	the	DET
ejpam-5605	326	22	hypotheses	hypothesis	NOUN
ejpam-5605	326	23	(	(	PUNCT
ejpam-5605	326	24	a2	a2	NOUN
ejpam-5605	326	25	)	)	PUNCT
ejpam-5605	326	26	holds	hold	VERB
ejpam-5605	326	27	with	with	ADP
ejpam-5605	326	28	φ1,1(ω	φ1,1(ω	ADJ
ejpam-5605	326	29	)	)	PUNCT
ejpam-5605	326	30	=	=	SYM
ejpam-5605	326	31	1	1	NUM
ejpam-5605	326	32	|ω|(1	|ω|(1	PROPN
ejpam-5605	326	33	+	+	CCONJ
ejpam-5605	326	34	|ω|	|ω|	PROPN
ejpam-5605	326	35	)	)	PUNCT
ejpam-5605	326	36	,	,	PUNCT
ejpam-5605	326	37	φ1,2(ω	φ1,2(ω	ADV
ejpam-5605	326	38	)	)	PUNCT
ejpam-5605	326	39	=	=	SYM
ejpam-5605	326	40	1	1	NUM
ejpam-5605	326	41	1	1	NUM
ejpam-5605	326	42	+	+	NUM
ejpam-5605	326	43	|ω|2	|ω|2	NOUN
ejpam-5605	326	44	,	,	PUNCT
ejpam-5605	326	45	for	for	ADP
ejpam-5605	326	46	all	all	DET
ejpam-5605	326	47	ω	ω	NUM
ejpam-5605	326	48	∈	∈	PROPN
ejpam-5605	326	49	ω	ω	NOUN
ejpam-5605	326	50	.	.	PUNCT
ejpam-5605	327	1	φ2,1(ω	φ2,1(ω	ADJ
ejpam-5605	327	2	)	)	PUNCT
ejpam-5605	327	3	=	=	SYM
ejpam-5605	328	1	1	1	NUM
ejpam-5605	328	2	1	1	NUM
ejpam-5605	328	3	+	+	NUM
ejpam-5605	328	4	|ω|	|ω|	PROPN
ejpam-5605	328	5	,	,	PUNCT
ejpam-5605	328	6	φ2,2(ω	φ2,2(ω	ADJ
ejpam-5605	328	7	)	)	PUNCT
ejpam-5605	328	8	=	=	SYM
ejpam-5605	328	9	1	1	NUM
ejpam-5605	328	10	e|ω|	e|ω|	NOUN
ejpam-5605	328	11	,	,	PUNCT
ejpam-5605	328	12	for	for	ADP
ejpam-5605	328	13	all	all	DET
ejpam-5605	328	14	ω	ω	NUM
ejpam-5605	328	15	∈	∈	PROPN
ejpam-5605	328	16	ω	ω	NOUN
ejpam-5605	328	17	.	.	PUNCT
ejpam-5605	329	1	an	an	DET
ejpam-5605	329	2	application	application	NOUN
ejpam-5605	329	3	of	of	ADP
ejpam-5605	329	4	theorem	theorem	NOUN
ejpam-5605	329	5	3	3	NUM
ejpam-5605	329	6	,	,	PUNCT
ejpam-5605	329	7	we	we	PRON
ejpam-5605	329	8	deduce	deduce	VERB
ejpam-5605	329	9	that	that	DET
ejpam-5605	329	10	system	system	NOUN
ejpam-5605	329	11	(	(	PUNCT
ejpam-5605	329	12	1	1	NUM
ejpam-5605	329	13	)	)	PUNCT
ejpam-5605	329	14	with	with	ADP
ejpam-5605	329	15	(	(	PUNCT
ejpam-5605	329	16	19	19	NUM
ejpam-5605	329	17	)	)	PUNCT
ejpam-5605	329	18	has	have	VERB
ejpam-5605	329	19	a	a	DET
ejpam-5605	329	20	unique	unique	ADJ
ejpam-5605	329	21	random	random	ADJ
ejpam-5605	329	22	solution	solution	NOUN
ejpam-5605	329	23	(	(	PUNCT
ejpam-5605	329	24	z1	z1	NOUN
ejpam-5605	329	25	,	,	PUNCT
ejpam-5605	329	26	z2	z2	PROPN
ejpam-5605	329	27	)	)	PUNCT
ejpam-5605	329	28	.	.	PUNCT
ejpam-5605	330	1	example	example	NOUN
ejpam-5605	331	1	2	2	NUM
ejpam-5605	331	2	:	:	PUNCT
ejpam-5605	331	3	illustration	illustration	NOUN
ejpam-5605	331	4	of	of	ADP
ejpam-5605	331	5	theorem	theorem	NOUN
ejpam-5605	331	6	4	4	NUM
ejpam-5605	331	7	.	.	PUNCT
ejpam-5605	331	8	for	for	ADP
ejpam-5605	331	9	(	(	PUNCT
ejpam-5605	331	10	ς	ς	PROPN
ejpam-5605	331	11	,	,	PUNCT
ejpam-5605	331	12	ω	ω	NOUN
ejpam-5605	331	13	)	)	PUNCT
ejpam-5605	331	14	∈	∈	PROPN
ejpam-5605	332	1	i×	i×	PROPN
ejpam-5605	332	2	ω	ω	PROPN
ejpam-5605	332	3	and	and	CCONJ
ejpam-5605	332	4	si	si	X
ejpam-5605	332	5	=	=	ADJ
ejpam-5605	332	6	{	{	PUNCT
ejpam-5605	332	7	si	si	X
ejpam-5605	332	8	,	,	PUNCT
ejpam-5605	332	9	n}n	n}n	PROPN
ejpam-5605	332	10	∈	∈	PROPN
ejpam-5605	332	11	c0	c0	NOUN
ejpam-5605	332	12	,	,	PUNCT
ejpam-5605	332	13	consider	consider	VERB
ejpam-5605	332	14	the	the	DET
ejpam-5605	332	15	nonlinear	nonlinear	ADJ
ejpam-5605	332	16	forcing	forcing	ADJ
ejpam-5605	332	17	terms	term	NOUN
ejpam-5605	332	18	,	,	PUNCT
ejpam-5605	332	19			PROPN
ejpam-5605	332	20	f1(ξ	f1(ξ	PROPN
ejpam-5605	332	21	,	,	PUNCT
ejpam-5605	332	22	z1(ξ	z1(ξ	PROPN
ejpam-5605	332	23	,	,	PUNCT
ejpam-5605	332	24	ω	ω	NOUN
ejpam-5605	332	25	)	)	PUNCT
ejpam-5605	332	26	,	,	PUNCT
ejpam-5605	332	27	z2(ξ	z2(ξ	PROPN
ejpam-5605	332	28	,	,	PUNCT
ejpam-5605	332	29	ω	ω	NOUN
ejpam-5605	332	30	)	)	PUNCT
ejpam-5605	332	31	,	,	PUNCT
ejpam-5605	332	32	ω	ω	X
ejpam-5605	332	33	)	)	PUNCT
ejpam-5605	332	34	=	=	SYM
ejpam-5605	332	35	2	2	NUM
ejpam-5605	332	36	sin(ω/5	sin(ω/5	NOUN
ejpam-5605	332	37	)	)	PUNCT
ejpam-5605	332	38	π	π	PROPN
ejpam-5605	332	39	arctan(ξ	arctan(ξ	NOUN
ejpam-5605	332	40	)	)	PUNCT
ejpam-5605	332	41	{	{	PUNCT
ejpam-5605	332	42	sin	sin	NOUN
ejpam-5605	332	43	|z1,n(ξ	|z1,n(ξ	NOUN
ejpam-5605	332	44	,	,	PUNCT
ejpam-5605	332	45	ω)|+	ω)|+	NOUN
ejpam-5605	332	46	loge(|z2,n(ξ	loge(|z2,n(ξ	NOUN
ejpam-5605	332	47	,	,	PUNCT
ejpam-5605	332	48	ω)|+	ω)|+	NOUN
ejpam-5605	332	49	1	1	NUM
ejpam-5605	332	50	)	)	PUNCT
ejpam-5605	332	51	+	+	NUM
ejpam-5605	332	52	5−n	5−n	NUM
ejpam-5605	332	53	}	}	PUNCT
ejpam-5605	332	54	n≥1	n≥1	NOUN
ejpam-5605	332	55	f2(ξ	f2(ξ	PROPN
ejpam-5605	332	56	,	,	PUNCT
ejpam-5605	332	57	z1(ξ	z1(ξ	PROPN
ejpam-5605	332	58	,	,	PUNCT
ejpam-5605	332	59	ω	ω	NOUN
ejpam-5605	332	60	)	)	PUNCT
ejpam-5605	332	61	,	,	PUNCT
ejpam-5605	332	62	z2(ξ	z2(ξ	PROPN
ejpam-5605	332	63	,	,	PUNCT
ejpam-5605	332	64	ω	ω	NOUN
ejpam-5605	332	65	)	)	PUNCT
ejpam-5605	332	66	,	,	PUNCT
ejpam-5605	332	67	ω	ω	X
ejpam-5605	332	68	)	)	PUNCT
ejpam-5605	332	69	=	=	VERB
ejpam-5605	332	70	|ω|(e2ξ	|ω|(e2ξ	VERB
ejpam-5605	332	71	−	−	NOUN
ejpam-5605	332	72	1	1	NUM
ejpam-5605	332	73	)	)	PUNCT
ejpam-5605	332	74	(	(	PUNCT
ejpam-5605	332	75	1	1	NUM
ejpam-5605	332	76	+	+	CCONJ
ejpam-5605	332	77	|ω|)(eξ	|ω|)(eξ	PUNCT
ejpam-5605	333	1	+	+	NUM
ejpam-5605	333	2	1	1	NUM
ejpam-5605	333	3	)	)	PUNCT
ejpam-5605	333	4	{	{	PUNCT
ejpam-5605	333	5	arctan(|z1,n(ξ	arctan(|z1,n(ξ	PROPN
ejpam-5605	333	6	,	,	PUNCT
ejpam-5605	333	7	ω)|	ω)|	ADJ
ejpam-5605	333	8	)	)	PUNCT
ejpam-5605	333	9	+	+	CCONJ
ejpam-5605	333	10	|z2,n(ξ	|z2,n(ξ	NOUN
ejpam-5605	333	11	,	,	PUNCT
ejpam-5605	333	12	ω)|+	ω)|+	NOUN
ejpam-5605	333	13	π−n	π−n	NOUN
ejpam-5605	333	14	}	}	PUNCT
ejpam-5605	333	15	n≥1	n≥1	NOUN
ejpam-5605	333	16	(	(	PUNCT
ejpam-5605	333	17	20	20	NUM
ejpam-5605	333	18	)	)	PUNCT
ejpam-5605	333	19	obviously	obviously	ADV
ejpam-5605	333	20	,	,	PUNCT
ejpam-5605	333	21	fi	fi	NOUN
ejpam-5605	333	22	,	,	PUNCT
ejpam-5605	333	23	(	(	PUNCT
ejpam-5605	333	24	i	i	NOUN
ejpam-5605	333	25	=	=	NOUN
ejpam-5605	333	26	1	1	NUM
ejpam-5605	333	27	,	,	PUNCT
ejpam-5605	333	28	2	2	X
ejpam-5605	333	29	)	)	PUNCT
ejpam-5605	333	30	satisfy	satisfy	NOUN
ejpam-5605	333	31	hypothesis	hypothesis	NOUN
ejpam-5605	333	32	(	(	PUNCT
ejpam-5605	333	33	a1	a1	NOUN
ejpam-5605	333	34	)	)	PUNCT
ejpam-5605	333	35	.	.	PUNCT
ejpam-5605	334	1	to	to	PART
ejpam-5605	334	2	illustrate	illustrate	VERB
ejpam-5605	334	3	(	(	PUNCT
ejpam-5605	334	4	a3	a3	NOUN
ejpam-5605	334	5	)	)	PUNCT
ejpam-5605	334	6	,	,	PUNCT
ejpam-5605	334	7	let	let	VERB
ejpam-5605	334	8	ξ	ξ	X
ejpam-5605	334	9	∈	∈	VERB
ejpam-5605	334	10	i	i	PRON
ejpam-5605	334	11	and	and	CCONJ
ejpam-5605	334	12	zi	zi	NOUN
ejpam-5605	334	13	=	=	SYM
ejpam-5605	334	14	{	{	PUNCT
ejpam-5605	334	15	zi	zi	PROPN
ejpam-5605	334	16	,	,	PUNCT
ejpam-5605	334	17	n}n	n}n	PROPN
ejpam-5605	334	18	∈	∈	PROPN
ejpam-5605	334	19	u	u	PROPN
ejpam-5605	334	20	⊂	⊂	PROPN
ejpam-5605	334	21	c0	c0	PROPN
ejpam-5605	334	22	,	,	PUNCT
ejpam-5605	334	23	i	i	PRON
ejpam-5605	334	24	=	=	NOUN
ejpam-5605	334	25	1	1	NUM
ejpam-5605	334	26	,	,	PUNCT
ejpam-5605	334	27	2	2	NUM
ejpam-5605	334	28	.	.	PUNCT
ejpam-5605	334	29	then	then	ADV
ejpam-5605	334	30	∥f1(ξ	∥f1(ξ	VERB
ejpam-5605	334	31	,	,	PUNCT
ejpam-5605	334	32	z1(ξ	z1(ξ	PROPN
ejpam-5605	334	33	,	,	PUNCT
ejpam-5605	334	34	ω	ω	NOUN
ejpam-5605	334	35	)	)	PUNCT
ejpam-5605	334	36	,	,	PUNCT
ejpam-5605	334	37	z2(ξ	z2(ξ	PROPN
ejpam-5605	334	38	,	,	PUNCT
ejpam-5605	334	39	ω	ω	NOUN
ejpam-5605	334	40	)	)	PUNCT
ejpam-5605	334	41	,	,	PUNCT
ejpam-5605	334	42	ω)∥	ω)∥	PUNCT
ejpam-5605	334	43	≤	≤	NUM
ejpam-5605	334	44	2	2	NUM
ejpam-5605	334	45	sin(ω/5	sin(ω/5	NOUN
ejpam-5605	334	46	)	)	PUNCT
ejpam-5605	334	47	π	π	PROPN
ejpam-5605	334	48	arctan(ξ	arctan(ξ	NOUN
ejpam-5605	334	49	)	)	PUNCT
ejpam-5605	334	50	(	(	PUNCT
ejpam-5605	334	51	∥z1,n(ξ	∥z1,n(ξ	NOUN
ejpam-5605	334	52	,	,	PUNCT
ejpam-5605	334	53	ω)∥+	ω)∥+	ADJ
ejpam-5605	334	54	∥z2,n(ξ	∥z2,n(ξ	NOUN
ejpam-5605	334	55	,	,	PUNCT
ejpam-5605	334	56	ω)∥+	ω)∥+	ADJ
ejpam-5605	334	57	1	1	NUM
ejpam-5605	334	58	)	)	PUNCT
ejpam-5605	334	59	,	,	PUNCT
ejpam-5605	334	60	(	(	PUNCT
ejpam-5605	334	61	21	21	NUM
ejpam-5605	334	62	)	)	PUNCT
ejpam-5605	334	63	and	and	CCONJ
ejpam-5605	334	64	∥f2(ξ	∥f2(ξ	NOUN
ejpam-5605	334	65	,	,	PUNCT
ejpam-5605	334	66	z1(ξ	z1(ξ	PROPN
ejpam-5605	334	67	,	,	PUNCT
ejpam-5605	334	68	ω	ω	NOUN
ejpam-5605	334	69	)	)	PUNCT
ejpam-5605	334	70	,	,	PUNCT
ejpam-5605	334	71	z2(ξ	z2(ξ	PROPN
ejpam-5605	334	72	,	,	PUNCT
ejpam-5605	334	73	ω	ω	NOUN
ejpam-5605	334	74	)	)	PUNCT
ejpam-5605	334	75	,	,	PUNCT
ejpam-5605	334	76	ω)∥	ω)∥	PUNCT
ejpam-5605	334	77	≤	≤	NOUN
ejpam-5605	334	78	|ω|(e2ξ	|ω|(e2ξ	VERB
ejpam-5605	334	79	−	−	PROPN
ejpam-5605	334	80	1	1	NUM
ejpam-5605	334	81	)	)	PUNCT
ejpam-5605	334	82	(	(	PUNCT
ejpam-5605	334	83	1	1	NUM
ejpam-5605	334	84	+	+	CCONJ
ejpam-5605	334	85	|ω|)(eξ	|ω|)(eξ	PUNCT
ejpam-5605	335	1	+	+	NUM
ejpam-5605	335	2	1	1	NUM
ejpam-5605	335	3	)	)	PUNCT
ejpam-5605	335	4	(	(	PUNCT
ejpam-5605	335	5	∥z1,n(ξ	∥z1,n(ξ	NOUN
ejpam-5605	335	6	,	,	PUNCT
ejpam-5605	335	7	ω)∥+	ω)∥+	ADJ
ejpam-5605	335	8	∥z2,n(ξ	∥z2,n(ξ	NOUN
ejpam-5605	335	9	,	,	PUNCT
ejpam-5605	335	10	ω)∥+	ω)∥+	ADJ
ejpam-5605	335	11	1	1	NUM
ejpam-5605	335	12	)	)	PUNCT
ejpam-5605	335	13	,	,	PUNCT
ejpam-5605	335	14	(	(	PUNCT
ejpam-5605	335	15	22	22	NUM
ejpam-5605	335	16	)	)	PUNCT
ejpam-5605	335	17	therefore	therefore	ADV
ejpam-5605	335	18	,	,	PUNCT
ejpam-5605	335	19	(	(	PUNCT
ejpam-5605	335	20	h3	h3	NOUN
ejpam-5605	335	21	)	)	PUNCT
ejpam-5605	335	22	is	be	AUX
ejpam-5605	335	23	verified	verify	VERB
ejpam-5605	335	24	with	with	ADP
ejpam-5605	335	25	ψ1(ξ	ψ1(ξ	PROPN
ejpam-5605	335	26	,	,	PUNCT
ejpam-5605	335	27	ω	ω	NOUN
ejpam-5605	335	28	)	)	PUNCT
ejpam-5605	335	29	=	=	SYM
ejpam-5605	335	30	2	2	NUM
ejpam-5605	335	31	sin(ω/5	sin(ω/5	NOUN
ejpam-5605	335	32	)	)	PUNCT
ejpam-5605	335	33	π	π	PROPN
ejpam-5605	335	34	arctan(ξ	arctan(ξ	NOUN
ejpam-5605	335	35	)	)	PUNCT
ejpam-5605	335	36	and	and	CCONJ
ejpam-5605	335	37	ψ2(ξ	ψ2(ξ	PROPN
ejpam-5605	335	38	,	,	PUNCT
ejpam-5605	335	39	ω	ω	NOUN
ejpam-5605	335	40	)	)	PUNCT
ejpam-5605	335	41	=	=	VERB
ejpam-5605	335	42	|ω|(e2ξ	|ω|(e2ξ	VERB
ejpam-5605	335	43	−	−	NOUN
ejpam-5605	335	44	1	1	NUM
ejpam-5605	335	45	)	)	PUNCT
ejpam-5605	335	46	(	(	PUNCT
ejpam-5605	335	47	1	1	NUM
ejpam-5605	335	48	+	+	CCONJ
ejpam-5605	335	49	|ω|)(eξ	|ω|)(eξ	PUNCT
ejpam-5605	336	1	+	+	NUM
ejpam-5605	336	2	1	1	NUM
ejpam-5605	336	3	)	)	PUNCT
ejpam-5605	336	4	for	for	ADP
ejpam-5605	336	5	all	all	DET
ejpam-5605	336	6	(	(	PUNCT
ejpam-5605	336	7	ξ	ξ	PROPN
ejpam-5605	336	8	,	,	PUNCT
ejpam-5605	336	9	ω	ω	NOUN
ejpam-5605	336	10	)	)	PUNCT
ejpam-5605	336	11	∈	∈	PROPN
ejpam-5605	336	12	i×ω	i×ω	PROPN
ejpam-5605	336	13	.	.	PUNCT
ejpam-5605	337	1	next	next	ADV
ejpam-5605	337	2	,	,	PUNCT
ejpam-5605	337	3	hypothesis	hypothesis	NOUN
ejpam-5605	337	4	(	(	PUNCT
ejpam-5605	337	5	a4	a4	NOUN
ejpam-5605	337	6	)	)	PUNCT
ejpam-5605	337	7	is	be	AUX
ejpam-5605	337	8	satisfied	satisfied	ADJ
ejpam-5605	337	9	.	.	PUNCT
ejpam-5605	338	1	indeed	indeed	ADV
ejpam-5605	338	2	,	,	PUNCT
ejpam-5605	338	3	we	we	PRON
ejpam-5605	338	4	recall	recall	VERB
ejpam-5605	338	5	that	that	SCONJ
ejpam-5605	338	6	the	the	DET
ejpam-5605	338	7	hausdorff	hausdorff	NOUN
ejpam-5605	338	8	mnc	mnc	PROPN
ejpam-5605	338	9	θ	θ	PROPN
ejpam-5605	338	10	in	in	ADP
ejpam-5605	338	11	(	(	PUNCT
ejpam-5605	338	12	c0	c0	NOUN
ejpam-5605	338	13	,	,	PUNCT
ejpam-5605	338	14	∥	∥	PROPN
ejpam-5605	338	15	·	·	PUNCT
ejpam-5605	338	16	∥c0	∥c0	X
ejpam-5605	338	17	)	)	PUNCT
ejpam-5605	338	18	can	can	AUX
ejpam-5605	338	19	be	be	AUX
ejpam-5605	338	20	computed	compute	VERB
ejpam-5605	338	21	by	by	ADP
ejpam-5605	338	22	means	mean	NOUN
ejpam-5605	338	23	of	of	ADP
ejpam-5605	338	24	the	the	DET
ejpam-5605	338	25	formula	formula	NOUN
ejpam-5605	338	26	θ(u	θ(u	NOUN
ejpam-5605	338	27	)	)	PUNCT
ejpam-5605	339	1	=	=	SYM
ejpam-5605	339	2	lim	lim	PROPN
ejpam-5605	339	3	n→∞	n→∞	NUM
ejpam-5605	339	4	sup	sup	PROPN
ejpam-5605	339	5	z∈u	z∈u	PROPN
ejpam-5605	339	6	∥(i−	∥(i−	PROPN
ejpam-5605	339	7	pn	pn	PROPN
ejpam-5605	339	8	)	)	PUNCT
ejpam-5605	339	9	z∥∞	z∥∞	PROPN
ejpam-5605	339	10	,	,	PUNCT
ejpam-5605	339	11	where	where	SCONJ
ejpam-5605	339	12	u	u	PROPN
ejpam-5605	339	13	∈	∈	PROPN
ejpam-5605	339	14	p(c0	p(c0	NOUN
ejpam-5605	339	15	)	)	PUNCT
ejpam-5605	339	16	,	,	PUNCT
ejpam-5605	339	17	pn	pn	PROPN
ejpam-5605	339	18	represents	represent	VERB
ejpam-5605	339	19	the	the	DET
ejpam-5605	339	20	projection	projection	NOUN
ejpam-5605	339	21	onto	onto	ADP
ejpam-5605	339	22	the	the	DET
ejpam-5605	339	23	linear	linear	ADJ
ejpam-5605	339	24	span	span	NOUN
ejpam-5605	339	25	of	of	ADP
ejpam-5605	339	26	the	the	DET
ejpam-5605	339	27	first	first	ADJ
ejpam-5605	339	28	n	n	PRON
ejpam-5605	339	29	vectors	vector	NOUN
ejpam-5605	339	30	in	in	ADP
ejpam-5605	339	31	the	the	DET
ejpam-5605	339	32	standard	standard	ADJ
ejpam-5605	339	33	basis	basis	NOUN
ejpam-5605	339	34	(	(	PUNCT
ejpam-5605	339	35	see	see	VERB
ejpam-5605	339	36	[	[	X
ejpam-5605	339	37	1	1	NUM
ejpam-5605	339	38	]	]	NUM
ejpam-5605	339	39	)	)	PUNCT
ejpam-5605	339	40	.	.	PUNCT
ejpam-5605	340	1	m.	m.	NOUN
ejpam-5605	340	2	ziane	ziane	PROPN
ejpam-5605	340	3	et	et	PROPN
ejpam-5605	340	4	al	al	PROPN
ejpam-5605	340	5	.	.	PUNCT
ejpam-5605	340	6	/	/	SYM
ejpam-5605	340	7	eur	eur	PROPN
ejpam-5605	340	8	.	.	PUNCT
ejpam-5605	341	1	j.	j.	PROPN
ejpam-5605	341	2	pure	pure	PROPN
ejpam-5605	341	3	appl	appl	PROPN
ejpam-5605	341	4	.	.	PROPN
ejpam-5605	341	5	math	math	PROPN
ejpam-5605	341	6	,	,	PUNCT
ejpam-5605	341	7	18	18	NUM
ejpam-5605	341	8	(	(	PUNCT
ejpam-5605	341	9	1	1	NUM
ejpam-5605	341	10	)	)	PUNCT
ejpam-5605	341	11	(	(	PUNCT
ejpam-5605	341	12	2025	2025	NUM
ejpam-5605	341	13	)	)	PUNCT
ejpam-5605	341	14	,	,	PUNCT
ejpam-5605	341	15	5605	5605	NUM
ejpam-5605	341	16	19	19	NUM
ejpam-5605	341	17	of	of	ADP
ejpam-5605	341	18	21	21	NUM
ejpam-5605	341	19	using	use	VERB
ejpam-5605	341	20	(	(	PUNCT
ejpam-5605	341	21	21	21	NUM
ejpam-5605	341	22	)	)	PUNCT
ejpam-5605	341	23	and	and	CCONJ
ejpam-5605	341	24	(	(	PUNCT
ejpam-5605	341	25	22	22	NUM
ejpam-5605	341	26	)	)	PUNCT
ejpam-5605	341	27	(	(	PUNCT
ejpam-5605	341	28	see	see	VERB
ejpam-5605	341	29	also	also	ADV
ejpam-5605	341	30	example	example	VERB
ejpam-5605	341	31	in	in	ADP
ejpam-5605	341	32	[	[	X
ejpam-5605	341	33	32	32	NUM
ejpam-5605	341	34	]	]	NUM
ejpam-5605	341	35	)	)	PUNCT
ejpam-5605	341	36	,	,	PUNCT
ejpam-5605	341	37	we	we	PRON
ejpam-5605	341	38	get	get	VERB
ejpam-5605	341	39	θ	θ	PROPN
ejpam-5605	341	40	(	(	PUNCT
ejpam-5605	341	41	fi(ξ	fi(ξ	X
ejpam-5605	341	42	,	,	PUNCT
ejpam-5605	341	43	u	u	NOUN
ejpam-5605	341	44	1	1	NUM
ejpam-5605	341	45	,	,	PUNCT
ejpam-5605	341	46	u2	u2	NOUN
ejpam-5605	341	47	)	)	PUNCT
ejpam-5605	341	48	)	)	PUNCT
ejpam-5605	342	1	≤	≤	NUM
ejpam-5605	342	2	ϱi,1(ω)θ(u1	ϱi,1(ω)θ(u1	PROPN
ejpam-5605	342	3	)	)	PUNCT
ejpam-5605	343	1	+	+	CCONJ
ejpam-5605	343	2	ϱi,2(ω)θ(u2	ϱi,2(ω)θ(u2	PROPN
ejpam-5605	343	3	)	)	PUNCT
ejpam-5605	343	4	,	,	PUNCT
ejpam-5605	343	5	for	for	ADP
ejpam-5605	343	6	all	all	PRON
ejpam-5605	343	7	(	(	PUNCT
ejpam-5605	343	8	ξ	ξ	PROPN
ejpam-5605	343	9	,	,	PUNCT
ejpam-5605	343	10	ω	ω	NOUN
ejpam-5605	343	11	)	)	PUNCT
ejpam-5605	343	12	∈	∈	PROPN
ejpam-5605	344	1	i×	i×	PROPN
ejpam-5605	344	2	ω	ω	PROPN
ejpam-5605	344	3	.	.	PUNCT
ejpam-5605	344	4	where	where	SCONJ
ejpam-5605	344	5	ϱ1,1(ω	ϱ1,1(ω	NOUN
ejpam-5605	344	6	)	)	PUNCT
ejpam-5605	344	7	=	=	SYM
ejpam-5605	344	8	ϱ1,2(ω	ϱ1,2(ω	PROPN
ejpam-5605	344	9	)	)	PUNCT
ejpam-5605	344	10	=	=	SYM
ejpam-5605	345	1	sin(ω/5	sin(ω/5	NOUN
ejpam-5605	345	2	)	)	PUNCT
ejpam-5605	345	3	,	,	PUNCT
ejpam-5605	345	4	ϱ2,1(ω	ϱ2,1(ω	NOUN
ejpam-5605	345	5	)	)	PUNCT
ejpam-5605	345	6	=	=	PUNCT
ejpam-5605	345	7	ϱ2,2(ω	ϱ2,2(ω	NOUN
ejpam-5605	345	8	)	)	PUNCT
ejpam-5605	345	9	=	=	SYM
ejpam-5605	345	10	|ω|	|ω|	ADP
ejpam-5605	345	11	1	1	NUM
ejpam-5605	345	12	+	+	NUM
ejpam-5605	345	13	|ω|	|ω|	NOUN
ejpam-5605	345	14	,	,	PUNCT
ejpam-5605	345	15	for	for	ADP
ejpam-5605	345	16	all	all	DET
ejpam-5605	345	17	ω	ω	NUM
ejpam-5605	345	18	∈	∈	PROPN
ejpam-5605	345	19	ω	ω	NOUN
ejpam-5605	345	20	.	.	PUNCT
ejpam-5605	346	1	the	the	DET
ejpam-5605	346	2	conclusion	conclusion	NOUN
ejpam-5605	346	3	of	of	ADP
ejpam-5605	346	4	teorem	teorem	ADJ
ejpam-5605	346	5	4	4	NUM
ejpam-5605	346	6	implies	imply	VERB
ejpam-5605	346	7	that	that	DET
ejpam-5605	346	8	problem	problem	NOUN
ejpam-5605	346	9	(	(	PUNCT
ejpam-5605	346	10	1	1	NUM
ejpam-5605	346	11	)	)	PUNCT
ejpam-5605	346	12	with	with	ADP
ejpam-5605	346	13	(	(	PUNCT
ejpam-5605	346	14	20	20	NUM
ejpam-5605	346	15	)	)	PUNCT
ejpam-5605	346	16	has	have	VERB
ejpam-5605	346	17	at	at	ADV
ejpam-5605	346	18	least	least	ADV
ejpam-5605	346	19	one	one	NUM
ejpam-5605	346	20	solution	solution	NOUN
ejpam-5605	346	21	(	(	PUNCT
ejpam-5605	346	22	z1	z1	NOUN
ejpam-5605	346	23	,	,	PUNCT
ejpam-5605	346	24	z2	z2	PROPN
ejpam-5605	346	25	)	)	PUNCT
ejpam-5605	346	26	.	.	PUNCT
ejpam-5605	347	1	5	5	X
ejpam-5605	347	2	.	.	X
ejpam-5605	347	3	conclusion	conclusion	NOUN
ejpam-5605	347	4	the	the	DET
ejpam-5605	347	5	fractional	fractional	ADJ
ejpam-5605	347	6	langevin	langevin	NOUN
ejpam-5605	347	7	system	system	NOUN
ejpam-5605	347	8	is	be	AUX
ejpam-5605	347	9	a	a	DET
ejpam-5605	347	10	crucial	crucial	ADJ
ejpam-5605	347	11	mathematical	mathematical	ADJ
ejpam-5605	347	12	model	model	NOUN
ejpam-5605	347	13	for	for	ADP
ejpam-5605	347	14	describing	describe	VERB
ejpam-5605	347	15	the	the	DET
ejpam-5605	347	16	random	random	ADJ
ejpam-5605	347	17	motion	motion	NOUN
ejpam-5605	347	18	of	of	ADP
ejpam-5605	347	19	particles	particle	NOUN
ejpam-5605	347	20	.	.	PUNCT
ejpam-5605	348	1	consequently	consequently	ADV
ejpam-5605	348	2	,	,	PUNCT
ejpam-5605	348	3	we	we	PRON
ejpam-5605	348	4	investigated	investigate	VERB
ejpam-5605	348	5	a	a	DET
ejpam-5605	348	6	class	class	NOUN
ejpam-5605	348	7	of	of	ADP
ejpam-5605	348	8	ψ	ψ	PROPN
ejpam-5605	348	9	-	-	PROPN
ejpam-5605	348	10	caputo	caputo	PROPN
ejpam-5605	348	11	langevin	langevin	PROPN
ejpam-5605	348	12	systems	system	NOUN
ejpam-5605	348	13	with	with	ADP
ejpam-5605	348	14	random	random	ADJ
ejpam-5605	348	15	effects	effect	NOUN
ejpam-5605	348	16	in	in	ADP
ejpam-5605	348	17	a	a	DET
ejpam-5605	348	18	generalized	generalize	VERB
ejpam-5605	348	19	separable	separable	ADJ
ejpam-5605	348	20	banach	banach	NOUN
ejpam-5605	348	21	space	space	NOUN
ejpam-5605	348	22	.	.	PUNCT
ejpam-5605	349	1	by	by	ADP
ejpam-5605	349	2	employing	employ	VERB
ejpam-5605	349	3	the	the	DET
ejpam-5605	349	4	bielecki	bielecki	ADJ
ejpam-5605	349	5	-	-	PUNCT
ejpam-5605	349	6	type	type	NOUN
ejpam-5605	349	7	vector	vector	NOUN
ejpam-5605	349	8	-	-	PUNCT
ejpam-5605	349	9	valued	value	VERB
ejpam-5605	349	10	norm	norm	NOUN
ejpam-5605	349	11	,	,	PUNCT
ejpam-5605	349	12	we	we	PRON
ejpam-5605	349	13	established	establish	VERB
ejpam-5605	349	14	a	a	DET
ejpam-5605	349	15	new	new	ADJ
ejpam-5605	349	16	uniqueness	uniqueness	NOUN
ejpam-5605	349	17	criterion	criterion	NOUN
ejpam-5605	349	18	.	.	PUNCT
ejpam-5605	350	1	additionally	additionally	ADV
ejpam-5605	350	2	,	,	PUNCT
ejpam-5605	350	3	we	we	PRON
ejpam-5605	350	4	imposed	impose	VERB
ejpam-5605	350	5	rather	rather	ADV
ejpam-5605	350	6	mild	mild	ADJ
ejpam-5605	350	7	assumptions	assumption	NOUN
ejpam-5605	350	8	to	to	PART
ejpam-5605	350	9	obtain	obtain	VERB
ejpam-5605	350	10	a	a	DET
ejpam-5605	350	11	new	new	ADJ
ejpam-5605	350	12	existence	existence	NOUN
ejpam-5605	350	13	result	result	NOUN
ejpam-5605	350	14	by	by	ADP
ejpam-5605	350	15	utilizing	utilize	VERB
ejpam-5605	350	16	a	a	DET
ejpam-5605	350	17	recent	recent	ADJ
ejpam-5605	350	18	random	random	ADJ
ejpam-5605	350	19	version	version	NOUN
ejpam-5605	350	20	of	of	ADP
ejpam-5605	350	21	sadovski	sadovski	PROPN
ejpam-5605	350	22	’s	’s	PART
ejpam-5605	350	23	fixed	fix	VERB
ejpam-5605	350	24	-	-	PUNCT
ejpam-5605	350	25	point	point	NOUN
ejpam-5605	350	26	theorem	theorem	VERB
ejpam-5605	350	27	.	.	PUNCT
ejpam-5605	351	1	as	as	ADP
ejpam-5605	351	2	a	a	DET
ejpam-5605	351	3	result	result	NOUN
ejpam-5605	351	4	,	,	PUNCT
ejpam-5605	351	5	numerous	numerous	ADJ
ejpam-5605	351	6	findings	finding	NOUN
ejpam-5605	351	7	in	in	ADP
ejpam-5605	351	8	the	the	DET
ejpam-5605	351	9	literature	literature	NOUN
ejpam-5605	351	10	can	can	AUX
ejpam-5605	351	11	be	be	AUX
ejpam-5605	351	12	recovered	recover	VERB
ejpam-5605	351	13	through	through	ADP
ejpam-5605	351	14	our	our	PRON
ejpam-5605	351	15	results	result	NOUN
ejpam-5605	351	16	.	.	PUNCT
ejpam-5605	352	1	acknowledgements	acknowledgement	NOUN
ejpam-5605	352	2	the	the	DET
ejpam-5605	352	3	authors	author	NOUN
ejpam-5605	352	4	would	would	AUX
ejpam-5605	352	5	like	like	VERB
ejpam-5605	352	6	to	to	PART
ejpam-5605	352	7	express	express	VERB
ejpam-5605	352	8	their	their	PRON
ejpam-5605	352	9	gratitude	gratitude	NOUN
ejpam-5605	352	10	to	to	ADP
ejpam-5605	352	11	the	the	DET
ejpam-5605	352	12	referees	referee	NOUN
ejpam-5605	352	13	for	for	ADP
ejpam-5605	352	14	their	their	PRON
ejpam-5605	352	15	insightful	insightful	ADJ
ejpam-5605	352	16	comments	comment	NOUN
ejpam-5605	352	17	,	,	PUNCT
ejpam-5605	352	18	which	which	PRON
ejpam-5605	352	19	have	have	AUX
ejpam-5605	352	20	improved	improve	VERB
ejpam-5605	352	21	the	the	DET
ejpam-5605	352	22	paper	paper	NOUN
ejpam-5605	352	23	.	.	PUNCT
ejpam-5605	353	1	references	reference	NOUN
ejpam-5605	353	2	[	[	X
ejpam-5605	353	3	1	1	NUM
ejpam-5605	353	4	]	]	X
ejpam-5605	353	5	r	r	NOUN
ejpam-5605	353	6	r	r	NOUN
ejpam-5605	353	7	akhmerov	akhmerov	NOUN
ejpam-5605	353	8	,	,	PUNCT
ejpam-5605	353	9	m	m	VERB
ejpam-5605	353	10	i	i	PRON
ejpam-5605	353	11	kamenskii	kamenskii	ADJ
ejpam-5605	353	12	,	,	PUNCT
ejpam-5605	353	13	a	a	DET
ejpam-5605	353	14	s	s	X
ejpam-5605	353	15	potapov	potapov	NOUN
ejpam-5605	353	16	,	,	PUNCT
ejpam-5605	353	17	a	a	DET
ejpam-5605	353	18	e	e	X
ejpam-5605	353	19	rodkina	rodkina	NOUN
ejpam-5605	353	20	,	,	PUNCT
ejpam-5605	353	21	and	and	CCONJ
ejpam-5605	353	22	b	b	X
ejpam-5605	353	23	n	n	ADV
ejpam-5605	353	24	sadovskii	sadovskii	NOUN
ejpam-5605	353	25	.	.	PUNCT
ejpam-5605	354	1	measures	measure	NOUN
ejpam-5605	354	2	of	of	ADP
ejpam-5605	354	3	noncompactness	noncompactness	ADJ
ejpam-5605	354	4	and	and	CCONJ
ejpam-5605	354	5	condensing	condense	VERB
ejpam-5605	354	6	operators	operator	NOUN
ejpam-5605	354	7	.	.	PUNCT
ejpam-5605	355	1	birkhäuser	birkhäuser	X
ejpam-5605	355	2	verlag	verlag	PROPN
ejpam-5605	355	3	,	,	PUNCT
ejpam-5605	355	4	baselboston	baselboston	PROPN
ejpam-5605	355	5	-	-	PUNCT
ejpam-5605	355	6	berlin	berlin	PROPN
ejpam-5605	355	7	,	,	PUNCT
ejpam-5605	355	8	1992	1992	NUM
ejpam-5605	355	9	.	.	PUNCT
ejpam-5605	356	1	[	[	X
ejpam-5605	356	2	2	2	X
ejpam-5605	356	3	]	]	PUNCT
ejpam-5605	356	4	i	i	PRON
ejpam-5605	356	5	alhribat	alhribat	VERB
ejpam-5605	356	6	and	and	CCONJ
ejpam-5605	356	7	m	m	PROPN
ejpam-5605	356	8	h	h	NOUN
ejpam-5605	356	9	samuh	samuh	ADJ
ejpam-5605	356	10	.	.	PUNCT
ejpam-5605	357	1	generating	generate	VERB
ejpam-5605	357	2	statistical	statistical	ADJ
ejpam-5605	357	3	distributions	distribution	NOUN
ejpam-5605	357	4	using	use	VERB
ejpam-5605	357	5	fractional	fractional	ADJ
ejpam-5605	357	6	differential	differential	ADJ
ejpam-5605	357	7	equations	equation	NOUN
ejpam-5605	357	8	.	.	PUNCT
ejpam-5605	358	1	jordan	jordan	PROPN
ejpam-5605	358	2	journal	journal	PROPN
ejpam-5605	358	3	of	of	ADP
ejpam-5605	358	4	mathematics	mathematics	PROPN
ejpam-5605	358	5	and	and	CCONJ
ejpam-5605	358	6	statistics	statistic	NOUN
ejpam-5605	358	7	,	,	PUNCT
ejpam-5605	358	8	16(2):379–396	16(2):379–396	NUM
ejpam-5605	358	9	,	,	PUNCT
ejpam-5605	358	10	2023	2023	NUM
ejpam-5605	358	11	.	.	PUNCT
ejpam-5605	359	1	[	[	X
ejpam-5605	359	2	3	3	NUM
ejpam-5605	359	3	]	]	X
ejpam-5605	359	4	r	r	PROPN
ejpam-5605	359	5	almeida	almeida	PROPN
ejpam-5605	359	6	.	.	PUNCT
ejpam-5605	360	1	a	a	DET
ejpam-5605	360	2	caputo	caputo	PROPN
ejpam-5605	360	3	fractional	fractional	PROPN
ejpam-5605	360	4	derivative	derivative	NOUN
ejpam-5605	360	5	of	of	ADP
ejpam-5605	360	6	a	a	DET
ejpam-5605	360	7	function	function	NOUN
ejpam-5605	360	8	with	with	ADP
ejpam-5605	360	9	respect	respect	NOUN
ejpam-5605	360	10	to	to	ADP
ejpam-5605	360	11	another	another	DET
ejpam-5605	360	12	function	function	NOUN
ejpam-5605	360	13	.	.	PUNCT
ejpam-5605	361	1	commun	commun	PROPN
ejpam-5605	361	2	.	.	PUNCT
ejpam-5605	362	1	nonlinear	nonlinear	PROPN
ejpam-5605	362	2	sci	sci	PROPN
ejpam-5605	362	3	.	.	PUNCT
ejpam-5605	362	4	numer	numer	PROPN
ejpam-5605	362	5	.	.	PUNCT
ejpam-5605	363	1	simul	simul	PROPN
ejpam-5605	363	2	.	.	PROPN
ejpam-5605	363	3	,	,	PUNCT
ejpam-5605	363	4	44:460–481	44:460–481	NUM
ejpam-5605	363	5	,	,	PUNCT
ejpam-5605	363	6	2017	2017	NUM
ejpam-5605	363	7	.	.	PUNCT
ejpam-5605	364	1	[	[	X
ejpam-5605	364	2	4	4	X
ejpam-5605	364	3	]	]	X
ejpam-5605	364	4	g	g	NOUN
ejpam-5605	364	5	alotta	alotta	NOUN
ejpam-5605	364	6	,	,	PUNCT
ejpam-5605	364	7	m	m	PROPN
ejpam-5605	364	8	di	di	PROPN
ejpam-5605	364	9	paola	paola	PROPN
ejpam-5605	364	10	,	,	PUNCT
ejpam-5605	364	11	and	and	CCONJ
ejpam-5605	364	12	f	f	PROPN
ejpam-5605	364	13	p	p	PROPN
ejpam-5605	364	14	pinnola	pinnola	PROPN
ejpam-5605	364	15	.	.	PUNCT
ejpam-5605	365	1	an	an	DET
ejpam-5605	365	2	unified	unified	ADJ
ejpam-5605	365	3	formulation	formulation	NOUN
ejpam-5605	365	4	of	of	ADP
ejpam-5605	365	5	strong	strong	ADJ
ejpam-5605	365	6	non	non	ADJ
ejpam-5605	365	7	-	-	ADJ
ejpam-5605	365	8	local	local	ADJ
ejpam-5605	365	9	elasticity	elasticity	NOUN
ejpam-5605	365	10	with	with	ADP
ejpam-5605	365	11	fractional	fractional	ADJ
ejpam-5605	365	12	order	order	NOUN
ejpam-5605	365	13	calculus	calculus	NOUN
ejpam-5605	365	14	.	.	PUNCT
ejpam-5605	366	1	commun	commun	PROPN
ejpam-5605	366	2	.	.	PUNCT
ejpam-5605	367	1	nonlinear	nonlinear	PROPN
ejpam-5605	367	2	sci	sci	PROPN
ejpam-5605	367	3	.	.	PUNCT
ejpam-5605	367	4	numer	numer	PROPN
ejpam-5605	367	5	.	.	PUNCT
ejpam-5605	368	1	simul	simul	PROPN
ejpam-5605	368	2	.	.	PROPN
ejpam-5605	368	3	,	,	PUNCT
ejpam-5605	368	4	57	57	NUM
ejpam-5605	368	5	:	:	PUNCT
ejpam-5605	368	6	meccanica	meccanica	PROPN
ejpam-5605	368	7	,	,	PUNCT
ejpam-5605	368	8	2022	2022	NUM
ejpam-5605	368	9	.	.	PUNCT
ejpam-5605	369	1	[	[	X
ejpam-5605	369	2	5	5	NUM
ejpam-5605	369	3	]	]	PUNCT
ejpam-5605	369	4	j	j	PROPN
ejpam-5605	369	5	alzabut	alzabut	PROPN
ejpam-5605	369	6	,	,	PUNCT
ejpam-5605	369	7	y	y	PROPN
ejpam-5605	369	8	adjabi	adjabi	PROPN
ejpam-5605	369	9	,	,	PUNCT
ejpam-5605	369	10	w	w	NOUN
ejpam-5605	369	11	sudsutad	sudsutad	NOUN
ejpam-5605	369	12	,	,	PUNCT
ejpam-5605	369	13	and	and	CCONJ
ejpam-5605	369	14	m	m	PROPN
ejpam-5605	369	15	rehman	rehman	PROPN
ejpam-5605	369	16	.	.	PUNCT
ejpam-5605	370	1	new	new	ADJ
ejpam-5605	370	2	generalizations	generalization	NOUN
ejpam-5605	370	3	for	for	ADP
ejpam-5605	370	4	gronwall	gronwall	ADJ
ejpam-5605	370	5	type	type	NOUN
ejpam-5605	370	6	inequalities	inequality	NOUN
ejpam-5605	370	7	involving	involve	VERB
ejpam-5605	370	8	a	a	DET
ejpam-5605	370	9	ϕ-fractional	ϕ-fractional	ADJ
ejpam-5605	370	10	operator	operator	NOUN
ejpam-5605	370	11	and	and	CCONJ
ejpam-5605	370	12	their	their	PRON
ejpam-5605	370	13	applications	application	NOUN
ejpam-5605	370	14	.	.	PUNCT
ejpam-5605	371	1	aims	aim	VERB
ejpam-5605	371	2	mathematics	mathematic	NOUN
ejpam-5605	371	3	,	,	PUNCT
ejpam-5605	371	4	6(5):5053–5077	6(5):5053–5077	PROPN
ejpam-5605	371	5	,	,	PUNCT
ejpam-5605	371	6	2021	2021	NUM
ejpam-5605	371	7	.	.	PUNCT
ejpam-5605	372	1	m.	m.	NOUN
ejpam-5605	372	2	ziane	ziane	PROPN
ejpam-5605	372	3	et	et	PROPN
ejpam-5605	372	4	al	al	PROPN
ejpam-5605	372	5	.	.	PUNCT
ejpam-5605	372	6	/	/	SYM
ejpam-5605	372	7	eur	eur	PROPN
ejpam-5605	372	8	.	.	PUNCT
ejpam-5605	373	1	j.	j.	PROPN
ejpam-5605	373	2	pure	pure	PROPN
ejpam-5605	373	3	appl	appl	PROPN
ejpam-5605	373	4	.	.	PROPN
ejpam-5605	373	5	math	math	PROPN
ejpam-5605	373	6	,	,	PUNCT
ejpam-5605	373	7	18	18	NUM
ejpam-5605	373	8	(	(	PUNCT
ejpam-5605	373	9	1	1	NUM
ejpam-5605	373	10	)	)	PUNCT
ejpam-5605	373	11	(	(	PUNCT
ejpam-5605	373	12	2025	2025	NUM
ejpam-5605	373	13	)	)	PUNCT
ejpam-5605	373	14	,	,	PUNCT
ejpam-5605	373	15	5605	5605	NUM
ejpam-5605	373	16	20	20	NUM
ejpam-5605	373	17	of	of	ADP
ejpam-5605	373	18	21	21	NUM
ejpam-5605	373	19	[	[	SYM
ejpam-5605	373	20	6	6	NUM
ejpam-5605	373	21	]	]	PUNCT
ejpam-5605	373	22	z	z	NOUN
ejpam-5605	373	23	baitiche	baitiche	NOUN
ejpam-5605	373	24	,	,	PUNCT
ejpam-5605	373	25	c	c	NOUN
ejpam-5605	373	26	derbazi	derbazi	NOUN
ejpam-5605	373	27	,	,	PUNCT
ejpam-5605	373	28	and	and	CCONJ
ejpam-5605	373	29	m	m	PROPN
ejpam-5605	373	30	matar	matar	NOUN
ejpam-5605	373	31	.	.	PUNCT
ejpam-5605	374	1	ulam	ulam	ADJ
ejpam-5605	374	2	-	-	PUNCT
ejpam-5605	374	3	stability	stability	NOUN
ejpam-5605	374	4	results	result	VERB
ejpam-5605	374	5	for	for	ADP
ejpam-5605	374	6	a	a	DET
ejpam-5605	374	7	new	new	ADJ
ejpam-5605	374	8	form	form	NOUN
ejpam-5605	374	9	of	of	ADP
ejpam-5605	374	10	nonlinear	nonlinear	ADJ
ejpam-5605	374	11	fractional	fractional	ADJ
ejpam-5605	374	12	langevin	langevin	PROPN
ejpam-5605	374	13	differential	differential	PROPN
ejpam-5605	374	14	equations	equation	NOUN
ejpam-5605	374	15	involving	involve	VERB
ejpam-5605	374	16	two	two	NUM
ejpam-5605	374	17	fractional	fractional	ADJ
ejpam-5605	374	18	orders	order	NOUN
ejpam-5605	374	19	in	in	ADP
ejpam-5605	374	20	the	the	DET
ejpam-5605	374	21	ψ	ψ	PROPN
ejpam-5605	374	22	–	–	PUNCT
ejpam-5605	374	23	caputo	caputo	NOUN
ejpam-5605	374	24	sense	sense	NOUN
ejpam-5605	374	25	.	.	PUNCT
ejpam-5605	375	1	applicable	applicable	ADJ
ejpam-5605	375	2	anal	anal	PROPN
ejpam-5605	375	3	.	.	PUNCT
ejpam-5605	375	4	,	,	PUNCT
ejpam-5605	375	5	101(14):4866–4881	101(14):4866–4881	NUM
ejpam-5605	375	6	,	,	PUNCT
ejpam-5605	375	7	2022	2022	NUM
ejpam-5605	375	8	.	.	PUNCT
ejpam-5605	376	1	[	[	X
ejpam-5605	376	2	7	7	X
ejpam-5605	376	3	]	]	X
ejpam-5605	376	4	a	a	DET
ejpam-5605	376	5	baliki	baliki	PROPN
ejpam-5605	376	6	,	,	PUNCT
ejpam-5605	376	7	j	j	PROPN
ejpam-5605	376	8	nieto	nieto	PROPN
ejpam-5605	376	9	,	,	PUNCT
ejpam-5605	376	10	a	a	DET
ejpam-5605	376	11	ouahab	ouahab	NOUN
ejpam-5605	376	12	,	,	PUNCT
ejpam-5605	376	13	and	and	CCONJ
ejpam-5605	376	14	m	m	PRON
ejpam-5605	376	15	sinacer	sinacer	ADJ
ejpam-5605	376	16	.	.	PUNCT
ejpam-5605	377	1	random	random	ADJ
ejpam-5605	377	2	semilinear	semilinear	NOUN
ejpam-5605	377	3	system	system	NOUN
ejpam-5605	377	4	of	of	ADP
ejpam-5605	377	5	differential	differential	ADJ
ejpam-5605	377	6	equations	equation	NOUN
ejpam-5605	377	7	with	with	ADP
ejpam-5605	377	8	impulses	impulse	NOUN
ejpam-5605	377	9	.	.	PUNCT
ejpam-5605	378	1	fixed	fix	VERB
ejpam-5605	378	2	point	point	NOUN
ejpam-5605	378	3	theory	theory	NOUN
ejpam-5605	378	4	appl	appl	PROPN
ejpam-5605	378	5	.	.	PROPN
ejpam-5605	378	6	,	,	PUNCT
ejpam-5605	378	7	2017:29	2017:29	NUM
ejpam-5605	378	8	p	p	NOUN
ejpam-5605	378	9	,	,	PUNCT
ejpam-5605	378	10	2017	2017	NUM
ejpam-5605	378	11	.	.	PUNCT
ejpam-5605	379	1	no	no	DET
ejpam-5605	379	2	27	27	NUM
ejpam-5605	379	3	.	.	PUNCT
ejpam-5605	380	1	[	[	X
ejpam-5605	380	2	8	8	NUM
ejpam-5605	380	3	]	]	X
ejpam-5605	380	4	r	r	NOUN
ejpam-5605	380	5	dhayal	dhayal	NOUN
ejpam-5605	380	6	,	,	PUNCT
ejpam-5605	380	7	m	m	PROPN
ejpam-5605	380	8	malik	malik	PROPN
ejpam-5605	380	9	,	,	PUNCT
ejpam-5605	380	10	and	and	CCONJ
ejpam-5605	380	11	s	s	VERB
ejpam-5605	380	12	abbas	abbas	NOUN
ejpam-5605	380	13	.	.	PUNCT
ejpam-5605	381	1	nonlinear	nonlinear	ADJ
ejpam-5605	381	2	heat	heat	NOUN
ejpam-5605	381	3	conduction	conduction	NOUN
ejpam-5605	381	4	equations	equation	NOUN
ejpam-5605	381	5	with	with	ADP
ejpam-5605	381	6	memory	memory	NOUN
ejpam-5605	381	7	:	:	PUNCT
ejpam-5605	381	8	physical	physical	ADJ
ejpam-5605	381	9	meaning	meaning	NOUN
ejpam-5605	381	10	and	and	CCONJ
ejpam-5605	381	11	analytical	analytical	ADJ
ejpam-5605	381	12	results	result	NOUN
ejpam-5605	381	13	.	.	PUNCT
ejpam-5605	382	1	j.	j.	PROPN
ejpam-5605	382	2	math	math	PROPN
ejpam-5605	382	3	.	.	PUNCT
ejpam-5605	383	1	phys	phy	NOUN
ejpam-5605	383	2	.	.	PUNCT
ejpam-5605	383	3	,	,	PUNCT
ejpam-5605	383	4	58:063501	58:063501	NUM
ejpam-5605	383	5	,	,	PUNCT
ejpam-5605	383	6	2017	2017	NUM
ejpam-5605	383	7	.	.	PUNCT
ejpam-5605	384	1	[	[	X
ejpam-5605	384	2	9	9	NUM
ejpam-5605	384	3	]	]	X
ejpam-5605	384	4	r	r	NOUN
ejpam-5605	384	5	dhayal	dhayal	NOUN
ejpam-5605	384	6	,	,	PUNCT
ejpam-5605	384	7	m	m	PROPN
ejpam-5605	384	8	malik	malik	PROPN
ejpam-5605	384	9	,	,	PUNCT
ejpam-5605	384	10	and	and	CCONJ
ejpam-5605	384	11	s	s	VERB
ejpam-5605	384	12	abbas	abbas	PROPN
ejpam-5605	384	13	.	.	PUNCT
ejpam-5605	384	14	solvability	solvability	NOUN
ejpam-5605	384	15	and	and	CCONJ
ejpam-5605	384	16	optimal	optimal	ADJ
ejpam-5605	384	17	controls	control	NOUN
ejpam-5605	384	18	of	of	ADP
ejpam-5605	384	19	noninstantaneous	noninstantaneous	ADJ
ejpam-5605	384	20	impulsive	impulsive	ADJ
ejpam-5605	384	21	stochastic	stochastic	ADJ
ejpam-5605	384	22	fractional	fractional	ADJ
ejpam-5605	384	23	differential	differential	ADJ
ejpam-5605	384	24	equation	equation	NOUN
ejpam-5605	384	25	of	of	ADP
ejpam-5605	384	26	order	order	NOUN
ejpam-5605	384	27	q	q	X
ejpam-5605	384	28	∈	∈	NOUN
ejpam-5605	384	29	(	(	PUNCT
ejpam-5605	384	30	1	1	NUM
ejpam-5605	384	31	,	,	PUNCT
ejpam-5605	384	32	2	2	NUM
ejpam-5605	384	33	)	)	PUNCT
ejpam-5605	384	34	.	.	PUNCT
ejpam-5605	385	1	stochastics	stochastic	NOUN
ejpam-5605	385	2	,	,	PUNCT
ejpam-5605	385	3	93(5):780–802	93(5):780–802	NOUN
ejpam-5605	385	4	,	,	PUNCT
ejpam-5605	385	5	2021	2021	NUM
ejpam-5605	385	6	.	.	PUNCT
ejpam-5605	386	1	[	[	X
ejpam-5605	386	2	10	10	NUM
ejpam-5605	386	3	]	]	X
ejpam-5605	386	4	h	h	NOUN
ejpam-5605	386	5	fu	fu	PROPN
ejpam-5605	386	6	,	,	PUNCT
ejpam-5605	386	7	g	g	PROPN
ejpam-5605	386	8	wu	wu	PROPN
ejpam-5605	386	9	,	,	PUNCT
ejpam-5605	386	10	g	g	PROPN
ejpam-5605	386	11	yang	yang	PROPN
ejpam-5605	386	12	,	,	PUNCT
ejpam-5605	386	13	and	and	CCONJ
ejpam-5605	386	14	l	l	PROPN
ejpam-5605	386	15	huang	huang	PROPN
ejpam-5605	386	16	.	.	PUNCT
ejpam-5605	387	1	continuous	continuous	ADJ
ejpam-5605	387	2	time	time	NOUN
ejpam-5605	387	3	random	random	ADJ
ejpam-5605	387	4	walk	walk	NOUN
ejpam-5605	387	5	to	to	ADP
ejpam-5605	387	6	a	a	DET
ejpam-5605	387	7	general	general	ADJ
ejpam-5605	387	8	fractional	fractional	ADJ
ejpam-5605	387	9	fokker	fokker	NOUN
ejpam-5605	387	10	–	–	PUNCT
ejpam-5605	387	11	planck	planck	NOUN
ejpam-5605	387	12	equation	equation	NOUN
ejpam-5605	387	13	on	on	ADP
ejpam-5605	387	14	fractal	fractal	ADJ
ejpam-5605	387	15	media	medium	NOUN
ejpam-5605	387	16	.	.	PUNCT
ejpam-5605	388	1	eur	eur	ADJ
ejpam-5605	388	2	.	.	PUNCT
ejpam-5605	389	1	phys	phy	NOUN
ejpam-5605	389	2	.	.	PUNCT
ejpam-5605	390	1	j.	j.	PROPN
ejpam-5605	390	2	spec	spec	PROPN
ejpam-5605	390	3	.	.	PUNCT
ejpam-5605	391	1	top	top	PROPN
ejpam-5605	391	2	.	.	PROPN
ejpam-5605	391	3	,	,	PUNCT
ejpam-5605	391	4	230:3927–3933	230:3927–3933	NUM
ejpam-5605	391	5	,	,	PUNCT
ejpam-5605	391	6	2021	2021	NUM
ejpam-5605	391	7	.	.	PUNCT
ejpam-5605	392	1	[	[	X
ejpam-5605	392	2	11	11	NUM
ejpam-5605	392	3	]	]	PUNCT
ejpam-5605	392	4	a	a	DET
ejpam-5605	392	5	giusti	giusti	NOUN
ejpam-5605	392	6	.	.	PUNCT
ejpam-5605	393	1	on	on	ADP
ejpam-5605	393	2	infinite	infinite	ADJ
ejpam-5605	393	3	order	order	NOUN
ejpam-5605	393	4	differential	differential	NOUN
ejpam-5605	393	5	operators	operator	NOUN
ejpam-5605	393	6	in	in	ADP
ejpam-5605	393	7	fractional	fractional	ADJ
ejpam-5605	393	8	viscoelasticity	viscoelasticity	NOUN
ejpam-5605	393	9	.	.	PUNCT
ejpam-5605	394	1	fract	fract	PROPN
ejpam-5605	394	2	.	.	PUNCT
ejpam-5605	395	1	calc	calc	PROPN
ejpam-5605	395	2	.	.	PUNCT
ejpam-5605	396	1	appl	appl	PROPN
ejpam-5605	396	2	.	.	PUNCT
ejpam-5605	397	1	anal	anal	PROPN
ejpam-5605	397	2	.	.	PROPN
ejpam-5605	397	3	,	,	PUNCT
ejpam-5605	397	4	20(4):854–867	20(4):854–867	NUM
ejpam-5605	397	5	,	,	PUNCT
ejpam-5605	397	6	2017	2017	NUM
ejpam-5605	397	7	.	.	PUNCT
ejpam-5605	398	1	[	[	X
ejpam-5605	398	2	12	12	NUM
ejpam-5605	398	3	]	]	X
ejpam-5605	398	4	j	j	PROPN
ejpam-5605	398	5	r	r	NOUN
ejpam-5605	398	6	graef	graef	NOUN
ejpam-5605	398	7	,	,	PUNCT
ejpam-5605	398	8	j	j	PROPN
ejpam-5605	398	9	henderson	henderson	PROPN
ejpam-5605	398	10	,	,	PUNCT
ejpam-5605	398	11	and	and	CCONJ
ejpam-5605	398	12	a	a	DET
ejpam-5605	398	13	ouahab	ouahab	NOUN
ejpam-5605	398	14	.	.	PUNCT
ejpam-5605	399	1	topological	topological	ADJ
ejpam-5605	399	2	methods	method	NOUN
ejpam-5605	399	3	for	for	ADP
ejpam-5605	399	4	differential	differential	ADJ
ejpam-5605	399	5	equations	equation	NOUN
ejpam-5605	399	6	and	and	CCONJ
ejpam-5605	399	7	inclusions	inclusion	NOUN
ejpam-5605	399	8	.	.	PUNCT
ejpam-5605	400	1	crc	crc	NOUN
ejpam-5605	400	2	press	press	PROPN
ejpam-5605	400	3	,	,	PUNCT
ejpam-5605	400	4	boca	boca	PROPN
ejpam-5605	400	5	raton	raton	PROPN
ejpam-5605	400	6	,	,	PUNCT
ejpam-5605	400	7	fl	fl	PROPN
ejpam-5605	400	8	,	,	PUNCT
ejpam-5605	400	9	2018	2018	NUM
ejpam-5605	400	10	.	.	PUNCT
ejpam-5605	401	1	[	[	X
ejpam-5605	401	2	13	13	NUM
ejpam-5605	401	3	]	]	SYM
ejpam-5605	401	4	m	m	VERB
ejpam-5605	401	5	abu	abu	PROPN
ejpam-5605	401	6	hammad	hammad	PROPN
ejpam-5605	401	7	,	,	PUNCT
ejpam-5605	401	8	o	o	NOUN
ejpam-5605	401	9	zentar	zentar	NOUN
ejpam-5605	401	10	,	,	PUNCT
ejpam-5605	401	11	s	s	NOUN
ejpam-5605	401	12	alshorm	alshorm	NOUN
ejpam-5605	401	13	,	,	PUNCT
ejpam-5605	401	14	m	m	VERB
ejpam-5605	401	15	ziane	ziane	NOUN
ejpam-5605	401	16	,	,	PUNCT
ejpam-5605	401	17	and	and	CCONJ
ejpam-5605	401	18	i	i	PROPN
ejpam-5605	401	19	zitouni	zitouni	PROPN
ejpam-5605	401	20	.	.	PUNCT
ejpam-5605	402	1	theoretical	theoretical	ADJ
ejpam-5605	402	2	analysis	analysis	NOUN
ejpam-5605	402	3	of	of	ADP
ejpam-5605	402	4	a	a	DET
ejpam-5605	402	5	class	class	NOUN
ejpam-5605	402	6	of	of	ADP
ejpam-5605	402	7	φ	φ	PROPN
ejpam-5605	402	8	-	-	PUNCT
ejpam-5605	402	9	caputo	caputo	PROPN
ejpam-5605	402	10	fractional	fractional	ADJ
ejpam-5605	402	11	differential	differential	ADJ
ejpam-5605	402	12	equations	equation	NOUN
ejpam-5605	402	13	in	in	ADP
ejpam-5605	402	14	banach	banach	NOUN
ejpam-5605	402	15	space	space	NOUN
ejpam-5605	402	16	.	.	PUNCT
ejpam-5605	403	1	aims	aim	VERB
ejpam-5605	403	2	mathematics	mathematics	PROPN
ejpam-5605	403	3	,	,	PUNCT
ejpam-5605	403	4	9(3):6411–6423	9(3):6411–6423	NUM
ejpam-5605	403	5	,	,	PUNCT
ejpam-5605	403	6	2024	2024	NUM
ejpam-5605	403	7	.	.	PUNCT
ejpam-5605	404	1	[	[	X
ejpam-5605	404	2	14	14	NUM
ejpam-5605	404	3	]	]	X
ejpam-5605	404	4	c	c	NOUN
ejpam-5605	404	5	ionescu	ionescu	PROPN
ejpam-5605	404	6	,	,	PUNCT
ejpam-5605	404	7	a	a	DET
ejpam-5605	404	8	lopes	lope	NOUN
ejpam-5605	404	9	,	,	PUNCT
ejpam-5605	404	10	d	d	ADP
ejpam-5605	404	11	copot	copot	NOUN
ejpam-5605	404	12	,	,	PUNCT
ejpam-5605	404	13	j	j	PROPN
ejpam-5605	404	14	a	a	DET
ejpam-5605	404	15	t	t	X
ejpam-5605	404	16	machado	machado	PROPN
ejpam-5605	404	17	,	,	PUNCT
ejpam-5605	404	18	and	and	CCONJ
ejpam-5605	404	19	j	j	PROPN
ejpam-5605	404	20	h	h	PROPN
ejpam-5605	404	21	t	t	PROPN
ejpam-5605	404	22	bates	bate	NOUN
ejpam-5605	404	23	.	.	PUNCT
ejpam-5605	405	1	the	the	DET
ejpam-5605	405	2	role	role	NOUN
ejpam-5605	405	3	of	of	ADP
ejpam-5605	405	4	fractional	fractional	ADJ
ejpam-5605	405	5	calculus	calculus	NOUN
ejpam-5605	405	6	in	in	ADP
ejpam-5605	405	7	modeling	model	VERB
ejpam-5605	405	8	biological	biological	ADJ
ejpam-5605	405	9	phenomena	phenomenon	NOUN
ejpam-5605	405	10	:	:	PUNCT
ejpam-5605	405	11	a	a	DET
ejpam-5605	405	12	review	review	NOUN
ejpam-5605	405	13	.	.	PUNCT
ejpam-5605	406	1	commun	commun	PROPN
ejpam-5605	406	2	.	.	PUNCT
ejpam-5605	407	1	nonlinear	nonlinear	PROPN
ejpam-5605	407	2	sci	sci	PROPN
ejpam-5605	407	3	.	.	PUNCT
ejpam-5605	407	4	numer	numer	PROPN
ejpam-5605	407	5	.	.	PUNCT
ejpam-5605	408	1	simul	simul	PROPN
ejpam-5605	408	2	.	.	PROPN
ejpam-5605	408	3	,	,	PUNCT
ejpam-5605	409	1	51:141–159	51:141–159	NUM
ejpam-5605	409	2	,	,	PUNCT
ejpam-5605	409	3	2017	2017	NUM
ejpam-5605	409	4	.	.	PUNCT
ejpam-5605	410	1	[	[	X
ejpam-5605	410	2	15	15	NUM
ejpam-5605	410	3	]	]	X
ejpam-5605	410	4	m	m	VERB
ejpam-5605	410	5	kamenskii	kamenskii	ADJ
ejpam-5605	410	6	,	,	PUNCT
ejpam-5605	410	7	v	v	ADP
ejpam-5605	410	8	obukhovskii	obukhovskii	NOUN
ejpam-5605	410	9	,	,	PUNCT
ejpam-5605	410	10	and	and	CCONJ
ejpam-5605	410	11	p	p	PROPN
ejpam-5605	410	12	zecca	zecca	NOUN
ejpam-5605	410	13	.	.	PUNCT
ejpam-5605	411	1	condensing	condense	VERB
ejpam-5605	411	2	multivalued	multivalue	VERB
ejpam-5605	411	3	maps	map	NOUN
ejpam-5605	411	4	and	and	CCONJ
ejpam-5605	411	5	semilinear	semilinear	NOUN
ejpam-5605	411	6	differential	differential	ADJ
ejpam-5605	411	7	inclusions	inclusion	NOUN
ejpam-5605	411	8	in	in	ADP
ejpam-5605	411	9	banach	banach	NOUN
ejpam-5605	411	10	spaces	space	NOUN
ejpam-5605	411	11	.	.	PUNCT
ejpam-5605	412	1	de	de	ADP
ejpam-5605	412	2	gruyter	gruyter	NOUN
ejpam-5605	412	3	,	,	PUNCT
ejpam-5605	412	4	berlin	berlin	PROPN
ejpam-5605	412	5	,	,	PUNCT
ejpam-5605	412	6	2001	2001	NUM
ejpam-5605	412	7	.	.	PUNCT
ejpam-5605	413	1	[	[	X
ejpam-5605	413	2	16	16	NUM
ejpam-5605	413	3	]	]	PUNCT
ejpam-5605	413	4	a	a	DET
ejpam-5605	413	5	a	a	DET
ejpam-5605	413	6	kilbas	kilbas	NOUN
ejpam-5605	413	7	,	,	PUNCT
ejpam-5605	413	8	h	h	PROPN
ejpam-5605	413	9	m	m	PROPN
ejpam-5605	413	10	srivastava	srivastava	PROPN
ejpam-5605	413	11	,	,	PUNCT
ejpam-5605	413	12	and	and	CCONJ
ejpam-5605	413	13	j	j	PROPN
ejpam-5605	413	14	j	j	PROPN
ejpam-5605	413	15	trujillo	trujillo	PROPN
ejpam-5605	413	16	.	.	PUNCT
ejpam-5605	413	17	theory	theory	NOUN
ejpam-5605	413	18	and	and	CCONJ
ejpam-5605	413	19	applications	application	NOUN
ejpam-5605	413	20	of	of	ADP
ejpam-5605	413	21	fractional	fractional	ADJ
ejpam-5605	413	22	differential	differential	ADJ
ejpam-5605	413	23	equations	equation	NOUN
ejpam-5605	413	24	.	.	PUNCT
ejpam-5605	414	1	north	north	NOUN
ejpam-5605	414	2	-	-	PUNCT
ejpam-5605	414	3	holland	holland	PROPN
ejpam-5605	414	4	mathematics	mathematics	PROPN
ejpam-5605	414	5	studies	study	NOUN
ejpam-5605	414	6	,	,	PUNCT
ejpam-5605	414	7	elsevier	elsevier	NOUN
ejpam-5605	414	8	,	,	PUNCT
ejpam-5605	414	9	amsterdam	amsterdam	PROPN
ejpam-5605	414	10	,	,	PUNCT
ejpam-5605	414	11	netherlands	netherlands	PROPN
ejpam-5605	414	12	,	,	PUNCT
ejpam-5605	414	13	2006	2006	NUM
ejpam-5605	414	14	.	.	PUNCT
ejpam-5605	415	1	[	[	X
ejpam-5605	415	2	17	17	NUM
ejpam-5605	415	3	]	]	SYM
ejpam-5605	415	4	v	v	NOUN
ejpam-5605	415	5	kobelev	kobelev	NOUN
ejpam-5605	415	6	and	and	CCONJ
ejpam-5605	415	7	e	e	PROPN
ejpam-5605	415	8	romanov	romanov	PROPN
ejpam-5605	415	9	.	.	PUNCT
ejpam-5605	415	10	fractional	fractional	ADJ
ejpam-5605	415	11	langevin	langevin	PROPN
ejpam-5605	415	12	equation	equation	NOUN
ejpam-5605	415	13	to	to	PART
ejpam-5605	415	14	describe	describe	VERB
ejpam-5605	415	15	anomalous	anomalous	ADJ
ejpam-5605	415	16	diffusion	diffusion	NOUN
ejpam-5605	415	17	.	.	PUNCT
ejpam-5605	416	1	prog	prog	PROPN
ejpam-5605	416	2	.	.	PUNCT
ejpam-5605	417	1	theor	theor	PROPN
ejpam-5605	417	2	.	.	PUNCT
ejpam-5605	418	1	phys	phy	NOUN
ejpam-5605	418	2	.	.	PUNCT
ejpam-5605	419	1	suppl	suppl	PROPN
ejpam-5605	419	2	.	.	PROPN
ejpam-5605	419	3	,	,	PUNCT
ejpam-5605	419	4	139:470–476	139:470–476	NUM
ejpam-5605	419	5	,	,	PUNCT
ejpam-5605	419	6	2000	2000	NUM
ejpam-5605	419	7	.	.	PUNCT
ejpam-5605	420	1	[	[	X
ejpam-5605	420	2	18	18	NUM
ejpam-5605	420	3	]	]	X
ejpam-5605	420	4	p	p	NOUN
ejpam-5605	420	5	langevin	langevin	NOUN
ejpam-5605	420	6	.	.	PUNCT
ejpam-5605	421	1	sur	sur	PROPN
ejpam-5605	421	2	la	la	PROPN
ejpam-5605	421	3	théorie	théorie	PROPN
ejpam-5605	421	4	du	du	PROPN
ejpam-5605	421	5	mouvement	mouvement	PROPN
ejpam-5605	421	6	brownien	brownien	NOUN
ejpam-5605	421	7	.	.	PUNCT
ejpam-5605	422	1	c.	c.	PROPN
ejpam-5605	422	2	r.	r.	PROPN
ejpam-5605	422	3	,	,	PUNCT
ejpam-5605	422	4	146:530–533	146:530–533	NUM
ejpam-5605	422	5	,	,	PUNCT
ejpam-5605	422	6	1908	1908	NUM
ejpam-5605	422	7	.	.	PUNCT
ejpam-5605	423	1	[	[	X
ejpam-5605	423	2	19	19	NUM
ejpam-5605	423	3	]	]	X
ejpam-5605	423	4	k	k	PROPN
ejpam-5605	423	5	b	b	PROPN
ejpam-5605	423	6	oldham	oldham	PROPN
ejpam-5605	423	7	.	.	PUNCT
ejpam-5605	424	1	fractional	fractional	ADJ
ejpam-5605	424	2	differential	differential	ADJ
ejpam-5605	424	3	equations	equation	NOUN
ejpam-5605	424	4	in	in	ADP
ejpam-5605	424	5	electrochemistry	electrochemistry	NOUN
ejpam-5605	424	6	.	.	PUNCT
ejpam-5605	425	1	adv	adv	PROPN
ejpam-5605	425	2	.	.	PUNCT
ejpam-5605	426	1	eng	eng	PROPN
ejpam-5605	426	2	.	.	PUNCT
ejpam-5605	427	1	softw	softw	PROPN
ejpam-5605	427	2	.	.	PUNCT
ejpam-5605	427	3	,	,	PUNCT
ejpam-5605	427	4	41(1):9–12	41(1):9–12	NOUN
ejpam-5605	427	5	,	,	PUNCT
ejpam-5605	427	6	2010	2010	NUM
ejpam-5605	427	7	.	.	PUNCT
ejpam-5605	428	1	[	[	X
ejpam-5605	428	2	20	20	NUM
ejpam-5605	428	3	]	]	X
ejpam-5605	428	4	r	r	NOUN
ejpam-5605	428	5	ozarslan	ozarslan	NOUN
ejpam-5605	428	6	,	,	PUNCT
ejpam-5605	428	7	e	e	X
ejpam-5605	428	8	bas	bas	X
ejpam-5605	428	9	,	,	PUNCT
ejpam-5605	428	10	d	d	NOUN
ejpam-5605	428	11	baleanu	baleanu	NOUN
ejpam-5605	428	12	,	,	PUNCT
ejpam-5605	428	13	and	and	CCONJ
ejpam-5605	428	14	b	b	NOUN
ejpam-5605	428	15	acay	acay	NOUN
ejpam-5605	428	16	.	.	PUNCT
ejpam-5605	429	1	fractional	fractional	ADJ
ejpam-5605	429	2	physical	physical	ADJ
ejpam-5605	429	3	problems	problem	NOUN
ejpam-5605	429	4	including	include	VERB
ejpam-5605	429	5	wind	wind	NOUN
ejpam-5605	429	6	-	-	PUNCT
ejpam-5605	429	7	influenced	influence	VERB
ejpam-5605	429	8	projectile	projectile	NOUN
ejpam-5605	429	9	motion	motion	NOUN
ejpam-5605	429	10	with	with	ADP
ejpam-5605	429	11	mittag	mittag	ADJ
ejpam-5605	429	12	-	-	PUNCT
ejpam-5605	429	13	leffler	leffler	NOUN
ejpam-5605	429	14	kernel	kernel	NOUN
ejpam-5605	429	15	.	.	PUNCT
ejpam-5605	430	1	aims	aim	VERB
ejpam-5605	430	2	mathematics	mathematic	NOUN
ejpam-5605	430	3	,	,	PUNCT
ejpam-5605	430	4	5(1):467–481	5(1):467–481	NUM
ejpam-5605	430	5	,	,	PUNCT
ejpam-5605	430	6	2020	2020	NUM
ejpam-5605	430	7	.	.	PUNCT
ejpam-5605	431	1	[	[	X
ejpam-5605	431	2	21	21	NUM
ejpam-5605	431	3	]	]	X
ejpam-5605	431	4	j	j	PROPN
ejpam-5605	431	5	c	c	PROPN
ejpam-5605	431	6	prajapati	prajapati	PROPN
ejpam-5605	431	7	,	,	PUNCT
ejpam-5605	431	8	a	a	DET
ejpam-5605	431	9	d	d	X
ejpam-5605	431	10	patel	patel	NOUN
ejpam-5605	431	11	,	,	PUNCT
ejpam-5605	431	12	k	k	PROPN
ejpam-5605	431	13	n	n	NUM
ejpam-5605	431	14	pathak	pathak	PROPN
ejpam-5605	431	15	,	,	PUNCT
ejpam-5605	431	16	and	and	CCONJ
ejpam-5605	431	17	a	a	DET
ejpam-5605	431	18	k	k	PROPN
ejpam-5605	431	19	shukla	shukla	NOUN
ejpam-5605	431	20	.	.	PUNCT
ejpam-5605	432	1	fractional	fractional	ADJ
ejpam-5605	432	2	calculus	calculus	NOUN
ejpam-5605	432	3	approach	approach	NOUN
ejpam-5605	432	4	in	in	ADP
ejpam-5605	432	5	the	the	DET
ejpam-5605	432	6	study	study	NOUN
ejpam-5605	432	7	of	of	ADP
ejpam-5605	432	8	instability	instability	NOUN
ejpam-5605	432	9	phenomenon	phenomenon	NOUN
ejpam-5605	432	10	in	in	ADP
ejpam-5605	432	11	fluid	fluid	ADJ
ejpam-5605	432	12	dynamics	dynamic	NOUN
ejpam-5605	432	13	.	.	PUNCT
ejpam-5605	433	1	palest	pale	ADJ
ejpam-5605	433	2	.	.	PUNCT
ejpam-5605	434	1	j.	j.	PROPN
ejpam-5605	434	2	math	math	PROPN
ejpam-5605	434	3	.	.	PROPN
ejpam-5605	434	4	,	,	PUNCT
ejpam-5605	434	5	1(2):95	1(2):95	NUM
ejpam-5605	434	6	–	–	PUNCT
ejpam-5605	434	7	103	103	NUM
ejpam-5605	434	8	,	,	PUNCT
ejpam-5605	434	9	2012	2012	NUM
ejpam-5605	434	10	.	.	PUNCT
ejpam-5605	435	1	[	[	X
ejpam-5605	435	2	22	22	NUM
ejpam-5605	435	3	]	]	PUNCT
ejpam-5605	435	4	z	z	NOUN
ejpam-5605	435	5	u	u	SYM
ejpam-5605	435	6	rehman	rehman	PROPN
ejpam-5605	435	7	,	,	PUNCT
ejpam-5605	435	8	s	s	PART
ejpam-5605	435	9	boulaaras	boulaaras	NOUN
ejpam-5605	435	10	,	,	PUNCT
ejpam-5605	435	11	r	r	PROPN
ejpam-5605	435	12	jan	jan	PROPN
ejpam-5605	435	13	,	,	PUNCT
ejpam-5605	435	14	i	i	PRON
ejpam-5605	435	15	ahmad	ahmad	PROPN
ejpam-5605	435	16	,	,	PUNCT
ejpam-5605	435	17	and	and	CCONJ
ejpam-5605	435	18	s	s	AUX
ejpam-5605	435	19	bahramand	bahramand	NOUN
ejpam-5605	435	20	.	.	PUNCT
ejpam-5605	436	1	computational	computational	ADJ
ejpam-5605	436	2	analysis	analysis	NOUN
ejpam-5605	436	3	of	of	ADP
ejpam-5605	436	4	financial	financial	ADJ
ejpam-5605	436	5	system	system	NOUN
ejpam-5605	436	6	through	through	ADP
ejpam-5605	436	7	non	non	ADJ
ejpam-5605	436	8	-	-	ADJ
ejpam-5605	436	9	integer	integer	ADJ
ejpam-5605	436	10	derivative	derivative	NOUN
ejpam-5605	436	11	.	.	PUNCT
ejpam-5605	437	1	journal	journal	PROPN
ejpam-5605	437	2	of	of	ADP
ejpam-5605	437	3	computational	computational	ADJ
ejpam-5605	437	4	science	science	NOUN
ejpam-5605	437	5	,	,	PUNCT
ejpam-5605	437	6	45:102204	45:102204	NUM
ejpam-5605	437	7	,	,	PUNCT
ejpam-5605	437	8	2024	2024	NUM
ejpam-5605	437	9	.	.	PUNCT
ejpam-5605	438	1	[	[	X
ejpam-5605	438	2	23	23	NUM
ejpam-5605	438	3	]	]	X
ejpam-5605	438	4	i	i	PRON
ejpam-5605	438	5	rus	rus	PROPN
ejpam-5605	438	6	.	.	PUNCT
ejpam-5605	438	7	generalized	generalized	ADJ
ejpam-5605	438	8	contractions	contraction	NOUN
ejpam-5605	438	9	and	and	CCONJ
ejpam-5605	438	10	applications	application	NOUN
ejpam-5605	438	11	.	.	PUNCT
ejpam-5605	439	1	cluj	cluj	PROPN
ejpam-5605	439	2	university	university	PROPN
ejpam-5605	439	3	press	press	NOUN
ejpam-5605	439	4	,	,	PUNCT
ejpam-5605	439	5	cluj	cluj	PROPN
ejpam-5605	439	6	-	-	PUNCT
ejpam-5605	439	7	napoca	napoca	NOUN
ejpam-5605	439	8	,	,	PUNCT
ejpam-5605	439	9	m.	m.	NOUN
ejpam-5605	439	10	ziane	ziane	PROPN
ejpam-5605	439	11	et	et	PROPN
ejpam-5605	439	12	al	al	PROPN
ejpam-5605	439	13	.	.	PUNCT
ejpam-5605	439	14	/	/	SYM
ejpam-5605	439	15	eur	eur	PROPN
ejpam-5605	439	16	.	.	PUNCT
ejpam-5605	440	1	j.	j.	PROPN
ejpam-5605	440	2	pure	pure	PROPN
ejpam-5605	440	3	appl	appl	PROPN
ejpam-5605	440	4	.	.	PROPN
ejpam-5605	440	5	math	math	PROPN
ejpam-5605	440	6	,	,	PUNCT
ejpam-5605	440	7	18	18	NUM
ejpam-5605	440	8	(	(	PUNCT
ejpam-5605	440	9	1	1	NUM
ejpam-5605	440	10	)	)	PUNCT
ejpam-5605	440	11	(	(	PUNCT
ejpam-5605	440	12	2025	2025	NUM
ejpam-5605	440	13	)	)	PUNCT
ejpam-5605	440	14	,	,	PUNCT
ejpam-5605	440	15	5605	5605	NUM
ejpam-5605	440	16	21	21	NUM
ejpam-5605	440	17	of	of	ADP
ejpam-5605	440	18	21	21	NUM
ejpam-5605	440	19	2001	2001	NUM
ejpam-5605	440	20	.	.	PUNCT
ejpam-5605	441	1	[	[	X
ejpam-5605	441	2	24	24	NUM
ejpam-5605	441	3	]	]	SYM
ejpam-5605	441	4	b	b	X
ejpam-5605	441	5	shiria	shiria	NOUN
ejpam-5605	441	6	and	and	CCONJ
ejpam-5605	441	7	d	d	NOUN
ejpam-5605	441	8	baleanu	baleanu	NOUN
ejpam-5605	441	9	.	.	PUNCT
ejpam-5605	442	1	numerical	numerical	ADJ
ejpam-5605	442	2	solution	solution	NOUN
ejpam-5605	442	3	of	of	ADP
ejpam-5605	442	4	some	some	DET
ejpam-5605	442	5	fractional	fractional	ADJ
ejpam-5605	442	6	dynamical	dynamical	ADJ
ejpam-5605	442	7	systems	system	NOUN
ejpam-5605	442	8	in	in	ADP
ejpam-5605	442	9	medicine	medicine	NOUN
ejpam-5605	442	10	involving	involve	VERB
ejpam-5605	442	11	non	non	ADJ
ejpam-5605	442	12	-	-	ADJ
ejpam-5605	442	13	singular	singular	ADJ
ejpam-5605	442	14	kernel	kernel	NOUN
ejpam-5605	442	15	with	with	ADP
ejpam-5605	442	16	vector	vector	NOUN
ejpam-5605	442	17	order	order	NOUN
ejpam-5605	442	18	.	.	PUNCT
ejpam-5605	443	1	results	result	NOUN
ejpam-5605	443	2	in	in	ADP
ejpam-5605	443	3	nonlinear	nonlinear	ADJ
ejpam-5605	443	4	analysis	analysis	NOUN
ejpam-5605	443	5	,	,	PUNCT
ejpam-5605	443	6	2(4):160–168	2(4):160–168	NOUN
ejpam-5605	443	7	,	,	PUNCT
ejpam-5605	443	8	2019	2019	NUM
ejpam-5605	443	9	.	.	PUNCT
ejpam-5605	444	1	[	[	X
ejpam-5605	444	2	25	25	NUM
ejpam-5605	444	3	]	]	PUNCT
ejpam-5605	444	4	m	m	NOUN
ejpam-5605	444	5	l	l	NOUN
ejpam-5605	444	6	sinacer	sinacer	NOUN
ejpam-5605	444	7	,	,	PUNCT
ejpam-5605	444	8	j	j	PROPN
ejpam-5605	444	9	j	j	PROPN
ejpam-5605	444	10	nieto	nieto	PROPN
ejpam-5605	444	11	,	,	PUNCT
ejpam-5605	444	12	and	and	CCONJ
ejpam-5605	444	13	a	a	DET
ejpam-5605	444	14	ouahab	ouahab	NOUN
ejpam-5605	444	15	.	.	PUNCT
ejpam-5605	445	1	random	random	ADJ
ejpam-5605	445	2	fixed	fix	VERB
ejpam-5605	445	3	point	point	NOUN
ejpam-5605	445	4	theorem	theorem	VERB
ejpam-5605	445	5	in	in	ADP
ejpam-5605	445	6	generalized	generalized	ADJ
ejpam-5605	445	7	banach	banach	NOUN
ejpam-5605	445	8	space	space	NOUN
ejpam-5605	445	9	and	and	CCONJ
ejpam-5605	445	10	applications	application	NOUN
ejpam-5605	445	11	.	.	PUNCT
ejpam-5605	446	1	random	random	ADJ
ejpam-5605	446	2	oper	oper	NOUN
ejpam-5605	446	3	.	.	PROPN
ejpam-5605	446	4	stoch	stoch	PROPN
ejpam-5605	446	5	.	.	PUNCT
ejpam-5605	447	1	equ	equ	PROPN
ejpam-5605	447	2	.	.	PROPN
ejpam-5605	447	3	,	,	PUNCT
ejpam-5605	447	4	24(2):93–112	24(2):93–112	NUM
ejpam-5605	447	5	,	,	PUNCT
ejpam-5605	447	6	2016	2016	NUM
ejpam-5605	447	7	.	.	PUNCT
ejpam-5605	448	1	[	[	X
ejpam-5605	448	2	26	26	NUM
ejpam-5605	448	3	]	]	X
ejpam-5605	448	4	j	j	PROPN
ejpam-5605	448	5	singh	singh	PROPN
ejpam-5605	448	6	,	,	PUNCT
ejpam-5605	448	7	d	d	PROPN
ejpam-5605	448	8	kumar	kumar	PROPN
ejpam-5605	448	9	,	,	PUNCT
ejpam-5605	448	10	and	and	CCONJ
ejpam-5605	448	11	d	d	ADP
ejpam-5605	448	12	baleanu	baleanu	NOUN
ejpam-5605	448	13	.	.	PUNCT
ejpam-5605	449	1	on	on	ADP
ejpam-5605	449	2	the	the	DET
ejpam-5605	449	3	analysis	analysis	NOUN
ejpam-5605	449	4	of	of	ADP
ejpam-5605	449	5	chemical	chemical	ADJ
ejpam-5605	449	6	kinetics	kinetic	NOUN
ejpam-5605	449	7	system	system	NOUN
ejpam-5605	449	8	pertaining	pertain	VERB
ejpam-5605	449	9	to	to	ADP
ejpam-5605	449	10	a	a	DET
ejpam-5605	449	11	fractional	fractional	ADJ
ejpam-5605	449	12	derivative	derivative	NOUN
ejpam-5605	449	13	with	with	ADP
ejpam-5605	449	14	mittag	mittag	ADJ
ejpam-5605	449	15	-	-	PUNCT
ejpam-5605	449	16	leffler	leffler	NOUN
ejpam-5605	449	17	type	type	NOUN
ejpam-5605	449	18	kernel	kernel	NOUN
ejpam-5605	449	19	.	.	PUNCT
ejpam-5605	450	1	chaos	chaos	NOUN
ejpam-5605	450	2	.	.	PUNCT
ejpam-5605	450	3	,	,	PUNCT
ejpam-5605	450	4	27:103113	27:103113	NUM
ejpam-5605	450	5	,	,	PUNCT
ejpam-5605	450	6	2017	2017	NUM
ejpam-5605	450	7	.	.	PUNCT
ejpam-5605	451	1	[	[	X
ejpam-5605	451	2	27	27	NUM
ejpam-5605	451	3	]	]	X
ejpam-5605	451	4	j	j	PROPN
ejpam-5605	451	5	sousa	sousa	PROPN
ejpam-5605	451	6	and	and	CCONJ
ejpam-5605	451	7	e	e	PROPN
ejpam-5605	451	8	oliveira	oliveira	PROPN
ejpam-5605	451	9	.	.	PUNCT
ejpam-5605	452	1	existence	existence	NOUN
ejpam-5605	452	2	,	,	PUNCT
ejpam-5605	452	3	uniqueness	uniqueness	NOUN
ejpam-5605	452	4	,	,	PUNCT
ejpam-5605	452	5	estimation	estimation	NOUN
ejpam-5605	452	6	and	and	CCONJ
ejpam-5605	452	7	continuous	continuous	ADJ
ejpam-5605	452	8	dependence	dependence	NOUN
ejpam-5605	452	9	of	of	ADP
ejpam-5605	452	10	the	the	DET
ejpam-5605	452	11	solutions	solution	NOUN
ejpam-5605	452	12	of	of	ADP
ejpam-5605	452	13	a	a	DET
ejpam-5605	452	14	nonlinear	nonlinear	ADJ
ejpam-5605	452	15	integral	integral	ADJ
ejpam-5605	452	16	and	and	CCONJ
ejpam-5605	452	17	an	an	DET
ejpam-5605	452	18	integrodifferential	integrodifferential	ADJ
ejpam-5605	452	19	equations	equation	NOUN
ejpam-5605	452	20	of	of	ADP
ejpam-5605	452	21	fractional	fractional	ADJ
ejpam-5605	452	22	order	order	NOUN
ejpam-5605	452	23	.	.	PUNCT
ejpam-5605	453	1	arxiv	arxiv	PROPN
ejpam-5605	453	2	preprint	preprint	PROPN
ejpam-5605	453	3	,	,	PUNCT
ejpam-5605	453	4	1806.01441	1806.01441	NUM
ejpam-5605	453	5	,	,	PUNCT
ejpam-5605	453	6	2018	2018	NUM
ejpam-5605	453	7	.	.	PUNCT
ejpam-5605	454	1	[	[	X
ejpam-5605	454	2	28	28	NUM
ejpam-5605	454	3	]	]	X
ejpam-5605	454	4	a	a	DET
ejpam-5605	454	5	traore	traore	NOUN
ejpam-5605	454	6	and	and	CCONJ
ejpam-5605	454	7	n	n	PRON
ejpam-5605	454	8	sene	sene	ADJ
ejpam-5605	454	9	.	.	PUNCT
ejpam-5605	455	1	model	model	NOUN
ejpam-5605	455	2	of	of	ADP
ejpam-5605	455	3	economic	economic	ADJ
ejpam-5605	455	4	growth	growth	NOUN
ejpam-5605	455	5	in	in	ADP
ejpam-5605	455	6	the	the	DET
ejpam-5605	455	7	context	context	NOUN
ejpam-5605	455	8	of	of	ADP
ejpam-5605	455	9	fractional	fractional	ADJ
ejpam-5605	455	10	derivative	derivative	NOUN
ejpam-5605	455	11	.	.	PUNCT
ejpam-5605	456	1	alex	alex	PROPN
ejpam-5605	456	2	.	.	PUNCT
ejpam-5605	457	1	eng	eng	PROPN
ejpam-5605	457	2	.	.	PUNCT
ejpam-5605	458	1	j.	j.	PROPN
ejpam-5605	458	2	,	,	PUNCT
ejpam-5605	458	3	59(6):4843–4850	59(6):4843–4850	NUM
ejpam-5605	458	4	,	,	PUNCT
ejpam-5605	458	5	2024	2024	NUM
ejpam-5605	458	6	.	.	PUNCT
ejpam-5605	459	1	[	[	X
ejpam-5605	459	2	29	29	NUM
ejpam-5605	459	3	]	]	SYM
ejpam-5605	459	4	v	v	X
ejpam-5605	459	5	v	v	ADP
ejpam-5605	459	6	uchaikin	uchaikin	X
ejpam-5605	459	7	.	.	PUNCT
ejpam-5605	460	1	fractional	fractional	ADJ
ejpam-5605	460	2	derivatives	derivative	NOUN
ejpam-5605	460	3	for	for	ADP
ejpam-5605	460	4	physicists	physicist	NOUN
ejpam-5605	460	5	and	and	CCONJ
ejpam-5605	460	6	engineers	engineer	NOUN
ejpam-5605	460	7	.	.	PUNCT
ejpam-5605	461	1	springer	springer	PROPN
ejpam-5605	461	2	,	,	PUNCT
ejpam-5605	461	3	berlin	berlin	PROPN
ejpam-5605	461	4	,	,	PUNCT
ejpam-5605	461	5	2013	2013	NUM
ejpam-5605	461	6	.	.	PUNCT
ejpam-5605	462	1	[	[	X
ejpam-5605	462	2	30	30	NUM
ejpam-5605	462	3	]	]	X
ejpam-5605	462	4	j	j	PROPN
ejpam-5605	462	5	vanterler	vanterler	NOUN
ejpam-5605	462	6	and	and	CCONJ
ejpam-5605	462	7	c	c	PROPN
ejpam-5605	462	8	sousa	sousa	PROPN
ejpam-5605	462	9	.	.	PUNCT
ejpam-5605	463	1	existence	existence	NOUN
ejpam-5605	463	2	results	result	NOUN
ejpam-5605	463	3	and	and	CCONJ
ejpam-5605	463	4	continuity	continuity	NOUN
ejpam-5605	463	5	dependence	dependence	NOUN
ejpam-5605	463	6	of	of	ADP
ejpam-5605	463	7	solutions	solution	NOUN
ejpam-5605	463	8	for	for	ADP
ejpam-5605	463	9	fractional	fractional	ADJ
ejpam-5605	463	10	equations	equation	NOUN
ejpam-5605	463	11	.	.	PUNCT
ejpam-5605	463	12	differ	differ	VERB
ejpam-5605	463	13	.	.	PUNCT
ejpam-5605	464	1	equ	equ	PROPN
ejpam-5605	464	2	.	.	PUNCT
ejpam-5605	464	3	appl	appl	PROPN
ejpam-5605	464	4	.	.	PROPN
ejpam-5605	464	5	,	,	PUNCT
ejpam-5605	464	6	12:377–396	12:377–396	NUM
ejpam-5605	464	7	,	,	PUNCT
ejpam-5605	464	8	2020	2020	NUM
ejpam-5605	464	9	.	.	PUNCT
ejpam-5605	465	1	[	[	X
ejpam-5605	465	2	31	31	NUM
ejpam-5605	465	3	]	]	PUNCT
ejpam-5605	465	4	x	x	PROPN
ejpam-5605	465	5	yang	yang	PROPN
ejpam-5605	465	6	,	,	PUNCT
ejpam-5605	465	7	j	j	PROPN
ejpam-5605	465	8	zeng	zeng	PROPN
ejpam-5605	465	9	,	,	PUNCT
ejpam-5605	465	10	c	c	PROPN
ejpam-5605	465	11	xu	xu	PROPN
ejpam-5605	465	12	,	,	PUNCT
ejpam-5605	465	13	l	l	PROPN
ejpam-5605	465	14	peng	peng	PROPN
ejpam-5605	465	15	,	,	PUNCT
ejpam-5605	465	16	and	and	CCONJ
ejpam-5605	465	17	j	j	PROPN
ejpam-5605	465	18	alsultan	alsultan	PROPN
ejpam-5605	465	19	.	.	PUNCT
ejpam-5605	466	1	modeling	modeling	NOUN
ejpam-5605	466	2	of	of	ADP
ejpam-5605	466	3	fractional	fractional	ADJ
ejpam-5605	466	4	differential	differential	ADJ
ejpam-5605	466	5	equation	equation	NOUN
ejpam-5605	466	6	in	in	ADP
ejpam-5605	466	7	cloud	cloud	NOUN
ejpam-5605	466	8	computing	compute	VERB
ejpam-5605	466	9	image	image	NOUN
ejpam-5605	466	10	fusion	fusion	NOUN
ejpam-5605	466	11	algorithm	algorithm	NOUN
ejpam-5605	466	12	.	.	PUNCT
ejpam-5605	467	1	appl	appl	PROPN
ejpam-5605	467	2	.	.	PROPN
ejpam-5605	467	3	math	math	PROPN
ejpam-5605	467	4	.	.	PUNCT
ejpam-5605	468	1	nonlinear	nonlinear	PROPN
ejpam-5605	468	2	sci	sci	PROPN
ejpam-5605	468	3	.	.	PROPN
ejpam-5605	468	4	,	,	PUNCT
ejpam-5605	468	5	8(1):1125–1134	8(1):1125–1134	PROPN
ejpam-5605	468	6	,	,	PUNCT
ejpam-5605	468	7	2023	2023	NUM
ejpam-5605	468	8	.	.	PUNCT
ejpam-5605	469	1	[	[	X
ejpam-5605	469	2	32	32	NUM
ejpam-5605	469	3	]	]	PUNCT
ejpam-5605	469	4	o	o	NOUN
ejpam-5605	469	5	zentar	zentar	NOUN
ejpam-5605	469	6	,	,	PUNCT
ejpam-5605	469	7	m	m	NOUN
ejpam-5605	469	8	ziane	ziane	NOUN
ejpam-5605	469	9	,	,	PUNCT
ejpam-5605	469	10	and	and	CCONJ
ejpam-5605	469	11	m	m	PROPN
ejpam-5605	469	12	al	al	PROPN
ejpam-5605	469	13	horani	horani	PROPN
ejpam-5605	469	14	.	.	PUNCT
ejpam-5605	470	1	theoretical	theoretical	ADJ
ejpam-5605	470	2	study	study	NOUN
ejpam-5605	470	3	of	of	ADP
ejpam-5605	470	4	a	a	DET
ejpam-5605	470	5	φ	φ	NUM
ejpam-5605	470	6	-	-	PUNCT
ejpam-5605	470	7	hilfer	hilfer	NOUN
ejpam-5605	470	8	fractional	fractional	ADJ
ejpam-5605	470	9	differential	differential	NOUN
ejpam-5605	470	10	system	system	NOUN
ejpam-5605	470	11	in	in	ADP
ejpam-5605	470	12	banach	banach	NOUN
ejpam-5605	470	13	spaces	space	NOUN
ejpam-5605	470	14	.	.	PUNCT
ejpam-5605	471	1	can	can	AUX
ejpam-5605	471	2	.	.	PUNCT
ejpam-5605	472	1	math	math	NOUN
ejpam-5605	472	2	.	.	PUNCT
ejpam-5605	473	1	bull	bull	PROPN
ejpam-5605	473	2	.	.	PUNCT
ejpam-5605	474	1	,	,	PUNCT
ejpam-5605	474	2	67(3):742–759	67(3):742–759	PROPN
ejpam-5605	474	3	,	,	PUNCT
ejpam-5605	474	4	2024	2024	NUM
ejpam-5605	474	5	.	.	PUNCT
ejpam-5605	475	1	[	[	X
ejpam-5605	475	2	33	33	NUM
ejpam-5605	475	3	]	]	PUNCT
ejpam-5605	475	4	o	o	NOUN
ejpam-5605	475	5	zentar	zentar	NOUN
ejpam-5605	475	6	,	,	PUNCT
ejpam-5605	475	7	m	m	NOUN
ejpam-5605	475	8	ziane	ziane	NOUN
ejpam-5605	475	9	,	,	PUNCT
ejpam-5605	475	10	m	m	PROPN
ejpam-5605	475	11	al	al	PROPN
ejpam-5605	475	12	horani	horani	PROPN
ejpam-5605	475	13	,	,	PUNCT
ejpam-5605	475	14	and	and	CCONJ
ejpam-5605	475	15	i	i	PROPN
ejpam-5605	475	16	zitouni	zitouni	PROPN
ejpam-5605	475	17	.	.	PUNCT
ejpam-5605	476	1	theoretical	theoretical	ADJ
ejpam-5605	476	2	study	study	NOUN
ejpam-5605	476	3	of	of	ADP
ejpam-5605	476	4	a	a	DET
ejpam-5605	476	5	class	class	NOUN
ejpam-5605	476	6	of	of	ADP
ejpam-5605	476	7	ζcaputo	ζcaputo	ADJ
ejpam-5605	476	8	fractional	fractional	ADJ
ejpam-5605	476	9	differential	differential	ADJ
ejpam-5605	476	10	equations	equation	NOUN
ejpam-5605	476	11	in	in	ADP
ejpam-5605	476	12	a	a	DET
ejpam-5605	476	13	banach	banach	NOUN
ejpam-5605	476	14	space	space	NOUN
ejpam-5605	476	15	.	.	PUNCT
ejpam-5605	477	1	j.	j.	PROPN
ejpam-5605	477	2	appl	appl	PROPN
ejpam-5605	477	3	.	.	PROPN
ejpam-5605	478	1	anal	anal	PROPN
ejpam-5605	478	2	.	.	PUNCT
ejpam-5605	479	1	comput	comput	PROPN
ejpam-5605	479	2	.	.	PUNCT
ejpam-5605	479	3	,	,	PUNCT
ejpam-5605	479	4	14(5):2808–2821	14(5):2808–2821	NUM
ejpam-5605	479	5	,	,	PUNCT
ejpam-5605	479	6	2024	2024	NUM
ejpam-5605	479	7	.	.	PUNCT
ejpam-5605	480	1	[	[	X
ejpam-5605	480	2	34	34	NUM
ejpam-5605	480	3	]	]	X
ejpam-5605	480	4	o	o	NOUN
ejpam-5605	480	5	zentar	zentar	NOUN
ejpam-5605	480	6	,	,	PUNCT
ejpam-5605	480	7	m	m	NOUN
ejpam-5605	480	8	ziane	ziane	NOUN
ejpam-5605	480	9	,	,	PUNCT
ejpam-5605	480	10	and	and	CCONJ
ejpam-5605	480	11	s	s	VERB
ejpam-5605	480	12	khelifa	khelifa	NOUN
ejpam-5605	480	13	.	.	PUNCT
ejpam-5605	480	14	coupled	couple	VERB
ejpam-5605	480	15	fractional	fractional	ADJ
ejpam-5605	480	16	differential	differential	NOUN
ejpam-5605	480	17	systems	system	NOUN
ejpam-5605	480	18	with	with	ADP
ejpam-5605	480	19	random	random	ADJ
ejpam-5605	480	20	effects	effect	NOUN
ejpam-5605	480	21	in	in	ADP
ejpam-5605	480	22	banach	banach	NOUN
ejpam-5605	480	23	spaces	space	NOUN
ejpam-5605	480	24	.	.	PUNCT
ejpam-5605	481	1	random	random	ADJ
ejpam-5605	481	2	oper	oper	NOUN
ejpam-5605	481	3	.	.	PROPN
ejpam-5605	481	4	stoch	stoch	PROPN
ejpam-5605	481	5	.	.	PUNCT
ejpam-5605	482	1	equ	equ	PROPN
ejpam-5605	482	2	.	.	PROPN
ejpam-5605	482	3	,	,	PUNCT
ejpam-5605	482	4	29(4):251–263	29(4):251–263	PROPN
ejpam-5605	482	5	,	,	PUNCT
ejpam-5605	482	6	2021	2021	NUM
ejpam-5605	482	7	.	.	PUNCT