id	sid	tid	token	lemma	pos
ma-44	1	1	2021	2021	NUM
ma-44	1	2	ada	ada	PROPN
ma-44	1	3	academica	academica	PROPN
ma-44	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-44	1	5	.	.	PUNCT
ma-44	2	1	j.	j.	PROPN
ma-44	2	2	math	math	PROPN
ma-44	2	3	.	.	PUNCT
ma-44	3	1	anal	anal	ADJ
ma-44	3	2	.	.	PUNCT
ma-44	4	1	1	1	NUM
ma-44	4	2	(	(	PUNCT
ma-44	4	3	2021	2021	NUM
ma-44	4	4	)	)	PUNCT
ma-44	4	5	164	164	NUM
ma-44	4	6	-	-	SYM
ma-44	4	7	181doi	181doi	NUM
ma-44	4	8	:	:	PUNCT
ma-44	4	9	10.28924	10.28924	NUM
ma-44	4	10	/	/	SYM
ma-44	4	11	ada	ada	NOUN
ma-44	4	12	/	/	SYM
ma-44	4	13	ma.1.164	ma.1.164	NOUN
ma-44	4	14	nonlinear	nonlinear	NOUN
ma-44	4	15	differential	differential	ADJ
ma-44	4	16	problem	problem	NOUN
ma-44	4	17	with	with	ADP
ma-44	4	18	p	p	NOUN
ma-44	4	19	-	-	PUNCT
ma-44	4	20	laplacian	laplacian	NOUN
ma-44	4	21	and	and	CCONJ
ma-44	4	22	via	via	ADP
ma-44	4	23	phi	phi	ADJ
ma-44	4	24	-	-	PUNCT
ma-44	4	25	hilfer	hilfer	NOUN
ma-44	4	26	approach	approach	NOUN
ma-44	4	27	:	:	PUNCT
ma-44	4	28	solvability	solvability	NOUN
ma-44	4	29	and	and	CCONJ
ma-44	4	30	stability	stability	NOUN
ma-44	4	31	analysis	analysis	NOUN
ma-44	4	32	hamid	hamid	PROPN
ma-44	4	33	beddani1,∗	beddani1,∗	PROPN
ma-44	4	34	,	,	PUNCT
ma-44	4	35	moustafa	moustafa	PROPN
ma-44	4	36	beddani2	beddani2	PROPN
ma-44	4	37	,	,	PUNCT
ma-44	4	38	zoubir	zoubir	NOUN
ma-44	4	39	dahmani3	dahmani3	X
ma-44	4	40	1laboratory	1laboratory	NUM
ma-44	4	41	of	of	ADP
ma-44	4	42	complex	complex	ADJ
ma-44	4	43	systems	system	NOUN
ma-44	4	44	of	of	ADP
ma-44	4	45	the	the	DET
ma-44	4	46	higher	high	ADJ
ma-44	4	47	school	school	NOUN
ma-44	4	48	of	of	ADP
ma-44	4	49	electrical	electrical	ADJ
ma-44	4	50	and	and	CCONJ
ma-44	4	51	energy	energy	NOUN
ma-44	4	52	engineering	engineering	NOUN
ma-44	4	53	of	of	ADP
ma-44	4	54	oran	oran	NOUN
ma-44	4	55	,	,	PUNCT
ma-44	4	56	31000	31000	NUM
ma-44	4	57	,	,	PUNCT
ma-44	4	58	algeria	algeria	PROPN
ma-44	4	59	beddanihamid@gmail.com	beddanihamid@gmail.com	X
ma-44	5	1	2department	2department	NUM
ma-44	5	2	of	of	ADP
ma-44	5	3	mathematics	mathematic	NOUN
ma-44	5	4	,	,	PUNCT
ma-44	5	5	university	university	NOUN
ma-44	5	6	of	of	ADP
ma-44	5	7	sidi	sidi	PROPN
ma-44	5	8	bel	bel	PROPN
ma-44	5	9	-	-	PROPN
ma-44	5	10	abbès	abbès	PROPN
ma-44	5	11	22000	22000	NUM
ma-44	5	12	,	,	PUNCT
ma-44	5	13	algeria	algeria	PROPN
ma-44	5	14	beddani2004@yahoo.fr	beddani2004@yahoo.fr	PROPN
ma-44	5	15	3laboratory	3laboratory	NUM
ma-44	5	16	of	of	ADP
ma-44	5	17	pure	pure	ADJ
ma-44	5	18	and	and	CCONJ
ma-44	5	19	applied	applied	ADJ
ma-44	5	20	mathematics	mathematic	NOUN
ma-44	5	21	,	,	PUNCT
ma-44	5	22	abdelhamid	abdelhamid	PROPN
ma-44	5	23	bni	bni	PROPN
ma-44	5	24	badis	badis	PROPN
ma-44	5	25	university	university	PROPN
ma-44	5	26	,	,	PUNCT
ma-44	5	27	27000	27000	NUM
ma-44	5	28	,	,	PUNCT
ma-44	5	29	algeria	algeria	PROPN
ma-44	5	30	zzdahmani@yahoo.fr	zzdahmani@yahoo.fr	PROPN
ma-44	5	31	∗correspondence	∗correspondence	NOUN
ma-44	5	32	:	:	PUNCT
ma-44	5	33	beddanihamid@gmail.com	beddanihamid@gmail.com	X
ma-44	6	1	abstract	abstract	ADJ
ma-44	6	2	.	.	PUNCT
ma-44	7	1	this	this	DET
ma-44	7	2	paper	paper	NOUN
ma-44	7	3	we	we	PRON
ma-44	7	4	consider	consider	VERB
ma-44	7	5	a	a	DET
ma-44	7	6	study	study	NOUN
ma-44	7	7	of	of	ADP
ma-44	7	8	a	a	DET
ma-44	7	9	general	general	ADJ
ma-44	7	10	class	class	NOUN
ma-44	7	11	of	of	ADP
ma-44	7	12	nonlinear	nonlinear	ADJ
ma-44	7	13	singular	singular	PROPN
ma-44	7	14	fractional	fractional	PROPN
ma-44	7	15	des	des	X
ma-44	7	16	withp	withp	PROPN
ma-44	7	17	-	-	PUNCT
ma-44	7	18	laplacian	laplacian	PROPN
ma-44	7	19	for	for	ADP
ma-44	7	20	the	the	DET
ma-44	7	21	existence	existence	NOUN
ma-44	7	22	and	and	CCONJ
ma-44	7	23	uniqueness	uniqueness	NOUN
ma-44	7	24	solution	solution	NOUN
ma-44	7	25	and	and	CCONJ
ma-44	7	26	the	the	DET
ma-44	7	27	hyers	hyer	NOUN
ma-44	7	28	-	-	PUNCT
ma-44	7	29	ulam	ulam	PROPN
ma-44	7	30	(	(	PUNCT
ma-44	7	31	hu	hu	NOUN
ma-44	7	32	)	)	PUNCT
ma-44	7	33	stability	stability	NOUN
ma-44	7	34	.	.	PUNCT
ma-44	8	1	result	result	VERB
ma-44	8	2	via	via	ADP
ma-44	8	3	ϕ−hilfer	ϕ−hilfer	VERB
ma-44	8	4	derivative	derivative	NOUN
ma-44	8	5	is	be	AUX
ma-44	8	6	studied	study	VERB
ma-44	8	7	.	.	PUNCT
ma-44	9	1	then	then	ADV
ma-44	9	2	,	,	PUNCT
ma-44	9	3	an	an	DET
ma-44	9	4	existence	existence	NOUN
ma-44	9	5	of	of	ADP
ma-44	9	6	one	one	NUM
ma-44	9	7	solution	solution	NOUN
ma-44	9	8	is	be	AUX
ma-44	9	9	investigated	investigate	VERB
ma-44	9	10	.	.	PUNCT
ma-44	10	1	some	some	DET
ma-44	10	2	illustrativeexamples	illustrativeexample	NOUN
ma-44	10	3	are	be	AUX
ma-44	10	4	discussed	discuss	VERB
ma-44	10	5	at	at	ADP
ma-44	10	6	the	the	DET
ma-44	10	7	end	end	NOUN
ma-44	10	8	.	.	PUNCT
ma-44	11	1	1	1	X
ma-44	11	2	.	.	X
ma-44	11	3	introduction	introduction	NOUN
ma-44	11	4	recently	recently	ADV
ma-44	11	5	,	,	PUNCT
ma-44	11	6	fractional	fractional	ADJ
ma-44	11	7	differential	differential	ADJ
ma-44	11	8	equations	equation	NOUN
ma-44	11	9	with	with	ADP
ma-44	11	10	boundary	boundary	ADJ
ma-44	11	11	conditions	condition	NOUN
ma-44	11	12	are	be	AUX
ma-44	11	13	being	be	AUX
ma-44	11	14	studied	study	VERB
ma-44	11	15	by	by	ADP
ma-44	11	16	manyinterested	manyintereste	VERB
ma-44	11	17	people	people	NOUN
ma-44	11	18	.	.	PUNCT
ma-44	12	1	this	this	PRON
ma-44	12	2	is	be	AUX
ma-44	12	3	because	because	SCONJ
ma-44	12	4	fractional	fractional	ADJ
ma-44	12	5	differential	differential	ADJ
ma-44	12	6	equations	equation	NOUN
ma-44	12	7	describe	describe	VERB
ma-44	12	8	many	many	ADJ
ma-44	12	9	more	more	ADJ
ma-44	12	10	real	real	ADJ
ma-44	12	11	op	op	NOUN
ma-44	12	12	-	-	PUNCT
ma-44	12	13	erations	eration	NOUN
ma-44	12	14	than	than	ADP
ma-44	12	15	classical	classical	ADJ
ma-44	12	16	differential	differential	ADJ
ma-44	12	17	equations	equation	NOUN
ma-44	12	18	.	.	PUNCT
ma-44	13	1	therefore	therefore	ADV
ma-44	13	2	,	,	PUNCT
ma-44	13	3	partial	partial	ADJ
ma-44	13	4	differential	differential	ADJ
ma-44	13	5	equations	equation	NOUN
ma-44	13	6	appearin	appearin	VERB
ma-44	13	7	many	many	ADJ
ma-44	13	8	engineering	engineering	NOUN
ma-44	13	9	and	and	CCONJ
ma-44	13	10	technological	technological	ADJ
ma-44	13	11	disciplines	discipline	NOUN
ma-44	13	12	that	that	PRON
ma-44	13	13	include	include	VERB
ma-44	13	14	several	several	ADJ
ma-44	13	15	sciences	science	NOUN
ma-44	13	16	;	;	PUNCT
ma-44	13	17	see	see	VERB
ma-44	13	18	for	for	ADP
ma-44	13	19	exam	exam	NOUN
ma-44	13	20	-	-	PUNCT
ma-44	13	21	ple	ple	NOUN
ma-44	13	22	[	[	X
ma-44	13	23	1	1	NUM
ma-44	13	24	,	,	PUNCT
ma-44	13	25	3–6,8	3–6,8	NUM
ma-44	13	26	,	,	PUNCT
ma-44	13	27	17,18,20,22,23,31	17,18,20,22,23,31	NUM
ma-44	13	28	]	]	PUNCT
ma-44	13	29	.	.	PUNCT
ma-44	14	1	currently	currently	ADV
ma-44	14	2	there	there	PRON
ma-44	14	3	are	be	VERB
ma-44	14	4	several	several	ADJ
ma-44	14	5	different	different	ADJ
ma-44	14	6	definitions	definition	NOUN
ma-44	14	7	of	of	ADP
ma-44	14	8	fractional	fractional	ADJ
ma-44	14	9	integrals	integral	NOUN
ma-44	14	10	and	and	CCONJ
ma-44	14	11	derivatives	derivative	NOUN
ma-44	14	12	,	,	PUNCT
ma-44	14	13	from	from	ADP
ma-44	14	14	themost	themost	ADJ
ma-44	14	15	famous	famous	ADJ
ma-44	14	16	of	of	ADP
ma-44	14	17	which	which	PRON
ma-44	14	18	are	be	AUX
ma-44	14	19	the	the	DET
ma-44	14	20	riemann	riemann	PROPN
ma-44	14	21	-	-	PUNCT
ma-44	14	22	liouville	liouville	PROPN
ma-44	14	23	and	and	CCONJ
ma-44	14	24	caputo	caputo	PROPN
ma-44	14	25	fractional	fractional	ADJ
ma-44	14	26	derivatives	derivative	NOUN
ma-44	14	27	to	to	ADP
ma-44	14	28	other	other	ADJ
ma-44	14	29	less	less	ADV
ma-44	14	30	wellknown	wellknown	ADJ
ma-44	14	31	definitions	definition	NOUN
ma-44	14	32	.	.	PUNCT
ma-44	15	1	a	a	DET
ma-44	15	2	generalization	generalization	NOUN
ma-44	15	3	of	of	ADP
ma-44	15	4	the	the	DET
ma-44	15	5	derivatives	derivative	NOUN
ma-44	15	6	of	of	ADP
ma-44	15	7	both	both	DET
ma-44	15	8	riemann	riemann	PROPN
ma-44	15	9	-	-	PUNCT
ma-44	15	10	liouville	liouville	PROPN
ma-44	15	11	and	and	CCONJ
ma-44	15	12	caputo	caputo	PROPN
ma-44	15	13	wasgiven	wasgiven	VERB
ma-44	15	14	by	by	ADP
ma-44	15	15	r.	r.	PROPN
ma-44	15	16	hilfer	hilfer	PROPN
ma-44	15	17	in	in	ADP
ma-44	15	18	[	[	X
ma-44	15	19	11	11	NUM
ma-44	15	20	]	]	PUNCT
ma-44	15	21	,	,	PUNCT
ma-44	15	22	known	know	VERB
ma-44	15	23	as	as	ADP
ma-44	15	24	the	the	DET
ma-44	15	25	fractional	fractional	ADJ
ma-44	15	26	hilfer	hilfer	NOUN
ma-44	15	27	derivative	derivative	NOUN
ma-44	15	28	of	of	ADP
ma-44	15	29	order	order	NOUN
ma-44	15	30	α	α	NOUN
ma-44	15	31	and	and	CCONJ
ma-44	15	32	type	type	VERB
ma-44	15	33	β	β	X
ma-44	15	34	∈	∈	PROPN
ma-44	15	35	[	[	X
ma-44	15	36	0	0	NUM
ma-44	15	37	,	,	PUNCT
ma-44	15	38	1].some	1].some	NUM
ma-44	15	39	properties	property	NOUN
ma-44	15	40	and	and	CCONJ
ma-44	15	41	applications	application	NOUN
ma-44	15	42	of	of	ADP
ma-44	15	43	the	the	DET
ma-44	15	44	helfer	helfer	PROPN
ma-44	15	45	derivative	derivative	NOUN
ma-44	15	46	are	be	AUX
ma-44	15	47	given	give	VERB
ma-44	15	48	in	in	ADP
ma-44	15	49	[	[	X
ma-44	15	50	12	12	NUM
ma-44	15	51	,	,	PUNCT
ma-44	15	52	13	13	NUM
ma-44	15	53	]	]	PUNCT
ma-44	15	54	and	and	CCONJ
ma-44	15	55	the	the	DET
ma-44	15	56	referencesmentioned	referencesmentioned	ADJ
ma-44	15	57	therein	therein	NOUN
ma-44	15	58	.	.	PUNCT
ma-44	16	1	prime	prime	ADJ
ma-44	16	2	value	value	NOUN
ma-44	16	3	problems	problem	NOUN
ma-44	16	4	involving	involve	VERB
ma-44	16	5	fractional	fractional	ADJ
ma-44	16	6	hilfer	hilfer	NOUN
ma-44	16	7	derivatives	derivative	NOUN
ma-44	16	8	have	have	AUX
ma-44	16	9	been	be	AUX
ma-44	16	10	studiedby	studiedby	ADJ
ma-44	16	11	several	several	ADJ
ma-44	16	12	authors	author	NOUN
ma-44	16	13	,	,	PUNCT
ma-44	16	14	see	see	VERB
ma-44	16	15	[	[	X
ma-44	16	16	9,10,26	9,10,26	NUM
ma-44	16	17	]	]	X
ma-44	16	18	.	.	PUNCT
ma-44	17	1	however	however	ADV
ma-44	17	2	,	,	PUNCT
ma-44	17	3	in	in	ADP
ma-44	17	4	the	the	DET
ma-44	17	5	literature	literature	NOUN
ma-44	17	6	there	there	PRON
ma-44	17	7	are	be	VERB
ma-44	17	8	few	few	ADJ
ma-44	17	9	papers	paper	NOUN
ma-44	17	10	on	on	ADP
ma-44	17	11	the	the	DET
ma-44	17	12	boundary	boundary	ADJ
ma-44	17	13	received	receive	VERB
ma-44	17	14	:	:	PUNCT
ma-44	17	15	8	8	NUM
ma-44	17	16	oct	oct	NOUN
ma-44	17	17	2021	2021	NUM
ma-44	17	18	.	.	PUNCT
ma-44	18	1	key	key	ADJ
ma-44	18	2	words	word	NOUN
ma-44	18	3	and	and	CCONJ
ma-44	18	4	phrases	phrase	NOUN
ma-44	18	5	.	.	PUNCT
ma-44	19	1	ϕ−hilfer	ϕ−hilfer	VERB
ma-44	19	2	derivative	derivative	ADJ
ma-44	19	3	;	;	PUNCT
ma-44	19	4	existence	existence	NOUN
ma-44	19	5	of	of	ADP
ma-44	19	6	solution	solution	NOUN
ma-44	19	7	;	;	PUNCT
ma-44	19	8	fixed	fix	VERB
ma-44	19	9	point	point	NOUN
ma-44	19	10	;	;	PUNCT
ma-44	19	11	hyers	hyer	NOUN
ma-44	19	12	-	-	PUNCT
ma-44	19	13	ulam	ulam	PROPN
ma-44	19	14	stability.164	stability.164	PROPN
ma-44	19	15	https://adac.ee	https://adac.ee	PROPN
ma-44	19	16	https://doi.org/10.28924/ada/ma.1.164	https://doi.org/10.28924/ada/ma.1.164	NOUN
ma-44	19	17	eur	eur	NOUN
ma-44	19	18	.	.	PUNCT
ma-44	20	1	j.	j.	PROPN
ma-44	20	2	math	math	PROPN
ma-44	20	3	.	.	PUNCT
ma-44	21	1	anal	anal	ADJ
ma-44	21	2	.	.	PUNCT
ma-44	22	1	1	1	NUM
ma-44	22	2	(	(	PUNCT
ma-44	22	3	2021	2021	NUM
ma-44	22	4	)	)	PUNCT
ma-44	22	5	165value	165value	PROPN
ma-44	22	6	problems	problem	NOUN
ma-44	22	7	of	of	ADP
ma-44	22	8	the	the	DET
ma-44	22	9	fractional	fractional	ADJ
ma-44	22	10	hilfer	hilfer	NOUN
ma-44	22	11	derivatives	derivative	NOUN
ma-44	22	12	.	.	PUNCT
ma-44	23	1	the	the	DET
ma-44	23	2	authors	author	NOUN
ma-44	23	3	set	set	VERB
ma-44	23	4	out	out	ADP
ma-44	23	5	in	in	ADP
ma-44	23	6	[	[	PUNCT
ma-44	23	7	2	2	NUM
ma-44	23	8	]	]	PUNCT
ma-44	23	9	non	non	ADJ
ma-44	23	10	-	-	ADJ
ma-44	23	11	local	local	ADJ
ma-44	23	12	value	value	NOUN
ma-44	23	13	prob	prob	NOUN
ma-44	23	14	-	-	PUNCT
ma-44	23	15	lems	lem	NOUN
ma-44	23	16	for	for	ADP
ma-44	23	17	derivatives	derivative	NOUN
ma-44	23	18	of	of	ADP
ma-44	23	19	helfer	helfer	PROPN
ma-44	23	20	’s	’s	PART
ma-44	23	21	fractions	fraction	NOUN
ma-44	23	22	.	.	PUNCT
ma-44	24	1	for	for	ADP
ma-44	24	2	some	some	DET
ma-44	24	3	recent	recent	ADJ
ma-44	24	4	work	work	NOUN
ma-44	24	5	on	on	ADP
ma-44	24	6	boundary	boundary	ADJ
ma-44	24	7	value	value	NOUN
ma-44	24	8	problems	problem	NOUN
ma-44	24	9	withfractional	withfractional	ADJ
ma-44	24	10	hilfer	hilfer	NOUN
ma-44	24	11	derivatives	derivative	NOUN
ma-44	24	12	,	,	PUNCT
ma-44	24	13	we	we	PRON
ma-44	24	14	refer	refer	VERB
ma-44	24	15	to	to	ADP
ma-44	24	16	the	the	DET
ma-44	24	17	papers	paper	NOUN
ma-44	24	18	in	in	ADP
ma-44	24	19	[	[	PUNCT
ma-44	24	20	28–30].some	28–30].some	NUM
ma-44	24	21	authors	author	NOUN
ma-44	24	22	have	have	AUX
ma-44	24	23	worked	work	VERB
ma-44	24	24	on	on	ADP
ma-44	24	25	the	the	DET
ma-44	24	26	eu	eu	PROPN
ma-44	24	27	of	of	ADP
ma-44	24	28	solutions	solution	NOUN
ma-44	24	29	for	for	ADP
ma-44	24	30	fractional	fractional	ADJ
ma-44	24	31	des	des	PROPN
ma-44	24	32	with	with	ADP
ma-44	24	33	p−laplacian	p−laplacian	PROPN
ma-44	24	34	operator.we	operator.we	PRON
ma-44	24	35	cite	cite	VERB
ma-44	24	36	,	,	PUNCT
ma-44	24	37	for	for	ADP
ma-44	24	38	example	example	NOUN
ma-44	24	39	;	;	PUNCT
ma-44	24	40	li	li	PROPN
ma-44	24	41	.	.	PROPN
ma-44	24	42	,	,	PUNCT
ma-44	24	43	wang	wang	PROPN
ma-44	24	44	.	.	PROPN
ma-44	24	45	,	,	PUNCT
ma-44	24	46	khan	khan	PROPN
ma-44	24	47	et	et	PROPN
ma-44	24	48	al	al	PROPN
ma-44	24	49	.	.	PUNCT
ma-44	25	1	[	[	X
ma-44	25	2	15	15	NUM
ma-44	25	3	,	,	PUNCT
ma-44	25	4	19	19	NUM
ma-44	25	5	,	,	PUNCT
ma-44	25	6	27	27	NUM
ma-44	25	7	]	]	PUNCT
ma-44	25	8	studieds	studied	VERB
ma-44	25	9	a	a	DET
ma-44	25	10	nonlinear	nonlinear	ADJ
ma-44	25	11	fractional	fractional	ADJ
ma-44	25	12	de	de	X
ma-44	25	13	withp	withp	PROPN
ma-44	25	14	-	-	PUNCT
ma-44	25	15	laplacian	laplacian	ADJ
ma-44	25	16	operator	operator	NOUN
ma-44	25	17	for	for	ADP
ma-44	25	18	the	the	DET
ma-44	25	19	eu	eu	PROPN
ma-44	25	20	of	of	ADP
ma-44	25	21	solutions	solution	NOUN
ma-44	25	22	.	.	PUNCT
ma-44	26	1	h.	h.	PROPN
ma-44	26	2	khan	khan	PROPN
ma-44	26	3	,	,	PUNCT
ma-44	26	4	t.	t.	PROPN
ma-44	26	5	abdeljawad	abdeljawad	PROPN
ma-44	26	6	,	,	PUNCT
ma-44	26	7	m.	m.	NOUN
ma-44	26	8	aslam	aslam	PROPN
ma-44	26	9	,	,	PUNCT
ma-44	26	10	r.	r.	PROPN
ma-44	26	11	a.	a.	PROPN
ma-44	26	12	khan	khan	PROPN
ma-44	26	13	and	and	CCONJ
ma-44	26	14	a.	a.	NOUN
ma-44	26	15	khan	khan	PROPN
ma-44	27	1	[	[	X
ma-44	27	2	16	16	NUM
ma-44	27	3	]	]	PUNCT
ma-44	27	4	.	.	PUNCT
ma-44	28	1	worked	work	VERB
ma-44	28	2	on	on	ADP
ma-44	28	3	the	the	DET
ma-44	28	4	followingproposal	followingproposal	NOUN
ma-44	28	5	for	for	ADP
ma-44	28	6	the	the	DET
ma-44	28	7	existence	existence	NOUN
ma-44	28	8	of	of	ADP
ma-44	28	9	a	a	DET
ma-44	28	10	positive	positive	ADJ
ma-44	28	11	solution	solution	NOUN
ma-44	28	12	(	(	PUNCT
ma-44	28	13	eps	eps	NOUN
ma-44	28	14	)	)	PUNCT
ma-44	28	15	and	and	CCONJ
ma-44	28	16	stability	stability	NOUN
ma-44	28	17	analysis	analysis	NOUN
ma-44	28	18	:	:	PUNCT
ma-44	28	19			NUM
ma-44	28	20	dr1ψp	dr1ψp	NOUN
ma-44	29	1	[	[	X
ma-44	29	2	dr2	dr2	X
ma-44	29	3	(	(	PUNCT
ma-44	29	4	u(t)−	u(t)−	PROPN
ma-44	29	5	v1(t	v1(t	PROPN
ma-44	29	6	,	,	PUNCT
ma-44	29	7	u(t	u(t	NOUN
ma-44	29	8	)	)	PUNCT
ma-44	29	9	)	)	PUNCT
ma-44	29	10	)	)	PUNCT
ma-44	29	11	]	]	PUNCT
ma-44	30	1	=	=	PUNCT
ma-44	30	2	−a(t)v2(t	−a(t)v2(t	NOUN
ma-44	30	3	,	,	PUNCT
ma-44	30	4	u(t	u(t	PROPN
ma-44	30	5	−	−	PROPN
ma-44	30	6	τ	τ	PROPN
ma-44	30	7	)	)	PUNCT
ma-44	30	8	)	)	PUNCT
ma-44	30	9	,	,	PUNCT
ma-44	30	10	ψp	ψp	PUNCT
ma-44	31	1	[	[	X
ma-44	31	2	dr2	dr2	X
ma-44	31	3	(	(	PUNCT
ma-44	31	4	u(t)−	u(t)−	PROPN
ma-44	31	5	v1(t	v1(t	PROPN
ma-44	31	6	,	,	PUNCT
ma-44	31	7	u(t)))]|t=0	u(t)))]|t=0	PROPN
ma-44	31	8	=	=	SYM
ma-44	31	9	ψp	ψp	PROPN
ma-44	31	10	[	[	PUNCT
ma-44	31	11	dr2	dr2	PROPN
ma-44	31	12	(	(	PUNCT
ma-44	31	13	u(t)−	u(t)−	PROPN
ma-44	31	14	v1(t	v1(t	PROPN
ma-44	31	15	,	,	PUNCT
ma-44	31	16	u(t)))′	u(t)))′	PROPN
ma-44	31	17	]	]	PUNCT
ma-44	31	18	∣∣	∣∣	X
ma-44	31	19	t=0	t=0	X
ma-44	31	20	=	=	SYM
ma-44	31	21	0	0	NUM
ma-44	31	22	,	,	PUNCT
ma-44	31	23	u(0	u(0	NOUN
ma-44	31	24	)	)	PUNCT
ma-44	31	25	=	=	SYM
ma-44	31	26	u(1	u(1	PROPN
ma-44	31	27	)	)	PUNCT
ma-44	31	28	=	=	SYM
ma-44	31	29	0	0	NUM
ma-44	31	30	,	,	PUNCT
ma-44	31	31	[	[	PUNCT
ma-44	31	32	i2−r2	i2−r2	PROPN
ma-44	31	33	(	(	PUNCT
ma-44	31	34	u(t)−	u(t)−	PROPN
ma-44	31	35	v1(t	v1(t	PROPN
ma-44	31	36	,	,	PUNCT
ma-44	31	37	u(t	u(t	NOUN
ma-44	31	38	)	)	PUNCT
ma-44	31	39	)	)	PUNCT
ma-44	31	40	)	)	PUNCT
ma-44	32	1	]	]	PUNCT
ma-44	32	2	∣∣	∣∣	X
ma-44	32	3	t=0	t=0	X
ma-44	32	4	=	=	SYM
ma-44	32	5	0	0	PROPN
ma-44	32	6	,	,	PUNCT
ma-44	32	7	where	where	SCONJ
ma-44	32	8	0	0	X
ma-44	32	9	<	<	X
ma-44	32	10	r1	r1	X
ma-44	32	11	<	<	X
ma-44	32	12	1	1	NUM
ma-44	32	13	<	<	X
ma-44	32	14	r2	r2	PROPN
ma-44	32	15	<	<	X
ma-44	32	16	2	2	NUM
ma-44	32	17	,	,	PUNCT
ma-44	32	18	and	and	CCONJ
ma-44	32	19	v1	v1	NOUN
ma-44	32	20	,	,	PUNCT
ma-44	32	21	v2	v2	PROPN
ma-44	32	22	are	be	AUX
ma-44	32	23	continuous	continuous	ADJ
ma-44	32	24	but	but	CCONJ
ma-44	32	25	singular	singular	ADJ
ma-44	32	26	at	at	ADP
ma-44	32	27	some	some	DET
ma-44	32	28	points	point	NOUN
ma-44	32	29	.	.	PUNCT
ma-44	33	1	thefractional	thefractional	ADJ
ma-44	33	2	derivatives	derivative	NOUN
ma-44	33	3	dr1	dr1	PROPN
ma-44	33	4	and	and	CCONJ
ma-44	33	5	dr2	dr2	PROPN
ma-44	33	6	are	be	AUX
ma-44	33	7	taken	take	VERB
ma-44	33	8	in	in	ADP
ma-44	33	9	the	the	DET
ma-44	33	10	caputo	caputo	PROPN
ma-44	33	11	sense	sense	NOUN
ma-44	33	12	and	and	CCONJ
ma-44	33	13	in	in	ADP
ma-44	33	14	the	the	DET
ma-44	33	15	riemann	riemann	PROPN
ma-44	33	16	–	–	PUNCT
ma-44	33	17	liouvillesense	liouvillesense	NOUN
ma-44	33	18	,	,	PUNCT
ma-44	33	19	respectively	respectively	ADV
ma-44	33	20	,	,	PUNCT
ma-44	33	21	and	and	CCONJ
ma-44	33	22	ψp(z	ψp(z	NUM
ma-44	33	23	)	)	PUNCT
ma-44	34	1	=	=	SYM
ma-44	34	2	|z	|z	PROPN
ma-44	34	3	|p−2	|p−2	PROPN
ma-44	34	4	z	z	PROPN
ma-44	34	5	denotes	denote	VERB
ma-44	34	6	the	the	DET
ma-44	34	7	p−laplacian	p−laplacian	ADJ
ma-44	34	8	operator	operator	NOUN
ma-44	34	9	and	and	CCONJ
ma-44	34	10	satisfies	satisfy	VERB
ma-44	34	11	1	1	NUM
ma-44	34	12	p	p	NOUN
ma-44	34	13	+	+	NOUN
ma-44	34	14	1	1	NUM
ma-44	34	15	q	q	NOUN
ma-44	34	16	=	=	SYM
ma-44	34	17	1	1	NUM
ma-44	34	18	,	,	PUNCT
ma-44	34	19	(	(	PUNCT
ma-44	34	20	ψp)−1	ψp)−1	NOUN
ma-44	34	21	=	=	SYM
ma-44	34	22	ψq.a	ψq.a	X
ma-44	34	23	.	.	PUNCT
ma-44	35	1	devi	devi	PROPN
ma-44	35	2	,	,	PUNCT
ma-44	35	3	a.	a.	PROPN
ma-44	35	4	kumar	kumar	PROPN
ma-44	35	5	,	,	PUNCT
ma-44	35	6	d.	d.	PROPN
ma-44	35	7	baleanu	baleanu	PROPN
ma-44	35	8	and	and	CCONJ
ma-44	35	9	a.	a.	NOUN
ma-44	35	10	khan	khan	PROPN
ma-44	36	1	[	[	X
ma-44	36	2	7	7	NUM
ma-44	36	3	]	]	PUNCT
ma-44	36	4	.	.	PUNCT
ma-44	36	5	worked	work	VERB
ma-44	36	6	on	on	ADP
ma-44	36	7	the	the	DET
ma-44	36	8	eu	eu	PROPN
ma-44	36	9	and	and	CCONJ
ma-44	36	10	hu	hu	PROPN
ma-44	36	11	stability	stability	NOUN
ma-44	36	12	results	result	NOUN
ma-44	36	13	,	,	PUNCT
ma-44	36	14	fornonliner	fornonliner	NOUN
ma-44	36	15	fdes	fde	NOUN
ma-44	36	16	involving	involve	VERB
ma-44	36	17	caputo	caputo	PROPN
ma-44	36	18	fractional	fractional	ADJ
ma-44	36	19	derivatives	derivative	NOUN
ma-44	36	20	of	of	ADP
ma-44	36	21	distinct	distinct	ADJ
ma-44	36	22	orders	order	NOUN
ma-44	36	23	with	with	ADP
ma-44	36	24	ψp	ψp	NOUN
ma-44	36	25	laplacian	laplacian	ADJ
ma-44	36	26	operator	operator	NOUN
ma-44	36	27	:	:	PUNCT
ma-44	36	28			NUM
ma-44	36	29	cdr1ψp	cdr1ψp	X
ma-44	36	30	[	[	PUNCT
ma-44	36	31	cdr2	cdr2	PROPN
ma-44	36	32	(	(	PUNCT
ma-44	36	33	u(t)−	u(t)−	PROPN
ma-44	36	34	∑m	∑m	PROPN
ma-44	36	35	i=1	i=1	PROPN
ma-44	36	36	vi(t	vi(t	PROPN
ma-44	36	37	)	)	PUNCT
ma-44	36	38	)	)	PUNCT
ma-44	36	39	]	]	PUNCT
ma-44	37	1	=	=	PUNCT
ma-44	37	2	−w(t	−w(t	PROPN
ma-44	37	3	,	,	PUNCT
ma-44	37	4	u(t	u(t	NOUN
ma-44	37	5	)	)	PUNCT
ma-44	37	6	)	)	PUNCT
ma-44	37	7	,	,	PUNCT
ma-44	37	8	t	t	PROPN
ma-44	37	9	∈	∈	PROPN
ma-44	37	10	(	(	PUNCT
ma-44	37	11	0	0	NUM
ma-44	37	12	,	,	PUNCT
ma-44	37	13	1	1	NUM
ma-44	37	14	]	]	PUNCT
ma-44	37	15	ψp	ψp	PROPN
ma-44	37	16	[	[	PUNCT
ma-44	37	17	cdr2	cdr2	PROPN
ma-44	37	18	(	(	PUNCT
ma-44	37	19	u(t)−	u(t)−	PROPN
ma-44	37	20	∑m	∑m	PROPN
ma-44	37	21	i=1	i=1	PROPN
ma-44	37	22	vi(t	vi(t	PROPN
ma-44	37	23	)	)	PUNCT
ma-44	37	24	)	)	PUNCT
ma-44	37	25	]	]	PUNCT
ma-44	37	26	∣∣	∣∣	X
ma-44	37	27	t=0	t=0	X
ma-44	37	28	=	=	SYM
ma-44	37	29	0	0	NUM
ma-44	37	30	,	,	PUNCT
ma-44	37	31	u(0	u(0	NOUN
ma-44	37	32	)	)	PUNCT
ma-44	37	33	=	=	PUNCT
ma-44	38	1	∑m	∑m	PROPN
ma-44	38	2	i=1	i=1	PROPN
ma-44	38	3	vi(0	vi(0	PROPN
ma-44	38	4	)	)	PUNCT
ma-44	38	5	,	,	PUNCT
ma-44	38	6	u′(1	u′(1	NOUN
ma-44	38	7	)	)	PUNCT
ma-44	38	8	=	=	PUNCT
ma-44	39	1	∑m	∑m	PROPN
ma-44	39	2	i=1	i=1	PROPN
ma-44	40	1	v	v	INTJ
ma-44	40	2	′	′	NUM
ma-44	41	1	i	i	PRON
ma-44	41	2	(	(	PUNCT
ma-44	41	3	1	1	NUM
ma-44	41	4	)	)	PUNCT
ma-44	41	5	,	,	PUNCT
ma-44	41	6	uj(0	uj(0	NOUN
ma-44	41	7	)	)	PUNCT
ma-44	41	8	=	=	VERB
ma-44	42	1	∑m	∑m	PROPN
ma-44	42	2	i=1	i=1	PROPN
ma-44	42	3	v	v	NUM
ma-44	43	1	j	j	PROPN
ma-44	43	2	i	i	PRON
ma-44	43	3	(	(	PUNCT
ma-44	43	4	0	0	NUM
ma-44	43	5	)	)	PUNCT
ma-44	43	6	,	,	PUNCT
ma-44	43	7	for	for	ADP
ma-44	43	8	j	j	PROPN
ma-44	43	9	=	=	SYM
ma-44	43	10	2	2	NUM
ma-44	43	11	,	,	PUNCT
ma-44	43	12	3	3	NUM
ma-44	43	13	,	,	PUNCT
ma-44	43	14	...	...	PUNCT
ma-44	43	15	,	,	PUNCT
ma-44	43	16	n	n	CCONJ
ma-44	43	17	−	−	PROPN
ma-44	43	18	1	1	NUM
ma-44	43	19	,	,	PUNCT
ma-44	43	20	where	where	SCONJ
ma-44	43	21	0	0	X
ma-44	43	22	<	<	X
ma-44	43	23	r1	r1	PROPN
ma-44	43	24	≤	≤	NUM
ma-44	43	25	1	1	NUM
ma-44	43	26	,	,	PUNCT
ma-44	43	27	n	n	CCONJ
ma-44	43	28	−	−	PROPN
ma-44	43	29	1	1	NUM
ma-44	43	30	<	<	X
ma-44	43	31	r2	r2	PROPN
ma-44	43	32	≤	≤	PUNCT
ma-44	43	33	n	n	CCONJ
ma-44	43	34	,	,	PUNCT
ma-44	43	35	n	n	PRON
ma-44	43	36	≥	≥	NOUN
ma-44	43	37	4	4	NUM
ma-44	43	38	,	,	PUNCT
ma-44	43	39	and	and	CCONJ
ma-44	43	40	vi	vi	PROPN
ma-44	43	41	,	,	PUNCT
ma-44	43	42	w	w	PROPN
ma-44	43	43	are	be	AUX
ma-44	43	44	continuous	continuous	ADJ
ma-44	43	45	functions	function	NOUN
ma-44	43	46	.	.	PUNCT
ma-44	44	1	cdr1	cdr1	PROPN
ma-44	44	2	and	and	CCONJ
ma-44	44	3	cdr2	cdr2	PROPN
ma-44	44	4	denotes	denote	VERB
ma-44	44	5	the	the	DET
ma-44	44	6	derivative	derivative	NOUN
ma-44	44	7	of	of	ADP
ma-44	44	8	fractional	fractional	ADJ
ma-44	44	9	order	order	NOUN
ma-44	44	10	r1	r1	NOUN
ma-44	44	11	and	and	CCONJ
ma-44	44	12	r2	r2	PROPN
ma-44	44	13	in	in	ADP
ma-44	44	14	caputo	caputo	PROPN
ma-44	44	15	’s	’s	PART
ma-44	44	16	sense	sense	NOUN
ma-44	44	17	,	,	PUNCT
ma-44	44	18	respectively	respectively	ADV
ma-44	44	19	,	,	PUNCT
ma-44	44	20	and	and	CCONJ
ma-44	44	21	ψp(z	ψp(z	NUM
ma-44	44	22	)	)	PUNCT
ma-44	45	1	=	=	SYM
ma-44	45	2	|z	|z	PROPN
ma-44	45	3	|p−2	|p−2	PROPN
ma-44	45	4	z	z	PROPN
ma-44	45	5	denotes	denote	VERB
ma-44	45	6	the	the	DET
ma-44	45	7	p−laplacian	p−laplacian	ADJ
ma-44	45	8	operator	operator	NOUN
ma-44	45	9	and	and	CCONJ
ma-44	45	10	satisfies	satisfy	VERB
ma-44	45	11	1	1	NUM
ma-44	45	12	p	p	NOUN
ma-44	45	13	+	+	NOUN
ma-44	45	14	1	1	NUM
ma-44	45	15	q	q	NOUN
ma-44	45	16	=	=	SYM
ma-44	45	17	1	1	NUM
ma-44	45	18	,	,	PUNCT
ma-44	45	19	(	(	PUNCT
ma-44	45	20	ψp)−1	ψp)−1	NOUN
ma-44	45	21	=	=	VERB
ma-44	45	22	ψq	ψq	NOUN
ma-44	45	23	.	.	PUNCT
ma-44	46	1	in	in	ADP
ma-44	46	2	the	the	DET
ma-44	46	3	present	present	ADJ
ma-44	46	4	research	research	NOUN
ma-44	46	5	work	work	NOUN
ma-44	46	6	,	,	PUNCT
ma-44	46	7	we	we	PRON
ma-44	46	8	study	study	VERB
ma-44	46	9	the	the	DET
ma-44	46	10	existence	existence	NOUN
ma-44	46	11	and	and	CCONJ
ma-44	46	12	uniqueness	uniqueness	NOUN
ma-44	46	13	of	of	ADP
ma-44	46	14	a	a	DET
ma-44	46	15	solution	solution	NOUN
ma-44	46	16	(	(	PUNCT
ma-44	46	17	eps	eps	NOUN
ma-44	46	18	)	)	PUNCT
ma-44	46	19	andstability	andstability	NOUN
ma-44	46	20	analysis	analysis	NOUN
ma-44	46	21	which	which	PRON
ma-44	46	22	includes	include	VERB
ma-44	46	23	the	the	DET
ma-44	46	24	ϕ−hilfer	ϕ−hilf	ADJ
ma-44	46	25	fractional	fractional	ADJ
ma-44	46	26	-	-	PUNCT
ma-44	46	27	order	order	NOUN
ma-44	46	28	of	of	ADP
ma-44	46	29	the	the	DET
ma-44	46	30	form	form	NOUN
ma-44	46	31	:	:	PUNCT
ma-44	46	32	eur	eur	PROPN
ma-44	46	33	.	.	PUNCT
ma-44	47	1	j.	j.	PROPN
ma-44	47	2	math	math	PROPN
ma-44	47	3	.	.	PUNCT
ma-44	48	1	anal	anal	ADJ
ma-44	48	2	.	.	PUNCT
ma-44	49	1	1	1	NUM
ma-44	49	2	(	(	PUNCT
ma-44	49	3	2021	2021	NUM
ma-44	49	4	)	)	PUNCT
ma-44	49	5	166	166	NUM
ma-44	49	6			PROPN
ma-44	49	7	hdα1,β1;ϕ	hdα1,β1;ϕ	PROPN
ma-44	49	8	a+	a+	PUNCT
ma-44	49	9	ψp	ψp	ADP
ma-44	49	10	(	(	PUNCT
ma-44	49	11	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	49	12	a+	a+	PUNCT
ma-44	49	13	u	u	NOUN
ma-44	49	14	)	)	PUNCT
ma-44	49	15	(	(	PUNCT
ma-44	49	16	t	t	NOUN
ma-44	49	17	)	)	PUNCT
ma-44	49	18	=	=	PUNCT
ma-44	50	1	h(t	h(t	PROPN
ma-44	50	2	,	,	PUNCT
ma-44	50	3	u(t),rldµ;ϕ	u(t),rldµ;ϕ	ADJ
ma-44	50	4	a+	a+	PUNCT
ma-44	50	5	u(t	u(t	NOUN
ma-44	50	6	)	)	PUNCT
ma-44	50	7	)	)	PUNCT
ma-44	50	8	,	,	PUNCT
ma-44	50	9	t	t	PROPN
ma-44	50	10	∈	∈	PROPN
ma-44	51	1	j	j	PROPN
ma-44	51	2	=	=	PRON
ma-44	51	3	(	(	PUNCT
ma-44	51	4	a	a	PRON
ma-44	51	5	,	,	PUNCT
ma-44	51	6	b	b	NOUN
ma-44	51	7	]	]	X
ma-44	51	8	u(a	u(a	PROPN
ma-44	51	9	)	)	PUNCT
ma-44	51	10	=	=	SYM
ma-44	51	11	0	0	NUM
ma-44	51	12	,	,	PUNCT
ma-44	51	13	u(b	u(b	NUM
ma-44	51	14	)	)	PUNCT
ma-44	52	1	=	=	PUNCT
ma-44	52	2	n∑	n∑	PROPN
ma-44	52	3	i=1	i=1	PROPN
ma-44	53	1	λiu	λiu	PROPN
ma-44	53	2	(	(	PUNCT
ma-44	53	3	ζi	ζi	PROPN
ma-44	53	4	)	)	PUNCT
ma-44	53	5	,	,	PUNCT
ma-44	53	6	ψp	ψp	ADP
ma-44	53	7	(	(	PUNCT
ma-44	53	8	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	53	9	a+	a+	PUNCT
ma-44	53	10	u	u	NOUN
ma-44	53	11	)	)	PUNCT
ma-44	53	12	(	(	PUNCT
ma-44	53	13	a	a	X
ma-44	53	14	)	)	PUNCT
ma-44	54	1	=	=	SYM
ma-44	54	2	0,and	0,and	NUM
ma-44	54	3	ψp	ψp	ADP
ma-44	54	4	(	(	PUNCT
ma-44	54	5	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	54	6	a+	a+	PUNCT
ma-44	54	7	u(b	u(b	NOUN
ma-44	54	8	)	)	PUNCT
ma-44	54	9	)	)	PUNCT
ma-44	54	10	=	=	PRON
ma-44	54	11	iρ;ϕ	iρ;ϕ	VERB
ma-44	54	12	a+	a+	PUNCT
ma-44	54	13	u	u	NOUN
ma-44	54	14	(	(	PUNCT
ma-44	54	15	ζ	ζ	NOUN
ma-44	54	16	)	)	PUNCT
ma-44	54	17	,	,	PUNCT
ma-44	54	18	a	a	DET
ma-44	54	19	<	<	X
ma-44	54	20	ζ	ζ	NOUN
ma-44	54	21	,	,	PUNCT
ma-44	54	22	ζi	ζi	ADP
ma-44	54	23	<	<	X
ma-44	54	24	b	b	PROPN
ma-44	54	25	,	,	PUNCT
ma-44	54	26	(	(	PUNCT
ma-44	54	27	1.1	1.1	NUM
ma-44	54	28	)	)	PUNCT
ma-44	54	29	here	here	ADV
ma-44	54	30	,	,	PUNCT
ma-44	54	31	we	we	PRON
ma-44	54	32	take	take	VERB
ma-44	54	33	hdα1,β;ϕ	hdα1,β;ϕ	PRON
ma-44	54	34	0	0	NUM
ma-44	55	1	+	+	NUM
ma-44	55	2	,	,	PUNCT
ma-44	55	3	h	h	NOUN
ma-44	55	4	dα2,β;ϕ	dα2,β;ϕ	NOUN
ma-44	55	5	0	0	NUM
ma-44	55	6	+	+	CCONJ
ma-44	55	7	,	,	PUNCT
ma-44	55	8	are	be	AUX
ma-44	55	9	the	the	DET
ma-44	55	10	ϕ−hilfer	ϕ−hilf	ADJ
ma-44	55	11	fractional	fractional	ADJ
ma-44	55	12	derivative	derivative	NOUN
ma-44	55	13	of	of	ADP
ma-44	55	14	orders	order	NOUN
ma-44	55	15	α1	α1	PROPN
ma-44	55	16	,	,	PUNCT
ma-44	55	17	α2	α2	VERB
ma-44	55	18	,	,	PUNCT
ma-44	55	19	1	1	NUM
ma-44	55	20	<	<	X
ma-44	55	21	α1	α1	PROPN
ma-44	55	22	,	,	PUNCT
ma-44	55	23	α2	α2	ADV
ma-44	55	24	<	<	X
ma-44	55	25	2	2	NUM
ma-44	55	26	and	and	CCONJ
ma-44	55	27	β1	β1	PROPN
ma-44	55	28	,	,	PUNCT
ma-44	55	29	β2	β2	VERB
ma-44	55	30	two	two	NUM
ma-44	55	31	parameters	parameter	NOUN
ma-44	56	1	0	0	NUM
ma-44	56	2	≤	≤	NUM
ma-44	56	3	β1	β1	NOUN
ma-44	56	4	,	,	PUNCT
ma-44	56	5	β2	β2	VERB
ma-44	56	6	≤	≤	NOUN
ma-44	56	7	1	1	NUM
ma-44	56	8	,	,	PUNCT
ma-44	56	9	rldκ;ϕ	rldκ;ϕ	PROPN
ma-44	56	10	a+	a+	PUNCT
ma-44	56	11	the	the	DET
ma-44	56	12	ϕ-riemann	ϕ-riemann	PROPN
ma-44	56	13	-	-	PUNCT
ma-44	56	14	liouville	liouville	VERB
ma-44	56	15	fractionalderivative	fractionalderivative	ADJ
ma-44	56	16	of	of	ADP
ma-44	56	17	order	order	NOUN
ma-44	56	18	µ	µ	PRON
ma-44	56	19	where	where	SCONJ
ma-44	56	20	µ	µ	X
ma-44	56	21	<	<	X
ma-44	56	22	α2	α2	PROPN
ma-44	56	23	,	,	PUNCT
ma-44	56	24	and	and	CCONJ
ma-44	56	25	iρ;ϕ	iρ;ϕ	VERB
ma-44	56	26	0	0	PUNCT
ma-44	56	27	+	+	CCONJ
ma-44	56	28	the	the	DET
ma-44	56	29	left	left	ADV
ma-44	56	30	-	-	PUNCT
ma-44	56	31	sided	sided	ADJ
ma-44	56	32	ϕ−riemann	ϕ−riemann	PROPN
ma-44	56	33	liouville	liouville	VERB
ma-44	56	34	fractional	fractional	ADJ
ma-44	56	35	integralof	integralof	PROPN
ma-44	56	36	order	order	PROPN
ma-44	56	37	ρ	ρ	PROPN
ma-44	56	38	,	,	PUNCT
ma-44	56	39	where	where	SCONJ
ma-44	56	40	ρ	ρ	PROPN
ma-44	56	41	>	>	X
ma-44	56	42	0	0	NUM
ma-44	56	43	,	,	PUNCT
ma-44	56	44	and	and	CCONJ
ma-44	56	45	ψp(z	ψp(z	NUM
ma-44	56	46	)	)	PUNCT
ma-44	56	47	=	=	SYM
ma-44	56	48	|z	|z	PROPN
ma-44	56	49	|p−2	|p−2	PROPN
ma-44	56	50	z	z	PROPN
ma-44	56	51	denotes	denote	VERB
ma-44	56	52	the	the	DET
ma-44	56	53	p−laplacian	p−laplacian	ADJ
ma-44	56	54	operator	operator	NOUN
ma-44	56	55	and	and	CCONJ
ma-44	56	56	satisfies	satisfy	VERB
ma-44	56	57	1	1	NUM
ma-44	56	58	p	p	NOUN
ma-44	56	59	+	+	NOUN
ma-44	56	60	1	1	NUM
ma-44	56	61	q	q	NOUN
ma-44	56	62	=	=	SYM
ma-44	56	63	1	1	NUM
ma-44	56	64	,	,	PUNCT
ma-44	56	65	(	(	PUNCT
ma-44	56	66	ψp)−1	ψp)−1	NOUN
ma-44	56	67	=	=	VERB
ma-44	56	68	ψq	ψq	NOUN
ma-44	56	69	,	,	PUNCT
ma-44	56	70	and	and	CCONJ
ma-44	56	71	ϕ	ϕ	NOUN
ma-44	56	72	:	:	PUNCT
ma-44	56	73	j	j	PROPN
ma-44	56	74	→	→	PUNCT
ma-44	56	75	r	r	NOUN
ma-44	56	76	be	be	AUX
ma-44	56	77	an	an	DET
ma-44	56	78	increasing	increase	VERB
ma-44	56	79	function	function	NOUN
ma-44	56	80	such	such	ADJ
ma-44	56	81	that	that	PRON
ma-44	56	82	ϕ′(t	ϕ′(t	NOUN
ma-44	56	83	)	)	PUNCT
ma-44	56	84	6=	6=	ADP
ma-44	56	85	0	0	NUM
ma-44	56	86	,	,	PUNCT
ma-44	56	87	for	for	ADP
ma-44	56	88	all	all	DET
ma-44	56	89	t	t	NOUN
ma-44	56	90	∈	∈	PROPN
ma-44	56	91	j	j	PROPN
ma-44	56	92	,	,	PUNCT
ma-44	56	93	and	and	CCONJ
ma-44	56	94	f	f	X
ma-44	56	95	:	:	PUNCT
ma-44	57	1	j	j	PROPN
ma-44	57	2	×	×	PROPN
ma-44	57	3	r×	r×	PROPN
ma-44	57	4	r→	r→	PROPN
ma-44	57	5	r	r	PROPN
ma-44	57	6	,	,	PUNCT
ma-44	57	7	is	be	AUX
ma-44	57	8	given	give	VERB
ma-44	57	9	function	function	NOUN
ma-44	57	10	will	will	AUX
ma-44	57	11	be	be	AUX
ma-44	57	12	"	"	PUNCT
ma-44	57	13	well	well	ADV
ma-44	57	14	defined	define	VERB
ma-44	57	15	"	"	PUNCT
ma-44	57	16	later	later	ADV
ma-44	57	17	.	.	PUNCT
ma-44	58	1	2	2	X
ma-44	58	2	.	.	X
ma-44	58	3	phi	phi	ADJ
ma-44	58	4	-	-	PUNCT
ma-44	58	5	hilfer	hilfer	NOUN
ma-44	58	6	derivatives	derivative	NOUN
ma-44	58	7	calculus	calculus	NOUN
ma-44	58	8	in	in	ADP
ma-44	58	9	this	this	DET
ma-44	58	10	section	section	NOUN
ma-44	58	11	,	,	PUNCT
ma-44	58	12	we	we	PRON
ma-44	58	13	introduce	introduce	VERB
ma-44	58	14	some	some	DET
ma-44	58	15	notations	notation	NOUN
ma-44	58	16	and	and	CCONJ
ma-44	58	17	definitions	definition	NOUN
ma-44	58	18	of	of	ADP
ma-44	58	19	phi	phi	ADJ
ma-44	58	20	-	-	PUNCT
ma-44	58	21	hilfer	hilfer	NOUN
ma-44	58	22	derivatives	derivative	NOUN
ma-44	58	23	calculusand	calculusand	VERB
ma-44	58	24	present	present	ADJ
ma-44	58	25	preliminary	preliminary	ADJ
ma-44	58	26	results	result	NOUN
ma-44	58	27	needed	need	VERB
ma-44	58	28	in	in	ADP
ma-44	58	29	our	our	PRON
ma-44	58	30	proofs	proof	NOUN
ma-44	58	31	later	later	ADV
ma-44	58	32	,	,	PUNCT
ma-44	58	33	for	for	ADP
ma-44	58	34	details	detail	NOUN
ma-44	58	35	,	,	PUNCT
ma-44	58	36	see	see	VERB
ma-44	58	37	[	[	X
ma-44	58	38	17,24,25].let	17,24,25].let	X
ma-44	58	39	ϕ	ϕ	NOUN
ma-44	58	40	:	:	PUNCT
ma-44	58	41	[	[	X
ma-44	58	42	a	a	X
ma-44	58	43	,	,	PUNCT
ma-44	58	44	b	b	NOUN
ma-44	58	45	]	]	X
ma-44	58	46	→	→	PUNCT
ma-44	58	47	r	r	NOUN
ma-44	58	48	be	be	AUX
ma-44	58	49	an	an	DET
ma-44	58	50	increasing	increase	VERB
ma-44	58	51	function	function	NOUN
ma-44	58	52	with	with	ADP
ma-44	58	53	ϕ′(t	ϕ′(t	NOUN
ma-44	58	54	)	)	PUNCT
ma-44	58	55	6=	6=	ADP
ma-44	58	56	0	0	NUM
ma-44	58	57	,	,	PUNCT
ma-44	58	58	for	for	ADP
ma-44	58	59	all	all	DET
ma-44	58	60	t	t	NOUN
ma-44	58	61	∈	∈	PROPN
ma-44	58	62	j	j	PROPN
ma-44	58	63	,	,	PUNCT
ma-44	58	64	and	and	CCONJ
ma-44	58	65	let	let	VERB
ma-44	58	66	c([a	c([a	PROPN
ma-44	58	67	,	,	PUNCT
ma-44	58	68	b	b	NOUN
ma-44	58	69	]	]	PUNCT
ma-44	58	70	,	,	PUNCT
ma-44	58	71	r	r	NOUN
ma-44	58	72	)	)	PUNCT
ma-44	58	73	bethe	bethe	ADJ
ma-44	58	74	banach	banach	NOUN
ma-44	58	75	space	space	NOUN
ma-44	58	76	.	.	PUNCT
ma-44	59	1	for	for	ADP
ma-44	59	2	all	all	PRON
ma-44	59	3	υ	υ	PRON
ma-44	59	4	>	>	X
ma-44	59	5	−1	−1	NOUN
ma-44	59	6	and	and	CCONJ
ma-44	59	7	s	s	PROPN
ma-44	59	8	,	,	PUNCT
ma-44	59	9	t	t	PROPN
ma-44	59	10	∈	∈	PROPN
ma-44	60	1	[	[	X
ma-44	60	2	0,∞	0,∞	NOUN
ma-44	60	3	)	)	PUNCT
ma-44	60	4	,	,	PUNCT
ma-44	60	5	(	(	PUNCT
ma-44	60	6	t	t	PROPN
ma-44	60	7	≥	≥	NOUN
ma-44	60	8	s	s	NOUN
ma-44	60	9	)	)	PUNCT
ma-44	60	10	,	,	PUNCT
ma-44	60	11	we	we	PRON
ma-44	60	12	pose	pose	VERB
ma-44	60	13	ϕυ(t	ϕυ(t	NUM
ma-44	60	14	,	,	PUNCT
ma-44	60	15	s	s	X
ma-44	60	16	)	)	PUNCT
ma-44	60	17	=	=	SYM
ma-44	60	18	(	(	PUNCT
ma-44	60	19	ϕ(t)−	ϕ(t)−	PROPN
ma-44	60	20	ϕ(s))υ	ϕ(s))υ	PROPN
ma-44	60	21	.	.	PUNCT
ma-44	61	1	definition	definition	NOUN
ma-44	61	2	1	1	NUM
ma-44	61	3	.	.	PUNCT
ma-44	62	1	let	let	VERB
ma-44	62	2	(	(	PUNCT
ma-44	62	3	a	a	DET
ma-44	62	4	,	,	PUNCT
ma-44	62	5	b	b	NOUN
ma-44	62	6	)	)	PUNCT
ma-44	62	7	,	,	PUNCT
ma-44	62	8	(	(	PUNCT
ma-44	62	9	−∞	−∞	X
ma-44	62	10	≤	≤	ADV
ma-44	62	11	a	a	DET
ma-44	62	12	<	<	X
ma-44	62	13	b	b	X
ma-44	62	14	≤	≤	NUM
ma-44	62	15	∞	∞	PROPN
ma-44	62	16	)	)	PUNCT
ma-44	62	17	be	be	AUX
ma-44	62	18	a	a	DET
ma-44	62	19	finite	finite	NOUN
ma-44	62	20	or	or	CCONJ
ma-44	62	21	infinite	infinite	ADJ
ma-44	62	22	interval	interval	NOUN
ma-44	62	23	of	of	ADP
ma-44	62	24	the	the	DET
ma-44	62	25	half	half	ADJ
ma-44	62	26	-	-	PUNCT
ma-44	62	27	axis	axis	NOUN
ma-44	62	28	(	(	PUNCT
ma-44	62	29	0,∞	0,∞	NUM
ma-44	62	30	)	)	PUNCT
ma-44	62	31	and	and	CCONJ
ma-44	62	32	α	α	X
ma-44	62	33	>	>	X
ma-44	62	34	0	0	X
ma-44	62	35	.	.	PUNCT
ma-44	63	1	in	in	ADP
ma-44	63	2	addition	addition	NOUN
ma-44	63	3	,	,	PUNCT
ma-44	63	4	let	let	VERB
ma-44	63	5	ϕ(t	ϕ(t	NUM
ma-44	63	6	)	)	PUNCT
ma-44	63	7	be	be	AUX
ma-44	63	8	a	a	DET
ma-44	63	9	positive	positive	ADJ
ma-44	63	10	increasing	increase	VERB
ma-44	63	11	function	function	NOUN
ma-44	63	12	on	on	ADP
ma-44	63	13	(	(	PUNCT
ma-44	63	14	a	a	DET
ma-44	63	15	,	,	PUNCT
ma-44	63	16	b	b	NOUN
ma-44	63	17	]	]	X
ma-44	63	18	,	,	PUNCT
ma-44	63	19	which	which	PRON
ma-44	63	20	has	have	VERB
ma-44	63	21	a	a	DET
ma-44	63	22	continuous	continuous	ADJ
ma-44	63	23	derivative	derivative	ADJ
ma-44	63	24	ϕ′(t	ϕ′(t	NOUN
ma-44	63	25	)	)	PUNCT
ma-44	63	26	on	on	ADP
ma-44	63	27	(	(	PUNCT
ma-44	63	28	a	a	DET
ma-44	63	29	,	,	PUNCT
ma-44	63	30	b	b	NOUN
ma-44	63	31	)	)	PUNCT
ma-44	63	32	.	.	PUNCT
ma-44	64	1	the	the	DET
ma-44	64	2	ϕ−riemann	ϕ−riemann	PROPN
ma-44	64	3	–	–	PUNCT
ma-44	64	4	liouville	liouville	VERB
ma-44	64	5	fractional	fractional	ADJ
ma-44	64	6	integral	integral	ADJ
ma-44	64	7	of	of	ADP
ma-44	64	8	a	a	DET
ma-44	64	9	function	function	NOUN
ma-44	64	10	u	u	NOUN
ma-44	64	11	with	with	ADP
ma-44	64	12	respect	respect	NOUN
ma-44	64	13	to	to	ADP
ma-44	64	14	another	another	DET
ma-44	64	15	function	function	NOUN
ma-44	64	16	ϕ	ϕ	NOUN
ma-44	64	17	on	on	ADP
ma-44	64	18	[	[	X
ma-44	64	19	a	a	X
ma-44	64	20	,	,	PUNCT
ma-44	64	21	b	b	NOUN
ma-44	64	22	]	]	PUNCT
ma-44	64	23	is	be	AUX
ma-44	64	24	defined	define	VERB
ma-44	64	25	by	by	ADP
ma-44	64	26	iα;ϕ	iα;ϕ	PROPN
ma-44	64	27	a+	a+	PUNCT
ma-44	64	28	u(t	u(t	PROPN
ma-44	64	29	)	)	PUNCT
ma-44	64	30	=	=	SYM
ma-44	64	31	1	1	NUM
ma-44	64	32	γ(α	γ(α	NOUN
ma-44	64	33	)	)	PUNCT
ma-44	65	1	t∫	t∫	PRON
ma-44	65	2	a	a	DET
ma-44	65	3	ϕ′(s)ϕα−1(t	ϕ′(s)ϕα−1(t	PROPN
ma-44	65	4	,	,	PUNCT
ma-44	65	5	s)u(s)ds	s)u(s)d	VERB
ma-44	65	6	,	,	PUNCT
ma-44	65	7	(	(	PUNCT
ma-44	65	8	2.1	2.1	NUM
ma-44	65	9	)	)	PUNCT
ma-44	65	10	where	where	SCONJ
ma-44	65	11	γ	γ	X
ma-44	65	12	(	(	PUNCT
ma-44	65	13	.	.	PUNCT
ma-44	65	14	)	)	PUNCT
ma-44	65	15	is	be	AUX
ma-44	65	16	the	the	DET
ma-44	65	17	gamma	gamma	PROPN
ma-44	65	18	function	function	NOUN
ma-44	65	19	.	.	PUNCT
ma-44	66	1	definition	definition	NOUN
ma-44	66	2	2	2	NUM
ma-44	66	3	.	.	PUNCT
ma-44	67	1	let	let	VERB
ma-44	67	2	n	n	PRON
ma-44	67	3	∈	∈	PROPN
ma-44	67	4	n	n	ADV
ma-44	67	5	and	and	CCONJ
ma-44	67	6	let	let	VERB
ma-44	67	7	ϕ	ϕ	NOUN
ma-44	67	8	,	,	PUNCT
ma-44	67	9	u	u	PROPN
ma-44	67	10	∈	∈	PROPN
ma-44	67	11	cn	cn	PROPN
ma-44	67	12	(	(	PUNCT
ma-44	67	13	j	j	NOUN
ma-44	67	14	)	)	PUNCT
ma-44	67	15	be	be	VERB
ma-44	67	16	two	two	NUM
ma-44	67	17	functions	function	NOUN
ma-44	67	18	such	such	ADJ
ma-44	67	19	that	that	SCONJ
ma-44	67	20	ϕ	ϕ	NOUN
ma-44	67	21	is	be	AUX
ma-44	67	22	increasing	increase	VERB
ma-44	67	23	and	and	CCONJ
ma-44	67	24	ϕ′(t	ϕ′(t	NOUN
ma-44	67	25	)	)	PUNCT
ma-44	67	26	6=	6=	ADP
ma-44	67	27	0	0	NUM
ma-44	67	28	,	,	PUNCT
ma-44	67	29	for	for	ADP
ma-44	67	30	all	all	DET
ma-44	67	31	t	t	NOUN
ma-44	67	32	∈	∈	PROPN
ma-44	67	33	(	(	PUNCT
ma-44	67	34	a	a	DET
ma-44	67	35	,	,	PUNCT
ma-44	67	36	b	b	NOUN
ma-44	67	37	]	]	X
ma-44	67	38	.	.	PUNCT
ma-44	68	1	the	the	DET
ma-44	68	2	left	left	ADV
ma-44	68	3	-	-	PUNCT
ma-44	68	4	sided	sided	ADJ
ma-44	68	5	ϕ−riemann	ϕ−riemann	PROPN
ma-44	68	6	liouville	liouville	VERB
ma-44	68	7	fractional	fractional	ADJ
ma-44	68	8	derivative	derivative	NOUN
ma-44	68	9	of	of	ADP
ma-44	68	10	a	a	DET
ma-44	68	11	function	function	NOUN
ma-44	68	12	u	u	NOUN
ma-44	68	13	of	of	ADP
ma-44	68	14	order	order	NOUN
ma-44	68	15	α	α	NOUN
ma-44	68	16	is	be	AUX
ma-44	68	17	defined	define	VERB
ma-44	68	18	by	by	ADP
ma-44	68	19	dα;ϕ	dα;ϕ	PROPN
ma-44	68	20	a+	a+	PUNCT
ma-44	68	21	u(t	u(t	PROPN
ma-44	68	22	)	)	PUNCT
ma-44	68	23	=	=	PUNCT
ma-44	68	24	(	(	PUNCT
ma-44	68	25	1	1	NUM
ma-44	68	26	ϕ′(t	ϕ′(t	NOUN
ma-44	68	27	)	)	PUNCT
ma-44	68	28	d	d	NOUN
ma-44	68	29	dt	dt	NOUN
ma-44	68	30	)	)	PUNCT
ma-44	68	31	n	n	CCONJ
ma-44	68	32	in−α;ϕ	in−α;ϕ	ADJ
ma-44	68	33	a+	a+	PUNCT
ma-44	68	34	u(t	u(t	PROPN
ma-44	68	35	)	)	PUNCT
ma-44	68	36	=	=	SYM
ma-44	69	1	1	1	NUM
ma-44	69	2	γ(n	γ(n	X
ma-44	69	3	−	−	PROPN
ma-44	69	4	α	α	NOUN
ma-44	69	5	)	)	PUNCT
ma-44	69	6	(	(	PUNCT
ma-44	69	7	1	1	NUM
ma-44	69	8	ϕ′(t	ϕ′(t	NOUN
ma-44	69	9	)	)	PUNCT
ma-44	69	10	d	d	NOUN
ma-44	69	11	dt	dt	NOUN
ma-44	69	12	)	)	PUNCT
ma-44	69	13	n	n	PROPN
ma-44	69	14	t∫	t∫	PROPN
ma-44	69	15	a	a	DET
ma-44	69	16	ϕ′(s)ϕn−α−1(t	ϕ′(s)ϕn−α−1(t	PRON
ma-44	69	17	,	,	PUNCT
ma-44	69	18	s)u(s)ds	s)u(s)d	VERB
ma-44	69	19	,	,	PUNCT
ma-44	69	20	eur	eur	PROPN
ma-44	69	21	.	.	PUNCT
ma-44	70	1	j.	j.	PROPN
ma-44	70	2	math	math	PROPN
ma-44	70	3	.	.	PUNCT
ma-44	71	1	anal	anal	ADJ
ma-44	71	2	.	.	PUNCT
ma-44	72	1	1	1	NUM
ma-44	72	2	(	(	PUNCT
ma-44	72	3	2021	2021	NUM
ma-44	72	4	)	)	PUNCT
ma-44	72	5	167	167	NUM
ma-44	73	1	where	where	SCONJ
ma-44	73	2	n	n	ADV
ma-44	73	3	=	=	PUNCT
ma-44	74	1	[	[	X
ma-44	74	2	α	α	X
ma-44	74	3	]	]	X
ma-44	74	4	+	+	NOUN
ma-44	74	5	1	1	NUM
ma-44	74	6	,	,	PUNCT
ma-44	74	7	[	[	X
ma-44	74	8	α	α	X
ma-44	74	9	]	]	PUNCT
ma-44	74	10	represents	represent	VERB
ma-44	74	11	the	the	DET
ma-44	74	12	integer	integer	NOUN
ma-44	74	13	part	part	NOUN
ma-44	74	14	of	of	ADP
ma-44	74	15	the	the	DET
ma-44	74	16	real	real	ADJ
ma-44	74	17	number	number	NOUN
ma-44	74	18	α	α	NOUN
ma-44	74	19	.	.	PUNCT
ma-44	75	1	definition	definition	NOUN
ma-44	75	2	3	3	NUM
ma-44	75	3	.	.	PUNCT
ma-44	76	1	let	let	VERB
ma-44	76	2	n−	n−	NOUN
ma-44	76	3	1	1	NUM
ma-44	76	4	<	<	X
ma-44	76	5	α	α	X
ma-44	76	6	<	<	X
ma-44	76	7	n	n	X
ma-44	76	8	with	with	ADP
ma-44	76	9	n	n	PRON
ma-44	76	10	∈	∈	PROPN
ma-44	76	11	n	n	CCONJ
ma-44	76	12	,	,	PUNCT
ma-44	76	13	[	[	X
ma-44	76	14	a	a	X
ma-44	76	15	,	,	PUNCT
ma-44	76	16	b	b	X
ma-44	76	17	]	]	X
ma-44	76	18	is	be	AUX
ma-44	76	19	the	the	DET
ma-44	76	20	interval	interval	NOUN
ma-44	76	21	such	such	ADJ
ma-44	76	22	that	that	PRON
ma-44	76	23	−∞	−∞	ADP
ma-44	76	24	≤	≤	ADV
ma-44	76	25	a	a	DET
ma-44	76	26	<	<	X
ma-44	76	27	b	b	X
ma-44	76	28	≤	≤	NUM
ma-44	76	29	∞	∞	PROPN
ma-44	76	30	and	and	CCONJ
ma-44	76	31	ϕ	ϕ	NOUN
ma-44	76	32	,	,	PUNCT
ma-44	76	33	u	u	PROPN
ma-44	76	34	∈	∈	PROPN
ma-44	76	35	cn	cn	X
ma-44	76	36	(	(	PUNCT
ma-44	76	37	[	[	X
ma-44	76	38	a	a	X
ma-44	76	39	,	,	PUNCT
ma-44	76	40	b	b	NOUN
ma-44	76	41	]	]	PUNCT
ma-44	76	42	,	,	PUNCT
ma-44	76	43	r	r	NOUN
ma-44	76	44	)	)	PUNCT
ma-44	76	45	two	two	NUM
ma-44	76	46	functions	function	NOUN
ma-44	76	47	such	such	ADJ
ma-44	76	48	that	that	SCONJ
ma-44	76	49	ϕ	ϕ	NOUN
ma-44	76	50	is	be	AUX
ma-44	76	51	increasing	increase	VERB
ma-44	76	52	and	and	CCONJ
ma-44	76	53	ϕ′(t	ϕ′(t	NOUN
ma-44	76	54	)	)	PUNCT
ma-44	76	55	6=	6=	ADP
ma-44	76	56	0	0	NUM
ma-44	76	57	,	,	PUNCT
ma-44	76	58	for	for	ADP
ma-44	76	59	all	all	DET
ma-44	76	60	t	t	NOUN
ma-44	76	61	∈	∈	PROPN
ma-44	77	1	[	[	X
ma-44	77	2	a	a	X
ma-44	77	3	,	,	PUNCT
ma-44	77	4	b	b	NOUN
ma-44	77	5	]	]	X
ma-44	77	6	.	.	PUNCT
ma-44	78	1	the	the	DET
ma-44	78	2	ϕ-hilfer	ϕ-hilfer	NOUN
ma-44	78	3	fractional	fractional	ADJ
ma-44	78	4	derivative	derivative	NOUN
ma-44	78	5	of	of	ADP
ma-44	78	6	a	a	DET
ma-44	78	7	function	function	NOUN
ma-44	78	8	u	u	NOUN
ma-44	78	9	of	of	ADP
ma-44	78	10	order	order	NOUN
ma-44	78	11	a	a	PRON
ma-44	78	12	and	and	CCONJ
ma-44	78	13	type	type	NOUN
ma-44	78	14	0	0	NUM
ma-44	78	15	≤	≤	NUM
ma-44	78	16	β	β	NOUN
ma-44	78	17	≤	≤	NUM
ma-44	78	18	1	1	NUM
ma-44	78	19	is	be	AUX
ma-44	78	20	defined	define	VERB
ma-44	78	21	by	by	ADP
ma-44	78	22	hdα	hdα	PROPN
ma-44	78	23	,	,	PUNCT
ma-44	78	24	β;ϕ	β;ϕ	NUM
ma-44	78	25	a+	a+	PUNCT
ma-44	78	26	u(t	u(t	PROPN
ma-44	78	27	)	)	PUNCT
ma-44	79	1	=	=	SYM
ma-44	80	1	iβ(n−α);ϕ	iβ(n−α);ϕ	INTJ
ma-44	80	2	a+	a+	PUNCT
ma-44	80	3	(	(	PUNCT
ma-44	80	4	1	1	NUM
ma-44	80	5	ϕ′(t	ϕ′(t	NOUN
ma-44	80	6	)	)	PUNCT
ma-44	80	7	d	d	NOUN
ma-44	80	8	dt	dt	NOUN
ma-44	80	9	)	)	PUNCT
ma-44	80	10	n	n	CCONJ
ma-44	80	11	i(1−β)(n−α);ϕ	i(1−β)(n−α);ϕ	ADV
ma-44	80	12	a+	a+	PUNCT
ma-44	80	13	u(t	u(t	NOUN
ma-44	80	14	)	)	PUNCT
ma-44	80	15	=	=	SYM
ma-44	80	16	iγ−α;ϕ	iγ−α;ϕ	PROPN
ma-44	80	17	a+	a+	PUNCT
ma-44	80	18	dγ;ϕ	dγ;ϕ	X
ma-44	80	19	a+	a+	PUNCT
ma-44	80	20	u(t	u(t	NOUN
ma-44	80	21	)	)	PUNCT
ma-44	80	22	,	,	PUNCT
ma-44	80	23	where	where	SCONJ
ma-44	80	24	n	n	ADV
ma-44	80	25	=	=	PUNCT
ma-44	81	1	[	[	X
ma-44	81	2	α	α	X
ma-44	81	3	]	]	X
ma-44	81	4	+	+	NOUN
ma-44	81	5	1	1	NUM
ma-44	81	6	,	,	PUNCT
ma-44	81	7	γ	γ	NOUN
ma-44	81	8	−	−	PROPN
ma-44	81	9	α	α	NOUN
ma-44	81	10	=	=	SYM
ma-44	81	11	β	β	X
ma-44	81	12	(	(	PUNCT
ma-44	81	13	n	n	CCONJ
ma-44	81	14	−	−	PROPN
ma-44	81	15	α	α	NOUN
ma-44	81	16	)	)	PUNCT
ma-44	81	17	.	.	PUNCT
ma-44	82	1	2.1	2.1	NUM
ma-44	82	2	.	.	PUNCT
ma-44	82	3	auxiliary	auxiliary	PROPN
ma-44	82	4	lemma	lemma	PROPN
ma-44	82	5	.	.	PUNCT
ma-44	83	1	lemma	lemma	PROPN
ma-44	83	2	1	1	X
ma-44	83	3	.	.	PUNCT
ma-44	84	1	let	let	VERB
ma-44	84	2	α	α	PRON
ma-44	84	3	,	,	PUNCT
ma-44	84	4	ρ	ρ	PROPN
ma-44	84	5	>	>	X
ma-44	84	6	0	0	PROPN
ma-44	84	7	.	.	PUNCT
ma-44	85	1	then	then	ADV
ma-44	85	2	,	,	PUNCT
ma-44	85	3	we	we	PRON
ma-44	85	4	have	have	VERB
ma-44	85	5	the	the	DET
ma-44	85	6	following	follow	VERB
ma-44	85	7	semigroup	semigroup	ADJ
ma-44	85	8	property	property	NOUN
ma-44	85	9	given	give	VERB
ma-44	85	10	by	by	ADP
ma-44	85	11	iα;ϕ	iα;ϕ	NOUN
ma-44	85	12	a+	a+	PUNCT
ma-44	85	13	iρ;ϕ	iρ;ϕ	VERB
ma-44	85	14	a+	a+	PUNCT
ma-44	85	15	u(t	u(t	NOUN
ma-44	85	16	)	)	PUNCT
ma-44	85	17	=	=	PUNCT
ma-44	85	18	iα+ρ;ϕ	iα+ρ;ϕ	VERB
ma-44	85	19	a+	a+	PUNCT
ma-44	85	20	u(t	u(t	NOUN
ma-44	85	21	)	)	PUNCT
ma-44	85	22	,	,	PUNCT
ma-44	85	23	t	t	X
ma-44	85	24	>	>	X
ma-44	85	25	a.	a.	PROPN
ma-44	85	26	next	next	ADV
ma-44	85	27	,	,	PUNCT
ma-44	85	28	we	we	PRON
ma-44	85	29	present	present	VERB
ma-44	85	30	the	the	DET
ma-44	85	31	ϕ-fractional	ϕ-fractional	ADJ
ma-44	85	32	integral	integral	ADJ
ma-44	85	33	and	and	CCONJ
ma-44	85	34	derivatives	derivative	NOUN
ma-44	85	35	of	of	ADP
ma-44	85	36	a	a	DET
ma-44	85	37	power	power	NOUN
ma-44	85	38	function	function	NOUN
ma-44	85	39	.	.	PUNCT
ma-44	86	1	proposition	proposition	NOUN
ma-44	86	2	1	1	NUM
ma-44	86	3	.	.	PUNCT
ma-44	87	1	let	let	VERB
ma-44	87	2	α	α	PRON
ma-44	87	3	≥	≥	NOUN
ma-44	87	4	0	0	NUM
ma-44	87	5	,	,	PUNCT
ma-44	87	6	σ	σ	X
ma-44	87	7	>	>	X
ma-44	87	8	0	0	PUNCT
ma-44	88	1	and	and	CCONJ
ma-44	88	2	t	t	PROPN
ma-44	88	3	>	>	PUNCT
ma-44	88	4	a.	a.	NOUN
ma-44	88	5	then	then	ADV
ma-44	88	6	,	,	PUNCT
ma-44	88	7	ϕ-fractional	ϕ-fractional	ADJ
ma-44	88	8	integral	integral	ADJ
ma-44	88	9	and	and	CCONJ
ma-44	88	10	derivative	derivative	NOUN
ma-44	88	11	of	of	ADP
ma-44	88	12	a	a	DET
ma-44	88	13	power	power	NOUN
ma-44	88	14	function	function	NOUN
ma-44	88	15	are	be	AUX
ma-44	88	16	given	give	VERB
ma-44	88	17	by(1	by(1	NOUN
ma-44	88	18	)	)	PUNCT
ma-44	88	19	iα,ϕ	iα,ϕ	NOUN
ma-44	88	20	a+	a+	PUNCT
ma-44	88	21	ϕσ−1(t	ϕσ−1(t	PROPN
ma-44	88	22	,	,	PUNCT
ma-44	88	23	a)(t	a)(t	X
ma-44	88	24	)	)	PUNCT
ma-44	88	25	=	=	SYM
ma-44	89	1	γ(σ	γ(σ	X
ma-44	89	2	)	)	PUNCT
ma-44	89	3	γ(α+σ)ϕσ+α−1(t	γ(α+σ)ϕσ+α−1(t	NOUN
ma-44	89	4	,	,	PUNCT
ma-44	89	5	a).(2	a).(2	VERB
ma-44	89	6	)	)	PUNCT
ma-44	89	7	hdα	hdα	ADJ
ma-44	89	8	,	,	PUNCT
ma-44	89	9	β;ϕ	β;ϕ	NUM
ma-44	89	10	a+	a+	PUNCT
ma-44	90	1	ϕσ−1(t	ϕσ−1(t	PROPN
ma-44	90	2	,	,	PUNCT
ma-44	90	3	a)(t	a)(t	X
ma-44	90	4	)	)	PUNCT
ma-44	90	5	=	=	SYM
ma-44	91	1	γ(σ	γ(σ	X
ma-44	91	2	)	)	PUNCT
ma-44	91	3	γ(σ−α)ϕσ−α−1(t	γ(σ−α)ϕσ−α−1(t	PROPN
ma-44	91	4	,	,	PUNCT
ma-44	91	5	a	a	PRON
ma-44	91	6	)	)	PUNCT
ma-44	91	7	,	,	PUNCT
ma-44	91	8	n	n	CCONJ
ma-44	91	9	−	−	PROPN
ma-44	91	10	1	1	NUM
ma-44	91	11	<	<	X
ma-44	91	12	α	α	X
ma-44	91	13	<	<	X
ma-44	91	14	n	n	PROPN
ma-44	91	15	,	,	PUNCT
ma-44	91	16	σ	σ	PROPN
ma-44	91	17	>	>	X
ma-44	91	18	n.	n.	PROPN
ma-44	91	19	lemma	lemma	PROPN
ma-44	92	1	2	2	NUM
ma-44	92	2	.	.	PUNCT
ma-44	93	1	if	if	SCONJ
ma-44	93	2	u	u	PROPN
ma-44	93	3	∈	∈	PROPN
ma-44	93	4	cn([a	cn([a	PROPN
ma-44	93	5	,	,	PUNCT
ma-44	93	6	b],r	b],r	NOUN
ma-44	93	7	)	)	PUNCT
ma-44	93	8	,	,	PUNCT
ma-44	93	9	n	n	CCONJ
ma-44	94	1	−	−	PROPN
ma-44	94	2	1	1	NUM
ma-44	94	3	<	<	X
ma-44	94	4	α	α	X
ma-44	94	5	<	<	X
ma-44	94	6	n	n	CCONJ
ma-44	94	7	,	,	PUNCT
ma-44	94	8	0	0	NUM
ma-44	94	9	≤	≤	NUM
ma-44	95	1	β	β	X
ma-44	95	2	≤	≤	NUM
ma-44	95	3	1	1	NUM
ma-44	95	4	and	and	CCONJ
ma-44	95	5	γ	γ	X
ma-44	95	6	=	=	SYM
ma-44	95	7	α+	α+	X
ma-44	95	8	β(n	β(n	NOUN
ma-44	95	9	−	−	PROPN
ma-44	95	10	α	α	X
ma-44	95	11	)	)	PUNCT
ma-44	95	12	.	.	PUNCT
ma-44	96	1	then	then	ADV
ma-44	96	2	iα,ϕ	iα,ϕ	X
ma-44	96	3	a+	a+	PUNCT
ma-44	96	4	(	(	PUNCT
ma-44	96	5	hdα	hdα	ADJ
ma-44	96	6	,	,	PUNCT
ma-44	96	7	β;ϕ	β;ϕ	NUM
ma-44	96	8	a+	a+	PUNCT
ma-44	96	9	u)(t	u)(t	ADJ
ma-44	96	10	)	)	PUNCT
ma-44	96	11	=	=	SYM
ma-44	97	1	u(t)−	u(t)−	PROPN
ma-44	97	2	k	k	PROPN
ma-44	98	1	=	=	PROPN
ma-44	98	2	n∑	n∑	NOUN
ma-44	98	3	k=1	k=1	X
ma-44	99	1	ϕγ−k(t	ϕγ−k(t	PROPN
ma-44	99	2	,	,	PUNCT
ma-44	99	3	s	s	X
ma-44	99	4	)	)	PUNCT
ma-44	99	5	γ(γ	γ(γ	PROPN
ma-44	99	6	−	−	PROPN
ma-44	100	1	k	k	PROPN
ma-44	100	2	+	+	CCONJ
ma-44	100	3	1	1	X
ma-44	100	4	)	)	PUNCT
ma-44	100	5	∇[n−k	∇[n−k	PROPN
ma-44	100	6	]	]	PUNCT
ma-44	100	7	ϕ	ϕ	NOUN
ma-44	100	8	i(1−β)(n−α);ϕ	i(1−β)(n−α);ϕ	ADV
ma-44	100	9	a+	a+	PUNCT
ma-44	100	10	u(a	u(a	PROPN
ma-44	100	11	)	)	PUNCT
ma-44	100	12	,	,	PUNCT
ma-44	100	13	t	t	PROPN
ma-44	100	14	∈	∈	PROPN
ma-44	101	1	[	[	X
ma-44	101	2	a	a	X
ma-44	101	3	,	,	PUNCT
ma-44	101	4	b	b	NOUN
ma-44	101	5	]	]	X
ma-44	101	6	,	,	PUNCT
ma-44	101	7	where	where	SCONJ
ma-44	101	8	∇[n	∇[n	PROPN
ma-44	101	9	]	]	X
ma-44	101	10	ϕ	ϕ	X
ma-44	101	11	u(t	u(t	PROPN
ma-44	101	12	)	)	PUNCT
ma-44	101	13	:	:	PUNCT
ma-44	102	1	=	=	SYM
ma-44	102	2	(	(	PUNCT
ma-44	102	3	1	1	NUM
ma-44	102	4	ψ′(t	ψ′(t	NOUN
ma-44	102	5	)	)	PUNCT
ma-44	102	6	d	d	NOUN
ma-44	102	7	dt	dt	NOUN
ma-44	102	8	)	)	PUNCT
ma-44	102	9	n	n	PRON
ma-44	102	10	u(t	u(t	NOUN
ma-44	102	11	)	)	PUNCT
ma-44	102	12	.	.	PUNCT
ma-44	103	1	lemma	lemma	PROPN
ma-44	103	2	3	3	X
ma-44	103	3	.	.	PUNCT
ma-44	104	1	let	let	VERB
ma-44	105	1	u	u	PRON
ma-44	105	2	∈	∈	PROPN
ma-44	105	3	cn	cn	PUNCT
ma-44	106	1	[	[	X
ma-44	106	2	a	a	X
ma-44	106	3	,	,	PUNCT
ma-44	106	4	b	b	NOUN
ma-44	106	5	]	]	X
ma-44	106	6	and	and	CCONJ
ma-44	106	7	0	0	NUM
ma-44	106	8	<	<	X
ma-44	106	9	q	q	X
ma-44	106	10	<	<	X
ma-44	106	11	1	1	NUM
ma-44	106	12	,	,	PUNCT
ma-44	106	13	we	we	PRON
ma-44	106	14	have∣∣iq;ϕ	have∣∣iq;ϕ	ADV
ma-44	106	15	a+	a+	PUNCT
ma-44	106	16	u(t2)−	u(t2)−	NOUN
ma-44	106	17	iq;ϕ	iq;ϕ	ADV
ma-44	106	18	a+	a+	PUNCT
ma-44	106	19	u(t1	u(t1	NOUN
ma-44	106	20	)	)	PUNCT
ma-44	106	21	∣∣	∣∣	VERB
ma-44	106	22	≤	≤	ADV
ma-44	106	23	2	2	NUM
ma-44	106	24	‖u‖	‖u‖	PROPN
ma-44	106	25	γ	γ	X
ma-44	106	26	(	(	PUNCT
ma-44	106	27	q	q	PROPN
ma-44	106	28	+	+	NUM
ma-44	106	29	1	1	NUM
ma-44	106	30	)	)	PUNCT
ma-44	106	31	ϕq(t2	ϕq(t2	NOUN
ma-44	106	32	,	,	PUNCT
ma-44	106	33	t1	t1	NOUN
ma-44	106	34	)	)	PUNCT
ma-44	106	35	.	.	PUNCT
ma-44	107	1	lemma	lemma	PROPN
ma-44	107	2	4	4	NUM
ma-44	107	3	.	.	PUNCT
ma-44	108	1	(	(	PUNCT
ma-44	108	2	[	[	X
ma-44	108	3	14	14	NUM
ma-44	108	4	]	]	PUNCT
ma-44	108	5	)	)	PUNCT
ma-44	108	6	for	for	ADP
ma-44	108	7	the	the	DET
ma-44	108	8	p−laplacian	p−laplacian	ADJ
ma-44	108	9	operator	operator	NOUN
ma-44	108	10	ψp	ψp	NOUN
ma-44	108	11	,	,	PUNCT
ma-44	108	12	the	the	DET
ma-44	108	13	following	follow	VERB
ma-44	108	14	conditions	condition	NOUN
ma-44	108	15	hold	hold	VERB
ma-44	108	16	true	true	ADJ
ma-44	108	17	:	:	PUNCT
ma-44	108	18	(	(	PUNCT
ma-44	108	19	1	1	X
ma-44	108	20	)	)	PUNCT
ma-44	108	21	if	if	SCONJ
ma-44	108	22	|δ1|	|δ1|	ADJ
ma-44	108	23	,	,	PUNCT
ma-44	108	24	|δ2|	|δ2|	NOUN
ma-44	108	25	≥	≥	PROPN
ma-44	108	26	ρ	ρ	PROPN
ma-44	108	27	>	>	X
ma-44	108	28	0	0	PROPN
ma-44	108	29	,	,	PUNCT
ma-44	108	30	1	1	NUM
ma-44	108	31	<	<	X
ma-44	108	32	p	p	X
ma-44	108	33	≤	≤	NUM
ma-44	108	34	2	2	NUM
ma-44	108	35	,	,	PUNCT
ma-44	108	36	δ1δ2	δ1δ2	X
ma-44	108	37	>	>	X
ma-44	108	38	0	0	PROPN
ma-44	108	39	,	,	PUNCT
ma-44	108	40	then	then	ADV
ma-44	108	41	|ψp(δ1)−	|ψp(δ1)−	PROPN
ma-44	108	42	ψp(δ2)|	ψp(δ2)|	PROPN
ma-44	108	43	≤	≤	NOUN
ma-44	108	44	(	(	PUNCT
ma-44	108	45	p	p	NOUN
ma-44	108	46	−	−	PROPN
ma-44	108	47	1	1	NUM
ma-44	108	48	)	)	PUNCT
ma-44	108	49	ρp−2	ρp−2	NOUN
ma-44	108	50	|δ1	|δ1	NOUN
ma-44	108	51	−	−	ADP
ma-44	108	52	δ2|	δ2|	NOUN
ma-44	108	53	.	.	PUNCT
ma-44	109	1	(	(	PUNCT
ma-44	109	2	2	2	X
ma-44	109	3	)	)	PUNCT
ma-44	109	4	if	if	SCONJ
ma-44	109	5	p	p	PROPN
ma-44	109	6	>	>	X
ma-44	109	7	2	2	NUM
ma-44	109	8	,	,	PUNCT
ma-44	109	9	|δ1|	|δ1|	NOUN
ma-44	109	10	,	,	PUNCT
ma-44	109	11	|δ2|	|δ2|	NOUN
ma-44	109	12	≤	≤	NUM
ma-44	109	13	ρ∗	ρ∗	PROPN
ma-44	109	14	>	>	X
ma-44	109	15	0	0	PROPN
ma-44	109	16	,	,	PUNCT
ma-44	109	17	then	then	ADV
ma-44	109	18	|ψp(δ1)−	|ψp(δ1)−	PROPN
ma-44	109	19	ψp(δ2)|	ψp(δ2)|	PROPN
ma-44	109	20	≤	≤	NOUN
ma-44	109	21	(	(	PUNCT
ma-44	109	22	p	p	NOUN
ma-44	109	23	−	−	PROPN
ma-44	109	24	1	1	NUM
ma-44	109	25	)	)	PUNCT
ma-44	109	26	ρp−2	ρp−2	NOUN
ma-44	109	27	∗	∗	NOUN
ma-44	109	28	|δ1	|δ1	PROPN
ma-44	110	1	−	−	PROPN
ma-44	110	2	δ2|	δ2|	NOUN
ma-44	110	3	.	.	PUNCT
ma-44	111	1	lemma	lemma	PROPN
ma-44	111	2	5	5	NUM
ma-44	111	3	.	.	PUNCT
ma-44	112	1	[	[	X
ma-44	112	2	9	9	NUM
ma-44	112	3	]	]	PUNCT
ma-44	112	4	for	for	ADP
ma-44	112	5	nonnegative	nonnegative	ADJ
ma-44	112	6	ai	ai	INTJ
ma-44	112	7	,	,	PUNCT
ma-44	112	8	i	i	PRON
ma-44	112	9	=	=	NOUN
ma-44	112	10	1	1	NUM
ma-44	112	11	,	,	PUNCT
ma-44	112	12	...	...	PUNCT
ma-44	112	13	,	,	PUNCT
ma-44	112	14	k	k	X
ma-44	112	15	,	,	PUNCT
ma-44	112	16	(	(	PUNCT
ma-44	112	17	k∑	k∑	VERB
ma-44	112	18	i=1	i=1	PROPN
ma-44	112	19	ai	ai	VERB
ma-44	112	20	)	)	PUNCT
ma-44	112	21	q	q	PROPN
ma-44	112	22	≤	≤	ADV
ma-44	112	23	kq−1	kq−1	ADV
ma-44	112	24	(	(	PUNCT
ma-44	112	25	k∑	k∑	NOUN
ma-44	112	26	i=1	i=1	PROPN
ma-44	112	27	aqi	aqi	PROPN
ma-44	112	28	)	)	PUNCT
ma-44	112	29	,	,	PUNCT
ma-44	112	30	q	q	X
ma-44	112	31	≥	≥	NOUN
ma-44	112	32	1	1	NUM
ma-44	112	33	.	.	PUNCT
ma-44	112	34	eur	eur	PROPN
ma-44	112	35	.	.	PUNCT
ma-44	113	1	j.	j.	PROPN
ma-44	113	2	math	math	PROPN
ma-44	113	3	.	.	PUNCT
ma-44	114	1	anal	anal	ADJ
ma-44	114	2	.	.	PUNCT
ma-44	115	1	1	1	NUM
ma-44	115	2	(	(	PUNCT
ma-44	115	3	2021	2021	NUM
ma-44	115	4	)	)	PUNCT
ma-44	115	5	168	168	NUM
ma-44	115	6	lemma	lemma	PROPN
ma-44	115	7	6	6	NUM
ma-44	115	8	.	.	PUNCT
ma-44	115	9	let	let	VERB
ma-44	115	10	a	a	DET
ma-44	115	11	≥	≥	NOUN
ma-44	115	12	0	0	NUM
ma-44	115	13	,	,	PUNCT
ma-44	115	14	1	1	NUM
ma-44	115	15	<	<	X
ma-44	115	16	α1	α1	PROPN
ma-44	115	17	,	,	PUNCT
ma-44	115	18	α2	α2	ADV
ma-44	115	19	<	<	X
ma-44	115	20	2	2	NUM
ma-44	115	21	,	,	PUNCT
ma-44	115	22	0	0	NUM
ma-44	115	23	≤	≤	NUM
ma-44	115	24	β1	β1	NOUN
ma-44	115	25	,	,	PUNCT
ma-44	115	26	β2	β2	VERB
ma-44	115	27	≤	≤	NOUN
ma-44	115	28	1	1	NUM
ma-44	115	29	,	,	PUNCT
ma-44	115	30	and	and	CCONJ
ma-44	115	31	2−	2−	NUM
ma-44	115	32	γ1	γ1	NOUN
ma-44	115	33	=	=	SYM
ma-44	115	34	(	(	PUNCT
ma-44	115	35	1−	1−	NUM
ma-44	115	36	β1	β1	PROPN
ma-44	115	37	)	)	PUNCT
ma-44	115	38	(	(	PUNCT
ma-44	115	39	2−	2−	NUM
ma-44	115	40	α1	α1	NOUN
ma-44	115	41	)	)	PUNCT
ma-44	115	42	,	,	PUNCT
ma-44	115	43	2−	2−	NUM
ma-44	115	44	γ2	γ2	NOUN
ma-44	115	45	=	=	SYM
ma-44	115	46	(	(	PUNCT
ma-44	115	47	1−	1−	NUM
ma-44	115	48	β2	β2	NOUN
ma-44	115	49	)	)	PUNCT
ma-44	115	50	(	(	PUNCT
ma-44	115	51	2−	2−	NUM
ma-44	115	52	α2	α2	ADJ
ma-44	115	53	)	)	PUNCT
ma-44	115	54	.	.	PUNCT
ma-44	116	1	for	for	ADP
ma-44	116	2	f	f	PROPN
ma-44	116	3	∈	∈	PROPN
ma-44	116	4	c(j	c(j	PROPN
ma-44	116	5	,	,	PUNCT
ma-44	116	6	,	,	PUNCT
ma-44	116	7	r	r	NOUN
ma-44	116	8	,	,	PUNCT
ma-44	116	9	r	r	NOUN
ma-44	116	10	)	)	PUNCT
ma-44	116	11	,	,	PUNCT
ma-44	116	12	the	the	DET
ma-44	116	13	unique	unique	ADJ
ma-44	116	14	solution	solution	NOUN
ma-44	116	15	of	of	ADP
ma-44	116	16	the	the	DET
ma-44	116	17	sequential	sequential	ADJ
ma-44	116	18	hilfer	hilfer	NOUN
ma-44	116	19	fractional	fractional	ADJ
ma-44	116	20	boundary	boundary	ADJ
ma-44	116	21	value	value	NOUN
ma-44	116	22	problem	problem	NOUN
ma-44	116	23	hdα1,β1;ϕ	hdα1,β1;ϕ	PROPN
ma-44	116	24	a+	a+	PUNCT
ma-44	116	25	ψp	ψp	ADP
ma-44	116	26	(	(	PUNCT
ma-44	116	27	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	116	28	a+	a+	PUNCT
ma-44	116	29	u	u	NOUN
ma-44	116	30	)	)	PUNCT
ma-44	116	31	(	(	PUNCT
ma-44	116	32	t	t	NOUN
ma-44	116	33	)	)	PUNCT
ma-44	116	34	=	=	SYM
ma-44	116	35	f	f	PROPN
ma-44	116	36	(	(	PUNCT
ma-44	116	37	t	t	PROPN
ma-44	116	38	)	)	PUNCT
ma-44	116	39	,	,	PUNCT
ma-44	116	40	t	t	PROPN
ma-44	116	41	∈	∈	PROPN
ma-44	117	1	j	j	PROPN
ma-44	118	1	=	=	PUNCT
ma-44	119	1	[	[	X
ma-44	119	2	a	a	X
ma-44	119	3	,	,	PUNCT
ma-44	119	4	b	b	NOUN
ma-44	119	5	]	]	X
ma-44	119	6	,	,	PUNCT
ma-44	119	7	(	(	PUNCT
ma-44	119	8	2.2	2.2	NUM
ma-44	119	9	)	)	PUNCT
ma-44	119	10			NOUN
ma-44	119	11	u(a	u(a	PROPN
ma-44	119	12	)	)	PUNCT
ma-44	119	13	=	=	SYM
ma-44	119	14	0	0	NUM
ma-44	119	15	,	,	PUNCT
ma-44	119	16	u(b	u(b	NUM
ma-44	119	17	)	)	PUNCT
ma-44	120	1	=	=	PUNCT
ma-44	120	2	n∑	n∑	PROPN
ma-44	120	3	i=1	i=1	PROPN
ma-44	121	1	λiu	λiu	PROPN
ma-44	121	2	(	(	PUNCT
ma-44	121	3	ζi	ζi	PROPN
ma-44	121	4	)	)	PUNCT
ma-44	121	5	,	,	PUNCT
ma-44	121	6	ψp	ψp	ADP
ma-44	121	7	(	(	PUNCT
ma-44	121	8	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	121	9	a+	a+	PUNCT
ma-44	121	10	u	u	NOUN
ma-44	121	11	)	)	PUNCT
ma-44	121	12	(	(	PUNCT
ma-44	121	13	a	a	X
ma-44	121	14	)	)	PUNCT
ma-44	121	15	=	=	SYM
ma-44	121	16	0	0	NUM
ma-44	121	17	,	,	PUNCT
ma-44	121	18	and	and	CCONJ
ma-44	121	19	ψp	ψp	PROPN
ma-44	121	20	(	(	PUNCT
ma-44	121	21	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	121	22	a+	a+	PUNCT
ma-44	121	23	u(b	u(b	NOUN
ma-44	121	24	)	)	PUNCT
ma-44	121	25	)	)	PUNCT
ma-44	122	1	=	=	PRON
ma-44	122	2	iρ;ϕ	iρ;ϕ	VERB
ma-44	122	3	a+	a+	PUNCT
ma-44	122	4	u	u	NOUN
ma-44	122	5	(	(	PUNCT
ma-44	122	6	ζ	ζ	NOUN
ma-44	122	7	)	)	PUNCT
ma-44	122	8	,	,	PUNCT
ma-44	122	9	a	a	DET
ma-44	122	10	<	<	X
ma-44	122	11	ζ	ζ	NOUN
ma-44	122	12	,	,	PUNCT
ma-44	122	13	ζi	ζi	ADP
ma-44	122	14	<	<	X
ma-44	122	15	b	b	PROPN
ma-44	122	16	,	,	PUNCT
ma-44	122	17	(	(	PUNCT
ma-44	122	18	2.3	2.3	NUM
ma-44	122	19	)	)	PUNCT
ma-44	122	20	is	be	AUX
ma-44	122	21	given	give	VERB
ma-44	122	22	by	by	ADP
ma-44	122	23	u(t	u(t	NOUN
ma-44	122	24	)	)	PUNCT
ma-44	122	25	=	=	SYM
ma-44	122	26	1	1	NUM
ma-44	122	27	γ(α2	γ(α2	NOUN
ma-44	122	28	)	)	PUNCT
ma-44	123	1	t∫	t∫	DET
ma-44	123	2	a	a	DET
ma-44	123	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	123	4	,	,	PUNCT
ma-44	123	5	s)x(s	s)x(s	NOUN
ma-44	123	6	,	,	PUNCT
ma-44	123	7	a)ds	a)ds	PROPN
ma-44	123	8	−	−	PROPN
ma-44	123	9	ϕγ2−1	ϕγ2−1	NOUN
ma-44	123	10	(	(	PUNCT
ma-44	123	11	t	t	PROPN
ma-44	123	12	,	,	PUNCT
ma-44	123	13	a	a	PRON
ma-44	123	14	)	)	PUNCT
ma-44	123	15	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	123	16	(	(	PUNCT
ma-44	123	17	b	b	NOUN
ma-44	123	18	,	,	PUNCT
ma-44	123	19	a	a	PRON
ma-44	123	20	)	)	PUNCT
ma-44	123	21	b∫	b∫	NOUN
ma-44	123	22	a	a	DET
ma-44	123	23	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	123	24	,	,	PUNCT
ma-44	123	25	t)x(t	t)x(t	PROPN
ma-44	123	26	,	,	PUNCT
ma-44	123	27	a)dt	a)dt	PROPN
ma-44	123	28	+	+	NUM
ma-44	123	29	ϕγ2−1	ϕγ2−1	NOUN
ma-44	123	30	(	(	PUNCT
ma-44	123	31	t	t	PROPN
ma-44	123	32	,	,	PUNCT
ma-44	123	33	a	a	PRON
ma-44	123	34	)	)	PUNCT
ma-44	123	35	ϕγ2−1	ϕγ2−1	NOUN
ma-44	123	36	(	(	PUNCT
ma-44	123	37	b	b	NOUN
ma-44	123	38	,	,	PUNCT
ma-44	123	39	a	a	PRON
ma-44	123	40	)	)	PUNCT
ma-44	123	41	n∑	n∑	NOUN
ma-44	123	42	i=1	i=1	PROPN
ma-44	124	1	λiu	λiu	PROPN
ma-44	125	1	(	(	PUNCT
ma-44	125	2	ζi	ζi	PROPN
ma-44	125	3	)	)	PUNCT
ma-44	125	4	.	.	PUNCT
ma-44	126	1	where	where	SCONJ
ma-44	126	2	x(s	x(s	PROPN
ma-44	126	3	,	,	PUNCT
ma-44	126	4	a	a	PRON
ma-44	126	5	)	)	PUNCT
ma-44	126	6	=	=	PUNCT
ma-44	126	7	ψq	ψq	PROPN
ma-44	126	8			PROPN
ma-44	126	9	1	1	NUM
ma-44	126	10	γ(α1	γ(α1	NOUN
ma-44	126	11	)	)	PUNCT
ma-44	126	12	s∫	s∫	PROPN
ma-44	126	13	a	a	DET
ma-44	126	14	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(s	PROPN
ma-44	126	15	,	,	PUNCT
ma-44	126	16	z)f	z)f	X
ma-44	126	17	(	(	PUNCT
ma-44	126	18	z)dz	z)dz	PROPN
ma-44	126	19	+	+	CCONJ
ma-44	126	20	(	(	PUNCT
ma-44	126	21	iρ;ϕ	iρ;ϕ	VERB
ma-44	126	22	0	0	NUM
ma-44	126	23	+	+	NUM
ma-44	126	24	u	u	SYM
ma-44	126	25	(	(	PUNCT
ma-44	126	26	ζ)−	ζ)−	PROPN
ma-44	126	27	iα1;ϕ	iα1;ϕ	PROPN
ma-44	126	28	0	0	PROPN
ma-44	126	29	+	+	NUM
ma-44	126	30	f	f	X
ma-44	126	31	(	(	PUNCT
ma-44	126	32	b	b	NOUN
ma-44	126	33	)	)	PUNCT
ma-44	126	34	)	)	PUNCT
ma-44	126	35	ϕγ1−1	ϕγ1−1	INTJ
ma-44	126	36	(	(	PUNCT
ma-44	126	37	b	b	NOUN
ma-44	126	38	,	,	PUNCT
ma-44	126	39	a	a	PRON
ma-44	126	40	)	)	PUNCT
ma-44	126	41	ϕγ1−1	ϕγ1−1	NOUN
ma-44	126	42	(	(	PUNCT
ma-44	126	43	s	s	PROPN
ma-44	126	44	,	,	PUNCT
ma-44	126	45	a	a	PRON
ma-44	126	46	)	)	PUNCT
ma-44	126	47			PROPN
ma-44	126	48	iρ;ϕ	iρ;ϕ	VERB
ma-44	126	49	0	0	NUM
ma-44	126	50	+	+	NUM
ma-44	126	51	u	u	SYM
ma-44	126	52	(	(	PUNCT
ma-44	126	53	ζ	ζ	NOUN
ma-44	126	54	)	)	PUNCT
ma-44	126	55	=	=	SYM
ma-44	126	56	1	1	NUM
ma-44	126	57	γ(ρ	γ(ρ	PROPN
ma-44	126	58	)	)	PUNCT
ma-44	126	59	ζ∫	ζ∫	NOUN
ma-44	126	60	a	a	DET
ma-44	126	61	ϕ′(s)ϕρ(ζ	ϕ′(s)ϕρ(ζ	NOUN
ma-44	126	62	,	,	PUNCT
ma-44	126	63	s)u	s)u	X
ma-44	126	64	(	(	PUNCT
ma-44	126	65	s	s	X
ma-44	126	66	)	)	PUNCT
ma-44	126	67	ds	ds	ADJ
ma-44	126	68	,	,	PUNCT
ma-44	126	69	iα1;ϕ	iα1;ϕ	NOUN
ma-44	126	70	0	0	PROPN
ma-44	126	71	+	+	NUM
ma-44	126	72	f	f	X
ma-44	126	73	(	(	PUNCT
ma-44	126	74	b	b	NOUN
ma-44	126	75	)	)	PUNCT
ma-44	126	76	=	=	SYM
ma-44	126	77	1	1	NUM
ma-44	126	78	γ(α1	γ(α1	NOUN
ma-44	126	79	)	)	PUNCT
ma-44	126	80	b∫	b∫	PROPN
ma-44	126	81	a	a	DET
ma-44	126	82	ϕ′(s)ϕα1−1(b	ϕ′(s)ϕα1−1(b	PROPN
ma-44	126	83	,	,	PUNCT
ma-44	126	84	s)f	s)f	NUM
ma-44	126	85	(	(	PUNCT
ma-44	126	86	s)ds	s)ds	PROPN
ma-44	126	87	.	.	PUNCT
ma-44	126	88	proof	proof	NOUN
ma-44	126	89	.	.	PUNCT
ma-44	127	1	assume	assume	VERB
ma-44	127	2	that	that	SCONJ
ma-44	127	3	u	u	PRON
ma-44	127	4	is	be	AUX
ma-44	127	5	a	a	DET
ma-44	127	6	solution	solution	NOUN
ma-44	127	7	of	of	ADP
ma-44	127	8	the	the	DET
ma-44	127	9	sequential	sequential	ADJ
ma-44	127	10	nonlocal	nonlocal	ADJ
ma-44	127	11	boundary	boundary	ADJ
ma-44	127	12	value	value	NOUN
ma-44	127	13	problems	problem	NOUN
ma-44	127	14	(	(	PUNCT
ma-44	127	15	3.6	3.6	NUM
ma-44	127	16	)	)	PUNCT
ma-44	127	17	and(2.3	and(2.3	NUM
ma-44	127	18	)	)	PUNCT
ma-44	127	19	.	.	PUNCT
ma-44	128	1	applying	apply	VERB
ma-44	128	2	the	the	DET
ma-44	128	3	two	two	NUM
ma-44	128	4	operators	operator	NOUN
ma-44	128	5	iα1;ϕ	iα1;ϕ	AUX
ma-44	128	6	a+	a+	PUNCT
ma-44	128	7	,	,	PUNCT
ma-44	128	8	iα2;ϕ	iα2;ϕ	PROPN
ma-44	128	9	a+	a+	PUNCT
ma-44	128	10	to	to	ADP
ma-44	128	11	both	both	DET
ma-44	128	12	sides	side	NOUN
ma-44	128	13	of	of	ADP
ma-44	128	14	equation	equation	NOUN
ma-44	128	15	(	(	PUNCT
ma-44	128	16	3.6	3.6	NUM
ma-44	128	17	)	)	PUNCT
ma-44	128	18	and	and	CCONJ
ma-44	128	19	using	use	VERB
ma-44	128	20	lemma	lemma	PROPN
ma-44	128	21	2and	2and	NUM
ma-44	128	22	proposition	proposition	NOUN
ma-44	128	23	1	1	NUM
ma-44	128	24	,	,	PUNCT
ma-44	128	25	we	we	PRON
ma-44	128	26	obtain	obtain	VERB
ma-44	128	27	ψp	ψp	ADP
ma-44	129	1	(	(	PUNCT
ma-44	129	2	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	129	3	a+	a+	PUNCT
ma-44	129	4	u	u	NOUN
ma-44	129	5	)	)	PUNCT
ma-44	129	6	(	(	PUNCT
ma-44	129	7	t	t	NOUN
ma-44	129	8	)	)	PUNCT
ma-44	130	1	=	=	PUNCT
ma-44	130	2	iα1;ϕ	iα1;ϕ	PROPN
ma-44	130	3	a+	a+	PUNCT
ma-44	130	4	f	f	PROPN
ma-44	130	5	(	(	PUNCT
ma-44	130	6	t	t	PROPN
ma-44	130	7	)	)	PUNCT
ma-44	130	8	+	+	CCONJ
ma-44	130	9	m0	m0	PROPN
ma-44	130	10	γ	γ	PROPN
ma-44	130	11	(	(	PUNCT
ma-44	130	12	γ1	γ1	PROPN
ma-44	130	13	−	−	PROPN
ma-44	130	14	1	1	NUM
ma-44	130	15	)	)	PUNCT
ma-44	130	16	ϕγ1−2	ϕγ1−2	NOUN
ma-44	130	17	(	(	PUNCT
ma-44	130	18	t	t	PROPN
ma-44	130	19	,	,	PUNCT
ma-44	130	20	a	a	PRON
ma-44	130	21	)	)	PUNCT
ma-44	130	22	+	+	CCONJ
ma-44	130	23	m1	m1	PROPN
ma-44	130	24	γ	γ	PROPN
ma-44	130	25	(	(	PUNCT
ma-44	130	26	γ1	γ1	PROPN
ma-44	130	27	)	)	PUNCT
ma-44	130	28	ϕγ1−1	ϕγ1−1	NOUN
ma-44	130	29	(	(	PUNCT
ma-44	130	30	t	t	PROPN
ma-44	130	31	,	,	PUNCT
ma-44	130	32	a	a	PRON
ma-44	130	33	)	)	PUNCT
ma-44	130	34	,	,	PUNCT
ma-44	130	35	(	(	PUNCT
ma-44	130	36	2.4	2.4	NUM
ma-44	130	37	)	)	PUNCT
ma-44	130	38	where	where	SCONJ
ma-44	130	39	m0	m0	NOUN
ma-44	130	40	,	,	PUNCT
ma-44	130	41	m1	m1	PROPN
ma-44	130	42	∈	∈	PROPN
ma-44	130	43	r	r	NOUN
ma-44	130	44	,	,	PUNCT
ma-44	130	45	and	and	CCONJ
ma-44	130	46	2−	2−	NUM
ma-44	130	47	γ1	γ1	NOUN
ma-44	130	48	=	=	SYM
ma-44	130	49	(	(	PUNCT
ma-44	130	50	1−	1−	NUM
ma-44	130	51	β1	β1	PROPN
ma-44	130	52	)	)	PUNCT
ma-44	130	53	(	(	PUNCT
ma-44	130	54	2−	2−	NUM
ma-44	130	55	α1	α1	NOUN
ma-44	130	56	)	)	PUNCT
ma-44	130	57	.	.	PUNCT
ma-44	131	1	from	from	ADP
ma-44	131	2	the	the	DET
ma-44	131	3	boundary	boundary	ADJ
ma-44	131	4	condition	condition	NOUN
ma-44	131	5	ψp	ψp	ADP
ma-44	131	6	(	(	PUNCT
ma-44	131	7	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	131	8	a+	a+	PUNCT
ma-44	131	9	u	u	NOUN
ma-44	131	10	)	)	PUNCT
ma-44	131	11	(	(	PUNCT
ma-44	131	12	a	a	X
ma-44	131	13	)	)	PUNCT
ma-44	131	14	=	=	SYM
ma-44	131	15	0	0	NUM
ma-44	131	16	,	,	PUNCT
ma-44	131	17	and	and	CCONJ
ma-44	131	18	if	if	SCONJ
ma-44	131	19	t	t	PROPN
ma-44	131	20	→	→	PUNCT
ma-44	131	21	a	a	DET
ma-44	131	22	then	then	ADV
ma-44	131	23	ϕγ1−2	ϕγ1−2	NOUN
ma-44	131	24	(	(	PUNCT
ma-44	131	25	t	t	PROPN
ma-44	131	26	,	,	PUNCT
ma-44	131	27	a)→∞	a)→∞	PROPN
ma-44	131	28	,	,	PUNCT
ma-44	131	29	we	we	PRON
ma-44	131	30	get	get	VERB
ma-44	131	31	m0	m0	NOUN
ma-44	131	32	=	=	PUNCT
ma-44	131	33	0	0	NUM
ma-44	131	34	.	.	X
ma-44	132	1	eur	eur	PROPN
ma-44	132	2	.	.	PUNCT
ma-44	133	1	j.	j.	PROPN
ma-44	133	2	math	math	PROPN
ma-44	133	3	.	.	PUNCT
ma-44	134	1	anal	anal	ADJ
ma-44	134	2	.	.	PUNCT
ma-44	135	1	1	1	NUM
ma-44	135	2	(	(	PUNCT
ma-44	135	3	2021	2021	NUM
ma-44	135	4	)	)	PUNCT
ma-44	135	5	169	169	NUM
ma-44	135	6	and	and	CCONJ
ma-44	135	7	by	by	ADP
ma-44	135	8	ψp	ψp	X
ma-44	135	9	(	(	PUNCT
ma-44	135	10	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	135	11	a+	a+	PUNCT
ma-44	135	12	u	u	NOUN
ma-44	135	13	)	)	PUNCT
ma-44	135	14	(	(	PUNCT
ma-44	135	15	b	b	X
ma-44	135	16	)	)	PUNCT
ma-44	135	17	=	=	VERB
ma-44	135	18	iρ;ϕ	iρ;ϕ	VERB
ma-44	135	19	a+	a+	PUNCT
ma-44	135	20	u	u	NOUN
ma-44	135	21	(	(	PUNCT
ma-44	135	22	ζ	ζ	NOUN
ma-44	135	23	)	)	PUNCT
ma-44	135	24	,	,	PUNCT
ma-44	135	25	we	we	PRON
ma-44	135	26	obtain	obtain	VERB
ma-44	135	27	m1	m1	NOUN
ma-44	135	28	=	=	PUNCT
ma-44	135	29	γ	γ	X
ma-44	135	30	(	(	PUNCT
ma-44	135	31	γ1	γ1	PROPN
ma-44	135	32	)	)	PUNCT
ma-44	135	33	ϕγ1−1	ϕγ1−1	NOUN
ma-44	135	34	(	(	PUNCT
ma-44	135	35	b	b	NOUN
ma-44	135	36	,	,	PUNCT
ma-44	135	37	a	a	PRON
ma-44	135	38	)	)	PUNCT
ma-44	135	39	(	(	PUNCT
ma-44	135	40	iρ;ϕ	iρ;ϕ	VERB
ma-44	135	41	0	0	NUM
ma-44	135	42	+	+	NUM
ma-44	135	43	u	u	SYM
ma-44	135	44	(	(	PUNCT
ma-44	135	45	ζ)−	ζ)−	PROPN
ma-44	135	46	iα1;ϕ	iα1;ϕ	PROPN
ma-44	135	47	0	0	PROPN
ma-44	135	48	+	+	NUM
ma-44	135	49	f	f	X
ma-44	135	50	(	(	PUNCT
ma-44	135	51	b	b	NOUN
ma-44	135	52	)	)	PUNCT
ma-44	135	53	)	)	PUNCT
ma-44	135	54	.	.	PUNCT
ma-44	136	1	so	so	ADV
ma-44	136	2	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	136	3	a+	a+	PUNCT
ma-44	136	4	u(t	u(t	NOUN
ma-44	136	5	)	)	PUNCT
ma-44	136	6	=	=	PUNCT
ma-44	137	1	ψq	ψq	PROPN
ma-44	137	2	(	(	PUNCT
ma-44	137	3	iα1;ϕ	iα1;ϕ	PROPN
ma-44	137	4	a+	a+	PUNCT
ma-44	137	5	f	f	PROPN
ma-44	137	6	(	(	PUNCT
ma-44	137	7	t	t	PROPN
ma-44	137	8	)	)	PUNCT
ma-44	138	1	+	+	CCONJ
ma-44	138	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	138	3	(	(	PUNCT
ma-44	138	4	t	t	PROPN
ma-44	138	5	,	,	PUNCT
ma-44	138	6	a	a	PRON
ma-44	138	7	)	)	PUNCT
ma-44	138	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	138	9	(	(	PUNCT
ma-44	138	10	b	b	NOUN
ma-44	138	11	,	,	PUNCT
ma-44	138	12	a	a	PRON
ma-44	138	13	)	)	PUNCT
ma-44	138	14	(	(	PUNCT
ma-44	138	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	138	16	0	0	NUM
ma-44	138	17	+	+	NUM
ma-44	138	18	u	u	SYM
ma-44	138	19	(	(	PUNCT
ma-44	138	20	ζ)−	ζ)−	PROPN
ma-44	138	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	138	22	0	0	PROPN
ma-44	138	23	+	+	NUM
ma-44	138	24	f	f	X
ma-44	138	25	(	(	PUNCT
ma-44	138	26	b	b	NOUN
ma-44	138	27	)	)	PUNCT
ma-44	138	28	)	)	PUNCT
ma-44	138	29	)	)	PUNCT
ma-44	138	30	,	,	PUNCT
ma-44	138	31	by	by	ADP
ma-44	138	32	(	(	PUNCT
ma-44	138	33	2.4)we	2.4)we	NOUN
ma-44	138	34	have	have	AUX
ma-44	138	35	u(t	u(t	NOUN
ma-44	138	36	)	)	PUNCT
ma-44	138	37	=	=	PUNCT
ma-44	139	1	iα2;ϕ	iα2;ϕ	X
ma-44	139	2	a+	a+	PUNCT
ma-44	139	3	[	[	PUNCT
ma-44	139	4	ψq	ψq	X
ma-44	139	5	(	(	PUNCT
ma-44	139	6	iα1;ϕ	iα1;ϕ	PROPN
ma-44	139	7	a+	a+	PUNCT
ma-44	139	8	f	f	PROPN
ma-44	139	9	(	(	PUNCT
ma-44	139	10	t	t	PROPN
ma-44	139	11	)	)	PUNCT
ma-44	140	1	+	+	CCONJ
ma-44	140	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	140	3	(	(	PUNCT
ma-44	140	4	t	t	PROPN
ma-44	140	5	,	,	PUNCT
ma-44	140	6	a	a	PRON
ma-44	140	7	)	)	PUNCT
ma-44	140	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	140	9	(	(	PUNCT
ma-44	140	10	b	b	NOUN
ma-44	140	11	,	,	PUNCT
ma-44	140	12	a	a	PRON
ma-44	140	13	)	)	PUNCT
ma-44	140	14	(	(	PUNCT
ma-44	140	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	140	16	0	0	NUM
ma-44	140	17	+	+	NUM
ma-44	140	18	u	u	SYM
ma-44	140	19	(	(	PUNCT
ma-44	140	20	ζ)−	ζ)−	PROPN
ma-44	140	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	140	22	0	0	PROPN
ma-44	140	23	+	+	NUM
ma-44	140	24	f	f	X
ma-44	140	25	(	(	PUNCT
ma-44	140	26	b	b	NOUN
ma-44	140	27	)	)	PUNCT
ma-44	140	28	)	)	PUNCT
ma-44	140	29	)	)	PUNCT
ma-44	140	30	]	]	PUNCT
ma-44	141	1	+	+	CCONJ
ma-44	141	2	m2	m2	PROPN
ma-44	141	3	γ	γ	PROPN
ma-44	141	4	(	(	PUNCT
ma-44	141	5	γ2	γ2	NOUN
ma-44	141	6	−	−	PROPN
ma-44	141	7	1	1	NUM
ma-44	141	8	)	)	PUNCT
ma-44	141	9	ϕγ2−2	ϕγ2−2	NOUN
ma-44	141	10	(	(	PUNCT
ma-44	141	11	t	t	PROPN
ma-44	141	12	,	,	PUNCT
ma-44	141	13	a	a	PRON
ma-44	141	14	)	)	PUNCT
ma-44	141	15	+	+	CCONJ
ma-44	141	16	m3	m3	PROPN
ma-44	141	17	γ	γ	PROPN
ma-44	141	18	(	(	PUNCT
ma-44	141	19	γ2	γ2	PROPN
ma-44	141	20	)	)	PUNCT
ma-44	141	21	ϕγ2−1	ϕγ2−1	NOUN
ma-44	141	22	(	(	PUNCT
ma-44	141	23	t	t	PROPN
ma-44	141	24	,	,	PUNCT
ma-44	141	25	a	a	PRON
ma-44	141	26	)	)	PUNCT
ma-44	141	27	,	,	PUNCT
ma-44	141	28	where	where	SCONJ
ma-44	141	29	m2	m2	PROPN
ma-44	141	30	,	,	PUNCT
ma-44	141	31	m3	m3	PROPN
ma-44	141	32	∈	∈	PROPN
ma-44	141	33	r	r	NOUN
ma-44	141	34	,	,	PUNCT
ma-44	141	35	and	and	CCONJ
ma-44	141	36	2−	2−	NUM
ma-44	141	37	(	(	PUNCT
ma-44	141	38	1−	1−	NUM
ma-44	141	39	β2	β2	NOUN
ma-44	141	40	)	)	PUNCT
ma-44	141	41	(	(	PUNCT
ma-44	141	42	2−	2−	NUM
ma-44	141	43	α2	α2	ADJ
ma-44	141	44	)	)	PUNCT
ma-44	141	45	=	=	SYM
ma-44	142	1	γ2.and	γ2.and	PUNCT
ma-44	142	2	if	if	SCONJ
ma-44	142	3	t	t	PROPN
ma-44	142	4	→	→	PUNCT
ma-44	142	5	a	a	DET
ma-44	142	6	then	then	ADV
ma-44	142	7	ϕγ2−2	ϕγ2−2	NOUN
ma-44	142	8	(	(	PUNCT
ma-44	142	9	t	t	PROPN
ma-44	142	10	,	,	PUNCT
ma-44	142	11	a)→∞	a)→∞	PROPN
ma-44	142	12	,	,	PUNCT
ma-44	142	13	we	we	PRON
ma-44	142	14	getby	getby	VERB
ma-44	142	15	conditions	condition	VERB
ma-44	142	16	u(a	u(a	NOUN
ma-44	142	17	)	)	PUNCT
ma-44	142	18	=	=	SYM
ma-44	142	19	0	0	NUM
ma-44	142	20	,	,	PUNCT
ma-44	142	21	and	and	CCONJ
ma-44	142	22	lim	lim	PROPN
ma-44	142	23	t→0	t→0	PROPN
ma-44	142	24	tγ2−2	tγ2−2	PROPN
ma-44	142	25	=	=	PROPN
ma-44	142	26	∞	∞	PROPN
ma-44	142	27	,	,	PUNCT
ma-44	142	28	we	we	PRON
ma-44	142	29	get	get	VERB
ma-44	142	30	m2	m2	PROPN
ma-44	143	1	=	=	PROPN
ma-44	143	2	0	0	PROPN
ma-44	143	3	.	.	PUNCT
ma-44	144	1	so	so	ADV
ma-44	144	2	u(t	u(t	NOUN
ma-44	144	3	)	)	PUNCT
ma-44	144	4	=	=	PUNCT
ma-44	145	1	iα2;ϕ	iα2;ϕ	X
ma-44	145	2	a+	a+	PUNCT
ma-44	145	3	[	[	PUNCT
ma-44	145	4	ψq	ψq	X
ma-44	145	5	(	(	PUNCT
ma-44	145	6	iα1;ϕ	iα1;ϕ	PROPN
ma-44	145	7	a+	a+	PUNCT
ma-44	145	8	f	f	PROPN
ma-44	145	9	(	(	PUNCT
ma-44	145	10	t	t	PROPN
ma-44	145	11	)	)	PUNCT
ma-44	146	1	+	+	CCONJ
ma-44	146	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	146	3	(	(	PUNCT
ma-44	146	4	t	t	PROPN
ma-44	146	5	,	,	PUNCT
ma-44	146	6	a	a	PRON
ma-44	146	7	)	)	PUNCT
ma-44	146	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	146	9	(	(	PUNCT
ma-44	146	10	b	b	NOUN
ma-44	146	11	,	,	PUNCT
ma-44	146	12	a	a	PRON
ma-44	146	13	)	)	PUNCT
ma-44	146	14	(	(	PUNCT
ma-44	146	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	146	16	0	0	NUM
ma-44	146	17	+	+	NUM
ma-44	146	18	u	u	SYM
ma-44	146	19	(	(	PUNCT
ma-44	146	20	ζ)−	ζ)−	PROPN
ma-44	146	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	146	22	0	0	PROPN
ma-44	146	23	+	+	NUM
ma-44	146	24	f	f	X
ma-44	146	25	(	(	PUNCT
ma-44	146	26	b	b	NOUN
ma-44	146	27	)	)	PUNCT
ma-44	146	28	)	)	PUNCT
ma-44	146	29	)	)	PUNCT
ma-44	146	30	]	]	PUNCT
ma-44	147	1	+	+	CCONJ
ma-44	147	2	m3	m3	PROPN
ma-44	147	3	γ	γ	X
ma-44	147	4	(	(	PUNCT
ma-44	147	5	γ2	γ2	PROPN
ma-44	147	6	)	)	PUNCT
ma-44	147	7	ϕγ2−1	ϕγ2−1	NOUN
ma-44	147	8	(	(	PUNCT
ma-44	147	9	t	t	PROPN
ma-44	147	10	,	,	PUNCT
ma-44	147	11	a	a	PRON
ma-44	147	12	)	)	PUNCT
ma-44	147	13	.	.	PUNCT
ma-44	148	1	by	by	ADP
ma-44	148	2	conditions	condition	NOUN
ma-44	148	3	u(b	u(b	NOUN
ma-44	148	4	)	)	PUNCT
ma-44	148	5	=	=	SYM
ma-44	149	1	n∑	n∑	PROPN
ma-44	149	2	i=1	i=1	PROPN
ma-44	149	3	λiu	λiu	PROPN
ma-44	149	4	(	(	PUNCT
ma-44	149	5	ζi	ζi	PROPN
ma-44	149	6	)	)	PUNCT
ma-44	149	7	,	,	PUNCT
ma-44	149	8	we	we	PRON
ma-44	149	9	get	get	VERB
ma-44	149	10	m3	m3	PROPN
ma-44	149	11	=	=	PUNCT
ma-44	149	12	γ	γ	X
ma-44	149	13	(	(	PUNCT
ma-44	149	14	γ2	γ2	PROPN
ma-44	149	15	)	)	PUNCT
ma-44	149	16	ϕγ2−1	ϕγ2−1	NOUN
ma-44	149	17	(	(	PUNCT
ma-44	149	18	b	b	NOUN
ma-44	149	19	,	,	PUNCT
ma-44	149	20	a	a	PRON
ma-44	149	21	)	)	PUNCT
ma-44	149	22	n∑	n∑	NOUN
ma-44	150	1	i=1	i=1	PROPN
ma-44	151	1	λiu	λiu	PROPN
ma-44	152	1	(	(	PUNCT
ma-44	152	2	ζi	ζi	PROPN
ma-44	152	3	)	)	PUNCT
ma-44	152	4	−	−	PROPN
ma-44	152	5	γ	γ	PROPN
ma-44	152	6	(	(	PUNCT
ma-44	152	7	γ2	γ2	PROPN
ma-44	152	8	)	)	PUNCT
ma-44	152	9	ϕγ2−1	ϕγ2−1	NOUN
ma-44	152	10	(	(	PUNCT
ma-44	152	11	b	b	NOUN
ma-44	152	12	,	,	PUNCT
ma-44	152	13	a	a	PRON
ma-44	152	14	)	)	PUNCT
ma-44	152	15	iα2;ϕ	iα2;ϕ	NOUN
ma-44	152	16	a+	a+	PUNCT
ma-44	153	1	[	[	PUNCT
ma-44	153	2	ψq	ψq	X
ma-44	153	3	(	(	PUNCT
ma-44	153	4	iα1;ϕ	iα1;ϕ	PROPN
ma-44	153	5	a+	a+	PUNCT
ma-44	153	6	f	f	PROPN
ma-44	153	7	(	(	PUNCT
ma-44	153	8	t	t	PROPN
ma-44	153	9	)	)	PUNCT
ma-44	154	1	+	+	CCONJ
ma-44	154	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	154	3	(	(	PUNCT
ma-44	154	4	t	t	PROPN
ma-44	154	5	,	,	PUNCT
ma-44	154	6	a	a	PRON
ma-44	154	7	)	)	PUNCT
ma-44	154	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	154	9	(	(	PUNCT
ma-44	154	10	b	b	NOUN
ma-44	154	11	,	,	PUNCT
ma-44	154	12	a	a	PRON
ma-44	154	13	)	)	PUNCT
ma-44	154	14	(	(	PUNCT
ma-44	154	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	154	16	0	0	NUM
ma-44	154	17	+	+	NUM
ma-44	154	18	u	u	SYM
ma-44	154	19	(	(	PUNCT
ma-44	154	20	ζ)−	ζ)−	PROPN
ma-44	154	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	154	22	0	0	PROPN
ma-44	154	23	+	+	NUM
ma-44	154	24	f	f	X
ma-44	154	25	(	(	PUNCT
ma-44	154	26	b	b	NOUN
ma-44	154	27	)	)	PUNCT
ma-44	154	28	)	)	PUNCT
ma-44	154	29	)	)	PUNCT
ma-44	154	30	]	]	PUNCT
ma-44	155	1	t	t	PROPN
ma-44	155	2	=	=	SYM
ma-44	155	3	b	b	PROPN
ma-44	155	4	.	.	PUNCT
ma-44	156	1	then	then	ADV
ma-44	156	2	u(t	u(t	VERB
ma-44	156	3	)	)	PUNCT
ma-44	156	4	=	=	PUNCT
ma-44	157	1	iα2;ϕ	iα2;ϕ	X
ma-44	157	2	a+	a+	PUNCT
ma-44	157	3	[	[	PUNCT
ma-44	157	4	ψq	ψq	X
ma-44	157	5	(	(	PUNCT
ma-44	157	6	iα1;ϕ	iα1;ϕ	PROPN
ma-44	157	7	a+	a+	PUNCT
ma-44	157	8	f	f	PROPN
ma-44	157	9	(	(	PUNCT
ma-44	157	10	t	t	PROPN
ma-44	157	11	)	)	PUNCT
ma-44	158	1	+	+	CCONJ
ma-44	158	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	158	3	(	(	PUNCT
ma-44	158	4	t	t	PROPN
ma-44	158	5	,	,	PUNCT
ma-44	158	6	a	a	PRON
ma-44	158	7	)	)	PUNCT
ma-44	158	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	158	9	(	(	PUNCT
ma-44	158	10	b	b	NOUN
ma-44	158	11	,	,	PUNCT
ma-44	158	12	a	a	PRON
ma-44	158	13	)	)	PUNCT
ma-44	158	14	(	(	PUNCT
ma-44	158	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	158	16	0	0	NUM
ma-44	158	17	+	+	NUM
ma-44	158	18	u	u	SYM
ma-44	158	19	(	(	PUNCT
ma-44	158	20	ζ)−	ζ)−	PROPN
ma-44	158	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	158	22	0	0	PROPN
ma-44	158	23	+	+	NUM
ma-44	158	24	f	f	X
ma-44	158	25	(	(	PUNCT
ma-44	158	26	b	b	NOUN
ma-44	158	27	)	)	PUNCT
ma-44	158	28	)	)	PUNCT
ma-44	158	29	)	)	PUNCT
ma-44	158	30	]	]	PUNCT
ma-44	159	1	+	+	CCONJ
ma-44	159	2	ϕγ2−1	ϕγ2−1	NOUN
ma-44	159	3	(	(	PUNCT
ma-44	159	4	t	t	PROPN
ma-44	159	5	,	,	PUNCT
ma-44	159	6	a	a	PRON
ma-44	159	7	)	)	PUNCT
ma-44	159	8	ϕγ2−1	ϕγ2−1	NOUN
ma-44	159	9	(	(	PUNCT
ma-44	159	10	b	b	NOUN
ma-44	159	11	,	,	PUNCT
ma-44	159	12	a	a	PRON
ma-44	159	13	)	)	PUNCT
ma-44	159	14	n∑	n∑	NOUN
ma-44	159	15	i=1	i=1	PROPN
ma-44	160	1	λiu	λiu	PROPN
ma-44	160	2	(	(	PUNCT
ma-44	160	3	ζi	ζi	PROPN
ma-44	160	4	)	)	PUNCT
ma-44	160	5	−	−	PROPN
ma-44	160	6	ϕγ2−1	ϕγ2−1	NOUN
ma-44	160	7	(	(	PUNCT
ma-44	160	8	t	t	PROPN
ma-44	160	9	,	,	PUNCT
ma-44	160	10	a	a	PRON
ma-44	160	11	)	)	PUNCT
ma-44	160	12	ϕγ2−1	ϕγ2−1	NOUN
ma-44	160	13	(	(	PUNCT
ma-44	160	14	b	b	NOUN
ma-44	160	15	,	,	PUNCT
ma-44	160	16	a	a	PRON
ma-44	160	17	)	)	PUNCT
ma-44	160	18	iα2;ϕ	iα2;ϕ	NOUN
ma-44	160	19	a+	a+	PUNCT
ma-44	160	20	[	[	PUNCT
ma-44	160	21	ψq	ψq	X
ma-44	160	22	(	(	PUNCT
ma-44	160	23	iα1;ϕ	iα1;ϕ	PROPN
ma-44	160	24	a+	a+	PUNCT
ma-44	160	25	f	f	PROPN
ma-44	160	26	(	(	PUNCT
ma-44	160	27	t	t	PROPN
ma-44	160	28	)	)	PUNCT
ma-44	161	1	+	+	CCONJ
ma-44	161	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	161	3	(	(	PUNCT
ma-44	161	4	t	t	PROPN
ma-44	161	5	,	,	PUNCT
ma-44	161	6	a	a	PRON
ma-44	161	7	)	)	PUNCT
ma-44	161	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	161	9	(	(	PUNCT
ma-44	161	10	b	b	NOUN
ma-44	161	11	,	,	PUNCT
ma-44	161	12	a	a	PRON
ma-44	161	13	)	)	PUNCT
ma-44	161	14	(	(	PUNCT
ma-44	161	15	iρ;ϕ	iρ;ϕ	VERB
ma-44	161	16	0	0	NUM
ma-44	161	17	+	+	NUM
ma-44	161	18	u	u	SYM
ma-44	161	19	(	(	PUNCT
ma-44	161	20	ζ)−	ζ)−	PROPN
ma-44	161	21	iα1;ϕ	iα1;ϕ	PROPN
ma-44	161	22	0	0	PROPN
ma-44	161	23	+	+	NUM
ma-44	161	24	f	f	X
ma-44	161	25	(	(	PUNCT
ma-44	161	26	b	b	NOUN
ma-44	161	27	)	)	PUNCT
ma-44	161	28	)	)	PUNCT
ma-44	161	29	)	)	PUNCT
ma-44	161	30	]	]	PUNCT
ma-44	162	1	t	t	PROPN
ma-44	162	2	=	=	SYM
ma-44	162	3	b	b	PROPN
ma-44	162	4	.	.	PUNCT
ma-44	163	1	this	this	PRON
ma-44	163	2	finishes	finish	VERB
ma-44	163	3	the	the	DET
ma-44	163	4	proof	proof	NOUN
ma-44	163	5	.	.	PUNCT
ma-44	164	1	�	�	PROPN
ma-44	164	2	eur	eur	PROPN
ma-44	164	3	.	.	PUNCT
ma-44	165	1	j.	j.	PROPN
ma-44	165	2	math	math	PROPN
ma-44	165	3	.	.	PUNCT
ma-44	166	1	anal	anal	ADJ
ma-44	166	2	.	.	PUNCT
ma-44	167	1	1	1	NUM
ma-44	167	2	(	(	PUNCT
ma-44	167	3	2021	2021	NUM
ma-44	167	4	)	)	PUNCT
ma-44	168	1	170	170	NUM
ma-44	168	2	conjecture	conjecture	NOUN
ma-44	168	3	1	1	NUM
ma-44	168	4	.	.	PUNCT
ma-44	168	5	rldµ;ϕ	rldµ;ϕ	ADJ
ma-44	168	6	a+	a+	PUNCT
ma-44	168	7	u(t	u(t	PROPN
ma-44	168	8	)	)	PUNCT
ma-44	168	9	=	=	SYM
ma-44	168	10	1	1	NUM
ma-44	168	11	γ(α2	γ(α2	NOUN
ma-44	168	12	−	−	PROPN
ma-44	168	13	µ	µ	X
ma-44	168	14	)	)	PUNCT
ma-44	168	15	t∫	t∫	PROPN
ma-44	168	16	a	a	DET
ma-44	168	17	ϕ′(s)ϕα2−µ−1(t	ϕ′(s)ϕα2−µ−1(t	PROPN
ma-44	168	18	,	,	PUNCT
ma-44	168	19	s)x(s	s)x(s	NOUN
ma-44	168	20	,	,	PUNCT
ma-44	168	21	a)ds	a)ds	PROPN
ma-44	168	22	+	+	CCONJ
ma-44	168	23	γ	γ	PROPN
ma-44	168	24	(	(	PUNCT
ma-44	168	25	γ2	γ2	ADJ
ma-44	168	26	)	)	PUNCT
ma-44	168	27	γ	γ	PROPN
ma-44	168	28	(	(	PUNCT
ma-44	168	29	γ2	γ2	PROPN
ma-44	168	30	−	−	PROPN
ma-44	168	31	µ	µ	NOUN
ma-44	168	32	)	)	PUNCT
ma-44	168	33	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	168	34	(	(	PUNCT
ma-44	168	35	t	t	PROPN
ma-44	168	36	,	,	PUNCT
ma-44	168	37	a	a	PRON
ma-44	168	38	)	)	PUNCT
ma-44	168	39	ϕγ2−1	ϕγ2−1	NOUN
ma-44	168	40	(	(	PUNCT
ma-44	168	41	b	b	NOUN
ma-44	168	42	,	,	PUNCT
ma-44	168	43	a	a	PRON
ma-44	168	44	)	)	PUNCT
ma-44	168	45	n∑	n∑	NOUN
ma-44	168	46	i=1	i=1	PROPN
ma-44	169	1	λiu	λiu	PROPN
ma-44	169	2	(	(	PUNCT
ma-44	169	3	ζi	ζi	PROPN
ma-44	169	4	)	)	PUNCT
ma-44	169	5	−	−	PROPN
ma-44	169	6	γ	γ	PROPN
ma-44	169	7	(	(	PUNCT
ma-44	169	8	γ2	γ2	ADJ
ma-44	169	9	)	)	PUNCT
ma-44	169	10	γ(α2)γ	γ(α2)γ	PROPN
ma-44	169	11	(	(	PUNCT
ma-44	169	12	γ2	γ2	PROPN
ma-44	169	13	−	−	PROPN
ma-44	169	14	µ	µ	NOUN
ma-44	169	15	)	)	PUNCT
ma-44	169	16	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	169	17	(	(	PUNCT
ma-44	169	18	t	t	PROPN
ma-44	169	19	,	,	PUNCT
ma-44	169	20	a	a	PRON
ma-44	169	21	)	)	PUNCT
ma-44	169	22	ϕγ2−1	ϕγ2−1	NOUN
ma-44	169	23	(	(	PUNCT
ma-44	169	24	b	b	NOUN
ma-44	169	25	,	,	PUNCT
ma-44	169	26	a	a	PRON
ma-44	169	27	)	)	PUNCT
ma-44	169	28	b∫	b∫	NOUN
ma-44	169	29	a	a	DET
ma-44	169	30	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	169	31	,	,	PUNCT
ma-44	169	32	t)x(t	t)x(t	NOUN
ma-44	169	33	,	,	PUNCT
ma-44	169	34	a)dt	a)dt	PROPN
ma-44	169	35	.	.	PROPN
ma-44	170	1	3	3	NUM
ma-44	170	2	.	.	X
ma-44	170	3	main	main	ADJ
ma-44	170	4	results	result	NOUN
ma-44	170	5	in	in	ADP
ma-44	170	6	this	this	DET
ma-44	170	7	section	section	NOUN
ma-44	170	8	,	,	PUNCT
ma-44	170	9	we	we	PRON
ma-44	170	10	present	present	VERB
ma-44	170	11	to	to	ADP
ma-44	170	12	the	the	DET
ma-44	170	13	reader	reader	NOUN
ma-44	170	14	our	our	PRON
ma-44	170	15	main	main	ADJ
ma-44	170	16	results	result	NOUN
ma-44	170	17	on	on	ADP
ma-44	170	18	the	the	DET
ma-44	170	19	existence	existence	NOUN
ma-44	170	20	and	and	CCONJ
ma-44	170	21	stability	stability	NOUN
ma-44	170	22	for	for	ADP
ma-44	170	23	theabove	theabove	NOUN
ma-44	170	24	problem	problem	NOUN
ma-44	170	25	.	.	PUNCT
ma-44	171	1	we	we	PRON
ma-44	171	2	begin	begin	VERB
ma-44	171	3	by	by	ADP
ma-44	171	4	considering	consider	VERB
ma-44	171	5	the	the	DET
ma-44	171	6	space	space	NOUN
ma-44	171	7	cµϕ	cµϕ	NOUN
ma-44	171	8	=	=	SYM
ma-44	171	9	{	{	PUNCT
ma-44	171	10	u	u	NOUN
ma-44	171	11	:	:	PUNCT
ma-44	171	12	u	u	NOUN
ma-44	171	13	,	,	PUNCT
ma-44	171	14	rldµ;ϕ	rldµ;ϕ	ADJ
ma-44	171	15	a+	a+	PUNCT
ma-44	171	16	u	u	PROPN
ma-44	171	17	∈	∈	PROPN
ma-44	171	18	c	c	X
ma-44	171	19	(	(	PUNCT
ma-44	171	20	[	[	X
ma-44	171	21	a	a	X
ma-44	171	22	,	,	PUNCT
ma-44	171	23	b	b	NOUN
ma-44	171	24	]	]	PUNCT
ma-44	171	25	,	,	PUNCT
ma-44	171	26	r	r	NOUN
ma-44	171	27	)	)	PUNCT
ma-44	171	28	}	}	PUNCT
ma-44	171	29	,	,	PUNCT
ma-44	171	30	with	with	ADP
ma-44	171	31	the	the	DET
ma-44	171	32	norm	norm	NOUN
ma-44	171	33	‖u‖cµϕ	‖u‖cµϕ	NOUN
ma-44	171	34	=	=	SYM
ma-44	171	35	‖u‖c	‖u‖c	NOUN
ma-44	171	36	+	+	CCONJ
ma-44	171	37	∥∥rldµ;ϕ	∥∥rldµ;ϕ	NUM
ma-44	171	38	a+	a+	SYM
ma-44	171	39	u	u	NOUN
ma-44	171	40	∥∥	∥∥	PROPN
ma-44	171	41	c	c	PROPN
ma-44	171	42	,	,	PUNCT
ma-44	171	43	such	such	ADJ
ma-44	171	44	that	that	DET
ma-44	171	45	‖u‖c	‖u‖c	NOUN
ma-44	171	46	=	=	SYM
ma-44	171	47	sup	sup	NOUN
ma-44	171	48	t∈[a	t∈[a	NOUN
ma-44	171	49	,	,	PUNCT
ma-44	171	50	b	b	NOUN
ma-44	171	51	]	]	X
ma-44	171	52	|u(t)|	|u(t)|	NOUN
ma-44	171	53	,	,	PUNCT
ma-44	171	54	and	and	CCONJ
ma-44	171	55	∥∥rldµ;ϕ	∥∥rldµ;ϕ	PROPN
ma-44	171	56	a+	a+	PUNCT
ma-44	171	57	u	u	NOUN
ma-44	171	58	∥∥	∥∥	X
ma-44	171	59	c	c	NOUN
ma-44	171	60	=	=	SYM
ma-44	171	61	sup	sup	NOUN
ma-44	171	62	t∈[a	t∈[a	NOUN
ma-44	171	63	,	,	PUNCT
ma-44	171	64	b	b	NOUN
ma-44	171	65	]	]	X
ma-44	171	66	∣∣rldµ;ϕ	∣∣rldµ;ϕ	PROPN
ma-44	171	67	a+	a+	PUNCT
ma-44	171	68	u(t	u(t	PROPN
ma-44	171	69	)	)	PUNCT
ma-44	171	70	∣∣	∣∣	NUM
ma-44	171	71	.	.	PUNCT
ma-44	172	1	3.1	3.1	NUM
ma-44	172	2	.	.	PUNCT
ma-44	172	3	criteria	criterion	NOUN
ma-44	172	4	for	for	ADP
ma-44	172	5	uniqueness	uniqueness	NOUN
ma-44	172	6	solution	solution	NOUN
ma-44	172	7	.	.	PUNCT
ma-44	173	1	now	now	ADV
ma-44	173	2	,	,	PUNCT
ma-44	173	3	wee	wee	ADJ
ma-44	173	4	need	need	VERB
ma-44	173	5	to	to	PART
ma-44	173	6	consider	consider	VERB
ma-44	173	7	the	the	DET
ma-44	173	8	following	follow	VERB
ma-44	173	9	assumptions	assumption	NOUN
ma-44	173	10	:	:	PUNCT
ma-44	173	11	h1	h1	NOUN
ma-44	173	12	)	)	PUNCT
ma-44	173	13	h	h	NOUN
ma-44	173	14	is	be	AUX
ma-44	173	15	continuous	continuous	ADJ
ma-44	173	16	function	function	NOUN
ma-44	173	17	.	.	PUNCT
ma-44	174	1	h2	h2	NOUN
ma-44	174	2	)	)	PUNCT
ma-44	174	3	there	there	PRON
ma-44	174	4	exists	exist	VERB
ma-44	174	5	a	a	DET
ma-44	174	6	constant	constant	ADJ
ma-44	174	7	υ	υ	X
ma-44	174	8	>	>	X
ma-44	174	9	0	0	NUM
ma-44	174	10	,	,	PUNCT
ma-44	174	11	such	such	ADJ
ma-44	174	12	that	that	SCONJ
ma-44	174	13	|h(t	|h(t	PROPN
ma-44	174	14	,	,	PUNCT
ma-44	174	15	u	u	NOUN
ma-44	174	16	,	,	PUNCT
ma-44	174	17	v)−	v)−	PROPN
ma-44	174	18	h(t	h(t	PROPN
ma-44	174	19	,	,	PUNCT
ma-44	174	20	x	x	PRON
ma-44	174	21	,	,	PUNCT
ma-44	174	22	y)|	y)|	PROPN
ma-44	174	23	≤	≤	NOUN
ma-44	174	24	υ	υ	PROPN
ma-44	175	1	(	(	PUNCT
ma-44	175	2	|u	|u	ADJ
ma-44	175	3	−	−	PROPN
ma-44	175	4	x	x	SYM
ma-44	175	5	|+	|+	NOUN
ma-44	175	6	|v	|v	PROPN
ma-44	175	7	−	−	PROPN
ma-44	175	8	y	y	PROPN
ma-44	175	9	|	|	NOUN
ma-44	175	10	)	)	PUNCT
ma-44	175	11	,	,	PUNCT
ma-44	175	12	with	with	ADP
ma-44	175	13	t	t	PROPN
ma-44	175	14	∈	∈	PROPN
ma-44	175	15	[	[	X
ma-44	175	16	a	a	X
ma-44	175	17	,	,	PUNCT
ma-44	175	18	b	b	NOUN
ma-44	175	19	]	]	PUNCT
ma-44	175	20	,	,	PUNCT
ma-44	175	21	(	(	PUNCT
ma-44	175	22	u	u	NOUN
ma-44	175	23	,	,	PUNCT
ma-44	175	24	v	v	INTJ
ma-44	175	25	,	,	PUNCT
ma-44	175	26	x	x	NOUN
ma-44	175	27	,	,	PUNCT
ma-44	175	28	y	y	NOUN
ma-44	175	29	)	)	PUNCT
ma-44	175	30	∈	∈	PROPN
ma-44	175	31	r4	r4	NOUN
ma-44	175	32	.	.	PUNCT
ma-44	176	1	h3	h3	NOUN
ma-44	176	2	)	)	PUNCT
ma-44	176	3	there	there	PRON
ma-44	176	4	exists	exist	VERB
ma-44	176	5	two	two	NUM
ma-44	176	6	continuous	continuous	ADJ
ma-44	176	7	functions	function	NOUN
ma-44	176	8	π1	π1	NOUN
ma-44	176	9	,	,	PUNCT
ma-44	176	10	π2	π2	NOUN
ma-44	176	11	:	:	PUNCT
ma-44	177	1	[	[	X
ma-44	177	2	a	a	DET
ma-44	177	3	,	,	PUNCT
ma-44	177	4	b]→	b]→	X
ma-44	177	5	r+	r+	ADV
ma-44	177	6	,	,	PUNCT
ma-44	177	7	such	such	ADJ
ma-44	177	8	that	that	SCONJ
ma-44	177	9	|h(t	|h(t	PROPN
ma-44	177	10	,	,	PUNCT
ma-44	177	11	u	u	NOUN
ma-44	177	12	,	,	PUNCT
ma-44	177	13	v)|	v)|	VERB
ma-44	177	14	≤	≤	NUM
ma-44	177	15	π1(t	π1(t	PROPN
ma-44	177	16	)	)	PUNCT
ma-44	177	17	|u(t)|+	|u(t)|+	VERB
ma-44	178	1	π2(t	π2(t	NOUN
ma-44	178	2	)	)	PUNCT
ma-44	179	1	|v(t)|	|v(t)|	ADV
ma-44	179	2	,	,	PUNCT
ma-44	179	3	where	where	SCONJ
ma-44	179	4	π∗1	π∗1	NOUN
ma-44	179	5	=	=	NOUN
ma-44	179	6	sup	sup	NOUN
ma-44	179	7	t∈[a	t∈[a	NOUN
ma-44	179	8	,	,	PUNCT
ma-44	179	9	b	b	NOUN
ma-44	179	10	]	]	PUNCT
ma-44	179	11	|π1(t)|	|π1(t)|	PUNCT
ma-44	179	12	,	,	PUNCT
ma-44	179	13	and	and	CCONJ
ma-44	179	14	π∗2	π∗2	NOUN
ma-44	179	15	=	=	SYM
ma-44	179	16	sup	sup	NOUN
ma-44	179	17	t∈[a	t∈[a	NOUN
ma-44	179	18	,	,	PUNCT
ma-44	179	19	b	b	NOUN
ma-44	179	20	]	]	PUNCT
ma-44	179	21	|π2(t)|	|π2(t)|	PUNCT
ma-44	179	22	.	.	PUNCT
ma-44	180	1	now	now	ADV
ma-44	180	2	,	,	PUNCT
ma-44	180	3	we	we	PRON
ma-44	180	4	define	define	VERB
ma-44	180	5	the	the	DET
ma-44	180	6	following	follow	VERB
ma-44	180	7	quantities	quantity	NOUN
ma-44	180	8	:	:	PUNCT
ma-44	180	9	eur	eur	PROPN
ma-44	180	10	.	.	PUNCT
ma-44	181	1	j.	j.	PROPN
ma-44	181	2	math	math	PROPN
ma-44	181	3	.	.	PUNCT
ma-44	182	1	anal	anal	ADJ
ma-44	182	2	.	.	PUNCT
ma-44	183	1	1	1	NUM
ma-44	183	2	(	(	PUNCT
ma-44	183	3	2021	2021	NUM
ma-44	183	4	)	)	PUNCT
ma-44	183	5	171	171	NUM
ma-44	183	6	ϕq(b	ϕq(b	ADV
ma-44	183	7	,	,	PUNCT
ma-44	183	8	a	a	PRON
ma-44	183	9	)	)	PUNCT
ma-44	183	10	=	=	SYM
ma-44	183	11	mq	mq	PROPN
ma-44	183	12	,	,	PUNCT
ma-44	183	13	ω	ω	PROPN
ma-44	183	14	=	=	PUNCT
ma-44	183	15	3q−2	3q−2	NUM
ma-44	183	16	[	[	X
ma-44	183	17	(	(	PUNCT
ma-44	183	18	2mα1	2mα1	NUM
ma-44	183	19	γ(α1	γ(α1	NOUN
ma-44	183	20	+	+	CCONJ
ma-44	183	21	1	1	NUM
ma-44	183	22	)	)	PUNCT
ma-44	183	23	)	)	PUNCT
ma-44	184	1	q−1	q−1	PROPN
ma-44	184	2	(	(	PUNCT
ma-44	184	3	(	(	PUNCT
ma-44	184	4	π∗1)q−1	π∗1)q−1	X
ma-44	184	5	+	+	CCONJ
ma-44	184	6	(	(	PUNCT
ma-44	184	7	π∗2)q−1	π∗2)q−1	X
ma-44	184	8	)	)	PUNCT
ma-44	185	1	+	+	CCONJ
ma-44	185	2	(	(	PUNCT
ma-44	185	3	mρ	mρ	INTJ
ma-44	185	4	γ	γ	X
ma-44	185	5	(	(	PUNCT
ma-44	185	6	ρ+	ρ+	NUM
ma-44	185	7	1	1	NUM
ma-44	185	8	)	)	PUNCT
ma-44	185	9	)	)	PUNCT
ma-44	186	1	q−1	q−1	PRON
ma-44	186	2	]	]	PUNCT
ma-44	187	1	λ1	λ1	PROPN
ma-44	187	2	=	=	SYM
ma-44	187	3	2.ω.mα2	2.ω.mα2	NUM
ma-44	187	4	γ(α2	γ(α2	NOUN
ma-44	188	1	+	+	NOUN
ma-44	188	2	1	1	X
ma-44	188	3	)	)	PUNCT
ma-44	188	4	,	,	PUNCT
ma-44	188	5	λ2	λ2	NOUN
ma-44	188	6	=	=	SYM
ma-44	188	7	(	(	PUNCT
ma-44	188	8	n∑	n∑	NOUN
ma-44	188	9	i=1	i=1	PROPN
ma-44	188	10	|λi	|λi	PROPN
ma-44	188	11	|	|	ADV
ma-44	188	12	)	)	PUNCT
ma-44	188	13	,	,	PUNCT
ma-44	188	14	λ3	λ3	PROPN
ma-44	188	15	=	=	SYM
ma-44	188	16	ω.mα2−µ	ω.mα2−µ	ADP
ma-44	188	17	γ(α2	γ(α2	NOUN
ma-44	188	18	−	−	PROPN
ma-44	188	19	µ+	µ+	PUNCT
ma-44	188	20	1	1	NUM
ma-44	188	21	)	)	PUNCT
ma-44	188	22	+	+	CCONJ
ma-44	188	23	ω.γ	ω.γ	PROPN
ma-44	188	24	(	(	PUNCT
ma-44	188	25	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	188	26	γ(α2	γ(α2	NOUN
ma-44	188	27	+	+	X
ma-44	188	28	1)γ	1)γ	PROPN
ma-44	188	29	(	(	PUNCT
ma-44	188	30	γ2	γ2	PROPN
ma-44	188	31	−	−	PROPN
ma-44	188	32	µ	µ	NUM
ma-44	188	33	)	)	PUNCT
ma-44	188	34	,	,	PUNCT
ma-44	188	35	λ4	λ4	PROPN
ma-44	188	36	=	=	SYM
ma-44	188	37	γ	γ	X
ma-44	188	38	(	(	PUNCT
ma-44	188	39	γ2)m−µ	γ2)m−µ	PROPN
ma-44	188	40	γ	γ	X
ma-44	188	41	(	(	PUNCT
ma-44	188	42	γ2	γ2	PROPN
ma-44	188	43	−	−	PROPN
ma-44	188	44	µ	µ	NUM
ma-44	188	45	)	)	PUNCT
ma-44	188	46	λ2	λ2	PROPN
ma-44	188	47	.	.	PUNCT
ma-44	189	1	based	base	VERB
ma-44	189	2	on	on	ADP
ma-44	189	3	the	the	DET
ma-44	189	4	above	above	ADJ
ma-44	189	5	hypotheses	hypothesis	NOUN
ma-44	189	6	,	,	PUNCT
ma-44	189	7	we	we	PRON
ma-44	189	8	present	present	VERB
ma-44	189	9	to	to	ADP
ma-44	189	10	the	the	DET
ma-44	189	11	reader	reader	NOUN
ma-44	189	12	the	the	DET
ma-44	189	13	following	following	ADJ
ma-44	189	14	result	result	NOUN
ma-44	189	15	.	.	PUNCT
ma-44	190	1	theorem	theorem	NOUN
ma-44	190	2	1	1	NUM
ma-44	190	3	.	.	PUNCT
ma-44	190	4	under	under	ADP
ma-44	190	5	h2	h2	NOUN
ma-44	190	6	and	and	CCONJ
ma-44	190	7	h3	h3	VERB
ma-44	190	8	the	the	DET
ma-44	190	9	equation	equation	NOUN
ma-44	190	10	(	(	PUNCT
ma-44	190	11	1.1	1.1	NUM
ma-44	190	12	)	)	PUNCT
ma-44	190	13	has	have	VERB
ma-44	190	14	a	a	DET
ma-44	190	15	solution	solution	NOUN
ma-44	190	16	.	.	PUNCT
ma-44	191	1	proof	proof	NOUN
ma-44	191	2	.	.	PUNCT
ma-44	192	1	firstly	firstly	ADV
ma-44	192	2	:	:	PUNCT
ma-44	192	3	we	we	PRON
ma-44	192	4	begin	begin	VERB
ma-44	192	5	this	this	DET
ma-44	192	6	proof	proof	NOUN
ma-44	192	7	by	by	ADP
ma-44	192	8	defining	define	VERB
ma-44	192	9	the	the	DET
ma-44	192	10	operator	operator	NOUN
ma-44	192	11	g	g	NOUN
ma-44	192	12	:	:	PUNCT
ma-44	192	13	cµϕ	cµϕ	NOUN
ma-44	192	14	→	→	SYM
ma-44	192	15	cµϕ	cµϕ	NOUN
ma-44	192	16	by	by	ADP
ma-44	192	17	:	:	PUNCT
ma-44	192	18	(	(	PUNCT
ma-44	192	19	gu	gu	NOUN
ma-44	192	20	)	)	PUNCT
ma-44	192	21	(	(	PUNCT
ma-44	192	22	t	t	NOUN
ma-44	192	23	)	)	PUNCT
ma-44	192	24	=	=	SYM
ma-44	192	25	1	1	NUM
ma-44	192	26	γ(α2	γ(α2	NOUN
ma-44	192	27	)	)	PUNCT
ma-44	193	1	t∫	t∫	PRON
ma-44	193	2	a	a	DET
ma-44	193	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	193	4	,	,	PUNCT
ma-44	193	5	s)xu(s	s)xu(s	NOUN
ma-44	193	6	,	,	PUNCT
ma-44	193	7	a)ds	a)ds	PROPN
ma-44	193	8	−	−	PROPN
ma-44	193	9	ϕγ2−1	ϕγ2−1	NOUN
ma-44	193	10	(	(	PUNCT
ma-44	193	11	t	t	PROPN
ma-44	193	12	,	,	PUNCT
ma-44	193	13	a	a	PRON
ma-44	193	14	)	)	PUNCT
ma-44	193	15	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	193	16	(	(	PUNCT
ma-44	193	17	b	b	NOUN
ma-44	193	18	,	,	PUNCT
ma-44	193	19	a	a	PRON
ma-44	193	20	)	)	PUNCT
ma-44	193	21	b∫	b∫	NOUN
ma-44	193	22	a	a	DET
ma-44	193	23	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	193	24	,	,	PUNCT
ma-44	193	25	t)xu(t	t)xu(t	PRON
ma-44	193	26	,	,	PUNCT
ma-44	193	27	a)dt	a)dt	PROPN
ma-44	193	28	+	+	NUM
ma-44	193	29	ϕγ2−1	ϕγ2−1	NOUN
ma-44	193	30	(	(	PUNCT
ma-44	193	31	t	t	PROPN
ma-44	193	32	,	,	PUNCT
ma-44	193	33	a	a	PRON
ma-44	193	34	)	)	PUNCT
ma-44	193	35	ϕγ2−1	ϕγ2−1	NOUN
ma-44	193	36	(	(	PUNCT
ma-44	193	37	b	b	NOUN
ma-44	193	38	,	,	PUNCT
ma-44	193	39	a	a	PRON
ma-44	193	40	)	)	PUNCT
ma-44	193	41	n∑	n∑	NOUN
ma-44	193	42	i=1	i=1	PROPN
ma-44	194	1	λiu	λiu	PROPN
ma-44	194	2	(	(	PUNCT
ma-44	194	3	ζi	ζi	PROPN
ma-44	194	4	)	)	PUNCT
ma-44	194	5	.	.	PUNCT
ma-44	195	1	where	where	SCONJ
ma-44	195	2	xu(s	xu(s	PUNCT
ma-44	195	3	,	,	PUNCT
ma-44	195	4	a	a	PRON
ma-44	195	5	)	)	PUNCT
ma-44	195	6	=	=	PUNCT
ma-44	195	7	ψq	ψq	PROPN
ma-44	195	8			PROPN
ma-44	195	9	1	1	NUM
ma-44	195	10	γ(α1	γ(α1	NOUN
ma-44	195	11	)	)	PUNCT
ma-44	195	12	s∫	s∫	PROPN
ma-44	195	13	a	a	DET
ma-44	195	14	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	195	15	,	,	PUNCT
ma-44	195	16	z)hu(z)dz	z)hu(z)dz	NOUN
ma-44	196	1	+	+	CCONJ
ma-44	196	2	(	(	PUNCT
ma-44	196	3	iρ;ϕ	iρ;ϕ	VERB
ma-44	196	4	0	0	NUM
ma-44	196	5	+	+	NUM
ma-44	196	6	u	u	SYM
ma-44	196	7	(	(	PUNCT
ma-44	196	8	ζ)−	ζ)−	PROPN
ma-44	196	9	iα1;ϕ	iα1;ϕ	PROPN
ma-44	196	10	0	0	PUNCT
ma-44	196	11	+	+	NUM
ma-44	196	12	hu(b	hu(b	NUM
ma-44	196	13	)	)	PUNCT
ma-44	196	14	)	)	PUNCT
ma-44	196	15	ϕγ1−1	ϕγ1−1	INTJ
ma-44	196	16	(	(	PUNCT
ma-44	196	17	b	b	NOUN
ma-44	196	18	,	,	PUNCT
ma-44	196	19	a	a	PRON
ma-44	196	20	)	)	PUNCT
ma-44	196	21	ϕγ1−1	ϕγ1−1	NOUN
ma-44	196	22	(	(	PUNCT
ma-44	196	23	s	s	PROPN
ma-44	196	24	,	,	PUNCT
ma-44	196	25	a	a	PRON
ma-44	196	26	)	)	PUNCT
ma-44	196	27			PROPN
ma-44	196	28	,	,	PUNCT
ma-44	196	29	where	where	SCONJ
ma-44	196	30	hu(t	hu(t	NUM
ma-44	196	31	)	)	PUNCT
ma-44	196	32	=	=	SYM
ma-44	196	33	h(t	h(t	PROPN
ma-44	196	34	,	,	PUNCT
ma-44	196	35	u(t),rldµ;ϕ	u(t),rldµ;ϕ	ADJ
ma-44	196	36	a+	a+	PUNCT
ma-44	196	37	u(t	u(t	NOUN
ma-44	196	38	)	)	PUNCT
ma-44	196	39	)	)	PUNCT
ma-44	196	40	.	.	PUNCT
ma-44	197	1	we	we	PRON
ma-44	197	2	consider	consider	VERB
ma-44	197	3	the	the	DET
ma-44	197	4	set	set	NOUN
ma-44	197	5	ur	ur	INTJ
ma-44	197	6	=	=	PUNCT
ma-44	197	7	{	{	PUNCT
ma-44	197	8	u	u	NOUN
ma-44	197	9	∈	∈	PROPN
ma-44	197	10	cµϕ	cµϕ	NOUN
ma-44	197	11	:	:	PUNCT
ma-44	197	12	‖u‖cµϕ	‖u‖cµϕ	INTJ
ma-44	197	13	≤	≤	NUM
ma-44	197	14	r	r	NOUN
ma-44	197	15	}	}	PUNCT
ma-44	197	16	,	,	PUNCT
ma-44	197	17	so	so	SCONJ
ma-44	197	18	that	that	SCONJ
ma-44	197	19	max	max	PROPN
ma-44	197	20	{	{	PUNCT
ma-44	197	21	(	(	PUNCT
ma-44	197	22	2	2	NUM
ma-44	197	23	(	(	PUNCT
ma-44	197	24	λ1	λ1	PROPN
ma-44	197	25	+	+	CCONJ
ma-44	197	26	λ3	λ3	PROPN
ma-44	197	27	)	)	PUNCT
ma-44	197	28	)	)	PUNCT
ma-44	197	29	1	1	NUM
ma-44	197	30	2−q	2−q	NUM
ma-44	197	31	,	,	PUNCT
ma-44	197	32	2	2	NUM
ma-44	197	33	(	(	PUNCT
ma-44	197	34	λ2	λ2	NOUN
ma-44	197	35	+	+	CCONJ
ma-44	197	36	λ4	λ4	ADJ
ma-44	197	37	)	)	PUNCT
ma-44	197	38	}	}	PUNCT
ma-44	197	39	≤	≤	PROPN
ma-44	197	40	r.	r.	PROPN
ma-44	197	41	eur	eur	PROPN
ma-44	197	42	.	.	PUNCT
ma-44	198	1	j.	j.	PROPN
ma-44	198	2	math	math	PROPN
ma-44	198	3	.	.	PUNCT
ma-44	199	1	anal	anal	ADJ
ma-44	199	2	.	.	PUNCT
ma-44	200	1	1	1	NUM
ma-44	200	2	(	(	PUNCT
ma-44	200	3	2021	2021	NUM
ma-44	200	4	)	)	PUNCT
ma-44	200	5	172we	172we	PROPN
ma-44	200	6	show	show	VERB
ma-44	200	7	that	that	SCONJ
ma-44	200	8	gur	gur	PROPN
ma-44	200	9	⊂	⊂	PROPN
ma-44	200	10	ur	ur	INTJ
ma-44	200	11	.	.	PUNCT
ma-44	201	1	for	for	ADP
ma-44	201	2	any	any	DET
ma-44	201	3	u	u	NOUN
ma-44	201	4	∈	∈	PROPN
ma-44	201	5	ur	ur	INTJ
ma-44	201	6	,	,	PUNCT
ma-44	201	7	and	and	CCONJ
ma-44	201	8	by	by	ADP
ma-44	201	9	lemma	lemma	PROPN
ma-44	201	10	5	5	NUM
ma-44	201	11	we	we	PRON
ma-44	201	12	have	have	VERB
ma-44	201	13	|xu(s	|xu(	NOUN
ma-44	201	14	,	,	PUNCT
ma-44	201	15	a)|	a)|	X
ma-44	201	16	=	=	SYM
ma-44	201	17	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	201	18	ψq	ψq	PROPN
ma-44	201	19			PROPN
ma-44	201	20	1	1	NUM
ma-44	201	21	γ(α1	γ(α1	NOUN
ma-44	201	22	)	)	PUNCT
ma-44	201	23	s∫	s∫	PROPN
ma-44	201	24	a	a	DET
ma-44	201	25	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	201	26	,	,	PUNCT
ma-44	201	27	z)hu(z)dz	z)hu(z)dz	NOUN
ma-44	201	28	+	+	CCONJ
ma-44	201	29	(	(	PUNCT
ma-44	201	30	iρ;ϕ	iρ;ϕ	VERB
ma-44	201	31	0	0	NUM
ma-44	202	1	+	+	NUM
ma-44	202	2	u	u	SYM
ma-44	202	3	(	(	PUNCT
ma-44	202	4	ζ)−	ζ)−	PROPN
ma-44	202	5	iα1;ϕ	iα1;ϕ	PROPN
ma-44	202	6	0	0	PUNCT
ma-44	202	7	+	+	NUM
ma-44	202	8	hu(b	hu(b	NUM
ma-44	202	9	)	)	PUNCT
ma-44	202	10	)	)	PUNCT
ma-44	202	11	ϕγ1−1	ϕγ1−1	INTJ
ma-44	202	12	(	(	PUNCT
ma-44	202	13	b	b	NOUN
ma-44	202	14	,	,	PUNCT
ma-44	202	15	a	a	PRON
ma-44	202	16	)	)	PUNCT
ma-44	202	17	ϕγ1−1	ϕγ1−1	NOUN
ma-44	202	18	(	(	PUNCT
ma-44	202	19	s	s	PROPN
ma-44	202	20	,	,	PUNCT
ma-44	202	21	a	a	PRON
ma-44	202	22	)	)	PUNCT
ma-44	202	23	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	202	24	≤	≤	PROPN
ma-44	202	25	sup	sup	NOUN
ma-44	202	26	t∈[a	t∈[a	NOUN
ma-44	202	27	,	,	PUNCT
ma-44	202	28	b	b	NOUN
ma-44	202	29	]	]	PUNCT
ma-44	202	30	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	202	31	1	1	NUM
ma-44	202	32	γ(α1	γ(α1	NOUN
ma-44	202	33	)	)	PUNCT
ma-44	202	34	s∫	s∫	PROPN
ma-44	202	35	a	a	DET
ma-44	202	36	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	202	37	,	,	PUNCT
ma-44	202	38	z)hu(z)dz	z)hu(z)dz	NOUN
ma-44	202	39	+	+	CCONJ
ma-44	202	40	iρ;ϕ	iρ;ϕ	VERB
ma-44	202	41	0	0	NUM
ma-44	202	42	+	+	NUM
ma-44	202	43	u	u	SYM
ma-44	202	44	(	(	PUNCT
ma-44	202	45	ζ	ζ	NOUN
ma-44	202	46	)	)	PUNCT
ma-44	202	47	+	+	PUNCT
ma-44	202	48	iα1;ϕ	iα1;ϕ	PROPN
ma-44	202	49	0	0	PUNCT
ma-44	202	50	+	+	NUM
ma-44	202	51	hu(b	hu(b	NUM
ma-44	202	52	)	)	PUNCT
ma-44	202	53	∣∣∣∣∣∣	∣∣∣∣∣∣	PUNCT
ma-44	203	1	q−1	q−1	PROPN
ma-44	203	2	≤	≤	ADV
ma-44	203	3	3q−2	3q−2	NUM
ma-44	203	4	sup	sup	NOUN
ma-44	203	5	t∈[a	t∈[a	NOUN
ma-44	203	6	,	,	PUNCT
ma-44	203	7	b	b	X
ma-44	203	8	]	]	X
ma-44	203	9			PROPN
ma-44	203	10	1	1	NUM
ma-44	203	11	γ(α1	γ(α1	NOUN
ma-44	203	12	)	)	PUNCT
ma-44	203	13	s∫	s∫	PROPN
ma-44	203	14	a	a	DET
ma-44	203	15	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	203	16	,	,	PUNCT
ma-44	203	17	z)hu(z)dz	z)hu(z)dz	NUM
ma-44	203	18	q−1	q−1	PRON
ma-44	204	1	+	+	CCONJ
ma-44	204	2	(	(	PUNCT
ma-44	204	3	iρ;ϕ	iρ;ϕ	VERB
ma-44	204	4	0	0	NUM
ma-44	204	5	+	+	NUM
ma-44	204	6	u	u	SYM
ma-44	204	7	(	(	PUNCT
ma-44	204	8	ζ	ζ	NOUN
ma-44	204	9	)	)	PUNCT
ma-44	204	10	)	)	PUNCT
ma-44	205	1	q−1	q−1	PROPN
ma-44	206	1	+	+	CCONJ
ma-44	206	2	(	(	PUNCT
ma-44	206	3	iα1;ϕ	iα1;ϕ	PROPN
ma-44	206	4	0	0	NUM
ma-44	206	5	+	+	NUM
ma-44	206	6	hu(b	hu(b	NUM
ma-44	206	7	)	)	PUNCT
ma-44	206	8	)	)	PUNCT
ma-44	207	1	q−1	q−1	PROPN
ma-44	207	2			VERB
ma-44	207	3	≤	≤	ADV
ma-44	207	4	3q−2	3q−2	NUM
ma-44	207	5	[	[	PUNCT
ma-44	207	6	2	2	NUM
ma-44	207	7	(	(	PUNCT
ma-44	207	8	π∗1	π∗1	PROPN
ma-44	207	9	m	m	PROPN
ma-44	207	10	α1	α1	PROPN
ma-44	207	11	γ(α1	γ(α1	NOUN
ma-44	207	12	+	+	CCONJ
ma-44	207	13	1	1	X
ma-44	207	14	)	)	PUNCT
ma-44	207	15	‖u‖c	‖u‖c	NOUN
ma-44	207	16	+	+	CCONJ
ma-44	208	1	π∗2	π∗2	PROPN
ma-44	208	2	m	m	PROPN
ma-44	208	3	α1	α1	PROPN
ma-44	208	4	γ(α1	γ(α1	NOUN
ma-44	208	5	+	+	CCONJ
ma-44	208	6	1	1	X
ma-44	208	7	)	)	PUNCT
ma-44	208	8	∥∥rldµ;ϕ	∥∥rldµ;ϕ	NOUN
ma-44	208	9	a+	a+	PUNCT
ma-44	208	10	u	u	NOUN
ma-44	208	11	∥∥	∥∥	PROPN
ma-44	208	12	c	c	NOUN
ma-44	208	13	)	)	PUNCT
ma-44	209	1	q−1	q−1	PROPN
ma-44	210	1	+	+	CCONJ
ma-44	210	2	(	(	PUNCT
ma-44	210	3	mρ	mρ	INTJ
ma-44	210	4	γ	γ	X
ma-44	210	5	(	(	PUNCT
ma-44	210	6	ρ+	ρ+	NUM
ma-44	210	7	1	1	NUM
ma-44	210	8	)	)	PUNCT
ma-44	210	9	)	)	PUNCT
ma-44	211	1	q−1	q−1	PROPN
ma-44	211	2	(	(	PUNCT
ma-44	211	3	‖u‖c)q−1	‖u‖c)q−1	X
ma-44	211	4	]	]	PUNCT
ma-44	211	5	≤	≤	NUM
ma-44	211	6	3q−2	3q−2	NUM
ma-44	211	7	[	[	X
ma-44	211	8	(	(	PUNCT
ma-44	211	9	2.π∗1	2.π∗1	NUM
ma-44	211	10	m	m	PROPN
ma-44	211	11	α1	α1	NOUN
ma-44	211	12	γ(α1	γ(α1	NOUN
ma-44	211	13	+	+	CCONJ
ma-44	211	14	1	1	NUM
ma-44	211	15	)	)	PUNCT
ma-44	211	16	)	)	PUNCT
ma-44	212	1	q−1	q−1	PROPN
ma-44	212	2	(	(	PUNCT
ma-44	212	3	‖u‖c)q−1	‖u‖c)q−1	X
ma-44	212	4	+	+	CCONJ
ma-44	212	5	(	(	PUNCT
ma-44	212	6	2.π∗2	2.π∗2	NUM
ma-44	212	7	m	m	PROPN
ma-44	212	8	α1	α1	NOUN
ma-44	212	9	γ(α1	γ(α1	NOUN
ma-44	212	10	+	+	CCONJ
ma-44	212	11	1	1	NUM
ma-44	212	12	)	)	PUNCT
ma-44	212	13	)	)	PUNCT
ma-44	213	1	q−1	q−1	PROPN
ma-44	213	2	(	(	PUNCT
ma-44	213	3	∥∥rldµ;ϕ	∥∥rldµ;ϕ	PROPN
ma-44	213	4	a+	a+	SYM
ma-44	213	5	u	u	NOUN
ma-44	213	6	∥∥	∥∥	PROPN
ma-44	213	7	c	c	NOUN
ma-44	213	8	)	)	PUNCT
ma-44	213	9	q−1	q−1	PROPN
ma-44	214	1	+	+	CCONJ
ma-44	214	2	(	(	PUNCT
ma-44	214	3	mρ	mρ	INTJ
ma-44	214	4	γ	γ	X
ma-44	214	5	(	(	PUNCT
ma-44	214	6	ρ+	ρ+	NUM
ma-44	214	7	1	1	NUM
ma-44	214	8	)	)	PUNCT
ma-44	214	9	)	)	PUNCT
ma-44	215	1	q−1	q−1	PROPN
ma-44	215	2	(	(	PUNCT
ma-44	215	3	‖u‖c)q−1	‖u‖c)q−1	X
ma-44	215	4	]	]	PUNCT
ma-44	215	5	≤	≤	NUM
ma-44	215	6	3q−2	3q−2	NUM
ma-44	215	7	[	[	X
ma-44	215	8	(	(	PUNCT
ma-44	215	9	2mα1	2mα1	NUM
ma-44	215	10	γ(α1	γ(α1	NOUN
ma-44	215	11	+	+	CCONJ
ma-44	215	12	1	1	NUM
ma-44	215	13	)	)	PUNCT
ma-44	215	14	)	)	PUNCT
ma-44	216	1	q−1	q−1	PROPN
ma-44	216	2	(	(	PUNCT
ma-44	216	3	(	(	PUNCT
ma-44	216	4	π∗1)q−1	π∗1)q−1	X
ma-44	216	5	+	+	CCONJ
ma-44	216	6	(	(	PUNCT
ma-44	216	7	π∗2)q−1	π∗2)q−1	X
ma-44	216	8	)	)	PUNCT
ma-44	217	1	+	+	CCONJ
ma-44	217	2	(	(	PUNCT
ma-44	217	3	mρ	mρ	INTJ
ma-44	217	4	γ	γ	X
ma-44	217	5	(	(	PUNCT
ma-44	217	6	ρ+	ρ+	NUM
ma-44	217	7	1	1	NUM
ma-44	217	8	)	)	PUNCT
ma-44	217	9	)	)	PUNCT
ma-44	218	1	q−1	q−1	PROPN
ma-44	218	2	]	]	PUNCT
ma-44	219	1	rq−1	rq−1	PROPN
ma-44	219	2	≤	≤	NUM
ma-44	219	3	ω.rq−1	ω.rq−1	NOUN
ma-44	219	4	.	.	PUNCT
ma-44	220	1	then	then	ADV
ma-44	220	2	sup	sup	NOUN
ma-44	220	3	t∈[a	t∈[a	NOUN
ma-44	220	4	,	,	PUNCT
ma-44	220	5	b	b	NOUN
ma-44	220	6	]	]	X
ma-44	220	7	|(gu	|(gu	NOUN
ma-44	220	8	)	)	PUNCT
ma-44	220	9	(	(	PUNCT
ma-44	220	10	t)|	t)|	NOUN
ma-44	220	11	(	(	PUNCT
ma-44	220	12	3.1	3.1	NUM
ma-44	220	13	)	)	PUNCT
ma-44	220	14	≤	≤	NUM
ma-44	220	15	sup	sup	NOUN
ma-44	220	16	t∈[a	t∈[a	NOUN
ma-44	220	17	,	,	PUNCT
ma-44	220	18	b	b	NOUN
ma-44	220	19	]	]	PUNCT
ma-44	220	20	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	220	21	1	1	NUM
ma-44	220	22	γ(α2	γ(α2	NOUN
ma-44	220	23	)	)	PUNCT
ma-44	221	1	t∫	t∫	PRON
ma-44	221	2	a	a	DET
ma-44	221	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	221	4	,	,	PUNCT
ma-44	221	5	s)xu(s	s)xu(s	NOUN
ma-44	221	6	,	,	PUNCT
ma-44	221	7	a)ds	a)ds	PROPN
ma-44	221	8	+	+	NUM
ma-44	221	9	ϕγ2−1	ϕγ2−1	NOUN
ma-44	221	10	(	(	PUNCT
ma-44	221	11	t	t	PROPN
ma-44	221	12	,	,	PUNCT
ma-44	221	13	a	a	PRON
ma-44	221	14	)	)	PUNCT
ma-44	221	15	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	221	16	(	(	PUNCT
ma-44	221	17	b	b	NOUN
ma-44	221	18	,	,	PUNCT
ma-44	221	19	a	a	PRON
ma-44	221	20	)	)	PUNCT
ma-44	221	21	b∫	b∫	NOUN
ma-44	221	22	a	a	DET
ma-44	221	23	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	221	24	,	,	PUNCT
ma-44	221	25	t)xu(t	t)xu(t	PRON
ma-44	221	26	,	,	PUNCT
ma-44	221	27	a)dt	a)dt	PROPN
ma-44	221	28	+	+	NUM
ma-44	221	29	ϕγ2−1	ϕγ2−1	NOUN
ma-44	221	30	(	(	PUNCT
ma-44	221	31	t	t	PROPN
ma-44	221	32	,	,	PUNCT
ma-44	221	33	a	a	PRON
ma-44	221	34	)	)	PUNCT
ma-44	221	35	ϕγ2−1	ϕγ2−1	NOUN
ma-44	221	36	(	(	PUNCT
ma-44	221	37	b	b	NOUN
ma-44	221	38	,	,	PUNCT
ma-44	221	39	a	a	PRON
ma-44	221	40	)	)	PUNCT
ma-44	221	41	n∑	n∑	NOUN
ma-44	221	42	i=1	i=1	PROPN
ma-44	222	1	λiu	λiu	PROPN
ma-44	222	2	(	(	PUNCT
ma-44	222	3	ζi	ζi	PROPN
ma-44	222	4	)	)	PUNCT
ma-44	222	5	∣∣∣∣∣	∣∣∣∣∣	ADJ
ma-44	222	6	≤	≤	NOUN
ma-44	222	7	2mα2	2mα2	NUM
ma-44	222	8	γ(α2	γ(α2	NOUN
ma-44	223	1	+	+	CCONJ
ma-44	223	2	1	1	X
ma-44	223	3	)	)	PUNCT
ma-44	223	4	|xu|+	|xu|+	NOUN
ma-44	223	5	(	(	PUNCT
ma-44	223	6	n∑	n∑	NOUN
ma-44	223	7	i=1	i=1	PROPN
ma-44	224	1	|λi	|λi	PROPN
ma-44	224	2	|	|	ADV
ma-44	224	3	)	)	PUNCT
ma-44	224	4	sup	sup	NOUN
ma-44	224	5	t∈[a	t∈[a	NOUN
ma-44	224	6	,	,	PUNCT
ma-44	224	7	b	b	NOUN
ma-44	224	8	]	]	X
ma-44	224	9	|u	|u	ADJ
ma-44	224	10	(	(	PUNCT
ma-44	224	11	t)|	t)|	ADV
ma-44	224	12	≤	≤	NUM
ma-44	224	13	2.ω.mα2	2.ω.mα2	NUM
ma-44	224	14	γ(α2	γ(α2	NOUN
ma-44	225	1	+	+	CCONJ
ma-44	225	2	1	1	X
ma-44	225	3	)	)	PUNCT
ma-44	225	4	rq	rq	NOUN
ma-44	225	5	+	+	CCONJ
ma-44	226	1	(	(	PUNCT
ma-44	226	2	n∑	n∑	INTJ
ma-44	226	3	i=1	i=1	PROPN
ma-44	226	4	|λi	|λi	PROPN
ma-44	226	5	|	|	ADV
ma-44	226	6	)	)	PUNCT
ma-44	226	7	r.	r.	NOUN
ma-44	226	8	≤	≤	NUM
ma-44	227	1	λ1r	λ1r	PROPN
ma-44	227	2	q	q	X
ma-44	228	1	+	+	NUM
ma-44	228	2	λ2r	λ2r	NOUN
ma-44	228	3	.	.	PUNCT
ma-44	229	1	also	also	ADV
ma-44	229	2	,	,	PUNCT
ma-44	229	3	we	we	PRON
ma-44	229	4	have	have	VERB
ma-44	229	5	sup	sup	NOUN
ma-44	229	6	t∈[a	t∈[a	NOUN
ma-44	229	7	,	,	PUNCT
ma-44	229	8	b	b	X
ma-44	229	9	]	]	X
ma-44	229	10	∣∣(rldµ;ϕ	∣∣(rldµ;ϕ	PROPN
ma-44	229	11	a+	a+	PUNCT
ma-44	229	12	gu	gu	NOUN
ma-44	229	13	)	)	PUNCT
ma-44	229	14	(	(	PUNCT
ma-44	229	15	t	t	NOUN
ma-44	229	16	)	)	PUNCT
ma-44	229	17	∣∣	∣∣	NUM
ma-44	229	18	(	(	PUNCT
ma-44	229	19	3.2	3.2	NUM
ma-44	229	20	)	)	PUNCT
ma-44	229	21	≤	≤	NUM
ma-44	229	22	sup	sup	NOUN
ma-44	229	23	t∈[a	t∈[a	NOUN
ma-44	229	24	,	,	PUNCT
ma-44	229	25	b	b	NOUN
ma-44	229	26	]	]	PUNCT
ma-44	229	27	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	229	28	1	1	NUM
ma-44	229	29	γ(α2	γ(α2	NOUN
ma-44	229	30	−	−	PROPN
ma-44	229	31	µ	µ	X
ma-44	229	32	)	)	PUNCT
ma-44	229	33	t∫	t∫	PROPN
ma-44	229	34	a	a	DET
ma-44	229	35	ϕ′(s)ϕα2−µ−1(t	ϕ′(s)ϕα2−µ−1(t	PROPN
ma-44	229	36	,	,	PUNCT
ma-44	229	37	s)xu(s	s)xu(s	ADJ
ma-44	229	38	,	,	PUNCT
ma-44	230	1	a)ds	a)ds	PROPN
ma-44	230	2	+	+	CCONJ
ma-44	230	3	γ	γ	PROPN
ma-44	230	4	(	(	PUNCT
ma-44	230	5	γ2	γ2	ADJ
ma-44	230	6	)	)	PUNCT
ma-44	230	7	γ	γ	PROPN
ma-44	230	8	(	(	PUNCT
ma-44	230	9	γ2	γ2	PROPN
ma-44	230	10	−	−	PROPN
ma-44	230	11	µ	µ	NOUN
ma-44	230	12	)	)	PUNCT
ma-44	230	13	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	230	14	(	(	PUNCT
ma-44	230	15	t	t	PROPN
ma-44	230	16	,	,	PUNCT
ma-44	230	17	a	a	PRON
ma-44	230	18	)	)	PUNCT
ma-44	230	19	ϕγ2−1	ϕγ2−1	NOUN
ma-44	230	20	(	(	PUNCT
ma-44	230	21	b	b	NOUN
ma-44	230	22	,	,	PUNCT
ma-44	230	23	a	a	PRON
ma-44	230	24	)	)	PUNCT
ma-44	230	25	n∑	n∑	NOUN
ma-44	230	26	i=1	i=1	PROPN
ma-44	230	27	λiu	λiu	PROPN
ma-44	230	28	(	(	PUNCT
ma-44	230	29	ζi	ζi	PROPN
ma-44	230	30	)	)	PUNCT
ma-44	230	31	eur	eur	PROPN
ma-44	230	32	.	.	PUNCT
ma-44	231	1	j.	j.	PROPN
ma-44	231	2	math	math	PROPN
ma-44	231	3	.	.	PUNCT
ma-44	232	1	anal	anal	ADJ
ma-44	232	2	.	.	PUNCT
ma-44	233	1	1	1	NUM
ma-44	233	2	(	(	PUNCT
ma-44	233	3	2021	2021	NUM
ma-44	233	4	)	)	PUNCT
ma-44	234	1	173	173	NUM
ma-44	234	2	−	−	PROPN
ma-44	234	3	γ	γ	PROPN
ma-44	234	4	(	(	PUNCT
ma-44	234	5	γ2	γ2	ADJ
ma-44	234	6	)	)	PUNCT
ma-44	234	7	γ(α2)γ	γ(α2)γ	PROPN
ma-44	234	8	(	(	PUNCT
ma-44	234	9	γ2	γ2	PROPN
ma-44	234	10	−	−	PROPN
ma-44	234	11	µ	µ	NOUN
ma-44	234	12	)	)	PUNCT
ma-44	234	13	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	234	14	(	(	PUNCT
ma-44	234	15	t	t	PROPN
ma-44	234	16	,	,	PUNCT
ma-44	234	17	a	a	PRON
ma-44	234	18	)	)	PUNCT
ma-44	234	19	ϕγ2−1	ϕγ2−1	NOUN
ma-44	234	20	(	(	PUNCT
ma-44	234	21	b	b	NOUN
ma-44	234	22	,	,	PUNCT
ma-44	234	23	a	a	PRON
ma-44	234	24	)	)	PUNCT
ma-44	234	25	b∫	b∫	NOUN
ma-44	234	26	a	a	DET
ma-44	234	27	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	234	28	,	,	PUNCT
ma-44	234	29	t)xu(t	t)xu(t	PRON
ma-44	234	30	,	,	PUNCT
ma-44	234	31	a)dt	a)dt	PROPN
ma-44	234	32	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	234	33	≤	≤	X
ma-44	234	34	[	[	PUNCT
ma-44	234	35	mα2−µ	mα2−µ	NOUN
ma-44	234	36	γ(α2	γ(α2	NOUN
ma-44	234	37	−	−	PROPN
ma-44	234	38	µ+	µ+	PUNCT
ma-44	234	39	1	1	NUM
ma-44	234	40	)	)	PUNCT
ma-44	234	41	+	+	CCONJ
ma-44	234	42	γ	γ	X
ma-44	234	43	(	(	PUNCT
ma-44	234	44	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	234	45	γ(α2	γ(α2	NOUN
ma-44	234	46	+	+	X
ma-44	234	47	1)γ	1)γ	PROPN
ma-44	234	48	(	(	PUNCT
ma-44	234	49	γ2	γ2	PROPN
ma-44	234	50	−	−	PROPN
ma-44	234	51	µ	µ	NUM
ma-44	234	52	)	)	PUNCT
ma-44	234	53	]	]	PUNCT
ma-44	234	54	|xu|+	|xu|+	VERB
ma-44	234	55	γ	γ	X
ma-44	234	56	(	(	PUNCT
ma-44	234	57	γ2)m−µ	γ2)m−µ	PROPN
ma-44	234	58	γ	γ	X
ma-44	234	59	(	(	PUNCT
ma-44	234	60	γ2	γ2	PROPN
ma-44	234	61	−	−	PROPN
ma-44	234	62	µ	µ	NUM
ma-44	234	63	)	)	PUNCT
ma-44	234	64	(	(	PUNCT
ma-44	234	65	n∑	n∑	NOUN
ma-44	234	66	i=1	i=1	PROPN
ma-44	235	1	|λi	|λi	PROPN
ma-44	235	2	|	|	ADV
ma-44	235	3	)	)	PUNCT
ma-44	235	4	sup	sup	NOUN
ma-44	235	5	t∈[a	t∈[a	NOUN
ma-44	235	6	,	,	PUNCT
ma-44	235	7	b	b	NOUN
ma-44	235	8	]	]	X
ma-44	235	9	|u	|u	ADJ
ma-44	235	10	(	(	PUNCT
ma-44	235	11	t)|	t)|	ADV
ma-44	235	12	≤	≤	NOUN
ma-44	235	13	[	[	PUNCT
ma-44	235	14	ω.mα2−µ	ω.mα2−µ	X
ma-44	235	15	γ(α2	γ(α2	NOUN
ma-44	235	16	−	−	PROPN
ma-44	235	17	µ+	µ+	PUNCT
ma-44	235	18	1	1	NUM
ma-44	235	19	)	)	PUNCT
ma-44	235	20	+	+	CCONJ
ma-44	235	21	ω.γ	ω.γ	PROPN
ma-44	235	22	(	(	PUNCT
ma-44	235	23	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	235	24	γ(α2	γ(α2	NOUN
ma-44	235	25	+	+	X
ma-44	235	26	1)γ	1)γ	PROPN
ma-44	235	27	(	(	PUNCT
ma-44	235	28	γ2	γ2	PROPN
ma-44	235	29	−	−	PROPN
ma-44	235	30	µ	µ	NUM
ma-44	235	31	)	)	PUNCT
ma-44	235	32	]	]	PUNCT
ma-44	236	1	rq−1	rq−1	NOUN
ma-44	236	2	+	+	CCONJ
ma-44	236	3	γ	γ	X
ma-44	236	4	(	(	PUNCT
ma-44	236	5	γ2)m−µ	γ2)m−µ	PROPN
ma-44	236	6	γ	γ	X
ma-44	236	7	(	(	PUNCT
ma-44	236	8	γ2	γ2	PROPN
ma-44	236	9	−	−	PROPN
ma-44	236	10	µ	µ	NUM
ma-44	236	11	)	)	PUNCT
ma-44	236	12	(	(	PUNCT
ma-44	236	13	n∑	n∑	NOUN
ma-44	236	14	i=1	i=1	PROPN
ma-44	236	15	|λi	|λi	X
ma-44	236	16	|	|	ADV
ma-44	236	17	)	)	PUNCT
ma-44	236	18	r	r	NOUN
ma-44	236	19	≤	≤	NUM
ma-44	236	20	λ3r	λ3r	X
ma-44	236	21	q−1	q−1	PROPN
ma-44	236	22	+	+	CCONJ
ma-44	236	23	λ4r	λ4r	PROPN
ma-44	236	24	.	.	PUNCT
ma-44	236	25	by	by	ADP
ma-44	236	26	(	(	PUNCT
ma-44	236	27	3.1	3.1	NUM
ma-44	236	28	)	)	PUNCT
ma-44	236	29	and	and	CCONJ
ma-44	236	30	(	(	PUNCT
ma-44	236	31	3.2	3.2	NUM
ma-44	236	32	)	)	PUNCT
ma-44	236	33	,	,	PUNCT
ma-44	236	34	we	we	PRON
ma-44	236	35	find	find	VERB
ma-44	236	36	‖u‖cµϕ	‖u‖cµϕ	PRON
ma-44	236	37	=	=	SYM
ma-44	236	38	sup	sup	NOUN
ma-44	236	39	t∈[a	t∈[a	NOUN
ma-44	236	40	,	,	PUNCT
ma-44	236	41	b	b	NOUN
ma-44	236	42	]	]	X
ma-44	236	43	|(gu	|(gu	NOUN
ma-44	236	44	)	)	PUNCT
ma-44	236	45	(	(	PUNCT
ma-44	236	46	t)|c	t)|c	VERB
ma-44	236	47	+	+	CCONJ
ma-44	236	48	sup	sup	NOUN
ma-44	236	49	t∈[a	t∈[a	NOUN
ma-44	236	50	,	,	PUNCT
ma-44	236	51	b	b	NOUN
ma-44	236	52	]	]	X
ma-44	236	53	∣∣(rldµ;ϕ	∣∣(rldµ;ϕ	PROPN
ma-44	236	54	a+	a+	PUNCT
ma-44	236	55	gu	gu	NOUN
ma-44	236	56	)	)	PUNCT
ma-44	236	57	(	(	PUNCT
ma-44	236	58	t	t	NOUN
ma-44	236	59	)	)	PUNCT
ma-44	236	60	∣∣	∣∣	X
ma-44	236	61	c	c	X
ma-44	236	62	(	(	PUNCT
ma-44	236	63	3.3	3.3	NUM
ma-44	236	64	)	)	PUNCT
ma-44	236	65	≤	≤	NOUN
ma-44	236	66	(	(	PUNCT
ma-44	236	67	λ1	λ1	PROPN
ma-44	236	68	+	+	CCONJ
ma-44	236	69	λ3	λ3	PROPN
ma-44	236	70	)	)	PUNCT
ma-44	236	71	rq−1	rq−1	NOUN
ma-44	236	72	+	+	CCONJ
ma-44	236	73	(	(	PUNCT
ma-44	236	74	λ2	λ2	NOUN
ma-44	236	75	+	+	CCONJ
ma-44	236	76	λ4	λ4	ADJ
ma-44	236	77	)	)	PUNCT
ma-44	236	78	r	r	NOUN
ma-44	236	79	≤	≤	PUNCT
ma-44	236	80	r.	r.	NOUN
ma-44	236	81	that	that	PRON
ma-44	236	82	is	be	AUX
ma-44	236	83	gur	gur	NOUN
ma-44	236	84	belongs	belong	VERB
ma-44	236	85	to	to	PART
ma-44	236	86	ur	ur	VERB
ma-44	236	87	on	on	ADP
ma-44	236	88	[	[	X
ma-44	236	89	a	a	X
ma-44	236	90	,	,	PUNCT
ma-44	236	91	b	b	NOUN
ma-44	236	92	]	]	X
ma-44	236	93	.	.	PUNCT
ma-44	237	1	next	next	ADV
ma-44	237	2	,	,	PUNCT
ma-44	237	3	we	we	PRON
ma-44	237	4	prove	prove	VERB
ma-44	237	5	that	that	SCONJ
ma-44	237	6	g	g	PROPN
ma-44	237	7	is	be	AUX
ma-44	237	8	completely	completely	ADV
ma-44	237	9	continuous	continuous	ADJ
ma-44	237	10	.	.	PUNCT
ma-44	238	1	for	for	ADP
ma-44	238	2	any	any	DET
ma-44	238	3	u	u	PROPN
ma-44	238	4	∈	∈	PROPN
ma-44	238	5	ur	ur	INTJ
ma-44	238	6	and	and	CCONJ
ma-44	238	7	t1	t1	PROPN
ma-44	238	8	,	,	PUNCT
ma-44	238	9	t2	t2	NOUN
ma-44	238	10	∈	∈	PROPN
ma-44	238	11	[	[	X
ma-44	238	12	a	a	X
ma-44	238	13	;	;	PUNCT
ma-44	238	14	b	b	X
ma-44	238	15	]	]	X
ma-44	238	16	such	such	ADJ
ma-44	238	17	that	that	SCONJ
ma-44	238	18	t1	t1	NOUN
ma-44	238	19	<	<	X
ma-44	238	20	t2	t2	PROPN
ma-44	238	21	,	,	PUNCT
ma-44	238	22	by	by	ADP
ma-44	238	23	lemma	lemma	PROPN
ma-44	238	24	3	3	NUM
ma-44	238	25	,	,	PUNCT
ma-44	238	26	we	we	PRON
ma-44	238	27	have	have	VERB
ma-44	238	28	sup	sup	NOUN
ma-44	238	29	t∈[a	t∈[a	NOUN
ma-44	238	30	,	,	PUNCT
ma-44	238	31	b	b	NOUN
ma-44	238	32	]	]	X
ma-44	238	33	|(gu	|(gu	NOUN
ma-44	238	34	)	)	PUNCT
ma-44	238	35	(	(	PUNCT
ma-44	238	36	t2)−	t2)−	NOUN
ma-44	238	37	(	(	PUNCT
ma-44	238	38	gu	gu	NOUN
ma-44	238	39	)	)	PUNCT
ma-44	238	40	(	(	PUNCT
ma-44	238	41	t1)|	t1)|	PROPN
ma-44	238	42	≤	≤	ADJ
ma-44	238	43	sup	sup	NOUN
ma-44	238	44	t∈[a	t∈[a	NOUN
ma-44	238	45	,	,	PUNCT
ma-44	238	46	b	b	NOUN
ma-44	238	47	]	]	PUNCT
ma-44	238	48	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	238	49	1	1	NUM
ma-44	238	50	γ(α2	γ(α2	NOUN
ma-44	238	51	)	)	PUNCT
ma-44	238	52	t2∫	t2∫	NOUN
ma-44	238	53	a	a	DET
ma-44	238	54	ϕ′(s)ϕα2−1(t2	ϕ′(s)ϕα2−1(t2	NOUN
ma-44	238	55	,	,	PUNCT
ma-44	238	56	s)xu(s	s)xu(s	NOUN
ma-44	238	57	,	,	PUNCT
ma-44	239	1	a)ds	a)ds	PROPN
ma-44	239	2	−	−	PROPN
ma-44	239	3	1	1	NUM
ma-44	239	4	γ(α2	γ(α2	NOUN
ma-44	239	5	)	)	PUNCT
ma-44	239	6	t1∫	t1∫	PUNCT
ma-44	240	1	a	a	DET
ma-44	240	2	ϕ′(s)ϕα2−1(t1	ϕ′(s)ϕα2−1(t1	PROPN
ma-44	240	3	,	,	PUNCT
ma-44	240	4	s)xu(s	s)xu(s	NOUN
ma-44	240	5	,	,	PUNCT
ma-44	240	6	a)ds	a)ds	PROPN
ma-44	240	7	+	+	NUM
ma-44	240	8	ϕγ2−1	ϕγ2−1	NOUN
ma-44	240	9	(	(	PUNCT
ma-44	240	10	t2	t2	NOUN
ma-44	240	11	,	,	PUNCT
ma-44	240	12	a)−	a)−	PROPN
ma-44	240	13	ϕγ2−1	ϕγ2−1	NOUN
ma-44	240	14	(	(	PUNCT
ma-44	240	15	t1	t1	NOUN
ma-44	240	16	,	,	PUNCT
ma-44	240	17	a	a	PRON
ma-44	240	18	)	)	PUNCT
ma-44	240	19	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	240	20	(	(	PUNCT
ma-44	240	21	b	b	NOUN
ma-44	240	22	,	,	PUNCT
ma-44	240	23	a	a	PRON
ma-44	240	24	)	)	PUNCT
ma-44	240	25	b∫	b∫	NOUN
ma-44	240	26	a	a	DET
ma-44	240	27	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	240	28	,	,	PUNCT
ma-44	240	29	t)xu(t	t)xu(t	PRON
ma-44	240	30	,	,	PUNCT
ma-44	240	31	a)dt	a)dt	PROPN
ma-44	240	32	+	+	NUM
ma-44	240	33	ϕγ2−1	ϕγ2−1	NOUN
ma-44	240	34	(	(	PUNCT
ma-44	240	35	t2	t2	NOUN
ma-44	240	36	,	,	PUNCT
ma-44	240	37	a)−	a)−	PROPN
ma-44	240	38	ϕγ2−1	ϕγ2−1	NOUN
ma-44	240	39	(	(	PUNCT
ma-44	240	40	t1	t1	NOUN
ma-44	240	41	,	,	PUNCT
ma-44	240	42	a	a	PRON
ma-44	240	43	)	)	PUNCT
ma-44	240	44	ϕγ2−1	ϕγ2−1	NOUN
ma-44	240	45	(	(	PUNCT
ma-44	240	46	b	b	NOUN
ma-44	240	47	,	,	PUNCT
ma-44	240	48	a	a	PRON
ma-44	240	49	)	)	PUNCT
ma-44	241	1	n∑	n∑	NOUN
ma-44	241	2	i=1	i=1	PROPN
ma-44	242	1	λiu	λiu	PROPN
ma-44	242	2	(	(	PUNCT
ma-44	242	3	ζi	ζi	PROPN
ma-44	242	4	)	)	PUNCT
ma-44	242	5	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-44	242	6	≤	≤	NOUN
ma-44	242	7	ω.rq−1	ω.rq−1	NOUN
ma-44	242	8	γ(α2	γ(α2	X
ma-44	243	1	+	+	CCONJ
ma-44	243	2	1	1	X
ma-44	243	3	)	)	PUNCT
ma-44	243	4	ϕα2	ϕα2	NOUN
ma-44	243	5	(	(	PUNCT
ma-44	243	6	t2	t2	NOUN
ma-44	243	7	,	,	PUNCT
ma-44	243	8	t1	t1	NOUN
ma-44	243	9	)	)	PUNCT
ma-44	243	10	+	+	CCONJ
ma-44	243	11	ω.mα2	ω.mα2	NOUN
ma-44	243	12	.rq−1	.rq−1	PUNCT
ma-44	244	1	+	+	CCONJ
ma-44	244	2	γ(α2	γ(α2	NOUN
ma-44	245	1	+	+	CCONJ
ma-44	245	2	1)λ2r	1)λ2r	NOUN
ma-44	245	3	γ(α2	γ(α2	NOUN
ma-44	246	1	+	+	CCONJ
ma-44	246	2	1)ϕγ2−1	1)ϕγ2−1	X
ma-44	246	3	(	(	PUNCT
ma-44	246	4	b	b	NOUN
ma-44	246	5	,	,	PUNCT
ma-44	246	6	a	a	DET
ma-44	246	7	)	)	PUNCT
ma-44	246	8	ϕγ2−1	ϕγ2−1	NOUN
ma-44	246	9	(	(	PUNCT
ma-44	246	10	t2	t2	NOUN
ma-44	246	11	,	,	PUNCT
ma-44	246	12	t1	t1	NOUN
ma-44	246	13	)	)	PUNCT
ma-44	246	14	.	.	PUNCT
ma-44	247	1	hence	hence	ADV
ma-44	247	2	,	,	PUNCT
ma-44	247	3	sup	sup	NOUN
ma-44	247	4	t∈[a	t∈[a	NOUN
ma-44	247	5	,	,	PUNCT
ma-44	247	6	b	b	NOUN
ma-44	247	7	]	]	X
ma-44	247	8	|(gu	|(gu	NOUN
ma-44	247	9	)	)	PUNCT
ma-44	247	10	(	(	PUNCT
ma-44	247	11	t2)−	t2)−	NOUN
ma-44	247	12	(	(	PUNCT
ma-44	247	13	gu	gu	NOUN
ma-44	247	14	)	)	PUNCT
ma-44	247	15	(	(	PUNCT
ma-44	247	16	t1)|	t1)|	PROPN
ma-44	247	17	→	→	SYM
ma-44	247	18	0	0	NUM
ma-44	247	19	,	,	PUNCT
ma-44	247	20	as	as	ADP
ma-44	247	21	t2	t2	PROPN
ma-44	247	22	→	→	SYM
ma-44	247	23	t1	t1	PROPN
ma-44	247	24	.	.	PUNCT
ma-44	248	1	eur	eur	PROPN
ma-44	248	2	.	.	PUNCT
ma-44	249	1	j.	j.	PROPN
ma-44	249	2	math	math	PROPN
ma-44	249	3	.	.	PUNCT
ma-44	250	1	anal	anal	ADJ
ma-44	250	2	.	.	PUNCT
ma-44	251	1	1	1	NUM
ma-44	251	2	(	(	PUNCT
ma-44	251	3	2021	2021	NUM
ma-44	251	4	)	)	PUNCT
ma-44	252	1	174also	174also	PROPN
ma-44	252	2	,	,	PUNCT
ma-44	252	3	we	we	PRON
ma-44	252	4	can	can	AUX
ma-44	252	5	say	say	VERB
ma-44	252	6	that	that	DET
ma-44	252	7	sup	sup	NOUN
ma-44	252	8	t∈[a	t∈[a	NOUN
ma-44	252	9	,	,	PUNCT
ma-44	252	10	b	b	X
ma-44	252	11	]	]	X
ma-44	252	12	∣∣(rldµ;ϕ	∣∣(rldµ;ϕ	PROPN
ma-44	252	13	a+	a+	PUNCT
ma-44	252	14	gu	gu	NOUN
ma-44	252	15	)	)	PUNCT
ma-44	252	16	(	(	PUNCT
ma-44	252	17	t2)−	t2)−	NOUN
ma-44	252	18	(	(	PUNCT
ma-44	252	19	rldµ;ϕ	rldµ;ϕ	ADJ
ma-44	252	20	a+	a+	PRON
ma-44	252	21	gu	gu	NOUN
ma-44	252	22	)	)	PUNCT
ma-44	252	23	(	(	PUNCT
ma-44	252	24	t1	t1	NOUN
ma-44	252	25	)	)	PUNCT
ma-44	252	26	∣∣	∣∣	PROPN
ma-44	252	27	≤	≤	NUM
ma-44	252	28	sup	sup	NOUN
ma-44	252	29	t∈[a	t∈[a	NOUN
ma-44	252	30	,	,	PUNCT
ma-44	252	31	b	b	NOUN
ma-44	252	32	]	]	PUNCT
ma-44	252	33	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	252	34	1	1	NUM
ma-44	252	35	γ(α2	γ(α2	NOUN
ma-44	252	36	−	−	PROPN
ma-44	252	37	µ	µ	X
ma-44	252	38	)	)	PUNCT
ma-44	252	39	t2∫	t2∫	NOUN
ma-44	252	40	a	a	DET
ma-44	252	41	ϕ′(s)ϕα2−µ−1(t2	ϕ′(s)ϕα2−µ−1(t2	NOUN
ma-44	252	42	,	,	PUNCT
ma-44	252	43	s)xu(s	s)xu(s	NOUN
ma-44	252	44	,	,	PUNCT
ma-44	253	1	a)ds	a)ds	PROPN
ma-44	253	2	−	−	PROPN
ma-44	253	3	1	1	NUM
ma-44	253	4	γ(α2	γ(α2	NOUN
ma-44	253	5	−	−	PROPN
ma-44	253	6	µ	µ	X
ma-44	253	7	)	)	PUNCT
ma-44	253	8	t1∫	t1∫	NOUN
ma-44	253	9	a	a	DET
ma-44	253	10	ϕ′(s)ϕα2−µ−1(t1	ϕ′(s)ϕα2−µ−1(t1	NOUN
ma-44	253	11	,	,	PUNCT
ma-44	253	12	s)xu(s	s)xu(s	NOUN
ma-44	253	13	,	,	PUNCT
ma-44	254	1	a)ds	a)ds	PROPN
ma-44	254	2	+	+	CCONJ
ma-44	254	3	γ	γ	PROPN
ma-44	254	4	(	(	PUNCT
ma-44	254	5	γ2	γ2	ADJ
ma-44	254	6	)	)	PUNCT
ma-44	254	7	γ	γ	PROPN
ma-44	254	8	(	(	PUNCT
ma-44	254	9	γ2	γ2	PROPN
ma-44	254	10	−	−	PROPN
ma-44	254	11	µ	µ	NOUN
ma-44	254	12	)	)	PUNCT
ma-44	254	13	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	254	14	(	(	PUNCT
ma-44	254	15	t2	t2	NOUN
ma-44	254	16	,	,	PUNCT
ma-44	254	17	a)−	a)−	PROPN
ma-44	254	18	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	254	19	(	(	PUNCT
ma-44	254	20	t1	t1	NOUN
ma-44	254	21	,	,	PUNCT
ma-44	254	22	a	a	DET
ma-44	254	23	)	)	PUNCT
ma-44	254	24	ϕγ2−1	ϕγ2−1	NOUN
ma-44	254	25	(	(	PUNCT
ma-44	254	26	b	b	NOUN
ma-44	254	27	,	,	PUNCT
ma-44	254	28	a	a	PRON
ma-44	254	29	)	)	PUNCT
ma-44	254	30	n∑	n∑	NOUN
ma-44	254	31	i=1	i=1	PROPN
ma-44	254	32	λiu	λiu	PROPN
ma-44	254	33	(	(	PUNCT
ma-44	254	34	ζi	ζi	PROPN
ma-44	254	35	)	)	PUNCT
ma-44	254	36	+	+	CCONJ
ma-44	254	37	γ	γ	PROPN
ma-44	254	38	(	(	PUNCT
ma-44	254	39	γ2	γ2	ADJ
ma-44	254	40	)	)	PUNCT
ma-44	254	41	γ(α2)γ	γ(α2)γ	PROPN
ma-44	254	42	(	(	PUNCT
ma-44	254	43	γ2	γ2	PROPN
ma-44	254	44	−	−	PROPN
ma-44	254	45	µ	µ	NOUN
ma-44	254	46	)	)	PUNCT
ma-44	254	47	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	254	48	(	(	PUNCT
ma-44	254	49	t2	t2	NOUN
ma-44	254	50	,	,	PUNCT
ma-44	254	51	a)−	a)−	PROPN
ma-44	254	52	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	254	53	(	(	PUNCT
ma-44	254	54	t1	t1	NOUN
ma-44	254	55	,	,	PUNCT
ma-44	254	56	a	a	DET
ma-44	254	57	)	)	PUNCT
ma-44	254	58	ϕγ2−1	ϕγ2−1	NOUN
ma-44	254	59	(	(	PUNCT
ma-44	254	60	b	b	NOUN
ma-44	254	61	,	,	PUNCT
ma-44	254	62	a	a	PRON
ma-44	254	63	)	)	PUNCT
ma-44	254	64	b∫	b∫	NOUN
ma-44	254	65	a	a	DET
ma-44	254	66	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	254	67	,	,	PUNCT
ma-44	254	68	t)xu(t	t)xu(t	PRON
ma-44	254	69	,	,	PUNCT
ma-44	254	70	a)dt	a)dt	PROPN
ma-44	254	71	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	254	72	≤	≤	NOUN
ma-44	254	73	ω.rq−1	ω.rq−1	NOUN
ma-44	254	74	γ(α2	γ(α2	PUNCT
ma-44	254	75	−	−	PROPN
ma-44	254	76	µ+	µ+	PUNCT
ma-44	254	77	1	1	NUM
ma-44	254	78	)	)	PUNCT
ma-44	254	79	ϕα2−µ(t2	ϕα2−µ(t2	NOUN
ma-44	254	80	,	,	PUNCT
ma-44	254	81	t1	t1	NOUN
ma-44	254	82	)	)	PUNCT
ma-44	254	83	+	+	CCONJ
ma-44	254	84	(	(	PUNCT
ma-44	254	85	γ	γ	X
ma-44	254	86	(	(	PUNCT
ma-44	254	87	γ2	γ2	PROPN
ma-44	254	88	)	)	PUNCT
ma-44	254	89	λ2r	λ2r	NOUN
ma-44	254	90	γ	γ	X
ma-44	254	91	(	(	PUNCT
ma-44	254	92	γ2	γ2	PROPN
ma-44	254	93	−	−	PROPN
ma-44	254	94	µ)ϕγ2−1	µ)ϕγ2−1	NOUN
ma-44	254	95	(	(	PUNCT
ma-44	254	96	b	b	NOUN
ma-44	254	97	,	,	PUNCT
ma-44	254	98	a	a	NOUN
ma-44	254	99	)	)	PUNCT
ma-44	255	1	+	+	CCONJ
ma-44	255	2	γ	γ	PROPN
ma-44	255	3	(	(	PUNCT
ma-44	255	4	γ2	γ2	PROPN
ma-44	255	5	)	)	PUNCT
ma-44	255	6	.ω.rq−1.mα2	.ω.rq−1.mα2	X
ma-44	256	1	γ(α2	γ(α2	NOUN
ma-44	257	1	+	+	CCONJ
ma-44	257	2	1)γ	1)γ	PROPN
ma-44	257	3	(	(	PUNCT
ma-44	257	4	γ2	γ2	NOUN
ma-44	257	5	−	−	PROPN
ma-44	257	6	µ)ϕγ2−1	µ)ϕγ2−1	NOUN
ma-44	257	7	(	(	PUNCT
ma-44	257	8	b	b	NOUN
ma-44	257	9	,	,	PUNCT
ma-44	257	10	a	a	PRON
ma-44	257	11	)	)	PUNCT
ma-44	257	12	)	)	PUNCT
ma-44	257	13	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	258	1	(	(	PUNCT
ma-44	258	2	t2	t2	NOUN
ma-44	258	3	,	,	PUNCT
ma-44	258	4	t1	t1	NOUN
ma-44	258	5	)	)	PUNCT
ma-44	258	6	.	.	PUNCT
ma-44	259	1	hence	hence	ADV
ma-44	259	2	,	,	PUNCT
ma-44	259	3	sup	sup	NOUN
ma-44	259	4	t∈[a	t∈[a	NOUN
ma-44	259	5	,	,	PUNCT
ma-44	259	6	b	b	NOUN
ma-44	259	7	]	]	X
ma-44	259	8	∣∣(rldµ;ϕ	∣∣(rldµ;ϕ	PROPN
ma-44	259	9	a+	a+	PUNCT
ma-44	259	10	gu	gu	NOUN
ma-44	259	11	)	)	PUNCT
ma-44	260	1	(	(	PUNCT
ma-44	260	2	t2)−	t2)−	NOUN
ma-44	260	3	(	(	PUNCT
ma-44	260	4	rldµ;ϕ	rldµ;ϕ	ADJ
ma-44	260	5	a+	a+	PRON
ma-44	260	6	gu	gu	NOUN
ma-44	260	7	)	)	PUNCT
ma-44	260	8	(	(	PUNCT
ma-44	260	9	t1	t1	NOUN
ma-44	260	10	)	)	PUNCT
ma-44	260	11	∣∣→	∣∣→	ADP
ma-44	260	12	0	0	NUM
ma-44	260	13	,	,	PUNCT
ma-44	260	14	as	as	ADP
ma-44	260	15	t2	t2	PROPN
ma-44	260	16	→	→	SYM
ma-44	260	17	t1	t1	PROPN
ma-44	260	18	.	.	PUNCT
ma-44	261	1	as	as	ADP
ma-44	261	2	a	a	DET
ma-44	261	3	consequence	consequence	NOUN
ma-44	261	4	of	of	ADP
ma-44	261	5	the	the	DET
ma-44	261	6	above	above	ADJ
ma-44	261	7	three	three	NUM
ma-44	261	8	steps	step	NOUN
ma-44	261	9	and	and	CCONJ
ma-44	261	10	thanks	thank	NOUN
ma-44	261	11	to	to	PART
ma-44	261	12	arzela	arzela	PROPN
ma-44	261	13	–	–	PUNCT
ma-44	261	14	ascoli	ascoli	PROPN
ma-44	261	15	theorem	theorem	PROPN
ma-44	261	16	,	,	PUNCT
ma-44	261	17	we	we	PRON
ma-44	261	18	conclude	conclude	VERB
ma-44	261	19	that	that	SCONJ
ma-44	261	20	g	g	PROPN
ma-44	261	21	is	be	AUX
ma-44	261	22	completely	completely	ADV
ma-44	261	23	continuous.the	continuous.the	DET
ma-44	261	24	proof	proof	NOUN
ma-44	261	25	of	of	ADP
ma-44	261	26	theorem	theorem	ADJ
ma-44	261	27	1	1	NUM
ma-44	261	28	is	be	AUX
ma-44	261	29	thus	thus	ADV
ma-44	261	30	completely	completely	ADV
ma-44	261	31	achieved	achieve	VERB
ma-44	261	32	.	.	PUNCT
ma-44	262	1	�	�	PROPN
ma-44	262	2	3.2	3.2	NUM
ma-44	262	3	.	.	PUNCT
ma-44	263	1	criteria	criterion	NOUN
ma-44	263	2	for	for	ADP
ma-44	263	3	existence	existence	NOUN
ma-44	263	4	of	of	ADP
ma-44	263	5	a	a	DET
ma-44	263	6	solution	solution	NOUN
ma-44	263	7	.	.	PUNCT
ma-44	264	1	theorem	theorem	NOUN
ma-44	264	2	2	2	NUM
ma-44	265	1	.	.	PUNCT
ma-44	265	2	assume	assume	VERB
ma-44	265	3	that	that	SCONJ
ma-44	265	4	h2	h2	NOUN
ma-44	265	5	and	and	CCONJ
ma-44	265	6	h3	h3	NOUN
ma-44	265	7	are	be	AUX
ma-44	265	8	satisfied	satisfied	ADJ
ma-44	265	9	.	.	PUNCT
ma-44	266	1	suppose	suppose	VERB
ma-44	266	2	that	that	SCONJ
ma-44	266	3	υ1	υ1	PROPN
ma-44	266	4	+	+	CCONJ
ma-44	266	5	υ2	υ2	VERB
ma-44	266	6	<	<	X
ma-44	266	7	1	1	NUM
ma-44	266	8	,	,	PUNCT
ma-44	266	9	where	where	SCONJ
ma-44	266	10	υ1	υ1	PROPN
ma-44	266	11	=	=	SYM
ma-44	266	12	2	2	NUM
ma-44	266	13	(	(	PUNCT
ma-44	266	14	q	q	NOUN
ma-44	266	15	−	−	PROPN
ma-44	266	16	1	1	NUM
ma-44	266	17	)	)	PUNCT
ma-44	266	18	∆q−2mα2	∆q−2mα2	NOUN
ma-44	266	19	γ(α2	γ(α2	NOUN
ma-44	267	1	+	+	CCONJ
ma-44	267	2	1	1	X
ma-44	267	3	)	)	PUNCT
ma-44	267	4	(	(	PUNCT
ma-44	267	5	4υmα1	4υmα1	NOUN
ma-44	267	6	γ(α1	γ(α1	NOUN
ma-44	267	7	+	+	CCONJ
ma-44	267	8	1	1	X
ma-44	267	9	)	)	PUNCT
ma-44	268	1	+	+	CCONJ
ma-44	268	2	mρ	mρ	X
ma-44	268	3	γ	γ	NOUN
ma-44	268	4	(	(	PUNCT
ma-44	268	5	ρ+	ρ+	NUM
ma-44	268	6	1	1	NUM
ma-44	268	7	)	)	PUNCT
ma-44	268	8	)	)	PUNCT
ma-44	269	1	+	+	CCONJ
ma-44	269	2	λ2	λ2	NOUN
ma-44	269	3	,	,	PUNCT
ma-44	269	4	and	and	CCONJ
ma-44	269	5	υ2	υ2	NOUN
ma-44	269	6	=	=	SYM
ma-44	269	7	(	(	PUNCT
ma-44	269	8	q	q	NOUN
ma-44	269	9	−	−	PROPN
ma-44	269	10	1	1	NUM
ma-44	269	11	)	)	PUNCT
ma-44	269	12	∆q−2	∆q−2	NOUN
ma-44	269	13	(	(	PUNCT
ma-44	269	14	4υmα1	4υmα1	NOUN
ma-44	269	15	γ(α1	γ(α1	NOUN
ma-44	269	16	+	+	CCONJ
ma-44	269	17	1	1	X
ma-44	269	18	)	)	PUNCT
ma-44	270	1	+	+	CCONJ
ma-44	270	2	mρ	mρ	X
ma-44	270	3	γ	γ	NOUN
ma-44	270	4	(	(	PUNCT
ma-44	270	5	ρ+	ρ+	NUM
ma-44	270	6	1	1	NUM
ma-44	270	7	)	)	PUNCT
ma-44	270	8	)	)	PUNCT
ma-44	270	9	(	(	PUNCT
ma-44	270	10	mα2−µ	mα2−µ	NOUN
ma-44	270	11	γ(α2	γ(α2	NOUN
ma-44	270	12	−	−	PROPN
ma-44	270	13	µ+	µ+	PUNCT
ma-44	270	14	1	1	NUM
ma-44	270	15	)	)	PUNCT
ma-44	270	16	+	+	CCONJ
ma-44	270	17	γ	γ	X
ma-44	270	18	(	(	PUNCT
ma-44	270	19	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	270	20	γ(α2	γ(α2	NOUN
ma-44	270	21	+	+	X
ma-44	270	22	1)γ	1)γ	PROPN
ma-44	270	23	(	(	PUNCT
ma-44	270	24	γ2	γ2	PROPN
ma-44	270	25	−	−	PROPN
ma-44	270	26	µ	µ	NUM
ma-44	270	27	)	)	PUNCT
ma-44	270	28	)	)	PUNCT
ma-44	271	1	+	+	CCONJ
ma-44	271	2	γ	γ	PROPN
ma-44	271	3	(	(	PUNCT
ma-44	271	4	γ2	γ2	ADJ
ma-44	271	5	)	)	PUNCT
ma-44	271	6	λ2	λ2	PROPN
ma-44	271	7	m	m	PROPN
ma-44	271	8	−µ	−µ	ADJ
ma-44	271	9	γ	γ	X
ma-44	271	10	(	(	PUNCT
ma-44	271	11	γ2	γ2	PROPN
ma-44	271	12	−	−	PROPN
ma-44	271	13	µ	µ	NUM
ma-44	271	14	)	)	PUNCT
ma-44	271	15	.	.	PUNCT
ma-44	272	1	then	then	ADV
ma-44	272	2	,	,	PUNCT
ma-44	272	3	(	(	PUNCT
ma-44	272	4	1.1	1.1	NUM
ma-44	272	5	)	)	PUNCT
ma-44	272	6	has	have	VERB
ma-44	272	7	a	a	DET
ma-44	272	8	uniqueness	uniqueness	NOUN
ma-44	272	9	solution	solution	NOUN
ma-44	272	10	.	.	PUNCT
ma-44	273	1	eur	eur	PROPN
ma-44	273	2	.	.	PUNCT
ma-44	274	1	j.	j.	PROPN
ma-44	274	2	math	math	PROPN
ma-44	274	3	.	.	PUNCT
ma-44	275	1	anal	anal	ADJ
ma-44	275	2	.	.	PUNCT
ma-44	276	1	1	1	NUM
ma-44	276	2	(	(	PUNCT
ma-44	276	3	2021	2021	NUM
ma-44	276	4	)	)	PUNCT
ma-44	276	5	175	175	NUM
ma-44	276	6	proof	proof	NOUN
ma-44	276	7	.	.	PUNCT
ma-44	277	1	we	we	PRON
ma-44	277	2	pass	pass	VERB
ma-44	277	3	to	to	PART
ma-44	277	4	prove	prove	VERB
ma-44	277	5	that	that	SCONJ
ma-44	277	6	g	g	PROPN
ma-44	277	7	is	be	AUX
ma-44	277	8	a	a	DET
ma-44	277	9	contraction	contraction	NOUN
ma-44	277	10	.	.	PUNCT
ma-44	278	1	for	for	ADP
ma-44	278	2	any	any	DET
ma-44	278	3	u	u	NOUN
ma-44	278	4	,	,	PUNCT
ma-44	278	5	v	v	X
ma-44	278	6	∈	∈	NOUN
ma-44	278	7	ur	ur	INTJ
ma-44	278	8	,	,	PUNCT
ma-44	278	9	we	we	PRON
ma-44	278	10	have	have	VERB
ma-44	278	11	the	the	DET
ma-44	278	12	following	follow	VERB
ma-44	278	13	estimate	estimate	NOUN
ma-44	278	14	|xu(s	|xu(s	NUM
ma-44	278	15	,	,	PUNCT
ma-44	278	16	a)−xv	a)−xv	PROPN
ma-44	278	17	(	(	PUNCT
ma-44	278	18	s	s	X
ma-44	278	19	,	,	PUNCT
ma-44	278	20	a)|	a)|	X
ma-44	279	1	=	=	NOUN
ma-44	279	2	∣∣∣∣∣∣ψq	∣∣∣∣∣∣ψq	PROPN
ma-44	279	3			PROPN
ma-44	279	4	1	1	NUM
ma-44	279	5	γ(α1	γ(α1	NOUN
ma-44	279	6	)	)	PUNCT
ma-44	279	7	s∫	s∫	PROPN
ma-44	279	8	a	a	DET
ma-44	279	9	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	279	10	,	,	PUNCT
ma-44	279	11	z)hu(z)dz	z)hu(z)dz	NOUN
ma-44	280	1	+	+	CCONJ
ma-44	280	2	(	(	PUNCT
ma-44	280	3	iρ;ϕ	iρ;ϕ	VERB
ma-44	280	4	0	0	NUM
ma-44	280	5	+	+	NUM
ma-44	280	6	u	u	SYM
ma-44	280	7	(	(	PUNCT
ma-44	280	8	ζ)−	ζ)−	PROPN
ma-44	280	9	iα1;ϕ	iα1;ϕ	PROPN
ma-44	280	10	0	0	PUNCT
ma-44	280	11	+	+	NUM
ma-44	280	12	hu(b	hu(b	NUM
ma-44	280	13	)	)	PUNCT
ma-44	280	14	)	)	PUNCT
ma-44	280	15	ϕγ1−1	ϕγ1−1	INTJ
ma-44	280	16	(	(	PUNCT
ma-44	280	17	b	b	NOUN
ma-44	280	18	,	,	PUNCT
ma-44	280	19	a	a	PRON
ma-44	280	20	)	)	PUNCT
ma-44	280	21	ϕγ1−1	ϕγ1−1	NOUN
ma-44	280	22	(	(	PUNCT
ma-44	280	23	s	s	PROPN
ma-44	280	24	,	,	PUNCT
ma-44	280	25	a	a	PRON
ma-44	280	26	)	)	PUNCT
ma-44	280	27			PROPN
ma-44	280	28	−	−	PROPN
ma-44	280	29	ψq	ψq	PROPN
ma-44	280	30			PROPN
ma-44	280	31	1	1	NUM
ma-44	280	32	γ(α1	γ(α1	NOUN
ma-44	280	33	)	)	PUNCT
ma-44	280	34	s∫	s∫	PROPN
ma-44	280	35	a	a	DET
ma-44	280	36	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	280	37	,	,	PUNCT
ma-44	280	38	z)hv	z)hv	PROPN
ma-44	280	39	(	(	PUNCT
ma-44	280	40	z)dz	z)dz	PROPN
ma-44	280	41	+	+	CCONJ
ma-44	280	42	(	(	PUNCT
ma-44	280	43	iρ;ϕ	iρ;ϕ	VERB
ma-44	280	44	0	0	NUM
ma-44	280	45	+	+	NUM
ma-44	280	46	v	v	X
ma-44	280	47	(	(	PUNCT
ma-44	280	48	ζ)−	ζ)−	PROPN
ma-44	280	49	iα1;ϕ	iα1;ϕ	PROPN
ma-44	280	50	0	0	PROPN
ma-44	280	51	+	+	NUM
ma-44	280	52	hv	hv	PROPN
ma-44	280	53	(	(	PUNCT
ma-44	280	54	b	b	NOUN
ma-44	280	55	)	)	PUNCT
ma-44	280	56	)	)	PUNCT
ma-44	280	57	ϕγ1−1	ϕγ1−1	INTJ
ma-44	280	58	(	(	PUNCT
ma-44	280	59	b	b	NOUN
ma-44	280	60	,	,	PUNCT
ma-44	280	61	a	a	PRON
ma-44	280	62	)	)	PUNCT
ma-44	280	63	ϕγ1−1	ϕγ1−1	NOUN
ma-44	280	64	(	(	PUNCT
ma-44	280	65	s	s	PROPN
ma-44	280	66	,	,	PUNCT
ma-44	280	67	a	a	PRON
ma-44	280	68	)	)	PUNCT
ma-44	280	69	∣∣∣∣∣∣	∣∣∣∣∣∣	PUNCT
ma-44	281	1	≤	≤	NOUN
ma-44	281	2	(	(	PUNCT
ma-44	281	3	q	q	NOUN
ma-44	281	4	−	−	PROPN
ma-44	281	5	1	1	X
ma-44	281	6	)	)	PUNCT
ma-44	281	7	yq−2	yq−2	NOUN
ma-44	281	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	281	9	1	1	NUM
ma-44	281	10	γ(α1	γ(α1	NOUN
ma-44	281	11	)	)	PUNCT
ma-44	281	12	s∫	s∫	PROPN
ma-44	281	13	a	a	DET
ma-44	281	14	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	281	15	,	,	PUNCT
ma-44	281	16	z)hu(z)dz	z)hu(z)dz	NOUN
ma-44	281	17	−	−	ADP
ma-44	281	18	1	1	NUM
ma-44	281	19	γ(α1	γ(α1	NOUN
ma-44	281	20	)	)	PUNCT
ma-44	281	21	s∫	s∫	PROPN
ma-44	281	22	a	a	DET
ma-44	281	23	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	281	24	,	,	PUNCT
ma-44	281	25	z)hv	z)hv	PROPN
ma-44	281	26	(	(	PUNCT
ma-44	281	27	z)dz	z)dz	PROPN
ma-44	281	28	+	+	NUM
ma-44	281	29	ϕγ1−1	ϕγ1−1	NOUN
ma-44	281	30	(	(	PUNCT
ma-44	281	31	s	s	PROPN
ma-44	281	32	,	,	PUNCT
ma-44	281	33	a	a	PRON
ma-44	281	34	)	)	PUNCT
ma-44	281	35	ϕγ1−1	ϕγ1−1	NOUN
ma-44	281	36	(	(	PUNCT
ma-44	281	37	b	b	NOUN
ma-44	281	38	,	,	PUNCT
ma-44	281	39	a	a	PRON
ma-44	281	40	)	)	PUNCT
ma-44	281	41	(	(	PUNCT
ma-44	281	42	iρ;ϕ	iρ;ϕ	VERB
ma-44	281	43	0	0	NUM
ma-44	281	44	+	+	NUM
ma-44	281	45	u	u	SYM
ma-44	281	46	(	(	PUNCT
ma-44	281	47	ζ)−	ζ)−	PROPN
ma-44	281	48	iρ;ϕ	iρ;ϕ	VERB
ma-44	281	49	0	0	NUM
ma-44	281	50	+	+	NUM
ma-44	281	51	v	v	ADJ
ma-44	281	52	(	(	PUNCT
ma-44	281	53	ζ	ζ	NOUN
ma-44	281	54	)	)	PUNCT
ma-44	281	55	)	)	PUNCT
ma-44	282	1	+	+	CCONJ
ma-44	282	2	ϕγ1−1	ϕγ1−1	NOUN
ma-44	282	3	(	(	PUNCT
ma-44	282	4	s	s	PROPN
ma-44	282	5	,	,	PUNCT
ma-44	282	6	a	a	PRON
ma-44	282	7	)	)	PUNCT
ma-44	282	8	ϕγ1−1	ϕγ1−1	NOUN
ma-44	282	9	(	(	PUNCT
ma-44	282	10	b	b	NOUN
ma-44	282	11	,	,	PUNCT
ma-44	282	12	a	a	PRON
ma-44	282	13	)	)	PUNCT
ma-44	282	14	(	(	PUNCT
ma-44	282	15	iα1;ϕ	iα1;ϕ	PROPN
ma-44	282	16	0	0	PUNCT
ma-44	282	17	+	+	NUM
ma-44	282	18	hu(b)−	hu(b)−	NOUN
ma-44	282	19	iα1;ϕ	iα1;ϕ	PROPN
ma-44	282	20	0	0	NUM
ma-44	282	21	+	+	NUM
ma-44	282	22	hv	hv	PROPN
ma-44	282	23	(	(	PUNCT
ma-44	282	24	b	b	NOUN
ma-44	282	25	)	)	PUNCT
ma-44	282	26	)	)	PUNCT
ma-44	282	27	∣∣∣∣	∣∣∣∣	NOUN
ma-44	282	28	≤	≤	NOUN
ma-44	282	29	(	(	PUNCT
ma-44	282	30	q	q	NOUN
ma-44	282	31	−	−	PROPN
ma-44	282	32	1	1	X
ma-44	282	33	)	)	PUNCT
ma-44	282	34	yq−2	yq−2	NOUN
ma-44	282	35	(	(	PUNCT
ma-44	282	36	2mα1	2mα1	NUM
ma-44	282	37	γ(α1	γ(α1	VERB
ma-44	282	38	+	+	CCONJ
ma-44	282	39	1	1	X
ma-44	282	40	)	)	PUNCT
ma-44	282	41	sup	sup	NOUN
ma-44	282	42	t∈[a	t∈[a	NOUN
ma-44	282	43	,	,	PUNCT
ma-44	282	44	b	b	NOUN
ma-44	282	45	]	]	X
ma-44	282	46	|hu(t)−	|hu(t)−	PROPN
ma-44	282	47	hv	hv	PROPN
ma-44	282	48	(	(	PUNCT
ma-44	282	49	t)|+	t)|+	PRON
ma-44	282	50	mρ	mρ	X
ma-44	282	51	γ	γ	X
ma-44	282	52	(	(	PUNCT
ma-44	282	53	ρ+	ρ+	NUM
ma-44	282	54	1	1	NUM
ma-44	282	55	)	)	PUNCT
ma-44	282	56	sup	sup	NOUN
ma-44	282	57	t∈[a	t∈[a	NOUN
ma-44	282	58	,	,	PUNCT
ma-44	282	59	b	b	NOUN
ma-44	282	60	]	]	PUNCT
ma-44	282	61	|u(t)−	|u(t)−	X
ma-44	282	62	v(t)|	v(t)|	PROPN
ma-44	282	63	)	)	PUNCT
ma-44	282	64	≤	≤	NOUN
ma-44	282	65	(	(	PUNCT
ma-44	282	66	q	q	NOUN
ma-44	282	67	−	−	PROPN
ma-44	282	68	1	1	NUM
ma-44	282	69	)	)	PUNCT
ma-44	282	70	yq−2	yq−2	NOUN
ma-44	282	71	(	(	PUNCT
ma-44	282	72	(	(	PUNCT
ma-44	282	73	2υmα1	2υmα1	NUM
ma-44	282	74	γ(α1	γ(α1	NOUN
ma-44	282	75	+	+	CCONJ
ma-44	282	76	1	1	X
ma-44	282	77	)	)	PUNCT
ma-44	283	1	+	+	CCONJ
ma-44	283	2	mρ	mρ	X
ma-44	283	3	γ	γ	NOUN
ma-44	283	4	(	(	PUNCT
ma-44	283	5	ρ+	ρ+	NUM
ma-44	283	6	1	1	NUM
ma-44	283	7	)	)	PUNCT
ma-44	283	8	)	)	PUNCT
ma-44	283	9	sup	sup	NOUN
ma-44	283	10	t∈[a	t∈[a	NOUN
ma-44	283	11	,	,	PUNCT
ma-44	283	12	b	b	NOUN
ma-44	283	13	]	]	PUNCT
ma-44	283	14	|u(t)−	|u(t)−	X
ma-44	283	15	v(t)|	v(t)|	ADJ
ma-44	284	1	+	+	X
ma-44	284	2	2υmα1	2υmα1	NUM
ma-44	284	3	γ(α1	γ(α1	NOUN
ma-44	284	4	+	+	CCONJ
ma-44	284	5	1	1	X
ma-44	284	6	)	)	PUNCT
ma-44	284	7	sup	sup	NOUN
ma-44	284	8	t∈[a	t∈[a	NOUN
ma-44	284	9	,	,	PUNCT
ma-44	284	10	b	b	NOUN
ma-44	284	11	]	]	X
ma-44	284	12	∣∣rldµ;ϕ	∣∣rldµ;ϕ	PROPN
ma-44	284	13	a+	a+	PUNCT
ma-44	284	14	u(t)−rl	u(t)−rl	PROPN
ma-44	285	1	dµ;ϕ	dµ;ϕ	PUNCT
ma-44	285	2	a+	a+	PUNCT
ma-44	285	3	v(t	v(t	NOUN
ma-44	285	4	)	)	PUNCT
ma-44	285	5	∣∣	∣∣	ADJ
ma-44	285	6	)	)	PUNCT
ma-44	285	7	≤	≤	NOUN
ma-44	285	8	(	(	PUNCT
ma-44	285	9	q	q	NOUN
ma-44	285	10	−	−	PROPN
ma-44	285	11	1	1	NUM
ma-44	285	12	)	)	PUNCT
ma-44	285	13	∆q−2	∆q−2	NOUN
ma-44	285	14	(	(	PUNCT
ma-44	285	15	4υmα1	4υmα1	NOUN
ma-44	285	16	γ(α1	γ(α1	NOUN
ma-44	285	17	+	+	CCONJ
ma-44	285	18	1	1	X
ma-44	285	19	)	)	PUNCT
ma-44	286	1	+	+	CCONJ
ma-44	286	2	mρ	mρ	X
ma-44	286	3	γ	γ	NOUN
ma-44	286	4	(	(	PUNCT
ma-44	286	5	ρ+	ρ+	NUM
ma-44	286	6	1	1	NUM
ma-44	286	7	)	)	PUNCT
ma-44	286	8	)	)	PUNCT
ma-44	286	9	‖u	‖u	NOUN
ma-44	286	10	−	−	PROPN
ma-44	287	1	v‖cµϕ	v‖cµϕ	X
ma-44	287	2	.	.	PUNCT
ma-44	288	1	where	where	SCONJ
ma-44	288	2			NUM
ma-44	288	3	∆	∆	X
ma-44	288	4	>	>	X
ma-44	288	5	2υmα1	2υmα1	NUM
ma-44	288	6	γ(α1	γ(α1	NOUN
ma-44	288	7	+	+	NOUN
ma-44	288	8	1	1	NUM
ma-44	288	9	)	)	PUNCT
ma-44	288	10	+	+	NUM
ma-44	288	11	mρ	mρ	ADJ
ma-44	288	12	γ(ρ+1	γ(ρ+1	NUM
ma-44	288	13	)	)	PUNCT
ma-44	288	14	,	,	PUNCT
ma-44	288	15	if	if	SCONJ
ma-44	288	16	q	q	X
ma-44	288	17	>	>	X
ma-44	288	18	2,ou	2,ou	NOUN
ma-44	288	19	0	0	PUNCT
ma-44	288	20	<	<	X
ma-44	288	21	∆	∆	PROPN
ma-44	288	22	≤	≤	NOUN
ma-44	288	23	2υmα1	2υmα1	NUM
ma-44	288	24	γ(α1	γ(α1	NOUN
ma-44	288	25	+	+	NOUN
ma-44	288	26	1	1	NUM
ma-44	288	27	)	)	PUNCT
ma-44	289	1	+	+	NUM
ma-44	289	2	mρ	mρ	ADJ
ma-44	289	3	γ(ρ+1	γ(ρ+1	NUM
ma-44	289	4	)	)	PUNCT
ma-44	289	5	,	,	PUNCT
ma-44	289	6	if	if	SCONJ
ma-44	289	7	1	1	NUM
ma-44	289	8	<	<	X
ma-44	289	9	q	q	X
ma-44	289	10	≤	≤	NUM
ma-44	289	11	2	2	NUM
ma-44	289	12	.	.	PUNCT
ma-44	290	1	then	then	ADV
ma-44	290	2	sup	sup	NOUN
ma-44	290	3	t∈[a	t∈[a	NOUN
ma-44	290	4	,	,	PUNCT
ma-44	290	5	b	b	NOUN
ma-44	290	6	]	]	X
ma-44	290	7	|(gu	|(gu	NOUN
ma-44	290	8	)	)	PUNCT
ma-44	290	9	(	(	PUNCT
ma-44	290	10	t)−	t)−	PROPN
ma-44	290	11	(	(	PUNCT
ma-44	290	12	gv	gv	ADP
ma-44	290	13	)	)	PUNCT
ma-44	290	14	(	(	PUNCT
ma-44	290	15	t)|	t)|	NOUN
ma-44	290	16	(	(	PUNCT
ma-44	290	17	3.4	3.4	NUM
ma-44	290	18	)	)	PUNCT
ma-44	290	19	≤	≤	NUM
ma-44	290	20	sup	sup	NOUN
ma-44	290	21	t∈[a	t∈[a	NOUN
ma-44	290	22	,	,	PUNCT
ma-44	290	23	b	b	NOUN
ma-44	290	24	]	]	PUNCT
ma-44	290	25	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	290	26	1	1	NUM
ma-44	290	27	γ(α2	γ(α2	NOUN
ma-44	290	28	)	)	PUNCT
ma-44	291	1	t∫	t∫	PRON
ma-44	291	2	a	a	DET
ma-44	291	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	291	4	,	,	PUNCT
ma-44	291	5	s	s	AUX
ma-44	291	6	)	)	PUNCT
ma-44	291	7	(	(	PUNCT
ma-44	291	8	xu	xu	INTJ
ma-44	291	9	−xv	−xv	PROPN
ma-44	291	10	)	)	PUNCT
ma-44	291	11	(	(	PUNCT
ma-44	291	12	s	s	X
ma-44	291	13	,	,	PUNCT
ma-44	291	14	a)ds	a)ds	PROPN
ma-44	291	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ma-44	291	16	+	+	CCONJ
ma-44	291	17	sup	sup	NOUN
ma-44	291	18	t∈[a	t∈[a	NOUN
ma-44	291	19	,	,	PUNCT
ma-44	291	20	b	b	NOUN
ma-44	291	21	]	]	PUNCT
ma-44	291	22	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	291	23	ϕγ2−1	ϕγ2−1	PROPN
ma-44	291	24	(	(	PUNCT
ma-44	291	25	t	t	PROPN
ma-44	291	26	,	,	PUNCT
ma-44	291	27	a	a	PRON
ma-44	291	28	)	)	PUNCT
ma-44	291	29	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	291	30	(	(	PUNCT
ma-44	291	31	b	b	NOUN
ma-44	291	32	,	,	PUNCT
ma-44	291	33	a	a	PRON
ma-44	291	34	)	)	PUNCT
ma-44	291	35	b∫	b∫	NOUN
ma-44	291	36	a	a	DET
ma-44	291	37	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	PROPN
ma-44	291	38	,	,	PUNCT
ma-44	291	39	t	t	PROPN
ma-44	291	40	)	)	PUNCT
ma-44	291	41	(	(	PUNCT
ma-44	291	42	xu	xu	INTJ
ma-44	291	43	−xv	−xv	PROPN
ma-44	291	44	)	)	PUNCT
ma-44	291	45	(	(	PUNCT
ma-44	291	46	t	t	PROPN
ma-44	291	47	,	,	PUNCT
ma-44	291	48	a)dt	a)dt	PROPN
ma-44	291	49	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	291	50	+	+	NUM
ma-44	291	51	sup	sup	NOUN
ma-44	291	52	t∈[a	t∈[a	NOUN
ma-44	291	53	,	,	PUNCT
ma-44	291	54	b	b	X
ma-44	291	55	]	]	X
ma-44	291	56	∣∣∣∣∣ϕγ2−1	∣∣∣∣∣ϕγ2−1	PROPN
ma-44	291	57	(	(	PUNCT
ma-44	291	58	t	t	PROPN
ma-44	291	59	,	,	PUNCT
ma-44	291	60	a	a	PRON
ma-44	291	61	)	)	PUNCT
ma-44	291	62	ϕγ2−1	ϕγ2−1	NOUN
ma-44	291	63	(	(	PUNCT
ma-44	291	64	b	b	NOUN
ma-44	291	65	,	,	PUNCT
ma-44	291	66	a	a	PRON
ma-44	291	67	)	)	PUNCT
ma-44	292	1	n∑	n∑	NOUN
ma-44	292	2	i=1	i=1	PRON
ma-44	293	1	λi	λi	INTJ
ma-44	293	2	(	(	PUNCT
ma-44	293	3	u	u	NOUN
ma-44	293	4	(	(	PUNCT
ma-44	293	5	ζi)−	ζi)−	NOUN
ma-44	293	6	v(ζi	v(ζi	NUM
ma-44	293	7	)	)	PUNCT
ma-44	293	8	)	)	PUNCT
ma-44	293	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-44	293	10	eur	eur	PROPN
ma-44	293	11	.	.	PUNCT
ma-44	294	1	j.	j.	PROPN
ma-44	294	2	math	math	PROPN
ma-44	294	3	.	.	PUNCT
ma-44	295	1	anal	anal	ADJ
ma-44	295	2	.	.	PUNCT
ma-44	296	1	1	1	NUM
ma-44	296	2	(	(	PUNCT
ma-44	296	3	2021	2021	NUM
ma-44	296	4	)	)	PUNCT
ma-44	296	5	176	176	NUM
ma-44	296	6	≤	≤	NOUN
ma-44	296	7	2mα2	2mα2	NUM
ma-44	296	8	γ(α2	γ(α2	NOUN
ma-44	297	1	+	+	CCONJ
ma-44	297	2	1	1	X
ma-44	297	3	)	)	PUNCT
ma-44	297	4	sup	sup	NOUN
ma-44	297	5	t∈[a	t∈[a	NOUN
ma-44	297	6	,	,	PUNCT
ma-44	297	7	b	b	NOUN
ma-44	297	8	]	]	X
ma-44	297	9	|xu(t	|xu(t	PRON
ma-44	297	10	,	,	PUNCT
ma-44	297	11	a)−xv	a)−xv	PROPN
ma-44	297	12	(	(	PUNCT
ma-44	297	13	t	t	PROPN
ma-44	297	14	,	,	PUNCT
ma-44	297	15	a)|+	a)|+	ADJ
ma-44	297	16	λ2	λ2	NOUN
ma-44	297	17	sup	sup	NOUN
ma-44	297	18	t∈[a	t∈[a	NOUN
ma-44	297	19	,	,	PUNCT
ma-44	297	20	b	b	NOUN
ma-44	297	21	]	]	X
ma-44	297	22	(	(	PUNCT
ma-44	297	23	|u	|u	ADJ
ma-44	297	24	(	(	PUNCT
ma-44	297	25	t)−	t)−	PROPN
ma-44	297	26	v(t)|	v(t)|	PROPN
ma-44	297	27	)	)	PUNCT
ma-44	297	28	≤	≤	NOUN
ma-44	297	29	(	(	PUNCT
ma-44	297	30	2	2	NUM
ma-44	297	31	(	(	PUNCT
ma-44	297	32	q	q	NOUN
ma-44	297	33	−	−	PROPN
ma-44	297	34	1	1	NUM
ma-44	297	35	)	)	PUNCT
ma-44	297	36	∆q−2mα2	∆q−2mα2	NOUN
ma-44	297	37	γ(α2	γ(α2	NOUN
ma-44	298	1	+	+	CCONJ
ma-44	298	2	1	1	X
ma-44	298	3	)	)	PUNCT
ma-44	298	4	(	(	PUNCT
ma-44	298	5	4υmα1	4υmα1	NOUN
ma-44	298	6	γ(α1	γ(α1	NOUN
ma-44	298	7	+	+	CCONJ
ma-44	298	8	1	1	X
ma-44	298	9	)	)	PUNCT
ma-44	299	1	+	+	CCONJ
ma-44	299	2	mρ	mρ	X
ma-44	299	3	γ	γ	NOUN
ma-44	299	4	(	(	PUNCT
ma-44	299	5	ρ+	ρ+	NUM
ma-44	299	6	1	1	NUM
ma-44	299	7	)	)	PUNCT
ma-44	299	8	)	)	PUNCT
ma-44	300	1	+	+	NUM
ma-44	300	2	λ2	λ2	NOUN
ma-44	300	3	)	)	PUNCT
ma-44	300	4	‖u	‖u	NOUN
ma-44	300	5	−	−	PROPN
ma-44	300	6	v‖cµϕ	v‖cµϕ	SYM
ma-44	300	7	≤	≤	PROPN
ma-44	300	8	υ1	υ1	PROPN
ma-44	300	9	‖u	‖u	PROPN
ma-44	300	10	−	−	PROPN
ma-44	300	11	v‖cµϕ	v‖cµϕ	SYM
ma-44	300	12	.also	.also	PUNCT
ma-44	300	13	sup	sup	PROPN
ma-44	300	14	t∈[a	t∈[a	NOUN
ma-44	300	15	,	,	PUNCT
ma-44	300	16	b	b	X
ma-44	300	17	]	]	X
ma-44	300	18	∣∣(rldµ;ϕ	∣∣(rldµ;ϕ	PROPN
ma-44	300	19	a+	a+	PUNCT
ma-44	300	20	gu	gu	NOUN
ma-44	300	21	)	)	PUNCT
ma-44	300	22	(	(	PUNCT
ma-44	300	23	t)−	t)−	PROPN
ma-44	300	24	(	(	PUNCT
ma-44	300	25	rldµ;ϕ	rldµ;ϕ	ADJ
ma-44	300	26	a+	a+	X
ma-44	300	27	gv	gv	PROPN
ma-44	300	28	)	)	PUNCT
ma-44	300	29	(	(	PUNCT
ma-44	300	30	t	t	NOUN
ma-44	300	31	)	)	PUNCT
ma-44	300	32	∣∣	∣∣	NUM
ma-44	300	33	(	(	PUNCT
ma-44	300	34	3.5	3.5	NUM
ma-44	300	35	)	)	PUNCT
ma-44	300	36	≤	≤	NUM
ma-44	300	37	sup	sup	NOUN
ma-44	300	38	t∈[a	t∈[a	NOUN
ma-44	300	39	,	,	PUNCT
ma-44	300	40	b	b	NOUN
ma-44	300	41	]	]	PUNCT
ma-44	300	42	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	300	43	1	1	NUM
ma-44	300	44	γ(α2	γ(α2	NOUN
ma-44	300	45	−	−	PROPN
ma-44	300	46	µ	µ	X
ma-44	300	47	)	)	PUNCT
ma-44	300	48	t∫	t∫	PROPN
ma-44	300	49	a	a	DET
ma-44	300	50	ϕ′(s)ϕα2−µ−1(t	ϕ′(s)ϕα2−µ−1(t	PROPN
ma-44	300	51	,	,	PUNCT
ma-44	300	52	s	s	AUX
ma-44	300	53	)	)	PUNCT
ma-44	300	54	(	(	PUNCT
ma-44	300	55	xu	xu	INTJ
ma-44	300	56	−xv	−xv	PROPN
ma-44	300	57	)	)	PUNCT
ma-44	300	58	(	(	PUNCT
ma-44	300	59	s	s	X
ma-44	300	60	,	,	PUNCT
ma-44	300	61	a)ds	a)ds	PROPN
ma-44	300	62	+	+	CCONJ
ma-44	300	63	γ	γ	PROPN
ma-44	300	64	(	(	PUNCT
ma-44	300	65	γ2	γ2	ADJ
ma-44	300	66	)	)	PUNCT
ma-44	300	67	γ	γ	PROPN
ma-44	300	68	(	(	PUNCT
ma-44	300	69	γ2	γ2	PROPN
ma-44	300	70	−	−	PROPN
ma-44	300	71	µ	µ	NOUN
ma-44	300	72	)	)	PUNCT
ma-44	300	73	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	300	74	(	(	PUNCT
ma-44	300	75	t	t	PROPN
ma-44	300	76	,	,	PUNCT
ma-44	300	77	a	a	PRON
ma-44	300	78	)	)	PUNCT
ma-44	300	79	ϕγ2−1	ϕγ2−1	NOUN
ma-44	300	80	(	(	PUNCT
ma-44	300	81	b	b	NOUN
ma-44	300	82	,	,	PUNCT
ma-44	300	83	a	a	PRON
ma-44	300	84	)	)	PUNCT
ma-44	300	85	n∑	n∑	NOUN
ma-44	301	1	i=1	i=1	PRON
ma-44	301	2	λi	λi	INTJ
ma-44	301	3	(	(	PUNCT
ma-44	301	4	u	u	NOUN
ma-44	301	5	(	(	PUNCT
ma-44	301	6	ζi)−	ζi)−	NOUN
ma-44	301	7	v(ζi	v(ζi	NUM
ma-44	301	8	)	)	PUNCT
ma-44	301	9	)	)	PUNCT
ma-44	302	1	+	+	CCONJ
ma-44	302	2	γ	γ	PROPN
ma-44	302	3	(	(	PUNCT
ma-44	302	4	γ2	γ2	ADJ
ma-44	302	5	)	)	PUNCT
ma-44	302	6	γ(α2)γ	γ(α2)γ	PROPN
ma-44	302	7	(	(	PUNCT
ma-44	302	8	γ2	γ2	PROPN
ma-44	302	9	−	−	PROPN
ma-44	302	10	µ	µ	NOUN
ma-44	302	11	)	)	PUNCT
ma-44	302	12	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	302	13	(	(	PUNCT
ma-44	302	14	t	t	PROPN
ma-44	302	15	,	,	PUNCT
ma-44	302	16	a	a	PRON
ma-44	302	17	)	)	PUNCT
ma-44	302	18	ϕγ2−1	ϕγ2−1	NOUN
ma-44	302	19	(	(	PUNCT
ma-44	302	20	b	b	NOUN
ma-44	302	21	,	,	PUNCT
ma-44	302	22	a	a	PRON
ma-44	302	23	)	)	PUNCT
ma-44	302	24	b∫	b∫	NOUN
ma-44	302	25	a	a	DET
ma-44	302	26	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	PROPN
ma-44	302	27	,	,	PUNCT
ma-44	302	28	t	t	PROPN
ma-44	302	29	)	)	PUNCT
ma-44	302	30	(	(	PUNCT
ma-44	302	31	xu	xu	INTJ
ma-44	302	32	−xv	−xv	PROPN
ma-44	302	33	)	)	PUNCT
ma-44	302	34	(	(	PUNCT
ma-44	302	35	t	t	PROPN
ma-44	302	36	,	,	PUNCT
ma-44	302	37	a)dt	a)dt	PROPN
ma-44	302	38	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	302	39	≤	≤	PROPN
ma-44	302	40	(	(	PUNCT
ma-44	302	41	mα2−µ	mα2−µ	NOUN
ma-44	302	42	γ(α2	γ(α2	NOUN
ma-44	302	43	−	−	PROPN
ma-44	302	44	µ+	µ+	PUNCT
ma-44	302	45	1	1	NUM
ma-44	302	46	)	)	PUNCT
ma-44	302	47	+	+	CCONJ
ma-44	302	48	γ	γ	X
ma-44	302	49	(	(	PUNCT
ma-44	302	50	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	302	51	γ(α2	γ(α2	NOUN
ma-44	302	52	+	+	X
ma-44	302	53	1)γ	1)γ	PROPN
ma-44	302	54	(	(	PUNCT
ma-44	302	55	γ2	γ2	PROPN
ma-44	302	56	−	−	PROPN
ma-44	302	57	µ	µ	NUM
ma-44	302	58	)	)	PUNCT
ma-44	302	59	)	)	PUNCT
ma-44	302	60	sup	sup	NOUN
ma-44	302	61	t∈[a	t∈[a	NOUN
ma-44	302	62	,	,	PUNCT
ma-44	302	63	b	b	NOUN
ma-44	302	64	]	]	X
ma-44	302	65	|xu	|xu	PRON
ma-44	302	66	−xv	−xv	NOUN
ma-44	303	1	|	|	ADV
ma-44	303	2	+	+	CCONJ
ma-44	303	3	γ	γ	X
ma-44	303	4	(	(	PUNCT
ma-44	303	5	γ2	γ2	ADJ
ma-44	303	6	)	)	PUNCT
ma-44	303	7	λ2	λ2	PROPN
ma-44	303	8	m	m	PROPN
ma-44	303	9	−µ	−µ	ADJ
ma-44	303	10	γ	γ	X
ma-44	303	11	(	(	PUNCT
ma-44	303	12	γ2	γ2	PROPN
ma-44	303	13	−	−	PROPN
ma-44	303	14	µ	µ	NUM
ma-44	303	15	)	)	PUNCT
ma-44	303	16	sup	sup	NOUN
ma-44	303	17	t∈[a	t∈[a	NOUN
ma-44	303	18	,	,	PUNCT
ma-44	303	19	b	b	NOUN
ma-44	303	20	]	]	X
ma-44	303	21	(	(	PUNCT
ma-44	303	22	|u	|u	ADJ
ma-44	303	23	(	(	PUNCT
ma-44	303	24	t)−	t)−	PROPN
ma-44	303	25	v(t)|	v(t)|	NOUN
ma-44	303	26	)	)	PUNCT
ma-44	303	27	≤	≤	NOUN
ma-44	303	28	{	{	PUNCT
ma-44	303	29	(	(	PUNCT
ma-44	303	30	q	q	NOUN
ma-44	303	31	−	−	PROPN
ma-44	303	32	1	1	NUM
ma-44	303	33	)	)	PUNCT
ma-44	303	34	∆q−2	∆q−2	NOUN
ma-44	303	35	(	(	PUNCT
ma-44	303	36	4υmα1	4υmα1	NOUN
ma-44	303	37	γ(α1	γ(α1	NOUN
ma-44	303	38	+	+	CCONJ
ma-44	303	39	1	1	X
ma-44	303	40	)	)	PUNCT
ma-44	304	1	+	+	CCONJ
ma-44	304	2	mρ	mρ	X
ma-44	304	3	γ	γ	NOUN
ma-44	304	4	(	(	PUNCT
ma-44	304	5	ρ+	ρ+	NUM
ma-44	304	6	1	1	NUM
ma-44	304	7	)	)	PUNCT
ma-44	304	8	)	)	PUNCT
ma-44	304	9	(	(	PUNCT
ma-44	304	10	mα2−µ	mα2−µ	NOUN
ma-44	304	11	γ(α2	γ(α2	NOUN
ma-44	304	12	−	−	PROPN
ma-44	304	13	µ+	µ+	PUNCT
ma-44	304	14	1	1	NUM
ma-44	304	15	)	)	PUNCT
ma-44	304	16	+	+	CCONJ
ma-44	304	17	γ	γ	X
ma-44	304	18	(	(	PUNCT
ma-44	304	19	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	304	20	γ(α2	γ(α2	NOUN
ma-44	304	21	+	+	X
ma-44	304	22	1)γ	1)γ	PROPN
ma-44	304	23	(	(	PUNCT
ma-44	304	24	γ2	γ2	PROPN
ma-44	304	25	−	−	PROPN
ma-44	304	26	µ	µ	NUM
ma-44	304	27	)	)	PUNCT
ma-44	304	28	)	)	PUNCT
ma-44	305	1	+	+	CCONJ
ma-44	305	2	γ	γ	PROPN
ma-44	305	3	(	(	PUNCT
ma-44	305	4	γ2	γ2	ADJ
ma-44	305	5	)	)	PUNCT
ma-44	305	6	λ2	λ2	PROPN
ma-44	305	7	m	m	PROPN
ma-44	305	8	−µ	−µ	ADJ
ma-44	305	9	γ	γ	X
ma-44	305	10	(	(	PUNCT
ma-44	305	11	γ2	γ2	PROPN
ma-44	305	12	−	−	PROPN
ma-44	305	13	µ	µ	NUM
ma-44	305	14	)	)	PUNCT
ma-44	305	15	}	}	PUNCT
ma-44	305	16	‖u	‖u	NOUN
ma-44	305	17	−	−	PROPN
ma-44	305	18	v‖cµϕ	v‖cµϕ	SYM
ma-44	305	19	≤	≤	NUM
ma-44	305	20	υ2	υ2	PROPN
ma-44	305	21	‖u	‖u	NOUN
ma-44	305	22	−	−	PROPN
ma-44	305	23	v‖cµϕ	v‖cµϕ	X
ma-44	305	24	.by	.by	X
ma-44	305	25	(	(	PUNCT
ma-44	305	26	3.4	3.4	NUM
ma-44	305	27	)	)	PUNCT
ma-44	305	28	and	and	CCONJ
ma-44	305	29	(	(	PUNCT
ma-44	305	30	3.5	3.5	NUM
ma-44	305	31	)	)	PUNCT
ma-44	305	32	,	,	PUNCT
ma-44	305	33	yields	yield	VERB
ma-44	305	34	the	the	DET
ma-44	305	35	following	follow	VERB
ma-44	305	36	inequality	inequality	NOUN
ma-44	305	37	‖gu	‖gu	PROPN
ma-44	305	38	−gv‖cµϕ	−gv‖cµϕ	PROPN
ma-44	305	39	≤	≤	NOUN
ma-44	305	40	(	(	PUNCT
ma-44	305	41	υ1	υ1	NOUN
ma-44	305	42	+	+	CCONJ
ma-44	305	43	υ2	υ2	NOUN
ma-44	305	44	)	)	PUNCT
ma-44	305	45	‖u	‖u	NOUN
ma-44	305	46	−	−	PROPN
ma-44	305	47	v‖cµϕ	v‖cµϕ	PUNCT
ma-44	305	48	.where	.where	X
ma-44	305	49	υ1	υ1	NOUN
ma-44	305	50	+	+	CCONJ
ma-44	305	51	υ2	υ2	VERB
ma-44	305	52	<	<	X
ma-44	305	53	1	1	NUM
ma-44	305	54	.	.	PUNCT
ma-44	305	55	hence	hence	ADV
ma-44	305	56	g	g	PROPN
ma-44	305	57	is	be	AUX
ma-44	305	58	a	a	DET
ma-44	305	59	contraction	contraction	NOUN
ma-44	305	60	operator	operator	NOUN
ma-44	305	61	and	and	CCONJ
ma-44	305	62	the	the	DET
ma-44	305	63	contraction	contraction	NOUN
ma-44	305	64	mapping	mapping	NOUN
ma-44	305	65	principleimplies	principleimplie	NOUN
ma-44	305	66	that	that	SCONJ
ma-44	305	67	(	(	PUNCT
ma-44	305	68	1.1	1.1	NUM
ma-44	305	69	)	)	PUNCT
ma-44	305	70	has	have	VERB
ma-44	305	71	a	a	DET
ma-44	305	72	unique	unique	ADJ
ma-44	305	73	solution	solution	NOUN
ma-44	305	74	.	.	PUNCT
ma-44	306	1	�	�	PROPN
ma-44	306	2	3.3	3.3	NUM
ma-44	306	3	.	.	PUNCT
ma-44	307	1	ulam	ulam	PROPN
ma-44	307	2	type	type	NOUN
ma-44	307	3	stability	stability	NOUN
ma-44	307	4	.	.	PUNCT
ma-44	308	1	we	we	PRON
ma-44	308	2	introduce	introduce	VERB
ma-44	308	3	the	the	DET
ma-44	308	4	following	follow	VERB
ma-44	308	5	two	two	NUM
ma-44	308	6	definitions	definition	NOUN
ma-44	308	7	definition	definition	NOUN
ma-44	308	8	4	4	NUM
ma-44	308	9	.	.	PUNCT
ma-44	309	1	the	the	DET
ma-44	309	2	problem	problem	NOUN
ma-44	309	3	(	(	PUNCT
ma-44	309	4	1.1	1.1	NUM
ma-44	309	5	)	)	PUNCT
ma-44	309	6	is	be	AUX
ma-44	309	7	ulam	ulam	NOUN
ma-44	309	8	–	–	PUNCT
ma-44	309	9	hyers	hyer	NOUN
ma-44	309	10	stable	stable	ADJ
ma-44	309	11	if	if	SCONJ
ma-44	309	12	∃	∃	PROPN
ma-44	309	13	λ	λ	PROPN
ma-44	309	14	∈	∈	PROPN
ma-44	309	15	r∗+	r∗+	PROPN
ma-44	309	16	,	,	PUNCT
ma-44	309	17	such	such	ADJ
ma-44	309	18	that	that	PRON
ma-44	309	19	for	for	ADP
ma-44	309	20	each	each	DET
ma-44	309	21	ε	ε	PROPN
ma-44	309	22	>	>	X
ma-44	309	23	0	0	PROPN
ma-44	309	24	,	,	PUNCT
ma-44	309	25	t	t	PROPN
ma-44	309	26	∈	∈	PROPN
ma-44	309	27	j	j	PROPN
ma-44	309	28	,	,	PUNCT
ma-44	309	29	and	and	CCONJ
ma-44	309	30	for	for	ADP
ma-44	309	31	each	each	DET
ma-44	309	32	u	u	PROPN
ma-44	309	33	∈	∈	NOUN
ma-44	309	34	cµϕ	cµϕ	NOUN
ma-44	309	35	solution	solution	NOUN
ma-44	309	36	of	of	ADP
ma-44	309	37	the	the	DET
ma-44	309	38	following	follow	VERB
ma-44	309	39	inequality∥∥∥hdα1,β1;ϕ	inequality∥∥∥hdα1,β1;ϕ	NUM
ma-44	309	40	a+	a+	PUNCT
ma-44	309	41	ψp	ψp	ADP
ma-44	309	42	(	(	PUNCT
ma-44	309	43	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	309	44	a+	a+	PUNCT
ma-44	309	45	u	u	NOUN
ma-44	309	46	)	)	PUNCT
ma-44	309	47	(	(	PUNCT
ma-44	309	48	t)−	t)−	PROPN
ma-44	309	49	h(t	h(t	PROPN
ma-44	309	50	,	,	PUNCT
ma-44	309	51	u(t),rldµ;ϕ	u(t),rldµ;ϕ	ADJ
ma-44	309	52	a+	a+	PUNCT
ma-44	309	53	u(t	u(t	NOUN
ma-44	309	54	)	)	PUNCT
ma-44	309	55	)	)	PUNCT
ma-44	310	1	∥∥∥	∥∥∥	PROPN
ma-44	310	2	cµϕ	cµϕ	VERB
ma-44	310	3	<	<	X
ma-44	310	4	ε	ε	PROPN
ma-44	310	5	,	,	PUNCT
ma-44	310	6	(	(	PUNCT
ma-44	310	7	3.6	3.6	NUM
ma-44	310	8	)	)	PUNCT
ma-44	310	9	∃v	∃v	PROPN
ma-44	310	10	∈	∈	NOUN
ma-44	310	11	cµϕ	cµϕ	NOUN
ma-44	310	12	solution	solution	NOUN
ma-44	310	13	of	of	ADP
ma-44	310	14	(	(	PUNCT
ma-44	310	15	1.1	1.1	NUM
ma-44	310	16	)	)	PUNCT
ma-44	310	17	,	,	PUNCT
ma-44	310	18	i.e.	i.e.	X
ma-44	310	19	hdα1,β1;ϕ	hdα1,β1;ϕ	X
ma-44	310	20	a+	a+	PUNCT
ma-44	310	21	ψp	ψp	ADP
ma-44	310	22	(	(	PUNCT
ma-44	310	23	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	310	24	a+	a+	PUNCT
ma-44	310	25	v	v	NOUN
ma-44	310	26	)	)	PUNCT
ma-44	310	27	(	(	PUNCT
ma-44	310	28	t	t	NOUN
ma-44	310	29	)	)	PUNCT
ma-44	310	30	=	=	PUNCT
ma-44	311	1	h(t	h(t	PROPN
ma-44	311	2	,	,	PUNCT
ma-44	311	3	v(t),rldµ;ϕ	v(t),rldµ;ϕ	PROPN
ma-44	311	4	a+	a+	PUNCT
ma-44	311	5	v(t	v(t	NOUN
ma-44	311	6	)	)	PUNCT
ma-44	311	7	)	)	PUNCT
ma-44	311	8	,	,	PUNCT
ma-44	311	9	(	(	PUNCT
ma-44	311	10	3.7	3.7	NUM
ma-44	311	11	)	)	PUNCT
ma-44	311	12	eur	eur	PROPN
ma-44	311	13	.	.	PUNCT
ma-44	312	1	j.	j.	PROPN
ma-44	312	2	math	math	PROPN
ma-44	312	3	.	.	PUNCT
ma-44	313	1	anal	anal	ADJ
ma-44	313	2	.	.	PUNCT
ma-44	314	1	1	1	NUM
ma-44	314	2	(	(	PUNCT
ma-44	314	3	2021	2021	NUM
ma-44	314	4	)	)	PUNCT
ma-44	314	5	177	177	NUM
ma-44	314	6	such	such	ADJ
ma-44	314	7	that	that	SCONJ
ma-44	314	8	,	,	PUNCT
ma-44	314	9	the	the	DET
ma-44	314	10	inequality	inequality	NOUN
ma-44	314	11	‖u	‖u	NOUN
ma-44	314	12	−	−	PROPN
ma-44	314	13	v‖cµϕ	v‖cµϕ	SYM
ma-44	314	14	≤	≤	NUM
ma-44	314	15	λε	λε	PROPN
ma-44	314	16	,	,	PUNCT
ma-44	314	17	holds	hold	VERB
ma-44	314	18	.	.	PUNCT
ma-44	315	1	definition	definition	NOUN
ma-44	315	2	5	5	NUM
ma-44	315	3	.	.	PUNCT
ma-44	316	1	the	the	DET
ma-44	316	2	equation	equation	NOUN
ma-44	316	3	(	(	PUNCT
ma-44	316	4	1.1	1.1	NUM
ma-44	316	5	)	)	PUNCT
ma-44	316	6	has	have	VERB
ma-44	316	7	the	the	DET
ma-44	316	8	ulam	ulam	NOUN
ma-44	316	9	–	–	PUNCT
ma-44	316	10	hyers	hyer	NOUN
ma-44	316	11	stability	stability	NOUN
ma-44	316	12	in	in	ADP
ma-44	316	13	the	the	DET
ma-44	316	14	generalized	generalized	ADJ
ma-44	316	15	sense	sense	NOUN
ma-44	316	16	if	if	SCONJ
ma-44	316	17	∃	∃	PROPN
ma-44	316	18	ϕ	ϕ	PROPN
ma-44	316	19	∈	∈	PROPN
ma-44	316	20	c	c	PROPN
ma-44	316	21	(	(	PUNCT
ma-44	316	22	j	j	NOUN
ma-44	316	23	,	,	PUNCT
ma-44	316	24	r+	r+	X
ma-44	316	25	)	)	PUNCT
ma-44	316	26	,	,	PUNCT
ma-44	316	27	such	such	ADJ
ma-44	316	28	that	that	PRON
ma-44	316	29	for	for	ADP
ma-44	316	30	each	each	DET
ma-44	316	31	ε	ε	PROPN
ma-44	316	32	>	>	X
ma-44	316	33	0	0	PROPN
ma-44	316	34	,	,	PUNCT
ma-44	316	35	t	t	PROPN
ma-44	316	36	∈	∈	PROPN
ma-44	316	37	j	j	PROPN
ma-44	316	38	,	,	PUNCT
ma-44	316	39	and	and	CCONJ
ma-44	316	40	for	for	ADP
ma-44	316	41	each	each	DET
ma-44	316	42	u	u	PROPN
ma-44	316	43	∈	∈	PROPN
ma-44	316	44	cµϕ	cµϕ	NOUN
ma-44	316	45	solution	solution	NOUN
ma-44	316	46	of:∥∥∥hdα1,β1;ϕ	of:∥∥∥hdα1,β1;ϕ	NUM
ma-44	316	47	a+	a+	PUNCT
ma-44	316	48	ψp	ψp	ADP
ma-44	316	49	(	(	PUNCT
ma-44	316	50	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	316	51	a+	a+	PUNCT
ma-44	316	52	u	u	NOUN
ma-44	316	53	)	)	PUNCT
ma-44	316	54	(	(	PUNCT
ma-44	316	55	t)−	t)−	PROPN
ma-44	316	56	h(t	h(t	PROPN
ma-44	316	57	,	,	PUNCT
ma-44	316	58	u(t),rldµ;ϕ	u(t),rldµ;ϕ	ADJ
ma-44	316	59	a+	a+	PUNCT
ma-44	316	60	u(t	u(t	NOUN
ma-44	316	61	)	)	PUNCT
ma-44	316	62	)	)	PUNCT
ma-44	316	63	∥∥∥	∥∥∥	PROPN
ma-44	316	64	cµϕ	cµϕ	VERB
ma-44	316	65	<	<	X
ma-44	316	66	ε	ε	PROPN
ma-44	316	67	,	,	PUNCT
ma-44	316	68	(	(	PUNCT
ma-44	316	69	3.8	3.8	NUM
ma-44	316	70	)	)	PUNCT
ma-44	316	71	∃v	∃v	PROPN
ma-44	316	72	∈	∈	NOUN
ma-44	316	73	cµϕ	cµϕ	NOUN
ma-44	316	74	solution	solution	NOUN
ma-44	316	75	of	of	ADP
ma-44	316	76	(	(	PUNCT
ma-44	316	77	1.1	1.1	NUM
ma-44	316	78	)	)	PUNCT
ma-44	316	79	that	that	PRON
ma-44	316	80	satisfies	satisfy	VERB
ma-44	316	81	‖u(t)−	‖u(t)−	PROPN
ma-44	316	82	v(t)‖cµϕ	v(t)‖cµϕ	PROPN
ma-44	316	83	≤	≤	NOUN
ma-44	316	84	εϕ(t	εϕ(t	NUM
ma-44	316	85	)	)	PUNCT
ma-44	316	86	.	.	PUNCT
ma-44	317	1	in	in	ADP
ma-44	317	2	the	the	DET
ma-44	317	3	light	light	NOUN
ma-44	317	4	of	of	ADP
ma-44	317	5	the	the	DET
ma-44	317	6	first	first	ADJ
ma-44	317	7	definition	definition	NOUN
ma-44	317	8	and	and	CCONJ
ma-44	317	9	using	use	VERB
ma-44	317	10	the	the	DET
ma-44	317	11	above	above	ADJ
ma-44	317	12	existence	existence	NOUN
ma-44	317	13	and	and	CCONJ
ma-44	317	14	uniqueness	uniqueness	NOUN
ma-44	317	15	theorem	theorem	VERB
ma-44	317	16	,	,	PUNCT
ma-44	317	17	wepresent	wepresent	ADJ
ma-44	317	18	to	to	ADP
ma-44	317	19	the	the	DET
ma-44	317	20	reader	reader	NOUN
ma-44	317	21	the	the	DET
ma-44	317	22	following	following	ADJ
ma-44	317	23	result	result	NOUN
ma-44	317	24	.	.	PUNCT
ma-44	318	1	theorem	theorem	NOUN
ma-44	318	2	3	3	NUM
ma-44	318	3	.	.	PUNCT
ma-44	319	1	if	if	SCONJ
ma-44	319	2	the	the	DET
ma-44	319	3	assumptions	assumption	NOUN
ma-44	319	4	(	(	PUNCT
ma-44	319	5	h2	h2	NOUN
ma-44	319	6	)	)	PUNCT
ma-44	319	7	are	be	AUX
ma-44	319	8	satisfied	satisfied	ADJ
ma-44	319	9	,	,	PUNCT
ma-44	319	10	then	then	ADV
ma-44	319	11	eq	eq	ADJ
ma-44	319	12	(	(	PUNCT
ma-44	319	13	1.1	1.1	NUM
ma-44	319	14	)	)	PUNCT
ma-44	319	15	is	be	AUX
ma-44	319	16	ulam	ulam	NOUN
ma-44	319	17	–	–	PUNCT
ma-44	319	18	hyers	hyer	NOUN
ma-44	319	19	stable	stable	ADJ
ma-44	319	20	under	under	ADP
ma-44	319	21	the	the	DET
ma-44	319	22	condition	condition	NOUN
ma-44	319	23	that	that	SCONJ
ma-44	319	24	n1	n1	PROPN
ma-44	319	25	+	+	CCONJ
ma-44	319	26	n2	n2	ADJ
ma-44	319	27	<	<	X
ma-44	319	28	1	1	NUM
ma-44	319	29	,	,	PUNCT
ma-44	319	30	where	where	SCONJ
ma-44	319	31	n1	n1	PROPN
ma-44	319	32	=	=	SYM
ma-44	319	33	2	2	NUM
ma-44	319	34	(	(	PUNCT
ma-44	319	35	q	q	NOUN
ma-44	319	36	−	−	PROPN
ma-44	319	37	1	1	NUM
ma-44	319	38	)	)	PUNCT
ma-44	319	39	∆q−2mα2	∆q−2mα2	NOUN
ma-44	319	40	γ(α2	γ(α2	NOUN
ma-44	319	41	+	+	CCONJ
ma-44	319	42	1	1	X
ma-44	319	43	)	)	PUNCT
ma-44	319	44	(	(	PUNCT
ma-44	319	45	4υmα1	4υmα1	NOUN
ma-44	319	46	γ(α1	γ(α1	NOUN
ma-44	319	47	+	+	CCONJ
ma-44	319	48	1	1	X
ma-44	319	49	)	)	PUNCT
ma-44	319	50	+	+	CCONJ
ma-44	319	51	mρ	mρ	X
ma-44	319	52	γ	γ	NOUN
ma-44	319	53	(	(	PUNCT
ma-44	319	54	ρ+	ρ+	NUM
ma-44	319	55	1	1	NUM
ma-44	319	56	)	)	PUNCT
ma-44	319	57	)	)	PUNCT
ma-44	319	58	,	,	PUNCT
ma-44	319	59	and	and	CCONJ
ma-44	319	60	n2	n2	NOUN
ma-44	319	61	=	=	SYM
ma-44	319	62	(	(	PUNCT
ma-44	319	63	4υ	4υ	X
ma-44	319	64	(	(	PUNCT
ma-44	319	65	q	q	NOUN
ma-44	319	66	−	−	PROPN
ma-44	319	67	1	1	NUM
ma-44	319	68	)	)	PUNCT
ma-44	319	69	∆q−2mα1	∆q−2mα1	NOUN
ma-44	319	70	γ(α1	γ(α1	NOUN
ma-44	320	1	+	+	CCONJ
ma-44	320	2	1	1	X
ma-44	320	3	)	)	PUNCT
ma-44	320	4	+	+	CCONJ
ma-44	320	5	(	(	PUNCT
ma-44	320	6	q	q	NOUN
ma-44	320	7	−	−	PROPN
ma-44	320	8	1	1	NUM
ma-44	320	9	)	)	PUNCT
ma-44	320	10	∆q−2mρ	∆q−2mρ	ADJ
ma-44	320	11	γ	γ	X
ma-44	320	12	(	(	PUNCT
ma-44	320	13	ρ+	ρ+	NUM
ma-44	320	14	1	1	NUM
ma-44	320	15	)	)	PUNCT
ma-44	320	16	)	)	PUNCT
ma-44	320	17	(	(	PUNCT
ma-44	320	18	mα2−µ	mα2−µ	NOUN
ma-44	320	19	γ(α2	γ(α2	NOUN
ma-44	320	20	−	−	PROPN
ma-44	320	21	µ+	µ+	PUNCT
ma-44	320	22	1	1	NUM
ma-44	320	23	)	)	PUNCT
ma-44	320	24	+	+	CCONJ
ma-44	320	25	γ	γ	X
ma-44	320	26	(	(	PUNCT
ma-44	320	27	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	320	28	γ(α2	γ(α2	NOUN
ma-44	320	29	+	+	X
ma-44	320	30	1)γ	1)γ	PROPN
ma-44	320	31	(	(	PUNCT
ma-44	320	32	γ2	γ2	PROPN
ma-44	320	33	−	−	PROPN
ma-44	320	34	µ	µ	NUM
ma-44	320	35	)	)	PUNCT
ma-44	320	36	)	)	PUNCT
ma-44	320	37	.	.	PUNCT
ma-44	321	1	proof	proof	NOUN
ma-44	321	2	.	.	PUNCT
ma-44	322	1	let	let	VERB
ma-44	322	2	u	u	PRON
ma-44	322	3	∈	∈	PROPN
ma-44	322	4	cµϕ	cµϕ	NOUN
ma-44	322	5	be	be	AUX
ma-44	322	6	a	a	DET
ma-44	322	7	solution	solution	NOUN
ma-44	322	8	of	of	ADP
ma-44	322	9	the	the	DET
ma-44	322	10	inequality	inequality	NOUN
ma-44	322	11	(	(	PUNCT
ma-44	322	12	3.6	3.6	NUM
ma-44	322	13	)	)	PUNCT
ma-44	322	14	,	,	PUNCT
ma-44	322	15	i.e.∥∥∥hdα1,β1;ϕ	i.e.∥∥∥hdα1,β1;ϕ	PROPN
ma-44	322	16	a+	a+	PUNCT
ma-44	322	17	ψp	ψp	ADP
ma-44	322	18	(	(	PUNCT
ma-44	322	19	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	322	20	a+	a+	PUNCT
ma-44	322	21	u	u	NOUN
ma-44	322	22	)	)	PUNCT
ma-44	322	23	(	(	PUNCT
ma-44	323	1	t)−	t)−	PROPN
ma-44	323	2	h(t	h(t	PROPN
ma-44	323	3	,	,	PUNCT
ma-44	323	4	u(t),rldµ;ϕ	u(t),rldµ;ϕ	ADJ
ma-44	323	5	a+	a+	PUNCT
ma-44	323	6	u(t	u(t	NOUN
ma-44	323	7	)	)	PUNCT
ma-44	323	8	)	)	PUNCT
ma-44	323	9	∥∥∥	∥∥∥	PROPN
ma-44	323	10	cµϕ	cµϕ	VERB
ma-44	323	11	<	<	X
ma-44	323	12	ε	ε	PROPN
ma-44	323	13	,	,	PUNCT
ma-44	323	14	∀t	∀t	PROPN
ma-44	323	15	∈	∈	PROPN
ma-44	323	16	j.	j.	PROPN
ma-44	323	17	(	(	PUNCT
ma-44	323	18	3.9	3.9	NUM
ma-44	323	19	)	)	PUNCT
ma-44	323	20	let	let	VERB
ma-44	323	21	v	v	NUM
ma-44	323	22	∈	∈	NOUN
ma-44	323	23	cµϕ	cµϕ	NOUN
ma-44	323	24	be	be	AUX
ma-44	323	25	a	a	DET
ma-44	323	26	unique	unique	ADJ
ma-44	323	27	solution	solution	NOUN
ma-44	323	28	of	of	ADP
ma-44	323	29	:	:	PUNCT
ma-44	323	30	hdα1,β1;ϕ	hdα1,β1;ϕ	PROPN
ma-44	323	31	a+	a+	PUNCT
ma-44	324	1	ψp	ψp	ADP
ma-44	325	1	(	(	PUNCT
ma-44	325	2	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	325	3	a+	a+	PUNCT
ma-44	325	4	v	v	NOUN
ma-44	325	5	)	)	PUNCT
ma-44	325	6	(	(	PUNCT
ma-44	325	7	t	t	NOUN
ma-44	325	8	)	)	PUNCT
ma-44	325	9	=	=	PUNCT
ma-44	326	1	h(t	h(t	PROPN
ma-44	326	2	,	,	PUNCT
ma-44	326	3	v(t),rldµ;ϕ	v(t),rldµ;ϕ	PROPN
ma-44	326	4	a+	a+	PUNCT
ma-44	326	5	v(t	v(t	NOUN
ma-44	326	6	)	)	PUNCT
ma-44	326	7	)	)	PUNCT
ma-44	326	8	,	,	PUNCT
ma-44	326	9	∀t	∀t	PROPN
ma-44	326	10	∈	∈	PROPN
ma-44	326	11	j	j	PROPN
ma-44	326	12	,	,	PUNCT
ma-44	326	13	and	and	CCONJ
ma-44	326	14			NUM
ma-44	326	15	u(a	u(a	NOUN
ma-44	326	16	)	)	PUNCT
ma-44	326	17	=	=	SYM
ma-44	326	18	v(a	v(a	NOUN
ma-44	326	19	)	)	PUNCT
ma-44	326	20	,	,	PUNCT
ma-44	326	21	u(b	u(b	NOUN
ma-44	326	22	)	)	PUNCT
ma-44	326	23	=	=	SYM
ma-44	326	24	v(b)and	v(b)and	NOUN
ma-44	327	1	ψp	ψp	ADP
ma-44	327	2	(	(	PUNCT
ma-44	327	3	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	327	4	a+	a+	PUNCT
ma-44	327	5	u	u	NOUN
ma-44	327	6	)	)	PUNCT
ma-44	327	7	(	(	PUNCT
ma-44	327	8	a	a	X
ma-44	327	9	)	)	PUNCT
ma-44	327	10	=	=	SYM
ma-44	327	11	ψp	ψp	ADP
ma-44	327	12	(	(	PUNCT
ma-44	327	13	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	327	14	a+	a+	PUNCT
ma-44	327	15	v	v	NOUN
ma-44	327	16	)	)	PUNCT
ma-44	327	17	(	(	PUNCT
ma-44	327	18	a	a	X
ma-44	327	19	)	)	PUNCT
ma-44	327	20	,	,	PUNCT
ma-44	327	21	ψp	ψp	ADP
ma-44	327	22	(	(	PUNCT
ma-44	327	23	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	327	24	a+	a+	PUNCT
ma-44	327	25	u	u	NOUN
ma-44	327	26	)	)	PUNCT
ma-44	327	27	(	(	PUNCT
ma-44	327	28	b	b	X
ma-44	327	29	)	)	PUNCT
ma-44	327	30	=	=	SYM
ma-44	327	31	ψp	ψp	ADP
ma-44	327	32	(	(	PUNCT
ma-44	327	33	hdα2,β2;ϕ	hdα2,β2;ϕ	PROPN
ma-44	327	34	a+	a+	PUNCT
ma-44	327	35	v	v	NOUN
ma-44	327	36	)	)	PUNCT
ma-44	327	37	(	(	PUNCT
ma-44	327	38	b	b	NOUN
ma-44	327	39	)	)	PUNCT
ma-44	327	40	,	,	PUNCT
ma-44	327	41	eur	eur	PROPN
ma-44	327	42	.	.	PUNCT
ma-44	328	1	j.	j.	PROPN
ma-44	328	2	math	math	PROPN
ma-44	328	3	.	.	PUNCT
ma-44	329	1	anal	anal	ADJ
ma-44	329	2	.	.	PUNCT
ma-44	330	1	1	1	NUM
ma-44	330	2	(	(	PUNCT
ma-44	330	3	2021	2021	NUM
ma-44	330	4	)	)	PUNCT
ma-44	330	5	178by	178by	NOUN
ma-44	330	6	using	use	VERB
ma-44	330	7	proof	proof	NOUN
ma-44	330	8	of	of	ADP
ma-44	330	9	lemma	lemma	PROPN
ma-44	330	10	6	6	NUM
ma-44	330	11	v(t	v(t	NOUN
ma-44	330	12	)	)	PUNCT
ma-44	330	13	=	=	SYM
ma-44	330	14	1	1	NUM
ma-44	330	15	γ(α2	γ(α2	NOUN
ma-44	330	16	)	)	PUNCT
ma-44	331	1	t∫	t∫	PRON
ma-44	331	2	a	a	PRON
ma-44	331	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	331	4	,	,	PUNCT
ma-44	331	5	s)xv	s)xv	PROPN
ma-44	331	6	(	(	PUNCT
ma-44	331	7	s	s	X
ma-44	331	8	,	,	PUNCT
ma-44	331	9	a)ds	a)ds	PROPN
ma-44	331	10	−	−	PROPN
ma-44	331	11	ϕγ2−1	ϕγ2−1	NOUN
ma-44	331	12	(	(	PUNCT
ma-44	331	13	t	t	PROPN
ma-44	331	14	,	,	PUNCT
ma-44	331	15	a	a	PRON
ma-44	331	16	)	)	PUNCT
ma-44	331	17	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	331	18	(	(	PUNCT
ma-44	331	19	b	b	NOUN
ma-44	331	20	,	,	PUNCT
ma-44	331	21	a	a	PRON
ma-44	331	22	)	)	PUNCT
ma-44	331	23	b∫	b∫	NOUN
ma-44	331	24	a	a	DET
ma-44	331	25	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	331	26	,	,	PUNCT
ma-44	331	27	t)xv	t)xv	PROPN
ma-44	331	28	(	(	PUNCT
ma-44	331	29	t	t	PROPN
ma-44	331	30	,	,	PUNCT
ma-44	331	31	a)dt	a)dt	PROPN
ma-44	331	32	+	+	NUM
ma-44	331	33	ϕγ2−1	ϕγ2−1	NOUN
ma-44	331	34	(	(	PUNCT
ma-44	331	35	t	t	PROPN
ma-44	331	36	,	,	PUNCT
ma-44	331	37	a	a	PRON
ma-44	331	38	)	)	PUNCT
ma-44	331	39	ϕγ2−1	ϕγ2−1	NOUN
ma-44	331	40	(	(	PUNCT
ma-44	331	41	b	b	NOUN
ma-44	331	42	,	,	PUNCT
ma-44	331	43	a	a	PRON
ma-44	331	44	)	)	PUNCT
ma-44	331	45	n∑	n∑	NOUN
ma-44	331	46	i=1	i=1	PROPN
ma-44	332	1	λiu	λiu	PROPN
ma-44	333	1	(	(	PUNCT
ma-44	333	2	ζi	ζi	PROPN
ma-44	333	3	)	)	PUNCT
ma-44	333	4	,	,	PUNCT
ma-44	334	1	where	where	SCONJ
ma-44	334	2	xv	xv	PROPN
ma-44	334	3	(	(	PUNCT
ma-44	334	4	s	s	PROPN
ma-44	334	5	,	,	PUNCT
ma-44	334	6	a	a	PRON
ma-44	334	7	)	)	PUNCT
ma-44	334	8	=	=	PUNCT
ma-44	334	9	ψq	ψq	PROPN
ma-44	334	10			PROPN
ma-44	334	11	1	1	NUM
ma-44	334	12	γ(α1	γ(α1	NOUN
ma-44	334	13	)	)	PUNCT
ma-44	334	14	s∫	s∫	PROPN
ma-44	334	15	a	a	DET
ma-44	334	16	ϕ′(s)ϕα1−1(s	ϕ′(s)ϕα1−1(	NOUN
ma-44	334	17	,	,	PUNCT
ma-44	334	18	z)hv	z)hv	PROPN
ma-44	334	19	(	(	PUNCT
ma-44	334	20	z)dz	z)dz	PROPN
ma-44	334	21	+	+	CCONJ
ma-44	334	22	(	(	PUNCT
ma-44	334	23	iρ;ϕ	iρ;ϕ	VERB
ma-44	334	24	0	0	NUM
ma-44	334	25	+	+	NUM
ma-44	334	26	u	u	SYM
ma-44	334	27	(	(	PUNCT
ma-44	334	28	ζ)−	ζ)−	PROPN
ma-44	334	29	iα1;ϕ	iα1;ϕ	PROPN
ma-44	334	30	0	0	PROPN
ma-44	334	31	+	+	NUM
ma-44	334	32	hv	hv	PROPN
ma-44	334	33	(	(	PUNCT
ma-44	334	34	b	b	NOUN
ma-44	334	35	)	)	PUNCT
ma-44	334	36	)	)	PUNCT
ma-44	335	1	ϕγ1−1	ϕγ1−1	INTJ
ma-44	335	2	(	(	PUNCT
ma-44	335	3	b	b	NOUN
ma-44	335	4	,	,	PUNCT
ma-44	335	5	a	a	PRON
ma-44	335	6	)	)	PUNCT
ma-44	335	7	ϕγ1−1	ϕγ1−1	NOUN
ma-44	335	8	(	(	PUNCT
ma-44	335	9	s	s	PROPN
ma-44	335	10	,	,	PUNCT
ma-44	335	11	a	a	PRON
ma-44	335	12	)	)	PUNCT
ma-44	335	13			PROPN
ma-44	335	14	.	.	PUNCT
ma-44	336	1	by	by	ADP
ma-44	336	2	integration	integration	NOUN
ma-44	336	3	of	of	ADP
ma-44	336	4	inequality	inequality	NOUN
ma-44	336	5	(	(	PUNCT
ma-44	336	6	3.9	3.9	NUM
ma-44	336	7	)	)	PUNCT
ma-44	336	8	,	,	PUNCT
ma-44	336	9	for	for	ADP
ma-44	336	10	any	any	DET
ma-44	336	11	t	t	PROPN
ma-44	336	12	∈	∈	PROPN
ma-44	336	13	j	j	PROPN
ma-44	336	14	,	,	PUNCT
ma-44	336	15	we	we	PRON
ma-44	336	16	have∥∥∥∥∥∥u(t)−	have∥∥∥∥∥∥u(t)−	PROPN
ma-44	336	17	1	1	NUM
ma-44	336	18	γ(α2	γ(α2	NOUN
ma-44	336	19	)	)	PUNCT
ma-44	337	1	t∫	t∫	PRON
ma-44	337	2	a	a	DET
ma-44	337	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	337	4	,	,	PUNCT
ma-44	337	5	s)xu(s	s)xu(s	NOUN
ma-44	337	6	,	,	PUNCT
ma-44	337	7	a)ds	a)ds	PROPN
ma-44	337	8	(	(	PUNCT
ma-44	337	9	3.10	3.10	NUM
ma-44	337	10	)	)	PUNCT
ma-44	338	1	+	+	CCONJ
ma-44	338	2	ϕγ2−1	ϕγ2−1	NOUN
ma-44	338	3	(	(	PUNCT
ma-44	338	4	t	t	PROPN
ma-44	338	5	,	,	PUNCT
ma-44	338	6	a	a	PRON
ma-44	338	7	)	)	PUNCT
ma-44	338	8	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	338	9	(	(	PUNCT
ma-44	338	10	b	b	NOUN
ma-44	338	11	,	,	PUNCT
ma-44	338	12	a	a	PRON
ma-44	338	13	)	)	PUNCT
ma-44	338	14	b∫	b∫	NOUN
ma-44	338	15	a	a	DET
ma-44	338	16	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	NOUN
ma-44	338	17	,	,	PUNCT
ma-44	338	18	t)xu(t	t)xu(t	PRON
ma-44	338	19	,	,	PUNCT
ma-44	338	20	a)dt	a)dt	PROPN
ma-44	338	21	−	−	PROPN
ma-44	338	22	ϕγ2−1	ϕγ2−1	NOUN
ma-44	338	23	(	(	PUNCT
ma-44	338	24	t	t	PROPN
ma-44	338	25	,	,	PUNCT
ma-44	338	26	a	a	PRON
ma-44	338	27	)	)	PUNCT
ma-44	338	28	ϕγ2−1	ϕγ2−1	NOUN
ma-44	338	29	(	(	PUNCT
ma-44	338	30	b	b	NOUN
ma-44	338	31	,	,	PUNCT
ma-44	338	32	a	a	PRON
ma-44	338	33	)	)	PUNCT
ma-44	339	1	n∑	n∑	NOUN
ma-44	339	2	i=1	i=1	PROPN
ma-44	340	1	λiu	λiu	PROPN
ma-44	340	2	(	(	PUNCT
ma-44	340	3	ζi	ζi	PROPN
ma-44	340	4	)	)	PUNCT
ma-44	340	5	∥∥∥∥∥	∥∥∥∥∥	PROPN
ma-44	340	6	c	c	NOUN
ma-44	340	7	≤	≤	NUM
ma-44	340	8	iα2;ϕ	iα2;ϕ	NOUN
ma-44	340	9	a+	a+	PUNCT
ma-44	340	10	ψq	ψq	PROPN
ma-44	340	11	(	(	PUNCT
ma-44	340	12	iα1;ϕ	iα1;ϕ	PROPN
ma-44	340	13	a+	a+	PUNCT
ma-44	340	14	ε	ε	PROPN
ma-44	340	15	)	)	PUNCT
ma-44	341	1	=	=	SYM
ma-44	341	2	mq−1ϕα1+α2	mq−1ϕα1+α2	X
ma-44	341	3	(	(	PUNCT
ma-44	341	4	t	t	PROPN
ma-44	341	5	,	,	PUNCT
ma-44	341	6	a	a	PRON
ma-44	341	7	)	)	PUNCT
ma-44	341	8	γ	γ	PROPN
ma-44	341	9	(	(	PUNCT
ma-44	341	10	α1	α1	PROPN
ma-44	341	11	+	+	CCONJ
ma-44	341	12	α2	α2	ADJ
ma-44	341	13	+	+	CCONJ
ma-44	341	14	1	1	X
ma-44	341	15	)	)	PUNCT
ma-44	341	16	ε	ε	PROPN
ma-44	341	17	.	.	PROPN
ma-44	342	1	on	on	ADP
ma-44	342	2	the	the	DET
ma-44	342	3	other	other	ADJ
ma-44	342	4	hand	hand	NOUN
ma-44	342	5	,	,	PUNCT
ma-44	342	6	for	for	ADP
ma-44	342	7	any	any	DET
ma-44	342	8	u	u	NOUN
ma-44	342	9	,	,	PUNCT
ma-44	342	10	v	v	PROPN
ma-44	342	11	∈	∈	PROPN
ma-44	342	12	cµϕ	cµϕ	NOUN
ma-44	342	13	,	,	PUNCT
ma-44	342	14	we	we	PRON
ma-44	342	15	have	have	VERB
ma-44	342	16	the	the	DET
ma-44	342	17	following	follow	VERB
ma-44	342	18	estimate	estimate	NOUN
ma-44	342	19	‖u(t)−	‖u(t)−	PROPN
ma-44	342	20	v(t)‖c	v(t)‖c	PROPN
ma-44	342	21	(	(	PUNCT
ma-44	342	22	3.11	3.11	NUM
ma-44	342	23	)	)	PUNCT
ma-44	342	24	<	<	X
ma-44	342	25	mq−1ϕα1+α2	mq−1ϕα1+α2	X
ma-44	342	26	(	(	PUNCT
ma-44	342	27	t	t	PROPN
ma-44	342	28	,	,	PUNCT
ma-44	342	29	a	a	PRON
ma-44	342	30	)	)	PUNCT
ma-44	342	31	γ	γ	PROPN
ma-44	342	32	(	(	PUNCT
ma-44	342	33	α1	α1	PROPN
ma-44	342	34	+	+	CCONJ
ma-44	342	35	α2	α2	ADJ
ma-44	342	36	+	+	CCONJ
ma-44	342	37	1	1	X
ma-44	342	38	)	)	PUNCT
ma-44	342	39	ε	ε	PROPN
ma-44	342	40	+	+	CCONJ
ma-44	342	41	sup	sup	NOUN
ma-44	342	42	t∈[a	t∈[a	NOUN
ma-44	342	43	,	,	PUNCT
ma-44	342	44	b	b	NOUN
ma-44	342	45	]	]	PUNCT
ma-44	342	46	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	342	47	1	1	NUM
ma-44	342	48	γ(α2	γ(α2	NOUN
ma-44	342	49	)	)	PUNCT
ma-44	343	1	t∫	t∫	DET
ma-44	343	2	a	a	DET
ma-44	343	3	ϕ′(s)ϕα2−1(t	ϕ′(s)ϕα2−1(t	X
ma-44	343	4	,	,	PUNCT
ma-44	343	5	s	s	AUX
ma-44	343	6	)	)	PUNCT
ma-44	343	7	(	(	PUNCT
ma-44	343	8	xu	xu	INTJ
ma-44	343	9	−xv	−xv	PROPN
ma-44	343	10	)	)	PUNCT
ma-44	343	11	(	(	PUNCT
ma-44	343	12	s	s	X
ma-44	343	13	,	,	PUNCT
ma-44	343	14	a)ds	a)ds	PROPN
ma-44	343	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ma-44	343	16	+	+	CCONJ
ma-44	343	17	sup	sup	NOUN
ma-44	343	18	t∈[a	t∈[a	NOUN
ma-44	343	19	,	,	PUNCT
ma-44	343	20	b	b	NOUN
ma-44	343	21	]	]	PUNCT
ma-44	343	22	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	343	23	ϕγ2−1	ϕγ2−1	PROPN
ma-44	343	24	(	(	PUNCT
ma-44	343	25	t	t	PROPN
ma-44	343	26	,	,	PUNCT
ma-44	343	27	a	a	PRON
ma-44	343	28	)	)	PUNCT
ma-44	343	29	γ(α2)ϕγ2−1	γ(α2)ϕγ2−1	NOUN
ma-44	343	30	(	(	PUNCT
ma-44	343	31	b	b	NOUN
ma-44	343	32	,	,	PUNCT
ma-44	343	33	a	a	PRON
ma-44	343	34	)	)	PUNCT
ma-44	343	35	b∫	b∫	NOUN
ma-44	343	36	a	a	DET
ma-44	343	37	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	PROPN
ma-44	343	38	,	,	PUNCT
ma-44	343	39	t	t	PROPN
ma-44	343	40	)	)	PUNCT
ma-44	343	41	(	(	PUNCT
ma-44	343	42	xu	xu	INTJ
ma-44	343	43	−xv	−xv	PROPN
ma-44	343	44	)	)	PUNCT
ma-44	343	45	(	(	PUNCT
ma-44	343	46	t	t	PROPN
ma-44	343	47	,	,	PUNCT
ma-44	343	48	a)dt	a)dt	PROPN
ma-44	343	49	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	343	50	<	<	X
ma-44	343	51	mα1+α2+q1	mα1+α2+q1	X
ma-44	343	52	γ	γ	X
ma-44	343	53	(	(	PUNCT
ma-44	343	54	α1	α1	PROPN
ma-44	343	55	+	+	CCONJ
ma-44	343	56	α2	α2	ADJ
ma-44	343	57	+	+	CCONJ
ma-44	343	58	1	1	NUM
ma-44	343	59	)	)	PUNCT
ma-44	343	60	ε+	ε+	X
ma-44	343	61	2	2	NUM
ma-44	343	62	(	(	PUNCT
ma-44	343	63	q	q	NOUN
ma-44	343	64	−	−	PROPN
ma-44	343	65	1	1	NUM
ma-44	343	66	)	)	PUNCT
ma-44	343	67	∆q−2mα2	∆q−2mα2	NOUN
ma-44	343	68	γ(α2	γ(α2	NOUN
ma-44	344	1	+	+	CCONJ
ma-44	344	2	1	1	X
ma-44	344	3	)	)	PUNCT
ma-44	344	4	(	(	PUNCT
ma-44	344	5	4υmα1	4υmα1	NOUN
ma-44	344	6	γ(α1	γ(α1	NOUN
ma-44	344	7	+	+	CCONJ
ma-44	344	8	1	1	X
ma-44	344	9	)	)	PUNCT
ma-44	345	1	+	+	CCONJ
ma-44	345	2	mρ	mρ	X
ma-44	345	3	γ	γ	NOUN
ma-44	345	4	(	(	PUNCT
ma-44	345	5	ρ+	ρ+	NUM
ma-44	345	6	1	1	NUM
ma-44	345	7	)	)	PUNCT
ma-44	345	8	)	)	PUNCT
ma-44	345	9	‖u	‖u	NOUN
ma-44	345	10	−	−	PROPN
ma-44	345	11	v‖cµϕ	v‖cµϕ	SYM
ma-44	345	12	<	<	X
ma-44	345	13	mα1+α2+q−1	mα1+α2+q−1	PROPN
ma-44	345	14	γ	γ	X
ma-44	345	15	(	(	PUNCT
ma-44	345	16	α1	α1	PROPN
ma-44	345	17	+	+	CCONJ
ma-44	345	18	α2	α2	ADJ
ma-44	345	19	+	+	CCONJ
ma-44	345	20	1	1	NUM
ma-44	345	21	)	)	PUNCT
ma-44	345	22	ε+	ε+	X
ma-44	345	23	n1	n1	PROPN
ma-44	345	24	‖u	‖u	NOUN
ma-44	345	25	−	−	PROPN
ma-44	345	26	v‖cµϕ	v‖cµϕ	X
ma-44	345	27	.	.	PUNCT
ma-44	346	1	eur	eur	PROPN
ma-44	346	2	.	.	PUNCT
ma-44	347	1	j.	j.	PROPN
ma-44	347	2	math	math	PROPN
ma-44	347	3	.	.	PUNCT
ma-44	348	1	anal	anal	ADJ
ma-44	348	2	.	.	PUNCT
ma-44	349	1	1	1	NUM
ma-44	349	2	(	(	PUNCT
ma-44	349	3	2021	2021	NUM
ma-44	349	4	)	)	PUNCT
ma-44	350	1	179also	179also	NUM
ma-44	350	2	,	,	PUNCT
ma-44	350	3	for	for	ADP
ma-44	350	4	any	any	DET
ma-44	350	5	t	t	PROPN
ma-44	350	6	∈	∈	PROPN
ma-44	350	7	j	j	PROPN
ma-44	350	8	,	,	PUNCT
ma-44	350	9	we	we	PRON
ma-44	350	10	have∥∥rldµ;ϕ	have∥∥rldµ;ϕ	VERB
ma-44	350	11	a+	a+	PUNCT
ma-44	350	12	(	(	PUNCT
ma-44	350	13	u(t)−	u(t)−	PROPN
ma-44	350	14	v(t	v(t	PROPN
ma-44	350	15	)	)	PUNCT
ma-44	350	16	)	)	PUNCT
ma-44	351	1	∥∥	∥∥	PROPN
ma-44	351	2	c	c	NOUN
ma-44	351	3	(	(	PUNCT
ma-44	351	4	3.12	3.12	NUM
ma-44	351	5	)	)	PUNCT
ma-44	351	6	≤	≤	NOUN
ma-44	351	7	mq−1ϕα1+α2−µ	mq−1ϕα1+α2−µ	NOUN
ma-44	351	8	(	(	PUNCT
ma-44	351	9	t	t	PROPN
ma-44	351	10	,	,	PUNCT
ma-44	351	11	a	a	PRON
ma-44	351	12	)	)	PUNCT
ma-44	351	13	γ	γ	PROPN
ma-44	351	14	(	(	PUNCT
ma-44	351	15	α1	α1	PROPN
ma-44	351	16	+	+	CCONJ
ma-44	351	17	α2	α2	ADJ
ma-44	351	18	−	−	PROPN
ma-44	351	19	µ+	µ+	PUNCT
ma-44	351	20	1	1	NUM
ma-44	351	21	)	)	PUNCT
ma-44	351	22	ε	ε	PROPN
ma-44	351	23	+	+	CCONJ
ma-44	351	24	sup	sup	NOUN
ma-44	351	25	t∈[a	t∈[a	NOUN
ma-44	351	26	,	,	PUNCT
ma-44	351	27	b	b	NOUN
ma-44	351	28	]	]	PUNCT
ma-44	351	29	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-44	351	30	1	1	NUM
ma-44	351	31	γ(α2	γ(α2	NOUN
ma-44	351	32	−	−	PROPN
ma-44	351	33	µ	µ	X
ma-44	351	34	)	)	PUNCT
ma-44	351	35	t∫	t∫	PROPN
ma-44	351	36	a	a	DET
ma-44	351	37	ϕ′(s)ϕα2−µ−1(t	ϕ′(s)ϕα2−µ−1(t	PROPN
ma-44	351	38	,	,	PUNCT
ma-44	351	39	s	s	AUX
ma-44	351	40	)	)	PUNCT
ma-44	351	41	(	(	PUNCT
ma-44	351	42	xu	xu	INTJ
ma-44	351	43	−xv	−xv	PROPN
ma-44	351	44	)	)	PUNCT
ma-44	351	45	(	(	PUNCT
ma-44	351	46	s	s	X
ma-44	351	47	,	,	PUNCT
ma-44	351	48	a)ds	a)ds	PROPN
ma-44	351	49	+	+	CCONJ
ma-44	351	50	γ	γ	PROPN
ma-44	351	51	(	(	PUNCT
ma-44	351	52	γ2	γ2	ADJ
ma-44	351	53	)	)	PUNCT
ma-44	351	54	γ(α2)γ	γ(α2)γ	PROPN
ma-44	351	55	(	(	PUNCT
ma-44	351	56	γ2	γ2	PROPN
ma-44	351	57	−	−	PROPN
ma-44	351	58	µ	µ	NOUN
ma-44	351	59	)	)	PUNCT
ma-44	351	60	ϕγ2−µ−1	ϕγ2−µ−1	PROPN
ma-44	351	61	(	(	PUNCT
ma-44	351	62	t	t	PROPN
ma-44	351	63	,	,	PUNCT
ma-44	351	64	a	a	PRON
ma-44	351	65	)	)	PUNCT
ma-44	351	66	ϕγ2−1	ϕγ2−1	NOUN
ma-44	351	67	(	(	PUNCT
ma-44	351	68	b	b	NOUN
ma-44	351	69	,	,	PUNCT
ma-44	351	70	a	a	PRON
ma-44	351	71	)	)	PUNCT
ma-44	351	72	b∫	b∫	NOUN
ma-44	351	73	a	a	DET
ma-44	351	74	ϕ′(t)ϕα2−1(b	ϕ′(t)ϕα2−1(b	PROPN
ma-44	351	75	,	,	PUNCT
ma-44	351	76	t	t	PROPN
ma-44	351	77	)	)	PUNCT
ma-44	351	78	(	(	PUNCT
ma-44	351	79	xu	xu	INTJ
ma-44	351	80	−xv	−xv	PROPN
ma-44	351	81	)	)	PUNCT
ma-44	351	82	(	(	PUNCT
ma-44	351	83	t	t	PROPN
ma-44	351	84	,	,	PUNCT
ma-44	351	85	a)dt	a)dt	PROPN
ma-44	351	86	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ma-44	351	87	≤	≤	PROPN
ma-44	352	1	mα1+α2+q−µ−1	mα1+α2+q−µ−1	PROPN
ma-44	352	2	γ	γ	PROPN
ma-44	352	3	(	(	PUNCT
ma-44	352	4	α1	α1	PROPN
ma-44	352	5	+	+	CCONJ
ma-44	352	6	α2	α2	ADJ
ma-44	352	7	−	−	PROPN
ma-44	352	8	µ+	µ+	PUNCT
ma-44	352	9	1	1	NUM
ma-44	352	10	)	)	PUNCT
ma-44	352	11	ε+	ε+	NOUN
ma-44	352	12	(	(	PUNCT
ma-44	352	13	mα2−µ	mα2−µ	NOUN
ma-44	352	14	γ(α2	γ(α2	NOUN
ma-44	352	15	−	−	PROPN
ma-44	352	16	µ+	µ+	PUNCT
ma-44	352	17	1	1	NUM
ma-44	352	18	)	)	PUNCT
ma-44	352	19	+	+	CCONJ
ma-44	352	20	γ	γ	X
ma-44	352	21	(	(	PUNCT
ma-44	352	22	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	352	23	γ(α2	γ(α2	NOUN
ma-44	352	24	+	+	X
ma-44	352	25	1)γ	1)γ	PROPN
ma-44	352	26	(	(	PUNCT
ma-44	352	27	γ2	γ2	PROPN
ma-44	352	28	−	−	PROPN
ma-44	352	29	µ	µ	NUM
ma-44	352	30	)	)	PUNCT
ma-44	352	31	)	)	PUNCT
ma-44	352	32	sup	sup	NOUN
ma-44	352	33	t∈[a	t∈[a	NOUN
ma-44	352	34	,	,	PUNCT
ma-44	352	35	b	b	NOUN
ma-44	352	36	]	]	X
ma-44	352	37	|xu	|xu	PRON
ma-44	352	38	−xv	−xv	NOUN
ma-44	352	39	|	|	ADV
ma-44	352	40	≤	≤	NUM
ma-44	353	1	mα1+α2+q−µ−1	mα1+α2+q−µ−1	NOUN
ma-44	353	2	γ	γ	X
ma-44	353	3	(	(	PUNCT
ma-44	353	4	α1	α1	PROPN
ma-44	353	5	+	+	CCONJ
ma-44	353	6	α2	α2	ADJ
ma-44	353	7	−	−	PROPN
ma-44	353	8	µ+	µ+	PUNCT
ma-44	353	9	1	1	NUM
ma-44	353	10	)	)	PUNCT
ma-44	353	11	ε	ε	PROPN
ma-44	354	1	+	+	CCONJ
ma-44	354	2	(	(	PUNCT
ma-44	354	3	4υ	4υ	X
ma-44	354	4	(	(	PUNCT
ma-44	354	5	q	q	NOUN
ma-44	354	6	−	−	PROPN
ma-44	354	7	1	1	NUM
ma-44	354	8	)	)	PUNCT
ma-44	354	9	∆q−2mα1	∆q−2mα1	NOUN
ma-44	354	10	γ(α1	γ(α1	NOUN
ma-44	355	1	+	+	CCONJ
ma-44	356	1	1	1	X
ma-44	356	2	)	)	PUNCT
ma-44	356	3	+	+	CCONJ
ma-44	356	4	(	(	PUNCT
ma-44	356	5	q	q	NOUN
ma-44	356	6	−	−	PROPN
ma-44	356	7	1	1	NUM
ma-44	356	8	)	)	PUNCT
ma-44	356	9	∆q−2mρ	∆q−2mρ	ADJ
ma-44	356	10	γ	γ	X
ma-44	356	11	(	(	PUNCT
ma-44	356	12	ρ+	ρ+	NUM
ma-44	356	13	1	1	NUM
ma-44	356	14	)	)	PUNCT
ma-44	356	15	)	)	PUNCT
ma-44	356	16	(	(	PUNCT
ma-44	356	17	mα2−µ	mα2−µ	NOUN
ma-44	356	18	γ(α2	γ(α2	NOUN
ma-44	356	19	−	−	PROPN
ma-44	356	20	µ+	µ+	PUNCT
ma-44	356	21	1	1	NUM
ma-44	356	22	)	)	PUNCT
ma-44	356	23	+	+	CCONJ
ma-44	356	24	γ	γ	X
ma-44	356	25	(	(	PUNCT
ma-44	356	26	γ2)mα2−µ	γ2)mα2−µ	PROPN
ma-44	356	27	γ(α2	γ(α2	NOUN
ma-44	356	28	+	+	X
ma-44	356	29	1)γ	1)γ	PROPN
ma-44	356	30	(	(	PUNCT
ma-44	356	31	γ2	γ2	PROPN
ma-44	356	32	−	−	PROPN
ma-44	356	33	µ	µ	NUM
ma-44	356	34	)	)	PUNCT
ma-44	356	35	)	)	PUNCT
ma-44	356	36	‖u	‖u	NOUN
ma-44	356	37	−	−	PROPN
ma-44	357	1	v‖cµϕ	v‖cµϕ	SYM
ma-44	357	2	≤	≤	NUM
ma-44	357	3	mα1+α2+q−µ−1	mα1+α2+q−µ−1	NOUN
ma-44	357	4	γ	γ	PROPN
ma-44	357	5	(	(	PUNCT
ma-44	357	6	α1	α1	PROPN
ma-44	357	7	+	+	CCONJ
ma-44	357	8	α2	α2	ADJ
ma-44	357	9	−	−	PROPN
ma-44	357	10	µ+	µ+	PUNCT
ma-44	357	11	1	1	NUM
ma-44	357	12	)	)	PUNCT
ma-44	357	13	ε+	ε+	X
ma-44	357	14	n2	n2	PROPN
ma-44	357	15	‖u	‖u	PROPN
ma-44	357	16	−	−	X
ma-44	357	17	v‖cµϕ	v‖cµϕ	X
ma-44	357	18	.	.	PUNCT
ma-44	358	1	so	so	ADV
ma-44	358	2	,	,	PUNCT
ma-44	358	3	by	by	ADP
ma-44	358	4	(	(	PUNCT
ma-44	358	5	3.11	3.11	NUM
ma-44	358	6	)	)	PUNCT
ma-44	358	7	and	and	CCONJ
ma-44	358	8	(	(	PUNCT
ma-44	358	9	3.12	3.12	NUM
ma-44	358	10	)	)	PUNCT
ma-44	358	11	we	we	PRON
ma-44	358	12	have	have	VERB
ma-44	358	13	‖u	‖u	NOUN
ma-44	358	14	−	−	PROPN
ma-44	358	15	v‖cµϕ	v‖cµϕ	SYM
ma-44	358	16	≤	≤	X
ma-44	358	17	ε	ε	PROPN
ma-44	358	18	(	(	PUNCT
ma-44	358	19	mα1+α2+q−1	mα1+α2+q−1	PROPN
ma-44	358	20	γ	γ	X
ma-44	358	21	(	(	PUNCT
ma-44	358	22	α1	α1	PROPN
ma-44	358	23	+	+	CCONJ
ma-44	358	24	α2	α2	ADJ
ma-44	358	25	+	+	CCONJ
ma-44	358	26	1	1	NUM
ma-44	358	27	)	)	PUNCT
ma-44	358	28	+	+	CCONJ
ma-44	358	29	mα1+α2+q−µ−1	mα1+α2+q−µ−1	PROPN
ma-44	358	30	γ	γ	X
ma-44	358	31	(	(	PUNCT
ma-44	358	32	α1	α1	PROPN
ma-44	358	33	+	+	CCONJ
ma-44	358	34	α2	α2	ADJ
ma-44	358	35	−	−	PROPN
ma-44	358	36	µ+	µ+	PUNCT
ma-44	358	37	1	1	NUM
ma-44	358	38	)	)	PUNCT
ma-44	358	39	)	)	PUNCT
ma-44	359	1	+	+	CCONJ
ma-44	359	2	(	(	PUNCT
ma-44	359	3	n1	n1	PROPN
ma-44	359	4	+	+	CCONJ
ma-44	359	5	n2	n2	ADJ
ma-44	359	6	)	)	PUNCT
ma-44	359	7	‖u	‖u	NOUN
ma-44	359	8	−	−	PROPN
ma-44	360	1	v‖cµϕ	v‖cµϕ	X
ma-44	360	2	.	.	PUNCT
ma-44	361	1	therefore	therefore	ADV
ma-44	361	2	,	,	PUNCT
ma-44	361	3	we	we	PRON
ma-44	361	4	get	get	VERB
ma-44	361	5	‖u	‖u	NOUN
ma-44	361	6	−	−	PROPN
ma-44	361	7	v‖cµϕ	v‖cµϕ	SYM
ma-44	361	8	≤	≤	NUM
ma-44	361	9	λε	λε	NOUN
ma-44	361	10	,	,	PUNCT
ma-44	361	11	such	such	ADJ
ma-44	361	12	that	that	SCONJ
ma-44	361	13	λ	λ	NOUN
ma-44	361	14	=	=	NOUN
ma-44	361	15	1	1	NUM
ma-44	361	16	1−	1−	NUM
ma-44	361	17	(	(	PUNCT
ma-44	361	18	n1	n1	PROPN
ma-44	361	19	+	+	CCONJ
ma-44	361	20	n2	n2	ADJ
ma-44	361	21	)	)	PUNCT
ma-44	361	22	(	(	PUNCT
ma-44	361	23	mα1+α2+q−1	mα1+α2+q−1	PROPN
ma-44	361	24	γ	γ	X
ma-44	361	25	(	(	PUNCT
ma-44	361	26	α1	α1	PROPN
ma-44	361	27	+	+	CCONJ
ma-44	361	28	α2	α2	ADJ
ma-44	361	29	+	+	CCONJ
ma-44	361	30	1	1	NUM
ma-44	361	31	)	)	PUNCT
ma-44	362	1	+	+	CCONJ
ma-44	362	2	mα1+α2+q−µ−1	mα1+α2+q−µ−1	AUX
ma-44	362	3	γ	γ	X
ma-44	362	4	(	(	PUNCT
ma-44	362	5	α1	α1	PROPN
ma-44	362	6	+	+	CCONJ
ma-44	362	7	α2	α2	ADJ
ma-44	362	8	−	−	PROPN
ma-44	362	9	µ+	µ+	PUNCT
ma-44	362	10	1	1	NUM
ma-44	362	11	)	)	PUNCT
ma-44	362	12	)	)	PUNCT
ma-44	363	1	,	,	PUNCT
ma-44	363	2	for	for	ADP
ma-44	363	3	any	any	DET
ma-44	363	4	t	t	NOUN
ma-44	363	5	∈	∈	PROPN
ma-44	363	6	j	j	PROPN
ma-44	363	7	.	.	PUNCT
ma-44	364	1	this	this	PRON
ma-44	364	2	implies	imply	VERB
ma-44	364	3	that	that	SCONJ
ma-44	364	4	the	the	DET
ma-44	364	5	ulam	ulam	PROPN
ma-44	364	6	-	-	PUNCT
ma-44	364	7	hyers	hyer	NOUN
ma-44	364	8	stability	stability	NOUN
ma-44	364	9	condition	condition	NOUN
ma-44	364	10	is	be	AUX
ma-44	364	11	satisfied	satisfied	ADJ
ma-44	364	12	.	.	PUNCT
ma-44	365	1	�	�	PROPN
ma-44	365	2	3.4	3.4	NUM
ma-44	365	3	.	.	PUNCT
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ma-44	366	2	exemple	exemple	NOUN
ma-44	366	3	.	.	PUNCT
ma-44	367	1	consider	consider	VERB
ma-44	367	2	the	the	DET
ma-44	367	3	following	follow	VERB
ma-44	367	4	problem	problem	NOUN
ma-44	367	5	hd	hd	VERB
ma-44	367	6	13	13	NUM
ma-44	367	7	10	10	NUM
ma-44	367	8	,	,	PUNCT
ma-44	367	9	6	6	NUM
ma-44	367	10	7	7	NUM
ma-44	367	11	;	;	PUNCT
ma-44	367	12	t2	t2	NOUN
ma-44	367	13	0	0	NUM
ma-44	367	14	+	+	NUM
ma-44	367	15	ψp	ψp	ADP
ma-44	367	16	(	(	PUNCT
ma-44	367	17	(	(	PUNCT
ma-44	367	18	hd	hd	PROPN
ma-44	367	19	17	17	NUM
ma-44	367	20	10	10	NUM
ma-44	367	21	,	,	PUNCT
ma-44	367	22	2	2	NUM
ma-44	367	23	3	3	NUM
ma-44	367	24	;	;	PUNCT
ma-44	367	25	t2	t2	NOUN
ma-44	367	26	0	0	NUM
ma-44	367	27	+	+	NUM
ma-44	367	28	u	u	NOUN
ma-44	367	29	)	)	PUNCT
ma-44	367	30	)	)	PUNCT
ma-44	367	31	(	(	PUNCT
ma-44	367	32	t	t	NOUN
ma-44	367	33	)	)	PUNCT
ma-44	367	34	=	=	SYM
ma-44	367	35	h(t	h(t	PROPN
ma-44	367	36	,	,	PUNCT
ma-44	367	37	u(t),rld	u(t),rld	PROPN
ma-44	367	38	1	1	NUM
ma-44	367	39	2	2	NUM
ma-44	367	40	;	;	PUNCT
ma-44	367	41	t2	t2	NOUN
ma-44	367	42	a+	a+	PUNCT
ma-44	367	43	u(t	u(t	NOUN
ma-44	367	44	)	)	PUNCT
ma-44	367	45	)	)	PUNCT
ma-44	367	46	,	,	PUNCT
ma-44	367	47	t	t	PROPN
ma-44	367	48	∈	∈	PROPN
ma-44	368	1	j	j	PROPN
ma-44	368	2	=	=	PUNCT
ma-44	369	1	[	[	X
ma-44	369	2	0	0	NUM
ma-44	369	3	,	,	PUNCT
ma-44	369	4	2	2	NUM
ma-44	369	5	]	]	PUNCT
ma-44	369	6	,	,	PUNCT
ma-44	369	7	(	(	PUNCT
ma-44	369	8	3.13	3.13	NUM
ma-44	369	9	)	)	PUNCT
ma-44	369	10	u(a	u(a	PROPN
ma-44	369	11	)	)	PUNCT
ma-44	369	12	=	=	SYM
ma-44	369	13	0	0	NUM
ma-44	369	14	,	,	PUNCT
ma-44	369	15	u(2	u(2	ADJ
ma-44	369	16	)	)	PUNCT
ma-44	369	17	=	=	PUNCT
ma-44	370	1	n∑	n∑	NOUN
ma-44	370	2	i=1	i=1	PROPN
ma-44	371	1	(	(	PUNCT
ma-44	371	2	3i	3i	NUM
ma-44	371	3	11	11	NUM
ma-44	371	4	)	)	PUNCT
ma-44	371	5	u	u	NOUN
ma-44	371	6	(	(	PUNCT
ma-44	371	7	i	i	NOUN
ma-44	371	8	2	2	NUM
ma-44	371	9	+	+	NUM
ma-44	371	10	i	i	NOUN
ma-44	371	11	)	)	PUNCT
ma-44	371	12	,	,	PUNCT
ma-44	371	13	ψp	ψp	ADP
ma-44	371	14	(	(	PUNCT
ma-44	371	15	(	(	PUNCT
ma-44	371	16	hd	hd	PROPN
ma-44	371	17	17	17	NUM
ma-44	371	18	10	10	NUM
ma-44	371	19	,	,	PUNCT
ma-44	371	20	2	2	NUM
ma-44	371	21	3	3	NUM
ma-44	371	22	;	;	PUNCT
ma-44	371	23	t2	t2	NOUN
ma-44	371	24	0	0	NUM
ma-44	371	25	+	+	NUM
ma-44	371	26	u	u	NOUN
ma-44	371	27	)	)	PUNCT
ma-44	371	28	)	)	PUNCT
ma-44	371	29	(	(	PUNCT
ma-44	371	30	0	0	X
ma-44	371	31	)	)	PUNCT
ma-44	371	32	=	=	SYM
ma-44	371	33	0	0	NUM
ma-44	371	34	,	,	PUNCT
ma-44	371	35	ψp	ψp	ADP
ma-44	371	36	(	(	PUNCT
ma-44	371	37	(	(	PUNCT
ma-44	371	38	hd	hd	PROPN
ma-44	371	39	17	17	NUM
ma-44	371	40	10	10	NUM
ma-44	371	41	,	,	PUNCT
ma-44	371	42	2	2	NUM
ma-44	371	43	3	3	NUM
ma-44	371	44	;	;	PUNCT
ma-44	371	45	t2	t2	NOUN
ma-44	371	46	0	0	NUM
ma-44	371	47	+	+	NUM
ma-44	371	48	u	u	NOUN
ma-44	371	49	)	)	PUNCT
ma-44	371	50	)	)	PUNCT
ma-44	371	51	(	(	PUNCT
ma-44	371	52	2	2	X
ma-44	371	53	)	)	PUNCT
ma-44	371	54	=	=	NOUN
ma-44	372	1	i	i	PRON
ma-44	372	2	3	3	NUM
ma-44	372	3	2	2	NUM
ma-44	372	4	;	;	PUNCT
ma-44	372	5	t2	t2	NOUN
ma-44	372	6	a+	a+	PUNCT
ma-44	372	7	u	u	NOUN
ma-44	372	8	(	(	PUNCT
ma-44	372	9	4	4	NUM
ma-44	372	10	3	3	NUM
ma-44	372	11	)	)	PUNCT
ma-44	372	12	f	f	PROPN
ma-44	372	13	(	(	PUNCT
ma-44	372	14	t	t	PROPN
ma-44	372	15	,	,	PUNCT
ma-44	372	16	u(t	u(t	PROPN
ma-44	372	17	)	)	PUNCT
ma-44	372	18	,	,	PUNCT
ma-44	372	19	v(t	v(t	NOUN
ma-44	372	20	)	)	PUNCT
ma-44	372	21	)	)	PUNCT
ma-44	373	1	=	=	SYM
ma-44	373	2	exp	exp	NOUN
ma-44	373	3	(	(	PUNCT
ma-44	373	4	1	1	NUM
ma-44	373	5	7	7	NUM
ma-44	373	6	(	(	PUNCT
ma-44	373	7	1	1	NUM
ma-44	373	8	+	+	NUM
ma-44	373	9	t2	t2	NOUN
ma-44	373	10	)	)	PUNCT
ma-44	373	11	)	)	PUNCT
ma-44	373	12	u(t	u(t	NOUN
ma-44	373	13	)	)	PUNCT
ma-44	373	14	+	+	CCONJ
ma-44	373	15	v(t	v(t	NUM
ma-44	373	16	)	)	PUNCT
ma-44	373	17	(	(	PUNCT
ma-44	373	18	1	1	NUM
ma-44	373	19	+	+	NUM
ma-44	373	20	et	et	NOUN
ma-44	373	21	)	)	PUNCT
ma-44	373	22	,	,	PUNCT
ma-44	373	23	eur	eur	PROPN
ma-44	373	24	.	.	PUNCT
ma-44	374	1	j.	j.	PROPN
ma-44	374	2	math	math	PROPN
ma-44	374	3	.	.	PUNCT
ma-44	375	1	anal	anal	ADJ
ma-44	375	2	.	.	PUNCT
ma-44	376	1	1	1	NUM
ma-44	376	2	(	(	PUNCT
ma-44	376	3	2021	2021	NUM
ma-44	376	4	)	)	PUNCT
ma-44	377	1	180then	180then	PROPN
ma-44	377	2	assumptions	assumption	NOUN
ma-44	377	3	(	(	PUNCT
ma-44	377	4	h1	h1	PROPN
ma-44	377	5	)	)	PUNCT
ma-44	377	6	,	,	PUNCT
ma-44	377	7	(	(	PUNCT
ma-44	377	8	h2	h2	NOUN
ma-44	377	9	)	)	PUNCT
ma-44	377	10	and	and	CCONJ
ma-44	377	11	(	(	PUNCT
ma-44	377	12	h3	h3	NOUN
ma-44	377	13	)	)	PUNCT
ma-44	377	14	are	be	AUX
ma-44	377	15	satisfied	satisfied	ADJ
ma-44	377	16	with	with	ADP
ma-44	377	17	υ	υ	PROPN
ma-44	377	18	=	=	PUNCT
ma-44	377	19	π∗2	π∗2	NOUN
ma-44	377	20	=	=	SYM
ma-44	377	21	1	1	NUM
ma-44	377	22	2	2	NUM
ma-44	377	23	,	,	PUNCT
ma-44	377	24	π∗1	π∗1	NOUN
ma-44	377	25	=	=	PUNCT
ma-44	378	1	e	e	NOUN
ma-44	378	2	1	1	NUM
ma-44	378	3	7	7	NUM
ma-44	378	4	,	,	PUNCT
ma-44	378	5	and	and	CCONJ
ma-44	378	6	m	m	NOUN
ma-44	378	7	=	=	ADJ
ma-44	378	8	4	4	X
ma-44	378	9	.	.	X
ma-44	379	1	we	we	PRON
ma-44	379	2	conclude	conclude	VERB
ma-44	379	3	that	that	SCONJ
ma-44	379	4	(	(	PUNCT
ma-44	379	5	3.13	3.13	NUM
ma-44	379	6	)	)	PUNCT
ma-44	379	7	has	have	VERB
ma-44	379	8	an	an	DET
ma-44	379	9	unique	unique	ADJ
ma-44	379	10	solution	solution	NOUN
ma-44	379	11	.	.	PUNCT
ma-44	380	1	references	reference	NOUN
ma-44	380	2	[	[	X
ma-44	380	3	1	1	NUM
ma-44	380	4	]	]	PUNCT
ma-44	380	5	b.	b.	PROPN
ma-44	380	6	ahmad	ahmad	PROPN
ma-44	380	7	,	,	PUNCT
ma-44	380	8	a.	a.	NOUN
ma-44	380	9	alsaedi	alsaedi	PROPN
ma-44	380	10	,	,	PUNCT
ma-44	380	11	s.	s.	PROPN
ma-44	380	12	k.	k.	PROPN
ma-44	380	13	ntouyas	ntouyas	PROPN
ma-44	380	14	,	,	PUNCT
ma-44	380	15	and	and	CCONJ
ma-44	380	16	j.	j.	PROPN
ma-44	380	17	tariboon	tariboon	PROPN
ma-44	380	18	,	,	PUNCT
ma-44	380	19	hadamard	hadamard	ADJ
ma-44	380	20	-	-	PUNCT
ma-44	380	21	type	type	NOUN
ma-44	380	22	fractional	fractional	ADJ
ma-44	380	23	differential	differential	NOUN
ma-44	380	24	equations	equation	NOUN
ma-44	380	25	,	,	PUNCT
ma-44	380	26	inclusionsand	inclusionsand	NOUN
ma-44	380	27	inequalities	inequality	NOUN
ma-44	380	28	,	,	PUNCT
ma-44	380	29	springer	springer	NOUN
ma-44	380	30	,	,	PUNCT
ma-44	380	31	cham	cham	PROPN
ma-44	380	32	,	,	PUNCT
ma-44	380	33	switzerland	switzerland	PROPN
ma-44	380	34	,	,	PUNCT
ma-44	380	35	2017.[2	2017.[2	NUM
ma-44	380	36	]	]	PUNCT
ma-44	380	37	s.	s.	PROPN
ma-44	380	38	asawasamrit	asawasamrit	PROPN
ma-44	380	39	,	,	PUNCT
ma-44	380	40	a.	a.	PROPN
ma-44	380	41	kijjathanakorn	kijjathanakorn	PROPN
ma-44	380	42	,	,	PUNCT
ma-44	380	43	s.	s.	PROPN
ma-44	380	44	k.	k.	PROPN
ma-44	380	45	ntouyas	ntouyas	PROPN
ma-44	380	46	,	,	PUNCT
ma-44	380	47	and	and	CCONJ
ma-44	380	48	j.	j.	PROPN
ma-44	380	49	tariboon	tariboon	PROPN
ma-44	380	50	,	,	PUNCT
ma-44	380	51	nonlocal	nonlocal	ADJ
ma-44	380	52	boundary	boundary	ADJ
ma-44	380	53	value	value	NOUN
ma-44	380	54	problems	problem	NOUN
ma-44	380	55	for	for	ADP
ma-44	380	56	hilferfractional	hilferfractional	ADJ
ma-44	380	57	differential	differential	ADJ
ma-44	380	58	equations	equation	NOUN
ma-44	380	59	,	,	PUNCT
ma-44	380	60	bull	bull	NOUN
ma-44	380	61	.	.	PUNCT
ma-44	381	1	korean	korean	ADJ
ma-44	381	2	math	math	PROPN
ma-44	381	3	.	.	PUNCT
ma-44	382	1	soc	soc	PROPN
ma-44	382	2	.	.	PUNCT
ma-44	383	1	55	55	NUM
ma-44	383	2	(	(	PUNCT
ma-44	383	3	2018	2018	NUM
ma-44	383	4	)	)	PUNCT
ma-44	383	5	1639	1639	NUM
ma-44	383	6	-	-	SYM
ma-44	383	7	1657	1657	NUM
ma-44	383	8	.	.	PUNCT
ma-44	384	1	https://doi.org/10.4134/bkms	https://doi.org/10.4134/bkms	PROPN
ma-44	384	2	.	.	PUNCT
ma-44	385	1	b170887.[3	b170887.[3	NOUN
ma-44	385	2	]	]	X
ma-44	385	3	h.	h.	PROPN
ma-44	385	4	beddani	beddani	PROPN
ma-44	385	5	,	,	PUNCT
ma-44	385	6	n	n	PROPN
ma-44	385	7	+	+	CCONJ
ma-44	385	8	1−parameter	1−parameter	NUM
ma-44	385	9	singular	singular	ADJ
ma-44	385	10	fractional	fractional	ADJ
ma-44	385	11	differential	differential	NOUN
ma-44	385	12	equation	equation	NOUN
ma-44	385	13	,	,	PUNCT
ma-44	385	14	asia	asia	PROPN
ma-44	385	15	math	math	NOUN
ma-44	385	16	.	.	PUNCT
ma-44	386	1	5	5	NUM
ma-44	386	2	(	(	PUNCT
ma-44	386	3	2021	2021	NUM
ma-44	386	4	)	)	PUNCT
ma-44	386	5	11	11	NUM
ma-44	386	6	-	-	SYM
ma-44	386	7	18	18	NUM
ma-44	386	8	.	.	PUNCT
ma-44	387	1	http://dx	http://dx	NOUN
ma-44	387	2	.	.	PUNCT
ma-44	388	1	doi.org/10.5281/zenodo.4721390.[4	doi.org/10.5281/zenodo.4721390.[4	PROPN
ma-44	388	2	]	]	PUNCT
ma-44	388	3	h.	h.	PROPN
ma-44	388	4	beddani	beddani	PROPN
ma-44	388	5	,	,	PUNCT
ma-44	388	6	z.	z.	PROPN
ma-44	388	7	dahmani	dahmani	PROPN
ma-44	388	8	,	,	PUNCT
ma-44	388	9	solvability	solvability	NOUN
ma-44	388	10	for	for	ADP
ma-44	388	11	a	a	DET
ma-44	388	12	nonlinear	nonlinear	ADJ
ma-44	388	13	differential	differential	ADJ
ma-44	388	14	problem	problem	NOUN
ma-44	388	15	of	of	ADP
ma-44	388	16	langevin	langevin	ADJ
ma-44	388	17	type	type	NOUN
ma-44	388	18	via	via	ADP
ma-44	388	19	phi	phi	NOUN
ma-44	388	20	-	-	PUNCT
ma-44	388	21	caputo	caputo	PROPN
ma-44	388	22	approach	approach	NOUN
ma-44	388	23	,	,	PUNCT
ma-44	388	24	eur	eur	PROPN
ma-44	388	25	.	.	PUNCT
ma-44	389	1	j.	j.	PROPN
ma-44	389	2	math	math	PROPN
ma-44	389	3	.	.	PUNCT
ma-44	390	1	appl	appl	PROPN
ma-44	390	2	.	.	PROPN
ma-44	391	1	1	1	NUM
ma-44	391	2	(	(	PUNCT
ma-44	391	3	2021	2021	NUM
ma-44	391	4	)	)	PUNCT
ma-44	391	5	,	,	PUNCT
ma-44	391	6	11	11	NUM
ma-44	391	7	.	.	PUNCT
ma-44	392	1	https://doi.org/10.28919/ejma.2021.1.11.[5	https://doi.org/10.28919/ejma.2021.1.11.[5	PROPN
ma-44	392	2	]	]	X
ma-44	392	3	h.	h.	PROPN
ma-44	392	4	beddani	beddani	PROPN
ma-44	392	5	,	,	PUNCT
ma-44	392	6	z.	z.	PROPN
ma-44	392	7	dahmani	dahmani	PROPN
ma-44	392	8	,	,	PUNCT
ma-44	392	9	i.	i.	PROPN
ma-44	392	10	jebril	jebril	PROPN
ma-44	392	11	,	,	PUNCT
ma-44	392	12	a	a	DET
ma-44	392	13	sequential	sequential	ADJ
ma-44	392	14	random	random	ADJ
ma-44	392	15	pronlem	pronlem	NOUN
ma-44	392	16	of	of	ADP
ma-44	392	17	airy	airy	ADJ
ma-44	392	18	type	type	NOUN
ma-44	392	19	solved	solve	VERB
ma-44	392	20	by	by	ADP
ma-44	392	21	the	the	DET
ma-44	392	22	lower	low	ADJ
ma-44	392	23	and	and	CCONJ
ma-44	392	24	upper	upper	ADJ
ma-44	392	25	method	method	NOUN
ma-44	392	26	,	,	PUNCT
ma-44	392	27	romai	romai	NOUN
ma-44	392	28	j.	j.	PROPN
ma-44	392	29	16	16	NUM
ma-44	392	30	(	(	PUNCT
ma-44	392	31	2020	2020	NUM
ma-44	392	32	)	)	PUNCT
ma-44	392	33	37	37	NUM
ma-44	392	34	-	-	SYM
ma-44	392	35	49[6	49[6	NUM
ma-44	392	36	]	]	X
ma-44	392	37	h.	h.	PROPN
ma-44	392	38	beddani	beddani	PROPN
ma-44	392	39	,	,	PUNCT
ma-44	392	40	m.	m.	NOUN
ma-44	392	41	beddani	beddani	PROPN
ma-44	392	42	,	,	PUNCT
ma-44	392	43	solvability	solvability	NOUN
ma-44	392	44	for	for	ADP
ma-44	392	45	a	a	DET
ma-44	392	46	differential	differential	ADJ
ma-44	392	47	systems	system	NOUN
ma-44	392	48	via	via	ADP
ma-44	392	49	phi	phi	NOUN
ma-44	392	50	-	-	PUNCT
ma-44	392	51	caputo	caputo	PROPN
ma-44	392	52	approach	approach	NOUN
ma-44	392	53	,	,	PUNCT
ma-44	392	54	j.	j.	PROPN
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ma-44	393	2	,	,	PUNCT
ma-44	393	3	3(56	3(56	NUM
ma-44	393	4	)	)	PUNCT
ma-44	393	5	(	(	PUNCT
ma-44	393	6	2021).[7	2021).[7	X
ma-44	393	7	]	]	X
ma-44	393	8	a.	a.	NOUN
ma-44	393	9	devi	devi	PROPN
ma-44	393	10	,	,	PUNCT
ma-44	393	11	a.	a.	PROPN
ma-44	393	12	kumar	kumar	PROPN
ma-44	393	13	,	,	PUNCT
ma-44	393	14	d.	d.	PROPN
ma-44	393	15	baleanu	baleanu	PROPN
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ma-44	393	17	a.	a.	PROPN
ma-44	393	18	khan	khan	PROPN
ma-44	393	19	,	,	PUNCT
ma-44	393	20	on	on	ADP
ma-44	393	21	stability	stability	NOUN
ma-44	393	22	analysis	analysis	NOUN
ma-44	393	23	and	and	CCONJ
ma-44	393	24	existence	existence	NOUN
ma-44	393	25	of	of	ADP
ma-44	393	26	positive	positive	ADJ
ma-44	393	27	solutions	solution	NOUN
ma-44	393	28	for	for	ADP
ma-44	393	29	a	a	DET
ma-44	393	30	generalnon	generalnon	NOUN
ma-44	393	31	-	-	PUNCT
ma-44	393	32	linear	linear	ADJ
ma-44	393	33	fractional	fractional	ADJ
ma-44	393	34	differential	differential	NOUN
ma-44	393	35	equations	equation	NOUN
ma-44	393	36	.	.	PUNCT
ma-44	394	1	adv	adv	PROPN
ma-44	394	2	.	.	PROPN
ma-44	394	3	differ	differ	VERB
ma-44	394	4	.	.	PUNCT
ma-44	395	1	equations	equation	NOUN
ma-44	395	2	2020	2020	NUM
ma-44	395	3	(	(	PUNCT
ma-44	395	4	2020	2020	NUM
ma-44	395	5	)	)	PUNCT
ma-44	395	6	300	300	NUM
ma-44	395	7	.	.	PUNCT
ma-44	396	1	https://doi.org/10.1186/	https://doi.org/10.1186/	PROPN
ma-44	396	2	s13662	s13662	PROPN
ma-44	396	3	-	-	PUNCT
ma-44	396	4	020	020	NUM
ma-44	396	5	-	-	PUNCT
ma-44	396	6	02729	02729	NUM
ma-44	396	7	-	-	PUNCT
ma-44	396	8	3.[8	3.[8	NUM
ma-44	396	9	]	]	X
ma-44	396	10	k.	k.	PROPN
ma-44	396	11	diethelm	diethelm	PROPN
ma-44	396	12	,	,	PUNCT
ma-44	396	13	the	the	DET
ma-44	396	14	analysis	analysis	NOUN
ma-44	396	15	of	of	ADP
ma-44	396	16	fractional	fractional	ADJ
ma-44	396	17	differential	differential	ADJ
ma-44	396	18	equations	equation	NOUN
ma-44	396	19	,	,	PUNCT
ma-44	396	20	lecture	lecture	NOUN
ma-44	396	21	notes	note	NOUN
ma-44	396	22	in	in	ADP
ma-44	396	23	mathematics	mathematic	NOUN
ma-44	396	24	,	,	PUNCT
ma-44	396	25	springer	springer	NOUN
ma-44	396	26	,	,	PUNCT
ma-44	396	27	new	new	PROPN
ma-44	396	28	york,2010.[9	york,2010.[9	PROPN
ma-44	396	29	]	]	X
ma-44	396	30	k.	k.	PROPN
ma-44	396	31	m.	m.	PROPN
ma-44	396	32	furati	furati	PROPN
ma-44	396	33	,	,	PUNCT
ma-44	396	34	n.	n.	PROPN
ma-44	396	35	d.	d.	PROPN
ma-44	396	36	kassim	kassim	PROPN
ma-44	396	37	,	,	PUNCT
ma-44	396	38	and	and	CCONJ
ma-44	396	39	n.	n.	PROPN
ma-44	396	40	e.	e.	PROPN
ma-44	396	41	tatar	tatar	PROPN
ma-44	396	42	,	,	PUNCT
ma-44	396	43	existence	existence	NOUN
ma-44	396	44	and	and	CCONJ
ma-44	396	45	uniqueness	uniqueness	NOUN
ma-44	396	46	for	for	ADP
ma-44	396	47	a	a	DET
ma-44	396	48	problem	problem	NOUN
ma-44	396	49	involving	involve	VERB
ma-44	396	50	hilfer	hilfer	NOUN
ma-44	396	51	fractionalderivative	fractionalderivative	ADJ
ma-44	396	52	,	,	PUNCT
ma-44	396	53	comput	comput	NOUN
ma-44	396	54	.	.	PUNCT
ma-44	397	1	math	math	NOUN
ma-44	397	2	.	.	PUNCT
ma-44	398	1	appl	appl	PROPN
ma-44	398	2	.	.	PUNCT
ma-44	399	1	64	64	NUM
ma-44	399	2	(	(	PUNCT
ma-44	399	3	2012	2012	NUM
ma-44	399	4	)	)	PUNCT
ma-44	399	5	,	,	PUNCT
ma-44	399	6	1616	1616	NUM
ma-44	399	7	-	-	SYM
ma-44	399	8	1626	1626	NUM
ma-44	399	9	.	.	PUNCT
ma-44	400	1	https://doi.org/10.1016/j.camwa.2012.01.009.[10	https://doi.org/10.1016/j.camwa.2012.01.009.[10	NOUN
ma-44	400	2	]	]	X
ma-44	400	3	h.	h.	PROPN
ma-44	400	4	gu	gu	PROPN
ma-44	400	5	and	and	CCONJ
ma-44	400	6	j.	j.	PROPN
ma-44	400	7	j.	j.	PROPN
ma-44	400	8	trujillo	trujillo	PROPN
ma-44	400	9	,	,	PUNCT
ma-44	400	10	existence	existence	NOUN
ma-44	400	11	of	of	ADP
ma-44	400	12	mild	mild	ADJ
ma-44	400	13	solution	solution	NOUN
ma-44	400	14	for	for	ADP
ma-44	400	15	evolution	evolution	NOUN
ma-44	400	16	equation	equation	NOUN
ma-44	400	17	with	with	ADP
ma-44	400	18	hilfer	hilfer	NOUN
ma-44	400	19	fractional	fractional	ADJ
ma-44	400	20	derivative	derivative	ADJ
ma-44	400	21	,	,	PUNCT
ma-44	400	22	appl	appl	PROPN
ma-44	400	23	.	.	PUNCT
ma-44	401	1	math.comput	math.comput	PROPN
ma-44	401	2	.	.	PUNCT
ma-44	402	1	257	257	NUM
ma-44	402	2	(	(	PUNCT
ma-44	402	3	2015	2015	NUM
ma-44	402	4	)	)	PUNCT
ma-44	402	5	344	344	NUM
ma-44	402	6	-	-	SYM
ma-44	402	7	354	354	NUM
ma-44	402	8	.	.	PUNCT
ma-44	403	1	https://doi.org/10.1016/j.amc.2014.10.083.[11	https://doi.org/10.1016/j.amc.2014.10.083.[11	PROPN
ma-44	403	2	]	]	PUNCT
ma-44	403	3	r.	r.	PROPN
ma-44	403	4	hilfer	hilfer	PROPN
ma-44	403	5	,	,	PUNCT
ma-44	403	6	applications	application	NOUN
ma-44	403	7	of	of	ADP
ma-44	403	8	fractional	fractional	ADJ
ma-44	403	9	calculus	calculus	NOUN
ma-44	403	10	in	in	ADP
ma-44	403	11	physics	physics	PROPN
ma-44	403	12	,	,	PUNCT
ma-44	403	13	world	world	NOUN
ma-44	403	14	scientific	scientific	PROPN
ma-44	403	15	,	,	PUNCT
ma-44	403	16	singapore	singapore	PROPN
ma-44	403	17	,	,	PUNCT
ma-44	403	18	2000.[12	2000.[12	PROPN
ma-44	403	19	]	]	X
ma-44	403	20	r.	r.	PROPN
ma-44	403	21	hilfer	hilfer	PROPN
ma-44	403	22	,	,	PUNCT
ma-44	403	23	experimental	experimental	ADJ
ma-44	403	24	evidence	evidence	NOUN
ma-44	403	25	for	for	ADP
ma-44	403	26	fractional	fractional	ADJ
ma-44	403	27	time	time	NOUN
ma-44	403	28	evolution	evolution	NOUN
ma-44	403	29	in	in	ADP
ma-44	403	30	glass	glass	NOUN
ma-44	403	31	forming	form	VERB
ma-44	403	32	materials	material	NOUN
ma-44	403	33	,	,	PUNCT
ma-44	403	34	j.	j.	PROPN
ma-44	403	35	chem	chem	PROPN
ma-44	403	36	.	.	PUNCT
ma-44	404	1	phys	phy	NOUN
ma-44	404	2	.	.	PUNCT
ma-44	405	1	284	284	NUM
ma-44	405	2	(	(	PUNCT
ma-44	405	3	2002)399	2002)399	PROPN
ma-44	405	4	-	-	SYM
ma-44	405	5	408	408	NUM
ma-44	405	6	.	.	PUNCT
ma-44	406	1	https://doi.org/10.1016/s0301-0104(02)00670-5.[13	https://doi.org/10.1016/s0301-0104(02)00670-5.[13	PROPN
ma-44	406	2	]	]	X
ma-44	406	3	r.	r.	PROPN
ma-44	406	4	hilfer	hilfer	PROPN
ma-44	406	5	,	,	PUNCT
ma-44	406	6	y.	y.	PROPN
ma-44	406	7	luchko	luchko	PROPN
ma-44	406	8	,	,	PUNCT
ma-44	406	9	and	and	CCONJ
ma-44	406	10	z.	z.	PROPN
ma-44	406	11	tomovski	tomovski	PROPN
ma-44	406	12	,	,	PUNCT
ma-44	406	13	operational	operational	ADJ
ma-44	406	14	method	method	NOUN
ma-44	406	15	for	for	ADP
ma-44	406	16	the	the	DET
ma-44	406	17	solution	solution	NOUN
ma-44	406	18	of	of	ADP
ma-44	406	19	fractional	fractional	ADJ
ma-44	406	20	differential	differential	ADJ
ma-44	406	21	equations	equation	NOUN
ma-44	406	22	withgeneralized	withgeneralize	VERB
ma-44	406	23	riemann	riemann	PROPN
ma-44	406	24	-	-	PUNCT
ma-44	406	25	liouville	liouville	VERB
ma-44	406	26	fractional	fractional	ADJ
ma-44	406	27	derivatives	derivative	NOUN
ma-44	406	28	,	,	PUNCT
ma-44	406	29	frac	frac	PROPN
ma-44	406	30	.	.	PUNCT
ma-44	407	1	calc	calc	PROPN
ma-44	407	2	.	.	PUNCT
ma-44	408	1	appl	appl	PROPN
ma-44	408	2	.	.	PUNCT
ma-44	409	1	anal	anal	PROPN
ma-44	409	2	.	.	PUNCT
ma-44	410	1	12	12	NUM
ma-44	410	2	(	(	PUNCT
ma-44	410	3	2009	2009	NUM
ma-44	410	4	)	)	PUNCT
ma-44	410	5	299	299	NUM
ma-44	410	6	-	-	SYM
ma-44	410	7	318.[14	318.[14	PROPN
ma-44	410	8	]	]	X
ma-44	410	9	h.	h.	PROPN
ma-44	410	10	khan	khan	PROPN
ma-44	410	11	,	,	PUNCT
ma-44	410	12	w.	w.	PROPN
ma-44	410	13	chen	chen	PROPN
ma-44	410	14	,	,	PUNCT
ma-44	410	15	h.	h.	PROPN
ma-44	410	16	sun	sun	PROPN
ma-44	410	17	,	,	PUNCT
ma-44	410	18	analysis	analysis	NOUN
ma-44	410	19	of	of	ADP
ma-44	410	20	positive	positive	ADJ
ma-44	410	21	solution	solution	NOUN
ma-44	410	22	and	and	CCONJ
ma-44	410	23	hyers	hyer	NOUN
ma-44	410	24	-	-	PUNCT
ma-44	410	25	ulam	ulam	PROPN
ma-44	410	26	stability	stability	NOUN
ma-44	410	27	for	for	ADP
ma-44	410	28	a	a	DET
ma-44	410	29	class	class	NOUN
ma-44	410	30	of	of	ADP
ma-44	410	31	singular	singular	ADJ
ma-44	410	32	fractionaldifferential	fractionaldifferential	ADJ
ma-44	410	33	equations	equation	NOUN
ma-44	410	34	with	with	ADP
ma-44	410	35	p	p	NOUN
ma-44	410	36	-	-	PUNCT
ma-44	410	37	laplacian	laplacian	NOUN
ma-44	410	38	in	in	ADP
ma-44	410	39	banach	banach	NOUN
ma-44	410	40	space	space	NOUN
ma-44	410	41	.	.	PUNCT
ma-44	411	1	math	math	NOUN
ma-44	411	2	.	.	PUNCT
ma-44	412	1	methods	method	NOUN
ma-44	412	2	appl	appl	PROPN
ma-44	412	3	.	.	PUNCT
ma-44	413	1	sci	sci	PROPN
ma-44	413	2	.	.	PROPN
ma-44	414	1	41	41	NUM
ma-44	414	2	(	(	PUNCT
ma-44	414	3	2018	2018	NUM
ma-44	414	4	)	)	PUNCT
ma-44	414	5	3430	3430	NUM
ma-44	414	6	-	-	SYM
ma-44	414	7	3440	3440	NUM
ma-44	414	8	.	.	PUNCT
ma-44	415	1	https	https	NOUN
ma-44	415	2	:	:	PUNCT
ma-44	415	3	//doi.org/10.1002	//doi.org/10.1002	NOUN
ma-44	415	4	/	/	SYM
ma-44	415	5	mma.4835.[15	mma.4835.[15	NOUN
ma-44	415	6	]	]	PUNCT
ma-44	415	7	a.	a.	PROPN
ma-44	415	8	khan	khan	PROPN
ma-44	415	9	,	,	PUNCT
ma-44	415	10	m.i	m.i	PROPN
ma-44	415	11	.	.	PROPN
ma-44	415	12	syam	syam	PROPN
ma-44	415	13	,	,	PUNCT
ma-44	415	14	a.	a.	PROPN
ma-44	415	15	,zada	,zada	PROPN
ma-44	415	16	,	,	PUNCT
ma-44	415	17	h.	h.	PROPN
ma-44	415	18	khan	khan	PROPN
ma-44	415	19	,	,	PUNCT
ma-44	415	20	:	:	PUNCT
ma-44	415	21	stability	stability	NOUN
ma-44	415	22	analysis	analysis	NOUN
ma-44	415	23	of	of	ADP
ma-44	415	24	nonlinear	nonlinear	ADJ
ma-44	415	25	fractional	fractional	ADJ
ma-44	415	26	differential	differential	ADJ
ma-44	415	27	equations	equation	NOUN
ma-44	415	28	withcaputo	withcaputo	NOUN
ma-44	415	29	and	and	CCONJ
ma-44	415	30	riemann	riemann	PROPN
ma-44	415	31	–	–	PUNCT
ma-44	415	32	liouville	liouville	VERB
ma-44	415	33	derivatives	derivative	NOUN
ma-44	415	34	.	.	PUNCT
ma-44	416	1	eur	eur	ADJ
ma-44	416	2	.	.	PUNCT
ma-44	416	3	phys	phy	NOUN
ma-44	416	4	.	.	PUNCT
ma-44	417	1	j.	j.	PROPN
ma-44	417	2	plus	plus	CCONJ
ma-44	417	3	133	133	NUM
ma-44	417	4	,	,	PUNCT
ma-44	417	5	26	26	NUM
ma-44	417	6	(	(	PUNCT
ma-44	417	7	2018	2018	NUM
ma-44	417	8	)	)	PUNCT
ma-44	417	9	.	.	PUNCT
ma-44	418	1	https://doi.org/10.1140/epjp/	https://doi.org/10.1140/epjp/	NOUN
ma-44	418	2	i2018	i2018	PROPN
ma-44	418	3	-	-	PUNCT
ma-44	418	4	12119	12119	NUM
ma-44	418	5	-	-	PUNCT
ma-44	418	6	6.[16	6.[16	NUM
ma-44	418	7	]	]	PUNCT
ma-44	419	1	h.	h.	PROPN
ma-44	419	2	khan	khan	PROPN
ma-44	419	3	,	,	PUNCT
ma-44	419	4	t.	t.	PROPN
ma-44	419	5	abdeljawad	abdeljawad	PROPN
ma-44	419	6	,	,	PUNCT
ma-44	419	7	m.	m.	NOUN
ma-44	419	8	aslam	aslam	PROPN
ma-44	419	9	,	,	PUNCT
ma-44	419	10	r.	r.	PROPN
ma-44	419	11	a.	a.	PROPN
ma-44	419	12	khan	khan	PROPN
ma-44	419	13	and	and	CCONJ
ma-44	419	14	a.	a.	PROPN
ma-44	419	15	khan	khan	PROPN
ma-44	419	16	,	,	PUNCT
ma-44	419	17	existence	existence	NOUN
ma-44	419	18	of	of	ADP
ma-44	419	19	positive	positive	ADJ
ma-44	419	20	solution	solution	NOUN
ma-44	419	21	and	and	CCONJ
ma-44	419	22	hyers	hyer	NOUN
ma-44	419	23	–	–	PUNCT
ma-44	419	24	ulamstability	ulamstability	NOUN
ma-44	419	25	for	for	ADP
ma-44	419	26	a	a	DET
ma-44	419	27	nonlinear	nonlinear	ADJ
ma-44	419	28	singular	singular	NOUN
ma-44	419	29	-	-	PUNCT
ma-44	419	30	delay	delay	NOUN
ma-44	419	31	-	-	PUNCT
ma-44	419	32	fractional	fractional	ADJ
ma-44	419	33	differential	differential	NOUN
ma-44	419	34	equation	equation	NOUN
ma-44	419	35	.	.	PUNCT
ma-44	420	1	adv	adv	PROPN
ma-44	420	2	.	.	PROPN
ma-44	420	3	differ	differ	VERB
ma-44	420	4	.	.	PUNCT
ma-44	421	1	equations	equation	NOUN
ma-44	421	2	2019	2019	NUM
ma-44	421	3	(	(	PUNCT
ma-44	421	4	2019	2019	NUM
ma-44	421	5	)	)	PUNCT
ma-44	421	6	104	104	NUM
ma-44	421	7	.	.	PUNCT
ma-44	422	1	https://doi.org/10.1186/s13662-019-2054-z.[17	https://doi.org/10.1186/s13662-019-2054-z.[17	PROPN
ma-44	422	2	]	]	X
ma-44	422	3	a.	a.	NOUN
ma-44	422	4	a.	a.	NOUN
ma-44	422	5	kilbas	kilbas	PROPN
ma-44	422	6	,	,	PUNCT
ma-44	422	7	h.	h.	PROPN
ma-44	422	8	m.	m.	PROPN
ma-44	422	9	srivastava	srivastava	PROPN
ma-44	422	10	,	,	PUNCT
ma-44	422	11	and	and	CCONJ
ma-44	422	12	j.	j.	PROPN
ma-44	422	13	j.	j.	PROPN
ma-44	422	14	trujillo	trujillo	PROPN
ma-44	422	15	,	,	PUNCT
ma-44	422	16	theory	theory	NOUN
ma-44	422	17	and	and	CCONJ
ma-44	422	18	applications	application	NOUN
ma-44	422	19	of	of	ADP
ma-44	422	20	the	the	DET
ma-44	422	21	fractional	fractional	ADJ
ma-44	422	22	differential	differential	ADJ
ma-44	422	23	equations	equation	NOUN
ma-44	422	24	,	,	PUNCT
ma-44	422	25	north	north	NOUN
ma-44	422	26	-	-	PUNCT
ma-44	422	27	holland	holland	PROPN
ma-44	422	28	mathematics	mathematics	PROPN
ma-44	422	29	studies	study	NOUN
ma-44	422	30	,	,	PUNCT
ma-44	422	31	vol	vol	NOUN
ma-44	422	32	.	.	PROPN
ma-44	422	33	204	204	NUM
ma-44	422	34	,	,	PUNCT
ma-44	422	35	elsevier	elsevier	NOUN
ma-44	422	36	,	,	PUNCT
ma-44	422	37	amsterdam	amsterdam	PROPN
ma-44	422	38	,	,	PUNCT
ma-44	422	39	2006	2006	NUM
ma-44	422	40	.	.	PUNCT
ma-44	423	1	https://doi.org/10.4134/bkms.b170887	https://doi.org/10.4134/bkms.b170887	PROPN
ma-44	423	2	https://doi.org/10.4134/bkms.b170887	https://doi.org/10.4134/bkms.b170887	INTJ
ma-44	423	3	http://dx.doi.org/10.5281/zenodo.4721390	http://dx.doi.org/10.5281/zenodo.4721390	PRON
ma-44	423	4	http://dx.doi.org/10.5281/zenodo.4721390	http://dx.doi.org/10.5281/zenodo.4721390	ADV
ma-44	423	5	https://doi.org/10.28919/ejma.2021.1.11	https://doi.org/10.28919/ejma.2021.1.11	PROPN
ma-44	423	6	https://doi.org/10.1186/s13662-020-02729-3	https://doi.org/10.1186/s13662-020-02729-3	NUM
ma-44	423	7	https://doi.org/10.1186/s13662-020-02729-3	https://doi.org/10.1186/s13662-020-02729-3	NUM
ma-44	423	8	https://doi.org/10.1016/j.camwa.2012.01.009	https://doi.org/10.1016/j.camwa.2012.01.009	VERB
ma-44	423	9	https://doi.org/10.1016/j.amc.2014.10.083	https://doi.org/10.1016/j.amc.2014.10.083	PROPN
ma-44	423	10	https://doi.org/10.1016/s0301-0104(02)00670-5	https://doi.org/10.1016/s0301-0104(02)00670-5	PROPN
ma-44	423	11	https://doi.org/10.1002/mma.4835	https://doi.org/10.1002/mma.4835	PROPN
ma-44	423	12	https://doi.org/10.1002/mma.4835	https://doi.org/10.1002/mma.4835	VERB
ma-44	423	13	https://doi.org/10.1140/epjp/i2018-12119-6	https://doi.org/10.1140/epjp/i2018-12119-6	DET
ma-44	423	14	https://doi.org/10.1140/epjp/i2018-12119-6	https://doi.org/10.1140/epjp/i2018-12119-6	PROPN
ma-44	423	15	https://doi.org/10.1186/s13662-019-2054-z	https://doi.org/10.1186/s13662-019-2054-z	PROPN
ma-44	423	16	eur	eur	PROPN
ma-44	423	17	.	.	PUNCT
ma-44	424	1	j.	j.	PROPN
ma-44	424	2	math	math	PROPN
ma-44	424	3	.	.	PUNCT
ma-44	425	1	anal	anal	ADJ
ma-44	425	2	.	.	PUNCT
ma-44	426	1	1	1	NUM
ma-44	426	2	(	(	PUNCT
ma-44	426	3	2021	2021	NUM
ma-44	426	4	)	)	PUNCT
ma-44	427	1	181	181	NUM
ma-44	428	1	[	[	X
ma-44	428	2	18	18	NUM
ma-44	428	3	]	]	PUNCT
ma-44	428	4	v.	v.	CCONJ
ma-44	428	5	lakshmikantham	lakshmikantham	PROPN
ma-44	428	6	,	,	PUNCT
ma-44	428	7	s.	s.	PROPN
ma-44	428	8	leela	leela	PROPN
ma-44	428	9	,	,	PUNCT
ma-44	428	10	and	and	CCONJ
ma-44	428	11	j.	j.	PROPN
ma-44	428	12	v.	v.	PROPN
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ma-44	428	16	of	of	ADP
ma-44	428	17	fractional	fractional	ADJ
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ma-44	428	19	systems	system	NOUN
ma-44	428	20	,	,	PUNCT
ma-44	428	21	cambridge	cambridge	NOUN
ma-44	428	22	scientific	scientific	ADJ
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ma-44	428	24	,	,	PUNCT
ma-44	428	25	cambridge	cambridge	PROPN
ma-44	428	26	,	,	PUNCT
ma-44	428	27	2009.[19	2009.[19	PROPN
ma-44	428	28	]	]	X
ma-44	428	29	y.	y.	PROPN
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ma-44	428	32	existence	existence	NOUN
ma-44	428	33	of	of	ADP
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ma-44	428	35	solutions	solution	NOUN
ma-44	428	36	for	for	ADP
ma-44	428	37	fractional	fractional	ADJ
ma-44	428	38	differential	differential	ADJ
ma-44	428	39	equation	equation	NOUN
ma-44	428	40	involving	involve	VERB
ma-44	428	41	integral	integral	ADJ
ma-44	428	42	boundary	boundary	ADJ
ma-44	428	43	conditions	condition	NOUN
ma-44	428	44	with	with	ADP
ma-44	428	45	p−	p−	NOUN
ma-44	428	46	laplacian	laplacian	ADJ
ma-44	428	47	operator	operator	NOUN
ma-44	428	48	.	.	PUNCT
ma-44	429	1	adv	adv	PROPN
ma-44	429	2	.	.	PROPN
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ma-44	429	4	.	.	PUNCT
ma-44	430	1	equ	equ	PROPN
ma-44	430	2	.	.	PROPN
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ma-44	430	4	(	(	PUNCT
ma-44	430	5	2017	2017	NUM
ma-44	430	6	)	)	PUNCT
ma-44	430	7	135	135	NUM
ma-44	430	8	.	.	PUNCT
ma-44	431	1	https://doi.org/10.1186/s13662-017-1172-8.[20	https://doi.org/10.1186/s13662-017-1172-8.[20	NOUN
ma-44	431	2	]	]	PUNCT
ma-44	431	3	k.	k.	PROPN
ma-44	431	4	s.	s.	PROPN
ma-44	431	5	miller	miller	PROPN
ma-44	431	6	and	and	CCONJ
ma-44	431	7	b.	b.	PROPN
ma-44	431	8	ross	ross	PROPN
ma-44	431	9	,	,	PUNCT
ma-44	431	10	an	an	DET
ma-44	431	11	introduction	introduction	NOUN
ma-44	431	12	to	to	ADP
ma-44	431	13	the	the	DET
ma-44	431	14	fractional	fractional	ADJ
ma-44	431	15	calculus	calculus	NOUN
ma-44	431	16	and	and	CCONJ
ma-44	431	17	differential	differential	ADJ
ma-44	431	18	equations	equation	NOUN
ma-44	431	19	,	,	PUNCT
ma-44	431	20	john	john	PROPN
ma-44	431	21	wiley	wiley	PROPN
ma-44	431	22	,	,	PUNCT
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ma-44	431	24	,	,	PUNCT
ma-44	431	25	1993.[21	1993.[21	NUM
ma-44	431	26	]	]	PUNCT
ma-44	431	27	c.	c.	PROPN
ma-44	431	28	nuchpong	nuchpong	PROPN
ma-44	431	29	,	,	PUNCT
ma-44	431	30	s.k	s.k	PROPN
ma-44	431	31	.	.	PROPN
ma-44	431	32	ntouyas	ntouyas	PROPN
ma-44	431	33	,	,	PUNCT
ma-44	431	34	and	and	CCONJ
ma-44	431	35	j.	j.	PROPN
ma-44	431	36	tariboon	tariboon	PROPN
ma-44	431	37	,	,	PUNCT
ma-44	431	38	.	.	PUNCT
ma-44	432	1	worked	work	VERB
ma-44	432	2	on	on	ADP
ma-44	432	3	boundary	boundary	ADJ
ma-44	432	4	value	value	NOUN
ma-44	432	5	problems	problem	NOUN
ma-44	432	6	of	of	ADP
ma-44	432	7	hilfer	hilfer	NOUN
ma-44	432	8	-	-	PUNCT
ma-44	432	9	type	type	NOUN
ma-44	432	10	fractional	fractional	ADJ
ma-44	432	11	integro	integro	ADJ
ma-44	432	12	-	-	PUNCT
ma-44	432	13	differential	differential	NOUN
ma-44	432	14	equations	equation	NOUN
ma-44	432	15	and	and	CCONJ
ma-44	432	16	inclusions	inclusion	NOUN
ma-44	432	17	with	with	ADP
ma-44	432	18	nonlocal	nonlocal	ADJ
ma-44	432	19	integro	integro	ADJ
ma-44	432	20	-	-	PUNCT
ma-44	432	21	multipoint	multipoint	NOUN
ma-44	432	22	boundary	boundary	ADJ
ma-44	432	23	conditions	condition	NOUN
ma-44	432	24	,	,	PUNCT
ma-44	432	25	open	open	ADJ
ma-44	432	26	math	math	NOUN
ma-44	432	27	.	.	PUNCT
ma-44	433	1	18	18	NUM
ma-44	433	2	(	(	PUNCT
ma-44	433	3	2020)1879	2020)1879	NUM
ma-44	433	4	-	-	SYM
ma-44	433	5	1894	1894	NUM
ma-44	433	6	.	.	PUNCT
ma-44	434	1	https://doi.org/10.1515/math-2020-0122[22	https://doi.org/10.1515/math-2020-0122[22	NOUN
ma-44	434	2	]	]	PUNCT
ma-44	434	3	i.	i.	NOUN
ma-44	434	4	podlubny	podlubny	PROPN
ma-44	434	5	,	,	PUNCT
ma-44	434	6	fractional	fractional	ADJ
ma-44	434	7	differential	differential	NOUN
ma-44	434	8	equations	equation	NOUN
ma-44	434	9	,	,	PUNCT
ma-44	434	10	academic	academic	ADJ
ma-44	434	11	press	press	NOUN
ma-44	434	12	,	,	PUNCT
ma-44	434	13	new	new	PROPN
ma-44	434	14	york	york	PROPN
ma-44	434	15	,	,	PUNCT
ma-44	434	16	1999.[23	1999.[23	NUM
ma-44	434	17	]	]	X
ma-44	434	18	s.	s.	PROPN
ma-44	434	19	g.	g.	PROPN
ma-44	434	20	samko	samko	PROPN
ma-44	434	21	,	,	PUNCT
ma-44	434	22	a.	a.	NOUN
ma-44	434	23	a.	a.	NOUN
ma-44	434	24	kilbas	kilbas	PROPN
ma-44	434	25	,	,	PUNCT
ma-44	434	26	and	and	CCONJ
ma-44	434	27	o.	o.	PROPN
ma-44	434	28	i.	i.	PROPN
ma-44	434	29	marichev	marichev	PROPN
ma-44	434	30	,	,	PUNCT
ma-44	434	31	fractional	fractional	ADJ
ma-44	434	32	integrals	integral	NOUN
ma-44	434	33	and	and	CCONJ
ma-44	434	34	derivatives	derivative	NOUN
ma-44	434	35	,	,	PUNCT
ma-44	434	36	gordon	gordon	PROPN
ma-44	434	37	and	and	CCONJ
ma-44	434	38	breach	breach	VERB
ma-44	434	39	science	science	NOUN
ma-44	434	40	,	,	PUNCT
ma-44	434	41	yverdon	yverdon	PROPN
ma-44	434	42	,	,	PUNCT
ma-44	434	43	1993[24	1993[24	NUM
ma-44	434	44	]	]	PUNCT
ma-44	434	45	a.	a.	NOUN
ma-44	434	46	seemab	seemab	PROPN
ma-44	434	47	,	,	PUNCT
ma-44	434	48	j.	j.	PROPN
ma-44	434	49	alzabut	alzabut	PROPN
ma-44	434	50	,	,	PUNCT
ma-44	434	51	m.	m.	PROPN
ma-44	434	52	rehman	rehman	PROPN
ma-44	434	53	,	,	PUNCT
ma-44	434	54	y.	y.	PROPN
ma-44	434	55	adjabi	adjabi	PROPN
ma-44	434	56	,	,	PUNCT
ma-44	434	57	m.s.abdo	m.s.abdo	NOUN
ma-44	434	58	,	,	PUNCT
ma-44	434	59	langevin	langevin	ADJ
ma-44	434	60	equation	equation	NOUN
ma-44	434	61	with	with	ADP
ma-44	434	62	nonlocal	nonlocal	ADJ
ma-44	434	63	boundary	boundary	NOUN
ma-44	434	64	conditionsinvolving	conditionsinvolve	VERB
ma-44	434	65	a	a	DET
ma-44	434	66	ϕ−caputo	ϕ−caputo	NOUN
ma-44	434	67	fractional	fractional	ADJ
ma-44	434	68	operator	operator	NOUN
ma-44	434	69	:	:	PUNCT
ma-44	434	70	arxiv:2006.00391v1	arxiv:2006.00391v1	ADJ
ma-44	434	71	[	[	X
ma-44	434	72	math.ap	math.ap	X
ma-44	434	73	]	]	X
ma-44	434	74	31	31	NUM
ma-44	434	75	may	may	PROPN
ma-44	434	76	2020.[25	2020.[25	NUM
ma-44	434	77	]	]	X
ma-44	434	78	c.	c.	PROPN
ma-44	434	79	vanterler	vanterler	PROPN
ma-44	434	80	da	da	PROPN
ma-44	434	81	,	,	PUNCT
ma-44	434	82	j.	j.	PROPN
ma-44	434	83	sousa	sousa	PROPN
ma-44	434	84	,	,	PUNCT
ma-44	434	85	;	;	PUNCT
ma-44	434	86	capelas	capelas	PROPN
ma-44	434	87	de	de	PROPN
ma-44	434	88	oliveira	oliveira	PROPN
ma-44	434	89	,	,	PUNCT
ma-44	434	90	e.	e.	PROPN
ma-44	434	91	on	on	ADP
ma-44	434	92	the	the	DET
ma-44	434	93	ϕ-hilfer	ϕ-hilfer	NOUN
ma-44	434	94	fractional	fractional	ADJ
ma-44	434	95	derivative	derivative	NOUN
ma-44	434	96	.	.	PUNCT
ma-44	435	1	commun	commun	PROPN
ma-44	435	2	.	.	PUNCT
ma-44	436	1	nonlinear	nonlinear	PROPN
ma-44	436	2	sci.numer	sci.numer	PROPN
ma-44	436	3	.	.	PUNCT
ma-44	437	1	simul	simul	PROPN
ma-44	437	2	.	.	PUNCT
ma-44	438	1	60	60	NUM
ma-44	438	2	(	(	PUNCT
ma-44	438	3	2018	2018	NUM
ma-44	438	4	)	)	PUNCT
ma-44	438	5	72	72	NUM
ma-44	438	6	-	-	SYM
ma-44	438	7	91.[26	91.[26	NUM
ma-44	438	8	]	]	X
ma-44	438	9	j.	j.	PROPN
ma-44	438	10	wang	wang	PROPN
ma-44	438	11	and	and	CCONJ
ma-44	438	12	y.	y.	PROPN
ma-44	438	13	zhang	zhang	PROPN
ma-44	438	14	,	,	PUNCT
ma-44	438	15	nonlocal	nonlocal	ADJ
ma-44	438	16	initial	initial	ADJ
ma-44	438	17	value	value	NOUN
ma-44	438	18	problems	problem	NOUN
ma-44	438	19	for	for	ADP
ma-44	438	20	differential	differential	ADJ
ma-44	438	21	equations	equation	NOUN
ma-44	438	22	with	with	ADP
ma-44	438	23	hilfer	hilfer	NOUN
ma-44	438	24	fractional	fractional	ADJ
ma-44	438	25	derivative	derivative	ADJ
ma-44	438	26	,	,	PUNCT
ma-44	438	27	appl	appl	PROPN
ma-44	438	28	.	.	PROPN
ma-44	438	29	math	math	NOUN
ma-44	438	30	.	.	PUNCT
ma-44	439	1	comput	comput	NOUN
ma-44	439	2	.	.	PUNCT
ma-44	440	1	266	266	NUM
ma-44	440	2	(	(	PUNCT
ma-44	440	3	2015	2015	NUM
ma-44	440	4	)	)	PUNCT
ma-44	440	5	,	,	PUNCT
ma-44	440	6	850	850	NUM
ma-44	440	7	-	-	SYM
ma-44	440	8	859	859	NUM
ma-44	440	9	.	.	PUNCT
ma-44	441	1	https://doi.org/10.1016/j.amc.2015.05.144.[27	https://doi.org/10.1016/j.amc.2015.05.144.[27	PROPN
ma-44	441	2	]	]	PUNCT
ma-44	441	3	y.	y.	PROPN
ma-44	441	4	wang	wang	PROPN
ma-44	441	5	,	,	PUNCT
ma-44	441	6	existence	existence	NOUN
ma-44	441	7	and	and	CCONJ
ma-44	441	8	nonexistence	nonexistence	NOUN
ma-44	441	9	of	of	ADP
ma-44	441	10	positive	positive	ADJ
ma-44	441	11	solutions	solution	NOUN
ma-44	441	12	for	for	ADP
ma-44	441	13	mixed	mixed	ADJ
ma-44	441	14	fractional	fractional	ADJ
ma-44	441	15	boundary	boundary	ADJ
ma-44	441	16	value	value	NOUN
ma-44	441	17	problem	problem	NOUN
ma-44	441	18	with	with	ADP
ma-44	441	19	parameterand	parameterand	NOUN
ma-44	441	20	p−laplacian	p−laplacian	NOUN
ma-44	441	21	operator	operator	NOUN
ma-44	441	22	.	.	PUNCT
ma-44	442	1	j.	j.	PROPN
ma-44	442	2	funct	funct	PROPN
ma-44	442	3	.	.	PUNCT
ma-44	443	1	spaces	space	VERB
ma-44	443	2	2018	2018	NUM
ma-44	443	3	(	(	PUNCT
ma-44	443	4	2018	2018	NUM
ma-44	443	5	)	)	PUNCT
ma-44	443	6	article	article	NOUN
ma-44	443	7	i	i	PROPN
ma-44	443	8	d	d	PROPN
ma-44	443	9	1462825	1462825	NUM
ma-44	443	10	.	.	PUNCT
ma-44	444	1	https://doi.org/10.1155/2018/	https://doi.org/10.1155/2018/	PROPN
ma-44	444	2	1462825.[28	1462825.[28	NUM
ma-44	444	3	]	]	X
ma-44	444	4	a.	a.	NOUN
ma-44	444	5	wongcharoen	wongcharoen	PROPN
ma-44	444	6	,	,	PUNCT
ma-44	444	7	b.	b.	PROPN
ma-44	444	8	ahmad	ahmad	PROPN
ma-44	444	9	,	,	PUNCT
ma-44	444	10	s.	s.	PROPN
ma-44	444	11	k.	k.	PROPN
ma-44	444	12	ntouyas	ntouyas	PROPN
ma-44	444	13	,	,	PUNCT
ma-44	444	14	and	and	CCONJ
ma-44	444	15	j.	j.	PROPN
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ma-44	444	17	,	,	PUNCT
ma-44	444	18	three	three	NUM
ma-44	444	19	-	-	PUNCT
ma-44	444	20	point	point	NOUN
ma-44	444	21	boundary	boundary	ADJ
ma-44	444	22	value	value	NOUN
ma-44	444	23	problems	problem	NOUN
ma-44	444	24	for	for	ADP
ma-44	444	25	langevinequation	langevinequation	NOUN
ma-44	444	26	with	with	ADP
ma-44	444	27	hilfer	hilfer	NOUN
ma-44	444	28	fractional	fractional	ADJ
ma-44	444	29	derivative	derivative	NOUN
ma-44	444	30	,	,	PUNCT
ma-44	444	31	adv	adv	PROPN
ma-44	444	32	.	.	PUNCT
ma-44	444	33	math	math	PROPN
ma-44	444	34	.	.	PUNCT
ma-44	445	1	phys	phy	NOUN
ma-44	445	2	.	.	PUNCT
ma-44	446	1	2020	2020	NUM
ma-44	446	2	(	(	PUNCT
ma-44	446	3	2020	2020	NUM
ma-44	446	4	)	)	PUNCT
ma-44	446	5	,	,	PUNCT
ma-44	446	6	9606428	9606428	NUM
ma-44	446	7	.	.	PUNCT
ma-44	447	1	https://doi.org/10.1155/	https://doi.org/10.1155/	PROPN
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ma-44	447	3	]	]	X
ma-44	447	4	a.	a.	NOUN
ma-44	447	5	wongcharoen	wongcharoen	PROPN
ma-44	447	6	,	,	PUNCT
ma-44	447	7	s.	s.	PROPN
ma-44	447	8	k.	k.	PROPN
ma-44	447	9	ntouyas	ntouyas	PROPN
ma-44	447	10	,	,	PUNCT
ma-44	447	11	and	and	CCONJ
ma-44	447	12	j.	j.	PROPN
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ma-44	447	14	,	,	PUNCT
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ma-44	447	16	boundary	boundary	ADJ
ma-44	447	17	value	value	NOUN
ma-44	447	18	problems	problem	NOUN
ma-44	447	19	for	for	ADP
ma-44	447	20	hilfer	hilfer	NOUN
ma-44	447	21	type	type	NOUN
ma-44	447	22	pantographfractional	pantographfractional	ADJ
ma-44	447	23	differential	differential	ADJ
ma-44	447	24	equations	equation	NOUN
ma-44	447	25	and	and	CCONJ
ma-44	447	26	inclusions	inclusion	NOUN
ma-44	447	27	,	,	PUNCT
ma-44	447	28	adv	adv	PROPN
ma-44	447	29	.	.	PUNCT
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ma-44	447	31	.	.	PUNCT
ma-44	448	1	equ	equ	PROPN
ma-44	448	2	.	.	PROPN
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ma-44	448	4	(	(	PUNCT
ma-44	448	5	2020	2020	NUM
ma-44	448	6	)	)	PUNCT
ma-44	448	7	,	,	PUNCT
ma-44	448	8	279	279	NUM
ma-44	448	9	.	.	PUNCT
ma-44	449	1	https://doi.org/10.1186/	https://doi.org/10.1186/	PROPN
ma-44	449	2	s13662	s13662	PROPN
ma-44	449	3	-	-	PUNCT
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ma-44	449	5	-	-	PUNCT
ma-44	449	6	02747	02747	NUM
ma-44	449	7	-	-	SYM
ma-44	449	8	1.[30	1.[30	NUM
ma-44	449	9	]	]	PUNCT
ma-44	449	10	a.	a.	NOUN
ma-44	449	11	wongcharoen	wongcharoen	PROPN
ma-44	449	12	,	,	PUNCT
ma-44	449	13	s.	s.	PROPN
ma-44	449	14	k.	k.	PROPN
ma-44	449	15	ntouyas	ntouyas	PROPN
ma-44	449	16	,	,	PUNCT
ma-44	449	17	and	and	CCONJ
ma-44	449	18	j.	j.	PROPN
ma-44	449	19	tariboon	tariboon	PROPN
ma-44	449	20	,	,	PUNCT
ma-44	449	21	boundary	boundary	ADJ
ma-44	449	22	value	value	NOUN
ma-44	449	23	problems	problem	NOUN
ma-44	449	24	for	for	ADP
ma-44	449	25	hilfer	hilfer	NOUN
ma-44	449	26	fractional	fractional	ADJ
ma-44	449	27	differential	differential	NOUN
ma-44	449	28	in	in	ADP
ma-44	449	29	-	-	PUNCT
ma-44	449	30	clusions	clusion	NOUN
ma-44	449	31	with	with	ADP
ma-44	449	32	nonlocal	nonlocal	ADJ
ma-44	449	33	integral	integral	ADJ
ma-44	449	34	boundary	boundary	ADJ
ma-44	449	35	conditions	condition	NOUN
ma-44	449	36	,	,	PUNCT
ma-44	449	37	mathematics	mathematic	NOUN
ma-44	449	38	8	8	NUM
ma-44	449	39	(	(	PUNCT
ma-44	449	40	2020	2020	NUM
ma-44	449	41	)	)	PUNCT
ma-44	449	42	,	,	PUNCT
ma-44	449	43	1905	1905	NUM
ma-44	449	44	.	.	PUNCT
ma-44	450	1	https://doi.org/10.3390/	https://doi.org/10.3390/	PROPN
ma-44	450	2	math8111905.[31	math8111905.[31	X
ma-44	450	3	]	]	X
ma-44	450	4	y.	y.	PROPN
ma-44	450	5	zhou	zhou	PROPN
ma-44	450	6	,	,	PUNCT
ma-44	450	7	basic	basic	ADJ
ma-44	450	8	theory	theory	NOUN
ma-44	450	9	of	of	ADP
ma-44	450	10	fractional	fractional	ADJ
ma-44	450	11	differential	differential	ADJ
ma-44	450	12	equations	equation	NOUN
ma-44	450	13	,	,	PUNCT
ma-44	450	14	world	world	NOUN
ma-44	450	15	scientific	scientific	PROPN
ma-44	450	16	,	,	PUNCT
ma-44	450	17	singapore	singapore	PROPN
ma-44	450	18	,	,	PUNCT
ma-44	450	19	2014	2014	NUM
ma-44	450	20	.	.	PUNCT
ma-44	451	1	https://doi.org/10.1186/s13662-017-1172-8	https://doi.org/10.1186/s13662-017-1172-8	NUM
ma-44	451	2	https://doi.org/10.1515/math-2020-0122	https://doi.org/10.1515/math-2020-0122	X
ma-44	452	1	https://doi.org/10.1016/j.amc.2015.05.144	https://doi.org/10.1016/j.amc.2015.05.144	ADJ
ma-44	452	2	https://doi.org/10.1155/2018/1462825	https://doi.org/10.1155/2018/1462825	PROPN
ma-44	452	3	https://doi.org/10.1155/2018/1462825	https://doi.org/10.1155/2018/1462825	PROPN
ma-44	452	4	https://doi.org/10.1155/2020/9606428	https://doi.org/10.1155/2020/9606428	PROPN
ma-44	452	5	https://doi.org/10.1155/2020/9606428	https://doi.org/10.1155/2020/9606428	PROPN
ma-44	452	6	https://doi.org/10.1186/s13662-020-02747-1	https://doi.org/10.1186/s13662-020-02747-1	NUM
ma-44	452	7	https://doi.org/10.1186/s13662-020-02747-1	https://doi.org/10.1186/s13662-020-02747-1	NUM
ma-44	452	8	https://doi.org/10.3390/math8111905	https://doi.org/10.3390/math8111905	VERB
ma-44	452	9	https://doi.org/10.3390/math8111905	https://doi.org/10.3390/math8111905	VERB
ma-44	452	10	1	1	NUM
ma-44	452	11	.	.	PUNCT
ma-44	453	1	introduction	introduction	NOUN
ma-44	453	2	2	2	NUM
ma-44	453	3	.	.	PUNCT
ma-44	453	4	phi	phi	ADJ
ma-44	453	5	-	-	PUNCT
ma-44	453	6	hilfer	hilfer	NOUN
ma-44	453	7	derivatives	derivative	NOUN
ma-44	453	8	calculus	calculus	NOUN
ma-44	453	9	2.1	2.1	NUM
ma-44	453	10	.	.	PUNCT
ma-44	454	1	auxiliary	auxiliary	PROPN
ma-44	454	2	lemma	lemma	PROPN
ma-44	454	3	.	.	PROPN
ma-44	455	1	3	3	NUM
ma-44	455	2	.	.	X
ma-44	455	3	main	main	ADJ
ma-44	455	4	results	result	NOUN
ma-44	455	5	3.1	3.1	NUM
ma-44	455	6	.	.	PUNCT
ma-44	455	7	criteria	criterion	NOUN
ma-44	455	8	for	for	ADP
ma-44	455	9	uniqueness	uniqueness	NOUN
ma-44	455	10	solution	solution	NOUN
ma-44	455	11	.	.	PUNCT
ma-44	456	1	3.2	3.2	NUM
ma-44	456	2	.	.	PUNCT
ma-44	456	3	criteria	criterion	NOUN
ma-44	456	4	for	for	ADP
ma-44	456	5	existence	existence	NOUN
ma-44	456	6	of	of	ADP
ma-44	456	7	a	a	DET
ma-44	456	8	solution	solution	NOUN
ma-44	456	9	.	.	PUNCT
ma-44	457	1	3.3	3.3	NUM
ma-44	457	2	.	.	PUNCT
ma-44	458	1	ulam	ulam	PROPN
ma-44	458	2	type	type	NOUN
ma-44	458	3	stability	stability	NOUN
ma-44	458	4	.	.	PUNCT
ma-44	459	1	3.4	3.4	NUM
ma-44	459	2	.	.	PUNCT
ma-44	459	3	illustrative	illustrative	ADJ
ma-44	459	4	exemple	exemple	NOUN
ma-44	459	5	.	.	PUNCT
ma-44	460	1	references	reference	NOUN