id	sid	tid	token	lemma	pos
ma-9	1	1	2021	2021	NUM
ma-9	1	2	ada	ada	PROPN
ma-9	1	3	academica	academica	PROPN
ma-9	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-9	1	5	.	.	PUNCT
ma-9	2	1	j.	j.	PROPN
ma-9	2	2	math	math	PROPN
ma-9	2	3	.	.	PUNCT
ma-9	3	1	anal	anal	ADJ
ma-9	3	2	.	.	PUNCT
ma-9	4	1	1	1	NUM
ma-9	4	2	(	(	PUNCT
ma-9	4	3	2021	2021	NUM
ma-9	4	4	)	)	PUNCT
ma-9	4	5	1	1	NUM
ma-9	4	6	-	-	NUM
ma-9	4	7	18doi	18doi	NUM
ma-9	4	8	:	:	PUNCT
ma-9	4	9	10.28924	10.28924	NUM
ma-9	4	10	/	/	SYM
ma-9	4	11	ada	ada	PROPN
ma-9	4	12	/	/	SYM
ma-9	4	13	ma.1.1	ma.1.1	PROPN
ma-9	4	14	existence	existence	NOUN
ma-9	4	15	and	and	CCONJ
ma-9	4	16	stability	stability	NOUN
ma-9	4	17	results	result	NOUN
ma-9	4	18	for	for	ADP
ma-9	4	19	second	second	ADJ
ma-9	4	20	-	-	PUNCT
ma-9	4	21	order	order	NOUN
ma-9	4	22	neutral	neutral	ADJ
ma-9	4	23	stochastic	stochastic	ADJ
ma-9	4	24	differential	differential	ADJ
ma-9	4	25	equations	equation	NOUN
ma-9	4	26	with	with	ADP
ma-9	4	27	random	random	ADJ
ma-9	4	28	impulses	impulse	NOUN
ma-9	4	29	and	and	CCONJ
ma-9	4	30	poisson	poisson	NOUN
ma-9	4	31	jumps	jump	VERB
ma-9	4	32	k.	k.	PROPN
ma-9	4	33	ravikumar1	ravikumar1	PROPN
ma-9	4	34	,	,	PUNCT
ma-9	4	35	k.	k.	PROPN
ma-9	4	36	ramkumar1	ramkumar1	PROPN
ma-9	4	37	,	,	PUNCT
ma-9	4	38	dimplekumar	dimplekumar	PROPN
ma-9	4	39	chalishajar2,∗	chalishajar2,∗	PROPN
ma-9	4	40	1department	1department	NUM
ma-9	4	41	of	of	ADP
ma-9	4	42	mathematics	mathematic	NOUN
ma-9	4	43	,	,	PUNCT
ma-9	4	44	psg	psg	PROPN
ma-9	4	45	college	college	PROPN
ma-9	4	46	of	of	ADP
ma-9	4	47	arts	art	NOUN
ma-9	4	48	and	and	CCONJ
ma-9	4	49	science	science	NOUN
ma-9	4	50	,	,	PUNCT
ma-9	4	51	coimbatore	coimbatore	PROPN
ma-9	4	52	,	,	PUNCT
ma-9	4	53	641	641	NUM
ma-9	4	54	046	046	NUM
ma-9	4	55	,	,	PUNCT
ma-9	4	56	india	india	PROPN
ma-9	4	57	;	;	PUNCT
ma-9	4	58	ravikumarkpsg@gmail.com	ravikumarkpsg@gmail.com	X
ma-9	4	59	,	,	PUNCT
ma-9	4	60	ramkumarkpsg@gmail.com2department	ramkumarkpsg@gmail.com2department	ADJ
ma-9	4	61	of	of	ADP
ma-9	4	62	applied	applied	ADJ
ma-9	4	63	mathematics	mathematic	NOUN
ma-9	4	64	,	,	PUNCT
ma-9	4	65	mallory	mallory	PROPN
ma-9	4	66	hall	hall	PROPN
ma-9	4	67	,	,	PUNCT
ma-9	4	68	virginia	virginia	PROPN
ma-9	4	69	military	military	PROPN
ma-9	4	70	institute	institute	PROPN
ma-9	4	71	,	,	PUNCT
ma-9	4	72	lexington	lexington	PROPN
ma-9	4	73	,	,	PUNCT
ma-9	4	74	va	va	PROPN
ma-9	4	75	24450	24450	NUM
ma-9	4	76	,	,	PUNCT
ma-9	4	77	usa	usa	PROPN
ma-9	4	78	∗correspondence	∗correspondence	NOUN
ma-9	4	79	:	:	PUNCT
ma-9	4	80	chalishajardn@vmi.edu	chalishajardn@vmi.edu	VERB
ma-9	4	81	abstract	abstract	NOUN
ma-9	4	82	.	.	PUNCT
ma-9	5	1	the	the	DET
ma-9	5	2	objective	objective	NOUN
ma-9	5	3	of	of	ADP
ma-9	5	4	this	this	DET
ma-9	5	5	paper	paper	NOUN
ma-9	5	6	is	be	AUX
ma-9	5	7	to	to	PART
ma-9	5	8	investigate	investigate	VERB
ma-9	5	9	the	the	DET
ma-9	5	10	existence	existence	NOUN
ma-9	5	11	and	and	CCONJ
ma-9	5	12	stability	stability	NOUN
ma-9	5	13	results	result	NOUN
ma-9	5	14	of	of	ADP
ma-9	5	15	second	second	ADJ
ma-9	5	16	-	-	PUNCT
ma-9	5	17	order	order	NOUN
ma-9	5	18	neutral	neutral	ADJ
ma-9	5	19	stochastic	stochastic	ADJ
ma-9	5	20	functional	functional	ADJ
ma-9	5	21	differential	differential	ADJ
ma-9	5	22	equations	equation	NOUN
ma-9	5	23	(	(	PUNCT
ma-9	5	24	nsfdes	nsfde	NOUN
ma-9	5	25	)	)	PUNCT
ma-9	5	26	in	in	ADP
ma-9	5	27	hilbert	hilbert	PROPN
ma-9	5	28	space	space	NOUN
ma-9	5	29	.	.	PUNCT
ma-9	6	1	initially	initially	ADV
ma-9	6	2	,	,	PUNCT
ma-9	6	3	weestablish	weestablish	VERB
ma-9	6	4	the	the	DET
ma-9	6	5	existence	existence	NOUN
ma-9	6	6	results	result	NOUN
ma-9	6	7	of	of	ADP
ma-9	6	8	mild	mild	ADJ
ma-9	6	9	solutions	solution	NOUN
ma-9	6	10	of	of	ADP
ma-9	6	11	the	the	DET
ma-9	6	12	aforementioned	aforementioned	ADJ
ma-9	6	13	system	system	NOUN
ma-9	6	14	using	use	VERB
ma-9	6	15	the	the	DET
ma-9	6	16	banachcontraction	banachcontraction	NOUN
ma-9	6	17	principle	principle	NOUN
ma-9	6	18	.	.	PUNCT
ma-9	7	1	the	the	DET
ma-9	7	2	results	result	NOUN
ma-9	7	3	are	be	AUX
ma-9	7	4	formulated	formulate	VERB
ma-9	7	5	using	use	VERB
ma-9	7	6	stochastic	stochastic	ADJ
ma-9	7	7	analysis	analysis	NOUN
ma-9	7	8	techniques	technique	NOUN
ma-9	7	9	.	.	PUNCT
ma-9	8	1	in	in	ADP
ma-9	8	2	the	the	DET
ma-9	8	3	laterpart	laterpart	NOUN
ma-9	8	4	,	,	PUNCT
ma-9	8	5	we	we	PRON
ma-9	8	6	investigate	investigate	VERB
ma-9	8	7	the	the	DET
ma-9	8	8	stability	stability	NOUN
ma-9	8	9	results	result	VERB
ma-9	8	10	through	through	ADP
ma-9	8	11	the	the	DET
ma-9	8	12	continuous	continuous	ADJ
ma-9	8	13	dependence	dependence	NOUN
ma-9	8	14	of	of	ADP
ma-9	8	15	solutions	solution	NOUN
ma-9	8	16	on	on	ADP
ma-9	8	17	initialconditions	initialcondition	NOUN
ma-9	8	18	.	.	PUNCT
ma-9	9	1	1	1	X
ma-9	9	2	.	.	X
ma-9	9	3	introduction	introduction	NOUN
ma-9	9	4	stochastic	stochastic	ADJ
ma-9	9	5	differential	differential	ADJ
ma-9	9	6	equations	equation	NOUN
ma-9	9	7	(	(	PUNCT
ma-9	9	8	sdes	sde	NOUN
ma-9	9	9	)	)	PUNCT
ma-9	9	10	captures	capture	VERB
ma-9	9	11	disturbances	disturbance	NOUN
ma-9	9	12	from	from	ADP
ma-9	9	13	random	random	ADJ
ma-9	9	14	factors	factor	NOUN
ma-9	9	15	.	.	PUNCT
ma-9	10	1	mathe	mathe	NOUN
ma-9	10	2	-	-	PUNCT
ma-9	10	3	matical	matical	ADJ
ma-9	10	4	models	model	NOUN
ma-9	10	5	obtained	obtain	VERB
ma-9	10	6	by	by	ADP
ma-9	10	7	integrating	integrate	VERB
ma-9	10	8	stochastic	stochastic	ADJ
ma-9	10	9	process	process	NOUN
ma-9	10	10	provide	provide	VERB
ma-9	10	11	a	a	DET
ma-9	10	12	better	well	ADJ
ma-9	10	13	understanding	understanding	NOUN
ma-9	10	14	of	of	ADP
ma-9	10	15	thereal	thereal	NOUN
ma-9	10	16	-	-	PUNCT
ma-9	10	17	world	world	NOUN
ma-9	10	18	system	system	NOUN
ma-9	10	19	[	[	X
ma-9	10	20	12	12	NUM
ma-9	10	21	]	]	PUNCT
ma-9	10	22	.	.	PUNCT
ma-9	11	1	for	for	ADP
ma-9	11	2	elementary	elementary	ADJ
ma-9	11	3	study	study	NOUN
ma-9	11	4	of	of	ADP
ma-9	11	5	stochastic	stochastic	ADJ
ma-9	11	6	differential	differential	ADJ
ma-9	11	7	equations	equation	NOUN
ma-9	11	8	,	,	PUNCT
ma-9	11	9	the	the	DET
ma-9	11	10	reader	reader	NOUN
ma-9	11	11	mayrefer	mayrefer	VERB
ma-9	11	12	to	to	ADP
ma-9	11	13	[	[	X
ma-9	11	14	7	7	NUM
ma-9	11	15	,	,	PUNCT
ma-9	11	16	12,14,24].impulsive	12,14,24].impulsive	NUM
ma-9	11	17	differential	differential	NOUN
ma-9	11	18	equations	equation	NOUN
ma-9	11	19	also	also	ADV
ma-9	11	20	attracted	attract	VERB
ma-9	11	21	the	the	DET
ma-9	11	22	attention	attention	NOUN
ma-9	11	23	of	of	ADP
ma-9	11	24	researchers	researcher	NOUN
ma-9	11	25	(	(	PUNCT
ma-9	11	26	see	see	VERB
ma-9	11	27	[	[	X
ma-9	11	28	4	4	NUM
ma-9	11	29	,	,	PUNCT
ma-9	11	30	11	11	NUM
ma-9	11	31	,	,	PUNCT
ma-9	11	32	13	13	NUM
ma-9	11	33	,	,	PUNCT
ma-9	11	34	21	21	NUM
ma-9	11	35	,	,	PUNCT
ma-9	11	36	22]etc	22]etc	NUM
ma-9	11	37	.	.	PUNCT
ma-9	11	38	)	)	PUNCT
ma-9	11	39	.	.	PUNCT
ma-9	12	1	impulse	impulse	ADJ
ma-9	12	2	in	in	ADP
ma-9	12	3	general	general	ADJ
ma-9	12	4	occurs	occur	VERB
ma-9	12	5	as	as	ADP
ma-9	12	6	deterministic	deterministic	ADJ
ma-9	12	7	or	or	CCONJ
ma-9	12	8	random	random	ADJ
ma-9	12	9	models	model	NOUN
ma-9	12	10	.	.	PUNCT
ma-9	13	1	nevertheless	nevertheless	ADV
ma-9	13	2	by	by	ADP
ma-9	13	3	naturalphenomena	naturalphenomena	PROPN
ma-9	13	4	,	,	PUNCT
ma-9	13	5	the	the	DET
ma-9	13	6	impulses	impulse	NOUN
ma-9	13	7	often	often	ADV
ma-9	13	8	occur	occur	VERB
ma-9	13	9	at	at	ADP
ma-9	13	10	random	random	ADJ
ma-9	13	11	time	time	NOUN
ma-9	13	12	points	point	NOUN
ma-9	13	13	.	.	PUNCT
ma-9	14	1	many	many	ADJ
ma-9	14	2	researches	research	NOUN
ma-9	14	3	have	have	AUX
ma-9	14	4	been	be	AUX
ma-9	14	5	undergonesolving	undergonesolve	VERB
ma-9	14	6	various	various	ADJ
ma-9	14	7	differential	differential	ADJ
ma-9	14	8	equations	equation	NOUN
ma-9	14	9	with	with	ADP
ma-9	14	10	fixed	fix	VERB
ma-9	14	11	time	time	NOUN
ma-9	14	12	impulses	impulse	NOUN
ma-9	14	13	[	[	X
ma-9	14	14	1	1	NUM
ma-9	14	15	,	,	PUNCT
ma-9	14	16	9	9	NUM
ma-9	14	17	,	,	PUNCT
ma-9	14	18	16	16	NUM
ma-9	14	19	,	,	PUNCT
ma-9	14	20	23	23	NUM
ma-9	14	21	]	]	PUNCT
ma-9	14	22	.	.	PUNCT
ma-9	15	1	random	random	ADJ
ma-9	15	2	impulsivedifferential	impulsivedifferential	ADJ
ma-9	15	3	equations	equation	NOUN
ma-9	15	4	involving	involve	VERB
ma-9	15	5	fractional	fractional	ADJ
ma-9	15	6	derivative	derivative	NOUN
ma-9	15	7	are	be	AUX
ma-9	15	8	also	also	ADV
ma-9	15	9	studied	study	VERB
ma-9	15	10	see	see	VERB
ma-9	16	1	[	[	PUNCT
ma-9	16	2	20,25].it	20,25].it	NOUN
ma-9	16	3	is	be	AUX
ma-9	16	4	known	know	VERB
ma-9	16	5	that	that	SCONJ
ma-9	16	6	impulsive	impulsive	ADJ
ma-9	16	7	stochastic	stochastic	ADJ
ma-9	16	8	differential	differential	NOUN
ma-9	16	9	equations	equation	NOUN
ma-9	16	10	play	play	VERB
ma-9	16	11	a	a	DET
ma-9	16	12	vital	vital	ADJ
ma-9	16	13	role	role	NOUN
ma-9	16	14	in	in	ADP
ma-9	16	15	modelling	model	VERB
ma-9	16	16	practicalprocesses	practicalprocesse	NOUN
ma-9	16	17	.	.	PUNCT
ma-9	17	1	not	not	PART
ma-9	17	2	only	only	ADV
ma-9	17	3	from	from	ADP
ma-9	17	4	guassian	guassian	PROPN
ma-9	17	5	white	white	PROPN
ma-9	17	6	noise	noise	NOUN
ma-9	17	7	there	there	PRON
ma-9	17	8	are	be	VERB
ma-9	17	9	certain	certain	ADJ
ma-9	17	10	other	other	ADJ
ma-9	17	11	factors	factor	NOUN
ma-9	17	12	that	that	PRON
ma-9	17	13	results	result	VERB
ma-9	17	14	in	in	ADP
ma-9	17	15	therise	therise	NOUN
ma-9	17	16	of	of	ADP
ma-9	17	17	random	random	ADJ
ma-9	17	18	effects	effect	NOUN
ma-9	17	19	.	.	PUNCT
ma-9	18	1	random	random	ADJ
ma-9	18	2	impulsive	impulsive	ADJ
ma-9	18	3	stochastic	stochastic	ADJ
ma-9	18	4	differential	differential	ADJ
ma-9	18	5	equations	equation	NOUN
ma-9	18	6	(	(	PUNCT
ma-9	18	7	isdes	isde	NOUN
ma-9	18	8	)	)	PUNCT
ma-9	18	9	are	be	AUX
ma-9	18	10	widely	widely	ADV
ma-9	18	11	used	use	VERB
ma-9	18	12	received	receive	VERB
ma-9	18	13	:	:	PUNCT
ma-9	18	14	20	20	NUM
ma-9	18	15	aug	aug	PROPN
ma-9	18	16	2021	2021	NUM
ma-9	18	17	.	.	PUNCT
ma-9	19	1	key	key	ADJ
ma-9	19	2	words	word	NOUN
ma-9	19	3	and	and	CCONJ
ma-9	19	4	phrases	phrase	NOUN
ma-9	19	5	.	.	PUNCT
ma-9	20	1	existence	existence	NOUN
ma-9	20	2	;	;	PUNCT
ma-9	20	3	stability	stability	NOUN
ma-9	20	4	;	;	PUNCT
ma-9	20	5	banach	banach	NOUN
ma-9	20	6	contraction	contraction	NOUN
ma-9	20	7	principle	principle	NOUN
ma-9	20	8	;	;	PUNCT
ma-9	20	9	second	second	ADJ
ma-9	20	10	-	-	PUNCT
ma-9	20	11	order	order	NOUN
ma-9	20	12	neutral	neutral	ADJ
ma-9	20	13	stochastic	stochastic	ADJ
ma-9	20	14	functionaldifferential	functionaldifferential	ADJ
ma-9	20	15	equations	equation	NOUN
ma-9	20	16	;	;	PUNCT
ma-9	20	17	random	random	ADJ
ma-9	20	18	impulse	impulse	ADJ
ma-9	20	19	;	;	PUNCT
ma-9	20	20	stochastic	stochastic	ADJ
ma-9	20	21	differential	differential	NOUN
ma-9	20	22	system.1	system.1	PROPN
ma-9	20	23	https://adac.ee	https://adac.ee	PROPN
ma-9	20	24	https://doi.org/10.28924/ada/ma.1.1	https://doi.org/10.28924/ada/ma.1.1	PROPN
ma-9	20	25	https://orcid.org/0000-0002-6146-5544	https://orcid.org/0000-0002-6146-5544	PROPN
ma-9	20	26	eur	eur	PROPN
ma-9	20	27	.	.	PUNCT
ma-9	21	1	j.	j.	PROPN
ma-9	21	2	math	math	PROPN
ma-9	21	3	.	.	PUNCT
ma-9	22	1	anal	anal	ADJ
ma-9	22	2	.	.	PUNCT
ma-9	23	1	1	1	NUM
ma-9	23	2	(	(	PUNCT
ma-9	23	3	2021	2021	NUM
ma-9	23	4	)	)	PUNCT
ma-9	23	5	2	2	NUM
ma-9	23	6	in	in	ADP
ma-9	23	7	the	the	DET
ma-9	23	8	fields	field	NOUN
ma-9	23	9	of	of	ADP
ma-9	23	10	medicine	medicine	NOUN
ma-9	23	11	,	,	PUNCT
ma-9	23	12	biology	biology	NOUN
ma-9	23	13	,	,	PUNCT
ma-9	23	14	economy	economy	NOUN
ma-9	23	15	,	,	PUNCT
ma-9	23	16	finance	finance	NOUN
ma-9	23	17	and	and	CCONJ
ma-9	23	18	so	so	ADV
ma-9	23	19	on	on	ADV
ma-9	23	20	.	.	PUNCT
ma-9	24	1	for	for	ADP
ma-9	24	2	example	example	NOUN
ma-9	24	3	,	,	PUNCT
ma-9	24	4	the	the	DET
ma-9	24	5	classical	classical	ADJ
ma-9	24	6	stockprice	stockprice	ADJ
ma-9	24	7	model	model	NOUN
ma-9	24	8	[	[	X
ma-9	24	9	28	28	NUM
ma-9	24	10	]	]	PUNCT
ma-9	24	11	.	.	PUNCT
ma-9	25	1	d[s(t	d[s(t	PROPN
ma-9	25	2	)	)	PUNCT
ma-9	25	3	]	]	PUNCT
ma-9	26	1	=	=	PUNCT
ma-9	26	2	fs(t)dt	fs(t)dt	PROPN
ma-9	26	3	+	+	CCONJ
ma-9	26	4	σs(t)dw(t	σs(t)dw(t	PROPN
ma-9	26	5	)	)	PUNCT
ma-9	26	6	,	,	PUNCT
ma-9	26	7	t	t	PROPN
ma-9	26	8	≥	≥	PROPN
ma-9	26	9	0	0	NUM
ma-9	26	10	,	,	PUNCT
ma-9	26	11	t	t	PROPN
ma-9	26	12	6=	6=	NUM
ma-9	26	13	τk	τk	ADP
ma-9	26	14	,	,	PUNCT
ma-9	26	15	s(τk	s(τk	X
ma-9	26	16	)	)	PUNCT
ma-9	26	17	=	=	SYM
ma-9	26	18	aks(τ−k	aks(τ−k	PROPN
ma-9	26	19	)	)	PUNCT
ma-9	26	20	,	,	PUNCT
ma-9	26	21	k	k	NOUN
ma-9	26	22	=	=	SYM
ma-9	26	23	1	1	NUM
ma-9	26	24	,	,	PUNCT
ma-9	26	25	2	2	NUM
ma-9	26	26	,	,	PUNCT
ma-9	26	27	...	...	PUNCT
ma-9	26	28	,	,	PUNCT
ma-9	26	29	s(0	s(0	PROPN
ma-9	26	30	)	)	PUNCT
ma-9	26	31	=	=	SYM
ma-9	26	32	s0	s0	PROPN
ma-9	26	33	,	,	PUNCT
ma-9	26	34	is	be	AUX
ma-9	26	35	described	describe	VERB
ma-9	26	36	using	use	VERB
ma-9	26	37	an	an	DET
ma-9	26	38	isdes	isde	NOUN
ma-9	26	39	.	.	PUNCT
ma-9	27	1	here	here	ADV
ma-9	27	2	wt	wt	PROPN
ma-9	27	3	is	be	AUX
ma-9	27	4	a	a	DET
ma-9	27	5	brownian	brownian	ADJ
ma-9	27	6	motion	motion	NOUN
ma-9	27	7	or	or	CCONJ
ma-9	27	8	wiener	wiener	NOUN
ma-9	27	9	process	process	NOUN
ma-9	27	10	,	,	PUNCT
ma-9	27	11	s(t	s(t	PROPN
ma-9	27	12	)	)	PUNCT
ma-9	27	13	representsthe	representsthe	ADJ
ma-9	27	14	price	price	NOUN
ma-9	27	15	of	of	ADP
ma-9	27	16	the	the	DET
ma-9	27	17	stock	stock	NOUN
ma-9	27	18	at	at	ADP
ma-9	27	19	time	time	NOUN
ma-9	27	20	t	t	PROPN
ma-9	27	21	,	,	PUNCT
ma-9	27	22	and	and	CCONJ
ma-9	27	23	{	{	PUNCT
ma-9	27	24	τk	τk	ADP
ma-9	27	25	}	}	PUNCT
ma-9	27	26	represents	represent	VERB
ma-9	27	27	the	the	DET
ma-9	27	28	release	release	NOUN
ma-9	27	29	time	time	NOUN
ma-9	27	30	of	of	ADP
ma-9	27	31	the	the	DET
ma-9	27	32	important	important	ADJ
ma-9	27	33	informationrelating	informationrelating	NOUN
ma-9	27	34	to	to	ADP
ma-9	27	35	the	the	DET
ma-9	27	36	stock	stock	NOUN
ma-9	27	37	.	.	PUNCT
ma-9	28	1	s(τ−k	s(τ−k	NOUN
ma-9	28	2	)	)	PUNCT
ma-9	29	1	=	=	SYM
ma-9	29	2	limt→τk−0	limt→τk−0	PROPN
ma-9	29	3	s(t	s(t	PROPN
ma-9	29	4	)	)	PUNCT
ma-9	29	5	and	and	CCONJ
ma-9	29	6	s0	s0	PROPN
ma-9	29	7	∈	∈	PROPN
ma-9	29	8	r.	r.	PROPN
ma-9	29	9	in	in	ADP
ma-9	29	10	reality	reality	NOUN
ma-9	29	11	,	,	PUNCT
ma-9	29	12	{	{	PUNCT
ma-9	29	13	τk	τk	ADP
ma-9	29	14	}	}	PUNCT
ma-9	29	15	is	be	AUX
ma-9	29	16	a	a	DET
ma-9	29	17	sequence	sequence	NOUN
ma-9	29	18	ofrandom	ofrandom	ADJ
ma-9	29	19	variables	variable	NOUN
ma-9	29	20	,	,	PUNCT
ma-9	29	21	which	which	PRON
ma-9	29	22	satisfies	satisfy	VERB
ma-9	29	23	0	0	X
ma-9	29	24	<	<	X
ma-9	29	25	τ2	τ2	NOUN
ma-9	29	26	<	<	X
ma-9	29	27	τ3	τ3	NOUN
ma-9	29	28	<	<	X
ma-9	29	29	·	·	PUNCT
ma-9	29	30	·	·	PUNCT
ma-9	29	31	·	·	PUNCT
ma-9	29	32	.	.	PUNCT
ma-9	30	1	recently	recently	ADV
ma-9	30	2	,	,	PUNCT
ma-9	30	3	in	in	ADP
ma-9	30	4	[	[	X
ma-9	30	5	10	10	NUM
ma-9	30	6	]	]	PUNCT
ma-9	30	7	the	the	DET
ma-9	30	8	authors	author	NOUN
ma-9	30	9	have	have	VERB
ma-9	30	10	contributedthe	contributedthe	DET
ma-9	30	11	existence	existence	NOUN
ma-9	30	12	and	and	CCONJ
ma-9	30	13	hyers	hyer	NOUN
ma-9	30	14	-	-	PUNCT
ma-9	30	15	ulam	ulam	PROPN
ma-9	30	16	stability	stability	NOUN
ma-9	30	17	of	of	ADP
ma-9	30	18	mild	mild	ADJ
ma-9	30	19	solutions	solution	NOUN
ma-9	30	20	for	for	ADP
ma-9	30	21	random	random	ADJ
ma-9	30	22	impulsive	impulsive	ADJ
ma-9	30	23	stochastic	stochastic	ADJ
ma-9	30	24	functionalordinary	functionalordinary	ADJ
ma-9	30	25	differential	differential	ADJ
ma-9	30	26	equations	equation	NOUN
ma-9	30	27	which	which	PRON
ma-9	30	28	are	be	AUX
ma-9	30	29	studied	study	VERB
ma-9	30	30	using	use	VERB
ma-9	30	31	krasnoselskii	krasnoselskii	PROPN
ma-9	30	32	’s	’s	PART
ma-9	30	33	fixed	fix	VERB
ma-9	30	34	point	point	NOUN
ma-9	30	35	theorem.solving	theorem.solve	VERB
ma-9	30	36	second	second	ADJ
ma-9	30	37	-	-	PUNCT
ma-9	30	38	order	order	NOUN
ma-9	30	39	differential	differential	ADJ
ma-9	30	40	equations	equation	NOUN
ma-9	30	41	has	have	AUX
ma-9	30	42	been	be	AUX
ma-9	30	43	observed	observe	VERB
ma-9	30	44	by	by	ADP
ma-9	30	45	many	many	ADJ
ma-9	30	46	scholars	scholar	NOUN
ma-9	30	47	.	.	PUNCT
ma-9	31	1	many	many	ADJ
ma-9	31	2	authorssolved	authorssolve	VERB
ma-9	31	3	second	second	ADJ
ma-9	31	4	-	-	PUNCT
ma-9	31	5	order	order	NOUN
ma-9	31	6	stochastic	stochastic	ADJ
ma-9	31	7	differential	differential	NOUN
ma-9	31	8	equations	equation	NOUN
ma-9	31	9	see	see	VERB
ma-9	31	10	[	[	X
ma-9	31	11	5	5	NUM
ma-9	31	12	,	,	PUNCT
ma-9	31	13	6	6	NUM
ma-9	31	14	,	,	PUNCT
ma-9	31	15	8	8	NUM
ma-9	31	16	,	,	PUNCT
ma-9	31	17	19	19	NUM
ma-9	31	18	]	]	PUNCT
ma-9	31	19	.	.	PUNCT
ma-9	32	1	however	however	ADV
ma-9	32	2	,	,	PUNCT
ma-9	32	3	there	there	PRON
ma-9	32	4	are	be	VERB
ma-9	32	5	not	not	PART
ma-9	32	6	manypapers	manypaper	NOUN
ma-9	32	7	considering	consider	VERB
ma-9	32	8	the	the	DET
ma-9	32	9	existence	existence	NOUN
ma-9	32	10	and	and	CCONJ
ma-9	32	11	stability	stability	NOUN
ma-9	32	12	results	result	NOUN
ma-9	32	13	on	on	ADP
ma-9	32	14	stochastic	stochastic	ADJ
ma-9	32	15	differential	differential	ADJ
ma-9	32	16	equations	equation	NOUN
ma-9	32	17	withrandom	withrandom	ADV
ma-9	32	18	impulse	impulse	ADJ
ma-9	32	19	.	.	PUNCT
ma-9	33	1	anguraj	anguraj	PROPN
ma-9	33	2	et.al	et.al	PROPN
ma-9	34	1	[	[	X
ma-9	34	2	3	3	NUM
ma-9	34	3	]	]	PUNCT
ma-9	34	4	,	,	PUNCT
ma-9	34	5	considered	consider	VERB
ma-9	34	6	the	the	DET
ma-9	34	7	sdes	sde	NOUN
ma-9	34	8	with	with	ADP
ma-9	34	9	random	random	ADJ
ma-9	34	10	impulses	impulse	NOUN
ma-9	34	11	and	and	CCONJ
ma-9	34	12	poisson	poisson	NOUN
ma-9	34	13	jumpsof	jumpsof	VERB
ma-9	34	14	the	the	DET
ma-9	34	15	form	form	NOUN
ma-9	34	16	d[x(t	d[x(t	NOUN
ma-9	34	17	)	)	PUNCT
ma-9	34	18	]	]	PUNCT
ma-9	35	1	=	=	SYM
ma-9	35	2	f(t	f(t	NOUN
ma-9	35	3	,	,	PUNCT
ma-9	35	4	xt	xt	X
ma-9	35	5	)	)	PUNCT
ma-9	35	6	+	+	CCONJ
ma-9	35	7	g(t	g(t	PROPN
ma-9	35	8	,	,	PUNCT
ma-9	35	9	xt)dw(t	xt)dw(t	PROPN
ma-9	35	10	)	)	PUNCT
ma-9	36	1	+	+	CCONJ
ma-9	37	1	∫	∫	PROPN
ma-9	37	2	u	u	X
ma-9	37	3	h(t	h(t	PROPN
ma-9	37	4	,	,	PUNCT
ma-9	37	5	xt	xt	PROPN
ma-9	37	6	,	,	PUNCT
ma-9	37	7	u)ñ(dt	u)ñ(dt	PROPN
ma-9	37	8	,	,	PUNCT
ma-9	37	9	du	du	NOUN
ma-9	37	10	)	)	PUNCT
ma-9	37	11	,	,	PUNCT
ma-9	37	12	t	t	PROPN
ma-9	37	13	≥	≥	PROPN
ma-9	37	14	t0	t0	PROPN
ma-9	37	15	,	,	PUNCT
ma-9	37	16	t	t	PROPN
ma-9	37	17	6=	6=	NUM
ma-9	37	18	τk	τk	ADP
ma-9	37	19	,	,	PUNCT
ma-9	37	20	x(ζk	x(ζk	PROPN
ma-9	37	21	)	)	PUNCT
ma-9	38	1	=	=	PUNCT
ma-9	38	2	bk	bk	INTJ
ma-9	38	3	(	(	PUNCT
ma-9	38	4	τk	τk	ADP
ma-9	38	5	)	)	PUNCT
ma-9	38	6	x(ζ−k	x(ζ−k	PROPN
ma-9	38	7	)	)	PUNCT
ma-9	38	8	,	,	PUNCT
ma-9	38	9	k	k	X
ma-9	38	10	=	=	SYM
ma-9	38	11	1	1	NUM
ma-9	38	12	,	,	PUNCT
ma-9	38	13	2	2	NUM
ma-9	38	14	,	,	PUNCT
ma-9	38	15	...	...	PUNCT
ma-9	38	16	,	,	PUNCT
ma-9	38	17	xt0	xt0	PROPN
ma-9	38	18	=	=	SYM
ma-9	38	19	ζ	ζ	PROPN
ma-9	38	20	=	=	SYM
ma-9	38	21	{	{	PUNCT
ma-9	38	22	ζ(θ	ζ(θ	NOUN
ma-9	38	23	)	)	PUNCT
ma-9	38	24	:	:	PUNCT
ma-9	38	25	−τ	−τ	VERB
ma-9	38	26	≤	≤	NUM
ma-9	38	27	θ	θ	PROPN
ma-9	38	28	≤	≤	ADV
ma-9	38	29	0	0	NUM
ma-9	38	30	}	}	PUNCT
ma-9	38	31	.	.	PUNCT
ma-9	39	1	the	the	DET
ma-9	39	2	authors	author	NOUN
ma-9	39	3	studied	study	VERB
ma-9	39	4	the	the	DET
ma-9	39	5	existence	existence	NOUN
ma-9	39	6	,	,	PUNCT
ma-9	39	7	uniqueness	uniqueness	NOUN
ma-9	39	8	,	,	PUNCT
ma-9	39	9	and	and	CCONJ
ma-9	39	10	stability	stability	NOUN
ma-9	39	11	through	through	ADP
ma-9	39	12	continuous	continuous	ADJ
ma-9	39	13	dependence	dependence	NOUN
ma-9	39	14	oninitial	oninitial	ADJ
ma-9	39	15	conditions	condition	NOUN
ma-9	39	16	for	for	ADP
ma-9	39	17	sdes	sde	NOUN
ma-9	39	18	with	with	ADP
ma-9	39	19	random	random	ADJ
ma-9	39	20	impulses	impulse	NOUN
ma-9	39	21	and	and	CCONJ
ma-9	39	22	poisson	poisson	NOUN
ma-9	39	23	jumps	jump	VERB
ma-9	39	24	by	by	ADP
ma-9	39	25	using	use	VERB
ma-9	39	26	banach	banach	NOUN
ma-9	39	27	fixed	fix	VERB
ma-9	39	28	pointtheorem	pointtheorem	VERB
ma-9	39	29	.	.	PUNCT
ma-9	40	1	very	very	ADV
ma-9	40	2	recently	recently	ADV
ma-9	40	3	,	,	PUNCT
ma-9	40	4	anguraj	anguraj	NOUN
ma-9	40	5	et.al	et.al	VERB
ma-9	41	1	[	[	X
ma-9	41	2	2	2	NUM
ma-9	41	3	]	]	PUNCT
ma-9	41	4	investigated	investigate	VERB
ma-9	41	5	the	the	DET
ma-9	41	6	existence	existence	NOUN
ma-9	41	7	and	and	CCONJ
ma-9	41	8	hyers	hyer	NOUN
ma-9	41	9	ulam	ulam	PROPN
ma-9	41	10	stability	stability	PROPN
ma-9	41	11	ofrandom	ofrandom	ADJ
ma-9	41	12	impulsive	impulsive	ADJ
ma-9	41	13	stochastic	stochastic	ADJ
ma-9	41	14	functional	functional	ADJ
ma-9	41	15	integrodifferential	integrodifferential	ADJ
ma-9	41	16	equations	equation	NOUN
ma-9	41	17	with	with	ADP
ma-9	41	18	finite	finite	NOUN
ma-9	41	19	delays.motivated	delays.motivate	VERB
ma-9	41	20	by	by	ADP
ma-9	41	21	the	the	DET
ma-9	41	22	above	above	ADJ
ma-9	41	23	discussion	discussion	NOUN
ma-9	41	24	,	,	PUNCT
ma-9	41	25	here	here	ADV
ma-9	41	26	we	we	PRON
ma-9	41	27	consider	consider	VERB
ma-9	41	28	the	the	DET
ma-9	41	29	following	follow	VERB
ma-9	41	30	second	second	ADJ
ma-9	41	31	-	-	PUNCT
ma-9	41	32	order	order	NOUN
ma-9	41	33	nsfdes	nsfde	NOUN
ma-9	41	34	withrandom	withrandom	ADJ
ma-9	41	35	impulses	impulse	NOUN
ma-9	41	36	and	and	CCONJ
ma-9	41	37	poisson	poisson	NOUN
ma-9	41	38	jumps	jump	VERB
ma-9	41	39	.	.	PUNCT
ma-9	42	1	d	d	X
ma-9	42	2	[	[	PUNCT
ma-9	42	3	x	x	PUNCT
ma-9	42	4	′(t)−	′(t)−	PROPN
ma-9	42	5	h(t	h(t	PROPN
ma-9	42	6	,	,	PUNCT
ma-9	42	7	xt	xt	ADJ
ma-9	42	8	)	)	PUNCT
ma-9	42	9	]	]	PUNCT
ma-9	43	1	=	=	PUNCT
ma-9	44	1	[	[	X
ma-9	44	2	ax(t	ax(t	X
ma-9	44	3	)	)	PUNCT
ma-9	45	1	+	+	CCONJ
ma-9	45	2	f(t	f(t	NOUN
ma-9	45	3	,	,	PUNCT
ma-9	45	4	xt)]dt	xt)]dt	PROPN
ma-9	45	5	+	+	NUM
ma-9	45	6	g(t	g(t	PROPN
ma-9	45	7	,	,	PUNCT
ma-9	45	8	xt)dω(t	xt)dω(t	PROPN
ma-9	45	9	)	)	PUNCT
ma-9	46	1	+	+	NUM
ma-9	46	2	∫	∫	PROPN
ma-9	46	3	u	u	PROPN
ma-9	46	4	σ	σ	PROPN
ma-9	46	5	(	(	PUNCT
ma-9	46	6	t	t	PROPN
ma-9	46	7	,	,	PUNCT
ma-9	46	8	xt	xt	PROPN
ma-9	46	9	,	,	PUNCT
ma-9	46	10	u)ñ(dt	u)ñ(dt	PROPN
ma-9	46	11	,	,	PUNCT
ma-9	46	12	du	du	NOUN
ma-9	46	13	)	)	PUNCT
ma-9	46	14	,	,	PUNCT
ma-9	46	15	,	,	PUNCT
ma-9	46	16	t	t	PROPN
ma-9	46	17	≥	≥	PROPN
ma-9	46	18	t0	t0	PROPN
ma-9	46	19	,	,	PUNCT
ma-9	46	20	t	t	PROPN
ma-9	46	21	6=	6=	PROPN
ma-9	46	22	ξk	ξk	ADP
ma-9	46	23	,	,	PUNCT
ma-9	46	24	x(ξk	x(ξk	PROPN
ma-9	46	25	)	)	PUNCT
ma-9	46	26	=	=	SYM
ma-9	46	27	bk(δk)x(ξ−k	bk(δk)x(ξ−k	PROPN
ma-9	46	28	)	)	PUNCT
ma-9	46	29	,	,	PUNCT
ma-9	46	30	x	x	SYM
ma-9	46	31	′(ξk	′(ξk	PROPN
ma-9	46	32	)	)	PUNCT
ma-9	46	33	=	=	VERB
ma-9	46	34	bk(δk)x	bk(δk)x	VERB
ma-9	46	35	′(ξ−k	′(ξ−k	NOUN
ma-9	46	36	)	)	PUNCT
ma-9	46	37	,	,	PUNCT
ma-9	46	38	k	k	X
ma-9	46	39	=	=	SYM
ma-9	46	40	1	1	NUM
ma-9	46	41	,	,	PUNCT
ma-9	46	42	2	2	NUM
ma-9	46	43	,	,	PUNCT
ma-9	46	44	...	...	PUNCT
ma-9	46	45	,	,	PUNCT
ma-9	46	46	(	(	PUNCT
ma-9	46	47	1.1	1.1	NUM
ma-9	46	48	)	)	PUNCT
ma-9	46	49	xt0	xt0	X
ma-9	46	50	=	=	SYM
ma-9	46	51	φ	φ	PROPN
ma-9	46	52	,	,	PUNCT
ma-9	46	53	x	x	PROPN
ma-9	46	54	′(t0	′(t0	NUM
ma-9	46	55	)	)	PUNCT
ma-9	46	56	=	=	PUNCT
ma-9	47	1	φ	φ	PROPN
ma-9	47	2	,	,	PUNCT
ma-9	47	3	where	where	SCONJ
ma-9	47	4	a	a	DET
ma-9	47	5	:	:	PUNCT
ma-9	47	6	d(a	d(a	PROPN
ma-9	47	7	)	)	PUNCT
ma-9	47	8	⊂	⊂	PROPN
ma-9	48	1	h	h	PROPN
ma-9	48	2	→	→	PUNCT
ma-9	48	3	h	h	NOUN
ma-9	48	4	is	be	AUX
ma-9	48	5	the	the	DET
ma-9	48	6	infinitesimal	infinitesimal	ADJ
ma-9	48	7	generator	generator	NOUN
ma-9	48	8	of	of	ADP
ma-9	48	9	a	a	DET
ma-9	48	10	strongly	strongly	ADV
ma-9	48	11	continuous	continuous	ADJ
ma-9	48	12	cosine	cosine	NOUN
ma-9	48	13	family	family	NOUN
ma-9	48	14	{	{	PUNCT
ma-9	48	15	c(t	c(t	PROPN
ma-9	48	16	)	)	PUNCT
ma-9	48	17	,	,	PUNCT
ma-9	48	18	t	t	PROPN
ma-9	48	19	≥	≥	NOUN
ma-9	48	20	0	0	NUM
ma-9	48	21	}	}	PUNCT
ma-9	48	22	.	.	PUNCT
ma-9	49	1	w(t	w(t	PROPN
ma-9	49	2	)	)	PUNCT
ma-9	49	3	is	be	AUX
ma-9	49	4	a	a	DET
ma-9	49	5	given	give	VERB
ma-9	49	6	q	q	ADJ
ma-9	49	7	-	-	PUNCT
ma-9	49	8	wiener	wiener	NOUN
ma-9	49	9	process	process	NOUN
ma-9	49	10	with	with	ADP
ma-9	49	11	a	a	DET
ma-9	49	12	finite	finite	ADJ
ma-9	49	13	trace	trace	NOUN
ma-9	49	14	nuclear	nuclear	ADJ
ma-9	49	15	covariance	covariance	NOUN
ma-9	49	16	operator	operator	NOUN
ma-9	49	17	q	q	PROPN
ma-9	49	18	>	>	X
ma-9	49	19	0	0	X
ma-9	49	20	.	.	PUNCT
ma-9	50	1	δk	δk	PROPN
ma-9	50	2	is	be	AUX
ma-9	50	3	a	a	DET
ma-9	50	4	random	random	ADJ
ma-9	50	5	variable	variable	NOUN
ma-9	50	6	defined	define	VERB
ma-9	50	7	from	from	ADP
ma-9	50	8	ω	ω	NUM
ma-9	50	9	to	to	ADP
ma-9	50	10	d	d	PROPN
ma-9	50	11	≡	≡	PROPN
ma-9	50	12	(	(	PUNCT
ma-9	50	13	0	0	NUM
ma-9	50	14	,	,	PUNCT
ma-9	50	15	dk	dk	PROPN
ma-9	50	16	)	)	PUNCT
ma-9	50	17	for	for	ADP
ma-9	50	18	k	k	PROPN
ma-9	50	19	=	=	SYM
ma-9	50	20	1	1	NUM
ma-9	50	21	,	,	PUNCT
ma-9	50	22	2	2	NUM
ma-9	50	23	·	·	PUNCT
ma-9	50	24	·	·	PUNCT
ma-9	50	25	·	·	PUNCT
ma-9	50	26	.	.	PUNCT
ma-9	51	1	suppose	suppose	VERB
ma-9	51	2	that	that	SCONJ
ma-9	51	3	δi	δi	PROPN
ma-9	51	4	and	and	CCONJ
ma-9	51	5	δj	δj	NOUN
ma-9	51	6	are	be	AUX
ma-9	51	7	independent	independent	ADJ
ma-9	51	8	of	of	ADP
ma-9	51	9	each	each	DET
ma-9	51	10	other	other	ADJ
ma-9	51	11	as	as	ADP
ma-9	51	12	i	i	PROPN
ma-9	51	13	6=	6=	PROPN
ma-9	51	14	j	j	PROPN
ma-9	51	15	,	,	PUNCT
ma-9	51	16	(	(	PUNCT
ma-9	51	17	i	i	PROPN
ma-9	51	18	,	,	PUNCT
ma-9	51	19	j	j	PROPN
ma-9	51	20	=	=	SYM
ma-9	51	21	1	1	NUM
ma-9	51	22	,	,	PUNCT
ma-9	51	23	2	2	NUM
ma-9	51	24	,	,	PUNCT
ma-9	51	25	·	·	PUNCT
ma-9	51	26	·	·	PUNCT
ma-9	51	27	·	·	PUNCT
ma-9	51	28	)	)	PUNCT
ma-9	51	29	.	.	PUNCT
ma-9	52	1	the	the	DET
ma-9	52	2	impulsive	impulsive	ADJ
ma-9	52	3	moments	moment	NOUN
ma-9	52	4	ξk	ξk	ADP
ma-9	52	5	are	be	AUX
ma-9	52	6	randomvariables	randomvariable	NOUN
ma-9	52	7	and	and	CCONJ
ma-9	52	8	satisfy	satisfy	VERB
ma-9	52	9	ξk	ξk	ADP
ma-9	52	10	=	=	PUNCT
ma-9	52	11	ξk−1	ξk−1	PROPN
ma-9	52	12	+	+	CCONJ
ma-9	52	13	δk	δk	PROPN
ma-9	52	14	,	,	PUNCT
ma-9	52	15	k	k	NOUN
ma-9	52	16	=	=	SYM
ma-9	52	17	1	1	NUM
ma-9	52	18	,	,	PUNCT
ma-9	52	19	2	2	NUM
ma-9	52	20	,	,	PUNCT
ma-9	52	21	·	·	PUNCT
ma-9	52	22	·	·	PUNCT
ma-9	52	23	·	·	PUNCT
ma-9	52	24	.	.	PUNCT
ma-9	53	1	obviously	obviously	ADV
ma-9	53	2	,	,	PUNCT
ma-9	53	3	{	{	PUNCT
ma-9	53	4	ξk	ξk	ADP
ma-9	53	5	}	}	PUNCT
ma-9	53	6	is	be	AUX
ma-9	53	7	a	a	DET
ma-9	53	8	process	process	NOUN
ma-9	53	9	with	with	ADP
ma-9	53	10	independentincrements	independentincrement	NOUN
ma-9	53	11	.	.	PUNCT
ma-9	53	12	0	0	PUNCT
ma-9	54	1	<	<	X
ma-9	54	2	t0	t0	PROPN
ma-9	54	3	=	=	SYM
ma-9	54	4	ξ0	ξ0	PROPN
ma-9	54	5	<	<	X
ma-9	54	6	ξ2	ξ2	NOUN
ma-9	54	7	<	<	X
ma-9	54	8	ξ3	ξ3	PROPN
ma-9	54	9	<	<	X
ma-9	54	10	·	·	PUNCT
ma-9	54	11	·	·	PUNCT
ma-9	54	12	·	·	PUNCT
ma-9	55	1	<	<	X
ma-9	55	2	limk→∞	limk→∞	NOUN
ma-9	55	3	ξk	ξk	ADP
ma-9	55	4	=	=	SYM
ma-9	55	5	∞	∞	PROPN
ma-9	55	6	,	,	PUNCT
ma-9	55	7	and	and	CCONJ
ma-9	55	8	x(ξ−k	x(ξ−k	NUM
ma-9	55	9	)	)	PUNCT
ma-9	56	1	=	=	SYM
ma-9	56	2	lim	lim	PROPN
ma-9	56	3	t→ξk−0	t→ξk−0	PRON
ma-9	56	4	x(t	x(t	PROPN
ma-9	56	5	)	)	PUNCT
ma-9	56	6	.	.	PUNCT
ma-9	57	1	bk	bk	INTJ
ma-9	57	2	:	:	PUNCT
ma-9	57	3	dk	dk	PROPN
ma-9	57	4	→	→	SYM
ma-9	57	5	h	h	PROPN
ma-9	57	6	,	,	PUNCT
ma-9	57	7	eur	eur	PROPN
ma-9	57	8	.	.	PUNCT
ma-9	58	1	j.	j.	PROPN
ma-9	58	2	math	math	PROPN
ma-9	58	3	.	.	PUNCT
ma-9	59	1	anal	anal	ADJ
ma-9	59	2	.	.	PUNCT
ma-9	60	1	1	1	NUM
ma-9	60	2	(	(	PUNCT
ma-9	60	3	2021	2021	NUM
ma-9	60	4	)	)	PUNCT
ma-9	61	1	3for	3for	ADP
ma-9	61	2	each	each	PRON
ma-9	61	3	k	k	NOUN
ma-9	62	1	=	=	SYM
ma-9	62	2	1	1	NUM
ma-9	62	3	,	,	PUNCT
ma-9	62	4	2	2	NUM
ma-9	62	5	,	,	PUNCT
ma-9	62	6	·	·	PUNCT
ma-9	62	7	·	·	PUNCT
ma-9	62	8	·	·	PUNCT
ma-9	62	9	.	.	PUNCT
ma-9	63	1	the	the	DET
ma-9	63	2	time	time	NOUN
ma-9	63	3	history	history	NOUN
ma-9	63	4	xt(θ	xt(θ	NUM
ma-9	63	5	)	)	PUNCT
ma-9	63	6	=	=	SYM
ma-9	63	7	{	{	PUNCT
ma-9	63	8	x(t	x(t	PROPN
ma-9	63	9	+	+	CCONJ
ma-9	63	10	θ	θ	NOUN
ma-9	63	11	)	)	PUNCT
ma-9	63	12	:	:	PUNCT
ma-9	63	13	−δ	−δ	ADJ
ma-9	63	14	≤	≤	NUM
ma-9	63	15	θ	θ	PROPN
ma-9	63	16	≤	≤	NOUN
ma-9	63	17	0	0	NUM
ma-9	63	18	}	}	PUNCT
ma-9	63	19	with	with	ADP
ma-9	63	20	some	some	PRON
ma-9	63	21	given	give	VERB
ma-9	63	22	δ	δ	PROPN
ma-9	63	23	>	>	X
ma-9	63	24	0.moreover	0.moreover	PROPN
ma-9	63	25	,	,	PUNCT
ma-9	63	26	h	h	NOUN
ma-9	63	27	,	,	PUNCT
ma-9	63	28	f	f	PROPN
ma-9	63	29	,	,	PUNCT
ma-9	63	30	g	g	PROPN
ma-9	63	31	,	,	PUNCT
ma-9	63	32	σ	σ	PROPN
ma-9	63	33	,	,	PUNCT
ma-9	63	34	and	and	CCONJ
ma-9	63	35	φ	φ	PROPN
ma-9	63	36	,	,	PUNCT
ma-9	63	37	φ	φ	PROPN
ma-9	63	38	will	will	AUX
ma-9	63	39	be	be	AUX
ma-9	63	40	specified	specify	VERB
ma-9	63	41	later.to	later.to	PRON
ma-9	63	42	the	the	DET
ma-9	63	43	best	good	ADJ
ma-9	63	44	of	of	ADP
ma-9	63	45	authors	author	NOUN
ma-9	63	46	knowledge	knowledge	NOUN
ma-9	63	47	,	,	PUNCT
ma-9	63	48	up	up	ADP
ma-9	63	49	to	to	ADP
ma-9	63	50	now	now	ADV
ma-9	63	51	,	,	PUNCT
ma-9	63	52	no	no	DET
ma-9	63	53	work	work	NOUN
ma-9	63	54	has	have	AUX
ma-9	63	55	been	be	AUX
ma-9	63	56	reported	report	VERB
ma-9	63	57	to	to	PART
ma-9	63	58	derive	derive	VERB
ma-9	63	59	the	the	DET
ma-9	63	60	second	second	ADJ
ma-9	63	61	-	-	PUNCT
ma-9	63	62	order	order	NOUN
ma-9	63	63	nsfdes	nsfde	NOUN
ma-9	63	64	with	with	ADP
ma-9	63	65	random	random	ADJ
ma-9	63	66	impulses	impulse	NOUN
ma-9	63	67	and	and	CCONJ
ma-9	63	68	poisson	poisson	NOUN
ma-9	63	69	jumps	jump	VERB
ma-9	63	70	.	.	PUNCT
ma-9	64	1	the	the	DET
ma-9	64	2	main	main	ADJ
ma-9	64	3	contributions	contribution	NOUN
ma-9	64	4	are	be	AUX
ma-9	64	5	summarizedas	summarizeda	VERB
ma-9	64	6	follows:(1	follows:(1	PROPN
ma-9	64	7	)	)	PUNCT
ma-9	64	8	second	second	ADJ
ma-9	64	9	-	-	PUNCT
ma-9	64	10	order	order	NOUN
ma-9	64	11	nsfdes	nsfde	NOUN
ma-9	64	12	with	with	ADP
ma-9	64	13	random	random	ADJ
ma-9	64	14	impulses	impulse	NOUN
ma-9	64	15	and	and	CCONJ
ma-9	64	16	poisson	poisson	NOUN
ma-9	64	17	jumps	jump	VERB
ma-9	64	18	is	be	AUX
ma-9	64	19	formulated.(2	formulated.(2	ADJ
ma-9	64	20	)	)	PUNCT
ma-9	64	21	initially	initially	ADV
ma-9	64	22	,	,	PUNCT
ma-9	64	23	we	we	PRON
ma-9	64	24	establish	establish	VERB
ma-9	64	25	the	the	DET
ma-9	64	26	existence	existence	NOUN
ma-9	64	27	results	result	NOUN
ma-9	64	28	of	of	ADP
ma-9	64	29	mild	mild	ADJ
ma-9	64	30	solutions	solution	NOUN
ma-9	64	31	of	of	ADP
ma-9	64	32	the	the	DET
ma-9	64	33	aforementioned	aforementioned	ADJ
ma-9	64	34	system	system	NOUN
ma-9	64	35	usingbanach	usingbanach	NOUN
ma-9	64	36	contraction	contraction	NOUN
ma-9	64	37	principle.(3	principle.(3	PROPN
ma-9	64	38	)	)	PUNCT
ma-9	64	39	next	next	ADV
ma-9	64	40	,	,	PUNCT
ma-9	64	41	we	we	PRON
ma-9	64	42	investigate	investigate	VERB
ma-9	64	43	the	the	DET
ma-9	64	44	stability	stability	NOUN
ma-9	64	45	results	result	VERB
ma-9	64	46	through	through	ADP
ma-9	64	47	continuous	continuous	ADJ
ma-9	64	48	dependence	dependence	NOUN
ma-9	64	49	of	of	ADP
ma-9	64	50	solutions	solution	NOUN
ma-9	64	51	on	on	ADP
ma-9	64	52	initialconditions.(4	initialconditions.(4	NOUN
ma-9	64	53	)	)	PUNCT
ma-9	64	54	an	an	DET
ma-9	64	55	example	example	NOUN
ma-9	64	56	is	be	AUX
ma-9	64	57	provided	provide	VERB
ma-9	64	58	to	to	PART
ma-9	64	59	illustrate	illustrate	VERB
ma-9	64	60	the	the	DET
ma-9	64	61	obtained	obtain	VERB
ma-9	64	62	theoretical	theoretical	ADJ
ma-9	64	63	results.the	results.the	DET
ma-9	64	64	rest	rest	NOUN
ma-9	64	65	of	of	ADP
ma-9	64	66	the	the	DET
ma-9	64	67	paper	paper	NOUN
ma-9	64	68	is	be	AUX
ma-9	64	69	organised	organise	VERB
ma-9	64	70	as	as	SCONJ
ma-9	64	71	follows	follow	VERB
ma-9	64	72	.	.	PUNCT
ma-9	65	1	section	section	NOUN
ma-9	65	2	2	2	NUM
ma-9	65	3	is	be	AUX
ma-9	65	4	devoted	devote	VERB
ma-9	65	5	to	to	ADP
ma-9	65	6	basic	basic	ADJ
ma-9	65	7	definitions	definition	NOUN
ma-9	65	8	,	,	PUNCT
ma-9	65	9	notions	notion	NOUN
ma-9	65	10	andlemma	andlemma	PROPN
ma-9	65	11	.	.	PUNCT
ma-9	66	1	in	in	ADP
ma-9	66	2	section	section	NOUN
ma-9	66	3	3	3	NUM
ma-9	66	4	,	,	PUNCT
ma-9	66	5	existence	existence	NOUN
ma-9	66	6	of	of	ADP
ma-9	66	7	mild	mild	ADJ
ma-9	66	8	solutions	solution	NOUN
ma-9	66	9	of	of	ADP
ma-9	66	10	the	the	DET
ma-9	66	11	aforementioned	aforementioned	ADJ
ma-9	66	12	system	system	NOUN
ma-9	66	13	(	(	PUNCT
ma-9	66	14	1.1	1.1	NUM
ma-9	66	15	)	)	PUNCT
ma-9	66	16	is	be	AUX
ma-9	66	17	investigatedusing	investigateduse	VERB
ma-9	66	18	banach	banach	NOUN
ma-9	66	19	contraction	contraction	NOUN
ma-9	66	20	principle	principle	NOUN
ma-9	66	21	.	.	PUNCT
ma-9	67	1	eventually	eventually	ADV
ma-9	67	2	in	in	ADP
ma-9	67	3	section	section	NOUN
ma-9	67	4	4	4	NUM
ma-9	67	5	,	,	PUNCT
ma-9	67	6	the	the	DET
ma-9	67	7	stability	stability	NOUN
ma-9	67	8	of	of	ADP
ma-9	67	9	mild	mild	ADJ
ma-9	67	10	solution	solution	NOUN
ma-9	67	11	is	be	AUX
ma-9	67	12	obtainedthrough	obtainedthrough	ADJ
ma-9	67	13	continuous	continuous	ADJ
ma-9	67	14	dependence	dependence	NOUN
ma-9	67	15	of	of	ADP
ma-9	67	16	solutions	solution	NOUN
ma-9	67	17	on	on	ADP
ma-9	67	18	initial	initial	ADJ
ma-9	67	19	conditions	condition	NOUN
ma-9	67	20	.	.	PUNCT
ma-9	68	1	2	2	X
ma-9	68	2	.	.	X
ma-9	68	3	preliminaries	preliminary	NOUN
ma-9	68	4	let	let	AUX
ma-9	68	5	(	(	PUNCT
ma-9	68	6	ω,=,p	ω,=,p	NUM
ma-9	68	7	)	)	PUNCT
ma-9	68	8	be	be	AUX
ma-9	68	9	a	a	DET
ma-9	68	10	complete	complete	ADJ
ma-9	68	11	probability	probability	NOUN
ma-9	68	12	space	space	NOUN
ma-9	68	13	equipped	equip	VERB
ma-9	68	14	with	with	ADP
ma-9	68	15	the	the	DET
ma-9	68	16	normal	normal	ADJ
ma-9	68	17	filtration	filtration	NOUN
ma-9	68	18	{	{	PUNCT
ma-9	68	19	=	=	NOUN
ma-9	68	20	}	}	SYM
ma-9	68	21	t≥t0	t≥t0	PUNCT
ma-9	68	22	.	.	PUNCT
ma-9	69	1	=	=	VERB
ma-9	69	2	t0containing	t0containe	VERB
ma-9	69	3	all	all	DET
ma-9	69	4	p	p	ADJ
ma-9	69	5	-	-	PUNCT
ma-9	69	6	null	null	ADJ
ma-9	69	7	sets	set	NOUN
ma-9	69	8	.	.	PUNCT
ma-9	70	1	h	h	NOUN
ma-9	70	2	and	and	CCONJ
ma-9	70	3	k	k	PROPN
ma-9	70	4	be	be	AUX
ma-9	70	5	two	two	NUM
ma-9	70	6	real	real	ADJ
ma-9	70	7	hilbert	hilbert	NOUN
ma-9	70	8	spaces	space	NOUN
ma-9	70	9	.	.	PUNCT
ma-9	71	1	l(h	l(h	PROPN
ma-9	71	2	,	,	PUNCT
ma-9	71	3	k	k	NOUN
ma-9	71	4	)	)	PUNCT
ma-9	71	5	denotes	denote	VERB
ma-9	71	6	the	the	DET
ma-9	71	7	space	space	NOUN
ma-9	71	8	of	of	ADP
ma-9	71	9	allbounded	allbounded	ADJ
ma-9	71	10	linear	linear	PROPN
ma-9	71	11	operators	operator	NOUN
ma-9	71	12	from	from	ADP
ma-9	71	13	k	k	PROPN
ma-9	71	14	to	to	ADP
ma-9	71	15	h.we	h.we	PROPN
ma-9	71	16	may	may	AUX
ma-9	71	17	assume	assume	VERB
ma-9	71	18	that	that	SCONJ
ma-9	71	19	,	,	PUNCT
ma-9	71	20	{	{	PUNCT
ma-9	71	21	n	n	X
ma-9	71	22	(	(	PUNCT
ma-9	71	23	t	t	PROPN
ma-9	71	24	)	)	PUNCT
ma-9	71	25	,	,	PUNCT
ma-9	71	26	t	t	PROPN
ma-9	71	27	≥	≥	PROPN
ma-9	71	28	t0	t0	PROPN
ma-9	71	29	}	}	PUNCT
ma-9	71	30	be	be	AUX
ma-9	71	31	a	a	DET
ma-9	71	32	counting	counting	NOUN
ma-9	71	33	process	process	NOUN
ma-9	71	34	generated	generate	VERB
ma-9	71	35	by	by	ADP
ma-9	71	36	{	{	PUNCT
ma-9	71	37	ξk	ξk	ADP
ma-9	71	38	,	,	PUNCT
ma-9	71	39	k	k	PROPN
ma-9	71	40	≥	≥	NOUN
ma-9	71	41	0	0	NUM
ma-9	71	42	}	}	PUNCT
ma-9	71	43	.	.	PUNCT
ma-9	72	1	=(	=(	PROPN
ma-9	72	2	1	1	NUM
ma-9	72	3	)	)	PUNCT
ma-9	72	4	t	t	NOUN
ma-9	72	5	denotethe	denotethe	PRON
ma-9	72	6	minimal	minimal	PROPN
ma-9	72	7	σ	σ	PROPN
ma-9	72	8	algebra	algebra	NOUN
ma-9	72	9	denoted	denote	VERB
ma-9	72	10	by	by	ADP
ma-9	72	11	{	{	PUNCT
ma-9	72	12	n	n	PROPN
ma-9	72	13	(	(	PUNCT
ma-9	72	14	r	r	NOUN
ma-9	72	15	)	)	PUNCT
ma-9	72	16	,	,	PUNCT
ma-9	72	17	r	r	NOUN
ma-9	72	18	≤	≤	PUNCT
ma-9	72	19	t	t	PROPN
ma-9	72	20	}	}	PUNCT
ma-9	72	21	and	and	CCONJ
ma-9	72	22	denote	denote	VERB
ma-9	72	23	=(	=(	NOUN
ma-9	72	24	2	2	NUM
ma-9	72	25	)	)	PUNCT
ma-9	72	26	t	t	NOUN
ma-9	72	27	the	the	DET
ma-9	72	28	σ	σ	PROPN
ma-9	72	29	-	-	PUNCT
ma-9	72	30	algebra	algebra	NOUN
ma-9	72	31	generated	generate	VERB
ma-9	72	32	by	by	ADP
ma-9	72	33	{	{	PUNCT
ma-9	72	34	ω(s	ω(s	PROPN
ma-9	72	35	)	)	PUNCT
ma-9	72	36	,	,	PUNCT
ma-9	72	37	s	s	VERB
ma-9	72	38	≤	≤	NUM
ma-9	72	39	t	t	PROPN
ma-9	72	40	}	}	PUNCT
ma-9	72	41	.	.	PUNCT
ma-9	73	1	we	we	PRON
ma-9	73	2	assume	assume	VERB
ma-9	73	3	that	that	SCONJ
ma-9	73	4	=(	=(	NOUN
ma-9	73	5	1	1	NUM
ma-9	73	6	)	)	PUNCT
ma-9	73	7	∞	∞	NUM
ma-9	73	8	,	,	PUNCT
ma-9	73	9	=(	=(	NOUN
ma-9	73	10	2	2	NUM
ma-9	73	11	)	)	PUNCT
ma-9	73	12	∞	∞	PROPN
ma-9	73	13	and	and	CCONJ
ma-9	73	14	ξ	ξ	PROPN
ma-9	73	15	are	be	AUX
ma-9	73	16	mutually	mutually	ADV
ma-9	73	17	independent	independent	ADJ
ma-9	73	18	and	and	CCONJ
ma-9	73	19	=	=	SYM
ma-9	73	20	t	t	NOUN
ma-9	73	21	=	=	SYM
ma-9	73	22	=(	=(	NOUN
ma-9	73	23	1	1	NUM
ma-9	73	24	)	)	PUNCT
ma-9	73	25	t	t	NOUN
ma-9	73	26	∨	∨	NUM
ma-9	73	27	=	=	SYM
ma-9	73	28	(	(	PUNCT
ma-9	73	29	2	2	NUM
ma-9	73	30	)	)	PUNCT
ma-9	73	31	t	t	PROPN
ma-9	73	32	.we	.we	PUNCT
ma-9	73	33	assume	assume	VERB
ma-9	73	34	that	that	SCONJ
ma-9	73	35	there	there	PRON
ma-9	73	36	exist	exist	VERB
ma-9	73	37	a	a	DET
ma-9	73	38	complete	complete	ADJ
ma-9	73	39	orthonormal	orthonormal	ADJ
ma-9	73	40	system	system	NOUN
ma-9	73	41	{	{	PUNCT
ma-9	73	42	en}∞n=1	en}∞n=1	NUM
ma-9	73	43	in	in	ADP
ma-9	73	44	k	k	PROPN
ma-9	73	45	,	,	PUNCT
ma-9	73	46	a	a	DET
ma-9	73	47	bounded	bound	VERB
ma-9	73	48	sequenceof	sequenceof	ADJ
ma-9	73	49	non	non	ADJ
ma-9	73	50	-	-	ADJ
ma-9	73	51	negative	negative	ADJ
ma-9	73	52	real	real	ADJ
ma-9	73	53	numbers	number	NOUN
ma-9	73	54	λn	λn	ADP
ma-9	73	55	such	such	ADJ
ma-9	73	56	that	that	SCONJ
ma-9	73	57	,	,	PUNCT
ma-9	73	58	qen	qen	PROPN
ma-9	73	59	=	=	PROPN
ma-9	73	60	λnen	λnen	NOUN
ma-9	73	61	,	,	PUNCT
ma-9	73	62	n	n	NOUN
ma-9	73	63	=	=	SYM
ma-9	73	64	1	1	NUM
ma-9	73	65	,	,	PUNCT
ma-9	73	66	2	2	NUM
ma-9	73	67	,	,	PUNCT
ma-9	73	68	·	·	PUNCT
ma-9	73	69	·	·	PUNCT
ma-9	73	70	·	·	PUNCT
ma-9	73	71	.	.	PUNCT
ma-9	74	1	let	let	VERB
ma-9	74	2	{	{	PUNCT
ma-9	74	3	βn(t)}(n	βn(t)}(n	PROPN
ma-9	74	4	=	=	SYM
ma-9	74	5	1	1	NUM
ma-9	74	6	,	,	PUNCT
ma-9	74	7	2	2	NUM
ma-9	74	8	,	,	PUNCT
ma-9	74	9	3	3	NUM
ma-9	74	10	...	...	PUNCT
ma-9	74	11	)	)	PUNCT
ma-9	74	12	bea	bea	PROPN
ma-9	74	13	sequence	sequence	NOUN
ma-9	74	14	of	of	ADP
ma-9	74	15	real	real	ADV
ma-9	74	16	valued	value	VERB
ma-9	74	17	one	one	NUM
ma-9	74	18	dimensional	dimensional	ADJ
ma-9	74	19	standard	standard	ADJ
ma-9	74	20	brownian	brownian	ADJ
ma-9	74	21	motion	motion	NOUN
ma-9	74	22	mutually	mutually	ADV
ma-9	74	23	independent	independent	ADJ
ma-9	74	24	over(ω,=,p	over(ω,=,p	PROPN
ma-9	74	25	)	)	PUNCT
ma-9	74	26	.	.	PUNCT
ma-9	75	1	a	a	DET
ma-9	75	2	q	q	ADJ
ma-9	75	3	-	-	PUNCT
ma-9	75	4	wiener	wiener	NOUN
ma-9	75	5	process	process	NOUN
ma-9	75	6	can	can	AUX
ma-9	75	7	be	be	AUX
ma-9	75	8	defined	define	VERB
ma-9	75	9	by	by	ADP
ma-9	75	10	ω(t	ω(t	NOUN
ma-9	75	11	)	)	PUNCT
ma-9	75	12	=	=	SYM
ma-9	76	1	∞∑	∞∑	NUM
ma-9	76	2	n=1	n=1	PROPN
ma-9	76	3	√	√	ADP
ma-9	76	4	λnβn(t)en	λnβn(t)en	NUM
ma-9	76	5	,	,	PUNCT
ma-9	76	6	(	(	PUNCT
ma-9	76	7	t	t	NOUN
ma-9	76	8	≥	≥	NOUN
ma-9	76	9	0	0	NUM
ma-9	76	10	)	)	PUNCT
ma-9	76	11	.	.	PUNCT
ma-9	77	1	set	set	VERB
ma-9	77	2	φ	φ	PROPN
ma-9	77	3	∈	∈	PROPN
ma-9	77	4	l(k	l(k	PROPN
ma-9	77	5	,	,	PUNCT
ma-9	77	6	h	h	NOUN
ma-9	77	7	)	)	PUNCT
ma-9	77	8	we	we	PRON
ma-9	77	9	define	define	VERB
ma-9	77	10	,	,	PUNCT
ma-9	77	11	∥∥φ∥∥2	∥∥φ∥∥2	NOUN
ma-9	77	12	q	q	NOUN
ma-9	78	1	=	=	PUNCT
ma-9	78	2	t	t	X
ma-9	78	3	r(φqφ∗	r(φqφ∗	PROPN
ma-9	78	4	)	)	PUNCT
ma-9	78	5	=	=	SYM
ma-9	79	1	∞∑	∞∑	NUM
ma-9	79	2	n=1	n=1	ADP
ma-9	79	3	∥∥∥√λnφen∥∥∥2	∥∥∥√λnφen∥∥∥2	X
ma-9	80	1	if	if	SCONJ
ma-9	80	2	∥∥φ∥∥2	∥∥φ∥∥2	PRON
ma-9	80	3	q	q	X
ma-9	80	4	<	<	X
ma-9	80	5	∞	∞	PROPN
ma-9	80	6	,	,	PUNCT
ma-9	80	7	then	then	ADV
ma-9	80	8	φ	φ	PROPN
ma-9	80	9	is	be	AUX
ma-9	80	10	called	call	VERB
ma-9	80	11	a	a	DET
ma-9	80	12	q	q	ADJ
ma-9	80	13	-	-	PUNCT
ma-9	80	14	hilbert	hilbert	ADJ
ma-9	80	15	-	-	PUNCT
ma-9	80	16	schmidt	schmidt	NOUN
ma-9	80	17	operator	operator	NOUN
ma-9	80	18	.	.	PUNCT
ma-9	81	1	let	let	AUX
ma-9	81	2	lq(k	lq(k	ADJ
ma-9	81	3	,	,	PUNCT
ma-9	81	4	h	h	NOUN
ma-9	81	5	)	)	PUNCT
ma-9	81	6	denote	denote	VERB
ma-9	81	7	the	the	DET
ma-9	81	8	space	space	NOUN
ma-9	81	9	ofall	ofall	ADJ
ma-9	82	1	q	q	ADJ
ma-9	82	2	-	-	PUNCT
ma-9	82	3	hilbert	hilbert	ADJ
ma-9	82	4	-	-	PUNCT
ma-9	82	5	schmidt	schmidt	NOUN
ma-9	82	6	operator	operator	NOUN
ma-9	82	7	φ	φ	NOUN
ma-9	82	8	:	:	PUNCT
ma-9	83	1	k	k	PROPN
ma-9	83	2	→	→	PUNCT
ma-9	83	3	h.	h.	PROPN
ma-9	83	4	the	the	DET
ma-9	83	5	completion	completion	NOUN
ma-9	83	6	lq(k	lq(k	NOUN
ma-9	83	7	,	,	PUNCT
ma-9	83	8	h	h	NOUN
ma-9	83	9	)	)	PUNCT
ma-9	83	10	of	of	ADP
ma-9	83	11	l(k	l(k	PROPN
ma-9	83	12	,	,	PUNCT
ma-9	83	13	h	h	NOUN
ma-9	83	14	)	)	PUNCT
ma-9	83	15	with	with	ADP
ma-9	83	16	respect	respect	NOUN
ma-9	83	17	tothe	tothe	NOUN
ma-9	83	18	topology	topology	NOUN
ma-9	83	19	induced	induce	VERB
ma-9	83	20	by	by	ADP
ma-9	83	21	the	the	DET
ma-9	83	22	norm	norm	NOUN
ma-9	83	23	∥.∥q	∥.∥q	PROPN
ma-9	83	24	,	,	PUNCT
ma-9	83	25	where	where	SCONJ
ma-9	83	26	∥∥φ∥∥2	∥∥φ∥∥2	PRON
ma-9	83	27	q	q	X
ma-9	83	28	=	=	SYM
ma-9	83	29	〈	〈	PROPN
ma-9	83	30	φ	φ	PROPN
ma-9	83	31	,	,	PUNCT
ma-9	83	32	φ	φ	PROPN
ma-9	83	33	〉	〉	PROPN
ma-9	83	34	is	be	AUX
ma-9	83	35	a	a	DET
ma-9	83	36	hilbert	hilbert	NOUN
ma-9	83	37	space.let	space.let	X
ma-9	83	38	t	t	PROPN
ma-9	83	39	∈	∈	PROPN
ma-9	83	40	(	(	PUNCT
ma-9	83	41	t0,+∞	t0,+∞	NUM
ma-9	83	42	)	)	PUNCT
ma-9	83	43	,	,	PUNCT
ma-9	83	44	j	j	NOUN
ma-9	83	45	:	:	PUNCT
ma-9	83	46	=	=	PUNCT
ma-9	84	1	[	[	X
ma-9	84	2	t0	t0	PROPN
ma-9	84	3	,	,	PUNCT
ma-9	84	4	t	t	X
ma-9	84	5	]	]	PUNCT
ma-9	84	6	,	,	PUNCT
ma-9	84	7	jk	jk	X
ma-9	84	8	=	=	PUNCT
ma-9	85	1	[	[	X
ma-9	85	2	ξk	ξk	ADP
ma-9	85	3	,	,	PUNCT
ma-9	85	4	ξk+1	ξk+1	NUM
ma-9	85	5	)	)	PUNCT
ma-9	85	6	,	,	PUNCT
ma-9	85	7	k	k	X
ma-9	85	8	=	=	SYM
ma-9	85	9	0	0	NUM
ma-9	85	10	,	,	PUNCT
ma-9	85	11	1	1	NUM
ma-9	85	12	,	,	PUNCT
ma-9	85	13	·	·	PUNCT
ma-9	85	14	·	·	PUNCT
ma-9	85	15	·	·	PUNCT
ma-9	85	16	,	,	PUNCT
ma-9	85	17	j̃	j̃	PROPN
ma-9	85	18	=	=	PUNCT
ma-9	85	19	{	{	PUNCT
ma-9	85	20	t	t	NOUN
ma-9	85	21	:	:	PUNCT
ma-9	85	22	t	t	PROPN
ma-9	85	23	∈	∈	PROPN
ma-9	85	24	j	j	PROPN
ma-9	85	25	,	,	PUNCT
ma-9	85	26	t	t	PROPN
ma-9	85	27	6=	6=	PROPN
ma-9	86	1	ξk	ξk	ADP
ma-9	86	2	,	,	PUNCT
ma-9	86	3	k	k	PROPN
ma-9	86	4	=	=	SYM
ma-9	86	5	1	1	NUM
ma-9	86	6	,	,	PUNCT
ma-9	86	7	2	2	NUM
ma-9	86	8	,	,	PUNCT
ma-9	86	9	·	·	PUNCT
ma-9	86	10	·	·	PUNCT
ma-9	86	11	·	·	PUNCT
ma-9	86	12	}	}	PUNCT
ma-9	86	13	.	.	PUNCT
ma-9	87	1	l2(ω	l2(ω	ADV
ma-9	87	2	,	,	PUNCT
ma-9	87	3	h	h	NOUN
ma-9	87	4	)	)	PUNCT
ma-9	87	5	be	be	VERB
ma-9	87	6	the	the	DET
ma-9	87	7	collection	collection	NOUN
ma-9	87	8	of	of	ADP
ma-9	87	9	square	square	ADJ
ma-9	87	10	integrable	integrable	ADJ
ma-9	87	11	=	=	PROPN
ma-9	87	12	t	t	NOUN
ma-9	87	13	-	-	PUNCT
ma-9	87	14	measurable	measurable	ADJ
ma-9	87	15	,	,	PUNCT
ma-9	87	16	h	h	NOUN
ma-9	87	17	-	-	PUNCT
ma-9	87	18	valued	value	VERB
ma-9	87	19	random	random	ADJ
ma-9	87	20	variables	variable	NOUN
ma-9	87	21	definedby	definedby	ADV
ma-9	87	22	the	the	DET
ma-9	87	23	norm	norm	NOUN
ma-9	87	24	∥x∥l2	∥x∥l2	NOUN
ma-9	87	25	=	=	SYM
ma-9	87	26	(	(	PUNCT
ma-9	87	27	e∥x∥2	e∥x∥2	PROPN
ma-9	87	28	)	)	PUNCT
ma-9	87	29	12	12	NUM
ma-9	87	30	,	,	PUNCT
ma-9	87	31	the	the	DET
ma-9	87	32	expectation	expectation	NOUN
ma-9	87	33	being	be	AUX
ma-9	87	34	expressed	express	VERB
ma-9	87	35	by	by	ADP
ma-9	87	36	the	the	DET
ma-9	87	37	form	form	NOUN
ma-9	88	1	e∥x∥2	e∥x∥2	NOUN
ma-9	88	2	=	=	SYM
ma-9	88	3	∫ω	∫ω	NOUN
ma-9	88	4	∥x∥2	∥x∥2	NOUN
ma-9	88	5	dp.let	dp.let	PROPN
ma-9	88	6	pc	pc	NOUN
ma-9	88	7	(	(	PUNCT
ma-9	88	8	j	j	NOUN
ma-9	88	9	,	,	PUNCT
ma-9	88	10	l2(ω	l2(ω	PROPN
ma-9	88	11	,	,	PUNCT
ma-9	88	12	h	h	NOUN
ma-9	88	13	)	)	PUNCT
ma-9	88	14	)	)	PUNCT
ma-9	89	1	=	=	PRON
ma-9	89	2	{	{	PUNCT
ma-9	90	1	x	x	X
ma-9	90	2	:	:	PUNCT
ma-9	90	3	j	j	PROPN
ma-9	90	4	→	→	SYM
ma-9	90	5	l2(ω	l2(ω	PROPN
ma-9	90	6	,	,	PUNCT
ma-9	90	7	h	h	NOUN
ma-9	90	8	)	)	PUNCT
ma-9	90	9	}	}	PUNCT
ma-9	90	10	,	,	PUNCT
ma-9	90	11	x	x	PRON
ma-9	90	12	is	be	AUX
ma-9	90	13	continuous	continuous	ADJ
ma-9	90	14	on	on	ADP
ma-9	90	15	every	every	DET
ma-9	90	16	jk	jk	PROPN
ma-9	90	17	,	,	PUNCT
ma-9	90	18	and	and	CCONJ
ma-9	90	19	the	the	DET
ma-9	90	20	left	left	ADJ
ma-9	90	21	limits	limit	NOUN
ma-9	90	22	x(ξ−k	x(ξ−k	PROPN
ma-9	90	23	)	)	PUNCT
ma-9	90	24	,	,	PUNCT
ma-9	90	25	x	x	X
ma-9	90	26	′(ξ−k	′(ξ−k	NOUN
ma-9	90	27	)	)	PUNCT
ma-9	90	28	exist	exist	VERB
ma-9	90	29	k	k	X
ma-9	90	30	=	=	SYM
ma-9	90	31	1	1	NUM
ma-9	90	32	,	,	PUNCT
ma-9	90	33	2	2	NUM
ma-9	90	34	,	,	PUNCT
ma-9	90	35	·	·	PUNCT
ma-9	90	36	·	·	PUNCT
ma-9	90	37	·	·	PUNCT
ma-9	90	38	be	be	AUX
ma-9	90	39	a	a	DET
ma-9	90	40	piecewise	piecewise	NOUN
ma-9	90	41	continuous	continuous	ADJ
ma-9	90	42	space	space	NOUN
ma-9	90	43	.	.	PUNCT
ma-9	91	1	eur	eur	PROPN
ma-9	91	2	.	.	PUNCT
ma-9	92	1	j.	j.	PROPN
ma-9	92	2	math	math	PROPN
ma-9	92	3	.	.	PUNCT
ma-9	93	1	anal	anal	ADJ
ma-9	93	2	.	.	PUNCT
ma-9	94	1	1	1	NUM
ma-9	94	2	(	(	PUNCT
ma-9	94	3	2021	2021	NUM
ma-9	94	4	)	)	PUNCT
ma-9	94	5	4we	4we	NOUN
ma-9	94	6	may	may	AUX
ma-9	94	7	define	define	VERB
ma-9	94	8	the	the	DET
ma-9	94	9	space	space	NOUN
ma-9	94	10	c	c	NOUN
ma-9	94	11	=	=	SYM
ma-9	94	12	c	c	X
ma-9	94	13	(	(	PUNCT
ma-9	94	14	[	[	X
ma-9	94	15	−δ	−δ	ADJ
ma-9	94	16	,	,	PUNCT
ma-9	94	17	0],h	0],h	NUM
ma-9	94	18	)	)	PUNCT
ma-9	94	19	which	which	PRON
ma-9	94	20	contains	contain	VERB
ma-9	94	21	all	all	DET
ma-9	94	22	piecewise	piecewise	NOUN
ma-9	94	23	continuous	continuous	ADJ
ma-9	94	24	functionsmapping	functionsmappe	VERB
ma-9	94	25	from	from	ADP
ma-9	94	26	[	[	X
ma-9	94	27	−δ	−δ	ADJ
ma-9	94	28	,	,	PUNCT
ma-9	94	29	0	0	NUM
ma-9	94	30	]	]	PUNCT
ma-9	94	31	to	to	ADP
ma-9	94	32	h	h	NOUN
ma-9	94	33	with	with	ADP
ma-9	94	34	the	the	DET
ma-9	94	35	norm	norm	NOUN
ma-9	94	36	∥x∥t	∥x∥t	PROPN
ma-9	94	37	=	=	PUNCT
ma-9	94	38	sup	sup	NOUN
ma-9	94	39	t−δ≤s≤t	t−δ≤s≤t	NOUN
ma-9	94	40	∥∥x(s)∥∥	∥∥x(s)∥∥	PROPN
ma-9	94	41	for	for	ADP
ma-9	94	42	each	each	DET
ma-9	94	43	t	t	PROPN
ma-9	94	44	≥	≥	PROPN
ma-9	94	45	t0	t0	PROPN
ma-9	94	46	.	.	PUNCT
ma-9	95	1	b	b	X
ma-9	95	2	be	be	AUX
ma-9	95	3	the	the	DET
ma-9	95	4	banachspace	banachspace	NOUN
ma-9	95	5	,	,	PUNCT
ma-9	95	6	b	b	PROPN
ma-9	95	7	(	(	PUNCT
ma-9	95	8	[	[	X
ma-9	95	9	t0−δ	t0−δ	PROPN
ma-9	95	10	,	,	PUNCT
ma-9	95	11	t	t	X
ma-9	95	12	]	]	PUNCT
ma-9	95	13	,	,	PUNCT
ma-9	95	14	l2(ω	l2(ω	PROPN
ma-9	95	15	,	,	PUNCT
ma-9	95	16	h	h	NOUN
ma-9	95	17	)	)	PUNCT
ma-9	95	18	)	)	PUNCT
ma-9	95	19	consists	consist	VERB
ma-9	95	20	of	of	ADP
ma-9	95	21	continuous	continuous	ADJ
ma-9	95	22	,	,	PUNCT
ma-9	95	23	=	=	NOUN
ma-9	95	24	t	t	NOUN
ma-9	95	25	-	-	PUNCT
ma-9	95	26	measurable	measurable	NOUN
ma-9	95	27	,	,	PUNCT
ma-9	95	28	c	c	NOUN
ma-9	95	29	-	-	PUNCT
ma-9	95	30	valued	value	VERB
ma-9	95	31	processes	process	NOUN
ma-9	95	32	.	.	PUNCT
ma-9	96	1	the	the	DET
ma-9	96	2	normis	normis	NOUN
ma-9	96	3	defined	define	VERB
ma-9	96	4	by	by	ADP
ma-9	96	5	∥x∥b	∥x∥b	NOUN
ma-9	96	6	=	=	SYM
ma-9	96	7	(	(	PUNCT
ma-9	96	8	sup	sup	NOUN
ma-9	96	9	t∈j	t∈j	VERB
ma-9	96	10	e∥x∥2	e∥x∥2	PROPN
ma-9	96	11	t	t	PROPN
ma-9	96	12	)	)	PUNCT
ma-9	96	13	12	12	NUM
ma-9	96	14	.	.	PUNCT
ma-9	97	1	in	in	ADP
ma-9	97	2	(	(	PUNCT
ma-9	97	3	1.1	1.1	NUM
ma-9	97	4	)	)	PUNCT
ma-9	97	5	,	,	PUNCT
ma-9	97	6	ñ(dt	ñ(dt	ADV
ma-9	97	7	,	,	PUNCT
ma-9	97	8	du	du	NOUN
ma-9	97	9	)	)	PUNCT
ma-9	97	10	=	=	SYM
ma-9	97	11	n(dt	n(dt	NUM
ma-9	97	12	,	,	PUNCT
ma-9	97	13	du)−	du)−	PRON
ma-9	97	14	dtv	dtv	PROPN
ma-9	97	15	(	(	PUNCT
ma-9	97	16	du	du	NOUN
ma-9	97	17	)	)	PUNCT
ma-9	97	18	denotes	denote	VERB
ma-9	97	19	the	the	DET
ma-9	97	20	compensated	compensate	VERB
ma-9	97	21	poisson	poisson	NOUN
ma-9	97	22	measure	measure	NOUN
ma-9	97	23	independentof	independentof	NOUN
ma-9	97	24	ω(t	ω(t	NOUN
ma-9	97	25	)	)	PUNCT
ma-9	97	26	and	and	CCONJ
ma-9	97	27	n(dt	n(dt	NUM
ma-9	97	28	,	,	PUNCT
ma-9	97	29	du	du	NOUN
ma-9	97	30	)	)	PUNCT
ma-9	97	31	represents	represent	VERB
ma-9	97	32	the	the	DET
ma-9	97	33	poisson	poisson	NOUN
ma-9	97	34	counting	counting	NOUN
ma-9	97	35	measure	measure	NOUN
ma-9	97	36	associated	associate	VERB
ma-9	97	37	with	with	ADP
ma-9	97	38	a	a	DET
ma-9	97	39	characteristicmeasure	characteristicmeasure	NOUN
ma-9	97	40	v	v	NOUN
ma-9	97	41	.	.	PUNCT
ma-9	98	1	for	for	ADP
ma-9	98	2	a	a	DET
ma-9	98	3	basic	basic	ADJ
ma-9	98	4	study	study	NOUN
ma-9	98	5	on	on	ADP
ma-9	98	6	the	the	DET
ma-9	98	7	poisson	poisson	NOUN
ma-9	98	8	jumps	jump	VERB
ma-9	98	9	we	we	PRON
ma-9	98	10	refer	refer	VERB
ma-9	98	11	to	to	ADP
ma-9	98	12	the	the	DET
ma-9	98	13	book	book	NOUN
ma-9	98	14	by	by	ADP
ma-9	98	15	[	[	X
ma-9	98	16	27].subsequently	27].subsequently	ADV
ma-9	98	17	,	,	PUNCT
ma-9	98	18	we	we	PRON
ma-9	98	19	introduce	introduce	VERB
ma-9	98	20	certain	certain	ADJ
ma-9	98	21	definitions	definition	NOUN
ma-9	98	22	of	of	ADP
ma-9	98	23	sine	sine	NOUN
ma-9	98	24	and	and	CCONJ
ma-9	98	25	cosine	cosine	NOUN
ma-9	99	1	operators.a	operators.a	PROPN
ma-9	99	2	bounded	bound	VERB
ma-9	99	3	linear	linear	PROPN
ma-9	99	4	operators	operators	PROPN
ma-9	99	5	family	family	PROPN
ma-9	99	6	{	{	PUNCT
ma-9	99	7	c(t	c(t	PROPN
ma-9	99	8	)	)	PUNCT
ma-9	99	9	,	,	PUNCT
ma-9	99	10	t	t	PROPN
ma-9	99	11	∈	∈	PROPN
ma-9	99	12	r	r	X
ma-9	99	13	}	}	PUNCT
ma-9	99	14	is	be	AUX
ma-9	99	15	called	call	VERB
ma-9	99	16	a	a	DET
ma-9	99	17	strongly	strongly	ADV
ma-9	99	18	continuous	continuous	ADJ
ma-9	99	19	cosine	cosine	NOUN
ma-9	99	20	family	family	NOUN
ma-9	99	21	ifand	ifand	NOUN
ma-9	99	22	only	only	ADV
ma-9	99	23	if(i	if(i	ADP
ma-9	99	24	)	)	PUNCT
ma-9	99	25	c(0	c(0	NOUN
ma-9	99	26	)	)	PUNCT
ma-9	100	1	=	=	SYM
ma-9	100	2	i	i	PRON
ma-9	100	3	(	(	PUNCT
ma-9	100	4	i	i	PRON
ma-9	100	5	is	be	AUX
ma-9	100	6	the	the	DET
ma-9	100	7	identity	identity	NOUN
ma-9	100	8	operator	operator	NOUN
ma-9	100	9	in	in	ADP
ma-9	100	10	h);(ii	h);(ii	NOUN
ma-9	100	11	)	)	PUNCT
ma-9	101	1	c(t)x	c(t)x	PROPN
ma-9	101	2	is	be	AUX
ma-9	101	3	continuous	continuous	ADJ
ma-9	101	4	in	in	ADP
ma-9	101	5	t	t	PROPN
ma-9	101	6	,	,	PUNCT
ma-9	101	7	for	for	ADP
ma-9	101	8	all	all	DET
ma-9	101	9	x	x	SYM
ma-9	101	10	∈	∈	PROPN
ma-9	101	11	h;(iii	h;(iii	NOUN
ma-9	101	12	)	)	PUNCT
ma-9	101	13	c(t	c(t	PROPN
ma-9	101	14	+	+	NUM
ma-9	101	15	s	s	X
ma-9	101	16	)	)	PUNCT
ma-9	101	17	+	+	CCONJ
ma-9	101	18	c(t	c(t	PROPN
ma-9	101	19	−	−	PROPN
ma-9	101	20	s	s	PART
ma-9	101	21	)	)	PUNCT
ma-9	101	22	=	=	PUNCT
ma-9	102	1	2c(t)c(s	2c(t)c(s	X
ma-9	102	2	)	)	PUNCT
ma-9	102	3	for	for	ADP
ma-9	102	4	all	all	DET
ma-9	102	5	t	t	PROPN
ma-9	102	6	,	,	PUNCT
ma-9	102	7	s	s	VERB
ma-9	102	8	∈	∈	PROPN
ma-9	102	9	r.the	r.the	DET
ma-9	102	10	corresponding	correspond	VERB
ma-9	102	11	strongly	strongly	ADV
ma-9	102	12	continuous	continuous	ADJ
ma-9	102	13	sine	sine	ADJ
ma-9	102	14	family	family	NOUN
ma-9	102	15	{	{	PUNCT
ma-9	102	16	s(t	s(t	PROPN
ma-9	102	17	)	)	PUNCT
ma-9	102	18	,	,	PUNCT
ma-9	102	19	t	t	PROPN
ma-9	102	20	∈	∈	PROPN
ma-9	103	1	r	r	X
ma-9	103	2	}	}	PUNCT
ma-9	103	3	is	be	AUX
ma-9	103	4	defined	define	VERB
ma-9	103	5	by	by	ADP
ma-9	103	6	s(t)x	s(t)x	PROPN
ma-9	103	7	=	=	SYM
ma-9	103	8	∫	∫	PROPN
ma-9	103	9	t	t	PROPN
ma-9	103	10	0	0	NUM
ma-9	103	11	c(s)xds	c(s)xds	PROPN
ma-9	103	12	,	,	PUNCT
ma-9	103	13	x	x	SYM
ma-9	103	14	∈	∈	PROPN
ma-9	103	15	h	h	NOUN
ma-9	103	16	,	,	PUNCT
ma-9	103	17	t	t	PROPN
ma-9	103	18	∈	∈	PROPN
ma-9	103	19	r	r	NOUN
ma-9	103	20	then	then	ADV
ma-9	103	21	the	the	DET
ma-9	103	22	following	follow	VERB
ma-9	103	23	property	property	NOUN
ma-9	103	24	holds	hold	VERB
ma-9	103	25	:	:	PUNCT
ma-9	103	26	a	a	DET
ma-9	103	27	∫	∫	PROPN
ma-9	103	28	t	t	PROPN
ma-9	103	29	t0	t0	PROPN
ma-9	103	30	s(s)xds	s(s)xds	PROPN
ma-9	103	31	=	=	PUNCT
ma-9	104	1	[	[	X
ma-9	104	2	c(t)−	c(t)−	PROPN
ma-9	104	3	c(t0	c(t0	PROPN
ma-9	104	4	)	)	PUNCT
ma-9	104	5	]	]	PUNCT
ma-9	105	1	x	x	X
ma-9	105	2	lemma	lemma	PROPN
ma-9	105	3	2.1	2.1	NUM
ma-9	105	4	.	.	PUNCT
ma-9	106	1	[	[	X
ma-9	106	2	18	18	NUM
ma-9	106	3	]	]	X
ma-9	106	4	let	let	VERB
ma-9	106	5	{	{	PUNCT
ma-9	106	6	c(t	c(t	PROPN
ma-9	106	7	)	)	PUNCT
ma-9	106	8	,	,	PUNCT
ma-9	106	9	t	t	PROPN
ma-9	106	10	∈	∈	PROPN
ma-9	106	11	r	r	AUX
ma-9	106	12	}	}	PUNCT
ma-9	106	13	be	be	AUX
ma-9	106	14	a	a	DET
ma-9	106	15	strongly	strongly	ADV
ma-9	106	16	continuous	continuous	ADJ
ma-9	106	17	cosine	cosine	NOUN
ma-9	106	18	family	family	NOUN
ma-9	106	19	in	in	ADP
ma-9	106	20	h	h	NOUN
ma-9	106	21	,	,	PUNCT
ma-9	106	22	then	then	ADV
ma-9	106	23	for	for	ADP
ma-9	106	24	all	all	DET
ma-9	106	25	s	s	PROPN
ma-9	106	26	,	,	PUNCT
ma-9	106	27	t	t	PROPN
ma-9	106	28	∈	∈	PROPN
ma-9	106	29	r	r	NOUN
ma-9	106	30	,	,	PUNCT
ma-9	106	31	the	the	DET
ma-9	106	32	following	follow	VERB
ma-9	106	33	results	result	NOUN
ma-9	106	34	are	be	AUX
ma-9	106	35	true	true	ADJ
ma-9	106	36	:	:	PUNCT
ma-9	106	37	(	(	PUNCT
ma-9	106	38	i	i	NOUN
ma-9	106	39	)	)	PUNCT
ma-9	106	40	c(t	c(t	PROPN
ma-9	106	41	)	)	PUNCT
ma-9	106	42	=	=	SYM
ma-9	106	43	c(−t	c(−t	NOUN
ma-9	106	44	)	)	PUNCT
ma-9	106	45	;	;	PUNCT
ma-9	106	46	(	(	PUNCT
ma-9	106	47	ii	ii	NOUN
ma-9	106	48	)	)	PUNCT
ma-9	106	49	s(s+	s(s+	NOUN
ma-9	106	50	t	t	PROPN
ma-9	106	51	)	)	PUNCT
ma-9	107	1	+	+	CCONJ
ma-9	107	2	s(s−	s(s−	PROPN
ma-9	107	3	t	t	PROPN
ma-9	107	4	)	)	PUNCT
ma-9	107	5	=	=	SYM
ma-9	108	1	2s(s)c(t	2s(s)c(t	NOUN
ma-9	108	2	)	)	PUNCT
ma-9	108	3	;	;	PUNCT
ma-9	108	4	(	(	PUNCT
ma-9	108	5	iii	iii	NOUN
ma-9	108	6	)	)	PUNCT
ma-9	108	7	s(s+	s(s+	NOUN
ma-9	108	8	t	t	PROPN
ma-9	108	9	)	)	PUNCT
ma-9	108	10	=	=	SYM
ma-9	108	11	s(s)c(t	s(s)c(t	NOUN
ma-9	108	12	)	)	PUNCT
ma-9	109	1	+	+	CCONJ
ma-9	109	2	s(t)c(s	s(t)c(	NOUN
ma-9	109	3	)	)	PUNCT
ma-9	109	4	;	;	PUNCT
ma-9	109	5	(	(	PUNCT
ma-9	109	6	iv	iv	X
ma-9	109	7	)	)	PUNCT
ma-9	109	8	s(t	s(t	PROPN
ma-9	109	9	)	)	PUNCT
ma-9	109	10	=	=	SYM
ma-9	109	11	−s(−t	−s(−t	NOUN
ma-9	109	12	)	)	PUNCT
ma-9	109	13	;	;	PUNCT
ma-9	109	14	(	(	PUNCT
ma-9	109	15	v	v	X
ma-9	109	16	)	)	PUNCT
ma-9	109	17	c(t	c(t	PROPN
ma-9	109	18	+	+	NUM
ma-9	109	19	s	s	X
ma-9	109	20	)	)	PUNCT
ma-9	109	21	+	+	NUM
ma-9	109	22	c(s−	c(s−	PROPN
ma-9	109	23	t	t	PROPN
ma-9	109	24	)	)	PUNCT
ma-9	109	25	=	=	SYM
ma-9	110	1	2c(s)c(t	2c(s)c(t	NOUN
ma-9	110	2	)	)	PUNCT
ma-9	110	3	;	;	PUNCT
ma-9	110	4	(	(	PUNCT
ma-9	110	5	vi	vi	X
ma-9	110	6	)	)	PUNCT
ma-9	110	7	c(t	c(t	PROPN
ma-9	110	8	+	+	PROPN
ma-9	110	9	s)−	s)−	PROPN
ma-9	110	10	c(t	c(t	PROPN
ma-9	110	11	−	−	PROPN
ma-9	110	12	s	s	PART
ma-9	110	13	)	)	PUNCT
ma-9	110	14	=	=	SYM
ma-9	110	15	2as(t)s(s	2as(t)s(s	NUM
ma-9	110	16	)	)	PUNCT
ma-9	110	17	.	.	PUNCT
ma-9	111	1	before	before	ADP
ma-9	111	2	investigating	investigate	VERB
ma-9	111	3	mild	mild	ADJ
ma-9	111	4	solution	solution	NOUN
ma-9	111	5	(	(	PUNCT
ma-9	111	6	1.1	1.1	NUM
ma-9	111	7	)	)	PUNCT
ma-9	111	8	,	,	PUNCT
ma-9	111	9	we	we	PRON
ma-9	111	10	consider	consider	VERB
ma-9	111	11	the	the	DET
ma-9	111	12	second	second	ADJ
ma-9	111	13	-	-	PUNCT
ma-9	111	14	order	order	NOUN
ma-9	111	15	neutral	neutral	ADJ
ma-9	111	16	functional	functional	ADJ
ma-9	111	17	differ	differ	NOUN
ma-9	111	18	-	-	PUNCT
ma-9	111	19	ential	ential	NOUN
ma-9	111	20	equation	equation	NOUN
ma-9	111	21	,	,	PUNCT
ma-9	111	22	which	which	PRON
ma-9	111	23	is	be	AUX
ma-9	111	24	given	give	VERB
ma-9	111	25	byd[u′(t)−	byd[u′(t)−	PROPN
ma-9	111	26	g(t	g(t	PROPN
ma-9	111	27	,	,	PUNCT
ma-9	111	28	u(t	u(t	NOUN
ma-9	111	29	)	)	PUNCT
ma-9	111	30	)	)	PUNCT
ma-9	111	31	]	]	PUNCT
ma-9	112	1	=	=	PUNCT
ma-9	112	2	autdt	autdt	PROPN
ma-9	112	3	+	+	CCONJ
ma-9	112	4	f(t	f(t	NOUN
ma-9	112	5	,	,	PUNCT
ma-9	112	6	ut)dt	ut)dt	PRON
ma-9	112	7	,	,	PUNCT
ma-9	112	8	t	t	PROPN
ma-9	112	9	≥	≥	NUM
ma-9	112	10	0	0	NUM
ma-9	112	11	,	,	PUNCT
ma-9	112	12	u0	u0	ADJ
ma-9	112	13	=	=	PROPN
ma-9	112	14	φ	φ	PROPN
ma-9	112	15	∈	∈	PROPN
ma-9	112	16	c	c	X
ma-9	112	17	,	,	PUNCT
ma-9	112	18	u′(0	u′(0	PROPN
ma-9	112	19	)	)	PUNCT
ma-9	112	20	=	=	PUNCT
ma-9	112	21	φ	φ	PROPN
ma-9	112	22	∈	∈	PROPN
ma-9	112	23	h	h	NOUN
ma-9	112	24	,	,	PUNCT
ma-9	112	25	t	t	PROPN
ma-9	112	26	∈	∈	PROPN
ma-9	112	27	(	(	PUNCT
ma-9	112	28	−r	−r	ADJ
ma-9	112	29	,	,	PUNCT
ma-9	112	30	0	0	NUM
ma-9	112	31	]	]	PUNCT
ma-9	112	32	,	,	PUNCT
ma-9	112	33	(	(	PUNCT
ma-9	112	34	2.1	2.1	NUM
ma-9	112	35	)	)	PUNCT
ma-9	112	36	where	where	SCONJ
ma-9	112	37	a	a	PRON
ma-9	112	38	is	be	AUX
ma-9	112	39	the	the	DET
ma-9	112	40	infinitesimal	infinitesimal	ADJ
ma-9	112	41	generator	generator	NOUN
ma-9	112	42	of	of	ADP
ma-9	112	43	a	a	DET
ma-9	112	44	strongly	strongly	ADV
ma-9	112	45	continuous	continuous	ADJ
ma-9	112	46	cosine	cosine	NOUN
ma-9	112	47	family	family	NOUN
ma-9	112	48	{	{	PUNCT
ma-9	112	49	c(t	c(t	PROPN
ma-9	112	50	)	)	PUNCT
ma-9	112	51	,	,	PUNCT
ma-9	112	52	t	t	PROPN
ma-9	112	53	∈	∈	PROPN
ma-9	112	54	r+	r+	PUNCT
ma-9	112	55	}	}	PUNCT
ma-9	112	56	andthe	andthe	ADJ
ma-9	112	57	functions	function	NOUN
ma-9	112	58	g	g	NOUN
ma-9	112	59	,	,	PUNCT
ma-9	112	60	f	f	PROPN
ma-9	112	61	∈	∈	PROPN
ma-9	112	62	l1(0	l1(0	PROPN
ma-9	112	63	,	,	PUNCT
ma-9	112	64	t	t	PROPN
ma-9	112	65	;	;	PUNCT
ma-9	112	66	h	h	X
ma-9	112	67	)	)	PUNCT
ma-9	112	68	.	.	PUNCT
ma-9	113	1	eur	eur	PROPN
ma-9	113	2	.	.	PUNCT
ma-9	114	1	j.	j.	PROPN
ma-9	114	2	math	math	PROPN
ma-9	114	3	.	.	PUNCT
ma-9	115	1	anal	anal	ADJ
ma-9	115	2	.	.	PUNCT
ma-9	116	1	1	1	NUM
ma-9	116	2	(	(	PUNCT
ma-9	116	3	2021	2021	NUM
ma-9	116	4	)	)	PUNCT
ma-9	116	5	5	5	NUM
ma-9	116	6	lemma	lemma	PROPN
ma-9	116	7	2.2	2.2	NUM
ma-9	116	8	.	.	PUNCT
ma-9	117	1	[	[	X
ma-9	117	2	15	15	NUM
ma-9	117	3	]	]	X
ma-9	117	4	a	a	DET
ma-9	117	5	continuously	continuously	ADV
ma-9	117	6	differentiable	differentiable	ADJ
ma-9	117	7	function	function	NOUN
ma-9	117	8	u(t	u(t	NOUN
ma-9	117	9	)	)	PUNCT
ma-9	117	10	:	:	PUNCT
ma-9	118	1	[	[	X
ma-9	118	2	0	0	NUM
ma-9	118	3	,	,	PUNCT
ma-9	118	4	t	t	X
ma-9	118	5	]	]	PUNCT
ma-9	118	6	→	→	SYM
ma-9	118	7	h	h	NOUN
ma-9	118	8	is	be	AUX
ma-9	118	9	called	call	VERB
ma-9	118	10	the	the	DET
ma-9	118	11	mild	mild	ADJ
ma-9	118	12	solution	solution	NOUN
ma-9	118	13	for	for	ADP
ma-9	118	14	the	the	DET
ma-9	118	15	cauchy	cauchy	ADJ
ma-9	118	16	problem	problem	NOUN
ma-9	118	17	(	(	PUNCT
ma-9	118	18	2.1	2.1	NUM
ma-9	118	19	)	)	PUNCT
ma-9	118	20	,	,	PUNCT
ma-9	118	21	if	if	SCONJ
ma-9	118	22	it	it	PRON
ma-9	118	23	satisfies	satisfy	VERB
ma-9	118	24	,	,	PUNCT
ma-9	118	25	u(t	u(t	NOUN
ma-9	118	26	)	)	PUNCT
ma-9	118	27	=	=	SYM
ma-9	118	28	c(t)φ(0	c(t)φ(0	NOUN
ma-9	118	29	)	)	PUNCT
ma-9	119	1	+	+	CCONJ
ma-9	119	2	s(t)[φ	s(t)[φ	NOUN
ma-9	119	3	−	−	NOUN
ma-9	119	4	g(0	g(0	PROPN
ma-9	119	5	,	,	PUNCT
ma-9	119	6	φ	φ	NOUN
ma-9	119	7	)	)	PUNCT
ma-9	119	8	]	]	PUNCT
ma-9	120	1	+	+	CCONJ
ma-9	120	2	∫	∫	PROPN
ma-9	120	3	t	t	NOUN
ma-9	120	4	0	0	NUM
ma-9	120	5	c(t	c(t	PROPN
ma-9	120	6	−	−	PROPN
ma-9	120	7	s)g(s	s)g(s	NOUN
ma-9	120	8	,	,	PUNCT
ma-9	120	9	us)ds+	us)ds+	ADJ
ma-9	120	10	∫	∫	PROPN
ma-9	120	11	t	t	NOUN
ma-9	120	12	0	0	PROPN
ma-9	121	1	s(t	s(t	PROPN
ma-9	121	2	−	−	PROPN
ma-9	121	3	s)f(s	s)f(	NOUN
ma-9	121	4	,	,	PUNCT
ma-9	121	5	xs)ds	xs)ds	PROPN
ma-9	121	6	,	,	PUNCT
ma-9	121	7	t	t	PROPN
ma-9	121	8	≥	≥	NUM
ma-9	121	9	0	0	NUM
ma-9	121	10	,	,	PUNCT
ma-9	121	11	where	where	SCONJ
ma-9	121	12	s(t	s(t	NOUN
ma-9	121	13	)	)	PUNCT
ma-9	121	14	=	=	SYM
ma-9	122	1	12πi	12πi	NOUN
ma-9	122	2	∫	∫	X
ma-9	122	3	γ	γ	X
ma-9	122	4	eλtr(λ2;a)dλ	eλtr(λ2;a)dλ	PROPN
ma-9	122	5	;	;	PUNCT
ma-9	122	6	c(t	c(t	PROPN
ma-9	122	7	)	)	PUNCT
ma-9	122	8	=	=	SYM
ma-9	122	9	12πi	12πi	NOUN
ma-9	122	10	∫	∫	X
ma-9	122	11	γ	γ	X
ma-9	122	12	eλtλr(λ2;a)dλ	eλtλr(λ2;a)dλ	PROPN
ma-9	122	13	,	,	PUNCT
ma-9	122	14	and	and	CCONJ
ma-9	122	15	γ	γ	NOUN
ma-9	122	16	is	be	AUX
ma-9	122	17	a	a	DET
ma-9	122	18	suitable	suitable	ADJ
ma-9	122	19	path	path	NOUN
ma-9	122	20	.	.	PUNCT
ma-9	123	1	consider	consider	VERB
ma-9	123	2	the	the	DET
ma-9	123	3	linear	linear	ADJ
ma-9	123	4	second	second	ADJ
ma-9	123	5	-	-	PUNCT
ma-9	123	6	order	order	NOUN
ma-9	123	7	linear	linear	ADJ
ma-9	123	8	differential	differential	NOUN
ma-9	123	9	equation	equation	NOUN
ma-9	123	10	with	with	ADP
ma-9	123	11	impulse	impulse	ADJ
ma-9	123	12	conditions,	conditions,	NOUN
ma-9	123	13	u′′(t	u′′(t	NOUN
ma-9	123	14	)	)	PUNCT
ma-9	123	15	=	=	SYM
ma-9	123	16	au(t	au(t	PRON
ma-9	123	17	)	)	PUNCT
ma-9	124	1	+	+	CCONJ
ma-9	124	2	f(t	f(t	NOUN
ma-9	124	3	)	)	PUNCT
ma-9	124	4	,	,	PUNCT
ma-9	124	5	t	t	PROPN
ma-9	124	6	≥	≥	NUM
ma-9	124	7	0	0	NUM
ma-9	124	8	,	,	PUNCT
ma-9	124	9	t	t	PROPN
ma-9	124	10	6=	6=	PROPN
ma-9	124	11	tk	tk	PROPN
ma-9	124	12	,	,	PUNCT
ma-9	124	13	u(0	u(0	PROPN
ma-9	124	14	)	)	PUNCT
ma-9	125	1	=	=	PUNCT
ma-9	125	2	u0	u0	ADJ
ma-9	125	3	,	,	PUNCT
ma-9	125	4	u′(0	u′(0	PROPN
ma-9	125	5	)	)	PUNCT
ma-9	125	6	=	=	SYM
ma-9	125	7	v0	v0	NOUN
ma-9	125	8	,	,	PUNCT
ma-9	125	9	u(tk	u(tk	NOUN
ma-9	125	10	)	)	PUNCT
ma-9	125	11	=	=	SYM
ma-9	125	12	bku(t−k	bku(t−k	NOUN
ma-9	125	13	)	)	PUNCT
ma-9	125	14	,	,	PUNCT
ma-9	125	15	u′(tk	u′(tk	PROPN
ma-9	125	16	)	)	PUNCT
ma-9	125	17	=	=	SYM
ma-9	125	18	bku′(t−k	bku′(t−k	NOUN
ma-9	125	19	)	)	PUNCT
ma-9	125	20	,	,	PUNCT
ma-9	125	21	k	k	PROPN
ma-9	125	22	=	=	SYM
ma-9	125	23	1	1	NUM
ma-9	125	24	,	,	PUNCT
ma-9	125	25	2	2	NUM
ma-9	125	26	,	,	PUNCT
ma-9	125	27	·	·	PUNCT
ma-9	125	28	·	·	PUNCT
ma-9	125	29	·	·	PUNCT
ma-9	125	30	,	,	PUNCT
ma-9	125	31	(	(	PUNCT
ma-9	125	32	2.2	2.2	NUM
ma-9	125	33	)	)	PUNCT
ma-9	126	1	where	where	SCONJ
ma-9	126	2	0	0	NUM
ma-9	126	3	=	=	SYM
ma-9	126	4	t0	t0	PROPN
ma-9	126	5	<	<	X
ma-9	126	6	t1	t1	NOUN
ma-9	126	7	<	<	X
ma-9	126	8	t2	t2	PROPN
ma-9	126	9	<	<	X
ma-9	126	10	·	·	PUNCT
ma-9	126	11	·	·	PUNCT
ma-9	126	12	·	·	PUNCT
ma-9	127	1	<	<	X
ma-9	127	2	tk	tk	X
ma-9	127	3	<	<	X
ma-9	127	4	·	·	PUNCT
ma-9	127	5	·	·	PUNCT
ma-9	127	6	·	·	PUNCT
ma-9	127	7	,	,	PUNCT
ma-9	127	8	{	{	PUNCT
ma-9	127	9	tk	tk	PROPN
ma-9	127	10	,	,	PUNCT
ma-9	127	11	k	k	PROPN
ma-9	127	12	≥	≥	NUM
ma-9	127	13	1	1	NUM
ma-9	127	14	}	}	PUNCT
ma-9	127	15	is	be	AUX
ma-9	127	16	a	a	DET
ma-9	127	17	sequence	sequence	NOUN
ma-9	127	18	of	of	ADP
ma-9	127	19	fixed	fix	VERB
ma-9	127	20	impulsive	impulsive	ADJ
ma-9	127	21	points	point	NOUN
ma-9	127	22	,	,	PUNCT
ma-9	127	23	f(t	f(t	PROPN
ma-9	127	24	)	)	PUNCT
ma-9	127	25	:	:	PUNCT
ma-9	128	1	[	[	X
ma-9	128	2	0	0	NUM
ma-9	128	3	,	,	PUNCT
ma-9	128	4	t	t	NOUN
ma-9	128	5	)	)	PUNCT
ma-9	128	6	→	→	SYM
ma-9	128	7	h	h	PROPN
ma-9	128	8	is	be	AUX
ma-9	128	9	an	an	DET
ma-9	128	10	integrable	integrable	ADJ
ma-9	128	11	function	function	NOUN
ma-9	128	12	.	.	PUNCT
ma-9	129	1	lemma	lemma	PROPN
ma-9	129	2	2.3	2.3	NUM
ma-9	129	3	.	.	PUNCT
ma-9	130	1	the	the	DET
ma-9	130	2	piecewise	piecewise	NOUN
ma-9	130	3	continuous	continuous	ADJ
ma-9	130	4	differentiable	differentiable	ADJ
ma-9	130	5	function	function	NOUN
ma-9	130	6	u(t	u(t	NOUN
ma-9	130	7	)	)	PUNCT
ma-9	130	8	:	:	PUNCT
ma-9	131	1	[	[	X
ma-9	131	2	0	0	NUM
ma-9	131	3	,	,	PUNCT
ma-9	131	4	t	t	X
ma-9	131	5	]	]	PUNCT
ma-9	131	6	→	→	SYM
ma-9	131	7	h	h	NOUN
ma-9	131	8	is	be	AUX
ma-9	131	9	a	a	DET
ma-9	131	10	mild	mild	ADJ
ma-9	131	11	solution	solution	NOUN
ma-9	131	12	of	of	ADP
ma-9	131	13	(	(	PUNCT
ma-9	131	14	2.2	2.2	NUM
ma-9	131	15	)	)	PUNCT
ma-9	131	16	,	,	PUNCT
ma-9	131	17	if	if	SCONJ
ma-9	131	18	and	and	CCONJ
ma-9	131	19	only	only	ADV
ma-9	131	20	if	if	SCONJ
ma-9	131	21	x(t	x(t	NOUN
ma-9	131	22	)	)	PUNCT
ma-9	131	23	satisfies	satisfy	VERB
ma-9	131	24	the	the	DET
ma-9	131	25	integral	integral	ADJ
ma-9	131	26	equation	equation	NOUN
ma-9	131	27	u(t	u(t	NOUN
ma-9	131	28	)	)	PUNCT
ma-9	131	29	=	=	PUNCT
ma-9	132	1	k∏	k∏	NOUN
ma-9	132	2	i=1	i=1	X
ma-9	132	3	bic(t)u0	bic(t)u0	ADV
ma-9	132	4	+	+	PUNCT
ma-9	132	5	k∏	k∏	PROPN
ma-9	132	6	i=1	i=1	PROPN
ma-9	132	7	bis(t)v0	bis(t)v0	NOUN
ma-9	132	8	+	+	CCONJ
ma-9	132	9	k∑	k∑	PROPN
ma-9	132	10	i=1	i=1	PROPN
ma-9	133	1	k∏	k∏	PROPN
ma-9	133	2	j	j	PROPN
ma-9	134	1	=	=	NOUN
ma-9	134	2	i	i	PRON
ma-9	134	3	bj	bj	VERB
ma-9	134	4	∫	∫	PROPN
ma-9	134	5	ti	ti	PROPN
ma-9	134	6	ti−1	ti−1	NOUN
ma-9	134	7	s(t	s(t	PROPN
ma-9	134	8	−	−	PROPN
ma-9	134	9	s)f(s)ds	s)f(s)ds	PROPN
ma-9	134	10	×	×	PROPN
ma-9	134	11	∫	∫	PROPN
ma-9	134	12	t	t	PROPN
ma-9	134	13	tk	tk	PROPN
ma-9	135	1	s(t	s(t	PROPN
ma-9	135	2	−	−	PROPN
ma-9	135	3	s)f(s)ds	s)f(s)ds	PROPN
ma-9	135	4	,	,	PUNCT
ma-9	135	5	t	t	PROPN
ma-9	135	6	∈	∈	PROPN
ma-9	136	1	[	[	X
ma-9	136	2	tk	tk	X
ma-9	136	3	,	,	PUNCT
ma-9	136	4	tk+1	tk+1	NUM
ma-9	136	5	)	)	PUNCT
ma-9	136	6	,	,	PUNCT
ma-9	136	7	k	k	PROPN
ma-9	136	8	=	=	SYM
ma-9	136	9	0	0	NUM
ma-9	136	10	,	,	PUNCT
ma-9	136	11	1	1	NUM
ma-9	136	12	,	,	PUNCT
ma-9	136	13	·	·	PUNCT
ma-9	136	14	·	·	PUNCT
ma-9	136	15	·	·	PUNCT
ma-9	136	16	.	.	PUNCT
ma-9	137	1	(	(	PUNCT
ma-9	137	2	2.3	2.3	NUM
ma-9	137	3	)	)	PUNCT
ma-9	137	4	proof	proof	NOUN
ma-9	137	5	.	.	PUNCT
ma-9	138	1	(	(	PUNCT
ma-9	138	2	i)for	i)for	PROPN
ma-9	138	3	t	t	PROPN
ma-9	138	4	∈	∈	PROPN
ma-9	139	1	[	[	X
ma-9	139	2	0	0	NUM
ma-9	139	3	,	,	PUNCT
ma-9	139	4	t1	t1	NOUN
ma-9	139	5	)	)	PUNCT
ma-9	139	6	,	,	PUNCT
ma-9	139	7	the	the	DET
ma-9	139	8	mild	mild	ADJ
ma-9	139	9	solution	solution	NOUN
ma-9	139	10	is	be	AUX
ma-9	139	11	studied	study	VERB
ma-9	139	12	in	in	ADP
ma-9	139	13	[	[	X
ma-9	139	14	17	17	NUM
ma-9	139	15	]	]	PUNCT
ma-9	139	16	,	,	PUNCT
ma-9	139	17	u(t	u(t	NOUN
ma-9	139	18	)	)	PUNCT
ma-9	139	19	=	=	VERB
ma-9	140	1	c(t)u0	c(t)u0	ADV
ma-9	140	2	+	+	CCONJ
ma-9	140	3	s(t)v0	s(t)v0	NOUN
ma-9	140	4	+	+	CCONJ
ma-9	140	5	∫	∫	PROPN
ma-9	140	6	t	t	PROPN
ma-9	140	7	0	0	NUM
ma-9	141	1	s(t	s(t	PROPN
ma-9	141	2	−	−	PROPN
ma-9	141	3	s)f(s)ds	s)f(s)ds	PROPN
ma-9	141	4	,	,	PUNCT
ma-9	141	5	t	t	PROPN
ma-9	141	6	∈	∈	PROPN
ma-9	142	1	[	[	X
ma-9	142	2	0	0	NUM
ma-9	142	3	,	,	PUNCT
ma-9	142	4	t1	t1	NOUN
ma-9	142	5	)	)	PUNCT
ma-9	142	6	.	.	PUNCT
ma-9	143	1	(	(	PUNCT
ma-9	143	2	ii	ii	NOUN
ma-9	143	3	)	)	PUNCT
ma-9	143	4	for	for	ADP
ma-9	143	5	t	t	PROPN
ma-9	143	6	∈	∈	PROPN
ma-9	144	1	[	[	X
ma-9	144	2	t1	t1	NOUN
ma-9	144	3	,	,	PUNCT
ma-9	144	4	t2	t2	NOUN
ma-9	144	5	)	)	PUNCT
ma-9	144	6	,	,	PUNCT
ma-9	144	7	we	we	PRON
ma-9	144	8	set	set	VERB
ma-9	144	9	u(t	u(t	NOUN
ma-9	144	10	)	)	PUNCT
ma-9	144	11	=	=	PUNCT
ma-9	144	12	c(t	c(t	PROPN
ma-9	144	13	−	−	NOUN
ma-9	144	14	t1)u(t1	t1)u(t1	NOUN
ma-9	144	15	)	)	PUNCT
ma-9	145	1	+	+	CCONJ
ma-9	145	2	s(t	s(t	PROPN
ma-9	145	3	−	−	NOUN
ma-9	145	4	t1)u′(t1	t1)u′(t1	NUM
ma-9	145	5	)	)	PUNCT
ma-9	146	1	+	+	CCONJ
ma-9	146	2	∫	∫	PROPN
ma-9	146	3	t	t	PROPN
ma-9	146	4	t1	t1	PROPN
ma-9	146	5	s(t	s(t	PROPN
ma-9	146	6	−	−	PROPN
ma-9	146	7	s)f(s)ds	s)f(s)ds	PROPN
ma-9	147	1	,	,	PUNCT
ma-9	147	2	t	t	PROPN
ma-9	147	3	∈	∈	PROPN
ma-9	148	1	[	[	X
ma-9	148	2	t1	t1	NOUN
ma-9	148	3	,	,	PUNCT
ma-9	148	4	t2	t2	NOUN
ma-9	148	5	)	)	PUNCT
ma-9	148	6	.	.	PUNCT
ma-9	149	1	(	(	PUNCT
ma-9	149	2	2.4	2.4	NUM
ma-9	149	3	)	)	PUNCT
ma-9	149	4	since	since	SCONJ
ma-9	149	5	,	,	PUNCT
ma-9	149	6	u(t1	u(t1	SYM
ma-9	149	7	)	)	PUNCT
ma-9	149	8	=	=	SYM
ma-9	149	9	b1u(t−1	b1u(t−1	PROPN
ma-9	149	10	)	)	PUNCT
ma-9	149	11	,	,	PUNCT
ma-9	149	12	u′(t1	u′(t1	PROPN
ma-9	149	13	)	)	PUNCT
ma-9	149	14	=	=	SYM
ma-9	149	15	b1u′(t−1	b1u′(t−1	PROPN
ma-9	149	16	)	)	PUNCT
ma-9	149	17	,	,	PUNCT
ma-9	149	18	and	and	CCONJ
ma-9	149	19	from	from	ADP
ma-9	149	20	(	(	PUNCT
ma-9	149	21	i	i	NOUN
ma-9	149	22	)	)	PUNCT
ma-9	149	23	we	we	PRON
ma-9	149	24	know	know	VERB
ma-9	149	25	u(t−1	u(t−1	PRON
ma-9	149	26	)	)	PUNCT
ma-9	149	27	=	=	SYM
ma-9	150	1	c(t1)u0	c(t1)u0	NOUN
ma-9	151	1	+	+	CCONJ
ma-9	151	2	s(t1)v0	s(t1)v0	NOUN
ma-9	151	3	+	+	CCONJ
ma-9	151	4	∫	∫	PROPN
ma-9	151	5	t1	t1	NOUN
ma-9	151	6	0	0	NUM
ma-9	151	7	s(t1	s(t1	NOUN
ma-9	151	8	−	−	PROPN
ma-9	151	9	s)f(s)ds	s)f(s)ds	NOUN
ma-9	151	10	;	;	PUNCT
ma-9	151	11	(	(	PUNCT
ma-9	151	12	2.5	2.5	NUM
ma-9	151	13	)	)	PUNCT
ma-9	151	14	u′(t−1	u′(t−1	NOUN
ma-9	151	15	)	)	PUNCT
ma-9	151	16	=	=	PUNCT
ma-9	152	1	as(t1)u0	as(t1)u0	ADV
ma-9	152	2	+	+	PUNCT
ma-9	152	3	c(t1)v0	c(t1)v0	PROPN
ma-9	152	4	+	+	CCONJ
ma-9	152	5	∫	∫	PROPN
ma-9	152	6	t1	t1	NOUN
ma-9	152	7	0	0	NUM
ma-9	152	8	c(t1	c(t1	PROPN
ma-9	152	9	−	−	PROPN
ma-9	152	10	s)f(s)ds	s)f(s)ds	PROPN
ma-9	152	11	.	.	PUNCT
ma-9	153	1	(	(	PUNCT
ma-9	153	2	2.6	2.6	NUM
ma-9	153	3	)	)	PUNCT
ma-9	153	4	eur	eur	PROPN
ma-9	153	5	.	.	PUNCT
ma-9	154	1	j.	j.	PROPN
ma-9	154	2	math	math	PROPN
ma-9	154	3	.	.	PUNCT
ma-9	155	1	anal	anal	ADJ
ma-9	155	2	.	.	PUNCT
ma-9	156	1	1	1	NUM
ma-9	156	2	(	(	PUNCT
ma-9	156	3	2021	2021	NUM
ma-9	156	4	)	)	PUNCT
ma-9	157	1	6thus	6thus	NUM
ma-9	157	2	,	,	PUNCT
ma-9	157	3	u(t	u(t	NOUN
ma-9	157	4	)	)	PUNCT
ma-9	157	5	=	=	SYM
ma-9	157	6	b1c(t	b1c(t	PROPN
ma-9	157	7	−	−	PROPN
ma-9	157	8	t1)c(t1)u0	t1)c(t1)u0	NOUN
ma-9	157	9	+	+	CCONJ
ma-9	157	10	b1s(t	b1s(t	PROPN
ma-9	157	11	−	−	PROPN
ma-9	157	12	t1)as(t1)u0	t1)as(t1)u0	PROPN
ma-9	157	13	+	+	PROPN
ma-9	157	14	b1c(t	b1c(t	NOUN
ma-9	157	15	−	−	NOUN
ma-9	157	16	t1)s(t1)v0	t1)s(t1)v0	NOUN
ma-9	157	17	+	+	CCONJ
ma-9	157	18	b1s(t	b1s(t	PROPN
ma-9	157	19	−	−	PROPN
ma-9	157	20	t1)c(t1)v0	t1)c(t1)v0	NOUN
ma-9	157	21	+	+	PROPN
ma-9	157	22	b1c(t	b1c(t	NOUN
ma-9	157	23	−	−	PROPN
ma-9	157	24	t1)∫	t1)∫	PROPN
ma-9	157	25	t1	t1	NOUN
ma-9	157	26	0	0	NUM
ma-9	158	1	s(t1	s(t1	NOUN
ma-9	158	2	−	−	PROPN
ma-9	158	3	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	158	4	b1s(t	b1s(t	PROPN
ma-9	158	5	−	−	PROPN
ma-9	159	1	t1)∫	t1)∫	PROPN
ma-9	159	2	t1	t1	NOUN
ma-9	159	3	0	0	NUM
ma-9	160	1	s(t1	s(t1	NOUN
ma-9	160	2	−	−	PROPN
ma-9	160	3	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	160	4	∫	∫	PROPN
ma-9	160	5	t	t	PROPN
ma-9	160	6	t1	t1	PROPN
ma-9	160	7	s(t	s(t	PROPN
ma-9	160	8	−	−	PROPN
ma-9	160	9	s)f(s)ds	s)f(s)ds	PROPN
ma-9	160	10	,	,	PUNCT
ma-9	160	11	t	t	PROPN
ma-9	160	12	∈	∈	PROPN
ma-9	161	1	[	[	X
ma-9	161	2	t1	t1	NOUN
ma-9	161	3	,	,	PUNCT
ma-9	161	4	t2	t2	NOUN
ma-9	161	5	)	)	PUNCT
ma-9	161	6	.	.	PUNCT
ma-9	162	1	applying	apply	VERB
ma-9	162	2	lemma	lemma	PROPN
ma-9	162	3	2.1	2.1	NUM
ma-9	162	4	,	,	PUNCT
ma-9	162	5	we	we	PRON
ma-9	162	6	get	get	VERB
ma-9	162	7	u(t	u(t	NOUN
ma-9	162	8	)	)	PUNCT
ma-9	162	9	=	=	PUNCT
ma-9	163	1	b1c(t)u0	b1c(t)u0	NOUN
ma-9	164	1	+	+	CCONJ
ma-9	164	2	b1s(t)v0	b1s(t)v0	NOUN
ma-9	164	3	+	+	CCONJ
ma-9	164	4	b1	b1	PROPN
ma-9	164	5	∫	∫	PROPN
ma-9	164	6	t1	t1	NOUN
ma-9	164	7	0	0	NUM
ma-9	164	8	s(t1	s(t1	NOUN
ma-9	164	9	−	−	PROPN
ma-9	164	10	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	164	11	∫	∫	PROPN
ma-9	164	12	t	t	PROPN
ma-9	164	13	t1	t1	PROPN
ma-9	164	14	s(t	s(t	PROPN
ma-9	164	15	−	−	PROPN
ma-9	164	16	s)f(s)ds	s)f(s)ds	PROPN
ma-9	164	17	,	,	PUNCT
ma-9	164	18	t	t	PROPN
ma-9	164	19	∈	∈	PROPN
ma-9	165	1	[	[	X
ma-9	165	2	t1	t1	NOUN
ma-9	165	3	,	,	PUNCT
ma-9	165	4	t2	t2	NOUN
ma-9	165	5	)	)	PUNCT
ma-9	165	6	.	.	PUNCT
ma-9	166	1	(	(	PUNCT
ma-9	166	2	iii	iii	X
ma-9	166	3	)	)	PUNCT
ma-9	166	4	for	for	ADP
ma-9	166	5	t	t	PROPN
ma-9	166	6	∈	∈	PROPN
ma-9	166	7	[	[	X
ma-9	166	8	t2	t2	NOUN
ma-9	166	9	,	,	PUNCT
ma-9	166	10	t3	t3	PROPN
ma-9	166	11	)	)	PUNCT
ma-9	166	12	,	,	PUNCT
ma-9	166	13	u(t	u(t	NOUN
ma-9	166	14	)	)	PUNCT
ma-9	166	15	=	=	SYM
ma-9	166	16	c(t	c(t	PROPN
ma-9	166	17	−	−	PROPN
ma-9	166	18	t2)u(t2	t2)u(t2	NOUN
ma-9	166	19	)	)	PUNCT
ma-9	167	1	+	+	CCONJ
ma-9	167	2	s(t	s(t	PROPN
ma-9	167	3	−	−	PROPN
ma-9	167	4	t2)u′(t2	t2)u′(t2	NUM
ma-9	167	5	)	)	PUNCT
ma-9	167	6	+	+	NUM
ma-9	167	7	∫	∫	PROPN
ma-9	167	8	t	t	PROPN
ma-9	167	9	t2	t2	PROPN
ma-9	167	10	s(t	s(t	PROPN
ma-9	167	11	−	−	PROPN
ma-9	167	12	s)f(s)ds=	s)f(s)ds=	NOUN
ma-9	167	13	c(t	c(t	PROPN
ma-9	167	14	−	−	PROPN
ma-9	167	15	t2)b2u(t−2	t2)b2u(t−2	PROPN
ma-9	167	16	)	)	PUNCT
ma-9	168	1	+	+	CCONJ
ma-9	168	2	s(t	s(t	PROPN
ma-9	168	3	−	−	NOUN
ma-9	168	4	t2)b2u′(t−2	t2)b2u′(t−2	NOUN
ma-9	168	5	)	)	PUNCT
ma-9	169	1	+	+	CCONJ
ma-9	169	2	∫	∫	PROPN
ma-9	169	3	t	t	PROPN
ma-9	169	4	t2	t2	PROPN
ma-9	169	5	s(t	s(t	PROPN
ma-9	169	6	−	−	PROPN
ma-9	169	7	s)f(s)ds	s)f(s)ds	PROPN
ma-9	169	8	.	.	PUNCT
ma-9	170	1	(	(	PUNCT
ma-9	170	2	2.7	2.7	NUM
ma-9	170	3	)	)	PUNCT
ma-9	170	4	from	from	ADP
ma-9	170	5	the	the	DET
ma-9	170	6	conclusions	conclusion	NOUN
ma-9	170	7	of	of	ADP
ma-9	170	8	(	(	PUNCT
ma-9	170	9	ii	ii	NOUN
ma-9	170	10	)	)	PUNCT
ma-9	170	11	,	,	PUNCT
ma-9	170	12	it	it	PRON
ma-9	170	13	is	be	AUX
ma-9	170	14	known	know	VERB
ma-9	170	15	that	that	SCONJ
ma-9	170	16	,	,	PUNCT
ma-9	170	17	u(t−2	u(t−2	NOUN
ma-9	170	18	)	)	PUNCT
ma-9	170	19	=	=	SYM
ma-9	170	20	b1c(t2)u0	b1c(t2)u0	NOUN
ma-9	171	1	+	+	NUM
ma-9	171	2	b1s(t2)v0	b1s(t2)v0	NOUN
ma-9	171	3	+	+	CCONJ
ma-9	171	4	b1	b1	PROPN
ma-9	171	5	∫	∫	PROPN
ma-9	171	6	t2	t2	PROPN
ma-9	171	7	0	0	NUM
ma-9	171	8	s(t2	s(t2	NOUN
ma-9	171	9	−	−	PROPN
ma-9	171	10	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	171	11	∫	∫	PROPN
ma-9	171	12	t2	t2	PROPN
ma-9	171	13	t1	t1	PROPN
ma-9	171	14	s(t2	s(t2	NOUN
ma-9	171	15	−	−	PROPN
ma-9	171	16	s)f(s)ds	s)f(s)ds	NOUN
ma-9	171	17	;	;	PUNCT
ma-9	171	18	(	(	PUNCT
ma-9	171	19	2.8	2.8	NUM
ma-9	171	20	)	)	PUNCT
ma-9	171	21	u′(t−2	u′(t−2	NOUN
ma-9	171	22	)	)	PUNCT
ma-9	172	1	=	=	SYM
ma-9	173	1	b1as(t2)u0	b1as(t2)u0	ADV
ma-9	173	2	+	+	NUM
ma-9	173	3	b1c(t2)v0	b1c(t2)v0	NOUN
ma-9	173	4	+	+	CCONJ
ma-9	173	5	b1	b1	PROPN
ma-9	173	6	∫	∫	PROPN
ma-9	173	7	t2	t2	PROPN
ma-9	173	8	0	0	NUM
ma-9	173	9	c(t2	c(t2	NOUN
ma-9	173	10	−	−	PROPN
ma-9	173	11	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	173	12	∫	∫	PROPN
ma-9	173	13	t2	t2	PROPN
ma-9	173	14	t1	t1	NOUN
ma-9	173	15	c(t2	c(t2	NOUN
ma-9	173	16	−	−	PROPN
ma-9	173	17	s)f(s)ds	s)f(s)ds	NOUN
ma-9	173	18	(	(	PUNCT
ma-9	173	19	2.9	2.9	NUM
ma-9	173	20	)	)	PUNCT
ma-9	173	21	along	along	ADP
ma-9	173	22	with	with	ADP
ma-9	173	23	(	(	PUNCT
ma-9	173	24	2.7	2.7	NUM
ma-9	173	25	)	)	PUNCT
ma-9	173	26	and	and	CCONJ
ma-9	173	27	using	use	VERB
ma-9	173	28	lemma	lemma	PROPN
ma-9	173	29	2.1	2.1	NUM
ma-9	173	30	,	,	PUNCT
ma-9	173	31	we	we	PRON
ma-9	173	32	have	have	VERB
ma-9	173	33	u(t	u(t	NOUN
ma-9	173	34	)	)	PUNCT
ma-9	173	35	=	=	PUNCT
ma-9	174	1	b2b1c(t)u0	b2b1c(t)u0	NOUN
ma-9	174	2	+	+	CCONJ
ma-9	174	3	b2b1s(t)v0	b2b1s(t)v0	NOUN
ma-9	175	1	+	+	CCONJ
ma-9	175	2	b2b1	b2b1	PROPN
ma-9	175	3	∫	∫	PROPN
ma-9	175	4	t1	t1	NOUN
ma-9	175	5	0	0	PROPN
ma-9	176	1	s(t	s(t	PROPN
ma-9	176	2	−	−	PROPN
ma-9	176	3	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	176	4	b2	b2	NOUN
ma-9	176	5	∫	∫	PROPN
ma-9	176	6	t2	t2	PROPN
ma-9	176	7	t1	t1	PROPN
ma-9	176	8	s(t	s(t	PROPN
ma-9	176	9	−	−	PROPN
ma-9	176	10	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	176	11	∫	∫	PROPN
ma-9	177	1	t2	t2	PROPN
ma-9	177	2	t1	t1	PROPN
ma-9	177	3	s(t	s(t	PROPN
ma-9	177	4	−	−	PROPN
ma-9	177	5	s)f(s)ds	s)f(s)ds	PROPN
ma-9	177	6	,	,	PUNCT
ma-9	177	7	t	t	PROPN
ma-9	177	8	∈	∈	PROPN
ma-9	178	1	[	[	X
ma-9	178	2	t2	t2	NOUN
ma-9	178	3	,	,	PUNCT
ma-9	178	4	t3	t3	PROPN
ma-9	178	5	)	)	PUNCT
ma-9	178	6	similarly	similarly	ADV
ma-9	178	7	,	,	PUNCT
ma-9	178	8	for	for	ADP
ma-9	178	9	all	all	DET
ma-9	178	10	t	t	NOUN
ma-9	178	11	∈	∈	PROPN
ma-9	179	1	[	[	X
ma-9	179	2	tk	tk	PROPN
ma-9	179	3	,	,	PUNCT
ma-9	179	4	tk−1	tk−1	PROPN
ma-9	179	5	)	)	PUNCT
ma-9	179	6	.	.	PUNCT
ma-9	180	1	x(t	x(t	PROPN
ma-9	180	2	)	)	PUNCT
ma-9	181	1	=	=	PUNCT
ma-9	182	1	k∏	k∏	NOUN
ma-9	182	2	i=1	i=1	X
ma-9	182	3	bic(t)u0	bic(t)u0	ADV
ma-9	182	4	+	+	PUNCT
ma-9	182	5	k∏	k∏	PROPN
ma-9	182	6	i=1	i=1	PROPN
ma-9	182	7	bis(t)v0	bis(t)v0	NOUN
ma-9	182	8	+	+	CCONJ
ma-9	182	9	k∑	k∑	PROPN
ma-9	182	10	i=1	i=1	PROPN
ma-9	183	1	k∏	k∏	PROPN
ma-9	183	2	j	j	PROPN
ma-9	184	1	=	=	NOUN
ma-9	184	2	i	i	PRON
ma-9	184	3	bj	bj	VERB
ma-9	184	4	∫	∫	PROPN
ma-9	184	5	ti	ti	PROPN
ma-9	184	6	ti−1	ti−1	NOUN
ma-9	184	7	s(t	s(t	PROPN
ma-9	184	8	−	−	PROPN
ma-9	184	9	s)f(s)ds+	s)f(s)ds+	PROPN
ma-9	184	10	∫	∫	PROPN
ma-9	185	1	t	t	PROPN
ma-9	185	2	ξk	ξk	ADP
ma-9	185	3	s(t	s(t	PROPN
ma-9	185	4	−	−	PROPN
ma-9	185	5	s)f(s)ds	s)f(s)ds	PROPN
ma-9	185	6	.	.	PUNCT
ma-9	186	1	�	�	PROPN
ma-9	186	2	by	by	ADP
ma-9	186	3	lemma	lemma	PROPN
ma-9	186	4	2.2	2.2	NUM
ma-9	186	5	,	,	PUNCT
ma-9	186	6	lemma	lemma	PROPN
ma-9	186	7	2.3	2.3	NUM
ma-9	186	8	the	the	DET
ma-9	186	9	mild	mild	ADJ
ma-9	186	10	solution	solution	NOUN
ma-9	186	11	of	of	ADP
ma-9	186	12	the	the	DET
ma-9	186	13	system	system	NOUN
ma-9	186	14	(	(	PUNCT
ma-9	186	15	1.1	1.1	NUM
ma-9	186	16	)	)	PUNCT
ma-9	186	17	applying	apply	VERB
ma-9	186	18	index	index	NOUN
ma-9	186	19	function	function	NOUN
ma-9	186	20	for	for	ADP
ma-9	186	21	t	t	PROPN
ma-9	186	22	∈	∈	PROPN
ma-9	186	23	j.	j.	PROPN
ma-9	186	24	definition	definition	NOUN
ma-9	186	25	2.1	2.1	NUM
ma-9	186	26	.	.	PUNCT
ma-9	187	1	for	for	ADP
ma-9	187	2	a	a	DET
ma-9	187	3	given	give	VERB
ma-9	187	4	t	t	PROPN
ma-9	187	5	∈	∈	PROPN
ma-9	187	6	(	(	PUNCT
ma-9	187	7	t0,+∞	t0,+∞	PROPN
ma-9	187	8	)	)	PUNCT
ma-9	187	9	,	,	PUNCT
ma-9	187	10	a	a	DET
ma-9	187	11	=	=	NUM
ma-9	187	12	-adapted	-adapted	ADJ
ma-9	187	13	process	process	NOUN
ma-9	187	14	function	function	NOUN
ma-9	187	15	{	{	PUNCT
ma-9	187	16	x	x	PROPN
ma-9	187	17	∈	∈	PROPN
ma-9	187	18	b	b	PROPN
ma-9	187	19	,	,	PUNCT
ma-9	187	20	t0	t0	PROPN
ma-9	187	21	−	−	PROPN
ma-9	187	22	δ	δ	PROPN
ma-9	187	23	≤	≤	PROPN
ma-9	187	24	t	t	PROPN
ma-9	187	25	≤	≤	PROPN
ma-9	187	26	t	t	PROPN
ma-9	187	27	}	}	PUNCT
ma-9	187	28	is	be	AUX
ma-9	187	29	called	call	VERB
ma-9	187	30	a	a	DET
ma-9	187	31	mild	mild	ADJ
ma-9	187	32	solution	solution	NOUN
ma-9	187	33	of	of	ADP
ma-9	187	34	system	system	NOUN
ma-9	187	35	(	(	PUNCT
ma-9	187	36	1.1	1.1	NUM
ma-9	187	37	)	)	PUNCT
ma-9	187	38	,	,	PUNCT
ma-9	187	39	if	if	SCONJ
ma-9	187	40	(	(	PUNCT
ma-9	187	41	i	i	NOUN
ma-9	187	42	)	)	PUNCT
ma-9	187	43	xt0(s	xt0(s	PROPN
ma-9	187	44	)	)	PUNCT
ma-9	187	45	=	=	PUNCT
ma-9	187	46	φ(s	φ(	VERB
ma-9	187	47	)	)	PUNCT
ma-9	187	48	∈	∈	PROPN
ma-9	187	49	l02(ω	l02(ω	PROPN
ma-9	187	50	,	,	PUNCT
ma-9	187	51	b	b	NOUN
ma-9	187	52	)	)	PUNCT
ma-9	187	53	for	for	ADP
ma-9	187	54	δ	δ	PROPN
ma-9	187	55	≤	≤	PROPN
ma-9	187	56	s	s	PART
ma-9	187	57	≤	≤	NOUN
ma-9	187	58	0	0	NUM
ma-9	187	59	;	;	PUNCT
ma-9	187	60	(	(	PUNCT
ma-9	187	61	ii	ii	NOUN
ma-9	187	62	)	)	PUNCT
ma-9	187	63	x	x	SYM
ma-9	187	64	′(t0	′(t0	NUM
ma-9	187	65	)	)	PUNCT
ma-9	187	66	=	=	SYM
ma-9	187	67	φ(t	φ(t	PROPN
ma-9	187	68	)	)	PUNCT
ma-9	187	69	∈	∈	NOUN
ma-9	187	70	l02(ω	l02(ω	ADJ
ma-9	187	71	,	,	PUNCT
ma-9	187	72	h	h	NOUN
ma-9	187	73	)	)	PUNCT
ma-9	187	74	for	for	ADP
ma-9	187	75	t	t	PROPN
ma-9	187	76	∈	∈	PROPN
ma-9	187	77	j	j	PROPN
ma-9	187	78	;	;	PUNCT
ma-9	187	79	(	(	PUNCT
ma-9	187	80	iii	iii	X
ma-9	187	81	)	)	PUNCT
ma-9	187	82	the	the	DET
ma-9	187	83	functions	function	NOUN
ma-9	187	84	f(s	f(s	ADV
ma-9	187	85	,	,	PUNCT
ma-9	187	86	xt	xt	ADJ
ma-9	187	87	)	)	PUNCT
ma-9	187	88	,	,	PUNCT
ma-9	187	89	g(s	g(s	PROPN
ma-9	187	90	,	,	PUNCT
ma-9	187	91	xt	xt	ADJ
ma-9	187	92	)	)	PUNCT
ma-9	187	93	,	,	PUNCT
ma-9	187	94	h(s	h(s	PROPN
ma-9	187	95	,	,	PUNCT
ma-9	187	96	xt	xt	NUM
ma-9	187	97	)	)	PUNCT
ma-9	187	98	and	and	CCONJ
ma-9	187	99	σ	σ	PROPN
ma-9	187	100	(	(	PUNCT
ma-9	187	101	s	s	PROPN
ma-9	187	102	,	,	PUNCT
ma-9	187	103	xs	xs	PROPN
ma-9	187	104	,	,	PUNCT
ma-9	187	105	u	u	NOUN
ma-9	187	106	)	)	PUNCT
ma-9	187	107	are	be	AUX
ma-9	187	108	integrable	integrable	ADJ
ma-9	187	109	,	,	PUNCT
ma-9	187	110	and	and	CCONJ
ma-9	187	111	for	for	ADP
ma-9	187	112	a.e	a.e	PROPN
ma-9	187	113	.	.	PROPN
ma-9	187	114	t	t	PROPN
ma-9	187	115	∈	∈	PROPN
ma-9	187	116	j	j	PROPN
ma-9	187	117	,	,	PUNCT
ma-9	187	118	the	the	DET
ma-9	187	119	eur	eur	PROPN
ma-9	187	120	.	.	PUNCT
ma-9	188	1	j.	j.	PROPN
ma-9	188	2	math	math	PROPN
ma-9	188	3	.	.	PUNCT
ma-9	189	1	anal	anal	ADJ
ma-9	189	2	.	.	PUNCT
ma-9	190	1	1	1	NUM
ma-9	190	2	(	(	PUNCT
ma-9	190	3	2021	2021	NUM
ma-9	190	4	)	)	PUNCT
ma-9	190	5	7	7	NUM
ma-9	191	1	following	follow	VERB
ma-9	191	2	integral	integral	ADJ
ma-9	191	3	equation	equation	NOUN
ma-9	191	4	is	be	AUX
ma-9	191	5	satisfied	satisfied	ADJ
ma-9	191	6	.	.	PUNCT
ma-9	192	1	x(t	x(t	PROPN
ma-9	192	2	)	)	PUNCT
ma-9	192	3	=	=	PUNCT
ma-9	193	1	+	+	PUNCT
ma-9	193	2	∞∑	∞∑	DET
ma-9	193	3	k=0	k=0	PROPN
ma-9	193	4	[	[	PUNCT
ma-9	193	5	k∏	k∏	PROPN
ma-9	193	6	i=1	i=1	PROPN
ma-9	193	7	bi(δi)c(t	bi(δi)c(t	PUNCT
ma-9	193	8	−	−	NOUN
ma-9	193	9	t0)φ(0	t0)φ(0	NOUN
ma-9	193	10	)	)	PUNCT
ma-9	193	11	+	+	CCONJ
ma-9	193	12	k∏	k∏	PROPN
ma-9	193	13	i=1	i=1	X
ma-9	193	14	bi(δi)s(t	bi(δi)s(t	VERB
ma-9	194	1	−	−	PROPN
ma-9	194	2	t0)[φ	t0)[φ	NOUN
ma-9	194	3	−	−	ADP
ma-9	194	4	h(0	h(0	PROPN
ma-9	194	5	,	,	PUNCT
ma-9	194	6	φ	φ	NOUN
ma-9	194	7	)	)	PUNCT
ma-9	194	8	]	]	PUNCT
ma-9	195	1	+	+	CCONJ
ma-9	195	2	k∑	k∑	ADJ
ma-9	195	3	i=1	i=1	PROPN
ma-9	196	1	k∏	k∏	PROPN
ma-9	196	2	j	j	PROPN
ma-9	197	1	=	=	NOUN
ma-9	197	2	i	i	PRON
ma-9	197	3	bj	bj	VERB
ma-9	197	4	(	(	PUNCT
ma-9	197	5	δj	δj	ADJ
ma-9	197	6	)	)	PUNCT
ma-9	197	7	×	×	NOUN
ma-9	197	8	∫	∫	PROPN
ma-9	197	9	ξi	ξi	PROPN
ma-9	197	10	ξi−1	ξi−1	PROPN
ma-9	197	11	c(t	c(t	PROPN
ma-9	197	12	−	−	PROPN
ma-9	197	13	s)h(s	s)h(s	NOUN
ma-9	197	14	,	,	PUNCT
ma-9	198	1	xs)ds+	xs)ds+	PROPN
ma-9	198	2	∫	∫	PROPN
ma-9	199	1	t	t	PROPN
ma-9	199	2	ξk	ξk	ADP
ma-9	199	3	c(t	c(t	PROPN
ma-9	199	4	−	−	PROPN
ma-9	199	5	s)h(s	s)h(s	NOUN
ma-9	199	6	,	,	PUNCT
ma-9	199	7	xs)ds+	xs)ds+	PROPN
ma-9	199	8	k∑	k∑	VERB
ma-9	199	9	i=1	i=1	PROPN
ma-9	200	1	k∏	k∏	PROPN
ma-9	200	2	j	j	PROPN
ma-9	201	1	=	=	NOUN
ma-9	201	2	i	i	PRON
ma-9	201	3	bj	bj	VERB
ma-9	201	4	(	(	PUNCT
ma-9	201	5	δj	δj	ADJ
ma-9	201	6	)	)	PUNCT
ma-9	201	7	∫	∫	PROPN
ma-9	201	8	ξi	ξi	PROPN
ma-9	201	9	ξi−1	ξi−1	PROPN
ma-9	201	10	s(t	s(t	PROPN
ma-9	201	11	−	−	PROPN
ma-9	201	12	s	s	PART
ma-9	201	13	)	)	PUNCT
ma-9	201	14	×	×	NOUN
ma-9	201	15	f(s	f(	NOUN
ma-9	201	16	,	,	PUNCT
ma-9	201	17	xs)ds+	xs)ds+	PROPN
ma-9	201	18	∫	∫	PROPN
ma-9	202	1	t	t	PROPN
ma-9	202	2	ξk	ξk	ADP
ma-9	202	3	s(t	s(t	PROPN
ma-9	202	4	−	−	PROPN
ma-9	202	5	s)f(s	s)f(	NOUN
ma-9	202	6	,	,	PUNCT
ma-9	202	7	xs)ds+	xs)ds+	PROPN
ma-9	202	8	k∑	k∑	VERB
ma-9	202	9	i=1	i=1	PROPN
ma-9	203	1	k∏	k∏	PROPN
ma-9	203	2	j	j	PROPN
ma-9	204	1	=	=	NOUN
ma-9	204	2	i	i	PRON
ma-9	204	3	bj	bj	VERB
ma-9	204	4	(	(	PUNCT
ma-9	204	5	δj	δj	ADJ
ma-9	204	6	)	)	PUNCT
ma-9	204	7	∫	∫	PROPN
ma-9	204	8	ξi	ξi	PROPN
ma-9	204	9	ξi−1	ξi−1	PROPN
ma-9	204	10	s(t	s(t	PROPN
ma-9	204	11	−	−	PROPN
ma-9	204	12	s)g(s	s)g(s	NOUN
ma-9	204	13	,	,	PUNCT
ma-9	204	14	xs)dω(s	xs)dω(s	PROPN
ma-9	204	15	)	)	PUNCT
ma-9	204	16	+	+	CCONJ
ma-9	204	17	∫	∫	PROPN
ma-9	204	18	t	t	PROPN
ma-9	204	19	ξk	ξk	ADP
ma-9	204	20	s(t	s(t	PROPN
ma-9	204	21	−	−	PROPN
ma-9	204	22	s)g(s	s)g(s	NOUN
ma-9	204	23	,	,	PUNCT
ma-9	204	24	xs)dω(s	xs)dω(s	PROPN
ma-9	204	25	)	)	PUNCT
ma-9	204	26	+	+	CCONJ
ma-9	204	27	k∑	k∑	VERB
ma-9	204	28	i=1	i=1	PROPN
ma-9	205	1	k∏	k∏	PROPN
ma-9	205	2	j	j	PROPN
ma-9	206	1	=	=	NOUN
ma-9	206	2	i	i	PRON
ma-9	206	3	bj	bj	VERB
ma-9	206	4	(	(	PUNCT
ma-9	206	5	δj	δj	ADJ
ma-9	206	6	)	)	PUNCT
ma-9	206	7	∫	∫	PROPN
ma-9	206	8	ξi	ξi	PROPN
ma-9	206	9	ξi−1	ξi−1	PROPN
ma-9	206	10	∫	∫	PROPN
ma-9	206	11	u	u	PROPN
ma-9	206	12	s(t	s(t	PROPN
ma-9	206	13	−	−	PROPN
ma-9	206	14	s)σ	s)σ	X
ma-9	206	15	(	(	PUNCT
ma-9	206	16	s	s	PROPN
ma-9	206	17	,	,	PUNCT
ma-9	206	18	xs	xs	PROPN
ma-9	206	19	,	,	PUNCT
ma-9	206	20	u)n(ds	u)n(ds	PROPN
ma-9	206	21	,	,	PUNCT
ma-9	206	22	du	du	NOUN
ma-9	206	23	)	)	PUNCT
ma-9	207	1	+	+	CCONJ
ma-9	207	2	∫	∫	PROPN
ma-9	207	3	t	t	X
ma-9	207	4	ξk	ξk	ADP
ma-9	207	5	∫	∫	PROPN
ma-9	207	6	u	u	PROPN
ma-9	207	7	s(t	s(t	PROPN
ma-9	207	8	−	−	PROPN
ma-9	207	9	s)σ	s)σ	X
ma-9	207	10	(	(	PUNCT
ma-9	207	11	s	s	PROPN
ma-9	207	12	,	,	PUNCT
ma-9	207	13	xs	xs	PROPN
ma-9	207	14	,	,	PUNCT
ma-9	207	15	u)n(ds	u)n(ds	PROPN
ma-9	207	16	,	,	PUNCT
ma-9	207	17	du)]i[ξk	du)]i[ξk	NOUN
ma-9	207	18	,	,	PUNCT
ma-9	207	19	ξk+1)(t	ξk+1)(t	PROPN
ma-9	207	20	)	)	PUNCT
ma-9	207	21	,	,	PUNCT
ma-9	207	22	t	t	PROPN
ma-9	207	23	∈	∈	PROPN
ma-9	207	24	[	[	X
ma-9	207	25	t0	t0	PROPN
ma-9	207	26	,	,	PUNCT
ma-9	207	27	t	t	X
ma-9	207	28	]	]	PUNCT
ma-9	207	29	.	.	PUNCT
ma-9	208	1	(	(	PUNCT
ma-9	208	2	2.10	2.10	NUM
ma-9	208	3	)	)	PUNCT
ma-9	208	4	where	where	SCONJ
ma-9	208	5	,	,	PUNCT
ma-9	208	6	k∏	k∏	PROPN
ma-9	208	7	j	j	PROPN
ma-9	209	1	=	=	NOUN
ma-9	209	2	i	i	PRON
ma-9	209	3	bj	bj	VERB
ma-9	209	4	(	(	PUNCT
ma-9	209	5	δj	δj	ADJ
ma-9	209	6	)	)	PUNCT
ma-9	209	7	=	=	SYM
ma-9	209	8	bk	bk	X
ma-9	209	9	(	(	PUNCT
ma-9	209	10	δk	δk	INTJ
ma-9	209	11	)	)	PUNCT
ma-9	209	12	bk−1(δk−1	bk−1(δk−1	PROPN
ma-9	209	13	)	)	PUNCT
ma-9	209	14	·	·	PUNCT
ma-9	209	15	·	·	PUNCT
ma-9	209	16	·	·	PUNCT
ma-9	209	17	bi(δi	bi(δi	ADJ
ma-9	209	18	)	)	PUNCT
ma-9	209	19	,	,	PUNCT
ma-9	209	20	and	and	CCONJ
ma-9	209	21	i(a	i(a	NOUN
ma-9	209	22	)	)	PUNCT
ma-9	209	23	(	(	PUNCT
ma-9	209	24	.	.	PUNCT
ma-9	209	25	)	)	PUNCT
ma-9	209	26	is	be	AUX
ma-9	209	27	the	the	DET
ma-9	209	28	index	index	NOUN
ma-9	209	29	function	function	NOUN
ma-9	209	30	,	,	PUNCT
ma-9	209	31	i.e.	i.e.	X
ma-9	209	32	,	,	PUNCT
ma-9	209	33	ia(t	ia(t	PUNCT
ma-9	209	34	)	)	PUNCT
ma-9	209	35	=	=	PUNCT
ma-9	210	1	1	1	NOUN
ma-9	210	2	,	,	PUNCT
ma-9	210	3	if	if	SCONJ
ma-9	210	4	t	t	PROPN
ma-9	210	5	∈	∈	PROPN
ma-9	210	6	a,0	a,0	NOUN
ma-9	210	7	,	,	PUNCT
ma-9	210	8	if	if	SCONJ
ma-9	210	9	t	t	PROPN
ma-9	210	10	/∈	/∈	PUNCT
ma-9	210	11	a.	a.	PROPN
ma-9	210	12	lemma	lemma	PROPN
ma-9	210	13	2.4	2.4	NUM
ma-9	210	14	.	.	PUNCT
ma-9	211	1	for	for	ADP
ma-9	211	2	any	any	DET
ma-9	211	3	p	p	NOUN
ma-9	211	4	≥	≥	NOUN
ma-9	211	5	1	1	NUM
ma-9	211	6	,	,	PUNCT
ma-9	211	7	and	and	CCONJ
ma-9	211	8	for	for	ADP
ma-9	211	9	lq(k	lq(k	ADV
ma-9	211	10	,	,	PUNCT
ma-9	211	11	h)-valued	h)-valued	PUNCT
ma-9	211	12	predictable	predictable	ADJ
ma-9	211	13	process	process	NOUN
ma-9	211	14	u	u	NOUN
ma-9	211	15	(	(	PUNCT
ma-9	211	16	.	.	PUNCT
ma-9	211	17	)	)	PUNCT
ma-9	212	1	such	such	ADJ
ma-9	212	2	that	that	PRON
ma-9	212	3	,	,	PUNCT
ma-9	212	4	sup	sup	NOUN
ma-9	212	5	s∈[0,t	s∈[0,t	NOUN
ma-9	212	6	]	]	PUNCT
ma-9	212	7	e	e	X
ma-9	212	8	∥∥∥∥∫	∥∥∥∥∫	PROPN
ma-9	212	9	s	s	PROPN
ma-9	212	10	0	0	NUM
ma-9	212	11	u(η)dω(η)∥∥∥∥2p	u(η)dω(η)∥∥∥∥2p	X
ma-9	212	12	≤	≤	X
ma-9	212	13	(	(	PUNCT
ma-9	212	14	p(2p−	p(2p−	NOUN
ma-9	212	15	1))p(∫	1))p(∫	NUM
ma-9	212	16	t	t	NOUN
ma-9	212	17	0	0	NUM
ma-9	213	1	(	(	PUNCT
ma-9	213	2	e	e	NOUN
ma-9	213	3	∥∥u(s)∥∥2p	∥∥u(s)∥∥2p	VERB
ma-9	213	4	q	q	NOUN
ma-9	213	5	)	)	PUNCT
ma-9	213	6	1	1	X
ma-9	213	7	/	/	SYM
ma-9	213	8	p	p	X
ma-9	213	9	ds	ds	ADJ
ma-9	213	10	)	)	PUNCT
ma-9	213	11	p	p	NOUN
ma-9	213	12	,	,	PUNCT
ma-9	213	13	t	t	PROPN
ma-9	213	14	∈	∈	PROPN
ma-9	213	15	j.	j.	PROPN
ma-9	213	16	3	3	PROPN
ma-9	213	17	.	.	PUNCT
ma-9	214	1	existence	existence	NOUN
ma-9	214	2	results	result	NOUN
ma-9	214	3	of	of	ADP
ma-9	214	4	mild	mild	ADJ
ma-9	214	5	solution	solution	NOUN
ma-9	214	6	to	to	PART
ma-9	214	7	prove	prove	VERB
ma-9	214	8	the	the	DET
ma-9	214	9	existence	existence	NOUN
ma-9	214	10	of	of	ADP
ma-9	214	11	mild	mild	ADJ
ma-9	214	12	solutions	solution	NOUN
ma-9	214	13	of	of	ADP
ma-9	214	14	random	random	ADJ
ma-9	214	15	impulsive	impulsive	ADJ
ma-9	214	16	stochastic	stochastic	ADJ
ma-9	214	17	differential	differential	ADJ
ma-9	214	18	equations	equation	NOUN
ma-9	214	19	,	,	PUNCT
ma-9	214	20	the	the	DET
ma-9	214	21	following	follow	VERB
ma-9	214	22	assumptions	assumption	NOUN
ma-9	214	23	are	be	AUX
ma-9	214	24	to	to	PART
ma-9	214	25	be	be	AUX
ma-9	214	26	made.(h1	made.(h1	NOUN
ma-9	214	27	)	)	PUNCT
ma-9	214	28	c(t	c(t	PROPN
ma-9	214	29	)	)	PUNCT
ma-9	214	30	,	,	PUNCT
ma-9	214	31	s(t)(t	s(t)(t	PROPN
ma-9	214	32	∈	∈	PROPN
ma-9	214	33	j	j	PROPN
ma-9	214	34	)	)	PUNCT
ma-9	214	35	are	be	AUX
ma-9	214	36	equicontinuous	equicontinuous	ADJ
ma-9	214	37	and	and	CCONJ
ma-9	214	38	there	there	PRON
ma-9	214	39	exist	exist	VERB
ma-9	214	40	positive	positive	ADJ
ma-9	214	41	constants	constant	NOUN
ma-9	214	42	m	m	VERB
ma-9	214	43	,	,	PUNCT
ma-9	214	44	m̃	m̃	PROPN
ma-9	214	45	such	such	ADJ
ma-9	214	46	that	that	DET
ma-9	214	47	sup	sup	PROPN
ma-9	214	48	t∈j	t∈j	PROPN
ma-9	214	49	∥∥c(t)∥∥	∥∥c(t)∥∥	PROPN
ma-9	214	50	≤m	≤m	NOUN
ma-9	214	51	,	,	PUNCT
ma-9	214	52	sup	sup	PROPN
ma-9	214	53	t∈j	t∈j	NOUN
ma-9	214	54	∥∥s(t)∥∥	∥∥s(t)∥∥	PROPN
ma-9	214	55	≤	≤	ADJ
ma-9	214	56	m̃.	m̃.	PROPN
ma-9	214	57	(	(	PUNCT
ma-9	214	58	3.1	3.1	NUM
ma-9	214	59	)	)	PUNCT
ma-9	214	60	(	(	PUNCT
ma-9	214	61	h2	h2	NOUN
ma-9	214	62	)	)	PUNCT
ma-9	215	1	the	the	DET
ma-9	215	2	functions	function	NOUN
ma-9	215	3	f	f	NOUN
ma-9	215	4	:	:	PUNCT
ma-9	215	5	j×	j×	PROPN
ma-9	215	6	c→	c→	PROPN
ma-9	215	7	h	h	NOUN
ma-9	215	8	;	;	PUNCT
ma-9	215	9	h	h	NOUN
ma-9	215	10	:	:	PUNCT
ma-9	216	1	j×	j×	PROPN
ma-9	216	2	c→	c→	PUNCT
ma-9	216	3	h	h	NOUN
ma-9	216	4	;	;	PUNCT
ma-9	216	5	g	g	NOUN
ma-9	216	6	:	:	PUNCT
ma-9	216	7	j×	j×	PROPN
ma-9	216	8	c→	c→	X
ma-9	216	9	lq(k	lq(k	ADJ
ma-9	216	10	,	,	PUNCT
ma-9	216	11	h	h	NOUN
ma-9	216	12	)	)	PUNCT
ma-9	216	13	and	and	CCONJ
ma-9	216	14	σ	σ	NUM
ma-9	216	15	:	:	PUNCT
ma-9	217	1	j×	j×	PROPN
ma-9	217	2	c×	c×	PROPN
ma-9	217	3	u→	u→	PROPN
ma-9	217	4	h	h	PROPN
ma-9	217	5	e	e	NOUN
ma-9	217	6	∥∥f(t	∥∥f(t	NOUN
ma-9	217	7	,	,	PUNCT
ma-9	217	8	xt)−	xt)−	PUNCT
ma-9	217	9	f(t	f(t	PROPN
ma-9	217	10	,	,	PUNCT
ma-9	217	11	yt)∥∥2	yt)∥∥2	PROPN
ma-9	217	12	≤	≤	PROPN
ma-9	217	13	lf	lf	ADP
ma-9	217	14	∥∥x	∥∥x	PROPN
ma-9	218	1	−	−	PROPN
ma-9	218	2	y∥∥2	y∥∥2	PROPN
ma-9	218	3	t	t	PROPN
ma-9	218	4	,	,	PUNCT
ma-9	218	5	e	e	PROPN
ma-9	218	6	∥∥g(t	∥∥g(t	PROPN
ma-9	218	7	,	,	PUNCT
ma-9	218	8	xt)−	xt)−	PROPN
ma-9	218	9	g(t	g(t	PROPN
ma-9	218	10	,	,	PUNCT
ma-9	218	11	yt)∥∥2	yt)∥∥2	PROPN
ma-9	218	12	≤	≤	PROPN
ma-9	218	13	lg	lg	PROPN
ma-9	218	14	∥∥x	∥∥x	PROPN
ma-9	218	15	−	−	PROPN
ma-9	218	16	y∥∥2	y∥∥2	PROPN
ma-9	218	17	t	t	PROPN
ma-9	218	18	,	,	PUNCT
ma-9	218	19	e	e	X
ma-9	218	20	∥∥h(t	∥∥h(t	PROPN
ma-9	218	21	,	,	PUNCT
ma-9	218	22	xt)−	xt)−	PROPN
ma-9	218	23	h(t	h(t	PROPN
ma-9	218	24	,	,	PUNCT
ma-9	218	25	yt)∥∥2	yt)∥∥2	PROPN
ma-9	218	26	≤	≤	PROPN
ma-9	218	27	lh	lh	PROPN
ma-9	218	28	∥∥x	∥∥x	PROPN
ma-9	218	29	−	−	PROPN
ma-9	218	30	y∥∥2	y∥∥2	PROPN
ma-9	218	31	t	t	PROPN
ma-9	218	32	,	,	PUNCT
ma-9	218	33	∫	∫	PROPN
ma-9	218	34	u	u	PROPN
ma-9	218	35	e	e	X
ma-9	218	36	∥∥σ	∥∥σ	NUM
ma-9	218	37	(	(	PUNCT
ma-9	218	38	t	t	PROPN
ma-9	218	39	,	,	PUNCT
ma-9	218	40	xt	xt	PROPN
ma-9	218	41	,	,	PUNCT
ma-9	218	42	u)−	u)−	PROPN
ma-9	218	43	σ	σ	PROPN
ma-9	218	44	(	(	PUNCT
ma-9	218	45	t	t	PROPN
ma-9	218	46	,	,	PUNCT
ma-9	218	47	yt	yt	PROPN
ma-9	218	48	,	,	PUNCT
ma-9	218	49	u)∥∥2	u)∥∥2	PROPN
ma-9	218	50	v	v	INTJ
ma-9	218	51	(	(	PUNCT
ma-9	218	52	du)ds	du)ds	PROPN
ma-9	218	53	∨	∨	NUM
ma-9	218	54	∫	∫	PROPN
ma-9	218	55	u	u	PROPN
ma-9	218	56	(	(	PUNCT
ma-9	218	57	e	e	PROPN
ma-9	218	58	∥∥σ	∥∥σ	PROPN
ma-9	218	59	(	(	PUNCT
ma-9	218	60	t	t	PROPN
ma-9	218	61	,	,	PUNCT
ma-9	218	62	xt	xt	PROPN
ma-9	218	63	,	,	PUNCT
ma-9	218	64	u)−	u)−	PROPN
ma-9	218	65	σ	σ	PROPN
ma-9	218	66	(	(	PUNCT
ma-9	218	67	t	t	PROPN
ma-9	218	68	,	,	PUNCT
ma-9	218	69	yt	yt	X
ma-9	218	70	,	,	PUNCT
ma-9	218	71	u)∥∥4	u)∥∥4	PROPN
ma-9	218	72	v	v	X
ma-9	218	73	(	(	PUNCT
ma-9	218	74	du)ds	du)ds	PROPN
ma-9	218	75	)	)	PUNCT
ma-9	218	76	12	12	NUM
ma-9	218	77	≤	≤	NUM
ma-9	218	78	lσ	lσ	PROPN
ma-9	218	79	∥∥x	∥∥x	PROPN
ma-9	218	80	−	−	PROPN
ma-9	218	81	y∥∥2	y∥∥2	PROPN
ma-9	218	82	t	t	PROPN
ma-9	218	83	,	,	PUNCT
ma-9	218	84	∫	∫	PROPN
ma-9	218	85	u	u	PROPN
ma-9	218	86	(	(	PUNCT
ma-9	218	87	e	e	PROPN
ma-9	218	88	∥∥σ	∥∥σ	PROPN
ma-9	218	89	(	(	PUNCT
ma-9	218	90	t	t	PROPN
ma-9	218	91	,	,	PUNCT
ma-9	218	92	xt	xt	PROPN
ma-9	218	93	,	,	PUNCT
ma-9	218	94	u)−	u)−	PROPN
ma-9	218	95	σ	σ	PROPN
ma-9	218	96	(	(	PUNCT
ma-9	218	97	t	t	PROPN
ma-9	218	98	,	,	PUNCT
ma-9	218	99	yt	yt	X
ma-9	218	100	,	,	PUNCT
ma-9	218	101	u)∥∥4	u)∥∥4	PROPN
ma-9	218	102	v	v	X
ma-9	218	103	(	(	PUNCT
ma-9	218	104	du)ds	du)ds	PROPN
ma-9	218	105	)	)	PUNCT
ma-9	218	106	12	12	NUM
ma-9	218	107	≤	≤	NUM
ma-9	218	108	lσ	lσ	NOUN
ma-9	218	109	∥x∥2	∥x∥2	NOUN
ma-9	218	110	t	t	PROPN
ma-9	218	111	.	.	PUNCT
ma-9	219	1	eur	eur	PROPN
ma-9	219	2	.	.	PUNCT
ma-9	220	1	j.	j.	PROPN
ma-9	220	2	math	math	PROPN
ma-9	220	3	.	.	PUNCT
ma-9	221	1	anal	anal	ADJ
ma-9	221	2	.	.	PUNCT
ma-9	222	1	1	1	NUM
ma-9	222	2	(	(	PUNCT
ma-9	222	3	2021	2021	NUM
ma-9	222	4	)	)	PUNCT
ma-9	222	5	8(h3	8(h3	NOUN
ma-9	222	6	)	)	PUNCT
ma-9	222	7	for	for	ADP
ma-9	222	8	all	all	DET
ma-9	222	9	t	t	NOUN
ma-9	222	10	∈	∈	PROPN
ma-9	222	11	j	j	PROPN
ma-9	222	12	,	,	PUNCT
ma-9	222	13	there	there	PRON
ma-9	222	14	exist	exist	VERB
ma-9	222	15	constants	constant	NOUN
ma-9	222	16	κf	κf	ADP
ma-9	222	17	,	,	PUNCT
ma-9	222	18	κg	κg	PROPN
ma-9	222	19	,	,	PUNCT
ma-9	222	20	κh	κh	PROPN
ma-9	222	21	,	,	PUNCT
ma-9	222	22	κσ	κσ	ADJ
ma-9	222	23	∈	∈	PROPN
ma-9	222	24	l′(j	l′(j	NOUN
ma-9	222	25	,	,	PUNCT
ma-9	222	26	r+	r+	NOUN
ma-9	222	27	)	)	PUNCT
ma-9	222	28	such	such	ADJ
ma-9	222	29	that	that	SCONJ
ma-9	222	30	,	,	PUNCT
ma-9	222	31	e	e	NOUN
ma-9	222	32	∥∥f(t	∥∥f(t	NOUN
ma-9	222	33	,	,	PUNCT
ma-9	222	34	0)∥∥2	0)∥∥2	NOUN
ma-9	222	35	≤	≤	PUNCT
ma-9	222	36	κf	κf	ADP
ma-9	222	37	,	,	PUNCT
ma-9	222	38	e∥∥g(t	e∥∥g(t	PROPN
ma-9	222	39	,	,	PUNCT
ma-9	222	40	0)∥∥2	0)∥∥2	NOUN
ma-9	222	41	≤	≤	PUNCT
ma-9	222	42	κg	κg	PROPN
ma-9	222	43	,	,	PUNCT
ma-9	222	44	e	e	NOUN
ma-9	222	45	∥∥h(t	∥∥h(t	NOUN
ma-9	222	46	,	,	PUNCT
ma-9	222	47	0)∥∥2	0)∥∥2	NOUN
ma-9	222	48	≤	≤	PUNCT
ma-9	222	49	κh	κh	PROPN
ma-9	222	50	,	,	PUNCT
ma-9	222	51	e∥∥σ	e∥∥σ	X
ma-9	222	52	(	(	PUNCT
ma-9	222	53	t	t	PROPN
ma-9	222	54	,	,	PUNCT
ma-9	222	55	0	0	NUM
ma-9	222	56	,	,	PUNCT
ma-9	222	57	u)∥∥2	u)∥∥2	PROPN
ma-9	222	58	≤	≤	NOUN
ma-9	222	59	κσ	κσ	NOUN
ma-9	222	60	.	.	PUNCT
ma-9	223	1	(	(	PUNCT
ma-9	223	2	h4	h4	PROPN
ma-9	223	3	)	)	PUNCT
ma-9	223	4	e	e	NOUN
ma-9	223	5	max	max	NOUN
ma-9	223	6	i	i	PRON
ma-9	223	7	,	,	PUNCT
ma-9	223	8	k	k	PROPN
ma-9	223	9	{	{	PUNCT
ma-9	223	10	k∏	k∏	PROPN
ma-9	223	11	j	j	PROPN
ma-9	223	12	=	=	NOUN
ma-9	223	13	i	i	NOUN
ma-9	223	14	∥∥bj	∥∥bj	VERB
ma-9	223	15	(	(	PUNCT
ma-9	223	16	δj	δj	PROPN
ma-9	223	17	)	)	PUNCT
ma-9	223	18	∥∥	∥∥	PROPN
ma-9	223	19	}	}	PUNCT
ma-9	223	20			NOUN
ma-9	223	21	is	be	AUX
ma-9	223	22	uniformly	uniformly	ADV
ma-9	223	23	bounded	bound	VERB
ma-9	223	24	then	then	ADV
ma-9	223	25	there	there	PRON
ma-9	223	26	exist	exist	VERB
ma-9	223	27	constant	constant	ADJ
ma-9	223	28	n	n	NOUN
ma-9	223	29	for	for	ADP
ma-9	223	30	all	all	DET
ma-9	223	31	δj	δj	NOUN
ma-9	223	32	∈	∈	NOUN
ma-9	223	33	dj	dj	NOUN
ma-9	223	34	such	such	DET
ma-9	224	1	that	that	SCONJ
ma-9	224	2	e	e	NOUN
ma-9	224	3	max	max	NOUN
ma-9	224	4	i	i	PRON
ma-9	224	5	,	,	PUNCT
ma-9	224	6	k	k	PROPN
ma-9	224	7	{	{	PUNCT
ma-9	224	8	k∏	k∏	PROPN
ma-9	224	9	j	j	PROPN
ma-9	224	10	=	=	NOUN
ma-9	224	11	i	i	NOUN
ma-9	224	12	∥∥bj	∥∥bj	VERB
ma-9	224	13	(	(	PUNCT
ma-9	224	14	δj	δj	PROPN
ma-9	224	15	)	)	PUNCT
ma-9	224	16	∥∥	∥∥	NOUN
ma-9	224	17	}	}	PUNCT
ma-9	224	18			ADP
ma-9	224	19	≤	≤	ADJ
ma-9	224	20	n	n	X
ma-9	224	21	.	.	PUNCT
ma-9	225	1	theorem	theorem	VERB
ma-9	225	2	3.1	3.1	NUM
ma-9	225	3	.	.	PUNCT
ma-9	226	1	if	if	SCONJ
ma-9	226	2	assumptions	assumption	NOUN
ma-9	226	3	(	(	PUNCT
ma-9	226	4	h1)-(h4	h1)-(h4	NOUN
ma-9	226	5	)	)	PUNCT
ma-9	226	6	gets	get	VERB
ma-9	226	7	satisfied	satisfied	ADJ
ma-9	226	8	then	then	ADV
ma-9	226	9	there	there	PRON
ma-9	226	10	exist	exist	VERB
ma-9	226	11	a	a	DET
ma-9	226	12	unique	unique	ADJ
ma-9	226	13	continuous	continuous	ADJ
ma-9	226	14	mild	mild	ADJ
ma-9	226	15	solution	solution	NOUN
ma-9	226	16	of	of	ADP
ma-9	226	17	the	the	DET
ma-9	226	18	system	system	NOUN
ma-9	226	19	(	(	PUNCT
ma-9	226	20	1.1	1.1	NUM
ma-9	226	21	)	)	PUNCT
ma-9	226	22	.	.	PUNCT
ma-9	227	1	proof	proof	NOUN
ma-9	227	2	.	.	PUNCT
ma-9	228	1	we	we	PRON
ma-9	228	2	define	define	VERB
ma-9	228	3	an	an	DET
ma-9	228	4	operator	operator	NOUN
ma-9	228	5	φ	φ	NOUN
ma-9	228	6	:	:	PUNCT
ma-9	228	7	b	b	X
ma-9	228	8	→	→	SYM
ma-9	228	9	b	b	NOUN
ma-9	228	10	by	by	ADP
ma-9	228	11	φx	φx	PRON
ma-9	228	12	such	such	ADJ
ma-9	228	13	that	that	SCONJ
ma-9	228	14	,	,	PUNCT
ma-9	228	15	(	(	PUNCT
ma-9	228	16	φx)(t	φx)(t	NOUN
ma-9	228	17	)	)	PUNCT
ma-9	228	18	=	=	SYM
ma-9	228	19			PROPN
ma-9	228	20	φ(t	φ(t	PROPN
ma-9	228	21	)	)	PUNCT
ma-9	228	22	,	,	PUNCT
ma-9	228	23	t	t	PROPN
ma-9	228	24	∈	∈	PROPN
ma-9	229	1	[	[	X
ma-9	229	2	t0	t0	X
ma-9	229	3	−	−	PROPN
ma-9	229	4	δ	δ	PROPN
ma-9	229	5	,	,	PUNCT
ma-9	229	6	t0],+∞∑	t0],+∞∑	PROPN
ma-9	229	7	k=0	k=0	PUNCT
ma-9	229	8	[	[	PUNCT
ma-9	229	9	k∏	k∏	PROPN
ma-9	229	10	i=1	i=1	PROPN
ma-9	229	11	bi(δi)c(t	bi(δi)c(t	PUNCT
ma-9	229	12	−	−	NOUN
ma-9	229	13	t0)φ(0	t0)φ(0	NOUN
ma-9	229	14	)	)	PUNCT
ma-9	229	15	+	+	CCONJ
ma-9	229	16	k∏	k∏	PROPN
ma-9	229	17	i=1	i=1	X
ma-9	229	18	bi(δi)s(t	bi(δi)s(t	VERB
ma-9	229	19	−	−	PROPN
ma-9	229	20	t0)[φ	t0)[φ	NOUN
ma-9	229	21	−	−	ADP
ma-9	229	22	h(0	h(0	PROPN
ma-9	229	23	,	,	PUNCT
ma-9	229	24	φ	φ	NOUN
ma-9	229	25	)	)	PUNCT
ma-9	229	26	]	]	PUNCT
ma-9	230	1	+	+	CCONJ
ma-9	230	2	k∑	k∑	ADJ
ma-9	230	3	i=1	i=1	PROPN
ma-9	231	1	k∏	k∏	PROPN
ma-9	231	2	j	j	PROPN
ma-9	232	1	=	=	NOUN
ma-9	232	2	i	i	PRON
ma-9	232	3	bj	bj	VERB
ma-9	232	4	(	(	PUNCT
ma-9	232	5	δj	δj	ADJ
ma-9	232	6	)	)	PUNCT
ma-9	232	7	×	×	NOUN
ma-9	232	8	∫	∫	PROPN
ma-9	232	9	ξi	ξi	PROPN
ma-9	232	10	ξi−1	ξi−1	PROPN
ma-9	232	11	c(t	c(t	PROPN
ma-9	232	12	−	−	PROPN
ma-9	232	13	s)h(s	s)h(s	NOUN
ma-9	232	14	,	,	PUNCT
ma-9	233	1	xs)ds+	xs)ds+	PROPN
ma-9	233	2	∫	∫	PROPN
ma-9	234	1	t	t	PROPN
ma-9	234	2	ξk	ξk	ADP
ma-9	234	3	c(t	c(t	PROPN
ma-9	234	4	−	−	PROPN
ma-9	234	5	s)h(s	s)h(s	NOUN
ma-9	234	6	,	,	PUNCT
ma-9	234	7	xs)ds+	xs)ds+	PROPN
ma-9	234	8	k∑	k∑	VERB
ma-9	234	9	i=1	i=1	PROPN
ma-9	235	1	k∏	k∏	PROPN
ma-9	235	2	j	j	PROPN
ma-9	236	1	=	=	NOUN
ma-9	236	2	i	i	PRON
ma-9	236	3	bj	bj	VERB
ma-9	236	4	(	(	PUNCT
ma-9	236	5	δj	δj	ADJ
ma-9	236	6	)	)	PUNCT
ma-9	236	7	∫	∫	PROPN
ma-9	236	8	ξi	ξi	PROPN
ma-9	236	9	ξi−1	ξi−1	PROPN
ma-9	236	10	s(t	s(t	PROPN
ma-9	236	11	−	−	PROPN
ma-9	236	12	s	s	PART
ma-9	236	13	)	)	PUNCT
ma-9	236	14	×	×	NOUN
ma-9	236	15	f(s	f(	NOUN
ma-9	236	16	,	,	PUNCT
ma-9	236	17	xs)ds+	xs)ds+	PROPN
ma-9	236	18	∫	∫	PROPN
ma-9	236	19	tξk	tξk	INTJ
ma-9	236	20	s(t	s(t	PROPN
ma-9	236	21	−	−	PROPN
ma-9	236	22	s)f(s	s)f(	NOUN
ma-9	236	23	,	,	PUNCT
ma-9	236	24	xs)ds+	xs)ds+	PROPN
ma-9	236	25	k∑	k∑	VERB
ma-9	236	26	i=1	i=1	PROPN
ma-9	237	1	k∏	k∏	PROPN
ma-9	237	2	j	j	PROPN
ma-9	238	1	=	=	NOUN
ma-9	238	2	i	i	PRON
ma-9	238	3	bj	bj	VERB
ma-9	238	4	(	(	PUNCT
ma-9	238	5	δj	δj	ADJ
ma-9	238	6	)	)	PUNCT
ma-9	238	7	∫	∫	PROPN
ma-9	238	8	ξi	ξi	PROPN
ma-9	238	9	ξi−1	ξi−1	PROPN
ma-9	238	10	s(t	s(t	PROPN
ma-9	238	11	−	−	PROPN
ma-9	238	12	s)g(s	s)g(s	NOUN
ma-9	238	13	,	,	PUNCT
ma-9	238	14	xs)dω(s	xs)dω(s	PROPN
ma-9	238	15	)	)	PUNCT
ma-9	239	1	+	+	NOUN
ma-9	239	2	∫	∫	PROPN
ma-9	239	3	t	t	PROPN
ma-9	239	4	ξk	ξk	ADP
ma-9	239	5	s(t	s(t	PROPN
ma-9	239	6	−	−	PROPN
ma-9	239	7	s)g(s	s)g(s	NOUN
ma-9	239	8	,	,	PUNCT
ma-9	239	9	xs)dω(s	xs)dω(s	PROPN
ma-9	239	10	)	)	PUNCT
ma-9	240	1	+	+	CCONJ
ma-9	240	2	k∑	k∑	VERB
ma-9	240	3	i=1	i=1	PROPN
ma-9	241	1	k∏	k∏	PROPN
ma-9	241	2	j	j	PROPN
ma-9	242	1	=	=	NOUN
ma-9	242	2	i	i	PRON
ma-9	242	3	bj	bj	VERB
ma-9	242	4	(	(	PUNCT
ma-9	242	5	δj	δj	ADJ
ma-9	242	6	)	)	PUNCT
ma-9	242	7	∫	∫	PROPN
ma-9	242	8	ξi	ξi	PROPN
ma-9	242	9	ξi−1	ξi−1	PROPN
ma-9	242	10	∫	∫	PROPN
ma-9	242	11	u	u	PROPN
ma-9	242	12	s(t	s(t	PROPN
ma-9	242	13	−	−	PROPN
ma-9	242	14	s)σ	s)σ	X
ma-9	242	15	(	(	PUNCT
ma-9	242	16	s	s	PROPN
ma-9	242	17	,	,	PUNCT
ma-9	242	18	xs	xs	PROPN
ma-9	242	19	,	,	PUNCT
ma-9	242	20	u)n(ds	u)n(ds	PROPN
ma-9	242	21	,	,	PUNCT
ma-9	242	22	du	du	NOUN
ma-9	242	23	)	)	PUNCT
ma-9	243	1	+	+	NOUN
ma-9	243	2	∫	∫	PROPN
ma-9	243	3	t	t	X
ma-9	243	4	ξk	ξk	ADP
ma-9	243	5	∫	∫	PROPN
ma-9	243	6	u	u	PROPN
ma-9	243	7	s(t	s(t	PROPN
ma-9	243	8	−	−	PROPN
ma-9	243	9	s)σ	s)σ	X
ma-9	243	10	(	(	PUNCT
ma-9	243	11	s	s	PROPN
ma-9	243	12	,	,	PUNCT
ma-9	243	13	xs	xs	PROPN
ma-9	243	14	,	,	PUNCT
ma-9	243	15	u)n(ds	u)n(ds	PROPN
ma-9	243	16	,	,	PUNCT
ma-9	243	17	du)]i[ξk	du)]i[ξk	NOUN
ma-9	243	18	,	,	PUNCT
ma-9	243	19	ξk+1)(t	ξk+1)(t	PROPN
ma-9	243	20	)	)	PUNCT
ma-9	244	1	,	,	PUNCT
ma-9	244	2	t	t	PROPN
ma-9	244	3	∈	∈	PROPN
ma-9	244	4	[	[	X
ma-9	244	5	t0	t0	PROPN
ma-9	244	6	,	,	PUNCT
ma-9	244	7	t	t	X
ma-9	244	8	]	]	PUNCT
ma-9	244	9	.	.	PUNCT
ma-9	245	1	we	we	PRON
ma-9	245	2	need	need	VERB
ma-9	245	3	to	to	PART
ma-9	245	4	prove	prove	VERB
ma-9	245	5	that	that	SCONJ
ma-9	245	6	φ	φ	PROPN
ma-9	245	7	maps	maps	PROPN
ma-9	245	8	b	b	PROPN
ma-9	245	9	into	into	ADP
ma-9	245	10	itself	itself	PRON
ma-9	245	11	.	.	PUNCT
ma-9	246	1	e	e	AUX
ma-9	246	2	∥∥(φx)(t)∥∥2	∥∥(φx)(t)∥∥2	VERB
ma-9	246	3	≤	≤	X
ma-9	246	4	e	e	NOUN
ma-9	246	5	∥∥∥∥	∥∥∥∥	PUNCT
ma-9	247	1	+	+	PUNCT
ma-9	247	2	∞∑	∞∑	DET
ma-9	247	3	k=0	k=0	PROPN
ma-9	247	4	[	[	PUNCT
ma-9	247	5	k∏	k∏	PROPN
ma-9	247	6	i=1	i=1	PROPN
ma-9	247	7	bi(δi)c(t	bi(δi)c(t	PUNCT
ma-9	247	8	−	−	NOUN
ma-9	247	9	t0)φ(0	t0)φ(0	NOUN
ma-9	247	10	)	)	PUNCT
ma-9	248	1	+	+	CCONJ
ma-9	248	2	k∏	k∏	PROPN
ma-9	248	3	i=1	i=1	X
ma-9	248	4	bi(δi)s(t	bi(δi)s(t	VERB
ma-9	249	1	−	−	PROPN
ma-9	249	2	t0)[φ	t0)[φ	NOUN
ma-9	249	3	−	−	ADP
ma-9	249	4	h(0	h(0	PROPN
ma-9	249	5	,	,	PUNCT
ma-9	249	6	φ	φ	NOUN
ma-9	249	7	)	)	PUNCT
ma-9	249	8	]	]	PUNCT
ma-9	250	1	+	+	CCONJ
ma-9	250	2	k∑	k∑	ADJ
ma-9	250	3	i=1	i=1	PROPN
ma-9	251	1	k∏	k∏	PROPN
ma-9	251	2	j	j	PROPN
ma-9	252	1	=	=	NOUN
ma-9	252	2	i	i	PRON
ma-9	252	3	bj	bj	VERB
ma-9	252	4	(	(	PUNCT
ma-9	252	5	δj	δj	ADJ
ma-9	252	6	)	)	PUNCT
ma-9	252	7	∫	∫	PROPN
ma-9	253	1	ξi	ξi	PROPN
ma-9	253	2	ξi−1	ξi−1	PROPN
ma-9	253	3	c(t	c(t	PROPN
ma-9	253	4	−	−	PROPN
ma-9	253	5	s)h(s	s)h(s	NOUN
ma-9	253	6	,	,	PUNCT
ma-9	253	7	xs)ds+	xs)ds+	PROPN
ma-9	253	8	∫	∫	PROPN
ma-9	254	1	t	t	PROPN
ma-9	254	2	ξk	ξk	ADP
ma-9	254	3	c(t	c(t	PROPN
ma-9	254	4	−	−	PROPN
ma-9	254	5	s)h(s	s)h(s	NOUN
ma-9	254	6	,	,	PUNCT
ma-9	254	7	xs)ds	xs)ds	PUNCT
ma-9	254	8	eur	eur	PROPN
ma-9	254	9	.	.	PUNCT
ma-9	255	1	j.	j.	PROPN
ma-9	255	2	math	math	PROPN
ma-9	255	3	.	.	PUNCT
ma-9	256	1	anal	anal	ADJ
ma-9	256	2	.	.	PUNCT
ma-9	257	1	1	1	NUM
ma-9	257	2	(	(	PUNCT
ma-9	257	3	2021	2021	NUM
ma-9	257	4	)	)	PUNCT
ma-9	257	5	9	9	NUM
ma-9	258	1	+	+	CCONJ
ma-9	258	2	k∑	k∑	ADJ
ma-9	258	3	i=1	i=1	PROPN
ma-9	259	1	k∏	k∏	PROPN
ma-9	259	2	j	j	PROPN
ma-9	260	1	=	=	NOUN
ma-9	260	2	i	i	PRON
ma-9	260	3	bj	bj	VERB
ma-9	260	4	(	(	PUNCT
ma-9	260	5	δj	δj	ADJ
ma-9	260	6	)	)	PUNCT
ma-9	260	7	∫	∫	PROPN
ma-9	260	8	ξi	ξi	PROPN
ma-9	260	9	ξi−1	ξi−1	PROPN
ma-9	260	10	s(t	s(t	PROPN
ma-9	260	11	−	−	PROPN
ma-9	260	12	s)f(s	s)f(	NOUN
ma-9	260	13	,	,	PUNCT
ma-9	261	1	xs)ds+	xs)ds+	PROPN
ma-9	261	2	∫	∫	PROPN
ma-9	261	3	t	t	PROPN
ma-9	261	4	ξk	ξk	ADP
ma-9	261	5	s(t	s(t	PROPN
ma-9	261	6	−	−	PROPN
ma-9	261	7	s)f(s	s)f(	NOUN
ma-9	261	8	,	,	PUNCT
ma-9	261	9	xs)ds	xs)ds	PUNCT
ma-9	262	1	+	+	CCONJ
ma-9	263	1	k∑	k∑	ADJ
ma-9	263	2	i=1	i=1	PROPN
ma-9	264	1	k∏	k∏	PROPN
ma-9	264	2	j	j	PROPN
ma-9	265	1	=	=	NOUN
ma-9	265	2	i	i	PRON
ma-9	265	3	bj	bj	VERB
ma-9	265	4	(	(	PUNCT
ma-9	265	5	δj	δj	ADJ
ma-9	265	6	)	)	PUNCT
ma-9	265	7	∫	∫	PROPN
ma-9	265	8	ξi	ξi	PROPN
ma-9	265	9	ξi−1	ξi−1	PROPN
ma-9	265	10	s(t	s(t	PROPN
ma-9	265	11	−	−	PROPN
ma-9	265	12	s)g(s	s)g(s	NOUN
ma-9	265	13	,	,	PUNCT
ma-9	265	14	xs)dω(s	xs)dω(s	PROPN
ma-9	265	15	)	)	PUNCT
ma-9	265	16	+	+	CCONJ
ma-9	265	17	∫	∫	PROPN
ma-9	265	18	t	t	PROPN
ma-9	265	19	ξk	ξk	ADP
ma-9	265	20	s(t	s(t	PROPN
ma-9	265	21	−	−	PROPN
ma-9	265	22	s)g(s	s)g(s	NOUN
ma-9	265	23	,	,	PUNCT
ma-9	265	24	xs)dω(s	xs)dω(s	PROPN
ma-9	265	25	)	)	PUNCT
ma-9	265	26	+	+	CCONJ
ma-9	265	27	k∑	k∑	VERB
ma-9	265	28	i=1	i=1	PROPN
ma-9	266	1	k∏	k∏	PROPN
ma-9	266	2	j	j	PROPN
ma-9	267	1	=	=	NOUN
ma-9	267	2	i	i	PRON
ma-9	267	3	bj	bj	VERB
ma-9	267	4	(	(	PUNCT
ma-9	267	5	δj	δj	ADJ
ma-9	267	6	)	)	PUNCT
ma-9	267	7	∫	∫	PROPN
ma-9	267	8	ξi	ξi	PROPN
ma-9	267	9	ξi−1	ξi−1	PROPN
ma-9	267	10	∫	∫	PROPN
ma-9	267	11	u	u	PROPN
ma-9	267	12	s(t	s(t	PROPN
ma-9	267	13	−	−	PROPN
ma-9	267	14	s)σ	s)σ	X
ma-9	267	15	(	(	PUNCT
ma-9	267	16	s	s	PROPN
ma-9	267	17	,	,	PUNCT
ma-9	267	18	xs	xs	PROPN
ma-9	267	19	,	,	PUNCT
ma-9	267	20	u)n(ds	u)n(ds	PROPN
ma-9	267	21	,	,	PUNCT
ma-9	267	22	du	du	NOUN
ma-9	267	23	)	)	PUNCT
ma-9	268	1	+	+	CCONJ
ma-9	268	2	∫	∫	PROPN
ma-9	268	3	t	t	X
ma-9	268	4	ξk	ξk	ADP
ma-9	268	5	∫	∫	PROPN
ma-9	268	6	u	u	PROPN
ma-9	268	7	s(t	s(t	PROPN
ma-9	268	8	−	−	PROPN
ma-9	268	9	s)σ	s)σ	X
ma-9	268	10	(	(	PUNCT
ma-9	268	11	s	s	PROPN
ma-9	268	12	,	,	PUNCT
ma-9	268	13	xs	xs	PROPN
ma-9	268	14	,	,	PUNCT
ma-9	268	15	u)n(ds	u)n(ds	PROPN
ma-9	268	16	,	,	PUNCT
ma-9	268	17	du)]i[ξk	du)]i[ξk	NOUN
ma-9	268	18	,	,	PUNCT
ma-9	268	19	ξk+1)(t)∥∥∥∥2	ξk+1)(t)∥∥∥∥2	PROPN
ma-9	268	20	≤	≤	NOUN
ma-9	269	1	6e[+∞∑	6e[+∞∑	NUM
ma-9	269	2	k=0	k=0	PROPN
ma-9	270	1	[	[	PUNCT
ma-9	270	2	k∏	k∏	PROPN
ma-9	270	3	i=1	i=1	PROPN
ma-9	270	4	∥∥bi(δi)∥∥∥∥c(t	∥∥bi(δi)∥∥∥∥c(t	PROPN
ma-9	270	5	−	−	PROPN
ma-9	270	6	t0)∥∥∥∥φ(0)∥∥	t0)∥∥∥∥φ(0)∥∥	PROPN
ma-9	270	7	]	]	X
ma-9	270	8	i[ξk	i[ξk	PROPN
ma-9	270	9	,	,	PUNCT
ma-9	270	10	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	270	11	+	+	NOUN
ma-9	270	12	6e	6e	NOUN
ma-9	270	13	[	[	PUNCT
ma-9	270	14	+	+	ADJ
ma-9	270	15	∞∑	∞∑	PRON
ma-9	270	16	k=0	k=0	PROPN
ma-9	270	17	[	[	PUNCT
ma-9	270	18	k∏	k∏	PROPN
ma-9	270	19	i=1	i=1	PROPN
ma-9	270	20	∥∥bi(δi)∥∥∥∥s(t	∥∥bi(δi)∥∥∥∥s(t	ADJ
ma-9	270	21	−	−	PROPN
ma-9	271	1	t0)∥∥	t0)∥∥	PROPN
ma-9	272	1	×	×	NOUN
ma-9	272	2	∥∥φ	∥∥φ	NOUN
ma-9	272	3	−	−	PROPN
ma-9	272	4	h(0	h(0	PROPN
ma-9	272	5	,	,	PUNCT
ma-9	272	6	φ)∥∥	φ)∥∥	NUM
ma-9	272	7	]	]	PUNCT
ma-9	272	8	i[ξk	i[ξk	NOUN
ma-9	272	9	,	,	PUNCT
ma-9	272	10	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	272	11	+	+	NOUN
ma-9	272	12	6e	6e	NOUN
ma-9	272	13	[	[	PUNCT
ma-9	272	14	+	+	ADJ
ma-9	272	15	∞∑	∞∑	PRON
ma-9	272	16	k=0	k=0	PROPN
ma-9	272	17	[	[	PUNCT
ma-9	272	18	k∏	k∏	PROPN
ma-9	272	19	j	j	PROPN
ma-9	272	20	=	=	NOUN
ma-9	272	21	i	i	NOUN
ma-9	272	22	∥∥bj	∥∥bj	VERB
ma-9	272	23	(	(	PUNCT
ma-9	272	24	δj	δj	ADJ
ma-9	272	25	)	)	PUNCT
ma-9	272	26	∥∥∫	∥∥∫	ADJ
ma-9	272	27	ξi	ξi	PROPN
ma-9	272	28	ξi−1	ξi−1	PROPN
ma-9	272	29	∥∥c(t	∥∥c(t	PROPN
ma-9	272	30	−	−	PROPN
ma-9	272	31	s)∥∥∥∥h(s	s)∥∥∥∥h(	NOUN
ma-9	272	32	,	,	PUNCT
ma-9	272	33	xs)∥∥ds	xs)∥∥ds	PUNCT
ma-9	273	1	+	+	CCONJ
ma-9	273	2	∫	∫	PROPN
ma-9	273	3	t	t	X
ma-9	273	4	ξk	ξk	ADP
ma-9	273	5	∥∥c(t	∥∥c(t	NOUN
ma-9	273	6	−	−	PROPN
ma-9	273	7	s)∥∥∥∥h(s	s)∥∥∥∥h(	NOUN
ma-9	273	8	,	,	PUNCT
ma-9	273	9	xs)∥∥ds]i[ξk	xs)∥∥ds]i[ξk	PROPN
ma-9	273	10	,	,	PUNCT
ma-9	273	11	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	273	12	+	+	NOUN
ma-9	273	13	6e	6e	NOUN
ma-9	273	14	[	[	PUNCT
ma-9	273	15	+	+	ADJ
ma-9	273	16	∞∑	∞∑	DET
ma-9	273	17	k=0	k=0	PROPN
ma-9	273	18	[	[	PUNCT
ma-9	273	19	k∏	k∏	PROPN
ma-9	273	20	j	j	PROPN
ma-9	274	1	=	=	NOUN
ma-9	274	2	i	i	NOUN
ma-9	274	3	∥∥bj	∥∥bj	VERB
ma-9	274	4	(	(	PUNCT
ma-9	274	5	δj	δj	ADJ
ma-9	274	6	)	)	PUNCT
ma-9	274	7	∥∥∫	∥∥∫	PROPN
ma-9	274	8	ξi	ξi	PROPN
ma-9	274	9	ξi−1	ξi−1	PROPN
ma-9	274	10	∥∥s(t	∥∥s(t	PROPN
ma-9	274	11	−	−	PROPN
ma-9	274	12	s)∥∥	s)∥∥	PROPN
ma-9	274	13	×	×	PROPN
ma-9	274	14	∥∥f(s	∥∥f(	NOUN
ma-9	274	15	,	,	PUNCT
ma-9	274	16	xs)∥∥ds+	xs)∥∥ds+	PROPN
ma-9	274	17	∫	∫	PROPN
ma-9	274	18	t	t	PROPN
ma-9	274	19	ξk	ξk	ADP
ma-9	274	20	∥∥s(t	∥∥s(t	ADJ
ma-9	274	21	−	−	PROPN
ma-9	274	22	s)∥∥∥∥f(s	s)∥∥∥∥f(	NOUN
ma-9	274	23	,	,	PUNCT
ma-9	274	24	xs)∥∥ds]i[ξk	xs)∥∥ds]i[ξk	PROPN
ma-9	274	25	,	,	PUNCT
ma-9	274	26	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	274	27	+	+	NOUN
ma-9	274	28	6e	6e	NOUN
ma-9	274	29	[	[	PUNCT
ma-9	274	30	+	+	ADJ
ma-9	274	31	∞∑	∞∑	DET
ma-9	274	32	k=0	k=0	PROPN
ma-9	274	33	[	[	PUNCT
ma-9	274	34	k∏	k∏	PROPN
ma-9	274	35	j	j	PROPN
ma-9	274	36	=	=	NOUN
ma-9	274	37	i	i	NOUN
ma-9	274	38	∥∥bj	∥∥bj	VERB
ma-9	274	39	(	(	PUNCT
ma-9	274	40	δj	δj	ADJ
ma-9	274	41	)	)	PUNCT
ma-9	274	42	∥∥	∥∥	PROPN
ma-9	274	43	×	×	PROPN
ma-9	274	44	∫	∫	PROPN
ma-9	274	45	ξi	ξi	PROPN
ma-9	274	46	ξi−1	ξi−1	PROPN
ma-9	274	47	∥∥s(t	∥∥s(t	PROPN
ma-9	274	48	−	−	PROPN
ma-9	274	49	s)∥∥∥∥g(s	s)∥∥∥∥g(s	ADJ
ma-9	274	50	,	,	PUNCT
ma-9	274	51	xs)∥∥dω(s	xs)∥∥dω(s	ADJ
ma-9	274	52	)	)	PUNCT
ma-9	275	1	+	+	CCONJ
ma-9	275	2	∫	∫	PROPN
ma-9	275	3	t	t	X
ma-9	275	4	ξk	ξk	ADP
ma-9	275	5	∥∥s(t	∥∥s(t	ADJ
ma-9	275	6	−	−	PROPN
ma-9	275	7	s)∥∥∥∥g(s	s)∥∥∥∥g(s	ADJ
ma-9	275	8	,	,	PUNCT
ma-9	275	9	xs)∥∥dω(s)]i[ξk	xs)∥∥dω(s)]i[ξk	PROPN
ma-9	275	10	,	,	PUNCT
ma-9	275	11	ξk+1)(t	ξk+1)(t	ADJ
ma-9	275	12	)	)	PUNCT
ma-9	276	1	+	+	CCONJ
ma-9	276	2	6e	6e	NOUN
ma-9	276	3	[	[	PUNCT
ma-9	276	4	+	+	ADJ
ma-9	276	5	∞∑	∞∑	DET
ma-9	276	6	k=0	k=0	PROPN
ma-9	276	7	[	[	PUNCT
ma-9	276	8	k∏	k∏	PROPN
ma-9	276	9	j	j	PROPN
ma-9	277	1	=	=	NOUN
ma-9	277	2	i	i	NOUN
ma-9	277	3	∥∥bj	∥∥bj	VERB
ma-9	277	4	(	(	PUNCT
ma-9	277	5	δj	δj	ADJ
ma-9	277	6	)	)	PUNCT
ma-9	277	7	∥∥×	∥∥×	PROPN
ma-9	277	8	∫	∫	PROPN
ma-9	277	9	ξi	ξi	PROPN
ma-9	277	10	ξi−1	ξi−1	PROPN
ma-9	277	11	∫	∫	PROPN
ma-9	277	12	u	u	PROPN
ma-9	277	13	∥∥s(t	∥∥s(t	X
ma-9	277	14	−	−	PROPN
ma-9	277	15	s)∥∥∥∥σ	s)∥∥∥∥σ	PROPN
ma-9	277	16	(	(	PUNCT
ma-9	277	17	s	s	PROPN
ma-9	277	18	,	,	PUNCT
ma-9	277	19	xs	xs	PROPN
ma-9	277	20	,	,	PUNCT
ma-9	277	21	u)∥∥	u)∥∥	PROPN
ma-9	277	22	ñ(ds	ñ(ds	PROPN
ma-9	277	23	,	,	PUNCT
ma-9	277	24	du	du	PROPN
ma-9	277	25	)	)	PUNCT
ma-9	278	1	+	+	CCONJ
ma-9	278	2	∫	∫	PROPN
ma-9	278	3	t	t	X
ma-9	278	4	ξk	ξk	ADP
ma-9	278	5	∫	∫	PROPN
ma-9	278	6	u	u	NOUN
ma-9	278	7	∥∥s(t	∥∥s(t	X
ma-9	278	8	−	−	PROPN
ma-9	278	9	s)∥∥∥∥σ	s)∥∥∥∥σ	PROPN
ma-9	278	10	(	(	PUNCT
ma-9	278	11	s	s	PROPN
ma-9	278	12	,	,	PUNCT
ma-9	278	13	xs	xs	PROPN
ma-9	278	14	,	,	PUNCT
ma-9	278	15	u)∥∥	u)∥∥	NOUN
ma-9	278	16	ñ(ds	ñ(ds	PROPN
ma-9	278	17	,	,	PUNCT
ma-9	278	18	du)]i[ξk	du)]i[ξk	NOUN
ma-9	278	19	,	,	PUNCT
ma-9	278	20	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	278	21	,	,	PUNCT
ma-9	278	22	=	=	PUNCT
ma-9	278	23	6	6	NUM
ma-9	278	24	6∑	6∑	NUM
ma-9	278	25	i=1	i=1	X
ma-9	279	1	gi	gi	INTJ
ma-9	279	2	.	.	PUNCT
ma-9	280	1	where	where	SCONJ
ma-9	280	2	,	,	PUNCT
ma-9	280	3	g1	g1	VERB
ma-9	280	4	≤	≤	PUNCT
ma-9	280	5	e	e	NOUN
ma-9	281	1	[	[	X
ma-9	281	2	+	+	ADP
ma-9	281	3	∞∑	∞∑	PRON
ma-9	281	4	k=0	k=0	PROPN
ma-9	281	5	[	[	PUNCT
ma-9	281	6	k∏	k∏	PROPN
ma-9	281	7	i=1	i=1	PROPN
ma-9	281	8	∥∥bi(δi)∥∥∥∥c(t	∥∥bi(δi)∥∥∥∥c(t	PROPN
ma-9	281	9	−	−	PROPN
ma-9	281	10	t0)∥∥∥∥φ(0)∥∥	t0)∥∥∥∥φ(0)∥∥	PROPN
ma-9	281	11	]	]	X
ma-9	281	12	i[ξk	i[ξk	PROPN
ma-9	281	13	,	,	PUNCT
ma-9	281	14	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	281	15	≤	≤	NUM
ma-9	281	16	m2e	m2e	NUM
ma-9	281	17	max	max	PROPN
ma-9	282	1	i	i	PRON
ma-9	282	2	,	,	PUNCT
ma-9	282	3	k	k	PROPN
ma-9	282	4	{	{	PUNCT
ma-9	282	5	k∏	k∏	PROPN
ma-9	282	6	j	j	PROPN
ma-9	282	7	=	=	NOUN
ma-9	282	8	i	i	NOUN
ma-9	282	9	∥∥bj	∥∥bj	VERB
ma-9	282	10	(	(	PUNCT
ma-9	282	11	δj	δj	PROPN
ma-9	282	12	)	)	PUNCT
ma-9	282	13	∥∥	∥∥	NOUN
ma-9	282	14	}	}	PUNCT
ma-9	282	15			ADP
ma-9	282	16	2	2	NUM
ma-9	282	17	e	e	NOUN
ma-9	282	18	∥∥φ(0)∥∥2	∥∥φ(0)∥∥2	NOUN
ma-9	282	19	≤	≤	ADJ
ma-9	282	20	m2n	m2n	NOUN
ma-9	282	21	2e∥∥φ(0)∥∥2	2e∥∥φ(0)∥∥2	NUM
ma-9	282	22	,	,	PUNCT
ma-9	282	23	g2	g2	PROPN
ma-9	282	24	≤	≤	PUNCT
ma-9	283	1	e	e	X
ma-9	284	1	[	[	PUNCT
ma-9	284	2	+	+	ADJ
ma-9	284	3	∞∑	∞∑	PRON
ma-9	284	4	k=0	k=0	PROPN
ma-9	284	5	[	[	PUNCT
ma-9	284	6	k∏	k∏	PROPN
ma-9	284	7	i=1	i=1	PROPN
ma-9	284	8	∥∥bi(δi)∥∥∥∥s(t	∥∥bi(δi)∥∥∥∥s(t	ADJ
ma-9	284	9	−	−	PROPN
ma-9	285	1	t0)∥∥∥∥φ	t0)∥∥∥∥φ	INTJ
ma-9	285	2	−	−	PROPN
ma-9	285	3	h(0	h(0	PROPN
ma-9	285	4	,	,	PUNCT
ma-9	285	5	φ)∥∥	φ)∥∥	NUM
ma-9	285	6	]	]	PUNCT
ma-9	285	7	i[ξk	i[ξk	NOUN
ma-9	285	8	,	,	PUNCT
ma-9	285	9	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	285	10	eur	eur	NOUN
ma-9	285	11	.	.	PUNCT
ma-9	286	1	j.	j.	PROPN
ma-9	286	2	math	math	PROPN
ma-9	286	3	.	.	PUNCT
ma-9	287	1	anal	anal	ADJ
ma-9	287	2	.	.	PUNCT
ma-9	288	1	1	1	NUM
ma-9	288	2	(	(	PUNCT
ma-9	288	3	2021	2021	NUM
ma-9	288	4	)	)	PUNCT
ma-9	288	5	10	10	NUM
ma-9	288	6	≤	≤	NOUN
ma-9	288	7	m̃2e	m̃2e	ADJ
ma-9	288	8	max	max	NOUN
ma-9	288	9	i	i	PRON
ma-9	288	10	,	,	PUNCT
ma-9	288	11	k	k	PROPN
ma-9	288	12	{	{	PUNCT
ma-9	288	13	k∏	k∏	PROPN
ma-9	288	14	j	j	PROPN
ma-9	288	15	=	=	NOUN
ma-9	288	16	i	i	NOUN
ma-9	288	17	∥∥bj	∥∥bj	VERB
ma-9	288	18	(	(	PUNCT
ma-9	288	19	δj	δj	PROPN
ma-9	288	20	)	)	PUNCT
ma-9	288	21	∥∥	∥∥	NOUN
ma-9	288	22	}	}	PUNCT
ma-9	288	23			ADP
ma-9	288	24	2	2	NUM
ma-9	288	25	e	e	NOUN
ma-9	288	26	∥∥φ	∥∥φ	VERB
ma-9	288	27	−	−	PROPN
ma-9	288	28	h(0	h(0	PROPN
ma-9	288	29	,	,	PUNCT
ma-9	288	30	φ)∥∥2	φ)∥∥2	NOUN
ma-9	288	31	≤	≤	NOUN
ma-9	288	32	m̃2n	m̃2n	NOUN
ma-9	288	33	2e∥∥φ	2e∥∥φ	NUM
ma-9	288	34	−	−	PROPN
ma-9	288	35	h(0	h(0	PROPN
ma-9	288	36	,	,	PUNCT
ma-9	288	37	φ)∥∥2	φ)∥∥2	NOUN
ma-9	288	38	,	,	PUNCT
ma-9	288	39	g3	g3	PROPN
ma-9	288	40	≤	≤	PUNCT
ma-9	288	41	e	e	X
ma-9	288	42	[	[	PUNCT
ma-9	288	43	+	+	ADJ
ma-9	288	44	∞∑	∞∑	DET
ma-9	288	45	k=0	k=0	PROPN
ma-9	288	46	[	[	PUNCT
ma-9	288	47	k∏	k∏	PROPN
ma-9	288	48	j	j	PROPN
ma-9	288	49	=	=	NOUN
ma-9	288	50	i	i	NOUN
ma-9	288	51	∥∥bj	∥∥bj	VERB
ma-9	288	52	(	(	PUNCT
ma-9	288	53	δj	δj	ADJ
ma-9	288	54	)	)	PUNCT
ma-9	288	55	∥∥∫	∥∥∫	ADJ
ma-9	288	56	ξi	ξi	PROPN
ma-9	288	57	ξi−1	ξi−1	PROPN
ma-9	288	58	∥∥c(t	∥∥c(t	PROPN
ma-9	288	59	−	−	PROPN
ma-9	288	60	s)∥∥∥∥h(s	s)∥∥∥∥h(s	PROPN
ma-9	288	61	,	,	PUNCT
ma-9	288	62	xs)∥∥ds+	xs)∥∥ds+	PROPN
ma-9	288	63	∫	∫	PROPN
ma-9	288	64	t	t	PROPN
ma-9	288	65	ξk	ξk	ADP
ma-9	288	66	∥∥c(t	∥∥c(t	NOUN
ma-9	288	67	−	−	PROPN
ma-9	288	68	s)∥∥∥∥h(s	s)∥∥∥∥h(	NOUN
ma-9	288	69	,	,	PUNCT
ma-9	288	70	xs)∥∥ds]i[ξk	xs)∥∥ds]i[ξk	PROPN
ma-9	288	71	,	,	PUNCT
ma-9	288	72	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	288	73	≤	≤	NUM
ma-9	288	74	m2e	m2e	ADJ
ma-9	288	75	max	max	PROPN
ma-9	289	1	i	i	PRON
ma-9	289	2	,	,	PUNCT
ma-9	289	3	k	k	PROPN
ma-9	289	4	{	{	PUNCT
ma-9	289	5	1	1	NUM
ma-9	289	6	,	,	PUNCT
ma-9	289	7	k∏	k∏	PROPN
ma-9	289	8	j	j	PROPN
ma-9	290	1	=	=	NOUN
ma-9	290	2	i	i	NOUN
ma-9	290	3	∥∥bj	∥∥bj	VERB
ma-9	290	4	(	(	PUNCT
ma-9	290	5	δj	δj	PROPN
ma-9	290	6	)	)	PUNCT
ma-9	290	7	∥∥	∥∥	NOUN
ma-9	290	8	}	}	PUNCT
ma-9	290	9			ADP
ma-9	290	10	2	2	NUM
ma-9	290	11	(	(	PUNCT
ma-9	290	12	t	t	NOUN
ma-9	290	13	−	−	PROPN
ma-9	290	14	t0)∫	t0)∫	PROPN
ma-9	290	15	t	t	PROPN
ma-9	290	16	t0	t0	PROPN
ma-9	290	17	e	e	X
ma-9	290	18	∥∥h(s	∥∥h(s	PROPN
ma-9	290	19	,	,	PUNCT
ma-9	290	20	xs)∥∥2	xs)∥∥2	PROPN
ma-9	290	21	ds	ds	ADJ
ma-9	290	22	≤	≤	NUM
ma-9	290	23	2m2	2m2	NUM
ma-9	290	24	max{1,n	max{1,n	NOUN
ma-9	290	25	2}(t	2}(t	NUM
ma-9	290	26	−	−	PROPN
ma-9	290	27	t0	t0	PROPN
ma-9	290	28	)	)	PUNCT
ma-9	291	1	[	[	X
ma-9	291	2	∫	∫	X
ma-9	291	3	t	t	PROPN
ma-9	291	4	t0	t0	PROPN
ma-9	291	5	e	e	X
ma-9	291	6	∥∥h(s	∥∥h(s	PROPN
ma-9	291	7	,	,	PUNCT
ma-9	291	8	xs)−	xs)−	PUNCT
ma-9	292	1	h(s	h(	NOUN
ma-9	292	2	,	,	PUNCT
ma-9	292	3	0)∥∥2	0)∥∥2	NOUN
ma-9	292	4	ds+	ds+	NOUN
ma-9	292	5	∫	∫	PROPN
ma-9	292	6	t	t	PROPN
ma-9	292	7	t0	t0	PROPN
ma-9	292	8	∥∥h(s	∥∥h(s	PROPN
ma-9	292	9	,	,	PUNCT
ma-9	292	10	0)∥∥2	0)∥∥2	NOUN
ma-9	292	11	ds	ds	X
ma-9	292	12	]	]	PUNCT
ma-9	292	13	≤	≤	NOUN
ma-9	292	14	2m2	2m2	NUM
ma-9	292	15	max{1,n	max{1,n	NOUN
ma-9	292	16	2}(t	2}(t	NUM
ma-9	292	17	−	−	NOUN
ma-9	292	18	t0)∫	t0)∫	PROPN
ma-9	292	19	t	t	PROPN
ma-9	292	20	t0	t0	PROPN
ma-9	292	21	[	[	PUNCT
ma-9	292	22	lhe	lhe	ADJ
ma-9	292	23	∥x∥2	∥x∥2	NOUN
ma-9	292	24	s	s	PART
ma-9	292	25	+	+	X
ma-9	292	26	κh	κh	ADJ
ma-9	292	27	]	]	PUNCT
ma-9	292	28	ds	ds	ADJ
ma-9	292	29	≤	≤	NOUN
ma-9	292	30	2m2	2m2	NUM
ma-9	292	31	max{1,n	max{1,n	NOUN
ma-9	292	32	2}(t	2}(t	NUM
ma-9	292	33	−	−	NOUN
ma-9	292	34	t0)∫	t0)∫	PROPN
ma-9	292	35	t	t	PROPN
ma-9	292	36	t0	t0	PROPN
ma-9	292	37	lhe	lhe	PROPN
ma-9	292	38	∥x∥2	∥x∥2	PROPN
ma-9	292	39	s	s	PART
ma-9	292	40	ds+	ds+	ADJ
ma-9	292	41	2m2	2m2	NUM
ma-9	292	42	max{1,n	max{1,n	NOUN
ma-9	293	1	2}(t	2}(t	NUM
ma-9	293	2	−	−	NOUN
ma-9	293	3	t0)2κh	t0)2κh	NOUN
ma-9	293	4	,	,	PUNCT
ma-9	293	5	g4	g4	NOUN
ma-9	293	6	≤	≤	NOUN
ma-9	293	7	e	e	NOUN
ma-9	293	8	[	[	PUNCT
ma-9	293	9	+	+	ADJ
ma-9	293	10	∞∑	∞∑	DET
ma-9	293	11	k=0	k=0	PROPN
ma-9	293	12	[	[	PUNCT
ma-9	293	13	k∏	k∏	PROPN
ma-9	293	14	j	j	PROPN
ma-9	294	1	=	=	NOUN
ma-9	294	2	i	i	NOUN
ma-9	294	3	∥∥bj	∥∥bj	VERB
ma-9	294	4	(	(	PUNCT
ma-9	294	5	δj	δj	ADJ
ma-9	294	6	)	)	PUNCT
ma-9	294	7	∥∥∫	∥∥∫	PROPN
ma-9	294	8	ξi	ξi	PROPN
ma-9	294	9	ξi−1	ξi−1	PROPN
ma-9	294	10	∥∥s(t	∥∥s(t	PROPN
ma-9	294	11	−	−	PROPN
ma-9	294	12	s)∥∥∥∥f(s	s)∥∥∥∥f(	NOUN
ma-9	294	13	,	,	PUNCT
ma-9	294	14	xs)∥∥ds+	xs)∥∥ds+	PROPN
ma-9	294	15	∫	∫	PROPN
ma-9	294	16	t	t	PROPN
ma-9	294	17	ξk	ξk	ADP
ma-9	294	18	∥∥s(t	∥∥s(t	PROPN
ma-9	294	19	−	−	PROPN
ma-9	294	20	s)∥∥	s)∥∥	PROPN
ma-9	294	21	∥∥f(s	∥∥f(s	PROPN
ma-9	294	22	,	,	PUNCT
ma-9	294	23	xs)∥∥ds]i[ξk	xs)∥∥ds]i[ξk	PROPN
ma-9	294	24	,	,	PUNCT
ma-9	294	25	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	294	26	≤	≤	PROPN
ma-9	294	27	m̃2e	m̃2e	ADJ
ma-9	294	28	max	max	NOUN
ma-9	294	29	i	i	PRON
ma-9	294	30	,	,	PUNCT
ma-9	294	31	k	k	PROPN
ma-9	294	32	{	{	PUNCT
ma-9	294	33	1	1	NUM
ma-9	294	34	,	,	PUNCT
ma-9	294	35	k∏	k∏	PROPN
ma-9	294	36	j	j	PROPN
ma-9	295	1	=	=	NOUN
ma-9	295	2	i	i	NOUN
ma-9	295	3	∥∥bj	∥∥bj	VERB
ma-9	295	4	(	(	PUNCT
ma-9	295	5	δj	δj	PROPN
ma-9	295	6	)	)	PUNCT
ma-9	295	7	∥∥	∥∥	NOUN
ma-9	295	8	}	}	PUNCT
ma-9	295	9			ADP
ma-9	295	10	2	2	NUM
ma-9	295	11	(	(	PUNCT
ma-9	295	12	t	t	NOUN
ma-9	295	13	−	−	PROPN
ma-9	295	14	t0)∫	t0)∫	PROPN
ma-9	295	15	t	t	PROPN
ma-9	295	16	t0	t0	PROPN
ma-9	295	17	e	e	X
ma-9	295	18	∥∥f(s	∥∥f(s	PROPN
ma-9	295	19	,	,	PUNCT
ma-9	295	20	xs)∥∥2	xs)∥∥2	PROPN
ma-9	295	21	ds	ds	ADJ
ma-9	295	22	≤	≤	ADJ
ma-9	295	23	2m̃2	2m̃2	ADJ
ma-9	295	24	max{1,n	max{1,n	NOUN
ma-9	295	25	2}(t	2}(t	NUM
ma-9	295	26	−	−	PROPN
ma-9	295	27	t0	t0	PROPN
ma-9	295	28	)	)	PUNCT
ma-9	296	1	[	[	X
ma-9	296	2	∫	∫	X
ma-9	296	3	t	t	PROPN
ma-9	296	4	t0	t0	PROPN
ma-9	296	5	e	e	X
ma-9	296	6	∥∥f(s	∥∥f(	NOUN
ma-9	296	7	,	,	PUNCT
ma-9	296	8	xs)−	xs)−	PUNCT
ma-9	296	9	f(s	f(	NOUN
ma-9	296	10	,	,	PUNCT
ma-9	296	11	0)∥∥2	0)∥∥2	NOUN
ma-9	296	12	ds+	ds+	PROPN
ma-9	296	13	∫	∫	PROPN
ma-9	296	14	t	t	PROPN
ma-9	296	15	t0	t0	PROPN
ma-9	296	16	∥∥f(s	∥∥f(s	PROPN
ma-9	296	17	,	,	PUNCT
ma-9	296	18	0)∥∥2	0)∥∥2	NOUN
ma-9	296	19	ds	ds	X
ma-9	296	20	]	]	PUNCT
ma-9	296	21	≤	≤	NOUN
ma-9	296	22	2m̃2	2m̃2	NUM
ma-9	296	23	max{1,n	max{1,n	NOUN
ma-9	297	1	2}(t	2}(t	NUM
ma-9	297	2	−	−	NOUN
ma-9	297	3	t0)∫	t0)∫	PROPN
ma-9	297	4	t	t	PROPN
ma-9	297	5	t0	t0	PROPN
ma-9	297	6	[	[	PUNCT
ma-9	297	7	lfe	lfe	PROPN
ma-9	297	8	∥x∥2	∥x∥2	PROPN
ma-9	297	9	s	s	PART
ma-9	298	1	+	+	CCONJ
ma-9	298	2	κf	κf	ADP
ma-9	298	3	]	]	X
ma-9	298	4	ds	ds	ADJ
ma-9	298	5	≤	≤	ADJ
ma-9	298	6	2m̃2	2m̃2	ADJ
ma-9	298	7	max{1,n	max{1,n	NOUN
ma-9	299	1	2}(t	2}(t	NUM
ma-9	299	2	−	−	NOUN
ma-9	299	3	t0)∫	t0)∫	PROPN
ma-9	299	4	t	t	PROPN
ma-9	299	5	t0	t0	PROPN
ma-9	299	6	lfe	lfe	PROPN
ma-9	299	7	∥x∥2	∥x∥2	PROPN
ma-9	299	8	s	s	PART
ma-9	299	9	ds+	ds+	ADJ
ma-9	299	10	2m̃2	2m̃2	ADJ
ma-9	299	11	max{1,n	max{1,n	NOUN
ma-9	300	1	2}(t	2}(t	NUM
ma-9	300	2	−	−	NOUN
ma-9	300	3	t0)2κf	t0)2κf	NOUN
ma-9	300	4	,	,	PUNCT
ma-9	300	5	g5	g5	NOUN
ma-9	300	6	≤	≤	ADJ
ma-9	300	7	e	e	NOUN
ma-9	300	8	[	[	PUNCT
ma-9	300	9	+	+	ADJ
ma-9	300	10	∞∑	∞∑	DET
ma-9	300	11	k=0	k=0	PROPN
ma-9	300	12	[	[	PUNCT
ma-9	300	13	k∏	k∏	PROPN
ma-9	300	14	j	j	PROPN
ma-9	301	1	=	=	NOUN
ma-9	301	2	i	i	NOUN
ma-9	301	3	∥∥bj	∥∥bj	VERB
ma-9	301	4	(	(	PUNCT
ma-9	301	5	δj	δj	ADJ
ma-9	301	6	)	)	PUNCT
ma-9	301	7	∥∥∫	∥∥∫	PROPN
ma-9	301	8	ξi	ξi	PROPN
ma-9	301	9	ξi−1	ξi−1	PROPN
ma-9	301	10	∥∥s(t	∥∥s(t	PROPN
ma-9	301	11	−	−	PROPN
ma-9	301	12	s)∥∥∥∥g(s	s)∥∥∥∥g(s	ADJ
ma-9	301	13	,	,	PUNCT
ma-9	301	14	xs)∥∥dω(s	xs)∥∥dω(s	ADJ
ma-9	301	15	)	)	PUNCT
ma-9	302	1	+	+	CCONJ
ma-9	302	2	∫	∫	PROPN
ma-9	302	3	t	t	X
ma-9	302	4	ξk	ξk	ADP
ma-9	302	5	∥∥s(t	∥∥s(t	ADJ
ma-9	302	6	−	−	PROPN
ma-9	302	7	s)∥∥∥∥g(s	s)∥∥∥∥g(s	ADJ
ma-9	302	8	,	,	PUNCT
ma-9	302	9	xs)∥∥dω(s)]i[ξk	xs)∥∥dω(s)]i[ξk	PROPN
ma-9	302	10	,	,	PUNCT
ma-9	302	11	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	302	12	≤	≤	PUNCT
ma-9	302	13	m̃2e	m̃2e	ADJ
ma-9	302	14	max	max	NOUN
ma-9	303	1	i	i	PRON
ma-9	303	2	,	,	PUNCT
ma-9	303	3	k	k	PROPN
ma-9	303	4	{	{	PUNCT
ma-9	303	5	1	1	NUM
ma-9	303	6	,	,	PUNCT
ma-9	303	7	k∏	k∏	PROPN
ma-9	303	8	j	j	PROPN
ma-9	303	9	=	=	NOUN
ma-9	303	10	i	i	NOUN
ma-9	303	11	∥∥bj	∥∥bj	VERB
ma-9	303	12	(	(	PUNCT
ma-9	303	13	δj	δj	PROPN
ma-9	303	14	)	)	PUNCT
ma-9	303	15	∥∥	∥∥	NOUN
ma-9	303	16	}	}	PUNCT
ma-9	303	17			ADP
ma-9	303	18	2	2	NUM
ma-9	303	19	∫	∫	NOUN
ma-9	303	20	t	t	PROPN
ma-9	303	21	t0	t0	PROPN
ma-9	303	22	e	e	PROPN
ma-9	303	23	∥∥g(s	∥∥g(s	PROPN
ma-9	303	24	,	,	PUNCT
ma-9	303	25	xs)∥∥2	xs)∥∥2	PROPN
ma-9	303	26	ds	ds	ADJ
ma-9	303	27	≤	≤	ADJ
ma-9	303	28	2m̃2	2m̃2	ADJ
ma-9	303	29	max{1,n	max{1,n	NOUN
ma-9	303	30	2}t	2}t	NUM
ma-9	303	31	r(q	r(q	NOUN
ma-9	303	32	)	)	PUNCT
ma-9	304	1	[	[	X
ma-9	304	2	∫	∫	X
ma-9	304	3	t	t	PROPN
ma-9	304	4	t0	t0	PROPN
ma-9	304	5	e	e	PROPN
ma-9	304	6	∥∥g(s	∥∥g(s	NUM
ma-9	304	7	,	,	PUNCT
ma-9	304	8	xs)−	xs)−	PUNCT
ma-9	305	1	g(s	g(	NOUN
ma-9	305	2	,	,	PUNCT
ma-9	305	3	0)∥∥2	0)∥∥2	NOUN
ma-9	305	4	ds+	ds+	NOUN
ma-9	305	5	∫	∫	PROPN
ma-9	305	6	t	t	PROPN
ma-9	305	7	t0	t0	PROPN
ma-9	305	8	∥∥g(s	∥∥g(s	PROPN
ma-9	305	9	,	,	PUNCT
ma-9	305	10	0)∥∥2	0)∥∥2	NOUN
ma-9	305	11	ds	ds	X
ma-9	305	12	]	]	PUNCT
ma-9	305	13	≤	≤	NOUN
ma-9	305	14	2m̃2	2m̃2	NUM
ma-9	305	15	max{1,n	max{1,n	NOUN
ma-9	305	16	2}t	2}t	NUM
ma-9	305	17	r(q)∫	r(q)∫	NOUN
ma-9	305	18	t	t	PROPN
ma-9	305	19	t0	t0	PROPN
ma-9	305	20	[	[	PUNCT
ma-9	305	21	lge	lge	PROPN
ma-9	305	22	∥x∥2	∥x∥2	NOUN
ma-9	305	23	s	s	PART
ma-9	305	24	+	+	CCONJ
ma-9	305	25	κg	κg	PRON
ma-9	305	26	]	]	PUNCT
ma-9	305	27	ds	ds	ADJ
ma-9	305	28	≤	≤	ADJ
ma-9	305	29	2m̃2	2m̃2	ADJ
ma-9	305	30	max{1,n	max{1,n	NOUN
ma-9	305	31	2}t	2}t	NUM
ma-9	305	32	r(q)∫	r(q)∫	NOUN
ma-9	305	33	t	t	PROPN
ma-9	305	34	t0	t0	PROPN
ma-9	305	35	lge	lge	PROPN
ma-9	305	36	∥x∥2	∥x∥2	PROPN
ma-9	305	37	s	s	PART
ma-9	305	38	ds+	ds+	ADJ
ma-9	305	39	2m̃2	2m̃2	ADJ
ma-9	305	40	max{1,n	max{1,n	NOUN
ma-9	306	1	2}(t	2}(t	NUM
ma-9	306	2	−	−	X
ma-9	306	3	t0)t	t0)t	PROPN
ma-9	306	4	r(q)κg	r(q)κg	PROPN
ma-9	306	5	.	.	PUNCT
ma-9	307	1	eur	eur	PROPN
ma-9	307	2	.	.	PUNCT
ma-9	308	1	j.	j.	PROPN
ma-9	308	2	math	math	PROPN
ma-9	308	3	.	.	PUNCT
ma-9	309	1	anal	anal	ADJ
ma-9	309	2	.	.	PUNCT
ma-9	310	1	1	1	NUM
ma-9	310	2	(	(	PUNCT
ma-9	310	3	2021	2021	NUM
ma-9	310	4	)	)	PUNCT
ma-9	311	1	11	11	NUM
ma-9	311	2	g6	g6	ADJ
ma-9	311	3	≤	≤	NUM
ma-9	311	4	e	e	X
ma-9	311	5	[	[	PUNCT
ma-9	311	6	+	+	ADJ
ma-9	311	7	∞∑	∞∑	DET
ma-9	311	8	k=0	k=0	PROPN
ma-9	311	9	[	[	PUNCT
ma-9	311	10	k∏	k∏	PROPN
ma-9	311	11	j	j	PROPN
ma-9	311	12	=	=	NOUN
ma-9	311	13	i	i	NOUN
ma-9	311	14	∥∥bj	∥∥bj	VERB
ma-9	311	15	(	(	PUNCT
ma-9	311	16	δj	δj	ADJ
ma-9	311	17	)	)	PUNCT
ma-9	311	18	∥∥×	∥∥×	PROPN
ma-9	311	19	∫	∫	PROPN
ma-9	311	20	ξi	ξi	PROPN
ma-9	311	21	ξi−1	ξi−1	PROPN
ma-9	311	22	∫	∫	PROPN
ma-9	311	23	u	u	PROPN
ma-9	311	24	∥∥s(t	∥∥s(t	X
ma-9	311	25	−	−	PROPN
ma-9	311	26	s)∥∥∥∥σ	s)∥∥∥∥σ	PROPN
ma-9	311	27	(	(	PUNCT
ma-9	311	28	s	s	PROPN
ma-9	311	29	,	,	PUNCT
ma-9	311	30	xs	xs	PROPN
ma-9	311	31	,	,	PUNCT
ma-9	311	32	u)∥∥	u)∥∥	PROPN
ma-9	311	33	ñ(ds	ñ(ds	PROPN
ma-9	311	34	,	,	PUNCT
ma-9	311	35	du	du	PROPN
ma-9	311	36	)	)	PUNCT
ma-9	311	37	+	+	CCONJ
ma-9	311	38	∫	∫	PROPN
ma-9	311	39	t	t	X
ma-9	311	40	ξk	ξk	ADP
ma-9	311	41	∫	∫	PROPN
ma-9	311	42	u	u	NOUN
ma-9	311	43	∥∥s(t	∥∥s(t	X
ma-9	311	44	−	−	PROPN
ma-9	311	45	s)∥∥∥∥σ	s)∥∥∥∥σ	PROPN
ma-9	311	46	(	(	PUNCT
ma-9	311	47	s	s	PROPN
ma-9	311	48	,	,	PUNCT
ma-9	311	49	xs	xs	PROPN
ma-9	311	50	,	,	PUNCT
ma-9	311	51	u)∥∥	u)∥∥	NOUN
ma-9	311	52	ñ(ds	ñ(ds	PROPN
ma-9	311	53	,	,	PUNCT
ma-9	311	54	du)]i[ξk	du)]i[ξk	NOUN
ma-9	311	55	,	,	PUNCT
ma-9	311	56	ξk+1)(t)]2	ξk+1)(t)]2	PROPN
ma-9	311	57	≤	≤	ADV
ma-9	311	58	2m̃2	2m̃2	NUM
ma-9	311	59	max{1,n	max{1,n	NOUN
ma-9	311	60	2	2	NUM
ma-9	311	61	}	}	PUNCT
ma-9	311	62	∫	∫	PROPN
ma-9	311	63	t	t	PROPN
ma-9	311	64	t0	t0	PROPN
ma-9	311	65	∫	∫	PROPN
ma-9	311	66	u	u	X
ma-9	311	67	[	[	PUNCT
ma-9	311	68	e	e	X
ma-9	311	69	∥∥σ	∥∥σ	NUM
ma-9	311	70	(	(	PUNCT
ma-9	311	71	s	s	PROPN
ma-9	311	72	,	,	PUNCT
ma-9	311	73	xs	xs	PROPN
ma-9	311	74	,	,	PUNCT
ma-9	311	75	u)−	u)−	PROPN
ma-9	311	76	σ	σ	PROPN
ma-9	311	77	(	(	PUNCT
ma-9	311	78	s	s	PROPN
ma-9	311	79	,	,	PUNCT
ma-9	311	80	0	0	NUM
ma-9	311	81	,	,	PUNCT
ma-9	311	82	u)∥∥2	u)∥∥2	PROPN
ma-9	311	83	+	+	CCONJ
ma-9	311	84	∥∥σ	∥∥σ	ADJ
ma-9	311	85	(	(	PUNCT
ma-9	311	86	s	s	NOUN
ma-9	311	87	,	,	PUNCT
ma-9	311	88	0	0	NUM
ma-9	311	89	,	,	PUNCT
ma-9	311	90	u)∥∥2]ds	u)∥∥2]ds	PUNCT
ma-9	311	91	+	+	CCONJ
ma-9	311	92	2m̃2	2m̃2	ADJ
ma-9	311	93	max{1,n	max{1,n	NOUN
ma-9	311	94	2}(∫	2}(∫	NOUN
ma-9	312	1	t	t	X
ma-9	312	2	t0	t0	PROPN
ma-9	312	3	∫	∫	PROPN
ma-9	312	4	u	u	PROPN
ma-9	312	5	e	e	X
ma-9	312	6	∥∥σ	∥∥σ	NUM
ma-9	312	7	(	(	PUNCT
ma-9	312	8	s	s	PROPN
ma-9	312	9	,	,	PUNCT
ma-9	312	10	xs	xs	PROPN
ma-9	312	11	,	,	PUNCT
ma-9	312	12	u)∥∥4	u)∥∥4	PROPN
ma-9	312	13	v	v	X
ma-9	312	14	(	(	PUNCT
ma-9	312	15	du)ds	du)ds	PROPN
ma-9	312	16	)	)	PUNCT
ma-9	312	17	12	12	NUM
ma-9	312	18	≤	≤	NOUN
ma-9	312	19	4m̃2	4m̃2	ADJ
ma-9	312	20	max{1,n	max{1,n	NOUN
ma-9	312	21	2	2	NUM
ma-9	312	22	}	}	PUNCT
ma-9	312	23	∫	∫	PROPN
ma-9	312	24	t	t	PROPN
ma-9	312	25	t0	t0	PROPN
ma-9	312	26	lσe	lσe	PROPN
ma-9	312	27	∥x∥2	∥x∥2	PROPN
ma-9	312	28	s	s	PART
ma-9	312	29	ds+	ds+	ADJ
ma-9	313	1	2m̃2	2m̃2	ADJ
ma-9	313	2	max{1,n	max{1,n	NOUN
ma-9	314	1	2}(t	2}(t	NUM
ma-9	314	2	−	−	NOUN
ma-9	314	3	t0)κσ	t0)κσ	NOUN
ma-9	314	4	,	,	PUNCT
ma-9	314	5	thus	thus	ADV
ma-9	314	6	we	we	PRON
ma-9	314	7	would	would	AUX
ma-9	314	8	obtain	obtain	VERB
ma-9	314	9	,	,	PUNCT
ma-9	314	10	e	e	X
ma-9	314	11	∥∥(φx)(t)∥∥2	∥∥(φx)(t)∥∥2	NOUN
ma-9	314	12	t	t	PROPN
ma-9	314	13	≤	≤	NUM
ma-9	314	14	6m2n	6m2n	NUM
ma-9	314	15	2e∥∥φ(0)∥∥2	2e∥∥φ(0)∥∥2	NUM
ma-9	315	1	+	+	CCONJ
ma-9	316	1	6m̃2n	6m̃2n	NUM
ma-9	316	2	2e∥∥φ	2e∥∥φ	NUM
ma-9	316	3	−	−	PROPN
ma-9	316	4	h(0	h(0	PROPN
ma-9	316	5	,	,	PUNCT
ma-9	316	6	φ)∥∥2	φ)∥∥2	NOUN
ma-9	316	7	+	+	CCONJ
ma-9	316	8	12m2	12m2	NUM
ma-9	316	9	max{1,n	max{1,n	NOUN
ma-9	316	10	2}(t	2}(t	NUM
ma-9	316	11	−	−	PROPN
ma-9	316	12	t0	t0	PROPN
ma-9	316	13	)	)	PUNCT
ma-9	316	14	×	×	NOUN
ma-9	316	15	∫	∫	PROPN
ma-9	316	16	t	t	PROPN
ma-9	316	17	t0	t0	PROPN
ma-9	316	18	lhe	lhe	PROPN
ma-9	316	19	∥x∥2	∥x∥2	PROPN
ma-9	316	20	s	s	PART
ma-9	316	21	ds+	ds+	ADJ
ma-9	316	22	12m2	12m2	NUM
ma-9	316	23	max{1,n	max{1,n	NOUN
ma-9	316	24	2}(t	2}(t	NUM
ma-9	316	25	−	−	NOUN
ma-9	317	1	t0)2κh	t0)2κh	NOUN
ma-9	318	1	+	+	CCONJ
ma-9	318	2	12m̃2	12m̃2	NUM
ma-9	318	3	max{1,n	max{1,n	NOUN
ma-9	318	4	2}(t	2}(t	NUM
ma-9	318	5	−	−	PROPN
ma-9	318	6	t0	t0	PROPN
ma-9	318	7	)	)	PUNCT
ma-9	318	8	×	×	NOUN
ma-9	318	9	∫	∫	PROPN
ma-9	318	10	t	t	PROPN
ma-9	318	11	t0	t0	PROPN
ma-9	318	12	lfe	lfe	PROPN
ma-9	318	13	∥x∥2	∥x∥2	PROPN
ma-9	318	14	s	s	PART
ma-9	318	15	ds+	ds+	ADJ
ma-9	318	16	12m̃2	12m̃2	ADJ
ma-9	318	17	max{1,n	max{1,n	NUM
ma-9	319	1	2}(t	2}(t	NUM
ma-9	319	2	−	−	NOUN
ma-9	319	3	t0)2κf	t0)2κf	NOUN
ma-9	319	4	+	+	CCONJ
ma-9	319	5	12m̃2	12m̃2	NUM
ma-9	319	6	max{1,n	max{1,n	NOUN
ma-9	319	7	2}t	2}t	NUM
ma-9	319	8	r(q	r(q	NOUN
ma-9	319	9	)	)	PUNCT
ma-9	319	10	×	×	NOUN
ma-9	319	11	∫	∫	PROPN
ma-9	319	12	t	t	PROPN
ma-9	319	13	t0	t0	PROPN
ma-9	319	14	lge	lge	PROPN
ma-9	319	15	∥x∥2	∥x∥2	PROPN
ma-9	319	16	s	s	PART
ma-9	319	17	ds+	ds+	ADJ
ma-9	319	18	12m̃2	12m̃2	ADJ
ma-9	319	19	max{1,n	max{1,n	NUM
ma-9	319	20	2}(t	2}(t	NUM
ma-9	319	21	−	−	NOUN
ma-9	319	22	t0)t	t0)t	NOUN
ma-9	319	23	r(q)κg	r(q)κg	X
ma-9	319	24	+	+	X
ma-9	319	25	24m̃2	24m̃2	NUM
ma-9	319	26	max{1,n	max{1,n	NOUN
ma-9	319	27	2}∫	2}∫	NUM
ma-9	319	28	t	t	PROPN
ma-9	319	29	t0	t0	PROPN
ma-9	319	30	lσe	lσe	PROPN
ma-9	319	31	∥x∥2	∥x∥2	PROPN
ma-9	319	32	s	s	PART
ma-9	319	33	ds+	ds+	ADJ
ma-9	319	34	12m̃2	12m̃2	ADJ
ma-9	319	35	max{1,n	max{1,n	NUM
ma-9	319	36	2}(t	2}(t	NUM
ma-9	319	37	−	−	NOUN
ma-9	319	38	t0)κσ	t0)κσ	NOUN
ma-9	319	39	.	.	PUNCT
ma-9	320	1	taking	take	VERB
ma-9	320	2	supremum	supremum	ADV
ma-9	320	3	over	over	ADP
ma-9	320	4	t	t	PROPN
ma-9	320	5	,	,	PUNCT
ma-9	320	6	sup	sup	ADJ
ma-9	320	7	t0≤t≤t	t0≤t≤t	PROPN
ma-9	320	8	e	e	PROPN
ma-9	320	9	∥∥(φx)(t)∥∥2	∥∥(φx)(t)∥∥2	NOUN
ma-9	320	10	t	t	NOUN
ma-9	320	11	≤	≤	NUM
ma-9	320	12	6m2n	6m2n	NUM
ma-9	320	13	2e∥∥φ(0)∥∥2	2e∥∥φ(0)∥∥2	NUM
ma-9	321	1	+	+	CCONJ
ma-9	321	2	6m̃2n	6m̃2n	NUM
ma-9	321	3	2e∥∥φ	2e∥∥φ	NUM
ma-9	321	4	−	−	PROPN
ma-9	321	5	h(0	h(0	PROPN
ma-9	321	6	,	,	PUNCT
ma-9	321	7	φ)∥∥2	φ)∥∥2	NOUN
ma-9	321	8	+	+	CCONJ
ma-9	321	9	12m2	12m2	NUM
ma-9	321	10	max{1,n	max{1,n	NOUN
ma-9	321	11	2}(t	2}(t	NUM
ma-9	321	12	−	−	PROPN
ma-9	321	13	t0	t0	PROPN
ma-9	321	14	)	)	PUNCT
ma-9	321	15	×	×	NOUN
ma-9	321	16	∫	∫	PROPN
ma-9	321	17	t	t	PROPN
ma-9	321	18	t0	t0	PROPN
ma-9	321	19	lh	lh	PROPN
ma-9	321	20	sup	sup	VERB
ma-9	321	21	t0≤t≤t	t0≤t≤t	PROPN
ma-9	321	22	e	e	NOUN
ma-9	321	23	∥x∥2	∥x∥2	NOUN
ma-9	321	24	s	s	PART
ma-9	321	25	ds+	ds+	ADJ
ma-9	321	26	12m2	12m2	NUM
ma-9	321	27	max{1,n	max{1,n	NOUN
ma-9	321	28	2}(t	2}(t	NUM
ma-9	322	1	−	−	NOUN
ma-9	322	2	t0)2κh	t0)2κh	NOUN
ma-9	322	3	+	+	CCONJ
ma-9	322	4	12m̃2max{1,n	12m̃2max{1,n	NUM
ma-9	322	5	2	2	NUM
ma-9	322	6	}	}	SYM
ma-9	322	7	×	×	NOUN
ma-9	322	8	(	(	PUNCT
ma-9	322	9	t	t	PROPN
ma-9	322	10	−	−	PROPN
ma-9	322	11	t0)∫	t0)∫	PROPN
ma-9	322	12	t	t	PROPN
ma-9	322	13	t0	t0	PROPN
ma-9	322	14	lf	lf	ADP
ma-9	322	15	sup	sup	NOUN
ma-9	322	16	t0≤t≤t	t0≤t≤t	PROPN
ma-9	322	17	e	e	NOUN
ma-9	322	18	∥x∥2	∥x∥2	NOUN
ma-9	322	19	s	s	PART
ma-9	322	20	ds+	ds+	ADJ
ma-9	322	21	12m̃2	12m̃2	ADJ
ma-9	322	22	max{1,n	max{1,n	NUM
ma-9	323	1	2}(t	2}(t	NUM
ma-9	323	2	−	−	NOUN
ma-9	323	3	t0)2κf	t0)2κf	NOUN
ma-9	323	4	+	+	CCONJ
ma-9	323	5	12m̃2	12m̃2	NUM
ma-9	323	6	×	×	NOUN
ma-9	323	7	max{1,n	max{1,n	NOUN
ma-9	323	8	2}t	2}t	NUM
ma-9	323	9	r(q)∫	r(q)∫	NOUN
ma-9	323	10	t	t	PROPN
ma-9	323	11	t0	t0	PROPN
ma-9	323	12	lg	lg	PROPN
ma-9	323	13	sup	sup	PROPN
ma-9	323	14	t0≤t≤t	t0≤t≤t	NOUN
ma-9	323	15	e	e	NOUN
ma-9	323	16	∥x∥2	∥x∥2	NOUN
ma-9	323	17	s	s	PART
ma-9	323	18	ds+	ds+	ADJ
ma-9	323	19	12m̃2max{1,n	12m̃2max{1,n	NUM
ma-9	323	20	2}(t	2}(t	NUM
ma-9	323	21	−	−	NOUN
ma-9	323	22	t0)t	t0)t	NOUN
ma-9	323	23	r(q)κg	r(q)κg	X
ma-9	323	24	+	+	NOUN
ma-9	324	1	24m̃2	24m̃2	NUM
ma-9	324	2	max{1,n	max{1,n	NOUN
ma-9	324	3	2	2	NUM
ma-9	324	4	}	}	PUNCT
ma-9	324	5	∫	∫	PROPN
ma-9	324	6	t	t	PROPN
ma-9	324	7	t0	t0	PROPN
ma-9	324	8	lσ	lσ	NOUN
ma-9	324	9	sup	sup	ADJ
ma-9	324	10	t0≤t≤t	t0≤t≤t	NOUN
ma-9	324	11	e	e	NOUN
ma-9	324	12	∥x∥2	∥x∥2	NOUN
ma-9	324	13	s	s	PART
ma-9	324	14	ds+	ds+	ADJ
ma-9	324	15	12m̃2	12m̃2	ADJ
ma-9	324	16	max{1,n	max{1,n	NUM
ma-9	324	17	2}(t	2}(t	NUM
ma-9	324	18	−	−	PROPN
ma-9	324	19	t0)κσ	t0)κσ	PROPN
ma-9	324	20	eur	eur	PROPN
ma-9	324	21	.	.	PUNCT
ma-9	325	1	j.	j.	PROPN
ma-9	325	2	math	math	PROPN
ma-9	325	3	.	.	PUNCT
ma-9	326	1	anal	anal	ADJ
ma-9	326	2	.	.	PUNCT
ma-9	327	1	1	1	NUM
ma-9	327	2	(	(	PUNCT
ma-9	327	3	2021	2021	NUM
ma-9	327	4	)	)	PUNCT
ma-9	328	1	12	12	NUM
ma-9	328	2	≤	≤	NUM
ma-9	328	3	6m2n	6m2n	NUM
ma-9	328	4	2e∥∥φ(0)∥∥2	2e∥∥φ(0)∥∥2	NUM
ma-9	328	5	+	+	CCONJ
ma-9	328	6	6m̃2n	6m̃2n	NUM
ma-9	328	7	2e∥∥φ	2e∥∥φ	NUM
ma-9	328	8	−	−	PROPN
ma-9	328	9	h(0	h(0	PROPN
ma-9	328	10	,	,	PUNCT
ma-9	328	11	φ)∥∥2	φ)∥∥2	NOUN
ma-9	328	12	+	+	CCONJ
ma-9	328	13	12m2	12m2	NUM
ma-9	328	14	max{1,n	max{1,n	NOUN
ma-9	328	15	2}(t	2}(t	NUM
ma-9	328	16	−	−	NOUN
ma-9	328	17	t0)2	t0)2	NUM
ma-9	328	18	×	×	NOUN
ma-9	328	19	lh	lh	PROPN
ma-9	328	20	sup	sup	NOUN
ma-9	328	21	t0≤t≤t	t0≤t≤t	PROPN
ma-9	328	22	e	e	NOUN
ma-9	328	23	∥x∥2	∥x∥2	NOUN
ma-9	328	24	t	t	NOUN
ma-9	328	25	+	+	CCONJ
ma-9	328	26	12m2	12m2	NUM
ma-9	328	27	max{1,n	max{1,n	NOUN
ma-9	328	28	2}(t	2}(t	NUM
ma-9	328	29	−	−	NOUN
ma-9	328	30	t0)2κh	t0)2κh	NOUN
ma-9	328	31	+	+	CCONJ
ma-9	328	32	12m̃2	12m̃2	NUM
ma-9	328	33	max{1,n	max{1,n	NOUN
ma-9	328	34	2	2	NUM
ma-9	328	35	}	}	PUNCT
ma-9	328	36	×	×	NOUN
ma-9	328	37	(	(	PUNCT
ma-9	328	38	t	t	NOUN
ma-9	328	39	−	−	PROPN
ma-9	328	40	t0)2lf	t0)2lf	PROPN
ma-9	328	41	sup	sup	VERB
ma-9	328	42	t0≤t≤t	t0≤t≤t	NOUN
ma-9	328	43	e	e	NOUN
ma-9	328	44	∥x∥2	∥x∥2	NOUN
ma-9	328	45	t	t	NOUN
ma-9	329	1	+	+	CCONJ
ma-9	329	2	12m̃2	12m̃2	NUM
ma-9	329	3	max{1,n	max{1,n	NOUN
ma-9	329	4	2}(t	2}(t	NUM
ma-9	329	5	−	−	NOUN
ma-9	329	6	t0)2κf	t0)2κf	NOUN
ma-9	329	7	+	+	CCONJ
ma-9	329	8	12m̃2	12m̃2	NUM
ma-9	329	9	max{1,n	max{1,n	NOUN
ma-9	329	10	2}t	2}t	NUM
ma-9	329	11	r(q)(t	r(q)(t	SYM
ma-9	329	12	−	−	NUM
ma-9	329	13	t0)lg	t0)lg	PROPN
ma-9	329	14	sup	sup	NOUN
ma-9	329	15	t0≤t≤t	t0≤t≤t	PROPN
ma-9	329	16	e	e	NOUN
ma-9	329	17	∥x∥2	∥x∥2	NOUN
ma-9	329	18	t	t	NOUN
ma-9	330	1	+	+	CCONJ
ma-9	330	2	12m̃2	12m̃2	NUM
ma-9	330	3	max{1,n	max{1,n	NOUN
ma-9	330	4	2}(t	2}(t	NUM
ma-9	330	5	−	−	NOUN
ma-9	330	6	t0)t	t0)t	NOUN
ma-9	330	7	r(q)κg+	r(q)κg+	NOUN
ma-9	330	8	24m̃2	24m̃2	NUM
ma-9	330	9	max{1,n	max{1,n	NOUN
ma-9	331	1	2}(t	2}(t	NUM
ma-9	331	2	−	−	NOUN
ma-9	331	3	t0)lσ	t0)lσ	VERB
ma-9	331	4	sup	sup	NOUN
ma-9	331	5	t0≤t≤t	t0≤t≤t	NOUN
ma-9	331	6	e	e	NOUN
ma-9	331	7	∥x∥2	∥x∥2	NOUN
ma-9	331	8	s	s	PART
ma-9	331	9	ds+	ds+	ADJ
ma-9	331	10	12m̃2	12m̃2	ADJ
ma-9	331	11	max{1,n	max{1,n	NUM
ma-9	332	1	2}(t	2}(t	NUM
ma-9	332	2	−	−	NOUN
ma-9	332	3	t0)κσ	t0)κσ	NOUN
ma-9	332	4	≤	≤	NOUN
ma-9	332	5	6[n	6[n	NUM
ma-9	332	6	2	2	NUM
ma-9	332	7	[	[	X
ma-9	332	8	m2e∥∥φ(0)∥∥2	m2e∥∥φ(0)∥∥2	NOUN
ma-9	332	9	+	+	CCONJ
ma-9	332	10	m̃2e∥∥φ	m̃2e∥∥φ	PROPN
ma-9	332	11	−	−	PROPN
ma-9	332	12	h(0	h(0	PROPN
ma-9	332	13	,	,	PUNCT
ma-9	332	14	φ)∥∥2	φ)∥∥2	NOUN
ma-9	332	15	]	]	PUNCT
ma-9	332	16	]	]	X
ma-9	332	17	+	+	CCONJ
ma-9	332	18	12	12	NUM
ma-9	332	19	max{1,n	max{1,n	NOUN
ma-9	332	20	2}(t	2}(t	NUM
ma-9	332	21	−	−	PROPN
ma-9	332	22	t0	t0	PROPN
ma-9	332	23	)	)	PUNCT
ma-9	332	24	×	×	NOUN
ma-9	332	25	[	[	PUNCT
ma-9	332	26	m2(t	m2(t	NOUN
ma-9	332	27	−	−	PROPN
ma-9	332	28	t0)κh	t0)κh	NOUN
ma-9	333	1	+	+	CCONJ
ma-9	333	2	m̃2(t	m̃2(t	NOUN
ma-9	333	3	−	−	NOUN
ma-9	333	4	t0)κf	t0)κf	NOUN
ma-9	333	5	+	+	CCONJ
ma-9	333	6	m̃2	m̃2	PROPN
ma-9	333	7	t	t	PROPN
ma-9	333	8	r(q)κg	r(q)κg	X
ma-9	334	1	+	+	CCONJ
ma-9	334	2	m̃2κσ	m̃2κσ	NOUN
ma-9	334	3	]	]	X
ma-9	334	4	+	+	CCONJ
ma-9	334	5	12	12	NUM
ma-9	334	6	max{1,n	max{1,n	SYM
ma-9	334	7	2	2	NUM
ma-9	334	8	}	}	PUNCT
ma-9	334	9	×	×	NOUN
ma-9	334	10	(	(	PUNCT
ma-9	334	11	t	t	PROPN
ma-9	334	12	−	−	PROPN
ma-9	334	13	t0	t0	PROPN
ma-9	334	14	)	)	PUNCT
ma-9	335	1	[	[	X
ma-9	335	2	m2(t	m2(t	X
ma-9	335	3	−	−	NOUN
ma-9	335	4	t0)lh	t0)lh	NOUN
ma-9	335	5	+	+	CCONJ
ma-9	335	6	m̃2(t	m̃2(t	PROPN
ma-9	335	7	−	−	PROPN
ma-9	335	8	t0)lf	t0)lf	NOUN
ma-9	335	9	+	+	CCONJ
ma-9	335	10	m̃2	m̃2	PROPN
ma-9	335	11	t	t	PROPN
ma-9	335	12	r(q)lg	r(q)lg	NOUN
ma-9	335	13	+	+	CCONJ
ma-9	335	14	2m̃2lσ	2m̃2lσ	NOUN
ma-9	335	15	]	]	X
ma-9	335	16	∥x∥2	∥x∥2	NOUN
ma-9	335	17	t∥∥φx∥∥2	t∥∥φx∥∥2	NOUN
ma-9	335	18	b	b	PROPN
ma-9	335	19	≤	≤	PROPN
ma-9	335	20	c1	c1	NOUN
ma-9	335	21	+	+	CCONJ
ma-9	335	22	c2	c2	PROPN
ma-9	335	23	∥x∥2	∥x∥2	PROPN
ma-9	335	24	b	b	PROPN
ma-9	335	25	.where	.where	PROPN
ma-9	335	26	,	,	PUNCT
ma-9	335	27	c1	c1	PROPN
ma-9	335	28	=	=	PROPN
ma-9	336	1	6[n	6[n	NUM
ma-9	336	2	2	2	NUM
ma-9	337	1	[	[	X
ma-9	337	2	m2e∥∥φ(0)∥∥2	m2e∥∥φ(0)∥∥2	NOUN
ma-9	337	3	+	+	CCONJ
ma-9	337	4	m̃2e∥∥φ	m̃2e∥∥φ	PROPN
ma-9	337	5	−	−	PROPN
ma-9	337	6	h(0	h(0	PROPN
ma-9	337	7	,	,	PUNCT
ma-9	337	8	φ)∥∥2	φ)∥∥2	NOUN
ma-9	337	9	]	]	PUNCT
ma-9	337	10	]	]	X
ma-9	337	11	+	+	CCONJ
ma-9	337	12	12	12	NUM
ma-9	337	13	max{1,n	max{1,n	NOUN
ma-9	337	14	2}(t	2}(t	NUM
ma-9	337	15	−	−	PROPN
ma-9	337	16	t0	t0	PROPN
ma-9	337	17	)	)	PUNCT
ma-9	337	18	×	×	NOUN
ma-9	337	19	[	[	PUNCT
ma-9	337	20	m2(t	m2(t	NOUN
ma-9	337	21	−	−	PROPN
ma-9	337	22	t0)κh	t0)κh	NOUN
ma-9	338	1	+	+	CCONJ
ma-9	338	2	m̃2(t	m̃2(t	NOUN
ma-9	338	3	−	−	NOUN
ma-9	338	4	t0)κf	t0)κf	NOUN
ma-9	338	5	+	+	CCONJ
ma-9	338	6	m̃2	m̃2	PROPN
ma-9	338	7	t	t	PROPN
ma-9	338	8	r(q)κg	r(q)κg	X
ma-9	338	9	+	+	X
ma-9	338	10	m̃2κσ	m̃2κσ	X
ma-9	338	11	]	]	PUNCT
ma-9	338	12	,	,	PUNCT
ma-9	338	13	c2	c2	PROPN
ma-9	338	14	=	=	PROPN
ma-9	338	15	12	12	NUM
ma-9	338	16	max{1,n	max{1,n	NOUN
ma-9	338	17	2}(t	2}(t	NUM
ma-9	338	18	−	−	PROPN
ma-9	338	19	t0	t0	PROPN
ma-9	338	20	)	)	PUNCT
ma-9	339	1	[	[	X
ma-9	339	2	m2(t	m2(t	X
ma-9	339	3	−	−	NOUN
ma-9	339	4	t0)lh	t0)lh	NOUN
ma-9	339	5	+	+	CCONJ
ma-9	339	6	m̃2(t	m̃2(t	PROPN
ma-9	339	7	−	−	PROPN
ma-9	339	8	t0)lf	t0)lf	NOUN
ma-9	339	9	+	+	CCONJ
ma-9	339	10	m̃2	m̃2	PROPN
ma-9	339	11	t	t	PROPN
ma-9	339	12	r(q)lg	r(q)lg	NOUN
ma-9	339	13	+	+	CCONJ
ma-9	339	14	2m̃2lσ	2m̃2lσ	NOUN
ma-9	339	15	]	]	PUNCT
ma-9	339	16	.	.	PUNCT
ma-9	340	1	where	where	SCONJ
ma-9	340	2	c1	c1	PROPN
ma-9	340	3	and	and	CCONJ
ma-9	340	4	c2	c2	PROPN
ma-9	340	5	are	be	AUX
ma-9	340	6	constants.hence	constants.hence	PROPN
ma-9	340	7	φ	φ	NOUN
ma-9	340	8	is	be	AUX
ma-9	340	9	bounded.now	bounded.now	ADJ
ma-9	340	10	we	we	PRON
ma-9	340	11	need	need	VERB
ma-9	340	12	to	to	PART
ma-9	340	13	prove	prove	VERB
ma-9	340	14	that	that	SCONJ
ma-9	340	15	φ	φ	PROPN
ma-9	340	16	is	be	AUX
ma-9	340	17	a	a	DET
ma-9	340	18	contraction	contraction	NOUN
ma-9	340	19	mapping	mapping	NOUN
ma-9	340	20	.	.	PUNCT
ma-9	341	1	for	for	ADP
ma-9	341	2	any	any	DET
ma-9	341	3	x	x	NOUN
ma-9	341	4	,	,	PUNCT
ma-9	341	5	y	y	PROPN
ma-9	341	6	∈	∈	PROPN
ma-9	341	7	b	b	NOUN
ma-9	341	8	we	we	PRON
ma-9	341	9	have,∥∥(φx)(t)−	have,∥∥(φx)(t)−	PROPN
ma-9	341	10	(	(	PUNCT
ma-9	341	11	φy)(t)∥∥2	φy)(t)∥∥2	PROPN
ma-9	341	12	≤	≤	PROPN
ma-9	341	13	∥∥∥∥	∥∥∥∥	NUM
ma-9	342	1	+	+	PUNCT
ma-9	342	2	∞∑	∞∑	PRON
ma-9	342	3	k=0	k=0	PROPN
ma-9	342	4	[	[	PUNCT
ma-9	342	5	k∑	k∑	NOUN
ma-9	342	6	i=1	i=1	PROPN
ma-9	343	1	k∏	k∏	PROPN
ma-9	343	2	j	j	PROPN
ma-9	344	1	=	=	NOUN
ma-9	344	2	i	i	PRON
ma-9	344	3	bj	bj	VERB
ma-9	344	4	(	(	PUNCT
ma-9	344	5	δj	δj	ADJ
ma-9	344	6	)	)	PUNCT
ma-9	344	7	∫	∫	PROPN
ma-9	345	1	ξi	ξi	PROPN
ma-9	345	2	ξi−1	ξi−1	PROPN
ma-9	345	3	c(t	c(t	PROPN
ma-9	345	4	−	−	PROPN
ma-9	345	5	s)h(s	s)h(s	NOUN
ma-9	345	6	,	,	PUNCT
ma-9	345	7	xs)ds+	xs)ds+	PROPN
ma-9	345	8	∫	∫	PROPN
ma-9	346	1	t	t	PROPN
ma-9	346	2	ξk	ξk	ADP
ma-9	346	3	c(t	c(t	PROPN
ma-9	346	4	−	−	PROPN
ma-9	346	5	s)h(s	s)h(s	NOUN
ma-9	346	6	,	,	PUNCT
ma-9	346	7	xs)ds	xs)ds	PUNCT
ma-9	347	1	+	+	CCONJ
ma-9	348	1	k∑	k∑	ADJ
ma-9	348	2	i=1	i=1	PROPN
ma-9	349	1	k∏	k∏	PROPN
ma-9	349	2	j	j	PROPN
ma-9	350	1	=	=	NOUN
ma-9	350	2	i	i	PRON
ma-9	350	3	bj	bj	VERB
ma-9	350	4	(	(	PUNCT
ma-9	350	5	δj	δj	ADJ
ma-9	350	6	)	)	PUNCT
ma-9	350	7	∫	∫	PROPN
ma-9	350	8	ξi	ξi	PROPN
ma-9	350	9	ξi−1	ξi−1	PROPN
ma-9	350	10	s(t	s(t	PROPN
ma-9	350	11	−	−	PROPN
ma-9	350	12	s)f(s	s)f(	NOUN
ma-9	350	13	,	,	PUNCT
ma-9	351	1	xs)ds+	xs)ds+	PROPN
ma-9	351	2	∫	∫	PROPN
ma-9	351	3	t	t	PROPN
ma-9	351	4	ξk	ξk	ADP
ma-9	351	5	s(t	s(t	PROPN
ma-9	351	6	−	−	PROPN
ma-9	351	7	s)f(s	s)f(	NOUN
ma-9	351	8	,	,	PUNCT
ma-9	351	9	xs)ds+	xs)ds+	PROPN
ma-9	351	10	k∑	k∑	VERB
ma-9	351	11	i=1	i=1	PROPN
ma-9	352	1	k∏	k∏	PROPN
ma-9	352	2	j	j	PROPN
ma-9	353	1	=	=	NOUN
ma-9	353	2	i	i	PRON
ma-9	353	3	bj	bj	VERB
ma-9	353	4	(	(	PUNCT
ma-9	353	5	δj	δj	ADJ
ma-9	353	6	)	)	PUNCT
ma-9	353	7	×	×	NOUN
ma-9	353	8	∫	∫	PROPN
ma-9	353	9	ξi	ξi	PROPN
ma-9	353	10	ξi−1	ξi−1	PROPN
ma-9	353	11	s(t	s(t	PROPN
ma-9	353	12	−	−	PROPN
ma-9	353	13	s)g(s	s)g(s	NOUN
ma-9	353	14	,	,	PUNCT
ma-9	353	15	xs)dω(s	xs)dω(s	PROPN
ma-9	353	16	)	)	PUNCT
ma-9	353	17	+	+	CCONJ
ma-9	353	18	∫	∫	PROPN
ma-9	353	19	t	t	PROPN
ma-9	353	20	ξk	ξk	ADP
ma-9	353	21	s(t	s(t	PROPN
ma-9	353	22	−	−	PROPN
ma-9	353	23	s)g(s	s)g(s	NOUN
ma-9	353	24	,	,	PUNCT
ma-9	353	25	xs)dω(s	xs)dω(s	PROPN
ma-9	353	26	)	)	PUNCT
ma-9	353	27	+	+	CCONJ
ma-9	353	28	k∑	k∑	VERB
ma-9	353	29	i=1	i=1	PROPN
ma-9	354	1	k∏	k∏	PROPN
ma-9	354	2	j	j	PROPN
ma-9	355	1	=	=	NOUN
ma-9	355	2	i	i	PRON
ma-9	355	3	bj	bj	VERB
ma-9	355	4	(	(	PUNCT
ma-9	355	5	δj	δj	ADJ
ma-9	355	6	)	)	PUNCT
ma-9	355	7	×	×	NOUN
ma-9	355	8	∫	∫	PROPN
ma-9	355	9	ξi	ξi	PROPN
ma-9	355	10	ξi−1	ξi−1	PROPN
ma-9	355	11	∫	∫	PROPN
ma-9	355	12	u	u	PROPN
ma-9	355	13	s(t	s(t	PROPN
ma-9	355	14	−	−	PROPN
ma-9	355	15	s)σ	s)σ	X
ma-9	355	16	(	(	PUNCT
ma-9	355	17	s	s	PROPN
ma-9	355	18	,	,	PUNCT
ma-9	355	19	xs	xs	PROPN
ma-9	355	20	,	,	PUNCT
ma-9	355	21	u)ñ(ds	u)ñ(ds	PROPN
ma-9	355	22	,	,	PUNCT
ma-9	355	23	dt	dt	PROPN
ma-9	355	24	)	)	PUNCT
ma-9	356	1	+	+	CCONJ
ma-9	356	2	∫	∫	PROPN
ma-9	356	3	t	t	X
ma-9	356	4	ξk	ξk	ADP
ma-9	356	5	∫	∫	PROPN
ma-9	356	6	u	u	PROPN
ma-9	356	7	s(t	s(t	PROPN
ma-9	356	8	−	−	PROPN
ma-9	356	9	s)σ	s)σ	X
ma-9	356	10	(	(	PUNCT
ma-9	356	11	s	s	PROPN
ma-9	356	12	,	,	PUNCT
ma-9	356	13	xs	xs	PROPN
ma-9	356	14	,	,	PUNCT
ma-9	356	15	u)ñ(ds	u)ñ(ds	PROPN
ma-9	356	16	,	,	PUNCT
ma-9	356	17	dt)]i[ξk	dt)]i[ξk	NOUN
ma-9	356	18	,	,	PUNCT
ma-9	356	19	ξk+1)(t)∥∥∥∥2	ξk+1)(t)∥∥∥∥2	PROPN
ma-9	356	20	−	−	NOUN
ma-9	356	21	∥∥∥∥	∥∥∥∥	PUNCT
ma-9	357	1	+	+	NOUN
ma-9	357	2	∞∑	∞∑	PRON
ma-9	357	3	k=0	k=0	PROPN
ma-9	357	4	[	[	PUNCT
ma-9	357	5	k∑	k∑	NOUN
ma-9	357	6	i=1	i=1	PROPN
ma-9	358	1	k∏	k∏	PROPN
ma-9	358	2	j	j	PROPN
ma-9	359	1	=	=	NOUN
ma-9	359	2	i	i	PRON
ma-9	359	3	bj	bj	VERB
ma-9	359	4	(	(	PUNCT
ma-9	359	5	δj	δj	ADJ
ma-9	359	6	)	)	PUNCT
ma-9	359	7	∫	∫	PROPN
ma-9	360	1	ξi	ξi	PROPN
ma-9	360	2	ξi−1	ξi−1	PROPN
ma-9	360	3	c(t	c(t	PROPN
ma-9	360	4	−	−	PROPN
ma-9	360	5	s)h(s	s)h(s	NOUN
ma-9	360	6	,	,	PUNCT
ma-9	360	7	ys)ds+	ys)ds+	ADJ
ma-9	360	8	∫	∫	PROPN
ma-9	360	9	t	t	NOUN
ma-9	360	10	ξk	ξk	ADP
ma-9	360	11	c(t	c(t	PROPN
ma-9	360	12	−	−	PROPN
ma-9	360	13	s)h(s	s)h(s	NOUN
ma-9	360	14	,	,	PUNCT
ma-9	360	15	ys)ds	ys)ds	X
ma-9	360	16	eur	eur	PROPN
ma-9	360	17	.	.	PUNCT
ma-9	361	1	j.	j.	PROPN
ma-9	361	2	math	math	PROPN
ma-9	361	3	.	.	PUNCT
ma-9	362	1	anal	anal	ADJ
ma-9	362	2	.	.	PUNCT
ma-9	363	1	1	1	NUM
ma-9	363	2	(	(	PUNCT
ma-9	363	3	2021	2021	NUM
ma-9	363	4	)	)	PUNCT
ma-9	363	5	13	13	NUM
ma-9	364	1	+	+	CCONJ
ma-9	364	2	k∑	k∑	ADJ
ma-9	364	3	i=1	i=1	PROPN
ma-9	365	1	k∏	k∏	PROPN
ma-9	365	2	j	j	PROPN
ma-9	366	1	=	=	NOUN
ma-9	366	2	i	i	PRON
ma-9	366	3	bj	bj	VERB
ma-9	366	4	(	(	PUNCT
ma-9	366	5	δj	δj	ADJ
ma-9	366	6	)	)	PUNCT
ma-9	366	7	∫	∫	PROPN
ma-9	366	8	ξi	ξi	PROPN
ma-9	366	9	ξi−1	ξi−1	PROPN
ma-9	366	10	s(t	s(t	PROPN
ma-9	366	11	−	−	PROPN
ma-9	366	12	s)f(s	s)f(	NOUN
ma-9	366	13	,	,	PUNCT
ma-9	366	14	ys)ds+	ys)ds+	ADJ
ma-9	366	15	∫	∫	PROPN
ma-9	366	16	t	t	NOUN
ma-9	366	17	ξk	ξk	ADP
ma-9	366	18	s(t	s(t	PROPN
ma-9	366	19	−	−	PROPN
ma-9	366	20	s)f(s	s)f(	NOUN
ma-9	366	21	,	,	PUNCT
ma-9	366	22	ys)ds+	ys)ds+	PROPN
ma-9	366	23	k∑	k∑	NOUN
ma-9	367	1	i=1	i=1	PROPN
ma-9	367	2	k∏	k∏	PROPN
ma-9	367	3	j	j	PROPN
ma-9	368	1	=	=	NOUN
ma-9	368	2	i	i	PRON
ma-9	368	3	bj	bj	VERB
ma-9	368	4	(	(	PUNCT
ma-9	368	5	δj	δj	ADJ
ma-9	368	6	)	)	PUNCT
ma-9	368	7	×	×	NOUN
ma-9	368	8	∫	∫	PROPN
ma-9	368	9	ξi	ξi	PROPN
ma-9	368	10	ξi−1	ξi−1	PROPN
ma-9	368	11	s(t	s(t	PROPN
ma-9	368	12	−	−	PROPN
ma-9	368	13	s)g(s	s)g(s	NOUN
ma-9	368	14	,	,	PUNCT
ma-9	368	15	ys)dω(s	ys)dω(s	PROPN
ma-9	368	16	)	)	PUNCT
ma-9	368	17	+	+	NUM
ma-9	368	18	∫	∫	PROPN
ma-9	368	19	t	t	PROPN
ma-9	368	20	ξk	ξk	ADP
ma-9	368	21	s(t	s(t	PROPN
ma-9	368	22	−	−	PROPN
ma-9	368	23	s)g(s	s)g(s	NOUN
ma-9	368	24	,	,	PUNCT
ma-9	368	25	ys)dω(s	ys)dω(s	PROPN
ma-9	368	26	)	)	PUNCT
ma-9	368	27	+	+	CCONJ
ma-9	368	28	k∑	k∑	VERB
ma-9	368	29	i=1	i=1	PROPN
ma-9	369	1	k∏	k∏	PROPN
ma-9	369	2	j	j	PROPN
ma-9	370	1	=	=	NOUN
ma-9	370	2	i	i	PRON
ma-9	370	3	bj	bj	VERB
ma-9	370	4	(	(	PUNCT
ma-9	370	5	δj	δj	ADJ
ma-9	370	6	)	)	PUNCT
ma-9	370	7	×	×	NOUN
ma-9	370	8	∫	∫	PROPN
ma-9	370	9	ξi	ξi	PROPN
ma-9	370	10	ξi−1	ξi−1	PROPN
ma-9	370	11	∫	∫	PROPN
ma-9	370	12	u	u	PROPN
ma-9	370	13	s(t	s(t	PROPN
ma-9	370	14	−	−	PROPN
ma-9	370	15	s)σ	s)σ	X
ma-9	370	16	(	(	PUNCT
ma-9	370	17	s	s	X
ma-9	370	18	,	,	PUNCT
ma-9	370	19	ys	ys	ADJ
ma-9	370	20	,	,	PUNCT
ma-9	370	21	u)ñ(ds	u)ñ(ds	PROPN
ma-9	370	22	,	,	PUNCT
ma-9	370	23	dt	dt	PROPN
ma-9	370	24	)	)	PUNCT
ma-9	371	1	+	+	CCONJ
ma-9	371	2	∫	∫	PROPN
ma-9	371	3	t	t	X
ma-9	371	4	ξk	ξk	ADP
ma-9	371	5	∫	∫	PROPN
ma-9	371	6	u	u	PROPN
ma-9	371	7	s(t	s(t	PROPN
ma-9	371	8	−	−	PROPN
ma-9	371	9	s)σ	s)σ	X
ma-9	371	10	(	(	PUNCT
ma-9	371	11	s	s	X
ma-9	371	12	,	,	PUNCT
ma-9	371	13	ys	ys	ADJ
ma-9	371	14	,	,	PUNCT
ma-9	371	15	u)ñ(ds	u)ñ(ds	PROPN
ma-9	371	16	,	,	PUNCT
ma-9	371	17	dt)]i[ξk	dt)]i[ξk	NOUN
ma-9	371	18	,	,	PUNCT
ma-9	371	19	ξk+1)(t)∥∥∥∥2	ξk+1)(t)∥∥∥∥2	PROPN
ma-9	371	20	≤	≤	NUM
ma-9	371	21	4	4	NUM
ma-9	371	22	max{1,n	max{1,n	NOUN
ma-9	371	23	2}m2(t	2}m2(t	NUM
ma-9	371	24	−	−	NOUN
ma-9	372	1	t0)∫	t0)∫	PROPN
ma-9	372	2	t	t	PROPN
ma-9	372	3	t0	t0	PROPN
ma-9	372	4	∥∥h(t	∥∥h(t	PROPN
ma-9	372	5	,	,	PUNCT
ma-9	372	6	xs)−	xs)−	PUNCT
ma-9	373	1	h(t	h(t	PROPN
ma-9	373	2	,	,	PUNCT
ma-9	373	3	ys)∥∥2	ys)∥∥2	PROPN
ma-9	373	4	ds+	ds+	NOUN
ma-9	373	5	4	4	NUM
ma-9	373	6	max{1,n	max{1,n	SYM
ma-9	373	7	2	2	NUM
ma-9	373	8	}	}	PUNCT
ma-9	373	9	×	×	NOUN
ma-9	373	10	m̃2(t	m̃2(t	PROPN
ma-9	373	11	−	−	PROPN
ma-9	374	1	t0)∫	t0)∫	PROPN
ma-9	374	2	t	t	PROPN
ma-9	374	3	t0	t0	PROPN
ma-9	374	4	∥∥f(t	∥∥f(t	NOUN
ma-9	374	5	,	,	PUNCT
ma-9	374	6	xs)−	xs)−	PUNCT
ma-9	375	1	f(t	f(t	NOUN
ma-9	375	2	,	,	PUNCT
ma-9	375	3	ys)∥∥2	ys)∥∥2	PROPN
ma-9	375	4	ds+	ds+	NOUN
ma-9	375	5	4	4	NUM
ma-9	375	6	max{1,n	max{1,n	NOUN
ma-9	375	7	2}m̃2	2}m̃2	NUM
ma-9	375	8	×	×	NOUN
ma-9	375	9	∫	∫	PROPN
ma-9	375	10	t	t	PROPN
ma-9	375	11	t0	t0	PROPN
ma-9	375	12	∥∥g(t	∥∥g(t	PROPN
ma-9	375	13	,	,	PUNCT
ma-9	375	14	xs)−	xs)−	PUNCT
ma-9	376	1	g(t	g(t	PROPN
ma-9	376	2	,	,	PUNCT
ma-9	376	3	ys)∥∥2	ys)∥∥2	PROPN
ma-9	376	4	ds+	ds+	NOUN
ma-9	376	5	4	4	NUM
ma-9	376	6	max{1,n	max{1,n	NOUN
ma-9	376	7	2}m̃2	2}m̃2	NUM
ma-9	376	8	×	×	NOUN
ma-9	376	9	[	[	PUNCT
ma-9	376	10	∫	∫	PROPN
ma-9	376	11	t	t	PROPN
ma-9	376	12	t0	t0	PROPN
ma-9	376	13	∫	∫	PROPN
ma-9	376	14	u	u	PROPN
ma-9	376	15	∥∥σ	∥∥σ	VERB
ma-9	376	16	(	(	PUNCT
ma-9	376	17	t	t	PROPN
ma-9	376	18	,	,	PUNCT
ma-9	376	19	xs	xs	PROPN
ma-9	376	20	,	,	PUNCT
ma-9	376	21	u)−	u)−	PROPN
ma-9	376	22	σ	σ	PROPN
ma-9	376	23	(	(	PUNCT
ma-9	376	24	t	t	PROPN
ma-9	376	25	,	,	PUNCT
ma-9	376	26	ys	ys	NOUN
ma-9	376	27	,	,	PUNCT
ma-9	376	28	u)∥∥2	u)∥∥2	NOUN
ma-9	376	29	v	v	X
ma-9	376	30	(	(	PUNCT
ma-9	376	31	du)ds	du)ds	X
ma-9	376	32	+	+	CCONJ
ma-9	376	33	(	(	PUNCT
ma-9	376	34	∫	∫	PROPN
ma-9	376	35	t	t	PROPN
ma-9	376	36	t0	t0	PROPN
ma-9	376	37	∫	∫	PROPN
ma-9	376	38	u	u	PROPN
ma-9	376	39	∥∥σ	∥∥σ	VERB
ma-9	376	40	(	(	PUNCT
ma-9	376	41	t	t	PROPN
ma-9	376	42	,	,	PUNCT
ma-9	376	43	xs	xs	PROPN
ma-9	376	44	,	,	PUNCT
ma-9	376	45	u)−	u)−	PROPN
ma-9	376	46	σ	σ	PROPN
ma-9	376	47	(	(	PUNCT
ma-9	376	48	t	t	PROPN
ma-9	376	49	,	,	PUNCT
ma-9	376	50	ys	ys	NOUN
ma-9	376	51	,	,	PUNCT
ma-9	376	52	u)∥∥4	u)∥∥4	PROPN
ma-9	376	53	v	v	X
ma-9	376	54	(	(	PUNCT
ma-9	376	55	du)ds	du)ds	PROPN
ma-9	376	56	)	)	PUNCT
ma-9	376	57	12	12	NUM
ma-9	376	58	]	]	PUNCT
ma-9	376	59	moreover	moreover	ADV
ma-9	376	60	,	,	PUNCT
ma-9	376	61	sup	sup	ADJ
ma-9	376	62	t0≤t≤t	t0≤t≤t	PROPN
ma-9	376	63	e	e	PROPN
ma-9	376	64	∥∥(φx)(t)−	∥∥(φx)(t)−	X
ma-9	376	65	(	(	PUNCT
ma-9	376	66	φy)(t)∥∥2	φy)(t)∥∥2	PROPN
ma-9	376	67	≤	≤	ADV
ma-9	376	68	4	4	NUM
ma-9	376	69	max{1,n	max{1,n	NOUN
ma-9	376	70	2}m2(t	2}m2(t	NUM
ma-9	376	71	−	−	NOUN
ma-9	377	1	t0)2lh	t0)2lh	NOUN
ma-9	377	2	sup	sup	NOUN
ma-9	377	3	t0≤t≤t	t0≤t≤t	PROPN
ma-9	377	4	e	e	PROPN
ma-9	377	5	∥∥x	∥∥x	VERB
ma-9	377	6	−	−	PROPN
ma-9	377	7	y∥∥2	y∥∥2	PROPN
ma-9	377	8	s	s	PART
ma-9	377	9	ds+	ds+	ADJ
ma-9	377	10	4	4	NUM
ma-9	377	11	max{1,n	max{1,n	SYM
ma-9	377	12	2	2	NUM
ma-9	377	13	}	}	PUNCT
ma-9	377	14	×	×	NOUN
ma-9	377	15	m̃2(t	m̃2(t	PROPN
ma-9	377	16	−	−	NOUN
ma-9	378	1	t0)2lf	t0)2lf	PROPN
ma-9	378	2	sup	sup	VERB
ma-9	378	3	t0≤t≤t	t0≤t≤t	PROPN
ma-9	378	4	e	e	PROPN
ma-9	378	5	∥∥x	∥∥x	NOUN
ma-9	378	6	−	−	PROPN
ma-9	378	7	y∥∥2	y∥∥2	PROPN
ma-9	378	8	s	s	PART
ma-9	378	9	ds+	ds+	ADJ
ma-9	378	10	4	4	NUM
ma-9	378	11	max{1,n	max{1,n	NOUN
ma-9	378	12	2}m̃2	2}m̃2	PROPN
ma-9	378	13	t	t	PROPN
ma-9	378	14	r(q	r(q	PROPN
ma-9	378	15	)	)	PUNCT
ma-9	378	16	×	×	NOUN
ma-9	378	17	(	(	PUNCT
ma-9	378	18	t	t	NOUN
ma-9	378	19	−	−	PROPN
ma-9	379	1	t0)lg	t0)lg	PROPN
ma-9	379	2	sup	sup	PROPN
ma-9	379	3	t0≤t≤t	t0≤t≤t	PROPN
ma-9	379	4	e	e	PROPN
ma-9	379	5	∥∥x	∥∥x	VERB
ma-9	379	6	−	−	PROPN
ma-9	379	7	y∥∥2	y∥∥2	PROPN
ma-9	379	8	s	s	PART
ma-9	379	9	ds+	ds+	ADJ
ma-9	379	10	4	4	NUM
ma-9	379	11	max{1,n	max{1,n	NOUN
ma-9	380	1	2}m̃2	2}m̃2	NUM
ma-9	380	2	×	×	NOUN
ma-9	380	3	(	(	PUNCT
ma-9	380	4	t	t	NOUN
ma-9	380	5	−	−	PROPN
ma-9	380	6	t0)lσ	t0)lσ	NOUN
ma-9	380	7	sup	sup	NOUN
ma-9	380	8	t0≤t≤t	t0≤t≤t	PROPN
ma-9	380	9	e	e	PROPN
ma-9	380	10	∥∥x	∥∥x	PROPN
ma-9	380	11	−	−	PROPN
ma-9	380	12	y∥∥2	y∥∥2	NOUN
ma-9	380	13	s	s	PART
ma-9	380	14	ds	ds	ADJ
ma-9	380	15	≤	≤	NOUN
ma-9	380	16	[	[	X
ma-9	380	17	4	4	NUM
ma-9	380	18	max{1,n	max{1,n	NOUN
ma-9	380	19	2}m2(t	2}m2(t	NUM
ma-9	380	20	−	−	NOUN
ma-9	381	1	t0)2lh	t0)2lh	NOUN
ma-9	381	2	+	+	CCONJ
ma-9	381	3	4	4	NUM
ma-9	381	4	max{1,n	max{1,n	NOUN
ma-9	381	5	2}m̃2(t	2}m̃2(t	NUM
ma-9	381	6	−	−	PROPN
ma-9	381	7	t0	t0	PROPN
ma-9	381	8	)	)	PUNCT
ma-9	381	9	×	×	NOUN
ma-9	381	10	[	[	X
ma-9	381	11	(	(	PUNCT
ma-9	381	12	t	t	PROPN
ma-9	381	13	−	−	PROPN
ma-9	381	14	t0)lf	t0)lf	PROPN
ma-9	381	15	+	+	CCONJ
ma-9	381	16	t	t	NOUN
ma-9	381	17	r(q)lg	r(q)lg	NOUN
ma-9	381	18	+	+	CCONJ
ma-9	381	19	lσ	lσ	X
ma-9	381	20	]	]	PUNCT
ma-9	381	21	]	]	PUNCT
ma-9	381	22	sup	sup	NOUN
ma-9	381	23	t0≤t≤t	t0≤t≤t	PROPN
ma-9	381	24	e	e	PROPN
ma-9	381	25	∥∥x	∥∥x	PROPN
ma-9	381	26	−	−	PROPN
ma-9	381	27	y∥∥2	y∥∥2	PROPN
ma-9	381	28	t	t	PROPN
ma-9	381	29	hence	hence	ADV
ma-9	381	30	,	,	PUNCT
ma-9	381	31	∥∥(φx)−	∥∥(φx)−	PROPN
ma-9	381	32	(	(	PUNCT
ma-9	381	33	φy)∥∥2	φy)∥∥2	PROPN
ma-9	381	34	b	b	PROPN
ma-9	381	35	≤	≤	PROPN
ma-9	381	36	γ(t	γ(t	PROPN
ma-9	381	37	)	)	PUNCT
ma-9	381	38	∥∥x	∥∥x	PROPN
ma-9	381	39	−	−	PROPN
ma-9	382	1	y∥∥2	y∥∥2	PROPN
ma-9	383	1	b	b	PROPN
ma-9	384	1	.where	.where	PROPN
ma-9	384	2	,	,	PUNCT
ma-9	384	3	γ(t	γ(t	NOUN
ma-9	384	4	)	)	PUNCT
ma-9	385	1	=	=	SYM
ma-9	385	2	3max{1,n	3max{1,n	NUM
ma-9	385	3	2}m2(t	2}m2(t	NUM
ma-9	385	4	−	−	NOUN
ma-9	386	1	t0)2lh	t0)2lh	NOUN
ma-9	386	2	+	+	CCONJ
ma-9	386	3	3	3	NUM
ma-9	386	4	max{1,n	max{1,n	NOUN
ma-9	386	5	2}m̃2(t	2}m̃2(t	NUM
ma-9	386	6	−	−	PROPN
ma-9	386	7	t0	t0	PROPN
ma-9	386	8	)	)	PUNCT
ma-9	387	1	[	[	X
ma-9	387	2	(	(	PUNCT
ma-9	387	3	t	t	PROPN
ma-9	387	4	−	−	PROPN
ma-9	387	5	t0)lf	t0)lf	PROPN
ma-9	387	6	+	+	CCONJ
ma-9	387	7	t	t	NOUN
ma-9	387	8	r(q)lg	r(q)lg	NOUN
ma-9	387	9	+	+	CCONJ
ma-9	387	10	lσ	lσ	X
ma-9	387	11	]	]	PUNCT
ma-9	387	12	.	.	PUNCT
ma-9	388	1	eur	eur	PROPN
ma-9	388	2	.	.	PUNCT
ma-9	389	1	j.	j.	PROPN
ma-9	389	2	math	math	PROPN
ma-9	389	3	.	.	PUNCT
ma-9	390	1	anal	anal	ADJ
ma-9	390	2	.	.	PUNCT
ma-9	391	1	1	1	NUM
ma-9	391	2	(	(	PUNCT
ma-9	391	3	2021	2021	NUM
ma-9	391	4	)	)	PUNCT
ma-9	391	5	14by	14by	NOUN
ma-9	391	6	taking	take	VERB
ma-9	391	7	suitable	suitable	ADJ
ma-9	391	8	0	0	NUM
ma-9	391	9	<	<	X
ma-9	391	10	t1	t1	NOUN
ma-9	391	11	<	<	X
ma-9	391	12	t	t	X
ma-9	391	13	sufficiently	sufficiently	ADV
ma-9	391	14	small	small	ADJ
ma-9	391	15	such	such	ADJ
ma-9	391	16	that	that	SCONJ
ma-9	391	17	,	,	PUNCT
ma-9	391	18	γ(t1	γ(t1	PROPN
ma-9	391	19	)	)	PUNCT
ma-9	392	1	<	<	X
ma-9	392	2	1.hence	1.hence	NUM
ma-9	392	3	φ	φ	NOUN
ma-9	392	4	is	be	AUX
ma-9	392	5	a	a	DET
ma-9	392	6	contraction	contraction	NOUN
ma-9	392	7	on	on	ADP
ma-9	392	8	b	b	PROPN
ma-9	392	9	.	.	PUNCT
ma-9	393	1	by	by	ADP
ma-9	393	2	banach	banach	NOUN
ma-9	393	3	contraction	contraction	NOUN
ma-9	393	4	principle	principle	NOUN
ma-9	393	5	,	,	PUNCT
ma-9	393	6	a	a	DET
ma-9	393	7	unique	unique	ADJ
ma-9	393	8	fixed	fixed	ADJ
ma-9	393	9	point	point	NOUN
ma-9	393	10	x	x	X
ma-9	393	11	∈	∈	PROPN
ma-9	393	12	b	b	NOUN
ma-9	393	13	isobtained	isobtaine	VERB
ma-9	393	14	for	for	ADP
ma-9	393	15	the	the	DET
ma-9	393	16	operator	operator	NOUN
ma-9	393	17	φ	φ	NOUN
ma-9	393	18	and	and	CCONJ
ma-9	393	19	therefore	therefore	ADV
ma-9	393	20	φx	φx	PROPN
ma-9	394	1	=	=	PUNCT
ma-9	394	2	x	x	X
ma-9	394	3	is	be	AUX
ma-9	394	4	a	a	DET
ma-9	394	5	mild	mild	ADJ
ma-9	394	6	solution	solution	NOUN
ma-9	394	7	of	of	ADP
ma-9	394	8	the	the	DET
ma-9	394	9	system.the	system.the	DET
ma-9	394	10	solution	solution	NOUN
ma-9	394	11	can	can	AUX
ma-9	394	12	be	be	AUX
ma-9	394	13	extended	extend	VERB
ma-9	394	14	to	to	ADP
ma-9	394	15	the	the	DET
ma-9	394	16	entire	entire	ADJ
ma-9	394	17	interval	interval	NOUN
ma-9	394	18	(	(	PUNCT
ma-9	394	19	−δ	−δ	ADJ
ma-9	394	20	,	,	PUNCT
ma-9	394	21	t	t	X
ma-9	394	22	]	]	PUNCT
ma-9	394	23	in	in	ADP
ma-9	394	24	finitely	finitely	ADV
ma-9	394	25	many	many	ADJ
ma-9	394	26	steps	step	NOUN
ma-9	394	27	.	.	PUNCT
ma-9	395	1	thus	thus	ADV
ma-9	395	2	the	the	DET
ma-9	395	3	existenceand	existenceand	ADJ
ma-9	395	4	uniqueness	uniqueness	NOUN
ma-9	395	5	of	of	ADP
ma-9	395	6	the	the	DET
ma-9	395	7	mild	mild	ADJ
ma-9	395	8	solution	solution	NOUN
ma-9	395	9	on	on	ADP
ma-9	395	10	(	(	PUNCT
ma-9	395	11	−δ	−δ	ADJ
ma-9	395	12	,	,	PUNCT
ma-9	395	13	t	t	PROPN
ma-9	395	14	]	]	PUNCT
ma-9	395	15	is	be	AUX
ma-9	395	16	proved	prove	VERB
ma-9	395	17	.	.	PUNCT
ma-9	396	1	�	�	PROPN
ma-9	396	2	4	4	NUM
ma-9	396	3	.	.	PUNCT
ma-9	396	4	stability	stability	VERB
ma-9	396	5	the	the	DET
ma-9	396	6	stability	stability	NOUN
ma-9	396	7	through	through	ADP
ma-9	396	8	continuous	continuous	ADJ
ma-9	396	9	dependence	dependence	NOUN
ma-9	396	10	of	of	ADP
ma-9	396	11	solutions	solution	NOUN
ma-9	396	12	on	on	ADP
ma-9	396	13	initial	initial	ADJ
ma-9	396	14	conditions	condition	NOUN
ma-9	396	15	are	be	AUX
ma-9	396	16	established	establish	VERB
ma-9	396	17	.	.	PUNCT
ma-9	397	1	definition	definition	NOUN
ma-9	397	2	4.1	4.1	NUM
ma-9	397	3	.	.	PUNCT
ma-9	398	1	a	a	DET
ma-9	398	2	mild	mild	ADJ
ma-9	398	3	solution	solution	NOUN
ma-9	398	4	xξ	xξ	NOUN
ma-9	398	5	,	,	PUNCT
ma-9	398	6	x	x	PROPN
ma-9	398	7	(	(	PUNCT
ma-9	398	8	t	t	NOUN
ma-9	398	9	)	)	PUNCT
ma-9	398	10	of	of	ADP
ma-9	398	11	the	the	DET
ma-9	398	12	system	system	NOUN
ma-9	398	13	(	(	PUNCT
ma-9	398	14	1.1	1.1	NUM
ma-9	398	15	)	)	PUNCT
ma-9	398	16	with	with	ADP
ma-9	398	17	the	the	DET
ma-9	398	18	initial	initial	ADJ
ma-9	398	19	value	value	NOUN
ma-9	398	20	(	(	PUNCT
ma-9	398	21	ξ	ξ	PROPN
ma-9	398	22	,	,	PUNCT
ma-9	398	23	x	x	X
ma-9	398	24	)	)	PUNCT
ma-9	398	25	is	be	AUX
ma-9	398	26	said	say	VERB
ma-9	398	27	to	to	PART
ma-9	398	28	be	be	AUX
ma-9	398	29	stable	stable	ADJ
ma-9	398	30	in	in	ADP
ma-9	398	31	mean	mean	ADJ
ma-9	398	32	square	square	ADJ
ma-9	398	33	if	if	SCONJ
ma-9	398	34	for	for	ADP
ma-9	398	35	all	all	DET
ma-9	398	36	ε	ε	PROPN
ma-9	398	37	>	>	X
ma-9	398	38	0	0	NUM
ma-9	398	39	such	such	ADJ
ma-9	398	40	that	that	SCONJ
ma-9	398	41	e	e	NOUN
ma-9	398	42	(	(	PUNCT
ma-9	398	43	sup0≤s≤t	sup0≤s≤t	PROPN
ma-9	398	44	∥∥∥xξ	∥∥∥xξ	PROPN
ma-9	398	45	,	,	PUNCT
ma-9	398	46	x	x	X
ma-9	398	47	(	(	PUNCT
ma-9	398	48	s)−	s)−	PROPN
ma-9	398	49	yξ	yξ	NOUN
ma-9	398	50	,	,	PUNCT
ma-9	398	51	x	x	INTJ
ma-9	398	52	(	(	PUNCT
ma-9	398	53	t)∥∥∥2	t)∥∥∥2	NOUN
ma-9	398	54	)	)	PUNCT
ma-9	398	55	≤	≤	PUNCT
ma-9	398	56	ε	ε	PROPN
ma-9	398	57	,	,	PUNCT
ma-9	398	58	when	when	SCONJ
ma-9	398	59	e	e	PROPN
ma-9	398	60	∥∥ξ	∥∥ξ	NOUN
ma-9	398	61	−	−	NOUN
ma-9	398	62	ζ∥∥2	ζ∥∥2	NOUN
ma-9	399	1	+	+	CCONJ
ma-9	399	2	e	e	NOUN
ma-9	399	3	∥∥x	∥∥x	VERB
ma-9	399	4	−	−	PROPN
ma-9	399	5	y∥∥2	y∥∥2	PROPN
ma-9	399	6	<	<	X
ma-9	399	7	δ	δ	PROPN
ma-9	399	8	,	,	PUNCT
ma-9	399	9	where	where	SCONJ
ma-9	399	10	xζ	xζ	NOUN
ma-9	399	11	,	,	PUNCT
ma-9	399	12	y(t	y(t	PROPN
ma-9	399	13	)	)	PUNCT
ma-9	399	14	is	be	AUX
ma-9	399	15	another	another	DET
ma-9	399	16	solution	solution	NOUN
ma-9	399	17	of	of	ADP
ma-9	399	18	the	the	DET
ma-9	399	19	system	system	NOUN
ma-9	399	20	(	(	PUNCT
ma-9	399	21	1.1	1.1	NUM
ma-9	399	22	)	)	PUNCT
ma-9	399	23	with	with	ADP
ma-9	399	24	initial	initial	ADJ
ma-9	399	25	value	value	NOUN
ma-9	399	26	(	(	PUNCT
ma-9	399	27	ζ	ζ	NOUN
ma-9	399	28	,	,	PUNCT
ma-9	399	29	y	y	NOUN
ma-9	399	30	)	)	PUNCT
ma-9	399	31	.	.	PUNCT
ma-9	399	32	theorem	theorem	VERB
ma-9	399	33	4.1	4.1	NUM
ma-9	399	34	.	.	PUNCT
ma-9	400	1	let	let	VERB
ma-9	400	2	x(t	x(t	PROPN
ma-9	400	3	)	)	PUNCT
ma-9	400	4	and	and	CCONJ
ma-9	400	5	x(t	x(t	PROPN
ma-9	400	6	)	)	PUNCT
ma-9	400	7	be	be	AUX
ma-9	400	8	mild	mild	ADJ
ma-9	400	9	solution	solution	NOUN
ma-9	400	10	of	of	ADP
ma-9	400	11	the	the	DET
ma-9	400	12	system	system	NOUN
ma-9	400	13	(	(	PUNCT
ma-9	400	14	1.1	1.1	NUM
ma-9	400	15	)	)	PUNCT
ma-9	400	16	with	with	ADP
ma-9	400	17	the	the	DET
ma-9	400	18	initial	initial	ADJ
ma-9	400	19	condition	condition	NOUN
ma-9	400	20	φ1	φ1	NOUN
ma-9	400	21	and	and	CCONJ
ma-9	400	22	φ2	φ2	PROPN
ma-9	400	23	respectively	respectively	ADV
ma-9	400	24	.	.	PUNCT
ma-9	401	1	if	if	SCONJ
ma-9	401	2	the	the	DET
ma-9	401	3	assumptions	assumption	NOUN
ma-9	401	4	of	of	ADP
ma-9	401	5	theorem	theorem	ADJ
ma-9	401	6	3.1	3.1	NUM
ma-9	401	7	gets	get	VERB
ma-9	401	8	satisfied	satisfied	ADJ
ma-9	401	9	,	,	PUNCT
ma-9	401	10	the	the	DET
ma-9	401	11	mean	mean	ADJ
ma-9	401	12	solution	solution	NOUN
ma-9	401	13	of	of	ADP
ma-9	401	14	the	the	DET
ma-9	401	15	system	system	NOUN
ma-9	401	16	(	(	PUNCT
ma-9	401	17	1.1	1.1	NUM
ma-9	401	18	)	)	PUNCT
ma-9	401	19	is	be	AUX
ma-9	401	20	stable	stable	ADJ
ma-9	401	21	in	in	ADP
ma-9	401	22	the	the	DET
ma-9	401	23	mean	mean	ADJ
ma-9	401	24	square	square	NOUN
ma-9	401	25	.	.	PUNCT
ma-9	402	1	proof	proof	NOUN
ma-9	402	2	.	.	PUNCT
ma-9	403	1	we	we	PRON
ma-9	403	2	may	may	AUX
ma-9	403	3	assume	assume	VERB
ma-9	403	4	that	that	SCONJ
ma-9	403	5	x(t	x(t	PROPN
ma-9	403	6	)	)	PUNCT
ma-9	403	7	and	and	CCONJ
ma-9	403	8	x(t	x(t	PROPN
ma-9	403	9	)	)	PUNCT
ma-9	403	10	be	be	VERB
ma-9	403	11	the	the	DET
ma-9	403	12	mild	mild	ADJ
ma-9	403	13	solutions	solution	NOUN
ma-9	403	14	of	of	ADP
ma-9	403	15	the	the	DET
ma-9	403	16	system	system	NOUN
ma-9	403	17	(	(	PUNCT
ma-9	403	18	1.1	1.1	NUM
ma-9	403	19	)	)	PUNCT
ma-9	403	20	with	with	ADP
ma-9	403	21	initialvalues	initialvalue	NOUN
ma-9	403	22	φ1	φ1	PROPN
ma-9	403	23	and	and	CCONJ
ma-9	403	24	φ2	φ2	PROPN
ma-9	403	25	respectively	respectively	ADV
ma-9	403	26	.	.	PUNCT
ma-9	404	1	x(t)−	x(t)−	PROPN
ma-9	404	2	x(t	x(t	PROPN
ma-9	404	3	)	)	PUNCT
ma-9	404	4	=	=	PUNCT
ma-9	405	1	+	+	PUNCT
ma-9	405	2	∞∑	∞∑	DET
ma-9	405	3	k=0	k=0	PROPN
ma-9	405	4	[	[	PUNCT
ma-9	405	5	k∏	k∏	PROPN
ma-9	405	6	i=1	i=1	PROPN
ma-9	405	7	bi(δi)c(t	bi(δi)c(t	PUNCT
ma-9	405	8	−	−	PROPN
ma-9	405	9	t0)[φ1	t0)[φ1	PROPN
ma-9	405	10	−	−	PROPN
ma-9	405	11	φ2	φ2	PROPN
ma-9	405	12	]	]	PUNCT
ma-9	406	1	+	+	CCONJ
ma-9	406	2	k∏	k∏	PROPN
ma-9	406	3	i=1	i=1	X
ma-9	406	4	bi(δi)s(t	bi(δi)s(t	VERB
ma-9	406	5	−	−	PROPN
ma-9	406	6	t0)[(φ1	t0)[(φ1	ADP
ma-9	406	7	−	−	PROPN
ma-9	406	8	φ2)−	φ2)−	ADV
ma-9	406	9	[	[	X
ma-9	406	10	(	(	PUNCT
ma-9	406	11	h(0	h(0	PROPN
ma-9	406	12	,	,	PUNCT
ma-9	406	13	φ1)−	φ1)−	PROPN
ma-9	406	14	(	(	PUNCT
ma-9	406	15	h(0	h(0	PROPN
ma-9	406	16	,	,	PUNCT
ma-9	406	17	φ2	φ2	PROPN
ma-9	406	18	)	)	PUNCT
ma-9	406	19	)	)	PUNCT
ma-9	406	20	]	]	PUNCT
ma-9	407	1	]	]	X
ma-9	408	1	+	+	CCONJ
ma-9	408	2	k∑	k∑	ADJ
ma-9	408	3	i=1	i=1	PROPN
ma-9	409	1	k∏	k∏	PROPN
ma-9	409	2	j	j	PROPN
ma-9	410	1	=	=	NOUN
ma-9	410	2	i	i	PRON
ma-9	410	3	bj	bj	VERB
ma-9	410	4	(	(	PUNCT
ma-9	410	5	δj	δj	ADJ
ma-9	410	6	)	)	PUNCT
ma-9	410	7	∫	∫	PROPN
ma-9	411	1	ξi	ξi	PROPN
ma-9	411	2	ξi−1	ξi−1	PROPN
ma-9	411	3	c(t	c(t	PROPN
ma-9	411	4	−	−	PROPN
ma-9	411	5	s	s	PART
ma-9	411	6	)	)	PUNCT
ma-9	412	1	[	[	X
ma-9	412	2	h(s	h(	NOUN
ma-9	412	3	,	,	PUNCT
ma-9	412	4	xs)−	xs)−	PUNCT
ma-9	413	1	h(s	h(s	PROPN
ma-9	413	2	,	,	PUNCT
ma-9	413	3	x(s))]ds+	x(s))]ds+	PROPN
ma-9	413	4	∫	∫	PROPN
ma-9	414	1	t	t	PROPN
ma-9	414	2	ξk	ξk	ADP
ma-9	414	3	c(t	c(t	PROPN
ma-9	414	4	−	−	PROPN
ma-9	414	5	s	s	PART
ma-9	414	6	)	)	PUNCT
ma-9	415	1	[	[	X
ma-9	415	2	h(s	h(	NOUN
ma-9	415	3	,	,	PUNCT
ma-9	415	4	xs)−	xs)−	PUNCT
ma-9	416	1	h(s	h(	NOUN
ma-9	416	2	,	,	PUNCT
ma-9	416	3	xs)]ds	xs)]ds	PROPN
ma-9	417	1	+	+	CCONJ
ma-9	417	2	k∑	k∑	VERB
ma-9	417	3	i=1	i=1	PROPN
ma-9	418	1	k∏	k∏	PROPN
ma-9	418	2	j	j	PROPN
ma-9	419	1	=	=	NOUN
ma-9	419	2	i	i	PRON
ma-9	419	3	bj	bj	VERB
ma-9	419	4	(	(	PUNCT
ma-9	419	5	δj	δj	ADJ
ma-9	419	6	)	)	PUNCT
ma-9	419	7	∫	∫	PROPN
ma-9	419	8	ξi	ξi	PROPN
ma-9	419	9	ξi−1	ξi−1	PROPN
ma-9	419	10	s(t	s(t	PROPN
ma-9	419	11	−	−	PROPN
ma-9	419	12	s	s	PART
ma-9	419	13	)	)	PUNCT
ma-9	420	1	[	[	X
ma-9	420	2	f(s	f(	NOUN
ma-9	420	3	,	,	PUNCT
ma-9	420	4	xs)−	xs)−	PUNCT
ma-9	421	1	f(s	f(	NOUN
ma-9	421	2	,	,	PUNCT
ma-9	421	3	xs)]ds+	xs)]ds+	PROPN
ma-9	422	1	∫	∫	PROPN
ma-9	422	2	t	t	PROPN
ma-9	422	3	ξk	ξk	ADP
ma-9	422	4	s(t	s(t	PROPN
ma-9	422	5	−	−	PROPN
ma-9	422	6	s	s	PART
ma-9	422	7	)	)	PUNCT
ma-9	423	1	[	[	X
ma-9	423	2	f(s	f(	NOUN
ma-9	423	3	,	,	PUNCT
ma-9	423	4	xs)−	xs)−	PUNCT
ma-9	424	1	f(s	f(	NOUN
ma-9	424	2	,	,	PUNCT
ma-9	424	3	xs)]ds	xs)]ds	PROPN
ma-9	425	1	+	+	CCONJ
ma-9	425	2	k∑	k∑	VERB
ma-9	425	3	i=1	i=1	PROPN
ma-9	426	1	k∏	k∏	PROPN
ma-9	426	2	j	j	PROPN
ma-9	427	1	=	=	NOUN
ma-9	427	2	i	i	PRON
ma-9	427	3	bj	bj	VERB
ma-9	427	4	(	(	PUNCT
ma-9	427	5	δj	δj	ADJ
ma-9	427	6	)	)	PUNCT
ma-9	427	7	∫	∫	PROPN
ma-9	427	8	ξi	ξi	PROPN
ma-9	427	9	ξi−1	ξi−1	PROPN
ma-9	427	10	s(t	s(t	PROPN
ma-9	427	11	−	−	PROPN
ma-9	427	12	s	s	PART
ma-9	427	13	)	)	PUNCT
ma-9	428	1	[	[	X
ma-9	428	2	g(s	g(s	X
ma-9	428	3	,	,	PUNCT
ma-9	428	4	xs)−	xs)−	PUNCT
ma-9	429	1	g(s	g(	NOUN
ma-9	429	2	,	,	PUNCT
ma-9	429	3	xs)]dω(s	xs)]dω(s	NOUN
ma-9	429	4	)	)	PUNCT
ma-9	430	1	+	+	CCONJ
ma-9	430	2	∫	∫	PROPN
ma-9	430	3	t	t	PROPN
ma-9	430	4	ξk	ξk	ADP
ma-9	430	5	s(t	s(t	PROPN
ma-9	430	6	−	−	PROPN
ma-9	430	7	s	s	PART
ma-9	430	8	)	)	PUNCT
ma-9	431	1	[	[	X
ma-9	431	2	g(s	g(s	X
ma-9	431	3	,	,	PUNCT
ma-9	431	4	xs)−	xs)−	PUNCT
ma-9	432	1	g(s	g(	NOUN
ma-9	432	2	,	,	PUNCT
ma-9	432	3	xs)]dω(s	xs)]dω(s	NOUN
ma-9	432	4	)	)	PUNCT
ma-9	433	1	+	+	CCONJ
ma-9	433	2	k∑	k∑	VERB
ma-9	433	3	i=1	i=1	PROPN
ma-9	434	1	k∏	k∏	PROPN
ma-9	434	2	j	j	PROPN
ma-9	435	1	=	=	NOUN
ma-9	435	2	i	i	PRON
ma-9	435	3	bj	bj	VERB
ma-9	435	4	(	(	PUNCT
ma-9	435	5	δj	δj	ADJ
ma-9	435	6	)	)	PUNCT
ma-9	435	7	∫	∫	PROPN
ma-9	435	8	ξi	ξi	PROPN
ma-9	435	9	ξi−1	ξi−1	PROPN
ma-9	435	10	∫	∫	PROPN
ma-9	435	11	u	u	PROPN
ma-9	435	12	s(t	s(t	PROPN
ma-9	435	13	−	−	PROPN
ma-9	435	14	s	s	PART
ma-9	435	15	)	)	PUNCT
ma-9	436	1	[	[	X
ma-9	436	2	σ	σ	X
ma-9	436	3	(	(	PUNCT
ma-9	436	4	s	s	PROPN
ma-9	436	5	,	,	PUNCT
ma-9	436	6	xs	xs	PROPN
ma-9	436	7	,	,	PUNCT
ma-9	436	8	u)−	u)−	PROPN
ma-9	436	9	σ	σ	PROPN
ma-9	436	10	(	(	PUNCT
ma-9	436	11	s	s	PROPN
ma-9	436	12	,	,	PUNCT
ma-9	436	13	xs	xs	PROPN
ma-9	436	14	,	,	PUNCT
ma-9	436	15	u	u	NOUN
ma-9	436	16	)	)	PUNCT
ma-9	436	17	]	]	X
ma-9	436	18	ñ(ds	ñ(ds	PROPN
ma-9	436	19	,	,	PUNCT
ma-9	436	20	du	du	PROPN
ma-9	436	21	)	)	PUNCT
ma-9	437	1	+	+	CCONJ
ma-9	437	2	∫	∫	PROPN
ma-9	437	3	t	t	X
ma-9	437	4	ξk	ξk	ADP
ma-9	437	5	∫	∫	PROPN
ma-9	437	6	u	u	PROPN
ma-9	437	7	s(t	s(t	PROPN
ma-9	437	8	−	−	PROPN
ma-9	437	9	s	s	PART
ma-9	437	10	)	)	PUNCT
ma-9	438	1	[	[	X
ma-9	438	2	σ	σ	X
ma-9	438	3	(	(	PUNCT
ma-9	438	4	s	s	PROPN
ma-9	438	5	,	,	PUNCT
ma-9	438	6	xs	xs	PROPN
ma-9	438	7	,	,	PUNCT
ma-9	438	8	u)−	u)−	PROPN
ma-9	438	9	σ	σ	PROPN
ma-9	438	10	(	(	PUNCT
ma-9	438	11	s	s	PROPN
ma-9	438	12	,	,	PUNCT
ma-9	438	13	xs	xs	PROPN
ma-9	438	14	,	,	PUNCT
ma-9	438	15	u	u	NOUN
ma-9	438	16	)	)	PUNCT
ma-9	438	17	]	]	X
ma-9	438	18	ñ(ds	ñ(ds	PROPN
ma-9	438	19	,	,	PUNCT
ma-9	438	20	du)]i[ξk	du)]i[ξk	NOUN
ma-9	438	21	,	,	PUNCT
ma-9	438	22	ξk+1)(t	ξk+1)(t	NOUN
ma-9	438	23	)	)	PUNCT
ma-9	438	24	eur	eur	NOUN
ma-9	438	25	.	.	PUNCT
ma-9	439	1	j.	j.	PROPN
ma-9	439	2	math	math	PROPN
ma-9	439	3	.	.	PUNCT
ma-9	440	1	anal	anal	ADJ
ma-9	440	2	.	.	PUNCT
ma-9	441	1	1	1	NUM
ma-9	441	2	(	(	PUNCT
ma-9	441	3	2021	2021	NUM
ma-9	441	4	)	)	PUNCT
ma-9	441	5	15	15	NUM
ma-9	441	6	e	e	NOUN
ma-9	441	7	∥∥x(t)−	∥∥x(t)−	PROPN
ma-9	441	8	x(t)∥∥2	x(t)∥∥2	PROPN
ma-9	442	1	≤	≤	NOUN
ma-9	443	1	6n	6n	NUM
ma-9	444	1	2m2e∥∥φ1	2m2e∥∥φ1	NUM
ma-9	445	1	−	−	ADP
ma-9	445	2	φ2∥∥2	φ2∥∥2	PROPN
ma-9	445	3	+	+	NUM
ma-9	445	4	12n	12n	NUM
ma-9	445	5	2m̃2e∥∥φ1	2m̃2e∥∥φ1	NUM
ma-9	445	6	−	−	NOUN
ma-9	446	1	φ2∥∥2	φ2∥∥2	PROPN
ma-9	446	2	+	+	NUM
ma-9	446	3	12n	12n	NOUN
ma-9	446	4	2m̃2e∥∥h(0	2m̃2e∥∥h(0	NUM
ma-9	446	5	,	,	PUNCT
ma-9	446	6	φ1)−	φ1)−	PROPN
ma-9	446	7	h(0	h(0	PROPN
ma-9	446	8	,	,	PUNCT
ma-9	446	9	φ2)∥∥2	φ2)∥∥2	NUM
ma-9	446	10	+	+	CCONJ
ma-9	446	11	6m2	6m2	NUM
ma-9	446	12	max{1,n	max{1,n	NOUN
ma-9	446	13	2	2	NUM
ma-9	446	14	}	}	PUNCT
ma-9	446	15	∫	∫	PROPN
ma-9	446	16	t	t	PROPN
ma-9	446	17	t0	t0	PROPN
ma-9	446	18	e	e	X
ma-9	446	19	∥∥h(s	∥∥h(s	PROPN
ma-9	446	20	,	,	PUNCT
ma-9	446	21	xs)−	xs)−	PUNCT
ma-9	447	1	h(s	h(	NOUN
ma-9	447	2	,	,	PUNCT
ma-9	447	3	xs)∥∥2	xs)∥∥2	PROPN
ma-9	447	4	ds+	ds+	NOUN
ma-9	447	5	6m̃2	6m̃2	ADJ
ma-9	447	6	max{1,n	max{1,n	NOUN
ma-9	447	7	2	2	NUM
ma-9	447	8	}	}	PUNCT
ma-9	447	9	×	×	NOUN
ma-9	447	10	∫	∫	NOUN
ma-9	447	11	t	t	PROPN
ma-9	447	12	t0	t0	PROPN
ma-9	447	13	e	e	X
ma-9	447	14	∥∥f(s	∥∥f(	NOUN
ma-9	447	15	,	,	PUNCT
ma-9	447	16	xs)−	xs)−	PUNCT
ma-9	448	1	f(s	f(s	PROPN
ma-9	448	2	,	,	PUNCT
ma-9	448	3	xs)∥∥2	xs)∥∥2	PROPN
ma-9	448	4	ds+	ds+	NOUN
ma-9	449	1	6m̃2	6m̃2	ADJ
ma-9	449	2	max{1,n	max{1,n	NOUN
ma-9	449	3	2	2	NUM
ma-9	449	4	}	}	PUNCT
ma-9	449	5	∫	∫	PROPN
ma-9	449	6	t	t	PROPN
ma-9	449	7	t0	t0	PROPN
ma-9	449	8	e	e	PROPN
ma-9	449	9	∥∥g(s	∥∥g(s	NUM
ma-9	449	10	,	,	PUNCT
ma-9	449	11	xs)−	xs)−	PUNCT
ma-9	450	1	g(s	g(	NOUN
ma-9	450	2	,	,	PUNCT
ma-9	450	3	xs)∥∥2	xs)∥∥2	PROPN
ma-9	450	4	ds	ds	ADJ
ma-9	450	5	+	+	CCONJ
ma-9	450	6	6	6	NUM
ma-9	450	7	max{1,n	max{1,n	NOUN
ma-9	450	8	2}m̃2	2}m̃2	NUM
ma-9	450	9	×	×	NOUN
ma-9	450	10	[	[	PUNCT
ma-9	450	11	∫	∫	PROPN
ma-9	450	12	t	t	PROPN
ma-9	450	13	t0	t0	PROPN
ma-9	450	14	∫	∫	PROPN
ma-9	450	15	u	u	PROPN
ma-9	450	16	∥∥σ	∥∥σ	VERB
ma-9	450	17	(	(	PUNCT
ma-9	450	18	t	t	PROPN
ma-9	450	19	,	,	PUNCT
ma-9	450	20	xs	xs	PROPN
ma-9	450	21	,	,	PUNCT
ma-9	450	22	u)−	u)−	PROPN
ma-9	450	23	σ	σ	PROPN
ma-9	450	24	(	(	PUNCT
ma-9	450	25	t	t	PROPN
ma-9	450	26	,	,	PUNCT
ma-9	450	27	xs	xs	PROPN
ma-9	450	28	,	,	PUNCT
ma-9	450	29	u)∥∥2	u)∥∥2	PROPN
ma-9	450	30	v	v	X
ma-9	450	31	(	(	PUNCT
ma-9	450	32	du)ds	du)ds	X
ma-9	450	33	+	+	CCONJ
ma-9	450	34	(	(	PUNCT
ma-9	450	35	∫	∫	PROPN
ma-9	450	36	t	t	PROPN
ma-9	450	37	t0	t0	PROPN
ma-9	450	38	∫	∫	PROPN
ma-9	450	39	u	u	PROPN
ma-9	450	40	∥∥σ	∥∥σ	VERB
ma-9	450	41	(	(	PUNCT
ma-9	450	42	t	t	PROPN
ma-9	450	43	,	,	PUNCT
ma-9	450	44	xs	xs	PROPN
ma-9	450	45	,	,	PUNCT
ma-9	450	46	u)−	u)−	PROPN
ma-9	450	47	σ	σ	PROPN
ma-9	450	48	(	(	PUNCT
ma-9	450	49	t	t	PROPN
ma-9	450	50	,	,	PUNCT
ma-9	450	51	xs	xs	PROPN
ma-9	450	52	,	,	PUNCT
ma-9	450	53	u)∥∥4	u)∥∥4	PROPN
ma-9	450	54	v	v	X
ma-9	450	55	(	(	PUNCT
ma-9	450	56	du)ds	du)ds	PROPN
ma-9	450	57	)	)	PUNCT
ma-9	450	58	12	12	NUM
ma-9	450	59	]	]	PUNCT
ma-9	450	60	≤	≤	NUM
ma-9	450	61	6n	6n	NOUN
ma-9	450	62	2m2e∥∥φ1	2m2e∥∥φ1	NUM
ma-9	451	1	−	−	PROPN
ma-9	451	2	φ2∥∥2	φ2∥∥2	PROPN
ma-9	451	3	+	+	NUM
ma-9	451	4	10n	10n	NOUN
ma-9	451	5	2m̃2e∥∥φ1	2m̃2e∥∥φ1	NUM
ma-9	451	6	−	−	NOUN
ma-9	452	1	φ2∥∥2	φ2∥∥2	PROPN
ma-9	452	2	+	+	NUM
ma-9	452	3	12n	12n	NOUN
ma-9	452	4	2m̃2lhe∥∥φ1	2m̃2lhe∥∥φ1	NUM
ma-9	452	5	−	−	PROPN
ma-9	453	1	φ2∥∥2	φ2∥∥2	NUM
ma-9	453	2	+	+	CCONJ
ma-9	453	3	6m2	6m2	NUM
ma-9	453	4	max{1,n	max{1,n	NOUN
ma-9	453	5	2	2	NUM
ma-9	453	6	}	}	PUNCT
ma-9	453	7	∫	∫	PROPN
ma-9	453	8	t	t	PROPN
ma-9	453	9	t0	t0	PROPN
ma-9	453	10	lhe	lhe	PROPN
ma-9	453	11	∥∥x	∥∥x	PROPN
ma-9	453	12	−	−	PROPN
ma-9	453	13	x∥∥2	x∥∥2	PROPN
ma-9	453	14	s	s	PART
ma-9	453	15	ds+	ds+	ADJ
ma-9	453	16	6m̃2	6m̃2	ADJ
ma-9	453	17	max{1,n	max{1,n	NOUN
ma-9	453	18	2	2	NUM
ma-9	453	19	}	}	PUNCT
ma-9	453	20	∫	∫	PROPN
ma-9	453	21	t	t	PROPN
ma-9	453	22	t0	t0	PROPN
ma-9	453	23	lfe	lfe	PROPN
ma-9	453	24	∥∥x	∥∥x	PROPN
ma-9	453	25	−	−	PROPN
ma-9	453	26	x∥∥2	x∥∥2	PROPN
ma-9	453	27	s	s	PART
ma-9	453	28	ds	ds	NOUN
ma-9	453	29	+	+	CCONJ
ma-9	453	30	6m̃2	6m̃2	ADJ
ma-9	453	31	max{1,n	max{1,n	NOUN
ma-9	453	32	2}t	2}t	NUM
ma-9	453	33	r(q	r(q	NOUN
ma-9	453	34	)	)	PUNCT
ma-9	453	35	∫	∫	PROPN
ma-9	453	36	t	t	PROPN
ma-9	453	37	t0	t0	PROPN
ma-9	453	38	lge	lge	PROPN
ma-9	453	39	∥∥x	∥∥x	PROPN
ma-9	453	40	−	−	PROPN
ma-9	454	1	x∥∥2	x∥∥2	PROPN
ma-9	454	2	s	s	PART
ma-9	454	3	ds	ds	ADJ
ma-9	454	4	+	+	CCONJ
ma-9	454	5	6m̃2	6m̃2	ADJ
ma-9	454	6	max{1,n	max{1,n	NOUN
ma-9	454	7	2	2	NUM
ma-9	454	8	}	}	PUNCT
ma-9	454	9	∫	∫	PROPN
ma-9	454	10	t	t	PROPN
ma-9	454	11	t0	t0	PROPN
ma-9	454	12	lσe	lσe	PROPN
ma-9	454	13	∥∥x	∥∥x	PROPN
ma-9	454	14	−	−	PROPN
ma-9	454	15	x∥∥2	x∥∥2	PROPN
ma-9	454	16	s	s	VERB
ma-9	454	17	ds	ds	NOUN
ma-9	454	18	furthermore	furthermore	ADV
ma-9	454	19	,	,	PUNCT
ma-9	454	20	sup	sup	VERB
ma-9	454	21	t0≤t≤t	t0≤t≤t	PROPN
ma-9	454	22	e	e	PROPN
ma-9	454	23	∥∥x	∥∥x	PROPN
ma-9	454	24	−	−	PROPN
ma-9	454	25	x∥∥2	x∥∥2	PROPN
ma-9	454	26	t	t	VERB
ma-9	454	27	≤	≤	NUM
ma-9	454	28	6n	6n	NOUN
ma-9	455	1	2m2e∥∥φ1	2m2e∥∥φ1	NUM
ma-9	456	1	−	−	ADP
ma-9	456	2	φ2∥∥2	φ2∥∥2	PROPN
ma-9	456	3	+	+	NUM
ma-9	456	4	12n	12n	NUM
ma-9	456	5	2m̃2e∥∥φ1	2m̃2e∥∥φ1	NUM
ma-9	456	6	−	−	NOUN
ma-9	457	1	φ2∥∥2	φ2∥∥2	PROPN
ma-9	457	2	+	+	NUM
ma-9	457	3	12n	12n	NOUN
ma-9	457	4	2m̃2lhe∥∥φ1	2m̃2lhe∥∥φ1	NUM
ma-9	457	5	−	−	PROPN
ma-9	458	1	φ2∥∥2	φ2∥∥2	NUM
ma-9	458	2	+	+	CCONJ
ma-9	458	3	6m2	6m2	NUM
ma-9	458	4	max{1,n	max{1,n	NOUN
ma-9	458	5	2}(t	2}(t	NUM
ma-9	458	6	−	−	NOUN
ma-9	458	7	t0)lh	t0)lh	NOUN
ma-9	458	8	sup	sup	NOUN
ma-9	458	9	t0≤t≤t	t0≤t≤t	PROPN
ma-9	458	10	e	e	PROPN
ma-9	458	11	∥∥x	∥∥x	PROPN
ma-9	458	12	−	−	PROPN
ma-9	458	13	x∥∥2	x∥∥2	PROPN
ma-9	458	14	t	t	PROPN
ma-9	458	15	+	+	CCONJ
ma-9	458	16	6m̃2	6m̃2	ADJ
ma-9	458	17	max{1,n	max{1,n	NOUN
ma-9	458	18	2}(t	2}(t	NUM
ma-9	458	19	−	−	PROPN
ma-9	458	20	t0	t0	PROPN
ma-9	458	21	)	)	PUNCT
ma-9	458	22	×	×	NOUN
ma-9	458	23	lf	lf	ADP
ma-9	458	24	sup	sup	NOUN
ma-9	458	25	t0≤t≤t	t0≤t≤t	PROPN
ma-9	458	26	e	e	PROPN
ma-9	458	27	∥∥x	∥∥x	PROPN
ma-9	458	28	−	−	PROPN
ma-9	458	29	x∥∥2	x∥∥2	PROPN
ma-9	458	30	t	t	PROPN
ma-9	458	31	+	+	CCONJ
ma-9	458	32	6m̃2	6m̃2	ADJ
ma-9	458	33	max{1,n	max{1,n	NOUN
ma-9	458	34	2}(t	2}(t	NUM
ma-9	458	35	−	−	NOUN
ma-9	458	36	t0)t	t0)t	ADJ
ma-9	458	37	r(q)lg	r(q)lg	NOUN
ma-9	458	38	sup	sup	NOUN
ma-9	458	39	t0≤t≤t	t0≤t≤t	PROPN
ma-9	458	40	e	e	PROPN
ma-9	458	41	∥∥x	∥∥x	PROPN
ma-9	458	42	−	−	PROPN
ma-9	458	43	x∥∥2	x∥∥2	PROPN
ma-9	458	44	t	t	PROPN
ma-9	458	45	+	+	CCONJ
ma-9	458	46	6m̃2	6m̃2	ADJ
ma-9	458	47	max{1,n	max{1,n	NOUN
ma-9	458	48	2}(t	2}(t	NUM
ma-9	458	49	−	−	NOUN
ma-9	458	50	t0)lσ	t0)lσ	VERB
ma-9	458	51	sup	sup	NOUN
ma-9	458	52	t0≤t≤t	t0≤t≤t	PROPN
ma-9	458	53	e	e	PROPN
ma-9	458	54	∥∥x	∥∥x	PROPN
ma-9	458	55	−	−	PROPN
ma-9	458	56	x∥∥2	x∥∥2	PROPN
ma-9	458	57	t	t	PROPN
ma-9	458	58	sup	sup	NOUN
ma-9	458	59	t0≤t≤t	t0≤t≤t	PROPN
ma-9	458	60	e	e	PROPN
ma-9	458	61	∥∥x	∥∥x	PROPN
ma-9	458	62	−	−	PROPN
ma-9	458	63	x∥∥2	x∥∥2	PROPN
ma-9	458	64	t	t	VERB
ma-9	458	65	≤	≤	NOUN
ma-9	458	66	6n	6n	NOUN
ma-9	458	67	2	2	NUM
ma-9	459	1	[	[	X
ma-9	459	2	m2	m2	PROPN
ma-9	459	3	+	+	CCONJ
ma-9	459	4	m̃2lh]1−	m̃2lh]1−	NOUN
ma-9	459	5	6	6	NUM
ma-9	459	6	max{1,n	max{1,n	NOUN
ma-9	459	7	2}(t	2}(t	NUM
ma-9	459	8	−	−	PROPN
ma-9	459	9	t0	t0	PROPN
ma-9	459	10	)	)	PUNCT
ma-9	460	1	[	[	X
ma-9	460	2	m2lh	m2lh	X
ma-9	460	3	+	+	CCONJ
ma-9	460	4	m̃2	m̃2	PROPN
ma-9	460	5	[	[	X
ma-9	460	6	lf	lf	ADP
ma-9	460	7	+	+	NUM
ma-9	460	8	t	t	NOUN
ma-9	460	9	r(q)lg	r(q)lg	NOUN
ma-9	460	10	+	+	CCONJ
ma-9	460	11	lσ	lσ	PRON
ma-9	460	12	]	]	X
ma-9	460	13	]	]	X
ma-9	460	14	e	e	X
ma-9	460	15	∥∥φ1	∥∥φ1	PUNCT
ma-9	460	16	−	−	PRON
ma-9	460	17	φ2∥∥2	φ2∥∥2	NOUN
ma-9	460	18	+	+	NUM
ma-9	460	19	12n	12n	NOUN
ma-9	460	20	2m̃2	2m̃2	PROPN
ma-9	460	21	1−	1−	NUM
ma-9	460	22	6	6	NUM
ma-9	460	23	max{1,n	max{1,n	NOUN
ma-9	460	24	2}(t	2}(t	NUM
ma-9	460	25	−	−	PROPN
ma-9	460	26	t0	t0	PROPN
ma-9	460	27	)	)	PUNCT
ma-9	461	1	[	[	X
ma-9	461	2	m2lh	m2lh	X
ma-9	461	3	+	+	CCONJ
ma-9	461	4	m̃2	m̃2	PROPN
ma-9	461	5	[	[	X
ma-9	461	6	lf	lf	ADP
ma-9	461	7	+	+	NUM
ma-9	461	8	t	t	NOUN
ma-9	461	9	r(q)lg	r(q)lg	NOUN
ma-9	461	10	+	+	CCONJ
ma-9	461	11	lσ	lσ	PRON
ma-9	461	12	]	]	X
ma-9	461	13	]	]	X
ma-9	461	14	e	e	X
ma-9	461	15	∥∥φ1	∥∥φ1	PUNCT
ma-9	461	16	−	−	PUNCT
ma-9	461	17	φ2∥∥2	φ2∥∥2	NOUN
ma-9	461	18	≤	≤	NUM
ma-9	461	19	ρe	ρe	VERB
ma-9	462	1	∥∥φ1	∥∥φ1	PROPN
ma-9	462	2	−	−	PUNCT
ma-9	462	3	φ2∥∥2	φ2∥∥2	PROPN
ma-9	462	4	+	+	CCONJ
ma-9	462	5	υe∥∥φ1	υe∥∥φ1	ADV
ma-9	462	6	−	−	PROPN
ma-9	463	1	φ2∥∥2	φ2∥∥2	NUM
ma-9	463	2	where	where	SCONJ
ma-9	463	3	,	,	PUNCT
ma-9	463	4	ρ	ρ	PROPN
ma-9	463	5	=	=	NOUN
ma-9	463	6	5n	5n	NUM
ma-9	463	7	2	2	NUM
ma-9	464	1	[	[	X
ma-9	464	2	m2	m2	PROPN
ma-9	464	3	+	+	CCONJ
ma-9	464	4	m̃2lh]1−	m̃2lh]1−	NOUN
ma-9	464	5	5	5	NUM
ma-9	464	6	max{1,n	max{1,n	SYM
ma-9	464	7	2}(t	2}(t	NUM
ma-9	464	8	−	−	PROPN
ma-9	464	9	t0	t0	PROPN
ma-9	464	10	)	)	PUNCT
ma-9	465	1	[	[	X
ma-9	465	2	m2lh	m2lh	X
ma-9	465	3	+	+	CCONJ
ma-9	465	4	m̃2	m̃2	PROPN
ma-9	465	5	[	[	X
ma-9	465	6	lf	lf	ADP
ma-9	465	7	+	+	NUM
ma-9	465	8	t	t	NOUN
ma-9	465	9	r(q)lg	r(q)lg	NOUN
ma-9	465	10	+	+	CCONJ
ma-9	465	11	lσ	lσ	PRON
ma-9	465	12	]	]	X
ma-9	465	13	]	]	X
ma-9	465	14	υ	υ	PROPN
ma-9	465	15	=	=	SYM
ma-9	465	16	10n	10n	NOUN
ma-9	465	17	2m̃2	2m̃2	PROPN
ma-9	465	18	1−	1−	NUM
ma-9	465	19	5	5	NUM
ma-9	465	20	max{1,n	max{1,n	NOUN
ma-9	465	21	2}(t	2}(t	NUM
ma-9	465	22	−	−	PROPN
ma-9	465	23	t0	t0	PROPN
ma-9	465	24	)	)	PUNCT
ma-9	466	1	[	[	X
ma-9	466	2	m2lh	m2lh	X
ma-9	466	3	+	+	CCONJ
ma-9	466	4	m̃2	m̃2	PROPN
ma-9	466	5	[	[	X
ma-9	466	6	lf	lf	ADP
ma-9	466	7	+	+	NUM
ma-9	466	8	t	t	NOUN
ma-9	466	9	r(q)lg	r(q)lg	NOUN
ma-9	466	10	+	+	CCONJ
ma-9	466	11	lσ	lσ	PRON
ma-9	466	12	]	]	X
ma-9	466	13	]	]	X
ma-9	466	14	eur	eur	PROPN
ma-9	466	15	.	.	PUNCT
ma-9	467	1	j.	j.	PROPN
ma-9	467	2	math	math	PROPN
ma-9	467	3	.	.	PUNCT
ma-9	468	1	anal	anal	ADJ
ma-9	468	2	.	.	PUNCT
ma-9	469	1	1	1	NUM
ma-9	469	2	(	(	PUNCT
ma-9	469	3	2021	2021	NUM
ma-9	469	4	)	)	PUNCT
ma-9	470	1	16given	16given	NUM
ma-9	470	2	ε	ε	X
ma-9	470	3	>	>	X
ma-9	470	4	0	0	PROPN
ma-9	470	5	,	,	PUNCT
ma-9	470	6	µ	µ	X
ma-9	470	7	>	>	X
ma-9	470	8	0	0	PUNCT
ma-9	470	9	choose	choose	NOUN
ma-9	470	10	,	,	PUNCT
ma-9	470	11	λ	λ	X
ma-9	470	12	=	=	SYM
ma-9	470	13	ε	ε	PROPN
ma-9	470	14	ρ	ρ	PROPN
ma-9	470	15	,	,	PUNCT
ma-9	470	16	µ	µ	X
ma-9	470	17	=	=	X
ma-9	470	18	συ	συ	ADP
ma-9	470	19	such	such	ADJ
ma-9	470	20	that	that	PRON
ma-9	470	21	,	,	PUNCT
ma-9	470	22	e	e	X
ma-9	470	23	∥∥φ1	∥∥φ1	PROPN
ma-9	470	24	−	−	PUNCT
ma-9	470	25	φ2∥∥2	φ2∥∥2	PROPN
ma-9	470	26	≤	≤	ADJ
ma-9	470	27	λ	λ	PROPN
ma-9	470	28	and	and	CCONJ
ma-9	470	29	e	e	X
ma-9	470	30	∥∥φ1	∥∥φ1	PROPN
ma-9	471	1	−	−	PRON
ma-9	471	2	φ2∥∥2	φ2∥∥2	NUM
ma-9	471	3	≤	≤	NOUN
ma-9	471	4	µ	µ	ADV
ma-9	471	5	therefore	therefore	ADV
ma-9	471	6	,	,	PUNCT
ma-9	471	7	∥∥x	∥∥x	PROPN
ma-9	471	8	−	−	PROPN
ma-9	471	9	y∥∥2	y∥∥2	PROPN
ma-9	471	10	b	b	PROPN
ma-9	471	11	≤	≤	PROPN
ma-9	471	12	ε.thus	ε.thus	ADV
ma-9	471	13	the	the	DET
ma-9	471	14	proof	proof	NOUN
ma-9	471	15	is	be	AUX
ma-9	471	16	complete	complete	ADJ
ma-9	471	17	.	.	PUNCT
ma-9	472	1	5	5	X
ma-9	472	2	.	.	X
ma-9	472	3	illustration	illustration	NOUN
ma-9	472	4	in	in	ADP
ma-9	472	5	this	this	DET
ma-9	472	6	section	section	NOUN
ma-9	472	7	,	,	PUNCT
ma-9	472	8	the	the	DET
ma-9	472	9	results	result	NOUN
ma-9	472	10	obtained	obtain	VERB
ma-9	472	11	are	be	AUX
ma-9	472	12	applied	apply	VERB
ma-9	472	13	to	to	ADP
ma-9	472	14	a	a	DET
ma-9	472	15	stochastic	stochastic	ADJ
ma-9	472	16	partial	partial	ADJ
ma-9	472	17	differential	differential	ADJ
ma-9	472	18	equations	equation	NOUN
ma-9	472	19	withrandom	withrandom	NOUN
ma-9	472	20	impulses	impulse	NOUN
ma-9	472	21	.	.	PUNCT
ma-9	473	1	let	let	VERB
ma-9	473	2	us	we	PRON
ma-9	473	3	consider	consider	VERB
ma-9	473	4	a	a	DET
ma-9	473	5	space	space	NOUN
ma-9	473	6	h	h	NOUN
ma-9	473	7	=	=	SYM
ma-9	473	8	l2([0	l2([0	PROPN
ma-9	473	9	,	,	PUNCT
ma-9	473	10	π	π	NOUN
ma-9	473	11	]	]	X
ma-9	473	12	)	)	PUNCT
ma-9	473	13	.	.	PUNCT
ma-9	474	1	the	the	DET
ma-9	474	2	infinitesimal	infinitesimal	ADJ
ma-9	474	3	generator	generator	NOUN
ma-9	474	4	a	a	PRON
ma-9	474	5	is	be	AUX
ma-9	474	6	definedto	definedto	NOUN
ma-9	474	7	be	be	AUX
ma-9	474	8	a	a	DET
ma-9	474	9	:	:	PUNCT
ma-9	474	10	d(a	d(a	PROPN
ma-9	474	11	)	)	PUNCT
ma-9	475	1	⊂	⊂	PROPN
ma-9	475	2	h→	h→	NOUN
ma-9	475	3	h	h	NOUN
ma-9	475	4	by	by	ADP
ma-9	475	5	a	a	DET
ma-9	475	6	=	=	SYM
ma-9	475	7	∂2	∂2	PROPN
ma-9	475	8	∂x2	∂x2	NOUN
ma-9	475	9	,	,	PUNCT
ma-9	475	10	with	with	ADP
ma-9	475	11	the	the	DET
ma-9	475	12	domain	domain	NOUN
ma-9	475	13	,	,	PUNCT
ma-9	475	14	d(a	d(a	PROPN
ma-9	475	15	)	)	PUNCT
ma-9	475	16	=	=	PRON
ma-9	476	1	{	{	PUNCT
ma-9	476	2	z	z	NOUN
ma-9	476	3	∈	∈	PROPN
ma-9	476	4	h	h	NOUN
ma-9	476	5	|	|	ADV
ma-9	476	6	z	z	PROPN
ma-9	477	1	and	and	CCONJ
ma-9	477	2	∂z	∂z	PROPN
ma-9	477	3	∂x	∂x	PROPN
ma-9	477	4	are	be	AUX
ma-9	477	5	absolutely	absolutely	ADV
ma-9	477	6	continuous	continuous	ADJ
ma-9	477	7	,	,	PUNCT
ma-9	477	8	∂2z	∂2z	ADJ
ma-9	477	9	∂x2	∂x2	NOUN
ma-9	477	10	∈	∈	NOUN
ma-9	477	11	h	h	NOUN
ma-9	477	12	,	,	PUNCT
ma-9	477	13	z(0	z(0	CCONJ
ma-9	477	14	)	)	PUNCT
ma-9	477	15	=	=	PUNCT
ma-9	477	16	z(π	z(π	X
ma-9	477	17	)	)	PUNCT
ma-9	477	18	=	=	SYM
ma-9	477	19	0	0	NUM
ma-9	477	20	}	}	PUNCT
ma-9	477	21	.	.	PUNCT
ma-9	478	1	for	for	ADP
ma-9	478	2	z	z	PROPN
ma-9	478	3	∈	∈	PROPN
ma-9	478	4	d(a),az	d(a),az	NOUN
ma-9	478	5	=	=	PUNCT
ma-9	478	6	−	−	PROPN
ma-9	478	7	∞∑	∞∑	NUM
ma-9	478	8	n=1	n=1	PROPN
ma-9	478	9	n	n	ADV
ma-9	478	10	2	2	NUM
ma-9	478	11	<	<	X
ma-9	478	12	z	z	PROPN
ma-9	478	13	,	,	PUNCT
ma-9	478	14	zn	zn	PROPN
ma-9	478	15	>	>	X
ma-9	478	16	zn	zn	PROPN
ma-9	478	17	,	,	PUNCT
ma-9	478	18	where	where	SCONJ
ma-9	478	19	{	{	PUNCT
ma-9	478	20	zn	zn	NOUN
ma-9	478	21	:	:	PUNCT
ma-9	479	1	n	n	X
ma-9	479	2	∈	∈	PROPN
ma-9	479	3	z	z	X
ma-9	479	4	}	}	PUNCT
ma-9	479	5	is	be	AUX
ma-9	479	6	an	an	DET
ma-9	479	7	orthonormal	orthonormal	ADJ
ma-9	479	8	basis	basis	NOUN
ma-9	479	9	of	of	ADP
ma-9	479	10	h	h	NOUN
ma-9	479	11	,	,	PUNCT
ma-9	479	12	zn(x	zn(x	NUM
ma-9	479	13	)	)	PUNCT
ma-9	479	14	:	:	PUNCT
ma-9	480	1	=	=	SYM
ma-9	480	2	1√2πeinx	1√2πeinx	NUM
ma-9	480	3	,	,	PUNCT
ma-9	480	4	n	n	PRON
ma-9	480	5	∈	∈	PROPN
ma-9	480	6	z+	z+	NUM
ma-9	480	7	,	,	PUNCT
ma-9	480	8	x	x	SYM
ma-9	480	9	∈	∈	PROPN
ma-9	481	1	[	[	X
ma-9	481	2	0	0	NUM
ma-9	481	3	,	,	PUNCT
ma-9	481	4	π	π	NOUN
ma-9	481	5	]	]	X
ma-9	481	6	.	.	PUNCT
ma-9	482	1	it	it	PRON
ma-9	482	2	is	be	AUX
ma-9	482	3	known	know	VERB
ma-9	482	4	that	that	SCONJ
ma-9	482	5	a	a	DET
ma-9	482	6	generates	generate	VERB
ma-9	482	7	strongly	strongly	ADV
ma-9	482	8	continuous	continuous	ADJ
ma-9	482	9	operators	operator	NOUN
ma-9	482	10	c(t	c(t	PROPN
ma-9	482	11	)	)	PUNCT
ma-9	482	12	and	and	CCONJ
ma-9	482	13	s(t	s(t	NUM
ma-9	482	14	)	)	PUNCT
ma-9	482	15	in	in	ADP
ma-9	482	16	a	a	DET
ma-9	482	17	hilbert	hilbert	NOUN
ma-9	482	18	space	space	NOUN
ma-9	482	19	h	h	NOUN
ma-9	482	20	,	,	PUNCT
ma-9	482	21	such	such	ADJ
ma-9	482	22	that	that	SCONJ
ma-9	482	23	c(t)z	c(t)z	NOUN
ma-9	482	24	=	=	NOUN
ma-9	483	1	∞∑	∞∑	NUM
ma-9	483	2	n=1	n=1	NUM
ma-9	483	3	cos(nt	cos(nt	NOUN
ma-9	483	4	)	)	PUNCT
ma-9	483	5	<	<	X
ma-9	484	1	z	z	X
ma-9	484	2	,	,	PUNCT
ma-9	484	3	zn	zn	PROPN
ma-9	484	4	>	>	X
ma-9	484	5	zn	zn	PROPN
ma-9	484	6	,	,	PUNCT
ma-9	484	7	and	and	CCONJ
ma-9	484	8	s(t)z	s(t)z	PROPN
ma-9	484	9	=	=	PROPN
ma-9	485	1	∞∑	∞∑	NUM
ma-9	485	2	n=1	n=1	ADP
ma-9	485	3	sin(nt)/n	sin(nt)/n	PROPN
ma-9	485	4	<	<	X
ma-9	485	5	z	z	PROPN
ma-9	485	6	,	,	PUNCT
ma-9	485	7	zn	zn	PROPN
ma-9	485	8	>	>	X
ma-9	485	9	zn	zn	PROPN
ma-9	485	10	,	,	PUNCT
ma-9	485	11	for	for	ADP
ma-9	485	12	t	t	PROPN
ma-9	485	13	∈	∈	PROPN
ma-9	485	14	r.	r.	PROPN
ma-9	485	15	and	and	CCONJ
ma-9	485	16	we	we	PRON
ma-9	485	17	assume	assume	VERB
ma-9	485	18	that	that	SCONJ
ma-9	485	19	s(t	s(t	PROPN
ma-9	485	20	)	)	PUNCT
ma-9	485	21	is	be	AUX
ma-9	485	22	not	not	PART
ma-9	485	23	a	a	DET
ma-9	485	24	compact	compact	ADJ
ma-9	485	25	semigroup	semigroup	NOUN
ma-9	485	26	and	and	CCONJ
ma-9	485	27	θ	θ	PROPN
ma-9	485	28	(	(	PUNCT
ma-9	485	29	s(t)d	s(t)d	PROPN
ma-9	485	30	)	)	PUNCT
ma-9	485	31	≤	≤	NUM
ma-9	485	32	θ	θ	PROPN
ma-9	485	33	(	(	PUNCT
ma-9	485	34	d	d	NOUN
ma-9	485	35	)	)	PUNCT
ma-9	485	36	,	,	PUNCT
ma-9	485	37	where	where	SCONJ
ma-9	485	38	d	d	PROPN
ma-9	485	39	∈	∈	PROPN
ma-9	485	40	h	h	NOUN
ma-9	485	41	denotes	denote	VERB
ma-9	485	42	a	a	DET
ma-9	485	43	bounded	bounded	ADJ
ma-9	485	44	set	set	NOUN
ma-9	485	45	,	,	PUNCT
ma-9	485	46	θ	θ	PROPN
ma-9	485	47	is	be	AUX
ma-9	485	48	the	the	DET
ma-9	485	49	hausdroff	hausdroff	ADJ
ma-9	485	50	measure	measure	NOUN
ma-9	485	51	of	of	ADP
ma-9	485	52	non-compactness.in	non-compactness.in	NOUN
ma-9	485	53	the	the	DET
ma-9	485	54	sequel	sequel	NOUN
ma-9	485	55	,	,	PUNCT
ma-9	485	56	we	we	PRON
ma-9	485	57	may	may	AUX
ma-9	485	58	consider	consider	VERB
ma-9	485	59	second	second	ADJ
ma-9	485	60	-	-	PUNCT
ma-9	485	61	order	order	NOUN
ma-9	485	62	neutral	neutral	ADJ
ma-9	485	63	stochastic	stochastic	ADJ
ma-9	485	64	functional	functional	ADJ
ma-9	485	65	differential	differential	NOUN
ma-9	485	66	equation	equation	NOUN
ma-9	485	67	ofthe	ofthe	NOUN
ma-9	485	68	form	form	NOUN
ma-9	485	69	,	,	PUNCT
ma-9	485	70	∂	∂	NUM
ma-9	485	71	∂t	∂t	PROPN
ma-9	485	72	[	[	PUNCT
ma-9	485	73	∂	∂	NOUN
ma-9	485	74	∂t	∂t	PROPN
ma-9	485	75	z(t	z(t	PROPN
ma-9	485	76	,	,	PUNCT
ma-9	485	77	x)−	x)−	PROPN
ma-9	485	78	m15	m15	PROPN
ma-9	485	79	∫	∫	PROPN
ma-9	485	80	0	0	NUM
ma-9	485	81	−r	−r	PROPN
ma-9	485	82	ε1(s)z(t	ε1(s)z(t	PROPN
ma-9	485	83	+	+	CCONJ
ma-9	485	84	s	s	PROPN
ma-9	485	85	,	,	PUNCT
ma-9	485	86	x)ds	x)ds	PROPN
ma-9	485	87	]	]	X
ma-9	485	88	(	(	PUNCT
ma-9	485	89	5.1	5.1	NUM
ma-9	485	90	)	)	PUNCT
ma-9	485	91	=	=	NOUN
ma-9	486	1	[	[	PUNCT
ma-9	486	2	∂2	∂2	NUM
ma-9	486	3	∂x2	∂x2	NOUN
ma-9	486	4	z(t	z(t	NOUN
ma-9	486	5	,	,	PUNCT
ma-9	486	6	x	x	PRON
ma-9	486	7	)	)	PUNCT
ma-9	487	1	+	+	CCONJ
ma-9	487	2	m25	m25	NUM
ma-9	487	3	∫	∫	PROPN
ma-9	487	4	0	0	NUM
ma-9	488	1	−r	−r	PROPN
ma-9	488	2	ε1(s)z(t	ε1(s)z(t	PROPN
ma-9	488	3	+	+	CCONJ
ma-9	488	4	s)ds]dt	s)ds]dt	PROPN
ma-9	488	5	+	+	CCONJ
ma-9	488	6	m35	m35	PROPN
ma-9	488	7	∫	∫	PROPN
ma-9	488	8	0	0	NUM
ma-9	489	1	−r	−r	ADJ
ma-9	489	2	ε3(s)z(t	ε3(s)z(t	PROPN
ma-9	489	3	+	+	PUNCT
ma-9	489	4	s)dω(t	s)dω(t	NOUN
ma-9	489	5	)	)	PUNCT
ma-9	490	1	+	+	CCONJ
ma-9	490	2	m45	m45	PROPN
ma-9	490	3	∫	∫	PROPN
ma-9	490	4	u	u	PROPN
ma-9	490	5	∫	∫	PROPN
ma-9	490	6	0	0	NUM
ma-9	490	7	−r	−r	ADJ
ma-9	490	8	ε4(s)z(t	ε4(s)z(t	PROPN
ma-9	490	9	+	+	CCONJ
ma-9	490	10	s)ñ(dt	s)ñ(dt	PROPN
ma-9	490	11	,	,	PUNCT
ma-9	490	12	du	du	PROPN
ma-9	490	13	)	)	PUNCT
ma-9	490	14	,	,	PUNCT
ma-9	490	15	t	t	PROPN
ma-9	490	16	≥	≥	PROPN
ma-9	490	17	t0	t0	PROPN
ma-9	490	18	,	,	PUNCT
ma-9	490	19	t	t	PROPN
ma-9	490	20	6=	6=	PROPN
ma-9	490	21	ξk	ξk	ADP
ma-9	490	22	,	,	PUNCT
ma-9	490	23	x	x	SYM
ma-9	490	24	∈	∈	PROPN
ma-9	491	1	[	[	X
ma-9	491	2	0	0	NUM
ma-9	491	3	,	,	PUNCT
ma-9	491	4	π	π	PROPN
ma-9	491	5	]	]	X
ma-9	491	6	,	,	PUNCT
ma-9	491	7	z(ξk	z(ξk	PROPN
ma-9	491	8	,	,	PUNCT
ma-9	491	9	x	x	X
ma-9	491	10	)	)	PUNCT
ma-9	491	11	=	=	SYM
ma-9	491	12	ρ(k)δkz(ξ−k	ρ(k)δkz(ξ−k	NOUN
ma-9	491	13	,	,	PUNCT
ma-9	491	14	x	x	NOUN
ma-9	491	15	)	)	PUNCT
ma-9	491	16	,	,	PUNCT
ma-9	491	17	k	k	X
ma-9	492	1	=	=	SYM
ma-9	492	2	1	1	NUM
ma-9	492	3	,	,	PUNCT
ma-9	492	4	2	2	NUM
ma-9	492	5	,	,	PUNCT
ma-9	492	6	3	3	NUM
ma-9	492	7	...	...	PUNCT
ma-9	492	8	,	,	PUNCT
ma-9	492	9	(	(	PUNCT
ma-9	492	10	5.2	5.2	NUM
ma-9	492	11	)	)	PUNCT
ma-9	492	12	∂	∂	NOUN
ma-9	493	1	∂t	∂t	PROPN
ma-9	493	2	z(ξk	z(ξk	PROPN
ma-9	493	3	,	,	PUNCT
ma-9	493	4	x	x	X
ma-9	493	5	)	)	PUNCT
ma-9	493	6	=	=	SYM
ma-9	494	1	ρ(k)δk	ρ(k)δk	PROPN
ma-9	494	2	∂∂t	∂∂t	NOUN
ma-9	494	3	z(ξ−k	z(ξ−k	NUM
ma-9	494	4	,	,	PUNCT
ma-9	494	5	x	x	NOUN
ma-9	494	6	)	)	PUNCT
ma-9	494	7	,	,	PUNCT
ma-9	494	8	z(t0	z(t0	NOUN
ma-9	494	9	,	,	PUNCT
ma-9	494	10	x	x	X
ma-9	494	11	)	)	PUNCT
ma-9	494	12	=	=	SYM
ma-9	494	13	φ(θ	φ(θ	PROPN
ma-9	494	14	,	,	PUNCT
ma-9	494	15	x	x	NOUN
ma-9	494	16	)	)	PUNCT
ma-9	494	17	,	,	PUNCT
ma-9	494	18	θ	θ	PROPN
ma-9	494	19	∈	∈	PROPN
ma-9	495	1	[	[	X
ma-9	495	2	−r	−r	ADJ
ma-9	495	3	,	,	PUNCT
ma-9	495	4	0	0	NUM
ma-9	495	5	]	]	PUNCT
ma-9	495	6	,	,	PUNCT
ma-9	495	7	x	x	SYM
ma-9	495	8	∈	∈	PROPN
ma-9	496	1	[	[	X
ma-9	496	2	0	0	NUM
ma-9	496	3	,	,	PUNCT
ma-9	496	4	π	π	PROPN
ma-9	496	5	]	]	X
ma-9	496	6	,	,	PUNCT
ma-9	496	7	r	r	NOUN
ma-9	496	8	>	>	X
ma-9	496	9	0	0	NUM
ma-9	496	10	,	,	PUNCT
ma-9	496	11	∂	∂	NUM
ma-9	496	12	∂t	∂t	PROPN
ma-9	496	13	z(t0	z(t0	NOUN
ma-9	496	14	,	,	PUNCT
ma-9	496	15	x	x	X
ma-9	496	16	)	)	PUNCT
ma-9	496	17	=	=	SYM
ma-9	496	18	φ(x	φ(x	NOUN
ma-9	496	19	)	)	PUNCT
ma-9	496	20	,	,	PUNCT
ma-9	496	21	x	x	PUNCT
ma-9	496	22	∈	∈	PROPN
ma-9	497	1	[	[	X
ma-9	497	2	0	0	NUM
ma-9	497	3	,	,	PUNCT
ma-9	497	4	π	π	PROPN
ma-9	497	5	]	]	X
ma-9	497	6	,	,	PUNCT
ma-9	497	7	z(t	z(t	PROPN
ma-9	497	8	,	,	PUNCT
ma-9	497	9	0	0	NUM
ma-9	497	10	)	)	PUNCT
ma-9	497	11	=	=	PUNCT
ma-9	497	12	z(t	z(t	NOUN
ma-9	497	13	,	,	PUNCT
ma-9	497	14	π	π	X
ma-9	497	15	)	)	PUNCT
ma-9	497	16	=	=	SYM
ma-9	497	17	0	0	X
ma-9	497	18	.	.	X
ma-9	497	19	eur	eur	PROPN
ma-9	497	20	.	.	PUNCT
ma-9	498	1	j.	j.	PROPN
ma-9	498	2	math	math	PROPN
ma-9	498	3	.	.	PUNCT
ma-9	499	1	anal	anal	ADJ
ma-9	499	2	.	.	PUNCT
ma-9	500	1	1	1	NUM
ma-9	500	2	(	(	PUNCT
ma-9	500	3	2021	2021	NUM
ma-9	500	4	)	)	PUNCT
ma-9	500	5	17let	17let	NOUN
ma-9	500	6	δk	δk	AUX
ma-9	500	7	be	be	AUX
ma-9	500	8	a	a	DET
ma-9	500	9	random	random	ADJ
ma-9	500	10	variable	variable	NOUN
ma-9	500	11	defined	define	VERB
ma-9	500	12	on	on	ADP
ma-9	500	13	dk	dk	PROPN
ma-9	500	14	≡	≡	PROPN
ma-9	500	15	(	(	PUNCT
ma-9	500	16	0	0	NUM
ma-9	500	17	,	,	PUNCT
ma-9	500	18	dk	dk	PROPN
ma-9	500	19	)	)	PUNCT
ma-9	500	20	where	where	SCONJ
ma-9	500	21	,	,	PUNCT
ma-9	500	22	0	0	PUNCT
ma-9	500	23	<	<	X
ma-9	500	24	dk	dk	X
ma-9	500	25	<	<	X
ma-9	500	26	+	+	PROPN
ma-9	500	27	∞	∞	PROPN
ma-9	500	28	,	,	PUNCT
ma-9	500	29	for	for	ADP
ma-9	500	30	k	k	PROPN
ma-9	500	31	=	=	SYM
ma-9	500	32	1	1	NUM
ma-9	500	33	,	,	PUNCT
ma-9	500	34	2	2	NUM
ma-9	500	35	,	,	PUNCT
ma-9	500	36	·	·	PUNCT
ma-9	500	37	·	·	PUNCT
ma-9	500	38	·	·	PUNCT
ma-9	500	39	.	.	PUNCT
ma-9	501	1	ξ0	ξ0	PROPN
ma-9	501	2	=	=	SYM
ma-9	501	3	t0	t0	PROPN
ma-9	501	4	>	>	PUNCT
ma-9	501	5	0	0	PUNCT
ma-9	502	1	and	and	CCONJ
ma-9	502	2	ξk	ξk	ADP
ma-9	502	3	=	=	PUNCT
ma-9	502	4	ξk−1	ξk−1	PROPN
ma-9	502	5	+	+	CCONJ
ma-9	502	6	δk	δk	PROPN
ma-9	502	7	for	for	ADP
ma-9	502	8	k	k	PROPN
ma-9	502	9	=	=	SYM
ma-9	502	10	1	1	NUM
ma-9	502	11	,	,	PUNCT
ma-9	502	12	2	2	NUM
ma-9	502	13	,	,	PUNCT
ma-9	502	14	·	·	PUNCT
ma-9	502	15	·	·	PUNCT
ma-9	502	16	·	·	PUNCT
ma-9	502	17	.	.	PUNCT
ma-9	503	1	ω(t	ω(t	NOUN
ma-9	503	2	)	)	PUNCT
ma-9	503	3	denotes	denote	VERB
ma-9	503	4	a	a	DET
ma-9	503	5	standard	standard	ADJ
ma-9	503	6	cylindrical	cylindrical	ADJ
ma-9	503	7	weiner	weiner	NOUN
ma-9	503	8	process	process	NOUN
ma-9	503	9	inh	inh	PROPN
ma-9	503	10	.	.	PUNCT
ma-9	504	1	furthermore	furthermore	ADV
ma-9	504	2	,	,	PUNCT
ma-9	504	3	let	let	VERB
ma-9	504	4	ρ	ρ	NOUN
ma-9	504	5	be	be	AUX
ma-9	504	6	a	a	DET
ma-9	504	7	function	function	NOUN
ma-9	504	8	of	of	ADP
ma-9	504	9	k.	k.	PROPN
ma-9	504	10	εi	εi	VERB
ma-9	504	11	:	:	PUNCT
ma-9	505	1	[	[	X
ma-9	505	2	−r	−r	ADJ
ma-9	505	3	,	,	PUNCT
ma-9	505	4	0	0	NUM
ma-9	505	5	]	]	PUNCT
ma-9	505	6	→	→	PUNCT
ma-9	505	7	r	r	NOUN
ma-9	505	8	are	be	AUX
ma-9	505	9	positive	positive	ADJ
ma-9	505	10	functions	function	NOUN
ma-9	505	11	and	and	CCONJ
ma-9	505	12	mi	mi	X
ma-9	505	13	>	>	X
ma-9	505	14	0	0	PUNCT
ma-9	506	1	for	for	ADP
ma-9	506	2	i	i	PRON
ma-9	506	3	=	=	NOUN
ma-9	506	4	1	1	NUM
ma-9	506	5	,	,	PUNCT
ma-9	506	6	2	2	NUM
ma-9	506	7	,	,	PUNCT
ma-9	506	8	3	3	NUM
ma-9	506	9	,	,	PUNCT
ma-9	506	10	4	4	NUM
ma-9	506	11	.	.	X
ma-9	506	12	∥∥c(t)∥∥	∥∥c(t)∥∥	PROPN
ma-9	506	13	,	,	PUNCT
ma-9	506	14	∥∥s(t)∥∥	∥∥s(t)∥∥	PROPN
ma-9	506	15	are	be	AUX
ma-9	506	16	bounded	bound	VERB
ma-9	506	17	on	on	ADP
ma-9	506	18	r.	r.	PROPN
ma-9	506	19	∥∥c(t)∥∥	∥∥c(t)∥∥	PROPN
ma-9	506	20	≤	≤	NUM
ma-9	506	21	e−π2	e−π2	PRON
ma-9	506	22	t	t	PROPN
ma-9	506	23	and	and	CCONJ
ma-9	506	24	∥∥s(t)∥∥	∥∥s(t)∥∥	PROPN
ma-9	506	25	≤	≤	PROPN
ma-9	507	1	e−π2t(t	e−π2t(t	NOUN
ma-9	507	2	≥	≥	NOUN
ma-9	507	3	0).we	0).we	NOUN
ma-9	507	4	may	may	AUX
ma-9	507	5	assume	assume	VERB
ma-9	507	6	that,(i)the	that,(i)the	DET
ma-9	507	7	function	function	NOUN
ma-9	507	8	ε(θ	ε(θ	PROPN
ma-9	507	9	)	)	PUNCT
ma-9	507	10	≥	≥	X
ma-9	507	11	0	0	NUM
ma-9	507	12	is	be	AUX
ma-9	507	13	continuous	continuous	ADJ
ma-9	507	14	on	on	ADP
ma-9	507	15	[	[	X
ma-9	508	1	−r	−r	ADJ
ma-9	508	2	,	,	PUNCT
ma-9	508	3	0],∫	0],∫	PROPN
ma-9	508	4	0	0	NUM
ma-9	508	5	−r	−r	PROPN
ma-9	508	6	ε2	ε2	PROPN
ma-9	509	1	i	i	PRON
ma-9	509	2	(	(	PUNCT
ma-9	509	3	θ)dθ	θ)dθ	PROPN
ma-9	509	4	<	<	X
ma-9	509	5	∞(i	∞(i	X
ma-9	509	6	=	=	SYM
ma-9	509	7	1	1	NUM
ma-9	509	8	,	,	PUNCT
ma-9	509	9	2	2	NUM
ma-9	509	10	,	,	PUNCT
ma-9	509	11	3	3	NUM
ma-9	509	12	,	,	PUNCT
ma-9	509	13	4	4	NUM
ma-9	509	14	.	.	NUM
ma-9	509	15	)	)	PUNCT
ma-9	509	16	(	(	PUNCT
ma-9	509	17	ii)max	ii)max	X
ma-9	509	18	i	i	PRON
ma-9	509	19	,	,	PUNCT
ma-9	509	20	k	k	PROPN
ma-9	509	21	=	=	PRON
ma-9	509	22	{	{	PUNCT
ma-9	509	23	k∏	k∏	PROPN
ma-9	509	24	j	j	PROPN
ma-9	509	25	=	=	PROPN
ma-9	509	26	i	i	PROPN
ma-9	509	27	e[∥∥ρ(j)δj∥∥2	e[∥∥ρ(j)δj∥∥2	PROPN
ma-9	509	28	]	]	PUNCT
ma-9	509	29	}	}	PUNCT
ma-9	509	30	<	<	X
ma-9	509	31	n	n	X
ma-9	509	32	.	.	PUNCT
ma-9	510	1	using	use	VERB
ma-9	510	2	above	above	ADP
ma-9	510	3	assumptions	assumption	NOUN
ma-9	510	4	and	and	CCONJ
ma-9	510	5	functions	function	NOUN
ma-9	510	6	ε1	ε1	VERB
ma-9	510	7	,	,	PUNCT
ma-9	510	8	ε2	ε2	PROPN
ma-9	510	9	,	,	PUNCT
ma-9	510	10	ε3	ε3	PROPN
ma-9	510	11	,	,	PUNCT
ma-9	510	12	ρ	ρ	NOUN
ma-9	510	13	we	we	PRON
ma-9	510	14	can	can	AUX
ma-9	510	15	show	show	VERB
ma-9	510	16	that	that	SCONJ
ma-9	510	17	lg	lg	PROPN
ma-9	510	18	=	=	PROPN
ma-9	510	19	rm125	rm125	PROPN
ma-9	510	20	∫	∫	PROPN
ma-9	510	21	0	0	NUM
ma-9	510	22	−r	−r	PROPN
ma-9	510	23	ε	ε	PROPN
ma-9	510	24	21(θ)dθ	21(θ)dθ	PROPN
ma-9	510	25	,	,	PUNCT
ma-9	510	26	lf	lf	ADP
ma-9	510	27	=	=	PUNCT
ma-9	510	28	rm225	rm225	NOUN
ma-9	510	29	∫	∫	NOUN
ma-9	510	30	0	0	NUM
ma-9	511	1	−r	−r	PROPN
ma-9	511	2	ε	ε	PROPN
ma-9	511	3	21(θ)dθ	21(θ)dθ	PROPN
ma-9	511	4	,	,	PUNCT
ma-9	511	5	lh	lh	PROPN
ma-9	512	1	=	=	PROPN
ma-9	513	1	rm325	rm325	PROPN
ma-9	513	2	∫	∫	PROPN
ma-9	513	3	0	0	NUM
ma-9	514	1	−r	−r	PROPN
ma-9	514	2	ε	ε	PROPN
ma-9	514	3	21(θ)dθ	21(θ)dθ	NUM
ma-9	514	4	and	and	CCONJ
ma-9	514	5	lσ	lσ	NOUN
ma-9	514	6	=	=	SYM
ma-9	514	7	rm425	rm425	PROPN
ma-9	514	8	∫	∫	PROPN
ma-9	514	9	0	0	NUM
ma-9	515	1	−r	−r	PROPN
ma-9	515	2	ε	ε	PROPN
ma-9	515	3	21(θ)dθ	21(θ)dθ	PROPN
ma-9	515	4	.	.	PROPN
ma-9	515	5	hence	hence	ADV
ma-9	515	6	stability	stability	NOUN
ma-9	515	7	in	in	ADP
ma-9	515	8	mean	mean	NOUN
ma-9	515	9	squareof	squareof	ADV
ma-9	515	10	mild	mild	ADJ
ma-9	515	11	solution	solution	NOUN
ma-9	515	12	(	(	PUNCT
ma-9	515	13	5.1	5.1	NUM
ma-9	515	14	)	)	PUNCT
ma-9	515	15	is	be	AUX
ma-9	515	16	obtained	obtain	VERB
ma-9	515	17	.	.	PUNCT
ma-9	516	1	�	�	PROPN
ma-9	516	2	6	6	NUM
ma-9	516	3	.	.	PUNCT
ma-9	516	4	conclusion	conclusion	NOUN
ma-9	516	5	in	in	ADP
ma-9	516	6	this	this	DET
ma-9	516	7	paper	paper	NOUN
ma-9	516	8	,	,	PUNCT
ma-9	516	9	the	the	DET
ma-9	516	10	existence	existence	NOUN
ma-9	516	11	and	and	CCONJ
ma-9	516	12	stability	stability	NOUN
ma-9	516	13	results	result	NOUN
ma-9	516	14	of	of	ADP
ma-9	516	15	second	second	ADJ
ma-9	516	16	-	-	PUNCT
ma-9	516	17	order	order	NOUN
ma-9	516	18	neutral	neutral	ADJ
ma-9	516	19	stochastic	stochastic	ADJ
ma-9	516	20	functionalsystems	functionalsystem	NOUN
ma-9	516	21	with	with	ADP
ma-9	516	22	random	random	ADJ
ma-9	516	23	impulse	impulse	NOUN
ma-9	516	24	is	be	AUX
ma-9	516	25	presented	present	VERB
ma-9	516	26	.	.	PUNCT
ma-9	517	1	the	the	DET
ma-9	517	2	existence	existence	NOUN
ma-9	517	3	results	result	NOUN
ma-9	517	4	of	of	ADP
ma-9	517	5	aforementioned	aforementioned	ADJ
ma-9	517	6	system	system	NOUN
ma-9	517	7	is	be	AUX
ma-9	517	8	estab	estab	NOUN
ma-9	517	9	-	-	PUNCT
ma-9	517	10	lished	lishe	VERB
ma-9	517	11	using	use	VERB
ma-9	517	12	banach	banach	NOUN
ma-9	517	13	contraction	contraction	NOUN
ma-9	517	14	principle	principle	NOUN
ma-9	517	15	.	.	PUNCT
ma-9	518	1	then	then	ADV
ma-9	518	2	the	the	DET
ma-9	518	3	stability	stability	NOUN
ma-9	518	4	of	of	ADP
ma-9	518	5	mild	mild	ADJ
ma-9	518	6	solutions	solution	NOUN
ma-9	518	7	through	through	ADP
ma-9	518	8	continuousdependence	continuousdependence	NOUN
ma-9	518	9	of	of	ADP
ma-9	518	10	solutions	solution	NOUN
ma-9	518	11	on	on	ADP
ma-9	518	12	initial	initial	ADJ
ma-9	518	13	conditions	condition	NOUN
ma-9	518	14	are	be	AUX
ma-9	518	15	calculated	calculate	VERB
ma-9	518	16	.	.	PUNCT
ma-9	519	1	references	reference	NOUN
ma-9	519	2	[	[	X
ma-9	519	3	1	1	NUM
ma-9	519	4	]	]	PUNCT
ma-9	519	5	a.	a.	NOUN
ma-9	519	6	anguraj	anguraj	PROPN
ma-9	519	7	,	,	PUNCT
ma-9	519	8	m.	m.	PROPN
ma-9	519	9	mallika	mallika	PROPN
ma-9	519	10	arjunan	arjunan	PROPN
ma-9	519	11	,	,	PUNCT
ma-9	519	12	e.	e.	PROPN
ma-9	519	13	hernández	hernández	PROPN
ma-9	519	14	m	m	PROPN
ma-9	519	15	,	,	PUNCT
ma-9	519	16	existence	existence	NOUN
ma-9	519	17	results	result	VERB
ma-9	519	18	for	for	ADP
ma-9	519	19	an	an	DET
ma-9	519	20	impulsive	impulsive	ADJ
ma-9	519	21	neutral	neutral	ADJ
ma-9	519	22	functional	functional	ADJ
ma-9	519	23	dif	dif	X
ma-9	519	24	-	-	ADJ
ma-9	519	25	ferential	ferential	ADJ
ma-9	519	26	equation	equation	NOUN
ma-9	519	27	with	with	ADP
ma-9	519	28	state	state	NOUN
ma-9	519	29	-	-	PUNCT
ma-9	519	30	dependent	dependent	ADJ
ma-9	519	31	delay	delay	NOUN
ma-9	519	32	,	,	PUNCT
ma-9	519	33	appl	appl	PROPN
ma-9	519	34	.	.	PROPN
ma-9	520	1	anal	anal	PROPN
ma-9	520	2	.	.	PUNCT
ma-9	521	1	86	86	NUM
ma-9	521	2	(	(	PUNCT
ma-9	521	3	2007	2007	NUM
ma-9	521	4	)	)	PUNCT
ma-9	522	1	861–872	861–872	NUM
ma-9	522	2	.	.	PUNCT
ma-9	523	1	https://doi.org/10.1080/	https://doi.org/10.1080/	NOUN
ma-9	523	2	00036810701354995.[2	00036810701354995.[2	NUM
ma-9	523	3	]	]	PUNCT
ma-9	523	4	a.	a.	NOUN
ma-9	523	5	anguraj	anguraj	PROPN
ma-9	523	6	,	,	PUNCT
ma-9	523	7	k.	k.	PROPN
ma-9	523	8	ramkumar	ramkumar	PROPN
ma-9	523	9	,	,	PUNCT
ma-9	523	10	k.	k.	PROPN
ma-9	523	11	ravikumar	ravikumar	PROPN
ma-9	523	12	,	,	PUNCT
ma-9	523	13	existence	existence	NOUN
ma-9	523	14	and	and	CCONJ
ma-9	523	15	hyers	hyers	PROPN
ma-9	523	16	-	-	PUNCT
ma-9	523	17	ulam	ulam	PROPN
ma-9	523	18	stability	stability	NOUN
ma-9	523	19	of	of	ADP
ma-9	523	20	random	random	ADJ
ma-9	523	21	impulsive	impulsive	ADJ
ma-9	523	22	stochastic	stochastic	ADJ
ma-9	523	23	func	func	ADJ
ma-9	523	24	-	-	PUNCT
ma-9	523	25	tional	tional	ADJ
ma-9	523	26	integrodifferential	integrodifferential	ADJ
ma-9	523	27	equations	equation	NOUN
ma-9	523	28	with	with	ADP
ma-9	523	29	finite	finite	ADJ
ma-9	523	30	delays	delay	NOUN
ma-9	523	31	,	,	PUNCT
ma-9	523	32	comput	comput	NOUN
ma-9	523	33	.	.	PUNCT
ma-9	524	1	methods	method	NOUN
ma-9	524	2	differ	differ	VERB
ma-9	524	3	.	.	PUNCT
ma-9	525	1	equ	equ	PROPN
ma-9	525	2	.	.	PUNCT
ma-9	525	3	(	(	PUNCT
ma-9	525	4	2021	2021	NUM
ma-9	525	5	)	)	PUNCT
ma-9	525	6	.	.	PUNCT
ma-9	526	1	https://doi.org/10	https://doi.org/10	PROPN
ma-9	526	2	.	.	PUNCT
ma-9	527	1	22034	22034	NUM
ma-9	527	2	/	/	SYM
ma-9	527	3	cmde.2020.32591.1512.[3	cmde.2020.32591.1512.[3	NOUN
ma-9	527	4	]	]	PUNCT
ma-9	527	5	a.	a.	NOUN
ma-9	527	6	anguraj	anguraj	PROPN
ma-9	527	7	,	,	PUNCT
ma-9	527	8	k.	k.	PROPN
ma-9	527	9	ravikumar	ravikumar	PROPN
ma-9	527	10	,	,	PUNCT
ma-9	527	11	j.j	j.j	PROPN
ma-9	527	12	.	.	PROPN
ma-9	527	13	nieto	nieto	PROPN
ma-9	527	14	,	,	PUNCT
ma-9	527	15	on	on	ADP
ma-9	527	16	stability	stability	NOUN
ma-9	527	17	of	of	ADP
ma-9	527	18	stochastic	stochastic	ADJ
ma-9	527	19	differential	differential	ADJ
ma-9	527	20	equations	equation	NOUN
ma-9	527	21	with	with	ADP
ma-9	527	22	random	random	ADJ
ma-9	527	23	impulses	impulse	NOUN
ma-9	527	24	drivenby	drivenby	PROPN
ma-9	527	25	poisson	poisson	NOUN
ma-9	527	26	jumps	jump	VERB
ma-9	527	27	,	,	PUNCT
ma-9	527	28	stochastics	stochastic	NOUN
ma-9	527	29	.	.	PUNCT
ma-9	528	1	93	93	NUM
ma-9	528	2	(	(	PUNCT
ma-9	528	3	2021	2021	NUM
ma-9	528	4	)	)	PUNCT
ma-9	529	1	682–696	682–696	NUM
ma-9	529	2	.	.	PUNCT
ma-9	530	1	https://doi.org/10.1080/17442508.2020.1783264.[4	https://doi.org/10.1080/17442508.2020.1783264.[4	NUM
ma-9	530	2	]	]	X
ma-9	530	3	a.	a.	NOUN
ma-9	530	4	anguraj	anguraj	PROPN
ma-9	530	5	,	,	PUNCT
ma-9	530	6	s.	s.	PROPN
ma-9	530	7	wu	wu	PROPN
ma-9	530	8	,	,	PUNCT
ma-9	530	9	a.	a.	PROPN
ma-9	530	10	vinodkumar	vinodkumar	PROPN
ma-9	530	11	,	,	PUNCT
ma-9	530	12	the	the	DET
ma-9	530	13	existence	existence	NOUN
ma-9	530	14	and	and	CCONJ
ma-9	530	15	exponential	exponential	ADJ
ma-9	530	16	stability	stability	NOUN
ma-9	530	17	of	of	ADP
ma-9	530	18	semilinear	semilinear	ADJ
ma-9	530	19	functional	functional	ADJ
ma-9	530	20	differentialequations	differentialequation	NOUN
ma-9	530	21	with	with	ADP
ma-9	530	22	random	random	ADJ
ma-9	530	23	impulses	impulse	NOUN
ma-9	530	24	under	under	ADP
ma-9	530	25	non	non	ADJ
ma-9	530	26	-	-	ADJ
ma-9	530	27	uniqueness	uniqueness	ADJ
ma-9	530	28	,	,	PUNCT
ma-9	530	29	nonlinear	nonlinear	ADJ
ma-9	530	30	anal	anal	NOUN
ma-9	530	31	.	.	PUNCT
ma-9	530	32	:	:	PUNCT
ma-9	531	1	theory	theory	NOUN
ma-9	531	2	methods	method	NOUN
ma-9	531	3	appl	appl	PROPN
ma-9	531	4	.	.	PUNCT
ma-9	532	1	74	74	NUM
ma-9	532	2	(	(	PUNCT
ma-9	532	3	2011	2011	NUM
ma-9	532	4	)	)	PUNCT
ma-9	533	1	331–342	331–342	NUM
ma-9	533	2	.	.	PUNCT
ma-9	534	1	https://doi.org/10.1016/j.na.2010.07.007.[5	https://doi.org/10.1016/j.na.2010.07.007.[5	NOUN
ma-9	534	2	]	]	PUNCT
ma-9	534	3	g.	g.	PROPN
ma-9	534	4	arthi	arthi	PROPN
ma-9	534	5	,	,	PUNCT
ma-9	534	6	j.h	j.h	PROPN
ma-9	534	7	.	.	PROPN
ma-9	534	8	park	park	PROPN
ma-9	534	9	,	,	PUNCT
ma-9	534	10	h.y	h.y	PROPN
ma-9	534	11	.	.	PROPN
ma-9	534	12	jung	jung	PROPN
ma-9	534	13	,	,	PUNCT
ma-9	534	14	exponential	exponential	ADJ
ma-9	534	15	stability	stability	NOUN
ma-9	534	16	for	for	ADP
ma-9	534	17	second	second	ADJ
ma-9	534	18	-	-	PUNCT
ma-9	534	19	order	order	NOUN
ma-9	534	20	neutral	neutral	ADJ
ma-9	534	21	stochastic	stochastic	ADJ
ma-9	534	22	differential	differential	ADJ
ma-9	534	23	equations	equation	NOUN
ma-9	534	24	withimpulses	withimpulse	NOUN
ma-9	534	25	,	,	PUNCT
ma-9	534	26	int	int	NOUN
ma-9	534	27	.	.	PUNCT
ma-9	535	1	j.	j.	PROPN
ma-9	535	2	control	control	PROPN
ma-9	535	3	.	.	PUNCT
ma-9	536	1	88	88	NUM
ma-9	536	2	(	(	PUNCT
ma-9	536	3	2015	2015	NUM
ma-9	536	4	)	)	PUNCT
ma-9	536	5	1300–1309	1300–1309	NUM
ma-9	536	6	.	.	PUNCT
ma-9	537	1	https://doi.org/10.1080/00207179.2015.1006683.[6	https://doi.org/10.1080/00207179.2015.1006683.[6	PUNCT
ma-9	537	2	]	]	PUNCT
ma-9	538	1	h.	h.	PROPN
ma-9	538	2	chen	chen	PROPN
ma-9	538	3	,	,	PUNCT
ma-9	538	4	the	the	DET
ma-9	538	5	asymptotic	asymptotic	ADJ
ma-9	538	6	behavior	behavior	NOUN
ma-9	538	7	for	for	ADP
ma-9	538	8	second	second	ADJ
ma-9	538	9	-	-	PUNCT
ma-9	538	10	order	order	NOUN
ma-9	538	11	neutral	neutral	ADJ
ma-9	538	12	stochastic	stochastic	ADJ
ma-9	538	13	partial	partial	ADJ
ma-9	538	14	differential	differential	NOUN
ma-9	538	15	equations	equation	NOUN
ma-9	538	16	with	with	ADP
ma-9	538	17	infinitedelay	infinitedelay	NOUN
ma-9	538	18	,	,	PUNCT
ma-9	538	19	discrete	discrete	ADJ
ma-9	538	20	dyn	dyn	NOUN
ma-9	538	21	.	.	PUNCT
ma-9	539	1	nat	nat	PROPN
ma-9	539	2	.	.	PUNCT
ma-9	540	1	soc	soc	PROPN
ma-9	540	2	.	.	PUNCT
ma-9	541	1	2011	2011	NUM
ma-9	541	2	(	(	PUNCT
ma-9	541	3	2011	2011	NUM
ma-9	541	4	)	)	PUNCT
ma-9	541	5	584510	584510	NUM
ma-9	541	6	.	.	PUNCT
ma-9	542	1	https://doi.org/10.1155/2011/584510.[7	https://doi.org/10.1155/2011/584510.[7	NOUN
ma-9	542	2	]	]	X
ma-9	542	3	g.	g.	PROPN
ma-9	542	4	da	da	PROPN
ma-9	542	5	prato	prato	PROPN
ma-9	542	6	,	,	PUNCT
ma-9	542	7	j.	j.	PROPN
ma-9	542	8	zabczyk	zabczyk	PROPN
ma-9	542	9	,	,	PUNCT
ma-9	542	10	stochastic	stochastic	ADJ
ma-9	542	11	equations	equation	NOUN
ma-9	542	12	in	in	ADP
ma-9	542	13	infinite	infinite	ADJ
ma-9	542	14	dimensions	dimension	NOUN
ma-9	542	15	,	,	PUNCT
ma-9	542	16	cambridge	cambridge	PROPN
ma-9	542	17	university	university	PROPN
ma-9	542	18	press	press	PROPN
ma-9	542	19	,	,	PUNCT
ma-9	542	20	cambridge	cambridge	PROPN
ma-9	542	21	,	,	PUNCT
ma-9	542	22	1992.[8	1992.[8	NUM
ma-9	542	23	]	]	X
ma-9	542	24	f.	f.	PROPN
ma-9	542	25	jiang	jiang	PROPN
ma-9	542	26	,	,	PUNCT
ma-9	542	27	h.	h.	PROPN
ma-9	542	28	yang	yang	PROPN
ma-9	542	29	,	,	PUNCT
ma-9	542	30	y.	y.	PROPN
ma-9	542	31	shen	shen	PROPN
ma-9	542	32	,	,	PUNCT
ma-9	542	33	a	a	DET
ma-9	542	34	note	note	NOUN
ma-9	542	35	on	on	ADP
ma-9	542	36	exponential	exponential	ADJ
ma-9	542	37	stability	stability	NOUN
ma-9	542	38	for	for	ADP
ma-9	542	39	second	second	ADJ
ma-9	542	40	-	-	PUNCT
ma-9	542	41	order	order	NOUN
ma-9	542	42	neutral	neutral	ADJ
ma-9	542	43	stochastic	stochastic	ADJ
ma-9	542	44	partial	partial	ADJ
ma-9	542	45	differentialequations	differentialequation	NOUN
ma-9	542	46	with	with	ADP
ma-9	542	47	infinite	infinite	ADJ
ma-9	542	48	delays	delay	NOUN
ma-9	542	49	in	in	ADP
ma-9	542	50	the	the	DET
ma-9	542	51	presence	presence	NOUN
ma-9	542	52	of	of	ADP
ma-9	542	53	impulses	impulse	NOUN
ma-9	542	54	,	,	PUNCT
ma-9	542	55	appl	appl	PROPN
ma-9	542	56	.	.	PROPN
ma-9	542	57	math	math	NOUN
ma-9	542	58	.	.	PUNCT
ma-9	543	1	comput	comput	NOUN
ma-9	543	2	.	.	PUNCT
ma-9	544	1	287–288	287–288	NUM
ma-9	544	2	(	(	PUNCT
ma-9	544	3	2016	2016	NUM
ma-9	544	4	)	)	PUNCT
ma-9	544	5	125–133	125–133	NUM
ma-9	544	6	.	.	PUNCT
ma-9	545	1	https	https	NOUN
ma-9	545	2	:	:	PUNCT
ma-9	546	1	//doi.org/10.1016	//doi.org/10.1016	PROPN
ma-9	546	2	/	/	SYM
ma-9	546	3	j.amc.2016.04.021.[9	j.amc.2016.04.021.[9	NOUN
ma-9	546	4	]	]	X
ma-9	547	1	v.	v.	CCONJ
ma-9	547	2	lakshmikantham	lakshmikantham	PROPN
ma-9	548	1	,	,	PUNCT
ma-9	548	2	d.d	d.d	PROPN
ma-9	548	3	.	.	PROPN
ma-9	548	4	bainov	bainov	PROPN
ma-9	548	5	,	,	PUNCT
ma-9	548	6	p.s	p.s	PROPN
ma-9	548	7	.	.	PROPN
ma-9	548	8	simeonov	simeonov	PROPN
ma-9	548	9	,	,	PUNCT
ma-9	548	10	theory	theory	NOUN
ma-9	548	11	of	of	ADP
ma-9	548	12	impulsive	impulsive	ADJ
ma-9	548	13	differential	differential	ADJ
ma-9	548	14	equations	equation	NOUN
ma-9	548	15	,	,	PUNCT
ma-9	548	16	world	world	NOUN
ma-9	548	17	scientific	scientific	ADJ
ma-9	548	18	,	,	PUNCT
ma-9	548	19	sin	sin	NOUN
ma-9	548	20	-	-	PUNCT
ma-9	548	21	gapore	gapore	NOUN
ma-9	548	22	,	,	PUNCT
ma-9	548	23	1989	1989	NUM
ma-9	548	24	.	.	PUNCT
ma-9	549	1	https://doi.org/10.1080/00036810701354995	https://doi.org/10.1080/00036810701354995	PROPN
ma-9	550	1	https://doi.org/10.1080/00036810701354995	https://doi.org/10.1080/00036810701354995	PROPN
ma-9	550	2	https://doi.org/10.22034/cmde.2020.32591.1512	https://doi.org/10.22034/cmde.2020.32591.1512	PROPN
ma-9	550	3	https://doi.org/10.22034/cmde.2020.32591.1512	https://doi.org/10.22034/cmde.2020.32591.1512	PROPN
ma-9	550	4	https://doi.org/10.1080/17442508.2020.1783264	https://doi.org/10.1080/17442508.2020.1783264	NOUN
ma-9	550	5	https://doi.org/10.1016/j.na.2010.07.007	https://doi.org/10.1016/j.na.2010.07.007	ADJ
ma-9	550	6	https://doi.org/10.1080/00207179.2015.1006683	https://doi.org/10.1080/00207179.2015.1006683	PROPN
ma-9	551	1	https://doi.org/10.1155/2011/584510	https://doi.org/10.1155/2011/584510	ADJ
ma-9	551	2	https://doi.org/10.1016/j.amc.2016.04.021	https://doi.org/10.1016/j.amc.2016.04.021	PROPN
ma-9	551	3	https://doi.org/10.1016/j.amc.2016.04.021	https://doi.org/10.1016/j.amc.2016.04.021	PROPN
ma-9	551	4	eur	eur	PROPN
ma-9	551	5	.	.	PUNCT
ma-9	552	1	j.	j.	PROPN
ma-9	552	2	math	math	PROPN
ma-9	552	3	.	.	PUNCT
ma-9	553	1	anal	anal	ADJ
ma-9	553	2	.	.	PUNCT
ma-9	554	1	1	1	NUM
ma-9	554	2	(	(	PUNCT
ma-9	554	3	2021	2021	NUM
ma-9	554	4	)	)	PUNCT
ma-9	554	5	18	18	NUM
ma-9	555	1	[	[	SYM
ma-9	555	2	10	10	NUM
ma-9	555	3	]	]	PUNCT
ma-9	555	4	s.	s.	PROPN
ma-9	555	5	li	li	PROPN
ma-9	555	6	,	,	PUNCT
ma-9	555	7	l.	l.	PROPN
ma-9	555	8	shu	shu	PROPN
ma-9	555	9	,	,	PUNCT
ma-9	555	10	x.-b	x.-b	PROPN
ma-9	555	11	.	.	PUNCT
ma-9	555	12	shu	shu	PROPN
ma-9	555	13	,	,	PUNCT
ma-9	555	14	f.	f.	PROPN
ma-9	555	15	xu	xu	PROPN
ma-9	555	16	,	,	PUNCT
ma-9	555	17	existence	existence	NOUN
ma-9	555	18	and	and	CCONJ
ma-9	555	19	hyers	hyers	PROPN
ma-9	555	20	-	-	PUNCT
ma-9	555	21	ulam	ulam	PROPN
ma-9	555	22	stability	stability	NOUN
ma-9	555	23	of	of	ADP
ma-9	555	24	random	random	ADJ
ma-9	555	25	impulsive	impulsive	ADJ
ma-9	555	26	stochastic	stochastic	ADJ
ma-9	555	27	functionaldifferential	functionaldifferential	ADJ
ma-9	555	28	equations	equation	NOUN
ma-9	555	29	with	with	ADP
ma-9	555	30	finite	finite	ADJ
ma-9	555	31	delays	delay	NOUN
ma-9	555	32	,	,	PUNCT
ma-9	555	33	stochastics	stochastic	NOUN
ma-9	555	34	.	.	PUNCT
ma-9	556	1	91	91	NUM
ma-9	556	2	(	(	PUNCT
ma-9	556	3	2019	2019	NUM
ma-9	556	4	)	)	PUNCT
ma-9	557	1	857–872	857–872	NUM
ma-9	557	2	.	.	PUNCT
ma-9	558	1	https://doi.org/10.1080/17442508	https://doi.org/10.1080/17442508	X
ma-9	558	2	.	.	PUNCT
ma-9	559	1	2018.1551400.[11	2018.1551400.[11	NOUN
ma-9	559	2	]	]	X
ma-9	559	3	c.	c.	PROPN
ma-9	559	4	loganathan	loganathan	PROPN
ma-9	559	5	,	,	PUNCT
ma-9	559	6	s.	s.	PROPN
ma-9	559	7	vijay	vijay	PROPN
ma-9	559	8	,	,	PUNCT
ma-9	559	9	approximate	approximate	ADJ
ma-9	559	10	controllability	controllability	NOUN
ma-9	559	11	of	of	ADP
ma-9	559	12	random	random	ADJ
ma-9	559	13	impulsive	impulsive	ADJ
ma-9	559	14	integro	integro	ADJ
ma-9	559	15	semilinear	semilinear	PROPN
ma-9	559	16	differential	differential	PROPN
ma-9	559	17	systems	system	NOUN
ma-9	559	18	,	,	PUNCT
ma-9	559	19	progress	progress	VERB
ma-9	559	20	nonlinear	nonlinear	ADJ
ma-9	559	21	dyn	dyn	PROPN
ma-9	559	22	.	.	PUNCT
ma-9	560	1	chaos	chaos	NOUN
ma-9	560	2	.	.	PUNCT
ma-9	561	1	5	5	NUM
ma-9	561	2	(	(	PUNCT
ma-9	561	3	2017	2017	NUM
ma-9	561	4	)	)	PUNCT
ma-9	561	5	,	,	PUNCT
ma-9	561	6	25	25	NUM
ma-9	561	7	-	-	SYM
ma-9	561	8	32.[12	32.[12	PROPN
ma-9	561	9	]	]	X
ma-9	561	10	x.	x.	NOUN
ma-9	561	11	mao	mao	PROPN
ma-9	561	12	,	,	PUNCT
ma-9	561	13	stochastic	stochastic	ADJ
ma-9	561	14	differential	differential	ADJ
ma-9	561	15	equations	equation	NOUN
ma-9	561	16	and	and	CCONJ
ma-9	561	17	applications	application	NOUN
ma-9	561	18	,	,	PUNCT
ma-9	561	19	m.	m.	NOUN
ma-9	561	20	horwood	horwood	PROPN
ma-9	561	21	,	,	PUNCT
ma-9	561	22	chichester	chichester	PROPN
ma-9	561	23	,	,	PUNCT
ma-9	561	24	1997.[13	1997.[13	PROPN
ma-9	561	25	]	]	X
ma-9	561	26	p.	p.	NOUN
ma-9	561	27	niu	niu	PROPN
ma-9	561	28	,	,	PUNCT
ma-9	561	29	x.	x.	PROPN
ma-9	561	30	shu	shu	PROPN
ma-9	561	31	,	,	PUNCT
ma-9	561	32	y.	y.	PROPN
ma-9	561	33	li	li	PROPN
ma-9	561	34	,	,	PUNCT
ma-9	561	35	the	the	DET
ma-9	561	36	existence	existence	NOUN
ma-9	561	37	and	and	CCONJ
ma-9	561	38	hyers	hyer	VERB
ma-9	561	39	ulam	ulam	PROPN
ma-9	561	40	stability	stability	NOUN
ma-9	561	41	for	for	ADP
ma-9	561	42	second	second	ADJ
ma-9	561	43	order	order	NOUN
ma-9	561	44	random	random	ADJ
ma-9	561	45	impulsive	impulsive	ADJ
ma-9	561	46	differential	differential	ADJ
ma-9	561	47	equations	equation	NOUN
ma-9	561	48	,	,	PUNCT
ma-9	561	49	dyn	dyn	NOUN
ma-9	561	50	.	.	PUNCT
ma-9	562	1	syst	syst	PROPN
ma-9	562	2	.	.	PUNCT
ma-9	563	1	appl	appl	PROPN
ma-9	563	2	.	.	PROPN
ma-9	564	1	28	28	NUM
ma-9	564	2	(	(	PUNCT
ma-9	564	3	2019	2019	NUM
ma-9	564	4	)	)	PUNCT
ma-9	565	1	,	,	PUNCT
ma-9	565	2	673	673	NUM
ma-9	565	3	-	-	SYM
ma-9	565	4	690.[14	690.[14	NUM
ma-9	565	5	]	]	X
ma-9	565	6	b.	b.	PROPN
ma-9	565	7	oksendal	oksendal	PROPN
ma-9	565	8	,	,	PUNCT
ma-9	565	9	stochastic	stochastic	ADJ
ma-9	565	10	differential	differential	ADJ
ma-9	565	11	equations	equation	NOUN
ma-9	565	12	:	:	PUNCT
ma-9	565	13	an	an	DET
ma-9	565	14	introduction	introduction	NOUN
ma-9	565	15	with	with	ADP
ma-9	565	16	applications	application	NOUN
ma-9	565	17	,	,	PUNCT
ma-9	565	18	springer	springer	NOUN
ma-9	565	19	science	science	NOUN
ma-9	565	20	and	and	CCONJ
ma-9	565	21	businessmedia	businessmedia	NOUN
ma-9	565	22	,	,	PUNCT
ma-9	565	23	2013.[15	2013.[15	NUM
ma-9	565	24	]	]	X
ma-9	565	25	l.	l.	PROPN
ma-9	565	26	shu	shu	PROPN
ma-9	565	27	,	,	PUNCT
ma-9	565	28	x.-b	x.-b	PROPN
ma-9	565	29	.	.	PUNCT
ma-9	566	1	shu	shu	PROPN
ma-9	566	2	,	,	PUNCT
ma-9	566	3	q.	q.	PROPN
ma-9	566	4	zhu	zhu	PROPN
ma-9	566	5	,	,	PUNCT
ma-9	566	6	f.	f.	PROPN
ma-9	566	7	xu	xu	PROPN
ma-9	566	8	,	,	PUNCT
ma-9	566	9	existence	existence	NOUN
ma-9	566	10	and	and	CCONJ
ma-9	566	11	exponential	exponential	ADJ
ma-9	566	12	stability	stability	NOUN
ma-9	566	13	of	of	ADP
ma-9	566	14	mild	mild	ADJ
ma-9	566	15	solutions	solution	NOUN
ma-9	566	16	for	for	ADP
ma-9	566	17	second	second	ADJ
ma-9	566	18	-	-	PUNCT
ma-9	566	19	order	order	NOUN
ma-9	566	20	neutralstochastic	neutralstochastic	ADJ
ma-9	566	21	functional	functional	ADJ
ma-9	566	22	differential	differential	NOUN
ma-9	566	23	equation	equation	NOUN
ma-9	566	24	with	with	ADP
ma-9	566	25	random	random	ADJ
ma-9	566	26	impulses	impulse	NOUN
ma-9	566	27	,	,	PUNCT
ma-9	566	28	j.	j.	PROPN
ma-9	566	29	appl	appl	PROPN
ma-9	566	30	.	.	PROPN
ma-9	567	1	anal	anal	PROPN
ma-9	567	2	.	.	PUNCT
ma-9	568	1	comput	comput	NOUN
ma-9	568	2	.	.	PUNCT
ma-9	569	1	11	11	NUM
ma-9	569	2	(	(	PUNCT
ma-9	569	3	2021	2021	NUM
ma-9	569	4	)	)	PUNCT
ma-9	570	1	59–80	59–80	NUM
ma-9	570	2	.	.	PUNCT
ma-9	570	3	https	https	NOUN
ma-9	570	4	:	:	PUNCT
ma-9	570	5	//doi.org/10.11948/20190089.[16	//doi.org/10.11948/20190089.[16	PUNCT
ma-9	570	6	]	]	PUNCT
ma-9	571	1	x.-b	x.-b	PROPN
ma-9	571	2	.	.	PUNCT
ma-9	572	1	shu	shu	PROPN
ma-9	572	2	,	,	PUNCT
ma-9	572	3	y.	y.	PROPN
ma-9	572	4	lai	lai	PROPN
ma-9	572	5	,	,	PUNCT
ma-9	572	6	y.	y.	PROPN
ma-9	572	7	chen	chen	PROPN
ma-9	572	8	,	,	PUNCT
ma-9	572	9	the	the	DET
ma-9	572	10	existence	existence	NOUN
ma-9	572	11	of	of	ADP
ma-9	572	12	mild	mild	ADJ
ma-9	572	13	solutions	solution	NOUN
ma-9	572	14	for	for	ADP
ma-9	572	15	impulsive	impulsive	ADJ
ma-9	572	16	fractional	fractional	ADJ
ma-9	572	17	partial	partial	ADJ
ma-9	572	18	differential	differential	NOUN
ma-9	572	19	equations	equation	NOUN
ma-9	572	20	,	,	PUNCT
ma-9	572	21	nonlinear	nonlinear	ADJ
ma-9	572	22	anal	anal	NOUN
ma-9	572	23	.	.	PUNCT
ma-9	572	24	:	:	PUNCT
ma-9	573	1	theory	theory	NOUN
ma-9	573	2	methods	method	NOUN
ma-9	573	3	appl	appl	PROPN
ma-9	573	4	.	.	PUNCT
ma-9	574	1	74	74	NUM
ma-9	574	2	(	(	PUNCT
ma-9	574	3	2011	2011	NUM
ma-9	574	4	)	)	PUNCT
ma-9	574	5	2003–2011	2003–2011	NUM
ma-9	574	6	.	.	PUNCT
ma-9	575	1	https://doi.org/10.1016/j.na.2010.11.007.[17	https://doi.org/10.1016/j.na.2010.11.007.[17	PROPN
ma-9	575	2	]	]	PUNCT
ma-9	575	3	c.	c.	PROPN
ma-9	575	4	travis	travis	PROPN
ma-9	575	5	,	,	PUNCT
ma-9	575	6	g.	g.	PROPN
ma-9	575	7	webb	webb	PROPN
ma-9	575	8	,	,	PUNCT
ma-9	575	9	compactness	compactness	NOUN
ma-9	575	10	,	,	PUNCT
ma-9	575	11	regularity	regularity	NOUN
ma-9	575	12	and	and	CCONJ
ma-9	575	13	uniform	uniform	ADJ
ma-9	575	14	continuity	continuity	NOUN
ma-9	575	15	properties	property	NOUN
ma-9	575	16	of	of	ADP
ma-9	575	17	strongly	strongly	ADV
ma-9	575	18	continuous	continuous	ADJ
ma-9	575	19	cosine	cosine	NOUN
ma-9	575	20	families	family	NOUN
ma-9	575	21	,	,	PUNCT
ma-9	575	22	houst	houst	NOUN
ma-9	575	23	.	.	PUNCT
ma-9	576	1	j.	j.	PROPN
ma-9	576	2	math	math	PROPN
ma-9	576	3	.	.	PUNCT
ma-9	577	1	3	3	NUM
ma-9	577	2	(	(	PUNCT
ma-9	577	3	1977	1977	NUM
ma-9	577	4	)	)	PUNCT
ma-9	577	5	,	,	PUNCT
ma-9	577	6	555	555	NUM
ma-9	577	7	-	-	SYM
ma-9	577	8	567.[18	567.[18	NUM
ma-9	577	9	]	]	PUNCT
ma-9	577	10	c.	c.	PROPN
ma-9	577	11	travis	travis	PROPN
ma-9	577	12	,	,	PUNCT
ma-9	577	13	g.	g.	PROPN
ma-9	577	14	webb	webb	PROPN
ma-9	577	15	,	,	PUNCT
ma-9	577	16	cosine	cosine	NOUN
ma-9	577	17	families	family	NOUN
ma-9	577	18	and	and	CCONJ
ma-9	577	19	abstract	abstract	ADJ
ma-9	577	20	nonlinear	nonlinear	ADJ
ma-9	577	21	second	second	ADJ
ma-9	577	22	order	order	NOUN
ma-9	577	23	differential	differential	NOUN
ma-9	577	24	equations	equation	NOUN
ma-9	577	25	,	,	PUNCT
ma-9	577	26	acta	acta	PROPN
ma-9	577	27	.	.	PUNCT
ma-9	577	28	math	math	NOUN
ma-9	577	29	.	.	PUNCT
ma-9	578	1	hung.32	hung.32	PROPN
ma-9	578	2	(	(	PUNCT
ma-9	578	3	1978	1978	NUM
ma-9	578	4	)	)	PUNCT
ma-9	578	5	,	,	PUNCT
ma-9	578	6	75	75	NUM
ma-9	578	7	-	-	SYM
ma-9	578	8	96.[19	96.[19	NUM
ma-9	578	9	]	]	X
ma-9	578	10	v.	v.	PROPN
ma-9	578	11	vijayakumar	vijayakumar	PROPN
ma-9	578	12	,	,	PUNCT
ma-9	578	13	r.	r.	PROPN
ma-9	578	14	murugesu	murugesu	PROPN
ma-9	578	15	,	,	PUNCT
ma-9	578	16	r.	r.	PROPN
ma-9	578	17	poongodi	poongodi	PROPN
ma-9	578	18	,	,	PUNCT
ma-9	578	19	s.	s.	PROPN
ma-9	578	20	dhanalakshmi	dhanalakshmi	PROPN
ma-9	578	21	,	,	PUNCT
ma-9	578	22	controllability	controllability	NOUN
ma-9	578	23	of	of	ADP
ma-9	578	24	second	second	ADJ
ma-9	578	25	-	-	PUNCT
ma-9	578	26	order	order	NOUN
ma-9	578	27	impulsive	impulsive	ADJ
ma-9	578	28	nonlocalcauchy	nonlocalcauchy	ADJ
ma-9	578	29	problem	problem	NOUN
ma-9	578	30	via	via	ADP
ma-9	578	31	measure	measure	NOUN
ma-9	578	32	of	of	ADP
ma-9	578	33	noncompactness	noncompactness	ADJ
ma-9	578	34	,	,	PUNCT
ma-9	578	35	mediterr	mediterr	NOUN
ma-9	578	36	.	.	PUNCT
ma-9	579	1	j.	j.	PROPN
ma-9	579	2	math	math	PROPN
ma-9	579	3	.	.	PUNCT
ma-9	580	1	14	14	NUM
ma-9	580	2	(	(	PUNCT
ma-9	580	3	2017	2017	NUM
ma-9	580	4	)	)	PUNCT
ma-9	580	5	3	3	NUM
ma-9	580	6	.	.	PUNCT
ma-9	580	7	https://doi.org/10.1007/s00009-016-0813-6.[20	https://doi.org/10.1007/s00009-016-0813-6.[20	NOUN
ma-9	580	8	]	]	PUNCT
ma-9	580	9	a.	a.	PROPN
ma-9	580	10	vinodkumar	vinodkumar	PROPN
ma-9	580	11	,	,	PUNCT
ma-9	580	12	k.	k.	PROPN
ma-9	581	1	malar	malar	PROPN
ma-9	581	2	,	,	PUNCT
ma-9	581	3	m.	m.	NOUN
ma-9	581	4	gowrisankar	gowrisankar	PROPN
ma-9	581	5	,	,	PUNCT
ma-9	581	6	p.	p.	PROPN
ma-9	581	7	mohankumar	mohankumar	PROPN
ma-9	581	8	,	,	PUNCT
ma-9	581	9	existence	existence	NOUN
ma-9	581	10	,	,	PUNCT
ma-9	581	11	uniqueness	uniqueness	NOUN
ma-9	581	12	and	and	CCONJ
ma-9	581	13	stability	stability	NOUN
ma-9	581	14	of	of	ADP
ma-9	581	15	random	random	ADJ
ma-9	581	16	impulsivefractional	impulsivefractional	ADJ
ma-9	581	17	differential	differential	NOUN
ma-9	581	18	equations	equation	NOUN
ma-9	581	19	,	,	PUNCT
ma-9	581	20	filomat	filomat	NOUN
ma-9	581	21	,	,	PUNCT
ma-9	581	22	32	32	NUM
ma-9	581	23	(	(	PUNCT
ma-9	581	24	2018	2018	NUM
ma-9	581	25	)	)	PUNCT
ma-9	581	26	,	,	PUNCT
ma-9	581	27	439	439	NUM
ma-9	581	28	-	-	SYM
ma-9	581	29	455.[21	455.[21	NOUN
ma-9	581	30	]	]	PUNCT
ma-9	581	31	s.	s.	PROPN
ma-9	581	32	wu	wu	PROPN
ma-9	581	33	,	,	PUNCT
ma-9	581	34	x.	x.	PROPN
ma-9	581	35	guo	guo	PROPN
ma-9	581	36	,	,	PUNCT
ma-9	581	37	y.	y.	PROPN
ma-9	581	38	zhou	zhou	PROPN
ma-9	581	39	,	,	PUNCT
ma-9	581	40	p	p	NOUN
ma-9	581	41	-	-	PUNCT
ma-9	581	42	moment	moment	NOUN
ma-9	581	43	stability	stability	NOUN
ma-9	581	44	of	of	ADP
ma-9	581	45	functional	functional	ADJ
ma-9	581	46	differential	differential	ADJ
ma-9	581	47	equations	equation	NOUN
ma-9	581	48	with	with	ADP
ma-9	581	49	random	random	ADJ
ma-9	581	50	impulses	impulse	NOUN
ma-9	581	51	,	,	PUNCT
ma-9	581	52	computersmath	computersmath	NOUN
ma-9	581	53	.	.	PUNCT
ma-9	582	1	appl	appl	PROPN
ma-9	582	2	.	.	PUNCT
ma-9	583	1	52	52	NUM
ma-9	583	2	(	(	PUNCT
ma-9	583	3	2006	2006	NUM
ma-9	583	4	)	)	PUNCT
ma-9	583	5	1683–1694	1683–1694	NUM
ma-9	583	6	.	.	PUNCT
ma-9	584	1	https://doi.org/10.1016/j.camwa.2006.04.026.[22	https://doi.org/10.1016/j.camwa.2006.04.026.[22	ADJ
ma-9	584	2	]	]	X
ma-9	584	3	s.	s.	PROPN
ma-9	584	4	wu	wu	PROPN
ma-9	584	5	,	,	PUNCT
ma-9	584	6	x.	x.	PROPN
ma-9	584	7	meng	meng	PROPN
ma-9	584	8	,	,	PUNCT
ma-9	584	9	boundedness	boundedness	NOUN
ma-9	584	10	of	of	ADP
ma-9	584	11	nonlinear	nonlinear	ADJ
ma-9	584	12	differential	differential	NOUN
ma-9	584	13	systems	system	NOUN
ma-9	584	14	with	with	ADP
ma-9	584	15	impulsive	impulsive	ADJ
ma-9	584	16	effect	effect	NOUN
ma-9	584	17	on	on	ADP
ma-9	584	18	random	random	ADJ
ma-9	584	19	moments	moment	NOUN
ma-9	584	20	,	,	PUNCT
ma-9	584	21	actamath	actamath	NOUN
ma-9	584	22	.	.	PUNCT
ma-9	585	1	appl	appl	PROPN
ma-9	585	2	.	.	PROPN
ma-9	586	1	sinica	sinica	PROPN
ma-9	586	2	,	,	PUNCT
ma-9	586	3	en	en	PROPN
ma-9	586	4	.	.	PUNCT
ma-9	586	5	ser	ser	PROPN
ma-9	586	6	.	.	PROPN
ma-9	586	7	20	20	NUM
ma-9	586	8	(	(	PUNCT
ma-9	586	9	2004	2004	NUM
ma-9	586	10	)	)	PUNCT
ma-9	586	11	147–154	147–154	NUM
ma-9	586	12	.	.	PUNCT
ma-9	586	13	https://doi.org/10.1007/s10255-004-0157-z.[23	https://doi.org/10.1007/s10255-004-0157-z.[23	PUNCT
ma-9	586	14	]	]	PUNCT
ma-9	586	15	x.	x.	PROPN
ma-9	586	16	yang	yang	PROPN
ma-9	586	17	,	,	PUNCT
ma-9	586	18	x.	x.	PROPN
ma-9	586	19	li	li	PROPN
ma-9	586	20	,	,	PUNCT
ma-9	586	21	q.	q.	PROPN
ma-9	586	22	xi	xi	PROPN
ma-9	586	23	,	,	PUNCT
ma-9	586	24	p.	p.	PROPN
ma-9	586	25	duan	duan	PROPN
ma-9	586	26	,	,	PUNCT
ma-9	586	27	review	review	NOUN
ma-9	586	28	of	of	ADP
ma-9	586	29	stability	stability	NOUN
ma-9	586	30	and	and	CCONJ
ma-9	586	31	stabilization	stabilization	NOUN
ma-9	586	32	for	for	ADP
ma-9	586	33	impulsive	impulsive	ADJ
ma-9	586	34	delayed	delay	VERB
ma-9	586	35	systems	system	NOUN
ma-9	586	36	,	,	PUNCT
ma-9	586	37	math	math	NOUN
ma-9	586	38	.	.	PUNCT
ma-9	587	1	biosci.eng	biosci.eng	X
ma-9	587	2	.	.	PROPN
ma-9	587	3	15	15	NUM
ma-9	587	4	(	(	PUNCT
ma-9	587	5	2018	2018	NUM
ma-9	587	6	)	)	PUNCT
ma-9	587	7	1495–1515	1495–1515	NOUN
ma-9	587	8	.	.	PUNCT
ma-9	587	9	https://doi.org/10.3934/mbe.2018069.[24	https://doi.org/10.3934/mbe.2018069.[24	PROPN
ma-9	587	10	]	]	PUNCT
ma-9	587	11	x.	x.	PROPN
ma-9	587	12	yang	yang	PROPN
ma-9	587	13	,	,	PUNCT
ma-9	587	14	q.	q.	PROPN
ma-9	587	15	zhu	zhu	PROPN
ma-9	587	16	,	,	PUNCT
ma-9	587	17	pth	pth	NOUN
ma-9	587	18	moment	moment	NOUN
ma-9	587	19	exponential	exponential	ADJ
ma-9	587	20	stability	stability	NOUN
ma-9	587	21	of	of	ADP
ma-9	587	22	stochastic	stochastic	ADJ
ma-9	587	23	partial	partial	ADJ
ma-9	587	24	differential	differential	ADJ
ma-9	587	25	equations	equation	NOUN
ma-9	587	26	with	with	ADP
ma-9	587	27	poisson	poisson	PROPN
ma-9	587	28	jumps	jump	VERB
ma-9	587	29	,	,	PUNCT
ma-9	587	30	asian	asian	PROPN
ma-9	587	31	j.	j.	PROPN
ma-9	587	32	control	control	PROPN
ma-9	587	33	.	.	PUNCT
ma-9	588	1	16	16	NUM
ma-9	588	2	(	(	PUNCT
ma-9	588	3	2014	2014	NUM
ma-9	588	4	)	)	PUNCT
ma-9	588	5	1482–1491	1482–1491	NUM
ma-9	588	6	.	.	PUNCT
ma-9	589	1	https://doi.org/10.1002/asjc.918.[25	https://doi.org/10.1002/asjc.918.[25	PROPN
ma-9	589	2	]	]	PUNCT
ma-9	590	1	s.	s.	PROPN
ma-9	590	2	zhang	zhang	PROPN
ma-9	590	3	,	,	PUNCT
ma-9	590	4	w.	w.	PROPN
ma-9	590	5	jiang	jiang	PROPN
ma-9	590	6	,	,	PUNCT
ma-9	590	7	the	the	DET
ma-9	590	8	existence	existence	NOUN
ma-9	590	9	and	and	CCONJ
ma-9	590	10	exponential	exponential	ADJ
ma-9	590	11	stability	stability	NOUN
ma-9	590	12	of	of	ADP
ma-9	590	13	random	random	ADJ
ma-9	590	14	impulsive	impulsive	ADJ
ma-9	590	15	fractional	fractional	ADJ
ma-9	590	16	differential	differential	NOUN
ma-9	590	17	equations	equation	NOUN
ma-9	590	18	,	,	PUNCT
ma-9	590	19	adv	adv	PROPN
ma-9	590	20	.	.	PUNCT
ma-9	590	21	differ	differ	VERB
ma-9	590	22	.	.	PUNCT
ma-9	591	1	equ	equ	PROPN
ma-9	591	2	.	.	PROPN
ma-9	591	3	2018	2018	NUM
ma-9	591	4	(	(	PUNCT
ma-9	591	5	2018	2018	NUM
ma-9	591	6	)	)	PUNCT
ma-9	591	7	404	404	NUM
ma-9	591	8	.	.	PUNCT
ma-9	592	1	https://doi.org/10.1186/s13662-018-1779-4.[26	https://doi.org/10.1186/s13662-018-1779-4.[26	ADP
ma-9	592	2	]	]	X
ma-9	592	3	y.	y.	PROPN
ma-9	592	4	zhou	zhou	PROPN
ma-9	592	5	,	,	PUNCT
ma-9	592	6	s.	s.	PROPN
ma-9	592	7	wu	wu	PROPN
ma-9	592	8	,	,	PUNCT
ma-9	592	9	existence	existence	NOUN
ma-9	592	10	and	and	CCONJ
ma-9	592	11	uniqueness	uniqueness	NOUN
ma-9	592	12	of	of	ADP
ma-9	592	13	solutions	solution	NOUN
ma-9	592	14	to	to	ADP
ma-9	592	15	stochastic	stochastic	ADJ
ma-9	592	16	differential	differential	ADJ
ma-9	592	17	equations	equation	NOUN
ma-9	592	18	with	with	ADP
ma-9	592	19	random	random	ADJ
ma-9	592	20	impulsesunder	impulsesunder	ADJ
ma-9	592	21	lipschitz	lipschitz	NOUN
ma-9	592	22	conditions	condition	NOUN
ma-9	592	23	,	,	PUNCT
ma-9	592	24	chinese	chinese	PROPN
ma-9	592	25	.	.	PUNCT
ma-9	593	1	j.	j.	PROPN
ma-9	593	2	appl	appl	PROPN
ma-9	593	3	.	.	PUNCT
ma-9	594	1	probab	probab	PROPN
ma-9	594	2	.	.	PUNCT
ma-9	595	1	statist	statist	PROPN
ma-9	595	2	.	.	PUNCT
ma-9	596	1	26	26	NUM
ma-9	596	2	(	(	PUNCT
ma-9	596	3	2010	2010	NUM
ma-9	596	4	)	)	PUNCT
ma-9	596	5	,	,	PUNCT
ma-9	596	6	347	347	NUM
ma-9	596	7	-	-	SYM
ma-9	596	8	356.[27	356.[27	NUM
ma-9	596	9	]	]	X
ma-9	596	10	d.	d.	PROPN
ma-9	596	11	applebaum	applebaum	PROPN
ma-9	596	12	,	,	PUNCT
ma-9	596	13	levy	levy	NOUN
ma-9	596	14	process	process	NOUN
ma-9	596	15	and	and	CCONJ
ma-9	596	16	stochastic	stochastic	ADJ
ma-9	596	17	calculus	calculus	NOUN
ma-9	596	18	,	,	PUNCT
ma-9	596	19	cambridge	cambridge	PROPN
ma-9	596	20	university	university	PROPN
ma-9	596	21	press	press	PROPN
ma-9	596	22	,	,	PUNCT
ma-9	596	23	cambridge	cambridge	PROPN
ma-9	596	24	,	,	PUNCT
ma-9	596	25	2009.[28	2009.[28	NUM
ma-9	596	26	]	]	PUNCT
ma-9	596	27	t.	t.	PROPN
ma-9	596	28	wang	wang	PROPN
ma-9	596	29	,	,	PUNCT
ma-9	596	30	s	s	PROPN
ma-9	596	31	wu	wu	PROPN
ma-9	596	32	,	,	PUNCT
ma-9	596	33	random	random	ADJ
ma-9	596	34	impulsive	impulsive	ADJ
ma-9	596	35	model	model	NOUN
ma-9	596	36	for	for	ADP
ma-9	596	37	stock	stock	NOUN
ma-9	596	38	prices	price	NOUN
ma-9	596	39	and	and	CCONJ
ma-9	596	40	its	its	PRON
ma-9	596	41	application	application	NOUN
ma-9	596	42	for	for	ADP
ma-9	596	43	insurers	insurer	NOUN
ma-9	596	44	,	,	PUNCT
ma-9	596	45	master	master	NOUN
ma-9	596	46	thesis	thesis	NOUN
ma-9	596	47	(	(	PUNCT
ma-9	596	48	in	in	ADP
ma-9	596	49	chinese),shanghai	chinese),shanghai	ADJ
ma-9	596	50	,	,	PUNCT
ma-9	596	51	east	east	PROPN
ma-9	596	52	china	china	PROPN
ma-9	596	53	normal	normal	ADJ
ma-9	596	54	university	university	NOUN
ma-9	596	55	,	,	PUNCT
ma-9	596	56	2008	2008	NUM
ma-9	596	57	.	.	PUNCT
ma-9	597	1	https://doi.org/10.1080/17442508.2018.1551400	https://doi.org/10.1080/17442508.2018.1551400	NOUN
ma-9	597	2	https://doi.org/10.1080/17442508.2018.1551400	https://doi.org/10.1080/17442508.2018.1551400	PROPN
ma-9	597	3	https://doi.org/10.11948/20190089	https://doi.org/10.11948/20190089	NOUN
ma-9	597	4	https://doi.org/10.11948/20190089	https://doi.org/10.11948/20190089	PUNCT
ma-9	598	1	https://doi.org/10.1016/j.na.2010.11.007	https://doi.org/10.1016/j.na.2010.11.007	PROPN
ma-9	598	2	https://doi.org/10.1016/j.camwa.2006.04.026	https://doi.org/10.1016/j.camwa.2006.04.026	PROPN
ma-9	598	3	https://doi.org/10.1007/s10255-004-0157-z	https://doi.org/10.1007/s10255-004-0157-z	PROPN
ma-9	598	4	https://doi.org/10.3934/mbe.2018069	https://doi.org/10.3934/mbe.2018069	PROPN
ma-9	598	5	https://doi.org/10.1002/asjc.918	https://doi.org/10.1002/asjc.918	NOUN
ma-9	598	6	https://doi.org/10.1186/s13662-018-1779-4	https://doi.org/10.1186/s13662-018-1779-4	NUM
ma-9	598	7	1	1	NUM
ma-9	598	8	.	.	PUNCT
ma-9	599	1	introduction	introduction	NOUN
ma-9	599	2	2	2	NUM
ma-9	599	3	.	.	PUNCT
ma-9	599	4	preliminaries	preliminary	NOUN
ma-9	599	5	3	3	NUM
ma-9	599	6	.	.	PUNCT
ma-9	600	1	existence	existence	NOUN
ma-9	600	2	results	result	NOUN
ma-9	600	3	of	of	ADP
ma-9	600	4	mild	mild	ADJ
ma-9	600	5	solution	solution	NOUN
ma-9	600	6	4	4	NUM
ma-9	600	7	.	.	PUNCT
ma-9	601	1	stability	stability	NOUN
ma-9	601	2	5	5	NUM
ma-9	601	3	.	.	PUNCT
ma-9	601	4	illustration	illustration	NOUN
ma-9	601	5	6	6	NUM
ma-9	601	6	.	.	PUNCT
ma-9	602	1	conclusion	conclusion	NOUN
ma-9	602	2	references	reference	NOUN