id	sid	tid	token	lemma	pos
ijassa-1131	1	1	adv	adv	PROPN
ijassa-1131	1	2	syst	syst	PROPN
ijassa-1131	1	3	sci	sci	PROPN
ijassa-1131	1	4	appl	appl	PROPN
ijassa-1131	1	5	2021	2021	NUM
ijassa-1131	1	6	;	;	PUNCT
ijassa-1131	1	7	03:113–118	03:113–118	NUM
ijassa-1131	1	8	published	publish	VERB
ijassa-1131	1	9	online	online	ADV
ijassa-1131	1	10	at	at	ADP
ijassa-1131	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1131	1	12	.	.	PUNCT
ijassa-1131	2	1	on	on	ADP
ijassa-1131	2	2	solvability	solvability	NOUN
ijassa-1131	2	3	of	of	ADP
ijassa-1131	2	4	equations	equation	NOUN
ijassa-1131	2	5	defined	define	VERB
ijassa-1131	2	6	by	by	ADP
ijassa-1131	2	7	continuous	continuous	ADJ
ijassa-1131	2	8	and	and	CCONJ
ijassa-1131	2	9	smooth	smooth	ADJ
ijassa-1131	2	10	regular	regular	ADJ
ijassa-1131	2	11	mappings	mapping	NOUN
ijassa-1131	2	12	sergey	sergey	PROPN
ijassa-1131	2	13	e.	e.	PROPN
ijassa-1131	2	14	zhukovskiy1	zhukovskiy1	PROPN
ijassa-1131	2	15	*	*	PROPN
ijassa-1131	2	16	1v	1v	NUM
ijassa-1131	2	17	.	.	PUNCT
ijassa-1131	3	1	a.	a.	NOUN
ijassa-1131	3	2	trapeznikov	trapeznikov	PROPN
ijassa-1131	3	3	institute	institute	PROPN
ijassa-1131	3	4	of	of	ADP
ijassa-1131	3	5	control	control	PROPN
ijassa-1131	3	6	sciences	sciences	PROPN
ijassa-1131	3	7	of	of	ADP
ijassa-1131	3	8	ras	ras	PROPN
ijassa-1131	3	9	,	,	PUNCT
ijassa-1131	3	10	moscow	moscow	PROPN
ijassa-1131	3	11	,	,	PUNCT
ijassa-1131	3	12	russia	russia	PROPN
ijassa-1131	3	13	abstract	abstract	NOUN
ijassa-1131	3	14	:	:	PUNCT
ijassa-1131	3	15	we	we	PRON
ijassa-1131	3	16	consider	consider	VERB
ijassa-1131	3	17	equations	equation	NOUN
ijassa-1131	3	18	defined	define	VERB
ijassa-1131	3	19	by	by	ADP
ijassa-1131	3	20	continuous	continuous	ADJ
ijassa-1131	3	21	mappings	mapping	NOUN
ijassa-1131	3	22	acting	act	VERB
ijassa-1131	3	23	between	between	ADP
ijassa-1131	3	24	finitedimensional	finitedimensional	ADJ
ijassa-1131	3	25	real	real	ADJ
ijassa-1131	3	26	vector	vector	NOUN
ijassa-1131	3	27	spaces	space	NOUN
ijassa-1131	3	28	.	.	PUNCT
ijassa-1131	4	1	it	it	PRON
ijassa-1131	4	2	is	be	AUX
ijassa-1131	4	3	assumed	assume	VERB
ijassa-1131	4	4	that	that	SCONJ
ijassa-1131	4	5	the	the	DET
ijassa-1131	4	6	mappings	mapping	NOUN
ijassa-1131	4	7	are	be	AUX
ijassa-1131	4	8	differentiable	differentiable	ADJ
ijassa-1131	4	9	in	in	ADP
ijassa-1131	4	10	the	the	DET
ijassa-1131	4	11	first	first	ADJ
ijassa-1131	4	12	variable	variable	NOUN
ijassa-1131	4	13	.	.	PUNCT
ijassa-1131	5	1	a	a	DET
ijassa-1131	5	2	regularity	regularity	NOUN
ijassa-1131	5	3	condition	condition	NOUN
ijassa-1131	5	4	for	for	ADP
ijassa-1131	5	5	this	this	DET
ijassa-1131	5	6	type	type	NOUN
ijassa-1131	5	7	of	of	ADP
ijassa-1131	5	8	equations	equation	NOUN
ijassa-1131	5	9	is	be	AUX
ijassa-1131	5	10	obtained	obtain	VERB
ijassa-1131	5	11	.	.	PUNCT
ijassa-1131	6	1	it	it	PRON
ijassa-1131	6	2	is	be	AUX
ijassa-1131	6	3	shown	show	VERB
ijassa-1131	6	4	that	that	SCONJ
ijassa-1131	6	5	the	the	DET
ijassa-1131	6	6	regularity	regularity	NOUN
ijassa-1131	6	7	assumption	assumption	NOUN
ijassa-1131	6	8	implies	imply	VERB
ijassa-1131	6	9	the	the	DET
ijassa-1131	6	10	existence	existence	NOUN
ijassa-1131	6	11	of	of	ADP
ijassa-1131	6	12	solutions	solution	NOUN
ijassa-1131	6	13	to	to	ADP
ijassa-1131	6	14	the	the	DET
ijassa-1131	6	15	considered	consider	VERB
ijassa-1131	6	16	equations	equation	NOUN
ijassa-1131	6	17	.	.	PUNCT
ijassa-1131	7	1	systems	system	NOUN
ijassa-1131	7	2	of	of	ADP
ijassa-1131	7	3	two	two	NUM
ijassa-1131	7	4	equations	equation	NOUN
ijassa-1131	7	5	defined	define	VERB
ijassa-1131	7	6	by	by	ADP
ijassa-1131	7	7	continuous	continuous	ADJ
ijassa-1131	7	8	mappings	mapping	NOUN
ijassa-1131	7	9	acting	act	VERB
ijassa-1131	7	10	between	between	ADP
ijassa-1131	7	11	finite	finite	ADJ
ijassa-1131	7	12	-	-	ADJ
ijassa-1131	7	13	dimensional	dimensional	ADJ
ijassa-1131	7	14	real	real	ADJ
ijassa-1131	7	15	vector	vector	NOUN
ijassa-1131	7	16	spaces	space	NOUN
ijassa-1131	7	17	are	be	AUX
ijassa-1131	7	18	considered	consider	VERB
ijassa-1131	7	19	.	.	PUNCT
ijassa-1131	8	1	it	it	PRON
ijassa-1131	8	2	is	be	AUX
ijassa-1131	8	3	assumed	assume	VERB
ijassa-1131	8	4	that	that	SCONJ
ijassa-1131	8	5	the	the	DET
ijassa-1131	8	6	first	first	ADJ
ijassa-1131	8	7	mapping	mapping	NOUN
ijassa-1131	8	8	is	be	AUX
ijassa-1131	8	9	differentiable	differentiable	ADJ
ijassa-1131	8	10	in	in	ADP
ijassa-1131	8	11	the	the	DET
ijassa-1131	8	12	first	first	ADJ
ijassa-1131	8	13	variable	variable	NOUN
ijassa-1131	8	14	and	and	CCONJ
ijassa-1131	8	15	the	the	DET
ijassa-1131	8	16	second	second	ADJ
ijassa-1131	8	17	mapping	mapping	NOUN
ijassa-1131	8	18	is	be	AUX
ijassa-1131	8	19	differentiable	differentiable	ADJ
ijassa-1131	8	20	in	in	ADP
ijassa-1131	8	21	the	the	DET
ijassa-1131	8	22	second	second	ADJ
ijassa-1131	8	23	variable	variable	NOUN
ijassa-1131	8	24	.	.	PUNCT
ijassa-1131	9	1	a	a	DET
ijassa-1131	9	2	regularity	regularity	NOUN
ijassa-1131	9	3	condition	condition	NOUN
ijassa-1131	9	4	for	for	ADP
ijassa-1131	9	5	this	this	DET
ijassa-1131	9	6	type	type	NOUN
ijassa-1131	9	7	of	of	ADP
ijassa-1131	9	8	systems	system	NOUN
ijassa-1131	9	9	is	be	AUX
ijassa-1131	9	10	obtained	obtain	VERB
ijassa-1131	9	11	.	.	PUNCT
ijassa-1131	10	1	it	it	PRON
ijassa-1131	10	2	is	be	AUX
ijassa-1131	10	3	shown	show	VERB
ijassa-1131	10	4	that	that	SCONJ
ijassa-1131	10	5	the	the	DET
ijassa-1131	10	6	regularity	regularity	NOUN
ijassa-1131	10	7	assumption	assumption	NOUN
ijassa-1131	10	8	implies	imply	VERB
ijassa-1131	10	9	the	the	DET
ijassa-1131	10	10	existence	existence	NOUN
ijassa-1131	10	11	of	of	ADP
ijassa-1131	10	12	solutions	solution	NOUN
ijassa-1131	10	13	to	to	ADP
ijassa-1131	10	14	the	the	DET
ijassa-1131	10	15	considered	consider	VERB
ijassa-1131	10	16	system	system	NOUN
ijassa-1131	10	17	.	.	PUNCT
ijassa-1131	11	1	the	the	DET
ijassa-1131	11	2	proofs	proof	NOUN
ijassa-1131	11	3	of	of	ADP
ijassa-1131	11	4	the	the	DET
ijassa-1131	11	5	main	main	ADJ
ijassa-1131	11	6	results	result	NOUN
ijassa-1131	11	7	of	of	ADP
ijassa-1131	11	8	the	the	DET
ijassa-1131	11	9	paper	paper	NOUN
ijassa-1131	11	10	are	be	AUX
ijassa-1131	11	11	based	base	VERB
ijassa-1131	11	12	on	on	ADP
ijassa-1131	11	13	brouwer	brouwer	PROPN
ijassa-1131	11	14	’s	’s	PART
ijassa-1131	11	15	fixed	fix	VERB
ijassa-1131	11	16	point	point	NOUN
ijassa-1131	11	17	theorem	theorem	ADJ
ijassa-1131	11	18	and	and	CCONJ
ijassa-1131	11	19	global	global	ADJ
ijassa-1131	11	20	implicit	implicit	ADJ
ijassa-1131	11	21	function	function	NOUN
ijassa-1131	11	22	theorem	theorem	VERB
ijassa-1131	11	23	.	.	PUNCT
ijassa-1131	12	1	keywords	keyword	NOUN
ijassa-1131	12	2	:	:	PUNCT
ijassa-1131	12	3	nonlinear	nonlinear	ADJ
ijassa-1131	12	4	equations	equation	NOUN
ijassa-1131	12	5	,	,	PUNCT
ijassa-1131	12	6	regularity	regularity	NOUN
ijassa-1131	12	7	,	,	PUNCT
ijassa-1131	12	8	covering	covering	NOUN
ijassa-1131	12	9	,	,	PUNCT
ijassa-1131	12	10	fixed	fix	VERB
ijassa-1131	12	11	point	point	NOUN
ijassa-1131	12	12	1	1	NUM
ijassa-1131	12	13	.	.	PUNCT
ijassa-1131	13	1	introduction	introduction	NOUN
ijassa-1131	13	2	given	give	VERB
ijassa-1131	13	3	positive	positive	ADJ
ijassa-1131	13	4	integers	integer	NOUN
ijassa-1131	13	5	n	n	CCONJ
ijassa-1131	13	6	,	,	PUNCT
ijassa-1131	13	7	k	k	PROPN
ijassa-1131	13	8	and	and	CCONJ
ijassa-1131	13	9	a	a	DET
ijassa-1131	13	10	continuous	continuous	ADJ
ijassa-1131	13	11	mapping	mapping	NOUN
ijassa-1131	13	12	f	f	NOUN
ijassa-1131	13	13	:	:	PUNCT
ijassa-1131	13	14	rn	rn	PROPN
ijassa-1131	13	15	×	×	PROPN
ijassa-1131	13	16	rn	rn	PROPN
ijassa-1131	13	17	→	→	SYM
ijassa-1131	13	18	rk	rk	PROPN
ijassa-1131	13	19	,	,	PUNCT
ijassa-1131	13	20	consider	consider	VERB
ijassa-1131	13	21	the	the	DET
ijassa-1131	13	22	following	follow	VERB
ijassa-1131	13	23	equation	equation	NOUN
ijassa-1131	13	24	f(x	f(x	PROPN
ijassa-1131	13	25	,	,	PUNCT
ijassa-1131	13	26	x	x	NOUN
ijassa-1131	13	27	)	)	PUNCT
ijassa-1131	13	28	=	=	SYM
ijassa-1131	13	29	0	0	PUNCT
ijassa-1131	13	30	(	(	PUNCT
ijassa-1131	13	31	1.1	1.1	NUM
ijassa-1131	13	32	)	)	PUNCT
ijassa-1131	13	33	with	with	ADP
ijassa-1131	13	34	unknown	unknown	ADJ
ijassa-1131	13	35	x	x	PROPN
ijassa-1131	13	36	∈	∈	PROPN
ijassa-1131	13	37	rn	rn	PROPN
ijassa-1131	13	38	.	.	PUNCT
ijassa-1131	14	1	our	our	PRON
ijassa-1131	14	2	goal	goal	NOUN
ijassa-1131	14	3	is	be	AUX
ijassa-1131	14	4	to	to	PART
ijassa-1131	14	5	obtain	obtain	VERB
ijassa-1131	14	6	sufficient	sufficient	ADJ
ijassa-1131	14	7	conditions	condition	NOUN
ijassa-1131	14	8	for	for	ADP
ijassa-1131	14	9	the	the	DET
ijassa-1131	14	10	existence	existence	NOUN
ijassa-1131	14	11	of	of	ADP
ijassa-1131	14	12	a	a	DET
ijassa-1131	14	13	solution	solution	NOUN
ijassa-1131	14	14	to	to	ADP
ijassa-1131	14	15	this	this	DET
ijassa-1131	14	16	equations	equation	NOUN
ijassa-1131	14	17	.	.	PUNCT
ijassa-1131	15	1	one	one	NUM
ijassa-1131	15	2	of	of	ADP
ijassa-1131	15	3	the	the	DET
ijassa-1131	15	4	standard	standard	ADJ
ijassa-1131	15	5	approaches	approach	NOUN
ijassa-1131	15	6	to	to	ADP
ijassa-1131	15	7	this	this	DET
ijassa-1131	15	8	problem	problem	NOUN
ijassa-1131	15	9	is	be	AUX
ijassa-1131	15	10	based	base	VERB
ijassa-1131	15	11	on	on	ADP
ijassa-1131	15	12	the	the	DET
ijassa-1131	15	13	application	application	NOUN
ijassa-1131	15	14	of	of	ADP
ijassa-1131	15	15	the	the	DET
ijassa-1131	15	16	covering	covering	NOUN
ijassa-1131	15	17	mappings	mapping	NOUN
ijassa-1131	15	18	theory	theory	NOUN
ijassa-1131	15	19	(	(	PUNCT
ijassa-1131	15	20	see	see	VERB
ijassa-1131	15	21	,	,	PUNCT
ijassa-1131	15	22	for	for	ADP
ijassa-1131	15	23	example	example	NOUN
ijassa-1131	15	24	,	,	PUNCT
ijassa-1131	15	25	[	[	X
ijassa-1131	15	26	1	1	NUM
ijassa-1131	15	27	,	,	PUNCT
ijassa-1131	15	28	2	2	NUM
ijassa-1131	15	29	]	]	NUM
ijassa-1131	15	30	)	)	PUNCT
ijassa-1131	15	31	.	.	PUNCT
ijassa-1131	16	1	the	the	DET
ijassa-1131	16	2	corresponding	corresponding	ADJ
ijassa-1131	16	3	results	result	NOUN
ijassa-1131	16	4	guarantee	guarantee	VERB
ijassa-1131	16	5	that	that	SCONJ
ijassa-1131	16	6	if	if	SCONJ
ijassa-1131	16	7	f	f	PROPN
ijassa-1131	16	8	is	be	AUX
ijassa-1131	16	9	covering	cover	VERB
ijassa-1131	16	10	in	in	ADP
ijassa-1131	16	11	the	the	DET
ijassa-1131	16	12	first	first	ADJ
ijassa-1131	16	13	variable	variable	NOUN
ijassa-1131	16	14	and	and	CCONJ
ijassa-1131	16	15	is	be	AUX
ijassa-1131	16	16	lipschitz	lipschitz	VERB
ijassa-1131	16	17	continuous	continuous	ADJ
ijassa-1131	16	18	in	in	ADP
ijassa-1131	16	19	the	the	DET
ijassa-1131	16	20	second	second	ADJ
ijassa-1131	16	21	variable	variable	NOUN
ijassa-1131	16	22	with	with	ADP
ijassa-1131	16	23	a	a	DET
ijassa-1131	16	24	sufficiently	sufficiently	ADV
ijassa-1131	16	25	small	small	ADJ
ijassa-1131	16	26	lipschitz	lipschitz	NOUN
ijassa-1131	16	27	constant	constant	ADJ
ijassa-1131	16	28	,	,	PUNCT
ijassa-1131	16	29	then	then	ADV
ijassa-1131	16	30	there	there	PRON
ijassa-1131	16	31	exists	exist	VERB
ijassa-1131	16	32	a	a	DET
ijassa-1131	16	33	solution	solution	NOUN
ijassa-1131	16	34	to	to	ADP
ijassa-1131	16	35	equation	equation	NOUN
ijassa-1131	16	36	(	(	PUNCT
ijassa-1131	16	37	1.1	1.1	NUM
ijassa-1131	16	38	)	)	PUNCT
ijassa-1131	16	39	.	.	PUNCT
ijassa-1131	17	1	in	in	ADP
ijassa-1131	17	2	the	the	DET
ijassa-1131	17	3	most	most	ADV
ijassa-1131	17	4	general	general	ADJ
ijassa-1131	17	5	settings	setting	NOUN
ijassa-1131	17	6	,	,	PUNCT
ijassa-1131	17	7	these	these	DET
ijassa-1131	17	8	assertions	assertion	NOUN
ijassa-1131	17	9	provide	provide	VERB
ijassa-1131	17	10	sufficient	sufficient	ADJ
ijassa-1131	17	11	solvability	solvability	NOUN
ijassa-1131	17	12	conditions	condition	NOUN
ijassa-1131	17	13	for	for	ADP
ijassa-1131	17	14	analogous	analogous	ADJ
ijassa-1131	17	15	equations	equation	NOUN
ijassa-1131	17	16	defined	define	VERB
ijassa-1131	17	17	by	by	ADP
ijassa-1131	17	18	mappings	mapping	NOUN
ijassa-1131	17	19	acting	act	VERB
ijassa-1131	17	20	between	between	ADP
ijassa-1131	17	21	metric	metric	ADJ
ijassa-1131	17	22	spaces	space	NOUN
ijassa-1131	17	23	.	.	PUNCT
ijassa-1131	18	1	in	in	ADP
ijassa-1131	18	2	this	this	DET
ijassa-1131	18	3	paper	paper	NOUN
ijassa-1131	18	4	,	,	PUNCT
ijassa-1131	18	5	we	we	PRON
ijassa-1131	18	6	consider	consider	VERB
ijassa-1131	18	7	a	a	DET
ijassa-1131	18	8	specific	specific	ADJ
ijassa-1131	18	9	case	case	NOUN
ijassa-1131	18	10	of	of	ADP
ijassa-1131	18	11	finite	finite	ADJ
ijassa-1131	18	12	-	-	ADJ
ijassa-1131	18	13	dimensional	dimensional	ADJ
ijassa-1131	18	14	real	real	ADJ
ijassa-1131	18	15	linear	linear	NOUN
ijassa-1131	18	16	spaces	space	NOUN
ijassa-1131	18	17	and	and	CCONJ
ijassa-1131	18	18	differential	differential	ADJ
ijassa-1131	18	19	mappings	mapping	NOUN
ijassa-1131	18	20	.	.	PUNCT
ijassa-1131	19	1	we	we	PRON
ijassa-1131	19	2	show	show	VERB
ijassa-1131	19	3	that	that	SCONJ
ijassa-1131	19	4	in	in	ADP
ijassa-1131	19	5	this	this	DET
ijassa-1131	19	6	specific	specific	ADJ
ijassa-1131	19	7	case	case	NOUN
ijassa-1131	19	8	,	,	PUNCT
ijassa-1131	19	9	the	the	DET
ijassa-1131	19	10	assumption	assumption	NOUN
ijassa-1131	19	11	of	of	ADP
ijassa-1131	19	12	lipschitz	lipschitz	NOUN
ijassa-1131	19	13	continuity	continuity	NOUN
ijassa-1131	19	14	is	be	AUX
ijassa-1131	19	15	redundant	redundant	ADJ
ijassa-1131	19	16	.	.	PUNCT
ijassa-1131	20	1	the	the	DET
ijassa-1131	20	2	proof	proof	NOUN
ijassa-1131	20	3	of	of	ADP
ijassa-1131	20	4	our	our	PRON
ijassa-1131	20	5	main	main	ADJ
ijassa-1131	20	6	result	result	NOUN
ijassa-1131	20	7	is	be	AUX
ijassa-1131	20	8	based	base	VERB
ijassa-1131	20	9	on	on	ADP
ijassa-1131	20	10	two	two	NUM
ijassa-1131	20	11	assertions	assertion	NOUN
ijassa-1131	20	12	.	.	PUNCT
ijassa-1131	21	1	one	one	NUM
ijassa-1131	21	2	of	of	ADP
ijassa-1131	21	3	them	they	PRON
ijassa-1131	21	4	is	be	AUX
ijassa-1131	21	5	the	the	DET
ijassa-1131	21	6	well	well	ADV
ijassa-1131	21	7	-	-	PUNCT
ijassa-1131	21	8	known	know	VERB
ijassa-1131	21	9	brouwer	brouwer	NOUN
ijassa-1131	21	10	’s	’s	PART
ijassa-1131	21	11	fixed	fix	VERB
ijassa-1131	21	12	-	-	PUNCT
ijassa-1131	21	13	point	point	NOUN
ijassa-1131	21	14	theorem	theorem	NOUN
ijassa-1131	21	15	(	(	PUNCT
ijassa-1131	21	16	see	see	VERB
ijassa-1131	21	17	,	,	PUNCT
ijassa-1131	21	18	for	for	ADP
ijassa-1131	21	19	example	example	NOUN
ijassa-1131	21	20	,	,	PUNCT
ijassa-1131	21	21	chapter	chapter	NOUN
ijassa-1131	21	22	ii	ii	PROPN
ijassa-1131	21	23	,	,	PUNCT
ijassa-1131	21	24	§	§	VERB
ijassa-1131	21	25	5.7	5.7	NUM
ijassa-1131	21	26	in	in	ADP
ijassa-1131	21	27	[	[	X
ijassa-1131	21	28	3	3	NUM
ijassa-1131	21	29	]	]	NUM
ijassa-1131	21	30	)	)	PUNCT
ijassa-1131	21	31	.	.	PUNCT
ijassa-1131	22	1	the	the	DET
ijassa-1131	22	2	second	second	NOUN
ijassa-1131	22	3	is	be	AUX
ijassa-1131	22	4	a	a	DET
ijassa-1131	22	5	global	global	ADJ
ijassa-1131	22	6	implicit	implicit	ADJ
ijassa-1131	22	7	function	function	NOUN
ijassa-1131	22	8	theorem	theorem	NOUN
ijassa-1131	22	9	(	(	PUNCT
ijassa-1131	22	10	see	see	VERB
ijassa-1131	22	11	theorem	theorem	NOUN
ijassa-1131	22	12	2	2	NUM
ijassa-1131	22	13	in	in	ADP
ijassa-1131	22	14	[	[	X
ijassa-1131	22	15	4	4	NUM
ijassa-1131	22	16	]	]	NUM
ijassa-1131	22	17	)	)	PUNCT
ijassa-1131	22	18	.	.	PUNCT
ijassa-1131	23	1	in	in	ADP
ijassa-1131	23	2	the	the	DET
ijassa-1131	23	3	second	second	ADJ
ijassa-1131	23	4	section	section	NOUN
ijassa-1131	23	5	of	of	ADP
ijassa-1131	23	6	this	this	DET
ijassa-1131	23	7	paper	paper	NOUN
ijassa-1131	23	8	,	,	PUNCT
ijassa-1131	23	9	we	we	PRON
ijassa-1131	23	10	recall	recall	VERB
ijassa-1131	23	11	this	this	DET
ijassa-1131	23	12	implicit	implicit	ADJ
ijassa-1131	23	13	function	function	NOUN
ijassa-1131	23	14	theorem	theorem	VERB
ijassa-1131	23	15	as	as	ADV
ijassa-1131	23	16	well	well	ADV
ijassa-1131	23	17	as	as	ADP
ijassa-1131	23	18	the	the	DET
ijassa-1131	23	19	related	relate	VERB
ijassa-1131	23	20	concepts	concept	NOUN
ijassa-1131	23	21	and	and	CCONJ
ijassa-1131	23	22	assertions	assertion	NOUN
ijassa-1131	23	23	.	.	PUNCT
ijassa-1131	24	1	in	in	ADP
ijassa-1131	24	2	the	the	DET
ijassa-1131	24	3	third	third	ADJ
ijassa-1131	24	4	section	section	NOUN
ijassa-1131	24	5	,	,	PUNCT
ijassa-1131	24	6	we	we	PRON
ijassa-1131	24	7	present	present	VERB
ijassa-1131	24	8	solvability	solvability	NOUN
ijassa-1131	24	9	conditions	condition	NOUN
ijassa-1131	24	10	for	for	ADP
ijassa-1131	24	11	equation	equation	NOUN
ijassa-1131	24	12	(	(	PUNCT
ijassa-1131	24	13	1.1	1.1	NUM
ijassa-1131	24	14	)	)	PUNCT
ijassa-1131	24	15	and	and	CCONJ
ijassa-1131	24	16	provide	provide	VERB
ijassa-1131	24	17	a	a	DET
ijassa-1131	24	18	proof	proof	NOUN
ijassa-1131	24	19	of	of	ADP
ijassa-1131	24	20	this	this	DET
ijassa-1131	24	21	result	result	NOUN
ijassa-1131	24	22	.	.	PUNCT
ijassa-1131	25	1	the	the	DET
ijassa-1131	25	2	last	last	ADJ
ijassa-1131	25	3	section	section	NOUN
ijassa-1131	25	4	is	be	AUX
ijassa-1131	25	5	devoted	devote	VERB
ijassa-1131	25	6	to	to	ADP
ijassa-1131	25	7	a	a	DET
ijassa-1131	25	8	development	development	NOUN
ijassa-1131	25	9	of	of	ADP
ijassa-1131	25	10	the	the	DET
ijassa-1131	25	11	main	main	ADJ
ijassa-1131	25	12	result	result	NOUN
ijassa-1131	25	13	to	to	ADP
ijassa-1131	25	14	systems	system	NOUN
ijassa-1131	25	15	of	of	ADP
ijassa-1131	25	16	equations	equation	NOUN
ijassa-1131	25	17	.	.	PUNCT
ijassa-1131	26	1	∗corresponding	∗corresponde	VERB
ijassa-1131	26	2	author	author	NOUN
ijassa-1131	26	3	:	:	PUNCT
ijassa-1131	26	4	s-e-zhuk@yandex.ru	s-e-zhuk@yandex.ru	PROPN
ijassa-1131	26	5	114	114	NUM
ijassa-1131	26	6	s.e	s.e	PROPN
ijassa-1131	26	7	.	.	PROPN
ijassa-1131	26	8	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	26	9	2	2	NUM
ijassa-1131	26	10	.	.	PUNCT
ijassa-1131	26	11	preliminaries	preliminary	NOUN
ijassa-1131	26	12	let	let	VERB
ijassa-1131	26	13	us	we	PRON
ijassa-1131	26	14	recall	recall	VERB
ijassa-1131	26	15	the	the	DET
ijassa-1131	26	16	concept	concept	NOUN
ijassa-1131	26	17	of	of	ADP
ijassa-1131	26	18	covering	cover	VERB
ijassa-1131	26	19	constant	constant	ADJ
ijassa-1131	26	20	of	of	ADP
ijassa-1131	26	21	a	a	DET
ijassa-1131	26	22	linear	linear	ADJ
ijassa-1131	26	23	operator	operator	NOUN
ijassa-1131	26	24	.	.	PUNCT
ijassa-1131	27	1	denote	denote	PROPN
ijassa-1131	27	2	byln×k	byln×k	VERB
ijassa-1131	27	3	the	the	DET
ijassa-1131	27	4	space	space	NOUN
ijassa-1131	27	5	of	of	ADP
ijassa-1131	27	6	linear	linear	PROPN
ijassa-1131	27	7	operators	operator	NOUN
ijassa-1131	27	8	a	a	DET
ijassa-1131	27	9	:	:	PUNCT
ijassa-1131	27	10	rn	rn	PROPN
ijassa-1131	27	11	→	→	SYM
ijassa-1131	27	12	rk	rk	PROPN
ijassa-1131	27	13	,	,	PUNCT
ijassa-1131	27	14	denote	denote	VERB
ijassa-1131	27	15	by	by	ADP
ijassa-1131	27	16	sln×k	sln×k	NOUN
ijassa-1131	27	17	the	the	DET
ijassa-1131	27	18	set	set	NOUN
ijassa-1131	27	19	of	of	ADP
ijassa-1131	27	20	all	all	DET
ijassa-1131	27	21	surjective	surjective	ADJ
ijassa-1131	27	22	operators	operator	NOUN
ijassa-1131	27	23	a	a	DET
ijassa-1131	27	24	∈	∈	PROPN
ijassa-1131	27	25	ln×k	ln×k	NOUN
ijassa-1131	27	26	.	.	PUNCT
ijassa-1131	28	1	denote	denote	VERB
ijassa-1131	28	2	by	by	ADP
ijassa-1131	28	3	bn(r	bn(r	NOUN
ijassa-1131	28	4	)	)	PUNCT
ijassa-1131	28	5	the	the	DET
ijassa-1131	28	6	closed	closed	ADJ
ijassa-1131	28	7	ball	ball	NOUN
ijassa-1131	28	8	in	in	ADP
ijassa-1131	28	9	the	the	DET
ijassa-1131	28	10	space	space	NOUN
ijassa-1131	28	11	rn	rn	PROPN
ijassa-1131	28	12	centered	center	VERB
ijassa-1131	28	13	at	at	ADP
ijassa-1131	28	14	a	a	DET
ijassa-1131	28	15	point	point	NOUN
ijassa-1131	28	16	x	x	X
ijassa-1131	28	17	∈	∈	PROPN
ijassa-1131	28	18	rn	rn	PROPN
ijassa-1131	28	19	with	with	ADP
ijassa-1131	28	20	a	a	DET
ijassa-1131	28	21	radius	radius	NOUN
ijassa-1131	28	22	r	r	NOUN
ijassa-1131	28	23	≥	≥	NOUN
ijassa-1131	28	24	0	0	NUM
ijassa-1131	28	25	.	.	PUNCT
ijassa-1131	29	1	here	here	ADV
ijassa-1131	29	2	and	and	CCONJ
ijassa-1131	29	3	below	below	ADV
ijassa-1131	29	4	we	we	PRON
ijassa-1131	29	5	assume	assume	VERB
ijassa-1131	29	6	that	that	SCONJ
ijassa-1131	29	7	rn	rn	PROPN
ijassa-1131	29	8	and	and	CCONJ
ijassa-1131	29	9	rk	rk	PRON
ijassa-1131	29	10	are	be	AUX
ijassa-1131	29	11	equipped	equip	VERB
ijassa-1131	29	12	with	with	ADP
ijassa-1131	29	13	norms	norm	NOUN
ijassa-1131	29	14	which	which	PRON
ijassa-1131	29	15	we	we	PRON
ijassa-1131	29	16	denote	denote	VERB
ijassa-1131	29	17	by	by	ADP
ijassa-1131	29	18	|	|	ADV
ijassa-1131	29	19	·	·	PUNCT
ijassa-1131	30	1	|	|	ADV
ijassa-1131	30	2	,	,	PUNCT
ijassa-1131	30	3	and	and	CCONJ
ijassa-1131	30	4	the	the	DET
ijassa-1131	30	5	space	space	NOUN
ijassa-1131	30	6	ln×k	ln×k	NOUN
ijassa-1131	30	7	is	be	AUX
ijassa-1131	30	8	equipped	equip	VERB
ijassa-1131	30	9	with	with	ADP
ijassa-1131	30	10	the	the	DET
ijassa-1131	30	11	corresponding	correspond	VERB
ijassa-1131	30	12	operator	operator	NOUN
ijassa-1131	30	13	norm	norm	NOUN
ijassa-1131	30	14	.	.	PUNCT
ijassa-1131	31	1	for	for	ADP
ijassa-1131	31	2	a	a	DET
ijassa-1131	31	3	linear	linear	ADJ
ijassa-1131	31	4	operator	operator	NOUN
ijassa-1131	31	5	a	a	DET
ijassa-1131	31	6	∈	∈	NOUN
ijassa-1131	31	7	ln×k	ln×k	NOUN
ijassa-1131	31	8	,	,	PUNCT
ijassa-1131	31	9	put	put	VERB
ijassa-1131	31	10	cova	cova	PROPN
ijassa-1131	31	11	:	:	PUNCT
ijassa-1131	31	12	=	=	PUNCT
ijassa-1131	31	13	sup{α	sup{α	ADJ
ijassa-1131	31	14	≥	≥	NOUN
ijassa-1131	31	15	0	0	NUM
ijassa-1131	31	16	:	:	PUNCT
ijassa-1131	31	17	bk(α	bk(α	X
ijassa-1131	31	18	)	)	PUNCT
ijassa-1131	31	19	⊂	⊂	PROPN
ijassa-1131	31	20	abn(1	abn(1	NOUN
ijassa-1131	31	21	)	)	PUNCT
ijassa-1131	31	22	}	}	PUNCT
ijassa-1131	31	23	.	.	PUNCT
ijassa-1131	32	1	it	it	PRON
ijassa-1131	32	2	is	be	AUX
ijassa-1131	32	3	a	a	DET
ijassa-1131	32	4	straightforward	straightforward	ADJ
ijassa-1131	32	5	task	task	NOUN
ijassa-1131	32	6	to	to	PART
ijassa-1131	32	7	ensure	ensure	VERB
ijassa-1131	32	8	that	that	SCONJ
ijassa-1131	32	9	cova	cova	PROPN
ijassa-1131	32	10	>	>	X
ijassa-1131	32	11	0	0	PUNCT
ijassa-1131	33	1	if	if	SCONJ
ijassa-1131	33	2	and	and	CCONJ
ijassa-1131	33	3	only	only	ADV
ijassa-1131	33	4	if	if	SCONJ
ijassa-1131	33	5	a	a	DET
ijassa-1131	33	6	∈	∈	NOUN
ijassa-1131	33	7	sln×k	sln×k	NOUN
ijassa-1131	33	8	.	.	PUNCT
ijassa-1131	34	1	let	let	VERB
ijassa-1131	34	2	us	we	PRON
ijassa-1131	34	3	recall	recall	VERB
ijassa-1131	34	4	the	the	DET
ijassa-1131	34	5	global	global	ADJ
ijassa-1131	34	6	implicit	implicit	ADJ
ijassa-1131	34	7	function	function	NOUN
ijassa-1131	34	8	theorem	theorem	VERB
ijassa-1131	34	9	from	from	ADP
ijassa-1131	34	10	[	[	X
ijassa-1131	34	11	4	4	NUM
ijassa-1131	34	12	]	]	PUNCT
ijassa-1131	34	13	.	.	PUNCT
ijassa-1131	35	1	given	give	VERB
ijassa-1131	35	2	a	a	DET
ijassa-1131	35	3	topological	topological	ADJ
ijassa-1131	35	4	space	space	NOUN
ijassa-1131	35	5	σ	σ	NOUN
ijassa-1131	35	6	and	and	CCONJ
ijassa-1131	35	7	a	a	DET
ijassa-1131	35	8	mapping	mapping	NOUN
ijassa-1131	35	9	f	f	NOUN
ijassa-1131	35	10	:	:	PUNCT
ijassa-1131	35	11	rn	rn	PROPN
ijassa-1131	35	12	×	×	PROPN
ijassa-1131	35	13	σ→	σ→	PROPN
ijassa-1131	35	14	rk	rk	NOUN
ijassa-1131	35	15	,	,	PUNCT
ijassa-1131	35	16	assume	assume	VERB
ijassa-1131	35	17	that	that	SCONJ
ijassa-1131	35	18	for	for	ADP
ijassa-1131	35	19	every	every	DET
ijassa-1131	35	20	σ	σ	PROPN
ijassa-1131	35	21	∈	∈	PROPN
ijassa-1131	35	22	σ	σ	NOUN
ijassa-1131	35	23	the	the	DET
ijassa-1131	35	24	mapping	mapping	NOUN
ijassa-1131	35	25	f	f	X
ijassa-1131	35	26	(	(	PUNCT
ijassa-1131	35	27	·	·	PUNCT
ijassa-1131	35	28	,	,	PUNCT
ijassa-1131	35	29	σ	σ	PROPN
ijassa-1131	35	30	)	)	PUNCT
ijassa-1131	35	31	:	:	PUNCT
ijassa-1131	35	32	rn	rn	PROPN
ijassa-1131	35	33	→	→	SYM
ijassa-1131	35	34	rk	rk	NOUN
ijassa-1131	35	35	is	be	AUX
ijassa-1131	35	36	differentiable	differentiable	ADJ
ijassa-1131	35	37	.	.	PUNCT
ijassa-1131	36	1	for	for	ADP
ijassa-1131	36	2	t	t	PROPN
ijassa-1131	36	3	≥	≥	NUM
ijassa-1131	36	4	0	0	NUM
ijassa-1131	36	5	,	,	PUNCT
ijassa-1131	36	6	put	put	VERB
ijassa-1131	36	7	α(t	α(t	NOUN
ijassa-1131	36	8	)	)	PUNCT
ijassa-1131	37	1	:	:	PUNCT
ijassa-1131	37	2	=	=	SYM
ijassa-1131	37	3	inf	inf	PROPN
ijassa-1131	37	4	{	{	PUNCT
ijassa-1131	37	5	cov	cov	NOUN
ijassa-1131	37	6	∂f	∂f	PROPN
ijassa-1131	37	7	∂x	∂x	PROPN
ijassa-1131	37	8	(	(	PUNCT
ijassa-1131	37	9	x	x	PROPN
ijassa-1131	37	10	,	,	PUNCT
ijassa-1131	37	11	σ	σ	PROPN
ijassa-1131	37	12	)	)	PUNCT
ijassa-1131	37	13	:	:	PUNCT
ijassa-1131	37	14	x	x	PUNCT
ijassa-1131	37	15	∈	∈	NOUN
ijassa-1131	37	16	bn(t	bn(t	NOUN
ijassa-1131	37	17	)	)	PUNCT
ijassa-1131	37	18	,	,	PUNCT
ijassa-1131	37	19	σ	σ	PROPN
ijassa-1131	37	20	∈	∈	PROPN
ijassa-1131	37	21	σ	σ	PROPN
ijassa-1131	37	22	}	}	PUNCT
ijassa-1131	37	23	.	.	PUNCT
ijassa-1131	38	1	theorem	theorem	VERB
ijassa-1131	38	2	2.1	2.1	NUM
ijassa-1131	38	3	:	:	PUNCT
ijassa-1131	38	4	(	(	PUNCT
ijassa-1131	38	5	see	see	VERB
ijassa-1131	38	6	theorem	theorem	NOUN
ijassa-1131	38	7	2	2	NUM
ijassa-1131	38	8	in	in	ADP
ijassa-1131	38	9	[	[	X
ijassa-1131	38	10	4	4	NUM
ijassa-1131	38	11	]	]	PUNCT
ijassa-1131	38	12	)	)	PUNCT
ijassa-1131	38	13	assume	assume	VERB
ijassa-1131	38	14	that	that	SCONJ
ijassa-1131	38	15	(	(	PUNCT
ijassa-1131	38	16	a1	a1	PROPN
ijassa-1131	38	17	)	)	PUNCT
ijassa-1131	38	18	the	the	DET
ijassa-1131	38	19	mapping	mapping	NOUN
ijassa-1131	38	20	f	f	X
ijassa-1131	38	21	(	(	PUNCT
ijassa-1131	38	22	·	·	PUNCT
ijassa-1131	38	23	,	,	PUNCT
ijassa-1131	38	24	·	·	PUNCT
ijassa-1131	38	25	)	)	PUNCT
ijassa-1131	38	26	is	be	AUX
ijassa-1131	38	27	continuous	continuous	ADJ
ijassa-1131	38	28	on	on	ADP
ijassa-1131	38	29	rn	rn	PROPN
ijassa-1131	38	30	×	×	PROPN
ijassa-1131	38	31	σ	σ	PROPN
ijassa-1131	38	32	,	,	PUNCT
ijassa-1131	38	33	for	for	ADP
ijassa-1131	38	34	every	every	DET
ijassa-1131	38	35	σ	σ	PROPN
ijassa-1131	38	36	∈	∈	PROPN
ijassa-1131	38	37	σ	σ	NOUN
ijassa-1131	38	38	the	the	DET
ijassa-1131	38	39	mapping	mapping	NOUN
ijassa-1131	38	40	f	f	X
ijassa-1131	38	41	(	(	PUNCT
ijassa-1131	38	42	·	·	PUNCT
ijassa-1131	38	43	,	,	PUNCT
ijassa-1131	38	44	σ	σ	PROPN
ijassa-1131	38	45	)	)	PUNCT
ijassa-1131	38	46	:	:	PUNCT
ijassa-1131	38	47	rn	rn	PROPN
ijassa-1131	38	48	→	→	SYM
ijassa-1131	38	49	rk	rk	PROPN
ijassa-1131	38	50	is	be	AUX
ijassa-1131	38	51	differentiable	differentiable	ADJ
ijassa-1131	38	52	on	on	ADP
ijassa-1131	38	53	rn	rn	PROPN
ijassa-1131	38	54	,	,	PUNCT
ijassa-1131	38	55	the	the	DET
ijassa-1131	38	56	mapping	mapping	NOUN
ijassa-1131	38	57	∂f	∂f	PROPN
ijassa-1131	38	58	∂x	∂x	PROPN
ijassa-1131	38	59	(	(	PUNCT
ijassa-1131	38	60	·	·	PUNCT
ijassa-1131	38	61	,	,	PUNCT
ijassa-1131	38	62	·	·	PUNCT
ijassa-1131	38	63	)	)	PUNCT
ijassa-1131	38	64	is	be	AUX
ijassa-1131	38	65	continuous	continuous	ADJ
ijassa-1131	38	66	on	on	ADP
ijassa-1131	38	67	rn	rn	PROPN
ijassa-1131	38	68	×	×	PROPN
ijassa-1131	38	69	σ	σ	PROPN
ijassa-1131	38	70	.	.	PUNCT
ijassa-1131	39	1	if	if	SCONJ
ijassa-1131	39	2	+	+	PROPN
ijassa-1131	39	3	∞∫	∞∫	PROPN
ijassa-1131	39	4	0	0	NUM
ijassa-1131	39	5	α(t	α(t	PROPN
ijassa-1131	39	6	)	)	PUNCT
ijassa-1131	39	7	dt	dt	NOUN
ijassa-1131	40	1	=	=	PUNCT
ijassa-1131	41	1	+	+	NOUN
ijassa-1131	41	2	∞	∞	NUM
ijassa-1131	41	3	or	or	CCONJ
ijassa-1131	41	4	sup	sup	NOUN
ijassa-1131	41	5	σ∈σ	σ∈σ	NOUN
ijassa-1131	41	6	|f(0	|f(0	NOUN
ijassa-1131	41	7	,	,	PUNCT
ijassa-1131	41	8	σ)|	σ)|	NOUN
ijassa-1131	41	9	<	<	X
ijassa-1131	41	10	+	+	PROPN
ijassa-1131	41	11	∞∫	∞∫	PROPN
ijassa-1131	41	12	0	0	NUM
ijassa-1131	41	13	α(t	α(t	PROPN
ijassa-1131	41	14	)	)	PUNCT
ijassa-1131	42	1	dt	dt	PROPN
ijassa-1131	42	2	,	,	PUNCT
ijassa-1131	42	3	then	then	ADV
ijassa-1131	42	4	for	for	ADP
ijassa-1131	42	5	every	every	DET
ijassa-1131	42	6	ε	ε	PROPN
ijassa-1131	42	7	>	>	X
ijassa-1131	42	8	0	0	PUNCT
ijassa-1131	42	9	there	there	PRON
ijassa-1131	42	10	exists	exist	VERB
ijassa-1131	42	11	a	a	DET
ijassa-1131	42	12	continuous	continuous	ADJ
ijassa-1131	42	13	mapping	mapping	NOUN
ijassa-1131	42	14	g	g	NOUN
ijassa-1131	42	15	:	:	PUNCT
ijassa-1131	42	16	σ→	σ→	PROPN
ijassa-1131	42	17	rn	rn	PROPN
ijassa-1131	42	18	such	such	ADJ
ijassa-1131	42	19	that	that	DET
ijassa-1131	42	20	f(g(σ	f(g(σ	PROPN
ijassa-1131	42	21	)	)	PUNCT
ijassa-1131	42	22	,	,	PUNCT
ijassa-1131	42	23	σ	σ	X
ijassa-1131	42	24	)	)	PUNCT
ijassa-1131	42	25	=	=	SYM
ijassa-1131	42	26	0	0	NUM
ijassa-1131	42	27	∀σ	∀σ	PROPN
ijassa-1131	42	28	∈	∈	PROPN
ijassa-1131	42	29	σ	σ	PROPN
ijassa-1131	42	30	,	,	PUNCT
ijassa-1131	42	31	|g(σ)|∫	|g(σ)|∫	PROPN
ijassa-1131	42	32	0	0	NUM
ijassa-1131	42	33	α(t	α(t	PROPN
ijassa-1131	42	34	)	)	PUNCT
ijassa-1131	42	35	dt	dt	PROPN
ijassa-1131	42	36	≤	≤	NUM
ijassa-1131	42	37	(	(	PUNCT
ijassa-1131	42	38	1	1	NUM
ijassa-1131	42	39	+	+	CCONJ
ijassa-1131	42	40	ε)|f(0	ε)|f(0	NOUN
ijassa-1131	42	41	,	,	PUNCT
ijassa-1131	42	42	σ)|	σ)|	PROPN
ijassa-1131	42	43	∀σ	∀σ	PROPN
ijassa-1131	42	44	∈	∈	PROPN
ijassa-1131	42	45	σ	σ	PROPN
ijassa-1131	42	46	.	.	PUNCT
ijassa-1131	43	1	below	below	ADP
ijassa-1131	43	2	we	we	PRON
ijassa-1131	43	3	also	also	ADV
ijassa-1131	43	4	use	use	VERB
ijassa-1131	43	5	the	the	DET
ijassa-1131	43	6	following	follow	VERB
ijassa-1131	43	7	corollary	corollary	NOUN
ijassa-1131	43	8	of	of	ADP
ijassa-1131	43	9	theorem	theorem	ADJ
ijassa-1131	43	10	2.1	2.1	NUM
ijassa-1131	43	11	.	.	PUNCT
ijassa-1131	44	1	corollary	corollary	ADJ
ijassa-1131	44	2	2.1	2.1	NUM
ijassa-1131	44	3	:	:	PUNCT
ijassa-1131	44	4	let	let	VERB
ijassa-1131	44	5	f	f	PROPN
ijassa-1131	44	6	satisfies	satisfy	VERB
ijassa-1131	44	7	the	the	DET
ijassa-1131	44	8	assumption	assumption	NOUN
ijassa-1131	44	9	(	(	PUNCT
ijassa-1131	44	10	a1	a1	NOUN
ijassa-1131	44	11	)	)	PUNCT
ijassa-1131	44	12	.	.	PUNCT
ijassa-1131	45	1	if	if	SCONJ
ijassa-1131	45	2	there	there	PRON
ijassa-1131	45	3	exists	exist	VERB
ijassa-1131	45	4	r̄	r̄	NOUN
ijassa-1131	45	5	>	>	X
ijassa-1131	45	6	0	0	NUM
ijassa-1131	45	7	such	such	ADJ
ijassa-1131	45	8	that	that	DET
ijassa-1131	45	9	sup	sup	NOUN
ijassa-1131	45	10	σ∈σ	σ∈σ	NOUN
ijassa-1131	45	11	|f(0	|f(0	NOUN
ijassa-1131	45	12	,	,	PUNCT
ijassa-1131	45	13	σ)|	σ)|	PROPN
ijassa-1131	45	14	<	<	X
ijassa-1131	45	15	α(r̄)r̄	α(r̄)r̄	PROPN
ijassa-1131	45	16	,	,	PUNCT
ijassa-1131	45	17	then	then	ADV
ijassa-1131	45	18	for	for	ADP
ijassa-1131	45	19	every	every	DET
ijassa-1131	45	20	ε	ε	PROPN
ijassa-1131	45	21	>	>	X
ijassa-1131	45	22	0	0	PUNCT
ijassa-1131	45	23	there	there	PRON
ijassa-1131	45	24	exists	exist	VERB
ijassa-1131	45	25	a	a	DET
ijassa-1131	45	26	continuous	continuous	ADJ
ijassa-1131	45	27	mapping	mapping	NOUN
ijassa-1131	45	28	g	g	NOUN
ijassa-1131	45	29	:	:	PUNCT
ijassa-1131	45	30	σ→	σ→	PROPN
ijassa-1131	45	31	rn	rn	PROPN
ijassa-1131	45	32	such	such	ADJ
ijassa-1131	45	33	that	that	DET
ijassa-1131	45	34	f(g(σ	f(g(σ	PROPN
ijassa-1131	45	35	)	)	PUNCT
ijassa-1131	45	36	,	,	PUNCT
ijassa-1131	45	37	σ	σ	X
ijassa-1131	45	38	)	)	PUNCT
ijassa-1131	45	39	=	=	SYM
ijassa-1131	45	40	0	0	NUM
ijassa-1131	45	41	∀σ	∀σ	PROPN
ijassa-1131	45	42	∈	∈	PROPN
ijassa-1131	45	43	σ	σ	PROPN
ijassa-1131	45	44	,	,	PUNCT
ijassa-1131	45	45	|g(σ)|	|g(σ)|	PROPN
ijassa-1131	45	46	≤	≤	X
ijassa-1131	45	47	(	(	PUNCT
ijassa-1131	45	48	1	1	NUM
ijassa-1131	45	49	+	+	CCONJ
ijassa-1131	45	50	ε)|f(0	ε)|f(0	NOUN
ijassa-1131	45	51	,	,	PUNCT
ijassa-1131	45	52	σ)|	σ)|	NOUN
ijassa-1131	45	53	α(r̄	α(r̄	NOUN
ijassa-1131	45	54	)	)	PUNCT
ijassa-1131	45	55	∀σ	∀σ	PROPN
ijassa-1131	46	1	∈	∈	PROPN
ijassa-1131	46	2	σ	σ	PROPN
ijassa-1131	46	3	.	.	PUNCT
ijassa-1131	46	4	note	note	VERB
ijassa-1131	46	5	that	that	SCONJ
ijassa-1131	46	6	in	in	ADP
ijassa-1131	46	7	[	[	X
ijassa-1131	46	8	4	4	X
ijassa-1131	46	9	]	]	PUNCT
ijassa-1131	46	10	these	these	DET
ijassa-1131	46	11	assertions	assertion	NOUN
ijassa-1131	46	12	were	be	AUX
ijassa-1131	46	13	proved	prove	VERB
ijassa-1131	46	14	under	under	ADP
ijassa-1131	46	15	more	more	ADJ
ijassa-1131	46	16	general	general	ADJ
ijassa-1131	46	17	assumptions	assumption	NOUN
ijassa-1131	46	18	.	.	PUNCT
ijassa-1131	47	1	in	in	ADP
ijassa-1131	47	2	particular	particular	ADJ
ijassa-1131	47	3	,	,	PUNCT
ijassa-1131	47	4	it	it	PRON
ijassa-1131	47	5	was	be	AUX
ijassa-1131	47	6	assumed	assume	VERB
ijassa-1131	47	7	that	that	SCONJ
ijassa-1131	47	8	the	the	DET
ijassa-1131	47	9	domain	domain	NOUN
ijassa-1131	47	10	of	of	ADP
ijassa-1131	47	11	f	f	PROPN
ijassa-1131	47	12	in	in	ADP
ijassa-1131	47	13	the	the	DET
ijassa-1131	47	14	variable	variable	NOUN
ijassa-1131	47	15	x	x	NOUN
ijassa-1131	47	16	as	as	ADV
ijassa-1131	47	17	well	well	ADV
ijassa-1131	47	18	as	as	ADP
ijassa-1131	47	19	the	the	DET
ijassa-1131	47	20	target	target	NOUN
ijassa-1131	47	21	space	space	NOUN
ijassa-1131	47	22	are	be	AUX
ijassa-1131	47	23	banach	banach	ADV
ijassa-1131	47	24	spaces	space	NOUN
ijassa-1131	47	25	.	.	PUNCT
ijassa-1131	48	1	however	however	ADV
ijassa-1131	48	2	,	,	PUNCT
ijassa-1131	48	3	the	the	DET
ijassa-1131	48	4	considered	consider	VERB
ijassa-1131	48	5	here	here	ADV
ijassa-1131	48	6	weak	weak	ADJ
ijassa-1131	48	7	form	form	NOUN
ijassa-1131	48	8	of	of	ADP
ijassa-1131	48	9	implicit	implicit	ADJ
ijassa-1131	48	10	function	function	NOUN
ijassa-1131	48	11	theorem	theorem	VERB
ijassa-1131	48	12	from	from	ADP
ijassa-1131	48	13	[	[	X
ijassa-1131	48	14	4	4	X
ijassa-1131	48	15	]	]	PUNCT
ijassa-1131	48	16	is	be	AUX
ijassa-1131	48	17	enough	enough	ADJ
ijassa-1131	48	18	for	for	ADP
ijassa-1131	48	19	the	the	DET
ijassa-1131	48	20	subsequent	subsequent	ADJ
ijassa-1131	48	21	constructions	construction	NOUN
ijassa-1131	48	22	.	.	PUNCT
ijassa-1131	49	1	copyright	copyright	NOUN
ijassa-1131	49	2	©	©	PROPN
ijassa-1131	49	3	2021	2021	NUM
ijassa-1131	49	4	assa	assa	NOUN
ijassa-1131	49	5	.	.	PUNCT
ijassa-1131	50	1	adv	adv	PROPN
ijassa-1131	50	2	syst	syst	PROPN
ijassa-1131	50	3	sci	sci	PROPN
ijassa-1131	50	4	appl	appl	PROPN
ijassa-1131	50	5	(	(	PUNCT
ijassa-1131	50	6	2021	2021	NUM
ijassa-1131	50	7	)	)	PUNCT
ijassa-1131	50	8	solvability	solvability	NOUN
ijassa-1131	50	9	of	of	ADP
ijassa-1131	50	10	equations	equation	NOUN
ijassa-1131	50	11	defined	define	VERB
ijassa-1131	50	12	by	by	ADP
ijassa-1131	50	13	continuous	continuous	ADJ
ijassa-1131	50	14	and	and	CCONJ
ijassa-1131	50	15	smooth	smooth	ADJ
ijassa-1131	50	16	mappings	mapping	NOUN
ijassa-1131	50	17	115	115	NUM
ijassa-1131	50	18	3	3	NUM
ijassa-1131	50	19	.	.	PUNCT
ijassa-1131	50	20	solvability	solvability	NOUN
ijassa-1131	50	21	condition	condition	NOUN
ijassa-1131	50	22	for	for	ADP
ijassa-1131	50	23	equations	equation	NOUN
ijassa-1131	50	24	let	let	VERB
ijassa-1131	50	25	us	we	PRON
ijassa-1131	50	26	turn	turn	VERB
ijassa-1131	50	27	back	back	ADV
ijassa-1131	50	28	to	to	ADP
ijassa-1131	50	29	equation	equation	NOUN
ijassa-1131	50	30	(	(	PUNCT
ijassa-1131	50	31	1.1	1.1	NUM
ijassa-1131	50	32	)	)	PUNCT
ijassa-1131	50	33	.	.	PUNCT
ijassa-1131	51	1	assume	assume	VERB
ijassa-1131	51	2	that	that	SCONJ
ijassa-1131	51	3	for	for	ADP
ijassa-1131	51	4	every	every	DET
ijassa-1131	51	5	x2	x2	PROPN
ijassa-1131	51	6	∈	∈	PROPN
ijassa-1131	51	7	rn	rn	PROPN
ijassa-1131	51	8	the	the	DET
ijassa-1131	51	9	mapping	mapping	NOUN
ijassa-1131	51	10	f	f	X
ijassa-1131	51	11	(	(	PUNCT
ijassa-1131	51	12	·	·	PUNCT
ijassa-1131	51	13	,	,	PUNCT
ijassa-1131	51	14	x2	x2	PROPN
ijassa-1131	51	15	)	)	PUNCT
ijassa-1131	51	16	is	be	AUX
ijassa-1131	51	17	differentiable	differentiable	ADJ
ijassa-1131	51	18	.	.	PUNCT
ijassa-1131	52	1	for	for	ADP
ijassa-1131	52	2	t	t	PROPN
ijassa-1131	52	3	>	>	SYM
ijassa-1131	52	4	0	0	PUNCT
ijassa-1131	52	5	put	put	NOUN
ijassa-1131	52	6	a(t	a(t	NOUN
ijassa-1131	52	7	,	,	PUNCT
ijassa-1131	52	8	r	r	NOUN
ijassa-1131	52	9	)	)	PUNCT
ijassa-1131	52	10	:	:	PUNCT
ijassa-1131	52	11	=	=	SYM
ijassa-1131	52	12	inf	inf	PROPN
ijassa-1131	52	13	{	{	PUNCT
ijassa-1131	52	14	cov	cov	NOUN
ijassa-1131	52	15	∂f	∂f	PROPN
ijassa-1131	52	16	∂x	∂x	PROPN
ijassa-1131	52	17	(	(	PUNCT
ijassa-1131	52	18	x1	x1	PROPN
ijassa-1131	52	19	,	,	PUNCT
ijassa-1131	52	20	x2	x2	PROPN
ijassa-1131	52	21	)	)	PUNCT
ijassa-1131	52	22	:	:	PUNCT
ijassa-1131	52	23	x1	x1	PROPN
ijassa-1131	52	24	∈	∈	PROPN
ijassa-1131	52	25	bn(t	bn(t	PUNCT
ijassa-1131	52	26	)	)	PUNCT
ijassa-1131	52	27	,	,	PUNCT
ijassa-1131	52	28	x2	x2	PROPN
ijassa-1131	52	29	∈	∈	PROPN
ijassa-1131	52	30	bn(r	bn(r	NOUN
ijassa-1131	52	31	)	)	PUNCT
ijassa-1131	52	32	}	}	PUNCT
ijassa-1131	52	33	,	,	PUNCT
ijassa-1131	52	34	b(r	b(r	PROPN
ijassa-1131	52	35	)	)	PUNCT
ijassa-1131	52	36	:	:	PUNCT
ijassa-1131	53	1	=	=	NUM
ijassa-1131	53	2	sup	sup	NOUN
ijassa-1131	53	3	x2∈bn(r	x2∈bn(r	NOUN
ijassa-1131	53	4	)	)	PUNCT
ijassa-1131	53	5	|f(0	|f(0	PROPN
ijassa-1131	53	6	,	,	PUNCT
ijassa-1131	53	7	x2)|	x2)|	PROPN
ijassa-1131	53	8	.	.	PUNCT
ijassa-1131	53	9	theorem	theorem	VERB
ijassa-1131	53	10	3.1	3.1	NUM
ijassa-1131	53	11	:	:	PUNCT
ijassa-1131	53	12	assume	assume	VERB
ijassa-1131	53	13	that	that	SCONJ
ijassa-1131	53	14	(	(	PUNCT
ijassa-1131	53	15	a	a	X
ijassa-1131	53	16	)	)	PUNCT
ijassa-1131	53	17	the	the	DET
ijassa-1131	53	18	mapping	mapping	NOUN
ijassa-1131	53	19	f	f	X
ijassa-1131	53	20	(	(	PUNCT
ijassa-1131	53	21	·	·	PUNCT
ijassa-1131	53	22	,	,	PUNCT
ijassa-1131	53	23	·	·	PUNCT
ijassa-1131	53	24	)	)	PUNCT
ijassa-1131	53	25	is	be	AUX
ijassa-1131	53	26	continuous	continuous	ADJ
ijassa-1131	53	27	on	on	ADP
ijassa-1131	53	28	rn	rn	PROPN
ijassa-1131	53	29	×	×	PROPN
ijassa-1131	53	30	rn	rn	PROPN
ijassa-1131	53	31	,	,	PUNCT
ijassa-1131	53	32	for	for	ADP
ijassa-1131	53	33	every	every	DET
ijassa-1131	53	34	x2	x2	PROPN
ijassa-1131	53	35	∈	∈	PROPN
ijassa-1131	53	36	rn	rn	PROPN
ijassa-1131	53	37	the	the	DET
ijassa-1131	53	38	mapping	mapping	NOUN
ijassa-1131	53	39	f	f	X
ijassa-1131	53	40	(	(	PUNCT
ijassa-1131	53	41	·	·	PUNCT
ijassa-1131	53	42	,	,	PUNCT
ijassa-1131	53	43	x2	x2	PROPN
ijassa-1131	53	44	)	)	PUNCT
ijassa-1131	53	45	:	:	PUNCT
ijassa-1131	53	46	rn	rn	PROPN
ijassa-1131	53	47	→	→	SYM
ijassa-1131	53	48	rk	rk	PROPN
ijassa-1131	53	49	is	be	AUX
ijassa-1131	53	50	differentiable	differentiable	ADJ
ijassa-1131	53	51	on	on	ADP
ijassa-1131	53	52	rn	rn	PROPN
ijassa-1131	53	53	,	,	PUNCT
ijassa-1131	53	54	the	the	DET
ijassa-1131	53	55	mapping	mapping	NOUN
ijassa-1131	53	56	∂f	∂f	PROPN
ijassa-1131	53	57	∂x	∂x	PROPN
ijassa-1131	53	58	(	(	PUNCT
ijassa-1131	53	59	·	·	PUNCT
ijassa-1131	53	60	,	,	PUNCT
ijassa-1131	53	61	·	·	PUNCT
ijassa-1131	53	62	)	)	PUNCT
ijassa-1131	53	63	is	be	AUX
ijassa-1131	53	64	continuous	continuous	ADJ
ijassa-1131	53	65	on	on	ADP
ijassa-1131	53	66	rn	rn	PROPN
ijassa-1131	53	67	×	×	PROPN
ijassa-1131	53	68	rn	rn	PROPN
ijassa-1131	53	69	.	.	PUNCT
ijassa-1131	54	1	if	if	SCONJ
ijassa-1131	54	2	there	there	PRON
ijassa-1131	54	3	exists	exist	VERB
ijassa-1131	54	4	r̄	r̄	NOUN
ijassa-1131	54	5	>	>	X
ijassa-1131	54	6	0	0	NUM
ijassa-1131	54	7	such	such	ADJ
ijassa-1131	54	8	that	that	SCONJ
ijassa-1131	54	9	b(r̄	b(r̄	NOUN
ijassa-1131	54	10	)	)	PUNCT
ijassa-1131	54	11	<	<	X
ijassa-1131	54	12	r̄∫	r̄∫	NOUN
ijassa-1131	54	13	0	0	SYM
ijassa-1131	54	14	a(t	a(t	NOUN
ijassa-1131	54	15	,	,	PUNCT
ijassa-1131	54	16	r̄	r̄	NOUN
ijassa-1131	54	17	)	)	PUNCT
ijassa-1131	54	18	dt	dt	NOUN
ijassa-1131	54	19	,	,	PUNCT
ijassa-1131	54	20	(	(	PUNCT
ijassa-1131	54	21	3.2	3.2	NUM
ijassa-1131	54	22	)	)	PUNCT
ijassa-1131	54	23	then	then	ADV
ijassa-1131	54	24	there	there	PRON
ijassa-1131	54	25	exists	exist	VERB
ijassa-1131	54	26	a	a	DET
ijassa-1131	54	27	point	point	NOUN
ijassa-1131	54	28	x̄	x̄	PRON
ijassa-1131	54	29	∈	∈	PROPN
ijassa-1131	54	30	bn(r̄	bn(r̄	PROPN
ijassa-1131	54	31	)	)	PUNCT
ijassa-1131	54	32	such	such	ADJ
ijassa-1131	54	33	that	that	SCONJ
ijassa-1131	54	34	such	such	ADJ
ijassa-1131	54	35	that	that	SCONJ
ijassa-1131	54	36	f(x̄	f(x̄	NOUN
ijassa-1131	54	37	,	,	PUNCT
ijassa-1131	54	38	x̄	x̄	NOUN
ijassa-1131	54	39	)	)	PUNCT
ijassa-1131	55	1	=	=	SYM
ijassa-1131	55	2	0	0	X
ijassa-1131	55	3	.	.	PUNCT
ijassa-1131	56	1	proof	proof	NOUN
ijassa-1131	56	2	apply	apply	VERB
ijassa-1131	56	3	theorem	theorem	VERB
ijassa-1131	56	4	2.1	2.1	NUM
ijassa-1131	56	5	to	to	ADP
ijassa-1131	56	6	the	the	DET
ijassa-1131	56	7	mapping	mapping	NOUN
ijassa-1131	56	8	f	f	NOUN
ijassa-1131	56	9	with	with	ADP
ijassa-1131	56	10	σ	σ	PROPN
ijassa-1131	56	11	=	=	SYM
ijassa-1131	56	12	bn(r̄	bn(r̄	PROPN
ijassa-1131	56	13	)	)	PUNCT
ijassa-1131	56	14	.	.	PUNCT
ijassa-1131	57	1	we	we	PRON
ijassa-1131	57	2	have	have	VERB
ijassa-1131	57	3	α(t	α(t	VERB
ijassa-1131	57	4	)	)	PUNCT
ijassa-1131	57	5	=	=	PUNCT
ijassa-1131	58	1	a(t	a(t	NOUN
ijassa-1131	58	2	,	,	PUNCT
ijassa-1131	58	3	r	r	NOUN
ijassa-1131	58	4	)	)	PUNCT
ijassa-1131	58	5	∀	∀	NOUN
ijassa-1131	59	1	r	r	NOUN
ijassa-1131	59	2	>	>	NOUN
ijassa-1131	59	3	0	0	NUM
ijassa-1131	59	4	.	.	PUNCT
ijassa-1131	60	1	therefore	therefore	ADV
ijassa-1131	60	2	,	,	PUNCT
ijassa-1131	60	3	assumption	assumption	NOUN
ijassa-1131	60	4	(	(	PUNCT
ijassa-1131	60	5	3.2	3.2	NUM
ijassa-1131	60	6	)	)	PUNCT
ijassa-1131	60	7	implies	imply	VERB
ijassa-1131	60	8	that	that	SCONJ
ijassa-1131	60	9	sup	sup	PROPN
ijassa-1131	60	10	x2∈bn(r̄	x2∈bn(r̄	PROPN
ijassa-1131	60	11	)	)	PUNCT
ijassa-1131	60	12	|f(0	|f(0	PROPN
ijassa-1131	60	13	,	,	PUNCT
ijassa-1131	60	14	x2)|	x2)|	PROPN
ijassa-1131	60	15	=	=	SYM
ijassa-1131	60	16	b(r̄	b(r̄	PROPN
ijassa-1131	60	17	)	)	PUNCT
ijassa-1131	60	18	<	<	X
ijassa-1131	60	19	r∫	r∫	PROPN
ijassa-1131	60	20	0	0	NUM
ijassa-1131	60	21	a(t	a(t	PROPN
ijassa-1131	60	22	,	,	PUNCT
ijassa-1131	60	23	r̄	r̄	NOUN
ijassa-1131	60	24	)	)	PUNCT
ijassa-1131	60	25	dt	dt	NOUN
ijassa-1131	61	1	=	=	PUNCT
ijassa-1131	62	1	+	+	PROPN
ijassa-1131	62	2	∞∫	∞∫	PROPN
ijassa-1131	62	3	0	0	NUM
ijassa-1131	62	4	α(t	α(t	PROPN
ijassa-1131	62	5	)	)	PUNCT
ijassa-1131	62	6	dt	dt	PROPN
ijassa-1131	62	7	.	.	PUNCT
ijassa-1131	62	8	take	take	VERB
ijassa-1131	62	9	an	an	DET
ijassa-1131	62	10	arbitrary	arbitrary	ADJ
ijassa-1131	62	11	ε	ε	NOUN
ijassa-1131	62	12	>	>	X
ijassa-1131	62	13	0	0	NUM
ijassa-1131	63	1	such	such	ADJ
ijassa-1131	63	2	that	that	SCONJ
ijassa-1131	63	3	(	(	PUNCT
ijassa-1131	63	4	1	1	NUM
ijassa-1131	63	5	+	+	X
ijassa-1131	63	6	ε)b(r̄	ε)b(r̄	NOUN
ijassa-1131	63	7	)	)	PUNCT
ijassa-1131	63	8	<	<	X
ijassa-1131	63	9	r̄∫	r̄∫	NOUN
ijassa-1131	63	10	0	0	SYM
ijassa-1131	63	11	a(t	a(t	NOUN
ijassa-1131	63	12	,	,	PUNCT
ijassa-1131	63	13	r̄	r̄	NOUN
ijassa-1131	63	14	)	)	PUNCT
ijassa-1131	63	15	dt	dt	NOUN
ijassa-1131	63	16	.	.	PUNCT
ijassa-1131	64	1	it	it	PRON
ijassa-1131	64	2	follows	follow	VERB
ijassa-1131	64	3	from	from	ADP
ijassa-1131	64	4	theorem	theorem	ADJ
ijassa-1131	64	5	2.1	2.1	NUM
ijassa-1131	64	6	that	that	SCONJ
ijassa-1131	64	7	there	there	PRON
ijassa-1131	64	8	exists	exist	VERB
ijassa-1131	64	9	a	a	DET
ijassa-1131	64	10	continuous	continuous	ADJ
ijassa-1131	64	11	mapping	mapping	NOUN
ijassa-1131	64	12	g	g	NOUN
ijassa-1131	64	13	:	:	PUNCT
ijassa-1131	64	14	bn(r̄)→	bn(r̄)→	PROPN
ijassa-1131	64	15	rn	rn	PROPN
ijassa-1131	64	16	such	such	ADJ
ijassa-1131	64	17	that	that	DET
ijassa-1131	64	18	f(g(x2	f(g(x2	NOUN
ijassa-1131	64	19	)	)	PUNCT
ijassa-1131	64	20	,	,	PUNCT
ijassa-1131	64	21	x2	x2	PROPN
ijassa-1131	64	22	)	)	PUNCT
ijassa-1131	64	23	=	=	SYM
ijassa-1131	64	24	0	0	NUM
ijassa-1131	64	25	,	,	PUNCT
ijassa-1131	64	26	|g(x2)|∫	|g(x2)|∫	NOUN
ijassa-1131	64	27	0	0	NUM
ijassa-1131	64	28	a(t	a(t	NOUN
ijassa-1131	64	29	,	,	PUNCT
ijassa-1131	64	30	r̄	r̄	NOUN
ijassa-1131	64	31	)	)	PUNCT
ijassa-1131	64	32	dt	dt	X
ijassa-1131	64	33	≤	≤	NUM
ijassa-1131	64	34	(	(	PUNCT
ijassa-1131	64	35	1	1	NUM
ijassa-1131	64	36	+	+	CCONJ
ijassa-1131	64	37	ε)|f(0	ε)|f(0	NOUN
ijassa-1131	64	38	,	,	PUNCT
ijassa-1131	64	39	x2)|	x2)|	PROPN
ijassa-1131	64	40	∀x2	∀x2	PUNCT
ijassa-1131	64	41	∈	∈	PROPN
ijassa-1131	64	42	bn(r̄	bn(r̄	PROPN
ijassa-1131	64	43	)	)	PUNCT
ijassa-1131	64	44	.	.	PUNCT
ijassa-1131	65	1	(	(	PUNCT
ijassa-1131	65	2	3.3	3.3	NUM
ijassa-1131	65	3	)	)	PUNCT
ijassa-1131	65	4	obviously	obviously	ADV
ijassa-1131	65	5	the	the	DET
ijassa-1131	65	6	function	function	NOUN
ijassa-1131	65	7	a	a	DET
ijassa-1131	65	8	(	(	PUNCT
ijassa-1131	65	9	·	·	PUNCT
ijassa-1131	65	10	,	,	PUNCT
ijassa-1131	65	11	r̄	r̄	NOUN
ijassa-1131	65	12	)	)	PUNCT
ijassa-1131	65	13	is	be	AUX
ijassa-1131	65	14	decreasing	decrease	VERB
ijassa-1131	65	15	.	.	PUNCT
ijassa-1131	66	1	thus	thus	ADV
ijassa-1131	66	2	,	,	PUNCT
ijassa-1131	66	3	the	the	DET
ijassa-1131	66	4	inequality	inequality	NOUN
ijassa-1131	66	5	in	in	ADP
ijassa-1131	66	6	(	(	PUNCT
ijassa-1131	66	7	3.3	3.3	NUM
ijassa-1131	66	8	)	)	PUNCT
ijassa-1131	66	9	and	and	CCONJ
ijassa-1131	66	10	the	the	DET
ijassa-1131	66	11	assumption	assumption	NOUN
ijassa-1131	66	12	(	(	PUNCT
ijassa-1131	66	13	3.2	3.2	NUM
ijassa-1131	66	14	)	)	PUNCT
ijassa-1131	66	15	imply	imply	VERB
ijassa-1131	66	16	that	that	SCONJ
ijassa-1131	66	17	|g(x2)|	|g(x2)|	PROPN
ijassa-1131	66	18	≤	≤	NOUN
ijassa-1131	66	19	r	r	NOUN
ijassa-1131	66	20	for	for	ADP
ijassa-1131	66	21	every	every	DET
ijassa-1131	66	22	x2	x2	PROPN
ijassa-1131	66	23	∈	∈	PROPN
ijassa-1131	66	24	bn(r̄	bn(r̄	PROPN
ijassa-1131	66	25	)	)	PUNCT
ijassa-1131	66	26	.	.	PUNCT
ijassa-1131	67	1	so	so	ADV
ijassa-1131	67	2	,	,	PUNCT
ijassa-1131	67	3	g(x2	g(x2	NOUN
ijassa-1131	67	4	)	)	PUNCT
ijassa-1131	67	5	∈	∈	PROPN
ijassa-1131	67	6	bn(r̄	bn(r̄	PROPN
ijassa-1131	67	7	)	)	PUNCT
ijassa-1131	67	8	∀x2	∀x2	NOUN
ijassa-1131	67	9	∈	∈	PROPN
ijassa-1131	67	10	bn(r̄	bn(r̄	PROPN
ijassa-1131	67	11	)	)	PUNCT
ijassa-1131	67	12	.	.	PUNCT
ijassa-1131	68	1	copyright	copyright	NOUN
ijassa-1131	68	2	©	©	PROPN
ijassa-1131	68	3	2021	2021	NUM
ijassa-1131	68	4	assa	assa	NOUN
ijassa-1131	68	5	.	.	PUNCT
ijassa-1131	69	1	adv	adv	PROPN
ijassa-1131	69	2	syst	syst	PROPN
ijassa-1131	69	3	sci	sci	PROPN
ijassa-1131	69	4	appl	appl	PROPN
ijassa-1131	69	5	(	(	PUNCT
ijassa-1131	69	6	2021	2021	NUM
ijassa-1131	69	7	)	)	PUNCT
ijassa-1131	69	8	116	116	NUM
ijassa-1131	69	9	s.e	s.e	PROPN
ijassa-1131	69	10	.	.	PROPN
ijassa-1131	69	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	69	12	therefore	therefore	ADV
ijassa-1131	69	13	,	,	PUNCT
ijassa-1131	69	14	by	by	ADP
ijassa-1131	69	15	virtue	virtue	NOUN
ijassa-1131	69	16	of	of	ADP
ijassa-1131	69	17	continuity	continuity	NOUN
ijassa-1131	69	18	of	of	ADP
ijassa-1131	69	19	g	g	PROPN
ijassa-1131	69	20	brouwer	brouwer	PROPN
ijassa-1131	69	21	’s	’s	PART
ijassa-1131	69	22	fixed	fix	VERB
ijassa-1131	69	23	-	-	PUNCT
ijassa-1131	69	24	point	point	NOUN
ijassa-1131	69	25	theorem	theorem	NOUN
ijassa-1131	69	26	implies	imply	VERB
ijassa-1131	69	27	that	that	SCONJ
ijassa-1131	69	28	there	there	PRON
ijassa-1131	69	29	exists	exist	VERB
ijassa-1131	69	30	a	a	DET
ijassa-1131	69	31	point	point	NOUN
ijassa-1131	69	32	x̄	x̄	PRON
ijassa-1131	69	33	∈	∈	PROPN
ijassa-1131	69	34	bn(r	bn(r	NOUN
ijassa-1131	69	35	)	)	PUNCT
ijassa-1131	69	36	such	such	ADJ
ijassa-1131	69	37	that	that	SCONJ
ijassa-1131	69	38	x̄	x̄	NOUN
ijassa-1131	69	39	=	=	PUNCT
ijassa-1131	69	40	g(x̄	g(x̄	NOUN
ijassa-1131	69	41	)	)	PUNCT
ijassa-1131	69	42	.	.	PUNCT
ijassa-1131	70	1	we	we	PRON
ijassa-1131	70	2	have	have	VERB
ijassa-1131	70	3	f(x̄	f(x̄	NOUN
ijassa-1131	70	4	,	,	PUNCT
ijassa-1131	70	5	x̄	x̄	NOUN
ijassa-1131	70	6	)	)	PUNCT
ijassa-1131	70	7	=	=	SYM
ijassa-1131	70	8	f(g(x̄	f(g(x̄	NOUN
ijassa-1131	70	9	)	)	PUNCT
ijassa-1131	70	10	,	,	PUNCT
ijassa-1131	70	11	x̄	x̄	X
ijassa-1131	70	12	)	)	PUNCT
ijassa-1131	71	1	=	=	PUNCT
ijassa-1131	71	2	0	0	X
ijassa-1131	71	3	.	.	PUNCT
ijassa-1131	72	1	so	so	ADV
ijassa-1131	72	2	,	,	PUNCT
ijassa-1131	72	3	the	the	DET
ijassa-1131	72	4	point	point	NOUN
ijassa-1131	72	5	x̄	x̄	PRON
ijassa-1131	72	6	is	be	AUX
ijassa-1131	72	7	the	the	DET
ijassa-1131	72	8	desired	desire	VERB
ijassa-1131	72	9	one	one	NUM
ijassa-1131	72	10	.	.	PUNCT
ijassa-1131	73	1	let	let	VERB
ijassa-1131	73	2	us	we	PRON
ijassa-1131	73	3	derive	derive	VERB
ijassa-1131	73	4	a	a	DET
ijassa-1131	73	5	stronger	strong	ADJ
ijassa-1131	73	6	but	but	CCONJ
ijassa-1131	73	7	simpler	simple	ADJ
ijassa-1131	73	8	solvability	solvability	NOUN
ijassa-1131	73	9	condition	condition	NOUN
ijassa-1131	73	10	for	for	ADP
ijassa-1131	73	11	the	the	DET
ijassa-1131	73	12	equation	equation	NOUN
ijassa-1131	73	13	(	(	PUNCT
ijassa-1131	73	14	1.1	1.1	NUM
ijassa-1131	73	15	)	)	PUNCT
ijassa-1131	73	16	.	.	PUNCT
ijassa-1131	74	1	corollary	corollary	ADJ
ijassa-1131	74	2	3.1	3.1	NUM
ijassa-1131	74	3	:	:	PUNCT
ijassa-1131	74	4	let	let	VERB
ijassa-1131	74	5	the	the	DET
ijassa-1131	74	6	assumption	assumption	NOUN
ijassa-1131	74	7	(	(	PUNCT
ijassa-1131	74	8	a	a	X
ijassa-1131	74	9	)	)	PUNCT
ijassa-1131	74	10	hold	hold	NOUN
ijassa-1131	74	11	.	.	PUNCT
ijassa-1131	75	1	if	if	SCONJ
ijassa-1131	75	2	there	there	PRON
ijassa-1131	75	3	exist	exist	VERB
ijassa-1131	75	4	ᾱ	ᾱ	NOUN
ijassa-1131	75	5	>	>	SYM
ijassa-1131	75	6	0	0	NUM
ijassa-1131	76	1	and	and	CCONJ
ijassa-1131	76	2	β̄	β̄	NUM
ijassa-1131	76	3	≥	≥	NUM
ijassa-1131	76	4	0	0	NUM
ijassa-1131	77	1	such	such	ADJ
ijassa-1131	77	2	that	that	DET
ijassa-1131	77	3	β̄	β̄	NOUN
ijassa-1131	77	4	<	<	X
ijassa-1131	77	5	ᾱ	ᾱ	NOUN
ijassa-1131	77	6	≤	≤	PROPN
ijassa-1131	77	7	cov	cov	NOUN
ijassa-1131	77	8	∂f	∂f	PROPN
ijassa-1131	77	9	∂x	∂x	PROPN
ijassa-1131	77	10	(	(	PUNCT
ijassa-1131	77	11	x1	x1	PROPN
ijassa-1131	77	12	,	,	PUNCT
ijassa-1131	77	13	x2	x2	PROPN
ijassa-1131	77	14	)	)	PUNCT
ijassa-1131	77	15	∀x1	∀x1	ADP
ijassa-1131	77	16	∈	∈	PROPN
ijassa-1131	77	17	rn	rn	PROPN
ijassa-1131	77	18	,	,	PUNCT
ijassa-1131	77	19	∀x2	∀x2	NOUN
ijassa-1131	77	20	∈	∈	PROPN
ijassa-1131	77	21	rn	rn	PROPN
ijassa-1131	77	22	,	,	PUNCT
ijassa-1131	77	23	|f(0	|f(0	PROPN
ijassa-1131	77	24	,	,	PUNCT
ijassa-1131	77	25	x2)|	x2)|	PROPN
ijassa-1131	77	26	≤	≤	NUM
ijassa-1131	77	27	|f(0	|f(0	NOUN
ijassa-1131	77	28	,	,	PUNCT
ijassa-1131	77	29	0)|+	0)|+	NUM
ijassa-1131	77	30	β̄|x2|	β̄|x2|	NUM
ijassa-1131	77	31	∀x2	∀x2	PROPN
ijassa-1131	77	32	∈	∈	PROPN
ijassa-1131	77	33	rn	rn	PROPN
ijassa-1131	77	34	,	,	PUNCT
ijassa-1131	77	35	then	then	ADV
ijassa-1131	77	36	there	there	PRON
ijassa-1131	77	37	exists	exist	VERB
ijassa-1131	77	38	a	a	DET
ijassa-1131	77	39	point	point	NOUN
ijassa-1131	77	40	x̄	x̄	PRON
ijassa-1131	77	41	∈	∈	PROPN
ijassa-1131	78	1	rn	rn	PROPN
ijassa-1131	78	2	such	such	ADJ
ijassa-1131	79	1	that	that	SCONJ
ijassa-1131	79	2	f(x̄	f(x̄	NOUN
ijassa-1131	79	3	,	,	PUNCT
ijassa-1131	79	4	x̄	x̄	NOUN
ijassa-1131	79	5	)	)	PUNCT
ijassa-1131	79	6	=	=	SYM
ijassa-1131	79	7	0	0	NUM
ijassa-1131	79	8	,	,	PUNCT
ijassa-1131	79	9	|x̄|	|x̄|	PROPN
ijassa-1131	79	10	≤	≤	NUM
ijassa-1131	79	11	|f(0	|f(0	NOUN
ijassa-1131	79	12	,	,	PUNCT
ijassa-1131	79	13	0)|	0)|	NOUN
ijassa-1131	79	14	ᾱ−	ᾱ−	NOUN
ijassa-1131	79	15	β̄	β̄	NOUN
ijassa-1131	79	16	.	.	PUNCT
ijassa-1131	80	1	(	(	PUNCT
ijassa-1131	80	2	3.4	3.4	NUM
ijassa-1131	80	3	)	)	PUNCT
ijassa-1131	80	4	proof	proof	NOUN
ijassa-1131	80	5	we	we	PRON
ijassa-1131	80	6	have	have	VERB
ijassa-1131	80	7	a(t	a(t	NOUN
ijassa-1131	80	8	,	,	PUNCT
ijassa-1131	80	9	r	r	NOUN
ijassa-1131	80	10	)	)	PUNCT
ijassa-1131	80	11	≥	≥	NOUN
ijassa-1131	80	12	ᾱ	ᾱ	NOUN
ijassa-1131	80	13	,	,	PUNCT
ijassa-1131	80	14	b(r	b(r	PROPN
ijassa-1131	80	15	)	)	PUNCT
ijassa-1131	80	16	≤	≤	NUM
ijassa-1131	80	17	|f(0	|f(0	NOUN
ijassa-1131	80	18	,	,	PUNCT
ijassa-1131	80	19	0)|+	0)|+	PUNCT
ijassa-1131	80	20	β̄r	β̄r	VERB
ijassa-1131	80	21	∀	∀	X
ijassa-1131	80	22	t	t	X
ijassa-1131	80	23	>	>	X
ijassa-1131	80	24	0	0	NUM
ijassa-1131	80	25	,	,	PUNCT
ijassa-1131	80	26	∀	∀	X
ijassa-1131	80	27	r	r	NOUN
ijassa-1131	80	28	≥	≥	NOUN
ijassa-1131	80	29	0	0	NUM
ijassa-1131	80	30	.	.	PUNCT
ijassa-1131	81	1	take	take	VERB
ijassa-1131	81	2	rj	rj	NOUN
ijassa-1131	81	3	:	:	PUNCT
ijassa-1131	81	4	=	=	SYM
ijassa-1131	81	5	|f(0	|f(0	ADJ
ijassa-1131	81	6	,	,	PUNCT
ijassa-1131	81	7	0)|	0)|	NOUN
ijassa-1131	81	8	ᾱ−	ᾱ−	NOUN
ijassa-1131	81	9	β̄	β̄	NOUN
ijassa-1131	82	1	+	+	SYM
ijassa-1131	82	2	1	1	NUM
ijassa-1131	82	3	j	j	PROPN
ijassa-1131	82	4	,	,	PUNCT
ijassa-1131	82	5	j	j	PROPN
ijassa-1131	82	6	=	=	SYM
ijassa-1131	82	7	1	1	NUM
ijassa-1131	82	8	,	,	PUNCT
ijassa-1131	82	9	2	2	NUM
ijassa-1131	82	10	,	,	PUNCT
ijassa-1131	82	11	...	...	PUNCT
ijassa-1131	82	12	.	.	PUNCT
ijassa-1131	83	1	by	by	ADP
ijassa-1131	83	2	construction	construction	NOUN
ijassa-1131	83	3	we	we	PRON
ijassa-1131	83	4	have	have	VERB
ijassa-1131	83	5	b(rj	b(rj	NOUN
ijassa-1131	83	6	)	)	PUNCT
ijassa-1131	83	7	≤	≤	NUM
ijassa-1131	83	8	|f(0	|f(0	NOUN
ijassa-1131	83	9	,	,	PUNCT
ijassa-1131	83	10	0)|+	0)|+	NUM
ijassa-1131	83	11	β̄	β̄	NOUN
ijassa-1131	83	12	|f(0	|f(0	X
ijassa-1131	83	13	,	,	PUNCT
ijassa-1131	83	14	0)|	0)|	NOUN
ijassa-1131	83	15	ᾱ−	ᾱ−	NOUN
ijassa-1131	83	16	β̄	β̄	NOUN
ijassa-1131	84	1	+	+	NUM
ijassa-1131	84	2	β̄	β̄	ADJ
ijassa-1131	84	3	j	j	PROPN
ijassa-1131	84	4	<	<	X
ijassa-1131	84	5	ᾱ	ᾱ	NOUN
ijassa-1131	84	6	(	(	PUNCT
ijassa-1131	84	7	|f(0	|f(0	ADJ
ijassa-1131	84	8	,	,	PUNCT
ijassa-1131	84	9	0)|	0)|	NOUN
ijassa-1131	84	10	ᾱ−	ᾱ−	NOUN
ijassa-1131	84	11	β̄	β̄	NOUN
ijassa-1131	85	1	+	+	SYM
ijassa-1131	85	2	1	1	NUM
ijassa-1131	85	3	j	j	NOUN
ijassa-1131	85	4	)	)	PUNCT
ijassa-1131	86	1	=	=	SYM
ijassa-1131	86	2	rj∫	rj∫	NOUN
ijassa-1131	86	3	0	0	NUM
ijassa-1131	86	4	a(t	a(t	PROPN
ijassa-1131	86	5	,	,	PUNCT
ijassa-1131	86	6	rj	rj	PROPN
ijassa-1131	86	7	)	)	PUNCT
ijassa-1131	86	8	dt	dt	PROPN
ijassa-1131	86	9	.	.	PUNCT
ijassa-1131	87	1	therefore	therefore	ADV
ijassa-1131	87	2	,	,	PUNCT
ijassa-1131	87	3	theorem	theorem	VERB
ijassa-1131	87	4	3.1	3.1	NUM
ijassa-1131	87	5	implies	imply	VERB
ijassa-1131	87	6	that	that	SCONJ
ijassa-1131	87	7	there	there	PRON
ijassa-1131	87	8	exists	exist	VERB
ijassa-1131	87	9	a	a	DET
ijassa-1131	87	10	point	point	NOUN
ijassa-1131	87	11	x̄j	x̄j	PROPN
ijassa-1131	87	12	∈	∈	PROPN
ijassa-1131	87	13	bn(rj	bn(rj	PROPN
ijassa-1131	87	14	)	)	PUNCT
ijassa-1131	87	15	such	such	ADJ
ijassa-1131	87	16	that	that	SCONJ
ijassa-1131	87	17	f(x̄j	f(x̄j	PROPN
ijassa-1131	87	18	,	,	PUNCT
ijassa-1131	87	19	x̄j	x̄j	PROPN
ijassa-1131	87	20	)	)	PUNCT
ijassa-1131	87	21	=	=	SYM
ijassa-1131	87	22	0	0	NUM
ijassa-1131	87	23	for	for	ADP
ijassa-1131	87	24	every	every	DET
ijassa-1131	87	25	j	j	NOUN
ijassa-1131	87	26	=	=	SYM
ijassa-1131	87	27	1	1	NUM
ijassa-1131	87	28	,	,	PUNCT
ijassa-1131	87	29	2	2	NUM
ijassa-1131	87	30	,	,	PUNCT
ijassa-1131	87	31	...	...	PUNCT
ijassa-1131	87	32	.	.	PUNCT
ijassa-1131	88	1	by	by	ADP
ijassa-1131	88	2	virtue	virtue	NOUN
ijassa-1131	88	3	of	of	ADP
ijassa-1131	88	4	the	the	DET
ijassa-1131	88	5	compactness	compactness	NOUN
ijassa-1131	88	6	of	of	ADP
ijassa-1131	88	7	bn(r1	bn(r1	NOUN
ijassa-1131	88	8	)	)	PUNCT
ijassa-1131	88	9	there	there	PRON
ijassa-1131	88	10	exists	exist	VERB
ijassa-1131	88	11	a	a	DET
ijassa-1131	88	12	subsequence	subsequence	NOUN
ijassa-1131	88	13	{	{	PUNCT
ijassa-1131	88	14	x̄ji	x̄ji	NOUN
ijassa-1131	88	15	}	}	PUNCT
ijassa-1131	88	16	of	of	ADP
ijassa-1131	88	17	the	the	DET
ijassa-1131	88	18	sequence	sequence	NOUN
ijassa-1131	88	19	{	{	PUNCT
ijassa-1131	88	20	x̄j	x̄j	NOUN
ijassa-1131	88	21	}	}	PUNCT
ijassa-1131	88	22	which	which	PRON
ijassa-1131	88	23	converges	converge	VERB
ijassa-1131	88	24	to	to	ADP
ijassa-1131	88	25	a	a	DET
ijassa-1131	88	26	point	point	NOUN
ijassa-1131	88	27	x̄.	x̄.	PUNCT
ijassa-1131	88	28	obviously	obviously	ADV
ijassa-1131	88	29	,	,	PUNCT
ijassa-1131	88	30	the	the	DET
ijassa-1131	88	31	point	point	NOUN
ijassa-1131	88	32	x̄	x̄	PRON
ijassa-1131	88	33	satisfies	satisfy	VERB
ijassa-1131	88	34	the	the	DET
ijassa-1131	88	35	inequality	inequality	NOUN
ijassa-1131	88	36	in	in	ADP
ijassa-1131	88	37	(	(	PUNCT
ijassa-1131	88	38	3.4	3.4	NUM
ijassa-1131	88	39	)	)	PUNCT
ijassa-1131	88	40	.	.	PUNCT
ijassa-1131	89	1	passing	pass	VERB
ijassa-1131	89	2	to	to	ADP
ijassa-1131	89	3	the	the	DET
ijassa-1131	89	4	limit	limit	NOUN
ijassa-1131	89	5	in	in	ADP
ijassa-1131	89	6	the	the	DET
ijassa-1131	89	7	equalities	equality	NOUN
ijassa-1131	89	8	f(x̄ji	f(x̄ji	PROPN
ijassa-1131	89	9	,	,	PUNCT
ijassa-1131	89	10	x̄ji	x̄ji	PROPN
ijassa-1131	89	11	)	)	PUNCT
ijassa-1131	90	1	=	=	SYM
ijassa-1131	90	2	0	0	PUNCT
ijassa-1131	91	1	as	as	SCONJ
ijassa-1131	91	2	i	i	PROPN
ijassa-1131	91	3	to∞	to∞	PROPN
ijassa-1131	91	4	we	we	PRON
ijassa-1131	91	5	obtain	obtain	VERB
ijassa-1131	91	6	that	that	SCONJ
ijassa-1131	91	7	f(x̄	f(x̄	NOUN
ijassa-1131	91	8	,	,	PUNCT
ijassa-1131	91	9	x̄	x̄	NOUN
ijassa-1131	91	10	)	)	PUNCT
ijassa-1131	92	1	=	=	PUNCT
ijassa-1131	92	2	0	0	X
ijassa-1131	92	3	.	.	NOUN
ijassa-1131	92	4	4	4	NUM
ijassa-1131	92	5	.	.	X
ijassa-1131	92	6	solvability	solvability	NOUN
ijassa-1131	92	7	condition	condition	NOUN
ijassa-1131	92	8	for	for	ADP
ijassa-1131	92	9	systems	system	NOUN
ijassa-1131	92	10	of	of	ADP
ijassa-1131	92	11	equations	equation	NOUN
ijassa-1131	92	12	consider	consider	VERB
ijassa-1131	92	13	now	now	ADV
ijassa-1131	92	14	the	the	DET
ijassa-1131	92	15	following	follow	VERB
ijassa-1131	92	16	system	system	NOUN
ijassa-1131	92	17	{	{	PUNCT
ijassa-1131	92	18	f1(x1	f1(x1	NOUN
ijassa-1131	92	19	,	,	PUNCT
ijassa-1131	92	20	x2	x2	PROPN
ijassa-1131	92	21	)	)	PUNCT
ijassa-1131	92	22	=	=	SYM
ijassa-1131	92	23	0	0	NUM
ijassa-1131	92	24	,	,	PUNCT
ijassa-1131	92	25	f2(x1	f2(x1	X
ijassa-1131	92	26	,	,	PUNCT
ijassa-1131	92	27	x2	x2	PROPN
ijassa-1131	92	28	)	)	PUNCT
ijassa-1131	92	29	=	=	SYM
ijassa-1131	93	1	0	0	X
ijassa-1131	93	2	.	.	PUNCT
ijassa-1131	94	1	(	(	PUNCT
ijassa-1131	94	2	4.5	4.5	NUM
ijassa-1131	94	3	)	)	PUNCT
ijassa-1131	94	4	here	here	ADV
ijassa-1131	94	5	f1	f1	NOUN
ijassa-1131	94	6	,	,	PUNCT
ijassa-1131	94	7	f2	f2	PROPN
ijassa-1131	94	8	:	:	PUNCT
ijassa-1131	94	9	rn	rn	PROPN
ijassa-1131	94	10	×	×	PROPN
ijassa-1131	94	11	rn	rn	PROPN
ijassa-1131	94	12	→	→	PROPN
ijassa-1131	94	13	rk	rk	NOUN
ijassa-1131	94	14	are	be	AUX
ijassa-1131	94	15	given	give	VERB
ijassa-1131	94	16	mappings	mapping	NOUN
ijassa-1131	94	17	.	.	PUNCT
ijassa-1131	95	1	let	let	VERB
ijassa-1131	95	2	us	we	PRON
ijassa-1131	95	3	derive	derive	VERB
ijassa-1131	95	4	solvability	solvability	NOUN
ijassa-1131	95	5	conditions	condition	NOUN
ijassa-1131	95	6	for	for	ADP
ijassa-1131	95	7	the	the	DET
ijassa-1131	95	8	system	system	NOUN
ijassa-1131	95	9	(	(	PUNCT
ijassa-1131	95	10	4.5	4.5	NUM
ijassa-1131	95	11	)	)	PUNCT
ijassa-1131	95	12	analogous	analogous	ADJ
ijassa-1131	95	13	to	to	ADP
ijassa-1131	95	14	those	those	PRON
ijassa-1131	95	15	in	in	ADP
ijassa-1131	95	16	section	section	NOUN
ijassa-1131	95	17	3	3	NUM
ijassa-1131	95	18	.	.	PUNCT
ijassa-1131	96	1	copyright	copyright	NOUN
ijassa-1131	96	2	©	©	PROPN
ijassa-1131	96	3	2021	2021	NUM
ijassa-1131	96	4	assa	assa	NOUN
ijassa-1131	96	5	.	.	PUNCT
ijassa-1131	97	1	adv	adv	PROPN
ijassa-1131	97	2	syst	syst	PROPN
ijassa-1131	97	3	sci	sci	PROPN
ijassa-1131	97	4	appl	appl	PROPN
ijassa-1131	97	5	(	(	PUNCT
ijassa-1131	97	6	2021	2021	NUM
ijassa-1131	97	7	)	)	PUNCT
ijassa-1131	97	8	solvability	solvability	NOUN
ijassa-1131	97	9	of	of	ADP
ijassa-1131	97	10	equations	equation	NOUN
ijassa-1131	97	11	defined	define	VERB
ijassa-1131	97	12	by	by	ADP
ijassa-1131	97	13	continuous	continuous	ADJ
ijassa-1131	97	14	and	and	CCONJ
ijassa-1131	97	15	smooth	smooth	ADJ
ijassa-1131	97	16	mappings	mapping	NOUN
ijassa-1131	97	17	117	117	NUM
ijassa-1131	97	18	assume	assume	VERB
ijassa-1131	97	19	that	that	SCONJ
ijassa-1131	97	20	f1	f1	NOUN
ijassa-1131	97	21	is	be	AUX
ijassa-1131	97	22	differentiable	differentiable	ADJ
ijassa-1131	97	23	in	in	ADP
ijassa-1131	97	24	x1	x1	PROPN
ijassa-1131	97	25	and	and	CCONJ
ijassa-1131	97	26	f2	f2	PROPN
ijassa-1131	97	27	is	be	AUX
ijassa-1131	97	28	differentiable	differentiable	ADJ
ijassa-1131	97	29	in	in	ADP
ijassa-1131	97	30	x2	x2	PROPN
ijassa-1131	97	31	.	.	PUNCT
ijassa-1131	98	1	given	give	VERB
ijassa-1131	98	2	numbers	number	NOUN
ijassa-1131	98	3	r̄1	r̄1	VERB
ijassa-1131	98	4	>	>	X
ijassa-1131	98	5	0	0	PUNCT
ijassa-1131	99	1	and	and	CCONJ
ijassa-1131	99	2	r̄2	r̄2	ADJ
ijassa-1131	99	3	>	>	X
ijassa-1131	99	4	0	0	NUM
ijassa-1131	99	5	,	,	PUNCT
ijassa-1131	99	6	denote	denote	VERB
ijassa-1131	99	7	a1	a1	NOUN
ijassa-1131	99	8	:	:	PUNCT
ijassa-1131	99	9	=	=	SYM
ijassa-1131	99	10	inf	inf	PROPN
ijassa-1131	99	11	{	{	PUNCT
ijassa-1131	99	12	cov	cov	NOUN
ijassa-1131	99	13	∂f1	∂f1	PROPN
ijassa-1131	99	14	∂x1	∂x1	PROPN
ijassa-1131	99	15	(	(	PUNCT
ijassa-1131	99	16	x1	x1	PROPN
ijassa-1131	99	17	,	,	PUNCT
ijassa-1131	99	18	x2	x2	PROPN
ijassa-1131	99	19	)	)	PUNCT
ijassa-1131	99	20	:	:	PUNCT
ijassa-1131	100	1	x1	x1	PROPN
ijassa-1131	100	2	∈	∈	PROPN
ijassa-1131	100	3	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	100	4	)	)	PUNCT
ijassa-1131	100	5	,	,	PUNCT
ijassa-1131	100	6	x2	x2	PROPN
ijassa-1131	100	7	∈	∈	PROPN
ijassa-1131	100	8	bn(r̄2	bn(r̄2	NOUN
ijassa-1131	100	9	)	)	PUNCT
ijassa-1131	100	10	}	}	PUNCT
ijassa-1131	100	11	,	,	PUNCT
ijassa-1131	100	12	b1	b1	NOUN
ijassa-1131	100	13	:	:	PUNCT
ijassa-1131	100	14	=	=	NOUN
ijassa-1131	100	15	sup	sup	NOUN
ijassa-1131	100	16	x2∈bn(r̄2	x2∈bn(r̄2	NOUN
ijassa-1131	100	17	)	)	PUNCT
ijassa-1131	100	18	|f1(0	|f1(0	PROPN
ijassa-1131	100	19	,	,	PUNCT
ijassa-1131	100	20	x2)|	x2)|	PROPN
ijassa-1131	100	21	,	,	PUNCT
ijassa-1131	100	22	a2	a2	PROPN
ijassa-1131	100	23	:	:	PUNCT
ijassa-1131	100	24	=	=	SYM
ijassa-1131	100	25	inf	inf	PROPN
ijassa-1131	100	26	{	{	PUNCT
ijassa-1131	100	27	cov	cov	NOUN
ijassa-1131	100	28	∂f1	∂f1	PROPN
ijassa-1131	100	29	∂x1	∂x1	PROPN
ijassa-1131	100	30	(	(	PUNCT
ijassa-1131	100	31	x1	x1	PROPN
ijassa-1131	100	32	,	,	PUNCT
ijassa-1131	100	33	x2	x2	PROPN
ijassa-1131	100	34	)	)	PUNCT
ijassa-1131	100	35	:	:	PUNCT
ijassa-1131	101	1	x1	x1	PROPN
ijassa-1131	101	2	∈	∈	PROPN
ijassa-1131	101	3	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	101	4	)	)	PUNCT
ijassa-1131	101	5	,	,	PUNCT
ijassa-1131	101	6	x2	x2	PROPN
ijassa-1131	101	7	∈	∈	PROPN
ijassa-1131	101	8	bn(r̄2	bn(r̄2	NOUN
ijassa-1131	101	9	)	)	PUNCT
ijassa-1131	101	10	}	}	PUNCT
ijassa-1131	101	11	,	,	PUNCT
ijassa-1131	101	12	b2	b2	NOUN
ijassa-1131	101	13	:	:	PUNCT
ijassa-1131	101	14	=	=	NUM
ijassa-1131	101	15	sup	sup	NOUN
ijassa-1131	101	16	x1∈bn(r̄1	x1∈bn(r̄1	NOUN
ijassa-1131	101	17	)	)	PUNCT
ijassa-1131	102	1	|f2(x1	|f2(x1	NOUN
ijassa-1131	102	2	,	,	PUNCT
ijassa-1131	102	3	0)|	0)|	NOUN
ijassa-1131	102	4	.	.	PUNCT
ijassa-1131	102	5	theorem	theorem	VERB
ijassa-1131	102	6	4.1	4.1	NUM
ijassa-1131	102	7	:	:	PUNCT
ijassa-1131	102	8	assume	assume	VERB
ijassa-1131	102	9	that	that	SCONJ
ijassa-1131	102	10	mappings	mapping	NOUN
ijassa-1131	102	11	f1	f1	NOUN
ijassa-1131	102	12	(	(	PUNCT
ijassa-1131	102	13	·	·	PUNCT
ijassa-1131	102	14	,	,	PUNCT
ijassa-1131	102	15	·	·	PUNCT
ijassa-1131	102	16	)	)	PUNCT
ijassa-1131	102	17	and	and	CCONJ
ijassa-1131	102	18	f2	f2	PROPN
ijassa-1131	102	19	(	(	PUNCT
ijassa-1131	102	20	·	·	PUNCT
ijassa-1131	102	21	,	,	PUNCT
ijassa-1131	102	22	·	·	PUNCT
ijassa-1131	102	23	)	)	PUNCT
ijassa-1131	102	24	are	be	AUX
ijassa-1131	102	25	continuous	continuous	ADJ
ijassa-1131	102	26	on	on	ADP
ijassa-1131	102	27	rn	rn	PROPN
ijassa-1131	102	28	×	×	PROPN
ijassa-1131	102	29	rn	rn	PROPN
ijassa-1131	102	30	,	,	PUNCT
ijassa-1131	102	31	for	for	ADP
ijassa-1131	102	32	every	every	DET
ijassa-1131	102	33	x1	x1	PROPN
ijassa-1131	102	34	,	,	PUNCT
ijassa-1131	102	35	x2	x2	PROPN
ijassa-1131	102	36	∈	∈	PROPN
ijassa-1131	102	37	rn	rn	PROPN
ijassa-1131	102	38	the	the	DET
ijassa-1131	102	39	mappings	mapping	NOUN
ijassa-1131	102	40	f1	f1	NOUN
ijassa-1131	102	41	(	(	PUNCT
ijassa-1131	102	42	·	·	PUNCT
ijassa-1131	102	43	,	,	PUNCT
ijassa-1131	102	44	x2	x2	PROPN
ijassa-1131	102	45	)	)	PUNCT
ijassa-1131	102	46	,	,	PUNCT
ijassa-1131	102	47	f2(x1	f2(x1	NOUN
ijassa-1131	102	48	,	,	PUNCT
ijassa-1131	102	49	·	·	PUNCT
ijassa-1131	102	50	)	)	PUNCT
ijassa-1131	102	51	:	:	PUNCT
ijassa-1131	103	1	rn	rn	PROPN
ijassa-1131	103	2	→	→	SYM
ijassa-1131	103	3	rk	rk	NOUN
ijassa-1131	103	4	are	be	AUX
ijassa-1131	103	5	differentiable	differentiable	ADJ
ijassa-1131	103	6	on	on	ADP
ijassa-1131	103	7	rn	rn	PROPN
ijassa-1131	103	8	,	,	PUNCT
ijassa-1131	103	9	the	the	DET
ijassa-1131	103	10	mappings	mapping	NOUN
ijassa-1131	103	11	∂f1	∂f1	PRON
ijassa-1131	103	12	∂x1	∂x1	NOUN
ijassa-1131	103	13	(	(	PUNCT
ijassa-1131	103	14	·	·	PUNCT
ijassa-1131	103	15	,	,	PUNCT
ijassa-1131	103	16	·	·	PUNCT
ijassa-1131	103	17	)	)	PUNCT
ijassa-1131	103	18	and	and	CCONJ
ijassa-1131	103	19	∂f2	∂f2	NOUN
ijassa-1131	103	20	∂x2	∂x2	NOUN
ijassa-1131	103	21	(	(	PUNCT
ijassa-1131	103	22	·	·	PUNCT
ijassa-1131	103	23	,	,	PUNCT
ijassa-1131	103	24	·	·	PUNCT
ijassa-1131	103	25	)	)	PUNCT
ijassa-1131	103	26	are	be	AUX
ijassa-1131	103	27	continuous	continuous	ADJ
ijassa-1131	103	28	on	on	ADP
ijassa-1131	103	29	rn	rn	PROPN
ijassa-1131	103	30	×	×	PROPN
ijassa-1131	103	31	rn	rn	PROPN
ijassa-1131	103	32	.	.	PROPN
ijassa-1131	104	1	if	if	SCONJ
ijassa-1131	104	2	b1	b1	NOUN
ijassa-1131	104	3	<	<	X
ijassa-1131	104	4	a1r̄1	a1r̄1	PROPN
ijassa-1131	104	5	,	,	PUNCT
ijassa-1131	104	6	b2	b2	NOUN
ijassa-1131	104	7	<	<	X
ijassa-1131	104	8	a2r̄2	a2r̄2	PROPN
ijassa-1131	104	9	,	,	PUNCT
ijassa-1131	104	10	(	(	PUNCT
ijassa-1131	104	11	4.6	4.6	NUM
ijassa-1131	104	12	)	)	PUNCT
ijassa-1131	104	13	then	then	ADV
ijassa-1131	104	14	there	there	PRON
ijassa-1131	104	15	exists	exist	VERB
ijassa-1131	104	16	a	a	DET
ijassa-1131	104	17	solution	solution	NOUN
ijassa-1131	104	18	(	(	PUNCT
ijassa-1131	104	19	x̄1	x̄1	PROPN
ijassa-1131	104	20	,	,	PUNCT
ijassa-1131	104	21	x̄2	x̄2	PROPN
ijassa-1131	104	22	)	)	PUNCT
ijassa-1131	104	23	∈	∈	PROPN
ijassa-1131	104	24	bn(r̄1)×bn(r̄2	bn(r̄1)×bn(r̄2	PROPN
ijassa-1131	104	25	)	)	PUNCT
ijassa-1131	104	26	to	to	ADP
ijassa-1131	104	27	the	the	DET
ijassa-1131	104	28	system	system	NOUN
ijassa-1131	104	29	(	(	PUNCT
ijassa-1131	104	30	4.5	4.5	NUM
ijassa-1131	104	31	)	)	PUNCT
ijassa-1131	104	32	,	,	PUNCT
ijassa-1131	104	33	i.e.	i.e.	X
ijassa-1131	104	34	{	{	PUNCT
ijassa-1131	104	35	f1(x̄1	f1(x̄1	NOUN
ijassa-1131	104	36	,	,	PUNCT
ijassa-1131	104	37	x̄2	x̄2	X
ijassa-1131	104	38	)	)	PUNCT
ijassa-1131	104	39	=	=	SYM
ijassa-1131	104	40	0	0	NUM
ijassa-1131	104	41	,	,	PUNCT
ijassa-1131	104	42	f2(x̄1	f2(x̄1	NOUN
ijassa-1131	104	43	,	,	PUNCT
ijassa-1131	104	44	x̄2	x̄2	X
ijassa-1131	104	45	)	)	PUNCT
ijassa-1131	105	1	=	=	SYM
ijassa-1131	105	2	0	0	X
ijassa-1131	105	3	.	.	PUNCT
ijassa-1131	106	1	proof	proof	NOUN
ijassa-1131	106	2	take	take	VERB
ijassa-1131	106	3	ε	ε	PROPN
ijassa-1131	106	4	>	>	X
ijassa-1131	106	5	0	0	NUM
ijassa-1131	107	1	such	such	ADJ
ijassa-1131	107	2	that	that	SCONJ
ijassa-1131	107	3	(	(	PUNCT
ijassa-1131	107	4	1	1	NUM
ijassa-1131	107	5	+	+	CCONJ
ijassa-1131	107	6	ε)b1	ε)b1	PROPN
ijassa-1131	107	7	a1	a1	NOUN
ijassa-1131	107	8	≤	≤	ADJ
ijassa-1131	107	9	r̄1	r̄1	NOUN
ijassa-1131	107	10	,	,	PUNCT
ijassa-1131	107	11	(	(	PUNCT
ijassa-1131	107	12	1	1	NUM
ijassa-1131	107	13	+	+	NUM
ijassa-1131	107	14	ε)b2	ε)b2	PROPN
ijassa-1131	107	15	a2	a2	PROPN
ijassa-1131	107	16	≤	≤	NOUN
ijassa-1131	107	17	r̄2	r̄2	NOUN
ijassa-1131	107	18	.	.	PUNCT
ijassa-1131	108	1	the	the	DET
ijassa-1131	108	2	existence	existence	NOUN
ijassa-1131	108	3	of	of	ADP
ijassa-1131	108	4	such	such	ADJ
ijassa-1131	108	5	number	number	NOUN
ijassa-1131	108	6	ε	ε	PROPN
ijassa-1131	108	7	follows	follow	VERB
ijassa-1131	108	8	from	from	ADP
ijassa-1131	108	9	the	the	DET
ijassa-1131	108	10	assumption	assumption	NOUN
ijassa-1131	108	11	(	(	PUNCT
ijassa-1131	108	12	4.6	4.6	NUM
ijassa-1131	108	13	)	)	PUNCT
ijassa-1131	108	14	.	.	PUNCT
ijassa-1131	109	1	since	since	SCONJ
ijassa-1131	109	2	b1	b1	NOUN
ijassa-1131	109	3	<	<	X
ijassa-1131	109	4	a1r̄1	a1r̄1	PROPN
ijassa-1131	109	5	,	,	PUNCT
ijassa-1131	109	6	applying	apply	VERB
ijassa-1131	109	7	corollary	corollary	NOUN
ijassa-1131	109	8	2.1	2.1	NUM
ijassa-1131	109	9	to	to	ADP
ijassa-1131	109	10	f	f	NOUN
ijassa-1131	109	11	=	=	SYM
ijassa-1131	109	12	f1	f1	PROPN
ijassa-1131	109	13	and	and	CCONJ
ijassa-1131	109	14	σ	σ	NOUN
ijassa-1131	109	15	=	=	PUNCT
ijassa-1131	109	16	bn(r̄2	bn(r̄2	X
ijassa-1131	109	17	)	)	PUNCT
ijassa-1131	109	18	we	we	PRON
ijassa-1131	109	19	obtain	obtain	VERB
ijassa-1131	109	20	that	that	SCONJ
ijassa-1131	109	21	there	there	PRON
ijassa-1131	109	22	exists	exist	VERB
ijassa-1131	109	23	a	a	DET
ijassa-1131	109	24	continuous	continuous	ADJ
ijassa-1131	109	25	mapping	mapping	NOUN
ijassa-1131	109	26	g1	g1	NOUN
ijassa-1131	109	27	:	:	PUNCT
ijassa-1131	109	28	bn(r̄2)→	bn(r̄2)→	PROPN
ijassa-1131	109	29	rn	rn	ADP
ijassa-1131	109	30	such	such	ADJ
ijassa-1131	109	31	that	that	DET
ijassa-1131	109	32	f1(g1(x2	f1(g1(x2	NOUN
ijassa-1131	109	33	)	)	PUNCT
ijassa-1131	109	34	,	,	PUNCT
ijassa-1131	109	35	x2	x2	PROPN
ijassa-1131	109	36	)	)	PUNCT
ijassa-1131	110	1	=	=	SYM
ijassa-1131	110	2	0	0	NUM
ijassa-1131	110	3	∀x2	∀x2	NOUN
ijassa-1131	110	4	∈	∈	PROPN
ijassa-1131	110	5	bn(r̄2	bn(r̄2	NOUN
ijassa-1131	110	6	)	)	PUNCT
ijassa-1131	110	7	,	,	PUNCT
ijassa-1131	110	8	|g1(x2)|	|g1(x2)|	PROPN
ijassa-1131	110	9	≤	≤	X
ijassa-1131	110	10	(	(	PUNCT
ijassa-1131	110	11	1	1	NUM
ijassa-1131	110	12	+	+	CCONJ
ijassa-1131	110	13	ε)|f1(0	ε)|f1(0	PROPN
ijassa-1131	110	14	,	,	PUNCT
ijassa-1131	110	15	x2)|	x2)|	PROPN
ijassa-1131	110	16	a1	a1	NOUN
ijassa-1131	110	17	≤	≤	NOUN
ijassa-1131	110	18	(	(	PUNCT
ijassa-1131	110	19	1	1	NUM
ijassa-1131	110	20	+	+	CCONJ
ijassa-1131	111	1	ε)b1	ε)b1	PROPN
ijassa-1131	111	2	a1	a1	NOUN
ijassa-1131	111	3	≤	≤	NUM
ijassa-1131	111	4	r̄1	r̄1	NOUN
ijassa-1131	111	5	∀x2	∀x2	NOUN
ijassa-1131	111	6	∈	∈	PROPN
ijassa-1131	111	7	bn(r̄2	bn(r̄2	NOUN
ijassa-1131	111	8	)	)	PUNCT
ijassa-1131	111	9	.	.	PUNCT
ijassa-1131	112	1	since	since	SCONJ
ijassa-1131	112	2	b2	b2	NOUN
ijassa-1131	112	3	<	<	X
ijassa-1131	112	4	a2r̄2	a2r̄2	PROPN
ijassa-1131	112	5	,	,	PUNCT
ijassa-1131	112	6	applying	apply	VERB
ijassa-1131	112	7	corollary	corollary	NOUN
ijassa-1131	112	8	2.1	2.1	NUM
ijassa-1131	112	9	to	to	ADP
ijassa-1131	112	10	f	f	PROPN
ijassa-1131	112	11	=	=	PUNCT
ijassa-1131	112	12	f2	f2	PROPN
ijassa-1131	112	13	and	and	CCONJ
ijassa-1131	112	14	σ	σ	NOUN
ijassa-1131	112	15	=	=	SYM
ijassa-1131	112	16	bn(r̄1	bn(r̄1	X
ijassa-1131	112	17	)	)	PUNCT
ijassa-1131	112	18	we	we	PRON
ijassa-1131	112	19	obtain	obtain	VERB
ijassa-1131	112	20	that	that	SCONJ
ijassa-1131	112	21	there	there	PRON
ijassa-1131	112	22	exists	exist	VERB
ijassa-1131	112	23	a	a	DET
ijassa-1131	112	24	continuous	continuous	ADJ
ijassa-1131	112	25	mapping	mapping	NOUN
ijassa-1131	112	26	g2	g2	PROPN
ijassa-1131	112	27	:	:	PUNCT
ijassa-1131	112	28	bn(r̄1)→	bn(r̄1)→	PROPN
ijassa-1131	112	29	rn	rn	PROPN
ijassa-1131	112	30	such	such	ADJ
ijassa-1131	112	31	that	that	SCONJ
ijassa-1131	112	32	f2(g2(x1	f2(g2(x1	NOUN
ijassa-1131	112	33	)	)	PUNCT
ijassa-1131	112	34	,	,	PUNCT
ijassa-1131	112	35	x1	x1	X
ijassa-1131	112	36	)	)	PUNCT
ijassa-1131	112	37	=	=	SYM
ijassa-1131	112	38	0	0	SYM
ijassa-1131	112	39	∀x1	∀x1	NUM
ijassa-1131	112	40	∈	∈	PROPN
ijassa-1131	112	41	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	112	42	)	)	PUNCT
ijassa-1131	112	43	,	,	PUNCT
ijassa-1131	112	44	|g2(x1)|	|g2(x1)|	PROPN
ijassa-1131	112	45	≤	≤	PROPN
ijassa-1131	112	46	(	(	PUNCT
ijassa-1131	112	47	1	1	NUM
ijassa-1131	112	48	+	+	SYM
ijassa-1131	112	49	ε)|f2(x1	ε)|f2(x1	NOUN
ijassa-1131	112	50	,	,	PUNCT
ijassa-1131	112	51	0)|	0)|	NOUN
ijassa-1131	112	52	a1	a1	NOUN
ijassa-1131	112	53	≤	≤	NOUN
ijassa-1131	112	54	(	(	PUNCT
ijassa-1131	112	55	1	1	NUM
ijassa-1131	112	56	+	+	NUM
ijassa-1131	112	57	ε)b2	ε)b2	PROPN
ijassa-1131	112	58	a2	a2	PROPN
ijassa-1131	112	59	≤	≤	PROPN
ijassa-1131	112	60	r̄2	r̄2	PUNCT
ijassa-1131	112	61	∀x1	∀x1	ADP
ijassa-1131	112	62	∈	∈	PROPN
ijassa-1131	112	63	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	112	64	)	)	PUNCT
ijassa-1131	112	65	.	.	PUNCT
ijassa-1131	113	1	consider	consider	VERB
ijassa-1131	113	2	the	the	DET
ijassa-1131	113	3	mapping	mapping	NOUN
ijassa-1131	113	4	g	g	NOUN
ijassa-1131	113	5	:	:	PUNCT
ijassa-1131	113	6	bn(r̄1)→	bn(r̄1)→	PROPN
ijassa-1131	113	7	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	113	8	)	)	PUNCT
ijassa-1131	113	9	,	,	PUNCT
ijassa-1131	113	10	g(x1	g(x1	NOUN
ijassa-1131	113	11	)	)	PUNCT
ijassa-1131	113	12	=	=	SYM
ijassa-1131	113	13	g1(g2(x1	g1(g2(x1	NOUN
ijassa-1131	113	14	)	)	PUNCT
ijassa-1131	113	15	)	)	PUNCT
ijassa-1131	113	16	,	,	PUNCT
ijassa-1131	113	17	x1	x1	PROPN
ijassa-1131	113	18	∈	∈	PROPN
ijassa-1131	113	19	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	113	20	)	)	PUNCT
ijassa-1131	113	21	.	.	PUNCT
ijassa-1131	114	1	this	this	DET
ijassa-1131	114	2	mapping	mapping	NOUN
ijassa-1131	114	3	is	be	AUX
ijassa-1131	114	4	well	well	ADV
ijassa-1131	114	5	-	-	PUNCT
ijassa-1131	114	6	defined	define	VERB
ijassa-1131	114	7	,	,	PUNCT
ijassa-1131	114	8	since	since	SCONJ
ijassa-1131	114	9	the	the	DET
ijassa-1131	114	10	above	above	ADJ
ijassa-1131	114	11	relations	relation	NOUN
ijassa-1131	114	12	imply	imply	VERB
ijassa-1131	114	13	g2(x1	g2(x1	ADJ
ijassa-1131	114	14	)	)	PUNCT
ijassa-1131	114	15	∈	∈	PROPN
ijassa-1131	114	16	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	114	17	)	)	PUNCT
ijassa-1131	114	18	and	and	CCONJ
ijassa-1131	114	19	g1(g2(x1	g1(g2(x1	NUM
ijassa-1131	114	20	)	)	PUNCT
ijassa-1131	114	21	)	)	PUNCT
ijassa-1131	115	1	∈	∈	PROPN
ijassa-1131	115	2	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	115	3	)	)	PUNCT
ijassa-1131	115	4	for	for	ADP
ijassa-1131	115	5	all	all	DET
ijassa-1131	115	6	x1	x1	PROPN
ijassa-1131	115	7	∈	∈	PROPN
ijassa-1131	115	8	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	115	9	)	)	PUNCT
ijassa-1131	115	10	.	.	PUNCT
ijassa-1131	116	1	moreover	moreover	ADV
ijassa-1131	116	2	,	,	PUNCT
ijassa-1131	116	3	g	g	PROPN
ijassa-1131	116	4	is	be	AUX
ijassa-1131	116	5	continuous	continuous	ADJ
ijassa-1131	116	6	since	since	SCONJ
ijassa-1131	116	7	it	it	PRON
ijassa-1131	116	8	is	be	AUX
ijassa-1131	116	9	a	a	DET
ijassa-1131	116	10	composition	composition	NOUN
ijassa-1131	116	11	copyright	copyright	NOUN
ijassa-1131	116	12	©	©	ADP
ijassa-1131	116	13	2021	2021	NUM
ijassa-1131	116	14	assa	assa	NOUN
ijassa-1131	116	15	.	.	PUNCT
ijassa-1131	117	1	adv	adv	PROPN
ijassa-1131	117	2	syst	syst	PROPN
ijassa-1131	117	3	sci	sci	PROPN
ijassa-1131	117	4	appl	appl	PROPN
ijassa-1131	117	5	(	(	PUNCT
ijassa-1131	117	6	2021	2021	NUM
ijassa-1131	117	7	)	)	PUNCT
ijassa-1131	117	8	118	118	NUM
ijassa-1131	117	9	s.e	s.e	PROPN
ijassa-1131	117	10	.	.	PROPN
ijassa-1131	117	11	zhukovskiy	zhukovskiy	NOUN
ijassa-1131	117	12	of	of	ADP
ijassa-1131	117	13	continuous	continuous	ADJ
ijassa-1131	117	14	mappings	mapping	NOUN
ijassa-1131	117	15	g1	g1	NOUN
ijassa-1131	117	16	and	and	CCONJ
ijassa-1131	117	17	g2	g2	PROPN
ijassa-1131	117	18	.	.	PUNCT
ijassa-1131	118	1	therefore	therefore	ADV
ijassa-1131	118	2	,	,	PUNCT
ijassa-1131	118	3	it	it	PRON
ijassa-1131	118	4	follows	follow	VERB
ijassa-1131	118	5	from	from	ADP
ijassa-1131	118	6	brouwer	brouwer	PROPN
ijassa-1131	118	7	’s	’s	PART
ijassa-1131	118	8	fixed	fix	VERB
ijassa-1131	118	9	point	point	NOUN
ijassa-1131	118	10	theorem	theorem	VERB
ijassa-1131	118	11	that	that	SCONJ
ijassa-1131	118	12	there	there	PRON
ijassa-1131	118	13	exists	exist	VERB
ijassa-1131	118	14	a	a	DET
ijassa-1131	118	15	point	point	NOUN
ijassa-1131	118	16	x̄1	x̄1	X
ijassa-1131	118	17	∈	∈	PROPN
ijassa-1131	118	18	bn(r̄1	bn(r̄1	PROPN
ijassa-1131	118	19	)	)	PUNCT
ijassa-1131	118	20	such	such	ADJ
ijassa-1131	118	21	that	that	SCONJ
ijassa-1131	118	22	x̄1	x̄1	X
ijassa-1131	118	23	=	=	SYM
ijassa-1131	118	24	g(x̄1	g(x̄1	NOUN
ijassa-1131	118	25	)	)	PUNCT
ijassa-1131	118	26	.	.	PUNCT
ijassa-1131	119	1	take	take	VERB
ijassa-1131	119	2	x̄2	x̄2	NOUN
ijassa-1131	119	3	:	:	PUNCT
ijassa-1131	119	4	=	=	SYM
ijassa-1131	119	5	g2(x̄1	g2(x̄1	NOUN
ijassa-1131	119	6	)	)	PUNCT
ijassa-1131	119	7	.	.	PUNCT
ijassa-1131	120	1	let	let	VERB
ijassa-1131	120	2	us	we	PRON
ijassa-1131	120	3	show	show	VERB
ijassa-1131	120	4	that	that	SCONJ
ijassa-1131	120	5	(	(	PUNCT
ijassa-1131	120	6	x̄1	x̄1	NOUN
ijassa-1131	120	7	,	,	PUNCT
ijassa-1131	120	8	x̄2	x̄2	PROPN
ijassa-1131	120	9	)	)	PUNCT
ijassa-1131	120	10	is	be	AUX
ijassa-1131	120	11	a	a	DET
ijassa-1131	120	12	desired	desire	VERB
ijassa-1131	120	13	point	point	NOUN
ijassa-1131	120	14	.	.	PUNCT
ijassa-1131	121	1	obviously	obviously	ADV
ijassa-1131	121	2	x̄2	x̄2	X
ijassa-1131	121	3	∈	∈	PROPN
ijassa-1131	121	4	bn(r̄2	bn(r̄2	NOUN
ijassa-1131	121	5	)	)	PUNCT
ijassa-1131	121	6	.	.	PUNCT
ijassa-1131	122	1	moreover	moreover	ADV
ijassa-1131	122	2	,	,	PUNCT
ijassa-1131	122	3	f1(x̄1	f1(x̄1	NOUN
ijassa-1131	122	4	,	,	PUNCT
ijassa-1131	122	5	x̄2	x̄2	X
ijassa-1131	122	6	)	)	PUNCT
ijassa-1131	123	1	=	=	SYM
ijassa-1131	123	2	f1(g(x̄1	f1(g(x̄1	NOUN
ijassa-1131	123	3	)	)	PUNCT
ijassa-1131	123	4	,	,	PUNCT
ijassa-1131	123	5	x̄2	x̄2	X
ijassa-1131	123	6	)	)	PUNCT
ijassa-1131	124	1	=	=	SYM
ijassa-1131	124	2	f1(g1(g2(x̄1	f1(g1(g2(x̄1	NOUN
ijassa-1131	124	3	)	)	PUNCT
ijassa-1131	124	4	)	)	PUNCT
ijassa-1131	124	5	,	,	PUNCT
ijassa-1131	124	6	g2(x̄1	g2(x̄1	NOUN
ijassa-1131	124	7	)	)	PUNCT
ijassa-1131	124	8	)	)	PUNCT
ijassa-1131	125	1	=	=	SYM
ijassa-1131	125	2	0	0	NUM
ijassa-1131	125	3	,	,	PUNCT
ijassa-1131	125	4	f2(x̄1	f2(x̄1	NOUN
ijassa-1131	125	5	,	,	PUNCT
ijassa-1131	125	6	x̄2	x̄2	X
ijassa-1131	125	7	)	)	PUNCT
ijassa-1131	126	1	=	=	SYM
ijassa-1131	126	2	f2(x̄1	f2(x̄1	NOUN
ijassa-1131	126	3	,	,	PUNCT
ijassa-1131	126	4	g2(x̄1	g2(x̄1	NOUN
ijassa-1131	126	5	)	)	PUNCT
ijassa-1131	126	6	)	)	PUNCT
ijassa-1131	127	1	=	=	PUNCT
ijassa-1131	127	2	0	0	X
ijassa-1131	127	3	.	.	PUNCT
ijassa-1131	128	1	so	so	ADV
ijassa-1131	128	2	,	,	PUNCT
ijassa-1131	128	3	(	(	PUNCT
ijassa-1131	128	4	x̄1	x̄1	PROPN
ijassa-1131	128	5	,	,	PUNCT
ijassa-1131	128	6	x̄2	x̄2	PROPN
ijassa-1131	128	7	)	)	PUNCT
ijassa-1131	128	8	is	be	AUX
ijassa-1131	128	9	a	a	DET
ijassa-1131	128	10	desired	desire	VERB
ijassa-1131	128	11	point	point	NOUN
ijassa-1131	128	12	.	.	PUNCT
ijassa-1131	129	1	acknowledgements	acknowledgement	NOUN
ijassa-1131	129	2	the	the	DET
ijassa-1131	129	3	research	research	NOUN
ijassa-1131	129	4	is	be	AUX
ijassa-1131	129	5	supported	support	VERB
ijassa-1131	129	6	by	by	ADP
ijassa-1131	129	7	the	the	DET
ijassa-1131	129	8	grant	grant	NOUN
ijassa-1131	129	9	of	of	ADP
ijassa-1131	129	10	the	the	DET
ijassa-1131	129	11	president	president	NOUN
ijassa-1131	129	12	of	of	ADP
ijassa-1131	129	13	russian	russian	PROPN
ijassa-1131	129	14	federation	federation	PROPN
ijassa-1131	129	15	(	(	PUNCT
ijassa-1131	129	16	project	project	VERB
ijassa-1131	129	17	no	no	DET
ijassa-1131	129	18	md-2658.2021.1.1	md-2658.2021.1.1	NOUN
ijassa-1131	129	19	)	)	PUNCT
ijassa-1131	129	20	and	and	CCONJ
ijassa-1131	129	21	by	by	ADP
ijassa-1131	129	22	the	the	DET
ijassa-1131	129	23	rfbr	rfbr	ADJ
ijassa-1131	129	24	grant	grant	NOUN
ijassa-1131	129	25	(	(	PUNCT
ijassa-1131	129	26	project	project	VERB
ijassa-1131	129	27	no	no	DET
ijassa-1131	129	28	19	19	NUM
ijassa-1131	129	29	-	-	PUNCT
ijassa-1131	129	30	01	01	NUM
ijassa-1131	129	31	-	-	PUNCT
ijassa-1131	129	32	00080	00080	NUM
ijassa-1131	129	33	)	)	PUNCT
ijassa-1131	129	34	.	.	PUNCT
ijassa-1131	130	1	the	the	DET
ijassa-1131	130	2	results	result	NOUN
ijassa-1131	130	3	in	in	ADP
ijassa-1131	130	4	section	section	NOUN
ijassa-1131	130	5	4	4	NUM
ijassa-1131	130	6	were	be	AUX
ijassa-1131	130	7	obtained	obtain	VERB
ijassa-1131	130	8	under	under	ADP
ijassa-1131	130	9	the	the	DET
ijassa-1131	130	10	financial	financial	ADJ
ijassa-1131	130	11	support	support	NOUN
ijassa-1131	130	12	of	of	ADP
ijassa-1131	130	13	the	the	DET
ijassa-1131	130	14	russian	russian	PROPN
ijassa-1131	130	15	science	science	PROPN
ijassa-1131	130	16	foundation	foundation	PROPN
ijassa-1131	130	17	(	(	PUNCT
ijassa-1131	130	18	project	project	VERB
ijassa-1131	130	19	no	no	DET
ijassa-1131	130	20	20	20	NUM
ijassa-1131	130	21	-	-	SYM
ijassa-1131	130	22	11	11	NUM
ijassa-1131	130	23	-	-	PUNCT
ijassa-1131	130	24	20131	20131	NUM
ijassa-1131	130	25	)	)	PUNCT
ijassa-1131	130	26	.	.	PUNCT
ijassa-1131	131	1	references	reference	NOUN
ijassa-1131	131	2	1	1	NUM
ijassa-1131	131	3	.	.	PUNCT
ijassa-1131	132	1	arutyunov	arutyunov	PROPN
ijassa-1131	132	2	,	,	PUNCT
ijassa-1131	132	3	a.v	a.v	PROPN
ijassa-1131	132	4	.	.	PROPN
ijassa-1131	132	5	,	,	PUNCT
ijassa-1131	132	6	avakov	avakov	PROPN
ijassa-1131	132	7	,	,	PUNCT
ijassa-1131	132	8	e.r	e.r	PROPN
ijassa-1131	132	9	.	.	PROPN
ijassa-1131	132	10	&	&	CCONJ
ijassa-1131	132	11	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	132	12	,	,	PUNCT
ijassa-1131	132	13	s.e	s.e	PROPN
ijassa-1131	132	14	.	.	PROPN
ijassa-1131	132	15	(	(	PUNCT
ijassa-1131	132	16	2009	2009	NUM
ijassa-1131	132	17	)	)	PUNCT
ijassa-1131	132	18	covering	cover	VERB
ijassa-1131	132	19	mappings	mapping	NOUN
ijassa-1131	132	20	and	and	CCONJ
ijassa-1131	132	21	their	their	PRON
ijassa-1131	132	22	applications	application	NOUN
ijassa-1131	132	23	to	to	PART
ijassa-1131	132	24	differential	differential	VERB
ijassa-1131	132	25	equations	equation	NOUN
ijassa-1131	132	26	unsolved	unsolve	VERB
ijassa-1131	132	27	for	for	ADP
ijassa-1131	132	28	the	the	DET
ijassa-1131	132	29	derivative	derivative	NOUN
ijassa-1131	132	30	,	,	PUNCT
ijassa-1131	132	31	differ	differ	VERB
ijassa-1131	132	32	.	.	PUNCT
ijassa-1131	133	1	equations	equation	NOUN
ijassa-1131	133	2	,	,	PUNCT
ijassa-1131	133	3	45(5	45(5	NOUN
ijassa-1131	133	4	)	)	PUNCT
ijassa-1131	133	5	,	,	PUNCT
ijassa-1131	133	6	627–649	627–649	NUM
ijassa-1131	133	7	.	.	NOUN
ijassa-1131	133	8	2	2	NUM
ijassa-1131	133	9	.	.	X
ijassa-1131	133	10	arutyunov	arutyunov	PROPN
ijassa-1131	133	11	,	,	PUNCT
ijassa-1131	133	12	a.	a.	PROPN
ijassa-1131	133	13	,	,	PUNCT
ijassa-1131	133	14	de	de	PROPN
ijassa-1131	133	15	oliveira	oliveira	PROPN
ijassa-1131	133	16	,	,	PUNCT
ijassa-1131	133	17	v.a	v.a	PROPN
ijassa-1131	133	18	.	.	PROPN
ijassa-1131	133	19	,	,	PUNCT
ijassa-1131	133	20	pereira	pereira	PROPN
ijassa-1131	133	21	,	,	PUNCT
ijassa-1131	133	22	f.l	f.l	PROPN
ijassa-1131	133	23	.	.	PROPN
ijassa-1131	133	24	,	,	PUNCT
ijassa-1131	133	25	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	133	26	,	,	PUNCT
ijassa-1131	133	27	e.	e.	PROPN
ijassa-1131	133	28	&	&	CCONJ
ijassa-1131	133	29	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	133	30	,	,	PUNCT
ijassa-1131	133	31	s.	s.	PROPN
ijassa-1131	133	32	(	(	PUNCT
ijassa-1131	133	33	2015	2015	NUM
ijassa-1131	133	34	)	)	PUNCT
ijassa-1131	133	35	on	on	ADP
ijassa-1131	133	36	the	the	DET
ijassa-1131	133	37	solvability	solvability	NOUN
ijassa-1131	133	38	of	of	ADP
ijassa-1131	133	39	implicit	implicit	ADJ
ijassa-1131	133	40	differential	differential	ADJ
ijassa-1131	133	41	inclusions	inclusion	NOUN
ijassa-1131	133	42	,	,	PUNCT
ijassa-1131	133	43	appl	appl	NOUN
ijassa-1131	133	44	.	.	PROPN
ijassa-1131	134	1	anal	anal	PROPN
ijassa-1131	134	2	.	.	PROPN
ijassa-1131	134	3	,	,	PUNCT
ijassa-1131	134	4	94(1	94(1	NUM
ijassa-1131	134	5	)	)	PUNCT
ijassa-1131	134	6	,	,	PUNCT
ijassa-1131	134	7	129–143	129–143	NUM
ijassa-1131	134	8	.	.	PUNCT
ijassa-1131	135	1	3	3	X
ijassa-1131	135	2	.	.	X
ijassa-1131	135	3	granas	grana	NOUN
ijassa-1131	135	4	,	,	PUNCT
ijassa-1131	135	5	a.	a.	PROPN
ijassa-1131	135	6	&	&	CCONJ
ijassa-1131	135	7	dugundji	dugundji	PROPN
ijassa-1131	135	8	,	,	PUNCT
ijassa-1131	135	9	j.	j.	PROPN
ijassa-1131	135	10	(	(	PUNCT
ijassa-1131	135	11	2003	2003	NUM
ijassa-1131	135	12	)	)	PUNCT
ijassa-1131	135	13	fixed	fix	VERB
ijassa-1131	135	14	point	point	NOUN
ijassa-1131	135	15	theory	theory	NOUN
ijassa-1131	135	16	,	,	PUNCT
ijassa-1131	135	17	n.y	n.y	PROPN
ijassa-1131	135	18	.	.	PROPN
ijassa-1131	135	19	,	,	PUNCT
ijassa-1131	135	20	usa	usa	PROPN
ijassa-1131	135	21	:	:	PUNCT
ijassa-1131	135	22	springer	springer	NOUN
ijassa-1131	135	23	.	.	PUNCT
ijassa-1131	136	1	4	4	X
ijassa-1131	136	2	.	.	X
ijassa-1131	136	3	arutyunov	arutyunov	PROPN
ijassa-1131	136	4	,	,	PUNCT
ijassa-1131	136	5	a.v	a.v	PROPN
ijassa-1131	136	6	.	.	PROPN
ijassa-1131	136	7	&	&	CCONJ
ijassa-1131	136	8	zhukovskiy	zhukovskiy	PROPN
ijassa-1131	136	9	,	,	PUNCT
ijassa-1131	136	10	s.e	s.e	PROPN
ijassa-1131	136	11	.	.	PROPN
ijassa-1131	136	12	(	(	PUNCT
ijassa-1131	136	13	2021	2021	NUM
ijassa-1131	136	14	)	)	PUNCT
ijassa-1131	136	15	on	on	ADP
ijassa-1131	136	16	global	global	ADJ
ijassa-1131	136	17	solvability	solvability	NOUN
ijassa-1131	136	18	of	of	ADP
ijassa-1131	136	19	nonlinear	nonlinear	ADJ
ijassa-1131	136	20	equations	equation	NOUN
ijassa-1131	136	21	with	with	ADP
ijassa-1131	136	22	parameters	parameter	NOUN
ijassa-1131	136	23	,	,	PUNCT
ijassa-1131	136	24	doklady	doklady	NOUN
ijassa-1131	136	25	mathematics	mathematic	NOUN
ijassa-1131	136	26	,	,	PUNCT
ijassa-1131	136	27	103(1	103(1	NUM
ijassa-1131	136	28	)	)	PUNCT
ijassa-1131	136	29	,	,	PUNCT
ijassa-1131	136	30	57–60	57–60	PROPN
ijassa-1131	136	31	.	.	PUNCT
ijassa-1131	137	1	copyright	copyright	NOUN
ijassa-1131	137	2	©	©	PROPN
ijassa-1131	137	3	2021	2021	NUM
ijassa-1131	137	4	assa	assa	NOUN
ijassa-1131	137	5	.	.	PUNCT
ijassa-1131	138	1	adv	adv	PROPN
ijassa-1131	138	2	syst	syst	PROPN
ijassa-1131	138	3	sci	sci	PROPN
ijassa-1131	138	4	appl	appl	PROPN
ijassa-1131	138	5	(	(	PUNCT
ijassa-1131	138	6	2021	2021	NUM
ijassa-1131	138	7	)	)	PUNCT
ijassa-1131	138	8	introduction	introduction	NOUN
ijassa-1131	138	9	preliminaries	preliminary	NOUN
ijassa-1131	138	10	solvability	solvability	NOUN
ijassa-1131	138	11	condition	condition	NOUN
ijassa-1131	138	12	for	for	ADP
ijassa-1131	138	13	equations	equation	NOUN
ijassa-1131	138	14	solvability	solvability	NOUN
ijassa-1131	138	15	condition	condition	NOUN
ijassa-1131	138	16	for	for	ADP
ijassa-1131	138	17	systems	system	NOUN
ijassa-1131	138	18	of	of	ADP
ijassa-1131	138	19	equations	equation	NOUN