id	sid	tid	token	lemma	pos
ejpam-3650	1	1	european	european	PROPN
ejpam-3650	1	2	journal	journal	PROPN
ejpam-3650	1	3	of	of	ADP
ejpam-3650	1	4	pure	pure	ADJ
ejpam-3650	1	5	and	and	CCONJ
ejpam-3650	1	6	applied	apply	VERB
ejpam-3650	1	7	mathematics	mathematic	NOUN
ejpam-3650	1	8	vol	vol	NOUN
ejpam-3650	1	9	.	.	PROPN
ejpam-3650	2	1	13	13	NUM
ejpam-3650	2	2	,	,	PUNCT
ejpam-3650	2	3	no	no	INTJ
ejpam-3650	2	4	.	.	NOUN
ejpam-3650	2	5	2	2	NUM
ejpam-3650	2	6	,	,	PUNCT
ejpam-3650	2	7	2020	2020	NUM
ejpam-3650	2	8	,	,	PUNCT
ejpam-3650	2	9	314	314	NUM
ejpam-3650	2	10	-	-	SYM
ejpam-3650	2	11	322	322	NUM
ejpam-3650	2	12	issn	issn	PROPN
ejpam-3650	2	13	1307	1307	NUM
ejpam-3650	2	14	-	-	SYM
ejpam-3650	2	15	5543	5543	NUM
ejpam-3650	2	16	–	–	PUNCT
ejpam-3650	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3650	2	18	published	publish	VERB
ejpam-3650	2	19	by	by	ADP
ejpam-3650	2	20	new	new	PROPN
ejpam-3650	2	21	york	york	PROPN
ejpam-3650	2	22	business	business	PROPN
ejpam-3650	2	23	global	global	PROPN
ejpam-3650	3	1	the	the	DET
ejpam-3650	3	2	problem	problem	NOUN
ejpam-3650	3	3	of	of	ADP
ejpam-3650	3	4	the	the	DET
ejpam-3650	3	5	optimal	optimal	ADJ
ejpam-3650	3	6	control	control	NOUN
ejpam-3650	3	7	with	with	ADP
ejpam-3650	3	8	a	a	DET
ejpam-3650	3	9	lower	low	ADJ
ejpam-3650	3	10	coefficient	coefficient	NOUN
ejpam-3650	3	11	for	for	ADP
ejpam-3650	3	12	weakly	weakly	ADJ
ejpam-3650	3	13	nonlinear	nonlinear	ADJ
ejpam-3650	3	14	wave	wave	NOUN
ejpam-3650	3	15	equation	equation	NOUN
ejpam-3650	3	16	in	in	ADP
ejpam-3650	3	17	the	the	DET
ejpam-3650	3	18	mixed	mixed	ADJ
ejpam-3650	3	19	problem	problem	NOUN
ejpam-3650	3	20	g.g	g.g	INTJ
ejpam-3650	3	21	ismayilova	ismayilova	PROPN
ejpam-3650	3	22	sumgait	sumgait	PROPN
ejpam-3650	3	23	state	state	PROPN
ejpam-3650	3	24	university	university	PROPN
ejpam-3650	3	25	,	,	PUNCT
ejpam-3650	3	26	sumgait	sumgait	NOUN
ejpam-3650	3	27	,	,	PUNCT
ejpam-3650	3	28	azerbaijan	azerbaijan	PROPN
ejpam-3650	3	29	abstract	abstract	NOUN
ejpam-3650	3	30	.	.	PUNCT
ejpam-3650	4	1	in	in	ADP
ejpam-3650	4	2	this	this	DET
ejpam-3650	4	3	paper	paper	NOUN
ejpam-3650	4	4	,	,	PUNCT
ejpam-3650	4	5	we	we	PRON
ejpam-3650	4	6	consider	consider	VERB
ejpam-3650	4	7	the	the	DET
ejpam-3650	4	8	problem	problem	NOUN
ejpam-3650	4	9	of	of	ADP
ejpam-3650	4	10	determining	determine	VERB
ejpam-3650	4	11	the	the	DET
ejpam-3650	4	12	lowest	low	ADJ
ejpam-3650	4	13	coefficient	coefficient	NOUN
ejpam-3650	4	14	of	of	ADP
ejpam-3650	4	15	weakly	weakly	ADJ
ejpam-3650	4	16	nonlinear	nonlinear	ADJ
ejpam-3650	4	17	wave	wave	NOUN
ejpam-3650	4	18	equation	equation	NOUN
ejpam-3650	4	19	.	.	PUNCT
ejpam-3650	5	1	the	the	DET
ejpam-3650	5	2	problem	problem	NOUN
ejpam-3650	5	3	is	be	AUX
ejpam-3650	5	4	reduced	reduce	VERB
ejpam-3650	5	5	to	to	ADP
ejpam-3650	5	6	the	the	DET
ejpam-3650	5	7	optimal	optimal	ADJ
ejpam-3650	5	8	control	control	NOUN
ejpam-3650	5	9	problem	problem	NOUN
ejpam-3650	5	10	,	,	PUNCT
ejpam-3650	5	11	in	in	ADP
ejpam-3650	5	12	the	the	DET
ejpam-3650	5	13	new	new	ADJ
ejpam-3650	5	14	problem	problem	NOUN
ejpam-3650	5	15	.	.	PUNCT
ejpam-3650	6	1	in	in	ADP
ejpam-3650	6	2	the	the	DET
ejpam-3650	6	3	this	this	DET
ejpam-3650	6	4	existence	existence	NOUN
ejpam-3650	6	5	theorem	theorem	NOUN
ejpam-3650	6	6	of	of	ADP
ejpam-3650	6	7	the	the	DET
ejpam-3650	6	8	optimal	optimal	ADJ
ejpam-3650	6	9	control	control	NOUN
ejpam-3650	6	10	and	and	CCONJ
ejpam-3650	6	11	,	,	PUNCT
ejpam-3650	6	12	the	the	DET
ejpam-3650	6	13	freéchet	freéchet	NOUN
ejpam-3650	6	14	differentiability	differentiability	NOUN
ejpam-3650	6	15	of	of	ADP
ejpam-3650	6	16	the	the	DET
ejpam-3650	6	17	functional	functional	ADJ
ejpam-3650	6	18	is	be	AUX
ejpam-3650	6	19	proved	prove	VERB
ejpam-3650	6	20	.	.	PUNCT
ejpam-3650	7	1	also	also	ADV
ejpam-3650	7	2	the	the	DET
ejpam-3650	7	3	necessary	necessary	ADJ
ejpam-3650	7	4	condition	condition	NOUN
ejpam-3650	7	5	of	of	ADP
ejpam-3650	7	6	optimality	optimality	NOUN
ejpam-3650	7	7	is	be	AUX
ejpam-3650	7	8	derived	derive	VERB
ejpam-3650	7	9	in	in	ADP
ejpam-3650	7	10	view	view	NOUN
ejpam-3650	7	11	of	of	ADP
ejpam-3650	7	12	variational	variational	ADJ
ejpam-3650	7	13	inequality	inequality	NOUN
ejpam-3650	7	14	.	.	PUNCT
ejpam-3650	8	1	2020	2020	NUM
ejpam-3650	8	2	mathematics	mathematic	NOUN
ejpam-3650	8	3	subject	subject	NOUN
ejpam-3650	8	4	classifications	classification	NOUN
ejpam-3650	8	5	:	:	PUNCT
ejpam-3650	8	6	49j15	49j15	NUM
ejpam-3650	8	7	,	,	PUNCT
ejpam-3650	8	8	49j40	49j40	DET
ejpam-3650	8	9	key	key	ADJ
ejpam-3650	8	10	words	word	NOUN
ejpam-3650	8	11	and	and	CCONJ
ejpam-3650	8	12	phrases	phrase	NOUN
ejpam-3650	8	13	:	:	PUNCT
ejpam-3650	8	14	coefficient	coefficient	NOUN
ejpam-3650	8	15	,	,	PUNCT
ejpam-3650	8	16	weakly	weakly	ADJ
ejpam-3650	8	17	nonlinear	nonlinear	ADJ
ejpam-3650	8	18	equation	equation	NOUN
ejpam-3650	8	19	,	,	PUNCT
ejpam-3650	8	20	optimal	optimal	ADJ
ejpam-3650	8	21	control	control	NOUN
ejpam-3650	8	22	,	,	PUNCT
ejpam-3650	8	23	necessary	necessary	ADJ
ejpam-3650	8	24	condition	condition	NOUN
ejpam-3650	8	25	.	.	PUNCT
ejpam-3650	9	1	1	1	X
ejpam-3650	9	2	.	.	X
ejpam-3650	9	3	introduction	introduction	NOUN
ejpam-3650	9	4	the	the	DET
ejpam-3650	9	5	problems	problem	NOUN
ejpam-3650	9	6	of	of	ADP
ejpam-3650	9	7	determining	determine	VERB
ejpam-3650	9	8	the	the	DET
ejpam-3650	9	9	coefficients	coefficient	NOUN
ejpam-3650	9	10	of	of	ADP
ejpam-3650	9	11	various	various	ADJ
ejpam-3650	9	12	partial	partial	ADJ
ejpam-3650	9	13	differential	differential	NOUN
ejpam-3650	9	14	equations	equation	NOUN
ejpam-3650	9	15	are	be	AUX
ejpam-3650	9	16	actual	actual	ADJ
ejpam-3650	9	17	problems	problem	NOUN
ejpam-3650	9	18	in	in	ADP
ejpam-3650	9	19	connection	connection	NOUN
ejpam-3650	9	20	with	with	ADP
ejpam-3650	9	21	of	of	ADP
ejpam-3650	9	22	applied	apply	VERB
ejpam-3650	9	23	significance	significance	NOUN
ejpam-3650	9	24	.	.	PUNCT
ejpam-3650	10	1	taking	take	VERB
ejpam-3650	10	2	into	into	ADP
ejpam-3650	10	3	account	account	NOUN
ejpam-3650	10	4	that	that	SCONJ
ejpam-3650	10	5	the	the	DET
ejpam-3650	10	6	coefficients	coefficient	NOUN
ejpam-3650	10	7	of	of	ADP
ejpam-3650	10	8	the	the	DET
ejpam-3650	10	9	equations	equation	NOUN
ejpam-3650	10	10	of	of	ADP
ejpam-3650	10	11	mathematical	mathematical	ADJ
ejpam-3650	10	12	physics	physics	NOUN
ejpam-3650	10	13	characterize	characterize	VERB
ejpam-3650	10	14	various	various	ADJ
ejpam-3650	10	15	properties	property	NOUN
ejpam-3650	10	16	of	of	ADP
ejpam-3650	10	17	the	the	DET
ejpam-3650	10	18	considered	consider	VERB
ejpam-3650	10	19	medium	medium	NOUN
ejpam-3650	10	20	,	,	PUNCT
ejpam-3650	10	21	finding	find	VERB
ejpam-3650	10	22	them	they	PRON
ejpam-3650	10	23	is	be	AUX
ejpam-3650	10	24	undoubtedly	undoubtedly	ADV
ejpam-3650	10	25	an	an	DET
ejpam-3650	10	26	important	important	ADJ
ejpam-3650	10	27	problem	problem	NOUN
ejpam-3650	10	28	.	.	PUNCT
ejpam-3650	11	1	such	such	ADJ
ejpam-3650	11	2	problems	problem	NOUN
ejpam-3650	11	3	arise	arise	VERB
ejpam-3650	11	4	in	in	ADP
ejpam-3650	11	5	various	various	ADJ
ejpam-3650	11	6	fields	field	NOUN
ejpam-3650	11	7	of	of	ADP
ejpam-3650	11	8	natural	natural	ADJ
ejpam-3650	11	9	science	science	NOUN
ejpam-3650	11	10	[	[	X
ejpam-3650	11	11	1–4	1–4	NOUN
ejpam-3650	11	12	]	]	X
ejpam-3650	11	13	.	.	PUNCT
ejpam-3650	12	1	recently	recently	ADV
ejpam-3650	12	2	,	,	PUNCT
ejpam-3650	12	3	various	various	ADJ
ejpam-3650	12	4	methods	method	NOUN
ejpam-3650	12	5	have	have	AUX
ejpam-3650	12	6	been	be	AUX
ejpam-3650	12	7	used	use	VERB
ejpam-3650	12	8	to	to	PART
ejpam-3650	12	9	solve	solve	VERB
ejpam-3650	12	10	such	such	ADJ
ejpam-3650	12	11	problems.one	problems.one	NOUN
ejpam-3650	12	12	of	of	ADP
ejpam-3650	12	13	these	these	DET
ejpam-3650	12	14	methods	method	NOUN
ejpam-3650	12	15	is	be	AUX
ejpam-3650	12	16	application	application	NOUN
ejpam-3650	12	17	of	of	ADP
ejpam-3650	12	18	the	the	DET
ejpam-3650	12	19	methods	method	NOUN
ejpam-3650	12	20	of	of	ADP
ejpam-3650	12	21	optimal	optimal	ADJ
ejpam-3650	12	22	control	control	NOUN
ejpam-3650	12	23	theory	theory	NOUN
ejpam-3650	12	24	,	,	PUNCT
ejpam-3650	12	25	which	which	PRON
ejpam-3650	12	26	is	be	AUX
ejpam-3650	12	27	also	also	ADV
ejpam-3650	12	28	called	call	VERB
ejpam-3650	12	29	variational	variational	ADJ
ejpam-3650	12	30	approach	approach	NOUN
ejpam-3650	12	31	.	.	PUNCT
ejpam-3650	13	1	to	to	PART
ejpam-3650	13	2	apply	apply	VERB
ejpam-3650	13	3	this	this	DET
ejpam-3650	13	4	approach	approach	NOUN
ejpam-3650	13	5	,	,	PUNCT
ejpam-3650	13	6	a	a	DET
ejpam-3650	13	7	residual	residual	ADJ
ejpam-3650	13	8	functional	functional	NOUN
ejpam-3650	13	9	is	be	AUX
ejpam-3650	13	10	constructed	construct	VERB
ejpam-3650	13	11	for	for	ADP
ejpam-3650	13	12	finding	find	VERB
ejpam-3650	13	13	the	the	DET
ejpam-3650	13	14	unknowns	unknown	NOUN
ejpam-3650	13	15	in	in	ADP
ejpam-3650	13	16	boundary	boundary	ADJ
ejpam-3650	13	17	value	value	NOUN
ejpam-3650	13	18	problems	problem	NOUN
ejpam-3650	13	19	using	use	VERB
ejpam-3650	13	20	additional	additional	ADJ
ejpam-3650	13	21	data	datum	NOUN
ejpam-3650	13	22	.	.	PUNCT
ejpam-3650	14	1	then	then	ADV
ejpam-3650	14	2	we	we	PRON
ejpam-3650	14	3	consider	consider	VERB
ejpam-3650	14	4	the	the	DET
ejpam-3650	14	5	problem	problem	NOUN
ejpam-3650	14	6	of	of	ADP
ejpam-3650	14	7	minimizing	minimize	VERB
ejpam-3650	14	8	the	the	DET
ejpam-3650	14	9	constructed	construct	VERB
ejpam-3650	14	10	functional	functional	NOUN
ejpam-3650	14	11	for	for	ADP
ejpam-3650	14	12	solving	solve	VERB
ejpam-3650	14	13	a	a	DET
ejpam-3650	14	14	boundary	boundary	ADJ
ejpam-3650	14	15	value	value	NOUN
ejpam-3650	14	16	problem	problem	NOUN
ejpam-3650	14	17	,	,	PUNCT
ejpam-3650	14	18	moreover	moreover	ADV
ejpam-3650	14	19	,	,	PUNCT
ejpam-3650	14	20	the	the	DET
ejpam-3650	14	21	unknown	unknown	NOUN
ejpam-3650	14	22	in	in	ADP
ejpam-3650	14	23	the	the	DET
ejpam-3650	14	24	boundary	boundary	ADJ
ejpam-3650	14	25	value	value	NOUN
ejpam-3650	14	26	problem	problem	NOUN
ejpam-3650	14	27	is	be	AUX
ejpam-3650	14	28	treated	treat	VERB
ejpam-3650	14	29	as	as	ADP
ejpam-3650	14	30	a	a	DET
ejpam-3650	14	31	control	control	NOUN
ejpam-3650	14	32	function	function	NOUN
ejpam-3650	14	33	and	and	CCONJ
ejpam-3650	14	34	the	the	DET
ejpam-3650	14	35	new	new	ADJ
ejpam-3650	14	36	problem	problem	NOUN
ejpam-3650	14	37	is	be	AUX
ejpam-3650	14	38	investigated	investigate	VERB
ejpam-3650	14	39	as	as	ADP
ejpam-3650	14	40	an	an	DET
ejpam-3650	14	41	optimal	optimal	ADJ
ejpam-3650	14	42	control	control	NOUN
ejpam-3650	14	43	problem	problem	NOUN
ejpam-3650	14	44	by	by	ADP
ejpam-3650	14	45	applying	apply	VERB
ejpam-3650	14	46	the	the	DET
ejpam-3650	14	47	methods	method	NOUN
ejpam-3650	14	48	of	of	ADP
ejpam-3650	14	49	control	control	NOUN
ejpam-3650	14	50	theory	theory	NOUN
ejpam-3650	14	51	.	.	PUNCT
ejpam-3650	15	1	doi	doi	NOUN
ejpam-3650	15	2	:	:	PUNCT
ejpam-3650	15	3	https://doi.org/10.29020/nybg.ejpam.v13i2.3650	https://doi.org/10.29020/nybg.ejpam.v13i2.3650	ADP
ejpam-3650	15	4	email	email	NOUN
ejpam-3650	15	5	address	address	NOUN
ejpam-3650	15	6	:	:	PUNCT
ejpam-3650	15	7	gunay	gunay	PROPN
ejpam-3650	15	8	ismayilova	ismayilova	PROPN
ejpam-3650	15	9	83@mail.ru	83@mail.ru	NUM
ejpam-3650	16	1	(	(	PUNCT
ejpam-3650	16	2	g.g	g.g	INTJ
ejpam-3650	16	3	ismayilova	ismayilova	PROPN
ejpam-3650	16	4	)	)	PUNCT
ejpam-3650	16	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3650	17	1	314	314	NUM
ejpam-3650	17	2	c	c	NOUN
ejpam-3650	17	3	©	©	PROPN
ejpam-3650	17	4	2020	2020	NUM
ejpam-3650	17	5	ejpam	ejpam	VERB
ejpam-3650	17	6	all	all	DET
ejpam-3650	17	7	rights	right	NOUN
ejpam-3650	17	8	reserved	reserve	VERB
ejpam-3650	17	9	.	.	PUNCT
ejpam-3650	18	1	g.g	g.g	INTJ
ejpam-3650	18	2	ismayilova	ismayilova	PROPN
ejpam-3650	18	3	/	/	SYM
ejpam-3650	18	4	eur	eur	PROPN
ejpam-3650	18	5	.	.	PUNCT
ejpam-3650	19	1	j.	j.	PROPN
ejpam-3650	19	2	pure	pure	PROPN
ejpam-3650	19	3	appl	appl	PROPN
ejpam-3650	19	4	.	.	PROPN
ejpam-3650	19	5	math	math	PROPN
ejpam-3650	19	6	,	,	PUNCT
ejpam-3650	19	7	13	13	NUM
ejpam-3650	19	8	(	(	PUNCT
ejpam-3650	19	9	2	2	NUM
ejpam-3650	19	10	)	)	PUNCT
ejpam-3650	19	11	(	(	PUNCT
ejpam-3650	19	12	2020	2020	NUM
ejpam-3650	19	13	)	)	PUNCT
ejpam-3650	19	14	,	,	PUNCT
ejpam-3650	19	15	314	314	NUM
ejpam-3650	19	16	-	-	SYM
ejpam-3650	19	17	322	322	NUM
ejpam-3650	19	18	315	315	NUM
ejpam-3650	19	19	2	2	NUM
ejpam-3650	19	20	.	.	PUNCT
ejpam-3650	20	1	statement	statement	NOUN
ejpam-3650	20	2	of	of	ADP
ejpam-3650	20	3	the	the	DET
ejpam-3650	20	4	problem	problem	NOUN
ejpam-3650	20	5	consider	consider	VERB
ejpam-3650	20	6	the	the	DET
ejpam-3650	20	7	problem	problem	NOUN
ejpam-3650	20	8	of	of	ADP
ejpam-3650	20	9	finding	find	VERB
ejpam-3650	20	10	a	a	DET
ejpam-3650	20	11	pair	pair	NOUN
ejpam-3650	20	12	of	of	ADP
ejpam-3650	20	13	functions	function	NOUN
ejpam-3650	20	14	{	{	PUNCT
ejpam-3650	20	15	u(x	u(x	PROPN
ejpam-3650	20	16	,	,	PUNCT
ejpam-3650	20	17	t	t	PROPN
ejpam-3650	20	18	)	)	PUNCT
ejpam-3650	20	19	,	,	PUNCT
ejpam-3650	20	20	v(x	v(x	PROPN
ejpam-3650	20	21	)	)	PUNCT
ejpam-3650	20	22	}	}	PUNCT
ejpam-3650	20	23	from	from	ADP
ejpam-3650	20	24	the	the	DET
ejpam-3650	20	25	following	follow	VERB
ejpam-3650	20	26	relations	relation	NOUN
ejpam-3650	20	27	∂2u	∂2u	PROPN
ejpam-3650	20	28	∂t2	∂t2	PROPN
ejpam-3650	20	29	−∆u+	−∆u+	NOUN
ejpam-3650	20	30	vu	vu	X
ejpam-3650	20	31	=	=	SYM
ejpam-3650	20	32	f(x	f(x	PROPN
ejpam-3650	20	33	,	,	PUNCT
ejpam-3650	20	34	t	t	PROPN
ejpam-3650	20	35	,	,	PUNCT
ejpam-3650	20	36	u	u	NOUN
ejpam-3650	20	37	)	)	PUNCT
ejpam-3650	20	38	,	,	PUNCT
ejpam-3650	20	39	(	(	PUNCT
ejpam-3650	20	40	x	x	X
ejpam-3650	20	41	,	,	PUNCT
ejpam-3650	20	42	t	t	PROPN
ejpam-3650	20	43	)	)	PUNCT
ejpam-3650	20	44	∈	∈	PROPN
ejpam-3650	21	1	q	q	NOUN
ejpam-3650	21	2	,	,	PUNCT
ejpam-3650	21	3	(	(	PUNCT
ejpam-3650	21	4	1	1	X
ejpam-3650	21	5	)	)	PUNCT
ejpam-3650	21	6	u	u	NOUN
ejpam-3650	21	7	=	=	NOUN
ejpam-3650	21	8	0	0	NUM
ejpam-3650	21	9	,	,	PUNCT
ejpam-3650	21	10	(	(	PUNCT
ejpam-3650	21	11	x	x	NOUN
ejpam-3650	21	12	,	,	PUNCT
ejpam-3650	21	13	t	t	PROPN
ejpam-3650	21	14	)	)	PUNCT
ejpam-3650	21	15	∈	∈	PROPN
ejpam-3650	21	16	s	s	PROPN
ejpam-3650	21	17	,	,	PUNCT
ejpam-3650	21	18	u|t=0	u|t=0	PUNCT
ejpam-3650	21	19	=	=	SYM
ejpam-3650	21	20	u0(x	u0(x	NUM
ejpam-3650	21	21	)	)	PUNCT
ejpam-3650	21	22	,	,	PUNCT
ejpam-3650	21	23	∂u	∂u	PROPN
ejpam-3650	21	24	∂t	∂t	PROPN
ejpam-3650	21	25	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3650	21	26	t=0	t=0	VERB
ejpam-3650	21	27	=	=	PUNCT
ejpam-3650	21	28	u1(x	u1(x	NOUN
ejpam-3650	21	29	)	)	PUNCT
ejpam-3650	21	30	,	,	PUNCT
ejpam-3650	21	31	x	x	PUNCT
ejpam-3650	21	32	∈	∈	PROPN
ejpam-3650	21	33	ω	ω	PROPN
ejpam-3650	21	34	,	,	PUNCT
ejpam-3650	21	35	(	(	PUNCT
ejpam-3650	21	36	2	2	X
ejpam-3650	21	37	)	)	PUNCT
ejpam-3650	21	38	t∫	t∫	NOUN
ejpam-3650	21	39	0	0	NUM
ejpam-3650	21	40	k(x	k(x	PROPN
ejpam-3650	21	41	,	,	PUNCT
ejpam-3650	21	42	t)u(x	t)u(x	NOUN
ejpam-3650	21	43	,	,	PUNCT
ejpam-3650	21	44	t)dt	t)dt	PROPN
ejpam-3650	21	45	=	=	PRON
ejpam-3650	21	46	ϕ(x	ϕ(x	PROPN
ejpam-3650	21	47	)	)	PUNCT
ejpam-3650	21	48	,	,	PUNCT
ejpam-3650	21	49	x	x	PUNCT
ejpam-3650	21	50	∈	∈	PROPN
ejpam-3650	21	51	ω	ω	PROPN
ejpam-3650	21	52	,	,	PUNCT
ejpam-3650	21	53	(	(	PUNCT
ejpam-3650	21	54	3	3	X
ejpam-3650	21	55	)	)	PUNCT
ejpam-3650	21	56	where	where	SCONJ
ejpam-3650	21	57	∆	∆	PROPN
ejpam-3650	21	58	is	be	AUX
ejpam-3650	21	59	the	the	DET
ejpam-3650	21	60	laplace	laplace	NOUN
ejpam-3650	21	61	operator	operator	NOUN
ejpam-3650	21	62	with	with	ADP
ejpam-3650	21	63	respect	respect	NOUN
ejpam-3650	21	64	to	to	ADP
ejpam-3650	21	65	x	x	PRON
ejpam-3650	21	66	,	,	PUNCT
ejpam-3650	21	67	f(x	f(x	PROPN
ejpam-3650	21	68	,	,	PUNCT
ejpam-3650	21	69	t	t	PROPN
ejpam-3650	21	70	,	,	PUNCT
ejpam-3650	21	71	u	u	NOUN
ejpam-3650	21	72	)	)	PUNCT
ejpam-3650	21	73	,	,	PUNCT
ejpam-3650	21	74	u0(x	u0(x	NOUN
ejpam-3650	21	75	)	)	PUNCT
ejpam-3650	21	76	,	,	PUNCT
ejpam-3650	21	77	u1(x),k(x	u1(x),k(x	PROPN
ejpam-3650	21	78	,	,	PUNCT
ejpam-3650	21	79	t	t	PROPN
ejpam-3650	21	80	)	)	PUNCT
ejpam-3650	21	81	,	,	PUNCT
ejpam-3650	21	82	ϕ(x	ϕ(x	X
ejpam-3650	21	83	)	)	PUNCT
ejpam-3650	21	84	are	be	AUX
ejpam-3650	21	85	given	give	VERB
ejpam-3650	21	86	functions	function	NOUN
ejpam-3650	21	87	.	.	PUNCT
ejpam-3650	22	1	let	let	VERB
ejpam-3650	22	2	q	q	NOUN
ejpam-3650	22	3	=	=	VERB
ejpam-3650	22	4	ω×	ω×	X
ejpam-3650	22	5	(	(	PUNCT
ejpam-3650	22	6	0	0	NUM
ejpam-3650	22	7	,	,	PUNCT
ejpam-3650	22	8	t	t	PROPN
ejpam-3650	22	9	)	)	PUNCT
ejpam-3650	22	10	be	be	AUX
ejpam-3650	22	11	a	a	DET
ejpam-3650	22	12	cylinder	cylinder	NOUN
ejpam-3650	22	13	in	in	ADP
ejpam-3650	22	14	rn+1(n	rn+1(n	NUM
ejpam-3650	22	15	≤	≤	NUM
ejpam-3650	22	16	4	4	NUM
ejpam-3650	22	17	)	)	PUNCT
ejpam-3650	22	18	,	,	PUNCT
ejpam-3650	22	19	ω	ω	X
ejpam-3650	22	20	be	be	AUX
ejpam-3650	22	21	a	a	DET
ejpam-3650	22	22	bounded	bounded	ADJ
ejpam-3650	22	23	domain	domain	NOUN
ejpam-3650	22	24	in	in	ADP
ejpam-3650	22	25	rn	rn	PROPN
ejpam-3650	22	26	with	with	ADP
ejpam-3650	22	27	a	a	DET
ejpam-3650	22	28	sufficiently	sufficiently	ADV
ejpam-3650	22	29	smooth	smooth	ADJ
ejpam-3650	22	30	boundary	boundary	ADJ
ejpam-3650	22	31	γ	γ	X
ejpam-3650	22	32	,	,	PUNCT
ejpam-3650	22	33	s	s	PART
ejpam-3650	22	34	=	=	X
ejpam-3650	22	35	γ	γ	X
ejpam-3650	22	36	×	×	NOUN
ejpam-3650	22	37	(	(	PUNCT
ejpam-3650	22	38	0	0	NUM
ejpam-3650	22	39	,	,	PUNCT
ejpam-3650	22	40	t	t	PROPN
ejpam-3650	22	41	)	)	PUNCT
ejpam-3650	22	42	is	be	AUX
ejpam-3650	22	43	the	the	DET
ejpam-3650	22	44	lateral	lateral	ADJ
ejpam-3650	22	45	surface	surface	NOUN
ejpam-3650	22	46	of	of	ADP
ejpam-3650	22	47	the	the	DET
ejpam-3650	22	48	cylinder	cylinder	NOUN
ejpam-3650	22	49	q	q	PROPN
ejpam-3650	22	50	,	,	PUNCT
ejpam-3650	22	51	t	t	PROPN
ejpam-3650	22	52	>	>	X
ejpam-3650	22	53	0	0	PUNCT
ejpam-3650	22	54	be	be	AUX
ejpam-3650	22	55	fixed	fix	VERB
ejpam-3650	22	56	number	number	NOUN
ejpam-3650	22	57	.	.	PUNCT
ejpam-3650	23	1	note	note	VERB
ejpam-3650	23	2	that	that	DET
ejpam-3650	23	3	problem	problem	NOUN
ejpam-3650	23	4	(	(	PUNCT
ejpam-3650	23	5	1	1	NUM
ejpam-3650	23	6	)	)	PUNCT
ejpam-3650	23	7	(	(	PUNCT
ejpam-3650	23	8	3	3	X
ejpam-3650	23	9	)	)	PUNCT
ejpam-3650	23	10	is	be	AUX
ejpam-3650	23	11	inverse	inverse	ADJ
ejpam-3650	23	12	to	to	ADP
ejpam-3650	23	13	the	the	DET
ejpam-3650	23	14	direct	direct	ADJ
ejpam-3650	23	15	problem	problem	NOUN
ejpam-3650	23	16	(	(	PUNCT
ejpam-3650	23	17	1	1	NUM
ejpam-3650	23	18	)	)	PUNCT
ejpam-3650	23	19	,	,	PUNCT
ejpam-3650	23	20	(	(	PUNCT
ejpam-3650	23	21	2	2	X
ejpam-3650	23	22	)	)	PUNCT
ejpam-3650	23	23	for	for	ADP
ejpam-3650	23	24	a	a	DET
ejpam-3650	23	25	given	give	VERB
ejpam-3650	23	26	function	function	NOUN
ejpam-3650	23	27	v(x	v(x	PROPN
ejpam-3650	23	28	)	)	PUNCT
ejpam-3650	23	29	.	.	PUNCT
ejpam-3650	24	1	we	we	PRON
ejpam-3650	24	2	reduce	reduce	VERB
ejpam-3650	24	3	this	this	DET
ejpam-3650	24	4	problem	problem	NOUN
ejpam-3650	24	5	to	to	ADP
ejpam-3650	24	6	the	the	DET
ejpam-3650	24	7	following	follow	VERB
ejpam-3650	24	8	optimal	optimal	ADJ
ejpam-3650	24	9	control	control	NOUN
ejpam-3650	24	10	problem	problem	NOUN
ejpam-3650	24	11	:	:	PUNCT
ejpam-3650	24	12	in	in	ADP
ejpam-3650	24	13	the	the	DET
ejpam-3650	24	14	class	class	NOUN
ejpam-3650	24	15	of	of	ADP
ejpam-3650	24	16	functions	function	NOUN
ejpam-3650	24	17	v	v	ADP
ejpam-3650	24	18	=	=	SYM
ejpam-3650	24	19	{	{	PUNCT
ejpam-3650	24	20	v(x	v(x	NOUN
ejpam-3650	24	21	)	)	PUNCT
ejpam-3650	24	22	∈	∈	PROPN
ejpam-3650	24	23	l2(ω)/a	l2(ω)/a	NOUN
ejpam-3650	24	24	≤	≤	NOUN
ejpam-3650	24	25	v(x	v(x	NOUN
ejpam-3650	24	26	)	)	PUNCT
ejpam-3650	24	27	≤	≤	PROPN
ejpam-3650	24	28	b	b	X
ejpam-3650	24	29	a.e.on	a.e.on	X
ejpam-3650	24	30	ω	ω	NUM
ejpam-3650	24	31	}	}	PUNCT
ejpam-3650	24	32	(	(	PUNCT
ejpam-3650	24	33	4	4	X
ejpam-3650	24	34	)	)	PUNCT
ejpam-3650	24	35	find	find	VERB
ejpam-3650	24	36	the	the	DET
ejpam-3650	24	37	minimum	minimum	NOUN
ejpam-3650	24	38	of	of	ADP
ejpam-3650	24	39	functional	functional	ADJ
ejpam-3650	24	40	j0(v	j0(v	PROPN
ejpam-3650	24	41	)	)	PUNCT
ejpam-3650	24	42	=	=	SYM
ejpam-3650	25	1	1	1	NUM
ejpam-3650	25	2	2	2	NUM
ejpam-3650	25	3	∫	∫	PROPN
ejpam-3650	25	4	ω	ω	NUM
ejpam-3650	25	5			PROPN
ejpam-3650	25	6	t∫	t∫	PRON
ejpam-3650	25	7	0	0	NUM
ejpam-3650	25	8	k(x	k(x	PROPN
ejpam-3650	25	9	,	,	PUNCT
ejpam-3650	25	10	t)u(x	t)u(x	NOUN
ejpam-3650	25	11	,	,	PUNCT
ejpam-3650	25	12	t	t	PROPN
ejpam-3650	25	13	;	;	PUNCT
ejpam-3650	25	14	v)dt−	v)dt−	PROPN
ejpam-3650	25	15	ϕ(x	ϕ(x	NOUN
ejpam-3650	25	16	)	)	PUNCT
ejpam-3650	25	17	2	2	NUM
ejpam-3650	25	18	dx	dx	PROPN
ejpam-3650	25	19	(	(	PUNCT
ejpam-3650	25	20	5	5	NUM
ejpam-3650	25	21	)	)	PUNCT
ejpam-3650	25	22	under	under	ADP
ejpam-3650	25	23	constraints	constraint	NOUN
ejpam-3650	25	24	(	(	PUNCT
ejpam-3650	25	25	1	1	NUM
ejpam-3650	25	26	)	)	PUNCT
ejpam-3650	25	27	,	,	PUNCT
ejpam-3650	25	28	(	(	PUNCT
ejpam-3650	25	29	2	2	NUM
ejpam-3650	25	30	)	)	PUNCT
ejpam-3650	25	31	,	,	PUNCT
ejpam-3650	25	32	where	where	SCONJ
ejpam-3650	25	33	a	a	PRON
ejpam-3650	25	34	and	and	CCONJ
ejpam-3650	25	35	b	b	NOUN
ejpam-3650	25	36	some	some	DET
ejpam-3650	25	37	constants	constant	NOUN
ejpam-3650	25	38	,	,	PUNCT
ejpam-3650	25	39	moreover	moreover	ADV
ejpam-3650	25	40	a	a	DET
ejpam-3650	25	41	<	<	X
ejpam-3650	25	42	b	b	PROPN
ejpam-3650	25	43	,	,	PUNCT
ejpam-3650	25	44	u(x	u(x	PROPN
ejpam-3650	25	45	,	,	PUNCT
ejpam-3650	25	46	t	t	PROPN
ejpam-3650	25	47	;	;	PUNCT
ejpam-3650	25	48	v	v	NOUN
ejpam-3650	25	49	)	)	PUNCT
ejpam-3650	25	50	is	be	AUX
ejpam-3650	25	51	the	the	DET
ejpam-3650	25	52	solution	solution	NOUN
ejpam-3650	25	53	of	of	ADP
ejpam-3650	25	54	the	the	DET
ejpam-3650	25	55	boundary	boundary	ADJ
ejpam-3650	25	56	value	value	NOUN
ejpam-3650	25	57	problem	problem	NOUN
ejpam-3650	25	58	(	(	PUNCT
ejpam-3650	25	59	1	1	NUM
ejpam-3650	25	60	)	)	PUNCT
ejpam-3650	25	61	,	,	PUNCT
ejpam-3650	25	62	(	(	PUNCT
ejpam-3650	25	63	2	2	X
ejpam-3650	25	64	)	)	PUNCT
ejpam-3650	25	65	for	for	ADP
ejpam-3650	25	66	v	v	NOUN
ejpam-3650	25	67	=	=	SYM
ejpam-3650	25	68	v(x	v(x	PROPN
ejpam-3650	25	69	)	)	PUNCT
ejpam-3650	25	70	∈	∈	PROPN
ejpam-3650	25	71	v	v	NOUN
ejpam-3650	25	72	.	.	PUNCT
ejpam-3650	26	1	we	we	PRON
ejpam-3650	26	2	call	call	VERB
ejpam-3650	26	3	a	a	DET
ejpam-3650	26	4	function	function	NOUN
ejpam-3650	26	5	v(x	v(x	NOUN
ejpam-3650	26	6	)	)	PUNCT
ejpam-3650	26	7	a	a	DET
ejpam-3650	26	8	control	control	NOUN
ejpam-3650	26	9	,	,	PUNCT
ejpam-3650	26	10	and	and	CCONJ
ejpam-3650	26	11	a	a	DET
ejpam-3650	26	12	set	set	NOUN
ejpam-3650	26	13	v	v	ADP
ejpam-3650	26	14	a	a	DET
ejpam-3650	26	15	class	class	NOUN
ejpam-3650	26	16	of	of	ADP
ejpam-3650	26	17	admissible	admissible	ADJ
ejpam-3650	26	18	controls	control	NOUN
ejpam-3650	26	19	.	.	PUNCT
ejpam-3650	27	1	note	note	VERB
ejpam-3650	27	2	that	that	SCONJ
ejpam-3650	27	3	between	between	ADP
ejpam-3650	27	4	problems	problem	NOUN
ejpam-3650	27	5	(	(	PUNCT
ejpam-3650	27	6	1	1	NUM
ejpam-3650	27	7	)	)	PUNCT
ejpam-3650	27	8	(	(	PUNCT
ejpam-3650	27	9	3	3	X
ejpam-3650	27	10	)	)	PUNCT
ejpam-3650	27	11	and	and	CCONJ
ejpam-3650	27	12	(	(	PUNCT
ejpam-3650	27	13	1	1	NUM
ejpam-3650	27	14	)	)	PUNCT
ejpam-3650	27	15	,	,	PUNCT
ejpam-3650	27	16	(	(	PUNCT
ejpam-3650	27	17	2	2	NUM
ejpam-3650	27	18	)	)	PUNCT
ejpam-3650	27	19	,	,	PUNCT
ejpam-3650	27	20	(	(	PUNCT
ejpam-3650	27	21	4	4	NUM
ejpam-3650	27	22	)	)	PUNCT
ejpam-3650	27	23	,	,	PUNCT
ejpam-3650	27	24	(	(	PUNCT
ejpam-3650	27	25	5	5	X
ejpam-3650	27	26	)	)	PUNCT
ejpam-3650	27	27	there	there	PRON
ejpam-3650	27	28	is	be	VERB
ejpam-3650	27	29	exist	exist	VERB
ejpam-3650	27	30	a	a	DET
ejpam-3650	27	31	closely	closely	ADV
ejpam-3650	27	32	connection	connection	NOUN
ejpam-3650	27	33	if	if	SCONJ
ejpam-3650	27	34	the	the	DET
ejpam-3650	27	35	minimum	minimum	NOUN
ejpam-3650	27	36	of	of	ADP
ejpam-3650	27	37	the	the	DET
ejpam-3650	27	38	functional	functional	ADJ
ejpam-3650	27	39	in	in	ADP
ejpam-3650	27	40	problem	problem	NOUN
ejpam-3650	27	41	(	(	PUNCT
ejpam-3650	27	42	1	1	NUM
ejpam-3650	27	43	)	)	PUNCT
ejpam-3650	27	44	,	,	PUNCT
ejpam-3650	27	45	(	(	PUNCT
ejpam-3650	27	46	2	2	NUM
ejpam-3650	27	47	)	)	PUNCT
ejpam-3650	27	48	,	,	PUNCT
ejpam-3650	27	49	(	(	PUNCT
ejpam-3650	27	50	4	4	NUM
ejpam-3650	27	51	)	)	PUNCT
ejpam-3650	27	52	,	,	PUNCT
ejpam-3650	27	53	(	(	PUNCT
ejpam-3650	27	54	5	5	X
ejpam-3650	27	55	)	)	PUNCT
ejpam-3650	27	56	is	be	AUX
ejpam-3650	27	57	equal	equal	ADJ
ejpam-3650	27	58	to	to	ADP
ejpam-3650	27	59	zero	zero	NUM
ejpam-3650	27	60	,	,	PUNCT
ejpam-3650	27	61	then	then	ADV
ejpam-3650	27	62	the	the	DET
ejpam-3650	27	63	additional	additional	ADJ
ejpam-3650	27	64	condition	condition	NOUN
ejpam-3650	27	65	(	(	PUNCT
ejpam-3650	27	66	3	3	X
ejpam-3650	27	67	)	)	PUNCT
ejpam-3650	27	68	is	be	AUX
ejpam-3650	27	69	satisfied	satisfied	ADJ
ejpam-3650	27	70	.	.	PUNCT
ejpam-3650	28	1	let	let	VERB
ejpam-3650	28	2	’s	’s	NOUN
ejpam-3650	28	3	consider	consider	VERB
ejpam-3650	28	4	the	the	DET
ejpam-3650	28	5	following	follow	VERB
ejpam-3650	28	6	problem	problem	NOUN
ejpam-3650	28	7	to	to	PART
ejpam-3650	28	8	avoid	avoid	VERB
ejpam-3650	28	9	the	the	DET
ejpam-3650	28	10	possible	possible	ADJ
ejpam-3650	28	11	degeneration	degeneration	NOUN
ejpam-3650	29	1	[	[	X
ejpam-3650	29	2	[	[	X
ejpam-3650	29	3	12	12	NUM
ejpam-3650	29	4	]	]	PUNCT
ejpam-3650	29	5	,	,	PUNCT
ejpam-3650	29	6	p.45	p.45	X
ejpam-3650	29	7	]	]	PUNCT
ejpam-3650	29	8	in	in	ADP
ejpam-3650	29	9	the	the	DET
ejpam-3650	29	10	obtained	obtain	VERB
ejpam-3650	29	11	necessary	necessary	ADJ
ejpam-3650	29	12	condition	condition	NOUN
ejpam-3650	29	13	of	of	ADP
ejpam-3650	29	14	optimality	optimality	NOUN
ejpam-3650	29	15	in	in	ADP
ejpam-3650	29	16	future	future	NOUN
ejpam-3650	29	17	:	:	PUNCT
ejpam-3650	29	18	find	find	VERB
ejpam-3650	29	19	the	the	DET
ejpam-3650	29	20	control	control	NOUN
ejpam-3650	29	21	v	v	ADP
ejpam-3650	29	22	∈	∈	PROPN
ejpam-3650	29	23	v	v	NOUN
ejpam-3650	29	24	that	that	PRON
ejpam-3650	29	25	gives	give	VERB
ejpam-3650	29	26	minimum	minimum	NOUN
ejpam-3650	29	27	to	to	ADP
ejpam-3650	29	28	the	the	DET
ejpam-3650	29	29	functional	functional	ADJ
ejpam-3650	29	30	.	.	PUNCT
ejpam-3650	30	1	jα(v	jα(v	PROPN
ejpam-3650	30	2	)	)	PUNCT
ejpam-3650	31	1	=	=	SYM
ejpam-3650	31	2	j0(v	j0(v	PROPN
ejpam-3650	31	3	)	)	PUNCT
ejpam-3650	32	1	+	+	CCONJ
ejpam-3650	32	2	α	α	PROPN
ejpam-3650	32	3	2	2	NUM
ejpam-3650	32	4	∫	∫	PROPN
ejpam-3650	32	5	ω	ω	PROPN
ejpam-3650	32	6	|v(x)|2dx	|v(x)|2dx	PROPN
ejpam-3650	32	7	(	(	PUNCT
ejpam-3650	32	8	6	6	NUM
ejpam-3650	32	9	)	)	PUNCT
ejpam-3650	32	10	under	under	ADP
ejpam-3650	32	11	the	the	DET
ejpam-3650	32	12	constraints	constraint	NOUN
ejpam-3650	32	13	(	(	PUNCT
ejpam-3650	32	14	1	1	NUM
ejpam-3650	32	15	)	)	PUNCT
ejpam-3650	32	16	,	,	PUNCT
ejpam-3650	32	17	(	(	PUNCT
ejpam-3650	32	18	2	2	NUM
ejpam-3650	32	19	)	)	PUNCT
ejpam-3650	32	20	,	,	PUNCT
ejpam-3650	32	21	where	where	SCONJ
ejpam-3650	32	22	α	α	PROPN
ejpam-3650	32	23	>	>	X
ejpam-3650	32	24	0	0	NUM
ejpam-3650	32	25	is	be	AUX
ejpam-3650	32	26	the	the	DET
ejpam-3650	32	27	given	give	VERB
ejpam-3650	32	28	number	number	NOUN
ejpam-3650	32	29	.	.	PUNCT
ejpam-3650	33	1	this	this	DET
ejpam-3650	33	2	problem	problem	NOUN
ejpam-3650	33	3	will	will	AUX
ejpam-3650	33	4	be	be	AUX
ejpam-3650	33	5	called	call	VERB
ejpam-3650	33	6	problem	problem	NOUN
ejpam-3650	33	7	(	(	PUNCT
ejpam-3650	33	8	1	1	NUM
ejpam-3650	33	9	)	)	PUNCT
ejpam-3650	33	10	,	,	PUNCT
ejpam-3650	33	11	(	(	PUNCT
ejpam-3650	33	12	2	2	NUM
ejpam-3650	33	13	)	)	PUNCT
ejpam-3650	33	14	,	,	PUNCT
ejpam-3650	33	15	(	(	PUNCT
ejpam-3650	33	16	4	4	NUM
ejpam-3650	33	17	)	)	PUNCT
ejpam-3650	33	18	,	,	PUNCT
ejpam-3650	33	19	(	(	PUNCT
ejpam-3650	33	20	6	6	NUM
ejpam-3650	33	21	)	)	PUNCT
ejpam-3650	33	22	.	.	PUNCT
ejpam-3650	34	1	let	let	VERB
ejpam-3650	34	2	the	the	DET
ejpam-3650	34	3	following	follow	VERB
ejpam-3650	34	4	conditions	condition	NOUN
ejpam-3650	34	5	be	be	AUX
ejpam-3650	34	6	fulfilled	fulfil	VERB
ejpam-3650	34	7	on	on	ADP
ejpam-3650	34	8	the	the	DET
ejpam-3650	34	9	data	datum	NOUN
ejpam-3650	34	10	of	of	ADP
ejpam-3650	34	11	problem	problem	NOUN
ejpam-3650	34	12	(	(	PUNCT
ejpam-3650	34	13	1	1	NUM
ejpam-3650	34	14	)	)	PUNCT
ejpam-3650	34	15	,	,	PUNCT
ejpam-3650	34	16	(	(	PUNCT
ejpam-3650	34	17	2	2	NUM
ejpam-3650	34	18	)	)	PUNCT
ejpam-3650	34	19	,	,	PUNCT
ejpam-3650	34	20	(	(	PUNCT
ejpam-3650	34	21	4	4	NUM
ejpam-3650	34	22	)	)	PUNCT
ejpam-3650	34	23	,	,	PUNCT
ejpam-3650	34	24	(	(	PUNCT
ejpam-3650	34	25	6	6	NUM
ejpam-3650	34	26	)	)	PUNCT
ejpam-3650	34	27	.	.	PUNCT
ejpam-3650	35	1	1	1	X
ejpam-3650	35	2	.	.	X
ejpam-3650	35	3	the	the	DET
ejpam-3650	35	4	function	function	NOUN
ejpam-3650	35	5	f(x	f(x	PROPN
ejpam-3650	35	6	,	,	PUNCT
ejpam-3650	35	7	t	t	PROPN
ejpam-3650	35	8	,	,	PUNCT
ejpam-3650	35	9	u	u	NOUN
ejpam-3650	35	10	)	)	PUNCT
ejpam-3650	35	11	satisfies	satisfy	VERB
ejpam-3650	35	12	the	the	DET
ejpam-3650	35	13	carathéodory	carathéodory	NOUN
ejpam-3650	35	14	conditions	condition	NOUN
ejpam-3650	35	15	,	,	PUNCT
ejpam-3650	35	16	has	have	VERB
ejpam-3650	35	17	a	a	DET
ejpam-3650	35	18	continuous	continuous	ADJ
ejpam-3650	35	19	partial	partial	ADJ
ejpam-3650	35	20	derivative	derivative	NOUN
ejpam-3650	35	21	with	with	ADP
ejpam-3650	35	22	respect	respect	NOUN
ejpam-3650	35	23	to	to	ADP
ejpam-3650	35	24	u	u	PROPN
ejpam-3650	35	25	∈	∈	PROPN
ejpam-3650	35	26	r	r	NOUN
ejpam-3650	35	27	,	,	PUNCT
ejpam-3650	35	28	for	for	ADP
ejpam-3650	35	29	almost	almost	ADV
ejpam-3650	35	30	all	all	PRON
ejpam-3650	35	31	(	(	PUNCT
ejpam-3650	35	32	x	x	NOUN
ejpam-3650	35	33	,	,	PUNCT
ejpam-3650	35	34	t	t	PROPN
ejpam-3650	35	35	)	)	PUNCT
ejpam-3650	35	36	∈	∈	PROPN
ejpam-3650	35	37	q	q	NOUN
ejpam-3650	35	38	and	and	CCONJ
ejpam-3650	35	39	for	for	ADP
ejpam-3650	35	40	all	all	DET
ejpam-3650	35	41	u	u	NOUN
ejpam-3650	35	42	∈	∈	PROPN
ejpam-3650	35	43	r	r	NOUN
ejpam-3650	35	44	,	,	PUNCT
ejpam-3650	35	45	moreover	moreover	ADV
ejpam-3650	35	46	g.g	g.g	INTJ
ejpam-3650	35	47	ismayilova	ismayilova	PROPN
ejpam-3650	35	48	/	/	SYM
ejpam-3650	35	49	eur	eur	PROPN
ejpam-3650	35	50	.	.	PUNCT
ejpam-3650	36	1	j.	j.	PROPN
ejpam-3650	36	2	pure	pure	PROPN
ejpam-3650	36	3	appl	appl	PROPN
ejpam-3650	36	4	.	.	PROPN
ejpam-3650	36	5	math	math	PROPN
ejpam-3650	36	6	,	,	PUNCT
ejpam-3650	36	7	13	13	NUM
ejpam-3650	36	8	(	(	PUNCT
ejpam-3650	36	9	2	2	NUM
ejpam-3650	36	10	)	)	PUNCT
ejpam-3650	36	11	(	(	PUNCT
ejpam-3650	36	12	2020	2020	NUM
ejpam-3650	36	13	)	)	PUNCT
ejpam-3650	36	14	,	,	PUNCT
ejpam-3650	36	15	314	314	NUM
ejpam-3650	36	16	-	-	SYM
ejpam-3650	36	17	322	322	NUM
ejpam-3650	36	18	316	316	NUM
ejpam-3650	36	19	the	the	DET
ejpam-3650	36	20	derivative	derivative	ADJ
ejpam-3650	36	21	∂f(x	∂f(x	PROPN
ejpam-3650	36	22	,	,	PUNCT
ejpam-3650	36	23	t	t	PROPN
ejpam-3650	36	24	,	,	PUNCT
ejpam-3650	36	25	u	u	NOUN
ejpam-3650	36	26	)	)	PUNCT
ejpam-3650	36	27	∂u	∂u	PROPN
ejpam-3650	36	28	is	be	AUX
ejpam-3650	36	29	bounded	bound	VERB
ejpam-3650	36	30	,	,	PUNCT
ejpam-3650	36	31	f(x	f(x	PROPN
ejpam-3650	36	32	,	,	PUNCT
ejpam-3650	36	33	t	t	PROPN
ejpam-3650	36	34	,	,	PUNCT
ejpam-3650	36	35	0	0	NUM
ejpam-3650	36	36	)	)	PUNCT
ejpam-3650	36	37	∈	∈	PROPN
ejpam-3650	36	38	l2(q	l2(q	PROPN
ejpam-3650	36	39	)	)	PUNCT
ejpam-3650	36	40	,	,	PUNCT
ejpam-3650	36	41	and	and	CCONJ
ejpam-3650	36	42	the	the	DET
ejpam-3650	36	43	operator	operator	NOUN
ejpam-3650	36	44	∂f(x	∂f(x	PROPN
ejpam-3650	36	45	,	,	PUNCT
ejpam-3650	36	46	t	t	PROPN
ejpam-3650	36	47	,	,	PUNCT
ejpam-3650	36	48	u(x	u(x	PROPN
ejpam-3650	36	49	,	,	PUNCT
ejpam-3650	36	50	t	t	NOUN
ejpam-3650	36	51	)	)	PUNCT
ejpam-3650	36	52	)	)	PUNCT
ejpam-3650	37	1	∂u	∂u	PROPN
ejpam-3650	37	2	acts	act	VERB
ejpam-3650	37	3	continuously	continuously	ADV
ejpam-3650	37	4	from	from	ADP
ejpam-3650	37	5	l2(q	l2(q	PROPN
ejpam-3650	37	6	)	)	PUNCT
ejpam-3650	37	7	to	to	ADP
ejpam-3650	37	8	l2(q	l2(q	PROPN
ejpam-3650	37	9	)	)	PUNCT
ejpam-3650	37	10	.	.	PUNCT
ejpam-3650	38	1	2	2	X
ejpam-3650	38	2	.	.	X
ejpam-3650	38	3	u0	u0	PROPN
ejpam-3650	38	4	∈	∈	PROPN
ejpam-3650	39	1	◦	◦	NOUN
ejpam-3650	39	2	w	w	ADP
ejpam-3650	39	3	1	1	NUM
ejpam-3650	39	4	2	2	NUM
ejpam-3650	39	5	(	(	PUNCT
ejpam-3650	39	6	ω	ω	NOUN
ejpam-3650	39	7	)	)	PUNCT
ejpam-3650	39	8	,	,	PUNCT
ejpam-3650	39	9	u1	u1	PROPN
ejpam-3650	39	10	∈	∈	PROPN
ejpam-3650	39	11	l2(ω),k	l2(ω),k	PROPN
ejpam-3650	39	12	∈	∈	PROPN
ejpam-3650	39	13	l∞(q	l∞(q	NOUN
ejpam-3650	39	14	)	)	PUNCT
ejpam-3650	39	15	,	,	PUNCT
ejpam-3650	39	16	ϕ	ϕ	PROPN
ejpam-3650	39	17	∈	∈	PROPN
ejpam-3650	39	18	l2(ω	l2(ω	PROPN
ejpam-3650	39	19	)	)	PUNCT
ejpam-3650	39	20	.	.	PUNCT
ejpam-3650	40	1	since	since	SCONJ
ejpam-3650	40	2	,	,	PUNCT
ejpam-3650	40	3	under	under	ADP
ejpam-3650	40	4	the	the	DET
ejpam-3650	40	5	imposed	impose	VERB
ejpam-3650	40	6	conditions	condition	NOUN
ejpam-3650	40	7	,	,	PUNCT
ejpam-3650	40	8	the	the	DET
ejpam-3650	40	9	function	function	NOUN
ejpam-3650	40	10	f(x	f(x	PROPN
ejpam-3650	40	11	,	,	PUNCT
ejpam-3650	40	12	t	t	PROPN
ejpam-3650	40	13	,	,	PUNCT
ejpam-3650	40	14	u	u	NOUN
ejpam-3650	40	15	)	)	PUNCT
ejpam-3650	40	16	satisfies	satisfy	VERB
ejpam-3650	40	17	the	the	DET
ejpam-3650	40	18	lipschitz	lipschitz	NOUN
ejpam-3650	40	19	condition	condition	NOUN
ejpam-3650	40	20	with	with	ADP
ejpam-3650	40	21	respect	respect	NOUN
ejpam-3650	40	22	to	to	ADP
ejpam-3650	40	23	u	u	NOUN
ejpam-3650	40	24	,	,	PUNCT
ejpam-3650	40	25	applying	apply	VERB
ejpam-3650	40	26	the	the	DET
ejpam-3650	40	27	faedo	faedo	NOUN
ejpam-3650	40	28	-	-	PUNCT
ejpam-3650	40	29	galarkin	galarkin	NOUN
ejpam-3650	40	30	method	method	NOUN
ejpam-3650	40	31	[	[	X
ejpam-3650	40	32	13],[14	13],[14	X
ejpam-3650	40	33	]	]	X
ejpam-3650	40	34	under	under	ADP
ejpam-3650	40	35	conditions	condition	NOUN
ejpam-3650	40	36	1.,2	1.,2	NUM
ejpam-3650	40	37	.	.	PUNCT
ejpam-3650	41	1	it	it	PRON
ejpam-3650	41	2	is	be	AUX
ejpam-3650	41	3	easy	easy	ADJ
ejpam-3650	41	4	to	to	PART
ejpam-3650	41	5	prove	prove	VERB
ejpam-3650	41	6	that	that	SCONJ
ejpam-3650	41	7	for	for	ADP
ejpam-3650	41	8	each	each	DET
ejpam-3650	41	9	v(x	v(x	PROPN
ejpam-3650	41	10	)	)	PUNCT
ejpam-3650	41	11	∈	∈	PROPN
ejpam-3650	41	12	v	v	ADP
ejpam-3650	41	13	the	the	DET
ejpam-3650	41	14	boundary	boundary	ADJ
ejpam-3650	41	15	value	value	NOUN
ejpam-3650	41	16	problem	problem	NOUN
ejpam-3650	41	17	(	(	PUNCT
ejpam-3650	41	18	1	1	NUM
ejpam-3650	41	19	)	)	PUNCT
ejpam-3650	41	20	,	,	PUNCT
ejpam-3650	41	21	(	(	PUNCT
ejpam-3650	41	22	2	2	X
ejpam-3650	41	23	)	)	PUNCT
ejpam-3650	41	24	has	have	VERB
ejpam-3650	41	25	a	a	DET
ejpam-3650	41	26	unique	unique	ADJ
ejpam-3650	41	27	generalized	generalized	ADJ
ejpam-3650	41	28	solution	solution	NOUN
ejpam-3650	41	29	from	from	ADP
ejpam-3650	41	30	u	u	NOUN
ejpam-3650	41	31	=	=	PUNCT
ejpam-3650	41	32	{	{	PUNCT
ejpam-3650	42	1	u|u	u|u	PROPN
ejpam-3650	42	2	∈	∈	PROPN
ejpam-3650	42	3	c	c	NOUN
ejpam-3650	42	4	(	(	PUNCT
ejpam-3650	42	5	[	[	X
ejpam-3650	42	6	0	0	NUM
ejpam-3650	42	7	,	,	PUNCT
ejpam-3650	42	8	t	t	X
ejpam-3650	42	9	]	]	PUNCT
ejpam-3650	42	10	;	;	PUNCT
ejpam-3650	42	11	◦	◦	NOUN
ejpam-3650	42	12	w	w	NUM
ejpam-3650	42	13	1	1	NUM
ejpam-3650	42	14	2	2	NUM
ejpam-3650	42	15	(	(	PUNCT
ejpam-3650	42	16	ω	ω	NOUN
ejpam-3650	42	17	)	)	PUNCT
ejpam-3650	42	18	)	)	PUNCT
ejpam-3650	42	19	,	,	PUNCT
ejpam-3650	42	20	∂u	∂u	PROPN
ejpam-3650	42	21	∂t	∂t	PROPN
ejpam-3650	42	22	∈	∈	PROPN
ejpam-3650	42	23	c	c	NOUN
ejpam-3650	42	24	(	(	PUNCT
ejpam-3650	42	25	[	[	X
ejpam-3650	42	26	0	0	NUM
ejpam-3650	42	27	,	,	PUNCT
ejpam-3650	42	28	t	t	X
ejpam-3650	42	29	]	]	PUNCT
ejpam-3650	42	30	;	;	PUNCT
ejpam-3650	42	31	l2(ω	l2(ω	NUM
ejpam-3650	42	32	)	)	PUNCT
ejpam-3650	42	33	)	)	PUNCT
ejpam-3650	42	34	}	}	PUNCT
ejpam-3650	42	35	and	and	CCONJ
ejpam-3650	42	36	following	follow	VERB
ejpam-3650	42	37	estimation	estimation	NOUN
ejpam-3650	42	38	is	be	AUX
ejpam-3650	42	39	true	true	ADJ
ejpam-3650	42	40	for	for	ADP
ejpam-3650	42	41	this	this	DET
ejpam-3650	42	42	solution	solution	NOUN
ejpam-3650	42	43	‖u‖	‖u‖	PROPN
ejpam-3650	42	44	◦	◦	VERB
ejpam-3650	42	45	w	w	NUM
ejpam-3650	42	46	1	1	NUM
ejpam-3650	42	47	2	2	NUM
ejpam-3650	42	48	(	(	PUNCT
ejpam-3650	42	49	ω	ω	NOUN
ejpam-3650	42	50	)	)	PUNCT
ejpam-3650	42	51	(	(	PUNCT
ejpam-3650	42	52	ω	ω	NOUN
ejpam-3650	42	53	)	)	PUNCT
ejpam-3650	42	54	+	+	CCONJ
ejpam-3650	42	55	∥∥∥∥∂u∂t	∥∥∥∥∂u∂t	NOUN
ejpam-3650	42	56	∥∥∥∥	∥∥∥∥	NUM
ejpam-3650	42	57	l2(ω	l2(ω	NOUN
ejpam-3650	42	58	)	)	PUNCT
ejpam-3650	42	59	≤	≤	NOUN
ejpam-3650	42	60	≤	≤	NUM
ejpam-3650	42	61	c	c	NOUN
ejpam-3650	42	62	[	[	PUNCT
ejpam-3650	42	63	‖u0‖	‖u0‖	NOUN
ejpam-3650	42	64	◦	◦	NOUN
ejpam-3650	42	65	w	w	NOUN
ejpam-3650	42	66	1	1	NUM
ejpam-3650	42	67	2	2	NUM
ejpam-3650	42	68	(	(	PUNCT
ejpam-3650	42	69	ω	ω	NOUN
ejpam-3650	42	70	)	)	PUNCT
ejpam-3650	42	71	+	+	CCONJ
ejpam-3650	42	72	‖u1‖l2(ω	‖u1‖l2(ω	NUM
ejpam-3650	42	73	)	)	PUNCT
ejpam-3650	43	1	+	+	CCONJ
ejpam-3650	43	2	‖f(x	‖f(x	NUM
ejpam-3650	43	3	,	,	PUNCT
ejpam-3650	43	4	t	t	PROPN
ejpam-3650	43	5	,	,	PUNCT
ejpam-3650	43	6	0)‖l2(q	0)‖l2(q	NUM
ejpam-3650	43	7	)	)	PUNCT
ejpam-3650	43	8	]	]	PUNCT
ejpam-3650	43	9	,	,	PUNCT
ejpam-3650	43	10	t	t	PROPN
ejpam-3650	43	11	∈	∈	PROPN
ejpam-3650	44	1	[	[	X
ejpam-3650	44	2	0	0	NUM
ejpam-3650	44	3	,	,	PUNCT
ejpam-3650	44	4	t	t	NOUN
ejpam-3650	44	5	]	]	PUNCT
ejpam-3650	44	6	.	.	PUNCT
ejpam-3650	45	1	(	(	PUNCT
ejpam-3650	45	2	7	7	X
ejpam-3650	45	3	)	)	PUNCT
ejpam-3650	45	4	here	here	ADV
ejpam-3650	45	5	and	and	CCONJ
ejpam-3650	45	6	in	in	ADP
ejpam-3650	45	7	the	the	DET
ejpam-3650	45	8	future	future	NOUN
ejpam-3650	45	9	,	,	PUNCT
ejpam-3650	45	10	with	with	ADP
ejpam-3650	45	11	c	c	NOUN
ejpam-3650	45	12	we	we	PRON
ejpam-3650	45	13	denote	denote	VERB
ejpam-3650	45	14	various	various	ADJ
ejpam-3650	45	15	constants	constant	NOUN
ejpam-3650	45	16	that	that	PRON
ejpam-3650	45	17	are	be	AUX
ejpam-3650	45	18	independent	independent	ADJ
ejpam-3650	45	19	of	of	ADP
ejpam-3650	45	20	the	the	DET
ejpam-3650	45	21	estimated	estimate	VERB
ejpam-3650	45	22	quantities	quantity	NOUN
ejpam-3650	45	23	and	and	CCONJ
ejpam-3650	45	24	of	of	ADP
ejpam-3650	45	25	the	the	DET
ejpam-3650	45	26	admissible	admissible	ADJ
ejpam-3650	45	27	controls	control	NOUN
ejpam-3650	45	28	.	.	PUNCT
ejpam-3650	46	1	by	by	ADP
ejpam-3650	46	2	a	a	DET
ejpam-3650	46	3	generalized	generalized	ADJ
ejpam-3650	46	4	solution	solution	NOUN
ejpam-3650	46	5	of	of	ADP
ejpam-3650	46	6	the	the	DET
ejpam-3650	46	7	problem	problem	NOUN
ejpam-3650	46	8	(	(	PUNCT
ejpam-3650	46	9	1	1	NUM
ejpam-3650	46	10	)	)	PUNCT
ejpam-3650	46	11	,	,	PUNCT
ejpam-3650	46	12	(	(	PUNCT
ejpam-3650	46	13	2	2	X
ejpam-3650	46	14	)	)	PUNCT
ejpam-3650	46	15	for	for	ADP
ejpam-3650	46	16	a	a	DET
ejpam-3650	46	17	given	give	VERB
ejpam-3650	46	18	function	function	NOUN
ejpam-3650	46	19	v(x	v(x	PROPN
ejpam-3650	46	20	)	)	PUNCT
ejpam-3650	46	21	∈	∈	PROPN
ejpam-3650	46	22	v	v	NOUN
ejpam-3650	46	23	we	we	PRON
ejpam-3650	46	24	mean	mean	VERB
ejpam-3650	46	25	a	a	DET
ejpam-3650	46	26	function	function	NOUN
ejpam-3650	46	27	u	u	NOUN
ejpam-3650	46	28	=	=	SYM
ejpam-3650	46	29	u(x	u(x	PROPN
ejpam-3650	46	30	,	,	PUNCT
ejpam-3650	46	31	t	t	PROPN
ejpam-3650	46	32	;	;	PUNCT
ejpam-3650	46	33	v	v	NOUN
ejpam-3650	46	34	)	)	PUNCT
ejpam-3650	46	35	from	from	ADP
ejpam-3650	46	36	u	u	PRON
ejpam-3650	46	37	such	such	ADJ
ejpam-3650	46	38	that	that	PRON
ejpam-3650	46	39	for	for	ADP
ejpam-3650	46	40	t	t	NOUN
ejpam-3650	47	1	=	=	SYM
ejpam-3650	47	2	0	0	NUM
ejpam-3650	48	1	it	it	PRON
ejpam-3650	48	2	satisfies	satisfy	VERB
ejpam-3650	48	3	the	the	DET
ejpam-3650	48	4	condition	condition	NOUN
ejpam-3650	48	5	u(x	u(x	NOUN
ejpam-3650	48	6	,	,	PUNCT
ejpam-3650	48	7	0	0	NUM
ejpam-3650	48	8	)	)	PUNCT
ejpam-3650	48	9	=	=	SYM
ejpam-3650	48	10	u0(x	u0(x	NOUN
ejpam-3650	48	11	)	)	PUNCT
ejpam-3650	48	12	and	and	CCONJ
ejpam-3650	48	13	the	the	DET
ejpam-3650	48	14	integral	integral	ADJ
ejpam-3650	48	15	identity∫	identity∫	X
ejpam-3650	48	16	q	q	X
ejpam-3650	48	17	[	[	PUNCT
ejpam-3650	48	18	−∂u	−∂u	NUM
ejpam-3650	48	19	∂t	∂t	PROPN
ejpam-3650	48	20	∂η	∂η	PROPN
ejpam-3650	48	21	∂t	∂t	PROPN
ejpam-3650	49	1	+	+	CCONJ
ejpam-3650	49	2	n∑	n∑	PROPN
ejpam-3650	49	3	i=1	i=1	PROPN
ejpam-3650	49	4	∂u	∂u	PROPN
ejpam-3650	49	5	∂xi	∂xi	PROPN
ejpam-3650	49	6	∂η	∂η	PROPN
ejpam-3650	49	7	∂xi	∂xi	NOUN
ejpam-3650	49	8	+	+	CCONJ
ejpam-3650	49	9	vuη	vuη	NOUN
ejpam-3650	49	10	]	]	PUNCT
ejpam-3650	49	11	dxdt−	dxdt−	NOUN
ejpam-3650	49	12	∫	∫	PROPN
ejpam-3650	49	13	ω	ω	PROPN
ejpam-3650	49	14	u1(x)η(x	u1(x)η(x	PROPN
ejpam-3650	49	15	,	,	PUNCT
ejpam-3650	49	16	0)dx	0)dx	PUNCT
ejpam-3650	49	17	=	=	SYM
ejpam-3650	49	18	∫	∫	PROPN
ejpam-3650	50	1	q	q	PROPN
ejpam-3650	50	2	f(x	f(x	PROPN
ejpam-3650	50	3	,	,	PUNCT
ejpam-3650	50	4	t	t	PROPN
ejpam-3650	50	5	,	,	PUNCT
ejpam-3650	50	6	u)ηdxdt	u)ηdxdt	PROPN
ejpam-3650	50	7	(	(	PUNCT
ejpam-3650	50	8	8)	8)	NUM
ejpam-3650	50	9	for	for	ADP
ejpam-3650	50	10	all	all	DET
ejpam-3650	50	11	η	η	X
ejpam-3650	50	12	=	=	SYM
ejpam-3650	50	13	η(x	η(x	PROPN
ejpam-3650	50	14	,	,	PUNCT
ejpam-3650	50	15	t	t	PROPN
ejpam-3650	50	16	)	)	PUNCT
ejpam-3650	50	17	from	from	ADP
ejpam-3650	50	18	u	u	PRON
ejpam-3650	50	19	and	and	CCONJ
ejpam-3650	50	20	are	be	AUX
ejpam-3650	50	21	equal	equal	ADJ
ejpam-3650	50	22	to	to	ADP
ejpam-3650	50	23	zero	zero	NUM
ejpam-3650	50	24	for	for	ADP
ejpam-3650	50	25	t	t	PROPN
ejpam-3650	50	26	=	=	SYM
ejpam-3650	50	27	t	t	PROPN
ejpam-3650	50	28	.	.	PUNCT
ejpam-3650	51	1	3	3	X
ejpam-3650	51	2	.	.	X
ejpam-3650	51	3	the	the	DET
ejpam-3650	51	4	existence	existence	NOUN
ejpam-3650	51	5	of	of	ADP
ejpam-3650	51	6	optimal	optimal	ADJ
ejpam-3650	51	7	control	control	NOUN
ejpam-3650	51	8	in	in	ADP
ejpam-3650	51	9	problem	problem	NOUN
ejpam-3650	51	10	(	(	PUNCT
ejpam-3650	51	11	1	1	NUM
ejpam-3650	51	12	)	)	PUNCT
ejpam-3650	51	13	,	,	PUNCT
ejpam-3650	51	14	(	(	PUNCT
ejpam-3650	51	15	2	2	NUM
ejpam-3650	51	16	)	)	PUNCT
ejpam-3650	51	17	,	,	PUNCT
ejpam-3650	51	18	(	(	PUNCT
ejpam-3650	51	19	4	4	NUM
ejpam-3650	51	20	)	)	PUNCT
ejpam-3650	51	21	,	,	PUNCT
ejpam-3650	51	22	(	(	PUNCT
ejpam-3650	51	23	6	6	X
ejpam-3650	51	24	)	)	PUNCT
ejpam-3650	51	25	theorem	theorem	NOUN
ejpam-3650	51	26	1	1	NUM
ejpam-3650	51	27	.	.	PUNCT
ejpam-3650	52	1	let	let	VERB
ejpam-3650	52	2	the	the	DET
ejpam-3650	52	3	conditions	condition	NOUN
ejpam-3650	52	4	accepted	accept	VERB
ejpam-3650	52	5	in	in	ADP
ejpam-3650	52	6	the	the	DET
ejpam-3650	52	7	statement	statement	NOUN
ejpam-3650	52	8	of	of	ADP
ejpam-3650	52	9	problem	problem	NOUN
ejpam-3650	52	10	(	(	PUNCT
ejpam-3650	52	11	1	1	NUM
ejpam-3650	52	12	)	)	PUNCT
ejpam-3650	52	13	,	,	PUNCT
ejpam-3650	52	14	(	(	PUNCT
ejpam-3650	52	15	2	2	NUM
ejpam-3650	52	16	)	)	PUNCT
ejpam-3650	52	17	,	,	PUNCT
ejpam-3650	52	18	(	(	PUNCT
ejpam-3650	52	19	4	4	NUM
ejpam-3650	52	20	)	)	PUNCT
ejpam-3650	52	21	,	,	PUNCT
ejpam-3650	52	22	(	(	PUNCT
ejpam-3650	52	23	6	6	X
ejpam-3650	52	24	)	)	PUNCT
ejpam-3650	52	25	be	be	AUX
ejpam-3650	52	26	satisfied	satisfied	ADJ
ejpam-3650	52	27	.	.	PUNCT
ejpam-3650	53	1	then	then	ADV
ejpam-3650	53	2	the	the	DET
ejpam-3650	53	3	set	set	NOUN
ejpam-3650	53	4	of	of	ADP
ejpam-3650	53	5	optimal	optimal	ADJ
ejpam-3650	53	6	controls	control	NOUN
ejpam-3650	53	7	of	of	ADP
ejpam-3650	53	8	problem	problem	NOUN
ejpam-3650	53	9	(	(	PUNCT
ejpam-3650	53	10	1	1	NUM
ejpam-3650	53	11	)	)	PUNCT
ejpam-3650	53	12	,	,	PUNCT
ejpam-3650	53	13	(	(	PUNCT
ejpam-3650	53	14	2	2	NUM
ejpam-3650	53	15	)	)	PUNCT
ejpam-3650	53	16	,	,	PUNCT
ejpam-3650	53	17	(	(	PUNCT
ejpam-3650	53	18	4	4	NUM
ejpam-3650	53	19	)	)	PUNCT
ejpam-3650	53	20	,	,	PUNCT
ejpam-3650	53	21	(	(	PUNCT
ejpam-3650	53	22	6	6	X
ejpam-3650	53	23	)	)	PUNCT
ejpam-3650	53	24	v∗	v∗	NOUN
ejpam-3650	53	25	=	=	NOUN
ejpam-3650	53	26	{	{	PUNCT
ejpam-3650	53	27	v	v	NUM
ejpam-3650	53	28	∈	∈	PROPN
ejpam-3650	53	29	v	v	NOUN
ejpam-3650	53	30	/	/	SYM
ejpam-3650	53	31	jα(v	jα(v	PROPN
ejpam-3650	53	32	)	)	PUNCT
ejpam-3650	54	1	=	=	PRON
ejpam-3650	54	2	jα∗	jα∗	NOUN
ejpam-3650	54	3	=	=	SYM
ejpam-3650	54	4	inf	inf	PROPN
ejpam-3650	54	5	v∈v	v∈v	NOUN
ejpam-3650	54	6	jα(v	jα(v	PROPN
ejpam-3650	54	7	)	)	PUNCT
ejpam-3650	54	8	}	}	PUNCT
ejpam-3650	54	9	is	be	AUX
ejpam-3650	54	10	nonempty	nonempty	ADJ
ejpam-3650	54	11	,	,	PUNCT
ejpam-3650	54	12	weakly	weakly	ADJ
ejpam-3650	54	13	compact	compact	ADJ
ejpam-3650	54	14	in	in	ADP
ejpam-3650	54	15	l2(ω	l2(ω	NOUN
ejpam-3650	54	16	)	)	PUNCT
ejpam-3650	54	17	,	,	PUNCT
ejpam-3650	54	18	and	and	CCONJ
ejpam-3650	54	19	any	any	DET
ejpam-3650	54	20	minimizing	minimize	VERB
ejpam-3650	54	21	sequence	sequence	NOUN
ejpam-3650	54	22	{	{	PUNCT
ejpam-3650	54	23	vm	vm	NOUN
ejpam-3650	54	24	}	}	PUNCT
ejpam-3650	54	25	weakly	weakly	ADJ
ejpam-3650	54	26	converges	converge	VERB
ejpam-3650	54	27	to	to	ADP
ejpam-3650	54	28	the	the	DET
ejpam-3650	54	29	set	set	NOUN
ejpam-3650	54	30	v∗	v∗	NOUN
ejpam-3650	54	31	in	in	ADP
ejpam-3650	54	32	l2(ω	l2(ω	NOUN
ejpam-3650	54	33	)	)	PUNCT
ejpam-3650	54	34	.	.	PUNCT
ejpam-3650	55	1	proof	proof	NOUN
ejpam-3650	55	2	.	.	PUNCT
ejpam-3650	56	1	the	the	DET
ejpam-3650	56	2	set	set	NOUN
ejpam-3650	56	3	v	v	NOUN
ejpam-3650	56	4	defined	define	VERB
ejpam-3650	56	5	by	by	ADP
ejpam-3650	56	6	relation	relation	NOUN
ejpam-3650	56	7	(	(	PUNCT
ejpam-3650	56	8	4	4	NUM
ejpam-3650	56	9	)	)	PUNCT
ejpam-3650	56	10	is	be	AUX
ejpam-3650	56	11	weakly	weakly	ADV
ejpam-3650	56	12	compact	compact	ADJ
ejpam-3650	56	13	in	in	ADP
ejpam-3650	56	14	l2(ω	l2(ω	NOUN
ejpam-3650	56	15	)	)	PUNCT
ejpam-3650	56	16	.	.	PUNCT
ejpam-3650	57	1	we	we	PRON
ejpam-3650	57	2	show	show	VERB
ejpam-3650	57	3	that	that	SCONJ
ejpam-3650	57	4	functional	functional	ADJ
ejpam-3650	57	5	(	(	PUNCT
ejpam-3650	57	6	6	6	NUM
ejpam-3650	57	7	)	)	PUNCT
ejpam-3650	57	8	is	be	AUX
ejpam-3650	57	9	weakly	weakly	ADV
ejpam-3650	57	10	lower	low	ADJ
ejpam-3650	57	11	semicontinuous	semicontinuous	ADJ
ejpam-3650	57	12	on	on	ADP
ejpam-3650	57	13	the	the	DET
ejpam-3650	57	14	set	set	NOUN
ejpam-3650	57	15	v	v	NOUN
ejpam-3650	57	16	.	.	PUNCT
ejpam-3650	58	1	let	let	VERB
ejpam-3650	58	2	v(x	v(x	NOUN
ejpam-3650	58	3	)	)	PUNCT
ejpam-3650	58	4	∈	∈	PROPN
ejpam-3650	58	5	v	v	NOUN
ejpam-3650	58	6	be	be	AUX
ejpam-3650	58	7	some	some	DET
ejpam-3650	58	8	element	element	NOUN
ejpam-3650	58	9	and	and	CCONJ
ejpam-3650	58	10	{	{	PUNCT
ejpam-3650	58	11	vm	vm	PROPN
ejpam-3650	58	12	}	}	PUNCT
ejpam-3650	58	13	⊂	⊂	PROPN
ejpam-3650	58	14	v	v	ADP
ejpam-3650	58	15	an	an	DET
ejpam-3650	58	16	arbitrary	arbitrary	ADJ
ejpam-3650	58	17	sequence	sequence	NOUN
ejpam-3650	58	18	such	such	ADJ
ejpam-3650	58	19	that	that	PRON
ejpam-3650	58	20	vm	vm	PROPN
ejpam-3650	58	21	→	→	SYM
ejpam-3650	58	22	v	v	NOUN
ejpam-3650	58	23	weakly	weakly	ADV
ejpam-3650	58	24	in	in	ADP
ejpam-3650	58	25	l2(ω	l2(ω	NOUN
ejpam-3650	58	26	)	)	PUNCT
ejpam-3650	58	27	.	.	PUNCT
ejpam-3650	59	1	due	due	ADP
ejpam-3650	59	2	to	to	ADP
ejpam-3650	59	3	the	the	DET
ejpam-3650	59	4	unique	unique	ADJ
ejpam-3650	59	5	solvability	solvability	NOUN
ejpam-3650	59	6	of	of	ADP
ejpam-3650	59	7	the	the	DET
ejpam-3650	59	8	boundary	boundary	ADJ
ejpam-3650	59	9	value	value	NOUN
ejpam-3650	59	10	problem	problem	NOUN
ejpam-3650	59	11	(	(	PUNCT
ejpam-3650	59	12	1	1	NUM
ejpam-3650	59	13	)	)	PUNCT
ejpam-3650	59	14	,	,	PUNCT
ejpam-3650	59	15	(	(	PUNCT
ejpam-3650	59	16	2	2	NUM
ejpam-3650	59	17	)	)	PUNCT
ejpam-3650	59	18	,	,	PUNCT
ejpam-3650	59	19	to	to	ADP
ejpam-3650	59	20	each	each	DET
ejpam-3650	59	21	control	control	NOUN
ejpam-3650	59	22	vm	vm	PROPN
ejpam-3650	59	23	∈	∈	PROPN
ejpam-3650	59	24	v	v	NOUN
ejpam-3650	59	25	corresponds	correspond	VERB
ejpam-3650	59	26	a	a	DET
ejpam-3650	59	27	unique	unique	ADJ
ejpam-3650	59	28	solution	solution	NOUN
ejpam-3650	59	29	um	um	INTJ
ejpam-3650	59	30	=	=	SYM
ejpam-3650	59	31	u(x	u(x	PROPN
ejpam-3650	59	32	,	,	PUNCT
ejpam-3650	59	33	t	t	PROPN
ejpam-3650	59	34	;	;	PUNCT
ejpam-3650	59	35	vm	vm	NOUN
ejpam-3650	59	36	)	)	PUNCT
ejpam-3650	59	37	of	of	ADP
ejpam-3650	59	38	the	the	DET
ejpam-3650	59	39	problem	problem	NOUN
ejpam-3650	59	40	(	(	PUNCT
ejpam-3650	59	41	1	1	NUM
ejpam-3650	59	42	)	)	PUNCT
ejpam-3650	59	43	,	,	PUNCT
ejpam-3650	59	44	(	(	PUNCT
ejpam-3650	59	45	2	2	X
ejpam-3650	59	46	)	)	PUNCT
ejpam-3650	59	47	and	and	CCONJ
ejpam-3650	59	48	,	,	PUNCT
ejpam-3650	59	49	by	by	ADP
ejpam-3650	59	50	g.g	g.g	INTJ
ejpam-3650	59	51	ismayilova	ismayilova	PROPN
ejpam-3650	59	52	/	/	SYM
ejpam-3650	59	53	eur	eur	PROPN
ejpam-3650	59	54	.	.	PUNCT
ejpam-3650	60	1	j.	j.	PROPN
ejpam-3650	60	2	pure	pure	PROPN
ejpam-3650	60	3	appl	appl	PROPN
ejpam-3650	60	4	.	.	PROPN
ejpam-3650	60	5	math	math	PROPN
ejpam-3650	60	6	,	,	PUNCT
ejpam-3650	60	7	13	13	NUM
ejpam-3650	60	8	(	(	PUNCT
ejpam-3650	60	9	2	2	NUM
ejpam-3650	60	10	)	)	PUNCT
ejpam-3650	60	11	(	(	PUNCT
ejpam-3650	60	12	2020	2020	NUM
ejpam-3650	60	13	)	)	PUNCT
ejpam-3650	60	14	,	,	PUNCT
ejpam-3650	60	15	314	314	NUM
ejpam-3650	60	16	-	-	SYM
ejpam-3650	60	17	322	322	NUM
ejpam-3650	60	18	317	317	NUM
ejpam-3650	60	19	virtue	virtue	NOUN
ejpam-3650	60	20	of	of	ADP
ejpam-3650	60	21	the	the	DET
ejpam-3650	60	22	estimate	estimate	NOUN
ejpam-3650	60	23	(	(	PUNCT
ejpam-3650	60	24	7	7	NUM
ejpam-3650	60	25	)	)	PUNCT
ejpam-3650	60	26	,	,	PUNCT
ejpam-3650	60	27	the	the	DET
ejpam-3650	60	28	estimate	estimate	NOUN
ejpam-3650	60	29	‖um‖w	‖um‖w	PROPN
ejpam-3650	60	30	1	1	NUM
ejpam-3650	60	31	2,0(q	2,0(q	NOUN
ejpam-3650	60	32	)	)	PUNCT
ejpam-3650	60	33	≤	≤	NOUN
ejpam-3650	61	1	c	c	X
ejpam-3650	61	2	,	,	PUNCT
ejpam-3650	61	3	∀m	∀m	NOUN
ejpam-3650	61	4	=	=	SYM
ejpam-3650	61	5	1	1	NUM
ejpam-3650	61	6	,	,	PUNCT
ejpam-3650	61	7	2	2	NUM
ejpam-3650	61	8	,	,	PUNCT
ejpam-3650	61	9	...	...	PUNCT
ejpam-3650	61	10	,	,	PUNCT
ejpam-3650	61	11	holds	hold	VERB
ejpam-3650	61	12	i.e.	i.e.	X
ejpam-3650	61	13	the	the	DET
ejpam-3650	61	14	sequence	sequence	NOUN
ejpam-3650	61	15	is	be	AUX
ejpam-3650	61	16	uniformly	uniformly	ADV
ejpam-3650	61	17	bounded	bound	VERB
ejpam-3650	61	18	in	in	ADP
ejpam-3650	61	19	the	the	DET
ejpam-3650	61	20	norm	norm	NOUN
ejpam-3650	61	21	of	of	ADP
ejpam-3650	61	22	the	the	DET
ejpam-3650	61	23	space	space	NOUN
ejpam-3650	61	24	w	w	PROPN
ejpam-3650	61	25	1	1	NUM
ejpam-3650	61	26	2,0(q	2,0(q	NOUN
ejpam-3650	61	27	)	)	PUNCT
ejpam-3650	61	28	.	.	PUNCT
ejpam-3650	62	1	then	then	ADV
ejpam-3650	62	2	it	it	PRON
ejpam-3650	62	3	follows	follow	VERB
ejpam-3650	62	4	from	from	ADP
ejpam-3650	62	5	the	the	DET
ejpam-3650	62	6	embedding	embed	VERB
ejpam-3650	62	7	theorem	theorem	NOUN
ejpam-3650	62	8	[	[	X
ejpam-3650	62	9	see	see	VERB
ejpam-3650	62	10	[	[	X
ejpam-3650	62	11	15	15	NUM
ejpam-3650	62	12	]	]	PUNCT
ejpam-3650	62	13	,	,	PUNCT
ejpam-3650	62	14	p.	p.	NOUN
ejpam-3650	62	15	106	106	NUM
ejpam-3650	62	16	]	]	PUNCT
ejpam-3650	62	17	that	that	SCONJ
ejpam-3650	62	18	,	,	PUNCT
ejpam-3650	62	19	from	from	ADP
ejpam-3650	62	20	sequence	sequence	NOUN
ejpam-3650	62	21	{	{	PUNCT
ejpam-3650	62	22	um	um	INTJ
ejpam-3650	62	23	}	}	PUNCT
ejpam-3650	62	24	can	can	AUX
ejpam-3650	62	25	be	be	AUX
ejpam-3650	62	26	chosen	choose	VERB
ejpam-3650	62	27	a	a	DET
ejpam-3650	62	28	sequence	sequence	NOUN
ejpam-3650	62	29	(	(	PUNCT
ejpam-3650	62	30	we	we	PRON
ejpam-3650	62	31	also	also	ADV
ejpam-3650	62	32	denote	denote	VERB
ejpam-3650	62	33	it	it	PRON
ejpam-3650	62	34	by	by	ADP
ejpam-3650	62	35	{	{	PUNCT
ejpam-3650	62	36	um	um	INTJ
ejpam-3650	62	37	}	}	PUNCT
ejpam-3650	62	38	)	)	PUNCT
ejpam-3650	62	39	that	that	SCONJ
ejpam-3650	62	40	um	um	INTJ
ejpam-3650	62	41	→	→	SYM
ejpam-3650	62	42	u	u	NOUN
ejpam-3650	62	43	strongly	strongly	ADV
ejpam-3650	62	44	in	in	ADP
ejpam-3650	62	45	l2(q	l2(q	PROPN
ejpam-3650	62	46	)	)	PUNCT
ejpam-3650	62	47	,	,	PUNCT
ejpam-3650	62	48	(	(	PUNCT
ejpam-3650	62	49	9	9	X
ejpam-3650	62	50	)	)	PUNCT
ejpam-3650	62	51	∂um	∂um	PROPN
ejpam-3650	62	52	∂t	∂t	PROPN
ejpam-3650	62	53	→	→	SYM
ejpam-3650	62	54	∂u	∂u	PROPN
ejpam-3650	62	55	∂t	∂t	PROPN
ejpam-3650	62	56	,	,	PUNCT
ejpam-3650	62	57	∂um	∂um	PROPN
ejpam-3650	62	58	∂xi	∂xi	PROPN
ejpam-3650	62	59	→	→	SYM
ejpam-3650	62	60	∂um	∂um	PROPN
ejpam-3650	62	61	∂xi	∂xi	NOUN
ejpam-3650	62	62	,	,	PUNCT
ejpam-3650	62	63	i	i	NOUN
ejpam-3650	62	64	=	=	NOUN
ejpam-3650	62	65	1	1	NUM
ejpam-3650	62	66	,	,	PUNCT
ejpam-3650	62	67	n	n	PRON
ejpam-3650	62	68	weakly	weakly	ADV
ejpam-3650	62	69	in	in	ADP
ejpam-3650	62	70	l2(q	l2(q	PROPN
ejpam-3650	62	71	)	)	PUNCT
ejpam-3650	62	72	,	,	PUNCT
ejpam-3650	62	73	(	(	PUNCT
ejpam-3650	62	74	10	10	NUM
ejpam-3650	62	75	)	)	PUNCT
ejpam-3650	62	76	where	where	SCONJ
ejpam-3650	62	77	u	u	NOUN
ejpam-3650	62	78	=	=	SYM
ejpam-3650	62	79	u(x	u(x	PROPN
ejpam-3650	62	80	,	,	PUNCT
ejpam-3650	62	81	t	t	NOUN
ejpam-3650	62	82	)	)	PUNCT
ejpam-3650	62	83	∈	∈	PROPN
ejpam-3650	62	84	u	u	NOUN
ejpam-3650	62	85	is	be	AUX
ejpam-3650	62	86	some	some	DET
ejpam-3650	62	87	element	element	NOUN
ejpam-3650	62	88	.	.	PUNCT
ejpam-3650	63	1	we	we	PRON
ejpam-3650	63	2	show	show	VERB
ejpam-3650	63	3	that	that	SCONJ
ejpam-3650	63	4	u(x	u(x	NOUN
ejpam-3650	63	5	,	,	PUNCT
ejpam-3650	63	6	t	t	NOUN
ejpam-3650	63	7	)	)	PUNCT
ejpam-3650	63	8	=	=	SYM
ejpam-3650	63	9	u(x	u(x	PROPN
ejpam-3650	63	10	,	,	PUNCT
ejpam-3650	63	11	t	t	PROPN
ejpam-3650	63	12	;	;	PUNCT
ejpam-3650	63	13	v	v	NOUN
ejpam-3650	63	14	)	)	PUNCT
ejpam-3650	63	15	,	,	PUNCT
ejpam-3650	63	16	i.e.	i.e.	X
ejpam-3650	63	17	the	the	DET
ejpam-3650	63	18	function	function	NOUN
ejpam-3650	63	19	u(x	u(x	NOUN
ejpam-3650	63	20	,	,	PUNCT
ejpam-3650	63	21	t	t	PROPN
ejpam-3650	63	22	)	)	PUNCT
ejpam-3650	63	23	is	be	AUX
ejpam-3650	63	24	a	a	DET
ejpam-3650	63	25	solution	solution	NOUN
ejpam-3650	63	26	of	of	ADP
ejpam-3650	63	27	problem	problem	NOUN
ejpam-3650	63	28	(	(	PUNCT
ejpam-3650	63	29	1	1	NUM
ejpam-3650	63	30	)	)	PUNCT
ejpam-3650	63	31	,	,	PUNCT
ejpam-3650	63	32	(	(	PUNCT
ejpam-3650	63	33	2	2	X
ejpam-3650	63	34	)	)	PUNCT
ejpam-3650	63	35	corresponding	correspond	VERB
ejpam-3650	63	36	to	to	ADP
ejpam-3650	63	37	the	the	DET
ejpam-3650	63	38	control	control	NOUN
ejpam-3650	63	39	v	v	ADP
ejpam-3650	63	40	∈	∈	PROPN
ejpam-3650	63	41	v	v	NOUN
ejpam-3650	63	42	.	.	PUNCT
ejpam-3650	64	1	it	it	PRON
ejpam-3650	64	2	is	be	AUX
ejpam-3650	64	3	clear	clear	ADJ
ejpam-3650	64	4	that	that	SCONJ
ejpam-3650	64	5	,	,	PUNCT
ejpam-3650	64	6	the	the	DET
ejpam-3650	64	7	identities∫	identities∫	ADP
ejpam-3650	64	8	q	q	NOUN
ejpam-3650	64	9	[	[	PUNCT
ejpam-3650	65	1	−∂um	−∂um	PROPN
ejpam-3650	65	2	∂t	∂t	PROPN
ejpam-3650	65	3	∂η	∂η	PROPN
ejpam-3650	65	4	∂t	∂t	PROPN
ejpam-3650	66	1	+	+	CCONJ
ejpam-3650	66	2	n∑	n∑	PROPN
ejpam-3650	66	3	i=1	i=1	PROPN
ejpam-3650	66	4	∂um	∂um	PROPN
ejpam-3650	66	5	∂xi	∂xi	PROPN
ejpam-3650	66	6	∂η	∂η	PROPN
ejpam-3650	66	7	∂xi	∂xi	NOUN
ejpam-3650	66	8	+	+	CCONJ
ejpam-3650	66	9	vmumη	vmumη	NOUN
ejpam-3650	66	10	]	]	PUNCT
ejpam-3650	66	11	dxdt−	dxdt−	VERB
ejpam-3650	66	12	−	−	PROPN
ejpam-3650	66	13	∫	∫	PROPN
ejpam-3650	66	14	ω	ω	PROPN
ejpam-3650	66	15	u1(x)η(x	u1(x)η(x	PROPN
ejpam-3650	66	16	,	,	PUNCT
ejpam-3650	66	17	0)dx	0)dx	PUNCT
ejpam-3650	66	18	=	=	SYM
ejpam-3650	66	19	∫	∫	PROPN
ejpam-3650	66	20	q	q	PROPN
ejpam-3650	66	21	f(x	f(x	PROPN
ejpam-3650	66	22	,	,	PUNCT
ejpam-3650	66	23	t	t	PROPN
ejpam-3650	66	24	,	,	PUNCT
ejpam-3650	66	25	um)ηdxdt	um)ηdxdt	PROPN
ejpam-3650	66	26	(	(	PUNCT
ejpam-3650	66	27	11	11	NUM
ejpam-3650	66	28	)	)	PUNCT
ejpam-3650	66	29	are	be	AUX
ejpam-3650	66	30	true	true	ADJ
ejpam-3650	66	31	for	for	ADP
ejpam-3650	66	32	all	all	DET
ejpam-3650	66	33	η	η	PROPN
ejpam-3650	66	34	∈	∈	PROPN
ejpam-3650	66	35	u	u	NOUN
ejpam-3650	66	36	which	which	PRON
ejpam-3650	66	37	are	be	AUX
ejpam-3650	66	38	equal	equal	ADJ
ejpam-3650	66	39	to	to	ADP
ejpam-3650	66	40	zero	zero	NUM
ejpam-3650	66	41	at	at	ADP
ejpam-3650	66	42	t	t	PROPN
ejpam-3650	66	43	=	=	SYM
ejpam-3650	66	44	t	t	PROPN
ejpam-3650	66	45	.	.	PUNCT
ejpam-3650	67	1	for	for	ADP
ejpam-3650	67	2	any	any	DET
ejpam-3650	67	3	η	η	PROPN
ejpam-3650	67	4	∈	∈	PROPN
ejpam-3650	67	5	u	u	NOUN
ejpam-3650	67	6	the	the	DET
ejpam-3650	67	7	following	follow	VERB
ejpam-3650	67	8	inequality	inequality	NOUN
ejpam-3650	67	9	is	be	AUX
ejpam-3650	67	10	true:∣∣∣∣∣∣∣	true:∣∣∣∣∣∣∣	PROPN
ejpam-3650	67	11	∫	∫	PROPN
ejpam-3650	67	12	q	q	PROPN
ejpam-3650	67	13	vmumηdxdt−	vmumηdxdt−	NUM
ejpam-3650	67	14	∫	∫	PROPN
ejpam-3650	67	15	q	q	PROPN
ejpam-3650	67	16	vuηdxdt	vuηdxdt	NOUN
ejpam-3650	67	17	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	NOUN
ejpam-3650	67	18	≤	≤	PUNCT
ejpam-3650	67	19	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-3650	68	1	∫	∫	PROPN
ejpam-3650	68	2	q	q	PROPN
ejpam-3650	69	1	(	(	PUNCT
ejpam-3650	69	2	vm	vm	PROPN
ejpam-3650	69	3	−	−	PROPN
ejpam-3650	69	4	v)uηdxdt	v)uηdxdt	PROPN
ejpam-3650	69	5	∣∣∣∣∣∣∣+	∣∣∣∣∣∣∣+	PROPN
ejpam-3650	69	6	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-3650	69	7	∫	∫	PROPN
ejpam-3650	69	8	q	q	PROPN
ejpam-3650	69	9	vm(um	vm(um	PROPN
ejpam-3650	69	10	−	−	ADP
ejpam-3650	69	11	u)ηdxdt	u)ηdxdt	PROPN
ejpam-3650	69	12	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-3650	69	13	.	.	PUNCT
ejpam-3650	70	1	since	since	SCONJ
ejpam-3650	70	2	u	u	PROPN
ejpam-3650	70	3	,	,	PUNCT
ejpam-3650	70	4	η	η	PROPN
ejpam-3650	70	5	∈	∈	PROPN
ejpam-3650	70	6	u	u	NOUN
ejpam-3650	70	7	and	and	CCONJ
ejpam-3650	70	8	n	n	PRON
ejpam-3650	70	9	≤	≤	NOUN
ejpam-3650	70	10	4	4	NUM
ejpam-3650	70	11	by	by	ADP
ejpam-3650	70	12	embedding	embed	VERB
ejpam-3650	70	13	theorem	theorem	NOUN
ejpam-3650	70	14	[	[	X
ejpam-3650	70	15	see	see	VERB
ejpam-3650	70	16	[	[	X
ejpam-3650	70	17	13	13	NUM
ejpam-3650	70	18	]	]	PUNCT
ejpam-3650	70	19	,	,	PUNCT
ejpam-3650	70	20	pp	pp	ADJ
ejpam-3650	70	21	.	.	PUNCT
ejpam-3650	70	22	83	83	NUM
ejpam-3650	70	23	-	-	SYM
ejpam-3650	70	24	84	84	NUM
ejpam-3650	70	25	]	]	SYM
ejpam-3650	70	26	u	u	NOUN
ejpam-3650	70	27	,	,	PUNCT
ejpam-3650	70	28	η	η	PROPN
ejpam-3650	70	29	∈	∈	PROPN
ejpam-3650	70	30	c([0	c([0	PROPN
ejpam-3650	70	31	,	,	PUNCT
ejpam-3650	70	32	t	t	X
ejpam-3650	70	33	]	]	PUNCT
ejpam-3650	70	34	;	;	PUNCT
ejpam-3650	70	35	l4(ω	l4(ω	X
ejpam-3650	70	36	)	)	PUNCT
ejpam-3650	70	37	)	)	PUNCT
ejpam-3650	70	38	,	,	PUNCT
ejpam-3650	70	39	therefore	therefore	ADV
ejpam-3650	70	40	uη	uη	ADP
ejpam-3650	70	41	∈	∈	PROPN
ejpam-3650	70	42	l2(q	l2(q	PROPN
ejpam-3650	70	43	)	)	PUNCT
ejpam-3650	70	44	.	.	PUNCT
ejpam-3650	71	1	take	take	VERB
ejpam-3650	71	2	into	into	ADP
ejpam-3650	71	3	account	account	NOUN
ejpam-3650	71	4	this	this	DET
ejpam-3650	71	5	inclusion	inclusion	NOUN
ejpam-3650	71	6	,	,	PUNCT
ejpam-3650	71	7	the	the	DET
ejpam-3650	71	8	boundedness	boundedness	NOUN
ejpam-3650	71	9	of	of	ADP
ejpam-3650	71	10	the	the	DET
ejpam-3650	71	11	sequence	sequence	NOUN
ejpam-3650	71	12	{	{	PUNCT
ejpam-3650	71	13	vm	vm	PROPN
ejpam-3650	71	14	,	,	PUNCT
ejpam-3650	71	15	η	η	NOUN
ejpam-3650	71	16	}	}	PUNCT
ejpam-3650	71	17	in	in	ADP
ejpam-3650	71	18	l2(q	l2(q	PROPN
ejpam-3650	71	19	)	)	PUNCT
ejpam-3650	71	20	,	,	PUNCT
ejpam-3650	71	21	and	and	CCONJ
ejpam-3650	71	22	also	also	ADV
ejpam-3650	71	23	the	the	DET
ejpam-3650	71	24	above	above	ADJ
ejpam-3650	71	25	established	establish	VERB
ejpam-3650	71	26	convergence	convergence	NOUN
ejpam-3650	71	27	sequences	sequence	NOUN
ejpam-3650	71	28	{	{	PUNCT
ejpam-3650	71	29	vm	vm	NOUN
ejpam-3650	71	30	}	}	PUNCT
ejpam-3650	71	31	and	and	CCONJ
ejpam-3650	71	32	{	{	PUNCT
ejpam-3650	71	33	um	um	INTJ
ejpam-3650	71	34	}	}	PUNCT
ejpam-3650	71	35	,	,	PUNCT
ejpam-3650	71	36	weakly	weakly	ADJ
ejpam-3650	71	37	l2(ω	l2(ω	NOUN
ejpam-3650	71	38	)	)	PUNCT
ejpam-3650	71	39	and	and	CCONJ
ejpam-3650	71	40	strongly	strongly	ADV
ejpam-3650	71	41	in	in	ADP
ejpam-3650	71	42	l2(q	l2(q	PROPN
ejpam-3650	71	43	)	)	PUNCT
ejpam-3650	71	44	,	,	PUNCT
ejpam-3650	71	45	respectively	respectively	ADV
ejpam-3650	71	46	we	we	PRON
ejpam-3650	71	47	establish	establish	VERB
ejpam-3650	71	48	from	from	ADP
ejpam-3650	71	49	the	the	DET
ejpam-3650	71	50	last	last	ADJ
ejpam-3650	71	51	inequality	inequality	NOUN
ejpam-3650	71	52	that	that	SCONJ
ejpam-3650	71	53	lim	lim	PROPN
ejpam-3650	71	54	m→∞	m→∞	NOUN
ejpam-3650	71	55	∫	∫	PROPN
ejpam-3650	71	56	q	q	PROPN
ejpam-3650	71	57	vmumηdxdt	vmumηdxdt	PROPN
ejpam-3650	71	58	=	=	PROPN
ejpam-3650	71	59	∫	∫	PROPN
ejpam-3650	71	60	q	q	PROPN
ejpam-3650	71	61	vuηdxdt	vuηdxdt	NOUN
ejpam-3650	71	62	.	.	PUNCT
ejpam-3650	72	1	(	(	PUNCT
ejpam-3650	72	2	12	12	NUM
ejpam-3650	72	3	)	)	PUNCT
ejpam-3650	72	4	since	since	SCONJ
ejpam-3650	72	5	the	the	DET
ejpam-3650	72	6	function	function	NOUN
ejpam-3650	72	7	f(x	f(x	PROPN
ejpam-3650	72	8	,	,	PUNCT
ejpam-3650	72	9	t	t	PROPN
ejpam-3650	72	10	,	,	PUNCT
ejpam-3650	72	11	u	u	NOUN
ejpam-3650	72	12	)	)	PUNCT
ejpam-3650	72	13	has	have	VERB
ejpam-3650	72	14	a	a	DET
ejpam-3650	72	15	bounded	bound	VERB
ejpam-3650	72	16	derivative	derivative	NOUN
ejpam-3650	72	17	with	with	ADP
ejpam-3650	72	18	respect	respect	NOUN
ejpam-3650	72	19	to	to	ADP
ejpam-3650	72	20	u	u	NOUN
ejpam-3650	72	21	,	,	PUNCT
ejpam-3650	72	22	it	it	PRON
ejpam-3650	72	23	satisfies	satisfy	VERB
ejpam-3650	72	24	the	the	DET
ejpam-3650	72	25	lipschitz	lipschitz	NOUN
ejpam-3650	72	26	condition	condition	NOUN
ejpam-3650	72	27	with	with	ADP
ejpam-3650	72	28	respect	respect	NOUN
ejpam-3650	72	29	to	to	ADP
ejpam-3650	72	30	the	the	DET
ejpam-3650	72	31	argument	argument	NOUN
ejpam-3650	72	32	u.	u.	VERB
ejpam-3650	72	33	therefore	therefore	ADV
ejpam-3650	72	34	|f(x	|f(x	PROPN
ejpam-3650	72	35	,	,	PUNCT
ejpam-3650	72	36	t	t	PROPN
ejpam-3650	72	37	,	,	PUNCT
ejpam-3650	72	38	u)|	u)|	NOUN
ejpam-3650	72	39	≤	≤	NUM
ejpam-3650	72	40	l|u|+	l|u|+	PROPN
ejpam-3650	72	41	|f(x	|f(x	PROPN
ejpam-3650	72	42	,	,	PUNCT
ejpam-3650	72	43	t	t	PROPN
ejpam-3650	72	44	,	,	PUNCT
ejpam-3650	72	45	0)|	0)|	NOUN
ejpam-3650	72	46	,	,	PUNCT
ejpam-3650	72	47	where	where	SCONJ
ejpam-3650	72	48	l	l	NOUN
ejpam-3650	72	49	>	>	X
ejpam-3650	72	50	0	0	PUNCT
ejpam-3650	72	51	is	be	AUX
ejpam-3650	72	52	the	the	DET
ejpam-3650	72	53	lipschitz	lipschitz	NOUN
ejpam-3650	72	54	constant	constant	ADJ
ejpam-3650	72	55	.	.	PUNCT
ejpam-3650	73	1	then	then	ADV
ejpam-3650	73	2	it	it	PRON
ejpam-3650	73	3	follows	follow	VERB
ejpam-3650	73	4	that	that	SCONJ
ejpam-3650	73	5	the	the	DET
ejpam-3650	73	6	operator	operator	NOUN
ejpam-3650	73	7	fu	fu	NOUN
ejpam-3650	73	8	=	=	SYM
ejpam-3650	73	9	f(x	f(x	PROPN
ejpam-3650	73	10	,	,	PUNCT
ejpam-3650	73	11	t	t	PROPN
ejpam-3650	73	12	,	,	PUNCT
ejpam-3650	73	13	u(x	u(x	PROPN
ejpam-3650	73	14	,	,	PUNCT
ejpam-3650	73	15	t	t	PROPN
ejpam-3650	73	16	)	)	PUNCT
ejpam-3650	73	17	)	)	PUNCT
ejpam-3650	73	18	generated	generate	VERB
ejpam-3650	73	19	by	by	ADP
ejpam-3650	73	20	the	the	DET
ejpam-3650	73	21	function	function	NOUN
ejpam-3650	73	22	f(x	f(x	PROPN
ejpam-3650	73	23	,	,	PUNCT
ejpam-3650	73	24	t	t	PROPN
ejpam-3650	73	25	,	,	PUNCT
ejpam-3650	73	26	u	u	NOUN
ejpam-3650	73	27	)	)	PUNCT
ejpam-3650	73	28	acts	act	VERB
ejpam-3650	73	29	continuously	continuously	ADV
ejpam-3650	73	30	from	from	ADP
ejpam-3650	73	31	l2(q	l2(q	PROPN
ejpam-3650	73	32	)	)	PUNCT
ejpam-3650	73	33	to	to	ADP
ejpam-3650	73	34	l2(q	l2(q	PROPN
ejpam-3650	73	35	)	)	PUNCT
ejpam-3650	74	1	[	[	X
ejpam-3650	74	2	16	16	NUM
ejpam-3650	74	3	]	]	PUNCT
ejpam-3650	74	4	.	.	PUNCT
ejpam-3650	75	1	therefore	therefore	ADV
ejpam-3650	75	2	,	,	PUNCT
ejpam-3650	75	3	the	the	DET
ejpam-3650	75	4	following	follow	VERB
ejpam-3650	75	5	relation	relation	NOUN
ejpam-3650	75	6	is	be	AUX
ejpam-3650	75	7	true	true	ADJ
ejpam-3650	75	8	:	:	PUNCT
ejpam-3650	75	9	lim	lim	PROPN
ejpam-3650	75	10	m→∞	m→∞	PROPN
ejpam-3650	75	11	∫	∫	PROPN
ejpam-3650	75	12	q	q	PROPN
ejpam-3650	75	13	f(x	f(x	PROPN
ejpam-3650	75	14	,	,	PUNCT
ejpam-3650	75	15	t	t	PROPN
ejpam-3650	75	16	,	,	PUNCT
ejpam-3650	76	1	um)ηdxdt	um)ηdxdt	PROPN
ejpam-3650	76	2	=	=	SYM
ejpam-3650	76	3	∫	∫	PROPN
ejpam-3650	77	1	q	q	PROPN
ejpam-3650	77	2	f(x	f(x	PROPN
ejpam-3650	77	3	,	,	PUNCT
ejpam-3650	77	4	t	t	PROPN
ejpam-3650	77	5	,	,	PUNCT
ejpam-3650	77	6	u)ηdxdt	u)ηdxdt	PROPN
ejpam-3650	77	7	.	.	PUNCT
ejpam-3650	78	1	(	(	PUNCT
ejpam-3650	78	2	13	13	NUM
ejpam-3650	78	3	)	)	PUNCT
ejpam-3650	78	4	g.g	g.g	INTJ
ejpam-3650	78	5	ismayilova	ismayilova	PROPN
ejpam-3650	78	6	/	/	SYM
ejpam-3650	78	7	eur	eur	PROPN
ejpam-3650	78	8	.	.	PUNCT
ejpam-3650	79	1	j.	j.	PROPN
ejpam-3650	79	2	pure	pure	PROPN
ejpam-3650	79	3	appl	appl	PROPN
ejpam-3650	79	4	.	.	PROPN
ejpam-3650	79	5	math	math	PROPN
ejpam-3650	79	6	,	,	PUNCT
ejpam-3650	79	7	13	13	NUM
ejpam-3650	79	8	(	(	PUNCT
ejpam-3650	79	9	2	2	NUM
ejpam-3650	79	10	)	)	PUNCT
ejpam-3650	79	11	(	(	PUNCT
ejpam-3650	79	12	2020	2020	NUM
ejpam-3650	79	13	)	)	PUNCT
ejpam-3650	79	14	,	,	PUNCT
ejpam-3650	79	15	314	314	NUM
ejpam-3650	79	16	-	-	SYM
ejpam-3650	79	17	322	322	NUM
ejpam-3650	79	18	318	318	NUM
ejpam-3650	79	19	passing	pass	VERB
ejpam-3650	79	20	to	to	ADP
ejpam-3650	79	21	the	the	DET
ejpam-3650	79	22	limit	limit	NOUN
ejpam-3650	79	23	in	in	ADP
ejpam-3650	79	24	(	(	PUNCT
ejpam-3650	79	25	11	11	NUM
ejpam-3650	79	26	)	)	PUNCT
ejpam-3650	79	27	as	as	ADP
ejpam-3650	79	28	m	m	PROPN
ejpam-3650	79	29	→	→	SYM
ejpam-3650	79	30	∞	∞	NUM
ejpam-3650	79	31	and	and	CCONJ
ejpam-3650	79	32	using	use	VERB
ejpam-3650	79	33	(	(	PUNCT
ejpam-3650	79	34	9	9	NUM
ejpam-3650	79	35	)	)	PUNCT
ejpam-3650	79	36	,	,	PUNCT
ejpam-3650	79	37	(	(	PUNCT
ejpam-3650	79	38	10	10	NUM
ejpam-3650	79	39	)	)	PUNCT
ejpam-3650	79	40	,	,	PUNCT
ejpam-3650	79	41	(	(	PUNCT
ejpam-3650	79	42	12	12	NUM
ejpam-3650	79	43	)	)	PUNCT
ejpam-3650	79	44	,	,	PUNCT
ejpam-3650	79	45	(	(	PUNCT
ejpam-3650	79	46	13	13	NUM
ejpam-3650	79	47	)	)	PUNCT
ejpam-3650	80	1	,	,	PUNCT
ejpam-3650	80	2	we	we	PRON
ejpam-3650	80	3	find	find	VERB
ejpam-3650	80	4	that	that	SCONJ
ejpam-3650	80	5	the	the	DET
ejpam-3650	80	6	function	function	NOUN
ejpam-3650	80	7	u(x	u(x	VERB
ejpam-3650	80	8	,	,	PUNCT
ejpam-3650	80	9	t	t	PROPN
ejpam-3650	80	10	)	)	PUNCT
ejpam-3650	80	11	is	be	AUX
ejpam-3650	80	12	equal	equal	ADJ
ejpam-3650	80	13	to	to	ADP
ejpam-3650	80	14	u0(x	u0(x	SYM
ejpam-3650	80	15	)	)	PUNCT
ejpam-3650	80	16	for	for	ADP
ejpam-3650	80	17	t	t	NOUN
ejpam-3650	80	18	=	=	SYM
ejpam-3650	80	19	0	0	PUNCT
ejpam-3650	80	20	and	and	CCONJ
ejpam-3650	80	21	satisfies	satisfy	VERB
ejpam-3650	80	22	the	the	DET
ejpam-3650	80	23	identity	identity	NOUN
ejpam-3650	80	24	(	(	PUNCT
ejpam-3650	80	25	8)	8)	NUM
ejpam-3650	80	26	.	.	PUNCT
ejpam-3650	80	27	from	from	ADP
ejpam-3650	80	28	this	this	PRON
ejpam-3650	80	29	and	and	CCONJ
ejpam-3650	80	30	the	the	DET
ejpam-3650	80	31	uniqueness	uniqueness	NOUN
ejpam-3650	80	32	of	of	ADP
ejpam-3650	80	33	the	the	DET
ejpam-3650	80	34	solution	solution	NOUN
ejpam-3650	80	35	of	of	ADP
ejpam-3650	80	36	problem	problem	NOUN
ejpam-3650	80	37	(	(	PUNCT
ejpam-3650	80	38	1	1	NUM
ejpam-3650	80	39	)	)	PUNCT
ejpam-3650	80	40	,	,	PUNCT
ejpam-3650	80	41	(	(	PUNCT
ejpam-3650	80	42	2	2	X
ejpam-3650	80	43	)	)	PUNCT
ejpam-3650	80	44	corresponding	correspond	VERB
ejpam-3650	80	45	to	to	ADP
ejpam-3650	80	46	the	the	DET
ejpam-3650	80	47	control	control	NOUN
ejpam-3650	80	48	v	v	ADP
ejpam-3650	80	49	∈	∈	PROPN
ejpam-3650	80	50	v	v	NOUN
ejpam-3650	80	51	imply	imply	NOUN
ejpam-3650	81	1	that	that	SCONJ
ejpam-3650	81	2	u(x	u(x	NOUN
ejpam-3650	81	3	,	,	PUNCT
ejpam-3650	81	4	t	t	NOUN
ejpam-3650	81	5	)	)	PUNCT
ejpam-3650	81	6	=	=	SYM
ejpam-3650	81	7	u(x	u(x	PROPN
ejpam-3650	81	8	,	,	PUNCT
ejpam-3650	81	9	t	t	PROPN
ejpam-3650	81	10	;	;	PUNCT
ejpam-3650	81	11	v	v	NOUN
ejpam-3650	81	12	)	)	PUNCT
ejpam-3650	81	13	.	.	PUNCT
ejpam-3650	82	1	thus	thus	ADV
ejpam-3650	82	2	,	,	PUNCT
ejpam-3650	82	3	it	it	PRON
ejpam-3650	82	4	follows	follow	VERB
ejpam-3650	82	5	from	from	ADP
ejpam-3650	82	6	this	this	PRON
ejpam-3650	82	7	that	that	SCONJ
ejpam-3650	82	8	the	the	DET
ejpam-3650	82	9	first	first	ADJ
ejpam-3650	82	10	term	term	NOUN
ejpam-3650	82	11	in	in	ADP
ejpam-3650	82	12	(	(	PUNCT
ejpam-3650	82	13	6	6	NUM
ejpam-3650	82	14	)	)	PUNCT
ejpam-3650	82	15	is	be	AUX
ejpam-3650	82	16	weakly	weakly	ADV
ejpam-3650	82	17	continuous	continuous	ADJ
ejpam-3650	82	18	in	in	ADP
ejpam-3650	82	19	l2(ω	l2(ω	PROPN
ejpam-3650	82	20	)	)	PUNCT
ejpam-3650	82	21	on	on	ADP
ejpam-3650	82	22	the	the	DET
ejpam-3650	82	23	set	set	NOUN
ejpam-3650	82	24	v	v	NOUN
ejpam-3650	82	25	.	.	PUNCT
ejpam-3650	83	1	the	the	DET
ejpam-3650	83	2	second	second	ADJ
ejpam-3650	83	3	term	term	NOUN
ejpam-3650	83	4	in	in	ADP
ejpam-3650	83	5	the	the	DET
ejpam-3650	83	6	expression	expression	NOUN
ejpam-3650	83	7	of	of	ADP
ejpam-3650	83	8	the	the	DET
ejpam-3650	83	9	functional	functional	ADJ
ejpam-3650	83	10	is	be	AUX
ejpam-3650	83	11	weakly	weakly	ADV
ejpam-3650	83	12	lower	low	ADJ
ejpam-3650	83	13	semicontinuous	semicontinuous	ADJ
ejpam-3650	83	14	in	in	ADP
ejpam-3650	83	15	l2(ω	l2(ω	PROPN
ejpam-3650	83	16	)	)	PUNCT
ejpam-3650	83	17	.	.	PUNCT
ejpam-3650	84	1	therefore	therefore	ADV
ejpam-3650	84	2	,	,	PUNCT
ejpam-3650	84	3	functional	functional	ADJ
ejpam-3650	84	4	(	(	PUNCT
ejpam-3650	84	5	6	6	NUM
ejpam-3650	84	6	)	)	PUNCT
ejpam-3650	84	7	is	be	AUX
ejpam-3650	84	8	weakly	weakly	ADV
ejpam-3650	84	9	lower	low	ADJ
ejpam-3650	84	10	semicontinuous	semicontinuous	ADJ
ejpam-3650	84	11	on	on	ADP
ejpam-3650	84	12	the	the	DET
ejpam-3650	84	13	set	set	NOUN
ejpam-3650	84	14	v	v	NOUN
ejpam-3650	84	15	.	.	PUNCT
ejpam-3650	85	1	then	then	ADV
ejpam-3650	85	2	,	,	PUNCT
ejpam-3650	85	3	by	by	ADP
ejpam-3650	85	4	virtue	virtue	NOUN
ejpam-3650	85	5	of	of	ADP
ejpam-3650	85	6	theorem	theorem	NOUN
ejpam-3650	85	7	2	2	NUM
ejpam-3650	85	8	from	from	ADP
ejpam-3650	85	9	[	[	PUNCT
ejpam-3650	85	10	see	see	NOUN
ejpam-3650	85	11	[	[	X
ejpam-3650	85	12	17	17	NUM
ejpam-3650	85	13	]	]	PUNCT
ejpam-3650	85	14	,	,	PUNCT
ejpam-3650	85	15	p.	p.	NOUN
ejpam-3650	85	16	49	49	NUM
ejpam-3650	85	17	]	]	PUNCT
ejpam-3650	85	18	,	,	PUNCT
ejpam-3650	85	19	we	we	PRON
ejpam-3650	85	20	obtain	obtain	VERB
ejpam-3650	85	21	that	that	SCONJ
ejpam-3650	85	22	all	all	DET
ejpam-3650	85	23	the	the	DET
ejpam-3650	85	24	statements	statement	NOUN
ejpam-3650	85	25	of	of	ADP
ejpam-3650	85	26	theorem	theorem	ADJ
ejpam-3650	85	27	1	1	NUM
ejpam-3650	85	28	are	be	AUX
ejpam-3650	85	29	true	true	ADJ
ejpam-3650	85	30	.	.	PUNCT
ejpam-3650	86	1	theorem	theorem	NOUN
ejpam-3650	86	2	1	1	NUM
ejpam-3650	86	3	is	be	AUX
ejpam-3650	86	4	proved	prove	VERB
ejpam-3650	86	5	.	.	PUNCT
ejpam-3650	87	1	4	4	X
ejpam-3650	87	2	.	.	X
ejpam-3650	87	3	the	the	DET
ejpam-3650	87	4	differentiability	differentiability	NOUN
ejpam-3650	87	5	of	of	ADP
ejpam-3650	87	6	functional	functional	ADJ
ejpam-3650	87	7	(	(	PUNCT
ejpam-3650	87	8	6	6	NUM
ejpam-3650	87	9	)	)	PUNCT
ejpam-3650	87	10	and	and	CCONJ
ejpam-3650	87	11	the	the	DET
ejpam-3650	87	12	necessary	necessary	ADJ
ejpam-3650	87	13	condition	condition	NOUN
ejpam-3650	87	14	of	of	ADP
ejpam-3650	87	15	optimality	optimality	NOUN
ejpam-3650	87	16	in	in	ADP
ejpam-3650	87	17	problem	problem	NOUN
ejpam-3650	87	18	(	(	PUNCT
ejpam-3650	87	19	1	1	NUM
ejpam-3650	87	20	)	)	PUNCT
ejpam-3650	87	21	,	,	PUNCT
ejpam-3650	87	22	(	(	PUNCT
ejpam-3650	87	23	2	2	NUM
ejpam-3650	87	24	)	)	PUNCT
ejpam-3650	87	25	,	,	PUNCT
ejpam-3650	87	26	(	(	PUNCT
ejpam-3650	87	27	4	4	NUM
ejpam-3650	87	28	)	)	PUNCT
ejpam-3650	87	29	,	,	PUNCT
ejpam-3650	87	30	(	(	PUNCT
ejpam-3650	87	31	6	6	X
ejpam-3650	87	32	)	)	PUNCT
ejpam-3650	87	33	now	now	ADV
ejpam-3650	87	34	we	we	PRON
ejpam-3650	87	35	study	study	VERB
ejpam-3650	87	36	the	the	DET
ejpam-3650	87	37	frechet	frechet	NOUN
ejpam-3650	87	38	differentiability	differentiability	NOUN
ejpam-3650	87	39	of	of	ADP
ejpam-3650	87	40	functional	functional	ADJ
ejpam-3650	87	41	(	(	PUNCT
ejpam-3650	87	42	6	6	NUM
ejpam-3650	87	43	)	)	PUNCT
ejpam-3650	87	44	and	and	CCONJ
ejpam-3650	87	45	establish	establish	VERB
ejpam-3650	87	46	the	the	DET
ejpam-3650	87	47	necessary	necessary	ADJ
ejpam-3650	87	48	condition	condition	NOUN
ejpam-3650	87	49	of	of	ADP
ejpam-3650	87	50	optimality	optimality	NOUN
ejpam-3650	87	51	in	in	ADP
ejpam-3650	87	52	problem	problem	NOUN
ejpam-3650	87	53	(	(	PUNCT
ejpam-3650	87	54	1	1	NUM
ejpam-3650	87	55	)	)	PUNCT
ejpam-3650	87	56	,	,	PUNCT
ejpam-3650	87	57	(	(	PUNCT
ejpam-3650	87	58	2	2	NUM
ejpam-3650	87	59	)	)	PUNCT
ejpam-3650	87	60	,	,	PUNCT
ejpam-3650	87	61	(	(	PUNCT
ejpam-3650	87	62	4	4	NUM
ejpam-3650	87	63	)	)	PUNCT
ejpam-3650	87	64	,	,	PUNCT
ejpam-3650	87	65	(	(	PUNCT
ejpam-3650	87	66	6	6	NUM
ejpam-3650	87	67	)	)	PUNCT
ejpam-3650	87	68	.	.	PUNCT
ejpam-3650	88	1	let	let	VERB
ejpam-3650	88	2	ψ	ψ	X
ejpam-3650	88	3	=	=	NOUN
ejpam-3650	88	4	ψ(x	ψ(x	PROPN
ejpam-3650	88	5	,	,	PUNCT
ejpam-3650	88	6	t	t	PROPN
ejpam-3650	88	7	;	;	PUNCT
ejpam-3650	88	8	v	v	NOUN
ejpam-3650	88	9	)	)	PUNCT
ejpam-3650	88	10	is	be	AUX
ejpam-3650	88	11	a	a	DET
ejpam-3650	88	12	generalized	generalized	ADJ
ejpam-3650	88	13	solution	solution	NOUN
ejpam-3650	88	14	from	from	ADP
ejpam-3650	88	15	the	the	DET
ejpam-3650	88	16	u	u	PROPN
ejpam-3650	88	17	of	of	ADP
ejpam-3650	88	18	adjoint	adjoint	PROPN
ejpam-3650	88	19	problem	problem	NOUN
ejpam-3650	88	20	∂2ψ	∂2ψ	PROPN
ejpam-3650	88	21	∂t2	∂t2	PROPN
ejpam-3650	88	22	−∆ψ	−∆ψ	X
ejpam-3650	89	1	+	+	CCONJ
ejpam-3650	89	2	vψ	vψ	ADP
ejpam-3650	89	3	=	=	SYM
ejpam-3650	89	4	∂f(x	∂f(x	PROPN
ejpam-3650	89	5	,	,	PUNCT
ejpam-3650	89	6	t	t	PROPN
ejpam-3650	89	7	,	,	PUNCT
ejpam-3650	89	8	u	u	NOUN
ejpam-3650	89	9	)	)	PUNCT
ejpam-3650	89	10	∂u	∂u	PROPN
ejpam-3650	89	11	ψ	ψ	SYM
ejpam-3650	89	12	−k(x	−k(x	PROPN
ejpam-3650	89	13	,	,	PUNCT
ejpam-3650	89	14	t	t	PROPN
ejpam-3650	89	15	)	)	PUNCT
ejpam-3650	89	16			NOUN
ejpam-3650	89	17	t∫	t∫	PRON
ejpam-3650	89	18	0	0	NUM
ejpam-3650	89	19	k(x	k(x	PROPN
ejpam-3650	89	20	,	,	PUNCT
ejpam-3650	89	21	t)u(x	t)u(x	NOUN
ejpam-3650	89	22	,	,	PUNCT
ejpam-3650	89	23	t)dt−	t)dt−	NOUN
ejpam-3650	89	24	ϕ(x	ϕ(x	NOUN
ejpam-3650	89	25	)	)	PUNCT
ejpam-3650	89	26			NOUN
ejpam-3650	89	27	,	,	PUNCT
ejpam-3650	89	28	(	(	PUNCT
ejpam-3650	89	29	x	x	NOUN
ejpam-3650	89	30	,	,	PUNCT
ejpam-3650	89	31	t	t	PROPN
ejpam-3650	89	32	)	)	PUNCT
ejpam-3650	89	33	∈	∈	PROPN
ejpam-3650	90	1	q	q	NOUN
ejpam-3650	90	2	,	,	PUNCT
ejpam-3650	90	3	(	(	PUNCT
ejpam-3650	90	4	14	14	NUM
ejpam-3650	90	5	)	)	PUNCT
ejpam-3650	90	6	ψ	ψ	NOUN
ejpam-3650	91	1	=	=	SYM
ejpam-3650	91	2	0	0	NUM
ejpam-3650	91	3	,	,	PUNCT
ejpam-3650	91	4	(	(	PUNCT
ejpam-3650	91	5	x	x	NOUN
ejpam-3650	91	6	,	,	PUNCT
ejpam-3650	91	7	t	t	PROPN
ejpam-3650	91	8	)	)	PUNCT
ejpam-3650	91	9	∈	∈	PROPN
ejpam-3650	91	10	s	s	PROPN
ejpam-3650	91	11	,	,	PUNCT
ejpam-3650	91	12	ψ|t	ψ|t	PUNCT
ejpam-3650	92	1	=	=	NOUN
ejpam-3650	92	2	t	t	NOUN
ejpam-3650	92	3	=	=	SYM
ejpam-3650	92	4	0	0	NUM
ejpam-3650	92	5	,	,	PUNCT
ejpam-3650	92	6	∂ψ	∂ψ	VERB
ejpam-3650	92	7	∂t	∂t	PROPN
ejpam-3650	92	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3650	92	9	t	t	PROPN
ejpam-3650	92	10	=	=	PROPN
ejpam-3650	92	11	t	t	NOUN
ejpam-3650	92	12	=	=	SYM
ejpam-3650	92	13	0	0	NUM
ejpam-3650	92	14	,	,	PUNCT
ejpam-3650	92	15	x	x	X
ejpam-3650	92	16	∈	∈	PROPN
ejpam-3650	92	17	ω	ω	PROPN
ejpam-3650	92	18	.	.	PUNCT
ejpam-3650	92	19	(	(	PUNCT
ejpam-3650	92	20	15	15	NUM
ejpam-3650	92	21	)	)	PUNCT
ejpam-3650	92	22	by	by	ADP
ejpam-3650	92	23	a	a	DET
ejpam-3650	92	24	generalized	generalized	ADJ
ejpam-3650	92	25	solution	solution	NOUN
ejpam-3650	92	26	of	of	ADP
ejpam-3650	92	27	the	the	DET
ejpam-3650	92	28	boundary	boundary	ADJ
ejpam-3650	92	29	value	value	NOUN
ejpam-3650	92	30	problem	problem	NOUN
ejpam-3650	92	31	(	(	PUNCT
ejpam-3650	92	32	14	14	NUM
ejpam-3650	92	33	)	)	PUNCT
ejpam-3650	92	34	,	,	PUNCT
ejpam-3650	92	35	(	(	PUNCT
ejpam-3650	92	36	15	15	NUM
ejpam-3650	92	37	)	)	PUNCT
ejpam-3650	92	38	for	for	ADP
ejpam-3650	92	39	a	a	DET
ejpam-3650	92	40	given	give	VERB
ejpam-3650	92	41	v	v	NUM
ejpam-3650	92	42	∈	∈	NOUN
ejpam-3650	92	43	v	v	NOUN
ejpam-3650	92	44	,	,	PUNCT
ejpam-3650	92	45	we	we	PRON
ejpam-3650	92	46	mean	mean	VERB
ejpam-3650	92	47	a	a	DET
ejpam-3650	92	48	function	function	NOUN
ejpam-3650	92	49	ψ	ψ	X
ejpam-3650	92	50	=	=	NOUN
ejpam-3650	92	51	ψ(x	ψ(x	PROPN
ejpam-3650	92	52	,	,	PUNCT
ejpam-3650	92	53	t	t	PROPN
ejpam-3650	92	54	;	;	PUNCT
ejpam-3650	92	55	v	v	NOUN
ejpam-3650	92	56	)	)	PUNCT
ejpam-3650	92	57	from	from	ADP
ejpam-3650	92	58	u	u	PRON
ejpam-3650	92	59	that	that	PRON
ejpam-3650	92	60	is	be	AUX
ejpam-3650	92	61	equal	equal	ADJ
ejpam-3650	92	62	to	to	ADP
ejpam-3650	92	63	zero	zero	NUM
ejpam-3650	92	64	for	for	ADP
ejpam-3650	92	65	t	t	PROPN
ejpam-3650	92	66	=	=	SYM
ejpam-3650	92	67	t	t	PROPN
ejpam-3650	92	68	and	and	CCONJ
ejpam-3650	92	69	satisfying	satisfy	VERB
ejpam-3650	92	70	the	the	DET
ejpam-3650	92	71	integral	integral	ADJ
ejpam-3650	92	72	identity∫	identity∫	X
ejpam-3650	92	73	q	q	NOUN
ejpam-3650	93	1	[	[	PUNCT
ejpam-3650	93	2	−∂ψ	−∂ψ	NUM
ejpam-3650	93	3	∂t	∂t	PROPN
ejpam-3650	93	4	∂g	∂g	PROPN
ejpam-3650	93	5	∂t	∂t	PROPN
ejpam-3650	94	1	+	+	CCONJ
ejpam-3650	94	2	n∑	n∑	ADJ
ejpam-3650	94	3	i=1	i=1	PROPN
ejpam-3650	94	4	∂ψ	∂ψ	VERB
ejpam-3650	94	5	∂xi	∂xi	NOUN
ejpam-3650	94	6	∂g	∂g	PROPN
ejpam-3650	94	7	∂xi	∂xi	NOUN
ejpam-3650	94	8	+	+	CCONJ
ejpam-3650	94	9	vψg	vψg	X
ejpam-3650	94	10	]	]	PUNCT
ejpam-3650	94	11	dxdt	dxdt	NOUN
ejpam-3650	94	12	=	=	SYM
ejpam-3650	95	1	=	=	SYM
ejpam-3650	95	2	∫	∫	PROPN
ejpam-3650	95	3	q	q	PROPN
ejpam-3650	95	4	{	{	PUNCT
ejpam-3650	95	5	∂f(x	∂f(x	PROPN
ejpam-3650	95	6	,	,	PUNCT
ejpam-3650	95	7	t	t	PROPN
ejpam-3650	95	8	,	,	PUNCT
ejpam-3650	95	9	u	u	NOUN
ejpam-3650	95	10	)	)	PUNCT
ejpam-3650	95	11	∂u	∂u	PROPN
ejpam-3650	95	12	ψ	ψ	SYM
ejpam-3650	95	13	−k(x	−k(x	PROPN
ejpam-3650	95	14	,	,	PUNCT
ejpam-3650	95	15	t	t	PROPN
ejpam-3650	95	16	)	)	PUNCT
ejpam-3650	95	17	[	[	PUNCT
ejpam-3650	95	18	t∫	t∫	PROPN
ejpam-3650	95	19	0	0	NUM
ejpam-3650	95	20	k(x	k(x	PROPN
ejpam-3650	95	21	,	,	PUNCT
ejpam-3650	95	22	t)u(x	t)u(x	NOUN
ejpam-3650	95	23	,	,	PUNCT
ejpam-3650	95	24	t)dt−	t)dt−	PROPN
ejpam-3650	95	25	ϕ(x	ϕ(x	NOUN
ejpam-3650	95	26	)	)	PUNCT
ejpam-3650	95	27	]	]	PUNCT
ejpam-3650	95	28	}	}	PUNCT
ejpam-3650	95	29	gdxdt	gdxdt	NOUN
ejpam-3650	95	30	(	(	PUNCT
ejpam-3650	95	31	16	16	NUM
ejpam-3650	95	32	)	)	PUNCT
ejpam-3650	95	33	for	for	ADP
ejpam-3650	95	34	all	all	PRON
ejpam-3650	95	35	g	g	PROPN
ejpam-3650	95	36	∈	∈	PROPN
ejpam-3650	95	37	u	u	NOUN
ejpam-3650	95	38	which	which	PRON
ejpam-3650	95	39	is	be	AUX
ejpam-3650	95	40	equal	equal	ADJ
ejpam-3650	95	41	to	to	ADP
ejpam-3650	95	42	zero	zero	NUM
ejpam-3650	95	43	for	for	ADP
ejpam-3650	95	44	t	t	NOUN
ejpam-3650	95	45	=	=	SYM
ejpam-3650	95	46	0	0	NUM
ejpam-3650	95	47	.	.	PUNCT
ejpam-3650	96	1	from	from	ADP
ejpam-3650	96	2	the	the	DET
ejpam-3650	96	3	results	result	NOUN
ejpam-3650	96	4	of	of	ADP
ejpam-3650	96	5	[	[	AUX
ejpam-3650	96	6	see	see	VERB
ejpam-3650	96	7	[	[	X
ejpam-3650	96	8	13	13	NUM
ejpam-3650	96	9	]	]	PUNCT
ejpam-3650	96	10	,	,	PUNCT
ejpam-3650	96	11	p.	p.	NOUN
ejpam-3650	96	12	209	209	NUM
ejpam-3650	96	13	-	-	SYM
ejpam-3650	96	14	215	215	NUM
ejpam-3650	96	15	]	]	PUNCT
ejpam-3650	96	16	it	it	PRON
ejpam-3650	96	17	follows	follow	VERB
ejpam-3650	96	18	that	that	SCONJ
ejpam-3650	96	19	under	under	ADP
ejpam-3650	96	20	the	the	DET
ejpam-3650	96	21	above	above	ADJ
ejpam-3650	96	22	assumptions	assumption	NOUN
ejpam-3650	96	23	,	,	PUNCT
ejpam-3650	96	24	for	for	ADP
ejpam-3650	96	25	each	each	PRON
ejpam-3650	96	26	given	give	VERB
ejpam-3650	96	27	v	v	NUM
ejpam-3650	96	28	∈	∈	NOUN
ejpam-3650	96	29	v	v	NOUN
ejpam-3650	96	30	problem	problem	NOUN
ejpam-3650	96	31	(	(	PUNCT
ejpam-3650	96	32	14	14	NUM
ejpam-3650	96	33	)	)	PUNCT
ejpam-3650	96	34	,	,	PUNCT
ejpam-3650	96	35	(	(	PUNCT
ejpam-3650	96	36	15	15	NUM
ejpam-3650	96	37	)	)	PUNCT
ejpam-3650	96	38	has	have	VERB
ejpam-3650	96	39	a	a	DET
ejpam-3650	96	40	unique	unique	ADJ
ejpam-3650	96	41	generalized	generalized	ADJ
ejpam-3650	96	42	solution	solution	NOUN
ejpam-3650	96	43	from	from	ADP
ejpam-3650	96	44	u	u	NOUN
ejpam-3650	96	45	and	and	CCONJ
ejpam-3650	96	46	the	the	DET
ejpam-3650	96	47	estimate	estimate	NOUN
ejpam-3650	96	48	is	be	AUX
ejpam-3650	96	49	true	true	ADJ
ejpam-3650	96	50	‖ψ‖	‖ψ‖	PROPN
ejpam-3650	96	51	◦	◦	NOUN
ejpam-3650	96	52	w	w	NOUN
ejpam-3650	96	53	1	1	NUM
ejpam-3650	96	54	2	2	NUM
ejpam-3650	96	55	(	(	PUNCT
ejpam-3650	96	56	ω	ω	NOUN
ejpam-3650	96	57	)	)	PUNCT
ejpam-3650	97	1	+	+	CCONJ
ejpam-3650	97	2	∥∥∥∥∂ψ∂t	∥∥∥∥∂ψ∂t	ADJ
ejpam-3650	97	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-3650	97	4	l2(ω	l2(ω	NOUN
ejpam-3650	97	5	)	)	PUNCT
ejpam-3650	97	6	≤	≤	NUM
ejpam-3650	97	7	c	c	NOUN
ejpam-3650	97	8	[	[	PUNCT
ejpam-3650	97	9	‖u‖l2(q	‖u‖l2(q	ADJ
ejpam-3650	97	10	)	)	PUNCT
ejpam-3650	97	11	+	+	CCONJ
ejpam-3650	97	12	‖ϕ‖l2(ω	‖ϕ‖l2(ω	NUM
ejpam-3650	97	13	)	)	PUNCT
ejpam-3650	97	14	]	]	PUNCT
ejpam-3650	97	15	,	,	PUNCT
ejpam-3650	97	16	t	t	PROPN
ejpam-3650	97	17	∈	∈	PROPN
ejpam-3650	98	1	[	[	X
ejpam-3650	98	2	0	0	NUM
ejpam-3650	98	3	,	,	PUNCT
ejpam-3650	98	4	t	t	X
ejpam-3650	98	5	]	]	PUNCT
ejpam-3650	98	6	.	.	PUNCT
ejpam-3650	99	1	taking	take	VERB
ejpam-3650	99	2	into	into	ADP
ejpam-3650	99	3	account	account	NOUN
ejpam-3650	99	4	(	(	PUNCT
ejpam-3650	99	5	7	7	NUM
ejpam-3650	99	6	)	)	PUNCT
ejpam-3650	99	7	,	,	PUNCT
ejpam-3650	99	8	we	we	PRON
ejpam-3650	99	9	obtain	obtain	VERB
ejpam-3650	99	10	‖ψ‖	‖ψ‖	PROPN
ejpam-3650	99	11	◦	◦	NOUN
ejpam-3650	99	12	w	w	ADP
ejpam-3650	99	13	1	1	NUM
ejpam-3650	99	14	2	2	NUM
ejpam-3650	99	15	(	(	PUNCT
ejpam-3650	99	16	ω	ω	NOUN
ejpam-3650	99	17	)	)	PUNCT
ejpam-3650	99	18	+	+	CCONJ
ejpam-3650	100	1	∥∥∥∥∂ψ∂t	∥∥∥∥∂ψ∂t	ADJ
ejpam-3650	100	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-3650	100	3	l2(ω	l2(ω	NOUN
ejpam-3650	100	4	)	)	PUNCT
ejpam-3650	100	5	≤	≤	NUM
ejpam-3650	100	6	c	c	NOUN
ejpam-3650	100	7	[	[	PUNCT
ejpam-3650	100	8	‖u0‖	‖u0‖	NOUN
ejpam-3650	100	9	◦	◦	NOUN
ejpam-3650	100	10	w	w	NOUN
ejpam-3650	100	11	1	1	NUM
ejpam-3650	100	12	2	2	NUM
ejpam-3650	100	13	(	(	PUNCT
ejpam-3650	100	14	ω	ω	NOUN
ejpam-3650	100	15	)	)	PUNCT
ejpam-3650	100	16	+	+	CCONJ
ejpam-3650	100	17	‖u1‖l2(ω	‖u1‖l2(ω	NUM
ejpam-3650	100	18	)	)	PUNCT
ejpam-3650	101	1	+	+	CCONJ
ejpam-3650	101	2	‖f(x	‖f(x	NUM
ejpam-3650	101	3	,	,	PUNCT
ejpam-3650	101	4	t	t	PROPN
ejpam-3650	101	5	,	,	PUNCT
ejpam-3650	101	6	0)‖l2(q	0)‖l2(q	NUM
ejpam-3650	101	7	)	)	PUNCT
ejpam-3650	102	1	+	+	CCONJ
ejpam-3650	102	2	‖ϕ‖l2(ω	‖ϕ‖l2(ω	NUM
ejpam-3650	102	3	)	)	PUNCT
ejpam-3650	102	4	]	]	PUNCT
ejpam-3650	103	1	,	,	PUNCT
ejpam-3650	103	2	t	t	PROPN
ejpam-3650	103	3	∈	∈	PROPN
ejpam-3650	104	1	[	[	X
ejpam-3650	104	2	0	0	NUM
ejpam-3650	104	3	,	,	PUNCT
ejpam-3650	104	4	t	t	X
ejpam-3650	104	5	]	]	PUNCT
ejpam-3650	104	6	.	.	PUNCT
ejpam-3650	105	1	(	(	PUNCT
ejpam-3650	105	2	17	17	NUM
ejpam-3650	105	3	)	)	PUNCT
ejpam-3650	105	4	g.g	g.g	INTJ
ejpam-3650	105	5	ismayilova	ismayilova	PROPN
ejpam-3650	105	6	/	/	SYM
ejpam-3650	105	7	eur	eur	PROPN
ejpam-3650	105	8	.	.	PUNCT
ejpam-3650	106	1	j.	j.	PROPN
ejpam-3650	106	2	pure	pure	PROPN
ejpam-3650	106	3	appl	appl	PROPN
ejpam-3650	106	4	.	.	PROPN
ejpam-3650	106	5	math	math	PROPN
ejpam-3650	106	6	,	,	PUNCT
ejpam-3650	106	7	13	13	NUM
ejpam-3650	106	8	(	(	PUNCT
ejpam-3650	106	9	2	2	NUM
ejpam-3650	106	10	)	)	PUNCT
ejpam-3650	106	11	(	(	PUNCT
ejpam-3650	106	12	2020	2020	NUM
ejpam-3650	106	13	)	)	PUNCT
ejpam-3650	106	14	,	,	PUNCT
ejpam-3650	106	15	314	314	NUM
ejpam-3650	106	16	-	-	SYM
ejpam-3650	106	17	322	322	NUM
ejpam-3650	106	18	319	319	NUM
ejpam-3650	106	19	theorem	theorem	NOUN
ejpam-3650	106	20	2	2	NUM
ejpam-3650	106	21	.	.	PUNCT
ejpam-3650	106	22	suppose	suppose	VERB
ejpam-3650	106	23	that	that	SCONJ
ejpam-3650	106	24	the	the	DET
ejpam-3650	106	25	conditions	condition	NOUN
ejpam-3650	106	26	of	of	ADP
ejpam-3650	106	27	theorem	theorem	NOUN
ejpam-3650	106	28	1	1	NUM
ejpam-3650	106	29	are	be	AUX
ejpam-3650	106	30	satisfied	satisfied	ADJ
ejpam-3650	106	31	.	.	PUNCT
ejpam-3650	107	1	then	then	ADV
ejpam-3650	107	2	functional	functional	ADJ
ejpam-3650	107	3	(	(	PUNCT
ejpam-3650	107	4	6	6	NUM
ejpam-3650	107	5	)	)	PUNCT
ejpam-3650	107	6	is	be	AUX
ejpam-3650	107	7	continuously	continuously	ADV
ejpam-3650	107	8	differentiable	differentiable	ADJ
ejpam-3650	107	9	in	in	ADP
ejpam-3650	107	10	v	v	NUM
ejpam-3650	107	11	by	by	ADP
ejpam-3650	107	12	frechet	frechet	NOUN
ejpam-3650	107	13	and	and	CCONJ
ejpam-3650	107	14	its	its	PRON
ejpam-3650	107	15	differential	differential	NOUN
ejpam-3650	107	16	at	at	ADP
ejpam-3650	107	17	a	a	DET
ejpam-3650	107	18	point	point	NOUN
ejpam-3650	107	19	v	v	ADP
ejpam-3650	107	20	∈	∈	NOUN
ejpam-3650	107	21	v	v	NOUN
ejpam-3650	107	22	in	in	ADP
ejpam-3650	107	23	with	with	ADP
ejpam-3650	107	24	increments	increment	NOUN
ejpam-3650	107	25	δv	δv	ADV
ejpam-3650	107	26	∈	∈	PROPN
ejpam-3650	107	27	l∞(ω	l∞(ω	NOUN
ejpam-3650	107	28	)	)	PUNCT
ejpam-3650	107	29	is	be	AUX
ejpam-3650	107	30	determined	determine	VERB
ejpam-3650	107	31	by	by	ADP
ejpam-3650	107	32	the	the	DET
ejpam-3650	107	33	expression	expression	NOUN
ejpam-3650	107	34	〈	〈	PROPN
ejpam-3650	107	35	j	j	PROPN
ejpam-3650	107	36	′α(v	′α(v	PROPN
ejpam-3650	107	37	)	)	PUNCT
ejpam-3650	107	38	,	,	PUNCT
ejpam-3650	107	39	δv	δv	ADV
ejpam-3650	107	40	〉	〉	NOUN
ejpam-3650	107	41	=	=	SYM
ejpam-3650	107	42	∫	∫	PROPN
ejpam-3650	107	43	ω	ω	PROPN
ejpam-3650	107	44	αv	αv	PROPN
ejpam-3650	107	45	+	+	CCONJ
ejpam-3650	107	46	t∫	t∫	ADJ
ejpam-3650	107	47	0	0	NUM
ejpam-3650	107	48	uψdt	uψdt	NOUN
ejpam-3650	107	49			NOUN
ejpam-3650	107	50	δv(x)dx	δv(x)dx	VERB
ejpam-3650	107	51	.	.	PUNCT
ejpam-3650	108	1	(	(	PUNCT
ejpam-3650	108	2	18	18	NUM
ejpam-3650	108	3	)	)	PUNCT
ejpam-3650	108	4	proof	proof	NOUN
ejpam-3650	108	5	.	.	PUNCT
ejpam-3650	109	1	let	let	VERB
ejpam-3650	109	2	the	the	DET
ejpam-3650	109	3	increment	increment	NOUN
ejpam-3650	109	4	δv	δv	ADV
ejpam-3650	109	5	∈	∈	PROPN
ejpam-3650	109	6	l∞(ω	l∞(ω	NOUN
ejpam-3650	109	7	)	)	PUNCT
ejpam-3650	109	8	of	of	ADP
ejpam-3650	109	9	the	the	DET
ejpam-3650	109	10	element	element	NOUN
ejpam-3650	109	11	v	v	ADP
ejpam-3650	109	12	∈	∈	PROPN
ejpam-3650	109	13	v	v	NOUN
ejpam-3650	109	14	be	be	AUX
ejpam-3650	109	15	v	v	ADP
ejpam-3650	109	16	+	+	NOUN
ejpam-3650	109	17	δv	δv	ADV
ejpam-3650	109	18	∈	∈	PROPN
ejpam-3650	109	19	v	v	NOUN
ejpam-3650	109	20	.	.	PUNCT
ejpam-3650	110	1	denote	denote	VERB
ejpam-3650	110	2	by	by	ADP
ejpam-3650	110	3	δu(x	δu(x	NOUN
ejpam-3650	110	4	,	,	PUNCT
ejpam-3650	110	5	t	t	PROPN
ejpam-3650	110	6	)	)	PUNCT
ejpam-3650	110	7	≡	≡	PROPN
ejpam-3650	110	8	u(x	u(x	PROPN
ejpam-3650	110	9	,	,	PUNCT
ejpam-3650	110	10	t	t	PROPN
ejpam-3650	110	11	;	;	PUNCT
ejpam-3650	110	12	v	v	NOUN
ejpam-3650	110	13	+	+	CCONJ
ejpam-3650	110	14	δv	δv	CCONJ
ejpam-3650	110	15	)	)	PUNCT
ejpam-3650	111	1	−	−	PROPN
ejpam-3650	112	1	u(x	u(x	PROPN
ejpam-3650	112	2	,	,	PUNCT
ejpam-3650	112	3	t	t	PROPN
ejpam-3650	112	4	;	;	PUNCT
ejpam-3650	112	5	v	v	NOUN
ejpam-3650	112	6	)	)	PUNCT
ejpam-3650	112	7	.	.	PUNCT
ejpam-3650	113	1	it	it	PRON
ejpam-3650	113	2	’s	’	VERB
ejpam-3650	113	3	clear	clear	ADJ
ejpam-3650	113	4	that	that	SCONJ
ejpam-3650	113	5	the	the	DET
ejpam-3650	113	6	function	function	NOUN
ejpam-3650	113	7	δu(x	δu(x	VERB
ejpam-3650	113	8	,	,	PUNCT
ejpam-3650	113	9	t	t	PROPN
ejpam-3650	113	10	)	)	PUNCT
ejpam-3650	113	11	is	be	AUX
ejpam-3650	113	12	a	a	DET
ejpam-3650	113	13	generalized	generalized	ADJ
ejpam-3650	113	14	solution	solution	NOUN
ejpam-3650	113	15	from	from	ADP
ejpam-3650	113	16	u	u	NOUN
ejpam-3650	113	17	of	of	ADP
ejpam-3650	113	18	the	the	DET
ejpam-3650	113	19	boundary	boundary	ADJ
ejpam-3650	113	20	value	value	NOUN
ejpam-3650	113	21	problem	problem	NOUN
ejpam-3650	113	22	∂2δu	∂2δu	X
ejpam-3650	113	23	∂t2	∂t2	NOUN
ejpam-3650	114	1	−∆δu+	−∆δu+	PUNCT
ejpam-3650	114	2	(	(	PUNCT
ejpam-3650	114	3	v	v	NOUN
ejpam-3650	114	4	+	+	NOUN
ejpam-3650	114	5	δv)δu	δv)δu	PUNCT
ejpam-3650	114	6	=	=	PUNCT
ejpam-3650	114	7	−uδv	−uδv	NOUN
ejpam-3650	114	8	+	+	X
ejpam-3650	115	1	[	[	X
ejpam-3650	115	2	f(x	f(x	PROPN
ejpam-3650	115	3	,	,	PUNCT
ejpam-3650	115	4	t	t	PROPN
ejpam-3650	115	5	,	,	PUNCT
ejpam-3650	115	6	u+	u+	NUM
ejpam-3650	115	7	δu)−	δu)−	PRON
ejpam-3650	115	8	f(x	f(x	PROPN
ejpam-3650	115	9	,	,	PUNCT
ejpam-3650	115	10	t	t	PROPN
ejpam-3650	115	11	,	,	PUNCT
ejpam-3650	115	12	u	u	NOUN
ejpam-3650	115	13	)	)	PUNCT
ejpam-3650	115	14	]	]	PUNCT
ejpam-3650	115	15	,	,	PUNCT
ejpam-3650	115	16	(	(	PUNCT
ejpam-3650	115	17	x	x	NOUN
ejpam-3650	115	18	,	,	PUNCT
ejpam-3650	115	19	t	t	PROPN
ejpam-3650	115	20	)	)	PUNCT
ejpam-3650	115	21	∈	∈	PROPN
ejpam-3650	115	22	q	q	NOUN
ejpam-3650	115	23	,	,	PUNCT
ejpam-3650	115	24	(	(	PUNCT
ejpam-3650	115	25	19	19	NUM
ejpam-3650	115	26	)	)	PUNCT
ejpam-3650	115	27	δu	δu	ADP
ejpam-3650	115	28	=	=	SYM
ejpam-3650	115	29	0	0	PROPN
ejpam-3650	115	30	,	,	PUNCT
ejpam-3650	115	31	(	(	PUNCT
ejpam-3650	115	32	x	x	NOUN
ejpam-3650	115	33	,	,	PUNCT
ejpam-3650	115	34	t	t	PROPN
ejpam-3650	115	35	)	)	PUNCT
ejpam-3650	115	36	∈	∈	PROPN
ejpam-3650	115	37	s	s	NOUN
ejpam-3650	115	38	,	,	PUNCT
ejpam-3650	115	39	δu|t=0	δu|t=0	ADJ
ejpam-3650	115	40	=	=	SYM
ejpam-3650	115	41	0	0	NUM
ejpam-3650	115	42	,	,	PUNCT
ejpam-3650	115	43	∂δu	∂δu	NOUN
ejpam-3650	115	44	∂t	∂t	PROPN
ejpam-3650	115	45	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3650	115	46	t=0	t=0	VERB
ejpam-3650	115	47	=	=	SYM
ejpam-3650	115	48	0	0	NUM
ejpam-3650	115	49	,	,	PUNCT
ejpam-3650	115	50	x	x	X
ejpam-3650	115	51	∈	∈	PROPN
ejpam-3650	115	52	ω	ω	PROPN
ejpam-3650	115	53	.	.	PUNCT
ejpam-3650	116	1	(	(	PUNCT
ejpam-3650	116	2	20	20	NUM
ejpam-3650	116	3	)	)	PUNCT
ejpam-3650	116	4	the	the	DET
ejpam-3650	116	5	generalized	generalize	VERB
ejpam-3650	116	6	solution	solution	NOUN
ejpam-3650	116	7	u	u	NOUN
ejpam-3650	116	8	of	of	ADP
ejpam-3650	116	9	the	the	DET
ejpam-3650	116	10	problem	problem	NOUN
ejpam-3650	116	11	(	(	PUNCT
ejpam-3650	116	12	19	19	NUM
ejpam-3650	116	13	)	)	PUNCT
ejpam-3650	116	14	,	,	PUNCT
ejpam-3650	116	15	(	(	PUNCT
ejpam-3650	116	16	20	20	NUM
ejpam-3650	116	17	)	)	PUNCT
ejpam-3650	116	18	from	from	ADP
ejpam-3650	116	19	is	be	AUX
ejpam-3650	116	20	equal	equal	ADJ
ejpam-3650	116	21	to	to	ADP
ejpam-3650	116	22	zero	zero	NUM
ejpam-3650	116	23	for	for	ADP
ejpam-3650	116	24	t	t	NOUN
ejpam-3650	116	25	=	=	SYM
ejpam-3650	116	26	0	0	PUNCT
ejpam-3650	116	27	and	and	CCONJ
ejpam-3650	116	28	satisfies	satisfy	VERB
ejpam-3650	116	29	the	the	DET
ejpam-3650	116	30	identity∫	identity∫	ADJ
ejpam-3650	116	31	q	q	X
ejpam-3650	116	32	[	[	PUNCT
ejpam-3650	116	33	∂δu	∂δu	NOUN
ejpam-3650	116	34	∂t	∂t	PROPN
ejpam-3650	116	35	∂η	∂η	PROPN
ejpam-3650	116	36	∂t	∂t	PROPN
ejpam-3650	116	37	−	−	PROPN
ejpam-3650	116	38	n∑	n∑	PROPN
ejpam-3650	117	1	i=1	i=1	PROPN
ejpam-3650	118	1	∂δu	∂δu	PROPN
ejpam-3650	118	2	∂xi	∂xi	NOUN
ejpam-3650	118	3	∂η	∂η	PROPN
ejpam-3650	118	4	∂xi	∂xi	PROPN
ejpam-3650	118	5	−	−	PROPN
ejpam-3650	118	6	(	(	PUNCT
ejpam-3650	118	7	v	v	NOUN
ejpam-3650	118	8	+	+	NOUN
ejpam-3650	118	9	δv)δuη	δv)δuη	X
ejpam-3650	118	10	]	]	X
ejpam-3650	118	11	dxdt	dxdt	NOUN
ejpam-3650	118	12	=	=	SYM
ejpam-3650	118	13	=	=	PUNCT
ejpam-3650	118	14	∫	∫	PROPN
ejpam-3650	118	15	q	q	X
ejpam-3650	119	1	uηδvdxdt−	uηδvdxdt−	ADJ
ejpam-3650	119	2	∫	∫	PROPN
ejpam-3650	119	3	q	q	PROPN
ejpam-3650	120	1	[	[	X
ejpam-3650	120	2	f(x	f(x	PROPN
ejpam-3650	120	3	,	,	PUNCT
ejpam-3650	120	4	t	t	PROPN
ejpam-3650	120	5	,	,	PUNCT
ejpam-3650	120	6	u+	u+	NUM
ejpam-3650	120	7	δu)−	δu)−	PRON
ejpam-3650	120	8	f(x	f(x	PROPN
ejpam-3650	120	9	,	,	PUNCT
ejpam-3650	120	10	t	t	PROPN
ejpam-3650	120	11	,	,	PUNCT
ejpam-3650	120	12	u	u	NOUN
ejpam-3650	120	13	)	)	PUNCT
ejpam-3650	120	14	]	]	PUNCT
ejpam-3650	120	15	ηdxdt	ηdxdt	NOUN
ejpam-3650	120	16	(	(	PUNCT
ejpam-3650	120	17	21	21	NUM
ejpam-3650	120	18	)	)	PUNCT
ejpam-3650	120	19	for	for	ADP
ejpam-3650	120	20	all	all	DET
ejpam-3650	120	21	η	η	X
ejpam-3650	120	22	=	=	SYM
ejpam-3650	120	23	η(x	η(x	PROPN
ejpam-3650	120	24	,	,	PUNCT
ejpam-3650	120	25	t	t	PROPN
ejpam-3650	120	26	)	)	PUNCT
ejpam-3650	120	27	from	from	ADP
ejpam-3650	120	28	u	u	PRON
ejpam-3650	120	29	which	which	PRON
ejpam-3650	120	30	equal	equal	ADJ
ejpam-3650	120	31	to	to	ADP
ejpam-3650	120	32	zero	zero	NUM
ejpam-3650	120	33	for	for	ADP
ejpam-3650	120	34	t	t	PROPN
ejpam-3650	120	35	=	=	SYM
ejpam-3650	120	36	t	t	PROPN
ejpam-3650	120	37	.	.	PUNCT
ejpam-3650	121	1	applying	apply	VERB
ejpam-3650	121	2	the	the	DET
ejpam-3650	121	3	faedogalerkin	faedogalerkin	NOUN
ejpam-3650	121	4	method	method	NOUN
ejpam-3650	121	5	and	and	CCONJ
ejpam-3650	121	6	taking	take	VERB
ejpam-3650	121	7	into	into	ADP
ejpam-3650	121	8	account	account	NOUN
ejpam-3650	121	9	that	that	SCONJ
ejpam-3650	121	10	the	the	DET
ejpam-3650	121	11	function	function	NOUN
ejpam-3650	121	12	f(x	f(x	PROPN
ejpam-3650	121	13	,	,	PUNCT
ejpam-3650	121	14	t	t	PROPN
ejpam-3650	121	15	,	,	PUNCT
ejpam-3650	121	16	u	u	NOUN
ejpam-3650	121	17	)	)	PUNCT
ejpam-3650	121	18	satisfies	satisfy	VERB
ejpam-3650	121	19	the	the	DET
ejpam-3650	121	20	lipschitz	lipschitz	NOUN
ejpam-3650	121	21	condition	condition	NOUN
ejpam-3650	121	22	with	with	ADP
ejpam-3650	121	23	respect	respect	NOUN
ejpam-3650	121	24	to	to	ADP
ejpam-3650	121	25	the	the	DET
ejpam-3650	121	26	argument	argument	NOUN
ejpam-3650	121	27	,	,	PUNCT
ejpam-3650	121	28	we	we	PRON
ejpam-3650	121	29	can	can	AUX
ejpam-3650	121	30	obtain	obtain	VERB
ejpam-3650	121	31	the	the	DET
ejpam-3650	121	32	estimate	estimate	NOUN
ejpam-3650	121	33	for	for	ADP
ejpam-3650	121	34	the	the	DET
ejpam-3650	121	35	solution	solution	NOUN
ejpam-3650	121	36	of	of	ADP
ejpam-3650	121	37	the	the	DET
ejpam-3650	121	38	problem	problem	NOUN
ejpam-3650	121	39	(	(	PUNCT
ejpam-3650	121	40	19	19	NUM
ejpam-3650	121	41	)	)	PUNCT
ejpam-3650	121	42	,	,	PUNCT
ejpam-3650	121	43	(	(	PUNCT
ejpam-3650	121	44	20	20	X
ejpam-3650	121	45	)	)	PUNCT
ejpam-3650	121	46	‖δu‖	‖δu‖	NOUN
ejpam-3650	121	47	◦	◦	NOUN
ejpam-3650	121	48	w	w	NOUN
ejpam-3650	121	49	1	1	NUM
ejpam-3650	121	50	2	2	NUM
ejpam-3650	121	51	(	(	PUNCT
ejpam-3650	121	52	ω	ω	NOUN
ejpam-3650	121	53	)	)	PUNCT
ejpam-3650	122	1	+	+	CCONJ
ejpam-3650	122	2	∥∥∥∥∂δu∂t	∥∥∥∥∂δu∂t	NOUN
ejpam-3650	122	3	∥∥∥∥	∥∥∥∥	PROPN
ejpam-3650	122	4	l2(ω	l2(ω	NOUN
ejpam-3650	122	5	)	)	PUNCT
ejpam-3650	122	6	≤	≤	NOUN
ejpam-3650	122	7	c	c	X
ejpam-3650	122	8	‖δv‖l∞(ω	‖δv‖l∞(ω	PROPN
ejpam-3650	122	9	)	)	PUNCT
ejpam-3650	122	10	,	,	PUNCT
ejpam-3650	122	11	t	t	PROPN
ejpam-3650	122	12	∈	∈	PROPN
ejpam-3650	123	1	[	[	X
ejpam-3650	123	2	0	0	NUM
ejpam-3650	123	3	,	,	PUNCT
ejpam-3650	123	4	t	t	X
ejpam-3650	123	5	]	]	PUNCT
ejpam-3650	123	6	.	.	PUNCT
ejpam-3650	124	1	(	(	PUNCT
ejpam-3650	124	2	22	22	NUM
ejpam-3650	124	3	)	)	PUNCT
ejpam-3650	124	4	we	we	PRON
ejpam-3650	124	5	consider	consider	VERB
ejpam-3650	124	6	the	the	DET
ejpam-3650	124	7	increment	increment	NOUN
ejpam-3650	124	8	of	of	ADP
ejpam-3650	124	9	functional	functional	ADJ
ejpam-3650	124	10	(	(	PUNCT
ejpam-3650	124	11	6	6	NUM
ejpam-3650	124	12	):	):	PUNCT
ejpam-3650	124	13	∆jα(v	∆jα(v	ADJ
ejpam-3650	124	14	)	)	PUNCT
ejpam-3650	124	15	=	=	SYM
ejpam-3650	124	16	jα(v	jα(v	X
ejpam-3650	125	1	+	+	X
ejpam-3650	125	2	δv)−	δv)−	ADJ
ejpam-3650	125	3	jα(v	jα(v	PUNCT
ejpam-3650	125	4	)	)	PUNCT
ejpam-3650	126	1	=	=	SYM
ejpam-3650	126	2	∫	∫	PROPN
ejpam-3650	126	3	ω	ω	PROPN
ejpam-3650	126	4	αvδvdx+	αvδvdx+	NUM
ejpam-3650	126	5	α	α	PROPN
ejpam-3650	126	6	2	2	NUM
ejpam-3650	126	7	∫	∫	PROPN
ejpam-3650	126	8	ω	ω	PROPN
ejpam-3650	126	9	|δv|2	|δv|2	PUNCT
ejpam-3650	126	10	dx+	dx+	PROPN
ejpam-3650	126	11	+	+	CCONJ
ejpam-3650	126	12	∫	∫	PROPN
ejpam-3650	126	13	ω	ω	X
ejpam-3650	126	14	[	[	PUNCT
ejpam-3650	126	15	t∫	t∫	PROPN
ejpam-3650	126	16	0	0	NUM
ejpam-3650	126	17	kudt−	kudt−	NOUN
ejpam-3650	126	18	ϕ(x	ϕ(x	PROPN
ejpam-3650	126	19	)	)	PUNCT
ejpam-3650	126	20	]	]	PUNCT
ejpam-3650	127	1	t∫	t∫	PRON
ejpam-3650	127	2	0	0	NUM
ejpam-3650	127	3	kδudtdx+	kδudtdx+	SYM
ejpam-3650	127	4	1	1	NUM
ejpam-3650	127	5	2	2	NUM
ejpam-3650	127	6	∫	∫	NOUN
ejpam-3650	127	7	ω	ω	NOUN
ejpam-3650	127	8	[	[	PUNCT
ejpam-3650	127	9	t∫	t∫	PROPN
ejpam-3650	127	10	0	0	NUM
ejpam-3650	127	11	kδudt	kδudt	NOUN
ejpam-3650	127	12	]	]	PUNCT
ejpam-3650	127	13	2	2	NUM
ejpam-3650	127	14	dx	dx	X
ejpam-3650	127	15	.	.	PUNCT
ejpam-3650	128	1	(	(	PUNCT
ejpam-3650	128	2	23	23	NUM
ejpam-3650	128	3	)	)	PUNCT
ejpam-3650	128	4	if	if	SCONJ
ejpam-3650	128	5	we	we	PRON
ejpam-3650	128	6	take	take	VERB
ejpam-3650	128	7	g	g	NOUN
ejpam-3650	128	8	=	=	SYM
ejpam-3650	128	9	δu(x	δu(x	NOUN
ejpam-3650	128	10	,	,	PUNCT
ejpam-3650	128	11	t	t	NOUN
ejpam-3650	128	12	)	)	PUNCT
ejpam-3650	128	13	in	in	ADP
ejpam-3650	128	14	(	(	PUNCT
ejpam-3650	128	15	16	16	NUM
ejpam-3650	128	16	)	)	PUNCT
ejpam-3650	128	17	and	and	CCONJ
ejpam-3650	128	18	take	take	VERB
ejpam-3650	128	19	η	η	NOUN
ejpam-3650	128	20	=	=	PROPN
ejpam-3650	128	21	ψ(x	ψ(x	PROPN
ejpam-3650	128	22	,	,	PUNCT
ejpam-3650	128	23	t	t	PROPN
ejpam-3650	128	24	;	;	PUNCT
ejpam-3650	128	25	v	v	NOUN
ejpam-3650	128	26	)	)	PUNCT
ejpam-3650	128	27	in	in	ADP
ejpam-3650	128	28	(	(	PUNCT
ejpam-3650	128	29	21	21	NUM
ejpam-3650	128	30	)	)	PUNCT
ejpam-3650	128	31	and	and	CCONJ
ejpam-3650	128	32	summing	sum	VERB
ejpam-3650	128	33	the	the	DET
ejpam-3650	128	34	obtained	obtain	VERB
ejpam-3650	128	35	relations	relation	NOUN
ejpam-3650	128	36	we	we	PRON
ejpam-3650	128	37	get	get	VERB
ejpam-3650	128	38	:	:	PUNCT
ejpam-3650	128	39	∫	∫	PROPN
ejpam-3650	128	40	q	q	PROPN
ejpam-3650	128	41	k(x	k(x	PROPN
ejpam-3650	128	42	,	,	PUNCT
ejpam-3650	128	43	t	t	PROPN
ejpam-3650	128	44	)	)	PUNCT
ejpam-3650	128	45	[	[	PUNCT
ejpam-3650	128	46	t∫	t∫	SYM
ejpam-3650	128	47	0	0	NUM
ejpam-3650	128	48	kudt−	kudt−	NOUN
ejpam-3650	128	49	ϕ(x	ϕ(x	PROPN
ejpam-3650	128	50	)	)	PUNCT
ejpam-3650	128	51	]	]	PUNCT
ejpam-3650	129	1	δudxdt	δudxdt	PROPN
ejpam-3650	129	2	=	=	SYM
ejpam-3650	129	3	∫	∫	PROPN
ejpam-3650	129	4	q	q	PROPN
ejpam-3650	130	1	uψδvdxdt+	uψδvdxdt+	ADP
ejpam-3650	130	2	∫	∫	PROPN
ejpam-3650	130	3	q	q	PROPN
ejpam-3650	130	4	ψδuδvdxdt+	ψδuδvdxdt+	X
ejpam-3650	131	1	+	+	NUM
ejpam-3650	131	2	∫	∫	PROPN
ejpam-3650	131	3	q	q	PROPN
ejpam-3650	131	4	∂f(x	∂f(x	PROPN
ejpam-3650	131	5	,	,	PUNCT
ejpam-3650	131	6	t	t	PROPN
ejpam-3650	131	7	,	,	PUNCT
ejpam-3650	131	8	u	u	NOUN
ejpam-3650	131	9	)	)	PUNCT
ejpam-3650	131	10	∂u	∂u	PROPN
ejpam-3650	131	11	ψδudxdt−	ψδudxdt−	PROPN
ejpam-3650	131	12	∫	∫	PROPN
ejpam-3650	131	13	q	q	PROPN
ejpam-3650	132	1	[	[	X
ejpam-3650	132	2	f(x	f(x	PROPN
ejpam-3650	132	3	,	,	PUNCT
ejpam-3650	132	4	t	t	PROPN
ejpam-3650	132	5	,	,	PUNCT
ejpam-3650	132	6	u+	u+	NUM
ejpam-3650	132	7	δu)−	δu)−	PRON
ejpam-3650	132	8	f(x	f(x	PROPN
ejpam-3650	132	9	,	,	PUNCT
ejpam-3650	132	10	t	t	PROPN
ejpam-3650	132	11	,	,	PUNCT
ejpam-3650	132	12	u)]ψdxdt	u)]ψdxdt	PROPN
ejpam-3650	132	13	.	.	PUNCT
ejpam-3650	133	1	g.g	g.g	INTJ
ejpam-3650	133	2	ismayilova	ismayilova	PROPN
ejpam-3650	133	3	/	/	SYM
ejpam-3650	133	4	eur	eur	PROPN
ejpam-3650	133	5	.	.	PUNCT
ejpam-3650	134	1	j.	j.	PROPN
ejpam-3650	134	2	pure	pure	PROPN
ejpam-3650	134	3	appl	appl	PROPN
ejpam-3650	134	4	.	.	PROPN
ejpam-3650	134	5	math	math	PROPN
ejpam-3650	134	6	,	,	PUNCT
ejpam-3650	134	7	13	13	NUM
ejpam-3650	134	8	(	(	PUNCT
ejpam-3650	134	9	2	2	NUM
ejpam-3650	134	10	)	)	PUNCT
ejpam-3650	134	11	(	(	PUNCT
ejpam-3650	134	12	2020	2020	NUM
ejpam-3650	134	13	)	)	PUNCT
ejpam-3650	134	14	,	,	PUNCT
ejpam-3650	134	15	314	314	NUM
ejpam-3650	134	16	-	-	SYM
ejpam-3650	134	17	322	322	NUM
ejpam-3650	134	18	320	320	NUM
ejpam-3650	134	19	taking	take	VERB
ejpam-3650	134	20	into	into	ADP
ejpam-3650	134	21	account	account	NOUN
ejpam-3650	134	22	this	this	DET
ejpam-3650	134	23	equality	equality	NOUN
ejpam-3650	134	24	in	in	ADP
ejpam-3650	134	25	(	(	PUNCT
ejpam-3650	134	26	23	23	NUM
ejpam-3650	134	27	)	)	PUNCT
ejpam-3650	135	1	,	,	PUNCT
ejpam-3650	135	2	we	we	PRON
ejpam-3650	135	3	obtain	obtain	VERB
ejpam-3650	135	4	∆jα(v	∆jα(v	ADJ
ejpam-3650	135	5	)	)	PUNCT
ejpam-3650	136	1	=	=	SYM
ejpam-3650	136	2	∫	∫	PROPN
ejpam-3650	136	3	ω	ω	NUM
ejpam-3650	136	4	αv	αv	PROPN
ejpam-3650	137	1	+	+	CCONJ
ejpam-3650	137	2	t∫	t∫	ADJ
ejpam-3650	137	3	0	0	NUM
ejpam-3650	137	4	uψdt	uψdt	PROPN
ejpam-3650	137	5	δvdx+r	δvdx+r	PROPN
ejpam-3650	137	6	,	,	PUNCT
ejpam-3650	137	7	(	(	PUNCT
ejpam-3650	137	8	24	24	NUM
ejpam-3650	137	9	)	)	PUNCT
ejpam-3650	137	10	where	where	SCONJ
ejpam-3650	137	11	r	r	NOUN
ejpam-3650	137	12	=	=	SYM
ejpam-3650	137	13	4∑	4∑	NUM
ejpam-3650	137	14	i=1	i=1	PROPN
ejpam-3650	137	15	ri	ri	PROPN
ejpam-3650	137	16	is	be	AUX
ejpam-3650	137	17	the	the	DET
ejpam-3650	137	18	remainder	remainder	ADJ
ejpam-3650	137	19	term	term	NOUN
ejpam-3650	137	20	and	and	CCONJ
ejpam-3650	137	21	r1	r1	NOUN
ejpam-3650	137	22	=	=	PUNCT
ejpam-3650	138	1	α	α	PROPN
ejpam-3650	138	2	2	2	NUM
ejpam-3650	138	3	∫	∫	PROPN
ejpam-3650	138	4	ω	ω	PROPN
ejpam-3650	138	5	|δv|2dx	|δv|2dx	PROPN
ejpam-3650	138	6	,	,	PUNCT
ejpam-3650	138	7	r2	r2	PROPN
ejpam-3650	138	8	=	=	NOUN
ejpam-3650	139	1	1	1	NUM
ejpam-3650	139	2	2	2	NUM
ejpam-3650	139	3	∫	∫	PROPN
ejpam-3650	139	4	ω	ω	NUM
ejpam-3650	139	5			PROPN
ejpam-3650	139	6	t∫	t∫	PRON
ejpam-3650	139	7	0	0	NUM
ejpam-3650	139	8	kδudt	kδudt	PROPN
ejpam-3650	139	9	2	2	NUM
ejpam-3650	139	10	dx	dx	PROPN
ejpam-3650	139	11	,	,	PUNCT
ejpam-3650	139	12	r3	r3	PROPN
ejpam-3650	139	13	=	=	SYM
ejpam-3650	139	14	∫	∫	PROPN
ejpam-3650	139	15	q	q	PROPN
ejpam-3650	139	16	ψδuδvdxdt	ψδuδvdxdt	NOUN
ejpam-3650	139	17	,	,	PUNCT
ejpam-3650	139	18	r4	r4	PROPN
ejpam-3650	139	19	=	=	SYM
ejpam-3650	139	20	∫	∫	PROPN
ejpam-3650	139	21	q	q	PROPN
ejpam-3650	139	22	{	{	PUNCT
ejpam-3650	139	23	∂f(x	∂f(x	PROPN
ejpam-3650	139	24	,	,	PUNCT
ejpam-3650	139	25	t	t	PROPN
ejpam-3650	139	26	,	,	PUNCT
ejpam-3650	139	27	u	u	NOUN
ejpam-3650	139	28	)	)	PUNCT
ejpam-3650	139	29	∂u	∂u	PROPN
ejpam-3650	139	30	δu−	δu−	PUNCT
ejpam-3650	140	1	[	[	X
ejpam-3650	140	2	f(x	f(x	PROPN
ejpam-3650	140	3	,	,	PUNCT
ejpam-3650	140	4	t	t	PROPN
ejpam-3650	140	5	,	,	PUNCT
ejpam-3650	140	6	u+	u+	NUM
ejpam-3650	140	7	δu)−	δu)−	PRON
ejpam-3650	140	8	f(x	f(x	PROPN
ejpam-3650	140	9	,	,	PUNCT
ejpam-3650	140	10	t	t	PROPN
ejpam-3650	140	11	,	,	PUNCT
ejpam-3650	140	12	u	u	NOUN
ejpam-3650	140	13	)	)	PUNCT
ejpam-3650	140	14	]	]	PUNCT
ejpam-3650	140	15	}	}	PUNCT
ejpam-3650	140	16	ψdxdt	ψdxdt	NOUN
ejpam-3650	140	17	.	.	PUNCT
ejpam-3650	141	1	the	the	DET
ejpam-3650	141	2	first	first	ADJ
ejpam-3650	141	3	term	term	NOUN
ejpam-3650	141	4	in	in	ADP
ejpam-3650	141	5	the	the	DET
ejpam-3650	141	6	right	right	ADJ
ejpam-3650	141	7	-	-	PUNCT
ejpam-3650	141	8	hand	hand	NOUN
ejpam-3650	141	9	side	side	NOUN
ejpam-3650	141	10	of	of	ADP
ejpam-3650	141	11	(	(	PUNCT
ejpam-3650	141	12	24	24	NUM
ejpam-3650	141	13	)	)	PUNCT
ejpam-3650	141	14	is	be	AUX
ejpam-3650	141	15	a	a	DET
ejpam-3650	141	16	linear	linear	ADV
ejpam-3650	141	17	bounded	bounded	ADJ
ejpam-3650	141	18	functional	functional	ADJ
ejpam-3650	141	19	in	in	ADP
ejpam-3650	141	20	l2(q	l2(q	PROPN
ejpam-3650	141	21	)	)	PUNCT
ejpam-3650	141	22	.	.	PUNCT
ejpam-3650	142	1	now	now	ADV
ejpam-3650	142	2	we	we	PRON
ejpam-3650	142	3	estimate	estimate	VERB
ejpam-3650	142	4	the	the	DET
ejpam-3650	142	5	remainder	remainder	NOUN
ejpam-3650	142	6	term	term	NOUN
ejpam-3650	142	7	of	of	ADP
ejpam-3650	142	8	or	or	CCONJ
ejpam-3650	142	9	r	r	NOUN
ejpam-3650	142	10	in	in	ADP
ejpam-3650	142	11	(	(	PUNCT
ejpam-3650	142	12	24	24	NUM
ejpam-3650	142	13	)	)	PUNCT
ejpam-3650	142	14	.	.	PUNCT
ejpam-3650	143	1	first	first	ADV
ejpam-3650	143	2	,	,	PUNCT
ejpam-3650	143	3	we	we	PRON
ejpam-3650	143	4	estimate	estimate	VERB
ejpam-3650	143	5	the	the	DET
ejpam-3650	143	6	fourth	fourth	ADJ
ejpam-3650	143	7	term	term	NOUN
ejpam-3650	143	8	in	in	ADP
ejpam-3650	143	9	the	the	DET
ejpam-3650	143	10	expression	expression	NOUN
ejpam-3650	143	11	r.	r.	NOUN
ejpam-3650	143	12	by	by	ADP
ejpam-3650	143	13	the	the	DET
ejpam-3650	143	14	lagrange	lagrange	PROPN
ejpam-3650	143	15	mean	mean	NOUN
ejpam-3650	143	16	value	value	NOUN
ejpam-3650	143	17	theorem	theorem	VERB
ejpam-3650	143	18	,	,	PUNCT
ejpam-3650	143	19	we	we	PRON
ejpam-3650	143	20	have	have	VERB
ejpam-3650	143	21	r4	r4	NOUN
ejpam-3650	143	22	=	=	PUNCT
ejpam-3650	144	1	∫	∫	PROPN
ejpam-3650	144	2	q	q	X
ejpam-3650	145	1	[	[	PUNCT
ejpam-3650	145	2	∂f(x	∂f(x	PROPN
ejpam-3650	145	3	,	,	PUNCT
ejpam-3650	145	4	t	t	PROPN
ejpam-3650	145	5	,	,	PUNCT
ejpam-3650	145	6	u	u	NOUN
ejpam-3650	145	7	)	)	PUNCT
ejpam-3650	145	8	∂u	∂u	PROPN
ejpam-3650	145	9	−	−	PROPN
ejpam-3650	145	10	∂f(x	∂f(x	PROPN
ejpam-3650	145	11	,	,	PUNCT
ejpam-3650	145	12	t	t	PROPN
ejpam-3650	145	13	,	,	PUNCT
ejpam-3650	145	14	u+	u+	NOUN
ejpam-3650	145	15	θδu	θδu	NOUN
ejpam-3650	145	16	)	)	PUNCT
ejpam-3650	145	17	∂u	∂u	PROPN
ejpam-3650	145	18	]	]	PUNCT
ejpam-3650	145	19	δuψdxdt	δuψdxdt	NOUN
ejpam-3650	145	20	,	,	PUNCT
ejpam-3650	145	21	where	where	SCONJ
ejpam-3650	145	22	0	0	NUM
ejpam-3650	145	23	≤	≤	NUM
ejpam-3650	145	24	θ	θ	PROPN
ejpam-3650	145	25	≤	≤	NUM
ejpam-3650	145	26	1	1	NUM
ejpam-3650	145	27	.	.	PUNCT
ejpam-3650	146	1	since	since	SCONJ
ejpam-3650	146	2	the	the	DET
ejpam-3650	146	3	operator	operator	NOUN
ejpam-3650	146	4	∂f(x	∂f(x	PROPN
ejpam-3650	146	5	,	,	PUNCT
ejpam-3650	146	6	t	t	PROPN
ejpam-3650	146	7	,	,	PUNCT
ejpam-3650	146	8	u(x	u(x	PROPN
ejpam-3650	146	9	,	,	PUNCT
ejpam-3650	146	10	t	t	NOUN
ejpam-3650	146	11	)	)	PUNCT
ejpam-3650	146	12	)	)	PUNCT
ejpam-3650	146	13	∂u	∂u	PROPN
ejpam-3650	146	14	acts	act	VERB
ejpam-3650	146	15	continuously	continuously	ADV
ejpam-3650	146	16	from	from	ADP
ejpam-3650	146	17	l2(q	l2(q	PROPN
ejpam-3650	146	18	)	)	PUNCT
ejpam-3650	146	19	to	to	ADP
ejpam-3650	146	20	l2(q	l2(q	PROPN
ejpam-3650	146	21	)	)	PUNCT
ejpam-3650	146	22	with	with	ADP
ejpam-3650	146	23	respect	respect	NOUN
ejpam-3650	146	24	to	to	ADP
ejpam-3650	146	25	u	u	NOUN
ejpam-3650	146	26	,	,	PUNCT
ejpam-3650	146	27	from	from	ADP
ejpam-3650	146	28	estimation	estimation	NOUN
ejpam-3650	146	29	(	(	PUNCT
ejpam-3650	146	30	22	22	NUM
ejpam-3650	146	31	)	)	PUNCT
ejpam-3650	146	32	it	it	PRON
ejpam-3650	146	33	follows	follow	VERB
ejpam-3650	146	34	that	that	SCONJ
ejpam-3650	146	35	∂f(x	∂f(x	PROPN
ejpam-3650	146	36	,	,	PUNCT
ejpam-3650	146	37	t	t	PROPN
ejpam-3650	146	38	,	,	PUNCT
ejpam-3650	146	39	u(x	u(x	PROPN
ejpam-3650	146	40	,	,	PUNCT
ejpam-3650	146	41	t	t	NOUN
ejpam-3650	146	42	)	)	PUNCT
ejpam-3650	146	43	)	)	PUNCT
ejpam-3650	147	1	∂u	∂u	PROPN
ejpam-3650	147	2	−	−	PROPN
ejpam-3650	147	3	∂f(x	∂f(x	PROPN
ejpam-3650	147	4	,	,	PUNCT
ejpam-3650	147	5	t	t	PROPN
ejpam-3650	147	6	,	,	PUNCT
ejpam-3650	147	7	u(x	u(x	NOUN
ejpam-3650	147	8	,	,	PUNCT
ejpam-3650	147	9	t)+θδu(x	t)+θδu(x	PROPN
ejpam-3650	147	10	,	,	PUNCT
ejpam-3650	147	11	t	t	PROPN
ejpam-3650	147	12	)	)	PUNCT
ejpam-3650	147	13	)	)	PUNCT
ejpam-3650	148	1	∂u	∂u	PROPN
ejpam-3650	148	2	→	→	SYM
ejpam-3650	148	3	0	0	NUM
ejpam-3650	148	4	strongly	strongly	ADV
ejpam-3650	148	5	in	in	ADP
ejpam-3650	148	6	l2(q	l2(q	PROPN
ejpam-3650	148	7	)	)	PUNCT
ejpam-3650	148	8	as	as	ADP
ejpam-3650	148	9	‖δv‖l∞(ω	‖δv‖l∞(ω	NOUN
ejpam-3650	148	10	)	)	PUNCT
ejpam-3650	148	11	→	→	SYM
ejpam-3650	148	12	0	0	X
ejpam-3650	148	13	.	.	PUNCT
ejpam-3650	149	1	therefore	therefore	ADV
ejpam-3650	149	2	,	,	PUNCT
ejpam-3650	149	3	from	from	ADP
ejpam-3650	149	4	this	this	PRON
ejpam-3650	149	5	and	and	CCONJ
ejpam-3650	149	6	estimation	estimation	NOUN
ejpam-3650	149	7	(	(	PUNCT
ejpam-3650	149	8	22	22	NUM
ejpam-3650	149	9	)	)	PUNCT
ejpam-3650	149	10	it	it	PRON
ejpam-3650	149	11	follows	follow	VERB
ejpam-3650	149	12	that	that	SCONJ
ejpam-3650	149	13	r4	r4	NOUN
ejpam-3650	149	14	=	=	SYM
ejpam-3650	149	15	0	0	NUM
ejpam-3650	149	16	(	(	PUNCT
ejpam-3650	149	17	‖δv‖l∞(ω	‖δv‖l∞(ω	NOUN
ejpam-3650	149	18	)	)	PUNCT
ejpam-3650	149	19	)	)	PUNCT
ejpam-3650	149	20	.	.	PUNCT
ejpam-3650	150	1	then	then	ADV
ejpam-3650	150	2	again	again	ADV
ejpam-3650	150	3	using	use	VERB
ejpam-3650	150	4	estimation	estimation	NOUN
ejpam-3650	150	5	(	(	PUNCT
ejpam-3650	150	6	22	22	NUM
ejpam-3650	150	7	)	)	PUNCT
ejpam-3650	150	8	,	,	PUNCT
ejpam-3650	150	9	we	we	PRON
ejpam-3650	150	10	obtain	obtain	VERB
ejpam-3650	150	11	|r|	|r|	NOUN
ejpam-3650	150	12	≤	≤	NOUN
ejpam-3650	150	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3650	150	14	4∑	4∑	NUM
ejpam-3650	150	15	i=1	i=1	PROPN
ejpam-3650	150	16	ri	ri	PROPN
ejpam-3650	150	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3650	150	18	≤	≤	NUM
ejpam-3650	150	19	c	c	NOUN
ejpam-3650	151	1	[	[	X
ejpam-3650	151	2	‖δv‖2l∞(ω	‖δv‖2l∞(ω	X
ejpam-3650	151	3	)	)	PUNCT
ejpam-3650	151	4	+	+	CCONJ
ejpam-3650	151	5	‖δu‖2	‖δu‖2	PROPN
ejpam-3650	151	6	l2(q	l2(q	PROPN
ejpam-3650	151	7	)	)	PUNCT
ejpam-3650	152	1	+	+	CCONJ
ejpam-3650	152	2	‖ψ‖	‖ψ‖	PROPN
ejpam-3650	152	3	l2(q	l2(q	PROPN
ejpam-3650	152	4	)	)	PUNCT
ejpam-3650	152	5	‖δu‖	‖δu‖	PROPN
ejpam-3650	152	6	l2(q	l2(q	PROPN
ejpam-3650	152	7	)	)	PUNCT
ejpam-3650	152	8	‖δv‖	‖δv‖	PROPN
ejpam-3650	152	9	l∞(ω	l∞(ω	NOUN
ejpam-3650	152	10	)	)	PUNCT
ejpam-3650	152	11	]	]	PUNCT
ejpam-3650	153	1	+	+	CCONJ
ejpam-3650	153	2	+	+	PUNCT
ejpam-3650	153	3	|r4|	|r4|	ADJ
ejpam-3650	153	4	≤	≤	NOUN
ejpam-3650	153	5	c	c	X
ejpam-3650	153	6	‖δv‖2	‖δv‖2	PROPN
ejpam-3650	153	7	l∞(ω	l∞(ω	ADJ
ejpam-3650	153	8	)	)	PUNCT
ejpam-3650	153	9	+	+	CCONJ
ejpam-3650	153	10	|r4|	|r4|	ADJ
ejpam-3650	153	11	.	.	PUNCT
ejpam-3650	153	12	therefore	therefore	ADV
ejpam-3650	153	13	r	r	NOUN
ejpam-3650	153	14	=	=	SYM
ejpam-3650	153	15	0	0	NUM
ejpam-3650	153	16	(	(	PUNCT
ejpam-3650	153	17	‖δv‖l∞(ω	‖δv‖l∞(ω	NOUN
ejpam-3650	153	18	)	)	PUNCT
ejpam-3650	153	19	)	)	PUNCT
ejpam-3650	153	20	.	.	PUNCT
ejpam-3650	154	1	then	then	ADV
ejpam-3650	154	2	it	it	PRON
ejpam-3650	154	3	follows	follow	VERB
ejpam-3650	154	4	from	from	ADP
ejpam-3650	154	5	(	(	PUNCT
ejpam-3650	154	6	24	24	NUM
ejpam-3650	154	7	)	)	PUNCT
ejpam-3650	154	8	that	that	ADV
ejpam-3650	154	9	functional	functional	ADJ
ejpam-3650	154	10	(	(	PUNCT
ejpam-3650	154	11	6	6	NUM
ejpam-3650	154	12	)	)	PUNCT
ejpam-3650	154	13	is	be	AUX
ejpam-3650	154	14	differentiable	differentiable	ADJ
ejpam-3650	154	15	by	by	ADP
ejpam-3650	154	16	freshet	freshet	NOUN
ejpam-3650	154	17	in	in	ADP
ejpam-3650	154	18	v	v	NOUN
ejpam-3650	154	19	and	and	CCONJ
ejpam-3650	154	20	formula	formula	NOUN
ejpam-3650	154	21	(	(	PUNCT
ejpam-3650	154	22	18	18	NUM
ejpam-3650	154	23	)	)	PUNCT
ejpam-3650	154	24	is	be	AUX
ejpam-3650	154	25	valid	valid	ADJ
ejpam-3650	154	26	.	.	PUNCT
ejpam-3650	155	1	we	we	PRON
ejpam-3650	155	2	show	show	VERB
ejpam-3650	155	3	that	that	SCONJ
ejpam-3650	155	4	the	the	DET
ejpam-3650	155	5	map	map	NOUN
ejpam-3650	155	6	v	v	ADP
ejpam-3650	155	7	→	→	SYM
ejpam-3650	155	8	j	j	PROPN
ejpam-3650	155	9	′α(v	′α(v	PROPN
ejpam-3650	155	10	)	)	PUNCT
ejpam-3650	155	11	defined	define	VERB
ejpam-3650	155	12	by	by	ADP
ejpam-3650	155	13	(	(	PUNCT
ejpam-3650	155	14	18	18	NUM
ejpam-3650	155	15	)	)	PUNCT
ejpam-3650	155	16	acts	act	VERB
ejpam-3650	155	17	continuously	continuously	ADV
ejpam-3650	155	18	from	from	ADP
ejpam-3650	155	19	v	v	PRON
ejpam-3650	155	20	to	to	ADP
ejpam-3650	155	21	(	(	PUNCT
ejpam-3650	155	22	l∞(ω))∗	l∞(ω))∗	PROPN
ejpam-3650	155	23	,	,	PUNCT
ejpam-3650	155	24	where	where	SCONJ
ejpam-3650	155	25	(	(	PUNCT
ejpam-3650	155	26	l∞(ω))∗	l∞(ω))∗	PROPN
ejpam-3650	155	27	is	be	AUX
ejpam-3650	155	28	adjoint	adjoint	NOUN
ejpam-3650	155	29	of	of	ADP
ejpam-3650	155	30	l∞(ω	l∞(ω	NOUN
ejpam-3650	155	31	)	)	PUNCT
ejpam-3650	155	32	.	.	PUNCT
ejpam-3650	156	1	let	let	VERB
ejpam-3650	156	2	δψ(x	δψ(x	NOUN
ejpam-3650	156	3	,	,	PUNCT
ejpam-3650	156	4	t	t	PROPN
ejpam-3650	156	5	)	)	PUNCT
ejpam-3650	156	6	=	=	SYM
ejpam-3650	156	7	ψ(x	ψ(x	PROPN
ejpam-3650	156	8	,	,	PUNCT
ejpam-3650	156	9	t	t	PROPN
ejpam-3650	156	10	;	;	PUNCT
ejpam-3650	156	11	v	v	NOUN
ejpam-3650	156	12	+	+	CCONJ
ejpam-3650	156	13	δv	δv	ADV
ejpam-3650	156	14	)	)	PUNCT
ejpam-3650	156	15	−	−	PROPN
ejpam-3650	157	1	ψ(x	ψ(x	PROPN
ejpam-3650	157	2	,	,	PUNCT
ejpam-3650	157	3	t	t	PROPN
ejpam-3650	157	4	;	;	PUNCT
ejpam-3650	157	5	v	v	NOUN
ejpam-3650	157	6	)	)	PUNCT
ejpam-3650	157	7	.	.	PUNCT
ejpam-3650	158	1	it	it	PRON
ejpam-3650	158	2	follows	follow	VERB
ejpam-3650	158	3	from	from	ADP
ejpam-3650	158	4	(	(	PUNCT
ejpam-3650	158	5	14	14	NUM
ejpam-3650	158	6	)	)	PUNCT
ejpam-3650	158	7	,	,	PUNCT
ejpam-3650	158	8	(	(	PUNCT
ejpam-3650	158	9	15	15	NUM
ejpam-3650	158	10	)	)	PUNCT
ejpam-3650	158	11	,	,	PUNCT
ejpam-3650	158	12	that	that	DET
ejpam-3650	158	13	δψ(x	δψ(x	NOUN
ejpam-3650	158	14	,	,	PUNCT
ejpam-3650	158	15	t	t	PROPN
ejpam-3650	158	16	)	)	PUNCT
ejpam-3650	158	17	is	be	AUX
ejpam-3650	158	18	a	a	DET
ejpam-3650	158	19	generalized	generalized	ADJ
ejpam-3650	158	20	solution	solution	NOUN
ejpam-3650	158	21	from	from	ADP
ejpam-3650	158	22	u	u	NOUN
ejpam-3650	158	23	of	of	ADP
ejpam-3650	158	24	the	the	DET
ejpam-3650	158	25	boundary	boundary	ADJ
ejpam-3650	158	26	value	value	NOUN
ejpam-3650	158	27	problem	problem	NOUN
ejpam-3650	158	28	∂2δψ	∂2δψ	PUNCT
ejpam-3650	158	29	∂t2	∂t2	NOUN
ejpam-3650	158	30	−∆δψ	−∆δψ	X
ejpam-3650	159	1	+	+	CCONJ
ejpam-3650	159	2	(	(	PUNCT
ejpam-3650	159	3	v	v	NOUN
ejpam-3650	159	4	+	+	CCONJ
ejpam-3650	159	5	δv)δψ	δv)δψ	PROPN
ejpam-3650	159	6	−	−	PROPN
ejpam-3650	159	7	∂f(x	∂f(x	PROPN
ejpam-3650	159	8	,	,	PUNCT
ejpam-3650	159	9	t	t	PROPN
ejpam-3650	159	10	,	,	PUNCT
ejpam-3650	159	11	u+δu	u+δu	PROPN
ejpam-3650	159	12	)	)	PUNCT
ejpam-3650	159	13	∂u	∂u	PROPN
ejpam-3650	159	14	δψ	δψ	NOUN
ejpam-3650	159	15	=	=	NOUN
ejpam-3650	159	16	−ψδv+	−ψδv+	NOUN
ejpam-3650	159	17	+	+	CCONJ
ejpam-3650	159	18	[	[	PUNCT
ejpam-3650	159	19	∂f(x	∂f(x	PROPN
ejpam-3650	159	20	,	,	PUNCT
ejpam-3650	159	21	t	t	PROPN
ejpam-3650	159	22	,	,	PUNCT
ejpam-3650	159	23	u+δu	u+δu	PROPN
ejpam-3650	159	24	)	)	PUNCT
ejpam-3650	159	25	∂u	∂u	PROPN
ejpam-3650	160	1	−	−	PROPN
ejpam-3650	160	2	∂f(x	∂f(x	PROPN
ejpam-3650	160	3	,	,	PUNCT
ejpam-3650	160	4	t	t	PROPN
ejpam-3650	160	5	,	,	PUNCT
ejpam-3650	160	6	u	u	NOUN
ejpam-3650	160	7	)	)	PUNCT
ejpam-3650	160	8	∂u	∂u	PROPN
ejpam-3650	160	9	]	]	PUNCT
ejpam-3650	160	10	ψ	ψ	X
ejpam-3650	160	11	−k(x	−k(x	PROPN
ejpam-3650	160	12	,	,	PUNCT
ejpam-3650	160	13	t	t	PROPN
ejpam-3650	160	14	)	)	PUNCT
ejpam-3650	160	15	t∫	t∫	PROPN
ejpam-3650	160	16	0	0	NUM
ejpam-3650	160	17	kδudt	kδudt	PROPN
ejpam-3650	160	18	,	,	PUNCT
ejpam-3650	160	19	(	(	PUNCT
ejpam-3650	160	20	x	x	NOUN
ejpam-3650	160	21	,	,	PUNCT
ejpam-3650	160	22	t	t	PROPN
ejpam-3650	160	23	)	)	PUNCT
ejpam-3650	160	24	∈	∈	PROPN
ejpam-3650	160	25	q	q	NOUN
ejpam-3650	160	26	,	,	PUNCT
ejpam-3650	160	27	(	(	PUNCT
ejpam-3650	160	28	25	25	NUM
ejpam-3650	160	29	)	)	PUNCT
ejpam-3650	160	30	references	reference	NOUN
ejpam-3650	160	31	321	321	NUM
ejpam-3650	160	32	δψ	δψ	NOUN
ejpam-3650	160	33	=	=	SYM
ejpam-3650	160	34	0	0	NUM
ejpam-3650	160	35	,	,	PUNCT
ejpam-3650	160	36	(	(	PUNCT
ejpam-3650	160	37	x	x	NOUN
ejpam-3650	160	38	,	,	PUNCT
ejpam-3650	160	39	t	t	PROPN
ejpam-3650	160	40	)	)	PUNCT
ejpam-3650	160	41	∈	∈	PROPN
ejpam-3650	160	42	s	s	PROPN
ejpam-3650	160	43	,	,	PUNCT
ejpam-3650	160	44	δψ|t	δψ|t	PROPN
ejpam-3650	160	45	=	=	NOUN
ejpam-3650	160	46	t	t	NOUN
ejpam-3650	160	47	=	=	SYM
ejpam-3650	160	48	0	0	NUM
ejpam-3650	160	49	,	,	PUNCT
ejpam-3650	160	50	∂δψ	∂δψ	PROPN
ejpam-3650	160	51	∂t	∂t	PROPN
ejpam-3650	160	52	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3650	160	53	t	t	PROPN
ejpam-3650	160	54	=	=	PROPN
ejpam-3650	160	55	t	t	NOUN
ejpam-3650	160	56	=	=	SYM
ejpam-3650	160	57	0	0	NUM
ejpam-3650	160	58	,	,	PUNCT
ejpam-3650	160	59	x	x	X
ejpam-3650	160	60	∈	∈	PROPN
ejpam-3650	160	61	ω	ω	PROPN
ejpam-3650	160	62	.	.	PUNCT
ejpam-3650	161	1	(	(	PUNCT
ejpam-3650	161	2	26	26	NUM
ejpam-3650	161	3	)	)	PUNCT
ejpam-3650	161	4	using	use	VERB
ejpam-3650	161	5	the	the	DET
ejpam-3650	161	6	results	result	NOUN
ejpam-3650	161	7	of	of	ADP
ejpam-3650	161	8	[	[	X
ejpam-3650	161	9	[	[	X
ejpam-3650	161	10	13	13	NUM
ejpam-3650	161	11	]	]	PUNCT
ejpam-3650	161	12	,	,	PUNCT
ejpam-3650	161	13	p.	p.	NOUN
ejpam-3650	161	14	209	209	NUM
ejpam-3650	161	15	-	-	SYM
ejpam-3650	161	16	215	215	NUM
ejpam-3650	161	17	]	]	PUNCT
ejpam-3650	161	18	,	,	PUNCT
ejpam-3650	161	19	it	it	PRON
ejpam-3650	161	20	can	can	AUX
ejpam-3650	161	21	be	be	AUX
ejpam-3650	161	22	shown	show	VERB
ejpam-3650	161	23	that	that	SCONJ
ejpam-3650	161	24	the	the	DET
ejpam-3650	161	25	following	follow	VERB
ejpam-3650	161	26	estimation	estimation	NOUN
ejpam-3650	161	27	is	be	AUX
ejpam-3650	161	28	true	true	ADJ
ejpam-3650	161	29	for	for	ADP
ejpam-3650	161	30	the	the	DET
ejpam-3650	161	31	solution	solution	NOUN
ejpam-3650	161	32	of	of	ADP
ejpam-3650	161	33	the	the	DET
ejpam-3650	161	34	problem	problem	NOUN
ejpam-3650	161	35	(	(	PUNCT
ejpam-3650	161	36	25	25	NUM
ejpam-3650	161	37	)	)	PUNCT
ejpam-3650	161	38	,	,	PUNCT
ejpam-3650	161	39	(	(	PUNCT
ejpam-3650	161	40	26	26	NUM
ejpam-3650	161	41	)	)	PUNCT
ejpam-3650	161	42	‖δψ‖	‖δψ‖	PROPN
ejpam-3650	161	43	◦	◦	NOUN
ejpam-3650	161	44	w	w	PROPN
ejpam-3650	161	45	1	1	NUM
ejpam-3650	161	46	2	2	NUM
ejpam-3650	161	47	(	(	PUNCT
ejpam-3650	161	48	ω	ω	NOUN
ejpam-3650	161	49	)	)	PUNCT
ejpam-3650	162	1	+	+	CCONJ
ejpam-3650	162	2	∥∥∥∥∂δψ∂t	∥∥∥∥∂δψ∂t	ADJ
ejpam-3650	162	3	∥∥∥∥	∥∥∥∥	NUM
ejpam-3650	162	4	l2(ω	l2(ω	NOUN
ejpam-3650	162	5	)	)	PUNCT
ejpam-3650	162	6	≤	≤	NOUN
ejpam-3650	162	7	c	c	X
ejpam-3650	162	8	‖δv‖l∞(ω	‖δv‖l∞(ω	PROPN
ejpam-3650	162	9	)	)	PUNCT
ejpam-3650	162	10	,	,	PUNCT
ejpam-3650	162	11	t	t	PROPN
ejpam-3650	162	12	∈	∈	PROPN
ejpam-3650	163	1	[	[	X
ejpam-3650	163	2	0	0	NUM
ejpam-3650	163	3	,	,	PUNCT
ejpam-3650	163	4	t	t	X
ejpam-3650	163	5	]	]	PUNCT
ejpam-3650	163	6	.	.	PUNCT
ejpam-3650	164	1	(	(	PUNCT
ejpam-3650	164	2	27	27	NUM
ejpam-3650	164	3	)	)	PUNCT
ejpam-3650	164	4	in	in	ADP
ejpam-3650	164	5	addition	addition	NOUN
ejpam-3650	164	6	,	,	PUNCT
ejpam-3650	164	7	using	use	VERB
ejpam-3650	164	8	(	(	PUNCT
ejpam-3650	164	9	18	18	NUM
ejpam-3650	164	10	)	)	PUNCT
ejpam-3650	164	11	we	we	PRON
ejpam-3650	164	12	obtain	obtain	VERB
ejpam-3650	164	13	‖j	‖j	NOUN
ejpam-3650	164	14	′α(v	′α(v	PROPN
ejpam-3650	165	1	+	+	CCONJ
ejpam-3650	165	2	δv)−	δv)−	ADJ
ejpam-3650	165	3	j	j	PROPN
ejpam-3650	165	4	′α(v)‖	′α(v)‖	X
ejpam-3650	165	5	(	(	PUNCT
ejpam-3650	165	6	l∞(ω))∗	l∞(ω))∗	PROPN
ejpam-3650	165	7	≤	≤	PROPN
ejpam-3650	166	1	c	c	X
ejpam-3650	166	2	[	[	PUNCT
ejpam-3650	166	3	‖δv‖	‖δv‖	NOUN
ejpam-3650	166	4	l∞(ω	l∞(ω	ADV
ejpam-3650	166	5	)	)	PUNCT
ejpam-3650	166	6	+	+	CCONJ
ejpam-3650	166	7	‖u‖	‖u‖	PROPN
ejpam-3650	166	8	l2(q	l2(q	PROPN
ejpam-3650	166	9	)	)	PUNCT
ejpam-3650	166	10	‖δψ‖	‖δψ‖	PROPN
ejpam-3650	166	11	l2(q	l2(q	PROPN
ejpam-3650	166	12	)	)	PUNCT
ejpam-3650	167	1	+	+	CCONJ
ejpam-3650	168	1	+	+	CCONJ
ejpam-3650	168	2	‖ψ‖	‖ψ‖	PROPN
ejpam-3650	168	3	l2(q	l2(q	PROPN
ejpam-3650	168	4	)	)	PUNCT
ejpam-3650	168	5	‖δu‖	‖δu‖	X
ejpam-3650	168	6	l2(q	l2(q	NOUN
ejpam-3650	168	7	)	)	PUNCT
ejpam-3650	168	8	+	+	CCONJ
ejpam-3650	168	9	‖δu‖	‖δu‖	ADJ
ejpam-3650	168	10	l2(q	l2(q	PROPN
ejpam-3650	168	11	)	)	PUNCT
ejpam-3650	168	12	‖δψ‖	‖δψ‖	PROPN
ejpam-3650	168	13	l2(q	l2(q	PROPN
ejpam-3650	168	14	)	)	PUNCT
ejpam-3650	168	15	]	]	PUNCT
ejpam-3650	168	16	.	.	PUNCT
ejpam-3650	169	1	by	by	ADP
ejpam-3650	169	2	virtue	virtue	NOUN
ejpam-3650	169	3	of	of	ADP
ejpam-3650	169	4	(	(	PUNCT
ejpam-3650	169	5	22	22	NUM
ejpam-3650	169	6	)	)	PUNCT
ejpam-3650	169	7	,	,	PUNCT
ejpam-3650	169	8	(	(	PUNCT
ejpam-3650	169	9	27	27	NUM
ejpam-3650	169	10	)	)	PUNCT
ejpam-3650	169	11	,	,	PUNCT
ejpam-3650	169	12	the	the	DET
ejpam-3650	169	13	right	right	ADJ
ejpam-3650	169	14	-	-	PUNCT
ejpam-3650	169	15	hand	hand	NOUN
ejpam-3650	169	16	side	side	NOUN
ejpam-3650	169	17	of	of	ADP
ejpam-3650	169	18	this	this	DET
ejpam-3650	169	19	inequality	inequality	NOUN
ejpam-3650	169	20	tends	tend	VERB
ejpam-3650	169	21	to	to	ADP
ejpam-3650	169	22	zero	zero	NUM
ejpam-3650	169	23	as	as	ADP
ejpam-3650	169	24	‖δv‖	‖δv‖	PROPN
ejpam-3650	169	25	l∞(ω	l∞(ω	ADV
ejpam-3650	169	26	)	)	PUNCT
ejpam-3650	169	27	→	→	SYM
ejpam-3650	169	28	0	0	X
ejpam-3650	169	29	.	.	PUNCT
ejpam-3650	170	1	it	it	PRON
ejpam-3650	170	2	follows	follow	VERB
ejpam-3650	170	3	that	that	SCONJ
ejpam-3650	170	4	v	v	X
ejpam-3650	170	5	→	→	SYM
ejpam-3650	170	6	j∗α(v	j∗α(v	PROPN
ejpam-3650	170	7	)	)	PUNCT
ejpam-3650	170	8	is	be	AUX
ejpam-3650	170	9	a	a	DET
ejpam-3650	170	10	continuous	continuous	ADJ
ejpam-3650	170	11	map	map	NOUN
ejpam-3650	170	12	from	from	ADP
ejpam-3650	170	13	v	v	PRON
ejpam-3650	170	14	to	to	ADP
ejpam-3650	170	15	(	(	PUNCT
ejpam-3650	170	16	l∞(ω))∗.	l∞(ω))∗.	PROPN
ejpam-3650	170	17	theorem	theorem	NOUN
ejpam-3650	170	18	2	2	NUM
ejpam-3650	170	19	is	be	AUX
ejpam-3650	170	20	proved	prove	VERB
ejpam-3650	170	21	.	.	PUNCT
ejpam-3650	171	1	theorem	theorem	NOUN
ejpam-3650	171	2	3	3	X
ejpam-3650	171	3	.	.	PUNCT
ejpam-3650	172	1	let	let	VERB
ejpam-3650	172	2	the	the	DET
ejpam-3650	172	3	conditions	condition	NOUN
ejpam-3650	172	4	of	of	ADP
ejpam-3650	172	5	theorem	theorem	ADJ
ejpam-3650	172	6	2	2	NUM
ejpam-3650	172	7	be	be	AUX
ejpam-3650	172	8	satisfied	satisfied	ADJ
ejpam-3650	172	9	.	.	PUNCT
ejpam-3650	173	1	then	then	ADV
ejpam-3650	173	2	,	,	PUNCT
ejpam-3650	173	3	for	for	ADP
ejpam-3650	173	4	the	the	DET
ejpam-3650	173	5	optimality	optimality	NOUN
ejpam-3650	173	6	of	of	ADP
ejpam-3650	173	7	control	control	NOUN
ejpam-3650	173	8	v∗	v∗	NOUN
ejpam-3650	173	9	=	=	PUNCT
ejpam-3650	173	10	v∗(x	v∗(x	NOUN
ejpam-3650	173	11	)	)	PUNCT
ejpam-3650	173	12	∈	∈	NOUN
ejpam-3650	173	13	v	v	NOUN
ejpam-3650	173	14	in	in	ADP
ejpam-3650	173	15	problem	problem	NOUN
ejpam-3650	173	16	(	(	PUNCT
ejpam-3650	173	17	1	1	NUM
ejpam-3650	173	18	)	)	PUNCT
ejpam-3650	173	19	,	,	PUNCT
ejpam-3650	173	20	(	(	PUNCT
ejpam-3650	173	21	2	2	NUM
ejpam-3650	173	22	)	)	PUNCT
ejpam-3650	173	23	,	,	PUNCT
ejpam-3650	173	24	(	(	PUNCT
ejpam-3650	173	25	4	4	NUM
ejpam-3650	173	26	)	)	PUNCT
ejpam-3650	173	27	,	,	PUNCT
ejpam-3650	173	28	(	(	PUNCT
ejpam-3650	173	29	6	6	NUM
ejpam-3650	173	30	)	)	PUNCT
ejpam-3650	173	31	,	,	PUNCT
ejpam-3650	173	32	it	it	PRON
ejpam-3650	173	33	is	be	AUX
ejpam-3650	173	34	necessary	necessary	ADJ
ejpam-3650	173	35	that	that	SCONJ
ejpam-3650	173	36	the	the	DET
ejpam-3650	173	37	inequality	inequality	NOUN
ejpam-3650	173	38	∫	∫	PROPN
ejpam-3650	173	39	ω	ω	PROPN
ejpam-3650	173	40	αv∗(x	αv∗(x	PROPN
ejpam-3650	173	41	)	)	PUNCT
ejpam-3650	173	42	+	+	CCONJ
ejpam-3650	173	43	t∫	t∫	NOUN
ejpam-3650	173	44	0	0	NUM
ejpam-3650	173	45	u∗(x	u∗(x	PROPN
ejpam-3650	173	46	,	,	PUNCT
ejpam-3650	173	47	t)ψ∗(x	t)ψ∗(x	NOUN
ejpam-3650	173	48	,	,	PUNCT
ejpam-3650	173	49	t)dt	t)dt	PROPN
ejpam-3650	173	50	(v(x)−	(v(x)−	PROPN
ejpam-3650	173	51	v∗(x))dx	v∗(x))dx	VERB
ejpam-3650	173	52	≥	≥	PRON
ejpam-3650	173	53	0	0	NUM
ejpam-3650	173	54	(	(	PUNCT
ejpam-3650	173	55	28	28	NUM
ejpam-3650	173	56	)	)	PUNCT
ejpam-3650	173	57	holds	hold	VERB
ejpam-3650	173	58	for	for	ADP
ejpam-3650	173	59	any	any	DET
ejpam-3650	173	60	control	control	NOUN
ejpam-3650	173	61	v	v	NOUN
ejpam-3650	173	62	=	=	SYM
ejpam-3650	173	63	v(x	v(x	PROPN
ejpam-3650	173	64	)	)	PUNCT
ejpam-3650	173	65	∈	∈	PROPN
ejpam-3650	173	66	v	v	ADP
ejpam-3650	173	67	here	here	ADV
ejpam-3650	173	68	u∗(x	u∗(x	PROPN
ejpam-3650	173	69	,	,	PUNCT
ejpam-3650	173	70	t	t	PROPN
ejpam-3650	173	71	)	)	PUNCT
ejpam-3650	173	72	=	=	SYM
ejpam-3650	173	73	u(x	u(x	PROPN
ejpam-3650	173	74	,	,	PUNCT
ejpam-3650	173	75	t	t	PROPN
ejpam-3650	173	76	;	;	PUNCT
ejpam-3650	173	77	v∗	v∗	PROPN
ejpam-3650	173	78	)	)	PUNCT
ejpam-3650	173	79	,	,	PUNCT
ejpam-3650	173	80	ψ∗(x	ψ∗(x	PROPN
ejpam-3650	173	81	,	,	PUNCT
ejpam-3650	173	82	t	t	PROPN
ejpam-3650	173	83	)	)	PUNCT
ejpam-3650	173	84	=	=	SYM
ejpam-3650	173	85	ψ(x	ψ(x	PROPN
ejpam-3650	173	86	,	,	PUNCT
ejpam-3650	173	87	t	t	PROPN
ejpam-3650	173	88	;	;	PUNCT
ejpam-3650	173	89	v∗	v∗	PROPN
ejpam-3650	173	90	)	)	PUNCT
ejpam-3650	173	91	are	be	AUX
ejpam-3650	173	92	the	the	DET
ejpam-3650	173	93	solutions	solution	NOUN
ejpam-3650	173	94	of	of	ADP
ejpam-3650	173	95	problems	problem	NOUN
ejpam-3650	173	96	(	(	PUNCT
ejpam-3650	173	97	1	1	NUM
ejpam-3650	173	98	)	)	PUNCT
ejpam-3650	173	99	,	,	PUNCT
ejpam-3650	173	100	(	(	PUNCT
ejpam-3650	173	101	2	2	X
ejpam-3650	173	102	)	)	PUNCT
ejpam-3650	173	103	and	and	CCONJ
ejpam-3650	173	104	(	(	PUNCT
ejpam-3650	173	105	14	14	NUM
ejpam-3650	173	106	)	)	PUNCT
ejpam-3650	173	107	,	,	PUNCT
ejpam-3650	173	108	(	(	PUNCT
ejpam-3650	173	109	15	15	NUM
ejpam-3650	173	110	)	)	PUNCT
ejpam-3650	173	111	,	,	PUNCT
ejpam-3650	173	112	respectively	respectively	ADV
ejpam-3650	173	113	,	,	PUNCT
ejpam-3650	173	114	for	for	ADP
ejpam-3650	173	115	v∗	v∗	ADJ
ejpam-3650	173	116	=	=	PUNCT
ejpam-3650	173	117	v∗(x	v∗(x	NOUN
ejpam-3650	173	118	)	)	PUNCT
ejpam-3650	173	119	.	.	PUNCT
ejpam-3650	174	1	proof	proof	NOUN
ejpam-3650	174	2	.	.	PUNCT
ejpam-3650	175	1	the	the	DET
ejpam-3650	175	2	set	set	NOUN
ejpam-3650	175	3	v	v	NOUN
ejpam-3650	175	4	defined	define	VERB
ejpam-3650	175	5	by	by	ADP
ejpam-3650	175	6	relation	relation	NOUN
ejpam-3650	175	7	(	(	PUNCT
ejpam-3650	175	8	4	4	NUM
ejpam-3650	175	9	)	)	PUNCT
ejpam-3650	175	10	is	be	AUX
ejpam-3650	175	11	convex	convex	ADJ
ejpam-3650	175	12	in	in	ADP
ejpam-3650	175	13	l∞(ω	l∞(ω	ADJ
ejpam-3650	175	14	)	)	PUNCT
ejpam-3650	175	15	.	.	PUNCT
ejpam-3650	176	1	in	in	ADP
ejpam-3650	176	2	addition	addition	NOUN
ejpam-3650	176	3	,	,	PUNCT
ejpam-3650	176	4	by	by	ADP
ejpam-3650	176	5	theorem	theorem	NOUN
ejpam-3650	176	6	2	2	NUM
ejpam-3650	176	7	,	,	PUNCT
ejpam-3650	176	8	the	the	DET
ejpam-3650	176	9	functional	functional	ADJ
ejpam-3650	176	10	jα(v	jα(v	PUNCT
ejpam-3650	176	11	)	)	PUNCT
ejpam-3650	176	12	is	be	AUX
ejpam-3650	176	13	continuously	continuously	ADV
ejpam-3650	176	14	differentiable	differentiable	ADJ
ejpam-3650	176	15	by	by	ADP
ejpam-3650	176	16	frechet	frechet	NOUN
ejpam-3650	176	17	on	on	ADP
ejpam-3650	176	18	v	v	NOUN
ejpam-3650	176	19	and	and	CCONJ
ejpam-3650	176	20	its	its	PRON
ejpam-3650	176	21	differential	differential	NOUN
ejpam-3650	176	22	at	at	ADP
ejpam-3650	176	23	the	the	DET
ejpam-3650	176	24	point	point	NOUN
ejpam-3650	176	25	v	v	ADP
ejpam-3650	176	26	∈	∈	NOUN
ejpam-3650	176	27	v	v	NOUN
ejpam-3650	176	28	is	be	AUX
ejpam-3650	176	29	determined	determine	VERB
ejpam-3650	176	30	by	by	ADP
ejpam-3650	176	31	equality	equality	NOUN
ejpam-3650	176	32	(	(	PUNCT
ejpam-3650	176	33	18	18	NUM
ejpam-3650	176	34	)	)	PUNCT
ejpam-3650	176	35	.	.	PUNCT
ejpam-3650	177	1	then	then	ADV
ejpam-3650	177	2	,	,	PUNCT
ejpam-3650	177	3	by	by	ADP
ejpam-3650	177	4	virtue	virtue	NOUN
ejpam-3650	177	5	of	of	ADP
ejpam-3650	177	6	theorem	theorem	NOUN
ejpam-3650	177	7	5	5	NUM
ejpam-3650	177	8	of	of	ADP
ejpam-3650	177	9	[	[	X
ejpam-3650	177	10	[	[	X
ejpam-3650	177	11	17	17	NUM
ejpam-3650	177	12	]	]	PUNCT
ejpam-3650	177	13	,	,	PUNCT
ejpam-3650	177	14	p.	p.	NOUN
ejpam-3650	177	15	28	28	NUM
ejpam-3650	177	16	]	]	PUNCT
ejpam-3650	177	17	inequality	inequality	NOUN
ejpam-3650	177	18	〈	〈	PROPN
ejpam-3650	177	19	j	j	PROPN
ejpam-3650	177	20	′α(v∗	′α(v∗	PROPN
ejpam-3650	177	21	)	)	PUNCT
ejpam-3650	177	22	,	,	PUNCT
ejpam-3650	177	23	v	v	ADP
ejpam-3650	177	24	−	−	PROPN
ejpam-3650	177	25	v∗	v∗	PROPN
ejpam-3650	177	26	〉	〉	PROPN
ejpam-3650	177	27	≥	≥	NOUN
ejpam-3650	177	28	0∀v	0∀v	X
ejpam-3650	178	1	∈	∈	PROPN
ejpam-3650	178	2	v	v	NOUN
ejpam-3650	178	3	must	must	AUX
ejpam-3650	178	4	be	be	AUX
ejpam-3650	178	5	satisfied	satisfied	ADJ
ejpam-3650	178	6	on	on	ADP
ejpam-3650	178	7	the	the	DET
ejpam-3650	178	8	element	element	NOUN
ejpam-3650	178	9	v∗	v∗	PROPN
ejpam-3650	178	10	∈	∈	PROPN
ejpam-3650	178	11	v	v	NOUN
ejpam-3650	178	12	.	.	PUNCT
ejpam-3650	179	1	from	from	ADP
ejpam-3650	179	2	here	here	ADV
ejpam-3650	179	3	and	and	CCONJ
ejpam-3650	179	4	(	(	PUNCT
ejpam-3650	179	5	18	18	NUM
ejpam-3650	179	6	)	)	PUNCT
ejpam-3650	179	7	follows	follow	VERB
ejpam-3650	179	8	the	the	DET
ejpam-3650	179	9	validity	validity	NOUN
ejpam-3650	179	10	of	of	ADP
ejpam-3650	179	11	inequality	inequality	NOUN
ejpam-3650	179	12	(	(	PUNCT
ejpam-3650	179	13	28	28	NUM
ejpam-3650	179	14	)	)	PUNCT
ejpam-3650	179	15	.	.	PUNCT
ejpam-3650	180	1	theorem	theorem	NOUN
ejpam-3650	180	2	3	3	NUM
ejpam-3650	180	3	is	be	AUX
ejpam-3650	180	4	proved	prove	VERB
ejpam-3650	180	5	.	.	PUNCT
ejpam-3650	181	1	references	reference	NOUN
ejpam-3650	181	2	[	[	X
ejpam-3650	181	3	1	1	NUM
ejpam-3650	181	4	]	]	X
ejpam-3650	181	5	kabanikhin	kabanikhin	PROPN
ejpam-3650	181	6	s.i	s.i	PROPN
ejpam-3650	181	7	.	.	PROPN
ejpam-3650	181	8	inverse	inverse	PROPN
ejpam-3650	181	9	and	and	CCONJ
ejpam-3650	181	10	ill	ill	ADV
ejpam-3650	181	11	-	-	PUNCT
ejpam-3650	181	12	posed	pose	VERB
ejpam-3650	181	13	problems	problem	NOUN
ejpam-3650	181	14	.	.	PUNCT
ejpam-3650	182	1	novosibirsk	novosibirsk	PROPN
ejpam-3650	182	2	:	:	PUNCT
ejpam-3650	182	3	sib.nauch	sib.nauch	X
ejpam-3650	182	4	.	.	PUNCT
ejpam-3650	183	1	publishing	publish	VERB
ejpam-3650	183	2	house	house	PROPN
ejpam-3650	183	3	,	,	PUNCT
ejpam-3650	183	4	2009	2009	NUM
ejpam-3650	183	5	,	,	PUNCT
ejpam-3650	183	6	457	457	NUM
ejpam-3650	184	1	p.	p.	NOUN
ejpam-3650	184	2	[	[	X
ejpam-3650	184	3	2	2	X
ejpam-3650	184	4	]	]	X
ejpam-3650	184	5	kabanikhin	kabanikhin	PROPN
ejpam-3650	184	6	s.i	s.i	PROPN
ejpam-3650	184	7	.	.	PROPN
ejpam-3650	184	8	,	,	PUNCT
ejpam-3650	184	9	iskakov	iskakov	PROPN
ejpam-3650	184	10	k.t	k.t	PROPN
ejpam-3650	184	11	.	.	PROPN
ejpam-3650	184	12	optimization	optimization	NOUN
ejpam-3650	184	13	methods	method	NOUN
ejpam-3650	184	14	for	for	ADP
ejpam-3650	184	15	solving	solve	VERB
ejpam-3650	184	16	coefficient	coefficient	ADJ
ejpam-3650	184	17	inverse	inverse	NOUN
ejpam-3650	184	18	problems	problem	NOUN
ejpam-3650	184	19	.	.	PUNCT
ejpam-3650	185	1	nsu	nsu	PROPN
ejpam-3650	185	2	,	,	PUNCT
ejpam-3650	185	3	novosibirsk	novosibirsk	PROPN
ejpam-3650	185	4	,	,	PUNCT
ejpam-3650	185	5	2001	2001	NUM
ejpam-3650	185	6	,	,	PUNCT
ejpam-3650	185	7	316	316	NUM
ejpam-3650	185	8	p.	p.	NOUN
ejpam-3650	186	1	[	[	X
ejpam-3650	186	2	3	3	X
ejpam-3650	186	3	]	]	X
ejpam-3650	186	4	kabanikhin	kabanikhin	PROPN
ejpam-3650	186	5	s.i	s.i	PROPN
ejpam-3650	186	6	.	.	PROPN
ejpam-3650	186	7	,	,	PUNCT
ejpam-3650	186	8	shishlenin	shishlenin	PROPN
ejpam-3650	186	9	m.a	m.a	PROPN
ejpam-3650	186	10	.	.	PROPN
ejpam-3650	186	11	,	,	PUNCT
ejpam-3650	186	12	krivorotko	krivorotko	PROPN
ejpam-3650	186	13	o.i	o.i	PROPN
ejpam-3650	186	14	.	.	PROPN
ejpam-3650	186	15	optimization	optimization	NOUN
ejpam-3650	186	16	methods	method	NOUN
ejpam-3650	186	17	for	for	ADP
ejpam-3650	186	18	solving	solve	VERB
ejpam-3650	186	19	the	the	DET
ejpam-3650	186	20	inverse	inverse	NOUN
ejpam-3650	186	21	problem	problem	NOUN
ejpam-3650	186	22	of	of	ADP
ejpam-3650	186	23	thermoacoustics	thermoacoustic	NOUN
ejpam-3650	186	24	//	//	SYM
ejpam-3650	186	25	journal	journal	PROPN
ejpam-3650	186	26	”	"	PUNCT
ejpam-3650	186	27	siberian	siberian	ADJ
ejpam-3650	186	28	electron	electron	PROPN
ejpam-3650	186	29	mathematical	mathematical	PROPN
ejpam-3650	186	30	izvestiya	izvestiya	PROPN
ejpam-3650	186	31	”	"	PUNCT
ejpam-3650	186	32	2011	2011	NUM
ejpam-3650	186	33	,	,	PUNCT
ejpam-3650	186	34	pp	pp	ADP
ejpam-3650	186	35	263	263	NUM
ejpam-3650	186	36	-	-	SYM
ejpam-3650	186	37	292	292	NUM
ejpam-3650	186	38	.	.	PUNCT
ejpam-3650	187	1	references	reference	NOUN
ejpam-3650	187	2	322	322	NUM
ejpam-3650	187	3	[	[	X
ejpam-3650	187	4	4	4	NUM
ejpam-3650	187	5	]	]	X
ejpam-3650	187	6	kabanikhin	kabanikhin	PROPN
ejpam-3650	187	7	s.i	s.i	PROPN
ejpam-3650	187	8	.	.	PROPN
ejpam-3650	187	9	,	,	PUNCT
ejpam-3650	187	10	shislenin	shislenin	PROPN
ejpam-3650	187	11	m.a	m.a	PROPN
ejpam-3650	187	12	.	.	PROPN
ejpam-3650	187	13	on	on	ADP
ejpam-3650	187	14	the	the	DET
ejpam-3650	187	15	use	use	NOUN
ejpam-3650	187	16	of	of	ADP
ejpam-3650	187	17	a	a	DET
ejpam-3650	187	18	priori	priori	ADJ
ejpam-3650	187	19	information	information	NOUN
ejpam-3650	187	20	in	in	ADP
ejpam-3650	187	21	coefficient	coefficient	ADJ
ejpam-3650	187	22	inverse	inverse	NOUN
ejpam-3650	187	23	problems	problem	NOUN
ejpam-3650	187	24	for	for	ADP
ejpam-3650	187	25	hyperbolic	hyperbolic	ADJ
ejpam-3650	187	26	equations	equation	NOUN
ejpam-3650	187	27	//	//	NUM
ejpam-3650	187	28	transactions	transaction	NOUN
ejpam-3650	187	29	of	of	ADP
ejpam-3650	187	30	imm	imm	PROPN
ejpam-3650	187	31	ur	ur	NOUN
ejpam-3650	187	32	sras	sra	NOUN
ejpam-3650	187	33	.	.	PUNCT
ejpam-3650	188	1	2012	2012	NUM
ejpam-3650	188	2	,	,	PUNCT
ejpam-3650	188	3	volume	volume	NOUN
ejpam-3650	188	4	18	18	NUM
ejpam-3650	188	5	,	,	PUNCT
ejpam-3650	188	6	no	no	DET
ejpam-3650	188	7	1	1	NUM
ejpam-3650	188	8	,	,	PUNCT
ejpam-3650	188	9	pp	pp	ADV
ejpam-3650	188	10	147	147	NUM
ejpam-3650	188	11	-	-	SYM
ejpam-3650	188	12	164	164	NUM
ejpam-3650	188	13	.	.	PUNCT
ejpam-3650	189	1	[	[	X
ejpam-3650	189	2	5	5	NUM
ejpam-3650	189	3	]	]	PUNCT
ejpam-3650	189	4	alifanov	alifanov	NOUN
ejpam-3650	189	5	o.m.artykhin	o.m.artykhin	NOUN
ejpam-3650	189	6	y.a	y.a	PROPN
ejpam-3650	189	7	.	.	PROPN
ejpam-3650	189	8	,	,	PUNCT
ejpam-3650	189	9	rumyancev	rumyancev	PROPN
ejpam-3650	189	10	s.v	s.v	PROPN
ejpam-3650	189	11	.	.	PROPN
ejpam-3650	189	12	exterme	exterme	ADJ
ejpam-3650	189	13	methods	method	NOUN
ejpam-3650	189	14	for	for	ADP
ejpam-3650	189	15	solving	solve	VERB
ejpam-3650	189	16	incorrect	incorrect	ADJ
ejpam-3650	189	17	problems	problem	NOUN
ejpam-3650	189	18	.	.	PUNCT
ejpam-3650	190	1	m.	m.	NOUN
ejpam-3650	190	2	:	:	PUNCT
ejpam-3650	190	3	science	science	NOUN
ejpam-3650	190	4	,	,	PUNCT
ejpam-3650	190	5	1988,p.288	1988,p.288	NUM
ejpam-3650	190	6	.	.	PUNCT
ejpam-3650	191	1	[	[	X
ejpam-3650	191	2	6	6	NUM
ejpam-3650	191	3	]	]	PUNCT
ejpam-3650	191	4	ayda	ayda	PROPN
ejpam-3650	191	5	-	-	PUNCT
ejpam-3650	191	6	zadeh	zadeh	PROPN
ejpam-3650	191	7	k.	k.	PROPN
ejpam-3650	191	8	r.	r.	PROPN
ejpam-3650	191	9	,	,	PUNCT
ejpam-3650	191	10	rahimov	rahimov	PROPN
ejpam-3650	191	11	a.b	a.b	PROPN
ejpam-3650	191	12	.	.	PROPN
ejpam-3650	191	13	on	on	ADP
ejpam-3650	191	14	the	the	DET
ejpam-3650	191	15	solution	solution	NOUN
ejpam-3650	191	16	of	of	ADP
ejpam-3650	191	17	solution	solution	NOUN
ejpam-3650	191	18	of	of	ADP
ejpam-3650	191	19	one	one	NUM
ejpam-3650	191	20	coefficient	coefficient	NOUN
ejpam-3650	191	21	-	-	PUNCT
ejpam-3650	191	22	inverse	inverse	NOUN
ejpam-3650	191	23	problem	problem	NOUN
ejpam-3650	191	24	.	.	PUNCT
ejpam-3650	192	1	seberian	seberian	ADJ
ejpam-3650	192	2	journal	journal	PROPN
ejpam-3650	192	3	industrial	industrial	ADJ
ejpam-3650	192	4	mathematics	mathematic	NOUN
ejpam-3650	192	5	2013	2013	NUM
ejpam-3650	192	6	,	,	PUNCT
ejpam-3650	192	7	vol	vol	NOUN
ejpam-3650	192	8	xvi	xvi	NOUN
ejpam-3650	192	9	,	,	PUNCT
ejpam-3650	192	10	no	no	DET
ejpam-3650	192	11	2(54	2(54	NUM
ejpam-3650	192	12	)	)	PUNCT
ejpam-3650	192	13	.	.	PUNCT
ejpam-3650	193	1	[	[	X
ejpam-3650	193	2	7	7	X
ejpam-3650	193	3	]	]	X
ejpam-3650	193	4	tagiev	tagiev	PROPN
ejpam-3650	193	5	r.k	r.k	PROPN
ejpam-3650	193	6	.	.	PROPN
ejpam-3650	193	7	,	,	PUNCT
ejpam-3650	193	8	karimov	karimov	PROPN
ejpam-3650	193	9	r.a	r.a	PROPN
ejpam-3650	193	10	.	.	PROPN
ejpam-3650	193	11	on	on	ADP
ejpam-3650	193	12	the	the	DET
ejpam-3650	193	13	optimization	optimization	NOUN
ejpam-3650	193	14	statement	statement	NOUN
ejpam-3650	193	15	of	of	ADP
ejpam-3650	193	16	coefficient	coefficient	NOUN
ejpam-3650	193	17	-	-	PUNCT
ejpam-3650	193	18	inverse	inverse	ADJ
ejpam-3650	193	19	problem	problem	NOUN
ejpam-3650	193	20	with	with	ADP
ejpam-3650	193	21	additional	additional	ADJ
ejpam-3650	193	22	integral	integral	ADJ
ejpam-3650	193	23	condition	condition	NOUN
ejpam-3650	193	24	for	for	ADP
ejpam-3650	193	25	parabolic	parabolic	ADJ
ejpam-3650	193	26	equation	equation	NOUN
ejpam-3650	193	27	.	.	PUNCT
ejpam-3650	194	1	seberian	seberian	ADJ
ejpam-3650	194	2	journal	journal	PROPN
ejpam-3650	194	3	industrial	industrial	ADJ
ejpam-3650	194	4	mathematics	mathematic	NOUN
ejpam-3650	194	5	2013	2013	NUM
ejpam-3650	194	6	,	,	PUNCT
ejpam-3650	194	7	vol	vol	NOUN
ejpam-3650	194	8	xvi	xvi	NOUN
ejpam-3650	194	9	,	,	PUNCT
ejpam-3650	194	10	no	no	DET
ejpam-3650	194	11	2(54	2(54	NUM
ejpam-3650	194	12	)	)	PUNCT
ejpam-3650	194	13	.	.	PUNCT
ejpam-3650	195	1	[	[	X
ejpam-3650	195	2	8	8	NUM
ejpam-3650	195	3	]	]	X
ejpam-3650	195	4	guliyev	guliyev	NOUN
ejpam-3650	195	5	h.f	h.f	PROPN
ejpam-3650	195	6	.	.	PROPN
ejpam-3650	195	7	,	,	PUNCT
ejpam-3650	195	8	nasibzadeh	nasibzadeh	PROPN
ejpam-3650	195	9	v.n	v.n	PRON
ejpam-3650	195	10	.	.	PROPN
ejpam-3650	195	11	on	on	ADP
ejpam-3650	195	12	determining	determine	VERB
ejpam-3650	195	13	the	the	DET
ejpam-3650	195	14	coefficient	coefficient	NOUN
ejpam-3650	195	15	of	of	ADP
ejpam-3650	195	16	a	a	DET
ejpam-3650	195	17	multi	multi	ADJ
ejpam-3650	195	18	-	-	ADJ
ejpam-3650	195	19	dimensional	dimensional	ADJ
ejpam-3650	195	20	hyperbolic	hyperbolic	ADJ
ejpam-3650	195	21	equation	equation	NOUN
ejpam-3650	195	22	with	with	ADP
ejpam-3650	195	23	integral	integral	ADJ
ejpam-3650	195	24	overdetrmination	overdetrmination	NOUN
ejpam-3650	195	25	condition	condition	NOUN
ejpam-3650	195	26	.	.	PUNCT
ejpam-3650	196	1	applied	apply	VERB
ejpam-3650	196	2	mathematics	mathematic	NOUN
ejpam-3650	196	3	,	,	PUNCT
ejpam-3650	196	4	informatics	informatic	NOUN
ejpam-3650	196	5	and	and	CCONJ
ejpam-3650	196	6	mechanics	mechanic	NOUN
ejpam-3650	196	7	.	.	PUNCT
ejpam-3650	197	1	tibilisi	tibilisi	ADJ
ejpam-3650	197	2	university	university	PROPN
ejpam-3650	197	3	press	press	NOUN
ejpam-3650	197	4	,	,	PUNCT
ejpam-3650	197	5	tbilisi	tbilisi	PROPN
ejpam-3650	197	6	vol.22	vol.22	PROPN
ejpam-3650	197	7	,	,	PUNCT
ejpam-3650	197	8	no	no	DET
ejpam-3650	197	9	1	1	NUM
ejpam-3650	197	10	,	,	PUNCT
ejpam-3650	197	11	2017	2017	NUM
ejpam-3650	197	12	,	,	PUNCT
ejpam-3650	197	13	pp.2231	pp.2231	PROPN
ejpam-3650	197	14	.	.	PUNCT
ejpam-3650	198	1	[	[	X
ejpam-3650	198	2	9	9	NUM
ejpam-3650	198	3	]	]	X
ejpam-3650	198	4	guliyev	guliyev	NOUN
ejpam-3650	198	5	h.f	h.f	PROPN
ejpam-3650	198	6	.	.	PROPN
ejpam-3650	198	7	,	,	PUNCT
ejpam-3650	198	8	nasibzadeh	nasibzadeh	PROPN
ejpam-3650	198	9	v.n	v.n	PROPN
ejpam-3650	198	10	.	.	PROPN
ejpam-3650	198	11	reduction	reduction	NOUN
ejpam-3650	198	12	of	of	ADP
ejpam-3650	198	13	the	the	DET
ejpam-3650	198	14	inverse	inverse	NOUN
ejpam-3650	198	15	problem	problem	NOUN
ejpam-3650	198	16	of	of	ADP
ejpam-3650	198	17	acoustics	acoustic	NOUN
ejpam-3650	198	18	to	to	ADP
ejpam-3650	198	19	the	the	DET
ejpam-3650	198	20	optimal	optimal	ADJ
ejpam-3650	198	21	control	control	NOUN
ejpam-3650	198	22	problem	problem	NOUN
ejpam-3650	198	23	and	and	CCONJ
ejpam-3650	198	24	its	its	PRON
ejpam-3650	198	25	investigation	investigation	NOUN
ejpam-3650	198	26	.	.	PUNCT
ejpam-3650	199	1	news	news	NOUN
ejpam-3650	199	2	of	of	ADP
ejpam-3650	199	3	tomsk	tomsk	PROPN
ejpam-3650	199	4	state	state	PROPN
ejpam-3650	199	5	university	university	PROPN
ejpam-3650	199	6	,	,	PUNCT
ejpam-3650	199	7	mathematics	mathematic	NOUN
ejpam-3650	199	8	and	and	CCONJ
ejpam-3650	199	9	mechanics	mechanic	NOUN
ejpam-3650	199	10	,	,	PUNCT
ejpam-3650	199	11	2018	2018	NUM
ejpam-3650	199	12	,	,	PUNCT
ejpam-3650	199	13	no	no	INTJ
ejpam-3650	199	14	,	,	PUNCT
ejpam-3650	199	15	54	54	NUM
ejpam-3650	199	16	,	,	PUNCT
ejpam-3650	199	17	p.5	p.5	NOUN
ejpam-3650	199	18	-	-	X
ejpam-3650	199	19	16	16	NUM
ejpam-3650	199	20	.	.	PUNCT
ejpam-3650	200	1	[	[	X
ejpam-3650	200	2	10	10	NUM
ejpam-3650	200	3	]	]	PUNCT
ejpam-3650	200	4	ismailova	ismailova	PROPN
ejpam-3650	200	5	g.g	g.g	INTJ
ejpam-3650	200	6	.	.	PROPN
ejpam-3650	200	7	on	on	ADP
ejpam-3650	200	8	determining	determine	VERB
ejpam-3650	200	9	the	the	DET
ejpam-3650	200	10	coefficient	coefficient	NOUN
ejpam-3650	200	11	of	of	ADP
ejpam-3650	200	12	the	the	DET
ejpam-3650	200	13	lowest	low	ADJ
ejpam-3650	200	14	term	term	NOUN
ejpam-3650	200	15	of	of	ADP
ejpam-3650	200	16	a	a	DET
ejpam-3650	200	17	multidimensional	multidimensional	ADJ
ejpam-3650	200	18	second	second	ADJ
ejpam-3650	200	19	-	-	PUNCT
ejpam-3650	200	20	order	order	NOUN
ejpam-3650	200	21	hyperbolic	hyperbolic	ADJ
ejpam-3650	200	22	equation	equation	NOUN
ejpam-3650	200	23	.	.	PUNCT
ejpam-3650	201	1	problem	problem	NOUN
ejpam-3650	201	2	of	of	ADP
ejpam-3650	201	3	control	control	NOUN
ejpam-3650	201	4	and	and	CCONJ
ejpam-3650	201	5	computer	computer	NOUN
ejpam-3650	201	6	science	science	NOUN
ejpam-3650	201	7	,	,	PUNCT
ejpam-3650	201	8	2019	2019	NUM
ejpam-3650	201	9	,	,	PUNCT
ejpam-3650	201	10	no	no	DET
ejpam-3650	201	11	1	1	NUM
ejpam-3650	201	12	,	,	PUNCT
ejpam-3650	201	13	p.13	p.13	AUX
ejpam-3650	201	14	-	-	X
ejpam-3650	201	15	19	19	NUM
ejpam-3650	201	16	.	.	PUNCT
ejpam-3650	202	1	[	[	X
ejpam-3650	202	2	11	11	NUM
ejpam-3650	202	3	]	]	PUNCT
ejpam-3650	202	4	safanova	safanova	PROPN
ejpam-3650	202	5	z.	z.	PROPN
ejpam-3650	202	6	r.	r.	PROPN
ejpam-3650	202	7	on	on	ADP
ejpam-3650	202	8	determining	determine	VERB
ejpam-3650	202	9	the	the	DET
ejpam-3650	202	10	coefficient	coefficient	NOUN
ejpam-3650	202	11	of	of	ADP
ejpam-3650	202	12	the	the	DET
ejpam-3650	202	13	derivative	derivative	NOUN
ejpam-3650	202	14	in	in	ADP
ejpam-3650	202	15	the	the	DET
ejpam-3650	202	16	vibration	vibration	NOUN
ejpam-3650	202	17	equation	equation	NOUN
ejpam-3650	202	18	of	of	ADP
ejpam-3650	202	19	a	a	DET
ejpam-3650	202	20	string	string	NOUN
ejpam-3650	202	21	with	with	ADP
ejpam-3650	202	22	a	a	DET
ejpam-3650	202	23	continuity	continuity	NOUN
ejpam-3650	202	24	problem	problem	NOUN
ejpam-3650	202	25	of	of	ADP
ejpam-3650	202	26	control	control	NOUN
ejpam-3650	202	27	and	and	CCONJ
ejpam-3650	202	28	computer	computer	NOUN
ejpam-3650	202	29	science	science	NOUN
ejpam-3650	202	30	,	,	PUNCT
ejpam-3650	202	31	2019	2019	NUM
ejpam-3650	202	32	,	,	PUNCT
ejpam-3650	202	33	no	no	DET
ejpam-3650	202	34	1	1	NUM
ejpam-3650	202	35	,	,	PUNCT
ejpam-3650	202	36	p.93	p.93	PROPN
ejpam-3650	202	37	-	-	PROPN
ejpam-3650	202	38	99	99	NUM
ejpam-3650	202	39	.	.	PUNCT
ejpam-3650	203	1	[	[	X
ejpam-3650	203	2	12	12	NUM
ejpam-3650	203	3	]	]	PUNCT
ejpam-3650	203	4	serovaysky	serovaysky	NOUN
ejpam-3650	203	5	s.ya	s.ya	PROPN
ejpam-3650	203	6	.	.	PUNCT
ejpam-3650	203	7	optimization	optimization	NOUN
ejpam-3650	203	8	and	and	CCONJ
ejpam-3650	203	9	differentiation	differentiation	NOUN
ejpam-3650	203	10	vol	vol	NOUN
ejpam-3650	203	11	.	.	PROPN
ejpam-3650	203	12	2	2	NUM
ejpam-3650	203	13	almaty	almaty	PROPN
ejpam-3650	203	14	,	,	PUNCT
ejpam-3650	203	15	kazak	kazak	PROPN
ejpam-3650	203	16	university	university	PROPN
ejpam-3650	203	17	,	,	PUNCT
ejpam-3650	203	18	2009	2009	NUM
ejpam-3650	203	19	,	,	PUNCT
ejpam-3650	203	20	p.329	p.329	NOUN
ejpam-3650	203	21	.	.	PUNCT
ejpam-3650	204	1	[	[	X
ejpam-3650	204	2	13	13	NUM
ejpam-3650	204	3	]	]	PUNCT
ejpam-3650	204	4	ladyzhenskaya	ladyzhenskaya	PROPN
ejpam-3650	204	5	o.a	o.a	PROPN
ejpam-3650	204	6	.	.	PROPN
ejpam-3650	204	7	boundary	boundary	ADJ
ejpam-3650	204	8	value	value	NOUN
ejpam-3650	204	9	problems	problem	NOUN
ejpam-3650	204	10	of	of	ADP
ejpam-3650	204	11	mathematical	mathematical	ADJ
ejpam-3650	204	12	physics	physics	NOUN
ejpam-3650	204	13	m.	m.	NOUN
ejpam-3650	204	14	:	:	PUNCT
ejpam-3650	204	15	nauka	nauka	PROPN
ejpam-3650	204	16	,	,	PUNCT
ejpam-3650	204	17	1973	1973	NUM
ejpam-3650	204	18	,	,	PUNCT
ejpam-3650	204	19	408	408	NUM
ejpam-3650	205	1	p.	p.	NOUN
ejpam-3650	206	1	[	[	X
ejpam-3650	206	2	14	14	NUM
ejpam-3650	206	3	]	]	PUNCT
ejpam-3650	206	4	lions	lion	NOUN
ejpam-3650	206	5	j.a	j.a	PROPN
ejpam-3650	206	6	.	.	PUNCT
ejpam-3650	207	1	some	some	DET
ejpam-3650	207	2	methods	method	NOUN
ejpam-3650	207	3	for	for	ADP
ejpam-3650	207	4	solving	solve	VERB
ejpam-3650	207	5	nonlinear	nonlinear	ADJ
ejpam-3650	207	6	boundary	boundary	ADJ
ejpam-3650	207	7	value	value	NOUN
ejpam-3650	207	8	problems	problem	NOUN
ejpam-3650	207	9	.	.	PUNCT
ejpam-3650	208	1	moscow	moscow	PROPN
ejpam-3650	208	2	:	:	PUNCT
ejpam-3650	208	3	mir	mir	PROPN
ejpam-3650	208	4	,	,	PUNCT
ejpam-3650	208	5	1972	1972	NUM
ejpam-3650	208	6	,	,	PUNCT
ejpam-3650	208	7	588	588	NUM
ejpam-3650	208	8	p.	p.	NOUN
ejpam-3650	209	1	[	[	X
ejpam-3650	209	2	15	15	NUM
ejpam-3650	209	3	]	]	X
ejpam-3650	209	4	sobolev	sobolev	PROPN
ejpam-3650	209	5	s.l	s.l	PROPN
ejpam-3650	209	6	.	.	PUNCT
ejpam-3650	210	1	some	some	DET
ejpam-3650	210	2	applications	application	NOUN
ejpam-3650	210	3	of	of	ADP
ejpam-3650	210	4	functional	functional	ADJ
ejpam-3650	210	5	analysis	analysis	NOUN
ejpam-3650	210	6	in	in	ADP
ejpam-3650	210	7	mathematical	mathematical	ADJ
ejpam-3650	210	8	physics	physics	NOUN
ejpam-3650	210	9	.	.	PUNCT
ejpam-3650	211	1	m.	m.	NOUN
ejpam-3650	211	2	:	:	PUNCT
ejpam-3650	211	3	nauka	nauka	PROPN
ejpam-3650	211	4	,	,	PUNCT
ejpam-3650	211	5	1988	1988	NUM
ejpam-3650	211	6	,	,	PUNCT
ejpam-3650	211	7	334	334	NUM
ejpam-3650	212	1	p.	p.	NOUN
ejpam-3650	213	1	[	[	X
ejpam-3650	213	2	16	16	NUM
ejpam-3650	213	3	]	]	X
ejpam-3650	213	4	vasilev	vasilev	PROPN
ejpam-3650	213	5	f.p	f.p	PROPN
ejpam-3650	213	6	.	.	PROPN
ejpam-3650	213	7	methods	method	NOUN
ejpam-3650	213	8	for	for	ADP
ejpam-3650	213	9	solving	solve	VERB
ejpam-3650	213	10	extremal	extremal	ADJ
ejpam-3650	213	11	problems	problem	NOUN
ejpam-3650	213	12	.	.	PUNCT
ejpam-3650	214	1	m.	m.	NOUN
ejpam-3650	214	2	:	:	PUNCT
ejpam-3650	214	3	nauka	nauka	PROPN
ejpam-3650	214	4	,	,	PUNCT
ejpam-3650	214	5	1981	1981	NUM
ejpam-3650	214	6	,	,	PUNCT
ejpam-3650	214	7	400	400	NUM
ejpam-3650	215	1	p.	p.	NOUN
ejpam-3650	216	1	[	[	X
ejpam-3650	216	2	17	17	NUM
ejpam-3650	216	3	]	]	X
ejpam-3650	217	1	zabreyko	zabreyko	PROPN
ejpam-3650	217	2	p.p	p.p	PROPN
ejpam-3650	217	3	.	.	PROPN
ejpam-3650	217	4	,	,	PUNCT
ejpam-3650	217	5	koshelov	koshelov	PROPN
ejpam-3650	217	6	a.i	a.i	PROPN
ejpam-3650	217	7	.	.	PROPN
ejpam-3650	217	8	,	,	PUNCT
ejpam-3650	217	9	krasnosel’skii	krasnosel’skii	PROPN
ejpam-3650	217	10	m.a	m.a	AUX
ejpam-3650	217	11	.	.	PROPN
ejpam-3650	217	12	,	,	PUNCT
ejpam-3650	217	13	mikhin	mikhin	PROPN
ejpam-3650	217	14	s.g	s.g	PROPN
ejpam-3650	217	15	.	.	PROPN
ejpam-3650	217	16	,	,	PUNCT
ejpam-3650	217	17	rakovshik	rakovshik	PROPN
ejpam-3650	217	18	l.s	l.s	PROPN
ejpam-3650	217	19	.	.	PROPN
ejpam-3650	217	20	stesenko	stesenko	PROPN
ejpam-3650	217	21	b.ya	b.ya	PROPN
ejpam-3650	217	22	.	.	PUNCT
ejpam-3650	218	1	integral	integral	ADJ
ejpam-3650	218	2	equations	equation	NOUN
ejpam-3650	218	3	,	,	PUNCT
ejpam-3650	218	4	reference	reference	NOUN
ejpam-3650	218	5	mathematical	mathematical	ADJ
ejpam-3650	218	6	library	library	NOUN
ejpam-3650	218	7	.	.	PUNCT
ejpam-3650	219	1	moscow	moscow	PROPN
ejpam-3650	219	2	:	:	PUNCT
ejpam-3650	219	3	nauka	nauka	PROPN
ejpam-3650	219	4	,	,	PUNCT
ejpam-3650	219	5	1968	1968	NUM
ejpam-3650	219	6	,	,	PUNCT
ejpam-3650	219	7	448	448	NUM
ejpam-3650	219	8	p.	p.	NOUN