id	sid	tid	token	lemma	pos
iajs-2557	1	1	ibn	ibn	PROPN
iajs-2557	1	2	al	al	PROPN
iajs-2557	1	3	-	-	PUNCT
iajs-2557	1	4	haitham	haitham	PROPN
iajs-2557	1	5	jour	jour	X
iajs-2557	1	6	.	.	PROPN
iajs-2557	1	7	for	for	ADP
iajs-2557	1	8	pure	pure	ADJ
iajs-2557	1	9	&	&	CCONJ
iajs-2557	1	10	appl	appl	PROPN
iajs-2557	1	11	.	.	PUNCT
iajs-2557	2	1	sci	sci	PROPN
iajs-2557	2	2	.	.	PROPN
iajs-2557	3	1	34	34	NUM
iajs-2557	3	2	(	(	PUNCT
iajs-2557	3	3	1	1	NUM
iajs-2557	3	4	)	)	PUNCT
iajs-2557	3	5	2021	2021	NUM
iajs-2557	3	6	60	60	NUM
iajs-2557	3	7	the	the	DET
iajs-2557	3	8	necessary	necessary	ADJ
iajs-2557	3	9	condition	condition	NOUN
iajs-2557	3	10	for	for	ADP
iajs-2557	3	11	optimal	optimal	ADJ
iajs-2557	3	12	boundary	boundary	ADJ
iajs-2557	3	13	control	control	NOUN
iajs-2557	3	14	problems	problem	NOUN
iajs-2557	3	15	for	for	ADP
iajs-2557	3	16	triple	triple	ADJ
iajs-2557	3	17	elliptic	elliptic	ADJ
iajs-2557	3	18	partial	partial	ADJ
iajs-2557	3	19	differential	differential	NOUN
iajs-2557	3	20	equations	equation	NOUN
iajs-2557	3	21	department	department	PROPN
iajs-2557	3	22	of	of	ADP
iajs-2557	3	23	mathematics	mathematics	PROPN
iajs-2557	3	24	,	,	PUNCT
iajs-2557	3	25	college	college	NOUN
iajs-2557	3	26	of	of	ADP
iajs-2557	3	27	science	science	NOUN
iajs-2557	3	28	,	,	PUNCT
iajs-2557	3	29	mustansiriyah	mustansiriyah	NOUN
iajs-2557	3	30	university	university	NOUN
iajs-2557	3	31	,	,	PUNCT
iajs-2557	3	32	baghdad	baghdad	PROPN
iajs-2557	3	33	,	,	PUNCT
iajs-2557	3	34	iraq	iraq	PROPN
iajs-2557	3	35	.	.	PUNCT
iajs-2557	4	1	hawasy20@yahoo.com	hawasy20@yahoo.com	X
iajs-2557	5	1	jhawassy17@mustansiriyah.edu.iq	jhawassy17@mustansiriyah.edu.iq	ADJ
iajs-2557	5	2	abstract	abstract	NOUN
iajs-2557	5	3	in	in	ADP
iajs-2557	5	4	this	this	DET
iajs-2557	5	5	work	work	NOUN
iajs-2557	5	6	,	,	PUNCT
iajs-2557	5	7	we	we	PRON
iajs-2557	5	8	prove	prove	VERB
iajs-2557	5	9	that	that	SCONJ
iajs-2557	5	10	the	the	DET
iajs-2557	5	11	triple	triple	ADJ
iajs-2557	5	12	linear	linear	ADJ
iajs-2557	5	13	partial	partial	ADJ
iajs-2557	5	14	differential	differential	NOUN
iajs-2557	5	15	equations	equation	NOUN
iajs-2557	5	16	(	(	PUNCT
iajs-2557	5	17	pdes	pde	NOUN
iajs-2557	5	18	)	)	PUNCT
iajs-2557	5	19	of	of	ADP
iajs-2557	5	20	the	the	DET
iajs-2557	5	21	elliptic	elliptic	ADJ
iajs-2557	5	22	type	type	NOUN
iajs-2557	5	23	(	(	PUNCT
iajs-2557	5	24	tlepdes	tlepdes	PROPN
iajs-2557	5	25	)	)	PUNCT
iajs-2557	5	26	with	with	ADP
iajs-2557	5	27	a	a	DET
iajs-2557	5	28	given	give	VERB
iajs-2557	5	29	classical	classical	ADJ
iajs-2557	5	30	continuous	continuous	ADJ
iajs-2557	5	31	boundary	boundary	ADJ
iajs-2557	5	32	control	control	NOUN
iajs-2557	5	33	vector	vector	NOUN
iajs-2557	5	34	(	(	PUNCT
iajs-2557	5	35	ccbcvr	ccbcvr	NOUN
iajs-2557	5	36	)	)	PUNCT
iajs-2557	5	37	has	have	VERB
iajs-2557	5	38	a	a	DET
iajs-2557	5	39	unique	unique	ADJ
iajs-2557	5	40	"	"	PUNCT
iajs-2557	5	41	state	state	NOUN
iajs-2557	5	42	"	"	PUNCT
iajs-2557	5	43	solution	solution	NOUN
iajs-2557	5	44	vector	vector	NOUN
iajs-2557	5	45	(	(	PUNCT
iajs-2557	5	46	ssv	ssv	NOUN
iajs-2557	5	47	)	)	PUNCT
iajs-2557	5	48	by	by	ADP
iajs-2557	5	49	utilizing	utilize	VERB
iajs-2557	5	50	the	the	DET
iajs-2557	5	51	galerkin	galerkin	NOUN
iajs-2557	5	52	's	's	PART
iajs-2557	5	53	method	method	NOUN
iajs-2557	5	54	(	(	PUNCT
iajs-2557	5	55	gme	gme	NOUN
iajs-2557	5	56	)	)	PUNCT
iajs-2557	5	57	.	.	PUNCT
iajs-2557	6	1	also	also	ADV
iajs-2557	6	2	,	,	PUNCT
iajs-2557	6	3	we	we	PRON
iajs-2557	6	4	prove	prove	VERB
iajs-2557	6	5	the	the	DET
iajs-2557	6	6	existence	existence	NOUN
iajs-2557	6	7	of	of	ADP
iajs-2557	6	8	a	a	DET
iajs-2557	6	9	classical	classical	ADJ
iajs-2557	6	10	continuous	continuous	ADJ
iajs-2557	6	11	boundary	boundary	ADJ
iajs-2557	6	12	optimal	optimal	ADJ
iajs-2557	6	13	control	control	NOUN
iajs-2557	6	14	vector	vector	NOUN
iajs-2557	6	15	(	(	PUNCT
iajs-2557	6	16	ccbocvr	ccbocvr	PROPN
iajs-2557	6	17	)	)	PUNCT
iajs-2557	6	18	ruled	rule	VERB
iajs-2557	6	19	by	by	ADP
iajs-2557	6	20	the	the	DET
iajs-2557	6	21	tlepdes	tlepde	NOUN
iajs-2557	6	22	.	.	PUNCT
iajs-2557	7	1	we	we	PRON
iajs-2557	7	2	study	study	VERB
iajs-2557	7	3	the	the	DET
iajs-2557	7	4	existence	existence	NOUN
iajs-2557	7	5	solution	solution	NOUN
iajs-2557	7	6	for	for	ADP
iajs-2557	7	7	the	the	DET
iajs-2557	7	8	triple	triple	ADJ
iajs-2557	7	9	adjoint	adjoint	PROPN
iajs-2557	7	10	equations	equation	NOUN
iajs-2557	7	11	(	(	PUNCT
iajs-2557	7	12	tajes	taje	NOUN
iajs-2557	7	13	)	)	PUNCT
iajs-2557	7	14	related	relate	VERB
iajs-2557	7	15	with	with	ADP
iajs-2557	7	16	the	the	DET
iajs-2557	7	17	triple	triple	ADJ
iajs-2557	7	18	state	state	NOUN
iajs-2557	7	19	equations	equation	NOUN
iajs-2557	7	20	(	(	PUNCT
iajs-2557	7	21	tses	tse	NOUN
iajs-2557	7	22	)	)	PUNCT
iajs-2557	7	23	.	.	PUNCT
iajs-2557	8	1	the	the	DET
iajs-2557	8	2	fréchet	fréchet	ADJ
iajs-2557	8	3	derivative	derivative	ADJ
iajs-2557	8	4	(	(	PUNCT
iajs-2557	8	5	fde	fde	PROPN
iajs-2557	8	6	)	)	PUNCT
iajs-2557	8	7	for	for	ADP
iajs-2557	8	8	the	the	DET
iajs-2557	8	9	objective	objective	ADJ
iajs-2557	8	10	function	function	NOUN
iajs-2557	8	11	is	be	AUX
iajs-2557	8	12	derived	derive	VERB
iajs-2557	8	13	.	.	PUNCT
iajs-2557	9	1	at	at	ADP
iajs-2557	9	2	the	the	DET
iajs-2557	9	3	end	end	NOUN
iajs-2557	9	4	we	we	PRON
iajs-2557	9	5	prove	prove	VERB
iajs-2557	9	6	the	the	DET
iajs-2557	9	7	necessary	necessary	ADJ
iajs-2557	9	8	"	"	PUNCT
iajs-2557	9	9	conditions	condition	NOUN
iajs-2557	9	10	"	"	PUNCT
iajs-2557	9	11	theorem	theorem	NOUN
iajs-2557	9	12	(	(	PUNCT
iajs-2557	9	13	ncth	ncth	NOUN
iajs-2557	9	14	)	)	PUNCT
iajs-2557	9	15	for	for	ADP
iajs-2557	9	16	optimality	optimality	NOUN
iajs-2557	9	17	for	for	ADP
iajs-2557	9	18	the	the	DET
iajs-2557	9	19	problem	problem	NOUN
iajs-2557	9	20	.	.	PUNCT
iajs-2557	10	1	keywords	keyword	NOUN
iajs-2557	10	2	:	:	PUNCT
iajs-2557	10	3	boundary	boundary	ADJ
iajs-2557	10	4	optimal	optimal	ADJ
iajs-2557	10	5	control	control	NOUN
iajs-2557	10	6	,	,	PUNCT
iajs-2557	10	7	triple	triple	ADJ
iajs-2557	10	8	linear	linear	ADJ
iajs-2557	10	9	partial	partial	ADJ
iajs-2557	10	10	differential	differential	ADJ
iajs-2557	10	11	equations	equation	NOUN
iajs-2557	10	12	of	of	ADP
iajs-2557	10	13	elliptic	elliptic	ADJ
iajs-2557	10	14	type	type	NOUN
iajs-2557	10	15	,	,	PUNCT
iajs-2557	10	16	fréchet	fréchet	NOUN
iajs-2557	10	17	derivative	derivative	ADJ
iajs-2557	10	18	,	,	PUNCT
iajs-2557	10	19	necessary	necessary	ADJ
iajs-2557	10	20	conditions	condition	NOUN
iajs-2557	10	21	.	.	PUNCT
iajs-2557	11	1	1	1	X
iajs-2557	11	2	.	.	X
iajs-2557	11	3	introduction	introduction	NOUN
iajs-2557	11	4	in	in	ADP
iajs-2557	11	5	many	many	ADJ
iajs-2557	11	6	scopes	scope	NOUN
iajs-2557	11	7	,	,	PUNCT
iajs-2557	11	8	the	the	DET
iajs-2557	11	9	optimal	optimal	ADJ
iajs-2557	11	10	control	control	NOUN
iajs-2557	11	11	problem	problem	NOUN
iajs-2557	11	12	(	(	PUNCT
iajs-2557	11	13	ocpr	ocpr	ADV
iajs-2557	11	14	)	)	PUNCT
iajs-2557	11	15	has	have	VERB
iajs-2557	11	16	a	a	DET
iajs-2557	11	17	significant	significant	ADJ
iajs-2557	11	18	base	base	NOUN
iajs-2557	11	19	of	of	ADP
iajs-2557	11	20	life	life	NOUN
iajs-2557	11	21	problems	problem	NOUN
iajs-2557	11	22	,	,	PUNCT
iajs-2557	11	23	different	different	ADJ
iajs-2557	11	24	examples	example	NOUN
iajs-2557	11	25	for	for	ADP
iajs-2557	11	26	applications	application	NOUN
iajs-2557	11	27	of	of	ADP
iajs-2557	11	28	such	such	ADJ
iajs-2557	11	29	problems	problem	NOUN
iajs-2557	11	30	are	be	AUX
iajs-2557	11	31	studied	study	VERB
iajs-2557	11	32	in	in	ADP
iajs-2557	11	33	medicine	medicine	NOUN
iajs-2557	12	1	[	[	X
iajs-2557	12	2	1	1	NUM
iajs-2557	12	3	]	]	PUNCT
iajs-2557	12	4	,	,	PUNCT
iajs-2557	12	5	in	in	ADP
iajs-2557	12	6	aircraft	aircraft	NOUN
iajs-2557	12	7	[	[	X
iajs-2557	12	8	2	2	NUM
iajs-2557	12	9	]	]	PUNCT
iajs-2557	12	10	,	,	PUNCT
iajs-2557	12	11	in	in	ADP
iajs-2557	12	12	electric	electric	ADJ
iajs-2557	12	13	power	power	NOUN
iajs-2557	12	14	[	[	X
iajs-2557	12	15	3	3	NUM
iajs-2557	12	16	]	]	PUNCT
iajs-2557	12	17	,	,	PUNCT
iajs-2557	12	18	in	in	ADP
iajs-2557	12	19	economic	economic	ADJ
iajs-2557	12	20	growth	growth	NOUN
iajs-2557	12	21	[	[	X
iajs-2557	12	22	4	4	NUM
iajs-2557	12	23	]	]	PUNCT
iajs-2557	12	24	,	,	PUNCT
iajs-2557	12	25	and	and	CCONJ
iajs-2557	12	26	many	many	ADJ
iajs-2557	12	27	other	other	ADJ
iajs-2557	12	28	fields	field	NOUN
iajs-2557	12	29	.	.	PUNCT
iajs-2557	13	1	this	this	DET
iajs-2557	13	2	role	role	NOUN
iajs-2557	13	3	push	push	VERB
iajs-2557	13	4	many	many	ADJ
iajs-2557	13	5	investigators	investigator	NOUN
iajs-2557	13	6	to	to	PART
iajs-2557	13	7	study	study	VERB
iajs-2557	13	8	the	the	DET
iajs-2557	13	9	ocpr	ocpr	NOUN
iajs-2557	13	10	for	for	ADP
iajs-2557	13	11	nonlinear	nonlinear	ADJ
iajs-2557	13	12	ordinary	ordinary	ADJ
iajs-2557	13	13	differential	differential	ADJ
iajs-2557	13	14	equations	equation	NOUN
iajs-2557	13	15	(	(	PUNCT
iajs-2557	13	16	nonodes	nonode	NOUN
iajs-2557	13	17	)	)	PUNCT
iajs-2557	13	18	as	as	ADP
iajs-2557	13	19	[	[	X
iajs-2557	13	20	5	5	NUM
iajs-2557	13	21	]	]	PUNCT
iajs-2557	13	22	,	,	PUNCT
iajs-2557	13	23	or	or	CCONJ
iajs-2557	13	24	for	for	ADP
iajs-2557	13	25	different	different	ADJ
iajs-2557	13	26	types	type	NOUN
iajs-2557	13	27	of	of	ADP
iajs-2557	13	28	linear	linear	ADJ
iajs-2557	13	29	pdes	pde	NOUN
iajs-2557	13	30	(	(	PUNCT
iajs-2557	13	31	lpdes	lpde	NOUN
iajs-2557	13	32	)	)	PUNCT
iajs-2557	13	33	hyperbolic	hyperbolic	ADJ
iajs-2557	13	34	,	,	PUNCT
iajs-2557	13	35	parabolic	parabolic	ADJ
iajs-2557	13	36	and	and	CCONJ
iajs-2557	13	37	elliptic	elliptic	ADJ
iajs-2557	13	38	as	as	ADP
iajs-2557	13	39	in	in	ADP
iajs-2557	13	40	[	[	NOUN
iajs-2557	13	41	6,7	6,7	NUM
iajs-2557	13	42	]	]	PUNCT
iajs-2557	13	43	and	and	CCONJ
iajs-2557	13	44	[	[	X
iajs-2557	13	45	8	8	NUM
iajs-2557	13	46	]	]	PUNCT
iajs-2557	13	47	respectively	respectively	ADV
iajs-2557	13	48	.	.	PUNCT
iajs-2557	14	1	however	however	ADV
iajs-2557	14	2	,	,	PUNCT
iajs-2557	14	3	many	many	ADJ
iajs-2557	14	4	others	other	NOUN
iajs-2557	14	5	interested	interested	ADJ
iajs-2557	14	6	to	to	PART
iajs-2557	14	7	study	study	VERB
iajs-2557	14	8	the	the	DET
iajs-2557	14	9	ocpr	ocpr	NOUN
iajs-2557	14	10	for	for	ADP
iajs-2557	14	11	couple	couple	NOUN
iajs-2557	14	12	nonlinear	nonlinear	ADJ
iajs-2557	14	13	pdes	pde	NOUN
iajs-2557	14	14	(	(	PUNCT
iajs-2557	14	15	cnonlpdes	cnonlpde	NOUN
iajs-2557	14	16	)	)	PUNCT
iajs-2557	14	17	of	of	ADP
iajs-2557	14	18	these	these	DET
iajs-2557	14	19	three	three	NUM
iajs-2557	14	20	types	type	NOUN
iajs-2557	14	21	[	[	X
iajs-2557	14	22	9,10	9,10	X
iajs-2557	14	23	]	]	X
iajs-2557	14	24	and	and	CCONJ
iajs-2557	14	25	[	[	X
iajs-2557	14	26	10	10	NUM
iajs-2557	14	27	]	]	PUNCT
iajs-2557	14	28	,	,	PUNCT
iajs-2557	14	29	whilst	whilst	SCONJ
iajs-2557	14	30	[	[	X
iajs-2557	14	31	11,12	11,12	NUM
iajs-2557	14	32	]	]	PUNCT
iajs-2557	14	33	and	and	CCONJ
iajs-2557	14	34	[	[	X
iajs-2557	14	35	13	13	NUM
iajs-2557	14	36	]	]	PUNCT
iajs-2557	14	37	studied	study	VERB
iajs-2557	14	38	these	these	DET
iajs-2557	14	39	three	three	NUM
iajs-2557	14	40	types	type	NOUN
iajs-2557	14	41	of	of	ADP
iajs-2557	14	42	the	the	DET
iajs-2557	14	43	cnonlpdes	cnonlpde	NOUN
iajs-2557	14	44	but	but	CCONJ
iajs-2557	14	45	involved	involve	VERB
iajs-2557	14	46	a	a	DET
iajs-2557	14	47	neumann	neumann	PROPN
iajs-2557	14	48	boundary	boundary	PROPN
iajs-2557	14	49	control	control	NOUN
iajs-2557	14	50	(	(	PUNCT
iajs-2557	14	51	nbc	nbc	PROPN
iajs-2557	14	52	)	)	PUNCT
iajs-2557	14	53	.	.	PUNCT
iajs-2557	15	1	on	on	ADP
iajs-2557	15	2	the	the	DET
iajs-2557	15	3	other	other	ADJ
iajs-2557	15	4	hand	hand	NOUN
iajs-2557	15	5	,	,	PUNCT
iajs-2557	15	6	[	[	X
iajs-2557	15	7	14,15	14,15	NUM
iajs-2557	15	8	]	]	PUNCT
iajs-2557	15	9	,	,	PUNCT
iajs-2557	15	10	and	and	CCONJ
iajs-2557	15	11	[	[	X
iajs-2557	15	12	16	16	NUM
iajs-2557	15	13	]	]	PUNCT
iajs-2557	15	14	in	in	ADP
iajs-2557	15	15	2019	2019	NUM
iajs-2557	15	16	studied	study	VERB
iajs-2557	15	17	ocpr	ocpr	ADV
iajs-2557	15	18	for	for	ADP
iajs-2557	15	19	triple	triple	ADJ
iajs-2557	15	20	pdes	pde	NOUN
iajs-2557	15	21	(	(	PUNCT
iajs-2557	15	22	tpdes	tpde	NOUN
iajs-2557	15	23	)	)	PUNCT
iajs-2557	15	24	of	of	ADP
iajs-2557	15	25	the	the	DET
iajs-2557	15	26	three	three	NUM
iajs-2557	15	27	types	type	NOUN
iajs-2557	15	28	,	,	PUNCT
iajs-2557	15	29	while	while	SCONJ
iajs-2557	15	30	[	[	X
iajs-2557	15	31	17	17	NUM
iajs-2557	15	32	]	]	PUNCT
iajs-2557	15	33	studied	study	VERB
iajs-2557	15	34	ocpr	ocpr	ADV
iajs-2557	15	35	involving	involve	VERB
iajs-2557	15	36	nbc	nbc	PROPN
iajs-2557	15	37	ibn	ibn	PROPN
iajs-2557	15	38	al	al	PROPN
iajs-2557	15	39	haitham	haitham	PROPN
iajs-2557	15	40	journal	journal	PROPN
iajs-2557	15	41	for	for	ADP
iajs-2557	15	42	pure	pure	ADJ
iajs-2557	15	43	and	and	CCONJ
iajs-2557	15	44	applied	apply	VERB
iajs-2557	15	45	science	science	NOUN
iajs-2557	15	46	journal	journal	PROPN
iajs-2557	15	47	homepage	homepage	NOUN
iajs-2557	15	48	:	:	PUNCT
iajs-2557	15	49	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2557	15	50	doi	doi	NOUN
iajs-2557	15	51	:	:	PUNCT
iajs-2557	15	52	10.30526/34.1.2557	10.30526/34.1.2557	NUM
iajs-2557	15	53	article	article	NOUN
iajs-2557	15	54	history	history	NOUN
iajs-2557	15	55	:	:	PUNCT
iajs-2557	15	56	received	receive	VERB
iajs-2557	15	57	3,february,2020	3,february,2020	NOUN
iajs-2557	15	58	,	,	PUNCT
iajs-2557	15	59	accepted15,march,2020	accepted15,march,2020	PROPN
iajs-2557	15	60	,	,	PUNCT
iajs-2557	15	61	published	publish	VERB
iajs-2557	15	62	in	in	ADP
iajs-2557	15	63	january	january	PROPN
iajs-2557	15	64	2021	2021	NUM
iajs-2557	15	65	jamil	jamil	PROPN
iajs-2557	15	66	a.	a.	PROPN
iajs-2557	15	67	ali	ali	PROPN
iajs-2557	15	68	al	al	PROPN
iajs-2557	15	69	-	-	PROPN
iajs-2557	15	70	hawasy	hawasy	PROPN
iajs-2557	15	71	nabeel	nabeel	PROPN
iajs-2557	15	72	a.	a.	PROPN
iajs-2557	15	73	thyab	thyab	PROPN
iajs-2557	16	1	al	al	PROPN
iajs-2557	16	2	-	-	PUNCT
iajs-2557	16	3	ajeeli	ajeeli	ADJ
iajs-2557	16	4	file:///c:/users/المجلة/desktop/math%20عدد%20خاص/hawasy20@yahoo.com	file:///c:/users/المجلة/desktop/math%20عدد%20خاص/hawasy20@yahoo.com	PROPN
iajs-2557	16	5	file:///c:/users/المجلة/desktop/math%20عدد%20خاص/hawasy20@yahoo.com	file:///c:/users/المجلة/desktop/math%20عدد%20خاص/hawasy20@yahoo.com	PROPN
iajs-2557	16	6	mailto:jhawassy17@mustansiriyah.edu.iq	mailto:jhawassy17@mustansiriyah.edu.iq	VERB
iajs-2557	16	7	61	61	NUM
iajs-2557	16	8	ibn	ibn	PROPN
iajs-2557	16	9	al	al	PROPN
iajs-2557	16	10	-	-	PUNCT
iajs-2557	16	11	haitham	haitham	PROPN
iajs-2557	16	12	jour	jour	X
iajs-2557	16	13	.	.	PROPN
iajs-2557	17	1	for	for	ADP
iajs-2557	17	2	pure	pure	ADJ
iajs-2557	17	3	&	&	CCONJ
iajs-2557	17	4	appl	appl	PROPN
iajs-2557	17	5	.	.	PUNCT
iajs-2557	18	1	sci	sci	PROPN
iajs-2557	18	2	.	.	PROPN
iajs-2557	19	1	34	34	NUM
iajs-2557	19	2	(	(	PUNCT
iajs-2557	19	3	1	1	NUM
iajs-2557	19	4	)	)	PUNCT
iajs-2557	19	5	2021	2021	NUM
iajs-2557	19	6	"	"	PUNCT
iajs-2557	19	7	ocprnbc	ocprnbc	NOUN
iajs-2557	19	8	"	"	PUNCT
iajs-2557	19	9	for	for	ADP
iajs-2557	19	10	tpdes	tpde	NOUN
iajs-2557	19	11	of	of	ADP
iajs-2557	19	12	parabolic	parabolic	ADJ
iajs-2557	19	13	type	type	NOUN
iajs-2557	19	14	(	(	PUNCT
iajs-2557	19	15	tpdesp	tpdesp	ADJ
iajs-2557	19	16	)	)	PUNCT
iajs-2557	19	17	.	.	PUNCT
iajs-2557	20	1	all	all	DET
iajs-2557	20	2	these	these	DET
iajs-2557	20	3	investigations	investigation	NOUN
iajs-2557	20	4	push	push	VERB
iajs-2557	20	5	us	we	PRON
iajs-2557	20	6	to	to	PART
iajs-2557	20	7	seek	seek	VERB
iajs-2557	20	8	the	the	DET
iajs-2557	20	9	ocprnbc	ocprnbc	NOUN
iajs-2557	20	10	governed	govern	VERB
iajs-2557	20	11	by	by	ADP
iajs-2557	20	12	the	the	DET
iajs-2557	20	13	tlepdes	tlepde	NOUN
iajs-2557	20	14	.	.	PUNCT
iajs-2557	21	1	in	in	ADP
iajs-2557	21	2	this	this	DET
iajs-2557	21	3	paper	paper	NOUN
iajs-2557	21	4	and	and	CCONJ
iajs-2557	21	5	at	at	ADP
iajs-2557	21	6	first	first	ADV
iajs-2557	21	7	,	,	PUNCT
iajs-2557	21	8	we	we	PRON
iajs-2557	21	9	prove	prove	VERB
iajs-2557	21	10	that	that	SCONJ
iajs-2557	21	11	the	the	DET
iajs-2557	21	12	tlepdes	tlepde	NOUN
iajs-2557	21	13	with	with	ADP
iajs-2557	21	14	a	a	DET
iajs-2557	21	15	given	give	VERB
iajs-2557	21	16	ccbcvr	ccbcvr	NOUN
iajs-2557	21	17	has	have	VERB
iajs-2557	21	18	a	a	DET
iajs-2557	21	19	unique	unique	ADJ
iajs-2557	21	20	ssv	ssv	NOUN
iajs-2557	21	21	utilizing	utilize	VERB
iajs-2557	21	22	the	the	DET
iajs-2557	21	23	gme	gme	NOUN
iajs-2557	21	24	.	.	PUNCT
iajs-2557	22	1	second	second	ADV
iajs-2557	22	2	we	we	PRON
iajs-2557	22	3	prove	prove	VERB
iajs-2557	22	4	the	the	DET
iajs-2557	22	5	existence	existence	NOUN
iajs-2557	22	6	theorem	theorem	NOUN
iajs-2557	22	7	of	of	ADP
iajs-2557	22	8	ccbocvr	ccbocvr	PROPN
iajs-2557	22	9	ruled	rule	VERB
iajs-2557	22	10	by	by	ADP
iajs-2557	22	11	the	the	DET
iajs-2557	22	12	tlepdes	tlepde	NOUN
iajs-2557	22	13	.	.	PUNCT
iajs-2557	23	1	we	we	PRON
iajs-2557	23	2	study	study	VERB
iajs-2557	23	3	the	the	DET
iajs-2557	23	4	existence	existence	NOUN
iajs-2557	23	5	for	for	ADP
iajs-2557	23	6	the	the	DET
iajs-2557	23	7	solution	solution	NOUN
iajs-2557	23	8	of	of	ADP
iajs-2557	23	9	the	the	DET
iajs-2557	23	10	taje	taje	NOUN
iajs-2557	23	11	related	relate	VERB
iajs-2557	23	12	with	with	ADP
iajs-2557	23	13	the	the	DET
iajs-2557	23	14	tses	tse	NOUN
iajs-2557	23	15	.	.	PUNCT
iajs-2557	24	1	the	the	DET
iajs-2557	24	2	fde	fde	NOUN
iajs-2557	24	3	of	of	ADP
iajs-2557	24	4	the	the	DET
iajs-2557	24	5	objective	objective	ADJ
iajs-2557	24	6	function	function	NOUN
iajs-2557	24	7	is	be	AUX
iajs-2557	24	8	derived	derive	VERB
iajs-2557	24	9	.	.	PUNCT
iajs-2557	25	1	at	at	ADP
iajs-2557	25	2	the	the	DET
iajs-2557	25	3	end	end	NOUN
iajs-2557	25	4	,	,	PUNCT
iajs-2557	25	5	the	the	DET
iajs-2557	25	6	ncth	ncth	NOUN
iajs-2557	25	7	of	of	ADP
iajs-2557	25	8	optimality	optimality	NOUN
iajs-2557	25	9	of	of	ADP
iajs-2557	25	10	is	be	AUX
iajs-2557	25	11	demonstrated	demonstrate	VERB
iajs-2557	25	12	.	.	PUNCT
iajs-2557	26	1	2	2	X
iajs-2557	26	2	.	.	X
iajs-2557	26	3	problem	problem	NOUN
iajs-2557	26	4	description	description	NOUN
iajs-2557	26	5	let	let	VERB
iajs-2557	26	6	ω	ω	NOUN
iajs-2557	26	7	be	be	AUX
iajs-2557	26	8	a	a	DET
iajs-2557	26	9	bounded	bounded	ADJ
iajs-2557	26	10	and	and	CCONJ
iajs-2557	26	11	open	open	ADJ
iajs-2557	26	12	connected	connected	ADJ
iajs-2557	26	13	subset	subset	NOUN
iajs-2557	26	14	in	in	ADP
iajs-2557	26	15	r2	r2	PROPN
iajs-2557	26	16	with	with	ADP
iajs-2557	26	17	"	"	PUNCT
iajs-2557	26	18	lipshitz	lipshitz	NOUN
iajs-2557	26	19	boundary	boundary	NOUN
iajs-2557	26	20	"	"	PUNCT
iajs-2557	26	21	∂ω	∂ω	PROPN
iajs-2557	26	22	,	,	PUNCT
iajs-2557	26	23	the	the	DET
iajs-2557	26	24	ocpr	ocpr	ADJ
iajs-2557	26	25	is	be	AUX
iajs-2557	26	26	considered	consider	VERB
iajs-2557	26	27	by	by	ADP
iajs-2557	26	28	the	the	DET
iajs-2557	26	29	"	"	PUNCT
iajs-2557	26	30	state	state	NOUN
iajs-2557	26	31	vector	vector	NOUN
iajs-2557	26	32	equation	equation	NOUN
iajs-2557	26	33	"	"	PUNCT
iajs-2557	26	34	which	which	PRON
iajs-2557	26	35	consists	consist	VERB
iajs-2557	26	36	of	of	ADP
iajs-2557	26	37	the	the	DET
iajs-2557	26	38	tlepdes	tlepde	NOUN
iajs-2557	26	39	with	with	ADP
iajs-2557	26	40	the	the	DET
iajs-2557	26	41	nbc	nbc	PROPN
iajs-2557	26	42	.	.	PUNCT
iajs-2557	27	1	a1y1	a1y1	X
iajs-2557	28	1	+	+	NUM
iajs-2557	28	2	y1	y1	NOUN
iajs-2557	28	3	−	−	PROPN
iajs-2557	28	4	y2	y2	NOUN
iajs-2557	28	5	−	−	PROPN
iajs-2557	28	6	y3	y3	NOUN
iajs-2557	28	7	=	=	SYM
iajs-2557	28	8	f1(x	f1(x	PROPN
iajs-2557	28	9	)	)	PUNCT
iajs-2557	28	10	,	,	PUNCT
iajs-2557	28	11	in	in	ADP
iajs-2557	28	12	ω	ω	PROPN
iajs-2557	28	13	(	(	PUNCT
iajs-2557	28	14	1	1	NUM
iajs-2557	28	15	)	)	PUNCT
iajs-2557	28	16	a2y2	a2y2	NOUN
iajs-2557	29	1	+	+	NUM
iajs-2557	29	2	y1	y1	NOUN
iajs-2557	29	3	+	+	CCONJ
iajs-2557	29	4	y2	y2	NOUN
iajs-2557	30	1	+	+	CCONJ
iajs-2557	30	2	y3	y3	NOUN
iajs-2557	30	3	=	=	SYM
iajs-2557	30	4	f2(x	f2(x	PROPN
iajs-2557	30	5	)	)	PUNCT
iajs-2557	30	6	,	,	PUNCT
iajs-2557	30	7	in	in	ADP
iajs-2557	30	8	ω	ω	PROPN
iajs-2557	30	9	(	(	PUNCT
iajs-2557	30	10	2	2	NUM
iajs-2557	30	11	)	)	PUNCT
iajs-2557	30	12	a3y3	a3y3	PROPN
iajs-2557	31	1	+	+	NUM
iajs-2557	31	2	y1	y1	NOUN
iajs-2557	31	3	−	−	PROPN
iajs-2557	31	4	y2	y2	NOUN
iajs-2557	31	5	+	+	CCONJ
iajs-2557	31	6	y3	y3	NOUN
iajs-2557	31	7	=	=	SYM
iajs-2557	31	8	f3(x	f3(x	PROPN
iajs-2557	31	9	)	)	PUNCT
iajs-2557	31	10	,	,	PUNCT
iajs-2557	31	11	in	in	ADP
iajs-2557	31	12	ω	ω	PROPN
iajs-2557	31	13	(	(	PUNCT
iajs-2557	31	14	3	3	NUM
iajs-2557	31	15	)	)	PUNCT
iajs-2557	31	16	∑	∑	PUNCT
iajs-2557	31	17	a1ij	a1ij	PROPN
iajs-2557	31	18	∂y1	∂y1	PROPN
iajs-2557	31	19	∂n1	∂n1	NOUN
iajs-2557	31	20	=	=	SYM
iajs-2557	31	21	u1	u1	NOUN
iajs-2557	31	22	,	,	PUNCT
iajs-2557	31	23	2	2	NUM
iajs-2557	31	24	i	i	NOUN
iajs-2557	31	25	,	,	PUNCT
iajs-2557	31	26	j=1	j=1	PROPN
iajs-2557	31	27	on	on	ADP
iajs-2557	31	28	∂ω	∂ω	PROPN
iajs-2557	31	29	(	(	PUNCT
iajs-2557	31	30	4	4	NUM
iajs-2557	31	31	)	)	PUNCT
iajs-2557	31	32	∑	∑	DET
iajs-2557	31	33	a2ij	a2ij	X
iajs-2557	31	34	∂y2	∂y2	ADJ
iajs-2557	31	35	∂n2	∂n2	PROPN
iajs-2557	31	36	=	=	SYM
iajs-2557	31	37	u2	u2	PROPN
iajs-2557	31	38	,	,	PUNCT
iajs-2557	31	39	2	2	NUM
iajs-2557	31	40	i	i	NOUN
iajs-2557	31	41	,	,	PUNCT
iajs-2557	31	42	j=1	j=1	ADJ
iajs-2557	31	43	on∂ω	on∂ω	NOUN
iajs-2557	31	44	(	(	PUNCT
iajs-2557	31	45	5	5	NUM
iajs-2557	31	46	)	)	PUNCT
iajs-2557	31	47	∑	∑	PUNCT
iajs-2557	31	48	a3ij	a3ij	PUNCT
iajs-2557	31	49	∂y3	∂y3	NOUN
iajs-2557	31	50	∂n3	∂n3	NOUN
iajs-2557	31	51	=	=	SYM
iajs-2557	31	52	u3	u3	PROPN
iajs-2557	31	53	,	,	PUNCT
iajs-2557	31	54	2	2	NUM
iajs-2557	31	55	i	i	NOUN
iajs-2557	31	56	,	,	PUNCT
iajs-2557	31	57	j=1	j=1	ADJ
iajs-2557	31	58	on∂ω	on∂ω	NOUN
iajs-2557	31	59	(	(	PUNCT
iajs-2557	31	60	6	6	NUM
iajs-2557	31	61	)	)	PUNCT
iajs-2557	31	62	where	where	SCONJ
iajs-2557	31	63	aryr	aryr	ADJ
iajs-2557	31	64	=	=	SYM
iajs-2557	31	65	−∑	−∑	PROPN
iajs-2557	31	66	∂	∂	NOUN
iajs-2557	31	67	∂xi	∂xi	NOUN
iajs-2557	31	68	(	(	PUNCT
iajs-2557	31	69	arij	arij	PROPN
iajs-2557	31	70	(	(	PUNCT
iajs-2557	31	71	x	x	X
iajs-2557	31	72	)	)	PUNCT
iajs-2557	31	73	∂yr	∂yr	PROPN
iajs-2557	31	74	∂xj	∂xj	PROPN
iajs-2557	31	75	)	)	PUNCT
iajs-2557	31	76	,	,	PUNCT
iajs-2557	31	77	r	r	NOUN
iajs-2557	31	78	=	=	SYM
iajs-2557	31	79	1,2,3	1,2,3	NUM
iajs-2557	31	80	,	,	PUNCT
iajs-2557	31	81	arij	arij	NOUN
iajs-2557	31	82	=	=	SYM
iajs-2557	31	83	arij	arij	PROPN
iajs-2557	31	84	(	(	PUNCT
iajs-2557	31	85	xij	xij	NOUN
iajs-2557	31	86	)	)	PUNCT
iajs-2557	31	87	∈	∈	PROPN
iajs-2557	31	88	l∞(ω	l∞(ω	NOUN
iajs-2557	31	89	)	)	PUNCT
iajs-2557	31	90	,	,	PUNCT
iajs-2557	31	91	and2	and2	VERB
iajs-2557	31	92	i	i	PRON
iajs-2557	31	93	,	,	PUNCT
iajs-2557	31	94	j=1	j=1	PROPN
iajs-2557	31	95	(	(	PUNCT
iajs-2557	31	96	u1	u1	PROPN
iajs-2557	31	97	,	,	PUNCT
iajs-2557	31	98	u2	u2	NOUN
iajs-2557	31	99	,	,	PUNCT
iajs-2557	31	100	u3	u3	NOUN
iajs-2557	31	101	)	)	PUNCT
iajs-2557	31	102	=	=	SYM
iajs-2557	31	103	(	(	PUNCT
iajs-2557	31	104	u1(x	u1(x	NOUN
iajs-2557	31	105	)	)	PUNCT
iajs-2557	31	106	,	,	PUNCT
iajs-2557	31	107	u2(x	u2(x	NOUN
iajs-2557	31	108	)	)	PUNCT
iajs-2557	31	109	,	,	PUNCT
iajs-2557	31	110	u3(x	u3(x	NOUN
iajs-2557	31	111	)	)	PUNCT
iajs-2557	31	112	)	)	PUNCT
iajs-2557	31	113	∈	∈	PROPN
iajs-2557	31	114	(	(	PUNCT
iajs-2557	31	115	l2(∂ω	l2(∂ω	NUM
iajs-2557	31	116	)	)	PUNCT
iajs-2557	31	117	)	)	PUNCT
iajs-2557	31	118	3	3	NUM
iajs-2557	31	119	is	be	AUX
iajs-2557	31	120	the	the	DET
iajs-2557	31	121	nbc	nbc	PROPN
iajs-2557	31	122	vector	vector	NOUN
iajs-2557	31	123	(	(	PUNCT
iajs-2557	31	124	nbcv	nbcv	PROPN
iajs-2557	31	125	)	)	PUNCT
iajs-2557	31	126	,	,	PUNCT
iajs-2557	31	127	(	(	PUNCT
iajs-2557	31	128	y1	y1	INTJ
iajs-2557	31	129	,	,	PUNCT
iajs-2557	31	130	y2	y2	PROPN
iajs-2557	31	131	,	,	PUNCT
iajs-2557	31	132	y3	y3	NOUN
iajs-2557	31	133	)	)	PUNCT
iajs-2557	31	134	=	=	SYM
iajs-2557	31	135	(	(	PUNCT
iajs-2557	31	136	y1(x	y1(x	NOUN
iajs-2557	31	137	)	)	PUNCT
iajs-2557	31	138	,	,	PUNCT
iajs-2557	31	139	y2(x	y2(x	PROPN
iajs-2557	31	140	)	)	PUNCT
iajs-2557	31	141	,	,	PUNCT
iajs-2557	31	142	y3(x	y3(x	PROPN
iajs-2557	31	143	)	)	PUNCT
iajs-2557	31	144	)	)	PUNCT
iajs-2557	31	145	∈	∈	PROPN
iajs-2557	31	146	(	(	PUNCT
iajs-2557	31	147	h1(ω	h1(ω	PROPN
iajs-2557	31	148	)	)	PUNCT
iajs-2557	31	149	)	)	PUNCT
iajs-2557	31	150	3	3	NUM
iajs-2557	31	151	is	be	AUX
iajs-2557	31	152	the	the	DET
iajs-2557	31	153	ssv	ssv	NOUN
iajs-2557	31	154	corresponding	correspond	VERB
iajs-2557	31	155	to	to	ADP
iajs-2557	31	156	nbcv	nbcv	PROPN
iajs-2557	31	157	,	,	PUNCT
iajs-2557	31	158	(	(	PUNCT
iajs-2557	31	159	f1	f1	NOUN
iajs-2557	31	160	,	,	PUNCT
iajs-2557	31	161	f2	f2	PROPN
iajs-2557	31	162	,	,	PUNCT
iajs-2557	31	163	f3	f3	NOUN
iajs-2557	31	164	)	)	PUNCT
iajs-2557	31	165	=	=	SYM
iajs-2557	31	166	(	(	PUNCT
iajs-2557	31	167	f1(x	f1(x	NOUN
iajs-2557	31	168	)	)	PUNCT
iajs-2557	31	169	,	,	PUNCT
iajs-2557	31	170	f2	f2	PROPN
iajs-2557	31	171	(	(	PUNCT
iajs-2557	31	172	x	x	NOUN
iajs-2557	31	173	)	)	PUNCT
iajs-2557	31	174	,	,	PUNCT
iajs-2557	31	175	f3(x	f3(x	NUM
iajs-2557	31	176	)	)	PUNCT
iajs-2557	31	177	)	)	PUNCT
iajs-2557	31	178	∈	∈	PROPN
iajs-2557	31	179	(	(	PUNCT
iajs-2557	31	180	l2(ω	l2(ω	NOUN
iajs-2557	31	181	)	)	PUNCT
iajs-2557	31	182	)	)	PUNCT
iajs-2557	31	183	3	3	NUM
iajs-2557	31	184	is	be	AUX
iajs-2557	31	185	given	give	VERB
iajs-2557	31	186	functions	function	NOUN
iajs-2557	31	187	,	,	PUNCT
iajs-2557	31	188	for	for	ADP
iajs-2557	31	189	all	all	DET
iajs-2557	31	190	x	x	SYM
iajs-2557	31	191	∈	∈	PROPN
iajs-2557	31	192	ω	ω	NOUN
iajs-2557	31	193	,	,	PUNCT
iajs-2557	31	194	and	and	CCONJ
iajs-2557	31	195	𝑛𝑙	𝑛𝑙	INTJ
iajs-2557	31	196	,	,	PUNCT
iajs-2557	31	197	∀	∀	X
iajs-2557	31	198	𝑙	𝑙	NOUN
iajs-2557	32	1	=	=	SYM
iajs-2557	32	2	1,2,3	1,2,3	NUM
iajs-2557	32	3	,	,	PUNCT
iajs-2557	32	4	is	be	AUX
iajs-2557	32	5	a	a	DET
iajs-2557	32	6	unit	unit	NOUN
iajs-2557	32	7	vector	vector	NOUN
iajs-2557	32	8	normal	normal	ADJ
iajs-2557	32	9	on	on	ADP
iajs-2557	32	10	σ	σ	PROPN
iajs-2557	32	11	.	.	PUNCT
iajs-2557	33	1	the	the	DET
iajs-2557	33	2	controls	control	NOUN
iajs-2557	33	3	are	be	AUX
iajs-2557	33	4	defined	define	VERB
iajs-2557	33	5	in	in	ADP
iajs-2557	33	6	the	the	DET
iajs-2557	33	7	set	set	NOUN
iajs-2557	33	8	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	33	9	⊂	⊂	PROPN
iajs-2557	33	10	(	(	PUNCT
iajs-2557	33	11	l2(∂ω	l2(∂ω	NUM
iajs-2557	33	12	)	)	PUNCT
iajs-2557	33	13	)	)	PUNCT
iajs-2557	33	14	3	3	NUM
iajs-2557	33	15	,	,	PUNCT
iajs-2557	33	16	with	with	ADP
iajs-2557	33	17	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	33	18	=	=	SYM
iajs-2557	33	19	{	{	PUNCT
iajs-2557	33	20	(	(	PUNCT
iajs-2557	33	21	u1	u1	PROPN
iajs-2557	33	22	,	,	PUNCT
iajs-2557	33	23	u2	u2	NOUN
iajs-2557	33	24	,	,	PUNCT
iajs-2557	33	25	u3	u3	NOUN
iajs-2557	33	26	)	)	PUNCT
iajs-2557	33	27	∈	∈	PROPN
iajs-2557	33	28	(	(	PUNCT
iajs-2557	33	29	l2(∂ω	l2(∂ω	NUM
iajs-2557	33	30	)	)	PUNCT
iajs-2557	33	31	)	)	PUNCT
iajs-2557	33	32	3	3	NUM
iajs-2557	33	33	|(u1	|(u1	NOUN
iajs-2557	33	34	,	,	PUNCT
iajs-2557	33	35	u2	u2	NOUN
iajs-2557	33	36	,	,	PUNCT
iajs-2557	33	37	u3	u3	PROPN
iajs-2557	33	38	)	)	PUNCT
iajs-2557	33	39	∈	∈	PROPN
iajs-2557	33	40	u⃗⃗	u⃗⃗	PROPN
iajs-2557	33	41	⊂	⊂	PROPN
iajs-2557	33	42	r3	r3	PROPN
iajs-2557	33	43	a.	a.	NOUN
iajs-2557	33	44	e	e	NOUN
iajs-2557	33	45	in	in	ADP
iajs-2557	33	46	∂ω	∂ω	PROPN
iajs-2557	33	47	}	}	PUNCT
iajs-2557	33	48	where	where	SCONJ
iajs-2557	33	49	u⃗⃗	u⃗⃗	PROPN
iajs-2557	33	50	is	be	AUX
iajs-2557	33	51	a	a	DET
iajs-2557	33	52	convex	convex	NOUN
iajs-2557	33	53	set	set	NOUN
iajs-2557	33	54	.	.	PUNCT
iajs-2557	34	1	the	the	DET
iajs-2557	34	2	objective	objective	ADJ
iajs-2557	34	3	functional	functional	NOUN
iajs-2557	34	4	is	be	AUX
iajs-2557	34	5	defined	define	VERB
iajs-2557	34	6	minu⃗⃗	minu⃗⃗	NOUN
iajs-2557	34	7	∈w⃗⃗⃗⃗	∈w⃗⃗⃗⃗	NOUN
iajs-2557	34	8	go(u⃗	go(u⃗	PROPN
iajs-2557	34	9	)	)	PUNCT
iajs-2557	35	1	=	=	PUNCT
iajs-2557	36	1	1	1	NUM
iajs-2557	36	2	2	2	NUM
iajs-2557	36	3	‖y1	‖y1	DET
iajs-2557	36	4	−	−	NOUN
iajs-2557	36	5	y1d‖l2(ω	y1d‖l2(ω	ADV
iajs-2557	36	6	)	)	PUNCT
iajs-2557	36	7	2	2	NUM
iajs-2557	37	1	+	+	CCONJ
iajs-2557	37	2	1	1	NUM
iajs-2557	37	3	2	2	NUM
iajs-2557	37	4	‖y2	‖y2	ADJ
iajs-2557	37	5	−	−	PROPN
iajs-2557	37	6	y2d‖l2(ω	y2d‖l2(ω	CCONJ
iajs-2557	37	7	)	)	PUNCT
iajs-2557	37	8	2	2	NUM
iajs-2557	38	1	+	+	CCONJ
iajs-2557	38	2	1	1	NUM
iajs-2557	38	3	2	2	NUM
iajs-2557	38	4	‖y3	‖y3	NOUN
iajs-2557	38	5	−	−	PROPN
iajs-2557	38	6	y3d‖l2(ω	y3d‖l2(ω	NOUN
iajs-2557	38	7	)	)	PUNCT
iajs-2557	38	8	2	2	NUM
iajs-2557	39	1	+	+	CCONJ
iajs-2557	39	2	α	α	NOUN
iajs-2557	39	3	2	2	NUM
iajs-2557	39	4	‖u1‖l2(∂ω	‖u1‖l2(∂ω	NOUN
iajs-2557	39	5	)	)	PUNCT
iajs-2557	39	6	2	2	NUM
iajs-2557	40	1	+	+	CCONJ
iajs-2557	40	2	α	α	NOUN
iajs-2557	40	3	2	2	NUM
iajs-2557	40	4	‖u2‖l2(∂ω	‖u2‖l2(∂ω	NOUN
iajs-2557	40	5	)	)	PUNCT
iajs-2557	40	6	2	2	NUM
iajs-2557	41	1	+	+	CCONJ
iajs-2557	41	2	α	α	NOUN
iajs-2557	41	3	2	2	NUM
iajs-2557	41	4	‖u3‖l2(∂ω	‖u3‖l2(∂ω	NOUN
iajs-2557	41	5	)	)	PUNCT
iajs-2557	41	6	2	2	NUM
iajs-2557	41	7	(	(	PUNCT
iajs-2557	41	8	7	7	X
iajs-2557	41	9	)	)	PUNCT
iajs-2557	41	10	let	let	VERB
iajs-2557	41	11	v⃗⃗	v⃗⃗	PROPN
iajs-2557	41	12	=	=	SYM
iajs-2557	41	13	(	(	PUNCT
iajs-2557	41	14	v)3	v)3	PROPN
iajs-2557	41	15	=	=	SYM
iajs-2557	41	16	(	(	PUNCT
iajs-2557	41	17	h1(ω	h1(ω	PROPN
iajs-2557	41	18	)	)	PUNCT
iajs-2557	41	19	)	)	PUNCT
iajs-2557	41	20	3	3	NUM
iajs-2557	41	21	.	.	PUNCT
iajs-2557	42	1	the	the	DET
iajs-2557	42	2	symbols	symbol	NOUN
iajs-2557	42	3	(	(	PUNCT
iajs-2557	42	4	v	v	NOUN
iajs-2557	42	5	,	,	PUNCT
iajs-2557	42	6	v)l2(ω	v)l2(ω	NOUN
iajs-2557	42	7	)	)	PUNCT
iajs-2557	42	8	,	,	PUNCT
iajs-2557	42	9	and	and	CCONJ
iajs-2557	42	10	‖	‖	PROPN
iajs-2557	42	11	v	v	PROPN
iajs-2557	42	12	‖l2(ω	‖l2(ω	NOUN
iajs-2557	42	13	)	)	PUNCT
iajs-2557	42	14	(	(	PUNCT
iajs-2557	42	15	‖	‖	PROPN
iajs-2557	42	16	v	v	NOUN
iajs-2557	42	17	‖l2(∂ω	‖l2(∂ω	NOUN
iajs-2557	42	18	)	)	PUNCT
iajs-2557	42	19	)	)	PUNCT
iajs-2557	42	20	are	be	AUX
iajs-2557	42	21	the	the	DET
iajs-2557	42	22	inner	inner	ADJ
iajs-2557	42	23	product	product	NOUN
iajs-2557	42	24	(	(	PUNCT
iajs-2557	42	25	ip	ip	NOUN
iajs-2557	42	26	)	)	PUNCT
iajs-2557	42	27	and	and	CCONJ
iajs-2557	42	28	the	the	DET
iajs-2557	42	29	norm	norm	NOUN
iajs-2557	42	30	in	in	ADP
iajs-2557	42	31	l2(ω	l2(ω	PROPN
iajs-2557	42	32	)	)	PUNCT
iajs-2557	42	33	(	(	PUNCT
iajs-2557	42	34	l2(∂ω	l2(∂ω	NUM
iajs-2557	42	35	)	)	PUNCT
iajs-2557	42	36	)	)	PUNCT
iajs-2557	42	37	,	,	PUNCT
iajs-2557	42	38	by	by	ADP
iajs-2557	42	39	(	(	PUNCT
iajs-2557	42	40	v	v	NOUN
iajs-2557	42	41	,	,	PUNCT
iajs-2557	42	42	v	v	NOUN
iajs-2557	42	43	)	)	PUNCT
iajs-2557	42	44	h1(ω	h1(ω	PROPN
iajs-2557	42	45	)	)	PUNCT
iajs-2557	42	46	,	,	PUNCT
iajs-2557	42	47	‖v‖h1(ω	‖v‖h1(ω	NOUN
iajs-2557	42	48	)	)	PUNCT
iajs-2557	42	49	the	the	DET
iajs-2557	42	50	in	in	ADV
iajs-2557	42	51	and	and	CCONJ
iajs-2557	42	52	the	the	DET
iajs-2557	42	53	norm	norm	NOUN
iajs-2557	42	54	in	in	ADP
iajs-2557	42	55	h1(ω	h1(ω	PROPN
iajs-2557	42	56	)	)	PUNCT
iajs-2557	42	57	,	,	PUNCT
iajs-2557	42	58	by	by	ADP
iajs-2557	42	59	(	(	PUNCT
iajs-2557	42	60	v⃗	v⃗	ADJ
iajs-2557	42	61	,	,	PUNCT
iajs-2557	42	62	v⃗	v⃗	ADJ
iajs-2557	42	63	)	)	PUNCT
iajs-2557	42	64	l2(ω	l2(ω	X
iajs-2557	42	65	)	)	PUNCT
iajs-2557	42	66	=	=	SYM
iajs-2557	42	67	∑	∑	PUNCT
iajs-2557	42	68	(	(	PUNCT
iajs-2557	42	69	vi	vi	PROPN
iajs-2557	42	70	,	,	PUNCT
iajs-2557	42	71	vi	vi	NOUN
iajs-2557	42	72	)	)	PUNCT
iajs-2557	42	73	2	2	NUM
iajs-2557	42	74	i=1	i=1	NOUN
iajs-2557	42	75	and	and	CCONJ
iajs-2557	42	76	‖	‖	PROPN
iajs-2557	42	77	v⃗	v⃗	PROPN
iajs-2557	42	78	‖	‖	PROPN
iajs-2557	42	79	(	(	PUNCT
iajs-2557	42	80	l2(ω	l2(ω	NOUN
iajs-2557	42	81	)	)	PUNCT
iajs-2557	42	82	)	)	PUNCT
iajs-2557	42	83	3	3	NUM
iajs-2557	42	84	=	=	SYM
iajs-2557	42	85	∑	∑	PUNCT
iajs-2557	42	86	‖	‖	PROPN
iajs-2557	42	87	vi‖l2(ω	vi‖l2(ω	ADJ
iajs-2557	42	88	)	)	PUNCT
iajs-2557	42	89	3	3	NUM
iajs-2557	42	90	i=1	i=1	PROPN
iajs-2557	42	91	the	the	DET
iajs-2557	42	92	ip	ip	NOUN
iajs-2557	42	93	and	and	CCONJ
iajs-2557	42	94	the	the	DET
iajs-2557	42	95	norm	norm	NOUN
iajs-2557	42	96	in	in	ADP
iajs-2557	42	97	(	(	PUNCT
iajs-2557	42	98	l2(ω	l2(ω	NOUN
iajs-2557	42	99	)	)	PUNCT
iajs-2557	42	100	)	)	PUNCT
iajs-2557	42	101	3	3	NUM
iajs-2557	42	102	,	,	PUNCT
iajs-2557	42	103	by	by	ADP
iajs-2557	42	104	(	(	PUNCT
iajs-2557	42	105	v⃗	v⃗	ADJ
iajs-2557	42	106	,	,	PUNCT
iajs-2557	42	107	v⃗	v⃗	ADJ
iajs-2557	42	108	)	)	PUNCT
iajs-2557	42	109	l2(ω	l2(ω	X
iajs-2557	42	110	)	)	PUNCT
iajs-2557	42	111	=	=	SYM
iajs-2557	42	112	∑	∑	PUNCT
iajs-2557	42	113	(	(	PUNCT
iajs-2557	42	114	vi	vi	PROPN
iajs-2557	42	115	,	,	PUNCT
iajs-2557	42	116	vi	vi	NOUN
iajs-2557	42	117	)	)	PUNCT
iajs-2557	42	118	3	3	NUM
iajs-2557	42	119	i=1	i=1	NOUN
iajs-2557	42	120	and	and	CCONJ
iajs-2557	42	121	‖	‖	PROPN
iajs-2557	42	122	v⃗	v⃗	PROPN
iajs-2557	42	123	‖	‖	PROPN
iajs-2557	42	124	(	(	PUNCT
iajs-2557	42	125	h1(ω	h1(ω	PROPN
iajs-2557	42	126	)	)	PUNCT
iajs-2557	42	127	)	)	PUNCT
iajs-2557	42	128	3	3	NUM
iajs-2557	42	129	=	=	SYM
iajs-2557	42	130	∑	∑	PUNCT
iajs-2557	42	131	‖	‖	PROPN
iajs-2557	42	132	vi‖h1(ω	vi‖h1(ω	PROPN
iajs-2557	42	133	)	)	PUNCT
iajs-2557	42	134	3	3	NUM
iajs-2557	42	135	i=1	i=1	PROPN
iajs-2557	42	136	the	the	DET
iajs-2557	42	137	ip	ip	NOUN
iajs-2557	42	138	and	and	CCONJ
iajs-2557	42	139	the	the	DET
iajs-2557	42	140	norm	norm	NOUN
iajs-2557	42	141	in	in	ADP
iajs-2557	42	142	v⃗⃗	v⃗⃗	PROPN
iajs-2557	42	143	and	and	CCONJ
iajs-2557	42	144	v⃗⃗	v⃗⃗	PROPN
iajs-2557	42	145	∗	∗	NOUN
iajs-2557	42	146	is	be	AUX
iajs-2557	42	147	the	the	DET
iajs-2557	42	148	dual	dual	ADJ
iajs-2557	42	149	of	of	ADP
iajs-2557	42	150	v⃗⃗	v⃗⃗	PROPN
iajs-2557	42	151	.	.	PUNCT
iajs-2557	43	1	3	3	X
iajs-2557	43	2	.	.	X
iajs-2557	43	3	weak	weak	ADJ
iajs-2557	43	4	formulation	formulation	NOUN
iajs-2557	43	5	:	:	PUNCT
iajs-2557	43	6	the	the	DET
iajs-2557	43	7	weak	weak	ADJ
iajs-2557	43	8	form	form	NOUN
iajs-2557	43	9	(	(	PUNCT
iajs-2557	43	10	wfo	wfo	NOUN
iajs-2557	43	11	)	)	PUNCT
iajs-2557	43	12	for	for	ADP
iajs-2557	43	13	(	(	PUNCT
iajs-2557	43	14	1	1	NUM
iajs-2557	43	15	-	-	SYM
iajs-2557	43	16	3	3	NUM
iajs-2557	43	17	)	)	PUNCT
iajs-2557	43	18	is	be	AUX
iajs-2557	43	19	obtained	obtain	VERB
iajs-2557	43	20	by	by	ADP
iajs-2557	43	21	multiplying	multiply	VERB
iajs-2557	43	22	their	their	PRON
iajs-2557	43	23	both	both	DET
iajs-2557	43	24	sides	side	NOUN
iajs-2557	43	25	by	by	ADP
iajs-2557	43	26	v1	v1	PROPN
iajs-2557	43	27	∈	∈	PROPN
iajs-2557	43	28	v	v	NOUN
iajs-2557	43	29	,	,	PUNCT
iajs-2557	43	30	v2	v2	PROPN
iajs-2557	43	31	∈	∈	PROPN
iajs-2557	43	32	v	v	NOUN
iajs-2557	43	33	and	and	CCONJ
iajs-2557	43	34	v3	v3	PROPN
iajs-2557	43	35	∈	∈	PROPN
iajs-2557	43	36	v	v	ADP
iajs-2557	43	37	respectively	respectively	ADV
iajs-2557	43	38	,	,	PUNCT
iajs-2557	43	39	then	then	ADV
iajs-2557	43	40	integrating	integrate	VERB
iajs-2557	43	41	them	they	PRON
iajs-2557	43	42	and	and	CCONJ
iajs-2557	43	43	then	then	ADV
iajs-2557	43	44	using	use	VERB
iajs-2557	43	45	the	the	DET
iajs-2557	43	46	generalized	generalize	VERB
iajs-2557	43	47	green	green	NOUN
iajs-2557	43	48	's	's	PART
iajs-2557	43	49	theorem	theorem	NOUN
iajs-2557	43	50	is	be	AUX
iajs-2557	43	51	applied	apply	VERB
iajs-2557	43	52	for	for	ADP
iajs-2557	43	53	the	the	DET
iajs-2557	43	54	terms	term	NOUN
iajs-2557	43	55	that	that	PRON
iajs-2557	43	56	contain	contain	VERB
iajs-2557	43	57	the	the	DET
iajs-2557	43	58	derivatives	derivative	NOUN
iajs-2557	43	59	of	of	ADP
iajs-2557	43	60	order	order	NOUN
iajs-2557	43	61	two	two	NUM
iajs-2557	43	62	,	,	PUNCT
iajs-2557	43	63	to	to	PART
iajs-2557	43	64	get	get	VERB
iajs-2557	43	65	:	:	PUNCT
iajs-2557	43	66	a1(y1	a1(y1	ADJ
iajs-2557	43	67	,	,	PUNCT
iajs-2557	43	68	v1	v1	NOUN
iajs-2557	43	69	)	)	PUNCT
iajs-2557	44	1	−	−	PROPN
iajs-2557	45	1	(	(	PUNCT
iajs-2557	45	2	y2	y2	NOUN
iajs-2557	45	3	+	+	CCONJ
iajs-2557	45	4	y3	y3	NOUN
iajs-2557	45	5	,	,	PUNCT
iajs-2557	45	6	v1	v1	NOUN
iajs-2557	45	7	)	)	PUNCT
iajs-2557	45	8	l2(ω	l2(ω	NOUN
iajs-2557	45	9	)	)	PUNCT
iajs-2557	45	10	=	=	SYM
iajs-2557	45	11	(	(	PUNCT
iajs-2557	45	12	f1	f1	NOUN
iajs-2557	45	13	,	,	PUNCT
iajs-2557	45	14	v1)l2(ω	v1)l2(ω	ADV
iajs-2557	45	15	)	)	PUNCT
iajs-2557	46	1	+	+	CCONJ
iajs-2557	46	2	(	(	PUNCT
iajs-2557	46	3	u1	u1	NOUN
iajs-2557	46	4	,	,	PUNCT
iajs-2557	46	5	v1)l2(∂ω	v1)l2(∂ω	PROPN
iajs-2557	46	6	)	)	PUNCT
iajs-2557	46	7	,	,	PUNCT
iajs-2557	46	8	∀	∀	NOUN
iajs-2557	46	9	v1	v1	NOUN
iajs-2557	46	10	∈	∈	PROPN
iajs-2557	46	11	v	v	NOUN
iajs-2557	46	12	(	(	PUNCT
iajs-2557	46	13	8)	8)	NUM
iajs-2557	46	14	62	62	NUM
iajs-2557	46	15	ibn	ibn	PROPN
iajs-2557	46	16	al	al	PROPN
iajs-2557	46	17	-	-	PUNCT
iajs-2557	46	18	haitham	haitham	PROPN
iajs-2557	46	19	jour	jour	X
iajs-2557	46	20	.	.	PROPN
iajs-2557	47	1	for	for	ADP
iajs-2557	47	2	pure	pure	ADJ
iajs-2557	47	3	&	&	CCONJ
iajs-2557	47	4	appl	appl	PROPN
iajs-2557	47	5	.	.	PUNCT
iajs-2557	48	1	sci	sci	PROPN
iajs-2557	48	2	.	.	PROPN
iajs-2557	49	1	34	34	NUM
iajs-2557	49	2	(	(	PUNCT
iajs-2557	49	3	1	1	NUM
iajs-2557	49	4	)	)	PUNCT
iajs-2557	49	5	2021	2021	NUM
iajs-2557	50	1	a2(y2	a2(y2	ADJ
iajs-2557	50	2	,	,	PUNCT
iajs-2557	50	3	v2	v2	NOUN
iajs-2557	50	4	)	)	PUNCT
iajs-2557	51	1	+	+	CCONJ
iajs-2557	51	2	(	(	PUNCT
iajs-2557	51	3	y1	y1	INTJ
iajs-2557	51	4	+	+	NUM
iajs-2557	51	5	y3	y3	NOUN
iajs-2557	51	6	,	,	PUNCT
iajs-2557	51	7	v2	v2	PROPN
iajs-2557	51	8	)	)	PUNCT
iajs-2557	51	9	l2(ω	l2(ω	NOUN
iajs-2557	51	10	)	)	PUNCT
iajs-2557	51	11	=	=	SYM
iajs-2557	51	12	(	(	PUNCT
iajs-2557	51	13	f2	f2	PROPN
iajs-2557	51	14	,	,	PUNCT
iajs-2557	51	15	v2)l2(ω	v2)l2(ω	ADJ
iajs-2557	51	16	)	)	PUNCT
iajs-2557	52	1	+	+	CCONJ
iajs-2557	52	2	(	(	PUNCT
iajs-2557	52	3	u2	u2	PROPN
iajs-2557	52	4	,	,	PUNCT
iajs-2557	52	5	v2)l2(∂ω	v2)l2(∂ω	PROPN
iajs-2557	52	6	)	)	PUNCT
iajs-2557	52	7	,	,	PUNCT
iajs-2557	52	8	∀	∀	PUNCT
iajs-2557	52	9	v2	v2	NOUN
iajs-2557	52	10	∈	∈	PROPN
iajs-2557	52	11	v	v	NOUN
iajs-2557	52	12	(	(	PUNCT
iajs-2557	52	13	9	9	NUM
iajs-2557	52	14	)	)	PUNCT
iajs-2557	52	15	a3(y3	a3(y3	PROPN
iajs-2557	52	16	,	,	PUNCT
iajs-2557	52	17	v3	v3	PROPN
iajs-2557	52	18	)	)	PUNCT
iajs-2557	52	19	+	+	CCONJ
iajs-2557	52	20	(	(	PUNCT
iajs-2557	52	21	y1	y1	INTJ
iajs-2557	52	22	−	−	PROPN
iajs-2557	52	23	y2	y2	PROPN
iajs-2557	52	24	,	,	PUNCT
iajs-2557	52	25	v3	v3	PROPN
iajs-2557	52	26	)	)	PUNCT
iajs-2557	52	27	l2(ω	l2(ω	PROPN
iajs-2557	52	28	)	)	PUNCT
iajs-2557	52	29	=	=	SYM
iajs-2557	52	30	(	(	PUNCT
iajs-2557	52	31	f3	f3	ADJ
iajs-2557	52	32	,	,	PUNCT
iajs-2557	52	33	v3)l2(ω	v3)l2(ω	ADV
iajs-2557	52	34	)	)	PUNCT
iajs-2557	52	35	+	+	CCONJ
iajs-2557	52	36	(	(	PUNCT
iajs-2557	52	37	u3	u3	NOUN
iajs-2557	52	38	,	,	PUNCT
iajs-2557	52	39	v3)l2(∂ω	v3)l2(∂ω	NOUN
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iajs-2557	52	41	,	,	PUNCT
iajs-2557	52	42	∀	∀	NUM
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iajs-2557	52	44	∈	∈	PROPN
iajs-2557	52	45	v	v	ADP
iajs-2557	52	46	(	(	PUNCT
iajs-2557	52	47	10	10	NUM
iajs-2557	52	48	)	)	PUNCT
iajs-2557	52	49	adding	add	VERB
iajs-2557	52	50	(	(	PUNCT
iajs-2557	52	51	8)	8)	NUM
iajs-2557	52	52	,	,	PUNCT
iajs-2557	52	53	(	(	PUNCT
iajs-2557	52	54	9	9	NUM
iajs-2557	52	55	)	)	PUNCT
iajs-2557	52	56	and	and	CCONJ
iajs-2557	52	57	(	(	PUNCT
iajs-2557	52	58	10	10	NUM
iajs-2557	52	59	)	)	PUNCT
iajs-2557	52	60	,	,	PUNCT
iajs-2557	52	61	to	to	PART
iajs-2557	52	62	get	get	VERB
iajs-2557	52	63	:	:	PUNCT
iajs-2557	52	64	a(y⃗	a(y⃗	NOUN
iajs-2557	52	65	,	,	PUNCT
iajs-2557	52	66	v⃗	v⃗	ADJ
iajs-2557	52	67	)	)	PUNCT
iajs-2557	53	1	=	=	SYM
iajs-2557	53	2	f	f	PROPN
iajs-2557	53	3	(	(	PUNCT
iajs-2557	53	4	v⃗	v⃗	PROPN
iajs-2557	53	5	)	)	PUNCT
iajs-2557	53	6	,	,	PUNCT
iajs-2557	53	7	∀	∀	X
iajs-2557	53	8	v⃗	v⃗	PROPN
iajs-2557	53	9	∈	∈	PROPN
iajs-2557	53	10	v	v	ADP
iajs-2557	53	11	(	(	PUNCT
iajs-2557	53	12	11	11	NUM
iajs-2557	53	13	)	)	PUNCT
iajs-2557	53	14	where	where	SCONJ
iajs-2557	53	15	a(y⃗	a(y⃗	NOUN
iajs-2557	53	16	,	,	PUNCT
iajs-2557	53	17	v⃗	v⃗	ADJ
iajs-2557	53	18	)	)	PUNCT
iajs-2557	54	1	=	=	SYM
iajs-2557	54	2	a1	a1	NOUN
iajs-2557	54	3	(	(	PUNCT
iajs-2557	54	4	y1	y1	INTJ
iajs-2557	54	5	,	,	PUNCT
iajs-2557	54	6	v1	v1	NOUN
iajs-2557	54	7	)	)	PUNCT
iajs-2557	54	8	−	−	PROPN
iajs-2557	55	1	(	(	PUNCT
iajs-2557	55	2	y2	y2	NOUN
iajs-2557	55	3	+	+	CCONJ
iajs-2557	55	4	y3	y3	NOUN
iajs-2557	55	5	,	,	PUNCT
iajs-2557	55	6	v1	v1	NOUN
iajs-2557	55	7	)	)	PUNCT
iajs-2557	55	8	l2(ω	l2(ω	NUM
iajs-2557	55	9	)	)	PUNCT
iajs-2557	55	10	+	+	NUM
iajs-2557	55	11	a2	a2	PROPN
iajs-2557	55	12	(	(	PUNCT
iajs-2557	55	13	y2	y2	INTJ
iajs-2557	55	14	,	,	PUNCT
iajs-2557	55	15	v2	v2	PROPN
iajs-2557	55	16	)	)	PUNCT
iajs-2557	55	17	(	(	PUNCT
iajs-2557	55	18	y1	y1	INTJ
iajs-2557	55	19	+	+	NUM
iajs-2557	55	20	y3	y3	NOUN
iajs-2557	55	21	,	,	PUNCT
iajs-2557	55	22	v2	v2	PROPN
iajs-2557	55	23	)	)	PUNCT
iajs-2557	55	24	l2(ω	l2(ω	NUM
iajs-2557	55	25	)	)	PUNCT
iajs-2557	55	26	+	+	NUM
iajs-2557	55	27	a3	a3	NOUN
iajs-2557	55	28	(	(	PUNCT
iajs-2557	55	29	y3	y3	NOUN
iajs-2557	55	30	,	,	PUNCT
iajs-2557	55	31	v3	v3	PROPN
iajs-2557	55	32	)	)	PUNCT
iajs-2557	55	33	+	+	CCONJ
iajs-2557	56	1	(	(	PUNCT
iajs-2557	56	2	y1	y1	INTJ
iajs-2557	56	3	−	−	PROPN
iajs-2557	56	4	y2	y2	PROPN
iajs-2557	56	5	,	,	PUNCT
iajs-2557	56	6	v3	v3	PROPN
iajs-2557	56	7	)	)	PUNCT
iajs-2557	56	8	l2(ω	l2(ω	NOUN
iajs-2557	56	9	)	)	PUNCT
iajs-2557	56	10	(	(	PUNCT
iajs-2557	56	11	12a	12a	NOUN
iajs-2557	56	12	)	)	PUNCT
iajs-2557	56	13	ar(yr	ar(yr	PROPN
iajs-2557	56	14	,	,	PUNCT
iajs-2557	56	15	vr	vr	NOUN
iajs-2557	56	16	)	)	PUNCT
iajs-2557	57	1	=	=	SYM
iajs-2557	57	2	∫	∫	PROPN
iajs-2557	57	3	(	(	PUNCT
iajs-2557	57	4	∑	∑	ADV
iajs-2557	57	5	arij	arij	VERB
iajs-2557	57	6	∂yr	∂yr	PROPN
iajs-2557	57	7	∂xi	∂xi	PROPN
iajs-2557	57	8	∂vr	∂vr	PROPN
iajs-2557	57	9	∂xj	∂xj	PROPN
iajs-2557	57	10	+	+	CCONJ
iajs-2557	57	11	yrvr	yrvr	NOUN
iajs-2557	57	12	2	2	NUM
iajs-2557	57	13	i	i	NOUN
iajs-2557	57	14	,	,	PUNCT
iajs-2557	57	15	j=1	j=1	PROPN
iajs-2557	57	16	)	)	PUNCT
iajs-2557	58	1	ω	ω	PROPN
iajs-2557	58	2	dx	dx	PROPN
iajs-2557	58	3	,	,	PUNCT
iajs-2557	58	4	with	with	ADP
iajs-2557	58	5	ar(yr	ar(yr	PROPN
iajs-2557	58	6	,	,	PUNCT
iajs-2557	58	7	vr	vr	PROPN
iajs-2557	58	8	)	)	PUNCT
iajs-2557	58	9	≥	≥	PROPN
iajs-2557	58	10	c1r	c1r	NOUN
iajs-2557	58	11	‖yr‖h1(ω	‖yr‖h1(ω	PROPN
iajs-2557	58	12	)	)	PUNCT
iajs-2557	58	13	2	2	NUM
iajs-2557	58	14	,	,	PUNCT
iajs-2557	58	15	where	where	SCONJ
iajs-2557	58	16	c1r	c1r	PROPN
iajs-2557	58	17	≥	≥	X
iajs-2557	58	18	0	0	NUM
iajs-2557	58	19	,	,	PUNCT
iajs-2557	58	20	r	r	NOUN
iajs-2557	58	21	=	=	SYM
iajs-2557	58	22	1	1	NUM
iajs-2557	58	23	,	,	PUNCT
iajs-2557	58	24	2	2	NUM
iajs-2557	58	25	,	,	PUNCT
iajs-2557	58	26	3	3	NUM
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iajs-2557	58	28	,	,	PUNCT
iajs-2557	58	29	vr	vr	NOUN
iajs-2557	58	30	)	)	PUNCT
iajs-2557	58	31	|	|	ADV
iajs-2557	58	32	≤	≤	NUM
iajs-2557	58	33	c2r	c2r	NOUN
iajs-2557	58	34	‖yr‖h1(ω	‖yr‖h1(ω	NOUN
iajs-2557	58	35	)	)	PUNCT
iajs-2557	58	36	2	2	NUM
iajs-2557	58	37	‖vr‖h1(ω	‖vr‖h1(ω	NUM
iajs-2557	58	38	)	)	PUNCT
iajs-2557	58	39	,	,	PUNCT
iajs-2557	58	40	2	2	NUM
iajs-2557	58	41	,	,	PUNCT
iajs-2557	58	42	where	where	SCONJ
iajs-2557	58	43	c2r	c2r	NOUN
iajs-2557	58	44	≥	≥	NOUN
iajs-2557	58	45	0	0	NUM
iajs-2557	58	46	,	,	PUNCT
iajs-2557	58	47	r	r	NOUN
iajs-2557	58	48	=	=	SYM
iajs-2557	58	49	1	1	NUM
iajs-2557	58	50	,	,	PUNCT
iajs-2557	58	51	2	2	NUM
iajs-2557	58	52	,	,	PUNCT
iajs-2557	58	53	3	3	NUM
iajs-2557	58	54	a(y⃗	a(y⃗	NOUN
iajs-2557	58	55	,	,	PUNCT
iajs-2557	58	56	y⃗	y⃗	NOUN
iajs-2557	58	57	)	)	PUNCT
iajs-2557	58	58	≥	≥	NOUN
iajs-2557	58	59	∝1	∝1	NUM
iajs-2557	58	60	‖	‖	NUM
iajs-2557	58	61	y⃗	y⃗	NOUN
iajs-2557	58	62	‖	‖	ADJ
iajs-2557	58	63	(	(	PUNCT
iajs-2557	58	64	h1(ω	h1(ω	PROPN
iajs-2557	58	65	)	)	PUNCT
iajs-2557	58	66	)	)	PUNCT
iajs-2557	58	67	3	3	NUM
iajs-2557	58	68	2	2	NUM
iajs-2557	58	69	|a(y⃗	|a(y⃗	NOUN
iajs-2557	58	70	,	,	PUNCT
iajs-2557	58	71	v⃗	v⃗	ADJ
iajs-2557	58	72	)	)	PUNCT
iajs-2557	58	73	|	|	ADV
iajs-2557	58	74	≤	≤	NUM
iajs-2557	58	75	∝2	∝2	NOUN
iajs-2557	58	76	‖	‖	PROPN
iajs-2557	58	77	y⃗	y⃗	NOUN
iajs-2557	58	78	‖	‖	ADJ
iajs-2557	58	79	(	(	PUNCT
iajs-2557	58	80	h1(ω	h1(ω	PROPN
iajs-2557	58	81	)	)	PUNCT
iajs-2557	58	82	)	)	PUNCT
iajs-2557	58	83	3	3	NUM
iajs-2557	58	84	‖	‖	VERB
iajs-2557	58	85	v⃗	v⃗	VERB
iajs-2557	58	86	‖	‖	PROPN
iajs-2557	58	87	(	(	PUNCT
iajs-2557	58	88	h1(ω	h1(ω	PROPN
iajs-2557	58	89	)	)	PUNCT
iajs-2557	58	90	)	)	PUNCT
iajs-2557	58	91	3	3	NUM
iajs-2557	58	92	where	where	SCONJ
iajs-2557	58	93	‖	‖	PROPN
iajs-2557	58	94	y⃗	y⃗	NOUN
iajs-2557	58	95	‖	‖	ADJ
iajs-2557	58	96	(	(	PUNCT
iajs-2557	58	97	h1(ω	h1(ω	PROPN
iajs-2557	58	98	)	)	PUNCT
iajs-2557	58	99	)	)	PUNCT
iajs-2557	58	100	3	3	NUM
iajs-2557	58	101	2	2	NUM
iajs-2557	58	102	=	=	SYM
iajs-2557	58	103	‖	‖	PROPN
iajs-2557	58	104	y⃗	y⃗	NOUN
iajs-2557	58	105	‖	‖	PROPN
iajs-2557	58	106	(	(	PUNCT
iajs-2557	58	107	l2(ω	l2(ω	NOUN
iajs-2557	58	108	)	)	PUNCT
iajs-2557	58	109	)	)	PUNCT
iajs-2557	58	110	3	3	NUM
iajs-2557	58	111	2	2	NUM
iajs-2557	58	112	+	+	NUM
iajs-2557	58	113	‖∇	‖∇	NUM
iajs-2557	58	114	y⃗	y⃗	NOUN
iajs-2557	58	115	‖	‖	PROPN
iajs-2557	58	116	(	(	PUNCT
iajs-2557	58	117	l2(ω	l2(ω	NOUN
iajs-2557	58	118	)	)	PUNCT
iajs-2557	58	119	)	)	PUNCT
iajs-2557	58	120	3	3	NUM
iajs-2557	58	121	2	2	NUM
iajs-2557	58	122	,	,	PUNCT
iajs-2557	58	123	and	and	CCONJ
iajs-2557	58	124	f	f	X
iajs-2557	58	125	(	(	PUNCT
iajs-2557	58	126	v⃗	v⃗	PROPN
iajs-2557	58	127	)	)	PUNCT
iajs-2557	58	128	=	=	SYM
iajs-2557	58	129	(	(	PUNCT
iajs-2557	58	130	f1	f1	NOUN
iajs-2557	58	131	,	,	PUNCT
iajs-2557	58	132	v1)l2(ω	v1)l2(ω	ADV
iajs-2557	58	133	)	)	PUNCT
iajs-2557	59	1	+	+	CCONJ
iajs-2557	59	2	(	(	PUNCT
iajs-2557	59	3	u1	u1	NOUN
iajs-2557	59	4	,	,	PUNCT
iajs-2557	59	5	v1)l2(∂ω	v1)l2(∂ω	PROPN
iajs-2557	59	6	)	)	PUNCT
iajs-2557	60	1	+	+	CCONJ
iajs-2557	60	2	(	(	PUNCT
iajs-2557	60	3	f2	f2	INTJ
iajs-2557	60	4	,	,	PUNCT
iajs-2557	60	5	v2)l2(ω	v2)l2(ω	ADJ
iajs-2557	60	6	)	)	PUNCT
iajs-2557	61	1	+	+	CCONJ
iajs-2557	61	2	(	(	PUNCT
iajs-2557	61	3	u2	u2	PROPN
iajs-2557	61	4	,	,	PUNCT
iajs-2557	61	5	v2)l2(∂ω	v2)l2(∂ω	PROPN
iajs-2557	61	6	)	)	PUNCT
iajs-2557	62	1	+	+	CCONJ
iajs-2557	62	2	(	(	PUNCT
iajs-2557	62	3	f3	f3	ADJ
iajs-2557	62	4	,	,	PUNCT
iajs-2557	62	5	v3)l2(ω	v3)l2(ω	ADV
iajs-2557	62	6	)	)	PUNCT
iajs-2557	63	1	+	+	CCONJ
iajs-2557	63	2	(	(	PUNCT
iajs-2557	63	3	u3	u3	NOUN
iajs-2557	63	4	,	,	PUNCT
iajs-2557	63	5	v3)l2(∂ω	v3)l2(∂ω	NOUN
iajs-2557	63	6	)	)	PUNCT
iajs-2557	63	7	(	(	PUNCT
iajs-2557	63	8	12b	12b	X
iajs-2557	63	9	)	)	PUNCT
iajs-2557	63	10	assumptions	assumption	NOUN
iajs-2557	63	11	(	(	PUNCT
iajs-2557	63	12	a	a	X
iajs-2557	63	13	):	):	PUNCT
iajs-2557	63	14	a	a	NOUN
iajs-2557	63	15	)	)	PUNCT
iajs-2557	63	16	a	a	PROPN
iajs-2557	63	17	(	(	PUNCT
iajs-2557	63	18	y⃗	y⃗	NOUN
iajs-2557	63	19	,	,	PUNCT
iajs-2557	63	20	v⃗	v⃗	PROPN
iajs-2557	63	21	)	)	PUNCT
iajs-2557	63	22	is	be	AUX
iajs-2557	63	23	coercive	coercive	ADJ
iajs-2557	63	24	,	,	PUNCT
iajs-2557	63	25	i.	i.	PROPN
iajs-2557	63	26	e	e	PROPN
iajs-2557	63	27	,	,	PUNCT
iajs-2557	63	28	a	a	DET
iajs-2557	63	29	(	(	PUNCT
iajs-2557	63	30	y⃗	y⃗	NOUN
iajs-2557	63	31	,	,	PUNCT
iajs-2557	63	32	y⃗	y⃗	NOUN
iajs-2557	63	33	)	)	PUNCT
iajs-2557	63	34	≥	≥	NOUN
iajs-2557	63	35	c‖	c‖	PROPN
iajs-2557	63	36	y⃗	y⃗	PROPN
iajs-2557	63	37	‖	‖	PROPN
iajs-2557	63	38	(	(	PUNCT
iajs-2557	63	39	h1(ω	h1(ω	PROPN
iajs-2557	63	40	)	)	PUNCT
iajs-2557	63	41	)	)	PUNCT
iajs-2557	63	42	3	3	NUM
iajs-2557	63	43	2	2	NUM
iajs-2557	63	44	.	.	PUNCT
iajs-2557	64	1	b	b	X
iajs-2557	64	2	)	)	PUNCT
iajs-2557	64	3	|a	|a	NOUN
iajs-2557	64	4	(	(	PUNCT
iajs-2557	64	5	y⃗	y⃗	NOUN
iajs-2557	64	6	,	,	PUNCT
iajs-2557	64	7	y⃗	y⃗	NOUN
iajs-2557	64	8	)	)	PUNCT
iajs-2557	64	9	|	|	ADV
iajs-2557	64	10	≤	≤	NUM
iajs-2557	64	11	c1‖	c1‖	VERB
iajs-2557	64	12	y⃗	y⃗	NOUN
iajs-2557	64	13	‖	‖	PROPN
iajs-2557	64	14	(	(	PUNCT
iajs-2557	64	15	h1(ω	h1(ω	PROPN
iajs-2557	64	16	)	)	PUNCT
iajs-2557	64	17	)	)	PUNCT
iajs-2557	64	18	3	3	NUM
iajs-2557	64	19	2	2	NUM
iajs-2557	64	20	‖	‖	VERB
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iajs-2557	64	22	‖	‖	PROPN
iajs-2557	64	23	(	(	PUNCT
iajs-2557	64	24	h1(ω	h1(ω	PROPN
iajs-2557	64	25	)	)	PUNCT
iajs-2557	64	26	)	)	PUNCT
iajs-2557	64	27	3	3	NUM
iajs-2557	65	1	where	where	SCONJ
iajs-2557	65	2	c1	c1	PROPN
iajs-2557	65	3	>	>	X
iajs-2557	65	4	0	0	PUNCT
iajs-2557	65	5	.	.	PUNCT
iajs-2557	66	1	c	c	X
iajs-2557	66	2	)	)	PUNCT
iajs-2557	66	3	|f	|f	PROPN
iajs-2557	66	4	(	(	PUNCT
iajs-2557	66	5	v⃗	v⃗	PROPN
iajs-2557	66	6	)	)	PUNCT
iajs-2557	66	7	|	|	ADV
iajs-2557	66	8	≤	≤	NUM
iajs-2557	67	1	c2‖	c2‖	PROPN
iajs-2557	67	2	v⃗	v⃗	VERB
iajs-2557	67	3	‖(l2(ω	‖(l2(ω	PROPN
iajs-2557	67	4	)	)	PUNCT
iajs-2557	67	5	)	)	PUNCT
iajs-2557	67	6	3	3	NUM
iajs-2557	67	7	,	,	PUNCT
iajs-2557	67	8	∀	∀	PUNCT
iajs-2557	67	9	v⃗	v⃗	PROPN
iajs-2557	67	10	∈	∈	PROPN
iajs-2557	67	11	v	v	NOUN
iajs-2557	67	12	,	,	PUNCT
iajs-2557	67	13	c2	c2	PROPN
iajs-2557	67	14	>	>	X
iajs-2557	67	15	0	0	PUNCT
iajs-2557	67	16	.	.	PUNCT
iajs-2557	68	1	to	to	PART
iajs-2557	68	2	find	find	VERB
iajs-2557	68	3	the	the	DET
iajs-2557	68	4	solution	solution	NOUN
iajs-2557	68	5	of	of	ADP
iajs-2557	68	6	(	(	PUNCT
iajs-2557	68	7	11	11	NUM
iajs-2557	68	8	)	)	PUNCT
iajs-2557	68	9	,	,	PUNCT
iajs-2557	68	10	the	the	DET
iajs-2557	68	11	gme	gme	NOUN
iajs-2557	68	12	is	be	AUX
iajs-2557	68	13	applied	apply	VERB
iajs-2557	68	14	,	,	PUNCT
iajs-2557	68	15	and	and	CCONJ
iajs-2557	68	16	an	an	DET
iajs-2557	68	17	approximation	approximation	NOUN
iajs-2557	68	18	(	(	PUNCT
iajs-2557	68	19	app	app	NOUN
iajs-2557	68	20	)	)	PUNCT
iajs-2557	68	21	subspace	subspace	NOUN
iajs-2557	68	22	v⃗⃗	v⃗⃗	PROPN
iajs-2557	68	23	n	n	PROPN
iajs-2557	68	24	⊂	⊂	PROPN
iajs-2557	68	25	v⃗⃗	v⃗⃗	PROPN
iajs-2557	68	26	(	(	PUNCT
iajs-2557	68	27	v⃗⃗	v⃗⃗	PROPN
iajs-2557	68	28	n	n	PROPN
iajs-2557	68	29	is	be	AUX
iajs-2557	68	30	the	the	DET
iajs-2557	68	31	set	set	NOUN
iajs-2557	68	32	of	of	ADP
iajs-2557	68	33	continuous	continuous	ADJ
iajs-2557	68	34	function	function	NOUN
iajs-2557	68	35	in	in	ADP
iajs-2557	68	36	ω	ω	PROPN
iajs-2557	68	37	)	)	PUNCT
iajs-2557	68	38	is	be	AUX
iajs-2557	68	39	chose	choose	VERB
iajs-2557	68	40	,	,	PUNCT
iajs-2557	68	41	thus	thus	ADV
iajs-2557	68	42	(	(	PUNCT
iajs-2557	68	43	11	11	NUM
iajs-2557	68	44	)	)	PUNCT
iajs-2557	68	45	will	will	AUX
iajs-2557	68	46	be	be	AUX
iajs-2557	68	47	in	in	ADP
iajs-2557	68	48	the	the	DET
iajs-2557	68	49	following	follow	VERB
iajs-2557	68	50	app	app	NOUN
iajs-2557	68	51	form	form	NOUN
iajs-2557	68	52	:	:	PUNCT
iajs-2557	68	53	a	a	DET
iajs-2557	68	54	(	(	PUNCT
iajs-2557	68	55	y⃗	y⃗	NOUN
iajs-2557	68	56	n	n	NOUN
iajs-2557	68	57	,	,	PUNCT
iajs-2557	68	58	v⃗	v⃗	ADJ
iajs-2557	68	59	)	)	PUNCT
iajs-2557	69	1	=	=	SYM
iajs-2557	70	1	f	f	X
iajs-2557	70	2	(	(	PUNCT
iajs-2557	70	3	v⃗	v⃗	PROPN
iajs-2557	70	4	)	)	PUNCT
iajs-2557	70	5	,	,	PUNCT
iajs-2557	70	6	∀	∀	PUNCT
iajs-2557	70	7	y⃗	y⃗	NOUN
iajs-2557	70	8	n	n	NOUN
iajs-2557	70	9	,	,	PUNCT
iajs-2557	70	10	v⃗	v⃗	PROPN
iajs-2557	70	11	∈	∈	PROPN
iajs-2557	70	12	v⃗⃗	v⃗⃗	PROPN
iajs-2557	70	13	n	n	PROPN
iajs-2557	70	14	(	(	PUNCT
iajs-2557	70	15	13	13	NUM
iajs-2557	70	16	)	)	PUNCT
iajs-2557	70	17	theorem	theorem	VERB
iajs-2557	70	18	3.1	3.1	NUM
iajs-2557	70	19	:	:	PUNCT
iajs-2557	70	20	if	if	SCONJ
iajs-2557	70	21	u⃗	u⃗	PROPN
iajs-2557	70	22	∈	∈	PROPN
iajs-2557	70	23	(	(	PUNCT
iajs-2557	70	24	l2(∂ω	l2(∂ω	NUM
iajs-2557	70	25	)	)	PUNCT
iajs-2557	70	26	)	)	PUNCT
iajs-2557	70	27	3	3	NUM
iajs-2557	70	28	,	,	PUNCT
iajs-2557	70	29	is	be	AUX
iajs-2557	70	30	a	a	DET
iajs-2557	70	31	given	give	VERB
iajs-2557	70	32	nbcv	nbcv	NOUN
iajs-2557	70	33	,	,	PUNCT
iajs-2557	70	34	then	then	ADV
iajs-2557	70	35	problem	problem	NOUN
iajs-2557	70	36	(	(	PUNCT
iajs-2557	70	37	13	13	NUM
iajs-2557	70	38	)	)	PUNCT
iajs-2557	70	39	has	have	VERB
iajs-2557	70	40	a	a	DET
iajs-2557	70	41	unique	unique	ADJ
iajs-2557	70	42	app	app	NOUN
iajs-2557	70	43	solution(apps	solution(app	NOUN
iajs-2557	70	44	)	)	PUNCT
iajs-2557	70	45	y⃗	y⃗	NOUN
iajs-2557	70	46	n	n	NOUN
iajs-2557	70	47	∈	∈	NOUN
iajs-2557	70	48	v⃗⃗	v⃗⃗	PROPN
iajs-2557	70	49	n	n	PRON
iajs-2557	70	50	proof	proof	NOUN
iajs-2557	70	51	:	:	PUNCT
iajs-2557	70	52	let	let	VERB
iajs-2557	70	53	{	{	PUNCT
iajs-2557	70	54	φ⃗⃗	φ⃗⃗	NOUN
iajs-2557	70	55	1	1	NUM
iajs-2557	70	56	,	,	PUNCT
iajs-2557	70	57	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	70	58	2	2	NUM
iajs-2557	70	59	,	,	PUNCT
iajs-2557	70	60	…	…	PUNCT
iajs-2557	70	61	……	……	NOUN
iajs-2557	70	62	,	,	PUNCT
iajs-2557	70	63	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	70	64	n	n	CCONJ
iajs-2557	70	65	}	}	PUNCT
iajs-2557	70	66	span	span	NOUN
iajs-2557	70	67	v⃗⃗	v⃗⃗	PROPN
iajs-2557	70	68	n	n	PROPN
iajs-2557	70	69	,	,	PUNCT
iajs-2557	70	70	then	then	ADV
iajs-2557	70	71	the	the	DET
iajs-2557	70	72	apps	app	NOUN
iajs-2557	70	73	of	of	ADP
iajs-2557	70	74	(	(	PUNCT
iajs-2557	70	75	13	13	NUM
iajs-2557	70	76	)	)	PUNCT
iajs-2557	70	77	is	be	AUX
iajs-2557	70	78	written	write	VERB
iajs-2557	70	79	by	by	ADP
iajs-2557	70	80	:	:	PUNCT
iajs-2557	70	81	y⃗	y⃗	NOUN
iajs-2557	71	1	n	n	NOUN
iajs-2557	71	2	=	=	SYM
iajs-2557	71	3	∑	∑	PUNCT
iajs-2557	71	4	dj	dj	PROPN
iajs-2557	71	5	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	71	6	j	j	PROPN
iajs-2557	71	7	(	(	PUNCT
iajs-2557	71	8	x1	x1	PROPN
iajs-2557	71	9	,	,	PUNCT
iajs-2557	71	10	x2	x2	PROPN
iajs-2557	71	11	)	)	PUNCT
iajs-2557	71	12	n	n	CCONJ
iajs-2557	72	1	j=1	j=1	NOUN
iajs-2557	73	1	(	(	PUNCT
iajs-2557	73	2	14	14	NUM
iajs-2557	73	3	)	)	PUNCT
iajs-2557	73	4	where	where	SCONJ
iajs-2557	73	5	∅⃗⃗	∅⃗⃗	NOUN
iajs-2557	73	6	j	j	NOUN
iajs-2557	73	7	=	=	PUNCT
iajs-2557	73	8	(	(	PUNCT
iajs-2557	73	9	(	(	PUNCT
iajs-2557	73	10	4	4	NUM
iajs-2557	73	11	ℓ	ℓ	NOUN
iajs-2557	73	12	mod	mod	NOUN
iajs-2557	73	13	(	(	PUNCT
iajs-2557	73	14	4	4	NUM
iajs-2557	73	15	−	−	NOUN
iajs-2557	73	16	ℓ	ℓ	NUM
iajs-2557	73	17	)	)	PUNCT
iajs-2557	73	18	)	)	PUNCT
iajs-2557	73	19	φk	φk	ADP
iajs-2557	73	20	,	,	PUNCT
iajs-2557	73	21	(	(	PUNCT
iajs-2557	73	22	4	4	NUM
iajs-2557	73	23	mod	mod	NOUN
iajs-2557	73	24	(	(	PUNCT
iajs-2557	73	25	ℓ	ℓ	PROPN
iajs-2557	73	26	+	+	PROPN
iajs-2557	73	27	1	1	NUM
iajs-2557	73	28	)	)	PUNCT
iajs-2557	73	29	)	)	PUNCT
iajs-2557	73	30	φk	φk	ADP
iajs-2557	73	31	,	,	PUNCT
iajs-2557	73	32	(	(	PUNCT
iajs-2557	73	33	(	(	PUNCT
iajs-2557	73	34	4	4	NUM
iajs-2557	73	35	+	+	CCONJ
iajs-2557	73	36	ℓ2)mod	ℓ2)mod	PROPN
iajs-2557	73	37	(	(	PUNCT
iajs-2557	73	38	ℓ	ℓ	NOUN
iajs-2557	73	39	)	)	PUNCT
iajs-2557	73	40	)	)	PUNCT
iajs-2557	73	41	φk	φk	ADP
iajs-2557	73	42	)	)	PUNCT
iajs-2557	73	43	,	,	PUNCT
iajs-2557	74	1	ℓ	ℓ	X
iajs-2557	74	2	=	=	SYM
iajs-2557	74	3	1	1	NUM
iajs-2557	74	4	,	,	PUNCT
iajs-2557	74	5	2,3	2,3	NUM
iajs-2557	74	6	j	j	X
iajs-2557	74	7	=	=	SYM
iajs-2557	74	8	k	k	PROPN
iajs-2557	75	1	+	+	CCONJ
iajs-2557	75	2	n(ℓ	n(ℓ	NOUN
iajs-2557	75	3	−	−	NOUN
iajs-2557	75	4	1	1	NUM
iajs-2557	75	5	)	)	PUNCT
iajs-2557	75	6	and	and	CCONJ
iajs-2557	75	7	dj	dj	NOUN
iajs-2557	75	8	=	=	NOUN
iajs-2557	75	9	dℓk	dℓk	NOUN
iajs-2557	75	10	is	be	AUX
iajs-2557	75	11	unknown	unknown	ADJ
iajs-2557	75	12	constant	constant	ADJ
iajs-2557	75	13	,	,	PUNCT
iajs-2557	75	14	∀	∀	X
iajs-2557	75	15	j	j	NOUN
iajs-2557	75	16	=	=	SYM
iajs-2557	75	17	1	1	NUM
iajs-2557	75	18	,	,	PUNCT
iajs-2557	75	19	2	2	NUM
iajs-2557	75	20	,	,	PUNCT
iajs-2557	75	21	…	…	PUNCT
iajs-2557	75	22	…	…	PUNCT
iajs-2557	75	23	,	,	PUNCT
iajs-2557	75	24	n	n	CCONJ
iajs-2557	75	25	,	,	PUNCT
iajs-2557	75	26	with	with	ADP
iajs-2557	75	27	n	n	NOUN
iajs-2557	75	28	=	=	SYM
iajs-2557	75	29	3n	3n	NOUN
iajs-2557	75	30	by	by	ADP
iajs-2557	75	31	substituting	substitute	VERB
iajs-2557	75	32	(	(	PUNCT
iajs-2557	75	33	14	14	NUM
iajs-2557	75	34	)	)	PUNCT
iajs-2557	75	35	in	in	ADP
iajs-2557	75	36	(	(	PUNCT
iajs-2557	75	37	13	13	NUM
iajs-2557	75	38	)	)	PUNCT
iajs-2557	75	39	,	,	PUNCT
iajs-2557	75	40	with	with	ADP
iajs-2557	75	41	v⃗	v⃗	PROPN
iajs-2557	75	42	=	=	SYM
iajs-2557	75	43	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	75	44	i	i	PRON
iajs-2557	75	45	,	,	PUNCT
iajs-2557	75	46	we	we	PRON
iajs-2557	75	47	get	get	VERB
iajs-2557	75	48	:	:	PUNCT
iajs-2557	75	49	∑	∑	PUNCT
iajs-2557	75	50	dj	dj	ADP
iajs-2557	75	51	a(φ⃗⃗	a(φ⃗⃗	PROPN
iajs-2557	75	52	j	j	PROPN
iajs-2557	75	53	,	,	PUNCT
iajs-2557	75	54	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	75	55	i	i	PROPN
iajs-2557	75	56	)	)	PUNCT
iajs-2557	76	1	=	=	SYM
iajs-2557	76	2	f(φ⃗⃗	f(φ⃗⃗	VERB
iajs-2557	76	3	i	i	PROPN
iajs-2557	76	4	)	)	PUNCT
iajs-2557	76	5	,	,	PUNCT
iajs-2557	76	6	∀	∀	PUNCT
iajs-2557	77	1	i	i	NOUN
iajs-2557	77	2	=	=	NOUN
iajs-2557	77	3	1	1	NUM
iajs-2557	77	4	,	,	PUNCT
iajs-2557	77	5	2	2	NUM
iajs-2557	77	6	,	,	PUNCT
iajs-2557	77	7	…	…	PUNCT
iajs-2557	77	8	,	,	PUNCT
iajs-2557	77	9	nn	nn	X
iajs-2557	77	10	j=1	j=1	X
iajs-2557	77	11	(	(	PUNCT
iajs-2557	77	12	15	15	NUM
iajs-2557	77	13	)	)	PUNCT
iajs-2557	77	14	it	it	PRON
iajs-2557	77	15	is	be	AUX
iajs-2557	77	16	clear	clear	ADJ
iajs-2557	77	17	that	that	SCONJ
iajs-2557	77	18	(	(	PUNCT
iajs-2557	77	19	15	15	NUM
iajs-2557	77	20	)	)	PUNCT
iajs-2557	77	21	is	be	AUX
iajs-2557	77	22	equivalent	equivalent	ADJ
iajs-2557	77	23	to	to	ADP
iajs-2557	77	24	the	the	DET
iajs-2557	77	25	algebraic	algebraic	ADJ
iajs-2557	77	26	system	system	NOUN
iajs-2557	77	27	.	.	PUNCT
iajs-2557	78	1	an×n	an×n	ADJ
iajs-2557	78	2	dn	dn	NOUN
iajs-2557	78	3	×1	×1	NOUN
iajs-2557	78	4	=	=	SYM
iajs-2557	78	5	bn	bn	NUM
iajs-2557	78	6	×1	×1	NOUN
iajs-2557	78	7	(	(	PUNCT
iajs-2557	78	8	16	16	NUM
iajs-2557	78	9	)	)	PUNCT
iajs-2557	78	10	where	where	SCONJ
iajs-2557	78	11	an×n	an×n	PROPN
iajs-2557	78	12	=	=	SYM
iajs-2557	78	13	(	(	PUNCT
iajs-2557	78	14	aij	aij	PROPN
iajs-2557	78	15	)	)	PUNCT
iajs-2557	78	16	n×n	n×n	PROPN
iajs-2557	78	17	,	,	PUNCT
iajs-2557	78	18	aij	aij	PROPN
iajs-2557	78	19	=	=	SYM
iajs-2557	78	20	a	a	PRON
iajs-2557	78	21	(	(	PUNCT
iajs-2557	78	22	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	78	23	j	j	PROPN
iajs-2557	78	24	,	,	PUNCT
iajs-2557	78	25	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	78	26	i	i	PROPN
iajs-2557	78	27	)	)	PUNCT
iajs-2557	78	28	,	,	PUNCT
iajs-2557	78	29	bn	bn	NOUN
iajs-2557	78	30	×1	×1	NOUN
iajs-2557	78	31	=	=	SYM
iajs-2557	78	32	(	(	PUNCT
iajs-2557	78	33	b1	b1	NOUN
iajs-2557	78	34	,	,	PUNCT
iajs-2557	78	35	b2	b2	NOUN
iajs-2557	78	36	,	,	PUNCT
iajs-2557	78	37	…	…	PUNCT
iajs-2557	78	38	.	.	PUNCT
iajs-2557	79	1	bn	bn	X
iajs-2557	79	2	)	)	PUNCT
iajs-2557	79	3	t	t	NOUN
iajs-2557	79	4	,	,	PUNCT
iajs-2557	79	5	bi	bi	NOUN
iajs-2557	79	6	=	=	PROPN
iajs-2557	79	7	f	f	PROPN
iajs-2557	79	8	(	(	PUNCT
iajs-2557	79	9	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	79	10	i	i	PROPN
iajs-2557	79	11	)	)	PUNCT
iajs-2557	79	12	63	63	NUM
iajs-2557	79	13	ibn	ibn	PROPN
iajs-2557	79	14	al	al	PROPN
iajs-2557	79	15	-	-	PUNCT
iajs-2557	79	16	haitham	haitham	PROPN
iajs-2557	79	17	jour	jour	X
iajs-2557	79	18	.	.	PROPN
iajs-2557	80	1	for	for	ADP
iajs-2557	80	2	pure	pure	ADJ
iajs-2557	80	3	&	&	CCONJ
iajs-2557	80	4	appl	appl	PROPN
iajs-2557	80	5	.	.	PUNCT
iajs-2557	81	1	sci	sci	PROPN
iajs-2557	81	2	.	.	PROPN
iajs-2557	82	1	34	34	NUM
iajs-2557	82	2	(	(	PUNCT
iajs-2557	82	3	1	1	NUM
iajs-2557	82	4	)	)	PUNCT
iajs-2557	82	5	2021	2021	NUM
iajs-2557	82	6	and	and	CCONJ
iajs-2557	82	7	dn	dn	NOUN
iajs-2557	82	8	×1	×1	NOUN
iajs-2557	82	9	=	=	SYM
iajs-2557	82	10	(	(	PUNCT
iajs-2557	82	11	d1	d1	PROPN
iajs-2557	82	12	,	,	PUNCT
iajs-2557	82	13	d2	d2	PROPN
iajs-2557	82	14	,	,	PUNCT
iajs-2557	82	15	…	…	PUNCT
iajs-2557	82	16	.	.	PUNCT
iajs-2557	83	1	dn	dn	X
iajs-2557	83	2	)	)	PUNCT
iajs-2557	83	3	t	t	PROPN
iajs-2557	83	4	,	,	PUNCT
iajs-2557	83	5	i	i	PRON
iajs-2557	83	6	,	,	PUNCT
iajs-2557	83	7	j	j	PROPN
iajs-2557	83	8	=	=	SYM
iajs-2557	83	9	1	1	NUM
iajs-2557	83	10	,	,	PUNCT
iajs-2557	83	11	2	2	NUM
iajs-2557	83	12	,	,	PUNCT
iajs-2557	83	13	…	…	PUNCT
iajs-2557	83	14	,	,	PUNCT
iajs-2557	83	15	n.	n.	NOUN
iajs-2557	83	16	since	since	SCONJ
iajs-2557	83	17	an×n	an×n	PROPN
iajs-2557	83	18	dn	dn	NOUN
iajs-2557	83	19	×1	×1	NOUN
iajs-2557	83	20	=	=	SYM
iajs-2557	83	21	0	0	NUM
iajs-2557	83	22	⟹	⟹	PROPN
iajs-2557	83	23	𝑎(∑	𝑎(∑	PROPN
iajs-2557	83	24	𝑑𝑗	𝑑𝑗	ADP
iajs-2557	83	25	𝑛	𝑛	DET
iajs-2557	83	26	𝑗=1	𝑗=1	PROPN
iajs-2557	83	27	�	�	PROPN
iajs-2557	83	28	⃗	⃗	NOUN
iajs-2557	83	29	�	�	X
iajs-2557	83	30	𝑗	𝑗	PROPN
iajs-2557	83	31	,	,	PUNCT
iajs-2557	83	32	�	�	PROPN
iajs-2557	83	33	⃗	⃗	NOUN
iajs-2557	83	34	�	�	PROPN
iajs-2557	83	35	𝑖	𝑖	NUM
iajs-2557	83	36	)	)	PUNCT
iajs-2557	83	37	=	=	SYM
iajs-2557	83	38	0	0	NUM
iajs-2557	83	39	,	,	PUNCT
iajs-2557	83	40	then	then	ADV
iajs-2557	83	41	from	from	ADP
iajs-2557	83	42	using	use	VERB
iajs-2557	83	43	(	(	PUNCT
iajs-2557	83	44	a	a	DET
iajs-2557	83	45	–	–	PUNCT
iajs-2557	83	46	a	a	NOUN
iajs-2557	83	47	)	)	PUNCT
iajs-2557	83	48	𝑐‖∑	𝑐‖∑	PROPN
iajs-2557	83	49	𝑑	𝑑	NOUN
iajs-2557	83	50	�	�	NOUN
iajs-2557	83	51	⃗	⃗	NOUN
iajs-2557	83	52	�	�	NOUN
iajs-2557	83	53	𝑗	𝑗	VERB
iajs-2557	83	54	𝑛	𝑛	PRON
iajs-2557	84	1	𝑗=1	𝑗=1	PROPN
iajs-2557	84	2	‖	‖	PROPN
iajs-2557	84	3	(	(	PUNCT
iajs-2557	84	4	𝐻¹(ω	𝐻¹(ω	ADJ
iajs-2557	84	5	)	)	PUNCT
iajs-2557	84	6	)	)	PUNCT
iajs-2557	84	7	2	2	NUM
iajs-2557	84	8	2	2	NUM
iajs-2557	84	9	≤	≤	NOUN
iajs-2557	84	10	∑	∑	PUNCT
iajs-2557	84	11	𝑑𝑖𝑎	𝑑𝑖𝑎	X
iajs-2557	84	12	𝑛	𝑛	ADP
iajs-2557	84	13	𝑖=1	𝑖=1	PROPN
iajs-2557	84	14	(	(	PUNCT
iajs-2557	84	15	∑	∑	PROPN
iajs-2557	84	16	𝑑𝑗	𝑑𝑗	PROPN
iajs-2557	84	17	�	�	NOUN
iajs-2557	84	18	⃗	⃗	NOUN
iajs-2557	84	19	�	�	PROPN
iajs-2557	84	20	𝑗	𝑗	PROPN
iajs-2557	84	21	𝑛	𝑛	PROPN
iajs-2557	84	22	𝑗=1	𝑗=1	PROPN
iajs-2557	84	23	,	,	PUNCT
iajs-2557	84	24	�	�	PROPN
iajs-2557	84	25	⃗	⃗	NOUN
iajs-2557	84	26	�	�	PROPN
iajs-2557	84	27	𝑖	𝑖	NUM
iajs-2557	84	28	)	)	PUNCT
iajs-2557	84	29	=	=	SYM
iajs-2557	84	30	0	0	NUM
iajs-2557	85	1	the	the	DET
iajs-2557	85	2	uniqueness	uniqueness	NOUN
iajs-2557	85	3	(	(	PUNCT
iajs-2557	85	4	16	16	NUM
iajs-2557	85	5	)	)	PUNCT
iajs-2557	85	6	is	be	AUX
iajs-2557	85	7	obtained	obtain	VERB
iajs-2557	85	8	from	from	ADP
iajs-2557	85	9	its	its	PRON
iajs-2557	85	10	corresponding	corresponding	ADJ
iajs-2557	85	11	homogeneous	homogeneous	ADJ
iajs-2557	85	12	system	system	NOUN
iajs-2557	85	13	.	.	PUNCT
iajs-2557	86	1	proposition	proposition	NOUN
iajs-2557	86	2	3.1	3.1	NUM
iajs-2557	87	1	[	[	X
iajs-2557	87	2	6	6	NUM
iajs-2557	87	3	]	]	X
iajs-2557	87	4	:	:	PUNCT
iajs-2557	87	5	for	for	ADP
iajs-2557	87	6	any	any	DET
iajs-2557	87	7	v⃗	v⃗	NOUN
iajs-2557	87	8	in	in	ADP
iajs-2557	87	9	v⃗⃗	v⃗⃗	PROPN
iajs-2557	87	10	,	,	PUNCT
iajs-2557	87	11	v⃗⃗	v⃗⃗	PROPN
iajs-2557	87	12	n	n	PRON
iajs-2557	87	13	has	have	VERB
iajs-2557	87	14	a	a	DET
iajs-2557	87	15	sequence	sequence	NOUN
iajs-2557	87	16	{	{	PUNCT
iajs-2557	87	17	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	87	18	n	n	CCONJ
iajs-2557	87	19	}	}	PUNCT
iajs-2557	87	20	with	with	ADP
iajs-2557	87	21	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	87	22	n	n	CCONJ
iajs-2557	87	23	∈	∈	PROPN
iajs-2557	87	24	v⃗⃗	v⃗⃗	PROPN
iajs-2557	87	25	n	n	PRON
iajs-2557	87	26	,	,	PUNCT
iajs-2557	87	27	∀	∀	X
iajs-2557	87	28	n	n	X
iajs-2557	87	29	for	for	ADP
iajs-2557	87	30	which	which	PRON
iajs-2557	87	31	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	87	32	n	n	PROPN
iajs-2557	87	33	→	→	PUNCT
iajs-2557	87	34	v⃗⃗	v⃗⃗	VERB
iajs-2557	87	35	strongly	strongly	ADV
iajs-2557	87	36	in	in	ADP
iajs-2557	87	37	v⃗⃗	v⃗⃗	PROPN
iajs-2557	87	38	.	.	PUNCT
iajs-2557	88	1	now	now	ADV
iajs-2557	88	2	,	,	PUNCT
iajs-2557	88	3	by	by	ADP
iajs-2557	88	4	theorem	theorem	NOUN
iajs-2557	88	5	3.1	3.1	NUM
iajs-2557	88	6	,	,	PUNCT
iajs-2557	88	7	the	the	DET
iajs-2557	88	8	following	follow	VERB
iajs-2557	88	9	sequence	sequence	NOUN
iajs-2557	88	10	of	of	ADP
iajs-2557	88	11	the	the	DET
iajs-2557	88	12	wfo	wfo	NOUN
iajs-2557	88	13	has	have	VERB
iajs-2557	88	14	a	a	DET
iajs-2557	88	15	sequence	sequence	NOUN
iajs-2557	88	16	for	for	ADP
iajs-2557	88	17	the	the	DET
iajs-2557	88	18	solutions	solution	NOUN
iajs-2557	88	19	{	{	PUNCT
iajs-2557	88	20	y⃗	y⃗	NOUN
iajs-2557	88	21	n	n	CCONJ
iajs-2557	88	22	}	}	PUNCT
iajs-2557	88	23	n=1	n=1	PROPN
iajs-2557	88	24	∞	∞	PROPN
iajs-2557	88	25	a	a	PROPN
iajs-2557	88	26	(	(	PUNCT
iajs-2557	88	27	y⃗	y⃗	NOUN
iajs-2557	88	28	n	n	NOUN
iajs-2557	88	29	,	,	PUNCT
iajs-2557	88	30	φ⃗⃗	φ⃗⃗	NOUN
iajs-2557	88	31	n	n	PROPN
iajs-2557	88	32	)	)	PUNCT
iajs-2557	89	1	=	=	SYM
iajs-2557	90	1	f	f	X
iajs-2557	90	2	(	(	PUNCT
iajs-2557	90	3	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	90	4	n	n	PROPN
iajs-2557	90	5	)	)	PUNCT
iajs-2557	90	6	,	,	PUNCT
iajs-2557	90	7	∀	∀	PUNCT
iajs-2557	90	8	y⃗	y⃗	NOUN
iajs-2557	90	9	n	n	NOUN
iajs-2557	90	10	,	,	PUNCT
iajs-2557	90	11	φ⃗⃗	φ⃗⃗	NOUN
iajs-2557	90	12	n	n	CCONJ
iajs-2557	90	13	∈	∈	PROPN
iajs-2557	90	14	v⃗⃗	v⃗⃗	PROPN
iajs-2557	90	15	n	n	PRON
iajs-2557	90	16	,	,	PUNCT
iajs-2557	90	17	∀	∀	X
iajs-2557	90	18	n	n	CCONJ
iajs-2557	90	19	(	(	PUNCT
iajs-2557	90	20	17	17	NUM
iajs-2557	90	21	)	)	PUNCT
iajs-2557	90	22	theorem	theorem	VERB
iajs-2557	90	23	3.2	3.2	NUM
iajs-2557	90	24	:	:	PUNCT
iajs-2557	90	25	the	the	DET
iajs-2557	90	26	sequence	sequence	NOUN
iajs-2557	90	27	{	{	PUNCT
iajs-2557	90	28	y⃗	y⃗	NOUN
iajs-2557	90	29	n	n	CCONJ
iajs-2557	90	30	}	}	PUNCT
iajs-2557	90	31	n=1	n=1	PROPN
iajs-2557	90	32	∞	∞	PROPN
iajs-2557	90	33	converges	converge	VERB
iajs-2557	90	34	to	to	ADP
iajs-2557	90	35	y⃗	y⃗	NOUN
iajs-2557	90	36	strongly	strongly	ADV
iajs-2557	90	37	in	in	ADP
iajs-2557	90	38	(	(	PUNCT
iajs-2557	90	39	h1(ω	h1(ω	PROPN
iajs-2557	90	40	)	)	PUNCT
iajs-2557	90	41	)	)	PUNCT
iajs-2557	90	42	3	3	NUM
iajs-2557	90	43	.	.	PUNCT
iajs-2557	91	1	proof	proof	NOUN
iajs-2557	91	2	:	:	PUNCT
iajs-2557	91	3	we	we	PRON
iajs-2557	91	4	have	have	VERB
iajs-2557	91	5	y⃗	y⃗	NOUN
iajs-2557	91	6	n	n	PART
iajs-2557	91	7	is	be	AUX
iajs-2557	91	8	a	a	DET
iajs-2557	91	9	solution	solution	NOUN
iajs-2557	91	10	of	of	ADP
iajs-2557	91	11	(	(	PUNCT
iajs-2557	91	12	17	17	NUM
iajs-2557	91	13	)	)	PUNCT
iajs-2557	91	14	,	,	PUNCT
iajs-2557	91	15	then	then	ADV
iajs-2557	91	16	by	by	ADP
iajs-2557	91	17	(	(	PUNCT
iajs-2557	91	18	a	a	PRON
iajs-2557	91	19	–	–	PUNCT
iajs-2557	91	20	a	a	PRON
iajs-2557	91	21	&	&	CCONJ
iajs-2557	91	22	c	c	NOUN
iajs-2557	91	23	)	)	PUNCT
iajs-2557	91	24	:	:	PUNCT
iajs-2557	92	1	‖	‖	NUM
iajs-2557	92	2	y⃗	y⃗	NOUN
iajs-2557	92	3	n	n	X
iajs-2557	92	4	‖	‖	PROPN
iajs-2557	92	5	(	(	PUNCT
iajs-2557	92	6	h1(ω	h1(ω	PROPN
iajs-2557	92	7	)	)	PUNCT
iajs-2557	92	8	)	)	PUNCT
iajs-2557	92	9	3	3	NUM
iajs-2557	92	10	≤	≤	NUM
iajs-2557	92	11	c̅1	c̅1	PROPN
iajs-2557	92	12	,	,	PUNCT
iajs-2557	92	13	where	where	SCONJ
iajs-2557	92	14	c̅1	c̅1	PROPN
iajs-2557	92	15	>	>	X
iajs-2557	92	16	0	0	PROPN
iajs-2557	92	17	,	,	PUNCT
iajs-2557	92	18	∀n	∀n	PROPN
iajs-2557	92	19	from	from	ADP
iajs-2557	92	20	the	the	DET
iajs-2557	92	21	alaoglu	alaoglu	NOUN
iajs-2557	92	22	's	's	PART
iajs-2557	92	23	theorem	theorem	NOUN
iajs-2557	92	24	(	(	PUNCT
iajs-2557	92	25	agth)[8	agth)[8	ADV
iajs-2557	92	26	]	]	PUNCT
iajs-2557	92	27	,	,	PUNCT
iajs-2557	92	28	{	{	PUNCT
iajs-2557	92	29	y⃗	y⃗	NOUN
iajs-2557	92	30	n	n	CCONJ
iajs-2557	92	31	}	}	PUNCT
iajs-2557	92	32	has	have	VERB
iajs-2557	92	33	a	a	DET
iajs-2557	92	34	subsequence	subsequence	NOUN
iajs-2557	92	35	.	.	PUNCT
iajs-2557	93	1	it	it	PRON
iajs-2557	93	2	is	be	AUX
iajs-2557	93	3	not	not	PART
iajs-2557	93	4	loss	loss	NOUN
iajs-2557	93	5	of	of	ADP
iajs-2557	93	6	generality	generality	NOUN
iajs-2557	93	7	to	to	PART
iajs-2557	93	8	say	say	VERB
iajs-2557	93	9	again	again	ADV
iajs-2557	93	10	{	{	PUNCT
iajs-2557	93	11	y⃗	y⃗	NOUN
iajs-2557	93	12	n	n	CCONJ
iajs-2557	93	13	}	}	PUNCT
iajs-2557	93	14	for	for	ADP
iajs-2557	93	15	which	which	PRON
iajs-2557	93	16	y⃗	y⃗	NOUN
iajs-2557	93	17	n	n	PRON
iajs-2557	93	18	→	→	SYM
iajs-2557	93	19	y⃗	y⃗	NOUN
iajs-2557	93	20	,	,	PUNCT
iajs-2557	93	21	weakly	weakly	ADV
iajs-2557	93	22	in	in	ADP
iajs-2557	93	23	v⃗⃗	v⃗⃗	PROPN
iajs-2557	93	24	.	.	PUNCT
iajs-2557	94	1	now	now	ADV
iajs-2557	94	2	,	,	PUNCT
iajs-2557	94	3	let	let	VERB
iajs-2557	94	4	v⃗	v⃗	PROPN
iajs-2557	94	5	∈	∈	PROPN
iajs-2557	94	6	v⃗⃗	v⃗⃗	PROPN
iajs-2557	94	7	be	be	AUX
iajs-2557	94	8	fixed	fix	VERB
iajs-2557	94	9	,	,	PUNCT
iajs-2557	94	10	then	then	ADV
iajs-2557	94	11	lv⃗⃗	lv⃗⃗	PROPN
iajs-2557	94	12	(	(	PUNCT
iajs-2557	94	13	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	94	14	)	)	PUNCT
iajs-2557	94	15	=	=	SYM
iajs-2557	95	1	a(w⃗⃗⃗	a(w⃗⃗⃗	ADV
iajs-2557	95	2	,	,	PUNCT
iajs-2557	95	3	v⃗	v⃗	PROPN
iajs-2557	95	4	)	)	PUNCT
iajs-2557	95	5	is	be	AUX
iajs-2557	95	6	a	a	DET
iajs-2557	95	7	bounded	bounded	ADJ
iajs-2557	95	8	linear	linear	ADJ
iajs-2557	95	9	functional	functional	PROPN
iajs-2557	95	10	i.e	i.e	PROPN
iajs-2557	95	11	,	,	PUNCT
iajs-2557	95	12	lv⃗⃗	lv⃗⃗	PROPN
iajs-2557	95	13	∈	∈	PROPN
iajs-2557	95	14	v⃗⃗	v⃗⃗	PROPN
iajs-2557	95	15	.	.	PUNCT
iajs-2557	96	1	to	to	PART
iajs-2557	96	2	prove	prove	VERB
iajs-2557	96	3	the	the	DET
iajs-2557	96	4	sequence	sequence	NOUN
iajs-2557	96	5	of	of	ADP
iajs-2557	96	6	the	the	DET
iajs-2557	96	7	solutions	solution	NOUN
iajs-2557	96	8	{	{	PUNCT
iajs-2557	96	9	y⃗	y⃗	NOUN
iajs-2557	96	10	n	n	CCONJ
iajs-2557	96	11	}	}	PUNCT
iajs-2557	96	12	n=1	n=1	PROPN
iajs-2557	96	13	∞	∞	PROPN
iajs-2557	96	14	of	of	ADP
iajs-2557	96	15	the	the	DET
iajs-2557	96	16	wfo	wfo	NOUN
iajs-2557	96	17	(	(	PUNCT
iajs-2557	96	18	17	17	NUM
iajs-2557	96	19	)	)	PUNCT
iajs-2557	96	20	converges	converge	NOUN
iajs-2557	96	21	to	to	ADP
iajs-2557	96	22	the	the	DET
iajs-2557	96	23	solution	solution	NOUN
iajs-2557	96	24	of	of	ADP
iajs-2557	96	25	the	the	DET
iajs-2557	96	26	wfo(11	wfo(11	NOUN
iajs-2557	96	27	)	)	PUNCT
iajs-2557	96	28	.	.	PUNCT
iajs-2557	97	1	step	step	NOUN
iajs-2557	97	2	1	1	NUM
iajs-2557	97	3	:	:	PUNCT
iajs-2557	97	4	since	since	SCONJ
iajs-2557	97	5	y⃗	y⃗	NOUN
iajs-2557	97	6	n	n	PRON
iajs-2557	97	7	→	→	SYM
iajs-2557	97	8	y⃗	y⃗	NOUN
iajs-2557	97	9	weakly	weakly	ADV
iajs-2557	97	10	in	in	ADP
iajs-2557	97	11	v⃗⃗	v⃗⃗	PROPN
iajs-2557	97	12	and	and	CCONJ
iajs-2557	97	13	by	by	ADP
iajs-2557	97	14	proposition3.1	proposition3.1	ADJ
iajs-2557	97	15	,	,	PUNCT
iajs-2557	97	16	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	97	17	n	n	PROPN
iajs-2557	97	18	→	→	PUNCT
iajs-2557	97	19	v⃗⃗	v⃗⃗	VERB
iajs-2557	97	20	strongly	strongly	ADV
iajs-2557	97	21	in	in	ADP
iajs-2557	97	22	v⃗⃗	v⃗⃗	PROPN
iajs-2557	97	23	,	,	PUNCT
iajs-2557	97	24	then	then	ADV
iajs-2557	97	25	|a	|a	PROPN
iajs-2557	97	26	(	(	PUNCT
iajs-2557	97	27	y⃗	y⃗	NOUN
iajs-2557	97	28	n	n	NOUN
iajs-2557	97	29	,	,	PUNCT
iajs-2557	97	30	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	97	31	n	n	PROPN
iajs-2557	97	32	)	)	PUNCT
iajs-2557	97	33	−	−	PROPN
iajs-2557	98	1	a	a	DET
iajs-2557	98	2	(	(	PUNCT
iajs-2557	98	3	y⃗	y⃗	NOUN
iajs-2557	98	4	,	,	PUNCT
iajs-2557	98	5	v⃗	v⃗	ADJ
iajs-2557	98	6	)	)	PUNCT
iajs-2557	98	7	|	|	ADV
iajs-2557	98	8	≤	≤	NUM
iajs-2557	98	9	|a	|a	NOUN
iajs-2557	98	10	(	(	PUNCT
iajs-2557	98	11	y⃗	y⃗	NOUN
iajs-2557	98	12	n	n	NOUN
iajs-2557	98	13	,	,	PUNCT
iajs-2557	98	14	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	98	15	n	n	CCONJ
iajs-2557	98	16	−	−	NOUN
iajs-2557	98	17	v⃗	v⃗	PROPN
iajs-2557	98	18	)	)	PUNCT
iajs-2557	99	1	+	+	CCONJ
iajs-2557	99	2	a	a	DET
iajs-2557	99	3	(	(	PUNCT
iajs-2557	99	4	y⃗	y⃗	NOUN
iajs-2557	99	5	n	n	CCONJ
iajs-2557	99	6	−	−	NOUN
iajs-2557	99	7	y⃗	y⃗	NOUN
iajs-2557	99	8	,	,	PUNCT
iajs-2557	99	9	v⃗	v⃗	ADJ
iajs-2557	99	10	)	)	PUNCT
iajs-2557	99	11	|	|	ADV
iajs-2557	99	12	≤	≤	NUM
iajs-2557	99	13	c1‖	c1‖	VERB
iajs-2557	99	14	y⃗	y⃗	NOUN
iajs-2557	99	15	n	n	X
iajs-2557	99	16	‖	‖	PROPN
iajs-2557	99	17	(	(	PUNCT
iajs-2557	99	18	h1(ω	h1(ω	PROPN
iajs-2557	99	19	)	)	PUNCT
iajs-2557	99	20	)	)	PUNCT
iajs-2557	99	21	3	3	NUM
iajs-2557	99	22	‖	‖	PROPN
iajs-2557	99	23	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	99	24	n	n	CCONJ
iajs-2557	99	25	−	−	ADP
iajs-2557	99	26	v⃗	v⃗	PROPN
iajs-2557	99	27	‖	‖	PROPN
iajs-2557	99	28	(	(	PUNCT
iajs-2557	99	29	h1(ω	h1(ω	PROPN
iajs-2557	99	30	)	)	PUNCT
iajs-2557	99	31	)	)	PUNCT
iajs-2557	99	32	3	3	NUM
iajs-2557	100	1	+	+	CCONJ
iajs-2557	100	2	c2‖	c2‖	PROPN
iajs-2557	100	3	y⃗	y⃗	NOUN
iajs-2557	100	4	n	n	CCONJ
iajs-2557	100	5	−	−	NOUN
iajs-2557	100	6	y⃗	y⃗	NOUN
iajs-2557	100	7	‖	‖	PROPN
iajs-2557	100	8	(	(	PUNCT
iajs-2557	100	9	h1(ω	h1(ω	PROPN
iajs-2557	100	10	)	)	PUNCT
iajs-2557	100	11	)	)	PUNCT
iajs-2557	100	12	3	3	NUM
iajs-2557	100	13	‖	‖	VERB
iajs-2557	100	14	v⃗	v⃗	VERB
iajs-2557	100	15	‖	‖	PROPN
iajs-2557	100	16	(	(	PUNCT
iajs-2557	100	17	h1(ω	h1(ω	PROPN
iajs-2557	100	18	)	)	PUNCT
iajs-2557	100	19	)	)	PUNCT
iajs-2557	100	20	3	3	NUM
iajs-2557	100	21	→	→	SYM
iajs-2557	100	22	0	0	NUM
iajs-2557	100	23	(	(	PUNCT
iajs-2557	100	24	18	18	NUM
iajs-2557	100	25	)	)	PUNCT
iajs-2557	100	26	hence	hence	ADV
iajs-2557	100	27	a	a	PRON
iajs-2557	100	28	(	(	PUNCT
iajs-2557	100	29	y⃗	y⃗	NOUN
iajs-2557	100	30	n	n	NOUN
iajs-2557	100	31	,	,	PUNCT
iajs-2557	100	32	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	100	33	n	n	PROPN
iajs-2557	100	34	)	)	PUNCT
iajs-2557	100	35	→	→	SYM
iajs-2557	100	36	a	a	DET
iajs-2557	100	37	(	(	PUNCT
iajs-2557	100	38	y⃗	y⃗	NOUN
iajs-2557	100	39	,	,	PUNCT
iajs-2557	100	40	v⃗	v⃗	ADJ
iajs-2557	100	41	)	)	PUNCT
iajs-2557	100	42	(	(	PUNCT
iajs-2557	100	43	19	19	NUM
iajs-2557	100	44	)	)	PUNCT
iajs-2557	100	45	step	step	NOUN
iajs-2557	100	46	2	2	NUM
iajs-2557	100	47	:	:	PUNCT
iajs-2557	100	48	since	since	SCONJ
iajs-2557	100	49	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	100	50	n	n	PROPN
iajs-2557	100	51	→	→	PUNCT
iajs-2557	100	52	v⃗	v⃗	VERB
iajs-2557	100	53	strongly	strongly	ADV
iajs-2557	100	54	in	in	ADP
iajs-2557	100	55	v⃗⃗	v⃗⃗	PROPN
iajs-2557	100	56	⟹	⟹	X
iajs-2557	100	57	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	100	58	n	n	CCONJ
iajs-2557	100	59	⟶	⟶	NOUN
iajs-2557	100	60	v⃗	v⃗	ADJ
iajs-2557	100	61	weakly	weakly	ADJ
iajs-2557	100	62	in	in	ADP
iajs-2557	100	63	v⃗⃗	v⃗⃗	PROPN
iajs-2557	100	64	,	,	PUNCT
iajs-2557	100	65	then	then	ADV
iajs-2557	100	66	f	f	X
iajs-2557	100	67	(	(	PUNCT
iajs-2557	100	68	φ⃗⃗	φ⃗⃗	PROPN
iajs-2557	100	69	n	n	ADJ
iajs-2557	100	70	)	)	PUNCT
iajs-2557	100	71	⟶	⟶	NOUN
iajs-2557	100	72	f	f	PROPN
iajs-2557	100	73	(	(	PUNCT
iajs-2557	100	74	v⃗	v⃗	PROPN
iajs-2557	100	75	)	)	PUNCT
iajs-2557	100	76	the	the	DET
iajs-2557	100	77	above	above	ADJ
iajs-2557	100	78	two	two	NUM
iajs-2557	100	79	steps	step	NOUN
iajs-2557	100	80	give	give	VERB
iajs-2557	100	81	the	the	DET
iajs-2557	100	82	following	follow	VERB
iajs-2557	100	83	a	a	DET
iajs-2557	100	84	(	(	PUNCT
iajs-2557	100	85	y⃗	y⃗	NOUN
iajs-2557	100	86	,	,	PUNCT
iajs-2557	100	87	v⃗	v⃗	ADJ
iajs-2557	100	88	)	)	PUNCT
iajs-2557	101	1	=	=	SYM
iajs-2557	102	1	f	f	X
iajs-2557	102	2	(	(	PUNCT
iajs-2557	102	3	v⃗	v⃗	PROPN
iajs-2557	102	4	)	)	PUNCT
iajs-2557	102	5	,	,	PUNCT
iajs-2557	102	6	∀	∀	PUNCT
iajs-2557	102	7	v⃗	v⃗	PROPN
iajs-2557	102	8	∈	∈	PROPN
iajs-2557	102	9	v⃗⃗	v⃗⃗	PROPN
iajs-2557	102	10	which	which	PRON
iajs-2557	102	11	means	mean	VERB
iajs-2557	102	12	y⃗	y⃗	NOUN
iajs-2557	102	13	is	be	AUX
iajs-2557	102	14	a	a	DET
iajs-2557	102	15	solution	solution	NOUN
iajs-2557	102	16	in	in	ADP
iajs-2557	102	17	(	(	PUNCT
iajs-2557	102	18	11	11	NUM
iajs-2557	102	19	)	)	PUNCT
iajs-2557	102	20	.	.	PUNCT
iajs-2557	103	1	now	now	ADV
iajs-2557	103	2	,	,	PUNCT
iajs-2557	103	3	to	to	PART
iajs-2557	103	4	prove	prove	VERB
iajs-2557	103	5	y⃗	y⃗	NOUN
iajs-2557	103	6	n	n	NOUN
iajs-2557	103	7	→	→	PUNCT
iajs-2557	103	8	y⃗	y⃗	NOUN
iajs-2557	103	9	strongly	strongly	ADV
iajs-2557	103	10	in	in	ADP
iajs-2557	103	11	v⃗⃗	v⃗⃗	PROPN
iajs-2557	103	12	,	,	PUNCT
iajs-2557	103	13	by	by	ADP
iajs-2557	103	14	using	use	VERB
iajs-2557	103	15	(	(	PUNCT
iajs-2557	103	16	a	a	DET
iajs-2557	103	17	−	−	NOUN
iajs-2557	103	18	a	a	NOUN
iajs-2557	103	19	)	)	PUNCT
iajs-2557	103	20	,	,	PUNCT
iajs-2557	103	21	it	it	PRON
iajs-2557	103	22	follows	follow	VERB
iajs-2557	103	23	that	that	PRON
iajs-2557	103	24	:	:	PUNCT
iajs-2557	103	25	c	c	X
iajs-2557	103	26	‖	‖	PROPN
iajs-2557	103	27	y⃗	y⃗	NOUN
iajs-2557	103	28	−	−	NOUN
iajs-2557	103	29	y⃗	y⃗	NOUN
iajs-2557	103	30	n‖	n‖	NOUN
iajs-2557	103	31	(	(	PUNCT
iajs-2557	103	32	h1(ω	h1(ω	PROPN
iajs-2557	103	33	)	)	PUNCT
iajs-2557	103	34	)	)	PUNCT
iajs-2557	103	35	3	3	NUM
iajs-2557	103	36	≤	≤	NUM
iajs-2557	103	37	a	a	DET
iajs-2557	103	38	(	(	PUNCT
iajs-2557	103	39	y⃗	y⃗	NOUN
iajs-2557	103	40	−	−	NOUN
iajs-2557	103	41	y⃗	y⃗	NOUN
iajs-2557	103	42	n	n	NOUN
iajs-2557	103	43	,	,	PUNCT
iajs-2557	103	44	y⃗	y⃗	NOUN
iajs-2557	103	45	)	)	PUNCT
iajs-2557	103	46	−	−	PROPN
iajs-2557	104	1	a	a	PRON
iajs-2557	104	2	(	(	PUNCT
iajs-2557	104	3	y⃗	y⃗	NOUN
iajs-2557	104	4	,	,	PUNCT
iajs-2557	104	5	y⃗	y⃗	NOUN
iajs-2557	104	6	n	n	NOUN
iajs-2557	104	7	)	)	PUNCT
iajs-2557	104	8	+	+	CCONJ
iajs-2557	104	9	a	a	DET
iajs-2557	104	10	(	(	PUNCT
iajs-2557	104	11	y⃗	y⃗	NOUN
iajs-2557	104	12	n	n	NOUN
iajs-2557	104	13	,	,	PUNCT
iajs-2557	104	14	y⃗	y⃗	NOUN
iajs-2557	104	15	n	n	CCONJ
iajs-2557	104	16	)	)	PUNCT
iajs-2557	104	17	=	=	SYM
iajs-2557	104	18	a	a	PROPN
iajs-2557	104	19	(	(	PUNCT
iajs-2557	104	20	y⃗	y⃗	NOUN
iajs-2557	104	21	−	−	NOUN
iajs-2557	104	22	y⃗	y⃗	NOUN
iajs-2557	104	23	n	n	NOUN
iajs-2557	104	24	,	,	PUNCT
iajs-2557	104	25	y⃗	y⃗	NOUN
iajs-2557	104	26	)	)	PUNCT
iajs-2557	104	27	=	=	SYM
iajs-2557	104	28	ly⃗⃗	ly⃗⃗	PROPN
iajs-2557	104	29	(	(	PUNCT
iajs-2557	104	30	y⃗	y⃗	NOUN
iajs-2557	104	31	−	−	NOUN
iajs-2557	104	32	y⃗	y⃗	NOUN
iajs-2557	104	33	n	n	NOUN
iajs-2557	104	34	)	)	PUNCT
iajs-2557	104	35	→	→	SYM
iajs-2557	104	36	0	0	NUM
iajs-2557	104	37	thus	thus	ADV
iajs-2557	104	38	{	{	PUNCT
iajs-2557	104	39	y⃗	y⃗	NOUN
iajs-2557	104	40	n	n	CCONJ
iajs-2557	104	41	}	}	PUNCT
iajs-2557	104	42	converges	converge	NOUN
iajs-2557	104	43	to	to	ADP
iajs-2557	104	44	y⃗	y⃗	NOUN
iajs-2557	104	45	strongly	strongly	ADV
iajs-2557	104	46	in	in	ADP
iajs-2557	104	47	(	(	PUNCT
iajs-2557	104	48	h1(ω	h1(ω	PROPN
iajs-2557	104	49	)	)	PUNCT
iajs-2557	104	50	)	)	PUNCT
iajs-2557	104	51	3	3	NUM
iajs-2557	104	52	.	.	X
iajs-2557	105	1	4	4	X
iajs-2557	105	2	.	.	X
iajs-2557	105	3	existence	existence	NOUN
iajs-2557	105	4	of	of	ADP
iajs-2557	105	5	a	a	DET
iajs-2557	105	6	ccbocvr	ccbocvr	NOUN
iajs-2557	105	7	:	:	PUNCT
iajs-2557	105	8	lemma	lemma	PROPN
iajs-2557	105	9	4.1	4.1	NUM
iajs-2557	105	10	:	:	PUNCT
iajs-2557	105	11	the	the	DET
iajs-2557	105	12	operator	operator	NOUN
iajs-2557	105	13	u⃗	u⃗	PROPN
iajs-2557	105	14	−	−	PROPN
iajs-2557	105	15	y⃗	y⃗	NOUN
iajs-2557	105	16	u⃗⃗	u⃗⃗	NOUN
iajs-2557	105	17	is	be	AUX
iajs-2557	105	18	lipschitz	lipschitz	NOUN
iajs-2557	105	19	continuous	continuous	ADJ
iajs-2557	105	20	from	from	ADP
iajs-2557	105	21	(	(	PUNCT
iajs-2557	105	22	l2(∂ω	l2(∂ω	NUM
iajs-2557	105	23	)	)	PUNCT
iajs-2557	105	24	)	)	PUNCT
iajs-2557	105	25	3	3	NUM
iajs-2557	105	26	into	into	ADP
iajs-2557	105	27	(	(	PUNCT
iajs-2557	105	28	l2(ω	l2(ω	NOUN
iajs-2557	105	29	)	)	PUNCT
iajs-2557	105	30	)	)	PUNCT
iajs-2557	105	31	3	3	NUM
iajs-2557	105	32	and	and	CCONJ
iajs-2557	105	33	is	be	AUX
iajs-2557	105	34	satisfied	satisfied	ADJ
iajs-2557	105	35	‖	‖	ADJ
iajs-2557	105	36	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	105	37	‖	‖	PROPN
iajs-2557	105	38	(	(	PUNCT
iajs-2557	105	39	l2(ω	l2(ω	NOUN
iajs-2557	105	40	)	)	PUNCT
iajs-2557	105	41	)	)	PUNCT
iajs-2557	105	42	3	3	NUM
iajs-2557	105	43	≤	≤	NOUN
iajs-2557	105	44	c3	c3	PROPN
iajs-2557	105	45	‖∆u⃗⃗	‖∆u⃗⃗	NOUN
iajs-2557	105	46	⃗⃗	⃗⃗	PROPN
iajs-2557	105	47	‖	‖	PROPN
iajs-2557	105	48	(	(	PUNCT
iajs-2557	105	49	l2(∂ω	l2(∂ω	NUM
iajs-2557	105	50	)	)	PUNCT
iajs-2557	105	51	)	)	PUNCT
iajs-2557	105	52	3	3	NUM
iajs-2557	105	53	,	,	PUNCT
iajs-2557	105	54	with	with	ADP
iajs-2557	105	55	c3	c3	PROPN
iajs-2557	105	56	>	>	X
iajs-2557	105	57	0	0	PUNCT
iajs-2557	105	58	.	.	PUNCT
iajs-2557	106	1	64	64	NUM
iajs-2557	106	2	ibn	ibn	PROPN
iajs-2557	106	3	al	al	PROPN
iajs-2557	106	4	-	-	PUNCT
iajs-2557	106	5	haitham	haitham	PROPN
iajs-2557	106	6	jour	jour	X
iajs-2557	106	7	.	.	PROPN
iajs-2557	106	8	for	for	ADP
iajs-2557	106	9	pure	pure	ADJ
iajs-2557	106	10	&	&	CCONJ
iajs-2557	106	11	appl	appl	PROPN
iajs-2557	106	12	.	.	PUNCT
iajs-2557	107	1	sci	sci	PROPN
iajs-2557	107	2	.	.	PROPN
iajs-2557	108	1	34	34	NUM
iajs-2557	108	2	(	(	PUNCT
iajs-2557	108	3	1	1	NUM
iajs-2557	108	4	)	)	PUNCT
iajs-2557	108	5	2021	2021	NUM
iajs-2557	108	6	proof	proof	NOUN
iajs-2557	108	7	:	:	PUNCT
iajs-2557	108	8	let	let	VERB
iajs-2557	108	9	u1́	u1́	NUM
iajs-2557	108	10	,	,	PUNCT
iajs-2557	108	11	u2́	u2́	PROPN
iajs-2557	108	12	,	,	PUNCT
iajs-2557	108	13	u3́	u3́	X
iajs-2557	108	14	be	be	VERB
iajs-2557	108	15	controls	control	NOUN
iajs-2557	108	16	of	of	ADP
iajs-2557	108	17	the	the	DET
iajs-2557	108	18	wfo	wfo	NOUN
iajs-2557	108	19	(	(	PUNCT
iajs-2557	108	20	11	11	NUM
iajs-2557	108	21	)	)	PUNCT
iajs-2557	108	22	y1́	y1́	NOUN
iajs-2557	108	23	,	,	PUNCT
iajs-2557	108	24	y2́	y2́	PUNCT
iajs-2557	108	25	and	and	CCONJ
iajs-2557	108	26	y3́	y3́	PROPN
iajs-2557	108	27	be	be	VERB
iajs-2557	108	28	their	their	PRON
iajs-2557	108	29	corresponding	corresponding	ADJ
iajs-2557	108	30	ssv	ssv	NOUN
iajs-2557	108	31	,	,	PUNCT
iajs-2557	108	32	subtracting	subtract	VERB
iajs-2557	108	33	the	the	DET
iajs-2557	108	34	obtaining	obtain	VERB
iajs-2557	108	35	wfo	wfo	NOUN
iajs-2557	108	36	from	from	ADP
iajs-2557	108	37	(	(	PUNCT
iajs-2557	108	38	11	11	NUM
iajs-2557	108	39	)	)	PUNCT
iajs-2557	108	40	,	,	PUNCT
iajs-2557	108	41	by	by	ADP
iajs-2557	108	42	letting	let	VERB
iajs-2557	108	43	∆y1	∆y1	PROPN
iajs-2557	108	44	=	=	SYM
iajs-2557	108	45	y1́	y1́	NOUN
iajs-2557	108	46	−	−	PROPN
iajs-2557	108	47	y1	y1	PROPN
iajs-2557	108	48	and	and	CCONJ
iajs-2557	108	49	∆u	∆u	PROPN
iajs-2557	108	50	=	=	SYM
iajs-2557	108	51	u1́	u1́	NUM
iajs-2557	108	52	−	−	ADP
iajs-2557	108	53	u	u	NOUN
iajs-2557	108	54	with	with	ADP
iajs-2557	108	55	v⃗	v⃗	ADJ
iajs-2557	108	56	=	=	SYM
iajs-2557	108	57	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	108	58	,	,	PUNCT
iajs-2557	108	59	to	to	PART
iajs-2557	108	60	get	get	VERB
iajs-2557	108	61	a	a	DET
iajs-2557	108	62	(	(	PUNCT
iajs-2557	108	63	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	NOUN
iajs-2557	108	64	,	,	PUNCT
iajs-2557	108	65	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	ADV
iajs-2557	108	66	)	)	PUNCT
iajs-2557	108	67	=	=	SYM
iajs-2557	109	1	(	(	PUNCT
iajs-2557	109	2	∆u1	∆u1	NOUN
iajs-2557	109	3	,	,	PUNCT
iajs-2557	109	4	∆y1	∆y1	PROPN
iajs-2557	109	5	)	)	PUNCT
iajs-2557	109	6	(	(	PUNCT
iajs-2557	109	7	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	109	8	)	)	PUNCT
iajs-2557	109	9	)	)	PUNCT
iajs-2557	110	1	+	+	CCONJ
iajs-2557	110	2	(	(	PUNCT
iajs-2557	110	3	∆u2	∆u2	PROPN
iajs-2557	110	4	,	,	PUNCT
iajs-2557	110	5	∆y2	∆y2	PROPN
iajs-2557	110	6	)	)	PUNCT
iajs-2557	110	7	(	(	PUNCT
iajs-2557	110	8	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	110	9	)	)	PUNCT
iajs-2557	110	10	)	)	PUNCT
iajs-2557	111	1	+	+	CCONJ
iajs-2557	111	2	(	(	PUNCT
iajs-2557	111	3	∆u3	∆u3	NOUN
iajs-2557	111	4	,	,	PUNCT
iajs-2557	111	5	∆y3	∆y3	PROPN
iajs-2557	111	6	)	)	PUNCT
iajs-2557	111	7	(	(	PUNCT
iajs-2557	111	8	l2(∂ω	l2(∂ω	NUM
iajs-2557	111	9	)	)	PUNCT
iajs-2557	111	10	)	)	PUNCT
iajs-2557	111	11	(	(	PUNCT
iajs-2557	111	12	20	20	NUM
iajs-2557	111	13	)	)	PUNCT
iajs-2557	111	14	which	which	PRON
iajs-2557	111	15	gives	give	VERB
iajs-2557	111	16	after	after	ADP
iajs-2557	111	17	using(a	using(a	NOUN
iajs-2557	111	18	-	-	PUNCT
iajs-2557	111	19	a	a	NOUN
iajs-2557	111	20	)	)	PUNCT
iajs-2557	111	21	,	,	PUNCT
iajs-2557	111	22	the	the	DET
iajs-2557	111	23	cauchy	cauchy	PROPN
iajs-2557	111	24	inequality(csin	inequality(csin	PROPN
iajs-2557	111	25	)	)	PUNCT
iajs-2557	111	26	and	and	CCONJ
iajs-2557	111	27	then	then	ADV
iajs-2557	111	28	the	the	DET
iajs-2557	111	29	trace	trace	NOUN
iajs-2557	111	30	operator	operator	NOUN
iajs-2557	111	31	to	to	PART
iajs-2557	111	32	obtain	obtain	VERB
iajs-2557	111	33	c‖	c‖	ADJ
iajs-2557	111	34	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	111	35	‖	‖	PROPN
iajs-2557	111	36	(	(	PUNCT
iajs-2557	111	37	h1(ω	h1(ω	PROPN
iajs-2557	111	38	)	)	PUNCT
iajs-2557	111	39	)	)	PUNCT
iajs-2557	111	40	3	3	NUM
iajs-2557	111	41	2	2	NUM
iajs-2557	111	42	≤	≤	NOUN
iajs-2557	111	43	|a	|a	VERB
iajs-2557	111	44	(	(	PUNCT
iajs-2557	111	45	∆y⃗⃗	∆y⃗⃗	PROPN
iajs-2557	111	46	⃗⃗	⃗⃗	PROPN
iajs-2557	111	47	,	,	PUNCT
iajs-2557	111	48	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	111	49	)	)	PUNCT
iajs-2557	111	50	|	|	ADV
iajs-2557	111	51	≤	≤	NUM
iajs-2557	111	52	c1‖	c1‖	VERB
iajs-2557	111	53	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	111	54	⃗⃗	⃗⃗	PROPN
iajs-2557	111	55	‖	‖	PROPN
iajs-2557	111	56	(	(	PUNCT
iajs-2557	111	57	l2(∂ω	l2(∂ω	NUM
iajs-2557	111	58	)	)	PUNCT
iajs-2557	111	59	)	)	PUNCT
iajs-2557	112	1	3	3	NUM
iajs-2557	112	2	‖	‖	PROPN
iajs-2557	112	3	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	112	4	‖	‖	PROPN
iajs-2557	112	5	(	(	PUNCT
iajs-2557	112	6	h1(ω	h1(ω	PROPN
iajs-2557	112	7	)	)	PUNCT
iajs-2557	112	8	)	)	PUNCT
iajs-2557	112	9	3	3	NUM
iajs-2557	112	10	then	then	ADV
iajs-2557	112	11	,	,	PUNCT
iajs-2557	112	12	‖	‖	ADJ
iajs-2557	112	13	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	112	14	‖	‖	PROPN
iajs-2557	112	15	(	(	PUNCT
iajs-2557	112	16	h1(ω	h1(ω	PROPN
iajs-2557	112	17	)	)	PUNCT
iajs-2557	112	18	)	)	PUNCT
iajs-2557	112	19	3	3	NUM
iajs-2557	112	20	≤	≤	NOUN
iajs-2557	112	21	c2‖	c2‖	PROPN
iajs-2557	112	22	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	112	23	⃗⃗	⃗⃗	PROPN
iajs-2557	112	24	‖	‖	PROPN
iajs-2557	112	25	(	(	PUNCT
iajs-2557	112	26	l2(∂ω	l2(∂ω	NUM
iajs-2557	112	27	)	)	PUNCT
iajs-2557	112	28	)	)	PUNCT
iajs-2557	112	29	3	3	NUM
iajs-2557	112	30	where	where	SCONJ
iajs-2557	112	31	c2	c2	PROPN
iajs-2557	112	32	=	=	PROPN
iajs-2557	112	33	c1	c1	PROPN
iajs-2557	112	34	c	c	PROPN
iajs-2557	112	35	since	since	SCONJ
iajs-2557	112	36	‖	‖	PROPN
iajs-2557	112	37	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	112	38	‖	‖	PROPN
iajs-2557	112	39	(	(	PUNCT
iajs-2557	112	40	l2(ω	l2(ω	NOUN
iajs-2557	112	41	)	)	PUNCT
iajs-2557	112	42	)	)	PUNCT
iajs-2557	112	43	3	3	NUM
iajs-2557	112	44	≤	≤	NOUN
iajs-2557	112	45	c	c	X
iajs-2557	113	1	‖	‖	PROPN
iajs-2557	113	2	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	113	3	‖	‖	PROPN
iajs-2557	113	4	(	(	PUNCT
iajs-2557	113	5	h1(ω	h1(ω	PROPN
iajs-2557	113	6	)	)	PUNCT
iajs-2557	113	7	)	)	PUNCT
iajs-2557	113	8	3	3	NUM
iajs-2557	113	9	,	,	PUNCT
iajs-2557	113	10	then	then	ADV
iajs-2557	113	11	the	the	DET
iajs-2557	113	12	above	above	ADJ
iajs-2557	113	13	inequality	inequality	NOUN
iajs-2557	113	14	becomes	become	VERB
iajs-2557	113	15	‖	‖	PROPN
iajs-2557	113	16	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	113	17	‖	‖	PROPN
iajs-2557	113	18	(	(	PUNCT
iajs-2557	113	19	l2(ω	l2(ω	NOUN
iajs-2557	113	20	)	)	PUNCT
iajs-2557	113	21	)	)	PUNCT
iajs-2557	113	22	3	3	NUM
iajs-2557	113	23	≤	≤	NOUN
iajs-2557	113	24	c3‖	c3‖	PROPN
iajs-2557	113	25	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	113	26	⃗⃗	⃗⃗	PROPN
iajs-2557	113	27	‖	‖	PROPN
iajs-2557	113	28	(	(	PUNCT
iajs-2557	113	29	l2(∂ω	l2(∂ω	NUM
iajs-2557	113	30	)	)	PUNCT
iajs-2557	113	31	)	)	PUNCT
iajs-2557	113	32	3	3	NUM
iajs-2557	113	33	,	,	PUNCT
iajs-2557	113	34	where	where	SCONJ
iajs-2557	113	35	c3	c3	PROPN
iajs-2557	113	36	=	=	PROPN
iajs-2557	114	1	c	c	PROPN
iajs-2557	114	2	∙	∙	PROPN
iajs-2557	114	3	c2	c2	PROPN
iajs-2557	114	4	(	(	PUNCT
iajs-2557	114	5	21	21	NUM
iajs-2557	114	6	)	)	PUNCT
iajs-2557	114	7	lemma	lemma	PROPN
iajs-2557	114	8	4.2	4.2	NUM
iajs-2557	115	1	[	[	NOUN
iajs-2557	115	2	3]:the	3]:the	DET
iajs-2557	115	3	norm	norm	NOUN
iajs-2557	115	4	‖	‖	PROPN
iajs-2557	115	5	‖l2(ω	‖l2(ω	PROPN
iajs-2557	115	6	)	)	PUNCT
iajs-2557	115	7	(	(	PUNCT
iajs-2557	115	8	or	or	CCONJ
iajs-2557	115	9	the	the	DET
iajs-2557	115	10	norm	norm	NOUN
iajs-2557	115	11	‖	‖	PROPN
iajs-2557	115	12	‖l2(∂ω	‖l2(∂ω	PROPN
iajs-2557	115	13	)	)	PUNCT
iajs-2557	115	14	)	)	PUNCT
iajs-2557	115	15	is	be	AUX
iajs-2557	115	16	weakly	weakly	ADV
iajs-2557	115	17	lower	low	ADJ
iajs-2557	115	18	semi	semi	ADV
iajs-2557	115	19	continuous	continuous	ADJ
iajs-2557	115	20	(	(	PUNCT
iajs-2557	115	21	welsc	welsc	PROPN
iajs-2557	115	22	)	)	PUNCT
iajs-2557	115	23	lemma	lemma	PROPN
iajs-2557	115	24	4.3	4.3	NUM
iajs-2557	115	25	:	:	PUNCT
iajs-2557	115	26	the	the	DET
iajs-2557	115	27	objective	objective	ADJ
iajs-2557	115	28	function	function	NOUN
iajs-2557	115	29	(	(	PUNCT
iajs-2557	115	30	7	7	X
iajs-2557	115	31	)	)	PUNCT
iajs-2557	115	32	is	be	AUX
iajs-2557	115	33	welsc	welsc	NOUN
iajs-2557	115	34	.	.	PUNCT
iajs-2557	116	1	proof	proof	NOUN
iajs-2557	116	2	:	:	PUNCT
iajs-2557	116	3	the	the	DET
iajs-2557	116	4	norm	norm	NOUN
iajs-2557	116	5	‖	‖	PROPN
iajs-2557	116	6	‖l2(∂ω	‖l2(∂ω	PROPN
iajs-2557	116	7	)	)	PUNCT
iajs-2557	116	8	is	be	AUX
iajs-2557	116	9	welsc	welsc	NOUN
iajs-2557	116	10	(	(	PUNCT
iajs-2557	116	11	by	by	ADP
iajs-2557	116	12	lemma	lemma	PROPN
iajs-2557	116	13	4.2	4.2	NUM
iajs-2557	116	14	)	)	PUNCT
iajs-2557	116	15	,	,	PUNCT
iajs-2557	116	16	but	but	CCONJ
iajs-2557	116	17	when	when	SCONJ
iajs-2557	116	18	u⃗	u⃗	PROPN
iajs-2557	116	19	n	n	PRON
iajs-2557	116	20	→	→	SYM
iajs-2557	116	21	u⃗	u⃗	PROPN
iajs-2557	116	22	weakly	weakly	ADV
iajs-2557	116	23	in	in	ADP
iajs-2557	116	24	(	(	PUNCT
iajs-2557	116	25	l2(ω	l2(ω	NOUN
iajs-2557	116	26	)	)	PUNCT
iajs-2557	116	27	)	)	PUNCT
iajs-2557	116	28	3	3	NUM
iajs-2557	116	29	,	,	PUNCT
iajs-2557	116	30	then	then	ADV
iajs-2557	116	31	by	by	ADP
iajs-2557	116	32	using	use	VERB
iajs-2557	116	33	lemma	lemma	PROPN
iajs-2557	116	34	4.1	4.1	NUM
iajs-2557	116	35	gives	give	VERB
iajs-2557	116	36	y⃗	y⃗	NOUN
iajs-2557	116	37	n	n	PRON
iajs-2557	116	38	→	→	SYM
iajs-2557	116	39	y⃗	y⃗	NOUN
iajs-2557	116	40	=	=	SYM
iajs-2557	116	41	y⃗	y⃗	NOUN
iajs-2557	116	42	u⃗⃗	u⃗⃗	NOUN
iajs-2557	116	43	weakly	weakly	ADV
iajs-2557	116	44	in	in	ADP
iajs-2557	116	45	(	(	PUNCT
iajs-2557	116	46	l2(ω	l2(ω	NOUN
iajs-2557	116	47	)	)	PUNCT
iajs-2557	116	48	)	)	PUNCT
iajs-2557	116	49	3	3	NUM
iajs-2557	116	50	,	,	PUNCT
iajs-2557	116	51	then	then	ADV
iajs-2557	116	52	by	by	ADP
iajs-2557	116	53	using	use	VERB
iajs-2557	116	54	lemma	lemma	PROPN
iajs-2557	116	55	4.2	4.2	NUM
iajs-2557	116	56	,	,	PUNCT
iajs-2557	116	57	‖y⃗	‖y⃗	NOUN
iajs-2557	116	58	−	−	NOUN
iajs-2557	116	59	y⃗	y⃗	NOUN
iajs-2557	116	60	n‖l2(ω	n‖l2(ω	NOUN
iajs-2557	116	61	)	)	PUNCT
iajs-2557	116	62	2	2	NUM
iajs-2557	116	63	is	be	AUX
iajs-2557	116	64	welsc	welsc	NOUN
iajs-2557	116	65	,	,	PUNCT
iajs-2557	116	66	i.e	i.e	PROPN
iajs-2557	116	67	,	,	PUNCT
iajs-2557	116	68	g0	g0	PROPN
iajs-2557	116	69	(	(	PUNCT
iajs-2557	116	70	u⃗	u⃗	PROPN
iajs-2557	116	71	)	)	PUNCT
iajs-2557	116	72	is	be	AUX
iajs-2557	116	73	welsc	welsc	NOUN
iajs-2557	116	74	.	.	PUNCT
iajs-2557	117	1	lemma	lemma	PROPN
iajs-2557	117	2	4.4	4.4	NUM
iajs-2557	118	1	[	[	X
iajs-2557	118	2	3]:the	3]:the	DET
iajs-2557	118	3	norm	norm	NOUN
iajs-2557	118	4	‖	‖	PROPN
iajs-2557	118	5	‖l2(ω	‖l2(ω	PROPN
iajs-2557	118	6	)	)	PUNCT
iajs-2557	118	7	(	(	PUNCT
iajs-2557	118	8	‖	‖	PROPN
iajs-2557	118	9	‖l2(∂ω	‖l2(∂ω	PROPN
iajs-2557	118	10	)	)	PUNCT
iajs-2557	118	11	)	)	PUNCT
iajs-2557	119	1	is	be	AUX
iajs-2557	119	2	strictly	strictly	ADV
iajs-2557	119	3	convex	convex	ADJ
iajs-2557	119	4	(	(	PUNCT
iajs-2557	119	5	sc	sc	PROPN
iajs-2557	119	6	)	)	PUNCT
iajs-2557	119	7	.	.	PUNCT
iajs-2557	120	1	remark	remark	VERB
iajs-2557	120	2	4.1	4.1	NUM
iajs-2557	120	3	:	:	PUNCT
iajs-2557	120	4	by	by	ADP
iajs-2557	120	5	applying	apply	VERB
iajs-2557	120	6	lemma	lemma	PROPN
iajs-2557	120	7	4.4	4.4	NUM
iajs-2557	120	8	,	,	PUNCT
iajs-2557	120	9	g0	g0	PROPN
iajs-2557	120	10	(	(	PUNCT
iajs-2557	120	11	u⃗	u⃗	PROPN
iajs-2557	120	12	)	)	PUNCT
iajs-2557	120	13	is	be	AUX
iajs-2557	120	14	(	(	PUNCT
iajs-2557	120	15	sc	sc	PROPN
iajs-2557	120	16	)	)	PUNCT
iajs-2557	120	17	.	.	PUNCT
iajs-2557	121	1	theorem	theorem	VERB
iajs-2557	121	2	4.1	4.1	NUM
iajs-2557	121	3	:	:	PUNCT
iajs-2557	121	4	if	if	SCONJ
iajs-2557	121	5	ui	ui	PROPN
iajs-2557	121	6	,	,	PUNCT
iajs-2557	121	7	∀	∀	VERB
iajs-2557	122	1	i	i	NOUN
iajs-2557	122	2	=	=	NOUN
iajs-2557	122	3	1	1	NUM
iajs-2557	122	4	,	,	PUNCT
iajs-2557	122	5	2	2	NUM
iajs-2557	122	6	,	,	PUNCT
iajs-2557	122	7	3	3	NUM
iajs-2557	122	8	is	be	AUX
iajs-2557	122	9	bounded	bound	VERB
iajs-2557	122	10	,	,	PUNCT
iajs-2557	122	11	then	then	ADV
iajs-2557	122	12	there	there	PRON
iajs-2557	122	13	is	be	VERB
iajs-2557	122	14	a	a	DET
iajs-2557	122	15	ccbocvr	ccbocvr	NOUN
iajs-2557	122	16	for	for	ADP
iajs-2557	122	17	the	the	DET
iajs-2557	122	18	problem	problem	NOUN
iajs-2557	122	19	(	(	PUNCT
iajs-2557	122	20	8)	8)	NUM
iajs-2557	122	21	.	.	PUNCT
iajs-2557	123	1	proof	proof	NOUN
iajs-2557	123	2	:	:	PUNCT
iajs-2557	123	3	since	since	SCONJ
iajs-2557	123	4	ui	ui	PROPN
iajs-2557	123	5	,	,	PUNCT
iajs-2557	123	6	∀	∀	VERB
iajs-2557	123	7	i	i	NOUN
iajs-2557	123	8	=	=	NOUN
iajs-2557	123	9	1	1	NUM
iajs-2557	123	10	,	,	PUNCT
iajs-2557	123	11	2	2	NUM
iajs-2557	123	12	,	,	PUNCT
iajs-2557	123	13	3	3	NUM
iajs-2557	123	14	is	be	AUX
iajs-2557	123	15	bounded	bound	VERB
iajs-2557	123	16	,	,	PUNCT
iajs-2557	123	17	then	then	ADV
iajs-2557	123	18	wi	wi	PROPN
iajs-2557	123	19	(	(	PUNCT
iajs-2557	123	20	∀	∀	X
iajs-2557	123	21	i	i	NOUN
iajs-2557	123	22	=	=	NOUN
iajs-2557	123	23	1	1	NUM
iajs-2557	123	24	,	,	PUNCT
iajs-2557	123	25	2	2	NUM
iajs-2557	123	26	,	,	PUNCT
iajs-2557	123	27	3	3	NUM
iajs-2557	123	28	)	)	PUNCT
iajs-2557	123	29	is	be	AUX
iajs-2557	123	30	a	a	DET
iajs-2557	123	31	bounded	bounded	ADJ
iajs-2557	123	32	and	and	CCONJ
iajs-2557	123	33	then	then	ADV
iajs-2557	123	34	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	123	35	is	be	AUX
iajs-2557	123	36	bounded	bound	VERB
iajs-2557	123	37	since	since	SCONJ
iajs-2557	123	38	g0	g0	PROPN
iajs-2557	123	39	(	(	PUNCT
iajs-2557	123	40	u⃗	u⃗	PROPN
iajs-2557	123	41	)	)	PUNCT
iajs-2557	123	42	≥	≥	NOUN
iajs-2557	123	43	0	0	NUM
iajs-2557	123	44	,	,	PUNCT
iajs-2557	123	45	then	then	ADV
iajs-2557	123	46	there	there	PRON
iajs-2557	123	47	is	be	VERB
iajs-2557	123	48	a	a	DET
iajs-2557	123	49	minimum	minimum	ADJ
iajs-2557	123	50	sequence	sequence	NOUN
iajs-2557	123	51	{	{	PUNCT
iajs-2557	123	52	u⃗	u⃗	PROPN
iajs-2557	123	53	n	n	CCONJ
iajs-2557	123	54	}	}	PUNCT
iajs-2557	123	55	=	=	SYM
iajs-2557	123	56	{	{	PUNCT
iajs-2557	123	57	(	(	PUNCT
iajs-2557	123	58	u1n	u1n	NOUN
iajs-2557	123	59	,	,	PUNCT
iajs-2557	123	60	u2n	u2n	PROPN
iajs-2557	123	61	,	,	PUNCT
iajs-2557	123	62	u3n	u3n	NOUN
iajs-2557	123	63	)	)	PUNCT
iajs-2557	123	64	}	}	PUNCT
iajs-2557	123	65	∈	∈	NOUN
iajs-2557	123	66	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	123	67	,	,	PUNCT
iajs-2557	123	68	for	for	ADP
iajs-2557	123	69	each	each	DET
iajs-2557	123	70	n	n	NOUN
iajs-2557	123	71	,	,	PUNCT
iajs-2557	123	72	such	such	ADJ
iajs-2557	123	73	that	that	SCONJ
iajs-2557	123	74	:	:	PUNCT
iajs-2557	123	75	lim	lim	PROPN
iajs-2557	123	76	n→∞	n→∞	NUM
iajs-2557	123	77	g0	g0	PROPN
iajs-2557	123	78	(	(	PUNCT
iajs-2557	123	79	u⃗	u⃗	PROPN
iajs-2557	123	80	n	n	NOUN
iajs-2557	123	81	)	)	PUNCT
iajs-2557	123	82	=	=	PUNCT
iajs-2557	123	83	infw⃗⃗⃗	infw⃗⃗⃗	NOUN
iajs-2557	123	84	∈w⃗⃗⃗⃗	∈w⃗⃗⃗⃗	NOUN
iajs-2557	123	85	g0	g0	PROPN
iajs-2557	123	86	(	(	PUNCT
iajs-2557	123	87	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	123	88	)	)	PUNCT
iajs-2557	123	89	from	from	ADP
iajs-2557	123	90	the	the	DET
iajs-2557	123	91	coercive	coercive	ADJ
iajs-2557	123	92	property	property	NOUN
iajs-2557	123	93	of	of	ADP
iajs-2557	123	94	g0	g0	PROPN
iajs-2557	123	95	(	(	PUNCT
iajs-2557	123	96	u⃗	u⃗	PROPN
iajs-2557	123	97	)	)	PUNCT
iajs-2557	123	98	,	,	PUNCT
iajs-2557	123	99	and	and	CCONJ
iajs-2557	123	100	its	its	PRON
iajs-2557	123	101	infimum	infimum	NOUN
iajs-2557	123	102	,	,	PUNCT
iajs-2557	123	103	there	there	PRON
iajs-2557	123	104	exists	exist	VERB
iajs-2557	123	105	a	a	DET
iajs-2557	123	106	constant	constant	ADJ
iajs-2557	123	107	c	c	NOUN
iajs-2557	123	108	>	>	X
iajs-2557	123	109	0	0	NUM
iajs-2557	123	110	such	such	ADJ
iajs-2557	123	111	that	that	SCONJ
iajs-2557	123	112	‖	‖	ADJ
iajs-2557	123	113	u⃗	u⃗	PROPN
iajs-2557	123	114	n‖(l2(∂ω	n‖(l2(∂ω	NOUN
iajs-2557	123	115	)	)	PUNCT
iajs-2557	123	116	)	)	PUNCT
iajs-2557	123	117	3	3	NUM
iajs-2557	123	118	≤	≤	NOUN
iajs-2557	123	119	c	c	NOUN
iajs-2557	123	120	,	,	PUNCT
iajs-2557	123	121	∀	∀	X
iajs-2557	123	122	n	n	CCONJ
iajs-2557	123	123	(	(	PUNCT
iajs-2557	123	124	22	22	NUM
iajs-2557	123	125	)	)	PUNCT
iajs-2557	123	126	then	then	ADV
iajs-2557	123	127	by	by	ADP
iajs-2557	123	128	agth	agth	NOUN
iajs-2557	123	129	,	,	PUNCT
iajs-2557	123	130	the	the	DET
iajs-2557	123	131	sequence	sequence	NOUN
iajs-2557	123	132	{	{	PUNCT
iajs-2557	123	133	u⃗	u⃗	PROPN
iajs-2557	123	134	n	n	CCONJ
iajs-2557	123	135	}	}	PUNCT
iajs-2557	123	136	has	have	VERB
iajs-2557	123	137	a	a	DET
iajs-2557	123	138	subsequence	subsequence	NOUN
iajs-2557	123	139	.	.	PUNCT
iajs-2557	124	1	it	it	PRON
iajs-2557	124	2	is	be	AUX
iajs-2557	124	3	not	not	PART
iajs-2557	124	4	loss	loss	NOUN
iajs-2557	124	5	of	of	ADP
iajs-2557	124	6	generality	generality	NOUN
iajs-2557	124	7	to	to	PART
iajs-2557	124	8	say	say	VERB
iajs-2557	124	9	again	again	ADV
iajs-2557	124	10	{	{	PUNCT
iajs-2557	124	11	u⃗	u⃗	PROPN
iajs-2557	124	12	n	n	CCONJ
iajs-2557	124	13	}	}	PUNCT
iajs-2557	124	14	for	for	ADP
iajs-2557	124	15	which	which	PRON
iajs-2557	124	16	u⃗	u⃗	PROPN
iajs-2557	124	17	n	n	NOUN
iajs-2557	124	18	→	→	SYM
iajs-2557	124	19	u⃗	u⃗	PROPN
iajs-2557	124	20	weakly	weakly	ADV
iajs-2557	124	21	in	in	ADP
iajs-2557	124	22	(	(	PUNCT
iajs-2557	124	23	l2(∂ω	l2(∂ω	NUM
iajs-2557	124	24	)	)	PUNCT
iajs-2557	124	25	)	)	PUNCT
iajs-2557	124	26	3	3	X
iajs-2557	124	27	.	.	PUNCT
iajs-2557	125	1	from	from	ADP
iajs-2557	125	2	theorem3.1	theorem3.1	PROPN
iajs-2557	125	3	,	,	PUNCT
iajs-2557	125	4	for	for	ADP
iajs-2557	125	5	each	each	DET
iajs-2557	125	6	control	control	NOUN
iajs-2557	125	7	u⃗	u⃗	PROPN
iajs-2557	125	8	n	n	NOUN
iajs-2557	125	9	=	=	SYM
iajs-2557	125	10	(	(	PUNCT
iajs-2557	125	11	u1n	u1n	NOUN
iajs-2557	125	12	,	,	PUNCT
iajs-2557	125	13	u2n	u2n	PROPN
iajs-2557	125	14	,	,	PUNCT
iajs-2557	125	15	u3n	u3n	PROPN
iajs-2557	125	16	)	)	PUNCT
iajs-2557	125	17	the	the	DET
iajs-2557	125	18	tepdese	tepdese	PROPN
iajs-2557	125	19	has	have	VERB
iajs-2557	125	20	a	a	DET
iajs-2557	125	21	unique	unique	ADJ
iajs-2557	125	22	apps	app	NOUN
iajs-2557	125	23	y⃗	y⃗	NOUN
iajs-2557	125	24	n	n	NOUN
iajs-2557	125	25	=	=	SYM
iajs-2557	125	26	y⃗	y⃗	NOUN
iajs-2557	125	27	un	un	PROPN
iajs-2557	125	28	.	.	PUNCT
iajs-2557	126	1	to	to	PART
iajs-2557	126	2	prove	prove	VERB
iajs-2557	126	3	(	(	PUNCT
iajs-2557	126	4	for	for	ADP
iajs-2557	126	5	each	each	DET
iajs-2557	126	6	n	n	NOUN
iajs-2557	126	7	)	)	PUNCT
iajs-2557	126	8	{	{	PUNCT
iajs-2557	126	9	y⃗	y⃗	NOUN
iajs-2557	126	10	n	n	CCONJ
iajs-2557	126	11	}	}	PUNCT
iajs-2557	126	12	,	,	PUNCT
iajs-2557	126	13	is	be	AUX
iajs-2557	126	14	bounded	bound	VERB
iajs-2557	126	15	in	in	ADP
iajs-2557	126	16	v⃗⃗	v⃗⃗	PROPN
iajs-2557	126	17	,	,	PUNCT
iajs-2557	126	18	using	use	VERB
iajs-2557	126	19	(	(	PUNCT
iajs-2557	126	20	a	a	PRON
iajs-2557	126	21	–	–	PUNCT
iajs-2557	126	22	a	a	PRON
iajs-2557	126	23	&	&	CCONJ
iajs-2557	126	24	c	c	NOUN
iajs-2557	126	25	)	)	PUNCT
iajs-2557	126	26	,	,	PUNCT
iajs-2557	126	27	csin	csin	VERB
iajs-2557	126	28	and	and	CCONJ
iajs-2557	126	29	the	the	DET
iajs-2557	126	30	trace	trace	NOUN
iajs-2557	126	31	operator	operator	NOUN
iajs-2557	126	32	,	,	PUNCT
iajs-2557	126	33	to	to	PART
iajs-2557	126	34	get	get	VERB
iajs-2557	126	35	c‖	c‖	ADJ
iajs-2557	126	36	y⃗	y⃗	NOUN
iajs-2557	126	37	n	n	X
iajs-2557	126	38	‖	‖	PROPN
iajs-2557	126	39	(	(	PUNCT
iajs-2557	126	40	h1(ω	h1(ω	PROPN
iajs-2557	126	41	)	)	PUNCT
iajs-2557	126	42	)	)	PUNCT
iajs-2557	126	43	3	3	NUM
iajs-2557	126	44	2	2	NUM
iajs-2557	126	45	≤	≤	NOUN
iajs-2557	126	46	a	a	DET
iajs-2557	126	47	(	(	PUNCT
iajs-2557	126	48	y⃗	y⃗	NOUN
iajs-2557	126	49	n	n	NOUN
iajs-2557	126	50	,	,	PUNCT
iajs-2557	126	51	y⃗	y⃗	NOUN
iajs-2557	126	52	n	n	NOUN
iajs-2557	126	53	)	)	PUNCT
iajs-2557	127	1	=	=	SYM
iajs-2557	127	2	f	f	X
iajs-2557	127	3	(	(	PUNCT
iajs-2557	127	4	y⃗	y⃗	NOUN
iajs-2557	127	5	n	n	CCONJ
iajs-2557	127	6	)	)	PUNCT
iajs-2557	127	7	≤	≤	NOUN
iajs-2557	127	8	ℓ1‖	ℓ1‖	ADJ
iajs-2557	127	9	y1n‖l2(ω	y1n‖l2(ω	NOUN
iajs-2557	127	10	)	)	PUNCT
iajs-2557	128	1	+	+	CCONJ
iajs-2557	128	2	c1‖	c1‖	X
iajs-2557	128	3	y1n‖h1(ω	y1n‖h1(ω	X
iajs-2557	128	4	)	)	PUNCT
iajs-2557	129	1	+	+	CCONJ
iajs-2557	129	2	ℓ2‖	ℓ2‖	PROPN
iajs-2557	129	3	y2n‖l2(ω	y2n‖l2(ω	PROPN
iajs-2557	129	4	)	)	PUNCT
iajs-2557	130	1	+	+	CCONJ
iajs-2557	131	1	c2‖	c2‖	PROPN
iajs-2557	131	2	y2n‖h1(ω	y2n‖h1(ω	NOUN
iajs-2557	131	3	)	)	PUNCT
iajs-2557	132	1	+	+	CCONJ
iajs-2557	132	2	ℓ3‖	ℓ3‖	PROPN
iajs-2557	132	3	y3n‖l2(ω	y3n‖l2(ω	ADV
iajs-2557	132	4	)	)	PUNCT
iajs-2557	133	1	+	+	CCONJ
iajs-2557	133	2	c3‖	c3‖	PROPN
iajs-2557	133	3	y3n‖h1(ω	y3n‖h1(ω	NOUN
iajs-2557	133	4	)	)	PUNCT
iajs-2557	133	5	≤	≤	NUM
iajs-2557	133	6	s‖	s‖	ADP
iajs-2557	133	7	y⃗	y⃗	NOUN
iajs-2557	133	8	n‖h1(ω	n‖h1(ω	ADJ
iajs-2557	133	9	)	)	PUNCT
iajs-2557	133	10	then	then	ADV
iajs-2557	133	11	‖	‖	PROPN
iajs-2557	133	12	y⃗	y⃗	NOUN
iajs-2557	133	13	n‖	n‖	NOUN
iajs-2557	133	14	(	(	PUNCT
iajs-2557	133	15	h1(ω	h1(ω	PROPN
iajs-2557	133	16	)	)	PUNCT
iajs-2557	133	17	)	)	PUNCT
iajs-2557	133	18	3	3	NUM
iajs-2557	133	19	≤	≤	NOUN
iajs-2557	133	20	a	a	PRON
iajs-2557	133	21	,	,	PUNCT
iajs-2557	133	22	for	for	ADP
iajs-2557	133	23	each	each	DET
iajs-2557	133	24	n	n	NOUN
iajs-2557	133	25	with	with	ADP
iajs-2557	133	26	a	a	DET
iajs-2557	133	27	=	=	X
iajs-2557	133	28	s	s	NOUN
iajs-2557	133	29	c	c	NOUN
iajs-2557	133	30	>	>	X
iajs-2557	133	31	0	0	PUNCT
iajs-2557	133	32	.	.	PUNCT
iajs-2557	134	1	where	where	SCONJ
iajs-2557	134	2	r1	r1	NOUN
iajs-2557	134	3	=	=	SYM
iajs-2557	134	4	max(ℓ1	max(ℓ1	PROPN
iajs-2557	134	5	,	,	PUNCT
iajs-2557	134	6	c1	c1	PROPN
iajs-2557	134	7	)	)	PUNCT
iajs-2557	134	8	,	,	PUNCT
iajs-2557	134	9	r2	r2	NOUN
iajs-2557	134	10	=	=	SYM
iajs-2557	134	11	max(ℓ2	max(ℓ2	PROPN
iajs-2557	134	12	,	,	PUNCT
iajs-2557	134	13	c2	c2	PROPN
iajs-2557	134	14	)	)	PUNCT
iajs-2557	134	15	,	,	PUNCT
iajs-2557	134	16	r3	r3	PROPN
iajs-2557	134	17	=	=	SYM
iajs-2557	134	18	(	(	PUNCT
iajs-2557	134	19	ℓ3	ℓ3	PROPN
iajs-2557	134	20	,	,	PUNCT
iajs-2557	134	21	c3	c3	PROPN
iajs-2557	134	22	)	)	PUNCT
iajs-2557	134	23	and	and	CCONJ
iajs-2557	134	24	s	s	X
iajs-2557	134	25	=	=	PUNCT
iajs-2557	134	26	max(r1	max(r1	NOUN
iajs-2557	134	27	,	,	PUNCT
iajs-2557	134	28	r2	r2	PROPN
iajs-2557	134	29	,	,	PUNCT
iajs-2557	134	30	r3	r3	PROPN
iajs-2557	134	31	)	)	PUNCT
iajs-2557	134	32	.	.	PUNCT
iajs-2557	135	1	65	65	NUM
iajs-2557	136	1	ibn	ibn	PROPN
iajs-2557	136	2	al	al	PROPN
iajs-2557	136	3	-	-	PUNCT
iajs-2557	136	4	haitham	haitham	PROPN
iajs-2557	136	5	jour	jour	X
iajs-2557	136	6	.	.	PROPN
iajs-2557	136	7	for	for	ADP
iajs-2557	136	8	pure	pure	ADJ
iajs-2557	136	9	&	&	CCONJ
iajs-2557	136	10	appl	appl	PROPN
iajs-2557	136	11	.	.	PUNCT
iajs-2557	137	1	sci	sci	PROPN
iajs-2557	137	2	.	.	PROPN
iajs-2557	138	1	34	34	NUM
iajs-2557	138	2	(	(	PUNCT
iajs-2557	138	3	1	1	NUM
iajs-2557	138	4	)	)	PUNCT
iajs-2557	138	5	2021	2021	NUM
iajs-2557	139	1	then	then	ADV
iajs-2557	139	2	by	by	ADP
iajs-2557	139	3	agth	agth	NOUN
iajs-2557	139	4	{	{	PUNCT
iajs-2557	139	5	y⃗	y⃗	NOUN
iajs-2557	139	6	n	n	CCONJ
iajs-2557	139	7	}	}	PUNCT
iajs-2557	139	8	has	have	VERB
iajs-2557	139	9	a	a	DET
iajs-2557	139	10	subsequence	subsequence	NOUN
iajs-2557	139	11	.	.	PUNCT
iajs-2557	140	1	it	it	PRON
iajs-2557	140	2	is	be	AUX
iajs-2557	140	3	not	not	PART
iajs-2557	140	4	loss	loss	NOUN
iajs-2557	140	5	of	of	ADP
iajs-2557	140	6	generality	generality	NOUN
iajs-2557	140	7	to	to	PART
iajs-2557	140	8	say	say	VERB
iajs-2557	140	9	again	again	ADV
iajs-2557	140	10	{	{	PUNCT
iajs-2557	140	11	y⃗	y⃗	NOUN
iajs-2557	140	12	n	n	CCONJ
iajs-2557	140	13	}	}	PUNCT
iajs-2557	140	14	for	for	ADP
iajs-2557	140	15	which	which	PRON
iajs-2557	140	16	y⃗	y⃗	NOUN
iajs-2557	140	17	n	n	PRON
iajs-2557	140	18	→	→	SYM
iajs-2557	140	19	y⃗	y⃗	NOUN
iajs-2557	140	20	weakly	weakly	ADV
iajs-2557	140	21	in	in	ADP
iajs-2557	140	22	v⃗⃗	v⃗⃗	PROPN
iajs-2557	140	23	,	,	PUNCT
iajs-2557	140	24	since	since	SCONJ
iajs-2557	140	25	∀n	∀n	NUM
iajs-2557	140	26	y⃗	y⃗	NOUN
iajs-2557	140	27	n	n	NOUN
iajs-2557	140	28	satisfies	satisfy	VERB
iajs-2557	140	29	the	the	DET
iajs-2557	140	30	wfo	wfo	NOUN
iajs-2557	140	31	(	(	PUNCT
iajs-2557	140	32	11	11	NUM
iajs-2557	140	33	)	)	PUNCT
iajs-2557	140	34	for	for	ADP
iajs-2557	140	35	each	each	PRON
iajs-2557	140	36	,	,	PUNCT
iajs-2557	140	37	or	or	CCONJ
iajs-2557	140	38	a	a	DET
iajs-2557	140	39	(	(	PUNCT
iajs-2557	140	40	y⃗	y⃗	NOUN
iajs-2557	140	41	n	n	CCONJ
iajs-2557	140	42	,	,	PUNCT
iajs-2557	140	43	v⃗	v⃗	ADJ
iajs-2557	140	44	)	)	PUNCT
iajs-2557	141	1	=	=	PUNCT
iajs-2557	141	2	fn(v⃗	fn(v⃗	NOUN
iajs-2557	141	3	)	)	PUNCT
iajs-2557	142	1	=	=	PRON
iajs-2557	142	2	(	(	PUNCT
iajs-2557	142	3	f1	f1	NOUN
iajs-2557	142	4	,	,	PUNCT
iajs-2557	142	5	v1)l2(ω	v1)l2(ω	ADV
iajs-2557	142	6	)	)	PUNCT
iajs-2557	143	1	+	+	CCONJ
iajs-2557	143	2	(	(	PUNCT
iajs-2557	143	3	u1n	u1n	NOUN
iajs-2557	143	4	,	,	PUNCT
iajs-2557	143	5	v1)l2(∂ω	v1)l2(∂ω	VERB
iajs-2557	143	6	)	)	PUNCT
iajs-2557	144	1	+	+	CCONJ
iajs-2557	144	2	(	(	PUNCT
iajs-2557	144	3	f2	f2	INTJ
iajs-2557	144	4	,	,	PUNCT
iajs-2557	144	5	v2)l2(ω	v2)l2(ω	ADJ
iajs-2557	144	6	)	)	PUNCT
iajs-2557	145	1	+	+	CCONJ
iajs-2557	145	2	(	(	PUNCT
iajs-2557	145	3	u2n	u2n	PROPN
iajs-2557	145	4	,	,	PUNCT
iajs-2557	145	5	v2)l2(∂ω	v2)l2(∂ω	PROPN
iajs-2557	145	6	)	)	PUNCT
iajs-2557	146	1	+	+	PROPN
iajs-2557	146	2	(	(	PUNCT
iajs-2557	146	3	f3	f3	ADJ
iajs-2557	146	4	,	,	PUNCT
iajs-2557	146	5	v3)l2(ω	v3)l2(ω	ADV
iajs-2557	146	6	)	)	PUNCT
iajs-2557	147	1	+	+	CCONJ
iajs-2557	147	2	(	(	PUNCT
iajs-2557	147	3	u3n	u3n	INTJ
iajs-2557	147	4	,	,	PUNCT
iajs-2557	147	5	v3)l2(∂ω	v3)l2(∂ω	NOUN
iajs-2557	147	6	)	)	PUNCT
iajs-2557	147	7	(	(	PUNCT
iajs-2557	147	8	23	23	NUM
iajs-2557	147	9	)	)	PUNCT
iajs-2557	147	10	to	to	PART
iajs-2557	147	11	show	show	VERB
iajs-2557	147	12	(	(	PUNCT
iajs-2557	147	13	23	23	NUM
iajs-2557	147	14	)	)	PUNCT
iajs-2557	147	15	converges	converge	VERB
iajs-2557	147	16	to	to	ADP
iajs-2557	147	17	a	a	DET
iajs-2557	147	18	(	(	PUNCT
iajs-2557	147	19	y⃗	y⃗	NOUN
iajs-2557	147	20	,	,	PUNCT
iajs-2557	147	21	v⃗	v⃗	ADJ
iajs-2557	147	22	)	)	PUNCT
iajs-2557	148	1	=	=	SYM
iajs-2557	148	2	f(v⃗	f(v⃗	NOUN
iajs-2557	148	3	)	)	PUNCT
iajs-2557	148	4	(	(	PUNCT
iajs-2557	148	5	24	24	NUM
iajs-2557	148	6	)	)	PUNCT
iajs-2557	148	7	first	first	ADV
iajs-2557	148	8	,	,	PUNCT
iajs-2557	148	9	since	since	SCONJ
iajs-2557	148	10	yin	yin	PROPN
iajs-2557	148	11	→	→	SYM
iajs-2557	148	12	yi	yi	PROPN
iajs-2557	148	13	weakly	weakly	ADV
iajs-2557	148	14	in	in	ADP
iajs-2557	148	15	l2(ω	l2(ω	NOUN
iajs-2557	148	16	)	)	PUNCT
iajs-2557	148	17	∀	∀	NOUN
iajs-2557	149	1	i	i	NOUN
iajs-2557	149	2	(	(	PUNCT
iajs-2557	149	3	for	for	ADP
iajs-2557	149	4	yin	yin	PROPN
iajs-2557	149	5	→	→	SYM
iajs-2557	149	6	yi	yi	PROPN
iajs-2557	149	7	weakly	weakly	ADV
iajs-2557	149	8	in	in	ADP
iajs-2557	149	9	vi	vi	PROPN
iajs-2557	149	10	)	)	PUNCT
iajs-2557	149	11	,	,	PUNCT
iajs-2557	149	12	then	then	ADV
iajs-2557	149	13	by	by	ADP
iajs-2557	149	14	csin	csin	NOUN
iajs-2557	149	15	,	,	PUNCT
iajs-2557	149	16	one	one	PRON
iajs-2557	149	17	has	have	VERB
iajs-2557	149	18	:	:	PUNCT
iajs-2557	149	19	│	│	NUM
iajs-2557	149	20	a1(y1n	a1(y1n	PROPN
iajs-2557	149	21	,	,	PUNCT
iajs-2557	149	22	v1	v1	NOUN
iajs-2557	149	23	)	)	PUNCT
iajs-2557	149	24	−	−	PROPN
iajs-2557	150	1	(	(	PUNCT
iajs-2557	150	2	y2n	y2n	PROPN
iajs-2557	150	3	+	+	CCONJ
iajs-2557	150	4	y3n	y3n	PROPN
iajs-2557	150	5	,	,	PUNCT
iajs-2557	150	6	v1	v1	NOUN
iajs-2557	150	7	)	)	PUNCT
iajs-2557	150	8	l2(ω	l2(ω	NUM
iajs-2557	150	9	)	)	PUNCT
iajs-2557	150	10	+	+	CCONJ
iajs-2557	150	11	a2(y2n	a2(y2n	PROPN
iajs-2557	150	12	,	,	PUNCT
iajs-2557	150	13	v2	v2	PROPN
iajs-2557	150	14	)	)	PUNCT
iajs-2557	151	1	+	+	CCONJ
iajs-2557	151	2	(	(	PUNCT
iajs-2557	151	3	y1n	y1n	PROPN
iajs-2557	151	4	+	+	CCONJ
iajs-2557	151	5	y3n	y3n	PROPN
iajs-2557	151	6	,	,	PUNCT
iajs-2557	151	7	v2	v2	PROPN
iajs-2557	151	8	)	)	PUNCT
iajs-2557	151	9	l2(ω	l2(ω	NUM
iajs-2557	151	10	)	)	PUNCT
iajs-2557	151	11	+	+	CCONJ
iajs-2557	151	12	a3(y3n	a3(y3n	PROPN
iajs-2557	151	13	,	,	PUNCT
iajs-2557	151	14	v3	v3	PROPN
iajs-2557	151	15	)	)	PUNCT
iajs-2557	152	1	+	+	CCONJ
iajs-2557	152	2	(	(	PUNCT
iajs-2557	152	3	y1n	y1n	PROPN
iajs-2557	152	4	−	−	NOUN
iajs-2557	152	5	y2n	y2n	PROPN
iajs-2557	152	6	,	,	PUNCT
iajs-2557	152	7	v3	v3	PROPN
iajs-2557	152	8	)	)	PUNCT
iajs-2557	152	9	l2(ω	l2(ω	NUM
iajs-2557	152	10	)	)	PUNCT
iajs-2557	152	11	−	−	PROPN
iajs-2557	152	12	a1(y1	a1(y1	PROPN
iajs-2557	152	13	,	,	PUNCT
iajs-2557	152	14	v1	v1	NOUN
iajs-2557	152	15	)	)	PUNCT
iajs-2557	152	16	+	+	CCONJ
iajs-2557	152	17	(	(	PUNCT
iajs-2557	152	18	y2	y2	INTJ
iajs-2557	152	19	+	+	CCONJ
iajs-2557	152	20	y3	y3	NOUN
iajs-2557	152	21	,	,	PUNCT
iajs-2557	152	22	v1	v1	NOUN
iajs-2557	152	23	)	)	PUNCT
iajs-2557	152	24	l2(ω	l2(ω	NOUN
iajs-2557	152	25	)	)	PUNCT
iajs-2557	152	26	−	−	PROPN
iajs-2557	152	27	a2(y2	a2(y2	ADJ
iajs-2557	152	28	,	,	PUNCT
iajs-2557	152	29	v2	v2	PROPN
iajs-2557	152	30	)	)	PUNCT
iajs-2557	152	31	−	−	PROPN
iajs-2557	153	1	(	(	PUNCT
iajs-2557	153	2	y1	y1	INTJ
iajs-2557	153	3	+	+	NUM
iajs-2557	153	4	y3	y3	NOUN
iajs-2557	153	5	,	,	PUNCT
iajs-2557	153	6	v2	v2	PROPN
iajs-2557	153	7	)	)	PUNCT
iajs-2557	153	8	l2(ω	l2(ω	NOUN
iajs-2557	153	9	)	)	PUNCT
iajs-2557	153	10	−	−	PROPN
iajs-2557	153	11	a3(y3	a3(y3	PROPN
iajs-2557	153	12	,	,	PUNCT
iajs-2557	153	13	v3	v3	PROPN
iajs-2557	153	14	)	)	PUNCT
iajs-2557	153	15	−	−	PROPN
iajs-2557	154	1	(	(	PUNCT
iajs-2557	154	2	y1	y1	INTJ
iajs-2557	154	3	−	−	PROPN
iajs-2557	154	4	y2	y2	PROPN
iajs-2557	154	5	,	,	PUNCT
iajs-2557	154	6	v3	v3	PROPN
iajs-2557	154	7	)	)	PUNCT
iajs-2557	154	8	l2(ω	l2(ω	NOUN
iajs-2557	154	9	)	)	PUNCT
iajs-2557	154	10	≤	≤	NOUN
iajs-2557	154	11	(	(	PUNCT
iajs-2557	154	12	c1‖	c1‖	NOUN
iajs-2557	154	13	y1n	y1n	PRON
iajs-2557	154	14	−	−	PROPN
iajs-2557	154	15	y1‖h1(ω	y1‖h1(ω	NOUN
iajs-2557	154	16	)	)	PUNCT
iajs-2557	155	1	+	+	CCONJ
iajs-2557	155	2	‖	‖	ADJ
iajs-2557	155	3	y2n	y2n	PROPN
iajs-2557	155	4	−	−	PROPN
iajs-2557	155	5	y2‖l2(ω	y2‖l2(ω	NOUN
iajs-2557	155	6	)	)	PUNCT
iajs-2557	156	1	+	+	CCONJ
iajs-2557	156	2	‖	‖	ADJ
iajs-2557	156	3	y3n	y3n	PROPN
iajs-2557	156	4	−	−	PROPN
iajs-2557	156	5	y3‖l2(ω	y3‖l2(ω	NOUN
iajs-2557	156	6	)	)	PUNCT
iajs-2557	156	7	)	)	PUNCT
iajs-2557	157	1	‖	‖	VERB
iajs-2557	157	2	v1‖l2(ω	v1‖l2(ω	ADV
iajs-2557	157	3	)	)	PUNCT
iajs-2557	158	1	+	+	PROPN
iajs-2557	158	2	(	(	PUNCT
iajs-2557	158	3	c2‖	c2‖	NOUN
iajs-2557	158	4	y2n	y2n	X
iajs-2557	158	5	−	−	PROPN
iajs-2557	158	6	y2‖h1(ω	y2‖h1(ω	NOUN
iajs-2557	158	7	)	)	PUNCT
iajs-2557	158	8	+	+	CCONJ
iajs-2557	158	9	‖	‖	PROPN
iajs-2557	158	10	y1n	y1n	PROPN
iajs-2557	158	11	−	−	PROPN
iajs-2557	158	12	y1‖l2(ω	y1‖l2(ω	PROPN
iajs-2557	158	13	)	)	PUNCT
iajs-2557	158	14	+	+	CCONJ
iajs-2557	158	15	‖	‖	ADJ
iajs-2557	158	16	y3n	y3n	PROPN
iajs-2557	158	17	−	−	PROPN
iajs-2557	158	18	y3‖l2(ω	y3‖l2(ω	NOUN
iajs-2557	158	19	)	)	PUNCT
iajs-2557	158	20	)	)	PUNCT
iajs-2557	159	1	‖	‖	PROPN
iajs-2557	159	2	v2‖l2(ω	v2‖l2(ω	NOUN
iajs-2557	159	3	)	)	PUNCT
iajs-2557	160	1	+	+	PROPN
iajs-2557	160	2	(	(	PUNCT
iajs-2557	160	3	c3‖	c3‖	NOUN
iajs-2557	160	4	y3n	y3n	X
iajs-2557	160	5	−	−	PROPN
iajs-2557	160	6	y3‖h1(ω	y3‖h1(ω	NOUN
iajs-2557	160	7	)	)	PUNCT
iajs-2557	160	8	+	+	CCONJ
iajs-2557	160	9	‖	‖	PROPN
iajs-2557	160	10	y1n	y1n	PROPN
iajs-2557	160	11	−	−	PROPN
iajs-2557	160	12	y1‖l2(ω	y1‖l2(ω	PROPN
iajs-2557	160	13	)	)	PUNCT
iajs-2557	160	14	+	+	CCONJ
iajs-2557	160	15	‖	‖	ADJ
iajs-2557	160	16	y2n	y2n	PROPN
iajs-2557	160	17	−	−	PROPN
iajs-2557	160	18	y2‖l2(ω	y2‖l2(ω	NOUN
iajs-2557	160	19	)	)	PUNCT
iajs-2557	160	20	)	)	PUNCT
iajs-2557	160	21	‖	‖	PROPN
iajs-2557	160	22	v3‖l2(ω	v3‖l2(ω	NOUN
iajs-2557	160	23	)	)	PUNCT
iajs-2557	160	24	→	→	SYM
iajs-2557	160	25	0	0	NUM
iajs-2557	160	26	second	second	NOUN
iajs-2557	160	27	,	,	PUNCT
iajs-2557	160	28	we	we	PRON
iajs-2557	160	29	have	have	VERB
iajs-2557	160	30	u⃗	u⃗	PROPN
iajs-2557	160	31	n	n	PROPN
iajs-2557	160	32	→	→	SYM
iajs-2557	160	33	u⃗	u⃗	PROPN
iajs-2557	160	34	weakly	weakly	ADV
iajs-2557	160	35	in	in	ADP
iajs-2557	160	36	(	(	PUNCT
iajs-2557	160	37	l2(∂ω	l2(∂ω	NUM
iajs-2557	160	38	)	)	PUNCT
iajs-2557	160	39	)	)	PUNCT
iajs-2557	160	40	3	3	NUM
iajs-2557	160	41	,	,	PUNCT
iajs-2557	160	42	then	then	ADV
iajs-2557	160	43	the	the	DET
iajs-2557	160	44	terms	term	NOUN
iajs-2557	160	45	in	in	ADP
iajs-2557	160	46	the	the	DET
iajs-2557	160	47	right	right	ADJ
iajs-2557	160	48	hand	hand	NOUN
iajs-2557	160	49	side	side	NOUN
iajs-2557	160	50	of	of	ADP
iajs-2557	160	51	(	(	PUNCT
iajs-2557	160	52	23	23	NUM
iajs-2557	160	53	)	)	PUNCT
iajs-2557	160	54	converges	converge	VERB
iajs-2557	160	55	to	to	ADP
iajs-2557	160	56	the	the	DET
iajs-2557	160	57	those	those	PRON
iajs-2557	160	58	in	in	ADP
iajs-2557	160	59	the	the	DET
iajs-2557	160	60	right	right	ADJ
iajs-2557	160	61	hand	hand	NOUN
iajs-2557	160	62	side	side	NOUN
iajs-2557	160	63	of	of	ADP
iajs-2557	160	64	(	(	PUNCT
iajs-2557	160	65	24	24	NUM
iajs-2557	160	66	)	)	PUNCT
iajs-2557	160	67	.	.	PUNCT
iajs-2557	161	1	thus	thus	ADV
iajs-2557	161	2	(	(	PUNCT
iajs-2557	161	3	23	23	X
iajs-2557	161	4	)	)	PUNCT
iajs-2557	161	5	converges	converge	VERB
iajs-2557	161	6	to	to	ADP
iajs-2557	161	7	(	(	PUNCT
iajs-2557	161	8	24	24	NUM
iajs-2557	161	9	)	)	PUNCT
iajs-2557	161	10	.	.	PUNCT
iajs-2557	162	1	but	but	CCONJ
iajs-2557	162	2	,	,	PUNCT
iajs-2557	162	3	we	we	PRON
iajs-2557	162	4	have	have	VERB
iajs-2557	162	5	u⃗	u⃗	PROPN
iajs-2557	162	6	n	n	PROPN
iajs-2557	162	7	→	→	SYM
iajs-2557	162	8	u⃗	u⃗	PROPN
iajs-2557	162	9	weakly	weakly	ADV
iajs-2557	162	10	in	in	ADP
iajs-2557	162	11	(	(	PUNCT
iajs-2557	162	12	l2(∂ω	l2(∂ω	NUM
iajs-2557	162	13	)	)	PUNCT
iajs-2557	162	14	)	)	PUNCT
iajs-2557	162	15	3	3	NUM
iajs-2557	162	16	and	and	CCONJ
iajs-2557	162	17	g0	g0	PROPN
iajs-2557	162	18	(	(	PUNCT
iajs-2557	162	19	u⃗	u⃗	PROPN
iajs-2557	162	20	)	)	PUNCT
iajs-2557	162	21	is	be	AUX
iajs-2557	162	22	welsc	welsc	NOUN
iajs-2557	162	23	,	,	PUNCT
iajs-2557	162	24	then	then	ADV
iajs-2557	162	25	g0	g0	PROPN
iajs-2557	162	26	(	(	PUNCT
iajs-2557	162	27	u⃗	u⃗	PROPN
iajs-2557	162	28	)	)	PUNCT
iajs-2557	162	29	≤	≤	PROPN
iajs-2557	163	1	lim	lim	PROPN
iajs-2557	163	2	n→∞	n→∞	NUM
iajs-2557	163	3	infu⃗⃗	infu⃗⃗	PRON
iajs-2557	163	4	n∈w⃗⃗⃗⃗	n∈w⃗⃗⃗⃗	PROPN
iajs-2557	163	5	g0	g0	PROPN
iajs-2557	163	6	(	(	PUNCT
iajs-2557	163	7	u⃗	u⃗	PROPN
iajs-2557	163	8	n	n	NOUN
iajs-2557	163	9	)	)	PUNCT
iajs-2557	164	1	=	=	SYM
iajs-2557	164	2	lim	lim	PROPN
iajs-2557	164	3	n→∞	n→∞	NUM
iajs-2557	164	4	g0	g0	PROPN
iajs-2557	164	5	(	(	PUNCT
iajs-2557	164	6	u⃗	u⃗	PROPN
iajs-2557	164	7	n	n	NOUN
iajs-2557	164	8	)	)	PUNCT
iajs-2557	164	9	=	=	PUNCT
iajs-2557	164	10	infw⃗⃗⃗	infw⃗⃗⃗	NOUN
iajs-2557	164	11	∈w⃗⃗⃗⃗	∈w⃗⃗⃗⃗	NOUN
iajs-2557	164	12	g0	g0	PROPN
iajs-2557	164	13	(	(	PUNCT
iajs-2557	164	14	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	164	15	)	)	PUNCT
iajs-2557	164	16	then	then	ADV
iajs-2557	164	17	g0	g0	PROPN
iajs-2557	164	18	(	(	PUNCT
iajs-2557	164	19	u⃗	u⃗	PROPN
iajs-2557	164	20	)	)	PUNCT
iajs-2557	164	21	=	=	PUNCT
iajs-2557	164	22	infw⃗⃗⃗	infw⃗⃗⃗	NOUN
iajs-2557	164	23	∈w⃗⃗⃗⃗	∈w⃗⃗⃗⃗	NOUN
iajs-2557	164	24	g0	g0	PROPN
iajs-2557	164	25	(	(	PUNCT
iajs-2557	164	26	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	164	27	)	)	PUNCT
iajs-2557	164	28	,	,	PUNCT
iajs-2557	164	29	i.e	i.e	PRON
iajs-2557	164	30	,	,	PUNCT
iajs-2557	164	31	u⃗	u⃗	PROPN
iajs-2557	164	32	a	a	DET
iajs-2557	164	33	ccbocvr	ccbocvr	NOUN
iajs-2557	164	34	.	.	PUNCT
iajs-2557	165	1	applying	apply	VERB
iajs-2557	165	2	remark	remark	NOUN
iajs-2557	165	3	4.1	4.1	NUM
iajs-2557	165	4	,	,	PUNCT
iajs-2557	165	5	gives	give	VERB
iajs-2557	165	6	us	we	PRON
iajs-2557	165	7	u⃗	u⃗	PROPN
iajs-2557	165	8	which	which	PRON
iajs-2557	165	9	is	be	AUX
iajs-2557	165	10	unique	unique	ADJ
iajs-2557	165	11	.	.	PUNCT
iajs-2557	166	1	5	5	X
iajs-2557	166	2	.	.	PUNCT
iajs-2557	166	3	the	the	DET
iajs-2557	166	4	ncth	ncth	NOUN
iajs-2557	166	5	for	for	ADP
iajs-2557	166	6	optimality	optimality	NOUN
iajs-2557	166	7	:	:	PUNCT
iajs-2557	166	8	theorem	theorem	VERB
iajs-2557	166	9	5.1	5.1	NUM
iajs-2557	166	10	:	:	PUNCT
iajs-2557	166	11	the	the	DET
iajs-2557	166	12	tajes(z1	tajes(z1	NOUN
iajs-2557	166	13	,	,	PUNCT
iajs-2557	166	14	z2	z2	PROPN
iajs-2557	166	15	,	,	PUNCT
iajs-2557	166	16	z3	z3	PROPN
iajs-2557	166	17	)	)	PUNCT
iajs-2557	166	18	=	=	SYM
iajs-2557	167	1	(	(	PUNCT
iajs-2557	167	2	z1u1	z1u1	PROPN
iajs-2557	167	3	,	,	PUNCT
iajs-2557	167	4	z2u2	z2u2	PROPN
iajs-2557	167	5	,	,	PUNCT
iajs-2557	167	6	z3u3	z3u3	PROPN
iajs-2557	167	7	)	)	PUNCT
iajs-2557	167	8	of	of	ADP
iajs-2557	167	9	the	the	DET
iajs-2557	167	10	wfo	wfo	NOUN
iajs-2557	167	11	of	of	ADP
iajs-2557	167	12	the	the	DET
iajs-2557	167	13	tses	tse	NOUN
iajs-2557	167	14	(	(	PUNCT
iajs-2557	167	15	1	1	NUM
iajs-2557	167	16	-	-	SYM
iajs-2557	167	17	6	6	NUM
iajs-2557	167	18	)	)	PUNCT
iajs-2557	167	19	are	be	AUX
iajs-2557	167	20	given	give	VERB
iajs-2557	167	21	by	by	ADP
iajs-2557	167	22	:	:	PUNCT
iajs-2557	167	23	a1	a1	NOUN
iajs-2557	167	24	z1	z1	NOUN
iajs-2557	167	25	+	+	CCONJ
iajs-2557	167	26	z1	z1	ADJ
iajs-2557	167	27	+	+	CCONJ
iajs-2557	167	28	z2	z2	PROPN
iajs-2557	167	29	+	+	CCONJ
iajs-2557	167	30	z3	z3	NOUN
iajs-2557	167	31	=	=	PUNCT
iajs-2557	167	32	(	(	PUNCT
iajs-2557	167	33	y1	y1	INTJ
iajs-2557	167	34	−	−	PROPN
iajs-2557	167	35	y1d	y1d	PROPN
iajs-2557	167	36	)	)	PUNCT
iajs-2557	167	37	,	,	PUNCT
iajs-2557	167	38	in	in	ADP
iajs-2557	167	39	ω	ω	PROPN
iajs-2557	167	40	(	(	PUNCT
iajs-2557	167	41	25	25	NUM
iajs-2557	167	42	)	)	PUNCT
iajs-2557	167	43	a2	a2	NOUN
iajs-2557	167	44	z1	z1	NOUN
iajs-2557	167	45	−	−	PROPN
iajs-2557	167	46	z1	z1	PROPN
iajs-2557	167	47	+	+	CCONJ
iajs-2557	167	48	z2	z2	PROPN
iajs-2557	167	49	−	−	PROPN
iajs-2557	167	50	z3	z3	NOUN
iajs-2557	167	51	=	=	PUNCT
iajs-2557	167	52	(	(	PUNCT
iajs-2557	167	53	y2	y2	INTJ
iajs-2557	167	54	−	−	PROPN
iajs-2557	167	55	y2d	y2d	NOUN
iajs-2557	167	56	)	)	PUNCT
iajs-2557	167	57	,	,	PUNCT
iajs-2557	167	58	in	in	ADP
iajs-2557	167	59	ω	ω	PROPN
iajs-2557	167	60	(	(	PUNCT
iajs-2557	167	61	26	26	NUM
iajs-2557	167	62	)	)	PUNCT
iajs-2557	167	63	a3	a3	NOUN
iajs-2557	167	64	z1	z1	VERB
iajs-2557	167	65	−	−	PROPN
iajs-2557	167	66	z1	z1	PROPN
iajs-2557	167	67	+	+	CCONJ
iajs-2557	167	68	z2	z2	PROPN
iajs-2557	167	69	+	+	CCONJ
iajs-2557	167	70	z3	z3	NOUN
iajs-2557	167	71	=	=	PUNCT
iajs-2557	167	72	(	(	PUNCT
iajs-2557	167	73	y3	y3	NOUN
iajs-2557	167	74	−	−	PROPN
iajs-2557	167	75	y3d	y3d	PROPN
iajs-2557	167	76	)	)	PUNCT
iajs-2557	167	77	,	,	PUNCT
iajs-2557	167	78	in	in	ADP
iajs-2557	167	79	ω	ω	PROPN
iajs-2557	167	80	(	(	PUNCT
iajs-2557	167	81	27	27	NUM
iajs-2557	167	82	)	)	PUNCT
iajs-2557	168	1	∂z1	∂z1	PROPN
iajs-2557	168	2	∂n1	∂n1	NOUN
iajs-2557	168	3	=	=	SYM
iajs-2557	168	4	0	0	NUM
iajs-2557	168	5	,	,	PUNCT
iajs-2557	168	6	in	in	ADP
iajs-2557	168	7	∂ω	∂ω	PROPN
iajs-2557	168	8	(	(	PUNCT
iajs-2557	168	9	28	28	NUM
iajs-2557	168	10	)	)	PUNCT
iajs-2557	168	11	∂z2	∂z2	NOUN
iajs-2557	168	12	∂n2	∂n2	NOUN
iajs-2557	168	13	=	=	SYM
iajs-2557	168	14	0	0	NUM
iajs-2557	168	15	,	,	PUNCT
iajs-2557	168	16	in	in	ADP
iajs-2557	168	17	∂ω	∂ω	PROPN
iajs-2557	168	18	(	(	PUNCT
iajs-2557	168	19	29	29	NUM
iajs-2557	168	20	)	)	PUNCT
iajs-2557	168	21	∂z3	∂z3	NOUN
iajs-2557	169	1	∂n3	∂n3	ADP
iajs-2557	169	2	=	=	SYM
iajs-2557	169	3	0	0	NUM
iajs-2557	169	4	,	,	PUNCT
iajs-2557	169	5	in	in	ADP
iajs-2557	169	6	∂ω	∂ω	PROPN
iajs-2557	169	7	(	(	PUNCT
iajs-2557	169	8	30	30	NUM
iajs-2557	169	9	)	)	PUNCT
iajs-2557	169	10	then	then	ADV
iajs-2557	169	11	the	the	DET
iajs-2557	169	12	fde	fde	NOUN
iajs-2557	169	13	of	of	ADP
iajs-2557	169	14	g0	g0	PROPN
iajs-2557	169	15	is	be	AUX
iajs-2557	169	16	given	give	VERB
iajs-2557	169	17	by	by	ADP
iajs-2557	169	18	:	:	PUNCT
iajs-2557	169	19	(	(	PUNCT
iajs-2557	169	20	g0	g0	ADJ
iajs-2557	169	21	′	′	PROPN
iajs-2557	169	22	(	(	PUNCT
iajs-2557	169	23	u⃗	u⃗	PROPN
iajs-2557	169	24	)	)	PUNCT
iajs-2557	169	25	,	,	PUNCT
iajs-2557	169	26	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	169	27	⃗⃗	⃗⃗	PROPN
iajs-2557	169	28	)	)	PUNCT
iajs-2557	169	29	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	169	30	)	)	PUNCT
iajs-2557	169	31	=	=	SYM
iajs-2557	170	1	(	(	PUNCT
iajs-2557	170	2	z	z	X
iajs-2557	170	3	+	+	NOUN
iajs-2557	170	4	∝	∝	PROPN
iajs-2557	170	5	u⃗	u⃗	PROPN
iajs-2557	170	6	,	,	PUNCT
iajs-2557	170	7	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	170	8	⃗⃗	⃗⃗	PROPN
iajs-2557	170	9	)	)	PUNCT
iajs-2557	170	10	l2(∂ω	l2(∂ω	NUM
iajs-2557	170	11	)	)	PUNCT
iajs-2557	170	12	proof	proof	NOUN
iajs-2557	170	13	:	:	PUNCT
iajs-2557	170	14	rewriting	rewrite	VERB
iajs-2557	170	15	the	the	DET
iajs-2557	170	16	tajes	taje	NOUN
iajs-2557	170	17	(	(	PUNCT
iajs-2557	170	18	25	25	NUM
iajs-2557	170	19	-	-	SYM
iajs-2557	170	20	30	30	NUM
iajs-2557	170	21	)	)	PUNCT
iajs-2557	170	22	by	by	ADP
iajs-2557	170	23	its	its	PRON
iajs-2557	170	24	wfo	wfo	NOUN
iajs-2557	170	25	,	,	PUNCT
iajs-2557	170	26	adding	add	VERB
iajs-2557	170	27	them	they	PRON
iajs-2557	170	28	,	,	PUNCT
iajs-2557	170	29	then	then	ADV
iajs-2557	170	30	substituting	substitute	VERB
iajs-2557	170	31	v⃗	v⃗	PROPN
iajs-2557	170	32	=	=	SYM
iajs-2557	170	33	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	170	34	,	,	PUNCT
iajs-2557	170	35	once	once	ADV
iajs-2557	170	36	get	get	VERB
iajs-2557	170	37	the	the	DET
iajs-2557	170	38	following	follow	VERB
iajs-2557	170	39	wfo	wfo	NOUN
iajs-2557	170	40	which	which	PRON
iajs-2557	170	41	has	have	VERB
iajs-2557	170	42	a	a	DET
iajs-2557	170	43	unique	unique	ADJ
iajs-2557	170	44	solution	solution	NOUN
iajs-2557	170	45	z	z	NOUN
iajs-2557	170	46	=	=	SYM
iajs-2557	170	47	z	z	X
iajs-2557	170	48	u⃗⃗	u⃗⃗	NOUN
iajs-2557	170	49	:	:	PUNCT
iajs-2557	170	50	a1(z1	a1(z1	ADJ
iajs-2557	170	51	,	,	PUNCT
iajs-2557	170	52	∆y1	∆y1	PROPN
iajs-2557	170	53	)	)	PUNCT
iajs-2557	171	1	+	+	CCONJ
iajs-2557	171	2	(	(	PUNCT
iajs-2557	171	3	z2	z2	NOUN
iajs-2557	171	4	+	+	CCONJ
iajs-2557	171	5	z3	z3	PROPN
iajs-2557	171	6	,	,	PUNCT
iajs-2557	171	7	∆y1	∆y1	NOUN
iajs-2557	171	8	)	)	PUNCT
iajs-2557	171	9	l2(ω	l2(ω	NUM
iajs-2557	171	10	)	)	PUNCT
iajs-2557	172	1	+	+	NUM
iajs-2557	172	2	a2(z2	a2(z2	NOUN
iajs-2557	172	3	,	,	PUNCT
iajs-2557	172	4	∆y2	∆y2	PROPN
iajs-2557	172	5	)	)	PUNCT
iajs-2557	173	1	−	−	PROPN
iajs-2557	173	2	(	(	PUNCT
iajs-2557	173	3	z1	z1	NOUN
iajs-2557	173	4	+	+	CCONJ
iajs-2557	173	5	z3	z3	NOUN
iajs-2557	173	6	,	,	PUNCT
iajs-2557	173	7	∆y1	∆y1	NOUN
iajs-2557	173	8	)	)	PUNCT
iajs-2557	173	9	l2(ω	l2(ω	NUM
iajs-2557	173	10	)	)	PUNCT
iajs-2557	174	1	+	+	CCONJ
iajs-2557	174	2	a3(z3	a3(z3	ADV
iajs-2557	174	3	,	,	PUNCT
iajs-2557	174	4	∆y3	∆y3	PROPN
iajs-2557	174	5	)	)	PUNCT
iajs-2557	175	1	−	−	PROPN
iajs-2557	176	1	(	(	PUNCT
iajs-2557	176	2	z1	z1	PROPN
iajs-2557	176	3	−	−	PROPN
iajs-2557	176	4	z2	z2	PROPN
iajs-2557	176	5	,	,	PUNCT
iajs-2557	176	6	∆y3	∆y3	PROPN
iajs-2557	176	7	)	)	PUNCT
iajs-2557	177	1	l2(ω	l2(ω	X
iajs-2557	177	2	)	)	PUNCT
iajs-2557	177	3	=	=	SYM
iajs-2557	178	1	(	(	PUNCT
iajs-2557	178	2	y1	y1	INTJ
iajs-2557	178	3	−	−	PROPN
iajs-2557	178	4	y1d	y1d	NOUN
iajs-2557	178	5	,	,	PUNCT
iajs-2557	178	6	∆y1	∆y1	PROPN
iajs-2557	178	7	)	)	PUNCT
iajs-2557	178	8	l2(ω	l2(ω	NUM
iajs-2557	178	9	)	)	PUNCT
iajs-2557	179	1	+	+	CCONJ
iajs-2557	179	2	(	(	PUNCT
iajs-2557	179	3	y2	y2	INTJ
iajs-2557	179	4	−	−	PROPN
iajs-2557	179	5	y2d	y2d	PROPN
iajs-2557	179	6	,	,	PUNCT
iajs-2557	179	7	∆y2	∆y2	PROPN
iajs-2557	179	8	)	)	PUNCT
iajs-2557	180	1	l2(ω	l2(ω	X
iajs-2557	180	2	)	)	PUNCT
iajs-2557	180	3	+	+	CCONJ
iajs-2557	180	4	66	66	NUM
iajs-2557	180	5	ibn	ibn	PROPN
iajs-2557	180	6	al	al	PROPN
iajs-2557	180	7	-	-	PUNCT
iajs-2557	180	8	haitham	haitham	PROPN
iajs-2557	180	9	jour	jour	X
iajs-2557	180	10	.	.	PROPN
iajs-2557	180	11	for	for	ADP
iajs-2557	180	12	pure	pure	ADJ
iajs-2557	180	13	&	&	CCONJ
iajs-2557	180	14	appl	appl	PROPN
iajs-2557	180	15	.	.	PUNCT
iajs-2557	181	1	sci	sci	PROPN
iajs-2557	181	2	.	.	PROPN
iajs-2557	182	1	34	34	NUM
iajs-2557	182	2	(	(	PUNCT
iajs-2557	182	3	1	1	NUM
iajs-2557	182	4	)	)	PUNCT
iajs-2557	182	5	2021	2021	NUM
iajs-2557	182	6	(	(	PUNCT
iajs-2557	182	7	y3	y3	NOUN
iajs-2557	182	8	−	−	PROPN
iajs-2557	182	9	y3d	y3d	NOUN
iajs-2557	182	10	,	,	PUNCT
iajs-2557	182	11	∆y3	∆y3	PROPN
iajs-2557	182	12	)	)	PUNCT
iajs-2557	183	1	l2(ω	l2(ω	PROPN
iajs-2557	183	2	)	)	PUNCT
iajs-2557	183	3	(	(	PUNCT
iajs-2557	183	4	31	31	NUM
iajs-2557	183	5	)	)	PUNCT
iajs-2557	183	6	utilizing	utilizing	NOUN
iajs-2557	183	7	(	(	PUNCT
iajs-2557	183	8	12a&b	12a&b	NOUN
iajs-2557	183	9	)	)	PUNCT
iajs-2557	183	10	in	in	ADP
iajs-2557	183	11	(	(	PUNCT
iajs-2557	183	12	11	11	NUM
iajs-2557	183	13	)	)	PUNCT
iajs-2557	183	14	,	,	PUNCT
iajs-2557	183	15	then	then	ADV
iajs-2557	183	16	substituting	substitute	VERB
iajs-2557	183	17	v⃗	v⃗	PROPN
iajs-2557	183	18	=	=	SYM
iajs-2557	183	19	z	z	NOUN
iajs-2557	184	1	once	once	ADV
iajs-2557	184	2	and	and	CCONJ
iajs-2557	184	3	once	once	ADV
iajs-2557	184	4	again	again	ADV
iajs-2557	184	5	v⃗	v⃗	PROPN
iajs-2557	184	6	=	=	SYM
iajs-2557	184	7	z	z	NOUN
iajs-2557	184	8	and	and	CCONJ
iajs-2557	184	9	setting	set	VERB
iajs-2557	184	10	y⃗	y⃗	NOUN
iajs-2557	184	11	+	+	CCONJ
iajs-2557	184	12	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	184	13	instead	instead	ADV
iajs-2557	184	14	of	of	ADP
iajs-2557	184	15	y⃗	y⃗	NOUN
iajs-2557	184	16	,	,	PUNCT
iajs-2557	184	17	then	then	ADV
iajs-2557	184	18	subtracting	subtract	VERB
iajs-2557	184	19	the	the	DET
iajs-2557	184	20	second	second	ADJ
iajs-2557	184	21	obtained	obtain	VERB
iajs-2557	184	22	equation	equation	NOUN
iajs-2557	184	23	from	from	ADP
iajs-2557	184	24	the	the	DET
iajs-2557	184	25	first	first	ADJ
iajs-2557	184	26	one	one	NUM
iajs-2557	184	27	,	,	PUNCT
iajs-2557	184	28	to	to	PART
iajs-2557	184	29	get	get	VERB
iajs-2557	184	30	a1(∆y1	a1(∆y1	PROPN
iajs-2557	184	31	,	,	PUNCT
iajs-2557	184	32	z1	z1	NOUN
iajs-2557	184	33	)	)	PUNCT
iajs-2557	184	34	−	−	PROPN
iajs-2557	185	1	(	(	PUNCT
iajs-2557	185	2	∆y2	∆y2	PROPN
iajs-2557	185	3	,	,	PUNCT
iajs-2557	185	4	z1	z1	PROPN
iajs-2557	185	5	)	)	PUNCT
iajs-2557	185	6	l2(ω	l2(ω	NOUN
iajs-2557	185	7	)	)	PUNCT
iajs-2557	185	8	−	−	PROPN
iajs-2557	185	9	(	(	PUNCT
iajs-2557	185	10	∆y3	∆y3	PROPN
iajs-2557	185	11	,	,	PUNCT
iajs-2557	185	12	z1	z1	PROPN
iajs-2557	185	13	)	)	PUNCT
iajs-2557	185	14	l2(ω	l2(ω	NUM
iajs-2557	185	15	)	)	PUNCT
iajs-2557	185	16	+	+	CCONJ
iajs-2557	185	17	a2(∆y2	a2(∆y2	PROPN
iajs-2557	185	18	,	,	PUNCT
iajs-2557	185	19	z2	z2	PROPN
iajs-2557	185	20	)	)	PUNCT
iajs-2557	186	1	+	+	CCONJ
iajs-2557	186	2	(	(	PUNCT
iajs-2557	186	3	∆y1	∆y1	NOUN
iajs-2557	186	4	,	,	PUNCT
iajs-2557	186	5	z2	z2	PROPN
iajs-2557	186	6	)	)	PUNCT
iajs-2557	186	7	l2(ω	l2(ω	NUM
iajs-2557	186	8	)	)	PUNCT
iajs-2557	186	9	+	+	CCONJ
iajs-2557	186	10	(	(	PUNCT
iajs-2557	186	11	∆y3	∆y3	ADJ
iajs-2557	186	12	,	,	PUNCT
iajs-2557	186	13	z2	z2	PROPN
iajs-2557	186	14	)	)	PUNCT
iajs-2557	186	15	l2(ω	l2(ω	NUM
iajs-2557	186	16	)	)	PUNCT
iajs-2557	186	17	+	+	CCONJ
iajs-2557	186	18	a3(∆y3	a3(∆y3	PROPN
iajs-2557	186	19	,	,	PUNCT
iajs-2557	186	20	z3	z3	PROPN
iajs-2557	186	21	)	)	PUNCT
iajs-2557	187	1	+	+	CCONJ
iajs-2557	187	2	(	(	PUNCT
iajs-2557	187	3	∆y1	∆y1	NOUN
iajs-2557	187	4	,	,	PUNCT
iajs-2557	187	5	z3	z3	PROPN
iajs-2557	187	6	)	)	PUNCT
iajs-2557	187	7	−	−	PROPN
iajs-2557	188	1	(	(	PUNCT
iajs-2557	188	2	∆y2	∆y2	PROPN
iajs-2557	188	3	,	,	PUNCT
iajs-2557	188	4	z3	z3	PROPN
iajs-2557	188	5	)	)	PUNCT
iajs-2557	189	1	=	=	PUNCT
iajs-2557	190	1	(	(	PUNCT
iajs-2557	190	2	∆u1	∆u1	PROPN
iajs-2557	190	3	,	,	PUNCT
iajs-2557	190	4	z1	z1	PROPN
iajs-2557	190	5	)	)	PUNCT
iajs-2557	190	6	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	190	7	)	)	PUNCT
iajs-2557	191	1	+	+	CCONJ
iajs-2557	191	2	(	(	PUNCT
iajs-2557	191	3	∆u2	∆u2	PROPN
iajs-2557	191	4	,	,	PUNCT
iajs-2557	191	5	z2	z2	PROPN
iajs-2557	191	6	)	)	PUNCT
iajs-2557	191	7	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	191	8	)	)	PUNCT
iajs-2557	192	1	+	+	CCONJ
iajs-2557	192	2	(	(	PUNCT
iajs-2557	192	3	∆u3	∆u3	NOUN
iajs-2557	192	4	,	,	PUNCT
iajs-2557	192	5	z3	z3	PROPN
iajs-2557	192	6	)	)	PUNCT
iajs-2557	192	7	l2(∂ω	l2(∂ω	NUM
iajs-2557	192	8	)	)	PUNCT
iajs-2557	192	9	(	(	PUNCT
iajs-2557	192	10	32	32	NUM
iajs-2557	192	11	)	)	PUNCT
iajs-2557	192	12	subtracting	subtract	VERB
iajs-2557	192	13	(	(	PUNCT
iajs-2557	192	14	32	32	NUM
iajs-2557	192	15	)	)	PUNCT
iajs-2557	192	16	from	from	ADP
iajs-2557	192	17	(	(	PUNCT
iajs-2557	192	18	31	31	NUM
iajs-2557	192	19	)	)	PUNCT
iajs-2557	192	20	,	,	PUNCT
iajs-2557	192	21	to	to	PART
iajs-2557	192	22	get	get	VERB
iajs-2557	192	23	(	(	PUNCT
iajs-2557	192	24	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	192	25	⃗⃗	⃗⃗	PROPN
iajs-2557	192	26	,	,	PUNCT
iajs-2557	192	27	z	z	NOUN
iajs-2557	192	28	)	)	PUNCT
iajs-2557	192	29	l2(∂ω	l2(∂ω	NUM
iajs-2557	192	30	)	)	PUNCT
iajs-2557	192	31	=	=	PRON
iajs-2557	192	32	(	(	PUNCT
iajs-2557	192	33	y⃗	y⃗	NOUN
iajs-2557	192	34	−	−	NOUN
iajs-2557	192	35	y⃗	y⃗	NOUN
iajs-2557	192	36	d	d	NOUN
iajs-2557	192	37	,	,	PUNCT
iajs-2557	192	38	∆y⃗⃗⃗⃗	∆y⃗⃗⃗⃗	PROPN
iajs-2557	192	39	)	)	PUNCT
iajs-2557	192	40	l2(ω	l2(ω	NOUN
iajs-2557	192	41	)	)	PUNCT
iajs-2557	192	42	(	(	PUNCT
iajs-2557	192	43	33	33	NUM
iajs-2557	192	44	)	)	PUNCT
iajs-2557	192	45	now	now	ADV
iajs-2557	192	46	,	,	PUNCT
iajs-2557	192	47	for	for	ADP
iajs-2557	192	48	the	the	DET
iajs-2557	192	49	cost	cost	NOUN
iajs-2557	192	50	function	function	NOUN
iajs-2557	192	51	,	,	PUNCT
iajs-2557	192	52	we	we	PRON
iajs-2557	192	53	have	have	VERB
iajs-2557	192	54	g0(u⃗	g0(u⃗	NOUN
iajs-2557	193	1	+	+	CCONJ
iajs-2557	193	2	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	193	3	⃗⃗	⃗⃗	PROPN
iajs-2557	193	4	)	)	PUNCT
iajs-2557	194	1	−	−	NOUN
iajs-2557	194	2	g0(u⃗	g0(u⃗	INTJ
iajs-2557	194	3	)	)	PUNCT
iajs-2557	194	4	=	=	SYM
iajs-2557	194	5	(	(	PUNCT
iajs-2557	194	6	y1	y1	INTJ
iajs-2557	194	7	−	−	PROPN
iajs-2557	194	8	y1d	y1d	NOUN
iajs-2557	194	9	,	,	PUNCT
iajs-2557	194	10	∆y1	∆y1	PROPN
iajs-2557	194	11	)	)	PUNCT
iajs-2557	194	12	l2(ω	l2(ω	NUM
iajs-2557	194	13	)	)	PUNCT
iajs-2557	195	1	+	+	CCONJ
iajs-2557	195	2	(	(	PUNCT
iajs-2557	195	3	y2	y2	INTJ
iajs-2557	195	4	−	−	PROPN
iajs-2557	195	5	y2d	y2d	PROPN
iajs-2557	195	6	,	,	PUNCT
iajs-2557	195	7	∆y2	∆y2	PROPN
iajs-2557	195	8	)	)	PUNCT
iajs-2557	196	1	l2(ω	l2(ω	X
iajs-2557	196	2	)	)	PUNCT
iajs-2557	196	3	+	+	CCONJ
iajs-2557	196	4	(	(	PUNCT
iajs-2557	196	5	y3	y3	PROPN
iajs-2557	196	6	−	−	PROPN
iajs-2557	196	7	y3d	y3d	NOUN
iajs-2557	196	8	,	,	PUNCT
iajs-2557	196	9	∆y3	∆y3	PROPN
iajs-2557	196	10	)	)	PUNCT
iajs-2557	197	1	l2(ω	l2(ω	NUM
iajs-2557	197	2	)	)	PUNCT
iajs-2557	198	1	+	+	CCONJ
iajs-2557	198	2	1	1	NUM
iajs-2557	198	3	2	2	NUM
iajs-2557	198	4	‖∆y⃗⃗⃗⃗	‖∆y⃗⃗⃗⃗	ADP
iajs-2557	198	5	‖	‖	PROPN
iajs-2557	198	6	(	(	PUNCT
iajs-2557	198	7	l2(ω	l2(ω	NOUN
iajs-2557	198	8	)	)	PUNCT
iajs-2557	198	9	)	)	PUNCT
iajs-2557	198	10	3	3	NUM
iajs-2557	198	11	2	2	NUM
iajs-2557	198	12	+	+	CCONJ
iajs-2557	198	13	∝	∝	PROPN
iajs-2557	198	14	2	2	NUM
iajs-2557	198	15	‖∆u⃗⃗	‖∆u⃗⃗	NUM
iajs-2557	198	16	⃗⃗	⃗⃗	NOUN
iajs-2557	198	17	‖	‖	PROPN
iajs-2557	198	18	(	(	PUNCT
iajs-2557	198	19	l2(∂ω	l2(∂ω	NUM
iajs-2557	198	20	)	)	PUNCT
iajs-2557	198	21	)	)	PUNCT
iajs-2557	198	22	3	3	NUM
iajs-2557	198	23	2	2	NUM
iajs-2557	198	24	(	(	PUNCT
iajs-2557	198	25	34	34	NUM
iajs-2557	198	26	)	)	PUNCT
iajs-2557	198	27	from	from	ADP
iajs-2557	198	28	(	(	PUNCT
iajs-2557	198	29	33	33	NUM
iajs-2557	198	30	)	)	PUNCT
iajs-2557	198	31	&	&	CCONJ
iajs-2557	198	32	(	(	PUNCT
iajs-2557	198	33	34	34	NUM
iajs-2557	198	34	)	)	PUNCT
iajs-2557	198	35	,	,	PUNCT
iajs-2557	198	36	we	we	PRON
iajs-2557	198	37	get	get	VERB
iajs-2557	198	38	g0(u⃗	g0(u⃗	NOUN
iajs-2557	199	1	+	+	CCONJ
iajs-2557	199	2	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	199	3	⃗⃗	⃗⃗	PROPN
iajs-2557	199	4	)	)	PUNCT
iajs-2557	200	1	−	−	NOUN
iajs-2557	200	2	g0(u⃗	g0(u⃗	INTJ
iajs-2557	200	3	)	)	PUNCT
iajs-2557	200	4	=	=	SYM
iajs-2557	200	5	(	(	PUNCT
iajs-2557	200	6	z	z	X
iajs-2557	200	7	+	+	NOUN
iajs-2557	200	8	∝	∝	PROPN
iajs-2557	200	9	u⃗	u⃗	PROPN
iajs-2557	200	10	,	,	PUNCT
iajs-2557	200	11	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	200	12	⃗⃗	⃗⃗	PROPN
iajs-2557	200	13	)	)	PUNCT
iajs-2557	200	14	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	200	15	)	)	PUNCT
iajs-2557	201	1	+	+	CCONJ
iajs-2557	201	2	1	1	NUM
iajs-2557	201	3	2	2	NUM
iajs-2557	201	4	‖∆y⃗⃗⃗⃗	‖∆y⃗⃗⃗⃗	ADP
iajs-2557	201	5	‖	‖	PROPN
iajs-2557	201	6	(	(	PUNCT
iajs-2557	201	7	l2(ω	l2(ω	NOUN
iajs-2557	201	8	)	)	PUNCT
iajs-2557	201	9	)	)	PUNCT
iajs-2557	201	10	3	3	NUM
iajs-2557	201	11	2	2	NUM
iajs-2557	201	12	+	+	CCONJ
iajs-2557	201	13	∝	∝	PROPN
iajs-2557	201	14	2	2	NUM
iajs-2557	201	15	‖∆u⃗⃗	‖∆u⃗⃗	NUM
iajs-2557	201	16	⃗⃗	⃗⃗	NOUN
iajs-2557	201	17	‖	‖	PROPN
iajs-2557	201	18	(	(	PUNCT
iajs-2557	201	19	l2(∂ω	l2(∂ω	NUM
iajs-2557	201	20	)	)	PUNCT
iajs-2557	201	21	)	)	PUNCT
iajs-2557	201	22	3	3	NUM
iajs-2557	201	23	2	2	NUM
iajs-2557	201	24	(	(	PUNCT
iajs-2557	201	25	35	35	NUM
iajs-2557	201	26	)	)	PUNCT
iajs-2557	201	27	from	from	ADP
iajs-2557	201	28	lemma	lemma	PROPN
iajs-2557	201	29	4.1	4.1	NUM
iajs-2557	201	30	,	,	PUNCT
iajs-2557	201	31	it	it	PRON
iajs-2557	201	32	yield	yield	VERB
iajs-2557	201	33	that	that	SCONJ
iajs-2557	201	34	1	1	NUM
iajs-2557	201	35	2	2	NUM
iajs-2557	201	36	‖∆y⃗⃗⃗⃗	‖∆y⃗⃗⃗⃗	ADP
iajs-2557	201	37	‖	‖	PROPN
iajs-2557	201	38	(	(	PUNCT
iajs-2557	201	39	l2(ω	l2(ω	NOUN
iajs-2557	201	40	)	)	PUNCT
iajs-2557	201	41	)	)	PUNCT
iajs-2557	201	42	3	3	NUM
iajs-2557	201	43	2	2	NUM
iajs-2557	201	44	+	+	CCONJ
iajs-2557	201	45	∝	∝	PROPN
iajs-2557	201	46	2	2	NUM
iajs-2557	201	47	‖∆u⃗⃗	‖∆u⃗⃗	NUM
iajs-2557	201	48	⃗⃗	⃗⃗	NOUN
iajs-2557	201	49	‖	‖	PROPN
iajs-2557	201	50	(	(	PUNCT
iajs-2557	201	51	l2(∂ω	l2(∂ω	NUM
iajs-2557	201	52	)	)	PUNCT
iajs-2557	201	53	)	)	PUNCT
iajs-2557	201	54	3	3	NUM
iajs-2557	201	55	2	2	NUM
iajs-2557	201	56	=	=	SYM
iajs-2557	201	57	є(∆u⃗⃗	є(∆u⃗⃗	PROPN
iajs-2557	201	58	⃗⃗	⃗⃗	PROPN
iajs-2557	201	59	)	)	PUNCT
iajs-2557	201	60	‖∆u⃗⃗	‖∆u⃗⃗	NUM
iajs-2557	201	61	⃗⃗	⃗⃗	PROPN
iajs-2557	201	62	‖	‖	PROPN
iajs-2557	201	63	(	(	PUNCT
iajs-2557	201	64	l2(∂ω	l2(∂ω	NUM
iajs-2557	201	65	)	)	PUNCT
iajs-2557	201	66	)	)	PUNCT
iajs-2557	201	67	3	3	NUM
iajs-2557	201	68	2	2	NUM
iajs-2557	201	69	(	(	PUNCT
iajs-2557	201	70	36	36	NUM
iajs-2557	201	71	)	)	PUNCT
iajs-2557	201	72	where	where	SCONJ
iajs-2557	201	73	є(∆u⃗⃗	є(∆u⃗⃗	PROPN
iajs-2557	201	74	⃗⃗	⃗⃗	PROPN
iajs-2557	201	75	)	)	PUNCT
iajs-2557	201	76	⟶	⟶	NOUN
iajs-2557	201	77	0	0	NUM
iajs-2557	201	78	,	,	PUNCT
iajs-2557	201	79	as	as	ADP
iajs-2557	201	80	‖∆u⃗⃗	‖∆u⃗⃗	NUM
iajs-2557	201	81	⃗⃗	⃗⃗	NOUN
iajs-2557	201	82	‖	‖	PROPN
iajs-2557	201	83	(	(	PUNCT
iajs-2557	201	84	l2(∂ω	l2(∂ω	NUM
iajs-2557	201	85	)	)	PUNCT
iajs-2557	201	86	)	)	PUNCT
iajs-2557	201	87	3	3	NUM
iajs-2557	201	88	2	2	NUM
iajs-2557	201	89	⟶	⟶	NOUN
iajs-2557	201	90	0	0	NUM
iajs-2557	201	91	with	with	ADP
iajs-2557	201	92	є(∆u⃗⃗	є(∆u⃗⃗	PROPN
iajs-2557	201	93	⃗⃗	⃗⃗	PROPN
iajs-2557	201	94	)	)	PUNCT
iajs-2557	201	95	=	=	PUNCT
iajs-2557	201	96	є1(∆u⃗⃗	є1(∆u⃗⃗	PROPN
iajs-2557	201	97	⃗⃗	⃗⃗	NOUN
iajs-2557	201	98	)	)	PUNCT
iajs-2557	202	1	+	+	CCONJ
iajs-2557	202	2	є2(∆u⃗⃗	є2(∆u⃗⃗	ADJ
iajs-2557	202	3	⃗⃗	⃗⃗	NOUN
iajs-2557	202	4	)	)	PUNCT
iajs-2557	202	5	then	then	ADV
iajs-2557	202	6	from	from	ADP
iajs-2557	202	7	the	the	DET
iajs-2557	202	8	fde	fde	NOUN
iajs-2557	202	9	of	of	ADP
iajs-2557	202	10	g0	g0	PROPN
iajs-2557	202	11	,	,	PUNCT
iajs-2557	202	12	and	and	CCONJ
iajs-2557	202	13	(	(	PUNCT
iajs-2557	202	14	35	35	NUM
iajs-2557	202	15	-	-	SYM
iajs-2557	202	16	36	36	NUM
iajs-2557	202	17	)	)	PUNCT
iajs-2557	202	18	,	,	PUNCT
iajs-2557	202	19	once	once	ADV
iajs-2557	202	20	get	get	VERB
iajs-2557	202	21	:	:	PUNCT
iajs-2557	202	22	(	(	PUNCT
iajs-2557	202	23	g0	g0	ADJ
iajs-2557	202	24	′	′	PROPN
iajs-2557	202	25	(	(	PUNCT
iajs-2557	202	26	u⃗	u⃗	PROPN
iajs-2557	202	27	)	)	PUNCT
iajs-2557	202	28	,	,	PUNCT
iajs-2557	202	29	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	202	30	⃗⃗	⃗⃗	PROPN
iajs-2557	202	31	)	)	PUNCT
iajs-2557	202	32	=	=	PUNCT
iajs-2557	203	1	(	(	PUNCT
iajs-2557	203	2	z	z	X
iajs-2557	203	3	+	+	NOUN
iajs-2557	203	4	∝	∝	PROPN
iajs-2557	203	5	u⃗	u⃗	PROPN
iajs-2557	203	6	,	,	PUNCT
iajs-2557	203	7	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	203	8	⃗⃗	⃗⃗	PROPN
iajs-2557	203	9	)	)	PUNCT
iajs-2557	203	10	l2(∂ω	l2(∂ω	PUNCT
iajs-2557	203	11	)	)	PUNCT
iajs-2557	203	12	.	.	PUNCT
iajs-2557	204	1	theorem	theorem	VERB
iajs-2557	204	2	5.2	5.2	NUM
iajs-2557	204	3	:	:	PUNCT
iajs-2557	204	4	the	the	DET
iajs-2557	204	5	(	(	PUNCT
iajs-2557	204	6	ccboc	ccboc	NOUN
iajs-2557	204	7	)	)	PUNCT
iajs-2557	204	8	of	of	ADP
iajs-2557	204	9	(	(	PUNCT
iajs-2557	204	10	1	1	NUM
iajs-2557	204	11	-	-	SYM
iajs-2557	204	12	6	6	NUM
iajs-2557	204	13	)	)	PUNCT
iajs-2557	204	14	is	be	AUX
iajs-2557	204	15	:	:	PUNCT
iajs-2557	204	16	g0	g0	ADJ
iajs-2557	204	17	′	′	PROPN
iajs-2557	204	18	(	(	PUNCT
iajs-2557	204	19	u⃗	u⃗	PROPN
iajs-2557	204	20	)	)	PUNCT
iajs-2557	204	21	=	=	PUNCT
iajs-2557	205	1	z	z	X
iajs-2557	206	1	+	+	NOUN
iajs-2557	206	2	∝	∝	X
iajs-2557	206	3	u⃗	u⃗	PROPN
iajs-2557	206	4	=	=	PUNCT
iajs-2557	206	5	0	0	NUM
iajs-2557	206	6	with	with	ADP
iajs-2557	206	7	y⃗	y⃗	NOUN
iajs-2557	206	8	=	=	SYM
iajs-2557	206	9	y⃗	y⃗	NOUN
iajs-2557	206	10	u⃗⃗	u⃗⃗	NOUN
iajs-2557	206	11	and	and	CCONJ
iajs-2557	206	12	z	z	NOUN
iajs-2557	206	13	=	=	SYM
iajs-2557	206	14	z	z	NOUN
iajs-2557	206	15	u⃗⃗	u⃗⃗	NOUN
iajs-2557	206	16	.	.	PUNCT
iajs-2557	207	1	proof	proof	NOUN
iajs-2557	207	2	:	:	PUNCT
iajs-2557	207	3	if	if	SCONJ
iajs-2557	207	4	u⃗	u⃗	PROPN
iajs-2557	207	5	is	be	AUX
iajs-2557	207	6	an	an	DET
iajs-2557	207	7	optimal	optimal	ADJ
iajs-2557	207	8	control	control	NOUN
iajs-2557	207	9	of	of	ADP
iajs-2557	207	10	the	the	DET
iajs-2557	207	11	problem	problem	NOUN
iajs-2557	207	12	,	,	PUNCT
iajs-2557	207	13	then	then	ADV
iajs-2557	207	14	g0(u⃗	g0(u⃗	INTJ
iajs-2557	207	15	)	)	PUNCT
iajs-2557	208	1	=	=	NOUN
iajs-2557	208	2	minw⃗⃗⃗	minw⃗⃗⃗	PROPN
iajs-2557	208	3	∈w⃗⃗⃗⃗	∈w⃗⃗⃗⃗	PROPN
iajs-2557	208	4	g0	g0	PROPN
iajs-2557	208	5	(	(	PUNCT
iajs-2557	208	6	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	208	7	)	)	PUNCT
iajs-2557	208	8	,	,	PUNCT
iajs-2557	208	9	∀	∀	X
iajs-2557	208	10	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	208	11	∈	∈	PROPN
iajs-2557	208	12	(	(	PUNCT
iajs-2557	208	13	l2(∂ω	l2(∂ω	NUM
iajs-2557	208	14	)	)	PUNCT
iajs-2557	208	15	)	)	PUNCT
iajs-2557	208	16	3	3	NUM
iajs-2557	209	1	i.e.	i.e.	X
iajs-2557	209	2	,	,	PUNCT
iajs-2557	209	3	g0	g0	ADJ
iajs-2557	209	4	′	′	NOUN
iajs-2557	209	5	(	(	PUNCT
iajs-2557	209	6	u⃗	u⃗	PROPN
iajs-2557	209	7	)	)	PUNCT
iajs-2557	209	8	=	=	SYM
iajs-2557	209	9	0	0	PUNCT
iajs-2557	209	10	⟹	⟹	NUM
iajs-2557	209	11	z	z	NOUN
iajs-2557	209	12	=	=	PUNCT
iajs-2557	210	1	−∝	−∝	PROPN
iajs-2557	210	2	u⃗	u⃗	PROPN
iajs-2557	210	3	,	,	PUNCT
iajs-2557	210	4	∆u⃗⃗	∆u⃗⃗	PROPN
iajs-2557	210	5	⃗⃗	⃗⃗	PROPN
iajs-2557	210	6	=	=	SYM
iajs-2557	210	7	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	210	8	−	−	PROPN
iajs-2557	210	9	u⃗	u⃗	PROPN
iajs-2557	210	10	the	the	DET
iajs-2557	210	11	necessary	necessary	ADJ
iajs-2557	210	12	condition	condition	NOUN
iajs-2557	210	13	for	for	ADP
iajs-2557	210	14	optimality	optimality	NOUN
iajs-2557	210	15	is	be	AUX
iajs-2557	210	16	:	:	PUNCT
iajs-2557	210	17	(	(	PUNCT
iajs-2557	210	18	z	z	X
iajs-2557	210	19	+	+	NOUN
iajs-2557	210	20	∝	∝	PROPN
iajs-2557	210	21	u⃗	u⃗	PROPN
iajs-2557	210	22	,	,	PUNCT
iajs-2557	210	23	u⃗	u⃗	PROPN
iajs-2557	210	24	)	)	PUNCT
iajs-2557	210	25	≤	≤	NOUN
iajs-2557	211	1	(	(	PUNCT
iajs-2557	211	2	z	z	X
iajs-2557	211	3	+	+	NOUN
iajs-2557	211	4	∝	∝	PROPN
iajs-2557	211	5	u⃗	u⃗	PROPN
iajs-2557	211	6	,	,	PUNCT
iajs-2557	211	7	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	211	8	)	)	PUNCT
iajs-2557	211	9	,	,	PUNCT
iajs-2557	211	10	∀	∀	X
iajs-2557	211	11	w⃗⃗⃗	w⃗⃗⃗	NOUN
iajs-2557	211	12	∈	∈	PROPN
iajs-2557	211	13	(	(	PUNCT
iajs-2557	211	14	l2(∂ω	l2(∂ω	NUM
iajs-2557	211	15	)	)	PUNCT
iajs-2557	211	16	)	)	PUNCT
iajs-2557	211	17	3	3	NUM
iajs-2557	211	18	.	.	X
iajs-2557	212	1	6	6	X
iajs-2557	212	2	.	.	PUNCT
iajs-2557	212	3	conclusions	conclusion	NOUN
iajs-2557	212	4	the	the	DET
iajs-2557	212	5	existence	existence	NOUN
iajs-2557	212	6	and	and	CCONJ
iajs-2557	212	7	uniqueness	uniqueness	NOUN
iajs-2557	212	8	theorem	theorem	VERB
iajs-2557	212	9	for	for	ADP
iajs-2557	212	10	the	the	DET
iajs-2557	212	11	ssv	ssv	NOUN
iajs-2557	212	12	of	of	ADP
iajs-2557	212	13	the	the	DET
iajs-2557	212	14	tlepdes	tlepde	NOUN
iajs-2557	212	15	is	be	AUX
iajs-2557	212	16	proved	prove	VERB
iajs-2557	212	17	successfully	successfully	ADV
iajs-2557	212	18	using	use	VERB
iajs-2557	212	19	the	the	DET
iajs-2557	212	20	gme	gme	NOUN
iajs-2557	212	21	when	when	SCONJ
iajs-2557	212	22	the	the	DET
iajs-2557	212	23	ccbcvr	ccbcvr	NOUN
iajs-2557	212	24	is	be	AUX
iajs-2557	212	25	given	give	VERB
iajs-2557	212	26	.	.	PUNCT
iajs-2557	213	1	the	the	DET
iajs-2557	213	2	proof	proof	NOUN
iajs-2557	213	3	of	of	ADP
iajs-2557	213	4	the	the	DET
iajs-2557	213	5	existence	existence	NOUN
iajs-2557	213	6	ccbocvr	ccbocvr	NOUN
iajs-2557	213	7	ruled	rule	VERB
iajs-2557	213	8	by	by	ADP
iajs-2557	213	9	the	the	DET
iajs-2557	213	10	considered	considered	ADJ
iajs-2557	213	11	tlepdes	tlepde	NOUN
iajs-2557	213	12	is	be	AUX
iajs-2557	213	13	demonstrated	demonstrate	VERB
iajs-2557	213	14	.	.	PUNCT
iajs-2557	214	1	the	the	DET
iajs-2557	214	2	studding	studding	NOUN
iajs-2557	214	3	of	of	ADP
iajs-2557	214	4	the	the	DET
iajs-2557	214	5	existence	existence	NOUN
iajs-2557	214	6	solution	solution	NOUN
iajs-2557	214	7	of	of	ADP
iajs-2557	214	8	the	the	DET
iajs-2557	214	9	tajes	taje	NOUN
iajs-2557	214	10	related	relate	VERB
iajs-2557	214	11	with	with	ADP
iajs-2557	214	12	the	the	DET
iajs-2557	214	13	tlepdes	tlepde	NOUN
iajs-2557	214	14	is	be	AUX
iajs-2557	214	15	demonstrated	demonstrate	VERB
iajs-2557	214	16	.	.	PUNCT
iajs-2557	215	1	the	the	DET
iajs-2557	215	2	fde	fde	PROPN
iajs-2557	215	3	is	be	AUX
iajs-2557	215	4	derived	derive	VERB
iajs-2557	215	5	.	.	PUNCT
iajs-2557	216	1	finally	finally	ADV
iajs-2557	216	2	the	the	DET
iajs-2557	216	3	ncth	ncth	NOUN
iajs-2557	216	4	of	of	ADP
iajs-2557	216	5	optimality	optimality	NOUN
iajs-2557	216	6	for	for	ADP
iajs-2557	216	7	the	the	DET
iajs-2557	216	8	considered	consider	VERB
iajs-2557	216	9	problem	problem	NOUN
iajs-2557	216	10	is	be	AUX
iajs-2557	216	11	demonstrated	demonstrate	VERB
iajs-2557	216	12	.	.	PUNCT
iajs-2557	217	1	references	reference	NOUN
iajs-2557	217	2	1	1	NUM
iajs-2557	217	3	.	.	PUNCT
iajs-2557	218	1	grigorenko	grigorenko	PROPN
iajs-2557	218	2	,	,	PUNCT
iajs-2557	218	3	n.l	n.l	PROPN
iajs-2557	218	4	.	.	PROPN
iajs-2557	218	5	;	;	PUNCT
iajs-2557	218	6	grigorieva	grigorieva	PROPN
iajs-2557	218	7	,	,	PUNCT
iajs-2557	218	8	ѐ.v	ѐ.v	PROPN
iajs-2557	218	9	.	.	PROPN
iajs-2557	218	10	;	;	PUNCT
iajs-2557	218	11	roi	roi	NOUN
iajs-2557	218	12	,	,	PUNCT
iajs-2557	218	13	p.k	p.k	PROPN
iajs-2557	218	14	.	.	PROPN
iajs-2557	218	15	;	;	PUNCT
iajs-2557	218	16	khailov	khailov	PROPN
iajs-2557	218	17	,	,	PUNCT
iajs-2557	218	18	e.n	e.n	PROPN
iajs-2557	218	19	.	.	PROPN
iajs-2557	218	20	optimal	optimal	ADJ
iajs-2557	218	21	control	control	NOUN
iajs-2557	218	22	problems	problem	NOUN
iajs-2557	218	23	for	for	ADP
iajs-2557	218	24	a	a	DET
iajs-2557	218	25	mathematical	mathematical	ADJ
iajs-2557	218	26	model	model	NOUN
iajs-2557	218	27	of	of	ADP
iajs-2557	218	28	the	the	DET
iajs-2557	218	29	treatment	treatment	NOUN
iajs-2557	218	30	of	of	ADP
iajs-2557	218	31	psoriasis	psoriasis	NOUN
iajs-2557	218	32	.	.	PUNCT
iajs-2557	219	1	computational	computational	ADJ
iajs-2557	219	2	mathimatics	mathimatic	NOUN
iajs-2557	219	3	and	and	CCONJ
iajs-2557	219	4	modeling	modeling	NOUN
iajs-2557	219	5	.	.	PUNCT
iajs-2557	220	1	2019	2019	NUM
iajs-2557	220	2	,	,	PUNCT
iajs-2557	220	3	30	30	NUM
iajs-2557	220	4	,	,	PUNCT
iajs-2557	220	5	352	352	NUM
iajs-2557	220	6	-	-	SYM
iajs-2557	220	7	363	363	NUM
iajs-2557	220	8	,	,	PUNCT
iajs-2557	220	9	doi	doi	NOUN
iajs-2557	220	10	:	:	PUNCT
iajs-2557	220	11	10.1007	10.1007	NUM
iajs-2557	220	12	/	/	SYM
iajs-2557	220	13	s10598	s10598	NOUN
iajs-2557	220	14	-	-	PUNCT
iajs-2557	220	15	019	019	NUM
iajs-2557	220	16	-	-	PUNCT
iajs-2557	220	17	09461	09461	NUM
iajs-2557	220	18	-	-	PUNCT
iajs-2557	220	19	y.	y.	NOUN
iajs-2557	220	20	2	2	NUM
iajs-2557	220	21	.	.	PUNCT
iajs-2557	221	1	kahina	kahina	PROPN
iajs-2557	221	2	,	,	PUNCT
iajs-2557	221	3	l.	l.	PROPN
iajs-2557	221	4	;	;	PUNCT
iajs-2557	221	5	spiteri	spiteri	NOUN
iajs-2557	221	6	,	,	PUNCT
iajs-2557	221	7	p.	p.	NOUN
iajs-2557	221	8	;	;	PUNCT
iajs-2557	221	9	demim	demim	PROPN
iajs-2557	221	10	,	,	PUNCT
iajs-2557	221	11	f.	f.	PROPN
iajs-2557	221	12	;	;	PUNCT
iajs-2557	221	13	mohamed	mohamed	PROPN
iajs-2557	221	14	,	,	PUNCT
iajs-2557	221	15	a.	a.	NOUN
iajs-2557	221	16	;	;	PUNCT
iajs-2557	221	17	nemra	nemra	PROPN
iajs-2557	221	18	,	,	PUNCT
iajs-2557	221	19	a.	a.	NOUN
iajs-2557	221	20	;	;	PUNCT
iajs-2557	221	21	messine	messine	PROPN
iajs-2557	221	22	,	,	PUNCT
iajs-2557	221	23	f.	f.	PROPN
iajs-2557	221	24	application	application	PROPN
iajs-2557	221	25	optimal	optimal	ADJ
iajs-2557	221	26	control	control	NOUN
iajs-2557	221	27	for	for	ADP
iajs-2557	221	28	a	a	DET
iajs-2557	221	29	problem	problem	NOUN
iajs-2557	221	30	aircraft	aircraft	NOUN
iajs-2557	221	31	flight	flight	NOUN
iajs-2557	221	32	.	.	PUNCT
iajs-2557	222	1	journal	journal	NOUN
iajs-2557	222	2	of	of	ADP
iajs-2557	222	3	engineering	engineering	NOUN
iajs-2557	222	4	science	science	NOUN
iajs-2557	222	5	and	and	CCONJ
iajs-2557	222	6	technology	technology	NOUN
iajs-2557	222	7	review	review	NOUN
iajs-2557	222	8	.	.	PUNCT
iajs-2557	223	1	2018	2018	NUM
iajs-2557	223	2	,	,	PUNCT
iajs-2557	223	3	11	11	NUM
iajs-2557	223	4	,	,	PUNCT
iajs-2557	223	5	156	156	NUM
iajs-2557	223	6	-	-	SYM
iajs-2557	223	7	164	164	NUM
iajs-2557	223	8	,	,	PUNCT
iajs-2557	223	9	doi	doi	NOUN
iajs-2557	223	10	:	:	PUNCT
iajs-2557	223	11	10.25103	10.25103	NUM
iajs-2557	223	12	/	/	SYM
iajs-2557	223	13	jestr.111.19	jestr.111.19	PROPN
iajs-2557	223	14	.	.	PUNCT
iajs-2557	224	1	67	67	NUM
iajs-2557	224	2	ibn	ibn	PROPN
iajs-2557	224	3	al	al	PROPN
iajs-2557	224	4	-	-	PUNCT
iajs-2557	224	5	haitham	haitham	PROPN
iajs-2557	224	6	jour	jour	X
iajs-2557	224	7	.	.	PROPN
iajs-2557	224	8	for	for	ADP
iajs-2557	224	9	pure	pure	ADJ
iajs-2557	224	10	&	&	CCONJ
iajs-2557	224	11	appl	appl	PROPN
iajs-2557	224	12	.	.	PUNCT
iajs-2557	225	1	sci	sci	PROPN
iajs-2557	225	2	.	.	PROPN
iajs-2557	226	1	34	34	NUM
iajs-2557	226	2	(	(	PUNCT
iajs-2557	226	3	1	1	NUM
iajs-2557	226	4	)	)	PUNCT
iajs-2557	226	5	2021	2021	NUM
iajs-2557	226	6	3	3	NUM
iajs-2557	226	7	.	.	X
iajs-2557	226	8	aderinto	aderinto	PROPN
iajs-2557	226	9	,	,	PUNCT
iajs-2557	226	10	y.o	y.o	PROPN
iajs-2557	226	11	.	.	PROPN
iajs-2557	226	12	;	;	PUNCT
iajs-2557	226	13	afolabi	afolabi	NOUN
iajs-2557	226	14	,	,	PUNCT
iajs-2557	226	15	a.o	a.o	PROPN
iajs-2557	226	16	.	.	PROPN
iajs-2557	226	17	;	;	PUNCT
iajs-2557	226	18	issa	issa	ADJ
iajs-2557	226	19	,	,	PUNCT
iajs-2557	226	20	i.t	i.t	PROPN
iajs-2557	226	21	.	.	PROPN
iajs-2557	226	22	on	on	ADP
iajs-2557	226	23	optimal	optimal	ADJ
iajs-2557	226	24	planning	planning	NOUN
iajs-2557	226	25	of	of	ADP
iajs-2557	226	26	electric	electric	ADJ
iajs-2557	226	27	power	power	NOUN
iajs-2557	226	28	generation	generation	NOUN
iajs-2557	226	29	systems	system	NOUN
iajs-2557	226	30	.	.	PUNCT
iajs-2557	227	1	punjab	punjab	PROPN
iajs-2557	227	2	university	university	PROPN
iajs-2557	227	3	.	.	PUNCT
iajs-2557	228	1	journal	journal	PROPN
iajs-2557	228	2	of	of	ADP
iajs-2557	228	3	mathematics	mathematic	NOUN
iajs-2557	228	4	.	.	PUNCT
iajs-2557	229	1	2017	2017	NUM
iajs-2557	229	2	,	,	PUNCT
iajs-2557	229	3	50	50	NUM
iajs-2557	229	4	,	,	PUNCT
iajs-2557	229	5	89	89	NUM
iajs-2557	229	6	-	-	SYM
iajs-2557	229	7	95,doi	95,doi	NUM
iajs-2557	229	8	:	:	PUNCT
iajs-2557	229	9	10.25103	10.25103	NUM
iajs-2557	229	10	/	/	SYM
iajs-2557	229	11	jestr.111.19	jestr.111.19	PROPN
iajs-2557	229	12	.	.	PUNCT
iajs-2557	230	1	4	4	X
iajs-2557	230	2	.	.	X
iajs-2557	230	3	kryazhimskii	kryazhimskii	PROPN
iajs-2557	230	4	,	,	PUNCT
iajs-2557	230	5	a.v	a.v	PROPN
iajs-2557	230	6	.	.	PROPN
iajs-2557	230	7	;	;	PUNCT
iajs-2557	230	8	taras'ev	taras'ev	NOUN
iajs-2557	230	9	,	,	PUNCT
iajs-2557	230	10	a.m.	a.m.	NOUN
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iajs-2557	230	12	control	control	NOUN
iajs-2557	230	13	for	for	ADP
iajs-2557	230	14	proportional	proportional	ADJ
iajs-2557	230	15	economic	economic	ADJ
iajs-2557	230	16	growth	growth	NOUN
iajs-2557	230	17	.	.	PUNCT
iajs-2557	231	1	pleiades	pleiades	PROPN
iajs-2557	231	2	publishing	publishing	PROPN
iajs-2557	231	3	.	.	PUNCT
iajs-2557	231	4	ltd	ltd	PROPN
iajs-2557	231	5	.	.	PROPN
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iajs-2557	231	7	,	,	PUNCT
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iajs-2557	231	9	,	,	PUNCT
iajs-2557	231	10	s101	s101	PROPN
iajs-2557	231	11	-	-	PUNCT
iajs-2557	231	12	s119	s119	PROPN
iajs-2557	231	13	,	,	PUNCT
iajs-2557	231	14	doi	doi	NOUN
iajs-2557	231	15	:	:	PUNCT
iajs-2557	231	16	10.1134	10.1134	NUM
iajs-2557	231	17	/	/	SYM
iajs-2557	231	18	s0081543816050102	s0081543816050102	NOUN
iajs-2557	231	19	.	.	NOUN
iajs-2557	231	20	5	5	NUM
iajs-2557	231	21	.	.	X
iajs-2557	232	1	afshar	afshar	ADJ
iajs-2557	232	2	,	,	PUNCT
iajs-2557	232	3	m.	m.	NOUN
iajs-2557	232	4	;	;	PUNCT
iajs-2557	232	5	merrikh	merrikh	NOUN
iajs-2557	232	6	-	-	PUNCT
iajs-2557	232	7	bayat	bayat	PROPN
iajs-2557	232	8	,	,	PUNCT
iajs-2557	232	9	f.	f.	PROPN
iajs-2557	232	10	;	;	PUNCT
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iajs-2557	232	12	,	,	PUNCT
iajs-2557	232	13	m.r	m.r	PROPN
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iajs-2557	232	17	for	for	ADP
iajs-2557	232	18	optimal	optimal	ADJ
iajs-2557	232	19	control	control	NOUN
iajs-2557	232	20	problems	problem	NOUN
iajs-2557	232	21	.	.	PUNCT
iajs-2557	233	1	çankaya	çankaya	PROPN
iajs-2557	233	2	university	university	PROPN
iajs-2557	233	3	.	.	PUNCT
iajs-2557	234	1	jornal	jornal	ADJ
iajs-2557	234	2	of	of	ADP
iajs-2557	234	3	science	science	NOUN
iajs-2557	234	4	and	and	CCONJ
iajs-2557	234	5	engineering	engineering	NOUN
iajs-2557	234	6	.	.	PUNCT
iajs-2557	235	1	2016	2016	NUM
iajs-2557	235	2	,	,	PUNCT
iajs-2557	235	3	13	13	NUM
iajs-2557	235	4	,	,	PUNCT
iajs-2557	235	5	024	024	NUM
iajs-2557	235	6	-	-	SYM
iajs-2557	235	7	037	037	NUM
iajs-2557	235	8	,	,	PUNCT
iajs-2557	235	9	doi	doi	NOUN
iajs-2557	235	10	:	:	PUNCT
iajs-2557	235	11	6	6	NUM
iajs-2557	235	12	.	.	X
iajs-2557	235	13	mabonzo	mabonzo	PROPN
iajs-2557	235	14	,	,	PUNCT
iajs-2557	235	15	v.d	v.d	PROPN
iajs-2557	235	16	.	.	PROPN
iajs-2557	235	17	;	;	PUNCT
iajs-2557	235	18	ampini	ampini	PROPN
iajs-2557	235	19	,	,	PUNCT
iajs-2557	235	20	d.	d.	PROPN
iajs-2557	235	21	existence	existence	NOUN
iajs-2557	235	22	of	of	ADP
iajs-2557	235	23	optimal	optimal	ADJ
iajs-2557	235	24	control	control	NOUN
iajs-2557	235	25	for	for	ADP
iajs-2557	235	26	a	a	DET
iajs-2557	235	27	nonlinear	nonlinear	ADJ
iajs-2557	235	28	partial	partial	ADJ
iajs-2557	235	29	differential	differential	NOUN
iajs-2557	235	30	equation	equation	NOUN
iajs-2557	235	31	of	of	ADP
iajs-2557	235	32	hyperbolic	hyperbolic	ADJ
iajs-2557	235	33	-	-	PUNCT
iajs-2557	235	34	type	type	NOUN
iajs-2557	235	35	.	.	PUNCT
iajs-2557	236	1	ejpam	ejpam	NOUN
iajs-2557	236	2	.	.	PUNCT
iajs-2557	237	1	2019	2019	NUM
iajs-2557	237	2	,	,	PUNCT
iajs-2557	237	3	12	12	NUM
iajs-2557	237	4	,	,	PUNCT
iajs-2557	237	5	1595	1595	NUM
iajs-2557	237	6	-	-	SYM
iajs-2557	237	7	1601	1601	NUM
iajs-2557	237	8	,	,	PUNCT
iajs-2557	237	9	doi	doi	NOUN
iajs-2557	237	10	:	:	PUNCT
iajs-2557	237	11	10.29020	10.29020	NUM
iajs-2557	237	12	/	/	SYM
iajs-2557	237	13	nybg.ejpam.v12i4.3577	nybg.ejpam.v12i4.3577	NOUN
iajs-2557	237	14	.	.	PUNCT
iajs-2557	238	1	7	7	X
iajs-2557	238	2	.	.	X
iajs-2557	238	3	kadhem	kadhem	PROPN
iajs-2557	238	4	,	,	PUNCT
iajs-2557	238	5	g.m	g.m	PROPN
iajs-2557	238	6	.	.	PUNCT
iajs-2557	239	1	the	the	DET
iajs-2557	239	2	continuous	continuous	ADJ
iajs-2557	239	3	classical	classical	ADJ
iajs-2557	239	4	optimal	optimal	ADJ
iajs-2557	239	5	control	control	NOUN
iajs-2557	239	6	problem	problem	NOUN
iajs-2557	239	7	of	of	ADP
iajs-2557	239	8	partial	partial	ADJ
iajs-2557	239	9	differential	differential	ADJ
iajs-2557	239	10	equations	equation	NOUN
iajs-2557	239	11	.	.	PUNCT
iajs-2557	240	1	m.sc	m.sc	PROPN
iajs-2557	240	2	.	.	PUNCT
iajs-2557	241	1	thesis	thesis	NOUN
iajs-2557	241	2	.	.	PUNCT
iajs-2557	242	1	university	university	NOUN
iajs-2557	242	2	of	of	ADP
iajs-2557	242	3	mustansiriyah	mustansiriyah	NOUN
iajs-2557	242	4	.	.	PUNCT
iajs-2557	243	1	2015	2015	NUM
iajs-2557	243	2	.	.	PUNCT
iajs-2557	244	1	8	8	X
iajs-2557	244	2	.	.	X
iajs-2557	245	1	al	al	PROPN
iajs-2557	245	2	-	-	PUNCT
iajs-2557	245	3	rawdanee	rawdanee	NOUN
iajs-2557	245	4	,	,	PUNCT
iajs-2557	245	5	e.h.m	e.h.m	ADJ
iajs-2557	245	6	.	.	PUNCT
iajs-2557	246	1	the	the	DET
iajs-2557	246	2	continuous	continuous	ADJ
iajs-2557	246	3	classical	classical	ADJ
iajs-2557	246	4	optimal	optimal	ADJ
iajs-2557	246	5	control	control	NOUN
iajs-2557	246	6	problem	problem	NOUN
iajs-2557	246	7	of	of	ADP
iajs-2557	246	8	a	a	DET
iajs-2557	246	9	non	non	ADJ
iajs-2557	246	10	-	-	ADJ
iajs-2557	246	11	linear	linear	ADJ
iajs-2557	246	12	partial	partial	ADJ
iajs-2557	246	13	differential	differential	ADJ
iajs-2557	246	14	equations	equation	NOUN
iajs-2557	246	15	of	of	ADP
iajs-2557	246	16	elliptic	elliptic	ADJ
iajs-2557	246	17	type	type	NOUN
iajs-2557	246	18	.	.	PUNCT
iajs-2557	247	1	m.sc	m.sc	PROPN
iajs-2557	247	2	.	.	PUNCT
iajs-2557	248	1	thesis	thesis	NOUN
iajs-2557	248	2	.	.	PUNCT
iajs-2557	249	1	university	university	NOUN
iajs-2557	249	2	of	of	ADP
iajs-2557	249	3	mustansiriyah	mustansiriyah	NOUN
iajs-2557	249	4	.	.	PUNCT
iajs-2557	250	1	2015	2015	NUM
iajs-2557	250	2	.	.	PUNCT
iajs-2557	251	1	9	9	X
iajs-2557	251	2	.	.	X
iajs-2557	252	1	al	al	PROPN
iajs-2557	252	2	-	-	PUNCT
iajs-2557	252	3	hawasy	hawasy	PROPN
iajs-2557	252	4	,	,	PUNCT
iajs-2557	252	5	j.	j.	PROPN
iajs-2557	252	6	the	the	DET
iajs-2557	252	7	continuous	continuous	ADJ
iajs-2557	252	8	classical	classical	ADJ
iajs-2557	252	9	optimal	optimal	ADJ
iajs-2557	252	10	control	control	NOUN
iajs-2557	252	11	of	of	ADP
iajs-2557	252	12	a	a	DET
iajs-2557	252	13	couple	couple	NOUN
iajs-2557	252	14	nonlinear	nonlinear	ADJ
iajs-2557	252	15	hyperbolic	hyperbolic	ADJ
iajs-2557	252	16	partial	partial	ADJ
iajs-2557	252	17	differential	differential	NOUN
iajs-2557	252	18	equations	equation	NOUN
iajs-2557	252	19	with	with	ADP
iajs-2557	252	20	equality	equality	NOUN
iajs-2557	252	21	and	and	CCONJ
iajs-2557	252	22	inequality	inequality	NOUN
iajs-2557	252	23	constraints	constraint	NOUN
iajs-2557	252	24	.	.	PUNCT
iajs-2557	253	1	iraqi	iraqi	ADJ
iajs-2557	253	2	journal	journal	PROPN
iajs-2557	253	3	of	of	ADP
iajs-2557	253	4	science	science	NOUN
iajs-2557	253	5	.	.	PUNCT
iajs-2557	254	1	2016	2016	NUM
iajs-2557	254	2	,	,	PUNCT
iajs-2557	254	3	57	57	NUM
iajs-2557	254	4	,	,	PUNCT
iajs-2557	254	5	1528	1528	NUM
iajs-2557	254	6	-	-	SYM
iajs-2557	254	7	1538	1538	NUM
iajs-2557	254	8	,	,	PUNCT
iajs-2557	254	9	issn	issn	PROPN
iajs-2557	254	10	:	:	PUNCT
iajs-2557	254	11	0067	0067	NUM
iajs-2557	254	12	-	-	SYM
iajs-2557	254	13	2904	2904	NUM
iajs-2557	254	14	.	.	PUNCT
iajs-2557	255	1	10	10	NUM
iajs-2557	255	2	.	.	PUNCT
iajs-2557	256	1	kadhem	kadhem	PROPN
iajs-2557	256	2	,	,	PUNCT
iajs-2557	256	3	g.m	g.m	PROPN
iajs-2557	256	4	.	.	PUNCT
iajs-2557	257	1	the	the	DET
iajs-2557	257	2	continuous	continuous	ADJ
iajs-2557	257	3	classical	classical	ADJ
iajs-2557	257	4	optimal	optimal	ADJ
iajs-2557	257	5	control	control	NOUN
iajs-2557	257	6	problem	problem	NOUN
iajs-2557	257	7	of	of	ADP
iajs-2557	257	8	partial	partial	ADJ
iajs-2557	257	9	differential	differential	ADJ
iajs-2557	257	10	equations	equation	NOUN
iajs-2557	257	11	.	.	PUNCT
iajs-2557	258	1	m.sc	m.sc	PROPN
iajs-2557	258	2	.	.	PUNCT
iajs-2557	259	1	thesis	thesis	NOUN
iajs-2557	259	2	.	.	PUNCT
iajs-2557	260	1	university	university	NOUN
iajs-2557	260	2	of	of	ADP
iajs-2557	260	3	mustansiriyah	mustansiriyah	NOUN
iajs-2557	260	4	.	.	PUNCT
iajs-2557	261	1	2015	2015	NUM
iajs-2557	261	2	.	.	PUNCT
iajs-2557	262	1	11	11	NUM
iajs-2557	262	2	.	.	PUNCT
iajs-2557	263	1	al	al	PROPN
iajs-2557	263	2	-	-	PUNCT
iajs-2557	263	3	hawasy	hawasy	PROPN
iajs-2557	263	4	,	,	PUNCT
iajs-2557	263	5	j.a.a	j.a.a	PROPN
iajs-2557	263	6	.	.	PUNCT
iajs-2557	263	7	;	;	PUNCT
iajs-2557	264	1	al	al	PROPN
iajs-2557	264	2	-	-	PUNCT
iajs-2557	264	3	qaisi	qaisi	PROPN
iajs-2557	264	4	,	,	PUNCT
iajs-2557	264	5	s.j.m	s.j.m	NOUN
iajs-2557	264	6	.	.	PUNCT
iajs-2557	265	1	the	the	DET
iajs-2557	265	2	solvability	solvability	NOUN
iajs-2557	265	3	of	of	ADP
iajs-2557	265	4	the	the	DET
iajs-2557	265	5	continuous	continuous	ADJ
iajs-2557	265	6	classical	classical	ADJ
iajs-2557	265	7	boundary	boundary	ADJ
iajs-2557	265	8	optimal	optimal	ADJ
iajs-2557	265	9	control	control	NOUN
iajs-2557	265	10	of	of	ADP
iajs-2557	265	11	couple	couple	NOUN
iajs-2557	265	12	nonlinear	nonlinear	ADJ
iajs-2557	265	13	elliptic	elliptic	ADJ
iajs-2557	265	14	partial	partial	ADJ
iajs-2557	265	15	differential	differential	ADJ
iajs-2557	265	16	equations	equation	NOUN
iajs-2557	265	17	with	with	ADP
iajs-2557	265	18	state	state	NOUN
iajs-2557	265	19	constraints	constraint	NOUN
iajs-2557	265	20	.	.	PUNCT
iajs-2557	266	1	al	al	PROPN
iajs-2557	266	2	-	-	PUNCT
iajs-2557	266	3	mustansiriyah	mustansiriyah	PROPN
iajs-2557	266	4	journal	journal	NOUN
iajs-2557	266	5	of	of	ADP
iajs-2557	266	6	science	science	NOUN
iajs-2557	266	7	.	.	PUNCT
iajs-2557	267	1	2019,30,143	2019,30,143	NOUN
iajs-2557	267	2	-	-	PUNCT
iajs-2557	267	3	151,doi	151,doi	NUM
iajs-2557	267	4	:	:	PUNCT
iajs-2557	267	5	10.23851	10.23851	NUM
iajs-2557	267	6	/	/	SYM
iajs-2557	267	7	mjs.v30il.464	mjs.v30il.464	NOUN
iajs-2557	267	8	.	.	PUNCT
iajs-2557	268	1	12	12	NUM
iajs-2557	268	2	.	.	PUNCT
iajs-2557	269	1	al	al	PROPN
iajs-2557	269	2	-	-	PUNCT
iajs-2557	269	3	hawasy	hawasy	PROPN
iajs-2557	269	4	,	,	PUNCT
iajs-2557	269	5	j.a.a	j.a.a	PROPN
iajs-2557	269	6	.	.	PROPN
iajs-2557	269	7	;	;	PUNCT
iajs-2557	269	8	naeif	naeif	NOUN
iajs-2557	269	9	,	,	PUNCT
iajs-2557	269	10	a.a.h	a.a.h	ADJ
iajs-2557	269	11	.	.	PUNCT
iajs-2557	270	1	the	the	DET
iajs-2557	270	2	continuous	continuous	ADJ
iajs-2557	270	3	classical	classical	ADJ
iajs-2557	270	4	boundary	boundary	ADJ
iajs-2557	270	5	optimal	optimal	ADJ
iajs-2557	270	6	control	control	NOUN
iajs-2557	270	7	of	of	ADP
iajs-2557	270	8	a	a	DET
iajs-2557	270	9	couple	couple	NOUN
iajs-2557	270	10	nonlinear	nonlinear	ADJ
iajs-2557	270	11	parabolic	parabolic	ADJ
iajs-2557	270	12	partial	partial	ADJ
iajs-2557	270	13	differential	differential	NOUN
iajs-2557	270	14	equations	equation	NOUN
iajs-2557	270	15	.	.	PUNCT
iajs-2557	271	1	1	1	NUM
iajs-2557	271	2	st	st	PROPN
iajs-2557	271	3	scientific	scientific	ADJ
iajs-2557	271	4	international	international	ADJ
iajs-2557	271	5	conference	conference	NOUN
iajs-2557	271	6	.	.	PUNCT
iajs-2557	272	1	college	college	NOUN
iajs-2557	272	2	of	of	ADP
iajs-2557	272	3	science	science	NOUN
iajs-2557	272	4	.	.	PUNCT
iajs-2557	273	1	al	al	PROPN
iajs-2557	273	2	-	-	PUNCT
iajs-2557	273	3	nahrain	nahrain	PROPN
iajs-2557	273	4	university	university	NOUN
iajs-2557	273	5	.	.	PUNCT
iajs-2557	274	1	2017	2017	NUM
iajs-2557	274	2	,	,	PUNCT
iajs-2557	274	3	special	special	ADJ
iajs-2557	274	4	issus	issus	NOUN
iajs-2557	274	5	,	,	PUNCT
iajs-2557	274	6	123	123	NUM
iajs-2557	274	7	-	-	SYM
iajs-2557	274	8	136	136	NUM
iajs-2557	274	9	,	,	PUNCT
iajs-2557	274	10	doi	doi	NOUN
iajs-2557	274	11	:	:	PUNCT
iajs-2557	274	12	10.22401	10.22401	NUM
iajs-2557	274	13	/	/	SYM
iajs-2557	274	14	anjs.00.1.17	anjs.00.1.17	PROPN
iajs-2557	274	15	.	.	PROPN
iajs-2557	274	16	13	13	NUM
iajs-2557	274	17	.	.	PUNCT
iajs-2557	275	1	al	al	PROPN
iajs-2557	275	2	-	-	PUNCT
iajs-2557	275	3	hawasy	hawasy	PROPN
iajs-2557	275	4	,	,	PUNCT
iajs-2557	275	5	j.a	j.a	PROPN
iajs-2557	275	6	.	.	PUNCT
iajs-2557	276	1	the	the	DET
iajs-2557	276	2	continuous	continuous	ADJ
iajs-2557	276	3	classical	classical	ADJ
iajs-2557	276	4	boundary	boundary	ADJ
iajs-2557	276	5	optimal	optimal	ADJ
iajs-2557	276	6	control	control	NOUN
iajs-2557	276	7	of	of	ADP
iajs-2557	276	8	couple	couple	NOUN
iajs-2557	276	9	nonlinear	nonlinear	ADJ
iajs-2557	276	10	hyperbolic	hyperbolic	ADJ
iajs-2557	276	11	boundary	boundary	ADJ
iajs-2557	276	12	value	value	NOUN
iajs-2557	276	13	problem	problem	NOUN
iajs-2557	276	14	with	with	ADP
iajs-2557	276	15	equality	equality	NOUN
iajs-2557	276	16	and	and	CCONJ
iajs-2557	276	17	inequality	inequality	NOUN
iajs-2557	276	18	constraints	constraint	NOUN
iajs-2557	276	19	.	.	PUNCT
iajs-2557	277	1	open1	open1	ADJ
iajs-2557	277	2	access	access	NOUN
iajs-2557	277	3	.	.	PUNCT
iajs-2557	278	1	baghdad	baghdad	PROPN
iajs-2557	278	2	science	science	PROPN
iajs-2557	278	3	journal	journal	PROPN
iajs-2557	278	4	.	.	PUNCT
iajs-2557	279	1	2019,16,1064	2019,16,1064	NUM
iajs-2557	279	2	-	-	SYM
iajs-2557	279	3	1074,doi	1074,doi	NUM
iajs-2557	279	4	:	:	PUNCT
iajs-2557	279	5	10.21123	10.21123	NUM
iajs-2557	279	6	/	/	SYM
iajs-2557	279	7	bsj.2019.16.4	bsj.2019.16.4	NOUN
iajs-2557	279	8	.	.	PUNCT
iajs-2557	280	1	14	14	NUM
iajs-2557	280	2	.	.	PUNCT
iajs-2557	281	1	al	al	PROPN
iajs-2557	281	2	-	-	PUNCT
iajs-2557	281	3	hawasy	hawasy	PROPN
iajs-2557	281	4	,	,	PUNCT
iajs-2557	281	5	j.	j.	PROPN
iajs-2557	281	6	;	;	PUNCT
iajs-2557	281	7	jaber	jaber	PROPN
iajs-2557	281	8	,	,	PUNCT
iajs-2557	281	9	m.a	m.a	PROPN
iajs-2557	281	10	.	.	PUNCT
iajs-2557	282	1	the	the	DET
iajs-2557	282	2	continuous	continuous	ADJ
iajs-2557	282	3	classical	classical	ADJ
iajs-2557	282	4	optimal	optimal	ADJ
iajs-2557	282	5	control	control	NOUN
iajs-2557	282	6	governing	govern	VERB
iajs-2557	282	7	by	by	ADP
iajs-2557	282	8	triple	triple	ADJ
iajs-2557	282	9	parabolic	parabolic	PROPN
iajs-2557	282	10	boundary	boundary	ADJ
iajs-2557	282	11	value	value	NOUN
iajs-2557	282	12	problem	problem	NOUN
iajs-2557	282	13	.	.	PUNCT
iajs-2557	283	1	ibn	ibn	PROPN
iajs-2557	283	2	al	al	PROPN
iajs-2557	283	3	-	-	PUNCT
iajs-2557	283	4	haitham	haitham	PROPN
iajs-2557	283	5	for	for	ADP
iajs-2557	283	6	pure	pure	ADJ
iajs-2557	283	7	and	and	CCONJ
iajs-2557	283	8	appl	appl	NOUN
iajs-2557	283	9	.	.	PUNCT
iajs-2557	284	1	sci	sci	PROPN
iajs-2557	284	2	.	.	PROPN
iajs-2557	284	3	2020	2020	NUM
iajs-2557	284	4	,	,	PUNCT
iajs-2557	284	5	33	33	NUM
iajs-2557	284	6	,	,	PUNCT
iajs-2557	284	7	129	129	NUM
iajs-2557	284	8	-	-	SYM
iajs-2557	284	9	142	142	NUM
iajs-2557	284	10	.	.	PUNCT
iajs-2557	285	1	15	15	NUM
iajs-2557	285	2	.	.	PUNCT
iajs-2557	286	1	al	al	PROPN
iajs-2557	286	2	-	-	PUNCT
iajs-2557	286	3	hawasy	hawasy	PROPN
iajs-2557	286	4	,	,	PUNCT
iajs-2557	286	5	j.	j.	PROPN
iajs-2557	286	6	;	;	PUNCT
iajs-2557	286	7	jasim	jasim	PROPN
iajs-2557	286	8	,	,	PUNCT
iajs-2557	286	9	d.k	d.k	PROPN
iajs-2557	286	10	.	.	PUNCT
iajs-2557	287	1	the	the	DET
iajs-2557	287	2	continuous	continuous	ADJ
iajs-2557	287	3	classical	classical	ADJ
iajs-2557	287	4	optimal	optimal	ADJ
iajs-2557	287	5	control	control	NOUN
iajs-2557	287	6	problems	problem	NOUN
iajs-2557	287	7	of	of	ADP
iajs-2557	287	8	a	a	DET
iajs-2557	287	9	triple	triple	ADJ
iajs-2557	287	10	elliptic	elliptic	ADJ
iajs-2557	287	11	partial	partial	ADJ
iajs-2557	287	12	differential	differential	NOUN
iajs-2557	287	13	equations	equation	NOUN
iajs-2557	287	14	.	.	PUNCT
iajs-2557	288	1	ibn	ibn	PROPN
iajs-2557	288	2	al	al	PROPN
iajs-2557	288	3	-	-	PUNCT
iajs-2557	288	4	haitham	haitham	PROPN
iajs-2557	288	5	for	for	ADP
iajs-2557	288	6	pure	pure	ADJ
iajs-2557	288	7	and	and	CCONJ
iajs-2557	288	8	appl	appl	NOUN
iajs-2557	288	9	.	.	PUNCT
iajs-2557	289	1	sci	sci	PROPN
iajs-2557	289	2	.	.	PROPN
iajs-2557	289	3	2020	2020	NUM
iajs-2557	289	4	,	,	PUNCT
iajs-2557	289	5	33	33	NUM
iajs-2557	289	6	,	,	PUNCT
iajs-2557	289	7	143	143	NUM
iajs-2557	289	8	-	-	SYM
iajs-2557	289	9	151	151	NUM
iajs-2557	289	10	.	.	PUNCT
iajs-2557	289	11	16	16	NUM
iajs-2557	289	12	.	.	PUNCT
iajs-2557	290	1	al	al	PROPN
iajs-2557	290	2	-	-	PUNCT
iajs-2557	290	3	hawasy	hawasy	PROPN
iajs-2557	290	4	,	,	PUNCT
iajs-2557	290	5	j.a.a	j.a.a	PROPN
iajs-2557	290	6	.	.	PROPN
iajs-2557	290	7	solvability	solvability	PROPN
iajs-2557	290	8	for	for	ADP
iajs-2557	290	9	continuous	continuous	ADJ
iajs-2557	290	10	classical	classical	ADJ
iajs-2557	290	11	optimal	optimal	ADJ
iajs-2557	290	12	control	control	NOUN
iajs-2557	290	13	associated	associate	VERB
iajs-2557	290	14	with	with	ADP
iajs-2557	290	15	triple	triple	ADJ
iajs-2557	290	16	hyperbolic	hyperbolic	ADJ
iajs-2557	290	17	boundary	boundary	ADJ
iajs-2557	290	18	value	value	NOUN
iajs-2557	290	19	problem	problem	NOUN
iajs-2557	290	20	.	.	PUNCT
iajs-2557	291	1	accepted	accept	VERB
iajs-2557	291	2	in	in	ADP
iajs-2557	291	3	ijpam	ijpam	NOUN
iajs-2557	291	4	,	,	PUNCT
iajs-2557	291	5	2019	2019	NUM
iajs-2557	291	6	.	.	PUNCT
iajs-2557	292	1	17	17	NUM
iajs-2557	292	2	.	.	PUNCT
iajs-2557	293	1	al	al	PROPN
iajs-2557	293	2	-	-	PUNCT
iajs-2557	293	3	hawasy	hawasy	PROPN
iajs-2557	293	4	,	,	PUNCT
iajs-2557	293	5	j.	j.	PROPN
iajs-2557	293	6	;	;	PUNCT
iajs-2557	293	7	jaber	jaber	PROPN
iajs-2557	293	8	,	,	PUNCT
iajs-2557	293	9	m.a	m.a	PROPN
iajs-2557	293	10	.	.	PUNCT
iajs-2557	294	1	the	the	DET
iajs-2557	294	2	continuous	continuous	ADJ
iajs-2557	294	3	classical	classical	ADJ
iajs-2557	294	4	boundary	boundary	ADJ
iajs-2557	294	5	optimal	optimal	ADJ
iajs-2557	294	6	control	control	NOUN
iajs-2557	294	7	vector	vector	NOUN
iajs-2557	294	8	governing	governing	NOUN
iajs-2557	294	9	by	by	ADP
iajs-2557	294	10	triple	triple	ADJ
iajs-2557	294	11	linear	linear	ADJ
iajs-2557	294	12	partial	partial	ADJ
iajs-2557	294	13	differential	differential	ADJ
iajs-2557	294	14	equations	equation	NOUN
iajs-2557	294	15	of	of	ADP
iajs-2557	294	16	parabolic	parabolic	ADJ
iajs-2557	294	17	type	type	NOUN
iajs-2557	294	18	.	.	PUNCT
iajs-2557	294	19	accepted	accept	VERB
iajs-2557	294	20	in	in	ADP
iajs-2557	294	21	ibn	ibn	PROPN
iajs-2557	294	22	al	al	PROPN
iajs-2557	294	23	-	-	PUNCT
iajs-2557	294	24	haitham	haitham	PROPN
iajs-2557	294	25	for	for	ADP
iajs-2557	294	26	pure	pure	ADJ
iajs-2557	294	27	and	and	CCONJ
iajs-2557	294	28	applied	applied	ADJ
iajs-2557	294	29	science	science	NOUN
iajs-2557	294	30	.	.	PUNCT
iajs-2557	295	1	2019	2019	NUM
iajs-2557	295	2	.	.	PUNCT