id	sid	tid	token	lemma	pos
iajs-2833	1	1	161	161	NUM
iajs-2833	1	2	this	this	DET
iajs-2833	1	3	work	work	NOUN
iajs-2833	1	4	is	be	AUX
iajs-2833	1	5	licensed	license	VERB
iajs-2833	1	6	under	under	ADP
iajs-2833	1	7	a	a	DET
iajs-2833	1	8	creative	creative	ADJ
iajs-2833	1	9	commons	common	NOUN
iajs-2833	1	10	attribution	attribution	NOUN
iajs-2833	1	11	4.0	4.0	NUM
iajs-2833	1	12	international	international	ADJ
iajs-2833	1	13	license	license	NOUN
iajs-2833	1	14	.	.	PUNCT
iajs-2833	2	1	the	the	DET
iajs-2833	2	2	optimal	optimal	ADJ
iajs-2833	2	3	classical	classical	ADJ
iajs-2833	2	4	continuous	continuous	ADJ
iajs-2833	2	5	control	control	NOUN
iajs-2833	2	6	quaternary	quaternary	ADJ
iajs-2833	2	7	vector	vector	NOUN
iajs-2833	2	8	of	of	ADP
iajs-2833	2	9	quaternary	quaternary	ADJ
iajs-2833	2	10	nonlinear	nonlinear	ADJ
iajs-2833	2	11	hyperbolic	hyperbolic	ADJ
iajs-2833	2	12	boundary	boundary	ADJ
iajs-2833	2	13	value	value	NOUN
iajs-2833	2	14	problem	problem	NOUN
iajs-2833	2	15	abstract	abstract	ADV
iajs-2833	2	16	this	this	DET
iajs-2833	2	17	work	work	NOUN
iajs-2833	2	18	is	be	AUX
iajs-2833	2	19	concerned	concern	VERB
iajs-2833	2	20	with	with	ADP
iajs-2833	2	21	studying	study	VERB
iajs-2833	2	22	the	the	DET
iajs-2833	2	23	optimal	optimal	ADJ
iajs-2833	2	24	classical	classical	ADJ
iajs-2833	2	25	continuous	continuous	ADJ
iajs-2833	2	26	control	control	NOUN
iajs-2833	2	27	quaternary	quaternary	ADJ
iajs-2833	2	28	vector	vector	NOUN
iajs-2833	2	29	problem	problem	NOUN
iajs-2833	2	30	.	.	PUNCT
iajs-2833	3	1	it	it	PRON
iajs-2833	3	2	is	be	AUX
iajs-2833	3	3	consisted	consist	VERB
iajs-2833	3	4	of	of	ADP
iajs-2833	3	5	;	;	PUNCT
iajs-2833	3	6	the	the	DET
iajs-2833	3	7	quaternary	quaternary	ADJ
iajs-2833	3	8	nonlinear	nonlinear	ADJ
iajs-2833	3	9	hyperbolic	hyperbolic	ADJ
iajs-2833	3	10	boundary	boundary	ADJ
iajs-2833	3	11	value	value	NOUN
iajs-2833	3	12	problem	problem	NOUN
iajs-2833	3	13	and	and	CCONJ
iajs-2833	3	14	the	the	DET
iajs-2833	3	15	cost	cost	NOUN
iajs-2833	3	16	functional	functional	ADJ
iajs-2833	3	17	.	.	PUNCT
iajs-2833	4	1	at	at	ADP
iajs-2833	4	2	first	first	ADV
iajs-2833	4	3	,	,	PUNCT
iajs-2833	4	4	the	the	DET
iajs-2833	4	5	weak	weak	ADJ
iajs-2833	4	6	form	form	NOUN
iajs-2833	4	7	of	of	ADP
iajs-2833	4	8	the	the	DET
iajs-2833	4	9	quaternary	quaternary	ADJ
iajs-2833	4	10	nonlinear	nonlinear	ADJ
iajs-2833	4	11	hyperbolic	hyperbolic	ADJ
iajs-2833	4	12	boundary	boundary	ADJ
iajs-2833	4	13	value	value	NOUN
iajs-2833	4	14	problem	problem	NOUN
iajs-2833	4	15	is	be	AUX
iajs-2833	4	16	obtained	obtain	VERB
iajs-2833	4	17	.	.	PUNCT
iajs-2833	5	1	then	then	ADV
iajs-2833	5	2	under	under	ADP
iajs-2833	5	3	suitable	suitable	ADJ
iajs-2833	5	4	hypotheses	hypothesis	NOUN
iajs-2833	5	5	,	,	PUNCT
iajs-2833	5	6	the	the	DET
iajs-2833	5	7	existence	existence	NOUN
iajs-2833	5	8	theorem	theorem	NOUN
iajs-2833	5	9	of	of	ADP
iajs-2833	5	10	a	a	DET
iajs-2833	5	11	unique	unique	ADJ
iajs-2833	5	12	state	state	NOUN
iajs-2833	5	13	quaternary	quaternary	ADJ
iajs-2833	5	14	vector	vector	NOUN
iajs-2833	5	15	solution	solution	NOUN
iajs-2833	5	16	for	for	ADP
iajs-2833	5	17	the	the	DET
iajs-2833	5	18	weak	weak	ADJ
iajs-2833	5	19	form	form	NOUN
iajs-2833	5	20	where	where	SCONJ
iajs-2833	5	21	the	the	DET
iajs-2833	5	22	classical	classical	ADJ
iajs-2833	5	23	continuous	continuous	ADJ
iajs-2833	5	24	control	control	NOUN
iajs-2833	5	25	quaternary	quaternary	ADJ
iajs-2833	5	26	vector	vector	NOUN
iajs-2833	5	27	is	be	AUX
iajs-2833	5	28	considered	consider	VERB
iajs-2833	5	29	known	know	VERB
iajs-2833	5	30	is	be	AUX
iajs-2833	5	31	stated	state	VERB
iajs-2833	5	32	and	and	CCONJ
iajs-2833	5	33	demonstrated	demonstrate	VERB
iajs-2833	5	34	by	by	ADP
iajs-2833	5	35	employing	employ	VERB
iajs-2833	5	36	the	the	DET
iajs-2833	5	37	method	method	NOUN
iajs-2833	5	38	of	of	ADP
iajs-2833	5	39	galerkin	galerkin	PROPN
iajs-2833	5	40	and	and	CCONJ
iajs-2833	5	41	the	the	DET
iajs-2833	5	42	compactness	compactness	NOUN
iajs-2833	5	43	theorem	theorem	VERB
iajs-2833	5	44	.	.	PUNCT
iajs-2833	6	1	in	in	ADP
iajs-2833	6	2	addition	addition	NOUN
iajs-2833	6	3	,	,	PUNCT
iajs-2833	6	4	the	the	DET
iajs-2833	6	5	continuity	continuity	NOUN
iajs-2833	6	6	operator	operator	NOUN
iajs-2833	6	7	between	between	ADP
iajs-2833	6	8	the	the	DET
iajs-2833	6	9	state	state	NOUN
iajs-2833	6	10	quaternary	quaternary	ADJ
iajs-2833	6	11	vector	vector	NOUN
iajs-2833	6	12	solution	solution	NOUN
iajs-2833	6	13	of	of	ADP
iajs-2833	6	14	the	the	DET
iajs-2833	6	15	weak	weak	ADJ
iajs-2833	6	16	form	form	NOUN
iajs-2833	6	17	and	and	CCONJ
iajs-2833	6	18	the	the	DET
iajs-2833	6	19	corresponding	corresponding	ADJ
iajs-2833	6	20	classical	classical	ADJ
iajs-2833	6	21	continuous	continuous	ADJ
iajs-2833	6	22	control	control	NOUN
iajs-2833	6	23	quaternary	quaternary	ADJ
iajs-2833	6	24	vector	vector	NOUN
iajs-2833	6	25	is	be	AUX
iajs-2833	6	26	demonstrated	demonstrate	VERB
iajs-2833	6	27	in	in	ADP
iajs-2833	6	28	three	three	NUM
iajs-2833	6	29	different	different	ADJ
iajs-2833	6	30	infinite	infinite	ADJ
iajs-2833	6	31	dimensional	dimensional	ADJ
iajs-2833	6	32	spaces	space	NOUN
iajs-2833	6	33	(	(	PUNCT
iajs-2833	6	34	hilbert	hilbert	NOUN
iajs-2833	6	35	spaces	space	NOUN
iajs-2833	6	36	)	)	PUNCT
iajs-2833	6	37	.	.	PUNCT
iajs-2833	7	1	furthermore	furthermore	ADV
iajs-2833	7	2	,	,	PUNCT
iajs-2833	7	3	with	with	ADP
iajs-2833	7	4	suitable	suitable	ADJ
iajs-2833	7	5	hypotheses	hypothesis	NOUN
iajs-2833	7	6	,	,	PUNCT
iajs-2833	7	7	the	the	DET
iajs-2833	7	8	existence	existence	NOUN
iajs-2833	7	9	theorem	theorem	NOUN
iajs-2833	7	10	of	of	ADP
iajs-2833	7	11	an	an	DET
iajs-2833	7	12	optimal	optimal	ADJ
iajs-2833	7	13	classical	classical	ADJ
iajs-2833	7	14	continuous	continuous	ADJ
iajs-2833	7	15	control	control	NOUN
iajs-2833	7	16	quaternary	quaternary	ADJ
iajs-2833	7	17	vector	vector	NOUN
iajs-2833	7	18	dominated	dominate	VERB
iajs-2833	7	19	by	by	ADP
iajs-2833	7	20	the	the	DET
iajs-2833	7	21	weak	weak	ADJ
iajs-2833	7	22	form	form	NOUN
iajs-2833	7	23	of	of	ADP
iajs-2833	7	24	the	the	DET
iajs-2833	7	25	quaternary	quaternary	ADJ
iajs-2833	7	26	nonlinear	nonlinear	ADJ
iajs-2833	7	27	hyperbolic	hyperbolic	ADJ
iajs-2833	7	28	boundary	boundary	ADJ
iajs-2833	7	29	value	value	NOUN
iajs-2833	7	30	problem	problem	NOUN
iajs-2833	7	31	is	be	AUX
iajs-2833	7	32	stated	state	VERB
iajs-2833	7	33	and	and	CCONJ
iajs-2833	7	34	demonstrated	demonstrate	VERB
iajs-2833	7	35	.	.	PUNCT
iajs-2833	8	1	keywords	keyword	NOUN
iajs-2833	8	2	:	:	PUNCT
iajs-2833	8	3	optimal	optimal	ADJ
iajs-2833	8	4	classical	classical	ADJ
iajs-2833	8	5	continuous	continuous	ADJ
iajs-2833	8	6	control	control	NOUN
iajs-2833	8	7	quaternary	quaternary	ADJ
iajs-2833	8	8	vector	vector	NOUN
iajs-2833	8	9	,	,	PUNCT
iajs-2833	8	10	quaternary	quaternary	ADJ
iajs-2833	8	11	nonlinear	nonlinear	ADJ
iajs-2833	8	12	hyperbolic	hyperbolic	ADJ
iajs-2833	8	13	boundary	boundary	ADJ
iajs-2833	8	14	value	value	NOUN
iajs-2833	8	15	problem	problem	NOUN
iajs-2833	8	16	,	,	PUNCT
iajs-2833	8	17	weak	weak	ADJ
iajs-2833	8	18	form	form	NOUN
iajs-2833	8	19	.	.	PUNCT
iajs-2833	9	1	1	1	X
iajs-2833	9	2	.	.	X
iajs-2833	9	3	introduction	introduction	NOUN
iajs-2833	9	4	different	different	ADJ
iajs-2833	9	5	applications	application	NOUN
iajs-2833	9	6	in	in	ADP
iajs-2833	9	7	real	real	ADJ
iajs-2833	9	8	-	-	PUNCT
iajs-2833	9	9	life	life	NOUN
iajs-2833	9	10	are	be	AUX
iajs-2833	9	11	classified	classify	VERB
iajs-2833	9	12	as	as	ADP
iajs-2833	9	13	optimal	optimal	ADJ
iajs-2833	9	14	control	control	NOUN
iajs-2833	9	15	problems	problem	NOUN
iajs-2833	9	16	(	(	PUNCT
iajs-2833	9	17	ocps	ocps	PROPN
iajs-2833	9	18	)	)	PUNCT
iajs-2833	9	19	.	.	PUNCT
iajs-2833	10	1	for	for	ADP
iajs-2833	10	2	example	example	NOUN
iajs-2833	10	3	,	,	PUNCT
iajs-2833	10	4	in	in	ADP
iajs-2833	10	5	medicine	medicine	NOUN
iajs-2833	10	6	[	[	X
iajs-2833	10	7	1	1	NUM
iajs-2833	10	8	]	]	PUNCT
iajs-2833	10	9	,	,	PUNCT
iajs-2833	10	10	economics	economic	NOUN
iajs-2833	10	11	[	[	X
iajs-2833	10	12	2	2	NUM
iajs-2833	10	13	]	]	PUNCT
iajs-2833	10	14	,	,	PUNCT
iajs-2833	10	15	robotics	robotic	NOUN
iajs-2833	10	16	[	[	X
iajs-2833	10	17	3	3	NUM
iajs-2833	10	18	]	]	PUNCT
iajs-2833	10	19	,	,	PUNCT
iajs-2833	10	20	aircraft	aircraft	NOUN
iajs-2833	10	21	[	[	X
iajs-2833	10	22	4	4	NUM
iajs-2833	10	23	]	]	PUNCT
iajs-2833	10	24	,	,	PUNCT
iajs-2833	10	25	and	and	CCONJ
iajs-2833	10	26	many	many	ADJ
iajs-2833	10	27	other	other	ADJ
iajs-2833	10	28	fields	field	NOUN
iajs-2833	10	29	.	.	PUNCT
iajs-2833	11	1	usually	usually	ADV
iajs-2833	11	2	,	,	PUNCT
iajs-2833	11	3	this	this	DET
iajs-2833	11	4	importance	importance	NOUN
iajs-2833	11	5	encouraged	encourage	VERB
iajs-2833	11	6	many	many	ADJ
iajs-2833	11	7	researchers	researcher	NOUN
iajs-2833	11	8	to	to	PART
iajs-2833	11	9	be	be	AUX
iajs-2833	11	10	interested	interested	ADJ
iajs-2833	11	11	in	in	ADP
iajs-2833	11	12	studying	study	VERB
iajs-2833	11	13	ocps	ocp	NOUN
iajs-2833	11	14	in	in	ADP
iajs-2833	11	15	general	general	ADJ
iajs-2833	11	16	and	and	CCONJ
iajs-2833	11	17	optimal	optimal	ADJ
iajs-2833	11	18	classical	classical	ADJ
iajs-2833	11	19	continuous	continuous	ADJ
iajs-2833	11	20	control	control	NOUN
iajs-2833	11	21	problems	problem	NOUN
iajs-2833	11	22	(	(	PUNCT
iajs-2833	11	23	occcp	occcp	ADV
iajs-2833	11	24	)	)	PUNCT
iajs-2833	11	25	in	in	ADP
iajs-2833	11	26	particular	particular	ADJ
iajs-2833	11	27	.	.	PUNCT
iajs-2833	12	1	during	during	ADP
iajs-2833	12	2	the	the	DET
iajs-2833	12	3	last	last	ADJ
iajs-2833	12	4	decade	decade	NOUN
iajs-2833	12	5	,	,	PUNCT
iajs-2833	12	6	great	great	ADJ
iajs-2833	12	7	attention	attention	NOUN
iajs-2833	12	8	has	have	AUX
iajs-2833	12	9	been	be	AUX
iajs-2833	12	10	made	make	VERB
iajs-2833	12	11	to	to	ADP
iajs-2833	12	12	studying	study	VERB
iajs-2833	12	13	the	the	DET
iajs-2833	12	14	subject	subject	NOUN
iajs-2833	12	15	of	of	ADP
iajs-2833	12	16	occcp	occcp	ADV
iajs-2833	12	17	for	for	ADP
iajs-2833	12	18	a	a	DET
iajs-2833	12	19	system	system	NOUN
iajs-2833	12	20	dominated	dominate	VERB
iajs-2833	12	21	by	by	ADP
iajs-2833	12	22	nonlinear	nonlinear	ADJ
iajs-2833	12	23	pdes	pde	NOUN
iajs-2833	12	24	(	(	PUNCT
iajs-2833	12	25	nlpdes	nlpde	NOUN
iajs-2833	12	26	)	)	PUNCT
iajs-2833	12	27	ibn	ibn	PROPN
iajs-2833	12	28	al	al	PROPN
iajs-2833	12	29	-	-	PUNCT
iajs-2833	12	30	haitham	haitham	PROPN
iajs-2833	12	31	journal	journal	PROPN
iajs-2833	12	32	for	for	ADP
iajs-2833	12	33	pure	pure	ADJ
iajs-2833	12	34	and	and	CCONJ
iajs-2833	12	35	applied	apply	VERB
iajs-2833	12	36	sciences	sciences	PROPN
iajs-2833	12	37	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2833	12	38	:	:	PUNCT
iajs-2833	12	39	journal	journal	PROPN
iajs-2833	12	40	homepage	homepage	NOUN
iajs-2833	12	41	doi	doi	PROPN
iajs-2833	12	42	:	:	PUNCT
iajs-2833	12	43	10.30526/35.3.2833	10.30526/35.3.2833	NUM
iajs-2833	12	44	article	article	NOUN
iajs-2833	12	45	history	history	NOUN
iajs-2833	12	46	:	:	PUNCT
iajs-2833	12	47	received	receive	VERB
iajs-2833	12	48	13	13	NUM
iajs-2833	12	49	march	march	NOUN
iajs-2833	12	50	2022	2022	NUM
iajs-2833	12	51	,	,	PUNCT
iajs-2833	12	52	accepted	accept	VERB
iajs-2833	12	53	17	17	NUM
iajs-2833	12	54	may	may	PROPN
iajs-2833	12	55	2022	2022	NUM
iajs-2833	12	56	,	,	PUNCT
iajs-2833	12	57	published	publish	VERB
iajs-2833	12	58	in	in	ADP
iajs-2833	12	59	july	july	PROPN
iajs-2833	12	60	2022	2022	NUM
iajs-2833	12	61	.	.	PUNCT
iajs-2833	13	1	jamil	jamil	PROPN
iajs-2833	13	2	a.	a.	PROPN
iajs-2833	13	3	ali	ali	PROPN
iajs-2833	13	4	al	al	PROPN
iajs-2833	13	5	-	-	PUNCT
iajs-2833	13	6	hawasy	hawasy	PROPN
iajs-2833	13	7	department	department	NOUN
iajs-2833	13	8	of	of	ADP
iajs-2833	13	9	mathematics	mathematics	PROPN
iajs-2833	13	10	,	,	PUNCT
iajs-2833	13	11	college	college	NOUN
iajs-2833	13	12	of	of	ADP
iajs-2833	13	13	sciences	sciences	PROPN
iajs-2833	13	14	,	,	PUNCT
iajs-2833	13	15	mustansiriyah	mustansiriyah	NOUN
iajs-2833	13	16	university	university	NOUN
iajs-2833	13	17	,	,	PUNCT
iajs-2833	13	18	baghdad	baghdad	PROPN
iajs-2833	13	19	,	,	PUNCT
iajs-2833	13	20	iraq	iraq	PROPN
iajs-2833	13	21	.	.	PUNCT
iajs-2833	14	1	jhawassy17@uomustanriyah.edu.iq	jhawassy17@uomustanriyah.edu.iq	PROPN
iajs-2833	14	2	mayeada	mayeada	PROPN
iajs-2833	14	3	abd	abd	PROPN
iajs-2833	14	4	alsatar	alsatar	PROPN
iajs-2833	14	5	hassan	hassan	PROPN
iajs-2833	14	6	baghdad	baghdad	PROPN
iajs-2833	14	7	directorate	directorate	NOUN
iajs-2833	14	8	of	of	ADP
iajs-2833	14	9	education	education	NOUN
iajs-2833	14	10	,	,	PUNCT
iajs-2833	14	11	baghdad	baghdad	PROPN
iajs-2833	14	12	,	,	PUNCT
iajs-2833	14	13	iraq	iraq	PROPN
iajs-2833	14	14	mayeadabd1989@uomustanriyah.edu.iq	mayeadabd1989@uomustanriyah.edu.iq	PROPN
iajs-2833	14	15	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2833	14	16	file:///f:/العدد%20الثاني%202022/:%20http:/jih.uobaghdad.edu.iq	file:///f:/العدد%20الثاني%202022/:%20http:/jih.uobaghdad.edu.iq	PROPN
iajs-2833	14	17	/	/	SYM
iajs-2833	14	18	index.php	index.php	VERB
iajs-2833	14	19	/	/	SYM
iajs-2833	14	20	j	j	NOUN
iajs-2833	14	21	/	/	SYM
iajs-2833	14	22	index	index	NOUN
iajs-2833	14	23	mailto:jhawassy17@uomustanriyah.edu.iq	mailto:jhawassy17@uomustanriyah.edu.iq	PROPN
iajs-2833	14	24	mailto:jhawassy17@uomustanriyah.edu.iq	mailto:jhawassy17@uomustanriyah.edu.iq	PROPN
iajs-2833	14	25	mailto	mailto	PROPN
iajs-2833	14	26	:	:	PUNCT
iajs-2833	14	27	mayeadabd1989@uomustanriyah.edu.iq%7d	mayeadabd1989@uomustanriyah.edu.iq%7d	PROPN
iajs-2833	14	28	ihjpas	ihjpas	PROPN
iajs-2833	14	29	.	.	PUNCT
iajs-2833	15	1	53	53	NUM
iajs-2833	15	2	(	(	PUNCT
iajs-2833	15	3	3)2022	3)2022	NOUN
iajs-2833	15	4	162	162	NUM
iajs-2833	15	5	of	of	ADP
iajs-2833	15	6	the	the	DET
iajs-2833	15	7	three	three	NUM
iajs-2833	15	8	types	type	NOUN
iajs-2833	15	9	elliptic	elliptic	ADJ
iajs-2833	15	10	[	[	X
iajs-2833	15	11	5	5	NUM
iajs-2833	15	12	]	]	PUNCT
iajs-2833	15	13	,	,	PUNCT
iajs-2833	15	14	hyperbolic	hyperbolic	ADJ
iajs-2833	15	15	[	[	X
iajs-2833	15	16	6	6	NUM
iajs-2833	15	17	]	]	PUNCT
iajs-2833	15	18	,	,	PUNCT
iajs-2833	15	19	and	and	CCONJ
iajs-2833	15	20	parabolic	parabolic	VERB
iajs-2833	16	1	[	[	X
iajs-2833	16	2	7	7	NUM
iajs-2833	16	3	]	]	PUNCT
iajs-2833	16	4	.	.	PUNCT
iajs-2833	17	1	latter	latter	ADJ
iajs-2833	17	2	,	,	PUNCT
iajs-2833	17	3	the	the	DET
iajs-2833	17	4	study	study	NOUN
iajs-2833	17	5	of	of	ADP
iajs-2833	17	6	this	this	DET
iajs-2833	17	7	subject	subject	NOUN
iajs-2833	17	8	expanded	expand	VERB
iajs-2833	17	9	to	to	PART
iajs-2833	17	10	include	include	VERB
iajs-2833	17	11	occcp	occcp	ADV
iajs-2833	17	12	for	for	ADP
iajs-2833	17	13	systems	system	NOUN
iajs-2833	17	14	dominated	dominate	VERB
iajs-2833	17	15	by	by	ADP
iajs-2833	17	16	a	a	DET
iajs-2833	17	17	couple	couple	NOUN
iajs-2833	17	18	of	of	ADP
iajs-2833	17	19	nlpdes	nlpde	NOUN
iajs-2833	17	20	of	of	ADP
iajs-2833	17	21	their	their	PRON
iajs-2833	17	22	three	three	NUM
iajs-2833	17	23	types	type	NOUN
iajs-2833	17	24	[	[	X
iajs-2833	17	25	8	8	NUM
iajs-2833	17	26	-	-	SYM
iajs-2833	17	27	10	10	NUM
iajs-2833	17	28	]	]	PUNCT
iajs-2833	17	29	;	;	PUNCT
iajs-2833	17	30	through	through	ADP
iajs-2833	17	31	recent	recent	ADJ
iajs-2833	17	32	years	year	NOUN
iajs-2833	17	33	,	,	PUNCT
iajs-2833	17	34	these	these	DET
iajs-2833	17	35	studies	study	NOUN
iajs-2833	17	36	for	for	ADP
iajs-2833	17	37	these	these	DET
iajs-2833	17	38	three	three	NUM
iajs-2833	17	39	types	type	NOUN
iajs-2833	17	40	expanded	expand	VERB
iajs-2833	17	41	to	to	PART
iajs-2833	17	42	deal	deal	VERB
iajs-2833	17	43	with	with	ADP
iajs-2833	17	44	occcp	occcp	PROPN
iajs-2833	17	45	for	for	ADP
iajs-2833	17	46	systems	system	NOUN
iajs-2833	17	47	dominated	dominate	VERB
iajs-2833	17	48	by	by	ADP
iajs-2833	17	49	triple	triple	ADJ
iajs-2833	17	50	nlpdes	nlpde	NOUN
iajs-2833	17	51	[	[	X
iajs-2833	17	52	11	11	NUM
iajs-2833	17	53	-	-	SYM
iajs-2833	17	54	13	13	NUM
iajs-2833	17	55	]	]	PUNCT
iajs-2833	17	56	.	.	PUNCT
iajs-2833	18	1	all	all	DET
iajs-2833	18	2	these	these	DET
iajs-2833	18	3	studies	study	NOUN
iajs-2833	18	4	encouraged	encourage	VERB
iajs-2833	18	5	us	we	PRON
iajs-2833	18	6	to	to	PART
iajs-2833	18	7	investigate	investigate	VERB
iajs-2833	18	8	the	the	DET
iajs-2833	18	9	occcp	occcp	ADV
iajs-2833	18	10	dominated	dominate	VERB
iajs-2833	18	11	by	by	ADP
iajs-2833	18	12	qnlhbvp	qnlhbvp	NOUN
iajs-2833	18	13	.	.	PUNCT
iajs-2833	19	1	this	this	DET
iajs-2833	19	2	article	article	NOUN
iajs-2833	19	3	first	first	ADV
iajs-2833	19	4	concerns	concern	VERB
iajs-2833	19	5	the	the	DET
iajs-2833	19	6	mathematical	mathematical	ADJ
iajs-2833	19	7	formulation	formulation	NOUN
iajs-2833	19	8	for	for	ADP
iajs-2833	19	9	the	the	DET
iajs-2833	19	10	optimal	optimal	ADJ
iajs-2833	19	11	classical	classical	ADJ
iajs-2833	19	12	continuous	continuous	ADJ
iajs-2833	19	13	control	control	NOUN
iajs-2833	19	14	quaternary	quaternary	ADJ
iajs-2833	19	15	vector	vector	NOUN
iajs-2833	19	16	problem	problem	NOUN
iajs-2833	19	17	.	.	PUNCT
iajs-2833	20	1	then	then	ADV
iajs-2833	20	2	the	the	DET
iajs-2833	20	3	existence	existence	NOUN
iajs-2833	20	4	theorem	theorem	NOUN
iajs-2833	20	5	(	(	PUNCT
iajs-2833	20	6	eth	eth	NOUN
iajs-2833	20	7	)	)	PUNCT
iajs-2833	20	8	of	of	ADP
iajs-2833	20	9	a	a	DET
iajs-2833	20	10	unique	unique	ADJ
iajs-2833	20	11	state	state	NOUN
iajs-2833	20	12	quaternary	quaternary	ADJ
iajs-2833	20	13	vector	vector	NOUN
iajs-2833	20	14	solution	solution	NOUN
iajs-2833	20	15	(	(	PUNCT
iajs-2833	20	16	sqvs	sqvs	PROPN
iajs-2833	20	17	)	)	PUNCT
iajs-2833	20	18	for	for	ADP
iajs-2833	20	19	the	the	DET
iajs-2833	20	20	weak	weak	ADJ
iajs-2833	20	21	form	form	NOUN
iajs-2833	20	22	(	(	PUNCT
iajs-2833	20	23	wf	wf	PROPN
iajs-2833	20	24	)	)	PUNCT
iajs-2833	20	25	“	"	PUNCT
iajs-2833	20	26	of	of	ADP
iajs-2833	20	27	the	the	DET
iajs-2833	20	28	quaternary	quaternary	ADJ
iajs-2833	20	29	nonlinear	nonlinear	ADJ
iajs-2833	20	30	hyperbolic	hyperbolic	ADJ
iajs-2833	20	31	boundary	boundary	ADJ
iajs-2833	20	32	value	value	NOUN
iajs-2833	20	33	problem	problem	NOUN
iajs-2833	20	34	(	(	PUNCT
iajs-2833	20	35	qnlhbvp	qnlhbvp	NOUN
iajs-2833	20	36	)	)	PUNCT
iajs-2833	20	37	”	"	PUNCT
iajs-2833	20	38	is	be	AUX
iajs-2833	20	39	stated	state	VERB
iajs-2833	20	40	and	and	CCONJ
iajs-2833	20	41	demonstrated	demonstrate	VERB
iajs-2833	20	42	using	use	VERB
iajs-2833	20	43	the	the	DET
iajs-2833	20	44	method	method	NOUN
iajs-2833	20	45	of	of	ADP
iajs-2833	20	46	galerkin	galerkin	PROPN
iajs-2833	20	47	(	(	PUNCT
iajs-2833	20	48	mga	mga	PROPN
iajs-2833	20	49	)	)	PUNCT
iajs-2833	20	50	and	and	CCONJ
iajs-2833	20	51	the	the	DET
iajs-2833	20	52	aubin	aubin	PROPN
iajs-2833	20	53	compactness	compactness	NOUN
iajs-2833	20	54	theorem	theorem	NOUN
iajs-2833	20	55	(	(	PUNCT
iajs-2833	20	56	acth	acth	NOUN
iajs-2833	20	57	)	)	PUNCT
iajs-2833	20	58	when	when	SCONJ
iajs-2833	20	59	the	the	DET
iajs-2833	20	60	classical	classical	ADJ
iajs-2833	20	61	continuous	continuous	ADJ
iajs-2833	20	62	control	control	NOUN
iajs-2833	20	63	quaternary	quaternary	ADJ
iajs-2833	20	64	vector	vector	NOUN
iajs-2833	20	65	(	(	PUNCT
iajs-2833	20	66	cccqv	cccqv	NOUN
iajs-2833	20	67	)	)	PUNCT
iajs-2833	20	68	is	be	AUX
iajs-2833	20	69	fixed	fix	VERB
iajs-2833	20	70	under	under	ADP
iajs-2833	20	71	suitable	suitable	ADJ
iajs-2833	20	72	hypotheses	hypothesis	NOUN
iajs-2833	20	73	.	.	PUNCT
iajs-2833	21	1	furthermore	furthermore	ADV
iajs-2833	21	2	,	,	PUNCT
iajs-2833	21	3	the	the	DET
iajs-2833	21	4	continuity	continuity	NOUN
iajs-2833	21	5	operator	operator	NOUN
iajs-2833	21	6	between	between	ADP
iajs-2833	21	7	the	the	DET
iajs-2833	21	8	sqvs	sqvs	NOUN
iajs-2833	21	9	of	of	ADP
iajs-2833	21	10	the	the	DET
iajs-2833	21	11	wf	wf	PROPN
iajs-2833	21	12	for	for	ADP
iajs-2833	21	13	the	the	DET
iajs-2833	21	14	qnlhbvp	qnlhbvp	NOUN
iajs-2833	21	15	and	and	CCONJ
iajs-2833	21	16	the	the	DET
iajs-2833	21	17	corresponding	corresponding	ADJ
iajs-2833	21	18	cccqv	cccqv	NOUN
iajs-2833	21	19	is	be	AUX
iajs-2833	21	20	demonstrated	demonstrate	VERB
iajs-2833	21	21	.	.	PUNCT
iajs-2833	22	1	lastly	lastly	ADV
iajs-2833	22	2	,	,	PUNCT
iajs-2833	22	3	the	the	DET
iajs-2833	22	4	eth	eth	NOUN
iajs-2833	22	5	of	of	ADP
iajs-2833	22	6	an	an	DET
iajs-2833	22	7	optimal	optimal	ADJ
iajs-2833	22	8	classical	classical	ADJ
iajs-2833	22	9	continuous	continuous	ADJ
iajs-2833	22	10	control	control	NOUN
iajs-2833	22	11	quaternary	quaternary	ADJ
iajs-2833	22	12	vector	vector	NOUN
iajs-2833	22	13	(	(	PUNCT
iajs-2833	22	14	occcqv	occcqv	NOUN
iajs-2833	22	15	)	)	PUNCT
iajs-2833	22	16	is	be	AUX
iajs-2833	22	17	stated	state	VERB
iajs-2833	22	18	and	and	CCONJ
iajs-2833	22	19	demonstrated	demonstrate	VERB
iajs-2833	22	20	with	with	ADP
iajs-2833	22	21	suitable	suitable	ADJ
iajs-2833	22	22	hypotheses	hypothesis	NOUN
iajs-2833	22	23	.	.	PUNCT
iajs-2833	23	1	2	2	X
iajs-2833	23	2	.	.	X
iajs-2833	23	3	problem	problem	NOUN
iajs-2833	23	4	description	description	NOUN
iajs-2833	23	5	let	let	VERB
iajs-2833	23	6	𝐼	𝐼	PROPN
iajs-2833	23	7	=	=	PUNCT
iajs-2833	24	1	[	[	X
iajs-2833	24	2	0	0	NUM
iajs-2833	24	3	,	,	PUNCT
iajs-2833	24	4	𝑇	𝑇	PROPN
iajs-2833	24	5	]	]	PUNCT
iajs-2833	24	6	,	,	PUNCT
iajs-2833	24	7	t	t	X
iajs-2833	24	8	<	<	X
iajs-2833	24	9	∞	∞	PROPN
iajs-2833	24	10	,	,	PUNCT
iajs-2833	24	11	ω	ω	PROPN
iajs-2833	24	12	⊂	⊂	PROPN
iajs-2833	24	13	ℝ2	ℝ2	PROPN
iajs-2833	24	14	,	,	PUNCT
iajs-2833	24	15	be	be	AUX
iajs-2833	24	16	an	an	DET
iajs-2833	24	17	open	open	ADJ
iajs-2833	24	18	bounded	bounded	ADJ
iajs-2833	24	19	region	region	NOUN
iajs-2833	24	20	with	with	ADP
iajs-2833	24	21	boundary	boundary	ADJ
iajs-2833	24	22	γ	γ	X
iajs-2833	24	23	=	=	SYM
iajs-2833	24	24	𝜕ω	𝜕ω	PROPN
iajs-2833	24	25	,	,	PUNCT
iajs-2833	24	26	𝑄	𝑄	PROPN
iajs-2833	24	27	=	=	SYM
iajs-2833	24	28	ω	ω	NUM
iajs-2833	24	29	×	×	NOUN
iajs-2833	24	30	𝐼	𝐼	PROPN
iajs-2833	24	31	,	,	PUNCT
iajs-2833	24	32	σ	σ	NOUN
iajs-2833	24	33	=	=	PUNCT
iajs-2833	24	34	γ	γ	X
iajs-2833	24	35	×	×	NOUN
iajs-2833	24	36	𝐼.	𝐼.	PROPN
iajs-2833	24	37	the	the	DET
iajs-2833	24	38	occcqv	occcqv	NOUN
iajs-2833	24	39	includes	include	VERB
iajs-2833	24	40	the	the	DET
iajs-2833	24	41	quaternary	quaternary	ADJ
iajs-2833	24	42	state	state	NOUN
iajs-2833	24	43	equations	equation	NOUN
iajs-2833	24	44	(	(	PUNCT
iajs-2833	24	45	qses	qse	NOUN
iajs-2833	24	46	)	)	PUNCT
iajs-2833	24	47	which	which	PRON
iajs-2833	24	48	are	be	AUX
iajs-2833	24	49	considered	consider	VERB
iajs-2833	24	50	by	by	ADP
iajs-2833	24	51	the	the	DET
iajs-2833	24	52	following	follow	VERB
iajs-2833	24	53	qnlhbvp	qnlhbvp	NOUN
iajs-2833	24	54	:	:	PUNCT
iajs-2833	24	55	𝑦1𝑡𝑡	𝑦1𝑡𝑡	PUNCT
iajs-2833	24	56	−	−	PROPN
iajs-2833	25	1	∆𝑦1	∆𝑦1	ADV
iajs-2833	25	2	+	+	CCONJ
iajs-2833	25	3	𝑦1	𝑦1	PROPN
iajs-2833	25	4	−	−	PROPN
iajs-2833	25	5	𝑦2	𝑦2	PROPN
iajs-2833	25	6	+	+	CCONJ
iajs-2833	25	7	𝑦3	𝑦3	PROPN
iajs-2833	25	8	+	+	CCONJ
iajs-2833	25	9	𝑦4	𝑦4	PROPN
iajs-2833	25	10	=	=	SYM
iajs-2833	25	11	𝑓1(𝑥	𝑓1(𝑥	NUM
iajs-2833	25	12	,	,	PUNCT
iajs-2833	25	13	𝑡	𝑡	NOUN
iajs-2833	25	14	,	,	PUNCT
iajs-2833	25	15	𝑦1	𝑦1	NOUN
iajs-2833	25	16	,	,	PUNCT
iajs-2833	25	17	𝑢1	𝑢1	NOUN
iajs-2833	25	18	)	)	PUNCT
iajs-2833	25	19	,	,	PUNCT
iajs-2833	25	20	in	in	ADP
iajs-2833	25	21	𝑄	𝑄	PROPN
iajs-2833	25	22	(	(	PUNCT
iajs-2833	25	23	1	1	NUM
iajs-2833	25	24	)	)	PUNCT
iajs-2833	25	25	𝑦2𝑡𝑡	𝑦2𝑡𝑡	PUNCT
iajs-2833	25	26	−	−	PUNCT
iajs-2833	26	1	∆𝑦2	∆𝑦2	NOUN
iajs-2833	26	2	+	+	CCONJ
iajs-2833	26	3	𝑦1	𝑦1	PROPN
iajs-2833	26	4	+	+	CCONJ
iajs-2833	26	5	𝑦2	𝑦2	PROPN
iajs-2833	26	6	−	−	PROPN
iajs-2833	26	7	𝑦3	𝑦3	PROPN
iajs-2833	26	8	−	−	PROPN
iajs-2833	26	9	𝑦4	𝑦4	PROPN
iajs-2833	26	10	=	=	SYM
iajs-2833	26	11	𝑓2(𝑥	𝑓2(𝑥	PROPN
iajs-2833	26	12	,	,	PUNCT
iajs-2833	26	13	𝑡	𝑡	PROPN
iajs-2833	26	14	,	,	PUNCT
iajs-2833	26	15	𝑦2	𝑦2	NOUN
iajs-2833	26	16	,	,	PUNCT
iajs-2833	26	17	𝑢2	𝑢2	PROPN
iajs-2833	26	18	)	)	PUNCT
iajs-2833	26	19	,	,	PUNCT
iajs-2833	26	20	in	in	ADP
iajs-2833	26	21	𝑄	𝑄	PROPN
iajs-2833	26	22	(	(	PUNCT
iajs-2833	26	23	2	2	NUM
iajs-2833	26	24	)	)	PUNCT
iajs-2833	26	25	𝑦3𝑡𝑡	𝑦3𝑡𝑡	X
iajs-2833	26	26	−	−	DET
iajs-2833	26	27	∆𝑦3	∆𝑦3	NOUN
iajs-2833	26	28	−	−	NOUN
iajs-2833	26	29	𝑦1	𝑦1	PROPN
iajs-2833	26	30	+	+	CCONJ
iajs-2833	26	31	𝑦2	𝑦2	PROPN
iajs-2833	26	32	+	+	CCONJ
iajs-2833	26	33	𝑦3	𝑦3	PROPN
iajs-2833	26	34	+	+	CCONJ
iajs-2833	26	35	𝑦4	𝑦4	PROPN
iajs-2833	26	36	=	=	SYM
iajs-2833	26	37	𝑓3(𝑥	𝑓3(𝑥	PROPN
iajs-2833	26	38	,	,	PUNCT
iajs-2833	26	39	𝑡	𝑡	PROPN
iajs-2833	26	40	,	,	PUNCT
iajs-2833	26	41	𝑦3	𝑦3	PROPN
iajs-2833	26	42	,	,	PUNCT
iajs-2833	26	43	𝑢3	𝑢3	PROPN
iajs-2833	26	44	)	)	PUNCT
iajs-2833	26	45	,	,	PUNCT
iajs-2833	26	46	in	in	ADP
iajs-2833	26	47	𝑄	𝑄	PROPN
iajs-2833	26	48	(	(	PUNCT
iajs-2833	26	49	3	3	NUM
iajs-2833	26	50	)	)	PUNCT
iajs-2833	26	51	𝑦4𝑡𝑡	𝑦4𝑡𝑡	NOUN
iajs-2833	26	52	−	−	PROPN
iajs-2833	26	53	∆𝑦4	∆𝑦4	PROPN
iajs-2833	26	54	−	−	PROPN
iajs-2833	26	55	𝑦1	𝑦1	PROPN
iajs-2833	26	56	+	+	CCONJ
iajs-2833	26	57	𝑦2	𝑦2	PROPN
iajs-2833	26	58	−	−	PROPN
iajs-2833	26	59	𝑦3	𝑦3	PROPN
iajs-2833	26	60	+	+	CCONJ
iajs-2833	26	61	𝑦4	𝑦4	PROPN
iajs-2833	26	62	=	=	SYM
iajs-2833	26	63	𝑓4(𝑥	𝑓4(𝑥	PROPN
iajs-2833	26	64	,	,	PUNCT
iajs-2833	26	65	𝑡	𝑡	PROPN
iajs-2833	26	66	,	,	PUNCT
iajs-2833	26	67	𝑦4	𝑦4	NOUN
iajs-2833	26	68	,	,	PUNCT
iajs-2833	26	69	𝑢4	𝑢4	NOUN
iajs-2833	26	70	)	)	PUNCT
iajs-2833	26	71	,	,	PUNCT
iajs-2833	26	72	in	in	ADP
iajs-2833	26	73	𝑄	𝑄	PROPN
iajs-2833	26	74	(	(	PUNCT
iajs-2833	26	75	4	4	NUM
iajs-2833	26	76	)	)	PUNCT
iajs-2833	26	77	with	with	ADP
iajs-2833	26	78	the	the	DET
iajs-2833	26	79	following	following	ADJ
iajs-2833	26	80	boundary	boundary	ADJ
iajs-2833	26	81	conditions	condition	NOUN
iajs-2833	26	82	(	(	PUNCT
iajs-2833	26	83	bcs	bcs	NOUN
iajs-2833	26	84	)	)	PUNCT
iajs-2833	26	85	and	and	CCONJ
iajs-2833	26	86	the	the	DET
iajs-2833	26	87	initial	initial	ADJ
iajs-2833	26	88	conditions	condition	NOUN
iajs-2833	26	89	(	(	PUNCT
iajs-2833	26	90	ics	ics	NOUN
iajs-2833	26	91	)	)	PUNCT
iajs-2833	26	92	𝑦𝑖(𝑥	𝑦𝑖(𝑥	PROPN
iajs-2833	26	93	,	,	PUNCT
iajs-2833	26	94	𝑡	𝑡	X
iajs-2833	26	95	)	)	PUNCT
iajs-2833	26	96	=	=	SYM
iajs-2833	26	97	0	0	NUM
iajs-2833	26	98	,	,	PUNCT
iajs-2833	26	99	on	on	ADP
iajs-2833	26	100	σ	σ	PROPN
iajs-2833	26	101	,	,	PUNCT
iajs-2833	26	102	for	for	ADP
iajs-2833	26	103	𝑖	𝑖	NOUN
iajs-2833	26	104	=	=	SYM
iajs-2833	26	105	1,2,3,4	1,2,3,4	NUM
iajs-2833	26	106	(	(	PUNCT
iajs-2833	26	107	5	5	NUM
iajs-2833	26	108	)	)	PUNCT
iajs-2833	26	109	𝑦1(𝑥	𝑦1(𝑥	NUM
iajs-2833	26	110	,	,	PUNCT
iajs-2833	26	111	0	0	NUM
iajs-2833	26	112	)	)	PUNCT
iajs-2833	26	113	=	=	SYM
iajs-2833	26	114	𝑦𝑖	𝑦𝑖	NUM
iajs-2833	26	115	0(𝑥),and	0(𝑥),and	NUM
iajs-2833	26	116	𝑦𝑖𝑡(𝑥	𝑦𝑖𝑡(𝑥	PROPN
iajs-2833	26	117	,	,	PUNCT
iajs-2833	26	118	0	0	NUM
iajs-2833	26	119	)	)	PUNCT
iajs-2833	26	120	=	=	SYM
iajs-2833	26	121	𝑦𝑖	𝑦𝑖	ADP
iajs-2833	26	122	1(𝑥	1(𝑥	NUM
iajs-2833	26	123	)	)	PUNCT
iajs-2833	26	124	,	,	PUNCT
iajs-2833	26	125	in	in	ADP
iajs-2833	26	126	ω	ω	NUM
iajs-2833	26	127	for	for	ADP
iajs-2833	26	128	𝑖	𝑖	NOUN
iajs-2833	26	129	=	=	SYM
iajs-2833	26	130	1,2,3,4	1,2,3,4	NUM
iajs-2833	26	131	(	(	PUNCT
iajs-2833	26	132	6	6	NUM
iajs-2833	26	133	)	)	PUNCT
iajs-2833	26	134	where	where	SCONJ
iajs-2833	26	135	�	�	NOUN
iajs-2833	26	136	⃗	⃗	X
iajs-2833	26	137	�	�	NOUN
iajs-2833	26	138	=	=	SYM
iajs-2833	26	139	(	(	PUNCT
iajs-2833	26	140	𝑦1	𝑦1	PROPN
iajs-2833	26	141	,	,	PUNCT
iajs-2833	26	142	𝑦2	𝑦2	PROPN
iajs-2833	26	143	,	,	PUNCT
iajs-2833	26	144	𝑦3	𝑦3	PROPN
iajs-2833	26	145	,	,	PUNCT
iajs-2833	26	146	𝑦4	𝑦4	NOUN
iajs-2833	26	147	)	)	PUNCT
iajs-2833	26	148	belongs	belong	VERB
iajs-2833	26	149	to	to	ADP
iajs-2833	26	150	the	the	DET
iajs-2833	26	151	hilbert	hilbert	NOUN
iajs-2833	26	152	space	space	NOUN
iajs-2833	26	153	(	(	PUNCT
iajs-2833	26	154	𝐻2(ω))4	𝐻2(ω))4	PROPN
iajs-2833	26	155	is	be	AUX
iajs-2833	26	156	the	the	DET
iajs-2833	26	157	sqvs	sqvs	NOUN
iajs-2833	26	158	,	,	PUNCT
iajs-2833	26	159	corresponding	correspond	VERB
iajs-2833	26	160	to	to	ADP
iajs-2833	26	161	the	the	DET
iajs-2833	26	162	cccqv	cccqv	PROPN
iajs-2833	26	163	�	�	PROPN
iajs-2833	26	164	⃗⃗	⃗⃗	PROPN
iajs-2833	26	165	�	�	PROPN
iajs-2833	26	166	=	=	SYM
iajs-2833	26	167	(	(	PUNCT
iajs-2833	26	168	𝑢1	𝑢1	PROPN
iajs-2833	26	169	,	,	PUNCT
iajs-2833	26	170	𝑢2	𝑢2	PROPN
iajs-2833	26	171	,	,	PUNCT
iajs-2833	26	172	𝑢3	𝑢3	PROPN
iajs-2833	26	173	,	,	PUNCT
iajs-2833	26	174	𝑢4	𝑢4	NOUN
iajs-2833	26	175	)	)	PUNCT
iajs-2833	26	176	∈	∈	PROPN
iajs-2833	26	177	(	(	PUNCT
iajs-2833	26	178	𝐿2(q))4	𝐿2(q))4	PROPN
iajs-2833	26	179	and	and	CCONJ
iajs-2833	26	180	(	(	PUNCT
iajs-2833	26	181	𝑓1	𝑓1	ADJ
iajs-2833	26	182	,	,	PUNCT
iajs-2833	26	183	𝑓2	𝑓2	ADJ
iajs-2833	26	184	,	,	PUNCT
iajs-2833	26	185	𝑓3	𝑓3	NOUN
iajs-2833	26	186	,	,	PUNCT
iajs-2833	26	187	𝑓4	𝑓4	PROPN
iajs-2833	26	188	)	)	PUNCT
iajs-2833	26	189	∈	∈	PROPN
iajs-2833	26	190	(	(	PUNCT
iajs-2833	26	191	𝐿2(q))4	𝐿2(q))4	PROPN
iajs-2833	26	192	is	be	AUX
iajs-2833	26	193	a	a	DET
iajs-2833	26	194	vector	vector	NOUN
iajs-2833	26	195	of	of	ADP
iajs-2833	26	196	a	a	DET
iajs-2833	26	197	given	give	VERB
iajs-2833	26	198	function	function	NOUN
iajs-2833	26	199	on	on	ADP
iajs-2833	26	200	(	(	PUNCT
iajs-2833	26	201	𝑄	𝑄	NOUN
iajs-2833	26	202	×	×	NOUN
iajs-2833	26	203	ℝ	ℝ	PROPN
iajs-2833	26	204	×	×	NOUN
iajs-2833	26	205	𝑈1	𝑈1	NOUN
iajs-2833	26	206	)	)	PUNCT
iajs-2833	26	207	×	×	NOUN
iajs-2833	26	208	(	(	PUNCT
iajs-2833	26	209	𝑄	𝑄	PROPN
iajs-2833	26	210	×	×	NOUN
iajs-2833	26	211	ℝ	ℝ	PROPN
iajs-2833	26	212	×	×	NOUN
iajs-2833	26	213	𝑈2	𝑈2	PROPN
iajs-2833	26	214	)	)	PUNCT
iajs-2833	26	215	×	×	NOUN
iajs-2833	26	216	(	(	PUNCT
iajs-2833	26	217	𝑄	𝑄	PROPN
iajs-2833	26	218	×	×	NOUN
iajs-2833	26	219	ℝ	ℝ	PROPN
iajs-2833	26	220	×	×	NOUN
iajs-2833	26	221	𝑈3	𝑈3	NOUN
iajs-2833	26	222	)	)	PUNCT
iajs-2833	26	223	×	×	NOUN
iajs-2833	26	224	(	(	PUNCT
iajs-2833	26	225	𝑄	𝑄	PROPN
iajs-2833	26	226	×	×	NOUN
iajs-2833	26	227	ℝ	ℝ	PROPN
iajs-2833	26	228	×	×	NOUN
iajs-2833	26	229	𝑈4	𝑈4	NOUN
iajs-2833	26	230	)	)	PUNCT
iajs-2833	26	231	,	,	PUNCT
iajs-2833	26	232	with	with	ADP
iajs-2833	26	233	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	26	234	⊂	⊂	PROPN
iajs-2833	26	235	ℝ	ℝ	PROPN
iajs-2833	26	236	,	,	PUNCT
iajs-2833	26	237	∀𝑖	∀𝑖	PROPN
iajs-2833	26	238	=	=	NOUN
iajs-2833	26	239	1,2,3,4	1,2,3,4	NUM
iajs-2833	26	240	.	.	PUNCT
iajs-2833	27	1	the	the	DET
iajs-2833	27	2	quaternary	quaternary	ADJ
iajs-2833	27	3	controls	control	NOUN
iajs-2833	27	4	constraints	constraint	NOUN
iajs-2833	27	5	(	(	PUNCT
iajs-2833	27	6	qccs	qccs	PROPN
iajs-2833	27	7	)	)	PUNCT
iajs-2833	27	8	are	be	AUX
iajs-2833	27	9	�	�	PROPN
iajs-2833	27	10	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	27	11	�	�	PROPN
iajs-2833	28	1	𝐴=	𝐴=	PROPN
iajs-2833	28	2	{	{	PUNCT
iajs-2833	28	3	�	�	PROPN
iajs-2833	28	4	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2833	28	5	�	�	PROPN
iajs-2833	28	6	∈	∈	PROPN
iajs-2833	28	7	𝑊	𝑊	PROPN
iajs-2833	28	8	⃗⃗⃗⃗⃗	⃗⃗⃗⃗⃗	NOUN
iajs-2833	28	9	⊂	⊂	PRON
iajs-2833	28	10	(	(	PUNCT
iajs-2833	28	11	𝐿2(q))4|	𝐿2(q))4|	NOUN
iajs-2833	28	12	�	�	PROPN
iajs-2833	28	13	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	28	14	�	�	PROPN
iajs-2833	28	15	∈	∈	PROPN
iajs-2833	28	16	�	�	PROPN
iajs-2833	28	17	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	28	18	�	�	PROPN
iajs-2833	28	19	⊂	⊂	PROPN
iajs-2833	28	20	ℝ4	ℝ4	PROPN
iajs-2833	28	21	𝑎.	𝑎.	PROPN
iajs-2833	28	22	𝑒.	𝑒.	PROPN
iajs-2833	28	23	𝑖𝑛	𝑖𝑛	PUNCT
iajs-2833	29	1	𝑄},with	𝑄},with	PROPN
iajs-2833	29	2	�	�	PROPN
iajs-2833	29	3	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	29	4	�	�	PROPN
iajs-2833	29	5	⊂	⊂	PROPN
iajs-2833	29	6	ℝ4is	ℝ4is	VERB
iajs-2833	29	7	a	a	DET
iajs-2833	29	8	convex	convex	NOUN
iajs-2833	29	9	.	.	PUNCT
iajs-2833	30	1	the	the	DET
iajs-2833	30	2	cost	cost	NOUN
iajs-2833	30	3	function	function	NOUN
iajs-2833	30	4	will	will	AUX
iajs-2833	30	5	is	be	AUX
iajs-2833	30	6	considered	consider	VERB
iajs-2833	30	7	as	as	ADP
iajs-2833	30	8	𝐺0(	𝐺0(	NOUN
iajs-2833	30	9	�	�	NOUN
iajs-2833	30	10	⃗⃗	⃗⃗	PROPN
iajs-2833	30	11	�	�	PROPN
iajs-2833	30	12	)	)	PUNCT
iajs-2833	31	1	=	=	PUNCT
iajs-2833	31	2	σ	σ	NOUN
iajs-2833	31	3	𝑖=1	𝑖=1	PROPN
iajs-2833	31	4	4	4	NUM
iajs-2833	31	5	∫	∫	NOUN
iajs-2833	31	6	𝑄	𝑄	PROPN
iajs-2833	31	7	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	31	8	(	(	PUNCT
iajs-2833	31	9	𝑥	𝑥	PROPN
iajs-2833	31	10	,	,	PUNCT
iajs-2833	31	11	𝑡	𝑡	PROPN
iajs-2833	31	12	,	,	PUNCT
iajs-2833	31	13	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	31	14	,	,	PUNCT
iajs-2833	31	15	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	X
iajs-2833	31	16	(	(	PUNCT
iajs-2833	31	17	7	7	X
iajs-2833	31	18	)	)	PUNCT
iajs-2833	31	19	the	the	DET
iajs-2833	31	20	occcp	occcp	NOUN
iajs-2833	31	21	is	be	AUX
iajs-2833	31	22	to	to	PART
iajs-2833	31	23	find	find	VERB
iajs-2833	31	24	�	�	PROPN
iajs-2833	31	25	⃗⃗	⃗⃗	PROPN
iajs-2833	31	26	�	�	PROPN
iajs-2833	31	27	∈	∈	PROPN
iajs-2833	31	28	�	�	PROPN
iajs-2833	31	29	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	31	30	�	�	PROPN
iajs-2833	31	31	𝐴	𝐴	PROPN
iajs-2833	31	32	,	,	PUNCT
iajs-2833	31	33	s.t	s.t	PROPN
iajs-2833	31	34	.	.	PROPN
iajs-2833	31	35	𝐺0(	𝐺0(	PROPN
iajs-2833	31	36	�	�	PROPN
iajs-2833	31	37	⃗⃗	⃗⃗	PROPN
iajs-2833	31	38	�	�	PROPN
iajs-2833	31	39	)	)	PUNCT
iajs-2833	31	40	=	=	SYM
iajs-2833	31	41	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
iajs-2833	31	42	�	�	PROPN
iajs-2833	31	43	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	31	44	�	�	PROPN
iajs-2833	31	45	∈	∈	PROPN
iajs-2833	31	46	�	�	PROPN
iajs-2833	31	47	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	31	48	�	�	PROPN
iajs-2833	31	49	𝐴	𝐴	PROPN
iajs-2833	31	50	𝐺0	𝐺0	NOUN
iajs-2833	31	51	(	(	PUNCT
iajs-2833	31	52	�	�	NOUN
iajs-2833	31	53	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	31	54	�	�	NOUN
iajs-2833	31	55	)	)	PUNCT
iajs-2833	31	56	let	let	VERB
iajs-2833	31	57	v⃗⃗⃗	v⃗⃗⃗	PUNCT
iajs-2833	31	58	=	=	PUNCT
iajs-2833	32	1	(	(	PUNCT
iajs-2833	32	2	𝑉)4	𝑉)4	PROPN
iajs-2833	32	3	;	;	PUNCT
iajs-2833	32	4	𝑉	𝑉	PROPN
iajs-2833	32	5	=	=	PROPN
iajs-2833	32	6	𝐻0	𝐻0	PROPN
iajs-2833	32	7	1(ω	1(ω	NUM
iajs-2833	32	8	)	)	PUNCT
iajs-2833	32	9	,	,	PUNCT
iajs-2833	32	10	and	and	CCONJ
iajs-2833	32	11	�	�	PROPN
iajs-2833	32	12	⃗⃗	⃗⃗	PROPN
iajs-2833	32	13	�	�	PROPN
iajs-2833	33	1	=	=	SYM
iajs-2833	33	2	{	{	PUNCT
iajs-2833	33	3	�	�	PROPN
iajs-2833	33	4	⃗	⃗	NOUN
iajs-2833	33	5	�	�	PROPN
iajs-2833	33	6	:	:	PUNCT
iajs-2833	33	7	�	�	PROPN
iajs-2833	33	8	⃗	⃗	NOUN
iajs-2833	33	9	�	�	PROPN
iajs-2833	33	10	∈	∈	PROPN
iajs-2833	33	11	(	(	PUNCT
iajs-2833	33	12	𝐻1(ω))4	𝐻1(ω))4	PROPN
iajs-2833	33	13	,	,	PUNCT
iajs-2833	33	14	𝑣1	𝑣1	NOUN
iajs-2833	33	15	=	=	SYM
iajs-2833	33	16	𝑣2	𝑣2	PROPN
iajs-2833	33	17	=	=	SYM
iajs-2833	33	18	𝑣3	𝑣3	PROPN
iajs-2833	33	19	=	=	SYM
iajs-2833	33	20	𝑣4	𝑣4	NOUN
iajs-2833	33	21	=	=	SYM
iajs-2833	33	22	0	0	NUM
iajs-2833	33	23	𝑜𝑛	𝑜𝑛	PROPN
iajs-2833	33	24	𝜕ω	𝜕ω	PROPN
iajs-2833	33	25	}	}	PUNCT
iajs-2833	33	26	.	.	PUNCT
iajs-2833	34	1	�	�	PROPN
iajs-2833	34	2	⃗	⃗	PROPN
iajs-2833	34	3	�	�	PROPN
iajs-2833	34	4	=	=	SYM
iajs-2833	34	5	(	(	PUNCT
iajs-2833	34	6	𝑣1	𝑣1	PROPN
iajs-2833	34	7	,	,	PUNCT
iajs-2833	34	8	𝑣2	𝑣2	PROPN
iajs-2833	34	9	,	,	PUNCT
iajs-2833	34	10	𝑣3	𝑣3	ADJ
iajs-2833	34	11	,	,	PUNCT
iajs-2833	34	12	𝑣4	𝑣4	NOUN
iajs-2833	34	13	)	)	PUNCT
iajs-2833	34	14	,	,	PUNCT
iajs-2833	34	15	we	we	PRON
iajs-2833	34	16	denote	denote	VERB
iajs-2833	34	17	by	by	ADP
iajs-2833	34	18	(	(	PUNCT
iajs-2833	34	19	𝑣	𝑣	NOUN
iajs-2833	34	20	,	,	PUNCT
iajs-2833	34	21	𝑣	𝑣	NOUN
iajs-2833	34	22	)	)	PUNCT
iajs-2833	34	23	and	and	CCONJ
iajs-2833	34	24	∥	∥	NUM
iajs-2833	34	25	𝑣	𝑣	PART
iajs-2833	34	26	∥0	∥0	VERB
iajs-2833	34	27	the	the	DET
iajs-2833	34	28	inner	inner	ADJ
iajs-2833	34	29	product	product	NOUN
iajs-2833	34	30	(	(	PUNCT
iajs-2833	34	31	ip	ip	NOUN
iajs-2833	34	32	)	)	PUNCT
iajs-2833	34	33	and	and	CCONJ
iajs-2833	34	34	the	the	DET
iajs-2833	34	35	norm	norm	NOUN
iajs-2833	34	36	in	in	ADP
iajs-2833	34	37	(	(	PUNCT
iajs-2833	34	38	𝐿2(ω))4	𝐿2(ω))4	INTJ
iajs-2833	34	39	,	,	PUNCT
iajs-2833	34	40	by	by	ADP
iajs-2833	34	41	(	(	PUNCT
iajs-2833	34	42	�	�	PROPN
iajs-2833	34	43	⃗	⃗	NOUN
iajs-2833	34	44	�	�	PROPN
iajs-2833	34	45	,	,	PUNCT
iajs-2833	34	46	�	�	PROPN
iajs-2833	34	47	⃗	⃗	NOUN
iajs-2833	34	48	�	�	PROPN
iajs-2833	34	49	)1	)1	PUNCT
iajs-2833	34	50	=	=	PROPN
iajs-2833	34	51	σ	σ	SYM
iajs-2833	34	52	𝑖=1	𝑖=1	PROPN
iajs-2833	34	53	4	4	NUM
iajs-2833	34	54	∥	∥	NOUN
iajs-2833	34	55	𝑣1	𝑣1	NOUN
iajs-2833	34	56	∥1	∥1	NOUN
iajs-2833	34	57	2	2	NUM
iajs-2833	34	58	the	the	DET
iajs-2833	34	59	ip	ip	NOUN
iajs-2833	34	60	and	and	CCONJ
iajs-2833	34	61	the	the	DET
iajs-2833	34	62	norm	norm	NOUN
iajs-2833	34	63	in	in	ADP
iajs-2833	34	64	v⃗⃗⃗	v⃗⃗⃗	PROPN
iajs-2833	34	65	,	,	PUNCT
iajs-2833	34	66	and	and	CCONJ
iajs-2833	34	67	v⃗⃗⃗∗	v⃗⃗⃗∗	ADV
iajs-2833	34	68	is	be	AUX
iajs-2833	34	69	the	the	DET
iajs-2833	34	70	dual	dual	ADJ
iajs-2833	34	71	of	of	ADP
iajs-2833	34	72	v⃗⃗⃗.	v⃗⃗⃗.	PROPN
iajs-2833	34	73	the	the	DET
iajs-2833	34	74	wf	wf	PROPN
iajs-2833	34	75	of	of	ADP
iajs-2833	34	76	(	(	PUNCT
iajs-2833	34	77	(	(	PUNCT
iajs-2833	34	78	1)-(6	1)-(6	NUM
iajs-2833	34	79	)	)	PUNCT
iajs-2833	34	80	)	)	PUNCT
iajs-2833	34	81	when	when	SCONJ
iajs-2833	34	82	𝑦⃗⃗⃗	𝑦⃗⃗⃗	X
iajs-2833	34	83	⃗	⃗	PROPN
iajs-2833	34	84	∈	∈	PROPN
iajs-2833	34	85	(	(	PUNCT
iajs-2833	34	86	𝐻0	𝐻0	PROPN
iajs-2833	34	87	1(ω))4	1(ω))4	PROPN
iajs-2833	34	88	is	be	AUX
iajs-2833	34	89	given	give	VERB
iajs-2833	34	90	a.e	a.e	PROPN
iajs-2833	34	91	.	.	PROPN
iajs-2833	35	1	on	on	ADP
iajs-2833	35	2	i	i	PRON
iajs-2833	35	3	and	and	CCONJ
iajs-2833	35	4	∀𝑣𝑖	∀𝑣𝑖	VERB
iajs-2833	35	5	∈	∈	PROPN
iajs-2833	35	6	𝑉𝑖	𝑉𝑖	PROPN
iajs-2833	35	7	(	(	PUNCT
iajs-2833	35	8	∀𝑖	∀𝑖	PROPN
iajs-2833	35	9	=	=	SYM
iajs-2833	35	10	1,2,3,4	1,2,3,4	NUM
iajs-2833	35	11	)	)	PUNCT
iajs-2833	35	12	by	by	ADP
iajs-2833	35	13	:	:	PUNCT
iajs-2833	35	14	(	(	PUNCT
iajs-2833	35	15	𝑦1𝑡𝑡	𝑦1𝑡𝑡	X
iajs-2833	35	16	,	,	PUNCT
iajs-2833	35	17	𝑣1	𝑣1	NOUN
iajs-2833	35	18	)	)	PUNCT
iajs-2833	35	19	+	+	CCONJ
iajs-2833	35	20	(	(	PUNCT
iajs-2833	35	21	∇𝑦1	∇𝑦1	NOUN
iajs-2833	35	22	,	,	PUNCT
iajs-2833	35	23	∇𝑣1	∇𝑣1	NOUN
iajs-2833	35	24	)	)	PUNCT
iajs-2833	35	25	+	+	CCONJ
iajs-2833	35	26	(	(	PUNCT
iajs-2833	35	27	𝑦1	𝑦1	PROPN
iajs-2833	35	28	,	,	PUNCT
iajs-2833	35	29	𝑣1	𝑣1	NOUN
iajs-2833	35	30	)	)	PUNCT
iajs-2833	35	31	−	−	PROPN
iajs-2833	35	32	(	(	PUNCT
iajs-2833	35	33	𝑦2	𝑦2	PROPN
iajs-2833	35	34	,	,	PUNCT
iajs-2833	35	35	𝑣1	𝑣1	PROPN
iajs-2833	35	36	)	)	PUNCT
iajs-2833	35	37	+	+	CCONJ
iajs-2833	35	38	(	(	PUNCT
iajs-2833	35	39	𝑦3	𝑦3	PROPN
iajs-2833	35	40	,	,	PUNCT
iajs-2833	35	41	𝑣1	𝑣1	PROPN
iajs-2833	35	42	)	)	PUNCT
iajs-2833	35	43	+	+	CCONJ
iajs-2833	35	44	(	(	PUNCT
iajs-2833	35	45	𝑦4	𝑦4	NOUN
iajs-2833	35	46	,	,	PUNCT
iajs-2833	35	47	𝑣1	𝑣1	NOUN
iajs-2833	35	48	)	)	PUNCT
iajs-2833	35	49	=	=	PUNCT
iajs-2833	35	50	(	(	PUNCT
iajs-2833	35	51	𝑓1	𝑓1	PROPN
iajs-2833	35	52	,	,	PUNCT
iajs-2833	35	53	𝑣1	𝑣1	PROPN
iajs-2833	35	54	)	)	PUNCT
iajs-2833	35	55	(	(	PUNCT
iajs-2833	35	56	8)	8)	NUM
iajs-2833	35	57	(	(	PUNCT
iajs-2833	35	58	𝑦1	𝑦1	PROPN
iajs-2833	35	59	0	0	NUM
iajs-2833	35	60	,	,	PUNCT
iajs-2833	35	61	𝑣1	𝑣1	NOUN
iajs-2833	35	62	)	)	PUNCT
iajs-2833	35	63	=	=	PUNCT
iajs-2833	35	64	(	(	PUNCT
iajs-2833	35	65	𝑦1(0	𝑦1(0	PROPN
iajs-2833	35	66	)	)	PUNCT
iajs-2833	35	67	,	,	PUNCT
iajs-2833	35	68	𝑣1	𝑣1	NOUN
iajs-2833	35	69	)	)	PUNCT
iajs-2833	35	70	,	,	PUNCT
iajs-2833	35	71	and	and	CCONJ
iajs-2833	35	72	(	(	PUNCT
iajs-2833	35	73	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2833	35	74	1	1	NUM
iajs-2833	35	75	,	,	PUNCT
iajs-2833	35	76	𝑣1	𝑣1	NOUN
iajs-2833	35	77	)	)	PUNCT
iajs-2833	35	78	=	=	PUNCT
iajs-2833	35	79	(	(	PUNCT
iajs-2833	35	80	𝑦1𝑡(0	𝑦1𝑡(0	PROPN
iajs-2833	35	81	)	)	PUNCT
iajs-2833	35	82	,	,	PUNCT
iajs-2833	35	83	𝑣1	𝑣1	PROPN
iajs-2833	35	84	)	)	PUNCT
iajs-2833	35	85	(	(	PUNCT
iajs-2833	35	86	9	9	X
iajs-2833	35	87	)	)	PUNCT
iajs-2833	35	88	ihjpas	ihjpa	NOUN
iajs-2833	35	89	.	.	PUNCT
iajs-2833	36	1	53	53	NUM
iajs-2833	36	2	(	(	PUNCT
iajs-2833	36	3	3)2022	3)2022	NOUN
iajs-2833	36	4	163	163	NUM
iajs-2833	36	5	(	(	PUNCT
iajs-2833	36	6	𝑦2𝑡𝑡	𝑦2𝑡𝑡	X
iajs-2833	36	7	,	,	PUNCT
iajs-2833	36	8	𝑣2	𝑣2	PROPN
iajs-2833	36	9	)	)	PUNCT
iajs-2833	36	10	+	+	CCONJ
iajs-2833	36	11	(	(	PUNCT
iajs-2833	36	12	∆𝑦2	∆𝑦2	PROPN
iajs-2833	36	13	,	,	PUNCT
iajs-2833	36	14	∇𝑣2	∇𝑣2	PROPN
iajs-2833	36	15	)	)	PUNCT
iajs-2833	37	1	+	+	CCONJ
iajs-2833	37	2	(	(	PUNCT
iajs-2833	37	3	𝑦1	𝑦1	PROPN
iajs-2833	37	4	,	,	PUNCT
iajs-2833	37	5	𝑣2	𝑣2	PROPN
iajs-2833	37	6	)	)	PUNCT
iajs-2833	37	7	+	+	CCONJ
iajs-2833	37	8	(	(	PUNCT
iajs-2833	37	9	𝑦2	𝑦2	PROPN
iajs-2833	37	10	,	,	PUNCT
iajs-2833	37	11	𝑣2	𝑣2	PROPN
iajs-2833	37	12	)	)	PUNCT
iajs-2833	37	13	−	−	PROPN
iajs-2833	37	14	(	(	PUNCT
iajs-2833	37	15	𝑦3	𝑦3	PROPN
iajs-2833	37	16	,	,	PUNCT
iajs-2833	37	17	𝑣2	𝑣2	PROPN
iajs-2833	37	18	)	)	PUNCT
iajs-2833	37	19	−	−	PROPN
iajs-2833	37	20	(	(	PUNCT
iajs-2833	37	21	𝑦4	𝑦4	PROPN
iajs-2833	37	22	,	,	PUNCT
iajs-2833	37	23	𝑣2	𝑣2	NOUN
iajs-2833	37	24	)	)	PUNCT
iajs-2833	37	25	=	=	SYM
iajs-2833	37	26	(	(	PUNCT
iajs-2833	37	27	𝑓2	𝑓2	PROPN
iajs-2833	37	28	,	,	PUNCT
iajs-2833	37	29	𝑣2	𝑣2	NUM
iajs-2833	37	30	)	)	PUNCT
iajs-2833	37	31	(	(	PUNCT
iajs-2833	37	32	10	10	NUM
iajs-2833	37	33	)	)	PUNCT
iajs-2833	37	34	(	(	PUNCT
iajs-2833	37	35	𝑦2	𝑦2	PROPN
iajs-2833	37	36	0	0	NUM
iajs-2833	37	37	,	,	PUNCT
iajs-2833	37	38	𝑣2	𝑣2	NUM
iajs-2833	37	39	)	)	PUNCT
iajs-2833	37	40	=	=	PUNCT
iajs-2833	37	41	(	(	PUNCT
iajs-2833	37	42	𝑦2(0	𝑦2(0	PROPN
iajs-2833	37	43	)	)	PUNCT
iajs-2833	37	44	,	,	PUNCT
iajs-2833	37	45	𝑣2	𝑣2	PROPN
iajs-2833	37	46	)	)	PUNCT
iajs-2833	37	47	,	,	PUNCT
iajs-2833	37	48	and	and	CCONJ
iajs-2833	37	49	(	(	PUNCT
iajs-2833	37	50	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	37	51	1	1	NUM
iajs-2833	37	52	,	,	PUNCT
iajs-2833	37	53	𝑣2	𝑣2	PROPN
iajs-2833	37	54	)	)	PUNCT
iajs-2833	37	55	=	=	PUNCT
iajs-2833	37	56	(	(	PUNCT
iajs-2833	37	57	𝑦2𝑡(0	𝑦2𝑡(0	PROPN
iajs-2833	37	58	)	)	PUNCT
iajs-2833	37	59	,	,	PUNCT
iajs-2833	37	60	𝑣2	𝑣2	PROPN
iajs-2833	37	61	)	)	PUNCT
iajs-2833	37	62	(	(	PUNCT
iajs-2833	37	63	11	11	NUM
iajs-2833	37	64	)	)	PUNCT
iajs-2833	37	65	(	(	PUNCT
iajs-2833	37	66	𝑦3𝑡𝑡	𝑦3𝑡𝑡	PROPN
iajs-2833	37	67	,	,	PUNCT
iajs-2833	37	68	𝑣3	𝑣3	ADJ
iajs-2833	37	69	)	)	PUNCT
iajs-2833	37	70	+	+	CCONJ
iajs-2833	37	71	(	(	PUNCT
iajs-2833	37	72	∇𝑦3	∇𝑦3	PROPN
iajs-2833	37	73	,	,	PUNCT
iajs-2833	37	74	∇𝑣3	∇𝑣3	NOUN
iajs-2833	37	75	)	)	PUNCT
iajs-2833	37	76	−	−	PROPN
iajs-2833	37	77	(	(	PUNCT
iajs-2833	37	78	𝑦1	𝑦1	NOUN
iajs-2833	37	79	,	,	PUNCT
iajs-2833	37	80	𝑣3	𝑣3	ADJ
iajs-2833	37	81	)	)	PUNCT
iajs-2833	37	82	+	+	CCONJ
iajs-2833	37	83	(	(	PUNCT
iajs-2833	37	84	𝑦2	𝑦2	NOUN
iajs-2833	37	85	,	,	PUNCT
iajs-2833	37	86	𝑣3	𝑣3	ADJ
iajs-2833	37	87	)	)	PUNCT
iajs-2833	37	88	+	+	CCONJ
iajs-2833	37	89	(	(	PUNCT
iajs-2833	37	90	𝑦3	𝑦3	PROPN
iajs-2833	37	91	,	,	PUNCT
iajs-2833	37	92	𝑣3	𝑣3	ADJ
iajs-2833	37	93	)	)	PUNCT
iajs-2833	37	94	+	+	CCONJ
iajs-2833	37	95	(	(	PUNCT
iajs-2833	37	96	𝑦4	𝑦4	NOUN
iajs-2833	37	97	,	,	PUNCT
iajs-2833	37	98	𝑣3	𝑣3	ADJ
iajs-2833	37	99	)	)	PUNCT
iajs-2833	37	100	=	=	SYM
iajs-2833	37	101	(	(	PUNCT
iajs-2833	37	102	𝑓3	𝑓3	NOUN
iajs-2833	37	103	,	,	PUNCT
iajs-2833	37	104	𝑣3	𝑣3	ADJ
iajs-2833	37	105	)	)	PUNCT
iajs-2833	37	106	(	(	PUNCT
iajs-2833	37	107	12	12	NUM
iajs-2833	37	108	)	)	PUNCT
iajs-2833	37	109	(	(	PUNCT
iajs-2833	37	110	𝑦3	𝑦3	PROPN
iajs-2833	37	111	0	0	NUM
iajs-2833	37	112	,	,	PUNCT
iajs-2833	37	113	𝑣3	𝑣3	ADJ
iajs-2833	37	114	)	)	PUNCT
iajs-2833	37	115	=	=	SYM
iajs-2833	37	116	(	(	PUNCT
iajs-2833	37	117	𝑦3(0	𝑦3(0	PROPN
iajs-2833	37	118	)	)	PUNCT
iajs-2833	37	119	,	,	PUNCT
iajs-2833	37	120	𝑣3	𝑣3	ADJ
iajs-2833	37	121	)	)	PUNCT
iajs-2833	37	122	,	,	PUNCT
iajs-2833	37	123	and	and	CCONJ
iajs-2833	37	124	(	(	PUNCT
iajs-2833	37	125	𝑦3𝑡	𝑦3𝑡	PROPN
iajs-2833	37	126	1	1	NUM
iajs-2833	37	127	,	,	PUNCT
iajs-2833	37	128	𝑣3	𝑣3	ADJ
iajs-2833	37	129	)	)	PUNCT
iajs-2833	37	130	=	=	SYM
iajs-2833	37	131	(	(	PUNCT
iajs-2833	37	132	𝑦3𝑡(0	𝑦3𝑡(0	PROPN
iajs-2833	37	133	)	)	PUNCT
iajs-2833	37	134	,	,	PUNCT
iajs-2833	37	135	𝑣3	𝑣3	ADJ
iajs-2833	37	136	)	)	PUNCT
iajs-2833	37	137	(	(	PUNCT
iajs-2833	37	138	13	13	NUM
iajs-2833	37	139	)	)	PUNCT
iajs-2833	37	140	(	(	PUNCT
iajs-2833	37	141	𝑦4𝑡𝑡	𝑦4𝑡𝑡	NOUN
iajs-2833	37	142	,	,	PUNCT
iajs-2833	37	143	𝑣4	𝑣4	NOUN
iajs-2833	37	144	)	)	PUNCT
iajs-2833	37	145	+	+	CCONJ
iajs-2833	37	146	(	(	PUNCT
iajs-2833	37	147	∇𝑦4	∇𝑦4	ADJ
iajs-2833	37	148	,	,	PUNCT
iajs-2833	37	149	∇𝑣4	∇𝑣4	NUM
iajs-2833	37	150	)	)	PUNCT
iajs-2833	37	151	−	−	PROPN
iajs-2833	37	152	(	(	PUNCT
iajs-2833	37	153	𝑦1	𝑦1	NOUN
iajs-2833	37	154	,	,	PUNCT
iajs-2833	37	155	𝑣4	𝑣4	NOUN
iajs-2833	37	156	)	)	PUNCT
iajs-2833	37	157	+	+	CCONJ
iajs-2833	37	158	(	(	PUNCT
iajs-2833	37	159	𝑦2	𝑦2	NOUN
iajs-2833	37	160	,	,	PUNCT
iajs-2833	37	161	𝑣4	𝑣4	NOUN
iajs-2833	37	162	)	)	PUNCT
iajs-2833	37	163	−	−	PROPN
iajs-2833	37	164	(	(	PUNCT
iajs-2833	37	165	𝑦3	𝑦3	PROPN
iajs-2833	37	166	,	,	PUNCT
iajs-2833	37	167	𝑣4	𝑣4	NOUN
iajs-2833	37	168	)	)	PUNCT
iajs-2833	37	169	+	+	CCONJ
iajs-2833	37	170	(	(	PUNCT
iajs-2833	37	171	𝑦4	𝑦4	NOUN
iajs-2833	37	172	,	,	PUNCT
iajs-2833	37	173	𝑣4	𝑣4	NOUN
iajs-2833	37	174	)	)	PUNCT
iajs-2833	37	175	=	=	PUNCT
iajs-2833	37	176	(	(	PUNCT
iajs-2833	37	177	𝑓4	𝑓4	PROPN
iajs-2833	37	178	,	,	PUNCT
iajs-2833	37	179	𝑣4	𝑣4	NOUN
iajs-2833	37	180	)	)	PUNCT
iajs-2833	37	181	(	(	PUNCT
iajs-2833	37	182	14	14	NUM
iajs-2833	37	183	)	)	PUNCT
iajs-2833	37	184	(	(	PUNCT
iajs-2833	37	185	𝑦4	𝑦4	PROPN
iajs-2833	37	186	0	0	NUM
iajs-2833	37	187	,	,	PUNCT
iajs-2833	37	188	𝑣2	𝑣2	NUM
iajs-2833	37	189	)	)	PUNCT
iajs-2833	37	190	=	=	PUNCT
iajs-2833	37	191	(	(	PUNCT
iajs-2833	37	192	𝑦4(0	𝑦4(0	NOUN
iajs-2833	37	193	)	)	PUNCT
iajs-2833	37	194	,	,	PUNCT
iajs-2833	37	195	𝑣4	𝑣4	NOUN
iajs-2833	37	196	)	)	PUNCT
iajs-2833	37	197	,	,	PUNCT
iajs-2833	37	198	and	and	CCONJ
iajs-2833	37	199	(	(	PUNCT
iajs-2833	37	200	𝑦4𝑡	𝑦4𝑡	NOUN
iajs-2833	37	201	1	1	NUM
iajs-2833	37	202	,	,	PUNCT
iajs-2833	37	203	𝑣4	𝑣4	NOUN
iajs-2833	37	204	)	)	PUNCT
iajs-2833	37	205	=	=	SYM
iajs-2833	37	206	(	(	PUNCT
iajs-2833	37	207	𝑦4𝑡(0	𝑦4𝑡(0	PROPN
iajs-2833	37	208	)	)	PUNCT
iajs-2833	37	209	,	,	PUNCT
iajs-2833	37	210	𝑣4	𝑣4	PROPN
iajs-2833	37	211	)	)	PUNCT
iajs-2833	37	212	(	(	PUNCT
iajs-2833	37	213	15	15	NUM
iajs-2833	37	214	)	)	PUNCT
iajs-2833	37	215	2.1	2.1	NUM
iajs-2833	37	216	.	.	PUNCT
iajs-2833	38	1	assumptions	assumption	NOUN
iajs-2833	38	2	(	(	PUNCT
iajs-2833	38	3	a	a	X
iajs-2833	38	4	):	):	PUNCT
iajs-2833	38	5	suppose	suppose	VERB
iajs-2833	38	6	that	that	SCONJ
iajs-2833	38	7	𝑓𝑖	𝑓𝑖	PROPN
iajs-2833	38	8	is	be	AUX
iajs-2833	38	9	of	of	ADP
iajs-2833	38	10	the	the	DET
iajs-2833	38	11	carathéodory	carathéodory	ADJ
iajs-2833	38	12	type	type	NOUN
iajs-2833	38	13	on	on	ADP
iajs-2833	38	14	𝑄	𝑄	PROPN
iajs-2833	38	15	×	×	NOUN
iajs-2833	38	16	(	(	PUNCT
iajs-2833	38	17	ℝ	ℝ	PROPN
iajs-2833	38	18	×	×	NOUN
iajs-2833	38	19	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	38	20	)	)	PUNCT
iajs-2833	38	21	and	and	CCONJ
iajs-2833	38	22	satisfies	satisfie	NOUN
iajs-2833	38	23	(	(	PUNCT
iajs-2833	38	24	for	for	ADP
iajs-2833	38	25	𝑖	𝑖	PRON
iajs-2833	38	26	=	=	NOUN
iajs-2833	38	27	1,2,3,4	1,2,3,4	NUM
iajs-2833	38	28	):	):	PUNCT
iajs-2833	38	29	(	(	PUNCT
iajs-2833	38	30	i)|𝑓𝑖(𝑥	i)|𝑓𝑖(𝑥	PROPN
iajs-2833	38	31	,	,	PUNCT
iajs-2833	38	32	𝑡	𝑡	PROPN
iajs-2833	38	33	,	,	PUNCT
iajs-2833	38	34	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	38	35	,	,	PUNCT
iajs-2833	38	36	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2833	38	37	≤	≤	ADJ
iajs-2833	38	38	𝐹𝑖(𝑥	𝐹𝑖(𝑥	NOUN
iajs-2833	38	39	,	,	PUNCT
iajs-2833	38	40	𝑡	𝑡	NOUN
iajs-2833	38	41	)	)	PUNCT
iajs-2833	39	1	+	+	CCONJ
iajs-2833	40	1	𝛾𝑖	𝛾𝑖	NUM
iajs-2833	40	2	∣	∣	ADJ
iajs-2833	40	3	𝑢𝑖|	𝑢𝑖|	PROPN
iajs-2833	40	4	+	+	CCONJ
iajs-2833	40	5	𝛽𝑖|𝑦𝑖|	𝛽𝑖|𝑦𝑖|	NOUN
iajs-2833	40	6	,	,	PUNCT
iajs-2833	40	7	where	where	SCONJ
iajs-2833	40	8	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	40	9	,	,	PUNCT
iajs-2833	40	10	𝑢𝑖	𝑢𝑖	PRON
iajs-2833	40	11	∈	∈	PROPN
iajs-2833	40	12	ℝ	ℝ	PROPN
iajs-2833	40	13	,	,	PUNCT
iajs-2833	40	14	𝛽𝑖	𝛽𝑖	ADJ
iajs-2833	40	15	,	,	PUNCT
iajs-2833	40	16	𝛾𝑖	𝛾𝑖	ADV
iajs-2833	40	17	∣	∣	NOUN
iajs-2833	40	18	>	>	X
iajs-2833	40	19	0	0	PUNCT
iajs-2833	41	1	and	and	CCONJ
iajs-2833	41	2	𝐹𝑖	𝐹𝑖	PROPN
iajs-2833	41	3	∈	∈	PROPN
iajs-2833	41	4	𝐿2(q	𝐿2(q	NUM
iajs-2833	41	5	)	)	PUNCT
iajs-2833	41	6	.	.	PUNCT
iajs-2833	42	1	(	(	PUNCT
iajs-2833	42	2	ii	ii	NOUN
iajs-2833	42	3	)	)	PUNCT
iajs-2833	42	4	𝑓𝑖	𝑓𝑖	PROPN
iajs-2833	42	5	is	be	AUX
iajs-2833	42	6	satisfied	satisfied	ADJ
iajs-2833	42	7	lipschitz	lipschitz	NOUN
iajs-2833	42	8	condition	condition	NOUN
iajs-2833	42	9	(	(	PUNCT
iajs-2833	42	10	lipc	lipc	PROPN
iajs-2833	42	11	)	)	PUNCT
iajs-2833	42	12	w.r.t	w.r.t	NOUN
iajs-2833	42	13	.	.	PUNCT
iajs-2833	43	1	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	43	2	,	,	PUNCT
iajs-2833	43	3	i.e.	i.e.	X
iajs-2833	43	4	|𝑓𝑖(𝑥	|𝑓𝑖(𝑥	X
iajs-2833	43	5	,	,	PUNCT
iajs-2833	43	6	𝑡	𝑡	PROPN
iajs-2833	43	7	,	,	PUNCT
iajs-2833	43	8	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	43	9	,	,	PUNCT
iajs-2833	43	10	𝑢𝑖	𝑢𝑖	PROPN
iajs-2833	43	11	)	)	PUNCT
iajs-2833	43	12	−	−	PROPN
iajs-2833	43	13	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2833	43	14	,	,	PUNCT
iajs-2833	43	15	𝑡	𝑡	PROPN
iajs-2833	43	16	,	,	PUNCT
iajs-2833	43	17	�	�	NOUN
iajs-2833	43	18	̅	̅	NOUN
iajs-2833	43	19	�	�	NOUN
iajs-2833	43	20	𝑖	𝑖	NUM
iajs-2833	43	21	,	,	PUNCT
iajs-2833	43	22	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2833	43	23	≤	≤	NUM
iajs-2833	43	24	𝐿𝑖|𝑦𝑖	𝐿𝑖|𝑦𝑖	VERB
iajs-2833	43	25	−	−	PROPN
iajs-2833	43	26	�	�	PROPN
iajs-2833	43	27	̅	̅	NOUN
iajs-2833	43	28	�	�	NOUN
iajs-2833	43	29	𝑖|	𝑖|	PROPN
iajs-2833	43	30	,	,	PUNCT
iajs-2833	43	31	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	43	32	,	,	PUNCT
iajs-2833	43	33	�	�	NOUN
iajs-2833	43	34	̅	̅	NOUN
iajs-2833	43	35	�	�	NOUN
iajs-2833	43	36	𝑖	𝑖	NOUN
iajs-2833	43	37	,	,	PUNCT
iajs-2833	43	38	𝑢𝑖	𝑢𝑖	DET
iajs-2833	43	39	∈	∈	PROPN
iajs-2833	43	40	ℝ	ℝ	PROPN
iajs-2833	43	41	,	,	PUNCT
iajs-2833	43	42	𝐿𝑖	𝐿𝑖	PROPN
iajs-2833	43	43	>	>	X
iajs-2833	43	44	0	0	NUM
iajs-2833	43	45	,	,	PUNCT
iajs-2833	43	46	for	for	ADP
iajs-2833	43	47	(	(	PUNCT
iajs-2833	43	48	𝑥	𝑥	PROPN
iajs-2833	43	49	,	,	PUNCT
iajs-2833	43	50	𝑡	𝑡	NOUN
iajs-2833	43	51	)	)	PUNCT
iajs-2833	43	52	∈	∈	PROPN
iajs-2833	43	53	𝑄.	𝑄.	PROPN
iajs-2833	43	54	2.2	2.2	NUM
iajs-2833	43	55	lemma1	lemma1	NOUN
iajs-2833	43	56	:	:	PUNCT
iajs-2833	43	57	(	(	PUNCT
iajs-2833	43	58	gronwall	gronwall	ADJ
iajs-2833	43	59	inequality	inequality	NOUN
iajs-2833	43	60	):	):	PUNCT
iajs-2833	43	61	let	let	VERB
iajs-2833	43	62	𝐾	𝐾	PRON
iajs-2833	43	63	be	be	AUX
iajs-2833	43	64	a	a	DET
iajs-2833	43	65	nonnegative	nonnegative	ADJ
iajs-2833	43	66	constant	constant	ADJ
iajs-2833	43	67	and	and	CCONJ
iajs-2833	43	68	let	let	VERB
iajs-2833	43	69	𝑓	𝑓	PRON
iajs-2833	43	70	and	and	CCONJ
iajs-2833	43	71	𝑔	𝑔	AUX
iajs-2833	43	72	be	be	AUX
iajs-2833	43	73	continuous	continuous	ADJ
iajs-2833	43	74	nonnegative	nonnegative	ADJ
iajs-2833	43	75	functions	function	NOUN
iajs-2833	43	76	on	on	ADP
iajs-2833	43	77	[	[	X
iajs-2833	43	78	𝛼	𝛼	X
iajs-2833	43	79	,	,	PUNCT
iajs-2833	43	80	𝛽	𝛽	NOUN
iajs-2833	43	81	]	]	PUNCT
iajs-2833	43	82	,	,	PUNCT
iajs-2833	43	83	satisfies	satisfie	NOUN
iajs-2833	43	84	:	:	PUNCT
iajs-2833	43	85	𝑓(𝑡	𝑓(𝑡	PROPN
iajs-2833	43	86	)	)	PUNCT
iajs-2833	43	87	≤	≤	NOUN
iajs-2833	43	88	𝐾	𝐾	PROPN
iajs-2833	43	89	+	+	CCONJ
iajs-2833	43	90	∫	∫	PROPN
iajs-2833	43	91	𝑓(𝑠)𝑔(𝑠)𝑑𝑠	𝑓(𝑠)𝑔(𝑠)𝑑𝑠	PROPN
iajs-2833	43	92	𝑡	𝑡	X
iajs-2833	43	93	𝛼	𝛼	PROPN
iajs-2833	43	94	.	.	PUNCT
iajs-2833	44	1	then	then	ADV
iajs-2833	44	2	,	,	PUNCT
iajs-2833	44	3	𝑓(𝑡	𝑓(𝑡	PROPN
iajs-2833	44	4	)	)	PUNCT
iajs-2833	44	5	≤	≤	NOUN
iajs-2833	44	6	𝐾𝑒∫	𝐾𝑒∫	NUM
iajs-2833	44	7	𝑔(𝑠)𝑑𝑠	𝑔(𝑠)𝑑𝑠	PROPN
iajs-2833	44	8	𝑡	𝑡	X
iajs-2833	44	9	𝛼	𝛼	NOUN
iajs-2833	44	10	,	,	PUNCT
iajs-2833	44	11	for	for	ADP
iajs-2833	44	12	𝛼	𝛼	PRON
iajs-2833	44	13	≤	≤	NUM
iajs-2833	44	14	𝑡	𝑡	PROPN
iajs-2833	44	15	≤	≤	PROPN
iajs-2833	44	16	𝛽.	𝛽.	NOUN
iajs-2833	44	17	3	3	NUM
iajs-2833	44	18	.	.	PUNCT
iajs-2833	45	1	the	the	DET
iajs-2833	45	2	solution	solution	NOUN
iajs-2833	45	3	for	for	ADP
iajs-2833	45	4	the	the	DET
iajs-2833	45	5	qses	qse	NOUN
iajs-2833	45	6	:	:	PUNCT
iajs-2833	45	7	3.1	3.1	NUM
iajs-2833	45	8	proposition	proposition	NOUN
iajs-2833	45	9	[	[	X
iajs-2833	45	10	14	14	NUM
iajs-2833	45	11	]	]	X
iajs-2833	45	12	:	:	PUNCT
iajs-2833	45	13	let	let	VERB
iajs-2833	45	14	𝐷	𝐷	NOUN
iajs-2833	45	15	is	be	AUX
iajs-2833	45	16	a	a	DET
iajs-2833	45	17	measurable	measurable	ADJ
iajs-2833	45	18	subset	subset	NOUN
iajs-2833	45	19	of	of	ADP
iajs-2833	45	20	ℝ𝑑	ℝ𝑑	PROPN
iajs-2833	45	21	(	(	PUNCT
iajs-2833	45	22	𝑑	𝑑	NOUN
iajs-2833	45	23	=	=	SYM
iajs-2833	45	24	2,3	2,3	NUM
iajs-2833	45	25	)	)	PUNCT
iajs-2833	45	26	,	,	PUNCT
iajs-2833	45	27	𝑓	𝑓	X
iajs-2833	45	28	:	:	PUNCT
iajs-2833	45	29	𝐷	𝐷	PROPN
iajs-2833	45	30	×	×	NOUN
iajs-2833	45	31	ℝ𝑛	ℝ𝑛	NOUN
iajs-2833	45	32	⟶	⟶	NOUN
iajs-2833	45	33	ℝ𝑚	ℝ𝑚	NOUN
iajs-2833	45	34	is	be	AUX
iajs-2833	45	35	of	of	ADP
iajs-2833	45	36	carathéodory	carathéodory	ADJ
iajs-2833	45	37	type	type	NOUN
iajs-2833	45	38	satisfies	satisfie	NOUN
iajs-2833	45	39	‖𝑓(𝑣	‖𝑓(𝑣	NUM
iajs-2833	45	40	,	,	PUNCT
iajs-2833	45	41	𝑥)‖	𝑥)‖	ADJ
iajs-2833	45	42	≤	≤	ADJ
iajs-2833	45	43	휁(𝑣	휁(𝑣	NOUN
iajs-2833	45	44	)	)	PUNCT
iajs-2833	46	1	+	+	SYM
iajs-2833	46	2	휂(𝑣)‖𝑥‖𝛼,∀(𝑣	휂(𝑣)‖𝑥‖𝛼,∀(𝑣	PROPN
iajs-2833	46	3	,	,	PUNCT
iajs-2833	46	4	𝑥	𝑥	NOUN
iajs-2833	46	5	)	)	PUNCT
iajs-2833	46	6	∈	∈	PROPN
iajs-2833	46	7	𝐷	𝐷	PROPN
iajs-2833	46	8	×	×	NOUN
iajs-2833	46	9	ℝ𝑛	ℝ𝑛	NOUN
iajs-2833	46	10	,	,	PUNCT
iajs-2833	46	11	where	where	SCONJ
iajs-2833	46	12	𝑥	𝑥	DET
iajs-2833	46	13	∈	∈	PROPN
iajs-2833	46	14	𝐿𝑝(𝐷	𝐿𝑝(𝐷	NOUN
iajs-2833	46	15	×	×	NOUN
iajs-2833	46	16	ℝ𝑛	ℝ𝑛	NOUN
iajs-2833	46	17	)	)	PUNCT
iajs-2833	46	18	,	,	PUNCT
iajs-2833	46	19	휁	휁	PROPN
iajs-2833	46	20	∈	∈	PROPN
iajs-2833	46	21	𝐿1(𝐷	𝐿1(𝐷	PROPN
iajs-2833	46	22	×	×	NOUN
iajs-2833	46	23	ℝ	ℝ	PROPN
iajs-2833	46	24	)	)	PUNCT
iajs-2833	46	25	,	,	PUNCT
iajs-2833	46	26	휂	휂	ADP
iajs-2833	46	27	∈	∈	PROPN
iajs-2833	46	28	𝐿	𝐿	PROPN
iajs-2833	46	29	𝑝	𝑝	PROPN
iajs-2833	46	30	𝑝−𝛼(𝐷	𝑝−𝛼(𝐷	NUM
iajs-2833	46	31	×	×	NOUN
iajs-2833	46	32	ℝ	ℝ	PROPN
iajs-2833	46	33	)	)	PUNCT
iajs-2833	46	34	,	,	PUNCT
iajs-2833	46	35	𝛼	𝛼	PROPN
iajs-2833	46	36	∈	∈	PROPN
iajs-2833	47	1	[	[	X
iajs-2833	47	2	0	0	NUM
iajs-2833	47	3	,	,	PUNCT
iajs-2833	47	4	𝑝	𝑝	NOUN
iajs-2833	47	5	]	]	PUNCT
iajs-2833	47	6	,	,	PUNCT
iajs-2833	47	7	if	if	SCONJ
iajs-2833	47	8	𝑝	𝑝	PROPN
iajs-2833	47	9	≠	≠	PROPN
iajs-2833	47	10	∞.	∞.	PROPN
iajs-2833	47	11	then	then	ADV
iajs-2833	47	12	,	,	PUNCT
iajs-2833	47	13	the	the	DET
iajs-2833	47	14	functional	functional	ADJ
iajs-2833	47	15	𝐹(𝑥	𝐹(𝑥	NUM
iajs-2833	47	16	)	)	PUNCT
iajs-2833	47	17	=	=	SYM
iajs-2833	47	18	∫	∫	PROPN
iajs-2833	47	19	𝐷	𝐷	PROPN
iajs-2833	47	20	𝑓(𝑣	𝑓(𝑣	PROPN
iajs-2833	47	21	,	,	PUNCT
iajs-2833	47	22	𝑥(𝑣))𝑑𝑣	𝑥(𝑣))𝑑𝑣	PROPN
iajs-2833	47	23	is	be	AUX
iajs-2833	47	24	continuous	continuous	ADJ
iajs-2833	47	25	.	.	PUNCT
iajs-2833	48	1	3.2	3.2	NUM
iajs-2833	48	2	theorem	theorem	NOUN
iajs-2833	48	3	(	(	PUNCT
iajs-2833	48	4	eth	eth	NOUN
iajs-2833	48	5	of	of	ADP
iajs-2833	48	6	a	a	DET
iajs-2833	48	7	unique	unique	ADJ
iajs-2833	48	8	sqvs	sqvs	NOUN
iajs-2833	48	9	):	):	PUNCT
iajs-2833	48	10	with	with	ADP
iajs-2833	48	11	assumptions	assumption	NOUN
iajs-2833	48	12	(	(	PUNCT
iajs-2833	48	13	a	a	X
iajs-2833	48	14	)	)	PUNCT
iajs-2833	48	15	,	,	PUNCT
iajs-2833	48	16	for	for	ADP
iajs-2833	48	17	each	each	DET
iajs-2833	48	18	given	give	VERB
iajs-2833	48	19	�	�	PROPN
iajs-2833	48	20	⃗⃗	⃗⃗	PROPN
iajs-2833	48	21	�	�	PROPN
iajs-2833	48	22	∈	∈	PROPN
iajs-2833	48	23	𝐿2(q	𝐿2(q	NUM
iajs-2833	48	24	)	)	PUNCT
iajs-2833	48	25	,	,	PUNCT
iajs-2833	48	26	the	the	DET
iajs-2833	48	27	wf	wf	PROPN
iajs-2833	48	28	(	(	PUNCT
iajs-2833	48	29	(	(	PUNCT
iajs-2833	48	30	8)-(15	8)-(15	NUM
iajs-2833	48	31	)	)	PUNCT
iajs-2833	48	32	)	)	PUNCT
iajs-2833	48	33	has	have	VERB
iajs-2833	48	34	a	a	DET
iajs-2833	48	35	unique	unique	ADJ
iajs-2833	48	36	solution	solution	NOUN
iajs-2833	48	37	�	�	NOUN
iajs-2833	48	38	⃗	⃗	NOUN
iajs-2833	48	39	�	�	NOUN
iajs-2833	48	40	=	=	SYM
iajs-2833	48	41	(	(	PUNCT
iajs-2833	48	42	𝑦1	𝑦1	PROPN
iajs-2833	48	43	,	,	PUNCT
iajs-2833	48	44	𝑦2	𝑦2	PROPN
iajs-2833	48	45	,	,	PUNCT
iajs-2833	48	46	𝑦3	𝑦3	PROPN
iajs-2833	48	47	,	,	PUNCT
iajs-2833	48	48	𝑦4	𝑦4	PROPN
iajs-2833	48	49	)	)	PUNCT
iajs-2833	48	50	∈	∈	PROPN
iajs-2833	48	51	(	(	PUNCT
iajs-2833	48	52	𝐿2(i	𝐿2(i	NOUN
iajs-2833	48	53	×	×	NOUN
iajs-2833	48	54	v))4	v))4	PROPN
iajs-2833	48	55	and	and	CCONJ
iajs-2833	48	56	�	�	PROPN
iajs-2833	48	57	⃗	⃗	NOUN
iajs-2833	48	58	�	�	NOUN
iajs-2833	48	59	𝑡	𝑡	NOUN
iajs-2833	48	60	=	=	SYM
iajs-2833	48	61	(	(	PUNCT
iajs-2833	48	62	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2833	48	63	,	,	PUNCT
iajs-2833	48	64	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	48	65	,	,	PUNCT
iajs-2833	48	66	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	48	67	,	,	PUNCT
iajs-2833	48	68	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	48	69	)	)	PUNCT
iajs-2833	48	70	∈	∈	PROPN
iajs-2833	48	71	(	(	PUNCT
iajs-2833	48	72	𝐿2(q))4	𝐿2(q))4	PROPN
iajs-2833	48	73	,	,	PUNCT
iajs-2833	48	74	�	�	PROPN
iajs-2833	48	75	⃗	⃗	NOUN
iajs-2833	48	76	�	�	NOUN
iajs-2833	48	77	𝑡𝑡	𝑡𝑡	ADJ
iajs-2833	48	78	=	=	SYM
iajs-2833	48	79	(	(	PUNCT
iajs-2833	48	80	𝑦1𝑡𝑡	𝑦1𝑡𝑡	X
iajs-2833	48	81	,	,	PUNCT
iajs-2833	48	82	𝑦2𝑡𝑡	𝑦2𝑡𝑡	NUM
iajs-2833	48	83	,	,	PUNCT
iajs-2833	48	84	𝑦3𝑡𝑡	𝑦3𝑡𝑡	PROPN
iajs-2833	48	85	,	,	PUNCT
iajs-2833	48	86	𝑦4𝑡𝑡	𝑦4𝑡𝑡	NOUN
iajs-2833	48	87	)	)	PUNCT
iajs-2833	48	88	∈	∈	PROPN
iajs-2833	48	89	(	(	PUNCT
iajs-2833	48	90	𝐿2(i	𝐿2(i	NOUN
iajs-2833	48	91	×	×	NOUN
iajs-2833	48	92	v∗))4	v∗))4	PROPN
iajs-2833	48	93	.	.	PUNCT
iajs-2833	49	1	proof	proof	NOUN
iajs-2833	49	2	:	:	PUNCT
iajs-2833	49	3	let	let	VERB
iajs-2833	49	4	𝑉𝑛	𝑉𝑛	PROPN
iajs-2833	49	5	⃗⃗	⃗⃗	PROPN
iajs-2833	49	6	⃗⃗	⃗⃗	PROPN
iajs-2833	49	7	=	=	PRON
iajs-2833	49	8	(	(	PUNCT
iajs-2833	49	9	𝑉𝑛)4	𝑉𝑛)4	PROPN
iajs-2833	49	10	⊂	⊂	PROPN
iajs-2833	49	11	𝑉	𝑉	PROPN
iajs-2833	49	12	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2833	49	13	(	(	PUNCT
iajs-2833	49	14	for	for	ADP
iajs-2833	49	15	each	each	DET
iajs-2833	49	16	n	n	CCONJ
iajs-2833	49	17	)	)	PUNCT
iajs-2833	49	18	be	be	AUX
iajs-2833	49	19	the	the	DET
iajs-2833	49	20	set	set	NOUN
iajs-2833	49	21	of	of	ADP
iajs-2833	49	22	piecewise	piecewise	NOUN
iajs-2833	49	23	affine	affine	NOUN
iajs-2833	49	24	functions	function	NOUN
iajs-2833	49	25	in	in	ADP
iajs-2833	49	26	ω	ω	NOUN
iajs-2833	49	27	,	,	PUNCT
iajs-2833	49	28	let	let	VERB
iajs-2833	49	29	{	{	PUNCT
iajs-2833	49	30	𝑣𝑛}𝑛=1	𝑣𝑛}𝑛=1	NOUN
iajs-2833	49	31	∞	∞	PRON
iajs-2833	49	32	be	be	AUX
iajs-2833	49	33	a	a	DET
iajs-2833	49	34	sequence	sequence	NOUN
iajs-2833	49	35	of	of	ADP
iajs-2833	49	36	subspaces	subspace	NOUN
iajs-2833	49	37	of	of	ADP
iajs-2833	49	38	𝑉	𝑉	PROPN
iajs-2833	49	39	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	49	40	,	,	PUNCT
iajs-2833	49	41	s.t	s.t	PROPN
iajs-2833	49	42	.	.	PROPN
iajs-2833	49	43	∀	∀	PROPN
iajs-2833	49	44	�	�	PROPN
iajs-2833	49	45	⃗	⃗	NOUN
iajs-2833	49	46	�	�	NOUN
iajs-2833	49	47	=	=	SYM
iajs-2833	49	48	(	(	PUNCT
iajs-2833	49	49	𝑣1	𝑣1	PROPN
iajs-2833	49	50	,	,	PUNCT
iajs-2833	49	51	𝑣2	𝑣2	PROPN
iajs-2833	49	52	,	,	PUNCT
iajs-2833	49	53	𝑣3	𝑣3	ADJ
iajs-2833	49	54	,	,	PUNCT
iajs-2833	49	55	𝑣4	𝑣4	NOUN
iajs-2833	49	56	)	)	PUNCT
iajs-2833	49	57	∈	∈	PROPN
iajs-2833	49	58	𝑉	𝑉	PROPN
iajs-2833	49	59	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	49	60	,	,	PUNCT
iajs-2833	49	61	there	there	PRON
iajs-2833	49	62	is	be	VERB
iajs-2833	49	63	a	a	DET
iajs-2833	49	64	sequence	sequence	NOUN
iajs-2833	49	65	{	{	PUNCT
iajs-2833	49	66	𝑣𝑛	𝑣𝑛	NOUN
iajs-2833	49	67	}	}	PUNCT
iajs-2833	49	68	with	with	ADP
iajs-2833	49	69	�	�	PROPN
iajs-2833	49	70	⃗	⃗	NOUN
iajs-2833	49	71	�	�	NOUN
iajs-2833	49	72	𝑛	𝑛	NOUN
iajs-2833	49	73	=	=	PUNCT
iajs-2833	49	74	(	(	PUNCT
iajs-2833	49	75	𝑣1𝑛	𝑣1𝑛	X
iajs-2833	49	76	,	,	PUNCT
iajs-2833	49	77	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	49	78	,	,	PUNCT
iajs-2833	49	79	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	49	80	,	,	PUNCT
iajs-2833	49	81	𝑣4𝑛	𝑣4𝑛	NOUN
iajs-2833	49	82	)	)	PUNCT
iajs-2833	49	83	∈	∈	PROPN
iajs-2833	49	84	�	�	PROPN
iajs-2833	49	85	⃗⃗	⃗⃗	PROPN
iajs-2833	49	86	�	�	PROPN
iajs-2833	49	87	𝑛	𝑛	PROPN
iajs-2833	49	88	,	,	PUNCT
iajs-2833	49	89	∀𝑛	∀𝑛	NOUN
iajs-2833	49	90	and	and	CCONJ
iajs-2833	49	91	�	�	PROPN
iajs-2833	49	92	⃗	⃗	NOUN
iajs-2833	49	93	�	�	NOUN
iajs-2833	49	94	𝑛	𝑛	PRON
iajs-2833	49	95	→	→	SYM
iajs-2833	49	96	�	�	NOUN
iajs-2833	49	97	⃗	⃗	NOUN
iajs-2833	49	98	�	�	PROPN
iajs-2833	49	99	strongly	strongly	ADV
iajs-2833	49	100	(	(	PUNCT
iajs-2833	49	101	st	st	PROPN
iajs-2833	49	102	)	)	PUNCT
iajs-2833	49	103	in	in	ADP
iajs-2833	49	104	𝑉	𝑉	PROPN
iajs-2833	49	105	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	49	106	then	then	ADV
iajs-2833	49	107	�	�	PROPN
iajs-2833	49	108	⃗	⃗	NOUN
iajs-2833	49	109	�	�	NOUN
iajs-2833	49	110	𝑛	𝑛	PRON
iajs-2833	49	111	→	→	SYM
iajs-2833	49	112	�	�	PROPN
iajs-2833	49	113	⃗	⃗	PROPN
iajs-2833	49	114	�	�	PROPN
iajs-2833	49	115	st	st	PROPN
iajs-2833	49	116	in	in	ADP
iajs-2833	49	117	(	(	PUNCT
iajs-2833	49	118	𝐿2(ω))4	𝐿2(ω))4	INTJ
iajs-2833	49	119	.	.	PUNCT
iajs-2833	50	1	let	let	VERB
iajs-2833	50	2	{	{	PUNCT
iajs-2833	50	3	𝑣𝑗⃗⃗⃗	𝑣𝑗⃗⃗⃗	NOUN
iajs-2833	50	4	⃗	⃗	PROPN
iajs-2833	50	5	=	=	PUNCT
iajs-2833	50	6	(	(	PUNCT
iajs-2833	50	7	𝑣1𝑗	𝑣1𝑗	NOUN
iajs-2833	50	8	,	,	PUNCT
iajs-2833	50	9	𝑣2𝑗	𝑣2𝑗	NOUN
iajs-2833	50	10	,	,	PUNCT
iajs-2833	50	11	𝑣3𝑗	𝑣3𝑗	ADV
iajs-2833	50	12	,	,	PUNCT
iajs-2833	50	13	𝑣4𝑗	𝑣4𝑗	NUM
iajs-2833	50	14	):	):	PUNCT
iajs-2833	50	15	𝑗	𝑗	NOUN
iajs-2833	50	16	=	=	SYM
iajs-2833	50	17	1,2	1,2	NUM
iajs-2833	50	18	,	,	PUNCT
iajs-2833	50	19	…	…	PUNCT
iajs-2833	50	20	,	,	PUNCT
iajs-2833	50	21	𝑀(𝑛	𝑀(𝑛	NUM
iajs-2833	50	22	)	)	PUNCT
iajs-2833	50	23	}	}	PUNCT
iajs-2833	50	24	be	be	AUX
iajs-2833	50	25	a	a	DET
iajs-2833	50	26	finite	finite	ADJ
iajs-2833	50	27	basis	basis	NOUN
iajs-2833	50	28	of	of	ADP
iajs-2833	50	29	�	�	PROPN
iajs-2833	50	30	⃗⃗	⃗⃗	PROPN
iajs-2833	50	31	�	�	PROPN
iajs-2833	50	32	𝑛	𝑛	PROPN
iajs-2833	50	33	(	(	PUNCT
iajs-2833	50	34	where	where	SCONJ
iajs-2833	50	35	𝑣𝑗⃗⃗⃗	𝑣𝑗⃗⃗⃗	NOUN
iajs-2833	50	36	⃗	⃗	PROPN
iajs-2833	50	37	is	be	AUX
iajs-2833	50	38	a	a	DET
iajs-2833	50	39	piecewise	piecewise	NOUN
iajs-2833	50	40	affine	affine	NOUN
iajs-2833	50	41	function	function	NOUN
iajs-2833	50	42	in	in	ADP
iajs-2833	50	43	ω	ω	PROPN
iajs-2833	50	44	,	,	PUNCT
iajs-2833	50	45	with	with	ADP
iajs-2833	50	46	𝑣𝑗⃗⃗⃗	𝑣𝑗⃗⃗⃗	NOUN
iajs-2833	50	47	⃗(𝑥	⃗(𝑥	NUM
iajs-2833	50	48	)	)	PUNCT
iajs-2833	51	1	=	=	SYM
iajs-2833	51	2	0	0	NUM
iajs-2833	52	1	on	on	ADP
iajs-2833	52	2	the	the	DET
iajs-2833	52	3	boundary	boundary	ADJ
iajs-2833	52	4	γ	γ	X
iajs-2833	52	5	)	)	PUNCT
iajs-2833	52	6	and	and	CCONJ
iajs-2833	52	7	let	let	VERB
iajs-2833	52	8	�	�	PROPN
iajs-2833	52	9	⃗	⃗	NOUN
iajs-2833	52	10	�	�	NOUN
iajs-2833	52	11	𝑛	𝑛	NOUN
iajs-2833	52	12	=	=	SYM
iajs-2833	52	13	(	(	PUNCT
iajs-2833	52	14	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	52	15	,	,	PUNCT
iajs-2833	52	16	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	52	17	,	,	PUNCT
iajs-2833	52	18	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	52	19	,	,	PUNCT
iajs-2833	52	20	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	52	21	)	)	PUNCT
iajs-2833	52	22	be	be	AUX
iajs-2833	52	23	the	the	DET
iajs-2833	52	24	galerkin	galerkin	ADJ
iajs-2833	52	25	approximate	approximate	ADJ
iajs-2833	52	26	solution	solution	NOUN
iajs-2833	52	27	(	(	PUNCT
iajs-2833	52	28	gas	gas	NOUN
iajs-2833	52	29	)	)	PUNCT
iajs-2833	52	30	to	to	ADP
iajs-2833	52	31	the	the	DET
iajs-2833	52	32	exact	exact	ADJ
iajs-2833	52	33	solution	solution	NOUN
iajs-2833	52	34	�	�	NOUN
iajs-2833	52	35	⃗	⃗	NOUN
iajs-2833	52	36	�	�	NOUN
iajs-2833	52	37	=	=	SYM
iajs-2833	52	38	(	(	PUNCT
iajs-2833	52	39	𝑦1	𝑦1	PROPN
iajs-2833	52	40	,	,	PUNCT
iajs-2833	52	41	𝑦2	𝑦2	PROPN
iajs-2833	52	42	,	,	PUNCT
iajs-2833	52	43	𝑦3	𝑦3	PROPN
iajs-2833	52	44	,	,	PUNCT
iajs-2833	52	45	𝑦4	𝑦4	PROPN
iajs-2833	52	46	)	)	PUNCT
iajs-2833	52	47	s.t	s.t	PROPN
iajs-2833	52	48	.	.	PUNCT
iajs-2833	52	49	:	:	PUNCT
iajs-2833	52	50	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	52	51	=	=	SYM
iajs-2833	52	52	σ	σ	PROPN
iajs-2833	52	53	𝑗=1	𝑗=1	PROPN
iajs-2833	52	54	𝑛	𝑛	PROPN
iajs-2833	52	55	𝑐𝑖𝑗(𝑡)𝑣𝑖𝑗(𝑥	𝑐𝑖𝑗(𝑡)𝑣𝑖𝑗(𝑥	X
iajs-2833	52	56	)	)	PUNCT
iajs-2833	52	57	(	(	PUNCT
iajs-2833	52	58	16	16	NUM
iajs-2833	52	59	)	)	PUNCT
iajs-2833	52	60	𝑧𝑖𝑛	𝑧𝑖𝑛	NOUN
iajs-2833	52	61	=	=	SYM
iajs-2833	52	62	σ	σ	PROPN
iajs-2833	52	63	𝑗=1	𝑗=1	PROPN
iajs-2833	52	64	𝑛	𝑛	X
iajs-2833	52	65	𝑑𝑖𝑗(𝑡)𝑣𝑖𝑗(𝑥	𝑑𝑖𝑗(𝑡)𝑣𝑖𝑗(𝑥	NOUN
iajs-2833	52	66	)	)	PUNCT
iajs-2833	52	67	(	(	PUNCT
iajs-2833	52	68	17	17	NUM
iajs-2833	52	69	)	)	PUNCT
iajs-2833	52	70	where	where	SCONJ
iajs-2833	52	71	𝑐𝑖𝑗(𝑡	𝑐𝑖𝑗(𝑡	NOUN
iajs-2833	52	72	)	)	PUNCT
iajs-2833	52	73	,	,	PUNCT
iajs-2833	52	74	𝑑𝑖𝑗(𝑡	𝑑𝑖𝑗(𝑡	PROPN
iajs-2833	52	75	)	)	PUNCT
iajs-2833	52	76	are	be	AUX
iajs-2833	52	77	unknown	unknown	ADJ
iajs-2833	52	78	functions	function	NOUN
iajs-2833	52	79	,	,	PUNCT
iajs-2833	52	80	∀𝑖	∀𝑖	PROPN
iajs-2833	52	81	=	=	SYM
iajs-2833	52	82	1,2,3,4	1,2,3,4	NUM
iajs-2833	52	83	,	,	PUNCT
iajs-2833	52	84	𝑗	𝑗	NOUN
iajs-2833	52	85	=	=	SYM
iajs-2833	52	86	1,2	1,2	NUM
iajs-2833	52	87	,	,	PUNCT
iajs-2833	52	88	…	…	PUNCT
iajs-2833	52	89	,	,	PUNCT
iajs-2833	52	90	𝑛.	𝑛.	NOUN
iajs-2833	52	91	the	the	DET
iajs-2833	52	92	mga	mga	PROPN
iajs-2833	52	93	is	be	AUX
iajs-2833	52	94	utilized	utilize	VERB
iajs-2833	52	95	to	to	PART
iajs-2833	52	96	approximate	approximate	VERB
iajs-2833	52	97	the	the	DET
iajs-2833	52	98	wf	wf	PROPN
iajs-2833	52	99	(	(	PUNCT
iajs-2833	52	100	(	(	PUNCT
iajs-2833	52	101	8)	8)	NUM
iajs-2833	52	102	,	,	PUNCT
iajs-2833	52	103	(	(	PUNCT
iajs-2833	52	104	10	10	NUM
iajs-2833	52	105	)	)	PUNCT
iajs-2833	52	106	,	,	PUNCT
iajs-2833	52	107	(	(	PUNCT
iajs-2833	52	108	12	12	NUM
iajs-2833	52	109	)	)	PUNCT
iajs-2833	52	110	,	,	PUNCT
iajs-2833	52	111	(	(	PUNCT
iajs-2833	52	112	14	14	NUM
iajs-2833	52	113	)	)	PUNCT
iajs-2833	52	114	)	)	PUNCT
iajs-2833	52	115	w.r.t	w.r.t	NOUN
iajs-2833	52	116	.	.	PUNCT
iajs-2833	53	1	𝑥	𝑥	X
iajs-2833	53	2	,	,	PUNCT
iajs-2833	53	3	they	they	PRON
iajs-2833	53	4	become	become	VERB
iajs-2833	53	5	after	after	ADP
iajs-2833	53	6	substituting	substitute	VERB
iajs-2833	53	7	𝑦𝑖𝑛𝑡	𝑦𝑖𝑛𝑡	NOUN
iajs-2833	53	8	=	=	SYM
iajs-2833	53	9	𝑧𝑖𝑛	𝑧𝑖𝑛	NOUN
iajs-2833	53	10	(	(	PUNCT
iajs-2833	53	11	∀𝑣𝑖	∀𝑣𝑖	NOUN
iajs-2833	53	12	∈	∈	PROPN
iajs-2833	53	13	𝑉𝑛	𝑉𝑛	PROPN
iajs-2833	53	14	,	,	PUNCT
iajs-2833	53	15	∀𝑖	∀𝑖	PROPN
iajs-2833	53	16	=	=	NOUN
iajs-2833	53	17	1,2,3,4	1,2,3,4	NUM
iajs-2833	53	18	):	):	PUNCT
iajs-2833	53	19	(	(	PUNCT
iajs-2833	53	20	𝑧1𝑛𝑡	𝑧1𝑛𝑡	X
iajs-2833	53	21	,	,	PUNCT
iajs-2833	53	22	𝑣1	𝑣1	NOUN
iajs-2833	53	23	)	)	PUNCT
iajs-2833	54	1	+	+	CCONJ
iajs-2833	54	2	(	(	PUNCT
iajs-2833	54	3	∇𝑦1𝑛	∇𝑦1𝑛	ADJ
iajs-2833	54	4	,	,	PUNCT
iajs-2833	54	5	∇𝑣1	∇𝑣1	NOUN
iajs-2833	54	6	)	)	PUNCT
iajs-2833	55	1	+	+	CCONJ
iajs-2833	55	2	(	(	PUNCT
iajs-2833	55	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	55	4	,	,	PUNCT
iajs-2833	55	5	𝑣1	𝑣1	NOUN
iajs-2833	55	6	)	)	PUNCT
iajs-2833	55	7	−	−	PROPN
iajs-2833	55	8	(	(	PUNCT
iajs-2833	55	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	55	10	,	,	PUNCT
iajs-2833	55	11	𝑣1	𝑣1	NOUN
iajs-2833	55	12	)	)	PUNCT
iajs-2833	55	13	+	+	CCONJ
iajs-2833	55	14	(	(	PUNCT
iajs-2833	55	15	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	55	16	,	,	PUNCT
iajs-2833	55	17	𝑣1	𝑣1	NOUN
iajs-2833	55	18	)	)	PUNCT
iajs-2833	55	19	+	+	CCONJ
iajs-2833	55	20	(	(	PUNCT
iajs-2833	55	21	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	55	22	,	,	PUNCT
iajs-2833	55	23	𝑣1	𝑣1	NOUN
iajs-2833	55	24	)	)	PUNCT
iajs-2833	55	25	=	=	PUNCT
iajs-2833	55	26	(	(	PUNCT
iajs-2833	55	27	𝑓1	𝑓1	PROPN
iajs-2833	55	28	,	,	PUNCT
iajs-2833	55	29	𝑣1	𝑣1	PROPN
iajs-2833	55	30	)	)	PUNCT
iajs-2833	55	31	(	(	PUNCT
iajs-2833	55	32	18	18	NUM
iajs-2833	55	33	)	)	PUNCT
iajs-2833	55	34	(	(	PUNCT
iajs-2833	55	35	𝑦1𝑛	𝑦1𝑛	NOUN
iajs-2833	55	36	0	0	NUM
iajs-2833	55	37	,	,	PUNCT
iajs-2833	55	38	𝑣1	𝑣1	NOUN
iajs-2833	55	39	)	)	PUNCT
iajs-2833	55	40	=	=	PUNCT
iajs-2833	56	1	(	(	PUNCT
iajs-2833	56	2	𝑦1	𝑦1	PROPN
iajs-2833	56	3	0	0	NUM
iajs-2833	56	4	,	,	PUNCT
iajs-2833	56	5	𝑣1	𝑣1	NOUN
iajs-2833	56	6	)	)	PUNCT
iajs-2833	56	7	,	,	PUNCT
iajs-2833	56	8	and	and	CCONJ
iajs-2833	56	9	(	(	PUNCT
iajs-2833	56	10	𝑧1𝑛	𝑧1𝑛	PROPN
iajs-2833	56	11	1	1	NUM
iajs-2833	56	12	,	,	PUNCT
iajs-2833	56	13	𝑣1	𝑣1	NOUN
iajs-2833	56	14	)	)	PUNCT
iajs-2833	56	15	=	=	PUNCT
iajs-2833	56	16	(	(	PUNCT
iajs-2833	56	17	𝑦1	𝑦1	NOUN
iajs-2833	56	18	1	1	NUM
iajs-2833	56	19	,	,	PUNCT
iajs-2833	56	20	𝑣1	𝑣1	PROPN
iajs-2833	56	21	)	)	PUNCT
iajs-2833	56	22	(	(	PUNCT
iajs-2833	56	23	19	19	NUM
iajs-2833	56	24	)	)	PUNCT
iajs-2833	56	25	(	(	PUNCT
iajs-2833	56	26	𝑧2𝑛𝑡	𝑧2𝑛𝑡	PROPN
iajs-2833	56	27	,	,	PUNCT
iajs-2833	56	28	𝑣2	𝑣2	PROPN
iajs-2833	56	29	)	)	PUNCT
iajs-2833	56	30	+	+	CCONJ
iajs-2833	56	31	(	(	PUNCT
iajs-2833	56	32	∇𝑦2𝑛	∇𝑦2𝑛	NOUN
iajs-2833	56	33	,	,	PUNCT
iajs-2833	56	34	∇𝑣2	∇𝑣2	PRON
iajs-2833	56	35	)	)	PUNCT
iajs-2833	56	36	+	+	CCONJ
iajs-2833	56	37	(	(	PUNCT
iajs-2833	56	38	𝑦1𝑛	𝑦1𝑛	PROPN
iajs-2833	56	39	,	,	PUNCT
iajs-2833	56	40	𝑣2	𝑣2	PROPN
iajs-2833	56	41	)	)	PUNCT
iajs-2833	56	42	+	+	CCONJ
iajs-2833	56	43	(	(	PUNCT
iajs-2833	56	44	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	56	45	,	,	PUNCT
iajs-2833	56	46	𝑣2	𝑣2	NOUN
iajs-2833	56	47	)	)	PUNCT
iajs-2833	56	48	−	−	PROPN
iajs-2833	56	49	(	(	PUNCT
iajs-2833	56	50	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	56	51	,	,	PUNCT
iajs-2833	56	52	𝑣2	𝑣2	PROPN
iajs-2833	56	53	)	)	PUNCT
iajs-2833	56	54	−	−	PROPN
iajs-2833	56	55	(	(	PUNCT
iajs-2833	56	56	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	56	57	,	,	PUNCT
iajs-2833	56	58	𝑣2	𝑣2	PROPN
iajs-2833	56	59	)	)	PUNCT
iajs-2833	56	60	=	=	SYM
iajs-2833	56	61	(	(	PUNCT
iajs-2833	56	62	𝑓2	𝑓2	PROPN
iajs-2833	56	63	,	,	PUNCT
iajs-2833	56	64	𝑣2	𝑣2	NUM
iajs-2833	56	65	)	)	PUNCT
iajs-2833	56	66	(	(	PUNCT
iajs-2833	56	67	20	20	NUM
iajs-2833	56	68	)	)	PUNCT
iajs-2833	56	69	(	(	PUNCT
iajs-2833	56	70	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	56	71	0	0	NUM
iajs-2833	56	72	,	,	PUNCT
iajs-2833	56	73	𝑣2	𝑣2	PROPN
iajs-2833	56	74	)	)	PUNCT
iajs-2833	56	75	=	=	PUNCT
iajs-2833	56	76	(	(	PUNCT
iajs-2833	56	77	𝑦2	𝑦2	PROPN
iajs-2833	56	78	0	0	NUM
iajs-2833	56	79	,	,	PUNCT
iajs-2833	56	80	𝑣2	𝑣2	NOUN
iajs-2833	56	81	)	)	PUNCT
iajs-2833	56	82	,	,	PUNCT
iajs-2833	56	83	and	and	CCONJ
iajs-2833	56	84	(	(	PUNCT
iajs-2833	56	85	𝑧2𝑛	𝑧2𝑛	X
iajs-2833	56	86	1	1	NUM
iajs-2833	56	87	,	,	PUNCT
iajs-2833	56	88	𝑣2	𝑣2	PROPN
iajs-2833	56	89	)	)	PUNCT
iajs-2833	56	90	=	=	PUNCT
iajs-2833	56	91	(	(	PUNCT
iajs-2833	56	92	𝑦2	𝑦2	PROPN
iajs-2833	56	93	1	1	NUM
iajs-2833	56	94	,	,	PUNCT
iajs-2833	56	95	𝑣2	𝑣2	PROPN
iajs-2833	56	96	)	)	PUNCT
iajs-2833	56	97	(	(	PUNCT
iajs-2833	56	98	21	21	NUM
iajs-2833	56	99	)	)	PUNCT
iajs-2833	56	100	(	(	PUNCT
iajs-2833	56	101	𝑧3𝑛𝑡	𝑧3𝑛𝑡	X
iajs-2833	56	102	,	,	PUNCT
iajs-2833	56	103	𝑣3	𝑣3	ADJ
iajs-2833	56	104	)	)	PUNCT
iajs-2833	57	1	+	+	CCONJ
iajs-2833	57	2	(	(	PUNCT
iajs-2833	57	3	∇𝑦3𝑛	∇𝑦3𝑛	ADJ
iajs-2833	57	4	,	,	PUNCT
iajs-2833	57	5	∇𝑣3	∇𝑣3	NOUN
iajs-2833	57	6	)	)	PUNCT
iajs-2833	57	7	−	−	PROPN
iajs-2833	57	8	(	(	PUNCT
iajs-2833	57	9	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	57	10	,	,	PUNCT
iajs-2833	57	11	𝑣3	𝑣3	ADJ
iajs-2833	57	12	)	)	PUNCT
iajs-2833	57	13	+	+	CCONJ
iajs-2833	57	14	(	(	PUNCT
iajs-2833	57	15	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	57	16	,	,	PUNCT
iajs-2833	57	17	𝑣3	𝑣3	NOUN
iajs-2833	57	18	)	)	PUNCT
iajs-2833	57	19	+	+	CCONJ
iajs-2833	57	20	(	(	PUNCT
iajs-2833	57	21	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	57	22	,	,	PUNCT
iajs-2833	57	23	𝑣3	𝑣3	ADJ
iajs-2833	57	24	)	)	PUNCT
iajs-2833	57	25	+	+	CCONJ
iajs-2833	57	26	(	(	PUNCT
iajs-2833	57	27	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	57	28	,	,	PUNCT
iajs-2833	57	29	𝑣3	𝑣3	ADJ
iajs-2833	57	30	)	)	PUNCT
iajs-2833	57	31	=	=	SYM
iajs-2833	57	32	(	(	PUNCT
iajs-2833	57	33	𝑓3	𝑓3	NOUN
iajs-2833	57	34	,	,	PUNCT
iajs-2833	57	35	𝑣3	𝑣3	ADJ
iajs-2833	57	36	)	)	PUNCT
iajs-2833	57	37	(	(	PUNCT
iajs-2833	57	38	22	22	NUM
iajs-2833	57	39	)	)	PUNCT
iajs-2833	57	40	ihjpas	ihjpa	NOUN
iajs-2833	57	41	.	.	PUNCT
iajs-2833	58	1	53	53	NUM
iajs-2833	58	2	(	(	PUNCT
iajs-2833	58	3	3)2022	3)2022	NOUN
iajs-2833	58	4	164	164	NUM
iajs-2833	58	5	(	(	PUNCT
iajs-2833	58	6	𝑦3𝑛	𝑦3𝑛	X
iajs-2833	58	7	0	0	NUM
iajs-2833	58	8	,	,	PUNCT
iajs-2833	58	9	𝑣3	𝑣3	ADJ
iajs-2833	58	10	)	)	PUNCT
iajs-2833	58	11	=	=	SYM
iajs-2833	58	12	(	(	PUNCT
iajs-2833	58	13	𝑦3	𝑦3	PROPN
iajs-2833	58	14	0	0	NUM
iajs-2833	58	15	,	,	PUNCT
iajs-2833	58	16	𝑣3	𝑣3	ADJ
iajs-2833	58	17	)	)	PUNCT
iajs-2833	58	18	,	,	PUNCT
iajs-2833	58	19	and	and	CCONJ
iajs-2833	58	20	(	(	PUNCT
iajs-2833	58	21	𝑧3𝑛	𝑧3𝑛	PROPN
iajs-2833	58	22	1	1	NUM
iajs-2833	58	23	,	,	PUNCT
iajs-2833	58	24	𝑣3	𝑣3	ADJ
iajs-2833	58	25	)	)	PUNCT
iajs-2833	58	26	=	=	SYM
iajs-2833	58	27	(	(	PUNCT
iajs-2833	58	28	(	(	PUNCT
iajs-2833	58	29	𝑦3	𝑦3	PROPN
iajs-2833	58	30	1	1	NUM
iajs-2833	58	31	,	,	PUNCT
iajs-2833	58	32	𝑣3	𝑣3	ADJ
iajs-2833	58	33	)	)	PUNCT
iajs-2833	58	34	(	(	PUNCT
iajs-2833	58	35	23	23	NUM
iajs-2833	58	36	)	)	PUNCT
iajs-2833	58	37	(	(	PUNCT
iajs-2833	58	38	𝑧4𝑛𝑡	𝑧4𝑛𝑡	NOUN
iajs-2833	58	39	,	,	PUNCT
iajs-2833	58	40	𝑣4	𝑣4	NOUN
iajs-2833	58	41	)	)	PUNCT
iajs-2833	58	42	+	+	CCONJ
iajs-2833	58	43	(	(	PUNCT
iajs-2833	58	44	∇𝑦4𝑛	∇𝑦4𝑛	ADV
iajs-2833	58	45	,	,	PUNCT
iajs-2833	58	46	∇𝑣4	∇𝑣4	ADJ
iajs-2833	58	47	)	)	PUNCT
iajs-2833	58	48	−	−	PROPN
iajs-2833	58	49	(	(	PUNCT
iajs-2833	58	50	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	58	51	,	,	PUNCT
iajs-2833	58	52	𝑣4	𝑣4	NOUN
iajs-2833	58	53	)	)	PUNCT
iajs-2833	58	54	+	+	CCONJ
iajs-2833	58	55	(	(	PUNCT
iajs-2833	58	56	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	58	57	,	,	PUNCT
iajs-2833	58	58	𝑣4	𝑣4	NOUN
iajs-2833	58	59	)	)	PUNCT
iajs-2833	58	60	−	−	PROPN
iajs-2833	58	61	(	(	PUNCT
iajs-2833	58	62	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	58	63	,	,	PUNCT
iajs-2833	58	64	𝑣4	𝑣4	NOUN
iajs-2833	58	65	)	)	PUNCT
iajs-2833	58	66	+	+	CCONJ
iajs-2833	58	67	(	(	PUNCT
iajs-2833	58	68	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	58	69	,	,	PUNCT
iajs-2833	58	70	𝑣4	𝑣4	NOUN
iajs-2833	58	71	)	)	PUNCT
iajs-2833	58	72	=	=	SYM
iajs-2833	58	73	(	(	PUNCT
iajs-2833	58	74	𝑓4	𝑓4	PROPN
iajs-2833	58	75	,	,	PUNCT
iajs-2833	58	76	𝑣4	𝑣4	NOUN
iajs-2833	58	77	)	)	PUNCT
iajs-2833	58	78	(	(	PUNCT
iajs-2833	58	79	24	24	NUM
iajs-2833	58	80	)	)	PUNCT
iajs-2833	58	81	(	(	PUNCT
iajs-2833	58	82	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	58	83	0	0	NUM
iajs-2833	58	84	,	,	PUNCT
iajs-2833	58	85	𝑣2	𝑣2	PROPN
iajs-2833	58	86	)	)	PUNCT
iajs-2833	58	87	=	=	PUNCT
iajs-2833	58	88	(	(	PUNCT
iajs-2833	58	89	𝑦4	𝑦4	PROPN
iajs-2833	58	90	0	0	NUM
iajs-2833	58	91	,	,	PUNCT
iajs-2833	58	92	𝑣4	𝑣4	NOUN
iajs-2833	58	93	)	)	PUNCT
iajs-2833	58	94	,	,	PUNCT
iajs-2833	58	95	and	and	CCONJ
iajs-2833	58	96	(	(	PUNCT
iajs-2833	58	97	𝑧4𝑛	𝑧4𝑛	NOUN
iajs-2833	58	98	1	1	NUM
iajs-2833	58	99	,	,	PUNCT
iajs-2833	58	100	𝑣4	𝑣4	NOUN
iajs-2833	58	101	)	)	PUNCT
iajs-2833	58	102	=	=	SYM
iajs-2833	58	103	(	(	PUNCT
iajs-2833	58	104	(	(	PUNCT
iajs-2833	58	105	𝑦4	𝑦4	PROPN
iajs-2833	58	106	1	1	NUM
iajs-2833	58	107	,	,	PUNCT
iajs-2833	58	108	𝑣4	𝑣4	NOUN
iajs-2833	58	109	)	)	PUNCT
iajs-2833	58	110	(	(	PUNCT
iajs-2833	58	111	25	25	NUM
iajs-2833	58	112	)	)	PUNCT
iajs-2833	58	113	where	where	SCONJ
iajs-2833	58	114	𝑦𝑖𝑛	𝑦𝑖𝑛	ADV
iajs-2833	58	115	0	0	NUM
iajs-2833	59	1	=	=	SYM
iajs-2833	59	2	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	59	3	0	0	NUM
iajs-2833	60	1	(	(	PUNCT
iajs-2833	60	2	𝑥	𝑥	NOUN
iajs-2833	60	3	)	)	PUNCT
iajs-2833	60	4	=	=	SYM
iajs-2833	60	5	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	60	6	(	(	PUNCT
iajs-2833	60	7	𝑥	𝑥	NOUN
iajs-2833	60	8	,	,	PUNCT
iajs-2833	60	9	0	0	NUM
iajs-2833	60	10	)	)	PUNCT
iajs-2833	60	11	∈	∈	PROPN
iajs-2833	61	1	𝑉𝑛	𝑉𝑛	PRON
iajs-2833	61	2	(	(	PUNCT
iajs-2833	61	3	respectively	respectively	ADV
iajs-2833	61	4	𝑧𝑖𝑛	𝑧𝑖𝑛	ADJ
iajs-2833	61	5	0	0	NUM
iajs-2833	61	6	=	=	SYM
iajs-2833	61	7	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	61	8	1	1	NUM
iajs-2833	61	9	=	=	SYM
iajs-2833	61	10	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	61	11	1	1	NUM
iajs-2833	61	12	(	(	PUNCT
iajs-2833	61	13	𝑥	𝑥	NOUN
iajs-2833	61	14	)	)	PUNCT
iajs-2833	61	15	=	=	SYM
iajs-2833	61	16	𝑦𝑖𝑛𝑡	𝑦𝑖𝑛𝑡	ADJ
iajs-2833	61	17	(	(	PUNCT
iajs-2833	61	18	𝑥	𝑥	NOUN
iajs-2833	61	19	,	,	PUNCT
iajs-2833	61	20	0	0	NUM
iajs-2833	61	21	)	)	PUNCT
iajs-2833	61	22	∈	∈	PROPN
iajs-2833	61	23	𝐿2(ω	𝐿2(ω	ADV
iajs-2833	61	24	)	)	PUNCT
iajs-2833	61	25	be	be	VERB
iajs-2833	61	26	the	the	DET
iajs-2833	61	27	projection	projection	NOUN
iajs-2833	61	28	of	of	ADP
iajs-2833	61	29	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	61	30	0	0	PROPN
iajs-2833	61	31	onto	onto	ADP
iajs-2833	61	32	𝑉	𝑉	PROPN
iajs-2833	61	33	(	(	PUNCT
iajs-2833	61	34	be	be	AUX
iajs-2833	61	35	the	the	DET
iajs-2833	61	36	projection	projection	NOUN
iajs-2833	61	37	of	of	ADP
iajs-2833	61	38	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	61	39	1	1	NUM
iajs-2833	61	40	=	=	NOUN
iajs-2833	61	41	𝑦𝑖𝑡	𝑦𝑖𝑡	NOUN
iajs-2833	61	42	on	on	ADP
iajs-2833	61	43	to	to	ADP
iajs-2833	61	44	𝐿2(ω	𝐿2(ω	NUM
iajs-2833	61	45	)	)	PUNCT
iajs-2833	61	46	,	,	PUNCT
iajs-2833	61	47	∀𝑖	∀𝑖	PROPN
iajs-2833	61	48	=	=	NOUN
iajs-2833	61	49	1,2,3,4	1,2,3,4	NUM
iajs-2833	61	50	)	)	PUNCT
iajs-2833	61	51	,	,	PUNCT
iajs-2833	61	52	i.e.	i.e.	X
iajs-2833	61	53	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	61	54	0	0	NUM
iajs-2833	61	55	→	→	SYM
iajs-2833	61	56	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	61	57	0	0	PROPN
iajs-2833	61	58	st	st	PROPN
iajs-2833	61	59	in	in	ADP
iajs-2833	61	60	𝑉	𝑉	PROPN
iajs-2833	61	61	,	,	PUNCT
iajs-2833	61	62	with	with	ADP
iajs-2833	61	63	∥	∥	PROPN
iajs-2833	61	64	�	�	NOUN
iajs-2833	61	65	⃗	⃗	NOUN
iajs-2833	61	66	�	�	NOUN
iajs-2833	61	67	𝑛	𝑛	PRON
iajs-2833	61	68	0	0	NUM
iajs-2833	61	69	∥1≤	∥1≤	NOUN
iajs-2833	61	70	𝑏0	𝑏0	NOUN
iajs-2833	61	71	and	and	CCONJ
iajs-2833	61	72	∥	∥	NUM
iajs-2833	61	73	�	�	NOUN
iajs-2833	61	74	⃗	⃗	NOUN
iajs-2833	61	75	�	�	NOUN
iajs-2833	61	76	𝑛	𝑛	ADJ
iajs-2833	61	77	0	0	NUM
iajs-2833	61	78	∥0≤	∥0≤	NOUN
iajs-2833	61	79	𝑏0	𝑏0	NOUN
iajs-2833	61	80	(	(	PUNCT
iajs-2833	61	81	26	26	NUM
iajs-2833	61	82	)	)	PUNCT
iajs-2833	61	83	𝑦𝑖𝑛	𝑦𝑖𝑛	NOUN
iajs-2833	61	84	1	1	NUM
iajs-2833	61	85	→	→	SYM
iajs-2833	61	86	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	61	87	1	1	NUM
iajs-2833	61	88	st	st	PROPN
iajs-2833	61	89	in	in	ADP
iajs-2833	61	90	𝐿2(ω	𝐿2(ω	PROPN
iajs-2833	61	91	)	)	PUNCT
iajs-2833	61	92	,	,	PUNCT
iajs-2833	61	93	with	with	ADP
iajs-2833	61	94	∥	∥	PROPN
iajs-2833	61	95	�	�	NOUN
iajs-2833	61	96	⃗	⃗	NOUN
iajs-2833	61	97	�	�	NOUN
iajs-2833	61	98	𝑛	𝑛	ADJ
iajs-2833	61	99	1	1	NUM
iajs-2833	61	100	∥≤	∥≤	NOUN
iajs-2833	61	101	𝑏1	𝑏1	NOUN
iajs-2833	61	102	(	(	PUNCT
iajs-2833	61	103	27	27	NUM
iajs-2833	61	104	)	)	PUNCT
iajs-2833	61	105	substituting	substitute	VERB
iajs-2833	61	106	(	(	PUNCT
iajs-2833	61	107	16	16	NUM
iajs-2833	61	108	)	)	PUNCT
iajs-2833	61	109	&	&	CCONJ
iajs-2833	61	110	(	(	PUNCT
iajs-2833	61	111	17	17	NUM
iajs-2833	61	112	)	)	PUNCT
iajs-2833	61	113	with	with	ADP
iajs-2833	61	114	𝑖	𝑖	NOUN
iajs-2833	61	115	=	=	SYM
iajs-2833	61	116	1,2,3,4	1,2,3,4	NUM
iajs-2833	61	117	in	in	ADP
iajs-2833	61	118	)	)	PUNCT
iajs-2833	61	119	(	(	PUNCT
iajs-2833	61	120	18)-(25	18)-(25	NUM
iajs-2833	61	121	)	)	PUNCT
iajs-2833	61	122	(	(	PUNCT
iajs-2833	61	123	and	and	CCONJ
iajs-2833	61	124	setting	set	VERB
iajs-2833	61	125	𝑣𝑖	𝑣𝑖	ADP
iajs-2833	61	126	=	=	NOUN
iajs-2833	61	127	𝑣𝑖𝑙	𝑣𝑖𝑙	PRON
iajs-2833	61	128	,	,	PUNCT
iajs-2833	61	129	∀𝑙	∀𝑙	NOUN
iajs-2833	61	130	=	=	SYM
iajs-2833	61	131	1,2	1,2	NUM
iajs-2833	61	132	,	,	PUNCT
iajs-2833	61	133	…	…	PUNCT
iajs-2833	61	134	,	,	PUNCT
iajs-2833	61	135	𝑛	𝑛	PROPN
iajs-2833	61	136	,	,	PUNCT
iajs-2833	61	137	then	then	ADV
iajs-2833	61	138	the	the	DET
iajs-2833	61	139	obtained	obtain	VERB
iajs-2833	61	140	equations	equation	NOUN
iajs-2833	61	141	are	be	AUX
iajs-2833	61	142	equivalent	equivalent	ADJ
iajs-2833	61	143	to	to	ADP
iajs-2833	61	144	the	the	DET
iajs-2833	61	145	following	follow	VERB
iajs-2833	61	146	system	system	NOUN
iajs-2833	61	147	of	of	ADP
iajs-2833	61	148	nonlinear	nonlinear	ADJ
iajs-2833	61	149	odes	ode	NOUN
iajs-2833	61	150	of	of	ADP
iajs-2833	61	151	1st	1st	ADJ
iajs-2833	61	152	order	order	NOUN
iajs-2833	61	153	with	with	ADP
iajs-2833	61	154	ics	ics	NOUN
iajs-2833	61	155	(	(	PUNCT
iajs-2833	61	156	which	which	PRON
iajs-2833	61	157	has	have	VERB
iajs-2833	61	158	a	a	DET
iajs-2833	61	159	unique	unique	ADJ
iajs-2833	61	160	solution	solution	NOUN
iajs-2833	61	161	)	)	PUNCT
iajs-2833	61	162	,	,	PUNCT
iajs-2833	61	163	i.e.	i.e.	X
iajs-2833	61	164	𝐴1𝐷1(𝑡	𝐴1𝐷1(𝑡	NOUN
iajs-2833	61	165	)	)	PUNCT
iajs-2833	62	1	+	+	NUM
iajs-2833	62	2	𝐵1𝐶1(𝑡	𝐵1𝐶1(𝑡	X
iajs-2833	62	3	)	)	PUNCT
iajs-2833	62	4	−	−	PROPN
iajs-2833	63	1	𝐸𝐶2(𝑡	𝐸𝐶2(𝑡	NOUN
iajs-2833	63	2	)	)	PUNCT
iajs-2833	63	3	+	+	SYM
iajs-2833	64	1	𝐹𝐶3(𝑡	𝐹𝐶3(𝑡	X
iajs-2833	64	2	)	)	PUNCT
iajs-2833	64	3	+	+	CCONJ
iajs-2833	64	4	𝐾𝐶4(𝑡	𝐾𝐶4(𝑡	X
iajs-2833	64	5	)	)	PUNCT
iajs-2833	64	6	=	=	SYM
iajs-2833	64	7	𝑏1(	𝑏1(	NUM
iajs-2833	64	8	�	�	NOUN
iajs-2833	64	9	̅	̅	NOUN
iajs-2833	64	10	�	�	NOUN
iajs-2833	64	11	1	1	NUM
iajs-2833	64	12	𝑇(𝑥)𝐶1(𝑡	𝑇(𝑥)𝐶1(𝑡	NOUN
iajs-2833	64	13	)	)	PUNCT
iajs-2833	64	14	)	)	PUNCT
iajs-2833	64	15	𝐴1𝐶1(0	𝐴1𝐶1(0	NOUN
iajs-2833	64	16	)	)	PUNCT
iajs-2833	65	1	=	=	SYM
iajs-2833	65	2	𝑏1	𝑏1	NOUN
iajs-2833	65	3	0	0	NUM
iajs-2833	65	4	and	and	CCONJ
iajs-2833	65	5	𝐴1𝐷1	𝐴1𝐷1	VERB
iajs-2833	65	6	̅̅	̅̅	PROPN
iajs-2833	65	7	̅(0	̅(0	X
iajs-2833	65	8	)	)	PUNCT
iajs-2833	65	9	=	=	SYM
iajs-2833	65	10	𝑏1	𝑏1	ADJ
iajs-2833	65	11	1	1	NUM
iajs-2833	65	12	𝐴2𝐷2(𝑡	𝐴2𝐷2(𝑡	NOUN
iajs-2833	65	13	)	)	PUNCT
iajs-2833	66	1	+	+	NUM
iajs-2833	66	2	𝐵2𝐶2(𝑡	𝐵2𝐶2(𝑡	NUM
iajs-2833	66	3	)	)	PUNCT
iajs-2833	67	1	+	+	NUM
iajs-2833	67	2	𝐻𝐶1(𝑡	𝐻𝐶1(𝑡	NOUN
iajs-2833	67	3	)	)	PUNCT
iajs-2833	67	4	−	−	PUNCT
iajs-2833	68	1	𝐺𝐶3(𝑡	𝐺𝐶3(𝑡	SYM
iajs-2833	68	2	)	)	PUNCT
iajs-2833	69	1	+	+	CCONJ
iajs-2833	69	2	𝐷𝐶4(𝑡	𝐷𝐶4(𝑡	X
iajs-2833	69	3	)	)	PUNCT
iajs-2833	69	4	=	=	SYM
iajs-2833	69	5	𝑏2	𝑏2	PROPN
iajs-2833	69	6	(	(	PUNCT
iajs-2833	69	7	�	�	NOUN
iajs-2833	69	8	̅	̅	NOUN
iajs-2833	69	9	�	�	NOUN
iajs-2833	69	10	2	2	NUM
iajs-2833	69	11	𝑇(𝑥)𝐶1(𝑡	𝑇(𝑥)𝐶1(𝑡	NOUN
iajs-2833	69	12	)	)	PUNCT
iajs-2833	69	13	)	)	PUNCT
iajs-2833	69	14	𝐴2𝐶2(0	𝐴2𝐶2(0	PROPN
iajs-2833	69	15	)	)	PUNCT
iajs-2833	69	16	=	=	SYM
iajs-2833	69	17	𝑏2	𝑏2	PROPN
iajs-2833	69	18	0	0	PROPN
iajs-2833	69	19	and	and	CCONJ
iajs-2833	69	20	𝐴2𝐷2	𝐴2𝐷2	PROPN
iajs-2833	69	21	̅̅	̅̅	PROPN
iajs-2833	69	22	̅(0	̅(0	PART
iajs-2833	69	23	)	)	PUNCT
iajs-2833	69	24	=	=	SYM
iajs-2833	69	25	𝑏2	𝑏2	PROPN
iajs-2833	69	26	1	1	NUM
iajs-2833	69	27	𝐴3𝐷3(𝑡	𝐴3𝐷3(𝑡	NOUN
iajs-2833	69	28	)	)	PUNCT
iajs-2833	70	1	+	+	CCONJ
iajs-2833	70	2	𝐵3𝐶3(𝑡	𝐵3𝐶3(𝑡	NOUN
iajs-2833	70	3	)	)	PUNCT
iajs-2833	70	4	−	−	PART
iajs-2833	70	5	𝑅𝐶1(𝑡	𝑅𝐶1(𝑡	SYM
iajs-2833	70	6	)	)	PUNCT
iajs-2833	70	7	+	+	CCONJ
iajs-2833	70	8	𝑊𝐶2(𝑡	𝑊𝐶2(𝑡	ADP
iajs-2833	70	9	)	)	PUNCT
iajs-2833	70	10	+	+	CCONJ
iajs-2833	70	11	𝑍𝐶4(𝑡	𝑍𝐶4(𝑡	X
iajs-2833	70	12	)	)	PUNCT
iajs-2833	70	13	=	=	PUNCT
iajs-2833	70	14	𝑏3(	𝑏3(	NOUN
iajs-2833	70	15	�	�	NOUN
iajs-2833	70	16	̅	̅	NOUN
iajs-2833	70	17	�	�	NOUN
iajs-2833	70	18	3	3	NUM
iajs-2833	70	19	𝑇(𝑥)𝐶1(𝑡	𝑇(𝑥)𝐶1(𝑡	NOUN
iajs-2833	70	20	)	)	PUNCT
iajs-2833	70	21	)	)	PUNCT
iajs-2833	71	1	𝐴3𝐶3(0	𝐴3𝐶3(0	NOUN
iajs-2833	71	2	)	)	PUNCT
iajs-2833	72	1	=	=	SYM
iajs-2833	72	2	𝑏3	𝑏3	NOUN
iajs-2833	72	3	0	0	NUM
iajs-2833	72	4	and	and	CCONJ
iajs-2833	72	5	𝐴3𝐷3	𝐴3𝐷3	PROPN
iajs-2833	72	6	̅̅	̅̅	PROPN
iajs-2833	72	7	̅(0	̅(0	X
iajs-2833	72	8	)	)	PUNCT
iajs-2833	73	1	=	=	PRON
iajs-2833	73	2	𝑏3	𝑏3	NOUN
iajs-2833	73	3	1	1	NUM
iajs-2833	73	4	𝐴4𝐷4(𝑡	𝐴4𝐷4(𝑡	ADJ
iajs-2833	73	5	)	)	PUNCT
iajs-2833	73	6	+	+	SYM
iajs-2833	73	7	𝐵4𝐶4(𝑡	𝐵4𝐶4(𝑡	X
iajs-2833	73	8	)	)	PUNCT
iajs-2833	73	9	−	−	NOUN
iajs-2833	73	10	𝑇𝐶1(𝑡	𝑇𝐶1(𝑡	NOUN
iajs-2833	73	11	)	)	PUNCT
iajs-2833	73	12	+	+	CCONJ
iajs-2833	73	13	𝑀𝐶2(𝑡	𝑀𝐶2(𝑡	NOUN
iajs-2833	73	14	)	)	PUNCT
iajs-2833	73	15	−	−	PROPN
iajs-2833	74	1	𝑁𝐶3(𝑡	𝑁𝐶3(𝑡	PROPN
iajs-2833	74	2	)	)	PUNCT
iajs-2833	74	3	=	=	SYM
iajs-2833	74	4	𝑏4(	𝑏4(	NOUN
iajs-2833	74	5	�	�	NOUN
iajs-2833	74	6	̅	̅	NOUN
iajs-2833	74	7	�	�	NOUN
iajs-2833	74	8	4	4	NUM
iajs-2833	74	9	𝑇(𝑥)𝐶1(𝑡	𝑇(𝑥)𝐶1(𝑡	NOUN
iajs-2833	74	10	)	)	PUNCT
iajs-2833	74	11	)	)	PUNCT
iajs-2833	74	12	𝐴4𝐶4(0	𝐴4𝐶4(0	PROPN
iajs-2833	74	13	)	)	PUNCT
iajs-2833	74	14	=	=	SYM
iajs-2833	74	15	𝑏4	𝑏4	PROPN
iajs-2833	74	16	0	0	NUM
iajs-2833	74	17	and	and	CCONJ
iajs-2833	74	18	𝐴4𝐷4	𝐴4𝐷4	PROPN
iajs-2833	74	19	̅̅	̅̅	PROPN
iajs-2833	74	20	̅(0	̅(0	PART
iajs-2833	74	21	)	)	PUNCT
iajs-2833	74	22	=	=	SYM
iajs-2833	74	23	𝑏4	𝑏4	PROPN
iajs-2833	74	24	1	1	NUM
iajs-2833	74	25	where	where	SCONJ
iajs-2833	74	26	𝐴𝑖	𝐴𝑖	PROPN
iajs-2833	74	27	=	=	SYM
iajs-2833	74	28	(	(	PUNCT
iajs-2833	74	29	𝑎𝑖𝑙𝑗)𝑛×𝑛	𝑎𝑖𝑙𝑗)𝑛×𝑛	ADJ
iajs-2833	74	30	,	,	PUNCT
iajs-2833	74	31	𝑎𝑖𝑙𝑗	𝑎𝑖𝑙𝑗	NOUN
iajs-2833	74	32	=	=	SYM
iajs-2833	74	33	(	(	PUNCT
iajs-2833	74	34	𝑣𝑖𝑗	𝑣𝑖𝑗	PROPN
iajs-2833	74	35	,	,	PUNCT
iajs-2833	74	36	𝑣𝑖𝑙	𝑣𝑖𝑙	NUM
iajs-2833	74	37	)	)	PUNCT
iajs-2833	74	38	,	,	PUNCT
iajs-2833	74	39	𝐵𝑖	𝐵𝑖	PROPN
iajs-2833	74	40	=	=	PUNCT
iajs-2833	74	41	(	(	PUNCT
iajs-2833	74	42	𝑏𝑖𝑙𝑗)𝑛×𝑛	𝑏𝑖𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	43	,	,	PUNCT
iajs-2833	74	44	𝑏𝑖𝑙𝑗	𝑏𝑖𝑙𝑗	ADJ
iajs-2833	74	45	=	=	PRON
iajs-2833	74	46	(	(	PUNCT
iajs-2833	74	47	∇𝑣𝑖𝑗	∇𝑣𝑖𝑗	NOUN
iajs-2833	74	48	,	,	PUNCT
iajs-2833	74	49	∇𝑣𝑖𝑙	∇𝑣𝑖𝑙	NOUN
iajs-2833	74	50	)	)	PUNCT
iajs-2833	74	51	+	+	CCONJ
iajs-2833	74	52	(	(	PUNCT
iajs-2833	74	53	𝑣𝑖𝑗	𝑣𝑖𝑗	PROPN
iajs-2833	74	54	,	,	PUNCT
iajs-2833	74	55	𝑣𝑖𝑙	𝑣𝑖𝑙	PRON
iajs-2833	74	56	)	)	PUNCT
iajs-2833	74	57	,	,	PUNCT
iajs-2833	74	58	𝐸	𝐸	PROPN
iajs-2833	74	59	=	=	SYM
iajs-2833	74	60	(	(	PUNCT
iajs-2833	74	61	𝑒𝑙𝑗)𝑛×𝑛,𝑒𝑙𝑗	𝑒𝑙𝑗)𝑛×𝑛,𝑒𝑙𝑗	X
iajs-2833	74	62	=	=	SYM
iajs-2833	74	63	(	(	PUNCT
iajs-2833	74	64	𝑣2𝑗	𝑣2𝑗	NUM
iajs-2833	74	65	,	,	PUNCT
iajs-2833	74	66	𝑣1𝑙),𝐹	𝑣1𝑙),𝐹	PROPN
iajs-2833	74	67	=	=	SYM
iajs-2833	74	68	(	(	PUNCT
iajs-2833	74	69	𝑓𝑙𝑗)𝑛×𝑛	𝑓𝑙𝑗)𝑛×𝑛	ADJ
iajs-2833	74	70	,	,	PUNCT
iajs-2833	74	71	𝑓𝑙𝑗	𝑓𝑙𝑗	NOUN
iajs-2833	74	72	=	=	SYM
iajs-2833	74	73	(	(	PUNCT
iajs-2833	74	74	𝑣3𝑗	𝑣3𝑗	ADP
iajs-2833	74	75	,	,	PUNCT
iajs-2833	74	76	𝑣1𝑙),𝐺	𝑣1𝑙),𝐺	NOUN
iajs-2833	74	77	=	=	SYM
iajs-2833	74	78	(	(	PUNCT
iajs-2833	74	79	𝑔𝑙𝑗)𝑛×𝑛	𝑔𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	80	,	,	PUNCT
iajs-2833	74	81	𝑔𝑙𝑗	𝑔𝑙𝑗	NOUN
iajs-2833	74	82	=	=	SYM
iajs-2833	74	83	(	(	PUNCT
iajs-2833	74	84	𝑣3𝑗	𝑣3𝑗	ADP
iajs-2833	74	85	,	,	PUNCT
iajs-2833	74	86	𝑣2𝑙	𝑣2𝑙	NOUN
iajs-2833	74	87	)	)	PUNCT
iajs-2833	74	88	,	,	PUNCT
iajs-2833	74	89	𝐻	𝐻	PROPN
iajs-2833	74	90	=	=	SYM
iajs-2833	74	91	(	(	PUNCT
iajs-2833	74	92	ℎ𝑙𝑗)𝑛×𝑛	ℎ𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	93	,	,	PUNCT
iajs-2833	74	94	ℎ𝑙𝑗	ℎ𝑙𝑗	NOUN
iajs-2833	74	95	=	=	SYM
iajs-2833	74	96	(	(	PUNCT
iajs-2833	74	97	𝑣1𝑗	𝑣1𝑗	NOUN
iajs-2833	74	98	,	,	PUNCT
iajs-2833	74	99	𝑣2𝑙),𝑅	𝑣2𝑙),𝑅	PROPN
iajs-2833	74	100	=	=	SYM
iajs-2833	74	101	(	(	PUNCT
iajs-2833	74	102	𝑟𝑙𝑗)𝑛×𝑛	𝑟𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	103	,	,	PUNCT
iajs-2833	74	104	𝑟𝑙𝑗	𝑟𝑙𝑗	NOUN
iajs-2833	74	105	=	=	SYM
iajs-2833	74	106	(	(	PUNCT
iajs-2833	74	107	𝑣1𝑗	𝑣1𝑗	NOUN
iajs-2833	74	108	,	,	PUNCT
iajs-2833	74	109	𝑣3𝑙	𝑣3𝑙	NOUN
iajs-2833	74	110	)	)	PUNCT
iajs-2833	74	111	,	,	PUNCT
iajs-2833	74	112	𝑊	𝑊	PROPN
iajs-2833	74	113	=	=	SYM
iajs-2833	74	114	(	(	PUNCT
iajs-2833	74	115	𝑤𝑙𝑗)𝑛×𝑛	𝑤𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	116	,	,	PUNCT
iajs-2833	74	117	𝑤𝑙𝑗	𝑤𝑙𝑗	X
iajs-2833	74	118	=	=	SYM
iajs-2833	74	119	(	(	PUNCT
iajs-2833	74	120	𝑣2𝑗	𝑣2𝑗	NOUN
iajs-2833	74	121	,	,	PUNCT
iajs-2833	74	122	𝑣3𝑙	𝑣3𝑙	NOUN
iajs-2833	74	123	)	)	PUNCT
iajs-2833	74	124	,	,	PUNCT
iajs-2833	74	125	𝐾	𝐾	PROPN
iajs-2833	74	126	=	=	SYM
iajs-2833	74	127	(	(	PUNCT
iajs-2833	74	128	𝑘𝑙𝑗)𝑛×𝑛	𝑘𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	129	,	,	PUNCT
iajs-2833	74	130	𝑘𝑙𝑗	𝑘𝑙𝑗	X
iajs-2833	74	131	=	=	SYM
iajs-2833	74	132	(	(	PUNCT
iajs-2833	74	133	𝑣4𝑗	𝑣4𝑗	NOUN
iajs-2833	74	134	,	,	PUNCT
iajs-2833	74	135	𝑣1𝑙	𝑣1𝑙	NUM
iajs-2833	74	136	)	)	PUNCT
iajs-2833	74	137	,	,	PUNCT
iajs-2833	74	138	𝐷	𝐷	PROPN
iajs-2833	74	139	=	=	SYM
iajs-2833	74	140	(	(	PUNCT
iajs-2833	74	141	𝑑𝑙𝑗)𝑛×𝑛	𝑑𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	142	,	,	PUNCT
iajs-2833	74	143	𝑑𝑙𝑗	𝑑𝑙𝑗	NOUN
iajs-2833	74	144	=	=	SYM
iajs-2833	74	145	(	(	PUNCT
iajs-2833	74	146	𝑣4𝑗	𝑣4𝑗	NOUN
iajs-2833	74	147	,	,	PUNCT
iajs-2833	74	148	𝑣2𝑙	𝑣2𝑙	NOUN
iajs-2833	74	149	)	)	PUNCT
iajs-2833	74	150	,	,	PUNCT
iajs-2833	74	151	𝑍	𝑍	PROPN
iajs-2833	74	152	=	=	SYM
iajs-2833	74	153	(	(	PUNCT
iajs-2833	74	154	𝑧𝑙𝑗)𝑛×𝑛	𝑧𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	155	,	,	PUNCT
iajs-2833	74	156	𝑧𝑙𝑗	𝑧𝑙𝑗	NOUN
iajs-2833	74	157	=	=	SYM
iajs-2833	74	158	(	(	PUNCT
iajs-2833	74	159	𝑣4𝑗	𝑣4𝑗	NOUN
iajs-2833	74	160	,	,	PUNCT
iajs-2833	74	161	𝑣3𝑙	𝑣3𝑙	NOUN
iajs-2833	74	162	)	)	PUNCT
iajs-2833	74	163	,	,	PUNCT
iajs-2833	74	164	𝑇	𝑇	PROPN
iajs-2833	74	165	=	=	SYM
iajs-2833	74	166	(	(	PUNCT
iajs-2833	74	167	𝑡𝑙𝑗)𝑛×𝑛	𝑡𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	168	,	,	PUNCT
iajs-2833	74	169	𝑡𝑙𝑗	𝑡𝑙𝑗	PROPN
iajs-2833	74	170	=	=	SYM
iajs-2833	74	171	(	(	PUNCT
iajs-2833	74	172	𝑣1𝑗	𝑣1𝑗	NOUN
iajs-2833	74	173	,	,	PUNCT
iajs-2833	74	174	𝑣4𝑙	𝑣4𝑙	PROPN
iajs-2833	74	175	)	)	PUNCT
iajs-2833	74	176	,	,	PUNCT
iajs-2833	74	177	𝑀	𝑀	PROPN
iajs-2833	74	178	=	=	SYM
iajs-2833	74	179	(	(	PUNCT
iajs-2833	74	180	𝑚𝑙𝑗)𝑛×𝑛	𝑚𝑙𝑗)𝑛×𝑛	ADJ
iajs-2833	74	181	,	,	PUNCT
iajs-2833	74	182	𝑚𝑙𝑗	𝑚𝑙𝑗	NOUN
iajs-2833	74	183	=	=	SYM
iajs-2833	74	184	(	(	PUNCT
iajs-2833	74	185	𝑣2𝑗	𝑣2𝑗	NUM
iajs-2833	74	186	,	,	PUNCT
iajs-2833	74	187	𝑣4𝑙	𝑣4𝑙	PROPN
iajs-2833	74	188	)	)	PUNCT
iajs-2833	74	189	,	,	PUNCT
iajs-2833	74	190	𝑁	𝑁	PROPN
iajs-2833	74	191	=	=	SYM
iajs-2833	74	192	(	(	PUNCT
iajs-2833	74	193	𝑛𝑙𝑗)𝑛×𝑛	𝑛𝑙𝑗)𝑛×𝑛	PROPN
iajs-2833	74	194	,	,	PUNCT
iajs-2833	74	195	𝑛𝑙𝑗	𝑛𝑙𝑗	NOUN
iajs-2833	74	196	=	=	SYM
iajs-2833	74	197	(	(	PUNCT
iajs-2833	74	198	𝑣3𝑗	𝑣3𝑗	ADV
iajs-2833	74	199	,	,	PUNCT
iajs-2833	74	200	𝑣4𝑙),𝑏𝑙	𝑣4𝑙),𝑏𝑙	PRON
iajs-2833	74	201	=	=	PUNCT
iajs-2833	74	202	(	(	PUNCT
iajs-2833	74	203	𝑏𝑙𝑖	𝑏𝑙𝑖	PROPN
iajs-2833	74	204	)	)	PUNCT
iajs-2833	74	205	=	=	SYM
iajs-2833	74	206	(	(	PUNCT
iajs-2833	74	207	𝑏𝑙𝑖)𝑛×1	𝑏𝑙𝑖)𝑛×1	NOUN
iajs-2833	74	208	,	,	PUNCT
iajs-2833	74	209	𝑏𝑙𝑖	𝑏𝑙𝑖	NOUN
iajs-2833	74	210	=	=	SYM
iajs-2833	74	211	(	(	PUNCT
iajs-2833	74	212	𝑓𝑖(	𝑓𝑖(	NOUN
iajs-2833	74	213	�	�	NOUN
iajs-2833	74	214	̅	̅	NOUN
iajs-2833	74	215	�	�	NOUN
iajs-2833	74	216	𝑙	𝑙	NOUN
iajs-2833	74	217	𝑇(𝑥)𝐶𝑙(𝑡	𝑇(𝑥)𝐶𝑙(𝑡	PROPN
iajs-2833	74	218	)	)	PUNCT
iajs-2833	74	219	,	,	PUNCT
iajs-2833	74	220	𝑢𝑖	𝑢𝑖	INTJ
iajs-2833	74	221	)	)	PUNCT
iajs-2833	74	222	,	,	PUNCT
iajs-2833	74	223	𝑣𝑙𝑖	𝑣𝑙𝑖	NOUN
iajs-2833	74	224	)	)	PUNCT
iajs-2833	74	225	,	,	PUNCT
iajs-2833	74	226	𝑏𝑙	𝑏𝑙	PROPN
iajs-2833	74	227	𝑘	𝑘	X
iajs-2833	74	228	=	=	PUNCT
iajs-2833	74	229	(	(	PUNCT
iajs-2833	74	230	𝑏𝑙𝑗	𝑏𝑙𝑗	PROPN
iajs-2833	74	231	𝑘	𝑘	PROPN
iajs-2833	74	232	)	)	PUNCT
iajs-2833	74	233	,	,	PUNCT
iajs-2833	74	234	𝑏𝑙𝑗	𝑏𝑙𝑗	PROPN
iajs-2833	74	235	0	0	PUNCT
iajs-2833	75	1	=	=	SYM
iajs-2833	75	2	(	(	PUNCT
iajs-2833	75	3	𝑦𝑙	𝑦𝑙	ADP
iajs-2833	75	4	𝑘	𝑘	PROPN
iajs-2833	75	5	,	,	PUNCT
iajs-2833	75	6	𝑣𝑙𝑗	𝑣𝑙𝑗	NOUN
iajs-2833	75	7	)	)	PUNCT
iajs-2833	75	8	,	,	PUNCT
iajs-2833	75	9	𝐶𝑖(𝑡	𝐶𝑖(𝑡	NUM
iajs-2833	75	10	)	)	PUNCT
iajs-2833	75	11	=	=	SYM
iajs-2833	75	12	(	(	PUNCT
iajs-2833	75	13	𝐶𝑖𝑗(𝑡))𝑛×1	𝐶𝑖𝑗(𝑡))𝑛×1	NOUN
iajs-2833	75	14	,	,	PUNCT
iajs-2833	75	15	𝐷𝑖(0	𝐷𝑖(0	NOUN
iajs-2833	75	16	)	)	PUNCT
iajs-2833	75	17	=	=	SYM
iajs-2833	75	18	(	(	PUNCT
iajs-2833	75	19	𝑑𝑖𝑗(0))𝑛×1	𝑑𝑖𝑗(0))𝑛×1	NUM
iajs-2833	75	20	,	,	PUNCT
iajs-2833	75	21	𝐶𝑖(0	𝐶𝑖(0	NOUN
iajs-2833	75	22	)	)	PUNCT
iajs-2833	75	23	=	=	PUNCT
iajs-2833	75	24	(	(	PUNCT
iajs-2833	75	25	𝐶𝑖𝑗(0))𝑛×1	𝐶𝑖𝑗(0))𝑛×1	PROPN
iajs-2833	75	26	,	,	PUNCT
iajs-2833	75	27	𝐷𝑖(𝑡	𝐷𝑖(𝑡	NOUN
iajs-2833	75	28	)	)	PUNCT
iajs-2833	75	29	=	=	PUNCT
iajs-2833	75	30	(	(	PUNCT
iajs-2833	75	31	𝑑𝑖𝑗(𝑡))𝑛×1	𝑑𝑖𝑗(𝑡))𝑛×1	NUM
iajs-2833	75	32	.	.	PUNCT
iajs-2833	75	33	then	then	ADV
iajs-2833	75	34	corresponding	correspond	VERB
iajs-2833	75	35	to	to	ADP
iajs-2833	75	36	the	the	DET
iajs-2833	75	37	sequence	sequence	NOUN
iajs-2833	75	38	{	{	PUNCT
iajs-2833	75	39	�	�	PROPN
iajs-2833	75	40	⃗	⃗	NOUN
iajs-2833	75	41	�	�	NOUN
iajs-2833	75	42	𝑛	𝑛	NOUN
iajs-2833	75	43	}	}	PUNCT
iajs-2833	75	44	,	,	PUNCT
iajs-2833	75	45	the	the	DET
iajs-2833	75	46	following	follow	VERB
iajs-2833	75	47	approximation	approximation	NOUN
iajs-2833	75	48	problems	problem	NOUN
iajs-2833	75	49	are	be	AUX
iajs-2833	75	50	held	hold	VERB
iajs-2833	75	51	,	,	PUNCT
iajs-2833	75	52	i.e.	i.e.	X
iajs-2833	75	53	for	for	ADP
iajs-2833	75	54	each	each	DET
iajs-2833	75	55	�	�	PROPN
iajs-2833	75	56	⃗	⃗	NOUN
iajs-2833	75	57	�	�	NOUN
iajs-2833	75	58	𝑛	𝑛	NOUN
iajs-2833	75	59	=	=	PUNCT
iajs-2833	75	60	(	(	PUNCT
iajs-2833	75	61	𝑣1𝑛	𝑣1𝑛	X
iajs-2833	75	62	,	,	PUNCT
iajs-2833	75	63	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	75	64	,	,	PUNCT
iajs-2833	75	65	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	75	66	,	,	PUNCT
iajs-2833	75	67	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	75	68	)	)	PUNCT
iajs-2833	75	69	⊂	⊂	PROPN
iajs-2833	76	1	𝑉𝑛	𝑉𝑛	PROPN
iajs-2833	76	2	⃗⃗	⃗⃗	PROPN
iajs-2833	76	3	⃗⃗	⃗⃗	PROPN
iajs-2833	76	4	,	,	PUNCT
iajs-2833	76	5	and	and	CCONJ
iajs-2833	76	6	𝑛	𝑛	PRON
iajs-2833	76	7	=	=	SYM
iajs-2833	76	8	1,2	1,2	NUM
iajs-2833	76	9	,	,	PUNCT
iajs-2833	76	10	…	…	PUNCT
iajs-2833	76	11	(	(	PUNCT
iajs-2833	76	12	𝑦1𝑛𝑡𝑡	𝑦1𝑛𝑡𝑡	NOUN
iajs-2833	76	13	,	,	PUNCT
iajs-2833	76	14	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	76	15	)	)	PUNCT
iajs-2833	77	1	+	+	CCONJ
iajs-2833	77	2	(	(	PUNCT
iajs-2833	77	3	∇𝑦1𝑛	∇𝑦1𝑛	ADJ
iajs-2833	77	4	,	,	PUNCT
iajs-2833	77	5	∇𝑣1𝑛	∇𝑣1𝑛	ADV
iajs-2833	77	6	)	)	PUNCT
iajs-2833	78	1	+	+	CCONJ
iajs-2833	78	2	(	(	PUNCT
iajs-2833	78	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	78	4	,	,	PUNCT
iajs-2833	78	5	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	6	)	)	PUNCT
iajs-2833	78	7	−	−	PROPN
iajs-2833	78	8	(	(	PUNCT
iajs-2833	78	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	78	10	,	,	PUNCT
iajs-2833	78	11	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	12	)	)	PUNCT
iajs-2833	78	13	+	+	CCONJ
iajs-2833	78	14	(	(	PUNCT
iajs-2833	78	15	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	78	16	,	,	PUNCT
iajs-2833	78	17	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	18	)	)	PUNCT
iajs-2833	78	19	+	+	CCONJ
iajs-2833	78	20	(	(	PUNCT
iajs-2833	78	21	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	78	22	,	,	PUNCT
iajs-2833	78	23	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	24	)	)	PUNCT
iajs-2833	78	25	=	=	SYM
iajs-2833	78	26	(	(	PUNCT
iajs-2833	78	27	𝑓1(𝑦1𝑛	𝑓1(𝑦1𝑛	NOUN
iajs-2833	78	28	,	,	PUNCT
iajs-2833	78	29	𝑢1	𝑢1	PROPN
iajs-2833	78	30	)	)	PUNCT
iajs-2833	78	31	,	,	PUNCT
iajs-2833	78	32	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	33	)	)	PUNCT
iajs-2833	78	34	(	(	PUNCT
iajs-2833	78	35	28	28	NUM
iajs-2833	78	36	)	)	PUNCT
iajs-2833	78	37	(	(	PUNCT
iajs-2833	78	38	𝑦1𝑛	𝑦1𝑛	NOUN
iajs-2833	78	39	0	0	NUM
iajs-2833	78	40	,	,	PUNCT
iajs-2833	78	41	𝑣1𝑛	𝑣1𝑛	NOUN
iajs-2833	78	42	)	)	PUNCT
iajs-2833	78	43	=	=	SYM
iajs-2833	78	44	(	(	PUNCT
iajs-2833	78	45	𝑦1	𝑦1	PROPN
iajs-2833	78	46	0	0	NUM
iajs-2833	78	47	,	,	PUNCT
iajs-2833	78	48	𝑣1𝑛	𝑣1𝑛	NOUN
iajs-2833	78	49	)	)	PUNCT
iajs-2833	78	50	,	,	PUNCT
iajs-2833	78	51	and	and	CCONJ
iajs-2833	78	52	(	(	PUNCT
iajs-2833	78	53	𝑦1𝑛	𝑦1𝑛	NOUN
iajs-2833	78	54	1	1	NUM
iajs-2833	78	55	,	,	PUNCT
iajs-2833	78	56	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	57	)	)	PUNCT
iajs-2833	78	58	=	=	SYM
iajs-2833	78	59	(	(	PUNCT
iajs-2833	78	60	𝑦1	𝑦1	PROPN
iajs-2833	78	61	1	1	NUM
iajs-2833	78	62	,	,	PUNCT
iajs-2833	78	63	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	78	64	)	)	PUNCT
iajs-2833	78	65	(	(	PUNCT
iajs-2833	78	66	29	29	NUM
iajs-2833	78	67	)	)	PUNCT
iajs-2833	78	68	(	(	PUNCT
iajs-2833	78	69	𝑦2𝑛𝑡𝑡	𝑦2𝑛𝑡𝑡	NOUN
iajs-2833	78	70	,	,	PUNCT
iajs-2833	78	71	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	78	72	)	)	PUNCT
iajs-2833	78	73	+	+	CCONJ
iajs-2833	78	74	(	(	PUNCT
iajs-2833	78	75	∇𝑦2𝑛	∇𝑦2𝑛	NOUN
iajs-2833	78	76	,	,	PUNCT
iajs-2833	78	77	∇𝑣2𝑛	∇𝑣2𝑛	NOUN
iajs-2833	78	78	)	)	PUNCT
iajs-2833	78	79	+	+	CCONJ
iajs-2833	78	80	(	(	PUNCT
iajs-2833	78	81	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	78	82	,	,	PUNCT
iajs-2833	78	83	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	78	84	)	)	PUNCT
iajs-2833	78	85	+	+	CCONJ
iajs-2833	78	86	(	(	PUNCT
iajs-2833	78	87	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	78	88	,	,	PUNCT
iajs-2833	78	89	𝑣2	𝑣2	NOUN
iajs-2833	78	90	)	)	PUNCT
iajs-2833	78	91	−	−	PROPN
iajs-2833	78	92	(	(	PUNCT
iajs-2833	78	93	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	78	94	,	,	PUNCT
iajs-2833	78	95	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	78	96	)	)	PUNCT
iajs-2833	78	97	−	−	PROPN
iajs-2833	78	98	(	(	PUNCT
iajs-2833	78	99	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	78	100	,	,	PUNCT
iajs-2833	78	101	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	78	102	)	)	PUNCT
iajs-2833	78	103	=	=	NOUN
iajs-2833	78	104	(	(	PUNCT
iajs-2833	78	105	𝑓2(𝑦2𝑛	𝑓2(𝑦2𝑛	NOUN
iajs-2833	78	106	,	,	PUNCT
iajs-2833	78	107	𝑢2	𝑢2	PROPN
iajs-2833	78	108	)	)	PUNCT
iajs-2833	78	109	,	,	PUNCT
iajs-2833	78	110	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	78	111	)	)	PUNCT
iajs-2833	78	112	(	(	PUNCT
iajs-2833	78	113	30	30	NUM
iajs-2833	78	114	)	)	PUNCT
iajs-2833	78	115	(	(	PUNCT
iajs-2833	78	116	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	78	117	0	0	NUM
iajs-2833	78	118	,	,	PUNCT
iajs-2833	78	119	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	78	120	)	)	PUNCT
iajs-2833	78	121	=	=	SYM
iajs-2833	78	122	(	(	PUNCT
iajs-2833	78	123	𝑦1	𝑦1	NOUN
iajs-2833	78	124	0	0	NUM
iajs-2833	78	125	,	,	PUNCT
iajs-2833	78	126	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	78	127	)	)	PUNCT
iajs-2833	78	128	,	,	PUNCT
iajs-2833	78	129	and	and	CCONJ
iajs-2833	78	130	(	(	PUNCT
iajs-2833	78	131	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	78	132	1	1	NUM
iajs-2833	78	133	,	,	PUNCT
iajs-2833	78	134	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	78	135	)	)	PUNCT
iajs-2833	78	136	=	=	PUNCT
iajs-2833	79	1	(	(	PUNCT
iajs-2833	79	2	𝑦1	𝑦1	NOUN
iajs-2833	79	3	1	1	NUM
iajs-2833	79	4	,	,	PUNCT
iajs-2833	79	5	𝑣2𝑛	𝑣2𝑛	PROPN
iajs-2833	79	6	)	)	PUNCT
iajs-2833	79	7	(	(	PUNCT
iajs-2833	79	8	31	31	NUM
iajs-2833	79	9	)	)	PUNCT
iajs-2833	79	10	(	(	PUNCT
iajs-2833	79	11	𝑦3𝑛𝑡𝑡	𝑦3𝑛𝑡𝑡	PROPN
iajs-2833	79	12	,	,	PUNCT
iajs-2833	79	13	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	14	)	)	PUNCT
iajs-2833	79	15	+	+	CCONJ
iajs-2833	79	16	(	(	PUNCT
iajs-2833	79	17	∇𝑦3𝑛	∇𝑦3𝑛	ADJ
iajs-2833	79	18	,	,	PUNCT
iajs-2833	79	19	∇𝑣3𝑛	∇𝑣3𝑛	PROPN
iajs-2833	79	20	)	)	PUNCT
iajs-2833	79	21	−	−	PROPN
iajs-2833	79	22	(	(	PUNCT
iajs-2833	79	23	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	79	24	,	,	PUNCT
iajs-2833	79	25	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	26	)	)	PUNCT
iajs-2833	79	27	+	+	CCONJ
iajs-2833	79	28	(	(	PUNCT
iajs-2833	79	29	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	79	30	,	,	PUNCT
iajs-2833	79	31	𝑣3𝑛	𝑣3𝑛	NUM
iajs-2833	79	32	)	)	PUNCT
iajs-2833	79	33	+	+	CCONJ
iajs-2833	79	34	(	(	PUNCT
iajs-2833	79	35	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	79	36	,	,	PUNCT
iajs-2833	79	37	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	38	)	)	PUNCT
iajs-2833	79	39	+	+	CCONJ
iajs-2833	79	40	(	(	PUNCT
iajs-2833	79	41	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	79	42	,	,	PUNCT
iajs-2833	79	43	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	44	)	)	PUNCT
iajs-2833	79	45	=	=	SYM
iajs-2833	79	46	(	(	PUNCT
iajs-2833	79	47	𝑓3(𝑦3𝑛	𝑓3(𝑦3𝑛	NOUN
iajs-2833	79	48	,	,	PUNCT
iajs-2833	79	49	𝑢3	𝑢3	NOUN
iajs-2833	79	50	)	)	PUNCT
iajs-2833	79	51	,	,	PUNCT
iajs-2833	79	52	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	53	)	)	PUNCT
iajs-2833	79	54	(	(	PUNCT
iajs-2833	79	55	32	32	NUM
iajs-2833	79	56	)	)	PUNCT
iajs-2833	79	57	(	(	PUNCT
iajs-2833	79	58	𝑦3𝑛	𝑦3𝑛	X
iajs-2833	79	59	0	0	NUM
iajs-2833	79	60	,	,	PUNCT
iajs-2833	79	61	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	62	)	)	PUNCT
iajs-2833	79	63	=	=	PUNCT
iajs-2833	79	64	(	(	PUNCT
iajs-2833	79	65	𝑦3	𝑦3	PROPN
iajs-2833	79	66	0	0	NUM
iajs-2833	79	67	,	,	PUNCT
iajs-2833	79	68	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	69	)	)	PUNCT
iajs-2833	79	70	,	,	PUNCT
iajs-2833	79	71	and	and	CCONJ
iajs-2833	79	72	(	(	PUNCT
iajs-2833	79	73	𝑦3𝑛	𝑦3𝑛	X
iajs-2833	79	74	1	1	NUM
iajs-2833	79	75	,	,	PUNCT
iajs-2833	79	76	𝑣3	𝑣3	ADJ
iajs-2833	79	77	)	)	PUNCT
iajs-2833	79	78	=	=	SYM
iajs-2833	79	79	(	(	PUNCT
iajs-2833	79	80	𝑦3	𝑦3	PROPN
iajs-2833	79	81	1	1	NUM
iajs-2833	79	82	,	,	PUNCT
iajs-2833	79	83	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	79	84	)	)	PUNCT
iajs-2833	79	85	(	(	PUNCT
iajs-2833	79	86	33	33	NUM
iajs-2833	79	87	)	)	PUNCT
iajs-2833	79	88	(	(	PUNCT
iajs-2833	79	89	𝑦4𝑛𝑡𝑡	𝑦4𝑛𝑡𝑡	PROPN
iajs-2833	79	90	,	,	PUNCT
iajs-2833	79	91	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	92	)	)	PUNCT
iajs-2833	79	93	+	+	CCONJ
iajs-2833	79	94	(	(	PUNCT
iajs-2833	79	95	∇𝑦4𝑛	∇𝑦4𝑛	ADV
iajs-2833	79	96	,	,	PUNCT
iajs-2833	79	97	∇𝑣4𝑛	∇𝑣4𝑛	NUM
iajs-2833	79	98	)	)	PUNCT
iajs-2833	79	99	−	−	PROPN
iajs-2833	79	100	(	(	PUNCT
iajs-2833	79	101	𝑦1𝑛	𝑦1𝑛	PROPN
iajs-2833	79	102	,	,	PUNCT
iajs-2833	79	103	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	104	)	)	PUNCT
iajs-2833	79	105	+	+	CCONJ
iajs-2833	79	106	(	(	PUNCT
iajs-2833	79	107	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	79	108	,	,	PUNCT
iajs-2833	79	109	𝑣4𝑛	𝑣4𝑛	NOUN
iajs-2833	79	110	)	)	PUNCT
iajs-2833	79	111	−	−	PROPN
iajs-2833	79	112	(	(	PUNCT
iajs-2833	79	113	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	79	114	,	,	PUNCT
iajs-2833	79	115	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	116	)	)	PUNCT
iajs-2833	79	117	+	+	CCONJ
iajs-2833	79	118	(	(	PUNCT
iajs-2833	79	119	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	79	120	,	,	PUNCT
iajs-2833	79	121	𝑣4𝑛	𝑣4𝑛	X
iajs-2833	79	122	)	)	PUNCT
iajs-2833	79	123	=	=	SYM
iajs-2833	79	124	(	(	PUNCT
iajs-2833	79	125	𝑓4(𝑦4𝑛	𝑓4(𝑦4𝑛	ADJ
iajs-2833	79	126	,	,	PUNCT
iajs-2833	79	127	𝑢4	𝑢4	NOUN
iajs-2833	79	128	)	)	PUNCT
iajs-2833	79	129	,	,	PUNCT
iajs-2833	79	130	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	131	)	)	PUNCT
iajs-2833	79	132	(	(	PUNCT
iajs-2833	79	133	34	34	NUM
iajs-2833	79	134	)	)	PUNCT
iajs-2833	79	135	(	(	PUNCT
iajs-2833	79	136	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	79	137	0	0	NUM
iajs-2833	79	138	,	,	PUNCT
iajs-2833	79	139	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	140	)	)	PUNCT
iajs-2833	79	141	=	=	PUNCT
iajs-2833	79	142	(	(	PUNCT
iajs-2833	79	143	𝑦4	𝑦4	PROPN
iajs-2833	79	144	0	0	NUM
iajs-2833	79	145	,	,	PUNCT
iajs-2833	79	146	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	147	)	)	PUNCT
iajs-2833	79	148	,	,	PUNCT
iajs-2833	79	149	and	and	CCONJ
iajs-2833	79	150	(	(	PUNCT
iajs-2833	79	151	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	79	152	1	1	NUM
iajs-2833	79	153	,	,	PUNCT
iajs-2833	79	154	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	155	)	)	PUNCT
iajs-2833	79	156	=	=	PUNCT
iajs-2833	79	157	(	(	PUNCT
iajs-2833	79	158	𝑦4	𝑦4	PROPN
iajs-2833	79	159	1	1	NUM
iajs-2833	79	160	,	,	PUNCT
iajs-2833	79	161	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	79	162	)	)	PUNCT
iajs-2833	79	163	(	(	PUNCT
iajs-2833	79	164	35	35	NUM
iajs-2833	79	165	)	)	PUNCT
iajs-2833	79	166	ihjpas	ihjpa	NOUN
iajs-2833	79	167	.	.	PUNCT
iajs-2833	80	1	53	53	NUM
iajs-2833	80	2	(	(	PUNCT
iajs-2833	80	3	3)2022	3)2022	PROPN
iajs-2833	80	4	165	165	NUM
iajs-2833	80	5	which	which	PRON
iajs-2833	80	6	have	have	VERB
iajs-2833	80	7	a	a	DET
iajs-2833	80	8	sequence	sequence	NOUN
iajs-2833	80	9	of	of	ADP
iajs-2833	80	10	unique	unique	ADJ
iajs-2833	80	11	solutions	solution	NOUN
iajs-2833	80	12	{	{	PUNCT
iajs-2833	80	13	�	�	PROPN
iajs-2833	80	14	⃗	⃗	NOUN
iajs-2833	80	15	�	�	NOUN
iajs-2833	80	16	𝑛	𝑛	NOUN
iajs-2833	80	17	}	}	PUNCT
iajs-2833	80	18	.	.	PUNCT
iajs-2833	81	1	substituting	substitute	VERB
iajs-2833	81	2	𝑣𝑖𝑛	𝑣𝑖𝑛	NOUN
iajs-2833	81	3	=	=	SYM
iajs-2833	81	4	𝑦𝑖𝑛𝑡	𝑦𝑖𝑛𝑡	ADJ
iajs-2833	81	5	,	,	PUNCT
iajs-2833	81	6	for	for	ADP
iajs-2833	81	7	𝑖	𝑖	DET
iajs-2833	81	8	=	=	SYM
iajs-2833	81	9	1,2,3,4	1,2,3,4	NUM
iajs-2833	81	10	in	in	ADP
iajs-2833	81	11	(	(	PUNCT
iajs-2833	81	12	28	28	NUM
iajs-2833	81	13	)	)	PUNCT
iajs-2833	81	14	,	,	PUNCT
iajs-2833	81	15	(	(	PUNCT
iajs-2833	81	16	30	30	NUM
iajs-2833	81	17	)	)	PUNCT
iajs-2833	81	18	,	,	PUNCT
iajs-2833	81	19	(	(	PUNCT
iajs-2833	81	20	32	32	NUM
iajs-2833	81	21	)	)	PUNCT
iajs-2833	81	22	and	and	CCONJ
iajs-2833	81	23	(	(	PUNCT
iajs-2833	81	24	34	34	NUM
iajs-2833	81	25	)	)	PUNCT
iajs-2833	81	26	resp	resp	NOUN
iajs-2833	81	27	.	.	PUNCT
iajs-2833	82	1	,	,	PUNCT
iajs-2833	82	2	using	use	VERB
iajs-2833	82	3	lemma	lemma	PROPN
iajs-2833	82	4	1.2	1.2	NUM
iajs-2833	82	5	in	in	ADP
iajs-2833	82	6	[	[	X
iajs-2833	82	7	15	15	NUM
iajs-2833	82	8	]	]	PUNCT
iajs-2833	82	9	for	for	ADP
iajs-2833	82	10	the	the	DET
iajs-2833	82	11	1st	1st	ADJ
iajs-2833	82	12	terms	term	NOUN
iajs-2833	82	13	of	of	ADP
iajs-2833	82	14	the	the	DET
iajs-2833	82	15	lhs	lhs	PROPN
iajs-2833	82	16	of	of	ADP
iajs-2833	82	17	each	each	DET
iajs-2833	82	18	equality	equality	NOUN
iajs-2833	82	19	,	,	PUNCT
iajs-2833	82	20	then	then	ADV
iajs-2833	82	21	adding	add	VERB
iajs-2833	82	22	the	the	DET
iajs-2833	82	23	resulting	result	VERB
iajs-2833	82	24	equation	equation	NOUN
iajs-2833	82	25	,	,	PUNCT
iajs-2833	82	26	to	to	PART
iajs-2833	82	27	get	get	VERB
iajs-2833	82	28	𝑑	𝑑	PRON
iajs-2833	82	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	82	30	[	[	X
iajs-2833	82	31	∥	∥	PROPN
iajs-2833	82	32	�	�	NOUN
iajs-2833	82	33	⃗	⃗	NOUN
iajs-2833	82	34	�	�	PROPN
iajs-2833	82	35	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	82	36	∥0	∥0	NOUN
iajs-2833	82	37	2	2	NUM
iajs-2833	82	38	+	+	CCONJ
iajs-2833	82	39	𝑑	𝑑	VERB
iajs-2833	82	40	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	82	41	∥	∥	PROPN
iajs-2833	82	42	�	�	NOUN
iajs-2833	82	43	⃗	⃗	NOUN
iajs-2833	82	44	�	�	NOUN
iajs-2833	82	45	𝑛	𝑛	VERB
iajs-2833	82	46	∥1	∥1	PRON
iajs-2833	82	47	2	2	NUM
iajs-2833	82	48	]	]	PUNCT
iajs-2833	82	49	=	=	SYM
iajs-2833	82	50	2[(𝑦2𝑛	2[(𝑦2𝑛	NUM
iajs-2833	82	51	,	,	PUNCT
iajs-2833	82	52	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	82	53	)	)	PUNCT
iajs-2833	82	54	−	−	PROPN
iajs-2833	82	55	(	(	PUNCT
iajs-2833	82	56	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	82	57	,	,	PUNCT
iajs-2833	82	58	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	82	59	)	)	PUNCT
iajs-2833	82	60	−	−	PROPN
iajs-2833	82	61	(	(	PUNCT
iajs-2833	82	62	𝑦4𝑛	𝑦4𝑛	NOUN
iajs-2833	82	63	,	,	PUNCT
iajs-2833	82	64	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	82	65	)	)	PUNCT
iajs-2833	82	66	−	−	PROPN
iajs-2833	82	67	(	(	PUNCT
iajs-2833	82	68	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	82	69	,	,	PUNCT
iajs-2833	82	70	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	82	71	)	)	PUNCT
iajs-2833	82	72	+	+	CCONJ
iajs-2833	82	73	(	(	PUNCT
iajs-2833	82	74	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	82	75	,	,	PUNCT
iajs-2833	82	76	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	82	77	)	)	PUNCT
iajs-2833	82	78	+	+	CCONJ
iajs-2833	82	79	(	(	PUNCT
iajs-2833	82	80	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	82	81	,	,	PUNCT
iajs-2833	82	82	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	82	83	)	)	PUNCT
iajs-2833	82	84	+	+	CCONJ
iajs-2833	82	85	(	(	PUNCT
iajs-2833	82	86	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	82	87	,	,	PUNCT
iajs-2833	82	88	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	82	89	)	)	PUNCT
iajs-2833	82	90	−	−	PROPN
iajs-2833	82	91	(	(	PUNCT
iajs-2833	82	92	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	82	93	,	,	PUNCT
iajs-2833	82	94	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	82	95	)	)	PUNCT
iajs-2833	82	96	−	−	PROPN
iajs-2833	82	97	(	(	PUNCT
iajs-2833	82	98	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	82	99	,	,	PUNCT
iajs-2833	82	100	𝑦3𝑛𝑡	𝑦3𝑛𝑡	X
iajs-2833	82	101	)	)	PUNCT
iajs-2833	83	1	+	+	CCONJ
iajs-2833	83	2	(	(	PUNCT
iajs-2833	83	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	83	4	,	,	PUNCT
iajs-2833	83	5	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	83	6	)	)	PUNCT
iajs-2833	83	7	−	−	PROPN
iajs-2833	83	8	(	(	PUNCT
iajs-2833	83	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	83	10	,	,	PUNCT
iajs-2833	83	11	𝑦4𝑛𝑡	𝑦4𝑛𝑡	PUNCT
iajs-2833	83	12	)	)	PUNCT
iajs-2833	84	1	+	+	CCONJ
iajs-2833	84	2	(	(	PUNCT
iajs-2833	84	3	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	84	4	,	,	PUNCT
iajs-2833	84	5	𝑦4𝑛𝑡)+(𝑓1(𝑦1𝑛	𝑦4𝑛𝑡)+(𝑓1(𝑦1𝑛	PROPN
iajs-2833	84	6	,	,	PUNCT
iajs-2833	84	7	𝑢1	𝑢1	PROPN
iajs-2833	84	8	)	)	PUNCT
iajs-2833	84	9	,	,	PUNCT
iajs-2833	84	10	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADV
iajs-2833	84	11	)	)	PUNCT
iajs-2833	84	12	+	+	CCONJ
iajs-2833	84	13	(	(	PUNCT
iajs-2833	84	14	𝑓2(𝑦2𝑛	𝑓2(𝑦2𝑛	NOUN
iajs-2833	84	15	,	,	PUNCT
iajs-2833	84	16	𝑢2	𝑢2	PROPN
iajs-2833	84	17	)	)	PUNCT
iajs-2833	84	18	,	,	PUNCT
iajs-2833	84	19	𝑦2𝑛𝑡	𝑦2𝑛𝑡	VERB
iajs-2833	84	20	)	)	PUNCT
iajs-2833	84	21	+	+	CCONJ
iajs-2833	84	22	(	(	PUNCT
iajs-2833	84	23	𝑓3(𝑦3𝑛	𝑓3(𝑦3𝑛	NOUN
iajs-2833	84	24	,	,	PUNCT
iajs-2833	84	25	𝑢3	𝑢3	NOUN
iajs-2833	84	26	)	)	PUNCT
iajs-2833	84	27	,	,	PUNCT
iajs-2833	84	28	𝑦3𝑛𝑡	𝑦3𝑛𝑡	X
iajs-2833	84	29	)	)	PUNCT
iajs-2833	84	30	+	+	CCONJ
iajs-2833	84	31	(	(	PUNCT
iajs-2833	84	32	𝑓4(𝑦4𝑛	𝑓4(𝑦4𝑛	ADJ
iajs-2833	84	33	,	,	PUNCT
iajs-2833	84	34	𝑢4	𝑢4	NOUN
iajs-2833	84	35	)	)	PUNCT
iajs-2833	84	36	,	,	PUNCT
iajs-2833	84	37	𝑦4𝑛𝑡	𝑦4𝑛𝑡	PROPN
iajs-2833	84	38	)	)	PUNCT
iajs-2833	84	39	]	]	PUNCT
iajs-2833	85	1	(	(	PUNCT
iajs-2833	85	2	36	36	X
iajs-2833	85	3	)	)	PUNCT
iajs-2833	85	4	taking	take	VERB
iajs-2833	85	5	the	the	DET
iajs-2833	85	6	absolute	absolute	ADJ
iajs-2833	85	7	value	value	NOUN
iajs-2833	85	8	for	for	ADP
iajs-2833	85	9	both	both	DET
iajs-2833	85	10	sides	side	NOUN
iajs-2833	85	11	,	,	PUNCT
iajs-2833	85	12	we	we	PRON
iajs-2833	85	13	get	get	VERB
iajs-2833	85	14	:	:	PUNCT
iajs-2833	85	15	𝑑	𝑑	NOUN
iajs-2833	85	16	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	85	17	[	[	X
iajs-2833	85	18	∥	∥	PROPN
iajs-2833	85	19	�	�	NOUN
iajs-2833	85	20	⃗	⃗	NOUN
iajs-2833	85	21	�	�	PROPN
iajs-2833	85	22	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	85	23	∥0	∥0	NOUN
iajs-2833	85	24	2+∥	2+∥	NUM
iajs-2833	85	25	�	�	PROPN
iajs-2833	85	26	⃗	⃗	NOUN
iajs-2833	85	27	�	�	NOUN
iajs-2833	85	28	𝑛	𝑛	VERB
iajs-2833	85	29	∥1	∥1	PRON
iajs-2833	85	30	2	2	NUM
iajs-2833	85	31	]	]	PUNCT
iajs-2833	85	32	≤	≤	NUM
iajs-2833	85	33	2[∣	2[∣	PROPN
iajs-2833	85	34	(	(	PUNCT
iajs-2833	85	35	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	85	36	,	,	PUNCT
iajs-2833	85	37	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	85	38	)	)	PUNCT
iajs-2833	85	39	∣	∣	ADJ
iajs-2833	85	40	+	+	PROPN
iajs-2833	85	41	∣	∣	PROPN
iajs-2833	85	42	(	(	PUNCT
iajs-2833	85	43	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	85	44	,	,	PUNCT
iajs-2833	85	45	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	85	46	)	)	PUNCT
iajs-2833	85	47	∣	∣	ADJ
iajs-2833	85	48	+	+	PROPN
iajs-2833	85	49	∣	∣	ADJ
iajs-2833	85	50	(	(	PUNCT
iajs-2833	85	51	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	85	52	,	,	PUNCT
iajs-2833	85	53	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	85	54	)	)	PUNCT
iajs-2833	85	55	∣	∣	ADJ
iajs-2833	85	56	+	+	NOUN
iajs-2833	85	57	∣(𝑦1𝑛	∣(𝑦1𝑛	ADJ
iajs-2833	85	58	,	,	PUNCT
iajs-2833	85	59	𝑦2𝑛𝑡)∣	𝑦2𝑛𝑡)∣	PROPN
iajs-2833	85	60	+	+	PROPN
iajs-2833	85	61	∣(𝑦3𝑛	∣(𝑦3𝑛	PROPN
iajs-2833	85	62	,	,	PUNCT
iajs-2833	85	63	𝑦2𝑛𝑡)∣+∣(𝑦4𝑛	𝑦2𝑛𝑡)∣+∣(𝑦4𝑛	NUM
iajs-2833	85	64	,	,	PUNCT
iajs-2833	85	65	𝑦2𝑛𝑡)∣+∣(𝑦1𝑛	𝑦2𝑛𝑡)∣+∣(𝑦1𝑛	ADJ
iajs-2833	85	66	,	,	PUNCT
iajs-2833	85	67	𝑦3𝑛𝑡)∣+∣(𝑦2𝑛	𝑦3𝑛𝑡)∣+∣(𝑦2𝑛	NOUN
iajs-2833	85	68	,	,	PUNCT
iajs-2833	85	69	𝑦3𝑛𝑡)∣+∣	𝑦3𝑛𝑡)∣+∣	PRON
iajs-2833	85	70	(	(	PUNCT
iajs-2833	85	71	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	85	72	,	,	PUNCT
iajs-2833	85	73	𝑦3𝑛𝑡	𝑦3𝑛𝑡	X
iajs-2833	85	74	)	)	PUNCT
iajs-2833	85	75	∣	∣	PROPN
iajs-2833	85	76	+	+	PROPN
iajs-2833	85	77	∣	∣	ADJ
iajs-2833	85	78	(	(	PUNCT
iajs-2833	85	79	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	85	80	,	,	PUNCT
iajs-2833	85	81	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	85	82	)	)	PUNCT
iajs-2833	85	83	∣	∣	PROPN
iajs-2833	85	84	+	+	PROPN
iajs-2833	85	85	∣	∣	ADJ
iajs-2833	85	86	(	(	PUNCT
iajs-2833	85	87	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	85	88	,	,	PUNCT
iajs-2833	85	89	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	85	90	)	)	PUNCT
iajs-2833	85	91	∣	∣	PROPN
iajs-2833	85	92	+	+	PROPN
iajs-2833	85	93	∣	∣	PROPN
iajs-2833	85	94	(	(	PUNCT
iajs-2833	85	95	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	85	96	,	,	PUNCT
iajs-2833	85	97	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	85	98	)	)	PUNCT
iajs-2833	85	99	∣	∣	PROPN
iajs-2833	85	100	+	+	PROPN
iajs-2833	85	101	∣	∣	ADJ
iajs-2833	85	102	(	(	PUNCT
iajs-2833	85	103	𝑓1(𝑦1𝑛	𝑓1(𝑦1𝑛	NOUN
iajs-2833	85	104	,	,	PUNCT
iajs-2833	85	105	𝑢1	𝑢1	PROPN
iajs-2833	85	106	)	)	PUNCT
iajs-2833	85	107	,	,	PUNCT
iajs-2833	85	108	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADV
iajs-2833	85	109	)	)	PUNCT
iajs-2833	85	110	∣	∣	ADJ
iajs-2833	85	111	+	+	PROPN
iajs-2833	85	112	∣	∣	ADJ
iajs-2833	85	113	(	(	PUNCT
iajs-2833	85	114	𝑓2(𝑦2𝑛	𝑓2(𝑦2𝑛	NOUN
iajs-2833	85	115	,	,	PUNCT
iajs-2833	85	116	𝑢2	𝑢2	PROPN
iajs-2833	85	117	)	)	PUNCT
iajs-2833	85	118	,	,	PUNCT
iajs-2833	85	119	𝑦2𝑛𝑡	𝑦2𝑛𝑡	VERB
iajs-2833	85	120	)	)	PUNCT
iajs-2833	85	121	∣	∣	ADJ
iajs-2833	85	122	+	+	CCONJ
iajs-2833	85	123	∣	∣	PROPN
iajs-2833	85	124	(	(	PUNCT
iajs-2833	85	125	𝑓3(𝑦3𝑛	𝑓3(𝑦3𝑛	NOUN
iajs-2833	85	126	,	,	PUNCT
iajs-2833	85	127	𝑢3	𝑢3	NOUN
iajs-2833	85	128	)	)	PUNCT
iajs-2833	85	129	,	,	PUNCT
iajs-2833	85	130	𝑦3𝑛𝑡	𝑦3𝑛𝑡	X
iajs-2833	85	131	)	)	PUNCT
iajs-2833	85	132	∣	∣	PROPN
iajs-2833	85	133	+	+	PROPN
iajs-2833	85	134	∣	∣	ADJ
iajs-2833	85	135	(	(	PUNCT
iajs-2833	85	136	𝑓4(𝑦4𝑛	𝑓4(𝑦4𝑛	ADJ
iajs-2833	85	137	,	,	PUNCT
iajs-2833	85	138	𝑢4	𝑢4	NOUN
iajs-2833	85	139	)	)	PUNCT
iajs-2833	85	140	,	,	PUNCT
iajs-2833	85	141	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	85	142	)	)	PUNCT
iajs-2833	85	143	∣	∣	NOUN
iajs-2833	85	144	]	]	X
iajs-2833	85	145	(	(	PUNCT
iajs-2833	85	146	37	37	NUM
iajs-2833	85	147	)	)	PUNCT
iajs-2833	85	148	using	use	VERB
iajs-2833	85	149	assumptions	assumption	NOUN
iajs-2833	85	150	(	(	PUNCT
iajs-2833	85	151	a	a	X
iajs-2833	85	152	)	)	PUNCT
iajs-2833	85	153	for	for	ADP
iajs-2833	85	154	the	the	DET
iajs-2833	85	155	r.h.l	r.h.l	NOUN
iajs-2833	85	156	.	.	PUNCT
iajs-2833	86	1	of	of	ADP
iajs-2833	86	2	(	(	PUNCT
iajs-2833	86	3	37	37	NUM
iajs-2833	86	4	)	)	PUNCT
iajs-2833	86	5	,	,	PUNCT
iajs-2833	86	6	integrating	integrate	VERB
iajs-2833	86	7	both	both	DET
iajs-2833	86	8	sides	side	NOUN
iajs-2833	86	9	(	(	PUNCT
iajs-2833	86	10	ibs	ibs	PROPN
iajs-2833	86	11	)	)	PUNCT
iajs-2833	86	12	on	on	ADP
iajs-2833	86	13	[	[	X
iajs-2833	86	14	0	0	NUM
iajs-2833	86	15	,	,	PUNCT
iajs-2833	86	16	𝑡	𝑡	X
iajs-2833	86	17	]	]	PUNCT
iajs-2833	86	18	,	,	PUNCT
iajs-2833	86	19	using	use	VERB
iajs-2833	86	20	∥	∥	PROPN
iajs-2833	86	21	𝑦𝑖𝑛	𝑦𝑖𝑛	PROPN
iajs-2833	86	22	∥0	∥0	PROPN
iajs-2833	86	23	≤∥	≤∥	ADJ
iajs-2833	86	24	�	�	PROPN
iajs-2833	86	25	⃗	⃗	NOUN
iajs-2833	86	26	�	�	NOUN
iajs-2833	86	27	𝑛	𝑛	PRON
iajs-2833	86	28	∥1	∥1	NOUN
iajs-2833	86	29	,	,	PUNCT
iajs-2833	86	30	∥	∥	PROPN
iajs-2833	86	31	�	�	NOUN
iajs-2833	86	32	⃗	⃗	NOUN
iajs-2833	86	33	�	�	PROPN
iajs-2833	86	34	𝑖𝑛𝑡	𝑖𝑛𝑡	PROPN
iajs-2833	86	35	∥0	∥0	PROPN
iajs-2833	86	36	≤∥	≤∥	ADJ
iajs-2833	86	37	�	�	PROPN
iajs-2833	86	38	⃗	⃗	NOUN
iajs-2833	86	39	�	�	NOUN
iajs-2833	86	40	𝑖𝑛𝑡	𝑖𝑛𝑡	VERB
iajs-2833	86	41	∥1	∥1	NOUN
iajs-2833	86	42	,	,	PUNCT
iajs-2833	86	43	∥	∥	PROPN
iajs-2833	86	44	�	�	NOUN
iajs-2833	86	45	⃗	⃗	NOUN
iajs-2833	86	46	�	�	PROPN
iajs-2833	86	47	𝑛𝑡	𝑛𝑡	NUM
iajs-2833	86	48	∥0	∥0	NOUN
iajs-2833	86	49	≤∥	≤∥	ADJ
iajs-2833	86	50	�	�	PROPN
iajs-2833	86	51	⃗	⃗	NOUN
iajs-2833	86	52	�	�	PROPN
iajs-2833	86	53	𝑛𝑡	𝑛𝑡	PRON
iajs-2833	86	54	∥1	∥1	NOUN
iajs-2833	86	55	,	,	PUNCT
iajs-2833	86	56	to	to	PART
iajs-2833	86	57	get	get	VERB
iajs-2833	86	58	∥	∥	NUM
iajs-2833	86	59	�	�	NOUN
iajs-2833	86	60	⃗	⃗	NOUN
iajs-2833	86	61	�	�	PROPN
iajs-2833	86	62	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	86	63	∥0	∥0	NOUN
iajs-2833	86	64	2+∥	2+∥	NUM
iajs-2833	86	65	�	�	PROPN
iajs-2833	86	66	⃗	⃗	NOUN
iajs-2833	86	67	�	�	NOUN
iajs-2833	86	68	𝑛	𝑛	PRON
iajs-2833	86	69	∥1	∥1	NOUN
iajs-2833	86	70	2≤	2≤	NUM
iajs-2833	86	71	3	3	NUM
iajs-2833	86	72	∫	∫	NOUN
iajs-2833	86	73	0	0	NUM
iajs-2833	87	1	𝑡	𝑡	PROPN
iajs-2833	88	1	[	[	X
iajs-2833	88	2	∥	∥	PROPN
iajs-2833	88	3	�	�	NOUN
iajs-2833	88	4	⃗	⃗	NOUN
iajs-2833	88	5	�	�	PROPN
iajs-2833	88	6	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	88	7	∥0	∥0	NOUN
iajs-2833	88	8	2+∥	2+∥	NUM
iajs-2833	88	9	�	�	PROPN
iajs-2833	88	10	⃗	⃗	NOUN
iajs-2833	88	11	�	�	NOUN
iajs-2833	88	12	𝑛	𝑛	PRON
iajs-2833	88	13	∥1	∥1	PRON
iajs-2833	88	14	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	88	15	+	+	CCONJ
iajs-2833	88	16	(	(	PUNCT
iajs-2833	88	17	∥	∥	X
iajs-2833	88	18	𝐹1	𝐹1	X
iajs-2833	88	19	∥𝑄	∥𝑄	NOUN
iajs-2833	88	20	2	2	NUM
iajs-2833	88	21	+	+	NOUN
iajs-2833	88	22	∥	∥	NOUN
iajs-2833	88	23	𝐹2	𝐹2	X
iajs-2833	88	24	∥𝑄	∥𝑄	NOUN
iajs-2833	88	25	2	2	NUM
iajs-2833	89	1	+	+	NOUN
iajs-2833	89	2	∥	∥	X
iajs-2833	89	3	𝐹3	𝐹3	X
iajs-2833	89	4	∥𝑄	∥𝑄	NOUN
iajs-2833	89	5	2	2	NUM
iajs-2833	89	6	+	+	NOUN
iajs-2833	89	7	∥	∥	PROPN
iajs-2833	89	8	𝐹4	𝐹4	NOUN
iajs-2833	89	9	∥𝑄	∥𝑄	PROPN
iajs-2833	89	10	2	2	NUM
iajs-2833	89	11	)	)	PUNCT
iajs-2833	89	12	+	+	CCONJ
iajs-2833	89	13	𝛽5	𝛽5	ADJ
iajs-2833	89	14	∫	∫	NOUN
iajs-2833	89	15	0	0	NUM
iajs-2833	89	16	𝑡	𝑡	PROPN
iajs-2833	89	17	∥	∥	PROPN
iajs-2833	89	18	�	�	NOUN
iajs-2833	89	19	⃗	⃗	NOUN
iajs-2833	89	20	�	�	NOUN
iajs-2833	89	21	𝑛	𝑛	VERB
iajs-2833	89	22	∥1	∥1	PRON
iajs-2833	89	23	2	2	NUM
iajs-2833	89	24	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	89	25	+	+	X
iajs-2833	89	26	(	(	PUNCT
iajs-2833	89	27	1	1	NUM
iajs-2833	89	28	+	+	CCONJ
iajs-2833	89	29	𝛽5	𝛽5	ADJ
iajs-2833	89	30	+	+	CCONJ
iajs-2833	89	31	𝛾5	𝛾5	ADJ
iajs-2833	89	32	)	)	PUNCT
iajs-2833	89	33	∫	∫	PROPN
iajs-2833	89	34	0	0	NUM
iajs-2833	89	35	𝑡	𝑡	PROPN
iajs-2833	89	36	∥	∥	PROPN
iajs-2833	89	37	�	�	NOUN
iajs-2833	89	38	⃗	⃗	NOUN
iajs-2833	89	39	�	�	PROPN
iajs-2833	89	40	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	89	41	∥0	∥0	NOUN
iajs-2833	89	42	2	2	NUM
iajs-2833	89	43	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	89	44	+	+	ADJ
iajs-2833	89	45	(	(	PUNCT
iajs-2833	89	46	𝛾5	𝛾5	PROPN
iajs-2833	89	47	+	+	CCONJ
iajs-2833	89	48	𝑐5	𝑐5	NOUN
iajs-2833	89	49	)	)	PUNCT
iajs-2833	89	50	∥	∥	PUNCT
iajs-2833	89	51	�	�	PROPN
iajs-2833	89	52	⃗⃗	⃗⃗	PROPN
iajs-2833	89	53	�	�	PROPN
iajs-2833	89	54	∥𝑄	∥𝑄	PROPN
iajs-2833	89	55	2	2	NUM
iajs-2833	89	56	+	+	CCONJ
iajs-2833	89	57	𝑏0	𝑏0	NOUN
iajs-2833	89	58	+	+	CCONJ
iajs-2833	89	59	𝑏1	𝑏1	ADJ
iajs-2833	89	60	≤	≤	NOUN
iajs-2833	89	61	𝑑6	𝑑6	VERB
iajs-2833	89	62	+	+	CCONJ
iajs-2833	89	63	3	3	NUM
iajs-2833	89	64	∫	∫	NOUN
iajs-2833	89	65	0	0	NUM
iajs-2833	89	66	𝑡	𝑡	PROPN
iajs-2833	90	1	[	[	X
iajs-2833	90	2	∥	∥	PROPN
iajs-2833	90	3	�	�	NOUN
iajs-2833	90	4	⃗	⃗	NOUN
iajs-2833	90	5	�	�	NOUN
iajs-2833	90	6	𝑛	𝑛	VERB
iajs-2833	90	7	∥1	∥1	NOUN
iajs-2833	90	8	2+∥	2+∥	NUM
iajs-2833	90	9	𝑦𝑛𝑡	𝑦𝑛𝑡	VERB
iajs-2833	90	10	∥0	∥0	NOUN
iajs-2833	90	11	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	90	12	+	+	CCONJ
iajs-2833	90	13	𝛽5	𝛽5	ADJ
iajs-2833	90	14	∫	∫	NOUN
iajs-2833	90	15	0	0	NUM
iajs-2833	91	1	𝑡	𝑡	NOUN
iajs-2833	91	2	∥	∥	PUNCT
iajs-2833	91	3	𝑦𝑛	𝑦𝑛	VERB
iajs-2833	91	4	∥1	∥1	PRON
iajs-2833	91	5	2	2	NUM
iajs-2833	91	6	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	91	7	+	+	ADJ
iajs-2833	91	8	𝛽6	𝛽6	NOUN
iajs-2833	91	9	∫	∫	PROPN
iajs-2833	91	10	0	0	NUM
iajs-2833	92	1	𝑡	𝑡	PROPN
iajs-2833	92	2	∥	∥	NUM
iajs-2833	92	3	𝑦𝑛𝑡	𝑦𝑛𝑡	VERB
iajs-2833	92	4	∥0	∥0	NOUN
iajs-2833	92	5	2	2	NUM
iajs-2833	92	6	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	92	7	≤	≤	NOUN
iajs-2833	92	8	𝑑6	𝑑6	VERB
iajs-2833	92	9	+	+	PROPN
iajs-2833	92	10	𝛽7	𝛽7	PROPN
iajs-2833	92	11	∫	∫	PROPN
iajs-2833	92	12	0	0	NUM
iajs-2833	93	1	𝑡	𝑡	PROPN
iajs-2833	93	2	[	[	X
iajs-2833	93	3	∥	∥	PROPN
iajs-2833	93	4	�	�	NOUN
iajs-2833	93	5	⃗	⃗	NOUN
iajs-2833	93	6	�	�	NOUN
iajs-2833	93	7	𝑛	𝑛	VERB
iajs-2833	93	8	∥1	∥1	NOUN
iajs-2833	93	9	2+∥	2+∥	NUM
iajs-2833	93	10	𝑦𝑛𝑡	𝑦𝑛𝑡	VERB
iajs-2833	93	11	∥0	∥0	NOUN
iajs-2833	93	12	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	93	13	(	(	PUNCT
iajs-2833	93	14	38	38	NUM
iajs-2833	93	15	)	)	PUNCT
iajs-2833	93	16	where𝛽5	where𝛽5	VERB
iajs-2833	94	1	=	=	SYM
iajs-2833	94	2	max	max	PROPN
iajs-2833	94	3	(	(	PUNCT
iajs-2833	94	4	𝛽1	𝛽1	NOUN
iajs-2833	94	5	,	,	PUNCT
iajs-2833	94	6	𝛽2	𝛽2	PROPN
iajs-2833	94	7	,	,	PUNCT
iajs-2833	94	8	𝛽3	𝛽3	NOUN
iajs-2833	94	9	,	,	PUNCT
iajs-2833	94	10	𝛽4	𝛽4	PROPN
iajs-2833	94	11	)	)	PUNCT
iajs-2833	94	12	,	,	PUNCT
iajs-2833	94	13	𝛾5	𝛾5	NOUN
iajs-2833	94	14	=	=	SYM
iajs-2833	94	15	max	max	PROPN
iajs-2833	94	16	(	(	PUNCT
iajs-2833	94	17	𝛾1	𝛾1	PROPN
iajs-2833	94	18	,	,	PUNCT
iajs-2833	94	19	𝛾2	𝛾2	NOUN
iajs-2833	94	20	,	,	PUNCT
iajs-2833	94	21	𝛾3	𝛾3	NOUN
iajs-2833	94	22	,	,	PUNCT
iajs-2833	94	23	𝛾4),∥	𝛾4),∥	PROPN
iajs-2833	94	24	𝑢𝑖	𝑢𝑖	ADP
iajs-2833	94	25	∥𝑄	∥𝑄	NUM
iajs-2833	94	26	2	2	NUM
iajs-2833	94	27	≤	≤	NUM
iajs-2833	94	28	𝑐𝑖(∀𝑖	𝑐𝑖(∀𝑖	NOUN
iajs-2833	94	29	=	=	NOUN
iajs-2833	94	30	1,2,3,4	1,2,3,4	NUM
iajs-2833	94	31	)	)	PUNCT
iajs-2833	94	32	,	,	PUNCT
iajs-2833	94	33	∥	∥	NUM
iajs-2833	94	34	𝐹𝑖	𝐹𝑖	NOUN
iajs-2833	94	35	∥𝑄	∥𝑄	NUM
iajs-2833	94	36	2	2	NUM
iajs-2833	94	37	≤	≤	NOUN
iajs-2833	94	38	𝑑𝑖	𝑑𝑖	PROPN
iajs-2833	94	39	,	,	PUNCT
iajs-2833	94	40	𝑑5	𝑑5	PROPN
iajs-2833	94	41	=	=	PUNCT
iajs-2833	94	42	∑	∑	PUNCT
iajs-2833	94	43	𝑖=1	𝑖=1	PROPN
iajs-2833	94	44	4	4	NUM
iajs-2833	94	45	𝑑𝑖	𝑑𝑖	NOUN
iajs-2833	94	46	,	,	PUNCT
iajs-2833	94	47	𝑐5	𝑐5	PROPN
iajs-2833	94	48	=	=	SYM
iajs-2833	94	49	max	max	PROPN
iajs-2833	94	50	(	(	PUNCT
iajs-2833	94	51	𝑐1	𝑐1	NOUN
iajs-2833	94	52	,	,	PUNCT
iajs-2833	94	53	𝑐2	𝑐2	NOUN
iajs-2833	94	54	,	,	PUNCT
iajs-2833	94	55	𝑐3	𝑐3	NOUN
iajs-2833	94	56	,	,	PUNCT
iajs-2833	94	57	𝑐4	𝑐4	PROPN
iajs-2833	94	58	)	)	PUNCT
iajs-2833	94	59	,	,	PUNCT
iajs-2833	94	60	𝑑6	𝑑6	NOUN
iajs-2833	94	61	=	=	SYM
iajs-2833	94	62	𝛾5	𝛾5	PROPN
iajs-2833	94	63	+	+	CCONJ
iajs-2833	94	64	𝑐5	𝑐5	ADJ
iajs-2833	94	65	+	+	CCONJ
iajs-2833	94	66	𝑑5	𝑑5	PROPN
iajs-2833	94	67	+	+	CCONJ
iajs-2833	94	68	𝑏0	𝑏0	NOUN
iajs-2833	94	69	+	+	CCONJ
iajs-2833	94	70	𝑏1	𝑏1	ADJ
iajs-2833	94	71	,	,	PUNCT
iajs-2833	94	72	𝛽6	𝛽6	NOUN
iajs-2833	94	73	=	=	SYM
iajs-2833	94	74	1	1	NUM
iajs-2833	94	75	+	+	NUM
iajs-2833	94	76	𝛽5	𝛽5	ADJ
iajs-2833	94	77	+	+	CCONJ
iajs-2833	94	78	𝛾5	𝛾5	ADJ
iajs-2833	94	79	𝛽7	𝛽7	NOUN
iajs-2833	94	80	=	=	SYM
iajs-2833	94	81	max	max	PROPN
iajs-2833	94	82	(	(	PUNCT
iajs-2833	94	83	3	3	NUM
iajs-2833	94	84	,	,	PUNCT
iajs-2833	94	85	𝛽6	𝛽6	NOUN
iajs-2833	94	86	)	)	PUNCT
iajs-2833	94	87	.	.	PUNCT
iajs-2833	95	1	using	use	VERB
iajs-2833	95	2	lemma	lemma	PROPN
iajs-2833	95	3	2.2	2.2	NUM
iajs-2833	95	4	,	,	PUNCT
iajs-2833	95	5	∀𝑡	∀𝑡	PROPN
iajs-2833	95	6	∈	∈	PROPN
iajs-2833	96	1	[	[	X
iajs-2833	96	2	0	0	NUM
iajs-2833	96	3	,	,	PUNCT
iajs-2833	96	4	𝑡	𝑡	X
iajs-2833	96	5	]	]	PUNCT
iajs-2833	96	6	to	to	PART
iajs-2833	96	7	get	get	VERB
iajs-2833	96	8	∥	∥	NUM
iajs-2833	96	9	�	�	NOUN
iajs-2833	96	10	⃗	⃗	NOUN
iajs-2833	96	11	�	�	NOUN
iajs-2833	96	12	𝑛𝑡(𝑡	𝑛𝑡(𝑡	NUM
iajs-2833	96	13	)	)	PUNCT
iajs-2833	96	14	∥0	∥0	VERB
iajs-2833	96	15	2+∥	2+∥	NUM
iajs-2833	96	16	�	�	PROPN
iajs-2833	96	17	⃗	⃗	NOUN
iajs-2833	96	18	�	�	NOUN
iajs-2833	96	19	𝑛(𝑡	𝑛(𝑡	NOUN
iajs-2833	96	20	)	)	PUNCT
iajs-2833	96	21	∥1	∥1	PRON
iajs-2833	96	22	2≤	2≤	NUM
iajs-2833	96	23	𝑑6𝑒	𝑑6𝑒	ADP
iajs-2833	96	24	𝛽7	𝛽7	PROPN
iajs-2833	96	25	∫	∫	PROPN
iajs-2833	96	26	0	0	PROPN
iajs-2833	97	1	𝑇	𝑇	PROPN
iajs-2833	97	2	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	97	3	=	=	PUNCT
iajs-2833	97	4	𝑏2(𝑐	𝑏2(𝑐	PROPN
iajs-2833	97	5	)	)	PUNCT
iajs-2833	97	6	⟹	⟹	NUM
iajs-2833	97	7	∥	∥	PUNCT
iajs-2833	97	8	�	�	NOUN
iajs-2833	97	9	⃗	⃗	NOUN
iajs-2833	97	10	�	�	NOUN
iajs-2833	97	11	𝑛𝑡(𝑡	𝑛𝑡(𝑡	NUM
iajs-2833	97	12	)	)	PUNCT
iajs-2833	97	13	∥0	∥0	VERB
iajs-2833	97	14	2≤	2≤	NUM
iajs-2833	97	15	𝑏2(𝑐	𝑏2(𝑐	ADP
iajs-2833	97	16	)	)	PUNCT
iajs-2833	97	17	and	and	CCONJ
iajs-2833	97	18	∥	∥	NUM
iajs-2833	97	19	�	�	NOUN
iajs-2833	97	20	⃗	⃗	NOUN
iajs-2833	97	21	�	�	NOUN
iajs-2833	97	22	𝑛(𝑡	𝑛(𝑡	NOUN
iajs-2833	97	23	)	)	PUNCT
iajs-2833	97	24	∥1	∥1	PRON
iajs-2833	97	25	2≤	2≤	NUM
iajs-2833	97	26	𝑏2(𝑐	𝑏2(𝑐	ADP
iajs-2833	97	27	)	)	PUNCT
iajs-2833	97	28	.	.	PUNCT
iajs-2833	98	1	easily	easily	ADV
iajs-2833	98	2	once	once	ADV
iajs-2833	98	3	can	can	AUX
iajs-2833	98	4	obtain	obtain	VERB
iajs-2833	98	5	that	that	DET
iajs-2833	98	6	∥	∥	PROPN
iajs-2833	98	7	�	�	PROPN
iajs-2833	98	8	⃗	⃗	NOUN
iajs-2833	98	9	�	�	NOUN
iajs-2833	98	10	𝑛𝑡(𝑡	𝑛𝑡(𝑡	NUM
iajs-2833	98	11	)	)	PUNCT
iajs-2833	98	12	∥𝑄	∥𝑄	PROPN
iajs-2833	98	13	≤	≤	NUM
iajs-2833	98	14	𝑏	𝑏	DET
iajs-2833	98	15	1(𝑐	1(𝑐	NUM
iajs-2833	98	16	)	)	PUNCT
iajs-2833	98	17	and	and	CCONJ
iajs-2833	98	18	∥	∥	NUM
iajs-2833	98	19	�	�	NOUN
iajs-2833	98	20	⃗	⃗	NOUN
iajs-2833	98	21	�	�	NOUN
iajs-2833	98	22	𝑛(𝑡	𝑛(𝑡	NOUN
iajs-2833	98	23	)	)	PUNCT
iajs-2833	98	24	∥𝐿2(𝐼,𝑉	∥𝐿2(𝐼,𝑉	PROPN
iajs-2833	98	25	)	)	PUNCT
iajs-2833	98	26	≤	≤	NOUN
iajs-2833	99	1	𝑏	𝑏	PROPN
iajs-2833	99	2	(	(	PUNCT
iajs-2833	99	3	𝑐	𝑐	NOUN
iajs-2833	99	4	)	)	PUNCT
iajs-2833	99	5	.	.	PUNCT
iajs-2833	100	1	then	then	ADV
iajs-2833	100	2	,	,	PUNCT
iajs-2833	100	3	by	by	ADP
iajs-2833	100	4	applying	apply	VERB
iajs-2833	100	5	the	the	DET
iajs-2833	100	6	alaoglu	alaoglu	NOUN
iajs-2833	100	7	’s	’s	PART
iajs-2833	100	8	theorem	theorem	NOUN
iajs-2833	100	9	(	(	PUNCT
iajs-2833	100	10	alth	alth	NOUN
iajs-2833	100	11	)	)	PUNCT
iajs-2833	100	12	,	,	PUNCT
iajs-2833	100	13	there	there	PRON
iajs-2833	100	14	is	be	VERB
iajs-2833	100	15	a	a	DET
iajs-2833	100	16	subsequence	subsequence	NOUN
iajs-2833	100	17	of	of	ADP
iajs-2833	100	18	{	{	PUNCT
iajs-2833	100	19	�	�	PROPN
iajs-2833	100	20	⃗	⃗	NOUN
iajs-2833	100	21	�	�	PROPN
iajs-2833	100	22	𝑛}𝑛∈𝑁	𝑛}𝑛∈𝑁	NOUN
iajs-2833	100	23	,	,	PUNCT
iajs-2833	100	24	for	for	ADP
iajs-2833	100	25	simplicity	simplicity	NOUN
iajs-2833	100	26	say	say	VERB
iajs-2833	100	27	{	{	PUNCT
iajs-2833	100	28	�	�	PROPN
iajs-2833	100	29	⃗	⃗	NOUN
iajs-2833	100	30	�	�	NOUN
iajs-2833	100	31	𝑛	𝑛	ADJ
iajs-2833	100	32	}	}	PUNCT
iajs-2833	100	33	s.t	s.t	PROPN
iajs-2833	100	34	.	.	PROPN
iajs-2833	100	35	�	�	PROPN
iajs-2833	100	36	⃗	⃗	PROPN
iajs-2833	100	37	�	�	PROPN
iajs-2833	100	38	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	100	39	→	→	SYM
iajs-2833	100	40	�	�	NOUN
iajs-2833	100	41	⃗	⃗	NOUN
iajs-2833	100	42	�	�	PROPN
iajs-2833	100	43	weakly	weakly	ADJ
iajs-2833	100	44	(	(	PUNCT
iajs-2833	100	45	wk	wk	NOUN
iajs-2833	100	46	)	)	PUNCT
iajs-2833	100	47	in	in	ADP
iajs-2833	100	48	(	(	PUNCT
iajs-2833	100	49	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	100	50	and	and	CCONJ
iajs-2833	100	51	�	�	PROPN
iajs-2833	100	52	⃗	⃗	NOUN
iajs-2833	100	53	�	�	NOUN
iajs-2833	100	54	𝑛	𝑛	PRON
iajs-2833	100	55	→	→	SYM
iajs-2833	100	56	�	�	NOUN
iajs-2833	100	57	⃗	⃗	NOUN
iajs-2833	100	58	�	�	PROPN
iajs-2833	100	59	wk	wk	X
iajs-2833	100	60	in	in	ADP
iajs-2833	100	61	(	(	PUNCT
iajs-2833	100	62	𝐿2(𝐼	𝐿2(𝐼	PROPN
iajs-2833	100	63	,	,	PUNCT
iajs-2833	100	64	𝑉))4	𝑉))4	PROPN
iajs-2833	100	65	.	.	PUNCT
iajs-2833	101	1	but	but	CCONJ
iajs-2833	101	2	(	(	PUNCT
iajs-2833	101	3	𝐿2(ℝ	𝐿2(ℝ	NOUN
iajs-2833	101	4	,	,	PUNCT
iajs-2833	101	5	𝑉))4	𝑉))4	PROPN
iajs-2833	101	6	⊂	⊂	PROPN
iajs-2833	101	7	(	(	PUNCT
iajs-2833	101	8	𝐿2(ℝ	𝐿2(ℝ	PROPN
iajs-2833	101	9	,	,	PUNCT
iajs-2833	101	10	ω))4	ω))4	PROPN
iajs-2833	101	11	≅	≅	PROPN
iajs-2833	101	12	(	(	PUNCT
iajs-2833	101	13	(	(	PUNCT
iajs-2833	101	14	𝐿2(ℝ	𝐿2(ℝ	NOUN
iajs-2833	101	15	,	,	PUNCT
iajs-2833	101	16	ω))∗)4	ω))∗)4	PROPN
iajs-2833	101	17	⊂	⊂	PROPN
iajs-2833	101	18	(	(	PUNCT
iajs-2833	101	19	𝐿2(ℝ	𝐿2(ℝ	PROPN
iajs-2833	101	20	,	,	PUNCT
iajs-2833	101	21	𝑉∗))4	𝑉∗))4	PROPN
iajs-2833	101	22	(	(	PUNCT
iajs-2833	101	23	39	39	NUM
iajs-2833	101	24	)	)	PUNCT
iajs-2833	101	25	then	then	ADV
iajs-2833	101	26	the	the	DET
iajs-2833	101	27	(	(	PUNCT
iajs-2833	101	28	acth)[15	acth)[15	PROPN
iajs-2833	101	29	]	]	PUNCT
iajs-2833	101	30	can	can	AUX
iajs-2833	101	31	be	be	AUX
iajs-2833	101	32	employed	employ	VERB
iajs-2833	101	33	here	here	ADV
iajs-2833	101	34	to	to	PART
iajs-2833	101	35	get	get	VERB
iajs-2833	101	36	that	that	DET
iajs-2833	101	37	�	�	PROPN
iajs-2833	101	38	⃗	⃗	NOUN
iajs-2833	101	39	�	�	NOUN
iajs-2833	101	40	𝑛	𝑛	PRON
iajs-2833	101	41	→	→	SYM
iajs-2833	101	42	�	�	PROPN
iajs-2833	101	43	⃗	⃗	PROPN
iajs-2833	101	44	�	�	PROPN
iajs-2833	101	45	st	st	PROPN
iajs-2833	101	46	in	in	ADP
iajs-2833	101	47	(	(	PUNCT
iajs-2833	101	48	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	101	49	.	.	PUNCT
iajs-2833	102	1	now	now	ADV
iajs-2833	102	2	multiplying	multiply	VERB
iajs-2833	102	3	both	both	DET
iajs-2833	102	4	sides	side	NOUN
iajs-2833	102	5	(	(	PUNCT
iajs-2833	102	6	mbs	mb	NOUN
iajs-2833	102	7	)	)	PUNCT
iajs-2833	102	8	of	of	ADP
iajs-2833	102	9	(	(	PUNCT
iajs-2833	102	10	(	(	PUNCT
iajs-2833	102	11	28	28	NUM
iajs-2833	102	12	)	)	PUNCT
iajs-2833	102	13	,	,	PUNCT
iajs-2833	102	14	(	(	PUNCT
iajs-2833	102	15	30),(32)&(34	30),(32)&(34	NOUN
iajs-2833	102	16	)	)	PUNCT
iajs-2833	102	17	)	)	PUNCT
iajs-2833	102	18	by	by	ADP
iajs-2833	102	19	𝜙𝑖(𝑇	𝜙𝑖(𝑇	NOUN
iajs-2833	102	20	)	)	PUNCT
iajs-2833	102	21	∈	∈	PROPN
iajs-2833	102	22	𝐶2[0	𝐶2[0	PROPN
iajs-2833	102	23	,	,	PUNCT
iajs-2833	102	24	𝑇	𝑇	PROPN
iajs-2833	102	25	]	]	PUNCT
iajs-2833	102	26	s.t	s.t	PROPN
iajs-2833	102	27	.	.	PROPN
iajs-2833	102	28	𝜙𝑖(𝑇	𝜙𝑖(𝑇	ADP
iajs-2833	102	29	)	)	PUNCT
iajs-2833	103	1	=	=	SYM
iajs-2833	103	2	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	103	3	′(𝑇	′(𝑇	NOUN
iajs-2833	103	4	)	)	PUNCT
iajs-2833	104	1	=	=	SYM
iajs-2833	104	2	0	0	NUM
iajs-2833	104	3	,	,	PUNCT
iajs-2833	104	4	𝜙𝑖(0	𝜙𝑖(0	NOUN
iajs-2833	104	5	)	)	PUNCT
iajs-2833	104	6	≠	≠	PROPN
iajs-2833	104	7	0	0	NUM
iajs-2833	104	8	,	,	PUNCT
iajs-2833	104	9	𝜙𝑖	𝜙𝑖	ADP
iajs-2833	104	10	′(0	′(0	NOUN
iajs-2833	104	11	)	)	PUNCT
iajs-2833	104	12	≠	≠	PROPN
iajs-2833	104	13	0	0	NUM
iajs-2833	104	14	,	,	PUNCT
iajs-2833	104	15	∀𝑖	∀𝑖	PROPN
iajs-2833	104	16	=	=	SYM
iajs-2833	104	17	1,2,3,4	1,2,3,4	NUM
iajs-2833	104	18	,	,	PUNCT
iajs-2833	104	19	ibs	ib	VERB
iajs-2833	104	20	on	on	ADP
iajs-2833	104	21	[	[	X
iajs-2833	104	22	0	0	NUM
iajs-2833	104	23	,	,	PUNCT
iajs-2833	104	24	𝑇	𝑇	PROPN
iajs-2833	104	25	]	]	PUNCT
iajs-2833	104	26	,	,	PUNCT
iajs-2833	104	27	finally	finally	ADV
iajs-2833	104	28	integrating	integrate	VERB
iajs-2833	104	29	by	by	ADP
iajs-2833	104	30	parts	part	NOUN
iajs-2833	104	31	twice	twice	ADV
iajs-2833	104	32	(	(	PUNCT
iajs-2833	104	33	ibps2	ibps2	NOUN
iajs-2833	104	34	)	)	PUNCT
iajs-2833	104	35	the	the	DET
iajs-2833	104	36	1st	1st	ADJ
iajs-2833	104	37	term	term	NOUN
iajs-2833	104	38	in	in	ADP
iajs-2833	104	39	each	each	DET
iajs-2833	104	40	equation	equation	NOUN
iajs-2833	104	41	yield	yield	VERB
iajs-2833	104	42	to	to	ADP
iajs-2833	104	43	−	−	PROPN
iajs-2833	104	44	∫	∫	PROPN
iajs-2833	104	45	0	0	PUNCT
iajs-2833	105	1	𝑇	𝑇	PROPN
iajs-2833	105	2	𝑑	𝑑	PRON
iajs-2833	105	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	105	4	(	(	PUNCT
iajs-2833	105	5	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	105	6	,	,	PUNCT
iajs-2833	105	7	𝑣1𝑛)𝜙1	𝑣1𝑛)𝜙1	NOUN
iajs-2833	105	8	′	′	NOUN
iajs-2833	105	9	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	105	10	+	+	CCONJ
iajs-2833	105	11	∫	∫	PROPN
iajs-2833	105	12	0	0	X
iajs-2833	105	13	𝑇	𝑇	PROPN
iajs-2833	106	1	[	[	X
iajs-2833	106	2	(	(	PUNCT
iajs-2833	106	3	∇𝑦1𝑛	∇𝑦1𝑛	ADJ
iajs-2833	106	4	,	,	PUNCT
iajs-2833	106	5	∇𝑣1𝑛	∇𝑣1𝑛	ADV
iajs-2833	106	6	)	)	PUNCT
iajs-2833	107	1	+	+	CCONJ
iajs-2833	107	2	(	(	PUNCT
iajs-2833	107	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	107	4	,	,	PUNCT
iajs-2833	107	5	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	107	6	)	)	PUNCT
iajs-2833	107	7	−	−	PROPN
iajs-2833	107	8	(	(	PUNCT
iajs-2833	107	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	107	10	,	,	PUNCT
iajs-2833	107	11	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	107	12	)	)	PUNCT
iajs-2833	107	13	+	+	CCONJ
iajs-2833	107	14	(	(	PUNCT
iajs-2833	107	15	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	107	16	,	,	PUNCT
iajs-2833	107	17	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	107	18	)	)	PUNCT
iajs-2833	107	19	+	+	CCONJ
iajs-2833	107	20	(	(	PUNCT
iajs-2833	107	21	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	107	22	,	,	PUNCT
iajs-2833	107	23	𝑣1𝑛)]𝜙1	𝑣1𝑛)]𝜙1	NOUN
iajs-2833	107	24	(	(	PUNCT
iajs-2833	107	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	107	26	=	=	SYM
iajs-2833	107	27	∫	∫	PROPN
iajs-2833	107	28	0	0	X
iajs-2833	107	29	𝑇	𝑇	PROPN
iajs-2833	107	30	(	(	PUNCT
iajs-2833	107	31	𝑓1(𝑦1𝑛	𝑓1(𝑦1𝑛	PROPN
iajs-2833	107	32	,	,	PUNCT
iajs-2833	107	33	𝑢1	𝑢1	PROPN
iajs-2833	107	34	)	)	PUNCT
iajs-2833	107	35	,	,	PUNCT
iajs-2833	107	36	𝑣1𝑛)𝜙1	𝑣1𝑛)𝜙1	NUM
iajs-2833	107	37	(	(	PUNCT
iajs-2833	107	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	107	39	+	+	CCONJ
iajs-2833	107	40	(	(	PUNCT
iajs-2833	107	41	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	107	42	′	′	NOUN
iajs-2833	107	43	,	,	PUNCT
iajs-2833	107	44	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	107	45	)	)	PUNCT
iajs-2833	107	46	𝜙1(0	𝜙1(0	NOUN
iajs-2833	107	47	)	)	PUNCT
iajs-2833	107	48	(	(	PUNCT
iajs-2833	107	49	40	40	NUM
iajs-2833	107	50	)	)	PUNCT
iajs-2833	107	51	ihjpas	ihjpa	NOUN
iajs-2833	107	52	.	.	PUNCT
iajs-2833	108	1	53	53	NUM
iajs-2833	108	2	(	(	PUNCT
iajs-2833	108	3	3)2022	3)2022	NOUN
iajs-2833	108	4	166	166	NUM
iajs-2833	108	5	∫	∫	PROPN
iajs-2833	108	6	0	0	PUNCT
iajs-2833	108	7	𝑇	𝑇	PROPN
iajs-2833	108	8	(	(	PUNCT
iajs-2833	108	9	𝑦1𝑛	𝑦1𝑛	PROPN
iajs-2833	108	10	,	,	PUNCT
iajs-2833	108	11	𝑣1𝑛)𝜙1	𝑣1𝑛)𝜙1	NOUN
iajs-2833	108	12	′′𝑑𝑡	′′𝑑𝑡	VERB
iajs-2833	108	13	+	+	X
iajs-2833	108	14	∫	∫	PROPN
iajs-2833	108	15	0	0	X
iajs-2833	108	16	𝑇	𝑇	PROPN
iajs-2833	109	1	[	[	X
iajs-2833	109	2	(	(	PUNCT
iajs-2833	109	3	∇𝑦1𝑛	∇𝑦1𝑛	ADJ
iajs-2833	109	4	,	,	PUNCT
iajs-2833	109	5	∇𝑣1𝑛	∇𝑣1𝑛	ADV
iajs-2833	109	6	)	)	PUNCT
iajs-2833	110	1	+	+	CCONJ
iajs-2833	110	2	(	(	PUNCT
iajs-2833	110	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	110	4	,	,	PUNCT
iajs-2833	110	5	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	110	6	)	)	PUNCT
iajs-2833	110	7	−	−	PROPN
iajs-2833	110	8	(	(	PUNCT
iajs-2833	110	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	110	10	,	,	PUNCT
iajs-2833	110	11	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	110	12	)	)	PUNCT
iajs-2833	110	13	+	+	CCONJ
iajs-2833	110	14	(	(	PUNCT
iajs-2833	110	15	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	110	16	,	,	PUNCT
iajs-2833	110	17	𝑣1𝑛	𝑣1𝑛	NUM
iajs-2833	110	18	)	)	PUNCT
iajs-2833	110	19	+	+	CCONJ
iajs-2833	110	20	(	(	PUNCT
iajs-2833	110	21	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	110	22	,	,	PUNCT
iajs-2833	110	23	𝑣1𝑛)]𝜙1	𝑣1𝑛)]𝜙1	NOUN
iajs-2833	110	24	(	(	PUNCT
iajs-2833	110	25	𝑡)𝑑𝑡=∫	𝑡)𝑑𝑡=∫	NOUN
iajs-2833	110	26	0	0	NUM
iajs-2833	110	27	𝑇	𝑇	PROPN
iajs-2833	110	28	(	(	PUNCT
iajs-2833	110	29	𝑓1(𝑦1𝑛	𝑓1(𝑦1𝑛	PROPN
iajs-2833	110	30	,	,	PUNCT
iajs-2833	110	31	𝑢1	𝑢1	PROPN
iajs-2833	110	32	)	)	PUNCT
iajs-2833	110	33	,	,	PUNCT
iajs-2833	110	34	𝑣1𝑛)𝜙1	𝑣1𝑛)𝜙1	NUM
iajs-2833	110	35	(	(	PUNCT
iajs-2833	110	36	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	110	37	+	+	CCONJ
iajs-2833	110	38	(	(	PUNCT
iajs-2833	110	39	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	110	40	′	′	NOUN
iajs-2833	110	41	,	,	PUNCT
iajs-2833	110	42	𝑣1𝑛)𝜙1(0	𝑣1𝑛)𝜙1(0	NOUN
iajs-2833	110	43	)	)	PUNCT
iajs-2833	110	44	−	−	PROPN
iajs-2833	110	45	(	(	PUNCT
iajs-2833	110	46	𝑦1𝑛	𝑦1𝑛	NOUN
iajs-2833	110	47	0	0	NUM
iajs-2833	110	48	,	,	PUNCT
iajs-2833	110	49	𝑣1𝑛)𝜙1	𝑣1𝑛)𝜙1	NOUN
iajs-2833	110	50	′	′	NUM
iajs-2833	110	51	(	(	PUNCT
iajs-2833	110	52	0	0	NUM
iajs-2833	110	53	)	)	PUNCT
iajs-2833	110	54	(	(	PUNCT
iajs-2833	110	55	41	41	NUM
iajs-2833	110	56	)	)	PUNCT
iajs-2833	110	57	−	−	NOUN
iajs-2833	111	1	∫	∫	NOUN
iajs-2833	111	2	0	0	NUM
iajs-2833	112	1	𝑇	𝑇	PROPN
iajs-2833	112	2	𝑑	𝑑	PRON
iajs-2833	112	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	112	4	(	(	PUNCT
iajs-2833	112	5	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	112	6	,	,	PUNCT
iajs-2833	112	7	𝑣2𝑛)𝜙2	𝑣2𝑛)𝜙2	ADP
iajs-2833	112	8	′	′	NUM
iajs-2833	112	9	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	112	10	+	+	CCONJ
iajs-2833	112	11	∫	∫	PROPN
iajs-2833	112	12	0	0	X
iajs-2833	112	13	𝑇	𝑇	PROPN
iajs-2833	113	1	[	[	X
iajs-2833	113	2	(	(	PUNCT
iajs-2833	113	3	∇𝑦2𝑛	∇𝑦2𝑛	NOUN
iajs-2833	113	4	,	,	PUNCT
iajs-2833	113	5	∇𝑣2𝑛	∇𝑣2𝑛	NOUN
iajs-2833	113	6	)	)	PUNCT
iajs-2833	114	1	+	+	CCONJ
iajs-2833	114	2	(	(	PUNCT
iajs-2833	114	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	114	4	,	,	PUNCT
iajs-2833	114	5	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	114	6	)	)	PUNCT
iajs-2833	114	7	+	+	CCONJ
iajs-2833	114	8	(	(	PUNCT
iajs-2833	114	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	114	10	,	,	PUNCT
iajs-2833	114	11	𝑣2𝑛	𝑣2𝑛	NUM
iajs-2833	114	12	)	)	PUNCT
iajs-2833	114	13	−	−	PROPN
iajs-2833	114	14	(	(	PUNCT
iajs-2833	114	15	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	114	16	,	,	PUNCT
iajs-2833	114	17	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	114	18	)	)	PUNCT
iajs-2833	114	19	−	−	PROPN
iajs-2833	114	20	(	(	PUNCT
iajs-2833	114	21	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	114	22	,	,	PUNCT
iajs-2833	114	23	𝑣2𝑛)]𝜙2	𝑣2𝑛)]𝜙2	PROPN
iajs-2833	114	24	(	(	PUNCT
iajs-2833	114	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	114	26	=	=	SYM
iajs-2833	114	27	∫	∫	PROPN
iajs-2833	114	28	0	0	X
iajs-2833	114	29	𝑇	𝑇	PROPN
iajs-2833	114	30	(	(	PUNCT
iajs-2833	114	31	𝑓2(𝑦2𝑛	𝑓2(𝑦2𝑛	NOUN
iajs-2833	114	32	,	,	PUNCT
iajs-2833	114	33	𝑢2	𝑢2	PROPN
iajs-2833	114	34	)	)	PUNCT
iajs-2833	114	35	,	,	PUNCT
iajs-2833	114	36	𝑣2𝑛)𝜙2	𝑣2𝑛)𝜙2	ADP
iajs-2833	114	37	(	(	PUNCT
iajs-2833	114	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	114	39	+	+	NUM
iajs-2833	114	40	(	(	PUNCT
iajs-2833	114	41	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	114	42	′	′	NUM
iajs-2833	114	43	,	,	PUNCT
iajs-2833	114	44	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	114	45	)	)	PUNCT
iajs-2833	114	46	𝜙1(0	𝜙1(0	NOUN
iajs-2833	114	47	)	)	PUNCT
iajs-2833	114	48	(	(	PUNCT
iajs-2833	114	49	42	42	NUM
iajs-2833	114	50	)	)	PUNCT
iajs-2833	114	51	∫	∫	PROPN
iajs-2833	114	52	0	0	X
iajs-2833	114	53	𝑇	𝑇	PROPN
iajs-2833	114	54	(	(	PUNCT
iajs-2833	114	55	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	114	56	,	,	PUNCT
iajs-2833	114	57	𝑣2𝑛)𝜙2	𝑣2𝑛)𝜙2	ADP
iajs-2833	115	1	′′(𝑡)𝑑𝑡	′′(𝑡)𝑑𝑡	PROPN
iajs-2833	115	2	+	+	NUM
iajs-2833	115	3	∫	∫	PROPN
iajs-2833	115	4	0	0	X
iajs-2833	115	5	𝑇	𝑇	PROPN
iajs-2833	116	1	[	[	X
iajs-2833	116	2	(	(	PUNCT
iajs-2833	116	3	∇𝑦2𝑛	∇𝑦2𝑛	NOUN
iajs-2833	116	4	,	,	PUNCT
iajs-2833	116	5	∇𝑣2𝑛	∇𝑣2𝑛	NOUN
iajs-2833	116	6	)	)	PUNCT
iajs-2833	116	7	+	+	CCONJ
iajs-2833	116	8	(	(	PUNCT
iajs-2833	116	9	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	116	10	,	,	PUNCT
iajs-2833	116	11	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	116	12	)	)	PUNCT
iajs-2833	116	13	+	+	CCONJ
iajs-2833	116	14	(	(	PUNCT
iajs-2833	116	15	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	116	16	,	,	PUNCT
iajs-2833	116	17	𝑣2𝑛	𝑣2𝑛	NUM
iajs-2833	116	18	)	)	PUNCT
iajs-2833	116	19	−	−	PROPN
iajs-2833	116	20	(	(	PUNCT
iajs-2833	116	21	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	116	22	,	,	PUNCT
iajs-2833	116	23	𝑣2𝑛	𝑣2𝑛	ADJ
iajs-2833	116	24	)	)	PUNCT
iajs-2833	116	25	−	−	PROPN
iajs-2833	116	26	(	(	PUNCT
iajs-2833	116	27	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	116	28	,	,	PUNCT
iajs-2833	116	29	𝑣2𝑛)]𝜙2	𝑣2𝑛)]𝜙2	PROPN
iajs-2833	116	30	(	(	PUNCT
iajs-2833	116	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	116	32	=	=	SYM
iajs-2833	116	33	∫	∫	PROPN
iajs-2833	116	34	0	0	X
iajs-2833	116	35	𝑇	𝑇	PROPN
iajs-2833	116	36	(	(	PUNCT
iajs-2833	116	37	𝑓2(𝑦2𝑛	𝑓2(𝑦2𝑛	NOUN
iajs-2833	116	38	,	,	PUNCT
iajs-2833	116	39	𝑢2	𝑢2	PROPN
iajs-2833	116	40	)	)	PUNCT
iajs-2833	116	41	,	,	PUNCT
iajs-2833	116	42	𝑣2𝑛)𝜙2	𝑣2𝑛)𝜙2	ADP
iajs-2833	116	43	(	(	PUNCT
iajs-2833	116	44	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	116	45	+	+	NUM
iajs-2833	116	46	(	(	PUNCT
iajs-2833	116	47	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	116	48	′	′	NUM
iajs-2833	116	49	,	,	PUNCT
iajs-2833	116	50	𝑣2𝑛)𝜙2(0	𝑣2𝑛)𝜙2(0	NOUN
iajs-2833	116	51	)	)	PUNCT
iajs-2833	116	52	−	−	PROPN
iajs-2833	116	53	(	(	PUNCT
iajs-2833	116	54	𝑦2𝑛	𝑦2𝑛	NUM
iajs-2833	116	55	0	0	NUM
iajs-2833	116	56	,	,	PUNCT
iajs-2833	116	57	𝑣2𝑛)𝜙2	𝑣2𝑛)𝜙2	ADP
iajs-2833	116	58	′	′	NUM
iajs-2833	116	59	(	(	PUNCT
iajs-2833	116	60	0	0	NUM
iajs-2833	116	61	)	)	PUNCT
iajs-2833	116	62	(	(	PUNCT
iajs-2833	116	63	43	43	NUM
iajs-2833	116	64	)	)	PUNCT
iajs-2833	116	65	−	−	ADP
iajs-2833	117	1	∫	∫	NOUN
iajs-2833	117	2	0	0	NUM
iajs-2833	118	1	𝑇	𝑇	PROPN
iajs-2833	118	2	𝑑	𝑑	PRON
iajs-2833	118	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	118	4	(	(	PUNCT
iajs-2833	118	5	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	118	6	,	,	PUNCT
iajs-2833	118	7	𝑣3𝑛)𝜙3	𝑣3𝑛)𝜙3	X
iajs-2833	118	8	′	′	NOUN
iajs-2833	118	9	(	(	PUNCT
iajs-2833	118	10	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	118	11	+	+	NUM
iajs-2833	118	12	∫	∫	PROPN
iajs-2833	118	13	0	0	X
iajs-2833	118	14	𝑇	𝑇	PROPN
iajs-2833	119	1	[	[	X
iajs-2833	119	2	(	(	PUNCT
iajs-2833	119	3	∇𝑦3𝑛	∇𝑦3𝑛	ADJ
iajs-2833	119	4	,	,	PUNCT
iajs-2833	119	5	∇𝑣3𝑛	∇𝑣3𝑛	NUM
iajs-2833	119	6	)	)	PUNCT
iajs-2833	119	7	−	−	PROPN
iajs-2833	119	8	(	(	PUNCT
iajs-2833	119	9	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	119	10	,	,	PUNCT
iajs-2833	119	11	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	119	12	)	)	PUNCT
iajs-2833	119	13	+	+	CCONJ
iajs-2833	119	14	(	(	PUNCT
iajs-2833	119	15	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	119	16	,	,	PUNCT
iajs-2833	119	17	𝑣3𝑛	𝑣3𝑛	NUM
iajs-2833	119	18	)	)	PUNCT
iajs-2833	119	19	+	+	CCONJ
iajs-2833	119	20	(	(	PUNCT
iajs-2833	119	21	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	119	22	,	,	PUNCT
iajs-2833	119	23	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	119	24	)	)	PUNCT
iajs-2833	119	25	+	+	CCONJ
iajs-2833	119	26	(	(	PUNCT
iajs-2833	119	27	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	119	28	,	,	PUNCT
iajs-2833	119	29	𝑣3𝑛)]𝜙3	𝑣3𝑛)]𝜙3	PROPN
iajs-2833	119	30	(	(	PUNCT
iajs-2833	119	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	119	32	=	=	SYM
iajs-2833	119	33	∫	∫	PROPN
iajs-2833	119	34	0	0	NUM
iajs-2833	119	35	𝑇	𝑇	PROPN
iajs-2833	119	36	(	(	PUNCT
iajs-2833	119	37	𝑓3(𝑦3𝑛	𝑓3(𝑦3𝑛	NOUN
iajs-2833	119	38	,	,	PUNCT
iajs-2833	119	39	𝑢3	𝑢3	NOUN
iajs-2833	119	40	)	)	PUNCT
iajs-2833	119	41	,	,	PUNCT
iajs-2833	119	42	𝑣3𝑛)𝜙3	𝑣3𝑛)𝜙3	PROPN
iajs-2833	119	43	(	(	PUNCT
iajs-2833	119	44	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	119	45	+	+	CCONJ
iajs-2833	119	46	(	(	PUNCT
iajs-2833	119	47	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	119	48	′	′	NUM
iajs-2833	119	49	,	,	PUNCT
iajs-2833	119	50	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	119	51	)	)	PUNCT
iajs-2833	119	52	𝜙3(0	𝜙3(0	PROPN
iajs-2833	119	53	)	)	PUNCT
iajs-2833	119	54	(	(	PUNCT
iajs-2833	119	55	44	44	NUM
iajs-2833	119	56	)	)	PUNCT
iajs-2833	119	57	∫	∫	PROPN
iajs-2833	119	58	0	0	X
iajs-2833	119	59	𝑇	𝑇	PROPN
iajs-2833	119	60	(	(	PUNCT
iajs-2833	119	61	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	119	62	,	,	PUNCT
iajs-2833	119	63	𝑣3𝑛)𝜙3	𝑣3𝑛)𝜙3	PROPN
iajs-2833	119	64	′′𝑑𝑡	′′𝑑𝑡	X
iajs-2833	119	65	+	+	X
iajs-2833	119	66	∫	∫	PROPN
iajs-2833	119	67	0	0	X
iajs-2833	119	68	𝑇	𝑇	PROPN
iajs-2833	120	1	[	[	X
iajs-2833	120	2	(	(	PUNCT
iajs-2833	120	3	∇𝑦3𝑛	∇𝑦3𝑛	ADJ
iajs-2833	120	4	,	,	PUNCT
iajs-2833	120	5	∇𝑣3𝑛	∇𝑣3𝑛	NUM
iajs-2833	120	6	)	)	PUNCT
iajs-2833	120	7	−	−	PROPN
iajs-2833	120	8	(	(	PUNCT
iajs-2833	120	9	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	120	10	,	,	PUNCT
iajs-2833	120	11	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	120	12	)	)	PUNCT
iajs-2833	120	13	+	+	CCONJ
iajs-2833	120	14	(	(	PUNCT
iajs-2833	120	15	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	120	16	,	,	PUNCT
iajs-2833	120	17	𝑣3𝑛	𝑣3𝑛	NUM
iajs-2833	120	18	)	)	PUNCT
iajs-2833	120	19	+	+	CCONJ
iajs-2833	120	20	(	(	PUNCT
iajs-2833	120	21	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	120	22	,	,	PUNCT
iajs-2833	120	23	𝑣3𝑛	𝑣3𝑛	PROPN
iajs-2833	120	24	)	)	PUNCT
iajs-2833	120	25	+	+	CCONJ
iajs-2833	120	26	(	(	PUNCT
iajs-2833	120	27	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	120	28	,	,	PUNCT
iajs-2833	120	29	𝑣3𝑛)]𝜙3	𝑣3𝑛)]𝜙3	PROPN
iajs-2833	120	30	(	(	PUNCT
iajs-2833	120	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	120	32	=	=	SYM
iajs-2833	120	33	∫	∫	PROPN
iajs-2833	120	34	0	0	NUM
iajs-2833	120	35	𝑇	𝑇	PROPN
iajs-2833	120	36	(	(	PUNCT
iajs-2833	120	37	𝑓3(𝑦3𝑛	𝑓3(𝑦3𝑛	NOUN
iajs-2833	120	38	,	,	PUNCT
iajs-2833	120	39	𝑢3	𝑢3	NOUN
iajs-2833	120	40	)	)	PUNCT
iajs-2833	120	41	,	,	PUNCT
iajs-2833	120	42	𝑣3𝑛)𝜙3	𝑣3𝑛)𝜙3	PROPN
iajs-2833	120	43	(	(	PUNCT
iajs-2833	120	44	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	120	45	+	+	CCONJ
iajs-2833	120	46	(	(	PUNCT
iajs-2833	120	47	𝑦3𝑛	𝑦3𝑛	ADJ
iajs-2833	120	48	′	′	NUM
iajs-2833	120	49	,	,	PUNCT
iajs-2833	120	50	𝑣3𝑛)𝜙3(0	𝑣3𝑛)𝜙3(0	PROPN
iajs-2833	120	51	)	)	PUNCT
iajs-2833	120	52	−	−	PROPN
iajs-2833	120	53	(	(	PUNCT
iajs-2833	120	54	𝑦3𝑛	𝑦3𝑛	X
iajs-2833	120	55	0	0	NUM
iajs-2833	120	56	,	,	PUNCT
iajs-2833	120	57	𝑣3𝑛)𝜙3	𝑣3𝑛)𝜙3	X
iajs-2833	120	58	′	′	NUM
iajs-2833	120	59	(	(	PUNCT
iajs-2833	120	60	0	0	NUM
iajs-2833	120	61	)	)	PUNCT
iajs-2833	120	62	(	(	PUNCT
iajs-2833	120	63	45	45	NUM
iajs-2833	120	64	)	)	PUNCT
iajs-2833	120	65	−	−	NOUN
iajs-2833	120	66	∫	∫	NOUN
iajs-2833	120	67	0	0	NUM
iajs-2833	121	1	𝑇	𝑇	PROPN
iajs-2833	121	2	𝑑	𝑑	PRON
iajs-2833	121	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	121	4	(	(	PUNCT
iajs-2833	121	5	𝑦4𝑛	𝑦4𝑛	ADV
iajs-2833	121	6	,	,	PUNCT
iajs-2833	121	7	𝑣4𝑛)𝜙4	𝑣4𝑛)𝜙4	NUM
iajs-2833	121	8	′	′	NUM
iajs-2833	121	9	(	(	PUNCT
iajs-2833	121	10	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	121	11	+	+	NUM
iajs-2833	121	12	∫	∫	PROPN
iajs-2833	121	13	0	0	X
iajs-2833	121	14	𝑇	𝑇	PROPN
iajs-2833	122	1	[	[	X
iajs-2833	122	2	(	(	PUNCT
iajs-2833	122	3	∇𝑦4𝑛	∇𝑦4𝑛	ADV
iajs-2833	122	4	,	,	PUNCT
iajs-2833	122	5	∇𝑣4𝑛	∇𝑣4𝑛	NUM
iajs-2833	122	6	)	)	PUNCT
iajs-2833	123	1	−	−	PROPN
iajs-2833	123	2	(	(	PUNCT
iajs-2833	123	3	𝑦1𝑛	𝑦1𝑛	PROPN
iajs-2833	123	4	,	,	PUNCT
iajs-2833	123	5	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	123	6	)	)	PUNCT
iajs-2833	123	7	+	+	CCONJ
iajs-2833	123	8	(	(	PUNCT
iajs-2833	123	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	123	10	,	,	PUNCT
iajs-2833	123	11	𝑣4𝑛	𝑣4𝑛	NOUN
iajs-2833	123	12	)	)	PUNCT
iajs-2833	123	13	−	−	PROPN
iajs-2833	123	14	(	(	PUNCT
iajs-2833	123	15	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	123	16	,	,	PUNCT
iajs-2833	123	17	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	123	18	)	)	PUNCT
iajs-2833	124	1	+	+	CCONJ
iajs-2833	124	2	(	(	PUNCT
iajs-2833	124	3	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	124	4	,	,	PUNCT
iajs-2833	124	5	𝑣4𝑛)]𝜙4	𝑣4𝑛)]𝜙4	NOUN
iajs-2833	124	6	(	(	PUNCT
iajs-2833	124	7	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	124	8	=	=	SYM
iajs-2833	124	9	∫	∫	PROPN
iajs-2833	124	10	0	0	NUM
iajs-2833	124	11	𝑇	𝑇	PROPN
iajs-2833	124	12	(	(	PUNCT
iajs-2833	124	13	𝑓4(𝑦4𝑛	𝑓4(𝑦4𝑛	ADJ
iajs-2833	124	14	,	,	PUNCT
iajs-2833	124	15	𝑢4	𝑢4	NOUN
iajs-2833	124	16	)	)	PUNCT
iajs-2833	124	17	,	,	PUNCT
iajs-2833	124	18	𝑣4𝑛)𝜙4	𝑣4𝑛)𝜙4	PRON
iajs-2833	124	19	(	(	PUNCT
iajs-2833	124	20	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	124	21	+	+	CCONJ
iajs-2833	124	22	(	(	PUNCT
iajs-2833	124	23	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	124	24	′	′	NUM
iajs-2833	124	25	,	,	PUNCT
iajs-2833	124	26	𝑣4𝑛	𝑣4𝑛	NOUN
iajs-2833	124	27	)	)	PUNCT
iajs-2833	124	28	𝜙4(0	𝜙4(0	NOUN
iajs-2833	124	29	)	)	PUNCT
iajs-2833	124	30	(	(	PUNCT
iajs-2833	124	31	46	46	NUM
iajs-2833	124	32	)	)	PUNCT
iajs-2833	124	33	∫	∫	PROPN
iajs-2833	124	34	0	0	X
iajs-2833	124	35	𝑇	𝑇	PROPN
iajs-2833	124	36	(	(	PUNCT
iajs-2833	124	37	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	124	38	,	,	PUNCT
iajs-2833	124	39	𝑣4𝑛)𝜙4	𝑣4𝑛)𝜙4	PRON
iajs-2833	124	40	′′𝑑𝑡	′′𝑑𝑡	VERB
iajs-2833	124	41	+	+	X
iajs-2833	124	42	∫	∫	PROPN
iajs-2833	124	43	0	0	X
iajs-2833	124	44	𝑇	𝑇	PROPN
iajs-2833	125	1	[	[	X
iajs-2833	125	2	(	(	PUNCT
iajs-2833	125	3	∇𝑦4𝑛	∇𝑦4𝑛	ADV
iajs-2833	125	4	,	,	PUNCT
iajs-2833	125	5	∇𝑣4𝑛	∇𝑣4𝑛	NUM
iajs-2833	125	6	)	)	PUNCT
iajs-2833	126	1	−	−	PROPN
iajs-2833	126	2	(	(	PUNCT
iajs-2833	126	3	𝑦1𝑛	𝑦1𝑛	PROPN
iajs-2833	126	4	,	,	PUNCT
iajs-2833	126	5	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	126	6	)	)	PUNCT
iajs-2833	126	7	+	+	CCONJ
iajs-2833	126	8	(	(	PUNCT
iajs-2833	126	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	126	10	,	,	PUNCT
iajs-2833	126	11	𝑣4𝑛	𝑣4𝑛	NOUN
iajs-2833	126	12	)	)	PUNCT
iajs-2833	126	13	−	−	PROPN
iajs-2833	126	14	(	(	PUNCT
iajs-2833	126	15	𝑦3𝑛	𝑦3𝑛	PROPN
iajs-2833	126	16	,	,	PUNCT
iajs-2833	126	17	𝑣4𝑛	𝑣4𝑛	PROPN
iajs-2833	126	18	)	)	PUNCT
iajs-2833	127	1	+	+	CCONJ
iajs-2833	127	2	(	(	PUNCT
iajs-2833	127	3	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	127	4	,	,	PUNCT
iajs-2833	127	5	𝑣4𝑛)]𝜙4	𝑣4𝑛)]𝜙4	NOUN
iajs-2833	127	6	(	(	PUNCT
iajs-2833	127	7	𝑡)𝑑𝑡=∫	𝑡)𝑑𝑡=∫	X
iajs-2833	127	8	0	0	NUM
iajs-2833	127	9	𝑇	𝑇	PROPN
iajs-2833	127	10	(	(	PUNCT
iajs-2833	127	11	𝑓4(𝑦4𝑛	𝑓4(𝑦4𝑛	ADJ
iajs-2833	127	12	,	,	PUNCT
iajs-2833	127	13	𝑢4	𝑢4	NOUN
iajs-2833	127	14	)	)	PUNCT
iajs-2833	127	15	,	,	PUNCT
iajs-2833	127	16	𝑣4𝑛)𝜙4	𝑣4𝑛)𝜙4	PRON
iajs-2833	127	17	(	(	PUNCT
iajs-2833	127	18	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	127	19	+	+	CCONJ
iajs-2833	127	20	(	(	PUNCT
iajs-2833	127	21	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	127	22	′	′	NUM
iajs-2833	127	23	,	,	PUNCT
iajs-2833	127	24	𝑣4𝑛)𝜙4(0	𝑣4𝑛)𝜙4(0	NOUN
iajs-2833	127	25	)	)	PUNCT
iajs-2833	127	26	−	−	PROPN
iajs-2833	127	27	(	(	PUNCT
iajs-2833	127	28	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	127	29	0	0	NUM
iajs-2833	127	30	,	,	PUNCT
iajs-2833	127	31	𝑣4𝑛)𝜙4	𝑣4𝑛)𝜙4	NUM
iajs-2833	127	32	′	′	NUM
iajs-2833	127	33	(	(	PUNCT
iajs-2833	127	34	0	0	NUM
iajs-2833	127	35	)	)	PUNCT
iajs-2833	127	36	(	(	PUNCT
iajs-2833	127	37	47	47	NUM
iajs-2833	127	38	)	)	PUNCT
iajs-2833	127	39	first	first	ADV
iajs-2833	127	40	,	,	PUNCT
iajs-2833	127	41	since	since	SCONJ
iajs-2833	127	42	𝑣𝑖𝑛	𝑣𝑖𝑛	NOUN
iajs-2833	127	43	→	→	SYM
iajs-2833	127	44	𝑣𝑖	𝑣𝑖	ADP
iajs-2833	127	45	st	st	PROPN
iajs-2833	127	46	in	in	ADP
iajs-2833	127	47	𝐿2(ω	𝐿2(ω	PROPN
iajs-2833	127	48	)	)	PUNCT
iajs-2833	127	49	⟹	⟹	VERB
iajs-2833	128	1	{	{	PUNCT
iajs-2833	128	2	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	PROPN
iajs-2833	128	3	(	(	PUNCT
iajs-2833	128	4	𝑡	𝑡	NOUN
iajs-2833	128	5	)	)	PUNCT
iajs-2833	128	6	→	→	SYM
iajs-2833	128	7	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	PROPN
iajs-2833	128	8	(	(	PUNCT
iajs-2833	128	9	𝑡	𝑡	NOUN
iajs-2833	128	10	)	)	PUNCT
iajs-2833	128	11	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	NOUN
iajs-2833	128	12	′(𝑡	′(𝑡	NOUN
iajs-2833	128	13	)	)	PUNCT
iajs-2833	128	14	→	→	SYM
iajs-2833	128	15	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	ADJ
iajs-2833	128	16	′(𝑡	′(𝑡	NOUN
iajs-2833	128	17	)	)	PUNCT
iajs-2833	128	18	st	st	PROPN
iajs-2833	128	19	in	in	ADP
iajs-2833	128	20	𝐿2(i	𝐿2(i	NOUN
iajs-2833	128	21	,	,	PUNCT
iajs-2833	128	22	v	v	NOUN
iajs-2833	128	23	)	)	PUNCT
iajs-2833	128	24	,	,	PUNCT
iajs-2833	128	25	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	PROPN
iajs-2833	128	26	(	(	PUNCT
iajs-2833	128	27	0	0	NUM
iajs-2833	128	28	)	)	PUNCT
iajs-2833	128	29	→	→	SYM
iajs-2833	128	30	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	PROPN
iajs-2833	128	31	(	(	PUNCT
iajs-2833	128	32	0	0	NUM
iajs-2833	128	33	)	)	PUNCT
iajs-2833	128	34	st	st	NOUN
iajs-2833	128	35	in	in	ADP
iajs-2833	128	36	𝐿2(ω	𝐿2(ω	PROPN
iajs-2833	128	37	)	)	PUNCT
iajs-2833	128	38	and	and	CCONJ
iajs-2833	128	39	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	PROPN
iajs-2833	128	40	′(0	′(0	PROPN
iajs-2833	128	41	)	)	PUNCT
iajs-2833	128	42	→	→	SYM
iajs-2833	128	43	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	PROPN
iajs-2833	128	44	′(0	′(0	PROPN
iajs-2833	128	45	)	)	PUNCT
iajs-2833	128	46	st	st	PROPN
iajs-2833	128	47	in	in	ADP
iajs-2833	128	48	𝐿2(ω	𝐿2(ω	PROPN
iajs-2833	128	49	)	)	PUNCT
iajs-2833	128	50	for	for	ADP
iajs-2833	128	51	𝑖	𝑖	NOUN
iajs-2833	128	52	=	=	NOUN
iajs-2833	128	53	1,2,3,4	1,2,3,4	NUM
iajs-2833	128	54	also	also	ADV
iajs-2833	128	55	since	since	SCONJ
iajs-2833	128	56	𝑣𝑖𝑛	𝑣𝑖𝑛	NOUN
iajs-2833	128	57	→	→	SYM
iajs-2833	128	58	𝑣𝑖	𝑣𝑖	ADP
iajs-2833	128	59	st	st	PROPN
iajs-2833	128	60	in	in	ADP
iajs-2833	128	61	𝑉	𝑉	PROPN
iajs-2833	128	62	⟹	⟹	PUNCT
iajs-2833	128	63	{	{	PUNCT
iajs-2833	128	64	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	NOUN
iajs-2833	128	65	′(𝑡	′(𝑡	NOUN
iajs-2833	128	66	)	)	PUNCT
iajs-2833	128	67	→	→	SYM
iajs-2833	128	68	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	ADJ
iajs-2833	128	69	′(𝑡	′(𝑡	NOUN
iajs-2833	128	70	)	)	PUNCT
iajs-2833	128	71	𝑣𝑖𝑛𝜙𝑖	𝑣𝑖𝑛𝜙𝑖	PROPN
iajs-2833	128	72	′′(𝑡	′′(𝑡	PROPN
iajs-2833	128	73	)	)	PUNCT
iajs-2833	128	74	→	→	SYM
iajs-2833	128	75	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	PROPN
iajs-2833	128	76	′′(𝑡	′′(𝑡	PROPN
iajs-2833	128	77	)	)	PUNCT
iajs-2833	128	78	st	st	NOUN
iajs-2833	128	79	in	in	ADP
iajs-2833	128	80	𝐿2(q	𝐿2(q	PROPN
iajs-2833	128	81	)	)	PUNCT
iajs-2833	128	82	.	.	PUNCT
iajs-2833	129	1	second	second	ADJ
iajs-2833	129	2	,	,	PUNCT
iajs-2833	129	3	we	we	PRON
iajs-2833	129	4	have	have	VERB
iajs-2833	129	5	𝑦𝑖𝑛𝑡	𝑦𝑖𝑛𝑡	NOUN
iajs-2833	129	6	→	→	SYM
iajs-2833	129	7	𝑦𝑖𝑡	𝑦𝑖𝑡	NOUN
iajs-2833	129	8	wk	wk	NOUN
iajs-2833	129	9	in	in	ADP
iajs-2833	129	10	𝐿2(q	𝐿2(q	NUM
iajs-2833	129	11	)	)	PUNCT
iajs-2833	129	12	and	and	CCONJ
iajs-2833	129	13	𝑦𝑖𝑛𝑡	𝑦𝑖𝑛𝑡	ADJ
iajs-2833	129	14	→	→	SYM
iajs-2833	129	15	𝑦𝑖𝑡	𝑦𝑖𝑡	NOUN
iajs-2833	129	16	wk	wk	NOUN
iajs-2833	129	17	in	in	ADP
iajs-2833	129	18	𝐿2(i	𝐿2(i	NOUN
iajs-2833	129	19	,	,	PUNCT
iajs-2833	129	20	v	v	NOUN
iajs-2833	129	21	)	)	PUNCT
iajs-2833	129	22	and	and	CCONJ
iajs-2833	129	23	st	st	PROPN
iajs-2833	129	24	in	in	ADP
iajs-2833	129	25	𝐿2(q	𝐿2(q	PROPN
iajs-2833	129	26	)	)	PUNCT
iajs-2833	129	27	.	.	PUNCT
iajs-2833	130	1	third	third	ADJ
iajs-2833	130	2	and	and	CCONJ
iajs-2833	130	3	on	on	ADP
iajs-2833	130	4	the	the	DET
iajs-2833	130	5	other	other	ADJ
iajs-2833	130	6	hand	hand	NOUN
iajs-2833	130	7	,	,	PUNCT
iajs-2833	130	8	let	let	VERB
iajs-2833	130	9	𝑤𝑖𝑛	𝑤𝑖𝑛	NOUN
iajs-2833	130	10	=	=	SYM
iajs-2833	130	11	𝑣𝑖𝑛	𝑣𝑖𝑛	NOUN
iajs-2833	130	12	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	130	13	and	and	CCONJ
iajs-2833	130	14	𝑤𝑖	𝑤𝑖	ADP
iajs-2833	130	15	=	=	SYM
iajs-2833	130	16	𝑣𝑖	𝑣𝑖	ADV
iajs-2833	130	17	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	130	18	then	then	ADV
iajs-2833	130	19	𝑤𝑖𝑛	𝑤𝑖𝑛	VERB
iajs-2833	130	20	→	→	PUNCT
iajs-2833	130	21	𝑤𝑖	𝑤𝑖	DET
iajs-2833	130	22	st	st	PROPN
iajs-2833	130	23	in	in	ADP
iajs-2833	130	24	𝐿2(q	𝐿2(q	PROPN
iajs-2833	130	25	)	)	PUNCT
iajs-2833	130	26	and	and	CCONJ
iajs-2833	130	27	then	then	ADV
iajs-2833	130	28	𝑤𝑖𝑛	𝑤𝑖𝑛	NOUN
iajs-2833	130	29	is	be	AUX
iajs-2833	130	30	measurable	measurable	ADJ
iajs-2833	130	31	w.r.t	w.r.t	NOUN
iajs-2833	130	32	.	.	PUNCT
iajs-2833	131	1	(	(	PUNCT
iajs-2833	131	2	𝑥	𝑥	NOUN
iajs-2833	131	3	,	,	PUNCT
iajs-2833	131	4	𝑡	𝑡	NOUN
iajs-2833	131	5	)	)	PUNCT
iajs-2833	131	6	,	,	PUNCT
iajs-2833	131	7	so	so	ADV
iajs-2833	131	8	using	use	VERB
iajs-2833	131	9	assm	assm	PROPN
iajs-2833	131	10	(	(	PUNCT
iajs-2833	131	11	a-(i	a-(i	ADJ
iajs-2833	131	12	)	)	PUNCT
iajs-2833	131	13	)	)	PUNCT
iajs-2833	131	14	,	,	PUNCT
iajs-2833	131	15	employing	employ	VERB
iajs-2833	131	16	proposition	proposition	NOUN
iajs-2833	131	17	1.3	1.3	NUM
iajs-2833	131	18	,	,	PUNCT
iajs-2833	131	19	the	the	DET
iajs-2833	131	20	(	(	PUNCT
iajs-2833	131	21	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2833	131	22	,	,	PUNCT
iajs-2833	131	23	𝑡	𝑡	PROPN
iajs-2833	131	24	,	,	PUNCT
iajs-2833	131	25	𝑦𝑖𝑛	𝑦𝑖𝑛	PROPN
iajs-2833	131	26	,	,	PUNCT
iajs-2833	131	27	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	131	28	)	)	PUNCT
iajs-2833	131	29	,	,	PUNCT
iajs-2833	131	30	𝑤𝑖𝑛)𝑑𝑥𝑑𝑡	𝑤𝑖𝑛)𝑑𝑥𝑑𝑡	PROPN
iajs-2833	131	31	is	be	AUX
iajs-2833	131	32	cont	cont	NOUN
iajs-2833	131	33	.	.	PUNCT
iajs-2833	132	1	w.r.t	w.r.t	PROPN
iajs-2833	132	2	.	.	PUNCT
iajs-2833	133	1	(	(	PUNCT
iajs-2833	133	2	𝑦𝑖𝑛	𝑦𝑖𝑛	PROPN
iajs-2833	133	3	,	,	PUNCT
iajs-2833	133	4	𝑢𝑖	𝑢𝑖	INTJ
iajs-2833	133	5	,	,	PUNCT
iajs-2833	133	6	𝑤𝑖𝑛	𝑤𝑖𝑛	NOUN
iajs-2833	133	7	)	)	PUNCT
iajs-2833	133	8	,	,	PUNCT
iajs-2833	133	9	then	then	ADV
iajs-2833	133	10	∫	∫	PROPN
iajs-2833	133	11	0	0	X
iajs-2833	133	12	𝑇	𝑇	PROPN
iajs-2833	133	13	(	(	PUNCT
iajs-2833	133	14	𝑓𝑖(𝑦𝑖𝑛	𝑓𝑖(𝑦𝑖𝑛	NOUN
iajs-2833	133	15	,	,	PUNCT
iajs-2833	133	16	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	133	17	)	)	PUNCT
iajs-2833	133	18	,	,	PUNCT
iajs-2833	133	19	𝑣𝑖𝑛)𝜙𝑖	𝑣𝑖𝑛)𝜙𝑖	NOUN
iajs-2833	133	20	(	(	PUNCT
iajs-2833	133	21	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	133	22	→	→	SYM
iajs-2833	133	23	∫	∫	PROPN
iajs-2833	133	24	0	0	NUM
iajs-2833	133	25	𝑇	𝑇	PROPN
iajs-2833	133	26	(	(	PUNCT
iajs-2833	133	27	𝑓𝑖(𝑦𝑖	𝑓𝑖(𝑦𝑖	PROPN
iajs-2833	133	28	,	,	PUNCT
iajs-2833	133	29	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	133	30	)	)	PUNCT
iajs-2833	133	31	,	,	PUNCT
iajs-2833	133	32	𝑣𝑖)𝜙𝑖	𝑣𝑖)𝜙𝑖	NUM
iajs-2833	133	33	(	(	PUNCT
iajs-2833	133	34	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	133	35	,	,	PUNCT
iajs-2833	133	36	∀𝑖	∀𝑖	PROPN
iajs-2833	133	37	=	=	NOUN
iajs-2833	133	38	1,2,3,4	1,2,3,4	NUM
iajs-2833	133	39	from	from	ADP
iajs-2833	133	40	these	these	DET
iajs-2833	133	41	convergences	convergence	NOUN
iajs-2833	133	42	,	,	PUNCT
iajs-2833	133	43	(	(	PUNCT
iajs-2833	133	44	26	26	NUM
iajs-2833	133	45	)	)	PUNCT
iajs-2833	133	46	,	,	PUNCT
iajs-2833	133	47	and	and	CCONJ
iajs-2833	133	48	(	(	PUNCT
iajs-2833	133	49	27	27	NUM
iajs-2833	133	50	)	)	PUNCT
iajs-2833	133	51	we	we	PRON
iajs-2833	133	52	can	can	AUX
iajs-2833	133	53	passage	passage	VERB
iajs-2833	133	54	the	the	DET
iajs-2833	133	55	limits	limit	NOUN
iajs-2833	133	56	in	in	ADP
iajs-2833	133	57	(	(	PUNCT
iajs-2833	133	58	(	(	PUNCT
iajs-2833	133	59	40)-(47	40)-(47	NOUN
iajs-2833	133	60	)	)	PUNCT
iajs-2833	133	61	)	)	PUNCT
iajs-2833	133	62	,	,	PUNCT
iajs-2833	133	63	to	to	PART
iajs-2833	133	64	get	get	VERB
iajs-2833	133	65	ihjpas	ihjpa	NOUN
iajs-2833	133	66	.	.	PUNCT
iajs-2833	134	1	53	53	NUM
iajs-2833	134	2	(	(	PUNCT
iajs-2833	134	3	3)2022	3)2022	NOUN
iajs-2833	134	4	167	167	NUM
iajs-2833	134	5	−	−	PROPN
iajs-2833	134	6	∫	∫	PROPN
iajs-2833	134	7	0	0	PUNCT
iajs-2833	134	8	𝑇	𝑇	PROPN
iajs-2833	134	9	(	(	PUNCT
iajs-2833	134	10	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2833	134	11	,	,	PUNCT
iajs-2833	134	12	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	134	13	′	′	NUM
iajs-2833	135	1	(	(	PUNCT
iajs-2833	135	2	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	135	3	+	+	NUM
iajs-2833	135	4	∫	∫	PROPN
iajs-2833	135	5	0	0	X
iajs-2833	135	6	𝑇	𝑇	PROPN
iajs-2833	135	7	[	[	X
iajs-2833	135	8	(	(	PUNCT
iajs-2833	135	9	∇𝑦1	∇𝑦1	NOUN
iajs-2833	135	10	,	,	PUNCT
iajs-2833	135	11	∇𝑣1	∇𝑣1	NOUN
iajs-2833	135	12	)	)	PUNCT
iajs-2833	135	13	+	+	CCONJ
iajs-2833	135	14	(	(	PUNCT
iajs-2833	135	15	𝑦1	𝑦1	PROPN
iajs-2833	135	16	,	,	PUNCT
iajs-2833	135	17	𝑣1	𝑣1	NOUN
iajs-2833	135	18	)	)	PUNCT
iajs-2833	135	19	−	−	PROPN
iajs-2833	136	1	(	(	PUNCT
iajs-2833	137	1	𝑦2	𝑦2	PROPN
iajs-2833	137	2	,	,	PUNCT
iajs-2833	137	3	𝑣1	𝑣1	PROPN
iajs-2833	137	4	)	)	PUNCT
iajs-2833	137	5	+	+	CCONJ
iajs-2833	137	6	(	(	PUNCT
iajs-2833	137	7	𝑦3	𝑦3	PROPN
iajs-2833	137	8	,	,	PUNCT
iajs-2833	137	9	𝑣1	𝑣1	PROPN
iajs-2833	137	10	)	)	PUNCT
iajs-2833	137	11	+	+	CCONJ
iajs-2833	137	12	(	(	PUNCT
iajs-2833	137	13	𝑦4	𝑦4	NOUN
iajs-2833	137	14	,	,	PUNCT
iajs-2833	137	15	𝑣1)]𝜙1	𝑣1)]𝜙1	INTJ
iajs-2833	137	16	(	(	PUNCT
iajs-2833	137	17	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	137	18	=	=	SYM
iajs-2833	137	19	∫	∫	PROPN
iajs-2833	137	20	0	0	X
iajs-2833	137	21	𝑇	𝑇	PROPN
iajs-2833	137	22	(	(	PUNCT
iajs-2833	137	23	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	137	24	,	,	PUNCT
iajs-2833	137	25	𝑢1	𝑢1	PROPN
iajs-2833	137	26	)	)	PUNCT
iajs-2833	137	27	,	,	PUNCT
iajs-2833	137	28	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	137	29	(	(	PUNCT
iajs-2833	137	30	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	137	31	+	+	CCONJ
iajs-2833	137	32	(	(	PUNCT
iajs-2833	137	33	𝑦1	𝑦1	PROPN
iajs-2833	137	34	′	′	NUM
iajs-2833	137	35	,	,	PUNCT
iajs-2833	137	36	𝑣1	𝑣1	NOUN
iajs-2833	137	37	)	)	PUNCT
iajs-2833	137	38	𝜙1(0	𝜙1(0	PROPN
iajs-2833	137	39	)	)	PUNCT
iajs-2833	137	40	(	(	PUNCT
iajs-2833	137	41	48	48	NUM
iajs-2833	137	42	)	)	PUNCT
iajs-2833	137	43	∫	∫	PROPN
iajs-2833	137	44	0	0	X
iajs-2833	137	45	𝑇	𝑇	PROPN
iajs-2833	137	46	(	(	PUNCT
iajs-2833	137	47	𝑦1	𝑦1	PROPN
iajs-2833	137	48	,	,	PUNCT
iajs-2833	137	49	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	137	50	′′𝑑𝑡	′′𝑑𝑡	VERB
iajs-2833	138	1	+	+	X
iajs-2833	138	2	∫	∫	PROPN
iajs-2833	138	3	0	0	X
iajs-2833	138	4	𝑇	𝑇	PROPN
iajs-2833	138	5	[	[	X
iajs-2833	138	6	(	(	PUNCT
iajs-2833	138	7	∇𝑦1	∇𝑦1	NOUN
iajs-2833	138	8	,	,	PUNCT
iajs-2833	138	9	∇𝑣1	∇𝑣1	NOUN
iajs-2833	138	10	)	)	PUNCT
iajs-2833	139	1	+	+	CCONJ
iajs-2833	139	2	(	(	PUNCT
iajs-2833	139	3	𝑦1	𝑦1	PROPN
iajs-2833	139	4	,	,	PUNCT
iajs-2833	139	5	𝑣1	𝑣1	NOUN
iajs-2833	139	6	)	)	PUNCT
iajs-2833	139	7	−	−	PROPN
iajs-2833	139	8	(	(	PUNCT
iajs-2833	139	9	𝑦2	𝑦2	PROPN
iajs-2833	139	10	,	,	PUNCT
iajs-2833	139	11	𝑣1	𝑣1	PROPN
iajs-2833	139	12	)	)	PUNCT
iajs-2833	139	13	+	+	CCONJ
iajs-2833	139	14	(	(	PUNCT
iajs-2833	139	15	𝑦3	𝑦3	PROPN
iajs-2833	139	16	,	,	PUNCT
iajs-2833	139	17	𝑣1	𝑣1	PROPN
iajs-2833	139	18	)	)	PUNCT
iajs-2833	139	19	+	+	CCONJ
iajs-2833	139	20	(	(	PUNCT
iajs-2833	139	21	𝑦4	𝑦4	NOUN
iajs-2833	139	22	,	,	PUNCT
iajs-2833	139	23	𝑣1)]𝜙1	𝑣1)]𝜙1	INTJ
iajs-2833	139	24	(	(	PUNCT
iajs-2833	139	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	139	26	=	=	SYM
iajs-2833	139	27	∫	∫	PROPN
iajs-2833	139	28	0	0	X
iajs-2833	139	29	𝑇	𝑇	PROPN
iajs-2833	139	30	(	(	PUNCT
iajs-2833	139	31	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	139	32	,	,	PUNCT
iajs-2833	139	33	𝑢1	𝑢1	PROPN
iajs-2833	139	34	)	)	PUNCT
iajs-2833	139	35	,	,	PUNCT
iajs-2833	139	36	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	139	37	(	(	PUNCT
iajs-2833	139	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	139	39	+	+	CCONJ
iajs-2833	139	40	(	(	PUNCT
iajs-2833	139	41	𝑦1	𝑦1	PROPN
iajs-2833	139	42	′	′	NUM
iajs-2833	139	43	,	,	PUNCT
iajs-2833	139	44	𝑣1)𝜙1(0	𝑣1)𝜙1(0	PROPN
iajs-2833	139	45	)	)	PUNCT
iajs-2833	139	46	−	−	PROPN
iajs-2833	140	1	(	(	PUNCT
iajs-2833	140	2	𝑦1	𝑦1	NOUN
iajs-2833	140	3	0	0	NUM
iajs-2833	140	4	,	,	PUNCT
iajs-2833	140	5	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	140	6	′	′	NUM
iajs-2833	140	7	(	(	PUNCT
iajs-2833	140	8	0	0	NUM
iajs-2833	140	9	)	)	PUNCT
iajs-2833	140	10	(	(	PUNCT
iajs-2833	140	11	49	49	NUM
iajs-2833	140	12	)	)	PUNCT
iajs-2833	140	13	−	−	NUM
iajs-2833	141	1	∫	∫	PROPN
iajs-2833	141	2	0	0	X
iajs-2833	141	3	𝑇	𝑇	PROPN
iajs-2833	141	4	(	(	PUNCT
iajs-2833	141	5	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	141	6	,	,	PUNCT
iajs-2833	141	7	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	141	8	′	′	NOUN
iajs-2833	141	9	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	141	10	+	+	CCONJ
iajs-2833	141	11	∫	∫	PROPN
iajs-2833	141	12	0	0	X
iajs-2833	141	13	𝑇	𝑇	PROPN
iajs-2833	142	1	[	[	X
iajs-2833	142	2	(	(	PUNCT
iajs-2833	142	3	∇𝑦2	∇𝑦2	NOUN
iajs-2833	142	4	,	,	PUNCT
iajs-2833	142	5	∇𝑣2	∇𝑣2	PRON
iajs-2833	142	6	)	)	PUNCT
iajs-2833	143	1	+	+	CCONJ
iajs-2833	143	2	(	(	PUNCT
iajs-2833	143	3	𝑦1	𝑦1	PROPN
iajs-2833	143	4	,	,	PUNCT
iajs-2833	143	5	𝑣2	𝑣2	PROPN
iajs-2833	143	6	)	)	PUNCT
iajs-2833	143	7	+	+	CCONJ
iajs-2833	143	8	(	(	PUNCT
iajs-2833	143	9	𝑦2	𝑦2	PROPN
iajs-2833	143	10	,	,	PUNCT
iajs-2833	143	11	𝑣2	𝑣2	PROPN
iajs-2833	143	12	)	)	PUNCT
iajs-2833	143	13	−	−	PROPN
iajs-2833	143	14	(	(	PUNCT
iajs-2833	143	15	𝑦3	𝑦3	PROPN
iajs-2833	143	16	,	,	PUNCT
iajs-2833	143	17	𝑣2	𝑣2	PROPN
iajs-2833	143	18	)	)	PUNCT
iajs-2833	143	19	−	−	PROPN
iajs-2833	143	20	(	(	PUNCT
iajs-2833	143	21	𝑦4	𝑦4	PROPN
iajs-2833	143	22	,	,	PUNCT
iajs-2833	143	23	𝑣2)]𝜙2	𝑣2)]𝜙2	PROPN
iajs-2833	143	24	(	(	PUNCT
iajs-2833	143	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	143	26	=	=	SYM
iajs-2833	143	27	∫	∫	PROPN
iajs-2833	143	28	0	0	X
iajs-2833	143	29	𝑇	𝑇	PROPN
iajs-2833	143	30	(	(	PUNCT
iajs-2833	143	31	𝑓2(𝑦2	𝑓2(𝑦2	PROPN
iajs-2833	143	32	,	,	PUNCT
iajs-2833	143	33	𝑢2	𝑢2	PROPN
iajs-2833	143	34	)	)	PUNCT
iajs-2833	143	35	,	,	PUNCT
iajs-2833	143	36	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	143	37	(	(	PUNCT
iajs-2833	143	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	143	39	+	+	CCONJ
iajs-2833	143	40	(	(	PUNCT
iajs-2833	143	41	𝑦2	𝑦2	NOUN
iajs-2833	143	42	′	′	PROPN
iajs-2833	143	43	,	,	PUNCT
iajs-2833	143	44	𝑣2	𝑣2	NOUN
iajs-2833	143	45	)	)	PUNCT
iajs-2833	143	46	𝜙1(0	𝜙1(0	NOUN
iajs-2833	143	47	)	)	PUNCT
iajs-2833	143	48	(	(	PUNCT
iajs-2833	143	49	50	50	NUM
iajs-2833	143	50	)	)	PUNCT
iajs-2833	143	51	∫	∫	PROPN
iajs-2833	143	52	0	0	X
iajs-2833	143	53	𝑇	𝑇	PROPN
iajs-2833	143	54	(	(	PUNCT
iajs-2833	143	55	𝑦2	𝑦2	PROPN
iajs-2833	143	56	,	,	PUNCT
iajs-2833	143	57	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	144	1	′′(𝑡)𝑑𝑡	′′(𝑡)𝑑𝑡	PROPN
iajs-2833	144	2	+	+	CCONJ
iajs-2833	144	3	∫	∫	PROPN
iajs-2833	144	4	0	0	X
iajs-2833	144	5	𝑇	𝑇	PROPN
iajs-2833	145	1	[	[	X
iajs-2833	145	2	(	(	PUNCT
iajs-2833	145	3	∇𝑦2	∇𝑦2	NOUN
iajs-2833	145	4	,	,	PUNCT
iajs-2833	145	5	∇𝑣2	∇𝑣2	PRON
iajs-2833	145	6	)	)	PUNCT
iajs-2833	146	1	+	+	CCONJ
iajs-2833	146	2	(	(	PUNCT
iajs-2833	146	3	𝑦1	𝑦1	PROPN
iajs-2833	146	4	,	,	PUNCT
iajs-2833	146	5	𝑣2	𝑣2	PROPN
iajs-2833	146	6	)	)	PUNCT
iajs-2833	146	7	+	+	CCONJ
iajs-2833	146	8	(	(	PUNCT
iajs-2833	146	9	𝑦2	𝑦2	PROPN
iajs-2833	146	10	,	,	PUNCT
iajs-2833	146	11	𝑣2	𝑣2	PROPN
iajs-2833	146	12	)	)	PUNCT
iajs-2833	146	13	−	−	PROPN
iajs-2833	146	14	(	(	PUNCT
iajs-2833	146	15	𝑦3	𝑦3	PROPN
iajs-2833	146	16	,	,	PUNCT
iajs-2833	146	17	𝑣2	𝑣2	PROPN
iajs-2833	146	18	)	)	PUNCT
iajs-2833	146	19	−	−	PROPN
iajs-2833	146	20	(	(	PUNCT
iajs-2833	146	21	𝑦4	𝑦4	PROPN
iajs-2833	146	22	,	,	PUNCT
iajs-2833	146	23	𝑣2)]𝜙2	𝑣2)]𝜙2	PROPN
iajs-2833	146	24	(	(	PUNCT
iajs-2833	146	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	146	26	=	=	SYM
iajs-2833	146	27	∫	∫	PROPN
iajs-2833	146	28	0	0	X
iajs-2833	146	29	𝑇	𝑇	PROPN
iajs-2833	146	30	(	(	PUNCT
iajs-2833	146	31	𝑓2(𝑦2	𝑓2(𝑦2	PROPN
iajs-2833	146	32	,	,	PUNCT
iajs-2833	146	33	𝑢2	𝑢2	PROPN
iajs-2833	146	34	)	)	PUNCT
iajs-2833	146	35	,	,	PUNCT
iajs-2833	146	36	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	146	37	(	(	PUNCT
iajs-2833	146	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	146	39	+	+	CCONJ
iajs-2833	146	40	(	(	PUNCT
iajs-2833	146	41	𝑦2	𝑦2	NOUN
iajs-2833	146	42	′	′	NUM
iajs-2833	146	43	,	,	PUNCT
iajs-2833	146	44	𝑣2)𝜙2(0	𝑣2)𝜙2(0	PROPN
iajs-2833	146	45	)	)	PUNCT
iajs-2833	146	46	−	−	PROPN
iajs-2833	146	47	(	(	PUNCT
iajs-2833	146	48	𝑦2	𝑦2	PROPN
iajs-2833	146	49	0	0	NUM
iajs-2833	146	50	,	,	PUNCT
iajs-2833	146	51	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	146	52	′	′	NUM
iajs-2833	146	53	(	(	PUNCT
iajs-2833	146	54	0	0	NUM
iajs-2833	146	55	)	)	PUNCT
iajs-2833	146	56	(	(	PUNCT
iajs-2833	146	57	51	51	NUM
iajs-2833	146	58	)	)	PUNCT
iajs-2833	146	59	−	−	ADP
iajs-2833	147	1	∫	∫	PROPN
iajs-2833	147	2	0	0	X
iajs-2833	147	3	𝑇	𝑇	PROPN
iajs-2833	147	4	(	(	PUNCT
iajs-2833	147	5	𝑦3𝑡	𝑦3𝑡	PROPN
iajs-2833	147	6	,	,	PUNCT
iajs-2833	147	7	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	147	8	′	′	NUM
iajs-2833	147	9	(	(	PUNCT
iajs-2833	147	10	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	147	11	+	+	NUM
iajs-2833	147	12	∫	∫	PROPN
iajs-2833	147	13	0	0	X
iajs-2833	147	14	𝑇	𝑇	PROPN
iajs-2833	148	1	[	[	X
iajs-2833	148	2	(	(	PUNCT
iajs-2833	148	3	∇𝑦3	∇𝑦3	PROPN
iajs-2833	148	4	,	,	PUNCT
iajs-2833	148	5	∇𝑣3	∇𝑣3	NOUN
iajs-2833	148	6	)	)	PUNCT
iajs-2833	148	7	−	−	PROPN
iajs-2833	149	1	(	(	PUNCT
iajs-2833	149	2	𝑦1	𝑦1	NOUN
iajs-2833	149	3	,	,	PUNCT
iajs-2833	149	4	𝑣3	𝑣3	ADJ
iajs-2833	149	5	)	)	PUNCT
iajs-2833	149	6	+	+	CCONJ
iajs-2833	149	7	(	(	PUNCT
iajs-2833	149	8	𝑦2	𝑦2	NOUN
iajs-2833	149	9	,	,	PUNCT
iajs-2833	149	10	𝑣3	𝑣3	ADJ
iajs-2833	149	11	)	)	PUNCT
iajs-2833	149	12	+	+	CCONJ
iajs-2833	149	13	(	(	PUNCT
iajs-2833	149	14	𝑦3	𝑦3	PROPN
iajs-2833	149	15	,	,	PUNCT
iajs-2833	149	16	𝑣3	𝑣3	ADJ
iajs-2833	149	17	)	)	PUNCT
iajs-2833	149	18	+	+	CCONJ
iajs-2833	149	19	(	(	PUNCT
iajs-2833	149	20	𝑦4	𝑦4	NOUN
iajs-2833	149	21	,	,	PUNCT
iajs-2833	149	22	𝑣3)]𝜙3	𝑣3)]𝜙3	PROPN
iajs-2833	149	23	(	(	PUNCT
iajs-2833	149	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	149	25	=	=	SYM
iajs-2833	149	26	∫	∫	PROPN
iajs-2833	149	27	0	0	NUM
iajs-2833	149	28	𝑇	𝑇	PROPN
iajs-2833	149	29	(	(	PUNCT
iajs-2833	149	30	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	149	31	,	,	PUNCT
iajs-2833	149	32	𝑢3	𝑢3	PROPN
iajs-2833	149	33	)	)	PUNCT
iajs-2833	149	34	,	,	PUNCT
iajs-2833	149	35	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	149	36	(	(	PUNCT
iajs-2833	149	37	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	149	38	+	+	CCONJ
iajs-2833	149	39	(	(	PUNCT
iajs-2833	149	40	𝑦3	𝑦3	PROPN
iajs-2833	149	41	′	′	NOUN
iajs-2833	149	42	,	,	PUNCT
iajs-2833	149	43	𝑣3	𝑣3	ADJ
iajs-2833	149	44	)	)	PUNCT
iajs-2833	149	45	𝜙3(0	𝜙3(0	PROPN
iajs-2833	149	46	)	)	PUNCT
iajs-2833	149	47	(	(	PUNCT
iajs-2833	149	48	52	52	NUM
iajs-2833	149	49	)	)	PUNCT
iajs-2833	149	50	∫	∫	PROPN
iajs-2833	149	51	0	0	X
iajs-2833	149	52	𝑇	𝑇	PROPN
iajs-2833	149	53	(	(	PUNCT
iajs-2833	149	54	𝑦3	𝑦3	PROPN
iajs-2833	149	55	,	,	PUNCT
iajs-2833	149	56	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	149	57	′′𝑑𝑡	′′𝑑𝑡	VERB
iajs-2833	150	1	+	+	X
iajs-2833	150	2	∫	∫	PROPN
iajs-2833	150	3	0	0	X
iajs-2833	150	4	𝑇	𝑇	PROPN
iajs-2833	150	5	[	[	X
iajs-2833	150	6	(	(	PUNCT
iajs-2833	150	7	∇𝑦3	∇𝑦3	PROPN
iajs-2833	150	8	,	,	PUNCT
iajs-2833	150	9	∇𝑣3	∇𝑣3	NOUN
iajs-2833	150	10	)	)	PUNCT
iajs-2833	150	11	−	−	PROPN
iajs-2833	151	1	(	(	PUNCT
iajs-2833	151	2	𝑦1	𝑦1	NOUN
iajs-2833	151	3	,	,	PUNCT
iajs-2833	151	4	𝑣3	𝑣3	ADJ
iajs-2833	151	5	)	)	PUNCT
iajs-2833	151	6	+	+	CCONJ
iajs-2833	151	7	(	(	PUNCT
iajs-2833	151	8	𝑦2	𝑦2	NOUN
iajs-2833	151	9	,	,	PUNCT
iajs-2833	151	10	𝑣3	𝑣3	ADJ
iajs-2833	151	11	)	)	PUNCT
iajs-2833	151	12	+	+	CCONJ
iajs-2833	151	13	(	(	PUNCT
iajs-2833	151	14	𝑦3	𝑦3	PROPN
iajs-2833	151	15	,	,	PUNCT
iajs-2833	151	16	𝑣3	𝑣3	ADJ
iajs-2833	151	17	)	)	PUNCT
iajs-2833	151	18	+	+	CCONJ
iajs-2833	151	19	(	(	PUNCT
iajs-2833	151	20	𝑦4	𝑦4	NOUN
iajs-2833	151	21	,	,	PUNCT
iajs-2833	151	22	𝑣3)]𝜙3	𝑣3)]𝜙3	PROPN
iajs-2833	151	23	(	(	PUNCT
iajs-2833	151	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	151	25	=	=	SYM
iajs-2833	151	26	∫	∫	PROPN
iajs-2833	151	27	0	0	NUM
iajs-2833	151	28	𝑇	𝑇	PROPN
iajs-2833	151	29	(	(	PUNCT
iajs-2833	151	30	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	151	31	,	,	PUNCT
iajs-2833	151	32	𝑢3	𝑢3	PROPN
iajs-2833	151	33	)	)	PUNCT
iajs-2833	151	34	,	,	PUNCT
iajs-2833	151	35	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	151	36	(	(	PUNCT
iajs-2833	151	37	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	151	38	+	+	CCONJ
iajs-2833	151	39	(	(	PUNCT
iajs-2833	151	40	𝑦3	𝑦3	PROPN
iajs-2833	151	41	′	′	NOUN
iajs-2833	151	42	,	,	PUNCT
iajs-2833	151	43	𝑣3)𝜙3(0	𝑣3)𝜙3(0	PROPN
iajs-2833	151	44	)	)	PUNCT
iajs-2833	151	45	−	−	PROPN
iajs-2833	151	46	(	(	PUNCT
iajs-2833	151	47	𝑦3	𝑦3	PROPN
iajs-2833	151	48	0	0	NUM
iajs-2833	151	49	,	,	PUNCT
iajs-2833	151	50	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	151	51	′	′	NUM
iajs-2833	151	52	(	(	PUNCT
iajs-2833	151	53	0	0	NUM
iajs-2833	151	54	)	)	PUNCT
iajs-2833	151	55	(	(	PUNCT
iajs-2833	151	56	53	53	NUM
iajs-2833	151	57	)	)	PUNCT
iajs-2833	151	58	−	−	ADP
iajs-2833	152	1	∫	∫	PROPN
iajs-2833	152	2	0	0	X
iajs-2833	152	3	𝑇	𝑇	PROPN
iajs-2833	152	4	(	(	PUNCT
iajs-2833	152	5	𝑦4𝑡	𝑦4𝑡	PROPN
iajs-2833	152	6	,	,	PUNCT
iajs-2833	152	7	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	152	8	′	′	NUM
iajs-2833	152	9	(	(	PUNCT
iajs-2833	152	10	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	152	11	+	+	NUM
iajs-2833	152	12	∫	∫	PROPN
iajs-2833	152	13	0	0	X
iajs-2833	152	14	𝑇	𝑇	PROPN
iajs-2833	153	1	[	[	X
iajs-2833	153	2	(	(	PUNCT
iajs-2833	153	3	∇𝑦4	∇𝑦4	ADJ
iajs-2833	153	4	,	,	PUNCT
iajs-2833	153	5	∇𝑣4	∇𝑣4	NUM
iajs-2833	153	6	)	)	PUNCT
iajs-2833	153	7	−	−	PROPN
iajs-2833	154	1	(	(	PUNCT
iajs-2833	154	2	𝑦1	𝑦1	NOUN
iajs-2833	154	3	,	,	PUNCT
iajs-2833	154	4	𝑣4	𝑣4	NOUN
iajs-2833	154	5	)	)	PUNCT
iajs-2833	154	6	+	+	CCONJ
iajs-2833	154	7	(	(	PUNCT
iajs-2833	154	8	𝑦2	𝑦2	NOUN
iajs-2833	154	9	,	,	PUNCT
iajs-2833	154	10	𝑣4	𝑣4	NOUN
iajs-2833	154	11	)	)	PUNCT
iajs-2833	154	12	−	−	PROPN
iajs-2833	154	13	(	(	PUNCT
iajs-2833	154	14	𝑦3	𝑦3	PROPN
iajs-2833	154	15	,	,	PUNCT
iajs-2833	154	16	𝑣4	𝑣4	NOUN
iajs-2833	154	17	)	)	PUNCT
iajs-2833	154	18	+	+	CCONJ
iajs-2833	154	19	(	(	PUNCT
iajs-2833	154	20	𝑦4	𝑦4	NOUN
iajs-2833	154	21	,	,	PUNCT
iajs-2833	154	22	𝑣4)]𝜙4	𝑣4)]𝜙4	NOUN
iajs-2833	154	23	(	(	PUNCT
iajs-2833	154	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	154	25	=	=	SYM
iajs-2833	154	26	∫	∫	PROPN
iajs-2833	154	27	0	0	NUM
iajs-2833	154	28	𝑇	𝑇	PROPN
iajs-2833	154	29	(	(	PUNCT
iajs-2833	154	30	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	154	31	,	,	PUNCT
iajs-2833	154	32	𝑢4	𝑢4	NOUN
iajs-2833	154	33	)	)	PUNCT
iajs-2833	154	34	,	,	PUNCT
iajs-2833	154	35	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	154	36	(	(	PUNCT
iajs-2833	154	37	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	154	38	+	+	CCONJ
iajs-2833	154	39	(	(	PUNCT
iajs-2833	154	40	𝑦4	𝑦4	PROPN
iajs-2833	154	41	′	′	NUM
iajs-2833	154	42	,	,	PUNCT
iajs-2833	154	43	𝑣4	𝑣4	NOUN
iajs-2833	154	44	)	)	PUNCT
iajs-2833	154	45	𝜙4(0	𝜙4(0	NOUN
iajs-2833	154	46	)	)	PUNCT
iajs-2833	154	47	(	(	PUNCT
iajs-2833	154	48	54	54	NUM
iajs-2833	154	49	)	)	PUNCT
iajs-2833	154	50	∫	∫	PROPN
iajs-2833	154	51	0	0	X
iajs-2833	155	1	𝑇	𝑇	PROPN
iajs-2833	155	2	(	(	PUNCT
iajs-2833	155	3	𝑦4	𝑦4	NOUN
iajs-2833	155	4	,	,	PUNCT
iajs-2833	155	5	𝑣4)𝜙4	𝑣4)𝜙4	VERB
iajs-2833	155	6	′′𝑑𝑡	′′𝑑𝑡	VERB
iajs-2833	156	1	+	+	CCONJ
iajs-2833	156	2	∫	∫	PROPN
iajs-2833	156	3	0	0	X
iajs-2833	156	4	𝑇	𝑇	PROPN
iajs-2833	156	5	[	[	X
iajs-2833	156	6	(	(	PUNCT
iajs-2833	156	7	∇𝑦4	∇𝑦4	ADJ
iajs-2833	156	8	,	,	PUNCT
iajs-2833	156	9	∇𝑣4	∇𝑣4	NUM
iajs-2833	156	10	)	)	PUNCT
iajs-2833	156	11	−	−	PROPN
iajs-2833	157	1	(	(	PUNCT
iajs-2833	157	2	𝑦1	𝑦1	NOUN
iajs-2833	157	3	,	,	PUNCT
iajs-2833	157	4	𝑣4	𝑣4	NOUN
iajs-2833	157	5	)	)	PUNCT
iajs-2833	157	6	+	+	CCONJ
iajs-2833	157	7	(	(	PUNCT
iajs-2833	157	8	𝑦2	𝑦2	NOUN
iajs-2833	157	9	,	,	PUNCT
iajs-2833	157	10	𝑣4	𝑣4	NOUN
iajs-2833	157	11	)	)	PUNCT
iajs-2833	157	12	−	−	PROPN
iajs-2833	157	13	(	(	PUNCT
iajs-2833	157	14	𝑦3	𝑦3	PROPN
iajs-2833	157	15	,	,	PUNCT
iajs-2833	157	16	𝑣4	𝑣4	NOUN
iajs-2833	157	17	)	)	PUNCT
iajs-2833	157	18	+	+	CCONJ
iajs-2833	157	19	(	(	PUNCT
iajs-2833	157	20	𝑦4	𝑦4	NOUN
iajs-2833	157	21	,	,	PUNCT
iajs-2833	157	22	𝑣4)]𝜙4	𝑣4)]𝜙4	NOUN
iajs-2833	157	23	(	(	PUNCT
iajs-2833	157	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	157	25	=	=	SYM
iajs-2833	157	26	∫	∫	PROPN
iajs-2833	157	27	0	0	X
iajs-2833	157	28	𝑇	𝑇	PROPN
iajs-2833	157	29	(	(	PUNCT
iajs-2833	157	30	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	157	31	,	,	PUNCT
iajs-2833	157	32	𝑢4	𝑢4	NOUN
iajs-2833	157	33	)	)	PUNCT
iajs-2833	157	34	,	,	PUNCT
iajs-2833	157	35	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	157	36	(	(	PUNCT
iajs-2833	157	37	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	157	38	+	+	CCONJ
iajs-2833	157	39	(	(	PUNCT
iajs-2833	157	40	𝑦4	𝑦4	PROPN
iajs-2833	157	41	′	′	NUM
iajs-2833	157	42	,	,	PUNCT
iajs-2833	157	43	𝑣4)𝜙4(0	𝑣4)𝜙4(0	AUX
iajs-2833	157	44	)	)	PUNCT
iajs-2833	157	45	−	−	PROPN
iajs-2833	157	46	(	(	PUNCT
iajs-2833	157	47	𝑦4	𝑦4	PROPN
iajs-2833	157	48	0	0	NUM
iajs-2833	157	49	,	,	PUNCT
iajs-2833	157	50	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	157	51	′	′	NUM
iajs-2833	157	52	(	(	PUNCT
iajs-2833	157	53	0	0	NUM
iajs-2833	157	54	)	)	PUNCT
iajs-2833	157	55	(	(	PUNCT
iajs-2833	157	56	55	55	NUM
iajs-2833	157	57	)	)	PUNCT
iajs-2833	157	58	case1	case1	PROPN
iajs-2833	157	59	:	:	PUNCT
iajs-2833	157	60	choose	choose	VERB
iajs-2833	157	61	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	157	62	∈	∈	PROPN
iajs-2833	157	63	𝐶2[0	𝐶2[0	PROPN
iajs-2833	157	64	,	,	PUNCT
iajs-2833	157	65	𝑇	𝑇	PROPN
iajs-2833	157	66	]	]	PUNCT
iajs-2833	157	67	s.t	s.t	PROPN
iajs-2833	157	68	.	.	PROPN
iajs-2833	157	69	𝜙𝑖(0	𝜙𝑖(0	PROPN
iajs-2833	157	70	)	)	PUNCT
iajs-2833	157	71	=	=	PUNCT
iajs-2833	157	72	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	157	73	′(0	′(0	NOUN
iajs-2833	157	74	)	)	PUNCT
iajs-2833	158	1	=	=	SYM
iajs-2833	158	2	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	158	3	′(𝑇	′(𝑇	NOUN
iajs-2833	158	4	)	)	PUNCT
iajs-2833	159	1	=	=	PRON
iajs-2833	159	2	𝜙𝑖	𝜙𝑖	X
iajs-2833	159	3	(	(	PUNCT
iajs-2833	159	4	𝑇	𝑇	PROPN
iajs-2833	159	5	)	)	PUNCT
iajs-2833	159	6	=	=	SYM
iajs-2833	159	7	0	0	NUM
iajs-2833	159	8	,	,	PUNCT
iajs-2833	159	9	∀𝑖	∀𝑖	PROPN
iajs-2833	159	10	=	=	NOUN
iajs-2833	159	11	1,2,3,4	1,2,3,4	NUM
iajs-2833	159	12	substituting	substituting	NOUN
iajs-2833	159	13	in	in	ADP
iajs-2833	159	14	(	(	PUNCT
iajs-2833	159	15	49	49	NUM
iajs-2833	159	16	)	)	PUNCT
iajs-2833	159	17	,	,	PUNCT
iajs-2833	159	18	(	(	PUNCT
iajs-2833	159	19	51	51	NUM
iajs-2833	159	20	)	)	PUNCT
iajs-2833	159	21	,	,	PUNCT
iajs-2833	159	22	(	(	PUNCT
iajs-2833	159	23	53	53	NUM
iajs-2833	159	24	)	)	PUNCT
iajs-2833	159	25	,	,	PUNCT
iajs-2833	159	26	(	(	PUNCT
iajs-2833	159	27	55	55	NUM
iajs-2833	159	28	)	)	PUNCT
iajs-2833	159	29	ibps2	ibps2	NOUN
iajs-2833	160	1	the	the	DET
iajs-2833	160	2	1st	1st	ADJ
iajs-2833	160	3	terms	term	NOUN
iajs-2833	160	4	in	in	ADP
iajs-2833	160	5	the	the	DET
iajs-2833	160	6	lhs	lhs	PROPN
iajs-2833	160	7	,	,	PUNCT
iajs-2833	160	8	i.e.	i.e.	X
iajs-2833	160	9	∫	∫	PROPN
iajs-2833	160	10	0	0	X
iajs-2833	160	11	𝑇	𝑇	PROPN
iajs-2833	160	12	(	(	PUNCT
iajs-2833	160	13	𝑦1𝑡𝑡	𝑦1𝑡𝑡	X
iajs-2833	160	14	,	,	PUNCT
iajs-2833	160	15	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	160	16	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	160	17	+	+	CCONJ
iajs-2833	160	18	∫	∫	PROPN
iajs-2833	160	19	0	0	X
iajs-2833	160	20	𝑇	𝑇	PROPN
iajs-2833	161	1	[	[	X
iajs-2833	161	2	(	(	PUNCT
iajs-2833	161	3	∇𝑦1	∇𝑦1	NOUN
iajs-2833	161	4	,	,	PUNCT
iajs-2833	161	5	∇𝑣1	∇𝑣1	NOUN
iajs-2833	161	6	)	)	PUNCT
iajs-2833	161	7	+	+	CCONJ
iajs-2833	161	8	(	(	PUNCT
iajs-2833	161	9	𝑦1	𝑦1	PROPN
iajs-2833	161	10	,	,	PUNCT
iajs-2833	161	11	𝑣1	𝑣1	NOUN
iajs-2833	161	12	)	)	PUNCT
iajs-2833	161	13	−	−	PROPN
iajs-2833	161	14	(	(	PUNCT
iajs-2833	161	15	𝑦2	𝑦2	PROPN
iajs-2833	161	16	,	,	PUNCT
iajs-2833	161	17	𝑣1	𝑣1	PROPN
iajs-2833	161	18	)	)	PUNCT
iajs-2833	161	19	+	+	CCONJ
iajs-2833	161	20	(	(	PUNCT
iajs-2833	161	21	𝑦3	𝑦3	PROPN
iajs-2833	161	22	,	,	PUNCT
iajs-2833	161	23	𝑣1	𝑣1	PROPN
iajs-2833	161	24	)	)	PUNCT
iajs-2833	161	25	+	+	CCONJ
iajs-2833	161	26	(	(	PUNCT
iajs-2833	161	27	𝑦4	𝑦4	NOUN
iajs-2833	161	28	,	,	PUNCT
iajs-2833	161	29	𝑣1)]𝜙1	𝑣1)]𝜙1	INTJ
iajs-2833	161	30	(	(	PUNCT
iajs-2833	161	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	161	32	=	=	SYM
iajs-2833	161	33	∫	∫	PROPN
iajs-2833	161	34	0	0	X
iajs-2833	161	35	𝑇	𝑇	PROPN
iajs-2833	161	36	(	(	PUNCT
iajs-2833	161	37	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	161	38	,	,	PUNCT
iajs-2833	161	39	𝑢1	𝑢1	PROPN
iajs-2833	161	40	)	)	PUNCT
iajs-2833	161	41	,	,	PUNCT
iajs-2833	161	42	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	161	43	(	(	PUNCT
iajs-2833	161	44	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	161	45	(	(	PUNCT
iajs-2833	161	46	56	56	NUM
iajs-2833	161	47	)	)	PUNCT
iajs-2833	161	48	∫	∫	PROPN
iajs-2833	161	49	0	0	X
iajs-2833	161	50	𝑇	𝑇	PROPN
iajs-2833	161	51	(	(	PUNCT
iajs-2833	161	52	𝑦2𝑡𝑡	𝑦2𝑡𝑡	X
iajs-2833	161	53	,	,	PUNCT
iajs-2833	161	54	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	161	55	(	(	PUNCT
iajs-2833	161	56	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	161	57	+	+	NUM
iajs-2833	161	58	∫	∫	PROPN
iajs-2833	161	59	0	0	X
iajs-2833	161	60	𝑇	𝑇	PROPN
iajs-2833	162	1	[	[	X
iajs-2833	162	2	(	(	PUNCT
iajs-2833	162	3	∇𝑦2	∇𝑦2	NOUN
iajs-2833	162	4	,	,	PUNCT
iajs-2833	162	5	∇𝑣2	∇𝑣2	PRON
iajs-2833	162	6	)	)	PUNCT
iajs-2833	163	1	+	+	CCONJ
iajs-2833	163	2	(	(	PUNCT
iajs-2833	163	3	𝑦1	𝑦1	PROPN
iajs-2833	163	4	,	,	PUNCT
iajs-2833	163	5	𝑣2	𝑣2	PROPN
iajs-2833	163	6	)	)	PUNCT
iajs-2833	163	7	+	+	CCONJ
iajs-2833	163	8	(	(	PUNCT
iajs-2833	163	9	𝑦2	𝑦2	PROPN
iajs-2833	163	10	,	,	PUNCT
iajs-2833	163	11	𝑣2	𝑣2	PROPN
iajs-2833	163	12	)	)	PUNCT
iajs-2833	163	13	−	−	PROPN
iajs-2833	163	14	(	(	PUNCT
iajs-2833	163	15	𝑦3	𝑦3	PROPN
iajs-2833	163	16	,	,	PUNCT
iajs-2833	163	17	𝑣2	𝑣2	PROPN
iajs-2833	163	18	)	)	PUNCT
iajs-2833	163	19	−	−	PROPN
iajs-2833	163	20	(	(	PUNCT
iajs-2833	163	21	𝑦4	𝑦4	PROPN
iajs-2833	163	22	,	,	PUNCT
iajs-2833	163	23	𝑣2)]𝜙2	𝑣2)]𝜙2	PROPN
iajs-2833	163	24	(	(	PUNCT
iajs-2833	163	25	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	163	26	=	=	SYM
iajs-2833	163	27	∫	∫	PROPN
iajs-2833	163	28	0	0	X
iajs-2833	163	29	𝑇	𝑇	PROPN
iajs-2833	163	30	(	(	PUNCT
iajs-2833	163	31	𝑓2(𝑦2	𝑓2(𝑦2	PROPN
iajs-2833	163	32	,	,	PUNCT
iajs-2833	163	33	𝑢2	𝑢2	PROPN
iajs-2833	163	34	)	)	PUNCT
iajs-2833	163	35	,	,	PUNCT
iajs-2833	163	36	𝑣2)𝜙2	𝑣2)𝜙2	CCONJ
iajs-2833	163	37	(	(	PUNCT
iajs-2833	163	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	NOUN
iajs-2833	163	39	)	)	PUNCT
iajs-2833	163	40	(	(	PUNCT
iajs-2833	163	41	57	57	NUM
iajs-2833	163	42	)	)	PUNCT
iajs-2833	163	43	∫	∫	PROPN
iajs-2833	163	44	0	0	X
iajs-2833	163	45	𝑇	𝑇	PROPN
iajs-2833	163	46	(	(	PUNCT
iajs-2833	163	47	𝑦3𝑡𝑡	𝑦3𝑡𝑡	PROPN
iajs-2833	163	48	,	,	PUNCT
iajs-2833	163	49	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	163	50	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	163	51	+	+	PROPN
iajs-2833	163	52	∫	∫	PROPN
iajs-2833	163	53	0	0	X
iajs-2833	163	54	𝑇	𝑇	PROPN
iajs-2833	164	1	[	[	X
iajs-2833	164	2	(	(	PUNCT
iajs-2833	164	3	∇𝑦3	∇𝑦3	PROPN
iajs-2833	164	4	,	,	PUNCT
iajs-2833	164	5	∇𝑣3	∇𝑣3	NOUN
iajs-2833	164	6	)	)	PUNCT
iajs-2833	164	7	−	−	PROPN
iajs-2833	165	1	(	(	PUNCT
iajs-2833	165	2	𝑦1	𝑦1	NOUN
iajs-2833	165	3	,	,	PUNCT
iajs-2833	165	4	𝑣3	𝑣3	ADJ
iajs-2833	165	5	)	)	PUNCT
iajs-2833	165	6	+	+	CCONJ
iajs-2833	165	7	(	(	PUNCT
iajs-2833	165	8	𝑦2	𝑦2	NOUN
iajs-2833	165	9	,	,	PUNCT
iajs-2833	165	10	𝑣3	𝑣3	ADJ
iajs-2833	165	11	)	)	PUNCT
iajs-2833	165	12	+	+	CCONJ
iajs-2833	165	13	(	(	PUNCT
iajs-2833	165	14	𝑦3	𝑦3	PROPN
iajs-2833	165	15	,	,	PUNCT
iajs-2833	165	16	𝑣3	𝑣3	ADJ
iajs-2833	165	17	)	)	PUNCT
iajs-2833	165	18	+	+	CCONJ
iajs-2833	165	19	(	(	PUNCT
iajs-2833	165	20	𝑦4	𝑦4	NOUN
iajs-2833	165	21	,	,	PUNCT
iajs-2833	165	22	𝑣3)]𝜙3	𝑣3)]𝜙3	PROPN
iajs-2833	165	23	(	(	PUNCT
iajs-2833	165	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	165	25	ihjpas	ihjpa	NOUN
iajs-2833	165	26	.	.	PUNCT
iajs-2833	166	1	53	53	NUM
iajs-2833	166	2	(	(	PUNCT
iajs-2833	166	3	3)2022	3)2022	NOUN
iajs-2833	166	4	168	168	NUM
iajs-2833	166	5	=	=	NOUN
iajs-2833	166	6	∫	∫	PROPN
iajs-2833	166	7	0	0	X
iajs-2833	166	8	𝑇	𝑇	PROPN
iajs-2833	166	9	(	(	PUNCT
iajs-2833	166	10	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	166	11	,	,	PUNCT
iajs-2833	166	12	𝑢3	𝑢3	PROPN
iajs-2833	166	13	)	)	PUNCT
iajs-2833	166	14	,	,	PUNCT
iajs-2833	166	15	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	166	16	(	(	PUNCT
iajs-2833	166	17	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	166	18	(	(	PUNCT
iajs-2833	166	19	58	58	NUM
iajs-2833	166	20	)	)	PUNCT
iajs-2833	166	21	∫	∫	PROPN
iajs-2833	166	22	0	0	X
iajs-2833	166	23	𝑇	𝑇	PROPN
iajs-2833	166	24	(	(	PUNCT
iajs-2833	166	25	𝑦4𝑡𝑡	𝑦4𝑡𝑡	NOUN
iajs-2833	166	26	,	,	PUNCT
iajs-2833	166	27	𝑣4)𝜙4	𝑣4)𝜙4	VERB
iajs-2833	166	28	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	166	29	+	+	CCONJ
iajs-2833	166	30	∫	∫	PROPN
iajs-2833	166	31	0	0	X
iajs-2833	166	32	𝑇	𝑇	PROPN
iajs-2833	167	1	[	[	X
iajs-2833	167	2	(	(	PUNCT
iajs-2833	167	3	∇𝑦4	∇𝑦4	ADJ
iajs-2833	167	4	,	,	PUNCT
iajs-2833	167	5	∇𝑣4	∇𝑣4	NUM
iajs-2833	167	6	)	)	PUNCT
iajs-2833	167	7	−	−	PROPN
iajs-2833	168	1	(	(	PUNCT
iajs-2833	168	2	𝑦1	𝑦1	NOUN
iajs-2833	168	3	,	,	PUNCT
iajs-2833	168	4	𝑣4	𝑣4	NOUN
iajs-2833	168	5	)	)	PUNCT
iajs-2833	168	6	+	+	CCONJ
iajs-2833	168	7	(	(	PUNCT
iajs-2833	168	8	𝑦2	𝑦2	NOUN
iajs-2833	168	9	,	,	PUNCT
iajs-2833	168	10	𝑣4	𝑣4	NOUN
iajs-2833	168	11	)	)	PUNCT
iajs-2833	168	12	−	−	PROPN
iajs-2833	168	13	(	(	PUNCT
iajs-2833	168	14	𝑦3	𝑦3	PROPN
iajs-2833	168	15	,	,	PUNCT
iajs-2833	168	16	𝑣4	𝑣4	NOUN
iajs-2833	168	17	)	)	PUNCT
iajs-2833	168	18	+	+	CCONJ
iajs-2833	168	19	(	(	PUNCT
iajs-2833	168	20	𝑦4	𝑦4	NOUN
iajs-2833	168	21	,	,	PUNCT
iajs-2833	168	22	𝑣4)]𝜙4	𝑣4)]𝜙4	NOUN
iajs-2833	168	23	(	(	PUNCT
iajs-2833	168	24	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	168	25	=	=	SYM
iajs-2833	168	26	∫	∫	PROPN
iajs-2833	168	27	0	0	X
iajs-2833	168	28	𝑇	𝑇	PROPN
iajs-2833	168	29	(	(	PUNCT
iajs-2833	168	30	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	168	31	,	,	PUNCT
iajs-2833	168	32	𝑢4	𝑢4	NOUN
iajs-2833	168	33	)	)	PUNCT
iajs-2833	168	34	,	,	PUNCT
iajs-2833	168	35	𝑣4)𝜙4	𝑣4)𝜙4	VERB
iajs-2833	168	36	(	(	PUNCT
iajs-2833	168	37	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	168	38	(	(	PUNCT
iajs-2833	168	39	59	59	NUM
iajs-2833	168	40	)	)	PUNCT
iajs-2833	168	41	hence	hence	ADV
iajs-2833	168	42	�	�	NOUN
iajs-2833	168	43	⃗	⃗	NOUN
iajs-2833	168	44	�	�	PROPN
iajs-2833	168	45	is	be	AUX
iajs-2833	168	46	a	a	DET
iajs-2833	168	47	solution	solution	NOUN
iajs-2833	168	48	of	of	ADP
iajs-2833	168	49	(	(	PUNCT
iajs-2833	168	50	16),(18	16),(18	NUM
iajs-2833	168	51	)	)	PUNCT
iajs-2833	168	52	,	,	PUNCT
iajs-2833	168	53	(	(	PUNCT
iajs-2833	168	54	20	20	NUM
iajs-2833	168	55	)	)	PUNCT
iajs-2833	168	56	&	&	CCONJ
iajs-2833	168	57	(	(	PUNCT
iajs-2833	168	58	22	22	NUM
iajs-2833	168	59	)	)	PUNCT
iajs-2833	168	60	a.e	a.e	PROPN
iajs-2833	168	61	.	.	PROPN
iajs-2833	169	1	on	on	ADP
iajs-2833	169	2	i	i	PROPN
iajs-2833	169	3	case2	case2	PROPN
iajs-2833	169	4	:	:	PUNCT
iajs-2833	169	5	choose	choose	VERB
iajs-2833	169	6	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	169	7	∈	∈	PROPN
iajs-2833	169	8	𝐶2[0	𝐶2[0	PROPN
iajs-2833	169	9	,	,	PUNCT
iajs-2833	169	10	𝑇	𝑇	PROPN
iajs-2833	169	11	]	]	PUNCT
iajs-2833	169	12	s.t	s.t	PROPN
iajs-2833	169	13	.	.	PROPN
iajs-2833	169	14	𝜙𝑖(𝑇	𝜙𝑖(𝑇	ADP
iajs-2833	169	15	)	)	PUNCT
iajs-2833	169	16	=	=	SYM
iajs-2833	169	17	0	0	NUM
iajs-2833	169	18	,	,	PUNCT
iajs-2833	169	19	&	&	CCONJ
iajs-2833	169	20	𝜙𝑖	𝜙𝑖	X
iajs-2833	169	21	(	(	PUNCT
iajs-2833	169	22	0	0	NUM
iajs-2833	169	23	)	)	PUNCT
iajs-2833	169	24	=	=	SYM
iajs-2833	169	25	0	0	NUM
iajs-2833	169	26	,	,	PUNCT
iajs-2833	169	27	∀𝑖	∀𝑖	PROPN
iajs-2833	169	28	=	=	NOUN
iajs-2833	169	29	1,2,3,4	1,2,3,4	NUM
iajs-2833	169	30	.	.	PUNCT
iajs-2833	170	1	mbs	mb	NOUN
iajs-2833	170	2	of	of	ADP
iajs-2833	170	3	(	(	PUNCT
iajs-2833	170	4	8)	8)	NUM
iajs-2833	170	5	,	,	PUNCT
iajs-2833	170	6	(	(	PUNCT
iajs-2833	170	7	10	10	NUM
iajs-2833	170	8	)	)	PUNCT
iajs-2833	170	9	,	,	PUNCT
iajs-2833	170	10	(	(	PUNCT
iajs-2833	170	11	12	12	NUM
iajs-2833	170	12	)	)	PUNCT
iajs-2833	170	13	and	and	CCONJ
iajs-2833	170	14	(	(	PUNCT
iajs-2833	170	15	14	14	NUM
iajs-2833	170	16	)	)	PUNCT
iajs-2833	170	17	by	by	ADP
iajs-2833	170	18	𝜙1(𝑡	𝜙1(𝑡	NOUN
iajs-2833	170	19	)	)	PUNCT
iajs-2833	170	20	,	,	PUNCT
iajs-2833	170	21	𝜙2(𝑡	𝜙2(𝑡	PROPN
iajs-2833	170	22	)	)	PUNCT
iajs-2833	170	23	,	,	PUNCT
iajs-2833	170	24	𝜙3(𝑡	𝜙3(𝑡	PROPN
iajs-2833	170	25	)	)	PUNCT
iajs-2833	170	26	,	,	PUNCT
iajs-2833	170	27	and	and	CCONJ
iajs-2833	170	28	𝜙4(𝑡)resp	𝜙4(𝑡)resp	NUM
iajs-2833	170	29	.	.	PUNCT
iajs-2833	170	30	,	,	PUNCT
iajs-2833	170	31	ibs	ib	VERB
iajs-2833	170	32	on	on	ADP
iajs-2833	170	33	[	[	X
iajs-2833	170	34	0	0	NUM
iajs-2833	170	35	,	,	PUNCT
iajs-2833	170	36	𝑇	𝑇	PROPN
iajs-2833	170	37	]	]	PUNCT
iajs-2833	170	38	,	,	PUNCT
iajs-2833	170	39	then	then	ADV
iajs-2833	170	40	ibps	ibps	VERB
iajs-2833	170	41	the	the	DET
iajs-2833	170	42	1st	1st	ADJ
iajs-2833	170	43	term	term	NOUN
iajs-2833	170	44	in	in	ADP
iajs-2833	170	45	the	the	DET
iajs-2833	170	46	lhs	lhs	NOUN
iajs-2833	170	47	of	of	ADP
iajs-2833	170	48	each	each	DET
iajs-2833	170	49	equation	equation	NOUN
iajs-2833	170	50	,	,	PUNCT
iajs-2833	170	51	then	then	ADV
iajs-2833	170	52	subtracting	subtract	VERB
iajs-2833	170	53	each	each	DET
iajs-2833	170	54	one	one	NUM
iajs-2833	170	55	of	of	ADP
iajs-2833	170	56	these	these	DET
iajs-2833	170	57	obtained	obtain	VERB
iajs-2833	170	58	equations	equation	NOUN
iajs-2833	170	59	from	from	ADP
iajs-2833	170	60	those	those	PRON
iajs-2833	170	61	corresponding	correspond	VERB
iajs-2833	170	62	in	in	ADP
iajs-2833	170	63	(	(	PUNCT
iajs-2833	170	64	48),(50),(52	48),(50),(52	PROPN
iajs-2833	170	65	)	)	PUNCT
iajs-2833	170	66	&	&	CCONJ
iajs-2833	170	67	(	(	PUNCT
iajs-2833	170	68	54	54	NUM
iajs-2833	170	69	)	)	PUNCT
iajs-2833	170	70	resp	resp	NOUN
iajs-2833	170	71	.	.	PUNCT
iajs-2833	171	1	to	to	PART
iajs-2833	171	2	get	get	VERB
iajs-2833	171	3	(	(	PUNCT
iajs-2833	171	4	𝑦𝑖𝑡(0	𝑦𝑖𝑡(0	NUM
iajs-2833	171	5	)	)	PUNCT
iajs-2833	171	6	,	,	PUNCT
iajs-2833	171	7	𝑣𝑖)𝜙𝑖	𝑣𝑖)𝜙𝑖	X
iajs-2833	171	8	(	(	PUNCT
iajs-2833	171	9	0	0	NUM
iajs-2833	171	10	)	)	PUNCT
iajs-2833	172	1	=	=	SYM
iajs-2833	172	2	(	(	PUNCT
iajs-2833	172	3	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	172	4	′(0	′(0	NOUN
iajs-2833	172	5	)	)	PUNCT
iajs-2833	172	6	,	,	PUNCT
iajs-2833	172	7	𝑣𝑖)𝜙𝑖	𝑣𝑖)𝜙𝑖	X
iajs-2833	172	8	(	(	PUNCT
iajs-2833	172	9	0	0	NUM
iajs-2833	172	10	)	)	PUNCT
iajs-2833	172	11	,	,	PUNCT
iajs-2833	172	12	∀𝑖	∀𝑖	PROPN
iajs-2833	172	13	=	=	NOUN
iajs-2833	172	14	1,2,3,4	1,2,3,4	NUM
iajs-2833	172	15	.	.	PUNCT
iajs-2833	173	1	case	case	NOUN
iajs-2833	173	2	3	3	NUM
iajs-2833	173	3	:	:	PUNCT
iajs-2833	173	4	choose	choose	VERB
iajs-2833	173	5	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	173	6	∈	∈	PROPN
iajs-2833	173	7	𝐶2[0	𝐶2[0	PROPN
iajs-2833	173	8	,	,	PUNCT
iajs-2833	173	9	𝑇	𝑇	PROPN
iajs-2833	173	10	]	]	PUNCT
iajs-2833	173	11	s.t	s.t	PROPN
iajs-2833	173	12	.	.	PROPN
iajs-2833	173	13	𝜙𝑖(0	𝜙𝑖(0	PROPN
iajs-2833	173	14	)	)	PUNCT
iajs-2833	173	15	=	=	SYM
iajs-2833	173	16	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	173	17	′(𝑇	′(𝑇	NOUN
iajs-2833	173	18	)	)	PUNCT
iajs-2833	174	1	=	=	PRON
iajs-2833	174	2	𝜙𝑖	𝜙𝑖	X
iajs-2833	174	3	(	(	PUNCT
iajs-2833	174	4	𝑇	𝑇	PROPN
iajs-2833	174	5	)	)	PUNCT
iajs-2833	174	6	=	=	SYM
iajs-2833	174	7	0	0	NUM
iajs-2833	174	8	,	,	PUNCT
iajs-2833	174	9	𝜙𝑖	𝜙𝑖	ADP
iajs-2833	174	10	′(0	′(0	NOUN
iajs-2833	174	11	)	)	PUNCT
iajs-2833	174	12	≠	≠	PROPN
iajs-2833	174	13	0	0	NUM
iajs-2833	174	14	,	,	PUNCT
iajs-2833	174	15	∀𝑖	∀𝑖	PROPN
iajs-2833	174	16	=	=	NOUN
iajs-2833	174	17	1,2,3,4	1,2,3,4	NUM
iajs-2833	174	18	.	.	PUNCT
iajs-2833	175	1	mbs	mb	NOUN
iajs-2833	175	2	of	of	ADP
iajs-2833	175	3	(	(	PUNCT
iajs-2833	175	4	8)	8)	NUM
iajs-2833	175	5	,	,	PUNCT
iajs-2833	175	6	(	(	PUNCT
iajs-2833	175	7	10	10	NUM
iajs-2833	175	8	)	)	PUNCT
iajs-2833	175	9	,	,	PUNCT
iajs-2833	175	10	(	(	PUNCT
iajs-2833	175	11	12	12	NUM
iajs-2833	175	12	)	)	PUNCT
iajs-2833	175	13	and	and	CCONJ
iajs-2833	175	14	(	(	PUNCT
iajs-2833	175	15	14	14	NUM
iajs-2833	175	16	)	)	PUNCT
iajs-2833	175	17	by	by	ADP
iajs-2833	175	18	𝜙1(𝑡	𝜙1(𝑡	NOUN
iajs-2833	175	19	)	)	PUNCT
iajs-2833	175	20	,	,	PUNCT
iajs-2833	175	21	𝜙2(𝑡	𝜙2(𝑡	PROPN
iajs-2833	175	22	)	)	PUNCT
iajs-2833	175	23	,	,	PUNCT
iajs-2833	175	24	𝜙3(𝑡	𝜙3(𝑡	PROPN
iajs-2833	175	25	)	)	PUNCT
iajs-2833	175	26	,	,	PUNCT
iajs-2833	175	27	and	and	CCONJ
iajs-2833	175	28	𝜙4(𝑡)resp	𝜙4(𝑡)resp	NUM
iajs-2833	175	29	.	.	PUNCT
iajs-2833	175	30	,	,	PUNCT
iajs-2833	175	31	ibs	ib	VERB
iajs-2833	175	32	on	on	ADP
iajs-2833	175	33	[	[	X
iajs-2833	175	34	0	0	NUM
iajs-2833	175	35	,	,	PUNCT
iajs-2833	175	36	𝑇	𝑇	PROPN
iajs-2833	175	37	]	]	PUNCT
iajs-2833	175	38	then	then	ADV
iajs-2833	175	39	ibps2	ibps2	VERB
iajs-2833	176	1	the	the	DET
iajs-2833	176	2	1st	1st	ADJ
iajs-2833	176	3	term	term	NOUN
iajs-2833	176	4	in	in	ADP
iajs-2833	176	5	the	the	DET
iajs-2833	176	6	lhs	lhs	NOUN
iajs-2833	176	7	of	of	ADP
iajs-2833	176	8	each	each	DET
iajs-2833	176	9	equation	equation	NOUN
iajs-2833	176	10	,	,	PUNCT
iajs-2833	176	11	then	then	ADV
iajs-2833	176	12	subtracting	subtract	VERB
iajs-2833	176	13	each	each	DET
iajs-2833	176	14	one	one	NUM
iajs-2833	176	15	of	of	ADP
iajs-2833	176	16	these	these	DET
iajs-2833	176	17	obtained	obtain	VERB
iajs-2833	176	18	equations	equation	NOUN
iajs-2833	176	19	from	from	ADP
iajs-2833	176	20	those	those	PRON
iajs-2833	176	21	corresponding	correspond	VERB
iajs-2833	176	22	in	in	ADP
iajs-2833	176	23	(	(	PUNCT
iajs-2833	176	24	49),(51),(53	49),(51),(53	NOUN
iajs-2833	176	25	)	)	PUNCT
iajs-2833	176	26	,	,	PUNCT
iajs-2833	176	27	and	and	CCONJ
iajs-2833	176	28	(	(	PUNCT
iajs-2833	176	29	55	55	NUM
iajs-2833	176	30	)	)	PUNCT
iajs-2833	176	31	resp	resp	NOUN
iajs-2833	176	32	.	.	PUNCT
iajs-2833	177	1	to	to	PART
iajs-2833	177	2	get	get	VERB
iajs-2833	177	3	(	(	PUNCT
iajs-2833	177	4	𝑦𝑖(0	𝑦𝑖(0	NOUN
iajs-2833	177	5	)	)	PUNCT
iajs-2833	177	6	,	,	PUNCT
iajs-2833	177	7	𝑣𝑖)𝜙𝑖	𝑣𝑖)𝜙𝑖	NUM
iajs-2833	177	8	′(0	′(0	NOUN
iajs-2833	177	9	)	)	PUNCT
iajs-2833	178	1	=	=	SYM
iajs-2833	178	2	(	(	PUNCT
iajs-2833	178	3	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	178	4	0	0	NUM
iajs-2833	178	5	,	,	PUNCT
iajs-2833	178	6	𝑣𝑖)𝜙𝑖	𝑣𝑖)𝜙𝑖	NUM
iajs-2833	178	7	′(0	′(0	NOUN
iajs-2833	178	8	)	)	PUNCT
iajs-2833	178	9	,	,	PUNCT
iajs-2833	178	10	∀𝑖	∀𝑖	PROPN
iajs-2833	178	11	=	=	NOUN
iajs-2833	178	12	1,2,3,4	1,2,3,4	NUM
iajs-2833	178	13	in	in	ADP
iajs-2833	178	14	the	the	DET
iajs-2833	178	15	last	last	ADJ
iajs-2833	178	16	two	two	NUM
iajs-2833	178	17	cases	case	NOUN
iajs-2833	178	18	,	,	PUNCT
iajs-2833	178	19	the	the	DET
iajs-2833	178	20	ics	ics	NOUN
iajs-2833	178	21	(	(	PUNCT
iajs-2833	178	22	19	19	NUM
iajs-2833	178	23	)	)	PUNCT
iajs-2833	178	24	,	,	PUNCT
iajs-2833	178	25	(	(	PUNCT
iajs-2833	178	26	11	11	NUM
iajs-2833	178	27	)	)	PUNCT
iajs-2833	178	28	,	,	PUNCT
iajs-2833	178	29	(	(	PUNCT
iajs-2833	178	30	13	13	NUM
iajs-2833	178	31	)	)	PUNCT
iajs-2833	178	32	and	and	CCONJ
iajs-2833	178	33	(	(	PUNCT
iajs-2833	178	34	14	14	NUM
iajs-2833	178	35	)	)	PUNCT
iajs-2833	178	36	are	be	AUX
iajs-2833	178	37	held	hold	VERB
iajs-2833	178	38	.	.	PUNCT
iajs-2833	179	1	to	to	PART
iajs-2833	179	2	prove	prove	VERB
iajs-2833	179	3	that	that	SCONJ
iajs-2833	179	4	�	�	PROPN
iajs-2833	179	5	⃗	⃗	NOUN
iajs-2833	179	6	�	�	NOUN
iajs-2833	179	7	𝑛	𝑛	PRON
iajs-2833	179	8	→	→	SYM
iajs-2833	179	9	�	�	PROPN
iajs-2833	179	10	⃗	⃗	PROPN
iajs-2833	179	11	�	�	PROPN
iajs-2833	179	12	st	st	PROPN
iajs-2833	179	13	in	in	ADP
iajs-2833	179	14	𝐿2(𝐼	𝐿2(𝐼	PROPN
iajs-2833	179	15	,	,	PUNCT
iajs-2833	179	16	𝑉	𝑉	PROPN
iajs-2833	179	17	)	)	PUNCT
iajs-2833	179	18	,	,	PUNCT
iajs-2833	179	19	we	we	PRON
iajs-2833	179	20	start	start	VERB
iajs-2833	179	21	by	by	ADP
iajs-2833	179	22	ibs	ibs	PROPN
iajs-2833	179	23	(	(	PUNCT
iajs-2833	179	24	36	36	NUM
iajs-2833	179	25	)	)	PUNCT
iajs-2833	179	26	on	on	ADP
iajs-2833	179	27	[	[	X
iajs-2833	179	28	0	0	NUM
iajs-2833	179	29	,	,	PUNCT
iajs-2833	179	30	𝑇	𝑇	PROPN
iajs-2833	179	31	]	]	PUNCT
iajs-2833	179	32	,	,	PUNCT
iajs-2833	179	33	to	to	PART
iajs-2833	179	34	get	get	VERB
iajs-2833	179	35	∫	∫	PROPN
iajs-2833	179	36	0	0	PUNCT
iajs-2833	180	1	𝑇	𝑇	PROPN
iajs-2833	180	2	𝑑	𝑑	PRON
iajs-2833	180	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	180	4	∥	∥	PROPN
iajs-2833	180	5	�	�	NOUN
iajs-2833	180	6	⃗	⃗	NOUN
iajs-2833	180	7	�	�	NOUN
iajs-2833	180	8	𝑛	𝑛	PRON
iajs-2833	180	9	∥0	∥0	NOUN
iajs-2833	180	10	2	2	NUM
iajs-2833	180	11	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	180	12	+	+	SYM
iajs-2833	180	13	2	2	NUM
iajs-2833	180	14	∫	∫	NOUN
iajs-2833	180	15	0	0	NUM
iajs-2833	180	16	𝑇	𝑇	PROPN
iajs-2833	180	17	∥	∥	PROPN
iajs-2833	180	18	�	�	NOUN
iajs-2833	180	19	⃗	⃗	NOUN
iajs-2833	180	20	�	�	NOUN
iajs-2833	180	21	𝑛	𝑛	VERB
iajs-2833	180	22	∥1	∥1	PRON
iajs-2833	180	23	2	2	NUM
iajs-2833	180	24	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	180	25	=	=	SYM
iajs-2833	180	26	2	2	NUM
iajs-2833	180	27	∫	∫	NOUN
iajs-2833	180	28	0	0	X
iajs-2833	181	1	𝑇	𝑇	PROPN
iajs-2833	181	2	[	[	X
iajs-2833	181	3	(	(	PUNCT
iajs-2833	181	4	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	181	5	,	,	PUNCT
iajs-2833	181	6	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	181	7	)	)	PUNCT
iajs-2833	181	8	−	−	PROPN
iajs-2833	181	9	(	(	PUNCT
iajs-2833	181	10	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	181	11	,	,	PUNCT
iajs-2833	181	12	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	181	13	)	)	PUNCT
iajs-2833	181	14	−	−	PROPN
iajs-2833	181	15	(	(	PUNCT
iajs-2833	181	16	𝑦4𝑛	𝑦4𝑛	NOUN
iajs-2833	181	17	,	,	PUNCT
iajs-2833	181	18	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	181	19	)	)	PUNCT
iajs-2833	181	20	−	−	PROPN
iajs-2833	181	21	(	(	PUNCT
iajs-2833	181	22	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	181	23	,	,	PUNCT
iajs-2833	181	24	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	181	25	)	)	PUNCT
iajs-2833	182	1	+	+	CCONJ
iajs-2833	182	2	(	(	PUNCT
iajs-2833	182	3	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	182	4	,	,	PUNCT
iajs-2833	182	5	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	182	6	)	)	PUNCT
iajs-2833	182	7	+	+	CCONJ
iajs-2833	182	8	(	(	PUNCT
iajs-2833	182	9	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	182	10	,	,	PUNCT
iajs-2833	182	11	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	182	12	)	)	PUNCT
iajs-2833	182	13	+	+	CCONJ
iajs-2833	182	14	(	(	PUNCT
iajs-2833	182	15	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	182	16	,	,	PUNCT
iajs-2833	182	17	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	182	18	)	)	PUNCT
iajs-2833	182	19	−	−	PROPN
iajs-2833	182	20	(	(	PUNCT
iajs-2833	182	21	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	182	22	,	,	PUNCT
iajs-2833	182	23	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	182	24	)	)	PUNCT
iajs-2833	183	1	−	−	PROPN
iajs-2833	183	2	(	(	PUNCT
iajs-2833	183	3	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	183	4	,	,	PUNCT
iajs-2833	183	5	𝑦4𝑛𝑡	𝑦4𝑛𝑡	PUNCT
iajs-2833	183	6	)	)	PUNCT
iajs-2833	184	1	+	+	CCONJ
iajs-2833	184	2	(	(	PUNCT
iajs-2833	184	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	184	4	,	,	PUNCT
iajs-2833	184	5	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	184	6	)	)	PUNCT
iajs-2833	184	7	−	−	PROPN
iajs-2833	184	8	(	(	PUNCT
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iajs-2833	184	10	,	,	PUNCT
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iajs-2833	185	6	+	+	CCONJ
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iajs-2833	185	14	,	,	PUNCT
iajs-2833	185	15	𝑢1	𝑢1	PROPN
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iajs-2833	185	17	,	,	PUNCT
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iajs-2833	185	20	+	+	CCONJ
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iajs-2833	185	26	,	,	PUNCT
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iajs-2833	185	29	+	+	CCONJ
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iajs-2833	185	35	,	,	PUNCT
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iajs-2833	185	38	+	+	CCONJ
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iajs-2833	185	41	,	,	PUNCT
iajs-2833	185	42	𝑢4	𝑢4	NOUN
iajs-2833	185	43	)	)	PUNCT
iajs-2833	185	44	,	,	PUNCT
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iajs-2833	185	47	60	60	NUM
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iajs-2833	185	56	36)&(60	36)&(60	NUM
iajs-2833	185	57	)	)	PUNCT
iajs-2833	185	58	,	,	PUNCT
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iajs-2833	185	60	be	be	AUX
iajs-2833	185	61	utilize	utilize	VERB
iajs-2833	185	62	here	here	ADV
iajs-2833	185	63	to	to	PART
iajs-2833	185	64	obtain	obtain	VERB
iajs-2833	185	65	,	,	PUNCT
iajs-2833	185	66	i.e.	i.e.	X
iajs-2833	185	67	∥	∥	X
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iajs-2833	185	69	)	)	PUNCT
iajs-2833	185	70	∥0	∥0	VERB
iajs-2833	185	71	2−∥	2−∥	NUM
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iajs-2833	185	73	)	)	PUNCT
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iajs-2833	186	2	+	+	SYM
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iajs-2833	186	12	)	)	PUNCT
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iajs-2833	186	14	2	2	NUM
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iajs-2833	186	23	𝑦1𝑡	𝑦1𝑡	PROPN
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iajs-2833	186	27	𝑦3	𝑦3	PROPN
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iajs-2833	189	7	+	+	CCONJ
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iajs-2833	189	17	𝑦3𝑡	𝑦3𝑡	NUM
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iajs-2833	190	1	+	+	CCONJ
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iajs-2833	191	1	+	+	CCONJ
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iajs-2833	192	3	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
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iajs-2833	193	5	𝑢2	𝑢2	PROPN
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iajs-2833	193	7	,	,	PUNCT
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iajs-2833	193	19	+	+	CCONJ
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iajs-2833	193	25	,	,	PUNCT
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iajs-2833	193	28	61	61	NUM
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iajs-2833	193	42	)	)	PUNCT
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iajs-2833	200	32	)	)	PUNCT
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iajs-2833	200	38	)	)	PUNCT
iajs-2833	200	39	)	)	PUNCT
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iajs-2833	201	4	⃗	⃗	X
iajs-2833	201	5	�	�	NOUN
iajs-2833	201	6	𝑡(0	𝑡(0	NOUN
iajs-2833	201	7	)	)	PUNCT
iajs-2833	201	8	,	,	PUNCT
iajs-2833	201	9	�	�	PROPN
iajs-2833	201	10	⃗	⃗	PROPN
iajs-2833	201	11	�	�	PROPN
iajs-2833	201	12	𝑛𝑡(0	𝑛𝑡(0	NOUN
iajs-2833	201	13	)	)	PUNCT
iajs-2833	201	14	−	−	PROPN
iajs-2833	201	15	�	�	PROPN
iajs-2833	201	16	⃗	⃗	NOUN
iajs-2833	201	17	�	�	NOUN
iajs-2833	201	18	𝑡(0	𝑡(0	NOUN
iajs-2833	201	19	)	)	PUNCT
iajs-2833	201	20	)	)	PUNCT
iajs-2833	202	1	+	+	CCONJ
iajs-2833	202	2	2	2	NUM
iajs-2833	202	3	∫	∫	NOUN
iajs-2833	202	4	0	0	NUM
iajs-2833	202	5	𝑇	𝑇	PROPN
iajs-2833	202	6	(	(	PUNCT
iajs-2833	202	7	𝑦	𝑦	NOUN
iajs-2833	202	8	⃗⃗⃗(𝑡	⃗⃗⃗(𝑡	PROPN
iajs-2833	202	9	)	)	PUNCT
iajs-2833	202	10	,	,	PUNCT
iajs-2833	202	11	�	�	PROPN
iajs-2833	202	12	⃗	⃗	PROPN
iajs-2833	202	13	�	�	NOUN
iajs-2833	202	14	𝑛(𝑡	𝑛(𝑡	NOUN
iajs-2833	202	15	)	)	PUNCT
iajs-2833	202	16	−	−	PROPN
iajs-2833	202	17	𝑦	𝑦	SYM
iajs-2833	202	18	⃗⃗⃗(𝑡	⃗⃗⃗(𝑡	PROPN
iajs-2833	202	19	)	)	PUNCT
iajs-2833	202	20	)	)	PUNCT
iajs-2833	202	21	1	1	NUM
iajs-2833	202	22	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	202	23	since	since	SCONJ
iajs-2833	202	24	�	�	PROPN
iajs-2833	202	25	⃗	⃗	NOUN
iajs-2833	202	26	�	�	NOUN
iajs-2833	202	27	𝑛	𝑛	PRON
iajs-2833	202	28	→	→	SYM
iajs-2833	202	29	�	�	PROPN
iajs-2833	202	30	⃗	⃗	PROPN
iajs-2833	202	31	�	�	PROPN
iajs-2833	202	32	st	st	PROPN
iajs-2833	202	33	in	in	ADP
iajs-2833	202	34	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	202	35	)	)	PUNCT
iajs-2833	202	36	,	,	PUNCT
iajs-2833	202	37	and	and	CCONJ
iajs-2833	202	38	�	�	PROPN
iajs-2833	202	39	⃗	⃗	NOUN
iajs-2833	202	40	�	�	PROPN
iajs-2833	202	41	𝑛𝑡	𝑛𝑡	NOUN
iajs-2833	202	42	→	→	SYM
iajs-2833	202	43	�	�	NOUN
iajs-2833	202	44	⃗	⃗	NOUN
iajs-2833	202	45	�	�	PROPN
iajs-2833	202	46	wk	wk	PROPN
iajs-2833	202	47	in	in	ADP
iajs-2833	202	48	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	202	49	)	)	PUNCT
iajs-2833	202	50	,	,	PUNCT
iajs-2833	202	51	then	then	ADV
iajs-2833	202	52	from	from	ADP
iajs-2833	202	53	(	(	PUNCT
iajs-2833	202	54	60	60	NUM
iajs-2833	202	55	)	)	PUNCT
iajs-2833	202	56	and	and	CCONJ
iajs-2833	202	57	the	the	DET
iajs-2833	202	58	assm	assm	PROPN
iajs-2833	202	59	on	on	ADP
iajs-2833	202	60	𝑓𝑖	𝑓𝑖	PROPN
iajs-2833	202	61	,	,	PUNCT
iajs-2833	202	62	for	for	ADP
iajs-2833	202	63	𝑖	𝑖	NOUN
iajs-2833	202	64	=	=	NOUN
iajs-2833	202	65	1,2,3,4	1,2,3,4	NUM
iajs-2833	202	66	,	,	PUNCT
iajs-2833	202	67	we	we	PRON
iajs-2833	202	68	get	get	VERB
iajs-2833	202	69	ihjpas	ihjpa	NOUN
iajs-2833	202	70	.	.	PUNCT
iajs-2833	203	1	53	53	NUM
iajs-2833	203	2	(	(	PUNCT
iajs-2833	203	3	3)2022	3)2022	NOUN
iajs-2833	203	4	169	169	NUM
iajs-2833	203	5	(	(	PUNCT
iajs-2833	203	6	𝑎	𝑎	NOUN
iajs-2833	203	7	)	)	PUNCT
iajs-2833	203	8	=	=	SYM
iajs-2833	203	9	2	2	NUM
iajs-2833	203	10	∫	∫	NOUN
iajs-2833	203	11	0	0	X
iajs-2833	203	12	𝑇	𝑇	PROPN
iajs-2833	203	13	[	[	X
iajs-2833	203	14	(	(	PUNCT
iajs-2833	203	15	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	203	16	,	,	PUNCT
iajs-2833	203	17	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	203	18	)	)	PUNCT
iajs-2833	203	19	−	−	PROPN
iajs-2833	203	20	(	(	PUNCT
iajs-2833	203	21	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	203	22	,	,	PUNCT
iajs-2833	203	23	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	203	24	)	)	PUNCT
iajs-2833	203	25	−	−	PROPN
iajs-2833	203	26	(	(	PUNCT
iajs-2833	203	27	𝑦4𝑛	𝑦4𝑛	NOUN
iajs-2833	203	28	,	,	PUNCT
iajs-2833	203	29	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADJ
iajs-2833	203	30	)	)	PUNCT
iajs-2833	203	31	−	−	PROPN
iajs-2833	203	32	(	(	PUNCT
iajs-2833	203	33	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	203	34	,	,	PUNCT
iajs-2833	203	35	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	203	36	)	)	PUNCT
iajs-2833	203	37	+	+	CCONJ
iajs-2833	203	38	(	(	PUNCT
iajs-2833	203	39	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	203	40	,	,	PUNCT
iajs-2833	203	41	𝑦2𝑛𝑡	𝑦2𝑛𝑡	PUNCT
iajs-2833	203	42	)	)	PUNCT
iajs-2833	203	43	+	+	CCONJ
iajs-2833	203	44	(	(	PUNCT
iajs-2833	203	45	𝑦4𝑛	𝑦4𝑛	NUM
iajs-2833	203	46	,	,	PUNCT
iajs-2833	203	47	𝑦2𝑛𝑡	𝑦2𝑛𝑡	NOUN
iajs-2833	203	48	)	)	PUNCT
iajs-2833	203	49	+	+	ADJ
iajs-2833	203	50	(	(	PUNCT
iajs-2833	203	51	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	203	52	,	,	PUNCT
iajs-2833	203	53	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	203	54	)	)	PUNCT
iajs-2833	203	55	−	−	PROPN
iajs-2833	203	56	(	(	PUNCT
iajs-2833	203	57	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	203	58	,	,	PUNCT
iajs-2833	203	59	𝑦3𝑛𝑡	𝑦3𝑛𝑡	NUM
iajs-2833	203	60	)	)	PUNCT
iajs-2833	204	1	−	−	PROPN
iajs-2833	204	2	(	(	PUNCT
iajs-2833	204	3	𝑦4𝑛	𝑦4𝑛	PROPN
iajs-2833	204	4	,	,	PUNCT
iajs-2833	204	5	𝑦4𝑛𝑡	𝑦4𝑛𝑡	PUNCT
iajs-2833	204	6	)	)	PUNCT
iajs-2833	205	1	+	+	CCONJ
iajs-2833	205	2	(	(	PUNCT
iajs-2833	205	3	𝑦1𝑛	𝑦1𝑛	ADJ
iajs-2833	205	4	,	,	PUNCT
iajs-2833	205	5	𝑦4𝑛𝑡	𝑦4𝑛𝑡	NOUN
iajs-2833	205	6	)	)	PUNCT
iajs-2833	205	7	−	−	PROPN
iajs-2833	205	8	(	(	PUNCT
iajs-2833	205	9	𝑦2𝑛	𝑦2𝑛	NOUN
iajs-2833	205	10	,	,	PUNCT
iajs-2833	205	11	𝑦4𝑛𝑡	𝑦4𝑛𝑡	PUNCT
iajs-2833	205	12	)	)	PUNCT
iajs-2833	206	1	+	+	CCONJ
iajs-2833	206	2	(	(	PUNCT
iajs-2833	206	3	𝑦3𝑛	𝑦3𝑛	NOUN
iajs-2833	206	4	,	,	PUNCT
iajs-2833	206	5	𝑦4𝑛𝑡)]𝑑𝑡	𝑦4𝑛𝑡)]𝑑𝑡	ADP
iajs-2833	206	6	+	+	CCONJ
iajs-2833	206	7	2	2	NUM
iajs-2833	206	8	∫	∫	NOUN
iajs-2833	206	9	0	0	NUM
iajs-2833	206	10	𝑇	𝑇	PROPN
iajs-2833	206	11	[	[	X
iajs-2833	206	12	(	(	PUNCT
iajs-2833	206	13	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	206	14	,	,	PUNCT
iajs-2833	206	15	𝑢1	𝑢1	PROPN
iajs-2833	206	16	)	)	PUNCT
iajs-2833	206	17	,	,	PUNCT
iajs-2833	206	18	𝑦1𝑛𝑡	𝑦1𝑛𝑡	ADV
iajs-2833	206	19	)	)	PUNCT
iajs-2833	206	20	+	+	CCONJ
iajs-2833	206	21	(	(	PUNCT
iajs-2833	206	22	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	206	23	,	,	PUNCT
iajs-2833	206	24	𝑢2	𝑢2	PROPN
iajs-2833	206	25	)	)	PUNCT
iajs-2833	206	26	,	,	PUNCT
iajs-2833	206	27	𝑦2𝑛𝑡	𝑦2𝑛𝑡	VERB
iajs-2833	206	28	)	)	PUNCT
iajs-2833	206	29	+	+	CCONJ
iajs-2833	206	30	(	(	PUNCT
iajs-2833	206	31	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	206	32	,	,	PUNCT
iajs-2833	206	33	𝑢3	𝑢3	PROPN
iajs-2833	206	34	)	)	PUNCT
iajs-2833	206	35	,	,	PUNCT
iajs-2833	206	36	𝑦3𝑛𝑡	𝑦3𝑛𝑡	X
iajs-2833	206	37	)	)	PUNCT
iajs-2833	206	38	+	+	CCONJ
iajs-2833	206	39	(	(	PUNCT
iajs-2833	206	40	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	206	41	,	,	PUNCT
iajs-2833	206	42	𝑢4	𝑢4	NOUN
iajs-2833	206	43	)	)	PUNCT
iajs-2833	206	44	,	,	PUNCT
iajs-2833	206	45	𝑦4𝑛𝑡)]𝑑𝑡	𝑦4𝑛𝑡)]𝑑𝑡	ADP
iajs-2833	206	46	⟶	⟶	NOUN
iajs-2833	206	47	2	2	NUM
iajs-2833	206	48	∫	∫	NOUN
iajs-2833	206	49	0	0	PUNCT
iajs-2833	206	50	𝑇	𝑇	PROPN
iajs-2833	207	1	[	[	X
iajs-2833	207	2	(	(	PUNCT
iajs-2833	207	3	𝑦2	𝑦2	PROPN
iajs-2833	207	4	,	,	PUNCT
iajs-2833	207	5	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2833	207	6	)	)	PUNCT
iajs-2833	207	7	−	−	PROPN
iajs-2833	207	8	(	(	PUNCT
iajs-2833	207	9	𝑦3	𝑦3	PROPN
iajs-2833	207	10	,	,	PUNCT
iajs-2833	207	11	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	207	12	)	)	PUNCT
iajs-2833	208	1	−	−	PROPN
iajs-2833	208	2	(	(	PUNCT
iajs-2833	208	3	𝑦4	𝑦4	NOUN
iajs-2833	208	4	,	,	PUNCT
iajs-2833	208	5	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	208	6	)	)	PUNCT
iajs-2833	208	7	−	−	PROPN
iajs-2833	209	1	(	(	PUNCT
iajs-2833	209	2	𝑦1	𝑦1	NOUN
iajs-2833	209	3	,	,	PUNCT
iajs-2833	209	4	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	209	5	)	)	PUNCT
iajs-2833	210	1	+	+	CCONJ
iajs-2833	210	2	(	(	PUNCT
iajs-2833	210	3	𝑦3	𝑦3	PROPN
iajs-2833	210	4	,	,	PUNCT
iajs-2833	210	5	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	210	6	)	)	PUNCT
iajs-2833	210	7	+	+	CCONJ
iajs-2833	210	8	(	(	PUNCT
iajs-2833	210	9	𝑦4	𝑦4	NOUN
iajs-2833	210	10	,	,	PUNCT
iajs-2833	210	11	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	210	12	)	)	PUNCT
iajs-2833	210	13	+	+	CCONJ
iajs-2833	210	14	(	(	PUNCT
iajs-2833	210	15	𝑦1	𝑦1	NOUN
iajs-2833	210	16	,	,	PUNCT
iajs-2833	210	17	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	210	18	)	)	PUNCT
iajs-2833	210	19	−	−	PROPN
iajs-2833	210	20	(	(	PUNCT
iajs-2833	210	21	𝑦2	𝑦2	PROPN
iajs-2833	210	22	,	,	PUNCT
iajs-2833	210	23	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	210	24	)	)	PUNCT
iajs-2833	210	25	−	−	PROPN
iajs-2833	210	26	(	(	PUNCT
iajs-2833	210	27	𝑦4	𝑦4	NOUN
iajs-2833	210	28	,	,	PUNCT
iajs-2833	210	29	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	210	30	)	)	PUNCT
iajs-2833	210	31	+	+	CCONJ
iajs-2833	210	32	(	(	PUNCT
iajs-2833	210	33	𝑦1	𝑦1	NOUN
iajs-2833	210	34	,	,	PUNCT
iajs-2833	210	35	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	210	36	)	)	PUNCT
iajs-2833	210	37	−	−	PROPN
iajs-2833	210	38	(	(	PUNCT
iajs-2833	210	39	𝑦2	𝑦2	PROPN
iajs-2833	210	40	,	,	PUNCT
iajs-2833	210	41	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	210	42	)	)	PUNCT
iajs-2833	211	1	+	+	CCONJ
iajs-2833	211	2	(	(	PUNCT
iajs-2833	211	3	𝑦3	𝑦3	PROPN
iajs-2833	211	4	,	,	PUNCT
iajs-2833	211	5	𝑦4𝑡)]𝑑𝑡	𝑦4𝑡)]𝑑𝑡	PROPN
iajs-2833	211	6	+2	+2	PROPN
iajs-2833	211	7	∫	∫	NOUN
iajs-2833	211	8	0	0	X
iajs-2833	211	9	𝑇	𝑇	PROPN
iajs-2833	212	1	[	[	X
iajs-2833	212	2	(	(	PUNCT
iajs-2833	212	3	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	212	4	,	,	PUNCT
iajs-2833	212	5	𝑢1	𝑢1	PROPN
iajs-2833	212	6	)	)	PUNCT
iajs-2833	212	7	,	,	PUNCT
iajs-2833	212	8	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	212	9	)	)	PUNCT
iajs-2833	213	1	+	+	CCONJ
iajs-2833	213	2	(	(	PUNCT
iajs-2833	213	3	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	213	4	,	,	PUNCT
iajs-2833	213	5	𝑢2	𝑢2	PROPN
iajs-2833	213	6	)	)	PUNCT
iajs-2833	213	7	,	,	PUNCT
iajs-2833	213	8	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	213	9	)	)	PUNCT
iajs-2833	213	10	+	+	CCONJ
iajs-2833	213	11	(	(	PUNCT
iajs-2833	213	12	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	213	13	,	,	PUNCT
iajs-2833	213	14	𝑢3	𝑢3	PROPN
iajs-2833	213	15	)	)	PUNCT
iajs-2833	213	16	,	,	PUNCT
iajs-2833	213	17	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	213	18	)	)	PUNCT
iajs-2833	213	19	+	+	CCONJ
iajs-2833	213	20	(	(	PUNCT
iajs-2833	213	21	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	213	22	,	,	PUNCT
iajs-2833	213	23	𝑢4	𝑢4	NOUN
iajs-2833	213	24	)	)	PUNCT
iajs-2833	213	25	,	,	PUNCT
iajs-2833	213	26	𝑦4𝑡)]𝑑𝑡	𝑦4𝑡)]𝑑𝑡	PROPN
iajs-2833	213	27	by	by	ADP
iajs-2833	213	28	the	the	DET
iajs-2833	213	29	same	same	ADJ
iajs-2833	213	30	way	way	NOUN
iajs-2833	213	31	that	that	PRON
iajs-2833	213	32	was	be	AUX
iajs-2833	213	33	employed	employ	VERB
iajs-2833	213	34	to	to	PART
iajs-2833	213	35	acquire	acquire	VERB
iajs-2833	213	36	(	(	PUNCT
iajs-2833	213	37	27	27	NUM
iajs-2833	213	38	)	)	PUNCT
iajs-2833	213	39	,	,	PUNCT
iajs-2833	213	40	it	it	PRON
iajs-2833	213	41	used	use	VERB
iajs-2833	213	42	here	here	ADV
iajs-2833	213	43	to	to	PART
iajs-2833	213	44	acquire	acquire	VERB
iajs-2833	213	45	�	�	PROPN
iajs-2833	213	46	⃗	⃗	NOUN
iajs-2833	213	47	�	�	NOUN
iajs-2833	213	48	𝑛𝑡(𝑇	𝑛𝑡(𝑇	NUM
iajs-2833	213	49	)	)	PUNCT
iajs-2833	213	50	→	→	SYM
iajs-2833	213	51	�	�	PROPN
iajs-2833	213	52	⃗	⃗	NOUN
iajs-2833	213	53	�	�	PROPN
iajs-2833	213	54	(𝑇	(𝑇	NUM
iajs-2833	213	55	)	)	PUNCT
iajs-2833	213	56	st	st	PROPN
iajs-2833	213	57	in	in	ADP
iajs-2833	213	58	𝐿2(ω	𝐿2(ω	PROPN
iajs-2833	213	59	)	)	PUNCT
iajs-2833	213	60	(	(	PUNCT
iajs-2833	213	61	63	63	NUM
iajs-2833	213	62	)	)	PUNCT
iajs-2833	213	63	on	on	ADP
iajs-2833	213	64	the	the	DET
iajs-2833	213	65	other	other	ADJ
iajs-2833	213	66	hand	hand	NOUN
iajs-2833	213	67	,	,	PUNCT
iajs-2833	213	68	since	since	SCONJ
iajs-2833	213	69	�	�	PROPN
iajs-2833	213	70	⃗	⃗	NOUN
iajs-2833	213	71	�	�	NOUN
iajs-2833	213	72	𝑛	𝑛	PRON
iajs-2833	213	73	→	→	SYM
iajs-2833	213	74	�	�	PROPN
iajs-2833	213	75	⃗	⃗	NOUN
iajs-2833	213	76	�	�	PROPN
iajs-2833	213	77	in	in	ADP
iajs-2833	213	78	𝐿2(i	𝐿2(i	NOUN
iajs-2833	213	79	,	,	PUNCT
iajs-2833	213	80	v	v	NOUN
iajs-2833	213	81	)	)	PUNCT
iajs-2833	213	82	,	,	PUNCT
iajs-2833	213	83	then	then	ADV
iajs-2833	213	84	using	use	VERB
iajs-2833	213	85	(	(	PUNCT
iajs-2833	213	86	27	27	NUM
iajs-2833	213	87	)	)	PUNCT
iajs-2833	213	88	&	&	CCONJ
iajs-2833	213	89	(	(	PUNCT
iajs-2833	213	90	63	63	NUM
iajs-2833	213	91	)	)	PUNCT
iajs-2833	213	92	,	,	PUNCT
iajs-2833	213	93	yield	yield	VERB
iajs-2833	213	94	to	to	PART
iajs-2833	213	95	(	(	PUNCT
iajs-2833	213	96	b)⟶	b)⟶	PROPN
iajs-2833	213	97	rhs	rhs	PROPN
iajs-2833	213	98	of	of	ADP
iajs-2833	213	99	(	(	PUNCT
iajs-2833	213	100	61)=	61)=	NUM
iajs-2833	213	101	2	2	NUM
iajs-2833	213	102	∫	∫	NOUN
iajs-2833	213	103	0	0	X
iajs-2833	213	104	𝑇	𝑇	PROPN
iajs-2833	214	1	[	[	X
iajs-2833	214	2	(	(	PUNCT
iajs-2833	214	3	𝑦2	𝑦2	PROPN
iajs-2833	214	4	,	,	PUNCT
iajs-2833	214	5	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2833	214	6	)	)	PUNCT
iajs-2833	214	7	−	−	PROPN
iajs-2833	214	8	(	(	PUNCT
iajs-2833	214	9	𝑦3	𝑦3	PROPN
iajs-2833	214	10	,	,	PUNCT
iajs-2833	214	11	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	214	12	)	)	PUNCT
iajs-2833	215	1	−	−	PROPN
iajs-2833	215	2	(	(	PUNCT
iajs-2833	215	3	𝑦4	𝑦4	NOUN
iajs-2833	215	4	,	,	PUNCT
iajs-2833	215	5	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	215	6	)	)	PUNCT
iajs-2833	215	7	−	−	PROPN
iajs-2833	216	1	(	(	PUNCT
iajs-2833	216	2	𝑦1	𝑦1	NOUN
iajs-2833	216	3	,	,	PUNCT
iajs-2833	216	4	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	216	5	)	)	PUNCT
iajs-2833	217	1	+	+	CCONJ
iajs-2833	217	2	(	(	PUNCT
iajs-2833	217	3	𝑦3	𝑦3	PROPN
iajs-2833	217	4	,	,	PUNCT
iajs-2833	217	5	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	217	6	)	)	PUNCT
iajs-2833	217	7	+	+	CCONJ
iajs-2833	217	8	(	(	PUNCT
iajs-2833	217	9	𝑦4	𝑦4	NOUN
iajs-2833	217	10	,	,	PUNCT
iajs-2833	217	11	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	217	12	)	)	PUNCT
iajs-2833	217	13	+	+	CCONJ
iajs-2833	217	14	(	(	PUNCT
iajs-2833	217	15	𝑦1	𝑦1	NOUN
iajs-2833	217	16	,	,	PUNCT
iajs-2833	217	17	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	217	18	)	)	PUNCT
iajs-2833	217	19	−	−	PROPN
iajs-2833	217	20	(	(	PUNCT
iajs-2833	217	21	𝑦2	𝑦2	PROPN
iajs-2833	217	22	,	,	PUNCT
iajs-2833	217	23	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	217	24	)	)	PUNCT
iajs-2833	217	25	−	−	PROPN
iajs-2833	217	26	(	(	PUNCT
iajs-2833	217	27	𝑦4	𝑦4	NOUN
iajs-2833	217	28	,	,	PUNCT
iajs-2833	217	29	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	217	30	)	)	PUNCT
iajs-2833	217	31	+	+	CCONJ
iajs-2833	217	32	(	(	PUNCT
iajs-2833	217	33	𝑦1	𝑦1	NOUN
iajs-2833	217	34	,	,	PUNCT
iajs-2833	217	35	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	217	36	)	)	PUNCT
iajs-2833	217	37	−	−	PROPN
iajs-2833	217	38	(	(	PUNCT
iajs-2833	217	39	𝑦2	𝑦2	PROPN
iajs-2833	217	40	,	,	PUNCT
iajs-2833	217	41	𝑦4𝑡	𝑦4𝑡	NUM
iajs-2833	217	42	)	)	PUNCT
iajs-2833	218	1	+	+	CCONJ
iajs-2833	218	2	(	(	PUNCT
iajs-2833	218	3	𝑦3	𝑦3	PROPN
iajs-2833	218	4	,	,	PUNCT
iajs-2833	218	5	𝑦4𝑡)]𝑑𝑡	𝑦4𝑡)]𝑑𝑡	NOUN
iajs-2833	218	6	+	+	CCONJ
iajs-2833	218	7	2	2	NUM
iajs-2833	218	8	∫	∫	NOUN
iajs-2833	218	9	0	0	NUM
iajs-2833	218	10	𝑇	𝑇	PROPN
iajs-2833	219	1	[	[	X
iajs-2833	219	2	(	(	PUNCT
iajs-2833	219	3	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	219	4	,	,	PUNCT
iajs-2833	219	5	𝑢1	𝑢1	PROPN
iajs-2833	219	6	)	)	PUNCT
iajs-2833	219	7	,	,	PUNCT
iajs-2833	219	8	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	219	9	)	)	PUNCT
iajs-2833	220	1	+	+	CCONJ
iajs-2833	220	2	(	(	PUNCT
iajs-2833	220	3	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	220	4	,	,	PUNCT
iajs-2833	220	5	𝑢2	𝑢2	PROPN
iajs-2833	220	6	)	)	PUNCT
iajs-2833	220	7	,	,	PUNCT
iajs-2833	220	8	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	220	9	)	)	PUNCT
iajs-2833	220	10	+	+	CCONJ
iajs-2833	220	11	(	(	PUNCT
iajs-2833	220	12	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	220	13	,	,	PUNCT
iajs-2833	220	14	𝑢3	𝑢3	PROPN
iajs-2833	220	15	)	)	PUNCT
iajs-2833	220	16	,	,	PUNCT
iajs-2833	220	17	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	220	18	)	)	PUNCT
iajs-2833	220	19	+	+	CCONJ
iajs-2833	220	20	(	(	PUNCT
iajs-2833	220	21	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	220	22	,	,	PUNCT
iajs-2833	220	23	𝑢4	𝑢4	NOUN
iajs-2833	220	24	)	)	PUNCT
iajs-2833	220	25	,	,	PUNCT
iajs-2833	220	26	𝑦4𝑡)]𝑑𝑡	𝑦4𝑡)]𝑑𝑡	PROPN
iajs-2833	220	27	all	all	DET
iajs-2833	220	28	the	the	DET
iajs-2833	220	29	term	term	NOUN
iajs-2833	220	30	in	in	ADP
iajs-2833	220	31	(	(	PUNCT
iajs-2833	220	32	c	c	NOUN
iajs-2833	220	33	)	)	PUNCT
iajs-2833	220	34	approach	approach	NOUN
iajs-2833	220	35	to	to	ADP
iajs-2833	220	36	zero	zero	NUM
iajs-2833	220	37	,	,	PUNCT
iajs-2833	220	38	so	so	SCONJ
iajs-2833	220	39	as	as	ADP
iajs-2833	220	40	the	the	DET
iajs-2833	220	41	1st	1st	ADJ
iajs-2833	220	42	two	two	NUM
iajs-2833	220	43	terms	term	NOUN
iajs-2833	220	44	in	in	ADP
iajs-2833	220	45	the	the	DET
iajs-2833	220	46	lhs	lhs	PROPN
iajs-2833	220	47	of	of	ADP
iajs-2833	220	48	(	(	PUNCT
iajs-2833	220	49	62	62	NUM
iajs-2833	220	50	)	)	PUNCT
iajs-2833	220	51	,	,	PUNCT
iajs-2833	220	52	hence	hence	ADV
iajs-2833	220	53	(	(	PUNCT
iajs-2833	220	54	62	62	NUM
iajs-2833	220	55	)	)	PUNCT
iajs-2833	220	56	gives	give	VERB
iajs-2833	220	57	∫	∫	PROPN
iajs-2833	220	58	0	0	PUNCT
iajs-2833	221	1	𝑇	𝑇	PROPN
iajs-2833	221	2	∥	∥	PROPN
iajs-2833	221	3	�	�	NOUN
iajs-2833	221	4	⃗	⃗	NOUN
iajs-2833	221	5	�	�	NOUN
iajs-2833	221	6	𝑛(𝑡	𝑛(𝑡	NOUN
iajs-2833	221	7	)	)	PUNCT
iajs-2833	222	1	−	−	PROPN
iajs-2833	222	2	𝑦	𝑦	SYM
iajs-2833	222	3	⃗⃗⃗(𝑡	⃗⃗⃗(𝑡	PROPN
iajs-2833	222	4	)	)	PUNCT
iajs-2833	222	5	∥1	∥1	PRON
iajs-2833	222	6	2	2	NUM
iajs-2833	222	7	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	222	8	→	→	SYM
iajs-2833	222	9	0	0	PROPN
iajs-2833	222	10	as	as	ADP
iajs-2833	222	11	𝑛	𝑛	PROPN
iajs-2833	222	12	→	→	SYM
iajs-2833	222	13	∞	∞	PROPN
iajs-2833	222	14	,	,	PUNCT
iajs-2833	222	15	therefore	therefore	ADV
iajs-2833	222	16	�	�	PROPN
iajs-2833	222	17	⃗	⃗	NOUN
iajs-2833	222	18	�	�	NOUN
iajs-2833	222	19	𝑛	𝑛	PRON
iajs-2833	222	20	→	→	SYM
iajs-2833	222	21	�	�	PROPN
iajs-2833	222	22	⃗	⃗	PROPN
iajs-2833	222	23	�	�	PROPN
iajs-2833	222	24	st	st	PROPN
iajs-2833	222	25	in	in	ADP
iajs-2833	222	26	𝐿2(i	𝐿2(i	NOUN
iajs-2833	222	27	,	,	PUNCT
iajs-2833	222	28	v	v	NOUN
iajs-2833	222	29	)	)	PUNCT
iajs-2833	222	30	uniqueness	uniqueness	NOUN
iajs-2833	222	31	of	of	ADP
iajs-2833	222	32	the	the	DET
iajs-2833	222	33	solution	solution	NOUN
iajs-2833	222	34	:	:	PUNCT
iajs-2833	222	35	let	let	VERB
iajs-2833	222	36	�	�	PROPN
iajs-2833	222	37	⃗	⃗	NOUN
iajs-2833	222	38	�	�	NOUN
iajs-2833	222	39	=	=	SYM
iajs-2833	222	40	(	(	PUNCT
iajs-2833	222	41	𝑦1	𝑦1	PROPN
iajs-2833	222	42	,	,	PUNCT
iajs-2833	222	43	𝑦2	𝑦2	PROPN
iajs-2833	222	44	,	,	PUNCT
iajs-2833	222	45	𝑦3	𝑦3	PROPN
iajs-2833	222	46	,	,	PUNCT
iajs-2833	222	47	𝑦4	𝑦4	PROPN
iajs-2833	222	48	)	)	PUNCT
iajs-2833	222	49	and	and	CCONJ
iajs-2833	222	50	�	�	PROPN
iajs-2833	222	51	⃗̅	⃗̅	PROPN
iajs-2833	222	52	�	�	PROPN
iajs-2833	222	53	=	=	SYM
iajs-2833	222	54	(	(	PUNCT
iajs-2833	222	55	�	�	NOUN
iajs-2833	222	56	̅	̅	NOUN
iajs-2833	222	57	�	�	NOUN
iajs-2833	222	58	1	1	NUM
iajs-2833	222	59	,	,	PUNCT
iajs-2833	222	60	�	�	NOUN
iajs-2833	222	61	̅	̅	NOUN
iajs-2833	222	62	�	�	NOUN
iajs-2833	222	63	2	2	NUM
iajs-2833	222	64	,	,	PUNCT
iajs-2833	222	65	�	�	NOUN
iajs-2833	222	66	̅	̅	NOUN
iajs-2833	222	67	�	�	NOUN
iajs-2833	222	68	3	3	NUM
iajs-2833	222	69	,	,	PUNCT
iajs-2833	222	70	�	�	NOUN
iajs-2833	222	71	̅	̅	NOUN
iajs-2833	222	72	�	�	NOUN
iajs-2833	222	73	4	4	NUM
iajs-2833	222	74	)	)	PUNCT
iajs-2833	222	75	be	be	VERB
iajs-2833	222	76	two	two	NUM
iajs-2833	222	77	solutions	solution	NOUN
iajs-2833	222	78	of	of	ADP
iajs-2833	222	79	the	the	DET
iajs-2833	222	80	sqvs	sqvs	NOUN
iajs-2833	222	81	of	of	ADP
iajs-2833	222	82	the	the	DET
iajs-2833	222	83	wf	wf	PROPN
iajs-2833	222	84	(	(	PUNCT
iajs-2833	222	85	(	(	PUNCT
iajs-2833	222	86	8)	8)	NUM
iajs-2833	222	87	,	,	PUNCT
iajs-2833	222	88	(	(	PUNCT
iajs-2833	222	89	10	10	NUM
iajs-2833	222	90	)	)	PUNCT
iajs-2833	222	91	,	,	PUNCT
iajs-2833	222	92	(	(	PUNCT
iajs-2833	222	93	12	12	NUM
iajs-2833	222	94	)	)	PUNCT
iajs-2833	222	95	,	,	PUNCT
iajs-2833	222	96	and	and	CCONJ
iajs-2833	222	97	(	(	PUNCT
iajs-2833	222	98	14	14	NUM
iajs-2833	222	99	)	)	PUNCT
iajs-2833	222	100	)	)	PUNCT
iajs-2833	222	101	,	,	PUNCT
iajs-2833	222	102	subtracting	subtract	VERB
iajs-2833	222	103	each	each	DET
iajs-2833	222	104	equation	equation	NOUN
iajs-2833	222	105	from	from	ADP
iajs-2833	222	106	the	the	DET
iajs-2833	222	107	other	other	ADJ
iajs-2833	222	108	and	and	CCONJ
iajs-2833	222	109	replace	replace	VERB
iajs-2833	222	110	𝑣𝑖	𝑣𝑖	ADP
iajs-2833	222	111	=	=	SYM
iajs-2833	222	112	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	222	113	−	−	PROPN
iajs-2833	222	114	�	�	PROPN
iajs-2833	222	115	̅	̅	NOUN
iajs-2833	222	116	�	�	NOUN
iajs-2833	222	117	𝑖	𝑖	X
iajs-2833	222	118	for	for	ADP
iajs-2833	222	119	each	each	PRON
iajs-2833	222	120	𝑖	𝑖	NOUN
iajs-2833	222	121	=	=	NOUN
iajs-2833	222	122	1,2,3,4	1,2,3,4	NUM
iajs-2833	222	123	,	,	PUNCT
iajs-2833	222	124	i.e.	i.e.	X
iajs-2833	222	125	(	(	PUNCT
iajs-2833	222	126	(	(	PUNCT
iajs-2833	222	127	𝑦1	𝑦1	PROPN
iajs-2833	222	128	−	−	PROPN
iajs-2833	222	129	�	�	PROPN
iajs-2833	222	130	̅	̅	NOUN
iajs-2833	222	131	�	�	NOUN
iajs-2833	222	132	1)𝑡𝑡	1)𝑡𝑡	NUM
iajs-2833	222	133	,	,	PUNCT
iajs-2833	222	134	𝑦1	𝑦1	PROPN
iajs-2833	222	135	−	−	PROPN
iajs-2833	222	136	�	�	PROPN
iajs-2833	222	137	̅	̅	NOUN
iajs-2833	222	138	�	�	NOUN
iajs-2833	222	139	1	1	NUM
iajs-2833	222	140	)	)	PUNCT
iajs-2833	223	1	+	+	CCONJ
iajs-2833	223	2	∇(𝑦1	∇(𝑦1	PROPN
iajs-2833	223	3	−	−	PROPN
iajs-2833	223	4	�	�	PROPN
iajs-2833	223	5	̅	̅	NOUN
iajs-2833	223	6	�	�	NOUN
iajs-2833	223	7	1	1	NUM
iajs-2833	223	8	,	,	PUNCT
iajs-2833	223	9	𝑦1	𝑦1	PROPN
iajs-2833	223	10	−	−	PROPN
iajs-2833	223	11	�	�	PROPN
iajs-2833	223	12	̅	̅	NOUN
iajs-2833	223	13	�	�	NOUN
iajs-2833	223	14	1	1	NUM
iajs-2833	223	15	)	)	PUNCT
iajs-2833	224	1	+	+	CCONJ
iajs-2833	224	2	(	(	PUNCT
iajs-2833	224	3	𝑦1	𝑦1	PROPN
iajs-2833	224	4	−	−	PROPN
iajs-2833	224	5	�	�	PROPN
iajs-2833	224	6	̅	̅	NOUN
iajs-2833	224	7	�	�	NOUN
iajs-2833	224	8	1	1	NUM
iajs-2833	224	9	,	,	PUNCT
iajs-2833	224	10	𝑦1	𝑦1	PROPN
iajs-2833	224	11	−	−	PROPN
iajs-2833	224	12	�	�	PROPN
iajs-2833	224	13	̅	̅	NOUN
iajs-2833	224	14	�	�	NOUN
iajs-2833	224	15	1	1	NUM
iajs-2833	224	16	)	)	PUNCT
iajs-2833	224	17	−	−	PROPN
iajs-2833	225	1	(	(	PUNCT
iajs-2833	225	2	𝑦2	𝑦2	PROPN
iajs-2833	225	3	−	−	PROPN
iajs-2833	225	4	�	�	PROPN
iajs-2833	225	5	̅	̅	NOUN
iajs-2833	225	6	�	�	NOUN
iajs-2833	225	7	2	2	NUM
iajs-2833	225	8	,	,	PUNCT
iajs-2833	225	9	𝑦1	𝑦1	PROPN
iajs-2833	225	10	−	−	PROPN
iajs-2833	225	11	�	�	PROPN
iajs-2833	225	12	̅	̅	NOUN
iajs-2833	225	13	�	�	NOUN
iajs-2833	225	14	1	1	NUM
iajs-2833	225	15	)	)	PUNCT
iajs-2833	225	16	+	+	CCONJ
iajs-2833	225	17	(	(	PUNCT
iajs-2833	225	18	𝑦3	𝑦3	PROPN
iajs-2833	225	19	−	−	PROPN
iajs-2833	225	20	�	�	PROPN
iajs-2833	225	21	̅	̅	NOUN
iajs-2833	225	22	�	�	NOUN
iajs-2833	225	23	3	3	NUM
iajs-2833	225	24	,	,	PUNCT
iajs-2833	225	25	𝑦1	𝑦1	PROPN
iajs-2833	225	26	−	−	PROPN
iajs-2833	225	27	�	�	PROPN
iajs-2833	225	28	̅	̅	NOUN
iajs-2833	225	29	�	�	NOUN
iajs-2833	225	30	1	1	NUM
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iajs-2833	228	78	equalities	equality	NOUN
iajs-2833	228	79	for	for	ADP
iajs-2833	228	80	𝑖	𝑖	NOUN
iajs-2833	228	81	=	=	NOUN
iajs-2833	228	82	1,2,3,4	1,2,3,4	NUM
iajs-2833	228	83	using	use	VERB
iajs-2833	228	84	lemma	lemma	PROPN
iajs-2833	228	85	1.2	1.2	NUM
iajs-2833	228	86	in	in	ADP
iajs-2833	228	87	ref	ref	NOUN
iajs-2833	228	88	.	.	PUNCT
iajs-2833	229	1	[	[	X
iajs-2833	229	2	15	15	NUM
iajs-2833	229	3	]	]	PUNCT
iajs-2833	229	4	for	for	ADP
iajs-2833	229	5	the	the	DET
iajs-2833	229	6	1st	1st	NOUN
iajs-2833	229	7	in	in	ADP
iajs-2833	229	8	lhs	lhs	PROPN
iajs-2833	229	9	of	of	ADP
iajs-2833	229	10	above	above	ADP
iajs-2833	229	11	equations	equation	NOUN
iajs-2833	229	12	,	,	PUNCT
iajs-2833	229	13	to	to	PART
iajs-2833	229	14	get	get	VERB
iajs-2833	229	15	1	1	NUM
iajs-2833	229	16	2	2	NUM
iajs-2833	229	17	𝑑	𝑑	NOUN
iajs-2833	229	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	229	19	∥	∥	X
iajs-2833	229	20	(	(	PUNCT
iajs-2833	229	21	�	�	NOUN
iajs-2833	229	22	⃗	⃗	NOUN
iajs-2833	229	23	�	�	PROPN
iajs-2833	229	24	−	−	PROPN
iajs-2833	229	25	�	�	PROPN
iajs-2833	229	26	⃗̅	⃗̅	PROPN
iajs-2833	229	27	�	�	PROPN
iajs-2833	229	28	)	)	PUNCT
iajs-2833	229	29	𝑡	𝑡	PROPN
iajs-2833	229	30	(	(	PUNCT
iajs-2833	229	31	𝑡	𝑡	NOUN
iajs-2833	229	32	)	)	PUNCT
iajs-2833	229	33	∥0	∥0	NOUN
iajs-2833	230	1	2	2	NUM
iajs-2833	230	2	+	+	NUM
iajs-2833	230	3	2	2	NUM
iajs-2833	230	4	∥	∥	NUM
iajs-2833	230	5	�	�	NOUN
iajs-2833	230	6	⃗	⃗	NOUN
iajs-2833	230	7	�	�	PROPN
iajs-2833	230	8	−	−	PROPN
iajs-2833	230	9	�	�	PROPN
iajs-2833	230	10	⃗̅	⃗̅	PROPN
iajs-2833	230	11	�	�	PROPN
iajs-2833	230	12	∥1	∥1	SYM
iajs-2833	230	13	2=	2=	NUM
iajs-2833	230	14	(	(	PUNCT
iajs-2833	230	15	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	230	16	,	,	PUNCT
iajs-2833	230	17	𝑢1	𝑢1	PROPN
iajs-2833	230	18	)	)	PUNCT
iajs-2833	230	19	−	−	ADP
iajs-2833	230	20	𝑓1(	𝑓1(	PROPN
iajs-2833	230	21	�	�	PROPN
iajs-2833	230	22	̅	̅	NOUN
iajs-2833	230	23	�	�	NOUN
iajs-2833	230	24	1	1	NUM
iajs-2833	230	25	,	,	PUNCT
iajs-2833	230	26	𝑢1	𝑢1	NOUN
iajs-2833	230	27	)	)	PUNCT
iajs-2833	230	28	,	,	PUNCT
iajs-2833	230	29	𝑦1	𝑦1	PROPN
iajs-2833	230	30	−	−	PROPN
iajs-2833	230	31	�	�	PROPN
iajs-2833	230	32	̅	̅	NOUN
iajs-2833	230	33	�	�	NOUN
iajs-2833	230	34	1	1	NUM
iajs-2833	230	35	)	)	PUNCT
iajs-2833	230	36	+	+	CCONJ
iajs-2833	230	37	(	(	PUNCT
iajs-2833	230	38	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	230	39	,	,	PUNCT
iajs-2833	230	40	𝑢2	𝑢2	PROPN
iajs-2833	230	41	)	)	PUNCT
iajs-2833	230	42	−	−	ADP
iajs-2833	230	43	𝑓2(	𝑓2(	X
iajs-2833	230	44	�	�	SYM
iajs-2833	230	45	̅	̅	NOUN
iajs-2833	230	46	�	�	NOUN
iajs-2833	230	47	2	2	NUM
iajs-2833	230	48	,	,	PUNCT
iajs-2833	230	49	𝑢2	𝑢2	PROPN
iajs-2833	230	50	)	)	PUNCT
iajs-2833	230	51	,	,	PUNCT
iajs-2833	230	52	𝑦2	𝑦2	PROPN
iajs-2833	230	53	−	−	PROPN
iajs-2833	230	54	�	�	PROPN
iajs-2833	230	55	̅	̅	NOUN
iajs-2833	230	56	�	�	NOUN
iajs-2833	230	57	2	2	NUM
iajs-2833	230	58	)	)	PUNCT
iajs-2833	230	59	+	+	CCONJ
iajs-2833	230	60	(	(	PUNCT
iajs-2833	230	61	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	230	62	,	,	PUNCT
iajs-2833	230	63	𝑢3	𝑢3	PROPN
iajs-2833	230	64	)	)	PUNCT
iajs-2833	230	65	−	−	PROPN
iajs-2833	230	66	𝑓3(	𝑓3(	SYM
iajs-2833	230	67	�	�	NOUN
iajs-2833	230	68	̅	̅	NOUN
iajs-2833	230	69	�	�	NOUN
iajs-2833	230	70	3	3	NUM
iajs-2833	230	71	,	,	PUNCT
iajs-2833	230	72	𝑢3	𝑢3	PROPN
iajs-2833	230	73	)	)	PUNCT
iajs-2833	230	74	,	,	PUNCT
iajs-2833	230	75	𝑦3	𝑦3	PROPN
iajs-2833	230	76	−	−	PROPN
iajs-2833	230	77	�	�	PROPN
iajs-2833	230	78	̅	̅	NOUN
iajs-2833	230	79	�	�	NOUN
iajs-2833	230	80	3	3	NUM
iajs-2833	230	81	)	)	PUNCT
iajs-2833	230	82	+	+	CCONJ
iajs-2833	230	83	(	(	PUNCT
iajs-2833	230	84	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	230	85	,	,	PUNCT
iajs-2833	230	86	𝑢4	𝑢4	NOUN
iajs-2833	230	87	)	)	PUNCT
iajs-2833	230	88	−	−	PROPN
iajs-2833	230	89	𝑓4(	𝑓4(	NOUN
iajs-2833	230	90	�	�	NOUN
iajs-2833	230	91	̅	̅	NOUN
iajs-2833	230	92	�	�	NOUN
iajs-2833	230	93	4	4	NUM
iajs-2833	230	94	,	,	PUNCT
iajs-2833	230	95	𝑢4	𝑢4	NOUN
iajs-2833	230	96	)	)	PUNCT
iajs-2833	230	97	,	,	PUNCT
iajs-2833	230	98	𝑦4	𝑦4	PROPN
iajs-2833	230	99	−	−	PROPN
iajs-2833	230	100	�	�	PROPN
iajs-2833	230	101	̅	̅	NOUN
iajs-2833	230	102	�	�	NOUN
iajs-2833	230	103	4	4	NUM
iajs-2833	230	104	)	)	PUNCT
iajs-2833	230	105	(	(	PUNCT
iajs-2833	230	106	68	68	NUM
iajs-2833	230	107	)	)	PUNCT
iajs-2833	230	108	the	the	DET
iajs-2833	230	109	lhs	lhs	PROPN
iajs-2833	230	110	of	of	ADP
iajs-2833	230	111	(	(	PUNCT
iajs-2833	230	112	68	68	NUM
iajs-2833	230	113	)	)	PUNCT
iajs-2833	230	114	is	be	AUX
iajs-2833	230	115	positive	positive	ADJ
iajs-2833	230	116	,	,	PUNCT
iajs-2833	230	117	ibs	ibs	PROPN
iajs-2833	230	118	of	of	ADP
iajs-2833	230	119	it	it	PRON
iajs-2833	230	120	w.r.t	w.r.t	VERB
iajs-2833	230	121	.	.	PUNCT
iajs-2833	231	1	𝑡	𝑡	VERB
iajs-2833	231	2	from	from	ADP
iajs-2833	231	3	0	0	NUM
iajs-2833	231	4	to	to	PART
iajs-2833	231	5	𝑡	𝑡	PROPN
iajs-2833	231	6	,	,	PUNCT
iajs-2833	231	7	and	and	CCONJ
iajs-2833	231	8	using	use	VERB
iajs-2833	231	9	assumptions	assumption	NOUN
iajs-2833	231	10	(	(	PUNCT
iajs-2833	231	11	a	a	DET
iajs-2833	231	12	-	-	PUNCT
iajs-2833	231	13	ii	ii	NOUN
iajs-2833	231	14	)	)	PUNCT
iajs-2833	231	15	of	of	ADP
iajs-2833	231	16	the	the	DET
iajs-2833	231	17	rhs	rhs	PROPN
iajs-2833	231	18	of	of	ADP
iajs-2833	231	19	it	it	PRON
iajs-2833	231	20	,	,	PUNCT
iajs-2833	231	21	yields	yield	NOUN
iajs-2833	231	22	to	to	PART
iajs-2833	231	23	∫	∫	PROPN
iajs-2833	231	24	0	0	PROPN
iajs-2833	231	25	𝑑	𝑑	PRON
iajs-2833	231	26	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	231	27	𝑡	𝑡	PROPN
iajs-2833	231	28	∥	∥	PROPN
iajs-2833	231	29	�	�	NOUN
iajs-2833	231	30	⃗	⃗	NOUN
iajs-2833	231	31	�	�	PROPN
iajs-2833	231	32	−	−	PROPN
iajs-2833	231	33	�	�	PROPN
iajs-2833	231	34	⃗̅	⃗̅	PROPN
iajs-2833	231	35	�	�	PROPN
iajs-2833	231	36	∥0	∥0	NUM
iajs-2833	231	37	2	2	NUM
iajs-2833	231	38	≤	≤	NUM
iajs-2833	231	39	2	2	NUM
iajs-2833	231	40	∫	∫	NOUN
iajs-2833	231	41	0	0	NUM
iajs-2833	231	42	𝑡	𝑡	PROPN
iajs-2833	231	43	𝐿	𝐿	PROPN
iajs-2833	231	44	∥	∥	PROPN
iajs-2833	231	45	�	�	NOUN
iajs-2833	231	46	⃗	⃗	NOUN
iajs-2833	231	47	�	�	PROPN
iajs-2833	231	48	−	−	PROPN
iajs-2833	231	49	�	�	PROPN
iajs-2833	231	50	⃗̅	⃗̅	PROPN
iajs-2833	231	51	�	�	PROPN
iajs-2833	231	52	∥0	∥0	PROPN
iajs-2833	231	53	2	2	NUM
iajs-2833	231	54	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	231	55	,	,	PUNCT
iajs-2833	231	56	where	where	SCONJ
iajs-2833	231	57	𝐿	𝐿	PROPN
iajs-2833	231	58	=	=	PROPN
iajs-2833	231	59	max	max	PROPN
iajs-2833	231	60	(	(	PUNCT
iajs-2833	231	61	𝐿1	𝐿1	PROPN
iajs-2833	231	62	,	,	PUNCT
iajs-2833	231	63	𝐿2	𝐿2	PROPN
iajs-2833	231	64	,	,	PUNCT
iajs-2833	231	65	𝐿3	𝐿3	PROPN
iajs-2833	231	66	,	,	PUNCT
iajs-2833	231	67	𝐿4	𝐿4	PROPN
iajs-2833	231	68	)	)	PUNCT
iajs-2833	231	69	ihjpas	ihjpas	PROPN
iajs-2833	231	70	.	.	PUNCT
iajs-2833	232	1	53	53	NUM
iajs-2833	232	2	(	(	PUNCT
iajs-2833	232	3	3)2022	3)2022	NOUN
iajs-2833	232	4	170	170	NUM
iajs-2833	232	5	then	then	ADV
iajs-2833	232	6	,	,	PUNCT
iajs-2833	232	7	∥	∥	PROPN
iajs-2833	232	8	�	�	NOUN
iajs-2833	232	9	⃗	⃗	NOUN
iajs-2833	232	10	�	�	PROPN
iajs-2833	232	11	−	−	PROPN
iajs-2833	232	12	�	�	PROPN
iajs-2833	232	13	⃗̅	⃗̅	PROPN
iajs-2833	232	14	�	�	PROPN
iajs-2833	232	15	∥0	∥0	PROPN
iajs-2833	232	16	2≤	2≤	NUM
iajs-2833	232	17	2	2	NUM
iajs-2833	232	18	∫	∫	NOUN
iajs-2833	232	19	0	0	NUM
iajs-2833	232	20	𝑇	𝑇	PROPN
iajs-2833	232	21	𝐿	𝐿	PROPN
iajs-2833	232	22	∥	∥	PROPN
iajs-2833	232	23	�	�	NOUN
iajs-2833	232	24	⃗	⃗	NOUN
iajs-2833	232	25	�	�	PROPN
iajs-2833	232	26	−	−	PROPN
iajs-2833	232	27	�	�	PROPN
iajs-2833	232	28	⃗̅	⃗̅	PROPN
iajs-2833	232	29	�	�	PROPN
iajs-2833	232	30	∥0	∥0	NUM
iajs-2833	232	31	2	2	NUM
iajs-2833	232	32	,	,	PUNCT
iajs-2833	232	33	.	.	PUNCT
iajs-2833	233	1	by	by	ADP
iajs-2833	233	2	using	use	VERB
iajs-2833	233	3	lemma	lemma	PROPN
iajs-2833	233	4	(	(	PUNCT
iajs-2833	233	5	1.2	1.2	NUM
iajs-2833	233	6	)	)	PUNCT
iajs-2833	233	7	,	,	PUNCT
iajs-2833	233	8	to	to	PART
iajs-2833	233	9	acquire	acquire	VERB
iajs-2833	233	10	∥	∥	NUM
iajs-2833	233	11	�	�	NOUN
iajs-2833	233	12	⃗	⃗	NOUN
iajs-2833	233	13	�	�	PROPN
iajs-2833	233	14	−	−	PROPN
iajs-2833	233	15	�	�	PROPN
iajs-2833	233	16	⃗̅	⃗̅	PROPN
iajs-2833	233	17	�	�	PROPN
iajs-2833	233	18	∥0	∥0	PROPN
iajs-2833	233	19	2≤	2≤	NUM
iajs-2833	233	20	0𝑒	0𝑒	ADJ
iajs-2833	233	21	∫	∫	PROPN
iajs-2833	233	22	0	0	NUM
iajs-2833	234	1	𝑇	𝑇	PROPN
iajs-2833	234	2	2𝐿𝑑𝑡	2𝐿𝑑𝑡	NUM
iajs-2833	234	3	=	=	SYM
iajs-2833	234	4	0	0	NUM
iajs-2833	234	5	,	,	PUNCT
iajs-2833	234	6	∀𝑡	∀𝑡	PROPN
iajs-2833	234	7	∈	∈	PROPN
iajs-2833	235	1	𝐼	𝐼	PROPN
iajs-2833	235	2	again	again	ADV
iajs-2833	235	3	ibs	ibs	PROPN
iajs-2833	235	4	of	of	ADP
iajs-2833	235	5	(	(	PUNCT
iajs-2833	235	6	68	68	NUM
iajs-2833	235	7	)	)	PUNCT
iajs-2833	235	8	w.r.t	w.r.t	NOUN
iajs-2833	235	9	.	.	PUNCT
iajs-2833	236	1	𝑡	𝑡	VERB
iajs-2833	236	2	from	from	ADP
iajs-2833	236	3	0	0	NUM
iajs-2833	236	4	to	to	ADP
iajs-2833	236	5	𝑇	𝑇	PROPN
iajs-2833	236	6	,	,	PUNCT
iajs-2833	236	7	using	use	VERB
iajs-2833	236	8	the	the	DET
iajs-2833	236	9	ics	ic	NOUN
iajs-2833	236	10	and	and	CCONJ
iajs-2833	236	11	the	the	DET
iajs-2833	236	12	above	above	ADJ
iajs-2833	236	13	result	result	NOUN
iajs-2833	236	14	for	for	ADP
iajs-2833	236	15	the	the	DET
iajs-2833	236	16	rhs	rhs	PROPN
iajs-2833	236	17	of	of	ADP
iajs-2833	236	18	the	the	DET
iajs-2833	236	19	equations	equation	NOUN
iajs-2833	236	20	,	,	PUNCT
iajs-2833	236	21	to	to	PART
iajs-2833	236	22	acquire	acquire	VERB
iajs-2833	236	23	∫	∫	PROPN
iajs-2833	236	24	0	0	PUNCT
iajs-2833	237	1	𝑇	𝑇	PROPN
iajs-2833	237	2	𝑑	𝑑	PRON
iajs-2833	237	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	237	4	∥	∥	PROPN
iajs-2833	237	5	�	�	NOUN
iajs-2833	237	6	⃗	⃗	NOUN
iajs-2833	237	7	�	�	PROPN
iajs-2833	237	8	−	−	PROPN
iajs-2833	237	9	�	�	PROPN
iajs-2833	237	10	⃗̅	⃗̅	PROPN
iajs-2833	237	11	�	�	PROPN
iajs-2833	237	12	∥0	∥0	VERB
iajs-2833	237	13	2	2	NUM
iajs-2833	237	14	+	+	NUM
iajs-2833	237	15	2	2	NUM
iajs-2833	237	16	∥	∥	NUM
iajs-2833	237	17	�	�	NOUN
iajs-2833	237	18	⃗	⃗	NOUN
iajs-2833	237	19	�	�	PROPN
iajs-2833	237	20	−	−	PROPN
iajs-2833	237	21	�	�	PROPN
iajs-2833	237	22	⃗̅	⃗̅	PROPN
iajs-2833	237	23	�	�	PROPN
iajs-2833	237	24	∥1	∥1	ADP
iajs-2833	237	25	2	2	NUM
iajs-2833	237	26	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	237	27	≤	≤	NUM
iajs-2833	237	28	𝐿	𝐿	PROPN
iajs-2833	237	29	∫	∫	PROPN
iajs-2833	237	30	0	0	NUM
iajs-2833	237	31	𝑇	𝑇	PROPN
iajs-2833	237	32	∥	∥	X
iajs-2833	237	33	(	(	PUNCT
iajs-2833	237	34	�	�	NOUN
iajs-2833	237	35	⃗	⃗	NOUN
iajs-2833	237	36	�	�	PROPN
iajs-2833	237	37	−	−	PROPN
iajs-2833	237	38	�	�	PROPN
iajs-2833	237	39	⃗̅	⃗̅	PROPN
iajs-2833	237	40	�	�	PROPN
iajs-2833	237	41	)	)	PUNCT
iajs-2833	237	42	∥0	∥0	NOUN
iajs-2833	237	43	2	2	NUM
iajs-2833	237	44	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	237	45	⟹	⟹	NUM
iajs-2833	237	46	∫	∫	PROPN
iajs-2833	237	47	0	0	NUM
iajs-2833	237	48	𝑇	𝑇	PROPN
iajs-2833	237	49	∥	∥	X
iajs-2833	237	50	(	(	PUNCT
iajs-2833	237	51	�	�	NOUN
iajs-2833	237	52	⃗	⃗	NOUN
iajs-2833	237	53	�	�	PROPN
iajs-2833	237	54	−	−	PROPN
iajs-2833	237	55	�	�	PROPN
iajs-2833	237	56	⃗̅	⃗̅	PROPN
iajs-2833	237	57	�	�	PROPN
iajs-2833	237	58	)	)	PUNCT
iajs-2833	237	59	(	(	PUNCT
iajs-2833	237	60	𝑡	𝑡	NOUN
iajs-2833	237	61	)	)	PUNCT
iajs-2833	237	62	∥1	∥1	PRON
iajs-2833	237	63	2≤	2≤	NUM
iajs-2833	237	64	0	0	NUM
iajs-2833	237	65	⟹∥	⟹∥	NOUN
iajs-2833	237	66	(	(	PUNCT
iajs-2833	237	67	�	�	NOUN
iajs-2833	237	68	⃗	⃗	NOUN
iajs-2833	237	69	�	�	PROPN
iajs-2833	237	70	−	−	PROPN
iajs-2833	237	71	�	�	PROPN
iajs-2833	237	72	⃗̅	⃗̅	PROPN
iajs-2833	237	73	�	�	PROPN
iajs-2833	237	74	)	)	PUNCT
iajs-2833	237	75	(	(	PUNCT
iajs-2833	237	76	𝑡	𝑡	X
iajs-2833	237	77	)	)	PUNCT
iajs-2833	237	78	∥𝐿2(i	∥𝐿2(i	NOUN
iajs-2833	237	79	,	,	PUNCT
iajs-2833	237	80	v	v	NOUN
iajs-2833	237	81	)	)	PUNCT
iajs-2833	237	82	=	=	SYM
iajs-2833	237	83	0	0	NUM
iajs-2833	237	84	⟹	⟹	NUM
iajs-2833	237	85	�	�	PROPN
iajs-2833	237	86	⃗	⃗	PROPN
iajs-2833	237	87	�	�	PROPN
iajs-2833	237	88	=	=	SYM
iajs-2833	237	89	�	�	PROPN
iajs-2833	237	90	⃗̅	⃗̅	PROPN
iajs-2833	237	91	�	�	PROPN
iajs-2833	237	92	i.e.	i.e.	X
iajs-2833	237	93	the	the	DET
iajs-2833	237	94	solution	solution	NOUN
iajs-2833	237	95	is	be	AUX
iajs-2833	237	96	unique	unique	ADJ
iajs-2833	237	97	3.1	3.1	NUM
iajs-2833	237	98	lemma	lemma	NOUN
iajs-2833	237	99	:	:	PUNCT
iajs-2833	237	100	in	in	ADP
iajs-2833	237	101	addition	addition	NOUN
iajs-2833	237	102	to	to	ADP
iajs-2833	237	103	assumptions	assumption	NOUN
iajs-2833	237	104	(	(	PUNCT
iajs-2833	237	105	a	a	X
iajs-2833	237	106	)	)	PUNCT
iajs-2833	237	107	,	,	PUNCT
iajs-2833	237	108	if	if	SCONJ
iajs-2833	237	109	the	the	DET
iajs-2833	237	110	functions	function	NOUN
iajs-2833	237	111	𝑓𝑖	𝑓𝑖	VERB
iajs-2833	237	112	(	(	PUNCT
iajs-2833	237	113	for	for	ADP
iajs-2833	237	114	each	each	PRON
iajs-2833	237	115	𝑖	𝑖	NOUN
iajs-2833	237	116	=	=	NOUN
iajs-2833	237	117	1,2,3,4	1,2,3,4	NUM
iajs-2833	237	118	)	)	PUNCT
iajs-2833	237	119	is	be	AUX
iajs-2833	237	120	lipschitz	lipschitz	NOUN
iajs-2833	237	121	w.r.t	w.r.t	NOUN
iajs-2833	237	122	.	.	PUNCT
iajs-2833	238	1	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	238	2	&	&	CCONJ
iajs-2833	238	3	𝑢𝑖	𝑢𝑖	PROPN
iajs-2833	238	4	,	,	PUNCT
iajs-2833	238	5	and	and	CCONJ
iajs-2833	238	6	if	if	SCONJ
iajs-2833	238	7	cccqv	cccqv	NOUN
iajs-2833	238	8	is	be	AUX
iajs-2833	238	9	bounded	bound	VERB
iajs-2833	238	10	,	,	PUNCT
iajs-2833	238	11	then	then	ADV
iajs-2833	238	12	the	the	DET
iajs-2833	238	13	operator	operator	NOUN
iajs-2833	238	14	�	�	PROPN
iajs-2833	238	15	⃗⃗	⃗⃗	PROPN
iajs-2833	238	16	�	�	PROPN
iajs-2833	238	17	→	→	SYM
iajs-2833	238	18	�	�	PROPN
iajs-2833	238	19	⃗	⃗	PROPN
iajs-2833	238	20	�	�	PROPN
iajs-2833	238	21	�	�	PROPN
iajs-2833	238	22	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	238	23	�	�	PROPN
iajs-2833	238	24	form	form	NOUN
iajs-2833	238	25	(	(	PUNCT
iajs-2833	238	26	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	238	27	to	to	PART
iajs-2833	238	28	(	(	PUNCT
iajs-2833	238	29	𝐿∞(𝐼	𝐿∞(𝐼	PROPN
iajs-2833	238	30	,	,	PUNCT
iajs-2833	238	31	𝐿2(ω)))4	𝐿2(ω)))4	NOUN
iajs-2833	238	32	or	or	CCONJ
iajs-2833	238	33	to	to	PART
iajs-2833	238	34	(	(	PUNCT
iajs-2833	238	35	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	238	36	or	or	CCONJ
iajs-2833	238	37	to	to	ADP
iajs-2833	238	38	(	(	PUNCT
iajs-2833	238	39	𝐿2(𝐼	𝐿2(𝐼	PROPN
iajs-2833	238	40	,	,	PUNCT
iajs-2833	238	41	𝑉))4	𝑉))4	PROPN
iajs-2833	238	42	is	be	AUX
iajs-2833	238	43	continuous	continuous	ADJ
iajs-2833	238	44	.	.	PUNCT
iajs-2833	239	1	proof	proof	NOUN
iajs-2833	239	2	:	:	PUNCT
iajs-2833	239	3	let	let	VERB
iajs-2833	239	4	�	�	PROPN
iajs-2833	239	5	⃗⃗	⃗⃗	PROPN
iajs-2833	239	6	�	�	PROPN
iajs-2833	239	7	=	=	SYM
iajs-2833	239	8	(	(	PUNCT
iajs-2833	239	9	𝑢1	𝑢1	PROPN
iajs-2833	239	10	,	,	PUNCT
iajs-2833	239	11	𝑢2	𝑢2	PROPN
iajs-2833	239	12	,	,	PUNCT
iajs-2833	239	13	𝑢3	𝑢3	PROPN
iajs-2833	239	14	,	,	PUNCT
iajs-2833	239	15	𝑢4	𝑢4	PROPN
iajs-2833	239	16	)	)	PUNCT
iajs-2833	239	17	,	,	PUNCT
iajs-2833	239	18	�	�	PROPN
iajs-2833	239	19	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	239	20	�	�	PROPN
iajs-2833	239	21	=	=	SYM
iajs-2833	239	22	(	(	PUNCT
iajs-2833	239	23	�	�	NOUN
iajs-2833	239	24	̅	̅	NOUN
iajs-2833	239	25	�	�	NOUN
iajs-2833	239	26	1	1	NUM
iajs-2833	239	27	,	,	PUNCT
iajs-2833	239	28	�	�	NOUN
iajs-2833	239	29	̅	̅	NOUN
iajs-2833	239	30	�	�	NOUN
iajs-2833	239	31	2	2	NUM
iajs-2833	239	32	,	,	PUNCT
iajs-2833	239	33	�	�	NOUN
iajs-2833	239	34	̅	̅	NOUN
iajs-2833	239	35	�	�	NOUN
iajs-2833	239	36	3	3	NUM
iajs-2833	239	37	,	,	PUNCT
iajs-2833	239	38	�	�	NOUN
iajs-2833	239	39	̅	̅	NOUN
iajs-2833	239	40	�	�	NOUN
iajs-2833	239	41	4	4	NUM
iajs-2833	239	42	)	)	PUNCT
iajs-2833	239	43	∈	∈	PROPN
iajs-2833	239	44	(	(	PUNCT
iajs-2833	239	45	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	239	46	,	,	PUNCT
iajs-2833	239	47	𝛿	𝛿	PROPN
iajs-2833	239	48	�	�	PROPN
iajs-2833	239	49	⃗⃗	⃗⃗	PROPN
iajs-2833	239	50	�	�	PROPN
iajs-2833	239	51	=	=	SYM
iajs-2833	239	52	�	�	PROPN
iajs-2833	239	53	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	239	54	�	�	PROPN
iajs-2833	239	55	−	−	PROPN
iajs-2833	239	56	�	�	PROPN
iajs-2833	239	57	⃗⃗	⃗⃗	PROPN
iajs-2833	239	58	�	�	PROPN
iajs-2833	239	59	,	,	PUNCT
iajs-2833	239	60	�	�	PROPN
iajs-2833	239	61	⃗⃗	⃗⃗	PROPN
iajs-2833	239	62	�	�	PROPN
iajs-2833	239	63	𝜀=	𝜀=	PROPN
iajs-2833	239	64	�	�	PROPN
iajs-2833	239	65	⃗⃗	⃗⃗	PROPN
iajs-2833	239	66	�	�	PROPN
iajs-2833	239	67	+	+	CCONJ
iajs-2833	239	68	휀𝛿	휀𝛿	PROPN
iajs-2833	239	69	�	�	PROPN
iajs-2833	239	70	⃗⃗	⃗⃗	PROPN
iajs-2833	239	71	�	�	PROPN
iajs-2833	239	72	∈	∈	PROPN
iajs-2833	239	73	(	(	PUNCT
iajs-2833	239	74	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	239	75	,	,	PUNCT
iajs-2833	239	76	for	for	ADP
iajs-2833	239	77	휀	휀	PRON
iajs-2833	239	78	>	>	X
iajs-2833	239	79	0	0	NUM
iajs-2833	239	80	,	,	PUNCT
iajs-2833	239	81	then	then	ADV
iajs-2833	239	82	by	by	ADP
iajs-2833	239	83	theorem	theorem	ADJ
iajs-2833	239	84	3.1	3.1	NUM
iajs-2833	239	85	,	,	PUNCT
iajs-2833	239	86	�	�	NOUN
iajs-2833	239	87	⃗	⃗	NOUN
iajs-2833	239	88	�	�	PROPN
iajs-2833	239	89	=	=	SYM
iajs-2833	239	90	�	�	PROPN
iajs-2833	239	91	⃗	⃗	PROPN
iajs-2833	239	92	�	�	PROPN
iajs-2833	239	93	�	�	PROPN
iajs-2833	239	94	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2833	239	95	�	�	X
iajs-2833	239	96	=	=	SYM
iajs-2833	239	97	(	(	PUNCT
iajs-2833	239	98	𝑦1	𝑦1	PROPN
iajs-2833	239	99	,	,	PUNCT
iajs-2833	239	100	𝑦2	𝑦2	PROPN
iajs-2833	239	101	,	,	PUNCT
iajs-2833	239	102	𝑦3	𝑦3	PROPN
iajs-2833	239	103	,	,	PUNCT
iajs-2833	239	104	𝑦4	𝑦4	PROPN
iajs-2833	239	105	)	)	PUNCT
iajs-2833	239	106	and	and	CCONJ
iajs-2833	239	107	�	�	PROPN
iajs-2833	239	108	⃗	⃗	NOUN
iajs-2833	239	109	�	�	PROPN
iajs-2833	239	110	𝜀	𝜀	NOUN
iajs-2833	239	111	=	=	SYM
iajs-2833	239	112	�	�	PROPN
iajs-2833	239	113	⃗	⃗	PROPN
iajs-2833	239	114	�	�	PROPN
iajs-2833	239	115	�	�	PROPN
iajs-2833	239	116	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2833	239	117	�	�	NOUN
iajs-2833	239	118	𝜀	𝜀	PROPN
iajs-2833	239	119	=	=	PUNCT
iajs-2833	239	120	(	(	PUNCT
iajs-2833	239	121	𝑦1𝜀	𝑦1𝜀	PROPN
iajs-2833	239	122	,	,	PUNCT
iajs-2833	239	123	𝑦2𝜀	𝑦2𝜀	PROPN
iajs-2833	239	124	,	,	PUNCT
iajs-2833	239	125	𝑦3𝜀	𝑦3𝜀	PROPN
iajs-2833	239	126	,	,	PUNCT
iajs-2833	239	127	𝑦4𝜀	𝑦4𝜀	NOUN
iajs-2833	239	128	)	)	PUNCT
iajs-2833	239	129	are	be	AUX
iajs-2833	239	130	their	their	PRON
iajs-2833	239	131	corresponding	correspond	VERB
iajs-2833	239	132	sqvs	sqvs	NOUN
iajs-2833	239	133	which	which	PRON
iajs-2833	239	134	satisfy	satisfy	VERB
iajs-2833	239	135	the	the	DET
iajs-2833	239	136	wf	wf	PROPN
iajs-2833	239	137	(	(	PUNCT
iajs-2833	239	138	(	(	PUNCT
iajs-2833	239	139	8)-(15	8)-(15	NUM
iajs-2833	239	140	)	)	PUNCT
iajs-2833	239	141	)	)	PUNCT
iajs-2833	239	142	.	.	PUNCT
iajs-2833	240	1	setting	set	VERB
iajs-2833	240	2	𝛿	𝛿	PROPN
iajs-2833	240	3	�	�	PROPN
iajs-2833	240	4	⃗	⃗	NOUN
iajs-2833	240	5	�	�	PROPN
iajs-2833	240	6	𝜀	𝜀	NOUN
iajs-2833	240	7	=	=	SYM
iajs-2833	240	8	(	(	PUNCT
iajs-2833	240	9	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	240	10	,	,	PUNCT
iajs-2833	240	11	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	240	12	,	,	PUNCT
iajs-2833	240	13	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	240	14	,	,	PUNCT
iajs-2833	240	15	𝛿𝑦4𝜀)=	𝛿𝑦4𝜀)=	PROPN
iajs-2833	240	16	�	�	PROPN
iajs-2833	240	17	⃗	⃗	PROPN
iajs-2833	240	18	�	�	PROPN
iajs-2833	240	19	𝜀	𝜀	ADP
iajs-2833	240	20	−	−	PROPN
iajs-2833	240	21	�	�	PROPN
iajs-2833	240	22	⃗	⃗	NOUN
iajs-2833	240	23	�	�	PROPN
iajs-2833	240	24	,	,	PUNCT
iajs-2833	240	25	to	to	PART
iajs-2833	240	26	obtain	obtain	VERB
iajs-2833	240	27	(	(	PUNCT
iajs-2833	240	28	𝛿𝑦1𝜀𝑡𝑡	𝛿𝑦1𝜀𝑡𝑡	PROPN
iajs-2833	240	29	,	,	PUNCT
iajs-2833	240	30	𝑣1	𝑣1	PROPN
iajs-2833	240	31	)	)	PUNCT
iajs-2833	240	32	+	+	CCONJ
iajs-2833	240	33	(	(	PUNCT
iajs-2833	240	34	∇𝛿𝑦1𝜀	∇𝛿𝑦1𝜀	INTJ
iajs-2833	240	35	,	,	PUNCT
iajs-2833	240	36	∇𝑣1	∇𝑣1	NOUN
iajs-2833	240	37	)	)	PUNCT
iajs-2833	241	1	+	+	CCONJ
iajs-2833	241	2	(	(	PUNCT
iajs-2833	241	3	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	241	4	,	,	PUNCT
iajs-2833	241	5	𝑣1	𝑣1	NOUN
iajs-2833	241	6	)	)	PUNCT
iajs-2833	241	7	−	−	PROPN
iajs-2833	242	1	(	(	PUNCT
iajs-2833	242	2	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	242	3	,	,	PUNCT
iajs-2833	242	4	𝑣1	𝑣1	PROPN
iajs-2833	242	5	)	)	PUNCT
iajs-2833	242	6	+	+	CCONJ
iajs-2833	242	7	(	(	PUNCT
iajs-2833	242	8	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	242	9	,	,	PUNCT
iajs-2833	242	10	𝑣1	𝑣1	PROPN
iajs-2833	242	11	)	)	PUNCT
iajs-2833	242	12	+	+	CCONJ
iajs-2833	242	13	(	(	PUNCT
iajs-2833	242	14	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	242	15	,	,	PUNCT
iajs-2833	242	16	𝑣1	𝑣1	NOUN
iajs-2833	242	17	)	)	PUNCT
iajs-2833	242	18	=	=	PUNCT
iajs-2833	242	19	(	(	PUNCT
iajs-2833	242	20	𝑓1(𝑦1	𝑓1(𝑦1	X
iajs-2833	242	21	+	+	X
iajs-2833	242	22	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	242	23	,	,	PUNCT
iajs-2833	242	24	𝑢1	𝑢1	NOUN
iajs-2833	242	25	+	+	CCONJ
iajs-2833	242	26	휀𝛿𝑢1	휀𝛿𝑢1	ADJ
iajs-2833	242	27	)	)	PUNCT
iajs-2833	243	1	−	−	PROPN
iajs-2833	243	2	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2833	243	3	,	,	PUNCT
iajs-2833	243	4	𝑢1	𝑢1	PROPN
iajs-2833	243	5	)	)	PUNCT
iajs-2833	243	6	,	,	PUNCT
iajs-2833	243	7	𝑣1	𝑣1	PROPN
iajs-2833	243	8	)	)	PUNCT
iajs-2833	243	9	(	(	PUNCT
iajs-2833	243	10	69	69	NUM
iajs-2833	243	11	)	)	PUNCT
iajs-2833	243	12	𝛿𝑦1𝜀(𝑥	𝛿𝑦1𝜀(𝑥	PROPN
iajs-2833	243	13	,	,	PUNCT
iajs-2833	243	14	0	0	NUM
iajs-2833	243	15	)	)	PUNCT
iajs-2833	243	16	=	=	SYM
iajs-2833	243	17	0	0	NUM
iajs-2833	243	18	and	and	CCONJ
iajs-2833	243	19	𝛿𝑦1𝜀𝑡(𝑥	𝛿𝑦1𝜀𝑡(𝑥	PROPN
iajs-2833	243	20	,	,	PUNCT
iajs-2833	243	21	0	0	NUM
iajs-2833	243	22	)	)	PUNCT
iajs-2833	243	23	=	=	SYM
iajs-2833	243	24	0	0	PUNCT
iajs-2833	243	25	(	(	PUNCT
iajs-2833	243	26	70	70	NUM
iajs-2833	243	27	)	)	PUNCT
iajs-2833	243	28	(	(	PUNCT
iajs-2833	243	29	𝛿𝑦2𝜀𝑡𝑡	𝛿𝑦2𝜀𝑡𝑡	PROPN
iajs-2833	243	30	,	,	PUNCT
iajs-2833	243	31	𝑣2	𝑣2	PROPN
iajs-2833	243	32	)	)	PUNCT
iajs-2833	243	33	+	+	CCONJ
iajs-2833	243	34	(	(	PUNCT
iajs-2833	243	35	∆𝛿𝑦2𝜀	∆𝛿𝑦2𝜀	PROPN
iajs-2833	243	36	,	,	PUNCT
iajs-2833	243	37	∇𝑣2	∇𝑣2	PROPN
iajs-2833	243	38	)	)	PUNCT
iajs-2833	244	1	+	+	CCONJ
iajs-2833	244	2	(	(	PUNCT
iajs-2833	244	3	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	244	4	,	,	PUNCT
iajs-2833	244	5	𝑣2	𝑣2	PROPN
iajs-2833	244	6	)	)	PUNCT
iajs-2833	244	7	+	+	CCONJ
iajs-2833	244	8	(	(	PUNCT
iajs-2833	244	9	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	244	10	,	,	PUNCT
iajs-2833	244	11	𝑣2	𝑣2	PROPN
iajs-2833	244	12	)	)	PUNCT
iajs-2833	244	13	−	−	PROPN
iajs-2833	244	14	(	(	PUNCT
iajs-2833	244	15	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	244	16	,	,	PUNCT
iajs-2833	244	17	𝑣2	𝑣2	PROPN
iajs-2833	244	18	)	)	PUNCT
iajs-2833	244	19	−	−	PROPN
iajs-2833	244	20	(	(	PUNCT
iajs-2833	244	21	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	244	22	,	,	PUNCT
iajs-2833	244	23	𝑣2	𝑣2	NOUN
iajs-2833	244	24	)	)	PUNCT
iajs-2833	244	25	=	=	PUNCT
iajs-2833	244	26	(	(	PUNCT
iajs-2833	244	27	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	244	28	+	+	CCONJ
iajs-2833	244	29	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	244	30	,	,	PUNCT
iajs-2833	244	31	𝑢2	𝑢2	PROPN
iajs-2833	244	32	+	+	CCONJ
iajs-2833	244	33	휀𝛿𝑢2	휀𝛿𝑢2	PROPN
iajs-2833	244	34	)	)	PUNCT
iajs-2833	244	35	−	−	PROPN
iajs-2833	244	36	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2833	244	37	,	,	PUNCT
iajs-2833	244	38	𝑢2	𝑢2	PROPN
iajs-2833	244	39	)	)	PUNCT
iajs-2833	244	40	,	,	PUNCT
iajs-2833	244	41	𝑣2	𝑣2	PROPN
iajs-2833	244	42	)	)	PUNCT
iajs-2833	244	43	(	(	PUNCT
iajs-2833	244	44	71	71	NUM
iajs-2833	244	45	)	)	PUNCT
iajs-2833	244	46	𝛿𝑦2𝜀(𝑥	𝛿𝑦2𝜀(𝑥	NOUN
iajs-2833	244	47	,	,	PUNCT
iajs-2833	244	48	0	0	NUM
iajs-2833	244	49	)	)	PUNCT
iajs-2833	244	50	=	=	SYM
iajs-2833	244	51	0	0	NUM
iajs-2833	244	52	and	and	CCONJ
iajs-2833	244	53	𝛿𝑦2𝜀𝑡(𝑥	𝛿𝑦2𝜀𝑡(𝑥	PROPN
iajs-2833	244	54	,	,	PUNCT
iajs-2833	244	55	0	0	NUM
iajs-2833	244	56	)	)	PUNCT
iajs-2833	244	57	=	=	SYM
iajs-2833	244	58	0	0	PUNCT
iajs-2833	244	59	(	(	PUNCT
iajs-2833	244	60	72	72	NUM
iajs-2833	244	61	)	)	PUNCT
iajs-2833	244	62	(	(	PUNCT
iajs-2833	244	63	𝛿𝑦3𝜀𝑡𝑡	𝛿𝑦3𝜀𝑡𝑡	PROPN
iajs-2833	244	64	,	,	PUNCT
iajs-2833	244	65	𝑣3	𝑣3	ADJ
iajs-2833	244	66	)	)	PUNCT
iajs-2833	244	67	+	+	CCONJ
iajs-2833	244	68	(	(	PUNCT
iajs-2833	244	69	∇δ𝑦3𝜀	∇δ𝑦3𝜀	INTJ
iajs-2833	244	70	,	,	PUNCT
iajs-2833	244	71	∇𝑣3	∇𝑣3	NOUN
iajs-2833	244	72	)	)	PUNCT
iajs-2833	244	73	−	−	PROPN
iajs-2833	244	74	(	(	PUNCT
iajs-2833	244	75	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	244	76	,	,	PUNCT
iajs-2833	244	77	𝑣3	𝑣3	ADJ
iajs-2833	244	78	)	)	PUNCT
iajs-2833	244	79	+	+	CCONJ
iajs-2833	244	80	(	(	PUNCT
iajs-2833	244	81	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	244	82	,	,	PUNCT
iajs-2833	244	83	𝑣3	𝑣3	ADJ
iajs-2833	244	84	)	)	PUNCT
iajs-2833	244	85	+	+	CCONJ
iajs-2833	244	86	(	(	PUNCT
iajs-2833	244	87	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	244	88	,	,	PUNCT
iajs-2833	244	89	𝑣3	𝑣3	ADJ
iajs-2833	244	90	)	)	PUNCT
iajs-2833	244	91	+	+	CCONJ
iajs-2833	244	92	(	(	PUNCT
iajs-2833	244	93	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	244	94	,	,	PUNCT
iajs-2833	244	95	𝑣3	𝑣3	ADJ
iajs-2833	244	96	)	)	PUNCT
iajs-2833	244	97	=	=	SYM
iajs-2833	244	98	(	(	PUNCT
iajs-2833	244	99	𝑓3(𝑦3	𝑓3(𝑦3	X
iajs-2833	244	100	+	+	CCONJ
iajs-2833	244	101	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	244	102	,	,	PUNCT
iajs-2833	244	103	𝑢3	𝑢3	PROPN
iajs-2833	244	104	+	+	CCONJ
iajs-2833	244	105	휀𝛿𝑢3	휀𝛿𝑢3	NOUN
iajs-2833	244	106	)	)	PUNCT
iajs-2833	244	107	−	−	PROPN
iajs-2833	244	108	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2833	244	109	,	,	PUNCT
iajs-2833	244	110	𝑢3	𝑢3	PROPN
iajs-2833	244	111	)	)	PUNCT
iajs-2833	244	112	,	,	PUNCT
iajs-2833	244	113	𝑣3	𝑣3	ADJ
iajs-2833	244	114	)	)	PUNCT
iajs-2833	244	115	(	(	PUNCT
iajs-2833	244	116	73	73	NUM
iajs-2833	244	117	)	)	PUNCT
iajs-2833	244	118	𝛿𝑦3𝜀(𝑥	𝛿𝑦3𝜀(𝑥	PROPN
iajs-2833	244	119	,	,	PUNCT
iajs-2833	244	120	0	0	NUM
iajs-2833	244	121	)	)	PUNCT
iajs-2833	244	122	=	=	SYM
iajs-2833	244	123	0	0	NUM
iajs-2833	244	124	and	and	CCONJ
iajs-2833	244	125	𝛿𝑦3𝜀𝑡(𝑥	𝛿𝑦3𝜀𝑡(𝑥	PROPN
iajs-2833	244	126	,	,	PUNCT
iajs-2833	244	127	0	0	NUM
iajs-2833	244	128	)	)	PUNCT
iajs-2833	244	129	=	=	SYM
iajs-2833	244	130	0	0	PUNCT
iajs-2833	244	131	(	(	PUNCT
iajs-2833	244	132	74	74	NUM
iajs-2833	244	133	)	)	PUNCT
iajs-2833	244	134	(	(	PUNCT
iajs-2833	244	135	𝛿𝑦4𝜀𝑡𝑡	𝛿𝑦4𝜀𝑡𝑡	PROPN
iajs-2833	244	136	,	,	PUNCT
iajs-2833	244	137	𝑣4	𝑣4	NOUN
iajs-2833	244	138	)	)	PUNCT
iajs-2833	244	139	+	+	CCONJ
iajs-2833	244	140	(	(	PUNCT
iajs-2833	244	141	∇δ𝑦4𝜀	∇δ𝑦4𝜀	INTJ
iajs-2833	244	142	,	,	PUNCT
iajs-2833	244	143	∇𝑣4	∇𝑣4	NUM
iajs-2833	244	144	)	)	PUNCT
iajs-2833	244	145	−	−	PROPN
iajs-2833	244	146	(	(	PUNCT
iajs-2833	244	147	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	244	148	,	,	PUNCT
iajs-2833	244	149	𝑣4	𝑣4	NOUN
iajs-2833	244	150	)	)	PUNCT
iajs-2833	244	151	+	+	CCONJ
iajs-2833	244	152	(	(	PUNCT
iajs-2833	244	153	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	244	154	,	,	PUNCT
iajs-2833	244	155	𝑣4	𝑣4	NOUN
iajs-2833	244	156	)	)	PUNCT
iajs-2833	244	157	−	−	PROPN
iajs-2833	244	158	(	(	PUNCT
iajs-2833	244	159	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	244	160	,	,	PUNCT
iajs-2833	244	161	𝑣4	𝑣4	NOUN
iajs-2833	244	162	)	)	PUNCT
iajs-2833	244	163	+	+	CCONJ
iajs-2833	244	164	(	(	PUNCT
iajs-2833	244	165	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	244	166	,	,	PUNCT
iajs-2833	244	167	𝑣4	𝑣4	NOUN
iajs-2833	244	168	)	)	PUNCT
iajs-2833	244	169	=	=	SYM
iajs-2833	244	170	(	(	PUNCT
iajs-2833	244	171	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	244	172	+	+	X
iajs-2833	244	173	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	244	174	,	,	PUNCT
iajs-2833	244	175	𝑢4	𝑢4	NOUN
iajs-2833	244	176	+	+	CCONJ
iajs-2833	244	177	휀𝛿𝑢4	휀𝛿𝑢4	NOUN
iajs-2833	244	178	)	)	PUNCT
iajs-2833	244	179	−	−	PROPN
iajs-2833	245	1	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2833	245	2	,	,	PUNCT
iajs-2833	245	3	𝑢4	𝑢4	NOUN
iajs-2833	245	4	)	)	PUNCT
iajs-2833	245	5	,	,	PUNCT
iajs-2833	245	6	𝑣4	𝑣4	PROPN
iajs-2833	245	7	)	)	PUNCT
iajs-2833	245	8	(	(	PUNCT
iajs-2833	245	9	75	75	NUM
iajs-2833	245	10	)	)	PUNCT
iajs-2833	245	11	𝛿𝑦4𝜀(𝑥	𝛿𝑦4𝜀(𝑥	PROPN
iajs-2833	245	12	,	,	PUNCT
iajs-2833	245	13	0	0	NUM
iajs-2833	245	14	)	)	PUNCT
iajs-2833	245	15	=	=	SYM
iajs-2833	245	16	0	0	NUM
iajs-2833	245	17	and	and	CCONJ
iajs-2833	245	18	𝛿𝑦4𝜀𝑡(𝑥	𝛿𝑦4𝜀𝑡(𝑥	PROPN
iajs-2833	245	19	,	,	PUNCT
iajs-2833	245	20	0	0	NUM
iajs-2833	245	21	)	)	PUNCT
iajs-2833	245	22	=	=	SYM
iajs-2833	245	23	0	0	PUNCT
iajs-2833	245	24	(	(	PUNCT
iajs-2833	245	25	76	76	NUM
iajs-2833	245	26	)	)	PUNCT
iajs-2833	245	27	substituting	substitute	VERB
iajs-2833	245	28	𝑣𝑖	𝑣𝑖	ADV
iajs-2833	245	29	=	=	PUNCT
iajs-2833	245	30	𝛿𝑦𝑖𝜀𝑡	𝛿𝑦𝑖𝜀𝑡	NOUN
iajs-2833	245	31	for	for	ADP
iajs-2833	245	32	𝑖	𝑖	NOUN
iajs-2833	245	33	=	=	NOUN
iajs-2833	245	34	1,2,3,4	1,2,3,4	NUM
iajs-2833	245	35	in	in	ADP
iajs-2833	245	36	(	(	PUNCT
iajs-2833	245	37	69),(71),(73)and	69),(71),(73)and	NUM
iajs-2833	245	38	(	(	PUNCT
iajs-2833	245	39	75	75	NUM
iajs-2833	245	40	)	)	PUNCT
iajs-2833	245	41	resp	resp	NOUN
iajs-2833	245	42	.	.	PUNCT
iajs-2833	245	43	,	,	PUNCT
iajs-2833	245	44	collecting	collect	VERB
iajs-2833	245	45	the	the	DET
iajs-2833	245	46	obtained	obtain	VERB
iajs-2833	245	47	equations	equation	NOUN
iajs-2833	245	48	.	.	PUNCT
iajs-2833	246	1	using	use	VERB
iajs-2833	246	2	the	the	DET
iajs-2833	246	3	same	same	ADJ
iajs-2833	246	4	way	way	NOUN
iajs-2833	246	5	that	that	PRON
iajs-2833	246	6	is	be	AUX
iajs-2833	246	7	used	use	VERB
iajs-2833	246	8	to	to	PART
iajs-2833	246	9	get	get	VERB
iajs-2833	246	10	(	(	PUNCT
iajs-2833	246	11	37	37	NUM
iajs-2833	246	12	)	)	PUNCT
iajs-2833	246	13	,	,	PUNCT
iajs-2833	246	14	a	a	DET
iajs-2833	246	15	similar	similar	ADJ
iajs-2833	246	16	equation	equation	NOUN
iajs-2833	246	17	can	can	AUX
iajs-2833	246	18	be	be	AUX
iajs-2833	246	19	obtained	obtain	VERB
iajs-2833	246	20	but	but	CCONJ
iajs-2833	246	21	with	with	ADP
iajs-2833	246	22	𝛿	𝛿	PROPN
iajs-2833	246	23	�	�	PROPN
iajs-2833	246	24	⃗	⃗	NOUN
iajs-2833	246	25	�	�	NOUN
iajs-2833	246	26	𝜀	𝜀	NOUN
iajs-2833	246	27	in	in	ADP
iajs-2833	246	28	position	position	NOUN
iajs-2833	246	29	of	of	ADP
iajs-2833	246	30	�	�	PROPN
iajs-2833	246	31	⃗	⃗	NOUN
iajs-2833	246	32	�	�	NOUN
iajs-2833	246	33	𝑛	𝑛	PROPN
iajs-2833	246	34	,	,	PUNCT
iajs-2833	246	35	then	then	ADV
iajs-2833	246	36	ibs	ib	VERB
iajs-2833	246	37	on	on	ADP
iajs-2833	246	38	[	[	X
iajs-2833	246	39	0	0	NUM
iajs-2833	246	40	,	,	PUNCT
iajs-2833	246	41	𝑡	𝑡	X
iajs-2833	246	42	]	]	PUNCT
iajs-2833	246	43	,	,	PUNCT
iajs-2833	246	44	using	use	VERB
iajs-2833	246	45	lip	lip	NOUN
iajs-2833	246	46	.	.	PUNCT
iajs-2833	247	1	on	on	ADP
iajs-2833	247	2	𝑓𝑖	𝑓𝑖	PROPN
iajs-2833	247	3	w.r.t	w.r.t	NOUN
iajs-2833	247	4	.	.	PUNCT
iajs-2833	248	1	(	(	PUNCT
iajs-2833	248	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	248	3	,	,	PUNCT
iajs-2833	248	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	248	5	)	)	PUNCT
iajs-2833	248	6	resp	resp	NOUN
iajs-2833	248	7	.	.	PUNCT
iajs-2833	249	1	for	for	ADP
iajs-2833	249	2	(	(	PUNCT
iajs-2833	249	3	𝑖	𝑖	NOUN
iajs-2833	249	4	=	=	NOUN
iajs-2833	249	5	1,2,3,4	1,2,3,4	NUM
iajs-2833	249	6	)	)	PUNCT
iajs-2833	249	7	to	to	PART
iajs-2833	249	8	get	get	VERB
iajs-2833	249	9	∫	∫	PROPN
iajs-2833	249	10	0	0	NUM
iajs-2833	249	11	𝑡	𝑡	PROPN
iajs-2833	249	12	𝑑	𝑑	VERB
iajs-2833	249	13	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	249	14	[	[	PUNCT
iajs-2833	249	15	∥	∥	PROPN
iajs-2833	249	16	𝛿	𝛿	PROPN
iajs-2833	249	17	�	�	PROPN
iajs-2833	249	18	⃗	⃗	NOUN
iajs-2833	249	19	�	�	NOUN
iajs-2833	249	20	𝜀𝑡(𝑡	𝜀𝑡(𝑡	NUM
iajs-2833	249	21	)	)	PUNCT
iajs-2833	249	22	∥0	∥0	VERB
iajs-2833	249	23	2+∥	2+∥	NUM
iajs-2833	249	24	𝛿	𝛿	DET
iajs-2833	249	25	�	�	PROPN
iajs-2833	249	26	⃗	⃗	NOUN
iajs-2833	249	27	�	�	NOUN
iajs-2833	249	28	𝜀	𝜀	ADP
iajs-2833	249	29	∥1	∥1	PRON
iajs-2833	249	30	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	249	31	≤	≤	NUM
iajs-2833	249	32	2	2	NUM
iajs-2833	249	33	∫	∫	NOUN
iajs-2833	249	34	0	0	PUNCT
iajs-2833	250	1	[	[	X
iajs-2833	250	2	(	(	PUNCT
iajs-2833	250	3	𝑡	𝑡	PROPN
iajs-2833	250	4	∣	∣	ADJ
iajs-2833	250	5	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	250	6	∣	∣	ADJ
iajs-2833	250	7	+	+	PROPN
iajs-2833	250	8	∣	∣	ADJ
iajs-2833	250	9	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	250	10	∣	∣	ADJ
iajs-2833	250	11	+	+	ADJ
iajs-2833	250	12	∣	∣	ADJ
iajs-2833	250	13	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	250	14	∣	∣	NOUN
iajs-2833	250	15	)	)	PUNCT
iajs-2833	250	16	∣	∣	ADJ
iajs-2833	250	17	𝛿𝑦1𝜀𝑡	𝛿𝑦1𝜀𝑡	ADJ
iajs-2833	250	18	∣	∣	PROPN
iajs-2833	250	19	+	+	PROPN
iajs-2833	250	20	�	�	NOUN
iajs-2833	250	21	̅	̅	NOUN
iajs-2833	250	22	�	�	NOUN
iajs-2833	250	23	1	1	NUM
iajs-2833	250	24	∣	∣	ADJ
iajs-2833	250	25	𝛿𝑦1𝜀𝑡	𝛿𝑦1𝜀𝑡	NOUN
iajs-2833	250	26	∣2	∣2	ADJ
iajs-2833	250	27	+	+	CCONJ
iajs-2833	250	28	휀	휀	PROPN
iajs-2833	250	29	�	�	PROPN
iajs-2833	250	30	̿	̿	NOUN
iajs-2833	250	31	�	�	PROPN
iajs-2833	250	32	1	1	NUM
iajs-2833	250	33	∣	∣	ADJ
iajs-2833	250	34	𝛿𝑢4	𝛿𝑢4	NOUN
iajs-2833	250	35	∣∣	∣∣	PUNCT
iajs-2833	250	36	𝛿𝑦1𝜀𝑡	𝛿𝑦1𝜀𝑡	NOUN
iajs-2833	250	37	∣]𝑑𝑡	∣]𝑑𝑡	PROPN
iajs-2833	250	38	+	+	CCONJ
iajs-2833	251	1	+	+	CCONJ
iajs-2833	251	2	2	2	NUM
iajs-2833	251	3	∫	∫	NOUN
iajs-2833	251	4	0	0	NUM
iajs-2833	252	1	𝑡	𝑡	PROPN
iajs-2833	253	1	[	[	X
iajs-2833	253	2	(	(	PUNCT
iajs-2833	253	3	∣	∣	ADJ
iajs-2833	253	4	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	253	5	∣	∣	ADJ
iajs-2833	253	6	+	+	ADJ
iajs-2833	253	7	∣	∣	ADJ
iajs-2833	253	8	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	253	9	∣	∣	ADJ
iajs-2833	253	10	+	+	ADJ
iajs-2833	253	11	∣	∣	ADJ
iajs-2833	253	12	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	253	13	∣	∣	NOUN
iajs-2833	253	14	)	)	PUNCT
iajs-2833	253	15	∣	∣	ADJ
iajs-2833	253	16	𝛿𝑦2𝜀𝑡	𝛿𝑦2𝜀𝑡	NUM
iajs-2833	253	17	∣	∣	ADJ
iajs-2833	253	18	+	+	PROPN
iajs-2833	253	19	�	�	NOUN
iajs-2833	253	20	̅	̅	NOUN
iajs-2833	253	21	�	�	NOUN
iajs-2833	253	22	2	2	NUM
iajs-2833	253	23	∣	∣	ADJ
iajs-2833	253	24	𝛿𝑦2𝜀𝑡	𝛿𝑦2𝜀𝑡	NOUN
iajs-2833	253	25	∣2	∣2	NOUN
iajs-2833	253	26	+	+	CCONJ
iajs-2833	253	27	휀	휀	PROPN
iajs-2833	253	28	�	�	PROPN
iajs-2833	253	29	̿	̿	NOUN
iajs-2833	253	30	�	�	PROPN
iajs-2833	253	31	2	2	NUM
iajs-2833	253	32	∣	∣	PROPN
iajs-2833	253	33	𝛿𝑢2	𝛿𝑢2	NOUN
iajs-2833	253	34	∣∣	∣∣	NUM
iajs-2833	253	35	𝛿𝑦2𝜀𝑡	𝛿𝑦2𝜀𝑡	NUM
iajs-2833	253	36	∣]𝑑𝑡	∣]𝑑𝑡	PROPN
iajs-2833	253	37	2∫	2∫	NUM
iajs-2833	253	38	0	0	NUM
iajs-2833	253	39	𝑡	𝑡	PROPN
iajs-2833	253	40	[	[	X
iajs-2833	253	41	(	(	PUNCT
iajs-2833	253	42	∣	∣	ADJ
iajs-2833	253	43	𝛿𝑦1𝜀	𝛿𝑦1𝜀	PROPN
iajs-2833	253	44	∣	∣	ADJ
iajs-2833	253	45	+	+	NOUN
iajs-2833	253	46	∣	∣	ADJ
iajs-2833	253	47	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	253	48	∣	∣	ADJ
iajs-2833	253	49	+	+	ADJ
iajs-2833	253	50	∣	∣	ADJ
iajs-2833	253	51	𝛿𝑦4𝜀	𝛿𝑦4𝜀	ADJ
iajs-2833	253	52	∣	∣	NOUN
iajs-2833	253	53	)	)	PUNCT
iajs-2833	253	54	∣	∣	ADJ
iajs-2833	253	55	𝛿𝑦3𝜀𝑡	𝛿𝑦3𝜀𝑡	NUM
iajs-2833	253	56	∣	∣	ADJ
iajs-2833	253	57	+	+	PROPN
iajs-2833	253	58	�	�	NOUN
iajs-2833	253	59	̅	̅	NOUN
iajs-2833	253	60	�	�	NOUN
iajs-2833	253	61	3	3	NUM
iajs-2833	253	62	∣	∣	NUM
iajs-2833	253	63	𝛿𝑦3𝜀𝑡	𝛿𝑦3𝜀𝑡	NUM
iajs-2833	253	64	∣2	∣2	ADJ
iajs-2833	253	65	+	+	ADP
iajs-2833	253	66	휀	휀	DET
iajs-2833	253	67	�	�	PROPN
iajs-2833	253	68	̅̅	̅̅	NOUN
iajs-2833	253	69	�	�	PROPN
iajs-2833	253	70	3	3	NUM
iajs-2833	253	71	∣	∣	PROPN
iajs-2833	253	72	𝛿𝑢3	𝛿𝑢3	NOUN
iajs-2833	253	73	∣	∣	PROPN
iajs-2833	253	74	∣	∣	PROPN
iajs-2833	253	75	𝛿𝑦3𝜀𝑡	𝛿𝑦3𝜀𝑡	NUM
iajs-2833	253	76	∣]𝑑𝑡	∣]𝑑𝑡	PROPN
iajs-2833	253	77	+2	+2	PROPN
iajs-2833	253	78	∫	∫	PROPN
iajs-2833	253	79	0	0	NUM
iajs-2833	254	1	𝑡	𝑡	PROPN
iajs-2833	255	1	[	[	X
iajs-2833	255	2	(	(	PUNCT
iajs-2833	255	3	∣	∣	PROPN
iajs-2833	255	4	𝛿𝑦1𝜀+∣	𝛿𝑦1𝜀+∣	PROPN
iajs-2833	255	5	𝛿𝑦2𝜀	𝛿𝑦2𝜀	PROPN
iajs-2833	255	6	∣	∣	ADJ
iajs-2833	255	7	+	+	PROPN
iajs-2833	255	8	∣	∣	ADJ
iajs-2833	255	9	𝛿𝑦3𝜀	𝛿𝑦3𝜀	PROPN
iajs-2833	255	10	∣	∣	NOUN
iajs-2833	255	11	)	)	PUNCT
iajs-2833	255	12	∣	∣	ADJ
iajs-2833	255	13	𝛿𝑦4𝜀𝑡	𝛿𝑦4𝜀𝑡	ADJ
iajs-2833	255	14	∣	∣	ADJ
iajs-2833	255	15	+	+	PROPN
iajs-2833	255	16	�	�	NOUN
iajs-2833	255	17	̅	̅	NOUN
iajs-2833	255	18	�	�	NOUN
iajs-2833	255	19	4	4	NUM
iajs-2833	255	20	∣	∣	ADJ
iajs-2833	255	21	𝛿𝑦4𝜀𝑡	𝛿𝑦4𝜀𝑡	ADJ
iajs-2833	255	22	∣2	∣2	NOUN
iajs-2833	255	23	+	+	CCONJ
iajs-2833	255	24	휀	휀	PROPN
iajs-2833	255	25	�	�	PROPN
iajs-2833	255	26	̅̅	̅̅	NOUN
iajs-2833	255	27	�	�	PROPN
iajs-2833	255	28	4	4	NUM
iajs-2833	255	29	∣	∣	ADJ
iajs-2833	255	30	𝛿𝑢4	𝛿𝑢4	ADJ
iajs-2833	255	31	∣∣	∣∣	PUNCT
iajs-2833	255	32	𝛿𝑦4𝜀𝑡	𝛿𝑦4𝜀𝑡	ADJ
iajs-2833	255	33	∣]𝑑𝑡	∣]𝑑𝑡	PROPN
iajs-2833	255	34	using	use	VERB
iajs-2833	255	35	the	the	DET
iajs-2833	255	36	definitions	definition	NOUN
iajs-2833	255	37	of	of	ADP
iajs-2833	255	38	the	the	DET
iajs-2833	255	39	norms	norm	NOUN
iajs-2833	255	40	and	and	CCONJ
iajs-2833	255	41	the	the	DET
iajs-2833	255	42	relations	relation	NOUN
iajs-2833	255	43	between	between	ADP
iajs-2833	255	44	them	they	PRON
iajs-2833	255	45	,	,	PUNCT
iajs-2833	255	46	to	to	PART
iajs-2833	255	47	get	get	VERB
iajs-2833	255	48	.	.	PUNCT
iajs-2833	256	1	∥	∥	X
iajs-2833	257	1	𝛿	𝛿	PRON
iajs-2833	257	2	�	�	PROPN
iajs-2833	257	3	⃗	⃗	NOUN
iajs-2833	257	4	�	�	NOUN
iajs-2833	257	5	𝜀𝑡	𝜀𝑡	NOUN
iajs-2833	257	6	∥0	∥0	NOUN
iajs-2833	257	7	2+∥	2+∥	NUM
iajs-2833	257	8	𝛿	𝛿	DET
iajs-2833	257	9	�	�	PROPN
iajs-2833	257	10	⃗	⃗	NOUN
iajs-2833	257	11	�	�	NOUN
iajs-2833	257	12	𝜀	𝜀	ADP
iajs-2833	257	13	∥1	∥1	PRON
iajs-2833	257	14	2≤	2≤	NUM
iajs-2833	257	15	3	3	NUM
iajs-2833	257	16	∫	∫	NOUN
iajs-2833	257	17	0	0	NUM
iajs-2833	258	1	𝑡	𝑡	PROPN
iajs-2833	259	1	[	[	X
iajs-2833	259	2	∥	∥	PUNCT
iajs-2833	259	3	𝛿	𝛿	PROPN
iajs-2833	259	4	�	�	PROPN
iajs-2833	259	5	⃗	⃗	NOUN
iajs-2833	259	6	�	�	NOUN
iajs-2833	259	7	𝜀	𝜀	NOUN
iajs-2833	259	8	∥0	∥0	NOUN
iajs-2833	260	1	2+∥	2+∥	NUM
iajs-2833	260	2	𝛿	𝛿	DET
iajs-2833	260	3	�	�	PROPN
iajs-2833	260	4	⃗	⃗	NOUN
iajs-2833	260	5	�	�	NOUN
iajs-2833	260	6	𝜀𝑡	𝜀𝑡	VERB
iajs-2833	260	7	∥1	∥1	PRON
iajs-2833	260	8	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	260	9	+	+	SYM
iajs-2833	260	10	�	�	PROPN
iajs-2833	260	11	̃	̃	PROPN
iajs-2833	260	12	�	�	NOUN
iajs-2833	260	13	3	3	NUM
iajs-2833	260	14	∫	∫	NOUN
iajs-2833	260	15	0	0	NUM
iajs-2833	260	16	𝑡	𝑡	PROPN
iajs-2833	261	1	[	[	X
iajs-2833	261	2	∥	∥	PUNCT
iajs-2833	261	3	𝛿	𝛿	PROPN
iajs-2833	261	4	�	�	PROPN
iajs-2833	261	5	⃗	⃗	NOUN
iajs-2833	261	6	�	�	NOUN
iajs-2833	261	7	𝜀	𝜀	NOUN
iajs-2833	261	8	∥0	∥0	NOUN
iajs-2833	262	1	2+∥	2+∥	NUM
iajs-2833	262	2	𝛿	𝛿	DET
iajs-2833	262	3	�	�	PROPN
iajs-2833	262	4	⃗	⃗	NOUN
iajs-2833	262	5	�	�	NOUN
iajs-2833	262	6	𝜀𝑡	𝜀𝑡	VERB
iajs-2833	262	7	∥1	∥1	PRON
iajs-2833	262	8	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	262	9	ihjpas	ihjpa	NOUN
iajs-2833	262	10	.	.	PUNCT
iajs-2833	263	1	53	53	NUM
iajs-2833	263	2	(	(	PUNCT
iajs-2833	263	3	3)2022	3)2022	NOUN
iajs-2833	263	4	171	171	NUM
iajs-2833	263	5	+	+	ADJ
iajs-2833	263	6	�	�	PROPN
iajs-2833	263	7	̃	̃	NOUN
iajs-2833	263	8	�	�	NOUN
iajs-2833	263	9	4	4	NUM
iajs-2833	263	10	∫	∫	NOUN
iajs-2833	263	11	0	0	NUM
iajs-2833	264	1	𝑡	𝑡	PROPN
iajs-2833	264	2	∥	∥	PUNCT
iajs-2833	264	3	𝛿	𝛿	PROPN
iajs-2833	264	4	�	�	PROPN
iajs-2833	264	5	⃗⃗	⃗⃗	PROPN
iajs-2833	264	6	�	�	PROPN
iajs-2833	264	7	∥0	∥0	NUM
iajs-2833	264	8	2	2	NUM
iajs-2833	264	9	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	264	10	+	+	PROPN
iajs-2833	264	11	�	�	PROPN
iajs-2833	264	12	̃	̃	PROPN
iajs-2833	264	13	�	�	NOUN
iajs-2833	264	14	4	4	NUM
iajs-2833	264	15	∫	∫	NOUN
iajs-2833	264	16	0	0	NUM
iajs-2833	265	1	𝑡	𝑡	PROPN
iajs-2833	265	2	∥	∥	PUNCT
iajs-2833	265	3	𝛿	𝛿	PROPN
iajs-2833	265	4	�	�	PROPN
iajs-2833	265	5	⃗	⃗	NOUN
iajs-2833	265	6	�	�	NOUN
iajs-2833	265	7	𝜀𝑡	𝜀𝑡	VERB
iajs-2833	265	8	∥1	∥1	PRON
iajs-2833	265	9	2	2	NUM
iajs-2833	265	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	265	11	≤	≤	NUM
iajs-2833	265	12	�	�	PROPN
iajs-2833	265	13	̃	̃	PROPN
iajs-2833	265	14	�	�	PROPN
iajs-2833	265	15	4	4	NUM
iajs-2833	265	16	∥	∥	NUM
iajs-2833	265	17	𝛿	𝛿	PROPN
iajs-2833	265	18	�	�	PROPN
iajs-2833	265	19	⃗⃗	⃗⃗	PROPN
iajs-2833	265	20	�	�	PROPN
iajs-2833	265	21	∥𝑄	∥𝑄	PROPN
iajs-2833	265	22	2	2	NUM
iajs-2833	265	23	+	+	CCONJ
iajs-2833	265	24	𝐿5	𝐿5	PROPN
iajs-2833	265	25	∫	∫	PROPN
iajs-2833	265	26	0	0	NUM
iajs-2833	266	1	𝑡	𝑡	PROPN
iajs-2833	267	1	[	[	X
iajs-2833	267	2	∥	∥	PUNCT
iajs-2833	267	3	𝛿	𝛿	PROPN
iajs-2833	267	4	�	�	PROPN
iajs-2833	267	5	⃗	⃗	NOUN
iajs-2833	267	6	�	�	NOUN
iajs-2833	267	7	𝜀	𝜀	NOUN
iajs-2833	267	8	∥0	∥0	NOUN
iajs-2833	267	9	2+∥	2+∥	NUM
iajs-2833	267	10	𝛿	𝛿	DET
iajs-2833	267	11	�	�	PROPN
iajs-2833	267	12	⃗	⃗	NOUN
iajs-2833	267	13	�	�	NOUN
iajs-2833	267	14	𝜀𝑡	𝜀𝑡	VERB
iajs-2833	267	15	∥1	∥1	PRON
iajs-2833	267	16	2]𝑑𝑡	2]𝑑𝑡	NUM
iajs-2833	267	17	where	where	SCONJ
iajs-2833	267	18	�	�	PROPN
iajs-2833	267	19	̃	̃	PROPN
iajs-2833	267	20	�	�	NOUN
iajs-2833	267	21	3	3	NUM
iajs-2833	267	22	=	=	SYM
iajs-2833	267	23	max	max	PROPN
iajs-2833	267	24	(	(	PUNCT
iajs-2833	267	25	�	�	NOUN
iajs-2833	267	26	̅	̅	NOUN
iajs-2833	267	27	�	�	NOUN
iajs-2833	267	28	1	1	NUM
iajs-2833	267	29	,	,	PUNCT
iajs-2833	267	30	�	�	NOUN
iajs-2833	267	31	̅	̅	NOUN
iajs-2833	267	32	�	�	NOUN
iajs-2833	267	33	2	2	NUM
iajs-2833	267	34	,	,	PUNCT
iajs-2833	267	35	�	�	NOUN
iajs-2833	267	36	̅	̅	NOUN
iajs-2833	267	37	�	�	NOUN
iajs-2833	267	38	3	3	NUM
iajs-2833	267	39	,	,	PUNCT
iajs-2833	267	40	�	�	NOUN
iajs-2833	267	41	̅	̅	NOUN
iajs-2833	267	42	�	�	NOUN
iajs-2833	267	43	4	4	NUM
iajs-2833	267	44	)	)	PUNCT
iajs-2833	267	45	,	,	PUNCT
iajs-2833	267	46	�	�	PROPN
iajs-2833	267	47	̃	̃	NOUN
iajs-2833	267	48	�	�	NOUN
iajs-2833	267	49	4	4	NUM
iajs-2833	267	50	=	=	SYM
iajs-2833	267	51	max	max	PROPN
iajs-2833	267	52	(	(	PUNCT
iajs-2833	267	53	�	�	PROPN
iajs-2833	267	54	̅̅	̅̅	NOUN
iajs-2833	267	55	�	�	PROPN
iajs-2833	267	56	1	1	NUM
iajs-2833	267	57	,	,	PUNCT
iajs-2833	267	58	�	�	PROPN
iajs-2833	267	59	̅̅	̅̅	NOUN
iajs-2833	267	60	�	�	PROPN
iajs-2833	267	61	2	2	NUM
iajs-2833	267	62	,	,	PUNCT
iajs-2833	267	63	�	�	PROPN
iajs-2833	267	64	̅̅	̅̅	NOUN
iajs-2833	267	65	�	�	PROPN
iajs-2833	267	66	3	3	NUM
iajs-2833	267	67	,	,	PUNCT
iajs-2833	267	68	�	�	PROPN
iajs-2833	267	69	̅̅	̅̅	NOUN
iajs-2833	267	70	�	�	PROPN
iajs-2833	267	71	4	4	NUM
iajs-2833	267	72	)	)	PUNCT
iajs-2833	267	73	,	,	PUNCT
iajs-2833	267	74	𝐿5	𝐿5	PROPN
iajs-2833	267	75	=	=	SYM
iajs-2833	267	76	max	max	PROPN
iajs-2833	267	77	(	(	PUNCT
iajs-2833	267	78	3	3	NUM
iajs-2833	267	79	+	+	NUM
iajs-2833	267	80	�	�	PROPN
iajs-2833	267	81	̃	̃	PROPN
iajs-2833	267	82	�	�	NOUN
iajs-2833	267	83	3	3	NUM
iajs-2833	267	84	,	,	PUNCT
iajs-2833	267	85	3	3	NUM
iajs-2833	267	86	+	+	NUM
iajs-2833	267	87	�	�	PROPN
iajs-2833	267	88	̃	̃	PROPN
iajs-2833	267	89	�	�	NOUN
iajs-2833	267	90	4	4	NUM
iajs-2833	267	91	+	+	SYM
iajs-2833	267	92	�	�	PROPN
iajs-2833	267	93	̃	̃	PROPN
iajs-2833	267	94	�	�	NOUN
iajs-2833	267	95	3	3	NUM
iajs-2833	267	96	)	)	PUNCT
iajs-2833	267	97	.	.	PUNCT
iajs-2833	268	1	applying	apply	VERB
iajs-2833	268	2	the	the	DET
iajs-2833	268	3	bgi	bgi	NOUN
iajs-2833	268	4	,	,	PUNCT
iajs-2833	268	5	with𝐿2	with𝐿2	ADP
iajs-2833	268	6	=	=	PUNCT
iajs-2833	268	7	�	�	PROPN
iajs-2833	268	8	̃	̃	PROPN
iajs-2833	268	9	�	�	PROPN
iajs-2833	268	10	4𝑒	4𝑒	PROPN
iajs-2833	268	11	𝐿5	𝐿5	PROPN
iajs-2833	268	12	∫	∫	PROPN
iajs-2833	268	13	0	0	NUM
iajs-2833	269	1	𝑡	𝑡	PROPN
iajs-2833	269	2	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	269	3	,	,	PUNCT
iajs-2833	269	4	to	to	PART
iajs-2833	269	5	get	get	VERB
iajs-2833	269	6	∥	∥	NUM
iajs-2833	269	7	𝛿	𝛿	DET
iajs-2833	269	8	�	�	PROPN
iajs-2833	269	9	⃗	⃗	NOUN
iajs-2833	269	10	�	�	NOUN
iajs-2833	269	11	𝜀𝑡	𝜀𝑡	NOUN
iajs-2833	269	12	∥0	∥0	NOUN
iajs-2833	269	13	2+∥	2+∥	NUM
iajs-2833	269	14	𝛿	𝛿	DET
iajs-2833	269	15	�	�	PROPN
iajs-2833	269	16	⃗	⃗	NOUN
iajs-2833	269	17	�	�	NOUN
iajs-2833	269	18	𝜀	𝜀	ADP
iajs-2833	269	19	∥1	∥1	PRON
iajs-2833	269	20	2≤	2≤	NUM
iajs-2833	269	21	𝐿2	𝐿2	PROPN
iajs-2833	269	22	∥	∥	PUNCT
iajs-2833	270	1	𝛿	𝛿	PROPN
iajs-2833	270	2	�	�	PROPN
iajs-2833	270	3	⃗⃗	⃗⃗	PROPN
iajs-2833	270	4	�	�	PROPN
iajs-2833	270	5	∥𝑄	∥𝑄	PROPN
iajs-2833	270	6	2	2	NUM
iajs-2833	270	7	,	,	PUNCT
iajs-2833	270	8	∀𝑡	∀𝑡	PROPN
iajs-2833	270	9	∈	∈	PROPN
iajs-2833	271	1	𝐼	𝐼	ADP
iajs-2833	271	2	⟹∥	⟹∥	NOUN
iajs-2833	271	3	𝛿	𝛿	PROPN
iajs-2833	271	4	�	�	PROPN
iajs-2833	271	5	⃗	⃗	NOUN
iajs-2833	271	6	�	�	NOUN
iajs-2833	271	7	𝜀	𝜀	ADP
iajs-2833	271	8	∥1	∥1	DET
iajs-2833	271	9	2≤	2≤	NUM
iajs-2833	272	1	𝐿2	𝐿2	PROPN
iajs-2833	272	2	∥	∥	PUNCT
iajs-2833	273	1	𝛿	𝛿	PROPN
iajs-2833	273	2	�	�	PROPN
iajs-2833	273	3	⃗⃗	⃗⃗	PROPN
iajs-2833	273	4	�	�	PROPN
iajs-2833	273	5	(𝑡	(𝑡	PROPN
iajs-2833	273	6	)	)	PUNCT
iajs-2833	273	7	∥𝑄	∥𝑄	PROPN
iajs-2833	273	8	2	2	NUM
iajs-2833	273	9	,	,	PUNCT
iajs-2833	273	10	∀𝑡	∀𝑡	PROPN
iajs-2833	273	11	∈	∈	PROPN
iajs-2833	274	1	𝐼	𝐼	ADP
iajs-2833	274	2	∥	∥	PUNCT
iajs-2833	274	3	𝛿	𝛿	PROPN
iajs-2833	274	4	�	�	PROPN
iajs-2833	274	5	⃗	⃗	NOUN
iajs-2833	274	6	�	�	PROPN
iajs-2833	274	7	𝜀	𝜀	NOUN
iajs-2833	274	8	∥𝐿∞(𝐼,𝐿2(ω))≤	∥𝐿∞(𝐼,𝐿2(ω))≤	NOUN
iajs-2833	274	9	𝐿	𝐿	PROPN
iajs-2833	274	10	∥	∥	PROPN
iajs-2833	274	11	𝛿	𝛿	PROPN
iajs-2833	274	12	�	�	PROPN
iajs-2833	274	13	⃗⃗	⃗⃗	PROPN
iajs-2833	274	14	�	�	PROPN
iajs-2833	274	15	∥𝑄	∥𝑄	PROPN
iajs-2833	274	16	,	,	PUNCT
iajs-2833	274	17	∥	∥	PUNCT
iajs-2833	274	18	𝛿	𝛿	PROPN
iajs-2833	274	19	�	�	PROPN
iajs-2833	274	20	⃗	⃗	NOUN
iajs-2833	274	21	�	�	ADP
iajs-2833	274	22	∈	∈	PROPN
iajs-2833	274	23	∥𝐿2(𝐼,𝑉)≤	∥𝐿2(𝐼,𝑉)≤	PROPN
iajs-2833	274	24	𝐿	𝐿	PROPN
iajs-2833	274	25	∥	∥	PROPN
iajs-2833	274	26	𝛿	𝛿	PROPN
iajs-2833	274	27	�	�	PROPN
iajs-2833	274	28	⃗⃗	⃗⃗	PROPN
iajs-2833	274	29	�	�	PROPN
iajs-2833	274	30	∥𝑄	∥𝑄	PROPN
iajs-2833	274	31	and	and	CCONJ
iajs-2833	274	32	∥	∥	PUNCT
iajs-2833	274	33	𝛿	𝛿	PROPN
iajs-2833	274	34	�	�	PROPN
iajs-2833	274	35	⃗	⃗	NOUN
iajs-2833	274	36	�	�	PROPN
iajs-2833	274	37	𝜀	𝜀	ADP
iajs-2833	274	38	∥𝑄≤	∥𝑄≤	PROPN
iajs-2833	274	39	𝐿	𝐿	PROPN
iajs-2833	274	40	∥	∥	PROPN
iajs-2833	274	41	𝛿	𝛿	PROPN
iajs-2833	274	42	�	�	PROPN
iajs-2833	274	43	⃗⃗	⃗⃗	PROPN
iajs-2833	274	44	�	�	PROPN
iajs-2833	274	45	∥𝑄	∥𝑄	PROPN
iajs-2833	274	46	.	.	PUNCT
iajs-2833	275	1	4	4	X
iajs-2833	275	2	.	.	X
iajs-2833	275	3	the	the	DET
iajs-2833	275	4	existence	existence	NOUN
iajs-2833	275	5	of	of	ADP
iajs-2833	275	6	an	an	DET
iajs-2833	275	7	occcqv	occcqv	NOUN
iajs-2833	275	8	4.1	4.1	NUM
iajs-2833	275	9	.	.	PUNCT
iajs-2833	275	10	assumptions	assumption	NOUN
iajs-2833	275	11	(	(	PUNCT
iajs-2833	275	12	b	b	NOUN
iajs-2833	275	13	):	):	PUNCT
iajs-2833	275	14	consider	consider	VERB
iajs-2833	275	15	𝑔𝑙𝑖	𝑔𝑙𝑖	NOUN
iajs-2833	275	16	for	for	ADP
iajs-2833	275	17	(	(	PUNCT
iajs-2833	275	18	𝑙	𝑙	NOUN
iajs-2833	275	19	=	=	SYM
iajs-2833	275	20	0	0	PROPN
iajs-2833	275	21	&	&	CCONJ
iajs-2833	275	22	𝑖	𝑖	SYM
iajs-2833	275	23	=	=	NOUN
iajs-2833	275	24	1,2,3,4	1,2,3,4	NUM
iajs-2833	275	25	)	)	PUNCT
iajs-2833	275	26	is	be	AUX
iajs-2833	275	27	of	of	ADP
iajs-2833	275	28	carathéodory	carathéodory	ADJ
iajs-2833	275	29	type	type	NOUN
iajs-2833	275	30	on	on	ADP
iajs-2833	275	31	𝑄	𝑄	PROPN
iajs-2833	275	32	×	×	NOUN
iajs-2833	275	33	(	(	PUNCT
iajs-2833	275	34	ℝ	ℝ	PROPN
iajs-2833	275	35	×	×	PROPN
iajs-2833	275	36	𝑈	𝑈	PROPN
iajs-2833	275	37	)	)	PUNCT
iajs-2833	275	38	,	,	PUNCT
iajs-2833	275	39	and	and	CCONJ
iajs-2833	275	40	satisfies	satisfy	VERB
iajs-2833	275	41	the	the	DET
iajs-2833	275	42	following	follow	VERB
iajs-2833	275	43	sub	sub	NOUN
iajs-2833	275	44	quadratic	quadratic	ADJ
iajs-2833	275	45	condition	condition	NOUN
iajs-2833	275	46	w.r.t	w.r.t	VERB
iajs-2833	275	47	.	.	PUNCT
iajs-2833	276	1	𝑦𝑖	𝑦𝑖	NUM
iajs-2833	276	2	∈	∈	PROPN
iajs-2833	276	3	ℝ	ℝ	PROPN
iajs-2833	276	4	and	and	CCONJ
iajs-2833	276	5	𝑢𝑖	𝑢𝑖	DET
iajs-2833	276	6	∈	∈	PROPN
iajs-2833	276	7	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	276	8	,	,	PUNCT
iajs-2833	276	9	|𝑔𝑙𝑖(𝑥	|𝑔𝑙𝑖(𝑥	PROPN
iajs-2833	276	10	,	,	PUNCT
iajs-2833	276	11	𝑡	𝑡	PROPN
iajs-2833	276	12	,	,	PUNCT
iajs-2833	276	13	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	276	14	,	,	PUNCT
iajs-2833	276	15	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2833	276	16	≤	≤	PROPN
iajs-2833	276	17	𝐺𝑙𝑖(𝑥	𝐺𝑙𝑖(𝑥	PROPN
iajs-2833	276	18	,	,	PUNCT
iajs-2833	276	19	𝑡	𝑡	X
iajs-2833	276	20	)	)	PUNCT
iajs-2833	276	21	+	+	CCONJ
iajs-2833	277	1	𝐶𝑙𝑖1𝑦𝑖	𝐶𝑙𝑖1𝑦𝑖	NOUN
iajs-2833	277	2	2	2	NUM
iajs-2833	277	3	+	+	CCONJ
iajs-2833	277	4	𝐶𝑙𝑖2𝑢𝑖	𝐶𝑙𝑖2𝑢𝑖	PROPN
iajs-2833	277	5	2	2	NUM
iajs-2833	277	6	,	,	PUNCT
iajs-2833	277	7	where	where	SCONJ
iajs-2833	277	8	𝐺𝑙𝑖	𝐺𝑙𝑖	PROPN
iajs-2833	277	9	∈	∈	PROPN
iajs-2833	277	10	𝐿1(q	𝐿1(q	ADV
iajs-2833	277	11	)	)	PUNCT
iajs-2833	277	12	,	,	PUNCT
iajs-2833	277	13	for	for	ADP
iajs-2833	277	14	(	(	PUNCT
iajs-2833	277	15	𝑥	𝑥	PROPN
iajs-2833	277	16	,	,	PUNCT
iajs-2833	277	17	𝑡	𝑡	NOUN
iajs-2833	277	18	)	)	PUNCT
iajs-2833	277	19	∈	∈	PROPN
iajs-2833	277	20	𝑄,𝑙	𝑄,𝑙	PUNCT
iajs-2833	278	1	=	=	SYM
iajs-2833	278	2	0	0	PROPN
iajs-2833	278	3	4.1	4.1	NUM
iajs-2833	278	4	lemma	lemma	PROPN
iajs-2833	278	5	:	:	PUNCT
iajs-2833	278	6	with	with	ADP
iajs-2833	278	7	assum	assum	VERB
iajs-2833	278	8	.	.	PUNCT
iajs-2833	279	1	(	(	PUNCT
iajs-2833	279	2	b	b	X
iajs-2833	279	3	)	)	PUNCT
iajs-2833	279	4	,	,	PUNCT
iajs-2833	279	5	the	the	DET
iajs-2833	279	6	functional	functional	ADJ
iajs-2833	279	7	�	�	PROPN
iajs-2833	279	8	⃗⃗	⃗⃗	PROPN
iajs-2833	279	9	�	�	PROPN
iajs-2833	279	10	→	→	SYM
iajs-2833	279	11	𝐺0(	𝐺0(	NOUN
iajs-2833	279	12	�	�	NOUN
iajs-2833	279	13	⃗⃗	⃗⃗	PROPN
iajs-2833	279	14	�	�	PROPN
iajs-2833	279	15	)	)	PUNCT
iajs-2833	279	16	is	be	AUX
iajs-2833	279	17	continuous	continuous	ADJ
iajs-2833	279	18	on	on	ADP
iajs-2833	279	19	(	(	PUNCT
iajs-2833	279	20	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	279	21	.	.	PUNCT
iajs-2833	280	1	proof	proof	NOUN
iajs-2833	280	2	:	:	PUNCT
iajs-2833	280	3	using	use	VERB
iajs-2833	280	4	assumptions	assumption	NOUN
iajs-2833	280	5	(	(	PUNCT
iajs-2833	280	6	b	b	NOUN
iajs-2833	280	7	)	)	PUNCT
iajs-2833	280	8	and	and	CCONJ
iajs-2833	280	9	proposition	proposition	NOUN
iajs-2833	280	10	1.3	1.3	NUM
iajs-2833	280	11	,	,	PUNCT
iajs-2833	280	12	the	the	DET
iajs-2833	280	13	integral∫	integral∫	NOUN
iajs-2833	280	14	𝑄	𝑄	PROPN
iajs-2833	280	15	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	280	16	(	(	PUNCT
iajs-2833	280	17	𝑥	𝑥	PROPN
iajs-2833	280	18	,	,	PUNCT
iajs-2833	280	19	𝑡	𝑡	PROPN
iajs-2833	280	20	,	,	PUNCT
iajs-2833	280	21	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	280	22	,	,	PUNCT
iajs-2833	280	23	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	280	24	is	be	AUX
iajs-2833	280	25	continuous	continuous	ADJ
iajs-2833	280	26	on	on	ADP
iajs-2833	280	27	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	280	28	)	)	PUNCT
iajs-2833	280	29	,	,	PUNCT
iajs-2833	280	30	∀𝑖	∀𝑖	PROPN
iajs-2833	280	31	=	=	NOUN
iajs-2833	280	32	1,2,3,4	1,2,3,4	NUM
iajs-2833	280	33	,	,	PUNCT
iajs-2833	280	34	hence	hence	ADV
iajs-2833	280	35	𝐺0(	𝐺0(	SYM
iajs-2833	280	36	�	�	PROPN
iajs-2833	280	37	⃗⃗	⃗⃗	PROPN
iajs-2833	280	38	�	�	PROPN
iajs-2833	280	39	)	)	PUNCT
iajs-2833	280	40	is	be	AUX
iajs-2833	280	41	continuous	continuous	ADJ
iajs-2833	280	42	on	on	ADP
iajs-2833	280	43	(	(	PUNCT
iajs-2833	280	44	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	280	45	.	.	PROPN
iajs-2833	280	46	4.2	4.2	NUM
iajs-2833	280	47	lemma	lemma	PROPN
iajs-2833	280	48	:	:	PUNCT
iajs-2833	280	49	let	let	VERB
iajs-2833	280	50	𝑔	𝑔	VERB
iajs-2833	280	51	:	:	PUNCT
iajs-2833	280	52	𝑄	𝑄	PROPN
iajs-2833	280	53	×	×	NOUN
iajs-2833	280	54	ℝ	ℝ	PROPN
iajs-2833	280	55	→	→	PUNCT
iajs-2833	280	56	ℝ	ℝ	PROPN
iajs-2833	280	57	is	be	AUX
iajs-2833	280	58	of	of	ADP
iajs-2833	280	59	carathéodory	carathéodory	ADJ
iajs-2833	280	60	type	type	NOUN
iajs-2833	280	61	on	on	ADP
iajs-2833	280	62	𝑄	𝑄	PROPN
iajs-2833	280	63	×	×	NOUN
iajs-2833	280	64	(	(	PUNCT
iajs-2833	280	65	ℝ	ℝ	PROPN
iajs-2833	280	66	×	×	NOUN
iajs-2833	280	67	ℝ	ℝ	PROPN
iajs-2833	280	68	)	)	PUNCT
iajs-2833	280	69	and	and	CCONJ
iajs-2833	280	70	satisfies	satisfie	NOUN
iajs-2833	280	71	|𝑔	|𝑔	NOUN
iajs-2833	280	72	(	(	PUNCT
iajs-2833	280	73	𝑥	𝑥	PROPN
iajs-2833	280	74	,	,	PUNCT
iajs-2833	280	75	𝑡	𝑡	PROPN
iajs-2833	280	76	,	,	PUNCT
iajs-2833	280	77	𝑦	𝑦	NUM
iajs-2833	280	78	,	,	PUNCT
iajs-2833	280	79	𝑢)|	𝑢)|	VERB
iajs-2833	280	80	≤	≤	PROPN
iajs-2833	280	81	𝐺	𝐺	PROPN
iajs-2833	280	82	(	(	PUNCT
iajs-2833	280	83	𝑥	𝑥	PROPN
iajs-2833	280	84	,	,	PUNCT
iajs-2833	280	85	𝑡	𝑡	NOUN
iajs-2833	280	86	)	)	PUNCT
iajs-2833	280	87	+	+	CCONJ
iajs-2833	280	88	𝑐	𝑐	PROPN
iajs-2833	280	89	𝑦	𝑦	SYM
iajs-2833	280	90	2	2	NUM
iajs-2833	280	91	+	+	NUM
iajs-2833	280	92	�	�	PROPN
iajs-2833	280	93	́	́	NOUN
iajs-2833	280	94	�	�	NOUN
iajs-2833	280	95	𝑢	𝑢	PRON
iajs-2833	280	96	2	2	NUM
iajs-2833	280	97	,	,	PUNCT
iajs-2833	280	98	where	where	SCONJ
iajs-2833	280	99	𝐺(𝑥	𝐺(𝑥	NOUN
iajs-2833	280	100	,	,	PUNCT
iajs-2833	280	101	𝑡	𝑡	NOUN
iajs-2833	280	102	)	)	PUNCT
iajs-2833	280	103	∈	∈	PROPN
iajs-2833	280	104	𝐿1(q),𝑢	𝐿1(q),𝑢	NUM
iajs-2833	280	105	∈	∈	PROPN
iajs-2833	280	106	𝑈	𝑈	PROPN
iajs-2833	280	107	,	,	PUNCT
iajs-2833	280	108	𝑐	𝑐	PROPN
iajs-2833	280	109	,	,	PUNCT
iajs-2833	280	110	𝑐́	𝑐́	VERB
iajs-2833	280	111	≥	≥	NOUN
iajs-2833	280	112	0	0	NUM
iajs-2833	280	113	,	,	PUNCT
iajs-2833	280	114	𝑈	𝑈	PROPN
iajs-2833	280	115	⊂	⊂	PUNCT
iajs-2833	280	116	ℝ	ℝ	PROPN
iajs-2833	280	117	,	,	PUNCT
iajs-2833	280	118	is	be	AUX
iajs-2833	280	119	compact	compact	ADJ
iajs-2833	280	120	..	..	PUNCT
iajs-2833	281	1	then	then	ADV
iajs-2833	281	2	,	,	PUNCT
iajs-2833	281	3	∫	∫	INTJ
iajs-2833	281	4	𝑄	𝑄	PROPN
iajs-2833	281	5	𝑔	𝑔	PROPN
iajs-2833	281	6	(	(	PUNCT
iajs-2833	281	7	𝑥	𝑥	PROPN
iajs-2833	281	8	,	,	PUNCT
iajs-2833	281	9	𝑦	𝑦	NOUN
iajs-2833	281	10	,	,	PUNCT
iajs-2833	281	11	𝑢	𝑢	NOUN
iajs-2833	281	12	)	)	PUNCT
iajs-2833	281	13	𝑑𝑥	𝑑𝑥	VERB
iajs-2833	281	14	is	be	AUX
iajs-2833	281	15	continuous	continuous	ADJ
iajs-2833	281	16	on	on	ADP
iajs-2833	281	17	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	281	18	)	)	PUNCT
iajs-2833	281	19	w.r.t	w.r.t	NOUN
iajs-2833	281	20	.	.	PUNCT
iajs-2833	282	1	𝑦.	𝑦.	PROPN
iajs-2833	282	2	4.1	4.1	NUM
iajs-2833	282	3	theorem	theorem	VERB
iajs-2833	282	4	:	:	PUNCT
iajs-2833	282	5	in	in	ADP
iajs-2833	282	6	addition	addition	NOUN
iajs-2833	282	7	to	to	ADP
iajs-2833	282	8	assumptions	assumption	NOUN
iajs-2833	282	9	(	(	PUNCT
iajs-2833	282	10	a&b	a&b	PROPN
iajs-2833	282	11	)	)	PUNCT
iajs-2833	282	12	,	,	PUNCT
iajs-2833	282	13	if	if	SCONJ
iajs-2833	282	14	the	the	DET
iajs-2833	282	15	set	set	NOUN
iajs-2833	282	16	�	�	PROPN
iajs-2833	282	17	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2833	282	18	�	�	PROPN
iajs-2833	282	19	is	be	AUX
iajs-2833	282	20	convex	convex	ADJ
iajs-2833	282	21	and	and	CCONJ
iajs-2833	282	22	compact	compact	ADJ
iajs-2833	282	23	.	.	PUNCT
iajs-2833	282	24	,	,	PUNCT
iajs-2833	282	25	�	�	PROPN
iajs-2833	282	26	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	282	27	�	�	PROPN
iajs-2833	282	28	𝐴	𝐴	PROPN
iajs-2833	282	29	≠	≠	PROPN
iajs-2833	282	30	𝜙	𝜙	NOUN
iajs-2833	282	31	,	,	PUNCT
iajs-2833	282	32	the	the	DET
iajs-2833	282	33	function	function	NOUN
iajs-2833	282	34	𝑓𝑖	𝑓𝑖	PROPN
iajs-2833	282	35	,	,	PUNCT
iajs-2833	282	36	for	for	ADP
iajs-2833	282	37	(	(	PUNCT
iajs-2833	282	38	𝑖	𝑖	NOUN
iajs-2833	282	39	=	=	NOUN
iajs-2833	282	40	1,2,3,4	1,2,3,4	NUM
iajs-2833	282	41	)	)	PUNCT
iajs-2833	282	42	have	have	VERB
iajs-2833	282	43	the	the	DET
iajs-2833	282	44	form	form	NOUN
iajs-2833	282	45	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2833	282	46	,	,	PUNCT
iajs-2833	282	47	𝑡	𝑡	PROPN
iajs-2833	282	48	,	,	PUNCT
iajs-2833	282	49	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	282	50	,	,	PUNCT
iajs-2833	282	51	𝑢𝑖	𝑢𝑖	INTJ
iajs-2833	282	52	)	)	PUNCT
iajs-2833	282	53	=	=	SYM
iajs-2833	282	54	𝑓𝑖1(𝑥	𝑓𝑖1(𝑥	PROPN
iajs-2833	282	55	,	,	PUNCT
iajs-2833	282	56	𝑡	𝑡	PROPN
iajs-2833	282	57	,	,	PUNCT
iajs-2833	282	58	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	282	59	)	)	PUNCT
iajs-2833	282	60	+	+	X
iajs-2833	283	1	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2833	283	2	,	,	PUNCT
iajs-2833	283	3	𝑡)𝑢𝑖,where	𝑡)𝑢𝑖,where	X
iajs-2833	283	4	|𝑓𝑖1(𝑥	|𝑓𝑖1(𝑥	PROPN
iajs-2833	283	5	,	,	PUNCT
iajs-2833	283	6	𝑡	𝑡	PROPN
iajs-2833	283	7	,	,	PUNCT
iajs-2833	283	8	𝑦𝑖)|	𝑦𝑖)|	PROPN
iajs-2833	283	9	≤	≤	X
iajs-2833	283	10	휂𝑖(𝑥	휂𝑖(𝑥	NUM
iajs-2833	283	11	,	,	PUNCT
iajs-2833	283	12	𝑡	𝑡	X
iajs-2833	283	13	)	)	PUNCT
iajs-2833	283	14	+	+	CCONJ
iajs-2833	283	15	𝑐𝑖	𝑐𝑖	PROPN
iajs-2833	283	16	∣	∣	ADJ
iajs-2833	283	17	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	283	18	∣	∣	PROPN
iajs-2833	283	19	,	,	PUNCT
iajs-2833	283	20	|𝑓𝑖2(𝑥	|𝑓𝑖2(𝑥	PROPN
iajs-2833	283	21	,	,	PUNCT
iajs-2833	283	22	𝑡)|	𝑡)|	PROPN
iajs-2833	283	23	≤	≤	PUNCT
iajs-2833	284	1	𝐾𝑖	𝐾𝑖	PROPN
iajs-2833	284	2	,	,	PUNCT
iajs-2833	284	3	휂𝑖	휂𝑖	PROPN
iajs-2833	284	4	∈	∈	PROPN
iajs-2833	284	5	𝐿2(q	𝐿2(q	NUM
iajs-2833	284	6	)	)	PUNCT
iajs-2833	284	7	,	,	PUNCT
iajs-2833	284	8	𝑐𝑖	𝑐𝑖	NOUN
iajs-2833	284	9	≥	≥	NOUN
iajs-2833	284	10	0	0	NUM
iajs-2833	284	11	,	,	PUNCT
iajs-2833	284	12	for	for	ADP
iajs-2833	284	13	𝑖	𝑖	NOUN
iajs-2833	284	14	=	=	NOUN
iajs-2833	284	15	1,2,3,4	1,2,3,4	NUM
iajs-2833	284	16	.	.	PUNCT
iajs-2833	285	1	then	then	ADV
iajs-2833	285	2	there	there	PRON
iajs-2833	285	3	exists	exist	VERB
iajs-2833	285	4	an	an	DET
iajs-2833	285	5	occqv	occqv	NOUN
iajs-2833	285	6	.	.	PUNCT
iajs-2833	286	1	proof	proof	NOUN
iajs-2833	286	2	:	:	PUNCT
iajs-2833	286	3	from	from	ADP
iajs-2833	286	4	the	the	DET
iajs-2833	286	5	assumptions	assumption	NOUN
iajs-2833	286	6	on	on	ADP
iajs-2833	286	7	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	286	8	⊂	⊂	PROPN
iajs-2833	286	9	ℝ	ℝ	PROPN
iajs-2833	286	10	for	for	ADP
iajs-2833	286	11	𝑖	𝑖	NOUN
iajs-2833	286	12	=	=	SYM
iajs-2833	286	13	1,2,3,4	1,2,3,4	NUM
iajs-2833	286	14	and	and	CCONJ
iajs-2833	286	15	the	the	DET
iajs-2833	286	16	egorov	egorov	PROPN
iajs-2833	286	17	’s	’s	PART
iajs-2833	286	18	theorem	theorem	ADJ
iajs-2833	286	19	,	,	PUNCT
iajs-2833	286	20	once	once	ADV
iajs-2833	286	21	get	get	VERB
iajs-2833	286	22	that	that	PRON
iajs-2833	286	23	�	�	PROPN
iajs-2833	286	24	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	286	25	�	�	PROPN
iajs-2833	286	26	is	be	AUX
iajs-2833	286	27	weakly	weakly	ADV
iajs-2833	286	28	compact	compact	ADJ
iajs-2833	286	29	,	,	PUNCT
iajs-2833	286	30	since	since	SCONJ
iajs-2833	286	31	�	�	PROPN
iajs-2833	286	32	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	286	33	�	�	PROPN
iajs-2833	286	34	𝐴	𝐴	PROPN
iajs-2833	286	35	≠	≠	PROPN
iajs-2833	286	36	𝜙	𝜙	NOUN
iajs-2833	286	37	,	,	PUNCT
iajs-2833	286	38	there	there	PRON
iajs-2833	286	39	exists	exist	VERB
iajs-2833	286	40	a	a	DET
iajs-2833	286	41	minimum	minimum	ADJ
iajs-2833	286	42	sequence	sequence	NOUN
iajs-2833	286	43	{	{	PUNCT
iajs-2833	286	44	�	�	PROPN
iajs-2833	286	45	⃗⃗	⃗⃗	PROPN
iajs-2833	286	46	�	�	PROPN
iajs-2833	286	47	𝑘	𝑘	NOUN
iajs-2833	286	48	}	}	PUNCT
iajs-2833	286	49	=	=	SYM
iajs-2833	286	50	{	{	PUNCT
iajs-2833	286	51	(	(	PUNCT
iajs-2833	286	52	𝑢1𝑘	𝑢1𝑘	PROPN
iajs-2833	286	53	,	,	PUNCT
iajs-2833	286	54	𝑢2𝑘	𝑢2𝑘	PROPN
iajs-2833	286	55	,	,	PUNCT
iajs-2833	286	56	𝑢3𝑘	𝑢3𝑘	X
iajs-2833	286	57	,	,	PUNCT
iajs-2833	286	58	𝑢4𝑘	𝑢4𝑘	NOUN
iajs-2833	286	59	)	)	PUNCT
iajs-2833	286	60	}	}	PUNCT
iajs-2833	286	61	∈	∈	PROPN
iajs-2833	286	62	�	�	PROPN
iajs-2833	286	63	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	286	64	�	�	PROPN
iajs-2833	286	65	𝐴	𝐴	PROPN
iajs-2833	286	66	,	,	PUNCT
iajs-2833	286	67	∀𝑘	∀𝑘	X
iajs-2833	286	68	s.t	s.t	PROPN
iajs-2833	286	69	.	.	PROPN
iajs-2833	286	70	𝑙𝑖𝑚	𝑙𝑖𝑚	PROPN
iajs-2833	286	71	𝑘→∞	𝑘→∞	NUM
iajs-2833	286	72	𝐺0(	𝐺0(	SYM
iajs-2833	286	73	�	�	NOUN
iajs-2833	286	74	⃗⃗	⃗⃗	PROPN
iajs-2833	286	75	�	�	PROPN
iajs-2833	286	76	𝑘	𝑘	NOUN
iajs-2833	286	77	)	)	PUNCT
iajs-2833	287	1	=	=	PUNCT
iajs-2833	287	2	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	287	3	�	�	PROPN
iajs-2833	287	4	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	287	5	�	�	NOUN
iajs-2833	287	6	𝑘∈	𝑘∈	PROPN
iajs-2833	287	7	�	�	PROPN
iajs-2833	287	8	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	287	9	�	�	PROPN
iajs-2833	287	10	𝐴	𝐴	PROPN
iajs-2833	287	11	𝐺0(	𝐺0(	NUM
iajs-2833	287	12	�	�	PROPN
iajs-2833	287	13	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	287	14	�	�	PROPN
iajs-2833	287	15	)	)	PUNCT
iajs-2833	287	16	.	.	PUNCT
iajs-2833	288	1	since	since	SCONJ
iajs-2833	288	2	{	{	PUNCT
iajs-2833	288	3	�	�	PROPN
iajs-2833	288	4	⃗⃗	⃗⃗	PROPN
iajs-2833	288	5	�	�	PROPN
iajs-2833	288	6	𝑘	𝑘	PRON
iajs-2833	288	7	}	}	PUNCT
iajs-2833	288	8	∈	∈	PROPN
iajs-2833	288	9	�	�	PROPN
iajs-2833	288	10	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	288	11	�	�	PROPN
iajs-2833	288	12	𝐴	𝐴	PROPN
iajs-2833	288	13	,	,	PUNCT
iajs-2833	288	14	∀𝑘	∀𝑘	NOUN
iajs-2833	288	15	and	and	CCONJ
iajs-2833	288	16	�	�	PROPN
iajs-2833	288	17	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2833	288	18	�	�	PROPN
iajs-2833	288	19	is	be	AUX
iajs-2833	288	20	weakly	weakly	ADV
iajs-2833	288	21	compact	compact	ADJ
iajs-2833	288	22	,	,	PUNCT
iajs-2833	288	23	there	there	PRON
iajs-2833	288	24	exists	exist	VERB
iajs-2833	288	25	a	a	DET
iajs-2833	288	26	subsequence	subsequence	NOUN
iajs-2833	288	27	of	of	ADP
iajs-2833	288	28	{	{	PUNCT
iajs-2833	288	29	�	�	PROPN
iajs-2833	288	30	⃗⃗	⃗⃗	PROPN
iajs-2833	288	31	�	�	PROPN
iajs-2833	288	32	𝑘	𝑘	PRON
iajs-2833	288	33	}	}	PUNCT
iajs-2833	288	34	say	say	VERB
iajs-2833	288	35	again	again	ADV
iajs-2833	288	36	{	{	PUNCT
iajs-2833	288	37	�	�	PROPN
iajs-2833	288	38	⃗⃗	⃗⃗	PROPN
iajs-2833	288	39	�	�	PROPN
iajs-2833	288	40	𝑘	𝑘	PROPN
iajs-2833	288	41	}	}	PUNCT
iajs-2833	288	42	s.t	s.t	PROPN
iajs-2833	288	43	.	.	PROPN
iajs-2833	288	44	.	.	PUNCT
iajs-2833	289	1	�	�	PROPN
iajs-2833	289	2	⃗⃗	⃗⃗	PROPN
iajs-2833	289	3	�	�	PROPN
iajs-2833	289	4	𝑘	𝑘	PROPN
iajs-2833	289	5	→	→	SYM
iajs-2833	289	6	�	�	PROPN
iajs-2833	289	7	⃗⃗	⃗⃗	PROPN
iajs-2833	289	8	�	�	PROPN
iajs-2833	289	9	wk	wk	X
iajs-2833	289	10	in	in	ADP
iajs-2833	289	11	(	(	PUNCT
iajs-2833	289	12	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	289	13	and	and	CCONJ
iajs-2833	289	14	∥	∥	PROPN
iajs-2833	289	15	�	�	PROPN
iajs-2833	289	16	⃗⃗	⃗⃗	PROPN
iajs-2833	289	17	�	�	PROPN
iajs-2833	289	18	𝑘	𝑘	PROPN
iajs-2833	289	19	∥𝑄≤	∥𝑄≤	PROPN
iajs-2833	289	20	𝑑,∀𝑘.	𝑑,∀𝑘.	PUNCT
iajs-2833	289	21	from	from	ADP
iajs-2833	289	22	theorem	theorem	ADJ
iajs-2833	289	23	3.1	3.1	NUM
iajs-2833	289	24	,	,	PUNCT
iajs-2833	289	25	for	for	ADP
iajs-2833	289	26	each	each	DET
iajs-2833	289	27	control	control	NOUN
iajs-2833	289	28	{	{	PUNCT
iajs-2833	289	29	�	�	PROPN
iajs-2833	289	30	⃗⃗	⃗⃗	PROPN
iajs-2833	289	31	�	�	PROPN
iajs-2833	289	32	𝑘	𝑘	NOUN
iajs-2833	289	33	}	}	PUNCT
iajs-2833	289	34	the	the	DET
iajs-2833	289	35	wf	wf	PROPN
iajs-2833	289	36	(	(	PUNCT
iajs-2833	289	37	18	18	NUM
iajs-2833	289	38	)	)	PUNCT
iajs-2833	289	39	,	,	PUNCT
iajs-2833	289	40	(	(	PUNCT
iajs-2833	289	41	20	20	NUM
iajs-2833	289	42	)	)	PUNCT
iajs-2833	289	43	,	,	PUNCT
iajs-2833	289	44	(	(	PUNCT
iajs-2833	289	45	22	22	NUM
iajs-2833	289	46	)	)	PUNCT
iajs-2833	289	47	,	,	PUNCT
iajs-2833	289	48	(	(	PUNCT
iajs-2833	289	49	24	24	NUM
iajs-2833	289	50	)	)	PUNCT
iajs-2833	289	51	has	have	VERB
iajs-2833	289	52	a	a	DET
iajs-2833	289	53	unique	unique	ADJ
iajs-2833	289	54	sqvs	sqvs	NOUN
iajs-2833	289	55	,	,	PUNCT
iajs-2833	289	56	{	{	PUNCT
iajs-2833	289	57	�	�	PROPN
iajs-2833	289	58	⃗	⃗	NOUN
iajs-2833	289	59	�	�	PROPN
iajs-2833	289	60	𝑘	𝑘	PRON
iajs-2833	289	61	=	=	SYM
iajs-2833	289	62	�	�	PROPN
iajs-2833	289	63	⃗	⃗	NOUN
iajs-2833	289	64	�	�	PROPN
iajs-2833	289	65	𝑢𝑘	𝑢𝑘	NOUN
iajs-2833	289	66	}	}	PUNCT
iajs-2833	289	67	s.t	s.t	PROPN
iajs-2833	289	68	.	.	PUNCT
iajs-2833	290	1	the	the	DET
iajs-2833	290	2	norm	norm	NOUN
iajs-2833	290	3	∥	∥	PUNCT
iajs-2833	290	4	�	�	NOUN
iajs-2833	290	5	⃗	⃗	NOUN
iajs-2833	290	6	�	�	PROPN
iajs-2833	290	7	𝑘	𝑘	PRON
iajs-2833	290	8	∥𝐿2(𝐼,𝑉	∥𝐿2(𝐼,𝑉	PROPN
iajs-2833	290	9	)	)	PUNCT
iajs-2833	290	10	,	,	PUNCT
iajs-2833	290	11	∥	∥	PROPN
iajs-2833	290	12	�	�	NOUN
iajs-2833	290	13	⃗	⃗	NOUN
iajs-2833	290	14	�	�	PROPN
iajs-2833	290	15	𝑘𝑡	𝑘𝑡	PROPN
iajs-2833	290	16	∥𝐿2(𝑄	∥𝐿2(𝑄	PROPN
iajs-2833	290	17	)	)	PUNCT
iajs-2833	290	18	are	be	AUX
iajs-2833	290	19	bounded	bound	VERB
iajs-2833	290	20	,	,	PUNCT
iajs-2833	290	21	then	then	ADV
iajs-2833	290	22	by	by	ADP
iajs-2833	290	23	ath	ath	NOUN
iajs-2833	290	24	there	there	PRON
iajs-2833	290	25	exists	exist	VERB
iajs-2833	290	26	a	a	DET
iajs-2833	290	27	subsequence	subsequence	NOUN
iajs-2833	290	28	of	of	ADP
iajs-2833	290	29	{	{	PUNCT
iajs-2833	290	30	�	�	PROPN
iajs-2833	290	31	⃗	⃗	NOUN
iajs-2833	290	32	�	�	NOUN
iajs-2833	290	33	𝑘	𝑘	PRON
iajs-2833	290	34	}	}	PUNCT
iajs-2833	290	35	and	and	CCONJ
iajs-2833	290	36	{	{	PUNCT
iajs-2833	290	37	�	�	PROPN
iajs-2833	290	38	⃗	⃗	NOUN
iajs-2833	290	39	�	�	NOUN
iajs-2833	290	40	𝑘𝑡	𝑘𝑡	NOUN
iajs-2833	290	41	}	}	PUNCT
iajs-2833	290	42	,	,	PUNCT
iajs-2833	290	43	say	say	VERB
iajs-2833	290	44	again	again	ADV
iajs-2833	290	45	{	{	PUNCT
iajs-2833	290	46	�	�	PROPN
iajs-2833	290	47	⃗	⃗	NOUN
iajs-2833	290	48	�	�	NOUN
iajs-2833	290	49	𝑘	𝑘	PRON
iajs-2833	290	50	}	}	PUNCT
iajs-2833	290	51	and	and	CCONJ
iajs-2833	290	52	{	{	PUNCT
iajs-2833	290	53	�	�	PROPN
iajs-2833	290	54	⃗	⃗	NOUN
iajs-2833	290	55	�	�	NOUN
iajs-2833	290	56	𝑘𝑡	𝑘𝑡	NOUN
iajs-2833	290	57	}	}	PUNCT
iajs-2833	290	58	,	,	PUNCT
iajs-2833	290	59	s.t	s.t	PROPN
iajs-2833	290	60	.	.	PROPN
iajs-2833	290	61	�	�	PROPN
iajs-2833	290	62	⃗	⃗	NOUN
iajs-2833	290	63	�	�	PROPN
iajs-2833	290	64	𝑘	𝑘	PRON
iajs-2833	290	65	→	→	SYM
iajs-2833	290	66	�	�	NOUN
iajs-2833	290	67	⃗	⃗	NOUN
iajs-2833	290	68	�	�	PROPN
iajs-2833	290	69	wk	wk	X
iajs-2833	290	70	in	in	ADP
iajs-2833	290	71	(	(	PUNCT
iajs-2833	290	72	𝐿2(𝐼	𝐿2(𝐼	PROPN
iajs-2833	290	73	,	,	PUNCT
iajs-2833	290	74	𝑉))4	𝑉))4	PROPN
iajs-2833	290	75	,	,	PUNCT
iajs-2833	290	76	�	�	PROPN
iajs-2833	290	77	⃗	⃗	NOUN
iajs-2833	290	78	�	�	NOUN
iajs-2833	290	79	𝑘𝑡	𝑘𝑡	PROPN
iajs-2833	290	80	→	→	SYM
iajs-2833	290	81	�	�	PROPN
iajs-2833	290	82	⃗	⃗	NOUN
iajs-2833	290	83	�	�	PROPN
iajs-2833	290	84	wk	wk	X
iajs-2833	290	85	in	in	ADP
iajs-2833	290	86	(	(	PUNCT
iajs-2833	290	87	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	290	88	.	.	PUNCT
iajs-2833	291	1	now	now	ADV
iajs-2833	291	2	for	for	ADP
iajs-2833	291	3	each	each	DET
iajs-2833	291	4	𝑘.	𝑘.	NOUN
iajs-2833	291	5	and	and	CCONJ
iajs-2833	291	6	by	by	ADP
iajs-2833	291	7	applying	apply	VERB
iajs-2833	291	8	the	the	DET
iajs-2833	291	9	acth	acth	NOUN
iajs-2833	291	10	[	[	X
iajs-2833	291	11	15	15	NUM
iajs-2833	291	12	]	]	PUNCT
iajs-2833	291	13	,	,	PUNCT
iajs-2833	291	14	we	we	PRON
iajs-2833	291	15	get	get	VERB
iajs-2833	291	16	that	that	SCONJ
iajs-2833	291	17	there	there	PRON
iajs-2833	291	18	exists	exist	VERB
iajs-2833	291	19	a	a	DET
iajs-2833	291	20	subsequence	subsequence	NOUN
iajs-2833	291	21	of{	of{	NUM
iajs-2833	291	22	�	�	NOUN
iajs-2833	291	23	⃗	⃗	NOUN
iajs-2833	291	24	�	�	PROPN
iajs-2833	291	25	𝑘	𝑘	PRON
iajs-2833	291	26	}	}	PUNCT
iajs-2833	291	27	say	say	VERB
iajs-2833	292	1	a	a	DET
iajs-2833	292	2	gain	gain	NOUN
iajs-2833	292	3	{	{	PUNCT
iajs-2833	292	4	�	�	PROPN
iajs-2833	292	5	⃗	⃗	NOUN
iajs-2833	292	6	�	�	PROPN
iajs-2833	292	7	𝑘	𝑘	PRON
iajs-2833	292	8	}	}	PUNCT
iajs-2833	292	9	s.t	s.t	PROPN
iajs-2833	292	10	.	.	PROPN
iajs-2833	292	11	�	�	PROPN
iajs-2833	292	12	⃗	⃗	NOUN
iajs-2833	292	13	�	�	PROPN
iajs-2833	292	14	𝑘	𝑘	PRON
iajs-2833	292	15	→	→	SYM
iajs-2833	292	16	�	�	NOUN
iajs-2833	292	17	⃗	⃗	PROPN
iajs-2833	292	18	�	�	PROPN
iajs-2833	292	19	st	st	PROPN
iajs-2833	292	20	in	in	ADP
iajs-2833	292	21	(	(	PUNCT
iajs-2833	292	22	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2833	292	23	.	.	PUNCT
iajs-2833	293	1	now	now	ADV
iajs-2833	293	2	since	since	SCONJ
iajs-2833	293	3	for	for	ADP
iajs-2833	293	4	each	each	PRON
iajs-2833	293	5	𝑘	𝑘	PROPN
iajs-2833	293	6	,	,	PUNCT
iajs-2833	293	7	�	�	PROPN
iajs-2833	293	8	⃗	⃗	NOUN
iajs-2833	293	9	�	�	NOUN
iajs-2833	293	10	𝑘	𝑘	PRON
iajs-2833	293	11	is	be	AUX
iajs-2833	293	12	a	a	DET
iajs-2833	293	13	sqvs	sqvs	NOUN
iajs-2833	293	14	of	of	ADP
iajs-2833	293	15	the	the	DET
iajs-2833	293	16	wf	wf	PROPN
iajs-2833	293	17	(	(	PUNCT
iajs-2833	293	18	(	(	PUNCT
iajs-2833	293	19	18	18	NUM
iajs-2833	293	20	)	)	PUNCT
iajs-2833	293	21	,	,	PUNCT
iajs-2833	293	22	(	(	PUNCT
iajs-2833	293	23	20	20	NUM
iajs-2833	293	24	)	)	PUNCT
iajs-2833	293	25	,	,	PUNCT
iajs-2833	293	26	(	(	PUNCT
iajs-2833	293	27	22	22	NUM
iajs-2833	293	28	)	)	PUNCT
iajs-2833	293	29	,	,	PUNCT
iajs-2833	293	30	(	(	PUNCT
iajs-2833	293	31	24	24	NUM
iajs-2833	293	32	)	)	PUNCT
iajs-2833	293	33	)	)	PUNCT
iajs-2833	293	34	resp	resp	NOUN
iajs-2833	293	35	.	.	PUNCT
iajs-2833	294	1	,	,	PUNCT
iajs-2833	294	2	substituting	substitute	VERB
iajs-2833	294	3	in	in	ADP
iajs-2833	294	4	these	these	DET
iajs-2833	294	5	equations	equation	NOUN
iajs-2833	294	6	,	,	PUNCT
iajs-2833	294	7	mbss	mbss	NOUN
iajs-2833	294	8	of	of	ADP
iajs-2833	294	9	each	each	DET
iajs-2833	294	10	equation	equation	NOUN
iajs-2833	294	11	by	by	ADP
iajs-2833	294	12	𝜙𝑖(𝑡	𝜙𝑖(𝑡	NUM
iajs-2833	294	13	)	)	PUNCT
iajs-2833	294	14	,	,	PUNCT
iajs-2833	294	15	∀𝑖	∀𝑖	PROPN
iajs-2833	294	16	=	=	SYM
iajs-2833	294	17	1,2,3,4	1,2,3,4	NUM
iajs-2833	294	18	(	(	PUNCT
iajs-2833	294	19	with	with	ADP
iajs-2833	294	20	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	294	21	∈	∈	PROPN
iajs-2833	294	22	𝐶2[0	𝐶2[0	PROPN
iajs-2833	294	23	,	,	PUNCT
iajs-2833	294	24	𝑇	𝑇	PROPN
iajs-2833	294	25	]	]	PUNCT
iajs-2833	294	26	,	,	PUNCT
iajs-2833	294	27	s.t	s.t	PROPN
iajs-2833	294	28	.	.	PROPN
iajs-2833	294	29	𝜙𝑖(𝑇	𝜙𝑖(𝑇	ADP
iajs-2833	294	30	)	)	PUNCT
iajs-2833	294	31	=	=	SYM
iajs-2833	294	32	𝜙𝑖	𝜙𝑖	NOUN
iajs-2833	294	33	′(𝑇	′(𝑇	NOUN
iajs-2833	294	34	)	)	PUNCT
iajs-2833	295	1	=	=	SYM
iajs-2833	295	2	0	0	NUM
iajs-2833	295	3	,	,	PUNCT
iajs-2833	295	4	𝜙𝑖(0	𝜙𝑖(0	NOUN
iajs-2833	295	5	)	)	PUNCT
iajs-2833	295	6	≠	≠	PROPN
iajs-2833	295	7	0	0	NUM
iajs-2833	295	8	,	,	PUNCT
iajs-2833	295	9	𝜙𝑖	𝜙𝑖	ADP
iajs-2833	295	10	′(0	′(0	NOUN
iajs-2833	295	11	)	)	PUNCT
iajs-2833	295	12	≠	≠	PROPN
iajs-2833	295	13	0	0	NUM
iajs-2833	295	14	)	)	PUNCT
iajs-2833	295	15	.	.	PUNCT
iajs-2833	296	1	rewriting	rewrite	VERB
iajs-2833	296	2	the	the	DET
iajs-2833	296	3	1st	1st	ADJ
iajs-2833	296	4	term	term	NOUN
iajs-2833	296	5	in	in	ADP
iajs-2833	296	6	the	the	DET
iajs-2833	296	7	lhs	lhs	NOUN
iajs-2833	296	8	of	of	ADP
iajs-2833	296	9	each	each	DET
iajs-2833	296	10	one	one	NOUN
iajs-2833	296	11	then	then	ADV
iajs-2833	296	12	ibs	ib	VERB
iajs-2833	296	13	on	on	ADP
iajs-2833	296	14	[	[	X
iajs-2833	296	15	0	0	NUM
iajs-2833	296	16	,	,	PUNCT
iajs-2833	296	17	𝑇	𝑇	PROPN
iajs-2833	296	18	]	]	PUNCT
iajs-2833	296	19	,	,	PUNCT
iajs-2833	296	20	finally	finally	ADV
iajs-2833	296	21	ibps	ibps	VERB
iajs-2833	296	22	for	for	ADP
iajs-2833	296	23	the	the	DET
iajs-2833	296	24	1st	1st	ADJ
iajs-2833	296	25	terms	term	NOUN
iajs-2833	296	26	,	,	PUNCT
iajs-2833	296	27	one	one	PRON
iajs-2833	296	28	has	have	VERB
iajs-2833	296	29	∫	∫	PROPN
iajs-2833	296	30	0	0	NUM
iajs-2833	296	31	𝑇	𝑇	PROPN
iajs-2833	296	32	𝑑	𝑑	PRON
iajs-2833	296	33	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	296	34	(	(	PUNCT
iajs-2833	296	35	𝑦1𝑘𝑡	𝑦1𝑘𝑡	PROPN
iajs-2833	296	36	,	,	PUNCT
iajs-2833	296	37	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	296	38	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	296	39	+	+	CCONJ
iajs-2833	296	40	∫	∫	PROPN
iajs-2833	297	1	0	0	X
iajs-2833	297	2	𝑇	𝑇	PROPN
iajs-2833	297	3	[	[	X
iajs-2833	297	4	(	(	PUNCT
iajs-2833	297	5	∇𝑦1𝑘	∇𝑦1𝑘	NOUN
iajs-2833	297	6	,	,	PUNCT
iajs-2833	297	7	∇𝑣1	∇𝑣1	NOUN
iajs-2833	297	8	)	)	PUNCT
iajs-2833	297	9	+	+	CCONJ
iajs-2833	297	10	(	(	PUNCT
iajs-2833	297	11	𝑦1𝑘	𝑦1𝑘	PROPN
iajs-2833	297	12	,	,	PUNCT
iajs-2833	297	13	𝑣1	𝑣1	PROPN
iajs-2833	297	14	)	)	PUNCT
iajs-2833	297	15	−	−	PROPN
iajs-2833	298	1	(	(	PUNCT
iajs-2833	299	1	𝑦2𝑘	𝑦2𝑘	PROPN
iajs-2833	299	2	,	,	PUNCT
iajs-2833	299	3	𝑣1	𝑣1	NOUN
iajs-2833	299	4	)	)	PUNCT
iajs-2833	299	5	+	+	CCONJ
iajs-2833	299	6	(	(	PUNCT
iajs-2833	299	7	𝑦3𝑘	𝑦3𝑘	NOUN
iajs-2833	299	8	,	,	PUNCT
iajs-2833	299	9	𝑣1	𝑣1	NOUN
iajs-2833	299	10	)	)	PUNCT
iajs-2833	299	11	+	+	CCONJ
iajs-2833	299	12	(	(	PUNCT
iajs-2833	299	13	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	299	14	,	,	PUNCT
iajs-2833	299	15	𝑣1)]𝜙1	𝑣1)]𝜙1	VERB
iajs-2833	299	16	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	299	17	=	=	NOUN
iajs-2833	299	18	∫	∫	PROPN
iajs-2833	299	19	0	0	NUM
iajs-2833	299	20	𝑇	𝑇	PROPN
iajs-2833	299	21	(	(	PUNCT
iajs-2833	299	22	𝑓11(𝑥	𝑓11(𝑥	NOUN
iajs-2833	299	23	,	,	PUNCT
iajs-2833	299	24	𝑡	𝑡	PROPN
iajs-2833	299	25	,	,	PUNCT
iajs-2833	299	26	𝑦1𝑘	𝑦1𝑘	PROPN
iajs-2833	299	27	)	)	PUNCT
iajs-2833	299	28	,	,	PUNCT
iajs-2833	299	29	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	299	30	(	(	PUNCT
iajs-2833	299	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	299	32	+	+	NUM
iajs-2833	299	33	∫	∫	PROPN
iajs-2833	299	34	0	0	X
iajs-2833	299	35	𝑇	𝑇	PROPN
iajs-2833	299	36	(	(	PUNCT
iajs-2833	299	37	𝑓12(𝑥	𝑓12(𝑥	NOUN
iajs-2833	299	38	,	,	PUNCT
iajs-2833	299	39	𝑡)𝑢1𝑘	𝑡)𝑢1𝑘	NOUN
iajs-2833	299	40	,	,	PUNCT
iajs-2833	299	41	𝑣1)𝜙1	𝑣1)𝜙1	NOUN
iajs-2833	299	42	(	(	PUNCT
iajs-2833	299	43	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	299	44	(	(	PUNCT
iajs-2833	299	45	77	77	NUM
iajs-2833	299	46	)	)	PUNCT
iajs-2833	299	47	∫	∫	NOUN
iajs-2833	299	48	0	0	NUM
iajs-2833	299	49	𝑇	𝑇	PROPN
iajs-2833	299	50	𝑑	𝑑	PRON
iajs-2833	299	51	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	299	52	(	(	PUNCT
iajs-2833	299	53	𝑦2𝑘𝑡	𝑦2𝑘𝑡	NOUN
iajs-2833	299	54	,	,	PUNCT
iajs-2833	299	55	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	299	56	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	299	57	+	+	CCONJ
iajs-2833	299	58	∫	∫	PROPN
iajs-2833	299	59	0	0	X
iajs-2833	300	1	𝑇	𝑇	PROPN
iajs-2833	301	1	[	[	X
iajs-2833	301	2	(	(	PUNCT
iajs-2833	301	3	∇𝑦2𝑘	∇𝑦2𝑘	PROPN
iajs-2833	301	4	,	,	PUNCT
iajs-2833	301	5	∇𝑣2	∇𝑣2	PRON
iajs-2833	301	6	)	)	PUNCT
iajs-2833	302	1	+	+	CCONJ
iajs-2833	302	2	(	(	PUNCT
iajs-2833	302	3	𝑦1𝑘	𝑦1𝑘	PROPN
iajs-2833	302	4	,	,	PUNCT
iajs-2833	302	5	𝑣2	𝑣2	PROPN
iajs-2833	302	6	)	)	PUNCT
iajs-2833	302	7	+	+	CCONJ
iajs-2833	302	8	(	(	PUNCT
iajs-2833	302	9	𝑦2𝑘	𝑦2𝑘	PROPN
iajs-2833	302	10	,	,	PUNCT
iajs-2833	302	11	𝑣2	𝑣2	NOUN
iajs-2833	302	12	)	)	PUNCT
iajs-2833	302	13	−	−	PROPN
iajs-2833	302	14	(	(	PUNCT
iajs-2833	302	15	𝑦3𝑘	𝑦3𝑘	PROPN
iajs-2833	302	16	,	,	PUNCT
iajs-2833	302	17	𝑣2	𝑣2	NOUN
iajs-2833	302	18	)	)	PUNCT
iajs-2833	302	19	−	−	PROPN
iajs-2833	302	20	(	(	PUNCT
iajs-2833	302	21	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	302	22	,	,	PUNCT
iajs-2833	302	23	𝑣2)]𝜙2	𝑣2)]𝜙2	PROPN
iajs-2833	302	24	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	302	25	ihjpas	ihjpas	PROPN
iajs-2833	302	26	.	.	PUNCT
iajs-2833	303	1	53	53	NUM
iajs-2833	303	2	(	(	PUNCT
iajs-2833	303	3	3)2022	3)2022	NOUN
iajs-2833	303	4	172	172	NUM
iajs-2833	303	5	=	=	SYM
iajs-2833	303	6	∫	∫	PROPN
iajs-2833	303	7	0	0	X
iajs-2833	303	8	𝑇	𝑇	PROPN
iajs-2833	303	9	(	(	PUNCT
iajs-2833	303	10	𝑓21(𝑥	𝑓21(𝑥	NOUN
iajs-2833	303	11	,	,	PUNCT
iajs-2833	303	12	𝑡	𝑡	NOUN
iajs-2833	303	13	,	,	PUNCT
iajs-2833	303	14	𝑦2𝑘	𝑦2𝑘	PROPN
iajs-2833	303	15	)	)	PUNCT
iajs-2833	303	16	,	,	PUNCT
iajs-2833	303	17	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	303	18	(	(	PUNCT
iajs-2833	303	19	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	303	20	+	+	NUM
iajs-2833	303	21	∫	∫	PROPN
iajs-2833	303	22	0	0	X
iajs-2833	303	23	𝑇	𝑇	PROPN
iajs-2833	303	24	(	(	PUNCT
iajs-2833	303	25	𝑓22(𝑥	𝑓22(𝑥	X
iajs-2833	303	26	,	,	PUNCT
iajs-2833	303	27	𝑡)𝑢2𝑘	𝑡)𝑢2𝑘	ADJ
iajs-2833	303	28	,	,	PUNCT
iajs-2833	303	29	𝑣2)𝜙2	𝑣2)𝜙2	ADP
iajs-2833	303	30	(	(	PUNCT
iajs-2833	303	31	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	303	32	(	(	PUNCT
iajs-2833	303	33	78	78	NUM
iajs-2833	303	34	)	)	PUNCT
iajs-2833	303	35	∫	∫	NOUN
iajs-2833	303	36	0	0	NUM
iajs-2833	303	37	𝑇	𝑇	PROPN
iajs-2833	303	38	𝑑	𝑑	PRON
iajs-2833	303	39	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	303	40	(	(	PUNCT
iajs-2833	303	41	𝑦3𝑘	𝑦3𝑘	PROPN
iajs-2833	303	42	,	,	PUNCT
iajs-2833	303	43	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	303	44	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	303	45	+	+	PROPN
iajs-2833	303	46	∫	∫	PROPN
iajs-2833	303	47	0	0	X
iajs-2833	303	48	𝑇	𝑇	PROPN
iajs-2833	304	1	[	[	X
iajs-2833	304	2	(	(	PUNCT
iajs-2833	304	3	∇𝑦3𝑘	∇𝑦3𝑘	PROPN
iajs-2833	304	4	,	,	PUNCT
iajs-2833	304	5	∇𝑣3	∇𝑣3	NOUN
iajs-2833	304	6	)	)	PUNCT
iajs-2833	304	7	−	−	PROPN
iajs-2833	304	8	(	(	PUNCT
iajs-2833	304	9	𝑦1𝑘	𝑦1𝑘	PROPN
iajs-2833	304	10	,	,	PUNCT
iajs-2833	304	11	𝑣3	𝑣3	ADJ
iajs-2833	304	12	)	)	PUNCT
iajs-2833	305	1	+	+	CCONJ
iajs-2833	305	2	(	(	PUNCT
iajs-2833	305	3	𝑦2𝑘	𝑦2𝑘	ADJ
iajs-2833	305	4	,	,	PUNCT
iajs-2833	305	5	𝑣3	𝑣3	ADJ
iajs-2833	305	6	)	)	PUNCT
iajs-2833	306	1	+	+	CCONJ
iajs-2833	306	2	(	(	PUNCT
iajs-2833	306	3	𝑦3𝑘	𝑦3𝑘	NOUN
iajs-2833	306	4	,	,	PUNCT
iajs-2833	306	5	𝑣3	𝑣3	ADJ
iajs-2833	306	6	)	)	PUNCT
iajs-2833	306	7	+	+	CCONJ
iajs-2833	306	8	(	(	PUNCT
iajs-2833	306	9	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	306	10	,	,	PUNCT
iajs-2833	306	11	𝑣3)]𝜙3	𝑣3)]𝜙3	PROPN
iajs-2833	306	12	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	306	13	=	=	SYM
iajs-2833	306	14	∫	∫	PROPN
iajs-2833	306	15	0	0	NUM
iajs-2833	306	16	𝑇	𝑇	PROPN
iajs-2833	306	17	(	(	PUNCT
iajs-2833	306	18	𝑓31(𝑥	𝑓31(𝑥	PROPN
iajs-2833	306	19	,	,	PUNCT
iajs-2833	306	20	𝑡	𝑡	NOUN
iajs-2833	306	21	,	,	PUNCT
iajs-2833	306	22	𝑦3𝑘	𝑦3𝑘	NOUN
iajs-2833	306	23	)	)	PUNCT
iajs-2833	306	24	,	,	PUNCT
iajs-2833	306	25	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	306	26	(	(	PUNCT
iajs-2833	306	27	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	306	28	+	+	NUM
iajs-2833	306	29	∫	∫	PROPN
iajs-2833	306	30	0	0	X
iajs-2833	306	31	𝑇	𝑇	PROPN
iajs-2833	306	32	(	(	PUNCT
iajs-2833	306	33	𝑓32(𝑥	𝑓32(𝑥	NOUN
iajs-2833	306	34	,	,	PUNCT
iajs-2833	306	35	𝑡)𝑢3𝑘	𝑡)𝑢3𝑘	PROPN
iajs-2833	306	36	,	,	PUNCT
iajs-2833	306	37	𝑣3)𝜙3	𝑣3)𝜙3	X
iajs-2833	306	38	(	(	PUNCT
iajs-2833	306	39	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	306	40	(	(	PUNCT
iajs-2833	306	41	79	79	NUM
iajs-2833	306	42	)	)	PUNCT
iajs-2833	306	43	∫	∫	NOUN
iajs-2833	306	44	0	0	NUM
iajs-2833	307	1	𝑇	𝑇	PROPN
iajs-2833	307	2	𝑑	𝑑	PRON
iajs-2833	307	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	307	4	(	(	PUNCT
iajs-2833	307	5	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	307	6	,	,	PUNCT
iajs-2833	307	7	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	307	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	307	9	+	+	CCONJ
iajs-2833	307	10	∫	∫	PROPN
iajs-2833	307	11	0	0	X
iajs-2833	308	1	𝑇	𝑇	PROPN
iajs-2833	308	2	[	[	X
iajs-2833	308	3	(	(	PUNCT
iajs-2833	308	4	∇𝑦4𝑘	∇𝑦4𝑘	NOUN
iajs-2833	308	5	,	,	PUNCT
iajs-2833	308	6	∇𝑣4	∇𝑣4	NUM
iajs-2833	308	7	)	)	PUNCT
iajs-2833	308	8	−	−	PROPN
iajs-2833	309	1	(	(	PUNCT
iajs-2833	309	2	𝑦1𝑘	𝑦1𝑘	PROPN
iajs-2833	309	3	,	,	PUNCT
iajs-2833	309	4	𝑣4	𝑣4	NOUN
iajs-2833	309	5	)	)	PUNCT
iajs-2833	309	6	+	+	CCONJ
iajs-2833	309	7	(	(	PUNCT
iajs-2833	309	8	𝑦2𝑘	𝑦2𝑘	PROPN
iajs-2833	309	9	,	,	PUNCT
iajs-2833	309	10	𝑣4	𝑣4	NOUN
iajs-2833	309	11	)	)	PUNCT
iajs-2833	309	12	−	−	PROPN
iajs-2833	309	13	(	(	PUNCT
iajs-2833	309	14	𝑦3𝑘	𝑦3𝑘	NOUN
iajs-2833	309	15	,	,	PUNCT
iajs-2833	309	16	𝑣4	𝑣4	NOUN
iajs-2833	309	17	)	)	PUNCT
iajs-2833	309	18	+	+	CCONJ
iajs-2833	309	19	(	(	PUNCT
iajs-2833	309	20	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	309	21	,	,	PUNCT
iajs-2833	309	22	𝑣4)]𝜙4	𝑣4)]𝜙4	NOUN
iajs-2833	309	23	𝑑𝑡	𝑑𝑡	ADP
iajs-2833	309	24	=	=	SYM
iajs-2833	309	25	∫	∫	PROPN
iajs-2833	309	26	0	0	X
iajs-2833	309	27	𝑇	𝑇	PROPN
iajs-2833	309	28	(	(	PUNCT
iajs-2833	309	29	𝑓41(𝑥	𝑓41(𝑥	NOUN
iajs-2833	309	30	,	,	PUNCT
iajs-2833	309	31	𝑡	𝑡	NOUN
iajs-2833	309	32	,	,	PUNCT
iajs-2833	309	33	𝑦4𝑘	𝑦4𝑘	NOUN
iajs-2833	309	34	)	)	PUNCT
iajs-2833	309	35	,	,	PUNCT
iajs-2833	309	36	𝑣4)𝜙4	𝑣4)𝜙4	VERB
iajs-2833	309	37	(	(	PUNCT
iajs-2833	309	38	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	309	39	+	+	NUM
iajs-2833	309	40	∫	∫	PROPN
iajs-2833	309	41	0	0	X
iajs-2833	309	42	𝑇	𝑇	PROPN
iajs-2833	309	43	(	(	PUNCT
iajs-2833	309	44	𝑓42(𝑥	𝑓42(𝑥	NOUN
iajs-2833	309	45	,	,	PUNCT
iajs-2833	309	46	𝑡)𝑢4𝑘	𝑡)𝑢4𝑘	NOUN
iajs-2833	309	47	,	,	PUNCT
iajs-2833	309	48	𝑣4)𝜙4	𝑣4)𝜙4	ADJ
iajs-2833	309	49	(	(	PUNCT
iajs-2833	309	50	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
iajs-2833	309	51	(	(	PUNCT
iajs-2833	309	52	80	80	NUM
iajs-2833	309	53	)	)	PUNCT
iajs-2833	309	54	the	the	DET
iajs-2833	309	55	same	same	ADJ
iajs-2833	309	56	steps	step	NOUN
iajs-2833	309	57	that	that	PRON
iajs-2833	309	58	are	be	AUX
iajs-2833	309	59	utilized	utilize	VERB
iajs-2833	309	60	in	in	ADP
iajs-2833	309	61	the	the	DET
iajs-2833	309	62	proof	proof	NOUN
iajs-2833	309	63	of	of	ADP
iajs-2833	309	64	theorem	theorem	ADJ
iajs-2833	309	65	3.1	3.1	NUM
iajs-2833	309	66	,	,	PUNCT
iajs-2833	309	67	can	can	AUX
iajs-2833	309	68	also	also	ADV
iajs-2833	309	69	be	be	AUX
iajs-2833	309	70	used	use	VERB
iajs-2833	309	71	here	here	ADV
iajs-2833	309	72	to	to	PART
iajs-2833	309	73	passage	passage	VERB
iajs-2833	309	74	the	the	DET
iajs-2833	309	75	limit	limit	NOUN
iajs-2833	309	76	in	in	ADP
iajs-2833	309	77	the	the	DET
iajs-2833	309	78	lhs	lhs	PROPN
iajs-2833	309	79	of	of	ADP
iajs-2833	309	80	(	(	PUNCT
iajs-2833	309	81	(	(	PUNCT
iajs-2833	309	82	77)-(80	77)-(80	NOUN
iajs-2833	309	83	)	)	PUNCT
iajs-2833	309	84	)	)	PUNCT
iajs-2833	309	85	.	.	PUNCT
iajs-2833	310	1	we	we	PRON
iajs-2833	310	2	persist	persist	VERB
iajs-2833	310	3	in	in	ADP
iajs-2833	310	4	the	the	DET
iajs-2833	310	5	passage	passage	NOUN
iajs-2833	310	6	of	of	ADP
iajs-2833	310	7	the	the	DET
iajs-2833	310	8	limit	limit	NOUN
iajs-2833	310	9	in	in	ADP
iajs-2833	310	10	rhs	rhs	PROPN
iajs-2833	310	11	of	of	ADP
iajs-2833	310	12	(	(	PUNCT
iajs-2833	310	13	(	(	PUNCT
iajs-2833	310	14	77))(80	77))(80	PROPN
iajs-2833	310	15	)	)	PUNCT
iajs-2833	310	16	)	)	PUNCT
iajs-2833	310	17	as	as	SCONJ
iajs-2833	310	18	follows	follow	VERB
iajs-2833	310	19	.	.	PUNCT
iajs-2833	311	1	let	let	VERB
iajs-2833	311	2	∀𝑖	∀𝑖	NOUN
iajs-2833	311	3	=	=	SYM
iajs-2833	311	4	1,2,3,4	1,2,3,4	NUM
iajs-2833	311	5	,	,	PUNCT
iajs-2833	311	6	𝑣𝑖	𝑣𝑖	ADP
iajs-2833	311	7	∈	∈	NOUN
iajs-2833	311	8	𝐶[ω̅	𝐶[ω̅	NOUN
iajs-2833	311	9	]	]	PUNCT
iajs-2833	311	10	,	,	PUNCT
iajs-2833	311	11	𝑤𝑖	𝑤𝑖	ADP
iajs-2833	311	12	=	=	PUNCT
iajs-2833	311	13	𝑣𝑖𝜙𝑖	𝑣𝑖𝜙𝑖	PROPN
iajs-2833	311	14	(	(	PUNCT
iajs-2833	311	15	𝑡	𝑡	NOUN
iajs-2833	311	16	)	)	PUNCT
iajs-2833	311	17	,	,	PUNCT
iajs-2833	311	18	then	then	ADV
iajs-2833	311	19	𝑤𝑖	𝑤𝑖	ADP
iajs-2833	311	20	∈	∈	PROPN
iajs-2833	311	21	𝐶[q̅	𝐶[q̅	NOUN
iajs-2833	311	22	]	]	X
iajs-2833	311	23	∈	∈	PROPN
iajs-2833	311	24	𝐿∞(𝑄	𝐿∞(𝑄	PROPN
iajs-2833	311	25	)	)	PUNCT
iajs-2833	311	26	⊂	⊂	PROPN
iajs-2833	311	27	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	311	28	)	)	PUNCT
iajs-2833	311	29	,	,	PUNCT
iajs-2833	311	30	set	set	VERB
iajs-2833	311	31	𝑓	𝑓	PRON
iajs-2833	311	32	�	�	PROPN
iajs-2833	311	33	̅	̅	NOUN
iajs-2833	311	34	�	�	NOUN
iajs-2833	311	35	1(𝑦𝑖𝑘	1(𝑦𝑖𝑘	NOUN
iajs-2833	311	36	)	)	PUNCT
iajs-2833	311	37	=	=	SYM
iajs-2833	311	38	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	NOUN
iajs-2833	311	39	,	,	PUNCT
iajs-2833	311	40	then	then	ADV
iajs-2833	311	41	𝑓	𝑓	PROPN
iajs-2833	311	42	�	�	PROPN
iajs-2833	311	43	̅	̅	NOUN
iajs-2833	311	44	�	�	NOUN
iajs-2833	311	45	1	1	NUM
iajs-2833	311	46	:	:	PUNCT
iajs-2833	311	47	𝑄	𝑄	PROPN
iajs-2833	311	48	×	×	NOUN
iajs-2833	311	49	ℝ	ℝ	PROPN
iajs-2833	311	50	→	→	PUNCT
iajs-2833	311	51	ℝ	ℝ	PROPN
iajs-2833	311	52	is	be	AUX
iajs-2833	311	53	of	of	ADP
iajs-2833	311	54	carathéodory	carathéodory	ADJ
iajs-2833	311	55	type	type	NOUN
iajs-2833	311	56	,	,	PUNCT
iajs-2833	311	57	utilizing	utilize	VERB
iajs-2833	311	58	proposition	proposition	NOUN
iajs-2833	311	59	3.1	3.1	NUM
iajs-2833	311	60	,	,	PUNCT
iajs-2833	311	61	to	to	PART
iajs-2833	311	62	get	get	VERB
iajs-2833	311	63	the	the	DET
iajs-2833	311	64	integral	integral	ADJ
iajs-2833	311	65	∫	∫	PROPN
iajs-2833	311	66	𝑄	𝑄	PROPN
iajs-2833	311	67	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	NOUN
iajs-2833	311	68	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	NOUN
iajs-2833	311	69	,	,	PUNCT
iajs-2833	311	70	is	be	AUX
iajs-2833	311	71	continuous	continuous	ADJ
iajs-2833	311	72	w.r.t	w.r.t	NOUN
iajs-2833	311	73	.	.	PUNCT
iajs-2833	312	1	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	312	2	∀𝑖	∀𝑖	PROPN
iajs-2833	312	3	=	=	ADJ
iajs-2833	312	4	1,2,3,4	1,2,3,4	NUM
iajs-2833	312	5	.	.	PUNCT
iajs-2833	313	1	but	but	CCONJ
iajs-2833	313	2	𝑦𝑖𝑘	𝑦𝑖𝑘	PROPN
iajs-2833	313	3	→	→	SYM
iajs-2833	313	4	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	313	5	st	st	PROPN
iajs-2833	313	6	in	in	ADP
iajs-2833	313	7	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	313	8	)	)	PUNCT
iajs-2833	313	9	and	and	CCONJ
iajs-2833	313	10	𝑢𝑖𝑘	𝑢𝑖𝑘	NOUN
iajs-2833	313	11	→	→	SYM
iajs-2833	313	12	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	313	13	wk	wk	INTJ
iajs-2833	313	14	in	in	ADP
iajs-2833	313	15	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2833	313	16	)	)	PUNCT
iajs-2833	313	17	,	,	PUNCT
iajs-2833	313	18	then	then	ADV
iajs-2833	313	19	∫	∫	PROPN
iajs-2833	313	20	𝑄	𝑄	PROPN
iajs-2833	313	21	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	𝑓𝑖1(𝑦𝑖𝑘)𝑤𝑖	NOUN
iajs-2833	313	22	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	NOUN
iajs-2833	313	23	→	→	SYM
iajs-2833	313	24	∫	∫	PROPN
iajs-2833	313	25	𝑄	𝑄	PROPN
iajs-2833	313	26	𝑓𝑖1(𝑦𝑖)𝑤𝑖	𝑓𝑖1(𝑦𝑖)𝑤𝑖	PROPN
iajs-2833	313	27	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	NOUN
iajs-2833	313	28	,	,	PUNCT
iajs-2833	313	29	∀	∀	NUM
iajs-2833	313	30	𝑤𝑖	𝑤𝑖	SCONJ
iajs-2833	313	31	∈	∈	PROPN
iajs-2833	313	32	𝐶[q̅	𝐶[q̅	NOUN
iajs-2833	313	33	]	]	PUNCT
iajs-2833	313	34	,	,	PUNCT
iajs-2833	313	35	for	for	ADP
iajs-2833	313	36	𝑖	𝑖	PRON
iajs-2833	313	37	=	=	SYM
iajs-2833	313	38	1,2,3,4	1,2,3,4	NUM
iajs-2833	313	39	(	(	PUNCT
iajs-2833	313	40	81	81	NUM
iajs-2833	313	41	)	)	PUNCT
iajs-2833	313	42	∫	∫	PROPN
iajs-2833	313	43	𝑄	𝑄	PROPN
iajs-2833	313	44	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2833	313	45	,	,	PUNCT
iajs-2833	313	46	𝑡)𝑢𝑖𝑘𝑤𝑖	𝑡)𝑢𝑖𝑘𝑤𝑖	ADV
iajs-2833	313	47	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	X
iajs-2833	313	48	→	→	SYM
iajs-2833	313	49	∫	∫	PROPN
iajs-2833	313	50	𝑄	𝑄	PROPN
iajs-2833	313	51	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2833	313	52	,	,	PUNCT
iajs-2833	313	53	𝑡)𝑢𝑖𝑤𝑖	𝑡)𝑢𝑖𝑤𝑖	NOUN
iajs-2833	313	54	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	ADJ
iajs-2833	313	55	,	,	PUNCT
iajs-2833	313	56	∀	∀	PUNCT
iajs-2833	313	57	𝑤𝑖	𝑤𝑖	SCONJ
iajs-2833	313	58	∈	∈	PROPN
iajs-2833	313	59	𝐶[q̅	𝐶[q̅	NOUN
iajs-2833	313	60	]	]	PUNCT
iajs-2833	313	61	,	,	PUNCT
iajs-2833	313	62	for	for	ADP
iajs-2833	313	63	𝑖	𝑖	PRON
iajs-2833	313	64	=	=	SYM
iajs-2833	313	65	1,2,3,4	1,2,3,4	NUM
iajs-2833	313	66	(	(	PUNCT
iajs-2833	313	67	82	82	NUM
iajs-2833	313	68	)	)	PUNCT
iajs-2833	313	69	form	form	VERB
iajs-2833	313	70	the	the	DET
iajs-2833	313	71	density	density	NOUN
iajs-2833	313	72	of	of	ADP
iajs-2833	313	73	𝐶(ω̅	𝐶(ω̅	NOUN
iajs-2833	313	74	)	)	PUNCT
iajs-2833	313	75	in	in	ADP
iajs-2833	313	76	𝑉	𝑉	PROPN
iajs-2833	313	77	,	,	PUNCT
iajs-2833	313	78	(	(	PUNCT
iajs-2833	313	79	81	81	NUM
iajs-2833	313	80	)	)	PUNCT
iajs-2833	313	81	&	&	CCONJ
iajs-2833	313	82	(	(	PUNCT
iajs-2833	313	83	82	82	NUM
iajs-2833	313	84	)	)	PUNCT
iajs-2833	313	85	are	be	AUX
iajs-2833	313	86	satisfies	satisfie	NOUN
iajs-2833	313	87	for	for	ADP
iajs-2833	313	88	each	each	DET
iajs-2833	313	89	𝑣𝑖	𝑣𝑖	NOUN
iajs-2833	313	90	∈	∈	PROPN
iajs-2833	313	91	𝑉	𝑉	PROPN
iajs-2833	313	92	for	for	ADP
iajs-2833	313	93	𝑖	𝑖	NOUN
iajs-2833	313	94	=	=	NOUN
iajs-2833	313	95	1,2,3,4	1,2,3,4	NUM
iajs-2833	313	96	,	,	PUNCT
iajs-2833	313	97	hence	hence	ADV
iajs-2833	313	98	the	the	DET
iajs-2833	313	99	following	follow	VERB
iajs-2833	313	100	wf	wf	PROPN
iajs-2833	313	101	is	be	AUX
iajs-2833	313	102	obtained	obtain	VERB
iajs-2833	313	103	(	(	PUNCT
iajs-2833	313	104	𝑦1𝑡	𝑦1𝑡	NOUN
iajs-2833	313	105	,	,	PUNCT
iajs-2833	313	106	𝑣1	𝑣1	PROPN
iajs-2833	313	107	)	)	PUNCT
iajs-2833	314	1	+	+	CCONJ
iajs-2833	314	2	(	(	PUNCT
iajs-2833	314	3	∇𝑦1	∇𝑦1	NOUN
iajs-2833	314	4	,	,	PUNCT
iajs-2833	314	5	∇𝑣1	∇𝑣1	NOUN
iajs-2833	314	6	)	)	PUNCT
iajs-2833	315	1	+	+	CCONJ
iajs-2833	315	2	(	(	PUNCT
iajs-2833	315	3	𝑦1	𝑦1	PROPN
iajs-2833	315	4	,	,	PUNCT
iajs-2833	315	5	𝑣1	𝑣1	NOUN
iajs-2833	315	6	)	)	PUNCT
iajs-2833	315	7	−	−	PROPN
iajs-2833	315	8	(	(	PUNCT
iajs-2833	315	9	𝑦2	𝑦2	PROPN
iajs-2833	315	10	,	,	PUNCT
iajs-2833	315	11	𝑣1	𝑣1	PROPN
iajs-2833	315	12	)	)	PUNCT
iajs-2833	315	13	+	+	CCONJ
iajs-2833	315	14	(	(	PUNCT
iajs-2833	315	15	𝑦3	𝑦3	PROPN
iajs-2833	315	16	,	,	PUNCT
iajs-2833	315	17	𝑣1	𝑣1	PROPN
iajs-2833	315	18	)	)	PUNCT
iajs-2833	315	19	+	+	CCONJ
iajs-2833	315	20	(	(	PUNCT
iajs-2833	315	21	𝑦4	𝑦4	NOUN
iajs-2833	315	22	,	,	PUNCT
iajs-2833	315	23	𝑣1	𝑣1	NOUN
iajs-2833	315	24	)	)	PUNCT
iajs-2833	315	25	=	=	PUNCT
iajs-2833	315	26	(	(	PUNCT
iajs-2833	315	27	𝑓11(𝑥	𝑓11(𝑥	NOUN
iajs-2833	315	28	,	,	PUNCT
iajs-2833	315	29	𝑡	𝑡	NOUN
iajs-2833	315	30	,	,	PUNCT
iajs-2833	315	31	𝑦1	𝑦1	NOUN
iajs-2833	315	32	)	)	PUNCT
iajs-2833	315	33	,	,	PUNCT
iajs-2833	315	34	𝑣1	𝑣1	NOUN
iajs-2833	315	35	)	)	PUNCT
iajs-2833	315	36	+	+	CCONJ
iajs-2833	315	37	(	(	PUNCT
iajs-2833	315	38	𝑓12(𝑥	𝑓12(𝑥	NOUN
iajs-2833	315	39	,	,	PUNCT
iajs-2833	315	40	𝑡)𝑢1	𝑡)𝑢1	PROPN
iajs-2833	315	41	,	,	PUNCT
iajs-2833	315	42	𝑣1	𝑣1	PROPN
iajs-2833	315	43	)	)	PUNCT
iajs-2833	315	44	,	,	PUNCT
iajs-2833	315	45	∀𝑣1	∀𝑣1	PROPN
iajs-2833	315	46	∈	∈	PROPN
iajs-2833	315	47	𝑉	𝑉	PROPN
iajs-2833	315	48	a.e	a.e	PROPN
iajs-2833	315	49	.	.	PROPN
iajs-2833	316	1	on	on	ADP
iajs-2833	316	2	i	i	PROPN
iajs-2833	316	3	(	(	PUNCT
iajs-2833	316	4	83	83	NUM
iajs-2833	316	5	)	)	PUNCT
iajs-2833	316	6	(	(	PUNCT
iajs-2833	316	7	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2833	316	8	,	,	PUNCT
iajs-2833	316	9	𝑣2	𝑣2	NOUN
iajs-2833	316	10	)	)	PUNCT
iajs-2833	316	11	+	+	CCONJ
iajs-2833	316	12	(	(	PUNCT
iajs-2833	316	13	∆𝑦2	∆𝑦2	PROPN
iajs-2833	316	14	,	,	PUNCT
iajs-2833	316	15	∇𝑣2	∇𝑣2	PROPN
iajs-2833	316	16	)	)	PUNCT
iajs-2833	316	17	+	+	CCONJ
iajs-2833	316	18	(	(	PUNCT
iajs-2833	316	19	𝑦1	𝑦1	PROPN
iajs-2833	316	20	,	,	PUNCT
iajs-2833	316	21	𝑣2	𝑣2	PROPN
iajs-2833	316	22	)	)	PUNCT
iajs-2833	316	23	+	+	CCONJ
iajs-2833	316	24	(	(	PUNCT
iajs-2833	316	25	𝑦2	𝑦2	PROPN
iajs-2833	316	26	,	,	PUNCT
iajs-2833	316	27	𝑣2	𝑣2	PROPN
iajs-2833	316	28	)	)	PUNCT
iajs-2833	316	29	−	−	PROPN
iajs-2833	316	30	(	(	PUNCT
iajs-2833	316	31	𝑦3	𝑦3	PROPN
iajs-2833	316	32	,	,	PUNCT
iajs-2833	316	33	𝑣2	𝑣2	PROPN
iajs-2833	316	34	)	)	PUNCT
iajs-2833	316	35	−	−	PROPN
iajs-2833	316	36	(	(	PUNCT
iajs-2833	316	37	𝑦4	𝑦4	PROPN
iajs-2833	316	38	,	,	PUNCT
iajs-2833	316	39	𝑣2	𝑣2	NOUN
iajs-2833	316	40	)	)	PUNCT
iajs-2833	316	41	=	=	PUNCT
iajs-2833	316	42	(	(	PUNCT
iajs-2833	316	43	𝑓21(𝑥	𝑓21(𝑥	NOUN
iajs-2833	316	44	,	,	PUNCT
iajs-2833	316	45	𝑡	𝑡	PROPN
iajs-2833	316	46	,	,	PUNCT
iajs-2833	316	47	𝑦2	𝑦2	NOUN
iajs-2833	316	48	)	)	PUNCT
iajs-2833	316	49	,	,	PUNCT
iajs-2833	316	50	𝑣2	𝑣2	PROPN
iajs-2833	316	51	)	)	PUNCT
iajs-2833	316	52	+	+	CCONJ
iajs-2833	316	53	(	(	PUNCT
iajs-2833	316	54	𝑓22(𝑥	𝑓22(𝑥	X
iajs-2833	316	55	,	,	PUNCT
iajs-2833	316	56	𝑡)𝑢2	𝑡)𝑢2	PROPN
iajs-2833	316	57	,	,	PUNCT
iajs-2833	316	58	𝑣2	𝑣2	PROPN
iajs-2833	316	59	)	)	PUNCT
iajs-2833	316	60	,	,	PUNCT
iajs-2833	316	61	∀𝑣2	∀𝑣2	PROPN
iajs-2833	316	62	∈	∈	PROPN
iajs-2833	316	63	𝑉	𝑉	PROPN
iajs-2833	316	64	a.e	a.e	PROPN
iajs-2833	316	65	.	.	PROPN
iajs-2833	317	1	on	on	ADP
iajs-2833	317	2	i	i	PRON
iajs-2833	317	3	(	(	PUNCT
iajs-2833	317	4	84	84	NUM
iajs-2833	317	5	)	)	PUNCT
iajs-2833	317	6	(	(	PUNCT
iajs-2833	317	7	𝑦3𝑡	𝑦3𝑡	NUM
iajs-2833	317	8	,	,	PUNCT
iajs-2833	317	9	𝑣3	𝑣3	ADJ
iajs-2833	317	10	)	)	PUNCT
iajs-2833	317	11	+	+	CCONJ
iajs-2833	317	12	(	(	PUNCT
iajs-2833	317	13	∇𝑦3	∇𝑦3	PROPN
iajs-2833	317	14	,	,	PUNCT
iajs-2833	317	15	∇𝑣3	∇𝑣3	NOUN
iajs-2833	317	16	)	)	PUNCT
iajs-2833	317	17	−	−	PROPN
iajs-2833	318	1	(	(	PUNCT
iajs-2833	318	2	𝑦1	𝑦1	NOUN
iajs-2833	318	3	,	,	PUNCT
iajs-2833	318	4	𝑣3	𝑣3	ADJ
iajs-2833	318	5	)	)	PUNCT
iajs-2833	318	6	+	+	CCONJ
iajs-2833	318	7	(	(	PUNCT
iajs-2833	318	8	𝑦2	𝑦2	NOUN
iajs-2833	318	9	,	,	PUNCT
iajs-2833	318	10	𝑣3	𝑣3	ADJ
iajs-2833	318	11	)	)	PUNCT
iajs-2833	318	12	+	+	CCONJ
iajs-2833	318	13	(	(	PUNCT
iajs-2833	318	14	𝑦3	𝑦3	PROPN
iajs-2833	318	15	,	,	PUNCT
iajs-2833	318	16	𝑣3	𝑣3	ADJ
iajs-2833	318	17	)	)	PUNCT
iajs-2833	318	18	+	+	CCONJ
iajs-2833	318	19	(	(	PUNCT
iajs-2833	318	20	𝑦4	𝑦4	NOUN
iajs-2833	318	21	,	,	PUNCT
iajs-2833	318	22	𝑣3	𝑣3	ADJ
iajs-2833	318	23	)	)	PUNCT
iajs-2833	318	24	=	=	SYM
iajs-2833	318	25	(	(	PUNCT
iajs-2833	318	26	𝑓31(𝑥	𝑓31(𝑥	NUM
iajs-2833	318	27	,	,	PUNCT
iajs-2833	318	28	𝑡	𝑡	PROPN
iajs-2833	318	29	,	,	PUNCT
iajs-2833	318	30	𝑦3	𝑦3	PROPN
iajs-2833	318	31	)	)	PUNCT
iajs-2833	318	32	,	,	PUNCT
iajs-2833	318	33	𝑣3	𝑣3	ADJ
iajs-2833	318	34	)	)	PUNCT
iajs-2833	318	35	+	+	CCONJ
iajs-2833	318	36	(	(	PUNCT
iajs-2833	318	37	𝑓32(𝑥	𝑓32(𝑥	NOUN
iajs-2833	318	38	,	,	PUNCT
iajs-2833	318	39	𝑡)𝑢3	𝑡)𝑢3	PROPN
iajs-2833	318	40	,	,	PUNCT
iajs-2833	318	41	𝑣3)∀𝑣3	𝑣3)∀𝑣3	PROPN
iajs-2833	318	42	∈	∈	PROPN
iajs-2833	318	43	𝑉	𝑉	PROPN
iajs-2833	318	44	a.e	a.e	PROPN
iajs-2833	318	45	.	.	PROPN
iajs-2833	319	1	on	on	ADP
iajs-2833	319	2	i	i	PROPN
iajs-2833	319	3	(	(	PUNCT
iajs-2833	319	4	85	85	NUM
iajs-2833	319	5	)	)	PUNCT
iajs-2833	319	6	(	(	PUNCT
iajs-2833	319	7	𝑦4𝑡	𝑦4𝑡	ADJ
iajs-2833	319	8	,	,	PUNCT
iajs-2833	319	9	𝑣4	𝑣4	NOUN
iajs-2833	319	10	)	)	PUNCT
iajs-2833	319	11	+	+	CCONJ
iajs-2833	319	12	(	(	PUNCT
iajs-2833	319	13	∇𝑦4	∇𝑦4	ADJ
iajs-2833	319	14	,	,	PUNCT
iajs-2833	319	15	∇𝑣4	∇𝑣4	NUM
iajs-2833	319	16	)	)	PUNCT
iajs-2833	319	17	−	−	PROPN
iajs-2833	320	1	(	(	PUNCT
iajs-2833	320	2	𝑦1	𝑦1	NOUN
iajs-2833	320	3	,	,	PUNCT
iajs-2833	320	4	𝑣4	𝑣4	NOUN
iajs-2833	320	5	)	)	PUNCT
iajs-2833	320	6	+	+	CCONJ
iajs-2833	320	7	(	(	PUNCT
iajs-2833	320	8	𝑦2	𝑦2	NOUN
iajs-2833	320	9	,	,	PUNCT
iajs-2833	320	10	𝑣4	𝑣4	NOUN
iajs-2833	320	11	)	)	PUNCT
iajs-2833	320	12	−	−	PROPN
iajs-2833	320	13	(	(	PUNCT
iajs-2833	320	14	𝑦3	𝑦3	PROPN
iajs-2833	320	15	,	,	PUNCT
iajs-2833	320	16	𝑣4	𝑣4	NOUN
iajs-2833	320	17	)	)	PUNCT
iajs-2833	320	18	+	+	CCONJ
iajs-2833	320	19	(	(	PUNCT
iajs-2833	320	20	𝑦4	𝑦4	NOUN
iajs-2833	320	21	,	,	PUNCT
iajs-2833	320	22	𝑣4	𝑣4	NOUN
iajs-2833	320	23	)	)	PUNCT
iajs-2833	320	24	=	=	PUNCT
iajs-2833	320	25	(	(	PUNCT
iajs-2833	320	26	𝑓41(𝑥	𝑓41(𝑥	NOUN
iajs-2833	320	27	,	,	PUNCT
iajs-2833	320	28	𝑡	𝑡	NOUN
iajs-2833	320	29	,	,	PUNCT
iajs-2833	320	30	𝑦4	𝑦4	NOUN
iajs-2833	320	31	)	)	PUNCT
iajs-2833	320	32	,	,	PUNCT
iajs-2833	320	33	𝑣4	𝑣4	NOUN
iajs-2833	320	34	)	)	PUNCT
iajs-2833	320	35	+	+	CCONJ
iajs-2833	320	36	(	(	PUNCT
iajs-2833	320	37	𝑓42(𝑥	𝑓42(𝑥	NOUN
iajs-2833	320	38	,	,	PUNCT
iajs-2833	320	39	𝑡)𝑢4	𝑡)𝑢4	PROPN
iajs-2833	320	40	,	,	PUNCT
iajs-2833	320	41	𝑣4	𝑣4	NOUN
iajs-2833	320	42	)	)	PUNCT
iajs-2833	320	43	∀𝑣4	∀𝑣4	NOUN
iajs-2833	320	44	∈	∈	PROPN
iajs-2833	320	45	𝑉	𝑉	PROPN
iajs-2833	320	46	a.e	a.e	PROPN
iajs-2833	320	47	.	.	PROPN
iajs-2833	321	1	on	on	ADP
iajs-2833	321	2	i	i	PROPN
iajs-2833	321	3	(	(	PUNCT
iajs-2833	321	4	86	86	NUM
iajs-2833	321	5	)	)	PUNCT
iajs-2833	321	6	also	also	ADV
iajs-2833	321	7	,	,	PUNCT
iajs-2833	321	8	the	the	DET
iajs-2833	321	9	same	same	ADJ
iajs-2833	321	10	steps	step	NOUN
iajs-2833	321	11	employed	employ	VERB
iajs-2833	321	12	in	in	ADP
iajs-2833	321	13	theorem	theorem	ADJ
iajs-2833	321	14	3.1	3.1	NUM
iajs-2833	321	15	can	can	AUX
iajs-2833	321	16	be	be	AUX
iajs-2833	321	17	employed	employ	VERB
iajs-2833	321	18	here	here	ADV
iajs-2833	321	19	to	to	PART
iajs-2833	321	20	obtain	obtain	VERB
iajs-2833	321	21	that	that	SCONJ
iajs-2833	321	22	the	the	DET
iajs-2833	321	23	ics	ic	NOUN
iajs-2833	321	24	are	be	AUX
iajs-2833	321	25	held	hold	VERB
iajs-2833	321	26	,	,	PUNCT
iajs-2833	321	27	hence	hence	ADV
iajs-2833	321	28	�	�	NOUN
iajs-2833	321	29	⃗	⃗	NOUN
iajs-2833	321	30	�	�	PROPN
iajs-2833	321	31	is	be	AUX
iajs-2833	321	32	the	the	DET
iajs-2833	321	33	sqvs	sqvs	NOUN
iajs-2833	321	34	.	.	PUNCT
iajs-2833	322	1	now	now	ADV
iajs-2833	322	2	since	since	SCONJ
iajs-2833	322	3	∀𝑖	∀𝑖	PROPN
iajs-2833	322	4	=	=	SYM
iajs-2833	322	5	1,2,3,4	1,2,3,4	NUM
iajs-2833	322	6	,	,	PUNCT
iajs-2833	322	7	𝑔0𝑖(𝑥	𝑔0𝑖(𝑥	PROPN
iajs-2833	322	8	,	,	PUNCT
iajs-2833	322	9	𝑡	𝑡	PROPN
iajs-2833	322	10	,	,	PUNCT
iajs-2833	322	11	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	322	12	,	,	PUNCT
iajs-2833	322	13	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	322	14	)	)	PUNCT
iajs-2833	322	15	is	be	AUX
iajs-2833	322	16	continuous	continuous	ADJ
iajs-2833	322	17	w.r.t	w.r.t	NOUN
iajs-2833	322	18	.	.	PUNCT
iajs-2833	323	1	(	(	PUNCT
iajs-2833	323	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	323	3	,	,	PUNCT
iajs-2833	323	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	323	5	)	)	PUNCT
iajs-2833	323	6	,	,	PUNCT
iajs-2833	323	7	and	and	CCONJ
iajs-2833	323	8	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	323	9	is	be	AUX
iajs-2833	323	10	compact	compact	ADJ
iajs-2833	323	11	.	.	PUNCT
iajs-2833	324	1	with	with	ADP
iajs-2833	324	2	𝑢𝑖(𝑥	𝑢𝑖(𝑥	NUM
iajs-2833	324	3	,	,	PUNCT
iajs-2833	324	4	𝑡	𝑡	NOUN
iajs-2833	324	5	)	)	PUNCT
iajs-2833	324	6	∈	∈	PROPN
iajs-2833	324	7	𝑈𝑖	𝑈𝑖	PROPN
iajs-2833	324	8	a.e	a.e	PROPN
iajs-2833	324	9	.	.	PROPN
iajs-2833	324	10	in	in	ADP
iajs-2833	324	11	𝑄	𝑄	PROPN
iajs-2833	324	12	,	,	PUNCT
iajs-2833	324	13	then	then	ADV
iajs-2833	324	14	using	use	VERB
iajs-2833	324	15	lemma	lemma	PROPN
iajs-2833	324	16	4.2	4.2	NUM
iajs-2833	324	17	,	,	PUNCT
iajs-2833	324	18	to	to	PART
iajs-2833	324	19	get	get	VERB
iajs-2833	324	20	∫	∫	PROPN
iajs-2833	324	21	𝑄	𝑄	PROPN
iajs-2833	324	22	𝑔0𝑖(𝑥	𝑔0𝑖(𝑥	PROPN
iajs-2833	324	23	,	,	PUNCT
iajs-2833	324	24	𝑡	𝑡	PROPN
iajs-2833	324	25	,	,	PUNCT
iajs-2833	324	26	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	324	27	,	,	PUNCT
iajs-2833	324	28	𝑢𝑖𝑘	𝑢𝑖𝑘	NOUN
iajs-2833	324	29	)	)	PUNCT
iajs-2833	324	30	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	ADJ
iajs-2833	324	31	→	→	SYM
iajs-2833	324	32	∫	∫	PROPN
iajs-2833	324	33	𝑄	𝑄	PROPN
iajs-2833	324	34	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	324	35	(	(	PUNCT
iajs-2833	324	36	𝑥	𝑥	PROPN
iajs-2833	324	37	,	,	PUNCT
iajs-2833	324	38	𝑡	𝑡	PROPN
iajs-2833	324	39	,	,	PUNCT
iajs-2833	324	40	𝑦𝑖	𝑦𝑖	NOUN
iajs-2833	324	41	,	,	PUNCT
iajs-2833	324	42	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	324	43	(	(	PUNCT
iajs-2833	324	44	87	87	NUM
iajs-2833	324	45	)	)	PUNCT
iajs-2833	324	46	but	but	CCONJ
iajs-2833	324	47	𝑔0𝑖(𝑥	𝑔0𝑖(𝑥	PROPN
iajs-2833	324	48	,	,	PUNCT
iajs-2833	324	49	𝑡	𝑡	PROPN
iajs-2833	324	50	,	,	PUNCT
iajs-2833	324	51	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	324	52	,	,	PUNCT
iajs-2833	324	53	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	324	54	)	)	PUNCT
iajs-2833	324	55	is	be	AUX
iajs-2833	324	56	continuous	continuous	ADJ
iajs-2833	324	57	and	and	CCONJ
iajs-2833	324	58	convex	convex	ADJ
iajs-2833	324	59	w.r.t	w.r.t	NOUN
iajs-2833	324	60	.	.	PUNCT
iajs-2833	325	1	𝑢𝑖	𝑢𝑖	NOUN
iajs-2833	325	2	then	then	ADV
iajs-2833	325	3	∫	∫	PROPN
iajs-2833	325	4	𝑄	𝑄	PROPN
iajs-2833	325	5	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	325	6	(	(	PUNCT
iajs-2833	325	7	𝑥	𝑥	PROPN
iajs-2833	325	8	,	,	PUNCT
iajs-2833	325	9	𝑡	𝑡	PROPN
iajs-2833	325	10	,	,	PUNCT
iajs-2833	325	11	𝑦𝑖	𝑦𝑖	PROPN
iajs-2833	325	12	,	,	PUNCT
iajs-2833	325	13	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	325	14	is	be	AUX
iajs-2833	325	15	weakly	weakly	ADJ
iajs-2833	325	16	lowe	lowe	NOUN
iajs-2833	325	17	semi	semi	ADJ
iajs-2833	325	18	cont	cont	PROPN
iajs-2833	325	19	.	.	PUNCT
iajs-2833	326	1	(	(	PUNCT
iajs-2833	326	2	wlsc	wlsc	NOUN
iajs-2833	326	3	)	)	PUNCT
iajs-2833	326	4	w.r.t	w.r.t	NOUN
iajs-2833	326	5	.	.	PUNCT
iajs-2833	327	1	𝑢𝑖	𝑢𝑖	ADP
iajs-2833	327	2	,	,	PUNCT
iajs-2833	327	3	∀𝑖	∀𝑖	PROPN
iajs-2833	327	4	=	=	NOUN
iajs-2833	327	5	1,2,3,4	1,2,3,4	NUM
iajs-2833	327	6	,	,	PUNCT
iajs-2833	327	7	i.e.	i.e.	X
iajs-2833	327	8	∫	∫	PROPN
iajs-2833	327	9	𝑄	𝑄	PROPN
iajs-2833	327	10	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	327	11	(	(	PUNCT
iajs-2833	327	12	𝑥	𝑥	PROPN
iajs-2833	327	13	,	,	PUNCT
iajs-2833	327	14	𝑡	𝑡	PROPN
iajs-2833	327	15	,	,	PUNCT
iajs-2833	327	16	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	327	17	,	,	PUNCT
iajs-2833	327	18	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	327	19	≤	≤	NUM
iajs-2833	327	20	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-2833	328	1	𝑘→∞	𝑘→∞	NUM
iajs-2833	328	2	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	328	3	∫	∫	INTJ
iajs-2833	329	1	𝑄	𝑄	PROPN
iajs-2833	329	2	[	[	X
iajs-2833	329	3	𝑔0𝑖	𝑔0𝑖	PROPN
iajs-2833	329	4	(	(	PUNCT
iajs-2833	329	5	𝑥	𝑥	PROPN
iajs-2833	329	6	,	,	PUNCT
iajs-2833	329	7	𝑡	𝑡	PROPN
iajs-2833	329	8	,	,	PUNCT
iajs-2833	329	9	𝑦𝑖	𝑦𝑖	NOUN
iajs-2833	329	10	,	,	PUNCT
iajs-2833	329	11	𝑢𝑖𝑘	𝑢𝑖𝑘	NOUN
iajs-2833	329	12	)	)	PUNCT
iajs-2833	329	13	−	−	PROPN
iajs-2833	329	14	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	329	15	(	(	PUNCT
iajs-2833	329	16	𝑥	𝑥	PROPN
iajs-2833	329	17	,	,	PUNCT
iajs-2833	329	18	𝑡	𝑡	PROPN
iajs-2833	329	19	,	,	PUNCT
iajs-2833	329	20	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	329	21	,	,	PUNCT
iajs-2833	329	22	𝑢𝑖𝑘)]𝑑𝑥𝑑𝑡	𝑢𝑖𝑘)]𝑑𝑥𝑑𝑡	X
iajs-2833	329	23	+	+	CCONJ
iajs-2833	329	24	𝑙𝑖𝑚	𝑙𝑖𝑚	NUM
iajs-2833	329	25	𝑘→∞	𝑘→∞	NUM
iajs-2833	329	26	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	329	27	∫	∫	PROPN
iajs-2833	329	28	𝑄	𝑄	PROPN
iajs-2833	329	29	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	329	30	(	(	PUNCT
iajs-2833	329	31	𝑥	𝑥	PROPN
iajs-2833	329	32	,	,	PUNCT
iajs-2833	329	33	𝑡	𝑡	PROPN
iajs-2833	329	34	,	,	PUNCT
iajs-2833	329	35	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	329	36	,	,	PUNCT
iajs-2833	329	37	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	329	38	,	,	PUNCT
iajs-2833	329	39	≤	≤	NUM
iajs-2833	329	40	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-2833	329	41	𝑘→∞	𝑘→∞	NUM
iajs-2833	329	42	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	329	43	∫	∫	PROPN
iajs-2833	329	44	𝑄	𝑄	PROPN
iajs-2833	329	45	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	329	46	(	(	PUNCT
iajs-2833	329	47	𝑥	𝑥	PROPN
iajs-2833	329	48	,	,	PUNCT
iajs-2833	329	49	𝑡	𝑡	PROPN
iajs-2833	329	50	,	,	PUNCT
iajs-2833	329	51	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	329	52	,	,	PUNCT
iajs-2833	329	53	𝑢𝑖𝑘)𝑑𝑥𝑑	𝑢𝑖𝑘)𝑑𝑥𝑑	PROPN
iajs-2833	329	54	⟹	⟹	PUNCT
iajs-2833	329	55	σ	σ	X
iajs-2833	329	56	𝑖=1	𝑖=1	PROPN
iajs-2833	329	57	4	4	NUM
iajs-2833	329	58	∫	∫	NOUN
iajs-2833	329	59	𝑄	𝑄	PROPN
iajs-2833	329	60	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	329	61	(	(	PUNCT
iajs-2833	329	62	𝑥	𝑥	PROPN
iajs-2833	329	63	,	,	PUNCT
iajs-2833	329	64	𝑡	𝑡	PROPN
iajs-2833	329	65	,	,	PUNCT
iajs-2833	329	66	𝑦𝑖	𝑦𝑖	INTJ
iajs-2833	329	67	,	,	PUNCT
iajs-2833	329	68	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	329	69	≤	≤	PUNCT
iajs-2833	329	70	σ	σ	X
iajs-2833	329	71	𝑖=1	𝑖=1	PROPN
iajs-2833	329	72	4	4	NUM
iajs-2833	329	73	∫	∫	NOUN
iajs-2833	329	74	𝑄	𝑄	PROPN
iajs-2833	329	75	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2833	329	76	(	(	PUNCT
iajs-2833	329	77	𝑥	𝑥	PROPN
iajs-2833	329	78	,	,	PUNCT
iajs-2833	329	79	𝑡	𝑡	PROPN
iajs-2833	329	80	,	,	PUNCT
iajs-2833	329	81	𝑦𝑖𝑘	𝑦𝑖𝑘	NOUN
iajs-2833	329	82	,	,	PUNCT
iajs-2833	329	83	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	𝑢𝑖𝑘)𝑑𝑥𝑑𝑡	NOUN
iajs-2833	329	84	,	,	PUNCT
iajs-2833	329	85	thus	thus	ADV
iajs-2833	329	86	ihjpas	ihjpa	VERB
iajs-2833	329	87	.	.	PUNCT
iajs-2833	330	1	53	53	NUM
iajs-2833	330	2	(	(	PUNCT
iajs-2833	330	3	3)2022	3)2022	NOUN
iajs-2833	330	4	173	173	NUM
iajs-2833	330	5	𝐺0(	𝐺0(	SYM
iajs-2833	330	6	�	�	NOUN
iajs-2833	330	7	⃗⃗	⃗⃗	PROPN
iajs-2833	330	8	�	�	PROPN
iajs-2833	330	9	)	)	PUNCT
iajs-2833	330	10	≤	≤	NUM
iajs-2833	330	11	𝑙𝑖𝑚	𝑙𝑖𝑚	VERB
iajs-2833	330	12	𝑘→∞	𝑘→∞	NUM
iajs-2833	330	13	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	330	14	�	�	PROPN
iajs-2833	330	15	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	330	16	�	�	NOUN
iajs-2833	330	17	𝑘∈	𝑘∈	PROPN
iajs-2833	330	18	�	�	PROPN
iajs-2833	330	19	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	330	20	�	�	PROPN
iajs-2833	330	21	𝐴	𝐴	PROPN
iajs-2833	330	22	𝐺0(	𝐺0(	NUM
iajs-2833	330	23	�	�	PROPN
iajs-2833	330	24	⃗⃗	⃗⃗	PROPN
iajs-2833	330	25	�	�	PROPN
iajs-2833	330	26	𝑘	𝑘	NOUN
iajs-2833	330	27	)	)	PUNCT
iajs-2833	330	28	=	=	SYM
iajs-2833	331	1	𝑙𝑖𝑚	𝑙𝑖𝑚	PROPN
iajs-2833	331	2	𝑘→∞	𝑘→∞	NUM
iajs-2833	331	3	𝐺0(	𝐺0(	NOUN
iajs-2833	331	4	�	�	NOUN
iajs-2833	331	5	⃗⃗	⃗⃗	PROPN
iajs-2833	331	6	�	�	PROPN
iajs-2833	331	7	𝑘	𝑘	NOUN
iajs-2833	331	8	)	)	PUNCT
iajs-2833	331	9	=	=	PUNCT
iajs-2833	331	10	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	331	11	�	�	PROPN
iajs-2833	331	12	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	331	13	�	�	NOUN
iajs-2833	331	14	𝑘∈	𝑘∈	PROPN
iajs-2833	331	15	�	�	PROPN
iajs-2833	331	16	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	331	17	�	�	PROPN
iajs-2833	331	18	𝐴	𝐴	PROPN
iajs-2833	331	19	𝐺0(	𝐺0(	NUM
iajs-2833	331	20	�	�	PROPN
iajs-2833	331	21	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	331	22	�	�	PROPN
iajs-2833	331	23	)	)	PUNCT
iajs-2833	331	24	,	,	PUNCT
iajs-2833	331	25	then	then	ADV
iajs-2833	331	26	𝐺0(	𝐺0(	VERB
iajs-2833	331	27	�	�	PROPN
iajs-2833	331	28	⃗⃗	⃗⃗	PROPN
iajs-2833	331	29	�	�	PROPN
iajs-2833	331	30	)	)	PUNCT
iajs-2833	331	31	≤	≤	NUM
iajs-2833	331	32	𝑖𝑛𝑓	𝑖𝑛𝑓	NOUN
iajs-2833	331	33	�	�	PROPN
iajs-2833	331	34	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	331	35	�	�	NOUN
iajs-2833	331	36	𝑘∈	𝑘∈	PROPN
iajs-2833	331	37	�	�	PROPN
iajs-2833	331	38	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	331	39	�	�	PROPN
iajs-2833	331	40	𝐴	𝐴	PROPN
iajs-2833	331	41	𝐺0(	𝐺0(	NUM
iajs-2833	331	42	�	�	PROPN
iajs-2833	331	43	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	331	44	�	�	PROPN
iajs-2833	331	45	)	)	PUNCT
iajs-2833	331	46	⟹	⟹	NUM
iajs-2833	331	47	𝐺0(	𝐺0(	SYM
iajs-2833	331	48	�	�	PROPN
iajs-2833	331	49	⃗⃗	⃗⃗	PROPN
iajs-2833	331	50	�	�	PROPN
iajs-2833	331	51	)	)	PUNCT
iajs-2833	331	52	≤	≤	NOUN
iajs-2833	331	53	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
iajs-2833	331	54	�	�	PROPN
iajs-2833	331	55	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2833	331	56	�	�	NOUN
iajs-2833	331	57	𝑘∈	𝑘∈	PROPN
iajs-2833	331	58	�	�	PROPN
iajs-2833	331	59	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2833	331	60	�	�	PROPN
iajs-2833	331	61	𝐴	𝐴	PROPN
iajs-2833	331	62	𝐺0(	𝐺0(	NUM
iajs-2833	331	63	�	�	PROPN
iajs-2833	331	64	⃗⃗̅	⃗⃗̅	NOUN
iajs-2833	331	65	�	�	PROPN
iajs-2833	331	66	)	)	PUNCT
iajs-2833	331	67	,	,	PUNCT
iajs-2833	331	68	then	then	ADV
iajs-2833	331	69	�	�	PROPN
iajs-2833	331	70	⃗⃗	⃗⃗	PROPN
iajs-2833	331	71	�	�	PROPN
iajs-2833	331	72	is	be	AUX
iajs-2833	331	73	oqcccv	oqcccv	ADJ
iajs-2833	331	74	.	.	PUNCT
iajs-2833	332	1	5	5	X
iajs-2833	332	2	.	.	X
iajs-2833	332	3	conclusion	conclusion	VERB
iajs-2833	332	4	the	the	DET
iajs-2833	332	5	method	method	NOUN
iajs-2833	332	6	of	of	ADP
iajs-2833	332	7	galerkin	galerkin	NOUN
iajs-2833	332	8	with	with	ADP
iajs-2833	332	9	the	the	DET
iajs-2833	332	10	aubin	aubin	PROPN
iajs-2833	332	11	compactness	compactness	NOUN
iajs-2833	332	12	theorem	theorem	NOUN
iajs-2833	332	13	is	be	AUX
iajs-2833	332	14	used	use	VERB
iajs-2833	332	15	successfully	successfully	ADV
iajs-2833	332	16	to	to	PART
iajs-2833	332	17	demonstrate	demonstrate	VERB
iajs-2833	332	18	the	the	DET
iajs-2833	332	19	existence	existence	NOUN
iajs-2833	332	20	theorem	theorem	VERB
iajs-2833	332	21	of	of	ADP
iajs-2833	332	22	a	a	DET
iajs-2833	332	23	unique	unique	ADJ
iajs-2833	332	24	state	state	NOUN
iajs-2833	332	25	quaternary	quaternary	ADJ
iajs-2833	332	26	vector	vector	NOUN
iajs-2833	332	27	solution	solution	NOUN
iajs-2833	332	28	for	for	ADP
iajs-2833	332	29	the	the	DET
iajs-2833	332	30	weak	weak	ADJ
iajs-2833	332	31	form	form	NOUN
iajs-2833	332	32	for	for	ADP
iajs-2833	332	33	the	the	DET
iajs-2833	332	34	quaternary	quaternary	ADJ
iajs-2833	332	35	nonlinear	nonlinear	ADJ
iajs-2833	332	36	hyperbolic	hyperbolic	ADJ
iajs-2833	332	37	boundary	boundary	ADJ
iajs-2833	332	38	value	value	NOUN
iajs-2833	332	39	problem	problem	NOUN
iajs-2833	332	40	where	where	SCONJ
iajs-2833	332	41	the	the	DET
iajs-2833	332	42	classical	classical	ADJ
iajs-2833	332	43	continuous	continuous	ADJ
iajs-2833	332	44	control	control	NOUN
iajs-2833	332	45	quaternary	quaternary	ADJ
iajs-2833	332	46	vector	vector	NOUN
iajs-2833	332	47	is	be	AUX
iajs-2833	332	48	considered	consider	VERB
iajs-2833	332	49	given	give	VERB
iajs-2833	332	50	under	under	ADP
iajs-2833	332	51	suitable	suitable	ADJ
iajs-2833	332	52	hypotheses	hypothesis	NOUN
iajs-2833	332	53	.	.	PUNCT
iajs-2833	333	1	the	the	DET
iajs-2833	333	2	continuity	continuity	NOUN
iajs-2833	333	3	operator	operator	NOUN
iajs-2833	333	4	between	between	ADP
iajs-2833	333	5	the	the	DET
iajs-2833	333	6	state	state	NOUN
iajs-2833	333	7	quaternary	quaternary	ADJ
iajs-2833	333	8	vector	vector	NOUN
iajs-2833	333	9	solution	solution	NOUN
iajs-2833	333	10	of	of	ADP
iajs-2833	333	11	the	the	DET
iajs-2833	333	12	weak	weak	ADJ
iajs-2833	333	13	form	form	NOUN
iajs-2833	333	14	for	for	ADP
iajs-2833	333	15	the	the	DET
iajs-2833	333	16	quaternary	quaternary	ADJ
iajs-2833	333	17	nonlinear	nonlinear	ADJ
iajs-2833	333	18	hyperbolic	hyperbolic	ADJ
iajs-2833	333	19	boundary	boundary	ADJ
iajs-2833	333	20	value	value	NOUN
iajs-2833	333	21	problem	problem	NOUN
iajs-2833	333	22	and	and	CCONJ
iajs-2833	333	23	the	the	DET
iajs-2833	333	24	corresponding	corresponding	ADJ
iajs-2833	333	25	classical	classical	ADJ
iajs-2833	333	26	continuous	continuous	ADJ
iajs-2833	333	27	control	control	NOUN
iajs-2833	333	28	quaternary	quaternary	ADJ
iajs-2833	333	29	vector	vector	NOUN
iajs-2833	333	30	is	be	AUX
iajs-2833	333	31	demonstrated	demonstrate	VERB
iajs-2833	333	32	.	.	PUNCT
iajs-2833	334	1	the	the	DET
iajs-2833	334	2	existence	existence	NOUN
iajs-2833	334	3	theorem	theorem	NOUN
iajs-2833	334	4	of	of	ADP
iajs-2833	334	5	an	an	DET
iajs-2833	334	6	optimal	optimal	ADJ
iajs-2833	334	7	classical	classical	ADJ
iajs-2833	334	8	continuous	continuous	ADJ
iajs-2833	334	9	control	control	NOUN
iajs-2833	334	10	quaternary	quaternary	ADJ
iajs-2833	334	11	vector	vector	NOUN
iajs-2833	334	12	under	under	ADP
iajs-2833	334	13	suitable	suitable	ADJ
iajs-2833	334	14	hypotheses	hypothesis	NOUN
iajs-2833	334	15	is	be	AUX
iajs-2833	334	16	demonstrated	demonstrate	VERB
iajs-2833	334	17	.	.	PUNCT
iajs-2833	335	1	references	reference	NOUN
iajs-2833	335	2	1	1	NUM
iajs-2833	335	3	.	.	PUNCT
iajs-2833	335	4	grigorenko	grigorenko	PROPN
iajs-2833	335	5	,	,	PUNCT
iajs-2833	335	6	n.	n.	PROPN
iajs-2833	335	7	;	;	PUNCT
iajs-2833	335	8	grigorieva	grigorieva	PROPN
iajs-2833	335	9	,	,	PUNCT
iajs-2833	335	10	ѐ	ѐ	X
iajs-2833	335	11	.	.	PUNCT
iajs-2833	336	1	v.	v.	ADP
iajs-2833	336	2	;	;	PUNCT
iajs-2833	336	3	roi	roi	NOUN
iajs-2833	336	4	,	,	PUNCT
iajs-2833	336	5	p.	p.	PROPN
iajs-2833	336	6	k.	k.	PROPN
iajs-2833	336	7	;	;	PUNCT
iajs-2833	336	8	khailov	khailov	VERB
iajs-2833	336	9	,	,	PUNCT
iajs-2833	336	10	e.n	e.n	PROPN
iajs-2833	336	11	.	.	PROPN
iajs-2833	336	12	optimal	optimal	ADJ
iajs-2833	336	13	control	control	NOUN
iajs-2833	336	14	problems	problem	NOUN
iajs-2833	336	15	for	for	ADP
iajs-2833	336	16	a	a	DET
iajs-2833	336	17	mathematical	mathematical	ADJ
iajs-2833	336	18	model	model	NOUN
iajs-2833	336	19	of	of	ADP
iajs-2833	336	20	the	the	DET
iajs-2833	336	21	treatment	treatment	NOUN
iajs-2833	336	22	of	of	ADP
iajs-2833	336	23	psoriasis	psoriasis	NOUN
iajs-2833	336	24	,	,	PUNCT
iajs-2833	336	25	computational	computational	ADJ
iajs-2833	336	26	mathematics	mathematic	NOUN
iajs-2833	336	27	and	and	CCONJ
iajs-2833	336	28	modeling	modeling	NOUN
iajs-2833	336	29	.	.	PUNCT
iajs-2833	337	1	2019	2019	NUM
iajs-2833	337	2	,	,	PUNCT
iajs-2833	337	3	304	304	NUM
iajs-2833	337	4	,	,	PUNCT
iajs-2833	337	5	352	352	NUM
iajs-2833	337	6	-	-	SYM
iajs-2833	337	7	363	363	NUM
iajs-2833	337	8	.	.	PUNCT
iajs-2833	338	1	2	2	NUM
iajs-2833	338	2	.	.	X
iajs-2833	338	3	syahrini	syahrini	PROPN
iajs-2833	338	4	,	,	PUNCT
iajs-2833	338	5	i.	i.	NOUN
iajs-2833	338	6	;	;	PUNCT
iajs-2833	338	7	masabar	masabar	PROPN
iajs-2833	338	8	,	,	PUNCT
iajs-2833	338	9	r.	r.	PROPN
iajs-2833	338	10	;	;	PUNCT
iajs-2833	338	11	aliasuddin	aliasuddin	PROPN
iajs-2833	338	12	,	,	PUNCT
iajs-2833	338	13	a.	a.	NOUN
iajs-2833	338	14	;	;	PUNCT
iajs-2833	338	15	munzir	munzir	NOUN
iajs-2833	338	16	,	,	PUNCT
iajs-2833	338	17	s.	s.	PROPN
iajs-2833	338	18	;	;	PUNCT
iajs-2833	338	19	hazim	hazim	NOUN
iajs-2833	338	20	,	,	PUNCT
iajs-2833	338	21	y.	y.	VERB
iajs-2833	338	22	the	the	DET
iajs-2833	338	23	application	application	NOUN
iajs-2833	338	24	of	of	ADP
iajs-2833	338	25	optimal	optimal	ADJ
iajs-2833	338	26	control	control	NOUN
iajs-2833	338	27	through	through	ADP
iajs-2833	338	28	fiscal	fiscal	ADJ
iajs-2833	338	29	policy	policy	NOUN
iajs-2833	338	30	on	on	ADP
iajs-2833	338	31	indonesian	indonesian	ADJ
iajs-2833	338	32	economy	economy	NOUN
iajs-2833	338	33	.	.	PUNCT
iajs-2833	339	1	the	the	DET
iajs-2833	339	2	journal	journal	NOUN
iajs-2833	339	3	of	of	ADP
iajs-2833	339	4	asian	asian	ADJ
iajs-2833	339	5	finance	finance	NOUN
iajs-2833	339	6	,	,	PUNCT
iajs-2833	339	7	economics	economic	NOUN
iajs-2833	339	8	and	and	CCONJ
iajs-2833	339	9	business	business	NOUN
iajs-2833	339	10	.	.	PUNCT
iajs-2833	340	1	2021	2021	NUM
iajs-2833	340	2	,	,	PUNCT
iajs-2833	340	3	8	8	NUM
iajs-2833	340	4	,	,	PUNCT
iajs-2833	340	5	3	3	NUM
iajs-2833	340	6	,	,	PUNCT
iajs-2833	340	7	0741	0741	NUM
iajs-2833	340	8	-	-	SYM
iajs-2833	340	9	0750	0750	NUM
iajs-2833	340	10	.	.	PUNCT
iajs-2833	341	1	3	3	X
iajs-2833	341	2	.	.	X
iajs-2833	341	3	rigatos	rigato	NOUN
iajs-2833	341	4	,	,	PUNCT
iajs-2833	341	5	g.	g.	PROPN
iajs-2833	341	6	;	;	PUNCT
iajs-2833	341	7	abbaszadeh	abbaszadeh	PROPN
iajs-2833	341	8	,	,	PUNCT
iajs-2833	341	9	m.	m.	NOUN
iajs-2833	341	10	nonlinear	nonlinear	PROPN
iajs-2833	341	11	optimal	optimal	ADJ
iajs-2833	341	12	control	control	NOUN
iajs-2833	341	13	for	for	ADP
iajs-2833	341	14	multi	multi	ADJ
iajs-2833	341	15	-	-	ADJ
iajs-2833	341	16	dof	dof	ADJ
iajs-2833	341	17	robotic	robotic	ADJ
iajs-2833	341	18	manipulators	manipulator	NOUN
iajs-2833	341	19	with	with	ADP
iajs-2833	341	20	flexible	flexible	ADJ
iajs-2833	341	21	joints	joint	NOUN
iajs-2833	341	22	.	.	PUNCT
iajs-2833	342	1	optimal	optimal	ADJ
iajs-2833	342	2	control	control	NOUN
iajs-2833	342	3	applications	application	NOUN
iajs-2833	342	4	and	and	CCONJ
iajs-2833	342	5	methods	method	NOUN
iajs-2833	342	6	.	.	PUNCT
iajs-2833	343	1	2021,6,1708	2021,6,1708	NUM
iajs-2833	343	2	1733	1733	NUM
iajs-2833	343	3	.	.	PUNCT
iajs-2833	344	1	4	4	X
iajs-2833	344	2	.	.	X
iajs-2833	344	3	kahina	kahina	PROPN
iajs-2833	344	4	,	,	PUNCT
iajs-2833	344	5	l.	l.	PROPN
iajs-2833	344	6	;	;	PUNCT
iajs-2833	344	7	spiteri	spiteri	NOUN
iajs-2833	344	8	,	,	PUNCT
iajs-2833	344	9	p.	p.	NOUN
iajs-2833	344	10	;	;	PUNCT
iajs-2833	344	11	demim	demim	PROPN
iajs-2833	344	12	,	,	PUNCT
iajs-2833	344	13	f.	f.	PROPN
iajs-2833	344	14	;	;	PUNCT
iajs-2833	344	15	mohamed	mohamed	PROPN
iajs-2833	344	16	,	,	PUNCT
iajs-2833	344	17	a.	a.	NOUN
iajs-2833	344	18	;	;	PUNCT
iajs-2833	344	19	nemra	nemra	NOUN
iajs-2833	344	20	,	,	PUNCT
iajs-2833	344	21	a.	a.	NOUN
iajs-2833	344	22	;	;	PUNCT
iajs-2833	344	23	messine	messine	PROPN
iajs-2833	344	24	,	,	PUNCT
iajs-2833	344	25	f.	f.	PROPN
iajs-2833	344	26	application	application	PROPN
iajs-2833	344	27	optimal	optimal	ADJ
iajs-2833	344	28	control	control	NOUN
iajs-2833	344	29	for	for	ADP
iajs-2833	344	30	a	a	DET
iajs-2833	344	31	problem	problem	NOUN
iajs-2833	344	32	aircraft	aircraft	NOUN
iajs-2833	344	33	flight	flight	NOUN
iajs-2833	344	34	,	,	PUNCT
iajs-2833	344	35	journal	journal	NOUN
iajs-2833	344	36	of	of	ADP
iajs-2833	344	37	engineering	engineering	NOUN
iajs-2833	344	38	science	science	NOUN
iajs-2833	344	39	and	and	CCONJ
iajs-2833	344	40	technology	technology	NOUN
iajs-2833	344	41	review	review	NOUN
iajs-2833	344	42	.	.	PUNCT
iajs-2833	345	1	2018	2018	NUM
iajs-2833	345	2	,	,	PUNCT
iajs-2833	345	3	11	11	NUM
iajs-2833	345	4	,	,	PUNCT
iajs-2833	345	5	156	156	NUM
iajs-2833	345	6	-	-	SYM
iajs-2833	345	7	164	164	NUM
iajs-2833	345	8	.	.	PUNCT
iajs-2833	346	1	5	5	NUM
iajs-2833	346	2	.	.	X
iajs-2833	346	3	bors	bor	NOUN
iajs-2833	346	4	,	,	PUNCT
iajs-2833	346	5	d.	d.	PROPN
iajs-2833	346	6	;	;	PUNCT
iajs-2833	346	7	walczak	walczak	PROPN
iajs-2833	346	8	,	,	PUNCT
iajs-2833	346	9	s.	s.	PROPN
iajs-2833	346	10	optimal	optimal	ADJ
iajs-2833	346	11	control	control	PROPN
iajs-2833	346	12	elliptic	elliptic	ADJ
iajs-2833	346	13	systems	system	NOUN
iajs-2833	346	14	with	with	ADP
iajs-2833	346	15	distributed	distribute	VERB
iajs-2833	346	16	and	and	CCONJ
iajs-2833	346	17	boundary	boundary	ADJ
iajs-2833	346	18	controls	control	NOUN
iajs-2833	346	19	.	.	PUNCT
iajs-2833	347	1	nonlinear	nonlinear	ADJ
iajs-2833	347	2	analysis	analysis	NOUN
iajs-2833	347	3	.	.	PUNCT
iajs-2833	348	1	2005	2005	NUM
iajs-2833	348	2	,	,	PUNCT
iajs-2833	348	3	63,5	63,5	NOUN
iajs-2833	348	4	-	-	SYM
iajs-2833	348	5	7,1367	7,1367	NOUN
iajs-2833	348	6	-	-	NOUN
iajs-2833	348	7	1376	1376	NUM
iajs-2833	348	8	.	.	PUNCT
iajs-2833	349	1	6	6	NUM
iajs-2833	349	2	.	.	X
iajs-2833	350	1	al	al	PROPN
iajs-2833	350	2	-	-	PUNCT
iajs-2833	350	3	hawasy	hawasy	PROPN
iajs-2833	350	4	,	,	PUNCT
iajs-2833	350	5	j.	j.	PROPN
iajs-2833	351	1	“	"	PUNCT
iajs-2833	351	2	the	the	DET
iajs-2833	351	3	continuous	continuous	ADJ
iajs-2833	351	4	classical	classical	ADJ
iajs-2833	351	5	optimal	optimal	ADJ
iajs-2833	351	6	control	control	NOUN
iajs-2833	351	7	problem	problem	NOUN
iajs-2833	351	8	of	of	ADP
iajs-2833	351	9	a	a	DET
iajs-2833	351	10	nonlinear	nonlinear	ADJ
iajs-2833	351	11	hyperbolic	hyperbolic	ADJ
iajs-2833	351	12	partial	partial	ADJ
iajs-2833	351	13	differential	differential	NOUN
iajs-2833	351	14	equations	equation	NOUN
iajs-2833	351	15	(	(	PUNCT
iajs-2833	351	16	ccocp	ccocp	NOUN
iajs-2833	351	17	)	)	PUNCT
iajs-2833	351	18	”	"	PUNCT
iajs-2833	351	19	,	,	PUNCT
iajs-2833	351	20	al	al	PROPN
iajs-2833	351	21	-	-	PUNCT
iajs-2833	351	22	mustansiriyah	mustansiriyah	PROPN
iajs-2833	351	23	journal	journal	NOUN
iajs-2833	351	24	of	of	ADP
iajs-2833	351	25	science	science	NOUN
iajs-2833	351	26	.	.	PUNCT
iajs-2833	352	1	2008	2008	NUM
iajs-2833	352	2	,	,	PUNCT
iajs-2833	352	3	19	19	NUM
iajs-2833	352	4	,	,	PUNCT
iajs-2833	352	5	3	3	NUM
iajs-2833	352	6	,	,	PUNCT
iajs-2833	352	7	96	96	NUM
iajs-2833	352	8	-	-	SYM
iajs-2833	352	9	110	110	NUM
iajs-2833	352	10	,	,	PUNCT
iajs-2833	352	11	.	.	PUNCT
iajs-2833	353	1	7	7	X
iajs-2833	353	2	.	.	NUM
iajs-2833	353	3	chryssoverghi	chryssoverghi	PROPN
iajs-2833	353	4	i.	i.	PROPN
iajs-2833	353	5	,	,	PUNCT
iajs-2833	353	6	al	al	PROPN
iajs-2833	353	7	-	-	PUNCT
iajs-2833	353	8	hawasy	hawasy	PROPN
iajs-2833	353	9	j.	j.	PROPN
iajs-2833	353	10	the	the	DET
iajs-2833	353	11	continuous	continuous	ADJ
iajs-2833	353	12	classical	classical	ADJ
iajs-2833	353	13	optimal	optimal	ADJ
iajs-2833	353	14	control	control	NOUN
iajs-2833	353	15	problem	problem	NOUN
iajs-2833	353	16	of	of	ADP
iajs-2833	353	17	semi	semi	ADJ
iajs-2833	353	18	linear	linear	PROPN
iajs-2833	353	19	parabolic	parabolic	ADJ
iajs-2833	353	20	equations	equation	NOUN
iajs-2833	353	21	(	(	PUNCT
iajs-2833	353	22	ccocp	ccocp	NOUN
iajs-2833	353	23	)	)	PUNCT
iajs-2833	353	24	,	,	PUNCT
iajs-2833	353	25	journal	journal	NOUN
iajs-2833	353	26	of	of	ADP
iajs-2833	353	27	karbala	karbala	PROPN
iajs-2833	353	28	university	university	PROPN
iajs-2833	353	29	.	.	PUNCT
iajs-2833	354	1	2010,8,3	2010,8,3	NUM
iajs-2833	354	2	.	.	NOUN
iajs-2833	354	3	8	8	NUM
iajs-2833	354	4	.	.	PUNCT
iajs-2833	355	1	al	al	PROPN
iajs-2833	355	2	-	-	PUNCT
iajs-2833	355	3	hawasy	hawasy	PROPN
iajs-2833	355	4	j.	j.	PROPN
iajs-2833	355	5	,	,	PUNCT
iajs-2833	355	6	and	and	CCONJ
iajs-2833	355	7	al	al	PROPN
iajs-2833	355	8	-	-	PUNCT
iajs-2833	355	9	rawdhanee	rawdhanee	NOUN
iajs-2833	355	10	e.	e.	PROPN
iajs-2833	355	11	h	h	PROPN
iajs-2833	355	12	,	,	PUNCT
iajs-2833	355	13	the	the	DET
iajs-2833	355	14	continuous	continuous	ADJ
iajs-2833	355	15	classical	classical	ADJ
iajs-2833	355	16	optimal	optimal	ADJ
iajs-2833	355	17	control	control	NOUN
iajs-2833	355	18	of	of	ADP
iajs-2833	355	19	a	a	DET
iajs-2833	355	20	couple	couple	NOUN
iajs-2833	355	21	of	of	ADP
iajs-2833	355	22	non	non	ADJ
iajs-2833	355	23	-	-	ADJ
iajs-2833	355	24	linear	linear	ADJ
iajs-2833	355	25	elliptic	elliptic	ADJ
iajs-2833	355	26	equation	equation	NOUN
iajs-2833	355	27	”	"	PUNCT
iajs-2833	355	28	,	,	PUNCT
iajs-2833	355	29	mathematical	mathematical	ADJ
iajs-2833	355	30	theory	theory	NOUN
iajs-2833	355	31	and	and	CCONJ
iajs-2833	355	32	modeling	modeling	NOUN
iajs-2833	355	33	.	.	PUNCT
iajs-2833	356	1	2014,4,14	2014,4,14	X
iajs-2833	356	2	.	.	PUNCT
iajs-2833	357	1	9	9	X
iajs-2833	357	2	.	.	X
iajs-2833	358	1	al	al	PROPN
iajs-2833	358	2	-	-	PUNCT
iajs-2833	358	3	hawasy	hawasy	PROPN
iajs-2833	358	4	j.	j.	PROPN
iajs-2833	358	5	the	the	DET
iajs-2833	358	6	continuous	continuous	ADJ
iajs-2833	358	7	classical	classical	ADJ
iajs-2833	358	8	optimal	optimal	ADJ
iajs-2833	358	9	control	control	NOUN
iajs-2833	358	10	of	of	ADP
iajs-2833	358	11	a	a	DET
iajs-2833	358	12	coupled	couple	VERB
iajs-2833	358	13	nonlinear	nonlinear	ADJ
iajs-2833	358	14	hyperbolic	hyperbolic	ADJ
iajs-2833	358	15	partial	partial	ADJ
iajs-2833	358	16	differential	differential	NOUN
iajs-2833	358	17	equations	equation	NOUN
iajs-2833	358	18	with	with	ADP
iajs-2833	358	19	equality	equality	NOUN
iajs-2833	358	20	and	and	CCONJ
iajs-2833	358	21	inequality	inequality	NOUN
iajs-2833	358	22	constraints	constraint	NOUN
iajs-2833	358	23	,	,	PUNCT
iajs-2833	358	24	iraqi	iraqi	ADJ
iajs-2833	358	25	journal	journal	NOUN
iajs-2833	358	26	of	of	ADP
iajs-2833	358	27	science	science	NOUN
iajs-2833	358	28	.	.	PUNCT
iajs-2833	359	1	2016,57	2016,57	NUM
iajs-2833	359	2	,	,	PUNCT
iajs-2833	359	3	2c	2c	NUM
iajs-2833	359	4	,	,	PUNCT
iajs-2833	359	5	1528	1528	NUM
iajs-2833	359	6	-	-	SYM
iajs-2833	359	7	1538	1538	NUM
iajs-2833	359	8	.	.	PUNCT
iajs-2833	360	1	ihjpas	ihjpas	PROPN
iajs-2833	360	2	.	.	PUNCT
iajs-2833	361	1	53	53	NUM
iajs-2833	361	2	(	(	PUNCT
iajs-2833	361	3	3)2022	3)2022	NOUN
iajs-2833	361	4	174	174	NUM
iajs-2833	361	5	10	10	NUM
iajs-2833	361	6	.	.	PUNCT
iajs-2833	362	1	al	al	PROPN
iajs-2833	362	2	-	-	PUNCT
iajs-2833	362	3	hawasy	hawasy	PROPN
iajs-2833	362	4	,	,	PUNCT
iajs-2833	362	5	j.	j.	PROPN
iajs-2833	362	6	;	;	PUNCT
iajs-2833	362	7	kadhem	kadhem	PROPN
iajs-2833	362	8	,	,	PUNCT
iajs-2833	362	9	g.m	g.m	PROPN
iajs-2833	362	10	.	.	PUNCT
iajs-2833	363	1	the	the	DET
iajs-2833	363	2	continuous	continuous	ADJ
iajs-2833	363	3	classical	classical	ADJ
iajs-2833	363	4	optimal	optimal	ADJ
iajs-2833	363	5	control	control	NOUN
iajs-2833	363	6	for	for	ADP
iajs-2833	363	7	a	a	DET
iajs-2833	363	8	coupled	couple	VERB
iajs-2833	363	9	nonlinear	nonlinear	ADJ
iajs-2833	363	10	parabolic	parabolic	ADJ
iajs-2833	363	11	partial	partial	ADJ
iajs-2833	363	12	differential	differential	NOUN
iajs-2833	363	13	equations	equation	NOUN
iajs-2833	363	14	with	with	ADP
iajs-2833	363	15	equality	equality	NOUN
iajs-2833	363	16	and	and	CCONJ
iajs-2833	363	17	inequality	inequality	NOUN
iajs-2833	363	18	constraints	constraint	NOUN
iajs-2833	363	19	.	.	PUNCT
iajs-2833	364	1	journal	journal	PROPN
iajs-2833	364	2	of	of	ADP
iajs-2833	364	3	al	al	PROPN
iajs-2833	364	4	-	-	PUNCT
iajs-2833	364	5	nahrain	nahrain	PROPN
iajs-2833	364	6	university	university	NOUN
iajs-2833	364	7	,	,	PUNCT
iajs-2833	364	8	2016,19	2016,19	NUM
iajs-2833	364	9	,	,	PUNCT
iajs-2833	364	10	1	1	NUM
iajs-2833	364	11	,	,	PUNCT
iajs-2833	364	12	173	173	NUM
iajs-2833	364	13	-	-	SYM
iajs-2833	364	14	186	186	NUM
iajs-2833	364	15	.	.	PUNCT
iajs-2833	364	16	11	11	NUM
iajs-2833	364	17	.	.	PUNCT
iajs-2833	365	1	al	al	PROPN
iajs-2833	365	2	-	-	PUNCT
iajs-2833	365	3	hawasy	hawasy	PROPN
iajs-2833	365	4	j.	j.	PROPN
iajs-2833	365	5	,	,	PUNCT
iajs-2833	365	6	jasim	jasim	PROPN
iajs-2833	365	7	d.	d.	PROPN
iajs-2833	365	8	k.the	k.the	PRON
iajs-2833	365	9	continuous	continuous	ADJ
iajs-2833	365	10	classical	classical	ADJ
iajs-2833	365	11	optimal	optimal	ADJ
iajs-2833	365	12	control	control	NOUN
iajs-2833	365	13	problems	problem	NOUN
iajs-2833	365	14	for	for	ADP
iajs-2833	365	15	triple	triple	ADJ
iajs-2833	365	16	nonlinear	nonlinear	ADJ
iajs-2833	365	17	elliptic	elliptic	ADJ
iajs-2833	365	18	boundary	boundary	ADJ
iajs-2833	365	19	value	value	NOUN
iajs-2833	365	20	problem	problem	NOUN
iajs-2833	365	21	.	.	PUNCT
iajs-2833	366	1	ibn	ibn	PROPN
iajs-2833	366	2	al	al	PROPN
iajs-2833	366	3	-	-	PUNCT
iajs-2833	366	4	haitham	haitham	PROPN
iajs-2833	366	5	jour	jour	X
iajs-2833	366	6	.	.	PUNCT
iajs-2833	367	1	for	for	ADP
iajs-2833	367	2	pure	pure	ADJ
iajs-2833	367	3	and	and	CCONJ
iajs-2833	367	4	applied	applied	ADJ
iajs-2833	367	5	sciences	science	NOUN
iajs-2833	367	6	.	.	PUNCT
iajs-2833	368	1	2020	2020	NUM
iajs-2833	368	2	,	,	PUNCT
iajs-2833	368	3	33	33	NUM
iajs-2833	368	4	,	,	PUNCT
iajs-2833	368	5	3	3	NUM
iajs-2833	368	6	,	,	PUNCT
iajs-2833	368	7	101	101	NUM
iajs-2833	368	8	-	-	SYM
iajs-2833	368	9	112	112	NUM
iajs-2833	368	10	.	.	PUNCT
iajs-2833	369	1	12	12	NUM
iajs-2833	369	2	.	.	PUNCT
iajs-2833	370	1	al	al	PROPN
iajs-2833	370	2	-	-	PUNCT
iajs-2833	370	3	hawasy	hawasy	PROPN
iajs-2833	370	4	,	,	PUNCT
iajs-2833	370	5	j.	j.	PROPN
iajs-2833	370	6	;	;	PUNCT
iajs-2833	370	7	rasheed	rasheed	PROPN
iajs-2833	370	8	,	,	PUNCT
iajs-2833	370	9	th	th	X
iajs-2833	370	10	.	.	PUNCT
iajs-2833	371	1	continuous	continuous	ADJ
iajs-2833	371	2	classical	classical	ADJ
iajs-2833	371	3	optimal	optimal	ADJ
iajs-2833	371	4	control	control	NOUN
iajs-2833	371	5	of	of	ADP
iajs-2833	371	6	triple	triple	ADJ
iajs-2833	371	7	nonlinear	nonlinear	ADJ
iajs-2833	371	8	parabolic	parabolic	ADJ
iajs-2833	371	9	partial	partial	ADJ
iajs-2833	371	10	differential	differential	NOUN
iajs-2833	371	11	equation	equation	NOUN
iajs-2833	371	12	,	,	PUNCT
iajs-2833	371	13	iraqi	iraqi	ADJ
iajs-2833	371	14	j.	j.	PROPN
iajs-2833	371	15	sci	sci	PROPN
iajs-2833	371	16	.	.	PUNCT
iajs-2833	372	1	2022,63,2,690	2022,63,2,690	NUM
iajs-2833	372	2	-	-	SYM
iajs-2833	372	3	701	701	NUM
iajs-2833	372	4	.	.	NOUN
iajs-2833	373	1	13	13	NUM
iajs-2833	373	2	.	.	PUNCT
iajs-2833	374	1	al	al	PROPN
iajs-2833	374	2	-	-	PUNCT
iajs-2833	374	3	hawasy	hawasy	PROPN
iajs-2833	374	4	,	,	PUNCT
iajs-2833	374	5	j.a	j.a	PROPN
iajs-2833	374	6	.	.	PROPN
iajs-2833	374	7	;	;	PUNCT
iajs-2833	374	8	ali	ali	PROPN
iajs-2833	374	9	,	,	PUNCT
iajs-2833	374	10	l.h	l.h	PROPN
iajs-2833	374	11	.	.	PROPN
iajs-2833	374	12	constraints	constraint	VERB
iajs-2833	374	13	optimal	optimal	ADJ
iajs-2833	374	14	control	control	NOUN
iajs-2833	374	15	governing	govern	VERB
iajs-2833	374	16	by	by	ADP
iajs-2833	374	17	triple	triple	ADJ
iajs-2833	374	18	nonlinear	nonlinear	ADJ
iajs-2833	374	19	hyperbolic	hyperbolic	ADJ
iajs-2833	374	20	boundary	boundary	ADJ
iajs-2833	374	21	value	value	NOUN
iajs-2833	374	22	problem	problem	NOUN
iajs-2833	374	23	.	.	PUNCT
iajs-2833	375	1	hindawi	hindawi	ADJ
iajs-2833	375	2	.	.	PUNCT
iajs-2833	376	1	journal	journal	PROPN
iajs-2833	376	2	of	of	ADP
iajs-2833	376	3	applied	apply	VERB
iajs-2833	376	4	mathematics	mathematic	NOUN
iajs-2833	376	5	,	,	PUNCT
iajs-2833	376	6	2020	2020	NUM
iajs-2833	376	7	.	.	PUNCT
iajs-2833	377	1	14	14	NUM
iajs-2833	377	2	.	.	X
iajs-2833	377	3	chryssoverghi	chryssoverghi	PROPN
iajs-2833	377	4	,	,	PUNCT
iajs-2833	377	5	i.	i.	NOUN
iajs-2833	377	6	optimization	optimization	NOUN
iajs-2833	377	7	.	.	PUNCT
iajs-2833	378	1	national	national	PROPN
iajs-2833	378	2	technical	technical	PROPN
iajs-2833	378	3	university	university	PROPN
iajs-2833	378	4	of	of	ADP
iajs-2833	378	5	athens	athens	PROPN
iajs-2833	378	6	-	-	PUNCT
iajs-2833	378	7	greece	greece	PROPN
iajs-2833	378	8	,	,	PUNCT
iajs-2833	378	9	2003	2003	NUM
iajs-2833	378	10	.	.	PUNCT
iajs-2833	379	1	15	15	NUM
iajs-2833	379	2	temam	temam	NOUN
iajs-2833	379	3	,	,	PUNCT
iajs-2833	379	4	r.	r.	PROPN
iajs-2833	379	5	navier	navier	PROPN
iajs-2833	379	6	-	-	PUNCT
iajs-2833	379	7	stokes	stokes	PROPN
iajs-2833	379	8	equations	equation	NOUN
iajs-2833	379	9	.	.	PUNCT
iajs-2833	380	1	northholand	northholand	PROPN
iajs-2833	380	2	publishing	publishing	PROPN
iajs-2833	380	3	company,1977	company,1977	PROPN
iajs-2833	380	4	.	.	PUNCT