id	sid	tid	token	lemma	pos
iajs-2816	1	1	135	135	NUM
iajs-2816	1	2	this	this	DET
iajs-2816	1	3	work	work	NOUN
iajs-2816	1	4	is	be	AUX
iajs-2816	1	5	licensed	license	VERB
iajs-2816	1	6	under	under	ADP
iajs-2816	1	7	a	a	DET
iajs-2816	1	8	creative	creative	ADJ
iajs-2816	1	9	commons	common	NOUN
iajs-2816	1	10	attribution	attribution	NOUN
iajs-2816	1	11	4.0	4.0	NUM
iajs-2816	1	12	international	international	ADJ
iajs-2816	1	13	license	license	NOUN
iajs-2816	1	14	.	.	PUNCT
iajs-2816	2	1	the	the	DET
iajs-2816	2	2	classical	classical	ADJ
iajs-2816	2	3	continuous	continuous	ADJ
iajs-2816	2	4	optimal	optimal	ADJ
iajs-2816	2	5	control	control	NOUN
iajs-2816	2	6	for	for	ADP
iajs-2816	2	7	quaternary	quaternary	ADJ
iajs-2816	2	8	nonlinear	nonlinear	ADJ
iajs-2816	2	9	parabolic	parabolic	PROPN
iajs-2816	2	10	boundary	boundary	ADJ
iajs-2816	2	11	value	value	NOUN
iajs-2816	2	12	problems	problem	NOUN
iajs-2816	2	13	with	with	ADP
iajs-2816	2	14	state	state	NOUN
iajs-2816	2	15	vector	vector	NOUN
iajs-2816	2	16	constraints	constraint	NOUN
iajs-2816	2	17	1jamil	1jamil	NUM
iajs-2816	2	18	a.	a.	NOUN
iajs-2816	2	19	ali	ali	PROPN
iajs-2816	3	1	al	al	PROPN
iajs-2816	3	2	-	-	PROPN
iajs-2816	3	3	hawasy	hawasy	PROPN
iajs-2816	3	4	2wissam	2wissam	NUM
iajs-2816	3	5	a.	a.	NOUN
iajs-2816	3	6	abdul	abdul	PROPN
iajs-2816	3	7	-	-	PUNCT
iajs-2816	3	8	hussien	hussien	PROPN
iajs-2816	3	9	al	al	PROPN
iajs-2816	3	10	-	-	PUNCT
iajs-2816	3	11	anbaki	anbaki	PROPN
iajs-2816	3	12	1	1	NUM
iajs-2816	3	13	-	-	SYM
iajs-2816	3	14	2department	2department	NUM
iajs-2816	3	15	of	of	ADP
iajs-2816	3	16	mathematics	mathematic	NOUN
iajs-2816	3	17	,	,	PUNCT
iajs-2816	3	18	college	college	NOUN
iajs-2816	3	19	of	of	ADP
iajs-2816	3	20	science	science	NOUN
iajs-2816	3	21	,	,	PUNCT
iajs-2816	3	22	mustansiriyah	mustansiriyah	NOUN
iajs-2816	3	23	university	university	NOUN
iajs-2816	3	24	,	,	PUNCT
iajs-2816	3	25	baghdad	baghdad	PROPN
iajs-2816	3	26	,	,	PUNCT
iajs-2816	3	27	iraq	iraq	PROPN
iajs-2816	3	28	.	.	PUNCT
iajs-2816	4	1	jhawassy17@uomustansiriyah.edu.iq	jhawassy17@uomustansiriyah.edu.iq	ADJ
iajs-2816	4	2	wissamali14595@uomustansiriyah.edu.iq	wissamali14595@uomustansiriyah.edu.iq	ADJ
iajs-2816	4	3	abstract	abstract	NOUN
iajs-2816	4	4	this	this	DET
iajs-2816	4	5	paper	paper	NOUN
iajs-2816	4	6	aims	aim	VERB
iajs-2816	4	7	to	to	PART
iajs-2816	4	8	study	study	VERB
iajs-2816	4	9	the	the	DET
iajs-2816	4	10	quaternary	quaternary	ADJ
iajs-2816	4	11	classical	classical	ADJ
iajs-2816	4	12	continuous	continuous	ADJ
iajs-2816	4	13	optimal	optimal	ADJ
iajs-2816	4	14	control	control	NOUN
iajs-2816	4	15	problem	problem	NOUN
iajs-2816	4	16	consisting	consist	VERB
iajs-2816	4	17	of	of	ADP
iajs-2816	4	18	the	the	DET
iajs-2816	4	19	quaternary	quaternary	ADJ
iajs-2816	4	20	nonlinear	nonlinear	PROPN
iajs-2816	4	21	parabolic	parabolic	PROPN
iajs-2816	4	22	boundary	boundary	ADJ
iajs-2816	4	23	value	value	NOUN
iajs-2816	4	24	problem	problem	NOUN
iajs-2816	4	25	,	,	PUNCT
iajs-2816	4	26	the	the	DET
iajs-2816	4	27	cost	cost	NOUN
iajs-2816	4	28	function	function	NOUN
iajs-2816	4	29	,	,	PUNCT
iajs-2816	4	30	and	and	CCONJ
iajs-2816	4	31	the	the	DET
iajs-2816	4	32	equality	equality	NOUN
iajs-2816	4	33	and	and	CCONJ
iajs-2816	4	34	inequality	inequality	NOUN
iajs-2816	4	35	constraints	constraint	NOUN
iajs-2816	4	36	on	on	ADP
iajs-2816	4	37	the	the	DET
iajs-2816	4	38	state	state	NOUN
iajs-2816	4	39	and	and	CCONJ
iajs-2816	4	40	the	the	DET
iajs-2816	4	41	control	control	NOUN
iajs-2816	4	42	.	.	PUNCT
iajs-2816	5	1	under	under	ADP
iajs-2816	5	2	appropriate	appropriate	ADJ
iajs-2816	5	3	hypotheses	hypothesis	NOUN
iajs-2816	5	4	,	,	PUNCT
iajs-2816	5	5	it	it	PRON
iajs-2816	5	6	is	be	AUX
iajs-2816	5	7	demonstrated	demonstrate	VERB
iajs-2816	5	8	that	that	SCONJ
iajs-2816	5	9	the	the	DET
iajs-2816	5	10	quaternary	quaternary	ADJ
iajs-2816	5	11	classical	classical	ADJ
iajs-2816	5	12	continuous	continuous	ADJ
iajs-2816	5	13	optimal	optimal	ADJ
iajs-2816	5	14	control	control	NOUN
iajs-2816	5	15	ruling	ruling	NOUN
iajs-2816	5	16	by	by	ADP
iajs-2816	5	17	the	the	DET
iajs-2816	5	18	quaternary	quaternary	PROPN
iajs-2816	5	19	nonlinear	nonlinear	PROPN
iajs-2816	5	20	parabolic	parabolic	PROPN
iajs-2816	5	21	boundary	boundary	ADJ
iajs-2816	5	22	value	value	NOUN
iajs-2816	5	23	problem	problem	NOUN
iajs-2816	5	24	has	have	VERB
iajs-2816	5	25	a	a	DET
iajs-2816	5	26	quaternary	quaternary	ADJ
iajs-2816	5	27	classical	classical	ADJ
iajs-2816	5	28	continuous	continuous	ADJ
iajs-2816	5	29	optimal	optimal	ADJ
iajs-2816	5	30	control	control	NOUN
iajs-2816	5	31	vector	vector	NOUN
iajs-2816	5	32	that	that	PRON
iajs-2816	5	33	satisfies	satisfy	VERB
iajs-2816	5	34	the	the	DET
iajs-2816	5	35	equality	equality	NOUN
iajs-2816	5	36	constraint	constraint	NOUN
iajs-2816	5	37	and	and	CCONJ
iajs-2816	5	38	inequality	inequality	NOUN
iajs-2816	5	39	state	state	NOUN
iajs-2816	5	40	and	and	CCONJ
iajs-2816	5	41	control	control	NOUN
iajs-2816	5	42	constraint	constraint	NOUN
iajs-2816	5	43	.	.	PUNCT
iajs-2816	6	1	moreover	moreover	ADV
iajs-2816	6	2	,	,	PUNCT
iajs-2816	6	3	mathematical	mathematical	ADJ
iajs-2816	6	4	formulation	formulation	NOUN
iajs-2816	6	5	of	of	ADP
iajs-2816	6	6	the	the	DET
iajs-2816	6	7	quaternary	quaternary	ADJ
iajs-2816	6	8	adjoint	adjoint	NOUN
iajs-2816	6	9	equations	equation	NOUN
iajs-2816	6	10	related	relate	VERB
iajs-2816	6	11	to	to	ADP
iajs-2816	6	12	the	the	DET
iajs-2816	6	13	quaternary	quaternary	ADJ
iajs-2816	6	14	state	state	NOUN
iajs-2816	6	15	equations	equation	NOUN
iajs-2816	6	16	is	be	AUX
iajs-2816	6	17	discovered	discover	VERB
iajs-2816	6	18	,	,	PUNCT
iajs-2816	6	19	and	and	CCONJ
iajs-2816	6	20	then	then	ADV
iajs-2816	6	21	the	the	DET
iajs-2816	6	22	weak	weak	ADJ
iajs-2816	6	23	form	form	NOUN
iajs-2816	6	24	of	of	ADP
iajs-2816	6	25	the	the	DET
iajs-2816	6	26	quaternary	quaternary	ADJ
iajs-2816	6	27	adjoint	adjoint	NOUN
iajs-2816	6	28	equations	equation	NOUN
iajs-2816	6	29	is	be	AUX
iajs-2816	6	30	obtained	obtain	VERB
iajs-2816	6	31	.	.	PUNCT
iajs-2816	7	1	lastly	lastly	ADV
iajs-2816	7	2	,	,	PUNCT
iajs-2816	7	3	both	both	CCONJ
iajs-2816	7	4	the	the	DET
iajs-2816	7	5	necessary	necessary	ADJ
iajs-2816	7	6	conditions	condition	NOUN
iajs-2816	7	7	for	for	ADP
iajs-2816	7	8	optimality	optimality	NOUN
iajs-2816	7	9	and	and	CCONJ
iajs-2816	7	10	sufficient	sufficient	ADJ
iajs-2816	7	11	conditions	condition	NOUN
iajs-2816	7	12	for	for	ADP
iajs-2816	7	13	optimality	optimality	NOUN
iajs-2816	7	14	of	of	ADP
iajs-2816	7	15	the	the	DET
iajs-2816	7	16	proposed	propose	VERB
iajs-2816	7	17	problem	problem	NOUN
iajs-2816	7	18	are	be	AUX
iajs-2816	7	19	stated	state	VERB
iajs-2816	7	20	and	and	CCONJ
iajs-2816	7	21	proved	prove	VERB
iajs-2816	7	22	.	.	PUNCT
iajs-2816	8	1	the	the	DET
iajs-2816	8	2	derivation	derivation	NOUN
iajs-2816	8	3	for	for	ADP
iajs-2816	8	4	the	the	DET
iajs-2816	8	5	fréchet	fréchet	NOUN
iajs-2816	8	6	derivative	derivative	NOUN
iajs-2816	8	7	of	of	ADP
iajs-2816	8	8	the	the	DET
iajs-2816	8	9	hamiltonian	hamiltonian	NOUN
iajs-2816	8	10	is	be	AUX
iajs-2816	8	11	attained	attain	VERB
iajs-2816	8	12	.	.	PUNCT
iajs-2816	9	1	keywords	keyword	NOUN
iajs-2816	9	2	:	:	PUNCT
iajs-2816	9	3	quaternary	quaternary	ADJ
iajs-2816	9	4	classical	classical	ADJ
iajs-2816	9	5	optimal	optimal	ADJ
iajs-2816	9	6	control	control	NOUN
iajs-2816	9	7	,	,	PUNCT
iajs-2816	9	8	quaternary	quaternary	ADJ
iajs-2816	9	9	nonlinear	nonlinear	ADJ
iajs-2816	9	10	parabolic	parabolic	PROPN
iajs-2816	9	11	boundary	boundary	ADJ
iajs-2816	9	12	value	value	NOUN
iajs-2816	9	13	problems	problem	NOUN
iajs-2816	9	14	,	,	PUNCT
iajs-2816	9	15	necessary	necessary	ADJ
iajs-2816	9	16	and	and	CCONJ
iajs-2816	9	17	sufficient	sufficient	ADJ
iajs-2816	9	18	for	for	ADP
iajs-2816	9	19	optimality	optimality	NOUN
iajs-2816	9	20	theorems	theorem	NOUN
iajs-2816	9	21	.	.	PUNCT
iajs-2816	10	1	1	1	X
iajs-2816	10	2	.	.	X
iajs-2816	10	3	introduction	introduction	NOUN
iajs-2816	10	4	it	it	PRON
iajs-2816	10	5	is	be	AUX
iajs-2816	10	6	a	a	DET
iajs-2816	10	7	well	well	ADV
iajs-2816	10	8	-	-	PUNCT
iajs-2816	10	9	known	know	VERB
iajs-2816	10	10	fact	fact	NOUN
iajs-2816	10	11	that	that	SCONJ
iajs-2816	10	12	optimal	optimal	ADJ
iajs-2816	10	13	control	control	NOUN
iajs-2816	10	14	problems	problem	NOUN
iajs-2816	10	15	(	(	PUNCT
iajs-2816	10	16	ocps	ocp	NOUN
iajs-2816	10	17	)	)	PUNCT
iajs-2816	10	18	are	be	AUX
iajs-2816	10	19	widely	widely	ADV
iajs-2816	10	20	used	use	VERB
iajs-2816	10	21	in	in	ADP
iajs-2816	10	22	a	a	DET
iajs-2816	10	23	variety	variety	NOUN
iajs-2816	10	24	of	of	ADP
iajs-2816	10	25	scientific	scientific	ADJ
iajs-2816	10	26	fields	field	NOUN
iajs-2816	10	27	,	,	PUNCT
iajs-2816	10	28	including	include	VERB
iajs-2816	10	29	biology	biology	NOUN
iajs-2816	10	30	[	[	X
iajs-2816	10	31	1	1	NUM
iajs-2816	10	32	]	]	PUNCT
iajs-2816	10	33	,	,	PUNCT
iajs-2816	10	34	economics	economic	NOUN
iajs-2816	11	1	[	[	X
iajs-2816	11	2	2	2	NUM
iajs-2816	11	3	]	]	PUNCT
iajs-2816	11	4	,	,	PUNCT
iajs-2816	11	5	robotics	robotic	NOUN
iajs-2816	11	6	[	[	X
iajs-2816	11	7	3	3	NUM
iajs-2816	11	8	]	]	PUNCT
iajs-2816	11	9	,	,	PUNCT
iajs-2816	11	10	aircraft	aircraft	NOUN
iajs-2816	11	11	[	[	X
iajs-2816	11	12	4	4	NUM
iajs-2816	11	13	]	]	PUNCT
iajs-2816	11	14	,	,	PUNCT
iajs-2816	11	15	and	and	CCONJ
iajs-2816	11	16	many	many	ADJ
iajs-2816	11	17	others	other	NOUN
iajs-2816	11	18	.	.	PUNCT
iajs-2816	12	1	ocps	ocp	NOUN
iajs-2816	12	2	are	be	AUX
iajs-2816	12	3	typically	typically	ADV
iajs-2816	12	4	ruled	rule	VERB
iajs-2816	12	5	by	by	ADP
iajs-2816	12	6	nonlinear	nonlinear	ADJ
iajs-2816	12	7	odes	ode	NOUN
iajs-2816	12	8	(	(	PUNCT
iajs-2816	12	9	nlodes	nlode	NOUN
iajs-2816	12	10	)	)	PUNCT
iajs-2816	13	1	[	[	X
iajs-2816	13	2	5	5	NUM
iajs-2816	13	3	]	]	PUNCT
iajs-2816	13	4	or	or	CCONJ
iajs-2816	13	5	nonlinear	nonlinear	ADJ
iajs-2816	13	6	pdes	pde	NOUN
iajs-2816	13	7	(	(	PUNCT
iajs-2816	13	8	nlpdes	nlpde	NOUN
iajs-2816	13	9	)	)	PUNCT
iajs-2816	14	1	[	[	X
iajs-2816	14	2	6	6	NUM
iajs-2816	14	3	]	]	PUNCT
iajs-2816	14	4	.	.	PUNCT
iajs-2816	15	1	during	during	ADP
iajs-2816	15	2	the	the	DET
iajs-2816	15	3	last	last	ADJ
iajs-2816	15	4	decade	decade	NOUN
iajs-2816	15	5	,	,	PUNCT
iajs-2816	15	6	great	great	ADJ
iajs-2816	15	7	attention	attention	NOUN
iajs-2816	15	8	has	have	AUX
iajs-2816	15	9	been	be	AUX
iajs-2816	15	10	made	make	VERB
iajs-2816	15	11	to	to	ADP
iajs-2816	15	12	studying	study	VERB
iajs-2816	15	13	ocps	ocp	NOUN
iajs-2816	15	14	for	for	ADP
iajs-2816	15	15	system	system	NOUN
iajs-2816	15	16	ruling	ruling	NOUN
iajs-2816	15	17	by	by	ADP
iajs-2816	15	18	nlpdes	nlpde	NOUN
iajs-2816	15	19	of	of	ADP
iajs-2816	15	20	elliptic	elliptic	ADJ
iajs-2816	15	21	,	,	PUNCT
iajs-2816	15	22	hyperbolic	hyperbolic	ADJ
iajs-2816	15	23	,	,	PUNCT
iajs-2816	15	24	and	and	CCONJ
iajs-2816	15	25	parabolic	parabolic	ADJ
iajs-2816	15	26	types	type	NOUN
iajs-2816	16	1	[	[	X
iajs-2816	16	2	7	7	NUM
iajs-2816	16	3	-	-	SYM
iajs-2816	16	4	9	9	NUM
iajs-2816	16	5	]	]	PUNCT
iajs-2816	16	6	.	.	PUNCT
iajs-2816	17	1	later	later	ADV
iajs-2816	17	2	,	,	PUNCT
iajs-2816	17	3	the	the	DET
iajs-2816	17	4	study	study	NOUN
iajs-2816	17	5	of	of	ADP
iajs-2816	17	6	this	this	DET
iajs-2816	17	7	subject	subject	NOUN
iajs-2816	17	8	is	be	AUX
iajs-2816	17	9	expanded	expand	VERB
iajs-2816	17	10	to	to	PART
iajs-2816	17	11	include	include	VERB
iajs-2816	17	12	classical	classical	ADJ
iajs-2816	17	13	continuous	continuous	ADJ
iajs-2816	17	14	optimal	optimal	ADJ
iajs-2816	17	15	control	control	NOUN
iajs-2816	17	16	problem	problem	NOUN
iajs-2816	17	17	(	(	PUNCT
iajs-2816	17	18	ccocp	ccocp	NOUN
iajs-2816	17	19	)	)	PUNCT
iajs-2816	17	20	for	for	ADP
iajs-2816	17	21	systems	system	NOUN
iajs-2816	17	22	ruling	rule	VERB
iajs-2816	17	23	by	by	ADP
iajs-2816	17	24	couple	couple	NOUN
iajs-2816	17	25	nlpdes	nlpde	NOUN
iajs-2816	17	26	and	and	CCONJ
iajs-2816	17	27	then	then	ADV
iajs-2816	17	28	recently	recently	ADV
iajs-2816	17	29	by	by	ADP
iajs-2816	17	30	triple	triple	ADJ
iajs-2816	17	31	nlpdes	nlpde	NOUN
iajs-2816	17	32	for	for	ADP
iajs-2816	17	33	the	the	DET
iajs-2816	17	34	above	above	ADJ
iajs-2816	17	35	three	three	NUM
iajs-2816	17	36	ibn	ibn	PROPN
iajs-2816	17	37	al	al	PROPN
iajs-2816	17	38	-	-	PUNCT
iajs-2816	17	39	haitham	haitham	PROPN
iajs-2816	17	40	journal	journal	PROPN
iajs-2816	17	41	for	for	ADP
iajs-2816	17	42	pure	pure	ADJ
iajs-2816	17	43	and	and	CCONJ
iajs-2816	17	44	applied	apply	VERB
iajs-2816	17	45	sciences	sciences	PROPN
iajs-2816	17	46	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2816	17	47	:	:	PUNCT
iajs-2816	17	48	journal	journal	PROPN
iajs-2816	17	49	homepage	homepage	NOUN
iajs-2816	17	50	doi	doi	PROPN
iajs-2816	17	51	:	:	PUNCT
iajs-2816	17	52	10.30526/35.3.2816	10.30526/35.3.2816	PROPN
iajs-2816	17	53	article	article	NOUN
iajs-2816	17	54	history	history	NOUN
iajs-2816	17	55	:	:	PUNCT
iajs-2816	17	56	received	receive	VERB
iajs-2816	17	57	1	1	NUM
iajs-2816	17	58	march	march	NOUN
iajs-2816	17	59	2022	2022	NUM
iajs-2816	17	60	,	,	PUNCT
iajs-2816	17	61	accepted	accept	VERB
iajs-2816	17	62	22	22	NUM
iajs-2816	17	63	march	march	NOUN
iajs-2816	17	64	2022	2022	NUM
iajs-2816	17	65	,	,	PUNCT
iajs-2816	17	66	published	publish	VERB
iajs-2816	17	67	in	in	ADP
iajs-2816	17	68	july	july	PROPN
iajs-2816	17	69	2022	2022	NUM
iajs-2816	17	70	.	.	PUNCT
iajs-2816	18	1	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2816	18	2	file:///d:/رسالة%20ماجستير/ibn%20al-haitham/jhawassy17@uomustansiriyah.edu.iq	file:///d:/رسالة%20ماجستير/ibn%20al-haitham/jhawassy17@uomustansiriyah.edu.iq	NOUN
iajs-2816	18	3	file:///d:/رسالة%20ماجستير/ibn%20al-haitham/wissamali14595@uomustansiriyah.edu.iq	file:///d:/رسالة%20ماجستير/ibn%20al-haitham/wissamali14595@uomustansiriyah.edu.iq	VERB
iajs-2816	18	4	file:///f:/العدد%20الثاني%202022/:%20http:/jih.uobaghdad.edu.iq	file:///f:/العدد%20الثاني%202022/:%20http:/jih.uobaghdad.edu.iq	PROPN
iajs-2816	18	5	/	/	SYM
iajs-2816	18	6	index.php	index.php	VERB
iajs-2816	18	7	/	/	SYM
iajs-2816	18	8	j	j	NOUN
iajs-2816	18	9	/	/	SYM
iajs-2816	18	10	index	index	NOUN
iajs-2816	18	11	ihjpas	ihjpa	NOUN
iajs-2816	18	12	.	.	PUNCT
iajs-2816	19	1	53	53	NUM
iajs-2816	19	2	(	(	PUNCT
iajs-2816	19	3	3)2022	3)2022	NOUN
iajs-2816	19	4	136	136	NUM
iajs-2816	19	5	indicated	indicate	VERB
iajs-2816	19	6	types	type	NOUN
iajs-2816	19	7	of	of	ADP
iajs-2816	19	8	nlpdes	nlpde	NOUN
iajs-2816	19	9	[	[	X
iajs-2816	19	10	10	10	NUM
iajs-2816	19	11	15	15	NUM
iajs-2816	19	12	]	]	PUNCT
iajs-2816	19	13	.	.	PUNCT
iajs-2816	20	1	as	as	ADP
iajs-2816	20	2	a	a	DET
iajs-2816	20	3	result	result	NOUN
iajs-2816	20	4	,	,	PUNCT
iajs-2816	20	5	these	these	DET
iajs-2816	20	6	concerns	concern	NOUN
iajs-2816	20	7	made	make	VERB
iajs-2816	20	8	us	we	PRON
iajs-2816	20	9	study	study	VERB
iajs-2816	20	10	the	the	DET
iajs-2816	20	11	quaternary	quaternary	ADJ
iajs-2816	20	12	classical	classical	ADJ
iajs-2816	20	13	continuous	continuous	ADJ
iajs-2816	20	14	optimal	optimal	ADJ
iajs-2816	20	15	control	control	NOUN
iajs-2816	20	16	problem	problem	NOUN
iajs-2816	20	17	(	(	PUNCT
iajs-2816	20	18	qccocp	qccocp	ADJ
iajs-2816	20	19	)	)	PUNCT
iajs-2816	20	20	ruling	ruling	NOUN
iajs-2816	20	21	by	by	ADP
iajs-2816	20	22	quaternary	quaternary	ADJ
iajs-2816	20	23	nonlinear	nonlinear	PROPN
iajs-2816	20	24	parabolic	parabolic	PROPN
iajs-2816	20	25	boundary	boundary	ADJ
iajs-2816	20	26	value	value	NOUN
iajs-2816	20	27	problems	problem	NOUN
iajs-2816	20	28	(	(	PUNCT
iajs-2816	20	29	qnlpbvps	qnlpbvps	NOUN
iajs-2816	20	30	)	)	PUNCT
iajs-2816	20	31	with	with	ADP
iajs-2816	20	32	equality	equality	NOUN
iajs-2816	20	33	constraint	constraint	NOUN
iajs-2816	20	34	(	(	PUNCT
iajs-2816	20	35	eqc	eqc	NOUN
iajs-2816	20	36	)	)	PUNCT
iajs-2816	20	37	and	and	CCONJ
iajs-2816	20	38	inequality	inequality	NOUN
iajs-2816	20	39	constraint	constraint	NOUN
iajs-2816	20	40	(	(	PUNCT
iajs-2816	20	41	ineqc	ineqc	PROPN
iajs-2816	20	42	)	)	PUNCT
iajs-2816	20	43	.	.	PUNCT
iajs-2816	21	1	this	this	DET
iajs-2816	21	2	paper	paper	NOUN
iajs-2816	21	3	is	be	AUX
iajs-2816	21	4	concerned	concern	VERB
iajs-2816	21	5	with	with	ADP
iajs-2816	21	6	studying	study	VERB
iajs-2816	21	7	the	the	DET
iajs-2816	21	8	qccocp	qccocp	ADJ
iajs-2816	21	9	ruling	ruling	NOUN
iajs-2816	21	10	by	by	ADP
iajs-2816	21	11	a	a	DET
iajs-2816	21	12	qnlpbvp	qnlpbvp	PROPN
iajs-2816	21	13	;	;	PUNCT
iajs-2816	21	14	it	it	PRON
iajs-2816	21	15	begins	begin	VERB
iajs-2816	21	16	with	with	ADP
iajs-2816	21	17	stating	state	VERB
iajs-2816	21	18	and	and	CCONJ
iajs-2816	21	19	demonstrating	demonstrate	VERB
iajs-2816	21	20	the	the	DET
iajs-2816	21	21	existence	existence	NOUN
iajs-2816	21	22	theorem	theorem	NOUN
iajs-2816	21	23	of	of	ADP
iajs-2816	21	24	a	a	DET
iajs-2816	21	25	quaternary	quaternary	ADJ
iajs-2816	21	26	classical	classical	ADJ
iajs-2816	21	27	continuous	continuous	ADJ
iajs-2816	21	28	optimal	optimal	ADJ
iajs-2816	21	29	control	control	NOUN
iajs-2816	21	30	vector	vector	NOUN
iajs-2816	21	31	(	(	PUNCT
iajs-2816	21	32	qccocv	qccocv	PROPN
iajs-2816	21	33	)	)	PUNCT
iajs-2816	21	34	ruling	ruling	NOUN
iajs-2816	21	35	by	by	ADP
iajs-2816	21	36	the	the	DET
iajs-2816	21	37	qnlpbvp	qnlpbvp	PROPN
iajs-2816	21	38	with	with	ADP
iajs-2816	21	39	eqc	eqc	NOUN
iajs-2816	21	40	and	and	CCONJ
iajs-2816	21	41	ineqc	ineqc	VERB
iajs-2816	21	42	under	under	ADP
iajs-2816	21	43	suitable	suitable	ADJ
iajs-2816	21	44	hypotheses	hypothesis	NOUN
iajs-2816	21	45	.	.	PUNCT
iajs-2816	22	1	in	in	ADP
iajs-2816	22	2	addition	addition	NOUN
iajs-2816	22	3	,	,	PUNCT
iajs-2816	22	4	the	the	DET
iajs-2816	22	5	mathematical	mathematical	ADJ
iajs-2816	22	6	formulation	formulation	NOUN
iajs-2816	22	7	of	of	ADP
iajs-2816	22	8	the	the	DET
iajs-2816	22	9	quaternary	quaternary	ADJ
iajs-2816	22	10	adjoint	adjoint	NOUN
iajs-2816	22	11	equations	equation	NOUN
iajs-2816	22	12	(	(	PUNCT
iajs-2816	22	13	qaes	qaes	PROPN
iajs-2816	22	14	)	)	PUNCT
iajs-2816	22	15	related	relate	VERB
iajs-2816	22	16	to	to	ADP
iajs-2816	22	17	the	the	DET
iajs-2816	22	18	quaternary	quaternary	ADJ
iajs-2816	22	19	state	state	NOUN
iajs-2816	22	20	equations	equation	NOUN
iajs-2816	22	21	(	(	PUNCT
iajs-2816	22	22	qses	qse	NOUN
iajs-2816	22	23	)	)	PUNCT
iajs-2816	22	24	is	be	AUX
iajs-2816	22	25	discovered	discover	VERB
iajs-2816	22	26	so	so	ADV
iajs-2816	22	27	as	as	ADP
iajs-2816	22	28	the	the	DET
iajs-2816	22	29	weak	weak	ADJ
iajs-2816	22	30	form	form	NOUN
iajs-2816	22	31	(	(	PUNCT
iajs-2816	22	32	wf	wf	PROPN
iajs-2816	22	33	)	)	PUNCT
iajs-2816	22	34	.	.	PUNCT
iajs-2816	23	1	moreover	moreover	ADV
iajs-2816	23	2	,	,	PUNCT
iajs-2816	23	3	the	the	DET
iajs-2816	23	4	fréchet	fréchet	NOUN
iajs-2816	23	5	derivative	derivative	ADJ
iajs-2816	23	6	(	(	PUNCT
iajs-2816	23	7	frd	frd	ADJ
iajs-2816	23	8	)	)	PUNCT
iajs-2816	23	9	of	of	ADP
iajs-2816	23	10	the	the	DET
iajs-2816	23	11	hamiltonian	hamiltonian	NOUN
iajs-2816	23	12	is	be	AUX
iajs-2816	23	13	attained	attain	VERB
iajs-2816	23	14	.	.	PUNCT
iajs-2816	24	1	lastly	lastly	ADV
iajs-2816	24	2	,	,	PUNCT
iajs-2816	24	3	both	both	CCONJ
iajs-2816	24	4	the	the	DET
iajs-2816	24	5	necessary	necessary	ADJ
iajs-2816	24	6	conditions	condition	NOUN
iajs-2816	24	7	for	for	ADP
iajs-2816	24	8	optimality	optimality	NOUN
iajs-2816	24	9	(	(	PUNCT
iajs-2816	24	10	ncsth	ncsth	NOUN
iajs-2816	24	11	)	)	PUNCT
iajs-2816	24	12	and	and	CCONJ
iajs-2816	24	13	sufficient	sufficient	ADJ
iajs-2816	24	14	conditions	condition	NOUN
iajs-2816	24	15	(	(	PUNCT
iajs-2816	24	16	scsth	scsth	NOUN
iajs-2816	24	17	)	)	PUNCT
iajs-2816	24	18	)	)	PUNCT
iajs-2816	24	19	for	for	ADP
iajs-2816	24	20	optimality	optimality	NOUN
iajs-2816	24	21	are	be	AUX
iajs-2816	24	22	stated	state	VERB
iajs-2816	24	23	and	and	CCONJ
iajs-2816	24	24	demonstrated	demonstrate	VERB
iajs-2816	24	25	.	.	PUNCT
iajs-2816	25	1	description	description	NOUN
iajs-2816	25	2	of	of	ADP
iajs-2816	25	3	the	the	DET
iajs-2816	25	4	problem	problem	NOUN
iajs-2816	25	5	let	let	VERB
iajs-2816	25	6	ω	ω	PROPN
iajs-2816	25	7	⊂	⊂	PROPN
iajs-2816	25	8	ℝ2	ℝ2	VERB
iajs-2816	25	9	be	be	AUX
iajs-2816	25	10	an	an	DET
iajs-2816	25	11	open	open	ADJ
iajs-2816	25	12	and	and	CCONJ
iajs-2816	25	13	bounded	bounded	ADJ
iajs-2816	25	14	region	region	NOUN
iajs-2816	25	15	with	with	ADP
iajs-2816	25	16	boundary	boundary	ADJ
iajs-2816	25	17	γ	γ	X
iajs-2816	25	18	=	=	SYM
iajs-2816	25	19	𝜕ω	𝜕ω	PROPN
iajs-2816	25	20	,	,	PUNCT
iajs-2816	25	21	𝑥	𝑥	X
iajs-2816	25	22	=	=	SYM
iajs-2816	25	23	(	(	PUNCT
iajs-2816	25	24	𝑥1	𝑥1	NOUN
iajs-2816	25	25	,	,	PUNCT
iajs-2816	25	26	𝑥2	𝑥2	NOUN
iajs-2816	25	27	)	)	PUNCT
iajs-2816	25	28	,	,	PUNCT
iajs-2816	26	1	𝑄	𝑄	PROPN
iajs-2816	26	2	=	=	PUNCT
iajs-2816	27	1	𝐼	𝐼	ADP
iajs-2816	27	2	×	×	PROPN
iajs-2816	27	3	ω	ω	NOUN
iajs-2816	27	4	,	,	PUNCT
iajs-2816	27	5	𝐼	𝐼	PROPN
iajs-2816	27	6	=	=	PUNCT
iajs-2816	28	1	[	[	X
iajs-2816	28	2	0	0	NUM
iajs-2816	28	3	,	,	PUNCT
iajs-2816	28	4	𝑇	𝑇	PROPN
iajs-2816	28	5	]	]	PUNCT
iajs-2816	28	6	,	,	PUNCT
iajs-2816	28	7	γ	γ	X
iajs-2816	28	8	=	=	SYM
iajs-2816	28	9	𝜕ω	𝜕ω	PROPN
iajs-2816	28	10	,	,	PUNCT
iajs-2816	28	11	σ	σ	PROPN
iajs-2816	28	12	=	=	PUNCT
iajs-2816	28	13	γ	γ	X
iajs-2816	28	14	×	×	PROPN
iajs-2816	28	15	i.	i.	NOUN
iajs-2816	28	16	the	the	DET
iajs-2816	28	17	qccoc	qccoc	PROPN
iajs-2816	28	18	consists	consist	VERB
iajs-2816	28	19	of	of	ADP
iajs-2816	28	20	the	the	DET
iajs-2816	28	21	continuous	continuous	ADJ
iajs-2816	28	22	quaternary	quaternary	ADJ
iajs-2816	28	23	state	state	NOUN
iajs-2816	28	24	vector	vector	NOUN
iajs-2816	28	25	solution	solution	NOUN
iajs-2816	28	26	(	(	PUNCT
iajs-2816	28	27	cqsvs	cqsvs	NOUN
iajs-2816	28	28	)	)	PUNCT
iajs-2816	28	29	,	,	PUNCT
iajs-2816	28	30	which	which	PRON
iajs-2816	28	31	is	be	AUX
iajs-2816	28	32	expressed	express	VERB
iajs-2816	28	33	by	by	ADP
iajs-2816	28	34	the	the	DET
iajs-2816	28	35	following	following	NOUN
iajs-2816	28	36	qnlpbvp	qnlpbvp	ADV
iajs-2816	28	37	:	:	PUNCT
iajs-2816	28	38	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2816	28	39	−	−	PROPN
iajs-2816	29	1	∆𝑦1	∆𝑦1	ADV
iajs-2816	29	2	+	+	CCONJ
iajs-2816	29	3	𝑦1	𝑦1	PROPN
iajs-2816	29	4	−	−	PROPN
iajs-2816	29	5	𝑦2	𝑦2	PROPN
iajs-2816	29	6	+	+	CCONJ
iajs-2816	29	7	𝑦3	𝑦3	PROPN
iajs-2816	29	8	+	+	CCONJ
iajs-2816	29	9	𝑦4	𝑦4	PROPN
iajs-2816	29	10	=	=	SYM
iajs-2816	29	11	𝑓1(𝑥	𝑓1(𝑥	NUM
iajs-2816	29	12	,	,	PUNCT
iajs-2816	29	13	𝑡	𝑡	NOUN
iajs-2816	29	14	,	,	PUNCT
iajs-2816	29	15	𝑦1	𝑦1	NOUN
iajs-2816	29	16	,	,	PUNCT
iajs-2816	29	17	𝑢1	𝑢1	NOUN
iajs-2816	29	18	)	)	PUNCT
iajs-2816	29	19	,	,	PUNCT
iajs-2816	29	20	in	in	ADP
iajs-2816	29	21	𝑄	𝑄	PROPN
iajs-2816	29	22	(	(	PUNCT
iajs-2816	29	23	1	1	NUM
iajs-2816	29	24	)	)	PUNCT
iajs-2816	29	25	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2816	29	26	−	−	PROPN
iajs-2816	29	27	∆𝑦2	∆𝑦2	PROPN
iajs-2816	29	28	+	+	CCONJ
iajs-2816	29	29	𝑦1	𝑦1	PROPN
iajs-2816	29	30	+	+	CCONJ
iajs-2816	29	31	𝑦2	𝑦2	PROPN
iajs-2816	29	32	−	−	PROPN
iajs-2816	29	33	𝑦3	𝑦3	PROPN
iajs-2816	29	34	−	−	PROPN
iajs-2816	29	35	𝑦4	𝑦4	PROPN
iajs-2816	29	36	=	=	SYM
iajs-2816	29	37	𝑓2(𝑥	𝑓2(𝑥	PROPN
iajs-2816	29	38	,	,	PUNCT
iajs-2816	29	39	𝑡	𝑡	PROPN
iajs-2816	29	40	,	,	PUNCT
iajs-2816	29	41	𝑦2	𝑦2	NOUN
iajs-2816	29	42	,	,	PUNCT
iajs-2816	29	43	𝑢2	𝑢2	PROPN
iajs-2816	29	44	)	)	PUNCT
iajs-2816	29	45	,	,	PUNCT
iajs-2816	29	46	in	in	ADP
iajs-2816	29	47	𝑄	𝑄	PROPN
iajs-2816	29	48	(	(	PUNCT
iajs-2816	29	49	2	2	NUM
iajs-2816	29	50	)	)	PUNCT
iajs-2816	29	51	𝑦3𝑡	𝑦3𝑡	NOUN
iajs-2816	29	52	−	−	NOUN
iajs-2816	29	53	∆𝑦3	∆𝑦3	NOUN
iajs-2816	29	54	−	−	NOUN
iajs-2816	29	55	𝑦1	𝑦1	PROPN
iajs-2816	29	56	+	+	CCONJ
iajs-2816	29	57	𝑦2	𝑦2	PROPN
iajs-2816	29	58	+	+	CCONJ
iajs-2816	29	59	𝑦3	𝑦3	PROPN
iajs-2816	29	60	+	+	CCONJ
iajs-2816	29	61	𝑦4	𝑦4	PROPN
iajs-2816	29	62	=	=	SYM
iajs-2816	29	63	𝑓3(𝑥	𝑓3(𝑥	PROPN
iajs-2816	29	64	,	,	PUNCT
iajs-2816	29	65	𝑡	𝑡	PROPN
iajs-2816	29	66	,	,	PUNCT
iajs-2816	29	67	𝑦3	𝑦3	PROPN
iajs-2816	29	68	,	,	PUNCT
iajs-2816	29	69	𝑢3	𝑢3	PROPN
iajs-2816	29	70	)	)	PUNCT
iajs-2816	29	71	,	,	PUNCT
iajs-2816	29	72	in	in	ADP
iajs-2816	29	73	𝑄	𝑄	PROPN
iajs-2816	29	74	(	(	PUNCT
iajs-2816	29	75	3	3	NUM
iajs-2816	29	76	)	)	PUNCT
iajs-2816	29	77	𝑦4𝑡	𝑦4𝑡	PART
iajs-2816	29	78	−	−	PROPN
iajs-2816	29	79	∆𝑦4	∆𝑦4	PROPN
iajs-2816	29	80	−	−	PROPN
iajs-2816	30	1	𝑦1	𝑦1	PROPN
iajs-2816	30	2	+	+	CCONJ
iajs-2816	30	3	𝑦2	𝑦2	PROPN
iajs-2816	30	4	−	−	PROPN
iajs-2816	30	5	𝑦3	𝑦3	PROPN
iajs-2816	30	6	+	+	CCONJ
iajs-2816	30	7	𝑦4	𝑦4	PROPN
iajs-2816	30	8	=	=	SYM
iajs-2816	30	9	𝑓4(𝑥	𝑓4(𝑥	PROPN
iajs-2816	30	10	,	,	PUNCT
iajs-2816	30	11	𝑡	𝑡	PROPN
iajs-2816	30	12	,	,	PUNCT
iajs-2816	30	13	𝑦4	𝑦4	NOUN
iajs-2816	30	14	,	,	PUNCT
iajs-2816	30	15	𝑢4	𝑢4	PROPN
iajs-2816	30	16	)	)	PUNCT
iajs-2816	30	17	,	,	PUNCT
iajs-2816	30	18	in	in	ADP
iajs-2816	30	19	𝑄	𝑄	PRON
iajs-2816	30	20	(	(	PUNCT
iajs-2816	30	21	4	4	NUM
iajs-2816	30	22	)	)	PUNCT
iajs-2816	30	23	with	with	ADP
iajs-2816	30	24	the	the	DET
iajs-2816	30	25	following	following	ADJ
iajs-2816	30	26	boundary	boundary	ADJ
iajs-2816	30	27	conditions	condition	NOUN
iajs-2816	30	28	(	(	PUNCT
iajs-2816	30	29	bcs	bcs	NOUN
iajs-2816	30	30	)	)	PUNCT
iajs-2816	30	31	and	and	CCONJ
iajs-2816	30	32	initial	initial	ADJ
iajs-2816	30	33	conditions	condition	NOUN
iajs-2816	30	34	(	(	PUNCT
iajs-2816	30	35	ics	ics	NOUN
iajs-2816	30	36	):	):	PUNCT
iajs-2816	30	37	𝑦𝑖(𝑥	𝑦𝑖(𝑥	NUM
iajs-2816	30	38	,	,	PUNCT
iajs-2816	30	39	𝑡	𝑡	X
iajs-2816	30	40	)	)	PUNCT
iajs-2816	30	41	=	=	SYM
iajs-2816	30	42	0	0	NUM
iajs-2816	30	43	,	,	PUNCT
iajs-2816	30	44	∀	∀	NOUN
iajs-2816	30	45	𝑖	𝑖	NOUN
iajs-2816	30	46	=	=	NOUN
iajs-2816	30	47	1,2,3,4	1,2,3,4	NUM
iajs-2816	30	48	.	.	PUNCT
iajs-2816	31	1	on	on	ADP
iajs-2816	31	2	σ	σ	PROPN
iajs-2816	31	3	(	(	PUNCT
iajs-2816	31	4	5	5	NUM
iajs-2816	31	5	)	)	PUNCT
iajs-2816	31	6	𝑦𝑖(𝑥	𝑦𝑖(𝑥	NOUN
iajs-2816	31	7	,	,	PUNCT
iajs-2816	31	8	0	0	NUM
iajs-2816	31	9	)	)	PUNCT
iajs-2816	31	10	=	=	SYM
iajs-2816	31	11	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	31	12	0(𝑥	0(𝑥	NUM
iajs-2816	31	13	)	)	PUNCT
iajs-2816	31	14	,	,	PUNCT
iajs-2816	31	15	∀	∀	PUNCT
iajs-2816	31	16	𝑖	𝑖	NOUN
iajs-2816	32	1	=	=	NOUN
iajs-2816	32	2	1,2,3,4	1,2,3,4	NUM
iajs-2816	32	3	.	.	PUNCT
iajs-2816	33	1	on	on	ADP
iajs-2816	33	2	ω	ω	PROPN
iajs-2816	33	3	(	(	PUNCT
iajs-2816	33	4	6	6	NUM
iajs-2816	33	5	)	)	PUNCT
iajs-2816	33	6	where	where	SCONJ
iajs-2816	33	7	�	�	NOUN
iajs-2816	33	8	⃗	⃗	X
iajs-2816	33	9	�	�	NOUN
iajs-2816	33	10	=	=	SYM
iajs-2816	33	11	(	(	PUNCT
iajs-2816	33	12	𝑦1	𝑦1	PROPN
iajs-2816	33	13	,	,	PUNCT
iajs-2816	33	14	𝑦2	𝑦2	PROPN
iajs-2816	33	15	,	,	PUNCT
iajs-2816	33	16	𝑦3	𝑦3	PROPN
iajs-2816	33	17	,	,	PUNCT
iajs-2816	33	18	𝑦4	𝑦4	PROPN
iajs-2816	33	19	)	)	PUNCT
iajs-2816	33	20	=	=	SYM
iajs-2816	33	21	(	(	PUNCT
iajs-2816	33	22	𝑦1(𝑥	𝑦1(𝑥	PROPN
iajs-2816	33	23	,	,	PUNCT
iajs-2816	33	24	𝑡	𝑡	NOUN
iajs-2816	33	25	)	)	PUNCT
iajs-2816	33	26	,	,	PUNCT
iajs-2816	33	27	𝑦2(𝑥	𝑦2(𝑥	PRON
iajs-2816	33	28	,	,	PUNCT
iajs-2816	33	29	𝑡	𝑡	PROPN
iajs-2816	33	30	)	)	PUNCT
iajs-2816	33	31	,	,	PUNCT
iajs-2816	33	32	𝑦3(𝑥	𝑦3(𝑥	PROPN
iajs-2816	33	33	,	,	PUNCT
iajs-2816	33	34	𝑡	𝑡	NOUN
iajs-2816	33	35	)	)	PUNCT
iajs-2816	33	36	,	,	PUNCT
iajs-2816	33	37	𝑦4(𝑥	𝑦4(𝑥	PROPN
iajs-2816	33	38	,	,	PUNCT
iajs-2816	33	39	𝑡	𝑡	NOUN
iajs-2816	33	40	)	)	PUNCT
iajs-2816	33	41	)	)	PUNCT
iajs-2816	33	42	∈	∈	PROPN
iajs-2816	33	43	(	(	PUNCT
iajs-2816	33	44	𝐻	𝐻	NOUN
iajs-2816	33	45	2(q̅	2(q̅	NUM
iajs-2816	33	46	)	)	PUNCT
iajs-2816	33	47	)	)	PUNCT
iajs-2816	33	48	4	4	NUM
iajs-2816	33	49	is	be	AUX
iajs-2816	33	50	the	the	DET
iajs-2816	33	51	quaternary	quaternary	ADJ
iajs-2816	33	52	state	state	NOUN
iajs-2816	33	53	vector	vector	NOUN
iajs-2816	33	54	solution	solution	NOUN
iajs-2816	33	55	(	(	PUNCT
iajs-2816	33	56	qsvs	qsvs	PROPN
iajs-2816	33	57	)	)	PUNCT
iajs-2816	33	58	,	,	PUNCT
iajs-2816	33	59	�	�	PROPN
iajs-2816	33	60	⃗⃗	⃗⃗	PROPN
iajs-2816	33	61	�	�	PROPN
iajs-2816	33	62	=	=	SYM
iajs-2816	33	63	(	(	PUNCT
iajs-2816	33	64	𝑢1	𝑢1	PROPN
iajs-2816	33	65	,	,	PUNCT
iajs-2816	33	66	𝑢2	𝑢2	PROPN
iajs-2816	33	67	,	,	PUNCT
iajs-2816	33	68	𝑢3	𝑢3	PROPN
iajs-2816	33	69	,	,	PUNCT
iajs-2816	33	70	𝑢4	𝑢4	NOUN
iajs-2816	33	71	)	)	PUNCT
iajs-2816	33	72	=	=	SYM
iajs-2816	33	73	(	(	PUNCT
iajs-2816	33	74	𝑢1(𝑥	𝑢1(𝑥	PROPN
iajs-2816	33	75	,	,	PUNCT
iajs-2816	33	76	𝑡	𝑡	NOUN
iajs-2816	33	77	)	)	PUNCT
iajs-2816	33	78	,	,	PUNCT
iajs-2816	33	79	𝑢2(𝑥	𝑢2(𝑥	PROPN
iajs-2816	33	80	,	,	PUNCT
iajs-2816	33	81	𝑡	𝑡	NOUN
iajs-2816	33	82	)	)	PUNCT
iajs-2816	33	83	,	,	PUNCT
iajs-2816	33	84	𝑢3(𝑥	𝑢3(𝑥	PROPN
iajs-2816	33	85	,	,	PUNCT
iajs-2816	33	86	𝑡	𝑡	NOUN
iajs-2816	33	87	)	)	PUNCT
iajs-2816	33	88	,	,	PUNCT
iajs-2816	33	89	𝑢4(𝑥	𝑢4(𝑥	NOUN
iajs-2816	33	90	,	,	PUNCT
iajs-2816	33	91	𝑡	𝑡	NOUN
iajs-2816	33	92	)	)	PUNCT
iajs-2816	33	93	)	)	PUNCT
iajs-2816	34	1	∈	∈	PROPN
iajs-2816	34	2	(	(	PUNCT
iajs-2816	34	3	𝐿	𝐿	PROPN
iajs-2816	34	4	2(q	2(q	NUM
iajs-2816	34	5	)	)	PUNCT
iajs-2816	34	6	)	)	PUNCT
iajs-2816	34	7	4	4	NUM
iajs-2816	34	8	is	be	AUX
iajs-2816	34	9	the	the	DET
iajs-2816	34	10	qcccv	qcccv	ADJ
iajs-2816	34	11	and	and	CCONJ
iajs-2816	34	12	(	(	PUNCT
iajs-2816	34	13	𝑓1	𝑓1	ADJ
iajs-2816	34	14	,	,	PUNCT
iajs-2816	34	15	𝑓2	𝑓2	ADJ
iajs-2816	34	16	,	,	PUNCT
iajs-2816	34	17	𝑓3	𝑓3	NOUN
iajs-2816	34	18	,	,	PUNCT
iajs-2816	34	19	𝑓4	𝑓4	PROPN
iajs-2816	34	20	)	)	PUNCT
iajs-2816	34	21	=	=	PUNCT
iajs-2816	34	22	(	(	PUNCT
iajs-2816	34	23	𝑓1(𝑥	𝑓1(𝑥	NOUN
iajs-2816	34	24	,	,	PUNCT
iajs-2816	34	25	𝑡	𝑡	NOUN
iajs-2816	34	26	)	)	PUNCT
iajs-2816	34	27	,	,	PUNCT
iajs-2816	34	28	𝑓2(𝑥	𝑓2(𝑥	PROPN
iajs-2816	34	29	,	,	PUNCT
iajs-2816	34	30	𝑡	𝑡	NOUN
iajs-2816	34	31	)	)	PUNCT
iajs-2816	34	32	,	,	PUNCT
iajs-2816	34	33	𝑓3(𝑥	𝑓3(𝑥	PROPN
iajs-2816	34	34	,	,	PUNCT
iajs-2816	34	35	𝑡	𝑡	NOUN
iajs-2816	34	36	)	)	PUNCT
iajs-2816	34	37	,	,	PUNCT
iajs-2816	34	38	𝑓4(𝑥	𝑓4(𝑥	PROPN
iajs-2816	34	39	,	,	PUNCT
iajs-2816	34	40	𝑡	𝑡	NOUN
iajs-2816	34	41	)	)	PUNCT
iajs-2816	34	42	)	)	PUNCT
iajs-2816	34	43	∈	∈	PROPN
iajs-2816	34	44	(	(	PUNCT
iajs-2816	34	45	𝐿	𝐿	PROPN
iajs-2816	34	46	2(q	2(q	NUM
iajs-2816	34	47	)	)	PUNCT
iajs-2816	34	48	)	)	PUNCT
iajs-2816	34	49	4	4	NUM
iajs-2816	34	50	is	be	AUX
iajs-2816	34	51	given	give	VERB
iajs-2816	34	52	,	,	PUNCT
iajs-2816	34	53	for	for	ADP
iajs-2816	34	54	all	all	PRON
iajs-2816	34	55	𝑥	𝑥	PRON
iajs-2816	34	56	=	=	SYM
iajs-2816	34	57	(	(	PUNCT
iajs-2816	34	58	𝑥1	𝑥1	NOUN
iajs-2816	34	59	,	,	PUNCT
iajs-2816	34	60	𝑥2	𝑥2	NOUN
iajs-2816	34	61	)	)	PUNCT
iajs-2816	34	62	∈	∈	PROPN
iajs-2816	34	63	ω	ω	PROPN
iajs-2816	34	64	.	.	PUNCT
iajs-2816	35	1	the	the	DET
iajs-2816	35	2	set	set	NOUN
iajs-2816	35	3	of	of	ADP
iajs-2816	35	4	admissible	admissible	ADJ
iajs-2816	35	5	control	control	NOUN
iajs-2816	35	6	(	(	PUNCT
iajs-2816	35	7	sac	sac	NOUN
iajs-2816	35	8	)	)	PUNCT
iajs-2816	35	9	is	be	AUX
iajs-2816	35	10	:	:	PUNCT
iajs-2816	35	11	�	�	PROPN
iajs-2816	35	12	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	35	13	�	�	PROPN
iajs-2816	36	1	𝐴=	𝐴=	PROPN
iajs-2816	36	2	{	{	PUNCT
iajs-2816	36	3	�	�	PROPN
iajs-2816	36	4	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	36	5	�	�	PROPN
iajs-2816	36	6	∈	∈	PROPN
iajs-2816	36	7	(	(	PUNCT
iajs-2816	36	8	𝐿	𝐿	PROPN
iajs-2816	36	9	2(q	2(q	NUM
iajs-2816	36	10	)	)	PUNCT
iajs-2816	36	11	)	)	PUNCT
iajs-2816	36	12	4	4	NUM
iajs-2816	36	13	|	|	NOUN
iajs-2816	36	14	�	�	NOUN
iajs-2816	36	15	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	36	16	�	�	PROPN
iajs-2816	36	17	∈	∈	PROPN
iajs-2816	36	18	�	�	PROPN
iajs-2816	36	19	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	36	20	�	�	PROPN
iajs-2816	36	21	⊂	⊂	PROPN
iajs-2816	36	22	ℝ4	ℝ4	PROPN
iajs-2816	36	23	a.	a.	PROPN
iajs-2816	36	24	e.	e.	PROPN
iajs-2816	37	1	in	in	ADP
iajs-2816	37	2	q	q	PROPN
iajs-2816	37	3	,	,	PUNCT
iajs-2816	37	4	𝐺1(	𝐺1(	PROPN
iajs-2816	37	5	�	�	PROPN
iajs-2816	37	6	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	37	7	�	�	PROPN
iajs-2816	37	8	)	)	PUNCT
iajs-2816	37	9	=	=	SYM
iajs-2816	37	10	0	0	NUM
iajs-2816	37	11	,	,	PUNCT
iajs-2816	37	12	𝐺2(	𝐺2(	PROPN
iajs-2816	37	13	�	�	PROPN
iajs-2816	37	14	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	37	15	�	�	NOUN
iajs-2816	37	16	)	)	PUNCT
iajs-2816	37	17	≤	≤	NOUN
iajs-2816	37	18	0	0	NUM
iajs-2816	37	19	}	}	PUNCT
iajs-2816	37	20	.	.	PUNCT
iajs-2816	38	1	the	the	DET
iajs-2816	38	2	cf	cf	NOUN
iajs-2816	38	3	is	be	AUX
iajs-2816	38	4	:	:	PUNCT
iajs-2816	38	5	𝐺0(	𝐺0(	X
iajs-2816	38	6	�	�	NOUN
iajs-2816	38	7	⃗⃗	⃗⃗	PROPN
iajs-2816	38	8	�	�	PROPN
iajs-2816	38	9	)	)	PUNCT
iajs-2816	38	10	=	=	SYM
iajs-2816	39	1	∫	∫	PROPN
iajs-2816	39	2	𝑔01(𝑥	𝑔01(𝑥	NOUN
iajs-2816	39	3	,	,	PUNCT
iajs-2816	39	4	𝑡	𝑡	PROPN
iajs-2816	39	5	,	,	PUNCT
iajs-2816	39	6	𝑦1	𝑦1	NOUN
iajs-2816	39	7	,	,	PUNCT
iajs-2816	39	8	𝑢1)𝑑𝑥𝑑𝑡	𝑢1)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	39	9	+	+	CCONJ
iajs-2816	39	10	∫	∫	PROPN
iajs-2816	39	11	𝑔02(𝑥	𝑔02(𝑥	X
iajs-2816	39	12	,	,	PUNCT
iajs-2816	39	13	𝑡	𝑡	PROPN
iajs-2816	39	14	,	,	PUNCT
iajs-2816	39	15	𝑦2	𝑦2	NOUN
iajs-2816	39	16	,	,	PUNCT
iajs-2816	39	17	𝑢2)𝑑𝑥𝑑𝑡	𝑢2)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	39	18	𝑄	𝑄	PROPN
iajs-2816	39	19	𝑄	𝑄	PROPN
iajs-2816	39	20	+	+	CCONJ
iajs-2816	39	21	∫	∫	PROPN
iajs-2816	39	22	𝑔03(𝑥	𝑔03(𝑥	NUM
iajs-2816	39	23	,	,	PUNCT
iajs-2816	39	24	𝑡	𝑡	PROPN
iajs-2816	39	25	,	,	PUNCT
iajs-2816	39	26	𝑦3	𝑦3	PROPN
iajs-2816	39	27	,	,	PUNCT
iajs-2816	39	28	𝑢3)𝑑𝑥𝑑𝑡	𝑢3)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	39	29	𝑄	𝑄	PROPN
iajs-2816	39	30	+	+	CCONJ
iajs-2816	39	31	∫	∫	NUM
iajs-2816	39	32	𝑔04(𝑥	𝑔04(𝑥	NOUN
iajs-2816	39	33	,	,	PUNCT
iajs-2816	39	34	𝑡	𝑡	NOUN
iajs-2816	39	35	,	,	PUNCT
iajs-2816	39	36	𝑦4	𝑦4	NOUN
iajs-2816	39	37	,	,	PUNCT
iajs-2816	39	38	𝑢4)𝑑𝑥𝑑𝑡	𝑢4)𝑑𝑥𝑑𝑡	ADJ
iajs-2816	39	39	𝑄	𝑄	PROPN
iajs-2816	39	40	,	,	PUNCT
iajs-2816	39	41	(	(	PUNCT
iajs-2816	39	42	7.a	7.a	X
iajs-2816	39	43	)	)	PUNCT
iajs-2816	39	44	the	the	DET
iajs-2816	39	45	constraints	constraint	NOUN
iajs-2816	39	46	on	on	ADP
iajs-2816	39	47	the	the	DET
iajs-2816	39	48	state	state	NOUN
iajs-2816	39	49	and	and	CCONJ
iajs-2816	39	50	the	the	DET
iajs-2816	39	51	control	control	NOUN
iajs-2816	39	52	(	(	PUNCT
iajs-2816	39	53	cssc	cssc	PROPN
iajs-2816	39	54	)	)	PUNCT
iajs-2816	39	55	are	be	AUX
iajs-2816	39	56	:	:	PUNCT
iajs-2816	39	57	𝐺1(	𝐺1(	NUM
iajs-2816	39	58	�	�	PROPN
iajs-2816	39	59	⃗⃗	⃗⃗	PROPN
iajs-2816	39	60	�	�	PROPN
iajs-2816	39	61	)	)	PUNCT
iajs-2816	39	62	=	=	SYM
iajs-2816	40	1	∫	∫	PROPN
iajs-2816	40	2	𝑔11(𝑥	𝑔11(𝑥	NOUN
iajs-2816	40	3	,	,	PUNCT
iajs-2816	40	4	𝑡	𝑡	NOUN
iajs-2816	40	5	,	,	PUNCT
iajs-2816	40	6	𝑦1	𝑦1	NOUN
iajs-2816	40	7	,	,	PUNCT
iajs-2816	40	8	𝑢1)𝑑𝑥𝑑𝑡	𝑢1)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	40	9	+	+	CCONJ
iajs-2816	40	10	∫	∫	PROPN
iajs-2816	40	11	𝑔12(𝑥	𝑔12(𝑥	PROPN
iajs-2816	40	12	,	,	PUNCT
iajs-2816	40	13	𝑡	𝑡	PROPN
iajs-2816	40	14	,	,	PUNCT
iajs-2816	40	15	𝑦2	𝑦2	NOUN
iajs-2816	40	16	,	,	PUNCT
iajs-2816	40	17	𝑢2)𝑑𝑥𝑑𝑡	𝑢2)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	40	18	𝑄	𝑄	PROPN
iajs-2816	40	19	𝑄	𝑄	PROPN
iajs-2816	40	20	+	+	CCONJ
iajs-2816	40	21	∫	∫	PROPN
iajs-2816	40	22	𝑔13(𝑥	𝑔13(𝑥	PROPN
iajs-2816	40	23	,	,	PUNCT
iajs-2816	40	24	𝑡	𝑡	PROPN
iajs-2816	40	25	,	,	PUNCT
iajs-2816	40	26	𝑦3	𝑦3	PROPN
iajs-2816	40	27	,	,	PUNCT
iajs-2816	40	28	𝑢3)𝑑𝑥𝑑𝑡	𝑢3)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	40	29	𝑄	𝑄	PROPN
iajs-2816	40	30	+	+	CCONJ
iajs-2816	40	31	∫	∫	PROPN
iajs-2816	40	32	𝑔14(𝑥	𝑔14(𝑥	NOUN
iajs-2816	40	33	,	,	PUNCT
iajs-2816	40	34	𝑡	𝑡	PROPN
iajs-2816	40	35	,	,	PUNCT
iajs-2816	40	36	𝑦4	𝑦4	NOUN
iajs-2816	40	37	,	,	PUNCT
iajs-2816	40	38	𝑢4)𝑑𝑥𝑑𝑡	𝑢4)𝑑𝑥𝑑𝑡	ADJ
iajs-2816	40	39	𝑄	𝑄	PROPN
iajs-2816	40	40	=	=	SYM
iajs-2816	40	41	0	0	NUM
iajs-2816	40	42	,	,	PUNCT
iajs-2816	40	43	(	(	PUNCT
iajs-2816	40	44	7.b	7.b	X
iajs-2816	40	45	)	)	PUNCT
iajs-2816	40	46	𝐺2(	𝐺2(	NUM
iajs-2816	40	47	�	�	PROPN
iajs-2816	40	48	⃗⃗	⃗⃗	PROPN
iajs-2816	40	49	�	�	PROPN
iajs-2816	40	50	)	)	PUNCT
iajs-2816	40	51	=	=	SYM
iajs-2816	41	1	∫	∫	PROPN
iajs-2816	41	2	𝑔21(𝑥	𝑔21(𝑥	PROPN
iajs-2816	41	3	,	,	PUNCT
iajs-2816	41	4	𝑡	𝑡	PROPN
iajs-2816	41	5	,	,	PUNCT
iajs-2816	41	6	𝑦1	𝑦1	NOUN
iajs-2816	41	7	,	,	PUNCT
iajs-2816	41	8	𝑢1)𝑑𝑥𝑑𝑡	𝑢1)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	41	9	+	+	CCONJ
iajs-2816	41	10	∫	∫	PROPN
iajs-2816	41	11	𝑔22(𝑥	𝑔22(𝑥	NUM
iajs-2816	41	12	,	,	PUNCT
iajs-2816	41	13	𝑡	𝑡	PROPN
iajs-2816	41	14	,	,	PUNCT
iajs-2816	41	15	𝑦2	𝑦2	NOUN
iajs-2816	41	16	,	,	PUNCT
iajs-2816	41	17	𝑢2)𝑑𝑥𝑑𝑡	𝑢2)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	41	18	𝑄	𝑄	PROPN
iajs-2816	41	19	𝑄	𝑄	PROPN
iajs-2816	41	20	+	+	CCONJ
iajs-2816	41	21	∫	∫	PROPN
iajs-2816	41	22	𝑔23(𝑥	𝑔23(𝑥	NUM
iajs-2816	41	23	,	,	PUNCT
iajs-2816	41	24	𝑡	𝑡	PROPN
iajs-2816	41	25	,	,	PUNCT
iajs-2816	41	26	𝑦3	𝑦3	PROPN
iajs-2816	41	27	,	,	PUNCT
iajs-2816	41	28	𝑢3)𝑑𝑥𝑑𝑡	𝑢3)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	41	29	𝑄	𝑄	PROPN
iajs-2816	41	30	+	+	CCONJ
iajs-2816	41	31	∫	∫	PROPN
iajs-2816	41	32	𝑔24(𝑥	𝑔24(𝑥	NOUN
iajs-2816	41	33	,	,	PUNCT
iajs-2816	41	34	𝑡	𝑡	PROPN
iajs-2816	41	35	,	,	PUNCT
iajs-2816	41	36	𝑦4	𝑦4	NOUN
iajs-2816	41	37	,	,	PUNCT
iajs-2816	41	38	𝑢4)𝑑𝑥𝑑𝑡	𝑢4)𝑑𝑥𝑑𝑡	VERB
iajs-2816	41	39	𝑄	𝑄	PROPN
iajs-2816	41	40	≤	≤	NOUN
iajs-2816	41	41	0	0	NUM
iajs-2816	41	42	,	,	PUNCT
iajs-2816	41	43	(	(	PUNCT
iajs-2816	41	44	7.c	7.c	NUM
iajs-2816	41	45	)	)	PUNCT
iajs-2816	41	46	where	where	SCONJ
iajs-2816	41	47	(	(	PUNCT
iajs-2816	41	48	𝑦1	𝑦1	NOUN
iajs-2816	41	49	,	,	PUNCT
iajs-2816	41	50	𝑦2	𝑦2	PROPN
iajs-2816	41	51	,	,	PUNCT
iajs-2816	41	52	𝑦3	𝑦3	PROPN
iajs-2816	41	53	,	,	PUNCT
iajs-2816	41	54	𝑦4	𝑦4	PROPN
iajs-2816	41	55	)	)	PUNCT
iajs-2816	41	56	=	=	SYM
iajs-2816	41	57	(	(	PUNCT
iajs-2816	41	58	𝑦𝑢1	𝑦𝑢1	PROPN
iajs-2816	41	59	,	,	PUNCT
iajs-2816	41	60	𝑦𝑢2	𝑦𝑢2	NOUN
iajs-2816	41	61	,	,	PUNCT
iajs-2816	41	62	𝑦𝑢3	𝑦𝑢3	PROPN
iajs-2816	41	63	,	,	PUNCT
iajs-2816	41	64	𝑦𝑢4	𝑦𝑢4	NOUN
iajs-2816	41	65	)	)	PUNCT
iajs-2816	41	66	is	be	AUX
iajs-2816	41	67	the	the	DET
iajs-2816	41	68	qsvs	qsvs	NOUN
iajs-2816	41	69	of	of	ADP
iajs-2816	41	70	(	(	PUNCT
iajs-2816	41	71	(	(	PUNCT
iajs-2816	41	72	1	1	NUM
iajs-2816	41	73	)	)	PUNCT
iajs-2816	41	74	–	–	PUNCT
iajs-2816	41	75	(	(	PUNCT
iajs-2816	41	76	6	6	NUM
iajs-2816	41	77	)	)	PUNCT
iajs-2816	41	78	)	)	PUNCT
iajs-2816	41	79	corresponding	correspond	VERB
iajs-2816	41	80	to	to	ADP
iajs-2816	41	81	the	the	DET
iajs-2816	41	82	qcccv	qcccv	ADJ
iajs-2816	41	83	(	(	PUNCT
iajs-2816	41	84	𝑢1	𝑢1	PROPN
iajs-2816	41	85	,	,	PUNCT
iajs-2816	41	86	𝑢2	𝑢2	PROPN
iajs-2816	41	87	,	,	PUNCT
iajs-2816	41	88	𝑢3	𝑢3	PROPN
iajs-2816	41	89	,	,	PUNCT
iajs-2816	41	90	𝑢4	𝑢4	PROPN
iajs-2816	41	91	)	)	PUNCT
iajs-2816	41	92	.	.	PUNCT
iajs-2816	42	1	ihjpas	ihjpas	PROPN
iajs-2816	42	2	.	.	PUNCT
iajs-2816	43	1	53	53	NUM
iajs-2816	43	2	(	(	PUNCT
iajs-2816	43	3	3)2022	3)2022	NOUN
iajs-2816	43	4	137	137	NUM
iajs-2816	43	5	let	let	VERB
iajs-2816	43	6	�	�	PROPN
iajs-2816	43	7	⃗⃗	⃗⃗	PROPN
iajs-2816	43	8	�	�	PROPN
iajs-2816	43	9	=	=	PRON
iajs-2816	43	10	𝑉1	𝑉1	PROPN
iajs-2816	43	11	×	×	PROPN
iajs-2816	43	12	𝑉2	𝑉2	NOUN
iajs-2816	43	13	×	×	PROPN
iajs-2816	43	14	v3	v3	PROPN
iajs-2816	43	15	×	×	PROPN
iajs-2816	43	16	v4	v4	PROPN
iajs-2816	43	17	=	=	SYM
iajs-2816	43	18	(	(	PUNCT
iajs-2816	43	19	ℋ0	ℋ0	PROPN
iajs-2816	43	20	1(ω	1(ω	NUM
iajs-2816	43	21	)	)	PUNCT
iajs-2816	43	22	)	)	PUNCT
iajs-2816	43	23	4	4	NUM
iajs-2816	43	24	and	and	CCONJ
iajs-2816	43	25	�	�	NOUN
iajs-2816	43	26	⃗	⃗	NOUN
iajs-2816	43	27	�	�	NOUN
iajs-2816	43	28	=	=	SYM
iajs-2816	43	29	(	(	PUNCT
iajs-2816	43	30	𝑣1	𝑣1	PROPN
iajs-2816	43	31	,	,	PUNCT
iajs-2816	43	32	𝑣2	𝑣2	PROPN
iajs-2816	43	33	,	,	PUNCT
iajs-2816	43	34	𝑣3	𝑣3	ADJ
iajs-2816	43	35	,	,	PUNCT
iajs-2816	43	36	𝑣4	𝑣4	NOUN
iajs-2816	43	37	)	)	PUNCT
iajs-2816	43	38	=	=	PUNCT
iajs-2816	43	39	(	(	PUNCT
iajs-2816	43	40	𝑣1(𝑥	𝑣1(𝑥	NOUN
iajs-2816	43	41	)	)	PUNCT
iajs-2816	43	42	,	,	PUNCT
iajs-2816	43	43	𝑣2(𝑥	𝑣2(𝑥	NOUN
iajs-2816	43	44	)	)	PUNCT
iajs-2816	43	45	,	,	PUNCT
iajs-2816	43	46	𝑣3(𝑥	𝑣3(𝑥	NUM
iajs-2816	43	47	)	)	PUNCT
iajs-2816	43	48	,	,	PUNCT
iajs-2816	43	49	𝑣4(𝑥	𝑣4(𝑥	NOUN
iajs-2816	43	50	)	)	PUNCT
iajs-2816	43	51	)	)	PUNCT
iajs-2816	43	52	.	.	PUNCT
iajs-2816	44	1	�	�	PROPN
iajs-2816	44	2	⃗⃗	⃗⃗	PROPN
iajs-2816	44	3	�	�	PROPN
iajs-2816	44	4	=	=	SYM
iajs-2816	44	5	{	{	PUNCT
iajs-2816	44	6	�	�	PROPN
iajs-2816	44	7	⃗	⃗	NOUN
iajs-2816	44	8	�	�	PROPN
iajs-2816	44	9	:	:	PUNCT
iajs-2816	44	10	�	�	PROPN
iajs-2816	44	11	⃗	⃗	NOUN
iajs-2816	44	12	�	�	PROPN
iajs-2816	44	13	∈	∈	PROPN
iajs-2816	44	14	(	(	PUNCT
iajs-2816	44	15	ℋ0	ℋ0	PROPN
iajs-2816	44	16	1(ω	1(ω	NUM
iajs-2816	44	17	)	)	PUNCT
iajs-2816	44	18	)	)	PUNCT
iajs-2816	44	19	4	4	NUM
iajs-2816	44	20	,	,	PUNCT
iajs-2816	44	21	with	with	ADP
iajs-2816	44	22	𝑣1	𝑣1	NOUN
iajs-2816	44	23	=	=	SYM
iajs-2816	44	24	𝑣2	𝑣2	PROPN
iajs-2816	44	25	=	=	SYM
iajs-2816	44	26	𝑣3	𝑣3	PROPN
iajs-2816	44	27	=	=	SYM
iajs-2816	44	28	𝑣4	𝑣4	NOUN
iajs-2816	44	29	=	=	SYM
iajs-2816	44	30	0	0	NUM
iajs-2816	44	31	on	on	ADP
iajs-2816	44	32	𝜕ω	𝜕ω	PROPN
iajs-2816	44	33	}	}	PUNCT
iajs-2816	44	34	.	.	PUNCT
iajs-2816	45	1	the	the	DET
iajs-2816	45	2	wf	wf	PROPN
iajs-2816	45	3	of	of	ADP
iajs-2816	45	4	the	the	DET
iajs-2816	45	5	qsves	qsve	NOUN
iajs-2816	45	6	:	:	PUNCT
iajs-2816	45	7	the	the	DET
iajs-2816	45	8	wf	wf	PROPN
iajs-2816	45	9	of	of	ADP
iajs-2816	45	10	(	(	PUNCT
iajs-2816	45	11	(	(	PUNCT
iajs-2816	45	12	1	1	NUM
iajs-2816	45	13	)	)	PUNCT
iajs-2816	45	14	−	−	PROPN
iajs-2816	45	15	(	(	PUNCT
iajs-2816	45	16	6	6	NUM
iajs-2816	45	17	)	)	PUNCT
iajs-2816	45	18	)	)	PUNCT
iajs-2816	45	19	with	with	ADP
iajs-2816	45	20	�	�	NOUN
iajs-2816	45	21	⃗	⃗	NOUN
iajs-2816	45	22	�	�	PROPN
iajs-2816	45	23	∈	∈	PROPN
iajs-2816	45	24	(	(	PUNCT
iajs-2816	45	25	ℋ0	ℋ0	PROPN
iajs-2816	45	26	1(ω	1(ω	NUM
iajs-2816	45	27	)	)	PUNCT
iajs-2816	45	28	)	)	PUNCT
iajs-2816	45	29	4	4	NUM
iajs-2816	45	30	is	be	AUX
iajs-2816	45	31	given	give	VERB
iajs-2816	45	32	by	by	ADP
iajs-2816	45	33	〈	〈	NOUN
iajs-2816	45	34	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2816	45	35	,	,	PUNCT
iajs-2816	45	36	𝑣1	𝑣1	NOUN
iajs-2816	45	37	〉	〉	NOUN
iajs-2816	45	38	+	+	CCONJ
iajs-2816	45	39	(	(	PUNCT
iajs-2816	45	40	∇𝑦1	∇𝑦1	NOUN
iajs-2816	45	41	,	,	PUNCT
iajs-2816	45	42	∇𝑣1	∇𝑣1	NOUN
iajs-2816	45	43	)	)	PUNCT
iajs-2816	45	44	+	+	CCONJ
iajs-2816	45	45	(	(	PUNCT
iajs-2816	45	46	𝑦1	𝑦1	PROPN
iajs-2816	45	47	,	,	PUNCT
iajs-2816	45	48	𝑣1	𝑣1	NOUN
iajs-2816	45	49	)	)	PUNCT
iajs-2816	45	50	−	−	PROPN
iajs-2816	45	51	(	(	PUNCT
iajs-2816	45	52	𝑦2	𝑦2	PROPN
iajs-2816	45	53	,	,	PUNCT
iajs-2816	45	54	𝑣1	𝑣1	PROPN
iajs-2816	45	55	)	)	PUNCT
iajs-2816	45	56	+	+	CCONJ
iajs-2816	45	57	(	(	PUNCT
iajs-2816	45	58	𝑦3	𝑦3	PROPN
iajs-2816	45	59	,	,	PUNCT
iajs-2816	45	60	𝑣1	𝑣1	PROPN
iajs-2816	45	61	)	)	PUNCT
iajs-2816	45	62	+	+	CCONJ
iajs-2816	45	63	(	(	PUNCT
iajs-2816	45	64	𝑦4	𝑦4	NOUN
iajs-2816	45	65	,	,	PUNCT
iajs-2816	45	66	𝑣1	𝑣1	NOUN
iajs-2816	45	67	)	)	PUNCT
iajs-2816	45	68	=	=	PUNCT
iajs-2816	45	69	(	(	PUNCT
iajs-2816	45	70	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2816	45	71	,	,	PUNCT
iajs-2816	45	72	𝑢1	𝑢1	PROPN
iajs-2816	45	73	)	)	PUNCT
iajs-2816	45	74	,	,	PUNCT
iajs-2816	45	75	𝑣1	𝑣1	PROPN
iajs-2816	45	76	)	)	PUNCT
iajs-2816	45	77	,	,	PUNCT
iajs-2816	45	78	(	(	PUNCT
iajs-2816	45	79	8.a	8.a	NUM
iajs-2816	45	80	)	)	PUNCT
iajs-2816	45	81	(	(	PUNCT
iajs-2816	45	82	𝑦1	𝑦1	NOUN
iajs-2816	45	83	0	0	NUM
iajs-2816	45	84	,	,	PUNCT
iajs-2816	45	85	𝑣1	𝑣1	NOUN
iajs-2816	45	86	)	)	PUNCT
iajs-2816	45	87	=	=	PUNCT
iajs-2816	45	88	(	(	PUNCT
iajs-2816	45	89	𝑦1(0	𝑦1(0	PROPN
iajs-2816	45	90	)	)	PUNCT
iajs-2816	45	91	,	,	PUNCT
iajs-2816	45	92	𝑣1	𝑣1	PROPN
iajs-2816	45	93	)	)	PUNCT
iajs-2816	45	94	,	,	PUNCT
iajs-2816	45	95	(	(	PUNCT
iajs-2816	45	96	8.b	8.b	NUM
iajs-2816	45	97	)	)	PUNCT
iajs-2816	45	98	〈	〈	NOUN
iajs-2816	45	99	𝑦2𝑡	𝑦2𝑡	NOUN
iajs-2816	45	100	,	,	PUNCT
iajs-2816	45	101	𝑣2	𝑣2	NOUN
iajs-2816	45	102	〉	〉	NOUN
iajs-2816	45	103	+	+	CCONJ
iajs-2816	45	104	(	(	PUNCT
iajs-2816	45	105	∇𝑦2	∇𝑦2	NUM
iajs-2816	45	106	,	,	PUNCT
iajs-2816	45	107	∇𝑣2	∇𝑣2	PRON
iajs-2816	45	108	)	)	PUNCT
iajs-2816	46	1	+	+	CCONJ
iajs-2816	46	2	(	(	PUNCT
iajs-2816	46	3	𝑦1	𝑦1	PROPN
iajs-2816	46	4	,	,	PUNCT
iajs-2816	46	5	𝑣2	𝑣2	PROPN
iajs-2816	46	6	)	)	PUNCT
iajs-2816	46	7	+	+	CCONJ
iajs-2816	46	8	(	(	PUNCT
iajs-2816	46	9	𝑦2	𝑦2	PROPN
iajs-2816	46	10	,	,	PUNCT
iajs-2816	46	11	𝑣2	𝑣2	PROPN
iajs-2816	46	12	)	)	PUNCT
iajs-2816	46	13	−	−	PROPN
iajs-2816	46	14	(	(	PUNCT
iajs-2816	46	15	𝑦3	𝑦3	PROPN
iajs-2816	46	16	,	,	PUNCT
iajs-2816	46	17	𝑣2	𝑣2	PROPN
iajs-2816	46	18	)	)	PUNCT
iajs-2816	46	19	−	−	PROPN
iajs-2816	46	20	(	(	PUNCT
iajs-2816	46	21	𝑦4	𝑦4	PROPN
iajs-2816	46	22	,	,	PUNCT
iajs-2816	46	23	𝑣2	𝑣2	NOUN
iajs-2816	46	24	)	)	PUNCT
iajs-2816	46	25	=	=	PUNCT
iajs-2816	46	26	(	(	PUNCT
iajs-2816	46	27	𝑓2(𝑦2	𝑓2(𝑦2	NOUN
iajs-2816	46	28	,	,	PUNCT
iajs-2816	46	29	𝑢2	𝑢2	PROPN
iajs-2816	46	30	)	)	PUNCT
iajs-2816	46	31	,	,	PUNCT
iajs-2816	46	32	𝑣2	𝑣2	PROPN
iajs-2816	46	33	)	)	PUNCT
iajs-2816	46	34	,	,	PUNCT
iajs-2816	46	35	(	(	PUNCT
iajs-2816	46	36	9.a	9.a	NUM
iajs-2816	46	37	)	)	PUNCT
iajs-2816	46	38	(	(	PUNCT
iajs-2816	46	39	𝑦2	𝑦2	PROPN
iajs-2816	46	40	0	0	NUM
iajs-2816	46	41	,	,	PUNCT
iajs-2816	46	42	𝑣2	𝑣2	NUM
iajs-2816	46	43	)	)	PUNCT
iajs-2816	46	44	=	=	PUNCT
iajs-2816	46	45	(	(	PUNCT
iajs-2816	46	46	𝑦2(0	𝑦2(0	PROPN
iajs-2816	46	47	)	)	PUNCT
iajs-2816	46	48	,	,	PUNCT
iajs-2816	46	49	𝑣2	𝑣2	PROPN
iajs-2816	46	50	)	)	PUNCT
iajs-2816	46	51	,	,	PUNCT
iajs-2816	46	52	(	(	PUNCT
iajs-2816	46	53	9.b	9.b	NUM
iajs-2816	46	54	)	)	PUNCT
iajs-2816	46	55	〈	〈	NOUN
iajs-2816	46	56	𝑦3𝑡	𝑦3𝑡	NOUN
iajs-2816	46	57	,	,	PUNCT
iajs-2816	46	58	𝑣3	𝑣3	ADJ
iajs-2816	46	59	〉	〉	NOUN
iajs-2816	46	60	+	+	CCONJ
iajs-2816	46	61	(	(	PUNCT
iajs-2816	46	62	∇𝑦3	∇𝑦3	PROPN
iajs-2816	46	63	,	,	PUNCT
iajs-2816	46	64	∇𝑣3	∇𝑣3	NOUN
iajs-2816	46	65	)	)	PUNCT
iajs-2816	46	66	−	−	PROPN
iajs-2816	46	67	(	(	PUNCT
iajs-2816	46	68	𝑦1	𝑦1	NOUN
iajs-2816	46	69	,	,	PUNCT
iajs-2816	46	70	𝑣3	𝑣3	ADJ
iajs-2816	46	71	)	)	PUNCT
iajs-2816	46	72	+	+	CCONJ
iajs-2816	46	73	(	(	PUNCT
iajs-2816	46	74	𝑦2	𝑦2	NOUN
iajs-2816	46	75	,	,	PUNCT
iajs-2816	46	76	𝑣3	𝑣3	ADJ
iajs-2816	46	77	)	)	PUNCT
iajs-2816	46	78	+	+	CCONJ
iajs-2816	46	79	(	(	PUNCT
iajs-2816	46	80	𝑦3	𝑦3	PROPN
iajs-2816	46	81	,	,	PUNCT
iajs-2816	46	82	𝑣3	𝑣3	ADJ
iajs-2816	46	83	)	)	PUNCT
iajs-2816	46	84	+	+	CCONJ
iajs-2816	46	85	(	(	PUNCT
iajs-2816	46	86	𝑦4	𝑦4	NOUN
iajs-2816	46	87	,	,	PUNCT
iajs-2816	46	88	𝑣3	𝑣3	ADJ
iajs-2816	46	89	)	)	PUNCT
iajs-2816	46	90	=	=	SYM
iajs-2816	46	91	(	(	PUNCT
iajs-2816	46	92	𝑓3(𝑦3	𝑓3(𝑦3	NOUN
iajs-2816	46	93	,	,	PUNCT
iajs-2816	46	94	𝑢3	𝑢3	PROPN
iajs-2816	46	95	)	)	PUNCT
iajs-2816	46	96	,	,	PUNCT
iajs-2816	46	97	𝑣3	𝑣3	NOUN
iajs-2816	46	98	)	)	PUNCT
iajs-2816	46	99	,	,	PUNCT
iajs-2816	46	100	(	(	PUNCT
iajs-2816	46	101	10.a	10.a	NUM
iajs-2816	46	102	)	)	PUNCT
iajs-2816	46	103	(	(	PUNCT
iajs-2816	46	104	𝑦3	𝑦3	PROPN
iajs-2816	46	105	0	0	NUM
iajs-2816	46	106	,	,	PUNCT
iajs-2816	46	107	𝑣3	𝑣3	ADJ
iajs-2816	46	108	)	)	PUNCT
iajs-2816	46	109	=	=	SYM
iajs-2816	46	110	(	(	PUNCT
iajs-2816	46	111	𝑦3(0	𝑦3(0	PROPN
iajs-2816	46	112	)	)	PUNCT
iajs-2816	46	113	,	,	PUNCT
iajs-2816	46	114	𝑣3	𝑣3	NOUN
iajs-2816	46	115	)	)	PUNCT
iajs-2816	46	116	,	,	PUNCT
iajs-2816	46	117	(	(	PUNCT
iajs-2816	46	118	10.b	10.b	NUM
iajs-2816	46	119	)	)	PUNCT
iajs-2816	46	120	〈	〈	NOUN
iajs-2816	46	121	𝑦4𝑡	𝑦4𝑡	PROPN
iajs-2816	46	122	,	,	PUNCT
iajs-2816	46	123	𝑣4	𝑣4	VERB
iajs-2816	46	124	〉	〉	NOUN
iajs-2816	46	125	+	+	CCONJ
iajs-2816	46	126	(	(	PUNCT
iajs-2816	46	127	∇𝑦4	∇𝑦4	ADJ
iajs-2816	46	128	,	,	PUNCT
iajs-2816	46	129	∇𝑣4	∇𝑣4	NUM
iajs-2816	46	130	)	)	PUNCT
iajs-2816	46	131	−	−	PROPN
iajs-2816	47	1	(	(	PUNCT
iajs-2816	47	2	𝑦1	𝑦1	NOUN
iajs-2816	47	3	,	,	PUNCT
iajs-2816	47	4	𝑣4	𝑣4	NOUN
iajs-2816	47	5	)	)	PUNCT
iajs-2816	47	6	+	+	CCONJ
iajs-2816	47	7	(	(	PUNCT
iajs-2816	47	8	𝑦2	𝑦2	NOUN
iajs-2816	47	9	,	,	PUNCT
iajs-2816	47	10	𝑣4	𝑣4	NOUN
iajs-2816	47	11	)	)	PUNCT
iajs-2816	47	12	−	−	PROPN
iajs-2816	47	13	(	(	PUNCT
iajs-2816	47	14	𝑦3	𝑦3	PROPN
iajs-2816	47	15	,	,	PUNCT
iajs-2816	47	16	𝑣4	𝑣4	NOUN
iajs-2816	47	17	)	)	PUNCT
iajs-2816	47	18	+	+	CCONJ
iajs-2816	47	19	(	(	PUNCT
iajs-2816	47	20	𝑦4	𝑦4	NOUN
iajs-2816	47	21	,	,	PUNCT
iajs-2816	47	22	𝑣4	𝑣4	NOUN
iajs-2816	47	23	)	)	PUNCT
iajs-2816	47	24	=	=	SYM
iajs-2816	47	25	(	(	PUNCT
iajs-2816	47	26	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2816	47	27	,	,	PUNCT
iajs-2816	47	28	𝑢4	𝑢4	NOUN
iajs-2816	47	29	)	)	PUNCT
iajs-2816	47	30	,	,	PUNCT
iajs-2816	47	31	𝑣4	𝑣4	NOUN
iajs-2816	47	32	)	)	PUNCT
iajs-2816	47	33	,	,	PUNCT
iajs-2816	47	34	(	(	PUNCT
iajs-2816	47	35	11.a	11.a	NUM
iajs-2816	47	36	)	)	PUNCT
iajs-2816	47	37	(	(	PUNCT
iajs-2816	47	38	𝑦4	𝑦4	PROPN
iajs-2816	47	39	0	0	NUM
iajs-2816	47	40	,	,	PUNCT
iajs-2816	47	41	𝑣4	𝑣4	NOUN
iajs-2816	47	42	)	)	PUNCT
iajs-2816	47	43	=	=	SYM
iajs-2816	47	44	(	(	PUNCT
iajs-2816	47	45	𝑦4(0	𝑦4(0	NOUN
iajs-2816	47	46	)	)	PUNCT
iajs-2816	47	47	,	,	PUNCT
iajs-2816	47	48	𝑣4	𝑣4	PROPN
iajs-2816	47	49	)	)	PUNCT
iajs-2816	47	50	,	,	PUNCT
iajs-2816	47	51	(	(	PUNCT
iajs-2816	47	52	11.b	11.b	X
iajs-2816	47	53	)	)	PUNCT
iajs-2816	47	54	the	the	DET
iajs-2816	47	55	following	follow	VERB
iajs-2816	47	56	hypotheses	hypothesis	NOUN
iajs-2816	47	57	are	be	AUX
iajs-2816	47	58	important	important	ADJ
iajs-2816	47	59	to	to	PART
iajs-2816	47	60	study	study	VERB
iajs-2816	47	61	the	the	DET
iajs-2816	47	62	qccoc	qccoc	PROPN
iajs-2816	47	63	.	.	PUNCT
iajs-2816	48	1	hypotheses	hypothesis	NOUN
iajs-2816	48	2	(	(	PUNCT
iajs-2816	48	3	𝐀	𝐀	NOUN
iajs-2816	48	4	):	):	PUNCT
iajs-2816	48	5	assume	assume	VERB
iajs-2816	48	6	∀𝒊	∀𝒊	X
iajs-2816	48	7	=	=	SYM
iajs-2816	48	8	𝟏	𝟏	NUM
iajs-2816	48	9	,	,	PUNCT
iajs-2816	48	10	𝟐	𝟐	NUM
iajs-2816	48	11	,	,	PUNCT
iajs-2816	48	12	𝟑	𝟑	NUM
iajs-2816	48	13	,	,	PUNCT
iajs-2816	48	14	𝟒	𝟒	NUM
iajs-2816	48	15	that	that	PRON
iajs-2816	48	16	:	:	PUNCT
iajs-2816	48	17	(	(	PUNCT
iajs-2816	48	18	i	i	NOUN
iajs-2816	48	19	)	)	PUNCT
iajs-2816	48	20	𝒇𝒊	𝒇𝒊	ADP
iajs-2816	48	21	is	be	AUX
iajs-2816	48	22	carathéodory	carathéodory	ADJ
iajs-2816	48	23	type	type	NOUN
iajs-2816	48	24	(	(	PUNCT
iajs-2816	48	25	cara	cara	INTJ
iajs-2816	48	26	.	.	PUNCT
iajs-2816	49	1	t.	t.	NOUN
iajs-2816	49	2	)	)	PUNCT
iajs-2816	50	1	on	on	ADP
iajs-2816	50	2	𝑸	𝑸	PROPN
iajs-2816	50	3	×	×	NOUN
iajs-2816	50	4	(	(	PUNCT
iajs-2816	50	5	ℝ)𝟒	ℝ)𝟒	PROPN
iajs-2816	50	6	,	,	PUNCT
iajs-2816	50	7	and	and	CCONJ
iajs-2816	50	8	satisfies	satisfy	VERB
iajs-2816	50	9	the	the	DET
iajs-2816	50	10	following	follow	VERB
iajs-2816	50	11	conditions	condition	NOUN
iajs-2816	50	12	w.r.t	w.r.t	VERB
iajs-2816	50	13	.	.	PUNCT
iajs-2816	51	1	𝒚𝒊	𝒚𝒊	PROPN
iajs-2816	51	2	&	&	CCONJ
iajs-2816	51	3	𝒖𝒊	𝒖𝒊	PROPN
iajs-2816	51	4	,	,	PUNCT
iajs-2816	51	5	i.e.	i.e.	X
iajs-2816	51	6	:	:	PUNCT
iajs-2816	51	7	|𝒇𝒊(𝒙	|𝒇𝒊(𝒙	NUM
iajs-2816	51	8	,	,	PUNCT
iajs-2816	51	9	𝒕	𝒕	NOUN
iajs-2816	51	10	,	,	PUNCT
iajs-2816	51	11	𝒚𝒊	𝒚𝒊	INTJ
iajs-2816	51	12	,	,	PUNCT
iajs-2816	51	13	𝒖𝒊)|	𝒖𝒊)|	ADJ
iajs-2816	51	14	≤	≤	PROPN
iajs-2816	51	15	𝜼𝒊(𝒙	𝜼𝒊(𝒙	NUM
iajs-2816	51	16	,	,	PUNCT
iajs-2816	51	17	𝒕	𝒕	X
iajs-2816	51	18	)	)	PUNCT
iajs-2816	51	19	+	+	NUM
iajs-2816	51	20	𝒄𝒊|𝒚𝒊|	𝒄𝒊|𝒚𝒊|	NOUN
iajs-2816	51	21	+	+	CCONJ
iajs-2816	51	22	�	�	PROPN
iajs-2816	51	23	́	́	NOUN
iajs-2816	51	24	�	�	NOUN
iajs-2816	51	25	𝒊|𝒖𝒊|	𝒊|𝒖𝒊|	NOUN
iajs-2816	51	26	,	,	PUNCT
iajs-2816	51	27	where	where	SCONJ
iajs-2816	51	28	(	(	PUNCT
iajs-2816	51	29	𝒙	𝒙	X
iajs-2816	51	30	,	,	PUNCT
iajs-2816	51	31	𝒕	𝒕	NOUN
iajs-2816	51	32	)	)	PUNCT
iajs-2816	51	33	∈	∈	PROPN
iajs-2816	51	34	𝑸	𝑸	PROPN
iajs-2816	51	35	,	,	PUNCT
iajs-2816	51	36	𝒄𝒊	𝒄𝒊	PROPN
iajs-2816	51	37	,	,	PUNCT
iajs-2816	51	38	�	�	PROPN
iajs-2816	51	39	́	́	NOUN
iajs-2816	51	40	�	�	NOUN
iajs-2816	51	41	𝒊	𝒊	X
iajs-2816	51	42	>	>	X
iajs-2816	51	43	𝟎	𝟎	NUM
iajs-2816	51	44	and	and	CCONJ
iajs-2816	51	45	𝜼𝒊	𝜼𝒊	ADP
iajs-2816	51	46	∈	∈	PROPN
iajs-2816	51	47	𝑳𝟐(𝑸,ℝ	𝑳𝟐(𝑸,ℝ	NOUN
iajs-2816	51	48	)	)	PUNCT
iajs-2816	51	49	.	.	PUNCT
iajs-2816	52	1	(	(	PUNCT
iajs-2816	52	2	ii	ii	NOUN
iajs-2816	52	3	)	)	PUNCT
iajs-2816	52	4	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	52	5	satisfies	satisfie	NOUN
iajs-2816	52	6	lipschitz	lipschitz	NOUN
iajs-2816	52	7	condition	condition	NOUN
iajs-2816	52	8	(	(	PUNCT
iajs-2816	52	9	lc	lc	NOUN
iajs-2816	52	10	)	)	PUNCT
iajs-2816	52	11	w.r.t	w.r.t	NOUN
iajs-2816	52	12	.	.	PUNCT
iajs-2816	53	1	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	53	2	,	,	PUNCT
iajs-2816	53	3	i.e.	i.e.	X
iajs-2816	53	4	:	:	PUNCT
iajs-2816	53	5	|𝑓𝑖(𝑥	|𝑓𝑖(𝑥	NUM
iajs-2816	53	6	,	,	PUNCT
iajs-2816	53	7	𝑡	𝑡	PROPN
iajs-2816	53	8	,	,	PUNCT
iajs-2816	53	9	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	53	10	,	,	PUNCT
iajs-2816	53	11	𝑢𝑖	𝑢𝑖	PROPN
iajs-2816	53	12	)	)	PUNCT
iajs-2816	53	13	−	−	PROPN
iajs-2816	53	14	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2816	53	15	,	,	PUNCT
iajs-2816	53	16	𝑡	𝑡	PROPN
iajs-2816	53	17	,	,	PUNCT
iajs-2816	53	18	�	�	NOUN
iajs-2816	53	19	̅	̅	NOUN
iajs-2816	53	20	�	�	NOUN
iajs-2816	53	21	𝑖	𝑖	NUM
iajs-2816	53	22	,	,	PUNCT
iajs-2816	53	23	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2816	53	24	≤	≤	NUM
iajs-2816	53	25	𝐿𝑖|𝑦𝑖	𝐿𝑖|𝑦𝑖	VERB
iajs-2816	53	26	−	−	PROPN
iajs-2816	53	27	�	�	PROPN
iajs-2816	53	28	̅	̅	NOUN
iajs-2816	53	29	�	�	NOUN
iajs-2816	53	30	𝑖|	𝑖|	PROPN
iajs-2816	53	31	.	.	PUNCT
iajs-2816	54	1	where	where	SCONJ
iajs-2816	54	2	(	(	PUNCT
iajs-2816	54	3	𝑥	𝑥	NOUN
iajs-2816	54	4	,	,	PUNCT
iajs-2816	54	5	𝑡	𝑡	NOUN
iajs-2816	54	6	)	)	PUNCT
iajs-2816	54	7	∈	∈	PROPN
iajs-2816	54	8	𝑄	𝑄	PROPN
iajs-2816	54	9	,	,	PUNCT
iajs-2816	54	10	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	54	11	,	,	PUNCT
iajs-2816	54	12	�	�	NOUN
iajs-2816	54	13	̅	̅	NOUN
iajs-2816	54	14	�	�	NOUN
iajs-2816	54	15	𝑖	𝑖	NOUN
iajs-2816	54	16	,	,	PUNCT
iajs-2816	54	17	𝑢𝑖	𝑢𝑖	DET
iajs-2816	54	18	∈	∈	PROPN
iajs-2816	54	19	ℝ	ℝ	PROPN
iajs-2816	54	20	and	and	CCONJ
iajs-2816	54	21	𝐿𝑖	𝐿𝑖	PROPN
iajs-2816	54	22	>	>	X
iajs-2816	54	23	0	0	X
iajs-2816	54	24	.	.	PUNCT
iajs-2816	55	1	theorem	theorem	NOUN
iajs-2816	55	2	(	(	PUNCT
iajs-2816	55	3	2.1	2.1	NUM
iajs-2816	55	4	)	)	PUNCT
iajs-2816	56	1	[	[	X
iajs-2816	56	2	13	13	NUM
iajs-2816	56	3	]	]	NUM
iajs-2816	56	4	:	:	PUNCT
iajs-2816	56	5	(	(	PUNCT
iajs-2816	56	6	euth	euth	NOUN
iajs-2816	56	7	for	for	ADP
iajs-2816	56	8	the	the	DET
iajs-2816	56	9	wf	wf	PROPN
iajs-2816	56	10	of	of	ADP
iajs-2816	56	11	the	the	DET
iajs-2816	56	12	qsves	qsve	NOUN
iajs-2816	56	13	)	)	PUNCT
iajs-2816	56	14	with	with	ADP
iajs-2816	56	15	hypotheses	hypothesis	NOUN
iajs-2816	56	16	(	(	PUNCT
iajs-2816	56	17	a	a	NOUN
iajs-2816	56	18	)	)	PUNCT
iajs-2816	56	19	,	,	PUNCT
iajs-2816	56	20	for	for	ADP
iajs-2816	56	21	each	each	PRON
iajs-2816	56	22	given	give	VERB
iajs-2816	56	23	qcccv	qcccv	ADV
iajs-2816	56	24	�	�	PROPN
iajs-2816	56	25	⃗⃗	⃗⃗	PROPN
iajs-2816	56	26	�	�	PROPN
iajs-2816	56	27	∈	∈	PROPN
iajs-2816	56	28	(	(	PUNCT
iajs-2816	56	29	𝐿2(𝑄	𝐿2(𝑄	NOUN
iajs-2816	56	30	)	)	PUNCT
iajs-2816	56	31	)	)	PUNCT
iajs-2816	56	32	4	4	NUM
iajs-2816	56	33	,	,	PUNCT
iajs-2816	56	34	the	the	DET
iajs-2816	56	35	wf	wf	PROPN
iajs-2816	56	36	(	(	PUNCT
iajs-2816	56	37	(	(	PUNCT
iajs-2816	56	38	8)	8)	NUM
iajs-2816	56	39	–	–	PUNCT
iajs-2816	56	40	(	(	PUNCT
iajs-2816	56	41	11	11	NUM
iajs-2816	56	42	)	)	PUNCT
iajs-2816	56	43	)	)	PUNCT
iajs-2816	56	44	has	have	VERB
iajs-2816	56	45	a	a	DET
iajs-2816	56	46	unique	unique	ADJ
iajs-2816	56	47	qsvs	qsvs	ADJ
iajs-2816	56	48	�	�	NOUN
iajs-2816	56	49	⃗	⃗	NOUN
iajs-2816	56	50	�	�	PROPN
iajs-2816	56	51	∈	∈	PROPN
iajs-2816	56	52	(	(	PUNCT
iajs-2816	56	53	𝐿2(𝐼	𝐿2(𝐼	PROPN
iajs-2816	56	54	,	,	PUNCT
iajs-2816	56	55	𝑉	𝑉	PROPN
iajs-2816	56	56	)	)	PUNCT
iajs-2816	56	57	)	)	PUNCT
iajs-2816	56	58	4	4	NUM
iajs-2816	56	59	,	,	PUNCT
iajs-2816	56	60	with	with	ADP
iajs-2816	56	61	�	�	PROPN
iajs-2816	56	62	⃗	⃗	NOUN
iajs-2816	56	63	�	�	PROPN
iajs-2816	56	64	𝑡	𝑡	ADP
iajs-2816	56	65	∈	∈	PROPN
iajs-2816	56	66	(	(	PUNCT
iajs-2816	56	67	𝐿	𝐿	NOUN
iajs-2816	56	68	2(𝐼	2(𝐼	NOUN
iajs-2816	56	69	,	,	PUNCT
iajs-2816	56	70	𝑉∗	𝑉∗	NOUN
iajs-2816	56	71	)	)	PUNCT
iajs-2816	56	72	)	)	PUNCT
iajs-2816	56	73	4	4	NUM
iajs-2816	56	74	.	.	PUNCT
iajs-2816	57	1	hypotheses	hypothesis	NOUN
iajs-2816	57	2	(	(	PUNCT
iajs-2816	57	3	b	b	NOUN
iajs-2816	57	4	):	):	PUNCT
iajs-2816	57	5	suppose	suppose	VERB
iajs-2816	57	6	that	that	SCONJ
iajs-2816	57	7	for	for	ADP
iajs-2816	57	8	each	each	PRON
iajs-2816	57	9	𝑙	𝑙	X
iajs-2816	57	10	=	=	SYM
iajs-2816	57	11	0,1,2	0,1,2	NOUN
iajs-2816	57	12	and	and	CCONJ
iajs-2816	57	13	𝑖	𝑖	NOUN
iajs-2816	57	14	=	=	NOUN
iajs-2816	57	15	1,2,3,4	1,2,3,4	NUM
iajs-2816	57	16	,	,	PUNCT
iajs-2816	57	17	that	that	SCONJ
iajs-2816	57	18	𝑔𝑙𝑖	𝑔𝑙𝑖	NOUN
iajs-2816	57	19	is	be	AUX
iajs-2816	57	20	of	of	ADP
iajs-2816	57	21	cara	cara	NOUN
iajs-2816	57	22	.	.	PUNCT
iajs-2816	58	1	t.	t.	NOUN
iajs-2816	58	2	on	on	ADP
iajs-2816	58	3	𝑄	𝑄	PROPN
iajs-2816	58	4	×	×	NOUN
iajs-2816	58	5	(	(	PUNCT
iajs-2816	58	6	ℝ)4	ℝ)4	NUM
iajs-2816	58	7	and	and	CCONJ
iajs-2816	58	8	satisfies	satisfy	VERB
iajs-2816	58	9	the	the	DET
iajs-2816	58	10	following	follow	VERB
iajs-2816	58	11	conditions	condition	NOUN
iajs-2816	58	12	w.r.t	w.r.t	VERB
iajs-2816	58	13	.	.	PUNCT
iajs-2816	59	1	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	59	2	and	and	CCONJ
iajs-2816	59	3	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	59	4	:	:	PUNCT
iajs-2816	59	5	|𝑔𝑙𝑖(𝑥	|𝑔𝑙𝑖(𝑥	PROPN
iajs-2816	59	6	,	,	PUNCT
iajs-2816	59	7	𝑡	𝑡	PROPN
iajs-2816	59	8	,	,	PUNCT
iajs-2816	59	9	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	59	10	,	,	PUNCT
iajs-2816	59	11	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2816	59	12	≤	≤	PROPN
iajs-2816	59	13	𝜂𝑙𝑖(𝑥	𝜂𝑙𝑖(𝑥	PROPN
iajs-2816	59	14	,	,	PUNCT
iajs-2816	59	15	𝑡	𝑡	PROPN
iajs-2816	59	16	)	)	PUNCT
iajs-2816	59	17	+	+	CCONJ
iajs-2816	59	18	𝑐𝑙𝑖1(𝑦𝑖	𝑐𝑙𝑖1(𝑦𝑖	PROPN
iajs-2816	59	19	)	)	PUNCT
iajs-2816	59	20	2	2	NUM
iajs-2816	59	21	+	+	X
iajs-2816	59	22	𝑐𝑙𝑖2(𝑢𝑖	𝑐𝑙𝑖2(𝑢𝑖	NOUN
iajs-2816	59	23	)	)	PUNCT
iajs-2816	59	24	2	2	NUM
iajs-2816	59	25	.	.	PUNCT
iajs-2816	60	1	where	where	SCONJ
iajs-2816	60	2	𝑦𝑖	𝑦𝑖	X
iajs-2816	60	3	,	,	PUNCT
iajs-2816	60	4	𝑢𝑖	𝑢𝑖	DET
iajs-2816	60	5	∈	∈	PROPN
iajs-2816	60	6	ℝ	ℝ	NOUN
iajs-2816	60	7	with	with	ADP
iajs-2816	60	8	𝜂𝑙𝑖	𝜂𝑙𝑖	NOUN
iajs-2816	60	9	∈	∈	PROPN
iajs-2816	60	10	𝐿	𝐿	PROPN
iajs-2816	60	11	1(𝑄	1(𝑄	PROPN
iajs-2816	60	12	)	)	PUNCT
iajs-2816	60	13	.	.	PUNCT
iajs-2816	61	1	lemma	lemma	PROPN
iajs-2816	61	2	(	(	PUNCT
iajs-2816	61	3	2.1	2.1	NUM
iajs-2816	61	4	):	):	PUNCT
iajs-2816	61	5	with	with	ADP
iajs-2816	61	6	hypotheses	hypothesis	NOUN
iajs-2816	61	7	(	(	PUNCT
iajs-2816	61	8	b	b	NOUN
iajs-2816	61	9	)	)	PUNCT
iajs-2816	61	10	,	,	PUNCT
iajs-2816	61	11	for	for	ADP
iajs-2816	61	12	each	each	PRON
iajs-2816	61	13	𝑙	𝑙	X
iajs-2816	61	14	=	=	SYM
iajs-2816	61	15	0,1,2	0,1,2	NUM
iajs-2816	61	16	,	,	PUNCT
iajs-2816	61	17	the	the	DET
iajs-2816	61	18	functional	functional	ADJ
iajs-2816	61	19	�	�	PROPN
iajs-2816	61	20	⃗⃗	⃗⃗	PROPN
iajs-2816	61	21	�	�	PROPN
iajs-2816	61	22	⟼	⟼	PROPN
iajs-2816	61	23	𝐺𝑙(	𝐺𝑙(	PROPN
iajs-2816	61	24	�	�	PROPN
iajs-2816	61	25	⃗⃗	⃗⃗	PROPN
iajs-2816	61	26	�	�	PROPN
iajs-2816	61	27	)	)	PUNCT
iajs-2816	61	28	is	be	AUX
iajs-2816	61	29	cont	cont	ADJ
iajs-2816	61	30	.	.	PUNCT
iajs-2816	62	1	on	on	ADP
iajs-2816	62	2	(	(	PUNCT
iajs-2816	62	3	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2816	62	4	.	.	PUNCT
iajs-2816	63	1	proof	proof	NOUN
iajs-2816	63	2	:	:	PUNCT
iajs-2816	63	3	the	the	DET
iajs-2816	63	4	requirement	requirement	NOUN
iajs-2816	63	5	result	result	NOUN
iajs-2816	63	6	is	be	AUX
iajs-2816	63	7	gotten	get	VERB
iajs-2816	63	8	(	(	PUNCT
iajs-2816	63	9	∀𝑙	∀𝑙	NOUN
iajs-2816	63	10	=	=	SYM
iajs-2816	63	11	0,1,2	0,1,2	NUM
iajs-2816	63	12	)	)	PUNCT
iajs-2816	63	13	directly	directly	ADV
iajs-2816	63	14	from	from	ADP
iajs-2816	63	15	hypotheses	hypothesis	NOUN
iajs-2816	63	16	(	(	PUNCT
iajs-2816	63	17	b	b	NOUN
iajs-2816	63	18	)	)	PUNCT
iajs-2816	63	19	and	and	CCONJ
iajs-2816	63	20	lemma	lemma	PROPN
iajs-2816	63	21	1.12	1.12	NUM
iajs-2816	63	22	in	in	ADP
iajs-2816	63	23	[	[	X
iajs-2816	63	24	16	16	NUM
iajs-2816	63	25	]	]	PUNCT
iajs-2816	63	26	.	.	PUNCT
iajs-2816	64	1	theorem	theorem	NOUN
iajs-2816	64	2	(	(	PUNCT
iajs-2816	64	3	2.2	2.2	NUM
iajs-2816	64	4	)	)	PUNCT
iajs-2816	65	1	[	[	X
iajs-2816	65	2	16	16	NUM
iajs-2816	65	3	]	]	X
iajs-2816	65	4	:	:	PUNCT
iajs-2816	65	5	consider	consider	VERB
iajs-2816	65	6	the	the	DET
iajs-2816	65	7	set	set	NOUN
iajs-2816	65	8	w⃗⃗⃗⃗a	w⃗⃗⃗⃗a	PRON
iajs-2816	65	9	≠	≠	PROPN
iajs-2816	65	10	∅	∅	NOUN
iajs-2816	65	11	,	,	PUNCT
iajs-2816	65	12	for	for	ADP
iajs-2816	65	13	each	each	PRON
iajs-2816	65	14	𝑖	𝑖	NOUN
iajs-2816	65	15	=	=	SYM
iajs-2816	65	16	1,2	1,2	NUM
iajs-2816	65	17	,	,	PUNCT
iajs-2816	65	18	3,4	3,4	NUM
iajs-2816	65	19	,	,	PUNCT
iajs-2816	65	20	the	the	DET
iajs-2816	65	21	functions	function	NOUN
iajs-2816	65	22	𝑓𝑖	𝑓𝑖	AUX
iajs-2816	65	23	has	have	VERB
iajs-2816	65	24	the	the	DET
iajs-2816	65	25	form	form	NOUN
iajs-2816	65	26	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2816	65	27	,	,	PUNCT
iajs-2816	65	28	𝑡	𝑡	PROPN
iajs-2816	65	29	,	,	PUNCT
iajs-2816	65	30	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	65	31	,	,	PUNCT
iajs-2816	65	32	𝑢𝑖	𝑢𝑖	INTJ
iajs-2816	65	33	)	)	PUNCT
iajs-2816	65	34	=	=	SYM
iajs-2816	65	35	𝑓𝑖1(𝑥	𝑓𝑖1(𝑥	PROPN
iajs-2816	65	36	,	,	PUNCT
iajs-2816	65	37	𝑡	𝑡	PROPN
iajs-2816	65	38	,	,	PUNCT
iajs-2816	65	39	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	65	40	)	)	PUNCT
iajs-2816	65	41	+	+	X
iajs-2816	65	42	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2816	65	43	,	,	PUNCT
iajs-2816	65	44	𝑡)𝑢𝑖	𝑡)𝑢𝑖	PROPN
iajs-2816	65	45	with	with	ADP
iajs-2816	65	46	|𝑓𝑖1	|𝑓𝑖1	PROPN
iajs-2816	65	47	(	(	PUNCT
iajs-2816	65	48	𝑥	𝑥	PROPN
iajs-2816	65	49	,	,	PUNCT
iajs-2816	65	50	𝑡	𝑡	PROPN
iajs-2816	65	51	,	,	PUNCT
iajs-2816	65	52	𝑦𝑖)|	𝑦𝑖)|	PROPN
iajs-2816	65	53	≤	≤	NOUN
iajs-2816	65	54	ƞ𝑖(𝑥	ƞ𝑖(𝑥	ADV
iajs-2816	65	55	,	,	PUNCT
iajs-2816	65	56	𝑡	𝑡	X
iajs-2816	65	57	)	)	PUNCT
iajs-2816	65	58	+	+	PUNCT
iajs-2816	65	59	𝑐𝑖|	𝑐𝑖|	PUNCT
iajs-2816	65	60	𝑦𝑖|	𝑦𝑖|	PRON
iajs-2816	65	61	where	where	SCONJ
iajs-2816	65	62	ƞ𝑖	ƞ𝑖	NOUN
iajs-2816	65	63	∈	∈	PROPN
iajs-2816	65	64	𝐿	𝐿	PROPN
iajs-2816	65	65	2(𝑄	2(𝑄	PROPN
iajs-2816	65	66	)	)	PUNCT
iajs-2816	65	67	and	and	CCONJ
iajs-2816	65	68	|𝑓𝑖2(𝑥	|𝑓𝑖2(𝑥	PROPN
iajs-2816	65	69	,	,	PUNCT
iajs-2816	65	70	𝑡)|	𝑡)|	PROPN
iajs-2816	65	71	≤	≤	NUM
iajs-2816	65	72	𝑘𝑖	𝑘𝑖	ADP
iajs-2816	65	73	,	,	PUNCT
iajs-2816	65	74	if	if	SCONJ
iajs-2816	65	75	∀𝑖	∀𝑖	PROPN
iajs-2816	65	76	=	=	SYM
iajs-2816	65	77	1,2	1,2	NUM
iajs-2816	65	78	,	,	PUNCT
iajs-2816	65	79	3,4	3,4	NUM
iajs-2816	65	80	,	,	PUNCT
iajs-2816	65	81	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2816	65	82	is	be	AUX
iajs-2816	65	83	convex	convex	NOUN
iajs-2816	65	84	(	(	PUNCT
iajs-2816	65	85	co	co	NOUN
iajs-2816	65	86	)	)	PUNCT
iajs-2816	65	87	w.r.t	w.r.t	NOUN
iajs-2816	65	88	.	.	PUNCT
iajs-2816	66	1	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	66	2	for	for	ADP
iajs-2816	66	3	fixed	fix	VERB
iajs-2816	66	4	(	(	PUNCT
iajs-2816	66	5	𝑥	𝑥	NOUN
iajs-2816	66	6	,	,	PUNCT
iajs-2816	66	7	𝑡	𝑡	PROPN
iajs-2816	66	8	,	,	PUNCT
iajs-2816	66	9	𝑦𝑖	𝑦𝑖	NOUN
iajs-2816	66	10	)	)	PUNCT
iajs-2816	66	11	.	.	PUNCT
iajs-2816	67	1	then	then	ADV
iajs-2816	67	2	there	there	PRON
iajs-2816	67	3	is	be	VERB
iajs-2816	67	4	a	a	DET
iajs-2816	67	5	qccocv	qccocv	NOUN
iajs-2816	67	6	.	.	PUNCT
iajs-2816	68	1	hypotheses	hypothesis	NOUN
iajs-2816	68	2	(	(	PUNCT
iajs-2816	68	3	c	c	NOUN
iajs-2816	68	4	):	):	PUNCT
iajs-2816	68	5	assume	assume	VERB
iajs-2816	68	6	that	that	SCONJ
iajs-2816	68	7	,	,	PUNCT
iajs-2816	68	8	for	for	ADP
iajs-2816	68	9	𝑙	𝑙	PRON
iajs-2816	68	10	=	=	SYM
iajs-2816	68	11	0,2	0,2	NUM
iajs-2816	68	12	and	and	CCONJ
iajs-2816	68	13	𝑖	𝑖	SYM
iajs-2816	68	14	=	=	SYM
iajs-2816	68	15	1,2,3,4	1,2,3,4	NUM
iajs-2816	68	16	𝑔𝑙𝑖𝑦𝑖	𝑔𝑙𝑖𝑦𝑖	NOUN
iajs-2816	68	17	and	and	CCONJ
iajs-2816	68	18	𝑔𝑙𝑖𝑢𝑖	𝑔𝑙𝑖𝑢𝑖	ADV
iajs-2816	68	19	are	be	AUX
iajs-2816	68	20	of	of	ADP
iajs-2816	68	21	cara	cara	NOUN
iajs-2816	68	22	.	.	PUNCT
iajs-2816	69	1	t.	t.	NOUN
iajs-2816	69	2	on	on	ADP
iajs-2816	69	3	×	×	PROPN
iajs-2816	69	4	(	(	PUNCT
iajs-2816	69	5	ℝ)4	ℝ)4	PROPN
iajs-2816	69	6	,	,	PUNCT
iajs-2816	69	7	|𝑔𝑙𝑖𝑦𝑖(𝑥	|𝑔𝑙𝑖𝑦𝑖(𝑥	PROPN
iajs-2816	69	8	,	,	PUNCT
iajs-2816	69	9	𝑡	𝑡	PROPN
iajs-2816	69	10	,	,	PUNCT
iajs-2816	69	11	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	69	12	,	,	PUNCT
iajs-2816	69	13	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2816	69	14	≤	≤	PROPN
iajs-2816	69	15	𝜂𝑙𝑖5(𝑥	𝜂𝑙𝑖5(𝑥	NUM
iajs-2816	69	16	,	,	PUNCT
iajs-2816	69	17	𝑡	𝑡	NOUN
iajs-2816	69	18	)	)	PUNCT
iajs-2816	69	19	+	+	NUM
iajs-2816	69	20	𝑐𝑙𝑖5|𝑦𝑖|	𝑐𝑙𝑖5|𝑦𝑖|	NOUN
iajs-2816	69	21	+	+	NUM
iajs-2816	69	22	�	�	PROPN
iajs-2816	69	23	́	́	NOUN
iajs-2816	69	24	�	�	NOUN
iajs-2816	69	25	𝑙𝑖5|𝑢𝑖|	𝑙𝑖5|𝑢𝑖|	NOUN
iajs-2816	69	26	,	,	PUNCT
iajs-2816	69	27	and	and	CCONJ
iajs-2816	69	28	|𝑔𝑙𝑖𝑢𝑖(𝑥	|𝑔𝑙𝑖𝑢𝑖(𝑥	PROPN
iajs-2816	69	29	,	,	PUNCT
iajs-2816	69	30	𝑡	𝑡	PROPN
iajs-2816	69	31	,	,	PUNCT
iajs-2816	69	32	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	69	33	,	,	PUNCT
iajs-2816	69	34	𝑢𝑖)|	𝑢𝑖)|	VERB
iajs-2816	69	35	≤	≤	PROPN
iajs-2816	69	36	𝜂𝑙𝑖6(𝑥	𝜂𝑙𝑖6(𝑥	NOUN
iajs-2816	69	37	,	,	PUNCT
iajs-2816	69	38	𝑡	𝑡	X
iajs-2816	69	39	)	)	PUNCT
iajs-2816	69	40	+	+	CCONJ
iajs-2816	69	41	𝑐𝑙𝑖6|𝑦𝑖|	𝑐𝑙𝑖6|𝑦𝑖|	PROPN
iajs-2816	69	42	+	+	CCONJ
iajs-2816	69	43	�	�	PROPN
iajs-2816	69	44	́	́	NOUN
iajs-2816	69	45	�	�	NOUN
iajs-2816	69	46	𝑙𝑖6|𝑢𝑖|	𝑙𝑖6|𝑢𝑖|	PROPN
iajs-2816	69	47	.	.	PUNCT
iajs-2816	70	1	where(𝑥	where(𝑥	PROPN
iajs-2816	70	2	,	,	PUNCT
iajs-2816	70	3	𝑡	𝑡	PROPN
iajs-2816	70	4	)	)	PUNCT
iajs-2816	70	5	∈	∈	PROPN
iajs-2816	70	6	𝑄	𝑄	PROPN
iajs-2816	70	7	,	,	PUNCT
iajs-2816	70	8	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	70	9	,	,	PUNCT
iajs-2816	70	10	𝑢𝑖	𝑢𝑖	PRON
iajs-2816	70	11	∈	∈	PROPN
iajs-2816	70	12	ℝ	ℝ	PROPN
iajs-2816	70	13	,	,	PUNCT
iajs-2816	70	14	𝜂𝑙𝑖5	𝜂𝑙𝑖5	NOUN
iajs-2816	70	15	,	,	PUNCT
iajs-2816	70	16	𝜂𝑙𝑖6	𝜂𝑙𝑖6	PROPN
iajs-2816	70	17	∈	∈	PROPN
iajs-2816	70	18	𝐿	𝐿	PROPN
iajs-2816	70	19	2(𝑄	2(𝑄	NOUN
iajs-2816	70	20	)	)	PUNCT
iajs-2816	70	21	.	.	PUNCT
iajs-2816	71	1	ihjpas	ihjpas	PROPN
iajs-2816	71	2	.	.	PUNCT
iajs-2816	72	1	53	53	NUM
iajs-2816	72	2	(	(	PUNCT
iajs-2816	72	3	3)2022	3)2022	NOUN
iajs-2816	72	4	138	138	NUM
iajs-2816	72	5	theorem	theorem	NOUN
iajs-2816	72	6	(	(	PUNCT
iajs-2816	72	7	2.3	2.3	NUM
iajs-2816	72	8	)	)	PUNCT
iajs-2816	73	1	[	[	X
iajs-2816	73	2	16	16	NUM
iajs-2816	73	3	]	]	X
iajs-2816	73	4	:	:	PUNCT
iajs-2816	73	5	in	in	ADP
iajs-2816	73	6	addition	addition	NOUN
iajs-2816	73	7	to	to	ADP
iajs-2816	73	8	hypotheses	hypothesis	NOUN
iajs-2816	73	9	(	(	PUNCT
iajs-2816	73	10	a	a	X
iajs-2816	73	11	)	)	PUNCT
iajs-2816	73	12	,	,	PUNCT
iajs-2816	73	13	if	if	SCONJ
iajs-2816	73	14	�	�	NOUN
iajs-2816	73	15	⃗	⃗	PART
iajs-2816	73	16	�	�	PROPN
iajs-2816	73	17	and	and	CCONJ
iajs-2816	73	18	�	�	PROPN
iajs-2816	73	19	⃗	⃗	PROPN
iajs-2816	73	20	�	�	PROPN
iajs-2816	73	21	+	+	CCONJ
iajs-2816	73	22	𝛿𝑦⃗⃗⃗⃗⃗	𝛿𝑦⃗⃗⃗⃗⃗	PROPN
iajs-2816	73	23	are	be	AUX
iajs-2816	73	24	the	the	DET
iajs-2816	73	25	qsvs	qsvs	NOUN
iajs-2816	73	26	corresponding	corresponding	NOUN
iajs-2816	73	27	to	to	ADP
iajs-2816	73	28	the	the	DET
iajs-2816	73	29	qcccv	qcccv	PROPN
iajs-2816	73	30	�	�	PROPN
iajs-2816	73	31	⃗⃗	⃗⃗	PROPN
iajs-2816	73	32	�	�	PROPN
iajs-2816	73	33	,	,	PUNCT
iajs-2816	73	34	�	�	PROPN
iajs-2816	73	35	⃗⃗	⃗⃗	PROPN
iajs-2816	73	36	�	�	PROPN
iajs-2816	73	37	+	+	CCONJ
iajs-2816	73	38	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	73	39	∈	∈	PROPN
iajs-2816	73	40	(	(	PUNCT
iajs-2816	73	41	𝐿2(𝑄))4	𝐿2(𝑄))4	PROPN
iajs-2816	73	42	,	,	PUNCT
iajs-2816	73	43	resp	resp	NOUN
iajs-2816	73	44	.	.	PUNCT
iajs-2816	73	45	,	,	PUNCT
iajs-2816	73	46	then	then	ADV
iajs-2816	73	47	‖𝛿𝑦⃗⃗⃗⃗⃗‖	‖𝛿𝑦⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	48	𝑳∞(𝑰,𝑳𝟐(𝜴	𝑳∞(𝑰,𝑳𝟐(𝜴	NOUN
iajs-2816	73	49	)	)	PUNCT
iajs-2816	73	50	≤	≤	NOUN
iajs-2816	73	51	m	m	VERB
iajs-2816	73	52	‖𝛿𝑢⃗⃗⃗⃗⃗‖	‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	53	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	73	54	)	)	PUNCT
iajs-2816	73	55	,	,	PUNCT
iajs-2816	73	56	‖𝛿𝑦⃗⃗⃗⃗⃗‖	‖𝛿𝑦⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	57	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	73	58	)	)	PUNCT
iajs-2816	73	59	≤	≤	NOUN
iajs-2816	73	60	m	m	VERB
iajs-2816	73	61	‖𝛿𝑢⃗⃗⃗⃗⃗‖	‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	62	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	73	63	)	)	PUNCT
iajs-2816	73	64	,	,	PUNCT
iajs-2816	73	65	‖𝛿𝑦⃗⃗⃗⃗⃗‖	‖𝛿𝑦⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	66	𝑳𝟐(𝑰,𝑽	𝑳𝟐(𝑰,𝑽	X
iajs-2816	73	67	)	)	PUNCT
iajs-2816	73	68	≤	≤	NUM
iajs-2816	73	69	m	m	VERB
iajs-2816	73	70	‖𝛿𝑢⃗⃗⃗⃗⃗‖	‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	73	71	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	73	72	)	)	PUNCT
iajs-2816	73	73	.	.	PUNCT
iajs-2816	74	1	theorem	theorem	NOUN
iajs-2816	74	2	(	(	PUNCT
iajs-2816	74	3	2.4	2.4	NUM
iajs-2816	74	4	)	)	PUNCT
iajs-2816	74	5	(	(	PUNCT
iajs-2816	74	6	the	the	DET
iajs-2816	74	7	kuhn	kuhn	PROPN
iajs-2816	74	8	-	-	PUNCT
iajs-2816	74	9	tucker	tucker	PROPN
iajs-2816	74	10	-	-	PUNCT
iajs-2816	74	11	lagrange	lagrange	NOUN
iajs-2816	74	12	conditions	condition	NOUN
iajs-2816	74	13	(	(	PUNCT
iajs-2816	74	14	ktl	ktl	NOUN
iajs-2816	74	15	)	)	PUNCT
iajs-2816	74	16	)	)	PUNCT
iajs-2816	75	1	[	[	X
iajs-2816	75	2	10	10	NUM
iajs-2816	75	3	]	]	PUNCT
iajs-2816	75	4	:	:	PUNCT
iajs-2816	75	5	let	let	VERB
iajs-2816	75	6	𝑈	𝑈	PROPN
iajs-2816	75	7	be	be	AUX
iajs-2816	75	8	a	a	DET
iajs-2816	75	9	nonempty	nonempty	ADJ
iajs-2816	75	10	co	co	NOUN
iajs-2816	75	11	subset	subset	NOUN
iajs-2816	75	12	of	of	ADP
iajs-2816	75	13	a	a	DET
iajs-2816	75	14	vector	vector	NOUN
iajs-2816	75	15	space	space	NOUN
iajs-2816	75	16	𝑋	𝑋	PROPN
iajs-2816	75	17	,	,	PUNCT
iajs-2816	75	18	𝐾	𝐾	PROPN
iajs-2816	75	19	be	be	VERB
iajs-2816	75	20	a	a	DET
iajs-2816	75	21	nonempty	nonempty	ADJ
iajs-2816	75	22	co	co	NOUN
iajs-2816	75	23	positive	positive	ADJ
iajs-2816	75	24	cone	cone	NOUN
iajs-2816	75	25	in	in	ADP
iajs-2816	75	26	a	a	DET
iajs-2816	75	27	normed	normed	ADJ
iajs-2816	75	28	space	space	NOUN
iajs-2816	75	29	𝑍	𝑍	NOUN
iajs-2816	75	30	,	,	PUNCT
iajs-2816	75	31	and	and	CCONJ
iajs-2816	75	32	𝑊	𝑊	PROPN
iajs-2816	75	33	=	=	PUNCT
iajs-2816	75	34	{	{	PUNCT
iajs-2816	75	35	𝑢	𝑢	X
iajs-2816	75	36	∈	∈	PROPN
iajs-2816	75	37	𝑈|𝐺1(𝑢	𝑈|𝐺1(𝑢	X
iajs-2816	75	38	)	)	PUNCT
iajs-2816	75	39	=	=	SYM
iajs-2816	75	40	0	0	NUM
iajs-2816	75	41	,	,	PUNCT
iajs-2816	75	42	𝐺1(𝑢	𝐺1(𝑢	NUM
iajs-2816	75	43	)	)	PUNCT
iajs-2816	75	44	∈	∈	PROPN
iajs-2816	75	45	−𝐾	−𝐾	PROPN
iajs-2816	75	46	}	}	PUNCT
iajs-2816	75	47	.	.	PUNCT
iajs-2816	76	1	the	the	DET
iajs-2816	76	2	functional	functional	ADJ
iajs-2816	76	3	𝐺0	𝐺0	NOUN
iajs-2816	76	4	:	:	PUNCT
iajs-2816	76	5	𝑈	𝑈	PROPN
iajs-2816	76	6	→	→	SYM
iajs-2816	76	7	ℝ	ℝ	PROPN
iajs-2816	76	8	,	,	PUNCT
iajs-2816	76	9	𝐺1	𝐺1	NOUN
iajs-2816	76	10	:	:	PUNCT
iajs-2816	76	11	𝑈	𝑈	PROPN
iajs-2816	76	12	→	→	SYM
iajs-2816	76	13	ℝ	ℝ	PROPN
iajs-2816	76	14	𝑚	𝑚	NOUN
iajs-2816	76	15	,	,	PUNCT
iajs-2816	76	16	𝐺2	𝐺2	ADJ
iajs-2816	76	17	:	:	PUNCT
iajs-2816	76	18	𝑈	𝑈	PROPN
iajs-2816	76	19	→	→	SYM
iajs-2816	76	20	𝑍	𝑍	NOUN
iajs-2816	76	21	are	be	AUX
iajs-2816	76	22	(	(	PUNCT
iajs-2816	76	23	𝑚	𝑚	X
iajs-2816	76	24	+	+	NOUN
iajs-2816	76	25	1	1	NUM
iajs-2816	76	26	)	)	PUNCT
iajs-2816	76	27	−	−	NOUN
iajs-2816	76	28	locally	locally	ADV
iajs-2816	76	29	continuous	continuous	ADJ
iajs-2816	76	30	at	at	ADP
iajs-2816	76	31	𝑢	𝑢	PROPN
iajs-2816	76	32	∈	∈	PROPN
iajs-2816	76	33	𝑈	𝑈	PROPN
iajs-2816	76	34	,	,	PUNCT
iajs-2816	76	35	and	and	CCONJ
iajs-2816	76	36	have	have	AUX
iajs-2816	76	37	(	(	PUNCT
iajs-2816	76	38	𝑚	𝑚	X
iajs-2816	76	39	+	+	NOUN
iajs-2816	76	40	1	1	NUM
iajs-2816	76	41	)	)	PUNCT
iajs-2816	76	42	−	−	NOUN
iajs-2816	76	43	derivatives	derivative	NOUN
iajs-2816	76	44	at	at	ADP
iajs-2816	76	45	𝑢	𝑢	PRON
iajs-2816	76	46	where	where	SCONJ
iajs-2816	76	47	𝑚	𝑚	ADP
iajs-2816	76	48	≠	≠	PROPN
iajs-2816	76	49	0	0	NUM
iajs-2816	76	50	.	.	PUNCT
iajs-2816	77	1	and	and	CCONJ
iajs-2816	77	2	if	if	SCONJ
iajs-2816	77	3	𝑚	𝑚	PROPN
iajs-2816	77	4	=	=	SYM
iajs-2816	77	5	0	0	NUM
iajs-2816	77	6	,	,	PUNCT
iajs-2816	77	7	we	we	PRON
iajs-2816	77	8	assume	assume	VERB
iajs-2816	77	9	that	that	SCONJ
iajs-2816	77	10	𝐷𝐺𝑙(𝑢	𝐷𝐺𝑙(𝑢	PROPN
iajs-2816	77	11	)	)	PUNCT
iajs-2816	77	12	,	,	PUNCT
iajs-2816	77	13	𝑙	𝑙	X
iajs-2816	78	1	=	=	PUNCT
iajs-2816	78	2	0,1,2	0,1,2	NOUN
iajs-2816	78	3	,	,	PUNCT
iajs-2816	78	4	are	be	AUX
iajs-2816	78	5	𝐾	𝐾	PROPN
iajs-2816	78	6	-linear	-linear	NOUN
iajs-2816	78	7	at	at	ADP
iajs-2816	78	8	the	the	DET
iajs-2816	78	9	point	point	NOUN
iajs-2816	78	10	𝑢.	𝑢.	NOUN
iajs-2816	78	11	if	if	SCONJ
iajs-2816	78	12	𝐺0(𝑢	𝐺0(𝑢	PROPN
iajs-2816	78	13	)	)	PUNCT
iajs-2816	78	14	has	have	AUX
iajs-2816	78	15	a	a	DET
iajs-2816	78	16	minimum	minimum	NOUN
iajs-2816	78	17	at	at	ADP
iajs-2816	78	18	𝑢	𝑢	NOUN
iajs-2816	78	19	in	in	ADP
iajs-2816	78	20	𝑊	𝑊	PROPN
iajs-2816	78	21	,	,	PUNCT
iajs-2816	78	22	then	then	ADV
iajs-2816	78	23	it	it	PRON
iajs-2816	78	24	satisfies	satisfy	VERB
iajs-2816	78	25	the	the	DET
iajs-2816	78	26	following	follow	VERB
iajs-2816	78	27	kutula	kutula	NOUN
iajs-2816	78	28	conditions	condition	NOUN
iajs-2816	78	29	,	,	PUNCT
iajs-2816	78	30	∀𝑤	∀𝑤	X
iajs-2816	78	31	∈	∈	PROPN
iajs-2816	78	32	𝑊	𝑊	PROPN
iajs-2816	78	33	:	:	PUNCT
iajs-2816	78	34	there	there	PRON
iajs-2816	78	35	exists	exist	VERB
iajs-2816	78	36	𝜆0	𝜆0	PROPN
iajs-2816	78	37	∈	∈	PROPN
iajs-2816	78	38	ℝ	ℝ	PROPN
iajs-2816	78	39	,	,	PUNCT
iajs-2816	78	40	𝜆1	𝜆1	NOUN
iajs-2816	78	41	∈	∈	PROPN
iajs-2816	78	42	ℝ	ℝ	PROPN
iajs-2816	78	43	𝑚	𝑚	NOUN
iajs-2816	78	44	,	,	PUNCT
iajs-2816	78	45	𝜆2	𝜆2	PROPN
iajs-2816	78	46	∈	∈	PROPN
iajs-2816	78	47	ℤ	ℤ	PROPN
iajs-2816	78	48	∗	∗	NOUN
iajs-2816	78	49	,	,	PUNCT
iajs-2816	78	50	with	with	ADP
iajs-2816	78	51	𝜆0	𝜆0	PROPN
iajs-2816	78	52	≥	≥	NUM
iajs-2816	78	53	0	0	NUM
iajs-2816	78	54	,	,	PUNCT
iajs-2816	78	55	𝜆2	𝜆2	NOUN
iajs-2816	78	56	≥	≥	NOUN
iajs-2816	78	57	0	0	NUM
iajs-2816	78	58	,	,	PUNCT
iajs-2816	78	59	∑	∑	PUNCT
iajs-2816	78	60	|𝜆𝑙|	|𝜆𝑙|	PROPN
iajs-2816	78	61	=	=	SYM
iajs-2816	78	62	1	1	NUM
iajs-2816	78	63	2	2	NUM
iajs-2816	78	64	𝑙=0	𝑙=0	NOUN
iajs-2816	78	65	s.t	s.t	PROPN
iajs-2816	78	66	𝜆0𝐷𝐺0(𝑢	𝜆0𝐷𝐺0(𝑢	PROPN
iajs-2816	78	67	,	,	PUNCT
iajs-2816	78	68	𝑤	𝑤	ADP
iajs-2816	78	69	−	−	NOUN
iajs-2816	78	70	𝑢	𝑢	X
iajs-2816	78	71	)	)	PUNCT
iajs-2816	78	72	+	+	CCONJ
iajs-2816	78	73	𝜆1	𝜆1	PROPN
iajs-2816	78	74	𝑇𝐷𝐺1(𝑢	𝑇𝐷𝐺1(𝑢	PROPN
iajs-2816	78	75	,	,	PUNCT
iajs-2816	78	76	𝑤	𝑤	ADP
iajs-2816	78	77	−	−	PROPN
iajs-2816	78	78	𝑢	𝑢	X
iajs-2816	78	79	)	)	PUNCT
iajs-2816	78	80	+	+	CCONJ
iajs-2816	78	81	〈	〈	PROPN
iajs-2816	78	82	𝜆2	𝜆2	NOUN
iajs-2816	78	83	,	,	PUNCT
iajs-2816	78	84	𝐷𝐺2(𝑢	𝐷𝐺2(𝑢	PROPN
iajs-2816	78	85	,	,	PUNCT
iajs-2816	78	86	𝑤	𝑤	ADP
iajs-2816	78	87	−	−	ADP
iajs-2816	78	88	𝑢	𝑢	NOUN
iajs-2816	78	89	)	)	PUNCT
iajs-2816	78	90	〉	〉	NOUN
iajs-2816	78	91	≥	≥	NUM
iajs-2816	78	92	0	0	NUM
iajs-2816	78	93	,	,	PUNCT
iajs-2816	78	94	〈	〈	PROPN
iajs-2816	78	95	𝜆2	𝜆2	NOUN
iajs-2816	78	96	,	,	PUNCT
iajs-2816	78	97	𝐺2(𝑢	𝐺2(𝑢	NOUN
iajs-2816	78	98	)	)	PUNCT
iajs-2816	78	99	〉	〉	NOUN
iajs-2816	78	100	=	=	SYM
iajs-2816	78	101	0	0	X
iajs-2816	78	102	.	.	PUNCT
iajs-2816	79	1	main	main	ADJ
iajs-2816	79	2	results	result	NOUN
iajs-2816	79	3	3	3	NUM
iajs-2816	79	4	.	.	PUNCT
iajs-2816	79	5	existence	existence	NOUN
iajs-2816	79	6	of	of	ADP
iajs-2816	79	7	the	the	DET
iajs-2816	79	8	qccocv	qccocv	NOUN
iajs-2816	79	9	and	and	CCONJ
iajs-2816	79	10	the	the	DET
iajs-2816	79	11	frd	frd	ADJ
iajs-2816	79	12	:	:	PUNCT
iajs-2816	79	13	this	this	DET
iajs-2816	79	14	section	section	NOUN
iajs-2816	79	15	deals	deal	VERB
iajs-2816	79	16	with	with	ADP
iajs-2816	79	17	the	the	DET
iajs-2816	79	18	existence	existence	NOUN
iajs-2816	79	19	theorem	theorem	NOUN
iajs-2816	79	20	of	of	ADP
iajs-2816	79	21	the	the	DET
iajs-2816	79	22	qccocv	qccocv	PROPN
iajs-2816	79	23	,	,	PUNCT
iajs-2816	79	24	the	the	DET
iajs-2816	79	25	discovery	discovery	NOUN
iajs-2816	79	26	of	of	ADP
iajs-2816	79	27	the	the	DET
iajs-2816	79	28	mathematical	mathematical	ADJ
iajs-2816	79	29	formulation	formulation	NOUN
iajs-2816	79	30	for	for	ADP
iajs-2816	79	31	the	the	DET
iajs-2816	79	32	qaes	qaes	NOUN
iajs-2816	79	33	and	and	CCONJ
iajs-2816	79	34	their	their	PRON
iajs-2816	79	35	wf	wf	PROPN
iajs-2816	79	36	is	be	AUX
iajs-2816	79	37	obtained	obtain	VERB
iajs-2816	79	38	,	,	PUNCT
iajs-2816	79	39	and	and	CCONJ
iajs-2816	79	40	the	the	DET
iajs-2816	79	41	derivation	derivation	NOUN
iajs-2816	79	42	of	of	ADP
iajs-2816	79	43	the	the	DET
iajs-2816	79	44	frd	frd	NOUN
iajs-2816	79	45	is	be	AUX
iajs-2816	79	46	derived	derive	VERB
iajs-2816	79	47	under	under	ADP
iajs-2816	79	48	some	some	DET
iajs-2816	79	49	appropriate	appropriate	ADJ
iajs-2816	79	50	hypotheses	hypothesis	NOUN
iajs-2816	79	51	.	.	PUNCT
iajs-2816	80	1	theorem	theorem	NOUN
iajs-2816	80	2	(	(	PUNCT
iajs-2816	80	3	3.1	3.1	NUM
iajs-2816	80	4	):	):	PUNCT
iajs-2816	80	5	consider	consider	VERB
iajs-2816	80	6	the	the	DET
iajs-2816	80	7	set	set	NOUN
iajs-2816	80	8	w⃗⃗⃗⃗a	w⃗⃗⃗⃗a	PRON
iajs-2816	80	9	≠	≠	PROPN
iajs-2816	80	10	∅	∅	NOUN
iajs-2816	80	11	,	,	PUNCT
iajs-2816	80	12	the	the	DET
iajs-2816	80	13	functions	function	NOUN
iajs-2816	80	14	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	80	15	,	,	PUNCT
iajs-2816	80	16	∀𝑖	∀𝑖	PROPN
iajs-2816	80	17	=	=	SYM
iajs-2816	80	18	1,2	1,2	NUM
iajs-2816	80	19	,	,	PUNCT
iajs-2816	80	20	3,4	3,4	NUM
iajs-2816	80	21	,	,	PUNCT
iajs-2816	80	22	has	have	VERB
iajs-2816	80	23	the	the	DET
iajs-2816	80	24	form	form	NOUN
iajs-2816	80	25	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2816	80	26	,	,	PUNCT
iajs-2816	80	27	𝑡	𝑡	PROPN
iajs-2816	80	28	,	,	PUNCT
iajs-2816	80	29	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	80	30	,	,	PUNCT
iajs-2816	80	31	𝑢𝑖	𝑢𝑖	INTJ
iajs-2816	80	32	)	)	PUNCT
iajs-2816	80	33	=	=	SYM
iajs-2816	80	34	𝑓𝑖1(𝑥	𝑓𝑖1(𝑥	PROPN
iajs-2816	80	35	,	,	PUNCT
iajs-2816	80	36	𝑡	𝑡	PROPN
iajs-2816	80	37	,	,	PUNCT
iajs-2816	80	38	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	80	39	)	)	PUNCT
iajs-2816	81	1	+	+	X
iajs-2816	82	1	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2816	82	2	,	,	PUNCT
iajs-2816	82	3	𝑡)𝑢𝑖	𝑡)𝑢𝑖	PROPN
iajs-2816	82	4	with	with	ADP
iajs-2816	82	5	|𝑓𝑖1	|𝑓𝑖1	PROPN
iajs-2816	82	6	(	(	PUNCT
iajs-2816	82	7	𝑥	𝑥	PROPN
iajs-2816	82	8	,	,	PUNCT
iajs-2816	82	9	𝑡	𝑡	PROPN
iajs-2816	82	10	,	,	PUNCT
iajs-2816	82	11	𝑦𝑖)|	𝑦𝑖)|	PROPN
iajs-2816	82	12	≤	≤	NOUN
iajs-2816	82	13	ƞ𝑖(𝑥	ƞ𝑖(𝑥	ADV
iajs-2816	82	14	,	,	PUNCT
iajs-2816	82	15	𝑡	𝑡	X
iajs-2816	82	16	)	)	PUNCT
iajs-2816	82	17	+	+	PUNCT
iajs-2816	82	18	𝑐𝑖|	𝑐𝑖|	VERB
iajs-2816	82	19	𝑦𝑖|	𝑦𝑖|	PROPN
iajs-2816	82	20	and	and	CCONJ
iajs-2816	82	21	|𝑓𝑖2(𝑥	|𝑓𝑖2(𝑥	PROPN
iajs-2816	82	22	,	,	PUNCT
iajs-2816	82	23	𝑡)|	𝑡)|	PROPN
iajs-2816	82	24	≤	≤	NUM
iajs-2816	82	25	𝑘𝑖	𝑘𝑖	ADP
iajs-2816	82	26	,	,	PUNCT
iajs-2816	82	27	where	where	SCONJ
iajs-2816	82	28	ƞ𝑖	ƞ𝑖	NOUN
iajs-2816	82	29	∈	∈	PROPN
iajs-2816	82	30	𝐿	𝐿	PROPN
iajs-2816	82	31	2(𝑄	2(𝑄	NOUN
iajs-2816	82	32	)	)	PUNCT
iajs-2816	82	33	.	.	PUNCT
iajs-2816	83	1	if	if	SCONJ
iajs-2816	83	2	∀𝑖	∀𝑖	PROPN
iajs-2816	83	3	=	=	SYM
iajs-2816	83	4	1,2	1,2	NUM
iajs-2816	83	5	,	,	PUNCT
iajs-2816	83	6	3,4	3,4	NUM
iajs-2816	83	7	,	,	PUNCT
iajs-2816	83	8	𝑔1𝑖	𝑔1𝑖	ADV
iajs-2816	83	9	is	be	AUX
iajs-2816	83	10	independent	independent	ADJ
iajs-2816	83	11	of	of	ADP
iajs-2816	83	12	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	83	13	,	,	PUNCT
iajs-2816	83	14	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2816	83	15	and	and	CCONJ
iajs-2816	83	16	𝑔2𝑖	𝑔2𝑖	NOUN
iajs-2816	83	17	are	be	AUX
iajs-2816	83	18	convex	convex	ADJ
iajs-2816	83	19	w.r.t	w.r.t	NOUN
iajs-2816	83	20	.	.	PUNCT
iajs-2816	84	1	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	84	2	for	for	ADP
iajs-2816	84	3	fixed	fix	VERB
iajs-2816	84	4	(	(	PUNCT
iajs-2816	84	5	𝑥	𝑥	NOUN
iajs-2816	84	6	,	,	PUNCT
iajs-2816	84	7	𝑡	𝑡	PROPN
iajs-2816	84	8	,	,	PUNCT
iajs-2816	84	9	𝑦𝑖	𝑦𝑖	NOUN
iajs-2816	84	10	)	)	PUNCT
iajs-2816	84	11	.	.	PUNCT
iajs-2816	85	1	then	then	ADV
iajs-2816	85	2	there	there	PRON
iajs-2816	85	3	is	be	VERB
iajs-2816	85	4	a	a	DET
iajs-2816	85	5	qccocv	qccocv	NOUN
iajs-2816	85	6	.	.	PUNCT
iajs-2816	86	1	proof	proof	NOUN
iajs-2816	86	2	:	:	PUNCT
iajs-2816	86	3	from	from	ADP
iajs-2816	86	4	the	the	DET
iajs-2816	86	5	hypotheses	hypothesis	NOUN
iajs-2816	86	6	on	on	ADP
iajs-2816	86	7	𝑊𝑖	𝑊𝑖	PROPN
iajs-2816	86	8	and	and	CCONJ
iajs-2816	86	9	𝑔1𝑖	𝑔1𝑖	PROPN
iajs-2816	86	10	(	(	PUNCT
iajs-2816	86	11	∀𝑖	∀𝑖	PROPN
iajs-2816	86	12	=	=	SYM
iajs-2816	86	13	1,2	1,2	NUM
iajs-2816	86	14	,	,	PUNCT
iajs-2816	86	15	3,4	3,4	NUM
iajs-2816	86	16	)	)	PUNCT
iajs-2816	86	17	,	,	PUNCT
iajs-2816	86	18	with	with	ADP
iajs-2816	86	19	using	use	VERB
iajs-2816	86	20	lemma	lemma	PROPN
iajs-2816	86	21	(	(	PUNCT
iajs-2816	86	22	2.1	2.1	NUM
iajs-2816	86	23	)	)	PUNCT
iajs-2816	86	24	and	and	CCONJ
iajs-2816	86	25	the	the	DET
iajs-2816	86	26	.	.	PROPN
iajs-2816	86	27	2.2	2.2	NUM
iajs-2816	86	28	,	,	PUNCT
iajs-2816	86	29	one	one	PRON
iajs-2816	86	30	can	can	AUX
iajs-2816	86	31	get	get	VERB
iajs-2816	86	32	that	that	SCONJ
iajs-2816	86	33	there	there	PRON
iajs-2816	86	34	is	be	VERB
iajs-2816	86	35	a	a	DET
iajs-2816	86	36	qccocv	qccocv	NOUN
iajs-2816	86	37	with	with	ADP
iajs-2816	86	38	the	the	DET
iajs-2816	86	39	eqc	eqc	NOUN
iajs-2816	86	40	and	and	CCONJ
iajs-2816	86	41	ineqc	ineqc	PROPN
iajs-2816	86	42	.	.	PUNCT
iajs-2816	87	1	theorem	theorem	NOUN
iajs-2816	87	2	(	(	PUNCT
iajs-2816	87	3	3.2	3.2	NUM
iajs-2816	87	4	):	):	PUNCT
iajs-2816	87	5	we	we	PRON
iajs-2816	87	6	drop	drop	VERB
iajs-2816	87	7	the	the	DET
iajs-2816	87	8	index	index	NOUN
iajs-2816	87	9	𝑙	𝑙	PROPN
iajs-2816	87	10	in	in	ADP
iajs-2816	87	11	𝑔𝑙	𝑔𝑙	PROPN
iajs-2816	87	12	and	and	CCONJ
iajs-2816	87	13	𝐺𝑙	𝐺𝑙	PROPN
iajs-2816	87	14	.	.	PUNCT
iajs-2816	88	1	in	in	ADP
iajs-2816	88	2	addition	addition	NOUN
iajs-2816	88	3	to	to	ADP
iajs-2816	88	4	hypotheses	hypothesis	NOUN
iajs-2816	88	5	(	(	PUNCT
iajs-2816	88	6	a	a	NOUN
iajs-2816	88	7	)	)	PUNCT
iajs-2816	88	8	,	,	PUNCT
iajs-2816	88	9	(	(	PUNCT
iajs-2816	88	10	b	b	NOUN
iajs-2816	88	11	)	)	PUNCT
iajs-2816	88	12	,	,	PUNCT
iajs-2816	88	13	and	and	CCONJ
iajs-2816	88	14	(	(	PUNCT
iajs-2816	88	15	c	c	NOUN
iajs-2816	88	16	)	)	PUNCT
iajs-2816	88	17	,	,	PUNCT
iajs-2816	88	18	the	the	DET
iajs-2816	88	19	following	follow	VERB
iajs-2816	88	20	adjoint	adjoint	NOUN
iajs-2816	88	21	(	(	PUNCT
iajs-2816	88	22	𝑧1	𝑧1	NOUN
iajs-2816	88	23	,	,	PUNCT
iajs-2816	88	24	𝑧2	𝑧2	NOUN
iajs-2816	88	25	,	,	PUNCT
iajs-2816	88	26	𝑧3	𝑧3	NOUN
iajs-2816	88	27	,	,	PUNCT
iajs-2816	88	28	𝑧4	𝑧4	ADJ
iajs-2816	88	29	)	)	PUNCT
iajs-2816	88	30	=	=	SYM
iajs-2816	88	31	(	(	PUNCT
iajs-2816	88	32	𝑧𝑢1	𝑧𝑢1	PROPN
iajs-2816	88	33	,	,	PUNCT
iajs-2816	88	34	𝑧𝑢2	𝑧𝑢2	X
iajs-2816	88	35	,	,	PUNCT
iajs-2816	88	36	𝑧𝑢3	𝑧𝑢3	NOUN
iajs-2816	88	37	,	,	PUNCT
iajs-2816	88	38	𝑧𝑢4	𝑧𝑢4	NOUN
iajs-2816	88	39	)	)	PUNCT
iajs-2816	88	40	equations	equation	NOUN
iajs-2816	88	41	corresponding	correspond	VERB
iajs-2816	88	42	to	to	ADP
iajs-2816	88	43	the	the	DET
iajs-2816	88	44	state	state	NOUN
iajs-2816	88	45	(	(	PUNCT
iajs-2816	88	46	𝑦1	𝑦1	PROPN
iajs-2816	88	47	,	,	PUNCT
iajs-2816	88	48	𝑦2	𝑦2	PROPN
iajs-2816	88	49	,	,	PUNCT
iajs-2816	88	50	𝑦3	𝑦3	PROPN
iajs-2816	88	51	,	,	PUNCT
iajs-2816	88	52	𝑦4	𝑦4	PROPN
iajs-2816	88	53	)	)	PUNCT
iajs-2816	88	54	=	=	SYM
iajs-2816	88	55	(	(	PUNCT
iajs-2816	88	56	𝑦𝑢1	𝑦𝑢1	PROPN
iajs-2816	88	57	,	,	PUNCT
iajs-2816	88	58	𝑦𝑢2	𝑦𝑢2	NOUN
iajs-2816	88	59	,	,	PUNCT
iajs-2816	88	60	𝑦𝑢3	𝑦𝑢3	PROPN
iajs-2816	88	61	,	,	PUNCT
iajs-2816	88	62	𝑦𝑢4	𝑦𝑢4	NOUN
iajs-2816	88	63	)	)	PUNCT
iajs-2816	88	64	equations	equation	NOUN
iajs-2816	88	65	(	(	PUNCT
iajs-2816	88	66	(	(	PUNCT
iajs-2816	88	67	1	1	NUM
iajs-2816	88	68	)	)	PUNCT
iajs-2816	88	69	–	–	PUNCT
iajs-2816	88	70	(	(	PUNCT
iajs-2816	88	71	6	6	NUM
iajs-2816	88	72	)	)	PUNCT
iajs-2816	88	73	)	)	PUNCT
iajs-2816	88	74	are	be	AUX
iajs-2816	88	75	expressed	express	VERB
iajs-2816	88	76	by	by	ADP
iajs-2816	88	77	:	:	PUNCT
iajs-2816	88	78	−𝑧1𝑡	−𝑧1𝑡	PUNCT
iajs-2816	89	1	−	−	PROPN
iajs-2816	89	2	∆𝑧1	∆𝑧1	NOUN
iajs-2816	89	3	+	+	NUM
iajs-2816	89	4	𝑧1	𝑧1	NOUN
iajs-2816	89	5	+	+	CCONJ
iajs-2816	89	6	𝑧2	𝑧2	NOUN
iajs-2816	89	7	−	−	PROPN
iajs-2816	89	8	𝑧3	𝑧3	ADJ
iajs-2816	89	9	−	−	PROPN
iajs-2816	89	10	𝑧4	𝑧4	PROPN
iajs-2816	89	11	=	=	SYM
iajs-2816	89	12	𝑧1𝑓𝑦1(𝑥	𝑧1𝑓𝑦1(𝑥	PROPN
iajs-2816	89	13	,	,	PUNCT
iajs-2816	89	14	𝑡	𝑡	NOUN
iajs-2816	89	15	,	,	PUNCT
iajs-2816	89	16	𝑦1	𝑦1	NOUN
iajs-2816	89	17	,	,	PUNCT
iajs-2816	89	18	𝑢1	𝑢1	NOUN
iajs-2816	89	19	)	)	PUNCT
iajs-2816	89	20	+	+	CCONJ
iajs-2816	89	21	𝑔𝑦1(𝑥	𝑔𝑦1(𝑥	PROPN
iajs-2816	89	22	,	,	PUNCT
iajs-2816	89	23	𝑡	𝑡	NOUN
iajs-2816	89	24	,	,	PUNCT
iajs-2816	89	25	𝑦1	𝑦1	NOUN
iajs-2816	89	26	,	,	PUNCT
iajs-2816	89	27	𝑢1	𝑢1	NOUN
iajs-2816	89	28	)	)	PUNCT
iajs-2816	89	29	,	,	PUNCT
iajs-2816	89	30	(	(	PUNCT
iajs-2816	89	31	12	12	NUM
iajs-2816	89	32	)	)	PUNCT
iajs-2816	89	33	−𝑧2𝑡	−𝑧2𝑡	NUM
iajs-2816	90	1	−	−	PROPN
iajs-2816	90	2	∆𝑧2	∆𝑧2	PROPN
iajs-2816	90	3	+	+	CCONJ
iajs-2816	90	4	𝑧2	𝑧2	NOUN
iajs-2816	90	5	−	−	NOUN
iajs-2816	90	6	𝑧1	𝑧1	NOUN
iajs-2816	90	7	+	+	CCONJ
iajs-2816	90	8	𝑧3	𝑧3	ADJ
iajs-2816	90	9	+	+	CCONJ
iajs-2816	90	10	𝑧4	𝑧4	ADJ
iajs-2816	90	11	=	=	SYM
iajs-2816	90	12	𝑧1𝑓𝑦1(𝑥	𝑧1𝑓𝑦1(𝑥	NOUN
iajs-2816	90	13	,	,	PUNCT
iajs-2816	90	14	𝑡	𝑡	NOUN
iajs-2816	90	15	,	,	PUNCT
iajs-2816	90	16	𝑦1	𝑦1	NOUN
iajs-2816	90	17	,	,	PUNCT
iajs-2816	90	18	𝑢1	𝑢1	NOUN
iajs-2816	90	19	)	)	PUNCT
iajs-2816	90	20	+	+	CCONJ
iajs-2816	90	21	𝑔𝑦1(𝑥	𝑔𝑦1(𝑥	PROPN
iajs-2816	90	22	,	,	PUNCT
iajs-2816	90	23	𝑡	𝑡	NOUN
iajs-2816	90	24	,	,	PUNCT
iajs-2816	90	25	𝑦1	𝑦1	NOUN
iajs-2816	90	26	,	,	PUNCT
iajs-2816	90	27	𝑢1	𝑢1	NOUN
iajs-2816	90	28	)	)	PUNCT
iajs-2816	90	29	,	,	PUNCT
iajs-2816	90	30	(	(	PUNCT
iajs-2816	90	31	13	13	NUM
iajs-2816	90	32	)	)	PUNCT
iajs-2816	90	33	−𝑧3𝑡	−𝑧3𝑡	NUM
iajs-2816	90	34	−	−	PROPN
iajs-2816	91	1	∆𝑧3	∆𝑧3	PROPN
iajs-2816	92	1	+	+	CCONJ
iajs-2816	92	2	𝑧3	𝑧3	ADJ
iajs-2816	92	3	+	+	NUM
iajs-2816	92	4	𝑧1	𝑧1	NOUN
iajs-2816	92	5	−	−	PROPN
iajs-2816	92	6	𝑧2	𝑧2	NOUN
iajs-2816	92	7	−	−	PROPN
iajs-2816	92	8	𝑧4	𝑧4	PROPN
iajs-2816	92	9	=	=	SYM
iajs-2816	92	10	𝑧1𝑓𝑦1(𝑥	𝑧1𝑓𝑦1(𝑥	PROPN
iajs-2816	92	11	,	,	PUNCT
iajs-2816	92	12	𝑡	𝑡	NOUN
iajs-2816	92	13	,	,	PUNCT
iajs-2816	92	14	𝑦1	𝑦1	NOUN
iajs-2816	92	15	,	,	PUNCT
iajs-2816	92	16	𝑢1	𝑢1	NOUN
iajs-2816	92	17	)	)	PUNCT
iajs-2816	92	18	+	+	CCONJ
iajs-2816	92	19	𝑔𝑦1(𝑥	𝑔𝑦1(𝑥	PROPN
iajs-2816	92	20	,	,	PUNCT
iajs-2816	92	21	𝑡	𝑡	NOUN
iajs-2816	92	22	,	,	PUNCT
iajs-2816	92	23	𝑦1	𝑦1	NOUN
iajs-2816	92	24	,	,	PUNCT
iajs-2816	92	25	𝑢1	𝑢1	NOUN
iajs-2816	92	26	)	)	PUNCT
iajs-2816	92	27	,	,	PUNCT
iajs-2816	92	28	(	(	PUNCT
iajs-2816	92	29	14	14	NUM
iajs-2816	92	30	)	)	PUNCT
iajs-2816	92	31	−𝑧4𝑡	−𝑧4𝑡	NUM
iajs-2816	92	32	−	−	PROPN
iajs-2816	93	1	∆𝑧4	∆𝑧4	NOUN
iajs-2816	94	1	+	+	CCONJ
iajs-2816	94	2	𝑧4	𝑧4	PROPN
iajs-2816	94	3	+	+	CCONJ
iajs-2816	94	4	𝑧1	𝑧1	NOUN
iajs-2816	94	5	−	−	PROPN
iajs-2816	94	6	𝑧2	𝑧2	PROPN
iajs-2816	94	7	+	+	CCONJ
iajs-2816	94	8	𝑧3	𝑧3	PROPN
iajs-2816	94	9	=	=	SYM
iajs-2816	94	10	𝑧1𝑓𝑦1(𝑥	𝑧1𝑓𝑦1(𝑥	PROPN
iajs-2816	94	11	,	,	PUNCT
iajs-2816	94	12	𝑡	𝑡	NOUN
iajs-2816	94	13	,	,	PUNCT
iajs-2816	94	14	𝑦1	𝑦1	NOUN
iajs-2816	94	15	,	,	PUNCT
iajs-2816	94	16	𝑢1	𝑢1	NOUN
iajs-2816	94	17	)	)	PUNCT
iajs-2816	94	18	+	+	CCONJ
iajs-2816	94	19	𝑔𝑦1(𝑥	𝑔𝑦1(𝑥	PROPN
iajs-2816	94	20	,	,	PUNCT
iajs-2816	94	21	𝑡	𝑡	NOUN
iajs-2816	94	22	,	,	PUNCT
iajs-2816	94	23	𝑦1	𝑦1	NOUN
iajs-2816	94	24	,	,	PUNCT
iajs-2816	94	25	𝑢1	𝑢1	NOUN
iajs-2816	94	26	)	)	PUNCT
iajs-2816	94	27	,	,	PUNCT
iajs-2816	94	28	(	(	PUNCT
iajs-2816	94	29	15	15	NUM
iajs-2816	94	30	)	)	PUNCT
iajs-2816	94	31	𝑧𝑖(𝑥	𝑧𝑖(𝑥	PUNCT
iajs-2816	94	32	,	,	PUNCT
iajs-2816	94	33	𝑡	𝑡	NOUN
iajs-2816	94	34	)	)	PUNCT
iajs-2816	94	35	=	=	SYM
iajs-2816	94	36	0	0	NUM
iajs-2816	94	37	,	,	PUNCT
iajs-2816	94	38	∀𝑖	∀𝑖	PROPN
iajs-2816	94	39	=	=	NOUN
iajs-2816	94	40	1,2,3,4	1,2,3,4	NUM
iajs-2816	94	41	,	,	PUNCT
iajs-2816	94	42	on	on	ADP
iajs-2816	94	43	σ	σ	PROPN
iajs-2816	94	44	,	,	PUNCT
iajs-2816	94	45	(	(	PUNCT
iajs-2816	94	46	16	16	NUM
iajs-2816	94	47	)	)	PUNCT
iajs-2816	94	48	𝑧𝑖(𝑇	𝑧𝑖(𝑇	NOUN
iajs-2816	94	49	)	)	PUNCT
iajs-2816	94	50	=	=	SYM
iajs-2816	94	51	0	0	NUM
iajs-2816	94	52	,	,	PUNCT
iajs-2816	94	53	∀𝑖	∀𝑖	PROPN
iajs-2816	94	54	=	=	NOUN
iajs-2816	94	55	1,2,3,4	1,2,3,4	NUM
iajs-2816	94	56	,	,	PUNCT
iajs-2816	94	57	on	on	ADP
iajs-2816	94	58	γ	γ	X
iajs-2816	94	59	,	,	PUNCT
iajs-2816	94	60	(	(	PUNCT
iajs-2816	94	61	17	17	NUM
iajs-2816	94	62	)	)	PUNCT
iajs-2816	94	63	also	also	ADV
iajs-2816	94	64	,	,	PUNCT
iajs-2816	94	65	the	the	DET
iajs-2816	94	66	hamiltonian	hamiltonian	NOUN
iajs-2816	94	67	is	be	AUX
iajs-2816	94	68	defined	define	VERB
iajs-2816	94	69	:	:	PUNCT
iajs-2816	94	70	𝐻(𝑥	𝐻(𝑥	NUM
iajs-2816	94	71	,	,	PUNCT
iajs-2816	94	72	𝑡	𝑡	PROPN
iajs-2816	94	73	,	,	PUNCT
iajs-2816	94	74	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	94	75	,	,	PUNCT
iajs-2816	94	76	𝑧𝑖	𝑧𝑖	NOUN
iajs-2816	94	77	,	,	PUNCT
iajs-2816	94	78	𝑢𝑖	𝑢𝑖	INTJ
iajs-2816	94	79	)	)	PUNCT
iajs-2816	94	80	=	=	SYM
iajs-2816	94	81	∑	∑	PUNCT
iajs-2816	94	82	𝑧𝑖𝑓𝑖(𝑥	𝑧𝑖𝑓𝑖(𝑥	PROPN
iajs-2816	94	83	,	,	PUNCT
iajs-2816	94	84	𝑡	𝑡	PROPN
iajs-2816	94	85	,	,	PUNCT
iajs-2816	94	86	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	94	87	,	,	PUNCT
iajs-2816	94	88	𝑢𝑖	𝑢𝑖	PROPN
iajs-2816	94	89	)	)	PUNCT
iajs-2816	94	90	+	+	CCONJ
iajs-2816	94	91	𝑔𝑖(𝑥	𝑔𝑖(𝑥	NUM
iajs-2816	94	92	,	,	PUNCT
iajs-2816	94	93	𝑡	𝑡	PROPN
iajs-2816	94	94	,	,	PUNCT
iajs-2816	94	95	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	94	96	,	,	PUNCT
iajs-2816	94	97	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	94	98	)	)	PUNCT
iajs-2816	94	99	4	4	NUM
iajs-2816	94	100	𝑖=1	𝑖=1	PUNCT
iajs-2816	94	101	,	,	PUNCT
iajs-2816	94	102	then	then	ADV
iajs-2816	94	103	the	the	DET
iajs-2816	94	104	frd	frd	NOUN
iajs-2816	94	105	of	of	ADP
iajs-2816	94	106	𝐺	𝐺	PROPN
iajs-2816	94	107	is	be	AUX
iajs-2816	94	108	given	give	VERB
iajs-2816	94	109	by	by	ADP
iajs-2816	94	110	�	�	PROPN
iajs-2816	94	111	́	́	PROPN
iajs-2816	94	112	�	�	PROPN
iajs-2816	94	113	(	(	PUNCT
iajs-2816	94	114	�	�	PROPN
iajs-2816	94	115	⃗⃗	⃗⃗	PROPN
iajs-2816	94	116	�	�	PROPN
iajs-2816	94	117	)	)	PUNCT
iajs-2816	95	1	∙	∙	PROPN
iajs-2816	95	2	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	95	3	=	=	SYM
iajs-2816	95	4	∫	∫	PROPN
iajs-2816	95	5	(	(	PUNCT
iajs-2816	95	6	𝑧1𝑓𝑢1	𝑧1𝑓𝑢1	NOUN
iajs-2816	95	7	+	+	CCONJ
iajs-2816	95	8	𝑔𝑢1	𝑔𝑢1	PROPN
iajs-2816	95	9	𝑧2𝑓𝑢2	𝑧2𝑓𝑢2	VERB
iajs-2816	95	10	+	+	NUM
iajs-2816	95	11	𝑔𝑢2	𝑔𝑢2	PROPN
iajs-2816	95	12	𝑧3𝑓𝑢3	𝑧3𝑓𝑢3	NOUN
iajs-2816	95	13	+	+	CCONJ
iajs-2816	95	14	𝑔𝑢3	𝑔𝑢3	VERB
iajs-2816	95	15	𝑧4𝑓𝑢4	𝑧4𝑓𝑢4	ADV
iajs-2816	95	16	+	+	CCONJ
iajs-2816	95	17	𝑔𝑢4	𝑔𝑢4	NOUN
iajs-2816	95	18	)	)	PUNCT
iajs-2816	95	19	𝑄	𝑄	PROPN
iajs-2816	95	20	∙	∙	PROPN
iajs-2816	95	21	(	(	PUNCT
iajs-2816	95	22	𝛿𝑢1	𝛿𝑢1	ADV
iajs-2816	95	23	𝛿𝑢2	𝛿𝑢2	PROPN
iajs-2816	95	24	𝛿𝑢3	𝛿𝑢3	NOUN
iajs-2816	95	25	𝛿𝑢4	𝛿𝑢4	PROPN
iajs-2816	95	26	)	)	PUNCT
iajs-2816	95	27	𝑑𝑥.	𝑑𝑥.	NOUN
iajs-2816	95	28	ihjpas	ihjpa	VERB
iajs-2816	95	29	.	.	PUNCT
iajs-2816	96	1	53	53	NUM
iajs-2816	96	2	(	(	PUNCT
iajs-2816	96	3	3)2022	3)2022	NOUN
iajs-2816	96	4	139	139	NUM
iajs-2816	96	5	proof	proof	NOUN
iajs-2816	96	6	:	:	PUNCT
iajs-2816	96	7	firstly	firstly	ADV
iajs-2816	96	8	,	,	PUNCT
iajs-2816	96	9	let	let	VERB
iajs-2816	96	10	�	�	PROPN
iajs-2816	96	11	⃗⃗	⃗⃗	PROPN
iajs-2816	96	12	�	�	PROPN
iajs-2816	96	13	be	be	AUX
iajs-2816	96	14	a	a	DET
iajs-2816	96	15	qcccv	qcccv	ADJ
iajs-2816	96	16	,	,	PUNCT
iajs-2816	96	17	and	and	CCONJ
iajs-2816	96	18	�	�	PROPN
iajs-2816	96	19	⃗	⃗	NOUN
iajs-2816	96	20	�	�	PROPN
iajs-2816	96	21	be	be	AUX
iajs-2816	96	22	its	its	PRON
iajs-2816	96	23	qsvs	qsvs	NOUN
iajs-2816	96	24	,	,	PUNCT
iajs-2816	96	25	and	and	CCONJ
iajs-2816	96	26	let	let	VERB
iajs-2816	96	27	𝐺(	𝐺(	PROPN
iajs-2816	96	28	�	�	PROPN
iajs-2816	96	29	⃗⃗	⃗⃗	PROPN
iajs-2816	96	30	�	�	PROPN
iajs-2816	96	31	)	)	PUNCT
iajs-2816	96	32	=	=	PUNCT
iajs-2816	97	1	∑	∑	PROPN
iajs-2816	97	2	∫	∫	PROPN
iajs-2816	97	3	𝑔𝑖(𝑥	𝑔𝑖(𝑥	X
iajs-2816	97	4	,	,	PUNCT
iajs-2816	97	5	𝑡	𝑡	PROPN
iajs-2816	97	6	,	,	PUNCT
iajs-2816	97	7	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	97	8	,	,	PUNCT
iajs-2816	97	9	𝑢𝑖)𝑑𝑥𝑑𝑡	𝑢𝑖)𝑑𝑥𝑑𝑡	NOUN
iajs-2816	97	10	𝑄	𝑄	PROPN
iajs-2816	97	11	4	4	NUM
iajs-2816	97	12	𝑖=1	𝑖=1	PUNCT
iajs-2816	97	13	,	,	PUNCT
iajs-2816	97	14	from	from	ADP
iajs-2816	97	15	the	the	DET
iajs-2816	97	16	hypotheses	hypothesis	NOUN
iajs-2816	97	17	on	on	ADP
iajs-2816	97	18	𝑔𝑙	𝑔𝑙	PROPN
iajs-2816	97	19	(	(	PUNCT
iajs-2816	97	20	𝑙	𝑙	NOUN
iajs-2816	97	21	=	=	NOUN
iajs-2816	97	22	1,2,3,4	1,2,3,4	NUM
iajs-2816	97	23	)	)	PUNCT
iajs-2816	97	24	,	,	PUNCT
iajs-2816	97	25	the	the	DET
iajs-2816	97	26	frd	frd	ADJ
iajs-2816	97	27	definition	definition	NOUN
iajs-2816	97	28	,	,	PUNCT
iajs-2816	97	29	the	the	DET
iajs-2816	97	30	result	result	NOUN
iajs-2816	97	31	of	of	ADP
iajs-2816	97	32	the	the	PRON
iajs-2816	97	33	.	.	PROPN
iajs-2816	97	34	2.3	2.3	NUM
iajs-2816	97	35	,	,	PUNCT
iajs-2816	97	36	and	and	CCONJ
iajs-2816	97	37	then	then	ADV
iajs-2816	97	38	using	use	VERB
iajs-2816	97	39	the	the	DET
iajs-2816	97	40	minkowski	minkowski	PROPN
iajs-2816	97	41	’s	’s	PART
iajs-2816	97	42	inequality	inequality	NOUN
iajs-2816	97	43	(	(	PUNCT
iajs-2816	97	44	mkin	mkin	PROPN
iajs-2816	97	45	)	)	PUNCT
iajs-2816	97	46	,	,	PUNCT
iajs-2816	97	47	one	one	PRON
iajs-2816	97	48	can	can	AUX
iajs-2816	97	49	get	get	VERB
iajs-2816	97	50	that	that	PRON
iajs-2816	97	51	:	:	PUNCT
iajs-2816	97	52	𝐺(	𝐺(	PROPN
iajs-2816	97	53	�	�	PROPN
iajs-2816	97	54	⃗⃗	⃗⃗	PROPN
iajs-2816	97	55	�	�	PROPN
iajs-2816	97	56	+	+	CCONJ
iajs-2816	97	57	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	97	58	)	)	PUNCT
iajs-2816	97	59	−	−	PROPN
iajs-2816	97	60	𝐺(	𝐺(	PROPN
iajs-2816	97	61	�	�	PROPN
iajs-2816	97	62	⃗⃗	⃗⃗	PROPN
iajs-2816	97	63	�	�	PROPN
iajs-2816	97	64	)	)	PUNCT
iajs-2816	97	65	=	=	SYM
iajs-2816	97	66	∫	∫	PROPN
iajs-2816	97	67	(	(	PUNCT
iajs-2816	97	68	𝑔𝑦1𝛿𝑦1	𝑔𝑦1𝛿𝑦1	NOUN
iajs-2816	97	69	+	+	CCONJ
iajs-2816	97	70	𝑔𝑢1𝛿𝑢1	𝑔𝑢1𝛿𝑢1	NOUN
iajs-2816	97	71	)	)	PUNCT
iajs-2816	97	72	𝑄	𝑄	PRON
iajs-2816	97	73	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	97	74	+	+	X
iajs-2816	97	75	∫	∫	PROPN
iajs-2816	97	76	(	(	PUNCT
iajs-2816	97	77	𝑔𝑦2𝛿𝑦2	𝑔𝑦2𝛿𝑦2	NOUN
iajs-2816	97	78	+	+	CCONJ
iajs-2816	97	79	𝑔𝑢2𝛿𝑢2	𝑔𝑢2𝛿𝑢2	ADJ
iajs-2816	97	80	)	)	PUNCT
iajs-2816	97	81	𝑄	𝑄	PRON
iajs-2816	97	82	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	97	83	+	+	X
iajs-2816	97	84	∫	∫	PROPN
iajs-2816	97	85	(	(	PUNCT
iajs-2816	97	86	𝑔𝑦3𝛿𝑦3	𝑔𝑦3𝛿𝑦3	PROPN
iajs-2816	97	87	+	+	SYM
iajs-2816	97	88	𝑔𝑢3𝛿𝑢3	𝑔𝑢3𝛿𝑢3	NOUN
iajs-2816	97	89	)	)	PUNCT
iajs-2816	97	90	𝑄	𝑄	PRON
iajs-2816	97	91	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	97	92	+	+	X
iajs-2816	97	93	∫	∫	PROPN
iajs-2816	97	94	(	(	PUNCT
iajs-2816	97	95	𝑔𝑦4𝛿𝑦4	𝑔𝑦4𝛿𝑦4	ADJ
iajs-2816	97	96	+	+	CCONJ
iajs-2816	97	97	𝑔𝑢4𝛿𝑢4	𝑔𝑢4𝛿𝑢4	ADJ
iajs-2816	97	98	)	)	PUNCT
iajs-2816	97	99	𝑄	𝑄	PRON
iajs-2816	97	100	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	97	101	+	+	CCONJ
iajs-2816	97	102	휀6(𝛿𝑢⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	휀6(𝛿𝑢⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	97	103	‖𝑳𝟐(𝑸	‖𝑳𝟐(𝑸	PROPN
iajs-2816	97	104	)	)	PUNCT
iajs-2816	97	105	(	(	PUNCT
iajs-2816	97	106	18	18	NUM
iajs-2816	97	107	)	)	PUNCT
iajs-2816	97	108	where	where	SCONJ
iajs-2816	97	109	휀6(𝛿𝑢⃗⃗⃗⃗⃗	휀6(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	97	110	)	)	PUNCT
iajs-2816	97	111	=	=	SYM
iajs-2816	97	112	휀2(𝛿𝑢⃗⃗⃗⃗⃗	휀2(𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	97	113	)	)	PUNCT
iajs-2816	97	114	+	+	NUM
iajs-2816	97	115	휀3(𝛿𝑢⃗⃗⃗⃗⃗	휀3(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	97	116	)	)	PUNCT
iajs-2816	97	117	+	+	CCONJ
iajs-2816	97	118	휀4(𝛿𝑢⃗⃗⃗⃗⃗	휀4(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	97	119	)	)	PUNCT
iajs-2816	97	120	+	+	NUM
iajs-2816	97	121	휀5(𝛿𝑢⃗⃗⃗⃗⃗	휀5(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	97	122	)	)	PUNCT
iajs-2816	97	123	⟶	⟶	NOUN
iajs-2816	97	124	0	0	NUM
iajs-2816	97	125	as	as	ADP
iajs-2816	97	126	‖𝛿𝑢⃗⃗⃗⃗⃗	‖𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	97	127	‖	‖	PROPN
iajs-2816	97	128	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	97	129	)	)	PUNCT
iajs-2816	97	130	⟶	⟶	NOUN
iajs-2816	97	131	0	0	NUM
iajs-2816	97	132	.	.	PUNCT
iajs-2816	98	1	on	on	ADP
iajs-2816	98	2	the	the	DET
iajs-2816	98	3	other	other	ADJ
iajs-2816	98	4	hand	hand	NOUN
iajs-2816	98	5	,	,	PUNCT
iajs-2816	98	6	the	the	DET
iajs-2816	98	7	wf	wf	PROPN
iajs-2816	98	8	of	of	ADP
iajs-2816	98	9	the	the	DET
iajs-2816	98	10	qaes	qaes	NOUN
iajs-2816	98	11	for	for	ADP
iajs-2816	98	12	𝑣𝑖	𝑣𝑖	ADP
iajs-2816	98	13	∈	∈	PROPN
iajs-2816	98	14	𝑉	𝑉	PROPN
iajs-2816	98	15	,	,	PUNCT
iajs-2816	98	16	∀	∀	NOUN
iajs-2816	98	17	𝑖	𝑖	NOUN
iajs-2816	99	1	=	=	NOUN
iajs-2816	99	2	1,2,3,4	1,2,3,4	NUM
iajs-2816	99	3	is	be	AUX
iajs-2816	99	4	given	give	VERB
iajs-2816	99	5	by	by	ADP
iajs-2816	99	6	:	:	PUNCT
iajs-2816	99	7	−〈𝑧1𝑡	−〈𝑧1𝑡	NUM
iajs-2816	99	8	,	,	PUNCT
iajs-2816	99	9	𝑣1	𝑣1	NOUN
iajs-2816	99	10	〉	〉	NOUN
iajs-2816	99	11	+	+	CCONJ
iajs-2816	99	12	(	(	PUNCT
iajs-2816	99	13	∇𝑧1	∇𝑧1	NOUN
iajs-2816	99	14	,	,	PUNCT
iajs-2816	99	15	∇𝑣1	∇𝑣1	NOUN
iajs-2816	99	16	)	)	PUNCT
iajs-2816	100	1	+	+	CCONJ
iajs-2816	100	2	(	(	PUNCT
iajs-2816	100	3	𝑧1	𝑧1	NOUN
iajs-2816	100	4	,	,	PUNCT
iajs-2816	100	5	𝑣1	𝑣1	NOUN
iajs-2816	100	6	)	)	PUNCT
iajs-2816	100	7	+	+	CCONJ
iajs-2816	100	8	(	(	PUNCT
iajs-2816	100	9	𝑧2	𝑧2	NOUN
iajs-2816	100	10	,	,	PUNCT
iajs-2816	100	11	𝑣1	𝑣1	PROPN
iajs-2816	100	12	)	)	PUNCT
iajs-2816	100	13	−	−	PROPN
iajs-2816	101	1	(	(	PUNCT
iajs-2816	101	2	𝑧3	𝑧3	PROPN
iajs-2816	101	3	,	,	PUNCT
iajs-2816	101	4	𝑣1	𝑣1	NOUN
iajs-2816	101	5	)	)	PUNCT
iajs-2816	101	6	−	−	PROPN
iajs-2816	101	7	(	(	PUNCT
iajs-2816	101	8	𝑧4	𝑧4	PROPN
iajs-2816	101	9	,	,	PUNCT
iajs-2816	101	10	𝑣1	𝑣1	NOUN
iajs-2816	101	11	)	)	PUNCT
iajs-2816	101	12	=	=	PUNCT
iajs-2816	101	13	(	(	PUNCT
iajs-2816	101	14	𝑧1𝑓1𝑦1	𝑧1𝑓1𝑦1	NOUN
iajs-2816	101	15	,	,	PUNCT
iajs-2816	101	16	𝑣1	𝑣1	PROPN
iajs-2816	101	17	)	)	PUNCT
iajs-2816	102	1	+	+	CCONJ
iajs-2816	102	2	(	(	PUNCT
iajs-2816	102	3	𝑔1𝑦1	𝑔1𝑦1	NUM
iajs-2816	102	4	,	,	PUNCT
iajs-2816	102	5	𝑣1	𝑣1	PROPN
iajs-2816	102	6	)	)	PUNCT
iajs-2816	102	7	,	,	PUNCT
iajs-2816	102	8	(	(	PUNCT
iajs-2816	102	9	19	19	NUM
iajs-2816	102	10	)	)	PUNCT
iajs-2816	102	11	−〈𝑧2𝑡	−〈𝑧2𝑡	NOUN
iajs-2816	102	12	,	,	PUNCT
iajs-2816	102	13	𝑣2	𝑣2	NOUN
iajs-2816	102	14	〉	〉	NOUN
iajs-2816	102	15	+	+	CCONJ
iajs-2816	102	16	(	(	PUNCT
iajs-2816	102	17	∇𝑧2	∇𝑧2	NOUN
iajs-2816	102	18	,	,	PUNCT
iajs-2816	102	19	∇𝑣2	∇𝑣2	PRON
iajs-2816	102	20	)	)	PUNCT
iajs-2816	103	1	+	+	CCONJ
iajs-2816	103	2	(	(	PUNCT
iajs-2816	103	3	𝑧2	𝑧2	PROPN
iajs-2816	103	4	,	,	PUNCT
iajs-2816	103	5	𝑣2	𝑣2	PROPN
iajs-2816	103	6	)	)	PUNCT
iajs-2816	103	7	−	−	PROPN
iajs-2816	104	1	(	(	PUNCT
iajs-2816	104	2	𝑧1	𝑧1	PROPN
iajs-2816	104	3	,	,	PUNCT
iajs-2816	104	4	𝑣2	𝑣2	PROPN
iajs-2816	104	5	)	)	PUNCT
iajs-2816	104	6	+	+	CCONJ
iajs-2816	104	7	(	(	PUNCT
iajs-2816	104	8	𝑧3	𝑧3	PROPN
iajs-2816	104	9	,	,	PUNCT
iajs-2816	104	10	𝑣2	𝑣2	PROPN
iajs-2816	104	11	)	)	PUNCT
iajs-2816	104	12	+	+	CCONJ
iajs-2816	104	13	(	(	PUNCT
iajs-2816	104	14	𝑧4	𝑧4	PROPN
iajs-2816	104	15	,	,	PUNCT
iajs-2816	104	16	𝑣2	𝑣2	NOUN
iajs-2816	104	17	)	)	PUNCT
iajs-2816	104	18	=	=	PUNCT
iajs-2816	104	19	(	(	PUNCT
iajs-2816	104	20	𝑧2𝑓2𝑦2	𝑧2𝑓2𝑦2	PROPN
iajs-2816	104	21	,	,	PUNCT
iajs-2816	104	22	𝑣2	𝑣2	PROPN
iajs-2816	104	23	)	)	PUNCT
iajs-2816	104	24	+	+	CCONJ
iajs-2816	104	25	(	(	PUNCT
iajs-2816	104	26	𝑔2𝑦2	𝑔2𝑦2	PROPN
iajs-2816	104	27	,	,	PUNCT
iajs-2816	104	28	𝑣2	𝑣2	PROPN
iajs-2816	104	29	)	)	PUNCT
iajs-2816	104	30	,	,	PUNCT
iajs-2816	104	31	(	(	PUNCT
iajs-2816	104	32	20	20	NUM
iajs-2816	104	33	)	)	PUNCT
iajs-2816	104	34	−〈𝑧3𝑡	−〈𝑧3𝑡	ADJ
iajs-2816	104	35	,	,	PUNCT
iajs-2816	104	36	𝑣3	𝑣3	ADJ
iajs-2816	104	37	〉	〉	NOUN
iajs-2816	104	38	+	+	CCONJ
iajs-2816	104	39	(	(	PUNCT
iajs-2816	104	40	∇𝑧3	∇𝑧3	NOUN
iajs-2816	104	41	,	,	PUNCT
iajs-2816	104	42	∇𝑣3	∇𝑣3	NOUN
iajs-2816	104	43	)	)	PUNCT
iajs-2816	104	44	+	+	CCONJ
iajs-2816	104	45	(	(	PUNCT
iajs-2816	104	46	𝑧3	𝑧3	ADJ
iajs-2816	104	47	,	,	PUNCT
iajs-2816	104	48	𝑣3	𝑣3	ADJ
iajs-2816	104	49	)	)	PUNCT
iajs-2816	104	50	+	+	CCONJ
iajs-2816	104	51	(	(	PUNCT
iajs-2816	104	52	𝑧1	𝑧1	NOUN
iajs-2816	104	53	,	,	PUNCT
iajs-2816	104	54	𝑣3	𝑣3	ADJ
iajs-2816	104	55	)	)	PUNCT
iajs-2816	104	56	−	−	PROPN
iajs-2816	105	1	(	(	PUNCT
iajs-2816	105	2	𝑧2	𝑧2	NOUN
iajs-2816	105	3	,	,	PUNCT
iajs-2816	105	4	𝑣3	𝑣3	ADJ
iajs-2816	105	5	)	)	PUNCT
iajs-2816	105	6	−	−	PROPN
iajs-2816	105	7	(	(	PUNCT
iajs-2816	105	8	𝑧4	𝑧4	ADJ
iajs-2816	105	9	,	,	PUNCT
iajs-2816	105	10	𝑣3	𝑣3	ADJ
iajs-2816	105	11	)	)	PUNCT
iajs-2816	105	12	=	=	SYM
iajs-2816	105	13	(	(	PUNCT
iajs-2816	105	14	𝑧3𝑓3𝑦3	𝑧3𝑓3𝑦3	PROPN
iajs-2816	105	15	,	,	PUNCT
iajs-2816	105	16	𝑣3	𝑣3	PROPN
iajs-2816	105	17	)	)	PUNCT
iajs-2816	105	18	+	+	CCONJ
iajs-2816	105	19	(	(	PUNCT
iajs-2816	105	20	𝑔3𝑦3	𝑔3𝑦3	INTJ
iajs-2816	105	21	,	,	PUNCT
iajs-2816	105	22	𝑣3	𝑣3	ADJ
iajs-2816	105	23	)	)	PUNCT
iajs-2816	105	24	,	,	PUNCT
iajs-2816	105	25	(	(	PUNCT
iajs-2816	105	26	21	21	NUM
iajs-2816	105	27	)	)	PUNCT
iajs-2816	106	1	−〈𝑧4𝑡	−〈𝑧4𝑡	PUNCT
iajs-2816	106	2	,	,	PUNCT
iajs-2816	106	3	𝑣4	𝑣4	VERB
iajs-2816	106	4	〉	〉	NOUN
iajs-2816	106	5	+	+	CCONJ
iajs-2816	106	6	(	(	PUNCT
iajs-2816	106	7	∇𝑧4	∇𝑧4	NOUN
iajs-2816	106	8	,	,	PUNCT
iajs-2816	106	9	∇𝑣4	∇𝑣4	NUM
iajs-2816	106	10	)	)	PUNCT
iajs-2816	107	1	+	+	CCONJ
iajs-2816	107	2	(	(	PUNCT
iajs-2816	107	3	𝑧4	𝑧4	ADJ
iajs-2816	107	4	,	,	PUNCT
iajs-2816	107	5	𝑣4	𝑣4	NOUN
iajs-2816	107	6	)	)	PUNCT
iajs-2816	107	7	+	+	CCONJ
iajs-2816	107	8	(	(	PUNCT
iajs-2816	107	9	𝑧1	𝑧1	NOUN
iajs-2816	107	10	,	,	PUNCT
iajs-2816	107	11	𝑣4	𝑣4	NOUN
iajs-2816	107	12	)	)	PUNCT
iajs-2816	107	13	−	−	PROPN
iajs-2816	107	14	(	(	PUNCT
iajs-2816	107	15	𝑧2	𝑧2	NOUN
iajs-2816	107	16	,	,	PUNCT
iajs-2816	107	17	𝑣4	𝑣4	NOUN
iajs-2816	107	18	)	)	PUNCT
iajs-2816	107	19	+	+	CCONJ
iajs-2816	107	20	(	(	PUNCT
iajs-2816	107	21	𝑧3	𝑧3	ADJ
iajs-2816	107	22	,	,	PUNCT
iajs-2816	107	23	𝑣4	𝑣4	NOUN
iajs-2816	107	24	)	)	PUNCT
iajs-2816	107	25	=	=	PRON
iajs-2816	107	26	(	(	PUNCT
iajs-2816	107	27	𝑧4𝑓4𝑦4	𝑧4𝑓4𝑦4	ADJ
iajs-2816	107	28	,	,	PUNCT
iajs-2816	107	29	𝑣4	𝑣4	NOUN
iajs-2816	107	30	)	)	PUNCT
iajs-2816	107	31	+	+	CCONJ
iajs-2816	107	32	(	(	PUNCT
iajs-2816	107	33	𝑔4𝑦4	𝑔4𝑦4	PROPN
iajs-2816	107	34	,	,	PUNCT
iajs-2816	107	35	𝑣4	𝑣4	NOUN
iajs-2816	107	36	)	)	PUNCT
iajs-2816	107	37	,	,	PUNCT
iajs-2816	107	38	(	(	PUNCT
iajs-2816	107	39	22	22	X
iajs-2816	107	40	)	)	PUNCT
iajs-2816	107	41	the	the	DET
iajs-2816	107	42	existence	existence	NOUN
iajs-2816	107	43	of	of	ADP
iajs-2816	107	44	a	a	DET
iajs-2816	107	45	unique	unique	ADJ
iajs-2816	107	46	solution	solution	NOUN
iajs-2816	107	47	of	of	ADP
iajs-2816	107	48	(	(	PUNCT
iajs-2816	107	49	(	(	PUNCT
iajs-2816	107	50	19	19	NUM
iajs-2816	107	51	)	)	PUNCT
iajs-2816	107	52	–	–	PUNCT
iajs-2816	107	53	(	(	PUNCT
iajs-2816	107	54	22	22	NUM
iajs-2816	107	55	)	)	PUNCT
iajs-2816	107	56	)	)	PUNCT
iajs-2816	107	57	can	can	AUX
iajs-2816	107	58	be	be	AUX
iajs-2816	107	59	proved	prove	VERB
iajs-2816	107	60	by	by	ADP
iajs-2816	107	61	the	the	DET
iajs-2816	107	62	same	same	ADJ
iajs-2816	107	63	manner	manner	NOUN
iajs-2816	107	64	which	which	PRON
iajs-2816	107	65	is	be	AUX
iajs-2816	107	66	used	use	VERB
iajs-2816	107	67	in	in	ADP
iajs-2816	107	68	the	the	DET
iajs-2816	107	69	proof	proof	NOUN
iajs-2816	107	70	of	of	ADP
iajs-2816	107	71	the	the	DET
iajs-2816	107	72	unique	unique	NOUN
iajs-2816	107	73	of	of	ADP
iajs-2816	107	74	the	the	DET
iajs-2816	107	75	qsvs	qsvs	NOUN
iajs-2816	107	76	.	.	PUNCT
iajs-2816	108	1	now	now	ADV
iajs-2816	108	2	,	,	PUNCT
iajs-2816	108	3	substituting	substitute	VERB
iajs-2816	108	4	𝑣𝑖	𝑣𝑖	ADP
iajs-2816	108	5	=	=	SYM
iajs-2816	108	6	𝛿𝑦𝑖	𝛿𝑦𝑖	PROPN
iajs-2816	108	7	,	,	PUNCT
iajs-2816	108	8	∀𝑖	∀𝑖	PROPN
iajs-2816	108	9	=	=	NOUN
iajs-2816	108	10	1,2,3,4	1,2,3,4	NUM
iajs-2816	108	11	in	in	ADP
iajs-2816	108	12	(	(	PUNCT
iajs-2816	108	13	(	(	PUNCT
iajs-2816	108	14	19	19	NUM
iajs-2816	108	15	)	)	PUNCT
iajs-2816	108	16	−	−	PROPN
iajs-2816	108	17	(	(	PUNCT
iajs-2816	108	18	22	22	NUM
iajs-2816	108	19	)	)	PUNCT
iajs-2816	108	20	)	)	PUNCT
iajs-2816	108	21	resp	resp	NOUN
iajs-2816	108	22	.	.	PUNCT
iajs-2816	108	23	,	,	PUNCT
iajs-2816	108	24	then	then	ADV
iajs-2816	108	25	taking	take	VERB
iajs-2816	108	26	the	the	DET
iajs-2816	108	27	integrating	integrating	NOUN
iajs-2816	108	28	both	both	DET
iajs-2816	108	29	sides	side	NOUN
iajs-2816	108	30	(	(	PUNCT
iajs-2816	108	31	ibs	ibs	PROPN
iajs-2816	108	32	)	)	PUNCT
iajs-2816	108	33	from	from	ADP
iajs-2816	108	34	0	0	NUM
iajs-2816	108	35	to	to	ADP
iajs-2816	108	36	𝑇	𝑇	PROPN
iajs-2816	108	37	,	,	PUNCT
iajs-2816	108	38	lastly	lastly	ADV
iajs-2816	108	39	,	,	PUNCT
iajs-2816	108	40	applying	apply	VERB
iajs-2816	108	41	integration	integration	NOUN
iajs-2816	108	42	by	by	ADP
iajs-2816	108	43	part	part	NOUN
iajs-2816	108	44	(	(	PUNCT
iajs-2816	108	45	ibp	ibp	NOUN
iajs-2816	108	46	)	)	PUNCT
iajs-2816	108	47	for	for	ADP
iajs-2816	108	48	the	the	DET
iajs-2816	108	49	1st	1st	ADJ
iajs-2816	108	50	terms	term	NOUN
iajs-2816	108	51	of	of	ADP
iajs-2816	108	52	each	each	DET
iajs-2816	108	53	resulting	result	VERB
iajs-2816	108	54	equation	equation	NOUN
iajs-2816	108	55	,	,	PUNCT
iajs-2816	108	56	to	to	PART
iajs-2816	108	57	get	get	VERB
iajs-2816	108	58	that	that	PRON
iajs-2816	108	59	:	:	PUNCT
iajs-2816	108	60	∫	∫	PROPN
iajs-2816	108	61	〈	〈	INTJ
iajs-2816	108	62	𝛿𝑦1	𝛿𝑦1	NOUN
iajs-2816	108	63	,	,	PUNCT
iajs-2816	108	64	𝑧1	𝑧1	VERB
iajs-2816	108	65	〉	〉	NOUN
iajs-2816	108	66	𝑇	𝑇	PROPN
iajs-2816	108	67	0	0	NUM
iajs-2816	108	68	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	108	69	+	+	NOUN
iajs-2816	108	70	∫	∫	PROPN
iajs-2816	109	1	[	[	X
iajs-2816	109	2	(	(	PUNCT
iajs-2816	109	3	∇𝑧1	∇𝑧1	NOUN
iajs-2816	109	4	,	,	PUNCT
iajs-2816	109	5	∇𝛿𝑦1	∇𝛿𝑦1	NOUN
iajs-2816	109	6	)	)	PUNCT
iajs-2816	109	7	+	+	CCONJ
iajs-2816	109	8	(	(	PUNCT
iajs-2816	109	9	𝑧1	𝑧1	NOUN
iajs-2816	109	10	,	,	PUNCT
iajs-2816	109	11	𝛿𝑦1	𝛿𝑦1	NOUN
iajs-2816	109	12	)	)	PUNCT
iajs-2816	110	1	+	+	CCONJ
iajs-2816	110	2	(	(	PUNCT
iajs-2816	110	3	𝑧2	𝑧2	NOUN
iajs-2816	110	4	,	,	PUNCT
iajs-2816	110	5	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	110	6	)	)	PUNCT
iajs-2816	110	7	−	−	PROPN
iajs-2816	111	1	(	(	PUNCT
iajs-2816	111	2	𝑧3	𝑧3	ADJ
iajs-2816	111	3	,	,	PUNCT
iajs-2816	111	4	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	111	5	)	)	PUNCT
iajs-2816	111	6	−	−	PROPN
iajs-2816	111	7	(	(	PUNCT
iajs-2816	111	8	𝑧4	𝑧4	PROPN
iajs-2816	111	9	,	,	PUNCT
iajs-2816	111	10	𝛿𝑦1	𝛿𝑦1	NOUN
iajs-2816	111	11	)	)	PUNCT
iajs-2816	111	12	]	]	PUNCT
iajs-2816	111	13	𝑇	𝑇	PROPN
iajs-2816	111	14	0	0	NUM
iajs-2816	111	15	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	111	16	=	=	SYM
iajs-2816	111	17	∫	∫	PROPN
iajs-2816	112	1	[	[	X
iajs-2816	112	2	(	(	PUNCT
iajs-2816	112	3	𝑧1𝑓1𝑦1	𝑧1𝑓1𝑦1	NOUN
iajs-2816	112	4	,	,	PUNCT
iajs-2816	112	5	𝛿𝑦1	𝛿𝑦1	NOUN
iajs-2816	112	6	)	)	PUNCT
iajs-2816	113	1	+	+	CCONJ
iajs-2816	113	2	(	(	PUNCT
iajs-2816	113	3	𝑔1𝑦1	𝑔1𝑦1	X
iajs-2816	113	4	,	,	PUNCT
iajs-2816	113	5	𝛿𝑦1)]𝑑𝑡	𝛿𝑦1)]𝑑𝑡	PROPN
iajs-2816	113	6	𝑇	𝑇	PROPN
iajs-2816	113	7	0	0	NUM
iajs-2816	113	8	,	,	PUNCT
iajs-2816	113	9	(	(	PUNCT
iajs-2816	113	10	23	23	NUM
iajs-2816	113	11	)	)	PUNCT
iajs-2816	113	12	∫	∫	PROPN
iajs-2816	114	1	〈	〈	INTJ
iajs-2816	114	2	𝛿𝑦2	𝛿𝑦2	PROPN
iajs-2816	114	3	,	,	PUNCT
iajs-2816	114	4	𝑧2	𝑧2	NOUN
iajs-2816	114	5	〉	〉	NOUN
iajs-2816	114	6	𝑇	𝑇	PROPN
iajs-2816	114	7	0	0	NUM
iajs-2816	114	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	114	9	+	+	NOUN
iajs-2816	114	10	∫	∫	PROPN
iajs-2816	115	1	[	[	X
iajs-2816	115	2	(	(	PUNCT
iajs-2816	115	3	∇𝑧2	∇𝑧2	NOUN
iajs-2816	115	4	,	,	PUNCT
iajs-2816	115	5	∇𝛿𝑦2	∇𝛿𝑦2	NOUN
iajs-2816	115	6	)	)	PUNCT
iajs-2816	115	7	+	+	CCONJ
iajs-2816	115	8	(	(	PUNCT
iajs-2816	115	9	𝑧2	𝑧2	PROPN
iajs-2816	115	10	,	,	PUNCT
iajs-2816	115	11	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	115	12	)	)	PUNCT
iajs-2816	115	13	−	−	PROPN
iajs-2816	115	14	(	(	PUNCT
iajs-2816	115	15	𝑧1	𝑧1	NOUN
iajs-2816	115	16	,	,	PUNCT
iajs-2816	115	17	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	115	18	)	)	PUNCT
iajs-2816	115	19	+	+	CCONJ
iajs-2816	115	20	(	(	PUNCT
iajs-2816	115	21	𝑧3	𝑧3	ADJ
iajs-2816	115	22	,	,	PUNCT
iajs-2816	115	23	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	115	24	)	)	PUNCT
iajs-2816	115	25	+	+	CCONJ
iajs-2816	115	26	(	(	PUNCT
iajs-2816	115	27	𝑧4	𝑧4	PROPN
iajs-2816	115	28	,	,	PUNCT
iajs-2816	115	29	𝛿𝑦2)]𝑑𝑡	𝛿𝑦2)]𝑑𝑡	PROPN
iajs-2816	115	30	𝑇	𝑇	PROPN
iajs-2816	115	31	0	0	NUM
iajs-2816	116	1	=	=	SYM
iajs-2816	117	1	∫	∫	PROPN
iajs-2816	118	1	[	[	X
iajs-2816	118	2	(	(	PUNCT
iajs-2816	118	3	𝑧2𝑓2𝑦2	𝑧2𝑓2𝑦2	PROPN
iajs-2816	118	4	,	,	PUNCT
iajs-2816	118	5	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	118	6	)	)	PUNCT
iajs-2816	118	7	+	+	CCONJ
iajs-2816	118	8	(	(	PUNCT
iajs-2816	118	9	𝑔2𝑦2	𝑔2𝑦2	X
iajs-2816	118	10	,	,	PUNCT
iajs-2816	118	11	𝛿𝑦2)]𝑑𝑡	𝛿𝑦2)]𝑑𝑡	PROPN
iajs-2816	118	12	𝑇	𝑇	PROPN
iajs-2816	118	13	0	0	NUM
iajs-2816	118	14	,	,	PUNCT
iajs-2816	118	15	(	(	PUNCT
iajs-2816	118	16	24	24	NUM
iajs-2816	118	17	)	)	PUNCT
iajs-2816	118	18	∫	∫	NOUN
iajs-2816	119	1	〈	〈	NOUN
iajs-2816	119	2	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	119	3	,	,	PUNCT
iajs-2816	119	4	𝑧3	𝑧3	ADJ
iajs-2816	119	5	〉	〉	NOUN
iajs-2816	119	6	𝑇	𝑇	PROPN
iajs-2816	119	7	0	0	NUM
iajs-2816	119	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	119	9	+	+	NOUN
iajs-2816	119	10	∫	∫	PROPN
iajs-2816	120	1	[	[	X
iajs-2816	120	2	(	(	PUNCT
iajs-2816	120	3	∇𝑧3	∇𝑧3	NOUN
iajs-2816	120	4	,	,	PUNCT
iajs-2816	120	5	∇𝛿𝑦3	∇𝛿𝑦3	NUM
iajs-2816	120	6	)	)	PUNCT
iajs-2816	120	7	+	+	CCONJ
iajs-2816	120	8	(	(	PUNCT
iajs-2816	120	9	𝑧3	𝑧3	ADJ
iajs-2816	120	10	,	,	PUNCT
iajs-2816	120	11	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	120	12	)	)	PUNCT
iajs-2816	120	13	+	+	CCONJ
iajs-2816	120	14	(	(	PUNCT
iajs-2816	120	15	𝑧1	𝑧1	NOUN
iajs-2816	120	16	,	,	PUNCT
iajs-2816	120	17	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	120	18	)	)	PUNCT
iajs-2816	120	19	−	−	PROPN
iajs-2816	121	1	(	(	PUNCT
iajs-2816	121	2	𝑧2	𝑧2	NOUN
iajs-2816	121	3	,	,	PUNCT
iajs-2816	121	4	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	121	5	)	)	PUNCT
iajs-2816	121	6	−	−	PROPN
iajs-2816	121	7	(	(	PUNCT
iajs-2816	121	8	𝑧4	𝑧4	ADV
iajs-2816	121	9	,	,	PUNCT
iajs-2816	121	10	𝛿𝑦3)]𝑑𝑡	𝛿𝑦3)]𝑑𝑡	PROPN
iajs-2816	121	11	𝑇	𝑇	PROPN
iajs-2816	121	12	0	0	NUM
iajs-2816	121	13	=	=	SYM
iajs-2816	121	14	∫	∫	PROPN
iajs-2816	122	1	[	[	X
iajs-2816	122	2	(	(	PUNCT
iajs-2816	122	3	𝑧3𝑓3𝑦3	𝑧3𝑓3𝑦3	PROPN
iajs-2816	122	4	,	,	PUNCT
iajs-2816	122	5	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	122	6	)	)	PUNCT
iajs-2816	122	7	+	+	CCONJ
iajs-2816	122	8	(	(	PUNCT
iajs-2816	122	9	𝑔3𝑦3	𝑔3𝑦3	INTJ
iajs-2816	122	10	,	,	PUNCT
iajs-2816	122	11	𝛿𝑦3)]𝑑𝑡	𝛿𝑦3)]𝑑𝑡	PROPN
iajs-2816	122	12	𝑇	𝑇	PROPN
iajs-2816	122	13	0	0	NUM
iajs-2816	122	14	,	,	PUNCT
iajs-2816	122	15	(	(	PUNCT
iajs-2816	122	16	25	25	NUM
iajs-2816	122	17	)	)	PUNCT
iajs-2816	122	18	∫	∫	PROPN
iajs-2816	123	1	〈	〈	PROPN
iajs-2816	123	2	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	123	3	,	,	PUNCT
iajs-2816	123	4	𝑧4	𝑧4	ADJ
iajs-2816	123	5	〉	〉	NOUN
iajs-2816	123	6	𝑇	𝑇	NOUN
iajs-2816	123	7	0	0	NUM
iajs-2816	123	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	123	9	+	+	NOUN
iajs-2816	123	10	∫	∫	PROPN
iajs-2816	124	1	[	[	X
iajs-2816	124	2	(	(	PUNCT
iajs-2816	124	3	∇𝑧4	∇𝑧4	NOUN
iajs-2816	124	4	,	,	PUNCT
iajs-2816	124	5	∇𝛿𝑦4	∇𝛿𝑦4	PROPN
iajs-2816	124	6	)	)	PUNCT
iajs-2816	125	1	+	+	CCONJ
iajs-2816	125	2	(	(	PUNCT
iajs-2816	125	3	𝑧4	𝑧4	PROPN
iajs-2816	125	4	,	,	PUNCT
iajs-2816	125	5	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	125	6	)	)	PUNCT
iajs-2816	126	1	+	+	CCONJ
iajs-2816	126	2	(	(	PUNCT
iajs-2816	126	3	𝑧1	𝑧1	NOUN
iajs-2816	126	4	,	,	PUNCT
iajs-2816	126	5	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	126	6	)	)	PUNCT
iajs-2816	126	7	−	−	PROPN
iajs-2816	127	1	(	(	PUNCT
iajs-2816	127	2	𝑧2	𝑧2	PROPN
iajs-2816	127	3	,	,	PUNCT
iajs-2816	127	4	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	127	5	)	)	PUNCT
iajs-2816	128	1	+	+	CCONJ
iajs-2816	128	2	(	(	PUNCT
iajs-2816	128	3	𝑧3	𝑧3	PROPN
iajs-2816	128	4	,	,	PUNCT
iajs-2816	128	5	𝛿𝑦4)]𝑑𝑡	𝛿𝑦4)]𝑑𝑡	PROPN
iajs-2816	128	6	𝑇	𝑇	PROPN
iajs-2816	128	7	0	0	NUM
iajs-2816	128	8	=	=	SYM
iajs-2816	128	9	∫	∫	PROPN
iajs-2816	129	1	[	[	X
iajs-2816	129	2	(	(	PUNCT
iajs-2816	129	3	𝑧4𝑓4𝑦4	𝑧4𝑓4𝑦4	ADJ
iajs-2816	129	4	,	,	PUNCT
iajs-2816	129	5	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	129	6	)	)	PUNCT
iajs-2816	130	1	+	+	CCONJ
iajs-2816	130	2	(	(	PUNCT
iajs-2816	130	3	𝑔4𝑦4	𝑔4𝑦4	PROPN
iajs-2816	130	4	,	,	PUNCT
iajs-2816	130	5	𝛿𝑦4)]𝑑𝑡	𝛿𝑦4)]𝑑𝑡	PROPN
iajs-2816	130	6	𝑇	𝑇	PROPN
iajs-2816	130	7	0	0	NUM
iajs-2816	130	8	,	,	PUNCT
iajs-2816	130	9	(	(	PUNCT
iajs-2816	130	10	26	26	NUM
iajs-2816	130	11	)	)	PUNCT
iajs-2816	130	12	also	also	ADV
iajs-2816	130	13	,	,	PUNCT
iajs-2816	130	14	substituting	substitute	VERB
iajs-2816	130	15	𝑣𝑖	𝑣𝑖	ADP
iajs-2816	130	16	=	=	SYM
iajs-2816	130	17	𝑧𝑖	𝑧𝑖	NOUN
iajs-2816	130	18	,	,	PUNCT
iajs-2816	130	19	∀𝑖	∀𝑖	PROPN
iajs-2816	130	20	=	=	NOUN
iajs-2816	130	21	1,2,3,4	1,2,3,4	NUM
iajs-2816	130	22	in	in	ADP
iajs-2816	130	23	(	(	PUNCT
iajs-2816	130	24	(	(	PUNCT
iajs-2816	130	25	8.a	8.a	NUM
iajs-2816	130	26	)	)	PUNCT
iajs-2816	130	27	−	−	PROPN
iajs-2816	130	28	(	(	PUNCT
iajs-2816	130	29	11.a	11.a	NUM
iajs-2816	130	30	)	)	PUNCT
iajs-2816	130	31	)	)	PUNCT
iajs-2816	130	32	resp	resp	NOUN
iajs-2816	130	33	.	.	PUNCT
iajs-2816	131	1	,	,	PUNCT
iajs-2816	131	2	then	then	ADV
iajs-2816	131	3	ibs	ib	VERB
iajs-2816	131	4	w.r.t	w.r.t	NOUN
iajs-2816	131	5	.	.	PUNCT
iajs-2816	132	1	𝑡	𝑡	PROPN
iajs-2816	132	2	from	from	ADP
iajs-2816	132	3	0	0	NUM
iajs-2816	132	4	to	to	ADP
iajs-2816	132	5	𝑇	𝑇	PROPN
iajs-2816	132	6	,	,	PUNCT
iajs-2816	132	7	to	to	PART
iajs-2816	132	8	obtain	obtain	VERB
iajs-2816	132	9	:	:	PUNCT
iajs-2816	132	10	∫	∫	PROPN
iajs-2816	132	11	〈	〈	PROPN
iajs-2816	132	12	𝛿𝑦1𝑡	𝛿𝑦1𝑡	PROPN
iajs-2816	132	13	,	,	PUNCT
iajs-2816	132	14	𝑧1	𝑧1	VERB
iajs-2816	132	15	〉	〉	NOUN
iajs-2816	132	16	𝑇	𝑇	PROPN
iajs-2816	132	17	0	0	NUM
iajs-2816	132	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	132	19	+	+	NOUN
iajs-2816	132	20	∫	∫	PROPN
iajs-2816	133	1	[	[	X
iajs-2816	133	2	(	(	PUNCT
iajs-2816	133	3	∇δ𝑦1	∇δ𝑦1	PROPN
iajs-2816	133	4	,	,	PUNCT
iajs-2816	133	5	∇𝑧1	∇𝑧1	NOUN
iajs-2816	133	6	)	)	PUNCT
iajs-2816	134	1	+	+	CCONJ
iajs-2816	134	2	(	(	PUNCT
iajs-2816	134	3	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	134	4	,	,	PUNCT
iajs-2816	134	5	𝑧1	𝑧1	NOUN
iajs-2816	134	6	)	)	PUNCT
iajs-2816	134	7	−	−	PROPN
iajs-2816	134	8	(	(	PUNCT
iajs-2816	134	9	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	134	10	,	,	PUNCT
iajs-2816	134	11	𝑧1	𝑧1	NOUN
iajs-2816	134	12	)	)	PUNCT
iajs-2816	135	1	+	+	CCONJ
iajs-2816	135	2	(	(	PUNCT
iajs-2816	135	3	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	135	4	,	,	PUNCT
iajs-2816	135	5	𝑧1	𝑧1	NOUN
iajs-2816	135	6	)	)	PUNCT
iajs-2816	136	1	+	+	CCONJ
iajs-2816	136	2	(	(	PUNCT
iajs-2816	136	3	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	136	4	,	,	PUNCT
iajs-2816	136	5	𝑧1	𝑧1	PROPN
iajs-2816	136	6	)	)	PUNCT
iajs-2816	136	7	]	]	PUNCT
iajs-2816	136	8	𝑇	𝑇	PROPN
iajs-2816	136	9	0	0	NUM
iajs-2816	136	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	136	11	=	=	SYM
iajs-2816	136	12	∫	∫	PROPN
iajs-2816	136	13	(	(	PUNCT
iajs-2816	136	14	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2816	136	15	+	+	CCONJ
iajs-2816	136	16	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	136	17	,	,	PUNCT
iajs-2816	136	18	𝑢1	𝑢1	NOUN
iajs-2816	136	19	+	+	CCONJ
iajs-2816	136	20	𝛿𝑢1	𝛿𝑢1	ADJ
iajs-2816	136	21	)	)	PUNCT
iajs-2816	136	22	,	,	PUNCT
iajs-2816	136	23	𝑧1)𝑑𝑡	𝑧1)𝑑𝑡	PROPN
iajs-2816	136	24	𝑇	𝑇	PROPN
iajs-2816	136	25	0	0	NUM
iajs-2816	136	26	−	−	PROPN
iajs-2816	137	1	∫	∫	PROPN
iajs-2816	137	2	(	(	PUNCT
iajs-2816	137	3	𝑓1(𝑦1	𝑓1(𝑦1	PROPN
iajs-2816	137	4	,	,	PUNCT
iajs-2816	137	5	𝑢1	𝑢1	PROPN
iajs-2816	137	6	)	)	PUNCT
iajs-2816	137	7	,	,	PUNCT
iajs-2816	137	8	𝑧1)𝑑𝑡	𝑧1)𝑑𝑡	PROPN
iajs-2816	137	9	𝑇	𝑇	PROPN
iajs-2816	137	10	0	0	NUM
iajs-2816	137	11	,	,	PUNCT
iajs-2816	137	12	(	(	PUNCT
iajs-2816	137	13	27	27	NUM
iajs-2816	137	14	)	)	PUNCT
iajs-2816	137	15	∫	∫	PROPN
iajs-2816	138	1	〈	〈	NOUN
iajs-2816	138	2	𝛿𝑦2𝑡	𝛿𝑦2𝑡	NOUN
iajs-2816	138	3	,	,	PUNCT
iajs-2816	138	4	𝑧2	𝑧2	NOUN
iajs-2816	138	5	〉	〉	NOUN
iajs-2816	138	6	𝑇	𝑇	PROPN
iajs-2816	138	7	0	0	NUM
iajs-2816	138	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	138	9	+	+	NOUN
iajs-2816	138	10	∫	∫	PROPN
iajs-2816	139	1	[	[	X
iajs-2816	139	2	(	(	PUNCT
iajs-2816	139	3	∇𝛿𝑦2	∇𝛿𝑦2	NOUN
iajs-2816	139	4	,	,	PUNCT
iajs-2816	139	5	∇𝑧2	∇𝑧2	NOUN
iajs-2816	139	6	)	)	PUNCT
iajs-2816	139	7	+	+	CCONJ
iajs-2816	139	8	(	(	PUNCT
iajs-2816	139	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	139	10	,	,	PUNCT
iajs-2816	139	11	𝑧2	𝑧2	NOUN
iajs-2816	139	12	)	)	PUNCT
iajs-2816	139	13	+	+	CCONJ
iajs-2816	139	14	(	(	PUNCT
iajs-2816	139	15	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	139	16	,	,	PUNCT
iajs-2816	139	17	𝑧2	𝑧2	NOUN
iajs-2816	139	18	)	)	PUNCT
iajs-2816	139	19	−	−	PROPN
iajs-2816	139	20	(	(	PUNCT
iajs-2816	139	21	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	139	22	,	,	PUNCT
iajs-2816	139	23	𝑧2	𝑧2	NOUN
iajs-2816	139	24	)	)	PUNCT
iajs-2816	139	25	−	−	PROPN
iajs-2816	140	1	(	(	PUNCT
iajs-2816	140	2	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	140	3	,	,	PUNCT
iajs-2816	140	4	𝑧2	𝑧2	PROPN
iajs-2816	140	5	)	)	PUNCT
iajs-2816	140	6	]	]	PUNCT
iajs-2816	141	1	𝑇	𝑇	PROPN
iajs-2816	141	2	0	0	NUM
iajs-2816	141	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	141	4	=	=	SYM
iajs-2816	141	5	∫	∫	PROPN
iajs-2816	141	6	(	(	PUNCT
iajs-2816	141	7	𝑓2(𝑦2	𝑓2(𝑦2	PROPN
iajs-2816	141	8	+	+	CCONJ
iajs-2816	141	9	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	141	10	,	,	PUNCT
iajs-2816	141	11	𝑢2	𝑢2	PROPN
iajs-2816	141	12	+	+	CCONJ
iajs-2816	141	13	𝛿𝑢2	𝛿𝑢2	PROPN
iajs-2816	141	14	)	)	PUNCT
iajs-2816	141	15	,	,	PUNCT
iajs-2816	141	16	𝑧2)𝑑𝑡	𝑧2)𝑑𝑡	NOUN
iajs-2816	141	17	𝑇	𝑇	PROPN
iajs-2816	141	18	0	0	NUM
iajs-2816	141	19	−	−	PROPN
iajs-2816	141	20	∫	∫	PROPN
iajs-2816	141	21	(	(	PUNCT
iajs-2816	141	22	𝑓2(𝑦2	𝑓2(𝑦2	PROPN
iajs-2816	141	23	,	,	PUNCT
iajs-2816	141	24	𝑢2	𝑢2	PROPN
iajs-2816	141	25	)	)	PUNCT
iajs-2816	141	26	,	,	PUNCT
iajs-2816	141	27	𝑧2)𝑑𝑡	𝑧2)𝑑𝑡	NOUN
iajs-2816	141	28	𝑇	𝑇	PROPN
iajs-2816	141	29	0	0	NUM
iajs-2816	141	30	,	,	PUNCT
iajs-2816	141	31	(	(	PUNCT
iajs-2816	141	32	28	28	NUM
iajs-2816	141	33	)	)	PUNCT
iajs-2816	141	34	ihjpas	ihjpa	NOUN
iajs-2816	141	35	.	.	PUNCT
iajs-2816	142	1	53	53	NUM
iajs-2816	142	2	(	(	PUNCT
iajs-2816	142	3	3)2022	3)2022	NOUN
iajs-2816	142	4	140	140	NUM
iajs-2816	142	5	∫	∫	NOUN
iajs-2816	142	6	〈	〈	NOUN
iajs-2816	142	7	𝛿𝑦3𝑡	𝛿𝑦3𝑡	NOUN
iajs-2816	142	8	,	,	PUNCT
iajs-2816	142	9	𝑧3	𝑧3	ADJ
iajs-2816	142	10	〉	〉	NOUN
iajs-2816	142	11	𝑇	𝑇	PROPN
iajs-2816	142	12	0	0	NUM
iajs-2816	142	13	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	142	14	+	+	NOUN
iajs-2816	142	15	∫	∫	PROPN
iajs-2816	143	1	[	[	X
iajs-2816	143	2	(	(	PUNCT
iajs-2816	143	3	∇𝛿𝑦3	∇𝛿𝑦3	NUM
iajs-2816	143	4	,	,	PUNCT
iajs-2816	143	5	∇𝑧3	∇𝑧3	NOUN
iajs-2816	143	6	)	)	PUNCT
iajs-2816	143	7	−	−	PROPN
iajs-2816	143	8	(	(	PUNCT
iajs-2816	143	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	143	10	,	,	PUNCT
iajs-2816	143	11	𝑧3	𝑧3	PROPN
iajs-2816	143	12	)	)	PUNCT
iajs-2816	144	1	+	+	CCONJ
iajs-2816	144	2	(	(	PUNCT
iajs-2816	144	3	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	144	4	,	,	PUNCT
iajs-2816	144	5	𝑧3	𝑧3	PROPN
iajs-2816	144	6	)	)	PUNCT
iajs-2816	144	7	+	+	CCONJ
iajs-2816	144	8	(	(	PUNCT
iajs-2816	144	9	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	144	10	,	,	PUNCT
iajs-2816	144	11	𝑧3	𝑧3	PROPN
iajs-2816	144	12	)	)	PUNCT
iajs-2816	145	1	+	+	CCONJ
iajs-2816	145	2	(	(	PUNCT
iajs-2816	145	3	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	145	4	,	,	PUNCT
iajs-2816	145	5	𝑧3	𝑧3	PROPN
iajs-2816	145	6	)	)	PUNCT
iajs-2816	145	7	]	]	PUNCT
iajs-2816	145	8	𝑇	𝑇	PROPN
iajs-2816	145	9	0	0	NUM
iajs-2816	145	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	145	11	=	=	SYM
iajs-2816	145	12	∫	∫	PROPN
iajs-2816	145	13	(	(	PUNCT
iajs-2816	145	14	𝑓3(𝑦3	𝑓3(𝑦3	X
iajs-2816	145	15	+	+	X
iajs-2816	145	16	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	145	17	,	,	PUNCT
iajs-2816	145	18	𝑢3	𝑢3	PROPN
iajs-2816	145	19	+	+	CCONJ
iajs-2816	145	20	𝛿𝑢3	𝛿𝑢3	NOUN
iajs-2816	145	21	)	)	PUNCT
iajs-2816	145	22	,	,	PUNCT
iajs-2816	145	23	𝑧3)𝑑𝑡	𝑧3)𝑑𝑡	PROPN
iajs-2816	145	24	𝑇	𝑇	PROPN
iajs-2816	145	25	0	0	NUM
iajs-2816	145	26	−	−	PROPN
iajs-2816	146	1	∫	∫	PROPN
iajs-2816	146	2	(	(	PUNCT
iajs-2816	146	3	𝑓3(𝑦3	𝑓3(𝑦3	PROPN
iajs-2816	146	4	,	,	PUNCT
iajs-2816	146	5	𝑢3	𝑢3	PROPN
iajs-2816	146	6	)	)	PUNCT
iajs-2816	146	7	,	,	PUNCT
iajs-2816	146	8	𝑧3)𝑑𝑡	𝑧3)𝑑𝑡	PROPN
iajs-2816	146	9	𝑇	𝑇	PROPN
iajs-2816	146	10	0	0	NUM
iajs-2816	146	11	,	,	PUNCT
iajs-2816	146	12	(	(	PUNCT
iajs-2816	146	13	29	29	NUM
iajs-2816	146	14	)	)	PUNCT
iajs-2816	146	15	∫	∫	PROPN
iajs-2816	147	1	〈	〈	PROPN
iajs-2816	147	2	𝛿𝑦4𝑡	𝛿𝑦4𝑡	PROPN
iajs-2816	147	3	,	,	PUNCT
iajs-2816	147	4	𝑧4	𝑧4	ADJ
iajs-2816	147	5	〉	〉	NOUN
iajs-2816	147	6	𝑇	𝑇	NOUN
iajs-2816	147	7	0	0	NUM
iajs-2816	147	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	147	9	+	+	NOUN
iajs-2816	147	10	∫	∫	PROPN
iajs-2816	148	1	[	[	X
iajs-2816	148	2	(	(	PUNCT
iajs-2816	148	3	∇𝛿𝑦4	∇𝛿𝑦4	PROPN
iajs-2816	148	4	,	,	PUNCT
iajs-2816	148	5	∇𝑧4	∇𝑧4	PROPN
iajs-2816	148	6	)	)	PUNCT
iajs-2816	148	7	−	−	PROPN
iajs-2816	148	8	(	(	PUNCT
iajs-2816	148	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	148	10	,	,	PUNCT
iajs-2816	148	11	𝑧4	𝑧4	ADJ
iajs-2816	148	12	)	)	PUNCT
iajs-2816	148	13	+	+	CCONJ
iajs-2816	148	14	(	(	PUNCT
iajs-2816	148	15	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	148	16	,	,	PUNCT
iajs-2816	148	17	𝑧4	𝑧4	ADJ
iajs-2816	148	18	)	)	PUNCT
iajs-2816	148	19	−	−	PROPN
iajs-2816	148	20	(	(	PUNCT
iajs-2816	148	21	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	148	22	,	,	PUNCT
iajs-2816	148	23	𝑧4	𝑧4	ADJ
iajs-2816	148	24	)	)	PUNCT
iajs-2816	149	1	+	+	CCONJ
iajs-2816	149	2	(	(	PUNCT
iajs-2816	149	3	𝛿𝑦4	𝛿𝑦4	ADJ
iajs-2816	149	4	,	,	PUNCT
iajs-2816	149	5	𝑧4	𝑧4	PROPN
iajs-2816	149	6	)	)	PUNCT
iajs-2816	149	7	]	]	PUNCT
iajs-2816	149	8	𝑇	𝑇	PROPN
iajs-2816	149	9	0	0	NUM
iajs-2816	149	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	149	11	=	=	SYM
iajs-2816	149	12	∫	∫	PROPN
iajs-2816	149	13	(	(	PUNCT
iajs-2816	149	14	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2816	149	15	+	+	CCONJ
iajs-2816	149	16	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	149	17	,	,	PUNCT
iajs-2816	149	18	𝑢4	𝑢4	NOUN
iajs-2816	149	19	+	+	CCONJ
iajs-2816	149	20	𝛿𝑢4	𝛿𝑢4	ADJ
iajs-2816	149	21	)	)	PUNCT
iajs-2816	149	22	,	,	PUNCT
iajs-2816	149	23	𝑧4)𝑑𝑡	𝑧4)𝑑𝑡	PROPN
iajs-2816	149	24	𝑇	𝑇	PROPN
iajs-2816	149	25	0	0	NUM
iajs-2816	149	26	−	−	PROPN
iajs-2816	149	27	∫	∫	PROPN
iajs-2816	149	28	(	(	PUNCT
iajs-2816	149	29	𝑓4(𝑦4	𝑓4(𝑦4	NOUN
iajs-2816	149	30	,	,	PUNCT
iajs-2816	149	31	𝑢4	𝑢4	NOUN
iajs-2816	149	32	)	)	PUNCT
iajs-2816	149	33	,	,	PUNCT
iajs-2816	149	34	𝑧4)𝑑𝑡	𝑧4)𝑑𝑡	NOUN
iajs-2816	149	35	𝑇	𝑇	PROPN
iajs-2816	149	36	0	0	NUM
iajs-2816	149	37	,	,	PUNCT
iajs-2816	149	38	(	(	PUNCT
iajs-2816	149	39	30	30	NUM
iajs-2816	149	40	)	)	PUNCT
iajs-2816	149	41	using	use	VERB
iajs-2816	149	42	the	the	DET
iajs-2816	149	43	hypotheses	hypothesis	NOUN
iajs-2816	149	44	on	on	ADP
iajs-2816	149	45	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	149	46	(	(	PUNCT
iajs-2816	149	47	for	for	ADP
iajs-2816	149	48	each	each	PRON
iajs-2816	149	49	𝑖	𝑖	NOUN
iajs-2816	149	50	=	=	NOUN
iajs-2816	149	51	1,23,4	1,23,4	NUM
iajs-2816	149	52	)	)	PUNCT
iajs-2816	149	53	,	,	PUNCT
iajs-2816	149	54	the	the	DET
iajs-2816	149	55	frd	frd	NOUN
iajs-2816	149	56	of	of	ADP
iajs-2816	149	57	it	it	PRON
iajs-2816	149	58	exists	exist	VERB
iajs-2816	149	59	,	,	PUNCT
iajs-2816	149	60	then	then	ADV
iajs-2816	149	61	from	from	ADP
iajs-2816	149	62	the	the	DET
iajs-2816	149	63	result	result	NOUN
iajs-2816	149	64	of	of	ADP
iajs-2816	149	65	the	the	PRON
iajs-2816	149	66	.	.	PROPN
iajs-2816	149	67	2.3	2.3	NUM
iajs-2816	149	68	,	,	PUNCT
iajs-2816	149	69	and	and	CCONJ
iajs-2816	149	70	the	the	DET
iajs-2816	149	71	mkin	mkin	X
iajs-2816	149	72	,	,	PUNCT
iajs-2816	149	73	the	the	DET
iajs-2816	149	74	followings	following	NOUN
iajs-2816	149	75	are	be	AUX
iajs-2816	149	76	yielded	yield	VERB
iajs-2816	149	77	:	:	PUNCT
iajs-2816	149	78	∫	∫	PROPN
iajs-2816	149	79	〈	〈	PROPN
iajs-2816	149	80	𝛿𝑦1𝑡	𝛿𝑦1𝑡	PROPN
iajs-2816	149	81	,	,	PUNCT
iajs-2816	149	82	𝑧1	𝑧1	VERB
iajs-2816	149	83	〉	〉	NOUN
iajs-2816	149	84	𝑇	𝑇	PROPN
iajs-2816	149	85	0	0	NUM
iajs-2816	149	86	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	149	87	+	+	NOUN
iajs-2816	149	88	∫	∫	PROPN
iajs-2816	150	1	[	[	X
iajs-2816	150	2	(	(	PUNCT
iajs-2816	150	3	∇δ𝑦1	∇δ𝑦1	PROPN
iajs-2816	150	4	,	,	PUNCT
iajs-2816	150	5	∇𝑧1	∇𝑧1	NOUN
iajs-2816	150	6	)	)	PUNCT
iajs-2816	151	1	+	+	CCONJ
iajs-2816	151	2	(	(	PUNCT
iajs-2816	151	3	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	151	4	,	,	PUNCT
iajs-2816	151	5	𝑧1	𝑧1	NOUN
iajs-2816	151	6	)	)	PUNCT
iajs-2816	151	7	−	−	PROPN
iajs-2816	151	8	(	(	PUNCT
iajs-2816	151	9	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	151	10	,	,	PUNCT
iajs-2816	151	11	𝑧1	𝑧1	NOUN
iajs-2816	151	12	)	)	PUNCT
iajs-2816	152	1	+	+	CCONJ
iajs-2816	152	2	(	(	PUNCT
iajs-2816	152	3	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	152	4	,	,	PUNCT
iajs-2816	152	5	𝑧1	𝑧1	NOUN
iajs-2816	152	6	)	)	PUNCT
iajs-2816	153	1	+	+	CCONJ
iajs-2816	153	2	(	(	PUNCT
iajs-2816	153	3	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	153	4	,	,	PUNCT
iajs-2816	153	5	𝑧1	𝑧1	PROPN
iajs-2816	153	6	)	)	PUNCT
iajs-2816	153	7	]	]	PUNCT
iajs-2816	153	8	𝑇	𝑇	PROPN
iajs-2816	153	9	0	0	NUM
iajs-2816	153	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	153	11	=	=	SYM
iajs-2816	153	12	∫	∫	PROPN
iajs-2816	153	13	(	(	PUNCT
iajs-2816	153	14	𝑇	𝑇	PROPN
iajs-2816	153	15	0	0	SYM
iajs-2816	153	16	𝑓1𝑦1𝛿𝑦1	𝑓1𝑦1𝛿𝑦1	PROPN
iajs-2816	153	17	+	+	CCONJ
iajs-2816	153	18	𝑓1𝑢1𝛿𝑢1	𝑓1𝑢1𝛿𝑢1	PROPN
iajs-2816	153	19	,	,	PUNCT
iajs-2816	153	20	𝑧1)𝑑𝑡	𝑧1)𝑑𝑡	NOUN
iajs-2816	153	21	+	+	CCONJ
iajs-2816	153	22	휀12(𝛿𝑢	휀12(𝛿𝑢	NUM
iajs-2816	153	23	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	153	24	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	153	25	)	)	PUNCT
iajs-2816	153	26	,	,	PUNCT
iajs-2816	153	27	(	(	PUNCT
iajs-2816	153	28	31	31	NUM
iajs-2816	153	29	)	)	PUNCT
iajs-2816	153	30	∫	∫	PROPN
iajs-2816	154	1	〈	〈	NOUN
iajs-2816	154	2	𝛿𝑦2𝑡	𝛿𝑦2𝑡	NOUN
iajs-2816	154	3	,	,	PUNCT
iajs-2816	154	4	𝑧2	𝑧2	NOUN
iajs-2816	154	5	〉	〉	NOUN
iajs-2816	154	6	𝑇	𝑇	PROPN
iajs-2816	154	7	0	0	NUM
iajs-2816	154	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	154	9	+	+	NOUN
iajs-2816	154	10	∫	∫	PROPN
iajs-2816	155	1	[	[	X
iajs-2816	155	2	(	(	PUNCT
iajs-2816	155	3	∇𝛿𝑦2	∇𝛿𝑦2	NOUN
iajs-2816	155	4	,	,	PUNCT
iajs-2816	155	5	∇𝑧2	∇𝑧2	NOUN
iajs-2816	155	6	)	)	PUNCT
iajs-2816	155	7	+	+	CCONJ
iajs-2816	155	8	(	(	PUNCT
iajs-2816	155	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	155	10	,	,	PUNCT
iajs-2816	155	11	𝑧2	𝑧2	NOUN
iajs-2816	155	12	)	)	PUNCT
iajs-2816	155	13	+	+	CCONJ
iajs-2816	155	14	(	(	PUNCT
iajs-2816	155	15	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	155	16	,	,	PUNCT
iajs-2816	155	17	𝑧2	𝑧2	NOUN
iajs-2816	155	18	)	)	PUNCT
iajs-2816	155	19	−	−	PROPN
iajs-2816	155	20	(	(	PUNCT
iajs-2816	155	21	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	155	22	,	,	PUNCT
iajs-2816	155	23	𝑧2	𝑧2	NOUN
iajs-2816	155	24	)	)	PUNCT
iajs-2816	155	25	−	−	PROPN
iajs-2816	156	1	(	(	PUNCT
iajs-2816	156	2	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	156	3	,	,	PUNCT
iajs-2816	156	4	𝑧2	𝑧2	PROPN
iajs-2816	156	5	)	)	PUNCT
iajs-2816	156	6	]	]	PUNCT
iajs-2816	157	1	𝑇	𝑇	PROPN
iajs-2816	157	2	0	0	NUM
iajs-2816	157	3	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	157	4	=	=	SYM
iajs-2816	157	5	∫	∫	PROPN
iajs-2816	157	6	(	(	PUNCT
iajs-2816	157	7	𝑇	𝑇	PROPN
iajs-2816	157	8	0	0	NUM
iajs-2816	157	9	𝑓2𝑦2𝛿𝑦2	𝑓2𝑦2𝛿𝑦2	PROPN
iajs-2816	157	10	+	+	NUM
iajs-2816	157	11	𝑓2𝑢2𝛿𝑢2	𝑓2𝑢2𝛿𝑢2	PROPN
iajs-2816	157	12	,	,	PUNCT
iajs-2816	157	13	𝑧2)𝑑𝑡	𝑧2)𝑑𝑡	NOUN
iajs-2816	157	14	+	+	CCONJ
iajs-2816	157	15	휀22(𝛿𝑢	휀22(𝛿𝑢	ADJ
iajs-2816	157	16	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	157	17	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	157	18	)	)	PUNCT
iajs-2816	157	19	,	,	PUNCT
iajs-2816	157	20	(	(	PUNCT
iajs-2816	157	21	32	32	NUM
iajs-2816	157	22	)	)	PUNCT
iajs-2816	157	23	∫	∫	PROPN
iajs-2816	158	1	〈	〈	NOUN
iajs-2816	158	2	𝛿𝑦3𝑡	𝛿𝑦3𝑡	NOUN
iajs-2816	158	3	,	,	PUNCT
iajs-2816	158	4	𝑧3	𝑧3	ADJ
iajs-2816	158	5	〉	〉	NOUN
iajs-2816	158	6	𝑇	𝑇	PROPN
iajs-2816	158	7	0	0	NUM
iajs-2816	158	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	158	9	+	+	NOUN
iajs-2816	158	10	∫	∫	PROPN
iajs-2816	159	1	[	[	X
iajs-2816	159	2	(	(	PUNCT
iajs-2816	159	3	∇𝛿𝑦3	∇𝛿𝑦3	NUM
iajs-2816	159	4	,	,	PUNCT
iajs-2816	159	5	∇𝑧3	∇𝑧3	NOUN
iajs-2816	159	6	)	)	PUNCT
iajs-2816	159	7	−	−	PROPN
iajs-2816	159	8	(	(	PUNCT
iajs-2816	159	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	159	10	,	,	PUNCT
iajs-2816	159	11	𝑧3	𝑧3	PROPN
iajs-2816	159	12	)	)	PUNCT
iajs-2816	160	1	+	+	CCONJ
iajs-2816	160	2	(	(	PUNCT
iajs-2816	160	3	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	160	4	,	,	PUNCT
iajs-2816	160	5	𝑧3	𝑧3	PROPN
iajs-2816	160	6	)	)	PUNCT
iajs-2816	160	7	+	+	CCONJ
iajs-2816	160	8	(	(	PUNCT
iajs-2816	160	9	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	160	10	,	,	PUNCT
iajs-2816	160	11	𝑧3	𝑧3	PROPN
iajs-2816	160	12	)	)	PUNCT
iajs-2816	161	1	+	+	CCONJ
iajs-2816	161	2	(	(	PUNCT
iajs-2816	161	3	𝛿𝑦4	𝛿𝑦4	PROPN
iajs-2816	161	4	,	,	PUNCT
iajs-2816	161	5	𝑧3	𝑧3	PROPN
iajs-2816	161	6	)	)	PUNCT
iajs-2816	161	7	]	]	PUNCT
iajs-2816	161	8	𝑇	𝑇	PROPN
iajs-2816	161	9	0	0	NUM
iajs-2816	161	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	161	11	=	=	SYM
iajs-2816	161	12	∫	∫	PROPN
iajs-2816	161	13	(	(	PUNCT
iajs-2816	161	14	𝑇	𝑇	PROPN
iajs-2816	161	15	0	0	SYM
iajs-2816	161	16	𝑓3𝑦3𝛿𝑦3	𝑓3𝑦3𝛿𝑦3	AUX
iajs-2816	161	17	+	+	CCONJ
iajs-2816	161	18	𝑓3𝑢3𝛿𝑢3	𝑓3𝑢3𝛿𝑢3	PROPN
iajs-2816	161	19	,	,	PUNCT
iajs-2816	161	20	𝑧3)𝑑𝑡	𝑧3)𝑑𝑡	NOUN
iajs-2816	161	21	+	+	CCONJ
iajs-2816	161	22	휀32(𝛿𝑢	휀32(𝛿𝑢	NUM
iajs-2816	161	23	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	161	24	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	161	25	)	)	PUNCT
iajs-2816	161	26	,	,	PUNCT
iajs-2816	161	27	(	(	PUNCT
iajs-2816	161	28	33	33	NUM
iajs-2816	161	29	)	)	PUNCT
iajs-2816	161	30	∫	∫	PROPN
iajs-2816	162	1	〈	〈	PROPN
iajs-2816	162	2	𝛿𝑦4𝑡	𝛿𝑦4𝑡	PROPN
iajs-2816	162	3	,	,	PUNCT
iajs-2816	162	4	𝑧4	𝑧4	ADJ
iajs-2816	162	5	〉	〉	NOUN
iajs-2816	162	6	𝑇	𝑇	NOUN
iajs-2816	162	7	0	0	NUM
iajs-2816	162	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	162	9	+	+	NOUN
iajs-2816	162	10	∫	∫	PROPN
iajs-2816	163	1	[	[	X
iajs-2816	163	2	(	(	PUNCT
iajs-2816	163	3	∇𝛿𝑦4	∇𝛿𝑦4	PROPN
iajs-2816	163	4	,	,	PUNCT
iajs-2816	163	5	∇𝑧4	∇𝑧4	PROPN
iajs-2816	163	6	)	)	PUNCT
iajs-2816	163	7	−	−	PROPN
iajs-2816	163	8	(	(	PUNCT
iajs-2816	163	9	𝛿𝑦1	𝛿𝑦1	ADJ
iajs-2816	163	10	,	,	PUNCT
iajs-2816	163	11	𝑧4	𝑧4	ADJ
iajs-2816	163	12	)	)	PUNCT
iajs-2816	163	13	+	+	CCONJ
iajs-2816	163	14	(	(	PUNCT
iajs-2816	163	15	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	163	16	,	,	PUNCT
iajs-2816	163	17	𝑧4	𝑧4	ADJ
iajs-2816	163	18	)	)	PUNCT
iajs-2816	163	19	−	−	PROPN
iajs-2816	163	20	(	(	PUNCT
iajs-2816	163	21	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	163	22	,	,	PUNCT
iajs-2816	163	23	𝑧4	𝑧4	ADJ
iajs-2816	163	24	)	)	PUNCT
iajs-2816	164	1	+	+	CCONJ
iajs-2816	164	2	(	(	PUNCT
iajs-2816	164	3	𝛿𝑦4	𝛿𝑦4	ADJ
iajs-2816	164	4	,	,	PUNCT
iajs-2816	164	5	𝑧4	𝑧4	PROPN
iajs-2816	164	6	)	)	PUNCT
iajs-2816	164	7	]	]	PUNCT
iajs-2816	164	8	𝑇	𝑇	PROPN
iajs-2816	164	9	0	0	NUM
iajs-2816	164	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2816	164	11	=	=	SYM
iajs-2816	164	12	∫	∫	PROPN
iajs-2816	164	13	(	(	PUNCT
iajs-2816	164	14	𝑇	𝑇	PROPN
iajs-2816	164	15	0	0	NUM
iajs-2816	164	16	𝑓4𝑦4𝛿𝑦4	𝑓4𝑦4𝛿𝑦4	PROPN
iajs-2816	164	17	+	+	CCONJ
iajs-2816	164	18	𝑓4𝑢4𝛿𝑢4	𝑓4𝑢4𝛿𝑢4	ADJ
iajs-2816	164	19	,	,	PUNCT
iajs-2816	164	20	𝑧4)𝑑𝑡	𝑧4)𝑑𝑡	NOUN
iajs-2816	164	21	+	+	CCONJ
iajs-2816	164	22	휀42(𝛿𝑢	휀42(𝛿𝑢	NUM
iajs-2816	164	23	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	164	24	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	164	25	)	)	PUNCT
iajs-2816	164	26	,	,	PUNCT
iajs-2816	164	27	(	(	PUNCT
iajs-2816	164	28	34	34	NUM
iajs-2816	164	29	)	)	PUNCT
iajs-2816	164	30	by	by	ADP
iajs-2816	164	31	subtracting	subtract	VERB
iajs-2816	164	32	(	(	PUNCT
iajs-2816	164	33	(	(	PUNCT
iajs-2816	164	34	31	31	NUM
iajs-2816	164	35	)	)	PUNCT
iajs-2816	164	36	–	–	PUNCT
iajs-2816	164	37	(	(	PUNCT
iajs-2816	164	38	34	34	NUM
iajs-2816	164	39	)	)	PUNCT
iajs-2816	164	40	)	)	PUNCT
iajs-2816	164	41	from	from	ADP
iajs-2816	164	42	(	(	PUNCT
iajs-2816	164	43	(	(	PUNCT
iajs-2816	164	44	23	23	NUM
iajs-2816	164	45	)	)	PUNCT
iajs-2816	164	46	−	−	PROPN
iajs-2816	164	47	(	(	PUNCT
iajs-2816	164	48	26	26	NUM
iajs-2816	164	49	)	)	PUNCT
iajs-2816	164	50	)	)	PUNCT
iajs-2816	164	51	resp	resp	NOUN
iajs-2816	164	52	.	.	PUNCT
iajs-2816	164	53	,	,	PUNCT
iajs-2816	164	54	and	and	CCONJ
iajs-2816	164	55	adding	add	VERB
iajs-2816	164	56	the	the	DET
iajs-2816	164	57	attained	attain	VERB
iajs-2816	164	58	equations	equation	NOUN
iajs-2816	164	59	,	,	PUNCT
iajs-2816	164	60	one	one	PRON
iajs-2816	164	61	obtains	obtain	VERB
iajs-2816	164	62	:	:	PUNCT
iajs-2816	164	63	∫	∫	PROPN
iajs-2816	164	64	[	[	PUNCT
iajs-2816	164	65	𝑇	𝑇	PROPN
iajs-2816	164	66	0	0	NUM
iajs-2816	164	67	(	(	PUNCT
iajs-2816	164	68	𝑓1𝑢1𝛿𝑢1	𝑓1𝑢1𝛿𝑢1	VERB
iajs-2816	164	69	,	,	PUNCT
iajs-2816	164	70	𝑧1	𝑧1	NOUN
iajs-2816	164	71	)	)	PUNCT
iajs-2816	164	72	+	+	CCONJ
iajs-2816	164	73	(	(	PUNCT
iajs-2816	164	74	𝑓2𝑢2𝛿𝑢2	𝑓2𝑢2𝛿𝑢2	PROPN
iajs-2816	164	75	,	,	PUNCT
iajs-2816	164	76	𝑧2	𝑧2	NOUN
iajs-2816	164	77	)	)	PUNCT
iajs-2816	164	78	+	+	CCONJ
iajs-2816	164	79	(	(	PUNCT
iajs-2816	164	80	𝑓3𝑢3𝛿𝑢3	𝑓3𝑢3𝛿𝑢3	NOUN
iajs-2816	164	81	,	,	PUNCT
iajs-2816	164	82	𝑧3	𝑧3	PROPN
iajs-2816	164	83	)	)	PUNCT
iajs-2816	164	84	+	+	CCONJ
iajs-2816	164	85	(	(	PUNCT
iajs-2816	164	86	𝑓4𝑢4𝛿𝑢4	𝑓4𝑢4𝛿𝑢4	PROPN
iajs-2816	164	87	,	,	PUNCT
iajs-2816	164	88	𝑧4)]𝑑𝑡	𝑧4)]𝑑𝑡	PROPN
iajs-2816	164	89	+	+	CCONJ
iajs-2816	164	90	휀5(𝛿𝑢	휀5(𝛿𝑢	PROPN
iajs-2816	164	91	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗‖	PROPN
iajs-2816	164	92	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	164	93	)	)	PUNCT
iajs-2816	164	94	=	=	SYM
iajs-2816	165	1	∫	∫	PROPN
iajs-2816	165	2	[	[	PUNCT
iajs-2816	165	3	𝑇	𝑇	PROPN
iajs-2816	165	4	0	0	NUM
iajs-2816	165	5	(	(	PUNCT
iajs-2816	165	6	𝑔1𝑦1	𝑔1𝑦1	NOUN
iajs-2816	165	7	,	,	PUNCT
iajs-2816	165	8	𝛿𝑦1	𝛿𝑦1	NOUN
iajs-2816	165	9	)	)	PUNCT
iajs-2816	165	10	+	+	CCONJ
iajs-2816	165	11	(	(	PUNCT
iajs-2816	165	12	𝑔2𝑦2	𝑔2𝑦2	X
iajs-2816	165	13	,	,	PUNCT
iajs-2816	165	14	𝛿𝑦2	𝛿𝑦2	NOUN
iajs-2816	165	15	)	)	PUNCT
iajs-2816	165	16	+	+	CCONJ
iajs-2816	165	17	(	(	PUNCT
iajs-2816	165	18	𝑔3𝑦3	𝑔3𝑦3	INTJ
iajs-2816	165	19	,	,	PUNCT
iajs-2816	165	20	𝛿𝑦3	𝛿𝑦3	NOUN
iajs-2816	165	21	)	)	PUNCT
iajs-2816	165	22	+	+	CCONJ
iajs-2816	165	23	(	(	PUNCT
iajs-2816	165	24	𝑔4𝑦4	𝑔4𝑦4	INTJ
iajs-2816	165	25	,	,	PUNCT
iajs-2816	165	26	𝛿𝑦4)]𝑑𝑡	𝛿𝑦4)]𝑑𝑡	PROPN
iajs-2816	165	27	,	,	PUNCT
iajs-2816	165	28	(	(	PUNCT
iajs-2816	165	29	35	35	NUM
iajs-2816	165	30	)	)	PUNCT
iajs-2816	165	31	where	where	SCONJ
iajs-2816	165	32	휀5(𝛿𝑢⃗⃗⃗⃗⃗	휀5(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	165	33	)	)	PUNCT
iajs-2816	165	34	=	=	SYM
iajs-2816	165	35	휀12(𝛿𝑢⃗⃗⃗⃗⃗	휀12(𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	165	36	)	)	PUNCT
iajs-2816	165	37	+	+	NUM
iajs-2816	166	1	휀22(𝛿𝑢⃗⃗⃗⃗⃗	휀22(𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	166	2	)	)	PUNCT
iajs-2816	167	1	+	+	X
iajs-2816	167	2	휀32(𝛿𝑢⃗⃗⃗⃗⃗	휀32(𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	167	3	)	)	PUNCT
iajs-2816	167	4	+	+	CCONJ
iajs-2816	167	5	휀42(𝛿𝑢⃗⃗⃗⃗⃗	휀42(𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	167	6	)	)	PUNCT
iajs-2816	167	7	⟶	⟶	NOUN
iajs-2816	167	8	0	0	NUM
iajs-2816	167	9	,	,	PUNCT
iajs-2816	167	10	as	as	ADP
iajs-2816	167	11	‖𝛿𝑢⃗⃗⃗⃗⃗	‖𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	167	12	‖	‖	PROPN
iajs-2816	167	13	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	167	14	)	)	PUNCT
iajs-2816	167	15	⟶	⟶	NOUN
iajs-2816	167	16	0	0	NUM
iajs-2816	167	17	,	,	PUNCT
iajs-2816	167	18	now	now	ADV
iajs-2816	167	19	,	,	PUNCT
iajs-2816	167	20	by	by	ADP
iajs-2816	167	21	substituting	substitute	VERB
iajs-2816	167	22	(	(	PUNCT
iajs-2816	167	23	35	35	NUM
iajs-2816	167	24	)	)	PUNCT
iajs-2816	167	25	in	in	ADP
iajs-2816	167	26	(	(	PUNCT
iajs-2816	167	27	18	18	NUM
iajs-2816	167	28	)	)	PUNCT
iajs-2816	167	29	,	,	PUNCT
iajs-2816	167	30	one	one	PRON
iajs-2816	167	31	gets	get	VERB
iajs-2816	167	32	:	:	PUNCT
iajs-2816	167	33	𝐺(	𝐺(	PROPN
iajs-2816	167	34	�	�	PROPN
iajs-2816	167	35	⃗⃗	⃗⃗	PROPN
iajs-2816	167	36	�	�	PROPN
iajs-2816	167	37	+	+	CCONJ
iajs-2816	167	38	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	167	39	)	)	PUNCT
iajs-2816	167	40	−	−	PROPN
iajs-2816	167	41	𝐺(	𝐺(	PROPN
iajs-2816	167	42	�	�	PROPN
iajs-2816	167	43	⃗⃗	⃗⃗	PROPN
iajs-2816	167	44	�	�	PROPN
iajs-2816	167	45	)	)	PUNCT
iajs-2816	167	46	=	=	SYM
iajs-2816	168	1	∫	∫	PROPN
iajs-2816	168	2	[	[	PUNCT
iajs-2816	168	3	𝑄	𝑄	PROPN
iajs-2816	168	4	(	(	PUNCT
iajs-2816	168	5	𝑧1𝑓1𝑢1	𝑧1𝑓1𝑢1	NOUN
iajs-2816	168	6	+	+	CCONJ
iajs-2816	168	7	𝑔1𝑢1)𝛿𝑢1	𝑔1𝑢1)𝛿𝑢1	PROPN
iajs-2816	168	8	+	+	CCONJ
iajs-2816	168	9	(	(	PUNCT
iajs-2816	168	10	𝑧2𝑓2𝑢2	𝑧2𝑓2𝑢2	PROPN
iajs-2816	169	1	+	+	X
iajs-2816	169	2	𝑔2𝑢2)𝛿𝑢2	𝑔2𝑢2)𝛿𝑢2	PROPN
iajs-2816	169	3	+	+	CCONJ
iajs-2816	169	4	(	(	PUNCT
iajs-2816	169	5	𝑧3𝑓3𝑢3	𝑧3𝑓3𝑢3	ADP
iajs-2816	169	6	+	+	CCONJ
iajs-2816	169	7	𝑔3𝑢3)𝛿𝑢3	𝑔3𝑢3)𝛿𝑢3	NOUN
iajs-2816	169	8	+	+	CCONJ
iajs-2816	169	9	(	(	PUNCT
iajs-2816	169	10	𝑧4𝑓4𝑢4	𝑧4𝑓4𝑢4	NOUN
iajs-2816	169	11	+	+	CCONJ
iajs-2816	169	12	𝑔4𝑢4)𝛿𝑢4]𝑑𝑥𝑑𝑡	𝑔4𝑢4)𝛿𝑢4]𝑑𝑥𝑑𝑡	NOUN
iajs-2816	169	13	+	+	CCONJ
iajs-2816	169	14	휀7(𝛿𝑢	휀7(𝛿𝑢	NUM
iajs-2816	169	15	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	169	16	‖	‖	PROPN
iajs-2816	169	17	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	169	18	)	)	PUNCT
iajs-2816	169	19	36	36	NUM
iajs-2816	169	20	)	)	PUNCT
iajs-2816	170	1	where	where	SCONJ
iajs-2816	170	2	휀7(𝛿𝑢⃗⃗⃗⃗⃗	휀7(𝛿𝑢⃗⃗⃗⃗⃗	VERB
iajs-2816	170	3	)	)	PUNCT
iajs-2816	170	4	=	=	SYM
iajs-2816	170	5	휀5(𝛿𝑢⃗⃗⃗⃗⃗	휀5(𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	170	6	)	)	PUNCT
iajs-2816	171	1	+	+	NUM
iajs-2816	171	2	휀6(𝛿𝑢⃗⃗⃗⃗⃗	휀6(𝛿𝑢⃗⃗⃗⃗⃗	NUM
iajs-2816	171	3	)	)	PUNCT
iajs-2816	171	4	⟶	⟶	NOUN
iajs-2816	171	5	0	0	NUM
iajs-2816	171	6	,	,	PUNCT
iajs-2816	171	7	as	as	ADP
iajs-2816	171	8	‖𝛿𝑢⃗⃗⃗⃗⃗	‖𝛿𝑢⃗⃗⃗⃗⃗	X
iajs-2816	171	9	‖	‖	PROPN
iajs-2816	171	10	𝑳𝟐(𝑸	𝑳𝟐(𝑸	PROPN
iajs-2816	171	11	)	)	PUNCT
iajs-2816	171	12	⟶	⟶	NOUN
iajs-2816	171	13	0	0	NUM
iajs-2816	171	14	,	,	PUNCT
iajs-2816	171	15	using	use	VERB
iajs-2816	171	16	the	the	DET
iajs-2816	171	17	frd	frd	ADJ
iajs-2816	171	18	definition	definition	NOUN
iajs-2816	171	19	of	of	ADP
iajs-2816	171	20	𝐺	𝐺	PROPN
iajs-2816	171	21	,	,	PUNCT
iajs-2816	171	22	one	one	PRON
iajs-2816	171	23	gets	get	VERB
iajs-2816	171	24	:	:	PUNCT
iajs-2816	171	25	𝐺(	𝐺(	PROPN
iajs-2816	171	26	�	�	PROPN
iajs-2816	171	27	⃗⃗	⃗⃗	PROPN
iajs-2816	171	28	�	�	PROPN
iajs-2816	171	29	+	+	CCONJ
iajs-2816	171	30	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	171	31	)	)	PUNCT
iajs-2816	171	32	−	−	PROPN
iajs-2816	171	33	𝐺(	𝐺(	PROPN
iajs-2816	171	34	�	�	PROPN
iajs-2816	171	35	⃗⃗	⃗⃗	PROPN
iajs-2816	171	36	�	�	PROPN
iajs-2816	171	37	)	)	PUNCT
iajs-2816	171	38	=	=	PRON
iajs-2816	171	39	(	(	PUNCT
iajs-2816	171	40	�	�	PROPN
iajs-2816	171	41	́	́	PROPN
iajs-2816	171	42	�	�	PROPN
iajs-2816	171	43	(	(	PUNCT
iajs-2816	171	44	�	�	PROPN
iajs-2816	171	45	⃗⃗	⃗⃗	PROPN
iajs-2816	171	46	�	�	PROPN
iajs-2816	171	47	)	)	PUNCT
iajs-2816	171	48	,	,	PUNCT
iajs-2816	171	49	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	171	50	)	)	PUNCT
iajs-2816	172	1	+	+	NUM
iajs-2816	172	2	휀7(𝛿𝑢⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	휀7(𝛿𝑢⃗⃗⃗⃗⃗)‖𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	172	3	‖𝑳𝟐(𝑸	‖𝑳𝟐(𝑸	NOUN
iajs-2816	172	4	)	)	PUNCT
iajs-2816	172	5	(	(	PUNCT
iajs-2816	172	6	37	37	NUM
iajs-2816	172	7	)	)	PUNCT
iajs-2816	172	8	from	from	ADP
iajs-2816	172	9	(	(	PUNCT
iajs-2816	172	10	36	36	NUM
iajs-2816	172	11	)	)	PUNCT
iajs-2816	172	12	and	and	CCONJ
iajs-2816	172	13	(	(	PUNCT
iajs-2816	172	14	37	37	NUM
iajs-2816	172	15	)	)	PUNCT
iajs-2816	172	16	,	,	PUNCT
iajs-2816	172	17	one	one	PRON
iajs-2816	172	18	can	can	AUX
iajs-2816	172	19	get	get	VERB
iajs-2816	172	20	:	:	PUNCT
iajs-2816	172	21	(	(	PUNCT
iajs-2816	172	22	�	�	PROPN
iajs-2816	172	23	́	́	NOUN
iajs-2816	172	24	�	�	PROPN
iajs-2816	172	25	(	(	PUNCT
iajs-2816	172	26	�	�	PROPN
iajs-2816	172	27	⃗⃗	⃗⃗	PROPN
iajs-2816	172	28	�	�	PROPN
iajs-2816	172	29	)	)	PUNCT
iajs-2816	172	30	,	,	PUNCT
iajs-2816	172	31	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	172	32	)	)	PUNCT
iajs-2816	172	33	=	=	SYM
iajs-2816	173	1	∫	∫	PROPN
iajs-2816	173	2	(	(	PUNCT
iajs-2816	173	3	𝑧1𝑓1𝑢1	𝑧1𝑓1𝑢1	NOUN
iajs-2816	173	4	+	+	CCONJ
iajs-2816	173	5	𝑔1𝑢1	𝑔1𝑢1	PROPN
iajs-2816	173	6	𝑧2𝑓2𝑢2	𝑧2𝑓2𝑢2	PROPN
iajs-2816	173	7	+	+	X
iajs-2816	173	8	𝑔2𝑢2	𝑔2𝑢2	X
iajs-2816	173	9	𝑧3𝑓3𝑢3	𝑧3𝑓3𝑢3	ADV
iajs-2816	173	10	+	+	CCONJ
iajs-2816	173	11	𝑔3𝑢3	𝑔3𝑢3	PROPN
iajs-2816	173	12	𝑧4𝑓4𝑢4	𝑧4𝑓4𝑢4	NOUN
iajs-2816	173	13	+	+	CCONJ
iajs-2816	173	14	𝑔4𝑢4	𝑔4𝑢4	X
iajs-2816	173	15	)	)	PUNCT
iajs-2816	173	16	∙	∙	PROPN
iajs-2816	173	17	(	(	PUNCT
iajs-2816	173	18	𝛿𝑢1	𝛿𝑢1	X
iajs-2816	173	19	𝛿𝑢2	𝛿𝑢2	PROPN
iajs-2816	173	20	𝛿𝑢3	𝛿𝑢3	NOUN
iajs-2816	173	21	𝛿𝑢4	𝛿𝑢4	ADV
iajs-2816	173	22	)	)	PUNCT
iajs-2816	174	1	𝑄	𝑄	PRON
iajs-2816	174	2	𝑑𝑥	𝑑𝑥	VERB
iajs-2816	174	3	.	.	PUNCT
iajs-2816	175	1	4	4	X
iajs-2816	175	2	.	.	X
iajs-2816	175	3	the	the	DET
iajs-2816	175	4	ncsth	ncsth	NOUN
iajs-2816	175	5	and	and	CCONJ
iajs-2816	175	6	the	the	DET
iajs-2816	175	7	scsth	scsth	NOUN
iajs-2816	175	8	for	for	ADP
iajs-2816	175	9	optimality	optimality	NOUN
iajs-2816	175	10	:	:	PUNCT
iajs-2816	175	11	this	this	DET
iajs-2816	175	12	section	section	NOUN
iajs-2816	175	13	deals	deal	VERB
iajs-2816	175	14	with	with	ADP
iajs-2816	175	15	the	the	DET
iajs-2816	175	16	state	state	NOUN
iajs-2816	175	17	and	and	CCONJ
iajs-2816	175	18	demonstration	demonstration	NOUN
iajs-2816	175	19	of	of	ADP
iajs-2816	175	20	the	the	DET
iajs-2816	175	21	ncsth	ncsth	NOUN
iajs-2816	175	22	,	,	PUNCT
iajs-2816	175	23	so	so	SCONJ
iajs-2816	175	24	as	as	ADP
iajs-2816	175	25	the	the	DET
iajs-2816	175	26	scsth	scsth	NOUN
iajs-2816	175	27	,	,	PUNCT
iajs-2816	175	28	under	under	ADP
iajs-2816	175	29	some	some	DET
iajs-2816	175	30	additional	additional	ADJ
iajs-2816	175	31	hypotheses	hypothesis	NOUN
iajs-2816	175	32	.	.	PUNCT
iajs-2816	176	1	ihjpas	ihjpas	PROPN
iajs-2816	176	2	.	.	PUNCT
iajs-2816	177	1	53	53	NUM
iajs-2816	177	2	(	(	PUNCT
iajs-2816	177	3	3)2022	3)2022	NOUN
iajs-2816	177	4	141	141	NUM
iajs-2816	177	5	theorem	theorem	NOUN
iajs-2816	177	6	(	(	PUNCT
iajs-2816	177	7	4.1	4.1	NUM
iajs-2816	177	8	):	):	PUNCT
iajs-2816	177	9	ncsth	ncsth	NOUN
iajs-2816	177	10	for	for	ADP
iajs-2816	177	11	optimality	optimality	NOUN
iajs-2816	177	12	:	:	PUNCT
iajs-2816	177	13	(	(	PUNCT
iajs-2816	177	14	a	a	X
iajs-2816	177	15	)	)	PUNCT
iajs-2816	177	16	in	in	ADP
iajs-2816	177	17	addition	addition	NOUN
iajs-2816	177	18	to	to	ADP
iajs-2816	177	19	hypotheses	hypothesis	NOUN
iajs-2816	177	20	(	(	PUNCT
iajs-2816	177	21	a	a	NOUN
iajs-2816	177	22	)	)	PUNCT
iajs-2816	177	23	,	,	PUNCT
iajs-2816	177	24	(	(	PUNCT
iajs-2816	177	25	b	b	X
iajs-2816	177	26	)	)	PUNCT
iajs-2816	177	27	and	and	CCONJ
iajs-2816	177	28	(	(	PUNCT
iajs-2816	177	29	c	c	NOUN
iajs-2816	177	30	)	)	PUNCT
iajs-2816	177	31	,	,	PUNCT
iajs-2816	177	32	if	if	SCONJ
iajs-2816	177	33	�	�	PROPN
iajs-2816	177	34	⃗⃗	⃗⃗	PROPN
iajs-2816	177	35	�	�	PROPN
iajs-2816	177	36	∈	∈	PROPN
iajs-2816	177	37	�	�	PROPN
iajs-2816	177	38	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	177	39	�	�	PROPN
iajs-2816	177	40	𝐴	𝐴	PROPN
iajs-2816	177	41	is	be	AUX
iajs-2816	177	42	qccocv	qccocv	ADJ
iajs-2816	177	43	,	,	PUNCT
iajs-2816	177	44	then	then	ADV
iajs-2816	177	45	there	there	PRON
iajs-2816	177	46	is	be	VERB
iajs-2816	177	47	"	"	PUNCT
iajs-2816	177	48	multiplier	multipli	ADJ
iajs-2816	177	49	"	"	PUNCT
iajs-2816	177	50	𝜆𝑙	𝜆𝑙	PROPN
iajs-2816	177	51	∈	∈	PROPN
iajs-2816	177	52	ℝ	ℝ	PROPN
iajs-2816	177	53	,	,	PUNCT
iajs-2816	177	54	𝑙	𝑙	X
iajs-2816	177	55	=	=	SYM
iajs-2816	177	56	0,1,2	0,1,2	NOUN
iajs-2816	177	57	,	,	PUNCT
iajs-2816	177	58	with	with	ADP
iajs-2816	177	59	𝜆0	𝜆0	PROPN
iajs-2816	177	60	≥	≥	NUM
iajs-2816	177	61	0	0	NUM
iajs-2816	177	62	,	,	PUNCT
iajs-2816	177	63	𝜆2	𝜆2	NOUN
iajs-2816	177	64	≥	≥	NOUN
iajs-2816	177	65	0	0	NUM
iajs-2816	177	66	,	,	PUNCT
iajs-2816	177	67	∑	∑	ADV
iajs-2816	177	68	|𝜆𝑙|	|𝜆𝑙|	PROPN
iajs-2816	177	69	=	=	SYM
iajs-2816	177	70	1	1	NUM
iajs-2816	177	71	2	2	NUM
iajs-2816	177	72	𝑙=0	𝑙=0	NOUN
iajs-2816	177	73	,	,	PUNCT
iajs-2816	177	74	s.t	s.t	PROPN
iajs-2816	177	75	.	.	PUNCT
iajs-2816	178	1	the	the	DET
iajs-2816	178	2	following	follow	VERB
iajs-2816	178	3	lagrange	lagrange	PROPN
iajs-2816	178	4	-kuhn	-kuhn	PROPN
iajs-2816	178	5	-	-	PUNCT
iajs-2816	178	6	tucker	tucker	PROPN
iajs-2816	178	7	conditions	condition	NOUN
iajs-2816	178	8	(	(	PUNCT
iajs-2816	178	9	lkt	lkt	ADJ
iajs-2816	178	10	)	)	PUNCT
iajs-2816	178	11	conditions	condition	NOUN
iajs-2816	178	12	are	be	AUX
iajs-2816	178	13	held	hold	VERB
iajs-2816	178	14	:	:	PUNCT
iajs-2816	178	15	∫	∫	PROPN
iajs-2816	178	16	𝐻	𝐻	PROPN
iajs-2816	178	17	�	�	PROPN
iajs-2816	178	18	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	178	19	�	�	PROPN
iajs-2816	178	20	(𝑥	(𝑥	PROPN
iajs-2816	178	21	,	,	PUNCT
iajs-2816	178	22	𝑡	𝑡	PROPN
iajs-2816	178	23	,	,	PUNCT
iajs-2816	178	24	�	�	PROPN
iajs-2816	178	25	⃗	⃗	NOUN
iajs-2816	178	26	�	�	PROPN
iajs-2816	178	27	,	,	PUNCT
iajs-2816	178	28	𝑧	𝑧	PROPN
iajs-2816	178	29	,	,	PUNCT
iajs-2816	178	30	�	�	PROPN
iajs-2816	178	31	⃗⃗	⃗⃗	PROPN
iajs-2816	178	32	�	�	PROPN
iajs-2816	178	33	)	)	PUNCT
iajs-2816	178	34	𝑄	𝑄	PROPN
iajs-2816	178	35	∙	∙	PROPN
iajs-2816	178	36	𝛿𝑢⃗⃗⃗⃗⃗𝑑𝑥𝑑𝑡	𝛿𝑢⃗⃗⃗⃗⃗𝑑𝑥𝑑𝑡	NOUN
iajs-2816	178	37	≥	≥	NOUN
iajs-2816	178	38	0	0	NUM
iajs-2816	178	39	,	,	PUNCT
iajs-2816	178	40	∀	∀	X
iajs-2816	178	41	�	�	NOUN
iajs-2816	178	42	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	178	43	�	�	PROPN
iajs-2816	178	44	∈	∈	PROPN
iajs-2816	178	45	�	�	PROPN
iajs-2816	178	46	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	178	47	�	�	PROPN
iajs-2816	178	48	,	,	PUNCT
iajs-2816	178	49	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	178	50	=	=	SYM
iajs-2816	178	51	�	�	PROPN
iajs-2816	178	52	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	178	53	�	�	PROPN
iajs-2816	178	54	−	−	PROPN
iajs-2816	178	55	�	�	PROPN
iajs-2816	178	56	⃗⃗	⃗⃗	PROPN
iajs-2816	178	57	�	�	PROPN
iajs-2816	178	58	(	(	PUNCT
iajs-2816	178	59	38.a	38.a	NUM
iajs-2816	178	60	)	)	PUNCT
iajs-2816	178	61	where	where	SCONJ
iajs-2816	178	62	𝑔𝑖	𝑔𝑖	NOUN
iajs-2816	178	63	=	=	PUNCT
iajs-2816	178	64	∑	∑	PUNCT
iajs-2816	178	65	𝜆𝑙𝑔𝑙𝑖	𝜆𝑙𝑔𝑙𝑖	NOUN
iajs-2816	178	66	2	2	NUM
iajs-2816	178	67	𝑙=0	𝑙=0	NOUN
iajs-2816	178	68	,	,	PUNCT
iajs-2816	178	69	∀𝑖	∀𝑖	PROPN
iajs-2816	179	1	=	=	NOUN
iajs-2816	179	2	1,2,3,4	1,2,3,4	NUM
iajs-2816	179	3	in	in	ADP
iajs-2816	179	4	the	the	DET
iajs-2816	179	5	definition	definition	NOUN
iajs-2816	179	6	of	of	ADP
iajs-2816	179	7	𝐻	𝐻	PROPN
iajs-2816	179	8	,	,	PUNCT
iajs-2816	179	9	and	and	CCONJ
iajs-2816	179	10	also	also	ADV
iajs-2816	179	11	𝜆2𝐺2(	𝜆2𝐺2(	PUNCT
iajs-2816	179	12	�	�	PROPN
iajs-2816	179	13	⃗⃗	⃗⃗	PROPN
iajs-2816	179	14	�	�	PROPN
iajs-2816	179	15	)	)	PUNCT
iajs-2816	179	16	=	=	SYM
iajs-2816	179	17	0	0	NUM
iajs-2816	179	18	,	,	PUNCT
iajs-2816	179	19	(	(	PUNCT
iajs-2816	179	20	38.b	38.b	NUM
iajs-2816	179	21	)	)	PUNCT
iajs-2816	179	22	(	(	PUNCT
iajs-2816	179	23	b	b	X
iajs-2816	179	24	)	)	PUNCT
iajs-2816	179	25	(	(	PUNCT
iajs-2816	179	26	minimum	minimum	ADJ
iajs-2816	179	27	principle	principle	NOUN
iajs-2816	179	28	in	in	ADP
iajs-2816	179	29	weak	weak	ADJ
iajs-2816	179	30	form	form	NOUN
iajs-2816	179	31	)	)	PUNCT
iajs-2816	179	32	if	if	SCONJ
iajs-2816	179	33	�	�	PROPN
iajs-2816	179	34	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	179	35	�	�	PROPN
iajs-2816	179	36	is	be	AUX
iajs-2816	179	37	of	of	ADP
iajs-2816	179	38	the	the	DET
iajs-2816	179	39	form	form	NOUN
iajs-2816	179	40	�	�	PROPN
iajs-2816	179	41	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	179	42	�	�	PROPN
iajs-2816	179	43	=	=	SYM
iajs-2816	179	44	{	{	PUNCT
iajs-2816	179	45	�	�	PROPN
iajs-2816	179	46	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	179	47	�	�	PROPN
iajs-2816	179	48	∈	∈	PROPN
iajs-2816	179	49	(	(	PUNCT
iajs-2816	179	50	𝐿2(𝑄,ℝ))4|	𝐿2(𝑄,ℝ))4|	VERB
iajs-2816	179	51	�	�	NOUN
iajs-2816	179	52	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	179	53	�	�	PROPN
iajs-2816	179	54	(𝑥	(𝑥	PROPN
iajs-2816	179	55	,	,	PUNCT
iajs-2816	179	56	𝑡	𝑡	NOUN
iajs-2816	179	57	)	)	PUNCT
iajs-2816	179	58	∈	∈	PROPN
iajs-2816	179	59	�	�	PROPN
iajs-2816	179	60	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	179	61	�	�	PROPN
iajs-2816	179	62	a.	a.	PROPN
iajs-2816	179	63	e.	e.	PROPN
iajs-2816	179	64	on	on	ADP
iajs-2816	179	65	𝑄	𝑄	PROPN
iajs-2816	179	66	}	}	PUNCT
iajs-2816	179	67	,	,	PUNCT
iajs-2816	179	68	with	with	ADP
iajs-2816	179	69	�	�	PROPN
iajs-2816	179	70	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	179	71	�	�	PROPN
iajs-2816	179	72	⊂	⊂	PROPN
iajs-2816	179	73	ℝ2	ℝ2	VERB
iajs-2816	179	74	.	.	PUNCT
iajs-2816	180	1	then	then	ADV
iajs-2816	180	2	,	,	PUNCT
iajs-2816	180	3	(	(	PUNCT
iajs-2816	180	4	37.a	37.a	NUM
iajs-2816	180	5	)	)	PUNCT
iajs-2816	180	6	is	be	AUX
iajs-2816	180	7	equivalent	equivalent	ADJ
iajs-2816	180	8	to	to	ADP
iajs-2816	180	9	the	the	DET
iajs-2816	180	10	minimum	minimum	ADJ
iajs-2816	180	11	principle	principle	NOUN
iajs-2816	180	12	in	in	ADP
iajs-2816	180	13	point	point	NOUN
iajs-2816	180	14	-	-	PUNCT
iajs-2816	180	15	wise	wise	ADJ
iajs-2816	180	16	form	form	NOUN
iajs-2816	180	17	(	(	PUNCT
iajs-2816	180	18	mppwf	mppwf	PROPN
iajs-2816	180	19	)	)	PUNCT
iajs-2816	180	20	𝐻	𝐻	PROPN
iajs-2816	180	21	�	�	PROPN
iajs-2816	180	22	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	180	23	�	�	PROPN
iajs-2816	180	24	(𝑥	(𝑥	PROPN
iajs-2816	180	25	,	,	PUNCT
iajs-2816	180	26	𝑡	𝑡	PROPN
iajs-2816	180	27	,	,	PUNCT
iajs-2816	180	28	�	�	PROPN
iajs-2816	180	29	⃗	⃗	NOUN
iajs-2816	180	30	�	�	PROPN
iajs-2816	180	31	,	,	PUNCT
iajs-2816	180	32	𝑧	𝑧	PROPN
iajs-2816	180	33	,	,	PUNCT
iajs-2816	180	34	�	�	PROPN
iajs-2816	180	35	⃗⃗	⃗⃗	PROPN
iajs-2816	180	36	�	�	PROPN
iajs-2816	180	37	)	)	PUNCT
iajs-2816	180	38	�	�	PROPN
iajs-2816	180	39	⃗⃗	⃗⃗	PROPN
iajs-2816	180	40	�	�	PROPN
iajs-2816	180	41	(𝑡	(𝑡	PROPN
iajs-2816	180	42	)	)	PUNCT
iajs-2816	181	1	=	=	SYM
iajs-2816	181	2	min	min	PROPN
iajs-2816	181	3	�	�	PROPN
iajs-2816	181	4	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	181	5	�	�	PROPN
iajs-2816	181	6	∈	∈	PROPN
iajs-2816	181	7	�	�	PROPN
iajs-2816	181	8	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	181	9	�	�	PROPN
iajs-2816	181	10	𝐻	𝐻	PROPN
iajs-2816	181	11	�	�	PROPN
iajs-2816	181	12	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	181	13	�	�	PROPN
iajs-2816	181	14	(𝑥	(𝑥	PROPN
iajs-2816	181	15	,	,	PUNCT
iajs-2816	181	16	𝑡	𝑡	PROPN
iajs-2816	181	17	,	,	PUNCT
iajs-2816	181	18	�	�	PROPN
iajs-2816	181	19	⃗	⃗	NOUN
iajs-2816	181	20	�	�	PROPN
iajs-2816	181	21	,	,	PUNCT
iajs-2816	181	22	𝑧	𝑧	PROPN
iajs-2816	181	23	,	,	PUNCT
iajs-2816	181	24	�	�	PROPN
iajs-2816	181	25	⃗⃗	⃗⃗	PROPN
iajs-2816	181	26	�	�	PROPN
iajs-2816	181	27	)	)	PUNCT
iajs-2816	181	28	�	�	PROPN
iajs-2816	181	29	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	181	30	�	�	PROPN
iajs-2816	181	31	a.e	a.e	PROPN
iajs-2816	181	32	.	.	PROPN
iajs-2816	181	33	on	on	ADP
iajs-2816	181	34	𝑄	𝑄	PROPN
iajs-2816	181	35	(	(	PUNCT
iajs-2816	181	36	39	39	NUM
iajs-2816	181	37	)	)	PUNCT
iajs-2816	181	38	proof	proof	NOUN
iajs-2816	181	39	:	:	PUNCT
iajs-2816	181	40	(	(	PUNCT
iajs-2816	181	41	a	a	X
iajs-2816	181	42	)	)	PUNCT
iajs-2816	181	43	the	the	DET
iajs-2816	181	44	functional	functional	ADJ
iajs-2816	181	45	𝐺𝑙(	𝐺𝑙(	PROPN
iajs-2816	181	46	�	�	PROPN
iajs-2816	181	47	⃗⃗	⃗⃗	PROPN
iajs-2816	181	48	�	�	PROPN
iajs-2816	181	49	)	)	PUNCT
iajs-2816	181	50	is	be	AUX
iajs-2816	181	51	𝜌	𝜌	ADP
iajs-2816	181	52	−locall	−locall	NOUN
iajs-2816	181	53	cont	cont	NOUN
iajs-2816	181	54	.	.	PUNCT
iajs-2816	182	1	at	at	ADP
iajs-2816	182	2	each	each	DET
iajs-2816	182	3	�	�	PROPN
iajs-2816	182	4	⃗⃗	⃗⃗	PROPN
iajs-2816	182	5	�	�	PROPN
iajs-2816	182	6	∈	∈	PROPN
iajs-2816	182	7	�	�	PROPN
iajs-2816	182	8	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	182	9	�	�	PROPN
iajs-2816	182	10	,	,	PUNCT
iajs-2816	182	11	∀𝑙	∀𝑙	NOUN
iajs-2816	182	12	=	=	SYM
iajs-2816	182	13	0,1,2	0,1,2	NOUN
iajs-2816	182	14	and	and	CCONJ
iajs-2816	182	15	for	for	ADP
iajs-2816	182	16	every	every	DET
iajs-2816	182	17	𝜌	𝜌	X
iajs-2816	182	18	(	(	PUNCT
iajs-2816	182	19	by	by	ADP
iajs-2816	182	20	hypotheses	hypothesis	NOUN
iajs-2816	182	21	(	(	PUNCT
iajs-2816	182	22	a	a	NOUN
iajs-2816	182	23	)	)	PUNCT
iajs-2816	182	24	,	,	PUNCT
iajs-2816	182	25	(	(	PUNCT
iajs-2816	182	26	b	b	X
iajs-2816	182	27	)	)	PUNCT
iajs-2816	182	28	and	and	CCONJ
iajs-2816	182	29	(	(	PUNCT
iajs-2816	182	30	c	c	X
iajs-2816	182	31	)	)	PUNCT
iajs-2816	182	32	and	and	CCONJ
iajs-2816	182	33	lemma	lemma	PROPN
iajs-2816	182	34	2.1	2.1	NUM
iajs-2816	182	35	)	)	PUNCT
iajs-2816	182	36	,	,	PUNCT
iajs-2816	182	37	and	and	CCONJ
iajs-2816	182	38	𝐺𝑙(	𝐺𝑙(	PROPN
iajs-2816	182	39	�	�	PROPN
iajs-2816	182	40	⃗⃗	⃗⃗	PROPN
iajs-2816	182	41	�	�	PROPN
iajs-2816	182	42	)	)	PUNCT
iajs-2816	182	43	is	be	AUX
iajs-2816	182	44	𝜌	𝜌	X
iajs-2816	182	45	−differentiable	−differentiable	ADJ
iajs-2816	182	46	at	at	ADP
iajs-2816	182	47	each	each	DET
iajs-2816	182	48	�	�	PROPN
iajs-2816	182	49	⃗⃗	⃗⃗	PROPN
iajs-2816	182	50	�	�	PROPN
iajs-2816	182	51	∈	∈	PROPN
iajs-2816	182	52	�	�	PROPN
iajs-2816	182	53	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	182	54	�	�	PROPN
iajs-2816	182	55	,	,	PUNCT
iajs-2816	182	56	∀𝜌	∀𝜌	PROPN
iajs-2816	182	57	(	(	PUNCT
iajs-2816	182	58	by	by	ADP
iajs-2816	182	59	hypotheses	hypothesis	NOUN
iajs-2816	182	60	(	(	PUNCT
iajs-2816	182	61	a	a	NOUN
iajs-2816	182	62	)	)	PUNCT
iajs-2816	182	63	,	,	PUNCT
iajs-2816	182	64	(	(	PUNCT
iajs-2816	182	65	b	b	X
iajs-2816	182	66	)	)	PUNCT
iajs-2816	182	67	and	and	CCONJ
iajs-2816	182	68	(	(	PUNCT
iajs-2816	182	69	c	c	NOUN
iajs-2816	182	70	)	)	PUNCT
iajs-2816	182	71	and	and	CCONJ
iajs-2816	182	72	the	the	DET
iajs-2816	182	73	.	.	NOUN
iajs-2816	182	74	3.2	3.2	NUM
iajs-2816	182	75	)	)	PUNCT
iajs-2816	182	76	and	and	CCONJ
iajs-2816	182	77	since	since	SCONJ
iajs-2816	182	78	�	�	PROPN
iajs-2816	182	79	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	182	80	�	�	PROPN
iajs-2816	182	81	⊂	⊂	PROPN
iajs-2816	182	82	(	(	PUNCT
iajs-2816	182	83	𝐿2(𝑄	𝐿2(𝑄	PROPN
iajs-2816	182	84	)	)	PUNCT
iajs-2816	182	85	)	)	PUNCT
iajs-2816	182	86	4	4	NUM
iajs-2816	182	87	,	,	PUNCT
iajs-2816	182	88	𝐿2(𝑄	𝐿2(𝑄	NOUN
iajs-2816	182	89	)	)	PUNCT
iajs-2816	182	90	is	be	AUX
iajs-2816	182	91	open	open	ADJ
iajs-2816	182	92	,	,	PUNCT
iajs-2816	182	93	then	then	ADV
iajs-2816	182	94	𝐷𝐺𝑙(	𝐷𝐺𝑙(	PROPN
iajs-2816	182	95	�	�	PROPN
iajs-2816	182	96	⃗⃗	⃗⃗	PROPN
iajs-2816	182	97	�	�	PROPN
iajs-2816	182	98	,	,	PUNCT
iajs-2816	182	99	�	�	PROPN
iajs-2816	182	100	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	182	101	�	�	PROPN
iajs-2816	182	102	−	−	PROPN
iajs-2816	182	103	�	�	PROPN
iajs-2816	182	104	⃗⃗	⃗⃗	PROPN
iajs-2816	182	105	�	�	PROPN
iajs-2816	182	106	)	)	PUNCT
iajs-2816	182	107	=	=	SYM
iajs-2816	182	108	�	�	PROPN
iajs-2816	182	109	́	́	PROPN
iajs-2816	182	110	�	�	NOUN
iajs-2816	182	111	𝑙(	𝑙(	PROPN
iajs-2816	182	112	�	�	PROPN
iajs-2816	182	113	⃗⃗	⃗⃗	PROPN
iajs-2816	182	114	�	�	PROPN
iajs-2816	182	115	)(	)(	PROPN
iajs-2816	182	116	�	�	PROPN
iajs-2816	182	117	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	182	118	�	�	PROPN
iajs-2816	182	119	−	−	PROPN
iajs-2816	182	120	�	�	PROPN
iajs-2816	182	121	⃗⃗	⃗⃗	PROPN
iajs-2816	182	122	�	�	PROPN
iajs-2816	182	123	)	)	PUNCT
iajs-2816	182	124	,	,	PUNCT
iajs-2816	182	125	𝑙	𝑙	X
iajs-2816	183	1	=	=	PUNCT
iajs-2816	183	2	0,1,2	0,1,2	NUM
iajs-2816	183	3	,	,	PUNCT
iajs-2816	183	4	and	and	CCONJ
iajs-2816	183	5	since	since	SCONJ
iajs-2816	183	6	�	�	PROPN
iajs-2816	183	7	⃗⃗	⃗⃗	PROPN
iajs-2816	183	8	�	�	PROPN
iajs-2816	183	9	∈	∈	PROPN
iajs-2816	183	10	�	�	PROPN
iajs-2816	183	11	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	183	12	�	�	PROPN
iajs-2816	183	13	𝐴	𝐴	PROPN
iajs-2816	183	14	is	be	AUX
iajs-2816	183	15	qccocv	qccocv	ADJ
iajs-2816	183	16	,	,	PUNCT
iajs-2816	183	17	by	by	ADP
iajs-2816	183	18	the	the	DET
iajs-2816	183	19	.	.	PROPN
iajs-2816	183	20	2.4	2.4	NUM
iajs-2816	183	21	,	,	PUNCT
iajs-2816	183	22	there	there	PRON
iajs-2816	183	23	is	be	VERB
iajs-2816	183	24	𝜆𝑙	𝜆𝑙	DET
iajs-2816	183	25	∈	∈	PROPN
iajs-2816	183	26	ℝ	ℝ	PROPN
iajs-2816	183	27	,	,	PUNCT
iajs-2816	183	28	𝑙	𝑙	X
iajs-2816	184	1	=	=	SYM
iajs-2816	184	2	0,1,2	0,1,2	NOUN
iajs-2816	184	3	,	,	PUNCT
iajs-2816	184	4	with	with	ADP
iajs-2816	184	5	𝜆0	𝜆0	PROPN
iajs-2816	184	6	≥	≥	NOUN
iajs-2816	184	7	0	0	NUM
iajs-2816	184	8	,	,	PUNCT
iajs-2816	184	9	𝜆2	𝜆2	PROPN
iajs-2816	184	10	≥	≥	NOUN
iajs-2816	184	11	0	0	NUM
iajs-2816	184	12	,	,	PUNCT
iajs-2816	184	13	∑	∑	PUNCT
iajs-2816	184	14	|𝜆𝑙|	|𝜆𝑙|	PROPN
iajs-2816	184	15	=	=	SYM
iajs-2816	184	16	1	1	NUM
iajs-2816	184	17	2	2	NUM
iajs-2816	184	18	𝑙=0	𝑙=0	PROPN
iajs-2816	184	19	s.t	s.t	PROPN
iajs-2816	184	20	.	.	PUNCT
iajs-2816	184	21	(	(	PUNCT
iajs-2816	184	22	38a&b	38a&b	NOUN
iajs-2816	184	23	)	)	PUNCT
iajs-2816	184	24	are	be	AUX
iajs-2816	184	25	held	hold	VERB
iajs-2816	184	26	.	.	PUNCT
iajs-2816	185	1	again	again	ADV
iajs-2816	185	2	by	by	ADP
iajs-2816	185	3	the	the	DET
iajs-2816	185	4	.	.	PROPN
iajs-2816	185	5	3.2	3.2	NUM
iajs-2816	185	6	,	,	PUNCT
iajs-2816	185	7	setting	set	VERB
iajs-2816	185	8	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	185	9	=	=	SYM
iajs-2816	185	10	�	�	PROPN
iajs-2816	185	11	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	185	12	�	�	PROPN
iajs-2816	185	13	−	−	PROPN
iajs-2816	185	14	�	�	PROPN
iajs-2816	185	15	⃗⃗	⃗⃗	PROPN
iajs-2816	185	16	�	�	PROPN
iajs-2816	185	17	and	and	CCONJ
iajs-2816	185	18	substituting	substitute	VERB
iajs-2816	185	19	the	the	DET
iajs-2816	185	20	frd	frd	NOUN
iajs-2816	185	21	of	of	ADP
iajs-2816	185	22	�	�	PROPN
iajs-2816	185	23	́	́	PROPN
iajs-2816	185	24	�	�	PROPN
iajs-2816	185	25	𝑙	𝑙	NUM
iajs-2816	185	26	,	,	PUNCT
iajs-2816	185	27	𝑙	𝑙	X
iajs-2816	185	28	=	=	SYM
iajs-2816	185	29	0,1,2	0,1,2	NOUN
iajs-2816	185	30	in	in	ADP
iajs-2816	185	31	(	(	PUNCT
iajs-2816	185	32	38.a	38.a	NUM
iajs-2816	185	33	)	)	PUNCT
iajs-2816	185	34	,	,	PUNCT
iajs-2816	185	35	one	one	PRON
iajs-2816	185	36	has	have	VERB
iajs-2816	185	37	:	:	PUNCT
iajs-2816	185	38	∑	∑	PUNCT
iajs-2816	185	39	∫	∫	PROPN
iajs-2816	186	1	[	[	X
iajs-2816	186	2	(	(	PUNCT
iajs-2816	186	3	𝜆0𝑧0𝑖	𝜆0𝑧0𝑖	NUM
iajs-2816	186	4	+	+	CCONJ
iajs-2816	186	5	𝜆1𝑧1𝑖	𝜆1𝑧1𝑖	PUNCT
iajs-2816	186	6	+	+	CCONJ
iajs-2816	186	7	𝜆2𝑧2𝑖)𝑓𝑖𝑢𝑖	𝜆2𝑧2𝑖)𝑓𝑖𝑢𝑖	ADJ
iajs-2816	186	8	𝑄	𝑄	PRON
iajs-2816	186	9	+	+	CCONJ
iajs-2816	186	10	(	(	PUNCT
iajs-2816	186	11	𝜆0𝑔0𝑖𝑢𝑖	𝜆0𝑔0𝑖𝑢𝑖	PROPN
iajs-2816	186	12	+	+	NUM
iajs-2816	186	13	𝜆1𝑔1𝑖𝑢𝑖	𝜆1𝑔1𝑖𝑢𝑖	NUM
iajs-2816	186	14	+	+	NUM
iajs-2816	186	15	𝜆2𝑔2𝑖𝑢𝑖)]𝛿𝑢𝑖𝑑𝑥𝑑𝑡	𝜆2𝑔2𝑖𝑢𝑖)]𝛿𝑢𝑖𝑑𝑥𝑑𝑡	X
iajs-2816	186	16	≥	≥	NOUN
iajs-2816	186	17	0	0	NUM
iajs-2816	186	18	4	4	NUM
iajs-2816	186	19	𝑖=1	𝑖=1	PUNCT
iajs-2816	186	20	,	,	PUNCT
iajs-2816	186	21	⇒	⇒	VERB
iajs-2816	186	22	∑	∑	PROPN
iajs-2816	186	23	∫	∫	PROPN
iajs-2816	187	1	[	[	X
iajs-2816	187	2	(	(	PUNCT
iajs-2816	187	3	𝑧𝑖𝑓𝑖𝑢𝑖	𝑧𝑖𝑓𝑖𝑢𝑖	NOUN
iajs-2816	187	4	+	+	CCONJ
iajs-2816	187	5	𝑔𝑖𝑢𝑖	𝑔𝑖𝑢𝑖	VERB
iajs-2816	187	6	)	)	PUNCT
iajs-2816	187	7	𝑄	𝑄	PROPN
iajs-2816	187	8	]	]	SYM
iajs-2816	187	9	4	4	NUM
iajs-2816	187	10	𝑖=1	𝑖=1	PROPN
iajs-2816	187	11	𝛿𝑢𝑖𝑑𝑥𝑑𝑡	𝛿𝑢𝑖𝑑𝑥𝑑𝑡	NOUN
iajs-2816	187	12	≥	≥	NOUN
iajs-2816	187	13	0	0	NUM
iajs-2816	187	14	,	,	PUNCT
iajs-2816	187	15	where	where	SCONJ
iajs-2816	187	16	𝑔𝑖	𝑔𝑖	NOUN
iajs-2816	187	17	=	=	PUNCT
iajs-2816	187	18	∑	∑	PUNCT
iajs-2816	187	19	𝜆𝑙	𝜆𝑙	PROPN
iajs-2816	187	20	2	2	NUM
iajs-2816	187	21	𝑙=0	𝑙=0	NOUN
iajs-2816	187	22	𝑔𝑙𝑖	𝑔𝑙𝑖	NOUN
iajs-2816	187	23	,	,	PUNCT
iajs-2816	187	24	𝑧𝑖	𝑧𝑖	NOUN
iajs-2816	187	25	=	=	NOUN
iajs-2816	187	26	∑	∑	PROPN
iajs-2816	187	27	𝜆𝑙	𝜆𝑙	PROPN
iajs-2816	187	28	2	2	NUM
iajs-2816	187	29	𝑙=0	𝑙=0	NOUN
iajs-2816	187	30	𝑧𝑙𝑖	𝑧𝑙𝑖	NOUN
iajs-2816	187	31	,	,	PUNCT
iajs-2816	187	32	∀𝑖	∀𝑖	PROPN
iajs-2816	187	33	=	=	NOUN
iajs-2816	187	34	1,2,3,4	1,2,3,4	NUM
iajs-2816	187	35	.	.	PUNCT
iajs-2816	188	1	⇒	⇒	PROPN
iajs-2816	188	2	∫	∫	PROPN
iajs-2816	188	3	(	(	PUNCT
iajs-2816	188	4	𝑧1𝑓1𝑢1	𝑧1𝑓1𝑢1	NOUN
iajs-2816	188	5	+	+	CCONJ
iajs-2816	188	6	𝑔1𝑢1	𝑔1𝑢1	PROPN
iajs-2816	188	7	𝑧2𝑓2𝑢2	𝑧2𝑓2𝑢2	PROPN
iajs-2816	188	8	+	+	X
iajs-2816	188	9	𝑔2𝑢2	𝑔2𝑢2	X
iajs-2816	188	10	𝑧3𝑓3𝑢3	𝑧3𝑓3𝑢3	ADV
iajs-2816	188	11	+	+	CCONJ
iajs-2816	188	12	𝑔3𝑢3	𝑔3𝑢3	PROPN
iajs-2816	188	13	𝑧4𝑓4𝑢4	𝑧4𝑓4𝑢4	NOUN
iajs-2816	188	14	+	+	CCONJ
iajs-2816	188	15	𝑔4𝑢4	𝑔4𝑢4	X
iajs-2816	188	16	)	)	PUNCT
iajs-2816	188	17	∙	∙	PROPN
iajs-2816	188	18	(	(	PUNCT
iajs-2816	188	19	𝛿𝑢1	𝛿𝑢1	X
iajs-2816	188	20	𝛿𝑢2	𝛿𝑢2	PROPN
iajs-2816	188	21	𝛿𝑢3	𝛿𝑢3	NOUN
iajs-2816	188	22	𝛿𝑢4	𝛿𝑢4	ADV
iajs-2816	188	23	)	)	PUNCT
iajs-2816	189	1	𝑄	𝑄	PRON
iajs-2816	189	2	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	189	3	≥	≥	NOUN
iajs-2816	189	4	0	0	NUM
iajs-2816	189	5	,	,	PUNCT
iajs-2816	189	6	or	or	CCONJ
iajs-2816	189	7	∫	∫	PROPN
iajs-2816	189	8	𝐻	𝐻	PROPN
iajs-2816	189	9	�	�	PROPN
iajs-2816	189	10	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	189	11	�	�	PROPN
iajs-2816	189	12	(𝑥	(𝑥	PROPN
iajs-2816	189	13	,	,	PUNCT
iajs-2816	189	14	𝑡	𝑡	PROPN
iajs-2816	189	15	,	,	PUNCT
iajs-2816	189	16	�	�	PROPN
iajs-2816	189	17	⃗	⃗	NOUN
iajs-2816	189	18	�	�	PROPN
iajs-2816	189	19	,	,	PUNCT
iajs-2816	189	20	𝑧	𝑧	PROPN
iajs-2816	189	21	,	,	PUNCT
iajs-2816	189	22	�	�	PROPN
iajs-2816	189	23	⃗⃗	⃗⃗	PROPN
iajs-2816	189	24	�	�	PROPN
iajs-2816	189	25	)	)	PUNCT
iajs-2816	189	26	𝑄	𝑄	PROPN
iajs-2816	189	27	∙	∙	PROPN
iajs-2816	189	28	𝛿𝑢⃗⃗⃗⃗⃗𝑑𝑥𝑑𝑡	𝛿𝑢⃗⃗⃗⃗⃗𝑑𝑥𝑑𝑡	NOUN
iajs-2816	189	29	≥	≥	NOUN
iajs-2816	189	30	0	0	NUM
iajs-2816	189	31	.	.	PUNCT
iajs-2816	190	1	(	(	PUNCT
iajs-2816	190	2	ii	ii	NOUN
iajs-2816	190	3	)	)	PUNCT
iajs-2816	190	4	to	to	PART
iajs-2816	190	5	prove	prove	VERB
iajs-2816	190	6	that	that	SCONJ
iajs-2816	190	7	(	(	PUNCT
iajs-2816	190	8	38.a	38.a	NUM
iajs-2816	190	9	)	)	PUNCT
iajs-2816	190	10	is	be	AUX
iajs-2816	190	11	equivalent	equivalent	ADJ
iajs-2816	190	12	to	to	ADP
iajs-2816	190	13	(	(	PUNCT
iajs-2816	190	14	39	39	NUM
iajs-2816	190	15	):	):	PUNCT
iajs-2816	190	16	let	let	VERB
iajs-2816	190	17	�	�	PROPN
iajs-2816	190	18	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	190	19	�	�	PROPN
iajs-2816	190	20	�	�	PROPN
iajs-2816	190	21	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	190	22	�	�	NOUN
iajs-2816	190	23	=	=	SYM
iajs-2816	190	24	{	{	PUNCT
iajs-2816	190	25	�	�	PROPN
iajs-2816	190	26	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	190	27	�	�	PROPN
iajs-2816	190	28	∈	∈	PROPN
iajs-2816	190	29	(	(	PUNCT
iajs-2816	190	30	𝐿	𝐿	PROPN
iajs-2816	190	31	2(𝑄,ℝ))4|	2(𝑄,ℝ))4|	PROPN
iajs-2816	190	32	�	�	PROPN
iajs-2816	190	33	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	34	�	�	PROPN
iajs-2816	190	35	(𝑥	(𝑥	PROPN
iajs-2816	190	36	,	,	PUNCT
iajs-2816	190	37	𝑡	𝑡	NOUN
iajs-2816	190	38	)	)	PUNCT
iajs-2816	190	39	∈	∈	PROPN
iajs-2816	190	40	�	�	PROPN
iajs-2816	190	41	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	42	�	�	PROPN
iajs-2816	190	43	a.	a.	PROPN
iajs-2816	190	44	e.	e.	PROPN
iajs-2816	190	45	in	in	ADP
iajs-2816	190	46	𝑄	𝑄	PROPN
iajs-2816	190	47	}	}	PUNCT
iajs-2816	190	48	with	with	ADP
iajs-2816	190	49	�	�	PROPN
iajs-2816	190	50	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	51	�	�	PROPN
iajs-2816	190	52	⊂	⊂	PROPN
iajs-2816	190	53	ℝ2	ℝ2	PROPN
iajs-2816	190	54	,	,	PUNCT
iajs-2816	190	55	let	let	VERB
iajs-2816	190	56	{	{	PUNCT
iajs-2816	190	57	�	�	NOUN
iajs-2816	190	58	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	190	59	�	�	NOUN
iajs-2816	190	60	𝑘	𝑘	NOUN
iajs-2816	190	61	}	}	PUNCT
iajs-2816	190	62	dense	dense	ADJ
iajs-2816	190	63	in	in	ADP
iajs-2816	190	64	a	a	DET
iajs-2816	190	65	set	set	VERB
iajs-2816	190	66	�	�	PROPN
iajs-2816	190	67	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	190	68	�	�	PROPN
iajs-2816	190	69	�	�	PROPN
iajs-2816	190	70	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	71	�	�	PROPN
iajs-2816	190	72	,	,	PUNCT
iajs-2816	190	73	𝜇	𝜇	X
iajs-2816	190	74	is	be	AUX
iajs-2816	190	75	“	"	PUNCT
iajs-2816	190	76	lebesgue	lebesgue	ADJ
iajs-2816	190	77	measure	measure	NOUN
iajs-2816	190	78	”	"	PUNCT
iajs-2816	190	79	on	on	ADP
iajs-2816	190	80	𝑄	𝑄	PRON
iajs-2816	190	81	and	and	CCONJ
iajs-2816	190	82	let	let	VERB
iajs-2816	190	83	𝑆	𝑆	PROPN
iajs-2816	190	84	⊂	⊂	PRON
iajs-2816	190	85	𝑄	𝑄	PRON
iajs-2816	190	86	be	be	VERB
iajs-2816	190	87	a	a	DET
iajs-2816	190	88	measurable	measurable	ADJ
iajs-2816	190	89	set	set	NOUN
iajs-2816	190	90	s.t	s.t	PROPN
iajs-2816	190	91	.	.	PROPN
iajs-2816	190	92	:	:	PUNCT
iajs-2816	190	93	�	�	PROPN
iajs-2816	190	94	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	95	�	�	PROPN
iajs-2816	190	96	(𝑥	(𝑥	PROPN
iajs-2816	190	97	,	,	PUNCT
iajs-2816	190	98	𝑡	𝑡	X
iajs-2816	190	99	)	)	PUNCT
iajs-2816	190	100	=	=	PRON
iajs-2816	190	101	{	{	PUNCT
iajs-2816	190	102	�	�	PROPN
iajs-2816	190	103	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	104	�	�	NOUN
iajs-2816	190	105	𝑘(𝑥	𝑘(𝑥	PROPN
iajs-2816	190	106	,	,	PUNCT
iajs-2816	190	107	𝑡	𝑡	PROPN
iajs-2816	190	108	)	)	PUNCT
iajs-2816	190	109	,	,	PUNCT
iajs-2816	190	110	if	if	SCONJ
iajs-2816	190	111	(	(	PUNCT
iajs-2816	190	112	𝑥	𝑥	NOUN
iajs-2816	190	113	,	,	PUNCT
iajs-2816	190	114	𝑡	𝑡	NOUN
iajs-2816	190	115	)	)	PUNCT
iajs-2816	190	116	∈	∈	PROPN
iajs-2816	190	117	𝑆	𝑆	PROPN
iajs-2816	190	118	�	�	PROPN
iajs-2816	190	119	⃗⃗	⃗⃗	PROPN
iajs-2816	190	120	�	�	PROPN
iajs-2816	190	121	(𝑥	(𝑥	PROPN
iajs-2816	190	122	,	,	PUNCT
iajs-2816	190	123	𝑡	𝑡	PROPN
iajs-2816	190	124	)	)	PUNCT
iajs-2816	190	125	,	,	PUNCT
iajs-2816	190	126	if	if	SCONJ
iajs-2816	190	127	(	(	PUNCT
iajs-2816	190	128	𝑥	𝑥	NOUN
iajs-2816	190	129	,	,	PUNCT
iajs-2816	190	130	𝑡	𝑡	PROPN
iajs-2816	190	131	)	)	PUNCT
iajs-2816	190	132	∉	∉	PROPN
iajs-2816	190	133	𝑆	𝑆	PROPN
iajs-2816	190	134	therefore	therefore	ADV
iajs-2816	190	135	(	(	PUNCT
iajs-2816	190	136	38.a	38.a	NUM
iajs-2816	190	137	)	)	PUNCT
iajs-2816	190	138	becomes	become	VERB
iajs-2816	190	139	:	:	PUNCT
iajs-2816	190	140	∫	∫	PROPN
iajs-2816	190	141	𝐻	𝐻	PROPN
iajs-2816	190	142	�	�	PROPN
iajs-2816	190	143	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	190	144	�	�	PROPN
iajs-2816	190	145	(𝑥	(𝑥	PROPN
iajs-2816	190	146	,	,	PUNCT
iajs-2816	190	147	𝑡	𝑡	PROPN
iajs-2816	190	148	,	,	PUNCT
iajs-2816	190	149	�	�	PROPN
iajs-2816	190	150	⃗	⃗	NOUN
iajs-2816	190	151	�	�	PROPN
iajs-2816	190	152	,	,	PUNCT
iajs-2816	190	153	𝑧	𝑧	PROPN
iajs-2816	190	154	,	,	PUNCT
iajs-2816	190	155	�	�	PROPN
iajs-2816	190	156	⃗⃗	⃗⃗	PROPN
iajs-2816	190	157	�	�	PROPN
iajs-2816	190	158	)	)	PUNCT
iajs-2816	190	159	𝑆	𝑆	PROPN
iajs-2816	190	160	(	(	PUNCT
iajs-2816	190	161	�	�	PROPN
iajs-2816	190	162	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	190	163	�	�	VERB
iajs-2816	190	164	𝑘	𝑘	PRON
iajs-2816	190	165	−	−	PROPN
iajs-2816	190	166	�	�	PROPN
iajs-2816	190	167	⃗⃗	⃗⃗	PROPN
iajs-2816	190	168	�	�	PROPN
iajs-2816	190	169	)	)	PUNCT
iajs-2816	190	170	≥	≥	NOUN
iajs-2816	190	171	0	0	NUM
iajs-2816	190	172	,	,	PUNCT
iajs-2816	190	173	∀𝑆.	∀𝑆.	PROPN
iajs-2816	190	174	using	use	VERB
iajs-2816	190	175	the	the	DET
iajs-2816	190	176	3.2	3.2	NUM
iajs-2816	190	177	,	,	PUNCT
iajs-2816	190	178	to	to	PART
iajs-2816	190	179	obtain	obtain	VERB
iajs-2816	191	1	:	:	PUNCT
iajs-2816	191	2	𝐻	𝐻	PROPN
iajs-2816	191	3	�	�	PROPN
iajs-2816	191	4	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	191	5	�	�	PROPN
iajs-2816	191	6	(𝑥	(𝑥	PROPN
iajs-2816	191	7	,	,	PUNCT
iajs-2816	191	8	𝑡	𝑡	PROPN
iajs-2816	191	9	,	,	PUNCT
iajs-2816	191	10	�	�	PROPN
iajs-2816	191	11	⃗	⃗	NOUN
iajs-2816	191	12	�	�	PROPN
iajs-2816	191	13	,	,	PUNCT
iajs-2816	191	14	𝑧	𝑧	PROPN
iajs-2816	191	15	,	,	PUNCT
iajs-2816	191	16	�	�	PROPN
iajs-2816	191	17	⃗⃗	⃗⃗	PROPN
iajs-2816	191	18	�	�	PROPN
iajs-2816	191	19	)(	)(	PROPN
iajs-2816	191	20	�	�	PROPN
iajs-2816	191	21	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	191	22	�	�	PROPN
iajs-2816	191	23	𝑘	𝑘	PRON
iajs-2816	191	24	−	−	PROPN
iajs-2816	191	25	�	�	PROPN
iajs-2816	191	26	⃗⃗	⃗⃗	PROPN
iajs-2816	191	27	�	�	PROPN
iajs-2816	191	28	)	)	PUNCT
iajs-2816	191	29	≥	≥	NOUN
iajs-2816	191	30	0	0	NUM
iajs-2816	191	31	,	,	PUNCT
iajs-2816	191	32	a.e	a.e	PROPN
iajs-2816	191	33	.	.	PROPN
iajs-2816	191	34	in	in	ADP
iajs-2816	191	35	𝑄	𝑄	PROPN
iajs-2816	191	36	,	,	PUNCT
iajs-2816	191	37	𝐻	𝐻	PROPN
iajs-2816	191	38	�	�	PROPN
iajs-2816	191	39	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	191	40	�	�	PROPN
iajs-2816	191	41	(𝑥	(𝑥	PROPN
iajs-2816	191	42	,	,	PUNCT
iajs-2816	191	43	𝑡	𝑡	PROPN
iajs-2816	191	44	,	,	PUNCT
iajs-2816	191	45	�	�	PROPN
iajs-2816	191	46	⃗	⃗	NOUN
iajs-2816	191	47	�	�	PROPN
iajs-2816	191	48	,	,	PUNCT
iajs-2816	191	49	𝑧	𝑧	PROPN
iajs-2816	191	50	,	,	PUNCT
iajs-2816	191	51	�	�	PROPN
iajs-2816	191	52	⃗⃗	⃗⃗	PROPN
iajs-2816	191	53	�	�	PROPN
iajs-2816	191	54	)(	)(	PROPN
iajs-2816	191	55	�	�	PROPN
iajs-2816	191	56	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	191	57	�	�	PROPN
iajs-2816	191	58	𝑘	𝑘	PRON
iajs-2816	191	59	−	−	PROPN
iajs-2816	191	60	�	�	PROPN
iajs-2816	191	61	⃗⃗	⃗⃗	PROPN
iajs-2816	191	62	�	�	PROPN
iajs-2816	191	63	)	)	PUNCT
iajs-2816	191	64	≥	≥	NOUN
iajs-2816	191	65	0	0	NUM
iajs-2816	191	66	,	,	PUNCT
iajs-2816	191	67	in	in	ADP
iajs-2816	191	68	𝑃	𝑃	NOUN
iajs-2816	191	69	=	=	SYM
iajs-2816	191	70	⋂	⋂	PROPN
iajs-2816	191	71	𝑃𝑘𝑘	𝑃𝑘𝑘	PROPN
iajs-2816	191	72	,	,	PUNCT
iajs-2816	191	73	where	where	SCONJ
iajs-2816	191	74	𝑃𝑘	𝑃𝑘	PROPN
iajs-2816	191	75	=	=	SYM
iajs-2816	191	76	𝑄	𝑄	PROPN
iajs-2816	191	77	−	−	PROPN
iajs-2816	191	78	𝑄𝑘	𝑄𝑘	PROPN
iajs-2816	191	79	with	with	ADP
iajs-2816	191	80	𝜇(𝑄𝑘	𝜇(𝑄𝑘	NOUN
iajs-2816	191	81	)	)	PUNCT
iajs-2816	191	82	=	=	SYM
iajs-2816	191	83	0	0	NUM
iajs-2816	191	84	,	,	PUNCT
iajs-2816	191	85	∀𝑘	∀𝑘	NOUN
iajs-2816	191	86	,	,	PUNCT
iajs-2816	191	87	since	since	SCONJ
iajs-2816	191	88	𝑃	𝑃	NOUN
iajs-2816	191	89	is	be	AUX
iajs-2816	191	90	independent	independent	ADJ
iajs-2816	191	91	of	of	ADP
iajs-2816	191	92	𝑘	𝑘	PRON
iajs-2816	191	93	,	,	PUNCT
iajs-2816	191	94	hence	hence	ADV
iajs-2816	191	95	𝜇(𝑄	𝜇(𝑄	ADJ
iajs-2816	191	96	−	−	PUNCT
iajs-2816	191	97	𝑃	𝑃	NOUN
iajs-2816	191	98	)	)	PUNCT
iajs-2816	191	99	=	=	PUNCT
iajs-2816	191	100	𝜇(⋃	𝜇(⋃	PROPN
iajs-2816	191	101	𝑄𝑘𝑘	𝑄𝑘𝑘	PROPN
iajs-2816	191	102	)	)	PUNCT
iajs-2816	192	1	=	=	SYM
iajs-2816	192	2	0	0	NUM
iajs-2816	192	3	,	,	PUNCT
iajs-2816	192	4	from	from	ADP
iajs-2816	192	5	the	the	DET
iajs-2816	192	6	density	density	NOUN
iajs-2816	192	7	of	of	ADP
iajs-2816	192	8	{	{	PUNCT
iajs-2816	192	9	�	�	PROPN
iajs-2816	192	10	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	192	11	�	�	NOUN
iajs-2816	192	12	𝑘	𝑘	NOUN
iajs-2816	192	13	}	}	PUNCT
iajs-2816	192	14	in	in	ADP
iajs-2816	192	15	�	�	PROPN
iajs-2816	192	16	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	192	17	�	�	PROPN
iajs-2816	192	18	�	�	PROPN
iajs-2816	192	19	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	192	20	�	�	PROPN
iajs-2816	192	21	,	,	PUNCT
iajs-2816	192	22	one	one	NUM
iajs-2816	192	23	has	have	VERB
iajs-2816	192	24	𝐻	𝐻	PROPN
iajs-2816	192	25	�	�	PROPN
iajs-2816	192	26	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	192	27	�	�	PROPN
iajs-2816	192	28	(𝑥	(𝑥	PROPN
iajs-2816	192	29	,	,	PUNCT
iajs-2816	192	30	𝑡	𝑡	PROPN
iajs-2816	192	31	,	,	PUNCT
iajs-2816	192	32	�	�	PROPN
iajs-2816	192	33	⃗	⃗	NOUN
iajs-2816	192	34	�	�	PROPN
iajs-2816	192	35	,	,	PUNCT
iajs-2816	192	36	𝑧	𝑧	PROPN
iajs-2816	192	37	,	,	PUNCT
iajs-2816	192	38	�	�	PROPN
iajs-2816	192	39	⃗⃗	⃗⃗	PROPN
iajs-2816	192	40	�	�	PROPN
iajs-2816	192	41	)(	)(	PROPN
iajs-2816	192	42	�	�	PROPN
iajs-2816	192	43	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	192	44	�	�	PROPN
iajs-2816	192	45	−	−	PROPN
iajs-2816	192	46	�	�	PROPN
iajs-2816	192	47	⃗⃗	⃗⃗	PROPN
iajs-2816	192	48	�	�	PROPN
iajs-2816	192	49	)	)	PUNCT
iajs-2816	192	50	≥	≥	NOUN
iajs-2816	192	51	0	0	NUM
iajs-2816	192	52	,	,	PUNCT
iajs-2816	192	53	a.e	a.e	PROPN
iajs-2816	192	54	.	.	PROPN
iajs-2816	193	1	in	in	ADP
iajs-2816	193	2	𝑄.	𝑄.	PROPN
iajs-2816	193	3	⇒	⇒	NOUN
iajs-2816	193	4	𝐻	𝐻	PROPN
iajs-2816	193	5	�	�	PROPN
iajs-2816	193	6	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	7	�	�	PROPN
iajs-2816	193	8	(𝑥	(𝑥	PROPN
iajs-2816	193	9	,	,	PUNCT
iajs-2816	193	10	𝑡	𝑡	PROPN
iajs-2816	193	11	,	,	PUNCT
iajs-2816	193	12	�	�	PROPN
iajs-2816	193	13	⃗	⃗	NOUN
iajs-2816	193	14	�	�	PROPN
iajs-2816	193	15	,	,	PUNCT
iajs-2816	193	16	𝑧	𝑧	PROPN
iajs-2816	193	17	,	,	PUNCT
iajs-2816	193	18	�	�	PROPN
iajs-2816	193	19	⃗⃗	⃗⃗	PROPN
iajs-2816	193	20	�	�	PROPN
iajs-2816	193	21	)	)	PUNCT
iajs-2816	193	22	�	�	PROPN
iajs-2816	193	23	⃗⃗	⃗⃗	PROPN
iajs-2816	193	24	�	�	PROPN
iajs-2816	193	25	=	=	SYM
iajs-2816	193	26	min	min	PROPN
iajs-2816	193	27	�	�	PROPN
iajs-2816	193	28	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	29	�	�	PROPN
iajs-2816	193	30	∈	∈	PROPN
iajs-2816	193	31	�	�	PROPN
iajs-2816	193	32	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	33	�	�	PROPN
iajs-2816	193	34	𝐻	𝐻	PROPN
iajs-2816	193	35	�	�	PROPN
iajs-2816	193	36	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	37	�	�	PROPN
iajs-2816	193	38	(𝑥	(𝑥	PROPN
iajs-2816	193	39	,	,	PUNCT
iajs-2816	193	40	𝑡	𝑡	PROPN
iajs-2816	193	41	,	,	PUNCT
iajs-2816	193	42	�	�	PROPN
iajs-2816	193	43	⃗	⃗	NOUN
iajs-2816	193	44	�	�	PROPN
iajs-2816	193	45	,	,	PUNCT
iajs-2816	193	46	𝑧	𝑧	PROPN
iajs-2816	193	47	,	,	PUNCT
iajs-2816	193	48	�	�	PROPN
iajs-2816	193	49	⃗⃗	⃗⃗	PROPN
iajs-2816	193	50	�	�	PROPN
iajs-2816	193	51	)	)	PUNCT
iajs-2816	193	52	�	�	PROPN
iajs-2816	193	53	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	54	�	�	PROPN
iajs-2816	193	55	,	,	PUNCT
iajs-2816	193	56	∀	∀	NUM
iajs-2816	193	57	�	�	NOUN
iajs-2816	193	58	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	59	�	�	PROPN
iajs-2816	193	60	∈	∈	PROPN
iajs-2816	193	61	�	�	PROPN
iajs-2816	193	62	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	193	63	�	�	PROPN
iajs-2816	193	64	,	,	PUNCT
iajs-2816	193	65	a.e	a.e	PROPN
iajs-2816	193	66	.	.	PROPN
iajs-2816	193	67	in	in	ADP
iajs-2816	193	68	𝑄.	𝑄.	NOUN
iajs-2816	193	69	conversely	conversely	ADV
iajs-2816	193	70	,	,	PUNCT
iajs-2816	193	71	if	if	SCONJ
iajs-2816	193	72	𝐻	𝐻	PROPN
iajs-2816	193	73	�	�	PROPN
iajs-2816	193	74	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	75	�	�	PROPN
iajs-2816	193	76	(𝑥	(𝑥	PROPN
iajs-2816	193	77	,	,	PUNCT
iajs-2816	193	78	𝑡	𝑡	PROPN
iajs-2816	193	79	,	,	PUNCT
iajs-2816	193	80	�	�	PROPN
iajs-2816	193	81	⃗	⃗	NOUN
iajs-2816	193	82	�	�	PROPN
iajs-2816	193	83	,	,	PUNCT
iajs-2816	193	84	𝑧	𝑧	PROPN
iajs-2816	193	85	,	,	PUNCT
iajs-2816	193	86	�	�	PROPN
iajs-2816	193	87	⃗⃗	⃗⃗	PROPN
iajs-2816	193	88	�	�	PROPN
iajs-2816	193	89	)	)	PUNCT
iajs-2816	193	90	�	�	PROPN
iajs-2816	193	91	⃗⃗	⃗⃗	PROPN
iajs-2816	193	92	�	�	PROPN
iajs-2816	193	93	=	=	SYM
iajs-2816	193	94	min	min	PROPN
iajs-2816	193	95	�	�	PROPN
iajs-2816	193	96	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	97	�	�	PROPN
iajs-2816	193	98	∈	∈	PROPN
iajs-2816	193	99	�	�	PROPN
iajs-2816	193	100	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	101	�	�	PROPN
iajs-2816	193	102	𝐻	𝐻	PROPN
iajs-2816	193	103	�	�	PROPN
iajs-2816	193	104	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	105	�	�	PROPN
iajs-2816	193	106	(𝑥	(𝑥	PROPN
iajs-2816	193	107	,	,	PUNCT
iajs-2816	193	108	𝑡	𝑡	PROPN
iajs-2816	193	109	,	,	PUNCT
iajs-2816	193	110	�	�	PROPN
iajs-2816	193	111	⃗	⃗	NOUN
iajs-2816	193	112	�	�	PROPN
iajs-2816	193	113	,	,	PUNCT
iajs-2816	193	114	𝑧	𝑧	PROPN
iajs-2816	193	115	,	,	PUNCT
iajs-2816	193	116	�	�	PROPN
iajs-2816	193	117	⃗⃗	⃗⃗	PROPN
iajs-2816	193	118	�	�	PROPN
iajs-2816	193	119	)	)	PUNCT
iajs-2816	193	120	�	�	PROPN
iajs-2816	193	121	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	193	122	�	�	PROPN
iajs-2816	193	123	,	,	PUNCT
iajs-2816	193	124	a.e	a.e	PROPN
iajs-2816	193	125	.	.	PROPN
iajs-2816	193	126	on	on	ADP
iajs-2816	193	127	𝑄	𝑄	PROPN
iajs-2816	193	128	ihjpas	ihjpa	VERB
iajs-2816	193	129	.	.	PUNCT
iajs-2816	194	1	53	53	NUM
iajs-2816	194	2	(	(	PUNCT
iajs-2816	194	3	3)2022	3)2022	NOUN
iajs-2816	194	4	142	142	NUM
iajs-2816	194	5	⇒	⇒	NOUN
iajs-2816	194	6	𝐻	𝐻	PROPN
iajs-2816	194	7	�	�	PROPN
iajs-2816	194	8	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	194	9	�	�	PROPN
iajs-2816	194	10	(𝑥	(𝑥	PROPN
iajs-2816	194	11	,	,	PUNCT
iajs-2816	194	12	𝑡	𝑡	PROPN
iajs-2816	194	13	,	,	PUNCT
iajs-2816	194	14	�	�	PROPN
iajs-2816	194	15	⃗	⃗	NOUN
iajs-2816	194	16	�	�	PROPN
iajs-2816	194	17	,	,	PUNCT
iajs-2816	194	18	𝑧	𝑧	PROPN
iajs-2816	194	19	,	,	PUNCT
iajs-2816	194	20	�	�	PROPN
iajs-2816	194	21	⃗⃗	⃗⃗	PROPN
iajs-2816	194	22	�	�	PROPN
iajs-2816	194	23	)(	)(	PROPN
iajs-2816	194	24	�	�	PROPN
iajs-2816	194	25	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	194	26	�	�	PROPN
iajs-2816	194	27	−	−	PROPN
iajs-2816	194	28	�	�	PROPN
iajs-2816	194	29	⃗⃗	⃗⃗	PROPN
iajs-2816	194	30	�	�	PROPN
iajs-2816	194	31	)	)	PUNCT
iajs-2816	194	32	≥	≥	NOUN
iajs-2816	194	33	0	0	NUM
iajs-2816	194	34	,	,	PUNCT
iajs-2816	194	35	∀	∀	X
iajs-2816	194	36	�	�	NOUN
iajs-2816	194	37	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	194	38	�	�	PROPN
iajs-2816	194	39	∈	∈	PROPN
iajs-2816	194	40	�	�	PROPN
iajs-2816	194	41	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	194	42	�	�	PROPN
iajs-2816	194	43	,	,	PUNCT
iajs-2816	194	44	a.e	a.e	PROPN
iajs-2816	194	45	.	.	PROPN
iajs-2816	194	46	on	on	ADP
iajs-2816	194	47	𝑄	𝑄	PROPN
iajs-2816	194	48	⇒	⇒	NOUN
iajs-2816	194	49	∫	∫	PROPN
iajs-2816	194	50	𝐻	𝐻	PROPN
iajs-2816	194	51	�	�	PROPN
iajs-2816	194	52	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	194	53	�	�	PROPN
iajs-2816	194	54	(𝑥	(𝑥	PROPN
iajs-2816	194	55	,	,	PUNCT
iajs-2816	194	56	𝑡	𝑡	PROPN
iajs-2816	194	57	,	,	PUNCT
iajs-2816	194	58	�	�	PROPN
iajs-2816	194	59	⃗	⃗	NOUN
iajs-2816	194	60	�	�	PROPN
iajs-2816	194	61	,	,	PUNCT
iajs-2816	194	62	𝑧	𝑧	PROPN
iajs-2816	194	63	,	,	PUNCT
iajs-2816	194	64	�	�	PROPN
iajs-2816	194	65	⃗⃗	⃗⃗	PROPN
iajs-2816	194	66	�	�	PROPN
iajs-2816	194	67	)𝛿𝑢⃗⃗⃗⃗⃗	)𝛿𝑢⃗⃗⃗⃗⃗	PUNCT
iajs-2816	194	68	𝑄	𝑄	PRON
iajs-2816	194	69	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	194	70	≥	≥	NOUN
iajs-2816	194	71	0	0	NUM
iajs-2816	194	72	,	,	PUNCT
iajs-2816	194	73	∀	∀	X
iajs-2816	194	74	�	�	NOUN
iajs-2816	194	75	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	194	76	�	�	PROPN
iajs-2816	194	77	∈	∈	PROPN
iajs-2816	194	78	�	�	PROPN
iajs-2816	194	79	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	194	80	�	�	PROPN
iajs-2816	194	81	.	.	PUNCT
iajs-2816	195	1	theorem	theorem	PROPN
iajs-2816	195	2	(	(	PUNCT
iajs-2816	195	3	4.2	4.2	NUM
iajs-2816	195	4	)	)	PUNCT
iajs-2816	195	5	:(	:(	PUNCT
iajs-2816	196	1	scsth	scsth	NOUN
iajs-2816	196	2	for	for	ADP
iajs-2816	196	3	optimality	optimality	NOUN
iajs-2816	196	4	)	)	PUNCT
iajs-2816	196	5	in	in	ADP
iajs-2816	196	6	addition	addition	NOUN
iajs-2816	196	7	to	to	ADP
iajs-2816	196	8	hypotheses	hypothesis	NOUN
iajs-2816	196	9	(	(	PUNCT
iajs-2816	196	10	a	a	NOUN
iajs-2816	196	11	)	)	PUNCT
iajs-2816	196	12	,	,	PUNCT
iajs-2816	196	13	(	(	PUNCT
iajs-2816	196	14	b	b	X
iajs-2816	196	15	)	)	PUNCT
iajs-2816	196	16	and	and	CCONJ
iajs-2816	196	17	(	(	PUNCT
iajs-2816	196	18	c	c	NOUN
iajs-2816	196	19	)	)	PUNCT
iajs-2816	196	20	,	,	PUNCT
iajs-2816	196	21	suppose	suppose	VERB
iajs-2816	196	22	that	that	SCONJ
iajs-2816	196	23	�	�	PROPN
iajs-2816	196	24	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	196	25	�	�	PROPN
iajs-2816	196	26	=	=	SYM
iajs-2816	196	27	�	�	PROPN
iajs-2816	196	28	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	196	29	�	�	PROPN
iajs-2816	196	30	�	�	PROPN
iajs-2816	196	31	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	196	32	�	�	PROPN
iajs-2816	196	33	is	be	AUX
iajs-2816	196	34	co	co	NOUN
iajs-2816	196	35	,	,	PUNCT
iajs-2816	196	36	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	196	37	,	,	PUNCT
iajs-2816	196	38	∀𝑖	∀𝑖	PROPN
iajs-2816	196	39	=	=	PUNCT
iajs-2816	196	40	1,2,3,4	1,2,3,4	NUM
iajs-2816	196	41	and	and	CCONJ
iajs-2816	196	42	𝑔1𝑖	𝑔1𝑖	NOUN
iajs-2816	196	43	are	be	AUX
iajs-2816	196	44	affine	affine	NOUN
iajs-2816	196	45	w.r.t	w.r.t	NOUN
iajs-2816	196	46	.	.	PUNCT
iajs-2816	197	1	(	(	PUNCT
iajs-2816	197	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	197	3	,	,	PUNCT
iajs-2816	197	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	197	5	)	)	PUNCT
iajs-2816	197	6	in	in	ADP
iajs-2816	197	7	𝑄	𝑄	PROPN
iajs-2816	197	8	,	,	PUNCT
iajs-2816	197	9	and	and	CCONJ
iajs-2816	197	10	𝑔0𝑖	𝑔0𝑖	NOUN
iajs-2816	197	11	and	and	CCONJ
iajs-2816	197	12	𝑔2𝑖	𝑔2𝑖	NOUN
iajs-2816	197	13	are	be	AUX
iajs-2816	197	14	co	co	VERB
iajs-2816	197	15	w.r.t	w.r.t	PROPN
iajs-2816	197	16	.	.	PUNCT
iajs-2816	198	1	(	(	PUNCT
iajs-2816	198	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	198	3	,	,	PUNCT
iajs-2816	198	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	198	5	)	)	PUNCT
iajs-2816	198	6	in	in	ADP
iajs-2816	198	7	𝑄	𝑄	PROPN
iajs-2816	198	8	∀𝑖	∀𝑖	PROPN
iajs-2816	199	1	=	=	VERB
iajs-2816	200	1	1,2,3,4	1,2,3,4	NUM
iajs-2816	200	2	.	.	PUNCT
iajs-2816	201	1	then	then	ADV
iajs-2816	201	2	the	the	DET
iajs-2816	201	3	ncs	ncs	NOUN
iajs-2816	201	4	in	in	ADP
iajs-2816	201	5	the	the	PRON
iajs-2816	201	6	.	.	PROPN
iajs-2816	201	7	4.1	4.1	NUM
iajs-2816	201	8	with	with	ADP
iajs-2816	201	9	𝜆0	𝜆0	NOUN
iajs-2816	201	10	>	>	X
iajs-2816	201	11	0	0	NUM
iajs-2816	201	12	are	be	AUX
iajs-2816	201	13	also	also	ADV
iajs-2816	201	14	sufficient	sufficient	ADJ
iajs-2816	201	15	.	.	PUNCT
iajs-2816	202	1	proof	proof	NOUN
iajs-2816	202	2	:	:	PUNCT
iajs-2816	202	3	from	from	ADP
iajs-2816	202	4	the	the	PRON
iajs-2816	202	5	.	.	PROPN
iajs-2816	202	6	4.1	4.1	NUM
iajs-2816	202	7	,	,	PUNCT
iajs-2816	202	8	𝐷𝐺𝑙(	𝐷𝐺𝑙(	PROPN
iajs-2816	202	9	�	�	PROPN
iajs-2816	202	10	⃗⃗	⃗⃗	PROPN
iajs-2816	202	11	�	�	PROPN
iajs-2816	202	12	,	,	PUNCT
iajs-2816	202	13	�	�	PROPN
iajs-2816	202	14	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	202	15	�	�	PROPN
iajs-2816	202	16	−	−	PROPN
iajs-2816	202	17	�	�	PROPN
iajs-2816	202	18	⃗⃗	⃗⃗	PROPN
iajs-2816	202	19	�	�	PROPN
iajs-2816	202	20	)	)	PUNCT
iajs-2816	202	21	=	=	SYM
iajs-2816	202	22	�	�	PROPN
iajs-2816	202	23	́	́	PROPN
iajs-2816	202	24	�	�	NOUN
iajs-2816	202	25	𝑙(	𝑙(	PROPN
iajs-2816	202	26	�	�	PROPN
iajs-2816	202	27	⃗⃗	⃗⃗	PROPN
iajs-2816	202	28	�	�	PROPN
iajs-2816	202	29	)(	)(	PROPN
iajs-2816	202	30	�	�	PROPN
iajs-2816	202	31	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	202	32	�	�	PROPN
iajs-2816	202	33	−	−	PROPN
iajs-2816	202	34	�	�	PROPN
iajs-2816	202	35	⃗⃗	⃗⃗	PROPN
iajs-2816	202	36	�	�	PROPN
iajs-2816	202	37	)	)	PUNCT
iajs-2816	202	38	,	,	PUNCT
iajs-2816	202	39	𝑙	𝑙	X
iajs-2816	203	1	=	=	SYM
iajs-2816	203	2	0,1,2	0,1,2	NOUN
iajs-2816	203	3	,	,	PUNCT
iajs-2816	203	4	assume	assume	VERB
iajs-2816	203	5	that	that	SCONJ
iajs-2816	203	6	�	�	PROPN
iajs-2816	203	7	⃗⃗	⃗⃗	PROPN
iajs-2816	203	8	�	�	PROPN
iajs-2816	203	9	satisfies	satisfie	NOUN
iajs-2816	203	10	(	(	PUNCT
iajs-2816	203	11	38	38	NUM
iajs-2816	203	12	)	)	PUNCT
iajs-2816	203	13	and	and	CCONJ
iajs-2816	203	14	�	�	PROPN
iajs-2816	203	15	⃗⃗	⃗⃗	PROPN
iajs-2816	203	16	�	�	PROPN
iajs-2816	203	17	∈	∈	PROPN
iajs-2816	203	18	�	�	PROPN
iajs-2816	203	19	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	203	20	�	�	PROPN
iajs-2816	203	21	𝐴	𝐴	PROPN
iajs-2816	203	22	,	,	PUNCT
iajs-2816	203	23	i.e.	i.e.	ADV
iajs-2816	203	24	:	:	PUNCT
iajs-2816	203	25	∫	∫	PROPN
iajs-2816	203	26	𝐻	𝐻	PROPN
iajs-2816	203	27	�	�	PROPN
iajs-2816	203	28	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	203	29	�	�	PROPN
iajs-2816	203	30	(𝑥	(𝑥	PROPN
iajs-2816	203	31	,	,	PUNCT
iajs-2816	203	32	𝑡	𝑡	PROPN
iajs-2816	203	33	,	,	PUNCT
iajs-2816	203	34	�	�	PROPN
iajs-2816	203	35	⃗	⃗	NOUN
iajs-2816	203	36	�	�	PROPN
iajs-2816	203	37	,	,	PUNCT
iajs-2816	203	38	𝑧	𝑧	PROPN
iajs-2816	203	39	,	,	PUNCT
iajs-2816	203	40	�	�	PROPN
iajs-2816	203	41	⃗⃗	⃗⃗	PROPN
iajs-2816	203	42	�	�	PROPN
iajs-2816	203	43	)𝛿𝑢⃗⃗⃗⃗⃗	)𝛿𝑢⃗⃗⃗⃗⃗	PUNCT
iajs-2816	203	44	𝑄	𝑄	PRON
iajs-2816	203	45	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	203	46	≥	≥	NOUN
iajs-2816	203	47	0	0	NUM
iajs-2816	203	48	,	,	PUNCT
iajs-2816	203	49	∀	∀	X
iajs-2816	203	50	�	�	NOUN
iajs-2816	203	51	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	203	52	�	�	PROPN
iajs-2816	203	53	∈	∈	PROPN
iajs-2816	203	54	�	�	PROPN
iajs-2816	203	55	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	203	56	�	�	PROPN
iajs-2816	203	57	.	.	PUNCT
iajs-2816	203	58	and	and	CCONJ
iajs-2816	203	59	𝜆2𝐺2(	𝜆2𝐺2(	PUNCT
iajs-2816	203	60	�	�	PROPN
iajs-2816	203	61	⃗⃗	⃗⃗	PROPN
iajs-2816	203	62	�	�	PROPN
iajs-2816	203	63	)	)	PUNCT
iajs-2816	203	64	=	=	SYM
iajs-2816	204	1	0	0	X
iajs-2816	204	2	.	.	PUNCT
iajs-2816	205	1	let	let	VERB
iajs-2816	205	2	(	(	PUNCT
iajs-2816	205	3	�	�	NOUN
iajs-2816	205	4	⃗⃗	⃗⃗	NOUN
iajs-2816	205	5	�	�	PROPN
iajs-2816	205	6	)	)	PUNCT
iajs-2816	205	7	=	=	SYM
iajs-2816	205	8	∑	∑	PUNCT
iajs-2816	205	9	𝜆𝑙𝐺𝑙(	𝜆𝑙𝐺𝑙(	PROPN
iajs-2816	205	10	�	�	PROPN
iajs-2816	205	11	⃗⃗	⃗⃗	PROPN
iajs-2816	205	12	�	�	PROPN
iajs-2816	205	13	)	)	PUNCT
iajs-2816	205	14	2	2	NUM
iajs-2816	205	15	𝑙=0	𝑙=0	NOUN
iajs-2816	205	16	,	,	PUNCT
iajs-2816	205	17	then	then	ADV
iajs-2816	205	18	�	�	PROPN
iajs-2816	205	19	́	́	PROPN
iajs-2816	205	20	�	�	PROPN
iajs-2816	205	21	(	(	PUNCT
iajs-2816	205	22	�	�	PROPN
iajs-2816	205	23	⃗⃗	⃗⃗	PROPN
iajs-2816	205	24	�	�	PROPN
iajs-2816	205	25	)	)	PUNCT
iajs-2816	205	26	∙	∙	PROPN
iajs-2816	205	27	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	206	1	=	=	PUNCT
iajs-2816	206	2	∑	∑	PUNCT
iajs-2816	206	3	𝜆𝑙	𝜆𝑙	PROPN
iajs-2816	206	4	�	�	PROPN
iajs-2816	206	5	́	́	PROPN
iajs-2816	206	6	�	�	NOUN
iajs-2816	206	7	𝑙(	𝑙(	PROPN
iajs-2816	206	8	�	�	PROPN
iajs-2816	206	9	⃗⃗	⃗⃗	PROPN
iajs-2816	206	10	�	�	PROPN
iajs-2816	206	11	)	)	PUNCT
iajs-2816	206	12	2	2	NUM
iajs-2816	206	13	𝑙=0	𝑙=0	PUNCT
iajs-2816	206	14	∙	∙	PROPN
iajs-2816	206	15	𝛿𝑢⃗⃗⃗⃗⃗	𝛿𝑢⃗⃗⃗⃗⃗	PROPN
iajs-2816	206	16	=	=	PUNCT
iajs-2816	207	1	𝜆0	𝜆0	NUM
iajs-2816	207	2	∫	∫	PROPN
iajs-2816	207	3	∑	∑	INTJ
iajs-2816	207	4	(	(	PUNCT
iajs-2816	207	5	𝑧0𝑖𝑓𝑖𝑢𝑖	𝑧0𝑖𝑓𝑖𝑢𝑖	VERB
iajs-2816	207	6	+	+	CCONJ
iajs-2816	207	7	𝑔0𝑖𝑢𝑖	𝑔0𝑖𝑢𝑖	PRON
iajs-2816	207	8	)	)	PUNCT
iajs-2816	207	9	4	4	NUM
iajs-2816	207	10	𝑖=1	𝑖=1	NUM
iajs-2816	207	11	𝛿𝑢𝑖	𝛿𝑢𝑖	VERB
iajs-2816	207	12	𝑄	𝑄	PRON
iajs-2816	207	13	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	ADV
iajs-2816	207	14	+	+	CCONJ
iajs-2816	207	15	𝜆1	𝜆1	VERB
iajs-2816	207	16	∫	∫	PROPN
iajs-2816	207	17	∑	∑	PROPN
iajs-2816	207	18	(	(	PUNCT
iajs-2816	207	19	𝑧1𝑖𝑓𝑖𝑢𝑖	𝑧1𝑖𝑓𝑖𝑢𝑖	VERB
iajs-2816	207	20	+	+	CCONJ
iajs-2816	207	21	𝑔1𝑖𝑢𝑖	𝑔1𝑖𝑢𝑖	NOUN
iajs-2816	207	22	)	)	PUNCT
iajs-2816	207	23	4	4	NUM
iajs-2816	207	24	𝑖=1	𝑖=1	NUM
iajs-2816	207	25	𝛿𝑢𝑖	𝛿𝑢𝑖	VERB
iajs-2816	207	26	𝑄	𝑄	PRON
iajs-2816	207	27	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	ADV
iajs-2816	208	1	+	+	CCONJ
iajs-2816	208	2	𝜆2	𝜆2	NOUN
iajs-2816	208	3	∫	∫	NOUN
iajs-2816	208	4	∑	∑	PROPN
iajs-2816	208	5	(	(	PUNCT
iajs-2816	208	6	𝑧2𝑖𝑓𝑖𝑢𝑖	𝑧2𝑖𝑓𝑖𝑢𝑖	PROPN
iajs-2816	208	7	+	+	CCONJ
iajs-2816	208	8	𝑔2𝑖𝑢𝑖	𝑔2𝑖𝑢𝑖	ADJ
iajs-2816	208	9	)	)	PUNCT
iajs-2816	208	10	4	4	NUM
iajs-2816	208	11	𝑖=1	𝑖=1	NUM
iajs-2816	208	12	𝛿𝑢𝑖	𝛿𝑢𝑖	VERB
iajs-2816	208	13	𝑄	𝑄	PRON
iajs-2816	208	14	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	ADV
iajs-2816	208	15	,	,	PUNCT
iajs-2816	208	16	=	=	SYM
iajs-2816	208	17	∫	∫	PROPN
iajs-2816	208	18	𝐻	𝐻	PROPN
iajs-2816	208	19	�	�	PROPN
iajs-2816	208	20	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	208	21	�	�	PROPN
iajs-2816	208	22	(𝑥	(𝑥	PROPN
iajs-2816	208	23	,	,	PUNCT
iajs-2816	208	24	𝑡	𝑡	PROPN
iajs-2816	208	25	,	,	PUNCT
iajs-2816	208	26	�	�	PROPN
iajs-2816	208	27	⃗	⃗	NOUN
iajs-2816	208	28	�	�	PROPN
iajs-2816	208	29	,	,	PUNCT
iajs-2816	208	30	𝑧	𝑧	PROPN
iajs-2816	208	31	,	,	PUNCT
iajs-2816	208	32	�	�	PROPN
iajs-2816	208	33	⃗⃗	⃗⃗	PROPN
iajs-2816	208	34	�	�	PROPN
iajs-2816	208	35	)𝛿𝑢⃗⃗⃗⃗⃗	)𝛿𝑢⃗⃗⃗⃗⃗	PUNCT
iajs-2816	208	36	𝑄	𝑄	PRON
iajs-2816	208	37	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	208	38	≥	≥	NOUN
iajs-2816	208	39	0	0	NUM
iajs-2816	208	40	,	,	PUNCT
iajs-2816	208	41	now	now	ADV
iajs-2816	208	42	,	,	PUNCT
iajs-2816	208	43	to	to	PART
iajs-2816	208	44	demonstrate	demonstrate	VERB
iajs-2816	208	45	�	�	PROPN
iajs-2816	208	46	⃗⃗	⃗⃗	PROPN
iajs-2816	208	47	�	�	PROPN
iajs-2816	208	48	⟼	⟼	PROPN
iajs-2816	208	49	�	�	PROPN
iajs-2816	208	50	⃗	⃗	NOUN
iajs-2816	208	51	�	�	PROPN
iajs-2816	208	52	�	�	PROPN
iajs-2816	208	53	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	208	54	�	�	PROPN
iajs-2816	208	55	is	be	AUX
iajs-2816	208	56	convex	convex	ADJ
iajs-2816	208	57	–	–	PUNCT
iajs-2816	208	58	linear	linear	PROPN
iajs-2816	208	59	(	(	PUNCT
iajs-2816	208	60	col	col	NOUN
iajs-2816	208	61	)	)	PUNCT
iajs-2816	208	62	,	,	PUNCT
iajs-2816	208	63	since	since	SCONJ
iajs-2816	208	64	∀𝑖	∀𝑖	PROPN
iajs-2816	208	65	=	=	SYM
iajs-2816	208	66	1,2,3,4	1,2,3,4	NUM
iajs-2816	208	67	,	,	PUNCT
iajs-2816	208	68	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	208	69	is	be	AUX
iajs-2816	208	70	affine	affine	NOUN
iajs-2816	208	71	from	from	ADP
iajs-2816	208	72	the	the	DET
iajs-2816	208	73	hypotheses	hypothesis	NOUN
iajs-2816	208	74	on	on	ADP
iajs-2816	208	75	𝑓𝑖	𝑓𝑖	PROPN
iajs-2816	208	76	,	,	PUNCT
iajs-2816	208	77	∀𝑖	∀𝑖	PROPN
iajs-2816	208	78	=	=	NOUN
iajs-2816	208	79	1,2,3,4	1,2,3,4	NUM
iajs-2816	208	80	:	:	PUNCT
iajs-2816	208	81	𝑓𝑖(𝑥	𝑓𝑖(𝑥	NUM
iajs-2816	208	82	,	,	PUNCT
iajs-2816	208	83	𝑡	𝑡	PROPN
iajs-2816	208	84	,	,	PUNCT
iajs-2816	208	85	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	208	86	,	,	PUNCT
iajs-2816	208	87	𝑢𝑖	𝑢𝑖	PROPN
iajs-2816	208	88	)	)	PUNCT
iajs-2816	209	1	=	=	SYM
iajs-2816	209	2	𝑓𝑖1(𝑥	𝑓𝑖1(𝑥	NOUN
iajs-2816	209	3	,	,	PUNCT
iajs-2816	209	4	𝑡)𝑦𝑖	𝑡)𝑦𝑖	PROPN
iajs-2816	209	5	+	+	SYM
iajs-2816	209	6	𝑓𝑖2(𝑥	𝑓𝑖2(𝑥	PROPN
iajs-2816	209	7	,	,	PUNCT
iajs-2816	209	8	𝑡)𝑢𝑖	𝑡)𝑢𝑖	PROPN
iajs-2816	209	9	+	+	CCONJ
iajs-2816	209	10	𝑓𝑖3(𝑥	𝑓𝑖3(𝑥	PROPN
iajs-2816	209	11	,	,	PUNCT
iajs-2816	209	12	𝑡	𝑡	NOUN
iajs-2816	209	13	)	)	PUNCT
iajs-2816	209	14	,	,	PUNCT
iajs-2816	209	15	∀𝑖	∀𝑖	PROPN
iajs-2816	209	16	=	=	NOUN
iajs-2816	209	17	1,2,3,4	1,2,3,4	NUM
iajs-2816	209	18	.	.	PUNCT
iajs-2816	210	1	let	let	VERB
iajs-2816	210	2	�	�	PROPN
iajs-2816	210	3	⃗⃗	⃗⃗	PROPN
iajs-2816	210	4	�	�	PROPN
iajs-2816	210	5	=	=	SYM
iajs-2816	210	6	(	(	PUNCT
iajs-2816	210	7	𝑢1	𝑢1	PROPN
iajs-2816	210	8	,	,	PUNCT
iajs-2816	210	9	𝑢2	𝑢2	PROPN
iajs-2816	210	10	,	,	PUNCT
iajs-2816	210	11	𝑢3	𝑢3	PROPN
iajs-2816	210	12	,	,	PUNCT
iajs-2816	210	13	𝑢4	𝑢4	PROPN
iajs-2816	210	14	)	)	PUNCT
iajs-2816	210	15	&	&	CCONJ
iajs-2816	210	16	�	�	PROPN
iajs-2816	210	17	⃗⃗̅	⃗⃗̅	NOUN
iajs-2816	210	18	�	�	PROPN
iajs-2816	210	19	=	=	SYM
iajs-2816	210	20	(	(	PUNCT
iajs-2816	210	21	�	�	NOUN
iajs-2816	210	22	̅	̅	NOUN
iajs-2816	210	23	�	�	NOUN
iajs-2816	210	24	1	1	NUM
iajs-2816	210	25	,	,	PUNCT
iajs-2816	210	26	�	�	NOUN
iajs-2816	210	27	̅	̅	NOUN
iajs-2816	210	28	�	�	NOUN
iajs-2816	210	29	2	2	NUM
iajs-2816	210	30	,	,	PUNCT
iajs-2816	210	31	�	�	NOUN
iajs-2816	210	32	̅	̅	NOUN
iajs-2816	210	33	�	�	NOUN
iajs-2816	210	34	3	3	NUM
iajs-2816	210	35	,	,	PUNCT
iajs-2816	210	36	�	�	NOUN
iajs-2816	210	37	̅	̅	NOUN
iajs-2816	210	38	�	�	NOUN
iajs-2816	210	39	4	4	NUM
iajs-2816	210	40	)	)	PUNCT
iajs-2816	210	41	be	be	VERB
iajs-2816	210	42	two	two	NUM
iajs-2816	210	43	given	give	VERB
iajs-2816	210	44	qcccvs	qcccvs	NOUN
iajs-2816	210	45	and	and	CCONJ
iajs-2816	210	46	from	from	ADP
iajs-2816	210	47	the	the	DET
iajs-2816	210	48	.	.	PROPN
iajs-2816	210	49	2.1	2.1	NUM
iajs-2816	210	50	,	,	PUNCT
iajs-2816	210	51	�	�	NOUN
iajs-2816	210	52	⃗	⃗	NOUN
iajs-2816	210	53	�	�	NOUN
iajs-2816	210	54	=	=	SYM
iajs-2816	210	55	(	(	PUNCT
iajs-2816	210	56	𝑦𝑢1	𝑦𝑢1	PROPN
iajs-2816	210	57	,	,	PUNCT
iajs-2816	210	58	𝑦𝑢2	𝑦𝑢2	NOUN
iajs-2816	210	59	,	,	PUNCT
iajs-2816	210	60	𝑦𝑢3	𝑦𝑢3	PROPN
iajs-2816	210	61	,	,	PUNCT
iajs-2816	210	62	𝑦𝑢4	𝑦𝑢4	NOUN
iajs-2816	210	63	)	)	PUNCT
iajs-2816	211	1	=	=	SYM
iajs-2816	212	1	(	(	PUNCT
iajs-2816	212	2	𝑦1	𝑦1	PROPN
iajs-2816	212	3	,	,	PUNCT
iajs-2816	212	4	𝑦2	𝑦2	PROPN
iajs-2816	212	5	,	,	PUNCT
iajs-2816	212	6	𝑦3	𝑦3	PROPN
iajs-2816	212	7	,	,	PUNCT
iajs-2816	212	8	𝑦4	𝑦4	PROPN
iajs-2816	212	9	)	)	PUNCT
iajs-2816	212	10	&	&	CCONJ
iajs-2816	212	11	�	�	PROPN
iajs-2816	212	12	⃗̅	⃗̅	PROPN
iajs-2816	212	13	�	�	PROPN
iajs-2816	212	14	=	=	SYM
iajs-2816	212	15	(	(	PUNCT
iajs-2816	212	16	�	�	NOUN
iajs-2816	212	17	̅	̅	NOUN
iajs-2816	212	18	�	�	NOUN
iajs-2816	212	19	𝑢1	𝑢1	NOUN
iajs-2816	212	20	,	,	PUNCT
iajs-2816	212	21	�	�	NOUN
iajs-2816	212	22	̅	̅	NOUN
iajs-2816	212	23	�	�	NOUN
iajs-2816	212	24	𝑢2	𝑢2	PROPN
iajs-2816	212	25	,	,	PUNCT
iajs-2816	212	26	�	�	PROPN
iajs-2816	212	27	̅	̅	NOUN
iajs-2816	212	28	�	�	NOUN
iajs-2816	212	29	𝑢3	𝑢3	NOUN
iajs-2816	212	30	,	,	PUNCT
iajs-2816	212	31	�	�	NOUN
iajs-2816	212	32	̅	̅	NOUN
iajs-2816	212	33	�	�	NOUN
iajs-2816	212	34	𝑢4	𝑢4	NOUN
iajs-2816	212	35	)	)	PUNCT
iajs-2816	212	36	=	=	SYM
iajs-2816	212	37	(	(	PUNCT
iajs-2816	212	38	�	�	NOUN
iajs-2816	212	39	̅	̅	NOUN
iajs-2816	212	40	�	�	NOUN
iajs-2816	212	41	1	1	NUM
iajs-2816	212	42	,	,	PUNCT
iajs-2816	212	43	�	�	NOUN
iajs-2816	212	44	̅	̅	NOUN
iajs-2816	212	45	�	�	NOUN
iajs-2816	212	46	2	2	NUM
iajs-2816	212	47	,	,	PUNCT
iajs-2816	212	48	�	�	NOUN
iajs-2816	212	49	̅	̅	NOUN
iajs-2816	212	50	�	�	NOUN
iajs-2816	212	51	3	3	NUM
iajs-2816	212	52	,	,	PUNCT
iajs-2816	212	53	�	�	NOUN
iajs-2816	212	54	̅	̅	NOUN
iajs-2816	212	55	�	�	NOUN
iajs-2816	212	56	4)are	4)are	PRON
iajs-2816	212	57	their	their	PRON
iajs-2816	212	58	corresponding	correspond	VERB
iajs-2816	212	59	qsvs	qsvs	ADJ
iajs-2816	212	60	,	,	PUNCT
iajs-2816	212	61	precisely	precisely	ADV
iajs-2816	212	62	from	from	ADP
iajs-2816	212	63	(	(	PUNCT
iajs-2816	212	64	1	1	NUM
iajs-2816	212	65	)	)	PUNCT
iajs-2816	212	66	,	,	PUNCT
iajs-2816	212	67	𝑦1𝑡	𝑦1𝑡	PROPN
iajs-2816	212	68	−	−	PROPN
iajs-2816	213	1	∆𝑦1	∆𝑦1	ADV
iajs-2816	213	2	+	+	CCONJ
iajs-2816	213	3	𝑦1	𝑦1	PROPN
iajs-2816	213	4	−	−	PROPN
iajs-2816	213	5	𝑦2	𝑦2	PROPN
iajs-2816	213	6	+	+	CCONJ
iajs-2816	213	7	𝑦3	𝑦3	PROPN
iajs-2816	213	8	+	+	CCONJ
iajs-2816	213	9	𝑦4	𝑦4	NOUN
iajs-2816	213	10	=	=	SYM
iajs-2816	213	11	𝑓11(𝑥	𝑓11(𝑥	NOUN
iajs-2816	213	12	,	,	PUNCT
iajs-2816	213	13	𝑡)𝑦1	𝑡)𝑦1	PROPN
iajs-2816	213	14	+	+	CCONJ
iajs-2816	213	15	𝑓12(𝑥	𝑓12(𝑥	NOUN
iajs-2816	213	16	,	,	PUNCT
iajs-2816	213	17	𝑡)𝑢1	𝑡)𝑢1	PROPN
iajs-2816	213	18	+	+	CCONJ
iajs-2816	213	19	𝑓13(𝑥	𝑓13(𝑥	NOUN
iajs-2816	213	20	,	,	PUNCT
iajs-2816	213	21	𝑡	𝑡	NOUN
iajs-2816	213	22	)	)	PUNCT
iajs-2816	213	23	,	,	PUNCT
iajs-2816	213	24	𝑦1(𝑥	𝑦1(𝑥	PROPN
iajs-2816	213	25	,	,	PUNCT
iajs-2816	213	26	0	0	NUM
iajs-2816	213	27	)	)	PUNCT
iajs-2816	214	1	=	=	SYM
iajs-2816	214	2	𝑦1	𝑦1	PROPN
iajs-2816	214	3	0(𝑥	0(𝑥	NUM
iajs-2816	214	4	)	)	PUNCT
iajs-2816	214	5	,	,	PUNCT
iajs-2816	214	6	�	�	PROPN
iajs-2816	214	7	̅	̅	NOUN
iajs-2816	214	8	�	�	NOUN
iajs-2816	214	9	1𝑡	1𝑡	NOUN
iajs-2816	214	10	−	−	NOUN
iajs-2816	214	11	∆	∆	PROPN
iajs-2816	214	12	�	�	PROPN
iajs-2816	214	13	̅	̅	NOUN
iajs-2816	214	14	�	�	NOUN
iajs-2816	214	15	1	1	NUM
iajs-2816	214	16	+	+	NUM
iajs-2816	214	17	�	�	NOUN
iajs-2816	214	18	̅	̅	NOUN
iajs-2816	214	19	�	�	NOUN
iajs-2816	214	20	1	1	NUM
iajs-2816	214	21	−	−	NOUN
iajs-2816	214	22	�	�	NOUN
iajs-2816	214	23	̅	̅	NOUN
iajs-2816	214	24	�	�	NOUN
iajs-2816	214	25	2	2	NUM
iajs-2816	214	26	+	+	NUM
iajs-2816	214	27	�	�	NOUN
iajs-2816	214	28	̅	̅	NOUN
iajs-2816	214	29	�	�	NOUN
iajs-2816	214	30	3	3	NUM
iajs-2816	214	31	+	+	NUM
iajs-2816	214	32	�	�	NOUN
iajs-2816	214	33	̅	̅	NOUN
iajs-2816	214	34	�	�	NOUN
iajs-2816	214	35	4	4	NUM
iajs-2816	214	36	=	=	SYM
iajs-2816	214	37	𝑓11(𝑥	𝑓11(𝑥	NOUN
iajs-2816	214	38	,	,	PUNCT
iajs-2816	214	39	𝑡)	𝑡)	PROPN
iajs-2816	214	40	�	�	NOUN
iajs-2816	214	41	̅	̅	NOUN
iajs-2816	214	42	�	�	NOUN
iajs-2816	214	43	1	1	NUM
iajs-2816	214	44	+	+	NUM
iajs-2816	214	45	𝑓12(𝑥	𝑓12(𝑥	NOUN
iajs-2816	214	46	,	,	PUNCT
iajs-2816	214	47	𝑡)	𝑡)	PROPN
iajs-2816	214	48	�	�	NOUN
iajs-2816	214	49	̅	̅	NOUN
iajs-2816	214	50	�	�	NOUN
iajs-2816	214	51	1	1	NUM
iajs-2816	214	52	+	+	CCONJ
iajs-2816	214	53	𝑓13(𝑥	𝑓13(𝑥	NOUN
iajs-2816	214	54	,	,	PUNCT
iajs-2816	214	55	𝑡	𝑡	NOUN
iajs-2816	214	56	)	)	PUNCT
iajs-2816	214	57	,	,	PUNCT
iajs-2816	214	58	�	�	PROPN
iajs-2816	214	59	̅	̅	NOUN
iajs-2816	214	60	�	�	NOUN
iajs-2816	214	61	1(𝑥	1(𝑥	NUM
iajs-2816	214	62	,	,	PUNCT
iajs-2816	214	63	0	0	NUM
iajs-2816	214	64	)	)	PUNCT
iajs-2816	215	1	=	=	SYM
iajs-2816	215	2	𝑦1	𝑦1	PROPN
iajs-2816	215	3	0(𝑥	0(𝑥	NUM
iajs-2816	215	4	)	)	PUNCT
iajs-2816	215	5	,	,	PUNCT
iajs-2816	215	6	by	by	ADP
iajs-2816	215	7	mbs	mb	NOUN
iajs-2816	215	8	the	the	DET
iajs-2816	215	9	1𝑠𝑡	1𝑠𝑡	NOUN
iajs-2816	215	10	above	above	ADP
iajs-2816	215	11	equation	equation	NOUN
iajs-2816	215	12	and	and	CCONJ
iajs-2816	215	13	its	its	PRON
iajs-2816	215	14	ic	ic	X
iajs-2816	215	15	by	by	ADP
iajs-2816	215	16	𝛼	𝛼	PROPN
iajs-2816	215	17	∈	∈	PROPN
iajs-2816	216	1	[	[	X
iajs-2816	216	2	0,1	0,1	NUM
iajs-2816	216	3	]	]	PUNCT
iajs-2816	216	4	,	,	PUNCT
iajs-2816	216	5	and	and	CCONJ
iajs-2816	216	6	the	the	DET
iajs-2816	216	7	2𝑛𝑑	2𝑛𝑑	ADJ
iajs-2816	216	8	equation	equation	NOUN
iajs-2816	216	9	and	and	CCONJ
iajs-2816	216	10	its	its	PRON
iajs-2816	216	11	ic	ic	INTJ
iajs-2816	216	12	by	by	ADP
iajs-2816	216	13	(	(	PUNCT
iajs-2816	216	14	1	1	NUM
iajs-2816	216	15	−	−	NOUN
iajs-2816	216	16	𝛼	𝛼	NOUN
iajs-2816	216	17	)	)	PUNCT
iajs-2816	216	18	,	,	PUNCT
iajs-2816	216	19	and	and	CCONJ
iajs-2816	216	20	adding	add	VERB
iajs-2816	216	21	the	the	DET
iajs-2816	216	22	attained	attain	VERB
iajs-2816	216	23	equations	equation	NOUN
iajs-2816	216	24	and	and	CCONJ
iajs-2816	216	25	their	their	PRON
iajs-2816	216	26	attained	attain	VERB
iajs-2816	216	27	ics	ics	NOUN
iajs-2816	216	28	,	,	PUNCT
iajs-2816	216	29	one	one	PRON
iajs-2816	216	30	gets	get	VERB
iajs-2816	216	31	that	that	PRON
iajs-2816	216	32	:	:	PUNCT
iajs-2816	216	33	(	(	PUNCT
iajs-2816	216	34	𝛼𝑦1	𝛼𝑦1	PROPN
iajs-2816	216	35	+	+	CCONJ
iajs-2816	216	36	(	(	PUNCT
iajs-2816	216	37	1	1	NUM
iajs-2816	216	38	−	−	PROPN
iajs-2816	216	39	𝛼)	𝛼)	PROPN
iajs-2816	216	40	�	�	SYM
iajs-2816	216	41	̅	̅	NOUN
iajs-2816	216	42	�	�	NOUN
iajs-2816	216	43	1	1	NUM
iajs-2816	216	44	)	)	PUNCT
iajs-2816	216	45	𝑡	𝑡	NOUN
iajs-2816	216	46	−	−	NOUN
iajs-2816	216	47	∆(𝛼𝑦1	∆(𝛼𝑦1	X
iajs-2816	216	48	+	+	X
iajs-2816	216	49	(	(	PUNCT
iajs-2816	216	50	1	1	NUM
iajs-2816	216	51	−	−	PROPN
iajs-2816	216	52	𝛼)	𝛼)	PROPN
iajs-2816	216	53	�	�	SYM
iajs-2816	216	54	̅	̅	NOUN
iajs-2816	216	55	�	�	NOUN
iajs-2816	216	56	1	1	NUM
iajs-2816	216	57	)	)	PUNCT
iajs-2816	217	1	+	+	CCONJ
iajs-2816	217	2	(	(	PUNCT
iajs-2816	217	3	𝛼𝑦1	𝛼𝑦1	PROPN
iajs-2816	217	4	+	+	CCONJ
iajs-2816	217	5	(	(	PUNCT
iajs-2816	217	6	1	1	NUM
iajs-2816	217	7	−	−	PROPN
iajs-2816	217	8	𝛼)	𝛼)	PROPN
iajs-2816	217	9	�	�	SYM
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iajs-2816	217	11	�	�	NOUN
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iajs-2816	217	14	−	−	PROPN
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iajs-2816	219	4	𝛼)	𝛼)	PROPN
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iajs-2816	219	6	̅	̅	NOUN
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iajs-2816	219	8	2	2	NUM
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iajs-2816	219	10	+	+	CCONJ
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iajs-2816	219	12	𝛼𝑦3	𝛼𝑦3	NOUN
iajs-2816	219	13	+	+	X
iajs-2816	219	14	(	(	PUNCT
iajs-2816	219	15	1	1	NUM
iajs-2816	219	16	−	−	PROPN
iajs-2816	219	17	𝛼)	𝛼)	PROPN
iajs-2816	219	18	�	�	SYM
iajs-2816	219	19	̅	̅	NOUN
iajs-2816	219	20	�	�	NOUN
iajs-2816	219	21	3	3	NUM
iajs-2816	219	22	)	)	PUNCT
iajs-2816	219	23	+	+	CCONJ
iajs-2816	219	24	(	(	PUNCT
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iajs-2816	219	26	+	+	CCONJ
iajs-2816	219	27	(	(	PUNCT
iajs-2816	219	28	1	1	NUM
iajs-2816	219	29	−	−	PROPN
iajs-2816	219	30	𝛼)	𝛼)	PROPN
iajs-2816	219	31	�	�	SYM
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iajs-2816	219	33	�	�	NOUN
iajs-2816	219	34	4	4	NUM
iajs-2816	219	35	)	)	PUNCT
iajs-2816	219	36	=	=	NOUN
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iajs-2816	219	39	𝑡)(𝛼𝑦1	𝑡)(𝛼𝑦1	X
iajs-2816	219	40	+	+	CCONJ
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iajs-2816	219	42	1	1	NUM
iajs-2816	219	43	−	−	PROPN
iajs-2816	219	44	𝛼)	𝛼)	PROPN
iajs-2816	219	45	�	�	SYM
iajs-2816	219	46	̅	̅	NOUN
iajs-2816	219	47	�	�	NOUN
iajs-2816	219	48	1	1	NUM
iajs-2816	219	49	)	)	PUNCT
iajs-2816	220	1	+	+	CCONJ
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iajs-2816	220	3	,	,	PUNCT
iajs-2816	220	4	𝑡)(𝛼𝑢1	𝑡)(𝛼𝑢1	PROPN
iajs-2816	220	5	+	+	CCONJ
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iajs-2816	220	7	1	1	NUM
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iajs-2816	220	9	𝛼)	𝛼)	PROPN
iajs-2816	220	10	�	�	SYM
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iajs-2816	220	13	1	1	NUM
iajs-2816	220	14	)	)	PUNCT
iajs-2816	220	15	+	+	CCONJ
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iajs-2816	220	17	,	,	PUNCT
iajs-2816	220	18	𝑡	𝑡	X
iajs-2816	220	19	)	)	PUNCT
iajs-2816	220	20	(	(	PUNCT
iajs-2816	220	21	40.a	40.a	NOUN
iajs-2816	220	22	)	)	PUNCT
iajs-2816	220	23	𝛼𝑦1(𝑥	𝛼𝑦1(𝑥	NUM
iajs-2816	220	24	,	,	PUNCT
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iajs-2816	220	27	+	+	CCONJ
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iajs-2816	220	30	−	−	PROPN
iajs-2816	220	31	𝛼)	𝛼)	PROPN
iajs-2816	220	32	�	�	SYM
iajs-2816	220	33	̅	̅	NOUN
iajs-2816	220	34	�	�	NOUN
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iajs-2816	221	19	+	+	CCONJ
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iajs-2816	221	21	1	1	NUM
iajs-2816	221	22	−	−	PROPN
iajs-2816	221	23	𝛼)	𝛼)	PROPN
iajs-2816	221	24	�	�	SYM
iajs-2816	221	25	̅	̅	NOUN
iajs-2816	221	26	�	�	NOUN
iajs-2816	221	27	2	2	NUM
iajs-2816	221	28	)	)	PUNCT
iajs-2816	221	29	𝑡	𝑡	NOUN
iajs-2816	221	30	−	−	PROPN
iajs-2816	221	31	∆(𝛼𝑦2	∆(𝛼𝑦2	X
iajs-2816	222	1	+	+	CCONJ
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iajs-2816	222	3	1	1	NUM
iajs-2816	222	4	−	−	PROPN
iajs-2816	222	5	𝛼)	𝛼)	PROPN
iajs-2816	222	6	�	�	SYM
iajs-2816	222	7	̅	̅	NOUN
iajs-2816	222	8	�	�	NOUN
iajs-2816	222	9	2	2	NUM
iajs-2816	222	10	)	)	PUNCT
iajs-2816	222	11	+	+	CCONJ
iajs-2816	222	12	(	(	PUNCT
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iajs-2816	222	14	+	+	CCONJ
iajs-2816	222	15	(	(	PUNCT
iajs-2816	222	16	1	1	NUM
iajs-2816	222	17	−	−	PROPN
iajs-2816	222	18	𝛼)	𝛼)	PROPN
iajs-2816	222	19	�	�	SYM
iajs-2816	222	20	̅	̅	NOUN
iajs-2816	222	21	�	�	NOUN
iajs-2816	222	22	2	2	NUM
iajs-2816	222	23	)	)	PUNCT
iajs-2816	222	24	+	+	CCONJ
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iajs-2816	222	26	𝛼𝑦1	𝛼𝑦1	PROPN
iajs-2816	222	27	+	+	CCONJ
iajs-2816	222	28	(	(	PUNCT
iajs-2816	222	29	1	1	NUM
iajs-2816	222	30	−	−	PROPN
iajs-2816	222	31	𝛼)	𝛼)	PROPN
iajs-2816	222	32	�	�	SYM
iajs-2816	222	33	̅	̅	NOUN
iajs-2816	222	34	�	�	NOUN
iajs-2816	222	35	1	1	NUM
iajs-2816	222	36	)	)	PUNCT
iajs-2816	222	37	−	−	PROPN
iajs-2816	223	1	(	(	PUNCT
iajs-2816	223	2	𝛼𝑦3	𝛼𝑦3	NOUN
iajs-2816	223	3	+	+	X
iajs-2816	223	4	(	(	PUNCT
iajs-2816	223	5	1	1	NUM
iajs-2816	223	6	−	−	PROPN
iajs-2816	223	7	𝛼)	𝛼)	PROPN
iajs-2816	223	8	�	�	SYM
iajs-2816	223	9	̅	̅	NOUN
iajs-2816	223	10	�	�	NOUN
iajs-2816	223	11	3	3	NUM
iajs-2816	223	12	)	)	PUNCT
iajs-2816	223	13	−	−	PROPN
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iajs-2816	223	15	𝛼𝑦4	𝛼𝑦4	PROPN
iajs-2816	223	16	+	+	CCONJ
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iajs-2816	223	18	1	1	NUM
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iajs-2816	223	20	𝛼)	𝛼)	PROPN
iajs-2816	223	21	�	�	SYM
iajs-2816	223	22	̅	̅	NOUN
iajs-2816	223	23	�	�	NOUN
iajs-2816	223	24	4	4	NUM
iajs-2816	223	25	)	)	PUNCT
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iajs-2816	223	29	𝑡)(𝛼𝑦2	𝑡)(𝛼𝑦2	PROPN
iajs-2816	224	1	+	+	CCONJ
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iajs-2816	224	3	1	1	NUM
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iajs-2816	224	5	𝛼)	𝛼)	PROPN
iajs-2816	224	6	�	�	SYM
iajs-2816	224	7	̅	̅	NOUN
iajs-2816	224	8	�	�	NOUN
iajs-2816	224	9	2	2	NUM
iajs-2816	224	10	)	)	PUNCT
iajs-2816	224	11	+	+	NUM
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iajs-2816	224	13	,	,	PUNCT
iajs-2816	224	14	𝑡)(𝛼𝑢2	𝑡)(𝛼𝑢2	NUM
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iajs-2816	224	17	1	1	NUM
iajs-2816	224	18	−	−	PROPN
iajs-2816	224	19	𝛼)	𝛼)	PROPN
iajs-2816	224	20	�	�	SYM
iajs-2816	224	21	̅	̅	NOUN
iajs-2816	224	22	�	�	NOUN
iajs-2816	224	23	2	2	NUM
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iajs-2816	224	25	+	+	CCONJ
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iajs-2816	224	27	,	,	PUNCT
iajs-2816	224	28	𝑡	𝑡	X
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iajs-2816	224	30	(	(	PUNCT
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iajs-2816	224	37	+	+	CCONJ
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iajs-2816	224	39	1	1	NUM
iajs-2816	224	40	−	−	PROPN
iajs-2816	224	41	𝛼)	𝛼)	PROPN
iajs-2816	224	42	�	�	SYM
iajs-2816	224	43	̅	̅	NOUN
iajs-2816	224	44	�	�	NOUN
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iajs-2816	224	53	(	(	PUNCT
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iajs-2816	224	56	(	(	PUNCT
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iajs-2816	224	62	𝛼)	𝛼)	PROPN
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iajs-2816	224	64	̅	̅	NOUN
iajs-2816	224	65	�	�	NOUN
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iajs-2816	224	67	)	)	PUNCT
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iajs-2816	225	5	𝛼)	𝛼)	PROPN
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iajs-2816	225	8	�	�	NOUN
iajs-2816	225	9	3	3	NUM
iajs-2816	225	10	)	)	PUNCT
iajs-2816	225	11	+	+	CCONJ
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iajs-2816	225	13	𝛼𝑦3	𝛼𝑦3	NOUN
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iajs-2816	225	18	𝛼)	𝛼)	PROPN
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iajs-2816	225	20	̅	̅	NOUN
iajs-2816	225	21	�	�	NOUN
iajs-2816	225	22	3	3	NUM
iajs-2816	225	23	)	)	PUNCT
iajs-2816	225	24	−	−	PROPN
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iajs-2816	225	26	𝛼𝑦1	𝛼𝑦1	PROPN
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iajs-2816	225	29	1	1	NUM
iajs-2816	225	30	−	−	PROPN
iajs-2816	225	31	𝛼)	𝛼)	PROPN
iajs-2816	225	32	�	�	SYM
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iajs-2816	225	34	�	�	NOUN
iajs-2816	225	35	1	1	NUM
iajs-2816	225	36	)	)	PUNCT
iajs-2816	225	37	+	+	CCONJ
iajs-2816	225	38	(	(	PUNCT
iajs-2816	225	39	𝛼𝑦2	𝛼𝑦2	PROPN
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iajs-2816	225	42	1	1	NUM
iajs-2816	225	43	−	−	PROPN
iajs-2816	225	44	𝛼)	𝛼)	PROPN
iajs-2816	225	45	�	�	SYM
iajs-2816	225	46	̅	̅	NOUN
iajs-2816	225	47	�	�	NOUN
iajs-2816	225	48	2	2	NUM
iajs-2816	225	49	)	)	PUNCT
iajs-2816	225	50	+	+	CCONJ
iajs-2816	225	51	(	(	PUNCT
iajs-2816	225	52	𝛼𝑦4	𝛼𝑦4	NOUN
iajs-2816	225	53	+	+	CCONJ
iajs-2816	225	54	(	(	PUNCT
iajs-2816	225	55	1	1	NUM
iajs-2816	225	56	−	−	PROPN
iajs-2816	225	57	𝛼)	𝛼)	PROPN
iajs-2816	225	58	�	�	SYM
iajs-2816	225	59	̅	̅	NOUN
iajs-2816	225	60	�	�	NOUN
iajs-2816	225	61	4	4	NUM
iajs-2816	225	62	)	)	PUNCT
iajs-2816	225	63	=	=	SYM
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iajs-2816	225	65	,	,	PUNCT
iajs-2816	225	66	𝑡)(𝛼𝑦3	𝑡)(𝛼𝑦3	VERB
iajs-2816	225	67	+	+	X
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iajs-2816	225	69	1	1	NUM
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iajs-2816	225	71	𝛼)	𝛼)	PROPN
iajs-2816	225	72	�	�	SYM
iajs-2816	225	73	̅	̅	NOUN
iajs-2816	225	74	�	�	NOUN
iajs-2816	225	75	3	3	NUM
iajs-2816	225	76	)	)	PUNCT
iajs-2816	225	77	+	+	NUM
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iajs-2816	226	2	,	,	PUNCT
iajs-2816	226	3	𝑡)(𝛼𝑢3	𝑡)(𝛼𝑢3	PROPN
iajs-2816	226	4	+	+	CCONJ
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iajs-2816	226	6	1	1	NUM
iajs-2816	226	7	−	−	PROPN
iajs-2816	226	8	𝛼)	𝛼)	PROPN
iajs-2816	226	9	�	�	SYM
iajs-2816	226	10	̅	̅	NOUN
iajs-2816	226	11	�	�	NOUN
iajs-2816	226	12	3	3	NUM
iajs-2816	226	13	)	)	PUNCT
iajs-2816	227	1	+	+	CCONJ
iajs-2816	227	2	𝑓33(𝑥	𝑓33(𝑥	ADJ
iajs-2816	227	3	,	,	PUNCT
iajs-2816	227	4	𝑡	𝑡	X
iajs-2816	227	5	)	)	PUNCT
iajs-2816	227	6	(	(	PUNCT
iajs-2816	227	7	42.a	42.a	NUM
iajs-2816	227	8	)	)	PUNCT
iajs-2816	227	9	𝛼𝑦3(𝑥	𝛼𝑦3(𝑥	PROPN
iajs-2816	227	10	,	,	PUNCT
iajs-2816	227	11	0	0	NUM
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iajs-2816	228	4	−	−	PROPN
iajs-2816	228	5	𝛼)	𝛼)	PROPN
iajs-2816	228	6	�	�	SYM
iajs-2816	228	7	̅	̅	NOUN
iajs-2816	228	8	�	�	NOUN
iajs-2816	228	9	3(𝑥	3(𝑥	NUM
iajs-2816	228	10	,	,	PUNCT
iajs-2816	228	11	0	0	NUM
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iajs-2816	228	16	)	)	PUNCT
iajs-2816	228	17	(	(	PUNCT
iajs-2816	228	18	42.b	42.b	NUM
iajs-2816	228	19	)	)	PUNCT
iajs-2816	228	20	(	(	PUNCT
iajs-2816	228	21	𝛼𝑦4	𝛼𝑦4	NOUN
iajs-2816	228	22	+	+	CCONJ
iajs-2816	228	23	(	(	PUNCT
iajs-2816	228	24	1	1	NUM
iajs-2816	228	25	−	−	PROPN
iajs-2816	228	26	𝛼)	𝛼)	PROPN
iajs-2816	228	27	�	�	SYM
iajs-2816	228	28	̅	̅	NOUN
iajs-2816	228	29	�	�	NOUN
iajs-2816	228	30	4	4	NUM
iajs-2816	228	31	)	)	PUNCT
iajs-2816	228	32	𝑡	𝑡	NOUN
iajs-2816	228	33	−	−	NOUN
iajs-2816	229	1	∆(𝛼𝑦4	∆(𝛼𝑦4	X
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iajs-2816	229	3	(	(	PUNCT
iajs-2816	229	4	1	1	NUM
iajs-2816	229	5	−	−	PROPN
iajs-2816	229	6	𝛼)	𝛼)	PROPN
iajs-2816	229	7	�	�	SYM
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iajs-2816	229	10	4	4	NUM
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iajs-2816	229	15	+	+	CCONJ
iajs-2816	229	16	(	(	PUNCT
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iajs-2816	229	18	−	−	PROPN
iajs-2816	229	19	𝛼)	𝛼)	PROPN
iajs-2816	229	20	�	�	SYM
iajs-2816	229	21	̅	̅	NOUN
iajs-2816	229	22	�	�	NOUN
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iajs-2816	229	26	(	(	PUNCT
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iajs-2816	229	28	+	+	CCONJ
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iajs-2816	229	30	1	1	NUM
iajs-2816	229	31	−	−	PROPN
iajs-2816	229	32	𝛼)	𝛼)	PROPN
iajs-2816	229	33	�	�	SYM
iajs-2816	229	34	̅	̅	NOUN
iajs-2816	229	35	�	�	NOUN
iajs-2816	229	36	1	1	NUM
iajs-2816	229	37	)	)	PUNCT
iajs-2816	229	38	+	+	CCONJ
iajs-2816	229	39	(	(	PUNCT
iajs-2816	229	40	𝛼𝑦2	𝛼𝑦2	PROPN
iajs-2816	229	41	+	+	CCONJ
iajs-2816	229	42	(	(	PUNCT
iajs-2816	229	43	1	1	NUM
iajs-2816	229	44	−	−	PROPN
iajs-2816	229	45	𝛼)	𝛼)	PROPN
iajs-2816	229	46	�	�	SYM
iajs-2816	229	47	̅	̅	NOUN
iajs-2816	229	48	�	�	NOUN
iajs-2816	229	49	2	2	NUM
iajs-2816	229	50	)	)	PUNCT
iajs-2816	229	51	−	−	PROPN
iajs-2816	230	1	(	(	PUNCT
iajs-2816	230	2	𝛼𝑦3	𝛼𝑦3	NOUN
iajs-2816	230	3	+	+	X
iajs-2816	230	4	(	(	PUNCT
iajs-2816	230	5	1	1	NUM
iajs-2816	230	6	−	−	PROPN
iajs-2816	230	7	𝛼)	𝛼)	PROPN
iajs-2816	230	8	�	�	SYM
iajs-2816	230	9	̅	̅	NOUN
iajs-2816	230	10	�	�	NOUN
iajs-2816	230	11	3	3	NUM
iajs-2816	230	12	)	)	PUNCT
iajs-2816	230	13	=	=	PUNCT
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iajs-2816	230	15	,	,	PUNCT
iajs-2816	230	16	𝑡)(𝛼𝑦4	𝑡)(𝛼𝑦4	PROPN
iajs-2816	230	17	+	+	CCONJ
iajs-2816	230	18	(	(	PUNCT
iajs-2816	230	19	1	1	NUM
iajs-2816	230	20	−	−	PROPN
iajs-2816	230	21	𝛼)	𝛼)	PROPN
iajs-2816	230	22	�	�	SYM
iajs-2816	230	23	̅	̅	NOUN
iajs-2816	230	24	�	�	NOUN
iajs-2816	230	25	4	4	NUM
iajs-2816	230	26	)	)	PUNCT
iajs-2816	230	27	+	+	CCONJ
iajs-2816	230	28	𝑓42(𝑥	𝑓42(𝑥	NOUN
iajs-2816	230	29	,	,	PUNCT
iajs-2816	230	30	𝑡)(𝛼𝑢4	𝑡)(𝛼𝑢4	AUX
iajs-2816	230	31	+	+	CCONJ
iajs-2816	230	32	(	(	PUNCT
iajs-2816	230	33	1	1	NUM
iajs-2816	230	34	−	−	PROPN
iajs-2816	230	35	𝛼)	𝛼)	PROPN
iajs-2816	230	36	�	�	SYM
iajs-2816	230	37	̅	̅	NOUN
iajs-2816	230	38	�	�	NOUN
iajs-2816	230	39	4	4	NUM
iajs-2816	230	40	)	)	PUNCT
iajs-2816	230	41	+	+	CCONJ
iajs-2816	230	42	𝑓43(𝑥	𝑓43(𝑥	ADJ
iajs-2816	230	43	,	,	PUNCT
iajs-2816	230	44	𝑡	𝑡	X
iajs-2816	230	45	)	)	PUNCT
iajs-2816	230	46	(	(	PUNCT
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iajs-2816	230	48	)	)	PUNCT
iajs-2816	230	49	ihjpas	ihjpa	NOUN
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iajs-2816	231	3	3)2022	3)2022	NOUN
iajs-2816	231	4	143	143	NUM
iajs-2816	231	5	𝛼𝑦4(𝑥	𝛼𝑦4(𝑥	PROPN
iajs-2816	231	6	,	,	PUNCT
iajs-2816	231	7	0	0	NUM
iajs-2816	231	8	)	)	PUNCT
iajs-2816	232	1	+	+	CCONJ
iajs-2816	232	2	(	(	PUNCT
iajs-2816	232	3	1	1	NUM
iajs-2816	232	4	−	−	PROPN
iajs-2816	232	5	𝛼)	𝛼)	PROPN
iajs-2816	232	6	�	�	SYM
iajs-2816	232	7	̅	̅	NOUN
iajs-2816	232	8	�	�	NOUN
iajs-2816	232	9	4(𝑥	4(𝑥	NUM
iajs-2816	232	10	,	,	PUNCT
iajs-2816	232	11	0	0	NUM
iajs-2816	232	12	)	)	PUNCT
iajs-2816	232	13	=	=	SYM
iajs-2816	232	14	𝑦4	𝑦4	NOUN
iajs-2816	232	15	0(𝑥	0(𝑥	NUM
iajs-2816	232	16	)	)	PUNCT
iajs-2816	232	17	(	(	PUNCT
iajs-2816	232	18	43.b	43.b	NUM
iajs-2816	232	19	)	)	PUNCT
iajs-2816	232	20	from	from	ADP
iajs-2816	232	21	equations	equation	NOUN
iajs-2816	232	22	(	(	PUNCT
iajs-2816	232	23	(	(	PUNCT
iajs-2816	232	24	40	40	NUM
iajs-2816	232	25	)	)	PUNCT
iajs-2816	232	26	−	−	PROPN
iajs-2816	232	27	(	(	PUNCT
iajs-2816	232	28	43	43	NUM
iajs-2816	232	29	)	)	PUNCT
iajs-2816	232	30	)	)	PUNCT
iajs-2816	232	31	,	,	PUNCT
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iajs-2816	232	33	qcccv	qcccv	PROPN
iajs-2816	232	34	�	�	PROPN
iajs-2816	232	35	⃗⃗̃	⃗⃗̃	NOUN
iajs-2816	232	36	�	�	PROPN
iajs-2816	232	37	=	=	SYM
iajs-2816	232	38	(	(	PUNCT
iajs-2816	232	39	�	�	PROPN
iajs-2816	232	40	̃	̃	NOUN
iajs-2816	232	41	�	�	NOUN
iajs-2816	232	42	1	1	NUM
iajs-2816	232	43	,	,	PUNCT
iajs-2816	232	44	�	�	PROPN
iajs-2816	232	45	̃	̃	NOUN
iajs-2816	232	46	�	�	NOUN
iajs-2816	232	47	2	2	NUM
iajs-2816	232	48	,	,	PUNCT
iajs-2816	232	49	�	�	PROPN
iajs-2816	232	50	̃	̃	PROPN
iajs-2816	232	51	�	�	NOUN
iajs-2816	232	52	3	3	NUM
iajs-2816	232	53	,	,	PUNCT
iajs-2816	232	54	�	�	PROPN
iajs-2816	232	55	̃	̃	NOUN
iajs-2816	232	56	�	�	NOUN
iajs-2816	232	57	4	4	NUM
iajs-2816	232	58	)	)	PUNCT
iajs-2816	232	59	,	,	PUNCT
iajs-2816	232	60	with	with	ADP
iajs-2816	232	61	�	�	PROPN
iajs-2816	232	62	⃗⃗̃	⃗⃗̃	NOUN
iajs-2816	232	63	�	�	PROPN
iajs-2816	232	64	=	=	SYM
iajs-2816	232	65	𝛼	𝛼	PROPN
iajs-2816	232	66	�	�	PROPN
iajs-2816	232	67	⃗⃗	⃗⃗	PROPN
iajs-2816	232	68	�	�	PROPN
iajs-2816	232	69	+	+	CCONJ
iajs-2816	232	70	(	(	PUNCT
iajs-2816	232	71	1	1	NUM
iajs-2816	232	72	−	−	PROPN
iajs-2816	232	73	𝛼)	𝛼)	PROPN
iajs-2816	232	74	�	�	PROPN
iajs-2816	232	75	⃗⃗̅	⃗⃗̅	NOUN
iajs-2816	232	76	�	�	PROPN
iajs-2816	232	77	has	have	VERB
iajs-2816	232	78	the	the	DET
iajs-2816	232	79	corresponding	corresponding	ADJ
iajs-2816	232	80	qsvs	qsvs	PROPN
iajs-2816	232	81	,	,	PUNCT
iajs-2816	232	82	�	�	PROPN
iajs-2816	232	83	⃗̃	⃗̃	NUM
iajs-2816	232	84	�	�	NOUN
iajs-2816	232	85	=	=	SYM
iajs-2816	232	86	(	(	PUNCT
iajs-2816	232	87	�	�	PROPN
iajs-2816	232	88	̃	̃	NOUN
iajs-2816	232	89	�	�	NOUN
iajs-2816	232	90	1	1	NUM
iajs-2816	232	91	,	,	PUNCT
iajs-2816	232	92	�	�	PROPN
iajs-2816	232	93	̃	̃	NOUN
iajs-2816	232	94	�	�	NOUN
iajs-2816	232	95	2	2	NUM
iajs-2816	232	96	,	,	PUNCT
iajs-2816	232	97	�	�	PROPN
iajs-2816	232	98	̃	̃	PROPN
iajs-2816	232	99	�	�	NOUN
iajs-2816	232	100	3	3	NUM
iajs-2816	232	101	,	,	PUNCT
iajs-2816	232	102	�	�	PROPN
iajs-2816	232	103	̃	̃	NOUN
iajs-2816	232	104	�	�	NOUN
iajs-2816	232	105	4	4	NUM
iajs-2816	232	106	)	)	PUNCT
iajs-2816	232	107	,	,	PUNCT
iajs-2816	232	108	�	�	PROPN
iajs-2816	232	109	⃗̃	⃗̃	NUM
iajs-2816	232	110	�	�	PROPN
iajs-2816	232	111	=	=	SYM
iajs-2816	232	112	𝛼	𝛼	PROPN
iajs-2816	232	113	�	�	PROPN
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iajs-2816	232	116	+	+	CCONJ
iajs-2816	232	117	(	(	PUNCT
iajs-2816	232	118	1	1	NUM
iajs-2816	232	119	−	−	PROPN
iajs-2816	232	120	𝛼)	𝛼)	PROPN
iajs-2816	232	121	�	�	PROPN
iajs-2816	232	122	⃗̅	⃗̅	PROPN
iajs-2816	232	123	�	�	PROPN
iajs-2816	232	124	,	,	PUNCT
iajs-2816	232	125	i.e.	i.e.	X
iajs-2816	232	126	:	:	PUNCT
iajs-2816	232	127	�	�	PROPN
iajs-2816	232	128	̃	̃	NOUN
iajs-2816	232	129	�	�	NOUN
iajs-2816	232	130	1𝑡	1𝑡	NOUN
iajs-2816	232	131	−	−	PROPN
iajs-2816	232	132	∆	∆	PROPN
iajs-2816	232	133	�	�	PROPN
iajs-2816	232	134	̃	̃	PROPN
iajs-2816	232	135	�	�	NOUN
iajs-2816	232	136	1	1	NUM
iajs-2816	232	137	+	+	NUM
iajs-2816	232	138	�	�	PROPN
iajs-2816	232	139	̃	̃	PROPN
iajs-2816	232	140	�	�	PROPN
iajs-2816	232	141	1	1	NUM
iajs-2816	232	142	−	−	PROPN
iajs-2816	232	143	�	�	PROPN
iajs-2816	232	144	̃	̃	PROPN
iajs-2816	232	145	�	�	PROPN
iajs-2816	232	146	2	2	NUM
iajs-2816	232	147	+	+	SYM
iajs-2816	232	148	�	�	PROPN
iajs-2816	232	149	̃	̃	PROPN
iajs-2816	232	150	�	�	NOUN
iajs-2816	232	151	3	3	NUM
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iajs-2816	232	153	�	�	PROPN
iajs-2816	232	154	̃	̃	PROPN
iajs-2816	232	155	�	�	NOUN
iajs-2816	232	156	4	4	NUM
iajs-2816	232	157	=	=	SYM
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iajs-2816	232	159	,	,	PUNCT
iajs-2816	232	160	𝑡)	𝑡)	PROPN
iajs-2816	232	161	�	�	PROPN
iajs-2816	232	162	̃	̃	PROPN
iajs-2816	232	163	�	�	NOUN
iajs-2816	232	164	1	1	NUM
iajs-2816	232	165	+	+	NUM
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iajs-2816	232	167	,	,	PUNCT
iajs-2816	232	168	𝑡)	𝑡)	PROPN
iajs-2816	232	169	�	�	PROPN
iajs-2816	232	170	̃	̃	PROPN
iajs-2816	232	171	�	�	NOUN
iajs-2816	232	172	1	1	NUM
iajs-2816	232	173	+	+	CCONJ
iajs-2816	232	174	𝑓13(𝑥	𝑓13(𝑥	NOUN
iajs-2816	232	175	,	,	PUNCT
iajs-2816	232	176	𝑡	𝑡	NOUN
iajs-2816	232	177	)	)	PUNCT
iajs-2816	232	178	,	,	PUNCT
iajs-2816	232	179	�	�	PROPN
iajs-2816	232	180	̃	̃	PROPN
iajs-2816	232	181	�	�	NOUN
iajs-2816	232	182	1(𝑥	1(𝑥	NUM
iajs-2816	232	183	,	,	PUNCT
iajs-2816	232	184	0	0	NUM
iajs-2816	232	185	)	)	PUNCT
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iajs-2816	232	194	2𝑡	2𝑡	NOUN
iajs-2816	232	195	−	−	PROPN
iajs-2816	232	196	∆	∆	PROPN
iajs-2816	232	197	�	�	PROPN
iajs-2816	232	198	̃	̃	PROPN
iajs-2816	232	199	�	�	PROPN
iajs-2816	232	200	2	2	NUM
iajs-2816	232	201	+	+	SYM
iajs-2816	232	202	�	�	PROPN
iajs-2816	232	203	̃	̃	PROPN
iajs-2816	232	204	�	�	NOUN
iajs-2816	232	205	2	2	NUM
iajs-2816	232	206	+	+	SYM
iajs-2816	232	207	�	�	PROPN
iajs-2816	232	208	̃	̃	PROPN
iajs-2816	232	209	�	�	PROPN
iajs-2816	232	210	1	1	NUM
iajs-2816	232	211	−	−	PROPN
iajs-2816	232	212	�	�	PROPN
iajs-2816	232	213	̃	̃	PROPN
iajs-2816	232	214	�	�	PROPN
iajs-2816	232	215	3	3	NUM
iajs-2816	232	216	−	−	PROPN
iajs-2816	232	217	�	�	PROPN
iajs-2816	232	218	̃	̃	NOUN
iajs-2816	232	219	�	�	NOUN
iajs-2816	232	220	4	4	NUM
iajs-2816	232	221	=	=	SYM
iajs-2816	232	222	𝑓21(𝑥	𝑓21(𝑥	NOUN
iajs-2816	232	223	,	,	PUNCT
iajs-2816	232	224	𝑡)	𝑡)	PROPN
iajs-2816	232	225	�	�	PROPN
iajs-2816	232	226	̃	̃	PROPN
iajs-2816	232	227	�	�	NOUN
iajs-2816	232	228	2	2	NUM
iajs-2816	232	229	+	+	NUM
iajs-2816	232	230	𝑓22(𝑥	𝑓22(𝑥	NOUN
iajs-2816	232	231	,	,	PUNCT
iajs-2816	232	232	𝑡)	𝑡)	PROPN
iajs-2816	232	233	�	�	PROPN
iajs-2816	232	234	̃	̃	PROPN
iajs-2816	232	235	�	�	NOUN
iajs-2816	232	236	2	2	NUM
iajs-2816	232	237	+	+	NUM
iajs-2816	232	238	𝑓23(𝑥	𝑓23(𝑥	NOUN
iajs-2816	232	239	,	,	PUNCT
iajs-2816	232	240	𝑡	𝑡	NOUN
iajs-2816	232	241	)	)	PUNCT
iajs-2816	232	242	,	,	PUNCT
iajs-2816	232	243	�	�	PROPN
iajs-2816	232	244	̃	̃	PROPN
iajs-2816	232	245	�	�	NOUN
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iajs-2816	232	247	,	,	PUNCT
iajs-2816	232	248	0	0	NUM
iajs-2816	232	249	)	)	PUNCT
iajs-2816	232	250	=	=	SYM
iajs-2816	232	251	𝑦2	𝑦2	NOUN
iajs-2816	232	252	0(𝑥	0(𝑥	NUM
iajs-2816	232	253	)	)	PUNCT
iajs-2816	232	254	,	,	PUNCT
iajs-2816	232	255	�	�	PROPN
iajs-2816	232	256	̃	̃	PROPN
iajs-2816	232	257	�	�	PROPN
iajs-2816	232	258	3𝑡	3𝑡	NOUN
iajs-2816	232	259	−	−	PROPN
iajs-2816	232	260	∆	∆	PROPN
iajs-2816	232	261	�	�	PROPN
iajs-2816	232	262	̃	̃	PROPN
iajs-2816	232	263	�	�	PROPN
iajs-2816	232	264	3	3	NUM
iajs-2816	232	265	+	+	SYM
iajs-2816	232	266	�	�	PROPN
iajs-2816	232	267	̃	̃	PROPN
iajs-2816	232	268	�	�	PROPN
iajs-2816	232	269	3	3	NUM
iajs-2816	232	270	−	−	PROPN
iajs-2816	232	271	�	�	PROPN
iajs-2816	232	272	̃	̃	PROPN
iajs-2816	232	273	�	�	NOUN
iajs-2816	232	274	1	1	NUM
iajs-2816	232	275	+	+	NUM
iajs-2816	232	276	�	�	PROPN
iajs-2816	232	277	̃	̃	PROPN
iajs-2816	232	278	�	�	NOUN
iajs-2816	232	279	2	2	NUM
iajs-2816	232	280	+	+	SYM
iajs-2816	232	281	�	�	PROPN
iajs-2816	232	282	̃	̃	NOUN
iajs-2816	232	283	�	�	NOUN
iajs-2816	232	284	4	4	NUM
iajs-2816	232	285	=	=	SYM
iajs-2816	232	286	𝑓31(𝑥	𝑓31(𝑥	NUM
iajs-2816	232	287	,	,	PUNCT
iajs-2816	232	288	𝑡)	𝑡)	PROPN
iajs-2816	232	289	�	�	PROPN
iajs-2816	232	290	̃	̃	PROPN
iajs-2816	232	291	�	�	PROPN
iajs-2816	232	292	3	3	NUM
iajs-2816	232	293	+	+	NUM
iajs-2816	232	294	𝑓32(𝑥	𝑓32(𝑥	NOUN
iajs-2816	232	295	,	,	PUNCT
iajs-2816	232	296	𝑡)	𝑡)	PROPN
iajs-2816	232	297	�	�	PROPN
iajs-2816	232	298	̃	̃	PROPN
iajs-2816	232	299	�	�	NOUN
iajs-2816	232	300	3	3	NUM
iajs-2816	232	301	+	+	CCONJ
iajs-2816	232	302	𝑓33(𝑥	𝑓33(𝑥	ADJ
iajs-2816	232	303	,	,	PUNCT
iajs-2816	232	304	𝑡	𝑡	NOUN
iajs-2816	232	305	)	)	PUNCT
iajs-2816	232	306	,	,	PUNCT
iajs-2816	232	307	�	�	PROPN
iajs-2816	232	308	̃	̃	PROPN
iajs-2816	232	309	�	�	NOUN
iajs-2816	232	310	3(𝑥	3(𝑥	NUM
iajs-2816	232	311	,	,	PUNCT
iajs-2816	232	312	0	0	NUM
iajs-2816	232	313	)	)	PUNCT
iajs-2816	232	314	=	=	SYM
iajs-2816	232	315	𝑦3	𝑦3	PROPN
iajs-2816	232	316	0(𝑥	0(𝑥	NUM
iajs-2816	232	317	)	)	PUNCT
iajs-2816	232	318	,	,	PUNCT
iajs-2816	232	319	�	�	PROPN
iajs-2816	232	320	̃	̃	PROPN
iajs-2816	232	321	�	�	NOUN
iajs-2816	232	322	4𝑡	4𝑡	NOUN
iajs-2816	232	323	−	−	PROPN
iajs-2816	232	324	∆	∆	PROPN
iajs-2816	232	325	�	�	PROPN
iajs-2816	232	326	̃	̃	PROPN
iajs-2816	232	327	�	�	NOUN
iajs-2816	232	328	4	4	NUM
iajs-2816	232	329	+	+	SYM
iajs-2816	232	330	�	�	PROPN
iajs-2816	232	331	̃	̃	PROPN
iajs-2816	232	332	�	�	NOUN
iajs-2816	232	333	4	4	NUM
iajs-2816	232	334	−	−	PROPN
iajs-2816	232	335	�	�	PROPN
iajs-2816	232	336	̃	̃	PROPN
iajs-2816	232	337	�	�	NOUN
iajs-2816	232	338	1	1	NUM
iajs-2816	232	339	+	+	NUM
iajs-2816	232	340	�	�	PROPN
iajs-2816	232	341	̃	̃	PROPN
iajs-2816	232	342	�	�	PROPN
iajs-2816	232	343	2	2	NUM
iajs-2816	232	344	−	−	PROPN
iajs-2816	232	345	�	�	PROPN
iajs-2816	232	346	̃	̃	PROPN
iajs-2816	232	347	�	�	NOUN
iajs-2816	232	348	3	3	NUM
iajs-2816	232	349	=	=	SYM
iajs-2816	232	350	𝑓41(𝑥	𝑓41(𝑥	NOUN
iajs-2816	232	351	,	,	PUNCT
iajs-2816	232	352	𝑡)	𝑡)	PROPN
iajs-2816	232	353	�	�	PROPN
iajs-2816	232	354	̃	̃	PROPN
iajs-2816	232	355	�	�	NOUN
iajs-2816	232	356	4	4	NUM
iajs-2816	232	357	+	+	SYM
iajs-2816	232	358	𝑓42(𝑥	𝑓42(𝑥	NOUN
iajs-2816	232	359	,	,	PUNCT
iajs-2816	232	360	𝑡)	𝑡)	PROPN
iajs-2816	232	361	�	�	PROPN
iajs-2816	232	362	̃	̃	PROPN
iajs-2816	232	363	�	�	NOUN
iajs-2816	232	364	4	4	NUM
iajs-2816	232	365	+	+	SYM
iajs-2816	232	366	𝑓43(𝑥	𝑓43(𝑥	ADJ
iajs-2816	232	367	,	,	PUNCT
iajs-2816	232	368	𝑡	𝑡	NOUN
iajs-2816	232	369	)	)	PUNCT
iajs-2816	232	370	,	,	PUNCT
iajs-2816	232	371	�	�	PROPN
iajs-2816	232	372	̃	̃	PROPN
iajs-2816	232	373	�	�	NOUN
iajs-2816	232	374	4(𝑥	4(𝑥	NUM
iajs-2816	232	375	,	,	PUNCT
iajs-2816	232	376	0	0	NUM
iajs-2816	232	377	)	)	PUNCT
iajs-2816	232	378	=	=	SYM
iajs-2816	232	379	𝑦4	𝑦4	NOUN
iajs-2816	232	380	0(𝑥	0(𝑥	NUM
iajs-2816	232	381	)	)	PUNCT
iajs-2816	232	382	,	,	PUNCT
iajs-2816	232	383	therefore	therefore	ADV
iajs-2816	232	384	�	�	PROPN
iajs-2816	232	385	⃗⃗	⃗⃗	PROPN
iajs-2816	232	386	�	�	PROPN
iajs-2816	232	387	⟼	⟼	PROPN
iajs-2816	232	388	�	�	PROPN
iajs-2816	232	389	⃗	⃗	NOUN
iajs-2816	232	390	�	�	PROPN
iajs-2816	232	391	�	�	PROPN
iajs-2816	232	392	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	232	393	�	�	PROPN
iajs-2816	232	394	is	be	AUX
iajs-2816	232	395	col	col	PROPN
iajs-2816	232	396	w.r.t	w.r.t	NOUN
iajs-2816	232	397	.	.	PUNCT
iajs-2816	233	1	(	(	PUNCT
iajs-2816	233	2	�	�	PROPN
iajs-2816	233	3	⃗	⃗	NOUN
iajs-2816	233	4	�	�	PROPN
iajs-2816	233	5	,	,	PUNCT
iajs-2816	233	6	�	�	PROPN
iajs-2816	233	7	⃗⃗	⃗⃗	PROPN
iajs-2816	233	8	�	�	PROPN
iajs-2816	233	9	)	)	PUNCT
iajs-2816	233	10	in	in	ADP
iajs-2816	233	11	𝑄.	𝑄.	NOUN
iajs-2816	233	12	from	from	ADP
iajs-2816	233	13	hypotheses	hypothesis	NOUN
iajs-2816	233	14	on	on	ADP
iajs-2816	233	15	𝑔1𝑖	𝑔1𝑖	NOUN
iajs-2816	233	16	in	in	ADP
iajs-2816	233	17	𝑄	𝑄	PROPN
iajs-2816	233	18	for	for	ADP
iajs-2816	233	19	each	each	PRON
iajs-2816	233	20	𝑖	𝑖	NOUN
iajs-2816	234	1	=	=	NOUN
iajs-2816	234	2	1,2,3,4	1,2,3,4	NUM
iajs-2816	234	3	:	:	PUNCT
iajs-2816	234	4	𝑔1𝑖(𝑥	𝑔1𝑖(𝑥	PROPN
iajs-2816	234	5	,	,	PUNCT
iajs-2816	234	6	𝑡	𝑡	PROPN
iajs-2816	234	7	,	,	PUNCT
iajs-2816	234	8	𝑦𝑖	𝑦𝑖	PROPN
iajs-2816	234	9	,	,	PUNCT
iajs-2816	234	10	𝑢𝑖	𝑢𝑖	INTJ
iajs-2816	234	11	)	)	PUNCT
iajs-2816	234	12	=	=	SYM
iajs-2816	234	13	ℎ1𝑖(𝑥	ℎ1𝑖(𝑥	PROPN
iajs-2816	234	14	,	,	PUNCT
iajs-2816	234	15	𝑡)𝑦𝑖	𝑡)𝑦𝑖	PROPN
iajs-2816	234	16	+	+	NUM
iajs-2816	234	17	ℎ2𝑖(𝑥	ℎ2𝑖(𝑥	PROPN
iajs-2816	234	18	,	,	PUNCT
iajs-2816	234	19	𝑡)𝑢𝑖	𝑡)𝑢𝑖	PROPN
iajs-2816	234	20	+	+	NUM
iajs-2816	234	21	ℎ3𝑖(𝑥	ℎ3𝑖(𝑥	PROPN
iajs-2816	234	22	,	,	PUNCT
iajs-2816	234	23	𝑡	𝑡	NOUN
iajs-2816	234	24	)	)	PUNCT
iajs-2816	234	25	.	.	PUNCT
iajs-2816	235	1	now	now	ADV
iajs-2816	235	2	,	,	PUNCT
iajs-2816	235	3	to	to	PART
iajs-2816	235	4	show	show	VERB
iajs-2816	235	5	𝑔1𝑖	𝑔1𝑖	ADJ
iajs-2816	235	6	is	be	AUX
iajs-2816	235	7	col	col	PROPN
iajs-2816	235	8	w.r.t	w.r.t	NOUN
iajs-2816	235	9	.	.	PUNCT
iajs-2816	236	1	(	(	PUNCT
iajs-2816	236	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	236	3	,	,	PUNCT
iajs-2816	236	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	236	5	)	)	PUNCT
iajs-2816	236	6	,	,	PUNCT
iajs-2816	236	7	in	in	ADP
iajs-2816	236	8	𝑄	𝑄	PROPN
iajs-2816	236	9	,	,	PUNCT
iajs-2816	236	10	since	since	SCONJ
iajs-2816	236	11	𝐺1(	𝐺1(	NUM
iajs-2816	236	12	�	�	PROPN
iajs-2816	236	13	⃗⃗	⃗⃗	PROPN
iajs-2816	236	14	�	�	PROPN
iajs-2816	236	15	+	+	CCONJ
iajs-2816	236	16	(	(	PUNCT
iajs-2816	236	17	1	1	NUM
iajs-2816	236	18	−	−	PROPN
iajs-2816	236	19	𝛼)	𝛼)	PROPN
iajs-2816	236	20	�	�	PROPN
iajs-2816	236	21	⃗⃗̅	⃗⃗̅	NOUN
iajs-2816	236	22	�	�	PROPN
iajs-2816	236	23	)	)	PUNCT
iajs-2816	236	24	=	=	PUNCT
iajs-2816	237	1	∑	∑	PUNCT
iajs-2816	238	1	[	[	X
iajs-2816	238	2	4	4	NUM
iajs-2816	238	3	𝑖=1	𝑖=1	PROPN
iajs-2816	238	4	∫	∫	PROPN
iajs-2816	238	5	𝑔1𝑖(𝑥	𝑔1𝑖(𝑥	PROPN
iajs-2816	238	6	,	,	PUNCT
iajs-2816	238	7	𝑡	𝑡	PROPN
iajs-2816	238	8	,	,	PUNCT
iajs-2816	238	9	𝑦𝑖(𝛼𝑢𝑖+(1−𝛼)𝑢𝑖	𝑦𝑖(𝛼𝑢𝑖+(1−𝛼)𝑢𝑖	PROPN
iajs-2816	238	10	)	)	PUNCT
iajs-2816	238	11	,	,	PUNCT
iajs-2816	238	12	𝛼𝑢𝑖	𝛼𝑢𝑖	ADJ
iajs-2816	238	13	+	+	SYM
iajs-2816	238	14	(	(	PUNCT
iajs-2816	238	15	1	1	NUM
iajs-2816	238	16	−	−	PROPN
iajs-2816	238	17	𝛼)	𝛼)	PROPN
iajs-2816	238	18	�	�	SYM
iajs-2816	238	19	̅	̅	NOUN
iajs-2816	238	20	�	�	NOUN
iajs-2816	238	21	𝑖	𝑖	NUM
iajs-2816	238	22	)	)	PUNCT
iajs-2816	238	23	𝑄	𝑄	PRON
iajs-2816	238	24	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2816	238	25	]	]	PUNCT
iajs-2816	238	26	=	=	SYM
iajs-2816	238	27	∑	∑	PUNCT
iajs-2816	238	28	{	{	PUNCT
iajs-2816	238	29	4	4	NUM
iajs-2816	238	30	𝑖=1	𝑖=1	PROPN
iajs-2816	238	31	∫	∫	PROPN
iajs-2816	238	32	[	[	PUNCT
iajs-2816	238	33	ℎ1𝑖(𝑥	ℎ1𝑖(𝑥	PROPN
iajs-2816	238	34	,	,	PUNCT
iajs-2816	238	35	𝑡)𝑦𝑖(𝛼𝑢𝑖+(1−𝛼)𝑢𝑖	𝑡)𝑦𝑖(𝛼𝑢𝑖+(1−𝛼)𝑢𝑖	PROPN
iajs-2816	238	36	)	)	PUNCT
iajs-2816	238	37	𝑄	𝑄	PRON
iajs-2816	238	38	]	]	PUNCT
iajs-2816	238	39	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	X
iajs-2816	238	40	+	+	NUM
iajs-2816	238	41	∫	∫	PROPN
iajs-2816	238	42	[	[	PUNCT
iajs-2816	238	43	𝑄	𝑄	PROPN
iajs-2816	238	44	ℎ2𝑖(𝑥	ℎ2𝑖(𝑥	PROPN
iajs-2816	238	45	,	,	PUNCT
iajs-2816	238	46	𝑡)(𝛼𝑢𝑖	𝑡)(𝛼𝑢𝑖	ADJ
iajs-2816	238	47	+	+	CCONJ
iajs-2816	238	48	(	(	PUNCT
iajs-2816	238	49	1	1	NUM
iajs-2816	238	50	−	−	PROPN
iajs-2816	238	51	𝛼)	𝛼)	PROPN
iajs-2816	238	52	�	�	SYM
iajs-2816	238	53	̅	̅	NOUN
iajs-2816	238	54	�	�	NOUN
iajs-2816	238	55	𝑖	𝑖	NUM
iajs-2816	238	56	)	)	PUNCT
iajs-2816	238	57	+	+	CCONJ
iajs-2816	238	58	ℎ3𝑖(𝑥	ℎ3𝑖(𝑥	PROPN
iajs-2816	238	59	,	,	PUNCT
iajs-2816	238	60	𝑡)]𝑑𝑥𝑑𝑡	𝑡)]𝑑𝑥𝑑𝑡	NUM
iajs-2816	238	61	}	}	PUNCT
iajs-2816	238	62	,	,	PUNCT
iajs-2816	238	63	since	since	SCONJ
iajs-2816	238	64	�	�	PROPN
iajs-2816	238	65	⃗⃗	⃗⃗	PROPN
iajs-2816	238	66	�	�	PROPN
iajs-2816	238	67	⟼	⟼	PROPN
iajs-2816	238	68	�	�	PROPN
iajs-2816	238	69	⃗	⃗	NOUN
iajs-2816	238	70	�	�	PROPN
iajs-2816	238	71	�	�	PROPN
iajs-2816	238	72	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	238	73	�	�	PROPN
iajs-2816	238	74	is	be	AUX
iajs-2816	238	75	col	col	PROPN
iajs-2816	238	76	.	.	PROPN
iajs-2816	239	1	then	then	ADV
iajs-2816	239	2	𝐺1(	𝐺1(	NUM
iajs-2816	239	3	�	�	PROPN
iajs-2816	239	4	⃗⃗	⃗⃗	PROPN
iajs-2816	239	5	�	�	PROPN
iajs-2816	239	6	)	)	PUNCT
iajs-2816	239	7	is	be	AUX
iajs-2816	239	8	col	col	PROPN
iajs-2816	239	9	w.r.t	w.r.t	NOUN
iajs-2816	239	10	.	.	PUNCT
iajs-2816	240	1	(	(	PUNCT
iajs-2816	240	2	�	�	PROPN
iajs-2816	240	3	⃗	⃗	NOUN
iajs-2816	240	4	�	�	PROPN
iajs-2816	240	5	,	,	PUNCT
iajs-2816	240	6	�	�	PROPN
iajs-2816	240	7	⃗⃗	⃗⃗	PROPN
iajs-2816	240	8	�	�	PROPN
iajs-2816	240	9	)	)	PUNCT
iajs-2816	241	1	,	,	PUNCT
iajs-2816	241	2	in	in	ADP
iajs-2816	241	3	𝑄	𝑄	PROPN
iajs-2816	241	4	,	,	PUNCT
iajs-2816	241	5	i.	i.	PROPN
iajs-2816	241	6	e.	e.	PROPN
iajs-2816	241	7	:	:	PUNCT
iajs-2816	241	8	𝐺1(	𝐺1(	PROPN
iajs-2816	241	9	�	�	PROPN
iajs-2816	241	10	⃗⃗	⃗⃗	PROPN
iajs-2816	241	11	�	�	PROPN
iajs-2816	241	12	+	+	CCONJ
iajs-2816	241	13	(	(	PUNCT
iajs-2816	241	14	1	1	NUM
iajs-2816	241	15	−	−	PROPN
iajs-2816	241	16	𝛼)	𝛼)	PROPN
iajs-2816	241	17	�	�	PROPN
iajs-2816	241	18	⃗⃗̅	⃗⃗̅	NOUN
iajs-2816	241	19	�	�	PROPN
iajs-2816	241	20	)	)	PUNCT
iajs-2816	242	1	=	=	PUNCT
iajs-2816	242	2	∑	∑	PROPN
iajs-2816	242	3	{	{	PUNCT
iajs-2816	242	4	4	4	NUM
iajs-2816	242	5	𝑖=1	𝑖=1	PROPN
iajs-2816	242	6	∫	∫	PROPN
iajs-2816	242	7	[	[	PUNCT
iajs-2816	242	8	ℎ1𝑖(𝑥	ℎ1𝑖(𝑥	PROPN
iajs-2816	242	9	,	,	PUNCT
iajs-2816	242	10	𝑡)(𝛼𝑦𝑖	𝑡)(𝛼𝑦𝑖	VERB
iajs-2816	242	11	+	+	CCONJ
iajs-2816	242	12	(	(	PUNCT
iajs-2816	242	13	1	1	NUM
iajs-2816	242	14	−	−	PROPN
iajs-2816	242	15	𝛼)	𝛼)	PROPN
iajs-2816	242	16	�	�	SYM
iajs-2816	242	17	̅	̅	NOUN
iajs-2816	242	18	�	�	NOUN
iajs-2816	242	19	𝑖	𝑖	NOUN
iajs-2816	242	20	)	)	PUNCT
iajs-2816	242	21	𝑄	𝑄	PRON
iajs-2816	242	22	]	]	PUNCT
iajs-2816	242	23	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	X
iajs-2816	242	24	+	+	NUM
iajs-2816	242	25	∫	∫	PROPN
iajs-2816	242	26	[	[	PUNCT
iajs-2816	242	27	𝑄	𝑄	PROPN
iajs-2816	242	28	ℎ2𝑖(𝑥	ℎ2𝑖(𝑥	PROPN
iajs-2816	242	29	,	,	PUNCT
iajs-2816	242	30	𝑡)(𝛼𝑢𝑖	𝑡)(𝛼𝑢𝑖	ADJ
iajs-2816	242	31	+	+	CCONJ
iajs-2816	242	32	(	(	PUNCT
iajs-2816	242	33	1	1	NUM
iajs-2816	242	34	−	−	PROPN
iajs-2816	242	35	𝛼)	𝛼)	PROPN
iajs-2816	242	36	�	�	SYM
iajs-2816	242	37	̅	̅	NOUN
iajs-2816	242	38	�	�	NOUN
iajs-2816	242	39	𝑖	𝑖	NUM
iajs-2816	242	40	)	)	PUNCT
iajs-2816	242	41	+	+	CCONJ
iajs-2816	242	42	ℎ3𝑖(𝑥	ℎ3𝑖(𝑥	PROPN
iajs-2816	242	43	,	,	PUNCT
iajs-2816	242	44	𝑡)]𝑑𝑥𝑑𝑡	𝑡)]𝑑𝑥𝑑𝑡	NUM
iajs-2816	242	45	}	}	PUNCT
iajs-2816	242	46	,	,	PUNCT
iajs-2816	242	47	=	=	PUNCT
iajs-2816	243	1	𝛼∑	𝛼∑	NUM
iajs-2816	243	2	∫	∫	PROPN
iajs-2816	243	3	[	[	PUNCT
iajs-2816	243	4	𝑄	𝑄	PROPN
iajs-2816	243	5	4	4	NUM
iajs-2816	243	6	𝑖=1	𝑖=1	PROPN
iajs-2816	243	7	ℎ1𝑖(𝑥	ℎ1𝑖(𝑥	PROPN
iajs-2816	243	8	,	,	PUNCT
iajs-2816	244	1	𝑡)𝑦𝑖	𝑡)𝑦𝑖	PROPN
iajs-2816	244	2	+	+	NUM
iajs-2816	244	3	ℎ2𝑖(𝑥	ℎ2𝑖(𝑥	PROPN
iajs-2816	244	4	,	,	PUNCT
iajs-2816	244	5	𝑡)𝑢𝑖	𝑡)𝑢𝑖	PROPN
iajs-2816	244	6	+	+	NUM
iajs-2816	244	7	ℎ3𝑖(𝑥	ℎ3𝑖(𝑥	PROPN
iajs-2816	244	8	,	,	PUNCT
iajs-2816	244	9	𝑡)]𝑑𝑥𝑑𝑡	𝑡)]𝑑𝑥𝑑𝑡	NUM
iajs-2816	244	10	+	+	CCONJ
iajs-2816	244	11	(	(	PUNCT
iajs-2816	244	12	1	1	NUM
iajs-2816	244	13	−	−	NUM
iajs-2816	244	14	𝛼)∑	𝛼)∑	NUM
iajs-2816	244	15	∫	∫	NOUN
iajs-2816	244	16	[	[	PUNCT
iajs-2816	244	17	𝑄	𝑄	PROPN
iajs-2816	244	18	4	4	NUM
iajs-2816	244	19	𝑖=1	𝑖=1	PROPN
iajs-2816	244	20	ℎ1𝑖(𝑥	ℎ1𝑖(𝑥	PROPN
iajs-2816	244	21	,	,	PUNCT
iajs-2816	244	22	𝑡)	𝑡)	PROPN
iajs-2816	244	23	�	�	NOUN
iajs-2816	244	24	̅	̅	NOUN
iajs-2816	244	25	�	�	NOUN
iajs-2816	244	26	𝑖	𝑖	NOUN
iajs-2816	244	27	+	+	PROPN
iajs-2816	244	28	ℎ2𝑖(𝑥	ℎ2𝑖(𝑥	PROPN
iajs-2816	244	29	,	,	PUNCT
iajs-2816	244	30	𝑡)	𝑡)	PROPN
iajs-2816	244	31	�	�	NOUN
iajs-2816	244	32	̅	̅	NOUN
iajs-2816	244	33	�	�	NOUN
iajs-2816	244	34	𝑖	𝑖	NOUN
iajs-2816	244	35	+	+	NOUN
iajs-2816	244	36	ℎ3𝑖(𝑥	ℎ3𝑖(𝑥	ADJ
iajs-2816	244	37	,	,	PUNCT
iajs-2816	244	38	𝑡)]𝑑𝑥𝑑𝑡	𝑡)]𝑑𝑥𝑑𝑡	NUM
iajs-2816	244	39	,	,	PUNCT
iajs-2816	244	40	=	=	PUNCT
iajs-2816	244	41	𝛼𝐺1(	𝛼𝐺1(	NUM
iajs-2816	244	42	�	�	PROPN
iajs-2816	244	43	⃗⃗	⃗⃗	PROPN
iajs-2816	244	44	�	�	PROPN
iajs-2816	244	45	)	)	PUNCT
iajs-2816	245	1	+	+	CCONJ
iajs-2816	245	2	(	(	PUNCT
iajs-2816	245	3	1	1	NUM
iajs-2816	245	4	−	−	PROPN
iajs-2816	245	5	𝛼)𝐺1(	𝛼)𝐺1(	PROPN
iajs-2816	245	6	�	�	PROPN
iajs-2816	245	7	⃗⃗̅	⃗⃗̅	NOUN
iajs-2816	245	8	�	�	PROPN
iajs-2816	245	9	)	)	PUNCT
iajs-2816	245	10	,	,	PUNCT
iajs-2816	245	11	since	since	SCONJ
iajs-2816	245	12	𝑔0𝑖	𝑔0𝑖	PROPN
iajs-2816	245	13	&	&	CCONJ
iajs-2816	245	14	𝑔2𝑖	𝑔2𝑖	NOUN
iajs-2816	245	15	are	be	AUX
iajs-2816	245	16	co	co	ADP
iajs-2816	245	17	w.r.t.(𝑦𝑖	w.r.t.(𝑦𝑖	ADV
iajs-2816	245	18	,	,	PUNCT
iajs-2816	245	19	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	245	20	)	)	PUNCT
iajs-2816	245	21	,	,	PUNCT
iajs-2816	245	22	in	in	ADP
iajs-2816	245	23	𝑄	𝑄	PRON
iajs-2816	245	24	,	,	PUNCT
iajs-2816	245	25	∀𝑖	∀𝑖	PROPN
iajs-2816	245	26	=	=	NOUN
iajs-2816	245	27	1,2,3,4	1,2,3,4	NUM
iajs-2816	245	28	,	,	PUNCT
iajs-2816	245	29	then	then	ADV
iajs-2816	245	30	∑	∑	PROPN
iajs-2816	245	31	∫	∫	PROPN
iajs-2816	245	32	𝑔0𝑖	𝑔0𝑖	PROPN
iajs-2816	245	33	𝑄	𝑄	PROPN
iajs-2816	245	34	4	4	NUM
iajs-2816	245	35	𝑖=1	𝑖=1	PROPN
iajs-2816	245	36	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	NOUN
iajs-2816	245	37	and	and	CCONJ
iajs-2816	245	38	∑	∑	ADP
iajs-2816	245	39	∫	∫	PROPN
iajs-2816	245	40	𝑔2𝑖	𝑔2𝑖	NOUN
iajs-2816	245	41	𝑄	𝑄	PROPN
iajs-2816	245	42	4	4	NUM
iajs-2816	245	43	𝑖=1	𝑖=1	PROPN
iajs-2816	245	44	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	PROPN
iajs-2816	245	45	are	be	AUX
iajs-2816	245	46	co	co	VERB
iajs-2816	245	47	w.r.t	w.r.t	ADJ
iajs-2816	245	48	.	.	PUNCT
iajs-2816	246	1	(	(	PUNCT
iajs-2816	246	2	𝑦𝑖	𝑦𝑖	INTJ
iajs-2816	246	3	,	,	PUNCT
iajs-2816	246	4	𝑢𝑖	𝑢𝑖	NOUN
iajs-2816	246	5	)	)	PUNCT
iajs-2816	246	6	,	,	PUNCT
iajs-2816	246	7	in	in	ADP
iajs-2816	246	8	𝑄	𝑄	PROPN
iajs-2816	246	9	,	,	PUNCT
iajs-2816	246	10	∀𝑖	∀𝑖	PROPN
iajs-2816	246	11	=	=	NOUN
iajs-2816	246	12	1,2,3,4	1,2,3,4	NUM
iajs-2816	246	13	,	,	PUNCT
iajs-2816	246	14	and	and	CCONJ
iajs-2816	246	15	then	then	ADV
iajs-2816	246	16	𝐺0(	𝐺0(	VERB
iajs-2816	246	17	�	�	PROPN
iajs-2816	246	18	⃗⃗	⃗⃗	PROPN
iajs-2816	246	19	�	�	PROPN
iajs-2816	246	20	)	)	PUNCT
iajs-2816	246	21	and	and	CCONJ
iajs-2816	246	22	𝐺2(	𝐺2(	NUM
iajs-2816	246	23	�	�	PROPN
iajs-2816	246	24	⃗⃗	⃗⃗	PROPN
iajs-2816	246	25	�	�	PROPN
iajs-2816	246	26	)	)	PUNCT
iajs-2816	246	27	are	be	AUX
iajs-2816	246	28	co	co	X
iajs-2816	246	29	w.r.t	w.r.t	PROPN
iajs-2816	246	30	.	.	PUNCT
iajs-2816	247	1	(	(	PUNCT
iajs-2816	247	2	�	�	PROPN
iajs-2816	247	3	⃗	⃗	NOUN
iajs-2816	247	4	�	�	PROPN
iajs-2816	247	5	,	,	PUNCT
iajs-2816	247	6	�	�	PROPN
iajs-2816	247	7	⃗⃗	⃗⃗	PROPN
iajs-2816	247	8	�	�	PROPN
iajs-2816	247	9	)	)	PUNCT
iajs-2816	247	10	,	,	PUNCT
iajs-2816	247	11	in	in	ADP
iajs-2816	247	12	𝑄	𝑄	PROPN
iajs-2816	247	13	,	,	PUNCT
iajs-2816	247	14	i.e.	i.e.	X
iajs-2816	247	15	𝐺(	𝐺(	X
iajs-2816	247	16	�	�	PROPN
iajs-2816	247	17	⃗⃗	⃗⃗	PROPN
iajs-2816	247	18	�	�	PROPN
iajs-2816	247	19	)	)	PUNCT
iajs-2816	247	20	is	be	AUX
iajs-2816	247	21	co	co	X
iajs-2816	247	22	w.r.t	w.r.t	PROPN
iajs-2816	247	23	.	.	PUNCT
iajs-2816	248	1	(	(	PUNCT
iajs-2816	248	2	�	�	PROPN
iajs-2816	248	3	⃗	⃗	NOUN
iajs-2816	248	4	�	�	PROPN
iajs-2816	248	5	,	,	PUNCT
iajs-2816	248	6	�	�	PROPN
iajs-2816	248	7	⃗⃗	⃗⃗	PROPN
iajs-2816	248	8	�	�	PROPN
iajs-2816	248	9	)	)	PUNCT
iajs-2816	248	10	,	,	PUNCT
iajs-2816	248	11	in	in	ADP
iajs-2816	248	12	𝑄	𝑄	PRON
iajs-2816	248	13	.	.	PUNCT
iajs-2816	249	1	on	on	ADP
iajs-2816	249	2	the	the	DET
iajs-2816	249	3	other	other	ADJ
iajs-2816	249	4	hand	hand	NOUN
iajs-2816	249	5	,	,	PUNCT
iajs-2816	249	6	since	since	SCONJ
iajs-2816	249	7	�	�	PROPN
iajs-2816	249	8	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	249	9	�	�	PROPN
iajs-2816	249	10	=	=	SYM
iajs-2816	249	11	�	�	PROPN
iajs-2816	249	12	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	249	13	�	�	PROPN
iajs-2816	249	14	�	�	PROPN
iajs-2816	249	15	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	249	16	�	�	PROPN
iajs-2816	249	17	is	be	AUX
iajs-2816	249	18	co	co	ADJ
iajs-2816	249	19	,	,	PUNCT
iajs-2816	249	20	and	and	CCONJ
iajs-2816	249	21	the	the	DET
iajs-2816	249	22	frd	frd	NOUN
iajs-2816	249	23	of	of	ADP
iajs-2816	249	24	𝐺𝑙(	𝐺𝑙(	PRON
iajs-2816	249	25	�	�	PROPN
iajs-2816	249	26	⃗⃗	⃗⃗	PROPN
iajs-2816	249	27	�	�	PROPN
iajs-2816	249	28	)	)	PUNCT
iajs-2816	249	29	,	,	PUNCT
iajs-2816	249	30	(	(	PUNCT
iajs-2816	249	31	𝑙	𝑙	X
iajs-2816	249	32	=	=	SYM
iajs-2816	249	33	0,1,2	0,1,2	NUM
iajs-2816	249	34	)	)	PUNCT
iajs-2816	249	35	exists	exist	VERB
iajs-2816	249	36	for	for	ADP
iajs-2816	249	37	each	each	DET
iajs-2816	249	38	�	�	PROPN
iajs-2816	249	39	⃗⃗	⃗⃗	PROPN
iajs-2816	249	40	�	�	PROPN
iajs-2816	249	41	∈	∈	PROPN
iajs-2816	249	42	�	�	PROPN
iajs-2816	249	43	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	249	44	�	�	PROPN
iajs-2816	249	45	and	and	CCONJ
iajs-2816	249	46	its	its	PRON
iajs-2816	249	47	cont	cont	NOUN
iajs-2816	249	48	.	.	PUNCT
iajs-2816	250	1	(	(	PUNCT
iajs-2816	250	2	by	by	ADP
iajs-2816	250	3	the	the	DET
iajs-2816	250	4	.	.	PROPN
iajs-2816	250	5	3.2	3.2	NUM
iajs-2816	250	6	and	and	CCONJ
iajs-2816	250	7	hypotheses	hypothesis	NOUN
iajs-2816	250	8	(	(	PUNCT
iajs-2816	250	9	a),(b	a),(b	NUM
iajs-2816	250	10	)	)	PUNCT
iajs-2816	250	11	and	and	CCONJ
iajs-2816	250	12	(	(	PUNCT
iajs-2816	250	13	c	c	NOUN
iajs-2816	250	14	)	)	PUNCT
iajs-2816	250	15	)	)	PUNCT
iajs-2816	250	16	,	,	PUNCT
iajs-2816	250	17	then	then	ADV
iajs-2816	250	18	𝐺(	𝐺(	PROPN
iajs-2816	250	19	�	�	PROPN
iajs-2816	250	20	⃗⃗	⃗⃗	PROPN
iajs-2816	250	21	�	�	PROPN
iajs-2816	250	22	)	)	PUNCT
iajs-2816	250	23	is	be	AUX
iajs-2816	250	24	co	co	X
iajs-2816	250	25	w.r.t	w.r.t	PROPN
iajs-2816	250	26	.	.	PUNCT
iajs-2816	251	1	(	(	PUNCT
iajs-2816	251	2	�	�	PROPN
iajs-2816	251	3	⃗	⃗	NOUN
iajs-2816	251	4	�	�	PROPN
iajs-2816	251	5	,	,	PUNCT
iajs-2816	251	6	�	�	PROPN
iajs-2816	251	7	⃗⃗	⃗⃗	PROPN
iajs-2816	251	8	�	�	PROPN
iajs-2816	251	9	)	)	PUNCT
iajs-2816	251	10	,	,	PUNCT
iajs-2816	251	11	in	in	ADP
iajs-2816	251	12	the	the	DET
iajs-2816	251	13	co	co	X
iajs-2816	251	14	set	set	PROPN
iajs-2816	251	15	�	�	PROPN
iajs-2816	251	16	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	251	17	�	�	PROPN
iajs-2816	252	1	and	and	CCONJ
iajs-2816	252	2	it	it	PRON
iajs-2816	252	3	has	have	VERB
iajs-2816	252	4	a	a	DET
iajs-2816	252	5	cont	cont	NOUN
iajs-2816	252	6	.	.	PUNCT
iajs-2816	253	1	frd	frd	ADJ
iajs-2816	253	2	,	,	PUNCT
iajs-2816	253	3	and	and	CCONJ
iajs-2816	253	4	satisfies	satisfy	VERB
iajs-2816	253	5	�	�	PROPN
iajs-2816	253	6	́	́	PROPN
iajs-2816	253	7	�	�	PROPN
iajs-2816	253	8	(	(	PUNCT
iajs-2816	253	9	�	�	PROPN
iajs-2816	253	10	⃗⃗	⃗⃗	PROPN
iajs-2816	253	11	�	�	PROPN
iajs-2816	253	12	)𝛿𝑢⃗⃗⃗⃗⃗	)𝛿𝑢⃗⃗⃗⃗⃗	PUNCT
iajs-2816	253	13	≥	≥	NOUN
iajs-2816	253	14	0	0	NUM
iajs-2816	253	15	,	,	PUNCT
iajs-2816	253	16	which	which	PRON
iajs-2816	253	17	means	mean	VERB
iajs-2816	253	18	𝐺(	𝐺(	PROPN
iajs-2816	253	19	�	�	PROPN
iajs-2816	253	20	⃗⃗	⃗⃗	PROPN
iajs-2816	253	21	�	�	PROPN
iajs-2816	253	22	)	)	PUNCT
iajs-2816	253	23	has	have	VERB
iajs-2816	253	24	a	a	DET
iajs-2816	253	25	minimum	minimum	NOUN
iajs-2816	253	26	at	at	ADP
iajs-2816	253	27	�	�	PROPN
iajs-2816	253	28	⃗⃗	⃗⃗	PROPN
iajs-2816	253	29	�	�	PROPN
iajs-2816	253	30	,	,	PUNCT
iajs-2816	253	31	i.e.	i.e.	X
iajs-2816	253	32	:	:	PUNCT
iajs-2816	253	33	𝐺(	𝐺(	PROPN
iajs-2816	253	34	�	�	PROPN
iajs-2816	253	35	⃗⃗	⃗⃗	PROPN
iajs-2816	253	36	�	�	PROPN
iajs-2816	253	37	)	)	PUNCT
iajs-2816	253	38	≤	≤	NUM
iajs-2816	253	39	𝐺(	𝐺(	NOUN
iajs-2816	253	40	�	�	PROPN
iajs-2816	253	41	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	42	�	�	PROPN
iajs-2816	253	43	)	)	PUNCT
iajs-2816	253	44	,	,	PUNCT
iajs-2816	253	45	∀	∀	X
iajs-2816	253	46	�	�	NOUN
iajs-2816	253	47	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	48	�	�	PROPN
iajs-2816	253	49	∈	∈	PROPN
iajs-2816	253	50	�	�	PROPN
iajs-2816	253	51	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	253	52	�	�	PROPN
iajs-2816	253	53	,	,	PUNCT
iajs-2816	253	54	⇒	⇒	NOUN
iajs-2816	253	55	𝜆0𝐺0(	𝜆0𝐺0(	PUNCT
iajs-2816	253	56	�	�	PROPN
iajs-2816	253	57	⃗⃗	⃗⃗	PROPN
iajs-2816	253	58	�	�	PROPN
iajs-2816	253	59	)	)	PUNCT
iajs-2816	253	60	+	+	CCONJ
iajs-2816	253	61	𝜆1𝐺1(	𝜆1𝐺1(	PROPN
iajs-2816	253	62	�	�	PROPN
iajs-2816	253	63	⃗⃗	⃗⃗	PROPN
iajs-2816	253	64	�	�	PROPN
iajs-2816	253	65	)	)	PUNCT
iajs-2816	253	66	+	+	CCONJ
iajs-2816	253	67	𝜆2𝐺2(	𝜆2𝐺2(	PUNCT
iajs-2816	253	68	�	�	PROPN
iajs-2816	253	69	⃗⃗	⃗⃗	PROPN
iajs-2816	253	70	�	�	PROPN
iajs-2816	253	71	)	)	PUNCT
iajs-2816	253	72	≤	≤	NOUN
iajs-2816	253	73	𝜆0𝐺0(	𝜆0𝐺0(	NUM
iajs-2816	253	74	�	�	PROPN
iajs-2816	253	75	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	253	76	�	�	PROPN
iajs-2816	253	77	)	)	PUNCT
iajs-2816	253	78	+	+	CCONJ
iajs-2816	253	79	𝜆1𝐺1(	𝜆1𝐺1(	NOUN
iajs-2816	253	80	�	�	PROPN
iajs-2816	253	81	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	253	82	�	�	PROPN
iajs-2816	253	83	)	)	PUNCT
iajs-2816	253	84	+	+	CCONJ
iajs-2816	253	85	𝜆2𝐺2(	𝜆2𝐺2(	PUNCT
iajs-2816	253	86	�	�	PROPN
iajs-2816	253	87	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	253	88	�	�	PROPN
iajs-2816	253	89	)	)	PUNCT
iajs-2816	253	90	(	(	PUNCT
iajs-2816	253	91	44	44	NUM
iajs-2816	253	92	)	)	PUNCT
iajs-2816	253	93	let	let	VERB
iajs-2816	253	94	�	�	PROPN
iajs-2816	253	95	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	96	�	�	PROPN
iajs-2816	253	97	∈	∈	PROPN
iajs-2816	253	98	�	�	PROPN
iajs-2816	253	99	⃗⃗⃗⃗	⃗⃗⃗⃗	SYM
iajs-2816	253	100	�	�	PROPN
iajs-2816	253	101	𝐴	𝐴	PROPN
iajs-2816	253	102	,	,	PUNCT
iajs-2816	253	103	with	with	ADP
iajs-2816	253	104	𝜆2	𝜆2	PROPN
iajs-2816	253	105	≥	≥	NOUN
iajs-2816	253	106	0	0	NUM
iajs-2816	253	107	,	,	PUNCT
iajs-2816	253	108	then	then	ADV
iajs-2816	253	109	from	from	ADP
iajs-2816	253	110	(	(	PUNCT
iajs-2816	253	111	38	38	NUM
iajs-2816	253	112	)	)	PUNCT
iajs-2816	253	113	and	and	CCONJ
iajs-2816	253	114	(	(	PUNCT
iajs-2816	253	115	44	44	NUM
iajs-2816	253	116	)	)	PUNCT
iajs-2816	253	117	gives	give	VERB
iajs-2816	253	118	:	:	PUNCT
iajs-2816	253	119	𝜆0𝐺0(	𝜆0𝐺0(	PUNCT
iajs-2816	253	120	�	�	PROPN
iajs-2816	253	121	⃗⃗	⃗⃗	PROPN
iajs-2816	253	122	�	�	PROPN
iajs-2816	253	123	)	)	PUNCT
iajs-2816	253	124	≤	≤	NOUN
iajs-2816	253	125	𝜆0𝐺0(	𝜆0𝐺0(	NUM
iajs-2816	253	126	�	�	PROPN
iajs-2816	253	127	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	128	�	�	PROPN
iajs-2816	253	129	)	)	PUNCT
iajs-2816	253	130	,	,	PUNCT
iajs-2816	253	131	∀	∀	X
iajs-2816	253	132	�	�	NOUN
iajs-2816	253	133	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	134	�	�	PROPN
iajs-2816	253	135	∈	∈	PROPN
iajs-2816	253	136	�	�	PROPN
iajs-2816	253	137	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2816	253	138	�	�	PROPN
iajs-2816	253	139	⇒	⇒	PROPN
iajs-2816	253	140	𝐺0(	𝐺0(	X
iajs-2816	253	141	�	�	PROPN
iajs-2816	253	142	⃗⃗	⃗⃗	PROPN
iajs-2816	253	143	�	�	PROPN
iajs-2816	253	144	)	)	PUNCT
iajs-2816	253	145	≤	≤	NUM
iajs-2816	253	146	𝐺0(	𝐺0(	SYM
iajs-2816	253	147	�	�	NOUN
iajs-2816	253	148	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2816	253	149	�	�	PROPN
iajs-2816	253	150	)	)	PUNCT
iajs-2816	253	151	,	,	PUNCT
iajs-2816	253	152	∀	∀	X
iajs-2816	253	153	�	�	NOUN
iajs-2816	253	154	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2816	253	155	�	�	PROPN
iajs-2816	253	156	∈	∈	PROPN
iajs-2816	253	157	�	�	PROPN
iajs-2816	253	158	⃗⃗⃗⃗	⃗⃗⃗⃗	NUM
iajs-2816	253	159	�	�	PROPN
iajs-2816	253	160	,	,	PUNCT
iajs-2816	253	161	since	since	SCONJ
iajs-2816	253	162	(	(	PUNCT
iajs-2816	253	163	𝜆0	𝜆0	NOUN
iajs-2816	253	164	>	>	X
iajs-2816	253	165	0	0	NUM
iajs-2816	253	166	)	)	PUNCT
iajs-2816	253	167	.	.	PUNCT
iajs-2816	254	1	⟹	⟹	PUNCT
iajs-2816	255	1	then	then	ADV
iajs-2816	255	2	�	�	PROPN
iajs-2816	255	3	⃗⃗	⃗⃗	PROPN
iajs-2816	255	4	�	�	PROPN
iajs-2816	255	5	is	be	AUX
iajs-2816	255	6	qccoc	qccoc	PROPN
iajs-2816	255	7	.	.	PUNCT
iajs-2816	256	1	quaternary	quaternary	ADJ
iajs-2816	256	2	classical	classical	ADJ
iajs-2816	256	3	continuous	continuous	ADJ
iajs-2816	256	4	optimal	optimal	ADJ
iajs-2816	256	5	control	control	NOUN
iajs-2816	256	6	consists	consist	VERB
iajs-2816	256	7	of	of	ADP
iajs-2816	256	8	a	a	DET
iajs-2816	256	9	quaternary	quaternary	ADJ
iajs-2816	256	10	nonlinear	nonlinear	ADJ
iajs-2816	256	11	parabolic	parabolic	PROPN
iajs-2816	256	12	boundary	boundary	ADJ
iajs-2816	256	13	value	value	NOUN
iajs-2816	256	14	problem	problem	NOUN
iajs-2816	256	15	with	with	ADP
iajs-2816	256	16	a	a	DET
iajs-2816	256	17	cost	cost	NOUN
iajs-2816	256	18	function	function	NOUN
iajs-2816	256	19	and	and	CCONJ
iajs-2816	256	20	the	the	DET
iajs-2816	256	21	constraints	constraint	NOUN
iajs-2816	256	22	on	on	ADP
iajs-2816	256	23	state	state	NOUN
iajs-2816	256	24	and	and	CCONJ
iajs-2816	256	25	control	control	NOUN
iajs-2816	256	26	(	(	PUNCT
iajs-2816	256	27	equality	equality	NOUN
iajs-2816	256	28	constraint	constraint	NOUN
iajs-2816	256	29	and	and	CCONJ
iajs-2816	256	30	inequality	inequality	NOUN
iajs-2816	256	31	constraint	constraint	NOUN
iajs-2816	256	32	)	)	PUNCT
iajs-2816	256	33	.	.	PUNCT
iajs-2816	257	1	under	under	ADP
iajs-2816	257	2	appropriate	appropriate	ADJ
iajs-2816	257	3	hypotheses	hypothesis	NOUN
iajs-2816	257	4	,	,	PUNCT
iajs-2816	257	5	the	the	DET
iajs-2816	257	6	quaternary	quaternary	ADJ
iajs-2816	257	7	classical	classical	ADJ
iajs-2816	257	8	continuous	continuous	ADJ
iajs-2816	257	9	optimal	optimal	ADJ
iajs-2816	257	10	control	control	NOUN
iajs-2816	257	11	ruling	ruling	NOUN
iajs-2816	257	12	by	by	ADP
iajs-2816	257	13	the	the	DET
iajs-2816	257	14	quaternary	quaternary	PROPN
iajs-2816	257	15	nonlinear	nonlinear	PROPN
iajs-2816	257	16	parabolic	parabolic	PROPN
iajs-2816	257	17	boundary	boundary	ADJ
iajs-2816	257	18	value	value	NOUN
iajs-2816	257	19	problem	problem	NOUN
iajs-2816	257	20	is	be	AUX
iajs-2816	257	21	demonstrated	demonstrate	VERB
iajs-2816	257	22	as	as	ADP
iajs-2816	257	23	a	a	DET
iajs-2816	257	24	quaternary	quaternary	ADJ
iajs-2816	257	25	classical	classical	ADJ
iajs-2816	257	26	continuous	continuous	ADJ
iajs-2816	257	27	optimal	optimal	ADJ
iajs-2816	257	28	control	control	NOUN
iajs-2816	257	29	vector	vector	NOUN
iajs-2816	257	30	that	that	PRON
iajs-2816	257	31	ihjpas	ihjpa	VERB
iajs-2816	257	32	.	.	PUNCT
iajs-2816	258	1	53	53	NUM
iajs-2816	258	2	(	(	PUNCT
iajs-2816	258	3	3)2022	3)2022	NOUN
iajs-2816	258	4	144	144	NUM
iajs-2816	258	5	satisfies	satisfie	NOUN
iajs-2816	258	6	the	the	DET
iajs-2816	258	7	equality	equality	NOUN
iajs-2816	258	8	constraint	constraint	NOUN
iajs-2816	258	9	and	and	CCONJ
iajs-2816	258	10	inequality	inequality	NOUN
iajs-2816	258	11	constraint	constraint	NOUN
iajs-2816	258	12	.	.	PUNCT
iajs-2816	259	1	moreover	moreover	ADV
iajs-2816	259	2	,	,	PUNCT
iajs-2816	259	3	mathematical	mathematical	ADJ
iajs-2816	259	4	formulation	formulation	NOUN
iajs-2816	259	5	of	of	ADP
iajs-2816	259	6	the	the	DET
iajs-2816	259	7	quaternary	quaternary	ADJ
iajs-2816	259	8	adjoint	adjoint	NOUN
iajs-2816	259	9	equations	equation	NOUN
iajs-2816	259	10	related	relate	VERB
iajs-2816	259	11	to	to	ADP
iajs-2816	259	12	the	the	DET
iajs-2816	259	13	quaternary	quaternary	ADJ
iajs-2816	259	14	state	state	NOUN
iajs-2816	259	15	equations	equation	NOUN
iajs-2816	259	16	is	be	AUX
iajs-2816	259	17	discovered	discover	VERB
iajs-2816	259	18	so	so	ADV
iajs-2816	259	19	as	as	ADP
iajs-2816	259	20	their	their	PRON
iajs-2816	259	21	weak	weak	ADJ
iajs-2816	259	22	form	form	NOUN
iajs-2816	259	23	.	.	PUNCT
iajs-2816	260	1	the	the	DET
iajs-2816	260	2	derivation	derivation	NOUN
iajs-2816	260	3	for	for	ADP
iajs-2816	260	4	the	the	DET
iajs-2816	260	5	fréchet	fréchet	NOUN
iajs-2816	260	6	derivative	derivative	NOUN
iajs-2816	260	7	of	of	ADP
iajs-2816	260	8	the	the	DET
iajs-2816	260	9	hamiltonian	hamiltonian	NOUN
iajs-2816	260	10	is	be	AUX
iajs-2816	260	11	attained	attain	VERB
iajs-2816	260	12	.	.	PUNCT
iajs-2816	261	1	lastly	lastly	ADV
iajs-2816	261	2	,	,	PUNCT
iajs-2816	261	3	both	both	CCONJ
iajs-2816	261	4	the	the	DET
iajs-2816	261	5	necessary	necessary	ADJ
iajs-2816	261	6	conditions	condition	NOUN
iajs-2816	261	7	for	for	ADP
iajs-2816	261	8	optimality	optimality	NOUN
iajs-2816	261	9	and	and	CCONJ
iajs-2816	261	10	sufficient	sufficient	ADJ
iajs-2816	261	11	conditions	condition	NOUN
iajs-2816	261	12	for	for	ADP
iajs-2816	261	13	optimality	optimality	NOUN
iajs-2816	261	14	of	of	ADP
iajs-2816	261	15	the	the	DET
iajs-2816	261	16	proposed	propose	VERB
iajs-2816	261	17	problem	problem	NOUN
iajs-2816	261	18	are	be	AUX
iajs-2816	261	19	stated	state	VERB
iajs-2816	261	20	and	and	CCONJ
iajs-2816	261	21	proved	prove	VERB
iajs-2816	261	22	.	.	PUNCT
iajs-2816	262	1	5	5	X
iajs-2816	262	2	.	.	X
iajs-2816	262	3	conclusion	conclusion	NOUN
iajs-2816	262	4	this	this	DET
iajs-2816	262	5	work	work	NOUN
iajs-2816	262	6	studies	study	VERB
iajs-2816	262	7	the	the	DET
iajs-2816	262	8	quaternary	quaternary	ADJ
iajs-2816	262	9	classical	classical	ADJ
iajs-2816	262	10	continuous	continuous	ADJ
iajs-2816	262	11	optimal	optimal	ADJ
iajs-2816	262	12	control	control	NOUN
iajs-2816	262	13	ruling	ruling	NOUN
iajs-2816	262	14	by	by	ADP
iajs-2816	262	15	a	a	DET
iajs-2816	262	16	quaternary	quaternary	ADJ
iajs-2816	262	17	nonlinear	nonlinear	ADJ
iajs-2816	262	18	parabolic	parabolic	PROPN
iajs-2816	262	19	boundary	boundary	ADJ
iajs-2816	262	20	value	value	NOUN
iajs-2816	262	21	problem	problem	NOUN
iajs-2816	262	22	.	.	PUNCT
iajs-2816	263	1	the	the	DET
iajs-2816	263	2	existence	existence	NOUN
iajs-2816	263	3	of	of	ADP
iajs-2816	263	4	a	a	DET
iajs-2816	263	5	quaternary	quaternary	ADJ
iajs-2816	263	6	classical	classical	ADJ
iajs-2816	263	7	continuous	continuous	ADJ
iajs-2816	263	8	optimal	optimal	ADJ
iajs-2816	263	9	control	control	NOUN
iajs-2816	263	10	vector	vector	NOUN
iajs-2816	263	11	ruling	ruling	NOUN
iajs-2816	263	12	by	by	ADP
iajs-2816	263	13	the	the	DET
iajs-2816	263	14	considered	consider	VERB
iajs-2816	263	15	the	the	DET
iajs-2816	263	16	quaternary	quaternary	ADJ
iajs-2816	263	17	nonlinear	nonlinear	PROPN
iajs-2816	263	18	parabolic	parabolic	PROPN
iajs-2816	263	19	boundary	boundary	ADJ
iajs-2816	263	20	value	value	NOUN
iajs-2816	263	21	problem	problem	NOUN
iajs-2816	263	22	satisfies	satisfy	VERB
iajs-2816	263	23	the	the	DET
iajs-2816	263	24	equality	equality	NOUN
iajs-2816	263	25	constraint	constraint	NOUN
iajs-2816	263	26	,	,	PUNCT
iajs-2816	263	27	and	and	CCONJ
iajs-2816	263	28	inequality	inequality	NOUN
iajs-2816	263	29	constraint	constraint	NOUN
iajs-2816	263	30	is	be	AUX
iajs-2816	263	31	proved	prove	VERB
iajs-2816	263	32	under	under	ADP
iajs-2816	263	33	appropriate	appropriate	ADJ
iajs-2816	263	34	hypotheses	hypothesis	NOUN
iajs-2816	263	35	.	.	PUNCT
iajs-2816	264	1	moreover	moreover	ADV
iajs-2816	264	2	,	,	PUNCT
iajs-2816	264	3	mathematical	mathematical	ADJ
iajs-2816	264	4	formulation	formulation	NOUN
iajs-2816	264	5	of	of	ADP
iajs-2816	264	6	the	the	DET
iajs-2816	264	7	quaternary	quaternary	ADJ
iajs-2816	264	8	adjoint	adjoint	NOUN
iajs-2816	264	9	equations	equation	NOUN
iajs-2816	264	10	related	relate	VERB
iajs-2816	264	11	to	to	ADP
iajs-2816	264	12	the	the	DET
iajs-2816	264	13	quaternary	quaternary	ADJ
iajs-2816	264	14	state	state	NOUN
iajs-2816	264	15	equations	equation	NOUN
iajs-2816	264	16	has	have	AUX
iajs-2816	264	17	been	be	AUX
iajs-2816	264	18	discovered	discover	VERB
iajs-2816	264	19	.	.	PUNCT
iajs-2816	265	1	the	the	DET
iajs-2816	265	2	derivation	derivation	NOUN
iajs-2816	265	3	of	of	ADP
iajs-2816	265	4	the	the	DET
iajs-2816	265	5	fréchet	fréchet	NOUN
iajs-2816	265	6	derivative	derivative	NOUN
iajs-2816	265	7	is	be	AUX
iajs-2816	265	8	attained	attain	VERB
iajs-2816	265	9	.	.	PUNCT
iajs-2816	266	1	lastly	lastly	ADV
iajs-2816	266	2	,	,	PUNCT
iajs-2816	266	3	the	the	DET
iajs-2816	266	4	necessary	necessary	ADJ
iajs-2816	266	5	(	(	PUNCT
iajs-2816	266	6	conditions	condition	NOUN
iajs-2816	266	7	)	)	PUNCT
iajs-2816	266	8	theorem	theorem	NOUN
iajs-2816	266	9	for	for	ADP
iajs-2816	266	10	optimality	optimality	NOUN
iajs-2816	266	11	and	and	CCONJ
iajs-2816	266	12	the	the	DET
iajs-2816	266	13	sufficient	sufficient	ADJ
iajs-2816	266	14	(	(	PUNCT
iajs-2816	266	15	conditions	condition	NOUN
iajs-2816	266	16	)	)	PUNCT
iajs-2816	266	17	for	for	ADP
iajs-2816	266	18	optimality	optimality	NOUN
iajs-2816	266	19	of	of	ADP
iajs-2816	266	20	the	the	DET
iajs-2816	266	21	proposed	propose	VERB
iajs-2816	266	22	problem	problem	NOUN
iajs-2816	266	23	are	be	AUX
iajs-2816	266	24	stated	state	VERB
iajs-2816	266	25	and	and	CCONJ
iajs-2816	266	26	demonstrated	demonstrate	VERB
iajs-2816	266	27	.	.	PUNCT
iajs-2816	267	1	references	reference	NOUN
iajs-2816	267	2	1	1	NUM
iajs-2816	267	3	.	.	PUNCT
iajs-2816	268	1	ameen	ameen	NOUN
iajs-2816	268	2	,	,	PUNCT
iajs-2816	268	3	at	at	ADP
iajs-2816	268	4	;	;	PUNCT
iajs-2816	268	5	ismael	ismael	PROPN
iajs-2816	268	6	,	,	PUNCT
iajs-2816	268	7	aj	aj	PROPN
iajs-2816	268	8	.	.	PUNCT
iajs-2816	269	1	a	a	DET
iajs-2816	269	2	detection	detection	NOUN
iajs-2816	269	3	of	of	ADP
iajs-2816	269	4	wheat	wheat	NOUN
iajs-2816	269	5	damping	damp	VERB
iajs-2816	269	6	off	off	ADP
iajs-2816	269	7	and	and	CCONJ
iajs-2816	269	8	root	root	NOUN
iajs-2816	269	9	rot	rot	NOUN
iajs-2816	269	10	disease	disease	NOUN
iajs-2816	269	11	pathogenic	pathogenic	ADJ
iajs-2816	269	12	fungi	fungus	NOUN
iajs-2816	269	13	and	and	CCONJ
iajs-2816	269	14	it	it	PRON
iajs-2816	269	15	bio	bio	INTJ
iajs-2816	269	16	control	control	PROPN
iajs-2816	269	17	by	by	ADP
iajs-2816	269	18	pseudomonas	pseudomona	NOUN
iajs-2816	269	19	fluorescens	fluorescen	NOUN
iajs-2816	269	20	.	.	PUNCT
iajs-2816	270	1	baghdad	baghdad	PROPN
iajs-2816	270	2	science	science	PROPN
iajs-2816	270	3	journal	journal	PROPN
iajs-2816	270	4	.	.	PUNCT
iajs-2816	271	1	2017,14,1	2017,14,1	NUM
iajs-2816	271	2	,	,	PUNCT
iajs-2816	271	3	22	22	NUM
iajs-2816	271	4	-	-	SYM
iajs-2816	271	5	31	31	NUM
iajs-2816	271	6	.	.	PUNCT
iajs-2816	272	1	2	2	NUM
iajs-2816	272	2	.	.	X
iajs-2816	272	3	syahrini	syahrini	PROPN
iajs-2816	272	4	,	,	PUNCT
iajs-2816	272	5	i.	i.	NOUN
iajs-2816	272	6	;	;	PUNCT
iajs-2816	272	7	masabar	masabar	PROPN
iajs-2816	272	8	,	,	PUNCT
iajs-2816	272	9	r.	r.	PROPN
iajs-2816	272	10	;	;	PUNCT
iajs-2816	272	11	aliasuddin	aliasuddin	PROPN
iajs-2816	272	12	,	,	PUNCT
iajs-2816	272	13	a.	a.	NOUN
iajs-2816	272	14	;	;	PUNCT
iajs-2816	272	15	munzir	munzir	NOUN
iajs-2816	272	16	,	,	PUNCT
iajs-2816	272	17	s.	s.	PROPN
iajs-2816	272	18	;	;	PUNCT
iajs-2816	272	19	hazim	hazim	NOUN
iajs-2816	272	20	,	,	PUNCT
iajs-2816	272	21	y.	y.	VERB
iajs-2816	272	22	the	the	DET
iajs-2816	272	23	application	application	NOUN
iajs-2816	272	24	of	of	ADP
iajs-2816	272	25	optimal	optimal	ADJ
iajs-2816	272	26	control	control	NOUN
iajs-2816	272	27	through	through	ADP
iajs-2816	272	28	fiscal	fiscal	ADJ
iajs-2816	272	29	policy	policy	NOUN
iajs-2816	272	30	on	on	ADP
iajs-2816	272	31	indonesian	indonesian	ADJ
iajs-2816	272	32	economy	economy	NOUN
iajs-2816	272	33	.	.	PUNCT
iajs-2816	273	1	the	the	DET
iajs-2816	273	2	journal	journal	NOUN
iajs-2816	273	3	of	of	ADP
iajs-2816	273	4	asian	asian	ADJ
iajs-2816	273	5	finance	finance	NOUN
iajs-2816	273	6	,	,	PUNCT
iajs-2816	273	7	economics	economic	NOUN
iajs-2816	273	8	and	and	CCONJ
iajs-2816	273	9	business	business	NOUN
iajs-2816	273	10	.	.	PUNCT
iajs-2816	274	1	2021	2021	NUM
iajs-2816	274	2	,	,	PUNCT
iajs-2816	274	3	8	8	NUM
iajs-2816	274	4	,	,	PUNCT
iajs-2816	274	5	3	3	NUM
iajs-2816	274	6	,	,	PUNCT
iajs-2816	274	7	0741	0741	NUM
iajs-2816	274	8	-	-	SYM
iajs-2816	274	9	0750	0750	NUM
iajs-2816	274	10	.	.	PUNCT
iajs-2816	275	1	3	3	X
iajs-2816	275	2	.	.	X
iajs-2816	275	3	rigatos	rigato	NOUN
iajs-2816	275	4	,	,	PUNCT
iajs-2816	275	5	g.	g.	PROPN
iajs-2816	275	6	;	;	PUNCT
iajs-2816	275	7	abbaszadeh	abbaszadeh	PROPN
iajs-2816	275	8	,	,	PUNCT
iajs-2816	275	9	m.	m.	NOUN
iajs-2816	275	10	nonlinear	nonlinear	PROPN
iajs-2816	275	11	optimal	optimal	ADJ
iajs-2816	275	12	control	control	NOUN
iajs-2816	275	13	for	for	ADP
iajs-2816	275	14	multi	multi	ADJ
iajs-2816	275	15	-	-	ADJ
iajs-2816	275	16	dof	dof	ADJ
iajs-2816	275	17	robotic	robotic	ADJ
iajs-2816	275	18	manipulators	manipulator	NOUN
iajs-2816	275	19	with	with	ADP
iajs-2816	275	20	flexible	flexible	ADJ
iajs-2816	275	21	joints	joint	NOUN
iajs-2816	275	22	.	.	PUNCT
iajs-2816	276	1	optim	optim	ADJ
iajs-2816	276	2	.	.	PUNCT
iajs-2816	277	1	control	control	PROPN
iajs-2816	277	2	appl	appl	PROPN
iajs-2816	277	3	.	.	PUNCT
iajs-2816	278	1	methods	method	NOUN
iajs-2816	278	2	.	.	PUNCT
iajs-2816	279	1	2021	2021	NUM
iajs-2816	279	2	,	,	PUNCT
iajs-2816	279	3	42,6	42,6	NOUN
iajs-2816	279	4	,	,	PUNCT
iajs-2816	279	5	1708	1708	NUM
iajs-2816	279	6	-	-	SYM
iajs-2816	279	7	1733	1733	NUM
iajs-2816	279	8	.	.	PUNCT
iajs-2816	280	1	staffetti	staffetti	NOUN
iajs-2816	280	2	e	e	PROPN
iajs-2816	280	3	;	;	PUNCT
iajs-2816	280	4	li	li	PROPN
iajs-2816	280	5	x	x	PROPN
iajs-2816	280	6	;	;	PUNCT
iajs-2816	280	7	matsuno	matsuno	PROPN
iajs-2816	280	8	y	y	PROPN
iajs-2816	280	9	;	;	PUNCT
iajs-2816	280	10	soler	soler	PROPN
iajs-2816	280	11	m.	m.	PROPN
iajs-2816	280	12	optimal	optimal	ADJ
iajs-2816	280	13	control	control	NOUN
iajs-2816	280	14	techniques	technique	NOUN
iajs-2816	280	15	in	in	ADP
iajs-2816	280	16	aircraft	aircraft	NOUN
iajs-2816	280	17	guidance	guidance	NOUN
iajs-2816	280	18	and	and	CCONJ
iajs-2816	280	19	control	control	VERB
iajs-2816	280	20	international	international	ADJ
iajs-2816	280	21	journal	journal	NOUN
iajs-2816	280	22	of	of	ADP
iajs-2816	280	23	aerospace	aerospace	NOUN
iajs-2816	280	24	engineering	engineering	NOUN
iajs-2816	280	25	.	.	PUNCT
iajs-2816	281	1	2019	2019	NUM
iajs-2816	281	2	.	.	X
iajs-2816	282	1	4	4	X
iajs-2816	282	2	.	.	NOUN
iajs-2816	282	3	warga	warga	PROPN
iajs-2816	282	4	,	,	PUNCT
iajs-2816	282	5	j.	j.	PROPN
iajs-2816	282	6	optimal	optimal	ADJ
iajs-2816	282	7	control	control	NOUN
iajs-2816	282	8	of	of	ADP
iajs-2816	282	9	differential	differential	ADJ
iajs-2816	282	10	and	and	CCONJ
iajs-2816	282	11	functional	functional	ADJ
iajs-2816	282	12	equations	equation	NOUN
iajs-2816	282	13	.	.	PUNCT
iajs-2816	282	14	;	;	PUNCT
iajs-2816	282	15	academic	academic	ADJ
iajs-2816	282	16	press	press	NOUN
iajs-2816	282	17	:	:	PUNCT
iajs-2816	282	18	new	new	PROPN
iajs-2816	282	19	york	york	PROPN
iajs-2816	282	20	and	and	CCONJ
iajs-2816	282	21	london	london	PROPN
iajs-2816	282	22	,	,	PUNCT
iajs-2816	282	23	1972	1972	NUM
iajs-2816	282	24	.	.	PUNCT
iajs-2816	283	1	isbn	isbn	NOUN
iajs-2816	283	2	:	:	PUNCT
iajs-2816	283	3	9781483259192	9781483259192	NUM
iajs-2816	283	4	.	.	PUNCT
iajs-2816	284	1	5	5	X
iajs-2816	284	2	.	.	X
iajs-2816	284	3	lions	lion	NOUN
iajs-2816	284	4	,	,	PUNCT
iajs-2816	284	5	j.l	j.l	PROPN
iajs-2816	284	6	.	.	PROPN
iajs-2816	284	7	optimal	optimal	ADJ
iajs-2816	284	8	control	control	NOUN
iajs-2816	284	9	of	of	ADP
iajs-2816	284	10	systems	system	NOUN
iajs-2816	284	11	governed	govern	VERB
iajs-2816	284	12	by	by	ADP
iajs-2816	284	13	partial	partial	ADJ
iajs-2816	284	14	differential	differential	NOUN
iajs-2816	284	15	equations	equation	NOUN
iajs-2816	284	16	;	;	PUNCT
iajs-2816	284	17	spriger	spriger	NOUN
iajs-2816	284	18	-	-	PUNCT
iajs-2816	284	19	verlag	verlag	PROPN
iajs-2816	284	20	:	:	PUNCT
iajs-2816	284	21	new	new	PROPN
iajs-2816	284	22	york	york	PROPN
iajs-2816	284	23	,	,	PUNCT
iajs-2816	284	24	1972	1972	NUM
iajs-2816	284	25	.	.	PUNCT
iajs-2816	285	1	6	6	NUM
iajs-2816	285	2	.	.	NUM
iajs-2816	285	3	chryssoverghi	chryssoverghi	PROPN
iajs-2816	285	4	,	,	PUNCT
iajs-2816	285	5	i.	i.	PROPN
iajs-2816	285	6	;	;	PUNCT
iajs-2816	285	7	al	al	PROPN
iajs-2816	285	8	-	-	PUNCT
iajs-2816	285	9	hawasy	hawasy	PROPN
iajs-2816	285	10	,	,	PUNCT
iajs-2816	285	11	j.	j.	PROPN
iajs-2816	285	12	the	the	DET
iajs-2816	285	13	continuous	continuous	ADJ
iajs-2816	285	14	classical	classical	ADJ
iajs-2816	285	15	optimal	optimal	ADJ
iajs-2816	285	16	control	control	NOUN
iajs-2816	285	17	problem	problem	NOUN
iajs-2816	285	18	of	of	ADP
iajs-2816	285	19	semi	semi	ADJ
iajs-2816	285	20	linear	linear	PROPN
iajs-2816	285	21	parabolic	parabolic	ADJ
iajs-2816	285	22	equations	equation	NOUN
iajs-2816	285	23	(	(	PUNCT
iajs-2816	285	24	ccocp	ccocp	NOUN
iajs-2816	285	25	)	)	PUNCT
iajs-2816	285	26	.	.	PUNCT
iajs-2816	286	1	j.	j.	PROPN
iajs-2816	286	2	of	of	ADP
iajs-2816	286	3	kerbala	kerbala	PROPN
iajs-2816	286	4	university.2010	university.2010	PROPN
iajs-2816	286	5	,	,	PUNCT
iajs-2816	286	6	8	8	NUM
iajs-2816	286	7	,	,	PUNCT
iajs-2816	286	8	3	3	NUM
iajs-2816	286	9	.	.	NOUN
iajs-2816	286	10	7	7	NUM
iajs-2816	286	11	.	.	X
iajs-2816	287	1	brett	brett	PROPN
iajs-2816	287	2	,	,	PUNCT
iajs-2816	287	3	c.	c.	PROPN
iajs-2816	287	4	;	;	PUNCT
iajs-2816	287	5	dedner	dedner	NOUN
iajs-2816	287	6	,	,	PUNCT
iajs-2816	287	7	a.	a.	PROPN
iajs-2816	287	8	;	;	PUNCT
iajs-2816	287	9	elliott	elliott	PROPN
iajs-2816	287	10	,	,	PUNCT
iajs-2816	287	11	c.	c.	PROPN
iajs-2816	287	12	optimal	optimal	ADJ
iajs-2816	287	13	control	control	NOUN
iajs-2816	287	14	of	of	ADP
iajs-2816	287	15	elliptic	elliptic	ADJ
iajs-2816	287	16	pdes	pde	NOUN
iajs-2816	287	17	at	at	ADP
iajs-2816	287	18	points	point	NOUN
iajs-2816	287	19	.	.	PUNCT
iajs-2816	288	1	i	i	PRON
iajs-2816	288	2	m	m	VERB
iajs-2816	288	3	a	a	DET
iajs-2816	288	4	journal	journal	NOUN
iajs-2816	288	5	of	of	ADP
iajs-2816	288	6	numerical	numerical	ADJ
iajs-2816	288	7	analysis	analysis	NOUN
iajs-2816	288	8	.	.	PUNCT
iajs-2816	289	1	2015	2015	NUM
iajs-2816	289	2	,	,	PUNCT
iajs-2816	289	3	36	36	NUM
iajs-2816	289	4	,	,	PUNCT
iajs-2816	289	5	3	3	NUM
iajs-2816	289	6	,	,	PUNCT
iajs-2816	289	7	1	1	NUM
iajs-2816	289	8	34	34	NUM
iajs-2816	289	9	.	.	NOUN
iajs-2816	289	10	8	8	NUM
iajs-2816	289	11	.	.	PUNCT
iajs-2816	290	1	al	al	PROPN
iajs-2816	290	2	-	-	PUNCT
iajs-2816	290	3	hawasy	hawasy	PROPN
iajs-2816	290	4	,	,	PUNCT
iajs-2816	290	5	j.	j.	PROPN
iajs-2816	290	6	the	the	DET
iajs-2816	290	7	continuous	continuous	ADJ
iajs-2816	290	8	classical	classical	ADJ
iajs-2816	290	9	optimal	optimal	ADJ
iajs-2816	290	10	control	control	NOUN
iajs-2816	290	11	of	of	ADP
iajs-2816	290	12	a	a	DET
iajs-2816	290	13	nonlinear	nonlinear	ADJ
iajs-2816	290	14	hyperbolic	hyperbolic	ADJ
iajs-2816	290	15	equation	equation	NOUN
iajs-2816	290	16	(	(	PUNCT
iajs-2816	290	17	ccocp	ccocp	NOUN
iajs-2816	290	18	)	)	PUNCT
iajs-2816	290	19	.	.	PUNCT
iajs-2816	291	1	al	al	PROPN
iajs-2816	291	2	-	-	PUNCT
iajs-2816	291	3	mustansiriyah	mustansiriyah	PROPN
iajs-2816	291	4	journal	journal	NOUN
iajs-2816	291	5	of	of	ADP
iajs-2816	291	6	science	science	NOUN
iajs-2816	291	7	.	.	PUNCT
iajs-2816	292	1	2008	2008	NUM
iajs-2816	292	2	,	,	PUNCT
iajs-2816	292	3	19	19	NUM
iajs-2816	292	4	,	,	PUNCT
iajs-2816	292	5	8	8	NUM
iajs-2816	292	6	,	,	PUNCT
iajs-2816	292	7	96	96	NUM
iajs-2816	292	8	110	110	NUM
iajs-2816	292	9	.	.	PUNCT
iajs-2816	293	1	9	9	NUM
iajs-2816	293	2	.	.	X
iajs-2816	294	1	al	al	PROPN
iajs-2816	294	2	-	-	PUNCT
iajs-2816	294	3	hawasy	hawasy	PROPN
iajs-2816	294	4	,	,	PUNCT
iajs-2816	294	5	j.	j.	PROPN
iajs-2816	294	6	;	;	PUNCT
iajs-2816	294	7	kadhem	kadhem	PROPN
iajs-2816	294	8	,	,	PUNCT
iajs-2816	294	9	g.m	g.m	PROPN
iajs-2816	294	10	.	.	PUNCT
iajs-2816	295	1	the	the	DET
iajs-2816	295	2	continuous	continuous	ADJ
iajs-2816	295	3	classical	classical	ADJ
iajs-2816	295	4	optimal	optimal	ADJ
iajs-2816	295	5	control	control	NOUN
iajs-2816	295	6	for	for	ADP
iajs-2816	295	7	coupled	couple	VERB
iajs-2816	295	8	nonlinear	nonlinear	ADJ
iajs-2816	295	9	parabolic	parabolic	ADJ
iajs-2816	295	10	partial	partial	ADJ
iajs-2816	295	11	differential	differential	NOUN
iajs-2816	295	12	equations	equation	NOUN
iajs-2816	295	13	with	with	ADP
iajs-2816	295	14	equality	equality	NOUN
iajs-2816	295	15	and	and	CCONJ
iajs-2816	295	16	inequality	inequality	NOUN
iajs-2816	295	17	constraints	constraint	NOUN
iajs-2816	295	18	.	.	PUNCT
iajs-2816	296	1	j.	j.	PROPN
iajs-2816	296	2	of	of	ADP
iajs-2816	296	3	al	al	PROPN
iajs-2816	296	4	-	-	PUNCT
iajs-2816	296	5	nahrain	nahrain	PROPN
iajs-2816	296	6	university	university	NOUN
iajs-2816	296	7	.	.	PUNCT
iajs-2816	297	1	2016	2016	NUM
iajs-2816	297	2	,	,	PUNCT
iajs-2816	297	3	19	19	NUM
iajs-2816	297	4	,	,	PUNCT
iajs-2816	297	5	1	1	NUM
iajs-2816	297	6	,	,	PUNCT
iajs-2816	297	7	173	173	NUM
iajs-2816	297	8	186	186	NUM
iajs-2816	297	9	.	.	PUNCT
iajs-2816	298	1	10	10	NUM
iajs-2816	298	2	.	.	PUNCT
iajs-2816	299	1	al	al	PROPN
iajs-2816	299	2	-	-	PUNCT
iajs-2816	299	3	rawdhanee	rawdhanee	NOUN
iajs-2816	299	4	,	,	PUNCT
iajs-2816	299	5	e.h	e.h	PROPN
iajs-2816	299	6	.	.	PROPN
iajs-2816	299	7	;	;	PUNCT
iajs-2816	299	8	the	the	DET
iajs-2816	299	9	continuous	continuous	ADJ
iajs-2816	299	10	classical	classical	ADJ
iajs-2816	299	11	optimal	optimal	ADJ
iajs-2816	299	12	control	control	NOUN
iajs-2816	299	13	of	of	ADP
iajs-2816	299	14	a	a	DET
iajs-2816	299	15	couple	couple	NOUN
iajs-2816	299	16	non	non	ADJ
iajs-2816	299	17	-	-	ADJ
iajs-2816	299	18	linear	linear	ADJ
iajs-2816	299	19	elliptic	elliptic	ADJ
iajs-2816	299	20	partial	partial	ADJ
iajs-2816	299	21	differential	differential	NOUN
iajs-2816	299	22	equations	equation	NOUN
iajs-2816	299	23	.	.	PUNCT
iajs-2816	300	1	m.sc	m.sc	PROPN
iajs-2816	300	2	.	.	PUNCT
iajs-2816	301	1	thesis	thesis	NOUN
iajs-2816	301	2	,	,	PUNCT
iajs-2816	301	3	baghdad	baghdad	PROPN
iajs-2816	301	4	-	-	PUNCT
iajs-2816	301	5	iraq	iraq	PROPN
iajs-2816	301	6	:	:	PUNCT
iajs-2816	301	7	al	al	ADJ
iajs-2816	301	8	-	-	PUNCT
iajs-2816	301	9	mustansiriyah	mustansiriyah	NOUN
iajs-2816	301	10	university;2015	university;2015	PROPN
iajs-2816	301	11	.	.	PROPN
iajs-2816	301	12	11	11	NUM
iajs-2816	301	13	.	.	PUNCT
iajs-2816	302	1	al	al	PROPN
iajs-2816	302	2	-	-	PUNCT
iajs-2816	302	3	hawasy	hawasy	PROPN
iajs-2816	302	4	,	,	PUNCT
iajs-2816	302	5	j.	j.	PROPN
iajs-2816	302	6	the	the	DET
iajs-2816	302	7	continuous	continuous	ADJ
iajs-2816	302	8	classical	classical	ADJ
iajs-2816	302	9	optimal	optimal	ADJ
iajs-2816	302	10	control	control	NOUN
iajs-2816	302	11	of	of	ADP
iajs-2816	302	12	a	a	DET
iajs-2816	302	13	couple	couple	NOUN
iajs-2816	302	14	nonlinear	nonlinear	ADJ
iajs-2816	302	15	hyperbolic	hyperbolic	ADJ
iajs-2816	302	16	partial	partial	ADJ
iajs-2816	302	17	differential	differential	NOUN
iajs-2816	302	18	equations	equation	NOUN
iajs-2816	302	19	with	with	ADP
iajs-2816	302	20	equality	equality	NOUN
iajs-2816	302	21	and	and	CCONJ
iajs-2816	302	22	inequality	inequality	NOUN
iajs-2816	302	23	constraints	constraint	NOUN
iajs-2816	302	24	.	.	PUNCT
iajs-2816	303	1	iraqi	iraqi	ADJ
iajs-2816	303	2	journal	journal	PROPN
iajs-2816	303	3	of	of	ADP
iajs-2816	303	4	science	science	NOUN
iajs-2816	303	5	.	.	PUNCT
iajs-2816	304	1	2016	2016	NUM
iajs-2816	304	2	,	,	PUNCT
iajs-2816	304	3	57	57	NUM
iajs-2816	304	4	,	,	PUNCT
iajs-2816	304	5	2c	2c	NUM
iajs-2816	304	6	,	,	PUNCT
iajs-2816	304	7	1528	1528	NUM
iajs-2816	304	8	1538	1538	NUM
iajs-2816	304	9	.	.	PUNCT
iajs-2816	305	1	13	13	NUM
iajs-2816	305	2	.	.	PUNCT
iajs-2816	306	1	al	al	PROPN
iajs-2816	306	2	-	-	PUNCT
iajs-2816	306	3	hawasy	hawasy	PROPN
iajs-2816	306	4	,	,	PUNCT
iajs-2816	306	5	j.	j.	PROPN
iajs-2816	306	6	;	;	PUNCT
iajs-2816	306	7	jaber	jaber	PROPN
iajs-2816	306	8	,	,	PUNCT
iajs-2816	306	9	m.a.k	m.a.k	NOUN
iajs-2816	306	10	.	.	PUNCT
iajs-2816	307	1	the	the	DET
iajs-2816	307	2	continuous	continuous	ADJ
iajs-2816	307	3	classical	classical	ADJ
iajs-2816	307	4	optimal	optimal	ADJ
iajs-2816	307	5	control	control	NOUN
iajs-2816	307	6	governing	govern	VERB
iajs-2816	307	7	by	by	ADP
iajs-2816	307	8	ihjpas	ihjpa	NOUN
iajs-2816	307	9	.	.	PUNCT
iajs-2816	308	1	53	53	NUM
iajs-2816	308	2	(	(	PUNCT
iajs-2816	308	3	3)2022	3)2022	NOUN
iajs-2816	308	4	145	145	NUM
iajs-2816	308	5	triple	triple	ADJ
iajs-2816	308	6	linear	linear	ADJ
iajs-2816	308	7	parabolic	parabolic	ADJ
iajs-2816	308	8	boundary	boundary	ADJ
iajs-2816	308	9	value	value	NOUN
iajs-2816	308	10	problem	problem	NOUN
iajs-2816	308	11	.	.	PUNCT
iajs-2816	309	1	ibn	ibn	PROPN
iajs-2816	309	2	al	al	PROPN
iajs-2816	309	3	haitham	haitham	PROPN
iajs-2816	309	4	jour	jour	PROPN
iajs-2816	309	5	.	.	PROPN
iajs-2816	310	1	for	for	ADP
iajs-2816	310	2	pure	pure	ADJ
iajs-2816	310	3	&	&	CCONJ
iajs-2816	310	4	appl	appl	PROPN
iajs-2816	310	5	.	.	PUNCT
iajs-2816	311	1	sci	sci	PROPN
iajs-2816	311	2	.	.	PROPN
iajs-2816	311	3	2020	2020	NUM
iajs-2816	311	4	,	,	PUNCT
iajs-2816	311	5	33	33	NUM
iajs-2816	311	6	,	,	PUNCT
iajs-2816	311	7	1	1	NUM
iajs-2816	311	8	,	,	PUNCT
iajs-2816	311	9	129	129	NUM
iajs-2816	311	10	142	142	NUM
iajs-2816	311	11	.	.	PUNCT
iajs-2816	312	1	14	14	NUM
iajs-2816	312	2	.	.	PUNCT
iajs-2816	313	1	al	al	PROPN
iajs-2816	313	2	-	-	PUNCT
iajs-2816	313	3	hawasy	hawasy	PROPN
iajs-2816	313	4	,	,	PUNCT
iajs-2816	313	5	j.	j.	PROPN
iajs-2816	313	6	;	;	PUNCT
iajs-2816	313	7	jasim	jasim	PROPN
iajs-2816	313	8	,	,	PUNCT
iajs-2816	313	9	d.a	d.a	PROPN
iajs-2816	313	10	.	.	PUNCT
iajs-2816	314	1	the	the	DET
iajs-2816	314	2	continuous	continuous	ADJ
iajs-2816	314	3	classical	classical	ADJ
iajs-2816	314	4	optimal	optimal	ADJ
iajs-2816	314	5	control	control	NOUN
iajs-2816	314	6	problems	problem	NOUN
iajs-2816	314	7	for	for	ADP
iajs-2816	314	8	triple	triple	ADJ
iajs-2816	314	9	nonlinear	nonlinear	ADJ
iajs-2816	314	10	elliptic	elliptic	ADJ
iajs-2816	314	11	partial	partial	ADJ
iajs-2816	314	12	differential	differential	NOUN
iajs-2816	314	13	equations	equation	NOUN
iajs-2816	314	14	.	.	PUNCT
iajs-2816	315	1	ibn	ibn	PROPN
iajs-2816	315	2	al	al	PROPN
iajs-2816	315	3	-	-	PUNCT
iajs-2816	315	4	haitham	haitham	PROPN
iajs-2816	315	5	jour	jour	X
iajs-2816	315	6	.	.	PROPN
iajs-2816	315	7	for	for	ADP
iajs-2816	315	8	pure	pure	ADJ
iajs-2816	315	9	&	&	CCONJ
iajs-2816	315	10	appl	appl	PROPN
iajs-2816	315	11	.	.	PUNCT
iajs-2816	316	1	sci	sci	PROPN
iajs-2816	316	2	.	.	PROPN
iajs-2816	316	3	2020	2020	NUM
iajs-2816	316	4	,	,	PUNCT
iajs-2816	316	5	33	33	NUM
iajs-2816	316	6	,	,	PUNCT
iajs-2816	316	7	3	3	NUM
iajs-2816	316	8	,	,	PUNCT
iajs-2816	316	9	101	101	NUM
iajs-2816	316	10	112	112	NUM
iajs-2816	316	11	.	.	PUNCT
iajs-2816	316	12	15	15	NUM
iajs-2816	316	13	.	.	PUNCT
iajs-2816	317	1	al	al	PROPN
iajs-2816	317	2	-	-	PUNCT
iajs-2816	317	3	hawasy	hawasy	PROPN
iajs-2816	317	4	,	,	PUNCT
iajs-2816	317	5	j.a	j.a	PROPN
iajs-2816	317	6	.	.	PROPN
iajs-2816	317	7	;	;	PUNCT
iajs-2816	317	8	ali	ali	PROPN
iajs-2816	317	9	,	,	PUNCT
iajs-2816	317	10	l.h	l.h	PROPN
iajs-2816	317	11	.	.	PROPN
iajs-2816	317	12	boundary	boundary	ADJ
iajs-2816	317	13	optimal	optimal	ADJ
iajs-2816	317	14	control	control	NOUN
iajs-2816	317	15	for	for	ADP
iajs-2816	317	16	triple	triple	ADJ
iajs-2816	317	17	nonlinear	nonlinear	ADJ
iajs-2816	317	18	hyperbolic	hyperbolic	ADJ
iajs-2816	317	19	boundary	boundary	ADJ
iajs-2816	317	20	value	value	NOUN
iajs-2816	317	21	problem	problem	NOUN
iajs-2816	317	22	with	with	ADP
iajs-2816	317	23	state	state	NOUN
iajs-2816	317	24	constraints	constraint	NOUN
iajs-2816	317	25	.	.	PUNCT
iajs-2816	318	1	iraqi	iraqi	ADJ
iajs-2816	318	2	journal	journal	PROPN
iajs-2816	318	3	of	of	ADP
iajs-2816	318	4	science	science	NOUN
iajs-2816	318	5	.	.	PUNCT
iajs-2816	319	1	2021	2021	NUM
iajs-2816	319	2	,	,	PUNCT
iajs-2816	319	3	62	62	NUM
iajs-2816	319	4	,	,	PUNCT
iajs-2816	319	5	6	6	NUM
iajs-2816	319	6	,	,	PUNCT
iajs-2816	319	7	2009	2009	NUM
iajs-2816	319	8	2021	2021	NUM
iajs-2816	319	9	.	.	PUNCT
iajs-2816	320	1	16	16	NUM
iajs-2816	320	2	.	.	PUNCT
iajs-2816	321	1	al	al	PROPN
iajs-2816	321	2	-	-	PUNCT
iajs-2816	321	3	anbaki	anbaki	PROPN
iajs-2816	321	4	,	,	PUNCT
iajs-2816	321	5	w.a	w.a	PROPN
iajs-2816	321	6	.	.	PUNCT
iajs-2816	322	1	the	the	DET
iajs-2816	322	2	classical	classical	ADJ
iajs-2816	322	3	continuous	continuous	ADJ
iajs-2816	322	4	optimal	optimal	ADJ
iajs-2816	322	5	control	control	NOUN
iajs-2816	322	6	for	for	ADP
iajs-2816	322	7	quaternary	quaternary	ADJ
iajs-2816	322	8	nonlinear	nonlinear	ADJ
iajs-2816	322	9	parabolic	parabolic	PROPN
iajs-2816	322	10	boundary	boundary	ADJ
iajs-2816	322	11	value	value	NOUN
iajs-2816	322	12	problem	problem	NOUN
iajs-2816	322	13	.	.	PUNCT
iajs-2816	323	1	msc	msc	PROPN
iajs-2816	323	2	.	.	PROPN
iajs-2816	324	1	thesis	thesis	PROPN
iajs-2816	324	2	,	,	PUNCT
iajs-2816	324	3	mustansiriyah	mustansiriyah	ADJ
iajs-2816	324	4	university	university	NOUN
iajs-2816	324	5	,	,	PUNCT
iajs-2816	324	6	college	college	NOUN
iajs-2816	324	7	of	of	ADP
iajs-2816	324	8	sciences	science	NOUN
iajs-2816	324	9	,	,	PUNCT
iajs-2816	324	10	department	department	NOUN
iajs-2816	324	11	of	of	ADP
iajs-2816	324	12	mathematics	mathematics	PROPN
iajs-2816	324	13	,	,	PUNCT
iajs-2816	324	14	baghdad	baghdad	PROPN
iajs-2816	324	15	,	,	PUNCT
iajs-2816	324	16	iraq	iraq	PROPN
iajs-2816	324	17	.	.	PUNCT
iajs-2816	325	1	2022	2022	NUM
iajs-2816	325	2	.	.	PUNCT