id	sid	tid	token	lemma	pos
iajs-2478	1	1	microsoft	microsoft	PROPN
iajs-2478	1	2	word	word	NOUN
iajs-2478	1	3	113	113	NUM
iajs-2478	1	4	-	-	SYM
iajs-2478	1	5	126	126	NUM
iajs-2478	1	6	  	  	SPACE
iajs-2478	1	7	113	113	NUM
iajs-2478	1	8	ibn	ibn	PROPN
iajs-2478	1	9	al	al	PROPN
iajs-2478	1	10	-	-	PUNCT
iajs-2478	1	11	haitham	haitham	PROPN
iajs-2478	1	12	jour	jour	X
iajs-2478	1	13	.	.	PROPN
iajs-2478	2	1	for	for	ADP
iajs-2478	2	2	pure	pure	ADJ
iajs-2478	2	3	&	&	CCONJ
iajs-2478	2	4	appl	appl	PROPN
iajs-2478	2	5	.	.	PUNCT
iajs-2478	3	1	sci	sci	PROPN
iajs-2478	3	2	.	.	PROPN
iajs-2478	4	1	33	33	NUM
iajs-2478	4	2	(	(	PUNCT
iajs-2478	4	3	3	3	NUM
iajs-2478	4	4	)	)	PUNCT
iajs-2478	4	5	2020	2020	NUM
iajs-2478	4	6	      	      	SPACE
iajs-2478	4	7	the	the	DET
iajs-2478	4	8	continuous	continuous	ADJ
iajs-2478	4	9	classical	classical	ADJ
iajs-2478	4	10	boundary	boundary	ADJ
iajs-2478	4	11	optimal	optimal	ADJ
iajs-2478	4	12	control	control	NOUN
iajs-2478	4	13	vector	vector	NOUN
iajs-2478	4	14	governing	governing	NOUN
iajs-2478	4	15	by	by	ADP
iajs-2478	4	16	triple	triple	ADJ
iajs-2478	4	17	linear	linear	ADJ
iajs-2478	4	18	partial	partial	ADJ
iajs-2478	4	19	differential	differential	ADJ
iajs-2478	4	20	equations	equation	NOUN
iajs-2478	4	21	of	of	ADP
iajs-2478	4	22	parabolic	parabolic	ADJ
iajs-2478	4	23	type	type	NOUN
iajs-2478	4	24	department	department	PROPN
iajs-2478	4	25	of	of	ADP
iajs-2478	4	26	mathematics	mathematics	PROPN
iajs-2478	4	27	,	,	PUNCT
iajs-2478	4	28	college	college	NOUN
iajs-2478	4	29	of	of	ADP
iajs-2478	4	30	science	science	NOUN
iajs-2478	4	31	,	,	PUNCT
iajs-2478	4	32	university	university	NOUN
iajs-2478	4	33	of	of	ADP
iajs-2478	4	34	mustansiriyah	mustansiriyah	NOUN
iajs-2478	4	35	,	,	PUNCT
iajs-2478	4	36	baghdad	baghdad	PROPN
iajs-2478	4	37	,	,	PUNCT
iajs-2478	4	38	iraq	iraq	PROPN
iajs-2478	4	39	.	.	PUNCT
iajs-2478	5	1	abstract	abstract	ADJ
iajs-2478	5	2	in	in	ADP
iajs-2478	5	3	this	this	DET
iajs-2478	5	4	paper	paper	NOUN
iajs-2478	5	5	,	,	PUNCT
iajs-2478	5	6	the	the	DET
iajs-2478	5	7	continuous	continuous	ADJ
iajs-2478	5	8	classical	classical	ADJ
iajs-2478	5	9	boundary	boundary	ADJ
iajs-2478	5	10	optimal	optimal	ADJ
iajs-2478	5	11	control	control	NOUN
iajs-2478	5	12	problem	problem	NOUN
iajs-2478	5	13	(	(	PUNCT
iajs-2478	5	14	ccbocp	ccbocp	NOUN
iajs-2478	5	15	)	)	PUNCT
iajs-2478	5	16	for	for	ADP
iajs-2478	5	17	triple	triple	ADJ
iajs-2478	5	18	linear	linear	ADJ
iajs-2478	5	19	partial	partial	ADJ
iajs-2478	5	20	differential	differential	ADJ
iajs-2478	5	21	equations	equation	NOUN
iajs-2478	5	22	of	of	ADP
iajs-2478	5	23	parabolic	parabolic	ADJ
iajs-2478	5	24	type	type	NOUN
iajs-2478	5	25	(	(	PUNCT
iajs-2478	5	26	tlpdepar	tlpdepar	NOUN
iajs-2478	5	27	)	)	PUNCT
iajs-2478	5	28	with	with	ADP
iajs-2478	5	29	initial	initial	ADJ
iajs-2478	5	30	and	and	CCONJ
iajs-2478	5	31	boundary	boundary	ADJ
iajs-2478	5	32	conditions	condition	NOUN
iajs-2478	5	33	(	(	PUNCT
iajs-2478	5	34	ics	ics	NOUN
iajs-2478	5	35	&	&	CCONJ
iajs-2478	5	36	bcs	bc	NOUN
iajs-2478	5	37	)	)	PUNCT
iajs-2478	5	38	is	be	AUX
iajs-2478	5	39	studied	study	VERB
iajs-2478	5	40	.	.	PUNCT
iajs-2478	6	1	the	the	DET
iajs-2478	6	2	galerkin	galerkin	ADJ
iajs-2478	6	3	method	method	NOUN
iajs-2478	6	4	(	(	PUNCT
iajs-2478	6	5	gm	gm	PROPN
iajs-2478	6	6	)	)	PUNCT
iajs-2478	6	7	is	be	AUX
iajs-2478	6	8	used	use	VERB
iajs-2478	6	9	to	to	PART
iajs-2478	6	10	prove	prove	VERB
iajs-2478	6	11	the	the	DET
iajs-2478	6	12	existence	existence	NOUN
iajs-2478	6	13	and	and	CCONJ
iajs-2478	6	14	uniqueness	uniqueness	NOUN
iajs-2478	6	15	theorem	theorem	NOUN
iajs-2478	6	16	of	of	ADP
iajs-2478	6	17	the	the	DET
iajs-2478	6	18	state	state	NOUN
iajs-2478	6	19	vector	vector	NOUN
iajs-2478	6	20	solution	solution	NOUN
iajs-2478	6	21	(	(	PUNCT
iajs-2478	6	22	svs	svs	NOUN
iajs-2478	6	23	)	)	PUNCT
iajs-2478	6	24	for	for	ADP
iajs-2478	6	25	given	give	VERB
iajs-2478	6	26	continuous	continuous	ADJ
iajs-2478	6	27	classical	classical	ADJ
iajs-2478	6	28	boundary	boundary	ADJ
iajs-2478	6	29	control	control	NOUN
iajs-2478	6	30	vector	vector	NOUN
iajs-2478	6	31	(	(	PUNCT
iajs-2478	6	32	ccbcv	ccbcv	PROPN
iajs-2478	6	33	)	)	PUNCT
iajs-2478	6	34	.	.	PUNCT
iajs-2478	7	1	the	the	DET
iajs-2478	7	2	proof	proof	NOUN
iajs-2478	7	3	of	of	ADP
iajs-2478	7	4	the	the	DET
iajs-2478	7	5	existence	existence	NOUN
iajs-2478	7	6	theorem	theorem	NOUN
iajs-2478	7	7	of	of	ADP
iajs-2478	7	8	a	a	DET
iajs-2478	7	9	continuous	continuous	ADJ
iajs-2478	7	10	classical	classical	ADJ
iajs-2478	7	11	boundary	boundary	ADJ
iajs-2478	7	12	optimal	optimal	ADJ
iajs-2478	7	13	control	control	NOUN
iajs-2478	7	14	vector	vector	NOUN
iajs-2478	7	15	(	(	PUNCT
iajs-2478	7	16	ccbocv	ccbocv	NOUN
iajs-2478	7	17	)	)	PUNCT
iajs-2478	7	18	associated	associate	VERB
iajs-2478	7	19	with	with	ADP
iajs-2478	7	20	the	the	DET
iajs-2478	7	21	tlpdepar	tlpdepar	NOUN
iajs-2478	7	22	is	be	AUX
iajs-2478	7	23	proved	prove	VERB
iajs-2478	7	24	.	.	PUNCT
iajs-2478	8	1	the	the	DET
iajs-2478	8	2	derivation	derivation	NOUN
iajs-2478	8	3	of	of	ADP
iajs-2478	8	4	the	the	DET
iajs-2478	8	5	fréchet	fréchet	NOUN
iajs-2478	8	6	derivative	derivative	ADJ
iajs-2478	8	7	(	(	PUNCT
iajs-2478	8	8	frd	frd	ADJ
iajs-2478	8	9	)	)	PUNCT
iajs-2478	8	10	for	for	ADP
iajs-2478	8	11	the	the	DET
iajs-2478	8	12	cost	cost	NOUN
iajs-2478	8	13	function	function	NOUN
iajs-2478	8	14	(	(	PUNCT
iajs-2478	8	15	cof	cof	PROPN
iajs-2478	8	16	)	)	PUNCT
iajs-2478	8	17	is	be	AUX
iajs-2478	8	18	obtained	obtain	VERB
iajs-2478	8	19	.	.	PUNCT
iajs-2478	9	1	at	at	ADP
iajs-2478	9	2	the	the	DET
iajs-2478	9	3	end	end	NOUN
iajs-2478	9	4	,	,	PUNCT
iajs-2478	9	5	the	the	DET
iajs-2478	9	6	theorem	theorem	NOUN
iajs-2478	9	7	of	of	ADP
iajs-2478	9	8	the	the	DET
iajs-2478	9	9	necessary	necessary	ADJ
iajs-2478	9	10	conditions	condition	NOUN
iajs-2478	9	11	for	for	ADP
iajs-2478	9	12	optimality	optimality	NOUN
iajs-2478	9	13	(	(	PUNCT
iajs-2478	9	14	ncsthop	ncsthop	NOUN
iajs-2478	9	15	)	)	PUNCT
iajs-2478	9	16	of	of	ADP
iajs-2478	9	17	this	this	DET
iajs-2478	9	18	problem	problem	NOUN
iajs-2478	9	19	is	be	AUX
iajs-2478	9	20	stated	state	VERB
iajs-2478	9	21	and	and	CCONJ
iajs-2478	9	22	proved	prove	VERB
iajs-2478	9	23	.	.	PUNCT
iajs-2478	10	1	keywords	keyword	NOUN
iajs-2478	10	2	:	:	PUNCT
iajs-2478	10	3	continuous	continuous	ADJ
iajs-2478	10	4	classical	classical	ADJ
iajs-2478	10	5	boundary	boundary	ADJ
iajs-2478	10	6	optimal	optimal	ADJ
iajs-2478	10	7	control	control	NOUN
iajs-2478	10	8	,	,	PUNCT
iajs-2478	10	9	triple	triple	ADJ
iajs-2478	10	10	linear	linear	ADJ
iajs-2478	10	11	partial	partial	ADJ
iajs-2478	10	12	differential	differential	NOUN
iajs-2478	10	13	equations	equation	NOUN
iajs-2478	10	14	,	,	PUNCT
iajs-2478	10	15	galerkin	galerkin	ADJ
iajs-2478	10	16	method	method	NOUN
iajs-2478	10	17	,	,	PUNCT
iajs-2478	10	18	necessary	necessary	ADJ
iajs-2478	10	19	conditions	condition	NOUN
iajs-2478	10	20	for	for	ADP
iajs-2478	10	21	optimality	optimality	NOUN
iajs-2478	10	22	.	.	PUNCT
iajs-2478	11	1	1	1	X
iajs-2478	11	2	.	.	X
iajs-2478	11	3	introduction	introduction	NOUN
iajs-2478	11	4	different	different	ADJ
iajs-2478	11	5	applications	application	NOUN
iajs-2478	11	6	for	for	ADP
iajs-2478	11	7	real	real	ADJ
iajs-2478	11	8	life	life	NOUN
iajs-2478	11	9	problems	problem	NOUN
iajs-2478	11	10	take	take	VERB
iajs-2478	11	11	a	a	DET
iajs-2478	11	12	main	main	ADJ
iajs-2478	11	13	place	place	NOUN
iajs-2478	11	14	in	in	ADP
iajs-2478	11	15	the	the	DET
iajs-2478	11	16	optimal	optimal	ADJ
iajs-2478	11	17	control	control	NOUN
iajs-2478	11	18	problems	problem	NOUN
iajs-2478	11	19	,	,	PUNCT
iajs-2478	11	20	for	for	ADP
iajs-2478	11	21	example	example	NOUN
iajs-2478	11	22	in	in	ADP
iajs-2478	11	23	medicine	medicine	NOUN
iajs-2478	11	24	[	[	X
iajs-2478	11	25	1	1	NUM
iajs-2478	11	26	]	]	PUNCT
iajs-2478	11	27	.	.	PUNCT
iajs-2478	12	1	robots	robot	NOUN
iajs-2478	12	2	[	[	X
iajs-2478	12	3	2	2	NUM
iajs-2478	12	4	]	]	PUNCT
iajs-2478	12	5	.	.	PUNCT
iajs-2478	13	1	engineering	engineer	VERB
iajs-2478	14	1	[	[	X
iajs-2478	14	2	3	3	NUM
iajs-2478	14	3	]	]	PUNCT
iajs-2478	14	4	.	.	PUNCT
iajs-2478	15	1	economic	economic	ADJ
iajs-2478	15	2	[	[	X
iajs-2478	15	3	4	4	NUM
iajs-2478	15	4	]	]	PUNCT
iajs-2478	15	5	.	.	PUNCT
iajs-2478	16	1	and	and	CCONJ
iajs-2478	16	2	many	many	ADJ
iajs-2478	16	3	others	other	NOUN
iajs-2478	16	4	fields	field	NOUN
iajs-2478	16	5	.	.	PUNCT
iajs-2478	17	1	in	in	ADP
iajs-2478	17	2	the	the	DET
iajs-2478	17	3	field	field	NOUN
iajs-2478	17	4	of	of	ADP
iajs-2478	17	5	mathematics	mathematic	NOUN
iajs-2478	17	6	,	,	PUNCT
iajs-2478	17	7	optimal	optimal	ADJ
iajs-2478	17	8	control	control	NOUN
iajs-2478	17	9	problem	problem	NOUN
iajs-2478	17	10	(	(	PUNCT
iajs-2478	17	11	ocp	ocp	PROPN
iajs-2478	17	12	)	)	PUNCT
iajs-2478	17	13	usually	usually	ADV
iajs-2478	17	14	governing	govern	VERB
iajs-2478	17	15	either	either	ADV
iajs-2478	17	16	by	by	ADP
iajs-2478	17	17	ordinary	ordinary	ADJ
iajs-2478	17	18	differential	differential	ADJ
iajs-2478	17	19	equations	equation	NOUN
iajs-2478	17	20	(	(	PUNCT
iajs-2478	17	21	odes	ode	NOUN
iajs-2478	17	22	)	)	PUNCT
iajs-2478	17	23	or	or	CCONJ
iajs-2478	17	24	partial	partial	ADJ
iajs-2478	17	25	differential	differential	ADJ
iajs-2478	17	26	equations	equation	NOUN
iajs-2478	17	27	(	(	PUNCT
iajs-2478	17	28	pdes	pde	NOUN
iajs-2478	17	29	)	)	PUNCT
iajs-2478	17	30	,	,	PUNCT
iajs-2478	17	31	examples	example	NOUN
iajs-2478	17	32	of	of	ADP
iajs-2478	17	33	ocp	ocp	PROPN
iajs-2478	17	34	which	which	PRON
iajs-2478	17	35	are	be	AUX
iajs-2478	17	36	governined	governine	VERB
iajs-2478	17	37	by	by	ADP
iajs-2478	17	38	parabolic	parabolic	ADJ
iajs-2478	17	39	,	,	PUNCT
iajs-2478	17	40	hyperbolic	hyperbolic	ADJ
iajs-2478	17	41	or	or	CCONJ
iajs-2478	17	42	elliptic	elliptic	ADJ
iajs-2478	17	43	pdes	pde	NOUN
iajs-2478	17	44	are	be	AUX
iajs-2478	17	45	studied	study	VERB
iajs-2478	17	46	by	by	ADP
iajs-2478	17	47	[	[	X
iajs-2478	17	48	5,-7	5,-7	NUM
iajs-2478	17	49	]	]	X
iajs-2478	17	50	.	.	PUNCT
iajs-2478	18	1	respectively	respectively	ADV
iajs-2478	18	2	,	,	PUNCT
iajs-2478	18	3	while	while	SCONJ
iajs-2478	18	4	ocp	ocp	PROPN
iajs-2478	18	5	which	which	PRON
iajs-2478	18	6	are	be	AUX
iajs-2478	18	7	governing	govern	VERB
iajs-2478	18	8	by	by	ADP
iajs-2478	18	9	couple	couple	NOUN
iajs-2478	18	10	of	of	ADP
iajs-2478	18	11	pdes	pde	NOUN
iajs-2478	18	12	(	(	PUNCT
iajs-2478	18	13	cpdes	cpde	NOUN
iajs-2478	18	14	)	)	PUNCT
iajs-2478	18	15	of	of	ADP
iajs-2478	18	16	parabolic	parabolic	ADJ
iajs-2478	18	17	,	,	PUNCT
iajs-2478	18	18	hyperbolic	hyperbolic	ADJ
iajs-2478	18	19	or	or	CCONJ
iajs-2478	18	20	elliptic	elliptic	ADJ
iajs-2478	18	21	type	type	NOUN
iajs-2478	18	22	are	be	AUX
iajs-2478	18	23	studied	study	VERB
iajs-2478	18	24	by	by	ADP
iajs-2478	18	25	[	[	PUNCT
iajs-2478	18	26	8	8	NUM
iajs-2478	18	27	-	-	SYM
iajs-2478	18	28	10	10	NUM
iajs-2478	18	29	]	]	PUNCT
iajs-2478	18	30	.	.	PUNCT
iajs-2478	19	1	on	on	ADP
iajs-2478	19	2	the	the	DET
iajs-2478	19	3	other	other	ADJ
iajs-2478	19	4	hand	hand	NOUN
iajs-2478	19	5	,	,	PUNCT
iajs-2478	19	6	[	[	X
iajs-2478	19	7	11	11	NUM
iajs-2478	19	8	-	-	SYM
iajs-2478	19	9	13	13	NUM
iajs-2478	19	10	]	]	PUNCT
iajs-2478	19	11	.	.	PUNCT
iajs-2478	19	12	are	be	AUX
iajs-2478	19	13	studied	study	VERB
iajs-2478	19	14	boundary	boundary	ADJ
iajs-2478	19	15	ocp	ocp	PROPN
iajs-2478	19	16	associated	associate	VERB
iajs-2478	19	17	with	with	ADP
iajs-2478	19	18	cpdes	cpde	NOUN
iajs-2478	19	19	of	of	ADP
iajs-2478	19	20	these	these	DET
iajs-2478	19	21	three	three	NUM
iajs-2478	19	22	types	type	NOUN
iajs-2478	19	23	;	;	PUNCT
iajs-2478	19	24	while	while	SCONJ
iajs-2478	19	25	[	[	X
iajs-2478	19	26	14	14	NUM
iajs-2478	19	27	,	,	PUNCT
iajs-2478	19	28	15	15	NUM
iajs-2478	19	29	]	]	PUNCT
iajs-2478	19	30	.	.	PUNCT
iajs-2478	20	1	are	be	AUX
iajs-2478	20	2	studied	study	VERB
iajs-2478	20	3	the	the	DET
iajs-2478	20	4	ocp	ocp	NOUN
iajs-2478	20	5	for	for	ADP
iajs-2478	20	6	triple	triple	ADJ
iajs-2478	20	7	pdes	pde	NOUN
iajs-2478	20	8	(	(	PUNCT
iajs-2478	20	9	tpdes	tpde	NOUN
iajs-2478	20	10	)	)	PUNCT
iajs-2478	20	11	of	of	ADP
iajs-2478	20	12	parabolic	parabolic	ADJ
iajs-2478	20	13	and	and	CCONJ
iajs-2478	20	14	elliptic	elliptic	ADJ
iajs-2478	20	15	type	type	NOUN
iajs-2478	20	16	respectively	respectively	ADV
iajs-2478	20	17	.	.	PUNCT
iajs-2478	21	1	all	all	DET
iajs-2478	21	2	these	these	DET
iajs-2478	21	3	works	work	NOUN
iajs-2478	21	4	push	push	VERB
iajs-2478	21	5	us	we	PRON
iajs-2478	21	6	to	to	PART
iajs-2478	21	7	seek	seek	VERB
iajs-2478	21	8	about	about	ADP
iajs-2478	21	9	the	the	DET
iajs-2478	21	10	ccbocv	ccbocv	NOUN
iajs-2478	21	11	for	for	ADP
iajs-2478	21	12	the	the	DET
iajs-2478	21	13	tlpdepar	tlpdepar	NOUN
iajs-2478	21	14	.	.	PUNCT
iajs-2478	22	1	this	this	DET
iajs-2478	22	2	work	work	NOUN
iajs-2478	22	3	starts	start	VERB
iajs-2478	22	4	with	with	ADP
iajs-2478	22	5	the	the	DET
iajs-2478	22	6	state	state	NOUN
iajs-2478	22	7	and	and	CCONJ
iajs-2478	22	8	prove	prove	VERB
iajs-2478	22	9	the	the	DET
iajs-2478	22	10	existence	existence	NOUN
iajs-2478	22	11	theorem	theorem	VERB
iajs-2478	22	12	of	of	ADP
iajs-2478	22	13	a	a	DET
iajs-2478	22	14	unique	unique	ADJ
iajs-2478	22	15	solution	solution	NOUN
iajs-2478	22	16	(	(	PUNCT
iajs-2478	22	17	svs	svs	NOUN
iajs-2478	22	18	)	)	PUNCT
iajs-2478	22	19	for	for	ADP
iajs-2478	22	20	the	the	DET
iajs-2478	22	21	triple	triple	ADJ
iajs-2478	22	22	state	state	NOUN
iajs-2478	22	23	equations	equation	NOUN
iajs-2478	22	24	(	(	PUNCT
iajs-2478	22	25	tses	tse	NOUN
iajs-2478	22	26	)	)	PUNCT
iajs-2478	22	27	of	of	ADP
iajs-2478	22	28	pdes	pde	NOUN
iajs-2478	22	29	of	of	ADP
iajs-2478	22	30	parabolic	parabolic	ADJ
iajs-2478	22	31	type	type	NOUN
iajs-2478	22	32	(	(	PUNCT
iajs-2478	22	33	tlpdepar	tlpdepar	NOUN
iajs-2478	22	34	)	)	PUNCT
iajs-2478	22	35	by	by	ADP
iajs-2478	22	36	using	use	VERB
iajs-2478	22	37	the	the	DET
iajs-2478	22	38	gm	gm	PROPN
iajs-2478	22	39	when	when	SCONJ
iajs-2478	22	40	the	the	DET
iajs-2478	22	41	ibn	ibn	PROPN
iajs-2478	22	42	al	al	PROPN
iajs-2478	22	43	haitham	haitham	PROPN
iajs-2478	22	44	journal	journal	PROPN
iajs-2478	22	45	for	for	ADP
iajs-2478	22	46	pure	pure	ADJ
iajs-2478	22	47	and	and	CCONJ
iajs-2478	22	48	applied	apply	VERB
iajs-2478	22	49	science	science	NOUN
iajs-2478	22	50	journal	journal	PROPN
iajs-2478	22	51	homepage	homepage	NOUN
iajs-2478	22	52	:	:	PUNCT
iajs-2478	22	53	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2478	22	54	doi	doi	NOUN
iajs-2478	22	55	:	:	PUNCT
iajs-2478	22	56	10.30526/33.3.2478	10.30526/33.3.2478	PROPN
iajs-2478	22	57	jamil	jamil	PROPN
iajs-2478	22	58	a.	a.	PROPN
iajs-2478	22	59	al	al	PROPN
iajs-2478	22	60	-	-	PUNCT
iajs-2478	22	61	hawasy	hawasy	PROPN
iajs-2478	22	62	article	article	NOUN
iajs-2478	22	63	history	history	NOUN
iajs-2478	22	64	:	:	PUNCT
iajs-2478	22	65	received	receive	VERB
iajs-2478	22	66	24	24	NUM
iajs-2478	22	67	september	september	PROPN
iajs-2478	22	68	2019	2019	NUM
iajs-2478	22	69	,	,	PUNCT
iajs-2478	22	70	accepted	accept	VERB
iajs-2478	22	71	4	4	NUM
iajs-2478	22	72	november	november	PROPN
iajs-2478	22	73	2019	2019	NUM
iajs-2478	22	74	,	,	PUNCT
iajs-2478	22	75	published	publish	VERB
iajs-2478	22	76	in	in	ADP
iajs-2478	22	77	july	july	PROPN
iajs-2478	22	78	2020	2020	NUM
iajs-2478	22	79	.	.	PUNCT
iajs-2478	23	1	mohammed	mohammed	PROPN
iajs-2478	23	2	a.	a.	PROPN
iajs-2478	23	3	k.	k.	PROPN
iajs-2478	23	4	jaber	jaber	PROPN
iajs-2478	23	5	jhawassy17@uomustansiriyah.edu.iq	jhawassy17@uomustansiriyah.edu.iq	PROPN
iajs-2478	23	6	  	  	SPACE
iajs-2478	23	7	hawasy20@	hawasy20@	X
iajs-2478	23	8	yahoo.com	yahoo.com	X
iajs-2478	23	9	  	  	SPACE
iajs-2478	23	10	114	114	NUM
iajs-2478	23	11	ibn	ibn	PROPN
iajs-2478	23	12	al	al	PROPN
iajs-2478	23	13	-	-	PUNCT
iajs-2478	23	14	haitham	haitham	PROPN
iajs-2478	23	15	jour	jour	X
iajs-2478	23	16	.	.	PROPN
iajs-2478	24	1	for	for	ADP
iajs-2478	24	2	pure	pure	ADJ
iajs-2478	24	3	&	&	CCONJ
iajs-2478	24	4	appl	appl	PROPN
iajs-2478	24	5	.	.	PUNCT
iajs-2478	25	1	sci	sci	PROPN
iajs-2478	25	2	.	.	PROPN
iajs-2478	26	1	33	33	NUM
iajs-2478	26	2	(	(	PUNCT
iajs-2478	26	3	3	3	NUM
iajs-2478	26	4	)	)	PUNCT
iajs-2478	26	5	2020	2020	NUM
iajs-2478	26	6	ccbcv	ccbcv	NOUN
iajs-2478	26	7	is	be	AUX
iajs-2478	26	8	fixed	fix	VERB
iajs-2478	26	9	,	,	PUNCT
iajs-2478	26	10	then	then	ADV
iajs-2478	26	11	we	we	PRON
iajs-2478	26	12	deals	deal	VERB
iajs-2478	26	13	with	with	ADP
iajs-2478	26	14	the	the	DET
iajs-2478	26	15	proof	proof	NOUN
iajs-2478	26	16	of	of	ADP
iajs-2478	26	17	the	the	DET
iajs-2478	26	18	existence	existence	NOUN
iajs-2478	26	19	theorem	theorem	NOUN
iajs-2478	26	20	of	of	ADP
iajs-2478	26	21	a	a	DET
iajs-2478	26	22	ccbocv	ccbocv	NOUN
iajs-2478	26	23	,	,	PUNCT
iajs-2478	26	24	the	the	DET
iajs-2478	26	25	solution	solution	NOUN
iajs-2478	26	26	vector	vector	NOUN
iajs-2478	26	27	of	of	ADP
iajs-2478	26	28	the	the	DET
iajs-2478	26	29	triple	triple	ADJ
iajs-2478	26	30	adjoint	adjoint	PROPN
iajs-2478	26	31	equations	equation	NOUN
iajs-2478	26	32	(	(	PUNCT
iajs-2478	26	33	tapes	tape	NOUN
iajs-2478	26	34	)	)	PUNCT
iajs-2478	26	35	associated	associate	VERB
iajs-2478	26	36	the	the	DET
iajs-2478	26	37	tlpdepar	tlpdepar	NOUN
iajs-2478	26	38	is	be	AUX
iajs-2478	26	39	studied	study	VERB
iajs-2478	26	40	.	.	PUNCT
iajs-2478	27	1	the	the	DET
iajs-2478	27	2	derivation	derivation	NOUN
iajs-2478	27	3	of	of	ADP
iajs-2478	27	4	the	the	DET
iajs-2478	27	5	frd	frd	NOUN
iajs-2478	27	6	for	for	ADP
iajs-2478	27	7	the	the	DET
iajs-2478	27	8	cof	cof	PROPN
iajs-2478	27	9	is	be	AUX
iajs-2478	27	10	obtained	obtain	VERB
iajs-2478	27	11	.	.	PUNCT
iajs-2478	28	1	at	at	ADP
iajs-2478	28	2	the	the	DET
iajs-2478	28	3	end	end	NOUN
iajs-2478	28	4	,	,	PUNCT
iajs-2478	28	5	the	the	DET
iajs-2478	28	6	ncsthop	ncsthop	NOUN
iajs-2478	28	7	of	of	ADP
iajs-2478	28	8	this	this	DET
iajs-2478	28	9	ocp	ocp	PROPN
iajs-2478	28	10	is	be	AUX
iajs-2478	28	11	sated	sate	VERB
iajs-2478	28	12	and	and	CCONJ
iajs-2478	28	13	proved	prove	VERB
iajs-2478	28	14	..	..	PUNCT
iajs-2478	29	1	2	2	X
iajs-2478	29	2	.	.	X
iajs-2478	29	3	description	description	NOUN
iajs-2478	29	4	of	of	ADP
iajs-2478	29	5	the	the	DET
iajs-2478	29	6	problem	problem	NOUN
iajs-2478	29	7	:	:	PUNCT
iajs-2478	29	8	let	let	VERB
iajs-2478	29	9	ω	ω	NUM
iajs-2478	29	10	⊂	⊂	X
iajs-2478	29	11	ℝ	ℝ	PROPN
iajs-2478	29	12	,	,	PUNCT
iajs-2478	29	13	𝓍	𝓍	PRON
iajs-2478	29	14	𝑥	𝑥	X
iajs-2478	29	15	,	,	PUNCT
iajs-2478	29	16	,	,	PUNCT
iajs-2478	29	17	𝑥	𝑥	X
iajs-2478	29	18	,	,	PUNCT
iajs-2478	29	19	𝑄	𝑄	PROPN
iajs-2478	29	20	0	0	NUM
iajs-2478	29	21	,	,	PUNCT
iajs-2478	29	22	t	t	PROPN
iajs-2478	29	23	ω	ω	PROPN
iajs-2478	29	24	,	,	PUNCT
iajs-2478	29	25	ĩ	ĩ	ADP
iajs-2478	29	26	0	0	NUM
iajs-2478	29	27	,	,	PUNCT
iajs-2478	29	28	t	t	PROPN
iajs-2478	29	29	,	,	PUNCT
iajs-2478	29	30	γ	γ	PROPN
iajs-2478	29	31	𝜕ω	𝜕ω	PROPN
iajs-2478	29	32	,	,	PUNCT
iajs-2478	29	33	σ	σ	PROPN
iajs-2478	29	34	γ	γ	X
iajs-2478	29	35	ĩ	ĩ	PROPN
iajs-2478	29	36	.	.	PUNCT
iajs-2478	30	1	the	the	DET
iajs-2478	30	2	ccbocp	ccbocp	NOUN
iajs-2478	30	3	consists	consist	VERB
iajs-2478	30	4	of	of	ADP
iajs-2478	30	5	the	the	DET
iajs-2478	30	6	tses	tse	NOUN
iajs-2478	30	7	which	which	PRON
iajs-2478	30	8	are	be	AUX
iajs-2478	30	9	given	give	VERB
iajs-2478	30	10	by	by	ADP
iajs-2478	30	11	the	the	DET
iajs-2478	30	12	following	follow	VERB
iajs-2478	30	13	tlpdepar	tlpdepar	NOUN
iajs-2478	30	14	𝑦	𝑦	PRON
iajs-2478	30	15	∆𝑦	∆𝑦	PROPN
iajs-2478	30	16	𝑦	𝑦	PRON
iajs-2478	30	17	𝑦	𝑦	PRON
iajs-2478	30	18	𝑦	𝑦	NOUN
iajs-2478	30	19	𝑓	𝑓	DET
iajs-2478	30	20	𝑥	𝑥	PROPN
iajs-2478	30	21	,	,	PUNCT
iajs-2478	30	22	𝑡	𝑡	PROPN
iajs-2478	30	23	,	,	PUNCT
iajs-2478	30	24	in	in	ADP
iajs-2478	30	25	𝑄	𝑄	PROPN
iajs-2478	30	26	(	(	PUNCT
iajs-2478	30	27	1	1	X
iajs-2478	30	28	)	)	PUNCT
iajs-2478	30	29	𝑦	𝑦	NOUN
iajs-2478	30	30	∆𝑦	∆𝑦	PROPN
iajs-2478	30	31	𝑦	𝑦	PRON
iajs-2478	30	32	𝑦	𝑦	PRON
iajs-2478	30	33	𝑦	𝑦	NOUN
iajs-2478	30	34	𝑓	𝑓	DET
iajs-2478	30	35	𝑥	𝑥	PROPN
iajs-2478	30	36	,	,	PUNCT
iajs-2478	30	37	𝑡	𝑡	PROPN
iajs-2478	30	38	,	,	PUNCT
iajs-2478	30	39	in	in	ADP
iajs-2478	30	40	𝑄	𝑄	PROPN
iajs-2478	30	41	(	(	PUNCT
iajs-2478	30	42	2	2	NUM
iajs-2478	30	43	)	)	PUNCT
iajs-2478	30	44	𝑦	𝑦	NOUN
iajs-2478	30	45	∆𝑦	∆𝑦	PROPN
iajs-2478	30	46	𝑦	𝑦	PRON
iajs-2478	30	47	𝑦	𝑦	PRON
iajs-2478	30	48	𝑦	𝑦	NOUN
iajs-2478	30	49	𝑓	𝑓	DET
iajs-2478	30	50	𝑥	𝑥	PROPN
iajs-2478	30	51	,	,	PUNCT
iajs-2478	30	52	𝑡	𝑡	PROPN
iajs-2478	30	53	,	,	PUNCT
iajs-2478	30	54	in	in	ADP
iajs-2478	30	55	𝑄	𝑄	PROPN
iajs-2478	30	56	(	(	PUNCT
iajs-2478	30	57	3	3	NUM
iajs-2478	30	58	)	)	PUNCT
iajs-2478	30	59	with	with	ADP
iajs-2478	30	60	the	the	DET
iajs-2478	30	61	bcs	bc	NOUN
iajs-2478	30	62	and	and	CCONJ
iajs-2478	30	63	ics	ic	NOUN
iajs-2478	30	64	.	.	PUNCT
iajs-2478	31	1	∑	∑	PROPN
iajs-2478	31	2	cos	cos	PROPN
iajs-2478	31	3	𝑛	𝑛	PROPN
iajs-2478	31	4	,	,	PUNCT
iajs-2478	31	5	𝑥	𝑥	PRON
iajs-2478	31	6	𝑢	𝑢	X
iajs-2478	31	7	𝑥	𝑥	PROPN
iajs-2478	31	8	,	,	PUNCT
iajs-2478	31	9	𝑡	𝑡	PROPN
iajs-2478	31	10	,	,	PUNCT
iajs-2478	31	11	on	on	ADP
iajs-2478	31	12	σ	σ	PROPN
iajs-2478	31	13	(	(	PUNCT
iajs-2478	31	14	4	4	NUM
iajs-2478	31	15	)	)	PUNCT
iajs-2478	31	16	∑	∑	PROPN
iajs-2478	31	17	cos	cos	PROPN
iajs-2478	31	18	𝑛	𝑛	PROPN
iajs-2478	31	19	,	,	PUNCT
iajs-2478	31	20	𝑥	𝑥	PRON
iajs-2478	31	21	𝑢	𝑢	X
iajs-2478	31	22	𝑥	𝑥	PROPN
iajs-2478	31	23	,	,	PUNCT
iajs-2478	31	24	𝑡	𝑡	PROPN
iajs-2478	31	25	,	,	PUNCT
iajs-2478	31	26	on	on	ADP
iajs-2478	31	27	σ	σ	PROPN
iajs-2478	31	28	(	(	PUNCT
iajs-2478	31	29	5	5	NUM
iajs-2478	31	30	)	)	PUNCT
iajs-2478	31	31	∑	∑	PUNCT
iajs-2478	31	32	cos	cos	PROPN
iajs-2478	31	33	𝑛	𝑛	PROPN
iajs-2478	31	34	,	,	PUNCT
iajs-2478	31	35	𝑥	𝑥	PRON
iajs-2478	31	36	𝑢	𝑢	X
iajs-2478	31	37	𝑥	𝑥	PROPN
iajs-2478	31	38	,	,	PUNCT
iajs-2478	31	39	𝑡	𝑡	PROPN
iajs-2478	31	40	,	,	PUNCT
iajs-2478	31	41	on	on	ADP
iajs-2478	31	42	σ	σ	PROPN
iajs-2478	31	43	(	(	PUNCT
iajs-2478	31	44	6	6	NUM
iajs-2478	31	45	)	)	PUNCT
iajs-2478	31	46	𝑦	𝑦	NOUN
iajs-2478	31	47	𝑥	𝑥	NOUN
iajs-2478	31	48	,	,	PUNCT
iajs-2478	31	49	0	0	NUM
iajs-2478	31	50	𝑦	𝑦	SYM
iajs-2478	31	51	𝑥	𝑥	X
iajs-2478	31	52	,	,	PUNCT
iajs-2478	31	53	on	on	ADP
iajs-2478	31	54	ω	ω	PROPN
iajs-2478	31	55	(	(	PUNCT
iajs-2478	31	56	7	7	NUM
iajs-2478	31	57	)	)	PUNCT
iajs-2478	31	58	𝑦	𝑦	NOUN
iajs-2478	31	59	𝑥	𝑥	NOUN
iajs-2478	31	60	,	,	PUNCT
iajs-2478	31	61	0	0	NUM
iajs-2478	31	62	𝑦	𝑦	SYM
iajs-2478	31	63	𝑥	𝑥	X
iajs-2478	31	64	,	,	PUNCT
iajs-2478	31	65	on	on	ADP
iajs-2478	31	66	ω	ω	PROPN
iajs-2478	31	67	(	(	PUNCT
iajs-2478	31	68	8)	8)	NUM
iajs-2478	31	69	𝑦	𝑦	SYM
iajs-2478	31	70	𝑥	𝑥	NOUN
iajs-2478	31	71	,	,	PUNCT
iajs-2478	31	72	0	0	NUM
iajs-2478	31	73	𝑦	𝑦	SYM
iajs-2478	31	74	𝑥	𝑥	X
iajs-2478	31	75	,	,	PUNCT
iajs-2478	31	76	on	on	ADP
iajs-2478	31	77	ω	ω	PROPN
iajs-2478	31	78	(	(	PUNCT
iajs-2478	31	79	9	9	NUM
iajs-2478	31	80	)	)	PUNCT
iajs-2478	31	81	where	where	SCONJ
iajs-2478	31	82	𝑛ℊ	𝑛ℊ	NOUN
iajs-2478	31	83	,	,	PUNCT
iajs-2478	31	84	∀	∀	X
iajs-2478	31	85	ℊ	ℊ	NOUN
iajs-2478	31	86	1,2,3	1,2,3	NOUN
iajs-2478	31	87	,	,	PUNCT
iajs-2478	31	88	is	be	AUX
iajs-2478	31	89	an	an	DET
iajs-2478	31	90	outer	outer	ADJ
iajs-2478	31	91	normal	normal	ADJ
iajs-2478	31	92	vector	vector	NOUN
iajs-2478	31	93	on	on	ADP
iajs-2478	31	94	the	the	DET
iajs-2478	31	95	boundary	boundary	ADJ
iajs-2478	31	96	σ	σ	PROPN
iajs-2478	31	97	,	,	PUNCT
iajs-2478	31	98	and	and	CCONJ
iajs-2478	31	99	(	(	PUNCT
iajs-2478	31	100	𝑛ℊ	𝑛ℊ	NOUN
iajs-2478	31	101	,	,	PUNCT
iajs-2478	31	102	𝑥	𝑥	PROPN
iajs-2478	31	103	is	be	AUX
iajs-2478	31	104	the	the	DET
iajs-2478	31	105	angle	angle	NOUN
iajs-2478	31	106	between	between	ADP
iajs-2478	31	107	𝑛ℊ	𝑛ℊ	ADP
iajs-2478	31	108	and	and	CCONJ
iajs-2478	31	109	the	the	DET
iajs-2478	31	110	𝑥	𝑥	PROPN
iajs-2478	31	111	axis	axis	NOUN
iajs-2478	31	112	,	,	PUNCT
iajs-2478	31	113	(	(	PUNCT
iajs-2478	31	114	𝑓	𝑓	X
iajs-2478	31	115	,	,	PUNCT
iajs-2478	31	116	𝑓	𝑓	X
iajs-2478	31	117	,	,	PUNCT
iajs-2478	31	118	𝑓	𝑓	X
iajs-2478	31	119	)	)	PUNCT
iajs-2478	31	120	is	be	AUX
iajs-2478	31	121	a	a	DET
iajs-2478	31	122	vector	vector	NOUN
iajs-2478	31	123	of	of	ADP
iajs-2478	31	124	a	a	DET
iajs-2478	31	125	given	give	VERB
iajs-2478	31	126	function	function	NOUN
iajs-2478	31	127	on	on	ADP
iajs-2478	31	128	ω,𝑢	ω,𝑢	PRON
iajs-2478	31	129	𝑢	𝑢	NOUN
iajs-2478	31	130	,	,	PUNCT
iajs-2478	31	131	𝑢	𝑢	X
iajs-2478	31	132	,	,	PUNCT
iajs-2478	31	133	𝑢	𝑢	PROPN
iajs-2478	31	134	∈	∈	PROPN
iajs-2478	31	135	𝐿	𝐿	PROPN
iajs-2478	31	136	σ	σ	PROPN
iajs-2478	31	137	is	be	AUX
iajs-2478	31	138	the	the	DET
iajs-2478	31	139	ccbcv	ccbcv	PROPN
iajs-2478	31	140	and	and	CCONJ
iajs-2478	31	141	�	�	NOUN
iajs-2478	31	142	⃗	⃗	NOUN
iajs-2478	31	143	�	�	PROPN
iajs-2478	31	144	𝑦	𝑦	PROPN
iajs-2478	31	145	,	,	PUNCT
iajs-2478	31	146	𝑦	𝑦	PRON
iajs-2478	31	147	,	,	PUNCT
iajs-2478	31	148	𝑦	𝑦	NOUN
iajs-2478	31	149	∈	∈	NOUN
iajs-2478	31	150	𝐻	𝐻	NOUN
iajs-2478	31	151	𝑄	𝑄	PROPN
iajs-2478	31	152	is	be	AUX
iajs-2478	31	153	their	their	PRON
iajs-2478	31	154	corresponding	correspond	VERB
iajs-2478	31	155	svs	svs	NOUN
iajs-2478	31	156	.	.	PUNCT
iajs-2478	32	1	the	the	DET
iajs-2478	32	2	set	set	NOUN
iajs-2478	32	3	of	of	ADP
iajs-2478	32	4	admissible	admissible	ADJ
iajs-2478	32	5	ccbcv	ccbcv	NOUN
iajs-2478	32	6	is	be	AUX
iajs-2478	32	7	defined	define	VERB
iajs-2478	32	8	by	by	ADP
iajs-2478	32	9	𝑊	𝑊	PROPN
iajs-2478	32	10	𝑢	𝑢	PRON
iajs-2478	32	11	𝑢	𝑢	PROPN
iajs-2478	32	12	,	,	PUNCT
iajs-2478	32	13	𝑢	𝑢	PRON
iajs-2478	32	14	,	,	PUNCT
iajs-2478	32	15	𝑢	𝑢	PROPN
iajs-2478	32	16	∈	∈	PROPN
iajs-2478	32	17	𝐿	𝐿	PROPN
iajs-2478	32	18	σ	σ	PROPN
iajs-2478	32	19	∣	∣	PROPN
iajs-2478	32	20	𝑢	𝑢	PROPN
iajs-2478	32	21	,	,	PUNCT
iajs-2478	32	22	𝑢	𝑢	X
iajs-2478	32	23	,	,	PUNCT
iajs-2478	32	24	𝑢	𝑢	PROPN
iajs-2478	32	25	∈	∈	PROPN
iajs-2478	32	26	�	�	NOUN
iajs-2478	32	27	⃗	⃗	PROPN
iajs-2478	32	28	�	�	PROPN
iajs-2478	32	29	𝑈	𝑈	PROPN
iajs-2478	32	30	𝑈	𝑈	PROPN
iajs-2478	32	31	𝑈	𝑈	PROPN
iajs-2478	32	32	⊂	⊂	PROPN
iajs-2478	32	33	𝑅	𝑅	PROPN
iajs-2478	32	34	a.e	a.e	PROPN
iajs-2478	32	35	.	.	PROPN
iajs-2478	33	1	in	in	ADP
iajs-2478	33	2	σ	σ	PROPN
iajs-2478	33	3	,	,	PUNCT
iajs-2478	33	4	where	where	SCONJ
iajs-2478	33	5	a.e	a.e	PROPN
iajs-2478	33	6	.	.	PROPN
iajs-2478	33	7	denotes	denote	NOUN
iajs-2478	33	8	to	to	ADP
iajs-2478	33	9	almost	almost	ADV
iajs-2478	33	10	everywhere	everywhere	ADV
iajs-2478	33	11	.	.	PUNCT
iajs-2478	34	1	the	the	DET
iajs-2478	34	2	cof	cof	PROPN
iajs-2478	34	3	is	be	AUX
iajs-2478	34	4	defined	define	VERB
iajs-2478	34	5	by	by	ADP
iajs-2478	34	6	𝐺	𝐺	PROPN
iajs-2478	34	7	𝑢	𝑢	PROPN
iajs-2478	34	8	‖𝑦	‖𝑦	VERB
iajs-2478	34	9	𝑦	𝑦	PROPN
iajs-2478	34	10	‖	‖	PROPN
iajs-2478	34	11	‖𝑦	‖𝑦	VERB
iajs-2478	34	12	𝑦	𝑦	X
iajs-2478	34	13	‖	‖	PROPN
iajs-2478	34	14	‖𝑦	‖𝑦	VERB
iajs-2478	34	15	𝑦	𝑦	X
iajs-2478	34	16	‖	‖	PROPN
iajs-2478	34	17	‖𝑢	‖𝑢	PROPN
iajs-2478	34	18	‖	‖	PROPN
iajs-2478	34	19	‖𝑢	‖𝑢	PROPN
iajs-2478	34	20	‖	‖	PROPN
iajs-2478	34	21	‖𝑢	‖𝑢	PROPN
iajs-2478	34	22	‖	‖	ADJ
iajs-2478	34	23	,	,	PUNCT
iajs-2478	34	24	𝑢	𝑢	PROPN
iajs-2478	34	25	∈	∈	PROPN
iajs-2478	34	26	𝑊	𝑊	PROPN
iajs-2478	34	27	,	,	PUNCT
iajs-2478	34	28	𝛽	𝛽	NOUN
iajs-2478	34	29	0	0	NUM
iajs-2478	34	30	(	(	PUNCT
iajs-2478	34	31	10	10	NUM
iajs-2478	34	32	)	)	PUNCT
iajs-2478	34	33	let	let	VERB
iajs-2478	34	34	�	�	NOUN
iajs-2478	34	35	⃗	⃗	NOUN
iajs-2478	34	36	�	�	PROPN
iajs-2478	34	37	𝑉	𝑉	PROPN
iajs-2478	34	38	𝑉	𝑉	PROPN
iajs-2478	34	39	𝑉	𝑉	PROPN
iajs-2478	34	40	𝐻	𝐻	PROPN
iajs-2478	34	41	ω	ω	PROPN
iajs-2478	34	42	,	,	PUNCT
iajs-2478	34	43	�	�	PROPN
iajs-2478	34	44	⃗	⃗	PROPN
iajs-2478	34	45	�	�	PROPN
iajs-2478	34	46	�	�	PROPN
iajs-2478	34	47	⃗	⃗	PROPN
iajs-2478	34	48	�	�	PROPN
iajs-2478	34	49	:	:	PUNCT
iajs-2478	34	50	�	�	PROPN
iajs-2478	34	51	⃗	⃗	NOUN
iajs-2478	34	52	�	�	PROPN
iajs-2478	34	53	𝑣	𝑣	ADP
iajs-2478	34	54	𝑥	𝑥	X
iajs-2478	34	55	,	,	PUNCT
iajs-2478	34	56	𝑣	𝑣	PRON
iajs-2478	34	57	𝑥	𝑥	X
iajs-2478	34	58	,	,	PUNCT
iajs-2478	34	59	𝑣	𝑣	PRON
iajs-2478	34	60	𝑥	𝑥	X
iajs-2478	34	61	∈	∈	NOUN
iajs-2478	34	62	𝐻	𝐻	PROPN
iajs-2478	34	63	ω	ω	NOUN
iajs-2478	34	64	.	.	PUNCT
iajs-2478	35	1	the	the	DET
iajs-2478	35	2	weak	weak	ADJ
iajs-2478	35	3	form	form	NOUN
iajs-2478	35	4	(	(	PUNCT
iajs-2478	35	5	wf	wf	PROPN
iajs-2478	35	6	)	)	PUNCT
iajs-2478	35	7	of	of	ADP
iajs-2478	35	8	the	the	DET
iajs-2478	35	9	boundary	boundary	ADJ
iajs-2478	35	10	value	value	NOUN
iajs-2478	35	11	problem	problem	NOUN
iajs-2478	35	12	(	(	PUNCT
iajs-2478	35	13	bvp	bvp	PROPN
iajs-2478	35	14	)	)	PUNCT
iajs-2478	35	15	(	(	PUNCT
iajs-2478	35	16	1)-(9	1)-(9	NOUN
iajs-2478	35	17	)	)	PUNCT
iajs-2478	35	18	,	,	PUNCT
iajs-2478	35	19	when	when	SCONJ
iajs-2478	35	20	�	�	NOUN
iajs-2478	35	21	⃗	⃗	NOUN
iajs-2478	35	22	�	�	NOUN
iajs-2478	35	23	∈	∈	PROPN
iajs-2478	35	24	𝐻	𝐻	PROPN
iajs-2478	35	25	𝑄	𝑄	PROPN
iajs-2478	35	26	is	be	AUX
iajs-2478	35	27	given	give	VERB
iajs-2478	35	28	by	by	ADP
iajs-2478	35	29	〈	〈	PROPN
iajs-2478	35	30	𝑦	𝑦	NOUN
iajs-2478	35	31	,	,	PUNCT
iajs-2478	35	32	𝑣	𝑣	ADP
iajs-2478	35	33	〉	〉	NOUN
iajs-2478	35	34	∇𝑦	∇𝑦	PROPN
iajs-2478	35	35	,	,	PUNCT
iajs-2478	35	36	∇𝑣	∇𝑣	PROPN
iajs-2478	35	37	𝑦	𝑦	PRON
iajs-2478	35	38	,	,	PUNCT
iajs-2478	35	39	𝑣	𝑣	DET
iajs-2478	35	40	𝑦	𝑦	NOUN
iajs-2478	35	41	,	,	PUNCT
iajs-2478	35	42	𝑣	𝑣	PRON
iajs-2478	35	43	𝑦	𝑦	NOUN
iajs-2478	35	44	,	,	PUNCT
iajs-2478	35	45	𝑣	𝑣	PRON
iajs-2478	35	46	𝑓	𝑓	X
iajs-2478	35	47	,	,	PUNCT
iajs-2478	35	48	𝑣	𝑣	PRON
iajs-2478	35	49	𝑢	𝑢	X
iajs-2478	35	50	,	,	PUNCT
iajs-2478	35	51	𝑣	𝑣	X
iajs-2478	35	52	,	,	PUNCT
iajs-2478	35	53	∀	∀	X
iajs-2478	35	54	𝑣	𝑣	ADP
iajs-2478	35	55	∈	∈	PROPN
iajs-2478	35	56	𝑉	𝑉	PROPN
iajs-2478	35	57	(	(	PUNCT
iajs-2478	35	58	11.a	11.a	NUM
iajs-2478	35	59	)	)	PUNCT
iajs-2478	35	60	𝑦	𝑦	NOUN
iajs-2478	35	61	0	0	NUM
iajs-2478	35	62	,	,	PUNCT
iajs-2478	35	63	𝑣	𝑣	PRON
iajs-2478	35	64	𝑦	𝑦	NOUN
iajs-2478	35	65	,	,	PUNCT
iajs-2478	35	66	𝑣	𝑣	X
iajs-2478	35	67	,	,	PUNCT
iajs-2478	35	68	∀	∀	VERB
iajs-2478	35	69	𝑣	𝑣	ADP
iajs-2478	35	70	∈	∈	PROPN
iajs-2478	35	71	𝑉	𝑉	PROPN
iajs-2478	35	72	(	(	PUNCT
iajs-2478	35	73	11.b	11.b	NUM
iajs-2478	35	74	)	)	PUNCT
iajs-2478	35	75	〈	〈	NOUN
iajs-2478	35	76	𝑦	𝑦	NOUN
iajs-2478	35	77	,	,	PUNCT
iajs-2478	35	78	𝑣	𝑣	ADP
iajs-2478	35	79	〉	〉	NOUN
iajs-2478	35	80	∇𝑦	∇𝑦	PROPN
iajs-2478	35	81	,	,	PUNCT
iajs-2478	35	82	∇𝑣	∇𝑣	PROPN
iajs-2478	35	83	𝑦	𝑦	PRON
iajs-2478	35	84	,	,	PUNCT
iajs-2478	35	85	𝑣	𝑣	PRON
iajs-2478	35	86	𝑦	𝑦	NOUN
iajs-2478	35	87	,	,	PUNCT
iajs-2478	35	88	𝑣	𝑣	PRON
iajs-2478	35	89	𝑦	𝑦	NOUN
iajs-2478	35	90	,	,	PUNCT
iajs-2478	35	91	𝑣	𝑣	PRON
iajs-2478	35	92	𝑓	𝑓	X
iajs-2478	35	93	,	,	PUNCT
iajs-2478	35	94	𝑣	𝑣	PRON
iajs-2478	35	95	𝑢	𝑢	X
iajs-2478	35	96	,	,	PUNCT
iajs-2478	35	97	𝑣	𝑣	X
iajs-2478	35	98	,	,	PUNCT
iajs-2478	35	99	∀	∀	X
iajs-2478	35	100	𝑣	𝑣	ADP
iajs-2478	35	101	∈	∈	PROPN
iajs-2478	35	102	𝑉	𝑉	PROPN
iajs-2478	35	103	(	(	PUNCT
iajs-2478	35	104	12.a	12.a	NUM
iajs-2478	35	105	)	)	PUNCT
iajs-2478	35	106	𝑦	𝑦	NOUN
iajs-2478	35	107	0	0	NUM
iajs-2478	35	108	,	,	PUNCT
iajs-2478	35	109	𝑣	𝑣	PRON
iajs-2478	35	110	𝑦	𝑦	NOUN
iajs-2478	35	111	,	,	PUNCT
iajs-2478	35	112	𝑣	𝑣	X
iajs-2478	35	113	,	,	PUNCT
iajs-2478	35	114	∀	∀	VERB
iajs-2478	35	115	𝑣	𝑣	ADP
iajs-2478	35	116	∈	∈	PROPN
iajs-2478	35	117	𝑉	𝑉	PROPN
iajs-2478	35	118	(	(	PUNCT
iajs-2478	35	119	12.b	12.b	NUM
iajs-2478	35	120	)	)	PUNCT
iajs-2478	35	121	〈	〈	NOUN
iajs-2478	35	122	𝑦	𝑦	NOUN
iajs-2478	35	123	,	,	PUNCT
iajs-2478	35	124	𝑣	𝑣	ADP
iajs-2478	35	125	〉	〉	NOUN
iajs-2478	35	126	∇𝑦	∇𝑦	PROPN
iajs-2478	35	127	,	,	PUNCT
iajs-2478	35	128	∇𝑣	∇𝑣	PROPN
iajs-2478	35	129	𝑦	𝑦	PRON
iajs-2478	35	130	,	,	PUNCT
iajs-2478	35	131	𝑣	𝑣	PRON
iajs-2478	35	132	𝑦	𝑦	NOUN
iajs-2478	35	133	,	,	PUNCT
iajs-2478	35	134	𝑣	𝑣	PRON
iajs-2478	35	135	𝑦	𝑦	NOUN
iajs-2478	35	136	,	,	PUNCT
iajs-2478	35	137	𝑣	𝑣	PRON
iajs-2478	35	138	𝑓	𝑓	X
iajs-2478	35	139	,	,	PUNCT
iajs-2478	35	140	𝑣	𝑣	PRON
iajs-2478	35	141	𝑢	𝑢	X
iajs-2478	35	142	,	,	PUNCT
iajs-2478	35	143	𝑣	𝑣	X
iajs-2478	35	144	,	,	PUNCT
iajs-2478	35	145	∀	∀	X
iajs-2478	35	146	𝑣	𝑣	SCONJ
iajs-2478	35	147	∈	∈	PROPN
iajs-2478	35	148	𝑉	𝑉	PROPN
iajs-2478	35	149	(	(	PUNCT
iajs-2478	35	150	13.a	13.a	NUM
iajs-2478	35	151	)	)	PUNCT
iajs-2478	35	152	𝑦	𝑦	NOUN
iajs-2478	35	153	0	0	NUM
iajs-2478	35	154	,	,	PUNCT
iajs-2478	35	155	𝑣	𝑣	PRON
iajs-2478	35	156	𝑦	𝑦	NOUN
iajs-2478	35	157	,	,	PUNCT
iajs-2478	35	158	𝑣	𝑣	X
iajs-2478	35	159	,	,	PUNCT
iajs-2478	35	160	∀	∀	VERB
iajs-2478	35	161	𝑣	𝑣	SCONJ
iajs-2478	35	162	∈	∈	PROPN
iajs-2478	35	163	𝑉	𝑉	PROPN
iajs-2478	35	164	(	(	PUNCT
iajs-2478	35	165	13.b	13.b	NUM
iajs-2478	35	166	)	)	PUNCT
iajs-2478	35	167	the	the	DET
iajs-2478	35	168	following	follow	VERB
iajs-2478	35	169	assumption	assumption	NOUN
iajs-2478	35	170	is	be	AUX
iajs-2478	35	171	important	important	ADJ
iajs-2478	35	172	to	to	PART
iajs-2478	35	173	study	study	VERB
iajs-2478	35	174	the	the	DET
iajs-2478	35	175	existence	existence	NOUN
iajs-2478	35	176	theorem	theorem	NOUN
iajs-2478	35	177	of	of	ADP
iajs-2478	35	178	the	the	DET
iajs-2478	35	179	svs	svs	NOUN
iajs-2478	35	180	for	for	ADP
iajs-2478	35	181	the	the	DET
iajs-2478	35	182	wf	wf	PROPN
iajs-2478	35	183	(	(	PUNCT
iajs-2478	35	184	11)−(13	11)−(13	NUM
iajs-2478	35	185	)	)	PUNCT
iajs-2478	35	186	.	.	PUNCT
iajs-2478	36	1	2.1	2.1	NUM
iajs-2478	36	2	.	.	PUNCT
iajs-2478	36	3	assumption	assumption	NOUN
iajs-2478	36	4	(	(	PUNCT
iajs-2478	36	5	a	a	X
iajs-2478	36	6	):	):	PUNCT
iajs-2478	36	7	the	the	DET
iajs-2478	36	8	function	function	NOUN
iajs-2478	36	9	𝑓	𝑓	X
iajs-2478	36	10	(	(	PUNCT
iajs-2478	36	11	∀	∀	NOUN
iajs-2478	36	12	𝑖	𝑖	SYM
iajs-2478	36	13	1,2,3	1,2,3	NOUN
iajs-2478	36	14	)	)	PUNCT
iajs-2478	36	15	is	be	AUX
iajs-2478	36	16	satisfied	satisfied	ADJ
iajs-2478	36	17	the	the	DET
iajs-2478	36	18	following	follow	VERB
iajs-2478	36	19	condition	condition	NOUN
iajs-2478	36	20	with	with	ADP
iajs-2478	36	21	respect	respect	NOUN
iajs-2478	36	22	to	to	ADP
iajs-2478	36	23	(	(	PUNCT
iajs-2478	36	24	w.r.t	w.r.t	NOUN
iajs-2478	36	25	.	.	PUNCT
iajs-2478	36	26	)	)	PUNCT
iajs-2478	37	1	𝑥	𝑥	PROPN
iajs-2478	37	2	&	&	CCONJ
iajs-2478	37	3	𝑡	𝑡	PROPN
iajs-2478	37	4	,	,	PUNCT
iajs-2478	37	5	that	that	ADV
iajs-2478	37	6	is	is	ADV
iajs-2478	37	7	(	(	PUNCT
iajs-2478	37	8	i.e.	i.e.	X
iajs-2478	37	9	)	)	PUNCT
iajs-2478	37	10	|𝑓	|𝑓	NOUN
iajs-2478	37	11	|	|	ADV
iajs-2478	37	12	𝜂	𝜂	PRON
iajs-2478	37	13	𝑥	𝑥	PROPN
iajs-2478	37	14	,	,	PUNCT
iajs-2478	37	15	𝑡	𝑡	PROPN
iajs-2478	37	16	,	,	PUNCT
iajs-2478	37	17	where	where	SCONJ
iajs-2478	37	18	𝑥	𝑥	NOUN
iajs-2478	37	19	,	,	PUNCT
iajs-2478	37	20	𝑡	𝑡	PROPN
iajs-2478	37	21	∈	∈	PROPN
iajs-2478	37	22	𝑄	𝑄	PROPN
iajs-2478	37	23	,	,	PUNCT
iajs-2478	37	24	𝜂	𝜂	PROPN
iajs-2478	37	25	∈	∈	PROPN
iajs-2478	37	26	𝐿	𝐿	PROPN
iajs-2478	37	27	𝑄	𝑄	PROPN
iajs-2478	37	28	,	,	PUNCT
iajs-2478	37	29	ℝ	ℝ	NOUN
iajs-2478	37	30	.	.	PUNCT
iajs-2478	38	1	3	3	X
iajs-2478	38	2	.	.	X
iajs-2478	38	3	the	the	DET
iajs-2478	38	4	existence	existence	NOUN
iajs-2478	38	5	solution	solution	NOUN
iajs-2478	38	6	for	for	ADP
iajs-2478	38	7	the	the	DET
iajs-2478	38	8	wf	wf	PROPN
iajs-2478	38	9	:	:	PUNCT
iajs-2478	38	10	  	  	SPACE
iajs-2478	38	11	115	115	NUM
iajs-2478	38	12	ibn	ibn	PROPN
iajs-2478	38	13	al	al	PROPN
iajs-2478	38	14	-	-	PUNCT
iajs-2478	38	15	haitham	haitham	PROPN
iajs-2478	38	16	jour	jour	X
iajs-2478	38	17	.	.	PROPN
iajs-2478	39	1	for	for	ADP
iajs-2478	39	2	pure	pure	ADJ
iajs-2478	39	3	&	&	CCONJ
iajs-2478	39	4	appl	appl	PROPN
iajs-2478	39	5	.	.	PUNCT
iajs-2478	40	1	sci	sci	PROPN
iajs-2478	40	2	.	.	PROPN
iajs-2478	41	1	33	33	NUM
iajs-2478	41	2	(	(	PUNCT
iajs-2478	41	3	3	3	NUM
iajs-2478	41	4	)	)	PUNCT
iajs-2478	41	5	2020	2020	NUM
iajs-2478	41	6	theorem	theorem	VERB
iajs-2478	41	7	3.1	3.1	NUM
iajs-2478	41	8	:	:	PUNCT
iajs-2478	41	9	existence	existence	NOUN
iajs-2478	41	10	of	of	ADP
iajs-2478	41	11	a	a	DET
iajs-2478	41	12	unique	unique	ADJ
iajs-2478	41	13	solution	solution	NOUN
iajs-2478	41	14	for	for	ADP
iajs-2478	41	15	the	the	DET
iajs-2478	41	16	wf	wf	PROPN
iajs-2478	41	17	of	of	ADP
iajs-2478	41	18	the	the	DET
iajs-2478	41	19	ses	se	NOUN
iajs-2478	41	20	:	:	PUNCT
iajs-2478	41	21	with	with	ADP
iajs-2478	41	22	assumption	assumption	NOUN
iajs-2478	41	23	(	(	PUNCT
iajs-2478	41	24	a	a	NOUN
iajs-2478	41	25	)	)	PUNCT
iajs-2478	41	26	,	,	PUNCT
iajs-2478	41	27	for	for	ADP
iajs-2478	41	28	each	each	DET
iajs-2478	41	29	given	give	VERB
iajs-2478	41	30	ccbcv	ccbcv	PROPN
iajs-2478	41	31	𝑢	𝑢	PROPN
iajs-2478	41	32	∈	∈	PROPN
iajs-2478	41	33	𝐿	𝐿	PROPN
iajs-2478	41	34	σ	σ	PROPN
iajs-2478	41	35	,	,	PUNCT
iajs-2478	41	36	the	the	DET
iajs-2478	41	37	wf	wf	PROPN
iajs-2478	41	38	(	(	PUNCT
iajs-2478	41	39	11)–(13	11)–(13	NUM
iajs-2478	41	40	)	)	PUNCT
iajs-2478	41	41	of	of	ADP
iajs-2478	41	42	the	the	DET
iajs-2478	41	43	tses	tse	NOUN
iajs-2478	41	44	has	have	VERB
iajs-2478	41	45	a	a	DET
iajs-2478	41	46	unique	unique	ADJ
iajs-2478	41	47	svs	svs	NOUN
iajs-2478	41	48	�	�	NOUN
iajs-2478	41	49	⃗	⃗	NOUN
iajs-2478	41	50	�	�	PROPN
iajs-2478	41	51	with	with	ADP
iajs-2478	41	52	�	�	NOUN
iajs-2478	41	53	⃗	⃗	NOUN
iajs-2478	41	54	�	�	PROPN
iajs-2478	41	55	∈	∈	PROPN
iajs-2478	41	56	𝐿	𝐿	PROPN
iajs-2478	41	57	ĩ	ĩ	PROPN
iajs-2478	41	58	,	,	PUNCT
iajs-2478	41	59	𝑉	𝑉	PROPN
iajs-2478	41	60	,	,	PUNCT
iajs-2478	41	61	�	�	PROPN
iajs-2478	41	62	⃗	⃗	PROPN
iajs-2478	41	63	�	�	PROPN
iajs-2478	41	64	𝑦	𝑦	PROPN
iajs-2478	41	65	,	,	PUNCT
iajs-2478	41	66	𝑦	𝑦	PRON
iajs-2478	41	67	,	,	PUNCT
iajs-2478	41	68	𝑦	𝑦	NOUN
iajs-2478	41	69	∈	∈	PROPN
iajs-2478	41	70	𝐿	𝐿	PROPN
iajs-2478	41	71	ĩ	ĩ	PROPN
iajs-2478	41	72	,	,	PUNCT
iajs-2478	41	73	𝑉∗	𝑉∗	NOUN
iajs-2478	41	74	.	.	PUNCT
iajs-2478	42	1	proof	proof	NOUN
iajs-2478	42	2	:	:	PUNCT
iajs-2478	42	3	let	let	VERB
iajs-2478	42	4	for	for	ADP
iajs-2478	42	5	each	each	DET
iajs-2478	42	6	n	n	NOUN
iajs-2478	42	7	,	,	PUNCT
iajs-2478	42	8	�	�	PROPN
iajs-2478	42	9	⃗	⃗	NOUN
iajs-2478	42	10	�	�	PROPN
iajs-2478	42	11	𝑉	𝑉	PROPN
iajs-2478	42	12	𝑉	𝑉	PROPN
iajs-2478	42	13	𝑉	𝑉	PROPN
iajs-2478	42	14	⊂	⊂	PROPN
iajs-2478	42	15	�	�	PROPN
iajs-2478	42	16	⃗	⃗	NOUN
iajs-2478	42	17	�	�	PROPN
iajs-2478	42	18	be	be	VERB
iajs-2478	42	19	the	the	DET
iajs-2478	42	20	set	set	NOUN
iajs-2478	42	21	of	of	ADP
iajs-2478	42	22	continuous	continuous	ADJ
iajs-2478	42	23	and	and	CCONJ
iajs-2478	42	24	piecewise	piecewise	NOUN
iajs-2478	42	25	affine	affine	NOUN
iajs-2478	42	26	functions	function	NOUN
iajs-2478	42	27	in	in	ADP
iajs-2478	42	28	ω	ω	PROPN
iajs-2478	42	29	,	,	PUNCT
iajs-2478	42	30	let	let	VERB
iajs-2478	42	31	𝑣	𝑣	ADP
iajs-2478	42	32	∈	∈	PROPN
iajs-2478	42	33	𝑉	𝑉	PROPN
iajs-2478	42	34	𝑉	𝑉	PROPN
iajs-2478	42	35	,	,	PUNCT
iajs-2478	42	36	𝑖	𝑖	NOUN
iajs-2478	42	37	1,2,3	1,2,3	NOUN
iajs-2478	42	38	,	,	PUNCT
iajs-2478	42	39	and	and	CCONJ
iajs-2478	42	40	𝑗	𝑗	PRON
iajs-2478	42	41	1,2	1,2	NUM
iajs-2478	42	42	,	,	PUNCT
iajs-2478	42	43	…	…	PUNCT
iajs-2478	42	44	,	,	PUNCT
iajs-2478	42	45	𝑛	𝑛	X
iajs-2478	42	46	,	,	PUNCT
iajs-2478	42	47	be	be	VERB
iajs-2478	42	48	a	a	DET
iajs-2478	42	49	basis	basis	NOUN
iajs-2478	42	50	of	of	ADP
iajs-2478	42	51	𝑉	𝑉	PROPN
iajs-2478	42	52	,	,	PUNCT
iajs-2478	42	53	let	let	VERB
iajs-2478	42	54	�	�	NOUN
iajs-2478	42	55	⃗	⃗	NOUN
iajs-2478	42	56	�	�	PROPN
iajs-2478	42	57	𝑦	𝑦	PROPN
iajs-2478	42	58	,	,	PUNCT
iajs-2478	42	59	𝑦	𝑦	PRON
iajs-2478	42	60	,	,	PUNCT
iajs-2478	42	61	𝑦	𝑦	PRON
iajs-2478	42	62	be	be	AUX
iajs-2478	42	63	an	an	DET
iajs-2478	42	64	approximate	approximate	ADJ
iajs-2478	42	65	solution	solution	NOUN
iajs-2478	42	66	for	for	ADP
iajs-2478	42	67	the	the	DET
iajs-2478	42	68	solution	solution	NOUN
iajs-2478	42	69	�	�	PROPN
iajs-2478	42	70	⃗	⃗	NOUN
iajs-2478	42	71	�	�	PROPN
iajs-2478	42	72	,	,	PUNCT
iajs-2478	42	73	then	then	ADV
iajs-2478	42	74	by	by	ADP
iajs-2478	42	75	gm	gm	PROPN
iajs-2478	42	76	:	:	PUNCT
iajs-2478	42	77	𝑦	𝑦	SYM
iajs-2478	42	78	∑	∑	PUNCT
iajs-2478	42	79	𝑐	𝑐	PROPN
iajs-2478	42	80	𝑡	𝑡	DET
iajs-2478	42	81	𝑣	𝑣	ADP
iajs-2478	42	82	𝑥	𝑥	NOUN
iajs-2478	42	83	,	,	PUNCT
iajs-2478	42	84	(	(	PUNCT
iajs-2478	42	85	14	14	NUM
iajs-2478	42	86	)	)	PUNCT
iajs-2478	42	87	𝑦	𝑦	NOUN
iajs-2478	42	88	∑	∑	PUNCT
iajs-2478	42	89	𝑐	𝑐	X
iajs-2478	42	90	𝑡	𝑡	DET
iajs-2478	42	91	𝑣	𝑣	ADP
iajs-2478	42	92	𝑥	𝑥	NOUN
iajs-2478	42	93	,	,	PUNCT
iajs-2478	42	94	(	(	PUNCT
iajs-2478	42	95	15	15	NUM
iajs-2478	42	96	)	)	PUNCT
iajs-2478	42	97	𝑦	𝑦	NOUN
iajs-2478	42	98	∑	∑	PUNCT
iajs-2478	42	99	𝑐	𝑐	X
iajs-2478	42	100	𝑡	𝑡	DET
iajs-2478	42	101	𝑣	𝑣	ADP
iajs-2478	42	102	𝑥	𝑥	NOUN
iajs-2478	42	103	,	,	PUNCT
iajs-2478	42	104	(	(	PUNCT
iajs-2478	42	105	16	16	NUM
iajs-2478	42	106	)	)	PUNCT
iajs-2478	42	107	where	where	SCONJ
iajs-2478	42	108	𝑐	𝑐	PROPN
iajs-2478	42	109	𝑡	𝑡	PROPN
iajs-2478	42	110	are	be	AUX
iajs-2478	42	111	unknown	unknown	ADJ
iajs-2478	42	112	functions	function	NOUN
iajs-2478	42	113	of	of	ADP
iajs-2478	42	114	𝑡	𝑡	NOUN
iajs-2478	42	115	,	,	PUNCT
iajs-2478	42	116	∀	∀	NOUN
iajs-2478	42	117	𝑖	𝑖	SYM
iajs-2478	42	118	1,2,3	1,2,3	NUM
iajs-2478	42	119	,	,	PUNCT
iajs-2478	42	120	𝑗	𝑗	PROPN
iajs-2478	42	121	1,2	1,2	NUM
iajs-2478	42	122	,	,	PUNCT
iajs-2478	42	123	…	…	PUNCT
iajs-2478	42	124	,	,	PUNCT
iajs-2478	42	125	𝑛.	𝑛.	NOUN
iajs-2478	42	126	the	the	DET
iajs-2478	42	127	wf	wf	PROPN
iajs-2478	42	128	(	(	PUNCT
iajs-2478	42	129	11	11	NUM
iajs-2478	42	130	13	13	NUM
iajs-2478	42	131	)	)	PUNCT
iajs-2478	42	132	is	be	AUX
iajs-2478	42	133	approximated	approximate	VERB
iajs-2478	42	134	by	by	ADP
iajs-2478	42	135	using	use	VERB
iajs-2478	42	136	(	(	PUNCT
iajs-2478	42	137	14	14	NUM
iajs-2478	42	138	)	)	PUNCT
iajs-2478	42	139	16	16	NUM
iajs-2478	42	140	)	)	PUNCT
iajs-2478	42	141	as	as	SCONJ
iajs-2478	42	142	follows	follow	VERB
iajs-2478	42	143	:	:	PUNCT
iajs-2478	42	144	〈	〈	PROPN
iajs-2478	42	145	𝑦	𝑦	NOUN
iajs-2478	42	146	,	,	PUNCT
iajs-2478	42	147	𝑣	𝑣	ADP
iajs-2478	42	148	〉	〉	NOUN
iajs-2478	42	149	∇𝑦	∇𝑦	PROPN
iajs-2478	42	150	,	,	PUNCT
iajs-2478	42	151	∇𝑣	∇𝑣	PROPN
iajs-2478	42	152	𝑦	𝑦	PRON
iajs-2478	42	153	,	,	PUNCT
iajs-2478	42	154	𝑣	𝑣	DET
iajs-2478	42	155	𝑦	𝑦	NOUN
iajs-2478	42	156	,	,	PUNCT
iajs-2478	42	157	𝑣	𝑣	PRON
iajs-2478	42	158	𝑦	𝑦	NOUN
iajs-2478	42	159	,	,	PUNCT
iajs-2478	42	160	𝑣	𝑣	PRON
iajs-2478	42	161	𝑓	𝑓	X
iajs-2478	42	162	,	,	PUNCT
iajs-2478	42	163	𝑣	𝑣	PRON
iajs-2478	42	164	𝑢	𝑢	X
iajs-2478	42	165	,	,	PUNCT
iajs-2478	42	166	𝑣	𝑣	X
iajs-2478	42	167	,	,	PUNCT
iajs-2478	42	168	∀	∀	X
iajs-2478	42	169	𝑣	𝑣	ADP
iajs-2478	42	170	∈	∈	PROPN
iajs-2478	42	171	𝑉	𝑉	PROPN
iajs-2478	42	172	(	(	PUNCT
iajs-2478	42	173	17.a	17.a	NUM
iajs-2478	42	174	)	)	PUNCT
iajs-2478	42	175	𝑦	𝑦	NOUN
iajs-2478	42	176	,	,	PUNCT
iajs-2478	42	177	𝑣	𝑣	PRON
iajs-2478	42	178	𝑦	𝑦	PROPN
iajs-2478	42	179	,	,	PUNCT
iajs-2478	42	180	𝑣	𝑣	X
iajs-2478	42	181	,	,	PUNCT
iajs-2478	42	182	∀	∀	VERB
iajs-2478	42	183	𝑣	𝑣	ADP
iajs-2478	42	184	∈	∈	PROPN
iajs-2478	42	185	𝑉	𝑉	PROPN
iajs-2478	42	186	(	(	PUNCT
iajs-2478	42	187	17.b	17.b	NUM
iajs-2478	42	188	)	)	PUNCT
iajs-2478	43	1	〈	〈	NOUN
iajs-2478	43	2	𝑦	𝑦	NOUN
iajs-2478	43	3	,	,	PUNCT
iajs-2478	43	4	𝑣	𝑣	ADP
iajs-2478	43	5	〉	〉	NOUN
iajs-2478	43	6	∇𝑦	∇𝑦	PROPN
iajs-2478	43	7	,	,	PUNCT
iajs-2478	43	8	∇𝑣	∇𝑣	PROPN
iajs-2478	43	9	𝑦	𝑦	PRON
iajs-2478	43	10	,	,	PUNCT
iajs-2478	43	11	𝑣	𝑣	PRON
iajs-2478	43	12	𝑦	𝑦	NOUN
iajs-2478	43	13	,	,	PUNCT
iajs-2478	43	14	𝑣	𝑣	PRON
iajs-2478	43	15	𝑦	𝑦	NOUN
iajs-2478	43	16	,	,	PUNCT
iajs-2478	43	17	𝑣	𝑣	PRON
iajs-2478	43	18	𝑓	𝑓	X
iajs-2478	43	19	,	,	PUNCT
iajs-2478	43	20	𝑣	𝑣	PRON
iajs-2478	43	21	𝑢	𝑢	X
iajs-2478	43	22	,	,	PUNCT
iajs-2478	43	23	𝑣	𝑣	X
iajs-2478	43	24	,	,	PUNCT
iajs-2478	43	25	∀	∀	X
iajs-2478	43	26	𝑣	𝑣	ADP
iajs-2478	43	27	∈	∈	PROPN
iajs-2478	43	28	𝑉	𝑉	PROPN
iajs-2478	43	29	(	(	PUNCT
iajs-2478	43	30	18.a	18.a	NUM
iajs-2478	43	31	)	)	PUNCT
iajs-2478	43	32	𝑦	𝑦	NOUN
iajs-2478	43	33	,	,	PUNCT
iajs-2478	43	34	𝑣	𝑣	PRON
iajs-2478	43	35	𝑦	𝑦	PROPN
iajs-2478	43	36	,	,	PUNCT
iajs-2478	43	37	𝑣	𝑣	X
iajs-2478	43	38	,	,	PUNCT
iajs-2478	43	39	∀	∀	VERB
iajs-2478	43	40	𝑣	𝑣	ADP
iajs-2478	43	41	∈	∈	PROPN
iajs-2478	43	42	𝑉	𝑉	PROPN
iajs-2478	43	43	(	(	PUNCT
iajs-2478	43	44	18.b	18.b	NUM
iajs-2478	43	45	)	)	PUNCT
iajs-2478	44	1	〈	〈	NOUN
iajs-2478	44	2	𝑦	𝑦	NOUN
iajs-2478	44	3	,	,	PUNCT
iajs-2478	44	4	𝑣	𝑣	ADP
iajs-2478	44	5	〉	〉	NOUN
iajs-2478	44	6	∇𝑦	∇𝑦	PROPN
iajs-2478	44	7	,	,	PUNCT
iajs-2478	44	8	∇𝑣	∇𝑣	PROPN
iajs-2478	44	9	𝑦	𝑦	PRON
iajs-2478	44	10	,	,	PUNCT
iajs-2478	44	11	𝑣	𝑣	DET
iajs-2478	44	12	𝑦	𝑦	NOUN
iajs-2478	44	13	,	,	PUNCT
iajs-2478	44	14	𝑣	𝑣	PRON
iajs-2478	44	15	𝑦	𝑦	NOUN
iajs-2478	44	16	,	,	PUNCT
iajs-2478	44	17	𝑣	𝑣	PRON
iajs-2478	44	18	𝑓	𝑓	X
iajs-2478	44	19	,	,	PUNCT
iajs-2478	44	20	𝑣	𝑣	PRON
iajs-2478	44	21	𝑢	𝑢	X
iajs-2478	44	22	,	,	PUNCT
iajs-2478	44	23	𝑣	𝑣	X
iajs-2478	44	24	,	,	PUNCT
iajs-2478	44	25	∀	∀	X
iajs-2478	44	26	𝑣	𝑣	ADP
iajs-2478	44	27	∈	∈	PROPN
iajs-2478	44	28	𝑉	𝑉	PROPN
iajs-2478	44	29	(	(	PUNCT
iajs-2478	44	30	19.a	19.a	NUM
iajs-2478	44	31	)	)	PUNCT
iajs-2478	44	32	𝑦	𝑦	NOUN
iajs-2478	44	33	,	,	PUNCT
iajs-2478	44	34	𝑣	𝑣	PRON
iajs-2478	44	35	𝑦	𝑦	PROPN
iajs-2478	44	36	,	,	PUNCT
iajs-2478	44	37	𝑣	𝑣	X
iajs-2478	44	38	,	,	PUNCT
iajs-2478	44	39	∀	∀	VERB
iajs-2478	44	40	𝑣	𝑣	ADP
iajs-2478	44	41	∈	∈	PROPN
iajs-2478	44	42	𝑉	𝑉	PROPN
iajs-2478	44	43	(	(	PUNCT
iajs-2478	44	44	19.b	19.b	NUM
iajs-2478	44	45	)	)	PUNCT
iajs-2478	44	46	where	where	SCONJ
iajs-2478	44	47	𝑦	𝑦	DET
iajs-2478	44	48	𝑦	𝑦	PART
iajs-2478	44	49	𝑥	𝑥	X
iajs-2478	44	50	𝑦	𝑦	NOUN
iajs-2478	44	51	𝑥	𝑥	NOUN
iajs-2478	44	52	,	,	PUNCT
iajs-2478	44	53	0	0	NUM
iajs-2478	44	54	∈	∈	PROPN
iajs-2478	44	55	𝑉	𝑉	PROPN
iajs-2478	44	56	⊂	⊂	PROPN
iajs-2478	44	57	𝑉	𝑉	PROPN
iajs-2478	44	58	⊂	⊂	PROPN
iajs-2478	44	59	𝐿	𝐿	PROPN
iajs-2478	44	60	ω	ω	PROPN
iajs-2478	44	61	is	be	AUX
iajs-2478	44	62	the	the	DET
iajs-2478	44	63	projection	projection	NOUN
iajs-2478	44	64	of	of	ADP
iajs-2478	44	65	𝑦	𝑦	NOUN
iajs-2478	44	66	,	,	PUNCT
iajs-2478	44	67	thus	thus	ADV
iajs-2478	44	68	𝑦	𝑦	NUM
iajs-2478	44	69	,	,	PUNCT
iajs-2478	44	70	𝑣	𝑣	PRON
iajs-2478	44	71	𝑦	𝑦	PROPN
iajs-2478	44	72	,	,	PUNCT
iajs-2478	44	73	𝑣	𝑣	X
iajs-2478	44	74	,	,	PUNCT
iajs-2478	44	75	∀	∀	X
iajs-2478	44	76	𝑣	𝑣	ADP
iajs-2478	44	77	∈	∈	PROPN
iajs-2478	44	78	𝑉	𝑉	PROPN
iajs-2478	44	79	⟺	⟺	NOUN
iajs-2478	44	80	∣∣	∣∣	NUM
iajs-2478	44	81	𝑦	𝑦	NOUN
iajs-2478	44	82	𝑦	𝑦	X
iajs-2478	44	83	∣∣	∣∣	X
iajs-2478	44	84	∣∣	∣∣	X
iajs-2478	44	85	𝑦	𝑦	NOUN
iajs-2478	44	86	𝑣	𝑣	ADP
iajs-2478	44	87	∣∣	∣∣	NUM
iajs-2478	44	88	,	,	PUNCT
iajs-2478	44	89	∀	∀	X
iajs-2478	44	90	𝑣	𝑣	ADP
iajs-2478	44	91	∈	∈	PROPN
iajs-2478	44	92	𝑉	𝑉	PROPN
iajs-2478	44	93	.	.	PUNCT
iajs-2478	45	1	substituting	substitute	VERB
iajs-2478	45	2	(	(	PUNCT
iajs-2478	45	3	14	14	NUM
iajs-2478	45	4	16	16	NUM
iajs-2478	45	5	)	)	PUNCT
iajs-2478	45	6	in	in	ADP
iajs-2478	45	7	(	(	PUNCT
iajs-2478	45	8	17	17	NUM
iajs-2478	45	9	)	)	SYM
iajs-2478	45	10	19	19	NUM
iajs-2478	45	11	)	)	PUNCT
iajs-2478	45	12	respectively	respectively	ADV
iajs-2478	45	13	,	,	PUNCT
iajs-2478	45	14	and	and	CCONJ
iajs-2478	45	15	then	then	ADV
iajs-2478	45	16	setting	set	VERB
iajs-2478	45	17	𝑣	𝑣	ADP
iajs-2478	45	18	𝑣	𝑣	NOUN
iajs-2478	45	19	,	,	PUNCT
iajs-2478	45	20	𝑣	𝑣	DET
iajs-2478	45	21	𝑣	𝑣	PROPN
iajs-2478	45	22	&	&	CCONJ
iajs-2478	45	23	𝑣	𝑣	DET
iajs-2478	45	24	𝑣	𝑣	ADP
iajs-2478	45	25	∀	∀	X
iajs-2478	45	26	𝑙	𝑙	X
iajs-2478	45	27	1,2	1,2	NUM
iajs-2478	45	28	,	,	PUNCT
iajs-2478	45	29	…	…	PUNCT
iajs-2478	45	30	,	,	PUNCT
iajs-2478	45	31	𝑛	𝑛	PROPN
iajs-2478	45	32	,	,	PUNCT
iajs-2478	45	33	the	the	DET
iajs-2478	45	34	obtained	obtain	VERB
iajs-2478	45	35	equations	equation	NOUN
iajs-2478	45	36	are	be	AUX
iajs-2478	45	37	equivalent	equivalent	ADJ
iajs-2478	45	38	to	to	ADP
iajs-2478	45	39	the	the	DET
iajs-2478	45	40	following	follow	VERB
iajs-2478	45	41	linear	linear	NOUN
iajs-2478	45	42	system	system	NOUN
iajs-2478	45	43	(	(	PUNCT
iajs-2478	45	44	ls	ls	PROPN
iajs-2478	45	45	)	)	PUNCT
iajs-2478	45	46	of	of	ADP
iajs-2478	45	47	1st	1st	ADJ
iajs-2478	45	48	order	order	NOUN
iajs-2478	45	49	odes	ode	VERB
iajs-2478	45	50	with	with	ADP
iajs-2478	45	51	ics	ic	NOUN
iajs-2478	45	52	(	(	PUNCT
iajs-2478	45	53	which	which	PRON
iajs-2478	45	54	has	have	VERB
iajs-2478	45	55	a	a	DET
iajs-2478	45	56	unique	unique	ADJ
iajs-2478	45	57	solution	solution	NOUN
iajs-2478	45	58	)	)	PUNCT
iajs-2478	45	59	,	,	PUNCT
iajs-2478	45	60	i.e.	i.e.	X
iajs-2478	45	61	𝐴𝐶	𝐴𝐶	PROPN
iajs-2478	45	62	´	´	PROPN
iajs-2478	45	63	𝑡	𝑡	PART
iajs-2478	45	64	𝐵𝐶	𝐵𝐶	PROPN
iajs-2478	45	65	𝑡	𝑡	VERB
iajs-2478	45	66	𝐷𝐶	𝐷𝐶	PROPN
iajs-2478	45	67	𝑡	𝑡	NOUN
iajs-2478	45	68	𝐸𝐶	𝐸𝐶	PROPN
iajs-2478	45	69	𝑡	𝑡	NOUN
iajs-2478	45	70	𝑏	𝑏	PROPN
iajs-2478	45	71	,	,	PUNCT
iajs-2478	45	72	(	(	PUNCT
iajs-2478	45	73	20.a	20.a	NUM
iajs-2478	45	74	)	)	PUNCT
iajs-2478	45	75	𝐴𝐶	𝐴𝐶	NOUN
iajs-2478	45	76	0	0	NUM
iajs-2478	45	77	𝑏	𝑏	NOUN
iajs-2478	45	78	,	,	PUNCT
iajs-2478	45	79	(	(	PUNCT
iajs-2478	45	80	20.b	20.b	NUM
iajs-2478	45	81	)	)	PUNCT
iajs-2478	45	82	𝐹𝐶	𝐹𝐶	PROPN
iajs-2478	45	83	´	´	NOUN
iajs-2478	45	84	𝑡	𝑡	PROPN
iajs-2478	45	85	𝐺𝐶	𝐺𝐶	PROPN
iajs-2478	45	86	𝑡	𝑡	PRON
iajs-2478	45	87	𝐻𝐶	𝐻𝐶	PROPN
iajs-2478	45	88	𝑡	𝑡	ADJ
iajs-2478	45	89	𝐾𝐶	𝐾𝐶	PROPN
iajs-2478	45	90	𝑡	𝑡	PROPN
iajs-2478	45	91	𝑏	𝑏	PROPN
iajs-2478	45	92	,	,	PUNCT
iajs-2478	45	93	(	(	PUNCT
iajs-2478	45	94	21.a	21.a	NUM
iajs-2478	45	95	)	)	PUNCT
iajs-2478	45	96	𝐹𝐶	𝐹𝐶	PROPN
iajs-2478	45	97	0	0	NUM
iajs-2478	45	98	𝑏	𝑏	NOUN
iajs-2478	45	99	,	,	PUNCT
iajs-2478	45	100	(	(	PUNCT
iajs-2478	45	101	21.b	21.b	NUM
iajs-2478	45	102	)	)	PUNCT
iajs-2478	45	103	𝑀𝐶	𝑀𝐶	PROPN
iajs-2478	45	104	´	´	NOUN
iajs-2478	45	105	𝑡	𝑡	PROPN
iajs-2478	45	106	𝑁𝐶	𝑁𝐶	PROPN
iajs-2478	45	107	𝑡	𝑡	PROPN
iajs-2478	45	108	𝑅𝐶	𝑅𝐶	PROPN
iajs-2478	45	109	𝑡	𝑡	X
iajs-2478	45	110	𝑊𝐶	𝑊𝐶	PROPN
iajs-2478	45	111	𝑡	𝑡	PROPN
iajs-2478	45	112	𝑏	𝑏	PROPN
iajs-2478	45	113	,	,	PUNCT
iajs-2478	45	114	(	(	PUNCT
iajs-2478	45	115	22.a	22.a	NUM
iajs-2478	45	116	)	)	PUNCT
iajs-2478	45	117	𝑀𝐶	𝑀𝐶	NOUN
iajs-2478	45	118	0	0	NUM
iajs-2478	46	1	𝑏	𝑏	NOUN
iajs-2478	46	2	,	,	PUNCT
iajs-2478	46	3	(	(	PUNCT
iajs-2478	46	4	22.b	22.b	NUM
iajs-2478	46	5	)	)	PUNCT
iajs-2478	46	6	where	where	SCONJ
iajs-2478	46	7	𝐴	𝐴	PROPN
iajs-2478	46	8	𝑎	𝑎	X
iajs-2478	46	9	,	,	PUNCT
iajs-2478	46	10	𝑎	𝑎	NOUN
iajs-2478	46	11	𝑣	𝑣	NOUN
iajs-2478	46	12	,	,	PUNCT
iajs-2478	46	13	𝑣	𝑣	X
iajs-2478	46	14	,	,	PUNCT
iajs-2478	46	15	𝐵	𝐵	PROPN
iajs-2478	46	16	𝑏	𝑏	PROPN
iajs-2478	46	17	,	,	PUNCT
iajs-2478	46	18	𝑏	𝑏	PROPN
iajs-2478	46	19	(	(	PUNCT
iajs-2478	46	20	∇𝑣	∇𝑣	INTJ
iajs-2478	46	21	,	,	PUNCT
iajs-2478	46	22	∇𝑣	∇𝑣	VERB
iajs-2478	46	23	𝑣	𝑣	ADP
iajs-2478	46	24	,	,	PUNCT
iajs-2478	46	25	𝑣	𝑣	X
iajs-2478	46	26	)	)	PUNCT
iajs-2478	46	27	,	,	PUNCT
iajs-2478	46	28	𝐷	𝐷	PROPN
iajs-2478	46	29	𝑑	𝑑	PROPN
iajs-2478	46	30	,	,	PUNCT
iajs-2478	46	31	𝑑	𝑑	PROPN
iajs-2478	46	32	𝑣	𝑣	PROPN
iajs-2478	46	33	,	,	PUNCT
iajs-2478	46	34	𝑣	𝑣	X
iajs-2478	46	35	,	,	PUNCT
iajs-2478	46	36	𝐸	𝐸	PROPN
iajs-2478	46	37	𝑒	𝑒	PROPN
iajs-2478	46	38	,	,	PUNCT
iajs-2478	46	39	𝑒	𝑒	PROPN
iajs-2478	46	40	𝑣	𝑣	NOUN
iajs-2478	46	41	,	,	PUNCT
iajs-2478	46	42	𝑣	𝑣	PROPN
iajs-2478	46	43	)	)	PUNCT
iajs-2478	46	44	,	,	PUNCT
iajs-2478	46	45	𝐹	𝐹	PROPN
iajs-2478	46	46	𝑓	𝑓	INTJ
iajs-2478	46	47	,	,	PUNCT
iajs-2478	46	48	𝑓	𝑓	PRON
iajs-2478	46	49	𝑣	𝑣	NOUN
iajs-2478	46	50	,	,	PUNCT
iajs-2478	46	51	𝑣	𝑣	X
iajs-2478	46	52	,	,	PUNCT
iajs-2478	46	53	𝐺	𝐺	PROPN
iajs-2478	46	54	𝑔	𝑔	PROPN
iajs-2478	46	55	,	,	PUNCT
iajs-2478	46	56	𝑔	𝑔	PROPN
iajs-2478	46	57	𝛻𝑣	𝛻𝑣	PUNCT
iajs-2478	46	58	,	,	PUNCT
iajs-2478	46	59	𝛻𝑣	𝛻𝑣	PUNCT
iajs-2478	46	60	𝑣	𝑣	X
iajs-2478	46	61	,	,	PUNCT
iajs-2478	46	62	𝑣	𝑣	PROPN
iajs-2478	46	63	)	)	PUNCT
iajs-2478	46	64	,	,	PUNCT
iajs-2478	46	65	𝐻	𝐻	PROPN
iajs-2478	46	66	ℎ	ℎ	NOUN
iajs-2478	46	67	,	,	PUNCT
iajs-2478	46	68	ℎ	ℎ	PROPN
iajs-2478	46	69	𝑣	𝑣	PROPN
iajs-2478	46	70	,	,	PUNCT
iajs-2478	46	71	𝑣	𝑣	INTJ
iajs-2478	46	72	,	,	PUNCT
iajs-2478	46	73	𝐾	𝐾	PROPN
iajs-2478	46	74	𝑘	𝑘	PROPN
iajs-2478	46	75	,	,	PUNCT
iajs-2478	46	76	𝑘	𝑘	PROPN
iajs-2478	46	77	𝑣	𝑣	X
iajs-2478	46	78	,	,	PUNCT
iajs-2478	46	79	𝑣	𝑣	PROPN
iajs-2478	46	80	)	)	PUNCT
iajs-2478	46	81	,	,	PUNCT
iajs-2478	46	82	𝑀	𝑀	PROPN
iajs-2478	46	83	𝑚	𝑚	PROPN
iajs-2478	46	84	,	,	PUNCT
iajs-2478	46	85	𝑚	𝑚	PROPN
iajs-2478	46	86	𝑣	𝑣	PROPN
iajs-2478	46	87	,	,	PUNCT
iajs-2478	46	88	𝑣	𝑣	X
iajs-2478	46	89	,	,	PUNCT
iajs-2478	46	90	𝑁	𝑁	PROPN
iajs-2478	46	91	𝑛	𝑛	NOUN
iajs-2478	46	92	,	,	PUNCT
iajs-2478	46	93	𝑛	𝑛	PRON
iajs-2478	46	94	𝛻𝑣	𝛻𝑣	PUNCT
iajs-2478	46	95	,	,	PUNCT
iajs-2478	46	96	𝛻𝑣	𝛻𝑣	PUNCT
iajs-2478	46	97	𝑣	𝑣	X
iajs-2478	46	98	,	,	PUNCT
iajs-2478	46	99	𝑣	𝑣	INTJ
iajs-2478	46	100	,	,	PUNCT
iajs-2478	46	101	𝑅	𝑅	PROPN
iajs-2478	46	102	𝑟	𝑟	NOUN
iajs-2478	46	103	,	,	PUNCT
iajs-2478	46	104	𝑟	𝑟	X
iajs-2478	46	105	𝑣	𝑣	X
iajs-2478	46	106	,	,	PUNCT
iajs-2478	46	107	𝑣	𝑣	PROPN
iajs-2478	46	108	)	)	PUNCT
iajs-2478	46	109	,	,	PUNCT
iajs-2478	46	110	𝑊	𝑊	PROPN
iajs-2478	46	111	𝑤	𝑤	PROPN
iajs-2478	46	112	,	,	PUNCT
iajs-2478	46	113	𝑤	𝑤	ADP
iajs-2478	46	114	𝑣	𝑣	NOUN
iajs-2478	46	115	,	,	PUNCT
iajs-2478	46	116	𝑣	𝑣	PROPN
iajs-2478	46	117	)	)	PUNCT
iajs-2478	46	118	,	,	PUNCT
iajs-2478	46	119	𝑏	𝑏	PROPN
iajs-2478	46	120	𝑏	𝑏	PROPN
iajs-2478	46	121	)	)	PUNCT
iajs-2478	46	122	,	,	PUNCT
iajs-2478	46	123	𝑏	𝑏	PROPN
iajs-2478	46	124	𝑦	𝑦	NOUN
iajs-2478	46	125	,	,	PUNCT
iajs-2478	46	126	𝑣	𝑣	X
iajs-2478	46	127	,	,	PUNCT
iajs-2478	46	128	𝑏	𝑏	PROPN
iajs-2478	46	129	𝑏	𝑏	PROPN
iajs-2478	46	130	,	,	PUNCT
iajs-2478	46	131	𝑏	𝑏	PROPN
iajs-2478	46	132	𝑓	𝑓	PROPN
iajs-2478	46	133	,	,	PUNCT
iajs-2478	46	134	𝑣	𝑣	PRON
iajs-2478	46	135	𝑢	𝑢	X
iajs-2478	46	136	,	,	PUNCT
iajs-2478	46	137	𝑣	𝑣	X
iajs-2478	46	138	,	,	PUNCT
iajs-2478	46	139	c	c	X
iajs-2478	46	140	´	´	NOUN
iajs-2478	46	141	t	t	NOUN
iajs-2478	47	1	c	c	NUM
iajs-2478	47	2	´	´	PROPN
iajs-2478	47	3	t	t	NOUN
iajs-2478	47	4	,	,	PUNCT
iajs-2478	47	5	𝐶	𝐶	PROPN
iajs-2478	47	6	t	t	PROPN
iajs-2478	47	7	𝑐	𝑐	PROPN
iajs-2478	47	8	t	t	PROPN
iajs-2478	47	9	,	,	PUNCT
iajs-2478	47	10	𝐶	𝐶	PROPN
iajs-2478	47	11	0	0	PUNCT
iajs-2478	47	12	𝑐	𝑐	PROPN
iajs-2478	47	13	0	0	NUM
iajs-2478	47	14	,	,	PUNCT
iajs-2478	47	15	∀	∀	NOUN
iajs-2478	47	16	𝑙	𝑙	SYM
iajs-2478	47	17	1,2,3	1,2,3	NUM
iajs-2478	47	18	…	…	PUNCT
iajs-2478	47	19	𝑛	𝑛	NOUN
iajs-2478	47	20	,	,	PUNCT
iajs-2478	47	21	𝑖	𝑖	NOUN
iajs-2478	47	22	1,2,3	1,2,3	NOUN
iajs-2478	47	23	.	.	PUNCT
iajs-2478	47	24	to	to	PART
iajs-2478	47	25	show	show	VERB
iajs-2478	47	26	the	the	DET
iajs-2478	47	27	norm	norm	NOUN
iajs-2478	47	28	𝐲𝐧	𝐲𝐧	ADP
iajs-2478	47	29	𝟎	𝟎	PROPN
iajs-2478	47	30	𝟎	𝟎	NUM
iajs-2478	47	31	is	be	AUX
iajs-2478	47	32	bounded	bound	VERB
iajs-2478	47	33	:	:	PUNCT
iajs-2478	47	34	since	since	SCONJ
iajs-2478	47	35	𝑦	𝑦	PROPN
iajs-2478	47	36	∈	∈	PROPN
iajs-2478	47	37	𝐿	𝐿	PROPN
iajs-2478	47	38	ω	ω	PROPN
iajs-2478	47	39	,	,	PUNCT
iajs-2478	47	40	there	there	PRON
iajs-2478	47	41	exists	exist	VERB
iajs-2478	47	42	a	a	DET
iajs-2478	47	43	sequence	sequence	NOUN
iajs-2478	47	44	𝑣	𝑣	NOUN
iajs-2478	47	45	with	with	ADP
iajs-2478	47	46	𝑣	𝑣	DET
iajs-2478	47	47	∈	∈	PROPN
iajs-2478	47	48	𝑉	𝑉	PROPN
iajs-2478	47	49	,	,	PUNCT
iajs-2478	47	50	such	such	ADJ
iajs-2478	47	51	that	that	SCONJ
iajs-2478	47	52	𝑣	𝑣	ADP
iajs-2478	47	53	⟶	⟶	NOUN
iajs-2478	47	54	𝑦	𝑦	NOUN
iajs-2478	47	55	strongly	strongly	ADV
iajs-2478	47	56	in	in	ADP
iajs-2478	47	57	𝐿	𝐿	PROPN
iajs-2478	47	58	ω	ω	PROPN
iajs-2478	47	59	,	,	PUNCT
iajs-2478	47	60	then	then	ADV
iajs-2478	47	61	from	from	ADP
iajs-2478	47	62	the	the	DET
iajs-2478	47	63	projection	projection	NOUN
iajs-2478	47	64	theorem	theorem	NOUN
iajs-2478	48	1	[	[	X
iajs-2478	48	2	16	16	NUM
iajs-2478	48	3	]	]	PUNCT
iajs-2478	48	4	.	.	PUNCT
iajs-2478	49	1	and	and	CCONJ
iajs-2478	49	2	(	(	PUNCT
iajs-2478	49	3	17.b	17.b	NUM
iajs-2478	49	4	)	)	PUNCT
iajs-2478	49	5	,	,	PUNCT
iajs-2478	49	6	‖𝑦	‖𝑦	VERB
iajs-2478	49	7	𝑦	𝑦	PROPN
iajs-2478	49	8	‖	‖	PROPN
iajs-2478	49	9	‖𝑦	‖𝑦	ADJ
iajs-2478	49	10	𝑣	𝑣	PRON
iajs-2478	49	11	‖	‖	PROPN
iajs-2478	49	12	,	,	PUNCT
iajs-2478	49	13	∀	∀	VERB
iajs-2478	49	14	𝑣	𝑣	ADP
iajs-2478	49	15	∈	∈	PROPN
iajs-2478	49	16	𝑉	𝑉	PROPN
iajs-2478	49	17	,	,	PUNCT
iajs-2478	49	18	and	and	CCONJ
iajs-2478	49	19	then	then	ADV
iajs-2478	49	20	‖𝑦	‖𝑦	VERB
iajs-2478	49	21	𝑦	𝑦	PROPN
iajs-2478	49	22	‖	‖	PROPN
iajs-2478	49	23	‖𝑦	‖𝑦	ADJ
iajs-2478	49	24	𝑣	𝑣	PRON
iajs-2478	49	25	‖	‖	PROPN
iajs-2478	49	26	,	,	PUNCT
iajs-2478	49	27	∀	∀	VERB
iajs-2478	49	28	𝑣	𝑣	ADP
iajs-2478	49	29	∈	∈	PROPN
iajs-2478	49	30	𝑉	𝑉	PROPN
iajs-2478	49	31	⊂	⊂	PROPN
iajs-2478	49	32	𝑉	𝑉	PROPN
iajs-2478	49	33	,	,	PUNCT
iajs-2478	49	34	∀𝑛	∀𝑛	NOUN
iajs-2478	49	35	⇒	⇒	VERB
iajs-2478	49	36	𝑦	𝑦	PROPN
iajs-2478	49	37	⟶	⟶	NOUN
iajs-2478	49	38	𝑦	𝑦	NOUN
iajs-2478	49	39	,	,	PUNCT
iajs-2478	49	40	strongly	strongly	ADV
iajs-2478	49	41	in	in	ADP
iajs-2478	49	42	𝐿	𝐿	PROPN
iajs-2478	49	43	ω	ω	PROPN
iajs-2478	49	44	,	,	PUNCT
iajs-2478	49	45	implies	imply	VERB
iajs-2478	49	46	to	to	ADP
iajs-2478	49	47	  	  	SPACE
iajs-2478	49	48	116	116	NUM
iajs-2478	49	49	ibn	ibn	PROPN
iajs-2478	49	50	al	al	PROPN
iajs-2478	49	51	-	-	PUNCT
iajs-2478	49	52	haitham	haitham	PROPN
iajs-2478	49	53	jour	jour	X
iajs-2478	49	54	.	.	PROPN
iajs-2478	50	1	for	for	ADP
iajs-2478	50	2	pure	pure	ADJ
iajs-2478	50	3	&	&	CCONJ
iajs-2478	50	4	appl	appl	PROPN
iajs-2478	50	5	.	.	PUNCT
iajs-2478	51	1	sci	sci	PROPN
iajs-2478	51	2	.	.	PROPN
iajs-2478	52	1	33	33	NUM
iajs-2478	52	2	(	(	PUNCT
iajs-2478	52	3	3	3	NUM
iajs-2478	52	4	)	)	PUNCT
iajs-2478	52	5	2020	2020	NUM
iajs-2478	52	6	‖𝑦	‖𝑦	VERB
iajs-2478	52	7	‖	‖	PROPN
iajs-2478	52	8	𝑏	𝑏	PROPN
iajs-2478	52	9	,	,	PUNCT
iajs-2478	52	10	similarly	similarly	ADV
iajs-2478	52	11	‖𝑦	‖𝑦	VERB
iajs-2478	52	12	‖	‖	PROPN
iajs-2478	52	13	𝑏	𝑏	PROPN
iajs-2478	52	14	&	&	CCONJ
iajs-2478	52	15	‖𝑦	‖𝑦	PROPN
iajs-2478	52	16	‖	‖	PROPN
iajs-2478	52	17	𝑏	𝑏	PROPN
iajs-2478	52	18	,	,	PUNCT
iajs-2478	52	19	thus	thus	ADV
iajs-2478	52	20	𝑦	𝑦	PRON
iajs-2478	52	21	⃗	⃗	PROPN
iajs-2478	52	22	𝟎	𝟎	NUM
iajs-2478	52	23	is	be	AUX
iajs-2478	52	24	bounded	bound	VERB
iajs-2478	52	25	in	in	ADP
iajs-2478	52	26	𝐿	𝐿	PROPN
iajs-2478	52	27	ω	ω	PROPN
iajs-2478	52	28	.	.	PUNCT
iajs-2478	53	1	the	the	DET
iajs-2478	53	2	norms	norm	NOUN
iajs-2478	53	3	‖	‖	PROPN
iajs-2478	53	4	�	�	NOUN
iajs-2478	53	5	⃗	⃗	NOUN
iajs-2478	53	6	�	�	PROPN
iajs-2478	53	7	𝒏	𝒏	PROPN
iajs-2478	53	8	𝒕	𝒕	X
iajs-2478	53	9	‖	‖	PROPN
iajs-2478	53	10	𝑳	𝑳	PROPN
iajs-2478	53	11	ĩ,𝑳𝟐	ĩ,𝑳𝟐	NOUN
iajs-2478	53	12	ω	ω	NUM
iajs-2478	53	13	and	and	CCONJ
iajs-2478	53	14	‖	‖	PROPN
iajs-2478	53	15	�	�	PROPN
iajs-2478	53	16	⃗	⃗	NOUN
iajs-2478	53	17	�	�	PROPN
iajs-2478	53	18	𝒏	𝒏	PROPN
iajs-2478	53	19	𝒕	𝒕	PRON
iajs-2478	53	20	‖𝑸	‖𝑸	PROPN
iajs-2478	53	21	are	be	AUX
iajs-2478	53	22	bounded	bound	VERB
iajs-2478	53	23	:	:	PUNCT
iajs-2478	53	24	setting	set	VERB
iajs-2478	53	25	𝑣	𝑣	ADP
iajs-2478	53	26	𝑦	𝑦	NOUN
iajs-2478	53	27	,	,	PUNCT
iajs-2478	53	28	𝑣	𝑣	DET
iajs-2478	53	29	𝑦	𝑦	NOUN
iajs-2478	53	30	and	and	CCONJ
iajs-2478	53	31	𝑣	𝑣	DET
iajs-2478	53	32	𝑦	𝑦	NOUN
iajs-2478	53	33	in	in	ADP
iajs-2478	53	34	(	(	PUNCT
iajs-2478	53	35	17	17	NUM
iajs-2478	53	36	)	)	PUNCT
iajs-2478	53	37	,	,	PUNCT
iajs-2478	53	38	(	(	PUNCT
iajs-2478	53	39	18	18	NUM
iajs-2478	53	40	)	)	PUNCT
iajs-2478	53	41	&	&	CCONJ
iajs-2478	53	42	(	(	PUNCT
iajs-2478	53	43	19	19	NUM
iajs-2478	53	44	)	)	PUNCT
iajs-2478	53	45	respectively	respectively	ADV
iajs-2478	53	46	,	,	PUNCT
iajs-2478	53	47	integrating	integrate	VERB
iajs-2478	53	48	w.r.t	w.r.t	NOUN
iajs-2478	53	49	.	.	PUNCT
iajs-2478	54	1	𝑡	𝑡	VERB
iajs-2478	54	2	from	from	ADP
iajs-2478	54	3	0	0	NUM
iajs-2478	54	4	to	to	ADP
iajs-2478	54	5	𝑇	𝑇	PROPN
iajs-2478	54	6	,	,	PUNCT
iajs-2478	54	7	and	and	CCONJ
iajs-2478	54	8	then	then	ADV
iajs-2478	54	9	adding	add	VERB
iajs-2478	54	10	the	the	DET
iajs-2478	54	11	obtained	obtain	VERB
iajs-2478	54	12	three	three	NUM
iajs-2478	54	13	equations	equation	NOUN
iajs-2478	54	14	,	,	PUNCT
iajs-2478	54	15	one	one	PRON
iajs-2478	54	16	gets	get	VERB
iajs-2478	54	17	〈	〈	PRON
iajs-2478	54	18	�	�	NOUN
iajs-2478	54	19	⃗	⃗	NOUN
iajs-2478	54	20	�	�	PROPN
iajs-2478	54	21	,	,	PUNCT
iajs-2478	54	22	�	�	PROPN
iajs-2478	54	23	⃗	⃗	PROPN
iajs-2478	54	24	�	�	PROPN
iajs-2478	54	25	〉	〉	PROPN
iajs-2478	54	26	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	54	27	‖	‖	PROPN
iajs-2478	54	28	�	�	PROPN
iajs-2478	54	29	⃗	⃗	PROPN
iajs-2478	54	30	�	�	PROPN
iajs-2478	54	31	‖	‖	PROPN
iajs-2478	54	32	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	54	33	𝑓	𝑓	PRON
iajs-2478	54	34	,	,	PUNCT
iajs-2478	54	35	𝑦	𝑦	NOUN
iajs-2478	54	36	𝑢	𝑢	X
iajs-2478	54	37	,	,	PUNCT
iajs-2478	54	38	𝑦	𝑦	PROPN
iajs-2478	54	39	𝑓	𝑓	PRON
iajs-2478	54	40	,	,	PUNCT
iajs-2478	54	41	𝑦	𝑦	NOUN
iajs-2478	54	42	𝑢	𝑢	X
iajs-2478	54	43	,	,	PUNCT
iajs-2478	54	44	𝑦	𝑦	PROPN
iajs-2478	54	45	𝑓	𝑓	PRON
iajs-2478	54	46	,	,	PUNCT
iajs-2478	54	47	𝑦	𝑦	NOUN
iajs-2478	54	48	𝑢	𝑢	NOUN
iajs-2478	54	49	,	,	PUNCT
iajs-2478	54	50	𝑦	𝑦	NOUN
iajs-2478	54	51	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	54	52	,	,	PUNCT
iajs-2478	54	53	(	(	PUNCT
iajs-2478	54	54	23	23	NUM
iajs-2478	54	55	)	)	PUNCT
iajs-2478	54	56	using	use	VERB
iajs-2478	54	57	lemma	lemma	PROPN
iajs-2478	54	58	(	(	PUNCT
iajs-2478	54	59	1.2	1.2	NUM
iajs-2478	54	60	)	)	PUNCT
iajs-2478	54	61	in	in	ADP
iajs-2478	54	62	[	[	X
iajs-2478	54	63	11	11	NUM
iajs-2478	54	64	]	]	PUNCT
iajs-2478	54	65	.	.	PUNCT
iajs-2478	55	1	for	for	ADP
iajs-2478	55	2	the	the	DET
iajs-2478	55	3	1st	1st	ADJ
iajs-2478	55	4	term	term	NOUN
iajs-2478	55	5	in	in	ADP
iajs-2478	55	6	the	the	DET
iajs-2478	55	7	l.h.s	l.h.s	NOUN
iajs-2478	55	8	.	.	PUNCT
iajs-2478	56	1	of	of	ADP
iajs-2478	56	2	(	(	PUNCT
iajs-2478	56	3	23	23	NUM
iajs-2478	56	4	)	)	PUNCT
iajs-2478	56	5	,	,	PUNCT
iajs-2478	56	6	and	and	CCONJ
iajs-2478	56	7	since	since	SCONJ
iajs-2478	56	8	the	the	DET
iajs-2478	56	9	2nd	2nd	ADJ
iajs-2478	56	10	term	term	NOUN
iajs-2478	56	11	is	be	AUX
iajs-2478	56	12	positive	positive	ADJ
iajs-2478	56	13	,	,	PUNCT
iajs-2478	56	14	taking	take	VERB
iajs-2478	56	15	𝑇	𝑇	PROPN
iajs-2478	56	16	𝑡	𝑡	ADP
iajs-2478	56	17	∈	∈	PROPN
iajs-2478	56	18	0	0	NUM
iajs-2478	56	19	,	,	PUNCT
iajs-2478	56	20	𝑇	𝑇	PROPN
iajs-2478	56	21	.	.	PUNCT
iajs-2478	57	1	finally	finally	ADV
iajs-2478	57	2	,	,	PUNCT
iajs-2478	57	3	using	use	VERB
iajs-2478	57	4	assumption	assumption	NOUN
iajs-2478	57	5	(	(	PUNCT
iajs-2478	57	6	a	a	X
iajs-2478	57	7	)	)	PUNCT
iajs-2478	57	8	for	for	ADP
iajs-2478	57	9	the	the	DET
iajs-2478	57	10	r.h.s	r.h.s	NOUN
iajs-2478	57	11	.	.	PUNCT
iajs-2478	58	1	of	of	ADP
iajs-2478	58	2	(	(	PUNCT
iajs-2478	58	3	23	23	NUM
iajs-2478	58	4	)	)	PUNCT
iajs-2478	58	5	,	,	PUNCT
iajs-2478	58	6	it	it	PRON
iajs-2478	58	7	yields	yield	VERB
iajs-2478	58	8	to	to	PART
iajs-2478	58	9	‖	‖	VERB
iajs-2478	58	10	⃗	⃗	PROPN
iajs-2478	58	11	‖	‖	PROPN
iajs-2478	58	12	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	58	13	𝜂	𝜂	PROPN
iajs-2478	58	14	|𝑦	|𝑦	PROPN
iajs-2478	58	15	|	|	ADV
iajs-2478	58	16	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2478	58	17	|𝑢	|𝑢	PROPN
iajs-2478	59	1	|	|	ADV
iajs-2478	59	2	|𝑦	|𝑦	PROPN
iajs-2478	59	3	|	|	ADV
iajs-2478	59	4	𝑑𝛾𝑑𝑡	𝑑𝛾𝑑𝑡	PROPN
iajs-2478	59	5	𝜂	𝜂	PROPN
iajs-2478	59	6	|𝑦	|𝑦	PROPN
iajs-2478	59	7	|	|	ADV
iajs-2478	59	8	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2478	59	9	|𝑢	|𝑢	PROPN
iajs-2478	60	1	|	|	ADV
iajs-2478	60	2	|𝑦	|𝑦	PROPN
iajs-2478	60	3	|	|	ADV
iajs-2478	60	4	𝑑𝛾𝑑𝑡	𝑑𝛾𝑑𝑡	PROPN
iajs-2478	60	5	𝜂	𝜂	PROPN
iajs-2478	60	6	|𝑦	|𝑦	PROPN
iajs-2478	60	7	|	|	ADV
iajs-2478	60	8	𝑑𝑥𝑑𝑡	𝑑𝑥𝑑𝑡	VERB
iajs-2478	60	9	|𝑢	|𝑢	PROPN
iajs-2478	61	1	|	|	ADV
iajs-2478	61	2	|𝑦	|𝑦	PROPN
iajs-2478	61	3	|	|	ADV
iajs-2478	61	4	𝑑𝛾𝑑𝑡	𝑑𝛾𝑑𝑡	PROPN
iajs-2478	61	5	]	]	PUNCT
iajs-2478	61	6	.	.	PUNCT
iajs-2478	62	1	using	use	VERB
iajs-2478	62	2	the	the	DET
iajs-2478	62	3	trace	trace	NOUN
iajs-2478	62	4	theorem	theorem	ADJ
iajs-2478	62	5	[	[	X
iajs-2478	62	6	17	17	NUM
iajs-2478	62	7	]	]	PUNCT
iajs-2478	62	8	.	.	PUNCT
iajs-2478	63	1	of	of	ADP
iajs-2478	63	2	the	the	DET
iajs-2478	63	3	r.h.s	r.h.s	NOUN
iajs-2478	63	4	.	.	PROPN
iajs-2478	63	5	,	,	PUNCT
iajs-2478	63	6	to	to	PART
iajs-2478	63	7	get	get	VERB
iajs-2478	63	8	‖	‖	PROPN
iajs-2478	63	9	�	�	NOUN
iajs-2478	63	10	⃗	⃗	NOUN
iajs-2478	63	11	�	�	PROPN
iajs-2478	63	12	𝑡	𝑡	PROPN
iajs-2478	63	13	‖	‖	PROPN
iajs-2478	63	14	‖	‖	PROPN
iajs-2478	63	15	�	�	PROPN
iajs-2478	63	16	⃗	⃗	NOUN
iajs-2478	63	17	�	�	PROPN
iajs-2478	63	18	0	0	NUM
iajs-2478	63	19	‖	‖	PROPN
iajs-2478	63	20	‖𝜂	‖𝜂	PROPN
iajs-2478	63	21	‖	‖	PROPN
iajs-2478	63	22	‖𝜂	‖𝜂	PROPN
iajs-2478	63	23	‖	‖	PROPN
iajs-2478	63	24	‖𝜂	‖𝜂	PROPN
iajs-2478	63	25	‖	‖	PROPN
iajs-2478	63	26	‖𝑢	‖𝑢	PROPN
iajs-2478	63	27	‖	‖	PROPN
iajs-2478	63	28	‖𝑢	‖𝑢	PROPN
iajs-2478	63	29	‖	‖	PROPN
iajs-2478	63	30	‖𝑢	‖𝑢	PROPN
iajs-2478	63	31	‖	‖	ADJ
iajs-2478	63	32	‖𝑦	‖𝑦	PROPN
iajs-2478	63	33	‖	‖	PROPN
iajs-2478	63	34	𝑑𝑡	𝑑𝑡	SCONJ
iajs-2478	63	35	𝑐	𝑐	PROPN
iajs-2478	63	36	‖𝑦	‖𝑦	PROPN
iajs-2478	63	37	‖	‖	ADJ
iajs-2478	63	38	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	63	39	‖𝑦	‖𝑦	ADJ
iajs-2478	63	40	‖	‖	PROPN
iajs-2478	63	41	𝑑𝑡	𝑑𝑡	SCONJ
iajs-2478	63	42	𝑐	𝑐	PROPN
iajs-2478	63	43	‖𝑦	‖𝑦	PROPN
iajs-2478	63	44	‖	‖	ADJ
iajs-2478	63	45	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	63	46	‖𝑦	‖𝑦	ADJ
iajs-2478	63	47	‖	‖	PROPN
iajs-2478	63	48	𝑑𝑡	𝑑𝑡	SCONJ
iajs-2478	63	49	𝑐	𝑐	PROPN
iajs-2478	63	50	‖𝑦	‖𝑦	ADJ
iajs-2478	63	51	‖	‖	PROPN
iajs-2478	63	52	𝑑𝑡.	𝑑𝑡.	PROPN
iajs-2478	63	53	since	since	SCONJ
iajs-2478	63	54	‖𝜂	‖𝜂	NOUN
iajs-2478	63	55	‖	‖	PROPN
iajs-2478	63	56	𝑏	𝑏	PROPN
iajs-2478	63	57	,	,	PUNCT
iajs-2478	63	58	‖𝑢	‖𝑢	PRON
iajs-2478	63	59	‖	‖	PROPN
iajs-2478	63	60	�	�	PROPN
iajs-2478	63	61	́	́	PROPN
iajs-2478	63	62	�	�	PROPN
iajs-2478	63	63	,	,	PUNCT
iajs-2478	63	64	∀	∀	NOUN
iajs-2478	63	65	𝑖	𝑖	SYM
iajs-2478	63	66	1,2,3	1,2,3	NUM
iajs-2478	63	67	,	,	PUNCT
iajs-2478	63	68	‖	‖	PROPN
iajs-2478	63	69	�	�	NOUN
iajs-2478	63	70	⃗	⃗	NOUN
iajs-2478	63	71	�	�	PROPN
iajs-2478	63	72	0	0	NUM
iajs-2478	63	73	‖	‖	PROPN
iajs-2478	63	74	𝑏	𝑏	PROPN
iajs-2478	63	75	,	,	PUNCT
iajs-2478	63	76	then	then	ADV
iajs-2478	63	77	‖	‖	PROPN
iajs-2478	63	78	�	�	PROPN
iajs-2478	63	79	⃗	⃗	NOUN
iajs-2478	63	80	�	�	PROPN
iajs-2478	63	81	𝑡	𝑡	PROPN
iajs-2478	63	82	‖	‖	PROPN
iajs-2478	63	83	𝑐∗	𝑐∗	PROPN
iajs-2478	63	84	ℏ	ℏ	PROPN
iajs-2478	63	85	‖	‖	PROPN
iajs-2478	63	86	�	�	PROPN
iajs-2478	63	87	⃗	⃗	PROPN
iajs-2478	63	88	�	�	PROPN
iajs-2478	63	89	‖	‖	PROPN
iajs-2478	63	90	𝑑𝑡	𝑑𝑡	PROPN
iajs-2478	63	91	,	,	PUNCT
iajs-2478	63	92	where	where	SCONJ
iajs-2478	63	93	𝑐∗	𝑐∗	PROPN
iajs-2478	63	94	𝑏	𝑏	PROPN
iajs-2478	63	95	𝑏	𝑏	PROPN
iajs-2478	63	96	𝑏	𝑏	PROPN
iajs-2478	63	97	�	�	PROPN
iajs-2478	63	98	́	́	PROPN
iajs-2478	63	99	�	�	PROPN
iajs-2478	63	100	�	�	PROPN
iajs-2478	63	101	́	́	PROPN
iajs-2478	63	102	�	�	PROPN
iajs-2478	63	103	�	�	PROPN
iajs-2478	63	104	́	́	PROPN
iajs-2478	63	105	�	�	PROPN
iajs-2478	63	106	𝑏	𝑏	PROPN
iajs-2478	63	107	and	and	CCONJ
iajs-2478	63	108	ℏ	ℏ	PROPN
iajs-2478	63	109	max	max	PROPN
iajs-2478	63	110	ℏ∗	ℏ∗	PROPN
iajs-2478	63	111	,	,	PUNCT
iajs-2478	63	112	ℏ∗	ℏ∗	NOUN
iajs-2478	63	113	,	,	PUNCT
iajs-2478	63	114	ℏ∗	ℏ∗	PROPN
iajs-2478	63	115	;	;	PUNCT
iajs-2478	63	116	ℏ∗	ℏ∗	PROPN
iajs-2478	63	117	1	1	NUM
iajs-2478	63	118	𝑐	𝑐	NOUN
iajs-2478	63	119	,	,	PUNCT
iajs-2478	63	120	ℏ∗	ℏ∗	PROPN
iajs-2478	63	121	1	1	NUM
iajs-2478	63	122	𝑐	𝑐	NOUN
iajs-2478	63	123	,	,	PUNCT
iajs-2478	63	124	ℏ∗	ℏ∗	PROPN
iajs-2478	63	125	1	1	NUM
iajs-2478	63	126	𝑐	𝑐	NOUN
iajs-2478	63	127	.	.	PUNCT
iajs-2478	64	1	using	use	VERB
iajs-2478	64	2	the	the	DET
iajs-2478	64	3	continuous	continuous	ADJ
iajs-2478	64	4	bellman	bellman	NOUN
iajs-2478	64	5	gronwall	gronwall	ADJ
iajs-2478	64	6	inequality	inequality	NOUN
iajs-2478	64	7	(	(	PUNCT
iajs-2478	64	8	bgi	bgi	PROPN
iajs-2478	64	9	)	)	PUNCT
iajs-2478	64	10	,	,	PUNCT
iajs-2478	64	11	one	one	PRON
iajs-2478	64	12	gets	get	VERB
iajs-2478	64	13	‖	‖	PROPN
iajs-2478	64	14	�	�	NOUN
iajs-2478	64	15	⃗	⃗	NOUN
iajs-2478	64	16	�	�	PROPN
iajs-2478	64	17	𝑡	𝑡	PROPN
iajs-2478	64	18	‖	‖	PROPN
iajs-2478	64	19	𝑐∗𝑒ℏ	𝑐∗𝑒ℏ	PROPN
iajs-2478	64	20	𝑏	𝑏	PROPN
iajs-2478	64	21	𝑐	𝑐	PROPN
iajs-2478	64	22	,	,	PUNCT
iajs-2478	64	23	∀	∀	PUNCT
iajs-2478	64	24	𝑡	𝑡	ADP
iajs-2478	64	25	∈	∈	PROPN
iajs-2478	64	26	0	0	NUM
iajs-2478	64	27	,	,	PUNCT
iajs-2478	64	28	𝑇	𝑇	PROPN
iajs-2478	64	29	or	or	CCONJ
iajs-2478	64	30	‖	‖	PROPN
iajs-2478	64	31	�	�	NOUN
iajs-2478	64	32	⃗	⃗	NOUN
iajs-2478	64	33	�	�	PROPN
iajs-2478	64	34	𝑡	𝑡	PROPN
iajs-2478	64	35	‖	‖	PROPN
iajs-2478	64	36	𝑳	𝑳	PROPN
iajs-2478	64	37	ĩ,𝑳𝟐	ĩ,𝑳𝟐	NOUN
iajs-2478	64	38	ω	ω	NUM
iajs-2478	65	1	𝑏	𝑏	PROPN
iajs-2478	65	2	𝑐	𝑐	PROPN
iajs-2478	65	3	⇒	⇒	PROPN
iajs-2478	65	4	‖	‖	PROPN
iajs-2478	65	5	�	�	PROPN
iajs-2478	65	6	⃗	⃗	NOUN
iajs-2478	65	7	�	�	PROPN
iajs-2478	65	8	𝑡	𝑡	PROPN
iajs-2478	65	9	‖𝑸	‖𝑸	PROPN
iajs-2478	65	10	𝑏	𝑏	PROPN
iajs-2478	65	11	𝑐	𝑐	PROPN
iajs-2478	65	12	.	.	PUNCT
iajs-2478	66	1	the	the	DET
iajs-2478	66	2	norm	norm	NOUN
iajs-2478	66	3	‖	‖	PROPN
iajs-2478	66	4	�	�	PROPN
iajs-2478	66	5	⃗	⃗	NOUN
iajs-2478	66	6	�	�	PROPN
iajs-2478	66	7	𝑡	𝑡	PROPN
iajs-2478	66	8	‖𝑳𝟐	‖𝑳𝟐	PROPN
iajs-2478	66	9	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	66	10	is	be	AUX
iajs-2478	66	11	bounded	bound	VERB
iajs-2478	66	12	:	:	PUNCT
iajs-2478	66	13	again	again	ADV
iajs-2478	66	14	for	for	ADP
iajs-2478	66	15	(	(	PUNCT
iajs-2478	66	16	23	23	NUM
iajs-2478	66	17	)	)	PUNCT
iajs-2478	66	18	by	by	ADP
iajs-2478	66	19	using	use	VERB
iajs-2478	66	20	lemma	lemma	PROPN
iajs-2478	66	21	(	(	PUNCT
iajs-2478	66	22	1.2	1.2	NUM
iajs-2478	66	23	)	)	PUNCT
iajs-2478	66	24	in	in	ADP
iajs-2478	66	25	[	[	X
iajs-2478	66	26	11	11	NUM
iajs-2478	66	27	]	]	PUNCT
iajs-2478	66	28	.	.	PUNCT
iajs-2478	67	1	for	for	ADP
iajs-2478	67	2	the	the	DET
iajs-2478	67	3	l.h.s	l.h.s	NOUN
iajs-2478	67	4	.	.	PUNCT
iajs-2478	68	1	the	the	DET
iajs-2478	68	2	same	same	ADJ
iajs-2478	68	3	results	result	NOUN
iajs-2478	68	4	may	may	AUX
iajs-2478	68	5	be	be	AUX
iajs-2478	68	6	obtained	obtain	VERB
iajs-2478	68	7	(	(	PUNCT
iajs-2478	68	8	from	from	ADP
iajs-2478	68	9	the	the	DET
iajs-2478	68	10	above	above	ADJ
iajs-2478	68	11	steps	step	NOUN
iajs-2478	68	12	)	)	PUNCT
iajs-2478	68	13	and	and	CCONJ
iajs-2478	68	14	since	since	SCONJ
iajs-2478	68	15	‖	‖	PROPN
iajs-2478	68	16	�	�	NOUN
iajs-2478	68	17	⃗	⃗	NOUN
iajs-2478	68	18	�	�	PROPN
iajs-2478	68	19	0	0	NUM
iajs-2478	68	20	‖	‖	PROPN
iajs-2478	68	21	is	be	AUX
iajs-2478	68	22	bounded	bound	VERB
iajs-2478	68	23	,	,	PUNCT
iajs-2478	68	24	equation	equation	NOUN
iajs-2478	68	25	(	(	PUNCT
iajs-2478	68	26	23	23	NUM
iajs-2478	68	27	)	)	PUNCT
iajs-2478	68	28	with	with	ADP
iajs-2478	68	29	𝑡	𝑡	PROPN
iajs-2478	68	30	=	=	PROPN
iajs-2478	68	31	t	t	PROPN
iajs-2478	68	32	,	,	PUNCT
iajs-2478	68	33	becomes	become	VERB
iajs-2478	68	34	‖	‖	PROPN
iajs-2478	69	1	�	�	NOUN
iajs-2478	69	2	⃗	⃗	NOUN
iajs-2478	69	3	�	�	PROPN
iajs-2478	69	4	𝑡	𝑡	PROPN
iajs-2478	69	5	‖	‖	PROPN
iajs-2478	69	6	‖	‖	PROPN
iajs-2478	69	7	�	�	PROPN
iajs-2478	69	8	⃗	⃗	NOUN
iajs-2478	69	9	�	�	PROPN
iajs-2478	69	10	0	0	SYM
iajs-2478	69	11	‖	‖	PROPN
iajs-2478	69	12	2	2	NUM
iajs-2478	69	13	‖	‖	PROPN
iajs-2478	69	14	�	�	PROPN
iajs-2478	69	15	⃗	⃗	NOUN
iajs-2478	69	16	�	�	PROPN
iajs-2478	69	17	‖	‖	PROPN
iajs-2478	69	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	69	19	‖𝜂	‖𝜂	PROPN
iajs-2478	69	20	‖	‖	PROPN
iajs-2478	69	21	‖𝜂	‖𝜂	PROPN
iajs-2478	69	22	‖	‖	PROPN
iajs-2478	69	23	‖𝜂	‖𝜂	PROPN
iajs-2478	69	24	‖	‖	PROPN
iajs-2478	69	25	‖𝑢	‖𝑢	PROPN
iajs-2478	69	26	‖	‖	PROPN
iajs-2478	69	27	‖𝑢	‖𝑢	PROPN
iajs-2478	69	28	‖	‖	PROPN
iajs-2478	69	29	‖𝑢	‖𝑢	PROPN
iajs-2478	69	30	‖	‖	ADJ
iajs-2478	69	31	ℏ‖	ℏ‖	NOUN
iajs-2478	69	32	�	�	NOUN
iajs-2478	69	33	⃗	⃗	NOUN
iajs-2478	69	34	�	�	PROPN
iajs-2478	69	35	‖𝑸	‖𝑸	PROPN
iajs-2478	69	36	.	.	PUNCT
iajs-2478	70	1	which	which	PRON
iajs-2478	70	2	gives	give	VERB
iajs-2478	70	3	‖	‖	PROPN
iajs-2478	70	4	�	�	PROPN
iajs-2478	70	5	⃗	⃗	NOUN
iajs-2478	70	6	�	�	PROPN
iajs-2478	70	7	‖	‖	PROPN
iajs-2478	70	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	70	9	𝑏	𝑏	PROPN
iajs-2478	70	10	𝑐	𝑐	PROPN
iajs-2478	70	11	,	,	PUNCT
iajs-2478	70	12	with	with	ADP
iajs-2478	70	13	𝑏	𝑏	PROPN
iajs-2478	70	14	𝑐	𝑐	PROPN
iajs-2478	70	15	́	́	PROPN
iajs-2478	70	16	́	́	PROPN
iajs-2478	70	17	́	́	PROPN
iajs-2478	71	1	ℏ	ℏ	X
iajs-2478	71	2	,	,	PUNCT
iajs-2478	71	3	thus	thus	ADV
iajs-2478	71	4	‖	‖	PROPN
iajs-2478	71	5	�	�	NOUN
iajs-2478	71	6	⃗	⃗	NOUN
iajs-2478	71	7	�	�	PROPN
iajs-2478	71	8	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	71	9	ĩ,𝑽	ĩ,𝑽	VERB
iajs-2478	71	10	𝑏	𝑏	PROPN
iajs-2478	71	11	𝑐	𝑐	PROPN
iajs-2478	71	12	.	.	PUNCT
iajs-2478	72	1	the	the	DET
iajs-2478	72	2	convergence	convergence	NOUN
iajs-2478	72	3	of	of	ADP
iajs-2478	72	4	the	the	DET
iajs-2478	72	5	solution	solution	NOUN
iajs-2478	72	6	:	:	PUNCT
iajs-2478	72	7	let	let	VERB
iajs-2478	72	8	�	�	PROPN
iajs-2478	72	9	⃗	⃗	NOUN
iajs-2478	72	10	�	�	PROPN
iajs-2478	72	11	be	be	VERB
iajs-2478	72	12	a	a	DET
iajs-2478	72	13	sequence	sequence	NOUN
iajs-2478	72	14	of	of	ADP
iajs-2478	72	15	subspaces	subspace	NOUN
iajs-2478	72	16	of	of	ADP
iajs-2478	72	17	�	�	PROPN
iajs-2478	72	18	⃗	⃗	NOUN
iajs-2478	72	19	�	�	PROPN
iajs-2478	72	20	,	,	PUNCT
iajs-2478	72	21	s.t	s.t	PROPN
iajs-2478	72	22	.	.	PROPN
iajs-2478	72	23	∀	∀	PROPN
iajs-2478	73	1	�	�	NOUN
iajs-2478	73	2	⃗	⃗	PROPN
iajs-2478	73	3	�	�	PROPN
iajs-2478	73	4	∈	∈	PROPN
iajs-2478	73	5	𝑉,⃗	𝑉,⃗	NOUN
iajs-2478	73	6	there	there	PRON
iajs-2478	73	7	exists	exist	VERB
iajs-2478	73	8	a	a	DET
iajs-2478	73	9	sequence	sequence	NOUN
iajs-2478	73	10	�	�	NOUN
iajs-2478	73	11	⃗	⃗	NOUN
iajs-2478	73	12	�	�	PROPN
iajs-2478	73	13	}	}	PUNCT
iajs-2478	73	14	with	with	ADP
iajs-2478	73	15	�	�	NOUN
iajs-2478	73	16	⃗	⃗	NOUN
iajs-2478	73	17	�	�	PROPN
iajs-2478	73	18	∈	∈	PROPN
iajs-2478	73	19	�	�	PROPN
iajs-2478	73	20	⃗	⃗	PROPN
iajs-2478	73	21	�	�	PROPN
iajs-2478	73	22	,	,	PUNCT
iajs-2478	73	23	∀	∀	NOUN
iajs-2478	73	24	𝑛	𝑛	DET
iajs-2478	73	25	and	and	CCONJ
iajs-2478	73	26	�	�	PROPN
iajs-2478	73	27	⃗	⃗	PROPN
iajs-2478	73	28	�	�	PROPN
iajs-2478	73	29	⟶	⟶	PROPN
iajs-2478	73	30	�	�	PROPN
iajs-2478	73	31	⃗	⃗	NOUN
iajs-2478	73	32	�	�	PROPN
iajs-2478	73	33	,	,	PUNCT
iajs-2478	73	34	strongly	strongly	ADV
iajs-2478	73	35	in	in	ADP
iajs-2478	73	36	�	�	NOUN
iajs-2478	73	37	⃗	⃗	NOUN
iajs-2478	73	38	�	�	PROPN
iajs-2478	73	39	⇒	⇒	PROPN
iajs-2478	73	40	�	�	PROPN
iajs-2478	73	41	⃗	⃗	PROPN
iajs-2478	73	42	�	�	PROPN
iajs-2478	73	43	⟶	⟶	PROPN
iajs-2478	73	44	�	�	PROPN
iajs-2478	73	45	⃗	⃗	NOUN
iajs-2478	73	46	�	�	PROPN
iajs-2478	73	47	,	,	PUNCT
iajs-2478	73	48	strongly	strongly	ADV
iajs-2478	73	49	in	in	ADP
iajs-2478	73	50	𝐿	𝐿	PROPN
iajs-2478	73	51	ω	ω	PROPN
iajs-2478	73	52	,	,	PUNCT
iajs-2478	73	53	since	since	SCONJ
iajs-2478	73	54	for	for	ADP
iajs-2478	73	55	each	each	DET
iajs-2478	73	56	𝑛	𝑛	NOUN
iajs-2478	73	57	,	,	PUNCT
iajs-2478	73	58	with	with	ADP
iajs-2478	73	59	�	�	NOUN
iajs-2478	73	60	⃗	⃗	PROPN
iajs-2478	73	61	�	�	PROPN
iajs-2478	73	62	⊂	⊂	PROPN
iajs-2478	73	63	�	�	PROPN
iajs-2478	73	64	⃗	⃗	PROPN
iajs-2478	73	65	�	�	PROPN
iajs-2478	73	66	,	,	PUNCT
iajs-2478	73	67	(	(	PUNCT
iajs-2478	73	68	17	17	NUM
iajs-2478	73	69	19	19	NUM
iajs-2478	73	70	)	)	PUNCT
iajs-2478	73	71	has	have	VERB
iajs-2478	73	72	a	a	DET
iajs-2478	73	73	unique	unique	ADJ
iajs-2478	73	74	solution	solution	NOUN
iajs-2478	73	75	�	�	NOUN
iajs-2478	73	76	⃗	⃗	PROPN
iajs-2478	73	77	�	�	PROPN
iajs-2478	73	78	𝑦	𝑦	PROPN
iajs-2478	73	79	,	,	PUNCT
iajs-2478	73	80	𝑦	𝑦	PRON
iajs-2478	73	81	,	,	PUNCT
iajs-2478	73	82	𝑦	𝑦	PRON
iajs-2478	73	83	,	,	PUNCT
iajs-2478	73	84	hence	hence	ADV
iajs-2478	73	85	corresponding	correspond	VERB
iajs-2478	73	86	to	to	ADP
iajs-2478	73	87	the	the	DET
iajs-2478	73	88	sequence	sequence	NOUN
iajs-2478	73	89	of	of	ADP
iajs-2478	73	90	subspaces	subspace	NOUN
iajs-2478	73	91	�	�	NOUN
iajs-2478	73	92	⃗	⃗	NOUN
iajs-2478	73	93	�	�	PROPN
iajs-2478	73	94	,	,	PUNCT
iajs-2478	73	95	there	there	PRON
iajs-2478	73	96	exists	exist	VERB
iajs-2478	73	97	a	a	DET
iajs-2478	73	98	sequence	sequence	NOUN
iajs-2478	73	99	of	of	ADP
iajs-2478	73	100	(	(	PUNCT
iajs-2478	73	101	approximation	approximation	NOUN
iajs-2478	73	102	)	)	PUNCT
iajs-2478	73	103	problems	problem	NOUN
iajs-2478	73	104	like	like	ADP
iajs-2478	73	105	(	(	PUNCT
iajs-2478	73	106	17	17	NUM
iajs-2478	73	107	19	19	NUM
iajs-2478	73	108	)	)	PUNCT
iajs-2478	73	109	,	,	PUNCT
iajs-2478	73	110	thus	thus	ADV
iajs-2478	73	111	by	by	ADP
iajs-2478	73	112	substituting	substitute	VERB
iajs-2478	73	113	�	�	NOUN
iajs-2478	73	114	⃗	⃗	PROPN
iajs-2478	73	115	�	�	PROPN
iajs-2478	73	116	�	�	PROPN
iajs-2478	73	117	⃗	⃗	NOUN
iajs-2478	73	118	�	�	PROPN
iajs-2478	73	119	𝑣	𝑣	PROPN
iajs-2478	73	120	,	,	PUNCT
iajs-2478	73	121	𝑣	𝑣	X
iajs-2478	73	122	,	,	PUNCT
iajs-2478	73	123	𝑣	𝑣	X
iajs-2478	73	124	,	,	PUNCT
iajs-2478	73	125	one	one	PRON
iajs-2478	73	126	has	have	VERB
iajs-2478	73	127	for	for	ADP
iajs-2478	73	128	𝑛	𝑛	DET
iajs-2478	73	129	1,2	1,2	NUM
iajs-2478	73	130	,	,	PUNCT
iajs-2478	73	131	…	…	PUNCT
iajs-2478	73	132	〈	〈	NOUN
iajs-2478	73	133	𝑦	𝑦	NOUN
iajs-2478	73	134	,	,	PUNCT
iajs-2478	73	135	𝑣	𝑣	ADP
iajs-2478	73	136	〉	〉	NOUN
iajs-2478	73	137	∇𝑦	∇𝑦	PROPN
iajs-2478	73	138	,	,	PUNCT
iajs-2478	73	139	∇𝑣	∇𝑣	PROPN
iajs-2478	73	140	𝑦	𝑦	PRON
iajs-2478	73	141	,	,	PUNCT
iajs-2478	73	142	𝑣	𝑣	DET
iajs-2478	73	143	𝑦	𝑦	NOUN
iajs-2478	73	144	,	,	PUNCT
iajs-2478	73	145	𝑣	𝑣	DET
iajs-2478	73	146	𝑦	𝑦	NOUN
iajs-2478	73	147	,	,	PUNCT
iajs-2478	73	148	𝑣	𝑣	X
iajs-2478	73	149	(	(	PUNCT
iajs-2478	73	150	𝑓	𝑓	X
iajs-2478	73	151	,	,	PUNCT
iajs-2478	73	152	𝑣	𝑣	NOUN
iajs-2478	73	153	)	)	PUNCT
iajs-2478	73	154	𝑢	𝑢	NOUN
iajs-2478	73	155	,	,	PUNCT
iajs-2478	73	156	𝑣	𝑣	X
iajs-2478	73	157	,	,	PUNCT
iajs-2478	73	158	∀	∀	X
iajs-2478	73	159	𝑣	𝑣	ADP
iajs-2478	73	160	∈	∈	PROPN
iajs-2478	73	161	𝑉	𝑉	PROPN
iajs-2478	73	162	(	(	PUNCT
iajs-2478	73	163	24.a	24.a	NUM
iajs-2478	73	164	)	)	PUNCT
iajs-2478	73	165	𝑦	𝑦	NOUN
iajs-2478	73	166	,	,	PUNCT
iajs-2478	73	167	𝑣	𝑣	PRON
iajs-2478	73	168	𝑦	𝑦	PROPN
iajs-2478	73	169	,	,	PUNCT
iajs-2478	73	170	𝑣	𝑣	X
iajs-2478	73	171	,	,	PUNCT
iajs-2478	73	172	∀	∀	VERB
iajs-2478	73	173	𝑣	𝑣	ADP
iajs-2478	73	174	∈	∈	PROPN
iajs-2478	73	175	𝑉	𝑉	PROPN
iajs-2478	73	176	(	(	PUNCT
iajs-2478	73	177	24.b	24.b	NUM
iajs-2478	73	178	)	)	PUNCT
iajs-2478	73	179	  	  	SPACE
iajs-2478	73	180	117	117	NUM
iajs-2478	73	181	ibn	ibn	PROPN
iajs-2478	73	182	al	al	PROPN
iajs-2478	73	183	-	-	PUNCT
iajs-2478	73	184	haitham	haitham	PROPN
iajs-2478	73	185	jour	jour	X
iajs-2478	73	186	.	.	PROPN
iajs-2478	74	1	for	for	ADP
iajs-2478	74	2	pure	pure	ADJ
iajs-2478	74	3	&	&	CCONJ
iajs-2478	74	4	appl	appl	PROPN
iajs-2478	74	5	.	.	PUNCT
iajs-2478	75	1	sci	sci	PROPN
iajs-2478	75	2	.	.	PROPN
iajs-2478	76	1	33	33	NUM
iajs-2478	76	2	(	(	PUNCT
iajs-2478	76	3	3	3	NUM
iajs-2478	76	4	)	)	PUNCT
iajs-2478	76	5	2020	2020	NUM
iajs-2478	77	1	〈	〈	PROPN
iajs-2478	77	2	𝑦	𝑦	NOUN
iajs-2478	77	3	,	,	PUNCT
iajs-2478	77	4	𝑣	𝑣	ADP
iajs-2478	77	5	〉	〉	NOUN
iajs-2478	77	6	∇𝑦	∇𝑦	PROPN
iajs-2478	77	7	,	,	PUNCT
iajs-2478	77	8	∇𝑣	∇𝑣	PROPN
iajs-2478	77	9	𝑦	𝑦	PRON
iajs-2478	77	10	,	,	PUNCT
iajs-2478	77	11	𝑣	𝑣	PRON
iajs-2478	77	12	𝑦	𝑦	NOUN
iajs-2478	77	13	,	,	PUNCT
iajs-2478	77	14	𝑣	𝑣	PRON
iajs-2478	77	15	𝑦	𝑦	NOUN
iajs-2478	77	16	,	,	PUNCT
iajs-2478	77	17	𝑣	𝑣	X
iajs-2478	77	18	(	(	PUNCT
iajs-2478	77	19	𝑓	𝑓	X
iajs-2478	77	20	,	,	PUNCT
iajs-2478	77	21	𝑣	𝑣	NOUN
iajs-2478	77	22	)	)	PUNCT
iajs-2478	77	23	𝑢	𝑢	NOUN
iajs-2478	77	24	,	,	PUNCT
iajs-2478	77	25	𝑣	𝑣	X
iajs-2478	77	26	,	,	PUNCT
iajs-2478	77	27	∀	∀	X
iajs-2478	77	28	𝑣	𝑣	ADP
iajs-2478	77	29	∈	∈	PROPN
iajs-2478	77	30	𝑉	𝑉	PROPN
iajs-2478	77	31	(	(	PUNCT
iajs-2478	77	32	25.a	25.a	NUM
iajs-2478	77	33	)	)	PUNCT
iajs-2478	77	34	𝑦	𝑦	NOUN
iajs-2478	77	35	,	,	PUNCT
iajs-2478	77	36	𝑣	𝑣	PRON
iajs-2478	77	37	𝑦	𝑦	PROPN
iajs-2478	77	38	,	,	PUNCT
iajs-2478	77	39	𝑣	𝑣	X
iajs-2478	77	40	,	,	PUNCT
iajs-2478	77	41	∀	∀	VERB
iajs-2478	77	42	𝑣	𝑣	ADP
iajs-2478	77	43	∈	∈	PROPN
iajs-2478	77	44	𝑉	𝑉	PROPN
iajs-2478	77	45	(	(	PUNCT
iajs-2478	77	46	25.b	25.b	NUM
iajs-2478	77	47	)	)	PUNCT
iajs-2478	78	1	〈	〈	NOUN
iajs-2478	78	2	𝑦	𝑦	NOUN
iajs-2478	78	3	,	,	PUNCT
iajs-2478	78	4	𝑣	𝑣	ADP
iajs-2478	78	5	〉	〉	NOUN
iajs-2478	78	6	∇𝑦	∇𝑦	PROPN
iajs-2478	78	7	,	,	PUNCT
iajs-2478	78	8	∇𝑣	∇𝑣	PROPN
iajs-2478	78	9	𝑦	𝑦	PRON
iajs-2478	78	10	,	,	PUNCT
iajs-2478	78	11	𝑣	𝑣	DET
iajs-2478	78	12	𝑦	𝑦	NOUN
iajs-2478	78	13	,	,	PUNCT
iajs-2478	78	14	𝑣	𝑣	PRON
iajs-2478	78	15	𝑦	𝑦	NOUN
iajs-2478	78	16	,	,	PUNCT
iajs-2478	78	17	𝑣	𝑣	X
iajs-2478	78	18	(	(	PUNCT
iajs-2478	78	19	𝑓	𝑓	X
iajs-2478	78	20	,	,	PUNCT
iajs-2478	78	21	𝑣	𝑣	NOUN
iajs-2478	78	22	)	)	PUNCT
iajs-2478	78	23	𝑢	𝑢	NOUN
iajs-2478	78	24	,	,	PUNCT
iajs-2478	78	25	𝑣	𝑣	X
iajs-2478	78	26	,	,	PUNCT
iajs-2478	78	27	∀	∀	X
iajs-2478	78	28	𝑣	𝑣	ADP
iajs-2478	78	29	∈	∈	PROPN
iajs-2478	78	30	𝑉	𝑉	PROPN
iajs-2478	78	31	(	(	PUNCT
iajs-2478	78	32	26.a	26.a	NUM
iajs-2478	78	33	)	)	PUNCT
iajs-2478	78	34	𝑦	𝑦	NOUN
iajs-2478	78	35	,	,	PUNCT
iajs-2478	78	36	𝑣	𝑣	PRON
iajs-2478	78	37	𝑦	𝑦	PROPN
iajs-2478	78	38	,	,	PUNCT
iajs-2478	78	39	𝑣	𝑣	X
iajs-2478	78	40	,	,	PUNCT
iajs-2478	78	41	∀	∀	VERB
iajs-2478	78	42	𝑣	𝑣	ADP
iajs-2478	78	43	∈	∈	PROPN
iajs-2478	78	44	𝑉	𝑉	PROPN
iajs-2478	78	45	(	(	PUNCT
iajs-2478	78	46	26.b	26.b	NUM
iajs-2478	78	47	)	)	PUNCT
iajs-2478	78	48	which	which	PRON
iajs-2478	78	49	has	have	VERB
iajs-2478	78	50	a	a	DET
iajs-2478	78	51	sequence	sequence	NOUN
iajs-2478	78	52	of	of	ADP
iajs-2478	78	53	solutions	solution	NOUN
iajs-2478	78	54	�	�	PROPN
iajs-2478	78	55	⃗	⃗	NOUN
iajs-2478	78	56	�	�	PROPN
iajs-2478	78	57	,	,	PUNCT
iajs-2478	78	58	with	with	ADP
iajs-2478	78	59	�	�	PROPN
iajs-2478	78	60	⃗	⃗	NOUN
iajs-2478	78	61	�	�	PROPN
iajs-2478	78	62	,	,	PUNCT
iajs-2478	78	63	but	but	CCONJ
iajs-2478	78	64	from	from	ADP
iajs-2478	78	65	the	the	DET
iajs-2478	78	66	above	above	ADJ
iajs-2478	78	67	steps	step	NOUN
iajs-2478	78	68	we	we	PRON
iajs-2478	78	69	have	have	VERB
iajs-2478	78	70	‖	‖	PROPN
iajs-2478	78	71	�	�	NOUN
iajs-2478	78	72	⃗	⃗	NOUN
iajs-2478	78	73	�	�	PROPN
iajs-2478	78	74	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	78	75	𝑸	𝑸	PROPN
iajs-2478	78	76	and	and	CCONJ
iajs-2478	78	77	‖	‖	PROPN
iajs-2478	78	78	�	�	NOUN
iajs-2478	78	79	⃗	⃗	NOUN
iajs-2478	78	80	�	�	PROPN
iajs-2478	78	81	‖𝑳𝟐	‖𝑳𝟐	PROPN
iajs-2478	78	82	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	78	83	are	be	AUX
iajs-2478	78	84	bounded	bound	VERB
iajs-2478	78	85	,	,	PUNCT
iajs-2478	78	86	then	then	ADV
iajs-2478	78	87	by	by	ADP
iajs-2478	78	88	alaoglu	alaoglu	PROPN
iajs-2478	78	89	’s	’s	PART
iajs-2478	78	90	theorem	theorem	NOUN
iajs-2478	78	91	(	(	PUNCT
iajs-2478	78	92	ath	ath	NOUN
iajs-2478	78	93	)	)	PUNCT
iajs-2478	78	94	,	,	PUNCT
iajs-2478	78	95	there	there	PRON
iajs-2478	78	96	exists	exist	VERB
iajs-2478	78	97	a	a	DET
iajs-2478	78	98	subsequence	subsequence	NOUN
iajs-2478	78	99	of	of	ADP
iajs-2478	78	100	�	�	NOUN
iajs-2478	78	101	⃗	⃗	NOUN
iajs-2478	78	102	�	�	PROPN
iajs-2478	78	103	∈	∈	PROPN
iajs-2478	78	104	,	,	PUNCT
iajs-2478	78	105	say	say	VERB
iajs-2478	78	106	again	again	ADV
iajs-2478	78	107	�	�	PROPN
iajs-2478	78	108	⃗	⃗	NOUN
iajs-2478	78	109	�	�	PROPN
iajs-2478	78	110	∈	∈	PROPN
iajs-2478	78	111	s.t	s.t	PROPN
iajs-2478	78	112	.	.	PROPN
iajs-2478	78	113	�	�	PROPN
iajs-2478	78	114	⃗	⃗	PROPN
iajs-2478	78	115	�	�	PROPN
iajs-2478	78	116	⟶	⟶	PROPN
iajs-2478	78	117	�	�	NOUN
iajs-2478	78	118	⃗	⃗	NOUN
iajs-2478	78	119	�	�	PROPN
iajs-2478	78	120	weakly	weakly	NOUN
iajs-2478	78	121	in	in	ADP
iajs-2478	78	122	𝐿	𝐿	PROPN
iajs-2478	78	123	𝑄	𝑄	PROPN
iajs-2478	78	124	and	and	CCONJ
iajs-2478	78	125	in	in	ADP
iajs-2478	78	126	𝐿	𝐿	PROPN
iajs-2478	78	127	ĩ	ĩ	PROPN
iajs-2478	78	128	,	,	PUNCT
iajs-2478	78	129	𝑉	𝑉	PROPN
iajs-2478	78	130	.	.	PUNCT
iajs-2478	79	1	multiplying	multiply	VERB
iajs-2478	79	2	both	both	DET
iajs-2478	79	3	sides	side	NOUN
iajs-2478	79	4	of	of	ADP
iajs-2478	79	5	(	(	PUNCT
iajs-2478	79	6	24.a	24.a	NUM
iajs-2478	79	7	)	)	PUNCT
iajs-2478	79	8	,	,	PUNCT
iajs-2478	79	9	(	(	PUNCT
iajs-2478	79	10	25.a	25.a	NUM
iajs-2478	79	11	)	)	PUNCT
iajs-2478	79	12	&	&	CCONJ
iajs-2478	79	13	(	(	PUNCT
iajs-2478	79	14	26.a	26.a	NUM
iajs-2478	79	15	)	)	PUNCT
iajs-2478	79	16	by	by	ADP
iajs-2478	79	17	𝜑	𝜑	X
iajs-2478	79	18	𝑡	𝑡	PROPN
iajs-2478	79	19	∈	∈	PROPN
iajs-2478	79	20	𝐶	𝐶	PROPN
iajs-2478	79	21	0	0	NUM
iajs-2478	79	22	,	,	PUNCT
iajs-2478	79	23	𝑇	𝑇	PROPN
iajs-2478	79	24	,	,	PUNCT
iajs-2478	79	25	∀𝑖	∀𝑖	PROPN
iajs-2478	79	26	1,2,3	1,2,3	NUM
iajs-2478	79	27	,	,	PUNCT
iajs-2478	79	28	respectively	respectively	ADV
iajs-2478	79	29	,	,	PUNCT
iajs-2478	79	30	s.t	s.t	PROPN
iajs-2478	79	31	.	.	PROPN
iajs-2478	79	32	𝜑	𝜑	PROPN
iajs-2478	79	33	𝑇	𝑇	PROPN
iajs-2478	79	34	0	0	NUM
iajs-2478	79	35	,	,	PUNCT
iajs-2478	79	36	𝜑	𝜑	PROPN
iajs-2478	79	37	0	0	NUM
iajs-2478	79	38	0	0	NUM
iajs-2478	79	39	,	,	PUNCT
iajs-2478	79	40	integrating	integrate	VERB
iajs-2478	79	41	both	both	DET
iajs-2478	79	42	sides	side	NOUN
iajs-2478	79	43	w.r.t	w.r.t	VERB
iajs-2478	79	44	.	.	PUNCT
iajs-2478	80	1	𝑡	𝑡	VERB
iajs-2478	80	2	on	on	ADP
iajs-2478	80	3	0	0	NUM
iajs-2478	80	4	,	,	PUNCT
iajs-2478	80	5	𝑇	𝑇	PROPN
iajs-2478	80	6	,	,	PUNCT
iajs-2478	80	7	then	then	ADV
iajs-2478	80	8	integrating	integrate	VERB
iajs-2478	80	9	by	by	ADP
iajs-2478	80	10	parts	part	NOUN
iajs-2478	80	11	the	the	DET
iajs-2478	80	12	1st	1st	ADJ
iajs-2478	80	13	terms	term	NOUN
iajs-2478	80	14	in	in	ADP
iajs-2478	80	15	the	the	DET
iajs-2478	80	16	l.h.s	l.h.s	NOUN
iajs-2478	80	17	.	.	PUNCT
iajs-2478	81	1	of	of	ADP
iajs-2478	81	2	each	each	DET
iajs-2478	81	3	one	one	NUM
iajs-2478	81	4	obtained	obtain	VERB
iajs-2478	81	5	equation	equation	NOUN
iajs-2478	81	6	,	,	PUNCT
iajs-2478	81	7	one	one	PRON
iajs-2478	81	8	gets	get	VERB
iajs-2478	81	9	𝑦	𝑦	NOUN
iajs-2478	81	10	,	,	PUNCT
iajs-2478	81	11	𝑣	𝑣	PRON
iajs-2478	81	12	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	81	13	𝑡	𝑡	PROPN
iajs-2478	81	14	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	15	∇𝑦	∇𝑦	PROPN
iajs-2478	81	16	,	,	PUNCT
iajs-2478	81	17	∇𝑣	∇𝑣	PROPN
iajs-2478	81	18	𝑦	𝑦	PRON
iajs-2478	81	19	,	,	PUNCT
iajs-2478	81	20	𝑣	𝑣	DET
iajs-2478	81	21	𝜑	𝜑	X
iajs-2478	81	22	𝑡	𝑡	NOUN
iajs-2478	81	23	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	24	𝑦	𝑦	NOUN
iajs-2478	81	25	,	,	PUNCT
iajs-2478	81	26	𝑣	𝑣	ADP
iajs-2478	81	27	𝜑	𝜑	X
iajs-2478	81	28	𝑡	𝑡	NOUN
iajs-2478	81	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	30	𝑦	𝑦	NOUN
iajs-2478	81	31	,	,	PUNCT
iajs-2478	81	32	𝑣	𝑣	ADP
iajs-2478	81	33	𝜑	𝜑	X
iajs-2478	81	34	𝑡	𝑡	NOUN
iajs-2478	81	35	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	36	𝑓	𝑓	PRON
iajs-2478	81	37	,	,	PUNCT
iajs-2478	81	38	𝑣	𝑣	DET
iajs-2478	81	39	𝜑	𝜑	X
iajs-2478	81	40	𝑡	𝑡	NOUN
iajs-2478	81	41	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	42	𝑢	𝑢	NOUN
iajs-2478	81	43	,	,	PUNCT
iajs-2478	81	44	𝑣	𝑣	PRON
iajs-2478	81	45	𝜑	𝜑	X
iajs-2478	81	46	𝑡	𝑡	NOUN
iajs-2478	81	47	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	48	𝑦	𝑦	NOUN
iajs-2478	81	49	,	,	PUNCT
iajs-2478	81	50	𝑣	𝑣	PRON
iajs-2478	81	51	𝜑	𝜑	NOUN
iajs-2478	81	52	0	0	NUM
iajs-2478	81	53	,	,	PUNCT
iajs-2478	81	54	(	(	PUNCT
iajs-2478	81	55	27	27	NUM
iajs-2478	81	56	)	)	PUNCT
iajs-2478	81	57	𝑦	𝑦	NOUN
iajs-2478	81	58	,	,	PUNCT
iajs-2478	81	59	𝑣	𝑣	PRON
iajs-2478	81	60	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	81	61	𝑡	𝑡	PROPN
iajs-2478	81	62	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	63	∇𝑦	∇𝑦	PROPN
iajs-2478	81	64	,	,	PUNCT
iajs-2478	81	65	∇𝑣	∇𝑣	PROPN
iajs-2478	81	66	𝑦	𝑦	PRON
iajs-2478	81	67	,	,	PUNCT
iajs-2478	81	68	𝑣	𝑣	DET
iajs-2478	81	69	𝜑	𝜑	X
iajs-2478	81	70	𝑡	𝑡	NOUN
iajs-2478	81	71	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	72	𝑦	𝑦	NOUN
iajs-2478	81	73	,	,	PUNCT
iajs-2478	81	74	𝑣	𝑣	ADP
iajs-2478	81	75	𝜑	𝜑	X
iajs-2478	81	76	𝑡	𝑡	NOUN
iajs-2478	81	77	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	78	𝑦	𝑦	NOUN
iajs-2478	81	79	,	,	PUNCT
iajs-2478	81	80	𝑣	𝑣	ADP
iajs-2478	81	81	𝜑	𝜑	X
iajs-2478	81	82	𝑡	𝑡	NOUN
iajs-2478	81	83	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	84	𝑓	𝑓	PRON
iajs-2478	81	85	,	,	PUNCT
iajs-2478	81	86	𝑣	𝑣	DET
iajs-2478	81	87	𝜑	𝜑	X
iajs-2478	81	88	𝑡	𝑡	NOUN
iajs-2478	81	89	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	90	𝑢	𝑢	NOUN
iajs-2478	81	91	,	,	PUNCT
iajs-2478	81	92	𝑣	𝑣	PRON
iajs-2478	81	93	𝜑	𝜑	X
iajs-2478	81	94	𝑡	𝑡	NOUN
iajs-2478	81	95	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	96	𝑦	𝑦	NOUN
iajs-2478	81	97	,	,	PUNCT
iajs-2478	81	98	𝑣	𝑣	PRON
iajs-2478	81	99	𝜑	𝜑	NOUN
iajs-2478	81	100	0	0	NUM
iajs-2478	81	101	,	,	PUNCT
iajs-2478	81	102	(	(	PUNCT
iajs-2478	81	103	28	28	NUM
iajs-2478	81	104	)	)	PUNCT
iajs-2478	81	105	𝑦	𝑦	NOUN
iajs-2478	81	106	,	,	PUNCT
iajs-2478	81	107	𝑣	𝑣	PRON
iajs-2478	81	108	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	81	109	𝑡	𝑡	PROPN
iajs-2478	81	110	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	111	∇𝑦	∇𝑦	PROPN
iajs-2478	81	112	,	,	PUNCT
iajs-2478	81	113	∇𝑣	∇𝑣	PROPN
iajs-2478	81	114	𝑦	𝑦	PRON
iajs-2478	81	115	,	,	PUNCT
iajs-2478	81	116	𝑣	𝑣	DET
iajs-2478	81	117	𝜑	𝜑	X
iajs-2478	81	118	𝑡	𝑡	NOUN
iajs-2478	81	119	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	120	𝑦	𝑦	NOUN
iajs-2478	81	121	,	,	PUNCT
iajs-2478	81	122	𝑣	𝑣	ADP
iajs-2478	81	123	𝜑	𝜑	X
iajs-2478	81	124	𝑡	𝑡	NOUN
iajs-2478	81	125	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	126	𝑦	𝑦	NOUN
iajs-2478	81	127	,	,	PUNCT
iajs-2478	81	128	𝑣	𝑣	ADP
iajs-2478	81	129	𝜑	𝜑	X
iajs-2478	81	130	𝑡	𝑡	NOUN
iajs-2478	81	131	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	132	𝑓	𝑓	PRON
iajs-2478	81	133	,	,	PUNCT
iajs-2478	81	134	𝑣	𝑣	DET
iajs-2478	81	135	𝜑	𝜑	X
iajs-2478	81	136	𝑡	𝑡	NOUN
iajs-2478	81	137	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	138	𝑢	𝑢	NOUN
iajs-2478	81	139	,	,	PUNCT
iajs-2478	81	140	𝑣	𝑣	PRON
iajs-2478	81	141	𝜑	𝜑	X
iajs-2478	81	142	𝑡	𝑡	NOUN
iajs-2478	81	143	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	81	144	𝑦	𝑦	NOUN
iajs-2478	81	145	,	,	PUNCT
iajs-2478	81	146	𝑣	𝑣	PRON
iajs-2478	81	147	𝜑	𝜑	NOUN
iajs-2478	81	148	0	0	NUM
iajs-2478	81	149	,	,	PUNCT
iajs-2478	81	150	(	(	PUNCT
iajs-2478	81	151	29	29	NUM
iajs-2478	81	152	)	)	PUNCT
iajs-2478	81	153	since	since	SCONJ
iajs-2478	81	154	𝑣	𝑣	NOUN
iajs-2478	81	155	⟶	⟶	NOUN
iajs-2478	81	156	𝑣	𝑣	X
iajs-2478	81	157	strongly	strongly	ADV
iajs-2478	81	158	in	in	ADP
iajs-2478	81	159	𝐿	𝐿	PROPN
iajs-2478	81	160	ω	ω	PROPN
iajs-2478	81	161	𝑣	𝑣	PROPN
iajs-2478	81	162	⟶	⟶	NOUN
iajs-2478	81	163	𝑣	𝑣	X
iajs-2478	81	164	strongly	strongly	ADV
iajs-2478	81	165	in	in	ADP
iajs-2478	81	166	𝑉	𝑉	PROPN
iajs-2478	81	167	⇒	⇒	NOUN
iajs-2478	81	168	𝑣	𝑣	ADP
iajs-2478	81	169	𝜑	𝜑	NOUN
iajs-2478	81	170	´	´	NOUN
iajs-2478	81	171	⟶	⟶	NOUN
iajs-2478	81	172	𝑣	𝑣	PART
iajs-2478	81	173	𝜑	𝜑	PRON
iajs-2478	81	174	´	´	VERB
iajs-2478	81	175	strongly	strongly	ADV
iajs-2478	81	176	in	in	ADP
iajs-2478	81	177	𝐿	𝐿	PROPN
iajs-2478	81	178	𝑄	𝑄	PROPN
iajs-2478	81	179	𝑣	𝑣	ADP
iajs-2478	81	180	𝜑	𝜑	NOUN
iajs-2478	81	181	⟶	⟶	NOUN
iajs-2478	81	182	𝑣	𝑣	ADP
iajs-2478	81	183	𝜑	𝜑	PRON
iajs-2478	81	184	strongly	strongly	ADV
iajs-2478	81	185	in	in	ADP
iajs-2478	81	186	𝐿	𝐿	PROPN
iajs-2478	81	187	ĩ	ĩ	PROPN
iajs-2478	81	188	,	,	PUNCT
iajs-2478	81	189	𝑉	𝑉	PROPN
iajs-2478	81	190	,	,	PUNCT
iajs-2478	81	191	also	also	ADV
iajs-2478	81	192	,	,	PUNCT
iajs-2478	81	193	since	since	SCONJ
iajs-2478	81	194	𝑦	𝑦	NOUN
iajs-2478	81	195	⟶	⟶	NOUN
iajs-2478	81	196	𝑦	𝑦	ADJ
iajs-2478	81	197	weakly	weakly	ADJ
iajs-2478	81	198	in	in	ADP
iajs-2478	81	199	𝐿	𝐿	PROPN
iajs-2478	81	200	𝑄	𝑄	PROPN
iajs-2478	81	201	,	,	PUNCT
iajs-2478	81	202	and	and	CCONJ
iajs-2478	81	203	𝑦	𝑦	NOUN
iajs-2478	81	204	⟶	⟶	NOUN
iajs-2478	81	205	𝑦	𝑦	ADJ
iajs-2478	81	206	weakly	weakly	ADJ
iajs-2478	81	207	in	in	ADP
iajs-2478	81	208	𝐿	𝐿	PROPN
iajs-2478	81	209	𝑄	𝑄	PROPN
iajs-2478	81	210	,	,	PUNCT
iajs-2478	81	211	∀	∀	NOUN
iajs-2478	81	212	𝑖	𝑖	SYM
iajs-2478	82	1	1,2,3	1,2,3	NUM
iajs-2478	82	2	,	,	PUNCT
iajs-2478	82	3	then	then	ADV
iajs-2478	82	4	𝑦	𝑦	NUM
iajs-2478	82	5	,	,	PUNCT
iajs-2478	82	6	𝑣	𝑣	ADP
iajs-2478	82	7	𝜑	𝜑	NOUN
iajs-2478	82	8	´	´	X
iajs-2478	82	9	𝑡	𝑡	NOUN
iajs-2478	82	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	11	∇𝑦	∇𝑦	PROPN
iajs-2478	82	12	,	,	PUNCT
iajs-2478	82	13	∇𝑣	∇𝑣	PROPN
iajs-2478	82	14	𝑦	𝑦	PRON
iajs-2478	82	15	,	,	PUNCT
iajs-2478	82	16	𝑣	𝑣	DET
iajs-2478	82	17	𝜑	𝜑	X
iajs-2478	82	18	𝑡	𝑡	NOUN
iajs-2478	82	19	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	20	𝑦	𝑦	NOUN
iajs-2478	82	21	,	,	PUNCT
iajs-2478	82	22	𝑣	𝑣	ADP
iajs-2478	82	23	𝜑	𝜑	X
iajs-2478	82	24	𝑡	𝑡	NOUN
iajs-2478	82	25	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	26	𝑦	𝑦	NOUN
iajs-2478	82	27	,	,	PUNCT
iajs-2478	82	28	𝑣	𝑣	ADP
iajs-2478	82	29	𝜑	𝜑	X
iajs-2478	82	30	𝑡	𝑡	NOUN
iajs-2478	82	31	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	32	⟶	⟶	NOUN
iajs-2478	82	33	𝑦	𝑦	PROPN
iajs-2478	82	34	,	,	PUNCT
iajs-2478	82	35	𝑣	𝑣	PRON
iajs-2478	82	36	𝜑	𝜑	NOUN
iajs-2478	82	37	´	´	X
iajs-2478	82	38	𝑡	𝑡	NOUN
iajs-2478	82	39	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	40	∇𝑦	∇𝑦	PROPN
iajs-2478	82	41	,	,	PUNCT
iajs-2478	82	42	∇𝑣	∇𝑣	PROPN
iajs-2478	82	43	𝑦	𝑦	PRON
iajs-2478	82	44	,	,	PUNCT
iajs-2478	82	45	𝑣	𝑣	PRON
iajs-2478	82	46	𝜑	𝜑	X
iajs-2478	82	47	𝑡	𝑡	NOUN
iajs-2478	82	48	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	49	𝑦	𝑦	NOUN
iajs-2478	82	50	,	,	PUNCT
iajs-2478	82	51	𝑣	𝑣	ADP
iajs-2478	82	52	𝜑	𝜑	X
iajs-2478	82	53	𝑡	𝑡	NOUN
iajs-2478	82	54	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	55	𝑦	𝑦	NOUN
iajs-2478	82	56	,	,	PUNCT
iajs-2478	82	57	𝑣	𝑣	ADP
iajs-2478	82	58	𝜑	𝜑	X
iajs-2478	82	59	𝑡	𝑡	NOUN
iajs-2478	82	60	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	61	,	,	PUNCT
iajs-2478	82	62	(	(	PUNCT
iajs-2478	82	63	30.a	30.a	NUM
iajs-2478	82	64	)	)	PUNCT
iajs-2478	82	65	𝑦	𝑦	NOUN
iajs-2478	82	66	,	,	PUNCT
iajs-2478	82	67	𝑣	𝑣	PRON
iajs-2478	82	68	𝜑	𝜑	NOUN
iajs-2478	82	69	´	´	X
iajs-2478	82	70	𝑡	𝑡	NOUN
iajs-2478	82	71	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	72	∇𝑦	∇𝑦	PROPN
iajs-2478	82	73	,	,	PUNCT
iajs-2478	82	74	∇𝑣	∇𝑣	PROPN
iajs-2478	82	75	𝑦	𝑦	PRON
iajs-2478	82	76	,	,	PUNCT
iajs-2478	82	77	𝑣	𝑣	PRON
iajs-2478	82	78	𝜑	𝜑	X
iajs-2478	82	79	𝑡	𝑡	NOUN
iajs-2478	82	80	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	81	𝑦	𝑦	NOUN
iajs-2478	82	82	,	,	PUNCT
iajs-2478	82	83	𝑣	𝑣	ADP
iajs-2478	82	84	𝜑	𝜑	X
iajs-2478	82	85	𝑡	𝑡	NOUN
iajs-2478	82	86	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	87	𝑦	𝑦	NOUN
iajs-2478	82	88	,	,	PUNCT
iajs-2478	82	89	𝑣	𝑣	ADP
iajs-2478	82	90	𝜑	𝜑	X
iajs-2478	82	91	𝑡	𝑡	NOUN
iajs-2478	82	92	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	93	⟶	⟶	NOUN
iajs-2478	82	94	𝑦	𝑦	PROPN
iajs-2478	82	95	,	,	PUNCT
iajs-2478	82	96	𝑣	𝑣	PRON
iajs-2478	82	97	𝜑	𝜑	NOUN
iajs-2478	82	98	´	´	X
iajs-2478	82	99	𝑡	𝑡	NOUN
iajs-2478	82	100	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	101	∇𝑦	∇𝑦	PROPN
iajs-2478	82	102	,	,	PUNCT
iajs-2478	82	103	∇𝑣	∇𝑣	PROPN
iajs-2478	82	104	𝑦	𝑦	PRON
iajs-2478	82	105	,	,	PUNCT
iajs-2478	82	106	𝑣	𝑣	PRON
iajs-2478	82	107	𝜑	𝜑	X
iajs-2478	82	108	𝑡	𝑡	NOUN
iajs-2478	82	109	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	110	𝑦	𝑦	NOUN
iajs-2478	82	111	,	,	PUNCT
iajs-2478	82	112	𝑣	𝑣	ADP
iajs-2478	82	113	𝜑	𝜑	X
iajs-2478	82	114	𝑡	𝑡	NOUN
iajs-2478	82	115	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	116	𝑦	𝑦	NOUN
iajs-2478	82	117	,	,	PUNCT
iajs-2478	82	118	𝑣	𝑣	ADP
iajs-2478	82	119	𝜑	𝜑	X
iajs-2478	82	120	𝑡	𝑡	NOUN
iajs-2478	82	121	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	122	,	,	PUNCT
iajs-2478	82	123	(	(	PUNCT
iajs-2478	82	124	31.a	31.a	NUM
iajs-2478	82	125	)	)	PUNCT
iajs-2478	82	126	𝑦	𝑦	NOUN
iajs-2478	82	127	,	,	PUNCT
iajs-2478	82	128	𝑣	𝑣	PRON
iajs-2478	82	129	𝜑	𝜑	NOUN
iajs-2478	82	130	´	´	X
iajs-2478	82	131	𝑡	𝑡	NOUN
iajs-2478	82	132	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	133	∇𝑦	∇𝑦	PROPN
iajs-2478	82	134	,	,	PUNCT
iajs-2478	82	135	∇𝑣	∇𝑣	PROPN
iajs-2478	82	136	𝑦	𝑦	PRON
iajs-2478	82	137	,	,	PUNCT
iajs-2478	82	138	𝑣	𝑣	PRON
iajs-2478	82	139	𝜑	𝜑	X
iajs-2478	82	140	𝑡	𝑡	NOUN
iajs-2478	82	141	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	142	𝑦	𝑦	NOUN
iajs-2478	82	143	,	,	PUNCT
iajs-2478	82	144	𝑣	𝑣	ADP
iajs-2478	82	145	𝜑	𝜑	X
iajs-2478	82	146	𝑡	𝑡	NOUN
iajs-2478	82	147	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	148	𝑦	𝑦	NOUN
iajs-2478	82	149	,	,	PUNCT
iajs-2478	82	150	𝑣	𝑣	ADP
iajs-2478	82	151	𝜑	𝜑	X
iajs-2478	82	152	𝑡	𝑡	NOUN
iajs-2478	82	153	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	154	⟶	⟶	NOUN
iajs-2478	82	155	𝑦	𝑦	PROPN
iajs-2478	82	156	,	,	PUNCT
iajs-2478	82	157	𝑣	𝑣	PRON
iajs-2478	82	158	𝜑	𝜑	NOUN
iajs-2478	82	159	´	´	X
iajs-2478	82	160	𝑡	𝑡	NOUN
iajs-2478	82	161	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	162	∇𝑦	∇𝑦	PROPN
iajs-2478	82	163	,	,	PUNCT
iajs-2478	82	164	∇𝑣	∇𝑣	PROPN
iajs-2478	82	165	𝑦	𝑦	PRON
iajs-2478	82	166	,	,	PUNCT
iajs-2478	82	167	𝑣	𝑣	PRON
iajs-2478	82	168	𝜑	𝜑	X
iajs-2478	82	169	𝑡	𝑡	NOUN
iajs-2478	82	170	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	171	𝑦	𝑦	NOUN
iajs-2478	82	172	,	,	PUNCT
iajs-2478	82	173	𝑣	𝑣	ADP
iajs-2478	82	174	𝜑	𝜑	X
iajs-2478	82	175	𝑡	𝑡	NOUN
iajs-2478	82	176	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	177	𝑦	𝑦	NOUN
iajs-2478	82	178	,	,	PUNCT
iajs-2478	82	179	𝑣	𝑣	ADP
iajs-2478	82	180	𝜑	𝜑	X
iajs-2478	82	181	𝑡	𝑡	NOUN
iajs-2478	82	182	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	82	183	,	,	PUNCT
iajs-2478	82	184	(	(	PUNCT
iajs-2478	82	185	32.a	32.a	NUM
iajs-2478	82	186	)	)	PUNCT
iajs-2478	82	187	𝑦	𝑦	NOUN
iajs-2478	82	188	,	,	PUNCT
iajs-2478	82	189	𝑣	𝑣	DET
iajs-2478	82	190	𝜑	𝜑	PROPN
iajs-2478	82	191	0	0	NUM
iajs-2478	82	192	⟶	⟶	NOUN
iajs-2478	82	193	𝑦	𝑦	NOUN
iajs-2478	82	194	,	,	PUNCT
iajs-2478	82	195	𝑣	𝑣	DET
iajs-2478	82	196	𝜑	𝜑	NOUN
iajs-2478	82	197	0	0	NUM
iajs-2478	82	198	,	,	PUNCT
iajs-2478	82	199	(	(	PUNCT
iajs-2478	82	200	30.b	30.b	NUM
iajs-2478	82	201	)	)	PUNCT
iajs-2478	82	202	𝑦	𝑦	NOUN
iajs-2478	82	203	,	,	PUNCT
iajs-2478	82	204	𝑣	𝑣	DET
iajs-2478	82	205	𝜑	𝜑	PROPN
iajs-2478	82	206	0	0	NUM
iajs-2478	82	207	⟶	⟶	NOUN
iajs-2478	82	208	𝑦	𝑦	NOUN
iajs-2478	82	209	,	,	PUNCT
iajs-2478	82	210	𝑣	𝑣	DET
iajs-2478	82	211	𝜑	𝜑	NOUN
iajs-2478	82	212	0	0	NUM
iajs-2478	82	213	,	,	PUNCT
iajs-2478	82	214	(	(	PUNCT
iajs-2478	82	215	31.b	31.b	NUM
iajs-2478	82	216	)	)	PUNCT
iajs-2478	82	217	𝑦	𝑦	NOUN
iajs-2478	82	218	,	,	PUNCT
iajs-2478	82	219	𝑣	𝑣	DET
iajs-2478	82	220	𝜑	𝜑	PROPN
iajs-2478	82	221	0	0	NUM
iajs-2478	82	222	⟶	⟶	NOUN
iajs-2478	82	223	𝑦	𝑦	NOUN
iajs-2478	82	224	,	,	PUNCT
iajs-2478	82	225	𝑣	𝑣	PRON
iajs-2478	82	226	𝜑	𝜑	NOUN
iajs-2478	82	227	0	0	NUM
iajs-2478	82	228	,	,	PUNCT
iajs-2478	82	229	(	(	PUNCT
iajs-2478	82	230	32.b	32.b	NUM
iajs-2478	82	231	)	)	PUNCT
iajs-2478	82	232	  	  	SPACE
iajs-2478	82	233	118	118	NUM
iajs-2478	82	234	ibn	ibn	PROPN
iajs-2478	82	235	al	al	PROPN
iajs-2478	82	236	-	-	PUNCT
iajs-2478	82	237	haitham	haitham	PROPN
iajs-2478	82	238	jour	jour	X
iajs-2478	82	239	.	.	PROPN
iajs-2478	83	1	for	for	ADP
iajs-2478	83	2	pure	pure	ADJ
iajs-2478	83	3	&	&	CCONJ
iajs-2478	83	4	appl	appl	PROPN
iajs-2478	83	5	.	.	PUNCT
iajs-2478	84	1	sci	sci	PROPN
iajs-2478	84	2	.	.	PROPN
iajs-2478	85	1	33	33	NUM
iajs-2478	85	2	(	(	PUNCT
iajs-2478	85	3	3	3	NUM
iajs-2478	85	4	)	)	PUNCT
iajs-2478	85	5	2020	2020	NUM
iajs-2478	86	1	since	since	SCONJ
iajs-2478	86	2	𝑣	𝑣	NOUN
iajs-2478	86	3	⟶	⟶	NOUN
iajs-2478	86	4	𝑣	𝑣	X
iajs-2478	86	5	,	,	PUNCT
iajs-2478	86	6	weakly	weakly	ADV
iajs-2478	86	7	in	in	ADP
iajs-2478	86	8	𝐿	𝐿	PROPN
iajs-2478	86	9	ω	ω	PROPN
iajs-2478	86	10	,	,	PUNCT
iajs-2478	86	11	then	then	ADV
iajs-2478	86	12	𝑓	𝑓	X
iajs-2478	86	13	,	,	PUNCT
iajs-2478	86	14	𝑣	𝑣	PRON
iajs-2478	86	15	𝑢	𝑢	X
iajs-2478	86	16	,	,	PUNCT
iajs-2478	86	17	𝑣	𝑣	DET
iajs-2478	86	18	𝜑	𝜑	X
iajs-2478	86	19	𝑡	𝑡	NOUN
iajs-2478	86	20	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	21	⟶	⟶	NOUN
iajs-2478	86	22	𝑓	𝑓	PROPN
iajs-2478	86	23	,	,	PUNCT
iajs-2478	86	24	𝑣	𝑣	PRON
iajs-2478	86	25	𝑢	𝑢	X
iajs-2478	86	26	,	,	PUNCT
iajs-2478	86	27	𝑣	𝑣	PRON
iajs-2478	86	28	𝜑	𝜑	X
iajs-2478	86	29	𝑡	𝑡	PROPN
iajs-2478	86	30	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	31	,	,	PUNCT
iajs-2478	86	32	(	(	PUNCT
iajs-2478	86	33	30.c	30.c	NUM
iajs-2478	86	34	)	)	PUNCT
iajs-2478	86	35	𝑓	𝑓	NOUN
iajs-2478	86	36	,	,	PUNCT
iajs-2478	86	37	𝑣	𝑣	PRON
iajs-2478	86	38	𝑢	𝑢	X
iajs-2478	86	39	,	,	PUNCT
iajs-2478	86	40	𝑣	𝑣	DET
iajs-2478	86	41	𝜑	𝜑	X
iajs-2478	86	42	𝑡	𝑡	NOUN
iajs-2478	86	43	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	44	⟶	⟶	NOUN
iajs-2478	86	45	𝑓	𝑓	PROPN
iajs-2478	86	46	,	,	PUNCT
iajs-2478	86	47	𝑣	𝑣	PRON
iajs-2478	86	48	𝑢	𝑢	X
iajs-2478	86	49	,	,	PUNCT
iajs-2478	86	50	𝑣	𝑣	PRON
iajs-2478	86	51	𝜑	𝜑	X
iajs-2478	86	52	𝑡	𝑡	PROPN
iajs-2478	86	53	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	54	,	,	PUNCT
iajs-2478	86	55	(	(	PUNCT
iajs-2478	86	56	31.c	31.c	NUM
iajs-2478	86	57	)	)	PUNCT
iajs-2478	86	58	𝑓	𝑓	NOUN
iajs-2478	86	59	,	,	PUNCT
iajs-2478	86	60	𝑣	𝑣	DET
iajs-2478	86	61	𝑢	𝑢	X
iajs-2478	86	62	,	,	PUNCT
iajs-2478	86	63	𝑣	𝑣	PRON
iajs-2478	86	64	𝜑	𝜑	X
iajs-2478	86	65	𝑡	𝑡	NOUN
iajs-2478	86	66	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	67	⟶	⟶	NOUN
iajs-2478	86	68	𝑓	𝑓	PROPN
iajs-2478	86	69	,	,	PUNCT
iajs-2478	86	70	𝑣	𝑣	DET
iajs-2478	86	71	𝑢	𝑢	X
iajs-2478	86	72	,	,	PUNCT
iajs-2478	86	73	𝑣	𝑣	DET
iajs-2478	86	74	𝜑	𝜑	X
iajs-2478	86	75	𝑡	𝑡	PROPN
iajs-2478	86	76	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	77	,	,	PUNCT
iajs-2478	86	78	(	(	PUNCT
iajs-2478	86	79	32.c	32.c	NUM
iajs-2478	86	80	)	)	PUNCT
iajs-2478	86	81	which	which	PRON
iajs-2478	86	82	means	mean	VERB
iajs-2478	86	83	(	(	PUNCT
iajs-2478	86	84	30	30	NUM
iajs-2478	86	85	32	32	NUM
iajs-2478	86	86	)	)	PUNCT
iajs-2478	86	87	,	,	PUNCT
iajs-2478	86	88	converge	converge	VERB
iajs-2478	86	89	to	to	ADP
iajs-2478	86	90	(	(	PUNCT
iajs-2478	86	91	33	33	NUM
iajs-2478	86	92	35	35	NUM
iajs-2478	86	93	)	)	PUNCT
iajs-2478	86	94	,	,	PUNCT
iajs-2478	86	95	respectively	respectively	ADV
iajs-2478	86	96	𝑦	𝑦	PRON
iajs-2478	86	97	,	,	PUNCT
iajs-2478	86	98	𝑣	𝑣	X
iajs-2478	86	99	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	86	100	𝑡	𝑡	PROPN
iajs-2478	86	101	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	102	∇𝑦	∇𝑦	PROPN
iajs-2478	86	103	,	,	PUNCT
iajs-2478	86	104	∇𝑣	∇𝑣	PROPN
iajs-2478	86	105	𝑦	𝑦	PRON
iajs-2478	86	106	,	,	PUNCT
iajs-2478	86	107	𝑣	𝑣	DET
iajs-2478	86	108	𝜑	𝜑	X
iajs-2478	86	109	𝑡	𝑡	NOUN
iajs-2478	86	110	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	111	𝑦	𝑦	NOUN
iajs-2478	86	112	,	,	PUNCT
iajs-2478	86	113	𝑣	𝑣	ADP
iajs-2478	86	114	𝜑	𝜑	X
iajs-2478	86	115	𝑡	𝑡	NOUN
iajs-2478	86	116	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	117	𝑦	𝑦	NOUN
iajs-2478	86	118	,	,	PUNCT
iajs-2478	86	119	𝑣	𝑣	ADP
iajs-2478	86	120	𝜑	𝜑	X
iajs-2478	86	121	𝑡	𝑡	NOUN
iajs-2478	86	122	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	123	𝑓	𝑓	PRON
iajs-2478	86	124	,	,	PUNCT
iajs-2478	86	125	𝑣	𝑣	DET
iajs-2478	86	126	𝜑	𝜑	X
iajs-2478	86	127	𝑡	𝑡	NOUN
iajs-2478	86	128	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	129	𝑢	𝑢	NOUN
iajs-2478	86	130	,	,	PUNCT
iajs-2478	86	131	𝑣	𝑣	DET
iajs-2478	86	132	𝜑	𝜑	X
iajs-2478	86	133	𝑡	𝑡	NOUN
iajs-2478	86	134	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	135	𝑦	𝑦	NOUN
iajs-2478	86	136	,	,	PUNCT
iajs-2478	86	137	𝑣	𝑣	PRON
iajs-2478	86	138	𝜑	𝜑	NOUN
iajs-2478	86	139	0	0	NUM
iajs-2478	86	140	,	,	PUNCT
iajs-2478	86	141	(	(	PUNCT
iajs-2478	86	142	33	33	NUM
iajs-2478	86	143	)	)	PUNCT
iajs-2478	86	144	𝑦	𝑦	NOUN
iajs-2478	86	145	,	,	PUNCT
iajs-2478	86	146	𝑣	𝑣	PRON
iajs-2478	86	147	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	86	148	𝑡	𝑡	PROPN
iajs-2478	86	149	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	150	∇𝑦	∇𝑦	PROPN
iajs-2478	86	151	,	,	PUNCT
iajs-2478	86	152	∇𝑣	∇𝑣	PROPN
iajs-2478	86	153	𝑦	𝑦	PRON
iajs-2478	86	154	,	,	PUNCT
iajs-2478	86	155	𝑣	𝑣	DET
iajs-2478	86	156	𝜑	𝜑	X
iajs-2478	86	157	𝑡	𝑡	NOUN
iajs-2478	86	158	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	159	𝑦	𝑦	NOUN
iajs-2478	86	160	,	,	PUNCT
iajs-2478	86	161	𝑣	𝑣	ADP
iajs-2478	86	162	𝜑	𝜑	X
iajs-2478	86	163	𝑡	𝑡	NOUN
iajs-2478	86	164	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	165	𝑦	𝑦	NOUN
iajs-2478	86	166	,	,	PUNCT
iajs-2478	86	167	𝑣	𝑣	ADP
iajs-2478	86	168	𝜑	𝜑	X
iajs-2478	86	169	𝑡	𝑡	NOUN
iajs-2478	86	170	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	171	𝑓	𝑓	PRON
iajs-2478	86	172	,	,	PUNCT
iajs-2478	86	173	𝑣	𝑣	DET
iajs-2478	86	174	𝜑	𝜑	X
iajs-2478	86	175	𝑡	𝑡	NOUN
iajs-2478	86	176	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	177	𝑢	𝑢	NOUN
iajs-2478	86	178	,	,	PUNCT
iajs-2478	86	179	𝑣	𝑣	PRON
iajs-2478	86	180	𝜑	𝜑	X
iajs-2478	86	181	𝑡	𝑡	NOUN
iajs-2478	86	182	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	183	𝑦	𝑦	NOUN
iajs-2478	86	184	,	,	PUNCT
iajs-2478	86	185	𝑣	𝑣	PRON
iajs-2478	86	186	𝜑	𝜑	NOUN
iajs-2478	86	187	0	0	NUM
iajs-2478	86	188	,	,	PUNCT
iajs-2478	86	189	(	(	PUNCT
iajs-2478	86	190	34	34	NUM
iajs-2478	86	191	)	)	PUNCT
iajs-2478	86	192	𝑦	𝑦	NOUN
iajs-2478	86	193	,	,	PUNCT
iajs-2478	86	194	𝑣	𝑣	PRON
iajs-2478	86	195	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	86	196	𝑡	𝑡	PROPN
iajs-2478	86	197	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	198	∇𝑦	∇𝑦	PROPN
iajs-2478	86	199	,	,	PUNCT
iajs-2478	86	200	∇𝑣	∇𝑣	PROPN
iajs-2478	86	201	𝑦	𝑦	PRON
iajs-2478	86	202	,	,	PUNCT
iajs-2478	86	203	𝑣	𝑣	DET
iajs-2478	86	204	𝜑	𝜑	X
iajs-2478	86	205	𝑡	𝑡	NOUN
iajs-2478	86	206	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	207	𝑦	𝑦	NOUN
iajs-2478	86	208	,	,	PUNCT
iajs-2478	86	209	𝑣	𝑣	ADP
iajs-2478	86	210	𝜑	𝜑	X
iajs-2478	86	211	𝑡	𝑡	NOUN
iajs-2478	86	212	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	213	𝑦	𝑦	NOUN
iajs-2478	86	214	,	,	PUNCT
iajs-2478	86	215	𝑣	𝑣	ADP
iajs-2478	86	216	𝜑	𝜑	X
iajs-2478	86	217	𝑡	𝑡	NOUN
iajs-2478	86	218	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	219	𝑓	𝑓	PRON
iajs-2478	86	220	,	,	PUNCT
iajs-2478	86	221	𝑣	𝑣	DET
iajs-2478	86	222	𝜑	𝜑	X
iajs-2478	86	223	𝑡	𝑡	NOUN
iajs-2478	86	224	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	225	𝑢	𝑢	NOUN
iajs-2478	86	226	,	,	PUNCT
iajs-2478	86	227	𝑣	𝑣	PRON
iajs-2478	86	228	𝜑	𝜑	X
iajs-2478	86	229	𝑡	𝑡	NOUN
iajs-2478	86	230	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	86	231	𝑦	𝑦	NOUN
iajs-2478	86	232	,	,	PUNCT
iajs-2478	86	233	𝑣	𝑣	DET
iajs-2478	86	234	𝜑	𝜑	NOUN
iajs-2478	86	235	0	0	NUM
iajs-2478	86	236	,	,	PUNCT
iajs-2478	86	237	(	(	PUNCT
iajs-2478	86	238	35	35	NUM
iajs-2478	86	239	)	)	PUNCT
iajs-2478	86	240	case1	case1	PROPN
iajs-2478	86	241	:	:	PUNCT
iajs-2478	86	242	choose	choose	VERB
iajs-2478	86	243	𝜑	𝜑	PRON
iajs-2478	86	244	∈	∈	PROPN
iajs-2478	86	245	𝐷	𝐷	PROPN
iajs-2478	86	246	0	0	NUM
iajs-2478	86	247	,	,	PUNCT
iajs-2478	86	248	𝑇	𝑇	PROPN
iajs-2478	86	249	,	,	PUNCT
iajs-2478	86	250	i.e.	i.e.	X
iajs-2478	86	251	𝜑	𝜑	NOUN
iajs-2478	86	252	0	0	PUNCT
iajs-2478	86	253	𝜑	𝜑	PROPN
iajs-2478	86	254	𝑇	𝑇	PROPN
iajs-2478	86	255	0	0	NUM
iajs-2478	86	256	,	,	PUNCT
iajs-2478	86	257	∀𝑖	∀𝑖	PROPN
iajs-2478	86	258	1,2	1,2	NUM
iajs-2478	86	259	,	,	PUNCT
iajs-2478	86	260	3	3	NUM
iajs-2478	86	261	.	.	PUNCT
iajs-2478	86	262	substituting	substitute	VERB
iajs-2478	86	263	in	in	ADP
iajs-2478	86	264	(	(	PUNCT
iajs-2478	86	265	33	33	NUM
iajs-2478	86	266	)	)	PUNCT
iajs-2478	86	267	35	35	NUM
iajs-2478	86	268	)	)	PUNCT
iajs-2478	86	269	,	,	PUNCT
iajs-2478	86	270	using	use	VERB
iajs-2478	86	271	integration	integration	NOUN
iajs-2478	86	272	by	by	ADP
iajs-2478	86	273	parts	part	NOUN
iajs-2478	86	274	for	for	ADP
iajs-2478	86	275	the	the	DET
iajs-2478	86	276	1st	1st	ADJ
iajs-2478	86	277	terms	term	NOUN
iajs-2478	86	278	in	in	ADP
iajs-2478	86	279	the	the	DET
iajs-2478	86	280	l.h.s	l.h.s	NOUN
iajs-2478	86	281	.	.	PUNCT
iajs-2478	87	1	of	of	ADP
iajs-2478	87	2	each	each	DET
iajs-2478	87	3	one	one	NUM
iajs-2478	87	4	of	of	ADP
iajs-2478	87	5	the	the	DET
iajs-2478	87	6	obtained	obtain	VERB
iajs-2478	87	7	equations	equation	NOUN
iajs-2478	87	8	,	,	PUNCT
iajs-2478	87	9	one	one	NUM
iajs-2478	87	10	has	have	VERB
iajs-2478	87	11	〈	〈	PROPN
iajs-2478	87	12	𝑦	𝑦	NOUN
iajs-2478	87	13	,	,	PUNCT
iajs-2478	87	14	𝑣	𝑣	PRON
iajs-2478	87	15	〉	〉	NOUN
iajs-2478	87	16	𝜑	𝜑	NOUN
iajs-2478	87	17	𝑡	𝑡	NOUN
iajs-2478	87	18	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	19	∇𝑦	∇𝑦	PROPN
iajs-2478	87	20	,	,	PUNCT
iajs-2478	87	21	∇𝑣	∇𝑣	PROPN
iajs-2478	87	22	𝑦	𝑦	PRON
iajs-2478	87	23	,	,	PUNCT
iajs-2478	87	24	𝑣	𝑣	PRON
iajs-2478	87	25	𝜑	𝜑	X
iajs-2478	87	26	𝑡	𝑡	NOUN
iajs-2478	87	27	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	28	𝑦	𝑦	NOUN
iajs-2478	87	29	,	,	PUNCT
iajs-2478	87	30	𝑣	𝑣	ADP
iajs-2478	87	31	𝜑	𝜑	X
iajs-2478	87	32	𝑡	𝑡	NOUN
iajs-2478	87	33	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	34	𝑦	𝑦	NOUN
iajs-2478	87	35	,	,	PUNCT
iajs-2478	87	36	𝑣	𝑣	ADP
iajs-2478	87	37	𝜑	𝜑	X
iajs-2478	87	38	𝑡	𝑡	NOUN
iajs-2478	87	39	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	40	𝑓	𝑓	PRON
iajs-2478	87	41	,	,	PUNCT
iajs-2478	87	42	𝑣	𝑣	DET
iajs-2478	87	43	𝜑	𝜑	X
iajs-2478	87	44	𝑡	𝑡	NOUN
iajs-2478	87	45	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	46	𝑢	𝑢	NOUN
iajs-2478	87	47	,	,	PUNCT
iajs-2478	87	48	𝑣	𝑣	DET
iajs-2478	87	49	𝜑	𝜑	X
iajs-2478	87	50	𝑡	𝑡	NOUN
iajs-2478	87	51	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	52	,	,	PUNCT
iajs-2478	87	53	(	(	PUNCT
iajs-2478	87	54	36	36	NUM
iajs-2478	87	55	)	)	PUNCT
iajs-2478	87	56	〈	〈	PROPN
iajs-2478	87	57	𝑦	𝑦	NOUN
iajs-2478	87	58	,	,	PUNCT
iajs-2478	87	59	𝑣	𝑣	PRON
iajs-2478	87	60	〉	〉	NOUN
iajs-2478	87	61	𝜑	𝜑	NOUN
iajs-2478	87	62	𝑡	𝑡	NOUN
iajs-2478	87	63	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	64	∇𝑦	∇𝑦	PROPN
iajs-2478	87	65	,	,	PUNCT
iajs-2478	87	66	∇𝑣	∇𝑣	PROPN
iajs-2478	87	67	𝑦	𝑦	PRON
iajs-2478	87	68	,	,	PUNCT
iajs-2478	87	69	𝑣	𝑣	DET
iajs-2478	87	70	𝜑	𝜑	X
iajs-2478	87	71	𝑡	𝑡	NOUN
iajs-2478	87	72	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	73	𝑦	𝑦	NOUN
iajs-2478	87	74	,	,	PUNCT
iajs-2478	87	75	𝑣	𝑣	ADP
iajs-2478	87	76	𝜑	𝜑	X
iajs-2478	87	77	𝑡	𝑡	NOUN
iajs-2478	87	78	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	79	𝑦	𝑦	NOUN
iajs-2478	87	80	,	,	PUNCT
iajs-2478	87	81	𝑣	𝑣	ADP
iajs-2478	87	82	𝜑	𝜑	X
iajs-2478	87	83	𝑡	𝑡	NOUN
iajs-2478	87	84	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	85	𝑓	𝑓	PRON
iajs-2478	87	86	,	,	PUNCT
iajs-2478	87	87	𝑣	𝑣	DET
iajs-2478	87	88	𝜑	𝜑	X
iajs-2478	87	89	𝑡	𝑡	NOUN
iajs-2478	87	90	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	91	𝑢	𝑢	NOUN
iajs-2478	87	92	,	,	PUNCT
iajs-2478	87	93	𝑣	𝑣	PRON
iajs-2478	87	94	𝜑	𝜑	X
iajs-2478	87	95	𝑡	𝑡	NOUN
iajs-2478	87	96	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	97	,	,	PUNCT
iajs-2478	87	98	(	(	PUNCT
iajs-2478	87	99	37	37	NUM
iajs-2478	87	100	)	)	PUNCT
iajs-2478	87	101	〈	〈	PROPN
iajs-2478	87	102	𝑦	𝑦	NOUN
iajs-2478	87	103	,	,	PUNCT
iajs-2478	87	104	𝑣	𝑣	PRON
iajs-2478	87	105	〉	〉	NOUN
iajs-2478	87	106	𝜑	𝜑	NOUN
iajs-2478	87	107	𝑡	𝑡	NOUN
iajs-2478	87	108	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	109	∇𝑦	∇𝑦	PROPN
iajs-2478	87	110	,	,	PUNCT
iajs-2478	87	111	∇𝑣	∇𝑣	PROPN
iajs-2478	87	112	𝑦	𝑦	PRON
iajs-2478	87	113	,	,	PUNCT
iajs-2478	87	114	𝑣	𝑣	PRON
iajs-2478	87	115	𝜑	𝜑	X
iajs-2478	87	116	𝑡	𝑡	NOUN
iajs-2478	87	117	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	118	𝑦	𝑦	NOUN
iajs-2478	87	119	,	,	PUNCT
iajs-2478	87	120	𝑣	𝑣	ADP
iajs-2478	87	121	𝜑	𝜑	X
iajs-2478	87	122	𝑡	𝑡	NOUN
iajs-2478	87	123	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	124	𝑦	𝑦	NOUN
iajs-2478	87	125	,	,	PUNCT
iajs-2478	87	126	𝑣	𝑣	ADP
iajs-2478	87	127	𝜑	𝜑	X
iajs-2478	87	128	𝑡	𝑡	NOUN
iajs-2478	87	129	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	130	𝑓	𝑓	PRON
iajs-2478	87	131	,	,	PUNCT
iajs-2478	87	132	𝑣	𝑣	DET
iajs-2478	87	133	𝜑	𝜑	X
iajs-2478	87	134	𝑡	𝑡	NOUN
iajs-2478	87	135	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	136	𝑢	𝑢	NOUN
iajs-2478	87	137	,	,	PUNCT
iajs-2478	87	138	𝑣	𝑣	PRON
iajs-2478	87	139	𝜑	𝜑	X
iajs-2478	87	140	𝑡	𝑡	NOUN
iajs-2478	87	141	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	87	142	,	,	PUNCT
iajs-2478	87	143	(	(	PUNCT
iajs-2478	87	144	38	38	NUM
iajs-2478	87	145	)	)	PUNCT
iajs-2478	87	146	i.e.	i.e.	X
iajs-2478	87	147	�	�	NOUN
iajs-2478	87	148	⃗	⃗	NOUN
iajs-2478	87	149	�	�	PROPN
iajs-2478	87	150	is	be	AUX
iajs-2478	87	151	a	a	DET
iajs-2478	87	152	solution	solution	NOUN
iajs-2478	87	153	of	of	ADP
iajs-2478	87	154	the	the	DET
iajs-2478	87	155	wf	wf	PROPN
iajs-2478	87	156	(	(	PUNCT
iajs-2478	87	157	11	11	NUM
iajs-2478	87	158	13	13	NUM
iajs-2478	87	159	)	)	PUNCT
iajs-2478	87	160	.	.	PUNCT
iajs-2478	88	1	case	case	NOUN
iajs-2478	88	2	2	2	NUM
iajs-2478	88	3	:	:	PUNCT
iajs-2478	88	4	choose	choose	VERB
iajs-2478	88	5	𝜑	𝜑	PRON
iajs-2478	88	6	∈	∈	PROPN
iajs-2478	88	7	𝐶	𝐶	PROPN
iajs-2478	88	8	0	0	PROPN
iajs-2478	88	9	,	,	PUNCT
iajs-2478	88	10	𝑇	𝑇	PROPN
iajs-2478	88	11	,	,	PUNCT
iajs-2478	88	12	s.t	s.t	PROPN
iajs-2478	88	13	.	.	PROPN
iajs-2478	88	14	𝜑	𝜑	PROPN
iajs-2478	88	15	𝑇	𝑇	PROPN
iajs-2478	88	16	0	0	NUM
iajs-2478	88	17	&	&	CCONJ
iajs-2478	88	18	𝜑	𝜑	PROPN
iajs-2478	88	19	0	0	NUM
iajs-2478	88	20	0	0	NUM
iajs-2478	88	21	,	,	PUNCT
iajs-2478	88	22	∀𝑖	∀𝑖	PROPN
iajs-2478	88	23	1,2,3	1,2,3	NOUN
iajs-2478	88	24	.	.	PUNCT
iajs-2478	89	1	using	use	VERB
iajs-2478	89	2	integration	integration	NOUN
iajs-2478	89	3	by	by	ADP
iajs-2478	89	4	parts	part	NOUN
iajs-2478	89	5	for	for	ADP
iajs-2478	89	6	1st	1st	ADJ
iajs-2478	89	7	term	term	NOUN
iajs-2478	89	8	in	in	ADP
iajs-2478	89	9	the	the	DET
iajs-2478	89	10	l.h.s	l.h.s	NOUN
iajs-2478	89	11	.	.	PUNCT
iajs-2478	90	1	of	of	ADP
iajs-2478	90	2	(	(	PUNCT
iajs-2478	90	3	36	36	NUM
iajs-2478	90	4	)	)	PUNCT
iajs-2478	90	5	,	,	PUNCT
iajs-2478	90	6	one	one	PRON
iajs-2478	90	7	gets	get	VERB
iajs-2478	90	8	𝑦	𝑦	NOUN
iajs-2478	90	9	,	,	PUNCT
iajs-2478	90	10	𝑣	𝑣	PRON
iajs-2478	90	11	𝜑ˊ	𝜑ˊ	ADP
iajs-2478	90	12	𝑡	𝑡	PROPN
iajs-2478	90	13	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	14	∇𝑦	∇𝑦	PROPN
iajs-2478	90	15	,	,	PUNCT
iajs-2478	90	16	∇𝑣	∇𝑣	PROPN
iajs-2478	90	17	𝑦	𝑦	PRON
iajs-2478	90	18	,	,	PUNCT
iajs-2478	90	19	𝑣	𝑣	DET
iajs-2478	90	20	𝜑	𝜑	X
iajs-2478	90	21	𝑡	𝑡	NOUN
iajs-2478	90	22	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	23	𝑦	𝑦	NOUN
iajs-2478	90	24	,	,	PUNCT
iajs-2478	90	25	𝑣	𝑣	ADP
iajs-2478	90	26	𝜑	𝜑	X
iajs-2478	90	27	𝑡	𝑡	NOUN
iajs-2478	90	28	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	29	𝑦	𝑦	NOUN
iajs-2478	90	30	,	,	PUNCT
iajs-2478	90	31	𝑣	𝑣	ADP
iajs-2478	90	32	𝜑	𝜑	X
iajs-2478	90	33	𝑡	𝑡	NOUN
iajs-2478	90	34	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	35	𝑓	𝑓	PRON
iajs-2478	90	36	,	,	PUNCT
iajs-2478	90	37	𝑣	𝑣	DET
iajs-2478	90	38	𝜑	𝜑	X
iajs-2478	90	39	𝑡	𝑡	NOUN
iajs-2478	90	40	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	41	𝑢	𝑢	NOUN
iajs-2478	90	42	,	,	PUNCT
iajs-2478	90	43	𝑣	𝑣	PRON
iajs-2478	90	44	𝜑	𝜑	X
iajs-2478	90	45	𝑡	𝑡	NOUN
iajs-2478	90	46	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	90	47	𝑦	𝑦	NOUN
iajs-2478	90	48	0	0	NUM
iajs-2478	90	49	,	,	PUNCT
iajs-2478	90	50	𝑣	𝑣	DET
iajs-2478	90	51	𝜑	𝜑	NOUN
iajs-2478	90	52	0	0	NUM
iajs-2478	90	53	,	,	PUNCT
iajs-2478	90	54	(	(	PUNCT
iajs-2478	90	55	39	39	NUM
iajs-2478	90	56	)	)	PUNCT
iajs-2478	90	57	subtracting	subtract	VERB
iajs-2478	90	58	(	(	PUNCT
iajs-2478	90	59	33	33	NUM
iajs-2478	90	60	)	)	PUNCT
iajs-2478	90	61	from	from	ADP
iajs-2478	90	62	(	(	PUNCT
iajs-2478	90	63	39	39	NUM
iajs-2478	90	64	)	)	PUNCT
iajs-2478	90	65	,	,	PUNCT
iajs-2478	90	66	one	one	PRON
iajs-2478	90	67	obtains	obtain	VERB
iajs-2478	90	68	that	that	PRON
iajs-2478	90	69	𝑦	𝑦	NOUN
iajs-2478	90	70	,	,	PUNCT
iajs-2478	90	71	𝑣	𝑣	PRON
iajs-2478	90	72	𝜑	𝜑	NOUN
iajs-2478	90	73	0	0	NUM
iajs-2478	90	74	𝑦	𝑦	NOUN
iajs-2478	90	75	0	0	NUM
iajs-2478	90	76	,	,	PUNCT
iajs-2478	90	77	𝑣	𝑣	DET
iajs-2478	90	78	𝜑	𝜑	NOUN
iajs-2478	90	79	0	0	NUM
iajs-2478	90	80	,	,	PUNCT
iajs-2478	90	81	𝜑	𝜑	PROPN
iajs-2478	90	82	0	0	NUM
iajs-2478	90	83	0,∀	0,∀	NUM
iajs-2478	90	84	𝜑	𝜑	NOUN
iajs-2478	90	85	∈	∈	PROPN
iajs-2478	90	86	𝐶	𝐶	PROPN
iajs-2478	90	87	0	0	PROPN
iajs-2478	90	88	,	,	PUNCT
iajs-2478	90	89	𝑇	𝑇	PROPN
iajs-2478	90	90	⇒	⇒	NOUN
iajs-2478	90	91	𝑦	𝑦	PRON
iajs-2478	90	92	,	,	PUNCT
iajs-2478	90	93	𝑣	𝑣	DET
iajs-2478	90	94	𝑦	𝑦	NOUN
iajs-2478	90	95	0	0	NUM
iajs-2478	90	96	,	,	PUNCT
iajs-2478	90	97	𝑣	𝑣	X
iajs-2478	90	98	,	,	PUNCT
iajs-2478	90	99	i.e.	i.e.	X
iajs-2478	90	100	the	the	DET
iajs-2478	90	101	ics	ics	NOUN
iajs-2478	90	102	(	(	PUNCT
iajs-2478	90	103	11.b	11.b	NUM
iajs-2478	90	104	)	)	PUNCT
iajs-2478	90	105	holds	hold	NOUN
iajs-2478	90	106	.	.	PUNCT
iajs-2478	91	1	by	by	ADP
iajs-2478	91	2	the	the	DET
iajs-2478	91	3	same	same	ADJ
iajs-2478	91	4	above	above	ADP
iajs-2478	91	5	way	way	NOUN
iajs-2478	91	6	one	one	PRON
iajs-2478	91	7	can	can	AUX
iajs-2478	91	8	show	show	VERB
iajs-2478	91	9	that	that	SCONJ
iajs-2478	91	10	𝑦	𝑦	NOUN
iajs-2478	91	11	,	,	PUNCT
iajs-2478	91	12	𝑣	𝑣	PRON
iajs-2478	91	13	𝑦	𝑦	NOUN
iajs-2478	91	14	0	0	NUM
iajs-2478	91	15	,	,	PUNCT
iajs-2478	91	16	𝑣	𝑣	X
iajs-2478	91	17	,	,	PUNCT
iajs-2478	91	18	𝑦	𝑦	NOUN
iajs-2478	91	19	,	,	PUNCT
iajs-2478	91	20	𝑣	𝑣	PRON
iajs-2478	91	21	𝑦	𝑦	NOUN
iajs-2478	91	22	0	0	NUM
iajs-2478	91	23	,	,	PUNCT
iajs-2478	91	24	𝑣	𝑣	PRON
iajs-2478	91	25	which	which	PRON
iajs-2478	91	26	means	mean	VERB
iajs-2478	91	27	the	the	DET
iajs-2478	91	28	ics	ics	NOUN
iajs-2478	91	29	(	(	PUNCT
iajs-2478	91	30	12.b	12.b	NUM
iajs-2478	91	31	)	)	PUNCT
iajs-2478	91	32	&	&	CCONJ
iajs-2478	91	33	(	(	PUNCT
iajs-2478	91	34	13.b	13.b	NUM
iajs-2478	91	35	)	)	PUNCT
iajs-2478	91	36	are	be	AUX
iajs-2478	91	37	holds	hold	NOUN
iajs-2478	91	38	.	.	PUNCT
iajs-2478	92	1	the	the	DET
iajs-2478	92	2	strongly	strongly	ADV
iajs-2478	92	3	convergence	convergence	NOUN
iajs-2478	92	4	for	for	ADP
iajs-2478	92	5	�	�	NOUN
iajs-2478	92	6	⃗	⃗	NOUN
iajs-2478	92	7	�	�	NOUN
iajs-2478	92	8	𝐧	𝐧	NOUN
iajs-2478	92	9	:	:	PUNCT
iajs-2478	92	10	substituting	substitute	VERB
iajs-2478	92	11	𝑣	𝑣	ADP
iajs-2478	92	12	𝑦	𝑦	NOUN
iajs-2478	92	13	,	,	PUNCT
iajs-2478	92	14	𝑣	𝑣	DET
iajs-2478	92	15	𝑦	𝑦	NOUN
iajs-2478	92	16	and	and	CCONJ
iajs-2478	92	17	𝑣	𝑣	DET
iajs-2478	92	18	𝑦	𝑦	NOUN
iajs-2478	92	19	in	in	ADP
iajs-2478	92	20	(	(	PUNCT
iajs-2478	92	21	17.a	17.a	NUM
iajs-2478	92	22	)	)	PUNCT
iajs-2478	92	23	,	,	PUNCT
iajs-2478	92	24	(	(	PUNCT
iajs-2478	92	25	18.a)&(19.a	18.a)&(19.a	NOUN
iajs-2478	92	26	)	)	PUNCT
iajs-2478	92	27	respectively	respectively	ADV
iajs-2478	92	28	,	,	PUNCT
iajs-2478	92	29	adding	add	VERB
iajs-2478	92	30	the	the	DET
iajs-2478	92	31	three	three	NUM
iajs-2478	92	32	obtained	obtain	VERB
iajs-2478	92	33	equations	equation	NOUN
iajs-2478	92	34	together	together	ADV
iajs-2478	92	35	,	,	PUNCT
iajs-2478	92	36	and	and	CCONJ
iajs-2478	92	37	then	then	ADV
iajs-2478	92	38	integrating	integrate	VERB
iajs-2478	92	39	the	the	DET
iajs-2478	92	40	obtained	obtain	VERB
iajs-2478	92	41	equation	equation	NOUN
iajs-2478	92	42	from	from	ADP
iajs-2478	92	43	0	0	NUM
iajs-2478	92	44	to	to	ADP
iajs-2478	92	45	𝑇	𝑇	PROPN
iajs-2478	92	46	,	,	PUNCT
iajs-2478	92	47	on	on	ADP
iajs-2478	92	48	the	the	DET
iajs-2478	92	49	other	other	ADJ
iajs-2478	92	50	hand	hand	NOUN
iajs-2478	92	51	substituting	substitute	VERB
iajs-2478	92	52	𝑣	𝑣	ADP
iajs-2478	92	53	𝑦	𝑦	NOUN
iajs-2478	92	54	,	,	PUNCT
iajs-2478	92	55	𝑣	𝑣	DET
iajs-2478	92	56	𝑦	𝑦	NOUN
iajs-2478	92	57	&	&	CCONJ
iajs-2478	92	58	𝑣	𝑣	DET
iajs-2478	92	59	𝑦	𝑦	NOUN
iajs-2478	92	60	in	in	ADP
iajs-2478	92	61	(	(	PUNCT
iajs-2478	92	62	11.a	11.a	NUM
iajs-2478	92	63	)	)	PUNCT
iajs-2478	92	64	,	,	PUNCT
iajs-2478	92	65	(	(	PUNCT
iajs-2478	92	66	12.a	12.a	NUM
iajs-2478	92	67	)	)	PUNCT
iajs-2478	92	68	&	&	CCONJ
iajs-2478	92	69	(	(	PUNCT
iajs-2478	92	70	13.a	13.a	NUM
iajs-2478	92	71	)	)	PUNCT
iajs-2478	92	72	respectively	respectively	ADV
iajs-2478	92	73	,	,	PUNCT
iajs-2478	92	74	adding	add	VERB
iajs-2478	92	75	them	they	PRON
iajs-2478	92	76	together	together	ADV
iajs-2478	92	77	,	,	PUNCT
iajs-2478	92	78	integrating	integrate	VERB
iajs-2478	92	79	the	the	DET
iajs-2478	92	80	obtained	obtain	VERB
iajs-2478	92	81	equations	equation	NOUN
iajs-2478	92	82	from	from	ADP
iajs-2478	92	83	0	0	NUM
iajs-2478	92	84	to	to	ADP
iajs-2478	92	85	𝑇	𝑇	PROPN
iajs-2478	92	86	,	,	PUNCT
iajs-2478	92	87	one	one	PRON
iajs-2478	92	88	gets	get	VERB
iajs-2478	92	89	〈	〈	PRON
iajs-2478	92	90	�	�	NOUN
iajs-2478	92	91	⃗	⃗	NOUN
iajs-2478	92	92	�	�	PROPN
iajs-2478	92	93	,	,	PUNCT
iajs-2478	92	94	�	�	PROPN
iajs-2478	92	95	⃗	⃗	NOUN
iajs-2478	92	96	�	�	PROPN
iajs-2478	92	97	〉	〉	NOUN
iajs-2478	92	98	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	92	99	𝑎	𝑎	PRON
iajs-2478	92	100	�	�	PROPN
iajs-2478	92	101	⃗	⃗	NOUN
iajs-2478	92	102	�	�	PROPN
iajs-2478	92	103	,	,	PUNCT
iajs-2478	92	104	�	�	PROPN
iajs-2478	92	105	⃗	⃗	PROPN
iajs-2478	92	106	�	�	PROPN
iajs-2478	92	107	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	92	108	𝑓	𝑓	PRON
iajs-2478	92	109	,	,	PUNCT
iajs-2478	92	110	𝑦	𝑦	NOUN
iajs-2478	92	111	𝑢	𝑢	X
iajs-2478	92	112	,	,	PUNCT
iajs-2478	92	113	𝑦	𝑦	PROPN
iajs-2478	92	114	𝑓	𝑓	PRON
iajs-2478	92	115	,	,	PUNCT
iajs-2478	92	116	𝑦	𝑦	NOUN
iajs-2478	92	117	𝑢	𝑢	X
iajs-2478	92	118	,	,	PUNCT
iajs-2478	92	119	𝑦	𝑦	PROPN
iajs-2478	92	120	𝑓	𝑓	PRON
iajs-2478	92	121	,	,	PUNCT
iajs-2478	92	122	𝑦	𝑦	NOUN
iajs-2478	92	123	𝑢	𝑢	NOUN
iajs-2478	92	124	,	,	PUNCT
iajs-2478	92	125	𝑦	𝑦	NOUN
iajs-2478	92	126	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	92	127	,	,	PUNCT
iajs-2478	92	128	(	(	PUNCT
iajs-2478	92	129	40.a	40.a	NOUN
iajs-2478	92	130	)	)	PUNCT
iajs-2478	93	1	〈	〈	PROPN
iajs-2478	93	2	�	�	PROPN
iajs-2478	93	3	⃗	⃗	PROPN
iajs-2478	93	4	�	�	PROPN
iajs-2478	93	5	,	,	PUNCT
iajs-2478	93	6	�	�	PROPN
iajs-2478	93	7	⃗	⃗	NOUN
iajs-2478	93	8	�	�	NOUN
iajs-2478	93	9	〉	〉	NOUN
iajs-2478	93	10	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	93	11	𝑎	𝑎	DET
iajs-2478	93	12	�	�	PROPN
iajs-2478	93	13	⃗	⃗	NOUN
iajs-2478	93	14	�	�	PROPN
iajs-2478	93	15	,	,	PUNCT
iajs-2478	93	16	�	�	PROPN
iajs-2478	93	17	⃗	⃗	PROPN
iajs-2478	93	18	�	�	PROPN
iajs-2478	93	19	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	93	20	𝑓	𝑓	PRON
iajs-2478	93	21	,	,	PUNCT
iajs-2478	93	22	𝑦	𝑦	NOUN
iajs-2478	93	23	𝑢	𝑢	X
iajs-2478	93	24	,	,	PUNCT
iajs-2478	93	25	𝑦	𝑦	PROPN
iajs-2478	93	26	𝑓	𝑓	PRON
iajs-2478	93	27	,	,	PUNCT
iajs-2478	93	28	𝑦	𝑦	NOUN
iajs-2478	93	29	𝑢	𝑢	X
iajs-2478	93	30	,	,	PUNCT
iajs-2478	93	31	𝑦	𝑦	PROPN
iajs-2478	93	32	𝑓	𝑓	PRON
iajs-2478	93	33	,	,	PUNCT
iajs-2478	93	34	𝑦	𝑦	NOUN
iajs-2478	93	35	𝑢	𝑢	NOUN
iajs-2478	93	36	,	,	PUNCT
iajs-2478	93	37	𝑦	𝑦	NOUN
iajs-2478	93	38	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	93	39	,	,	PUNCT
iajs-2478	93	40	(	(	PUNCT
iajs-2478	93	41	40.b	40.b	NUM
iajs-2478	93	42	)	)	PUNCT
iajs-2478	93	43	using	use	VERB
iajs-2478	93	44	lemma(1.2	lemma(1.2	NOUN
iajs-2478	93	45	)	)	PUNCT
iajs-2478	93	46	in	in	ADP
iajs-2478	93	47	[	[	X
iajs-2478	93	48	11	11	NUM
iajs-2478	93	49	]	]	PUNCT
iajs-2478	93	50	for	for	ADP
iajs-2478	93	51	the	the	DET
iajs-2478	93	52	1st	1st	ADJ
iajs-2478	93	53	terms	term	NOUN
iajs-2478	93	54	in	in	ADP
iajs-2478	93	55	the	the	DET
iajs-2478	93	56	l.h.s	l.h.s	NOUN
iajs-2478	93	57	.	.	PUNCT
iajs-2478	94	1	of	of	ADP
iajs-2478	94	2	(	(	PUNCT
iajs-2478	94	3	40.a&b	40.a&b	NOUN
iajs-2478	94	4	)	)	PUNCT
iajs-2478	94	5	,	,	PUNCT
iajs-2478	94	6	they	they	PRON
iajs-2478	94	7	become	become	VERB
iajs-2478	94	8	‖	‖	PROPN
iajs-2478	94	9	�	�	NOUN
iajs-2478	94	10	⃗	⃗	NOUN
iajs-2478	94	11	�	�	PROPN
iajs-2478	94	12	𝑇	𝑇	PROPN
iajs-2478	94	13	‖	‖	PROPN
iajs-2478	94	14	‖	‖	PROPN
iajs-2478	94	15	�	�	PROPN
iajs-2478	94	16	⃗	⃗	NOUN
iajs-2478	94	17	�	�	PROPN
iajs-2478	94	18	0	0	NUM
iajs-2478	94	19	‖	‖	PROPN
iajs-2478	94	20	𝑎	𝑎	DET
iajs-2478	94	21	�	�	PROPN
iajs-2478	94	22	⃗	⃗	NOUN
iajs-2478	94	23	�	�	PROPN
iajs-2478	94	24	,	,	PUNCT
iajs-2478	94	25	�	�	PROPN
iajs-2478	94	26	⃗	⃗	PROPN
iajs-2478	94	27	�	�	PROPN
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iajs-2478	98	355	𝑢	𝑢	X
iajs-2478	98	356	,	,	PUNCT
iajs-2478	98	357	𝑦	𝑦	PROPN
iajs-2478	98	358	𝑓	𝑓	PRON
iajs-2478	98	359	,	,	PUNCT
iajs-2478	98	360	𝑦	𝑦	NOUN
iajs-2478	98	361	𝑢	𝑢	NOUN
iajs-2478	98	362	,	,	PUNCT
iajs-2478	98	363	𝑦	𝑦	NOUN
iajs-2478	98	364	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	98	365	⟶	⟶	NOUN
iajs-2478	98	366	𝑓	𝑓	PROPN
iajs-2478	98	367	,	,	PUNCT
iajs-2478	98	368	𝑦	𝑦	NOUN
iajs-2478	98	369	𝑢	𝑢	X
iajs-2478	98	370	,	,	PUNCT
iajs-2478	98	371	𝑦	𝑦	PROPN
iajs-2478	98	372	𝑓	𝑓	PRON
iajs-2478	98	373	,	,	PUNCT
iajs-2478	98	374	𝑦	𝑦	NOUN
iajs-2478	98	375	𝑢	𝑢	X
iajs-2478	98	376	,	,	PUNCT
iajs-2478	98	377	𝑦	𝑦	PROPN
iajs-2478	98	378	𝑓	𝑓	PRON
iajs-2478	98	379	,	,	PUNCT
iajs-2478	98	380	𝑦	𝑦	NOUN
iajs-2478	98	381	𝑢	𝑢	NOUN
iajs-2478	98	382	,	,	PUNCT
iajs-2478	98	383	𝑦	𝑦	NOUN
iajs-2478	98	384	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	98	385	,	,	PUNCT
iajs-2478	98	386	(	(	PUNCT
iajs-2478	98	387	42.f	42.f	NUM
iajs-2478	98	388	)	)	PUNCT
iajs-2478	98	389	i.e.	i.e.	X
iajs-2478	98	390	when	when	SCONJ
iajs-2478	98	391	𝑛	𝑛	PROPN
iajs-2478	98	392	→	→	SYM
iajs-2478	98	393	∞	∞	NUM
iajs-2478	98	394	in	in	ADP
iajs-2478	98	395	both	both	DET
iajs-2478	98	396	sides	side	NOUN
iajs-2478	98	397	of	of	ADP
iajs-2478	98	398	(	(	PUNCT
iajs-2478	98	399	42	42	NUM
iajs-2478	98	400	)	)	PUNCT
iajs-2478	98	401	,	,	PUNCT
iajs-2478	98	402	one	one	PRON
iajs-2478	98	403	has	have	VERB
iajs-2478	98	404	the	the	DET
iajs-2478	98	405	following	follow	VERB
iajs-2478	98	406	results	result	NOUN
iajs-2478	98	407	:	:	PUNCT
iajs-2478	98	408	(	(	PUNCT
iajs-2478	98	409	1	1	X
iajs-2478	98	410	)	)	PUNCT
iajs-2478	98	411	the	the	DET
iajs-2478	98	412	first	first	ADJ
iajs-2478	98	413	two	two	NUM
iajs-2478	98	414	terms	term	NOUN
iajs-2478	98	415	in	in	ADP
iajs-2478	98	416	the	the	DET
iajs-2478	98	417	l.h.s	l.h.s	NOUN
iajs-2478	98	418	.	.	PUNCT
iajs-2478	99	1	of	of	ADP
iajs-2478	99	2	(	(	PUNCT
iajs-2478	99	3	42	42	NUM
iajs-2478	99	4	)	)	PUNCT
iajs-2478	99	5	are	be	AUX
iajs-2478	99	6	tending	tend	VERB
iajs-2478	99	7	to	to	ADP
iajs-2478	99	8	zero	zero	NUM
iajs-2478	99	9	from	from	ADP
iajs-2478	99	10	(	(	PUNCT
iajs-2478	99	11	42.d	42.d	NUM
iajs-2478	99	12	)	)	PUNCT
iajs-2478	99	13	.	.	PUNCT
iajs-2478	100	1	(	(	PUNCT
iajs-2478	100	2	2	2	X
iajs-2478	100	3	)	)	PUNCT
iajs-2478	100	4	from	from	ADP
iajs-2478	100	5	(	(	PUNCT
iajs-2478	100	6	41.a	41.a	NUM
iajs-2478	100	7	)	)	PUNCT
iajs-2478	100	8	eq	eq	NOUN
iajs-2478	100	9	.	.	PUNCT
iajs-2478	101	1	𝐴	𝐴	PROPN
iajs-2478	101	2	𝑓	𝑓	PROPN
iajs-2478	101	3	,	,	PUNCT
iajs-2478	101	4	𝑦	𝑦	NOUN
iajs-2478	101	5	𝑢	𝑢	X
iajs-2478	101	6	,	,	PUNCT
iajs-2478	101	7	𝑦	𝑦	PROPN
iajs-2478	101	8	𝑓	𝑓	PRON
iajs-2478	101	9	,	,	PUNCT
iajs-2478	101	10	𝑦	𝑦	NOUN
iajs-2478	101	11	𝑢	𝑢	NOUN
iajs-2478	101	12	,	,	PUNCT
iajs-2478	101	13	𝑦	𝑦	X
iajs-2478	101	14	(	(	PUNCT
iajs-2478	101	15	𝑓	𝑓	PROPN
iajs-2478	101	16	,	,	PUNCT
iajs-2478	101	17	𝑦	𝑦	NOUN
iajs-2478	101	18	)	)	PUNCT
iajs-2478	101	19	𝑢	𝑢	PROPN
iajs-2478	101	20	,	,	PUNCT
iajs-2478	101	21	𝑦	𝑦	NOUN
iajs-2478	101	22	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	101	23	from	from	ADP
iajs-2478	101	24	⟶	⟶	NOUN
iajs-2478	101	25	42	42	NUM
iajs-2478	101	26	.	.	PUNCT
iajs-2478	102	1	f	f	PROPN
iajs-2478	102	2	𝑓	𝑓	PROPN
iajs-2478	102	3	,	,	PUNCT
iajs-2478	102	4	𝑦	𝑦	NOUN
iajs-2478	102	5	𝑢	𝑢	X
iajs-2478	102	6	,	,	PUNCT
iajs-2478	102	7	𝑦	𝑦	PROPN
iajs-2478	102	8	𝑓	𝑓	PRON
iajs-2478	102	9	,	,	PUNCT
iajs-2478	102	10	𝑦	𝑦	NOUN
iajs-2478	102	11	𝑢	𝑢	X
iajs-2478	102	12	,	,	PUNCT
iajs-2478	102	13	𝑦	𝑦	PROPN
iajs-2478	102	14	𝑓	𝑓	PRON
iajs-2478	102	15	,	,	PUNCT
iajs-2478	102	16	𝑦	𝑦	NOUN
iajs-2478	102	17	𝑢	𝑢	NOUN
iajs-2478	102	18	,	,	PUNCT
iajs-2478	102	19	𝑦	𝑦	NOUN
iajs-2478	102	20	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	102	21	,	,	PUNCT
iajs-2478	102	22	(	(	PUNCT
iajs-2478	102	23	3	3	X
iajs-2478	102	24	)	)	PUNCT
iajs-2478	102	25	eq	eq	NOUN
iajs-2478	102	26	.	.	PUNCT
iajs-2478	103	1	𝐵	𝐵	NOUN
iajs-2478	103	2	⟶	⟶	NOUN
iajs-2478	103	3	l.h.s	l.h.s	NOUN
iajs-2478	103	4	.	.	PUNCT
iajs-2478	104	1	of	of	ADP
iajs-2478	104	2	(	(	PUNCT
iajs-2478	104	3	3.41.b	3.41.b	NUM
iajs-2478	104	4	)	)	PUNCT
iajs-2478	104	5	𝑓	𝑓	PRON
iajs-2478	104	6	,	,	PUNCT
iajs-2478	104	7	𝑦	𝑦	NOUN
iajs-2478	104	8	𝑢	𝑢	X
iajs-2478	104	9	,	,	PUNCT
iajs-2478	104	10	𝑦	𝑦	PROPN
iajs-2478	104	11	𝑓	𝑓	PRON
iajs-2478	104	12	,	,	PUNCT
iajs-2478	104	13	𝑦	𝑦	NOUN
iajs-2478	104	14	𝑢	𝑢	X
iajs-2478	104	15	,	,	PUNCT
iajs-2478	104	16	𝑦	𝑦	PROPN
iajs-2478	104	17	𝑓	𝑓	PRON
iajs-2478	104	18	,	,	PUNCT
iajs-2478	104	19	𝑦	𝑦	NOUN
iajs-2478	104	20	𝑢	𝑢	NOUN
iajs-2478	104	21	,	,	PUNCT
iajs-2478	104	22	𝑦	𝑦	NOUN
iajs-2478	104	23	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	104	24	,	,	PUNCT
iajs-2478	104	25	(	(	PUNCT
iajs-2478	104	26	4	4	X
iajs-2478	104	27	)	)	PUNCT
iajs-2478	104	28	the	the	DET
iajs-2478	104	29	1st	1st	ADJ
iajs-2478	104	30	two	two	NUM
iajs-2478	104	31	terms	term	NOUN
iajs-2478	104	32	in	in	ADP
iajs-2478	104	33	eq	eq	ADP
iajs-2478	104	34	.	.	PUNCT
iajs-2478	105	1	𝐶	𝐶	PROPN
iajs-2478	105	2	are	be	AUX
iajs-2478	105	3	tending	tend	VERB
iajs-2478	105	4	to	to	ADP
iajs-2478	105	5	zero	zero	NUM
iajs-2478	105	6	from	from	ADP
iajs-2478	105	7	(	(	PUNCT
iajs-2478	105	8	42.c	42.c	NOUN
iajs-2478	105	9	)	)	PUNCT
iajs-2478	105	10	,	,	PUNCT
iajs-2478	105	11	and	and	CCONJ
iajs-2478	105	12	the	the	DET
iajs-2478	105	13	last	last	ADJ
iajs-2478	105	14	one	one	NUM
iajs-2478	105	15	term	term	NOUN
iajs-2478	105	16	also	also	ADV
iajs-2478	105	17	tend	tend	VERB
iajs-2478	105	18	to	to	PART
iajs-2478	105	19	zero	zero	NUM
iajs-2478	105	20	from	from	ADP
iajs-2478	105	21	(	(	PUNCT
iajs-2478	105	22	42.e	42.e	NUM
iajs-2478	105	23	)	)	PUNCT
iajs-2478	105	24	,	,	PUNCT
iajs-2478	105	25	from	from	ADP
iajs-2478	105	26	these	these	DET
iajs-2478	105	27	results	result	NOUN
iajs-2478	105	28	(	(	PUNCT
iajs-2478	105	29	42	42	NUM
iajs-2478	105	30	)	)	PUNCT
iajs-2478	105	31	gives	give	VERB
iajs-2478	105	32	when	when	SCONJ
iajs-2478	105	33	𝑛	𝑛	PROPN
iajs-2478	105	34	→	→	SYM
iajs-2478	105	35	∞	∞	PROPN
iajs-2478	105	36	‖	‖	PROPN
iajs-2478	105	37	�	�	PROPN
iajs-2478	105	38	⃗	⃗	PROPN
iajs-2478	105	39	�	�	PROPN
iajs-2478	105	40	�	�	PROPN
iajs-2478	105	41	⃗	⃗	NOUN
iajs-2478	105	42	�	�	PROPN
iajs-2478	105	43	‖	‖	PROPN
iajs-2478	105	44	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	105	45	𝑎	𝑎	PRON
iajs-2478	105	46	�	�	PROPN
iajs-2478	105	47	⃗	⃗	NOUN
iajs-2478	105	48	�	�	PROPN
iajs-2478	105	49	�	�	PROPN
iajs-2478	105	50	⃗	⃗	PROPN
iajs-2478	105	51	�	�	PROPN
iajs-2478	105	52	,	,	PUNCT
iajs-2478	105	53	�	�	PROPN
iajs-2478	105	54	⃗	⃗	PROPN
iajs-2478	105	55	�	�	PROPN
iajs-2478	105	56	�	�	PROPN
iajs-2478	105	57	⃗	⃗	PROPN
iajs-2478	105	58	�	�	PROPN
iajs-2478	105	59	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	105	60	⟶	⟶	NOUN
iajs-2478	106	1	0	0	NUM
iajs-2478	106	2	⇒	⇒	PROPN
iajs-2478	106	3	�	�	PROPN
iajs-2478	106	4	⃗	⃗	PROPN
iajs-2478	106	5	�	�	PROPN
iajs-2478	106	6	⟶	⟶	NOUN
iajs-2478	106	7	�	�	NOUN
iajs-2478	106	8	⃗	⃗	NOUN
iajs-2478	106	9	�	�	NOUN
iajs-2478	106	10	strongly	strongly	ADV
iajs-2478	106	11	in	in	ADP
iajs-2478	106	12	𝐿	𝐿	PROPN
iajs-2478	106	13	ĩ	ĩ	PROPN
iajs-2478	106	14	,	,	PUNCT
iajs-2478	106	15	𝑉	𝑉	PROPN
iajs-2478	106	16	.	.	PUNCT
iajs-2478	107	1	uniqueness	uniqueness	NOUN
iajs-2478	107	2	of	of	ADP
iajs-2478	107	3	the	the	DET
iajs-2478	107	4	solution	solution	NOUN
iajs-2478	107	5	:	:	PUNCT
iajs-2478	107	6	let	let	VERB
iajs-2478	107	7	�	�	PROPN
iajs-2478	107	8	⃗	⃗	ADJ
iajs-2478	107	9	�	�	PROPN
iajs-2478	107	10	,	,	PUNCT
iajs-2478	107	11	�	�	NOUN
iajs-2478	107	12	⃗	⃗	NOUN
iajs-2478	107	13	�	�	NOUN
iajs-2478	107	14	are	be	AUX
iajs-2478	107	15	two	two	NUM
iajs-2478	107	16	solutions	solution	NOUN
iajs-2478	107	17	of	of	ADP
iajs-2478	107	18	the	the	DET
iajs-2478	107	19	wf	wf	PROPN
iajs-2478	107	20	(	(	PUNCT
iajs-2478	107	21	11	11	NUM
iajs-2478	107	22	)	)	PUNCT
iajs-2478	107	23	13	13	NUM
iajs-2478	107	24	)	)	PUNCT
iajs-2478	107	25	i.e.	i.e.	X
iajs-2478	107	26	𝑦	𝑦	NOUN
iajs-2478	107	27	and	and	CCONJ
iajs-2478	107	28	𝑦	𝑦	NOUN
iajs-2478	107	29	are	be	AUX
iajs-2478	107	30	satisfied	satisfied	ADJ
iajs-2478	107	31	(	(	PUNCT
iajs-2478	107	32	11.a	11.a	NUM
iajs-2478	107	33	)	)	PUNCT
iajs-2478	107	34	,	,	PUNCT
iajs-2478	107	35	or	or	CCONJ
iajs-2478	107	36	〈	〈	NOUN
iajs-2478	107	37	𝑦	𝑦	NOUN
iajs-2478	107	38	,	,	PUNCT
iajs-2478	107	39	𝑣	𝑣	ADP
iajs-2478	107	40	〉	〉	NOUN
iajs-2478	107	41	𝑎	𝑎	PUNCT
iajs-2478	107	42	𝑦	𝑦	NOUN
iajs-2478	107	43	,	,	PUNCT
iajs-2478	107	44	𝑣	𝑣	PRON
iajs-2478	107	45	𝑦	𝑦	NOUN
iajs-2478	107	46	,	,	PUNCT
iajs-2478	107	47	𝑣	𝑣	PRON
iajs-2478	107	48	𝑦	𝑦	NOUN
iajs-2478	107	49	,	,	PUNCT
iajs-2478	107	50	𝑣	𝑣	PRON
iajs-2478	107	51	𝑓	𝑓	X
iajs-2478	107	52	,	,	PUNCT
iajs-2478	107	53	𝑣	𝑣	PRON
iajs-2478	107	54	𝑢	𝑢	X
iajs-2478	107	55	,	,	PUNCT
iajs-2478	107	56	𝑣	𝑣	X
iajs-2478	107	57	,	,	PUNCT
iajs-2478	107	58	∀	∀	X
iajs-2478	107	59	𝑣	𝑣	ADP
iajs-2478	107	60	∈	∈	PROPN
iajs-2478	107	61	𝑉	𝑉	PROPN
iajs-2478	107	62	〈	〈	PROPN
iajs-2478	107	63	𝑦	𝑦	NOUN
iajs-2478	107	64	,	,	PUNCT
iajs-2478	107	65	𝑣	𝑣	ADP
iajs-2478	107	66	〉	〉	NOUN
iajs-2478	107	67	𝑎	𝑎	PUNCT
iajs-2478	107	68	𝑦	𝑦	NOUN
iajs-2478	107	69	,	,	PUNCT
iajs-2478	107	70	𝑣	𝑣	PRON
iajs-2478	107	71	𝑦	𝑦	NOUN
iajs-2478	107	72	,	,	PUNCT
iajs-2478	107	73	𝑣	𝑣	PRON
iajs-2478	107	74	𝑦	𝑦	NOUN
iajs-2478	107	75	,	,	PUNCT
iajs-2478	107	76	𝑣	𝑣	PRON
iajs-2478	107	77	𝑓	𝑓	X
iajs-2478	107	78	,	,	PUNCT
iajs-2478	107	79	𝑣	𝑣	PRON
iajs-2478	107	80	𝑢	𝑢	X
iajs-2478	107	81	,	,	PUNCT
iajs-2478	107	82	𝑣	𝑣	X
iajs-2478	107	83	,	,	PUNCT
iajs-2478	107	84	∀	∀	VERB
iajs-2478	107	85	𝑣	𝑣	ADP
iajs-2478	107	86	∈	∈	PROPN
iajs-2478	107	87	𝑉	𝑉	PROPN
iajs-2478	107	88	subtracting	subtract	VERB
iajs-2478	107	89	the	the	DET
iajs-2478	107	90	2	2	NUM
iajs-2478	107	91	equation	equation	NOUN
iajs-2478	107	92	from	from	ADP
iajs-2478	107	93	the	the	DET
iajs-2478	107	94	1st	1st	ADJ
iajs-2478	107	95	one	one	NOUN
iajs-2478	107	96	and	and	CCONJ
iajs-2478	107	97	substituting	substitute	VERB
iajs-2478	107	98	𝑣	𝑣	ADP
iajs-2478	107	99	𝑦	𝑦	PROPN
iajs-2478	107	100	𝑦	𝑦	NOUN
iajs-2478	107	101	in	in	ADP
iajs-2478	107	102	the	the	DET
iajs-2478	107	103	obtained	obtain	VERB
iajs-2478	107	104	equation	equation	NOUN
iajs-2478	107	105	,	,	PUNCT
iajs-2478	107	106	one	one	PRON
iajs-2478	107	107	gets	get	VERB
iajs-2478	107	108	that	that	PRON
iajs-2478	107	109	〈	〈	PROPN
iajs-2478	107	110	𝑦	𝑦	NOUN
iajs-2478	107	111	𝑦	𝑦	NOUN
iajs-2478	107	112	,	,	PUNCT
iajs-2478	107	113	𝑦	𝑦	PRON
iajs-2478	107	114	𝑦	𝑦	PRON
iajs-2478	107	115	〉	〉	NOUN
iajs-2478	107	116	𝑎	𝑎	X
iajs-2478	107	117	𝑦	𝑦	NUM
iajs-2478	107	118	𝑦	𝑦	NOUN
iajs-2478	107	119	,	,	PUNCT
iajs-2478	107	120	𝑦	𝑦	PRON
iajs-2478	107	121	𝑦	𝑦	NOUN
iajs-2478	107	122	𝑦	𝑦	PRON
iajs-2478	107	123	𝑦	𝑦	NOUN
iajs-2478	107	124	,	,	PUNCT
iajs-2478	107	125	𝑦	𝑦	PRON
iajs-2478	107	126	𝑦	𝑦	NOUN
iajs-2478	107	127	𝑦	𝑦	PRON
iajs-2478	107	128	𝑦	𝑦	NOUN
iajs-2478	107	129	,	,	PUNCT
iajs-2478	107	130	𝑦	𝑦	PRON
iajs-2478	107	131	𝑦	𝑦	NOUN
iajs-2478	107	132	0	0	NUM
iajs-2478	107	133	,	,	PUNCT
iajs-2478	107	134	(	(	PUNCT
iajs-2478	107	135	43	43	NUM
iajs-2478	107	136	)	)	PUNCT
iajs-2478	107	137	by	by	ADP
iajs-2478	107	138	the	the	DET
iajs-2478	107	139	same	same	ADJ
iajs-2478	107	140	way	way	NOUN
iajs-2478	107	141	,	,	PUNCT
iajs-2478	107	142	one	one	PRON
iajs-2478	107	143	gets	get	VERB
iajs-2478	107	144	〈	〈	PROPN
iajs-2478	107	145	𝑦	𝑦	PRON
iajs-2478	107	146	𝑦	𝑦	NOUN
iajs-2478	107	147	,	,	PUNCT
iajs-2478	107	148	𝑦	𝑦	PRON
iajs-2478	107	149	𝑦	𝑦	PRON
iajs-2478	107	150	〉	〉	NOUN
iajs-2478	107	151	𝑎	𝑎	X
iajs-2478	107	152	𝑦	𝑦	NUM
iajs-2478	107	153	𝑦	𝑦	NOUN
iajs-2478	107	154	,	,	PUNCT
iajs-2478	107	155	𝑦	𝑦	PRON
iajs-2478	107	156	𝑦	𝑦	NOUN
iajs-2478	107	157	𝑦	𝑦	PRON
iajs-2478	107	158	𝑦	𝑦	NOUN
iajs-2478	107	159	,	,	PUNCT
iajs-2478	107	160	𝑦	𝑦	PRON
iajs-2478	107	161	𝑦	𝑦	NOUN
iajs-2478	107	162	𝑦	𝑦	PRON
iajs-2478	107	163	𝑦	𝑦	NOUN
iajs-2478	107	164	,	,	PUNCT
iajs-2478	107	165	𝑦	𝑦	PRON
iajs-2478	107	166	𝑦	𝑦	NOUN
iajs-2478	107	167	0	0	NUM
iajs-2478	107	168	,	,	PUNCT
iajs-2478	107	169	(	(	PUNCT
iajs-2478	107	170	44	44	NUM
iajs-2478	107	171	)	)	PUNCT
iajs-2478	107	172	  	  	SPACE
iajs-2478	107	173	120	120	NUM
iajs-2478	107	174	ibn	ibn	PROPN
iajs-2478	107	175	al	al	PROPN
iajs-2478	107	176	-	-	PUNCT
iajs-2478	107	177	haitham	haitham	PROPN
iajs-2478	107	178	jour	jour	X
iajs-2478	107	179	.	.	PROPN
iajs-2478	108	1	for	for	ADP
iajs-2478	108	2	pure	pure	ADJ
iajs-2478	108	3	&	&	CCONJ
iajs-2478	108	4	appl	appl	PROPN
iajs-2478	108	5	.	.	PUNCT
iajs-2478	109	1	sci	sci	PROPN
iajs-2478	109	2	.	.	PROPN
iajs-2478	110	1	33	33	NUM
iajs-2478	110	2	(	(	PUNCT
iajs-2478	110	3	3	3	NUM
iajs-2478	110	4	)	)	PUNCT
iajs-2478	110	5	2020	2020	NUM
iajs-2478	111	1	〈	〈	PROPN
iajs-2478	111	2	𝑦	𝑦	NUM
iajs-2478	111	3	𝑦	𝑦	NOUN
iajs-2478	111	4	,	,	PUNCT
iajs-2478	111	5	𝑦	𝑦	PRON
iajs-2478	111	6	𝑦	𝑦	DET
iajs-2478	111	7	〉	〉	NOUN
iajs-2478	111	8	𝑎	𝑎	X
iajs-2478	111	9	𝑦	𝑦	NUM
iajs-2478	111	10	𝑦	𝑦	NOUN
iajs-2478	111	11	,	,	PUNCT
iajs-2478	111	12	𝑦	𝑦	PRON
iajs-2478	111	13	𝑦	𝑦	NOUN
iajs-2478	111	14	𝑦	𝑦	PRON
iajs-2478	111	15	𝑦	𝑦	NOUN
iajs-2478	111	16	,	,	PUNCT
iajs-2478	111	17	𝑦	𝑦	PRON
iajs-2478	111	18	𝑦	𝑦	NOUN
iajs-2478	111	19	𝑦	𝑦	PRON
iajs-2478	111	20	𝑦	𝑦	NOUN
iajs-2478	111	21	,	,	PUNCT
iajs-2478	111	22	𝑦	𝑦	PRON
iajs-2478	111	23	𝑦	𝑦	NOUN
iajs-2478	111	24	0	0	NUM
iajs-2478	111	25	,	,	PUNCT
iajs-2478	111	26	(	(	PUNCT
iajs-2478	111	27	45	45	NUM
iajs-2478	111	28	)	)	PUNCT
iajs-2478	111	29	adding	add	VERB
iajs-2478	111	30	(	(	PUNCT
iajs-2478	111	31	43	43	NUM
iajs-2478	111	32	45	45	NUM
iajs-2478	111	33	)	)	PUNCT
iajs-2478	111	34	,	,	PUNCT
iajs-2478	111	35	using	use	VERB
iajs-2478	111	36	lemma(1.2	lemma(1.2	NOUN
iajs-2478	111	37	)	)	PUNCT
iajs-2478	111	38	in	in	ADP
iajs-2478	111	39	[	[	X
iajs-2478	111	40	11	11	NUM
iajs-2478	111	41	]	]	PUNCT
iajs-2478	111	42	.	.	PUNCT
iajs-2478	112	1	in	in	ADP
iajs-2478	112	2	the	the	DET
iajs-2478	112	3	1st	1st	ADJ
iajs-2478	112	4	term	term	NOUN
iajs-2478	112	5	of	of	ADP
iajs-2478	112	6	the	the	DET
iajs-2478	112	7	obtained	obtain	VERB
iajs-2478	112	8	equations	equation	NOUN
iajs-2478	112	9	,	,	PUNCT
iajs-2478	112	10	to	to	PART
iajs-2478	112	11	get	get	VERB
iajs-2478	112	12	�	�	NOUN
iajs-2478	112	13	⃗	⃗	PROPN
iajs-2478	112	14	�	�	PROPN
iajs-2478	112	15	�	�	PROPN
iajs-2478	112	16	⃗	⃗	PROPN
iajs-2478	112	17	�	�	PROPN
iajs-2478	112	18	�	�	PROPN
iajs-2478	112	19	⃗	⃗	PROPN
iajs-2478	112	20	�	�	PROPN
iajs-2478	112	21	�	�	PROPN
iajs-2478	112	22	⃗	⃗	NOUN
iajs-2478	112	23	�	�	PROPN
iajs-2478	112	24	0	0	NUM
iajs-2478	112	25	,	,	PUNCT
iajs-2478	112	26	(	(	PUNCT
iajs-2478	112	27	46	46	NUM
iajs-2478	112	28	)	)	PUNCT
iajs-2478	112	29	the	the	DET
iajs-2478	112	30	2nd	2nd	ADJ
iajs-2478	112	31	term	term	NOUN
iajs-2478	112	32	of	of	ADP
iajs-2478	112	33	the	the	DET
iajs-2478	112	34	l.h.s	l.h.s	NOUN
iajs-2478	112	35	.	.	PUNCT
iajs-2478	113	1	of	of	ADP
iajs-2478	113	2	(	(	PUNCT
iajs-2478	113	3	46	46	NUM
iajs-2478	113	4	)	)	PUNCT
iajs-2478	113	5	is	be	AUX
iajs-2478	113	6	positive	positive	ADJ
iajs-2478	113	7	,	,	PUNCT
iajs-2478	113	8	integrating	integrate	VERB
iajs-2478	113	9	both	both	DET
iajs-2478	113	10	sides	side	NOUN
iajs-2478	113	11	of	of	ADP
iajs-2478	113	12	(	(	PUNCT
iajs-2478	113	13	46	46	NUM
iajs-2478	113	14	)	)	PUNCT
iajs-2478	113	15	w.r.t	w.r.t	NOUN
iajs-2478	113	16	.	.	PUNCT
iajs-2478	114	1	𝑡	𝑡	VERB
iajs-2478	114	2	from	from	ADP
iajs-2478	114	3	0	0	NUM
iajs-2478	114	4	to	to	ADP
iajs-2478	114	5	𝑡	𝑡	PROPN
iajs-2478	114	6	,	,	PUNCT
iajs-2478	114	7	one	one	PRON
iajs-2478	114	8	gets	get	VERB
iajs-2478	114	9	⃗	⃗	PROPN
iajs-2478	114	10	⃗	⃗	PROPN
iajs-2478	114	11	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	114	12	0	0	NUM
iajs-2478	114	13	⇒	⇒	PROPN
iajs-2478	114	14	�	�	PROPN
iajs-2478	114	15	⃗	⃗	PROPN
iajs-2478	114	16	�	�	PROPN
iajs-2478	114	17	�	�	PROPN
iajs-2478	114	18	⃗	⃗	NOUN
iajs-2478	114	19	�	�	PROPN
iajs-2478	114	20	𝑡	𝑡	PROPN
iajs-2478	114	21	0	0	NUM
iajs-2478	114	22	⇒	⇒	PROPN
iajs-2478	114	23	�	�	PROPN
iajs-2478	114	24	⃗	⃗	PROPN
iajs-2478	114	25	�	�	PROPN
iajs-2478	114	26	�	�	PROPN
iajs-2478	114	27	⃗	⃗	NOUN
iajs-2478	114	28	�	�	NOUN
iajs-2478	114	29	0	0	NUM
iajs-2478	114	30	∀𝑡	∀𝑡	NUM
iajs-2478	114	31	∈	∈	PROPN
iajs-2478	114	32	ĩ	ĩ	ADP
iajs-2478	114	33	,	,	PUNCT
iajs-2478	114	34	integrating	integrate	VERB
iajs-2478	114	35	both	both	DET
iajs-2478	114	36	sides	side	NOUN
iajs-2478	114	37	of	of	ADP
iajs-2478	114	38	(	(	PUNCT
iajs-2478	114	39	46	46	NUM
iajs-2478	114	40	)	)	PUNCT
iajs-2478	114	41	from	from	ADP
iajs-2478	114	42	0	0	NUM
iajs-2478	114	43	to	to	ADP
iajs-2478	114	44	𝑇	𝑇	PROPN
iajs-2478	114	45	,	,	PUNCT
iajs-2478	114	46	using	use	VERB
iajs-2478	114	47	the	the	DET
iajs-2478	114	48	given	give	VERB
iajs-2478	114	49	ics	ic	NOUN
iajs-2478	114	50	,	,	PUNCT
iajs-2478	114	51	one	one	NUM
iajs-2478	114	52	has	have	VERB
iajs-2478	114	53	�	�	NOUN
iajs-2478	114	54	⃗	⃗	NOUN
iajs-2478	114	55	�	�	PROPN
iajs-2478	114	56	�	�	PROPN
iajs-2478	114	57	⃗	⃗	PROPN
iajs-2478	114	58	�	�	PROPN
iajs-2478	114	59	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	114	60	0	0	NUM
iajs-2478	114	61	⇒	⇒	PROPN
iajs-2478	114	62	�	�	PROPN
iajs-2478	114	63	⃗	⃗	PROPN
iajs-2478	114	64	�	�	PROPN
iajs-2478	114	65	�	�	PROPN
iajs-2478	114	66	⃗	⃗	NOUN
iajs-2478	114	67	�	�	PROPN
iajs-2478	114	68	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	114	69	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	114	70	0	0	NUM
iajs-2478	115	1	⇒	⇒	NOUN
iajs-2478	115	2	�	�	PROPN
iajs-2478	115	3	⃗	⃗	PROPN
iajs-2478	115	4	�	�	PROPN
iajs-2478	115	5	�	�	PROPN
iajs-2478	115	6	⃗	⃗	PROPN
iajs-2478	115	7	�	�	PROPN
iajs-2478	115	8	.	.	PUNCT
iajs-2478	116	1	4	4	X
iajs-2478	116	2	.	.	X
iajs-2478	116	3	existence	existence	NOUN
iajs-2478	116	4	of	of	ADP
iajs-2478	116	5	a	a	DET
iajs-2478	116	6	ccbocp	ccbocp	NOUN
iajs-2478	116	7	:	:	PUNCT
iajs-2478	116	8	theorem	theorem	NOUN
iajs-2478	116	9	4.1	4.1	NUM
iajs-2478	116	10	:	:	PUNCT
iajs-2478	116	11	in	in	ADP
iajs-2478	116	12	addition	addition	NOUN
iajs-2478	116	13	to	to	ADP
iajs-2478	116	14	assumptions	assumption	NOUN
iajs-2478	116	15	(	(	PUNCT
iajs-2478	116	16	a	a	X
iajs-2478	116	17	)	)	PUNCT
iajs-2478	116	18	,	,	PUNCT
iajs-2478	116	19	assume	assume	VERB
iajs-2478	116	20	that	that	SCONJ
iajs-2478	116	21	�	�	NOUN
iajs-2478	116	22	⃗	⃗	PART
iajs-2478	116	23	�	�	PROPN
iajs-2478	116	24	and	and	CCONJ
iajs-2478	116	25	�	�	PROPN
iajs-2478	116	26	⃗	⃗	PROPN
iajs-2478	116	27	�	�	PROPN
iajs-2478	116	28	δ	δ	PROPN
iajs-2478	116	29	�	�	PROPN
iajs-2478	116	30	⃗	⃗	NOUN
iajs-2478	116	31	�	�	PROPN
iajs-2478	116	32	are	be	AUX
iajs-2478	116	33	the	the	DET
iajs-2478	116	34	svs	svs	NOUN
iajs-2478	116	35	corresponding	correspond	VERB
iajs-2478	116	36	to	to	ADP
iajs-2478	116	37	the	the	DET
iajs-2478	116	38	cvs	cvs	NOUN
iajs-2478	116	39	𝑢	𝑢	PROPN
iajs-2478	116	40	and	and	CCONJ
iajs-2478	116	41	𝑢	𝑢	PRON
iajs-2478	116	42	δ𝑢	δ𝑢	VERB
iajs-2478	116	43	respectively	respectively	ADV
iajs-2478	116	44	with	with	ADP
iajs-2478	116	45	𝑢	𝑢	PRON
iajs-2478	116	46	and	and	CCONJ
iajs-2478	116	47	δ𝑢	δ𝑢	PROPN
iajs-2478	116	48	are	be	AUX
iajs-2478	116	49	bounded	bound	VERB
iajs-2478	116	50	in	in	ADP
iajs-2478	116	51	𝐿	𝐿	PROPN
iajs-2478	116	52	σ	σ	PROPN
iajs-2478	116	53	,	,	PUNCT
iajs-2478	116	54	then	then	ADV
iajs-2478	116	55	‖δ	‖δ	ADP
iajs-2478	116	56	�	�	NOUN
iajs-2478	116	57	⃗	⃗	NOUN
iajs-2478	116	58	�	�	PROPN
iajs-2478	116	59	‖𝑳	‖𝑳	PROPN
iajs-2478	116	60	ĩ,𝑳𝟐	ĩ,𝑳𝟐	PROPN
iajs-2478	116	61	ω	ω	PROPN
iajs-2478	116	62	𝐿‖δ𝑢‖	𝐿‖δ𝑢‖	PROPN
iajs-2478	116	63	,	,	PUNCT
iajs-2478	116	64	𝐿	𝐿	PROPN
iajs-2478	116	65	∈	∈	PROPN
iajs-2478	116	66	ℝ	ℝ	PROPN
iajs-2478	116	67	‖δ	‖δ	ADJ
iajs-2478	116	68	�	�	NOUN
iajs-2478	116	69	⃗	⃗	NOUN
iajs-2478	116	70	�	�	NOUN
iajs-2478	116	71	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	116	72	𝑸	𝑸	PROPN
iajs-2478	116	73	𝐿‖δ𝑢‖	𝐿‖δ𝑢‖	PROPN
iajs-2478	116	74	,	,	PUNCT
iajs-2478	116	75	𝐿	𝐿	PROPN
iajs-2478	116	76	∈	∈	PROPN
iajs-2478	116	77	ℝ	ℝ	PROPN
iajs-2478	116	78	‖δ	‖δ	ADJ
iajs-2478	116	79	�	�	NOUN
iajs-2478	116	80	⃗	⃗	NOUN
iajs-2478	116	81	�	�	NOUN
iajs-2478	116	82	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	116	83	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	116	84	𝐿	𝐿	PROPN
iajs-2478	116	85	‖δ𝑢‖	‖δ𝑢‖	PROPN
iajs-2478	116	86	,	,	PUNCT
iajs-2478	116	87	𝐿	𝐿	PROPN
iajs-2478	116	88	∈	∈	PROPN
iajs-2478	116	89	ℝ	ℝ	NOUN
iajs-2478	116	90	proof	proof	NOUN
iajs-2478	116	91	:	:	PUNCT
iajs-2478	116	92	let	let	VERB
iajs-2478	116	93	𝑢	𝑢	PRON
iajs-2478	116	94	𝑢	𝑢	X
iajs-2478	116	95	,	,	PUNCT
iajs-2478	116	96	𝑢	𝑢	PRON
iajs-2478	116	97	,	,	PUNCT
iajs-2478	116	98	𝑢	𝑢	PROPN
iajs-2478	116	99	∈	∈	PROPN
iajs-2478	116	100	𝐿	𝐿	PROPN
iajs-2478	116	101	σ	σ	PROPN
iajs-2478	116	102	be	be	AUX
iajs-2478	116	103	given	give	VERB
iajs-2478	116	104	,	,	PUNCT
iajs-2478	116	105	then	then	ADV
iajs-2478	116	106	by	by	ADP
iajs-2478	116	107	theorem3.1	theorem3.1	NUM
iajs-2478	116	108	,	,	PUNCT
iajs-2478	116	109	there	there	PRON
iajs-2478	116	110	exists	exist	VERB
iajs-2478	116	111	�	�	NOUN
iajs-2478	116	112	⃗	⃗	NOUN
iajs-2478	116	113	�	�	PROPN
iajs-2478	116	114	𝑦	𝑦	SYM
iajs-2478	116	115	𝑦	𝑦	PROPN
iajs-2478	116	116	,	,	PUNCT
iajs-2478	116	117	𝑦	𝑦	PROPN
iajs-2478	116	118	𝑦	𝑦	NOUN
iajs-2478	116	119	,	,	PUNCT
iajs-2478	116	120	𝑦	𝑦	PRON
iajs-2478	116	121	𝑦	𝑦	NOUN
iajs-2478	116	122	which	which	PRON
iajs-2478	116	123	is	be	AUX
iajs-2478	116	124	satisfied	satisfied	ADJ
iajs-2478	116	125	(	(	PUNCT
iajs-2478	116	126	11	11	NUM
iajs-2478	116	127	)	)	PUNCT
iajs-2478	116	128	13	13	NUM
iajs-2478	116	129	)	)	PUNCT
iajs-2478	116	130	and	and	CCONJ
iajs-2478	116	131	also	also	ADV
iajs-2478	116	132	let	let	VERB
iajs-2478	116	133	�	�	NOUN
iajs-2478	116	134	⃗	⃗	NOUN
iajs-2478	116	135	�	�	PROPN
iajs-2478	116	136	𝑦	𝑦	PROPN
iajs-2478	116	137	,	,	PUNCT
iajs-2478	116	138	𝑦	𝑦	PRON
iajs-2478	116	139	,	,	PUNCT
iajs-2478	116	140	𝑦	𝑦	PRON
iajs-2478	116	141	be	be	AUX
iajs-2478	116	142	the	the	DET
iajs-2478	116	143	solution	solution	NOUN
iajs-2478	116	144	of	of	ADP
iajs-2478	116	145	(	(	PUNCT
iajs-2478	116	146	11	11	NUM
iajs-2478	116	147	13	13	NUM
iajs-2478	116	148	)	)	PUNCT
iajs-2478	116	149	,	,	PUNCT
iajs-2478	116	150	corresponds	correspond	VERB
iajs-2478	116	151	to	to	ADP
iajs-2478	116	152	the	the	DET
iajs-2478	116	153	cv	cv	PROPN
iajs-2478	116	154	𝑢	𝑢	ADP
iajs-2478	116	155	𝑢	𝑢	PROPN
iajs-2478	116	156	,	,	PUNCT
iajs-2478	116	157	𝑢	𝑢	PRON
iajs-2478	116	158	,	,	PUNCT
iajs-2478	116	159	𝑢	𝑢	PROPN
iajs-2478	116	160	∈	∈	PROPN
iajs-2478	116	161	𝐿	𝐿	PROPN
iajs-2478	116	162	σ	σ	X
iajs-2478	116	163	i.e.	i.e.	X
iajs-2478	116	164	〈	〈	PROPN
iajs-2478	116	165	𝑦	𝑦	NOUN
iajs-2478	116	166	,	,	PUNCT
iajs-2478	116	167	𝑣	𝑣	ADP
iajs-2478	116	168	〉	〉	NOUN
iajs-2478	116	169	∇𝑦	∇𝑦	PROPN
iajs-2478	116	170	,	,	PUNCT
iajs-2478	116	171	∇𝑣	∇𝑣	PROPN
iajs-2478	116	172	𝑦	𝑦	PRON
iajs-2478	116	173	,	,	PUNCT
iajs-2478	116	174	𝑣	𝑣	DET
iajs-2478	116	175	𝑦	𝑦	NOUN
iajs-2478	116	176	,	,	PUNCT
iajs-2478	116	177	𝑣	𝑣	PRON
iajs-2478	116	178	𝑦	𝑦	NOUN
iajs-2478	116	179	,	,	PUNCT
iajs-2478	116	180	𝑣	𝑣	PRON
iajs-2478	116	181	𝑓	𝑓	X
iajs-2478	116	182	,	,	PUNCT
iajs-2478	116	183	𝑣	𝑣	PRON
iajs-2478	116	184	𝑢	𝑢	X
iajs-2478	116	185	,	,	PUNCT
iajs-2478	116	186	𝑣	𝑣	X
iajs-2478	116	187	,	,	PUNCT
iajs-2478	116	188	(	(	PUNCT
iajs-2478	116	189	47.a	47.a	NUM
iajs-2478	116	190	)	)	PUNCT
iajs-2478	116	191	𝑦	𝑦	NOUN
iajs-2478	116	192	0	0	NUM
iajs-2478	116	193	,	,	PUNCT
iajs-2478	116	194	𝑣	𝑣	PRON
iajs-2478	116	195	𝑦	𝑦	NOUN
iajs-2478	116	196	,	,	PUNCT
iajs-2478	116	197	𝑣	𝑣	X
iajs-2478	116	198	,	,	PUNCT
iajs-2478	116	199	(	(	PUNCT
iajs-2478	116	200	47.b	47.b	NOUN
iajs-2478	116	201	)	)	PUNCT
iajs-2478	117	1	〈	〈	PROPN
iajs-2478	117	2	𝑦	𝑦	NOUN
iajs-2478	117	3	,	,	PUNCT
iajs-2478	117	4	𝑣	𝑣	ADP
iajs-2478	117	5	〉	〉	NOUN
iajs-2478	117	6	∇𝑦	∇𝑦	PROPN
iajs-2478	117	7	,	,	PUNCT
iajs-2478	117	8	∇𝑣	∇𝑣	PROPN
iajs-2478	117	9	𝑦	𝑦	PRON
iajs-2478	117	10	,	,	PUNCT
iajs-2478	117	11	𝑣	𝑣	PRON
iajs-2478	117	12	𝑦	𝑦	NOUN
iajs-2478	117	13	,	,	PUNCT
iajs-2478	117	14	𝑣	𝑣	PRON
iajs-2478	117	15	𝑦	𝑦	NOUN
iajs-2478	117	16	,	,	PUNCT
iajs-2478	117	17	𝑣	𝑣	PRON
iajs-2478	117	18	𝑓	𝑓	X
iajs-2478	117	19	,	,	PUNCT
iajs-2478	117	20	𝑣	𝑣	PRON
iajs-2478	117	21	𝑢	𝑢	X
iajs-2478	117	22	,	,	PUNCT
iajs-2478	117	23	𝑣	𝑣	X
iajs-2478	117	24	,	,	PUNCT
iajs-2478	117	25	(	(	PUNCT
iajs-2478	117	26	48.a	48.a	NUM
iajs-2478	117	27	)	)	PUNCT
iajs-2478	117	28	𝑦	𝑦	NOUN
iajs-2478	117	29	0	0	NUM
iajs-2478	117	30	,	,	PUNCT
iajs-2478	117	31	𝑣	𝑣	PRON
iajs-2478	117	32	𝑦	𝑦	NOUN
iajs-2478	117	33	,	,	PUNCT
iajs-2478	117	34	𝑣	𝑣	X
iajs-2478	117	35	,	,	PUNCT
iajs-2478	117	36	(	(	PUNCT
iajs-2478	117	37	48.b	48.b	NOUN
iajs-2478	117	38	)	)	PUNCT
iajs-2478	118	1	〈	〈	NOUN
iajs-2478	118	2	𝑦	𝑦	NOUN
iajs-2478	118	3	,	,	PUNCT
iajs-2478	118	4	𝑣	𝑣	ADP
iajs-2478	118	5	〉	〉	NOUN
iajs-2478	118	6	∇𝑦	∇𝑦	PROPN
iajs-2478	118	7	,	,	PUNCT
iajs-2478	118	8	∇𝑣	∇𝑣	PROPN
iajs-2478	118	9	𝑦	𝑦	PRON
iajs-2478	118	10	,	,	PUNCT
iajs-2478	118	11	𝑣	𝑣	PRON
iajs-2478	118	12	𝑦	𝑦	NOUN
iajs-2478	118	13	,	,	PUNCT
iajs-2478	118	14	𝑣	𝑣	PRON
iajs-2478	118	15	𝑦	𝑦	NOUN
iajs-2478	118	16	,	,	PUNCT
iajs-2478	118	17	𝑣	𝑣	PRON
iajs-2478	118	18	𝑓	𝑓	X
iajs-2478	118	19	,	,	PUNCT
iajs-2478	118	20	𝑣	𝑣	PRON
iajs-2478	118	21	𝑢	𝑢	X
iajs-2478	118	22	,	,	PUNCT
iajs-2478	118	23	𝑣	𝑣	X
iajs-2478	118	24	,	,	PUNCT
iajs-2478	118	25	(	(	PUNCT
iajs-2478	118	26	49.a	49.a	NUM
iajs-2478	118	27	)	)	PUNCT
iajs-2478	118	28	𝑦	𝑦	NOUN
iajs-2478	118	29	0	0	NUM
iajs-2478	118	30	,	,	PUNCT
iajs-2478	118	31	𝑣	𝑣	PRON
iajs-2478	118	32	𝑦	𝑦	NOUN
iajs-2478	118	33	,	,	PUNCT
iajs-2478	118	34	𝑣	𝑣	X
iajs-2478	118	35	,	,	PUNCT
iajs-2478	118	36	(	(	PUNCT
iajs-2478	118	37	49.b	49.b	NUM
iajs-2478	118	38	)	)	PUNCT
iajs-2478	118	39	subtracting	subtracting	NOUN
iajs-2478	118	40	(	(	PUNCT
iajs-2478	118	41	11.a&b	11.a&b	NUM
iajs-2478	118	42	)	)	PUNCT
iajs-2478	118	43	from	from	ADP
iajs-2478	118	44	(	(	PUNCT
iajs-2478	118	45	47.a&b	47.a&b	NUM
iajs-2478	118	46	)	)	PUNCT
iajs-2478	118	47	,	,	PUNCT
iajs-2478	118	48	(	(	PUNCT
iajs-2478	118	49	12.a&b	12.a&b	NOUN
iajs-2478	118	50	)	)	PUNCT
iajs-2478	118	51	from	from	ADP
iajs-2478	118	52	(	(	PUNCT
iajs-2478	118	53	48.a&b	48.a&b	NOUN
iajs-2478	118	54	)	)	PUNCT
iajs-2478	118	55	,	,	PUNCT
iajs-2478	118	56	and	and	CCONJ
iajs-2478	118	57	(	(	PUNCT
iajs-2478	118	58	13.a&b	13.a&b	NUM
iajs-2478	118	59	)	)	PUNCT
iajs-2478	118	60	from	from	ADP
iajs-2478	118	61	(	(	PUNCT
iajs-2478	118	62	49.a&b	49.a&b	NOUN
iajs-2478	118	63	)	)	PUNCT
iajs-2478	118	64	and	and	CCONJ
iajs-2478	118	65	setting	set	VERB
iajs-2478	118	66	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	118	67	𝑦	𝑦	PROPN
iajs-2478	118	68	𝑦	𝑦	PROPN
iajs-2478	118	69	,	,	PUNCT
iajs-2478	118	70	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	118	71	𝑦	𝑦	PROPN
iajs-2478	118	72	𝑦	𝑦	PROPN
iajs-2478	118	73	,	,	PUNCT
iajs-2478	118	74	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	118	75	𝑦	𝑦	PROPN
iajs-2478	118	76	𝑦	𝑦	NOUN
iajs-2478	118	77	,	,	PUNCT
iajs-2478	118	78	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	79	𝑢	𝑢	PROPN
iajs-2478	118	80	𝑢	𝑢	PROPN
iajs-2478	118	81	,	,	PUNCT
iajs-2478	118	82	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	83	𝑢	𝑢	PROPN
iajs-2478	118	84	𝑢	𝑢	PROPN
iajs-2478	118	85	and	and	CCONJ
iajs-2478	118	86	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	87	𝑢	𝑢	PROPN
iajs-2478	118	88	𝑢	𝑢	NOUN
iajs-2478	118	89	in	in	ADP
iajs-2478	118	90	the	the	DET
iajs-2478	118	91	obtained	obtain	VERB
iajs-2478	118	92	equations	equation	NOUN
iajs-2478	118	93	,	,	PUNCT
iajs-2478	118	94	they	they	PRON
iajs-2478	118	95	give	give	VERB
iajs-2478	118	96	〈	〈	PROPN
iajs-2478	118	97	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	98	,	,	PUNCT
iajs-2478	118	99	𝑣	𝑣	ADP
iajs-2478	118	100	〉	〉	NOUN
iajs-2478	118	101	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	118	102	,	,	PUNCT
iajs-2478	118	103	∇𝑣	∇𝑣	PROPN
iajs-2478	118	104	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	105	,	,	PUNCT
iajs-2478	118	106	𝑣	𝑣	DET
iajs-2478	118	107	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	108	,	,	PUNCT
iajs-2478	118	109	𝑣	𝑣	DET
iajs-2478	118	110	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	111	,	,	PUNCT
iajs-2478	118	112	𝑣	𝑣	PRON
iajs-2478	118	113	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	114	,	,	PUNCT
iajs-2478	118	115	𝑣	𝑣	X
iajs-2478	118	116	,	,	PUNCT
iajs-2478	118	117	(	(	PUNCT
iajs-2478	118	118	50.a	50.a	NUM
iajs-2478	118	119	)	)	PUNCT
iajs-2478	118	120	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	121	0	0	NUM
iajs-2478	118	122	,	,	PUNCT
iajs-2478	118	123	𝑣	𝑣	PROPN
iajs-2478	118	124	0	0	NUM
iajs-2478	118	125	,	,	PUNCT
iajs-2478	118	126	(	(	PUNCT
iajs-2478	118	127	50.b	50.b	ADV
iajs-2478	118	128	)	)	PUNCT
iajs-2478	118	129	〈	〈	NOUN
iajs-2478	118	130	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	131	,	,	PUNCT
iajs-2478	118	132	𝑣	𝑣	ADP
iajs-2478	118	133	〉	〉	NOUN
iajs-2478	118	134	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	118	135	,	,	PUNCT
iajs-2478	118	136	∇𝑣	∇𝑣	PROPN
iajs-2478	118	137	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	138	,	,	PUNCT
iajs-2478	118	139	𝑣	𝑣	DET
iajs-2478	118	140	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	141	,	,	PUNCT
iajs-2478	118	142	𝑣	𝑣	DET
iajs-2478	118	143	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	144	,	,	PUNCT
iajs-2478	118	145	𝑣	𝑣	DET
iajs-2478	118	146	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	147	,	,	PUNCT
iajs-2478	118	148	𝑣	𝑣	X
iajs-2478	118	149	,	,	PUNCT
iajs-2478	118	150	(	(	PUNCT
iajs-2478	118	151	51.a	51.a	NUM
iajs-2478	118	152	)	)	PUNCT
iajs-2478	118	153	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	154	0	0	NUM
iajs-2478	118	155	,	,	PUNCT
iajs-2478	118	156	𝑣	𝑣	PROPN
iajs-2478	118	157	0	0	NUM
iajs-2478	118	158	,	,	PUNCT
iajs-2478	118	159	(	(	PUNCT
iajs-2478	118	160	51.b	51.b	NUM
iajs-2478	118	161	)	)	PUNCT
iajs-2478	118	162	〈	〈	NOUN
iajs-2478	118	163	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	164	,	,	PUNCT
iajs-2478	118	165	𝑣	𝑣	ADP
iajs-2478	118	166	〉	〉	NOUN
iajs-2478	118	167	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	118	168	,	,	PUNCT
iajs-2478	118	169	∇𝑣	∇𝑣	PROPN
iajs-2478	118	170	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	171	,	,	PUNCT
iajs-2478	118	172	𝑣	𝑣	DET
iajs-2478	118	173	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	174	,	,	PUNCT
iajs-2478	118	175	𝑣	𝑣	DET
iajs-2478	118	176	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	177	,	,	PUNCT
iajs-2478	118	178	𝑣	𝑣	PRON
iajs-2478	118	179	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	118	180	,	,	PUNCT
iajs-2478	118	181	𝑣	𝑣	X
iajs-2478	118	182	,	,	PUNCT
iajs-2478	118	183	(	(	PUNCT
iajs-2478	118	184	52.a	52.a	NUM
iajs-2478	118	185	)	)	PUNCT
iajs-2478	118	186	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	187	0	0	NUM
iajs-2478	118	188	,	,	PUNCT
iajs-2478	118	189	𝑣	𝑣	PROPN
iajs-2478	118	190	0	0	NUM
iajs-2478	118	191	,	,	PUNCT
iajs-2478	118	192	(	(	PUNCT
iajs-2478	118	193	52.b	52.b	X
iajs-2478	118	194	)	)	PUNCT
iajs-2478	118	195	substituting	substitute	VERB
iajs-2478	118	196	𝑣	𝑣	DET
iajs-2478	118	197	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	198	,	,	PUNCT
iajs-2478	118	199	𝑣	𝑣	DET
iajs-2478	118	200	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	118	201	&	&	CCONJ
iajs-2478	118	202	𝑣	𝑣	DET
iajs-2478	118	203	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	118	204	in	in	ADP
iajs-2478	118	205	(	(	PUNCT
iajs-2478	118	206	3.50	3.50	NUM
iajs-2478	118	207	)	)	PUNCT
iajs-2478	118	208	,	,	PUNCT
iajs-2478	118	209	(	(	PUNCT
iajs-2478	118	210	3.51	3.51	NUM
iajs-2478	118	211	)	)	PUNCT
iajs-2478	118	212	&	&	CCONJ
iajs-2478	118	213	(	(	PUNCT
iajs-2478	118	214	3.52	3.52	NUM
iajs-2478	118	215	)	)	PUNCT
iajs-2478	118	216	respectively	respectively	ADV
iajs-2478	118	217	,	,	PUNCT
iajs-2478	118	218	adding	add	VERB
iajs-2478	118	219	the	the	DET
iajs-2478	118	220	obtained	obtain	VERB
iajs-2478	118	221	equations	equation	NOUN
iajs-2478	118	222	,	,	PUNCT
iajs-2478	118	223	using	use	VERB
iajs-2478	118	224	lemma(1.2	lemma(1.2	NOUN
iajs-2478	118	225	)	)	PUNCT
iajs-2478	118	226	in[11	in[11	VERB
iajs-2478	118	227	]	]	PUNCT
iajs-2478	118	228	.	.	PUNCT
iajs-2478	119	1	they	they	PRON
iajs-2478	119	2	give	give	VERB
iajs-2478	119	3	‖𝛿	‖𝛿	PROPN
iajs-2478	119	4	�	�	NOUN
iajs-2478	119	5	⃗	⃗	NOUN
iajs-2478	119	6	�	�	PROPN
iajs-2478	119	7	‖	‖	PROPN
iajs-2478	119	8	‖𝛿	‖𝛿	PROPN
iajs-2478	119	9	�	�	PROPN
iajs-2478	119	10	⃗	⃗	NOUN
iajs-2478	119	11	�	�	PROPN
iajs-2478	119	12	‖	‖	PROPN
iajs-2478	119	13	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	119	14	,	,	PUNCT
iajs-2478	119	15	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	119	16	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	119	17	,	,	PUNCT
iajs-2478	119	18	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	119	19	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	119	20	,	,	PUNCT
iajs-2478	119	21	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	119	22	,	,	PUNCT
iajs-2478	119	23	(	(	PUNCT
iajs-2478	119	24	53	53	NUM
iajs-2478	119	25	)	)	PUNCT
iajs-2478	119	26	since	since	SCONJ
iajs-2478	119	27	the	the	DET
iajs-2478	119	28	2nd	2nd	ADJ
iajs-2478	119	29	term	term	NOUN
iajs-2478	119	30	of	of	ADP
iajs-2478	119	31	(	(	PUNCT
iajs-2478	119	32	53	53	NUM
iajs-2478	119	33	)	)	PUNCT
iajs-2478	119	34	is	be	AUX
iajs-2478	119	35	positive	positive	ADJ
iajs-2478	119	36	,	,	PUNCT
iajs-2478	119	37	integrating	integrate	VERB
iajs-2478	119	38	w.r.t	w.r.t	NOUN
iajs-2478	119	39	.	.	PUNCT
iajs-2478	120	1	𝑡	𝑡	VERB
iajs-2478	120	2	from	from	ADP
iajs-2478	120	3	0	0	NUM
iajs-2478	120	4	to	to	ADP
iajs-2478	120	5	𝑡	𝑡	PROPN
iajs-2478	120	6	,	,	PUNCT
iajs-2478	120	7	and	and	CCONJ
iajs-2478	120	8	then	then	ADV
iajs-2478	120	9	using	use	VERB
iajs-2478	120	10	the	the	DET
iajs-2478	120	11	cauchy	cauchy	ADJ
iajs-2478	120	12	schwartz	schwartz	PROPN
iajs-2478	120	13	inequality	inequality	PROPN
iajs-2478	120	14	(	(	PUNCT
iajs-2478	120	15	csi	csi	PROPN
iajs-2478	120	16	)	)	PUNCT
iajs-2478	120	17	,	,	PUNCT
iajs-2478	120	18	it	it	PRON
iajs-2478	120	19	becomes	become	VERB
iajs-2478	120	20	‖𝛿	‖𝛿	PROPN
iajs-2478	120	21	�	�	NOUN
iajs-2478	120	22	⃗	⃗	NOUN
iajs-2478	120	23	�	�	PROPN
iajs-2478	120	24	‖	‖	PROPN
iajs-2478	120	25	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	120	26	‖𝛿𝑢	‖𝛿𝑢	PROPN
iajs-2478	120	27	‖	‖	PROPN
iajs-2478	120	28	‖𝛿𝑦	‖𝛿𝑦	PROPN
iajs-2478	120	29	‖	‖	ADJ
iajs-2478	120	30	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	120	31	‖𝛿𝑢	‖𝛿𝑢	PROPN
iajs-2478	120	32	‖	‖	PROPN
iajs-2478	120	33	‖𝛿𝑦	‖𝛿𝑦	PROPN
iajs-2478	120	34	‖	‖	ADJ
iajs-2478	120	35	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	120	36	‖𝛿𝑢	‖𝛿𝑢	PROPN
iajs-2478	120	37	‖	‖	PROPN
iajs-2478	120	38	‖𝛿𝑦	‖𝛿𝑦	PROPN
iajs-2478	120	39	‖	‖	ADJ
iajs-2478	120	40	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	120	41	,	,	PUNCT
iajs-2478	120	42	which	which	PRON
iajs-2478	120	43	gives	give	VERB
iajs-2478	120	44	by	by	ADP
iajs-2478	120	45	using	use	VERB
iajs-2478	120	46	the	the	DET
iajs-2478	120	47	trace	trace	NOUN
iajs-2478	120	48	theorem	theorem	ADJ
iajs-2478	120	49	[	[	X
iajs-2478	120	50	17	17	NUM
iajs-2478	120	51	]	]	PUNCT
iajs-2478	120	52	.	.	PUNCT
iajs-2478	121	1	‖𝛿	‖𝛿	PROPN
iajs-2478	121	2	�	�	NOUN
iajs-2478	121	3	⃗	⃗	NOUN
iajs-2478	121	4	�	�	PROPN
iajs-2478	121	5	𝑡	𝑡	PROPN
iajs-2478	121	6	‖	‖	PROPN
iajs-2478	121	7	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	121	8	𝑐	𝑐	PROPN
iajs-2478	121	9	‖𝛿	‖𝛿	PROPN
iajs-2478	121	10	�	�	PROPN
iajs-2478	121	11	⃗	⃗	PROPN
iajs-2478	121	12	�	�	PROPN
iajs-2478	121	13	‖	‖	NOUN
iajs-2478	121	14	𝑑𝑡	𝑑𝑡	PROPN
iajs-2478	121	15	,	,	PUNCT
iajs-2478	121	16	∀	∀	X
iajs-2478	121	17	𝑡	𝑡	ADP
iajs-2478	121	18	∈	∈	PROPN
iajs-2478	121	19	0	0	NUM
iajs-2478	121	20	,	,	PUNCT
iajs-2478	121	21	𝑇	𝑇	PROPN
iajs-2478	121	22	using	use	VERB
iajs-2478	121	23	the	the	DET
iajs-2478	121	24	bgi	bgi	NOUN
iajs-2478	121	25	,	,	PUNCT
iajs-2478	121	26	one	one	PRON
iajs-2478	121	27	gets	get	VERB
iajs-2478	121	28	‖𝛿	‖𝛿	PROPN
iajs-2478	121	29	�	�	NOUN
iajs-2478	121	30	⃗	⃗	NOUN
iajs-2478	121	31	�	�	PROPN
iajs-2478	121	32	𝑡	𝑡	PROPN
iajs-2478	121	33	‖	‖	PROPN
iajs-2478	121	34	𝑒	𝑒	PROPN
iajs-2478	121	35	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	121	36	𝐿	𝐿	PROPN
iajs-2478	121	37	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	121	38	,	,	PUNCT
iajs-2478	121	39	𝑒	𝑒	PROPN
iajs-2478	121	40	𝐿	𝐿	PROPN
iajs-2478	121	41	,	,	PUNCT
iajs-2478	121	42	𝐿	𝐿	PROPN
iajs-2478	121	43	0	0	NUM
iajs-2478	121	44	  	  	SPACE
iajs-2478	121	45	121	121	NUM
iajs-2478	121	46	ibn	ibn	PROPN
iajs-2478	121	47	al	al	PROPN
iajs-2478	121	48	-	-	PUNCT
iajs-2478	121	49	haitham	haitham	PROPN
iajs-2478	121	50	jour	jour	X
iajs-2478	121	51	.	.	PROPN
iajs-2478	122	1	for	for	ADP
iajs-2478	122	2	pure	pure	ADJ
iajs-2478	122	3	&	&	CCONJ
iajs-2478	122	4	appl	appl	PROPN
iajs-2478	122	5	.	.	PUNCT
iajs-2478	123	1	sci	sci	PROPN
iajs-2478	123	2	.	.	PROPN
iajs-2478	124	1	33	33	NUM
iajs-2478	124	2	(	(	PUNCT
iajs-2478	124	3	3	3	NUM
iajs-2478	124	4	)	)	PUNCT
iajs-2478	124	5	2020	2020	NUM
iajs-2478	124	6	or	or	CCONJ
iajs-2478	124	7	‖𝛿	‖𝛿	PROPN
iajs-2478	124	8	�	�	NOUN
iajs-2478	124	9	⃗	⃗	NOUN
iajs-2478	124	10	�	�	PROPN
iajs-2478	124	11	‖𝑳	‖𝑳	PROPN
iajs-2478	124	12	ĩ,𝑳𝟐	ĩ,𝑳𝟐	PROPN
iajs-2478	124	13	ω	ω	NUM
iajs-2478	124	14	𝐿‖𝛿𝑢‖𝚺	𝐿‖𝛿𝑢‖𝚺	NOUN
iajs-2478	124	15	since	since	SCONJ
iajs-2478	124	16	‖𝛿	‖𝛿	PROPN
iajs-2478	124	17	�	�	NOUN
iajs-2478	124	18	⃗	⃗	NOUN
iajs-2478	124	19	�	�	NOUN
iajs-2478	124	20	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	124	21	𝑸	𝑸	PROPN
iajs-2478	124	22	𝑇𝐿	𝑇𝐿	PROPN
iajs-2478	124	23	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	124	24	,	,	PUNCT
iajs-2478	124	25	thus	thus	ADV
iajs-2478	124	26	‖𝛿	‖𝛿	PROPN
iajs-2478	124	27	�	�	NOUN
iajs-2478	124	28	⃗	⃗	NOUN
iajs-2478	124	29	�	�	NOUN
iajs-2478	124	30	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	124	31	𝑸	𝑸	NOUN
iajs-2478	124	32	𝐿‖𝛿𝑢‖𝚺	𝐿‖𝛿𝑢‖𝚺	NOUN
iajs-2478	124	33	,	,	PUNCT
iajs-2478	124	34	𝑇𝐿	𝑇𝐿	PROPN
iajs-2478	124	35	𝐿	𝐿	PROPN
iajs-2478	124	36	using	use	VERB
iajs-2478	124	37	a	a	DET
iajs-2478	124	38	similar	similar	ADJ
iajs-2478	124	39	way	way	NOUN
iajs-2478	124	40	which	which	PRON
iajs-2478	124	41	is	be	AUX
iajs-2478	124	42	used	use	VERB
iajs-2478	124	43	in	in	ADP
iajs-2478	124	44	the	the	DET
iajs-2478	124	45	above	above	ADJ
iajs-2478	124	46	steps	step	NOUN
iajs-2478	124	47	,	,	PUNCT
iajs-2478	124	48	gives	give	VERB
iajs-2478	124	49	‖𝛿	‖𝛿	PROPN
iajs-2478	124	50	�	�	NOUN
iajs-2478	124	51	⃗	⃗	NOUN
iajs-2478	124	52	�	�	PROPN
iajs-2478	124	53	‖	‖	PROPN
iajs-2478	124	54	2	2	NUM
iajs-2478	124	55	‖𝛿	‖𝛿	PROPN
iajs-2478	124	56	�	�	NOUN
iajs-2478	124	57	⃗	⃗	NOUN
iajs-2478	124	58	�	�	PROPN
iajs-2478	124	59	‖	‖	PROPN
iajs-2478	124	60	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	124	61	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	124	62	𝑐	𝑐	PROPN
iajs-2478	124	63	‖𝛿	‖𝛿	PROPN
iajs-2478	124	64	�	�	PROPN
iajs-2478	124	65	⃗	⃗	NOUN
iajs-2478	124	66	�	�	PROPN
iajs-2478	124	67	‖	‖	VERB
iajs-2478	124	68	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	124	69	⇒	⇒	PROPN
iajs-2478	124	70	‖𝛿	‖𝛿	PROPN
iajs-2478	124	71	�	�	PROPN
iajs-2478	124	72	⃗	⃗	NOUN
iajs-2478	124	73	�	�	NOUN
iajs-2478	124	74	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	124	75	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	124	76	𝐿	𝐿	PROPN
iajs-2478	124	77	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	124	78	where	where	SCONJ
iajs-2478	124	79	𝐿	𝐿	PROPN
iajs-2478	124	80	1	1	NUM
iajs-2478	124	81	𝐿	𝐿	PROPN
iajs-2478	124	82	𝑐	𝑐	PROPN
iajs-2478	124	83	/2	/2	PUNCT
iajs-2478	124	84	or	or	CCONJ
iajs-2478	124	85	‖𝛿	‖𝛿	PROPN
iajs-2478	124	86	�	�	NOUN
iajs-2478	124	87	⃗	⃗	NOUN
iajs-2478	124	88	�	�	PROPN
iajs-2478	124	89	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	124	90	ĩ,𝑽	ĩ,𝑽	VERB
iajs-2478	124	91	𝐿	𝐿	PROPN
iajs-2478	124	92	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	124	93	.	.	PUNCT
iajs-2478	125	1	theorem	theorem	VERB
iajs-2478	125	2	4.2	4.2	NUM
iajs-2478	125	3	:	:	PUNCT
iajs-2478	125	4	with	with	ADP
iajs-2478	125	5	assumption	assumption	NOUN
iajs-2478	125	6	(	(	PUNCT
iajs-2478	125	7	a	a	X
iajs-2478	125	8	)	)	PUNCT
iajs-2478	125	9	,	,	PUNCT
iajs-2478	125	10	the	the	DET
iajs-2478	125	11	operator	operator	NOUN
iajs-2478	125	12	𝑢	𝑢	PART
iajs-2478	125	13	↦	↦	PROPN
iajs-2478	125	14	�	�	SYM
iajs-2478	125	15	⃗	⃗	NOUN
iajs-2478	125	16	�	�	PROPN
iajs-2478	125	17	⃗	⃗	PROPN
iajs-2478	125	18	is	be	AUX
iajs-2478	125	19	continuous	continuous	ADJ
iajs-2478	125	20	from	from	ADP
iajs-2478	125	21	𝐿	𝐿	PROPN
iajs-2478	125	22	σ	σ	NOUN
iajs-2478	125	23	in	in	ADP
iajs-2478	125	24	to	to	ADP
iajs-2478	125	25	𝐿	𝐿	PROPN
iajs-2478	125	26	ĩ,𝑳𝟐	ĩ,𝑳𝟐	PROPN
iajs-2478	125	27	ω	ω	PROPN
iajs-2478	125	28	or	or	CCONJ
iajs-2478	125	29	in	in	ADP
iajs-2478	125	30	to	to	ADP
iajs-2478	125	31	𝐿	𝐿	PROPN
iajs-2478	125	32	ĩ	ĩ	PROPN
iajs-2478	125	33	,	,	PUNCT
iajs-2478	125	34	𝑉	𝑉	X
iajs-2478	125	35	𝟑	𝟑	X
iajs-2478	125	36	or	or	CCONJ
iajs-2478	125	37	in	in	ADP
iajs-2478	125	38	to	to	ADP
iajs-2478	125	39	𝐿	𝐿	PROPN
iajs-2478	125	40	𝑄	𝑄	PROPN
iajs-2478	125	41	𝟑	𝟑	NUM
iajs-2478	125	42	.	.	PUNCT
iajs-2478	126	1	proof	proof	NOUN
iajs-2478	126	2	:	:	PUNCT
iajs-2478	126	3	let	let	VERB
iajs-2478	126	4	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	126	5	𝑢	𝑢	PROPN
iajs-2478	126	6	𝑢	𝑢	PROPN
iajs-2478	126	7	and	and	CCONJ
iajs-2478	126	8	�	�	PROPN
iajs-2478	126	9	⃗	⃗	PROPN
iajs-2478	126	10	�	�	PROPN
iajs-2478	126	11	�	�	PROPN
iajs-2478	126	12	⃗	⃗	PROPN
iajs-2478	126	13	�	�	PROPN
iajs-2478	126	14	�	�	PROPN
iajs-2478	126	15	⃗	⃗	PROPN
iajs-2478	126	16	�	�	PROPN
iajs-2478	126	17	,	,	PUNCT
iajs-2478	126	18	where	where	SCONJ
iajs-2478	126	19	�	�	NOUN
iajs-2478	126	20	⃗	⃗	PART
iajs-2478	126	21	�	�	PROPN
iajs-2478	126	22	and	and	CCONJ
iajs-2478	126	23	�	�	PROPN
iajs-2478	126	24	⃗	⃗	NOUN
iajs-2478	126	25	�	�	NOUN
iajs-2478	126	26	are	be	AUX
iajs-2478	126	27	the	the	DET
iajs-2478	126	28	corresponding	correspond	VERB
iajs-2478	126	29	svs	svs	NOUN
iajs-2478	126	30	to	to	ADP
iajs-2478	126	31	the	the	DET
iajs-2478	126	32	cvs	cvs	NOUN
iajs-2478	126	33	𝑢	𝑢	NOUN
iajs-2478	126	34	and	and	CCONJ
iajs-2478	126	35	𝑢	𝑢	PRON
iajs-2478	126	36	respectively	respectively	ADV
iajs-2478	126	37	,	,	PUNCT
iajs-2478	126	38	using	use	VERB
iajs-2478	126	39	the	the	DET
iajs-2478	126	40	first	first	ADJ
iajs-2478	126	41	result	result	NOUN
iajs-2478	126	42	in	in	ADP
iajs-2478	126	43	theorem4.1	theorem4.1	NUM
iajs-2478	126	44	,	,	PUNCT
iajs-2478	126	45	we	we	PRON
iajs-2478	126	46	get	get	VERB
iajs-2478	126	47	�	�	NOUN
iajs-2478	126	48	⃗	⃗	NOUN
iajs-2478	126	49	�	�	PROPN
iajs-2478	126	50	ĩ	ĩ	PROPN
iajs-2478	126	51	,	,	PUNCT
iajs-2478	126	52	ω	ω	NUM
iajs-2478	126	53	⎯⎯⎯⎯⎯⎯⎯	⎯⎯⎯⎯⎯⎯⎯	PUNCT
iajs-2478	126	54	�	�	NOUN
iajs-2478	126	55	⃗	⃗	NOUN
iajs-2478	126	56	�	�	PROPN
iajs-2478	126	57	if	if	SCONJ
iajs-2478	126	58	𝑢	𝑢	PROPN
iajs-2478	126	59	⎯⎯	⎯⎯	X
iajs-2478	126	60	𝑢	𝑢	X
iajs-2478	126	61	,	,	PUNCT
iajs-2478	126	62	i.e.	i.e.	X
iajs-2478	126	63	the	the	DET
iajs-2478	126	64	operator	operator	NOUN
iajs-2478	126	65	𝑢	𝑢	PART
iajs-2478	126	66	↦	↦	PROPN
iajs-2478	126	67	�	�	SYM
iajs-2478	126	68	⃗	⃗	NOUN
iajs-2478	126	69	�	�	PROPN
iajs-2478	126	70	⃗	⃗	PROPN
iajs-2478	126	71	is	be	AUX
iajs-2478	126	72	lipschitz	lipschitz	ADJ
iajs-2478	126	73	continuous	continuous	ADJ
iajs-2478	126	74	(	(	PUNCT
iajs-2478	126	75	lc	lc	NOUN
iajs-2478	126	76	)	)	PUNCT
iajs-2478	126	77	from	from	ADP
iajs-2478	126	78	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	126	79	𝚺	𝚺	PROPN
iajs-2478	126	80	in	in	ADP
iajs-2478	126	81	to	to	ADP
iajs-2478	126	82	𝐋	𝐋	PROPN
iajs-2478	126	83	ĩ	ĩ	PROPN
iajs-2478	126	84	,	,	PUNCT
iajs-2478	126	85	𝐋𝟐	𝐋𝟐	PROPN
iajs-2478	126	86	ω	ω	PROPN
iajs-2478	126	87	.	.	PUNCT
iajs-2478	127	1	easily	easily	ADV
iajs-2478	127	2	,	,	PUNCT
iajs-2478	127	3	one	one	PRON
iajs-2478	127	4	can	can	AUX
iajs-2478	127	5	get	get	VERB
iajs-2478	127	6	this	this	DET
iajs-2478	127	7	operator	operator	NOUN
iajs-2478	127	8	is	be	AUX
iajs-2478	127	9	also	also	ADV
iajs-2478	127	10	lc	lc	NOUN
iajs-2478	127	11	from	from	ADP
iajs-2478	127	12	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	127	13	𝚺	𝚺	PROPN
iajs-2478	127	14	into	into	ADP
iajs-2478	127	15	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	127	16	𝑸	𝑸	PROPN
iajs-2478	127	17	and	and	CCONJ
iajs-2478	127	18	into	into	ADP
iajs-2478	127	19	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	127	20	ĩ	ĩ	PROPN
iajs-2478	127	21	,	,	PUNCT
iajs-2478	127	22	𝑽	𝑽	PROPN
iajs-2478	127	23	.	.	PUNCT
iajs-2478	128	1	lemma	lemma	PROPN
iajs-2478	128	2	4.1	4.1	NUM
iajs-2478	128	3	:	:	PUNCT
iajs-2478	129	1	[	[	X
iajs-2478	129	2	10	10	NUM
iajs-2478	129	3	]	]	PUNCT
iajs-2478	129	4	.	.	PUNCT
iajs-2478	130	1	the	the	DET
iajs-2478	130	2	norm	norm	NOUN
iajs-2478	130	3	∥.	∥.	ADP
iajs-2478	130	4	∥𝟎	∥𝟎	NOUN
iajs-2478	130	5	is	be	AUX
iajs-2478	130	6	weakly	weakly	ADV
iajs-2478	130	7	lower	low	ADJ
iajs-2478	130	8	semi	semi	ADV
iajs-2478	130	9	continuous	continuous	ADJ
iajs-2478	130	10	(	(	PUNCT
iajs-2478	130	11	w.l.s.c	w.l.s.c	PROPN
iajs-2478	130	12	.	.	PUNCT
iajs-2478	130	13	)	)	PUNCT
iajs-2478	130	14	.	.	PUNCT
iajs-2478	131	1	lemma	lemma	PROPN
iajs-2478	131	2	4.2	4.2	NUM
iajs-2478	131	3	:	:	PUNCT
iajs-2478	131	4	the	the	DET
iajs-2478	131	5	cof	cof	PROPN
iajs-2478	131	6	which	which	PRON
iajs-2478	131	7	is	be	AUX
iajs-2478	131	8	given	give	VERB
iajs-2478	131	9	by	by	ADP
iajs-2478	131	10	(	(	PUNCT
iajs-2478	131	11	10	10	NUM
iajs-2478	131	12	)	)	PUNCT
iajs-2478	131	13	is	be	AUX
iajs-2478	131	14	w.l.s.c	w.l.s.c	PROPN
iajs-2478	131	15	.	.	PUNCT
iajs-2478	132	1	proof	proof	NOUN
iajs-2478	132	2	:	:	PUNCT
iajs-2478	132	3	from	from	ADP
iajs-2478	132	4	lemma(4.1	lemma(4.1	ADV
iajs-2478	132	5	)	)	PUNCT
iajs-2478	132	6	,	,	PUNCT
iajs-2478	132	7	we	we	PRON
iajs-2478	132	8	got	get	VERB
iajs-2478	132	9	that	that	SCONJ
iajs-2478	132	10	the	the	DET
iajs-2478	132	11	norm	norm	NOUN
iajs-2478	132	12	‖𝑢	‖𝑢	DET
iajs-2478	132	13	‖𝚺	‖𝚺	NOUN
iajs-2478	132	14	is	be	AUX
iajs-2478	132	15	w.l.s.c	w.l.s.c	PROPN
iajs-2478	132	16	.	.	PROPN
iajs-2478	132	17	,	,	PUNCT
iajs-2478	132	18	𝑢	𝑢	X
iajs-2478	132	19	→	→	SYM
iajs-2478	132	20	𝑢	𝑢	NOUN
iajs-2478	132	21	weakly	weakly	ADJ
iajs-2478	132	22	in	in	ADP
iajs-2478	132	23	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	132	24	𝚺	𝚺	PROPN
iajs-2478	132	25	,	,	PUNCT
iajs-2478	132	26	then	then	ADV
iajs-2478	132	27	by	by	ADP
iajs-2478	132	28	(	(	PUNCT
iajs-2478	132	29	theorem	theorem	VERB
iajs-2478	132	30	4.2	4.2	NUM
iajs-2478	132	31	)	)	PUNCT
iajs-2478	132	32	�	�	PROPN
iajs-2478	133	1	⃗	⃗	PROPN
iajs-2478	133	2	�	�	PROPN
iajs-2478	133	3	→	→	SYM
iajs-2478	133	4	�	�	PROPN
iajs-2478	133	5	⃗	⃗	PROPN
iajs-2478	133	6	�	�	PROPN
iajs-2478	133	7	�	�	PROPN
iajs-2478	133	8	⃗	⃗	NOUN
iajs-2478	133	9	�	�	PROPN
iajs-2478	133	10	⃗	⃗	PROPN
iajs-2478	133	11	is	be	AUX
iajs-2478	133	12	weakly	weakly	ADJ
iajs-2478	133	13	in	in	ADP
iajs-2478	133	14	𝑳𝟐	𝑳𝟐	PROPN
iajs-2478	133	15	𝚺	𝚺	PROPN
iajs-2478	133	16	,	,	PUNCT
iajs-2478	133	17	which	which	PRON
iajs-2478	133	18	gives	give	VERB
iajs-2478	133	19	that	that	SCONJ
iajs-2478	133	20	the	the	DET
iajs-2478	133	21	norm	norm	NOUN
iajs-2478	133	22	‖	‖	PROPN
iajs-2478	133	23	�	�	PROPN
iajs-2478	133	24	⃗	⃗	PROPN
iajs-2478	133	25	�	�	PROPN
iajs-2478	133	26	�	�	PROPN
iajs-2478	133	27	⃗	⃗	NOUN
iajs-2478	133	28	�	�	PROPN
iajs-2478	133	29	‖𝚺	‖𝚺	NOUN
iajs-2478	133	30	is	be	AUX
iajs-2478	133	31	w.l.s.c	w.l.s.c	PROPN
iajs-2478	133	32	.	.	PUNCT
iajs-2478	134	1	(	(	PUNCT
iajs-2478	134	2	by	by	ADP
iajs-2478	134	3	lemma	lemma	PROPN
iajs-2478	134	4	4.1	4.1	NUM
iajs-2478	134	5	)	)	PUNCT
iajs-2478	134	6	,	,	PUNCT
iajs-2478	134	7	hence	hence	ADV
iajs-2478	134	8	𝐺	𝐺	PROPN
iajs-2478	134	9	𝑢	𝑢	PROPN
iajs-2478	134	10	is	be	AUX
iajs-2478	134	11	w.l.s.c	w.l.s.c	PROPN
iajs-2478	134	12	.	.	PUNCT
iajs-2478	134	13	.	.	PUNCT
iajs-2478	135	1	theorem	theorem	VERB
iajs-2478	135	2	4.3	4.3	NUM
iajs-2478	135	3	:	:	PUNCT
iajs-2478	135	4	consider	consider	VERB
iajs-2478	135	5	the	the	DET
iajs-2478	135	6	cost	cost	NOUN
iajs-2478	135	7	function	function	NOUN
iajs-2478	135	8	(	(	PUNCT
iajs-2478	135	9	10	10	NUM
iajs-2478	135	10	)	)	PUNCT
iajs-2478	135	11	,	,	PUNCT
iajs-2478	135	12	if	if	SCONJ
iajs-2478	135	13	𝐺	𝐺	PROPN
iajs-2478	135	14	𝑢	𝑢	PROPN
iajs-2478	135	15	is	be	AUX
iajs-2478	135	16	coercive	coercive	ADJ
iajs-2478	135	17	,	,	PUNCT
iajs-2478	135	18	then	then	ADV
iajs-2478	135	19	there	there	PRON
iajs-2478	135	20	exists	exist	VERB
iajs-2478	135	21	a	a	DET
iajs-2478	135	22	ccbocv	ccbocv	NOUN
iajs-2478	135	23	.	.	PUNCT
iajs-2478	136	1	proof	proof	NOUN
iajs-2478	136	2	:	:	PUNCT
iajs-2478	136	3	since	since	SCONJ
iajs-2478	136	4	𝐺	𝐺	PROPN
iajs-2478	136	5	𝑢	𝑢	X
iajs-2478	136	6	0	0	NUM
iajs-2478	136	7	and	and	CCONJ
iajs-2478	136	8	𝐺	𝐺	PROPN
iajs-2478	136	9	𝑢	𝑢	PROPN
iajs-2478	136	10	is	be	AUX
iajs-2478	136	11	coercive	coercive	ADJ
iajs-2478	136	12	,	,	PUNCT
iajs-2478	136	13	then	then	ADV
iajs-2478	136	14	there	there	PRON
iajs-2478	136	15	exists	exist	VERB
iajs-2478	136	16	a	a	DET
iajs-2478	136	17	minimizing	minimize	VERB
iajs-2478	136	18	sequence	sequence	NOUN
iajs-2478	136	19	𝑢	𝑢	ADP
iajs-2478	136	20	𝑢	𝑢	PROPN
iajs-2478	136	21	,	,	PUNCT
iajs-2478	136	22	𝑢	𝑢	PRON
iajs-2478	136	23	,	,	PUNCT
iajs-2478	136	24	𝑢	𝑢	PROPN
iajs-2478	136	25	∈	∈	PROPN
iajs-2478	136	26	𝑊	𝑊	PROPN
iajs-2478	136	27	,	,	PUNCT
iajs-2478	136	28	∀𝑘	∀𝑘	NOUN
iajs-2478	136	29	such	such	ADJ
iajs-2478	136	30	that	that	SCONJ
iajs-2478	136	31	lim	lim	PROPN
iajs-2478	136	32	→	→	PROPN
iajs-2478	136	33	𝐺	𝐺	PROPN
iajs-2478	136	34	𝑢	𝑢	PROPN
iajs-2478	136	35	inf	inf	PROPN
iajs-2478	136	36	⃗∈	⃗∈	NUM
iajs-2478	136	37	⃗	⃗	PROPN
iajs-2478	136	38	𝐺	𝐺	PROPN
iajs-2478	136	39	𝑢	𝑢	NOUN
iajs-2478	136	40	,	,	PUNCT
iajs-2478	136	41	then	then	ADV
iajs-2478	136	42	‖𝑢	‖𝑢	DET
iajs-2478	136	43	‖𝚺	‖𝚺	NOUN
iajs-2478	136	44	ĉ	ĉ	X
iajs-2478	136	45	,	,	PUNCT
iajs-2478	136	46	ĉ	ĉ	PROPN
iajs-2478	136	47	0	0	NUM
iajs-2478	136	48	,	,	PUNCT
iajs-2478	136	49	then	then	ADV
iajs-2478	136	50	by	by	ADP
iajs-2478	136	51	ath	ath	NOUN
iajs-2478	136	52	there	there	PRON
iajs-2478	136	53	exists	exist	VERB
iajs-2478	136	54	a	a	DET
iajs-2478	136	55	subsequence	subsequence	NOUN
iajs-2478	136	56	of	of	ADP
iajs-2478	136	57	𝑢	𝑢	NOUN
iajs-2478	136	58	,	,	PUNCT
iajs-2478	136	59	for	for	ADP
iajs-2478	136	60	simplicity	simplicity	NOUN
iajs-2478	136	61	say	say	VERB
iajs-2478	136	62	again	again	ADV
iajs-2478	136	63	𝑢	𝑢	X
iajs-2478	136	64	s.t	s.t	PROPN
iajs-2478	136	65	.	.	PROPN
iajs-2478	136	66	𝑢	𝑢	PROPN
iajs-2478	136	67	⟶	⟶	NOUN
iajs-2478	136	68	𝑢	𝑢	NOUN
iajs-2478	136	69	weakly	weakly	ADJ
iajs-2478	136	70	in	in	ADP
iajs-2478	136	71	𝐿	𝐿	PROPN
iajs-2478	136	72	σ	σ	PROPN
iajs-2478	136	73	,	,	PUNCT
iajs-2478	136	74	𝑎s	𝑎s	ADP
iajs-2478	136	75	𝑘	𝑘	PROPN
iajs-2478	136	76	→	→	SYM
iajs-2478	136	77	∞	∞	PROPN
iajs-2478	136	78	,	,	PUNCT
iajs-2478	136	79	from	from	ADP
iajs-2478	136	80	theorem	theorem	ADJ
iajs-2478	136	81	3.1	3.1	NUM
iajs-2478	136	82	,	,	PUNCT
iajs-2478	136	83	corresponding	correspond	VERB
iajs-2478	136	84	to	to	ADP
iajs-2478	136	85	the	the	DET
iajs-2478	136	86	sequence	sequence	NOUN
iajs-2478	136	87	of	of	ADP
iajs-2478	136	88	controls	control	NOUN
iajs-2478	136	89	𝑢	𝑢	NOUN
iajs-2478	136	90	,	,	PUNCT
iajs-2478	136	91	there	there	PRON
iajs-2478	136	92	exists	exist	VERB
iajs-2478	136	93	a	a	DET
iajs-2478	136	94	sequence	sequence	NOUN
iajs-2478	136	95	of	of	ADP
iajs-2478	136	96	solutions	solution	NOUN
iajs-2478	136	97	�	�	NOUN
iajs-2478	136	98	⃗	⃗	NOUN
iajs-2478	136	99	�	�	PROPN
iajs-2478	136	100	,	,	PUNCT
iajs-2478	136	101	but	but	CCONJ
iajs-2478	136	102	the	the	DET
iajs-2478	136	103	norms	norm	NOUN
iajs-2478	136	104	‖	‖	PROPN
iajs-2478	136	105	�	�	NOUN
iajs-2478	136	106	⃗	⃗	NOUN
iajs-2478	136	107	�	�	PROPN
iajs-2478	136	108	‖	‖	PROPN
iajs-2478	136	109	𝑳	𝑳	PROPN
iajs-2478	136	110	ĩ,𝑳𝟐	ĩ,𝑳𝟐	NOUN
iajs-2478	136	111	ω	ω	PROPN
iajs-2478	136	112	,	,	PUNCT
iajs-2478	136	113	‖	‖	PROPN
iajs-2478	136	114	�	�	NOUN
iajs-2478	136	115	⃗	⃗	NOUN
iajs-2478	136	116	�	�	PROPN
iajs-2478	136	117	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	136	118	𝑸	𝑸	PROPN
iajs-2478	136	119	&	&	CCONJ
iajs-2478	136	120	‖	‖	PROPN
iajs-2478	136	121	�	�	PROPN
iajs-2478	136	122	⃗	⃗	NOUN
iajs-2478	136	123	�	�	PROPN
iajs-2478	136	124	‖𝑳𝟐	‖𝑳𝟐	PROPN
iajs-2478	136	125	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	136	126	are	be	AUX
iajs-2478	136	127	bounded	bound	VERB
iajs-2478	136	128	,	,	PUNCT
iajs-2478	136	129	then	then	ADV
iajs-2478	136	130	by	by	ADP
iajs-2478	136	131	ath	ath	NOUN
iajs-2478	136	132	there	there	PRON
iajs-2478	136	133	exists	exist	VERB
iajs-2478	136	134	a	a	DET
iajs-2478	136	135	subsequence	subsequence	NOUN
iajs-2478	136	136	of	of	ADP
iajs-2478	136	137	�	�	PROPN
iajs-2478	136	138	⃗	⃗	NOUN
iajs-2478	136	139	�	�	PROPN
iajs-2478	136	140	,	,	PUNCT
iajs-2478	136	141	for	for	ADP
iajs-2478	136	142	simplicity	simplicity	NOUN
iajs-2478	136	143	,	,	PUNCT
iajs-2478	136	144	say	say	VERB
iajs-2478	136	145	again	again	ADV
iajs-2478	136	146	�	�	PROPN
iajs-2478	136	147	⃗	⃗	PROPN
iajs-2478	136	148	�	�	PROPN
iajs-2478	136	149	,	,	PUNCT
iajs-2478	136	150	such	such	ADJ
iajs-2478	136	151	that	that	SCONJ
iajs-2478	136	152	�	�	NOUN
iajs-2478	136	153	⃗	⃗	NOUN
iajs-2478	136	154	�	�	PROPN
iajs-2478	136	155	⟶	⟶	NOUN
iajs-2478	136	156	�	�	NOUN
iajs-2478	136	157	⃗	⃗	NOUN
iajs-2478	136	158	�	�	PROPN
iajs-2478	136	159	weakly	weakly	NOUN
iajs-2478	136	160	in	in	ADP
iajs-2478	136	161	𝐿	𝐿	PROPN
iajs-2478	136	162	ĩ	ĩ	PROPN
iajs-2478	136	163	,	,	PUNCT
iajs-2478	136	164	𝐿	𝐿	PROPN
iajs-2478	136	165	ω	ω	PROPN
iajs-2478	136	166	,	,	PUNCT
iajs-2478	136	167	in	in	ADP
iajs-2478	136	168	𝐿	𝐿	PROPN
iajs-2478	136	169	𝑄	𝑄	PROPN
iajs-2478	136	170	,	,	PUNCT
iajs-2478	136	171	and	and	CCONJ
iajs-2478	136	172	in	in	ADP
iajs-2478	136	173	𝐿	𝐿	PROPN
iajs-2478	136	174	ĩ	ĩ	PROPN
iajs-2478	136	175	,	,	PUNCT
iajs-2478	136	176	𝑉	𝑉	PROPN
iajs-2478	136	177	,	,	PUNCT
iajs-2478	136	178	suppose	suppose	VERB
iajs-2478	136	179	that	that	SCONJ
iajs-2478	136	180	(	(	PUNCT
iajs-2478	136	181	17.a	17.a	NUM
iajs-2478	136	182	)	)	PUNCT
iajs-2478	136	183	,	,	PUNCT
iajs-2478	136	184	(	(	PUNCT
iajs-2478	136	185	18.a	18.a	NUM
iajs-2478	136	186	)	)	PUNCT
iajs-2478	136	187	&	&	CCONJ
iajs-2478	136	188	(	(	PUNCT
iajs-2478	136	189	19.a	19.a	NUM
iajs-2478	136	190	)	)	PUNCT
iajs-2478	136	191	can	can	AUX
iajs-2478	136	192	be	be	AUX
iajs-2478	136	193	rewritten	rewrite	VERB
iajs-2478	136	194	as	as	ADP
iajs-2478	136	195	〈	〈	NOUN
iajs-2478	136	196	𝑦	𝑦	NOUN
iajs-2478	136	197	,	,	PUNCT
iajs-2478	136	198	𝑣	𝑣	ADP
iajs-2478	136	199	〉	〉	NOUN
iajs-2478	136	200	∇𝑦	∇𝑦	PROPN
iajs-2478	136	201	,	,	PUNCT
iajs-2478	136	202	∇𝑣	∇𝑣	PROPN
iajs-2478	136	203	𝑦	𝑦	PRON
iajs-2478	136	204	,	,	PUNCT
iajs-2478	136	205	𝑣	𝑣	DET
iajs-2478	136	206	𝑦	𝑦	NOUN
iajs-2478	136	207	,	,	PUNCT
iajs-2478	136	208	𝑣	𝑣	PRON
iajs-2478	136	209	𝑦	𝑦	NOUN
iajs-2478	136	210	,	,	PUNCT
iajs-2478	136	211	𝑣	𝑣	PRON
iajs-2478	136	212	𝑓	𝑓	X
iajs-2478	136	213	,	,	PUNCT
iajs-2478	136	214	𝑣	𝑣	PRON
iajs-2478	136	215	𝑢	𝑢	X
iajs-2478	136	216	,	,	PUNCT
iajs-2478	136	217	𝑣	𝑣	X
iajs-2478	136	218	,	,	PUNCT
iajs-2478	136	219	〈	〈	PROPN
iajs-2478	136	220	𝑦	𝑦	NOUN
iajs-2478	136	221	,	,	PUNCT
iajs-2478	136	222	𝑣	𝑣	ADP
iajs-2478	136	223	〉	〉	NOUN
iajs-2478	136	224	∇𝑦	∇𝑦	PROPN
iajs-2478	136	225	,	,	PUNCT
iajs-2478	136	226	∇𝑣	∇𝑣	PROPN
iajs-2478	136	227	𝑦	𝑦	PRON
iajs-2478	136	228	,	,	PUNCT
iajs-2478	136	229	𝑣	𝑣	DET
iajs-2478	136	230	𝑦	𝑦	NOUN
iajs-2478	136	231	,	,	PUNCT
iajs-2478	136	232	𝑣	𝑣	PRON
iajs-2478	136	233	𝑦	𝑦	NOUN
iajs-2478	136	234	,	,	PUNCT
iajs-2478	136	235	𝑣	𝑣	PRON
iajs-2478	136	236	𝑓	𝑓	X
iajs-2478	136	237	,	,	PUNCT
iajs-2478	136	238	𝑣	𝑣	PRON
iajs-2478	136	239	𝑢	𝑢	X
iajs-2478	136	240	,	,	PUNCT
iajs-2478	136	241	𝑣	𝑣	X
iajs-2478	136	242	,	,	PUNCT
iajs-2478	136	243	〈	〈	PROPN
iajs-2478	136	244	𝑦	𝑦	NOUN
iajs-2478	136	245	,	,	PUNCT
iajs-2478	136	246	𝑣	𝑣	ADP
iajs-2478	136	247	〉	〉	NOUN
iajs-2478	136	248	∇𝑦	∇𝑦	PROPN
iajs-2478	136	249	,	,	PUNCT
iajs-2478	136	250	∇𝑣	∇𝑣	PROPN
iajs-2478	136	251	𝑦	𝑦	PRON
iajs-2478	136	252	,	,	PUNCT
iajs-2478	136	253	𝑣	𝑣	DET
iajs-2478	136	254	𝑦	𝑦	NOUN
iajs-2478	136	255	,	,	PUNCT
iajs-2478	136	256	𝑣	𝑣	PRON
iajs-2478	136	257	𝑦	𝑦	NOUN
iajs-2478	136	258	,	,	PUNCT
iajs-2478	136	259	𝑣	𝑣	PRON
iajs-2478	136	260	𝑓	𝑓	X
iajs-2478	136	261	,	,	PUNCT
iajs-2478	136	262	𝑣	𝑣	PRON
iajs-2478	136	263	𝑢	𝑢	X
iajs-2478	136	264	,	,	PUNCT
iajs-2478	136	265	𝑣	𝑣	ADP
iajs-2478	136	266	,	,	PUNCT
iajs-2478	136	267	adding	add	VERB
iajs-2478	136	268	the	the	DET
iajs-2478	136	269	above	above	ADJ
iajs-2478	136	270	three	three	NUM
iajs-2478	136	271	equations	equation	NOUN
iajs-2478	136	272	and	and	CCONJ
iajs-2478	136	273	integrating	integrate	VERB
iajs-2478	136	274	both	both	DET
iajs-2478	136	275	sides	side	NOUN
iajs-2478	136	276	of	of	ADP
iajs-2478	136	277	the	the	DET
iajs-2478	136	278	obtained	obtain	VERB
iajs-2478	136	279	equation	equation	NOUN
iajs-2478	136	280	from	from	ADP
iajs-2478	136	281	0	0	NUM
iajs-2478	136	282	to	to	ADP
iajs-2478	136	283	𝑇	𝑇	PROPN
iajs-2478	136	284	,	,	PUNCT
iajs-2478	136	285	taking	take	VERB
iajs-2478	136	286	the	the	DET
iajs-2478	136	287	absolute	absolute	ADJ
iajs-2478	136	288	value	value	NOUN
iajs-2478	136	289	,	,	PUNCT
iajs-2478	136	290	then	then	ADV
iajs-2478	136	291	using	use	VERB
iajs-2478	136	292	csi	csi	PROPN
iajs-2478	136	293	.	.	PUNCT
iajs-2478	137	1	finally	finally	ADV
iajs-2478	137	2	,	,	PUNCT
iajs-2478	137	3	using	use	VERB
iajs-2478	137	4	assumption	assumption	NOUN
iajs-2478	137	5	(	(	PUNCT
iajs-2478	137	6	a	a	X
iajs-2478	137	7	)	)	PUNCT
iajs-2478	137	8	,	,	PUNCT
iajs-2478	137	9	it	it	PRON
iajs-2478	137	10	yields	yield	VERB
iajs-2478	137	11	〈	〈	PROPN
iajs-2478	137	12	�	�	PROPN
iajs-2478	137	13	⃗	⃗	PART
iajs-2478	137	14	�	�	PROPN
iajs-2478	137	15	,	,	PUNCT
iajs-2478	137	16	�	�	PROPN
iajs-2478	137	17	⃗	⃗	NOUN
iajs-2478	137	18	�	�	NOUN
iajs-2478	137	19	〉𝑑𝑡	〉𝑑𝑡	DET
iajs-2478	137	20	‖∇𝑦	‖∇𝑦	PROPN
iajs-2478	137	21	‖	‖	PROPN
iajs-2478	137	22	‖∇𝑣	‖∇𝑣	PROPN
iajs-2478	137	23	‖	‖	PROPN
iajs-2478	137	24	‖𝑦	‖𝑦	ADJ
iajs-2478	137	25	‖	‖	PROPN
iajs-2478	137	26	‖𝑣	‖𝑣	PROPN
iajs-2478	137	27	‖	‖	PROPN
iajs-2478	137	28	‖𝑦	‖𝑦	PROPN
iajs-2478	138	1	‖	‖	PROPN
iajs-2478	138	2	‖𝑣	‖𝑣	PROPN
iajs-2478	138	3	‖	‖	PROPN
iajs-2478	138	4	‖𝑦	‖𝑦	PROPN
iajs-2478	138	5	‖	‖	PROPN
iajs-2478	138	6	‖𝑣	‖𝑣	PROPN
iajs-2478	138	7	‖	‖	PROPN
iajs-2478	139	1	‖∇𝑦	‖∇𝑦	NOUN
iajs-2478	139	2	‖	‖	PROPN
iajs-2478	139	3	‖∇𝑣	‖∇𝑣	PROPN
iajs-2478	139	4	‖	‖	PROPN
iajs-2478	139	5	‖𝑦	‖𝑦	ADJ
iajs-2478	139	6	‖	‖	PROPN
iajs-2478	139	7	‖𝑣	‖𝑣	PROPN
iajs-2478	139	8	‖	‖	PROPN
iajs-2478	139	9	‖𝑦	‖𝑦	PROPN
iajs-2478	139	10	‖	‖	PROPN
iajs-2478	139	11	‖𝑣	‖𝑣	PROPN
iajs-2478	139	12	‖	‖	PROPN
iajs-2478	139	13	‖𝑦	‖𝑦	PROPN
iajs-2478	139	14	‖	‖	PROPN
iajs-2478	139	15	‖𝑣	‖𝑣	PROPN
iajs-2478	139	16	‖	‖	PROPN
iajs-2478	140	1	‖∇𝑦	‖∇𝑦	NOUN
iajs-2478	140	2	‖	‖	PROPN
iajs-2478	140	3	‖∇𝑣	‖∇𝑣	PROPN
iajs-2478	140	4	‖	‖	PROPN
iajs-2478	140	5	‖𝑦	‖𝑦	ADJ
iajs-2478	141	1	‖	‖	PROPN
iajs-2478	141	2	‖𝑣	‖𝑣	PROPN
iajs-2478	141	3	‖	‖	PROPN
iajs-2478	141	4	‖𝑦	‖𝑦	PROPN
iajs-2478	141	5	‖	‖	PROPN
iajs-2478	141	6	‖𝑣	‖𝑣	PROPN
iajs-2478	141	7	‖	‖	PROPN
iajs-2478	141	8	‖𝑦	‖𝑦	PROPN
iajs-2478	141	9	‖	‖	PROPN
iajs-2478	141	10	‖𝑣	‖𝑣	PROPN
iajs-2478	141	11	‖	‖	PROPN
iajs-2478	141	12	‖𝜂	‖𝜂	PROPN
iajs-2478	141	13	‖	‖	PROPN
iajs-2478	141	14	‖𝑣	‖𝑣	PROPN
iajs-2478	141	15	‖	‖	PROPN
iajs-2478	141	16	‖𝜂	‖𝜂	PROPN
iajs-2478	141	17	‖	‖	PROPN
iajs-2478	141	18	‖𝑣	‖𝑣	PROPN
iajs-2478	141	19	‖	‖	PROPN
iajs-2478	141	20	‖𝜂	‖𝜂	PROPN
iajs-2478	141	21	‖	‖	PROPN
iajs-2478	141	22	‖𝑣	‖𝑣	PROPN
iajs-2478	141	23	‖	‖	PROPN
iajs-2478	141	24	‖𝑢	‖𝑢	PROPN
iajs-2478	141	25	‖	‖	PROPN
iajs-2478	141	26	‖𝑣	‖𝑣	PROPN
iajs-2478	141	27	‖	‖	PROPN
iajs-2478	141	28	‖𝑢	‖𝑢	PROPN
iajs-2478	141	29	‖	‖	PROPN
iajs-2478	141	30	‖𝑣	‖𝑣	PROPN
iajs-2478	141	31	‖	‖	PROPN
iajs-2478	141	32	‖𝑢	‖𝑢	PROPN
iajs-2478	141	33	‖	‖	PROPN
iajs-2478	141	34	‖𝑣	‖𝑣	PROPN
iajs-2478	141	35	‖	‖	PROPN
iajs-2478	141	36	.	.	PUNCT
iajs-2478	142	1	since	since	SCONJ
iajs-2478	142	2	for	for	ADP
iajs-2478	142	3	each	each	PRON
iajs-2478	142	4	𝑖	𝑖	SYM
iajs-2478	142	5	1,2,3	1,2,3	NUM
iajs-2478	142	6	,	,	PUNCT
iajs-2478	142	7	the	the	DET
iajs-2478	142	8	following	follow	VERB
iajs-2478	142	9	inequalities	inequality	NOUN
iajs-2478	142	10	are	be	AUX
iajs-2478	142	11	satisfied	satisfied	ADJ
iajs-2478	142	12	  	  	SPACE
iajs-2478	142	13	122	122	NUM
iajs-2478	142	14	ibn	ibn	PROPN
iajs-2478	142	15	al	al	PROPN
iajs-2478	142	16	-	-	PUNCT
iajs-2478	142	17	haitham	haitham	PROPN
iajs-2478	142	18	jour	jour	X
iajs-2478	142	19	.	.	PROPN
iajs-2478	143	1	for	for	ADP
iajs-2478	143	2	pure	pure	ADJ
iajs-2478	143	3	&	&	CCONJ
iajs-2478	143	4	appl	appl	PROPN
iajs-2478	143	5	.	.	PUNCT
iajs-2478	144	1	sci	sci	PROPN
iajs-2478	144	2	.	.	PROPN
iajs-2478	145	1	33	33	NUM
iajs-2478	145	2	(	(	PUNCT
iajs-2478	145	3	3	3	NUM
iajs-2478	145	4	)	)	PUNCT
iajs-2478	145	5	2020	2020	NUM
iajs-2478	146	1	‖∇𝑦	‖∇𝑦	AUX
iajs-2478	146	2	‖	‖	PROPN
iajs-2478	146	3	‖∇	‖∇	NUM
iajs-2478	146	4	�	�	NOUN
iajs-2478	146	5	⃗	⃗	NOUN
iajs-2478	146	6	�	�	PROPN
iajs-2478	146	7	‖𝑸	‖𝑸	PROPN
iajs-2478	146	8	‖	‖	PROPN
iajs-2478	146	9	�	�	PROPN
iajs-2478	146	10	⃗	⃗	NOUN
iajs-2478	146	11	�	�	PROPN
iajs-2478	146	12	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	146	13	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	146	14	,	,	PUNCT
iajs-2478	146	15	‖∇𝑣	‖∇𝑣	PROPN
iajs-2478	146	16	‖	‖	PROPN
iajs-2478	146	17	‖∇	‖∇	NUM
iajs-2478	146	18	�	�	PROPN
iajs-2478	146	19	⃗	⃗	NOUN
iajs-2478	146	20	�	�	PROPN
iajs-2478	146	21	‖𝑸	‖𝑸	PROPN
iajs-2478	146	22	‖	‖	PROPN
iajs-2478	146	23	�	�	PROPN
iajs-2478	146	24	⃗	⃗	NOUN
iajs-2478	146	25	�	�	NOUN
iajs-2478	146	26	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	146	27	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	146	28	,	,	PUNCT
iajs-2478	146	29	‖𝑦	‖𝑦	ADJ
iajs-2478	146	30	‖	‖	PROPN
iajs-2478	146	31	‖	‖	PROPN
iajs-2478	146	32	�	�	PROPN
iajs-2478	146	33	⃗	⃗	PROPN
iajs-2478	146	34	�	�	PROPN
iajs-2478	146	35	‖𝑸	‖𝑸	PROPN
iajs-2478	146	36	‖	‖	PROPN
iajs-2478	146	37	�	�	PROPN
iajs-2478	146	38	⃗	⃗	NOUN
iajs-2478	146	39	�	�	PROPN
iajs-2478	146	40	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	146	41	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	146	42	,	,	PUNCT
iajs-2478	146	43	‖𝑣	‖𝑣	PROPN
iajs-2478	146	44	‖	‖	PROPN
iajs-2478	146	45	‖	‖	PROPN
iajs-2478	146	46	�	�	PROPN
iajs-2478	146	47	⃗	⃗	PROPN
iajs-2478	146	48	�	�	PROPN
iajs-2478	146	49	‖𝑸	‖𝑸	PROPN
iajs-2478	146	50	‖	‖	PROPN
iajs-2478	146	51	�	�	PROPN
iajs-2478	146	52	⃗	⃗	NOUN
iajs-2478	146	53	�	�	NOUN
iajs-2478	146	54	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	146	55	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	146	56	,	,	PUNCT
iajs-2478	147	1	‖𝑢	‖𝑢	DET
iajs-2478	147	2	‖	‖	PROPN
iajs-2478	147	3	‖𝑢	‖𝑢	NOUN
iajs-2478	147	4	‖𝚺	‖𝚺	NOUN
iajs-2478	147	5	ĉ	ĉ	PROPN
iajs-2478	147	6	,	,	PUNCT
iajs-2478	147	7	‖𝑣	‖𝑣	ADJ
iajs-2478	147	8	‖𝚺	‖𝚺	PROPN
iajs-2478	147	9	‖	‖	PROPN
iajs-2478	147	10	�	�	PROPN
iajs-2478	147	11	⃗	⃗	NOUN
iajs-2478	147	12	�	�	PROPN
iajs-2478	147	13	‖𝚺	‖𝚺	PROPN
iajs-2478	147	14	ĥ	ĥ	PROPN
iajs-2478	147	15	‖	‖	PROPN
iajs-2478	147	16	�	�	PROPN
iajs-2478	147	17	⃗	⃗	NOUN
iajs-2478	147	18	�	�	NOUN
iajs-2478	147	19	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	147	20	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	147	21	,	,	PUNCT
iajs-2478	147	22	‖𝜂	‖𝜂	NOUN
iajs-2478	147	23	‖	‖	PROPN
iajs-2478	148	1	𝑏	𝑏	DET
iajs-2478	148	2	´	´	NOUN
iajs-2478	148	3	,	,	PUNCT
iajs-2478	148	4	then	then	ADV
iajs-2478	148	5	〈	〈	PROPN
iajs-2478	148	6	�	�	PROPN
iajs-2478	148	7	⃗	⃗	PROPN
iajs-2478	148	8	�	�	PROPN
iajs-2478	148	9	,	,	PUNCT
iajs-2478	148	10	�	�	PROPN
iajs-2478	148	11	⃗	⃗	NOUN
iajs-2478	148	12	�	�	NOUN
iajs-2478	148	13	〉	〉	NOUN
iajs-2478	148	14	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	148	15	12‖	12‖	NUM
iajs-2478	148	16	�	�	NOUN
iajs-2478	148	17	⃗	⃗	NOUN
iajs-2478	148	18	�	�	PROPN
iajs-2478	148	19	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	20	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	148	21	‖	‖	NUM
iajs-2478	148	22	�	�	NOUN
iajs-2478	148	23	⃗	⃗	NOUN
iajs-2478	148	24	�	�	NOUN
iajs-2478	148	25	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	26	ĩ,𝑽	ĩ,𝑽	VERB
iajs-2478	148	27	𝑏	𝑏	NUM
iajs-2478	148	28	´	´	NOUN
iajs-2478	148	29	𝑏	𝑏	NUM
iajs-2478	148	30	´	´	NOUN
iajs-2478	148	31	𝑏	𝑏	NUM
iajs-2478	148	32	´	´	NOUN
iajs-2478	148	33	3ĉ	3ĉ	NUM
iajs-2478	148	34	ĥ	ĥ	DET
iajs-2478	148	35	‖	‖	PROPN
iajs-2478	148	36	�	�	PROPN
iajs-2478	148	37	⃗	⃗	NOUN
iajs-2478	148	38	�	�	NOUN
iajs-2478	148	39	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	40	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	148	41	or	or	CCONJ
iajs-2478	148	42	〈	〈	PRON
iajs-2478	148	43	�	�	NOUN
iajs-2478	148	44	⃗	⃗	NOUN
iajs-2478	148	45	�	�	PROPN
iajs-2478	148	46	,	,	PUNCT
iajs-2478	148	47	�	�	PROPN
iajs-2478	148	48	⃗	⃗	NOUN
iajs-2478	148	49	�	�	NOUN
iajs-2478	148	50	〉𝑑𝑡	〉𝑑𝑡	NOUN
iajs-2478	148	51	12𝑏	12𝑏	NUM
iajs-2478	148	52	𝑐	𝑐	ADP
iajs-2478	148	53	𝑏	𝑏	NUM
iajs-2478	148	54	´	´	PROPN
iajs-2478	148	55	𝑐	𝑐	PROPN
iajs-2478	148	56	‖	‖	PROPN
iajs-2478	148	57	�	�	PROPN
iajs-2478	148	58	⃗	⃗	NOUN
iajs-2478	148	59	�	�	NOUN
iajs-2478	148	60	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	61	ĩ,𝑽	ĩ,𝑽	PROPN
iajs-2478	148	62	with	with	ADP
iajs-2478	148	63	‖	‖	PROPN
iajs-2478	148	64	�	�	NOUN
iajs-2478	148	65	⃗	⃗	NOUN
iajs-2478	148	66	�	�	PROPN
iajs-2478	148	67	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	68	ĩ,𝑽	ĩ,𝑽	VERB
iajs-2478	148	69	𝑏	𝑏	PROPN
iajs-2478	148	70	𝑐	𝑐	PROPN
iajs-2478	148	71	&	&	CCONJ
iajs-2478	148	72	𝑏	𝑏	PROPN
iajs-2478	148	73	´	´	PROPN
iajs-2478	148	74	𝑐	𝑐	NOUN
iajs-2478	148	75	𝑏	𝑏	NOUN
iajs-2478	148	76	´	´	NOUN
iajs-2478	148	77	𝑏	𝑏	NUM
iajs-2478	148	78	´	´	NOUN
iajs-2478	148	79	𝑏	𝑏	NUM
iajs-2478	148	80	´	´	NOUN
iajs-2478	148	81	3ĉ	3ĉ	NUM
iajs-2478	148	82	ĥ	ĥ	X
iajs-2478	148	83	⇒	⇒	NOUN
iajs-2478	148	84	〈	〈	PROPN
iajs-2478	148	85	⃗	⃗	PROPN
iajs-2478	148	86	,	,	PUNCT
iajs-2478	148	87	⃗	⃗	X
iajs-2478	148	88	〉	〉	NOUN
iajs-2478	148	89	‖	‖	ADJ
iajs-2478	148	90	⃗‖𝑳𝟐	⃗‖𝑳𝟐	PUNCT
iajs-2478	148	91	ĩ,𝑽	ĩ,𝑽	VERB
iajs-2478	148	92	𝑏	𝑏	PROPN
iajs-2478	148	93	𝑐	𝑐	PROPN
iajs-2478	148	94	,	,	PUNCT
iajs-2478	148	95	with	with	ADP
iajs-2478	148	96	𝑏	𝑏	PROPN
iajs-2478	148	97	𝑐	𝑐	PROPN
iajs-2478	148	98	12𝑏	12𝑏	NUM
iajs-2478	148	99	𝑐	𝑐	ADP
iajs-2478	148	100	𝑏	𝑏	NUM
iajs-2478	148	101	´	´	NOUN
iajs-2478	148	102	𝑐	𝑐	PROPN
iajs-2478	148	103	⇒	⇒	PROPN
iajs-2478	148	104	‖	‖	PROPN
iajs-2478	148	105	�	�	PROPN
iajs-2478	148	106	⃗	⃗	NOUN
iajs-2478	148	107	�	�	PROPN
iajs-2478	148	108	‖𝑳𝟐	‖𝑳𝟐	NOUN
iajs-2478	148	109	ĩ,𝑽∗	ĩ,𝑽∗	PROPN
iajs-2478	148	110	𝑏	𝑏	DET
iajs-2478	148	111	𝑐	𝑐	PROPN
iajs-2478	148	112	since	since	SCONJ
iajs-2478	148	113	for	for	ADP
iajs-2478	148	114	each	each	DET
iajs-2478	148	115	𝑘	𝑘	PROPN
iajs-2478	148	116	,	,	PUNCT
iajs-2478	148	117	�	�	NOUN
iajs-2478	148	118	⃗	⃗	NOUN
iajs-2478	148	119	�	�	PROPN
iajs-2478	148	120	is	be	AUX
iajs-2478	148	121	a	a	DET
iajs-2478	148	122	solution	solution	NOUN
iajs-2478	148	123	of	of	ADP
iajs-2478	148	124	the	the	DET
iajs-2478	148	125	tses	tse	NOUN
iajs-2478	148	126	(	(	PUNCT
iajs-2478	148	127	1	1	NUM
iajs-2478	148	128	9	9	NUM
iajs-2478	148	129	)	)	PUNCT
iajs-2478	148	130	,	,	PUNCT
iajs-2478	148	131	then	then	ADV
iajs-2478	148	132	〈	〈	PROPN
iajs-2478	148	133	𝑦	𝑦	NOUN
iajs-2478	148	134	,	,	PUNCT
iajs-2478	148	135	𝑣	𝑣	ADP
iajs-2478	148	136	〉	〉	NOUN
iajs-2478	148	137	∇𝑦	∇𝑦	PROPN
iajs-2478	148	138	,	,	PUNCT
iajs-2478	148	139	∇𝑣	∇𝑣	PROPN
iajs-2478	148	140	𝑦	𝑦	PRON
iajs-2478	148	141	,	,	PUNCT
iajs-2478	148	142	𝑣	𝑣	DET
iajs-2478	148	143	𝑦	𝑦	NOUN
iajs-2478	148	144	,	,	PUNCT
iajs-2478	148	145	𝑣	𝑣	PRON
iajs-2478	148	146	𝑦	𝑦	NOUN
iajs-2478	148	147	,	,	PUNCT
iajs-2478	148	148	𝑣	𝑣	X
iajs-2478	148	149	(	(	PUNCT
iajs-2478	148	150	𝑓	𝑓	PROPN
iajs-2478	148	151	,	,	PUNCT
iajs-2478	148	152	𝑣	𝑣	NOUN
iajs-2478	148	153	)	)	PUNCT
iajs-2478	149	1	+	+	NUM
iajs-2478	149	2	𝑢	𝑢	X
iajs-2478	149	3	,	,	PUNCT
iajs-2478	149	4	𝑣	𝑣	X
iajs-2478	149	5	,	,	PUNCT
iajs-2478	149	6	(	(	PUNCT
iajs-2478	149	7	54	54	NUM
iajs-2478	149	8	)	)	PUNCT
iajs-2478	150	1	〈	〈	NOUN
iajs-2478	150	2	𝑦	𝑦	NOUN
iajs-2478	150	3	,	,	PUNCT
iajs-2478	150	4	𝑣	𝑣	ADP
iajs-2478	150	5	〉	〉	NOUN
iajs-2478	150	6	∇𝑦	∇𝑦	PROPN
iajs-2478	150	7	,	,	PUNCT
iajs-2478	150	8	∇𝑣	∇𝑣	PROPN
iajs-2478	150	9	𝑦	𝑦	PRON
iajs-2478	150	10	,	,	PUNCT
iajs-2478	150	11	𝑣	𝑣	DET
iajs-2478	150	12	𝑦	𝑦	NOUN
iajs-2478	150	13	,	,	PUNCT
iajs-2478	150	14	𝑣	𝑣	PRON
iajs-2478	150	15	𝑦	𝑦	NOUN
iajs-2478	150	16	,	,	PUNCT
iajs-2478	150	17	𝑣	𝑣	X
iajs-2478	150	18	(	(	PUNCT
iajs-2478	150	19	𝑓	𝑓	PROPN
iajs-2478	150	20	,	,	PUNCT
iajs-2478	150	21	𝑣	𝑣	NOUN
iajs-2478	150	22	)	)	PUNCT
iajs-2478	151	1	+	+	NUM
iajs-2478	151	2	𝑢	𝑢	X
iajs-2478	151	3	,	,	PUNCT
iajs-2478	151	4	𝑣	𝑣	X
iajs-2478	151	5	,	,	PUNCT
iajs-2478	151	6	(	(	PUNCT
iajs-2478	151	7	55	55	NUM
iajs-2478	151	8	)	)	PUNCT
iajs-2478	152	1	〈	〈	PROPN
iajs-2478	152	2	𝑦	𝑦	NOUN
iajs-2478	152	3	,	,	PUNCT
iajs-2478	152	4	𝑣	𝑣	ADP
iajs-2478	152	5	〉	〉	NOUN
iajs-2478	152	6	∇𝑦	∇𝑦	PROPN
iajs-2478	152	7	,	,	PUNCT
iajs-2478	152	8	∇𝑣	∇𝑣	PROPN
iajs-2478	152	9	𝑦	𝑦	PRON
iajs-2478	152	10	,	,	PUNCT
iajs-2478	152	11	𝑣	𝑣	PRON
iajs-2478	152	12	𝑦	𝑦	NOUN
iajs-2478	152	13	,	,	PUNCT
iajs-2478	152	14	𝑣	𝑣	DET
iajs-2478	152	15	𝑦	𝑦	NOUN
iajs-2478	152	16	,	,	PUNCT
iajs-2478	152	17	𝑣	𝑣	X
iajs-2478	152	18	(	(	PUNCT
iajs-2478	152	19	𝑓	𝑓	PROPN
iajs-2478	152	20	,	,	PUNCT
iajs-2478	152	21	𝑣	𝑣	NOUN
iajs-2478	152	22	)	)	PUNCT
iajs-2478	153	1	+	+	NUM
iajs-2478	153	2	𝑢	𝑢	X
iajs-2478	153	3	,	,	PUNCT
iajs-2478	153	4	𝑣	𝑣	X
iajs-2478	153	5	,	,	PUNCT
iajs-2478	153	6	(	(	PUNCT
iajs-2478	153	7	56	56	NUM
iajs-2478	153	8	)	)	PUNCT
iajs-2478	153	9	let	let	VERB
iajs-2478	153	10	𝜑	𝜑	PROPN
iajs-2478	153	11	∈	∈	PROPN
iajs-2478	153	12	𝐶	𝐶	PROPN
iajs-2478	153	13	0	0	PROPN
iajs-2478	153	14	,	,	PUNCT
iajs-2478	153	15	𝑇	𝑇	PROPN
iajs-2478	153	16	,	,	PUNCT
iajs-2478	153	17	s.t	s.t	PROPN
iajs-2478	153	18	.	.	PROPN
iajs-2478	153	19	𝜑	𝜑	PROPN
iajs-2478	153	20	𝑇	𝑇	PROPN
iajs-2478	153	21	0	0	NUM
iajs-2478	153	22	,	,	PUNCT
iajs-2478	153	23	𝜑	𝜑	PROPN
iajs-2478	153	24	0	0	NUM
iajs-2478	153	25	0	0	NUM
iajs-2478	153	26	,	,	PUNCT
iajs-2478	153	27	∀𝑖	∀𝑖	PROPN
iajs-2478	153	28	1,2,3	1,2,3	NUM
iajs-2478	153	29	,	,	PUNCT
iajs-2478	153	30	rewriting	rewrite	VERB
iajs-2478	153	31	the	the	DET
iajs-2478	153	32	1st	1st	ADJ
iajs-2478	153	33	terms	term	NOUN
iajs-2478	153	34	in	in	ADP
iajs-2478	153	35	the	the	DET
iajs-2478	153	36	l.h.s	l.h.s	NOUN
iajs-2478	153	37	.	.	PUNCT
iajs-2478	154	1	of	of	ADP
iajs-2478	154	2	(	(	PUNCT
iajs-2478	154	3	54	54	NUM
iajs-2478	154	4	56	56	NUM
iajs-2478	154	5	)	)	PUNCT
iajs-2478	154	6	multiplying	multiply	VERB
iajs-2478	154	7	their	their	PRON
iajs-2478	154	8	both	both	DET
iajs-2478	154	9	sides	side	NOUN
iajs-2478	154	10	by	by	ADP
iajs-2478	154	11	𝜑	𝜑	PROPN
iajs-2478	154	12	𝑡	𝑡	PROPN
iajs-2478	154	13	,	,	PUNCT
iajs-2478	154	14	∀𝑖	∀𝑖	PROPN
iajs-2478	154	15	1,2,3	1,2,3	NUM
iajs-2478	154	16	,	,	PUNCT
iajs-2478	154	17	respectively	respectively	ADV
iajs-2478	154	18	,	,	PUNCT
iajs-2478	154	19	integrating	integrate	VERB
iajs-2478	154	20	both	both	DET
iajs-2478	154	21	sides	side	NOUN
iajs-2478	154	22	w.r.t	w.r.t	VERB
iajs-2478	154	23	.	.	PUNCT
iajs-2478	155	1	𝑡	𝑡	VERB
iajs-2478	155	2	from	from	ADP
iajs-2478	155	3	0	0	NUM
iajs-2478	155	4	to	to	ADP
iajs-2478	155	5	𝑇	𝑇	PROPN
iajs-2478	155	6	,	,	PUNCT
iajs-2478	155	7	and	and	CCONJ
iajs-2478	155	8	integration	integration	NOUN
iajs-2478	155	9	by	by	ADP
iajs-2478	155	10	parts	part	NOUN
iajs-2478	155	11	for	for	ADP
iajs-2478	155	12	the	the	DET
iajs-2478	155	13	1st	1st	ADJ
iajs-2478	155	14	terms	term	NOUN
iajs-2478	155	15	in	in	ADP
iajs-2478	155	16	the	the	DET
iajs-2478	155	17	l.h.s	l.h.s	NOUN
iajs-2478	155	18	.	.	PUNCT
iajs-2478	156	1	of	of	ADP
iajs-2478	156	2	each	each	DET
iajs-2478	156	3	obtained	obtain	VERB
iajs-2478	156	4	equations	equation	NOUN
iajs-2478	156	5	,	,	PUNCT
iajs-2478	156	6	one	one	PRON
iajs-2478	156	7	gets	get	VERB
iajs-2478	156	8	that	that	PRON
iajs-2478	156	9	𝑦	𝑦	NOUN
iajs-2478	156	10	,	,	PUNCT
iajs-2478	156	11	𝑣	𝑣	ADP
iajs-2478	156	12	𝜑	𝜑	NOUN
iajs-2478	156	13	´	´	X
iajs-2478	156	14	𝑡	𝑡	NOUN
iajs-2478	156	15	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	16	∇𝑦	∇𝑦	PROPN
iajs-2478	156	17	,	,	PUNCT
iajs-2478	156	18	∇𝑣	∇𝑣	PROPN
iajs-2478	156	19	𝑦	𝑦	PRON
iajs-2478	156	20	,	,	PUNCT
iajs-2478	156	21	𝑣	𝑣	PRON
iajs-2478	156	22	𝜑	𝜑	X
iajs-2478	156	23	𝑡	𝑡	NOUN
iajs-2478	156	24	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	25	𝑦	𝑦	NOUN
iajs-2478	156	26	,	,	PUNCT
iajs-2478	156	27	𝑣	𝑣	ADP
iajs-2478	156	28	𝜑	𝜑	X
iajs-2478	156	29	𝑡	𝑡	NOUN
iajs-2478	156	30	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	31	𝑦	𝑦	NOUN
iajs-2478	156	32	,	,	PUNCT
iajs-2478	156	33	𝑣	𝑣	ADP
iajs-2478	156	34	𝜑	𝜑	X
iajs-2478	156	35	𝑡	𝑡	NOUN
iajs-2478	156	36	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	37	𝑓	𝑓	PRON
iajs-2478	156	38	,	,	PUNCT
iajs-2478	156	39	𝑣	𝑣	DET
iajs-2478	156	40	𝜑	𝜑	X
iajs-2478	156	41	𝑡	𝑡	NOUN
iajs-2478	156	42	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	43	𝑢	𝑢	NOUN
iajs-2478	156	44	,	,	PUNCT
iajs-2478	156	45	𝑣	𝑣	DET
iajs-2478	156	46	𝜑	𝜑	X
iajs-2478	156	47	𝑡	𝑡	NOUN
iajs-2478	156	48	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	49	𝑦	𝑦	NOUN
iajs-2478	156	50	0	0	NUM
iajs-2478	156	51	,	,	PUNCT
iajs-2478	156	52	𝑣	𝑣	DET
iajs-2478	156	53	𝜑	𝜑	NOUN
iajs-2478	156	54	0	0	NUM
iajs-2478	156	55	,	,	PUNCT
iajs-2478	156	56	(	(	PUNCT
iajs-2478	156	57	57	57	NUM
iajs-2478	156	58	)	)	PUNCT
iajs-2478	156	59	𝑦	𝑦	NOUN
iajs-2478	156	60	,	,	PUNCT
iajs-2478	156	61	𝑣	𝑣	PRON
iajs-2478	156	62	𝜑	𝜑	NOUN
iajs-2478	156	63	´	´	X
iajs-2478	156	64	𝑡	𝑡	NOUN
iajs-2478	156	65	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	66	∇𝑦	∇𝑦	PROPN
iajs-2478	156	67	,	,	PUNCT
iajs-2478	156	68	∇𝑣	∇𝑣	PROPN
iajs-2478	156	69	𝑦	𝑦	PRON
iajs-2478	156	70	,	,	PUNCT
iajs-2478	156	71	𝑣	𝑣	PRON
iajs-2478	156	72	𝜑	𝜑	X
iajs-2478	156	73	𝑡	𝑡	NOUN
iajs-2478	156	74	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	75	𝑦	𝑦	NOUN
iajs-2478	156	76	,	,	PUNCT
iajs-2478	156	77	𝑣	𝑣	ADP
iajs-2478	156	78	𝜑	𝜑	X
iajs-2478	156	79	𝑡	𝑡	NOUN
iajs-2478	156	80	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	81	𝑦	𝑦	NOUN
iajs-2478	156	82	,	,	PUNCT
iajs-2478	156	83	𝑣	𝑣	ADP
iajs-2478	156	84	𝜑	𝜑	X
iajs-2478	156	85	𝑡	𝑡	NOUN
iajs-2478	156	86	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	87	𝑓	𝑓	PRON
iajs-2478	156	88	,	,	PUNCT
iajs-2478	156	89	𝑣	𝑣	DET
iajs-2478	156	90	𝜑	𝜑	X
iajs-2478	156	91	𝑡	𝑡	NOUN
iajs-2478	156	92	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	93	𝑢	𝑢	NOUN
iajs-2478	156	94	,	,	PUNCT
iajs-2478	156	95	𝑣	𝑣	PRON
iajs-2478	156	96	𝜑	𝜑	X
iajs-2478	156	97	𝑡	𝑡	NOUN
iajs-2478	156	98	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	99	𝑦	𝑦	NOUN
iajs-2478	156	100	0	0	NUM
iajs-2478	156	101	,	,	PUNCT
iajs-2478	156	102	𝑣	𝑣	PRON
iajs-2478	156	103	𝜑	𝜑	NOUN
iajs-2478	156	104	0	0	NUM
iajs-2478	156	105	,	,	PUNCT
iajs-2478	156	106	(	(	PUNCT
iajs-2478	156	107	58	58	NUM
iajs-2478	156	108	)	)	PUNCT
iajs-2478	156	109	𝑦	𝑦	NOUN
iajs-2478	156	110	,	,	PUNCT
iajs-2478	156	111	𝑣	𝑣	PRON
iajs-2478	156	112	𝜑	𝜑	NOUN
iajs-2478	156	113	´	´	X
iajs-2478	156	114	𝑡	𝑡	NOUN
iajs-2478	156	115	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	116	∇𝑦	∇𝑦	PROPN
iajs-2478	156	117	,	,	PUNCT
iajs-2478	156	118	∇𝑣	∇𝑣	PROPN
iajs-2478	156	119	𝑦	𝑦	PRON
iajs-2478	156	120	,	,	PUNCT
iajs-2478	156	121	𝑣	𝑣	PRON
iajs-2478	156	122	𝜑	𝜑	X
iajs-2478	156	123	𝑡	𝑡	NOUN
iajs-2478	156	124	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	125	𝑦	𝑦	NOUN
iajs-2478	156	126	,	,	PUNCT
iajs-2478	156	127	𝑣	𝑣	ADP
iajs-2478	156	128	𝜑	𝜑	X
iajs-2478	156	129	𝑡	𝑡	NOUN
iajs-2478	156	130	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	131	𝑦	𝑦	NOUN
iajs-2478	156	132	,	,	PUNCT
iajs-2478	156	133	𝑣	𝑣	ADP
iajs-2478	156	134	𝜑	𝜑	X
iajs-2478	156	135	𝑡	𝑡	NOUN
iajs-2478	156	136	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	137	𝑓	𝑓	PRON
iajs-2478	156	138	,	,	PUNCT
iajs-2478	156	139	𝑣	𝑣	DET
iajs-2478	156	140	𝜑	𝜑	X
iajs-2478	156	141	𝑡	𝑡	NOUN
iajs-2478	156	142	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	143	𝑢	𝑢	NOUN
iajs-2478	156	144	,	,	PUNCT
iajs-2478	156	145	𝑣	𝑣	PRON
iajs-2478	156	146	𝜑	𝜑	X
iajs-2478	156	147	𝑡	𝑡	NOUN
iajs-2478	156	148	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	149	𝑦	𝑦	NOUN
iajs-2478	156	150	0	0	NUM
iajs-2478	156	151	,	,	PUNCT
iajs-2478	156	152	𝑣	𝑣	DET
iajs-2478	156	153	𝜑	𝜑	NOUN
iajs-2478	156	154	0	0	NUM
iajs-2478	156	155	,	,	PUNCT
iajs-2478	156	156	(	(	PUNCT
iajs-2478	156	157	59	59	NUM
iajs-2478	156	158	)	)	PUNCT
iajs-2478	156	159	since	since	SCONJ
iajs-2478	156	160	�	�	NOUN
iajs-2478	156	161	⃗	⃗	NOUN
iajs-2478	156	162	�	�	PROPN
iajs-2478	156	163	⟶	⟶	NOUN
iajs-2478	156	164	�	�	NOUN
iajs-2478	156	165	⃗	⃗	NOUN
iajs-2478	156	166	�	�	PROPN
iajs-2478	156	167	weakly	weakly	NOUN
iajs-2478	156	168	in	in	ADP
iajs-2478	156	169	𝐿	𝐿	PROPN
iajs-2478	156	170	𝑄	𝑄	PROPN
iajs-2478	156	171	and	and	CCONJ
iajs-2478	156	172	in	in	ADP
iajs-2478	156	173	𝐿	𝐿	PROPN
iajs-2478	156	174	ĩ	ĩ	PROPN
iajs-2478	156	175	,	,	PUNCT
iajs-2478	156	176	𝑉	𝑉	PROPN
iajs-2478	156	177	,	,	PUNCT
iajs-2478	156	178	then	then	ADV
iajs-2478	156	179	the	the	DET
iajs-2478	156	180	following	follow	VERB
iajs-2478	156	181	convergences	convergence	NOUN
iajs-2478	156	182	are	be	AUX
iajs-2478	156	183	held	hold	VERB
iajs-2478	156	184	𝑦	𝑦	PRON
iajs-2478	156	185	,	,	PUNCT
iajs-2478	156	186	𝑣	𝑣	ADP
iajs-2478	156	187	𝜑	𝜑	NOUN
iajs-2478	156	188	´	´	X
iajs-2478	156	189	𝑡	𝑡	NOUN
iajs-2478	156	190	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	191	∇𝑦	∇𝑦	PROPN
iajs-2478	156	192	,	,	PUNCT
iajs-2478	156	193	∇𝑣	∇𝑣	PROPN
iajs-2478	156	194	𝑦	𝑦	PRON
iajs-2478	156	195	,	,	PUNCT
iajs-2478	156	196	𝑣	𝑣	PRON
iajs-2478	156	197	𝜑	𝜑	X
iajs-2478	156	198	𝑡	𝑡	NOUN
iajs-2478	156	199	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	200	𝑦	𝑦	NOUN
iajs-2478	156	201	,	,	PUNCT
iajs-2478	156	202	𝑣	𝑣	ADP
iajs-2478	156	203	𝜑	𝜑	X
iajs-2478	156	204	𝑡	𝑡	NOUN
iajs-2478	156	205	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	206	𝑦	𝑦	NOUN
iajs-2478	156	207	,	,	PUNCT
iajs-2478	156	208	𝑣	𝑣	ADP
iajs-2478	156	209	𝜑	𝜑	X
iajs-2478	156	210	𝑡	𝑡	NOUN
iajs-2478	156	211	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	212	⟶	⟶	NOUN
iajs-2478	156	213	𝑦	𝑦	PROPN
iajs-2478	156	214	,	,	PUNCT
iajs-2478	156	215	𝑣	𝑣	PRON
iajs-2478	156	216	𝜑	𝜑	NOUN
iajs-2478	156	217	´	´	X
iajs-2478	156	218	𝑡	𝑡	NOUN
iajs-2478	156	219	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	220	∇𝑦	∇𝑦	PROPN
iajs-2478	156	221	,	,	PUNCT
iajs-2478	156	222	∇𝑣	∇𝑣	PROPN
iajs-2478	156	223	𝑦	𝑦	PRON
iajs-2478	156	224	,	,	PUNCT
iajs-2478	156	225	𝑣	𝑣	PRON
iajs-2478	156	226	𝜑	𝜑	X
iajs-2478	156	227	𝑡	𝑡	NOUN
iajs-2478	156	228	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	229	𝑦	𝑦	NOUN
iajs-2478	156	230	,	,	PUNCT
iajs-2478	156	231	𝑣	𝑣	ADP
iajs-2478	156	232	𝜑	𝜑	X
iajs-2478	156	233	𝑡	𝑡	NOUN
iajs-2478	156	234	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	235	𝑦	𝑦	NOUN
iajs-2478	156	236	,	,	PUNCT
iajs-2478	156	237	𝑣	𝑣	ADP
iajs-2478	156	238	𝜑	𝜑	X
iajs-2478	156	239	𝑡	𝑡	NOUN
iajs-2478	156	240	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	241	,	,	PUNCT
iajs-2478	156	242	(	(	PUNCT
iajs-2478	156	243	60	60	NUM
iajs-2478	156	244	)	)	PUNCT
iajs-2478	156	245	𝑦	𝑦	NOUN
iajs-2478	156	246	,	,	PUNCT
iajs-2478	156	247	𝑣	𝑣	PRON
iajs-2478	156	248	𝜑	𝜑	NOUN
iajs-2478	156	249	´	´	X
iajs-2478	156	250	𝑡	𝑡	NOUN
iajs-2478	156	251	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	252	∇𝑦	∇𝑦	PROPN
iajs-2478	156	253	,	,	PUNCT
iajs-2478	156	254	∇𝑣	∇𝑣	PROPN
iajs-2478	156	255	𝑦	𝑦	PRON
iajs-2478	156	256	,	,	PUNCT
iajs-2478	156	257	𝑣	𝑣	DET
iajs-2478	156	258	𝜑	𝜑	X
iajs-2478	156	259	𝑡	𝑡	NOUN
iajs-2478	156	260	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	261	𝑦	𝑦	NOUN
iajs-2478	156	262	,	,	PUNCT
iajs-2478	156	263	𝑣	𝑣	ADP
iajs-2478	156	264	𝜑	𝜑	X
iajs-2478	156	265	𝑡	𝑡	NOUN
iajs-2478	156	266	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	267	𝑦	𝑦	NOUN
iajs-2478	156	268	,	,	PUNCT
iajs-2478	156	269	𝑣	𝑣	ADP
iajs-2478	156	270	𝜑	𝜑	X
iajs-2478	156	271	𝑡	𝑡	NOUN
iajs-2478	156	272	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	273	⟶	⟶	NOUN
iajs-2478	156	274	𝑦	𝑦	PROPN
iajs-2478	156	275	,	,	PUNCT
iajs-2478	156	276	𝑣	𝑣	PRON
iajs-2478	156	277	𝜑	𝜑	NOUN
iajs-2478	156	278	´	´	X
iajs-2478	156	279	𝑡	𝑡	NOUN
iajs-2478	156	280	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	281	∇𝑦	∇𝑦	PROPN
iajs-2478	156	282	,	,	PUNCT
iajs-2478	156	283	∇𝑣	∇𝑣	PROPN
iajs-2478	156	284	𝑦	𝑦	PRON
iajs-2478	156	285	,	,	PUNCT
iajs-2478	156	286	𝑣	𝑣	PRON
iajs-2478	156	287	𝜑	𝜑	X
iajs-2478	156	288	𝑡	𝑡	NOUN
iajs-2478	156	289	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	290	𝑦	𝑦	NOUN
iajs-2478	156	291	,	,	PUNCT
iajs-2478	156	292	𝑣	𝑣	ADP
iajs-2478	156	293	𝜑	𝜑	X
iajs-2478	156	294	𝑡	𝑡	NOUN
iajs-2478	156	295	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	296	𝑦	𝑦	NOUN
iajs-2478	156	297	,	,	PUNCT
iajs-2478	156	298	𝑣	𝑣	ADP
iajs-2478	156	299	𝜑	𝜑	X
iajs-2478	156	300	𝑡	𝑡	PROPN
iajs-2478	156	301	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	302	,	,	PUNCT
iajs-2478	156	303	(	(	PUNCT
iajs-2478	156	304	61	61	NUM
iajs-2478	156	305	)	)	PUNCT
iajs-2478	156	306	𝑦	𝑦	NOUN
iajs-2478	156	307	,	,	PUNCT
iajs-2478	156	308	𝑣	𝑣	PRON
iajs-2478	156	309	𝜑	𝜑	NOUN
iajs-2478	156	310	´	´	X
iajs-2478	156	311	𝑡	𝑡	NOUN
iajs-2478	156	312	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	313	∇𝑦	∇𝑦	PROPN
iajs-2478	156	314	,	,	PUNCT
iajs-2478	156	315	∇𝑣	∇𝑣	PROPN
iajs-2478	156	316	𝑦	𝑦	PRON
iajs-2478	156	317	,	,	PUNCT
iajs-2478	156	318	𝑣	𝑣	DET
iajs-2478	156	319	𝜑	𝜑	X
iajs-2478	156	320	𝑡	𝑡	NOUN
iajs-2478	156	321	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	322	𝑦	𝑦	NOUN
iajs-2478	156	323	,	,	PUNCT
iajs-2478	156	324	𝑣	𝑣	ADP
iajs-2478	156	325	𝜑	𝜑	X
iajs-2478	156	326	𝑡	𝑡	NOUN
iajs-2478	156	327	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	328	𝑦	𝑦	NOUN
iajs-2478	156	329	,	,	PUNCT
iajs-2478	156	330	𝑣	𝑣	ADP
iajs-2478	156	331	𝜑	𝜑	X
iajs-2478	156	332	𝑡	𝑡	NOUN
iajs-2478	156	333	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	334	⟶	⟶	NOUN
iajs-2478	156	335	𝑦	𝑦	PROPN
iajs-2478	156	336	,	,	PUNCT
iajs-2478	156	337	𝑣	𝑣	PRON
iajs-2478	156	338	𝜑	𝜑	NOUN
iajs-2478	156	339	´	´	X
iajs-2478	156	340	𝑡	𝑡	NOUN
iajs-2478	156	341	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	342	∇𝑦	∇𝑦	PROPN
iajs-2478	156	343	,	,	PUNCT
iajs-2478	156	344	∇𝑣	∇𝑣	PROPN
iajs-2478	156	345	𝑦	𝑦	PRON
iajs-2478	156	346	,	,	PUNCT
iajs-2478	156	347	𝑣	𝑣	PRON
iajs-2478	156	348	𝜑	𝜑	X
iajs-2478	156	349	𝑡	𝑡	NOUN
iajs-2478	156	350	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	351	𝑦	𝑦	NOUN
iajs-2478	156	352	,	,	PUNCT
iajs-2478	156	353	𝑣	𝑣	ADP
iajs-2478	156	354	𝜑	𝜑	X
iajs-2478	156	355	𝑡	𝑡	NOUN
iajs-2478	156	356	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	357	𝑦	𝑦	NOUN
iajs-2478	156	358	,	,	PUNCT
iajs-2478	156	359	𝑣	𝑣	ADP
iajs-2478	156	360	𝜑	𝜑	X
iajs-2478	156	361	𝑡	𝑡	NOUN
iajs-2478	156	362	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	156	363	,	,	PUNCT
iajs-2478	156	364	(	(	PUNCT
iajs-2478	156	365	62	62	NUM
iajs-2478	156	366	)	)	PUNCT
iajs-2478	156	367	since	since	SCONJ
iajs-2478	156	368	𝑦	𝑦	NOUN
iajs-2478	156	369	0	0	NUM
iajs-2478	156	370	is	be	AUX
iajs-2478	156	371	bounded	bound	VERB
iajs-2478	156	372	in	in	ADP
iajs-2478	156	373	𝐿	𝐿	PROPN
iajs-2478	156	374	ω	ω	X
iajs-2478	156	375	∀	∀	X
iajs-2478	156	376	𝑖	𝑖	SYM
iajs-2478	156	377	1,2,3	1,2,3	NUM
iajs-2478	156	378	,	,	PUNCT
iajs-2478	156	379	then	then	ADV
iajs-2478	156	380	𝑦	𝑦	NOUN
iajs-2478	156	381	,	,	PUNCT
iajs-2478	156	382	𝑣	𝑣	PRON
iajs-2478	156	383	𝜑	𝜑	PROPN
iajs-2478	156	384	0	0	NUM
iajs-2478	156	385	⟶	⟶	NOUN
iajs-2478	156	386	𝑦	𝑦	NOUN
iajs-2478	156	387	,	,	PUNCT
iajs-2478	156	388	𝑣	𝑣	PRON
iajs-2478	156	389	𝜑	𝜑	NOUN
iajs-2478	156	390	0	0	NUM
iajs-2478	156	391	,	,	PUNCT
iajs-2478	156	392	(	(	PUNCT
iajs-2478	156	393	63	63	NUM
iajs-2478	156	394	)	)	PUNCT
iajs-2478	156	395	𝑦	𝑦	NOUN
iajs-2478	156	396	,	,	PUNCT
iajs-2478	156	397	𝑣	𝑣	DET
iajs-2478	156	398	𝜑	𝜑	PROPN
iajs-2478	156	399	0	0	NUM
iajs-2478	156	400	⟶	⟶	NOUN
iajs-2478	156	401	𝑦	𝑦	NOUN
iajs-2478	156	402	,	,	PUNCT
iajs-2478	156	403	𝑣	𝑣	PRON
iajs-2478	156	404	𝜑	𝜑	NOUN
iajs-2478	156	405	0	0	NUM
iajs-2478	156	406	,	,	PUNCT
iajs-2478	156	407	(	(	PUNCT
iajs-2478	156	408	64	64	NUM
iajs-2478	156	409	)	)	PUNCT
iajs-2478	156	410	𝑦	𝑦	NOUN
iajs-2478	156	411	,	,	PUNCT
iajs-2478	156	412	𝑣	𝑣	DET
iajs-2478	156	413	𝜑	𝜑	PROPN
iajs-2478	156	414	0	0	NUM
iajs-2478	156	415	⟶	⟶	NOUN
iajs-2478	156	416	𝑦	𝑦	NOUN
iajs-2478	156	417	,	,	PUNCT
iajs-2478	156	418	𝑣	𝑣	DET
iajs-2478	156	419	𝜑	𝜑	NOUN
iajs-2478	156	420	0	0	NUM
iajs-2478	156	421	,	,	PUNCT
iajs-2478	156	422	(	(	PUNCT
iajs-2478	156	423	65	65	NUM
iajs-2478	156	424	)	)	PUNCT
iajs-2478	156	425	and	and	CCONJ
iajs-2478	156	426	since	since	SCONJ
iajs-2478	156	427	𝑢	𝑢	NOUN
iajs-2478	156	428	⟶	⟶	NOUN
iajs-2478	156	429	𝑢	𝑢	NOUN
iajs-2478	156	430	weakly	weakly	ADJ
iajs-2478	156	431	in	in	ADP
iajs-2478	156	432	𝐿	𝐿	PROPN
iajs-2478	156	433	σ	σ	PROPN
iajs-2478	156	434	,	,	PUNCT
iajs-2478	156	435	then	then	ADV
iajs-2478	156	436	  	  	SPACE
iajs-2478	156	437	123	123	NUM
iajs-2478	156	438	ibn	ibn	PROPN
iajs-2478	156	439	al	al	PROPN
iajs-2478	156	440	-	-	PUNCT
iajs-2478	156	441	haitham	haitham	PROPN
iajs-2478	156	442	jour	jour	X
iajs-2478	156	443	.	.	PROPN
iajs-2478	157	1	for	for	ADP
iajs-2478	157	2	pure	pure	ADJ
iajs-2478	157	3	&	&	CCONJ
iajs-2478	157	4	appl	appl	PROPN
iajs-2478	157	5	.	.	PUNCT
iajs-2478	158	1	sci	sci	PROPN
iajs-2478	158	2	.	.	PROPN
iajs-2478	159	1	33	33	NUM
iajs-2478	159	2	(	(	PUNCT
iajs-2478	159	3	3	3	NUM
iajs-2478	159	4	)	)	PUNCT
iajs-2478	159	5	2020	2020	NUM
iajs-2478	160	1	𝑓	𝑓	PRON
iajs-2478	160	2	,	,	PUNCT
iajs-2478	160	3	𝑣	𝑣	PRON
iajs-2478	160	4	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	5	𝑢	𝑢	NOUN
iajs-2478	160	6	,	,	PUNCT
iajs-2478	160	7	𝑣	𝑣	PRON
iajs-2478	160	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	9	→	→	SYM
iajs-2478	160	10	𝑓	𝑓	X
iajs-2478	160	11	,	,	PUNCT
iajs-2478	160	12	𝑣	𝑣	PRON
iajs-2478	160	13	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	14	𝑢	𝑢	NOUN
iajs-2478	160	15	,	,	PUNCT
iajs-2478	160	16	𝑣	𝑣	PRON
iajs-2478	160	17	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	18	,	,	PUNCT
iajs-2478	160	19	(	(	PUNCT
iajs-2478	160	20	66	66	NUM
iajs-2478	160	21	)	)	PUNCT
iajs-2478	160	22	𝑓	𝑓	PRON
iajs-2478	160	23	,	,	PUNCT
iajs-2478	160	24	𝑣	𝑣	PRON
iajs-2478	160	25	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	26	𝑢	𝑢	NOUN
iajs-2478	160	27	,	,	PUNCT
iajs-2478	160	28	𝑣	𝑣	PRON
iajs-2478	160	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	30	→	→	SYM
iajs-2478	160	31	𝑓	𝑓	X
iajs-2478	160	32	,	,	PUNCT
iajs-2478	160	33	𝑣	𝑣	PRON
iajs-2478	160	34	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	35	𝑢	𝑢	NOUN
iajs-2478	160	36	,	,	PUNCT
iajs-2478	160	37	𝑣	𝑣	PRON
iajs-2478	160	38	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	39	,	,	PUNCT
iajs-2478	160	40	(	(	PUNCT
iajs-2478	160	41	67	67	NUM
iajs-2478	160	42	)	)	PUNCT
iajs-2478	160	43	𝑓	𝑓	PROPN
iajs-2478	160	44	,	,	PUNCT
iajs-2478	160	45	𝑣	𝑣	PRON
iajs-2478	160	46	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	47	𝑢	𝑢	NOUN
iajs-2478	160	48	,	,	PUNCT
iajs-2478	160	49	𝑣	𝑣	PRON
iajs-2478	160	50	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	51	→	→	SYM
iajs-2478	160	52	𝑓	𝑓	X
iajs-2478	160	53	,	,	PUNCT
iajs-2478	160	54	𝑣	𝑣	PRON
iajs-2478	160	55	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	56	𝑢	𝑢	NOUN
iajs-2478	160	57	,	,	PUNCT
iajs-2478	160	58	𝑣	𝑣	PRON
iajs-2478	160	59	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	60	,	,	PUNCT
iajs-2478	160	61	(	(	PUNCT
iajs-2478	160	62	68	68	NUM
iajs-2478	160	63	)	)	PUNCT
iajs-2478	160	64	finally	finally	ADV
iajs-2478	160	65	,	,	PUNCT
iajs-2478	160	66	using	use	VERB
iajs-2478	160	67	(	(	PUNCT
iajs-2478	160	68	60	60	NUM
iajs-2478	160	69	)	)	PUNCT
iajs-2478	160	70	62	62	NUM
iajs-2478	160	71	)	)	PUNCT
iajs-2478	160	72	,	,	PUNCT
iajs-2478	160	73	(	(	PUNCT
iajs-2478	160	74	63	63	NUM
iajs-2478	160	75	65),(66	65),(66	NUM
iajs-2478	160	76	68	68	NUM
iajs-2478	160	77	)	)	PUNCT
iajs-2478	160	78	in	in	ADP
iajs-2478	160	79	(	(	PUNCT
iajs-2478	160	80	57	57	NUM
iajs-2478	160	81	59	59	NUM
iajs-2478	160	82	)	)	PUNCT
iajs-2478	160	83	,	,	PUNCT
iajs-2478	160	84	one	one	PRON
iajs-2478	160	85	gets	get	VERB
iajs-2478	160	86	𝑦	𝑦	NOUN
iajs-2478	160	87	,	,	PUNCT
iajs-2478	160	88	𝑣	𝑣	ADP
iajs-2478	160	89	𝜑	𝜑	NOUN
iajs-2478	160	90	´	´	X
iajs-2478	160	91	𝑡	𝑡	NOUN
iajs-2478	160	92	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	93	∇𝑦	∇𝑦	PROPN
iajs-2478	160	94	,	,	PUNCT
iajs-2478	160	95	∇𝑣	∇𝑣	PROPN
iajs-2478	160	96	𝑦	𝑦	PRON
iajs-2478	160	97	,	,	PUNCT
iajs-2478	160	98	𝑣	𝑣	PRON
iajs-2478	160	99	𝜑	𝜑	X
iajs-2478	160	100	𝑡	𝑡	NOUN
iajs-2478	160	101	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	102	𝑦	𝑦	NOUN
iajs-2478	160	103	,	,	PUNCT
iajs-2478	160	104	𝑣	𝑣	ADP
iajs-2478	160	105	𝜑	𝜑	X
iajs-2478	160	106	𝑡	𝑡	NOUN
iajs-2478	160	107	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	108	𝑦	𝑦	NOUN
iajs-2478	160	109	,	,	PUNCT
iajs-2478	160	110	𝑣	𝑣	ADP
iajs-2478	160	111	𝜑	𝜑	X
iajs-2478	160	112	𝑡	𝑡	NOUN
iajs-2478	160	113	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	114	𝑓	𝑓	PRON
iajs-2478	160	115	,	,	PUNCT
iajs-2478	160	116	𝑣	𝑣	DET
iajs-2478	160	117	𝜑	𝜑	X
iajs-2478	160	118	𝑡	𝑡	NOUN
iajs-2478	160	119	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	120	𝑢	𝑢	NOUN
iajs-2478	160	121	,	,	PUNCT
iajs-2478	160	122	𝑣	𝑣	PRON
iajs-2478	160	123	𝜑	𝜑	X
iajs-2478	160	124	𝑡	𝑡	NOUN
iajs-2478	160	125	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	126	𝑦	𝑦	NOUN
iajs-2478	160	127	,	,	PUNCT
iajs-2478	160	128	𝑣	𝑣	PRON
iajs-2478	160	129	𝜑	𝜑	NOUN
iajs-2478	160	130	0	0	NUM
iajs-2478	160	131	,	,	PUNCT
iajs-2478	160	132	(	(	PUNCT
iajs-2478	160	133	69	69	NUM
iajs-2478	160	134	)	)	PUNCT
iajs-2478	160	135	𝑦	𝑦	NOUN
iajs-2478	160	136	,	,	PUNCT
iajs-2478	160	137	𝑣	𝑣	PRON
iajs-2478	160	138	𝜑	𝜑	NOUN
iajs-2478	160	139	´	´	X
iajs-2478	160	140	𝑡	𝑡	NOUN
iajs-2478	160	141	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	142	∇𝑦	∇𝑦	PROPN
iajs-2478	160	143	,	,	PUNCT
iajs-2478	160	144	∇𝑣	∇𝑣	PROPN
iajs-2478	160	145	𝑦	𝑦	PRON
iajs-2478	160	146	,	,	PUNCT
iajs-2478	160	147	𝑣	𝑣	PRON
iajs-2478	160	148	𝜑	𝜑	X
iajs-2478	160	149	𝑡	𝑡	NOUN
iajs-2478	160	150	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	151	𝑦	𝑦	NOUN
iajs-2478	160	152	,	,	PUNCT
iajs-2478	160	153	𝑣	𝑣	ADP
iajs-2478	160	154	𝜑	𝜑	X
iajs-2478	160	155	𝑡	𝑡	NOUN
iajs-2478	160	156	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	157	𝑦	𝑦	NOUN
iajs-2478	160	158	,	,	PUNCT
iajs-2478	160	159	𝑣	𝑣	ADP
iajs-2478	160	160	𝜑	𝜑	X
iajs-2478	160	161	𝑡	𝑡	NOUN
iajs-2478	160	162	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	163	𝑓	𝑓	PRON
iajs-2478	160	164	,	,	PUNCT
iajs-2478	160	165	𝑣	𝑣	DET
iajs-2478	160	166	𝜑	𝜑	X
iajs-2478	160	167	𝑡	𝑡	NOUN
iajs-2478	160	168	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	169	𝑢	𝑢	NOUN
iajs-2478	160	170	,	,	PUNCT
iajs-2478	160	171	𝑣	𝑣	PRON
iajs-2478	160	172	𝜑	𝜑	X
iajs-2478	160	173	𝑡	𝑡	NOUN
iajs-2478	160	174	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	175	𝑦	𝑦	NOUN
iajs-2478	160	176	,	,	PUNCT
iajs-2478	160	177	𝑣	𝑣	PRON
iajs-2478	160	178	𝜑	𝜑	NOUN
iajs-2478	160	179	0	0	NUM
iajs-2478	160	180	,	,	PUNCT
iajs-2478	160	181	(	(	PUNCT
iajs-2478	160	182	70	70	NUM
iajs-2478	160	183	)	)	PUNCT
iajs-2478	160	184	𝑦	𝑦	NOUN
iajs-2478	160	185	,	,	PUNCT
iajs-2478	160	186	𝑣	𝑣	PRON
iajs-2478	160	187	𝜑	𝜑	NOUN
iajs-2478	160	188	´	´	X
iajs-2478	160	189	𝑡	𝑡	NOUN
iajs-2478	160	190	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	191	∇𝑦	∇𝑦	PROPN
iajs-2478	160	192	,	,	PUNCT
iajs-2478	160	193	∇𝑣	∇𝑣	PROPN
iajs-2478	160	194	𝑦	𝑦	PRON
iajs-2478	160	195	,	,	PUNCT
iajs-2478	160	196	𝑣	𝑣	PRON
iajs-2478	160	197	𝜑	𝜑	X
iajs-2478	160	198	𝑡	𝑡	NOUN
iajs-2478	160	199	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	200	𝑦	𝑦	NOUN
iajs-2478	160	201	,	,	PUNCT
iajs-2478	160	202	𝑣	𝑣	ADP
iajs-2478	160	203	𝜑	𝜑	X
iajs-2478	160	204	𝑡	𝑡	NOUN
iajs-2478	160	205	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	206	𝑦	𝑦	NOUN
iajs-2478	160	207	,	,	PUNCT
iajs-2478	160	208	𝑣	𝑣	ADP
iajs-2478	160	209	𝜑	𝜑	X
iajs-2478	160	210	𝑡	𝑡	NOUN
iajs-2478	160	211	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	212	𝑓	𝑓	PRON
iajs-2478	160	213	,	,	PUNCT
iajs-2478	160	214	𝑣	𝑣	DET
iajs-2478	160	215	𝜑	𝜑	X
iajs-2478	160	216	𝑡	𝑡	NOUN
iajs-2478	160	217	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	218	𝑢	𝑢	NOUN
iajs-2478	160	219	,	,	PUNCT
iajs-2478	160	220	𝑣	𝑣	PRON
iajs-2478	160	221	𝜑	𝜑	X
iajs-2478	160	222	𝑡	𝑡	NOUN
iajs-2478	160	223	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	160	224	𝑦	𝑦	NOUN
iajs-2478	160	225	,	,	PUNCT
iajs-2478	160	226	𝑣	𝑣	DET
iajs-2478	160	227	𝜑	𝜑	NOUN
iajs-2478	160	228	0	0	NUM
iajs-2478	160	229	,	,	PUNCT
iajs-2478	160	230	(	(	PUNCT
iajs-2478	160	231	71	71	NUM
iajs-2478	160	232	)	)	PUNCT
iajs-2478	160	233	case1	case1	PROPN
iajs-2478	160	234	:	:	PUNCT
iajs-2478	160	235	we	we	PRON
iajs-2478	160	236	choose	choose	VERB
iajs-2478	160	237	𝜑	𝜑	PRON
iajs-2478	160	238	∈	∈	PROPN
iajs-2478	160	239	𝐷	𝐷	PROPN
iajs-2478	160	240	0	0	NUM
iajs-2478	160	241	,	,	PUNCT
iajs-2478	160	242	𝑇	𝑇	PROPN
iajs-2478	160	243	,	,	PUNCT
iajs-2478	160	244	i.e.	i.e.	X
iajs-2478	160	245	𝜑	𝜑	NOUN
iajs-2478	160	246	0	0	PUNCT
iajs-2478	160	247	𝜑	𝜑	PROPN
iajs-2478	160	248	𝑇	𝑇	PROPN
iajs-2478	160	249	0	0	NUM
iajs-2478	160	250	,	,	PUNCT
iajs-2478	160	251	∀𝑖	∀𝑖	PROPN
iajs-2478	160	252	1,2,3	1,2,3	NUM
iajs-2478	160	253	,	,	PUNCT
iajs-2478	160	254	now	now	ADV
iajs-2478	160	255	by	by	ADP
iajs-2478	160	256	using	use	VERB
iajs-2478	160	257	integration	integration	NOUN
iajs-2478	160	258	by	by	ADP
iajs-2478	160	259	parts	part	NOUN
iajs-2478	160	260	for	for	ADP
iajs-2478	160	261	the	the	DET
iajs-2478	160	262	1	1	NUM
iajs-2478	160	263	terms	term	NOUN
iajs-2478	160	264	in	in	ADP
iajs-2478	160	265	the	the	DET
iajs-2478	160	266	l.h.s	l.h.s	NOUN
iajs-2478	160	267	.	.	PUNCT
iajs-2478	161	1	of	of	ADP
iajs-2478	161	2	(	(	PUNCT
iajs-2478	161	3	69	69	NUM
iajs-2478	161	4	71	71	NUM
iajs-2478	161	5	)	)	PUNCT
iajs-2478	161	6	,	,	PUNCT
iajs-2478	161	7	one	one	PRON
iajs-2478	161	8	gets	get	VERB
iajs-2478	161	9	〈	〈	PROPN
iajs-2478	161	10	𝑦	𝑦	NOUN
iajs-2478	161	11	,	,	PUNCT
iajs-2478	161	12	𝑣	𝑣	PRON
iajs-2478	161	13	〉	〉	NOUN
iajs-2478	161	14	𝜑	𝜑	NOUN
iajs-2478	161	15	𝑡	𝑡	NOUN
iajs-2478	161	16	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	17	∇𝑦	∇𝑦	PROPN
iajs-2478	161	18	,	,	PUNCT
iajs-2478	161	19	∇𝑣	∇𝑣	PROPN
iajs-2478	161	20	𝑦	𝑦	PRON
iajs-2478	161	21	,	,	PUNCT
iajs-2478	161	22	𝑣	𝑣	PRON
iajs-2478	161	23	𝜑	𝜑	X
iajs-2478	161	24	𝑡	𝑡	NOUN
iajs-2478	161	25	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	26	𝑦	𝑦	NOUN
iajs-2478	161	27	,	,	PUNCT
iajs-2478	161	28	𝑣	𝑣	ADP
iajs-2478	161	29	𝜑	𝜑	X
iajs-2478	161	30	𝑡	𝑡	NOUN
iajs-2478	161	31	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	32	𝑦	𝑦	NOUN
iajs-2478	161	33	,	,	PUNCT
iajs-2478	161	34	𝑣	𝑣	ADP
iajs-2478	161	35	𝜑	𝜑	X
iajs-2478	161	36	𝑡	𝑡	NOUN
iajs-2478	161	37	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	38	𝑓	𝑓	PRON
iajs-2478	161	39	,	,	PUNCT
iajs-2478	161	40	𝑣	𝑣	DET
iajs-2478	161	41	𝜑	𝜑	X
iajs-2478	161	42	𝑡	𝑡	NOUN
iajs-2478	161	43	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	44	𝑢	𝑢	NOUN
iajs-2478	161	45	,	,	PUNCT
iajs-2478	161	46	𝑣	𝑣	DET
iajs-2478	161	47	𝜑	𝜑	X
iajs-2478	161	48	𝑡	𝑡	NOUN
iajs-2478	161	49	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	161	50	,	,	PUNCT
iajs-2478	161	51	∀𝑣	∀𝑣	PROPN
iajs-2478	161	52	∈	∈	PROPN
iajs-2478	161	53	𝑉	𝑉	PROPN
iajs-2478	161	54	,	,	PUNCT
iajs-2478	161	55	∀𝜑	∀𝜑	NUM
iajs-2478	161	56	∈	∈	PROPN
iajs-2478	161	57	𝐷	𝐷	PROPN
iajs-2478	161	58	0	0	NUM
iajs-2478	161	59	,	,	PUNCT
iajs-2478	161	60	𝑇	𝑇	PROPN
iajs-2478	161	61	(	(	PUNCT
iajs-2478	161	62	72	72	NUM
iajs-2478	161	63	)	)	PUNCT
iajs-2478	162	1	〈	〈	NOUN
iajs-2478	162	2	𝑦	𝑦	NOUN
iajs-2478	162	3	,	,	PUNCT
iajs-2478	162	4	𝑣	𝑣	PRON
iajs-2478	162	5	〉	〉	NOUN
iajs-2478	162	6	𝜑	𝜑	NOUN
iajs-2478	162	7	𝑡	𝑡	NOUN
iajs-2478	162	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	9	∇𝑦	∇𝑦	PROPN
iajs-2478	162	10	,	,	PUNCT
iajs-2478	162	11	∇𝑣	∇𝑣	PROPN
iajs-2478	162	12	𝑦	𝑦	PRON
iajs-2478	162	13	,	,	PUNCT
iajs-2478	162	14	𝑣	𝑣	DET
iajs-2478	162	15	𝜑	𝜑	X
iajs-2478	162	16	𝑡	𝑡	NOUN
iajs-2478	162	17	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	18	𝑦	𝑦	NOUN
iajs-2478	162	19	,	,	PUNCT
iajs-2478	162	20	𝑣	𝑣	ADP
iajs-2478	162	21	𝜑	𝜑	X
iajs-2478	162	22	𝑡	𝑡	NOUN
iajs-2478	162	23	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	24	𝑦	𝑦	NOUN
iajs-2478	162	25	,	,	PUNCT
iajs-2478	162	26	𝑣	𝑣	ADP
iajs-2478	162	27	𝜑	𝜑	X
iajs-2478	162	28	𝑡	𝑡	NOUN
iajs-2478	162	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	30	𝑓	𝑓	PRON
iajs-2478	162	31	,	,	PUNCT
iajs-2478	162	32	𝑣	𝑣	DET
iajs-2478	162	33	𝜑	𝜑	X
iajs-2478	162	34	𝑡	𝑡	NOUN
iajs-2478	162	35	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	36	𝑢	𝑢	NOUN
iajs-2478	162	37	,	,	PUNCT
iajs-2478	162	38	𝑣	𝑣	PRON
iajs-2478	162	39	𝜑	𝜑	X
iajs-2478	162	40	𝑡	𝑡	NOUN
iajs-2478	162	41	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	162	42	,	,	PUNCT
iajs-2478	162	43	∀𝑣	∀𝑣	PROPN
iajs-2478	162	44	∈	∈	PROPN
iajs-2478	162	45	𝑉	𝑉	PROPN
iajs-2478	162	46	,	,	PUNCT
iajs-2478	162	47	∀𝜑	∀𝜑	NUM
iajs-2478	162	48	∈	∈	PROPN
iajs-2478	162	49	𝐷	𝐷	PROPN
iajs-2478	162	50	0	0	NUM
iajs-2478	162	51	,	,	PUNCT
iajs-2478	162	52	𝑇	𝑇	PROPN
iajs-2478	162	53	(	(	PUNCT
iajs-2478	162	54	73	73	NUM
iajs-2478	162	55	)	)	PUNCT
iajs-2478	163	1	〈	〈	NOUN
iajs-2478	163	2	𝑦	𝑦	NOUN
iajs-2478	163	3	,	,	PUNCT
iajs-2478	163	4	𝑣	𝑣	PRON
iajs-2478	163	5	〉	〉	NOUN
iajs-2478	163	6	𝜑	𝜑	NOUN
iajs-2478	163	7	𝑡	𝑡	NOUN
iajs-2478	163	8	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	9	∇𝑦	∇𝑦	PROPN
iajs-2478	163	10	,	,	PUNCT
iajs-2478	163	11	∇𝑣	∇𝑣	PROPN
iajs-2478	163	12	𝑦	𝑦	PRON
iajs-2478	163	13	,	,	PUNCT
iajs-2478	163	14	𝑣	𝑣	DET
iajs-2478	163	15	𝜑	𝜑	X
iajs-2478	163	16	𝑡	𝑡	NOUN
iajs-2478	163	17	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	18	𝑦	𝑦	NOUN
iajs-2478	163	19	,	,	PUNCT
iajs-2478	163	20	𝑣	𝑣	ADP
iajs-2478	163	21	𝜑	𝜑	X
iajs-2478	163	22	𝑡	𝑡	NOUN
iajs-2478	163	23	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	24	𝑦	𝑦	NOUN
iajs-2478	163	25	,	,	PUNCT
iajs-2478	163	26	𝑣	𝑣	ADP
iajs-2478	163	27	𝜑	𝜑	X
iajs-2478	163	28	𝑡	𝑡	NOUN
iajs-2478	163	29	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	30	𝑓	𝑓	PRON
iajs-2478	163	31	,	,	PUNCT
iajs-2478	163	32	𝑣	𝑣	DET
iajs-2478	163	33	𝜑	𝜑	X
iajs-2478	163	34	𝑡	𝑡	NOUN
iajs-2478	163	35	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	36	𝑢	𝑢	NOUN
iajs-2478	163	37	,	,	PUNCT
iajs-2478	163	38	𝑣	𝑣	PRON
iajs-2478	163	39	𝜑	𝜑	PROPN
iajs-2478	163	40	𝑡	𝑡	PROPN
iajs-2478	163	41	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	163	42	,	,	PUNCT
iajs-2478	163	43	∀𝑣	∀𝑣	PROPN
iajs-2478	163	44	∈	∈	PROPN
iajs-2478	163	45	𝑉	𝑉	PROPN
iajs-2478	163	46	,	,	PUNCT
iajs-2478	163	47	∀𝜑	∀𝜑	NUM
iajs-2478	163	48	∈	∈	PROPN
iajs-2478	163	49	𝐷	𝐷	PROPN
iajs-2478	163	50	0	0	NUM
iajs-2478	163	51	,	,	PUNCT
iajs-2478	163	52	𝑇	𝑇	PROPN
iajs-2478	163	53	(	(	PUNCT
iajs-2478	163	54	74	74	NUM
iajs-2478	163	55	)	)	PUNCT
iajs-2478	163	56	then	then	ADV
iajs-2478	163	57	〈	〈	PROPN
iajs-2478	163	58	𝑦	𝑦	NOUN
iajs-2478	163	59	,	,	PUNCT
iajs-2478	163	60	𝑣	𝑣	ADP
iajs-2478	163	61	〉	〉	NOUN
iajs-2478	163	62	∇𝑦	∇𝑦	PROPN
iajs-2478	163	63	,	,	PUNCT
iajs-2478	163	64	∇𝑣	∇𝑣	PROPN
iajs-2478	163	65	𝑦	𝑦	PRON
iajs-2478	163	66	,	,	PUNCT
iajs-2478	163	67	𝑣	𝑣	DET
iajs-2478	163	68	𝑦	𝑦	NOUN
iajs-2478	163	69	,	,	PUNCT
iajs-2478	163	70	𝑣	𝑣	PRON
iajs-2478	163	71	𝑦	𝑦	NOUN
iajs-2478	163	72	,	,	PUNCT
iajs-2478	163	73	𝑣	𝑣	DET
iajs-2478	163	74	𝑓	𝑓	X
iajs-2478	163	75	,	,	PUNCT
iajs-2478	163	76	𝑣	𝑣	PRON
iajs-2478	163	77	𝑢	𝑢	X
iajs-2478	163	78	,	,	PUNCT
iajs-2478	163	79	𝑣	𝑣	INTJ
iajs-2478	163	80	,	,	PUNCT
iajs-2478	163	81	∀𝑣	∀𝑣	PROPN
iajs-2478	163	82	∈	∈	PROPN
iajs-2478	163	83	𝑉	𝑉	PROPN
iajs-2478	163	84	,	,	PUNCT
iajs-2478	163	85	a.e	a.e	PROPN
iajs-2478	163	86	.	.	PROPN
iajs-2478	164	1	on	on	ADP
iajs-2478	164	2	ĩ	ĩ	ADP
iajs-2478	164	3	〈	〈	NOUN
iajs-2478	164	4	𝑦	𝑦	NOUN
iajs-2478	164	5	,	,	PUNCT
iajs-2478	164	6	𝑣	𝑣	ADP
iajs-2478	164	7	〉	〉	NOUN
iajs-2478	164	8	∇𝑦	∇𝑦	PROPN
iajs-2478	164	9	,	,	PUNCT
iajs-2478	164	10	∇𝑣	∇𝑣	PROPN
iajs-2478	164	11	𝑦	𝑦	PRON
iajs-2478	164	12	,	,	PUNCT
iajs-2478	164	13	𝑣	𝑣	DET
iajs-2478	164	14	𝑦	𝑦	NOUN
iajs-2478	164	15	,	,	PUNCT
iajs-2478	164	16	𝑣	𝑣	PRON
iajs-2478	164	17	𝑦	𝑦	NOUN
iajs-2478	164	18	,	,	PUNCT
iajs-2478	164	19	𝑣	𝑣	DET
iajs-2478	164	20	𝑓	𝑓	X
iajs-2478	164	21	,	,	PUNCT
iajs-2478	164	22	𝑣	𝑣	PRON
iajs-2478	164	23	𝑢	𝑢	X
iajs-2478	164	24	,	,	PUNCT
iajs-2478	164	25	𝑣	𝑣	INTJ
iajs-2478	164	26	,	,	PUNCT
iajs-2478	164	27	∀𝑣	∀𝑣	PROPN
iajs-2478	164	28	∈	∈	PROPN
iajs-2478	164	29	𝑉	𝑉	PROPN
iajs-2478	164	30	,	,	PUNCT
iajs-2478	164	31	a.e	a.e	PROPN
iajs-2478	164	32	.	.	PROPN
iajs-2478	164	33	on	on	ADP
iajs-2478	164	34	ĩ	ĩ	ADP
iajs-2478	164	35	〈	〈	NOUN
iajs-2478	164	36	𝑦	𝑦	NOUN
iajs-2478	164	37	,	,	PUNCT
iajs-2478	164	38	𝑣	𝑣	ADP
iajs-2478	164	39	〉	〉	NOUN
iajs-2478	164	40	∇𝑦	∇𝑦	PROPN
iajs-2478	164	41	,	,	PUNCT
iajs-2478	164	42	∇𝑣	∇𝑣	PROPN
iajs-2478	164	43	𝑦	𝑦	PRON
iajs-2478	164	44	,	,	PUNCT
iajs-2478	164	45	𝑣	𝑣	DET
iajs-2478	164	46	𝑦	𝑦	NOUN
iajs-2478	164	47	,	,	PUNCT
iajs-2478	164	48	𝑣	𝑣	PRON
iajs-2478	164	49	𝑦	𝑦	NOUN
iajs-2478	164	50	,	,	PUNCT
iajs-2478	164	51	𝑣	𝑣	DET
iajs-2478	164	52	𝑓	𝑓	X
iajs-2478	164	53	,	,	PUNCT
iajs-2478	164	54	𝑣	𝑣	PRON
iajs-2478	164	55	𝑢	𝑢	X
iajs-2478	164	56	,	,	PUNCT
iajs-2478	164	57	𝑣	𝑣	INTJ
iajs-2478	164	58	,	,	PUNCT
iajs-2478	164	59	∀𝑣	∀𝑣	PROPN
iajs-2478	164	60	∈	∈	PROPN
iajs-2478	164	61	𝑉	𝑉	PROPN
iajs-2478	164	62	,	,	PUNCT
iajs-2478	164	63	a.e	a.e	PROPN
iajs-2478	164	64	.	.	PROPN
iajs-2478	165	1	on	on	ADP
iajs-2478	165	2	ĩ	ĩ	DET
iajs-2478	165	3	i.e.	i.e.	X
iajs-2478	165	4	�	�	NOUN
iajs-2478	165	5	⃗	⃗	NOUN
iajs-2478	165	6	�	�	PROPN
iajs-2478	165	7	is	be	AUX
iajs-2478	165	8	satisfied	satisfied	ADJ
iajs-2478	165	9	the	the	DET
iajs-2478	165	10	wf	wf	PROPN
iajs-2478	165	11	of	of	ADP
iajs-2478	165	12	the	the	DET
iajs-2478	165	13	tses	tse	NOUN
iajs-2478	165	14	.	.	PUNCT
iajs-2478	166	1	case2	case2	PROPN
iajs-2478	166	2	:	:	PUNCT
iajs-2478	166	3	we	we	PRON
iajs-2478	166	4	choose	choose	VERB
iajs-2478	166	5	𝜑	𝜑	PRON
iajs-2478	166	6	∈	∈	PROPN
iajs-2478	166	7	𝐶	𝐶	PROPN
iajs-2478	166	8	ĩ	ĩ	PROPN
iajs-2478	166	9	,	,	PUNCT
iajs-2478	166	10	s.t	s.t	PROPN
iajs-2478	167	1	.	.	PROPN
iajs-2478	167	2	𝜑	𝜑	PROPN
iajs-2478	167	3	𝑇	𝑇	PROPN
iajs-2478	167	4	0	0	NUM
iajs-2478	167	5	&	&	CCONJ
iajs-2478	167	6	𝜑	𝜑	PROPN
iajs-2478	167	7	0	0	NUM
iajs-2478	167	8	0	0	NUM
iajs-2478	167	9	,	,	PUNCT
iajs-2478	167	10	∀𝑖	∀𝑖	PROPN
iajs-2478	167	11	1,2,3	1,2,3	NUM
iajs-2478	167	12	,	,	PUNCT
iajs-2478	167	13	by	by	ADP
iajs-2478	167	14	using	use	VERB
iajs-2478	167	15	integration	integration	NOUN
iajs-2478	167	16	by	by	ADP
iajs-2478	167	17	parts	part	NOUN
iajs-2478	167	18	for	for	ADP
iajs-2478	167	19	the	the	DET
iajs-2478	167	20	1	1	NUM
iajs-2478	167	21	terms	term	NOUN
iajs-2478	167	22	in	in	ADP
iajs-2478	167	23	the	the	DET
iajs-2478	167	24	l.h.s	l.h.s	NOUN
iajs-2478	167	25	.	.	PUNCT
iajs-2478	168	1	of	of	ADP
iajs-2478	168	2	(	(	PUNCT
iajs-2478	168	3	72	72	NUM
iajs-2478	168	4	74	74	NUM
iajs-2478	168	5	)	)	PUNCT
iajs-2478	168	6	,	,	PUNCT
iajs-2478	168	7	one	one	PRON
iajs-2478	168	8	has	have	VERB
iajs-2478	168	9	𝑦	𝑦	PRON
iajs-2478	168	10	,	,	PUNCT
iajs-2478	168	11	𝑣	𝑣	ADP
iajs-2478	168	12	𝜑	𝜑	NOUN
iajs-2478	168	13	´	´	X
iajs-2478	168	14	𝑡	𝑡	NOUN
iajs-2478	168	15	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	16	∇𝑦	∇𝑦	PROPN
iajs-2478	168	17	,	,	PUNCT
iajs-2478	168	18	∇𝑣	∇𝑣	PROPN
iajs-2478	168	19	𝑦	𝑦	PRON
iajs-2478	168	20	,	,	PUNCT
iajs-2478	168	21	𝑣	𝑣	DET
iajs-2478	168	22	𝜑	𝜑	X
iajs-2478	168	23	𝑡	𝑡	NOUN
iajs-2478	168	24	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	25	𝑦	𝑦	NOUN
iajs-2478	168	26	,	,	PUNCT
iajs-2478	168	27	𝑣	𝑣	ADP
iajs-2478	168	28	𝜑	𝜑	X
iajs-2478	168	29	𝑡	𝑡	NOUN
iajs-2478	168	30	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	31	𝑦	𝑦	NOUN
iajs-2478	168	32	,	,	PUNCT
iajs-2478	168	33	𝑣	𝑣	ADP
iajs-2478	168	34	𝜑	𝜑	X
iajs-2478	168	35	𝑡	𝑡	NOUN
iajs-2478	168	36	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	37	𝑓	𝑓	PRON
iajs-2478	168	38	,	,	PUNCT
iajs-2478	168	39	𝑣	𝑣	DET
iajs-2478	168	40	𝜑	𝜑	X
iajs-2478	168	41	𝑡	𝑡	NOUN
iajs-2478	168	42	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	43	𝑢	𝑢	NOUN
iajs-2478	168	44	,	,	PUNCT
iajs-2478	168	45	𝑣	𝑣	PRON
iajs-2478	168	46	𝜑	𝜑	X
iajs-2478	168	47	𝑡	𝑡	NOUN
iajs-2478	168	48	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	49	𝑦	𝑦	NOUN
iajs-2478	168	50	0	0	NUM
iajs-2478	168	51	,	,	PUNCT
iajs-2478	168	52	𝑣	𝑣	PRON
iajs-2478	168	53	𝜑	𝜑	NOUN
iajs-2478	168	54	0	0	NUM
iajs-2478	168	55	,	,	PUNCT
iajs-2478	168	56	(	(	PUNCT
iajs-2478	168	57	75	75	NUM
iajs-2478	168	58	)	)	PUNCT
iajs-2478	168	59	𝑦	𝑦	NOUN
iajs-2478	168	60	,	,	PUNCT
iajs-2478	168	61	𝑣	𝑣	PRON
iajs-2478	168	62	𝜑	𝜑	NOUN
iajs-2478	168	63	´	´	X
iajs-2478	168	64	𝑡	𝑡	NOUN
iajs-2478	168	65	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	66	∇𝑦	∇𝑦	PROPN
iajs-2478	168	67	,	,	PUNCT
iajs-2478	168	68	∇𝑣	∇𝑣	PROPN
iajs-2478	168	69	𝑦	𝑦	PRON
iajs-2478	168	70	,	,	PUNCT
iajs-2478	168	71	𝑣	𝑣	PRON
iajs-2478	168	72	𝜑	𝜑	X
iajs-2478	168	73	𝑡	𝑡	NOUN
iajs-2478	168	74	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	75	𝑦	𝑦	NOUN
iajs-2478	168	76	,	,	PUNCT
iajs-2478	168	77	𝑣	𝑣	ADP
iajs-2478	168	78	𝜑	𝜑	X
iajs-2478	168	79	𝑡	𝑡	NOUN
iajs-2478	168	80	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	81	𝑦	𝑦	NOUN
iajs-2478	168	82	,	,	PUNCT
iajs-2478	168	83	𝑣	𝑣	ADP
iajs-2478	168	84	𝜑	𝜑	X
iajs-2478	168	85	𝑡	𝑡	NOUN
iajs-2478	168	86	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	87	𝑓	𝑓	PRON
iajs-2478	168	88	,	,	PUNCT
iajs-2478	168	89	𝑣	𝑣	DET
iajs-2478	168	90	𝜑	𝜑	X
iajs-2478	168	91	𝑡	𝑡	NOUN
iajs-2478	168	92	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	93	𝑢	𝑢	NOUN
iajs-2478	168	94	,	,	PUNCT
iajs-2478	168	95	𝑣	𝑣	PRON
iajs-2478	168	96	𝜑	𝜑	X
iajs-2478	168	97	𝑡	𝑡	NOUN
iajs-2478	168	98	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	99	𝑦	𝑦	NOUN
iajs-2478	168	100	0	0	NUM
iajs-2478	168	101	,	,	PUNCT
iajs-2478	168	102	𝑣	𝑣	DET
iajs-2478	168	103	𝜑	𝜑	NOUN
iajs-2478	168	104	0	0	NUM
iajs-2478	168	105	,	,	PUNCT
iajs-2478	168	106	(	(	PUNCT
iajs-2478	168	107	76	76	NUM
iajs-2478	168	108	)	)	PUNCT
iajs-2478	168	109	𝑦	𝑦	NOUN
iajs-2478	168	110	,	,	PUNCT
iajs-2478	168	111	𝑣	𝑣	PRON
iajs-2478	168	112	𝜑	𝜑	NOUN
iajs-2478	168	113	´	´	X
iajs-2478	168	114	𝑡	𝑡	NOUN
iajs-2478	168	115	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	116	∇𝑦	∇𝑦	PROPN
iajs-2478	168	117	,	,	PUNCT
iajs-2478	168	118	∇𝑣	∇𝑣	PROPN
iajs-2478	168	119	𝑦	𝑦	PRON
iajs-2478	168	120	,	,	PUNCT
iajs-2478	168	121	𝑣	𝑣	PRON
iajs-2478	168	122	𝜑	𝜑	X
iajs-2478	168	123	𝑡	𝑡	NOUN
iajs-2478	168	124	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	125	𝑦	𝑦	NOUN
iajs-2478	168	126	,	,	PUNCT
iajs-2478	168	127	𝑣	𝑣	ADP
iajs-2478	168	128	𝜑	𝜑	X
iajs-2478	168	129	𝑡	𝑡	NOUN
iajs-2478	168	130	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	131	𝑦	𝑦	NOUN
iajs-2478	168	132	,	,	PUNCT
iajs-2478	168	133	𝑣	𝑣	ADP
iajs-2478	168	134	𝜑	𝜑	X
iajs-2478	168	135	𝑡	𝑡	NOUN
iajs-2478	168	136	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	137	𝑓	𝑓	PRON
iajs-2478	168	138	,	,	PUNCT
iajs-2478	168	139	𝑣	𝑣	DET
iajs-2478	168	140	𝜑	𝜑	X
iajs-2478	168	141	𝑡	𝑡	NOUN
iajs-2478	168	142	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	143	𝑢	𝑢	NOUN
iajs-2478	168	144	,	,	PUNCT
iajs-2478	168	145	𝑣	𝑣	PRON
iajs-2478	168	146	𝜑	𝜑	X
iajs-2478	168	147	𝑡	𝑡	NOUN
iajs-2478	168	148	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	168	149	𝑦	𝑦	NOUN
iajs-2478	168	150	0	0	NUM
iajs-2478	168	151	,	,	PUNCT
iajs-2478	168	152	𝑣	𝑣	DET
iajs-2478	168	153	𝜑	𝜑	NOUN
iajs-2478	168	154	0	0	NUM
iajs-2478	168	155	,	,	PUNCT
iajs-2478	168	156	(	(	PUNCT
iajs-2478	168	157	77	77	NUM
iajs-2478	168	158	)	)	PUNCT
iajs-2478	168	159	and	and	CCONJ
iajs-2478	168	160	subtracting	subtract	VERB
iajs-2478	168	161	(	(	PUNCT
iajs-2478	168	162	75	75	NUM
iajs-2478	168	163	77	77	NUM
iajs-2478	168	164	)	)	PUNCT
iajs-2478	168	165	from	from	ADP
iajs-2478	168	166	(	(	PUNCT
iajs-2478	168	167	69	69	NUM
iajs-2478	168	168	71	71	NUM
iajs-2478	168	169	)	)	PUNCT
iajs-2478	168	170	respectively	respectively	ADV
iajs-2478	168	171	,	,	PUNCT
iajs-2478	168	172	one	one	PRON
iajs-2478	168	173	gets	get	VERB
iajs-2478	168	174	𝑦	𝑦	NOUN
iajs-2478	168	175	,	,	PUNCT
iajs-2478	168	176	𝑣	𝑣	PRON
iajs-2478	168	177	𝜑	𝜑	NOUN
iajs-2478	168	178	0	0	NUM
iajs-2478	168	179	𝑦	𝑦	NOUN
iajs-2478	168	180	0	0	NUM
iajs-2478	168	181	,	,	PUNCT
iajs-2478	168	182	𝑣	𝑣	DET
iajs-2478	168	183	𝜑	𝜑	NOUN
iajs-2478	168	184	0	0	NUM
iajs-2478	168	185	,	,	PUNCT
iajs-2478	168	186	𝜑	𝜑	PROPN
iajs-2478	168	187	0	0	NUM
iajs-2478	168	188	0	0	NUM
iajs-2478	168	189	,	,	PUNCT
iajs-2478	168	190	∀	∀	X
iajs-2478	168	191	𝜑	𝜑	PART
iajs-2478	168	192	∈	∈	PROPN
iajs-2478	168	193	𝐷	𝐷	PROPN
iajs-2478	168	194	0	0	NUM
iajs-2478	168	195	,	,	PUNCT
iajs-2478	168	196	𝑇	𝑇	PROPN
iajs-2478	168	197	⇒	⇒	VERB
iajs-2478	168	198	𝑦	𝑦	PRON
iajs-2478	168	199	𝑦	𝑦	NOUN
iajs-2478	168	200	0	0	NUM
iajs-2478	168	201	𝑦	𝑦	SYM
iajs-2478	168	202	𝑥	𝑥	X
iajs-2478	168	203	,	,	PUNCT
iajs-2478	168	204	by	by	ADP
iajs-2478	168	205	the	the	DET
iajs-2478	168	206	same	same	ADJ
iajs-2478	168	207	above	above	ADP
iajs-2478	168	208	way	way	NOUN
iajs-2478	168	209	one	one	PRON
iajs-2478	168	210	can	can	AUX
iajs-2478	168	211	show	show	VERB
iajs-2478	168	212	that	that	SCONJ
iajs-2478	168	213	𝑦	𝑦	PRON
iajs-2478	168	214	𝑦	𝑦	NOUN
iajs-2478	168	215	0	0	NUM
iajs-2478	168	216	𝑦	𝑦	SYM
iajs-2478	168	217	𝑥	𝑥	PROPN
iajs-2478	168	218	and	and	CCONJ
iajs-2478	168	219	𝑦	𝑦	NOUN
iajs-2478	168	220	𝑦	𝑦	NOUN
iajs-2478	168	221	0	0	NUM
iajs-2478	168	222	𝑦	𝑦	SYM
iajs-2478	168	223	𝑥	𝑥	NOUN
iajs-2478	168	224	.	.	PUNCT
iajs-2478	169	1	then	then	ADV
iajs-2478	169	2	�	�	PROPN
iajs-2478	169	3	⃗	⃗	NOUN
iajs-2478	169	4	�	�	PROPN
iajs-2478	169	5	is	be	AUX
iajs-2478	169	6	a	a	DET
iajs-2478	169	7	solutions	solution	NOUN
iajs-2478	169	8	of	of	ADP
iajs-2478	169	9	the	the	DET
iajs-2478	169	10	wf	wf	PROPN
iajs-2478	169	11	of	of	ADP
iajs-2478	169	12	the	the	DET
iajs-2478	169	13	tses	tse	NOUN
iajs-2478	169	14	,	,	PUNCT
iajs-2478	169	15	since	since	SCONJ
iajs-2478	169	16	𝐺	𝐺	PROPN
iajs-2478	169	17	𝑢	𝑢	PROPN
iajs-2478	169	18	is	be	AUX
iajs-2478	169	19	w.l.s.c	w.l.s.c	PROPN
iajs-2478	169	20	.	.	PUNCT
iajs-2478	169	21	from	from	ADP
iajs-2478	169	22	lemma	lemma	PROPN
iajs-2478	169	23	4.2	4.2	NUM
iajs-2478	169	24	and	and	CCONJ
iajs-2478	169	25	𝑢	𝑢	NOUN
iajs-2478	169	26	⟶	⟶	NOUN
iajs-2478	169	27	𝑢	𝑢	X
iajs-2478	169	28	weakly	weakly	ADJ
iajs-2478	169	29	in	in	ADP
iajs-2478	169	30	𝐿	𝐿	PROPN
iajs-2478	169	31	σ	σ	PROPN
iajs-2478	169	32	,	,	PUNCT
iajs-2478	169	33	then	then	ADV
iajs-2478	169	34	  	  	SPACE
iajs-2478	169	35	124	124	NUM
iajs-2478	169	36	ibn	ibn	PROPN
iajs-2478	169	37	al	al	PROPN
iajs-2478	169	38	-	-	PUNCT
iajs-2478	169	39	haitham	haitham	PROPN
iajs-2478	169	40	jour	jour	X
iajs-2478	169	41	.	.	PROPN
iajs-2478	170	1	for	for	ADP
iajs-2478	170	2	pure	pure	ADJ
iajs-2478	170	3	&	&	CCONJ
iajs-2478	170	4	appl	appl	PROPN
iajs-2478	170	5	.	.	PUNCT
iajs-2478	171	1	sci	sci	PROPN
iajs-2478	171	2	.	.	PROPN
iajs-2478	172	1	33	33	NUM
iajs-2478	172	2	(	(	PUNCT
iajs-2478	172	3	3	3	NUM
iajs-2478	172	4	)	)	PUNCT
iajs-2478	172	5	2020	2020	NUM
iajs-2478	173	1	𝐺	𝐺	PROPN
iajs-2478	173	2	𝑢	𝑢	PROPN
iajs-2478	173	3	lim	lim	PROPN
iajs-2478	173	4	→	→	SYM
iajs-2478	173	5	inf	inf	PROPN
iajs-2478	173	6	⃗	⃗	PROPN
iajs-2478	173	7	∈	∈	PROPN
iajs-2478	173	8	⃗	⃗	PROPN
iajs-2478	173	9	𝐺	𝐺	PROPN
iajs-2478	173	10	𝑢	𝑢	PROPN
iajs-2478	173	11	lim	lim	PROPN
iajs-2478	173	12	→	→	SYM
iajs-2478	173	13	𝐺	𝐺	PROPN
iajs-2478	173	14	𝑢	𝑢	PROPN
iajs-2478	173	15	inf	inf	PROPN
iajs-2478	173	16	⃗∈	⃗∈	NUM
iajs-2478	173	17	⃗	⃗	PROPN
iajs-2478	173	18	𝐺	𝐺	PROPN
iajs-2478	173	19	𝑢	𝑢	PROPN
iajs-2478	173	20	⇒	⇒	PROPN
iajs-2478	173	21	𝐺	𝐺	PROPN
iajs-2478	173	22	𝑢	𝑢	PROPN
iajs-2478	173	23	inf	inf	PROPN
iajs-2478	173	24	⃗∈	⃗∈	NUM
iajs-2478	173	25	⃗	⃗	PROPN
iajs-2478	173	26	𝐺	𝐺	PROPN
iajs-2478	173	27	𝑢	𝑢	X
iajs-2478	173	28	min	min	PROPN
iajs-2478	173	29	⃗∈	⃗∈	PUNCT
iajs-2478	173	30	⃗	⃗	PROPN
iajs-2478	173	31	𝐺	𝐺	PROPN
iajs-2478	173	32	𝑢	𝑢	NOUN
iajs-2478	173	33	,	,	PUNCT
iajs-2478	173	34	then	then	ADV
iajs-2478	173	35	𝑢	𝑢	PROPN
iajs-2478	173	36	is	be	AUX
iajs-2478	173	37	a	a	DET
iajs-2478	173	38	ccbocv	ccbocv	NOUN
iajs-2478	173	39	.	.	PUNCT
iajs-2478	174	1	5	5	X
iajs-2478	174	2	.	.	X
iajs-2478	174	3	ncsthop	ncsthop	NOUN
iajs-2478	174	4	:	:	PUNCT
iajs-2478	174	5	in	in	SCONJ
iajs-2478	174	6	order	order	NOUN
iajs-2478	174	7	to	to	PART
iajs-2478	174	8	state	state	VERB
iajs-2478	174	9	the	the	DET
iajs-2478	174	10	nccthop	nccthop	NOUN
iajs-2478	174	11	for	for	ADP
iajs-2478	174	12	ccbocv	ccbocv	NOUN
iajs-2478	174	13	,	,	PUNCT
iajs-2478	174	14	the	the	DET
iajs-2478	174	15	frd	frd	NOUN
iajs-2478	174	16	of	of	ADP
iajs-2478	174	17	the	the	DET
iajs-2478	174	18	cof	cof	PROPN
iajs-2478	174	19	is	be	AUX
iajs-2478	174	20	derived	derive	VERB
iajs-2478	174	21	and	and	CCONJ
iajs-2478	174	22	the	the	DET
iajs-2478	174	23	nccthop	nccthop	NOUN
iajs-2478	174	24	is	be	AUX
iajs-2478	174	25	proved	prove	VERB
iajs-2478	174	26	.	.	PUNCT
iajs-2478	175	1	theorem	theorem	VERB
iajs-2478	175	2	5.1	5.1	NUM
iajs-2478	175	3	:	:	PUNCT
iajs-2478	175	4	consider	consider	VERB
iajs-2478	175	5	cof	cof	PROPN
iajs-2478	175	6	(	(	PUNCT
iajs-2478	175	7	10	10	NUM
iajs-2478	175	8	)	)	PUNCT
iajs-2478	175	9	,	,	PUNCT
iajs-2478	175	10	then	then	ADV
iajs-2478	175	11	the	the	DET
iajs-2478	175	12	tapes	tape	NOUN
iajs-2478	175	13	of	of	ADP
iajs-2478	175	14	the	the	DET
iajs-2478	175	15	tses	tse	NOUN
iajs-2478	175	16	are	be	AUX
iajs-2478	175	17	given	give	VERB
iajs-2478	175	18	by	by	ADP
iajs-2478	175	19	𝑧	𝑧	PROPN
iajs-2478	175	20	∆𝑧	∆𝑧	PROPN
iajs-2478	175	21	𝑧	𝑧	VERB
iajs-2478	175	22	𝑧	𝑧	PRON
iajs-2478	175	23	𝑧	𝑧	PRON
iajs-2478	175	24	𝑦	𝑦	X
iajs-2478	175	25	𝑦	𝑦	NOUN
iajs-2478	175	26	,	,	PUNCT
iajs-2478	175	27	in	in	ADP
iajs-2478	175	28	𝑄	𝑄	PROPN
iajs-2478	175	29	(	(	PUNCT
iajs-2478	175	30	78	78	NUM
iajs-2478	175	31	)	)	PUNCT
iajs-2478	175	32	𝑧	𝑧	DET
iajs-2478	175	33	∆𝑧	∆𝑧	NOUN
iajs-2478	175	34	𝑧	𝑧	VERB
iajs-2478	175	35	𝑧	𝑧	X
iajs-2478	175	36	𝑧	𝑧	PRON
iajs-2478	175	37	𝑦	𝑦	X
iajs-2478	175	38	𝑦	𝑦	NOUN
iajs-2478	175	39	,	,	PUNCT
iajs-2478	175	40	in	in	ADP
iajs-2478	175	41	𝑄	𝑄	PROPN
iajs-2478	175	42	(	(	PUNCT
iajs-2478	175	43	79	79	NUM
iajs-2478	175	44	)	)	PUNCT
iajs-2478	175	45	𝑧	𝑧	DET
iajs-2478	175	46	∆𝑧	∆𝑧	NOUN
iajs-2478	175	47	𝑧	𝑧	VERB
iajs-2478	175	48	𝑧	𝑧	X
iajs-2478	175	49	𝑧	𝑧	PRON
iajs-2478	175	50	𝑦	𝑦	X
iajs-2478	175	51	𝑦	𝑦	NOUN
iajs-2478	175	52	,	,	PUNCT
iajs-2478	175	53	in	in	ADP
iajs-2478	175	54	𝑄	𝑄	PROPN
iajs-2478	175	55	(	(	PUNCT
iajs-2478	175	56	80	80	NUM
iajs-2478	175	57	)	)	PUNCT
iajs-2478	175	58	𝑧	𝑧	PRON
iajs-2478	175	59	𝑥	𝑥	PROPN
iajs-2478	175	60	,	,	PUNCT
iajs-2478	175	61	𝑇	𝑇	PROPN
iajs-2478	175	62	0	0	NUM
iajs-2478	175	63	,	,	PUNCT
iajs-2478	175	64	in	in	ADP
iajs-2478	175	65	ω	ω	PROPN
iajs-2478	175	66	(	(	PUNCT
iajs-2478	175	67	81	81	NUM
iajs-2478	175	68	)	)	PUNCT
iajs-2478	175	69	𝑧	𝑧	PRON
iajs-2478	176	1	𝑥	𝑥	PROPN
iajs-2478	176	2	,	,	PUNCT
iajs-2478	176	3	𝑇	𝑇	PROPN
iajs-2478	176	4	0	0	NUM
iajs-2478	176	5	,	,	PUNCT
iajs-2478	176	6	in	in	ADP
iajs-2478	176	7	ω	ω	PROPN
iajs-2478	176	8	(	(	PUNCT
iajs-2478	176	9	82	82	NUM
iajs-2478	176	10	)	)	PUNCT
iajs-2478	176	11	𝑧	𝑧	PRON
iajs-2478	176	12	𝑥	𝑥	PROPN
iajs-2478	176	13	,	,	PUNCT
iajs-2478	176	14	𝑇	𝑇	PROPN
iajs-2478	176	15	0	0	NUM
iajs-2478	176	16	,	,	PUNCT
iajs-2478	176	17	in	in	ADP
iajs-2478	176	18	ω	ω	PROPN
iajs-2478	176	19	(	(	PUNCT
iajs-2478	176	20	83	83	NUM
iajs-2478	176	21	)	)	PUNCT
iajs-2478	176	22	∑	∑	PUNCT
iajs-2478	176	23	cos	cos	PROPN
iajs-2478	176	24	𝑛	𝑛	PROPN
iajs-2478	176	25	,	,	PUNCT
iajs-2478	176	26	𝑥	𝑥	PROPN
iajs-2478	176	27	0	0	NUM
iajs-2478	176	28	,	,	PUNCT
iajs-2478	176	29	on	on	ADP
iajs-2478	176	30	σ	σ	PROPN
iajs-2478	176	31	(	(	PUNCT
iajs-2478	176	32	84	84	NUM
iajs-2478	176	33	)	)	PUNCT
iajs-2478	176	34	∑	∑	PROPN
iajs-2478	176	35	cos	cos	PROPN
iajs-2478	176	36	𝑛	𝑛	PROPN
iajs-2478	176	37	,	,	PUNCT
iajs-2478	176	38	𝑥	𝑥	PROPN
iajs-2478	176	39	0	0	NUM
iajs-2478	176	40	,	,	PUNCT
iajs-2478	176	41	on	on	ADP
iajs-2478	176	42	σ	σ	PROPN
iajs-2478	176	43	(	(	PUNCT
iajs-2478	176	44	85	85	NUM
iajs-2478	176	45	)	)	PUNCT
iajs-2478	176	46	∑	∑	PUNCT
iajs-2478	176	47	cos	cos	PROPN
iajs-2478	176	48	𝑛	𝑛	PROPN
iajs-2478	176	49	,	,	PUNCT
iajs-2478	176	50	𝑥	𝑥	PROPN
iajs-2478	176	51	0	0	NUM
iajs-2478	176	52	,	,	PUNCT
iajs-2478	176	53	on	on	ADP
iajs-2478	176	54	σ	σ	PROPN
iajs-2478	176	55	(	(	PUNCT
iajs-2478	176	56	86	86	NUM
iajs-2478	176	57	)	)	PUNCT
iajs-2478	176	58	then	then	ADV
iajs-2478	176	59	𝑢	𝑢	X
iajs-2478	176	60	,	,	PUNCT
iajs-2478	176	61	𝑢	𝑢	PRON
iajs-2478	176	62	,	,	PUNCT
iajs-2478	176	63	𝑢	𝑢	PROPN
iajs-2478	176	64	∈	∈	PROPN
iajs-2478	176	65	𝑊	𝑊	PROPN
iajs-2478	176	66	and	and	CCONJ
iajs-2478	176	67	the	the	DET
iajs-2478	176	68	frd	frd	NOUN
iajs-2478	176	69	of	of	ADP
iajs-2478	176	70	the	the	DET
iajs-2478	176	71	cof	cof	PROPN
iajs-2478	176	72	is	be	AUX
iajs-2478	176	73	given	give	VERB
iajs-2478	176	74	by	by	ADP
iajs-2478	176	75	𝐺	𝐺	NOUN
iajs-2478	176	76	´	´	NOUN
iajs-2478	176	77	𝑢	𝑢	NOUN
iajs-2478	176	78	,	,	PUNCT
iajs-2478	176	79	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	176	80	𝚺	𝚺	ADP
iajs-2478	176	81	𝑧	𝑧	ADP
iajs-2478	176	82	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	176	83	,	,	PUNCT
iajs-2478	176	84	𝛿𝑢	𝛿𝑢	NOUN
iajs-2478	176	85	𝚺	𝚺	ADV
iajs-2478	176	86	proof	proof	NOUN
iajs-2478	176	87	:	:	PUNCT
iajs-2478	176	88	the	the	DET
iajs-2478	176	89	wf	wf	PROPN
iajs-2478	176	90	of	of	ADP
iajs-2478	176	91	(	(	PUNCT
iajs-2478	176	92	78	78	NUM
iajs-2478	176	93	86	86	NUM
iajs-2478	176	94	)	)	PUNCT
iajs-2478	176	95	for	for	ADP
iajs-2478	176	96	𝑣	𝑣	DET
iajs-2478	176	97	∈	∈	PROPN
iajs-2478	176	98	𝑉	𝑉	PROPN
iajs-2478	176	99	,	,	PUNCT
iajs-2478	176	100	∀	∀	NOUN
iajs-2478	176	101	𝑖	𝑖	SYM
iajs-2478	176	102	1,2,3	1,2,3	NUM
iajs-2478	176	103	,	,	PUNCT
iajs-2478	176	104	is	be	AUX
iajs-2478	176	105	given	give	VERB
iajs-2478	176	106	by	by	ADP
iajs-2478	176	107	〈	〈	PROPN
iajs-2478	176	108	𝑧	𝑧	PROPN
iajs-2478	176	109	,	,	PUNCT
iajs-2478	176	110	𝑣	𝑣	DET
iajs-2478	176	111	〉	〉	NOUN
iajs-2478	176	112	∇𝑧	∇𝑧	ADV
iajs-2478	176	113	,	,	PUNCT
iajs-2478	176	114	∇𝑣	∇𝑣	VERB
iajs-2478	176	115	𝑧	𝑧	PRON
iajs-2478	176	116	,	,	PUNCT
iajs-2478	176	117	𝑣	𝑣	PRON
iajs-2478	176	118	𝑧	𝑧	NOUN
iajs-2478	176	119	,	,	PUNCT
iajs-2478	176	120	𝑣	𝑣	PRON
iajs-2478	176	121	𝑧	𝑧	NOUN
iajs-2478	176	122	,	,	PUNCT
iajs-2478	176	123	𝑣	𝑣	DET
iajs-2478	176	124	𝑦	𝑦	PRON
iajs-2478	176	125	𝑦	𝑦	NOUN
iajs-2478	176	126	,	,	PUNCT
iajs-2478	176	127	𝑣	𝑣	X
iajs-2478	176	128	,	,	PUNCT
iajs-2478	176	129	(	(	PUNCT
iajs-2478	176	130	87	87	NUM
iajs-2478	176	131	)	)	PUNCT
iajs-2478	176	132	〈	〈	PROPN
iajs-2478	176	133	𝑧	𝑧	NOUN
iajs-2478	176	134	,	,	PUNCT
iajs-2478	176	135	𝑣	𝑣	DET
iajs-2478	176	136	〉	〉	NOUN
iajs-2478	176	137	∇𝑧	∇𝑧	ADV
iajs-2478	176	138	,	,	PUNCT
iajs-2478	176	139	∇𝑣	∇𝑣	VERB
iajs-2478	176	140	𝑧	𝑧	PRON
iajs-2478	176	141	,	,	PUNCT
iajs-2478	176	142	𝑣	𝑣	PRON
iajs-2478	176	143	𝑧	𝑧	NOUN
iajs-2478	176	144	,	,	PUNCT
iajs-2478	176	145	𝑣	𝑣	PRON
iajs-2478	176	146	𝑧	𝑧	NOUN
iajs-2478	176	147	,	,	PUNCT
iajs-2478	176	148	𝑣	𝑣	PRON
iajs-2478	176	149	𝑦	𝑦	PRON
iajs-2478	176	150	𝑦	𝑦	NOUN
iajs-2478	176	151	,	,	PUNCT
iajs-2478	176	152	𝑣	𝑣	X
iajs-2478	176	153	,	,	PUNCT
iajs-2478	176	154	(	(	PUNCT
iajs-2478	176	155	88	88	NUM
iajs-2478	176	156	)	)	PUNCT
iajs-2478	176	157	〈	〈	PROPN
iajs-2478	176	158	𝑧	𝑧	NOUN
iajs-2478	176	159	,	,	PUNCT
iajs-2478	176	160	𝑣	𝑣	DET
iajs-2478	176	161	〉	〉	NOUN
iajs-2478	176	162	∇𝑧	∇𝑧	ADV
iajs-2478	176	163	,	,	PUNCT
iajs-2478	176	164	∇𝑣	∇𝑣	VERB
iajs-2478	176	165	𝑧	𝑧	PRON
iajs-2478	176	166	,	,	PUNCT
iajs-2478	176	167	𝑣	𝑣	PRON
iajs-2478	176	168	𝑧	𝑧	NOUN
iajs-2478	176	169	,	,	PUNCT
iajs-2478	176	170	𝑣	𝑣	PRON
iajs-2478	176	171	𝑧	𝑧	NOUN
iajs-2478	176	172	,	,	PUNCT
iajs-2478	176	173	𝑣	𝑣	PRON
iajs-2478	176	174	𝑦	𝑦	PRON
iajs-2478	176	175	𝑦	𝑦	NOUN
iajs-2478	176	176	,	,	PUNCT
iajs-2478	176	177	𝑣	𝑣	X
iajs-2478	176	178	,	,	PUNCT
iajs-2478	176	179	(	(	PUNCT
iajs-2478	176	180	89	89	NUM
iajs-2478	176	181	)	)	PUNCT
iajs-2478	176	182	the	the	DET
iajs-2478	176	183	existence	existence	NOUN
iajs-2478	176	184	of	of	ADP
iajs-2478	176	185	a	a	DET
iajs-2478	176	186	unique	unique	ADJ
iajs-2478	176	187	solution	solution	NOUN
iajs-2478	176	188	of	of	ADP
iajs-2478	176	189	(	(	PUNCT
iajs-2478	176	190	87	87	NUM
iajs-2478	176	191	89	89	NUM
iajs-2478	176	192	)	)	PUNCT
iajs-2478	176	193	can	can	AUX
iajs-2478	176	194	be	be	AUX
iajs-2478	176	195	proved	prove	VERB
iajs-2478	176	196	by	by	ADP
iajs-2478	176	197	the	the	DET
iajs-2478	176	198	same	same	ADJ
iajs-2478	176	199	manner	manner	NOUN
iajs-2478	176	200	which	which	PRON
iajs-2478	176	201	is	be	AUX
iajs-2478	176	202	used	use	VERB
iajs-2478	176	203	in	in	ADP
iajs-2478	176	204	the	the	DET
iajs-2478	176	205	proof	proof	NOUN
iajs-2478	176	206	of	of	ADP
iajs-2478	176	207	theorem	theorem	NOUN
iajs-2478	176	208	3.1	3.1	NUM
iajs-2478	176	209	.	.	PUNCT
iajs-2478	177	1	now	now	ADV
iajs-2478	177	2	substituting	substitute	VERB
iajs-2478	177	3	𝑣	𝑣	ADP
iajs-2478	177	4	𝑧	𝑧	NOUN
iajs-2478	177	5	,	,	PUNCT
iajs-2478	177	6	𝑣	𝑣	DET
iajs-2478	177	7	𝑧	𝑧	NOUN
iajs-2478	177	8	and	and	CCONJ
iajs-2478	177	9	𝑣	𝑣	ADP
iajs-2478	177	10	𝑧	𝑧	X
iajs-2478	177	11	in	in	ADP
iajs-2478	177	12	(	(	PUNCT
iajs-2478	177	13	50.a	50.a	NUM
iajs-2478	177	14	)	)	PUNCT
iajs-2478	177	15	,	,	PUNCT
iajs-2478	177	16	(	(	PUNCT
iajs-2478	177	17	51.a	51.a	NUM
iajs-2478	177	18	)	)	PUNCT
iajs-2478	177	19	and	and	CCONJ
iajs-2478	177	20	(	(	PUNCT
iajs-2478	177	21	52.a	52.a	NUM
iajs-2478	177	22	)	)	PUNCT
iajs-2478	177	23	respectively	respectively	ADV
iajs-2478	177	24	,	,	PUNCT
iajs-2478	177	25	to	to	PART
iajs-2478	177	26	get	get	VERB
iajs-2478	177	27	〈	〈	PROPN
iajs-2478	177	28	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	29	,	,	PUNCT
iajs-2478	177	30	𝑧	𝑧	PRON
iajs-2478	177	31	〉	〉	NOUN
iajs-2478	177	32	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	177	33	,	,	PUNCT
iajs-2478	177	34	∇𝑧	∇𝑧	PROPN
iajs-2478	177	35	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	36	,	,	PUNCT
iajs-2478	177	37	𝑧	𝑧	PROPN
iajs-2478	177	38	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	39	,	,	PUNCT
iajs-2478	177	40	𝑧	𝑧	PROPN
iajs-2478	177	41	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	42	,	,	PUNCT
iajs-2478	177	43	𝑧	𝑧	PROPN
iajs-2478	177	44	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	177	45	,	,	PUNCT
iajs-2478	177	46	𝑧	𝑧	PROPN
iajs-2478	177	47	,	,	PUNCT
iajs-2478	177	48	(	(	PUNCT
iajs-2478	177	49	90.a	90.a	NUM
iajs-2478	177	50	)	)	PUNCT
iajs-2478	177	51	〈	〈	NOUN
iajs-2478	177	52	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	53	,	,	PUNCT
iajs-2478	177	54	𝑧	𝑧	PRON
iajs-2478	177	55	〉	〉	NOUN
iajs-2478	177	56	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	177	57	,	,	PUNCT
iajs-2478	177	58	∇𝑧	∇𝑧	PROPN
iajs-2478	177	59	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	60	,	,	PUNCT
iajs-2478	177	61	𝑧	𝑧	PROPN
iajs-2478	177	62	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	63	,	,	PUNCT
iajs-2478	177	64	𝑧	𝑧	PROPN
iajs-2478	177	65	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	66	,	,	PUNCT
iajs-2478	177	67	𝑧	𝑧	PROPN
iajs-2478	177	68	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	177	69	,	,	PUNCT
iajs-2478	177	70	𝑧	𝑧	PROPN
iajs-2478	177	71	,	,	PUNCT
iajs-2478	177	72	(	(	PUNCT
iajs-2478	177	73	90.b	90.b	NUM
iajs-2478	177	74	)	)	PUNCT
iajs-2478	177	75	〈	〈	NOUN
iajs-2478	177	76	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	77	,	,	PUNCT
iajs-2478	177	78	𝑧	𝑧	PRON
iajs-2478	177	79	〉	〉	NOUN
iajs-2478	177	80	∇δ𝑦	∇δ𝑦	PROPN
iajs-2478	177	81	,	,	PUNCT
iajs-2478	177	82	∇𝑧	∇𝑧	PROPN
iajs-2478	177	83	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	84	,	,	PUNCT
iajs-2478	177	85	𝑧	𝑧	PROPN
iajs-2478	177	86	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	87	,	,	PUNCT
iajs-2478	177	88	𝑧	𝑧	PROPN
iajs-2478	177	89	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	90	,	,	PUNCT
iajs-2478	177	91	𝑧	𝑧	PROPN
iajs-2478	177	92	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	177	93	,	,	PUNCT
iajs-2478	177	94	𝑧	𝑧	PROPN
iajs-2478	177	95	,	,	PUNCT
iajs-2478	177	96	(	(	PUNCT
iajs-2478	177	97	90.c	90.c	NUM
iajs-2478	177	98	)	)	PUNCT
iajs-2478	177	99	also	also	ADV
iajs-2478	177	100	,	,	PUNCT
iajs-2478	177	101	substituting	substitute	VERB
iajs-2478	177	102	𝑣	𝑣	ADP
iajs-2478	177	103	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	104	,	,	PUNCT
iajs-2478	177	105	𝑣	𝑣	DET
iajs-2478	177	106	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	107	and	and	CCONJ
iajs-2478	177	108	𝑣	𝑣	DET
iajs-2478	177	109	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	110	in	in	ADP
iajs-2478	177	111	(	(	PUNCT
iajs-2478	177	112	87),(88)&(89	87),(88)&(89	PROPN
iajs-2478	177	113	)	)	PUNCT
iajs-2478	177	114	respectively	respectively	ADV
iajs-2478	177	115	,	,	PUNCT
iajs-2478	177	116	to	to	PART
iajs-2478	177	117	get	get	VERB
iajs-2478	177	118	〈	〈	ADP
iajs-2478	177	119	𝑧	𝑧	PROPN
iajs-2478	177	120	,	,	PUNCT
iajs-2478	177	121	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	177	122	〉	〉	NOUN
iajs-2478	177	123	∇𝑧	∇𝑧	PROPN
iajs-2478	177	124	,	,	PUNCT
iajs-2478	177	125	∇𝛿𝑦	∇𝛿𝑦	NOUN
iajs-2478	177	126	𝑧	𝑧	X
iajs-2478	177	127	,	,	PUNCT
iajs-2478	177	128	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	129	𝑧	𝑧	PROPN
iajs-2478	177	130	,	,	PUNCT
iajs-2478	177	131	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	177	132	𝑧	𝑧	PROPN
iajs-2478	177	133	,	,	PUNCT
iajs-2478	177	134	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	177	135	𝑦	𝑦	PROPN
iajs-2478	177	136	𝑦	𝑦	PROPN
iajs-2478	177	137	,	,	PUNCT
iajs-2478	177	138	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	177	139	,	,	PUNCT
iajs-2478	177	140	(	(	PUNCT
iajs-2478	177	141	91.a	91.a	NUM
iajs-2478	177	142	)	)	PUNCT
iajs-2478	178	1	〈	〈	PROPN
iajs-2478	178	2	𝑧	𝑧	PROPN
iajs-2478	178	3	,	,	PUNCT
iajs-2478	178	4	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	5	〉	〉	NOUN
iajs-2478	178	6	∇𝑧	∇𝑧	PROPN
iajs-2478	178	7	,	,	PUNCT
iajs-2478	178	8	∇𝛿𝑦	∇𝛿𝑦	NOUN
iajs-2478	178	9	𝑧	𝑧	X
iajs-2478	178	10	,	,	PUNCT
iajs-2478	178	11	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	178	12	𝑧	𝑧	PROPN
iajs-2478	178	13	,	,	PUNCT
iajs-2478	178	14	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	15	𝑧	𝑧	PROPN
iajs-2478	178	16	,	,	PUNCT
iajs-2478	178	17	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	18	𝑦	𝑦	PROPN
iajs-2478	178	19	𝑦	𝑦	PROPN
iajs-2478	178	20	,	,	PUNCT
iajs-2478	178	21	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	178	22	,	,	PUNCT
iajs-2478	178	23	(	(	PUNCT
iajs-2478	178	24	91.b	91.b	NUM
iajs-2478	178	25	)	)	PUNCT
iajs-2478	178	26	〈	〈	PROPN
iajs-2478	178	27	𝑧	𝑧	PROPN
iajs-2478	178	28	,	,	PUNCT
iajs-2478	178	29	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	30	〉	〉	NOUN
iajs-2478	178	31	∇𝑧	∇𝑧	PROPN
iajs-2478	178	32	,	,	PUNCT
iajs-2478	178	33	∇𝛿𝑦	∇𝛿𝑦	NOUN
iajs-2478	178	34	𝑧	𝑧	X
iajs-2478	178	35	,	,	PUNCT
iajs-2478	178	36	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	178	37	𝑧	𝑧	PROPN
iajs-2478	178	38	,	,	PUNCT
iajs-2478	178	39	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	40	𝑧	𝑧	PROPN
iajs-2478	178	41	,	,	PUNCT
iajs-2478	178	42	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	178	43	𝑦	𝑦	PROPN
iajs-2478	178	44	𝑦	𝑦	PROPN
iajs-2478	178	45	,	,	PUNCT
iajs-2478	178	46	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	178	47	,	,	PUNCT
iajs-2478	178	48	(	(	PUNCT
iajs-2478	178	49	91.c	91.c	X
iajs-2478	178	50	)	)	PUNCT
iajs-2478	178	51	integrating	integrate	VERB
iajs-2478	178	52	both	both	DET
iajs-2478	178	53	sides	side	NOUN
iajs-2478	178	54	of	of	ADP
iajs-2478	178	55	equations	equation	NOUN
iajs-2478	178	56	(	(	PUNCT
iajs-2478	178	57	90.a	90.a	NUM
iajs-2478	178	58	,	,	PUNCT
iajs-2478	178	59	b	b	PROPN
iajs-2478	178	60	&	&	CCONJ
iajs-2478	178	61	c	c	NOUN
iajs-2478	178	62	)	)	PUNCT
iajs-2478	178	63	and	and	CCONJ
iajs-2478	178	64	(	(	PUNCT
iajs-2478	178	65	91.a	91.a	NUM
iajs-2478	178	66	,	,	PUNCT
iajs-2478	178	67	b	b	PROPN
iajs-2478	178	68	&	&	CCONJ
iajs-2478	178	69	c	c	NOUN
iajs-2478	178	70	)	)	PUNCT
iajs-2478	178	71	,	,	PUNCT
iajs-2478	178	72	w.r.t	w.r.t	NOUN
iajs-2478	178	73	.	.	PUNCT
iajs-2478	179	1	𝑡	𝑡	PROPN
iajs-2478	179	2	from	from	ADP
iajs-2478	179	3	0	0	NUM
iajs-2478	179	4	to	to	ADP
iajs-2478	179	5	𝑇	𝑇	PROPN
iajs-2478	179	6	,	,	PUNCT
iajs-2478	179	7	using	use	VERB
iajs-2478	179	8	integration	integration	NOUN
iajs-2478	179	9	by	by	ADP
iajs-2478	179	10	parts	part	NOUN
iajs-2478	179	11	for	for	ADP
iajs-2478	179	12	the	the	DET
iajs-2478	179	13	1st	1st	ADJ
iajs-2478	179	14	terms	term	NOUN
iajs-2478	179	15	of	of	ADP
iajs-2478	179	16	the	the	DET
iajs-2478	179	17	l.h.s	l.h.s	NOUN
iajs-2478	179	18	.	.	PUNCT
iajs-2478	180	1	of	of	ADP
iajs-2478	180	2	each	each	PRON
iajs-2478	180	3	of	of	ADP
iajs-2478	180	4	the	the	DET
iajs-2478	180	5	obtained	obtain	VERB
iajs-2478	180	6	equations	equation	NOUN
iajs-2478	180	7	from	from	ADP
iajs-2478	180	8	(	(	PUNCT
iajs-2478	180	9	91.a	91.a	NUM
iajs-2478	180	10	)	)	PUNCT
iajs-2478	180	11	,	,	PUNCT
iajs-2478	180	12	(	(	PUNCT
iajs-2478	180	13	91.b	91.b	NUM
iajs-2478	180	14	)	)	PUNCT
iajs-2478	180	15	&	&	CCONJ
iajs-2478	180	16	(	(	PUNCT
iajs-2478	180	17	91.c	91.c	NUM
iajs-2478	180	18	)	)	PUNCT
iajs-2478	180	19	,	,	PUNCT
iajs-2478	180	20	then	then	ADV
iajs-2478	180	21	subtracting	subtract	VERB
iajs-2478	180	22	each	each	DET
iajs-2478	180	23	one	one	NUM
iajs-2478	180	24	of	of	ADP
iajs-2478	180	25	the	the	DET
iajs-2478	180	26	obtained	obtain	VERB
iajs-2478	180	27	equations	equation	NOUN
iajs-2478	180	28	from	from	ADP
iajs-2478	180	29	its	its	PRON
iajs-2478	180	30	corresponding	correspond	VERB
iajs-2478	180	31	equation	equation	NOUN
iajs-2478	180	32	(	(	PUNCT
iajs-2478	180	33	90.a	90.a	NUM
iajs-2478	180	34	,	,	PUNCT
iajs-2478	180	35	b	b	PROPN
iajs-2478	180	36	&	&	CCONJ
iajs-2478	180	37	c	c	NOUN
iajs-2478	180	38	)	)	PUNCT
iajs-2478	180	39	,	,	PUNCT
iajs-2478	180	40	and	and	CCONJ
iajs-2478	180	41	adding	add	VERB
iajs-2478	180	42	all	all	DET
iajs-2478	180	43	the	the	DET
iajs-2478	180	44	obtained	obtain	VERB
iajs-2478	180	45	equations	equation	NOUN
iajs-2478	180	46	,	,	PUNCT
iajs-2478	180	47	give	give	VERB
iajs-2478	180	48	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	180	49	,	,	PUNCT
iajs-2478	180	50	𝑧	𝑧	PROPN
iajs-2478	180	51	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	180	52	,	,	PUNCT
iajs-2478	180	53	𝑧	𝑧	PROPN
iajs-2478	180	54	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	180	55	,	,	PUNCT
iajs-2478	180	56	𝑧	𝑧	PROPN
iajs-2478	180	57	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	180	58	𝑦	𝑦	PRON
iajs-2478	180	59	𝑦	𝑦	PROPN
iajs-2478	180	60	,	,	PUNCT
iajs-2478	180	61	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	180	62	𝑦	𝑦	PROPN
iajs-2478	180	63	𝑦	𝑦	PROPN
iajs-2478	180	64	,	,	PUNCT
iajs-2478	180	65	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	180	66	𝑦	𝑦	PROPN
iajs-2478	180	67	𝑦	𝑦	PROPN
iajs-2478	180	68	,	,	PUNCT
iajs-2478	180	69	𝛿𝑦	𝛿𝑦	PROPN
iajs-2478	180	70	𝑑𝑡	𝑑𝑡	ADP
iajs-2478	180	71	,	,	PUNCT
iajs-2478	180	72	(	(	PUNCT
iajs-2478	180	73	92	92	NUM
iajs-2478	180	74	)	)	PUNCT
iajs-2478	180	75	now	now	ADV
iajs-2478	180	76	,	,	PUNCT
iajs-2478	180	77	adding	add	VERB
iajs-2478	180	78	together	together	ADV
iajs-2478	180	79	each	each	PRON
iajs-2478	180	80	of	of	ADP
iajs-2478	180	81	the	the	DET
iajs-2478	180	82	pair	pair	NOUN
iajs-2478	180	83	of	of	ADP
iajs-2478	180	84	equations	equation	NOUN
iajs-2478	180	85	(	(	PUNCT
iajs-2478	180	86	11.a&50.a	11.a&50.a	NUM
iajs-2478	180	87	)	)	PUNCT
iajs-2478	180	88	,	,	PUNCT
iajs-2478	180	89	(	(	PUNCT
iajs-2478	180	90	12.a&51.a	12.a&51.a	NUM
iajs-2478	180	91	)	)	PUNCT
iajs-2478	180	92	and	and	CCONJ
iajs-2478	180	93	(	(	PUNCT
iajs-2478	180	94	13.a&52.a	13.a&52.a	NUM
iajs-2478	180	95	)	)	PUNCT
iajs-2478	180	96	,	,	PUNCT
iajs-2478	180	97	one	one	PRON
iajs-2478	180	98	has	have	VERB
iajs-2478	180	99	〈	〈	PROPN
iajs-2478	180	100	𝑦	𝑦	DET
iajs-2478	180	101	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	102	,	,	PUNCT
iajs-2478	180	103	𝑣	𝑣	ADP
iajs-2478	180	104	〉	〉	X
iajs-2478	180	105	∇	∇	X
iajs-2478	180	106	𝑦	𝑦	NOUN
iajs-2478	180	107	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	108	,	,	PUNCT
iajs-2478	180	109	∇𝑣	∇𝑣	PROPN
iajs-2478	180	110	𝑦	𝑦	NUM
iajs-2478	180	111	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	112	,	,	PUNCT
iajs-2478	180	113	𝑣	𝑣	DET
iajs-2478	180	114	𝑦	𝑦	PRON
iajs-2478	180	115	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	116	,	,	PUNCT
iajs-2478	180	117	𝑣	𝑣	DET
iajs-2478	180	118	𝑦	𝑦	NOUN
iajs-2478	180	119	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	120	,	,	PUNCT
iajs-2478	180	121	𝑣	𝑣	PRON
iajs-2478	180	122	𝑓	𝑓	X
iajs-2478	180	123	,	,	PUNCT
iajs-2478	180	124	𝑣	𝑣	ADP
iajs-2478	180	125	𝑢	𝑢	X
iajs-2478	180	126	𝛿𝑢	𝛿𝑢	NOUN
iajs-2478	180	127	,	,	PUNCT
iajs-2478	180	128	𝑣	𝑣	X
iajs-2478	180	129	,	,	PUNCT
iajs-2478	180	130	(	(	PUNCT
iajs-2478	180	131	93	93	NUM
iajs-2478	180	132	)	)	PUNCT
iajs-2478	180	133	〈	〈	PROPN
iajs-2478	180	134	𝑦	𝑦	NUM
iajs-2478	180	135	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	136	,	,	PUNCT
iajs-2478	180	137	𝑣	𝑣	ADP
iajs-2478	180	138	〉	〉	X
iajs-2478	180	139	∇	∇	X
iajs-2478	180	140	𝑦	𝑦	NOUN
iajs-2478	180	141	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	142	,	,	PUNCT
iajs-2478	180	143	∇𝑣	∇𝑣	PROPN
iajs-2478	180	144	𝑦	𝑦	NUM
iajs-2478	180	145	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	146	,	,	PUNCT
iajs-2478	180	147	𝑣	𝑣	DET
iajs-2478	180	148	𝑦	𝑦	PRON
iajs-2478	180	149	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	150	,	,	PUNCT
iajs-2478	180	151	𝑣	𝑣	DET
iajs-2478	180	152	𝑦	𝑦	NOUN
iajs-2478	180	153	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	180	154	,	,	PUNCT
iajs-2478	180	155	𝑣	𝑣	PRON
iajs-2478	180	156	𝑓	𝑓	X
iajs-2478	180	157	,	,	PUNCT
iajs-2478	180	158	𝑣	𝑣	ADP
iajs-2478	180	159	𝑢	𝑢	X
iajs-2478	180	160	𝛿𝑢	𝛿𝑢	NOUN
iajs-2478	180	161	,	,	PUNCT
iajs-2478	180	162	𝑣	𝑣	X
iajs-2478	180	163	,	,	PUNCT
iajs-2478	180	164	(	(	PUNCT
iajs-2478	180	165	94	94	NUM
iajs-2478	180	166	)	)	PUNCT
iajs-2478	180	167	  	  	SPACE
iajs-2478	181	1	125	125	NUM
iajs-2478	181	2	ibn	ibn	PROPN
iajs-2478	181	3	al	al	PROPN
iajs-2478	181	4	-	-	PUNCT
iajs-2478	181	5	haitham	haitham	PROPN
iajs-2478	181	6	jour	jour	X
iajs-2478	181	7	.	.	PROPN
iajs-2478	181	8	for	for	ADP
iajs-2478	181	9	pure	pure	ADJ
iajs-2478	181	10	&	&	CCONJ
iajs-2478	181	11	appl	appl	PROPN
iajs-2478	181	12	.	.	PUNCT
iajs-2478	182	1	sci	sci	PROPN
iajs-2478	182	2	.	.	PROPN
iajs-2478	183	1	33	33	NUM
iajs-2478	183	2	(	(	PUNCT
iajs-2478	183	3	3	3	NUM
iajs-2478	183	4	)	)	PUNCT
iajs-2478	183	5	2020	2020	NUM
iajs-2478	184	1	〈	〈	PROPN
iajs-2478	184	2	𝑦	𝑦	PROPN
iajs-2478	184	3	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	4	,	,	PUNCT
iajs-2478	184	5	𝑣	𝑣	ADP
iajs-2478	184	6	〉	〉	X
iajs-2478	184	7	∇	∇	X
iajs-2478	184	8	𝑦	𝑦	NOUN
iajs-2478	184	9	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	10	,	,	PUNCT
iajs-2478	184	11	∇𝑣	∇𝑣	PROPN
iajs-2478	184	12	𝑦	𝑦	NUM
iajs-2478	184	13	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	14	,	,	PUNCT
iajs-2478	184	15	𝑣	𝑣	DET
iajs-2478	184	16	𝑦	𝑦	PRON
iajs-2478	184	17	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	18	,	,	PUNCT
iajs-2478	184	19	𝑣	𝑣	DET
iajs-2478	184	20	𝑦	𝑦	NOUN
iajs-2478	184	21	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	22	,	,	PUNCT
iajs-2478	184	23	𝑣	𝑣	PRON
iajs-2478	184	24	𝑓	𝑓	X
iajs-2478	184	25	,	,	PUNCT
iajs-2478	184	26	𝑣	𝑣	ADP
iajs-2478	184	27	𝑢	𝑢	X
iajs-2478	184	28	𝛿𝑢	𝛿𝑢	NOUN
iajs-2478	184	29	,	,	PUNCT
iajs-2478	184	30	𝑣	𝑣	X
iajs-2478	184	31	,	,	PUNCT
iajs-2478	184	32	(	(	PUNCT
iajs-2478	184	33	95	95	NUM
iajs-2478	184	34	)	)	PUNCT
iajs-2478	184	35	which	which	PRON
iajs-2478	184	36	means	mean	VERB
iajs-2478	184	37	the	the	DET
iajs-2478	184	38	cv	cv	PROPN
iajs-2478	184	39	(	(	PUNCT
iajs-2478	184	40	𝑢	𝑢	X
iajs-2478	184	41	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	184	42	,	,	PUNCT
iajs-2478	184	43	𝑢	𝑢	PROPN
iajs-2478	184	44	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	184	45	,	,	PUNCT
iajs-2478	184	46	𝑢	𝑢	PROPN
iajs-2478	184	47	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	184	48	gives	give	VERB
iajs-2478	184	49	that	that	SCONJ
iajs-2478	184	50	the	the	DET
iajs-2478	184	51	solution	solution	NOUN
iajs-2478	184	52	(	(	PUNCT
iajs-2478	184	53	𝑦	𝑦	NOUN
iajs-2478	184	54	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	55	,	,	PUNCT
iajs-2478	184	56	𝑦	𝑦	NOUN
iajs-2478	184	57	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	58	,	,	PUNCT
iajs-2478	184	59	𝑦	𝑦	PRON
iajs-2478	184	60	𝛿𝑦	𝛿𝑦	NOUN
iajs-2478	184	61	of	of	ADP
iajs-2478	184	62	(	(	PUNCT
iajs-2478	184	63	93	93	NUM
iajs-2478	184	64	)	)	PUNCT
iajs-2478	184	65	–	–	PUNCT
iajs-2478	184	66	(	(	PUNCT
iajs-2478	184	67	95	95	NUM
iajs-2478	184	68	)	)	PUNCT
iajs-2478	184	69	.	.	PUNCT
iajs-2478	185	1	on	on	ADP
iajs-2478	185	2	the	the	DET
iajs-2478	185	3	other	other	ADJ
iajs-2478	185	4	hand	hand	NOUN
iajs-2478	185	5	,	,	PUNCT
iajs-2478	185	6	from	from	ADP
iajs-2478	185	7	(	(	PUNCT
iajs-2478	185	8	92	92	NUM
iajs-2478	185	9	)	)	PUNCT
iajs-2478	185	10	and	and	CCONJ
iajs-2478	185	11	the	the	DET
iajs-2478	185	12	cof	cof	PROPN
iajs-2478	185	13	,	,	PUNCT
iajs-2478	185	14	we	we	PRON
iajs-2478	185	15	have	have	VERB
iajs-2478	185	16	𝐺	𝐺	PROPN
iajs-2478	185	17	𝑢	𝑢	PROPN
iajs-2478	185	18	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	19	𝐺	𝐺	PROPN
iajs-2478	185	20	𝑢	𝑢	PROPN
iajs-2478	185	21	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	22	,	,	PUNCT
iajs-2478	185	23	𝑧	𝑧	PROPN
iajs-2478	185	24	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	25	,	,	PUNCT
iajs-2478	185	26	𝑧	𝑧	PROPN
iajs-2478	185	27	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	28	,	,	PUNCT
iajs-2478	185	29	𝑧	𝑧	PROPN
iajs-2478	185	30	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	185	31	,	,	PUNCT
iajs-2478	185	32	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	33	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	185	34	,	,	PUNCT
iajs-2478	185	35	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	36	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	185	37	,	,	PUNCT
iajs-2478	185	38	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	39	‖𝛿	‖𝛿	PROPN
iajs-2478	185	40	�	�	PROPN
iajs-2478	185	41	⃗	⃗	NOUN
iajs-2478	185	42	�	�	PROPN
iajs-2478	185	43	‖	‖	PROPN
iajs-2478	185	44	‖𝛿𝑢‖	‖𝛿𝑢‖	PROPN
iajs-2478	185	45	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	46	,	,	PUNCT
iajs-2478	185	47	𝑧	𝑧	PROPN
iajs-2478	185	48	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	185	49	,	,	PUNCT
iajs-2478	185	50	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	51	‖𝛿	‖𝛿	PROPN
iajs-2478	185	52	�	�	PROPN
iajs-2478	185	53	⃗	⃗	NOUN
iajs-2478	185	54	�	�	PROPN
iajs-2478	185	55	‖	‖	PROPN
iajs-2478	185	56	‖𝛿𝑢‖	‖𝛿𝑢‖	PROPN
iajs-2478	185	57	or	or	CCONJ
iajs-2478	185	58	𝐺	𝐺	PROPN
iajs-2478	185	59	𝑢	𝑢	PROPN
iajs-2478	185	60	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	185	61	𝐺	𝐺	PROPN
iajs-2478	185	62	𝑢	𝑢	PROPN
iajs-2478	185	63	𝑧	𝑧	PRON
iajs-2478	185	64	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	185	65	,	,	PUNCT
iajs-2478	186	1	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	186	2	𝚺	𝚺	PROPN
iajs-2478	186	3	‖𝛿	‖𝛿	PROPN
iajs-2478	186	4	�	�	PROPN
iajs-2478	186	5	⃗	⃗	PROPN
iajs-2478	186	6	�	�	PROPN
iajs-2478	186	7	‖𝑸	‖𝑸	PROPN
iajs-2478	186	8	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	186	9	.	.	PUNCT
iajs-2478	187	1	from	from	ADP
iajs-2478	187	2	theorem	theorem	ADJ
iajs-2478	187	3	4.1	4.1	NUM
iajs-2478	187	4	,	,	PUNCT
iajs-2478	187	5	we	we	PRON
iajs-2478	187	6	have	have	VERB
iajs-2478	187	7	‖𝛿	‖𝛿	PROPN
iajs-2478	187	8	�	�	NOUN
iajs-2478	187	9	⃗	⃗	NOUN
iajs-2478	187	10	�	�	PROPN
iajs-2478	187	11	‖𝑸	‖𝑸	PROPN
iajs-2478	187	12	𝜀	𝜀	PROPN
iajs-2478	187	13	𝛿𝑢	𝛿𝑢	X
iajs-2478	187	14	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	187	15	and	and	CCONJ
iajs-2478	187	16	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	187	17	𝜀	𝜀	PROPN
iajs-2478	187	18	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	187	19	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	187	20	with	with	ADP
iajs-2478	187	21	𝜀	𝜀	X
iajs-2478	187	22	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	187	23	𝑀	𝑀	PROPN
iajs-2478	187	24	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	187	25	,	,	PUNCT
iajs-2478	187	26	where	where	SCONJ
iajs-2478	187	27	𝜀	𝜀	ADP
iajs-2478	187	28	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	187	29	,	,	PUNCT
iajs-2478	187	30	𝜀	𝜀	X
iajs-2478	187	31	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	187	32	⟶	⟶	PROPN
iajs-2478	187	33	0	0	NUM
iajs-2478	187	34	as	as	ADP
iajs-2478	187	35	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	187	36	⟶	⟶	NOUN
iajs-2478	187	37	0	0	NUM
iajs-2478	188	1	then	then	ADV
iajs-2478	188	2	𝐺	𝐺	PROPN
iajs-2478	188	3	𝑢	𝑢	PROPN
iajs-2478	188	4	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	5	𝐺	𝐺	PROPN
iajs-2478	188	6	𝑢	𝑢	PROPN
iajs-2478	188	7	𝑧	𝑧	PRON
iajs-2478	188	8	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	188	9	,	,	PUNCT
iajs-2478	188	10	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	11	𝚺	𝚺	ADV
iajs-2478	188	12	𝜀	𝜀	VERB
iajs-2478	188	13	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	14	‖𝛿𝑢‖𝚺	‖𝛿𝑢‖𝚺	PROPN
iajs-2478	188	15	where	where	SCONJ
iajs-2478	188	16	𝜀	𝜀	ADP
iajs-2478	188	17	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	18	𝜀	𝜀	PROPN
iajs-2478	188	19	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	20	𝜀	𝜀	PROPN
iajs-2478	188	21	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	22	⟶	⟶	PROPN
iajs-2478	188	23	0	0	NUM
iajs-2478	188	24	as	as	ADP
iajs-2478	188	25	‖𝛿𝑢‖	‖𝛿𝑢‖	PROPN
iajs-2478	188	26	⟶	⟶	NOUN
iajs-2478	188	27	0	0	NUM
iajs-2478	188	28	using	use	VERB
iajs-2478	188	29	the	the	DET
iajs-2478	188	30	definition	definition	NOUN
iajs-2478	188	31	of	of	ADP
iajs-2478	188	32	frd	frd	NOUN
iajs-2478	188	33	of	of	ADP
iajs-2478	188	34	𝐺	𝐺	PROPN
iajs-2478	188	35	,	,	PUNCT
iajs-2478	188	36	one	one	PRON
iajs-2478	188	37	has	have	VERB
iajs-2478	188	38	𝐺	𝐺	NOUN
iajs-2478	188	39	´	´	NOUN
iajs-2478	188	40	𝑢	𝑢	NOUN
iajs-2478	188	41	,	,	PUNCT
iajs-2478	188	42	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	43	𝚺	𝚺	ADP
iajs-2478	188	44	𝑧	𝑧	ADP
iajs-2478	188	45	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	188	46	,	,	PUNCT
iajs-2478	188	47	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	188	48	𝚺	𝚺	NOUN
iajs-2478	188	49	.	.	PUNCT
iajs-2478	189	1	theorem	theorem	VERB
iajs-2478	189	2	5.2	5.2	NUM
iajs-2478	189	3	:	:	PUNCT
iajs-2478	189	4	the	the	DET
iajs-2478	189	5	ncsthop	ncsthop	NOUN
iajs-2478	189	6	for	for	ADP
iajs-2478	189	7	the	the	DET
iajs-2478	189	8	ccbocv	ccbocv	NOUN
iajs-2478	189	9	of	of	ADP
iajs-2478	189	10	the	the	DET
iajs-2478	189	11	above	above	ADJ
iajs-2478	189	12	problem	problem	NOUN
iajs-2478	189	13	is	be	AUX
iajs-2478	189	14	𝐺	𝐺	NOUN
iajs-2478	189	15	´	´	NOUN
iajs-2478	189	16	𝑢	𝑢	X
iajs-2478	189	17	𝑧	𝑧	PRON
iajs-2478	189	18	𝛽𝑢	𝛽𝑢	ADP
iajs-2478	189	19	0	0	NUM
iajs-2478	189	20	with	with	ADP
iajs-2478	189	21	�	�	NOUN
iajs-2478	189	22	⃗	⃗	PROPN
iajs-2478	189	23	�	�	PROPN
iajs-2478	189	24	�	�	PROPN
iajs-2478	189	25	⃗	⃗	NOUN
iajs-2478	189	26	�	�	PROPN
iajs-2478	189	27	⃗	⃗	PROPN
iajs-2478	189	28	and	and	CCONJ
iajs-2478	189	29	𝑧	𝑧	ADP
iajs-2478	189	30	𝑧	𝑧	DET
iajs-2478	189	31	⃗	⃗	PROPN
iajs-2478	189	32	.	.	PUNCT
iajs-2478	190	1	proof	proof	NOUN
iajs-2478	190	2	:	:	PUNCT
iajs-2478	190	3	if	if	SCONJ
iajs-2478	190	4	𝑢	𝑢	NOUN
iajs-2478	190	5	is	be	AUX
iajs-2478	190	6	an	an	DET
iajs-2478	190	7	ccbocv	ccbocv	NOUN
iajs-2478	190	8	of	of	ADP
iajs-2478	190	9	the	the	DET
iajs-2478	190	10	problem	problem	NOUN
iajs-2478	190	11	,	,	PUNCT
iajs-2478	190	12	then	then	ADV
iajs-2478	190	13	𝐺	𝐺	PROPN
iajs-2478	190	14	𝑢	𝑢	PROPN
iajs-2478	190	15	min	min	PROPN
iajs-2478	190	16	⃗∈	⃗∈	PUNCT
iajs-2478	190	17	⃗	⃗	PROPN
iajs-2478	190	18	𝐺	𝐺	PROPN
iajs-2478	190	19	𝑢	𝑢	PROPN
iajs-2478	190	20	∀𝑢	∀𝑢	PRON
iajs-2478	190	21	∈	∈	PROPN
iajs-2478	190	22	𝐿	𝐿	PROPN
iajs-2478	190	23	σ	σ	PROPN
iajs-2478	190	24	,	,	PUNCT
iajs-2478	190	25	i.e.	i.e.	X
iajs-2478	190	26	𝐺	𝐺	NOUN
iajs-2478	190	27	´	´	PROPN
iajs-2478	190	28	𝑢	𝑢	X
iajs-2478	190	29	0	0	PROPN
iajs-2478	190	30	⇒	⇒	NOUN
iajs-2478	190	31	𝑧	𝑧	PROPN
iajs-2478	190	32	𝛽𝑢	𝛽𝑢	ADP
iajs-2478	190	33	0	0	NUM
iajs-2478	190	34	from	from	ADP
iajs-2478	190	35	theorem	theorem	ADJ
iajs-2478	190	36	5.1	5.1	NUM
iajs-2478	190	37	𝑧	𝑧	PRON
iajs-2478	190	38	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	190	39	,	,	PUNCT
iajs-2478	190	40	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	190	41	0	0	NUM
iajs-2478	190	42	with	with	ADP
iajs-2478	190	43	𝛿𝑢	𝛿𝑢	PROPN
iajs-2478	190	44	𝑤	𝑤	ADP
iajs-2478	190	45	𝑢	𝑢	PROPN
iajs-2478	190	46	⇒	⇒	PROPN
iajs-2478	190	47	𝑧	𝑧	PROPN
iajs-2478	190	48	𝛽𝑢	𝛽𝑢	X
iajs-2478	190	49	,	,	PUNCT
iajs-2478	190	50	𝑤	𝑤	VERB
iajs-2478	190	51	𝚺	𝚺	ADV
iajs-2478	190	52	𝑧	𝑧	PRON
iajs-2478	190	53	𝛽𝑢	𝛽𝑢	PROPN
iajs-2478	190	54	,	,	PUNCT
iajs-2478	190	55	𝑢	𝑢	X
iajs-2478	190	56	𝚺	𝚺	ADV
iajs-2478	190	57	,	,	PUNCT
iajs-2478	190	58	∀	∀	NOUN
iajs-2478	190	59	𝑤	𝑤	ADP
iajs-2478	190	60	∈	∈	PROPN
iajs-2478	190	61	𝐿	𝐿	PROPN
iajs-2478	190	62	σ	σ	PROPN
iajs-2478	190	63	.	.	PUNCT
iajs-2478	191	1	6	6	X
iajs-2478	191	2	.	.	X
iajs-2478	191	3	conclusions	conclusion	NOUN
iajs-2478	191	4	in	in	ADP
iajs-2478	191	5	this	this	DET
iajs-2478	191	6	paper	paper	NOUN
iajs-2478	191	7	,	,	PUNCT
iajs-2478	191	8	the	the	DET
iajs-2478	191	9	gm	gm	PROPN
iajs-2478	191	10	is	be	AUX
iajs-2478	191	11	employed	employ	VERB
iajs-2478	191	12	to	to	PART
iajs-2478	191	13	prove	prove	VERB
iajs-2478	191	14	the	the	DET
iajs-2478	191	15	existence	existence	NOUN
iajs-2478	191	16	theorem	theorem	VERB
iajs-2478	191	17	of	of	ADP
iajs-2478	191	18	a	a	DET
iajs-2478	191	19	unique	unique	ADJ
iajs-2478	191	20	solution	solution	NOUN
iajs-2478	191	21	for	for	ADP
iajs-2478	191	22	a	a	DET
iajs-2478	191	23	svs	svs	NOUN
iajs-2478	191	24	of	of	ADP
iajs-2478	191	25	the	the	DET
iajs-2478	191	26	tlpdepar	tlpdepar	NOUN
iajs-2478	191	27	when	when	SCONJ
iajs-2478	191	28	the	the	DET
iajs-2478	191	29	ccbocv	ccbocv	NOUN
iajs-2478	191	30	is	be	AUX
iajs-2478	191	31	fixed	fix	VERB
iajs-2478	191	32	.	.	PUNCT
iajs-2478	192	1	the	the	DET
iajs-2478	192	2	existence	existence	NOUN
iajs-2478	192	3	theorem	theorem	NOUN
iajs-2478	192	4	of	of	ADP
iajs-2478	192	5	a	a	DET
iajs-2478	192	6	ccbocv	ccbocv	NOUN
iajs-2478	192	7	governed	govern	VERB
iajs-2478	192	8	by	by	ADP
iajs-2478	192	9	the	the	DET
iajs-2478	192	10	tlpdepar	tlpdepar	NOUN
iajs-2478	192	11	is	be	AUX
iajs-2478	192	12	developed	develop	VERB
iajs-2478	192	13	and	and	CCONJ
iajs-2478	192	14	proved	prove	VERB
iajs-2478	192	15	.	.	PUNCT
iajs-2478	193	1	the	the	DET
iajs-2478	193	2	existence	existence	NOUN
iajs-2478	193	3	and	and	CCONJ
iajs-2478	193	4	uniqueness	uniqueness	NOUN
iajs-2478	193	5	of	of	ADP
iajs-2478	193	6	a	a	DET
iajs-2478	193	7	solution	solution	NOUN
iajs-2478	193	8	for	for	ADP
iajs-2478	193	9	the	the	DET
iajs-2478	193	10	tapes	tape	NOUN
iajs-2478	193	11	associated	associate	VERB
iajs-2478	193	12	with	with	ADP
iajs-2478	193	13	the	the	DET
iajs-2478	193	14	tlpdepar	tlpdepar	NOUN
iajs-2478	193	15	is	be	AUX
iajs-2478	193	16	studied	study	VERB
iajs-2478	193	17	,	,	PUNCT
iajs-2478	193	18	the	the	DET
iajs-2478	193	19	frd	frd	NOUN
iajs-2478	193	20	for	for	ADP
iajs-2478	193	21	the	the	DET
iajs-2478	193	22	cof	cof	PROPN
iajs-2478	193	23	is	be	AUX
iajs-2478	193	24	obtained	obtain	VERB
iajs-2478	193	25	.	.	PUNCT
iajs-2478	194	1	at	at	ADP
iajs-2478	194	2	the	the	DET
iajs-2478	194	3	end	end	NOUN
iajs-2478	194	4	,	,	PUNCT
iajs-2478	194	5	the	the	DET
iajs-2478	194	6	ncsthop	ncsthop	NOUN
iajs-2478	194	7	of	of	ADP
iajs-2478	194	8	the	the	DET
iajs-2478	194	9	ccbocv	ccbocv	NOUN
iajs-2478	194	10	problem	problem	NOUN
iajs-2478	194	11	is	be	AUX
iajs-2478	194	12	stated	state	VERB
iajs-2478	194	13	and	and	CCONJ
iajs-2478	194	14	proved	prove	VERB
iajs-2478	194	15	.	.	PUNCT
iajs-2478	195	1	acknowledgement	acknowledgement	NOUN
iajs-2478	195	2	i	i	PRON
iajs-2478	195	3	wish	wish	VERB
iajs-2478	195	4	to	to	PART
iajs-2478	195	5	express	express	VERB
iajs-2478	195	6	my	my	PRON
iajs-2478	195	7	sincere	sincere	ADJ
iajs-2478	195	8	thanks	thank	NOUN
iajs-2478	195	9	to	to	ADP
iajs-2478	195	10	the	the	DET
iajs-2478	195	11	university	university	NOUN
iajs-2478	195	12	of	of	ADP
iajs-2478	195	13	mustansiriyah	mustansiriyah	NOUN
iajs-2478	195	14	for	for	ADP
iajs-2478	195	15	providing	provide	VERB
iajs-2478	195	16	a	a	DET
iajs-2478	195	17	pleasurable	pleasurable	ADJ
iajs-2478	195	18	and	and	CCONJ
iajs-2478	195	19	stimulating	stimulate	VERB
iajs-2478	195	20	environment	environment	NOUN
iajs-2478	195	21	to	to	PART
iajs-2478	195	22	carry	carry	VERB
iajs-2478	195	23	out	out	ADP
iajs-2478	195	24	research	research	NOUN
iajs-2478	195	25	.	.	PUNCT
iajs-2478	196	1	also	also	ADV
iajs-2478	196	2	,	,	PUNCT
iajs-2478	196	3	i	i	PRON
iajs-2478	196	4	would	would	AUX
iajs-2478	196	5	like	like	VERB
iajs-2478	196	6	to	to	PART
iajs-2478	196	7	extend	extend	VERB
iajs-2478	196	8	our	our	PRON
iajs-2478	196	9	sincere	sincere	ADJ
iajs-2478	196	10	esteems	esteem	NOUN
iajs-2478	196	11	to	to	ADP
iajs-2478	196	12	the	the	DET
iajs-2478	196	13	college	college	NOUN
iajs-2478	196	14	of	of	ADP
iajs-2478	196	15	sciencedepartment	sciencedepartment	NOUN
iajs-2478	196	16	of	of	ADP
iajs-2478	196	17	mathematics	mathematic	NOUN
iajs-2478	196	18	for	for	ADP
iajs-2478	196	19	their	their	PRON
iajs-2478	196	20	timely	timely	ADJ
iajs-2478	196	21	support	support	NOUN
iajs-2478	196	22	references	reference	NOUN
iajs-2478	196	23	1	1	NUM
iajs-2478	196	24	.	.	PUNCT
iajs-2478	197	1	aro	aro	PROPN
iajs-2478	197	2	,	,	PUNCT
iajs-2478	197	3	m.k	m.k	PROPN
iajs-2478	197	4	.	.	PUNCT
iajs-2478	197	5	;	;	PUNCT
iajs-2478	197	6	luboobi	luboobi	PROPN
iajs-2478	197	7	,	,	PUNCT
iajs-2478	197	8	l.	l.	PROPN
iajs-2478	197	9	;	;	PUNCT
iajs-2478	197	10	shahada	shahada	PROPN
iajs-2478	197	11	,	,	PUNCT
iajs-2478	197	12	f.	f.	PROPN
iajs-2478	197	13	application	application	NOUN
iajs-2478	197	14	of	of	ADP
iajs-2478	197	15	optimal	optimal	ADJ
iajs-2478	197	16	control	control	NOUN
iajs-2478	197	17	strategies	strategy	NOUN
iajs-2478	197	18	for	for	ADP
iajs-2478	197	19	the	the	DET
iajs-2478	197	20	dynamics	dynamic	NOUN
iajs-2478	197	21	of	of	ADP
iajs-2478	197	22	yellow	yellow	ADJ
iajs-2478	197	23	fever	fever	NOUN
iajs-2478	197	24	.	.	PUNCT
iajs-2478	198	1	j.	j.	PROPN
iajs-2478	198	2	math	math	PROPN
iajs-2478	198	3	.	.	PUNCT
iajs-2478	199	1	computer	computer	NOUN
iajs-2478	199	2	.	.	PUNCT
iajs-2478	200	1	sci.2015	sci.2015	X
iajs-2478	200	2	,	,	PUNCT
iajs-2478	200	3	5	5	NUM
iajs-2478	200	4	,	,	PUNCT
iajs-2478	200	5	3	3	NUM
iajs-2478	200	6	,	,	PUNCT
iajs-2478	200	7	430	430	NUM
iajs-2478	200	8	-	-	SYM
iajs-2478	200	9	453	453	NUM
iajs-2478	200	10	.	.	NOUN
iajs-2478	201	1	2	2	NUM
iajs-2478	201	2	.	.	X
iajs-2478	201	3	hajiabadi	hajiabadi	PROPN
iajs-2478	201	4	,	,	PUNCT
iajs-2478	201	5	m.e	m.e	PROPN
iajs-2478	201	6	.	.	PROPN
iajs-2478	201	7	;	;	PUNCT
iajs-2478	201	8	mashhadi	mashhadi	NOUN
iajs-2478	201	9	,	,	PUNCT
iajs-2478	201	10	h.r	h.r	PROPN
iajs-2478	201	11	.	.	NOUN
iajs-2478	201	12	modeling	modeling	NOUN
iajs-2478	201	13	of	of	ADP
iajs-2478	201	14	the	the	DET
iajs-2478	201	15	maximum	maximum	PROPN
iajs-2478	201	16	entropy	entropy	NOUN
iajs-2478	201	17	problem	problem	NOUN
iajs-2478	201	18	as	as	ADP
iajs-2478	201	19	an	an	DET
iajs-2478	201	20	optimal	optimal	ADJ
iajs-2478	201	21	control	control	NOUN
iajs-2478	201	22	problem	problem	NOUN
iajs-2478	201	23	and	and	CCONJ
iajs-2478	201	24	its	its	PRON
iajs-2478	201	25	application	application	NOUN
iajs-2478	201	26	to	to	ADP
iajs-2478	201	27	pdf	pdf	NOUN
iajs-2478	201	28	estimation	estimation	NOUN
iajs-2478	201	29	of	of	ADP
iajs-2478	201	30	electricity	electricity	NOUN
iajs-2478	201	31	price	price	NOUN
iajs-2478	201	32	.	.	PUNCT
iajs-2478	202	1	ijeee	ijeee	NOUN
iajs-2478	202	2	.	.	PUNCT
iajs-2478	203	1	iran	iran	PROPN
iajs-2478	203	2	university	university	PROPN
iajs-2478	203	3	of	of	ADP
iajs-2478	203	4	science	science	NOUN
iajs-2478	203	5	and	and	CCONJ
iajs-2478	203	6	technology.2013	technology.2013	PROPN
iajs-2478	203	7	,	,	PUNCT
iajs-2478	203	8	9	9	NUM
iajs-2478	203	9	,	,	PUNCT
iajs-2478	203	10	3	3	NUM
iajs-2478	203	11	,	,	PUNCT
iajs-2478	203	12	150	150	NUM
iajs-2478	203	13	-	-	SYM
iajs-2478	203	14	157	157	NUM
iajs-2478	203	15	.	.	PUNCT
iajs-2478	203	16	  	  	SPACE
iajs-2478	204	1	126	126	NUM
iajs-2478	204	2	ibn	ibn	PROPN
iajs-2478	204	3	al	al	PROPN
iajs-2478	204	4	-	-	PUNCT
iajs-2478	204	5	haitham	haitham	PROPN
iajs-2478	204	6	jour	jour	X
iajs-2478	204	7	.	.	PROPN
iajs-2478	204	8	for	for	ADP
iajs-2478	204	9	pure	pure	ADJ
iajs-2478	204	10	&	&	CCONJ
iajs-2478	204	11	appl	appl	PROPN
iajs-2478	204	12	.	.	PUNCT
iajs-2478	205	1	sci	sci	PROPN
iajs-2478	205	2	.	.	PROPN
iajs-2478	206	1	33	33	NUM
iajs-2478	206	2	(	(	PUNCT
iajs-2478	206	3	3	3	NUM
iajs-2478	206	4	)	)	PUNCT
iajs-2478	206	5	2020	2020	NUM
iajs-2478	206	6	3	3	NUM
iajs-2478	206	7	.	.	PUNCT
iajs-2478	206	8	bermudez	bermudez	PROPN
iajs-2478	206	9	,	,	PUNCT
iajs-2478	206	10	a.	a.	NOUN
iajs-2478	206	11	some	some	DET
iajs-2478	206	12	applications	application	NOUN
iajs-2478	206	13	of	of	ADP
iajs-2478	206	14	optimal	optimal	ADJ
iajs-2478	206	15	control	control	NOUN
iajs-2478	206	16	theory	theory	NOUN
iajs-2478	206	17	of	of	ADP
iajs-2478	206	18	distributed	distribute	VERB
iajs-2478	206	19	systems	system	NOUN
iajs-2478	206	20	.	.	PUNCT
iajs-2478	207	1	esaim	esaim	NOUN
iajs-2478	207	2	:	:	PUNCT
iajs-2478	207	3	control	control	NOUN
iajs-2478	207	4	,	,	PUNCT
iajs-2478	207	5	optimisation	optimisation	NOUN
iajs-2478	207	6	and	and	CCONJ
iajs-2478	207	7	calculus	calculus	NOUN
iajs-2478	207	8	of	of	ADP
iajs-2478	207	9	variations	variation	NOUN
iajs-2478	207	10	.2002	.2002	PROPN
iajs-2478	207	11	,	,	PUNCT
iajs-2478	207	12	8,195	8,195	NUM
iajs-2478	207	13	-	-	SYM
iajs-2478	207	14	218	218	NUM
iajs-2478	207	15	.	.	PUNCT
iajs-2478	208	1	4	4	X
iajs-2478	208	2	.	.	X
iajs-2478	208	3	torre	torre	PROPN
iajs-2478	208	4	,	,	PUNCT
iajs-2478	208	5	d.la	d.la	PROPN
iajs-2478	208	6	.	.	PROPN
iajs-2478	208	7	;	;	PUNCT
iajs-2478	208	8	kunze	kunze	PROPN
iajs-2478	208	9	,	,	PUNCT
iajs-2478	208	10	h.	h.	PROPN
iajs-2478	208	11	;	;	PUNCT
iajs-2478	208	12	ruiz	ruiz	NOUN
iajs-2478	208	13	-	-	PUNCT
iajs-2478	208	14	galan	galan	NOUN
iajs-2478	208	15	,	,	PUNCT
iajs-2478	208	16	m.	m.	NOUN
iajs-2478	208	17	;	;	PUNCT
iajs-2478	208	18	malik	malik	PROPN
iajs-2478	208	19	,	,	PUNCT
iajs-2478	208	20	t.	t.	PROPN
iajs-2478	208	21	;	;	PUNCT
iajs-2478	208	22	marsiglio	marsiglio	PROPN
iajs-2478	208	23	,	,	PUNCT
iajs-2478	208	24	s.	s.	PROPN
iajs-2478	208	25	optimal	optimal	ADJ
iajs-2478	208	26	control	control	NOUN
iajs-2478	208	27	:	:	PUNCT
iajs-2478	208	28	theory	theory	NOUN
iajs-2478	208	29	and	and	CCONJ
iajs-2478	208	30	application	application	NOUN
iajs-2478	208	31	to	to	ADP
iajs-2478	208	32	science	science	NOUN
iajs-2478	208	33	engineering	engineering	NOUN
iajs-2478	208	34	and	and	CCONJ
iajs-2478	208	35	social	social	ADJ
iajs-2478	208	36	sciences	science	NOUN
iajs-2478	208	37	.	.	PUNCT
iajs-2478	209	1	hindawi	hindawi	ADJ
iajs-2478	209	2	publishing	publishing	NOUN
iajs-2478	209	3	corporation	corporation	NOUN
iajs-2478	209	4	.	.	PUNCT
iajs-2478	210	1	abstract	abstract	ADJ
iajs-2478	210	2	and	and	CCONJ
iajs-2478	210	3	applied	apply	VERB
iajs-2478	210	4	analysis.2015	analysis.2015	PROPN
iajs-2478	210	5	,	,	PUNCT
iajs-2478	210	6	i	i	PROPN
iajs-2478	210	7	d	d	PROPN
iajs-2478	210	8	890527,2pages.doi:10.1155/2015/890527	890527,2pages.doi:10.1155/2015/890527	NUM
iajs-2478	210	9	.	.	PUNCT
iajs-2478	211	1	5	5	NUM
iajs-2478	211	2	.	.	NUM
iajs-2478	211	3	chryssoverghi	chryssoverghi	PROPN
iajs-2478	211	4	,	,	PUNCT
iajs-2478	211	5	i.	i.	PROPN
iajs-2478	211	6	;	;	PUNCT
iajs-2478	211	7	al	al	PROPN
iajs-2478	211	8	-	-	PUNCT
iajs-2478	211	9	hawasy	hawasy	PROPN
iajs-2478	211	10	,	,	PUNCT
iajs-2478	211	11	j.	j.	PROPN
iajs-2478	211	12	the	the	DET
iajs-2478	211	13	continuous	continuous	ADJ
iajs-2478	211	14	classical	classical	ADJ
iajs-2478	211	15	optimal	optimal	ADJ
iajs-2478	211	16	control	control	NOUN
iajs-2478	211	17	problem	problem	NOUN
iajs-2478	211	18	of	of	ADP
iajs-2478	211	19	semi	semi	ADJ
iajs-2478	211	20	linear	linear	PROPN
iajs-2478	211	21	parabolic	parabolic	ADJ
iajs-2478	211	22	equations	equation	NOUN
iajs-2478	211	23	(	(	PUNCT
iajs-2478	211	24	ccocp	ccocp	NOUN
iajs-2478	211	25	)	)	PUNCT
iajs-2478	211	26	,	,	PUNCT
iajs-2478	211	27	journal	journal	NOUN
iajs-2478	211	28	of	of	ADP
iajs-2478	211	29	kerbala	kerbala	PROPN
iajs-2478	211	30	university.2010	university.2010	PROPN
iajs-2478	211	31	,	,	PUNCT
iajs-2478	211	32	8	8	NUM
iajs-2478	211	33	,	,	PUNCT
iajs-2478	211	34	3	3	NUM
iajs-2478	211	35	.	.	NOUN
iajs-2478	211	36	6	6	NUM
iajs-2478	211	37	.	.	PUNCT
iajs-2478	212	1	al	al	PROPN
iajs-2478	212	2	-	-	PUNCT
iajs-2478	212	3	hawasy	hawasy	PROPN
iajs-2478	212	4	,	,	PUNCT
iajs-2478	212	5	j	j	PROPN
iajs-2478	212	6	.	.	PUNCT
iajs-2478	213	1	the	the	DET
iajs-2478	213	2	continuous	continuous	ADJ
iajs-2478	213	3	classical	classical	ADJ
iajs-2478	213	4	optimal	optimal	ADJ
iajs-2478	213	5	control	control	NOUN
iajs-2478	213	6	problem	problem	NOUN
iajs-2478	213	7	of	of	ADP
iajs-2478	213	8	a	a	DET
iajs-2478	213	9	nonlinear	nonlinear	ADJ
iajs-2478	213	10	hyperbolic	hyperbolic	ADJ
iajs-2478	213	11	partial	partial	ADJ
iajs-2478	213	12	differential	differential	NOUN
iajs-2478	213	13	equations	equation	NOUN
iajs-2478	213	14	(	(	PUNCT
iajs-2478	213	15	ccocp	ccocp	NOUN
iajs-2478	213	16	)	)	PUNCT
iajs-2478	213	17	.	.	PUNCT
iajs-2478	214	1	al	al	PROPN
iajs-2478	214	2	-	-	PUNCT
iajs-2478	214	3	mustansiriyah	mustansiriyah	PROPN
iajs-2478	214	4	journal	journal	NOUN
iajs-2478	214	5	of	of	ADP
iajs-2478	214	6	science.2008	science.2008	PROPN
iajs-2478	214	7	,	,	PUNCT
iajs-2478	214	8	19	19	NUM
iajs-2478	214	9	,	,	PUNCT
iajs-2478	214	10	8	8	NUM
iajs-2478	214	11	,	,	PUNCT
iajs-2478	214	12	96	96	NUM
iajs-2478	214	13	-	-	SYM
iajs-2478	214	14	110	110	NUM
iajs-2478	214	15	.	.	PUNCT
iajs-2478	215	1	7	7	X
iajs-2478	215	2	.	.	X
iajs-2478	215	3	brett	brett	PROPN
iajs-2478	215	4	,	,	PUNCT
iajs-2478	215	5	c.	c.	PROPN
iajs-2478	215	6	;	;	PUNCT
iajs-2478	215	7	dedner	dedner	NOUN
iajs-2478	215	8	,	,	PUNCT
iajs-2478	215	9	a.	a.	PROPN
iajs-2478	215	10	;	;	PUNCT
iajs-2478	215	11	elliott	elliott	PROPN
iajs-2478	215	12	,	,	PUNCT
iajs-2478	215	13	c.	c.	PROPN
iajs-2478	215	14	optimal	optimal	ADJ
iajs-2478	215	15	control	control	NOUN
iajs-2478	215	16	of	of	ADP
iajs-2478	215	17	elliptic	elliptic	ADJ
iajs-2478	215	18	pdes	pde	NOUN
iajs-2478	215	19	at	at	ADP
iajs-2478	215	20	points	point	NOUN
iajs-2478	215	21	.	.	PUNCT
iajs-2478	216	1	i	i	PRON
iajs-2478	216	2	m	m	VERB
iajs-2478	216	3	a	a	DET
iajs-2478	216	4	journal	journal	NOUN
iajs-2478	216	5	of	of	ADP
iajs-2478	216	6	numerical	numerical	PROPN
iajs-2478	216	7	analysis.2015	analysis.2015	PROPN
iajs-2478	216	8	,	,	PUNCT
iajs-2478	216	9	36	36	NUM
iajs-2478	216	10	,	,	PUNCT
iajs-2478	216	11	3	3	NUM
iajs-2478	216	12	,	,	PUNCT
iajs-2478	216	13	1	1	NUM
iajs-2478	216	14	-	-	SYM
iajs-2478	216	15	34	34	NUM
iajs-2478	216	16	8	8	NUM
iajs-2478	216	17	.	.	PUNCT
iajs-2478	217	1	al	al	PROPN
iajs-2478	217	2	-	-	PUNCT
iajs-2478	217	3	hawasy	hawasy	PROPN
iajs-2478	217	4	,	,	PUNCT
iajs-2478	217	5	j.	j.	PROPN
iajs-2478	217	6	;	;	PUNCT
iajs-2478	217	7	kadhem	kadhem	PROPN
iajs-2478	217	8	,	,	PUNCT
iajs-2478	217	9	g.m	g.m	PROPN
iajs-2478	217	10	.	.	PUNCT
iajs-2478	218	1	the	the	DET
iajs-2478	218	2	continuous	continuous	ADJ
iajs-2478	218	3	classical	classical	ADJ
iajs-2478	218	4	optimal	optimal	ADJ
iajs-2478	218	5	control	control	NOUN
iajs-2478	218	6	for	for	ADP
iajs-2478	218	7	a	a	DET
iajs-2478	218	8	coupled	couple	VERB
iajs-2478	218	9	nonlinear	nonlinear	ADJ
iajs-2478	218	10	parabolic	parabolic	ADJ
iajs-2478	218	11	partial	partial	ADJ
iajs-2478	218	12	differential	differential	NOUN
iajs-2478	218	13	equations	equation	NOUN
iajs-2478	218	14	with	with	ADP
iajs-2478	218	15	equality	equality	NOUN
iajs-2478	218	16	and	and	CCONJ
iajs-2478	218	17	inequality	inequality	NOUN
iajs-2478	218	18	constraints	constraint	NOUN
iajs-2478	218	19	.	.	PUNCT
iajs-2478	219	1	journal	journal	PROPN
iajs-2478	219	2	of	of	ADP
iajs-2478	219	3	al	al	PROPN
iajs-2478	219	4	-	-	PUNCT
iajs-2478	219	5	nahrain	nahrain	PROPN
iajs-2478	219	6	university.2016	university.2016	PROPN
iajs-2478	219	7	,	,	PUNCT
iajs-2478	219	8	19	19	NUM
iajs-2478	219	9	,	,	PUNCT
iajs-2478	219	10	1	1	NUM
iajs-2478	219	11	,	,	PUNCT
iajs-2478	219	12	173	173	NUM
iajs-2478	219	13	-	-	SYM
iajs-2478	219	14	186	186	NUM
iajs-2478	219	15	.	.	PUNCT
iajs-2478	219	16	9	9	NUM
iajs-2478	219	17	.	.	X
iajs-2478	220	1	al	al	PROPN
iajs-2478	220	2	-	-	PUNCT
iajs-2478	220	3	hawasy	hawasy	PROPN
iajs-2478	220	4	,	,	PUNCT
iajs-2478	220	5	j.	j.	PROPN
iajs-2478	220	6	the	the	DET
iajs-2478	220	7	continuous	continuous	ADJ
iajs-2478	220	8	classical	classical	ADJ
iajs-2478	220	9	optimal	optimal	ADJ
iajs-2478	220	10	control	control	NOUN
iajs-2478	220	11	of	of	ADP
iajs-2478	220	12	a	a	DET
iajs-2478	220	13	couple	couple	NOUN
iajs-2478	220	14	nonlinear	nonlinear	ADJ
iajs-2478	220	15	hyperbolic	hyperbolic	ADJ
iajs-2478	220	16	partial	partial	ADJ
iajs-2478	220	17	differential	differential	NOUN
iajs-2478	220	18	equations	equation	NOUN
iajs-2478	220	19	with	with	ADP
iajs-2478	220	20	equality	equality	NOUN
iajs-2478	220	21	and	and	CCONJ
iajs-2478	220	22	inequality	inequality	NOUN
iajs-2478	220	23	constraints	constraint	NOUN
iajs-2478	220	24	.	.	PUNCT
iajs-2478	221	1	iraqi	iraqi	ADJ
iajs-2478	221	2	journal	journal	NOUN
iajs-2478	221	3	of	of	ADP
iajs-2478	221	4	science.2016	science.2016	PROPN
iajs-2478	221	5	,	,	PUNCT
iajs-2478	221	6	57	57	NUM
iajs-2478	221	7	,	,	PUNCT
iajs-2478	221	8	2c	2c	NUM
iajs-2478	221	9	,	,	PUNCT
iajs-2478	221	10	1528	1528	NUM
iajs-2478	221	11	-	-	SYM
iajs-2478	221	12	1538	1538	NUM
iajs-2478	221	13	.	.	PUNCT
iajs-2478	222	1	10	10	NUM
iajs-2478	222	2	.	.	PUNCT
iajs-2478	223	1	al	al	PROPN
iajs-2478	223	2	-	-	PUNCT
iajs-2478	223	3	rawdhanee	rawdhanee	NOUN
iajs-2478	223	4	,	,	PUNCT
iajs-2478	223	5	e.h	e.h	PROPN
iajs-2478	223	6	.	.	PUNCT
iajs-2478	224	1	the	the	DET
iajs-2478	224	2	continuous	continuous	ADJ
iajs-2478	224	3	classical	classical	ADJ
iajs-2478	224	4	optimal	optimal	ADJ
iajs-2478	224	5	control	control	NOUN
iajs-2478	224	6	of	of	ADP
iajs-2478	224	7	a	a	DET
iajs-2478	224	8	couple	couple	NOUN
iajs-2478	224	9	nonlinear	nonlinear	ADJ
iajs-2478	224	10	elliptic	elliptic	ADJ
iajs-2478	224	11	partial	partial	ADJ
iajs-2478	224	12	differential	differential	NOUN
iajs-2478	224	13	equations	equation	NOUN
iajs-2478	224	14	.	.	PUNCT
iajs-2478	225	1	master	master	NOUN
iajs-2478	225	2	thesis	thesis	PROPN
iajs-2478	225	3	;	;	PUNCT
iajs-2478	225	4	al	al	PROPN
iajs-2478	225	5	-	-	PUNCT
iajs-2478	225	6	mustansiriyah	mustansiriyah	PROPN
iajs-2478	225	7	university	university	NOUN
iajs-2478	225	8	,	,	PUNCT
iajs-2478	225	9	2015	2015	NUM
iajs-2478	225	10	.	.	PUNCT
iajs-2478	226	1	11	11	NUM
iajs-2478	226	2	.	.	PUNCT
iajs-2478	227	1	al	al	PROPN
iajs-2478	227	2	-	-	PUNCT
iajs-2478	227	3	hawasy	hawasy	PROPN
iajs-2478	227	4	,	,	PUNCT
iajs-2478	227	5	j.	j.	PROPN
iajs-2478	227	6	;	;	PUNCT
iajs-2478	227	7	naeif	naeif	NOUN
iajs-2478	227	8	,	,	PUNCT
iajs-2478	227	9	a.a	a.a	PROPN
iajs-2478	227	10	.	.	PROPN
iajs-2478	227	11	the	the	DET
iajs-2478	227	12	continuous	continuous	ADJ
iajs-2478	227	13	classical	classical	ADJ
iajs-2478	227	14	boundary	boundary	ADJ
iajs-2478	227	15	optimal	optimal	ADJ
iajs-2478	227	16	control	control	NOUN
iajs-2478	227	17	of	of	ADP
iajs-2478	227	18	a	a	DET
iajs-2478	227	19	couple	couple	NOUN
iajs-2478	227	20	linear	linear	NOUN
iajs-2478	227	21	of	of	ADP
iajs-2478	227	22	parabolic	parabolic	ADJ
iajs-2478	227	23	partial	partial	ADJ
iajs-2478	227	24	differential	differential	NOUN
iajs-2478	227	25	equations	equation	NOUN
iajs-2478	227	26	.	.	PUNCT
iajs-2478	228	1	al	al	PROPN
iajs-2478	228	2	-	-	PUNCT
iajs-2478	228	3	mustansiriyah	mustansiriyah	PROPN
iajs-2478	228	4	journal	journal	NOUN
iajs-2478	228	5	of	of	ADP
iajs-2478	228	6	science	science	NOUN
iajs-2478	228	7	.	.	PUNCT
iajs-2478	229	1	2018	2018	NUM
iajs-2478	229	2	,	,	PUNCT
iajs-2478	229	3	29	29	NUM
iajs-2478	229	4	,	,	PUNCT
iajs-2478	229	5	1	1	NUM
iajs-2478	229	6	,	,	PUNCT
iajs-2478	229	7	118	118	NUM
iajs-2478	229	8	-	-	SYM
iajs-2478	229	9	126	126	NUM
iajs-2478	229	10	.	.	PUNCT
iajs-2478	230	1	doi	doi	NOUN
iajs-2478	230	2	:	:	PUNCT
iajs-2478	230	3	http://dx.doi.org/10.23851/mjs.v29i1.159	http://dx.doi.org/10.23851/mjs.v29i1.159	PROPN
iajs-2478	230	4	.	.	PROPN
iajs-2478	230	5	12	12	NUM
iajs-2478	230	6	.	.	PUNCT
iajs-2478	231	1	al	al	PROPN
iajs-2478	231	2	-	-	PUNCT
iajs-2478	231	3	hawasy	hawasy	PROPN
iajs-2478	231	4	,	,	PUNCT
iajs-2478	231	5	j.	j.	PROPN
iajs-2478	231	6	the	the	DET
iajs-2478	231	7	continuous	continuous	ADJ
iajs-2478	231	8	classical	classical	ADJ
iajs-2478	231	9	boundary	boundary	ADJ
iajs-2478	231	10	optimal	optimal	ADJ
iajs-2478	231	11	control	control	NOUN
iajs-2478	231	12	of	of	ADP
iajs-2478	231	13	couple	couple	NOUN
iajs-2478	231	14	nonlinear	nonlinear	ADJ
iajs-2478	231	15	hyperbolic	hyperbolic	ADJ
iajs-2478	231	16	boundary	boundary	ADJ
iajs-2478	231	17	value	value	NOUN
iajs-2478	231	18	problem	problem	NOUN
iajs-2478	231	19	with	with	ADP
iajs-2478	231	20	equality	equality	NOUN
iajs-2478	231	21	and	and	CCONJ
iajs-2478	231	22	inequality	inequality	NOUN
iajs-2478	231	23	constraints	constraint	NOUN
iajs-2478	231	24	.	.	PUNCT
iajs-2478	232	1	baghdad	baghdad	PROPN
iajs-2478	232	2	science	science	PROPN
iajs-2478	232	3	journal.2019	journal.2019	PROPN
iajs-2478	232	4	,	,	PUNCT
iajs-2478	232	5	(	(	PUNCT
iajs-2478	232	6	accepted	accept	VERB
iajs-2478	232	7	for	for	ADP
iajs-2478	232	8	publishing	publishing	NOUN
iajs-2478	232	9	)	)	PUNCT
iajs-2478	232	10	.	.	PUNCT
iajs-2478	233	1	13	13	NUM
iajs-2478	233	2	.	.	PUNCT
iajs-2478	234	1	al	al	PROPN
iajs-2478	234	2	-	-	PUNCT
iajs-2478	234	3	hawasy	hawasy	PROPN
iajs-2478	234	4	,	,	PUNCT
iajs-2478	234	5	j.	j.	PROPN
iajs-2478	234	6	;	;	PUNCT
iajs-2478	234	7	al	al	PROPN
iajs-2478	234	8	-	-	PUNCT
iajs-2478	234	9	qaisi	qaisi	PROPN
iajs-2478	234	10	,	,	PUNCT
iajs-2478	234	11	s.j	s.j	PROPN
iajs-2478	234	12	.	.	PUNCT
iajs-2478	235	1	the	the	DET
iajs-2478	235	2	continuous	continuous	ADJ
iajs-2478	235	3	classical	classical	ADJ
iajs-2478	235	4	optimal	optimal	ADJ
iajs-2478	235	5	boundary	boundary	ADJ
iajs-2478	235	6	control	control	NOUN
iajs-2478	235	7	of	of	ADP
iajs-2478	235	8	a	a	DET
iajs-2478	235	9	couple	couple	NOUN
iajs-2478	235	10	linear	linear	NOUN
iajs-2478	235	11	elliptic	elliptic	ADJ
iajs-2478	235	12	partial	partial	ADJ
iajs-2478	235	13	differential	differential	NOUN
iajs-2478	235	14	equations	equation	NOUN
iajs-2478	235	15	.	.	PUNCT
iajs-2478	236	1	special	special	ADJ
iajs-2478	236	2	issue	issue	NOUN
iajs-2478	236	3	,	,	PUNCT
iajs-2478	236	4	1st	1st	ADJ
iajs-2478	236	5	scientific	scientific	ADJ
iajs-2478	236	6	international	international	ADJ
iajs-2478	236	7	conference	conference	NOUN
iajs-2478	236	8	,	,	PUNCT
iajs-2478	236	9	college	college	NOUN
iajs-2478	236	10	of	of	ADP
iajs-2478	236	11	science	science	PROPN
iajs-2478	236	12	,	,	PUNCT
iajs-2478	236	13	al	al	PROPN
iajs-2478	236	14	-	-	PUNCT
iajs-2478	236	15	nahrain	nahrain	PROPN
iajs-2478	236	16	university.2017	university.2017	PROPN
iajs-2478	236	17	,	,	PUNCT
iajs-2478	236	18	i	i	PRON
iajs-2478	236	19	,	,	PUNCT
iajs-2478	236	20	137	137	NUM
iajs-2478	236	21	-	-	SYM
iajs-2478	236	22	142	142	NUM
iajs-2478	236	23	.	.	PUNCT
iajs-2478	237	1	doi	doi	NOUN
iajs-2478	237	2	:	:	PUNCT
iajs-2478	237	3	10.22401	10.22401	NUM
iajs-2478	237	4	/	/	SYM
iajs-2478	237	5	anjs.00.1.18	anjs.00.1.18	NOUN
iajs-2478	237	6	.	.	PROPN
iajs-2478	237	7	14	14	NUM
iajs-2478	237	8	.	.	PUNCT
iajs-2478	238	1	al	al	PROPN
iajs-2478	238	2	-	-	PUNCT
iajs-2478	238	3	hawasy	hawasy	PROPN
iajs-2478	238	4	,	,	PUNCT
iajs-2478	238	5	j.	j.	PROPN
iajs-2478	238	6	;	;	PUNCT
iajs-2478	238	7	mohamed	mohamed	PROPN
iajs-2478	238	8	,	,	PUNCT
iajs-2478	238	9	a.j	a.j	PROPN
iajs-2478	238	10	.	.	PROPN
iajs-2478	239	1	the	the	DET
iajs-2478	239	2	continuous	continuous	ADJ
iajs-2478	239	3	classical	classical	ADJ
iajs-2478	239	4	optimal	optimal	ADJ
iajs-2478	239	5	control	control	NOUN
iajs-2478	239	6	governing	govern	VERB
iajs-2478	239	7	by	by	ADP
iajs-2478	239	8	triple	triple	ADJ
iajs-2478	239	9	parabolic	parabolic	PROPN
iajs-2478	239	10	boundary	boundary	ADJ
iajs-2478	239	11	value	value	NOUN
iajs-2478	239	12	problem	problem	NOUN
iajs-2478	239	13	,	,	PUNCT
iajs-2478	239	14	submitted	submit	VERB
iajs-2478	239	15	in	in	ADP
iajs-2478	239	16	ibn	ibn	PROPN
iajs-2478	239	17	al	al	PROPN
iajs-2478	239	18	-	-	PUNCT
iajs-2478	239	19	haitham	haitham	PROPN
iajs-2478	239	20	for	for	ADP
iajs-2478	239	21	pure	pure	ADJ
iajs-2478	239	22	and	and	CCONJ
iajs-2478	239	23	applied	apply	VERB
iajs-2478	239	24	science	science	NOUN
iajs-2478	239	25	in	in	ADP
iajs-2478	239	26	,	,	PUNCT
iajs-2478	239	27	2020	2020	NUM
iajs-2478	239	28	.	.	PUNCT
iajs-2478	240	1	15	15	NUM
iajs-2478	240	2	.	.	PUNCT
iajs-2478	241	1	al	al	PROPN
iajs-2478	241	2	-	-	PUNCT
iajs-2478	241	3	hawasy	hawasy	PROPN
iajs-2478	241	4	,	,	PUNCT
iajs-2478	241	5	j.	j.	PROPN
iajs-2478	241	6	;	;	PUNCT
iajs-2478	241	7	jasim	jasim	PROPN
iajs-2478	241	8	,	,	PUNCT
iajs-2478	241	9	d.a	d.a	PROPN
iajs-2478	241	10	.	.	PUNCT
iajs-2478	242	1	the	the	DET
iajs-2478	242	2	continuous	continuous	ADJ
iajs-2478	242	3	classical	classical	ADJ
iajs-2478	242	4	optimal	optimal	ADJ
iajs-2478	242	5	control	control	NOUN
iajs-2478	242	6	problems	problem	NOUN
iajs-2478	242	7	for	for	ADP
iajs-2478	242	8	triple	triple	ADJ
iajs-2478	242	9	elliptic	elliptic	ADJ
iajs-2478	242	10	partial	partial	ADJ
iajs-2478	242	11	differential	differential	NOUN
iajs-2478	242	12	equations	equation	NOUN
iajs-2478	242	13	,	,	PUNCT
iajs-2478	242	14	submitted	submit	VERB
iajs-2478	242	15	in	in	ADP
iajs-2478	242	16	ibn	ibn	PROPN
iajs-2478	242	17	al	al	PROPN
iajs-2478	242	18	-	-	PUNCT
iajs-2478	242	19	haitham	haitham	PROPN
iajs-2478	242	20	for	for	ADP
iajs-2478	242	21	pure	pure	ADJ
iajs-2478	242	22	and	and	CCONJ
iajs-2478	242	23	applied	apply	VERB
iajs-2478	242	24	science	science	NOUN
iajs-2478	242	25	in	in	ADP
iajs-2478	242	26	,	,	PUNCT
iajs-2478	242	27	2020	2020	NUM
iajs-2478	242	28	.	.	PUNCT
iajs-2478	243	1	16	16	NUM
iajs-2478	243	2	.	.	PUNCT
iajs-2478	243	3	albiac	albiac	PROPN
iajs-2478	243	4	,	,	PUNCT
iajs-2478	243	5	f.	f.	PROPN
iajs-2478	243	6	;	;	PUNCT
iajs-2478	243	7	kalton	kalton	PROPN
iajs-2478	243	8	,	,	PUNCT
iajs-2478	243	9	n.j	n.j	PROPN
iajs-2478	243	10	.	.	PROPN
iajs-2478	243	11	topics	topic	NOUN
iajs-2478	243	12	in	in	ADP
iajs-2478	243	13	banach	banach	NOUN
iajs-2478	243	14	space	space	NOUN
iajs-2478	243	15	theory	theory	NOUN
iajs-2478	243	16	,	,	PUNCT
iajs-2478	243	17	2nd	2nd	ADJ
iajs-2478	243	18	ed	ed	NOUN
iajs-2478	243	19	.	.	PUNCT
iajs-2478	243	20	;	;	PUNCT
iajs-2478	243	21	springer	springer	NOUN
iajs-2478	243	22	,	,	PUNCT
iajs-2478	243	23	switzerland.2015	switzerland.2015	PROPN
iajs-2478	243	24	,	,	PUNCT
iajs-2478	243	25	isbn	isbn	ADJ
iajs-2478	243	26	978	978	NUM
iajs-2478	243	27	-	-	SYM
iajs-2478	243	28	3	3	NUM
iajs-2478	243	29	-	-	NUM
iajs-2478	243	30	319	319	NUM
iajs-2478	243	31	-	-	PUNCT
iajs-2478	243	32	31557	31557	NUM
iajs-2478	243	33	-	-	SYM
iajs-2478	243	34	7	7	NUM
iajs-2478	243	35	.	.	NUM
iajs-2478	243	36	17	17	NUM
iajs-2478	243	37	.	.	PUNCT
iajs-2478	244	1	marsden	marsden	PROPN
iajs-2478	244	2	,	,	PUNCT
iajs-2478	244	3	j.e	j.e	PROPN
iajs-2478	244	4	.	.	PROPN
iajs-2478	244	5	;	;	PUNCT
iajs-2478	244	6	sirovich	sirovich	PROPN
iajs-2478	244	7	,	,	PUNCT
iajs-2478	244	8	l.	l.	PROPN
iajs-2478	244	9	;	;	PUNCT
iajs-2478	244	10	golubitsky	golubitsky	ADJ
iajs-2478	244	11	,	,	PUNCT
iajs-2478	244	12	m.	m.	NOUN
iajs-2478	244	13	;	;	PUNCT
iajs-2478	244	14	jäger	jäger	PROPN
iajs-2478	244	15	,	,	PUNCT
iajs-2478	244	16	w.	w.	PROPN
iajs-2478	244	17	;	;	PUNCT
iajs-2478	244	18	john	john	PROPN
iajs-2478	244	19	,	,	PUNCT
iajs-2478	244	20	f.	f.	PROPN
iajs-2478	244	21	introductory	introductory	PROPN
iajs-2478	244	22	functional	functional	ADJ
iajs-2478	244	23	analysis	analysis	NOUN
iajs-2478	244	24	with	with	ADP
iajs-2478	244	25	applications	application	NOUN
iajs-2478	244	26	to	to	ADP
iajs-2478	244	27	boundary	boundary	ADJ
iajs-2478	244	28	value	value	NOUN
iajs-2478	244	29	problems	problem	NOUN
iajs-2478	244	30	and	and	CCONJ
iajs-2478	244	31	finite	finite	ADJ
iajs-2478	244	32	elements	element	NOUN
iajs-2478	244	33	.	.	PUNCT
iajs-2478	245	1	springer	springer	NOUN
iajs-2478	245	2	science	science	PROPN
iajs-2478	245	3	business	business	NOUN
iajs-2478	245	4	media	media	PROPN
iajs-2478	245	5	new	new	PROPN
iajs-2478	245	6	york	york	PROPN
iajs-2478	245	7	,	,	PUNCT
iajs-2478	245	8	1998	1998	NUM
iajs-2478	245	9	.	.	PUNCT