id	sid	tid	token	lemma	pos
iajs-2379	1	1	129	129	NUM
iajs-2379	1	2	ibn	ibn	PROPN
iajs-2379	1	3	al	al	PROPN
iajs-2379	1	4	-	-	PUNCT
iajs-2379	1	5	haitham	haitham	PROPN
iajs-2379	1	6	jour	jour	X
iajs-2379	1	7	.	.	PROPN
iajs-2379	1	8	for	for	ADP
iajs-2379	1	9	pure	pure	ADJ
iajs-2379	1	10	&	&	CCONJ
iajs-2379	1	11	appl	appl	PROPN
iajs-2379	1	12	.	.	PUNCT
iajs-2379	2	1	sci	sci	PROPN
iajs-2379	2	2	.	.	PROPN
iajs-2379	3	1	33	33	NUM
iajs-2379	3	2	(	(	PUNCT
iajs-2379	3	3	1	1	NUM
iajs-2379	3	4	)	)	PUNCT
iajs-2379	3	5	2020	2020	NUM
iajs-2379	3	6	doi	doi	NOUN
iajs-2379	3	7	:	:	PUNCT
iajs-2379	3	8	10.30526/33.1.2379	10.30526/33.1.2379	PROPN
iajs-2379	3	9	abstract	abstract	NOUN
iajs-2379	3	10	this	this	DET
iajs-2379	3	11	paper	paper	NOUN
iajs-2379	3	12	deals	deal	NOUN
iajs-2379	3	13	with	with	ADP
iajs-2379	3	14	the	the	DET
iajs-2379	3	15	continuous	continuous	ADJ
iajs-2379	3	16	classical	classical	ADJ
iajs-2379	3	17	optimal	optimal	ADJ
iajs-2379	3	18	control	control	NOUN
iajs-2379	3	19	problem	problem	NOUN
iajs-2379	3	20	for	for	ADP
iajs-2379	3	21	triple	triple	ADJ
iajs-2379	3	22	partial	partial	ADJ
iajs-2379	3	23	differential	differential	ADJ
iajs-2379	3	24	equations	equation	NOUN
iajs-2379	3	25	of	of	ADP
iajs-2379	3	26	parabolic	parabolic	ADJ
iajs-2379	3	27	type	type	NOUN
iajs-2379	3	28	with	with	ADP
iajs-2379	3	29	initial	initial	ADJ
iajs-2379	3	30	and	and	CCONJ
iajs-2379	3	31	boundary	boundary	ADJ
iajs-2379	3	32	conditions	condition	NOUN
iajs-2379	3	33	;	;	PUNCT
iajs-2379	3	34	the	the	DET
iajs-2379	3	35	galerkin	galerkin	ADJ
iajs-2379	3	36	method	method	NOUN
iajs-2379	3	37	is	be	AUX
iajs-2379	3	38	used	use	VERB
iajs-2379	3	39	to	to	PART
iajs-2379	3	40	prove	prove	VERB
iajs-2379	3	41	the	the	DET
iajs-2379	3	42	existence	existence	NOUN
iajs-2379	3	43	and	and	CCONJ
iajs-2379	3	44	uniqueness	uniqueness	NOUN
iajs-2379	3	45	theorem	theorem	NOUN
iajs-2379	3	46	of	of	ADP
iajs-2379	3	47	the	the	DET
iajs-2379	3	48	state	state	NOUN
iajs-2379	3	49	vector	vector	NOUN
iajs-2379	3	50	solution	solution	NOUN
iajs-2379	3	51	for	for	ADP
iajs-2379	3	52	given	give	VERB
iajs-2379	3	53	continuous	continuous	ADJ
iajs-2379	3	54	classical	classical	ADJ
iajs-2379	3	55	control	control	NOUN
iajs-2379	3	56	vector	vector	NOUN
iajs-2379	3	57	.	.	PUNCT
iajs-2379	4	1	the	the	DET
iajs-2379	4	2	proof	proof	NOUN
iajs-2379	4	3	of	of	ADP
iajs-2379	4	4	the	the	DET
iajs-2379	4	5	existence	existence	NOUN
iajs-2379	4	6	theorem	theorem	NOUN
iajs-2379	4	7	of	of	ADP
iajs-2379	4	8	a	a	DET
iajs-2379	4	9	continuous	continuous	ADJ
iajs-2379	4	10	classical	classical	ADJ
iajs-2379	4	11	optimal	optimal	ADJ
iajs-2379	4	12	control	control	NOUN
iajs-2379	4	13	vector	vector	NOUN
iajs-2379	4	14	associated	associate	VERB
iajs-2379	4	15	with	with	ADP
iajs-2379	4	16	the	the	DET
iajs-2379	4	17	triple	triple	ADJ
iajs-2379	4	18	linear	linear	ADJ
iajs-2379	4	19	partial	partial	ADJ
iajs-2379	4	20	differential	differential	ADJ
iajs-2379	4	21	equations	equation	NOUN
iajs-2379	4	22	of	of	ADP
iajs-2379	4	23	parabolic	parabolic	ADJ
iajs-2379	4	24	type	type	NOUN
iajs-2379	4	25	is	be	AUX
iajs-2379	4	26	given	give	VERB
iajs-2379	4	27	.	.	PUNCT
iajs-2379	5	1	the	the	DET
iajs-2379	5	2	derivation	derivation	NOUN
iajs-2379	5	3	of	of	ADP
iajs-2379	5	4	the	the	DET
iajs-2379	5	5	fréchet	fréchet	NOUN
iajs-2379	5	6	derivative	derivative	NOUN
iajs-2379	5	7	for	for	ADP
iajs-2379	5	8	the	the	DET
iajs-2379	5	9	cost	cost	NOUN
iajs-2379	5	10	function	function	NOUN
iajs-2379	5	11	is	be	AUX
iajs-2379	5	12	obtained	obtain	VERB
iajs-2379	5	13	.	.	PUNCT
iajs-2379	6	1	at	at	ADP
iajs-2379	6	2	the	the	DET
iajs-2379	6	3	end	end	NOUN
iajs-2379	6	4	,	,	PUNCT
iajs-2379	6	5	the	the	DET
iajs-2379	6	6	theorem	theorem	NOUN
iajs-2379	6	7	of	of	ADP
iajs-2379	6	8	the	the	DET
iajs-2379	6	9	necessary	necessary	ADJ
iajs-2379	6	10	conditions	condition	NOUN
iajs-2379	6	11	for	for	ADP
iajs-2379	6	12	optimality	optimality	NOUN
iajs-2379	6	13	of	of	ADP
iajs-2379	6	14	this	this	DET
iajs-2379	6	15	problem	problem	NOUN
iajs-2379	6	16	is	be	AUX
iajs-2379	6	17	stated	state	VERB
iajs-2379	6	18	and	and	CCONJ
iajs-2379	6	19	is	be	AUX
iajs-2379	6	20	proved	prove	VERB
iajs-2379	6	21	.	.	PUNCT
iajs-2379	7	1	keywords	keyword	NOUN
iajs-2379	7	2	:	:	PUNCT
iajs-2379	7	3	continuous	continuous	ADJ
iajs-2379	7	4	classical	classical	ADJ
iajs-2379	7	5	optimal	optimal	ADJ
iajs-2379	7	6	control	control	NOUN
iajs-2379	7	7	,	,	PUNCT
iajs-2379	7	8	triple	triple	ADJ
iajs-2379	7	9	parabolic	parabolic	ADJ
iajs-2379	7	10	partial	partial	ADJ
iajs-2379	7	11	differential	differential	NOUN
iajs-2379	7	12	equations	equation	NOUN
iajs-2379	7	13	,	,	PUNCT
iajs-2379	7	14	galerkin	galerkin	ADJ
iajs-2379	7	15	method	method	NOUN
iajs-2379	7	16	,	,	PUNCT
iajs-2379	7	17	the	the	DET
iajs-2379	7	18	necessary	necessary	ADJ
iajs-2379	7	19	conditions	condition	NOUN
iajs-2379	7	20	for	for	ADP
iajs-2379	7	21	optimality	optimality	NOUN
iajs-2379	7	22	.	.	PUNCT
iajs-2379	8	1	1	1	X
iajs-2379	8	2	.	.	X
iajs-2379	8	3	introduction	introduction	NOUN
iajs-2379	8	4	different	different	ADJ
iajs-2379	8	5	applications	application	NOUN
iajs-2379	8	6	for	for	ADP
iajs-2379	8	7	real	real	ADJ
iajs-2379	8	8	life	life	NOUN
iajs-2379	8	9	problems	problem	NOUN
iajs-2379	8	10	take	take	VERB
iajs-2379	8	11	a	a	DET
iajs-2379	8	12	main	main	ADJ
iajs-2379	8	13	place	place	NOUN
iajs-2379	8	14	in	in	ADP
iajs-2379	8	15	the	the	DET
iajs-2379	8	16	optimal	optimal	ADJ
iajs-2379	8	17	control	control	NOUN
iajs-2379	8	18	problems	problem	NOUN
iajs-2379	8	19	,	,	PUNCT
iajs-2379	8	20	for	for	ADP
iajs-2379	8	21	examples	example	NOUN
iajs-2379	8	22	in	in	ADP
iajs-2379	8	23	medicine	medicine	NOUN
iajs-2379	8	24	[	[	X
iajs-2379	8	25	1	1	NUM
iajs-2379	8	26	]	]	PUNCT
iajs-2379	8	27	.	.	PUNCT
iajs-2379	9	1	robots	robot	NOUN
iajs-2379	9	2	[	[	X
iajs-2379	9	3	2	2	NUM
iajs-2379	9	4	]	]	PUNCT
iajs-2379	9	5	.	.	PUNCT
iajs-2379	10	1	engineering	engineer	VERB
iajs-2379	11	1	[	[	X
iajs-2379	11	2	3	3	NUM
iajs-2379	11	3	]	]	PUNCT
iajs-2379	11	4	.	.	PUNCT
iajs-2379	12	1	economic	economic	ADJ
iajs-2379	12	2	[	[	X
iajs-2379	12	3	4	4	NUM
iajs-2379	12	4	]	]	PUNCT
iajs-2379	12	5	.	.	PUNCT
iajs-2379	13	1	and	and	CCONJ
iajs-2379	13	2	many	many	ADJ
iajs-2379	13	3	others	other	NOUN
iajs-2379	13	4	fields	field	NOUN
iajs-2379	13	5	.	.	PUNCT
iajs-2379	14	1	in	in	ADP
iajs-2379	14	2	the	the	DET
iajs-2379	14	3	field	field	NOUN
iajs-2379	14	4	of	of	ADP
iajs-2379	14	5	mathematics	mathematic	NOUN
iajs-2379	14	6	,	,	PUNCT
iajs-2379	14	7	optimal	optimal	ADJ
iajs-2379	14	8	control	control	NOUN
iajs-2379	14	9	problem	problem	NOUN
iajs-2379	14	10	(	(	PUNCT
iajs-2379	14	11	ocp	ocp	PROPN
iajs-2379	14	12	)	)	PUNCT
iajs-2379	14	13	usually	usually	ADV
iajs-2379	14	14	governing	govern	VERB
iajs-2379	14	15	either	either	ADV
iajs-2379	14	16	by	by	ADP
iajs-2379	14	17	ordinary	ordinary	ADJ
iajs-2379	14	18	differential	differential	ADJ
iajs-2379	14	19	equations	equation	NOUN
iajs-2379	14	20	(	(	PUNCT
iajs-2379	14	21	odes	ode	NOUN
iajs-2379	14	22	)	)	PUNCT
iajs-2379	14	23	or	or	CCONJ
iajs-2379	14	24	partial	partial	ADJ
iajs-2379	14	25	differential	differential	NOUN
iajs-2379	14	26	equations	equation	NOUN
iajs-2379	14	27	(	(	PUNCT
iajs-2379	14	28	pdes	pde	NOUN
iajs-2379	14	29	)	)	PUNCT
iajs-2379	14	30	,	,	PUNCT
iajs-2379	14	31	examples	example	NOUN
iajs-2379	14	32	for	for	ADP
iajs-2379	14	33	ocp	ocp	PROPN
iajs-2379	14	34	which	which	PRON
iajs-2379	14	35	are	be	AUX
iajs-2379	14	36	governing	govern	VERB
iajs-2379	14	37	by	by	ADP
iajs-2379	14	38	parabolic	parabolic	ADJ
iajs-2379	14	39	or	or	CCONJ
iajs-2379	14	40	hyperbolic	hyperbolic	ADJ
iajs-2379	14	41	or	or	CCONJ
iajs-2379	14	42	elliptic	elliptic	ADJ
iajs-2379	14	43	pdes	pde	NOUN
iajs-2379	14	44	are	be	AUX
iajs-2379	14	45	studied	study	VERB
iajs-2379	14	46	by	by	ADP
iajs-2379	14	47	[	[	PUNCT
iajs-2379	14	48	5	5	NUM
iajs-2379	14	49	-	-	SYM
iajs-2379	14	50	7	7	NUM
iajs-2379	14	51	]	]	PUNCT
iajs-2379	14	52	.	.	PUNCT
iajs-2379	15	1	respectively	respectively	ADV
iajs-2379	15	2	,	,	PUNCT
iajs-2379	15	3	while	while	SCONJ
iajs-2379	15	4	which	which	PRON
iajs-2379	15	5	are	be	AUX
iajs-2379	15	6	governing	govern	VERB
iajs-2379	15	7	by	by	ADP
iajs-2379	15	8	couple	couple	NOUN
iajs-2379	15	9	of	of	ADP
iajs-2379	15	10	pdes	pde	NOUN
iajs-2379	15	11	(	(	PUNCT
iajs-2379	15	12	cpdes	cpde	NOUN
iajs-2379	15	13	)	)	PUNCT
iajs-2379	15	14	of	of	ADP
iajs-2379	15	15	parabolic	parabolic	NOUN
iajs-2379	15	16	or	or	CCONJ
iajs-2379	15	17	of	of	ADP
iajs-2379	15	18	hyperbolic	hyperbolic	ADJ
iajs-2379	15	19	or	or	CCONJ
iajs-2379	15	20	of	of	ADP
iajs-2379	15	21	elliptic	elliptic	ADJ
iajs-2379	15	22	type	type	NOUN
iajs-2379	15	23	are	be	AUX
iajs-2379	15	24	studied	study	VERB
iajs-2379	15	25	by	by	ADP
iajs-2379	15	26	[	[	PUNCT
iajs-2379	15	27	8	8	NUM
iajs-2379	15	28	-	-	SYM
iajs-2379	15	29	10	10	NUM
iajs-2379	15	30	]	]	PUNCT
iajs-2379	15	31	.	.	PUNCT
iajs-2379	16	1	on	on	ADP
iajs-2379	16	2	the	the	DET
iajs-2379	16	3	other	other	ADJ
iajs-2379	16	4	hand	hand	NOUN
iajs-2379	16	5	[	[	X
iajs-2379	16	6	11	11	NUM
iajs-2379	16	7	-	-	SYM
iajs-2379	16	8	13	13	NUM
iajs-2379	16	9	]	]	PUNCT
iajs-2379	16	10	.	.	PUNCT
iajs-2379	17	1	rre	rre	PROPN
iajs-2379	17	2	studied	study	VERB
iajs-2379	17	3	boundary	boundary	ADJ
iajs-2379	17	4	ocp	ocp	PROPN
iajs-2379	17	5	associated	associate	VERB
iajs-2379	17	6	with	with	ADP
iajs-2379	17	7	cpdes	cpde	NOUN
iajs-2379	17	8	of	of	ADP
iajs-2379	17	9	parabolic	parabolic	ADJ
iajs-2379	17	10	,	,	PUNCT
iajs-2379	17	11	hyperbolic	hyperbolic	ADJ
iajs-2379	17	12	and	and	CCONJ
iajs-2379	17	13	elliptic	elliptic	ADJ
iajs-2379	17	14	;	;	PUNCT
iajs-2379	17	15	while	while	SCONJ
iajs-2379	17	16	[	[	X
iajs-2379	17	17	14	14	NUM
iajs-2379	17	18	]	]	PUNCT
iajs-2379	17	19	.	.	PUNCT
iajs-2379	17	20	studied	study	VERB
iajs-2379	17	21	the	the	DET
iajs-2379	17	22	ocp	ocp	NOUN
iajs-2379	17	23	for	for	ADP
iajs-2379	17	24	triple	triple	ADJ
iajs-2379	17	25	pdes	pde	NOUN
iajs-2379	17	26	(	(	PUNCT
iajs-2379	17	27	tpdes	tpde	NOUN
iajs-2379	17	28	)	)	PUNCT
iajs-2379	17	29	of	of	ADP
iajs-2379	17	30	elliptic	elliptic	ADJ
iajs-2379	17	31	type	type	NOUN
iajs-2379	17	32	.	.	PUNCT
iajs-2379	18	1	these	these	DET
iajs-2379	18	2	works	work	NOUN
iajs-2379	18	3	push	push	VERB
iajs-2379	18	4	us	we	PRON
iajs-2379	18	5	to	to	PART
iajs-2379	18	6	seek	seek	VERB
iajs-2379	18	7	about	about	ADP
iajs-2379	18	8	the	the	DET
iajs-2379	18	9	ocp	ocp	NOUN
iajs-2379	18	10	for	for	ADP
iajs-2379	18	11	tpdes	tpde	NOUN
iajs-2379	18	12	of	of	ADP
iajs-2379	18	13	parabolic	parabolic	ADJ
iajs-2379	18	14	type	type	NOUN
iajs-2379	18	15	.	.	PUNCT
iajs-2379	19	1	this	this	DET
iajs-2379	19	2	work	work	NOUN
iajs-2379	19	3	consists	consist	VERB
iajs-2379	19	4	of	of	ADP
iajs-2379	19	5	the	the	DET
iajs-2379	19	6	study	study	NOUN
iajs-2379	19	7	of	of	ADP
iajs-2379	19	8	the	the	DET
iajs-2379	19	9	continuous	continuous	ADJ
iajs-2379	19	10	classical	classical	ADJ
iajs-2379	19	11	optimal	optimal	ADJ
iajs-2379	19	12	control	control	NOUN
iajs-2379	19	13	governing	govern	VERB
iajs-2379	19	14	by	by	ADP
iajs-2379	19	15	triple	triple	ADJ
iajs-2379	19	16	linear	linear	PROPN
iajs-2379	19	17	parabolic	parabolic	ADJ
iajs-2379	19	18	boundary	boundary	ADJ
iajs-2379	19	19	value	value	NOUN
iajs-2379	19	20	problem	problem	NOUN
iajs-2379	19	21	ibn	ibn	PROPN
iajs-2379	19	22	al	al	PROPN
iajs-2379	19	23	haitham	haitham	PROPN
iajs-2379	19	24	journal	journal	PROPN
iajs-2379	19	25	for	for	ADP
iajs-2379	19	26	pure	pure	ADJ
iajs-2379	19	27	and	and	CCONJ
iajs-2379	19	28	applied	apply	VERB
iajs-2379	19	29	science	science	NOUN
iajs-2379	19	30	journal	journal	PROPN
iajs-2379	19	31	homepage	homepage	NOUN
iajs-2379	19	32	:	:	PUNCT
iajs-2379	19	33	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	PROPN
iajs-2379	19	34	department	department	PROPN
iajs-2379	19	35	of	of	ADP
iajs-2379	19	36	mathematics	mathematics	PROPN
iajs-2379	19	37	,	,	PUNCT
iajs-2379	19	38	college	college	NOUN
iajs-2379	19	39	of	of	ADP
iajs-2379	19	40	science	science	NOUN
iajs-2379	19	41	,	,	PUNCT
iajs-2379	19	42	mustansiriyah	mustansiriyah	NOUN
iajs-2379	19	43	of	of	ADP
iajs-2379	19	44	university	university	NOUN
iajs-2379	19	45	,	,	PUNCT
iajs-2379	19	46	baghdad	baghdad	PROPN
iajs-2379	19	47	,	,	PUNCT
iajs-2379	19	48	iraq	iraq	PROPN
iajs-2379	19	49	jamil	jamil	PROPN
iajs-2379	19	50	amir	amir	PROPN
iajs-2379	19	51	ali	ali	PROPN
iajs-2379	19	52	al	al	PROPN
iajs-2379	19	53	-	-	PROPN
iajs-2379	19	54	hawasy	hawasy	PROPN
iajs-2379	19	55	mohammed	mohammed	PROPN
iajs-2379	19	56	a.	a.	PROPN
iajs-2379	19	57	k.	k.	PROPN
iajs-2379	20	1	jaber	jaber	PROPN
iajs-2379	20	2	jhawassy17@uomustansiriyah.edu.iq	jhawassy17@uomustansiriyah.edu.iq	PROPN
iajs-2379	20	3	article	article	NOUN
iajs-2379	20	4	history	history	NOUN
iajs-2379	20	5	:	:	PUNCT
iajs-2379	20	6	received	receive	VERB
iajs-2379	20	7	3	3	NUM
iajs-2379	20	8	may	may	PROPN
iajs-2379	20	9	2019	2019	NUM
iajs-2379	20	10	,	,	PUNCT
iajs-2379	20	11	accepted	accept	VERB
iajs-2379	20	12	17	17	NUM
iajs-2379	20	13	june	june	PROPN
iajs-2379	20	14	2019	2019	NUM
iajs-2379	20	15	,	,	PUNCT
iajs-2379	20	16	publish	publish	VERB
iajs-2379	20	17	january	january	PROPN
iajs-2379	20	18	2020	2020	NUM
iajs-2379	20	19	.	.	PUNCT
iajs-2379	21	1	hawasy20@	hawasy20@	X
iajs-2379	21	2	yahoo.com	yahoo.com	X
iajs-2379	21	3	file:///d:/فزياء%20العدد%20الثالث%202019/moaayed99@gmail.com	file:///d:/فزياء%20العدد%20الثالث%202019/moaayed99@gmail.com	PROPN
iajs-2379	21	4	file:///c:/users/mustafa/desktop/2020/رياضيات/new%20folder/jhawassy17@uomustansiriyah.edu.iq	file:///c:/users/mustafa/desktop/2020/رياضيات/new%20folder/jhawassy17@uomustansiriyah.edu.iq	VERB
iajs-2379	21	5	file:///c:/users	file:///c:/user	NOUN
iajs-2379	21	6	/	/	SYM
iajs-2379	21	7	mustafa	mustafa	PROPN
iajs-2379	21	8	/	/	SYM
iajs-2379	21	9	desktop/2020	desktop/2020	PROPN
iajs-2379	21	10	/	/	SYM
iajs-2379	21	11	رياضيات	رياضيات	NOUN
iajs-2379	21	12	/	/	SYM
iajs-2379	21	13	new%20folder	new%20folder	NOUN
iajs-2379	21	14	/	/	SYM
iajs-2379	21	15	جميل%20ا.docx	جميل%20ا.docx	NOUN
iajs-2379	21	16	130	130	NUM
iajs-2379	21	17	ibn	ibn	PROPN
iajs-2379	21	18	al	al	PROPN
iajs-2379	21	19	-	-	PUNCT
iajs-2379	21	20	haitham	haitham	PROPN
iajs-2379	21	21	jour	jour	X
iajs-2379	21	22	.	.	PROPN
iajs-2379	21	23	for	for	ADP
iajs-2379	21	24	pure	pure	ADJ
iajs-2379	21	25	&	&	CCONJ
iajs-2379	21	26	appl	appl	PROPN
iajs-2379	21	27	.	.	PUNCT
iajs-2379	22	1	sci	sci	PROPN
iajs-2379	22	2	.	.	PROPN
iajs-2379	23	1	33	33	NUM
iajs-2379	23	2	(	(	PUNCT
iajs-2379	23	3	1	1	NUM
iajs-2379	23	4	)	)	PUNCT
iajs-2379	23	5	2020	2020	NUM
iajs-2379	24	1	the	the	DET
iajs-2379	24	2	continuous	continuous	ADJ
iajs-2379	24	3	classical	classical	ADJ
iajs-2379	24	4	optimal	optimal	ADJ
iajs-2379	24	5	control	control	NOUN
iajs-2379	24	6	problem	problem	NOUN
iajs-2379	24	7	(	(	PUNCT
iajs-2379	24	8	ccocp	ccocp	NOUN
iajs-2379	24	9	)	)	PUNCT
iajs-2379	24	10	,	,	PUNCT
iajs-2379	24	11	starting	start	VERB
iajs-2379	24	12	with	with	ADP
iajs-2379	24	13	the	the	DET
iajs-2379	24	14	state	state	NOUN
iajs-2379	24	15	and	and	CCONJ
iajs-2379	24	16	prove	prove	VERB
iajs-2379	24	17	the	the	DET
iajs-2379	24	18	existence	existence	NOUN
iajs-2379	24	19	theorem	theorem	VERB
iajs-2379	24	20	of	of	ADP
iajs-2379	24	21	a	a	DET
iajs-2379	24	22	unique	unique	ADJ
iajs-2379	24	23	solution	solution	NOUN
iajs-2379	24	24	(	(	PUNCT
iajs-2379	24	25	state	state	NOUN
iajs-2379	24	26	vector	vector	NOUN
iajs-2379	24	27	solution	solution	NOUN
iajs-2379	24	28	svs	sv	VERB
iajs-2379	24	29	)	)	PUNCT
iajs-2379	24	30	for	for	ADP
iajs-2379	24	31	the	the	DET
iajs-2379	24	32	triple	triple	ADJ
iajs-2379	24	33	state	state	NOUN
iajs-2379	24	34	equations	equation	NOUN
iajs-2379	24	35	(	(	PUNCT
iajs-2379	24	36	tse	tse	PROPN
iajs-2379	24	37	)	)	PUNCT
iajs-2379	24	38	of	of	ADP
iajs-2379	24	39	pdes	pde	NOUN
iajs-2379	24	40	of	of	ADP
iajs-2379	24	41	parabolic	parabolic	ADJ
iajs-2379	24	42	type	type	NOUN
iajs-2379	24	43	(	(	PUNCT
iajs-2379	24	44	tppdes	tppde	NOUN
iajs-2379	24	45	)	)	PUNCT
iajs-2379	24	46	by	by	ADP
iajs-2379	24	47	using	use	VERB
iajs-2379	24	48	the	the	DET
iajs-2379	24	49	galerkin	galerkin	ADJ
iajs-2379	24	50	method	method	NOUN
iajs-2379	24	51	(	(	PUNCT
iajs-2379	24	52	gm	gm	PROPN
iajs-2379	24	53	)	)	PUNCT
iajs-2379	24	54	when	when	SCONJ
iajs-2379	24	55	the	the	DET
iajs-2379	24	56	continuous	continuous	ADJ
iajs-2379	24	57	classical	classical	ADJ
iajs-2379	24	58	control	control	NOUN
iajs-2379	24	59	vector	vector	NOUN
iajs-2379	24	60	(	(	PUNCT
iajs-2379	24	61	cccv	cccv	PROPN
iajs-2379	24	62	)	)	PUNCT
iajs-2379	24	63	is	be	AUX
iajs-2379	24	64	fixed	fix	VERB
iajs-2379	24	65	then	then	ADV
iajs-2379	24	66	it	it	PRON
iajs-2379	24	67	deals	deal	VERB
iajs-2379	24	68	with	with	ADP
iajs-2379	24	69	the	the	DET
iajs-2379	24	70	state	state	NOUN
iajs-2379	24	71	and	and	CCONJ
iajs-2379	24	72	proof	proof	NOUN
iajs-2379	24	73	of	of	ADP
iajs-2379	24	74	the	the	DET
iajs-2379	24	75	existence	existence	NOUN
iajs-2379	24	76	theorem	theorem	NOUN
iajs-2379	24	77	of	of	ADP
iajs-2379	24	78	a	a	DET
iajs-2379	24	79	continuous	continuous	ADJ
iajs-2379	24	80	classical	classical	ADJ
iajs-2379	24	81	optimal	optimal	ADJ
iajs-2379	24	82	control	control	NOUN
iajs-2379	24	83	vector	vector	NOUN
iajs-2379	24	84	(	(	PUNCT
iajs-2379	24	85	ccocv	ccocv	PROPN
iajs-2379	24	86	)	)	PUNCT
iajs-2379	24	87	,	,	PUNCT
iajs-2379	24	88	the	the	DET
iajs-2379	24	89	solution	solution	NOUN
iajs-2379	24	90	vector	vector	NOUN
iajs-2379	24	91	of	of	ADP
iajs-2379	24	92	the	the	DET
iajs-2379	24	93	triple	triple	ADJ
iajs-2379	24	94	adjoint	adjoint	NOUN
iajs-2379	24	95	equations	equation	NOUN
iajs-2379	24	96	(	(	PUNCT
iajs-2379	24	97	tapes	tape	NOUN
iajs-2379	24	98	)	)	PUNCT
iajs-2379	24	99	associated	associate	VERB
iajs-2379	24	100	the	the	DET
iajs-2379	24	101	(	(	PUNCT
iajs-2379	24	102	tppdes	tppde	NOUN
iajs-2379	24	103	)	)	PUNCT
iajs-2379	24	104	is	be	AUX
iajs-2379	24	105	studied	study	VERB
iajs-2379	24	106	.	.	PUNCT
iajs-2379	25	1	the	the	DET
iajs-2379	25	2	derivation	derivation	NOUN
iajs-2379	25	3	of	of	ADP
iajs-2379	25	4	the	the	DET
iajs-2379	25	5	fréchet	fréchet	NOUN
iajs-2379	25	6	derivative	derivative	NOUN
iajs-2379	25	7	(	(	PUNCT
iajs-2379	25	8	fd	fd	PROPN
iajs-2379	25	9	)	)	PUNCT
iajs-2379	25	10	for	for	ADP
iajs-2379	25	11	the	the	DET
iajs-2379	25	12	cost	cost	NOUN
iajs-2379	25	13	function	function	NOUN
iajs-2379	25	14	is	be	AUX
iajs-2379	25	15	obtained	obtain	VERB
iajs-2379	25	16	,	,	PUNCT
iajs-2379	25	17	at	at	ADP
iajs-2379	25	18	the	the	DET
iajs-2379	25	19	end	end	NOUN
iajs-2379	25	20	;	;	PUNCT
iajs-2379	25	21	the	the	DET
iajs-2379	25	22	theorem	theorem	NOUN
iajs-2379	25	23	of	of	ADP
iajs-2379	25	24	the	the	DET
iajs-2379	25	25	necessary	necessary	ADJ
iajs-2379	25	26	conditions	condition	NOUN
iajs-2379	25	27	for	for	ADP
iajs-2379	25	28	optimality	optimality	NOUN
iajs-2379	25	29	(	(	PUNCT
iajs-2379	25	30	nco	nco	NOUN
iajs-2379	25	31	)	)	PUNCT
iajs-2379	25	32	of	of	ADP
iajs-2379	25	33	this	this	DET
iajs-2379	25	34	ocp	ocp	PROPN
iajs-2379	25	35	is	be	AUX
iajs-2379	25	36	sated	sate	VERB
iajs-2379	25	37	and	and	CCONJ
iajs-2379	25	38	proved	prove	VERB
iajs-2379	25	39	.	.	PUNCT
iajs-2379	26	1	2	2	X
iajs-2379	26	2	.	.	X
iajs-2379	26	3	description	description	NOUN
iajs-2379	26	4	of	of	ADP
iajs-2379	26	5	the	the	DET
iajs-2379	26	6	problem	problem	NOUN
iajs-2379	26	7	let	let	VERB
iajs-2379	26	8	ω	ω	PROPN
iajs-2379	26	9	⊂	⊂	PRON
iajs-2379	26	10	𝑅2	𝑅2	ADP
iajs-2379	26	11	,	,	PUNCT
iajs-2379	26	12	=(	=(	ADV
iajs-2379	26	13	)	)	PUNCT
iajs-2379	26	14	,	,	PUNCT
iajs-2379	26	15	=[	=[	NOUN
iajs-2379	26	16	0,t]×ω	0,t]×ω	NUM
iajs-2379	26	17	,	,	PUNCT
iajs-2379	26	18	ĩ=	ĩ=	ADJ
iajs-2379	26	19	[	[	X
iajs-2379	26	20	0,t	0,t	X
iajs-2379	26	21	]	]	X
iajs-2379	26	22	,	,	PUNCT
iajs-2379	26	23	=	=	SYM
iajs-2379	26	24	𝜕ω	𝜕ω	PROPN
iajs-2379	26	25	,	,	PUNCT
iajs-2379	26	26	,	,	PUNCT
iajs-2379	26	27	the	the	DET
iajs-2379	26	28	ccocp	ccocp	NOUN
iajs-2379	26	29	consists	consist	VERB
iajs-2379	26	30	of	of	ADP
iajs-2379	26	31	tse	tse	PROPN
iajs-2379	26	32	are	be	AUX
iajs-2379	26	33	given	give	VERB
iajs-2379	26	34	by	by	ADP
iajs-2379	26	35	the	the	DET
iajs-2379	26	36	following	follow	VERB
iajs-2379	26	37	tpdes	tpde	NOUN
iajs-2379	26	38	:	:	PUNCT
iajs-2379	26	39	(	(	PUNCT
iajs-2379	26	40	)	)	PUNCT
iajs-2379	26	41	(	(	PUNCT
iajs-2379	26	42	1	1	X
iajs-2379	26	43	)	)	PUNCT
iajs-2379	26	44	(	(	PUNCT
iajs-2379	26	45	)	)	PUNCT
iajs-2379	26	46	in	in	ADP
iajs-2379	26	47	(	(	PUNCT
iajs-2379	26	48	2	2	NUM
iajs-2379	26	49	)	)	PUNCT
iajs-2379	26	50	(	(	PUNCT
iajs-2379	26	51	)	)	PUNCT
iajs-2379	26	52	in	in	ADP
iajs-2379	26	53	(	(	PUNCT
iajs-2379	26	54	3	3	X
iajs-2379	26	55	)	)	PUNCT
iajs-2379	26	56	with	with	ADP
iajs-2379	26	57	the	the	DET
iajs-2379	26	58	following	following	ADJ
iajs-2379	26	59	boundary	boundary	ADJ
iajs-2379	26	60	conditions	condition	NOUN
iajs-2379	26	61	(	(	PUNCT
iajs-2379	26	62	bcs	bcs	NOUN
iajs-2379	26	63	)	)	PUNCT
iajs-2379	26	64	and	and	CCONJ
iajs-2379	26	65	the	the	DET
iajs-2379	26	66	initial	initial	ADJ
iajs-2379	26	67	conditions	condition	NOUN
iajs-2379	26	68	(	(	PUNCT
iajs-2379	26	69	ics	ics	NOUN
iajs-2379	26	70	)	)	PUNCT
iajs-2379	26	71	(	(	PUNCT
iajs-2379	26	72	)	)	PUNCT
iajs-2379	26	73	,	,	PUNCT
iajs-2379	26	74	on	on	ADP
iajs-2379	26	75	∑	∑	PROPN
iajs-2379	26	76	(	(	PUNCT
iajs-2379	26	77	4	4	NUM
iajs-2379	26	78	)	)	PUNCT
iajs-2379	26	79	(	(	PUNCT
iajs-2379	26	80	)	)	PUNCT
iajs-2379	26	81	,	,	PUNCT
iajs-2379	26	82	on	on	ADP
iajs-2379	26	83	∑	∑	PROPN
iajs-2379	26	84	(	(	PUNCT
iajs-2379	26	85	5	5	NUM
iajs-2379	26	86	)	)	PUNCT
iajs-2379	26	87	(	(	PUNCT
iajs-2379	26	88	)	)	PUNCT
iajs-2379	26	89	,	,	PUNCT
iajs-2379	26	90	on	on	ADP
iajs-2379	26	91	∑	∑	PROPN
iajs-2379	26	92	(	(	PUNCT
iajs-2379	26	93	6	6	NUM
iajs-2379	26	94	)	)	PUNCT
iajs-2379	26	95	(	(	PUNCT
iajs-2379	26	96	)	)	PUNCT
iajs-2379	26	97	(	(	PUNCT
iajs-2379	26	98	)	)	PUNCT
iajs-2379	26	99	,	,	PUNCT
iajs-2379	26	100	on	on	ADP
iajs-2379	26	101	ω	ω	PROPN
iajs-2379	26	102	(	(	PUNCT
iajs-2379	26	103	7	7	NUM
iajs-2379	26	104	)	)	PUNCT
iajs-2379	26	105	(	(	PUNCT
iajs-2379	26	106	)	)	PUNCT
iajs-2379	26	107	(	(	PUNCT
iajs-2379	26	108	)	)	PUNCT
iajs-2379	26	109	,	,	PUNCT
iajs-2379	26	110	on	on	ADP
iajs-2379	26	111	ω	ω	PROPN
iajs-2379	26	112	(	(	PUNCT
iajs-2379	26	113	8)	8)	NUM
iajs-2379	26	114	(	(	PUNCT
iajs-2379	26	115	)	)	PUNCT
iajs-2379	26	116	(	(	PUNCT
iajs-2379	26	117	)	)	PUNCT
iajs-2379	26	118	,	,	PUNCT
iajs-2379	26	119	on	on	ADP
iajs-2379	26	120	ω	ω	PROPN
iajs-2379	26	121	(	(	PUNCT
iajs-2379	26	122	9	9	NUM
iajs-2379	26	123	)	)	PUNCT
iajs-2379	26	124	where	where	SCONJ
iajs-2379	26	125	(	(	PUNCT
iajs-2379	26	126	,	,	PUNCT
iajs-2379	26	127	,	,	PUNCT
iajs-2379	26	128	)	)	PUNCT
iajs-2379	26	129	is	be	AUX
iajs-2379	26	130	a	a	DET
iajs-2379	26	131	vector	vector	NOUN
iajs-2379	26	132	of	of	ADP
iajs-2379	26	133	given	give	VERB
iajs-2379	26	134	function	function	NOUN
iajs-2379	26	135	for	for	ADP
iajs-2379	26	136	each	each	PRON
iajs-2379	26	137	(	(	PUNCT
iajs-2379	26	138	)	)	PUNCT
iajs-2379	26	139	,	,	PUNCT
iajs-2379	26	140	⃗	⃗	PROPN
iajs-2379	26	141	(	(	PUNCT
iajs-2379	26	142	,	,	PUNCT
iajs-2379	26	143	,	,	PUNCT
iajs-2379	26	144	)	)	PUNCT
iajs-2379	26	145	(	(	PUNCT
iajs-2379	26	146	(	(	PUNCT
iajs-2379	26	147	)	)	PUNCT
iajs-2379	26	148	)	)	PUNCT
iajs-2379	26	149	is	be	AUX
iajs-2379	26	150	a	a	DET
iajs-2379	26	151	cccv	cccv	NOUN
iajs-2379	26	152	and	and	CCONJ
iajs-2379	26	153	(	(	PUNCT
iajs-2379	26	154	,	,	PUNCT
iajs-2379	26	155	,	,	PUNCT
iajs-2379	26	156	)	)	PUNCT
iajs-2379	26	157	(	(	PUNCT
iajs-2379	26	158	(	(	PUNCT
iajs-2379	26	159	)	)	PUNCT
iajs-2379	26	160	)	)	PUNCT
iajs-2379	26	161	,	,	PUNCT
iajs-2379	26	162	is	be	AUX
iajs-2379	26	163	its	its	PRON
iajs-2379	26	164	corresponding	correspond	VERB
iajs-2379	26	165	svs	svs	NOUN
iajs-2379	26	166	the	the	DET
iajs-2379	26	167	set	set	NOUN
iajs-2379	26	168	of	of	ADP
iajs-2379	26	169	admissible	admissible	ADJ
iajs-2379	26	170	cccv	cccv	NOUN
iajs-2379	26	171	is	be	AUX
iajs-2379	26	172	defined	define	VERB
iajs-2379	26	173	by	by	ADP
iajs-2379	26	174	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	26	175	=	=	NOUN
iajs-2379	26	176	{	{	PUNCT
iajs-2379	26	177	(	(	PUNCT
iajs-2379	26	178	,	,	PUNCT
iajs-2379	26	179	,	,	PUNCT
iajs-2379	26	180	)	)	PUNCT
iajs-2379	26	181	(	(	PUNCT
iajs-2379	26	182	(	(	PUNCT
iajs-2379	26	183	)	)	PUNCT
iajs-2379	26	184	)	)	PUNCT
iajs-2379	26	185	∣	∣	PROPN
iajs-2379	26	186	(	(	PUNCT
iajs-2379	26	187	,	,	PUNCT
iajs-2379	26	188	,	,	PUNCT
iajs-2379	26	189	)	)	PUNCT
iajs-2379	27	1	⃗⃗	⃗⃗	PROPN
iajs-2379	27	2	⊂	⊂	PROPN
iajs-2379	27	3	𝑅	𝑅	PROPN
iajs-2379	27	4	a.e	a.e	PROPN
iajs-2379	27	5	.	.	PROPN
iajs-2379	28	1	in	in	ADP
iajs-2379	28	2	q	q	PROPN
iajs-2379	28	3	}	}	PUNCT
iajs-2379	28	4	,	,	PUNCT
iajs-2379	28	5	⃗⃗	⃗⃗	PROPN
iajs-2379	28	6	is	be	AUX
iajs-2379	28	7	convex	convex	PROPN
iajs-2379	28	8	.	.	PUNCT
iajs-2379	29	1	the	the	DET
iajs-2379	29	2	cost	cost	NOUN
iajs-2379	29	3	function	function	NOUN
iajs-2379	29	4	is	be	AUX
iajs-2379	29	5	defined	define	VERB
iajs-2379	29	6	for	for	ADP
iajs-2379	29	7	by	by	ADP
iajs-2379	29	8	(	(	PUNCT
iajs-2379	29	9	⃗	⃗	PROPN
iajs-2379	29	10	)	)	PUNCT
iajs-2379	29	11	(	(	PUNCT
iajs-2379	29	12	‖	‖	PROPN
iajs-2379	29	13	‖	‖	PROPN
iajs-2379	29	14	‖	‖	PROPN
iajs-2379	29	15	‖	‖	PROPN
iajs-2379	29	16	‖	‖	PROPN
iajs-2379	29	17	‖	‖	PROPN
iajs-2379	29	18	)	)	PUNCT
iajs-2379	29	19	(	(	PUNCT
iajs-2379	29	20	‖	‖	PROPN
iajs-2379	29	21	‖	‖	PROPN
iajs-2379	29	22	‖	‖	PROPN
iajs-2379	29	23	‖	‖	PROPN
iajs-2379	29	24	‖	‖	PROPN
iajs-2379	29	25	‖	‖	PROPN
iajs-2379	29	26	)	)	PUNCT
iajs-2379	29	27	(	(	PUNCT
iajs-2379	29	28	10	10	NUM
iajs-2379	29	29	)	)	PUNCT
iajs-2379	29	30	⃗	⃗	PROPN
iajs-2379	29	31	;	;	PUNCT
iajs-2379	29	32	(	(	PUNCT
iajs-2379	29	33	)	)	PUNCT
iajs-2379	29	34	⃗	⃗	PROPN
iajs-2379	29	35	{	{	PUNCT
iajs-2379	29	36	:	:	PUNCT
iajs-2379	29	37	=(	=(	INTJ
iajs-2379	29	38	,	,	PUNCT
iajs-2379	29	39	,	,	PUNCT
iajs-2379	29	40	)	)	PUNCT
iajs-2379	29	41	(	(	PUNCT
iajs-2379	29	42	(	(	PUNCT
iajs-2379	29	43	)	)	PUNCT
iajs-2379	29	44	)	)	PUNCT
iajs-2379	29	45	,	,	PUNCT
iajs-2379	29	46	on𝜕	on𝜕	VERB
iajs-2379	29	47	}	}	PUNCT
iajs-2379	29	48	.	.	PUNCT
iajs-2379	30	1	the	the	DET
iajs-2379	30	2	weak	weak	ADJ
iajs-2379	30	3	form(wf	form(wf	NOUN
iajs-2379	30	4	)	)	PUNCT
iajs-2379	30	5	of	of	ADP
iajs-2379	30	6	problem	problem	NOUN
iajs-2379	30	7	(	(	PUNCT
iajs-2379	30	8	19	19	NUM
iajs-2379	30	9	)	)	PUNCT
iajs-2379	30	10	when	when	SCONJ
iajs-2379	30	11	(	(	PUNCT
iajs-2379	30	12	(	(	PUNCT
iajs-2379	30	13	)	)	PUNCT
iajs-2379	30	14	)	)	PUNCT
iajs-2379	30	15	is	be	AUX
iajs-2379	30	16	given	give	VERB
iajs-2379	30	17	by	by	ADP
iajs-2379	30	18	〈	〈	PROPN
iajs-2379	30	19	〉	〉	NOUN
iajs-2379	30	20	(	(	PUNCT
iajs-2379	30	21	)	)	PUNCT
iajs-2379	30	22	(	(	PUNCT
iajs-2379	30	23	)	)	PUNCT
iajs-2379	30	24	(	(	PUNCT
iajs-2379	30	25	)	)	PUNCT
iajs-2379	30	26	(	(	PUNCT
iajs-2379	30	27	)	)	PUNCT
iajs-2379	30	28	=	=	SYM
iajs-2379	30	29	(	(	PUNCT
iajs-2379	30	30	)	)	PUNCT
iajs-2379	30	31	,	,	PUNCT
iajs-2379	30	32	(	(	PUNCT
iajs-2379	30	33	11.a	11.a	NUM
iajs-2379	30	34	)	)	PUNCT
iajs-2379	30	35	(	(	PUNCT
iajs-2379	30	36	)	)	PUNCT
iajs-2379	30	37	(	(	PUNCT
iajs-2379	30	38	(	(	PUNCT
iajs-2379	30	39	)	)	PUNCT
iajs-2379	30	40	)	)	PUNCT
iajs-2379	30	41	,	,	PUNCT
iajs-2379	30	42	(	(	PUNCT
iajs-2379	30	43	11.b	11.b	X
iajs-2379	30	44	)	)	PUNCT
iajs-2379	30	45	〈	〈	NOUN
iajs-2379	30	46	〉	〉	NOUN
iajs-2379	30	47	(	(	PUNCT
iajs-2379	30	48	)	)	PUNCT
iajs-2379	30	49	(	(	PUNCT
iajs-2379	30	50	)	)	PUNCT
iajs-2379	30	51	(	(	PUNCT
iajs-2379	30	52	)	)	PUNCT
iajs-2379	30	53	(	(	PUNCT
iajs-2379	30	54	)	)	PUNCT
iajs-2379	30	55	(	(	PUNCT
iajs-2379	30	56	)	)	PUNCT
iajs-2379	30	57	(	(	PUNCT
iajs-2379	30	58	11.a	11.a	NUM
iajs-2379	30	59	)	)	PUNCT
iajs-2379	30	60	(	(	PUNCT
iajs-2379	30	61	)	)	PUNCT
iajs-2379	30	62	(	(	PUNCT
iajs-2379	30	63	(	(	PUNCT
iajs-2379	30	64	)	)	PUNCT
iajs-2379	30	65	)	)	PUNCT
iajs-2379	30	66	,	,	PUNCT
iajs-2379	30	67	(	(	PUNCT
iajs-2379	30	68	11.b	11.b	X
iajs-2379	30	69	)	)	PUNCT
iajs-2379	30	70	〈	〈	NOUN
iajs-2379	30	71	〉	〉	NOUN
iajs-2379	30	72	(	(	PUNCT
iajs-2379	30	73	)	)	PUNCT
iajs-2379	30	74	(	(	PUNCT
iajs-2379	30	75	)	)	PUNCT
iajs-2379	30	76	(	(	PUNCT
iajs-2379	30	77	)	)	PUNCT
iajs-2379	30	78	(	(	PUNCT
iajs-2379	30	79	)	)	PUNCT
iajs-2379	30	80	(	(	PUNCT
iajs-2379	30	81	)	)	PUNCT
iajs-2379	30	82	(	(	PUNCT
iajs-2379	30	83	11.a	11.a	NUM
iajs-2379	30	84	)	)	PUNCT
iajs-2379	30	85	(	(	PUNCT
iajs-2379	30	86	)	)	PUNCT
iajs-2379	30	87	(	(	PUNCT
iajs-2379	30	88	(	(	PUNCT
iajs-2379	30	89	)	)	PUNCT
iajs-2379	30	90	)	)	PUNCT
iajs-2379	30	91	,	,	PUNCT
iajs-2379	30	92	(	(	PUNCT
iajs-2379	30	93	11.b	11.b	X
iajs-2379	30	94	)	)	PUNCT
iajs-2379	30	95	the	the	DET
iajs-2379	30	96	following	follow	VERB
iajs-2379	30	97	assumption	assumption	NOUN
iajs-2379	30	98	is	be	AUX
iajs-2379	30	99	important	important	ADJ
iajs-2379	30	100	to	to	PART
iajs-2379	30	101	study	study	VERB
iajs-2379	30	102	the	the	DET
iajs-2379	30	103	ccocv	ccocv	ADJ
iajs-2379	30	104	problem	problem	NOUN
iajs-2379	30	105	(	(	PUNCT
iajs-2379	30	106	ccocvp	ccocvp	NOUN
iajs-2379	30	107	)	)	PUNCT
iajs-2379	30	108	2.1	2.1	NUM
iajs-2379	30	109	.	.	PUNCT
iajs-2379	31	1	assumption	assumption	NOUN
iajs-2379	31	2	(	(	PUNCT
iajs-2379	31	3	a	a	X
iajs-2379	31	4	):	):	PUNCT
iajs-2379	31	5	the	the	DET
iajs-2379	31	6	function	function	NOUN
iajs-2379	31	7	(	(	PUNCT
iajs-2379	31	8	)	)	PUNCT
iajs-2379	31	9	is	be	AUX
iajs-2379	31	10	satisfied	satisfied	ADJ
iajs-2379	31	11	the	the	DET
iajs-2379	31	12	following	follow	VERB
iajs-2379	31	13	condition	condition	NOUN
iajs-2379	31	14	w.r.t	w.r.t	NOUN
iajs-2379	31	15	.	.	PUNCT
iajs-2379	32	1	&	&	CCONJ
iajs-2379	32	2	,	,	PUNCT
iajs-2379	32	3	i.e.	i.e.	X
iajs-2379	32	4	|	|	ADV
iajs-2379	32	5	|	|	ADV
iajs-2379	32	6	(	(	PUNCT
iajs-2379	32	7	)	)	PUNCT
iajs-2379	32	8	,	,	PUNCT
iajs-2379	32	9	where	where	SCONJ
iajs-2379	32	10	(	(	PUNCT
iajs-2379	32	11	)	)	PUNCT
iajs-2379	32	12	,	,	PUNCT
iajs-2379	32	13	(	(	PUNCT
iajs-2379	32	14	)	)	PUNCT
iajs-2379	32	15	.	.	PUNCT
iajs-2379	33	1	3	3	X
iajs-2379	33	2	.	.	X
iajs-2379	33	3	the	the	DET
iajs-2379	33	4	solution	solution	NOUN
iajs-2379	33	5	for	for	ADP
iajs-2379	33	6	the	the	DET
iajs-2379	33	7	wf	wf	PROPN
iajs-2379	33	8	:	:	PUNCT
iajs-2379	33	9	theorem	theorem	VERB
iajs-2379	33	10	3.1	3.1	NUM
iajs-2379	33	11	:	:	PUNCT
iajs-2379	33	12	existence	existence	NOUN
iajs-2379	33	13	of	of	ADP
iajs-2379	33	14	a	a	DET
iajs-2379	33	15	unique	unique	ADJ
iajs-2379	33	16	solution	solution	NOUN
iajs-2379	33	17	for	for	ADP
iajs-2379	33	18	the	the	DET
iajs-2379	33	19	wf	wf	PROPN
iajs-2379	33	20	:	:	PUNCT
iajs-2379	33	21	with	with	ADP
iajs-2379	33	22	assumption	assumption	NOUN
iajs-2379	33	23	(	(	PUNCT
iajs-2379	33	24	a	a	NOUN
iajs-2379	33	25	)	)	PUNCT
iajs-2379	33	26	,	,	PUNCT
iajs-2379	33	27	for	for	ADP
iajs-2379	33	28	each	each	DET
iajs-2379	33	29	given	give	VERB
iajs-2379	33	30	cccv	cccv	PROPN
iajs-2379	33	31	⃗	⃗	PROPN
iajs-2379	33	32	(	(	PUNCT
iajs-2379	33	33	(	(	PUNCT
iajs-2379	33	34	)	)	PUNCT
iajs-2379	33	35	)	)	PUNCT
iajs-2379	33	36	,	,	PUNCT
iajs-2379	33	37	the	the	DET
iajs-2379	33	38	wf(11−13	wf(11−13	PROPN
iajs-2379	33	39	(	(	PUNCT
iajs-2379	33	40	has	have	VERB
iajs-2379	33	41	a	a	DET
iajs-2379	33	42	unique	unique	ADJ
iajs-2379	33	43	solution	solution	NOUN
iajs-2379	33	44	(	(	PUNCT
iajs-2379	33	45	)	)	PUNCT
iajs-2379	33	46	with	with	ADP
iajs-2379	33	47	(	(	PUNCT
iajs-2379	33	48	(	(	PUNCT
iajs-2379	33	49	)	)	PUNCT
iajs-2379	33	50	)	)	PUNCT
iajs-2379	33	51	and	and	CCONJ
iajs-2379	33	52	(	(	PUNCT
iajs-2379	33	53	)	)	PUNCT
iajs-2379	33	54	(	(	PUNCT
iajs-2379	33	55	(	(	PUNCT
iajs-2379	33	56	)	)	PUNCT
iajs-2379	33	57	)	)	PUNCT
iajs-2379	34	1	131	131	NUM
iajs-2379	34	2	ibn	ibn	PROPN
iajs-2379	34	3	al	al	PROPN
iajs-2379	34	4	-	-	PUNCT
iajs-2379	34	5	haitham	haitham	PROPN
iajs-2379	34	6	jour	jour	X
iajs-2379	34	7	.	.	PROPN
iajs-2379	34	8	for	for	ADP
iajs-2379	34	9	pure	pure	ADJ
iajs-2379	34	10	&	&	CCONJ
iajs-2379	34	11	appl	appl	PROPN
iajs-2379	34	12	.	.	PUNCT
iajs-2379	35	1	sci	sci	PROPN
iajs-2379	35	2	.	.	PROPN
iajs-2379	36	1	33	33	NUM
iajs-2379	36	2	(	(	PUNCT
iajs-2379	36	3	1	1	NUM
iajs-2379	36	4	)	)	PUNCT
iajs-2379	36	5	2020	2020	NUM
iajs-2379	37	1	proof	proof	NOUN
iajs-2379	37	2	:	:	PUNCT
iajs-2379	37	3	let	let	VERB
iajs-2379	37	4	for	for	ADP
iajs-2379	37	5	each	each	PRON
iajs-2379	37	6	,	,	PUNCT
iajs-2379	37	7	⃗	⃗	PROPN
iajs-2379	37	8	⊂	⊂	X
iajs-2379	37	9	⃗	⃗	AUX
iajs-2379	37	10	be	be	AUX
iajs-2379	37	11	the	the	DET
iajs-2379	37	12	set	set	NOUN
iajs-2379	37	13	of	of	ADP
iajs-2379	37	14	continuous	continuous	ADJ
iajs-2379	37	15	and	and	CCONJ
iajs-2379	37	16	piecewise	piecewise	NOUN
iajs-2379	37	17	affine	affine	NOUN
iajs-2379	37	18	functions	function	NOUN
iajs-2379	37	19	in	in	ADP
iajs-2379	37	20	let	let	VERB
iajs-2379	37	21	,	,	PUNCT
iajs-2379	37	22	be	be	AUX
iajs-2379	37	23	a	a	DET
iajs-2379	37	24	basis	basis	NOUN
iajs-2379	37	25	of	of	ADP
iajs-2379	37	26	=	=	PUNCT
iajs-2379	37	27	,	,	PUNCT
iajs-2379	37	28	and	and	CCONJ
iajs-2379	37	29	let	let	VERB
iajs-2379	37	30	be	be	AUX
iajs-2379	37	31	an	an	DET
iajs-2379	37	32	approximate	approximate	ADJ
iajs-2379	37	33	solution	solution	NOUN
iajs-2379	37	34	for	for	ADP
iajs-2379	37	35	the	the	DET
iajs-2379	37	36	solution	solution	NOUN
iajs-2379	37	37	,	,	PUNCT
iajs-2379	37	38	then	then	ADV
iajs-2379	37	39	by	by	ADP
iajs-2379	37	40	gm	gm	PROPN
iajs-2379	37	41	:	:	PUNCT
iajs-2379	37	42	∑	∑	PUNCT
iajs-2379	37	43	(	(	PUNCT
iajs-2379	37	44	)	)	PUNCT
iajs-2379	37	45	(	(	PUNCT
iajs-2379	37	46	)	)	PUNCT
iajs-2379	37	47	(	(	PUNCT
iajs-2379	37	48	14	14	NUM
iajs-2379	37	49	)	)	PUNCT
iajs-2379	37	50	∑	∑	PUNCT
iajs-2379	37	51	(	(	PUNCT
iajs-2379	37	52	)	)	PUNCT
iajs-2379	37	53	(	(	PUNCT
iajs-2379	37	54	)	)	PUNCT
iajs-2379	37	55	(	(	PUNCT
iajs-2379	37	56	15	15	NUM
iajs-2379	37	57	)	)	PUNCT
iajs-2379	37	58	∑	∑	PUNCT
iajs-2379	37	59	(	(	PUNCT
iajs-2379	37	60	)	)	PUNCT
iajs-2379	37	61	(	(	PUNCT
iajs-2379	37	62	)	)	PUNCT
iajs-2379	37	63	(	(	PUNCT
iajs-2379	37	64	16	16	NUM
iajs-2379	37	65	)	)	PUNCT
iajs-2379	37	66	where	where	SCONJ
iajs-2379	37	67	(	(	PUNCT
iajs-2379	37	68	)	)	PUNCT
iajs-2379	37	69	is	be	AUX
iajs-2379	37	70	unknown	unknown	ADJ
iajs-2379	37	71	function	function	NOUN
iajs-2379	37	72	of	of	ADP
iajs-2379	37	73	,	,	PUNCT
iajs-2379	37	74	,	,	PUNCT
iajs-2379	37	75	.	.	PUNCT
iajs-2379	38	1	the	the	DET
iajs-2379	38	2	wf	wf	PROPN
iajs-2379	38	3	(	(	PUNCT
iajs-2379	38	4	11–13	11–13	NUM
iajs-2379	38	5	)	)	PUNCT
iajs-2379	38	6	is	be	AUX
iajs-2379	38	7	approximated	approximate	VERB
iajs-2379	38	8	by	by	ADP
iajs-2379	38	9	using	use	VERB
iajs-2379	38	10	(	(	PUNCT
iajs-2379	38	11	14−16	14−16	NOUN
iajs-2379	38	12	)	)	PUNCT
iajs-2379	38	13	as	as	ADP
iajs-2379	38	14	,	,	PUNCT
iajs-2379	38	15	〈	〈	NOUN
iajs-2379	38	16	〉	〉	NOUN
iajs-2379	38	17	(	(	PUNCT
iajs-2379	38	18	)	)	PUNCT
iajs-2379	38	19	(	(	PUNCT
iajs-2379	38	20	)	)	PUNCT
iajs-2379	38	21	(	(	PUNCT
iajs-2379	38	22	)	)	PUNCT
iajs-2379	38	23	(	(	PUNCT
iajs-2379	38	24	)	)	PUNCT
iajs-2379	38	25	(	(	PUNCT
iajs-2379	38	26	)	)	PUNCT
iajs-2379	38	27	,	,	PUNCT
iajs-2379	38	28	(	(	PUNCT
iajs-2379	38	29	11.a	11.a	NUM
iajs-2379	38	30	)	)	PUNCT
iajs-2379	38	31	(	(	PUNCT
iajs-2379	38	32	)	)	PUNCT
iajs-2379	38	33	(	(	PUNCT
iajs-2379	38	34	)	)	PUNCT
iajs-2379	38	35	,	,	PUNCT
iajs-2379	38	36	(	(	PUNCT
iajs-2379	38	37	11.b	11.b	X
iajs-2379	38	38	)	)	PUNCT
iajs-2379	38	39	〈	〈	NOUN
iajs-2379	38	40	〉	〉	NOUN
iajs-2379	38	41	(	(	PUNCT
iajs-2379	38	42	)	)	PUNCT
iajs-2379	38	43	(	(	PUNCT
iajs-2379	38	44	)	)	PUNCT
iajs-2379	38	45	(	(	PUNCT
iajs-2379	38	46	)	)	PUNCT
iajs-2379	38	47	(	(	PUNCT
iajs-2379	38	48	)	)	PUNCT
iajs-2379	38	49	(	(	PUNCT
iajs-2379	38	50	)	)	PUNCT
iajs-2379	38	51	,	,	PUNCT
iajs-2379	38	52	(	(	PUNCT
iajs-2379	38	53	11.a	11.a	NUM
iajs-2379	38	54	)	)	PUNCT
iajs-2379	38	55	(	(	PUNCT
iajs-2379	38	56	)	)	PUNCT
iajs-2379	38	57	(	(	PUNCT
iajs-2379	38	58	)	)	PUNCT
iajs-2379	38	59	,	,	PUNCT
iajs-2379	38	60	(	(	PUNCT
iajs-2379	38	61	11.b	11.b	X
iajs-2379	38	62	)	)	PUNCT
iajs-2379	38	63	〈	〈	NOUN
iajs-2379	38	64	〉	〉	NOUN
iajs-2379	38	65	(	(	PUNCT
iajs-2379	38	66	)	)	PUNCT
iajs-2379	38	67	(	(	PUNCT
iajs-2379	38	68	)	)	PUNCT
iajs-2379	38	69	(	(	PUNCT
iajs-2379	38	70	)	)	PUNCT
iajs-2379	38	71	(	(	PUNCT
iajs-2379	38	72	)	)	PUNCT
iajs-2379	38	73	(	(	PUNCT
iajs-2379	38	74	)	)	PUNCT
iajs-2379	38	75	,	,	PUNCT
iajs-2379	38	76	(	(	PUNCT
iajs-2379	38	77	11.a	11.a	NUM
iajs-2379	38	78	)	)	PUNCT
iajs-2379	38	79	(	(	PUNCT
iajs-2379	38	80	)	)	PUNCT
iajs-2379	38	81	(	(	PUNCT
iajs-2379	38	82	)	)	PUNCT
iajs-2379	38	83	,	,	PUNCT
iajs-2379	38	84	(	(	PUNCT
iajs-2379	38	85	11.b	11.b	NUM
iajs-2379	38	86	)	)	PUNCT
iajs-2379	38	87	where	where	SCONJ
iajs-2379	38	88	(	(	PUNCT
iajs-2379	38	89	)	)	PUNCT
iajs-2379	38	90	(	(	PUNCT
iajs-2379	38	91	)	)	PUNCT
iajs-2379	38	92	⊂	⊂	PROPN
iajs-2379	38	93	⊂	⊂	X
iajs-2379	38	94	(	(	PUNCT
iajs-2379	38	95	)	)	PUNCT
iajs-2379	38	96	is	be	AUX
iajs-2379	38	97	the	the	DET
iajs-2379	38	98	projection	projection	NOUN
iajs-2379	38	99	of	of	ADP
iajs-2379	38	100	,	,	PUNCT
iajs-2379	38	101	thus	thus	ADV
iajs-2379	38	102	(	(	PUNCT
iajs-2379	38	103	)	)	PUNCT
iajs-2379	38	104	(	(	PUNCT
iajs-2379	38	105	)	)	PUNCT
iajs-2379	38	106	∣∣	∣∣	NUM
iajs-2379	39	1	∣∣	∣∣	NUM
iajs-2379	39	2	∣∣	∣∣	NUM
iajs-2379	39	3	∣∣	∣∣	PROPN
iajs-2379	39	4	,	,	PUNCT
iajs-2379	39	5	substituting	substitute	VERB
iajs-2379	39	6	(	(	PUNCT
iajs-2379	39	7	14−16	14−16	NOUN
iajs-2379	39	8	)	)	PUNCT
iajs-2379	39	9	in	in	ADP
iajs-2379	39	10	(	(	PUNCT
iajs-2379	39	11	17−19	17−19	NOUN
iajs-2379	39	12	)	)	PUNCT
iajs-2379	39	13	respectively	respectively	ADV
iajs-2379	39	14	and	and	CCONJ
iajs-2379	39	15	then	then	ADV
iajs-2379	39	16	setting	set	VERB
iajs-2379	39	17	,	,	PUNCT
iajs-2379	39	18	&	&	CCONJ
iajs-2379	39	19	then	then	ADV
iajs-2379	39	20	the	the	DET
iajs-2379	39	21	obtained	obtain	VERB
iajs-2379	39	22	equations	equation	NOUN
iajs-2379	39	23	are	be	AUX
iajs-2379	39	24	equivalent	equivalent	ADJ
iajs-2379	39	25	to	to	ADP
iajs-2379	39	26	the	the	DET
iajs-2379	39	27	following	follow	VERB
iajs-2379	39	28	linear	linear	NOUN
iajs-2379	39	29	system	system	NOUN
iajs-2379	39	30	(	(	PUNCT
iajs-2379	39	31	ls	ls	PROPN
iajs-2379	39	32	)	)	PUNCT
iajs-2379	39	33	of	of	ADP
iajs-2379	39	34	order	order	NOUN
iajs-2379	39	35	odes	ode	VERB
iajs-2379	39	36	with	with	ADP
iajs-2379	39	37	ics	ic	NOUN
iajs-2379	39	38	(	(	PUNCT
iajs-2379	39	39	which	which	PRON
iajs-2379	39	40	has	have	VERB
iajs-2379	39	41	a	a	DET
iajs-2379	39	42	unique	unique	ADJ
iajs-2379	39	43	solution	solution	NOUN
iajs-2379	39	44	)	)	PUNCT
iajs-2379	39	45	,	,	PUNCT
iajs-2379	39	46	i.e.	i.e.	X
iajs-2379	39	47	(	(	PUNCT
iajs-2379	39	48	)	)	PUNCT
iajs-2379	39	49	(	(	PUNCT
iajs-2379	39	50	)	)	PUNCT
iajs-2379	39	51	(	(	PUNCT
iajs-2379	39	52	)	)	PUNCT
iajs-2379	39	53	(	(	PUNCT
iajs-2379	39	54	)	)	PUNCT
iajs-2379	39	55	(	(	PUNCT
iajs-2379	39	56	20.a	20.a	NUM
iajs-2379	39	57	)	)	PUNCT
iajs-2379	39	58	(	(	PUNCT
iajs-2379	39	59	)	)	PUNCT
iajs-2379	39	60	(	(	PUNCT
iajs-2379	39	61	20.b	20.b	NUM
iajs-2379	39	62	)	)	PUNCT
iajs-2379	39	63	(	(	PUNCT
iajs-2379	39	64	)	)	PUNCT
iajs-2379	39	65	(	(	PUNCT
iajs-2379	39	66	)	)	PUNCT
iajs-2379	39	67	(	(	PUNCT
iajs-2379	39	68	)	)	PUNCT
iajs-2379	39	69	(	(	PUNCT
iajs-2379	39	70	)	)	PUNCT
iajs-2379	39	71	(	(	PUNCT
iajs-2379	39	72	21.a	21.a	NUM
iajs-2379	39	73	)	)	PUNCT
iajs-2379	39	74	(	(	PUNCT
iajs-2379	39	75	)	)	PUNCT
iajs-2379	39	76	(	(	PUNCT
iajs-2379	39	77	21.b	21.b	NUM
iajs-2379	39	78	)	)	PUNCT
iajs-2379	39	79	(	(	PUNCT
iajs-2379	39	80	)	)	PUNCT
iajs-2379	39	81	(	(	PUNCT
iajs-2379	39	82	)	)	PUNCT
iajs-2379	39	83	𝑅	𝑅	PROPN
iajs-2379	39	84	(	(	PUNCT
iajs-2379	39	85	)	)	PUNCT
iajs-2379	39	86	(	(	PUNCT
iajs-2379	39	87	)	)	PUNCT
iajs-2379	39	88	(	(	PUNCT
iajs-2379	39	89	22.a	22.a	NUM
iajs-2379	39	90	)	)	PUNCT
iajs-2379	39	91	(	(	PUNCT
iajs-2379	39	92	)	)	PUNCT
iajs-2379	39	93	(	(	PUNCT
iajs-2379	39	94	22.b	22.b	NUM
iajs-2379	39	95	)	)	PUNCT
iajs-2379	39	96	where	where	SCONJ
iajs-2379	39	97	a	a	PRON
iajs-2379	39	98	(	(	PUNCT
iajs-2379	39	99	)	)	PUNCT
iajs-2379	39	100	,	,	PUNCT
iajs-2379	39	101	(	(	PUNCT
iajs-2379	39	102	,	,	PUNCT
iajs-2379	39	103	)	)	PUNCT
iajs-2379	39	104	,	,	PUNCT
iajs-2379	39	105	b	b	X
iajs-2379	39	106	=	=	SYM
iajs-2379	39	107	(	(	PUNCT
iajs-2379	39	108	)	)	PUNCT
iajs-2379	39	109	,	,	PUNCT
iajs-2379	39	110	=	=	PUNCT
iajs-2379	39	111	(	(	PUNCT
iajs-2379	39	112	,	,	PUNCT
iajs-2379	39	113	)	)	PUNCT
iajs-2379	39	114	+	+	CCONJ
iajs-2379	39	115	(	(	PUNCT
iajs-2379	39	116	,	,	PUNCT
iajs-2379	39	117	)	)	PUNCT
iajs-2379	39	118	,	,	PUNCT
iajs-2379	39	119	d	d	NOUN
iajs-2379	39	120	=	=	PRON
iajs-2379	39	121	(	(	PUNCT
iajs-2379	39	122	)	)	PUNCT
iajs-2379	39	123	,	,	PUNCT
iajs-2379	39	124	(	(	PUNCT
iajs-2379	39	125	,	,	PUNCT
iajs-2379	39	126	)	)	PUNCT
iajs-2379	39	127	,	,	PUNCT
iajs-2379	39	128	e	e	X
iajs-2379	39	129	=	=	PUNCT
iajs-2379	39	130	(	(	PUNCT
iajs-2379	39	131	)	)	PUNCT
iajs-2379	39	132	,	,	PUNCT
iajs-2379	39	133	(	(	PUNCT
iajs-2379	39	134	,	,	PUNCT
iajs-2379	39	135	)	)	PUNCT
iajs-2379	39	136	,	,	PUNCT
iajs-2379	39	137	f	f	X
iajs-2379	39	138	=	=	PRON
iajs-2379	39	139	(	(	PUNCT
iajs-2379	39	140	)	)	PUNCT
iajs-2379	39	141	,	,	PUNCT
iajs-2379	39	142	(	(	PUNCT
iajs-2379	39	143	,	,	PUNCT
iajs-2379	39	144	)	)	PUNCT
iajs-2379	39	145	,	,	PUNCT
iajs-2379	39	146	g	g	NOUN
iajs-2379	39	147	=	=	SYM
iajs-2379	39	148	(	(	PUNCT
iajs-2379	39	149	)	)	PUNCT
iajs-2379	39	150	=	=	SYM
iajs-2379	39	151	(	(	PUNCT
iajs-2379	39	152	,	,	PUNCT
iajs-2379	39	153	)	)	PUNCT
iajs-2379	39	154	+	+	CCONJ
iajs-2379	39	155	(	(	PUNCT
iajs-2379	39	156	,	,	PUNCT
iajs-2379	39	157	)	)	PUNCT
iajs-2379	39	158	,	,	PUNCT
iajs-2379	39	159	h	h	NOUN
iajs-2379	39	160	=	=	PRON
iajs-2379	39	161	(	(	PUNCT
iajs-2379	39	162	)	)	PUNCT
iajs-2379	39	163	,	,	PUNCT
iajs-2379	39	164	(	(	PUNCT
iajs-2379	39	165	,	,	PUNCT
iajs-2379	39	166	)	)	PUNCT
iajs-2379	39	167	,	,	PUNCT
iajs-2379	39	168	k	k	PROPN
iajs-2379	39	169	=	=	PRON
iajs-2379	39	170	(	(	PUNCT
iajs-2379	39	171	)	)	PUNCT
iajs-2379	39	172	,	,	PUNCT
iajs-2379	39	173	(	(	PUNCT
iajs-2379	39	174	,	,	PUNCT
iajs-2379	39	175	)	)	PUNCT
iajs-2379	39	176	,	,	PUNCT
iajs-2379	39	177	m	m	VERB
iajs-2379	39	178	=	=	SYM
iajs-2379	39	179	(	(	PUNCT
iajs-2379	39	180	)	)	PUNCT
iajs-2379	39	181	,	,	PUNCT
iajs-2379	39	182	(	(	PUNCT
iajs-2379	39	183	,	,	PUNCT
iajs-2379	39	184	)	)	PUNCT
iajs-2379	39	185	,	,	PUNCT
iajs-2379	39	186	n	n	NOUN
iajs-2379	39	187	=	=	SYM
iajs-2379	39	188	(	(	PUNCT
iajs-2379	39	189	)	)	PUNCT
iajs-2379	39	190	,	,	PUNCT
iajs-2379	39	191	=	=	PUNCT
iajs-2379	39	192	(	(	PUNCT
iajs-2379	39	193	,	,	PUNCT
iajs-2379	39	194	)	)	PUNCT
iajs-2379	39	195	+	+	ADJ
iajs-2379	39	196	(	(	PUNCT
iajs-2379	39	197	,	,	PUNCT
iajs-2379	39	198	)	)	PUNCT
iajs-2379	39	199	r	r	NOUN
iajs-2379	39	200	(	(	PUNCT
iajs-2379	39	201	)	)	PUNCT
iajs-2379	39	202	,	,	PUNCT
iajs-2379	39	203	(	(	PUNCT
iajs-2379	39	204	,	,	PUNCT
iajs-2379	39	205	)	)	PUNCT
iajs-2379	39	206	,	,	PUNCT
iajs-2379	39	207	w	w	NOUN
iajs-2379	39	208	=	=	SYM
iajs-2379	39	209	(	(	PUNCT
iajs-2379	39	210	)	)	PUNCT
iajs-2379	39	211	,	,	PUNCT
iajs-2379	39	212	(	(	PUNCT
iajs-2379	39	213	,	,	PUNCT
iajs-2379	39	214	)	)	PUNCT
iajs-2379	39	215	,	,	PUNCT
iajs-2379	39	216	(	(	PUNCT
iajs-2379	39	217	)	)	PUNCT
iajs-2379	39	218	,	,	PUNCT
iajs-2379	39	219	=	=	PRON
iajs-2379	39	220	(	(	PUNCT
iajs-2379	39	221	)	)	PUNCT
iajs-2379	39	222	,	,	PUNCT
iajs-2379	39	223	=	=	PRON
iajs-2379	39	224	(	(	PUNCT
iajs-2379	39	225	)	)	PUNCT
iajs-2379	39	226	,	,	PUNCT
iajs-2379	39	227	=	=	PUNCT
iajs-2379	39	228	(	(	PUNCT
iajs-2379	39	229	,	,	PUNCT
iajs-2379	39	230	)	)	PUNCT
iajs-2379	39	231	,	,	PUNCT
iajs-2379	39	232	(	(	PUNCT
iajs-2379	39	233	)	)	PUNCT
iajs-2379	39	234	=	=	SYM
iajs-2379	39	235	(	(	PUNCT
iajs-2379	39	236	(	(	PUNCT
iajs-2379	39	237	)	)	PUNCT
iajs-2379	39	238	)	)	PUNCT
iajs-2379	39	239	,	,	PUNCT
iajs-2379	39	240	(	(	PUNCT
iajs-2379	39	241	t	t	NOUN
iajs-2379	39	242	)	)	PUNCT
iajs-2379	39	243	=	=	SYM
iajs-2379	39	244	(	(	PUNCT
iajs-2379	39	245	(	(	PUNCT
iajs-2379	39	246	)	)	PUNCT
iajs-2379	39	247	)	)	PUNCT
iajs-2379	39	248	,	,	PUNCT
iajs-2379	39	249	(	(	PUNCT
iajs-2379	39	250	0	0	X
iajs-2379	39	251	)	)	PUNCT
iajs-2379	39	252	=	=	SYM
iajs-2379	39	253	(	(	PUNCT
iajs-2379	39	254	(	(	PUNCT
iajs-2379	39	255	)	)	PUNCT
iajs-2379	39	256	)	)	PUNCT
iajs-2379	39	257	,	,	PUNCT
iajs-2379	39	258	=	=	PUNCT
iajs-2379	39	259	1,2,3,	1,2,3,	NUM
iajs-2379	39	260	…	…	PUNCT
iajs-2379	39	261	,n	,n	NOUN
iajs-2379	39	262	,	,	PUNCT
iajs-2379	39	263	=	=	NOUN
iajs-2379	39	264	1,2,3	1,2,3	NOUN
iajs-2379	39	265	.	.	PUNCT
iajs-2379	39	266	to	to	PART
iajs-2379	39	267	show	show	VERB
iajs-2379	39	268	the	the	DET
iajs-2379	39	269	norm	norm	NOUN
iajs-2379	39	270	‖	‖	PROPN
iajs-2379	39	271	⃗⃗⃗⃗	⃗⃗⃗⃗	NOUN
iajs-2379	39	272	‖	‖	ADJ
iajs-2379	39	273	is	be	AUX
iajs-2379	39	274	bounded	bound	VERB
iajs-2379	39	275	since	since	SCONJ
iajs-2379	39	276	(	(	PUNCT
iajs-2379	39	277	)	)	PUNCT
iajs-2379	39	278	,	,	PUNCT
iajs-2379	39	279	then	then	ADV
iajs-2379	39	280	there	there	PRON
iajs-2379	39	281	exists	exist	VERB
iajs-2379	39	282	a	a	DET
iajs-2379	39	283	sequence	sequence	NOUN
iajs-2379	39	284	*	*	PUNCT
iajs-2379	39	285	+	+	CCONJ
iajs-2379	39	286	with	with	ADP
iajs-2379	39	287	,	,	PUNCT
iajs-2379	39	288	such	such	ADJ
iajs-2379	39	289	that	that	SCONJ
iajs-2379	39	290	strongly	strongly	ADV
iajs-2379	39	291	in	in	ADP
iajs-2379	39	292	(	(	PUNCT
iajs-2379	39	293	)	)	PUNCT
iajs-2379	39	294	,	,	PUNCT
iajs-2379	39	295	then	then	ADV
iajs-2379	39	296	from	from	ADP
iajs-2379	39	297	the	the	DET
iajs-2379	39	298	projection	projection	NOUN
iajs-2379	39	299	theorem	theorem	NOUN
iajs-2379	39	300	[	[	X
iajs-2379	39	301	15	15	NUM
iajs-2379	39	302	]	]	PUNCT
iajs-2379	39	303	.	.	PUNCT
iajs-2379	40	1	and	and	CCONJ
iajs-2379	40	2	(	(	PUNCT
iajs-2379	40	3	11.b	11.b	NUM
iajs-2379	40	4	)	)	PUNCT
iajs-2379	40	5	,	,	PUNCT
iajs-2379	40	6	‖	‖	PROPN
iajs-2379	40	7	‖	‖	PROPN
iajs-2379	40	8	‖	‖	PROPN
iajs-2379	40	9	‖	‖	PROPN
iajs-2379	40	10	then	then	ADV
iajs-2379	40	11	‖	‖	PROPN
iajs-2379	40	12	‖	‖	PROPN
iajs-2379	40	13	‖	‖	PROPN
iajs-2379	40	14	‖	‖	PROPN
iajs-2379	40	15	⊂	⊂	PROPN
iajs-2379	40	16	,	,	PUNCT
iajs-2379	40	17	strongly	strongly	ADV
iajs-2379	40	18	in	in	ADP
iajs-2379	40	19	(	(	PUNCT
iajs-2379	40	20	)	)	PUNCT
iajs-2379	40	21	with	with	ADP
iajs-2379	40	22	‖	‖	PROPN
iajs-2379	40	23	‖	‖	PROPN
iajs-2379	40	24	,	,	PUNCT
iajs-2379	40	25	by	by	ADP
iajs-2379	40	26	the	the	DET
iajs-2379	40	27	same	same	ADJ
iajs-2379	40	28	way	way	NOUN
iajs-2379	40	29	,	,	PUNCT
iajs-2379	40	30	one	one	PRON
iajs-2379	40	31	can	can	AUX
iajs-2379	40	32	show	show	VERB
iajs-2379	40	33	that	that	SCONJ
iajs-2379	40	34	‖	‖	PROPN
iajs-2379	40	35	‖	‖	PROPN
iajs-2379	40	36	&	&	CCONJ
iajs-2379	40	37	‖	‖	PROPN
iajs-2379	40	38	‖	‖	PROPN
iajs-2379	40	39	,	,	PUNCT
iajs-2379	40	40	then	then	ADV
iajs-2379	40	41	‖	‖	PROPN
iajs-2379	40	42	⃗⃗⃗⃗	⃗⃗⃗⃗	PROPN
iajs-2379	40	43	‖	‖	ADJ
iajs-2379	40	44	is	be	AUX
iajs-2379	40	45	bounded	bound	VERB
iajs-2379	40	46	in	in	ADP
iajs-2379	40	47	(	(	PUNCT
iajs-2379	40	48	(	(	PUNCT
iajs-2379	40	49	)	)	PUNCT
iajs-2379	40	50	)	)	PUNCT
iajs-2379	40	51	.	.	PUNCT
iajs-2379	41	1	132	132	NUM
iajs-2379	41	2	ibn	ibn	PROPN
iajs-2379	41	3	al	al	PROPN
iajs-2379	41	4	-	-	PUNCT
iajs-2379	41	5	haitham	haitham	PROPN
iajs-2379	41	6	jour	jour	X
iajs-2379	41	7	.	.	PROPN
iajs-2379	41	8	for	for	ADP
iajs-2379	41	9	pure	pure	ADJ
iajs-2379	41	10	&	&	CCONJ
iajs-2379	41	11	appl	appl	PROPN
iajs-2379	41	12	.	.	PUNCT
iajs-2379	42	1	sci	sci	PROPN
iajs-2379	42	2	.	.	PROPN
iajs-2379	43	1	33	33	NUM
iajs-2379	43	2	(	(	PUNCT
iajs-2379	43	3	1	1	NUM
iajs-2379	43	4	)	)	PUNCT
iajs-2379	43	5	2020	2020	NUM
iajs-2379	43	6	the	the	DET
iajs-2379	43	7	norms‖	norms‖	PROPN
iajs-2379	43	8	⃗⃗⃗⃗	⃗⃗⃗⃗	NOUN
iajs-2379	43	9	(	(	PUNCT
iajs-2379	43	10	)	)	PUNCT
iajs-2379	43	11	‖	‖	PROPN
iajs-2379	43	12	.	.	PUNCT
iajs-2379	44	1	(	(	PUNCT
iajs-2379	44	2	)	)	PUNCT
iajs-2379	44	3	/	/	SYM
iajs-2379	44	4	and‖	and‖	ADJ
iajs-2379	44	5	⃗⃗⃗⃗	⃗⃗⃗⃗	NOUN
iajs-2379	44	6	(	(	PUNCT
iajs-2379	44	7	)	)	PUNCT
iajs-2379	44	8	‖	‖	PROPN
iajs-2379	44	9	are	be	AUX
iajs-2379	44	10	bounded	bound	VERB
iajs-2379	44	11	setting	setting	NOUN
iajs-2379	44	12	,	,	PUNCT
iajs-2379	44	13	and	and	CCONJ
iajs-2379	44	14	in	in	ADP
iajs-2379	44	15	(	(	PUNCT
iajs-2379	44	16	11	11	NUM
iajs-2379	44	17	–	–	SYM
iajs-2379	44	18	19	19	NUM
iajs-2379	44	19	)	)	PUNCT
iajs-2379	44	20	respectively	respectively	ADV
iajs-2379	44	21	,	,	PUNCT
iajs-2379	44	22	integrating	integrate	VERB
iajs-2379	44	23	w.r.t	w.r.t	NOUN
iajs-2379	44	24	.	.	PUNCT
iajs-2379	45	1	from	from	ADP
iajs-2379	45	2	to	to	ADP
iajs-2379	45	3	,	,	PUNCT
iajs-2379	45	4	adding	add	VERB
iajs-2379	45	5	the	the	DET
iajs-2379	45	6	obtained	obtain	VERB
iajs-2379	45	7	three	three	NUM
iajs-2379	45	8	equations	equation	NOUN
iajs-2379	45	9	,	,	PUNCT
iajs-2379	45	10	one	one	PRON
iajs-2379	45	11	gets	get	VERB
iajs-2379	45	12	∫	∫	PROPN
iajs-2379	46	1	〈	〈	PROPN
iajs-2379	46	2	〉	〉	NOUN
iajs-2379	46	3	∫	∫	PROPN
iajs-2379	46	4	‖	‖	PROPN
iajs-2379	46	5	‖	‖	PROPN
iajs-2379	46	6	∫	∫	PROPN
iajs-2379	46	7	,	,	PUNCT
iajs-2379	46	8	(	(	PUNCT
iajs-2379	46	9	)	)	PUNCT
iajs-2379	46	10	(	(	PUNCT
iajs-2379	46	11	)	)	PUNCT
iajs-2379	46	12	(	(	PUNCT
iajs-2379	46	13	)	)	PUNCT
iajs-2379	46	14	(	(	PUNCT
iajs-2379	46	15	23	23	NUM
iajs-2379	46	16	)	)	PUNCT
iajs-2379	46	17	using	use	VERB
iajs-2379	46	18	lemma	lemma	PROPN
iajs-2379	46	19	(	(	PUNCT
iajs-2379	46	20	1.2	1.2	NUM
iajs-2379	46	21	)	)	PUNCT
iajs-2379	46	22	in	in	ADP
iajs-2379	46	23	[	[	X
iajs-2379	46	24	11	11	NUM
iajs-2379	46	25	]	]	PUNCT
iajs-2379	46	26	.	.	PUNCT
iajs-2379	47	1	for	for	ADP
iajs-2379	47	2	the	the	DET
iajs-2379	47	3	term	term	NOUN
iajs-2379	47	4	in	in	ADP
iajs-2379	47	5	the	the	DET
iajs-2379	47	6	l.h.s	l.h.s	NOUN
iajs-2379	47	7	.	.	PUNCT
iajs-2379	48	1	of	of	ADP
iajs-2379	48	2	(	(	PUNCT
iajs-2379	48	3	23	23	NUM
iajs-2379	48	4	)	)	PUNCT
iajs-2379	48	5	and	and	CCONJ
iajs-2379	48	6	since	since	SCONJ
iajs-2379	48	7	the	the	DET
iajs-2379	48	8	term	term	NOUN
iajs-2379	48	9	is	be	AUX
iajs-2379	48	10	positive	positive	ADJ
iajs-2379	48	11	,	,	PUNCT
iajs-2379	48	12	using	use	VERB
iajs-2379	48	13	assumptions	assumption	NOUN
iajs-2379	48	14	(	(	PUNCT
iajs-2379	48	15	a	a	X
iajs-2379	48	16	)	)	PUNCT
iajs-2379	48	17	for	for	ADP
iajs-2379	48	18	the	the	DET
iajs-2379	48	19	r.h.s	r.h.s	NOUN
iajs-2379	48	20	.	.	PUNCT
iajs-2379	49	1	of	of	ADP
iajs-2379	49	2	(	(	PUNCT
iajs-2379	49	3	23	23	NUM
iajs-2379	49	4	)	)	PUNCT
iajs-2379	49	5	,	,	PUNCT
iajs-2379	49	6	it	it	PRON
iajs-2379	49	7	yields	yield	VERB
iajs-2379	49	8	∫	∫	PROPN
iajs-2379	50	1	‖	‖	PROPN
iajs-2379	51	1	(	(	PUNCT
iajs-2379	51	2	)	)	PUNCT
iajs-2379	51	3	‖	‖	PROPN
iajs-2379	51	4	∫	∫	PROPN
iajs-2379	51	5	∫	∫	PROPN
iajs-2379	52	1	|	|	ADV
iajs-2379	52	2	|	|	ADV
iajs-2379	53	1	∫	∫	PROPN
iajs-2379	53	2	∫	∫	PROPN
iajs-2379	54	1	|	|	ADV
iajs-2379	54	2	||	||	PUNCT
iajs-2379	55	1	|	|	ADV
iajs-2379	55	2	∫	∫	PROPN
iajs-2379	56	1	∫	∫	PROPN
iajs-2379	57	1	|	|	ADV
iajs-2379	57	2	|	|	ADV
iajs-2379	58	1	∫	∫	PROPN
iajs-2379	58	2	∫	∫	PROPN
iajs-2379	59	1	|	|	ADV
iajs-2379	59	2	||	||	NOUN
iajs-2379	60	1	|	|	ADV
iajs-2379	61	1	+	+	NUM
iajs-2379	61	2	∫	∫	PROPN
iajs-2379	61	3	∫	∫	PROPN
iajs-2379	62	1	|	|	ADV
iajs-2379	62	2	|	|	ADV
iajs-2379	63	1	∫	∫	PROPN
iajs-2379	63	2	∫	∫	PROPN
iajs-2379	64	1	|	|	ADV
iajs-2379	64	2	||	||	PUNCT
iajs-2379	65	1	|	|	ADV
iajs-2379	65	2	∫	∫	PROPN
iajs-2379	65	3	‖	‖	PROPN
iajs-2379	66	1	(	(	PUNCT
iajs-2379	66	2	)	)	PUNCT
iajs-2379	66	3	‖	‖	PROPN
iajs-2379	66	4	‖	‖	PROPN
iajs-2379	66	5	‖	‖	PROPN
iajs-2379	66	6	‖	‖	PROPN
iajs-2379	66	7	‖	‖	PROPN
iajs-2379	66	8	‖	‖	PROPN
iajs-2379	66	9	‖	‖	PROPN
iajs-2379	66	10	‖	‖	PROPN
iajs-2379	66	11	‖	‖	PROPN
iajs-2379	66	12	‖	‖	PROPN
iajs-2379	66	13	‖	‖	PROPN
iajs-2379	66	14	‖	‖	PROPN
iajs-2379	66	15	‖	‖	PROPN
iajs-2379	66	16	∫	∫	PROPN
iajs-2379	66	17	‖	‖	PROPN
iajs-2379	66	18	‖	‖	PROPN
iajs-2379	66	19	∫	∫	PROPN
iajs-2379	66	20	‖	‖	PROPN
iajs-2379	66	21	‖	‖	PROPN
iajs-2379	66	22	∫	∫	PROPN
iajs-2379	66	23	‖	‖	PROPN
iajs-2379	66	24	‖	‖	PROPN
iajs-2379	66	25	since‖	since‖	PROPN
iajs-2379	66	26	‖	‖	PROPN
iajs-2379	66	27	́	́	PROPN
iajs-2379	66	28	‖	‖	ADJ
iajs-2379	66	29	‖	‖	ADJ
iajs-2379	66	30	,	,	PUNCT
iajs-2379	66	31	,	,	PUNCT
iajs-2379	66	32	‖	‖	PROPN
iajs-2379	66	33	(	(	PUNCT
iajs-2379	66	34	)	)	PUNCT
iajs-2379	66	35	‖	‖	PROPN
iajs-2379	66	36	.	.	PUNCT
iajs-2379	67	1	‖	‖	PROPN
iajs-2379	67	2	(	(	PUNCT
iajs-2379	67	3	)	)	PUNCT
iajs-2379	67	4	‖	‖	PROPN
iajs-2379	67	5	∫	∫	PROPN
iajs-2379	67	6	‖	‖	PROPN
iajs-2379	67	7	‖	‖	PROPN
iajs-2379	67	8	́	́	PROPN
iajs-2379	67	9	́	́	PROPN
iajs-2379	67	10	́	́	PROPN
iajs-2379	67	11	,	,	PUNCT
iajs-2379	67	12	using	use	VERB
iajs-2379	67	13	the	the	DET
iajs-2379	67	14	continuous	continuous	ADJ
iajs-2379	67	15	bellman	bellman	NOUN
iajs-2379	67	16	gronwall	gronwall	ADJ
iajs-2379	67	17	inequality	inequality	NOUN
iajs-2379	67	18	(	(	PUNCT
iajs-2379	67	19	bgi	bgi	PROPN
iajs-2379	67	20	)	)	PUNCT
iajs-2379	67	21	,	,	PUNCT
iajs-2379	67	22	one	one	PRON
iajs-2379	67	23	gets	get	VERB
iajs-2379	67	24	‖	‖	ADJ
iajs-2379	67	25	(	(	PUNCT
iajs-2379	67	26	)	)	PUNCT
iajs-2379	67	27	‖	‖	PROPN
iajs-2379	67	28	(	(	PUNCT
iajs-2379	67	29	)	)	PUNCT
iajs-2379	67	30	,	,	PUNCT
iajs-2379	67	31	,	,	PUNCT
iajs-2379	67	32	‖	‖	PROPN
iajs-2379	67	33	(	(	PUNCT
iajs-2379	67	34	)	)	PUNCT
iajs-2379	67	35	‖	‖	PROPN
iajs-2379	67	36	.	.	PUNCT
iajs-2379	68	1	(	(	PUNCT
iajs-2379	68	2	)	)	PUNCT
iajs-2379	68	3	/	/	SYM
iajs-2379	68	4	(	(	PUNCT
iajs-2379	68	5	)	)	PUNCT
iajs-2379	68	6	‖	‖	PROPN
iajs-2379	68	7	(	(	PUNCT
iajs-2379	68	8	)	)	PUNCT
iajs-2379	68	9	‖	‖	PROPN
iajs-2379	68	10	(	(	PUNCT
iajs-2379	68	11	)	)	PUNCT
iajs-2379	68	12	.	.	PUNCT
iajs-2379	69	1	the	the	DET
iajs-2379	69	2	norm	norm	NOUN
iajs-2379	69	3	‖	‖	PROPN
iajs-2379	69	4	(	(	PUNCT
iajs-2379	69	5	)	)	PUNCT
iajs-2379	69	6	‖	‖	PROPN
iajs-2379	69	7	(	(	PUNCT
iajs-2379	69	8	)	)	PUNCT
iajs-2379	69	9	is	be	AUX
iajs-2379	69	10	bounded	bound	VERB
iajs-2379	69	11	again	again	ADV
iajs-2379	69	12	for	for	ADP
iajs-2379	69	13	(	(	PUNCT
iajs-2379	69	14	23	23	NUM
iajs-2379	69	15	)	)	PUNCT
iajs-2379	69	16	by	by	ADP
iajs-2379	69	17	using	use	VERB
iajs-2379	69	18	lemma	lemma	PROPN
iajs-2379	69	19	(	(	PUNCT
iajs-2379	69	20	1.2	1.2	NUM
iajs-2379	69	21	)	)	PUNCT
iajs-2379	69	22	in	in	ADP
iajs-2379	69	23	[	[	X
iajs-2379	69	24	11	11	NUM
iajs-2379	69	25	]	]	PUNCT
iajs-2379	69	26	.	.	PUNCT
iajs-2379	70	1	for	for	ADP
iajs-2379	70	2	the	the	DET
iajs-2379	70	3	r.h.s	r.h.s	NOUN
iajs-2379	70	4	.	.	PUNCT
iajs-2379	71	1	the	the	DET
iajs-2379	71	2	same	same	ADJ
iajs-2379	71	3	results	result	NOUN
iajs-2379	71	4	will	will	AUX
iajs-2379	71	5	be	be	AUX
iajs-2379	71	6	obtained	obtain	VERB
iajs-2379	71	7	(	(	PUNCT
iajs-2379	71	8	from	from	ADP
iajs-2379	71	9	the	the	DET
iajs-2379	71	10	above	above	ADJ
iajs-2379	71	11	steps	step	NOUN
iajs-2379	71	12	)	)	PUNCT
iajs-2379	71	13	and	and	CCONJ
iajs-2379	71	14	since	since	SCONJ
iajs-2379	71	15	‖	‖	PROPN
iajs-2379	71	16	(	(	PUNCT
iajs-2379	71	17	)	)	PUNCT
iajs-2379	71	18	‖	‖	PROPN
iajs-2379	71	19	is	be	AUX
iajs-2379	71	20	positive	positive	ADJ
iajs-2379	71	21	,	,	PUNCT
iajs-2379	71	22	equation	equation	NOUN
iajs-2379	71	23	(	(	PUNCT
iajs-2379	71	24	23	23	NUM
iajs-2379	71	25	)	)	PUNCT
iajs-2379	71	26	with	with	ADP
iajs-2379	71	27	=	=	NOUN
iajs-2379	71	28	t	t	PROPN
iajs-2379	71	29	,	,	PUNCT
iajs-2379	71	30	becomes	become	VERB
iajs-2379	71	31	‖	‖	ADJ
iajs-2379	71	32	(	(	PUNCT
iajs-2379	71	33	)	)	PUNCT
iajs-2379	71	34	‖	‖	PROPN
iajs-2379	71	35	‖	‖	PROPN
iajs-2379	71	36	(	(	PUNCT
iajs-2379	71	37	)	)	PUNCT
iajs-2379	72	1	‖	‖	PROPN
iajs-2379	72	2	∫	∫	PROPN
iajs-2379	73	1	‖	‖	PROPN
iajs-2379	73	2	‖	‖	PROPN
iajs-2379	73	3	‖	‖	PROPN
iajs-2379	73	4	‖	‖	PROPN
iajs-2379	73	5	‖	‖	PROPN
iajs-2379	73	6	‖	‖	PROPN
iajs-2379	73	7	‖	‖	PROPN
iajs-2379	73	8	‖	‖	PROPN
iajs-2379	73	9	‖	‖	PROPN
iajs-2379	73	10	‖	‖	PROPN
iajs-2379	73	11	‖	‖	PROPN
iajs-2379	73	12	‖	‖	PROPN
iajs-2379	73	13	‖	‖	PROPN
iajs-2379	73	14	‖	‖	PROPN
iajs-2379	73	15	‖	‖	PROPN
iajs-2379	73	16	‖	‖	PROPN
iajs-2379	73	17	,	,	PUNCT
iajs-2379	73	18	which	which	PRON
iajs-2379	73	19	gives	give	VERB
iajs-2379	73	20	∫	∫	PROPN
iajs-2379	73	21	‖	‖	PROPN
iajs-2379	73	22	‖	‖	PROPN
iajs-2379	73	23	(	(	PUNCT
iajs-2379	73	24	)	)	PUNCT
iajs-2379	73	25	,	,	PUNCT
iajs-2379	73	26	with	with	ADP
iajs-2379	73	27	(	(	PUNCT
iajs-2379	73	28	)	)	PUNCT
iajs-2379	73	29	.	.	PUNCT
iajs-2379	74	1	(	(	PUNCT
iajs-2379	74	2	)	)	PUNCT
iajs-2379	74	3	/	/	SYM
iajs-2379	74	4	,	,	PUNCT
iajs-2379	74	5	thus	thus	ADV
iajs-2379	74	6	‖	‖	ADJ
iajs-2379	74	7	‖	‖	PROPN
iajs-2379	74	8	(	(	PUNCT
iajs-2379	74	9	)	)	PUNCT
iajs-2379	74	10	(	(	PUNCT
iajs-2379	74	11	)	)	PUNCT
iajs-2379	74	12	.	.	PUNCT
iajs-2379	75	1	the	the	DET
iajs-2379	75	2	solution	solution	NOUN
iajs-2379	75	3	convergence	convergence	NOUN
iajs-2379	75	4	let	let	VERB
iajs-2379	75	5	{	{	PUNCT
iajs-2379	75	6	⃗	⃗	PROPN
iajs-2379	75	7	}	}	PUNCT
iajs-2379	75	8	be	be	AUX
iajs-2379	75	9	a	a	DET
iajs-2379	75	10	sequence	sequence	NOUN
iajs-2379	75	11	of	of	ADP
iajs-2379	75	12	subspaces	subspace	NOUN
iajs-2379	75	13	of	of	ADP
iajs-2379	75	14	⃗	⃗	PROPN
iajs-2379	75	15	,	,	PUNCT
iajs-2379	75	16	s.t	s.t	PROPN
iajs-2379	75	17	.	.	PROPN
iajs-2379	75	18	⃗⃗	⃗⃗	PROPN
iajs-2379	75	19	⃗	⃗	PROPN
iajs-2379	75	20	there	there	PRON
iajs-2379	75	21	exists	exist	VERB
iajs-2379	75	22	a	a	DET
iajs-2379	75	23	sequence	sequence	NOUN
iajs-2379	75	24	{	{	PUNCT
iajs-2379	75	25	}	}	PUNCT
iajs-2379	75	26	with	with	ADP
iajs-2379	75	27	⃗	⃗	PROPN
iajs-2379	75	28	,	,	PUNCT
iajs-2379	75	29	n	n	PROPN
iajs-2379	75	30	and	and	CCONJ
iajs-2379	75	31	strongly	strongly	ADV
iajs-2379	75	32	in	in	ADP
iajs-2379	75	33	⃗	⃗	PROPN
iajs-2379	75	34	strongly	strongly	ADV
iajs-2379	75	35	in	in	ADP
iajs-2379	75	36	(	(	PUNCT
iajs-2379	75	37	(	(	PUNCT
iajs-2379	75	38	)	)	PUNCT
iajs-2379	75	39	)	)	PUNCT
iajs-2379	75	40	,	,	PUNCT
iajs-2379	75	41	since	since	SCONJ
iajs-2379	75	42	for	for	ADP
iajs-2379	75	43	each	each	PRON
iajs-2379	75	44	,	,	PUNCT
iajs-2379	75	45	with	with	ADP
iajs-2379	75	46	⃗	⃗	PROPN
iajs-2379	75	47	⊂	⊂	X
iajs-2379	75	48	⃗	⃗	PROPN
iajs-2379	75	49	,	,	PUNCT
iajs-2379	75	50	(	(	PUNCT
iajs-2379	75	51	17	17	NUM
iajs-2379	75	52	19	19	NUM
iajs-2379	75	53	)	)	PUNCT
iajs-2379	75	54	has	have	VERB
iajs-2379	75	55	a	a	DET
iajs-2379	75	56	unique	unique	ADJ
iajs-2379	75	57	solution	solution	NOUN
iajs-2379	75	58	(	(	PUNCT
iajs-2379	75	59	,	,	PUNCT
iajs-2379	75	60	,	,	PUNCT
iajs-2379	75	61	)	)	PUNCT
iajs-2379	75	62	,	,	PUNCT
iajs-2379	75	63	hence	hence	ADV
iajs-2379	75	64	corresponding	correspond	VERB
iajs-2379	75	65	to	to	ADP
iajs-2379	75	66	the	the	DET
iajs-2379	75	67	sequence	sequence	NOUN
iajs-2379	75	68	of	of	ADP
iajs-2379	75	69	subspaces	subspace	NOUN
iajs-2379	75	70	{	{	PUNCT
iajs-2379	75	71	⃗	⃗	PROPN
iajs-2379	75	72	}	}	PUNCT
iajs-2379	75	73	,	,	PUNCT
iajs-2379	75	74	there	there	PRON
iajs-2379	75	75	exist	exist	VERB
iajs-2379	75	76	a	a	DET
iajs-2379	75	77	sequence	sequence	NOUN
iajs-2379	75	78	of	of	ADP
iajs-2379	75	79	(	(	PUNCT
iajs-2379	75	80	approximation	approximation	NOUN
iajs-2379	75	81	)	)	PUNCT
iajs-2379	75	82	problems	problem	NOUN
iajs-2379	75	83	like	like	ADP
iajs-2379	75	84	(	(	PUNCT
iajs-2379	75	85	17	17	NUM
iajs-2379	75	86	19	19	NUM
iajs-2379	75	87	)	)	PUNCT
iajs-2379	75	88	now	now	ADV
iajs-2379	75	89	,	,	PUNCT
iajs-2379	75	90	by	by	ADP
iajs-2379	75	91	substituting	substitute	VERB
iajs-2379	75	92	(	(	PUNCT
iajs-2379	75	93	)	)	PUNCT
iajs-2379	75	94	,	,	PUNCT
iajs-2379	75	95	in	in	ADP
iajs-2379	75	96	these	these	DET
iajs-2379	75	97	equations	equation	NOUN
iajs-2379	75	98	for	for	ADP
iajs-2379	75	99	,	,	PUNCT
iajs-2379	75	100	one	one	PRON
iajs-2379	75	101	has	have	VERB
iajs-2379	75	102	〈	〈	PROPN
iajs-2379	75	103	〉	〉	NOUN
iajs-2379	75	104	(	(	PUNCT
iajs-2379	75	105	)	)	PUNCT
iajs-2379	75	106	(	(	PUNCT
iajs-2379	75	107	)	)	PUNCT
iajs-2379	75	108	(	(	PUNCT
iajs-2379	75	109	)	)	PUNCT
iajs-2379	75	110	(	(	PUNCT
iajs-2379	75	111	)	)	PUNCT
iajs-2379	75	112	(	(	PUNCT
iajs-2379	75	113	)	)	PUNCT
iajs-2379	75	114	(	(	PUNCT
iajs-2379	75	115	24.a	24.a	NUM
iajs-2379	75	116	)	)	PUNCT
iajs-2379	75	117	(	(	PUNCT
iajs-2379	75	118	)	)	PUNCT
iajs-2379	75	119	(	(	PUNCT
iajs-2379	75	120	)	)	PUNCT
iajs-2379	75	121	(	(	PUNCT
iajs-2379	75	122	24.b	24.b	NUM
iajs-2379	75	123	)	)	PUNCT
iajs-2379	75	124	〈	〈	NOUN
iajs-2379	75	125	〉	〉	NOUN
iajs-2379	75	126	(	(	PUNCT
iajs-2379	75	127	)	)	PUNCT
iajs-2379	75	128	(	(	PUNCT
iajs-2379	75	129	)	)	PUNCT
iajs-2379	75	130	(	(	PUNCT
iajs-2379	75	131	)	)	PUNCT
iajs-2379	75	132	(	(	PUNCT
iajs-2379	75	133	)	)	PUNCT
iajs-2379	75	134	(	(	PUNCT
iajs-2379	75	135	)	)	PUNCT
iajs-2379	75	136	(	(	PUNCT
iajs-2379	75	137	25.a	25.a	NUM
iajs-2379	75	138	)	)	PUNCT
iajs-2379	75	139	(	(	PUNCT
iajs-2379	75	140	)	)	PUNCT
iajs-2379	75	141	(	(	PUNCT
iajs-2379	75	142	)	)	PUNCT
iajs-2379	75	143	)	)	PUNCT
iajs-2379	75	144	,	,	PUNCT
iajs-2379	75	145	(	(	PUNCT
iajs-2379	75	146	25.b	25.b	NUM
iajs-2379	75	147	)	)	PUNCT
iajs-2379	75	148	〈	〈	NOUN
iajs-2379	75	149	〉	〉	NOUN
iajs-2379	75	150	(	(	PUNCT
iajs-2379	75	151	)	)	PUNCT
iajs-2379	75	152	(	(	PUNCT
iajs-2379	75	153	)	)	PUNCT
iajs-2379	75	154	(	(	PUNCT
iajs-2379	75	155	)	)	PUNCT
iajs-2379	75	156	(	(	PUNCT
iajs-2379	75	157	)	)	PUNCT
iajs-2379	75	158	(	(	PUNCT
iajs-2379	75	159	)	)	PUNCT
iajs-2379	75	160	(	(	PUNCT
iajs-2379	75	161	26.a	26.a	NUM
iajs-2379	75	162	)	)	PUNCT
iajs-2379	75	163	(	(	PUNCT
iajs-2379	75	164	)	)	PUNCT
iajs-2379	75	165	(	(	PUNCT
iajs-2379	75	166	)	)	PUNCT
iajs-2379	75	167	(	(	PUNCT
iajs-2379	75	168	26.b	26.b	NUM
iajs-2379	75	169	)	)	PUNCT
iajs-2379	75	170	which	which	PRON
iajs-2379	75	171	has	have	VERB
iajs-2379	75	172	a	a	DET
iajs-2379	75	173	sequence	sequence	NOUN
iajs-2379	75	174	of	of	ADP
iajs-2379	75	175	solutions	solution	NOUN
iajs-2379	75	176	*	*	PUNCT
iajs-2379	76	1	+	+	CCONJ
iajs-2379	76	2	,	,	PUNCT
iajs-2379	76	3	(	(	PUNCT
iajs-2379	76	4	)	)	PUNCT
iajs-2379	76	5	but	but	CCONJ
iajs-2379	76	6	from	from	ADP
iajs-2379	76	7	the	the	DET
iajs-2379	76	8	above	above	ADJ
iajs-2379	76	9	steps	step	NOUN
iajs-2379	76	10	we	we	PRON
iajs-2379	76	11	have	have	VERB
iajs-2379	76	12	‖	‖	ADJ
iajs-2379	76	13	‖	‖	PROPN
iajs-2379	76	14	(	(	PUNCT
iajs-2379	76	15	)	)	PUNCT
iajs-2379	76	16	and‖	and‖	PUNCT
iajs-2379	76	17	‖	‖	PROPN
iajs-2379	76	18	(	(	PUNCT
iajs-2379	76	19	)	)	PUNCT
iajs-2379	76	20	are	be	AUX
iajs-2379	76	21	bounded	bound	VERB
iajs-2379	76	22	,	,	PUNCT
iajs-2379	76	23	then	then	ADV
iajs-2379	76	24	by	by	ADP
iajs-2379	76	25	alaoglu	alaoglu	PROPN
iajs-2379	76	26	’s	’s	PART
iajs-2379	76	27	theorem	theorem	NOUN
iajs-2379	76	28	(	(	PUNCT
iajs-2379	76	29	at	at	ADP
iajs-2379	76	30	)	)	PUNCT
iajs-2379	76	31	,	,	PUNCT
iajs-2379	76	32	there	there	PRON
iajs-2379	76	33	exists	exist	VERB
iajs-2379	76	34	a	a	DET
iajs-2379	76	35	subsequence	subsequence	NOUN
iajs-2379	76	36	of	of	ADP
iajs-2379	76	37	*	*	PUNCT
iajs-2379	76	38	+	+	CCONJ
iajs-2379	76	39	,	,	PUNCT
iajs-2379	76	40	say	say	VERB
iajs-2379	76	41	again	again	ADV
iajs-2379	76	42	*	*	PUNCT
iajs-2379	77	1	+	+	CCONJ
iajs-2379	77	2	s.t	s.t	PROPN
iajs-2379	77	3	.	.	PROPN
iajs-2379	77	4	weakly	weakly	ADV
iajs-2379	77	5	in	in	ADP
iajs-2379	77	6	(	(	PUNCT
iajs-2379	77	7	(	(	PUNCT
iajs-2379	77	8	)	)	PUNCT
iajs-2379	77	9	)	)	PUNCT
iajs-2379	77	10	and	and	CCONJ
iajs-2379	77	11	133	133	NUM
iajs-2379	77	12	ibn	ibn	PROPN
iajs-2379	77	13	al	al	PROPN
iajs-2379	77	14	-	-	PUNCT
iajs-2379	77	15	haitham	haitham	PROPN
iajs-2379	77	16	jour	jour	X
iajs-2379	77	17	.	.	PROPN
iajs-2379	77	18	for	for	ADP
iajs-2379	77	19	pure	pure	ADJ
iajs-2379	77	20	&	&	CCONJ
iajs-2379	77	21	appl	appl	PROPN
iajs-2379	77	22	.	.	PUNCT
iajs-2379	78	1	sci	sci	PROPN
iajs-2379	78	2	.	.	PROPN
iajs-2379	79	1	33	33	NUM
iajs-2379	79	2	(	(	PUNCT
iajs-2379	79	3	1	1	NUM
iajs-2379	79	4	)	)	PUNCT
iajs-2379	79	5	2020	2020	NUM
iajs-2379	79	6	weakly	weakly	ADV
iajs-2379	79	7	in	in	ADV
iajs-2379	79	8	.	.	PUNCT
iajs-2379	80	1	(	(	PUNCT
iajs-2379	80	2	)	)	PUNCT
iajs-2379	80	3	/	/	SYM
iajs-2379	80	4	,	,	PUNCT
iajs-2379	80	5	multiplying	multiply	VERB
iajs-2379	80	6	both	both	DET
iajs-2379	80	7	sides	side	NOUN
iajs-2379	80	8	of	of	ADP
iajs-2379	80	9	(	(	PUNCT
iajs-2379	80	10	24.a	24.a	NUM
iajs-2379	80	11	)	)	PUNCT
iajs-2379	80	12	,	,	PUNCT
iajs-2379	80	13	(	(	PUNCT
iajs-2379	80	14	25.a	25.a	NUM
iajs-2379	80	15	)	)	PUNCT
iajs-2379	80	16	(	(	PUNCT
iajs-2379	80	17	26.a	26.a	NUM
iajs-2379	80	18	)	)	PUNCT
iajs-2379	80	19	by	by	ADP
iajs-2379	80	20	(	(	PUNCT
iajs-2379	80	21	)	)	PUNCT
iajs-2379	80	22	,	,	PUNCT
iajs-2379	80	23	respectively	respectively	ADV
iajs-2379	80	24	,	,	PUNCT
iajs-2379	80	25	s.t	s.t	PROPN
iajs-2379	80	26	.	.	PROPN
iajs-2379	80	27	(	(	PUNCT
iajs-2379	80	28	)	)	PUNCT
iajs-2379	80	29	,	,	PUNCT
iajs-2379	80	30	,	,	PUNCT
iajs-2379	80	31	3	3	NUM
iajs-2379	80	32	,	,	PUNCT
iajs-2379	80	33	then	then	ADV
iajs-2379	80	34	integrating	integrate	VERB
iajs-2379	80	35	both	both	DET
iajs-2379	80	36	sides	side	NOUN
iajs-2379	80	37	w.r.t	w.r.t	VERB
iajs-2379	80	38	.	.	PUNCT
iajs-2379	81	1	on	on	ADP
iajs-2379	81	2	,	,	PUNCT
iajs-2379	81	3	,	,	PUNCT
iajs-2379	81	4	then	then	ADV
iajs-2379	81	5	integrating	integrate	VERB
iajs-2379	81	6	by	by	ADP
iajs-2379	81	7	parts	part	NOUN
iajs-2379	81	8	the	the	DET
iajs-2379	81	9	terms	term	NOUN
iajs-2379	81	10	in	in	ADP
iajs-2379	81	11	the	the	DET
iajs-2379	81	12	l.h.s	l.h.s	NOUN
iajs-2379	81	13	.	.	PUNCT
iajs-2379	82	1	of	of	ADP
iajs-2379	82	2	each	each	DET
iajs-2379	82	3	one	one	NUM
iajs-2379	82	4	obtained	obtain	VERB
iajs-2379	82	5	equation	equation	NOUN
iajs-2379	82	6	,	,	PUNCT
iajs-2379	82	7	one	one	PRON
iajs-2379	82	8	gets	get	VERB
iajs-2379	82	9	∫	∫	NOUN
iajs-2379	82	10	(	(	PUNCT
iajs-2379	82	11	)	)	PUNCT
iajs-2379	82	12	(	(	PUNCT
iajs-2379	82	13	)	)	PUNCT
iajs-2379	82	14	∫	∫	PROPN
iajs-2379	82	15	,	,	PUNCT
iajs-2379	82	16	(	(	PUNCT
iajs-2379	82	17	)	)	PUNCT
iajs-2379	82	18	(	(	PUNCT
iajs-2379	82	19	)	)	PUNCT
iajs-2379	82	20	(	(	PUNCT
iajs-2379	82	21	)	)	PUNCT
iajs-2379	82	22	∫	∫	PROPN
iajs-2379	82	23	(	(	PUNCT
iajs-2379	82	24	)	)	PUNCT
iajs-2379	82	25	(	(	PUNCT
iajs-2379	82	26	)	)	PUNCT
iajs-2379	82	27	∫	∫	PROPN
iajs-2379	82	28	(	(	PUNCT
iajs-2379	82	29	)	)	PUNCT
iajs-2379	82	30	(	(	PUNCT
iajs-2379	82	31	)	)	PUNCT
iajs-2379	82	32	∫	∫	PROPN
iajs-2379	82	33	(	(	PUNCT
iajs-2379	82	34	)	)	PUNCT
iajs-2379	82	35	(	(	PUNCT
iajs-2379	82	36	)	)	PUNCT
iajs-2379	82	37	(	(	PUNCT
iajs-2379	82	38	)	)	PUNCT
iajs-2379	82	39	(	(	PUNCT
iajs-2379	82	40	)	)	PUNCT
iajs-2379	82	41	(	(	PUNCT
iajs-2379	82	42	)	)	PUNCT
iajs-2379	82	43	∫	∫	PROPN
iajs-2379	82	44	(	(	PUNCT
iajs-2379	82	45	)	)	PUNCT
iajs-2379	82	46	(	(	PUNCT
iajs-2379	82	47	)	)	PUNCT
iajs-2379	82	48	∫	∫	PROPN
iajs-2379	82	49	,	,	PUNCT
iajs-2379	82	50	(	(	PUNCT
iajs-2379	82	51	)	)	PUNCT
iajs-2379	82	52	(	(	PUNCT
iajs-2379	82	53	)	)	PUNCT
iajs-2379	82	54	(	(	PUNCT
iajs-2379	82	55	)	)	PUNCT
iajs-2379	82	56	∫	∫	PROPN
iajs-2379	82	57	(	(	PUNCT
iajs-2379	82	58	)	)	PUNCT
iajs-2379	82	59	(	(	PUNCT
iajs-2379	82	60	)	)	PUNCT
iajs-2379	82	61	∫	∫	PROPN
iajs-2379	82	62	(	(	PUNCT
iajs-2379	82	63	)	)	PUNCT
iajs-2379	82	64	(	(	PUNCT
iajs-2379	82	65	)	)	PUNCT
iajs-2379	82	66	∫	∫	PROPN
iajs-2379	82	67	(	(	PUNCT
iajs-2379	82	68	)	)	PUNCT
iajs-2379	82	69	(	(	PUNCT
iajs-2379	82	70	)	)	PUNCT
iajs-2379	82	71	(	(	PUNCT
iajs-2379	82	72	)	)	PUNCT
iajs-2379	82	73	(	(	PUNCT
iajs-2379	82	74	)	)	PUNCT
iajs-2379	82	75	(	(	PUNCT
iajs-2379	82	76	)	)	PUNCT
iajs-2379	82	77	∫	∫	PROPN
iajs-2379	82	78	(	(	PUNCT
iajs-2379	82	79	)	)	PUNCT
iajs-2379	82	80	(	(	PUNCT
iajs-2379	82	81	)	)	PUNCT
iajs-2379	82	82	∫	∫	PROPN
iajs-2379	82	83	,	,	PUNCT
iajs-2379	82	84	(	(	PUNCT
iajs-2379	82	85	)	)	PUNCT
iajs-2379	82	86	(	(	PUNCT
iajs-2379	82	87	)	)	PUNCT
iajs-2379	82	88	(	(	PUNCT
iajs-2379	82	89	)	)	PUNCT
iajs-2379	82	90	∫	∫	PROPN
iajs-2379	82	91	(	(	PUNCT
iajs-2379	82	92	)	)	PUNCT
iajs-2379	82	93	(	(	PUNCT
iajs-2379	82	94	)	)	PUNCT
iajs-2379	82	95	∫	∫	PROPN
iajs-2379	82	96	(	(	PUNCT
iajs-2379	82	97	)	)	PUNCT
iajs-2379	82	98	(	(	PUNCT
iajs-2379	82	99	)	)	PUNCT
iajs-2379	82	100	∫	∫	PROPN
iajs-2379	82	101	(	(	PUNCT
iajs-2379	82	102	)	)	PUNCT
iajs-2379	82	103	(	(	PUNCT
iajs-2379	82	104	)	)	PUNCT
iajs-2379	82	105	(	(	PUNCT
iajs-2379	82	106	)	)	PUNCT
iajs-2379	82	107	(	(	PUNCT
iajs-2379	82	108	)	)	PUNCT
iajs-2379	82	109	(	(	PUNCT
iajs-2379	82	110	)	)	PUNCT
iajs-2379	82	111	since	since	SCONJ
iajs-2379	82	112	(	(	PUNCT
iajs-2379	82	113	)	)	PUNCT
iajs-2379	82	114	}	}	PUNCT
iajs-2379	82	115	{	{	PUNCT
iajs-2379	82	116	(	(	PUNCT
iajs-2379	82	117	)	)	PUNCT
iajs-2379	82	118	(	(	PUNCT
iajs-2379	82	119	)	)	PUNCT
iajs-2379	82	120	since	since	SCONJ
iajs-2379	82	121	weakly	weakly	ADV
iajs-2379	82	122	in	in	ADP
iajs-2379	82	123	(	(	PUNCT
iajs-2379	82	124	)	)	PUNCT
iajs-2379	82	125	,	,	PUNCT
iajs-2379	82	126	also	also	ADV
iajs-2379	82	127	(	(	PUNCT
iajs-2379	82	128	)	)	PUNCT
iajs-2379	82	129	,	,	PUNCT
iajs-2379	82	130	3	3	X
iajs-2379	82	131	.	.	PUNCT
iajs-2379	83	1	then	then	ADV
iajs-2379	83	2	∫	∫	PROPN
iajs-2379	83	3	(	(	PUNCT
iajs-2379	83	4	)	)	PUNCT
iajs-2379	83	5	(	(	PUNCT
iajs-2379	83	6	)	)	PUNCT
iajs-2379	83	7	∫	∫	PROPN
iajs-2379	83	8	,	,	PUNCT
iajs-2379	83	9	(	(	PUNCT
iajs-2379	83	10	)	)	PUNCT
iajs-2379	83	11	(	(	PUNCT
iajs-2379	83	12	)	)	PUNCT
iajs-2379	83	13	(	(	PUNCT
iajs-2379	83	14	)	)	PUNCT
iajs-2379	83	15	∫	∫	PROPN
iajs-2379	83	16	(	(	PUNCT
iajs-2379	83	17	)	)	PUNCT
iajs-2379	83	18	(	(	PUNCT
iajs-2379	83	19	)	)	PUNCT
iajs-2379	83	20	∫	∫	PROPN
iajs-2379	83	21	(	(	PUNCT
iajs-2379	83	22	)	)	PUNCT
iajs-2379	83	23	(	(	PUNCT
iajs-2379	83	24	)	)	PUNCT
iajs-2379	83	25	∫	∫	PROPN
iajs-2379	83	26	(	(	PUNCT
iajs-2379	83	27	)	)	PUNCT
iajs-2379	83	28	(	(	PUNCT
iajs-2379	83	29	)	)	PUNCT
iajs-2379	83	30	∫	∫	PROPN
iajs-2379	83	31	,	,	PUNCT
iajs-2379	83	32	(	(	PUNCT
iajs-2379	83	33	)	)	PUNCT
iajs-2379	83	34	(	(	PUNCT
iajs-2379	83	35	)	)	PUNCT
iajs-2379	83	36	(	(	PUNCT
iajs-2379	83	37	)	)	PUNCT
iajs-2379	83	38	∫	∫	PROPN
iajs-2379	83	39	(	(	PUNCT
iajs-2379	83	40	)	)	PUNCT
iajs-2379	83	41	(	(	PUNCT
iajs-2379	83	42	)	)	PUNCT
iajs-2379	83	43	∫	∫	PROPN
iajs-2379	83	44	(	(	PUNCT
iajs-2379	83	45	)	)	PUNCT
iajs-2379	83	46	(	(	PUNCT
iajs-2379	83	47	)	)	PUNCT
iajs-2379	83	48	(	(	PUNCT
iajs-2379	83	49	30.a	30.a	NUM
iajs-2379	83	50	)	)	PUNCT
iajs-2379	83	51	∫	∫	PROPN
iajs-2379	83	52	(	(	PUNCT
iajs-2379	83	53	)	)	PUNCT
iajs-2379	83	54	(	(	PUNCT
iajs-2379	83	55	)	)	PUNCT
iajs-2379	83	56	∫	∫	PROPN
iajs-2379	83	57	,	,	PUNCT
iajs-2379	83	58	(	(	PUNCT
iajs-2379	83	59	)	)	PUNCT
iajs-2379	83	60	(	(	PUNCT
iajs-2379	83	61	)	)	PUNCT
iajs-2379	83	62	(	(	PUNCT
iajs-2379	83	63	)	)	PUNCT
iajs-2379	83	64	∫	∫	PROPN
iajs-2379	83	65	(	(	PUNCT
iajs-2379	83	66	)	)	PUNCT
iajs-2379	83	67	(	(	PUNCT
iajs-2379	83	68	)	)	PUNCT
iajs-2379	83	69	∫	∫	PROPN
iajs-2379	83	70	(	(	PUNCT
iajs-2379	83	71	)	)	PUNCT
iajs-2379	83	72	(	(	PUNCT
iajs-2379	83	73	)	)	PUNCT
iajs-2379	83	74	∫	∫	PROPN
iajs-2379	83	75	(	(	PUNCT
iajs-2379	83	76	)	)	PUNCT
iajs-2379	83	77	(	(	PUNCT
iajs-2379	83	78	)	)	PUNCT
iajs-2379	83	79	∫	∫	PROPN
iajs-2379	83	80	,	,	PUNCT
iajs-2379	83	81	(	(	PUNCT
iajs-2379	83	82	)	)	PUNCT
iajs-2379	83	83	(	(	PUNCT
iajs-2379	83	84	)	)	PUNCT
iajs-2379	83	85	(	(	PUNCT
iajs-2379	83	86	)	)	PUNCT
iajs-2379	83	87	∫	∫	PROPN
iajs-2379	83	88	(	(	PUNCT
iajs-2379	83	89	)	)	PUNCT
iajs-2379	83	90	(	(	PUNCT
iajs-2379	83	91	)	)	PUNCT
iajs-2379	83	92	∫	∫	PROPN
iajs-2379	83	93	(	(	PUNCT
iajs-2379	83	94	)	)	PUNCT
iajs-2379	83	95	(	(	PUNCT
iajs-2379	83	96	)	)	PUNCT
iajs-2379	83	97	(	(	PUNCT
iajs-2379	83	98	31.a	31.a	NUM
iajs-2379	83	99	)	)	PUNCT
iajs-2379	83	100	∫	∫	PROPN
iajs-2379	83	101	(	(	PUNCT
iajs-2379	83	102	)	)	PUNCT
iajs-2379	83	103	(	(	PUNCT
iajs-2379	83	104	)	)	PUNCT
iajs-2379	83	105	∫	∫	PROPN
iajs-2379	83	106	,	,	PUNCT
iajs-2379	83	107	(	(	PUNCT
iajs-2379	83	108	)	)	PUNCT
iajs-2379	83	109	(	(	PUNCT
iajs-2379	83	110	)	)	PUNCT
iajs-2379	83	111	(	(	PUNCT
iajs-2379	83	112	)	)	PUNCT
iajs-2379	83	113	∫	∫	PROPN
iajs-2379	83	114	(	(	PUNCT
iajs-2379	83	115	)	)	PUNCT
iajs-2379	83	116	(	(	PUNCT
iajs-2379	83	117	)	)	PUNCT
iajs-2379	83	118	∫	∫	PROPN
iajs-2379	83	119	(	(	PUNCT
iajs-2379	83	120	)	)	PUNCT
iajs-2379	83	121	(	(	PUNCT
iajs-2379	83	122	)	)	PUNCT
iajs-2379	83	123	∫	∫	PROPN
iajs-2379	83	124	(	(	PUNCT
iajs-2379	83	125	)	)	PUNCT
iajs-2379	83	126	(	(	PUNCT
iajs-2379	83	127	)	)	PUNCT
iajs-2379	83	128	∫	∫	PROPN
iajs-2379	83	129	,	,	PUNCT
iajs-2379	83	130	(	(	PUNCT
iajs-2379	83	131	)	)	PUNCT
iajs-2379	83	132	(	(	PUNCT
iajs-2379	83	133	)	)	PUNCT
iajs-2379	83	134	(	(	PUNCT
iajs-2379	83	135	)	)	PUNCT
iajs-2379	83	136	∫	∫	PROPN
iajs-2379	83	137	(	(	PUNCT
iajs-2379	83	138	)	)	PUNCT
iajs-2379	83	139	(	(	PUNCT
iajs-2379	83	140	)	)	PUNCT
iajs-2379	83	141	∫	∫	PROPN
iajs-2379	83	142	(	(	PUNCT
iajs-2379	83	143	)	)	PUNCT
iajs-2379	83	144	(	(	PUNCT
iajs-2379	83	145	)	)	PUNCT
iajs-2379	83	146	(	(	PUNCT
iajs-2379	83	147	32.a	32.a	NUM
iajs-2379	83	148	)	)	PUNCT
iajs-2379	83	149	(	(	PUNCT
iajs-2379	83	150	)	)	PUNCT
iajs-2379	83	151	(	(	PUNCT
iajs-2379	83	152	)	)	PUNCT
iajs-2379	83	153	(	(	PUNCT
iajs-2379	83	154	)	)	PUNCT
iajs-2379	83	155	(	(	PUNCT
iajs-2379	83	156	)	)	PUNCT
iajs-2379	83	157	(	(	PUNCT
iajs-2379	83	158	30.b	30.b	NUM
iajs-2379	83	159	)	)	PUNCT
iajs-2379	83	160	(	(	PUNCT
iajs-2379	83	161	)	)	PUNCT
iajs-2379	83	162	(	(	PUNCT
iajs-2379	83	163	)	)	PUNCT
iajs-2379	83	164	(	(	PUNCT
iajs-2379	83	165	)	)	PUNCT
iajs-2379	83	166	(	(	PUNCT
iajs-2379	83	167	)	)	PUNCT
iajs-2379	83	168	(	(	PUNCT
iajs-2379	83	169	31.b	31.b	NUM
iajs-2379	83	170	)	)	PUNCT
iajs-2379	83	171	(	(	PUNCT
iajs-2379	83	172	)	)	PUNCT
iajs-2379	83	173	(	(	PUNCT
iajs-2379	83	174	)	)	PUNCT
iajs-2379	83	175	(	(	PUNCT
iajs-2379	83	176	)	)	PUNCT
iajs-2379	83	177	(	(	PUNCT
iajs-2379	83	178	)	)	PUNCT
iajs-2379	83	179	(	(	PUNCT
iajs-2379	83	180	32.b	32.b	NUM
iajs-2379	83	181	)	)	PUNCT
iajs-2379	83	182	since	since	SCONJ
iajs-2379	83	183	(	(	PUNCT
iajs-2379	83	184	)	)	PUNCT
iajs-2379	83	185	,	,	PUNCT
iajs-2379	83	186	then	then	ADV
iajs-2379	83	187	∫	∫	PROPN
iajs-2379	83	188	(	(	PUNCT
iajs-2379	83	189	)	)	PUNCT
iajs-2379	83	190	(	(	PUNCT
iajs-2379	83	191	)	)	PUNCT
iajs-2379	83	192	∫	∫	PROPN
iajs-2379	83	193	(	(	PUNCT
iajs-2379	83	194	)	)	PUNCT
iajs-2379	83	195	(	(	PUNCT
iajs-2379	83	196	)	)	PUNCT
iajs-2379	83	197	(	(	PUNCT
iajs-2379	83	198	30.c	30.c	NUM
iajs-2379	83	199	)	)	PUNCT
iajs-2379	83	200	∫	∫	PROPN
iajs-2379	83	201	(	(	PUNCT
iajs-2379	83	202	)	)	PUNCT
iajs-2379	83	203	(	(	PUNCT
iajs-2379	83	204	)	)	PUNCT
iajs-2379	83	205	∫	∫	PROPN
iajs-2379	83	206	(	(	PUNCT
iajs-2379	83	207	)	)	PUNCT
iajs-2379	83	208	(	(	PUNCT
iajs-2379	83	209	)	)	PUNCT
iajs-2379	83	210	(	(	PUNCT
iajs-2379	83	211	31.c	31.c	NUM
iajs-2379	83	212	)	)	PUNCT
iajs-2379	83	213	∫	∫	PROPN
iajs-2379	83	214	(	(	PUNCT
iajs-2379	83	215	)	)	PUNCT
iajs-2379	83	216	(	(	PUNCT
iajs-2379	83	217	)	)	PUNCT
iajs-2379	83	218	∫	∫	PROPN
iajs-2379	83	219	(	(	PUNCT
iajs-2379	83	220	)	)	PUNCT
iajs-2379	83	221	(	(	PUNCT
iajs-2379	83	222	)	)	PUNCT
iajs-2379	83	223	(	(	PUNCT
iajs-2379	83	224	32.c	32.c	NUM
iajs-2379	83	225	)	)	PUNCT
iajs-2379	83	226	which	which	PRON
iajs-2379	83	227	means	mean	VERB
iajs-2379	83	228	(	(	PUNCT
iajs-2379	83	229	30	30	NUM
iajs-2379	83	230	32	32	NUM
iajs-2379	83	231	)	)	PUNCT
iajs-2379	83	232	converge	converge	VERB
iajs-2379	83	233	to	to	ADP
iajs-2379	83	234	(	(	PUNCT
iajs-2379	83	235	33–35	33–35	NUM
iajs-2379	83	236	)	)	PUNCT
iajs-2379	83	237	respectively	respectively	ADV
iajs-2379	83	238	,	,	PUNCT
iajs-2379	83	239	with	with	ADP
iajs-2379	83	240	∫	∫	PROPN
iajs-2379	83	241	(	(	PUNCT
iajs-2379	83	242	)	)	PUNCT
iajs-2379	83	243	(	(	PUNCT
iajs-2379	83	244	)	)	PUNCT
iajs-2379	83	245	∫	∫	PROPN
iajs-2379	83	246	,	,	PUNCT
iajs-2379	83	247	(	(	PUNCT
iajs-2379	83	248	)	)	PUNCT
iajs-2379	83	249	(	(	PUNCT
iajs-2379	83	250	)	)	PUNCT
iajs-2379	83	251	(	(	PUNCT
iajs-2379	83	252	)	)	PUNCT
iajs-2379	83	253	∫	∫	PROPN
iajs-2379	83	254	(	(	PUNCT
iajs-2379	83	255	)	)	PUNCT
iajs-2379	83	256	(	(	PUNCT
iajs-2379	83	257	)	)	PUNCT
iajs-2379	83	258	∫	∫	PROPN
iajs-2379	83	259	(	(	PUNCT
iajs-2379	83	260	)	)	PUNCT
iajs-2379	83	261	(	(	PUNCT
iajs-2379	83	262	)	)	PUNCT
iajs-2379	83	263	=	=	SYM
iajs-2379	83	264	∫	∫	PROPN
iajs-2379	83	265	(	(	PUNCT
iajs-2379	83	266	)	)	PUNCT
iajs-2379	83	267	(	(	PUNCT
iajs-2379	83	268	)	)	PUNCT
iajs-2379	83	269	(	(	PUNCT
iajs-2379	83	270	)	)	PUNCT
iajs-2379	83	271	(	(	PUNCT
iajs-2379	83	272	)	)	PUNCT
iajs-2379	83	273	(	(	PUNCT
iajs-2379	83	274	33	33	NUM
iajs-2379	83	275	)	)	PUNCT
iajs-2379	83	276	∫	∫	PROPN
iajs-2379	83	277	(	(	PUNCT
iajs-2379	83	278	)	)	PUNCT
iajs-2379	83	279	(	(	PUNCT
iajs-2379	83	280	)	)	PUNCT
iajs-2379	83	281	∫	∫	PROPN
iajs-2379	83	282	,	,	PUNCT
iajs-2379	83	283	(	(	PUNCT
iajs-2379	83	284	)	)	PUNCT
iajs-2379	83	285	(	(	PUNCT
iajs-2379	83	286	)	)	PUNCT
iajs-2379	83	287	(	(	PUNCT
iajs-2379	83	288	)	)	PUNCT
iajs-2379	83	289	∫	∫	PROPN
iajs-2379	83	290	(	(	PUNCT
iajs-2379	83	291	)	)	PUNCT
iajs-2379	83	292	(	(	PUNCT
iajs-2379	83	293	)	)	PUNCT
iajs-2379	83	294	∫	∫	PROPN
iajs-2379	83	295	(	(	PUNCT
iajs-2379	83	296	)	)	PUNCT
iajs-2379	83	297	(	(	PUNCT
iajs-2379	83	298	)	)	PUNCT
iajs-2379	83	299	∫	∫	PROPN
iajs-2379	83	300	(	(	PUNCT
iajs-2379	83	301	)	)	PUNCT
iajs-2379	83	302	(	(	PUNCT
iajs-2379	83	303	)	)	PUNCT
iajs-2379	83	304	(	(	PUNCT
iajs-2379	83	305	)	)	PUNCT
iajs-2379	83	306	(	(	PUNCT
iajs-2379	83	307	)	)	PUNCT
iajs-2379	83	308	(	(	PUNCT
iajs-2379	83	309	34	34	NUM
iajs-2379	83	310	)	)	PUNCT
iajs-2379	83	311	134	134	NUM
iajs-2379	83	312	ibn	ibn	PROPN
iajs-2379	83	313	al	al	PROPN
iajs-2379	83	314	-	-	PUNCT
iajs-2379	83	315	haitham	haitham	PROPN
iajs-2379	83	316	jour	jour	X
iajs-2379	83	317	.	.	PROPN
iajs-2379	84	1	for	for	ADP
iajs-2379	84	2	pure	pure	ADJ
iajs-2379	84	3	&	&	CCONJ
iajs-2379	84	4	appl	appl	PROPN
iajs-2379	84	5	.	.	PUNCT
iajs-2379	85	1	sci	sci	PROPN
iajs-2379	85	2	.	.	PROPN
iajs-2379	86	1	33	33	NUM
iajs-2379	86	2	(	(	PUNCT
iajs-2379	86	3	1	1	NUM
iajs-2379	86	4	)	)	PUNCT
iajs-2379	86	5	2020	2020	NUM
iajs-2379	86	6	∫	∫	PROPN
iajs-2379	86	7	(	(	PUNCT
iajs-2379	86	8	)	)	PUNCT
iajs-2379	86	9	(	(	PUNCT
iajs-2379	86	10	)	)	PUNCT
iajs-2379	86	11	∫	∫	PROPN
iajs-2379	86	12	,	,	PUNCT
iajs-2379	86	13	(	(	PUNCT
iajs-2379	86	14	)	)	PUNCT
iajs-2379	86	15	(	(	PUNCT
iajs-2379	86	16	)	)	PUNCT
iajs-2379	86	17	(	(	PUNCT
iajs-2379	86	18	)	)	PUNCT
iajs-2379	86	19	∫	∫	PROPN
iajs-2379	86	20	(	(	PUNCT
iajs-2379	86	21	)	)	PUNCT
iajs-2379	86	22	(	(	PUNCT
iajs-2379	86	23	)	)	PUNCT
iajs-2379	86	24	∫	∫	PROPN
iajs-2379	86	25	(	(	PUNCT
iajs-2379	86	26	)	)	PUNCT
iajs-2379	86	27	(	(	PUNCT
iajs-2379	86	28	)	)	PUNCT
iajs-2379	86	29	∫	∫	PROPN
iajs-2379	86	30	(	(	PUNCT
iajs-2379	86	31	)	)	PUNCT
iajs-2379	86	32	(	(	PUNCT
iajs-2379	86	33	)	)	PUNCT
iajs-2379	86	34	(	(	PUNCT
iajs-2379	86	35	)	)	PUNCT
iajs-2379	86	36	(	(	PUNCT
iajs-2379	86	37	)	)	PUNCT
iajs-2379	86	38	(	(	PUNCT
iajs-2379	86	39	35	35	NUM
iajs-2379	86	40	)	)	PUNCT
iajs-2379	86	41	case1	case1	PROPN
iajs-2379	86	42	:	:	PUNCT
iajs-2379	86	43	choose	choose	VERB
iajs-2379	86	44	,	,	PUNCT
iajs-2379	86	45	-	-	PUNCT
iajs-2379	86	46	,	,	PUNCT
iajs-2379	86	47	i.e.	i.e.	X
iajs-2379	86	48	(	(	PUNCT
iajs-2379	86	49	)	)	PUNCT
iajs-2379	86	50	(	(	PUNCT
iajs-2379	86	51	)	)	PUNCT
iajs-2379	86	52	,	,	PUNCT
iajs-2379	86	53	,	,	PUNCT
iajs-2379	86	54	3	3	X
iajs-2379	86	55	.	.	X
iajs-2379	87	1	substituting	substitute	VERB
iajs-2379	87	2	in	in	ADP
iajs-2379	87	3	(	(	PUNCT
iajs-2379	87	4	33	33	NUM
iajs-2379	87	5	35	35	NUM
iajs-2379	87	6	)	)	PUNCT
iajs-2379	87	7	,	,	PUNCT
iajs-2379	87	8	using	use	VERB
iajs-2379	87	9	integration	integration	NOUN
iajs-2379	87	10	by	by	ADP
iajs-2379	87	11	parts	part	NOUN
iajs-2379	87	12	for	for	ADP
iajs-2379	87	13	the	the	DET
iajs-2379	87	14	terms	term	NOUN
iajs-2379	87	15	in	in	ADP
iajs-2379	87	16	l.h.s	l.h.s	NOUN
iajs-2379	87	17	.	.	PUNCT
iajs-2379	88	1	of	of	ADP
iajs-2379	88	2	each	each	DET
iajs-2379	88	3	one	one	NUM
iajs-2379	88	4	of	of	ADP
iajs-2379	88	5	the	the	DET
iajs-2379	88	6	obtained	obtain	VERB
iajs-2379	88	7	equations	equation	NOUN
iajs-2379	88	8	,	,	PUNCT
iajs-2379	88	9	to	to	PART
iajs-2379	88	10	get	get	VERB
iajs-2379	88	11	∫	∫	PROPN
iajs-2379	88	12	〈	〈	PROPN
iajs-2379	88	13	〉	〉	NOUN
iajs-2379	88	14	(	(	PUNCT
iajs-2379	88	15	)	)	PUNCT
iajs-2379	88	16	∫	∫	PROPN
iajs-2379	88	17	,	,	PUNCT
iajs-2379	88	18	(	(	PUNCT
iajs-2379	88	19	)	)	PUNCT
iajs-2379	88	20	(	(	PUNCT
iajs-2379	88	21	)	)	PUNCT
iajs-2379	88	22	(	(	PUNCT
iajs-2379	88	23	)	)	PUNCT
iajs-2379	88	24	∫	∫	PROPN
iajs-2379	88	25	(	(	PUNCT
iajs-2379	88	26	)	)	PUNCT
iajs-2379	88	27	(	(	PUNCT
iajs-2379	88	28	)	)	PUNCT
iajs-2379	88	29	∫	∫	PROPN
iajs-2379	88	30	(	(	PUNCT
iajs-2379	88	31	)	)	PUNCT
iajs-2379	88	32	(	(	PUNCT
iajs-2379	88	33	)	)	PUNCT
iajs-2379	88	34	∫	∫	PROPN
iajs-2379	88	35	(	(	PUNCT
iajs-2379	88	36	)	)	PUNCT
iajs-2379	88	37	(	(	PUNCT
iajs-2379	88	38	)	)	PUNCT
iajs-2379	88	39	(	(	PUNCT
iajs-2379	88	40	36	36	NUM
iajs-2379	88	41	)	)	PUNCT
iajs-2379	88	42	∫	∫	NOUN
iajs-2379	88	43	〈	〈	PROPN
iajs-2379	88	44	〉	〉	NOUN
iajs-2379	88	45	(	(	PUNCT
iajs-2379	88	46	t)dt	t)dt	PROPN
iajs-2379	88	47	∫	∫	PROPN
iajs-2379	88	48	,	,	PUNCT
iajs-2379	88	49	(	(	PUNCT
iajs-2379	88	50	)	)	PUNCT
iajs-2379	88	51	(	(	PUNCT
iajs-2379	88	52	)	)	PUNCT
iajs-2379	88	53	(	(	PUNCT
iajs-2379	88	54	)	)	PUNCT
iajs-2379	88	55	∫	∫	PROPN
iajs-2379	88	56	(	(	PUNCT
iajs-2379	88	57	)	)	PUNCT
iajs-2379	88	58	(	(	PUNCT
iajs-2379	88	59	)	)	PUNCT
iajs-2379	88	60	∫	∫	PROPN
iajs-2379	88	61	(	(	PUNCT
iajs-2379	88	62	)	)	PUNCT
iajs-2379	88	63	(	(	PUNCT
iajs-2379	88	64	t	t	PROPN
iajs-2379	88	65	)	)	PUNCT
iajs-2379	88	66	∫	∫	PROPN
iajs-2379	88	67	(	(	PUNCT
iajs-2379	88	68	)	)	PUNCT
iajs-2379	88	69	(	(	PUNCT
iajs-2379	88	70	)	)	PUNCT
iajs-2379	88	71	(	(	PUNCT
iajs-2379	88	72	37	37	NUM
iajs-2379	88	73	)	)	PUNCT
iajs-2379	88	74	∫	∫	NOUN
iajs-2379	88	75	〈	〈	PROPN
iajs-2379	88	76	〉	〉	NOUN
iajs-2379	88	77	(	(	PUNCT
iajs-2379	88	78	)	)	PUNCT
iajs-2379	88	79	∫	∫	PROPN
iajs-2379	88	80	,	,	PUNCT
iajs-2379	88	81	(	(	PUNCT
iajs-2379	88	82	)	)	PUNCT
iajs-2379	88	83	(	(	PUNCT
iajs-2379	88	84	)	)	PUNCT
iajs-2379	88	85	(	(	PUNCT
iajs-2379	88	86	)	)	PUNCT
iajs-2379	88	87	∫	∫	PROPN
iajs-2379	88	88	(	(	PUNCT
iajs-2379	88	89	)	)	PUNCT
iajs-2379	88	90	(	(	PUNCT
iajs-2379	88	91	)	)	PUNCT
iajs-2379	88	92	∫	∫	PROPN
iajs-2379	88	93	(	(	PUNCT
iajs-2379	88	94	)	)	PUNCT
iajs-2379	88	95	(	(	PUNCT
iajs-2379	88	96	)	)	PUNCT
iajs-2379	88	97	∫	∫	PROPN
iajs-2379	88	98	(	(	PUNCT
iajs-2379	88	99	)	)	PUNCT
iajs-2379	88	100	(	(	PUNCT
iajs-2379	88	101	)	)	PUNCT
iajs-2379	88	102	(	(	PUNCT
iajs-2379	88	103	38	38	NUM
iajs-2379	88	104	)	)	PUNCT
iajs-2379	88	105	i.e.	i.e.	X
iajs-2379	88	106	(	(	PUNCT
iajs-2379	88	107	,	,	PUNCT
iajs-2379	88	108	)	)	PUNCT
iajs-2379	88	109	is	be	AUX
iajs-2379	88	110	solution	solution	NOUN
iajs-2379	88	111	of	of	ADP
iajs-2379	88	112	the	the	DET
iajs-2379	88	113	wf	wf	PROPN
iajs-2379	88	114	(	(	PUNCT
iajs-2379	88	115	11	11	NUM
iajs-2379	88	116	13	13	NUM
iajs-2379	88	117	)	)	PUNCT
iajs-2379	88	118	.	.	PUNCT
iajs-2379	89	1	case	case	NOUN
iajs-2379	89	2	2	2	NUM
iajs-2379	89	3	:	:	PUNCT
iajs-2379	89	4	choose	choose	VERB
iajs-2379	89	5	,	,	PUNCT
iajs-2379	89	6	s.t	s.t	PROPN
iajs-2379	89	7	.	.	PROPN
iajs-2379	90	1	(	(	PUNCT
iajs-2379	90	2	)	)	PUNCT
iajs-2379	90	3	&	&	CCONJ
iajs-2379	90	4	(	(	PUNCT
iajs-2379	90	5	)	)	PUNCT
iajs-2379	90	6	,	,	PUNCT
iajs-2379	90	7	using	use	VERB
iajs-2379	90	8	integration	integration	NOUN
iajs-2379	90	9	by	by	ADP
iajs-2379	90	10	parts	part	NOUN
iajs-2379	90	11	for	for	ADP
iajs-2379	90	12	the	the	DET
iajs-2379	90	13	term	term	NOUN
iajs-2379	90	14	in	in	ADP
iajs-2379	90	15	the	the	DET
iajs-2379	90	16	l.h.s	l.h.s	NOUN
iajs-2379	90	17	.	.	PUNCT
iajs-2379	91	1	of	of	ADP
iajs-2379	91	2	(	(	PUNCT
iajs-2379	91	3	36	36	NUM
iajs-2379	91	4	)	)	PUNCT
iajs-2379	91	5	,	,	PUNCT
iajs-2379	91	6	one	one	PRON
iajs-2379	91	7	gets	get	VERB
iajs-2379	91	8	∫	∫	NOUN
iajs-2379	91	9	(	(	PUNCT
iajs-2379	91	10	)	)	PUNCT
iajs-2379	91	11	(	(	PUNCT
iajs-2379	91	12	)	)	PUNCT
iajs-2379	91	13	∫	∫	PROPN
iajs-2379	91	14	,	,	PUNCT
iajs-2379	91	15	(	(	PUNCT
iajs-2379	91	16	)	)	PUNCT
iajs-2379	91	17	(	(	PUNCT
iajs-2379	91	18	)	)	PUNCT
iajs-2379	91	19	(	(	PUNCT
iajs-2379	91	20	)	)	PUNCT
iajs-2379	91	21	∫	∫	PROPN
iajs-2379	91	22	(	(	PUNCT
iajs-2379	91	23	)	)	PUNCT
iajs-2379	91	24	(	(	PUNCT
iajs-2379	91	25	)	)	PUNCT
iajs-2379	91	26	∫	∫	PROPN
iajs-2379	91	27	(	(	PUNCT
iajs-2379	91	28	)	)	PUNCT
iajs-2379	91	29	(	(	PUNCT
iajs-2379	91	30	)	)	PUNCT
iajs-2379	91	31	∫	∫	PROPN
iajs-2379	91	32	(	(	PUNCT
iajs-2379	91	33	)	)	PUNCT
iajs-2379	91	34	(	(	PUNCT
iajs-2379	91	35	)	)	PUNCT
iajs-2379	91	36	(	(	PUNCT
iajs-2379	91	37	(	(	PUNCT
iajs-2379	91	38	)	)	PUNCT
iajs-2379	91	39	)	)	PUNCT
iajs-2379	92	1	(	(	PUNCT
iajs-2379	92	2	)	)	PUNCT
iajs-2379	92	3	(	(	PUNCT
iajs-2379	92	4	39	39	NUM
iajs-2379	92	5	)	)	PUNCT
iajs-2379	92	6	subtracting	subtract	VERB
iajs-2379	92	7	(	(	PUNCT
iajs-2379	92	8	33	33	NUM
iajs-2379	92	9	)	)	PUNCT
iajs-2379	92	10	from	from	ADP
iajs-2379	92	11	(	(	PUNCT
iajs-2379	92	12	39	39	NUM
iajs-2379	92	13	)	)	PUNCT
iajs-2379	92	14	,	,	PUNCT
iajs-2379	92	15	one	one	PRON
iajs-2379	92	16	obtains	obtain	VERB
iajs-2379	92	17	that	that	PRON
iajs-2379	92	18	(	(	PUNCT
iajs-2379	92	19	)	)	PUNCT
iajs-2379	92	20	(	(	PUNCT
iajs-2379	92	21	)	)	PUNCT
iajs-2379	92	22	=	=	SYM
iajs-2379	92	23	(	(	PUNCT
iajs-2379	92	24	(	(	PUNCT
iajs-2379	92	25	)	)	PUNCT
iajs-2379	92	26	)	)	PUNCT
iajs-2379	92	27	(	(	PUNCT
iajs-2379	92	28	)	)	PUNCT
iajs-2379	92	29	,	,	PUNCT
iajs-2379	92	30	(	(	PUNCT
iajs-2379	92	31	)	)	PUNCT
iajs-2379	92	32	,	,	PUNCT
iajs-2379	92	33	,	,	PUNCT
iajs-2379	92	34	(	(	PUNCT
iajs-2379	92	35	)	)	PUNCT
iajs-2379	92	36	(	(	PUNCT
iajs-2379	92	37	(	(	PUNCT
iajs-2379	92	38	)	)	PUNCT
iajs-2379	92	39	)	)	PUNCT
iajs-2379	92	40	i.e.	i.e.	X
iajs-2379	92	41	the	the	DET
iajs-2379	92	42	ic	ic	PROPN
iajs-2379	92	43	(	(	PUNCT
iajs-2379	92	44	11.b	11.b	NUM
iajs-2379	92	45	)	)	PUNCT
iajs-2379	92	46	holds	hold	NOUN
iajs-2379	92	47	.	.	PUNCT
iajs-2379	93	1	by	by	ADP
iajs-2379	93	2	the	the	DET
iajs-2379	93	3	same	same	ADJ
iajs-2379	93	4	above	above	ADP
iajs-2379	93	5	way	way	NOUN
iajs-2379	93	6	one	one	PRON
iajs-2379	93	7	can	can	AUX
iajs-2379	93	8	show	show	VERB
iajs-2379	93	9	that	that	SCONJ
iajs-2379	93	10	(	(	PUNCT
iajs-2379	93	11	)	)	PUNCT
iajs-2379	93	12	(	(	PUNCT
iajs-2379	93	13	(	(	PUNCT
iajs-2379	93	14	)	)	PUNCT
iajs-2379	93	15	)	)	PUNCT
iajs-2379	93	16	&	&	CCONJ
iajs-2379	93	17	(	(	PUNCT
iajs-2379	93	18	)	)	PUNCT
iajs-2379	93	19	(	(	PUNCT
iajs-2379	93	20	(	(	PUNCT
iajs-2379	93	21	)	)	PUNCT
iajs-2379	93	22	)	)	PUNCT
iajs-2379	93	23	that	that	PRON
iajs-2379	93	24	means	mean	VERB
iajs-2379	93	25	the	the	DET
iajs-2379	93	26	ics	ics	NOUN
iajs-2379	93	27	(	(	PUNCT
iajs-2379	93	28	12.b)&(13.b	12.b)&(13.b	NUM
iajs-2379	93	29	)	)	PUNCT
iajs-2379	93	30	are	be	AUX
iajs-2379	93	31	hold	hold	ADJ
iajs-2379	93	32	.	.	PUNCT
iajs-2379	94	1	the	the	DET
iajs-2379	94	2	strongly	strongly	ADV
iajs-2379	94	3	convergence	convergence	NOUN
iajs-2379	94	4	for	for	ADP
iajs-2379	94	5	:	:	PUNCT
iajs-2379	94	6	substituting	substituting	NOUN
iajs-2379	94	7	,	,	PUNCT
iajs-2379	94	8	and	and	CCONJ
iajs-2379	94	9	in	in	ADP
iajs-2379	94	10	(	(	PUNCT
iajs-2379	94	11	17.a),(18.a)&(19.a	17.a),(18.a)&(19.a	ADJ
iajs-2379	94	12	)	)	PUNCT
iajs-2379	94	13	respectively	respectively	ADV
iajs-2379	94	14	,	,	PUNCT
iajs-2379	94	15	adding	add	VERB
iajs-2379	94	16	the	the	DET
iajs-2379	94	17	three	three	NUM
iajs-2379	94	18	obtained	obtain	VERB
iajs-2379	94	19	equations	equation	NOUN
iajs-2379	94	20	together	together	ADV
iajs-2379	94	21	,	,	PUNCT
iajs-2379	94	22	and	and	CCONJ
iajs-2379	94	23	then	then	ADV
iajs-2379	94	24	integrating	integrate	VERB
iajs-2379	94	25	the	the	DET
iajs-2379	94	26	obtained	obtain	VERB
iajs-2379	94	27	equation	equation	NOUN
iajs-2379	94	28	from	from	ADP
iajs-2379	94	29	0	0	NUM
iajs-2379	94	30	to	to	ADP
iajs-2379	94	31	t	t	PROPN
iajs-2379	94	32	,	,	PUNCT
iajs-2379	94	33	on	on	ADP
iajs-2379	94	34	the	the	DET
iajs-2379	94	35	other	other	ADJ
iajs-2379	94	36	hand	hand	NOUN
iajs-2379	94	37	substituting	substituting	NOUN
iajs-2379	94	38	,	,	PUNCT
iajs-2379	94	39	&	&	CCONJ
iajs-2379	94	40	in	in	ADP
iajs-2379	94	41	(	(	PUNCT
iajs-2379	94	42	11.a),(12.a)&(13.a	11.a),(12.a)&(13.a	NOUN
iajs-2379	94	43	)	)	PUNCT
iajs-2379	94	44	respectively	respectively	ADV
iajs-2379	94	45	,	,	PUNCT
iajs-2379	94	46	adding	add	VERB
iajs-2379	94	47	them	they	PRON
iajs-2379	94	48	and	and	CCONJ
iajs-2379	94	49	then	then	ADV
iajs-2379	94	50	integrating	integrate	VERB
iajs-2379	94	51	the	the	DET
iajs-2379	94	52	three	three	NUM
iajs-2379	94	53	obtained	obtain	VERB
iajs-2379	94	54	equations	equation	NOUN
iajs-2379	94	55	from	from	ADP
iajs-2379	94	56	0	0	NUM
iajs-2379	94	57	to	to	ADP
iajs-2379	94	58	t	t	PROPN
iajs-2379	94	59	,	,	PUNCT
iajs-2379	94	60	to	to	PART
iajs-2379	94	61	get	get	VERB
iajs-2379	94	62	∫	∫	PROPN
iajs-2379	94	63	〈	〈	PROPN
iajs-2379	94	64	〉	〉	NOUN
iajs-2379	94	65	∫	∫	PROPN
iajs-2379	94	66	(	(	PUNCT
iajs-2379	94	67	)	)	PUNCT
iajs-2379	94	68	∫	∫	PROPN
iajs-2379	94	69	,	,	PUNCT
iajs-2379	94	70	(	(	PUNCT
iajs-2379	94	71	)	)	PUNCT
iajs-2379	94	72	(	(	PUNCT
iajs-2379	94	73	)	)	PUNCT
iajs-2379	94	74	(	(	PUNCT
iajs-2379	94	75	)	)	PUNCT
iajs-2379	94	76	(	(	PUNCT
iajs-2379	94	77	40	40	NUM
iajs-2379	94	78	)	)	PUNCT
iajs-2379	94	79	and	and	CCONJ
iajs-2379	94	80	∫	∫	PROPN
iajs-2379	94	81	〈	〈	PROPN
iajs-2379	94	82	〉	〉	NOUN
iajs-2379	94	83	∫	∫	PROPN
iajs-2379	94	84	(	(	PUNCT
iajs-2379	94	85	)	)	PUNCT
iajs-2379	94	86	∫	∫	PROPN
iajs-2379	94	87	,	,	PUNCT
iajs-2379	94	88	(	(	PUNCT
iajs-2379	94	89	)	)	PUNCT
iajs-2379	94	90	(	(	PUNCT
iajs-2379	94	91	)	)	PUNCT
iajs-2379	94	92	(	(	PUNCT
iajs-2379	94	93	)	)	PUNCT
iajs-2379	94	94	(	(	PUNCT
iajs-2379	94	95	41	41	NUM
iajs-2379	94	96	)	)	PUNCT
iajs-2379	94	97	using	use	VERB
iajs-2379	94	98	lemma	lemma	PROPN
iajs-2379	94	99	(	(	PUNCT
iajs-2379	94	100	1.2	1.2	NUM
iajs-2379	94	101	)	)	PUNCT
iajs-2379	94	102	in	in	ADP
iajs-2379	94	103	[	[	X
iajs-2379	94	104	11	11	NUM
iajs-2379	94	105	]	]	PUNCT
iajs-2379	94	106	.	.	PUNCT
iajs-2379	95	1	for	for	ADP
iajs-2379	95	2	the	the	DET
iajs-2379	95	3	terms	term	NOUN
iajs-2379	95	4	in	in	ADP
iajs-2379	95	5	the	the	DET
iajs-2379	95	6	l.h.s	l.h.s	NOUN
iajs-2379	95	7	.	.	PUNCT
iajs-2379	96	1	of	of	ADP
iajs-2379	96	2	(	(	PUNCT
iajs-2379	96	3	40	40	NUM
iajs-2379	96	4	)	)	PUNCT
iajs-2379	96	5	and	and	CCONJ
iajs-2379	96	6	(	(	PUNCT
iajs-2379	96	7	41	41	NUM
iajs-2379	96	8	)	)	PUNCT
iajs-2379	96	9	,	,	PUNCT
iajs-2379	96	10	they	they	PRON
iajs-2379	96	11	become	become	VERB
iajs-2379	96	12	‖	‖	ADJ
iajs-2379	96	13	(	(	PUNCT
iajs-2379	96	14	)	)	PUNCT
iajs-2379	96	15	‖	‖	PROPN
iajs-2379	96	16	‖	‖	PROPN
iajs-2379	96	17	(	(	PUNCT
iajs-2379	96	18	)	)	PUNCT
iajs-2379	96	19	‖	‖	PROPN
iajs-2379	96	20	∫	∫	PROPN
iajs-2379	96	21	(	(	PUNCT
iajs-2379	96	22	)	)	PUNCT
iajs-2379	96	23	∫	∫	PROPN
iajs-2379	96	24	,	,	PUNCT
iajs-2379	96	25	(	(	PUNCT
iajs-2379	96	26	+	+	CCONJ
iajs-2379	96	27	,	,	PUNCT
iajs-2379	96	28	)	)	PUNCT
iajs-2379	97	1	(	(	PUNCT
iajs-2379	97	2	+	+	X
iajs-2379	97	3	,	,	PUNCT
iajs-2379	97	4	)	)	PUNCT
iajs-2379	97	5	(	(	PUNCT
iajs-2379	97	6	+	+	X
iajs-2379	97	7	,	,	PUNCT
iajs-2379	97	8	)	)	PUNCT
iajs-2379	97	9	]	]	X
iajs-2379	97	10	dt	dt	X
iajs-2379	97	11	(	(	PUNCT
iajs-2379	97	12	42	42	NUM
iajs-2379	97	13	)	)	PUNCT
iajs-2379	97	14	‖	‖	PROPN
iajs-2379	97	15	(	(	PUNCT
iajs-2379	97	16	)	)	PUNCT
iajs-2379	97	17	‖	‖	PROPN
iajs-2379	97	18	‖	‖	PROPN
iajs-2379	97	19	(	(	PUNCT
iajs-2379	97	20	)	)	PUNCT
iajs-2379	97	21	‖	‖	PROPN
iajs-2379	97	22	∫	∫	PROPN
iajs-2379	97	23	(	(	PUNCT
iajs-2379	97	24	)	)	PUNCT
iajs-2379	97	25	∫	∫	PROPN
iajs-2379	97	26	,	,	PUNCT
iajs-2379	97	27	(	(	PUNCT
iajs-2379	97	28	+	+	CCONJ
iajs-2379	97	29	,	,	PUNCT
iajs-2379	97	30	)	)	PUNCT
iajs-2379	97	31	(	(	PUNCT
iajs-2379	97	32	+	+	X
iajs-2379	97	33	,	,	PUNCT
iajs-2379	97	34	)	)	PUNCT
iajs-2379	97	35	(	(	PUNCT
iajs-2379	97	36	+	+	X
iajs-2379	97	37	,	,	PUNCT
iajs-2379	97	38	)	)	PUNCT
iajs-2379	97	39	]	]	X
iajs-2379	97	40	dt	dt	X
iajs-2379	97	41	(	(	PUNCT
iajs-2379	97	42	43	43	NUM
iajs-2379	97	43	)	)	PUNCT
iajs-2379	97	44	since	since	SCONJ
iajs-2379	97	45	‖	‖	PROPN
iajs-2379	97	46	(	(	PUNCT
iajs-2379	97	47	)	)	PUNCT
iajs-2379	97	48	(	(	PUNCT
iajs-2379	97	49	)	)	PUNCT
iajs-2379	97	50	‖	‖	PROPN
iajs-2379	97	51	‖	‖	PROPN
iajs-2379	97	52	(	(	PUNCT
iajs-2379	97	53	)	)	PUNCT
iajs-2379	97	54	(	(	PUNCT
iajs-2379	97	55	)	)	PUNCT
iajs-2379	97	56	‖	‖	PROPN
iajs-2379	97	57	∫	∫	PROPN
iajs-2379	97	58	(	(	PUNCT
iajs-2379	97	59	)	)	PUNCT
iajs-2379	97	60	(	(	PUNCT
iajs-2379	97	61	44	44	NUM
iajs-2379	97	62	)	)	PUNCT
iajs-2379	97	63	where	where	SCONJ
iajs-2379	97	64	‖	‖	PROPN
iajs-2379	97	65	(	(	PUNCT
iajs-2379	97	66	)	)	PUNCT
iajs-2379	97	67	‖	‖	PROPN
iajs-2379	97	68	‖	‖	PROPN
iajs-2379	97	69	(	(	PUNCT
iajs-2379	97	70	)	)	PUNCT
iajs-2379	97	71	‖	‖	PROPN
iajs-2379	97	72	∫	∫	PROPN
iajs-2379	97	73	(	(	PUNCT
iajs-2379	97	74	(	(	PUNCT
iajs-2379	97	75	)	)	PUNCT
iajs-2379	97	76	(	(	PUNCT
iajs-2379	97	77	)	)	PUNCT
iajs-2379	97	78	)	)	PUNCT
iajs-2379	97	79	(	(	PUNCT
iajs-2379	97	80	(	(	PUNCT
iajs-2379	97	81	)	)	PUNCT
iajs-2379	97	82	(	(	PUNCT
iajs-2379	97	83	)	)	PUNCT
iajs-2379	97	84	)	)	PUNCT
iajs-2379	97	85	(	(	PUNCT
iajs-2379	97	86	(	(	PUNCT
iajs-2379	97	87	)	)	PUNCT
iajs-2379	97	88	(	(	PUNCT
iajs-2379	97	89	)	)	PUNCT
iajs-2379	97	90	)	)	PUNCT
iajs-2379	97	91	∫	∫	PROPN
iajs-2379	98	1	(	(	PUNCT
iajs-2379	98	2	(	(	PUNCT
iajs-2379	98	3	)	)	PUNCT
iajs-2379	98	4	(	(	PUNCT
iajs-2379	98	5	)	)	PUNCT
iajs-2379	98	6	)	)	PUNCT
iajs-2379	98	7	(	(	PUNCT
iajs-2379	98	8	(	(	PUNCT
iajs-2379	98	9	)	)	PUNCT
iajs-2379	98	10	(	(	PUNCT
iajs-2379	98	11	)	)	PUNCT
iajs-2379	98	12	(	(	PUNCT
iajs-2379	98	13	)	)	PUNCT
iajs-2379	98	14	)	)	PUNCT
iajs-2379	98	15	(	(	PUNCT
iajs-2379	98	16	(	(	PUNCT
iajs-2379	98	17	)	)	PUNCT
iajs-2379	98	18	(	(	PUNCT
iajs-2379	98	19	)	)	PUNCT
iajs-2379	98	20	(	(	PUNCT
iajs-2379	98	21	)	)	PUNCT
iajs-2379	98	22	)	)	PUNCT
iajs-2379	98	23	∫	∫	PROPN
iajs-2379	99	1	(	(	PUNCT
iajs-2379	99	2	(	(	PUNCT
iajs-2379	99	3	)	)	PUNCT
iajs-2379	99	4	(	(	PUNCT
iajs-2379	99	5	)	)	PUNCT
iajs-2379	99	6	(	(	PUNCT
iajs-2379	99	7	)	)	PUNCT
iajs-2379	99	8	)	)	PUNCT
iajs-2379	99	9	135	135	NUM
iajs-2379	99	10	ibn	ibn	PROPN
iajs-2379	99	11	al	al	PROPN
iajs-2379	99	12	-	-	PUNCT
iajs-2379	99	13	haitham	haitham	PROPN
iajs-2379	99	14	jour	jour	X
iajs-2379	99	15	.	.	PROPN
iajs-2379	99	16	for	for	ADP
iajs-2379	99	17	pure	pure	ADJ
iajs-2379	99	18	&	&	CCONJ
iajs-2379	99	19	appl	appl	PROPN
iajs-2379	99	20	.	.	PUNCT
iajs-2379	100	1	sci	sci	PROPN
iajs-2379	100	2	.	.	PROPN
iajs-2379	101	1	33	33	NUM
iajs-2379	101	2	(	(	PUNCT
iajs-2379	101	3	1	1	NUM
iajs-2379	101	4	)	)	PUNCT
iajs-2379	101	5	2020	2020	NUM
iajs-2379	101	6	since	since	SCONJ
iajs-2379	101	7	(	(	PUNCT
iajs-2379	101	8	)	)	PUNCT
iajs-2379	101	9	(	(	PUNCT
iajs-2379	101	10	)	)	PUNCT
iajs-2379	101	11	strongly	strongly	ADV
iajs-2379	101	12	in	in	ADP
iajs-2379	101	13	(	(	PUNCT
iajs-2379	101	14	(	(	PUNCT
iajs-2379	101	15	)	)	PUNCT
iajs-2379	101	16	)	)	PUNCT
iajs-2379	101	17	(	(	PUNCT
iajs-2379	101	18	44.a	44.a	NOUN
iajs-2379	101	19	)	)	PUNCT
iajs-2379	101	20	(	(	PUNCT
iajs-2379	101	21	)	)	PUNCT
iajs-2379	101	22	(	(	PUNCT
iajs-2379	101	23	)	)	PUNCT
iajs-2379	101	24	strongly	strongly	ADV
iajs-2379	101	25	in	in	ADP
iajs-2379	101	26	(	(	PUNCT
iajs-2379	101	27	(	(	PUNCT
iajs-2379	101	28	)	)	PUNCT
iajs-2379	101	29	)	)	PUNCT
iajs-2379	101	30	(	(	PUNCT
iajs-2379	101	31	44.b	44.b	NOUN
iajs-2379	101	32	)	)	PUNCT
iajs-2379	101	33	then	then	ADV
iajs-2379	101	34	(	(	PUNCT
iajs-2379	101	35	(	(	PUNCT
iajs-2379	101	36	)	)	PUNCT
iajs-2379	101	37	(	(	PUNCT
iajs-2379	101	38	)	)	PUNCT
iajs-2379	101	39	(	(	PUNCT
iajs-2379	101	40	)	)	PUNCT
iajs-2379	101	41	)	)	PUNCT
iajs-2379	101	42	(	(	PUNCT
iajs-2379	101	43	(	(	PUNCT
iajs-2379	101	44	)	)	PUNCT
iajs-2379	101	45	(	(	PUNCT
iajs-2379	101	46	)	)	PUNCT
iajs-2379	101	47	(	(	PUNCT
iajs-2379	101	48	)	)	PUNCT
iajs-2379	101	49	)	)	PUNCT
iajs-2379	101	50	(	(	PUNCT
iajs-2379	101	51	44.c	44.c	NOUN
iajs-2379	101	52	)	)	PUNCT
iajs-2379	101	53	‖	‖	PROPN
iajs-2379	101	54	(	(	PUNCT
iajs-2379	101	55	)	)	PUNCT
iajs-2379	101	56	(	(	PUNCT
iajs-2379	101	57	)	)	PUNCT
iajs-2379	101	58	‖	‖	PROPN
iajs-2379	101	59	and	and	CCONJ
iajs-2379	101	60	‖	‖	PROPN
iajs-2379	101	61	(	(	PUNCT
iajs-2379	101	62	)	)	PUNCT
iajs-2379	101	63	(	(	PUNCT
iajs-2379	101	64	)	)	PUNCT
iajs-2379	101	65	‖	‖	PROPN
iajs-2379	101	66	(	(	PUNCT
iajs-2379	101	67	44.d	44.d	NUM
iajs-2379	101	68	)	)	PUNCT
iajs-2379	101	69	since	since	SCONJ
iajs-2379	101	70	weakly	weakly	ADV
iajs-2379	101	71	in	in	ADP
iajs-2379	101	72	(	(	PUNCT
iajs-2379	101	73	(	(	PUNCT
iajs-2379	101	74	)	)	PUNCT
iajs-2379	101	75	)	)	PUNCT
iajs-2379	101	76	,	,	PUNCT
iajs-2379	101	77	then	then	ADV
iajs-2379	101	78	∫	∫	PROPN
iajs-2379	101	79	(	(	PUNCT
iajs-2379	101	80	(	(	PUNCT
iajs-2379	101	81	)	)	PUNCT
iajs-2379	101	82	(	(	PUNCT
iajs-2379	101	83	)	)	PUNCT
iajs-2379	101	84	(	(	PUNCT
iajs-2379	101	85	)	)	PUNCT
iajs-2379	101	86	)	)	PUNCT
iajs-2379	101	87	(	(	PUNCT
iajs-2379	101	88	44.e	44.e	NUM
iajs-2379	101	89	)	)	PUNCT
iajs-2379	101	90	also	also	ADV
iajs-2379	101	91	since	since	SCONJ
iajs-2379	101	92	weakly	weakly	ADJ
iajs-2379	101	93	in	in	ADP
iajs-2379	101	94	(	(	PUNCT
iajs-2379	101	95	(	(	PUNCT
iajs-2379	101	96	)	)	PUNCT
iajs-2379	101	97	)	)	PUNCT
iajs-2379	101	98	,	,	PUNCT
iajs-2379	101	99	then	then	ADV
iajs-2379	101	100	∫	∫	INTJ
iajs-2379	101	101	,	,	PUNCT
iajs-2379	101	102	(	(	PUNCT
iajs-2379	101	103	)	)	PUNCT
iajs-2379	101	104	(	(	PUNCT
iajs-2379	101	105	)	)	PUNCT
iajs-2379	101	106	(	(	PUNCT
iajs-2379	101	107	)	)	PUNCT
iajs-2379	101	108	∫	∫	PROPN
iajs-2379	101	109	,	,	PUNCT
iajs-2379	101	110	(	(	PUNCT
iajs-2379	101	111	)	)	PUNCT
iajs-2379	101	112	(	(	PUNCT
iajs-2379	101	113	)	)	PUNCT
iajs-2379	101	114	(	(	PUNCT
iajs-2379	101	115	)	)	PUNCT
iajs-2379	101	116	(	(	PUNCT
iajs-2379	101	117	44.f	44.f	NUM
iajs-2379	101	118	)	)	PUNCT
iajs-2379	101	119	i.e.	i.e.	X
iajs-2379	101	120	when	when	SCONJ
iajs-2379	101	121	in	in	ADP
iajs-2379	101	122	both	both	DET
iajs-2379	101	123	sides	side	NOUN
iajs-2379	101	124	of	of	ADP
iajs-2379	101	125	(	(	PUNCT
iajs-2379	101	126	44	44	NUM
iajs-2379	101	127	)	)	PUNCT
iajs-2379	101	128	,	,	PUNCT
iajs-2379	101	129	one	one	PRON
iajs-2379	101	130	has	have	VERB
iajs-2379	101	131	the	the	DET
iajs-2379	101	132	following	follow	VERB
iajs-2379	101	133	results	result	NOUN
iajs-2379	101	134	:	:	PUNCT
iajs-2379	101	135	(	(	PUNCT
iajs-2379	101	136	1)the	1)the	DET
iajs-2379	101	137	first	first	ADJ
iajs-2379	101	138	two	two	NUM
iajs-2379	101	139	terms	term	NOUN
iajs-2379	101	140	in	in	ADP
iajs-2379	101	141	the	the	DET
iajs-2379	101	142	l.h.s	l.h.s	NOUN
iajs-2379	101	143	.	.	PUNCT
iajs-2379	102	1	of	of	ADP
iajs-2379	102	2	(	(	PUNCT
iajs-2379	102	3	44	44	NUM
iajs-2379	102	4	)	)	PUNCT
iajs-2379	102	5	are	be	AUX
iajs-2379	102	6	tending	tend	VERB
iajs-2379	102	7	to	to	ADP
iajs-2379	102	8	zero	zero	NUM
iajs-2379	102	9	(	(	PUNCT
iajs-2379	102	10	from	from	ADP
iajs-2379	102	11	(	(	PUNCT
iajs-2379	102	12	44.d	44.d	NUM
iajs-2379	102	13	)	)	PUNCT
iajs-2379	102	14	)	)	PUNCT
iajs-2379	102	15	,	,	PUNCT
iajs-2379	102	16	(	(	PUNCT
iajs-2379	102	17	2	2	X
iajs-2379	102	18	)	)	PUNCT
iajs-2379	102	19	eq	eq	NOUN
iajs-2379	102	20	.	.	PUNCT
iajs-2379	103	1	(	(	PUNCT
iajs-2379	103	2	)	)	PUNCT
iajs-2379	103	3	∫	∫	PROPN
iajs-2379	103	4	,	,	PUNCT
iajs-2379	103	5	(	(	PUNCT
iajs-2379	103	6	)	)	PUNCT
iajs-2379	103	7	(	(	PUNCT
iajs-2379	103	8	)	)	PUNCT
iajs-2379	103	9	(	(	PUNCT
iajs-2379	103	10	)	)	PUNCT
iajs-2379	103	11	(	(	PUNCT
iajs-2379	103	12	)	)	PUNCT
iajs-2379	103	13	∫	∫	PROPN
iajs-2379	103	14	,	,	PUNCT
iajs-2379	103	15	(	(	PUNCT
iajs-2379	103	16	)	)	PUNCT
iajs-2379	103	17	(	(	PUNCT
iajs-2379	103	18	)	)	PUNCT
iajs-2379	103	19	(	(	PUNCT
iajs-2379	103	20	)	)	PUNCT
iajs-2379	103	21	(	(	PUNCT
iajs-2379	103	22	3	3	X
iajs-2379	103	23	)	)	PUNCT
iajs-2379	103	24	eq	eq	NOUN
iajs-2379	103	25	.	.	PUNCT
iajs-2379	103	26	l.h.s	l.h.s	PROPN
iajs-2379	103	27	.	.	PUNCT
iajs-2379	104	1	of	of	ADP
iajs-2379	104	2	(	(	PUNCT
iajs-2379	104	3	43	43	NUM
iajs-2379	104	4	)	)	PUNCT
iajs-2379	104	5	∫	∫	NOUN
iajs-2379	104	6	,	,	PUNCT
iajs-2379	104	7	(	(	PUNCT
iajs-2379	104	8	)	)	PUNCT
iajs-2379	104	9	(	(	PUNCT
iajs-2379	104	10	)	)	PUNCT
iajs-2379	104	11	(	(	PUNCT
iajs-2379	104	12	)	)	PUNCT
iajs-2379	104	13	(	(	PUNCT
iajs-2379	104	14	4	4	X
iajs-2379	104	15	)	)	PUNCT
iajs-2379	104	16	the	the	DET
iajs-2379	104	17	two	two	NUM
iajs-2379	104	18	terms	term	NOUN
iajs-2379	104	19	in	in	ADP
iajs-2379	104	20	eq	eq	ADP
iajs-2379	104	21	.	.	PROPN
iajs-2379	104	22	are	be	AUX
iajs-2379	104	23	tending	tend	VERB
iajs-2379	104	24	to	to	ADP
iajs-2379	104	25	zero	zero	NUM
iajs-2379	104	26	from	from	ADP
iajs-2379	104	27	(	(	PUNCT
iajs-2379	104	28	44.c	44.c	NOUN
iajs-2379	104	29	)	)	PUNCT
iajs-2379	104	30	,	,	PUNCT
iajs-2379	104	31	and	and	CCONJ
iajs-2379	104	32	the	the	DET
iajs-2379	104	33	last	last	ADJ
iajs-2379	104	34	one	one	NUM
iajs-2379	104	35	term	term	NOUN
iajs-2379	104	36	also	also	ADV
iajs-2379	104	37	tend	tend	VERB
iajs-2379	104	38	to	to	PART
iajs-2379	104	39	zero	zero	NUM
iajs-2379	104	40	from	from	ADP
iajs-2379	104	41	(	(	PUNCT
iajs-2379	104	42	44.e	44.e	NUM
iajs-2379	104	43	)	)	PUNCT
iajs-2379	104	44	,	,	PUNCT
iajs-2379	104	45	from	from	ADP
iajs-2379	104	46	these	these	DET
iajs-2379	104	47	results	result	NOUN
iajs-2379	104	48	(	(	PUNCT
iajs-2379	104	49	44	44	NUM
iajs-2379	104	50	)	)	PUNCT
iajs-2379	104	51	gives	give	VERB
iajs-2379	104	52	when	when	SCONJ
iajs-2379	104	53	∫	∫	PROPN
iajs-2379	104	54	‖	‖	PROPN
iajs-2379	104	55	‖	‖	PROPN
iajs-2379	104	56	∫	∫	PROPN
iajs-2379	104	57	(	(	PUNCT
iajs-2379	104	58	)	)	PUNCT
iajs-2379	104	59	strongly	strongly	ADV
iajs-2379	104	60	in	in	ADP
iajs-2379	104	61	(	(	PUNCT
iajs-2379	104	62	(	(	PUNCT
iajs-2379	104	63	)	)	PUNCT
iajs-2379	104	64	)	)	PUNCT
iajs-2379	104	65	.	.	PUNCT
iajs-2379	105	1	uniqueness	uniqueness	NOUN
iajs-2379	105	2	of	of	ADP
iajs-2379	105	3	the	the	DET
iajs-2379	105	4	solution	solution	NOUN
iajs-2379	105	5	:	:	PUNCT
iajs-2379	105	6	let	let	VERB
iajs-2379	105	7	⃗	⃗	PROPN
iajs-2379	105	8	,	,	PUNCT
iajs-2379	105	9	̅	̅	NOUN
iajs-2379	105	10	are	be	AUX
iajs-2379	105	11	two	two	NUM
iajs-2379	105	12	solutions	solution	NOUN
iajs-2379	105	13	of	of	ADP
iajs-2379	105	14	the	the	DET
iajs-2379	105	15	wf	wf	PROPN
iajs-2379	105	16	(	(	PUNCT
iajs-2379	105	17	11–13	11–13	NUM
iajs-2379	105	18	)	)	PUNCT
iajs-2379	105	19	,	,	PUNCT
iajs-2379	105	20	i.e.	i.e.	X
iajs-2379	105	21	and	and	CCONJ
iajs-2379	105	22	̅	̅	NOUN
iajs-2379	105	23	are	be	AUX
iajs-2379	105	24	satisfied	satisfied	ADJ
iajs-2379	105	25	(	(	PUNCT
iajs-2379	105	26	11.a	11.a	NUM
iajs-2379	105	27	)	)	PUNCT
iajs-2379	105	28	,	,	PUNCT
iajs-2379	105	29	or	or	CCONJ
iajs-2379	105	30	〈	〈	PRON
iajs-2379	105	31	〉	〉	NOUN
iajs-2379	105	32	(	(	PUNCT
iajs-2379	105	33	)	)	PUNCT
iajs-2379	105	34	(	(	PUNCT
iajs-2379	105	35	)	)	PUNCT
iajs-2379	105	36	(	(	PUNCT
iajs-2379	105	37	)	)	PUNCT
iajs-2379	105	38	(	(	PUNCT
iajs-2379	105	39	)	)	PUNCT
iajs-2379	105	40	,	,	PUNCT
iajs-2379	105	41	〈	〈	PROPN
iajs-2379	105	42	̅	̅	NOUN
iajs-2379	105	43	〉	〉	NOUN
iajs-2379	105	44	(	(	PUNCT
iajs-2379	105	45	̅	̅	NOUN
iajs-2379	105	46	)	)	PUNCT
iajs-2379	105	47	(	(	PUNCT
iajs-2379	105	48	̅	̅	NOUN
iajs-2379	105	49	)	)	PUNCT
iajs-2379	105	50	(	(	PUNCT
iajs-2379	105	51	̅	̅	NOUN
iajs-2379	105	52	)	)	PUNCT
iajs-2379	105	53	(	(	PUNCT
iajs-2379	105	54	)	)	PUNCT
iajs-2379	105	55	,	,	PUNCT
iajs-2379	105	56	subtracting	subtract	VERB
iajs-2379	105	57	the	the	DET
iajs-2379	105	58	equation	equation	NOUN
iajs-2379	105	59	from	from	ADP
iajs-2379	105	60	the	the	DET
iajs-2379	105	61	one	one	NUM
iajs-2379	105	62	and	and	CCONJ
iajs-2379	105	63	substituting	substitute	VERB
iajs-2379	105	64	̅	̅	NOUN
iajs-2379	105	65	in	in	ADP
iajs-2379	105	66	the	the	DET
iajs-2379	105	67	obtained	obtain	VERB
iajs-2379	105	68	equation	equation	NOUN
iajs-2379	105	69	,	,	PUNCT
iajs-2379	105	70	one	one	PRON
iajs-2379	105	71	gets	get	VERB
iajs-2379	105	72	that	that	PRON
iajs-2379	105	73	〈	〈	NOUN
iajs-2379	105	74	(	(	PUNCT
iajs-2379	105	75	̅	̅	NOUN
iajs-2379	105	76	)	)	PUNCT
iajs-2379	105	77	̅	̅	NOUN
iajs-2379	105	78	〉	〉	NOUN
iajs-2379	105	79	(	(	PUNCT
iajs-2379	105	80	̅	̅	NOUN
iajs-2379	105	81	̅	̅	NOUN
iajs-2379	105	82	)	)	PUNCT
iajs-2379	105	83	(	(	PUNCT
iajs-2379	105	84	̅	̅	NOUN
iajs-2379	105	85	̅	̅	NOUN
iajs-2379	105	86	)	)	PUNCT
iajs-2379	105	87	(	(	PUNCT
iajs-2379	105	88	̅	̅	NUM
iajs-2379	105	89	̅	̅	NOUN
iajs-2379	105	90	)	)	PUNCT
iajs-2379	105	91	(	(	PUNCT
iajs-2379	105	92	45	45	NUM
iajs-2379	105	93	)	)	PUNCT
iajs-2379	105	94	by	by	ADP
iajs-2379	105	95	the	the	DET
iajs-2379	105	96	similar	similar	ADJ
iajs-2379	105	97	manner	manner	NOUN
iajs-2379	105	98	,	,	PUNCT
iajs-2379	105	99	one	one	PRON
iajs-2379	105	100	gets	get	VERB
iajs-2379	105	101	〈	〈	NOUN
iajs-2379	105	102	(	(	SYM
iajs-2379	105	103	̅	̅	NOUN
iajs-2379	105	104	)	)	PUNCT
iajs-2379	105	105	̅	̅	NOUN
iajs-2379	105	106	〉	〉	NOUN
iajs-2379	105	107	(	(	PUNCT
iajs-2379	105	108	̅	̅	NOUN
iajs-2379	105	109	̅	̅	NOUN
iajs-2379	105	110	)	)	PUNCT
iajs-2379	105	111	(	(	PUNCT
iajs-2379	105	112	̅	̅	NOUN
iajs-2379	105	113	̅	̅	NOUN
iajs-2379	105	114	)	)	PUNCT
iajs-2379	105	115	(	(	PUNCT
iajs-2379	105	116	̅	̅	NUM
iajs-2379	105	117	̅	̅	NOUN
iajs-2379	105	118	)	)	PUNCT
iajs-2379	105	119	(	(	PUNCT
iajs-2379	105	120	46	46	NUM
iajs-2379	105	121	)	)	PUNCT
iajs-2379	105	122	〈	〈	PROPN
iajs-2379	105	123	(	(	PUNCT
iajs-2379	105	124	̅	̅	NOUN
iajs-2379	105	125	)	)	PUNCT
iajs-2379	105	126	̅	̅	NOUN
iajs-2379	105	127	〉	〉	NOUN
iajs-2379	105	128	(	(	PUNCT
iajs-2379	105	129	̅	̅	NOUN
iajs-2379	105	130	̅	̅	NOUN
iajs-2379	105	131	)	)	PUNCT
iajs-2379	105	132	(	(	PUNCT
iajs-2379	105	133	̅	̅	NOUN
iajs-2379	105	134	̅	̅	NOUN
iajs-2379	105	135	)	)	PUNCT
iajs-2379	105	136	(	(	PUNCT
iajs-2379	105	137	̅	̅	NUM
iajs-2379	105	138	̅	̅	NOUN
iajs-2379	105	139	)	)	PUNCT
iajs-2379	105	140	(	(	PUNCT
iajs-2379	105	141	47	47	NUM
iajs-2379	105	142	)	)	PUNCT
iajs-2379	105	143	adding	add	VERB
iajs-2379	105	144	(	(	PUNCT
iajs-2379	105	145	45	45	NUM
iajs-2379	105	146	47	47	NUM
iajs-2379	105	147	)	)	PUNCT
iajs-2379	105	148	,	,	PUNCT
iajs-2379	105	149	using	use	VERB
iajs-2379	105	150	lemma(1.2	lemma(1.2	NOUN
iajs-2379	105	151	)	)	PUNCT
iajs-2379	105	152	in	in	ADP
iajs-2379	105	153	[	[	X
iajs-2379	105	154	11	11	NUM
iajs-2379	105	155	]	]	PUNCT
iajs-2379	105	156	.	.	PUNCT
iajs-2379	106	1	in	in	ADP
iajs-2379	106	2	the	the	DET
iajs-2379	106	3	term	term	NOUN
iajs-2379	106	4	of	of	ADP
iajs-2379	106	5	the	the	DET
iajs-2379	106	6	obtained	obtain	VERB
iajs-2379	106	7	equation	equation	NOUN
iajs-2379	106	8	,	,	PUNCT
iajs-2379	106	9	to	to	PART
iajs-2379	106	10	get	get	VERB
iajs-2379	106	11	‖	‖	ADJ
iajs-2379	106	12	̅	̅	NOUN
iajs-2379	106	13	‖	‖	ADJ
iajs-2379	106	14	‖	‖	PROPN
iajs-2379	106	15	̅	̅	NOUN
iajs-2379	106	16	‖	‖	PROPN
iajs-2379	106	17	(	(	PUNCT
iajs-2379	106	18	48	48	NUM
iajs-2379	106	19	)	)	PUNCT
iajs-2379	106	20	since	since	SCONJ
iajs-2379	106	21	the	the	DET
iajs-2379	106	22	term	term	NOUN
iajs-2379	106	23	of	of	ADP
iajs-2379	106	24	the	the	DET
iajs-2379	106	25	l.h.s	l.h.s	NOUN
iajs-2379	106	26	.	.	PUNCT
iajs-2379	107	1	of	of	ADP
iajs-2379	107	2	(	(	PUNCT
iajs-2379	107	3	48	48	NUM
iajs-2379	107	4	)	)	PUNCT
iajs-2379	107	5	is	be	AUX
iajs-2379	107	6	positive	positive	ADJ
iajs-2379	107	7	,	,	PUNCT
iajs-2379	107	8	integrating	integrate	VERB
iajs-2379	107	9	both	both	DET
iajs-2379	107	10	sides	side	NOUN
iajs-2379	107	11	of	of	ADP
iajs-2379	107	12	(	(	PUNCT
iajs-2379	107	13	48	48	NUM
iajs-2379	107	14	)	)	PUNCT
iajs-2379	107	15	w.r.t	w.r.t	NOUN
iajs-2379	107	16	.	.	PUNCT
iajs-2379	108	1	from	from	ADP
iajs-2379	108	2	to	to	ADP
iajs-2379	108	3	,	,	PUNCT
iajs-2379	108	4	one	one	PRON
iajs-2379	108	5	gets	get	VERB
iajs-2379	108	6	∫	∫	PROPN
iajs-2379	108	7	‖	‖	PROPN
iajs-2379	108	8	̅	̅	NOUN
iajs-2379	108	9	‖	‖	ADJ
iajs-2379	108	10	‖	‖	ADJ
iajs-2379	108	11	(	(	PUNCT
iajs-2379	108	12	̅	̅	NOUN
iajs-2379	108	13	)	)	PUNCT
iajs-2379	108	14	(	(	PUNCT
iajs-2379	108	15	)	)	PUNCT
iajs-2379	108	16	‖	‖	PROPN
iajs-2379	108	17	‖	‖	PROPN
iajs-2379	108	18	̅	̅	PROPN
iajs-2379	108	19	‖	‖	ADJ
iajs-2379	108	20	,	,	PUNCT
iajs-2379	108	21	integrating	integrate	VERB
iajs-2379	108	22	both	both	DET
iajs-2379	108	23	sides	side	NOUN
iajs-2379	108	24	of	of	ADP
iajs-2379	108	25	(	(	PUNCT
iajs-2379	108	26	48	48	NUM
iajs-2379	108	27	)	)	PUNCT
iajs-2379	108	28	from	from	ADP
iajs-2379	108	29	to	to	ADP
iajs-2379	108	30	,	,	PUNCT
iajs-2379	108	31	using	use	VERB
iajs-2379	108	32	the	the	DET
iajs-2379	108	33	given	give	VERB
iajs-2379	108	34	ics	ic	NOUN
iajs-2379	108	35	and	and	CCONJ
iajs-2379	108	36	the	the	DET
iajs-2379	108	37	above	above	ADJ
iajs-2379	108	38	result	result	NOUN
iajs-2379	108	39	,	,	PUNCT
iajs-2379	108	40	one	one	PRON
iajs-2379	108	41	has	have	VERB
iajs-2379	108	42	136	136	NUM
iajs-2379	108	43	ibn	ibn	PROPN
iajs-2379	108	44	al	al	PROPN
iajs-2379	108	45	-	-	PUNCT
iajs-2379	108	46	haitham	haitham	PROPN
iajs-2379	108	47	jour	jour	X
iajs-2379	108	48	.	.	PROPN
iajs-2379	109	1	for	for	ADP
iajs-2379	109	2	pure	pure	ADJ
iajs-2379	109	3	&	&	CCONJ
iajs-2379	109	4	appl	appl	PROPN
iajs-2379	109	5	.	.	PUNCT
iajs-2379	110	1	sci	sci	PROPN
iajs-2379	110	2	.	.	PROPN
iajs-2379	111	1	33	33	NUM
iajs-2379	111	2	(	(	PUNCT
iajs-2379	111	3	1	1	NUM
iajs-2379	111	4	)	)	PUNCT
iajs-2379	111	5	2020	2020	NUM
iajs-2379	111	6	∫	∫	PROPN
iajs-2379	111	7	‖	‖	PROPN
iajs-2379	111	8	̅	̅	PROPN
iajs-2379	111	9	‖	‖	ADJ
iajs-2379	111	10	‖	‖	PROPN
iajs-2379	111	11	̅	̅	NOUN
iajs-2379	111	12	‖	‖	ADJ
iajs-2379	111	13	(	(	PUNCT
iajs-2379	111	14	)	)	PUNCT
iajs-2379	111	15	̅	̅	NOUN
iajs-2379	111	16	.	.	PUNCT
iajs-2379	112	1	4	4	X
iajs-2379	112	2	.	.	X
iajs-2379	112	3	existence	existence	NOUN
iajs-2379	112	4	of	of	ADP
iajs-2379	112	5	a	a	DET
iajs-2379	112	6	ccocp	ccocp	NOUN
iajs-2379	112	7	theorem	theorem	VERB
iajs-2379	112	8	4.1	4.1	NUM
iajs-2379	112	9	:	:	PUNCT
iajs-2379	112	10	in	in	ADP
iajs-2379	112	11	addition	addition	NOUN
iajs-2379	112	12	to	to	ADP
iajs-2379	112	13	assumptions	assumption	NOUN
iajs-2379	112	14	(	(	PUNCT
iajs-2379	112	15	a	a	X
iajs-2379	112	16	)	)	PUNCT
iajs-2379	112	17	,	,	PUNCT
iajs-2379	112	18	assume	assume	VERB
iajs-2379	112	19	that	that	SCONJ
iajs-2379	112	20	and	and	CCONJ
iajs-2379	112	21	are	be	AUX
iajs-2379	112	22	the	the	DET
iajs-2379	112	23	svs	svs	NOUN
iajs-2379	112	24	corresponding	correspond	VERB
iajs-2379	112	25	to	to	ADP
iajs-2379	112	26	the	the	DET
iajs-2379	112	27	cvs	cvs	NOUN
iajs-2379	112	28	⃗	⃗	PROPN
iajs-2379	112	29	and	and	CCONJ
iajs-2379	112	30	⃗	⃗	PROPN
iajs-2379	112	31	⃗	⃗	PROPN
iajs-2379	112	32	respectively	respectively	ADV
iajs-2379	112	33	with	with	SCONJ
iajs-2379	112	34	⃗	⃗	PROPN
iajs-2379	112	35	and	and	CCONJ
iajs-2379	112	36	⃗	⃗	PROPN
iajs-2379	112	37	are	be	AUX
iajs-2379	112	38	bounded	bound	VERB
iajs-2379	112	39	in	in	ADP
iajs-2379	112	40	(	(	PUNCT
iajs-2379	112	41	(	(	PUNCT
iajs-2379	112	42	)	)	PUNCT
iajs-2379	112	43	)	)	PUNCT
iajs-2379	112	44	then	then	ADV
iajs-2379	112	45	‖	‖	PROPN
iajs-2379	112	46	‖	‖	PROPN
iajs-2379	112	47	.	.	PUNCT
iajs-2379	113	1	(	(	PUNCT
iajs-2379	113	2	)	)	PUNCT
iajs-2379	113	3	/	/	SYM
iajs-2379	113	4	‖	‖	PROPN
iajs-2379	113	5	⃗	⃗	PROPN
iajs-2379	113	6	‖	‖	PROPN
iajs-2379	113	7	,	,	PUNCT
iajs-2379	113	8	‖	‖	PROPN
iajs-2379	113	9	‖	‖	PROPN
iajs-2379	113	10	(	(	PUNCT
iajs-2379	113	11	)	)	PUNCT
iajs-2379	113	12	‖	‖	PROPN
iajs-2379	113	13	⃗	⃗	PROPN
iajs-2379	113	14	‖	‖	PROPN
iajs-2379	113	15	,	,	PUNCT
iajs-2379	113	16	‖	‖	PROPN
iajs-2379	113	17	‖	‖	PROPN
iajs-2379	113	18	(	(	PUNCT
iajs-2379	113	19	)	)	PUNCT
iajs-2379	113	20	‖	‖	PROPN
iajs-2379	114	1	⃗	⃗	PROPN
iajs-2379	114	2	‖	‖	PROPN
iajs-2379	114	3	,	,	PUNCT
iajs-2379	114	4	proof	proof	NOUN
iajs-2379	114	5	:	:	PUNCT
iajs-2379	114	6	let	let	VERB
iajs-2379	114	7	⃗	⃗	PROPN
iajs-2379	114	8	(	(	PUNCT
iajs-2379	114	9	)	)	PUNCT
iajs-2379	114	10	(	(	PUNCT
iajs-2379	114	11	(	(	PUNCT
iajs-2379	114	12	)	)	PUNCT
iajs-2379	114	13	)	)	PUNCT
iajs-2379	114	14	then	then	ADV
iajs-2379	114	15	by	by	ADP
iajs-2379	114	16	theorem	theorem	NOUN
iajs-2379	114	17	3.1	3.1	NUM
iajs-2379	114	18	there	there	ADV
iajs-2379	114	19	exists	exist	VERB
iajs-2379	114	20	(	(	PUNCT
iajs-2379	114	21	)	)	PUNCT
iajs-2379	114	22	which	which	PRON
iajs-2379	114	23	is	be	AUX
iajs-2379	114	24	satisfied	satisfied	ADJ
iajs-2379	114	25	(	(	PUNCT
iajs-2379	114	26	11	11	NUM
iajs-2379	114	27	13	13	NUM
iajs-2379	114	28	)	)	PUNCT
iajs-2379	114	29	and	and	CCONJ
iajs-2379	114	30	also	also	ADV
iajs-2379	114	31	let	let	VERB
iajs-2379	114	32	̅	̅	NOUN
iajs-2379	114	33	(	(	PUNCT
iajs-2379	114	34	̅	̅	NOUN
iajs-2379	114	35	̅	̅	NOUN
iajs-2379	114	36	̅	̅	NOUN
iajs-2379	114	37	)	)	PUNCT
iajs-2379	114	38	be	be	AUX
iajs-2379	114	39	the	the	DET
iajs-2379	114	40	solution	solution	NOUN
iajs-2379	114	41	of	of	ADP
iajs-2379	114	42	(	(	PUNCT
iajs-2379	114	43	11	11	NUM
iajs-2379	114	44	13	13	NUM
iajs-2379	114	45	)	)	PUNCT
iajs-2379	114	46	corresponds	correspond	VERB
iajs-2379	114	47	to	to	ADP
iajs-2379	114	48	the	the	DET
iajs-2379	114	49	cv	cv	PROPN
iajs-2379	114	50	⃗̅	⃗̅	PROPN
iajs-2379	114	51	(	(	PUNCT
iajs-2379	114	52	̅	̅	NOUN
iajs-2379	114	53	̅	̅	NOUN
iajs-2379	114	54	̅	̅	NOUN
iajs-2379	114	55	)	)	PUNCT
iajs-2379	114	56	(	(	PUNCT
iajs-2379	114	57	(	(	PUNCT
iajs-2379	114	58	)	)	PUNCT
iajs-2379	114	59	)	)	PUNCT
iajs-2379	114	60	i.e.	i.e.	X
iajs-2379	114	61	〈	〈	DET
iajs-2379	114	62	̅	̅	NOUN
iajs-2379	114	63	〉	〉	NOUN
iajs-2379	114	64	(	(	PUNCT
iajs-2379	114	65	̅	̅	NOUN
iajs-2379	114	66	)	)	PUNCT
iajs-2379	114	67	(	(	PUNCT
iajs-2379	114	68	̅	̅	NOUN
iajs-2379	114	69	)	)	PUNCT
iajs-2379	114	70	(	(	PUNCT
iajs-2379	114	71	̅	̅	NOUN
iajs-2379	114	72	)	)	PUNCT
iajs-2379	114	73	(	(	PUNCT
iajs-2379	114	74	̅	̅	NOUN
iajs-2379	114	75	)	)	PUNCT
iajs-2379	114	76	(	(	PUNCT
iajs-2379	114	77	̅	̅	NOUN
iajs-2379	114	78	)	)	PUNCT
iajs-2379	114	79	(	(	PUNCT
iajs-2379	114	80	49.a	49.a	NUM
iajs-2379	114	81	)	)	PUNCT
iajs-2379	114	82	(	(	PUNCT
iajs-2379	114	83	̅	̅	X
iajs-2379	114	84	(	(	PUNCT
iajs-2379	114	85	)	)	PUNCT
iajs-2379	114	86	)	)	PUNCT
iajs-2379	114	87	(	(	PUNCT
iajs-2379	114	88	)	)	PUNCT
iajs-2379	114	89	(	(	PUNCT
iajs-2379	114	90	49.b	49.b	NUM
iajs-2379	114	91	)	)	PUNCT
iajs-2379	114	92	〈	〈	NOUN
iajs-2379	114	93	̅	̅	NOUN
iajs-2379	114	94	〉	〉	NOUN
iajs-2379	114	95	(	(	PUNCT
iajs-2379	114	96	̅	̅	NOUN
iajs-2379	114	97	)	)	PUNCT
iajs-2379	114	98	(	(	PUNCT
iajs-2379	114	99	̅	̅	NOUN
iajs-2379	114	100	)	)	PUNCT
iajs-2379	114	101	(	(	PUNCT
iajs-2379	114	102	̅	̅	NOUN
iajs-2379	114	103	)	)	PUNCT
iajs-2379	114	104	(	(	PUNCT
iajs-2379	114	105	̅	̅	NOUN
iajs-2379	114	106	)	)	PUNCT
iajs-2379	114	107	(	(	PUNCT
iajs-2379	114	108	̅	̅	NOUN
iajs-2379	114	109	)	)	PUNCT
iajs-2379	114	110	(	(	PUNCT
iajs-2379	114	111	50.a	50.a	NUM
iajs-2379	114	112	)	)	PUNCT
iajs-2379	114	113	(	(	PUNCT
iajs-2379	114	114	̅	̅	X
iajs-2379	114	115	(	(	PUNCT
iajs-2379	114	116	)	)	PUNCT
iajs-2379	114	117	)	)	PUNCT
iajs-2379	114	118	(	(	PUNCT
iajs-2379	114	119	)	)	PUNCT
iajs-2379	114	120	(	(	PUNCT
iajs-2379	114	121	50.b	50.b	ADJ
iajs-2379	114	122	)	)	PUNCT
iajs-2379	114	123	〈	〈	NOUN
iajs-2379	114	124	̅	̅	NOUN
iajs-2379	114	125	〉	〉	NOUN
iajs-2379	114	126	(	(	PUNCT
iajs-2379	114	127	̅	̅	NOUN
iajs-2379	114	128	)	)	PUNCT
iajs-2379	114	129	(	(	PUNCT
iajs-2379	114	130	̅	̅	NOUN
iajs-2379	114	131	)	)	PUNCT
iajs-2379	114	132	(	(	PUNCT
iajs-2379	114	133	̅	̅	NOUN
iajs-2379	114	134	)	)	PUNCT
iajs-2379	114	135	(	(	PUNCT
iajs-2379	114	136	̅	̅	NOUN
iajs-2379	114	137	)	)	PUNCT
iajs-2379	114	138	(	(	PUNCT
iajs-2379	114	139	̅	̅	NOUN
iajs-2379	114	140	)	)	PUNCT
iajs-2379	114	141	(	(	PUNCT
iajs-2379	114	142	51.a	51.a	NUM
iajs-2379	114	143	)	)	PUNCT
iajs-2379	114	144	(	(	PUNCT
iajs-2379	114	145	̅	̅	X
iajs-2379	114	146	(	(	PUNCT
iajs-2379	114	147	)	)	PUNCT
iajs-2379	114	148	)	)	PUNCT
iajs-2379	114	149	(	(	PUNCT
iajs-2379	114	150	)	)	PUNCT
iajs-2379	114	151	(	(	PUNCT
iajs-2379	114	152	51.b	51.b	NUM
iajs-2379	114	153	)	)	PUNCT
iajs-2379	114	154	subtracting	subtracting	NOUN
iajs-2379	114	155	(	(	PUNCT
iajs-2379	114	156	11.a&b	11.a&b	NUM
iajs-2379	114	157	)	)	PUNCT
iajs-2379	114	158	from	from	ADP
iajs-2379	114	159	(	(	PUNCT
iajs-2379	114	160	49.a&b	49.a&b	NOUN
iajs-2379	114	161	)	)	PUNCT
iajs-2379	114	162	,	,	PUNCT
iajs-2379	114	163	(	(	PUNCT
iajs-2379	114	164	12.a&b	12.a&b	NOUN
iajs-2379	114	165	)	)	PUNCT
iajs-2379	114	166	from	from	ADP
iajs-2379	114	167	(	(	PUNCT
iajs-2379	114	168	50.a&b	50.a&b	NUM
iajs-2379	114	169	)	)	PUNCT
iajs-2379	114	170	,	,	PUNCT
iajs-2379	114	171	and	and	CCONJ
iajs-2379	114	172	(	(	PUNCT
iajs-2379	114	173	13.a&b	13.a&b	NUM
iajs-2379	114	174	)	)	PUNCT
iajs-2379	114	175	from	from	ADP
iajs-2379	114	176	(	(	PUNCT
iajs-2379	114	177	51.a&b	51.a&b	NOUN
iajs-2379	114	178	)	)	PUNCT
iajs-2379	114	179	and	and	CCONJ
iajs-2379	114	180	setting	set	VERB
iajs-2379	114	181	̅	̅	NOUN
iajs-2379	114	182	̅	̅	NOUN
iajs-2379	114	183	,	,	PUNCT
iajs-2379	114	184	̅	̅	NOUN
iajs-2379	114	185	,	,	PUNCT
iajs-2379	114	186	̅	̅	NOUN
iajs-2379	114	187	̅	̅	NOUN
iajs-2379	114	188	and	and	CCONJ
iajs-2379	114	189	̅	̅	NOUN
iajs-2379	114	190	in	in	ADP
iajs-2379	114	191	the	the	DET
iajs-2379	114	192	obtained	obtain	VERB
iajs-2379	114	193	equations	equation	NOUN
iajs-2379	114	194	,	,	PUNCT
iajs-2379	114	195	they	they	PRON
iajs-2379	114	196	give	give	VERB
iajs-2379	114	197	〈	〈	PROPN
iajs-2379	114	198	〉	〉	NOUN
iajs-2379	114	199	(	(	PUNCT
iajs-2379	114	200	)	)	PUNCT
iajs-2379	114	201	(	(	PUNCT
iajs-2379	114	202	)	)	PUNCT
iajs-2379	114	203	(	(	PUNCT
iajs-2379	114	204	)	)	PUNCT
iajs-2379	114	205	(	(	PUNCT
iajs-2379	114	206	)	)	PUNCT
iajs-2379	114	207	(	(	PUNCT
iajs-2379	114	208	)	)	PUNCT
iajs-2379	114	209	(	(	PUNCT
iajs-2379	114	210	52.a	52.a	NUM
iajs-2379	114	211	)	)	PUNCT
iajs-2379	114	212	(	(	PUNCT
iajs-2379	114	213	(	(	PUNCT
iajs-2379	114	214	)	)	PUNCT
iajs-2379	114	215	)	)	PUNCT
iajs-2379	115	1	(	(	PUNCT
iajs-2379	115	2	52.b	52.b	X
iajs-2379	115	3	)	)	PUNCT
iajs-2379	115	4	〈	〈	NOUN
iajs-2379	115	5	〉	〉	NOUN
iajs-2379	115	6	(	(	PUNCT
iajs-2379	115	7	)	)	PUNCT
iajs-2379	115	8	(	(	PUNCT
iajs-2379	115	9	)	)	PUNCT
iajs-2379	115	10	(	(	PUNCT
iajs-2379	115	11	)	)	PUNCT
iajs-2379	115	12	(	(	PUNCT
iajs-2379	115	13	)	)	PUNCT
iajs-2379	115	14	(	(	PUNCT
iajs-2379	115	15	)	)	PUNCT
iajs-2379	115	16	(	(	PUNCT
iajs-2379	115	17	53.a	53.a	NUM
iajs-2379	115	18	)	)	PUNCT
iajs-2379	115	19	(	(	PUNCT
iajs-2379	115	20	(	(	PUNCT
iajs-2379	115	21	)	)	PUNCT
iajs-2379	115	22	)	)	PUNCT
iajs-2379	115	23	(	(	PUNCT
iajs-2379	115	24	53.b	53.b	NUM
iajs-2379	115	25	)	)	PUNCT
iajs-2379	115	26	〈	〈	NOUN
iajs-2379	115	27	〉	〉	NOUN
iajs-2379	115	28	(	(	PUNCT
iajs-2379	115	29	)	)	PUNCT
iajs-2379	115	30	(	(	PUNCT
iajs-2379	115	31	)	)	PUNCT
iajs-2379	115	32	(	(	PUNCT
iajs-2379	115	33	)	)	PUNCT
iajs-2379	115	34	(	(	PUNCT
iajs-2379	115	35	)	)	PUNCT
iajs-2379	115	36	(	(	PUNCT
iajs-2379	115	37	)	)	PUNCT
iajs-2379	115	38	(	(	PUNCT
iajs-2379	115	39	54.a	54.a	NUM
iajs-2379	115	40	)	)	PUNCT
iajs-2379	115	41	(	(	PUNCT
iajs-2379	115	42	(	(	PUNCT
iajs-2379	115	43	)	)	PUNCT
iajs-2379	115	44	)	)	PUNCT
iajs-2379	115	45	(	(	PUNCT
iajs-2379	115	46	54.b	54.b	X
iajs-2379	115	47	)	)	PUNCT
iajs-2379	115	48	substituting	substituting	NOUN
iajs-2379	115	49	,	,	PUNCT
iajs-2379	115	50	&	&	CCONJ
iajs-2379	115	51	in	in	ADP
iajs-2379	115	52	(	(	PUNCT
iajs-2379	115	53	52.a&b	52.a&b	NOUN
iajs-2379	115	54	)	)	PUNCT
iajs-2379	115	55	,	,	PUNCT
iajs-2379	115	56	(	(	PUNCT
iajs-2379	115	57	53.a&b	53.a&b	NOUN
iajs-2379	115	58	)	)	PUNCT
iajs-2379	115	59	and	and	CCONJ
iajs-2379	115	60	(	(	PUNCT
iajs-2379	115	61	54.a&b	54.a&b	NOUN
iajs-2379	115	62	)	)	PUNCT
iajs-2379	115	63	respectively	respectively	ADV
iajs-2379	115	64	,	,	PUNCT
iajs-2379	115	65	adding	add	VERB
iajs-2379	115	66	the	the	DET
iajs-2379	115	67	obtained	obtain	VERB
iajs-2379	115	68	equations	equation	NOUN
iajs-2379	115	69	,	,	PUNCT
iajs-2379	115	70	using	use	VERB
iajs-2379	115	71	lemma	lemma	PROPN
iajs-2379	115	72	(	(	PUNCT
iajs-2379	115	73	1.2	1.2	NUM
iajs-2379	115	74	)	)	PUNCT
iajs-2379	115	75	in	in	ADP
iajs-2379	115	76	[	[	X
iajs-2379	115	77	11	11	NUM
iajs-2379	115	78	]	]	PUNCT
iajs-2379	115	79	.	.	PUNCT
iajs-2379	116	1	they	they	PRON
iajs-2379	116	2	give	give	VERB
iajs-2379	116	3	‖	‖	PROPN
iajs-2379	116	4	‖	‖	PROPN
iajs-2379	116	5	‖	‖	PROPN
iajs-2379	116	6	‖	‖	PROPN
iajs-2379	116	7	(	(	PUNCT
iajs-2379	116	8	)	)	PUNCT
iajs-2379	116	9	(	(	PUNCT
iajs-2379	116	10	)	)	PUNCT
iajs-2379	116	11	(	(	PUNCT
iajs-2379	116	12	)	)	PUNCT
iajs-2379	116	13	(	(	PUNCT
iajs-2379	116	14	55	55	NUM
iajs-2379	116	15	)	)	PUNCT
iajs-2379	116	16	since	since	SCONJ
iajs-2379	116	17	the	the	DET
iajs-2379	116	18	term	term	NOUN
iajs-2379	116	19	of	of	ADP
iajs-2379	116	20	(	(	PUNCT
iajs-2379	116	21	55	55	NUM
iajs-2379	116	22	)	)	PUNCT
iajs-2379	116	23	is	be	AUX
iajs-2379	116	24	positive	positive	ADJ
iajs-2379	116	25	,	,	PUNCT
iajs-2379	116	26	integrating	integrate	VERB
iajs-2379	116	27	w.r.t	w.r.t	NOUN
iajs-2379	116	28	.	.	PUNCT
iajs-2379	117	1	from	from	ADP
iajs-2379	117	2	to	to	ADP
iajs-2379	117	3	,	,	PUNCT
iajs-2379	117	4	and	and	CCONJ
iajs-2379	117	5	then	then	ADV
iajs-2379	117	6	using	use	VERB
iajs-2379	117	7	the	the	DET
iajs-2379	117	8	cauchy	cauchy	ADJ
iajs-2379	117	9	schwartz	schwartz	PROPN
iajs-2379	117	10	inequality	inequality	PROPN
iajs-2379	117	11	(	(	PUNCT
iajs-2379	117	12	csi	csi	PROPN
iajs-2379	117	13	)	)	PUNCT
iajs-2379	117	14	,	,	PUNCT
iajs-2379	117	15	it	it	PRON
iajs-2379	117	16	becomes	become	VERB
iajs-2379	117	17	∫	∫	PROPN
iajs-2379	117	18	‖	‖	PROPN
iajs-2379	117	19	‖	‖	PROPN
iajs-2379	117	20	dt	dt	PROPN
iajs-2379	117	21	2	2	NUM
iajs-2379	117	22	∫	∫	NOUN
iajs-2379	117	23	∫	∫	PROPN
iajs-2379	118	1	|	|	ADV
iajs-2379	118	2	||	||	NOUN
iajs-2379	119	1	|	|	ADV
iajs-2379	120	1	2∫	2∫	NUM
iajs-2379	120	2	∫	∫	NOUN
iajs-2379	121	1	|	|	ADV
iajs-2379	121	2	||	||	PUNCT
iajs-2379	122	1	|	|	ADV
iajs-2379	122	2	∫	∫	PROPN
iajs-2379	123	1	∫	∫	PROPN
iajs-2379	124	1	|	|	ADV
iajs-2379	124	2	||	||	PUNCT
iajs-2379	125	1	|	|	ADV
iajs-2379	125	2	∫	∫	PROPN
iajs-2379	125	3	‖	‖	PROPN
iajs-2379	126	1	⃗	⃗	PROPN
iajs-2379	126	2	‖	‖	PROPN
iajs-2379	126	3	∫	∫	PROPN
iajs-2379	126	4	‖	‖	PROPN
iajs-2379	126	5	‖	‖	PROPN
iajs-2379	126	6	,	,	PUNCT
iajs-2379	126	7	,	,	PUNCT
iajs-2379	126	8	-	-	PUNCT
iajs-2379	126	9	,	,	PUNCT
iajs-2379	126	10	by	by	ADP
iajs-2379	126	11	the	the	DET
iajs-2379	126	12	bgi	bgi	PROPN
iajs-2379	126	13	,	,	PUNCT
iajs-2379	126	14	once	once	ADV
iajs-2379	126	15	get	get	VERB
iajs-2379	126	16	‖	‖	ADJ
iajs-2379	126	17	(	(	PUNCT
iajs-2379	126	18	)	)	PUNCT
iajs-2379	126	19	‖	‖	PROPN
iajs-2379	126	20	‖	‖	PROPN
iajs-2379	126	21	⃗	⃗	PROPN
iajs-2379	126	22	‖	‖	PROPN
iajs-2379	126	23	‖	‖	PROPN
iajs-2379	126	24	(	(	PUNCT
iajs-2379	126	25	)	)	PUNCT
iajs-2379	126	26	‖	‖	PROPN
iajs-2379	126	27	‖	‖	PROPN
iajs-2379	126	28	⃗	⃗	PROPN
iajs-2379	126	29	‖	‖	PROPN
iajs-2379	126	30	,	,	PUNCT
iajs-2379	126	31	where	where	SCONJ
iajs-2379	126	32	,	,	PUNCT
iajs-2379	126	33	‖	‖	PROPN
iajs-2379	126	34	‖	‖	PROPN
iajs-2379	126	35	.	.	PUNCT
iajs-2379	127	1	(	(	PUNCT
iajs-2379	127	2	)	)	PUNCT
iajs-2379	127	3	/	/	SYM
iajs-2379	127	4	‖	‖	PROPN
iajs-2379	127	5	⃗	⃗	PROPN
iajs-2379	127	6	‖	‖	PROPN
iajs-2379	127	7	since	since	SCONJ
iajs-2379	127	8	‖	‖	ADJ
iajs-2379	127	9	‖	‖	PROPN
iajs-2379	127	10	(	(	PUNCT
iajs-2379	127	11	)	)	PUNCT
iajs-2379	127	12	‖	‖	PROPN
iajs-2379	128	1	⃗	⃗	PROPN
iajs-2379	128	2	‖	‖	PROPN
iajs-2379	128	3	,	,	PUNCT
iajs-2379	128	4	then	then	ADV
iajs-2379	128	5	‖	‖	PROPN
iajs-2379	128	6	‖	‖	PROPN
iajs-2379	128	7	(	(	PUNCT
iajs-2379	128	8	)	)	PUNCT
iajs-2379	128	9	‖	‖	PROPN
iajs-2379	129	1	⃗	⃗	PROPN
iajs-2379	129	2	‖	‖	ADJ
iajs-2379	129	3	,	,	PUNCT
iajs-2379	129	4	̅	̅	NOUN
iajs-2379	129	5	using	use	VERB
iajs-2379	129	6	a	a	DET
iajs-2379	129	7	similar	similar	ADJ
iajs-2379	129	8	way	way	NOUN
iajs-2379	129	9	which	which	PRON
iajs-2379	129	10	is	be	AUX
iajs-2379	129	11	used	use	VERB
iajs-2379	129	12	in	in	ADP
iajs-2379	129	13	above	above	ADP
iajs-2379	129	14	steps	step	NOUN
iajs-2379	129	15	,	,	PUNCT
iajs-2379	129	16	gives	give	VERB
iajs-2379	129	17	∫	∫	PROPN
iajs-2379	130	1	‖	‖	PROPN
iajs-2379	130	2	‖	‖	PROPN
iajs-2379	130	3	∫	∫	PROPN
iajs-2379	130	4	‖	‖	PROPN
iajs-2379	130	5	‖	‖	PROPN
iajs-2379	130	6	‖	‖	PROPN
iajs-2379	130	7	⃗	⃗	PROPN
iajs-2379	130	8	‖	‖	PROPN
iajs-2379	130	9	∫	∫	PROPN
iajs-2379	130	10	‖	‖	PROPN
iajs-2379	130	11	‖	‖	PROPN
iajs-2379	130	12	̅	̅	PROPN
iajs-2379	130	13	‖	‖	ADJ
iajs-2379	130	14	⃗	⃗	PROPN
iajs-2379	130	15	‖	‖	PROPN
iajs-2379	130	16	137	137	NUM
iajs-2379	130	17	ibn	ibn	PROPN
iajs-2379	130	18	al	al	PROPN
iajs-2379	130	19	-	-	PUNCT
iajs-2379	130	20	haitham	haitham	PROPN
iajs-2379	130	21	jour	jour	X
iajs-2379	130	22	.	.	PROPN
iajs-2379	131	1	for	for	ADP
iajs-2379	131	2	pure	pure	ADJ
iajs-2379	131	3	&	&	CCONJ
iajs-2379	131	4	appl	appl	PROPN
iajs-2379	131	5	.	.	PUNCT
iajs-2379	132	1	sci	sci	PROPN
iajs-2379	132	2	.	.	PROPN
iajs-2379	133	1	33	33	NUM
iajs-2379	133	2	(	(	PUNCT
iajs-2379	133	3	1	1	NUM
iajs-2379	133	4	)	)	PUNCT
iajs-2379	133	5	2020	2020	NUM
iajs-2379	133	6	‖	‖	PROPN
iajs-2379	133	7	‖	‖	PROPN
iajs-2379	133	8	(	(	PUNCT
iajs-2379	133	9	)	)	PUNCT
iajs-2379	133	10	̅	̅	NOUN
iajs-2379	133	11	‖	‖	PROPN
iajs-2379	133	12	⃗	⃗	PROPN
iajs-2379	133	13	‖	‖	PROPN
iajs-2379	133	14	where	where	SCONJ
iajs-2379	133	15	̅	̅	NOUN
iajs-2379	133	16	(	(	PUNCT
iajs-2379	133	17	̅	̅	NOUN
iajs-2379	133	18	)	)	PUNCT
iajs-2379	133	19	‖	‖	PROPN
iajs-2379	133	20	‖	‖	PROPN
iajs-2379	133	21	(	(	PUNCT
iajs-2379	133	22	)	)	PUNCT
iajs-2379	133	23	‖	‖	PROPN
iajs-2379	134	1	⃗	⃗	PROPN
iajs-2379	134	2	‖	‖	PROPN
iajs-2379	134	3	.	.	PUNCT
iajs-2379	134	4	theorem	theorem	VERB
iajs-2379	134	5	4.2	4.2	NUM
iajs-2379	134	6	:	:	PUNCT
iajs-2379	134	7	with	with	ADP
iajs-2379	134	8	assumptions	assumption	NOUN
iajs-2379	134	9	(	(	PUNCT
iajs-2379	134	10	a	a	X
iajs-2379	134	11	)	)	PUNCT
iajs-2379	134	12	,	,	PUNCT
iajs-2379	134	13	the	the	DET
iajs-2379	134	14	operator	operator	NOUN
iajs-2379	134	15	⃗	⃗	PROPN
iajs-2379	134	16	⃗⃗	⃗⃗	NOUN
iajs-2379	134	17	is	be	AUX
iajs-2379	134	18	continuous	continuous	ADJ
iajs-2379	134	19	from	from	ADP
iajs-2379	134	20	(	(	PUNCT
iajs-2379	134	21	(	(	PUNCT
iajs-2379	134	22	)	)	PUNCT
iajs-2379	134	23	)	)	PUNCT
iajs-2379	135	1	in	in	ADP
iajs-2379	135	2	to	to	ADP
iajs-2379	135	3	(	(	PUNCT
iajs-2379	135	4	(	(	PUNCT
iajs-2379	135	5	(	(	PUNCT
iajs-2379	135	6	)	)	PUNCT
iajs-2379	135	7	)	)	PUNCT
iajs-2379	135	8	)	)	PUNCT
iajs-2379	135	9	or	or	CCONJ
iajs-2379	135	10	in	in	ADP
iajs-2379	135	11	to	to	ADP
iajs-2379	135	12	(	(	PUNCT
iajs-2379	135	13	(	(	PUNCT
iajs-2379	135	14	)	)	PUNCT
iajs-2379	135	15	)	)	PUNCT
iajs-2379	135	16	or	or	CCONJ
iajs-2379	135	17	in	in	ADP
iajs-2379	135	18	to	to	ADP
iajs-2379	135	19	(	(	PUNCT
iajs-2379	135	20	(	(	PUNCT
iajs-2379	135	21	)	)	PUNCT
iajs-2379	135	22	)	)	PUNCT
iajs-2379	135	23	.	.	PUNCT
iajs-2379	136	1	proof	proof	NOUN
iajs-2379	136	2	:	:	PUNCT
iajs-2379	136	3	let	let	VERB
iajs-2379	136	4	⃗	⃗	PROPN
iajs-2379	136	5	⃗̅	⃗̅	VERB
iajs-2379	136	6	⃗	⃗	PROPN
iajs-2379	136	7	and	and	CCONJ
iajs-2379	136	8	̅	̅	NOUN
iajs-2379	136	9	,	,	PUNCT
iajs-2379	136	10	where	where	SCONJ
iajs-2379	136	11	̅	̅	NOUN
iajs-2379	136	12	are	be	AUX
iajs-2379	136	13	the	the	DET
iajs-2379	136	14	correspond	correspond	NOUN
iajs-2379	136	15	svs	sv	VERB
iajs-2379	136	16	to	to	ADP
iajs-2379	136	17	the	the	DET
iajs-2379	136	18	cvs	cvs	NOUN
iajs-2379	136	19	⃗̅	⃗̅	NOUN
iajs-2379	136	20	and	and	CCONJ
iajs-2379	136	21	⃗	⃗	PROPN
iajs-2379	136	22	using	use	VERB
iajs-2379	136	23	the	the	DET
iajs-2379	136	24	first	first	ADJ
iajs-2379	136	25	result	result	NOUN
iajs-2379	136	26	in	in	ADP
iajs-2379	136	27	theorem	theorem	NOUN
iajs-2379	136	28	4.1	4.1	NUM
iajs-2379	136	29	,	,	PUNCT
iajs-2379	136	30	one	one	PRON
iajs-2379	136	31	has	have	VERB
iajs-2379	136	32	‖	‖	ADJ
iajs-2379	136	33	̅	̅	NOUN
iajs-2379	136	34	‖	‖	ADJ
iajs-2379	136	35	.	.	PUNCT
iajs-2379	137	1	(	(	PUNCT
iajs-2379	137	2	)	)	PUNCT
iajs-2379	137	3	/	/	SYM
iajs-2379	137	4	‖	‖	PROPN
iajs-2379	137	5	⃗̅	⃗̅	PROPN
iajs-2379	137	6	⃗	⃗	PROPN
iajs-2379	137	7	‖	‖	PROPN
iajs-2379	137	8	,	,	PUNCT
iajs-2379	137	9	if	if	SCONJ
iajs-2379	137	10	⃗̅	⃗̅	PROPN
iajs-2379	137	11	(	(	PUNCT
iajs-2379	137	12	)	)	PUNCT
iajs-2379	137	13	→	→	SYM
iajs-2379	137	14	⃗	⃗	PROPN
iajs-2379	137	15	then	then	ADV
iajs-2379	137	16	̅	̅	VERB
iajs-2379	137	17	.	.	PUNCT
iajs-2379	138	1	(	(	PUNCT
iajs-2379	138	2	)	)	PUNCT
iajs-2379	138	3	/	/	SYM
iajs-2379	138	4	→	→	ADP
iajs-2379	138	5	i.e.	i.e.	X
iajs-2379	138	6	the	the	DET
iajs-2379	138	7	operator	operator	NOUN
iajs-2379	138	8	⃗	⃗	PROPN
iajs-2379	138	9	⃗⃗	⃗⃗	NOUN
iajs-2379	138	10	is	be	AUX
iajs-2379	138	11	lipschitz	lipschitz	VERB
iajs-2379	138	12	continuous	continuous	ADJ
iajs-2379	138	13	(	(	PUNCT
iajs-2379	138	14	lc	lc	NOUN
iajs-2379	138	15	)	)	PUNCT
iajs-2379	138	16	from	from	ADP
iajs-2379	138	17	(	(	PUNCT
iajs-2379	138	18	(	(	PUNCT
iajs-2379	138	19	)	)	PUNCT
iajs-2379	138	20	)	)	PUNCT
iajs-2379	138	21	in	in	ADP
iajs-2379	138	22	to	to	ADP
iajs-2379	138	23	(	(	PUNCT
iajs-2379	138	24	(	(	PUNCT
iajs-2379	138	25	(	(	PUNCT
iajs-2379	138	26	)	)	PUNCT
iajs-2379	138	27	)	)	PUNCT
iajs-2379	138	28	)	)	PUNCT
iajs-2379	139	1	by	by	ADP
iajs-2379	139	2	a	a	DET
iajs-2379	139	3	similar	similar	ADJ
iajs-2379	139	4	way	way	NOUN
iajs-2379	139	5	this	this	DET
iajs-2379	139	6	operator	operator	NOUN
iajs-2379	139	7	is	be	AUX
iajs-2379	139	8	also	also	ADV
iajs-2379	139	9	lc	lc	NOUN
iajs-2379	139	10	from	from	ADP
iajs-2379	139	11	(	(	PUNCT
iajs-2379	139	12	(	(	PUNCT
iajs-2379	139	13	)	)	PUNCT
iajs-2379	139	14	)	)	PUNCT
iajs-2379	139	15	into	into	ADP
iajs-2379	139	16	(	(	PUNCT
iajs-2379	139	17	(	(	PUNCT
iajs-2379	139	18	)	)	PUNCT
iajs-2379	139	19	)	)	PUNCT
iajs-2379	139	20	and	and	CCONJ
iajs-2379	139	21	into	into	ADP
iajs-2379	139	22	(	(	PUNCT
iajs-2379	139	23	(	(	PUNCT
iajs-2379	139	24	)	)	PUNCT
iajs-2379	139	25	)	)	PUNCT
iajs-2379	139	26	.	.	PUNCT
iajs-2379	140	1	lemma	lemma	PROPN
iajs-2379	140	2	4.1	4.1	NUM
iajs-2379	141	1	[	[	X
iajs-2379	141	2	10	10	NUM
iajs-2379	141	3	]	]	PUNCT
iajs-2379	141	4	:	:	PUNCT
iajs-2379	141	5	the	the	DET
iajs-2379	141	6	norm	norm	NOUN
iajs-2379	141	7	is	be	AUX
iajs-2379	141	8	weakly	weakly	ADV
iajs-2379	141	9	lower	low	ADJ
iajs-2379	141	10	semi	semi	ADV
iajs-2379	141	11	continuous	continuous	ADJ
iajs-2379	141	12	(	(	PUNCT
iajs-2379	141	13	w.l.s.c	w.l.s.c	PROPN
iajs-2379	141	14	.	.	PUNCT
iajs-2379	141	15	)	)	PUNCT
iajs-2379	141	16	.	.	PUNCT
iajs-2379	142	1	lemma	lemma	PROPN
iajs-2379	142	2	(	(	PUNCT
iajs-2379	142	3	4.2	4.2	NUM
iajs-2379	142	4	)	)	PUNCT
iajs-2379	142	5	:	:	PUNCT
iajs-2379	142	6	the	the	DET
iajs-2379	142	7	cost	cost	NOUN
iajs-2379	142	8	function	function	NOUN
iajs-2379	142	9	which	which	PRON
iajs-2379	142	10	is	be	AUX
iajs-2379	142	11	given	give	VERB
iajs-2379	142	12	by	by	ADP
iajs-2379	142	13	(	(	PUNCT
iajs-2379	142	14	)	)	PUNCT
iajs-2379	142	15	is	be	AUX
iajs-2379	142	16	w.l.s.c	w.l.s.c	PROPN
iajs-2379	142	17	.	.	PUNCT
iajs-2379	143	1	proof	proof	NOUN
iajs-2379	143	2	:	:	PUNCT
iajs-2379	143	3	from	from	ADP
iajs-2379	143	4	lemma	lemma	PROPN
iajs-2379	143	5	(	(	PUNCT
iajs-2379	143	6	3.1	3.1	NUM
iajs-2379	143	7	)	)	PUNCT
iajs-2379	143	8	‖	‖	PROPN
iajs-2379	144	1	⃗	⃗	PROPN
iajs-2379	144	2	‖	‖	PROPN
iajs-2379	144	3	(	(	PUNCT
iajs-2379	144	4	)	)	PUNCT
iajs-2379	144	5	,	,	PUNCT
iajs-2379	144	6	is	be	AUX
iajs-2379	144	7	w.l.s.c	w.l.s.c	PROPN
iajs-2379	144	8	.	.	PUNCT
iajs-2379	145	1	when	when	SCONJ
iajs-2379	145	2	⃗	⃗	PROPN
iajs-2379	145	3	⃗	⃗	PROPN
iajs-2379	145	4	weakly	weakly	ADV
iajs-2379	145	5	in	in	ADP
iajs-2379	145	6	(	(	PUNCT
iajs-2379	145	7	(	(	PUNCT
iajs-2379	145	8	)	)	PUNCT
iajs-2379	145	9	)	)	PUNCT
iajs-2379	145	10	then	then	ADV
iajs-2379	145	11	weakly	weakly	ADV
iajs-2379	145	12	in	in	ADP
iajs-2379	145	13	(	(	PUNCT
iajs-2379	145	14	(	(	PUNCT
iajs-2379	145	15	)	)	PUNCT
iajs-2379	145	16	)	)	PUNCT
iajs-2379	145	17	by	by	ADP
iajs-2379	145	18	theorem	theorem	VERB
iajs-2379	145	19	4.1	4.1	NUM
iajs-2379	145	20	then	then	ADV
iajs-2379	145	21	‖	‖	PROPN
iajs-2379	145	22	⃗⃗	⃗⃗	PROPN
iajs-2379	145	23	⃗⃗	⃗⃗	PROPN
iajs-2379	145	24	‖	‖	PROPN
iajs-2379	145	25	‖	‖	PROPN
iajs-2379	145	26	⃗⃗	⃗⃗	PROPN
iajs-2379	145	27	⃗⃗	⃗⃗	PROPN
iajs-2379	145	28	‖	‖	PROPN
iajs-2379	145	29	then	then	ADV
iajs-2379	145	30	‖	‖	ADJ
iajs-2379	145	31	⃗	⃗	PROPN
iajs-2379	145	32	⃗	⃗	PROPN
iajs-2379	145	33	‖	‖	PROPN
iajs-2379	145	34	is	be	AUX
iajs-2379	145	35	w.l.s.c	w.l.s.c	PROPN
iajs-2379	145	36	.	.	PROPN
iajs-2379	145	37	,	,	PUNCT
iajs-2379	145	38	hence	hence	ADV
iajs-2379	145	39	(	(	PUNCT
iajs-2379	145	40	⃗	⃗	PROPN
iajs-2379	145	41	)	)	PUNCT
iajs-2379	145	42	is	be	AUX
iajs-2379	145	43	w.l.s.c	w.l.s.c	PROPN
iajs-2379	145	44	.	.	PUNCT
iajs-2379	146	1	lemma	lemma	PROPN
iajs-2379	146	2	4.3	4.3	NUM
iajs-2379	147	1	[	[	X
iajs-2379	147	2	13	13	NUM
iajs-2379	147	3	]	]	PUNCT
iajs-2379	147	4	:	:	PUNCT
iajs-2379	147	5	the	the	DET
iajs-2379	147	6	norm	norm	NOUN
iajs-2379	147	7	‖	‖	PROPN
iajs-2379	147	8	‖	‖	PROPN
iajs-2379	147	9	is	be	AUX
iajs-2379	147	10	strictly	strictly	ADV
iajs-2379	147	11	convex	convex	ADJ
iajs-2379	147	12	.	.	PUNCT
iajs-2379	148	1	theorem	theorem	VERB
iajs-2379	148	2	4.3	4.3	NUM
iajs-2379	148	3	:	:	PUNCT
iajs-2379	148	4	consider	consider	VERB
iajs-2379	148	5	the	the	DET
iajs-2379	148	6	cost	cost	NOUN
iajs-2379	148	7	function	function	NOUN
iajs-2379	148	8	(	(	PUNCT
iajs-2379	148	9	)	)	PUNCT
iajs-2379	148	10	,	,	PUNCT
iajs-2379	148	11	if	if	SCONJ
iajs-2379	148	12	(	(	PUNCT
iajs-2379	148	13	⃗	⃗	PROPN
iajs-2379	148	14	)	)	PUNCT
iajs-2379	148	15	is	be	AUX
iajs-2379	148	16	coercive	coercive	ADJ
iajs-2379	148	17	,	,	PUNCT
iajs-2379	148	18	then	then	ADV
iajs-2379	148	19	there	there	PRON
iajs-2379	148	20	exists	exist	VERB
iajs-2379	148	21	ccoc	ccoc	NOUN
iajs-2379	148	22	.	.	PUNCT
iajs-2379	149	1	proof	proof	NOUN
iajs-2379	149	2	:	:	PUNCT
iajs-2379	149	3	since	since	SCONJ
iajs-2379	149	4	(	(	PUNCT
iajs-2379	149	5	⃗	⃗	PROPN
iajs-2379	149	6	)	)	PUNCT
iajs-2379	149	7	and	and	CCONJ
iajs-2379	149	8	(	(	PUNCT
iajs-2379	149	9	⃗	⃗	PROPN
iajs-2379	149	10	)	)	PUNCT
iajs-2379	149	11	is	be	AUX
iajs-2379	149	12	coercive	coercive	ADJ
iajs-2379	149	13	,	,	PUNCT
iajs-2379	149	14	then	then	ADV
iajs-2379	149	15	there	there	PRON
iajs-2379	149	16	exists	exist	VERB
iajs-2379	149	17	a	a	DET
iajs-2379	149	18	minimizing	minimize	VERB
iajs-2379	149	19	sequence	sequence	NOUN
iajs-2379	149	20	*	*	PUNCT
iajs-2379	150	1	⃗	⃗	PROPN
iajs-2379	150	2	+	+	PUNCT
iajs-2379	150	3	*	*	PUNCT
iajs-2379	150	4	(	(	PUNCT
iajs-2379	150	5	)	)	PUNCT
iajs-2379	150	6	+	+	NUM
iajs-2379	150	7	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	150	8	,	,	PUNCT
iajs-2379	150	9	such	such	ADJ
iajs-2379	150	10	that	that	SCONJ
iajs-2379	150	11	(	(	PUNCT
iajs-2379	150	12	⃗	⃗	PROPN
iajs-2379	150	13	)	)	PUNCT
iajs-2379	150	14	⃗⃗̅	⃗⃗̅	NOUN
iajs-2379	150	15	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	150	16	(	(	PUNCT
iajs-2379	150	17	⃗̅	⃗̅	PROPN
iajs-2379	150	18	)	)	PUNCT
iajs-2379	150	19	,	,	PUNCT
iajs-2379	150	20	and	and	CCONJ
iajs-2379	150	21	‖	‖	PROPN
iajs-2379	150	22	⃗	⃗	PROPN
iajs-2379	150	23	‖	‖	PROPN
iajs-2379	150	24	,	,	PUNCT
iajs-2379	150	25	then	then	ADV
iajs-2379	150	26	by	by	ADP
iajs-2379	150	27	at	at	ADP
iajs-2379	150	28	there	there	ADV
iajs-2379	150	29	exists	exist	VERB
iajs-2379	150	30	a	a	DET
iajs-2379	150	31	subsequence	subsequence	NOUN
iajs-2379	150	32	of	of	ADP
iajs-2379	150	33	*	*	PUNCT
iajs-2379	150	34	⃗	⃗	PROPN
iajs-2379	150	35	+	+	CCONJ
iajs-2379	150	36	,	,	PUNCT
iajs-2379	150	37	for	for	ADP
iajs-2379	150	38	simplicity	simplicity	NOUN
iajs-2379	150	39	say	say	VERB
iajs-2379	150	40	again	again	ADV
iajs-2379	150	41	*	*	PUNCT
iajs-2379	151	1	⃗	⃗	PROPN
iajs-2379	151	2	+	+	X
iajs-2379	151	3	s.t	s.t	PROPN
iajs-2379	151	4	.	.	PUNCT
iajs-2379	152	1	⃗	⃗	PROPN
iajs-2379	152	2	⃗	⃗	X
iajs-2379	152	3	weakly	weakly	ADJ
iajs-2379	152	4	in	in	ADP
iajs-2379	152	5	(	(	PUNCT
iajs-2379	152	6	(	(	PUNCT
iajs-2379	152	7	)	)	PUNCT
iajs-2379	152	8	)	)	PUNCT
iajs-2379	152	9	,	,	PUNCT
iajs-2379	152	10	as	as	ADP
iajs-2379	152	11	.	.	PUNCT
iajs-2379	152	12	from	from	ADP
iajs-2379	152	13	theorem	theorem	ADJ
iajs-2379	152	14	3.1	3.1	NUM
iajs-2379	152	15	we	we	PRON
iajs-2379	152	16	got	get	VERB
iajs-2379	152	17	that	that	PRON
iajs-2379	152	18	for	for	ADP
iajs-2379	152	19	each	each	DET
iajs-2379	152	20	control	control	NOUN
iajs-2379	152	21	⃗	⃗	PROPN
iajs-2379	152	22	there	there	PRON
iajs-2379	152	23	exists	exist	VERB
iajs-2379	152	24	a	a	DET
iajs-2379	152	25	unique	unique	ADJ
iajs-2379	152	26	solution	solution	NOUN
iajs-2379	152	27	⃗⃗	⃗⃗	NOUN
iajs-2379	152	28	then	then	ADV
iajs-2379	152	29	corresponding	correspond	VERB
iajs-2379	152	30	to	to	ADP
iajs-2379	152	31	the	the	DET
iajs-2379	152	32	sequence	sequence	NOUN
iajs-2379	152	33	of	of	ADP
iajs-2379	152	34	control	control	NOUN
iajs-2379	152	35	*	*	PUNCT
iajs-2379	153	1	⃗	⃗	PROPN
iajs-2379	153	2	+	+	CCONJ
iajs-2379	153	3	there	there	PRON
iajs-2379	153	4	exists	exist	VERB
iajs-2379	153	5	a	a	DET
iajs-2379	153	6	sequence	sequence	NOUN
iajs-2379	153	7	of	of	ADP
iajs-2379	153	8	solutions	solution	NOUN
iajs-2379	153	9	*	*	PUNCT
iajs-2379	154	1	+	+	PUNCT
iajs-2379	154	2	such	such	ADJ
iajs-2379	154	3	that	that	SCONJ
iajs-2379	154	4	the	the	DET
iajs-2379	154	5	norms	norm	NOUN
iajs-2379	154	6	‖	‖	PROPN
iajs-2379	154	7	‖	‖	PROPN
iajs-2379	154	8	.	.	PUNCT
iajs-2379	155	1	(	(	PUNCT
iajs-2379	155	2	)	)	PUNCT
iajs-2379	155	3	/	/	SYM
iajs-2379	155	4	,	,	PUNCT
iajs-2379	155	5	‖	‖	PROPN
iajs-2379	155	6	‖	‖	PROPN
iajs-2379	155	7	(	(	PUNCT
iajs-2379	155	8	)	)	PUNCT
iajs-2379	155	9	&	&	CCONJ
iajs-2379	155	10	‖	‖	PROPN
iajs-2379	155	11	‖	‖	PROPN
iajs-2379	155	12	(	(	PUNCT
iajs-2379	155	13	)	)	PUNCT
iajs-2379	155	14	are	be	AUX
iajs-2379	155	15	bounded	bound	VERB
iajs-2379	155	16	,	,	PUNCT
iajs-2379	155	17	then	then	ADV
iajs-2379	155	18	by	by	ADP
iajs-2379	155	19	at	at	ADP
iajs-2379	155	20	there	there	ADV
iajs-2379	155	21	exists	exist	VERB
iajs-2379	155	22	a	a	DET
iajs-2379	155	23	subsequence	subsequence	NOUN
iajs-2379	155	24	of	of	ADP
iajs-2379	155	25	*	*	PUNCT
iajs-2379	155	26	+	+	CCONJ
iajs-2379	155	27	,	,	PUNCT
iajs-2379	155	28	for	for	ADP
iajs-2379	155	29	simplicity	simplicity	NOUN
iajs-2379	155	30	say	say	VERB
iajs-2379	155	31	again	again	ADV
iajs-2379	155	32	*	*	PUNCT
iajs-2379	156	1	+	+	CCONJ
iajs-2379	156	2	,	,	PUNCT
iajs-2379	156	3	such	such	ADJ
iajs-2379	156	4	that	that	DET
iajs-2379	156	5	weakly	weakly	ADJ
iajs-2379	156	6	in	in	ADP
iajs-2379	156	7	(	(	PUNCT
iajs-2379	156	8	.	.	PUNCT
iajs-2379	157	1	(	(	PUNCT
iajs-2379	157	2	)	)	PUNCT
iajs-2379	157	3	/	/	SYM
iajs-2379	157	4	)	)	PUNCT
iajs-2379	157	5	,	,	PUNCT
iajs-2379	157	6	weakly	weakly	ADV
iajs-2379	157	7	in	in	ADP
iajs-2379	157	8	(	(	PUNCT
iajs-2379	157	9	(	(	PUNCT
iajs-2379	157	10	)	)	PUNCT
iajs-2379	157	11	)	)	PUNCT
iajs-2379	157	12	,	,	PUNCT
iajs-2379	157	13	and	and	CCONJ
iajs-2379	157	14	weakly	weakly	ADV
iajs-2379	157	15	in	in	ADV
iajs-2379	157	16	.	.	PUNCT
iajs-2379	158	1	(	(	PUNCT
iajs-2379	158	2	)	)	PUNCT
iajs-2379	158	3	/	/	PUNCT
iajs-2379	158	4	,	,	PUNCT
iajs-2379	158	5	to	to	PART
iajs-2379	158	6	show	show	VERB
iajs-2379	158	7	the	the	DET
iajs-2379	158	8	norm	norm	NOUN
iajs-2379	158	9	‖	‖	PROPN
iajs-2379	158	10	‖	‖	PROPN
iajs-2379	158	11	.	.	PUNCT
iajs-2379	159	1	(	(	PUNCT
iajs-2379	159	2	)	)	PUNCT
iajs-2379	159	3	/	/	PUNCT
iajs-2379	159	4	is	be	AUX
iajs-2379	159	5	bounded	bound	VERB
iajs-2379	159	6	,	,	PUNCT
iajs-2379	159	7	let	let	INTJ
iajs-2379	159	8	(	(	PUNCT
iajs-2379	159	9	2.19.a),(2.20.a)&(2.21.a	2.19.a),(2.20.a)&(2.21.a	NUM
iajs-2379	159	10	)	)	PUNCT
iajs-2379	159	11	be	be	AUX
iajs-2379	159	12	rewritten	rewrite	VERB
iajs-2379	159	13	as	as	ADP
iajs-2379	159	14	〈	〈	PROPN
iajs-2379	159	15	〉	〉	NOUN
iajs-2379	159	16	(	(	PUNCT
iajs-2379	159	17	)	)	PUNCT
iajs-2379	159	18	(	(	PUNCT
iajs-2379	159	19	)	)	PUNCT
iajs-2379	159	20	(	(	PUNCT
iajs-2379	159	21	)	)	PUNCT
iajs-2379	159	22	(	(	PUNCT
iajs-2379	159	23	)	)	PUNCT
iajs-2379	159	24	(	(	PUNCT
iajs-2379	159	25	)	)	PUNCT
iajs-2379	159	26	〈	〈	NOUN
iajs-2379	159	27	〉	〉	NOUN
iajs-2379	159	28	(	(	PUNCT
iajs-2379	159	29	)	)	PUNCT
iajs-2379	159	30	(	(	PUNCT
iajs-2379	159	31	)	)	PUNCT
iajs-2379	159	32	(	(	PUNCT
iajs-2379	159	33	)	)	PUNCT
iajs-2379	159	34	(	(	PUNCT
iajs-2379	159	35	)	)	PUNCT
iajs-2379	159	36	(	(	PUNCT
iajs-2379	159	37	)	)	PUNCT
iajs-2379	159	38	〈	〈	NOUN
iajs-2379	159	39	〉	〉	NOUN
iajs-2379	159	40	(	(	PUNCT
iajs-2379	159	41	)	)	PUNCT
iajs-2379	159	42	(	(	PUNCT
iajs-2379	159	43	)	)	PUNCT
iajs-2379	159	44	(	(	PUNCT
iajs-2379	159	45	)	)	PUNCT
iajs-2379	159	46	(	(	PUNCT
iajs-2379	159	47	)	)	PUNCT
iajs-2379	159	48	(	(	PUNCT
iajs-2379	159	49	)	)	PUNCT
iajs-2379	159	50	.	.	PUNCT
iajs-2379	160	1	by	by	ADP
iajs-2379	160	2	adding	add	VERB
iajs-2379	160	3	the	the	DET
iajs-2379	160	4	above	above	ADJ
iajs-2379	160	5	equations	equation	NOUN
iajs-2379	160	6	and	and	CCONJ
iajs-2379	160	7	integrating	integrate	VERB
iajs-2379	160	8	both	both	DET
iajs-2379	160	9	sides	side	NOUN
iajs-2379	160	10	of	of	ADP
iajs-2379	160	11	the	the	DET
iajs-2379	160	12	obtained	obtain	VERB
iajs-2379	160	13	equation	equation	NOUN
iajs-2379	160	14	from	from	ADP
iajs-2379	160	15	to	to	ADP
iajs-2379	160	16	,	,	PUNCT
iajs-2379	160	17	taking	take	VERB
iajs-2379	160	18	the	the	DET
iajs-2379	160	19	absolute	absolute	ADJ
iajs-2379	160	20	value	value	NOUN
iajs-2379	160	21	then	then	ADV
iajs-2379	160	22	using	use	VERB
iajs-2379	160	23	the	the	DET
iajs-2379	160	24	csi	csi	PROPN
iajs-2379	160	25	,	,	PUNCT
iajs-2379	160	26	and	and	CCONJ
iajs-2379	160	27	finally	finally	ADV
iajs-2379	160	28	using	use	VERB
iajs-2379	160	29	assumptions	assumption	NOUN
iajs-2379	160	30	(	(	PUNCT
iajs-2379	160	31	a	a	X
iajs-2379	160	32	)	)	PUNCT
iajs-2379	160	33	,	,	PUNCT
iajs-2379	160	34	it	it	PRON
iajs-2379	160	35	yields	yield	VERB
iajs-2379	160	36	|∫	|∫	ADV
iajs-2379	160	37	〈	〈	PROPN
iajs-2379	160	38	〉	〉	NOUN
iajs-2379	160	39	|	|	ADV
iajs-2379	160	40	|∫	|∫	ADV
iajs-2379	160	41	,	,	PUNCT
iajs-2379	160	42	(	(	PUNCT
iajs-2379	160	43	)	)	PUNCT
iajs-2379	160	44	(	(	PUNCT
iajs-2379	160	45	)	)	PUNCT
iajs-2379	160	46	(	(	PUNCT
iajs-2379	160	47	)	)	PUNCT
iajs-2379	160	48	(	(	PUNCT
iajs-2379	160	49	)	)	PUNCT
iajs-2379	160	50	(	(	PUNCT
iajs-2379	160	51	)	)	PUNCT
iajs-2379	160	52	(	(	PUNCT
iajs-2379	160	53	)	)	PUNCT
iajs-2379	160	54	–	–	PUNCT
iajs-2379	160	55	(	(	PUNCT
iajs-2379	160	56	)	)	PUNCT
iajs-2379	160	57	(	(	PUNCT
iajs-2379	160	58	)	)	PUNCT
iajs-2379	160	59	(	(	PUNCT
iajs-2379	160	60	)	)	PUNCT
iajs-2379	160	61	(	(	PUNCT
iajs-2379	160	62	)	)	PUNCT
iajs-2379	160	63	(	(	PUNCT
iajs-2379	160	64	)	)	PUNCT
iajs-2379	160	65	(	(	PUNCT
iajs-2379	160	66	)	)	PUNCT
iajs-2379	160	67	(	(	PUNCT
iajs-2379	160	68	)	)	PUNCT
iajs-2379	160	69	(	(	PUNCT
iajs-2379	160	70	)	)	PUNCT
iajs-2379	160	71	(	(	PUNCT
iajs-2379	160	72	)	)	PUNCT
iajs-2379	161	1	]	]	X
iajs-2379	161	2	dt|	dt|	CCONJ
iajs-2379	161	3	,	,	PUNCT
iajs-2379	161	4	gives	give	VERB
iajs-2379	161	5	|∫	|∫	PRON
iajs-2379	161	6	〈	〈	NOUN
iajs-2379	161	7	〉	〉	NOUN
iajs-2379	161	8	|	|	CCONJ
iajs-2379	161	9	s‖	s‖	VERB
iajs-2379	161	10	‖	‖	PROPN
iajs-2379	161	11	‖	‖	PROPN
iajs-2379	161	12	‖	‖	PROPN
iajs-2379	161	13	‖	‖	PROPN
iajs-2379	161	14	‖	‖	PROPN
iajs-2379	161	15	‖	‖	PROPN
iajs-2379	161	16	‖	‖	PROPN
iajs-2379	161	17	‖	‖	PROPN
iajs-2379	161	18	‖	‖	PROPN
iajs-2379	161	19	‖	‖	PROPN
iajs-2379	161	20	‖	‖	PROPN
iajs-2379	161	21	‖	‖	PROPN
iajs-2379	161	22	‖	‖	PROPN
iajs-2379	161	23	‖	‖	PROPN
iajs-2379	161	24	‖	‖	PROPN
iajs-2379	161	25	‖	‖	PROPN
iajs-2379	161	26	‖	‖	PROPN
iajs-2379	161	27	‖	‖	PROPN
iajs-2379	161	28	‖	‖	PROPN
iajs-2379	161	29	‖	‖	PROPN
iajs-2379	161	30	‖	‖	PROPN
iajs-2379	161	31	‖	‖	PROPN
iajs-2379	161	32	‖	‖	PROPN
iajs-2379	161	33	‖	‖	PROPN
iajs-2379	161	34	‖	‖	PROPN
iajs-2379	161	35	‖	‖	PROPN
iajs-2379	161	36	‖	‖	PROPN
iajs-2379	161	37	‖	‖	PROPN
iajs-2379	161	38	‖	‖	PROPN
iajs-2379	161	39	‖	‖	PROPN
iajs-2379	161	40	‖	‖	PROPN
iajs-2379	161	41	‖	‖	PROPN
iajs-2379	161	42	‖	‖	PROPN
iajs-2379	161	43	‖	‖	PROPN
iajs-2379	161	44	‖	‖	PROPN
iajs-2379	161	45	‖	‖	PROPN
iajs-2379	161	46	‖	‖	PROPN
iajs-2379	161	47	‖	‖	PROPN
iajs-2379	161	48	‖	‖	PROPN
iajs-2379	161	49	‖	‖	PROPN
iajs-2379	161	50	‖	‖	PROPN
iajs-2379	161	51	‖	‖	PROPN
iajs-2379	161	52	‖	‖	PROPN
iajs-2379	161	53	‖	‖	PROPN
iajs-2379	161	54	‖	‖	PROPN
iajs-2379	161	55	‖	‖	PROPN
iajs-2379	161	56	‖	‖	PROPN
iajs-2379	161	57	138	138	NUM
iajs-2379	161	58	ibn	ibn	PROPN
iajs-2379	161	59	al	al	PROPN
iajs-2379	161	60	-	-	PUNCT
iajs-2379	161	61	haitham	haitham	PROPN
iajs-2379	161	62	jour	jour	X
iajs-2379	161	63	.	.	PROPN
iajs-2379	162	1	for	for	ADP
iajs-2379	162	2	pure	pure	ADJ
iajs-2379	162	3	&	&	CCONJ
iajs-2379	162	4	appl	appl	PROPN
iajs-2379	162	5	.	.	PUNCT
iajs-2379	163	1	sci	sci	PROPN
iajs-2379	163	2	.	.	PROPN
iajs-2379	164	1	33	33	NUM
iajs-2379	164	2	(	(	PUNCT
iajs-2379	164	3	1	1	NUM
iajs-2379	164	4	)	)	PUNCT
iajs-2379	164	5	2020	2020	NUM
iajs-2379	164	6	‖	‖	PROPN
iajs-2379	164	7	‖	‖	PROPN
iajs-2379	164	8	‖	‖	PROPN
iajs-2379	164	9	‖	‖	PROPN
iajs-2379	164	10	‖	‖	PROPN
iajs-2379	164	11	‖	‖	PROPN
iajs-2379	164	12	‖	‖	PROPN
iajs-2379	164	13	‖	‖	PROPN
iajs-2379	164	14	‖	‖	PROPN
iajs-2379	164	15	‖	‖	PROPN
iajs-2379	164	16	‖	‖	PROPN
iajs-2379	164	17	‖	‖	PROPN
iajs-2379	164	18	‖	‖	PROPN
iajs-2379	164	19	‖	‖	PROPN
iajs-2379	164	20	‖	‖	PROPN
iajs-2379	164	21	‖	‖	PROPN
iajs-2379	164	22	‖	‖	PROPN
iajs-2379	164	23	‖	‖	PROPN
iajs-2379	164	24	‖	‖	PROPN
iajs-2379	164	25	‖	‖	PROPN
iajs-2379	164	26	‖	‖	PROPN
iajs-2379	164	27	‖	‖	PROPN
iajs-2379	164	28	‖	‖	PROPN
iajs-2379	164	29	‖	‖	PROPN
iajs-2379	164	30	.	.	PUNCT
iajs-2379	165	1	since	since	SCONJ
iajs-2379	165	2	for	for	ADP
iajs-2379	165	3	each	each	DET
iajs-2379	165	4	i	i	NOUN
iajs-2379	165	5	=	=	NOUN
iajs-2379	165	6	1,2,3	1,2,3	NUM
iajs-2379	165	7	the	the	DET
iajs-2379	165	8	following	follow	VERB
iajs-2379	165	9	inequalities	inequality	NOUN
iajs-2379	165	10	are	be	AUX
iajs-2379	165	11	satisfied	satisfied	ADJ
iajs-2379	165	12	‖	‖	PROPN
iajs-2379	165	13	‖	‖	PROPN
iajs-2379	165	14	‖	‖	PROPN
iajs-2379	165	15	‖	‖	PROPN
iajs-2379	165	16	,	,	PUNCT
iajs-2379	165	17	‖	‖	PROPN
iajs-2379	165	18	‖	‖	PROPN
iajs-2379	165	19	‖	‖	PROPN
iajs-2379	165	20	‖	‖	PROPN
iajs-2379	165	21	,	,	PUNCT
iajs-2379	165	22	‖	‖	PROPN
iajs-2379	165	23	‖	‖	PROPN
iajs-2379	165	24	‖	‖	PROPN
iajs-2379	166	1	⃗	⃗	PROPN
iajs-2379	166	2	‖	‖	PROPN
iajs-2379	166	3	,	,	PUNCT
iajs-2379	166	4	‖	‖	PROPN
iajs-2379	166	5	⃗	⃗	PROPN
iajs-2379	166	6	‖	‖	PROPN
iajs-2379	166	7	,	,	PUNCT
iajs-2379	166	8	‖	‖	PROPN
iajs-2379	166	9	‖	‖	PROPN
iajs-2379	166	10	‖	‖	PROPN
iajs-2379	166	11	‖	‖	PROPN
iajs-2379	166	12	‖	‖	PROPN
iajs-2379	166	13	‖	‖	PROPN
iajs-2379	166	14	‖	‖	PROPN
iajs-2379	166	15	‖	‖	PROPN
iajs-2379	166	16	,	,	PUNCT
iajs-2379	166	17	‖	‖	PROPN
iajs-2379	166	18	‖	‖	PROPN
iajs-2379	166	19	‖	‖	PROPN
iajs-2379	166	20	‖	‖	PROPN
iajs-2379	166	21	(	(	PUNCT
iajs-2379	166	22	)	)	PUNCT
iajs-2379	166	23	,	,	PUNCT
iajs-2379	166	24	‖	‖	PROPN
iajs-2379	166	25	‖	‖	PROPN
iajs-2379	166	26	,	,	PUNCT
iajs-2379	166	27	‖	‖	PROPN
iajs-2379	166	28	‖	‖	PROPN
iajs-2379	166	29	‖	‖	PROPN
iajs-2379	166	30	‖	‖	PROPN
iajs-2379	166	31	(	(	PUNCT
iajs-2379	166	32	)	)	PUNCT
iajs-2379	166	33	,	,	PUNCT
iajs-2379	166	34	‖	‖	PROPN
iajs-2379	166	35	‖	‖	PROPN
iajs-2379	166	36	‖	‖	PROPN
iajs-2379	166	37	‖	‖	PROPN
iajs-2379	166	38	(	(	PUNCT
iajs-2379	166	39	)	)	PUNCT
iajs-2379	166	40	,	,	PUNCT
iajs-2379	166	41	‖	‖	PROPN
iajs-2379	166	42	‖	‖	PROPN
iajs-2379	166	43	‖	‖	PROPN
iajs-2379	166	44	‖	‖	PROPN
iajs-2379	166	45	(	(	PUNCT
iajs-2379	166	46	)	)	PUNCT
iajs-2379	166	47	,	,	PUNCT
iajs-2379	166	48	then	then	ADV
iajs-2379	166	49	|∫	|∫	ADV
iajs-2379	166	50	〈	〈	PROPN
iajs-2379	166	51	〉	〉	NOUN
iajs-2379	166	52	|	|	ADV
iajs-2379	166	53	,	,	PUNCT
iajs-2379	166	54	‖	‖	PROPN
iajs-2379	166	55	‖	‖	PROPN
iajs-2379	166	56	(	(	PUNCT
iajs-2379	166	57	)	)	PUNCT
iajs-2379	166	58	‖	‖	PROPN
iajs-2379	166	59	‖	‖	PROPN
iajs-2379	166	60	(	(	PUNCT
iajs-2379	166	61	)	)	PUNCT
iajs-2379	166	62	(	(	PUNCT
iajs-2379	166	63	)	)	PUNCT
iajs-2379	166	64	-‖	-‖	PROPN
iajs-2379	166	65	‖	‖	PROPN
iajs-2379	166	66	(	(	PUNCT
iajs-2379	166	67	)	)	PUNCT
iajs-2379	166	68	or	or	CCONJ
iajs-2379	166	69	|∫	|∫	PRON
iajs-2379	166	70	〈	〈	NOUN
iajs-2379	166	71	〉	〉	NOUN
iajs-2379	166	72	|	|	ADV
iajs-2379	166	73	.	.	PUNCT
iajs-2379	167	1	(	(	PUNCT
iajs-2379	167	2	)	)	PUNCT
iajs-2379	167	3	(	(	PUNCT
iajs-2379	167	4	)	)	PUNCT
iajs-2379	167	5	/	/	SYM
iajs-2379	167	6	‖	‖	PROPN
iajs-2379	167	7	‖	‖	PROPN
iajs-2379	167	8	(	(	PUNCT
iajs-2379	167	9	)	)	PUNCT
iajs-2379	167	10	,	,	PUNCT
iajs-2379	167	11	where	where	SCONJ
iajs-2379	167	12	‖	‖	PROPN
iajs-2379	167	13	‖	‖	PROPN
iajs-2379	167	14	(	(	PUNCT
iajs-2379	167	15	)	)	PUNCT
iajs-2379	167	16	(	(	PUNCT
iajs-2379	167	17	)	)	PUNCT
iajs-2379	167	18	and	and	CCONJ
iajs-2379	167	19	(	(	PUNCT
iajs-2379	167	20	)	)	PUNCT
iajs-2379	167	21	|∫	|∫	NOUN
iajs-2379	167	22	〈	〈	PROPN
iajs-2379	167	23	⃗	⃗	NOUN
iajs-2379	167	24	⃗	⃗	PROPN
iajs-2379	167	25	〉	〉	NOUN
iajs-2379	167	26	|	|	ADV
iajs-2379	167	27	‖	‖	ADJ
iajs-2379	167	28	⃗	⃗	PROPN
iajs-2379	167	29	‖	‖	PROPN
iajs-2379	167	30	(	(	PUNCT
iajs-2379	167	31	)	)	PUNCT
iajs-2379	167	32	(	(	PUNCT
iajs-2379	167	33	)	)	PUNCT
iajs-2379	167	34	,	,	PUNCT
iajs-2379	167	35	with	with	ADP
iajs-2379	167	36	(	(	PUNCT
iajs-2379	167	37	)	)	PUNCT
iajs-2379	167	38	(	(	PUNCT
iajs-2379	167	39	)	)	PUNCT
iajs-2379	167	40	(	(	PUNCT
iajs-2379	167	41	)	)	PUNCT
iajs-2379	167	42	‖	‖	PROPN
iajs-2379	167	43	‖	‖	PROPN
iajs-2379	167	44	(	(	PUNCT
iajs-2379	167	45	)	)	PUNCT
iajs-2379	167	46	(	(	PUNCT
iajs-2379	167	47	)	)	PUNCT
iajs-2379	167	48	since	since	SCONJ
iajs-2379	167	49	is	be	AUX
iajs-2379	167	50	solution	solution	NOUN
iajs-2379	167	51	of	of	ADP
iajs-2379	167	52	the	the	DET
iajs-2379	167	53	ses	se	NOUN
iajs-2379	167	54	(	(	PUNCT
iajs-2379	167	55	1	1	NUM
iajs-2379	167	56	)	)	PUNCT
iajs-2379	167	57	,	,	PUNCT
iajs-2379	167	58	then	then	ADV
iajs-2379	167	59	〈	〈	PROPN
iajs-2379	167	60	〉	〉	NOUN
iajs-2379	167	61	(	(	PUNCT
iajs-2379	167	62	)	)	PUNCT
iajs-2379	167	63	(	(	PUNCT
iajs-2379	167	64	)	)	PUNCT
iajs-2379	167	65	(	(	PUNCT
iajs-2379	167	66	)	)	PUNCT
iajs-2379	167	67	(	(	PUNCT
iajs-2379	167	68	)	)	PUNCT
iajs-2379	167	69	=	=	SYM
iajs-2379	167	70	(	(	PUNCT
iajs-2379	167	71	)	)	PUNCT
iajs-2379	167	72	(	(	PUNCT
iajs-2379	167	73	56	56	NUM
iajs-2379	167	74	)	)	PUNCT
iajs-2379	167	75	〈	〈	PROPN
iajs-2379	167	76	〉	〉	NOUN
iajs-2379	167	77	(	(	PUNCT
iajs-2379	167	78	)	)	PUNCT
iajs-2379	167	79	(	(	PUNCT
iajs-2379	167	80	)	)	PUNCT
iajs-2379	167	81	(	(	PUNCT
iajs-2379	167	82	)	)	PUNCT
iajs-2379	167	83	(	(	PUNCT
iajs-2379	167	84	)	)	PUNCT
iajs-2379	167	85	=(	=(	NOUN
iajs-2379	167	86	)	)	PUNCT
iajs-2379	167	87	(	(	PUNCT
iajs-2379	167	88	57	57	NUM
iajs-2379	167	89	)	)	PUNCT
iajs-2379	167	90	〈	〈	PROPN
iajs-2379	167	91	〉	〉	NOUN
iajs-2379	167	92	(	(	PUNCT
iajs-2379	167	93	)	)	PUNCT
iajs-2379	167	94	(	(	PUNCT
iajs-2379	167	95	)	)	PUNCT
iajs-2379	167	96	(	(	PUNCT
iajs-2379	167	97	)	)	PUNCT
iajs-2379	167	98	(	(	PUNCT
iajs-2379	167	99	)	)	PUNCT
iajs-2379	167	100	=(	=(	NOUN
iajs-2379	167	101	)	)	PUNCT
iajs-2379	167	102	(	(	PUNCT
iajs-2379	167	103	58	58	X
iajs-2379	167	104	)	)	PUNCT
iajs-2379	167	105	let	let	VERB
iajs-2379	167	106	,	,	PUNCT
iajs-2379	167	107	-	-	PUNCT
iajs-2379	167	108	,	,	PUNCT
iajs-2379	167	109	s.t	s.t	PROPN
iajs-2379	167	110	.	.	PROPN
iajs-2379	167	111	(	(	PUNCT
iajs-2379	167	112	)	)	PUNCT
iajs-2379	167	113	,	,	PUNCT
iajs-2379	167	114	,	,	PUNCT
iajs-2379	167	115	3	3	NUM
iajs-2379	167	116	,	,	PUNCT
iajs-2379	167	117	rewriting	rewrite	VERB
iajs-2379	167	118	the	the	DET
iajs-2379	167	119	terms	term	NOUN
iajs-2379	167	120	in	in	ADP
iajs-2379	167	121	the	the	DET
iajs-2379	167	122	l.h.s	l.h.s	NOUN
iajs-2379	167	123	.	.	PUNCT
iajs-2379	168	1	of	of	ADP
iajs-2379	168	2	(	(	PUNCT
iajs-2379	168	3	56–58	56–58	NUM
iajs-2379	168	4	)	)	PUNCT
iajs-2379	168	5	multiplying	multiply	VERB
iajs-2379	168	6	their	their	PRON
iajs-2379	168	7	both	both	DET
iajs-2379	168	8	sides	side	NOUN
iajs-2379	168	9	by	by	ADP
iajs-2379	168	10	(	(	PUNCT
iajs-2379	168	11	)	)	PUNCT
iajs-2379	168	12	,	,	PUNCT
iajs-2379	168	13	(	(	PUNCT
iajs-2379	168	14	)	)	PUNCT
iajs-2379	168	15	&	&	CCONJ
iajs-2379	168	16	(	(	PUNCT
iajs-2379	168	17	)	)	PUNCT
iajs-2379	168	18	respectively	respectively	ADV
iajs-2379	168	19	,	,	PUNCT
iajs-2379	168	20	integrating	integrate	VERB
iajs-2379	168	21	both	both	DET
iajs-2379	168	22	sides	side	NOUN
iajs-2379	168	23	w.r.t	w.r.t	VERB
iajs-2379	168	24	.	.	PUNCT
iajs-2379	169	1	from	from	ADP
iajs-2379	169	2	to	to	ADP
iajs-2379	169	3	,	,	PUNCT
iajs-2379	169	4	and	and	CCONJ
iajs-2379	169	5	integration	integration	NOUN
iajs-2379	169	6	by	by	ADP
iajs-2379	169	7	parts	part	NOUN
iajs-2379	169	8	for	for	ADP
iajs-2379	169	9	the	the	DET
iajs-2379	169	10	terms	term	NOUN
iajs-2379	169	11	in	in	ADP
iajs-2379	169	12	the	the	DET
iajs-2379	169	13	l.h.s	l.h.s	NOUN
iajs-2379	169	14	.	.	PUNCT
iajs-2379	170	1	of	of	ADP
iajs-2379	170	2	each	each	DET
iajs-2379	170	3	obtained	obtain	VERB
iajs-2379	170	4	equation	equation	NOUN
iajs-2379	170	5	,	,	PUNCT
iajs-2379	170	6	one	one	PRON
iajs-2379	170	7	gets	get	VERB
iajs-2379	170	8	that	that	DET
iajs-2379	170	9	∫	∫	PROPN
iajs-2379	170	10	(	(	PUNCT
iajs-2379	170	11	)	)	PUNCT
iajs-2379	170	12	(	(	PUNCT
iajs-2379	170	13	)	)	PUNCT
iajs-2379	170	14	∫	∫	PROPN
iajs-2379	170	15	,	,	PUNCT
iajs-2379	170	16	(	(	PUNCT
iajs-2379	170	17	)	)	PUNCT
iajs-2379	170	18	(	(	PUNCT
iajs-2379	170	19	)	)	PUNCT
iajs-2379	170	20	(	(	PUNCT
iajs-2379	170	21	)	)	PUNCT
iajs-2379	170	22	∫	∫	PROPN
iajs-2379	170	23	(	(	PUNCT
iajs-2379	170	24	)	)	PUNCT
iajs-2379	170	25	(	(	PUNCT
iajs-2379	170	26	)	)	PUNCT
iajs-2379	170	27	∫	∫	PROPN
iajs-2379	170	28	(	(	PUNCT
iajs-2379	170	29	)	)	PUNCT
iajs-2379	170	30	(	(	PUNCT
iajs-2379	170	31	)	)	PUNCT
iajs-2379	170	32	∫	∫	PROPN
iajs-2379	170	33	(	(	PUNCT
iajs-2379	170	34	)	)	PUNCT
iajs-2379	170	35	(	(	PUNCT
iajs-2379	170	36	)	)	PUNCT
iajs-2379	170	37	(	(	PUNCT
iajs-2379	170	38	(	(	PUNCT
iajs-2379	170	39	)	)	PUNCT
iajs-2379	170	40	)	)	PUNCT
iajs-2379	170	41	(	(	PUNCT
iajs-2379	170	42	)	)	PUNCT
iajs-2379	170	43	(	(	PUNCT
iajs-2379	170	44	59	59	NUM
iajs-2379	170	45	)	)	PUNCT
iajs-2379	170	46	∫	∫	PROPN
iajs-2379	170	47	(	(	PUNCT
iajs-2379	170	48	)	)	PUNCT
iajs-2379	170	49	(	(	PUNCT
iajs-2379	170	50	)	)	PUNCT
iajs-2379	170	51	∫	∫	PROPN
iajs-2379	170	52	,	,	PUNCT
iajs-2379	170	53	(	(	PUNCT
iajs-2379	170	54	)	)	PUNCT
iajs-2379	170	55	(	(	PUNCT
iajs-2379	170	56	)	)	PUNCT
iajs-2379	170	57	(	(	PUNCT
iajs-2379	170	58	)	)	PUNCT
iajs-2379	170	59	∫	∫	PROPN
iajs-2379	170	60	(	(	PUNCT
iajs-2379	170	61	)	)	PUNCT
iajs-2379	170	62	(	(	PUNCT
iajs-2379	170	63	)	)	PUNCT
iajs-2379	170	64	∫	∫	PROPN
iajs-2379	170	65	(	(	PUNCT
iajs-2379	170	66	)	)	PUNCT
iajs-2379	170	67	(	(	PUNCT
iajs-2379	170	68	)	)	PUNCT
iajs-2379	170	69	∫	∫	PROPN
iajs-2379	170	70	(	(	PUNCT
iajs-2379	170	71	)	)	PUNCT
iajs-2379	170	72	(	(	PUNCT
iajs-2379	170	73	)	)	PUNCT
iajs-2379	170	74	(	(	PUNCT
iajs-2379	170	75	(	(	PUNCT
iajs-2379	170	76	)	)	PUNCT
iajs-2379	170	77	)	)	PUNCT
iajs-2379	171	1	(	(	PUNCT
iajs-2379	171	2	)	)	PUNCT
iajs-2379	171	3	(	(	PUNCT
iajs-2379	171	4	60	60	NUM
iajs-2379	171	5	)	)	PUNCT
iajs-2379	171	6	∫	∫	PROPN
iajs-2379	171	7	(	(	PUNCT
iajs-2379	171	8	)	)	PUNCT
iajs-2379	171	9	(	(	PUNCT
iajs-2379	171	10	)	)	PUNCT
iajs-2379	171	11	∫	∫	PROPN
iajs-2379	171	12	,	,	PUNCT
iajs-2379	171	13	(	(	PUNCT
iajs-2379	171	14	)	)	PUNCT
iajs-2379	171	15	(	(	PUNCT
iajs-2379	171	16	)	)	PUNCT
iajs-2379	171	17	(	(	PUNCT
iajs-2379	171	18	)	)	PUNCT
iajs-2379	171	19	∫	∫	PROPN
iajs-2379	171	20	(	(	PUNCT
iajs-2379	171	21	)	)	PUNCT
iajs-2379	171	22	(	(	PUNCT
iajs-2379	171	23	)	)	PUNCT
iajs-2379	171	24	∫	∫	PROPN
iajs-2379	171	25	(	(	PUNCT
iajs-2379	171	26	)	)	PUNCT
iajs-2379	171	27	(	(	PUNCT
iajs-2379	171	28	)	)	PUNCT
iajs-2379	171	29	∫	∫	PROPN
iajs-2379	171	30	(	(	PUNCT
iajs-2379	171	31	)	)	PUNCT
iajs-2379	171	32	(	(	PUNCT
iajs-2379	171	33	)	)	PUNCT
iajs-2379	171	34	(	(	PUNCT
iajs-2379	171	35	(	(	PUNCT
iajs-2379	171	36	)	)	PUNCT
iajs-2379	171	37	)	)	PUNCT
iajs-2379	171	38	(	(	PUNCT
iajs-2379	171	39	)	)	PUNCT
iajs-2379	171	40	(	(	PUNCT
iajs-2379	171	41	61	61	NUM
iajs-2379	171	42	)	)	PUNCT
iajs-2379	171	43	since	since	SCONJ
iajs-2379	171	44	weakly	weakly	ADV
iajs-2379	171	45	in	in	ADP
iajs-2379	171	46	(	(	PUNCT
iajs-2379	171	47	(	(	PUNCT
iajs-2379	171	48	)	)	PUNCT
iajs-2379	171	49	)	)	PUNCT
iajs-2379	171	50	and	and	CCONJ
iajs-2379	171	51	weakly	weakly	ADV
iajs-2379	171	52	in	in	ADV
iajs-2379	171	53	.	.	PUNCT
iajs-2379	172	1	(	(	PUNCT
iajs-2379	172	2	)	)	PUNCT
iajs-2379	172	3	/	/	SYM
iajs-2379	172	4	,	,	PUNCT
iajs-2379	172	5	then	then	ADV
iajs-2379	172	6	the	the	DET
iajs-2379	172	7	following	follow	VERB
iajs-2379	172	8	convergences	convergence	NOUN
iajs-2379	172	9	are	be	AUX
iajs-2379	172	10	hold	hold	NOUN
iajs-2379	172	11	∫	∫	PROPN
iajs-2379	172	12	(	(	PUNCT
iajs-2379	172	13	)	)	PUNCT
iajs-2379	172	14	(	(	PUNCT
iajs-2379	172	15	)	)	PUNCT
iajs-2379	172	16	∫	∫	PROPN
iajs-2379	172	17	,	,	PUNCT
iajs-2379	172	18	(	(	PUNCT
iajs-2379	172	19	)	)	PUNCT
iajs-2379	172	20	(	(	PUNCT
iajs-2379	172	21	)	)	PUNCT
iajs-2379	172	22	(	(	PUNCT
iajs-2379	172	23	)	)	PUNCT
iajs-2379	172	24	∫	∫	PROPN
iajs-2379	172	25	(	(	PUNCT
iajs-2379	172	26	)	)	PUNCT
iajs-2379	172	27	(	(	PUNCT
iajs-2379	172	28	)	)	PUNCT
iajs-2379	172	29	∫	∫	PROPN
iajs-2379	172	30	(	(	PUNCT
iajs-2379	172	31	)	)	PUNCT
iajs-2379	172	32	(	(	PUNCT
iajs-2379	172	33	)	)	PUNCT
iajs-2379	172	34	∫	∫	PROPN
iajs-2379	172	35	(	(	PUNCT
iajs-2379	172	36	)	)	PUNCT
iajs-2379	172	37	(	(	PUNCT
iajs-2379	172	38	)	)	PUNCT
iajs-2379	172	39	∫	∫	PROPN
iajs-2379	172	40	,	,	PUNCT
iajs-2379	172	41	(	(	PUNCT
iajs-2379	172	42	)	)	PUNCT
iajs-2379	172	43	(	(	PUNCT
iajs-2379	172	44	)	)	PUNCT
iajs-2379	172	45	(	(	PUNCT
iajs-2379	172	46	)	)	PUNCT
iajs-2379	172	47	∫	∫	PROPN
iajs-2379	172	48	(	(	PUNCT
iajs-2379	172	49	)	)	PUNCT
iajs-2379	172	50	(	(	PUNCT
iajs-2379	172	51	)	)	PUNCT
iajs-2379	172	52	∫	∫	PROPN
iajs-2379	172	53	(	(	PUNCT
iajs-2379	172	54	)	)	PUNCT
iajs-2379	172	55	(	(	PUNCT
iajs-2379	172	56	)	)	PUNCT
iajs-2379	172	57	(	(	PUNCT
iajs-2379	172	58	62	62	NUM
iajs-2379	172	59	)	)	PUNCT
iajs-2379	172	60	∫	∫	PROPN
iajs-2379	172	61	(	(	PUNCT
iajs-2379	172	62	)	)	PUNCT
iajs-2379	172	63	(	(	PUNCT
iajs-2379	172	64	)	)	PUNCT
iajs-2379	172	65	∫	∫	PROPN
iajs-2379	172	66	,	,	PUNCT
iajs-2379	172	67	(	(	PUNCT
iajs-2379	172	68	)	)	PUNCT
iajs-2379	172	69	(	(	PUNCT
iajs-2379	172	70	)	)	PUNCT
iajs-2379	172	71	(	(	PUNCT
iajs-2379	172	72	)	)	PUNCT
iajs-2379	172	73	∫	∫	PROPN
iajs-2379	172	74	(	(	PUNCT
iajs-2379	172	75	)	)	PUNCT
iajs-2379	172	76	(	(	PUNCT
iajs-2379	172	77	)	)	PUNCT
iajs-2379	172	78	∫	∫	PROPN
iajs-2379	172	79	(	(	PUNCT
iajs-2379	172	80	)	)	PUNCT
iajs-2379	172	81	(	(	PUNCT
iajs-2379	172	82	)	)	PUNCT
iajs-2379	172	83	∫	∫	PROPN
iajs-2379	172	84	(	(	PUNCT
iajs-2379	172	85	)	)	PUNCT
iajs-2379	172	86	(	(	PUNCT
iajs-2379	172	87	)	)	PUNCT
iajs-2379	172	88	∫	∫	PROPN
iajs-2379	172	89	,	,	PUNCT
iajs-2379	172	90	(	(	PUNCT
iajs-2379	172	91	)	)	PUNCT
iajs-2379	172	92	(	(	PUNCT
iajs-2379	172	93	)	)	PUNCT
iajs-2379	172	94	(	(	PUNCT
iajs-2379	172	95	)	)	PUNCT
iajs-2379	172	96	∫	∫	PROPN
iajs-2379	172	97	(	(	PUNCT
iajs-2379	172	98	)	)	PUNCT
iajs-2379	172	99	(	(	PUNCT
iajs-2379	172	100	)	)	PUNCT
iajs-2379	172	101	∫	∫	PROPN
iajs-2379	172	102	(	(	PUNCT
iajs-2379	172	103	)	)	PUNCT
iajs-2379	172	104	(	(	PUNCT
iajs-2379	172	105	)	)	PUNCT
iajs-2379	172	106	(	(	PUNCT
iajs-2379	172	107	63	63	NUM
iajs-2379	172	108	)	)	PUNCT
iajs-2379	172	109	139	139	NUM
iajs-2379	172	110	ibn	ibn	PROPN
iajs-2379	172	111	al	al	PROPN
iajs-2379	172	112	-	-	PUNCT
iajs-2379	172	113	haitham	haitham	PROPN
iajs-2379	172	114	jour	jour	X
iajs-2379	172	115	.	.	PROPN
iajs-2379	173	1	for	for	ADP
iajs-2379	173	2	pure	pure	ADJ
iajs-2379	173	3	&	&	CCONJ
iajs-2379	173	4	appl	appl	PROPN
iajs-2379	173	5	.	.	PUNCT
iajs-2379	174	1	sci	sci	PROPN
iajs-2379	174	2	.	.	PROPN
iajs-2379	175	1	33	33	NUM
iajs-2379	175	2	(	(	PUNCT
iajs-2379	175	3	1	1	NUM
iajs-2379	175	4	)	)	PUNCT
iajs-2379	175	5	2020	2020	NUM
iajs-2379	175	6	∫	∫	PROPN
iajs-2379	175	7	(	(	PUNCT
iajs-2379	175	8	)	)	PUNCT
iajs-2379	175	9	(	(	PUNCT
iajs-2379	175	10	)	)	PUNCT
iajs-2379	175	11	∫	∫	PROPN
iajs-2379	175	12	,	,	PUNCT
iajs-2379	175	13	(	(	PUNCT
iajs-2379	175	14	)	)	PUNCT
iajs-2379	175	15	(	(	PUNCT
iajs-2379	175	16	)	)	PUNCT
iajs-2379	175	17	(	(	PUNCT
iajs-2379	175	18	)	)	PUNCT
iajs-2379	175	19	∫	∫	PROPN
iajs-2379	175	20	(	(	PUNCT
iajs-2379	175	21	)	)	PUNCT
iajs-2379	175	22	(	(	PUNCT
iajs-2379	175	23	)	)	PUNCT
iajs-2379	175	24	∫	∫	PROPN
iajs-2379	175	25	(	(	PUNCT
iajs-2379	175	26	)	)	PUNCT
iajs-2379	175	27	(	(	PUNCT
iajs-2379	175	28	)	)	PUNCT
iajs-2379	175	29	∫	∫	PROPN
iajs-2379	175	30	(	(	PUNCT
iajs-2379	175	31	)	)	PUNCT
iajs-2379	175	32	(	(	PUNCT
iajs-2379	175	33	)	)	PUNCT
iajs-2379	175	34	∫	∫	PROPN
iajs-2379	175	35	,	,	PUNCT
iajs-2379	175	36	(	(	PUNCT
iajs-2379	175	37	)	)	PUNCT
iajs-2379	175	38	(	(	PUNCT
iajs-2379	175	39	)	)	PUNCT
iajs-2379	175	40	(	(	PUNCT
iajs-2379	175	41	)	)	PUNCT
iajs-2379	175	42	∫	∫	PROPN
iajs-2379	175	43	(	(	PUNCT
iajs-2379	175	44	)	)	PUNCT
iajs-2379	175	45	(	(	PUNCT
iajs-2379	175	46	)	)	PUNCT
iajs-2379	175	47	∫	∫	PROPN
iajs-2379	175	48	(	(	PUNCT
iajs-2379	175	49	)	)	PUNCT
iajs-2379	175	50	(	(	PUNCT
iajs-2379	175	51	)	)	PUNCT
iajs-2379	175	52	(	(	PUNCT
iajs-2379	175	53	64	64	NUM
iajs-2379	175	54	)	)	PUNCT
iajs-2379	175	55	since	since	SCONJ
iajs-2379	175	56	(	(	PUNCT
iajs-2379	175	57	(	(	PUNCT
iajs-2379	175	58	)	)	PUNCT
iajs-2379	175	59	(	(	PUNCT
iajs-2379	175	60	)	)	PUNCT
iajs-2379	175	61	(	(	PUNCT
iajs-2379	175	62	)	)	PUNCT
iajs-2379	175	63	)	)	PUNCT
iajs-2379	175	64	bounded	bound	VERB
iajs-2379	175	65	in	in	ADP
iajs-2379	175	66	(	(	PUNCT
iajs-2379	175	67	(	(	PUNCT
iajs-2379	175	68	)	)	PUNCT
iajs-2379	175	69	)	)	PUNCT
iajs-2379	175	70	and	and	CCONJ
iajs-2379	175	71	from	from	ADP
iajs-2379	175	72	the	the	DET
iajs-2379	175	73	projection	projection	NOUN
iajs-2379	175	74	theorem	theorem	NOUN
iajs-2379	175	75	one	one	PRON
iajs-2379	175	76	has	have	VERB
iajs-2379	175	77	(	(	PUNCT
iajs-2379	175	78	)	)	PUNCT
iajs-2379	175	79	(	(	PUNCT
iajs-2379	175	80	)	)	PUNCT
iajs-2379	175	81	(	(	PUNCT
iajs-2379	175	82	)	)	PUNCT
iajs-2379	175	83	(	(	PUNCT
iajs-2379	175	84	)	)	PUNCT
iajs-2379	175	85	(	(	PUNCT
iajs-2379	175	86	65	65	NUM
iajs-2379	175	87	)	)	PUNCT
iajs-2379	175	88	(	(	PUNCT
iajs-2379	175	89	)	)	PUNCT
iajs-2379	175	90	(	(	PUNCT
iajs-2379	175	91	)	)	PUNCT
iajs-2379	175	92	(	(	PUNCT
iajs-2379	175	93	)	)	PUNCT
iajs-2379	175	94	(	(	PUNCT
iajs-2379	175	95	)	)	PUNCT
iajs-2379	175	96	(	(	PUNCT
iajs-2379	175	97	66	66	NUM
iajs-2379	175	98	)	)	PUNCT
iajs-2379	175	99	(	(	PUNCT
iajs-2379	175	100	)	)	PUNCT
iajs-2379	175	101	(	(	PUNCT
iajs-2379	175	102	)	)	PUNCT
iajs-2379	175	103	(	(	PUNCT
iajs-2379	175	104	)	)	PUNCT
iajs-2379	175	105	(	(	PUNCT
iajs-2379	175	106	)	)	PUNCT
iajs-2379	175	107	(	(	PUNCT
iajs-2379	175	108	67	67	NUM
iajs-2379	175	109	)	)	PUNCT
iajs-2379	175	110	and	and	CCONJ
iajs-2379	175	111	since	since	SCONJ
iajs-2379	175	112	⃗	⃗	PROPN
iajs-2379	175	113	⃗	⃗	PROPN
iajs-2379	175	114	weakly	weakly	ADJ
iajs-2379	175	115	in	in	ADP
iajs-2379	175	116	(	(	PUNCT
iajs-2379	175	117	(	(	PUNCT
iajs-2379	175	118	)	)	PUNCT
iajs-2379	175	119	)	)	PUNCT
iajs-2379	175	120	,	,	PUNCT
iajs-2379	175	121	then	then	ADV
iajs-2379	175	122	∫	∫	PROPN
iajs-2379	175	123	(	(	PUNCT
iajs-2379	175	124	)	)	PUNCT
iajs-2379	175	125	(	(	PUNCT
iajs-2379	175	126	)	)	PUNCT
iajs-2379	175	127	∫	∫	PROPN
iajs-2379	175	128	(	(	PUNCT
iajs-2379	175	129	)	)	PUNCT
iajs-2379	175	130	(	(	PUNCT
iajs-2379	175	131	)	)	PUNCT
iajs-2379	175	132	(	(	PUNCT
iajs-2379	175	133	68	68	NUM
iajs-2379	175	134	)	)	PUNCT
iajs-2379	175	135	∫	∫	PROPN
iajs-2379	175	136	(	(	PUNCT
iajs-2379	175	137	)	)	PUNCT
iajs-2379	175	138	(	(	PUNCT
iajs-2379	175	139	)	)	PUNCT
iajs-2379	175	140	∫	∫	PROPN
iajs-2379	175	141	(	(	PUNCT
iajs-2379	175	142	)	)	PUNCT
iajs-2379	175	143	(	(	PUNCT
iajs-2379	175	144	)	)	PUNCT
iajs-2379	175	145	(	(	PUNCT
iajs-2379	175	146	69	69	NUM
iajs-2379	175	147	)	)	PUNCT
iajs-2379	175	148	∫	∫	PROPN
iajs-2379	175	149	(	(	PUNCT
iajs-2379	175	150	)	)	PUNCT
iajs-2379	175	151	(	(	PUNCT
iajs-2379	175	152	)	)	PUNCT
iajs-2379	175	153	∫	∫	PROPN
iajs-2379	175	154	(	(	PUNCT
iajs-2379	175	155	)	)	PUNCT
iajs-2379	175	156	(	(	PUNCT
iajs-2379	175	157	)	)	PUNCT
iajs-2379	175	158	(	(	PUNCT
iajs-2379	175	159	70	70	NUM
iajs-2379	175	160	)	)	PUNCT
iajs-2379	175	161	finally	finally	ADV
iajs-2379	175	162	using(62	using(62	ADJ
iajs-2379	175	163	64	64	NUM
iajs-2379	175	164	)	)	PUNCT
iajs-2379	175	165	,	,	PUNCT
iajs-2379	175	166	(	(	PUNCT
iajs-2379	175	167	65	65	NUM
iajs-2379	175	168	67	67	NUM
iajs-2379	175	169	)	)	PUNCT
iajs-2379	175	170	,	,	PUNCT
iajs-2379	175	171	(	(	PUNCT
iajs-2379	175	172	68	68	NUM
iajs-2379	175	173	70	70	NUM
iajs-2379	175	174	)	)	PUNCT
iajs-2379	175	175	in	in	ADP
iajs-2379	175	176	(	(	PUNCT
iajs-2379	175	177	59	59	NUM
iajs-2379	175	178	61	61	NUM
iajs-2379	175	179	)	)	PUNCT
iajs-2379	175	180	respectively	respectively	ADV
iajs-2379	175	181	,	,	PUNCT
iajs-2379	175	182	one	one	PRON
iajs-2379	175	183	gets	get	VERB
iajs-2379	175	184	∫	∫	NOUN
iajs-2379	175	185	(	(	PUNCT
iajs-2379	175	186	)	)	PUNCT
iajs-2379	175	187	(	(	PUNCT
iajs-2379	175	188	)	)	PUNCT
iajs-2379	175	189	∫	∫	PROPN
iajs-2379	175	190	,	,	PUNCT
iajs-2379	175	191	(	(	PUNCT
iajs-2379	175	192	)	)	PUNCT
iajs-2379	175	193	(	(	PUNCT
iajs-2379	175	194	)	)	PUNCT
iajs-2379	175	195	(	(	PUNCT
iajs-2379	175	196	)	)	PUNCT
iajs-2379	175	197	∫	∫	PROPN
iajs-2379	175	198	(	(	PUNCT
iajs-2379	175	199	)	)	PUNCT
iajs-2379	175	200	(	(	PUNCT
iajs-2379	175	201	)	)	PUNCT
iajs-2379	175	202	∫	∫	PROPN
iajs-2379	175	203	(	(	PUNCT
iajs-2379	175	204	)	)	PUNCT
iajs-2379	175	205	(	(	PUNCT
iajs-2379	175	206	)	)	PUNCT
iajs-2379	175	207	∫	∫	PROPN
iajs-2379	175	208	(	(	PUNCT
iajs-2379	175	209	)	)	PUNCT
iajs-2379	175	210	(	(	PUNCT
iajs-2379	175	211	)	)	PUNCT
iajs-2379	175	212	(	(	PUNCT
iajs-2379	175	213	)	)	PUNCT
iajs-2379	175	214	(	(	PUNCT
iajs-2379	175	215	)	)	PUNCT
iajs-2379	175	216	(	(	PUNCT
iajs-2379	175	217	71	71	NUM
iajs-2379	175	218	)	)	PUNCT
iajs-2379	175	219	∫	∫	PROPN
iajs-2379	175	220	(	(	PUNCT
iajs-2379	175	221	)	)	PUNCT
iajs-2379	175	222	(	(	PUNCT
iajs-2379	175	223	)	)	PUNCT
iajs-2379	175	224	∫	∫	PROPN
iajs-2379	175	225	,	,	PUNCT
iajs-2379	175	226	(	(	PUNCT
iajs-2379	175	227	)	)	PUNCT
iajs-2379	175	228	(	(	PUNCT
iajs-2379	175	229	)	)	PUNCT
iajs-2379	175	230	(	(	PUNCT
iajs-2379	175	231	)	)	PUNCT
iajs-2379	175	232	∫	∫	PROPN
iajs-2379	175	233	(	(	PUNCT
iajs-2379	175	234	)	)	PUNCT
iajs-2379	175	235	(	(	PUNCT
iajs-2379	175	236	)	)	PUNCT
iajs-2379	175	237	∫	∫	PROPN
iajs-2379	175	238	(	(	PUNCT
iajs-2379	175	239	)	)	PUNCT
iajs-2379	175	240	(	(	PUNCT
iajs-2379	175	241	)	)	PUNCT
iajs-2379	175	242	∫	∫	PROPN
iajs-2379	175	243	(	(	PUNCT
iajs-2379	175	244	)	)	PUNCT
iajs-2379	175	245	(	(	PUNCT
iajs-2379	175	246	)	)	PUNCT
iajs-2379	175	247	(	(	PUNCT
iajs-2379	175	248	)	)	PUNCT
iajs-2379	175	249	(	(	PUNCT
iajs-2379	175	250	)	)	PUNCT
iajs-2379	175	251	(	(	PUNCT
iajs-2379	175	252	72	72	NUM
iajs-2379	175	253	)	)	PUNCT
iajs-2379	175	254	∫	∫	PROPN
iajs-2379	175	255	(	(	PUNCT
iajs-2379	175	256	)	)	PUNCT
iajs-2379	175	257	(	(	PUNCT
iajs-2379	175	258	)	)	PUNCT
iajs-2379	175	259	∫	∫	PROPN
iajs-2379	175	260	,	,	PUNCT
iajs-2379	175	261	(	(	PUNCT
iajs-2379	175	262	)	)	PUNCT
iajs-2379	175	263	(	(	PUNCT
iajs-2379	175	264	)	)	PUNCT
iajs-2379	175	265	(	(	PUNCT
iajs-2379	175	266	)	)	PUNCT
iajs-2379	175	267	∫	∫	PROPN
iajs-2379	175	268	(	(	PUNCT
iajs-2379	175	269	)	)	PUNCT
iajs-2379	175	270	(	(	PUNCT
iajs-2379	175	271	)	)	PUNCT
iajs-2379	175	272	∫	∫	PROPN
iajs-2379	175	273	(	(	PUNCT
iajs-2379	175	274	)	)	PUNCT
iajs-2379	175	275	(	(	PUNCT
iajs-2379	175	276	)	)	PUNCT
iajs-2379	175	277	∫	∫	PROPN
iajs-2379	175	278	(	(	PUNCT
iajs-2379	175	279	)	)	PUNCT
iajs-2379	175	280	(	(	PUNCT
iajs-2379	175	281	)	)	PUNCT
iajs-2379	175	282	(	(	PUNCT
iajs-2379	175	283	)	)	PUNCT
iajs-2379	175	284	(	(	PUNCT
iajs-2379	175	285	)	)	PUNCT
iajs-2379	175	286	(	(	PUNCT
iajs-2379	175	287	73	73	NUM
iajs-2379	175	288	)	)	PUNCT
iajs-2379	175	289	case	case	NOUN
iajs-2379	175	290	1	1	NUM
iajs-2379	175	291	:	:	PUNCT
iajs-2379	175	292	we	we	PRON
iajs-2379	175	293	choose	choose	VERB
iajs-2379	175	294	,	,	PUNCT
iajs-2379	175	295	,	,	PUNCT
iajs-2379	175	296	i.e.	i.e.	X
iajs-2379	175	297	(	(	PUNCT
iajs-2379	175	298	)	)	PUNCT
iajs-2379	175	299	(	(	PUNCT
iajs-2379	175	300	)	)	PUNCT
iajs-2379	175	301	,	,	PUNCT
iajs-2379	175	302	.now	.now	PUNCT
iajs-2379	176	1	using	use	VERB
iajs-2379	176	2	integration	integration	NOUN
iajs-2379	176	3	by	by	ADP
iajs-2379	176	4	parts	part	NOUN
iajs-2379	176	5	for	for	ADP
iajs-2379	176	6	the	the	DET
iajs-2379	176	7	terms	term	NOUN
iajs-2379	176	8	in	in	ADP
iajs-2379	176	9	the	the	DET
iajs-2379	176	10	l.h.s	l.h.s	NOUN
iajs-2379	176	11	.	.	PUNCT
iajs-2379	177	1	of	of	ADP
iajs-2379	177	2	(	(	PUNCT
iajs-2379	177	3	71	71	NUM
iajs-2379	177	4	73	73	NUM
iajs-2379	177	5	)	)	PUNCT
iajs-2379	177	6	,	,	PUNCT
iajs-2379	177	7	one	one	PRON
iajs-2379	177	8	gets	get	VERB
iajs-2379	177	9	that	that	DET
iajs-2379	177	10	∫	∫	PROPN
iajs-2379	177	11	〈	〈	PROPN
iajs-2379	177	12	〉	〉	NOUN
iajs-2379	177	13	(	(	PUNCT
iajs-2379	177	14	)	)	PUNCT
iajs-2379	177	15	∫	∫	PROPN
iajs-2379	177	16	,	,	PUNCT
iajs-2379	177	17	(	(	PUNCT
iajs-2379	177	18	)	)	PUNCT
iajs-2379	177	19	(	(	PUNCT
iajs-2379	177	20	)	)	PUNCT
iajs-2379	177	21	(	(	PUNCT
iajs-2379	177	22	)	)	PUNCT
iajs-2379	177	23	∫	∫	PROPN
iajs-2379	177	24	(	(	PUNCT
iajs-2379	177	25	)	)	PUNCT
iajs-2379	177	26	(	(	PUNCT
iajs-2379	177	27	)	)	PUNCT
iajs-2379	177	28	∫	∫	PROPN
iajs-2379	177	29	(	(	PUNCT
iajs-2379	177	30	)	)	PUNCT
iajs-2379	177	31	(	(	PUNCT
iajs-2379	177	32	)	)	PUNCT
iajs-2379	177	33	∫	∫	PROPN
iajs-2379	177	34	(	(	PUNCT
iajs-2379	177	35	)	)	PUNCT
iajs-2379	177	36	(	(	PUNCT
iajs-2379	177	37	)	)	PUNCT
iajs-2379	177	38	,	,	PUNCT
iajs-2379	177	39	(	(	PUNCT
iajs-2379	177	40	74	74	X
iajs-2379	177	41	)	)	PUNCT
iajs-2379	177	42	∫	∫	NOUN
iajs-2379	177	43	〈	〈	PROPN
iajs-2379	177	44	〉	〉	NOUN
iajs-2379	177	45	(	(	PUNCT
iajs-2379	177	46	)	)	PUNCT
iajs-2379	177	47	∫	∫	PROPN
iajs-2379	177	48	,	,	PUNCT
iajs-2379	177	49	(	(	PUNCT
iajs-2379	177	50	)	)	PUNCT
iajs-2379	177	51	(	(	PUNCT
iajs-2379	177	52	)	)	PUNCT
iajs-2379	177	53	(	(	PUNCT
iajs-2379	177	54	)	)	PUNCT
iajs-2379	177	55	∫	∫	PROPN
iajs-2379	177	56	(	(	PUNCT
iajs-2379	177	57	)	)	PUNCT
iajs-2379	177	58	(	(	PUNCT
iajs-2379	177	59	)	)	PUNCT
iajs-2379	177	60	∫	∫	PROPN
iajs-2379	177	61	(	(	PUNCT
iajs-2379	177	62	)	)	PUNCT
iajs-2379	177	63	(	(	PUNCT
iajs-2379	177	64	)	)	PUNCT
iajs-2379	177	65	∫	∫	PROPN
iajs-2379	177	66	(	(	PUNCT
iajs-2379	177	67	)	)	PUNCT
iajs-2379	177	68	(	(	PUNCT
iajs-2379	177	69	)	)	PUNCT
iajs-2379	177	70	,	,	PUNCT
iajs-2379	177	71	(	(	PUNCT
iajs-2379	177	72	75	75	NUM
iajs-2379	177	73	)	)	PUNCT
iajs-2379	177	74	∫	∫	NOUN
iajs-2379	177	75	〈	〈	PROPN
iajs-2379	177	76	〉	〉	NOUN
iajs-2379	177	77	(	(	PUNCT
iajs-2379	177	78	)	)	PUNCT
iajs-2379	177	79	∫	∫	PROPN
iajs-2379	177	80	,	,	PUNCT
iajs-2379	177	81	(	(	PUNCT
iajs-2379	177	82	)	)	PUNCT
iajs-2379	177	83	(	(	PUNCT
iajs-2379	177	84	)	)	PUNCT
iajs-2379	177	85	(	(	PUNCT
iajs-2379	177	86	)	)	PUNCT
iajs-2379	177	87	∫	∫	PROPN
iajs-2379	177	88	(	(	PUNCT
iajs-2379	177	89	)	)	PUNCT
iajs-2379	177	90	(	(	PUNCT
iajs-2379	177	91	)	)	PUNCT
iajs-2379	177	92	∫	∫	PROPN
iajs-2379	177	93	(	(	PUNCT
iajs-2379	177	94	)	)	PUNCT
iajs-2379	177	95	(	(	PUNCT
iajs-2379	177	96	)	)	PUNCT
iajs-2379	177	97	∫	∫	PROPN
iajs-2379	177	98	(	(	PUNCT
iajs-2379	177	99	)	)	PUNCT
iajs-2379	177	100	(	(	PUNCT
iajs-2379	177	101	)	)	PUNCT
iajs-2379	177	102	,	,	PUNCT
iajs-2379	177	103	(	(	PUNCT
iajs-2379	177	104	76	76	NUM
iajs-2379	177	105	)	)	PUNCT
iajs-2379	177	106	then	then	ADV
iajs-2379	177	107	〈	〈	PROPN
iajs-2379	177	108	〉	〉	NOUN
iajs-2379	177	109	(	(	PUNCT
iajs-2379	177	110	)	)	PUNCT
iajs-2379	177	111	(	(	PUNCT
iajs-2379	177	112	)	)	PUNCT
iajs-2379	177	113	(	(	PUNCT
iajs-2379	177	114	)	)	PUNCT
iajs-2379	177	115	(	(	PUNCT
iajs-2379	177	116	)	)	PUNCT
iajs-2379	177	117	(	(	PUNCT
iajs-2379	177	118	)	)	PUNCT
iajs-2379	177	119	,	,	PUNCT
iajs-2379	177	120	,	,	PUNCT
iajs-2379	177	121	a.e	a.e	PROPN
iajs-2379	177	122	.	.	PROPN
iajs-2379	177	123	on	on	ADP
iajs-2379	177	124	〈	〈	PROPN
iajs-2379	177	125	〉	〉	NOUN
iajs-2379	177	126	(	(	PUNCT
iajs-2379	177	127	)	)	PUNCT
iajs-2379	177	128	(	(	PUNCT
iajs-2379	177	129	)	)	PUNCT
iajs-2379	177	130	(	(	PUNCT
iajs-2379	177	131	)	)	PUNCT
iajs-2379	177	132	(	(	PUNCT
iajs-2379	177	133	)	)	PUNCT
iajs-2379	177	134	=	=	SYM
iajs-2379	177	135	(	(	PUNCT
iajs-2379	177	136	)	)	PUNCT
iajs-2379	177	137	,	,	PUNCT
iajs-2379	177	138	,	,	PUNCT
iajs-2379	177	139	a.e	a.e	PROPN
iajs-2379	177	140	.	.	PROPN
iajs-2379	177	141	on	on	ADP
iajs-2379	177	142	〈	〈	PROPN
iajs-2379	177	143	〉	〉	NOUN
iajs-2379	177	144	(	(	PUNCT
iajs-2379	177	145	)	)	PUNCT
iajs-2379	177	146	(	(	PUNCT
iajs-2379	177	147	)	)	PUNCT
iajs-2379	177	148	(	(	PUNCT
iajs-2379	177	149	)	)	PUNCT
iajs-2379	177	150	(	(	PUNCT
iajs-2379	177	151	)	)	PUNCT
iajs-2379	177	152	=	=	SYM
iajs-2379	177	153	(	(	PUNCT
iajs-2379	177	154	)	)	PUNCT
iajs-2379	177	155	,	,	PUNCT
iajs-2379	177	156	i.e.	i.e.	X
iajs-2379	177	157	(	(	PUNCT
iajs-2379	177	158	,	,	PUNCT
iajs-2379	177	159	,	,	PUNCT
iajs-2379	177	160	)	)	PUNCT
iajs-2379	177	161	satisfies	satisfy	VERB
iajs-2379	177	162	the	the	DET
iajs-2379	177	163	wf	wf	PROPN
iajs-2379	177	164	of	of	ADP
iajs-2379	177	165	the	the	DET
iajs-2379	177	166	ses	se	NOUN
iajs-2379	177	167	case	case	NOUN
iajs-2379	177	168	2	2	NUM
iajs-2379	177	169	:	:	PUNCT
iajs-2379	177	170	we	we	PRON
iajs-2379	177	171	choose	choose	VERB
iajs-2379	177	172	,	,	PUNCT
iajs-2379	177	173	,	,	PUNCT
iajs-2379	177	174	s.t	s.t	PROPN
iajs-2379	177	175	.	.	PROPN
iajs-2379	177	176	(	(	PUNCT
iajs-2379	177	177	)	)	PUNCT
iajs-2379	177	178	,	,	PUNCT
iajs-2379	177	179	(	(	PUNCT
iajs-2379	177	180	)	)	PUNCT
iajs-2379	177	181	,	,	PUNCT
iajs-2379	177	182	using	use	VERB
iajs-2379	177	183	integration	integration	NOUN
iajs-2379	177	184	by	by	ADP
iajs-2379	177	185	parts	part	NOUN
iajs-2379	177	186	for	for	ADP
iajs-2379	177	187	the	the	DET
iajs-2379	177	188	terms	term	NOUN
iajs-2379	177	189	in	in	ADP
iajs-2379	177	190	the	the	DET
iajs-2379	177	191	l.h.s	l.h.s	NOUN
iajs-2379	177	192	.	.	PUNCT
iajs-2379	178	1	of	of	ADP
iajs-2379	178	2	(	(	PUNCT
iajs-2379	178	3	74	74	NUM
iajs-2379	178	4	76),one	76),one	PROPN
iajs-2379	178	5	has	have	AUX
iajs-2379	178	6	∫	∫	PROPN
iajs-2379	178	7	(	(	PUNCT
iajs-2379	178	8	)	)	PUNCT
iajs-2379	178	9	(	(	PUNCT
iajs-2379	178	10	)	)	PUNCT
iajs-2379	178	11	∫	∫	PROPN
iajs-2379	178	12	,	,	PUNCT
iajs-2379	178	13	(	(	PUNCT
iajs-2379	178	14	)	)	PUNCT
iajs-2379	178	15	(	(	PUNCT
iajs-2379	178	16	)	)	PUNCT
iajs-2379	178	17	(	(	PUNCT
iajs-2379	178	18	)	)	PUNCT
iajs-2379	178	19	∫	∫	PROPN
iajs-2379	178	20	(	(	PUNCT
iajs-2379	178	21	)	)	PUNCT
iajs-2379	178	22	(	(	PUNCT
iajs-2379	178	23	)	)	PUNCT
iajs-2379	178	24	∫	∫	PROPN
iajs-2379	178	25	(	(	PUNCT
iajs-2379	178	26	)	)	PUNCT
iajs-2379	178	27	(	(	PUNCT
iajs-2379	178	28	)	)	PUNCT
iajs-2379	178	29	∫	∫	PROPN
iajs-2379	178	30	(	(	PUNCT
iajs-2379	178	31	)	)	PUNCT
iajs-2379	178	32	(	(	PUNCT
iajs-2379	178	33	)	)	PUNCT
iajs-2379	178	34	(	(	PUNCT
iajs-2379	178	35	(	(	PUNCT
iajs-2379	178	36	)	)	PUNCT
iajs-2379	178	37	)	)	PUNCT
iajs-2379	178	38	(	(	PUNCT
iajs-2379	178	39	)	)	PUNCT
iajs-2379	178	40	(	(	PUNCT
iajs-2379	178	41	77	77	NUM
iajs-2379	178	42	)	)	PUNCT
iajs-2379	178	43	140	140	NUM
iajs-2379	178	44	ibn	ibn	PROPN
iajs-2379	178	45	al	al	PROPN
iajs-2379	178	46	-	-	PUNCT
iajs-2379	178	47	haitham	haitham	PROPN
iajs-2379	178	48	jour	jour	X
iajs-2379	178	49	.	.	PROPN
iajs-2379	179	1	for	for	ADP
iajs-2379	179	2	pure	pure	ADJ
iajs-2379	179	3	&	&	CCONJ
iajs-2379	179	4	appl	appl	PROPN
iajs-2379	179	5	.	.	PUNCT
iajs-2379	180	1	sci	sci	PROPN
iajs-2379	180	2	.	.	PROPN
iajs-2379	181	1	33	33	NUM
iajs-2379	181	2	(	(	PUNCT
iajs-2379	181	3	1	1	NUM
iajs-2379	181	4	)	)	PUNCT
iajs-2379	181	5	2020	2020	NUM
iajs-2379	181	6	∫	∫	PROPN
iajs-2379	181	7	(	(	PUNCT
iajs-2379	181	8	)	)	PUNCT
iajs-2379	181	9	(	(	PUNCT
iajs-2379	181	10	)	)	PUNCT
iajs-2379	181	11	∫	∫	PROPN
iajs-2379	181	12	,	,	PUNCT
iajs-2379	181	13	(	(	PUNCT
iajs-2379	181	14	)	)	PUNCT
iajs-2379	181	15	(	(	PUNCT
iajs-2379	181	16	)	)	PUNCT
iajs-2379	181	17	(	(	PUNCT
iajs-2379	181	18	)	)	PUNCT
iajs-2379	181	19	∫	∫	PROPN
iajs-2379	181	20	(	(	PUNCT
iajs-2379	181	21	)	)	PUNCT
iajs-2379	181	22	(	(	PUNCT
iajs-2379	181	23	)	)	PUNCT
iajs-2379	181	24	∫	∫	PROPN
iajs-2379	181	25	(	(	PUNCT
iajs-2379	181	26	)	)	PUNCT
iajs-2379	181	27	(	(	PUNCT
iajs-2379	181	28	)	)	PUNCT
iajs-2379	181	29	∫	∫	PROPN
iajs-2379	181	30	(	(	PUNCT
iajs-2379	181	31	)	)	PUNCT
iajs-2379	181	32	(	(	PUNCT
iajs-2379	181	33	)	)	PUNCT
iajs-2379	181	34	(	(	PUNCT
iajs-2379	181	35	(	(	PUNCT
iajs-2379	181	36	)	)	PUNCT
iajs-2379	181	37	)	)	PUNCT
iajs-2379	181	38	(	(	PUNCT
iajs-2379	181	39	)	)	PUNCT
iajs-2379	181	40	(	(	PUNCT
iajs-2379	181	41	78	78	NUM
iajs-2379	181	42	)	)	PUNCT
iajs-2379	181	43	∫	∫	PROPN
iajs-2379	181	44	(	(	PUNCT
iajs-2379	181	45	)	)	PUNCT
iajs-2379	181	46	(	(	PUNCT
iajs-2379	181	47	)	)	PUNCT
iajs-2379	181	48	∫	∫	PROPN
iajs-2379	181	49	,	,	PUNCT
iajs-2379	181	50	(	(	PUNCT
iajs-2379	181	51	)	)	PUNCT
iajs-2379	181	52	(	(	PUNCT
iajs-2379	181	53	)	)	PUNCT
iajs-2379	181	54	(	(	PUNCT
iajs-2379	181	55	)	)	PUNCT
iajs-2379	181	56	∫	∫	PROPN
iajs-2379	181	57	(	(	PUNCT
iajs-2379	181	58	)	)	PUNCT
iajs-2379	181	59	(	(	PUNCT
iajs-2379	181	60	)	)	PUNCT
iajs-2379	181	61	∫	∫	PROPN
iajs-2379	181	62	(	(	PUNCT
iajs-2379	181	63	)	)	PUNCT
iajs-2379	181	64	(	(	PUNCT
iajs-2379	181	65	)	)	PUNCT
iajs-2379	181	66	∫	∫	PROPN
iajs-2379	181	67	(	(	PUNCT
iajs-2379	181	68	)	)	PUNCT
iajs-2379	181	69	(	(	PUNCT
iajs-2379	181	70	)	)	PUNCT
iajs-2379	181	71	(	(	PUNCT
iajs-2379	181	72	(	(	PUNCT
iajs-2379	181	73	)	)	PUNCT
iajs-2379	181	74	)	)	PUNCT
iajs-2379	181	75	(	(	PUNCT
iajs-2379	181	76	)	)	PUNCT
iajs-2379	181	77	(	(	PUNCT
iajs-2379	181	78	79	79	NUM
iajs-2379	181	79	)	)	PUNCT
iajs-2379	181	80	by	by	ADP
iajs-2379	181	81	subtracting(77	subtracting(77	ADV
iajs-2379	181	82	79	79	NUM
iajs-2379	181	83	)	)	PUNCT
iajs-2379	181	84	from	from	ADP
iajs-2379	181	85	(	(	PUNCT
iajs-2379	181	86	71	71	NUM
iajs-2379	181	87	73	73	NUM
iajs-2379	181	88	)	)	PUNCT
iajs-2379	181	89	respectively	respectively	ADV
iajs-2379	181	90	,	,	PUNCT
iajs-2379	181	91	one	one	NUM
iajs-2379	181	92	obtain	obtain	NOUN
iajs-2379	181	93	(	(	PUNCT
iajs-2379	181	94	)	)	PUNCT
iajs-2379	181	95	(	(	PUNCT
iajs-2379	181	96	)	)	PUNCT
iajs-2379	181	97	=(	=(	NOUN
iajs-2379	181	98	(	(	PUNCT
iajs-2379	181	99	)	)	PUNCT
iajs-2379	181	100	)	)	PUNCT
iajs-2379	181	101	(	(	PUNCT
iajs-2379	181	102	)	)	PUNCT
iajs-2379	181	103	,	,	PUNCT
iajs-2379	181	104	(	(	PUNCT
iajs-2379	181	105	)	)	PUNCT
iajs-2379	181	106	(	(	PUNCT
iajs-2379	181	107	)	)	PUNCT
iajs-2379	181	108	,	,	PUNCT
iajs-2379	181	109	by	by	ADP
iajs-2379	181	110	the	the	DET
iajs-2379	181	111	same	same	ADJ
iajs-2379	181	112	way	way	NOUN
iajs-2379	181	113	show	show	VERB
iajs-2379	181	114	that	that	SCONJ
iajs-2379	181	115	(	(	PUNCT
iajs-2379	181	116	)	)	PUNCT
iajs-2379	181	117	(	(	PUNCT
iajs-2379	181	118	)	)	PUNCT
iajs-2379	181	119	and	and	CCONJ
iajs-2379	181	120	(	(	PUNCT
iajs-2379	181	121	)	)	PUNCT
iajs-2379	181	122	(	(	PUNCT
iajs-2379	181	123	)	)	PUNCT
iajs-2379	181	124	(	(	PUNCT
iajs-2379	181	125	,	,	PUNCT
iajs-2379	181	126	,	,	PUNCT
iajs-2379	181	127	)	)	PUNCT
iajs-2379	181	128	is	be	AUX
iajs-2379	181	129	a	a	DET
iajs-2379	181	130	solution	solution	NOUN
iajs-2379	181	131	of	of	ADP
iajs-2379	181	132	the	the	DET
iajs-2379	181	133	wf	wf	PROPN
iajs-2379	181	134	of	of	ADP
iajs-2379	181	135	the	the	DET
iajs-2379	181	136	se	se	PROPN
iajs-2379	181	137	,	,	PUNCT
iajs-2379	181	138	since	since	SCONJ
iajs-2379	181	139	(	(	PUNCT
iajs-2379	181	140	⃗	⃗	PROPN
iajs-2379	181	141	)	)	PUNCT
iajs-2379	181	142	is	be	AUX
iajs-2379	181	143	w.l.s.c	w.l.s.c	PROPN
iajs-2379	181	144	.	.	PUNCT
iajs-2379	181	145	from	from	ADP
iajs-2379	181	146	lemma4.1	lemma4.1	PUNCT
iajs-2379	181	147	and	and	CCONJ
iajs-2379	181	148	since	since	SCONJ
iajs-2379	181	149	⃗	⃗	PROPN
iajs-2379	181	150	⃗̅	⃗̅	NOUN
iajs-2379	181	151	weakly	weakly	ADV
iajs-2379	181	152	in	in	ADP
iajs-2379	181	153	(	(	PUNCT
iajs-2379	181	154	(	(	PUNCT
iajs-2379	181	155	)	)	PUNCT
iajs-2379	181	156	)	)	PUNCT
iajs-2379	181	157	,	,	PUNCT
iajs-2379	181	158	then	then	ADV
iajs-2379	181	159	(	(	PUNCT
iajs-2379	181	160	⃗	⃗	PROPN
iajs-2379	181	161	)	)	PUNCT
iajs-2379	181	162	⃗⃗	⃗⃗	PROPN
iajs-2379	181	163	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	181	164	(	(	PUNCT
iajs-2379	181	165	⃗	⃗	PROPN
iajs-2379	181	166	)	)	PUNCT
iajs-2379	181	167	(	(	PUNCT
iajs-2379	181	168	⃗	⃗	PROPN
iajs-2379	181	169	)	)	PUNCT
iajs-2379	181	170	(	(	PUNCT
iajs-2379	181	171	⃗̅	⃗̅	NOUN
iajs-2379	181	172	)	)	PUNCT
iajs-2379	181	173	(	(	PUNCT
iajs-2379	181	174	⃗	⃗	PROPN
iajs-2379	181	175	)	)	PUNCT
iajs-2379	181	176	⃗⃗̅	⃗⃗̅	NOUN
iajs-2379	181	177	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	181	178	(	(	PUNCT
iajs-2379	181	179	⃗̅	⃗̅	PROPN
iajs-2379	181	180	)	)	PUNCT
iajs-2379	181	181	⃗⃗̅	⃗⃗̅	PROPN
iajs-2379	181	182	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	181	183	(	(	PUNCT
iajs-2379	181	184	⃗̅	⃗̅	PROPN
iajs-2379	181	185	)	)	PUNCT
iajs-2379	181	186	.	.	PUNCT
iajs-2379	182	1	then	then	ADV
iajs-2379	182	2	⃗	⃗	PROPN
iajs-2379	182	3	is	be	AUX
iajs-2379	182	4	a	a	DET
iajs-2379	182	5	ccoc	ccoc	NOUN
iajs-2379	182	6	.	.	PUNCT
iajs-2379	183	1	5	5	X
iajs-2379	183	2	.	.	X
iajs-2379	183	3	the	the	DET
iajs-2379	183	4	nco	nco	NOUN
iajs-2379	183	5	:	:	PUNCT
iajs-2379	183	6	in	in	ADP
iajs-2379	183	7	order	order	NOUN
iajs-2379	183	8	to	to	PART
iajs-2379	183	9	state	state	VERB
iajs-2379	183	10	the	the	DET
iajs-2379	183	11	ncs	ncs	NOUN
iajs-2379	183	12	for	for	ADP
iajs-2379	183	13	ccoc	ccoc	PROPN
iajs-2379	183	14	,	,	PUNCT
iajs-2379	183	15	the	the	DET
iajs-2379	183	16	fd	fd	PROPN
iajs-2379	183	17	of	of	ADP
iajs-2379	183	18	the	the	DET
iajs-2379	183	19	cost	cost	NOUN
iajs-2379	183	20	function	function	NOUN
iajs-2379	183	21	(	(	PUNCT
iajs-2379	183	22	10	10	NUM
iajs-2379	183	23	)	)	PUNCT
iajs-2379	183	24	is	be	AUX
iajs-2379	183	25	derived	derive	VERB
iajs-2379	183	26	and	and	CCONJ
iajs-2379	183	27	the	the	DET
iajs-2379	183	28	theorem	theorem	NOUN
iajs-2379	183	29	for	for	ADP
iajs-2379	183	30	the	the	DET
iajs-2379	183	31	nco	nco	NOUN
iajs-2379	183	32	is	be	AUX
iajs-2379	183	33	proved	prove	VERB
iajs-2379	183	34	.	.	PUNCT
iajs-2379	184	1	theorem	theorem	VERB
iajs-2379	184	2	5.1	5.1	NUM
iajs-2379	184	3	:	:	PUNCT
iajs-2379	184	4	consider	consider	VERB
iajs-2379	184	5	(	(	PUNCT
iajs-2379	184	6	⃗	⃗	PROPN
iajs-2379	184	7	)	)	PUNCT
iajs-2379	184	8	is	be	AUX
iajs-2379	184	9	given	give	VERB
iajs-2379	184	10	by	by	ADP
iajs-2379	184	11	(	(	PUNCT
iajs-2379	184	12	10	10	NUM
iajs-2379	184	13	)	)	PUNCT
iajs-2379	184	14	and	and	CCONJ
iajs-2379	184	15	the	the	DET
iajs-2379	184	16	taes	taes	NOUN
iajs-2379	184	17	of	of	ADP
iajs-2379	184	18	the	the	DET
iajs-2379	184	19	ste	ste	PROPN
iajs-2379	184	20	(	(	PUNCT
iajs-2379	184	21	1	1	NUM
iajs-2379	184	22	-	-	SYM
iajs-2379	184	23	9	9	NUM
iajs-2379	184	24	)	)	PUNCT
iajs-2379	184	25	are	be	AUX
iajs-2379	184	26	given	give	VERB
iajs-2379	184	27	by	by	ADP
iajs-2379	184	28	(	(	PUNCT
iajs-2379	184	29	)	)	PUNCT
iajs-2379	184	30	(	(	PUNCT
iajs-2379	184	31	80	80	NUM
iajs-2379	184	32	)	)	PUNCT
iajs-2379	184	33	(	(	PUNCT
iajs-2379	184	34	)	)	PUNCT
iajs-2379	184	35	(	(	PUNCT
iajs-2379	184	36	81	81	NUM
iajs-2379	184	37	)	)	PUNCT
iajs-2379	184	38	(	(	PUNCT
iajs-2379	184	39	)	)	PUNCT
iajs-2379	184	40	(	(	PUNCT
iajs-2379	184	41	82	82	NUM
iajs-2379	184	42	)	)	PUNCT
iajs-2379	184	43	(	(	PUNCT
iajs-2379	184	44	)	)	PUNCT
iajs-2379	184	45	(	(	PUNCT
iajs-2379	184	46	83	83	NUM
iajs-2379	184	47	)	)	PUNCT
iajs-2379	184	48	(	(	PUNCT
iajs-2379	184	49	)	)	PUNCT
iajs-2379	184	50	(	(	PUNCT
iajs-2379	184	51	84	84	NUM
iajs-2379	184	52	)	)	PUNCT
iajs-2379	184	53	(	(	PUNCT
iajs-2379	184	54	)	)	PUNCT
iajs-2379	184	55	(	(	PUNCT
iajs-2379	184	56	85	85	NUM
iajs-2379	184	57	)	)	PUNCT
iajs-2379	184	58	then	then	ADV
iajs-2379	184	59	(	(	PUNCT
iajs-2379	184	60	)	)	PUNCT
iajs-2379	184	61	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	184	62	and	and	CCONJ
iajs-2379	184	63	the	the	DET
iajs-2379	184	64	fd	fd	PROPN
iajs-2379	184	65	of	of	ADP
iajs-2379	184	66	is	be	AUX
iajs-2379	184	67	given	give	VERB
iajs-2379	184	68	by	by	ADP
iajs-2379	184	69	(	(	PUNCT
iajs-2379	184	70	(	(	PUNCT
iajs-2379	184	71	⃗	⃗	PROPN
iajs-2379	184	72	)	)	PUNCT
iajs-2379	184	73	⃗	⃗	PROPN
iajs-2379	184	74	)	)	PUNCT
iajs-2379	184	75	(	(	PUNCT
iajs-2379	184	76	⃗	⃗	PROPN
iajs-2379	184	77	⃗	⃗	PROPN
iajs-2379	184	78	)	)	PUNCT
iajs-2379	184	79	proof	proof	NOUN
iajs-2379	184	80	:	:	PUNCT
iajs-2379	184	81	the	the	DET
iajs-2379	184	82	wf	wf	PROPN
iajs-2379	184	83	of	of	ADP
iajs-2379	184	84	(	(	PUNCT
iajs-2379	184	85	80–85	80–85	NUM
iajs-2379	184	86	)	)	PUNCT
iajs-2379	184	87	for	for	ADP
iajs-2379	184	88	is	be	AUX
iajs-2379	184	89	given	give	VERB
iajs-2379	184	90	by	by	ADP
iajs-2379	184	91	〈	〈	PROPN
iajs-2379	184	92	〉	〉	NOUN
iajs-2379	184	93	(	(	PUNCT
iajs-2379	184	94	)	)	PUNCT
iajs-2379	184	95	(	(	PUNCT
iajs-2379	184	96	)	)	PUNCT
iajs-2379	184	97	(	(	PUNCT
iajs-2379	184	98	)	)	PUNCT
iajs-2379	184	99	(	(	PUNCT
iajs-2379	184	100	)	)	PUNCT
iajs-2379	184	101	(	(	PUNCT
iajs-2379	184	102	)	)	PUNCT
iajs-2379	184	103	(	(	PUNCT
iajs-2379	184	104	86	86	NUM
iajs-2379	184	105	)	)	PUNCT
iajs-2379	184	106	〈	〈	PROPN
iajs-2379	184	107	〉	〉	NOUN
iajs-2379	184	108	(	(	PUNCT
iajs-2379	184	109	)	)	PUNCT
iajs-2379	184	110	(	(	PUNCT
iajs-2379	184	111	)	)	PUNCT
iajs-2379	184	112	(	(	PUNCT
iajs-2379	184	113	)	)	PUNCT
iajs-2379	184	114	(	(	PUNCT
iajs-2379	184	115	)	)	PUNCT
iajs-2379	184	116	=	=	SYM
iajs-2379	184	117	(	(	PUNCT
iajs-2379	184	118	)	)	PUNCT
iajs-2379	184	119	(	(	PUNCT
iajs-2379	184	120	87	87	NUM
iajs-2379	184	121	)	)	PUNCT
iajs-2379	184	122	〈	〈	PROPN
iajs-2379	184	123	〉	〉	NOUN
iajs-2379	184	124	(	(	PUNCT
iajs-2379	184	125	)	)	PUNCT
iajs-2379	184	126	(	(	PUNCT
iajs-2379	184	127	)	)	PUNCT
iajs-2379	184	128	(	(	PUNCT
iajs-2379	184	129	)	)	PUNCT
iajs-2379	184	130	(	(	PUNCT
iajs-2379	184	131	)	)	PUNCT
iajs-2379	184	132	=	=	SYM
iajs-2379	184	133	(	(	PUNCT
iajs-2379	184	134	)	)	PUNCT
iajs-2379	184	135	(	(	PUNCT
iajs-2379	184	136	88	88	NUM
iajs-2379	184	137	)	)	PUNCT
iajs-2379	184	138	the	the	DET
iajs-2379	184	139	existence	existence	NOUN
iajs-2379	184	140	of	of	ADP
iajs-2379	184	141	a	a	DET
iajs-2379	184	142	unique	unique	ADJ
iajs-2379	184	143	solution	solution	NOUN
iajs-2379	184	144	of	of	ADP
iajs-2379	184	145	(	(	PUNCT
iajs-2379	184	146	86	86	NUM
iajs-2379	184	147	88	88	NUM
iajs-2379	184	148	)	)	PUNCT
iajs-2379	184	149	can	can	AUX
iajs-2379	184	150	be	be	AUX
iajs-2379	184	151	proved	prove	VERB
iajs-2379	184	152	by	by	ADP
iajs-2379	184	153	the	the	DET
iajs-2379	184	154	same	same	ADJ
iajs-2379	184	155	manner	manner	NOUN
iajs-2379	184	156	which	which	PRON
iajs-2379	184	157	is	be	AUX
iajs-2379	184	158	used	use	VERB
iajs-2379	184	159	in	in	ADP
iajs-2379	184	160	the	the	DET
iajs-2379	184	161	proof	proof	NOUN
iajs-2379	184	162	of	of	ADP
iajs-2379	184	163	theorem	theorem	NOUN
iajs-2379	184	164	in	in	ADP
iajs-2379	184	165	(	(	PUNCT
iajs-2379	184	166	52.a	52.a	NUM
iajs-2379	184	167	)	)	PUNCT
iajs-2379	184	168	,	,	PUNCT
iajs-2379	184	169	(	(	PUNCT
iajs-2379	184	170	53.a	53.a	NUM
iajs-2379	184	171	)	)	PUNCT
iajs-2379	184	172	and	and	CCONJ
iajs-2379	184	173	(	(	PUNCT
iajs-2379	184	174	54.a	54.a	NOUN
iajs-2379	184	175	)	)	PUNCT
iajs-2379	184	176	respectively	respectively	ADV
iajs-2379	184	177	,	,	PUNCT
iajs-2379	184	178	these	these	DET
iajs-2379	184	179	equations	equation	NOUN
iajs-2379	184	180	become	become	VERB
iajs-2379	184	181	,	,	PUNCT
iajs-2379	184	182	〈	〈	PROPN
iajs-2379	184	183	〉	〉	NOUN
iajs-2379	184	184	(	(	PUNCT
iajs-2379	184	185	)	)	PUNCT
iajs-2379	184	186	(	(	PUNCT
iajs-2379	184	187	)	)	PUNCT
iajs-2379	184	188	(	(	PUNCT
iajs-2379	184	189	)	)	PUNCT
iajs-2379	184	190	(	(	PUNCT
iajs-2379	184	191	)	)	PUNCT
iajs-2379	184	192	(	(	PUNCT
iajs-2379	184	193	)	)	PUNCT
iajs-2379	184	194	(	(	PUNCT
iajs-2379	184	195	89	89	NUM
iajs-2379	184	196	)	)	PUNCT
iajs-2379	184	197	〈	〈	PROPN
iajs-2379	184	198	〉	〉	NOUN
iajs-2379	184	199	(	(	PUNCT
iajs-2379	184	200	)	)	PUNCT
iajs-2379	184	201	(	(	PUNCT
iajs-2379	184	202	)	)	PUNCT
iajs-2379	184	203	(	(	PUNCT
iajs-2379	184	204	)	)	PUNCT
iajs-2379	184	205	(	(	PUNCT
iajs-2379	184	206	)	)	PUNCT
iajs-2379	184	207	(	(	PUNCT
iajs-2379	184	208	)	)	PUNCT
iajs-2379	184	209	(	(	PUNCT
iajs-2379	184	210	90	90	NUM
iajs-2379	184	211	)	)	PUNCT
iajs-2379	184	212	〈	〈	NOUN
iajs-2379	184	213	〉	〉	NOUN
iajs-2379	184	214	(	(	PUNCT
iajs-2379	184	215	)	)	PUNCT
iajs-2379	184	216	(	(	PUNCT
iajs-2379	184	217	)	)	PUNCT
iajs-2379	184	218	(	(	PUNCT
iajs-2379	184	219	)	)	PUNCT
iajs-2379	184	220	(	(	PUNCT
iajs-2379	184	221	)	)	PUNCT
iajs-2379	184	222	(	(	PUNCT
iajs-2379	184	223	)	)	PUNCT
iajs-2379	184	224	(	(	PUNCT
iajs-2379	184	225	91	91	NUM
iajs-2379	184	226	)	)	PUNCT
iajs-2379	184	227	also	also	ADV
iajs-2379	184	228	,	,	PUNCT
iajs-2379	184	229	substituting	substitute	VERB
iajs-2379	184	230	and	and	CCONJ
iajs-2379	184	231	in	in	ADP
iajs-2379	184	232	(	(	PUNCT
iajs-2379	184	233	86	86	NUM
iajs-2379	184	234	88	88	NUM
iajs-2379	184	235	)	)	PUNCT
iajs-2379	184	236	respectively	respectively	ADV
iajs-2379	184	237	,	,	PUNCT
iajs-2379	184	238	to	to	PART
iajs-2379	184	239	get	get	VERB
iajs-2379	184	240	〈	〈	PROPN
iajs-2379	184	241	〉	〉	NOUN
iajs-2379	184	242	(	(	PUNCT
iajs-2379	184	243	)	)	PUNCT
iajs-2379	184	244	(	(	PUNCT
iajs-2379	184	245	)	)	PUNCT
iajs-2379	184	246	(	(	PUNCT
iajs-2379	184	247	)	)	PUNCT
iajs-2379	184	248	(	(	PUNCT
iajs-2379	184	249	)	)	PUNCT
iajs-2379	184	250	(	(	PUNCT
iajs-2379	184	251	)	)	PUNCT
iajs-2379	184	252	(	(	PUNCT
iajs-2379	184	253	92	92	NUM
iajs-2379	184	254	)	)	PUNCT
iajs-2379	184	255	〈	〈	NOUN
iajs-2379	184	256	〉	〉	NOUN
iajs-2379	184	257	(	(	PUNCT
iajs-2379	184	258	)	)	PUNCT
iajs-2379	184	259	(	(	PUNCT
iajs-2379	184	260	)	)	PUNCT
iajs-2379	184	261	(	(	PUNCT
iajs-2379	184	262	)	)	PUNCT
iajs-2379	184	263	(	(	PUNCT
iajs-2379	184	264	)	)	PUNCT
iajs-2379	184	265	(	(	PUNCT
iajs-2379	184	266	)	)	PUNCT
iajs-2379	184	267	(	(	PUNCT
iajs-2379	184	268	93	93	NUM
iajs-2379	184	269	)	)	PUNCT
iajs-2379	184	270	〈	〈	NOUN
iajs-2379	184	271	〉	〉	NOUN
iajs-2379	184	272	(	(	PUNCT
iajs-2379	184	273	)	)	PUNCT
iajs-2379	184	274	(	(	PUNCT
iajs-2379	184	275	)	)	PUNCT
iajs-2379	184	276	(	(	PUNCT
iajs-2379	184	277	)	)	PUNCT
iajs-2379	184	278	(	(	PUNCT
iajs-2379	184	279	)	)	PUNCT
iajs-2379	184	280	(	(	PUNCT
iajs-2379	184	281	)	)	PUNCT
iajs-2379	184	282	(	(	PUNCT
iajs-2379	184	283	94	94	X
iajs-2379	184	284	)	)	PUNCT
iajs-2379	184	285	integrating	integrate	VERB
iajs-2379	184	286	both	both	DET
iajs-2379	184	287	sides	side	NOUN
iajs-2379	184	288	of	of	ADP
iajs-2379	184	289	equations	equation	NOUN
iajs-2379	184	290	(	(	PUNCT
iajs-2379	184	291	89	89	NUM
iajs-2379	184	292	94	94	NUM
iajs-2379	184	293	)	)	PUNCT
iajs-2379	184	294	w.r.t	w.r.t	NOUN
iajs-2379	184	295	.	.	PUNCT
iajs-2379	185	1	t	t	PROPN
iajs-2379	185	2	from	from	ADP
iajs-2379	185	3	0	0	NUM
iajs-2379	185	4	to	to	ADP
iajs-2379	185	5	t	t	PROPN
iajs-2379	185	6	,	,	PUNCT
iajs-2379	185	7	using	use	VERB
iajs-2379	185	8	integration	integration	NOUN
iajs-2379	185	9	by	by	ADP
iajs-2379	185	10	parts	part	NOUN
iajs-2379	185	11	for	for	ADP
iajs-2379	185	12	the	the	DET
iajs-2379	185	13	terms	term	NOUN
iajs-2379	185	14	of	of	ADP
iajs-2379	185	15	the	the	DET
iajs-2379	185	16	l.h.s	l.h.s	NOUN
iajs-2379	185	17	.	.	PUNCT
iajs-2379	186	1	of	of	ADP
iajs-2379	186	2	each	each	PRON
iajs-2379	186	3	of	of	ADP
iajs-2379	186	4	the	the	DET
iajs-2379	186	5	obtained	obtain	VERB
iajs-2379	186	6	equations	equation	NOUN
iajs-2379	186	7	from	from	ADP
iajs-2379	186	8	(	(	PUNCT
iajs-2379	186	9	92–94	92–94	NUM
iajs-2379	186	10	)	)	PUNCT
iajs-2379	186	11	,	,	PUNCT
iajs-2379	186	12	then	then	ADV
iajs-2379	186	13	subtracting	subtract	VERB
iajs-2379	186	14	each	each	DET
iajs-2379	186	15	one	one	NUM
iajs-2379	186	16	of	of	ADP
iajs-2379	186	17	the	the	DET
iajs-2379	186	18	obtained	obtain	VERB
iajs-2379	186	19	equations	equation	NOUN
iajs-2379	186	20	from	from	ADP
iajs-2379	186	21	it	it	PRON
iajs-2379	186	22	's	's	PART
iajs-2379	186	23	corresponding	correspond	VERB
iajs-2379	186	24	equation	equation	NOUN
iajs-2379	186	25	of	of	ADP
iajs-2379	186	26	(	(	PUNCT
iajs-2379	186	27	89–91	89–91	NUM
iajs-2379	186	28	)	)	PUNCT
iajs-2379	186	29	,	,	PUNCT
iajs-2379	186	30	add	add	VERB
iajs-2379	186	31	all	all	DET
iajs-2379	186	32	three	three	NUM
iajs-2379	186	33	result	result	NOUN
iajs-2379	186	34	get	get	VERB
iajs-2379	186	35	141	141	NUM
iajs-2379	186	36	ibn	ibn	PROPN
iajs-2379	186	37	al	al	PROPN
iajs-2379	186	38	-	-	PUNCT
iajs-2379	186	39	haitham	haitham	PROPN
iajs-2379	186	40	jour	jour	X
iajs-2379	186	41	.	.	PROPN
iajs-2379	187	1	for	for	ADP
iajs-2379	187	2	pure	pure	ADJ
iajs-2379	187	3	&	&	CCONJ
iajs-2379	187	4	appl	appl	PROPN
iajs-2379	187	5	.	.	PUNCT
iajs-2379	188	1	sci	sci	PROPN
iajs-2379	188	2	.	.	PROPN
iajs-2379	189	1	33	33	NUM
iajs-2379	189	2	(	(	PUNCT
iajs-2379	189	3	1	1	NUM
iajs-2379	189	4	)	)	PUNCT
iajs-2379	189	5	2020	2020	NUM
iajs-2379	190	1	〈	〈	PROPN
iajs-2379	190	2	(	(	PUNCT
iajs-2379	190	3	)	)	PUNCT
iajs-2379	190	4	〉	〉	NOUN
iajs-2379	190	5	(	(	PUNCT
iajs-2379	190	6	(	(	PUNCT
iajs-2379	190	7	)	)	PUNCT
iajs-2379	190	8	)	)	PUNCT
iajs-2379	190	9	(	(	PUNCT
iajs-2379	190	10	)	)	PUNCT
iajs-2379	190	11	(	(	PUNCT
iajs-2379	190	12	)	)	PUNCT
iajs-2379	190	13	(	(	PUNCT
iajs-2379	190	14	)	)	PUNCT
iajs-2379	190	15	(	(	PUNCT
iajs-2379	190	16	)	)	PUNCT
iajs-2379	190	17	(	(	PUNCT
iajs-2379	190	18	95	95	NUM
iajs-2379	190	19	)	)	PUNCT
iajs-2379	190	20	〈	〈	PROPN
iajs-2379	190	21	(	(	PUNCT
iajs-2379	190	22	)	)	PUNCT
iajs-2379	190	23	〉	〉	NOUN
iajs-2379	190	24	(	(	PUNCT
iajs-2379	190	25	(	(	PUNCT
iajs-2379	190	26	)	)	PUNCT
iajs-2379	190	27	)	)	PUNCT
iajs-2379	190	28	(	(	PUNCT
iajs-2379	190	29	)	)	PUNCT
iajs-2379	190	30	(	(	PUNCT
iajs-2379	190	31	)	)	PUNCT
iajs-2379	190	32	(	(	PUNCT
iajs-2379	190	33	)	)	PUNCT
iajs-2379	190	34	(	(	PUNCT
iajs-2379	190	35	)	)	PUNCT
iajs-2379	190	36	(	(	PUNCT
iajs-2379	190	37	96	96	NUM
iajs-2379	190	38	)	)	PUNCT
iajs-2379	190	39	〈	〈	PROPN
iajs-2379	190	40	(	(	PUNCT
iajs-2379	190	41	)	)	PUNCT
iajs-2379	190	42	〉	〉	NOUN
iajs-2379	190	43	(	(	PUNCT
iajs-2379	190	44	(	(	PUNCT
iajs-2379	190	45	)	)	PUNCT
iajs-2379	190	46	)	)	PUNCT
iajs-2379	190	47	(	(	PUNCT
iajs-2379	190	48	)	)	PUNCT
iajs-2379	190	49	(	(	PUNCT
iajs-2379	190	50	)	)	PUNCT
iajs-2379	190	51	(	(	PUNCT
iajs-2379	190	52	)	)	PUNCT
iajs-2379	190	53	(	(	PUNCT
iajs-2379	190	54	)	)	PUNCT
iajs-2379	190	55	(	(	PUNCT
iajs-2379	190	56	97	97	NUM
iajs-2379	190	57	)	)	PUNCT
iajs-2379	190	58	which	which	PRON
iajs-2379	190	59	means	mean	VERB
iajs-2379	190	60	the	the	DET
iajs-2379	190	61	cv	cv	PROPN
iajs-2379	190	62	(	(	PUNCT
iajs-2379	190	63	,	,	PUNCT
iajs-2379	190	64	,	,	PUNCT
iajs-2379	190	65	)	)	PUNCT
iajs-2379	190	66	gives	give	VERB
iajs-2379	190	67	the	the	DET
iajs-2379	190	68	solution	solution	NOUN
iajs-2379	190	69	(	(	PUNCT
iajs-2379	190	70	,	,	PUNCT
iajs-2379	190	71	)	)	PUNCT
iajs-2379	190	72	of	of	ADP
iajs-2379	190	73	(	(	PUNCT
iajs-2379	190	74	95	95	NUM
iajs-2379	190	75	97	97	NUM
iajs-2379	190	76	)	)	PUNCT
iajs-2379	190	77	.	.	PUNCT
iajs-2379	191	1	now	now	ADV
iajs-2379	191	2	,	,	PUNCT
iajs-2379	191	3	from	from	ADP
iajs-2379	191	4	the	the	DET
iajs-2379	191	5	cost	cost	NOUN
iajs-2379	191	6	function	function	NOUN
iajs-2379	191	7	,	,	PUNCT
iajs-2379	191	8	we	we	PRON
iajs-2379	191	9	have	have	VERB
iajs-2379	191	10	(	(	PUNCT
iajs-2379	191	11	⃗	⃗	PROPN
iajs-2379	191	12	⃗	⃗	PROPN
iajs-2379	191	13	)	)	PUNCT
iajs-2379	191	14	(	(	PUNCT
iajs-2379	191	15	⃗	⃗	PROPN
iajs-2379	191	16	)	)	PUNCT
iajs-2379	191	17	=	=	SYM
iajs-2379	192	1	(	(	PUNCT
iajs-2379	192	2	,	,	PUNCT
iajs-2379	192	3	)	)	PUNCT
iajs-2379	192	4	(	(	PUNCT
iajs-2379	192	5	,	,	PUNCT
iajs-2379	192	6	)	)	PUNCT
iajs-2379	192	7	(	(	PUNCT
iajs-2379	192	8	,	,	PUNCT
iajs-2379	192	9	)	)	PUNCT
iajs-2379	192	10	(	(	PUNCT
iajs-2379	192	11	,	,	PUNCT
iajs-2379	192	12	)	)	PUNCT
iajs-2379	192	13	(	(	PUNCT
iajs-2379	192	14	,	,	PUNCT
iajs-2379	192	15	)	)	PUNCT
iajs-2379	192	16	(	(	PUNCT
iajs-2379	192	17	,	,	PUNCT
iajs-2379	192	18	)	)	PUNCT
iajs-2379	192	19	‖	‖	PROPN
iajs-2379	193	1	‖	‖	PROPN
iajs-2379	193	2	‖	‖	PROPN
iajs-2379	193	3	⃗	⃗	PROPN
iajs-2379	193	4	‖	‖	PROPN
iajs-2379	193	5	,	,	PUNCT
iajs-2379	193	6	or	or	CCONJ
iajs-2379	193	7	(	(	PUNCT
iajs-2379	193	8	⃗	⃗	PROPN
iajs-2379	193	9	⃗	⃗	PROPN
iajs-2379	193	10	)	)	PUNCT
iajs-2379	193	11	(	(	PUNCT
iajs-2379	193	12	⃗	⃗	PROPN
iajs-2379	193	13	)	)	PUNCT
iajs-2379	193	14	=	=	SYM
iajs-2379	193	15	(	(	PUNCT
iajs-2379	193	16	⃗	⃗	PROPN
iajs-2379	193	17	⃗	⃗	X
iajs-2379	193	18	)	)	PUNCT
iajs-2379	193	19	‖	‖	PROPN
iajs-2379	193	20	‖	‖	PROPN
iajs-2379	193	21	‖	‖	PROPN
iajs-2379	193	22	⃗	⃗	PROPN
iajs-2379	193	23	‖	‖	PROPN
iajs-2379	193	24	from	from	ADP
iajs-2379	193	25	the	the	DET
iajs-2379	193	26	first	first	ADJ
iajs-2379	193	27	results	result	NOUN
iajs-2379	193	28	of	of	ADP
iajs-2379	193	29	theorem	theorem	NOUN
iajs-2379	193	30	4.1	4.1	NUM
iajs-2379	193	31	,	,	PUNCT
iajs-2379	193	32	we	we	PRON
iajs-2379	193	33	have	have	VERB
iajs-2379	193	34	‖	‖	ADJ
iajs-2379	194	1	‖	‖	PROPN
iajs-2379	194	2	(	(	PUNCT
iajs-2379	194	3	⃗	⃗	PROPN
iajs-2379	194	4	)	)	PUNCT
iajs-2379	194	5	‖	‖	PROPN
iajs-2379	195	1	⃗	⃗	PROPN
iajs-2379	195	2	‖	‖	PROPN
iajs-2379	195	3	and	and	CCONJ
iajs-2379	195	4	‖	‖	PROPN
iajs-2379	195	5	⃗	⃗	PROPN
iajs-2379	195	6	‖	‖	PROPN
iajs-2379	195	7	(	(	PUNCT
iajs-2379	195	8	⃗	⃗	PROPN
iajs-2379	195	9	)	)	PUNCT
iajs-2379	195	10	‖	‖	PROPN
iajs-2379	196	1	⃗	⃗	PROPN
iajs-2379	196	2	‖	‖	PROPN
iajs-2379	196	3	with	with	ADP
iajs-2379	196	4	(	(	PUNCT
iajs-2379	196	5	⃗	⃗	PROPN
iajs-2379	196	6	)	)	PUNCT
iajs-2379	196	7	‖	‖	PROPN
iajs-2379	196	8	⃗	⃗	PROPN
iajs-2379	196	9	‖	‖	PROPN
iajs-2379	196	10	where	where	SCONJ
iajs-2379	196	11	(	(	PUNCT
iajs-2379	196	12	⃗	⃗	PROPN
iajs-2379	196	13	)	)	PUNCT
iajs-2379	196	14	(	(	PUNCT
iajs-2379	196	15	⃗	⃗	PROPN
iajs-2379	196	16	)	)	PUNCT
iajs-2379	196	17	,	,	PUNCT
iajs-2379	196	18	as	as	SCONJ
iajs-2379	196	19	‖	‖	PROPN
iajs-2379	196	20	⃗	⃗	PROPN
iajs-2379	196	21	‖	‖	PROPN
iajs-2379	196	22	then	then	ADV
iajs-2379	196	23	(	(	PUNCT
iajs-2379	196	24	⃗	⃗	PROPN
iajs-2379	196	25	⃗	⃗	PROPN
iajs-2379	196	26	)	)	PUNCT
iajs-2379	196	27	(	(	PUNCT
iajs-2379	196	28	⃗	⃗	PROPN
iajs-2379	196	29	)	)	PUNCT
iajs-2379	196	30	(	(	PUNCT
iajs-2379	196	31	⃗	⃗	PROPN
iajs-2379	196	32	⃗	⃗	PROPN
iajs-2379	196	33	)	)	PUNCT
iajs-2379	196	34	(	(	PUNCT
iajs-2379	196	35	⃗	⃗	PROPN
iajs-2379	196	36	)	)	PUNCT
iajs-2379	196	37	‖	‖	PROPN
iajs-2379	197	1	⃗	⃗	PROPN
iajs-2379	197	2	‖	‖	PROPN
iajs-2379	197	3	with	with	ADP
iajs-2379	197	4	(	(	PUNCT
iajs-2379	197	5	⃗	⃗	PROPN
iajs-2379	197	6	)	)	PUNCT
iajs-2379	197	7	(	(	PUNCT
iajs-2379	197	8	⃗	⃗	PROPN
iajs-2379	197	9	)	)	PUNCT
iajs-2379	197	10	(	(	PUNCT
iajs-2379	197	11	⃗	⃗	PROPN
iajs-2379	197	12	)	)	PUNCT
iajs-2379	197	13	where	where	SCONJ
iajs-2379	197	14	(	(	PUNCT
iajs-2379	197	15	⃗	⃗	PROPN
iajs-2379	197	16	)	)	PUNCT
iajs-2379	197	17	as	as	SCONJ
iajs-2379	197	18	‖	‖	PROPN
iajs-2379	197	19	⃗	⃗	PROPN
iajs-2379	197	20	‖	‖	ADJ
iajs-2379	197	21	using	use	VERB
iajs-2379	197	22	the	the	DET
iajs-2379	197	23	definition	definition	NOUN
iajs-2379	197	24	of	of	ADP
iajs-2379	197	25	fd	fd	PROPN
iajs-2379	197	26	of	of	ADP
iajs-2379	197	27	,	,	PUNCT
iajs-2379	197	28	one	one	PRON
iajs-2379	197	29	has	have	VERB
iajs-2379	197	30	(	(	PUNCT
iajs-2379	197	31	(	(	PUNCT
iajs-2379	197	32	⃗	⃗	PROPN
iajs-2379	197	33	)	)	PUNCT
iajs-2379	197	34	⃗	⃗	PROPN
iajs-2379	197	35	)	)	PUNCT
iajs-2379	198	1	(	(	PUNCT
iajs-2379	198	2	⃗	⃗	PROPN
iajs-2379	198	3	⃗	⃗	X
iajs-2379	198	4	)	)	PUNCT
iajs-2379	198	5	theorem	theorem	VERB
iajs-2379	198	6	5.2	5.2	NUM
iajs-2379	198	7	:	:	PUNCT
iajs-2379	198	8	the	the	DET
iajs-2379	198	9	ccoc	ccoc	NOUN
iajs-2379	198	10	of	of	ADP
iajs-2379	198	11	the	the	DET
iajs-2379	198	12	above	above	ADJ
iajs-2379	198	13	problem	problem	NOUN
iajs-2379	198	14	is	be	AUX
iajs-2379	198	15	(	(	PUNCT
iajs-2379	198	16	⃗	⃗	PROPN
iajs-2379	198	17	)	)	PUNCT
iajs-2379	198	18	⃗	⃗	PROPN
iajs-2379	198	19	with	with	ADP
iajs-2379	198	20	⃗⃗	⃗⃗	PROPN
iajs-2379	198	21	and	and	CCONJ
iajs-2379	198	22	⃗⃗	⃗⃗	NOUN
iajs-2379	198	23	.	.	PUNCT
iajs-2379	199	1	proof	proof	NOUN
iajs-2379	199	2	:	:	PUNCT
iajs-2379	199	3	if	if	SCONJ
iajs-2379	199	4	⃗	⃗	PROPN
iajs-2379	199	5	is	be	AUX
iajs-2379	199	6	an	an	DET
iajs-2379	199	7	ccoc	ccoc	NOUN
iajs-2379	199	8	of	of	ADP
iajs-2379	199	9	the	the	DET
iajs-2379	199	10	problem	problem	NOUN
iajs-2379	199	11	,	,	PUNCT
iajs-2379	199	12	then	then	ADV
iajs-2379	199	13	(	(	PUNCT
iajs-2379	199	14	⃗̅	⃗̅	PROPN
iajs-2379	199	15	)	)	PUNCT
iajs-2379	199	16	⃗⃗	⃗⃗	PROPN
iajs-2379	199	17	⃗⃗⃗	⃗⃗⃗	NOUN
iajs-2379	199	18	(	(	PUNCT
iajs-2379	199	19	⃗	⃗	PROPN
iajs-2379	199	20	)	)	PUNCT
iajs-2379	199	21	,	,	PUNCT
iajs-2379	199	22	⃗	⃗	PROPN
iajs-2379	199	23	(	(	PUNCT
iajs-2379	199	24	(	(	PUNCT
iajs-2379	199	25	)	)	PUNCT
iajs-2379	199	26	)	)	PUNCT
iajs-2379	199	27	,	,	PUNCT
iajs-2379	199	28	i.e.	i.e.	X
iajs-2379	199	29	(	(	PUNCT
iajs-2379	199	30	⃗̅	⃗̅	PROPN
iajs-2379	199	31	)	)	PUNCT
iajs-2379	199	32	⃗̅	⃗̅	NOUN
iajs-2379	199	33	the	the	DET
iajs-2379	199	34	nco	nco	NOUN
iajs-2379	199	35	is	be	AUX
iajs-2379	199	36	(	(	PUNCT
iajs-2379	199	37	⃗̅	⃗̅	PROPN
iajs-2379	199	38	⃗	⃗	PROPN
iajs-2379	199	39	)	)	PUNCT
iajs-2379	200	1	⃗	⃗	PROPN
iajs-2379	200	2	⃗⃗	⃗⃗	PROPN
iajs-2379	200	3	⃗̅	⃗̅	PROPN
iajs-2379	200	4	(	(	PUNCT
iajs-2379	200	5	⃗̅	⃗̅	PROPN
iajs-2379	200	6	⃗⃗	⃗⃗	PROPN
iajs-2379	200	7	)	)	PUNCT
iajs-2379	200	8	(	(	PUNCT
iajs-2379	200	9	̅	̅	NOUN
iajs-2379	200	10	⃗⃗⃗	⃗⃗⃗	PROPN
iajs-2379	200	11	⃗̅	⃗̅	NOUN
iajs-2379	200	12	)	)	PUNCT
iajs-2379	200	13	,	,	PUNCT
iajs-2379	200	14	⃗⃗	⃗⃗	NOUN
iajs-2379	200	15	(	(	PUNCT
iajs-2379	200	16	(	(	PUNCT
iajs-2379	200	17	)	)	PUNCT
iajs-2379	200	18	)	)	PUNCT
iajs-2379	200	19	6	6	X
iajs-2379	200	20	.	.	PUNCT
iajs-2379	200	21	conclusions	conclusion	NOUN
iajs-2379	200	22	the	the	DET
iajs-2379	200	23	gm	gm	PROPN
iajs-2379	200	24	is	be	AUX
iajs-2379	200	25	employed	employ	VERB
iajs-2379	200	26	to	to	PART
iajs-2379	200	27	prove	prove	VERB
iajs-2379	200	28	the	the	DET
iajs-2379	200	29	existence	existence	NOUN
iajs-2379	200	30	and	and	CCONJ
iajs-2379	200	31	unique	unique	ADJ
iajs-2379	200	32	theorem	theorem	NOUN
iajs-2379	200	33	for	for	ADP
iajs-2379	200	34	a	a	DET
iajs-2379	200	35	svs	svs	NOUN
iajs-2379	200	36	of	of	ADP
iajs-2379	200	37	the	the	DET
iajs-2379	200	38	tspdes	tspde	NOUN
iajs-2379	200	39	of	of	ADP
iajs-2379	200	40	parabolic	parabolic	ADJ
iajs-2379	200	41	type	type	NOUN
iajs-2379	200	42	for	for	ADP
iajs-2379	200	43	fixed	fix	VERB
iajs-2379	200	44	cccv	cccv	NOUN
iajs-2379	200	45	.	.	PUNCT
iajs-2379	201	1	the	the	DET
iajs-2379	201	2	existence	existence	NOUN
iajs-2379	201	3	of	of	ADP
iajs-2379	201	4	a	a	DET
iajs-2379	201	5	ccocv	ccocv	NOUN
iajs-2379	201	6	governing	govern	VERB
iajs-2379	201	7	with	with	ADP
iajs-2379	201	8	the	the	DET
iajs-2379	201	9	considered	consider	VERB
iajs-2379	201	10	tlpdes	tlpde	NOUN
iajs-2379	201	11	of	of	ADP
iajs-2379	201	12	parabolic	parabolic	ADJ
iajs-2379	201	13	type	type	NOUN
iajs-2379	201	14	is	be	AUX
iajs-2379	201	15	proved	prove	VERB
iajs-2379	201	16	.	.	PUNCT
iajs-2379	202	1	the	the	DET
iajs-2379	202	2	existence	existence	NOUN
iajs-2379	202	3	and	and	CCONJ
iajs-2379	202	4	uniqueness	uniqueness	ADJ
iajs-2379	202	5	solution	solution	NOUN
iajs-2379	202	6	of	of	ADP
iajs-2379	202	7	the	the	DET
iajs-2379	202	8	taes	taes	NOUN
iajs-2379	202	9	associated	associate	VERB
iajs-2379	202	10	with	with	ADP
iajs-2379	202	11	the	the	DET
iajs-2379	202	12	tspdes	tspde	NOUN
iajs-2379	202	13	.	.	PUNCT
iajs-2379	203	1	the	the	DET
iajs-2379	203	2	derivation	derivation	NOUN
iajs-2379	203	3	of	of	ADP
iajs-2379	203	4	the	the	DET
iajs-2379	203	5	fréchet	fréchet	NOUN
iajs-2379	203	6	derivative	derivative	NOUN
iajs-2379	203	7	for	for	ADP
iajs-2379	203	8	the	the	DET
iajs-2379	203	9	cost	cost	NOUN
iajs-2379	203	10	function	function	NOUN
iajs-2379	203	11	is	be	AUX
iajs-2379	203	12	obtained	obtain	VERB
iajs-2379	203	13	.	.	PUNCT
iajs-2379	204	1	the	the	DET
iajs-2379	204	2	theorem	theorem	NOUN
iajs-2379	204	3	of	of	ADP
iajs-2379	204	4	the	the	DET
iajs-2379	204	5	nco	nco	NOUN
iajs-2379	204	6	is	be	AUX
iajs-2379	204	7	stated	state	VERB
iajs-2379	204	8	and	and	CCONJ
iajs-2379	204	9	proved	prove	VERB
iajs-2379	204	10	.	.	PUNCT
iajs-2379	205	1	references	reference	NOUN
iajs-2379	205	2	1	1	NUM
iajs-2379	205	3	.	.	PUNCT
iajs-2379	206	1	aro	aro	PROPN
iajs-2379	206	2	,	,	PUNCT
iajs-2379	206	3	m.k	m.k	PROPN
iajs-2379	206	4	.	.	PUNCT
iajs-2379	206	5	;	;	PUNCT
iajs-2379	206	6	luboobi	luboobi	PROPN
iajs-2379	206	7	l.	l.	PROPN
iajs-2379	206	8	;	;	PUNCT
iajs-2379	206	9	shahada	shahada	PROPN
iajs-2379	206	10	,	,	PUNCT
iajs-2379	206	11	f.	f.	PROPN
iajs-2379	206	12	application	application	NOUN
iajs-2379	206	13	of	of	ADP
iajs-2379	206	14	optimal	optimal	ADJ
iajs-2379	206	15	control	control	NOUN
iajs-2379	206	16	strategies	strategy	NOUN
iajs-2379	206	17	for	for	ADP
iajs-2379	206	18	the	the	DET
iajs-2379	206	19	dynamics	dynamic	NOUN
iajs-2379	206	20	of	of	ADP
iajs-2379	206	21	yellow	yellow	ADJ
iajs-2379	206	22	fever	fever	NOUN
iajs-2379	206	23	.	.	PUNCT
iajs-2379	207	1	j.	j.	PROPN
iajs-2379	207	2	math	math	PROPN
iajs-2379	207	3	.	.	PUNCT
iajs-2379	208	1	computer	computer	NOUN
iajs-2379	208	2	.	.	PUNCT
iajs-2379	209	1	sci.2015	sci.2015	X
iajs-2379	209	2	,	,	PUNCT
iajs-2379	209	3	5	5	NUM
iajs-2379	209	4	,	,	PUNCT
iajs-2379	209	5	3	3	NUM
iajs-2379	209	6	,	,	PUNCT
iajs-2379	209	7	430	430	NUM
iajs-2379	209	8	-	-	SYM
iajs-2379	209	9	453	453	NUM
iajs-2379	209	10	.	.	NOUN
iajs-2379	210	1	2	2	NUM
iajs-2379	210	2	.	.	X
iajs-2379	210	3	hajiabadi	hajiabadi	PROPN
iajs-2379	210	4	,	,	PUNCT
iajs-2379	210	5	m.e	m.e	PROPN
iajs-2379	210	6	.	.	PROPN
iajs-2379	210	7	;	;	PUNCT
iajs-2379	210	8	mashhadi	mashhadi	NOUN
iajs-2379	210	9	,	,	PUNCT
iajs-2379	210	10	h.r	h.r	PROPN
iajs-2379	210	11	.	.	NOUN
iajs-2379	210	12	modeling	modeling	NOUN
iajs-2379	210	13	of	of	ADP
iajs-2379	210	14	the	the	DET
iajs-2379	210	15	maximum	maximum	PROPN
iajs-2379	210	16	entropy	entropy	NOUN
iajs-2379	210	17	problem	problem	NOUN
iajs-2379	210	18	as	as	ADP
iajs-2379	210	19	an	an	DET
iajs-2379	210	20	optimal	optimal	ADJ
iajs-2379	210	21	control	control	NOUN
iajs-2379	210	22	problem	problem	NOUN
iajs-2379	210	23	and	and	CCONJ
iajs-2379	210	24	its	its	PRON
iajs-2379	210	25	application	application	NOUN
iajs-2379	210	26	to	to	ADP
iajs-2379	210	27	pdf	pdf	NOUN
iajs-2379	210	28	estimation	estimation	NOUN
iajs-2379	210	29	of	of	ADP
iajs-2379	210	30	electricity	electricity	NOUN
iajs-2379	210	31	price	price	NOUN
iajs-2379	210	32	.	.	PUNCT
iajs-2379	211	1	ijeee	ijeee	NOUN
iajs-2379	211	2	.	.	PUNCT
iajs-2379	212	1	iran	iran	PROPN
iajs-2379	212	2	university	university	PROPN
iajs-2379	212	3	of	of	ADP
iajs-2379	212	4	science	science	NOUN
iajs-2379	212	5	and	and	CCONJ
iajs-2379	212	6	technology.2013	technology.2013	PROPN
iajs-2379	212	7	,	,	PUNCT
iajs-2379	212	8	9	9	NUM
iajs-2379	212	9	,	,	PUNCT
iajs-2379	212	10	3	3	NUM
iajs-2379	212	11	,	,	PUNCT
iajs-2379	212	12	150	150	NUM
iajs-2379	212	13	-	-	SYM
iajs-2379	212	14	157	157	NUM
iajs-2379	212	15	.	.	PUNCT
iajs-2379	213	1	3	3	X
iajs-2379	213	2	.	.	X
iajs-2379	213	3	bermudez	bermudez	PROPN
iajs-2379	213	4	,	,	PUNCT
iajs-2379	213	5	a.	a.	NOUN
iajs-2379	213	6	some	some	DET
iajs-2379	213	7	applications	application	NOUN
iajs-2379	213	8	of	of	ADP
iajs-2379	213	9	optimal	optimal	ADJ
iajs-2379	213	10	control	control	NOUN
iajs-2379	213	11	theory	theory	NOUN
iajs-2379	213	12	of	of	ADP
iajs-2379	213	13	distributed	distribute	VERB
iajs-2379	213	14	systems	system	NOUN
iajs-2379	213	15	.	.	PUNCT
iajs-2379	214	1	esaim	esaim	NOUN
iajs-2379	214	2	:	:	PUNCT
iajs-2379	214	3	control	control	NOUN
iajs-2379	214	4	,	,	PUNCT
iajs-2379	214	5	optimisation	optimisation	NOUN
iajs-2379	214	6	and	and	CCONJ
iajs-2379	214	7	calculus	calculus	NOUN
iajs-2379	214	8	of	of	ADP
iajs-2379	214	9	variations.2002	variations.2002	PROPN
iajs-2379	214	10	,	,	PUNCT
iajs-2379	214	11	8	8	NUM
iajs-2379	214	12	,	,	PUNCT
iajs-2379	214	13	195	195	NUM
iajs-2379	214	14	-	-	SYM
iajs-2379	214	15	218	218	NUM
iajs-2379	214	16	.	.	PUNCT
iajs-2379	215	1	142	142	NUM
iajs-2379	215	2	ibn	ibn	PROPN
iajs-2379	215	3	al	al	PROPN
iajs-2379	215	4	-	-	PUNCT
iajs-2379	215	5	haitham	haitham	PROPN
iajs-2379	215	6	jour	jour	X
iajs-2379	215	7	.	.	PROPN
iajs-2379	215	8	for	for	ADP
iajs-2379	215	9	pure	pure	ADJ
iajs-2379	215	10	&	&	CCONJ
iajs-2379	215	11	appl	appl	PROPN
iajs-2379	215	12	.	.	PUNCT
iajs-2379	216	1	sci	sci	PROPN
iajs-2379	216	2	.	.	PROPN
iajs-2379	217	1	33	33	NUM
iajs-2379	217	2	(	(	PUNCT
iajs-2379	217	3	1	1	NUM
iajs-2379	217	4	)	)	PUNCT
iajs-2379	217	5	2020	2020	NUM
iajs-2379	217	6	4	4	NUM
iajs-2379	217	7	.	.	X
iajs-2379	218	1	tawfiq	tawfiq	PROPN
iajs-2379	218	2	,	,	PUNCT
iajs-2379	218	3	l.n.m	l.n.m	NOUN
iajs-2379	218	4	.	.	PUNCT
iajs-2379	218	5	;	;	PUNCT
iajs-2379	219	1	jabber	jabber	PROPN
iajs-2379	219	2	,	,	PUNCT
iajs-2379	219	3	a.k	a.k	PROPN
iajs-2379	219	4	.	.	PROPN
iajs-2379	219	5	steady	steady	ADJ
iajs-2379	219	6	state	state	NOUN
iajs-2379	219	7	radial	radial	ADJ
iajs-2379	219	8	flow	flow	NOUN
iajs-2379	219	9	in	in	ADP
iajs-2379	219	10	anisotropic	anisotropic	NOUN
iajs-2379	219	11	and	and	CCONJ
iajs-2379	219	12	homogenous	homogenous	ADJ
iajs-2379	219	13	in	in	ADP
iajs-2379	219	14	confined	confine	VERB
iajs-2379	219	15	aquifers	aquifer	NOUN
iajs-2379	219	16	.	.	PUNCT
iajs-2379	220	1	journal	journal	PROPN
iajs-2379	220	2	of	of	ADP
iajs-2379	220	3	physics	physics	PROPN
iajs-2379	220	4	:	:	PUNCT
iajs-2379	220	5	conference	conference	NOUN
iajs-2379	220	6	series.2018	series.2018	PROPN
iajs-2379	220	7	,	,	PUNCT
iajs-2379	220	8	1003	1003	NUM
iajs-2379	220	9	,	,	PUNCT
iajs-2379	220	10	012056	012056	NUM
iajs-2379	220	11	,	,	PUNCT
iajs-2379	220	12	1	1	NUM
iajs-2379	220	13	-	-	SYM
iajs-2379	220	14	12	12	NUM
iajs-2379	220	15	.	.	PUNCT
iajs-2379	221	1	5	5	NUM
iajs-2379	221	2	.	.	NUM
iajs-2379	221	3	chryssoverghi	chryssoverghi	PROPN
iajs-2379	221	4	,	,	PUNCT
iajs-2379	221	5	i.	i.	PROPN
iajs-2379	221	6	;	;	PUNCT
iajs-2379	221	7	al	al	PROPN
iajs-2379	221	8	-	-	PUNCT
iajs-2379	221	9	hawasy	hawasy	PROPN
iajs-2379	221	10	,	,	PUNCT
iajs-2379	221	11	j.	j.	PROPN
iajs-2379	221	12	the	the	DET
iajs-2379	221	13	continuous	continuous	ADJ
iajs-2379	221	14	classical	classical	ADJ
iajs-2379	221	15	optimal	optimal	ADJ
iajs-2379	221	16	control	control	NOUN
iajs-2379	221	17	problem	problem	NOUN
iajs-2379	221	18	of	of	ADP
iajs-2379	221	19	semi	semi	ADJ
iajs-2379	221	20	linear	linear	PROPN
iajs-2379	221	21	parabolic	parabolic	ADJ
iajs-2379	221	22	equations	equation	NOUN
iajs-2379	221	23	(	(	PUNCT
iajs-2379	221	24	ccocp	ccocp	NOUN
iajs-2379	221	25	)	)	PUNCT
iajs-2379	221	26	,	,	PUNCT
iajs-2379	221	27	journal	journal	NOUN
iajs-2379	221	28	of	of	ADP
iajs-2379	221	29	kerbala	kerbala	PROPN
iajs-2379	221	30	university.2010	university.2010	PROPN
iajs-2379	221	31	,	,	PUNCT
iajs-2379	221	32	8	8	NUM
iajs-2379	221	33	,	,	PUNCT
iajs-2379	221	34	3	3	NUM
iajs-2379	221	35	.	.	NOUN
iajs-2379	221	36	6	6	NUM
iajs-2379	221	37	.	.	X
iajs-2379	222	1	tawfiq	tawfiq	PROPN
iajs-2379	222	2	,	,	PUNCT
iajs-2379	222	3	l.n.m	l.n.m	NOUN
iajs-2379	222	4	.	.	PUNCT
iajs-2379	222	5	;	;	PUNCT
iajs-2379	222	6	jasim	jasim	PROPN
iajs-2379	222	7	,	,	PUNCT
iajs-2379	222	8	k.a	k.a	PROPN
iajs-2379	222	9	.	.	PROPN
iajs-2379	222	10	;	;	PUNCT
iajs-2379	222	11	abdulhmeed	abdulhmee	VERB
iajs-2379	222	12	,	,	PUNCT
iajs-2379	222	13	e.o	e.o	PROPN
iajs-2379	222	14	.	.	PROPN
iajs-2379	222	15	pollution	pollution	NOUN
iajs-2379	222	16	of	of	ADP
iajs-2379	222	17	soils	soil	NOUN
iajs-2379	222	18	by	by	ADP
iajs-2379	222	19	heavy	heavy	ADJ
iajs-2379	222	20	metals	metal	NOUN
iajs-2379	222	21	in	in	ADP
iajs-2379	222	22	east	east	PROPN
iajs-2379	222	23	baghdad	baghdad	PROPN
iajs-2379	222	24	in	in	ADP
iajs-2379	222	25	iraq	iraq	PROPN
iajs-2379	222	26	.	.	PUNCT
iajs-2379	223	1	international	international	ADJ
iajs-2379	223	2	journal	journal	PROPN
iajs-2379	223	3	of	of	ADP
iajs-2379	223	4	innovative	innovative	ADJ
iajs-2379	223	5	science	science	NOUN
iajs-2379	223	6	engineering	engineering	NOUN
iajs-2379	223	7	&	&	CCONJ
iajs-2379	223	8	technology.2015	technology.2015	PROPN
iajs-2379	223	9	,	,	PUNCT
iajs-2379	223	10	2	2	NUM
iajs-2379	223	11	,	,	PUNCT
iajs-2379	223	12	6	6	NUM
iajs-2379	223	13	,	,	PUNCT
iajs-2379	223	14	181	181	NUM
iajs-2379	223	15	-	-	SYM
iajs-2379	223	16	187	187	NUM
iajs-2379	223	17	.	.	PUNCT
iajs-2379	224	1	7	7	X
iajs-2379	224	2	.	.	X
iajs-2379	224	3	brett	brett	PROPN
iajs-2379	224	4	,	,	PUNCT
iajs-2379	224	5	c.	c.	PROPN
iajs-2379	224	6	;	;	PUNCT
iajs-2379	224	7	dedner	dedner	NOUN
iajs-2379	224	8	,	,	PUNCT
iajs-2379	224	9	a.	a.	PROPN
iajs-2379	224	10	;	;	PUNCT
iajs-2379	224	11	elliott	elliott	PROPN
iajs-2379	224	12	,	,	PUNCT
iajs-2379	224	13	c.	c.	PROPN
iajs-2379	224	14	optimal	optimal	ADJ
iajs-2379	224	15	control	control	NOUN
iajs-2379	224	16	of	of	ADP
iajs-2379	224	17	elliptic	elliptic	ADJ
iajs-2379	224	18	pdes	pde	NOUN
iajs-2379	224	19	at	at	ADP
iajs-2379	224	20	points	point	NOUN
iajs-2379	224	21	.	.	PUNCT
iajs-2379	225	1	i	i	PRON
iajs-2379	225	2	m	m	VERB
iajs-2379	225	3	a	a	DET
iajs-2379	225	4	journal	journal	NOUN
iajs-2379	225	5	of	of	ADP
iajs-2379	225	6	numerical	numerical	PROPN
iajs-2379	225	7	analysis.2015	analysis.2015	PROPN
iajs-2379	225	8	,	,	PUNCT
iajs-2379	225	9	36	36	NUM
iajs-2379	225	10	,	,	PUNCT
iajs-2379	225	11	3	3	NUM
iajs-2379	225	12	,	,	PUNCT
iajs-2379	225	13	1	1	NUM
iajs-2379	225	14	-	-	SYM
iajs-2379	225	15	34	34	NUM
iajs-2379	225	16	.	.	NOUN
iajs-2379	225	17	8	8	NUM
iajs-2379	225	18	.	.	PUNCT
iajs-2379	226	1	al	al	PROPN
iajs-2379	226	2	-	-	PUNCT
iajs-2379	226	3	hawasy	hawasy	PROPN
iajs-2379	226	4	,	,	PUNCT
iajs-2379	226	5	j.	j.	PROPN
iajs-2379	226	6	;	;	PUNCT
iajs-2379	226	7	kadhem	kadhem	PROPN
iajs-2379	226	8	,	,	PUNCT
iajs-2379	226	9	g.m	g.m	PROPN
iajs-2379	226	10	.	.	PUNCT
iajs-2379	227	1	the	the	DET
iajs-2379	227	2	continuous	continuous	ADJ
iajs-2379	227	3	classical	classical	ADJ
iajs-2379	227	4	optimal	optimal	ADJ
iajs-2379	227	5	control	control	NOUN
iajs-2379	227	6	for	for	ADP
iajs-2379	227	7	coupled	couple	VERB
iajs-2379	227	8	nonlinear	nonlinear	ADJ
iajs-2379	227	9	parabolic	parabolic	ADJ
iajs-2379	227	10	partial	partial	ADJ
iajs-2379	227	11	differential	differential	NOUN
iajs-2379	227	12	equations	equation	NOUN
iajs-2379	227	13	with	with	ADP
iajs-2379	227	14	equality	equality	NOUN
iajs-2379	227	15	and	and	CCONJ
iajs-2379	227	16	inequality	inequality	NOUN
iajs-2379	227	17	constraints	constraint	NOUN
iajs-2379	227	18	.	.	PUNCT
iajs-2379	228	1	journal	journal	PROPN
iajs-2379	228	2	of	of	ADP
iajs-2379	228	3	al	al	PROPN
iajs-2379	228	4	-	-	PUNCT
iajs-2379	228	5	nahrain	nahrain	PROPN
iajs-2379	228	6	university.2016	university.2016	PROPN
iajs-2379	228	7	,	,	PUNCT
iajs-2379	228	8	19	19	NUM
iajs-2379	228	9	,	,	PUNCT
iajs-2379	228	10	1,173	1,173	NUM
iajs-2379	228	11	-	-	SYM
iajs-2379	228	12	186	186	NUM
iajs-2379	228	13	.	.	PUNCT
iajs-2379	229	1	9	9	NUM
iajs-2379	229	2	.	.	X
iajs-2379	230	1	al	al	PROPN
iajs-2379	230	2	-	-	PUNCT
iajs-2379	230	3	hawasy	hawasy	PROPN
iajs-2379	230	4	,	,	PUNCT
iajs-2379	230	5	j.	j.	PROPN
iajs-2379	230	6	the	the	DET
iajs-2379	230	7	continuous	continuous	ADJ
iajs-2379	230	8	classical	classical	ADJ
iajs-2379	230	9	optimal	optimal	ADJ
iajs-2379	230	10	control	control	NOUN
iajs-2379	230	11	of	of	ADP
iajs-2379	230	12	a	a	DET
iajs-2379	230	13	couple	couple	NOUN
iajs-2379	230	14	nonlinear	nonlinear	ADJ
iajs-2379	230	15	hyperbolic	hyperbolic	ADJ
iajs-2379	230	16	29,1partial	29,1partial	NUM
iajs-2379	230	17	differential	differential	ADJ
iajs-2379	230	18	equations	equation	NOUN
iajs-2379	230	19	with	with	ADP
iajs-2379	230	20	equality	equality	NOUN
iajs-2379	230	21	and	and	CCONJ
iajs-2379	230	22	inequality	inequality	NOUN
iajs-2379	230	23	constraints	constraint	NOUN
iajs-2379	230	24	.	.	PUNCT
iajs-2379	231	1	iraqi	iraqi	ADJ
iajs-2379	231	2	journal	journal	NOUN
iajs-2379	231	3	of	of	ADP
iajs-2379	231	4	science.2016	science.2016	PROPN
iajs-2379	231	5	,	,	PUNCT
iajs-2379	231	6	57	57	NUM
iajs-2379	231	7	,	,	PUNCT
iajs-2379	231	8	2c	2c	NUM
iajs-2379	231	9	,	,	PUNCT
iajs-2379	231	10	1528	1528	NUM
iajs-2379	231	11	-	-	SYM
iajs-2379	231	12	1538	1538	NUM
iajs-2379	231	13	.	.	PUNCT
iajs-2379	232	1	10	10	NUM
iajs-2379	232	2	.	.	PUNCT
iajs-2379	233	1	al	al	PROPN
iajs-2379	233	2	-	-	PUNCT
iajs-2379	233	3	rawdhanee	rawdhanee	NOUN
iajs-2379	233	4	,	,	PUNCT
iajs-2379	233	5	e.h	e.h	PROPN
iajs-2379	233	6	.	.	PUNCT
iajs-2379	234	1	the	the	DET
iajs-2379	234	2	continuous	continuous	ADJ
iajs-2379	234	3	classical	classical	ADJ
iajs-2379	234	4	optimal	optimal	ADJ
iajs-2379	234	5	control	control	NOUN
iajs-2379	234	6	of	of	ADP
iajs-2379	234	7	a	a	DET
iajs-2379	234	8	couple	couple	NOUN
iajs-2379	234	9	non	non	ADJ
iajs-2379	234	10	-	-	ADJ
iajs-2379	234	11	linear	linear	ADJ
iajs-2379	234	12	elliptic	elliptic	ADJ
iajs-2379	234	13	partial	partial	ADJ
iajs-2379	234	14	differential	differential	NOUN
iajs-2379	234	15	equations	equation	NOUN
iajs-2379	234	16	.	.	PUNCT
iajs-2379	235	1	master	master	NOUN
iajs-2379	235	2	thesis	thesis	PROPN
iajs-2379	235	3	,	,	PUNCT
iajs-2379	235	4	al	al	PROPN
iajs-2379	235	5	-	-	PUNCT
iajs-2379	235	6	mustansiriyah	mustansiriyah	PROPN
iajs-2379	235	7	university	university	NOUN
iajs-2379	235	8	,	,	PUNCT
iajs-2379	235	9	2015	2015	NUM
iajs-2379	235	10	.	.	PUNCT
iajs-2379	236	1	11	11	NUM
iajs-2379	236	2	.	.	PUNCT
iajs-2379	237	1	al	al	PROPN
iajs-2379	237	2	-	-	PUNCT
iajs-2379	237	3	hawasy	hawasy	PROPN
iajs-2379	237	4	,	,	PUNCT
iajs-2379	237	5	j.	j.	PROPN
iajs-2379	237	6	;	;	PUNCT
iajs-2379	237	7	naeif	naeif	NOUN
iajs-2379	237	8	,	,	PUNCT
iajs-2379	237	9	a.a	a.a	PROPN
iajs-2379	237	10	.	.	PROPN
iajs-2379	237	11	the	the	DET
iajs-2379	237	12	continuous	continuous	ADJ
iajs-2379	237	13	classical	classical	ADJ
iajs-2379	237	14	boundary	boundary	ADJ
iajs-2379	237	15	optimal	optimal	ADJ
iajs-2379	237	16	control	control	NOUN
iajs-2379	237	17	of	of	ADP
iajs-2379	237	18	a	a	DET
iajs-2379	237	19	couple	couple	NOUN
iajs-2379	237	20	linear	linear	NOUN
iajs-2379	237	21	of	of	ADP
iajs-2379	237	22	parabolic	parabolic	ADJ
iajs-2379	237	23	partial	partial	ADJ
iajs-2379	237	24	differential	differential	NOUN
iajs-2379	237	25	equations	equation	NOUN
iajs-2379	237	26	.	.	PUNCT
iajs-2379	238	1	al	al	PROPN
iajs-2379	238	2	-	-	PUNCT
iajs-2379	238	3	mustansiriyah	mustansiriyah	PROPN
iajs-2379	238	4	journal	journal	NOUN
iajs-2379	238	5	of	of	ADP
iajs-2379	238	6	science.2018	science.2018	PROPN
iajs-2379	238	7	,	,	PUNCT
iajs-2379	238	8	29	29	NUM
iajs-2379	238	9	,	,	PUNCT
iajs-2379	238	10	1	1	NUM
iajs-2379	238	11	,	,	PUNCT
iajs-2379	238	12	118	118	NUM
iajs-2379	238	13	-	-	SYM
iajs-2379	238	14	126	126	NUM
iajs-2379	238	15	.	.	PUNCT
iajs-2379	239	1	doi	doi	NOUN
iajs-2379	239	2	:	:	PUNCT
iajs-2379	239	3	http://dx.doi.org/10.23851/mjs.v29i1.159	http://dx.doi.org/10.23851/mjs.v29i1.159	PROPN
iajs-2379	239	4	.	.	PROPN
iajs-2379	239	5	12	12	NUM
iajs-2379	239	6	.	.	PUNCT
iajs-2379	240	1	al	al	PROPN
iajs-2379	240	2	-	-	PUNCT
iajs-2379	240	3	hawasy	hawasy	PROPN
iajs-2379	240	4	,	,	PUNCT
iajs-2379	240	5	j.	j.	PROPN
iajs-2379	240	6	the	the	DET
iajs-2379	240	7	continuous	continuous	ADJ
iajs-2379	240	8	classical	classical	ADJ
iajs-2379	240	9	boundary	boundary	ADJ
iajs-2379	240	10	optimal	optimal	ADJ
iajs-2379	240	11	control	control	NOUN
iajs-2379	240	12	of	of	ADP
iajs-2379	240	13	couple	couple	NOUN
iajs-2379	240	14	nonlinear	nonlinear	ADJ
iajs-2379	240	15	hyperbolic	hyperbolic	ADJ
iajs-2379	240	16	boundary	boundary	ADJ
iajs-2379	240	17	value	value	NOUN
iajs-2379	240	18	problem	problem	NOUN
iajs-2379	240	19	with	with	ADP
iajs-2379	240	20	equality	equality	NOUN
iajs-2379	240	21	and	and	CCONJ
iajs-2379	240	22	inequality	inequality	NOUN
iajs-2379	240	23	constraints	constraint	NOUN
iajs-2379	240	24	.	.	PUNCT
iajs-2379	241	1	baghdad	baghdad	PROPN
iajs-2379	241	2	science	science	NOUN
iajs-2379	241	3	journal.2019	journal.2019	PROPN
iajs-2379	241	4	16	16	NUM
iajs-2379	241	5	,	,	PUNCT
iajs-2379	241	6	4	4	NUM
iajs-2379	241	7	,	,	PUNCT
iajs-2379	241	8	1064	1064	NUM
iajs-2379	241	9	-	-	SYM
iajs-2379	241	10	1064	1064	NUM
iajs-2379	241	11	.	.	PUNCT
iajs-2379	242	1	13	13	NUM
iajs-2379	242	2	.	.	PUNCT
iajs-2379	243	1	al	al	PROPN
iajs-2379	243	2	-	-	PUNCT
iajs-2379	243	3	hawasy	hawasy	PROPN
iajs-2379	243	4	,	,	PUNCT
iajs-2379	243	5	j.	j.	PROPN
iajs-2379	243	6	;	;	PUNCT
iajs-2379	243	7	al	al	PROPN
iajs-2379	243	8	-	-	PUNCT
iajs-2379	243	9	qaisi	qaisi	PROPN
iajs-2379	243	10	,	,	PUNCT
iajs-2379	243	11	s.j	s.j	PROPN
iajs-2379	243	12	.	.	PUNCT
iajs-2379	244	1	the	the	DET
iajs-2379	244	2	continuous	continuous	ADJ
iajs-2379	244	3	classical	classical	ADJ
iajs-2379	244	4	optimal	optimal	ADJ
iajs-2379	244	5	boundary	boundary	ADJ
iajs-2379	244	6	control	control	NOUN
iajs-2379	244	7	of	of	ADP
iajs-2379	244	8	a	a	DET
iajs-2379	244	9	couple	couple	NOUN
iajs-2379	244	10	linear	linear	NOUN
iajs-2379	244	11	elliptic	elliptic	ADJ
iajs-2379	244	12	partial	partial	ADJ
iajs-2379	244	13	differential	differential	NOUN
iajs-2379	244	14	equations	equation	NOUN
iajs-2379	244	15	.	.	PUNCT
iajs-2379	245	1	special	special	ADJ
iajs-2379	245	2	issue	issue	NOUN
iajs-2379	245	3	,	,	PUNCT
iajs-2379	245	4	1	1	NUM
iajs-2379	245	5	st	st	NOUN
iajs-2379	245	6	scientific	scientific	ADJ
iajs-2379	245	7	international	international	ADJ
iajs-2379	245	8	conference	conference	NOUN
iajs-2379	245	9	,	,	PUNCT
iajs-2379	245	10	college	college	NOUN
iajs-2379	245	11	of	of	ADP
iajs-2379	245	12	science	science	PROPN
iajs-2379	245	13	,	,	PUNCT
iajs-2379	245	14	al	al	PROPN
iajs-2379	245	15	-	-	PUNCT
iajs-2379	245	16	nahrain	nahrain	PROPN
iajs-2379	245	17	journal	journal	NOUN
iajs-2379	245	18	of	of	ADP
iajs-2379	245	19	science.2017	science.2017	PROPN
iajs-2379	245	20	,	,	PUNCT
iajs-2379	245	21	1	1	NUM
iajs-2379	245	22	,	,	PUNCT
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