id	sid	tid	token	lemma	pos
ejpam-4406	1	1	european	european	PROPN
ejpam-4406	1	2	journal	journal	PROPN
ejpam-4406	1	3	of	of	ADP
ejpam-4406	1	4	pure	pure	ADJ
ejpam-4406	1	5	and	and	CCONJ
ejpam-4406	1	6	applied	apply	VERB
ejpam-4406	1	7	mathematics	mathematic	NOUN
ejpam-4406	1	8	vol	vol	NOUN
ejpam-4406	1	9	.	.	PROPN
ejpam-4406	2	1	15	15	NUM
ejpam-4406	2	2	,	,	PUNCT
ejpam-4406	2	3	no	no	INTJ
ejpam-4406	2	4	.	.	NOUN
ejpam-4406	2	5	3	3	NUM
ejpam-4406	2	6	,	,	PUNCT
ejpam-4406	2	7	2022	2022	NUM
ejpam-4406	2	8	,	,	PUNCT
ejpam-4406	2	9	1144	1144	NUM
ejpam-4406	2	10	-	-	SYM
ejpam-4406	2	11	1157	1157	NUM
ejpam-4406	2	12	issn	issn	PROPN
ejpam-4406	2	13	1307	1307	NUM
ejpam-4406	2	14	-	-	SYM
ejpam-4406	2	15	5543	5543	NUM
ejpam-4406	2	16	–	–	PUNCT
ejpam-4406	2	17	ejpam.com	ejpam.com	X
ejpam-4406	2	18	published	publish	VERB
ejpam-4406	2	19	by	by	ADP
ejpam-4406	2	20	new	new	PROPN
ejpam-4406	2	21	york	york	PROPN
ejpam-4406	2	22	business	business	PROPN
ejpam-4406	2	23	global	global	ADJ
ejpam-4406	2	24	fractional	fractional	ADJ
ejpam-4406	2	25	order	order	NOUN
ejpam-4406	2	26	techniques	technique	NOUN
ejpam-4406	2	27	for	for	ADP
ejpam-4406	2	28	stiff	stiff	ADJ
ejpam-4406	2	29	differential	differential	ADJ
ejpam-4406	2	30	equations	equation	NOUN
ejpam-4406	2	31	arising	arise	VERB
ejpam-4406	2	32	from	from	ADP
ejpam-4406	2	33	chemistry	chemistry	NOUN
ejpam-4406	2	34	kinetics	kinetic	NOUN
ejpam-4406	2	35	rania	rania	PROPN
ejpam-4406	2	36	wannan1	wannan1	PROPN
ejpam-4406	2	37	,	,	PUNCT
ejpam-4406	2	38	muhammad	muhammad	PROPN
ejpam-4406	2	39	aslam2	aslam2	PROPN
ejpam-4406	2	40	,	,	PUNCT
ejpam-4406	2	41	muhammad	muhammad	PROPN
ejpam-4406	2	42	farman3	farman3	PROPN
ejpam-4406	2	43	,	,	PUNCT
ejpam-4406	2	44	ali	ali	PROPN
ejpam-4406	2	45	akgül4	akgül4	PROPN
ejpam-4406	2	46	,	,	PUNCT
ejpam-4406	2	47	farhina	farhina	PROPN
ejpam-4406	2	48	kouser5	kouser5	PROPN
ejpam-4406	2	49	,	,	PUNCT
ejpam-4406	2	50	jihad	jihad	VERB
ejpam-4406	2	51	asad1,∗	asad1,∗	ADP
ejpam-4406	2	52	1	1	NUM
ejpam-4406	2	53	faculty	faculty	NOUN
ejpam-4406	2	54	of	of	ADP
ejpam-4406	2	55	applied	apply	VERB
ejpam-4406	2	56	science	science	NOUN
ejpam-4406	2	57	,	,	PUNCT
ejpam-4406	2	58	palestine	palestine	PROPN
ejpam-4406	2	59	technical	technical	PROPN
ejpam-4406	2	60	university	university	PROPN
ejpam-4406	2	61	kadoorie	kadoorie	NOUN
ejpam-4406	2	62	,	,	PUNCT
ejpam-4406	2	63	tulkarem	tulkarem	VERB
ejpam-4406	2	64	,	,	PUNCT
ejpam-4406	2	65	palestine	palestine	PROPN
ejpam-4406	2	66	.	.	PROPN
ejpam-4406	3	1	2	2	NUM
ejpam-4406	3	2	key	key	ADJ
ejpam-4406	3	3	laboratory	laboratory	NOUN
ejpam-4406	3	4	of	of	ADP
ejpam-4406	3	5	synthetic	synthetic	ADJ
ejpam-4406	3	6	and	and	CCONJ
ejpam-4406	3	7	natural	natural	ADJ
ejpam-4406	3	8	functional	functional	ADJ
ejpam-4406	3	9	molecule	molecule	NOUN
ejpam-4406	3	10	chemistry	chemistry	NOUN
ejpam-4406	3	11	of	of	ADP
ejpam-4406	3	12	ministry	ministry	PROPN
ejpam-4406	3	13	of	of	ADP
ejpam-4406	3	14	education	education	PROPN
ejpam-4406	3	15	,	,	PUNCT
ejpam-4406	3	16	department	department	NOUN
ejpam-4406	3	17	of	of	ADP
ejpam-4406	3	18	chemistry	chemistry	NOUN
ejpam-4406	3	19	and	and	CCONJ
ejpam-4406	3	20	materials	material	NOUN
ejpam-4406	3	21	science	science	NOUN
ejpam-4406	3	22	,	,	PUNCT
ejpam-4406	3	23	northwest	northwest	PROPN
ejpam-4406	3	24	university	university	PROPN
ejpam-4406	3	25	,	,	PUNCT
ejpam-4406	3	26	xi’an	xi’an	PROPN
ejpam-4406	3	27	710127	710127	NUM
ejpam-4406	3	28	,	,	PUNCT
ejpam-4406	3	29	p.r	p.r	PROPN
ejpam-4406	3	30	china	china	PROPN
ejpam-4406	3	31	3	3	NUM
ejpam-4406	3	32	department	department	NOUN
ejpam-4406	3	33	of	of	ADP
ejpam-4406	3	34	mathematics	mathematics	PROPN
ejpam-4406	3	35	,	,	PUNCT
ejpam-4406	3	36	khawaja	khawaja	PROPN
ejpam-4406	3	37	fareed	fareed	PROPN
ejpam-4406	3	38	university	university	PROPN
ejpam-4406	3	39	of	of	ADP
ejpam-4406	3	40	engineering	engineering	NOUN
ejpam-4406	3	41	and	and	CCONJ
ejpam-4406	3	42	information	information	NOUN
ejpam-4406	3	43	technology	technology	NOUN
ejpam-4406	3	44	,	,	PUNCT
ejpam-4406	3	45	rahim	rahim	PROPN
ejpam-4406	3	46	yar	yar	PROPN
ejpam-4406	3	47	khan	khan	PROPN
ejpam-4406	3	48	,	,	PUNCT
ejpam-4406	3	49	pakistan	pakistan	PROPN
ejpam-4406	3	50	.	.	PUNCT
ejpam-4406	4	1	4	4	NUM
ejpam-4406	4	2	department	department	NOUN
ejpam-4406	4	3	of	of	ADP
ejpam-4406	4	4	mathematics	mathematic	NOUN
ejpam-4406	4	5	,	,	PUNCT
ejpam-4406	4	6	art	art	NOUN
ejpam-4406	4	7	and	and	CCONJ
ejpam-4406	4	8	science	science	NOUN
ejpam-4406	4	9	faculty	faculty	NOUN
ejpam-4406	4	10	,	,	PUNCT
ejpam-4406	4	11	siirt	siirt	PROPN
ejpam-4406	4	12	university	university	NOUN
ejpam-4406	4	13	,	,	PUNCT
ejpam-4406	4	14	56100	56100	NUM
ejpam-4406	4	15	siirt	siirt	NOUN
ejpam-4406	4	16	,	,	PUNCT
ejpam-4406	4	17	turkey	turkey	PROPN
ejpam-4406	4	18	5	5	NUM
ejpam-4406	4	19	department	department	NOUN
ejpam-4406	4	20	of	of	ADP
ejpam-4406	4	21	mathematics	mathematic	NOUN
ejpam-4406	4	22	and	and	CCONJ
ejpam-4406	4	23	statistics	statistic	NOUN
ejpam-4406	4	24	,	,	PUNCT
ejpam-4406	4	25	the	the	DET
ejpam-4406	4	26	university	university	NOUN
ejpam-4406	4	27	of	of	ADP
ejpam-4406	4	28	lahore	lahore	PROPN
ejpam-4406	4	29	,	,	PUNCT
ejpam-4406	4	30	lahore	lahore	NOUN
ejpam-4406	4	31	,	,	PUNCT
ejpam-4406	4	32	pakistan	pakistan	PROPN
ejpam-4406	4	33	abstract	abstract	NOUN
ejpam-4406	4	34	.	.	PUNCT
ejpam-4406	5	1	in	in	ADP
ejpam-4406	5	2	this	this	DET
ejpam-4406	5	3	paper	paper	NOUN
ejpam-4406	5	4	,	,	PUNCT
ejpam-4406	5	5	we	we	PRON
ejpam-4406	5	6	consider	consider	VERB
ejpam-4406	5	7	the	the	DET
ejpam-4406	5	8	stiff	stiff	ADJ
ejpam-4406	5	9	systems	system	NOUN
ejpam-4406	5	10	of	of	ADP
ejpam-4406	5	11	ordinary	ordinary	ADJ
ejpam-4406	5	12	differential	differential	ADJ
ejpam-4406	5	13	equations	equation	NOUN
ejpam-4406	5	14	arising	arise	VERB
ejpam-4406	5	15	from	from	ADP
ejpam-4406	5	16	chemistry	chemistry	NOUN
ejpam-4406	5	17	kinetics	kinetic	NOUN
ejpam-4406	5	18	.	.	PUNCT
ejpam-4406	6	1	we	we	PRON
ejpam-4406	6	2	develop	develop	VERB
ejpam-4406	6	3	the	the	DET
ejpam-4406	6	4	fractional	fractional	ADJ
ejpam-4406	6	5	order	order	NOUN
ejpam-4406	6	6	model	model	NOUN
ejpam-4406	6	7	for	for	ADP
ejpam-4406	6	8	chemistry	chemistry	NOUN
ejpam-4406	6	9	kinetics	kinetic	NOUN
ejpam-4406	6	10	problems	problem	NOUN
ejpam-4406	6	11	by	by	ADP
ejpam-4406	6	12	using	use	VERB
ejpam-4406	6	13	the	the	DET
ejpam-4406	6	14	caputo	caputo	PROPN
ejpam-4406	6	15	fabrizio	fabrizio	PROPN
ejpam-4406	6	16	and	and	CCONJ
ejpam-4406	6	17	atangana	atangana	PROPN
ejpam-4406	6	18	-	-	PUNCT
ejpam-4406	6	19	baleanu	baleanu	ADJ
ejpam-4406	6	20	derivatives	derivative	NOUN
ejpam-4406	6	21	in	in	ADP
ejpam-4406	6	22	caputo	caputo	PROPN
ejpam-4406	6	23	sense	sense	NOUN
ejpam-4406	6	24	.	.	PUNCT
ejpam-4406	7	1	we	we	PRON
ejpam-4406	7	2	apply	apply	VERB
ejpam-4406	7	3	the	the	DET
ejpam-4406	7	4	sumudu	sumudu	NOUN
ejpam-4406	7	5	transform	transform	NOUN
ejpam-4406	7	6	to	to	PART
ejpam-4406	7	7	obtain	obtain	VERB
ejpam-4406	7	8	the	the	DET
ejpam-4406	7	9	solutions	solution	NOUN
ejpam-4406	7	10	of	of	ADP
ejpam-4406	7	11	the	the	DET
ejpam-4406	7	12	models	model	NOUN
ejpam-4406	7	13	.	.	PUNCT
ejpam-4406	8	1	uniqueness	uniqueness	NOUN
ejpam-4406	8	2	and	and	CCONJ
ejpam-4406	8	3	stability	stability	NOUN
ejpam-4406	8	4	analysis	analysis	NOUN
ejpam-4406	8	5	of	of	ADP
ejpam-4406	8	6	the	the	DET
ejpam-4406	8	7	problem	problem	NOUN
ejpam-4406	8	8	are	be	AUX
ejpam-4406	8	9	also	also	ADV
ejpam-4406	8	10	established	establish	VERB
ejpam-4406	8	11	by	by	ADP
ejpam-4406	8	12	using	use	VERB
ejpam-4406	8	13	the	the	DET
ejpam-4406	8	14	fixed	fix	VERB
ejpam-4406	8	15	point	point	NOUN
ejpam-4406	8	16	theory	theory	NOUN
ejpam-4406	8	17	results	result	VERB
ejpam-4406	8	18	.	.	PUNCT
ejpam-4406	9	1	numerical	numerical	ADJ
ejpam-4406	9	2	results	result	NOUN
ejpam-4406	9	3	are	be	AUX
ejpam-4406	9	4	obtained	obtain	VERB
ejpam-4406	9	5	by	by	ADP
ejpam-4406	9	6	using	use	VERB
ejpam-4406	9	7	the	the	DET
ejpam-4406	9	8	proposed	propose	VERB
ejpam-4406	9	9	schemes	scheme	NOUN
ejpam-4406	9	10	which	which	PRON
ejpam-4406	9	11	supports	support	VERB
ejpam-4406	9	12	theoretical	theoretical	ADJ
ejpam-4406	9	13	results	result	NOUN
ejpam-4406	9	14	.	.	PUNCT
ejpam-4406	10	1	these	these	DET
ejpam-4406	10	2	concepts	concept	NOUN
ejpam-4406	10	3	are	be	AUX
ejpam-4406	10	4	very	very	ADV
ejpam-4406	10	5	important	important	ADJ
ejpam-4406	10	6	for	for	ADP
ejpam-4406	10	7	using	use	VERB
ejpam-4406	10	8	the	the	DET
ejpam-4406	10	9	real	real	ADJ
ejpam-4406	10	10	-	-	PUNCT
ejpam-4406	10	11	life	life	NOUN
ejpam-4406	10	12	problems	problem	NOUN
ejpam-4406	10	13	like	like	ADP
ejpam-4406	10	14	brine	brine	NOUN
ejpam-4406	10	15	tank	tank	NOUN
ejpam-4406	10	16	cascade	cascade	NOUN
ejpam-4406	10	17	,	,	PUNCT
ejpam-4406	10	18	recycled	recycle	VERB
ejpam-4406	10	19	brine	brine	NOUN
ejpam-4406	10	20	tank	tank	NOUN
ejpam-4406	10	21	cascade	cascade	NOUN
ejpam-4406	10	22	,	,	PUNCT
ejpam-4406	10	23	pond	pond	NOUN
ejpam-4406	10	24	pollution	pollution	NOUN
ejpam-4406	10	25	,	,	PUNCT
ejpam-4406	10	26	home	home	NOUN
ejpam-4406	10	27	heating	heating	NOUN
ejpam-4406	10	28	and	and	CCONJ
ejpam-4406	10	29	biomass	biomass	NOUN
ejpam-4406	10	30	transfer	transfer	NOUN
ejpam-4406	10	31	problem	problem	NOUN
ejpam-4406	10	32	.	.	PUNCT
ejpam-4406	11	1	these	these	DET
ejpam-4406	11	2	results	result	NOUN
ejpam-4406	11	3	are	be	AUX
ejpam-4406	11	4	crucial	crucial	ADJ
ejpam-4406	11	5	for	for	ADP
ejpam-4406	11	6	solving	solve	VERB
ejpam-4406	11	7	the	the	DET
ejpam-4406	11	8	nonlinear	nonlinear	ADJ
ejpam-4406	11	9	model	model	NOUN
ejpam-4406	11	10	in	in	ADP
ejpam-4406	11	11	chemistry	chemistry	NOUN
ejpam-4406	11	12	kinetics	kinetic	NOUN
ejpam-4406	11	13	.	.	PUNCT
ejpam-4406	12	1	2020	2020	NUM
ejpam-4406	12	2	mathematics	mathematic	NOUN
ejpam-4406	12	3	subject	subject	NOUN
ejpam-4406	12	4	classifications	classification	NOUN
ejpam-4406	12	5	:	:	PUNCT
ejpam-4406	12	6	65p40	65p40	NUM
ejpam-4406	12	7	,	,	PUNCT
ejpam-4406	12	8	68m07	68m07	NUM
ejpam-4406	12	9	key	key	ADJ
ejpam-4406	12	10	words	word	NOUN
ejpam-4406	12	11	and	and	CCONJ
ejpam-4406	12	12	phrases	phrase	NOUN
ejpam-4406	12	13	:	:	PUNCT
ejpam-4406	12	14	chemistry	chemistry	NOUN
ejpam-4406	12	15	kinetics	kinetic	NOUN
ejpam-4406	12	16	,	,	PUNCT
ejpam-4406	12	17	fractional	fractional	ADJ
ejpam-4406	12	18	technique	technique	NOUN
ejpam-4406	12	19	,	,	PUNCT
ejpam-4406	12	20	stability	stability	NOUN
ejpam-4406	12	21	,	,	PUNCT
ejpam-4406	12	22	uniqueness	uniqueness	NOUN
ejpam-4406	12	23	,	,	PUNCT
ejpam-4406	12	24	sumudu	sumudu	NOUN
ejpam-4406	12	25	transform	transform	NOUN
ejpam-4406	12	26	.	.	PUNCT
ejpam-4406	13	1	1	1	X
ejpam-4406	13	2	.	.	X
ejpam-4406	13	3	introduction	introduction	NOUN
ejpam-4406	13	4	some	some	DET
ejpam-4406	13	5	problems	problem	NOUN
ejpam-4406	13	6	with	with	ADP
ejpam-4406	13	7	the	the	DET
ejpam-4406	13	8	fractional	fractional	ADJ
ejpam-4406	13	9	derivatives	derivative	NOUN
ejpam-4406	13	10	which	which	PRON
ejpam-4406	13	11	include	include	VERB
ejpam-4406	13	12	the	the	DET
ejpam-4406	13	13	trigonometric	trigonometric	ADJ
ejpam-4406	13	14	and	and	CCONJ
ejpam-4406	13	15	exponential	exponential	ADJ
ejpam-4406	13	16	functions	function	NOUN
ejpam-4406	13	17	[	[	X
ejpam-4406	13	18	3–8	3–8	NUM
ejpam-4406	13	19	,	,	PUNCT
ejpam-4406	13	20	12	12	NUM
ejpam-4406	13	21	,	,	PUNCT
ejpam-4406	13	22	14	14	NUM
ejpam-4406	13	23	]	]	PUNCT
ejpam-4406	13	24	show	show	VERB
ejpam-4406	13	25	some	some	DET
ejpam-4406	13	26	related	related	ADJ
ejpam-4406	13	27	approaches	approach	NOUN
ejpam-4406	13	28	for	for	ADP
ejpam-4406	13	29	models	model	NOUN
ejpam-4406	13	30	of	of	ADP
ejpam-4406	13	31	epidemic	epidemic	NOUN
ejpam-4406	13	32	.	.	PUNCT
ejpam-4406	14	1	different	different	ADJ
ejpam-4406	14	2	fractional	fractional	ADJ
ejpam-4406	14	3	operator	operator	NOUN
ejpam-4406	14	4	is	be	AUX
ejpam-4406	14	5	used	use	VERB
ejpam-4406	14	6	in	in	ADP
ejpam-4406	14	7	literature	literature	NOUN
ejpam-4406	14	8	to	to	PART
ejpam-4406	14	9	solve	solve	VERB
ejpam-4406	14	10	the	the	DET
ejpam-4406	14	11	real	real	ADJ
ejpam-4406	14	12	life	life	NOUN
ejpam-4406	14	13	problems	problem	NOUN
ejpam-4406	14	14	[	[	X
ejpam-4406	14	15	2	2	NUM
ejpam-4406	14	16	,	,	PUNCT
ejpam-4406	14	17	9	9	NUM
ejpam-4406	14	18	,	,	PUNCT
ejpam-4406	14	19	10	10	NUM
ejpam-4406	14	20	,	,	PUNCT
ejpam-4406	14	21	13	13	NUM
ejpam-4406	14	22	,	,	PUNCT
ejpam-4406	14	23	15	15	NUM
ejpam-4406	14	24	]	]	PUNCT
ejpam-4406	14	25	.	.	PUNCT
ejpam-4406	15	1	the	the	DET
ejpam-4406	15	2	chemical	chemical	NOUN
ejpam-4406	15	3	reaction	reaction	NOUN
ejpam-4406	15	4	has	have	AUX
ejpam-4406	15	5	been	be	AUX
ejpam-4406	15	6	introduced	introduce	VERB
ejpam-4406	15	7	by	by	ADP
ejpam-4406	15	8	robertson	robertson	PROPN
ejpam-4406	15	9	as	as	ADP
ejpam-4406	15	10	[	[	X
ejpam-4406	15	11	1	1	NUM
ejpam-4406	15	12	]	]	X
ejpam-4406	15	13	:	:	PUNCT
ejpam-4406	15	14	∗corresponding	∗corresponde	VERB
ejpam-4406	15	15	author	author	NOUN
ejpam-4406	15	16	.	.	PUNCT
ejpam-4406	16	1	doi	doi	NOUN
ejpam-4406	16	2	:	:	PUNCT
ejpam-4406	16	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4406	https://doi.org/10.29020/nybg.ejpam.v15i3.4406	ADJ
ejpam-4406	16	4	email	email	NOUN
ejpam-4406	16	5	addresses	address	VERB
ejpam-4406	16	6	:	:	PUNCT
ejpam-4406	17	1	j.asad@ptuk.edu.ps	j.asad@ptuk.edu.ps	NOUN
ejpam-4406	17	2	(	(	PUNCT
ejpam-4406	17	3	jihad	jihad	PROPN
ejpam-4406	17	4	asad	asad	PROPN
ejpam-4406	17	5	)	)	PUNCT
ejpam-4406	17	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4406	17	7	1144	1144	NUM
ejpam-4406	18	1	©	©	PROPN
ejpam-4406	18	2	2022	2022	NUM
ejpam-4406	18	3	ejpam	ejpam	VERB
ejpam-4406	18	4	all	all	DET
ejpam-4406	18	5	rights	right	NOUN
ejpam-4406	18	6	reserved	reserve	VERB
ejpam-4406	18	7	.	.	PUNCT
ejpam-4406	19	1	j.	j.	PROPN
ejpam-4406	19	2	asad	asad	PROPN
ejpam-4406	19	3	et	et	PROPN
ejpam-4406	19	4	al	al	PROPN
ejpam-4406	19	5	.	.	PUNCT
ejpam-4406	19	6	/	/	SYM
ejpam-4406	19	7	eur	eur	PROPN
ejpam-4406	19	8	.	.	PUNCT
ejpam-4406	20	1	j.	j.	PROPN
ejpam-4406	20	2	pure	pure	PROPN
ejpam-4406	20	3	appl	appl	PROPN
ejpam-4406	20	4	.	.	PROPN
ejpam-4406	20	5	math	math	PROPN
ejpam-4406	20	6	,	,	PUNCT
ejpam-4406	20	7	15	15	NUM
ejpam-4406	20	8	(	(	PUNCT
ejpam-4406	20	9	3	3	NUM
ejpam-4406	20	10	)	)	PUNCT
ejpam-4406	20	11	(	(	PUNCT
ejpam-4406	20	12	2022	2022	NUM
ejpam-4406	20	13	)	)	PUNCT
ejpam-4406	20	14	,	,	PUNCT
ejpam-4406	20	15	1144	1144	NUM
ejpam-4406	20	16	-	-	SYM
ejpam-4406	20	17	1157	1157	NUM
ejpam-4406	20	18	1145	1145	NUM
ejpam-4406	20	19	a	a	DET
ejpam-4406	20	20	k1→	k1→	X
ejpam-4406	20	21	b.	b.	PROPN
ejpam-4406	20	22	(	(	PUNCT
ejpam-4406	20	23	1	1	NUM
ejpam-4406	20	24	)	)	PUNCT
ejpam-4406	20	25	b	b	NOUN
ejpam-4406	21	1	+	+	NOUN
ejpam-4406	21	2	b	b	X
ejpam-4406	21	3	k2→	k2→	X
ejpam-4406	21	4	c	c	PROPN
ejpam-4406	21	5	+	+	PROPN
ejpam-4406	21	6	b.	b.	PROPN
ejpam-4406	21	7	(	(	PUNCT
ejpam-4406	21	8	2	2	NUM
ejpam-4406	21	9	)	)	PUNCT
ejpam-4406	21	10	b	b	NOUN
ejpam-4406	22	1	+	+	CCONJ
ejpam-4406	22	2	c	c	NOUN
ejpam-4406	22	3	k3→	k3→	X
ejpam-4406	22	4	a+	a+	PUNCT
ejpam-4406	22	5	c.	c.	NOUN
ejpam-4406	22	6	(	(	PUNCT
ejpam-4406	22	7	3	3	X
ejpam-4406	22	8	)	)	PUNCT
ejpam-4406	22	9	the	the	DET
ejpam-4406	22	10	problem	problem	NOUN
ejpam-4406	22	11	has	have	VERB
ejpam-4406	22	12	three	three	NUM
ejpam-4406	22	13	equations	equation	NOUN
ejpam-4406	22	14	,	,	PUNCT
ejpam-4406	22	15	where	where	SCONJ
ejpam-4406	22	16	k1,k2	k1,k2	PROPN
ejpam-4406	22	17	and	and	CCONJ
ejpam-4406	22	18	k3	k3	VERB
ejpam-4406	22	19	describe	describe	VERB
ejpam-4406	22	20	the	the	DET
ejpam-4406	22	21	rate	rate	NOUN
ejpam-4406	22	22	constants	constant	NOUN
ejpam-4406	22	23	and	and	CCONJ
ejpam-4406	22	24	a	a	DET
ejpam-4406	22	25	,	,	PUNCT
ejpam-4406	22	26	b	b	NOUN
ejpam-4406	22	27	and	and	CCONJ
ejpam-4406	22	28	c	c	PROPN
ejpam-4406	22	29	are	be	AUX
ejpam-4406	22	30	the	the	DET
ejpam-4406	22	31	chemical	chemical	ADJ
ejpam-4406	22	32	species	specie	NOUN
ejpam-4406	22	33	contained	contain	VERB
ejpam-4406	22	34	.	.	PUNCT
ejpam-4406	23	1	by	by	ADP
ejpam-4406	23	2	using	use	VERB
ejpam-4406	23	3	the	the	DET
ejpam-4406	23	4	mass	mass	ADJ
ejpam-4406	23	5	action	action	NOUN
ejpam-4406	23	6	law	law	NOUN
ejpam-4406	23	7	,	,	PUNCT
ejpam-4406	23	8	the	the	PRON
ejpam-4406	23	9	get	get	VERB
ejpam-4406	23	10	y′1	y′1	NOUN
ejpam-4406	24	1	=	=	PUNCT
ejpam-4406	24	2	−m1y1	−m1y1	PROPN
ejpam-4406	24	3	+	+	ADP
ejpam-4406	24	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	24	5	,	,	PUNCT
ejpam-4406	24	6	y′2	y′2	NOUN
ejpam-4406	24	7	=	=	SYM
ejpam-4406	24	8	m1y1	m1y1	PROPN
ejpam-4406	24	9	−m2y	−m2y	PROPN
ejpam-4406	24	10	2	2	NUM
ejpam-4406	24	11	2	2	NUM
ejpam-4406	24	12	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	24	13	,	,	PUNCT
ejpam-4406	24	14	y′3	y′3	NOUN
ejpam-4406	25	1	=	=	SYM
ejpam-4406	25	2	m2y	m2y	ADJ
ejpam-4406	25	3	2	2	NUM
ejpam-4406	25	4	2	2	NUM
ejpam-4406	25	5	.	.	PUNCT
ejpam-4406	25	6	(	(	PUNCT
ejpam-4406	25	7	4	4	NUM
ejpam-4406	25	8	)	)	PUNCT
ejpam-4406	25	9	in	in	ADP
ejpam-4406	25	10	this	this	DET
ejpam-4406	25	11	system	system	NOUN
ejpam-4406	25	12	y1(t	y1(t	PROPN
ejpam-4406	25	13	)	)	PUNCT
ejpam-4406	25	14	,	,	PUNCT
ejpam-4406	25	15	y2(t	y2(t	PROPN
ejpam-4406	25	16	)	)	PUNCT
ejpam-4406	25	17	and	and	CCONJ
ejpam-4406	25	18	y3(t	y3(t	NUM
ejpam-4406	25	19	)	)	PUNCT
ejpam-4406	25	20	are	be	AUX
ejpam-4406	25	21	the	the	DET
ejpam-4406	25	22	concentrations	concentration	NOUN
ejpam-4406	25	23	of	of	ADP
ejpam-4406	25	24	the	the	DET
ejpam-4406	25	25	chemical	chemical	NOUN
ejpam-4406	25	26	species	specie	NOUN
ejpam-4406	25	27	a	a	DET
ejpam-4406	25	28	,	,	PUNCT
ejpam-4406	25	29	b	b	NOUN
ejpam-4406	25	30	and	and	CCONJ
ejpam-4406	25	31	c.	c.	NOUN
ejpam-4406	25	32	the	the	DET
ejpam-4406	25	33	initial	initial	ADJ
ejpam-4406	25	34	time	time	NOUN
ejpam-4406	25	35	t	t	PROPN
ejpam-4406	25	36	=	=	SYM
ejpam-4406	25	37	0	0	PROPN
ejpam-4406	25	38	can	can	AUX
ejpam-4406	25	39	be	be	AUX
ejpam-4406	25	40	given	give	VERB
ejpam-4406	25	41	by	by	ADP
ejpam-4406	25	42	(	(	PUNCT
ejpam-4406	25	43	y01	y01	PROPN
ejpam-4406	25	44	,	,	PUNCT
ejpam-4406	25	45	y02	y02	NOUN
ejpam-4406	25	46	,	,	PUNCT
ejpam-4406	25	47	y03	y03	NOUN
ejpam-4406	25	48	)	)	PUNCT
ejpam-4406	25	49	t	t	PROPN
ejpam-4406	25	50	.	.	PUNCT
ejpam-4406	26	1	where	where	SCONJ
ejpam-4406	26	2	m1	m1	PROPN
ejpam-4406	26	3	=	=	SYM
ejpam-4406	26	4	0.04,m2	0.04,m2	NUM
ejpam-4406	27	1	=	=	SYM
ejpam-4406	27	2	3×	3×	NUM
ejpam-4406	27	3	107	107	NUM
ejpam-4406	27	4	and	and	CCONJ
ejpam-4406	27	5	m3	m3	PROPN
ejpam-4406	27	6	=	=	SYM
ejpam-4406	27	7	104	104	NUM
ejpam-4406	27	8	,	,	PUNCT
ejpam-4406	27	9	and	and	CCONJ
ejpam-4406	27	10	the	the	DET
ejpam-4406	27	11	initial	initial	ADJ
ejpam-4406	27	12	concentrations	concentration	NOUN
ejpam-4406	27	13	were	be	AUX
ejpam-4406	27	14	y01	y01	NOUN
ejpam-4406	27	15	=	=	SYM
ejpam-4406	27	16	1/100000	1/100000	NUM
ejpam-4406	27	17	,	,	PUNCT
ejpam-4406	27	18	y02	y02	NOUN
ejpam-4406	27	19	=	=	SYM
ejpam-4406	27	20	0	0	NUM
ejpam-4406	27	21	and	and	CCONJ
ejpam-4406	27	22	y03	y03	NOUN
ejpam-4406	27	23	=	=	SYM
ejpam-4406	27	24	0	0	X
ejpam-4406	27	25	.	.	PUNCT
ejpam-4406	28	1	our	our	PRON
ejpam-4406	28	2	new	new	PROPN
ejpam-4406	28	3	caputo	caputo	PROPN
ejpam-4406	28	4	–	–	PUNCT
ejpam-4406	28	5	fabrizio	fabrizio	PROPN
ejpam-4406	28	6	fractional	fractional	ADJ
ejpam-4406	28	7	model	model	NOUN
ejpam-4406	28	8	for	for	ADP
ejpam-4406	28	9	robertson	robertson	PROPN
ejpam-4406	28	10	problem	problem	NOUN
ejpam-4406	28	11	can	can	AUX
ejpam-4406	28	12	therefore	therefore	ADV
ejpam-4406	28	13	be	be	AUX
ejpam-4406	28	14	written	write	VERB
ejpam-4406	28	15	as	as	SCONJ
ejpam-4406	28	16	follows	follow	VERB
ejpam-4406	28	17	:	:	PUNCT
ejpam-4406	29	1	cf	cf	NOUN
ejpam-4406	29	2	0	0	NUM
ejpam-4406	30	1	dρ	dρ	NOUN
ejpam-4406	30	2	t	t	NOUN
ejpam-4406	30	3	y1	y1	NOUN
ejpam-4406	30	4	=	=	PUNCT
ejpam-4406	31	1	−m1y1	−m1y1	PROPN
ejpam-4406	31	2	+	+	ADJ
ejpam-4406	31	3	m3y2y3	m3y2y3	NOUN
ejpam-4406	31	4	,	,	PUNCT
ejpam-4406	31	5	cf	cf	NOUN
ejpam-4406	31	6	0	0	NUM
ejpam-4406	32	1	dρ	dρ	NOUN
ejpam-4406	32	2	t	t	NOUN
ejpam-4406	33	1	y2	y2	NOUN
ejpam-4406	34	1	=	=	SYM
ejpam-4406	35	1	m1y1	m1y1	PROPN
ejpam-4406	35	2	−m2y	−m2y	PROPN
ejpam-4406	35	3	2	2	NUM
ejpam-4406	35	4	2	2	NUM
ejpam-4406	35	5	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	35	6	,	,	PUNCT
ejpam-4406	35	7	cf	cf	NOUN
ejpam-4406	35	8	0	0	NUM
ejpam-4406	35	9	dρ	dρ	ADJ
ejpam-4406	35	10	t	t	NOUN
ejpam-4406	35	11	y3	y3	NOUN
ejpam-4406	36	1	=	=	PUNCT
ejpam-4406	36	2	m2y	m2y	PROPN
ejpam-4406	36	3	2	2	NUM
ejpam-4406	36	4	2	2	NUM
ejpam-4406	36	5	.	.	PUNCT
ejpam-4406	36	6	(	(	PUNCT
ejpam-4406	36	7	5	5	NUM
ejpam-4406	36	8	)	)	PUNCT
ejpam-4406	36	9	2	2	NUM
ejpam-4406	36	10	.	.	PUNCT
ejpam-4406	36	11	basic	basic	ADJ
ejpam-4406	36	12	definitions	definition	NOUN
ejpam-4406	36	13	some	some	DET
ejpam-4406	36	14	basic	basic	ADJ
ejpam-4406	36	15	definitions	definition	NOUN
ejpam-4406	36	16	are	be	AUX
ejpam-4406	36	17	given	give	VERB
ejpam-4406	36	18	in	in	ADP
ejpam-4406	36	19	this	this	DET
ejpam-4406	36	20	section	section	NOUN
ejpam-4406	37	1	[	[	X
ejpam-4406	37	2	3–5	3–5	NOUN
ejpam-4406	37	3	,	,	PUNCT
ejpam-4406	37	4	12	12	NUM
ejpam-4406	37	5	]	]	PUNCT
ejpam-4406	37	6	.	.	PUNCT
ejpam-4406	38	1	definition	definition	NOUN
ejpam-4406	38	2	1	1	NUM
ejpam-4406	38	3	.	.	PUNCT
ejpam-4406	38	4	sumudu	sumudu	NOUN
ejpam-4406	38	5	transform	transform	NOUN
ejpam-4406	38	6	for	for	ADP
ejpam-4406	38	7	any	any	DET
ejpam-4406	38	8	function	function	NOUN
ejpam-4406	38	9	ϕ(t	ϕ(t	NUM
ejpam-4406	38	10	)	)	PUNCT
ejpam-4406	38	11	over	over	ADP
ejpam-4406	38	12	a	a	DET
ejpam-4406	38	13	set	set	NOUN
ejpam-4406	38	14	is	be	AUX
ejpam-4406	38	15	given	give	VERB
ejpam-4406	38	16	as	as	ADP
ejpam-4406	38	17	,	,	PUNCT
ejpam-4406	38	18	a	a	PRON
ejpam-4406	38	19	=	=	X
ejpam-4406	38	20	{	{	PUNCT
ejpam-4406	38	21	ϕ(t	ϕ(t	NUM
ejpam-4406	38	22	)	)	PUNCT
ejpam-4406	38	23	:	:	PUNCT
ejpam-4406	38	24	there	there	PRON
ejpam-4406	38	25	exist	exist	VERB
ejpam-4406	38	26	λ	λ	PROPN
ejpam-4406	38	27	,	,	PUNCT
ejpam-4406	38	28	τ1	τ1	NOUN
ejpam-4406	38	29	,	,	PUNCT
ejpam-4406	38	30	τ2	τ2	NOUN
ejpam-4406	38	31	>	>	X
ejpam-4406	38	32	0	0	NUM
ejpam-4406	38	33	,	,	PUNCT
ejpam-4406	38	34	|ϕ(t)|	|ϕ(t)|	NUM
ejpam-4406	38	35	<	<	X
ejpam-4406	38	36	λexp(|t|/τi	λexp(|t|/τi	PROPN
ejpam-4406	38	37	)	)	PUNCT
ejpam-4406	38	38	,	,	PUNCT
ejpam-4406	38	39	if	if	SCONJ
ejpam-4406	38	40	t	t	PROPN
ejpam-4406	38	41	∈	∈	PROPN
ejpam-4406	38	42	(	(	PUNCT
ejpam-4406	38	43	−1)i	−1)i	X
ejpam-4406	38	44	×	×	NOUN
ejpam-4406	38	45	[	[	X
ejpam-4406	38	46	0,∞	0,∞	NOUN
ejpam-4406	38	47	)	)	PUNCT
ejpam-4406	38	48	}	}	PUNCT
ejpam-4406	38	49	is	be	AUX
ejpam-4406	38	50	described	describe	VERB
ejpam-4406	38	51	by	by	ADP
ejpam-4406	38	52	f	f	PROPN
ejpam-4406	38	53	(	(	PUNCT
ejpam-4406	38	54	u	u	NOUN
ejpam-4406	38	55	)	)	PUNCT
ejpam-4406	38	56	=	=	SYM
ejpam-4406	39	1	st	st	PROPN
ejpam-4406	40	1	[	[	X
ejpam-4406	40	2	ϕ(t	ϕ(t	NUM
ejpam-4406	40	3	)	)	PUNCT
ejpam-4406	40	4	]	]	PUNCT
ejpam-4406	41	1	=	=	PUNCT
ejpam-4406	41	2	∫	∫	PROPN
ejpam-4406	41	3	∞	∞	PROPN
ejpam-4406	41	4	0	0	NUM
ejpam-4406	41	5	exp(−t)ϕ(ut)dt	exp(−t)ϕ(ut)dt	PROPN
ejpam-4406	41	6	,	,	PUNCT
ejpam-4406	41	7	u	u	NOUN
ejpam-4406	41	8	∈	∈	PROPN
ejpam-4406	41	9	(	(	PUNCT
ejpam-4406	41	10	−τ1	−τ1	PROPN
ejpam-4406	41	11	,	,	PUNCT
ejpam-4406	41	12	τ2	τ2	NOUN
ejpam-4406	41	13	)	)	PUNCT
ejpam-4406	41	14	.	.	PUNCT
ejpam-4406	42	1	(	(	PUNCT
ejpam-4406	42	2	6	6	X
ejpam-4406	42	3	)	)	PUNCT
ejpam-4406	42	4	definition	definition	NOUN
ejpam-4406	42	5	2	2	NUM
ejpam-4406	42	6	.	.	PUNCT
ejpam-4406	42	7	atangana	atangana	PROPN
ejpam-4406	42	8	-	-	PUNCT
ejpam-4406	42	9	baleanu	baleanu	PROPN
ejpam-4406	42	10	derivative	derivative	NOUN
ejpam-4406	42	11	in	in	ADP
ejpam-4406	42	12	caputo	caputo	PROPN
ejpam-4406	42	13	sense	sense	NOUN
ejpam-4406	42	14	is	be	AUX
ejpam-4406	42	15	described	describe	VERB
ejpam-4406	42	16	as	as	ADP
ejpam-4406	42	17	[	[	X
ejpam-4406	42	18	13	13	NUM
ejpam-4406	42	19	]	]	PUNCT
ejpam-4406	42	20	:	:	PUNCT
ejpam-4406	42	21	abc	abc	PROPN
ejpam-4406	42	22	a	a	DET
ejpam-4406	42	23	dα	dα	PROPN
ejpam-4406	42	24	τ	τ	PROPN
ejpam-4406	42	25	ϕ(t	ϕ(t	NUM
ejpam-4406	42	26	)	)	PUNCT
ejpam-4406	42	27	=	=	SYM
ejpam-4406	42	28	ab(α	ab(α	X
ejpam-4406	42	29	)	)	PUNCT
ejpam-4406	42	30	n−	n−	NOUN
ejpam-4406	42	31	α	α	PRON
ejpam-4406	42	32	∫	∫	PROPN
ejpam-4406	42	33	t	t	PROPN
ejpam-4406	42	34	a	a	DET
ejpam-4406	42	35	dn	dn	NOUN
ejpam-4406	42	36	dwn	dwn	VERB
ejpam-4406	42	37	ϕ(w)eα	ϕ(w)eα	PROPN
ejpam-4406	42	38	−α(t−	−α(t−	PRON
ejpam-4406	42	39	w)α	w)α	ADJ
ejpam-4406	42	40	(	(	PUNCT
ejpam-4406	42	41	n−	n−	NOUN
ejpam-4406	42	42	α	α	NOUN
ejpam-4406	42	43	)	)	PUNCT
ejpam-4406	42	44	dw	dw	PROPN
ejpam-4406	42	45	,	,	PUNCT
ejpam-4406	42	46	n−	n−	NOUN
ejpam-4406	42	47	1	1	NUM
ejpam-4406	42	48	<	<	X
ejpam-4406	42	49	α	α	X
ejpam-4406	42	50	<	<	X
ejpam-4406	42	51	n.	n.	NOUN
ejpam-4406	42	52	(	(	PUNCT
ejpam-4406	42	53	7	7	NUM
ejpam-4406	42	54	)	)	PUNCT
ejpam-4406	42	55	the	the	DET
ejpam-4406	42	56	laplace	laplace	NOUN
ejpam-4406	42	57	transform	transform	NOUN
ejpam-4406	42	58	of	of	ADP
ejpam-4406	42	59	equation	equation	NOUN
ejpam-4406	42	60	(	(	PUNCT
ejpam-4406	42	61	7	7	X
ejpam-4406	42	62	)	)	PUNCT
ejpam-4406	42	63	is	be	AUX
ejpam-4406	42	64	acquired	acquire	VERB
ejpam-4406	42	65	as	as	ADP
ejpam-4406	42	66	:	:	PUNCT
ejpam-4406	42	67	l[abc	l[abc	X
ejpam-4406	42	68	a	a	DET
ejpam-4406	42	69	dα	dα	ADJ
ejpam-4406	42	70	τ	τ	PROPN
ejpam-4406	42	71	ϕ(t)](s	ϕ(t)](s	NUM
ejpam-4406	42	72	)	)	PUNCT
ejpam-4406	42	73	=	=	SYM
ejpam-4406	42	74	ab(α	ab(α	NUM
ejpam-4406	42	75	)	)	PUNCT
ejpam-4406	42	76	1−	1−	NUM
ejpam-4406	42	77	α	α	NOUN
ejpam-4406	42	78	(	(	PUNCT
ejpam-4406	42	79	sαl[ϕ(t)](s)−	sαl[ϕ(t)](s)−	PROPN
ejpam-4406	42	80	sα−1ϕ(0	sα−1ϕ(0	PROPN
ejpam-4406	42	81	)	)	PUNCT
ejpam-4406	42	82	)	)	PUNCT
ejpam-4406	43	1	sα	sα	ADV
ejpam-4406	44	1	+	+	CCONJ
ejpam-4406	44	2	α	α	PROPN
ejpam-4406	44	3	1−α	1−α	NUM
ejpam-4406	44	4	.	.	PUNCT
ejpam-4406	45	1	(	(	PUNCT
ejpam-4406	45	2	8)	8)	NUM
ejpam-4406	45	3	by	by	ADP
ejpam-4406	45	4	using	use	VERB
ejpam-4406	45	5	sumudu	sumudu	NOUN
ejpam-4406	45	6	transform	transform	NOUN
ejpam-4406	45	7	(	(	PUNCT
ejpam-4406	45	8	st	st	NOUN
ejpam-4406	45	9	)	)	PUNCT
ejpam-4406	45	10	for	for	ADP
ejpam-4406	45	11	equation	equation	NOUN
ejpam-4406	45	12	(	(	PUNCT
ejpam-4406	45	13	7	7	NUM
ejpam-4406	45	14	)	)	PUNCT
ejpam-4406	45	15	,	,	PUNCT
ejpam-4406	45	16	we	we	PRON
ejpam-4406	45	17	obtain	obtain	VERB
ejpam-4406	45	18	st	st	PROPN
ejpam-4406	46	1	[	[	X
ejpam-4406	46	2	abc	abc	PROPN
ejpam-4406	46	3	0	0	PROPN
ejpam-4406	46	4	dα	dα	PROPN
ejpam-4406	46	5	τ	τ	PROPN
ejpam-4406	46	6	ϕ(t)](s	ϕ(t)](s	NUM
ejpam-4406	46	7	)	)	PUNCT
ejpam-4406	46	8	=	=	SYM
ejpam-4406	46	9	b(α	b(α	PROPN
ejpam-4406	46	10	)	)	PUNCT
ejpam-4406	46	11	1−	1−	NUM
ejpam-4406	46	12	α	α	NOUN
ejpam-4406	46	13	αγ(α+	αγ(α+	PROPN
ejpam-4406	46	14	1)eα	1)eα	PROPN
ejpam-4406	46	15	(	(	PUNCT
ejpam-4406	46	16	−1	−1	NOUN
ejpam-4406	46	17	1−	1−	NUM
ejpam-4406	46	18	α	α	NOUN
ejpam-4406	46	19	wα)[st	wα)[st	NOUN
ejpam-4406	46	20	(	(	PUNCT
ejpam-4406	46	21	ϕ(t))−	ϕ(t))−	ADJ
ejpam-4406	46	22	ϕ(0	ϕ(0	PROPN
ejpam-4406	46	23	)	)	PUNCT
ejpam-4406	46	24	]	]	PUNCT
ejpam-4406	46	25	.	.	PUNCT
ejpam-4406	47	1	(	(	PUNCT
ejpam-4406	47	2	9	9	X
ejpam-4406	47	3	)	)	PUNCT
ejpam-4406	47	4	j.	j.	PROPN
ejpam-4406	47	5	asad	asad	PROPN
ejpam-4406	47	6	et	et	PROPN
ejpam-4406	47	7	al	al	PROPN
ejpam-4406	47	8	.	.	PUNCT
ejpam-4406	47	9	/	/	SYM
ejpam-4406	47	10	eur	eur	PROPN
ejpam-4406	47	11	.	.	PUNCT
ejpam-4406	48	1	j.	j.	PROPN
ejpam-4406	48	2	pure	pure	PROPN
ejpam-4406	48	3	appl	appl	PROPN
ejpam-4406	48	4	.	.	PROPN
ejpam-4406	48	5	math	math	PROPN
ejpam-4406	48	6	,	,	PUNCT
ejpam-4406	48	7	15	15	NUM
ejpam-4406	48	8	(	(	PUNCT
ejpam-4406	48	9	3	3	NUM
ejpam-4406	48	10	)	)	PUNCT
ejpam-4406	48	11	(	(	PUNCT
ejpam-4406	48	12	2022	2022	NUM
ejpam-4406	48	13	)	)	PUNCT
ejpam-4406	48	14	,	,	PUNCT
ejpam-4406	48	15	1144	1144	NUM
ejpam-4406	48	16	-	-	SYM
ejpam-4406	48	17	1157	1157	NUM
ejpam-4406	48	18	1146	1146	NUM
ejpam-4406	48	19	3	3	NUM
ejpam-4406	48	20	.	.	PUNCT
ejpam-4406	49	1	caputo	caputo	PROPN
ejpam-4406	49	2	fabrizio	fabrizio	PROPN
ejpam-4406	49	3	derivative	derivative	NOUN
ejpam-4406	49	4	by	by	ADP
ejpam-4406	49	5	using	use	VERB
ejpam-4406	49	6	sumudu	sumudu	NOUN
ejpam-4406	49	7	transform	transform	NOUN
ejpam-4406	49	8	on	on	ADP
ejpam-4406	49	9	system	system	NOUN
ejpam-4406	49	10	(	(	PUNCT
ejpam-4406	49	11	5	5	NUM
ejpam-4406	49	12	)	)	PUNCT
ejpam-4406	49	13	,	,	PUNCT
ejpam-4406	49	14	we	we	PRON
ejpam-4406	49	15	have	have	VERB
ejpam-4406	49	16	m(ρ	m(ρ	PRON
ejpam-4406	49	17	)	)	PUNCT
ejpam-4406	49	18	st	st	NOUN
ejpam-4406	49	19	(	(	PUNCT
ejpam-4406	49	20	y1(t))−	y1(t))−	PROPN
ejpam-4406	49	21	y1(0	y1(0	PROPN
ejpam-4406	49	22	)	)	PUNCT
ejpam-4406	49	23	1−	1−	NUM
ejpam-4406	49	24	ρ+	ρ+	NOUN
ejpam-4406	49	25	ρu	ρu	ADP
ejpam-4406	49	26	=	=	SYM
ejpam-4406	49	27	st	st	PROPN
ejpam-4406	50	1	[	[	X
ejpam-4406	50	2	−m1y1	−m1y1	PROPN
ejpam-4406	50	3	+	+	ADJ
ejpam-4406	50	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	50	5	]	]	SYM
ejpam-4406	50	6	,	,	PUNCT
ejpam-4406	50	7	m(ρ	m(ρ	NUM
ejpam-4406	50	8	)	)	PUNCT
ejpam-4406	50	9	st	st	PROPN
ejpam-4406	50	10	(	(	PUNCT
ejpam-4406	50	11	y2(t))−	y2(t))−	PROPN
ejpam-4406	50	12	y2(0	y2(0	PROPN
ejpam-4406	50	13	)	)	PUNCT
ejpam-4406	50	14	1−	1−	NUM
ejpam-4406	50	15	ρ+	ρ+	NOUN
ejpam-4406	50	16	ρu	ρu	ADP
ejpam-4406	50	17	=	=	SYM
ejpam-4406	50	18	st	st	PROPN
ejpam-4406	51	1	[	[	X
ejpam-4406	51	2	m1y1	m1y1	NOUN
ejpam-4406	51	3	−m2y	−m2y	PROPN
ejpam-4406	51	4	2	2	NUM
ejpam-4406	51	5	2	2	NUM
ejpam-4406	51	6	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	51	7	]	]	X
ejpam-4406	51	8	,	,	PUNCT
ejpam-4406	51	9	m(ρ	m(ρ	NUM
ejpam-4406	51	10	)	)	PUNCT
ejpam-4406	51	11	st	st	PROPN
ejpam-4406	51	12	(	(	PUNCT
ejpam-4406	51	13	y3(t))−	y3(t))−	PROPN
ejpam-4406	51	14	y3(0	y3(0	PROPN
ejpam-4406	51	15	)	)	PUNCT
ejpam-4406	51	16	1−	1−	NUM
ejpam-4406	51	17	ρ+	ρ+	NOUN
ejpam-4406	51	18	ρu	ρu	ADP
ejpam-4406	51	19	=	=	SYM
ejpam-4406	51	20	st	st	PROPN
ejpam-4406	52	1	[	[	X
ejpam-4406	52	2	m2y	m2y	PROPN
ejpam-4406	52	3	2	2	NUM
ejpam-4406	52	4	2	2	NUM
ejpam-4406	52	5	]	]	PUNCT
ejpam-4406	52	6	.	.	PUNCT
ejpam-4406	53	1	(	(	PUNCT
ejpam-4406	53	2	10	10	NUM
ejpam-4406	53	3	)	)	PUNCT
ejpam-4406	53	4	rearranging	rearrange	VERB
ejpam-4406	53	5	the	the	DET
ejpam-4406	53	6	above	above	ADJ
ejpam-4406	53	7	equations	equation	NOUN
ejpam-4406	53	8	yields	yield	VERB
ejpam-4406	53	9	:	:	PUNCT
ejpam-4406	53	10	st	st	PROPN
ejpam-4406	53	11	(	(	PUNCT
ejpam-4406	53	12	y1(t	y1(t	PROPN
ejpam-4406	53	13	)	)	PUNCT
ejpam-4406	53	14	)	)	PUNCT
ejpam-4406	53	15	=	=	SYM
ejpam-4406	53	16	y1(0	y1(0	PROPN
ejpam-4406	53	17	)	)	PUNCT
ejpam-4406	54	1	+	+	SYM
ejpam-4406	54	2	1−	1−	NUM
ejpam-4406	54	3	ρ+	ρ+	NOUN
ejpam-4406	54	4	ρu	ρu	ADP
ejpam-4406	54	5	m(ρ	m(ρ	NUM
ejpam-4406	54	6	)	)	PUNCT
ejpam-4406	54	7	st	st	NOUN
ejpam-4406	55	1	[	[	X
ejpam-4406	55	2	−m1y1	−m1y1	PROPN
ejpam-4406	55	3	+	+	ADJ
ejpam-4406	55	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	55	5	]	]	X
ejpam-4406	55	6	,	,	PUNCT
ejpam-4406	55	7	st	st	PROPN
ejpam-4406	55	8	(	(	PUNCT
ejpam-4406	55	9	y2(t	y2(t	PROPN
ejpam-4406	55	10	)	)	PUNCT
ejpam-4406	55	11	)	)	PUNCT
ejpam-4406	55	12	=	=	SYM
ejpam-4406	55	13	y2(0	y2(0	PROPN
ejpam-4406	55	14	)	)	PUNCT
ejpam-4406	56	1	+	+	SYM
ejpam-4406	56	2	1−	1−	NUM
ejpam-4406	56	3	ρ+	ρ+	NOUN
ejpam-4406	56	4	ρu	ρu	ADP
ejpam-4406	56	5	m(ρ	m(ρ	NUM
ejpam-4406	56	6	)	)	PUNCT
ejpam-4406	56	7	st	st	NOUN
ejpam-4406	57	1	[	[	X
ejpam-4406	57	2	m1y1	m1y1	NOUN
ejpam-4406	57	3	−m2y	−m2y	PROPN
ejpam-4406	57	4	2	2	NUM
ejpam-4406	57	5	2	2	NUM
ejpam-4406	57	6	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	57	7	]	]	PUNCT
ejpam-4406	57	8	,	,	PUNCT
ejpam-4406	57	9	st	st	PROPN
ejpam-4406	57	10	(	(	PUNCT
ejpam-4406	57	11	y3(t	y3(t	PROPN
ejpam-4406	57	12	)	)	PUNCT
ejpam-4406	57	13	)	)	PUNCT
ejpam-4406	58	1	=	=	SYM
ejpam-4406	58	2	y3(0	y3(0	PROPN
ejpam-4406	58	3	)	)	PUNCT
ejpam-4406	59	1	+	+	SYM
ejpam-4406	59	2	1−	1−	NUM
ejpam-4406	59	3	ρ+	ρ+	NOUN
ejpam-4406	59	4	ρu	ρu	ADP
ejpam-4406	59	5	m(ρ	m(ρ	NUM
ejpam-4406	59	6	)	)	PUNCT
ejpam-4406	59	7	st	st	NOUN
ejpam-4406	60	1	[	[	X
ejpam-4406	60	2	m2y	m2y	PROPN
ejpam-4406	60	3	2	2	NUM
ejpam-4406	60	4	2	2	NUM
ejpam-4406	60	5	]	]	PUNCT
ejpam-4406	60	6	.	.	PUNCT
ejpam-4406	61	1	(	(	PUNCT
ejpam-4406	61	2	11	11	X
ejpam-4406	61	3	)	)	PUNCT
ejpam-4406	61	4	taking	take	VERB
ejpam-4406	61	5	inverse	inverse	NOUN
ejpam-4406	61	6	transform	transform	NOUN
ejpam-4406	61	7	for	for	ADP
ejpam-4406	61	8	system	system	NOUN
ejpam-4406	61	9	(	(	PUNCT
ejpam-4406	61	10	11	11	NUM
ejpam-4406	61	11	)	)	PUNCT
ejpam-4406	61	12	gives	give	VERB
ejpam-4406	61	13	:	:	PUNCT
ejpam-4406	61	14	y1(t	y1(t	X
ejpam-4406	61	15	)	)	PUNCT
ejpam-4406	61	16	=	=	SYM
ejpam-4406	61	17	y1(0	y1(0	PROPN
ejpam-4406	61	18	)	)	PUNCT
ejpam-4406	62	1	+	+	CCONJ
ejpam-4406	62	2	st−1	st−1	PROPN
ejpam-4406	62	3	[	[	PUNCT
ejpam-4406	62	4	1−	1−	NUM
ejpam-4406	62	5	ρ+	ρ+	NOUN
ejpam-4406	62	6	ρu	ρu	ADP
ejpam-4406	62	7	m(ρ	m(ρ	NUM
ejpam-4406	62	8	)	)	PUNCT
ejpam-4406	62	9	st	st	PROPN
ejpam-4406	62	10	(	(	PUNCT
ejpam-4406	62	11	−m1y1	−m1y1	PROPN
ejpam-4406	62	12	+	+	ADJ
ejpam-4406	62	13	m3y2y3	m3y2y3	NOUN
ejpam-4406	62	14	)	)	PUNCT
ejpam-4406	62	15	]	]	PUNCT
ejpam-4406	62	16	,	,	PUNCT
ejpam-4406	62	17	y2(t	y2(t	PROPN
ejpam-4406	62	18	)	)	PUNCT
ejpam-4406	62	19	=	=	SYM
ejpam-4406	62	20	y2(0	y2(0	PROPN
ejpam-4406	62	21	)	)	PUNCT
ejpam-4406	63	1	+	+	CCONJ
ejpam-4406	63	2	st−1	st−1	PROPN
ejpam-4406	63	3	[	[	PUNCT
ejpam-4406	63	4	1−	1−	NUM
ejpam-4406	63	5	ρ+	ρ+	NOUN
ejpam-4406	63	6	ρu	ρu	ADP
ejpam-4406	63	7	m(ρ	m(ρ	NUM
ejpam-4406	63	8	)	)	PUNCT
ejpam-4406	63	9	st	st	PROPN
ejpam-4406	63	10	(	(	PUNCT
ejpam-4406	63	11	m1y1	m1y1	PROPN
ejpam-4406	63	12	−m2y	−m2y	PROPN
ejpam-4406	63	13	2	2	NUM
ejpam-4406	63	14	2	2	NUM
ejpam-4406	63	15	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	63	16	)	)	PUNCT
ejpam-4406	63	17	]	]	PUNCT
ejpam-4406	63	18	,	,	PUNCT
ejpam-4406	63	19	y3(t	y3(t	NUM
ejpam-4406	63	20	)	)	PUNCT
ejpam-4406	63	21	=	=	SYM
ejpam-4406	63	22	y3(0	y3(0	PROPN
ejpam-4406	63	23	)	)	PUNCT
ejpam-4406	64	1	+	+	PUNCT
ejpam-4406	64	2	st−1	st−1	PROPN
ejpam-4406	64	3	[	[	PUNCT
ejpam-4406	64	4	1−	1−	NUM
ejpam-4406	64	5	ρ+	ρ+	NOUN
ejpam-4406	64	6	ρu	ρu	ADP
ejpam-4406	64	7	m(ρ	m(ρ	NUM
ejpam-4406	64	8	)	)	PUNCT
ejpam-4406	64	9	st	st	NOUN
ejpam-4406	65	1	(	(	PUNCT
ejpam-4406	65	2	m2y	m2y	PROPN
ejpam-4406	65	3	2	2	NUM
ejpam-4406	65	4	2	2	NUM
ejpam-4406	65	5	)	)	PUNCT
ejpam-4406	65	6	]	]	PUNCT
ejpam-4406	65	7	.	.	PUNCT
ejpam-4406	66	1	(	(	PUNCT
ejpam-4406	66	2	12	12	NUM
ejpam-4406	66	3	)	)	PUNCT
ejpam-4406	66	4	we	we	PRON
ejpam-4406	66	5	get	get	VERB
ejpam-4406	66	6	this	this	DET
ejpam-4406	66	7	recursive	recursive	ADJ
ejpam-4406	66	8	form	form	NOUN
ejpam-4406	66	9	as	as	ADP
ejpam-4406	66	10	:	:	PUNCT
ejpam-4406	66	11	y1(n+1)(t	y1(n+1)(t	NUM
ejpam-4406	66	12	)	)	PUNCT
ejpam-4406	66	13	=	=	SYM
ejpam-4406	66	14	y1(n)(0	y1(n)(0	X
ejpam-4406	66	15	)	)	PUNCT
ejpam-4406	66	16	+	+	CCONJ
ejpam-4406	66	17	st−1	st−1	PROPN
ejpam-4406	66	18	[	[	PUNCT
ejpam-4406	66	19	1−	1−	NUM
ejpam-4406	66	20	ρ+	ρ+	NOUN
ejpam-4406	66	21	ρu	ρu	ADP
ejpam-4406	66	22	m(ρ	m(ρ	PRON
ejpam-4406	66	23	)	)	PUNCT
ejpam-4406	66	24	st	st	PROPN
ejpam-4406	66	25	(	(	PUNCT
ejpam-4406	66	26	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	66	27	)	)	PUNCT
ejpam-4406	66	28	+	+	NOUN
ejpam-4406	66	29	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	66	30	)	)	PUNCT
ejpam-4406	66	31	)	)	PUNCT
ejpam-4406	66	32	]	]	PUNCT
ejpam-4406	66	33	,	,	PUNCT
ejpam-4406	66	34	y2(n+1)(t	y2(n+1)(t	X
ejpam-4406	66	35	)	)	PUNCT
ejpam-4406	66	36	=	=	SYM
ejpam-4406	67	1	y2(n)(0	y2(n)(0	NUM
ejpam-4406	67	2	)	)	PUNCT
ejpam-4406	67	3	+	+	CCONJ
ejpam-4406	67	4	st−1	st−1	PROPN
ejpam-4406	67	5	[	[	PUNCT
ejpam-4406	67	6	1−	1−	NUM
ejpam-4406	67	7	ρ+	ρ+	NOUN
ejpam-4406	67	8	ρu	ρu	ADP
ejpam-4406	67	9	m(ρ	m(ρ	PRON
ejpam-4406	67	10	)	)	PUNCT
ejpam-4406	67	11	st	st	PROPN
ejpam-4406	67	12	(	(	PUNCT
ejpam-4406	67	13	m1y1(n	m1y1(n	PROPN
ejpam-4406	67	14	)	)	PUNCT
ejpam-4406	67	15	−m2y	−m2y	NUM
ejpam-4406	67	16	2	2	NUM
ejpam-4406	67	17	2(n	2(n	NUM
ejpam-4406	67	18	)	)	PUNCT
ejpam-4406	67	19	−m3y2(n)y3(n	−m3y2(n)y3(n	NOUN
ejpam-4406	67	20	)	)	PUNCT
ejpam-4406	67	21	)	)	PUNCT
ejpam-4406	68	1	]	]	PUNCT
ejpam-4406	68	2	,	,	PUNCT
ejpam-4406	68	3	y3(n+1)(t	y3(n+1)(t	PROPN
ejpam-4406	68	4	)	)	PUNCT
ejpam-4406	68	5	=	=	SYM
ejpam-4406	68	6	y3(n)(0	y3(n)(0	X
ejpam-4406	68	7	)	)	PUNCT
ejpam-4406	69	1	+	+	CCONJ
ejpam-4406	69	2	st−1	st−1	PROPN
ejpam-4406	69	3	[	[	PUNCT
ejpam-4406	69	4	1−	1−	NUM
ejpam-4406	69	5	ρ+	ρ+	NOUN
ejpam-4406	69	6	ρu	ρu	ADP
ejpam-4406	69	7	m(ρ	m(ρ	NUM
ejpam-4406	69	8	)	)	PUNCT
ejpam-4406	69	9	st	st	NOUN
ejpam-4406	70	1	(	(	PUNCT
ejpam-4406	70	2	m2y	m2y	PROPN
ejpam-4406	70	3	2	2	NUM
ejpam-4406	70	4	2(n	2(n	NUM
ejpam-4406	70	5	)	)	PUNCT
ejpam-4406	70	6	)	)	PUNCT
ejpam-4406	70	7	]	]	PUNCT
ejpam-4406	70	8	.	.	PUNCT
ejpam-4406	71	1	(	(	PUNCT
ejpam-4406	71	2	13	13	NUM
ejpam-4406	71	3	)	)	PUNCT
ejpam-4406	71	4	and	and	CCONJ
ejpam-4406	71	5	the	the	DET
ejpam-4406	71	6	solution	solution	NOUN
ejpam-4406	71	7	of	of	ADP
ejpam-4406	71	8	system	system	NOUN
ejpam-4406	71	9	(	(	PUNCT
ejpam-4406	71	10	13	13	NUM
ejpam-4406	71	11	)	)	PUNCT
ejpam-4406	71	12	is	be	AUX
ejpam-4406	71	13	obtained	obtain	VERB
ejpam-4406	71	14	as	as	ADP
ejpam-4406	71	15	:	:	PUNCT
ejpam-4406	71	16	y1(t	y1(t	X
ejpam-4406	71	17	)	)	PUNCT
ejpam-4406	71	18	=	=	SYM
ejpam-4406	71	19	lim	lim	PROPN
ejpam-4406	71	20	n→∞	n→∞	X
ejpam-4406	71	21	y1(n)(t	y1(n)(t	PROPN
ejpam-4406	71	22	)	)	PUNCT
ejpam-4406	71	23	,	,	PUNCT
ejpam-4406	71	24	y2(t	y2(t	PROPN
ejpam-4406	71	25	)	)	PUNCT
ejpam-4406	72	1	=	=	SYM
ejpam-4406	72	2	lim	lim	PROPN
ejpam-4406	72	3	n→∞	n→∞	NUM
ejpam-4406	72	4	y2(n)(t	y2(n)(t	NOUN
ejpam-4406	72	5	)	)	PUNCT
ejpam-4406	72	6	,	,	PUNCT
ejpam-4406	72	7	y3(t	y3(t	NUM
ejpam-4406	72	8	)	)	PUNCT
ejpam-4406	73	1	=	=	SYM
ejpam-4406	73	2	lim	lim	PROPN
ejpam-4406	73	3	n→∞	n→∞	NUM
ejpam-4406	73	4	y3(n)(t	y3(n)(t	PROPN
ejpam-4406	73	5	)	)	PUNCT
ejpam-4406	73	6	.	.	PUNCT
ejpam-4406	74	1	(	(	PUNCT
ejpam-4406	74	2	14	14	NUM
ejpam-4406	74	3	)	)	PUNCT
ejpam-4406	74	4	3.1	3.1	NUM
ejpam-4406	74	5	.	.	PUNCT
ejpam-4406	75	1	stability	stability	NOUN
ejpam-4406	75	2	analysis	analysis	NOUN
ejpam-4406	75	3	of	of	ADP
ejpam-4406	75	4	the	the	DET
ejpam-4406	75	5	problem	problem	NOUN
ejpam-4406	75	6	theorem	theorem	VERB
ejpam-4406	75	7	1	1	X
ejpam-4406	75	8	.	.	PUNCT
ejpam-4406	76	1	let	let	VERB
ejpam-4406	76	2	(	(	PUNCT
ejpam-4406	76	3	x1	x1	ADJ
ejpam-4406	76	4	,	,	PUNCT
ejpam-4406	76	5	.	.	PUNCT
ejpam-4406	76	6	)	)	PUNCT
ejpam-4406	77	1	be	be	AUX
ejpam-4406	77	2	a	a	DET
ejpam-4406	77	3	banach	banach	NOUN
ejpam-4406	77	4	space	space	NOUN
ejpam-4406	77	5	and	and	CCONJ
ejpam-4406	77	6	p	p	NOUN
ejpam-4406	77	7	be	be	AUX
ejpam-4406	77	8	a	a	DET
ejpam-4406	77	9	self	self	NOUN
ejpam-4406	77	10	-	-	PUNCT
ejpam-4406	77	11	map	map	NOUN
ejpam-4406	77	12	of	of	ADP
ejpam-4406	77	13	x1	x1	PROPN
ejpam-4406	77	14	satisfying	satisfy	VERB
ejpam-4406	77	15	∥px	∥px	PROPN
ejpam-4406	77	16	−	−	PROPN
ejpam-4406	78	1	py∥	py∥	PROPN
ejpam-4406	78	2	≤	≤	PROPN
ejpam-4406	78	3	c∥x−	c∥x−	ADV
ejpam-4406	79	1	px∥+	px∥+	X
ejpam-4406	79	2	c∥x−	c∥x−	PROPN
ejpam-4406	79	3	y∥	y∥	VERB
ejpam-4406	79	4	j.	j.	PROPN
ejpam-4406	79	5	asad	asad	PROPN
ejpam-4406	79	6	et	et	PROPN
ejpam-4406	79	7	al	al	PROPN
ejpam-4406	79	8	.	.	PUNCT
ejpam-4406	79	9	/	/	SYM
ejpam-4406	79	10	eur	eur	PROPN
ejpam-4406	79	11	.	.	PUNCT
ejpam-4406	80	1	j.	j.	PROPN
ejpam-4406	80	2	pure	pure	PROPN
ejpam-4406	80	3	appl	appl	PROPN
ejpam-4406	80	4	.	.	PROPN
ejpam-4406	80	5	math	math	PROPN
ejpam-4406	80	6	,	,	PUNCT
ejpam-4406	80	7	15	15	NUM
ejpam-4406	80	8	(	(	PUNCT
ejpam-4406	80	9	3	3	NUM
ejpam-4406	80	10	)	)	PUNCT
ejpam-4406	80	11	(	(	PUNCT
ejpam-4406	80	12	2022	2022	NUM
ejpam-4406	80	13	)	)	PUNCT
ejpam-4406	80	14	,	,	PUNCT
ejpam-4406	80	15	1144	1144	NUM
ejpam-4406	80	16	-	-	SYM
ejpam-4406	80	17	1157	1157	NUM
ejpam-4406	80	18	1147	1147	NUM
ejpam-4406	80	19	for	for	ADP
ejpam-4406	80	20	all	all	DET
ejpam-4406	80	21	x	x	NOUN
ejpam-4406	80	22	,	,	PUNCT
ejpam-4406	80	23	y	y	PROPN
ejpam-4406	80	24	∈	∈	PROPN
ejpam-4406	80	25	x1	x1	PROPN
ejpam-4406	80	26	,	,	PUNCT
ejpam-4406	80	27	where	where	SCONJ
ejpam-4406	80	28	0	0	NUM
ejpam-4406	80	29	≤	≤	NUM
ejpam-4406	80	30	c	c	NOUN
ejpam-4406	80	31	,	,	PUNCT
ejpam-4406	80	32	0	0	NUM
ejpam-4406	80	33	≤	≤	NUM
ejpam-4406	81	1	c	c	AUX
ejpam-4406	81	2	<	<	X
ejpam-4406	81	3	1	1	X
ejpam-4406	81	4	.	.	PUNCT
ejpam-4406	81	5	consider	consider	VERB
ejpam-4406	81	6	that	that	SCONJ
ejpam-4406	81	7	p	p	NOUN
ejpam-4406	81	8	is	be	AUX
ejpam-4406	81	9	a	a	DET
ejpam-4406	81	10	p	p	NOUN
ejpam-4406	81	11	-	-	PUNCT
ejpam-4406	81	12	stable	stable	ADJ
ejpam-4406	81	13	.	.	PUNCT
ejpam-4406	82	1	we	we	PRON
ejpam-4406	82	2	have	have	VERB
ejpam-4406	82	3	y1(n+1)(t	y1(n+1)(t	PRON
ejpam-4406	82	4	)	)	PUNCT
ejpam-4406	82	5	=	=	SYM
ejpam-4406	82	6	y1(n)(0	y1(n)(0	NUM
ejpam-4406	82	7	)	)	PUNCT
ejpam-4406	82	8	+	+	CCONJ
ejpam-4406	82	9	st−1	st−1	PROPN
ejpam-4406	82	10	[	[	PUNCT
ejpam-4406	82	11	1−	1−	NUM
ejpam-4406	82	12	ρ+	ρ+	NOUN
ejpam-4406	82	13	ρu	ρu	ADP
ejpam-4406	82	14	m(ρ	m(ρ	PRON
ejpam-4406	82	15	)	)	PUNCT
ejpam-4406	82	16	st	st	PROPN
ejpam-4406	82	17	(	(	PUNCT
ejpam-4406	82	18	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	82	19	)	)	PUNCT
ejpam-4406	82	20	+	+	NOUN
ejpam-4406	82	21	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	82	22	)	)	PUNCT
ejpam-4406	82	23	)	)	PUNCT
ejpam-4406	82	24	]	]	PUNCT
ejpam-4406	82	25	,	,	PUNCT
ejpam-4406	82	26	y2(n+1)(t	y2(n+1)(t	X
ejpam-4406	82	27	)	)	PUNCT
ejpam-4406	82	28	=	=	SYM
ejpam-4406	82	29	y2(n)(0	y2(n)(0	NUM
ejpam-4406	82	30	)	)	PUNCT
ejpam-4406	83	1	+	+	CCONJ
ejpam-4406	83	2	st−1	st−1	PROPN
ejpam-4406	83	3	[	[	PUNCT
ejpam-4406	83	4	1−	1−	NUM
ejpam-4406	83	5	ρ+	ρ+	NOUN
ejpam-4406	83	6	ρu	ρu	ADP
ejpam-4406	83	7	m(ρ	m(ρ	PRON
ejpam-4406	83	8	)	)	PUNCT
ejpam-4406	83	9	st	st	PROPN
ejpam-4406	83	10	(	(	PUNCT
ejpam-4406	83	11	m1y1(n	m1y1(n	PROPN
ejpam-4406	83	12	)	)	PUNCT
ejpam-4406	83	13	−m2y	−m2y	NUM
ejpam-4406	83	14	2	2	NUM
ejpam-4406	83	15	2(n	2(n	NUM
ejpam-4406	83	16	)	)	PUNCT
ejpam-4406	83	17	−m3y2(n)y3(n	−m3y2(n)y3(n	NOUN
ejpam-4406	83	18	)	)	PUNCT
ejpam-4406	83	19	)	)	PUNCT
ejpam-4406	84	1	]	]	PUNCT
ejpam-4406	84	2	,	,	PUNCT
ejpam-4406	84	3	y3(n+1)(t	y3(n+1)(t	PROPN
ejpam-4406	84	4	)	)	PUNCT
ejpam-4406	84	5	=	=	SYM
ejpam-4406	84	6	y3(n)(0	y3(n)(0	X
ejpam-4406	84	7	)	)	PUNCT
ejpam-4406	85	1	+	+	CCONJ
ejpam-4406	85	2	st−1	st−1	PROPN
ejpam-4406	85	3	[	[	PUNCT
ejpam-4406	85	4	1−	1−	NUM
ejpam-4406	85	5	ρ+	ρ+	NOUN
ejpam-4406	85	6	ρu	ρu	ADP
ejpam-4406	85	7	m(ρ	m(ρ	NUM
ejpam-4406	85	8	)	)	PUNCT
ejpam-4406	85	9	st	st	NOUN
ejpam-4406	86	1	(	(	PUNCT
ejpam-4406	86	2	m2y	m2y	PROPN
ejpam-4406	86	3	2	2	NUM
ejpam-4406	86	4	2(n	2(n	NUM
ejpam-4406	86	5	)	)	PUNCT
ejpam-4406	86	6	)	)	PUNCT
ejpam-4406	86	7	]	]	PUNCT
ejpam-4406	86	8	.	.	PUNCT
ejpam-4406	87	1	(	(	PUNCT
ejpam-4406	87	2	15	15	NUM
ejpam-4406	87	3	)	)	PUNCT
ejpam-4406	87	4	where	where	SCONJ
ejpam-4406	87	5	1−ρ+ρu	1−ρ+ρu	PROPN
ejpam-4406	87	6	m(ρ	m(ρ	PRON
ejpam-4406	87	7	)	)	PUNCT
ejpam-4406	87	8	is	be	AUX
ejpam-4406	87	9	the	the	DET
ejpam-4406	87	10	fractional	fractional	ADJ
ejpam-4406	87	11	lagrange	lagrange	NOUN
ejpam-4406	87	12	multiplier	multiplier	NOUN
ejpam-4406	87	13	.	.	PUNCT
ejpam-4406	88	1	theorem	theorem	NOUN
ejpam-4406	88	2	2	2	NUM
ejpam-4406	88	3	.	.	PUNCT
ejpam-4406	89	1	let	let	VERB
ejpam-4406	89	2	us	we	PRON
ejpam-4406	89	3	describe	describe	VERB
ejpam-4406	89	4	a	a	DET
ejpam-4406	89	5	self	self	NOUN
ejpam-4406	89	6	-	-	PUNCT
ejpam-4406	89	7	map	map	NOUN
ejpam-4406	89	8	p	p	NOUN
ejpam-4406	89	9	as	as	ADP
ejpam-4406	89	10	p	p	PROPN
ejpam-4406	89	11	(	(	PUNCT
ejpam-4406	89	12	y1(n)(t	y1(n)(t	PROPN
ejpam-4406	89	13	)	)	PUNCT
ejpam-4406	89	14	)	)	PUNCT
ejpam-4406	90	1	=	=	SYM
ejpam-4406	90	2	y1(n+1)(t	y1(n+1)(t	X
ejpam-4406	90	3	)	)	PUNCT
ejpam-4406	90	4	=	=	SYM
ejpam-4406	90	5	y1(n)(0	y1(n)(0	X
ejpam-4406	90	6	)	)	PUNCT
ejpam-4406	90	7	+	+	CCONJ
ejpam-4406	90	8	st−1	st−1	PROPN
ejpam-4406	90	9	[	[	PUNCT
ejpam-4406	90	10	1−	1−	NUM
ejpam-4406	90	11	ρ+	ρ+	NOUN
ejpam-4406	90	12	ρu	ρu	ADP
ejpam-4406	90	13	m(ρ	m(ρ	PRON
ejpam-4406	90	14	)	)	PUNCT
ejpam-4406	90	15	st	st	PROPN
ejpam-4406	90	16	(	(	PUNCT
ejpam-4406	90	17	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	90	18	)	)	PUNCT
ejpam-4406	90	19	+	+	NOUN
ejpam-4406	90	20	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	90	21	)	)	PUNCT
ejpam-4406	90	22	)	)	PUNCT
ejpam-4406	91	1	]	]	PUNCT
ejpam-4406	91	2	,	,	PUNCT
ejpam-4406	91	3	p	p	X
ejpam-4406	91	4	(	(	PUNCT
ejpam-4406	91	5	y2(n)(t	y2(n)(t	ADJ
ejpam-4406	91	6	)	)	PUNCT
ejpam-4406	91	7	)	)	PUNCT
ejpam-4406	91	8	=	=	SYM
ejpam-4406	91	9	y2(n+1)(t	y2(n+1)(t	PROPN
ejpam-4406	91	10	)	)	PUNCT
ejpam-4406	91	11	=	=	SYM
ejpam-4406	91	12	y2(n)(0	y2(n)(0	NUM
ejpam-4406	91	13	)	)	PUNCT
ejpam-4406	91	14	+	+	CCONJ
ejpam-4406	91	15	st−1	st−1	PROPN
ejpam-4406	91	16	[	[	PUNCT
ejpam-4406	91	17	1−	1−	NUM
ejpam-4406	91	18	ρ+	ρ+	NOUN
ejpam-4406	91	19	ρu	ρu	ADP
ejpam-4406	91	20	m(ρ	m(ρ	PRON
ejpam-4406	91	21	)	)	PUNCT
ejpam-4406	91	22	st	st	PROPN
ejpam-4406	91	23	(	(	PUNCT
ejpam-4406	91	24	m1y1(n	m1y1(n	PROPN
ejpam-4406	91	25	)	)	PUNCT
ejpam-4406	91	26	−m2y	−m2y	NUM
ejpam-4406	91	27	2	2	NUM
ejpam-4406	91	28	2(n	2(n	NUM
ejpam-4406	91	29	)	)	PUNCT
ejpam-4406	91	30	−m3y2(n)y3(n	−m3y2(n)y3(n	NOUN
ejpam-4406	91	31	)	)	PUNCT
ejpam-4406	91	32	)	)	PUNCT
ejpam-4406	92	1	]	]	PUNCT
ejpam-4406	92	2	,	,	PUNCT
ejpam-4406	92	3	p	p	X
ejpam-4406	92	4	(	(	PUNCT
ejpam-4406	92	5	y3(n)(t	y3(n)(t	PROPN
ejpam-4406	92	6	)	)	PUNCT
ejpam-4406	92	7	)	)	PUNCT
ejpam-4406	92	8	=	=	SYM
ejpam-4406	92	9	y3(n+1)(t	y3(n+1)(t	X
ejpam-4406	92	10	)	)	PUNCT
ejpam-4406	92	11	=	=	SYM
ejpam-4406	92	12	y3(n)(0	y3(n)(0	X
ejpam-4406	92	13	)	)	PUNCT
ejpam-4406	92	14	+	+	CCONJ
ejpam-4406	92	15	st−1	st−1	PROPN
ejpam-4406	92	16	[	[	PUNCT
ejpam-4406	92	17	1−	1−	NUM
ejpam-4406	92	18	ρ+	ρ+	NOUN
ejpam-4406	92	19	ρu	ρu	ADP
ejpam-4406	92	20	m(ρ	m(ρ	NUM
ejpam-4406	92	21	)	)	PUNCT
ejpam-4406	92	22	st	st	NOUN
ejpam-4406	93	1	(	(	PUNCT
ejpam-4406	93	2	m2y	m2y	PROPN
ejpam-4406	93	3	2	2	NUM
ejpam-4406	93	4	2(n	2(n	NUM
ejpam-4406	93	5	)	)	PUNCT
ejpam-4406	93	6	)	)	PUNCT
ejpam-4406	93	7	]	]	PUNCT
ejpam-4406	93	8	.	.	PUNCT
ejpam-4406	94	1	(	(	PUNCT
ejpam-4406	94	2	16	16	NUM
ejpam-4406	94	3	)	)	PUNCT
ejpam-4406	94	4	is	be	AUX
ejpam-4406	94	5	p	p	NOUN
ejpam-4406	94	6	-stable	-stable	ADJ
ejpam-4406	94	7	in	in	ADP
ejpam-4406	94	8	l1(a	l1(a	ADP
ejpam-4406	94	9	,	,	PUNCT
ejpam-4406	94	10	b	b	NOUN
ejpam-4406	94	11	)	)	PUNCT
ejpam-4406	94	12	if	if	SCONJ
ejpam-4406	94	13	c	c	NOUN
ejpam-4406	94	14	=	=	SYM
ejpam-4406	94	15	(	(	PUNCT
ejpam-4406	94	16	[	[	X
ejpam-4406	94	17	1−m1f(γ	1−m1f(γ	NUM
ejpam-4406	94	18	)	)	PUNCT
ejpam-4406	94	19	+	+	NOUN
ejpam-4406	94	20	m3(k	m3(k	PROPN
ejpam-4406	94	21	+	+	ADJ
ejpam-4406	94	22	l)h(γ	l)h(γ	PROPN
ejpam-4406	94	23	)	)	PUNCT
ejpam-4406	94	24	]	]	PUNCT
ejpam-4406	94	25	,	,	PUNCT
ejpam-4406	94	26	[	[	X
ejpam-4406	94	27	1	1	NUM
ejpam-4406	94	28	+	+	NOUN
ejpam-4406	94	29	m1f(γ)−m2g(γ)−m3(k	m1f(γ)−m2g(γ)−m3(k	NOUN
ejpam-4406	94	30	+	+	ADJ
ejpam-4406	94	31	l)h(γ	l)h(γ	PROPN
ejpam-4406	94	32	)	)	PUNCT
ejpam-4406	94	33	]	]	PUNCT
ejpam-4406	94	34	,	,	PUNCT
ejpam-4406	95	1	[	[	X
ejpam-4406	95	2	1	1	NUM
ejpam-4406	95	3	+	+	ADJ
ejpam-4406	95	4	m2g(γ	m2g(γ	NOUN
ejpam-4406	95	5	)	)	PUNCT
ejpam-4406	95	6	]	]	PUNCT
ejpam-4406	95	7	)	)	PUNCT
ejpam-4406	95	8	,	,	PUNCT
ejpam-4406	95	9	c	c	X
ejpam-4406	95	10	=	=	SYM
ejpam-4406	95	11	(	(	PUNCT
ejpam-4406	95	12	0	0	NUM
ejpam-4406	95	13	,	,	PUNCT
ejpam-4406	95	14	0	0	NUM
ejpam-4406	95	15	,	,	PUNCT
ejpam-4406	95	16	0	0	NUM
ejpam-4406	95	17	)	)	PUNCT
ejpam-4406	95	18	.	.	PUNCT
ejpam-4406	96	1	(	(	PUNCT
ejpam-4406	96	2	17	17	NUM
ejpam-4406	96	3	)	)	PUNCT
ejpam-4406	96	4	proof	proof	NOUN
ejpam-4406	96	5	.	.	PUNCT
ejpam-4406	97	1	we	we	PRON
ejpam-4406	97	2	prove	prove	VERB
ejpam-4406	97	3	that	that	SCONJ
ejpam-4406	97	4	p	p	PROPN
ejpam-4406	97	5	has	have	VERB
ejpam-4406	97	6	a	a	DET
ejpam-4406	97	7	fixed	fix	VERB
ejpam-4406	97	8	point	point	NOUN
ejpam-4406	97	9	.	.	PUNCT
ejpam-4406	98	1	for	for	ADP
ejpam-4406	98	2	this	this	PRON
ejpam-4406	98	3	,	,	PUNCT
ejpam-4406	98	4	we	we	PRON
ejpam-4406	98	5	evaluate	evaluate	VERB
ejpam-4406	98	6	the	the	DET
ejpam-4406	98	7	following	following	NOUN
ejpam-4406	98	8	for	for	ADP
ejpam-4406	98	9	all	all	DET
ejpam-4406	98	10	(	(	PUNCT
ejpam-4406	98	11	m	m	NOUN
ejpam-4406	98	12	,	,	PUNCT
ejpam-4406	98	13	n	n	CCONJ
ejpam-4406	98	14	)	)	PUNCT
ejpam-4406	98	15	∈	∈	PROPN
ejpam-4406	98	16	n×	n×	PROPN
ejpam-4406	98	17	n.	n.	NOUN
ejpam-4406	98	18	p	p	NOUN
ejpam-4406	98	19	(	(	PUNCT
ejpam-4406	98	20	y1(n)(t))−	y1(n)(t))−	PROPN
ejpam-4406	98	21	p	p	NOUN
ejpam-4406	98	22	(	(	PUNCT
ejpam-4406	98	23	y1(m)(t	y1(m)(t	PROPN
ejpam-4406	98	24	)	)	PUNCT
ejpam-4406	98	25	)	)	PUNCT
ejpam-4406	99	1	=	=	SYM
ejpam-4406	99	2	y1(n)(t)−	y1(n)(t)−	PROPN
ejpam-4406	99	3	y1(m)(t	y1(m)(t	PROPN
ejpam-4406	99	4	)	)	PUNCT
ejpam-4406	100	1	+	+	CCONJ
ejpam-4406	100	2	st−1	st−1	PROPN
ejpam-4406	100	3	[	[	PUNCT
ejpam-4406	100	4	1−	1−	NUM
ejpam-4406	100	5	ρ+	ρ+	NOUN
ejpam-4406	100	6	ρu	ρu	ADP
ejpam-4406	100	7	m(ρ	m(ρ	PRON
ejpam-4406	100	8	)	)	PUNCT
ejpam-4406	100	9	st	st	PROPN
ejpam-4406	100	10	(	(	PUNCT
ejpam-4406	100	11	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	100	12	)	)	PUNCT
ejpam-4406	100	13	+	+	NOUN
ejpam-4406	100	14	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	100	15	)	)	PUNCT
ejpam-4406	100	16	)	)	PUNCT
ejpam-4406	100	17	]	]	PUNCT
ejpam-4406	101	1	−	−	PROPN
ejpam-4406	101	2	st−1	st−1	PROPN
ejpam-4406	101	3	[	[	PUNCT
ejpam-4406	101	4	1−	1−	NUM
ejpam-4406	101	5	ρ+	ρ+	NOUN
ejpam-4406	101	6	ρu	ρu	ADP
ejpam-4406	101	7	m(ρ	m(ρ	PRON
ejpam-4406	101	8	)	)	PUNCT
ejpam-4406	101	9	st	st	PROPN
ejpam-4406	101	10	(	(	PUNCT
ejpam-4406	101	11	−m1y1(m	−m1y1(m	PROPN
ejpam-4406	101	12	)	)	PUNCT
ejpam-4406	101	13	+	+	NOUN
ejpam-4406	101	14	m3y2(m)y3(m	m3y2(m)y3(m	NOUN
ejpam-4406	101	15	)	)	PUNCT
ejpam-4406	101	16	)	)	PUNCT
ejpam-4406	102	1	]	]	PUNCT
ejpam-4406	102	2	,	,	PUNCT
ejpam-4406	102	3	p	p	X
ejpam-4406	102	4	(	(	PUNCT
ejpam-4406	102	5	y2(n)(t))−	y2(n)(t))−	NOUN
ejpam-4406	102	6	p	p	X
ejpam-4406	102	7	(	(	PUNCT
ejpam-4406	102	8	y2(m)(t	y2(m)(t	PROPN
ejpam-4406	102	9	)	)	PUNCT
ejpam-4406	102	10	)	)	PUNCT
ejpam-4406	103	1	=	=	SYM
ejpam-4406	103	2	y2(n)(t)−	y2(n)(t)−	PROPN
ejpam-4406	103	3	y2(m)(t	y2(m)(t	PROPN
ejpam-4406	103	4	)	)	PUNCT
ejpam-4406	104	1	+	+	CCONJ
ejpam-4406	104	2	st−1	st−1	PROPN
ejpam-4406	104	3	[	[	PUNCT
ejpam-4406	104	4	1−	1−	NUM
ejpam-4406	104	5	ρ+	ρ+	NOUN
ejpam-4406	104	6	ρu	ρu	ADP
ejpam-4406	104	7	m(ρ	m(ρ	PRON
ejpam-4406	104	8	)	)	PUNCT
ejpam-4406	104	9	st	st	PROPN
ejpam-4406	104	10	(	(	PUNCT
ejpam-4406	104	11	m1y1(n	m1y1(n	PROPN
ejpam-4406	104	12	)	)	PUNCT
ejpam-4406	104	13	−m2y	−m2y	NUM
ejpam-4406	104	14	2	2	NUM
ejpam-4406	104	15	2(n	2(n	NUM
ejpam-4406	104	16	)	)	PUNCT
ejpam-4406	105	1	+	+	PROPN
ejpam-4406	105	2	m3y2(n)y3(n))]−	m3y2(n)y3(n))]−	PROPN
ejpam-4406	105	3	st−1	st−1	PROPN
ejpam-4406	105	4	[	[	PUNCT
ejpam-4406	105	5	1−	1−	NUM
ejpam-4406	105	6	ρ+	ρ+	NOUN
ejpam-4406	105	7	ρu	ρu	ADP
ejpam-4406	105	8	m(ρ	m(ρ	PRON
ejpam-4406	105	9	)	)	PUNCT
ejpam-4406	105	10	st	st	PROPN
ejpam-4406	105	11	(	(	PUNCT
ejpam-4406	105	12	m1y1(m	m1y1(m	PROPN
ejpam-4406	105	13	)	)	PUNCT
ejpam-4406	105	14	−m2y	−m2y	NUM
ejpam-4406	105	15	2	2	NUM
ejpam-4406	105	16	2(m	2(m	NUM
ejpam-4406	105	17	)	)	PUNCT
ejpam-4406	105	18	−m3y2(m)y3(m	−m3y2(m)y3(m	NUM
ejpam-4406	105	19	)	)	PUNCT
ejpam-4406	105	20	)	)	PUNCT
ejpam-4406	105	21	]	]	PUNCT
ejpam-4406	105	22	,	,	PUNCT
ejpam-4406	105	23	p	p	X
ejpam-4406	105	24	(	(	PUNCT
ejpam-4406	105	25	y3(n)(t))−	y3(n)(t))−	X
ejpam-4406	105	26	p	p	X
ejpam-4406	105	27	(	(	PUNCT
ejpam-4406	105	28	y3(m)(t	y3(m)(t	NOUN
ejpam-4406	105	29	)	)	PUNCT
ejpam-4406	105	30	)	)	PUNCT
ejpam-4406	106	1	=	=	PUNCT
ejpam-4406	107	1	y3(n)(t)−	y3(n)(t)−	PROPN
ejpam-4406	107	2	y3(m)(t	y3(m)(t	PROPN
ejpam-4406	107	3	)	)	PUNCT
ejpam-4406	107	4	+	+	CCONJ
ejpam-4406	107	5	st−1	st−1	PROPN
ejpam-4406	107	6	[	[	PUNCT
ejpam-4406	107	7	1−	1−	NUM
ejpam-4406	107	8	ρ+	ρ+	NOUN
ejpam-4406	107	9	ρu	ρu	ADP
ejpam-4406	107	10	m(ρ	m(ρ	NUM
ejpam-4406	107	11	)	)	PUNCT
ejpam-4406	107	12	st	st	NOUN
ejpam-4406	108	1	(	(	PUNCT
ejpam-4406	108	2	m2y	m2y	PROPN
ejpam-4406	108	3	2	2	NUM
ejpam-4406	108	4	2(n	2(n	NUM
ejpam-4406	108	5	)	)	PUNCT
ejpam-4406	108	6	)	)	PUNCT
ejpam-4406	108	7	]	]	PUNCT
ejpam-4406	109	1	−	−	PROPN
ejpam-4406	109	2	st−1	st−1	PROPN
ejpam-4406	109	3	[	[	PUNCT
ejpam-4406	109	4	1−	1−	NUM
ejpam-4406	109	5	ρ+	ρ+	NOUN
ejpam-4406	109	6	ρu	ρu	ADP
ejpam-4406	109	7	m(ρ	m(ρ	NUM
ejpam-4406	109	8	)	)	PUNCT
ejpam-4406	109	9	st	st	NOUN
ejpam-4406	109	10	(	(	PUNCT
ejpam-4406	109	11	m2y	m2y	PROPN
ejpam-4406	109	12	2	2	NUM
ejpam-4406	109	13	2(m	2(m	NUM
ejpam-4406	109	14	)	)	PUNCT
ejpam-4406	109	15	)	)	PUNCT
ejpam-4406	109	16	]	]	PUNCT
ejpam-4406	109	17	.	.	PUNCT
ejpam-4406	110	1	(	(	PUNCT
ejpam-4406	110	2	18	18	NUM
ejpam-4406	110	3	)	)	PUNCT
ejpam-4406	110	4	j.	j.	PROPN
ejpam-4406	110	5	asad	asad	PROPN
ejpam-4406	110	6	et	et	PROPN
ejpam-4406	110	7	al	al	PROPN
ejpam-4406	110	8	.	.	PUNCT
ejpam-4406	110	9	/	/	SYM
ejpam-4406	110	10	eur	eur	PROPN
ejpam-4406	110	11	.	.	PUNCT
ejpam-4406	111	1	j.	j.	PROPN
ejpam-4406	111	2	pure	pure	PROPN
ejpam-4406	111	3	appl	appl	PROPN
ejpam-4406	111	4	.	.	PROPN
ejpam-4406	111	5	math	math	PROPN
ejpam-4406	111	6	,	,	PUNCT
ejpam-4406	111	7	15	15	NUM
ejpam-4406	111	8	(	(	PUNCT
ejpam-4406	111	9	3	3	NUM
ejpam-4406	111	10	)	)	PUNCT
ejpam-4406	111	11	(	(	PUNCT
ejpam-4406	111	12	2022	2022	NUM
ejpam-4406	111	13	)	)	PUNCT
ejpam-4406	111	14	,	,	PUNCT
ejpam-4406	111	15	1144	1144	NUM
ejpam-4406	111	16	-	-	SYM
ejpam-4406	111	17	1157	1157	NUM
ejpam-4406	111	18	1148	1148	NUM
ejpam-4406	111	19	considering	consider	VERB
ejpam-4406	111	20	equation	equation	NOUN
ejpam-4406	111	21	(	(	PUNCT
ejpam-4406	111	22	18	18	NUM
ejpam-4406	111	23	)	)	PUNCT
ejpam-4406	111	24	,	,	PUNCT
ejpam-4406	111	25	we	we	PRON
ejpam-4406	111	26	get	get	VERB
ejpam-4406	111	27	∥p	∥p	ADJ
ejpam-4406	111	28	(	(	PUNCT
ejpam-4406	111	29	y1(n)(t))−	y1(n)(t))−	NOUN
ejpam-4406	111	30	p	p	NOUN
ejpam-4406	111	31	(	(	PUNCT
ejpam-4406	111	32	y1(m)(t))∥	y1(m)(t))∥	PROPN
ejpam-4406	111	33	=	=	SYM
ejpam-4406	111	34	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	111	35	y1(m)(t)|	y1(m)(t)|	PROPN
ejpam-4406	112	1	+	+	ADJ
ejpam-4406	112	2	st−1	st−1	PROPN
ejpam-4406	112	3	[	[	PUNCT
ejpam-4406	112	4	1−	1−	NUM
ejpam-4406	112	5	ρ+	ρ+	NOUN
ejpam-4406	112	6	ρu	ρu	ADP
ejpam-4406	112	7	m(ρ	m(ρ	PRON
ejpam-4406	112	8	)	)	PUNCT
ejpam-4406	112	9	st	st	PROPN
ejpam-4406	112	10	(	(	PUNCT
ejpam-4406	112	11	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	112	12	)	)	PUNCT
ejpam-4406	112	13	+	+	NOUN
ejpam-4406	112	14	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	112	15	)	)	PUNCT
ejpam-4406	112	16	)	)	PUNCT
ejpam-4406	112	17	]	]	PUNCT
ejpam-4406	113	1	−st−1	−st−1	X
ejpam-4406	113	2	[	[	PUNCT
ejpam-4406	113	3	1−	1−	NUM
ejpam-4406	113	4	ρ+	ρ+	NOUN
ejpam-4406	113	5	ρu	ρu	ADP
ejpam-4406	113	6	m(ρ	m(ρ	PRON
ejpam-4406	113	7	)	)	PUNCT
ejpam-4406	113	8	st	st	PROPN
ejpam-4406	113	9	(	(	PUNCT
ejpam-4406	113	10	−m1y1(m	−m1y1(m	PROPN
ejpam-4406	113	11	)	)	PUNCT
ejpam-4406	113	12	+	+	PROPN
ejpam-4406	113	13	m3y2(m)y3(m))]∥.	m3y2(m)y3(m))]∥.	PROPN
ejpam-4406	113	14	(	(	PUNCT
ejpam-4406	113	15	19	19	NUM
ejpam-4406	113	16	)	)	PUNCT
ejpam-4406	113	17	using	use	VERB
ejpam-4406	113	18	triangular	triangular	NOUN
ejpam-4406	113	19	inequality	inequality	NOUN
ejpam-4406	113	20	for	for	ADP
ejpam-4406	113	21	equation	equation	NOUN
ejpam-4406	113	22	(	(	PUNCT
ejpam-4406	113	23	19	19	NUM
ejpam-4406	113	24	)	)	PUNCT
ejpam-4406	113	25	,	,	PUNCT
ejpam-4406	113	26	we	we	PRON
ejpam-4406	113	27	get	get	VERB
ejpam-4406	113	28	∥p	∥p	ADJ
ejpam-4406	113	29	(	(	PUNCT
ejpam-4406	113	30	y1(n)(t))−	y1(n)(t))−	NOUN
ejpam-4406	113	31	p	p	NOUN
ejpam-4406	113	32	(	(	PUNCT
ejpam-4406	113	33	y1(m)(t))∥	y1(m)(t))∥	PROPN
ejpam-4406	113	34	=	=	SYM
ejpam-4406	113	35	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	113	36	y1(m)(t)∥	y1(m)(t)∥	PROPN
ejpam-4406	114	1	+	+	CCONJ
ejpam-4406	114	2	∥st−1	∥st−1	PROPN
ejpam-4406	114	3	[	[	PUNCT
ejpam-4406	114	4	1−	1−	NUM
ejpam-4406	114	5	ρ+	ρ+	NOUN
ejpam-4406	114	6	ρu	ρu	ADP
ejpam-4406	114	7	m(ρ	m(ρ	PRON
ejpam-4406	114	8	)	)	PUNCT
ejpam-4406	114	9	st	st	PROPN
ejpam-4406	114	10	(	(	PUNCT
ejpam-4406	114	11	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	114	12	)	)	PUNCT
ejpam-4406	114	13	+	+	NOUN
ejpam-4406	114	14	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	114	15	)	)	PUNCT
ejpam-4406	114	16	)	)	PUNCT
ejpam-4406	114	17	]	]	PUNCT
ejpam-4406	115	1	−	−	PROPN
ejpam-4406	115	2	st−1	st−1	PROPN
ejpam-4406	115	3	[	[	PUNCT
ejpam-4406	115	4	1−	1−	NUM
ejpam-4406	115	5	ρ+	ρ+	NOUN
ejpam-4406	115	6	ρu	ρu	ADP
ejpam-4406	115	7	m(ρ	m(ρ	PRON
ejpam-4406	115	8	)	)	PUNCT
ejpam-4406	115	9	st	st	PROPN
ejpam-4406	115	10	(	(	PUNCT
ejpam-4406	115	11	−m1y1(m	−m1y1(m	PROPN
ejpam-4406	115	12	)	)	PUNCT
ejpam-4406	115	13	+	+	NOUN
ejpam-4406	115	14	m3y2(m)y3(m))]∥	m3y2(m)y3(m))]∥	NUM
ejpam-4406	115	15	(	(	PUNCT
ejpam-4406	115	16	20	20	NUM
ejpam-4406	115	17	)	)	PUNCT
ejpam-4406	115	18	upon	upon	SCONJ
ejpam-4406	115	19	further	further	ADJ
ejpam-4406	115	20	simplification	simplification	NOUN
ejpam-4406	115	21	gives	give	VERB
ejpam-4406	115	22	:	:	PUNCT
ejpam-4406	115	23	∥p	∥p	ADJ
ejpam-4406	115	24	(	(	PUNCT
ejpam-4406	115	25	y1(n)(t))−	y1(n)(t))−	PROPN
ejpam-4406	115	26	p	p	NOUN
ejpam-4406	115	27	(	(	PUNCT
ejpam-4406	115	28	y1(m)(t))∥	y1(m)(t))∥	PROPN
ejpam-4406	115	29	=	=	SYM
ejpam-4406	115	30	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	115	31	y1(m)(t)∥	y1(m)(t)∥	PROPN
ejpam-4406	115	32	+	+	CCONJ
ejpam-4406	115	33	∥st−1	∥st−1	PROPN
ejpam-4406	115	34	[	[	PUNCT
ejpam-4406	115	35	1−	1−	NUM
ejpam-4406	115	36	ρ+	ρ+	NOUN
ejpam-4406	115	37	ρu	ρu	ADP
ejpam-4406	115	38	m(ρ	m(ρ	PRON
ejpam-4406	115	39	)	)	PUNCT
ejpam-4406	115	40	st	st	PROPN
ejpam-4406	115	41	(	(	PUNCT
ejpam-4406	115	42	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	115	43	)	)	PUNCT
ejpam-4406	116	1	+	+	NOUN
ejpam-4406	116	2	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	116	3	)	)	PUNCT
ejpam-4406	117	1	+	+	NOUN
ejpam-4406	118	1	m1y1(m	m1y1(m	X
ejpam-4406	118	2	)	)	PUNCT
ejpam-4406	118	3	−m3y2(m)y3(m))]∥	−m3y2(m)y3(m))]∥	ADP
ejpam-4406	118	4	(	(	PUNCT
ejpam-4406	118	5	21	21	NUM
ejpam-4406	118	6	)	)	PUNCT
ejpam-4406	118	7	∥p	∥p	PROPN
ejpam-4406	118	8	(	(	PUNCT
ejpam-4406	118	9	y1(n)(t))−	y1(n)(t))−	PROPN
ejpam-4406	118	10	p	p	NOUN
ejpam-4406	118	11	(	(	PUNCT
ejpam-4406	118	12	y1(m)(t))∥	y1(m)(t))∥	PROPN
ejpam-4406	118	13	=	=	SYM
ejpam-4406	118	14	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	118	15	y1(m)(t)∥	y1(m)(t)∥	PROPN
ejpam-4406	118	16	+	+	CCONJ
ejpam-4406	118	17	st−1	st−1	PROPN
ejpam-4406	118	18	[	[	PUNCT
ejpam-4406	118	19	1−	1−	NUM
ejpam-4406	118	20	ρ+	ρ+	NOUN
ejpam-4406	118	21	ρu	ρu	ADP
ejpam-4406	118	22	m(ρ	m(ρ	PRON
ejpam-4406	118	23	)	)	PUNCT
ejpam-4406	118	24	st	st	NOUN
ejpam-4406	118	25	(	(	PUNCT
ejpam-4406	118	26	∥	∥	X
ejpam-4406	118	27	−m1(y1(n	−m1(y1(n	NOUN
ejpam-4406	118	28	)	)	PUNCT
ejpam-4406	118	29	−	−	ADP
ejpam-4406	118	30	y1(m))∥+	y1(m))∥+	ADJ
ejpam-4406	118	31	∥m3y2(n)(y3(n	∥m3y2(n)(y3(n	NOUN
ejpam-4406	118	32	)	)	PUNCT
ejpam-4406	118	33	−	−	PROPN
ejpam-4406	118	34	y3(m))∥	y3(m))∥	NOUN
ejpam-4406	119	1	+	+	CCONJ
ejpam-4406	119	2	∥m3y3(m)(y2(n	∥m3y3(m)(y2(n	PROPN
ejpam-4406	119	3	)	)	PUNCT
ejpam-4406	119	4	−	−	PROPN
ejpam-4406	119	5	y2(m))∥	y2(m))∥	NOUN
ejpam-4406	119	6	)	)	PUNCT
ejpam-4406	119	7	]	]	PUNCT
ejpam-4406	119	8	.	.	PUNCT
ejpam-4406	120	1	(	(	PUNCT
ejpam-4406	120	2	22	22	X
ejpam-4406	120	3	)	)	PUNCT
ejpam-4406	120	4	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	120	5	y1(m)(t)∥	y1(m)(t)∥	PROPN
ejpam-4406	121	1	≈	≈	PROPN
ejpam-4406	121	2	∥y2(n)(t)−	∥y2(n)(t)−	PROPN
ejpam-4406	121	3	y2(m)(t)∥	y2(m)(t)∥	X
ejpam-4406	121	4	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	122	1	y1(m)(t)∥	y1(m)(t)∥	PRON
ejpam-4406	123	1	≈	≈	PROPN
ejpam-4406	123	2	∥y3(n)(t)−	∥y3(n)(t)−	PROPN
ejpam-4406	123	3	y3(m)(t)∥	y3(m)(t)∥	PRON
ejpam-4406	123	4	replacing	replace	VERB
ejpam-4406	123	5	this	this	PRON
ejpam-4406	123	6	in	in	ADP
ejpam-4406	123	7	equation	equation	NOUN
ejpam-4406	123	8	(	(	PUNCT
ejpam-4406	123	9	22	22	NUM
ejpam-4406	123	10	)	)	PUNCT
ejpam-4406	123	11	gives	give	VERB
ejpam-4406	123	12	:	:	PUNCT
ejpam-4406	123	13	∥p	∥p	ADJ
ejpam-4406	123	14	(	(	PUNCT
ejpam-4406	123	15	y1(n)(t))−	y1(n)(t))−	PROPN
ejpam-4406	123	16	p	p	NOUN
ejpam-4406	123	17	(	(	PUNCT
ejpam-4406	123	18	y1(m)(t))∥	y1(m)(t))∥	PROPN
ejpam-4406	123	19	=	=	SYM
ejpam-4406	123	20	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	123	21	y1(m)(t)∥	y1(m)(t)∥	PROPN
ejpam-4406	124	1	+	+	PROPN
ejpam-4406	124	2	st−1	st−1	PROPN
ejpam-4406	124	3	[	[	PUNCT
ejpam-4406	124	4	1−	1−	NUM
ejpam-4406	124	5	ρ+	ρ+	NOUN
ejpam-4406	124	6	ρu	ρu	ADP
ejpam-4406	124	7	m(ρ	m(ρ	PRON
ejpam-4406	124	8	)	)	PUNCT
ejpam-4406	124	9	st	st	NOUN
ejpam-4406	124	10	(	(	PUNCT
ejpam-4406	124	11	∥	∥	X
ejpam-4406	124	12	−m1(y1(n	−m1(y1(n	NOUN
ejpam-4406	124	13	)	)	PUNCT
ejpam-4406	124	14	−	−	ADP
ejpam-4406	124	15	y1(m))∥+	y1(m))∥+	ADJ
ejpam-4406	124	16	∥m3y2(n)(y1(n	∥m3y2(n)(y1(n	NOUN
ejpam-4406	124	17	)	)	PUNCT
ejpam-4406	124	18	−	−	NOUN
ejpam-4406	124	19	y1(m))∥	y1(m))∥	X
ejpam-4406	125	1	+	+	NOUN
ejpam-4406	125	2	∥m3y3(m)(y1(n	∥m3y3(m)(y1(n	PROPN
ejpam-4406	125	3	)	)	PUNCT
ejpam-4406	125	4	−	−	PROPN
ejpam-4406	125	5	y1(m))∥	y1(m))∥	PROPN
ejpam-4406	125	6	)	)	PUNCT
ejpam-4406	125	7	]	]	X
ejpam-4406	126	1	∥p	∥p	INTJ
ejpam-4406	126	2	(	(	PUNCT
ejpam-4406	126	3	y1(n)(t))−	y1(n)(t))−	PROPN
ejpam-4406	126	4	p	p	NOUN
ejpam-4406	126	5	(	(	PUNCT
ejpam-4406	126	6	y1(m)(t))∥	y1(m)(t))∥	NOUN
ejpam-4406	126	7	=	=	SYM
ejpam-4406	126	8	∥y1(n	∥y1(n	NOUN
ejpam-4406	126	9	)	)	PUNCT
ejpam-4406	126	10	−	−	NOUN
ejpam-4406	127	1	y1(m)∥[1	y1(m)∥[1	PRON
ejpam-4406	128	1	+	+	NOUN
ejpam-4406	128	2	st−1st	st−1st	NUM
ejpam-4406	128	3	(	(	PUNCT
ejpam-4406	128	4	1−	1−	NUM
ejpam-4406	128	5	ρ+	ρ+	NOUN
ejpam-4406	128	6	ρu	ρu	ADP
ejpam-4406	128	7	m(ρ	m(ρ	NUM
ejpam-4406	128	8	)	)	PUNCT
ejpam-4406	128	9	)	)	PUNCT
ejpam-4406	128	10	∥	∥	PUNCT
ejpam-4406	128	11	−m1∥+	−m1∥+	NOUN
ejpam-4406	128	12	st−1(st	st−1(st	NOUN
ejpam-4406	128	13	1−	1−	NUM
ejpam-4406	128	14	ρ+	ρ+	NOUN
ejpam-4406	128	15	ρu	ρu	ADP
ejpam-4406	128	16	m(ρ	m(ρ	NUM
ejpam-4406	128	17	)	)	PUNCT
ejpam-4406	128	18	)	)	PUNCT
ejpam-4406	128	19	∥m3(y2(n	∥m3(y2(n	PROPN
ejpam-4406	128	20	)	)	PUNCT
ejpam-4406	129	1	+	+	NUM
ejpam-4406	129	2	y3(m))∥	y3(m))∥	NOUN
ejpam-4406	129	3	]	]	X
ejpam-4406	129	4	(	(	PUNCT
ejpam-4406	129	5	23	23	NUM
ejpam-4406	129	6	)	)	PUNCT
ejpam-4406	129	7	j.	j.	PROPN
ejpam-4406	129	8	asad	asad	PROPN
ejpam-4406	129	9	et	et	PROPN
ejpam-4406	129	10	al	al	PROPN
ejpam-4406	129	11	.	.	PUNCT
ejpam-4406	129	12	/	/	SYM
ejpam-4406	129	13	eur	eur	PROPN
ejpam-4406	129	14	.	.	PUNCT
ejpam-4406	130	1	j.	j.	PROPN
ejpam-4406	130	2	pure	pure	PROPN
ejpam-4406	130	3	appl	appl	PROPN
ejpam-4406	130	4	.	.	PROPN
ejpam-4406	130	5	math	math	PROPN
ejpam-4406	130	6	,	,	PUNCT
ejpam-4406	130	7	15	15	NUM
ejpam-4406	130	8	(	(	PUNCT
ejpam-4406	130	9	3	3	NUM
ejpam-4406	130	10	)	)	PUNCT
ejpam-4406	130	11	(	(	PUNCT
ejpam-4406	130	12	2022	2022	NUM
ejpam-4406	130	13	)	)	PUNCT
ejpam-4406	130	14	,	,	PUNCT
ejpam-4406	130	15	1144	1144	NUM
ejpam-4406	130	16	-	-	SYM
ejpam-4406	130	17	1157	1157	NUM
ejpam-4406	130	18	1149	1149	NUM
ejpam-4406	130	19	since	since	SCONJ
ejpam-4406	130	20	y2(n	y2(n	PROPN
ejpam-4406	130	21	)	)	PUNCT
ejpam-4406	130	22	,	,	PUNCT
ejpam-4406	130	23	y3(m	y3(m	PROPN
ejpam-4406	130	24	)	)	PUNCT
ejpam-4406	130	25	are	be	AUX
ejpam-4406	130	26	bounded	bound	VERB
ejpam-4406	130	27	as	as	SCONJ
ejpam-4406	130	28	they	they	PRON
ejpam-4406	130	29	are	be	AUX
ejpam-4406	130	30	convergent	convergent	ADJ
ejpam-4406	130	31	sequence	sequence	NOUN
ejpam-4406	130	32	,	,	PUNCT
ejpam-4406	130	33	therefore	therefore	ADV
ejpam-4406	130	34	,	,	PUNCT
ejpam-4406	130	35	we	we	PRON
ejpam-4406	130	36	can	can	AUX
ejpam-4406	130	37	obtain	obtain	VERB
ejpam-4406	130	38	two	two	NUM
ejpam-4406	130	39	different	different	ADJ
ejpam-4406	130	40	constants	constant	NOUN
ejpam-4406	130	41	k	k	PROPN
ejpam-4406	130	42	,	,	PUNCT
ejpam-4406	130	43	l	l	NOUN
ejpam-4406	130	44	for	for	ADP
ejpam-4406	130	45	all	all	DET
ejpam-4406	130	46	“	"	PUNCT
ejpam-4406	130	47	t	t	PROPN
ejpam-4406	130	48	”	"	PUNCT
ejpam-4406	130	49	such	such	ADJ
ejpam-4406	130	50	that	that	SCONJ
ejpam-4406	130	51	∥y2(n)∥	∥y2(n)∥	ADJ
ejpam-4406	130	52	<	<	X
ejpam-4406	130	53	k	k	PROPN
ejpam-4406	130	54	,	,	PUNCT
ejpam-4406	130	55	∥y3(m)∥	∥y3(m)∥	ADJ
ejpam-4406	130	56	<	<	X
ejpam-4406	130	57	l	l	NOUN
ejpam-4406	130	58	,	,	PUNCT
ejpam-4406	130	59	(	(	PUNCT
ejpam-4406	130	60	m	m	NOUN
ejpam-4406	130	61	,	,	PUNCT
ejpam-4406	130	62	n	n	CCONJ
ejpam-4406	130	63	)	)	PUNCT
ejpam-4406	130	64	∈	∈	PROPN
ejpam-4406	130	65	n×	n×	PROPN
ejpam-4406	130	66	n.	n.	NOUN
ejpam-4406	130	67	(	(	PUNCT
ejpam-4406	130	68	24	24	NUM
ejpam-4406	130	69	)	)	PUNCT
ejpam-4406	130	70	now	now	ADV
ejpam-4406	130	71	considering	consider	VERB
ejpam-4406	130	72	equation	equation	NOUN
ejpam-4406	130	73	(	(	PUNCT
ejpam-4406	130	74	22	22	NUM
ejpam-4406	130	75	)	)	PUNCT
ejpam-4406	130	76	with	with	ADP
ejpam-4406	130	77	equation	equation	NOUN
ejpam-4406	130	78	(	(	PUNCT
ejpam-4406	130	79	23	23	NUM
ejpam-4406	130	80	)	)	PUNCT
ejpam-4406	130	81	,	,	PUNCT
ejpam-4406	130	82	we	we	PRON
ejpam-4406	130	83	get	get	VERB
ejpam-4406	130	84	∥p	∥p	ADJ
ejpam-4406	130	85	(	(	PUNCT
ejpam-4406	130	86	y1(n)(t))−	y1(n)(t))−	NOUN
ejpam-4406	130	87	p	p	NOUN
ejpam-4406	130	88	(	(	PUNCT
ejpam-4406	130	89	y1(m)(t))∥	y1(m)(t))∥	NOUN
ejpam-4406	130	90	=	=	SYM
ejpam-4406	130	91	(	(	PUNCT
ejpam-4406	130	92	1−m1f(γ	1−m1f(γ	NUM
ejpam-4406	130	93	)	)	PUNCT
ejpam-4406	131	1	+	+	NOUN
ejpam-4406	131	2	m3(k	m3(k	PROPN
ejpam-4406	131	3	+	+	NUM
ejpam-4406	131	4	l)h(γ))∥y1(n	l)h(γ))∥y1(n	NOUN
ejpam-4406	131	5	)	)	PUNCT
ejpam-4406	131	6	−	−	PROPN
ejpam-4406	131	7	y1(m)∥	y1(m)∥	NOUN
ejpam-4406	131	8	(	(	PUNCT
ejpam-4406	131	9	25	25	NUM
ejpam-4406	131	10	)	)	PUNCT
ejpam-4406	131	11	where	where	SCONJ
ejpam-4406	131	12	f	f	X
ejpam-4406	131	13	,	,	PUNCT
ejpam-4406	131	14	g	g	PROPN
ejpam-4406	131	15	and	and	CCONJ
ejpam-4406	131	16	h	h	NOUN
ejpam-4406	131	17	are	be	AUX
ejpam-4406	131	18	functions	function	NOUN
ejpam-4406	131	19	from	from	ADP
ejpam-4406	131	20	st−1st	st−1st	NUM
ejpam-4406	131	21	(	(	PUNCT
ejpam-4406	131	22	1−ρ+ρu	1−ρ+ρu	NUM
ejpam-4406	131	23	m(ρ	m(ρ	NUM
ejpam-4406	131	24	)	)	PUNCT
ejpam-4406	131	25	)	)	PUNCT
ejpam-4406	131	26	.	.	PUNCT
ejpam-4406	132	1	similarly	similarly	ADV
ejpam-4406	132	2	we	we	PRON
ejpam-4406	132	3	get	get	VERB
ejpam-4406	132	4	∥p	∥p	ADJ
ejpam-4406	132	5	(	(	PUNCT
ejpam-4406	132	6	y2(n)(t))−	y2(n)(t))−	NOUN
ejpam-4406	132	7	p	p	X
ejpam-4406	132	8	(	(	PUNCT
ejpam-4406	132	9	y2(m)(t))∥	y2(m)(t))∥	PROPN
ejpam-4406	132	10	=	=	SYM
ejpam-4406	132	11	(	(	PUNCT
ejpam-4406	132	12	1	1	NUM
ejpam-4406	132	13	+	+	NOUN
ejpam-4406	132	14	m1f(γ)−m2g(γ)−m3(k	m1f(γ)−m2g(γ)−m3(k	NOUN
ejpam-4406	132	15	+	+	SYM
ejpam-4406	132	16	l)h(γ))∥y2(n	l)h(γ))∥y2(n	NOUN
ejpam-4406	132	17	)	)	PUNCT
ejpam-4406	133	1	−	−	PROPN
ejpam-4406	134	1	y2(m)∥	y2(m)∥	NOUN
ejpam-4406	134	2	(	(	PUNCT
ejpam-4406	134	3	26	26	NUM
ejpam-4406	134	4	)	)	PUNCT
ejpam-4406	134	5	∥p	∥p	NOUN
ejpam-4406	134	6	(	(	PUNCT
ejpam-4406	134	7	y3(n)(t))−	y3(n)(t))−	PRON
ejpam-4406	134	8	p	p	X
ejpam-4406	134	9	(	(	PUNCT
ejpam-4406	134	10	y3(m)(t))∥	y3(m)(t))∥	PROPN
ejpam-4406	134	11	=	=	SYM
ejpam-4406	134	12	(	(	PUNCT
ejpam-4406	134	13	1	1	NUM
ejpam-4406	134	14	+	+	NOUN
ejpam-4406	134	15	m2g(γ))∥y3((n))−	m2g(γ))∥y3((n))−	X
ejpam-4406	134	16	y3(m)∥	y3(m)∥	PROPN
ejpam-4406	134	17	(	(	PUNCT
ejpam-4406	134	18	27	27	NUM
ejpam-4406	134	19	)	)	PUNCT
ejpam-4406	134	20	where	where	SCONJ
ejpam-4406	134	21	1−m1f(γ	1−m1f(γ	NUM
ejpam-4406	134	22	)	)	PUNCT
ejpam-4406	134	23	+	+	NOUN
ejpam-4406	134	24	m3(k	m3(k	PROPN
ejpam-4406	134	25	+	+	ADJ
ejpam-4406	134	26	l)h(γ	l)h(γ	PROPN
ejpam-4406	134	27	)	)	PUNCT
ejpam-4406	134	28	<	<	X
ejpam-4406	134	29	1	1	NUM
ejpam-4406	134	30	,	,	PUNCT
ejpam-4406	134	31	1+m1f(γ)−m2g(γ)−m3(k	1+m1f(γ)−m2g(γ)−m3(k	NUM
ejpam-4406	134	32	+	+	CCONJ
ejpam-4406	134	33	l)h(γ	l)h(γ	PROPN
ejpam-4406	134	34	)	)	PUNCT
ejpam-4406	134	35	<	<	X
ejpam-4406	134	36	1	1	NUM
ejpam-4406	134	37	,	,	PUNCT
ejpam-4406	134	38	1+m2g(γ	1+m2g(γ	NUM
ejpam-4406	134	39	)	)	PUNCT
ejpam-4406	134	40	<	<	X
ejpam-4406	134	41	1	1	NUM
ejpam-4406	134	42	,	,	PUNCT
ejpam-4406	134	43	then	then	ADV
ejpam-4406	134	44	,	,	PUNCT
ejpam-4406	134	45	we	we	PRON
ejpam-4406	134	46	get	get	VERB
ejpam-4406	134	47	c	c	NOUN
ejpam-4406	134	48	=	=	SYM
ejpam-4406	134	49	(	(	PUNCT
ejpam-4406	134	50	0	0	NUM
ejpam-4406	134	51	,	,	PUNCT
ejpam-4406	134	52	0	0	NUM
ejpam-4406	134	53	,	,	PUNCT
ejpam-4406	134	54	0	0	NUM
ejpam-4406	134	55	)	)	PUNCT
ejpam-4406	134	56	,	,	PUNCT
ejpam-4406	134	57	c	c	X
ejpam-4406	134	58	=	=	SYM
ejpam-4406	134	59	(	(	PUNCT
ejpam-4406	134	60	1−m1f(γ	1−m1f(γ	NUM
ejpam-4406	134	61	)	)	PUNCT
ejpam-4406	134	62	+	+	NOUN
ejpam-4406	134	63	m3(k	m3(k	PROPN
ejpam-4406	134	64	+	+	ADJ
ejpam-4406	134	65	l)h(γ	l)h(γ	PROPN
ejpam-4406	134	66	)	)	PUNCT
ejpam-4406	134	67	,	,	PUNCT
ejpam-4406	134	68	1	1	NUM
ejpam-4406	134	69	+	+	NOUN
ejpam-4406	134	70	m1f(γ)−m2g(γ)−m3(k	m1f(γ)−m2g(γ)−m3(k	NOUN
ejpam-4406	134	71	+	+	ADJ
ejpam-4406	134	72	l)h(γ	l)h(γ	PROPN
ejpam-4406	134	73	)	)	PUNCT
ejpam-4406	134	74	,	,	PUNCT
ejpam-4406	134	75	1	1	NUM
ejpam-4406	134	76	+	+	ADJ
ejpam-4406	134	77	m2g(γ	m2g(γ	NOUN
ejpam-4406	134	78	)	)	PUNCT
ejpam-4406	134	79	)	)	PUNCT
ejpam-4406	134	80	.	.	PUNCT
ejpam-4406	135	1	4	4	X
ejpam-4406	135	2	.	.	X
ejpam-4406	135	3	atangana	atangana	PROPN
ejpam-4406	135	4	-	-	PUNCT
ejpam-4406	135	5	baleanu	baleanu	PROPN
ejpam-4406	135	6	derivative	derivative	NOUN
ejpam-4406	135	7	in	in	ADP
ejpam-4406	135	8	caputo	caputo	PROPN
ejpam-4406	135	9	sense	sense	NOUN
ejpam-4406	135	10	we	we	PRON
ejpam-4406	135	11	consider	consider	VERB
ejpam-4406	135	12	abc	abc	PROPN
ejpam-4406	135	13	0	0	PROPN
ejpam-4406	135	14	dα	dα	PROPN
ejpam-4406	135	15	t	t	PROPN
ejpam-4406	135	16	y1	y1	NOUN
ejpam-4406	136	1	=	=	PUNCT
ejpam-4406	136	2	−m1y1	−m1y1	PROPN
ejpam-4406	136	3	+	+	ADP
ejpam-4406	136	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	136	5	,	,	PUNCT
ejpam-4406	136	6	abc	abc	PROPN
ejpam-4406	136	7	0	0	PROPN
ejpam-4406	137	1	dα	dα	PROPN
ejpam-4406	137	2	t	t	PROPN
ejpam-4406	137	3	y2	y2	PROPN
ejpam-4406	138	1	=	=	SYM
ejpam-4406	138	2	m1y1	m1y1	PROPN
ejpam-4406	138	3	−m2y	−m2y	PROPN
ejpam-4406	138	4	2	2	NUM
ejpam-4406	138	5	2	2	NUM
ejpam-4406	138	6	−m3y2y3	−m3y2y3	ADV
ejpam-4406	138	7	,	,	PUNCT
ejpam-4406	138	8	abc	abc	PROPN
ejpam-4406	138	9	0	0	PROPN
ejpam-4406	138	10	dα	dα	PROPN
ejpam-4406	138	11	t	t	NOUN
ejpam-4406	138	12	y3	y3	NOUN
ejpam-4406	139	1	=	=	PUNCT
ejpam-4406	139	2	m2y	m2y	NOUN
ejpam-4406	139	3	2	2	NUM
ejpam-4406	139	4	2	2	NUM
ejpam-4406	139	5	.	.	PUNCT
ejpam-4406	140	1	(	(	PUNCT
ejpam-4406	140	2	28	28	NUM
ejpam-4406	140	3	)	)	PUNCT
ejpam-4406	140	4	by	by	ADP
ejpam-4406	140	5	using	use	VERB
ejpam-4406	140	6	sumudu	sumudu	NOUN
ejpam-4406	140	7	transform	transform	NOUN
ejpam-4406	140	8	,	,	PUNCT
ejpam-4406	140	9	we	we	PRON
ejpam-4406	140	10	have	have	VERB
ejpam-4406	140	11	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	140	12	1	1	NUM
ejpam-4406	140	13	)	)	PUNCT
ejpam-4406	140	14	(	(	PUNCT
ejpam-4406	140	15	1−	1−	NUM
ejpam-4406	140	16	α	α	NOUN
ejpam-4406	140	17	)	)	PUNCT
ejpam-4406	140	18	eα(−	eα(−	SYM
ejpam-4406	140	19	1	1	NUM
ejpam-4406	140	20	(	(	PUNCT
ejpam-4406	140	21	1−	1−	NUM
ejpam-4406	140	22	α	α	NOUN
ejpam-4406	140	23	)	)	PUNCT
ejpam-4406	140	24	wα)st	wα)st	PROPN
ejpam-4406	140	25	(	(	PUNCT
ejpam-4406	140	26	y1(t)−	y1(t)−	PROPN
ejpam-4406	140	27	y1(0	y1(0	PROPN
ejpam-4406	140	28	)	)	PUNCT
ejpam-4406	140	29	)	)	PUNCT
ejpam-4406	141	1	=	=	PUNCT
ejpam-4406	141	2	st	st	PROPN
ejpam-4406	142	1	[	[	X
ejpam-4406	142	2	−m1y1	−m1y1	PROPN
ejpam-4406	142	3	+	+	ADJ
ejpam-4406	142	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	142	5	]	]	X
ejpam-4406	142	6	,	,	PUNCT
ejpam-4406	142	7	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	142	8	1	1	NUM
ejpam-4406	142	9	)	)	PUNCT
ejpam-4406	142	10	(	(	PUNCT
ejpam-4406	142	11	1−	1−	NUM
ejpam-4406	142	12	α	α	NOUN
ejpam-4406	142	13	)	)	PUNCT
ejpam-4406	142	14	eα(−	eα(−	SYM
ejpam-4406	142	15	1	1	NUM
ejpam-4406	142	16	(	(	PUNCT
ejpam-4406	142	17	1−	1−	NUM
ejpam-4406	142	18	α	α	NOUN
ejpam-4406	142	19	)	)	PUNCT
ejpam-4406	142	20	wα)st	wα)st	PROPN
ejpam-4406	142	21	(	(	PUNCT
ejpam-4406	142	22	y2(t)−	y2(t)−	PROPN
ejpam-4406	142	23	y2(0	y2(0	PROPN
ejpam-4406	142	24	)	)	PUNCT
ejpam-4406	142	25	)	)	PUNCT
ejpam-4406	143	1	=	=	PUNCT
ejpam-4406	143	2	st	st	PROPN
ejpam-4406	144	1	[	[	X
ejpam-4406	144	2	m1y1	m1y1	NOUN
ejpam-4406	144	3	−m2y	−m2y	PROPN
ejpam-4406	144	4	2	2	NUM
ejpam-4406	144	5	2	2	NUM
ejpam-4406	144	6	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	144	7	]	]	PUNCT
ejpam-4406	144	8	,	,	PUNCT
ejpam-4406	144	9	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	144	10	1	1	NUM
ejpam-4406	144	11	)	)	PUNCT
ejpam-4406	144	12	(	(	PUNCT
ejpam-4406	144	13	1−	1−	NUM
ejpam-4406	144	14	α	α	NOUN
ejpam-4406	144	15	)	)	PUNCT
ejpam-4406	144	16	eα(−	eα(−	SYM
ejpam-4406	144	17	1	1	NUM
ejpam-4406	144	18	(	(	PUNCT
ejpam-4406	144	19	1−	1−	NUM
ejpam-4406	144	20	α	α	NOUN
ejpam-4406	144	21	)	)	PUNCT
ejpam-4406	144	22	wα)st	wα)st	PROPN
ejpam-4406	144	23	(	(	PUNCT
ejpam-4406	144	24	y3(t)−	y3(t)−	PROPN
ejpam-4406	144	25	y3(0	y3(0	PROPN
ejpam-4406	144	26	)	)	PUNCT
ejpam-4406	144	27	)	)	PUNCT
ejpam-4406	145	1	=	=	PUNCT
ejpam-4406	145	2	st	st	PROPN
ejpam-4406	146	1	[	[	X
ejpam-4406	146	2	m2y	m2y	PROPN
ejpam-4406	146	3	2	2	NUM
ejpam-4406	146	4	2	2	NUM
ejpam-4406	146	5	]	]	PUNCT
ejpam-4406	146	6	.	.	PUNCT
ejpam-4406	147	1	(	(	PUNCT
ejpam-4406	147	2	29	29	NUM
ejpam-4406	147	3	)	)	PUNCT
ejpam-4406	147	4	j.	j.	PROPN
ejpam-4406	147	5	asad	asad	PROPN
ejpam-4406	147	6	et	et	PROPN
ejpam-4406	147	7	al	al	PROPN
ejpam-4406	147	8	.	.	PUNCT
ejpam-4406	147	9	/	/	SYM
ejpam-4406	147	10	eur	eur	PROPN
ejpam-4406	147	11	.	.	PUNCT
ejpam-4406	148	1	j.	j.	PROPN
ejpam-4406	148	2	pure	pure	PROPN
ejpam-4406	148	3	appl	appl	PROPN
ejpam-4406	148	4	.	.	PROPN
ejpam-4406	148	5	math	math	PROPN
ejpam-4406	148	6	,	,	PUNCT
ejpam-4406	148	7	15	15	NUM
ejpam-4406	148	8	(	(	PUNCT
ejpam-4406	148	9	3	3	NUM
ejpam-4406	148	10	)	)	PUNCT
ejpam-4406	148	11	(	(	PUNCT
ejpam-4406	148	12	2022	2022	NUM
ejpam-4406	148	13	)	)	PUNCT
ejpam-4406	148	14	,	,	PUNCT
ejpam-4406	148	15	1144	1144	NUM
ejpam-4406	148	16	-	-	SYM
ejpam-4406	148	17	1157	1157	NUM
ejpam-4406	148	18	1150	1150	NUM
ejpam-4406	148	19	rearranging	rearrange	VERB
ejpam-4406	148	20	the	the	DET
ejpam-4406	148	21	above	above	ADJ
ejpam-4406	148	22	equations	equation	NOUN
ejpam-4406	148	23	gives	give	VERB
ejpam-4406	148	24	:	:	PUNCT
ejpam-4406	148	25	st	st	PROPN
ejpam-4406	148	26	(	(	PUNCT
ejpam-4406	148	27	y1(t	y1(t	PROPN
ejpam-4406	148	28	)	)	PUNCT
ejpam-4406	148	29	)	)	PUNCT
ejpam-4406	149	1	=	=	SYM
ejpam-4406	149	2	y1(0	y1(0	PROPN
ejpam-4406	149	3	)	)	PUNCT
ejpam-4406	150	1	+	+	CCONJ
ejpam-4406	150	2	1−	1−	NUM
ejpam-4406	150	3	α	α	DET
ejpam-4406	150	4	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	150	5	1)eα(−	1)eα(−	NUM
ejpam-4406	150	6	1	1	NUM
ejpam-4406	150	7	(	(	PUNCT
ejpam-4406	150	8	1−α)w	1−α)w	NUM
ejpam-4406	150	9	α	α	NOUN
ejpam-4406	150	10	)	)	PUNCT
ejpam-4406	150	11	×	×	PROPN
ejpam-4406	150	12	st	st	PROPN
ejpam-4406	151	1	[	[	X
ejpam-4406	151	2	−m1y1	−m1y1	PROPN
ejpam-4406	151	3	+	+	ADJ
ejpam-4406	151	4	m3y2y3	m3y2y3	NOUN
ejpam-4406	151	5	]	]	X
ejpam-4406	151	6	,	,	PUNCT
ejpam-4406	151	7	st	st	PROPN
ejpam-4406	151	8	(	(	PUNCT
ejpam-4406	151	9	y2(t	y2(t	PROPN
ejpam-4406	151	10	)	)	PUNCT
ejpam-4406	151	11	)	)	PUNCT
ejpam-4406	152	1	=	=	SYM
ejpam-4406	152	2	y2(0	y2(0	PROPN
ejpam-4406	152	3	)	)	PUNCT
ejpam-4406	153	1	+	+	CCONJ
ejpam-4406	153	2	1−	1−	NUM
ejpam-4406	153	3	α	α	DET
ejpam-4406	153	4	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	153	5	1)eα(−	1)eα(−	NUM
ejpam-4406	153	6	1	1	NUM
ejpam-4406	153	7	(	(	PUNCT
ejpam-4406	153	8	1−α)w	1−α)w	NUM
ejpam-4406	153	9	α	α	NOUN
ejpam-4406	153	10	)	)	PUNCT
ejpam-4406	153	11	×	×	PROPN
ejpam-4406	153	12	st	st	PROPN
ejpam-4406	154	1	[	[	X
ejpam-4406	154	2	m1y1	m1y1	NOUN
ejpam-4406	154	3	−m2y	−m2y	ADP
ejpam-4406	154	4	2	2	NUM
ejpam-4406	154	5	2	2	NUM
ejpam-4406	154	6	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	154	7	]	]	PUNCT
ejpam-4406	154	8	,	,	PUNCT
ejpam-4406	154	9	st	st	PROPN
ejpam-4406	154	10	(	(	PUNCT
ejpam-4406	154	11	y3(t	y3(t	PROPN
ejpam-4406	154	12	)	)	PUNCT
ejpam-4406	154	13	)	)	PUNCT
ejpam-4406	155	1	=	=	SYM
ejpam-4406	155	2	y3(0	y3(0	PROPN
ejpam-4406	155	3	)	)	PUNCT
ejpam-4406	156	1	+	+	NUM
ejpam-4406	156	2	1−	1−	NUM
ejpam-4406	156	3	α	α	DET
ejpam-4406	156	4	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	156	5	1)eα(−	1)eα(−	NUM
ejpam-4406	156	6	1	1	NUM
ejpam-4406	156	7	(	(	PUNCT
ejpam-4406	156	8	1−α)w	1−α)w	NUM
ejpam-4406	156	9	α	α	NOUN
ejpam-4406	156	10	)	)	PUNCT
ejpam-4406	156	11	×	×	PROPN
ejpam-4406	156	12	st	st	PROPN
ejpam-4406	157	1	[	[	X
ejpam-4406	157	2	m2y	m2y	PROPN
ejpam-4406	157	3	2	2	NUM
ejpam-4406	157	4	2	2	NUM
ejpam-4406	157	5	]	]	PUNCT
ejpam-4406	157	6	.	.	PUNCT
ejpam-4406	158	1	(	(	PUNCT
ejpam-4406	158	2	30	30	NUM
ejpam-4406	158	3	)	)	PUNCT
ejpam-4406	158	4	y1(t	y1(t	PROPN
ejpam-4406	158	5	)	)	PUNCT
ejpam-4406	158	6	=	=	SYM
ejpam-4406	158	7	y1(0	y1(0	PROPN
ejpam-4406	158	8	)	)	PUNCT
ejpam-4406	159	1	+	+	PUNCT
ejpam-4406	159	2	st−1	st−1	PROPN
ejpam-4406	159	3	[	[	PUNCT
ejpam-4406	159	4	1−	1−	NUM
ejpam-4406	159	5	α	α	DET
ejpam-4406	159	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	159	7	1)eα(−	1)eα(−	NUM
ejpam-4406	159	8	1	1	NUM
ejpam-4406	159	9	(	(	PUNCT
ejpam-4406	159	10	1−α)w	1−α)w	NUM
ejpam-4406	159	11	α	α	NOUN
ejpam-4406	159	12	)	)	PUNCT
ejpam-4406	159	13	×	×	PROPN
ejpam-4406	159	14	st	st	PROPN
ejpam-4406	159	15	(	(	PUNCT
ejpam-4406	159	16	−m1y1	−m1y1	PROPN
ejpam-4406	159	17	+	+	ADJ
ejpam-4406	159	18	m3y2y3	m3y2y3	NOUN
ejpam-4406	159	19	)	)	PUNCT
ejpam-4406	159	20	]	]	PUNCT
ejpam-4406	159	21	,	,	PUNCT
ejpam-4406	159	22	y2(t	y2(t	PROPN
ejpam-4406	159	23	)	)	PUNCT
ejpam-4406	159	24	=	=	SYM
ejpam-4406	159	25	y2(0	y2(0	PROPN
ejpam-4406	159	26	)	)	PUNCT
ejpam-4406	160	1	+	+	PUNCT
ejpam-4406	160	2	st−1	st−1	PROPN
ejpam-4406	160	3	[	[	PUNCT
ejpam-4406	160	4	1−	1−	NUM
ejpam-4406	160	5	α	α	DET
ejpam-4406	160	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	160	7	1)eα(−	1)eα(−	NUM
ejpam-4406	160	8	1	1	NUM
ejpam-4406	160	9	(	(	PUNCT
ejpam-4406	160	10	1−α)w	1−α)w	NUM
ejpam-4406	160	11	α	α	NOUN
ejpam-4406	160	12	)	)	PUNCT
ejpam-4406	160	13	×	×	PROPN
ejpam-4406	160	14	st	st	PROPN
ejpam-4406	160	15	(	(	PUNCT
ejpam-4406	160	16	m1y1	m1y1	PROPN
ejpam-4406	160	17	−m2y	−m2y	PROPN
ejpam-4406	160	18	2	2	NUM
ejpam-4406	160	19	2	2	NUM
ejpam-4406	160	20	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	160	21	)	)	PUNCT
ejpam-4406	160	22	]	]	PUNCT
ejpam-4406	160	23	,	,	PUNCT
ejpam-4406	160	24	y3(t	y3(t	NUM
ejpam-4406	160	25	)	)	PUNCT
ejpam-4406	160	26	=	=	SYM
ejpam-4406	160	27	y3(0	y3(0	PROPN
ejpam-4406	160	28	)	)	PUNCT
ejpam-4406	161	1	+	+	PUNCT
ejpam-4406	161	2	st−1	st−1	PROPN
ejpam-4406	161	3	[	[	PUNCT
ejpam-4406	161	4	1−	1−	NUM
ejpam-4406	161	5	α	α	DET
ejpam-4406	161	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	161	7	1)eα(−	1)eα(−	NUM
ejpam-4406	161	8	1	1	NUM
ejpam-4406	161	9	(	(	PUNCT
ejpam-4406	161	10	1−α)w	1−α)w	NUM
ejpam-4406	161	11	α	α	NOUN
ejpam-4406	161	12	)	)	PUNCT
ejpam-4406	161	13	×	×	PROPN
ejpam-4406	161	14	st	st	PROPN
ejpam-4406	161	15	(	(	PUNCT
ejpam-4406	161	16	m2y	m2y	PROPN
ejpam-4406	161	17	2	2	NUM
ejpam-4406	161	18	2	2	NUM
ejpam-4406	161	19	)	)	PUNCT
ejpam-4406	161	20	]	]	PUNCT
ejpam-4406	161	21	.	.	PUNCT
ejpam-4406	162	1	(	(	PUNCT
ejpam-4406	162	2	31	31	NUM
ejpam-4406	162	3	)	)	PUNCT
ejpam-4406	162	4	then	then	ADV
ejpam-4406	162	5	,	,	PUNCT
ejpam-4406	162	6	we	we	PRON
ejpam-4406	162	7	get	get	VERB
ejpam-4406	162	8	y1(n+1)(t	y1(n+1)(t	PRON
ejpam-4406	162	9	)	)	PUNCT
ejpam-4406	162	10	=	=	SYM
ejpam-4406	162	11	y1(n)(0	y1(n)(0	NUM
ejpam-4406	162	12	)	)	PUNCT
ejpam-4406	163	1	+	+	CCONJ
ejpam-4406	163	2	st−1	st−1	PROPN
ejpam-4406	163	3	[	[	PUNCT
ejpam-4406	163	4	1−	1−	NUM
ejpam-4406	163	5	α	α	DET
ejpam-4406	163	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	163	7	1)eα(−	1)eα(−	NUM
ejpam-4406	163	8	1	1	NUM
ejpam-4406	163	9	(	(	PUNCT
ejpam-4406	163	10	1−α)w	1−α)w	NUM
ejpam-4406	163	11	α	α	NOUN
ejpam-4406	163	12	)	)	PUNCT
ejpam-4406	163	13	×	×	PROPN
ejpam-4406	163	14	st	st	PROPN
ejpam-4406	163	15	(	(	PUNCT
ejpam-4406	163	16	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	163	17	)	)	PUNCT
ejpam-4406	163	18	+	+	NOUN
ejpam-4406	163	19	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	163	20	)	)	PUNCT
ejpam-4406	163	21	)	)	PUNCT
ejpam-4406	163	22	]	]	PUNCT
ejpam-4406	163	23	,	,	PUNCT
ejpam-4406	163	24	y2(n+1)(t	y2(n+1)(t	X
ejpam-4406	163	25	)	)	PUNCT
ejpam-4406	163	26	=	=	SYM
ejpam-4406	163	27	y2(n)(0	y2(n)(0	NUM
ejpam-4406	163	28	)	)	PUNCT
ejpam-4406	163	29	+	+	CCONJ
ejpam-4406	163	30	st−1	st−1	PROPN
ejpam-4406	163	31	[	[	PUNCT
ejpam-4406	163	32	1−	1−	NUM
ejpam-4406	163	33	α	α	DET
ejpam-4406	163	34	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	163	35	1)eα(−	1)eα(−	NUM
ejpam-4406	163	36	1	1	NUM
ejpam-4406	163	37	(	(	PUNCT
ejpam-4406	163	38	1−α)w	1−α)w	NUM
ejpam-4406	163	39	α	α	NOUN
ejpam-4406	163	40	)	)	PUNCT
ejpam-4406	163	41	×	×	PROPN
ejpam-4406	163	42	st	st	PROPN
ejpam-4406	163	43	(	(	PUNCT
ejpam-4406	163	44	m1y1(n	m1y1(n	NOUN
ejpam-4406	163	45	)	)	PUNCT
ejpam-4406	163	46	−m2y	−m2y	NUM
ejpam-4406	163	47	2	2	NUM
ejpam-4406	163	48	2(n	2(n	NUM
ejpam-4406	163	49	)	)	PUNCT
ejpam-4406	163	50	−m3y2(n)y3(n	−m3y2(n)y3(n	NOUN
ejpam-4406	163	51	)	)	PUNCT
ejpam-4406	163	52	)	)	PUNCT
ejpam-4406	163	53	]	]	PUNCT
ejpam-4406	163	54	,	,	PUNCT
ejpam-4406	163	55	y3(n+1)(t	y3(n+1)(t	PROPN
ejpam-4406	163	56	)	)	PUNCT
ejpam-4406	163	57	=	=	SYM
ejpam-4406	163	58	y3((n))(0	y3((n))(0	X
ejpam-4406	163	59	)	)	PUNCT
ejpam-4406	164	1	+	+	CCONJ
ejpam-4406	164	2	st	st	X
ejpam-4406	164	3	(	(	PUNCT
ejpam-4406	164	4	−	−	PROPN
ejpam-4406	164	5	1	1	NUM
ejpam-4406	164	6	)	)	PUNCT
ejpam-4406	164	7	[	[	PUNCT
ejpam-4406	164	8	1−	1−	NUM
ejpam-4406	164	9	α	α	PRON
ejpam-4406	164	10	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	164	11	1)eα(−	1)eα(−	NUM
ejpam-4406	164	12	1	1	NUM
ejpam-4406	164	13	(	(	PUNCT
ejpam-4406	164	14	1−α)w	1−α)w	NUM
ejpam-4406	164	15	α	α	NOUN
ejpam-4406	164	16	)	)	PUNCT
ejpam-4406	164	17	×	×	PROPN
ejpam-4406	164	18	st	st	PROPN
ejpam-4406	164	19	(	(	PUNCT
ejpam-4406	164	20	m2y	m2y	PROPN
ejpam-4406	164	21	2	2	NUM
ejpam-4406	164	22	2(n	2(n	NUM
ejpam-4406	164	23	)	)	PUNCT
ejpam-4406	164	24	)	)	PUNCT
ejpam-4406	164	25	]	]	PUNCT
ejpam-4406	164	26	.	.	PUNCT
ejpam-4406	165	1	(	(	PUNCT
ejpam-4406	165	2	32	32	NUM
ejpam-4406	165	3	)	)	PUNCT
ejpam-4406	165	4	and	and	CCONJ
ejpam-4406	165	5	the	the	DET
ejpam-4406	165	6	solution	solution	NOUN
ejpam-4406	165	7	of	of	ADP
ejpam-4406	165	8	system	system	NOUN
ejpam-4406	165	9	(	(	PUNCT
ejpam-4406	165	10	32	32	NUM
ejpam-4406	165	11	)	)	PUNCT
ejpam-4406	165	12	is	be	AUX
ejpam-4406	165	13	obtained	obtain	VERB
ejpam-4406	165	14	as	as	ADP
ejpam-4406	165	15	:	:	PUNCT
ejpam-4406	165	16	y1(t	y1(t	X
ejpam-4406	165	17	)	)	PUNCT
ejpam-4406	165	18	=	=	SYM
ejpam-4406	165	19	lim	lim	PROPN
ejpam-4406	165	20	n→∞	n→∞	X
ejpam-4406	165	21	y1(n)(t	y1(n)(t	PROPN
ejpam-4406	165	22	)	)	PUNCT
ejpam-4406	165	23	,	,	PUNCT
ejpam-4406	165	24	y2(t	y2(t	PROPN
ejpam-4406	165	25	)	)	PUNCT
ejpam-4406	166	1	=	=	SYM
ejpam-4406	166	2	lim	lim	PROPN
ejpam-4406	166	3	n→∞	n→∞	NUM
ejpam-4406	166	4	y2(n)(t	y2(n)(t	NOUN
ejpam-4406	166	5	)	)	PUNCT
ejpam-4406	166	6	,	,	PUNCT
ejpam-4406	166	7	y3(t	y3(t	NUM
ejpam-4406	166	8	)	)	PUNCT
ejpam-4406	167	1	=	=	SYM
ejpam-4406	167	2	lim	lim	PROPN
ejpam-4406	167	3	n→∞	n→∞	NUM
ejpam-4406	167	4	y3(n)(t	y3(n)(t	PROPN
ejpam-4406	167	5	)	)	PUNCT
ejpam-4406	167	6	.	.	PUNCT
ejpam-4406	168	1	(	(	PUNCT
ejpam-4406	168	2	33	33	NUM
ejpam-4406	168	3	)	)	PUNCT
ejpam-4406	168	4	4.1	4.1	NUM
ejpam-4406	168	5	.	.	PUNCT
ejpam-4406	169	1	stability	stability	NOUN
ejpam-4406	169	2	and	and	CCONJ
ejpam-4406	169	3	uniqueness	uniqueness	NOUN
ejpam-4406	169	4	of	of	ADP
ejpam-4406	169	5	the	the	DET
ejpam-4406	169	6	proposed	propose	VERB
ejpam-4406	169	7	scheme	scheme	NOUN
ejpam-4406	169	8	assume	assume	VERB
ejpam-4406	169	9	that	that	SCONJ
ejpam-4406	169	10	(	(	PUNCT
ejpam-4406	169	11	x	x	NOUN
ejpam-4406	169	12	,	,	PUNCT
ejpam-4406	169	13	|.|	|.|	NOUN
ejpam-4406	169	14	)	)	PUNCT
ejpam-4406	169	15	is	be	AUX
ejpam-4406	169	16	a	a	DET
ejpam-4406	169	17	banach	banach	NOUN
ejpam-4406	169	18	space	space	NOUN
ejpam-4406	169	19	and	and	CCONJ
ejpam-4406	169	20	h	h	DET
ejpam-4406	169	21	a	a	DET
ejpam-4406	169	22	self	self	NOUN
ejpam-4406	169	23	-	-	PUNCT
ejpam-4406	169	24	map	map	NOUN
ejpam-4406	169	25	of	of	ADP
ejpam-4406	169	26	x.	x.	NOUN
ejpam-4406	169	27	let	let	VERB
ejpam-4406	169	28	rn+1	rn+1	VERB
ejpam-4406	169	29	=	=	SYM
ejpam-4406	169	30	f(hrn	f(hrn	NOUN
ejpam-4406	169	31	)	)	PUNCT
ejpam-4406	169	32	be	be	AUX
ejpam-4406	169	33	specific	specific	ADJ
ejpam-4406	169	34	recursive	recursive	ADJ
ejpam-4406	169	35	procedure	procedure	NOUN
ejpam-4406	169	36	.	.	PUNCT
ejpam-4406	170	1	the	the	DET
ejpam-4406	170	2	following	follow	VERB
ejpam-4406	170	3	condition	condition	NOUN
ejpam-4406	170	4	must	must	AUX
ejpam-4406	170	5	be	be	AUX
ejpam-4406	170	6	fulfilled	fulfil	VERB
ejpam-4406	170	7	for	for	ADP
ejpam-4406	170	8	rn+1	rn+1	NOUN
ejpam-4406	170	9	=	=	SYM
ejpam-4406	170	10	hrn	hrn	NOUN
ejpam-4406	170	11	•	•	NOUN
ejpam-4406	170	12	the	the	DET
ejpam-4406	170	13	fixed	fix	VERB
ejpam-4406	170	14	point	point	NOUN
ejpam-4406	170	15	set	set	NOUN
ejpam-4406	170	16	of	of	ADP
ejpam-4406	170	17	h	h	NOUN
ejpam-4406	170	18	possesses	possesse	NOUN
ejpam-4406	170	19	at	at	ADV
ejpam-4406	170	20	least	least	ADV
ejpam-4406	170	21	one	one	NUM
ejpam-4406	170	22	element	element	NOUN
ejpam-4406	170	23	.	.	PUNCT
ejpam-4406	171	1	•	•	NUM
ejpam-4406	171	2	rn	rn	PROPN
ejpam-4406	171	3	converges	converge	VERB
ejpam-4406	171	4	to	to	ADP
ejpam-4406	171	5	a	a	DET
ejpam-4406	171	6	point	point	NOUN
ejpam-4406	171	7	p	p	X
ejpam-4406	171	8	∈	∈	PROPN
ejpam-4406	171	9	f	f	X
ejpam-4406	171	10	(	(	PUNCT
ejpam-4406	171	11	h	h	NOUN
ejpam-4406	171	12	)	)	PUNCT
ejpam-4406	171	13	.	.	PUNCT
ejpam-4406	172	1	•	•	NUM
ejpam-4406	172	2	limn→∞	limn→∞	PROPN
ejpam-4406	172	3	xn(t	xn(t	NUM
ejpam-4406	172	4	)	)	PUNCT
ejpam-4406	173	1	=	=	VERB
ejpam-4406	174	1	p.	p.	NOUN
ejpam-4406	174	2	j.	j.	PROPN
ejpam-4406	174	3	asad	asad	PROPN
ejpam-4406	174	4	et	et	PROPN
ejpam-4406	174	5	al	al	PROPN
ejpam-4406	174	6	.	.	PUNCT
ejpam-4406	174	7	/	/	SYM
ejpam-4406	174	8	eur	eur	PROPN
ejpam-4406	174	9	.	.	PUNCT
ejpam-4406	175	1	j.	j.	PROPN
ejpam-4406	175	2	pure	pure	PROPN
ejpam-4406	175	3	appl	appl	PROPN
ejpam-4406	175	4	.	.	PROPN
ejpam-4406	175	5	math	math	PROPN
ejpam-4406	175	6	,	,	PUNCT
ejpam-4406	175	7	15	15	NUM
ejpam-4406	175	8	(	(	PUNCT
ejpam-4406	175	9	3	3	NUM
ejpam-4406	175	10	)	)	PUNCT
ejpam-4406	175	11	(	(	PUNCT
ejpam-4406	175	12	2022	2022	NUM
ejpam-4406	175	13	)	)	PUNCT
ejpam-4406	175	14	,	,	PUNCT
ejpam-4406	175	15	1144	1144	NUM
ejpam-4406	175	16	-	-	SYM
ejpam-4406	175	17	1157	1157	NUM
ejpam-4406	175	18	1151	1151	NUM
ejpam-4406	175	19	.	.	PUNCT
ejpam-4406	176	1	theorem	theorem	NOUN
ejpam-4406	176	2	3	3	X
ejpam-4406	176	3	.	.	PUNCT
ejpam-4406	176	4	suppose	suppose	VERB
ejpam-4406	176	5	that	that	SCONJ
ejpam-4406	176	6	(	(	PUNCT
ejpam-4406	176	7	x	x	NOUN
ejpam-4406	176	8	,	,	PUNCT
ejpam-4406	176	9	|.|	|.|	NOUN
ejpam-4406	176	10	)	)	PUNCT
ejpam-4406	176	11	is	be	AUX
ejpam-4406	176	12	a	a	DET
ejpam-4406	176	13	banach	banach	NOUN
ejpam-4406	176	14	space	space	NOUN
ejpam-4406	176	15	and	and	CCONJ
ejpam-4406	176	16	h	h	DET
ejpam-4406	176	17	a	a	DET
ejpam-4406	176	18	self	self	NOUN
ejpam-4406	176	19	-	-	PUNCT
ejpam-4406	176	20	map	map	NOUN
ejpam-4406	176	21	of	of	ADP
ejpam-4406	176	22	x	x	PUNCT
ejpam-4406	176	23	satisfying	satisfy	VERB
ejpam-4406	176	24	∥hx	∥hx	ADP
ejpam-4406	176	25	−hr∥	−hr∥	NOUN
ejpam-4406	176	26	≤	≤	NOUN
ejpam-4406	176	27	θ∥x−hx∥+	θ∥x−hx∥+	NUM
ejpam-4406	176	28	θ∥x−	θ∥x−	ADP
ejpam-4406	176	29	r∥	r∥	NOUN
ejpam-4406	176	30	,	,	PUNCT
ejpam-4406	176	31	for	for	ADP
ejpam-4406	176	32	all	all	DET
ejpam-4406	176	33	x	x	NOUN
ejpam-4406	176	34	,	,	PUNCT
ejpam-4406	176	35	r	r	NOUN
ejpam-4406	176	36	∈	∈	PROPN
ejpam-4406	176	37	x	x	NOUN
ejpam-4406	176	38	,	,	PUNCT
ejpam-4406	176	39	where	where	SCONJ
ejpam-4406	176	40	0≤	0≤	ADJ
ejpam-4406	176	41	θ	θ	NOUN
ejpam-4406	176	42	,	,	PUNCT
ejpam-4406	176	43	0≤	0≤	NUM
ejpam-4406	176	44	θ	θ	NOUN
ejpam-4406	176	45	<	<	X
ejpam-4406	176	46	1	1	NUM
ejpam-4406	176	47	.	.	PUNCT
ejpam-4406	177	1	then	then	ADV
ejpam-4406	177	2	h	h	PROPN
ejpam-4406	177	3	is	be	AUX
ejpam-4406	177	4	picard	picard	NOUN
ejpam-4406	177	5	h	h	NOUN
ejpam-4406	177	6	-	-	PUNCT
ejpam-4406	177	7	stable	stable	ADJ
ejpam-4406	177	8	.	.	PUNCT
ejpam-4406	178	1	theorem	theorem	NOUN
ejpam-4406	178	2	4	4	NUM
ejpam-4406	178	3	.	.	PUNCT
ejpam-4406	179	1	describe	describe	VERB
ejpam-4406	179	2	h	h	NOUN
ejpam-4406	179	3	as	as	ADP
ejpam-4406	179	4	a	a	DET
ejpam-4406	179	5	self	self	NOUN
ejpam-4406	179	6	-	-	PUNCT
ejpam-4406	179	7	map	map	NOUN
ejpam-4406	179	8	:	:	PUNCT
ejpam-4406	179	9	h[y1(n+1)(t	h[y1(n+1)(t	NOUN
ejpam-4406	179	10	)	)	PUNCT
ejpam-4406	179	11	]	]	PUNCT
ejpam-4406	180	1	=	=	SYM
ejpam-4406	180	2	y1(n+1)(t	y1(n+1)(t	X
ejpam-4406	180	3	)	)	PUNCT
ejpam-4406	180	4	=	=	SYM
ejpam-4406	180	5	y1(n)(t	y1(n)(t	PROPN
ejpam-4406	180	6	)	)	PUNCT
ejpam-4406	181	1	+	+	CCONJ
ejpam-4406	181	2	st−1	st−1	PROPN
ejpam-4406	181	3	[	[	PUNCT
ejpam-4406	181	4	1−	1−	NUM
ejpam-4406	181	5	α	α	DET
ejpam-4406	181	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	181	7	1)eα(−	1)eα(−	NUM
ejpam-4406	181	8	1	1	NUM
ejpam-4406	181	9	(	(	PUNCT
ejpam-4406	181	10	1−α)w	1−α)w	NUM
ejpam-4406	181	11	α	α	NOUN
ejpam-4406	181	12	)	)	PUNCT
ejpam-4406	181	13	×st	×st	PROPN
ejpam-4406	181	14	(	(	PUNCT
ejpam-4406	181	15	−m1y1(n	−m1y1(n	NOUN
ejpam-4406	181	16	)	)	PUNCT
ejpam-4406	181	17	+	+	NOUN
ejpam-4406	181	18	m3y2(n)y3(n	m3y2(n)y3(n	NOUN
ejpam-4406	181	19	)	)	PUNCT
ejpam-4406	181	20	)	)	PUNCT
ejpam-4406	181	21	]	]	PUNCT
ejpam-4406	181	22	,	,	PUNCT
ejpam-4406	181	23	h[y2(n+1)(t	h[y2(n+1)(t	PROPN
ejpam-4406	181	24	)	)	PUNCT
ejpam-4406	181	25	]	]	PUNCT
ejpam-4406	182	1	=	=	SYM
ejpam-4406	182	2	y2(n+1)(t	y2(n+1)(t	PROPN
ejpam-4406	182	3	)	)	PUNCT
ejpam-4406	182	4	=	=	SYM
ejpam-4406	182	5	y2(n)(0	y2(n)(0	NUM
ejpam-4406	182	6	)	)	PUNCT
ejpam-4406	182	7	+	+	CCONJ
ejpam-4406	182	8	st−1	st−1	PROPN
ejpam-4406	182	9	[	[	PUNCT
ejpam-4406	182	10	1−	1−	NUM
ejpam-4406	182	11	α	α	DET
ejpam-4406	182	12	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	182	13	1)eα(−	1)eα(−	NUM
ejpam-4406	182	14	1	1	NUM
ejpam-4406	182	15	(	(	PUNCT
ejpam-4406	182	16	1−α)w	1−α)w	NUM
ejpam-4406	182	17	α	α	NOUN
ejpam-4406	182	18	)	)	PUNCT
ejpam-4406	182	19	×st	×st	NOUN
ejpam-4406	182	20	(	(	PUNCT
ejpam-4406	182	21	m1y1(n	m1y1(n	NOUN
ejpam-4406	182	22	)	)	PUNCT
ejpam-4406	182	23	−m2y	−m2y	NUM
ejpam-4406	182	24	2	2	NUM
ejpam-4406	182	25	2(n	2(n	NUM
ejpam-4406	182	26	)	)	PUNCT
ejpam-4406	182	27	−m3y2(n)y3(n	−m3y2(n)y3(n	NOUN
ejpam-4406	182	28	)	)	PUNCT
ejpam-4406	182	29	)	)	PUNCT
ejpam-4406	183	1	]	]	PUNCT
ejpam-4406	183	2	,	,	PUNCT
ejpam-4406	183	3	h[y3(n+1)(t	h[y3(n+1)(t	PROPN
ejpam-4406	183	4	)	)	PUNCT
ejpam-4406	183	5	]	]	PUNCT
ejpam-4406	184	1	=	=	SYM
ejpam-4406	184	2	y3(n+1)(t	y3(n+1)(t	X
ejpam-4406	184	3	)	)	PUNCT
ejpam-4406	184	4	=	=	SYM
ejpam-4406	184	5	y3(n)(0	y3(n)(0	X
ejpam-4406	184	6	)	)	PUNCT
ejpam-4406	185	1	+	+	CCONJ
ejpam-4406	185	2	st−1	st−1	PROPN
ejpam-4406	185	3	[	[	PUNCT
ejpam-4406	185	4	1−	1−	NUM
ejpam-4406	185	5	α	α	DET
ejpam-4406	185	6	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	185	7	1)eα(−	1)eα(−	NUM
ejpam-4406	185	8	1	1	NUM
ejpam-4406	185	9	(	(	PUNCT
ejpam-4406	185	10	1−α)w	1−α)w	NUM
ejpam-4406	185	11	α	α	NOUN
ejpam-4406	185	12	)	)	PUNCT
ejpam-4406	185	13	×st	×st	NOUN
ejpam-4406	185	14	(	(	PUNCT
ejpam-4406	185	15	m2y	m2y	PROPN
ejpam-4406	185	16	2	2	NUM
ejpam-4406	185	17	2(n	2(n	NUM
ejpam-4406	185	18	)	)	PUNCT
ejpam-4406	185	19	)	)	PUNCT
ejpam-4406	185	20	]	]	PUNCT
ejpam-4406	185	21	.	.	PUNCT
ejpam-4406	186	1	(	(	PUNCT
ejpam-4406	186	2	34	34	NUM
ejpam-4406	186	3	)	)	PUNCT
ejpam-4406	186	4	proof	proof	NOUN
ejpam-4406	186	5	.	.	PUNCT
ejpam-4406	187	1	by	by	ADP
ejpam-4406	187	2	using	use	VERB
ejpam-4406	187	3	norm	norm	NOUN
ejpam-4406	187	4	properties	property	NOUN
ejpam-4406	187	5	,	,	PUNCT
ejpam-4406	187	6	then	then	ADV
ejpam-4406	187	7	the	the	DET
ejpam-4406	187	8	iteration	iteration	NOUN
ejpam-4406	187	9	is	be	AUX
ejpam-4406	187	10	h	h	NOUN
ejpam-4406	187	11	-	-	PUNCT
ejpam-4406	187	12	stable	stable	ADJ
ejpam-4406	187	13	∥h[y1(n)(t)]−h[y1(m)(t)]∥	∥h[y1(n)(t)]−h[y1(m)(t)]∥	ADJ
ejpam-4406	187	14	≤	≤	NUM
ejpam-4406	187	15	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	187	16	y1(m)(t)∥+	y1(m)(t)∥+	ADJ
ejpam-4406	187	17	st−1	st−1	PROPN
ejpam-4406	187	18	[	[	PUNCT
ejpam-4406	187	19	1−	1−	NUM
ejpam-4406	187	20	α	α	DET
ejpam-4406	187	21	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	187	22	1)eα(−	1)eα(−	NUM
ejpam-4406	187	23	1	1	NUM
ejpam-4406	187	24	(	(	PUNCT
ejpam-4406	187	25	1−α)w	1−α)w	NUM
ejpam-4406	187	26	α	α	NOUN
ejpam-4406	187	27	)	)	PUNCT
ejpam-4406	187	28	×st	×st	NOUN
ejpam-4406	187	29	(	(	PUNCT
ejpam-4406	187	30	−m1∥y1(n	−m1∥y1(n	PROPN
ejpam-4406	187	31	)	)	PUNCT
ejpam-4406	187	32	−	−	PROPN
ejpam-4406	188	1	y1(m)∥+m3∥y2(n)y3(n	y1(m)∥+m3∥y2(n)y3(n	NOUN
ejpam-4406	188	2	)	)	PUNCT
ejpam-4406	188	3	−	−	PROPN
ejpam-4406	188	4	y2(m)y3(m)∥	y2(m)y3(m)∥	NUM
ejpam-4406	188	5	)	)	PUNCT
ejpam-4406	188	6	]	]	PUNCT
ejpam-4406	188	7	,	,	PUNCT
ejpam-4406	188	8	∥h[y2(n)(t)]−h[y2(m)(t)]∥	∥h[y2(n)(t)]−h[y2(m)(t)]∥	VERB
ejpam-4406	188	9	≤	≤	NUM
ejpam-4406	188	10	∥y2(n)(t)−	∥y2(n)(t)−	PROPN
ejpam-4406	188	11	y2(m)(t)∥+	y2(m)(t)∥+	PROPN
ejpam-4406	188	12	st−1	st−1	PROPN
ejpam-4406	188	13	[	[	PUNCT
ejpam-4406	188	14	1−	1−	NUM
ejpam-4406	188	15	α	α	DET
ejpam-4406	188	16	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	188	17	1)eα(−	1)eα(−	NUM
ejpam-4406	188	18	1	1	NUM
ejpam-4406	188	19	(	(	PUNCT
ejpam-4406	188	20	1−α)w	1−α)w	NUM
ejpam-4406	188	21	α	α	NOUN
ejpam-4406	188	22	)	)	PUNCT
ejpam-4406	188	23	×st	×st	PROPN
ejpam-4406	188	24	(	(	PUNCT
ejpam-4406	188	25	m1∥y1(n	m1∥y1(n	NOUN
ejpam-4406	188	26	)	)	PUNCT
ejpam-4406	188	27	−	−	PROPN
ejpam-4406	188	28	y1(m)∥	y1(m)∥	PROPN
ejpam-4406	188	29	−m2∥y22(n	−m2∥y22(n	PROPN
ejpam-4406	188	30	)	)	PUNCT
ejpam-4406	188	31	−	−	PROPN
ejpam-4406	188	32	y22(m)∥	y22(m)∥	INTJ
ejpam-4406	188	33	−m3∥y2(n)y3(n	−m3∥y2(n)y3(n	NOUN
ejpam-4406	188	34	)	)	PUNCT
ejpam-4406	188	35	−	−	PROPN
ejpam-4406	188	36	y2(m)y3(m)∥	y2(m)y3(m)∥	PROPN
ejpam-4406	188	37	)	)	PUNCT
ejpam-4406	188	38	]	]	PUNCT
ejpam-4406	188	39	,	,	PUNCT
ejpam-4406	188	40	∥h[y3(n)(t)]−h[y3(m)(t)]∥	∥h[y3(n)(t)]−h[y3(m)(t)]∥	NUM
ejpam-4406	188	41	≤	≤	PUNCT
ejpam-4406	188	42	∥y3(n)(t)−	∥y3(n)(t)−	PROPN
ejpam-4406	188	43	y3(n)(t)∥+	y3(n)(t)∥+	PROPN
ejpam-4406	188	44	st−1	st−1	PROPN
ejpam-4406	188	45	[	[	PUNCT
ejpam-4406	188	46	1−	1−	NUM
ejpam-4406	188	47	α	α	DET
ejpam-4406	188	48	b(α)αγ(α+	b(α)αγ(α+	NOUN
ejpam-4406	188	49	1)eα(−	1)eα(−	NUM
ejpam-4406	188	50	1	1	NUM
ejpam-4406	188	51	(	(	PUNCT
ejpam-4406	188	52	1−α)w	1−α)w	NUM
ejpam-4406	188	53	α	α	NOUN
ejpam-4406	188	54	)	)	PUNCT
ejpam-4406	188	55	×st	×st	PROPN
ejpam-4406	188	56	(	(	PUNCT
ejpam-4406	188	57	m2∥y22(n	m2∥y22(n	PROPN
ejpam-4406	188	58	)	)	PUNCT
ejpam-4406	188	59	−	−	PROPN
ejpam-4406	188	60	y22(m)∥	y22(m)∥	NOUN
ejpam-4406	188	61	)	)	PUNCT
ejpam-4406	188	62	]	]	PUNCT
ejpam-4406	188	63	.	.	PUNCT
ejpam-4406	189	1	(	(	PUNCT
ejpam-4406	189	2	35	35	NUM
ejpam-4406	189	3	)	)	PUNCT
ejpam-4406	189	4	its	its	PRON
ejpam-4406	189	5	satisfied	satisfied	ADJ
ejpam-4406	189	6	in	in	ADP
ejpam-4406	189	7	theorem	theorem	NOUN
ejpam-4406	189	8	3	3	NUM
ejpam-4406	189	9	,	,	PUNCT
ejpam-4406	189	10	when	when	SCONJ
ejpam-4406	189	11	θ	θ	PROPN
ejpam-4406	189	12	=	=	SYM
ejpam-4406	189	13	(	(	PUNCT
ejpam-4406	189	14	0	0	NUM
ejpam-4406	189	15	,	,	PUNCT
ejpam-4406	189	16	0	0	NUM
ejpam-4406	189	17	,	,	PUNCT
ejpam-4406	189	18	0	0	NUM
ejpam-4406	189	19	)	)	PUNCT
ejpam-4406	189	20	,	,	PUNCT
ejpam-4406	189	21	θ	θ	X
ejpam-4406	189	22	=	=	PUNCT
ejpam-4406	190	1	(	(	PUNCT
ejpam-4406	190	2	∥y1(n)(t)−	∥y1(n)(t)−	PROPN
ejpam-4406	190	3	y1(m)(t)∥	y1(m)(t)∥	PRON
ejpam-4406	190	4	×	×	VERB
ejpam-4406	190	5	∥	∥	PUNCT
ejpam-4406	190	6	−	−	PROPN
ejpam-4406	191	1	(	(	PUNCT
ejpam-4406	191	2	y1(n)(t	y1(n)(t	PROPN
ejpam-4406	191	3	)	)	PUNCT
ejpam-4406	192	1	+	+	CCONJ
ejpam-4406	192	2	y1(m)(t))∥	y1(m)(t))∥	PRON
ejpam-4406	192	3	−m1∥y1(n	−m1∥y1(n	NOUN
ejpam-4406	192	4	)	)	PUNCT
ejpam-4406	193	1	−	−	PROPN
ejpam-4406	193	2	y1(m)∥+	y1(m)∥+	ADJ
ejpam-4406	193	3	m3∥y2(n)y3(n	m3∥y2(n)y3(n	PROPN
ejpam-4406	193	4	)	)	PUNCT
ejpam-4406	194	1	−	−	PROPN
ejpam-4406	194	2	y2(m)y3(m)∥	y2(m)y3(m)∥	INTJ
ejpam-4406	194	3	×	×	PROPN
ejpam-4406	194	4	∥y2(n)(t)−	∥y2(n)(t)−	PROPN
ejpam-4406	194	5	y2(m)(t)∥	y2(m)(t)∥	X
ejpam-4406	194	6	×	×	NOUN
ejpam-4406	194	7	∥	∥	PUNCT
ejpam-4406	194	8	−	−	PROPN
ejpam-4406	194	9	(	(	PUNCT
ejpam-4406	194	10	y2(n)(t	y2(n)(t	PROPN
ejpam-4406	194	11	)	)	PUNCT
ejpam-4406	194	12	+	+	CCONJ
ejpam-4406	194	13	y2(m)(t))∥+	y2(m)(t))∥+	NUM
ejpam-4406	194	14	m1∥y1(n	m1∥y1(n	NOUN
ejpam-4406	194	15	)	)	PUNCT
ejpam-4406	194	16	−	−	PROPN
ejpam-4406	194	17	y1(m)∥	y1(m)∥	PROPN
ejpam-4406	194	18	−m2∥y22(n	−m2∥y22(n	PROPN
ejpam-4406	194	19	)	)	PUNCT
ejpam-4406	194	20	−	−	PROPN
ejpam-4406	194	21	y22(m)∥	y22(m)∥	INTJ
ejpam-4406	194	22	−m3∥y2(n)y3(n	−m3∥y2(n)y3(n	NOUN
ejpam-4406	194	23	)	)	PUNCT
ejpam-4406	195	1	−	−	PROPN
ejpam-4406	195	2	y2(m)y3(m)∥×	y2(m)y3(m)∥×	NOUN
ejpam-4406	195	3	∥y3(n)(t)−	∥y3(n)(t)−	PROPN
ejpam-4406	195	4	y3(m)(t)∥	y3(m)(t)∥	PRON
ejpam-4406	196	1	×	×	VERB
ejpam-4406	196	2	∥	∥	PUNCT
ejpam-4406	196	3	−	−	PROPN
ejpam-4406	196	4	(	(	PUNCT
ejpam-4406	196	5	y3(n)(t	y3(n)(t	PROPN
ejpam-4406	196	6	)	)	PUNCT
ejpam-4406	197	1	+	+	NUM
ejpam-4406	197	2	y3(m)(t))∥+m2∥y22(n	y3(m)(t))∥+m2∥y22(n	ADJ
ejpam-4406	197	3	)	)	PUNCT
ejpam-4406	197	4	−	−	PROPN
ejpam-4406	197	5	y22(m)∥	y22(m)∥	NOUN
ejpam-4406	197	6	)	)	PUNCT
ejpam-4406	197	7	(	(	PUNCT
ejpam-4406	197	8	36	36	NUM
ejpam-4406	197	9	)	)	PUNCT
ejpam-4406	197	10	j.	j.	PROPN
ejpam-4406	197	11	asad	asad	PROPN
ejpam-4406	197	12	et	et	PROPN
ejpam-4406	197	13	al	al	PROPN
ejpam-4406	197	14	.	.	PUNCT
ejpam-4406	197	15	/	/	SYM
ejpam-4406	197	16	eur	eur	PROPN
ejpam-4406	197	17	.	.	PUNCT
ejpam-4406	198	1	j.	j.	PROPN
ejpam-4406	198	2	pure	pure	PROPN
ejpam-4406	198	3	appl	appl	PROPN
ejpam-4406	198	4	.	.	PROPN
ejpam-4406	198	5	math	math	PROPN
ejpam-4406	198	6	,	,	PUNCT
ejpam-4406	198	7	15	15	NUM
ejpam-4406	198	8	(	(	PUNCT
ejpam-4406	198	9	3	3	NUM
ejpam-4406	198	10	)	)	PUNCT
ejpam-4406	198	11	(	(	PUNCT
ejpam-4406	198	12	2022	2022	NUM
ejpam-4406	198	13	)	)	PUNCT
ejpam-4406	198	14	,	,	PUNCT
ejpam-4406	198	15	1144	1144	NUM
ejpam-4406	198	16	-	-	SYM
ejpam-4406	198	17	1157	1157	NUM
ejpam-4406	198	18	1152	1152	NUM
ejpam-4406	198	19	theorem	theorem	NOUN
ejpam-4406	198	20	5	5	NUM
ejpam-4406	198	21	.	.	PUNCT
ejpam-4406	199	1	the	the	DET
ejpam-4406	199	2	special	special	ADJ
ejpam-4406	199	3	solution	solution	NOUN
ejpam-4406	199	4	of	of	ADP
ejpam-4406	199	5	system	system	NOUN
ejpam-4406	199	6	(	(	PUNCT
ejpam-4406	199	7	28	28	NUM
ejpam-4406	199	8	)	)	PUNCT
ejpam-4406	199	9	using	use	VERB
ejpam-4406	199	10	the	the	DET
ejpam-4406	199	11	iteration	iteration	NOUN
ejpam-4406	199	12	method	method	NOUN
ejpam-4406	199	13	is	be	AUX
ejpam-4406	199	14	unique	unique	ADJ
ejpam-4406	199	15	singular	singular	ADJ
ejpam-4406	199	16	solution	solution	NOUN
ejpam-4406	199	17	.	.	PUNCT
ejpam-4406	200	1	proof	proof	NOUN
ejpam-4406	200	2	.	.	PUNCT
ejpam-4406	201	1	by	by	ADP
ejpam-4406	201	2	using	use	VERB
ejpam-4406	201	3	hilbert	hilbert	NOUN
ejpam-4406	201	4	space	space	NOUN
ejpam-4406	201	5	h	h	NOUN
ejpam-4406	201	6	=	=	PUNCT
ejpam-4406	201	7	l2((p	l2((p	PROPN
ejpam-4406	201	8	,	,	PUNCT
ejpam-4406	201	9	q)×	q)×	PUNCT
ejpam-4406	201	10	(	(	PUNCT
ejpam-4406	201	11	0	0	NUM
ejpam-4406	201	12	,	,	PUNCT
ejpam-4406	201	13	r	r	NOUN
ejpam-4406	201	14	)	)	PUNCT
ejpam-4406	201	15	)	)	PUNCT
ejpam-4406	201	16	which	which	PRON
ejpam-4406	201	17	can	can	AUX
ejpam-4406	201	18	be	be	AUX
ejpam-4406	201	19	described	describe	VERB
ejpam-4406	201	20	as	as	ADP
ejpam-4406	201	21	h	h	NOUN
ejpam-4406	201	22	:	:	PUNCT
ejpam-4406	201	23	(	(	PUNCT
ejpam-4406	201	24	p	p	X
ejpam-4406	201	25	,	,	PUNCT
ejpam-4406	201	26	q)×	q)×	X
ejpam-4406	201	27	(	(	PUNCT
ejpam-4406	201	28	0	0	NUM
ejpam-4406	201	29	,	,	PUNCT
ejpam-4406	201	30	t	t	NOUN
ejpam-4406	201	31	)	)	PUNCT
ejpam-4406	201	32	→	→	PUNCT
ejpam-4406	201	33	r	r	NOUN
ejpam-4406	201	34	considering	consider	VERB
ejpam-4406	201	35	θ	θ	PROPN
ejpam-4406	201	36	=	=	SYM
ejpam-4406	201	37	(	(	PUNCT
ejpam-4406	201	38	0	0	NUM
ejpam-4406	201	39	,	,	PUNCT
ejpam-4406	201	40	0	0	NUM
ejpam-4406	201	41	,	,	PUNCT
ejpam-4406	201	42	0	0	NUM
ejpam-4406	201	43	)	)	PUNCT
ejpam-4406	201	44	,	,	PUNCT
ejpam-4406	201	45	θ	θ	X
ejpam-4406	201	46	=	=	PUNCT
ejpam-4406	201	47	(	(	PUNCT
ejpam-4406	202	1	−m1y1	−m1y1	PROPN
ejpam-4406	202	2	+	+	NOUN
ejpam-4406	202	3	m3y2y3	m3y2y3	NOUN
ejpam-4406	202	4	,	,	PUNCT
ejpam-4406	202	5	m1y1	m1y1	NOUN
ejpam-4406	202	6	−m2y	−m2y	PROPN
ejpam-4406	202	7	2	2	NUM
ejpam-4406	202	8	2	2	NUM
ejpam-4406	202	9	−m3y2y3	−m3y2y3	NOUN
ejpam-4406	202	10	,	,	PUNCT
ejpam-4406	202	11	m2y	m2y	PROPN
ejpam-4406	202	12	2	2	NUM
ejpam-4406	202	13	2	2	NUM
ejpam-4406	202	14	)	)	PUNCT
ejpam-4406	202	15	.	.	PUNCT
ejpam-4406	203	1	we	we	PRON
ejpam-4406	203	2	have	have	VERB
ejpam-4406	203	3	t	t	X
ejpam-4406	203	4	(	(	PUNCT
ejpam-4406	203	5	(	(	PUNCT
ejpam-4406	203	6	y1(11)(t)−	y1(11)(t)−	PROPN
ejpam-4406	203	7	y1(12)(t	y1(12)(t	PROPN
ejpam-4406	203	8	)	)	PUNCT
ejpam-4406	203	9	,	,	PUNCT
ejpam-4406	203	10	y2(21)(t)−	y2(21)(t)−	PROPN
ejpam-4406	203	11	y2(22)(t	y2(22)(t	PROPN
ejpam-4406	203	12	)	)	PUNCT
ejpam-4406	203	13	,	,	PUNCT
ejpam-4406	203	14	y3(31)(t)−	y3(31)(t)−	PROPN
ejpam-4406	203	15	y3(32)(t	y3(32)(t	PROPN
ejpam-4406	203	16	)	)	PUNCT
ejpam-4406	203	17	)	)	PUNCT
ejpam-4406	203	18	,	,	PUNCT
ejpam-4406	203	19	(	(	PUNCT
ejpam-4406	203	20	v1	v1	NOUN
ejpam-4406	203	21	,	,	PUNCT
ejpam-4406	203	22	v2	v2	PROPN
ejpam-4406	203	23	,	,	PUNCT
ejpam-4406	203	24	v3	v3	PROPN
ejpam-4406	203	25	)	)	PUNCT
ejpam-4406	203	26	)	)	PUNCT
ejpam-4406	203	27	.	.	PUNCT
ejpam-4406	204	1	(	(	PUNCT
ejpam-4406	204	2	37	37	NUM
ejpam-4406	204	3	)	)	PUNCT
ejpam-4406	204	4	we	we	PRON
ejpam-4406	204	5	get	get	VERB
ejpam-4406	204	6	(	(	PUNCT
ejpam-4406	204	7	−m1(y1(11	−m1(y1(11	NOUN
ejpam-4406	204	8	)	)	PUNCT
ejpam-4406	204	9	−	−	PROPN
ejpam-4406	204	10	y1(12	y1(12	PROPN
ejpam-4406	204	11	)	)	PUNCT
ejpam-4406	204	12	)	)	PUNCT
ejpam-4406	205	1	+	+	X
ejpam-4406	205	2	m3(y2(21	m3(y2(21	NOUN
ejpam-4406	205	3	)	)	PUNCT
ejpam-4406	205	4	−	−	NOUN
ejpam-4406	205	5	y2(22))(y3(31	y2(22))(y3(31	NOUN
ejpam-4406	205	6	)	)	PUNCT
ejpam-4406	205	7	−	−	PROPN
ejpam-4406	205	8	y3(32	y3(32	NOUN
ejpam-4406	205	9	)	)	PUNCT
ejpam-4406	205	10	)	)	PUNCT
ejpam-4406	205	11	,	,	PUNCT
ejpam-4406	205	12	v1	v1	NOUN
ejpam-4406	205	13	)	)	PUNCT
ejpam-4406	205	14	≤	≤	NOUN
ejpam-4406	205	15	m1∥y1(11	m1∥y1(11	NUM
ejpam-4406	205	16	)	)	PUNCT
ejpam-4406	205	17	−	−	ADP
ejpam-4406	205	18	y1(12)∥	y1(12)∥	NUM
ejpam-4406	205	19	∥v1∥+m3∥y2(21	∥v1∥+m3∥y2(21	NOUN
ejpam-4406	205	20	)	)	PUNCT
ejpam-4406	205	21	−	−	NUM
ejpam-4406	205	22	y2(22)∥∥y3(31	y2(22)∥∥y3(31	NOUN
ejpam-4406	205	23	)	)	PUNCT
ejpam-4406	205	24	−	−	PROPN
ejpam-4406	205	25	y3(32)∥∥v1∥	y3(32)∥∥v1∥	PROPN
ejpam-4406	205	26	,	,	PUNCT
ejpam-4406	205	27	(	(	PUNCT
ejpam-4406	205	28	m1(y1(11	m1(y1(11	PROPN
ejpam-4406	205	29	)	)	PUNCT
ejpam-4406	205	30	−	−	PROPN
ejpam-4406	206	1	y1(12))−m2(y	y1(12))−m2(y	ADJ
ejpam-4406	206	2	2	2	NUM
ejpam-4406	206	3	2(21	2(21	NUM
ejpam-4406	206	4	)	)	PUNCT
ejpam-4406	206	5	−	−	PROPN
ejpam-4406	206	6	y22(22))−m3(y2(21	y22(22))−m3(y2(21	NUM
ejpam-4406	206	7	)	)	PUNCT
ejpam-4406	206	8	−	−	NOUN
ejpam-4406	206	9	y2(22))(y3(31	y2(22))(y3(31	NOUN
ejpam-4406	206	10	)	)	PUNCT
ejpam-4406	206	11	−	−	PROPN
ejpam-4406	206	12	y3(32	y3(32	NOUN
ejpam-4406	206	13	)	)	PUNCT
ejpam-4406	206	14	)	)	PUNCT
ejpam-4406	206	15	,	,	PUNCT
ejpam-4406	206	16	v2	v2	PROPN
ejpam-4406	206	17	)	)	PUNCT
ejpam-4406	206	18	≤	≤	NOUN
ejpam-4406	206	19	m1∥y1(11	m1∥y1(11	NUM
ejpam-4406	206	20	)	)	PUNCT
ejpam-4406	206	21	−	−	PROPN
ejpam-4406	207	1	y1(12)∥∥v2∥+m2∥(y22(21	y1(12)∥∥v2∥+m2∥(y22(21	NOUN
ejpam-4406	207	2	)	)	PUNCT
ejpam-4406	207	3	−	−	PROPN
ejpam-4406	207	4	y22(22))∥	y22(22))∥	PROPN
ejpam-4406	207	5	∥v2∥+	∥v2∥+	PROPN
ejpam-4406	207	6	∥+m3∥y2(21	∥+m3∥y2(21	PROPN
ejpam-4406	207	7	)	)	PUNCT
ejpam-4406	207	8	−	−	NUM
ejpam-4406	207	9	y2(22)∥∥y3(31	y2(22)∥∥y3(31	NOUN
ejpam-4406	207	10	)	)	PUNCT
ejpam-4406	207	11	−	−	PROPN
ejpam-4406	207	12	y3(32)∥∥v2∥	y3(32)∥∥v2∥	PROPN
ejpam-4406	207	13	,	,	PUNCT
ejpam-4406	207	14	(	(	PUNCT
ejpam-4406	207	15	m2(y	m2(y	ADP
ejpam-4406	207	16	2	2	NUM
ejpam-4406	207	17	2(21	2(21	NUM
ejpam-4406	207	18	)	)	PUNCT
ejpam-4406	207	19	−	−	PROPN
ejpam-4406	208	1	y22(22	y22(22	NOUN
ejpam-4406	208	2	)	)	PUNCT
ejpam-4406	208	3	)	)	PUNCT
ejpam-4406	208	4	,	,	PUNCT
ejpam-4406	208	5	v3	v3	PROPN
ejpam-4406	208	6	)	)	PUNCT
ejpam-4406	208	7	≤	≤	NOUN
ejpam-4406	209	1	m2∥(y22(21	m2∥(y22(21	CCONJ
ejpam-4406	209	2	)	)	PUNCT
ejpam-4406	210	1	−	−	PROPN
ejpam-4406	210	2	y22(22))∥∥v3∥.	y22(22))∥∥v3∥.	NOUN
ejpam-4406	210	3	(	(	PUNCT
ejpam-4406	210	4	38	38	NUM
ejpam-4406	210	5	)	)	PUNCT
ejpam-4406	210	6	by	by	ADP
ejpam-4406	210	7	using	use	VERB
ejpam-4406	210	8	conditions	condition	NOUN
ejpam-4406	210	9	,	,	PUNCT
ejpam-4406	210	10	we	we	PRON
ejpam-4406	210	11	get	get	AUX
ejpam-4406	210	12	∥y1	∥y1	NOUN
ejpam-4406	210	13	−	−	PROPN
ejpam-4406	210	14	y1(11)∥	y1(11)∥	PROPN
ejpam-4406	210	15	,	,	PUNCT
ejpam-4406	210	16	∥y1	∥y1	NOUN
ejpam-4406	211	1	−	−	PROPN
ejpam-4406	211	2	y1(12)∥	y1(12)∥	X
ejpam-4406	211	3	≤	≤	NUM
ejpam-4406	212	1	χe1	χe1	PROPN
ejpam-4406	212	2	ω	ω	PROPN
ejpam-4406	212	3	,	,	PUNCT
ejpam-4406	212	4	∥y2	∥y2	X
ejpam-4406	213	1	−	−	PROPN
ejpam-4406	213	2	y2(21)∥	y2(21)∥	PROPN
ejpam-4406	213	3	,	,	PUNCT
ejpam-4406	213	4	∥y2	∥y2	PUNCT
ejpam-4406	214	1	−	−	PROPN
ejpam-4406	214	2	y2(22)∥	y2(22)∥	SYM
ejpam-4406	214	3	≤	≤	PUNCT
ejpam-4406	214	4	χe2	χe2	PROPN
ejpam-4406	214	5	ς	ς	PROPN
ejpam-4406	214	6	,	,	PUNCT
ejpam-4406	214	7	∥y3	∥y3	VERB
ejpam-4406	214	8	−	−	PROPN
ejpam-4406	214	9	y3(31)∥	y3(31)∥	NUM
ejpam-4406	214	10	,	,	PUNCT
ejpam-4406	214	11	∥y3	∥y3	VERB
ejpam-4406	214	12	−	−	PROPN
ejpam-4406	214	13	y3(32)∥	y3(32)∥	NUM
ejpam-4406	214	14	≤	≤	NUM
ejpam-4406	214	15	χe3	χe3	NOUN
ejpam-4406	214	16	υ	υ	PROPN
ejpam-4406	214	17	.	.	PUNCT
ejpam-4406	215	1	(	(	PUNCT
ejpam-4406	215	2	39	39	NUM
ejpam-4406	215	3	)	)	PUNCT
ejpam-4406	215	4	where	where	SCONJ
ejpam-4406	215	5	ω	ω	NOUN
ejpam-4406	215	6	=	=	SYM
ejpam-4406	215	7	3(m1∥y1(11	3(m1∥y1(11	PROPN
ejpam-4406	215	8	)	)	PUNCT
ejpam-4406	215	9	−	−	PROPN
ejpam-4406	215	10	y1(12)∥+m3∥y2(21	y1(12)∥+m3∥y2(21	PROPN
ejpam-4406	215	11	)	)	PUNCT
ejpam-4406	215	12	−	−	NUM
ejpam-4406	215	13	y2(22)∥∥y3(31	y2(22)∥∥y3(31	NOUN
ejpam-4406	215	14	)	)	PUNCT
ejpam-4406	215	15	−	−	PROPN
ejpam-4406	215	16	y3(32)∥)∥v1∥	y3(32)∥)∥v1∥	NOUN
ejpam-4406	215	17	,	,	PUNCT
ejpam-4406	215	18	ς	ς	PROPN
ejpam-4406	215	19	=	=	SYM
ejpam-4406	215	20	3(m1∥y1(11	3(m1∥y1(11	PROPN
ejpam-4406	215	21	)	)	PUNCT
ejpam-4406	215	22	−	−	NUM
ejpam-4406	215	23	y1(12)∥+m2∥(y22(21	y1(12)∥+m2∥(y22(21	NOUN
ejpam-4406	215	24	)	)	PUNCT
ejpam-4406	215	25	−	−	PROPN
ejpam-4406	215	26	y22(22))∥+m3∥y2(21	y22(22))∥+m3∥y2(21	SYM
ejpam-4406	215	27	)	)	PUNCT
ejpam-4406	216	1	−	−	PROPN
ejpam-4406	216	2	y2(22)∥	y2(22)∥	NUM
ejpam-4406	216	3	∥y3(31	∥y3(31	NUM
ejpam-4406	216	4	)	)	PUNCT
ejpam-4406	216	5	−	−	PROPN
ejpam-4406	216	6	y3(32)∥)∥v2∥	y3(32)∥)∥v2∥	PROPN
ejpam-4406	216	7	,	,	PUNCT
ejpam-4406	216	8	υ	υ	PROPN
ejpam-4406	216	9	=	=	SYM
ejpam-4406	216	10	3(m2∥(y22(21	3(m2∥(y22(21	NUM
ejpam-4406	216	11	)	)	PUNCT
ejpam-4406	216	12	−	−	PROPN
ejpam-4406	217	1	y22(22))∥)∥v3∥.	y22(22))∥)∥v3∥.	PROPN
ejpam-4406	217	2	(	(	PUNCT
ejpam-4406	217	3	40	40	NUM
ejpam-4406	217	4	)	)	PUNCT
ejpam-4406	218	1	but	but	CCONJ
ejpam-4406	218	2	,	,	PUNCT
ejpam-4406	218	3	it	it	PRON
ejpam-4406	218	4	is	be	AUX
ejpam-4406	218	5	obvious	obvious	ADJ
ejpam-4406	218	6	that	that	SCONJ
ejpam-4406	218	7	(	(	PUNCT
ejpam-4406	218	8	m1∥y1(11	m1∥y1(11	NUM
ejpam-4406	218	9	)	)	PUNCT
ejpam-4406	218	10	−	−	PROPN
ejpam-4406	218	11	y1(12)∥+m3∥y2(21	y1(12)∥+m3∥y2(21	PROPN
ejpam-4406	218	12	)	)	PUNCT
ejpam-4406	218	13	−	−	NUM
ejpam-4406	218	14	y2(22)∥∥y3(31	y2(22)∥∥y3(31	NOUN
ejpam-4406	218	15	)	)	PUNCT
ejpam-4406	218	16	−	−	PROPN
ejpam-4406	218	17	y3(32)∥	y3(32)∥	PROPN
ejpam-4406	218	18	)	)	PUNCT
ejpam-4406	218	19	̸=	̸=	PROPN
ejpam-4406	218	20	0	0	NUM
ejpam-4406	218	21	(	(	PUNCT
ejpam-4406	218	22	m1∥y1(11	m1∥y1(11	NUM
ejpam-4406	218	23	)	)	PUNCT
ejpam-4406	218	24	−	−	PROPN
ejpam-4406	219	1	y1(12)∥+m2∥(y22(21	y1(12)∥+m2∥(y22(21	NOUN
ejpam-4406	219	2	)	)	PUNCT
ejpam-4406	219	3	−	−	PROPN
ejpam-4406	219	4	y22(22))∥+m3∥y2(21	y22(22))∥+m3∥y2(21	SYM
ejpam-4406	219	5	)	)	PUNCT
ejpam-4406	219	6	−	−	NUM
ejpam-4406	219	7	y2(22)∥∥y3(31	y2(22)∥∥y3(31	NOUN
ejpam-4406	219	8	)	)	PUNCT
ejpam-4406	219	9	−	−	PROPN
ejpam-4406	219	10	y3(32)∥	y3(32)∥	PROPN
ejpam-4406	219	11	)	)	PUNCT
ejpam-4406	219	12	̸=	̸=	PROPN
ejpam-4406	219	13	0	0	NUM
ejpam-4406	219	14	(	(	PUNCT
ejpam-4406	219	15	m2∥(y22(21	m2∥(y22(21	NOUN
ejpam-4406	219	16	)	)	PUNCT
ejpam-4406	219	17	−	−	PROPN
ejpam-4406	219	18	y22(22))∥	y22(22))∥	NOUN
ejpam-4406	219	19	)	)	PUNCT
ejpam-4406	219	20	̸=	̸=	PROPN
ejpam-4406	219	21	0	0	NUM
ejpam-4406	219	22	where∥v1∥	where∥v1∥	PROPN
ejpam-4406	219	23	,	,	PUNCT
ejpam-4406	219	24	∥v2∥	∥v2∥	PROPN
ejpam-4406	219	25	,	,	PUNCT
ejpam-4406	219	26	∥v3∥	∥v3∥	PROPN
ejpam-4406	219	27	=	=	AUX
ejpam-4406	219	28	̸	̸	NUM
ejpam-4406	219	29	0	0	NUM
ejpam-4406	219	30	(	(	PUNCT
ejpam-4406	219	31	41	41	NUM
ejpam-4406	219	32	)	)	PUNCT
ejpam-4406	219	33	j.	j.	PROPN
ejpam-4406	219	34	asad	asad	PROPN
ejpam-4406	219	35	et	et	PROPN
ejpam-4406	219	36	al	al	PROPN
ejpam-4406	219	37	.	.	PUNCT
ejpam-4406	219	38	/	/	SYM
ejpam-4406	219	39	eur	eur	PROPN
ejpam-4406	219	40	.	.	PUNCT
ejpam-4406	220	1	j.	j.	PROPN
ejpam-4406	220	2	pure	pure	PROPN
ejpam-4406	220	3	appl	appl	PROPN
ejpam-4406	220	4	.	.	PROPN
ejpam-4406	220	5	math	math	PROPN
ejpam-4406	220	6	,	,	PUNCT
ejpam-4406	220	7	15	15	NUM
ejpam-4406	220	8	(	(	PUNCT
ejpam-4406	220	9	3	3	NUM
ejpam-4406	220	10	)	)	PUNCT
ejpam-4406	220	11	(	(	PUNCT
ejpam-4406	220	12	2022	2022	NUM
ejpam-4406	220	13	)	)	PUNCT
ejpam-4406	220	14	,	,	PUNCT
ejpam-4406	220	15	1144	1144	NUM
ejpam-4406	220	16	-	-	SYM
ejpam-4406	220	17	1157	1157	NUM
ejpam-4406	220	18	1153	1153	NUM
ejpam-4406	220	19	therefore	therefore	ADV
ejpam-4406	220	20	,	,	PUNCT
ejpam-4406	220	21	we	we	PRON
ejpam-4406	220	22	have	have	AUX
ejpam-4406	220	23	∥y1(11	∥y1(11	NUM
ejpam-4406	220	24	)	)	PUNCT
ejpam-4406	221	1	−	−	PROPN
ejpam-4406	221	2	y1(12)∥	y1(12)∥	NUM
ejpam-4406	221	3	=	=	SYM
ejpam-4406	221	4	0	0	NUM
ejpam-4406	221	5	,	,	PUNCT
ejpam-4406	221	6	∥y2(21	∥y2(21	NUM
ejpam-4406	221	7	)	)	PUNCT
ejpam-4406	222	1	−	−	PUNCT
ejpam-4406	223	1	y2(22)∥	y2(22)∥	NUM
ejpam-4406	223	2	=	=	SYM
ejpam-4406	223	3	0	0	NUM
ejpam-4406	223	4	,	,	PUNCT
ejpam-4406	223	5	∥y3(31	∥y3(31	NUM
ejpam-4406	223	6	)	)	PUNCT
ejpam-4406	224	1	−	−	PROPN
ejpam-4406	224	2	y3(32)∥	y3(32)∥	NUM
ejpam-4406	225	1	=	=	SYM
ejpam-4406	225	2	0	0	PROPN
ejpam-4406	225	3	,	,	PUNCT
ejpam-4406	225	4	(	(	PUNCT
ejpam-4406	225	5	42	42	NUM
ejpam-4406	225	6	)	)	PUNCT
ejpam-4406	225	7	which	which	PRON
ejpam-4406	225	8	yields	yield	VERB
ejpam-4406	225	9	that	that	PRON
ejpam-4406	225	10	y1(11	y1(11	PROPN
ejpam-4406	225	11	)	)	PUNCT
ejpam-4406	225	12	=	=	SYM
ejpam-4406	225	13	y1(12	y1(12	PROPN
ejpam-4406	225	14	)	)	PUNCT
ejpam-4406	225	15	,	,	PUNCT
ejpam-4406	226	1	y2(21	y2(21	NOUN
ejpam-4406	226	2	)	)	PUNCT
ejpam-4406	226	3	=	=	SYM
ejpam-4406	226	4	y2(22	y2(22	PROPN
ejpam-4406	226	5	)	)	PUNCT
ejpam-4406	226	6	,	,	PUNCT
ejpam-4406	226	7	y3(31	y3(31	PROPN
ejpam-4406	226	8	)	)	PUNCT
ejpam-4406	226	9	=	=	SYM
ejpam-4406	226	10	y3(32	y3(32	NOUN
ejpam-4406	226	11	)	)	PUNCT
ejpam-4406	226	12	(	(	PUNCT
ejpam-4406	226	13	43	43	NUM
ejpam-4406	226	14	)	)	PUNCT
ejpam-4406	226	15	this	this	PRON
ejpam-4406	226	16	completes	complete	VERB
ejpam-4406	226	17	the	the	DET
ejpam-4406	226	18	proof	proof	NOUN
ejpam-4406	226	19	of	of	ADP
ejpam-4406	226	20	uniqueness	uniqueness	NOUN
ejpam-4406	226	21	.	.	PUNCT
ejpam-4406	227	1	5	5	X
ejpam-4406	227	2	.	.	NOUN
ejpam-4406	227	3	results	result	NOUN
ejpam-4406	227	4	and	and	CCONJ
ejpam-4406	227	5	discussion	discussion	VERB
ejpam-4406	227	6	the	the	DET
ejpam-4406	227	7	mathematical	mathematical	ADJ
ejpam-4406	227	8	analysis	analysis	NOUN
ejpam-4406	227	9	of	of	ADP
ejpam-4406	227	10	chemistry	chemistry	NOUN
ejpam-4406	227	11	kinetics	kinetic	NOUN
ejpam-4406	227	12	model	model	NOUN
ejpam-4406	227	13	with	with	ADP
ejpam-4406	227	14	non	non	ADJ
ejpam-4406	227	15	-	-	ADJ
ejpam-4406	227	16	linear	linear	ADJ
ejpam-4406	227	17	occurrence	occurrence	NOUN
ejpam-4406	227	18	has	have	AUX
ejpam-4406	227	19	been	be	AUX
ejpam-4406	227	20	offered	offer	VERB
ejpam-4406	227	21	.	.	PUNCT
ejpam-4406	228	1	some	some	DET
ejpam-4406	228	2	convergence	convergence	NOUN
ejpam-4406	228	3	of	of	ADP
ejpam-4406	228	4	theoretical	theoretical	ADJ
ejpam-4406	228	5	results	result	NOUN
ejpam-4406	228	6	with	with	ADP
ejpam-4406	228	7	some	some	DET
ejpam-4406	228	8	numerical	numerical	ADJ
ejpam-4406	228	9	method	method	NOUN
ejpam-4406	228	10	is	be	AUX
ejpam-4406	228	11	also	also	ADV
ejpam-4406	228	12	given	give	VERB
ejpam-4406	228	13	in	in	ADP
ejpam-4406	228	14	[	[	PUNCT
ejpam-4406	228	15	11	11	NUM
ejpam-4406	228	16	]	]	PUNCT
ejpam-4406	228	17	.	.	PUNCT
ejpam-4406	229	1	in	in	ADP
ejpam-4406	229	2	figures	figure	NOUN
ejpam-4406	229	3	1	1	NUM
ejpam-4406	229	4	,	,	PUNCT
ejpam-4406	229	5	2	2	NUM
ejpam-4406	229	6	,	,	PUNCT
ejpam-4406	229	7	3	3	NUM
ejpam-4406	229	8	,	,	PUNCT
ejpam-4406	229	9	4	4	NUM
ejpam-4406	229	10	,	,	PUNCT
ejpam-4406	229	11	5	5	NUM
ejpam-4406	229	12	,	,	PUNCT
ejpam-4406	229	13	6	6	NUM
ejpam-4406	229	14	the	the	DET
ejpam-4406	229	15	memory	memory	NOUN
ejpam-4406	229	16	effect	effect	NOUN
ejpam-4406	229	17	of	of	ADP
ejpam-4406	229	18	fractional	fractional	ADJ
ejpam-4406	229	19	order	order	NOUN
ejpam-4406	229	20	technique	technique	NOUN
ejpam-4406	229	21	for	for	ADP
ejpam-4406	229	22	robertson	robertson	PROPN
ejpam-4406	229	23	problem	problem	NOUN
ejpam-4406	229	24	has	have	AUX
ejpam-4406	229	25	been	be	AUX
ejpam-4406	229	26	demonstrated	demonstrate	VERB
ejpam-4406	229	27	.	.	PUNCT
ejpam-4406	230	1	figures	figure	NOUN
ejpam-4406	230	2	1	1	NUM
ejpam-4406	230	3	,	,	PUNCT
ejpam-4406	230	4	2	2	NUM
ejpam-4406	230	5	,	,	PUNCT
ejpam-4406	230	6	3	3	NUM
ejpam-4406	230	7	represent	represent	VERB
ejpam-4406	230	8	the	the	DET
ejpam-4406	230	9	results	result	NOUN
ejpam-4406	230	10	by	by	ADP
ejpam-4406	230	11	using	use	VERB
ejpam-4406	230	12	caputo	caputo	PROPN
ejpam-4406	230	13	-	-	PUNCT
ejpam-4406	230	14	fabrizio	fabrizio	PROPN
ejpam-4406	230	15	derivative	derivative	NOUN
ejpam-4406	230	16	and	and	CCONJ
ejpam-4406	230	17	figures	figure	NOUN
ejpam-4406	230	18	4	4	NUM
ejpam-4406	230	19	,	,	PUNCT
ejpam-4406	230	20	5	5	NUM
ejpam-4406	230	21	,	,	PUNCT
ejpam-4406	230	22	6	6	NUM
ejpam-4406	230	23	are	be	AUX
ejpam-4406	230	24	obtained	obtain	VERB
ejpam-4406	230	25	with	with	ADP
ejpam-4406	230	26	abc	abc	PROPN
ejpam-4406	230	27	derivative	derivative	NOUN
ejpam-4406	230	28	.	.	PUNCT
ejpam-4406	231	1	we	we	PRON
ejpam-4406	231	2	can	can	AUX
ejpam-4406	231	3	get	get	VERB
ejpam-4406	231	4	better	well	ADJ
ejpam-4406	231	5	concentration	concentration	NOUN
ejpam-4406	231	6	of	of	ADP
ejpam-4406	231	7	the	the	DET
ejpam-4406	231	8	components	component	NOUN
ejpam-4406	231	9	by	by	ADP
ejpam-4406	231	10	using	use	VERB
ejpam-4406	231	11	the	the	DET
ejpam-4406	231	12	fractional	fractional	ADJ
ejpam-4406	231	13	derivative	derivative	NOUN
ejpam-4406	231	14	which	which	PRON
ejpam-4406	231	15	are	be	AUX
ejpam-4406	231	16	very	very	ADV
ejpam-4406	231	17	important	important	ADJ
ejpam-4406	231	18	for	for	SCONJ
ejpam-4406	231	19	chemical	chemical	ADJ
ejpam-4406	231	20	problem	problem	NOUN
ejpam-4406	231	21	to	to	PART
ejpam-4406	231	22	check	check	VERB
ejpam-4406	231	23	the	the	DET
ejpam-4406	231	24	actual	actual	ADJ
ejpam-4406	231	25	behavior	behavior	NOUN
ejpam-4406	231	26	of	of	ADP
ejpam-4406	231	27	the	the	DET
ejpam-4406	231	28	concentration	concentration	NOUN
ejpam-4406	231	29	of	of	ADP
ejpam-4406	231	30	the	the	DET
ejpam-4406	231	31	chemical	chemical	NOUN
ejpam-4406	231	32	with	with	ADP
ejpam-4406	231	33	smallest	small	ADJ
ejpam-4406	231	34	changes	change	NOUN
ejpam-4406	231	35	in	in	ADP
ejpam-4406	231	36	derivative	derivative	NOUN
ejpam-4406	231	37	with	with	ADP
ejpam-4406	231	38	respect	respect	NOUN
ejpam-4406	231	39	to	to	ADP
ejpam-4406	231	40	time	time	NOUN
ejpam-4406	231	41	.	.	PUNCT
ejpam-4406	232	1	figure	figure	VERB
ejpam-4406	232	2	1	1	NUM
ejpam-4406	232	3	:	:	PUNCT
ejpam-4406	232	4	concentration	concentration	NOUN
ejpam-4406	232	5	results	result	NOUN
ejpam-4406	232	6	of	of	ADP
ejpam-4406	232	7	y1(t	y1(t	PROPN
ejpam-4406	232	8	)	)	PUNCT
ejpam-4406	232	9	with	with	ADP
ejpam-4406	232	10	cf	cf	NOUN
ejpam-4406	232	11	operator	operator	NOUN
ejpam-4406	232	12	at	at	ADP
ejpam-4406	232	13	different	different	ADJ
ejpam-4406	232	14	fractional	fractional	ADJ
ejpam-4406	232	15	order	order	NOUN
ejpam-4406	232	16	.	.	PUNCT
ejpam-4406	233	1	j.	j.	PROPN
ejpam-4406	233	2	asad	asad	PROPN
ejpam-4406	233	3	et	et	PROPN
ejpam-4406	233	4	al	al	PROPN
ejpam-4406	233	5	.	.	PUNCT
ejpam-4406	233	6	/	/	SYM
ejpam-4406	233	7	eur	eur	PROPN
ejpam-4406	233	8	.	.	PUNCT
ejpam-4406	234	1	j.	j.	PROPN
ejpam-4406	234	2	pure	pure	PROPN
ejpam-4406	234	3	appl	appl	PROPN
ejpam-4406	234	4	.	.	PROPN
ejpam-4406	234	5	math	math	PROPN
ejpam-4406	234	6	,	,	PUNCT
ejpam-4406	234	7	15	15	NUM
ejpam-4406	234	8	(	(	PUNCT
ejpam-4406	234	9	3	3	NUM
ejpam-4406	234	10	)	)	PUNCT
ejpam-4406	234	11	(	(	PUNCT
ejpam-4406	234	12	2022	2022	NUM
ejpam-4406	234	13	)	)	PUNCT
ejpam-4406	234	14	,	,	PUNCT
ejpam-4406	234	15	1144	1144	NUM
ejpam-4406	234	16	-	-	SYM
ejpam-4406	234	17	1157	1157	NUM
ejpam-4406	234	18	1154	1154	NUM
ejpam-4406	234	19	figure	figure	NOUN
ejpam-4406	234	20	2	2	NUM
ejpam-4406	234	21	:	:	PUNCT
ejpam-4406	234	22	concentration	concentration	NOUN
ejpam-4406	234	23	results	result	NOUN
ejpam-4406	234	24	of	of	ADP
ejpam-4406	234	25	y2(t	y2(t	PROPN
ejpam-4406	234	26	)	)	PUNCT
ejpam-4406	234	27	with	with	ADP
ejpam-4406	234	28	cf	cf	NOUN
ejpam-4406	234	29	operator	operator	NOUN
ejpam-4406	234	30	at	at	ADP
ejpam-4406	234	31	different	different	ADJ
ejpam-4406	234	32	fractional	fractional	ADJ
ejpam-4406	234	33	order	order	NOUN
ejpam-4406	234	34	.	.	PUNCT
ejpam-4406	235	1	figure	figure	VERB
ejpam-4406	235	2	3	3	NUM
ejpam-4406	235	3	:	:	PUNCT
ejpam-4406	235	4	concentration	concentration	NOUN
ejpam-4406	235	5	results	result	NOUN
ejpam-4406	235	6	of	of	ADP
ejpam-4406	235	7	y3(t	y3(t	PROPN
ejpam-4406	235	8	)	)	PUNCT
ejpam-4406	235	9	with	with	ADP
ejpam-4406	235	10	cf	cf	NOUN
ejpam-4406	235	11	operator	operator	NOUN
ejpam-4406	235	12	at	at	ADP
ejpam-4406	235	13	different	different	ADJ
ejpam-4406	235	14	fractional	fractional	ADJ
ejpam-4406	235	15	order	order	NOUN
ejpam-4406	235	16	.	.	PUNCT
ejpam-4406	236	1	6	6	X
ejpam-4406	236	2	.	.	X
ejpam-4406	236	3	conclusion	conclusion	NOUN
ejpam-4406	236	4	in	in	ADP
ejpam-4406	236	5	this	this	DET
ejpam-4406	236	6	paper	paper	NOUN
ejpam-4406	236	7	,	,	PUNCT
ejpam-4406	236	8	we	we	PRON
ejpam-4406	236	9	considered	consider	VERB
ejpam-4406	236	10	the	the	DET
ejpam-4406	236	11	stiff	stiff	ADJ
ejpam-4406	236	12	systems	system	NOUN
ejpam-4406	236	13	of	of	ADP
ejpam-4406	236	14	nonlinear	nonlinear	ADJ
ejpam-4406	236	15	ordinary	ordinary	ADJ
ejpam-4406	236	16	equations	equation	NOUN
ejpam-4406	236	17	which	which	PRON
ejpam-4406	236	18	are	be	AUX
ejpam-4406	236	19	depend	depend	ADJ
ejpam-4406	236	20	on	on	ADP
ejpam-4406	236	21	time	time	NOUN
ejpam-4406	236	22	t	t	NOUN
ejpam-4406	236	23	with	with	ADP
ejpam-4406	236	24	given	give	VERB
ejpam-4406	236	25	initial	initial	ADJ
ejpam-4406	236	26	conditions	condition	NOUN
ejpam-4406	236	27	.	.	PUNCT
ejpam-4406	237	1	the	the	DET
ejpam-4406	237	2	new	new	ADJ
ejpam-4406	237	3	fractional	fractional	ADJ
ejpam-4406	237	4	operator	operator	NOUN
ejpam-4406	237	5	has	have	AUX
ejpam-4406	237	6	been	be	AUX
ejpam-4406	237	7	implemented	implement	VERB
ejpam-4406	237	8	to	to	ADP
ejpam-4406	237	9	several	several	ADJ
ejpam-4406	237	10	initial	initial	ADJ
ejpam-4406	237	11	value	value	NOUN
ejpam-4406	237	12	problems	problem	NOUN
ejpam-4406	237	13	arising	arise	VERB
ejpam-4406	237	14	from	from	ADP
ejpam-4406	237	15	chemical	chemical	ADJ
ejpam-4406	237	16	reactions	reaction	NOUN
ejpam-4406	237	17	composed	compose	VERB
ejpam-4406	237	18	of	of	ADP
ejpam-4406	237	19	large	large	ADJ
ejpam-4406	237	20	systems	system	NOUN
ejpam-4406	237	21	of	of	ADP
ejpam-4406	237	22	stiff	stiff	ADJ
ejpam-4406	237	23	ordinary	ordinary	ADJ
ejpam-4406	237	24	differential	differential	ADJ
ejpam-4406	237	25	equations	equation	NOUN
ejpam-4406	237	26	.	.	PUNCT
ejpam-4406	238	1	by	by	ADP
ejpam-4406	238	2	using	use	VERB
ejpam-4406	238	3	the	the	DET
ejpam-4406	238	4	fixed	fix	VERB
ejpam-4406	238	5	point	point	NOUN
ejpam-4406	238	6	theory	theory	NOUN
ejpam-4406	238	7	results	result	NOUN
ejpam-4406	238	8	,	,	PUNCT
ejpam-4406	238	9	stability	stability	NOUN
ejpam-4406	238	10	and	and	CCONJ
ejpam-4406	238	11	uniqueness	uniqueness	NOUN
ejpam-4406	238	12	of	of	ADP
ejpam-4406	238	13	the	the	DET
ejpam-4406	238	14	chemistry	chemistry	NOUN
ejpam-4406	238	15	kinetic	kinetic	NOUN
ejpam-4406	238	16	model	model	NOUN
ejpam-4406	238	17	have	have	AUX
ejpam-4406	238	18	been	be	AUX
ejpam-4406	238	19	researched	research	VERB
ejpam-4406	238	20	.	.	PUNCT
ejpam-4406	239	1	the	the	DET
ejpam-4406	239	2	arbitrary	arbitrary	ADJ
ejpam-4406	239	3	derivative	derivative	NOUN
ejpam-4406	239	4	of	of	ADP
ejpam-4406	239	5	fractional	fractional	ADJ
ejpam-4406	239	6	order	order	NOUN
ejpam-4406	239	7	has	have	AUX
ejpam-4406	239	8	been	be	AUX
ejpam-4406	239	9	taken	take	VERB
ejpam-4406	239	10	in	in	ADP
ejpam-4406	239	11	the	the	DET
ejpam-4406	239	12	caputo	caputo	PROPN
ejpam-4406	239	13	-	-	PUNCT
ejpam-4406	239	14	fabrizio	fabrizio	PROPN
ejpam-4406	239	15	sense	sense	NOUN
ejpam-4406	239	16	j.	j.	PROPN
ejpam-4406	239	17	asad	asad	PROPN
ejpam-4406	239	18	et	et	PROPN
ejpam-4406	239	19	al	al	PROPN
ejpam-4406	239	20	.	.	PUNCT
ejpam-4406	239	21	/	/	SYM
ejpam-4406	239	22	eur	eur	PROPN
ejpam-4406	239	23	.	.	PUNCT
ejpam-4406	240	1	j.	j.	PROPN
ejpam-4406	240	2	pure	pure	PROPN
ejpam-4406	240	3	appl	appl	PROPN
ejpam-4406	240	4	.	.	PROPN
ejpam-4406	240	5	math	math	PROPN
ejpam-4406	240	6	,	,	PUNCT
ejpam-4406	240	7	15	15	NUM
ejpam-4406	240	8	(	(	PUNCT
ejpam-4406	240	9	3	3	NUM
ejpam-4406	240	10	)	)	PUNCT
ejpam-4406	240	11	(	(	PUNCT
ejpam-4406	240	12	2022	2022	NUM
ejpam-4406	240	13	)	)	PUNCT
ejpam-4406	240	14	,	,	PUNCT
ejpam-4406	240	15	1144	1144	NUM
ejpam-4406	240	16	-	-	SYM
ejpam-4406	240	17	1157	1157	NUM
ejpam-4406	240	18	1155	1155	NUM
ejpam-4406	240	19	figure	figure	NOUN
ejpam-4406	240	20	4	4	NUM
ejpam-4406	240	21	:	:	PUNCT
ejpam-4406	240	22	concentration	concentration	NOUN
ejpam-4406	240	23	results	result	NOUN
ejpam-4406	240	24	of	of	ADP
ejpam-4406	240	25	y1(t	y1(t	PROPN
ejpam-4406	240	26	)	)	PUNCT
ejpam-4406	240	27	with	with	ADP
ejpam-4406	240	28	abc	abc	PROPN
ejpam-4406	240	29	operator	operator	NOUN
ejpam-4406	240	30	at	at	ADP
ejpam-4406	240	31	different	different	ADJ
ejpam-4406	240	32	fractional	fractional	ADJ
ejpam-4406	240	33	order	order	NOUN
ejpam-4406	240	34	.	.	PUNCT
ejpam-4406	241	1	figure	figure	VERB
ejpam-4406	241	2	5	5	NUM
ejpam-4406	241	3	:	:	PUNCT
ejpam-4406	241	4	concentration	concentration	NOUN
ejpam-4406	241	5	results	result	NOUN
ejpam-4406	241	6	of	of	ADP
ejpam-4406	241	7	y2(t	y2(t	PROPN
ejpam-4406	241	8	)	)	PUNCT
ejpam-4406	241	9	with	with	ADP
ejpam-4406	241	10	abc	abc	PROPN
ejpam-4406	241	11	operator	operator	NOUN
ejpam-4406	241	12	at	at	ADP
ejpam-4406	241	13	different	different	ADJ
ejpam-4406	241	14	fractional	fractional	ADJ
ejpam-4406	241	15	order	order	NOUN
ejpam-4406	241	16	.	.	PUNCT
ejpam-4406	242	1	with	with	ADP
ejpam-4406	242	2	no	no	DET
ejpam-4406	242	3	singular	singular	ADJ
ejpam-4406	242	4	kernel	kernel	NOUN
ejpam-4406	242	5	and	and	CCONJ
ejpam-4406	242	6	atangana	atangana	PROPN
ejpam-4406	242	7	-	-	PUNCT
ejpam-4406	242	8	baleanu	baleanu	PROPN
ejpam-4406	242	9	in	in	ADP
ejpam-4406	242	10	caputo	caputo	PROPN
ejpam-4406	242	11	sense	sense	NOUN
ejpam-4406	242	12	with	with	ADP
ejpam-4406	242	13	mittag	mittag	ADJ
ejpam-4406	242	14	-	-	PUNCT
ejpam-4406	242	15	leffler	leffler	NOUN
ejpam-4406	242	16	kernel	kernel	NOUN
ejpam-4406	242	17	respectively	respectively	ADV
ejpam-4406	242	18	.	.	PUNCT
ejpam-4406	243	1	sumudu	sumudu	NOUN
ejpam-4406	243	2	transform	transform	NOUN
ejpam-4406	243	3	is	be	AUX
ejpam-4406	243	4	used	use	VERB
ejpam-4406	243	5	to	to	PART
ejpam-4406	243	6	obtain	obtain	VERB
ejpam-4406	243	7	the	the	DET
ejpam-4406	243	8	results	result	NOUN
ejpam-4406	243	9	for	for	ADP
ejpam-4406	243	10	proposed	propose	VERB
ejpam-4406	243	11	schemes	scheme	NOUN
ejpam-4406	243	12	.	.	PUNCT
ejpam-4406	244	1	these	these	DET
ejpam-4406	244	2	concepts	concept	NOUN
ejpam-4406	244	3	are	be	AUX
ejpam-4406	244	4	very	very	ADV
ejpam-4406	244	5	important	important	ADJ
ejpam-4406	244	6	to	to	PART
ejpam-4406	244	7	use	use	VERB
ejpam-4406	244	8	real	real	ADJ
ejpam-4406	244	9	life	life	NOUN
ejpam-4406	244	10	problems	problem	NOUN
ejpam-4406	244	11	like	like	ADP
ejpam-4406	244	12	brine	brine	NOUN
ejpam-4406	244	13	tank	tank	NOUN
ejpam-4406	244	14	cascade	cascade	NOUN
ejpam-4406	244	15	,	,	PUNCT
ejpam-4406	244	16	recycled	recycle	VERB
ejpam-4406	244	17	brine	brine	NOUN
ejpam-4406	244	18	tank	tank	NOUN
ejpam-4406	244	19	cascade	cascade	NOUN
ejpam-4406	244	20	,	,	PUNCT
ejpam-4406	244	21	pond	pond	NOUN
ejpam-4406	244	22	pollution	pollution	NOUN
ejpam-4406	244	23	,	,	PUNCT
ejpam-4406	244	24	home	home	NOUN
ejpam-4406	244	25	heating	heating	NOUN
ejpam-4406	244	26	and	and	CCONJ
ejpam-4406	244	27	biomass	biomass	NOUN
ejpam-4406	244	28	transfer	transfer	NOUN
ejpam-4406	244	29	problem	problem	NOUN
ejpam-4406	244	30	.	.	PUNCT
ejpam-4406	245	1	references	reference	NOUN
ejpam-4406	245	2	1156	1156	NUM
ejpam-4406	245	3	figure	figure	NOUN
ejpam-4406	245	4	6	6	NUM
ejpam-4406	245	5	:	:	PUNCT
ejpam-4406	245	6	concentration	concentration	NOUN
ejpam-4406	245	7	results	result	NOUN
ejpam-4406	245	8	of	of	ADP
ejpam-4406	245	9	y3(t	y3(t	PROPN
ejpam-4406	245	10	)	)	PUNCT
ejpam-4406	245	11	with	with	ADP
ejpam-4406	245	12	abc	abc	PROPN
ejpam-4406	245	13	operator	operator	NOUN
ejpam-4406	245	14	at	at	ADP
ejpam-4406	245	15	different	different	ADJ
ejpam-4406	245	16	fractional	fractional	ADJ
ejpam-4406	245	17	order	order	NOUN
ejpam-4406	245	18	.	.	PUNCT
ejpam-4406	246	1	acknowledgements	acknowledgement	NOUN
ejpam-4406	246	2	jihad	jihad	PROPN
ejpam-4406	246	3	asad	asad	PROPN
ejpam-4406	246	4	,	,	PUNCT
ejpam-4406	246	5	and	and	CCONJ
ejpam-4406	246	6	rania	rania	PROPN
ejpam-4406	246	7	wannan	wannan	PROPN
ejpam-4406	246	8	would	would	AUX
ejpam-4406	246	9	like	like	VERB
ejpam-4406	246	10	to	to	PART
ejpam-4406	246	11	thank	thank	VERB
ejpam-4406	246	12	palestine	palestine	PROPN
ejpam-4406	246	13	technical	technical	PROPN
ejpam-4406	246	14	university	university	PROPN
ejpam-4406	246	15	–	–	PUNCT
ejpam-4406	246	16	kadoorie	kadoorie	NOUN
ejpam-4406	246	17	for	for	ADP
ejpam-4406	246	18	supporting	support	VERB
ejpam-4406	246	19	this	this	DET
ejpam-4406	246	20	project	project	NOUN
ejpam-4406	246	21	financially	financially	ADV
ejpam-4406	246	22	.	.	PUNCT
ejpam-4406	247	1	references	reference	NOUN
ejpam-4406	247	2	[	[	X
ejpam-4406	247	3	1	1	NUM
ejpam-4406	247	4	]	]	X
ejpam-4406	247	5	sergio	sergio	PROPN
ejpam-4406	247	6	amat	amat	PROPN
ejpam-4406	247	7	,	,	PUNCT
ejpam-4406	247	8	maŕıa	maŕıa	ADP
ejpam-4406	247	9	josé	josé	ADJ
ejpam-4406	247	10	legaz	legaz	NOUN
ejpam-4406	247	11	,	,	PUNCT
ejpam-4406	247	12	and	and	CCONJ
ejpam-4406	247	13	juan	juan	PROPN
ejpam-4406	247	14	ruiz	ruiz	PROPN
ejpam-4406	247	15	-	-	PUNCT
ejpam-4406	247	16	álvarez	álvarez	PROPN
ejpam-4406	247	17	.	.	PUNCT
ejpam-4406	248	1	on	on	ADP
ejpam-4406	248	2	a	a	DET
ejpam-4406	248	3	variational	variational	ADJ
ejpam-4406	248	4	method	method	NOUN
ejpam-4406	248	5	for	for	ADP
ejpam-4406	248	6	stiff	stiff	ADJ
ejpam-4406	248	7	differential	differential	ADJ
ejpam-4406	248	8	equations	equation	NOUN
ejpam-4406	248	9	arising	arise	VERB
ejpam-4406	248	10	from	from	ADP
ejpam-4406	248	11	chemistry	chemistry	NOUN
ejpam-4406	248	12	kinetics	kinetic	NOUN
ejpam-4406	248	13	.	.	PUNCT
ejpam-4406	249	1	mathematics	mathematic	NOUN
ejpam-4406	249	2	,	,	PUNCT
ejpam-4406	249	3	7(5):459	7(5):459	NUM
ejpam-4406	249	4	,	,	PUNCT
ejpam-4406	249	5	2019	2019	NUM
ejpam-4406	249	6	.	.	PUNCT
ejpam-4406	250	1	[	[	X
ejpam-4406	250	2	2	2	X
ejpam-4406	250	3	]	]	PUNCT
ejpam-4406	250	4	a	a	DET
ejpam-4406	250	5	atangana	atangana	PROPN
ejpam-4406	250	6	,	,	PUNCT
ejpam-4406	250	7	e	e	PROPN
ejpam-4406	250	8	bonyah	bonyah	NOUN
ejpam-4406	250	9	,	,	PUNCT
ejpam-4406	250	10	and	and	CCONJ
ejpam-4406	250	11	aa	aa	PROPN
ejpam-4406	250	12	elsadany	elsadany	NOUN
ejpam-4406	250	13	.	.	PUNCT
ejpam-4406	251	1	a	a	DET
ejpam-4406	251	2	fractional	fractional	ADJ
ejpam-4406	251	3	order	order	NOUN
ejpam-4406	251	4	optimal	optimal	ADJ
ejpam-4406	251	5	4d	4d	NUM
ejpam-4406	251	6	chaotic	chaotic	ADJ
ejpam-4406	251	7	financial	financial	ADJ
ejpam-4406	251	8	model	model	NOUN
ejpam-4406	251	9	with	with	ADP
ejpam-4406	251	10	mittag	mittag	ADJ
ejpam-4406	251	11	-	-	PUNCT
ejpam-4406	251	12	leffler	leffler	NOUN
ejpam-4406	251	13	law	law	NOUN
ejpam-4406	251	14	.	.	PUNCT
ejpam-4406	252	1	chinese	chinese	ADJ
ejpam-4406	252	2	journal	journal	PROPN
ejpam-4406	252	3	of	of	ADP
ejpam-4406	252	4	physics	physics	PROPN
ejpam-4406	252	5	,	,	PUNCT
ejpam-4406	252	6	65:38–53	65:38–53	PROPN
ejpam-4406	252	7	,	,	PUNCT
ejpam-4406	252	8	2020	2020	NUM
ejpam-4406	252	9	.	.	PUNCT
ejpam-4406	253	1	[	[	X
ejpam-4406	253	2	3	3	NUM
ejpam-4406	253	3	]	]	X
ejpam-4406	253	4	abdon	abdon	NOUN
ejpam-4406	253	5	atangana	atangana	PROPN
ejpam-4406	253	6	and	and	CCONJ
ejpam-4406	253	7	badr	badr	PROPN
ejpam-4406	253	8	saad	saad	PROPN
ejpam-4406	253	9	t	t	PROPN
ejpam-4406	253	10	alkahtani	alkahtani	PROPN
ejpam-4406	253	11	.	.	PUNCT
ejpam-4406	254	1	analysis	analysis	NOUN
ejpam-4406	254	2	of	of	ADP
ejpam-4406	254	3	the	the	DET
ejpam-4406	254	4	keller	keller	PROPN
ejpam-4406	254	5	–	–	PUNCT
ejpam-4406	254	6	segel	segel	NOUN
ejpam-4406	254	7	model	model	NOUN
ejpam-4406	254	8	with	with	ADP
ejpam-4406	254	9	a	a	DET
ejpam-4406	254	10	fractional	fractional	ADJ
ejpam-4406	254	11	derivative	derivative	NOUN
ejpam-4406	254	12	without	without	ADP
ejpam-4406	254	13	singular	singular	ADJ
ejpam-4406	254	14	kernel	kernel	PROPN
ejpam-4406	254	15	.	.	PUNCT
ejpam-4406	255	1	entropy	entropy	PROPN
ejpam-4406	255	2	,	,	PUNCT
ejpam-4406	255	3	17(6):4439–4453	17(6):4439–4453	NUM
ejpam-4406	255	4	,	,	PUNCT
ejpam-4406	255	5	2015	2015	NUM
ejpam-4406	255	6	.	.	PUNCT
ejpam-4406	256	1	[	[	X
ejpam-4406	256	2	4	4	NUM
ejpam-4406	256	3	]	]	X
ejpam-4406	256	4	abdon	abdon	NOUN
ejpam-4406	256	5	atangana	atangana	PROPN
ejpam-4406	256	6	and	and	CCONJ
ejpam-4406	256	7	dumitru	dumitru	PROPN
ejpam-4406	256	8	baleanu	baleanu	NOUN
ejpam-4406	256	9	.	.	PUNCT
ejpam-4406	257	1	new	new	ADJ
ejpam-4406	257	2	fractional	fractional	ADJ
ejpam-4406	257	3	derivatives	derivative	NOUN
ejpam-4406	257	4	with	with	ADP
ejpam-4406	257	5	nonlocal	nonlocal	ADJ
ejpam-4406	257	6	and	and	CCONJ
ejpam-4406	257	7	non	non	ADJ
ejpam-4406	257	8	-	-	ADJ
ejpam-4406	257	9	singular	singular	ADJ
ejpam-4406	257	10	kernel	kernel	NOUN
ejpam-4406	257	11	:	:	PUNCT
ejpam-4406	257	12	theory	theory	NOUN
ejpam-4406	257	13	and	and	CCONJ
ejpam-4406	257	14	application	application	NOUN
ejpam-4406	257	15	to	to	PART
ejpam-4406	257	16	heat	heat	NOUN
ejpam-4406	257	17	transfer	transfer	NOUN
ejpam-4406	257	18	model	model	NOUN
ejpam-4406	257	19	.	.	PUNCT
ejpam-4406	258	1	arxiv	arxiv	PROPN
ejpam-4406	258	2	preprint	preprint	VERB
ejpam-4406	258	3	arxiv:1602.03408	arxiv:1602.03408	PROPN
ejpam-4406	258	4	,	,	PUNCT
ejpam-4406	258	5	2016	2016	NUM
ejpam-4406	258	6	.	.	PUNCT
ejpam-4406	259	1	[	[	X
ejpam-4406	259	2	5	5	X
ejpam-4406	259	3	]	]	PUNCT
ejpam-4406	259	4	michele	michele	PROPN
ejpam-4406	259	5	caputo	caputo	PROPN
ejpam-4406	259	6	and	and	CCONJ
ejpam-4406	259	7	mauro	mauro	PROPN
ejpam-4406	259	8	fabrizio	fabrizio	PROPN
ejpam-4406	259	9	.	.	PUNCT
ejpam-4406	260	1	a	a	DET
ejpam-4406	260	2	new	new	ADJ
ejpam-4406	260	3	definition	definition	NOUN
ejpam-4406	260	4	of	of	ADP
ejpam-4406	260	5	fractional	fractional	ADJ
ejpam-4406	260	6	derivative	derivative	NOUN
ejpam-4406	260	7	without	without	ADP
ejpam-4406	260	8	singular	singular	ADJ
ejpam-4406	260	9	kernel	kernel	PROPN
ejpam-4406	260	10	.	.	PUNCT
ejpam-4406	261	1	progress	progress	NOUN
ejpam-4406	261	2	in	in	ADP
ejpam-4406	261	3	fractional	fractional	ADJ
ejpam-4406	261	4	differentiation	differentiation	NOUN
ejpam-4406	261	5	&	&	CCONJ
ejpam-4406	261	6	applications	application	NOUN
ejpam-4406	261	7	,	,	PUNCT
ejpam-4406	261	8	1(2):73–85	1(2):73–85	NUM
ejpam-4406	261	9	,	,	PUNCT
ejpam-4406	261	10	2015	2015	NUM
ejpam-4406	261	11	.	.	PUNCT
ejpam-4406	262	1	[	[	X
ejpam-4406	262	2	6	6	X
ejpam-4406	262	3	]	]	PUNCT
ejpam-4406	262	4	muhammad	muhammad	PROPN
ejpam-4406	262	5	farman	farman	PROPN
ejpam-4406	262	6	,	,	PUNCT
ejpam-4406	262	7	ali	ali	PROPN
ejpam-4406	262	8	akgül	akgül	PROPN
ejpam-4406	262	9	,	,	PUNCT
ejpam-4406	262	10	dumitru	dumitru	PROPN
ejpam-4406	262	11	baleanu	baleanu	PROPN
ejpam-4406	262	12	,	,	PUNCT
ejpam-4406	262	13	sumaiyah	sumaiyah	PROPN
ejpam-4406	262	14	imtiaz	imtiaz	PROPN
ejpam-4406	262	15	,	,	PUNCT
ejpam-4406	262	16	and	and	CCONJ
ejpam-4406	262	17	aqeel	aqeel	PROPN
ejpam-4406	262	18	ahmad	ahmad	PROPN
ejpam-4406	262	19	.	.	PUNCT
ejpam-4406	263	1	analysis	analysis	NOUN
ejpam-4406	263	2	of	of	ADP
ejpam-4406	263	3	fractional	fractional	ADJ
ejpam-4406	263	4	order	order	NOUN
ejpam-4406	263	5	chaotic	chaotic	ADJ
ejpam-4406	263	6	financial	financial	ADJ
ejpam-4406	263	7	model	model	NOUN
ejpam-4406	263	8	with	with	ADP
ejpam-4406	263	9	minimum	minimum	ADJ
ejpam-4406	263	10	interest	interest	NOUN
ejpam-4406	263	11	rate	rate	NOUN
ejpam-4406	263	12	impact	impact	NOUN
ejpam-4406	263	13	.	.	PUNCT
ejpam-4406	264	1	fractal	fractal	ADJ
ejpam-4406	264	2	and	and	CCONJ
ejpam-4406	264	3	fractional	fractional	ADJ
ejpam-4406	264	4	,	,	PUNCT
ejpam-4406	264	5	4(3):43	4(3):43	NUM
ejpam-4406	264	6	,	,	PUNCT
ejpam-4406	264	7	2020	2020	NUM
ejpam-4406	264	8	.	.	PUNCT
ejpam-4406	265	1	references	reference	NOUN
ejpam-4406	265	2	1157	1157	NUM
ejpam-4406	265	3	[	[	X
ejpam-4406	265	4	7	7	X
ejpam-4406	265	5	]	]	X
ejpam-4406	265	6	muhammad	muhammad	PROPN
ejpam-4406	265	7	farman	farman	PROPN
ejpam-4406	265	8	,	,	PUNCT
ejpam-4406	265	9	muhammad	muhammad	PROPN
ejpam-4406	265	10	umer	umer	PROPN
ejpam-4406	265	11	saleem	saleem	PROPN
ejpam-4406	265	12	,	,	PUNCT
ejpam-4406	265	13	aqeel	aqeel	PROPN
ejpam-4406	265	14	ahmad	ahmad	PROPN
ejpam-4406	265	15	,	,	PUNCT
ejpam-4406	265	16	sumaiyah	sumaiyah	PROPN
ejpam-4406	265	17	imtiaz	imtiaz	PROPN
ejpam-4406	265	18	,	,	PUNCT
ejpam-4406	265	19	muhammad	muhammad	PROPN
ejpam-4406	265	20	farhan	farhan	PROPN
ejpam-4406	265	21	tabassum	tabassum	PROPN
ejpam-4406	265	22	,	,	PUNCT
ejpam-4406	265	23	sana	sana	PROPN
ejpam-4406	265	24	akram	akram	PROPN
ejpam-4406	265	25	,	,	PUNCT
ejpam-4406	265	26	and	and	CCONJ
ejpam-4406	265	27	mo	mo	PROPN
ejpam-4406	265	28	ahmad	ahmad	PROPN
ejpam-4406	265	29	.	.	PUNCT
ejpam-4406	266	1	a	a	DET
ejpam-4406	266	2	control	control	NOUN
ejpam-4406	266	3	of	of	ADP
ejpam-4406	266	4	glucose	glucose	NOUN
ejpam-4406	266	5	level	level	NOUN
ejpam-4406	266	6	in	in	ADP
ejpam-4406	266	7	insulin	insulin	NOUN
ejpam-4406	266	8	therapies	therapy	NOUN
ejpam-4406	266	9	for	for	ADP
ejpam-4406	266	10	the	the	DET
ejpam-4406	266	11	development	development	NOUN
ejpam-4406	266	12	of	of	ADP
ejpam-4406	266	13	artificial	artificial	ADJ
ejpam-4406	266	14	pancreas	pancrea	NOUN
ejpam-4406	266	15	by	by	ADP
ejpam-4406	266	16	atangana	atangana	PROPN
ejpam-4406	266	17	baleanu	baleanu	PROPN
ejpam-4406	266	18	derivative	derivative	PROPN
ejpam-4406	266	19	.	.	PUNCT
ejpam-4406	267	1	alexandria	alexandria	PROPN
ejpam-4406	267	2	engineering	engineering	PROPN
ejpam-4406	267	3	journal	journal	PROPN
ejpam-4406	267	4	,	,	PUNCT
ejpam-4406	267	5	59(4):2639–2648	59(4):2639–2648	NUM
ejpam-4406	267	6	,	,	PUNCT
ejpam-4406	267	7	2020	2020	NUM
ejpam-4406	267	8	.	.	PUNCT
ejpam-4406	268	1	[	[	X
ejpam-4406	268	2	8	8	X
ejpam-4406	268	3	]	]	X
ejpam-4406	268	4	muhammad	muhammad	PROPN
ejpam-4406	268	5	farman	farman	PROPN
ejpam-4406	268	6	,	,	PUNCT
ejpam-4406	268	7	muhammad	muhammad	PROPN
ejpam-4406	268	8	umer	umer	PROPN
ejpam-4406	268	9	saleem	saleem	PROPN
ejpam-4406	268	10	,	,	PUNCT
ejpam-4406	268	11	mf	mf	NOUN
ejpam-4406	268	12	tabassum	tabassum	NOUN
ejpam-4406	268	13	,	,	PUNCT
ejpam-4406	268	14	aqeel	aqeel	PROPN
ejpam-4406	268	15	ahmad	ahmad	PROPN
ejpam-4406	268	16	,	,	PUNCT
ejpam-4406	268	17	and	and	CCONJ
ejpam-4406	268	18	mo	mo	PROPN
ejpam-4406	268	19	ahmad	ahmad	PROPN
ejpam-4406	268	20	.	.	PUNCT
ejpam-4406	269	1	a	a	DET
ejpam-4406	269	2	linear	linear	ADJ
ejpam-4406	269	3	control	control	NOUN
ejpam-4406	269	4	of	of	ADP
ejpam-4406	269	5	composite	composite	ADJ
ejpam-4406	269	6	model	model	NOUN
ejpam-4406	269	7	for	for	ADP
ejpam-4406	269	8	glucose	glucose	NOUN
ejpam-4406	269	9	insulin	insulin	NOUN
ejpam-4406	269	10	glucagon	glucagon	NOUN
ejpam-4406	269	11	pump	pump	NOUN
ejpam-4406	269	12	.	.	PUNCT
ejpam-4406	270	1	ain	ain	PROPN
ejpam-4406	270	2	shams	sham	VERB
ejpam-4406	270	3	engineering	engineering	NOUN
ejpam-4406	270	4	journal	journal	NOUN
ejpam-4406	270	5	,	,	PUNCT
ejpam-4406	270	6	10(4):867–872	10(4):867–872	PROPN
ejpam-4406	270	7	,	,	PUNCT
ejpam-4406	270	8	2019	2019	NUM
ejpam-4406	270	9	.	.	PUNCT
ejpam-4406	271	1	[	[	X
ejpam-4406	271	2	9	9	NUM
ejpam-4406	271	3	]	]	X
ejpam-4406	271	4	hai	hai	PROPN
ejpam-4406	271	5	-	-	PUNCT
ejpam-4406	271	6	feng	feng	PROPN
ejpam-4406	271	7	huo	huo	PROPN
ejpam-4406	271	8	,	,	PUNCT
ejpam-4406	271	9	rui	rui	PROPN
ejpam-4406	271	10	chen	chen	PROPN
ejpam-4406	271	11	,	,	PUNCT
ejpam-4406	271	12	and	and	CCONJ
ejpam-4406	271	13	xun	xun	PROPN
ejpam-4406	271	14	-	-	PUNCT
ejpam-4406	271	15	yang	yang	PROPN
ejpam-4406	271	16	wang	wang	PROPN
ejpam-4406	271	17	.	.	PUNCT
ejpam-4406	272	1	modelling	modelling	NOUN
ejpam-4406	272	2	and	and	CCONJ
ejpam-4406	272	3	stability	stability	NOUN
ejpam-4406	272	4	of	of	ADP
ejpam-4406	272	5	hiv	hiv	PROPN
ejpam-4406	272	6	/	/	SYM
ejpam-4406	272	7	aids	aids	PROPN
ejpam-4406	272	8	epidemic	epidemic	NOUN
ejpam-4406	272	9	model	model	NOUN
ejpam-4406	272	10	with	with	ADP
ejpam-4406	272	11	treatment	treatment	NOUN
ejpam-4406	272	12	.	.	PUNCT
ejpam-4406	273	1	applied	apply	VERB
ejpam-4406	273	2	mathematical	mathematical	ADJ
ejpam-4406	273	3	modelling	modelling	NOUN
ejpam-4406	273	4	,	,	PUNCT
ejpam-4406	273	5	40(13	40(13	NOUN
ejpam-4406	273	6	-	-	SYM
ejpam-4406	273	7	14):6550	14):6550	NUM
ejpam-4406	273	8	–	–	PUNCT
ejpam-4406	273	9	6559	6559	NUM
ejpam-4406	273	10	,	,	PUNCT
ejpam-4406	273	11	2016	2016	NUM
ejpam-4406	273	12	.	.	PUNCT
ejpam-4406	274	1	[	[	X
ejpam-4406	274	2	10	10	NUM
ejpam-4406	274	3	]	]	X
ejpam-4406	274	4	muhammad	muhammad	PROPN
ejpam-4406	274	5	altaf	altaf	PROPN
ejpam-4406	274	6	khan	khan	PROPN
ejpam-4406	274	7	and	and	CCONJ
ejpam-4406	274	8	abdon	abdon	PROPN
ejpam-4406	274	9	atangana	atangana	PROPN
ejpam-4406	274	10	.	.	PUNCT
ejpam-4406	275	1	modeling	model	VERB
ejpam-4406	275	2	the	the	DET
ejpam-4406	275	3	dynamics	dynamic	NOUN
ejpam-4406	275	4	of	of	ADP
ejpam-4406	275	5	novel	novel	ADJ
ejpam-4406	275	6	coronavirus	coronavirus	NOUN
ejpam-4406	275	7	(	(	PUNCT
ejpam-4406	275	8	2019	2019	NUM
ejpam-4406	275	9	-	-	PUNCT
ejpam-4406	275	10	ncov	ncov	NOUN
ejpam-4406	275	11	)	)	PUNCT
ejpam-4406	275	12	with	with	ADP
ejpam-4406	275	13	fractional	fractional	ADJ
ejpam-4406	275	14	derivative	derivative	NOUN
ejpam-4406	275	15	.	.	PUNCT
ejpam-4406	276	1	alexandria	alexandria	PROPN
ejpam-4406	276	2	engineering	engineering	PROPN
ejpam-4406	276	3	journal	journal	PROPN
ejpam-4406	276	4	,	,	PUNCT
ejpam-4406	276	5	59(4):2379–2389	59(4):2379–2389	NUM
ejpam-4406	276	6	,	,	PUNCT
ejpam-4406	276	7	2020	2020	NUM
ejpam-4406	276	8	.	.	PUNCT
ejpam-4406	277	1	[	[	X
ejpam-4406	277	2	11	11	NUM
ejpam-4406	277	3	]	]	X
ejpam-4406	277	4	mj	mj	PROPN
ejpam-4406	277	5	legaz	legaz	PROPN
ejpam-4406	277	6	.	.	PUNCT
ejpam-4406	278	1	approximation	approximation	NOUN
ejpam-4406	278	2	of	of	ADP
ejpam-4406	278	3	differential	differential	ADJ
ejpam-4406	278	4	equations	equation	NOUN
ejpam-4406	278	5	through	through	ADP
ejpam-4406	278	6	a	a	DET
ejpam-4406	278	7	new	new	ADJ
ejpam-4406	278	8	variational	variational	ADJ
ejpam-4406	278	9	technique	technique	NOUN
ejpam-4406	278	10	and	and	CCONJ
ejpam-4406	278	11	applications	application	NOUN
ejpam-4406	278	12	.	.	PUNCT
ejpam-4406	279	1	2012	2012	NUM
ejpam-4406	279	2	.	.	PUNCT
ejpam-4406	280	1	[	[	X
ejpam-4406	280	2	12	12	NUM
ejpam-4406	280	3	]	]	PUNCT
ejpam-4406	280	4	jorge	jorge	PROPN
ejpam-4406	280	5	losada	losada	PROPN
ejpam-4406	280	6	and	and	CCONJ
ejpam-4406	280	7	juan	juan	PROPN
ejpam-4406	280	8	j	j	PROPN
ejpam-4406	280	9	nieto	nieto	PROPN
ejpam-4406	280	10	.	.	PUNCT
ejpam-4406	281	1	properties	property	NOUN
ejpam-4406	281	2	of	of	ADP
ejpam-4406	281	3	a	a	DET
ejpam-4406	281	4	new	new	ADJ
ejpam-4406	281	5	fractional	fractional	ADJ
ejpam-4406	281	6	derivative	derivative	NOUN
ejpam-4406	281	7	without	without	ADP
ejpam-4406	281	8	singular	singular	ADJ
ejpam-4406	281	9	kernel	kernel	PROPN
ejpam-4406	281	10	.	.	PUNCT
ejpam-4406	282	1	progr	progr	NOUN
ejpam-4406	282	2	.	.	PUNCT
ejpam-4406	283	1	fract	fract	PROPN
ejpam-4406	283	2	.	.	PUNCT
ejpam-4406	284	1	differ	differ	VERB
ejpam-4406	284	2	.	.	PUNCT
ejpam-4406	285	1	appl	appl	PROPN
ejpam-4406	285	2	,	,	PUNCT
ejpam-4406	285	3	1(2):87–92	1(2):87–92	NUM
ejpam-4406	285	4	,	,	PUNCT
ejpam-4406	285	5	2015	2015	NUM
ejpam-4406	285	6	.	.	PUNCT
ejpam-4406	286	1	[	[	X
ejpam-4406	286	2	13	13	NUM
ejpam-4406	286	3	]	]	X
ejpam-4406	286	4	sirisubtawee	sirisubtawee	PROPN
ejpam-4406	286	5	moore	moore	PROPN
ejpam-4406	286	6	and	and	CCONJ
ejpam-4406	286	7	koonprasert	koonprasert	PROPN
ejpam-4406	286	8	.	.	PUNCT
ejpam-4406	287	1	a	a	DET
ejpam-4406	287	2	caputo	caputo	PROPN
ejpam-4406	287	3	–	–	PUNCT
ejpam-4406	287	4	fabrizio	fabrizio	PROPN
ejpam-4406	287	5	fractional	fractional	ADJ
ejpam-4406	287	6	differential	differential	NOUN
ejpam-4406	287	7	equation	equation	NOUN
ejpam-4406	287	8	model	model	NOUN
ejpam-4406	287	9	for	for	ADP
ejpam-4406	287	10	hiv	hiv	PROPN
ejpam-4406	287	11	/	/	SYM
ejpam-4406	287	12	aids	aids	PROPN
ejpam-4406	287	13	with	with	ADP
ejpam-4406	287	14	treatment	treatment	NOUN
ejpam-4406	287	15	compartment	compartment	NOUN
ejpam-4406	287	16	.	.	PUNCT
ejpam-4406	288	1	advances	advance	NOUN
ejpam-4406	288	2	in	in	ADP
ejpam-4406	288	3	difference	difference	NOUN
ejpam-4406	288	4	equations	equation	NOUN
ejpam-4406	288	5	,	,	PUNCT
ejpam-4406	288	6	2019(200):1–20	2019(200):1–20	NUM
ejpam-4406	288	7	,	,	PUNCT
ejpam-4406	288	8	2019	2019	NUM
ejpam-4406	288	9	.	.	PUNCT
ejpam-4406	289	1	[	[	X
ejpam-4406	289	2	14	14	NUM
ejpam-4406	289	3	]	]	X
ejpam-4406	289	4	muhammad	muhammad	PROPN
ejpam-4406	289	5	umer	umer	PROPN
ejpam-4406	289	6	saleem	saleem	PROPN
ejpam-4406	289	7	,	,	PUNCT
ejpam-4406	289	8	muhammad	muhammad	PROPN
ejpam-4406	289	9	farman	farman	PROPN
ejpam-4406	289	10	,	,	PUNCT
ejpam-4406	289	11	aqeel	aqeel	PROPN
ejpam-4406	289	12	ahmad	ahmad	PROPN
ejpam-4406	289	13	,	,	PUNCT
ejpam-4406	289	14	ehsan	ehsan	PROPN
ejpam-4406	289	15	ul	ul	PROPN
ejpam-4406	289	16	haque	haque	PROPN
ejpam-4406	289	17	,	,	PUNCT
ejpam-4406	289	18	and	and	CCONJ
ejpam-4406	289	19	mo	mo	PROPN
ejpam-4406	289	20	ahmad	ahmad	PROPN
ejpam-4406	289	21	.	.	PUNCT
ejpam-4406	290	1	a	a	DET
ejpam-4406	290	2	caputo	caputo	PROPN
ejpam-4406	290	3	fabrizio	fabrizio	PROPN
ejpam-4406	290	4	fractional	fractional	PROPN
ejpam-4406	290	5	order	order	NOUN
ejpam-4406	290	6	model	model	NOUN
ejpam-4406	290	7	for	for	ADP
ejpam-4406	290	8	control	control	NOUN
ejpam-4406	290	9	of	of	ADP
ejpam-4406	290	10	glucose	glucose	NOUN
ejpam-4406	290	11	in	in	ADP
ejpam-4406	290	12	insulin	insulin	NOUN
ejpam-4406	290	13	therapies	therapy	NOUN
ejpam-4406	290	14	for	for	ADP
ejpam-4406	290	15	diabetes	diabetes	NOUN
ejpam-4406	290	16	.	.	PUNCT
ejpam-4406	291	1	ain	ain	PROPN
ejpam-4406	291	2	shams	sham	VERB
ejpam-4406	291	3	engineering	engineering	NOUN
ejpam-4406	291	4	journal	journal	NOUN
ejpam-4406	291	5	,	,	PUNCT
ejpam-4406	291	6	11(4):1309–1316	11(4):1309–1316	NUM
ejpam-4406	291	7	,	,	PUNCT
ejpam-4406	291	8	2020	2020	NUM
ejpam-4406	291	9	.	.	PUNCT
ejpam-4406	292	1	[	[	X
ejpam-4406	292	2	15	15	NUM
ejpam-4406	292	3	]	]	PUNCT
ejpam-4406	292	4	mekkaoui	mekkaoui	ADJ
ejpam-4406	292	5	toufik	toufik	NOUN
ejpam-4406	292	6	and	and	CCONJ
ejpam-4406	292	7	abdon	abdon	PROPN
ejpam-4406	292	8	atangana	atangana	PROPN
ejpam-4406	292	9	.	.	PUNCT
ejpam-4406	293	1	new	new	ADJ
ejpam-4406	293	2	numerical	numerical	ADJ
ejpam-4406	293	3	approximation	approximation	NOUN
ejpam-4406	293	4	of	of	ADP
ejpam-4406	293	5	fractional	fractional	ADJ
ejpam-4406	293	6	derivative	derivative	NOUN
ejpam-4406	293	7	with	with	ADP
ejpam-4406	293	8	non	non	ADJ
ejpam-4406	293	9	-	-	ADJ
ejpam-4406	293	10	local	local	ADJ
ejpam-4406	293	11	and	and	CCONJ
ejpam-4406	293	12	non	non	ADJ
ejpam-4406	293	13	-	-	ADJ
ejpam-4406	293	14	singular	singular	ADJ
ejpam-4406	293	15	kernel	kernel	NOUN
ejpam-4406	293	16	:	:	PUNCT
ejpam-4406	293	17	application	application	NOUN
ejpam-4406	293	18	to	to	ADP
ejpam-4406	293	19	chaotic	chaotic	ADJ
ejpam-4406	293	20	models	model	NOUN
ejpam-4406	293	21	.	.	PUNCT
ejpam-4406	294	1	the	the	DET
ejpam-4406	294	2	european	european	PROPN
ejpam-4406	294	3	physical	physical	PROPN
ejpam-4406	294	4	journal	journal	PROPN
ejpam-4406	294	5	plus	plus	CCONJ
ejpam-4406	294	6	,	,	PUNCT
ejpam-4406	294	7	132(10):1–16	132(10):1–16	NOUN
ejpam-4406	294	8	,	,	PUNCT
ejpam-4406	294	9	2017	2017	NUM
ejpam-4406	294	10	.	.	PUNCT