id	sid	tid	token	lemma	pos
ejpam-5396	1	1	european	european	PROPN
ejpam-5396	1	2	journal	journal	PROPN
ejpam-5396	1	3	of	of	ADP
ejpam-5396	1	4	pure	pure	ADJ
ejpam-5396	1	5	and	and	CCONJ
ejpam-5396	1	6	applied	apply	VERB
ejpam-5396	1	7	mathematics	mathematic	NOUN
ejpam-5396	1	8	vol	vol	NOUN
ejpam-5396	1	9	.	.	PROPN
ejpam-5396	2	1	17	17	NUM
ejpam-5396	2	2	,	,	PUNCT
ejpam-5396	2	3	no	no	INTJ
ejpam-5396	2	4	.	.	NOUN
ejpam-5396	2	5	4	4	NUM
ejpam-5396	2	6	,	,	PUNCT
ejpam-5396	2	7	2024	2024	NUM
ejpam-5396	2	8	,	,	PUNCT
ejpam-5396	2	9	2763	2763	NUM
ejpam-5396	2	10	-	-	SYM
ejpam-5396	2	11	2799	2799	NUM
ejpam-5396	2	12	issn	issn	PROPN
ejpam-5396	2	13	1307	1307	NUM
ejpam-5396	2	14	-	-	SYM
ejpam-5396	2	15	5543	5543	NUM
ejpam-5396	2	16	–	–	PUNCT
ejpam-5396	2	17	ejpam.com	ejpam.com	X
ejpam-5396	2	18	published	publish	VERB
ejpam-5396	2	19	by	by	ADP
ejpam-5396	2	20	new	new	PROPN
ejpam-5396	2	21	york	york	PROPN
ejpam-5396	2	22	business	business	PROPN
ejpam-5396	2	23	global	global	PROPN
ejpam-5396	2	24	on	on	ADP
ejpam-5396	2	25	the	the	DET
ejpam-5396	2	26	solution	solution	NOUN
ejpam-5396	2	27	of	of	ADP
ejpam-5396	2	28	the	the	DET
ejpam-5396	2	29	fractional	fractional	ADJ
ejpam-5396	2	30	-	-	PUNCT
ejpam-5396	2	31	order	order	NOUN
ejpam-5396	2	32	pneumonia	pneumonia	NOUN
ejpam-5396	2	33	model	model	NOUN
ejpam-5396	2	34	using	use	VERB
ejpam-5396	2	35	numerical	numerical	ADJ
ejpam-5396	2	36	computational	computational	ADJ
ejpam-5396	2	37	methods	method	NOUN
ejpam-5396	2	38	ahmad	ahmad	PROPN
ejpam-5396	2	39	alalyani	alalyani	PROPN
ejpam-5396	2	40	department	department	PROPN
ejpam-5396	2	41	of	of	ADP
ejpam-5396	2	42	mathematics	mathematic	NOUN
ejpam-5396	2	43	,	,	PUNCT
ejpam-5396	2	44	faculty	faculty	NOUN
ejpam-5396	2	45	of	of	ADP
ejpam-5396	2	46	science	science	NOUN
ejpam-5396	2	47	,	,	PUNCT
ejpam-5396	2	48	al	al	PROPN
ejpam-5396	2	49	-	-	PUNCT
ejpam-5396	2	50	baha	baha	PROPN
ejpam-5396	2	51	university	university	PROPN
ejpam-5396	2	52	,	,	PUNCT
ejpam-5396	2	53	al	al	PROPN
ejpam-5396	2	54	-	-	PUNCT
ejpam-5396	2	55	baha	baha	PROPN
ejpam-5396	2	56	,	,	PUNCT
ejpam-5396	3	1	saudi	saudi	PROPN
ejpam-5396	3	2	arabia	arabia	PROPN
ejpam-5396	3	3	abstract	abstract	NOUN
ejpam-5396	3	4	.	.	PUNCT
ejpam-5396	4	1	this	this	DET
ejpam-5396	4	2	paper	paper	NOUN
ejpam-5396	4	3	deals	deal	NOUN
ejpam-5396	4	4	with	with	ADP
ejpam-5396	4	5	the	the	DET
ejpam-5396	4	6	solution	solution	NOUN
ejpam-5396	4	7	and	and	CCONJ
ejpam-5396	4	8	the	the	DET
ejpam-5396	4	9	dynamics	dynamic	NOUN
ejpam-5396	4	10	of	of	ADP
ejpam-5396	4	11	the	the	DET
ejpam-5396	4	12	pneumonia	pneumonia	NOUN
ejpam-5396	4	13	fractional	fractional	ADJ
ejpam-5396	4	14	-	-	PUNCT
ejpam-5396	4	15	order	order	NOUN
ejpam-5396	4	16	mathematical	mathematical	ADJ
ejpam-5396	4	17	model	model	NOUN
ejpam-5396	4	18	using	use	VERB
ejpam-5396	4	19	numerical	numerical	ADJ
ejpam-5396	4	20	computational	computational	ADJ
ejpam-5396	4	21	methods	method	NOUN
ejpam-5396	4	22	.	.	PUNCT
ejpam-5396	5	1	we	we	PRON
ejpam-5396	5	2	study	study	VERB
ejpam-5396	5	3	positivity	positivity	NOUN
ejpam-5396	5	4	,	,	PUNCT
ejpam-5396	5	5	boundedness	boundedness	NOUN
ejpam-5396	5	6	,	,	PUNCT
ejpam-5396	5	7	equilibria	equilibrium	NOUN
ejpam-5396	5	8	,	,	PUNCT
ejpam-5396	5	9	local	local	ADJ
ejpam-5396	5	10	and	and	CCONJ
ejpam-5396	5	11	global	global	ADJ
ejpam-5396	5	12	stability	stability	NOUN
ejpam-5396	5	13	,	,	PUNCT
ejpam-5396	5	14	and	and	CCONJ
ejpam-5396	5	15	the	the	DET
ejpam-5396	5	16	basic	basic	ADJ
ejpam-5396	5	17	reproductive	reproductive	ADJ
ejpam-5396	5	18	number	number	NOUN
ejpam-5396	5	19	r0	r0	NOUN
ejpam-5396	5	20	of	of	ADP
ejpam-5396	5	21	the	the	DET
ejpam-5396	5	22	proposed	propose	VERB
ejpam-5396	5	23	model	model	NOUN
ejpam-5396	5	24	,	,	PUNCT
ejpam-5396	5	25	which	which	PRON
ejpam-5396	5	26	is	be	AUX
ejpam-5396	5	27	the	the	DET
ejpam-5396	5	28	one	one	NUM
ejpam-5396	5	29	most	most	ADV
ejpam-5396	5	30	significant	significant	ADJ
ejpam-5396	5	31	parameter	parameter	NOUN
ejpam-5396	5	32	in	in	ADP
ejpam-5396	5	33	epidemiological	epidemiological	ADJ
ejpam-5396	5	34	modeling	modeling	NOUN
ejpam-5396	5	35	.	.	PUNCT
ejpam-5396	6	1	it	it	PRON
ejpam-5396	6	2	estimates	estimate	VERB
ejpam-5396	6	3	the	the	DET
ejpam-5396	6	4	average	average	ADJ
ejpam-5396	6	5	number	number	NOUN
ejpam-5396	6	6	of	of	ADP
ejpam-5396	6	7	additional	additional	ADJ
ejpam-5396	6	8	infections	infection	NOUN
ejpam-5396	6	9	induced	induce	VERB
ejpam-5396	6	10	by	by	ADP
ejpam-5396	6	11	a	a	DET
ejpam-5396	6	12	sole	sole	ADJ
ejpam-5396	6	13	infectious	infectious	ADJ
ejpam-5396	6	14	individual	individual	NOUN
ejpam-5396	6	15	within	within	ADP
ejpam-5396	6	16	a	a	DET
ejpam-5396	6	17	fully	fully	ADV
ejpam-5396	6	18	susceptible	susceptible	ADJ
ejpam-5396	6	19	group	group	NOUN
ejpam-5396	6	20	during	during	ADP
ejpam-5396	6	21	the	the	DET
ejpam-5396	6	22	mean	mean	ADJ
ejpam-5396	6	23	period	period	NOUN
ejpam-5396	6	24	of	of	ADP
ejpam-5396	6	25	infection	infection	NOUN
ejpam-5396	6	26	.	.	PUNCT
ejpam-5396	7	1	to	to	PART
ejpam-5396	7	2	verify	verify	VERB
ejpam-5396	7	3	the	the	DET
ejpam-5396	7	4	theoretical	theoretical	ADJ
ejpam-5396	7	5	analysis	analysis	NOUN
ejpam-5396	7	6	of	of	ADP
ejpam-5396	7	7	the	the	DET
ejpam-5396	7	8	proposed	propose	VERB
ejpam-5396	7	9	model	model	NOUN
ejpam-5396	7	10	,	,	PUNCT
ejpam-5396	7	11	we	we	PRON
ejpam-5396	7	12	use	use	VERB
ejpam-5396	7	13	numerical	numerical	ADJ
ejpam-5396	7	14	techniques	technique	NOUN
ejpam-5396	7	15	including	include	VERB
ejpam-5396	7	16	the	the	DET
ejpam-5396	7	17	adams	adams	PROPN
ejpam-5396	7	18	-	-	PUNCT
ejpam-5396	7	19	bashforth	bashforth	PROPN
ejpam-5396	7	20	-	-	PUNCT
ejpam-5396	7	21	moulton	moulton	PROPN
ejpam-5396	7	22	method	method	NOUN
ejpam-5396	7	23	,	,	PUNCT
ejpam-5396	7	24	the	the	DET
ejpam-5396	7	25	generalized	generalize	VERB
ejpam-5396	7	26	euler	euler	NOUN
ejpam-5396	7	27	method	method	NOUN
ejpam-5396	7	28	,	,	PUNCT
ejpam-5396	7	29	the	the	DET
ejpam-5396	7	30	generalized	generalize	VERB
ejpam-5396	7	31	runge	runge	NOUN
ejpam-5396	7	32	-	-	PUNCT
ejpam-5396	7	33	kutta	kutta	NOUN
ejpam-5396	7	34	method	method	NOUN
ejpam-5396	7	35	,	,	PUNCT
ejpam-5396	7	36	and	and	CCONJ
ejpam-5396	7	37	the	the	DET
ejpam-5396	7	38	multistep	multistep	ADJ
ejpam-5396	7	39	generalized	generalize	VERB
ejpam-5396	7	40	differential	differential	NOUN
ejpam-5396	7	41	transform	transform	NOUN
ejpam-5396	7	42	method	method	NOUN
ejpam-5396	7	43	.	.	PUNCT
ejpam-5396	8	1	the	the	DET
ejpam-5396	8	2	numerical	numerical	ADJ
ejpam-5396	8	3	results	result	NOUN
ejpam-5396	8	4	and	and	CCONJ
ejpam-5396	8	5	simulations	simulation	NOUN
ejpam-5396	8	6	confirm	confirm	VERB
ejpam-5396	8	7	the	the	DET
ejpam-5396	8	8	convergence	convergence	NOUN
ejpam-5396	8	9	between	between	ADP
ejpam-5396	8	10	the	the	DET
ejpam-5396	8	11	presented	present	VERB
ejpam-5396	8	12	fractional	fractional	ADJ
ejpam-5396	8	13	-	-	PUNCT
ejpam-5396	8	14	order	order	NOUN
ejpam-5396	8	15	model	model	NOUN
ejpam-5396	8	16	and	and	CCONJ
ejpam-5396	8	17	its	its	PRON
ejpam-5396	8	18	integer	integer	NOUN
ejpam-5396	8	19	-	-	PUNCT
ejpam-5396	8	20	order	order	NOUN
ejpam-5396	8	21	form	form	NOUN
ejpam-5396	8	22	.	.	PUNCT
ejpam-5396	9	1	the	the	DET
ejpam-5396	9	2	proposed	propose	VERB
ejpam-5396	9	3	model	model	NOUN
ejpam-5396	9	4	proves	prove	VERB
ejpam-5396	9	5	to	to	PART
ejpam-5396	9	6	be	be	AUX
ejpam-5396	9	7	a	a	DET
ejpam-5396	9	8	valuable	valuable	ADJ
ejpam-5396	9	9	tool	tool	NOUN
ejpam-5396	9	10	for	for	ADP
ejpam-5396	9	11	investigating	investigate	VERB
ejpam-5396	9	12	dynamical	dynamical	ADJ
ejpam-5396	9	13	and	and	CCONJ
ejpam-5396	9	14	numerical	numerical	ADJ
ejpam-5396	9	15	analysis	analysis	NOUN
ejpam-5396	9	16	for	for	ADP
ejpam-5396	9	17	a	a	DET
ejpam-5396	9	18	variety	variety	NOUN
ejpam-5396	9	19	of	of	ADP
ejpam-5396	9	20	disease	disease	NOUN
ejpam-5396	9	21	models	model	NOUN
ejpam-5396	9	22	in	in	ADP
ejpam-5396	9	23	epidemiology	epidemiology	NOUN
ejpam-5396	9	24	.	.	PUNCT
ejpam-5396	10	1	2020	2020	NUM
ejpam-5396	10	2	mathematics	mathematic	NOUN
ejpam-5396	10	3	subject	subject	NOUN
ejpam-5396	10	4	classifications	classification	NOUN
ejpam-5396	10	5	:	:	PUNCT
ejpam-5396	10	6	26a33	26a33	NUM
ejpam-5396	10	7	,	,	PUNCT
ejpam-5396	10	8	34a08	34a08	NUM
ejpam-5396	10	9	,	,	PUNCT
ejpam-5396	10	10	34d20	34d20	NUM
ejpam-5396	10	11	,	,	PUNCT
ejpam-5396	10	12	65l99	65l99	NUM
ejpam-5396	10	13	,	,	PUNCT
ejpam-5396	10	14	92	92	NUM
ejpam-5396	10	15	-	-	SYM
ejpam-5396	10	16	10	10	NUM
ejpam-5396	10	17	,	,	PUNCT
ejpam-5396	10	18	92c42	92c42	NUM
ejpam-5396	10	19	,	,	PUNCT
ejpam-5396	10	20	92d25	92d25	NUM
ejpam-5396	10	21	,	,	PUNCT
ejpam-5396	10	22	92d30	92d30	NUM
ejpam-5396	10	23	key	key	ADJ
ejpam-5396	10	24	words	word	NOUN
ejpam-5396	10	25	and	and	CCONJ
ejpam-5396	10	26	phrases	phrase	NOUN
ejpam-5396	10	27	:	:	PUNCT
ejpam-5396	10	28	pneumonia	pneumonia	NOUN
ejpam-5396	10	29	disease	disease	NOUN
ejpam-5396	10	30	,	,	PUNCT
ejpam-5396	10	31	fractional	fractional	ADJ
ejpam-5396	10	32	-	-	PUNCT
ejpam-5396	10	33	order	order	NOUN
ejpam-5396	10	34	mathematical	mathematical	ADJ
ejpam-5396	10	35	model	model	NOUN
ejpam-5396	10	36	,	,	PUNCT
ejpam-5396	10	37	caputo	caputo	PROPN
ejpam-5396	10	38	fractional	fractional	PROPN
ejpam-5396	10	39	derivative	derivative	PROPN
ejpam-5396	10	40	,	,	PUNCT
ejpam-5396	10	41	stability	stability	NOUN
ejpam-5396	10	42	analysis	analysis	NOUN
ejpam-5396	10	43	,	,	PUNCT
ejpam-5396	10	44	numerical	numerical	ADJ
ejpam-5396	10	45	techniques	technique	NOUN
ejpam-5396	10	46	1	1	NUM
ejpam-5396	10	47	.	.	PUNCT
ejpam-5396	11	1	introduction	introduction	NOUN
ejpam-5396	11	2	according	accord	VERB
ejpam-5396	11	3	to	to	ADP
ejpam-5396	11	4	johns	johns	PROPN
ejpam-5396	11	5	hopkins	hopkins	PROPN
ejpam-5396	11	6	medicine	medicine	PROPN
ejpam-5396	11	7	[	[	X
ejpam-5396	11	8	34	34	NUM
ejpam-5396	11	9	]	]	PUNCT
ejpam-5396	11	10	,	,	PUNCT
ejpam-5396	11	11	pneumonia	pneumonia	NOUN
ejpam-5396	11	12	is	be	AUX
ejpam-5396	11	13	a	a	DET
ejpam-5396	11	14	disease	disease	NOUN
ejpam-5396	11	15	of	of	ADP
ejpam-5396	11	16	one	one	NUM
ejpam-5396	11	17	or	or	CCONJ
ejpam-5396	11	18	both	both	PRON
ejpam-5396	11	19	of	of	ADP
ejpam-5396	11	20	the	the	DET
ejpam-5396	11	21	lungs	lung	NOUN
ejpam-5396	11	22	caused	cause	VERB
ejpam-5396	11	23	by	by	ADP
ejpam-5396	11	24	infection	infection	NOUN
ejpam-5396	11	25	with	with	ADP
ejpam-5396	11	26	bacteria	bacteria	NOUN
ejpam-5396	11	27	,	,	PUNCT
ejpam-5396	11	28	viruses	virus	NOUN
ejpam-5396	11	29	,	,	PUNCT
ejpam-5396	11	30	or	or	CCONJ
ejpam-5396	11	31	fungi	fungus	NOUN
ejpam-5396	11	32	.	.	PUNCT
ejpam-5396	12	1	pneumonia	pneumonia	NOUN
ejpam-5396	12	2	has	have	VERB
ejpam-5396	12	3	more	more	ADJ
ejpam-5396	12	4	than	than	ADP
ejpam-5396	12	5	30	30	NUM
ejpam-5396	12	6	different	different	ADJ
ejpam-5396	12	7	causes	cause	NOUN
ejpam-5396	12	8	,	,	PUNCT
ejpam-5396	12	9	which	which	PRON
ejpam-5396	12	10	are	be	AUX
ejpam-5396	12	11	grouped	group	VERB
ejpam-5396	12	12	according	accord	VERB
ejpam-5396	12	13	to	to	ADP
ejpam-5396	12	14	the	the	DET
ejpam-5396	12	15	cause	cause	NOUN
ejpam-5396	12	16	.	.	PUNCT
ejpam-5396	13	1	the	the	DET
ejpam-5396	13	2	main	main	ADJ
ejpam-5396	13	3	species	specie	NOUN
ejpam-5396	13	4	of	of	ADP
ejpam-5396	13	5	pneumonia	pneumonia	NOUN
ejpam-5396	13	6	include	include	VERB
ejpam-5396	13	7	bacterial	bacterial	ADJ
ejpam-5396	13	8	pneumonia	pneumonia	NOUN
ejpam-5396	13	9	,	,	PUNCT
ejpam-5396	13	10	viral	viral	ADJ
ejpam-5396	13	11	pneumonia	pneumonia	NOUN
ejpam-5396	13	12	,	,	PUNCT
ejpam-5396	13	13	mycoplasma	mycoplasma	NOUN
ejpam-5396	13	14	pneumonia	pneumonia	NOUN
ejpam-5396	13	15	,	,	PUNCT
ejpam-5396	13	16	and	and	CCONJ
ejpam-5396	13	17	other	other	ADJ
ejpam-5396	13	18	pneumonias	pneumonia	NOUN
ejpam-5396	13	19	.	.	PUNCT
ejpam-5396	14	1	people	people	NOUN
ejpam-5396	14	2	of	of	ADP
ejpam-5396	14	3	different	different	ADJ
ejpam-5396	14	4	ages	age	NOUN
ejpam-5396	14	5	can	can	AUX
ejpam-5396	14	6	get	get	VERB
ejpam-5396	14	7	pneumonia	pneumonia	NOUN
ejpam-5396	14	8	,	,	PUNCT
ejpam-5396	14	9	but	but	CCONJ
ejpam-5396	14	10	the	the	DET
ejpam-5396	14	11	groups	group	NOUN
ejpam-5396	14	12	at	at	ADP
ejpam-5396	14	13	the	the	DET
ejpam-5396	14	14	highest	high	ADJ
ejpam-5396	14	15	risk	risk	NOUN
ejpam-5396	14	16	are	be	AUX
ejpam-5396	14	17	children	child	NOUN
ejpam-5396	14	18	under	under	ADP
ejpam-5396	14	19	the	the	DET
ejpam-5396	14	20	age	age	NOUN
ejpam-5396	14	21	of	of	ADP
ejpam-5396	14	22	2	2	NUM
ejpam-5396	14	23	,	,	PUNCT
ejpam-5396	14	24	adults	adult	NOUN
ejpam-5396	14	25	ages	age	NOUN
ejpam-5396	14	26	65	65	NUM
ejpam-5396	14	27	and	and	CCONJ
ejpam-5396	14	28	older	old	ADJ
ejpam-5396	14	29	,	,	PUNCT
ejpam-5396	14	30	individuals	individual	NOUN
ejpam-5396	14	31	with	with	ADP
ejpam-5396	14	32	specific	specific	ADJ
ejpam-5396	14	33	medical	medical	ADJ
ejpam-5396	14	34	conditions	condition	NOUN
ejpam-5396	14	35	,	,	PUNCT
ejpam-5396	14	36	and	and	CCONJ
ejpam-5396	14	37	individuals	individual	NOUN
ejpam-5396	14	38	who	who	PRON
ejpam-5396	14	39	smoke	smoke	VERB
ejpam-5396	14	40	.	.	PUNCT
ejpam-5396	15	1	the	the	DET
ejpam-5396	15	2	majority	majority	NOUN
ejpam-5396	15	3	of	of	ADP
ejpam-5396	15	4	people	people	NOUN
ejpam-5396	15	5	with	with	ADP
ejpam-5396	15	6	pneumonia	pneumonia	NOUN
ejpam-5396	15	7	have	have	VERB
ejpam-5396	15	8	a	a	DET
ejpam-5396	15	9	good	good	ADJ
ejpam-5396	15	10	reaction	reaction	NOUN
ejpam-5396	15	11	to	to	ADP
ejpam-5396	15	12	medicine	medicine	NOUN
ejpam-5396	15	13	,	,	PUNCT
ejpam-5396	15	14	but	but	CCONJ
ejpam-5396	15	15	pneumonia	pneumonia	NOUN
ejpam-5396	15	16	can	can	AUX
ejpam-5396	15	17	be	be	AUX
ejpam-5396	15	18	lethal	lethal	ADJ
ejpam-5396	15	19	.	.	PUNCT
ejpam-5396	16	1	in	in	ADP
ejpam-5396	16	2	2013	2013	NUM
ejpam-5396	16	3	,	,	PUNCT
ejpam-5396	16	4	ong’ala	ong’ala	PROPN
ejpam-5396	16	5	et	et	PROPN
ejpam-5396	16	6	al	al	PROPN
ejpam-5396	16	7	.	.	PUNCT
ejpam-5396	17	1	[	[	X
ejpam-5396	17	2	46	46	NUM
ejpam-5396	17	3	]	]	PUNCT
ejpam-5396	17	4	created	create	VERB
ejpam-5396	17	5	a	a	DET
ejpam-5396	17	6	mathematical	mathematical	ADJ
ejpam-5396	17	7	model	model	NOUN
ejpam-5396	17	8	for	for	ADP
ejpam-5396	17	9	pneumonia	pneumonia	NOUN
ejpam-5396	17	10	dynamics	dynamic	NOUN
ejpam-5396	17	11	with	with	ADP
ejpam-5396	17	12	carriers	carrier	NOUN
ejpam-5396	17	13	.	.	PUNCT
ejpam-5396	18	1	doi	doi	NOUN
ejpam-5396	18	2	:	:	PUNCT
ejpam-5396	18	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5396	https://doi.org/10.29020/nybg.ejpam.v17i4.5396	PROPN
ejpam-5396	18	4	email	email	NOUN
ejpam-5396	18	5	address	address	NOUN
ejpam-5396	18	6	:	:	PUNCT
ejpam-5396	18	7	azaher@bu.edu.sa	azaher@bu.edu.sa	PROPN
ejpam-5396	18	8	(	(	PUNCT
ejpam-5396	18	9	a.	a.	NOUN
ejpam-5396	18	10	alalyani	alalyani	PROPN
ejpam-5396	18	11	)	)	PUNCT
ejpam-5396	18	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5396	19	1	2763	2763	NUM
ejpam-5396	19	2	copyright	copyright	NOUN
ejpam-5396	19	3	:	:	PUNCT
ejpam-5396	19	4	©	©	PROPN
ejpam-5396	19	5	2024	2024	NUM
ejpam-5396	19	6	the	the	DET
ejpam-5396	19	7	author(s	author(s	NOUN
ejpam-5396	19	8	)	)	PUNCT
ejpam-5396	19	9	.	.	PUNCT
ejpam-5396	20	1	(	(	PUNCT
ejpam-5396	20	2	cc	cc	NOUN
ejpam-5396	20	3	by	by	ADP
ejpam-5396	20	4	-	-	PUNCT
ejpam-5396	20	5	nc	nc	PROPN
ejpam-5396	20	6	4.0	4.0	NUM
ejpam-5396	20	7	)	)	PUNCT
ejpam-5396	20	8	a.	a.	NOUN
ejpam-5396	20	9	alalyani	alalyani	PROPN
ejpam-5396	20	10	/	/	SYM
ejpam-5396	20	11	eur	eur	PROPN
ejpam-5396	20	12	.	.	PUNCT
ejpam-5396	21	1	j.	j.	PROPN
ejpam-5396	21	2	pure	pure	PROPN
ejpam-5396	21	3	appl	appl	PROPN
ejpam-5396	21	4	.	.	PROPN
ejpam-5396	21	5	math	math	PROPN
ejpam-5396	21	6	,	,	PUNCT
ejpam-5396	21	7	17	17	NUM
ejpam-5396	21	8	(	(	PUNCT
ejpam-5396	21	9	4	4	NUM
ejpam-5396	21	10	)	)	PUNCT
ejpam-5396	21	11	(	(	PUNCT
ejpam-5396	21	12	2024	2024	NUM
ejpam-5396	21	13	)	)	PUNCT
ejpam-5396	21	14	,	,	PUNCT
ejpam-5396	21	15	2763	2763	NUM
ejpam-5396	21	16	-	-	SYM
ejpam-5396	21	17	2799	2799	NUM
ejpam-5396	21	18	2764	2764	NUM
ejpam-5396	21	19	they	they	PRON
ejpam-5396	21	20	use	use	VERB
ejpam-5396	21	21	bifurcation	bifurcation	NOUN
ejpam-5396	21	22	and	and	CCONJ
ejpam-5396	21	23	stability	stability	NOUN
ejpam-5396	21	24	of	of	ADP
ejpam-5396	21	25	equilibrium	equilibrium	NOUN
ejpam-5396	21	26	points	point	NOUN
ejpam-5396	21	27	to	to	PART
ejpam-5396	21	28	study	study	VERB
ejpam-5396	21	29	the	the	DET
ejpam-5396	21	30	reduction	reduction	NOUN
ejpam-5396	21	31	paths	path	NOUN
ejpam-5396	21	32	or	or	CCONJ
ejpam-5396	21	33	transfer	transfer	NOUN
ejpam-5396	21	34	rates	rate	NOUN
ejpam-5396	21	35	between	between	ADP
ejpam-5396	21	36	infected	infect	VERB
ejpam-5396	21	37	individuals	individual	NOUN
ejpam-5396	21	38	and	and	CCONJ
ejpam-5396	21	39	the	the	DET
ejpam-5396	21	40	carriers	carrier	NOUN
ejpam-5396	21	41	.	.	PUNCT
ejpam-5396	22	1	in	in	ADP
ejpam-5396	22	2	2014	2014	NUM
ejpam-5396	22	3	,	,	PUNCT
ejpam-5396	22	4	a	a	DET
ejpam-5396	22	5	simple	simple	ADJ
ejpam-5396	22	6	model	model	NOUN
ejpam-5396	22	7	of	of	ADP
ejpam-5396	22	8	ode	ode	PROPN
ejpam-5396	22	9	was	be	AUX
ejpam-5396	22	10	presented	present	VERB
ejpam-5396	22	11	by	by	ADP
ejpam-5396	22	12	mochan	mochan	PROPN
ejpam-5396	22	13	et	et	PROPN
ejpam-5396	22	14	al	al	PROPN
ejpam-5396	22	15	.	.	PUNCT
ejpam-5396	23	1	[	[	X
ejpam-5396	23	2	36	36	NUM
ejpam-5396	23	3	]	]	PUNCT
ejpam-5396	23	4	to	to	PART
ejpam-5396	23	5	dynamically	dynamically	ADV
ejpam-5396	23	6	describe	describe	VERB
ejpam-5396	23	7	the	the	DET
ejpam-5396	23	8	host	host	NOUN
ejpam-5396	23	9	’s	’s	PART
ejpam-5396	23	10	immune	immune	ADJ
ejpam-5396	23	11	response	response	NOUN
ejpam-5396	23	12	to	to	ADP
ejpam-5396	23	13	pneumonia	pneumonia	NOUN
ejpam-5396	23	14	caused	cause	VERB
ejpam-5396	23	15	by	by	ADP
ejpam-5396	23	16	bacteria	bacteria	NOUN
ejpam-5396	23	17	infection	infection	NOUN
ejpam-5396	23	18	in	in	ADP
ejpam-5396	23	19	murine	murine	ADJ
ejpam-5396	23	20	strains	strain	NOUN
ejpam-5396	23	21	.	.	PUNCT
ejpam-5396	24	1	in	in	ADP
ejpam-5396	24	2	2014	2014	NUM
ejpam-5396	24	3	,	,	PUNCT
ejpam-5396	24	4	drusano	drusano	PROPN
ejpam-5396	24	5	et	et	PROPN
ejpam-5396	24	6	al	al	PROPN
ejpam-5396	24	7	.	.	PUNCT
ejpam-5396	25	1	[	[	X
ejpam-5396	25	2	21	21	NUM
ejpam-5396	25	3	]	]	PUNCT
ejpam-5396	25	4	examined	examine	VERB
ejpam-5396	25	5	how	how	SCONJ
ejpam-5396	25	6	granulates	granulate	NOUN
ejpam-5396	25	7	work	work	VERB
ejpam-5396	25	8	to	to	PART
ejpam-5396	25	9	kill	kill	VERB
ejpam-5396	25	10	bacteria	bacteria	NOUN
ejpam-5396	25	11	and	and	CCONJ
ejpam-5396	25	12	found	find	VERB
ejpam-5396	25	13	no	no	DET
ejpam-5396	25	14	role	role	NOUN
ejpam-5396	25	15	for	for	ADP
ejpam-5396	25	16	antibiotics	antibiotic	NOUN
ejpam-5396	25	17	.	.	PUNCT
ejpam-5396	26	1	ndelwa	ndelwa	PROPN
ejpam-5396	26	2	et	et	PROPN
ejpam-5396	26	3	al	al	PROPN
ejpam-5396	26	4	.	.	PUNCT
ejpam-5396	27	1	[	[	X
ejpam-5396	27	2	39	39	NUM
ejpam-5396	27	3	]	]	PUNCT
ejpam-5396	27	4	created	create	VERB
ejpam-5396	27	5	in	in	ADP
ejpam-5396	27	6	2015	2015	NUM
ejpam-5396	27	7	a	a	DET
ejpam-5396	27	8	mathematical	mathematical	ADJ
ejpam-5396	27	9	model	model	NOUN
ejpam-5396	27	10	to	to	PART
ejpam-5396	27	11	describe	describe	VERB
ejpam-5396	27	12	the	the	DET
ejpam-5396	27	13	pneumonia	pneumonia	NOUN
ejpam-5396	27	14	transmission	transmission	NOUN
ejpam-5396	27	15	process	process	NOUN
ejpam-5396	27	16	in	in	ADP
ejpam-5396	27	17	order	order	NOUN
ejpam-5396	27	18	to	to	PART
ejpam-5396	27	19	estimate	estimate	VERB
ejpam-5396	27	20	transmission	transmission	NOUN
ejpam-5396	27	21	and	and	CCONJ
ejpam-5396	27	22	effects	effect	NOUN
ejpam-5396	27	23	.	.	PUNCT
ejpam-5396	28	1	in	in	ADP
ejpam-5396	28	2	2015	2015	NUM
ejpam-5396	28	3	,	,	PUNCT
ejpam-5396	28	4	kosasih	kosasih	PROPN
ejpam-5396	28	5	et	et	PROPN
ejpam-5396	28	6	al	al	PROPN
ejpam-5396	28	7	.	.	PUNCT
ejpam-5396	29	1	[	[	X
ejpam-5396	29	2	29	29	NUM
ejpam-5396	29	3	]	]	PUNCT
ejpam-5396	29	4	used	use	VERB
ejpam-5396	29	5	wavelet	wavelet	NOUN
ejpam-5396	29	6	-	-	PUNCT
ejpam-5396	29	7	based	base	VERB
ejpam-5396	29	8	crackle	crackle	NOUN
ejpam-5396	29	9	detection	detection	NOUN
ejpam-5396	29	10	to	to	PART
ejpam-5396	29	11	analyze	analyze	VERB
ejpam-5396	29	12	a	a	DET
ejpam-5396	29	13	mathematical	mathematical	ADJ
ejpam-5396	29	14	model	model	NOUN
ejpam-5396	29	15	of	of	ADP
ejpam-5396	29	16	cough	cough	NOUN
ejpam-5396	29	17	sounds	sound	VERB
ejpam-5396	29	18	for	for	ADP
ejpam-5396	29	19	quick	quick	ADJ
ejpam-5396	29	20	identification	identification	NOUN
ejpam-5396	29	21	of	of	ADP
ejpam-5396	29	22	pneumonia	pneumonia	NOUN
ejpam-5396	29	23	caused	cause	VERB
ejpam-5396	29	24	by	by	ADP
ejpam-5396	29	25	bacteria	bacteria	NOUN
ejpam-5396	29	26	in	in	ADP
ejpam-5396	29	27	children	child	NOUN
ejpam-5396	29	28	.	.	PUNCT
ejpam-5396	30	1	cesar	cesar	PROPN
ejpam-5396	30	2	et	et	PROPN
ejpam-5396	30	3	al	al	PROPN
ejpam-5396	30	4	.	.	PUNCT
ejpam-5396	31	1	[	[	X
ejpam-5396	31	2	16	16	NUM
ejpam-5396	31	3	]	]	PUNCT
ejpam-5396	31	4	mathematically	mathematically	ADV
ejpam-5396	31	5	evaluated	evaluate	VERB
ejpam-5396	31	6	in	in	ADP
ejpam-5396	31	7	2016	2016	NUM
ejpam-5396	31	8	a	a	DET
ejpam-5396	31	9	fine	fine	ADJ
ejpam-5396	31	10	particulate	particulate	NOUN
ejpam-5396	31	11	matter	matter	NOUN
ejpam-5396	31	12	using	use	VERB
ejpam-5396	31	13	a	a	DET
ejpam-5396	31	14	model	model	NOUN
ejpam-5396	31	15	and	and	CCONJ
ejpam-5396	31	16	assessed	assess	VERB
ejpam-5396	31	17	medicines	medicine	NOUN
ejpam-5396	31	18	for	for	ADP
ejpam-5396	31	19	pediatric	pediatric	ADJ
ejpam-5396	31	20	asthma	asthma	NOUN
ejpam-5396	31	21	and	and	CCONJ
ejpam-5396	31	22	pneumonia	pneumonia	NOUN
ejpam-5396	31	23	.	.	PUNCT
ejpam-5396	32	1	atypical	atypical	ADJ
ejpam-5396	32	2	bacterial	bacterial	ADJ
ejpam-5396	32	3	pathogens	pathogen	NOUN
ejpam-5396	32	4	were	be	AUX
ejpam-5396	32	5	recorded	record	VERB
ejpam-5396	32	6	as	as	ADP
ejpam-5396	32	7	the	the	DET
ejpam-5396	32	8	primary	primary	ADJ
ejpam-5396	32	9	reasons	reason	NOUN
ejpam-5396	32	10	for	for	ADP
ejpam-5396	32	11	lower	low	ADJ
ejpam-5396	32	12	respiratory	respiratory	ADJ
ejpam-5396	32	13	illnesses	illness	NOUN
ejpam-5396	32	14	such	such	ADJ
ejpam-5396	32	15	as	as	ADP
ejpam-5396	32	16	cap	cap	NOUN
ejpam-5396	32	17	,	,	PUNCT
ejpam-5396	32	18	bronchitis	bronchitis	NOUN
ejpam-5396	32	19	,	,	PUNCT
ejpam-5396	32	20	and	and	CCONJ
ejpam-5396	32	21	coughs	cough	NOUN
ejpam-5396	32	22	by	by	ADP
ejpam-5396	32	23	marchello	marchello	PROPN
ejpam-5396	32	24	et	et	PROPN
ejpam-5396	32	25	al	al	PROPN
ejpam-5396	32	26	.	.	PUNCT
ejpam-5396	33	1	[	[	X
ejpam-5396	33	2	32	32	NUM
ejpam-5396	33	3	]	]	PUNCT
ejpam-5396	33	4	in	in	ADP
ejpam-5396	33	5	2016	2016	NUM
ejpam-5396	33	6	.	.	PUNCT
ejpam-5396	34	1	cheng	cheng	PROPN
ejpam-5396	34	2	et	et	PROPN
ejpam-5396	34	3	al	al	PROPN
ejpam-5396	34	4	.	.	PROPN
ejpam-5396	35	1	in	in	ADP
ejpam-5396	35	2	2017	2017	NUM
ejpam-5396	35	3	estimated	estimate	VERB
ejpam-5396	35	4	an	an	DET
ejpam-5396	35	5	iav	iav	NOUN
ejpam-5396	35	6	-	-	PUNCT
ejpam-5396	35	7	sp	sp	NOUN
ejpam-5396	35	8	model	model	NOUN
ejpam-5396	35	9	dynamically	dynamically	ADV
ejpam-5396	35	10	and	and	CCONJ
ejpam-5396	35	11	mathematically	mathematically	ADV
ejpam-5396	35	12	[	[	X
ejpam-5396	35	13	17	17	NUM
ejpam-5396	35	14	]	]	PUNCT
ejpam-5396	35	15	.	.	PUNCT
ejpam-5396	36	1	to	to	PART
ejpam-5396	36	2	develop	develop	VERB
ejpam-5396	36	3	the	the	DET
ejpam-5396	36	4	respiratory	respiratory	ADJ
ejpam-5396	36	5	health	health	NOUN
ejpam-5396	36	6	of	of	ADP
ejpam-5396	36	7	copd	copd	PROPN
ejpam-5396	36	8	patients	patient	NOUN
ejpam-5396	36	9	,	,	PUNCT
ejpam-5396	36	10	they	they	PRON
ejpam-5396	36	11	created	create	VERB
ejpam-5396	36	12	a	a	DET
ejpam-5396	36	13	quantitative	quantitative	ADJ
ejpam-5396	36	14	risk	risk	NOUN
ejpam-5396	36	15	-	-	PUNCT
ejpam-5396	36	16	assessment	assessment	NOUN
ejpam-5396	36	17	structure	structure	NOUN
ejpam-5396	36	18	.	.	PUNCT
ejpam-5396	37	1	in	in	ADP
ejpam-5396	37	2	2017	2017	NUM
ejpam-5396	37	3	,	,	PUNCT
ejpam-5396	37	4	kosasih	kosasih	NOUN
ejpam-5396	37	5	and	and	CCONJ
ejpam-5396	37	6	abeyratne	abeyratne	NOUN
ejpam-5396	37	7	[	[	X
ejpam-5396	37	8	28	28	NUM
ejpam-5396	37	9	]	]	PUNCT
ejpam-5396	37	10	proposed	propose	VERB
ejpam-5396	37	11	a	a	DET
ejpam-5396	37	12	straightforward	straightforward	ADJ
ejpam-5396	37	13	mathematical	mathematical	ADJ
ejpam-5396	37	14	model	model	NOUN
ejpam-5396	37	15	to	to	PART
ejpam-5396	37	16	illustrate	illustrate	VERB
ejpam-5396	37	17	the	the	DET
ejpam-5396	37	18	measurement	measurement	NOUN
ejpam-5396	37	19	analysis	analysis	NOUN
ejpam-5396	37	20	for	for	ADP
ejpam-5396	37	21	the	the	DET
ejpam-5396	37	22	clinical	clinical	ADJ
ejpam-5396	37	23	identification	identification	NOUN
ejpam-5396	37	24	of	of	ADP
ejpam-5396	37	25	pediatric	pediatric	ADJ
ejpam-5396	37	26	pneumonia	pneumonia	NOUN
ejpam-5396	37	27	.	.	PUNCT
ejpam-5396	38	1	tilahun	tilahun	PROPN
ejpam-5396	38	2	et	et	PROPN
ejpam-5396	38	3	al	al	PROPN
ejpam-5396	38	4	.	.	PUNCT
ejpam-5396	39	1	[	[	X
ejpam-5396	39	2	55	55	NUM
ejpam-5396	39	3	]	]	PUNCT
ejpam-5396	39	4	presented	present	VERB
ejpam-5396	39	5	in	in	ADP
ejpam-5396	39	6	2017	2017	NUM
ejpam-5396	39	7	a	a	DET
ejpam-5396	39	8	non	non	ADJ
ejpam-5396	39	9	-	-	ADJ
ejpam-5396	39	10	linear	linear	ADJ
ejpam-5396	39	11	mathematical	mathematical	ADJ
ejpam-5396	39	12	model	model	NOUN
ejpam-5396	39	13	along	along	ADP
ejpam-5396	39	14	with	with	ADP
ejpam-5396	39	15	an	an	DET
ejpam-5396	39	16	analysis	analysis	NOUN
ejpam-5396	39	17	of	of	ADP
ejpam-5396	39	18	optical	optical	ADJ
ejpam-5396	39	19	control	control	NOUN
ejpam-5396	39	20	approaches	approach	NOUN
ejpam-5396	39	21	for	for	ADP
ejpam-5396	39	22	pneumonia	pneumonia	NOUN
ejpam-5396	39	23	disease	disease	NOUN
ejpam-5396	39	24	.	.	PUNCT
ejpam-5396	40	1	tilahun	tilahun	PROPN
ejpam-5396	40	2	et	et	PROPN
ejpam-5396	40	3	al	al	PROPN
ejpam-5396	40	4	.	.	PUNCT
ejpam-5396	41	1	[	[	X
ejpam-5396	41	2	56	56	NUM
ejpam-5396	41	3	]	]	PUNCT
ejpam-5396	41	4	considered	consider	VERB
ejpam-5396	41	5	in	in	ADP
ejpam-5396	41	6	2018	2018	NUM
ejpam-5396	41	7	a	a	DET
ejpam-5396	41	8	co	co	ADJ
ejpam-5396	41	9	-	-	ADJ
ejpam-5396	41	10	infection	infection	ADJ
ejpam-5396	41	11	model	model	NOUN
ejpam-5396	41	12	for	for	ADP
ejpam-5396	41	13	the	the	DET
ejpam-5396	41	14	diseases	disease	NOUN
ejpam-5396	41	15	of	of	ADP
ejpam-5396	41	16	pneumonia	pneumonia	NOUN
ejpam-5396	41	17	and	and	CCONJ
ejpam-5396	41	18	typhoid	typhoid	NOUN
ejpam-5396	41	19	fever	fever	NOUN
ejpam-5396	41	20	,	,	PUNCT
ejpam-5396	41	21	and	and	CCONJ
ejpam-5396	41	22	their	their	PRON
ejpam-5396	41	23	distinctive	distinctive	ADJ
ejpam-5396	41	24	relation	relation	NOUN
ejpam-5396	41	25	in	in	ADP
ejpam-5396	41	26	the	the	DET
ejpam-5396	41	27	case	case	NOUN
ejpam-5396	41	28	of	of	ADP
ejpam-5396	41	29	a	a	DET
ejpam-5396	41	30	treatment	treatment	NOUN
ejpam-5396	41	31	and	and	CCONJ
ejpam-5396	41	32	medical	medical	ADJ
ejpam-5396	41	33	plans	plan	NOUN
ejpam-5396	41	34	of	of	ADP
ejpam-5396	41	35	action	action	NOUN
ejpam-5396	41	36	was	be	AUX
ejpam-5396	41	37	mathematically	mathematically	ADV
ejpam-5396	41	38	analyzed	analyze	VERB
ejpam-5396	41	39	.	.	PUNCT
ejpam-5396	42	1	based	base	VERB
ejpam-5396	42	2	on	on	ADP
ejpam-5396	42	3	mathematical	mathematical	ADJ
ejpam-5396	42	4	characteristics	characteristic	NOUN
ejpam-5396	42	5	of	of	ADP
ejpam-5396	42	6	cough	cough	NOUN
ejpam-5396	42	7	sounds	sound	NOUN
ejpam-5396	42	8	,	,	PUNCT
ejpam-5396	42	9	raj	raj	PROPN
ejpam-5396	42	10	et	et	PROPN
ejpam-5396	42	11	al	al	PROPN
ejpam-5396	42	12	.	.	PROPN
ejpam-5396	43	1	in	in	ADP
ejpam-5396	43	2	2018	2018	NUM
ejpam-5396	43	3	[	[	SYM
ejpam-5396	43	4	49	49	NUM
ejpam-5396	43	5	]	]	PUNCT
ejpam-5396	43	6	studied	study	VERB
ejpam-5396	43	7	the	the	DET
ejpam-5396	43	8	classification	classification	NOUN
ejpam-5396	43	9	of	of	ADP
ejpam-5396	43	10	pneumonia	pneumonia	NOUN
ejpam-5396	43	11	and	and	CCONJ
ejpam-5396	43	12	asthma	asthma	NOUN
ejpam-5396	43	13	in	in	ADP
ejpam-5396	43	14	poor	poor	ADJ
ejpam-5396	43	15	populations	population	NOUN
ejpam-5396	43	16	.	.	PUNCT
ejpam-5396	44	1	kizito	kizito	NOUN
ejpam-5396	44	2	and	and	CCONJ
ejpam-5396	44	3	tumwiine	tumwiine	NOUN
ejpam-5396	44	4	[	[	X
ejpam-5396	44	5	27	27	NUM
ejpam-5396	44	6	]	]	PUNCT
ejpam-5396	44	7	provided	provide	VERB
ejpam-5396	44	8	a	a	DET
ejpam-5396	44	9	mathematical	mathematical	ADJ
ejpam-5396	44	10	model	model	NOUN
ejpam-5396	44	11	in	in	ADP
ejpam-5396	44	12	2018	2018	NUM
ejpam-5396	44	13	that	that	PRON
ejpam-5396	44	14	illustrates	illustrate	VERB
ejpam-5396	44	15	how	how	SCONJ
ejpam-5396	44	16	bacteria	bacteria	NOUN
ejpam-5396	44	17	control	control	VERB
ejpam-5396	44	18	the	the	DET
ejpam-5396	44	19	spread	spread	NOUN
ejpam-5396	44	20	of	of	ADP
ejpam-5396	44	21	pneumonia	pneumonia	NOUN
ejpam-5396	44	22	.	.	PUNCT
ejpam-5396	45	1	in	in	ADP
ejpam-5396	45	2	addition	addition	NOUN
ejpam-5396	45	3	,	,	PUNCT
ejpam-5396	45	4	the	the	DET
ejpam-5396	45	5	dynamics	dynamic	NOUN
ejpam-5396	45	6	of	of	ADP
ejpam-5396	45	7	vaccine	vaccine	NOUN
ejpam-5396	45	8	formulation	formulation	NOUN
ejpam-5396	45	9	and	and	CCONJ
ejpam-5396	45	10	treatment	treatment	NOUN
ejpam-5396	45	11	were	be	AUX
ejpam-5396	45	12	discussed	discuss	VERB
ejpam-5396	45	13	.	.	PUNCT
ejpam-5396	46	1	a	a	DET
ejpam-5396	46	2	non	non	ADJ
ejpam-5396	46	3	-	-	ADJ
ejpam-5396	46	4	linear	linear	ADJ
ejpam-5396	46	5	mathematical	mathematical	ADJ
ejpam-5396	46	6	model	model	NOUN
ejpam-5396	46	7	that	that	PRON
ejpam-5396	46	8	describes	describe	VERB
ejpam-5396	46	9	the	the	DET
ejpam-5396	46	10	modeling	modeling	NOUN
ejpam-5396	46	11	of	of	ADP
ejpam-5396	46	12	co	co	NOUN
ejpam-5396	46	13	-	-	NOUN
ejpam-5396	46	14	infection	infection	NOUN
ejpam-5396	46	15	of	of	ADP
ejpam-5396	46	16	the	the	DET
ejpam-5396	46	17	influenza	influenza	NOUN
ejpam-5396	46	18	a	a	DET
ejpam-5396	46	19	virus	virus	NOUN
ejpam-5396	46	20	and	and	CCONJ
ejpam-5396	46	21	pneumonia	pneumonia	NOUN
ejpam-5396	46	22	within	within	ADP
ejpam-5396	46	23	the	the	DET
ejpam-5396	46	24	host	host	NOUN
ejpam-5396	46	25	was	be	AUX
ejpam-5396	46	26	studied	study	VERB
ejpam-5396	46	27	in	in	ADP
ejpam-5396	46	28	2018	2018	NUM
ejpam-5396	46	29	by	by	ADP
ejpam-5396	46	30	mbabazi	mbabazi	PROPN
ejpam-5396	46	31	et	et	PROPN
ejpam-5396	46	32	al	al	PROPN
ejpam-5396	46	33	.	.	PUNCT
ejpam-5396	47	1	[	[	X
ejpam-5396	47	2	33	33	NUM
ejpam-5396	47	3	]	]	PUNCT
ejpam-5396	47	4	.	.	PUNCT
ejpam-5396	48	1	tilahun	tilahun	PROPN
ejpam-5396	48	2	in	in	ADP
ejpam-5396	48	3	2019	2019	NUM
ejpam-5396	49	1	[	[	X
ejpam-5396	49	2	54	54	NUM
ejpam-5396	49	3	]	]	PUNCT
ejpam-5396	49	4	used	use	VERB
ejpam-5396	49	5	theorems	theorem	NOUN
ejpam-5396	49	6	and	and	CCONJ
ejpam-5396	49	7	ordinary	ordinary	ADJ
ejpam-5396	49	8	differential	differential	ADJ
ejpam-5396	49	9	equations	equation	NOUN
ejpam-5396	49	10	to	to	PART
ejpam-5396	49	11	describe	describe	VERB
ejpam-5396	49	12	a	a	DET
ejpam-5396	49	13	pneumonia	pneumonia	NOUN
ejpam-5396	49	14	-	-	PUNCT
ejpam-5396	49	15	meningitis	meningitis	ADJ
ejpam-5396	49	16	co	co	NOUN
ejpam-5396	49	17	-	-	NOUN
ejpam-5396	49	18	infection	infection	NOUN
ejpam-5396	49	19	model	model	NOUN
ejpam-5396	49	20	.	.	PUNCT
ejpam-5396	50	1	tilahun	tilahun	PROPN
ejpam-5396	50	2	provided	provide	VERB
ejpam-5396	50	3	an	an	DET
ejpam-5396	50	4	explanation	explanation	NOUN
ejpam-5396	50	5	of	of	ADP
ejpam-5396	50	6	different	different	ADJ
ejpam-5396	50	7	disease	disease	NOUN
ejpam-5396	50	8	clearance	clearance	NOUN
ejpam-5396	50	9	methods	method	NOUN
ejpam-5396	50	10	.	.	PUNCT
ejpam-5396	51	1	in	in	ADP
ejpam-5396	51	2	2019	2019	NUM
ejpam-5396	51	3	,	,	PUNCT
ejpam-5396	51	4	diah	diah	NOUN
ejpam-5396	51	5	and	and	CCONJ
ejpam-5396	51	6	aziz	aziz	PROPN
ejpam-5396	51	7	[	[	X
ejpam-5396	51	8	19	19	NUM
ejpam-5396	51	9	]	]	PUNCT
ejpam-5396	51	10	reviewed	review	VERB
ejpam-5396	51	11	dynamic	dynamic	ADJ
ejpam-5396	51	12	mathematical	mathematical	ADJ
ejpam-5396	51	13	models	model	NOUN
ejpam-5396	51	14	of	of	ADP
ejpam-5396	51	15	pneumonia	pneumonia	NOUN
ejpam-5396	51	16	,	,	PUNCT
ejpam-5396	51	17	followed	follow	VERB
ejpam-5396	51	18	by	by	ADP
ejpam-5396	51	19	earlier	early	ADJ
ejpam-5396	51	20	research	research	NOUN
ejpam-5396	51	21	.	.	PUNCT
ejpam-5396	52	1	tilahun	tilahun	NOUN
ejpam-5396	52	2	in	in	ADP
ejpam-5396	52	3	2019	2019	NUM
ejpam-5396	52	4	[	[	X
ejpam-5396	52	5	53	53	NUM
ejpam-5396	52	6	]	]	PUNCT
ejpam-5396	52	7	investigated	investigate	VERB
ejpam-5396	52	8	a	a	DET
ejpam-5396	52	9	mathematical	mathematical	ADJ
ejpam-5396	52	10	model	model	NOUN
ejpam-5396	52	11	of	of	ADP
ejpam-5396	52	12	co	co	NOUN
ejpam-5396	52	13	-	-	NOUN
ejpam-5396	52	14	dynamics	dynamic	NOUN
ejpam-5396	52	15	for	for	ADP
ejpam-5396	52	16	the	the	DET
ejpam-5396	52	17	diseases	disease	NOUN
ejpam-5396	52	18	meningitis	meningiti	NOUN
ejpam-5396	52	19	and	and	CCONJ
ejpam-5396	52	20	pneumonia	pneumonia	NOUN
ejpam-5396	52	21	.	.	PUNCT
ejpam-5396	53	1	in	in	ADP
ejpam-5396	53	2	2020	2020	NUM
ejpam-5396	53	3	,	,	PUNCT
ejpam-5396	53	4	otoo	otoo	PROPN
ejpam-5396	53	5	et	et	PROPN
ejpam-5396	53	6	al	al	PROPN
ejpam-5396	53	7	.	.	PUNCT
ejpam-5396	54	1	[	[	X
ejpam-5396	54	2	47	47	NUM
ejpam-5396	54	3	]	]	PUNCT
ejpam-5396	54	4	studied	study	VERB
ejpam-5396	54	5	a	a	DET
ejpam-5396	54	6	model	model	NOUN
ejpam-5396	54	7	that	that	PRON
ejpam-5396	54	8	illustrates	illustrate	VERB
ejpam-5396	54	9	how	how	SCONJ
ejpam-5396	54	10	bacteria	bacteria	NOUN
ejpam-5396	54	11	spread	spread	VERB
ejpam-5396	54	12	pneumonia	pneumonia	NOUN
ejpam-5396	54	13	,	,	PUNCT
ejpam-5396	54	14	and	and	CCONJ
ejpam-5396	54	15	the	the	DET
ejpam-5396	54	16	analysis	analysis	NOUN
ejpam-5396	54	17	in	in	ADP
ejpam-5396	54	18	this	this	DET
ejpam-5396	54	19	study	study	NOUN
ejpam-5396	54	20	was	be	AUX
ejpam-5396	54	21	helpful	helpful	ADJ
ejpam-5396	54	22	in	in	ADP
ejpam-5396	54	23	determining	determine	VERB
ejpam-5396	54	24	the	the	DET
ejpam-5396	54	25	effects	effect	NOUN
ejpam-5396	54	26	of	of	ADP
ejpam-5396	54	27	vaccination	vaccination	NOUN
ejpam-5396	54	28	on	on	ADP
ejpam-5396	54	29	disease	disease	NOUN
ejpam-5396	54	30	control	control	NOUN
ejpam-5396	54	31	.	.	PUNCT
ejpam-5396	55	1	in	in	ADP
ejpam-5396	55	2	2020	2020	NUM
ejpam-5396	55	3	,	,	PUNCT
ejpam-5396	55	4	the	the	DET
ejpam-5396	55	5	graphical	graphical	ADJ
ejpam-5396	55	6	result	result	NOUN
ejpam-5396	55	7	for	for	ADP
ejpam-5396	55	8	the	the	DET
ejpam-5396	55	9	dynamics	dynamic	NOUN
ejpam-5396	55	10	of	of	ADP
ejpam-5396	55	11	a	a	DET
ejpam-5396	55	12	mathematical	mathematical	ADJ
ejpam-5396	55	13	model	model	NOUN
ejpam-5396	55	14	for	for	ADP
ejpam-5396	55	15	pneumonia	pneumonia	NOUN
ejpam-5396	55	16	was	be	AUX
ejpam-5396	55	17	provided	provide	VERB
ejpam-5396	55	18	by	by	ADP
ejpam-5396	55	19	zephaniah	zephaniah	PROPN
ejpam-5396	55	20	et	et	PROPN
ejpam-5396	55	21	al	al	PROPN
ejpam-5396	55	22	.	.	PUNCT
ejpam-5396	56	1	[	[	X
ejpam-5396	56	2	60	60	NUM
ejpam-5396	56	3	]	]	PUNCT
ejpam-5396	56	4	.	.	PUNCT
ejpam-5396	57	1	ming	ming	PROPN
ejpam-5396	57	2	et	et	PROPN
ejpam-5396	57	3	al	al	PROPN
ejpam-5396	57	4	.	.	PUNCT
ejpam-5396	58	1	[	[	X
ejpam-5396	58	2	35	35	NUM
ejpam-5396	58	3	]	]	PUNCT
ejpam-5396	58	4	discussed	discuss	VERB
ejpam-5396	58	5	in	in	ADP
ejpam-5396	58	6	2020	2020	NUM
ejpam-5396	58	7	the	the	DET
ejpam-5396	58	8	growing	grow	VERB
ejpam-5396	58	9	number	number	NOUN
ejpam-5396	58	10	of	of	ADP
ejpam-5396	58	11	coronavirus	coronavirus	NOUN
ejpam-5396	58	12	pneumonia	pneumonia	NOUN
ejpam-5396	58	13	cases	case	NOUN
ejpam-5396	58	14	and	and	CCONJ
ejpam-5396	58	15	the	the	DET
ejpam-5396	58	16	spread	spread	NOUN
ejpam-5396	58	17	of	of	ADP
ejpam-5396	58	18	this	this	DET
ejpam-5396	58	19	disease	disease	NOUN
ejpam-5396	58	20	in	in	ADP
ejpam-5396	58	21	wuhan	wuhan	PROPN
ejpam-5396	58	22	,	,	PUNCT
ejpam-5396	58	23	china	china	PROPN
ejpam-5396	58	24	.	.	PUNCT
ejpam-5396	59	1	in	in	ADP
ejpam-5396	59	2	2020	2020	NUM
ejpam-5396	59	3	,	,	PUNCT
ejpam-5396	59	4	jung	jung	PROPN
ejpam-5396	59	5	et	et	PROPN
ejpam-5396	59	6	al	al	PROPN
ejpam-5396	59	7	.	.	PUNCT
ejpam-5396	60	1	[	[	X
ejpam-5396	60	2	26	26	NUM
ejpam-5396	60	3	]	]	PUNCT
ejpam-5396	60	4	exhibited	exhibit	VERB
ejpam-5396	60	5	the	the	DET
ejpam-5396	60	6	observations	observation	NOUN
ejpam-5396	60	7	through	through	ADP
ejpam-5396	60	8	a	a	DET
ejpam-5396	60	9	variety	variety	NOUN
ejpam-5396	60	10	of	of	ADP
ejpam-5396	60	11	clinical	clinical	ADJ
ejpam-5396	60	12	tests	test	NOUN
ejpam-5396	60	13	and	and	CCONJ
ejpam-5396	60	14	revealed	reveal	VERB
ejpam-5396	60	15	a	a	DET
ejpam-5396	60	16	novel	novel	ADJ
ejpam-5396	60	17	pathogen	pathogen	NOUN
ejpam-5396	60	18	as	as	ADP
ejpam-5396	60	19	the	the	DET
ejpam-5396	60	20	cause	cause	NOUN
ejpam-5396	60	21	of	of	ADP
ejpam-5396	60	22	disease	disease	NOUN
ejpam-5396	60	23	.	.	PUNCT
ejpam-5396	61	1	in	in	ADP
ejpam-5396	61	2	2021	2021	NUM
ejpam-5396	61	3	,	,	PUNCT
ejpam-5396	61	4	wafula	wafula	VERB
ejpam-5396	61	5	et	et	PROPN
ejpam-5396	61	6	al	al	PROPN
ejpam-5396	61	7	.	.	PUNCT
ejpam-5396	62	1	[	[	X
ejpam-5396	62	2	59	59	NUM
ejpam-5396	62	3	]	]	PUNCT
ejpam-5396	62	4	established	establish	VERB
ejpam-5396	62	5	a	a	DET
ejpam-5396	62	6	deterministic	deterministic	ADJ
ejpam-5396	62	7	mathematical	mathematical	ADJ
ejpam-5396	62	8	model	model	NOUN
ejpam-5396	62	9	of	of	ADP
ejpam-5396	62	10	pneumonia	pneumonia	NOUN
ejpam-5396	62	11	-	-	PUNCT
ejpam-5396	62	12	hiv	hiv	PROPN
ejpam-5396	62	13	coinfection	coinfection	NOUN
ejpam-5396	62	14	with	with	ADP
ejpam-5396	62	15	the	the	DET
ejpam-5396	62	16	utilization	utilization	NOUN
ejpam-5396	62	17	of	of	ADP
ejpam-5396	62	18	anti	anti	ADJ
ejpam-5396	62	19	-	-	NOUN
ejpam-5396	62	20	pneumonia	pneumonia	NOUN
ejpam-5396	62	21	and	and	CCONJ
ejpam-5396	62	22	art	art	NOUN
ejpam-5396	62	23	therapy	therapy	NOUN
ejpam-5396	62	24	strategies	strategy	NOUN
ejpam-5396	62	25	as	as	ADP
ejpam-5396	62	26	control	control	NOUN
ejpam-5396	62	27	to	to	PART
ejpam-5396	62	28	describe	describe	VERB
ejpam-5396	62	29	optimal	optimal	ADJ
ejpam-5396	62	30	control	control	NOUN
ejpam-5396	62	31	treatment	treatment	NOUN
ejpam-5396	62	32	.	.	PUNCT
ejpam-5396	63	1	oluwatobi	oluwatobi	PROPN
ejpam-5396	63	2	and	and	CCONJ
ejpam-5396	63	3	erinle	erinle	ADV
ejpam-5396	63	4	-	-	ADJ
ejpam-5396	63	5	ibrahim	ibrahim	ADJ
ejpam-5396	63	6	in	in	ADP
ejpam-5396	63	7	2021	2021	NUM
ejpam-5396	63	8	[	[	X
ejpam-5396	63	9	45	45	NUM
ejpam-5396	63	10	]	]	PUNCT
ejpam-5396	63	11	investigated	investigate	VERB
ejpam-5396	63	12	the	the	DET
ejpam-5396	63	13	impact	impact	NOUN
ejpam-5396	63	14	of	of	ADP
ejpam-5396	63	15	treating	treat	VERB
ejpam-5396	63	16	pneumonia	pneumonia	NOUN
ejpam-5396	63	17	disease	disease	NOUN
ejpam-5396	63	18	,	,	PUNCT
ejpam-5396	63	19	the	the	DET
ejpam-5396	63	20	existence	existence	NOUN
ejpam-5396	63	21	of	of	ADP
ejpam-5396	63	22	efficient	efficient	ADJ
ejpam-5396	63	23	reproduction	reproduction	NOUN
ejpam-5396	63	24	a.	a.	NOUN
ejpam-5396	63	25	alalyani	alalyani	PROPN
ejpam-5396	63	26	/	/	SYM
ejpam-5396	63	27	eur	eur	PROPN
ejpam-5396	63	28	.	.	PUNCT
ejpam-5396	64	1	j.	j.	PROPN
ejpam-5396	64	2	pure	pure	PROPN
ejpam-5396	64	3	appl	appl	PROPN
ejpam-5396	64	4	.	.	PROPN
ejpam-5396	64	5	math	math	PROPN
ejpam-5396	64	6	,	,	PUNCT
ejpam-5396	64	7	17	17	NUM
ejpam-5396	64	8	(	(	PUNCT
ejpam-5396	64	9	4	4	NUM
ejpam-5396	64	10	)	)	PUNCT
ejpam-5396	64	11	(	(	PUNCT
ejpam-5396	64	12	2024	2024	NUM
ejpam-5396	64	13	)	)	PUNCT
ejpam-5396	64	14	,	,	PUNCT
ejpam-5396	64	15	2763	2763	NUM
ejpam-5396	64	16	-	-	SYM
ejpam-5396	64	17	2799	2799	NUM
ejpam-5396	64	18	2765	2765	NUM
ejpam-5396	64	19	numbers	number	NOUN
ejpam-5396	64	20	,	,	PUNCT
ejpam-5396	64	21	and	and	CCONJ
ejpam-5396	64	22	the	the	DET
ejpam-5396	64	23	stability	stability	NOUN
ejpam-5396	64	24	of	of	ADP
ejpam-5396	64	25	equilibrium	equilibrium	NOUN
ejpam-5396	64	26	points	point	NOUN
ejpam-5396	64	27	.	.	PUNCT
ejpam-5396	65	1	in	in	ADP
ejpam-5396	65	2	2021	2021	NUM
ejpam-5396	65	3	,	,	PUNCT
ejpam-5396	65	4	a	a	DET
ejpam-5396	65	5	delayed	delay	VERB
ejpam-5396	65	6	mathematical	mathematical	ADJ
ejpam-5396	65	7	modeling	modeling	NOUN
ejpam-5396	65	8	technique	technique	NOUN
ejpam-5396	65	9	was	be	AUX
ejpam-5396	65	10	implemented	implement	VERB
ejpam-5396	65	11	by	by	ADP
ejpam-5396	65	12	muhammad	muhammad	PROPN
ejpam-5396	65	13	naveed	naveed	PROPN
ejpam-5396	65	14	et	et	PROPN
ejpam-5396	65	15	al	al	PROPN
ejpam-5396	65	16	.	.	PUNCT
ejpam-5396	66	1	[	[	X
ejpam-5396	66	2	38	38	NUM
ejpam-5396	66	3	]	]	PUNCT
ejpam-5396	66	4	to	to	PART
ejpam-5396	66	5	analyze	analyze	VERB
ejpam-5396	66	6	pneumonia	pneumonia	NOUN
ejpam-5396	66	7	disease	disease	NOUN
ejpam-5396	66	8	.	.	PUNCT
ejpam-5396	67	1	olumuyiwa	olumuyiwa	PROPN
ejpam-5396	67	2	james	james	PROPN
ejpam-5396	67	3	peter	peter	PROPN
ejpam-5396	67	4	et	et	PROPN
ejpam-5396	67	5	al	al	PROPN
ejpam-5396	67	6	.	.	PROPN
ejpam-5396	68	1	in	in	ADP
ejpam-5396	68	2	2021	2021	NUM
ejpam-5396	68	3	[	[	X
ejpam-5396	68	4	44	44	NUM
ejpam-5396	68	5	]	]	PUNCT
ejpam-5396	68	6	introduced	introduce	VERB
ejpam-5396	68	7	a	a	DET
ejpam-5396	68	8	model	model	NOUN
ejpam-5396	68	9	for	for	ADP
ejpam-5396	68	10	pneumococcal	pneumococcal	ADJ
ejpam-5396	68	11	pneumonia	pneumonia	NOUN
ejpam-5396	68	12	infection	infection	NOUN
ejpam-5396	68	13	using	use	VERB
ejpam-5396	68	14	fractional	fractional	ADJ
ejpam-5396	68	15	order	order	NOUN
ejpam-5396	68	16	derivatives	derivative	NOUN
ejpam-5396	68	17	in	in	ADP
ejpam-5396	68	18	the	the	DET
ejpam-5396	68	19	sense	sense	NOUN
ejpam-5396	68	20	of	of	ADP
ejpam-5396	68	21	the	the	DET
ejpam-5396	68	22	caputo	caputo	PROPN
ejpam-5396	68	23	-	-	PUNCT
ejpam-5396	68	24	fabrizio	fabrizio	PROPN
ejpam-5396	68	25	operator	operator	NOUN
ejpam-5396	68	26	.	.	PUNCT
ejpam-5396	69	1	in	in	ADP
ejpam-5396	69	2	2022	2022	NUM
ejpam-5396	69	3	,	,	PUNCT
ejpam-5396	69	4	sayed	say	VERB
ejpam-5396	69	5	saber	saber	PROPN
ejpam-5396	69	6	et	et	PROPN
ejpam-5396	69	7	al	al	PROPN
ejpam-5396	69	8	.	.	PUNCT
ejpam-5396	70	1	[	[	X
ejpam-5396	70	2	52	52	NUM
ejpam-5396	70	3	]	]	PUNCT
ejpam-5396	70	4	studied	study	VERB
ejpam-5396	70	5	a	a	DET
ejpam-5396	70	6	fractional	fractional	ADJ
ejpam-5396	70	7	mathematical	mathematical	ADJ
ejpam-5396	70	8	svcir	svcir	NOUN
ejpam-5396	70	9	model	model	NOUN
ejpam-5396	70	10	to	to	PART
ejpam-5396	70	11	estimate	estimate	VERB
ejpam-5396	70	12	the	the	DET
ejpam-5396	70	13	pneumonia	pneumonia	NOUN
ejpam-5396	70	14	disease	disease	NOUN
ejpam-5396	70	15	transmission	transmission	NOUN
ejpam-5396	70	16	dynamics	dynamic	NOUN
ejpam-5396	70	17	in	in	ADP
ejpam-5396	70	18	sheep	sheep	NOUN
ejpam-5396	70	19	and	and	CCONJ
ejpam-5396	70	20	goats	goat	NOUN
ejpam-5396	70	21	in	in	ADP
ejpam-5396	70	22	al	al	PROPN
ejpam-5396	70	23	-	-	PUNCT
ejpam-5396	70	24	baha	baha	PROPN
ejpam-5396	70	25	region	region	NOUN
ejpam-5396	70	26	of	of	ADP
ejpam-5396	70	27	saudi	saudi	PROPN
ejpam-5396	70	28	arabia	arabia	PROPN
ejpam-5396	70	29	with	with	ADP
ejpam-5396	70	30	cost	cost	NOUN
ejpam-5396	70	31	-	-	PUNCT
ejpam-5396	70	32	effective	effective	ADJ
ejpam-5396	70	33	strategies	strategy	NOUN
ejpam-5396	70	34	.	.	PUNCT
ejpam-5396	71	1	the	the	DET
ejpam-5396	71	2	research	research	NOUN
ejpam-5396	71	3	conducted	conduct	VERB
ejpam-5396	71	4	by	by	ADP
ejpam-5396	71	5	sayed	sayed	PROPN
ejpam-5396	71	6	saber	saber	PROPN
ejpam-5396	71	7	et	et	PROPN
ejpam-5396	71	8	al	al	PROPN
ejpam-5396	71	9	.	.	PROPN
ejpam-5396	71	10	investigated	investigate	VERB
ejpam-5396	71	11	critical	critical	ADJ
ejpam-5396	71	12	parameters	parameter	NOUN
ejpam-5396	71	13	that	that	PRON
ejpam-5396	71	14	impact	impact	VERB
ejpam-5396	71	15	the	the	DET
ejpam-5396	71	16	transmission	transmission	NOUN
ejpam-5396	71	17	of	of	ADP
ejpam-5396	71	18	pneumonia	pneumonia	NOUN
ejpam-5396	71	19	in	in	ADP
ejpam-5396	71	20	livestock	livestock	NOUN
ejpam-5396	71	21	.	.	PUNCT
ejpam-5396	72	1	they	they	PRON
ejpam-5396	72	2	provided	provide	VERB
ejpam-5396	72	3	evidence	evidence	NOUN
ejpam-5396	72	4	that	that	SCONJ
ejpam-5396	72	5	the	the	DET
ejpam-5396	72	6	implementation	implementation	NOUN
ejpam-5396	72	7	of	of	ADP
ejpam-5396	72	8	cost	cost	NOUN
ejpam-5396	72	9	-	-	PUNCT
ejpam-5396	72	10	effective	effective	ADJ
ejpam-5396	72	11	vaccination	vaccination	NOUN
ejpam-5396	72	12	and	and	CCONJ
ejpam-5396	72	13	treatment	treatment	NOUN
ejpam-5396	72	14	strategies	strategy	NOUN
ejpam-5396	72	15	led	lead	VERB
ejpam-5396	72	16	to	to	ADP
ejpam-5396	72	17	a	a	DET
ejpam-5396	72	18	substantial	substantial	ADJ
ejpam-5396	72	19	reduction	reduction	NOUN
ejpam-5396	72	20	in	in	ADP
ejpam-5396	72	21	disease	disease	NOUN
ejpam-5396	72	22	prevalence	prevalence	NOUN
ejpam-5396	72	23	.	.	PUNCT
ejpam-5396	73	1	furthermore	furthermore	ADV
ejpam-5396	73	2	,	,	PUNCT
ejpam-5396	73	3	the	the	DET
ejpam-5396	73	4	fractional	fractional	ADJ
ejpam-5396	73	5	models	model	NOUN
ejpam-5396	73	6	usually	usually	ADV
ejpam-5396	73	7	have	have	VERB
ejpam-5396	73	8	more	more	ADJ
ejpam-5396	73	9	accurate	accurate	ADJ
ejpam-5396	73	10	predictions	prediction	NOUN
ejpam-5396	73	11	compared	compare	VERB
ejpam-5396	73	12	to	to	ADP
ejpam-5396	73	13	the	the	DET
ejpam-5396	73	14	traditional	traditional	ADJ
ejpam-5396	73	15	integer	integer	NOUN
ejpam-5396	73	16	models	model	NOUN
ejpam-5396	73	17	.	.	PUNCT
ejpam-5396	74	1	in	in	ADP
ejpam-5396	74	2	2022	2022	NUM
ejpam-5396	74	3	,	,	PUNCT
ejpam-5396	74	4	kamaledin	kamaledin	ADJ
ejpam-5396	74	5	abodayeh	abodayeh	NOUN
ejpam-5396	74	6	et	et	PROPN
ejpam-5396	74	7	al	al	PROPN
ejpam-5396	74	8	.	.	PUNCT
ejpam-5396	75	1	[	[	X
ejpam-5396	75	2	1	1	X
ejpam-5396	75	3	]	]	PUNCT
ejpam-5396	75	4	discussed	discuss	VERB
ejpam-5396	75	5	the	the	DET
ejpam-5396	75	6	dynamical	dynamical	ADJ
ejpam-5396	75	7	and	and	CCONJ
ejpam-5396	75	8	numerical	numerical	ADJ
ejpam-5396	75	9	analysis	analysis	NOUN
ejpam-5396	75	10	of	of	ADP
ejpam-5396	75	11	a	a	DET
ejpam-5396	75	12	pneumonia	pneumonia	NOUN
ejpam-5396	75	13	model	model	NOUN
ejpam-5396	75	14	using	use	VERB
ejpam-5396	75	15	appropriate	appropriate	ADJ
ejpam-5396	75	16	numerical	numerical	ADJ
ejpam-5396	75	17	techniques	technique	NOUN
ejpam-5396	75	18	.	.	PUNCT
ejpam-5396	76	1	fractional	fractional	ADJ
ejpam-5396	76	2	epidemic	epidemic	NOUN
ejpam-5396	76	3	models	model	NOUN
ejpam-5396	76	4	provide	provide	VERB
ejpam-5396	76	5	various	various	ADJ
ejpam-5396	76	6	advantages	advantage	NOUN
ejpam-5396	76	7	,	,	PUNCT
ejpam-5396	76	8	such	such	ADJ
ejpam-5396	76	9	as	as	ADP
ejpam-5396	76	10	improved	improved	ADJ
ejpam-5396	76	11	accuracy	accuracy	NOUN
ejpam-5396	76	12	in	in	ADP
ejpam-5396	76	13	representing	represent	VERB
ejpam-5396	76	14	the	the	DET
ejpam-5396	76	15	memory	memory	NOUN
ejpam-5396	76	16	and	and	CCONJ
ejpam-5396	76	17	hereditary	hereditary	ADJ
ejpam-5396	76	18	properties	property	NOUN
ejpam-5396	76	19	of	of	ADP
ejpam-5396	76	20	disease	disease	NOUN
ejpam-5396	76	21	transmission	transmission	NOUN
ejpam-5396	76	22	.	.	PUNCT
ejpam-5396	77	1	they	they	PRON
ejpam-5396	77	2	offer	offer	VERB
ejpam-5396	77	3	improved	improved	ADJ
ejpam-5396	77	4	capacity	capacity	NOUN
ejpam-5396	77	5	to	to	PART
ejpam-5396	77	6	explain	explain	VERB
ejpam-5396	77	7	the	the	DET
ejpam-5396	77	8	complex	complex	ADJ
ejpam-5396	77	9	dynamics	dynamic	NOUN
ejpam-5396	77	10	of	of	ADP
ejpam-5396	77	11	disease	disease	NOUN
ejpam-5396	77	12	transmission	transmission	NOUN
ejpam-5396	77	13	over	over	ADP
ejpam-5396	77	14	time	time	NOUN
ejpam-5396	77	15	,	,	PUNCT
ejpam-5396	77	16	a	a	DET
ejpam-5396	77	17	facet	facet	NOUN
ejpam-5396	77	18	that	that	SCONJ
ejpam-5396	77	19	traditional	traditional	ADJ
ejpam-5396	77	20	integer	integer	NOUN
ejpam-5396	77	21	models	model	NOUN
ejpam-5396	77	22	may	may	AUX
ejpam-5396	77	23	neglect	neglect	VERB
ejpam-5396	77	24	.	.	PUNCT
ejpam-5396	78	1	this	this	DET
ejpam-5396	78	2	results	result	NOUN
ejpam-5396	78	3	in	in	ADP
ejpam-5396	78	4	heightened	heightened	ADJ
ejpam-5396	78	5	predictive	predictive	ADJ
ejpam-5396	78	6	accuracy	accuracy	NOUN
ejpam-5396	78	7	and	and	CCONJ
ejpam-5396	78	8	more	more	ADV
ejpam-5396	78	9	efficacious	efficacious	ADJ
ejpam-5396	78	10	intervention	intervention	NOUN
ejpam-5396	78	11	strategies	strategy	NOUN
ejpam-5396	78	12	.	.	PUNCT
ejpam-5396	79	1	there	there	PRON
ejpam-5396	79	2	is	be	VERB
ejpam-5396	79	3	also	also	ADV
ejpam-5396	79	4	substantial	substantial	ADJ
ejpam-5396	79	5	literature	literature	NOUN
ejpam-5396	79	6	dealing	deal	VERB
ejpam-5396	79	7	with	with	ADP
ejpam-5396	79	8	the	the	DET
ejpam-5396	79	9	mathematical	mathematical	ADJ
ejpam-5396	79	10	investigation	investigation	NOUN
ejpam-5396	79	11	of	of	ADP
ejpam-5396	79	12	a	a	DET
ejpam-5396	79	13	disease	disease	NOUN
ejpam-5396	79	14	model	model	NOUN
ejpam-5396	79	15	;	;	PUNCT
ejpam-5396	79	16	(	(	PUNCT
ejpam-5396	79	17	see	see	VERB
ejpam-5396	79	18	,	,	PUNCT
ejpam-5396	79	19	for	for	ADP
ejpam-5396	79	20	example	example	NOUN
ejpam-5396	79	21	,	,	PUNCT
ejpam-5396	79	22	but	but	CCONJ
ejpam-5396	79	23	not	not	PART
ejpam-5396	79	24	limited	limit	VERB
ejpam-5396	79	25	to	to	ADP
ejpam-5396	79	26	,	,	PUNCT
ejpam-5396	79	27	(	(	PUNCT
ejpam-5396	79	28	[	[	X
ejpam-5396	79	29	13	13	NUM
ejpam-5396	79	30	]	]	PUNCT
ejpam-5396	79	31	,	,	PUNCT
ejpam-5396	79	32	[	[	X
ejpam-5396	79	33	5	5	NUM
ejpam-5396	79	34	]	]	PUNCT
ejpam-5396	79	35	,	,	PUNCT
ejpam-5396	79	36	[	[	X
ejpam-5396	79	37	50	50	NUM
ejpam-5396	79	38	]	]	PUNCT
ejpam-5396	79	39	,	,	PUNCT
ejpam-5396	79	40	[	[	X
ejpam-5396	79	41	7	7	NUM
ejpam-5396	79	42	]	]	PUNCT
ejpam-5396	79	43	,	,	PUNCT
ejpam-5396	79	44	[	[	X
ejpam-5396	79	45	3	3	NUM
ejpam-5396	79	46	]	]	PUNCT
ejpam-5396	79	47	,	,	PUNCT
ejpam-5396	79	48	[	[	X
ejpam-5396	79	49	14	14	NUM
ejpam-5396	79	50	]	]	PUNCT
ejpam-5396	79	51	,	,	PUNCT
ejpam-5396	79	52	[	[	X
ejpam-5396	79	53	2	2	NUM
ejpam-5396	79	54	]	]	PUNCT
ejpam-5396	79	55	,	,	PUNCT
ejpam-5396	79	56	[	[	X
ejpam-5396	79	57	12	12	NUM
ejpam-5396	79	58	]	]	PUNCT
ejpam-5396	79	59	)	)	PUNCT
ejpam-5396	79	60	.	.	PUNCT
ejpam-5396	80	1	we	we	PRON
ejpam-5396	80	2	develop	develop	VERB
ejpam-5396	80	3	in	in	ADP
ejpam-5396	80	4	this	this	DET
ejpam-5396	80	5	research	research	NOUN
ejpam-5396	80	6	a	a	DET
ejpam-5396	80	7	fractional	fractional	ADJ
ejpam-5396	80	8	-	-	PUNCT
ejpam-5396	80	9	order	order	NOUN
ejpam-5396	80	10	model	model	NOUN
ejpam-5396	80	11	for	for	ADP
ejpam-5396	80	12	the	the	DET
ejpam-5396	80	13	presented	present	VERB
ejpam-5396	80	14	model	model	NOUN
ejpam-5396	80	15	in	in	ADP
ejpam-5396	80	16	[	[	X
ejpam-5396	80	17	1	1	NUM
ejpam-5396	80	18	]	]	PUNCT
ejpam-5396	80	19	to	to	PART
ejpam-5396	80	20	describe	describe	VERB
ejpam-5396	80	21	the	the	DET
ejpam-5396	80	22	dynamics	dynamic	NOUN
ejpam-5396	80	23	of	of	ADP
ejpam-5396	80	24	transmission	transmission	NOUN
ejpam-5396	80	25	for	for	ADP
ejpam-5396	80	26	pneumonia	pneumonia	NOUN
ejpam-5396	80	27	disease	disease	NOUN
ejpam-5396	80	28	.	.	PUNCT
ejpam-5396	81	1	more	more	ADV
ejpam-5396	81	2	precisely	precisely	ADV
ejpam-5396	81	3	,	,	PUNCT
ejpam-5396	81	4	for	for	ADP
ejpam-5396	81	5	any	any	DET
ejpam-5396	81	6	arbitrary	arbitrary	ADJ
ejpam-5396	81	7	time	time	NOUN
ejpam-5396	81	8	t	t	PROPN
ejpam-5396	81	9	,	,	PUNCT
ejpam-5396	81	10	a	a	DET
ejpam-5396	81	11	fractional	fractional	ADJ
ejpam-5396	81	12	-	-	PUNCT
ejpam-5396	81	13	order	order	NOUN
ejpam-5396	81	14	scir	scir	NOUN
ejpam-5396	81	15	model	model	NOUN
ejpam-5396	81	16	is	be	AUX
ejpam-5396	81	17	taken	take	VERB
ejpam-5396	81	18	into	into	ADP
ejpam-5396	81	19	consideration	consideration	NOUN
ejpam-5396	81	20	in	in	ADP
ejpam-5396	81	21	the	the	DET
ejpam-5396	81	22	context	context	NOUN
ejpam-5396	81	23	of	of	ADP
ejpam-5396	81	24	the	the	DET
ejpam-5396	81	25	caputo	caputo	PROPN
ejpam-5396	81	26	derivative	derivative	PROPN
ejpam-5396	81	27	dα	dα	PROPN
ejpam-5396	81	28	,	,	PUNCT
ejpam-5396	81	29	0	0	PUNCT
ejpam-5396	81	30	<	<	X
ejpam-5396	81	31	α	α	PROPN
ejpam-5396	81	32	≤	≤	NUM
ejpam-5396	81	33	1	1	NUM
ejpam-5396	81	34	,	,	PUNCT
ejpam-5396	81	35	and	and	CCONJ
ejpam-5396	81	36	is	be	AUX
ejpam-5396	81	37	provided	provide	VERB
ejpam-5396	81	38	by	by	ADP
ejpam-5396	81	39	:	:	PUNCT
ejpam-5396	81	40	dαs(t	dαs(t	ADJ
ejpam-5396	81	41	)	)	PUNCT
ejpam-5396	81	42	=	=	SYM
ejpam-5396	82	1	λ−	λ−	PROPN
ejpam-5396	82	2	δ(i(t	δ(i(t	PROPN
ejpam-5396	82	3	)	)	PUNCT
ejpam-5396	82	4	+	+	NUM
ejpam-5396	82	5	ωc(t	ωc(t	NOUN
ejpam-5396	82	6	)	)	PUNCT
ejpam-5396	82	7	)	)	PUNCT
ejpam-5396	83	1	n	n	CCONJ
ejpam-5396	83	2	s(t)−	s(t)−	PROPN
ejpam-5396	83	3	µs(t	µs(t	PROPN
ejpam-5396	83	4	)	)	PUNCT
ejpam-5396	83	5	+	+	NUM
ejpam-5396	83	6	ηr(t	ηr(t	NOUN
ejpam-5396	83	7	)	)	PUNCT
ejpam-5396	83	8	,	,	PUNCT
ejpam-5396	83	9	dαc(t	dαc(t	NOUN
ejpam-5396	83	10	)	)	PUNCT
ejpam-5396	83	11	=	=	PUNCT
ejpam-5396	83	12	δ(i(t	δ(i(t	PROPN
ejpam-5396	83	13	)	)	PUNCT
ejpam-5396	83	14	+	+	NUM
ejpam-5396	83	15	ωc(t	ωc(t	NOUN
ejpam-5396	83	16	)	)	PUNCT
ejpam-5396	83	17	)	)	PUNCT
ejpam-5396	84	1	n	n	CCONJ
ejpam-5396	84	2	θs(t)−	θs(t)−	PROPN
ejpam-5396	84	3	z1c(t	z1c(t	PROPN
ejpam-5396	84	4	)	)	PUNCT
ejpam-5396	84	5	,	,	PUNCT
ejpam-5396	84	6	dαi(t	dαi(t	PROPN
ejpam-5396	84	7	)	)	PUNCT
ejpam-5396	84	8	=	=	SYM
ejpam-5396	84	9	δ(i(t	δ(i(t	PROPN
ejpam-5396	84	10	)	)	PUNCT
ejpam-5396	84	11	+	+	NUM
ejpam-5396	84	12	ωc(t	ωc(t	NOUN
ejpam-5396	84	13	)	)	PUNCT
ejpam-5396	84	14	)	)	PUNCT
ejpam-5396	85	1	n	n	CCONJ
ejpam-5396	85	2	(	(	PUNCT
ejpam-5396	85	3	1−	1−	NUM
ejpam-5396	85	4	θ)s(t	θ)s(t	NOUN
ejpam-5396	85	5	)	)	PUNCT
ejpam-5396	85	6	+	+	CCONJ
ejpam-5396	85	7	πc(t)−	πc(t)−	PROPN
ejpam-5396	85	8	z2i(t	z2i(t	PROPN
ejpam-5396	85	9	)	)	PUNCT
ejpam-5396	85	10	,	,	PUNCT
ejpam-5396	85	11	dαr(t	dαr(t	PROPN
ejpam-5396	85	12	)	)	PUNCT
ejpam-5396	85	13	=	=	SYM
ejpam-5396	85	14	βc(t	βc(t	NOUN
ejpam-5396	85	15	)	)	PUNCT
ejpam-5396	86	1	+	+	CCONJ
ejpam-5396	86	2	τi(t)−	τi(t)−	PROPN
ejpam-5396	86	3	(	(	PUNCT
ejpam-5396	86	4	µ+	µ+	X
ejpam-5396	86	5	η)r(t	η)r(t	NOUN
ejpam-5396	86	6	)	)	PUNCT
ejpam-5396	86	7	,	,	PUNCT
ejpam-5396	86	8	(	(	PUNCT
ejpam-5396	86	9	1	1	X
ejpam-5396	86	10	)	)	PUNCT
ejpam-5396	86	11	with	with	ADP
ejpam-5396	86	12	the	the	DET
ejpam-5396	86	13	initial	initial	ADJ
ejpam-5396	86	14	conditions	condition	NOUN
ejpam-5396	86	15	s(0	s(0	PROPN
ejpam-5396	86	16	)	)	PUNCT
ejpam-5396	86	17	=	=	SYM
ejpam-5396	86	18	s0	s0	PROPN
ejpam-5396	86	19	,	,	PUNCT
ejpam-5396	86	20	c(0	c(0	NOUN
ejpam-5396	86	21	)	)	PUNCT
ejpam-5396	86	22	=	=	SYM
ejpam-5396	86	23	c0	c0	NOUN
ejpam-5396	86	24	,	,	PUNCT
ejpam-5396	86	25	i(0	i(0	PROPN
ejpam-5396	86	26	)	)	PUNCT
ejpam-5396	86	27	=	=	SYM
ejpam-5396	86	28	i0	i0	PROPN
ejpam-5396	86	29	,	,	PUNCT
ejpam-5396	86	30	and	and	CCONJ
ejpam-5396	86	31	r(0	r(0	PROPN
ejpam-5396	86	32	)	)	PUNCT
ejpam-5396	86	33	=	=	SYM
ejpam-5396	86	34	r0	r0	NOUN
ejpam-5396	86	35	.	.	PUNCT
ejpam-5396	87	1	here	here	ADV
ejpam-5396	87	2	,	,	PUNCT
ejpam-5396	87	3	the	the	DET
ejpam-5396	87	4	infection	infection	NOUN
ejpam-5396	87	5	force	force	NOUN
ejpam-5396	87	6	is	be	AUX
ejpam-5396	87	7	give	give	VERB
ejpam-5396	87	8	by	by	ADP
ejpam-5396	87	9	δ(i(t)+ωc(t	δ(i(t)+ωc(t	NOUN
ejpam-5396	87	10	)	)	PUNCT
ejpam-5396	87	11	)	)	PUNCT
ejpam-5396	88	1	n	n	X
ejpam-5396	88	2	.	.	PUNCT
ejpam-5396	89	1	the	the	DET
ejpam-5396	89	2	fractional	fractional	ADJ
ejpam-5396	89	3	-	-	PUNCT
ejpam-5396	89	4	order	order	NOUN
ejpam-5396	89	5	scir	scir	PROPN
ejpam-5396	89	6	model	model	NOUN
ejpam-5396	89	7	,	,	PUNCT
ejpam-5396	89	8	as	as	SCONJ
ejpam-5396	89	9	expressed	express	VERB
ejpam-5396	89	10	in	in	ADP
ejpam-5396	89	11	eq	eq	ADP
ejpam-5396	89	12	.	.	PUNCT
ejpam-5396	89	13	(	(	PUNCT
ejpam-5396	89	14	1	1	NUM
ejpam-5396	89	15	)	)	PUNCT
ejpam-5396	89	16	,	,	PUNCT
ejpam-5396	89	17	serves	serve	VERB
ejpam-5396	89	18	as	as	ADP
ejpam-5396	89	19	a	a	DET
ejpam-5396	89	20	mathematical	mathematical	ADJ
ejpam-5396	89	21	representation	representation	NOUN
ejpam-5396	89	22	tailored	tailor	VERB
ejpam-5396	89	23	to	to	PART
ejpam-5396	89	24	elucidate	elucidate	VERB
ejpam-5396	89	25	the	the	DET
ejpam-5396	89	26	dynamics	dynamic	NOUN
ejpam-5396	89	27	of	of	ADP
ejpam-5396	89	28	pneumonia	pneumonia	NOUN
ejpam-5396	89	29	transmission	transmission	NOUN
ejpam-5396	89	30	.	.	PUNCT
ejpam-5396	90	1	the	the	DET
ejpam-5396	90	2	model	model	NOUN
ejpam-5396	90	3	employs	employ	VERB
ejpam-5396	90	4	the	the	DET
ejpam-5396	90	5	caputo	caputo	PROPN
ejpam-5396	90	6	derivative	derivative	PROPN
ejpam-5396	90	7	dα	dα	NOUN
ejpam-5396	90	8	,	,	PUNCT
ejpam-5396	90	9	where	where	SCONJ
ejpam-5396	90	10	0	0	X
ejpam-5396	90	11	<	<	X
ejpam-5396	90	12	α	α	X
ejpam-5396	90	13	≤	≤	NUM
ejpam-5396	90	14	1	1	NUM
ejpam-5396	90	15	,	,	PUNCT
ejpam-5396	90	16	to	to	PART
ejpam-5396	90	17	incorporate	incorporate	VERB
ejpam-5396	90	18	memory	memory	NOUN
ejpam-5396	90	19	effects	effect	NOUN
ejpam-5396	90	20	in	in	ADP
ejpam-5396	90	21	the	the	DET
ejpam-5396	90	22	system	system	NOUN
ejpam-5396	90	23	dynamics	dynamic	NOUN
ejpam-5396	90	24	.	.	PUNCT
ejpam-5396	91	1	this	this	DET
ejpam-5396	91	2	approach	approach	NOUN
ejpam-5396	91	3	facilitates	facilitate	VERB
ejpam-5396	91	4	a	a	DET
ejpam-5396	91	5	more	more	ADV
ejpam-5396	91	6	precise	precise	ADJ
ejpam-5396	91	7	characterization	characterization	NOUN
ejpam-5396	91	8	of	of	ADP
ejpam-5396	91	9	biological	biological	ADJ
ejpam-5396	91	10	processes	process	NOUN
ejpam-5396	91	11	in	in	ADP
ejpam-5396	91	12	the	the	DET
ejpam-5396	91	13	real	real	ADJ
ejpam-5396	91	14	-	-	PUNCT
ejpam-5396	91	15	world	world	NOUN
ejpam-5396	91	16	,	,	PUNCT
ejpam-5396	91	17	frequently	frequently	ADV
ejpam-5396	91	18	exhibited	exhibit	VERB
ejpam-5396	91	19	by	by	ADP
ejpam-5396	91	20	fractional	fractional	ADJ
ejpam-5396	91	21	dynamics	dynamic	NOUN
ejpam-5396	91	22	.	.	PUNCT
ejpam-5396	92	1	fractional	fractional	ADJ
ejpam-5396	92	2	mathematical	mathematical	ADJ
ejpam-5396	92	3	modeling	modeling	NOUN
ejpam-5396	92	4	has	have	AUX
ejpam-5396	92	5	been	be	AUX
ejpam-5396	92	6	shown	show	VERB
ejpam-5396	92	7	to	to	PART
ejpam-5396	92	8	be	be	AUX
ejpam-5396	92	9	an	an	DET
ejpam-5396	92	10	effective	effective	ADJ
ejpam-5396	92	11	mathematical	mathematical	ADJ
ejpam-5396	92	12	tool	tool	NOUN
ejpam-5396	92	13	with	with	ADP
ejpam-5396	92	14	uses	use	NOUN
ejpam-5396	92	15	in	in	ADP
ejpam-5396	92	16	a	a	DET
ejpam-5396	92	17	variety	variety	NOUN
ejpam-5396	92	18	of	of	ADP
ejpam-5396	92	19	fields	field	NOUN
ejpam-5396	92	20	of	of	ADP
ejpam-5396	92	21	study	study	NOUN
ejpam-5396	92	22	(	(	PUNCT
ejpam-5396	92	23	see	see	VERB
ejpam-5396	92	24	,	,	PUNCT
ejpam-5396	92	25	for	for	ADP
ejpam-5396	92	26	example	example	NOUN
ejpam-5396	92	27	,	,	PUNCT
ejpam-5396	92	28	but	but	CCONJ
ejpam-5396	92	29	not	not	PART
ejpam-5396	92	30	limited	limit	VERB
ejpam-5396	92	31	to	to	ADP
ejpam-5396	92	32	,	,	PUNCT
ejpam-5396	92	33	(	(	PUNCT
ejpam-5396	92	34	[	[	X
ejpam-5396	92	35	4	4	NUM
ejpam-5396	92	36	]	]	PUNCT
ejpam-5396	92	37	,	,	PUNCT
ejpam-5396	92	38	[	[	X
ejpam-5396	92	39	8	8	NUM
ejpam-5396	92	40	]	]	PUNCT
ejpam-5396	92	41	,	,	PUNCT
ejpam-5396	92	42	[	[	X
ejpam-5396	92	43	10	10	NUM
ejpam-5396	92	44	]	]	PUNCT
ejpam-5396	92	45	,	,	PUNCT
ejpam-5396	93	1	[	[	X
ejpam-5396	93	2	11	11	NUM
ejpam-5396	93	3	]	]	PUNCT
ejpam-5396	93	4	,	,	PUNCT
ejpam-5396	93	5	[	[	X
ejpam-5396	93	6	48	48	NUM
ejpam-5396	93	7	]	]	PUNCT
ejpam-5396	93	8	,	,	PUNCT
ejpam-5396	94	1	[	[	X
ejpam-5396	94	2	9	9	NUM
ejpam-5396	94	3	]	]	PUNCT
ejpam-5396	94	4	,	,	PUNCT
ejpam-5396	94	5	[	[	X
ejpam-5396	94	6	51	51	NUM
ejpam-5396	94	7	]	]	PUNCT
ejpam-5396	94	8	,	,	PUNCT
ejpam-5396	94	9	[	[	X
ejpam-5396	94	10	57	57	NUM
ejpam-5396	94	11	]	]	PUNCT
ejpam-5396	94	12	,	,	PUNCT
ejpam-5396	94	13	[	[	X
ejpam-5396	94	14	6	6	NUM
ejpam-5396	94	15	]	]	PUNCT
ejpam-5396	94	16	)	)	PUNCT
ejpam-5396	94	17	.	.	PUNCT
ejpam-5396	95	1	in	in	ADP
ejpam-5396	95	2	eq	eq	ADP
ejpam-5396	95	3	.	.	PUNCT
ejpam-5396	96	1	(	(	PUNCT
ejpam-5396	96	2	1	1	NUM
ejpam-5396	96	3	)	)	PUNCT
ejpam-5396	96	4	,	,	PUNCT
ejpam-5396	96	5	s(t	s(t	PROPN
ejpam-5396	96	6	)	)	PUNCT
ejpam-5396	96	7	represents	represent	VERB
ejpam-5396	96	8	the	the	DET
ejpam-5396	96	9	susceptible	susceptible	ADJ
ejpam-5396	96	10	who	who	PRON
ejpam-5396	96	11	is	be	AUX
ejpam-5396	96	12	susceptible	susceptible	ADJ
ejpam-5396	96	13	to	to	ADP
ejpam-5396	96	14	infection	infection	NOUN
ejpam-5396	96	15	with	with	ADP
ejpam-5396	96	16	pneumonia	pneumonia	NOUN
ejpam-5396	96	17	.	.	PUNCT
ejpam-5396	97	1	c(t	c(t	PROPN
ejpam-5396	97	2	)	)	PUNCT
ejpam-5396	97	3	stands	stand	VERB
ejpam-5396	97	4	for	for	ADP
ejpam-5396	97	5	the	the	DET
ejpam-5396	97	6	individuals	individual	NOUN
ejpam-5396	97	7	who	who	PRON
ejpam-5396	97	8	carry	carry	VERB
ejpam-5396	97	9	pneumonia	pneumonia	NOUN
ejpam-5396	97	10	bacteria	bacteria	NOUN
ejpam-5396	97	11	and	and	CCONJ
ejpam-5396	97	12	can	can	AUX
ejpam-5396	97	13	transmit	transmit	VERB
ejpam-5396	97	14	the	the	DET
ejpam-5396	97	15	infection	infection	NOUN
ejpam-5396	97	16	.	.	PUNCT
ejpam-5396	98	1	i(t	i(t	NOUN
ejpam-5396	98	2	)	)	PUNCT
ejpam-5396	98	3	stands	stand	VERB
ejpam-5396	98	4	for	for	ADP
ejpam-5396	98	5	the	the	DET
ejpam-5396	98	6	infectious	infectious	ADJ
ejpam-5396	98	7	a.	a.	NOUN
ejpam-5396	98	8	alalyani	alalyani	PROPN
ejpam-5396	98	9	/	/	SYM
ejpam-5396	98	10	eur	eur	PROPN
ejpam-5396	98	11	.	.	PUNCT
ejpam-5396	99	1	j.	j.	PROPN
ejpam-5396	99	2	pure	pure	PROPN
ejpam-5396	99	3	appl	appl	PROPN
ejpam-5396	99	4	.	.	PROPN
ejpam-5396	99	5	math	math	PROPN
ejpam-5396	99	6	,	,	PUNCT
ejpam-5396	99	7	17	17	NUM
ejpam-5396	99	8	(	(	PUNCT
ejpam-5396	99	9	4	4	NUM
ejpam-5396	99	10	)	)	PUNCT
ejpam-5396	99	11	(	(	PUNCT
ejpam-5396	99	12	2024	2024	NUM
ejpam-5396	99	13	)	)	PUNCT
ejpam-5396	99	14	,	,	PUNCT
ejpam-5396	99	15	2763	2763	NUM
ejpam-5396	99	16	-	-	SYM
ejpam-5396	99	17	2799	2799	NUM
ejpam-5396	99	18	2766	2766	NUM
ejpam-5396	99	19	individuals	individual	NOUN
ejpam-5396	99	20	who	who	PRON
ejpam-5396	99	21	have	have	VERB
ejpam-5396	99	22	the	the	DET
ejpam-5396	99	23	potential	potential	NOUN
ejpam-5396	99	24	to	to	PART
ejpam-5396	99	25	transfer	transfer	VERB
ejpam-5396	99	26	the	the	DET
ejpam-5396	99	27	infection	infection	NOUN
ejpam-5396	99	28	to	to	ADP
ejpam-5396	99	29	the	the	DET
ejpam-5396	99	30	susceptible	susceptible	ADJ
ejpam-5396	99	31	;	;	PUNCT
ejpam-5396	99	32	and	and	CCONJ
ejpam-5396	99	33	r(t	r(t	NOUN
ejpam-5396	99	34	)	)	PUNCT
ejpam-5396	99	35	stands	stand	VERB
ejpam-5396	99	36	for	for	ADP
ejpam-5396	99	37	the	the	DET
ejpam-5396	99	38	individuals	individual	NOUN
ejpam-5396	99	39	who	who	PRON
ejpam-5396	99	40	received	receive	VERB
ejpam-5396	99	41	treatment	treatment	NOUN
ejpam-5396	99	42	for	for	ADP
ejpam-5396	99	43	pneumonia	pneumonia	NOUN
ejpam-5396	99	44	and	and	CCONJ
ejpam-5396	99	45	made	make	VERB
ejpam-5396	99	46	a	a	DET
ejpam-5396	99	47	recovery	recovery	NOUN
ejpam-5396	99	48	.	.	PUNCT
ejpam-5396	100	1	over	over	ADP
ejpam-5396	100	2	time	time	NOUN
ejpam-5396	100	3	,	,	PUNCT
ejpam-5396	100	4	susceptibility	susceptibility	NOUN
ejpam-5396	100	5	to	to	ADP
ejpam-5396	100	6	the	the	DET
ejpam-5396	100	7	disease	disease	NOUN
ejpam-5396	100	8	may	may	AUX
ejpam-5396	100	9	be	be	AUX
ejpam-5396	100	10	regained	regain	VERB
ejpam-5396	100	11	by	by	ADP
ejpam-5396	100	12	these	these	DET
ejpam-5396	100	13	individuals	individual	NOUN
ejpam-5396	100	14	,	,	PUNCT
ejpam-5396	100	15	contingent	contingent	ADJ
ejpam-5396	100	16	upon	upon	SCONJ
ejpam-5396	100	17	factors	factor	NOUN
ejpam-5396	100	18	such	such	ADJ
ejpam-5396	100	19	as	as	ADP
ejpam-5396	100	20	waning	wane	VERB
ejpam-5396	100	21	immunity	immunity	NOUN
ejpam-5396	100	22	.	.	PUNCT
ejpam-5396	101	1	λ	λ	NOUN
ejpam-5396	101	2	represents	represent	VERB
ejpam-5396	101	3	the	the	DET
ejpam-5396	101	4	per	per	ADP
ejpam-5396	101	5	capita	capita	X
ejpam-5396	101	6	recruitment	recruitment	NOUN
ejpam-5396	101	7	rate	rate	NOUN
ejpam-5396	101	8	of	of	ADP
ejpam-5396	101	9	new	new	ADJ
ejpam-5396	101	10	susceptible	susceptible	ADJ
ejpam-5396	101	11	individuals	individual	NOUN
ejpam-5396	101	12	into	into	ADP
ejpam-5396	101	13	the	the	DET
ejpam-5396	101	14	population	population	NOUN
ejpam-5396	101	15	,	,	PUNCT
ejpam-5396	101	16	which	which	PRON
ejpam-5396	101	17	may	may	AUX
ejpam-5396	101	18	occur	occur	VERB
ejpam-5396	101	19	through	through	ADP
ejpam-5396	101	20	processes	process	NOUN
ejpam-5396	101	21	such	such	ADJ
ejpam-5396	101	22	as	as	ADP
ejpam-5396	101	23	births	birth	NOUN
ejpam-5396	101	24	or	or	CCONJ
ejpam-5396	101	25	immigration	immigration	NOUN
ejpam-5396	101	26	.	.	PUNCT
ejpam-5396	102	1	δ	δ	PROPN
ejpam-5396	102	2	stands	stand	VERB
ejpam-5396	102	3	for	for	ADP
ejpam-5396	102	4	the	the	DET
ejpam-5396	102	5	transmission	transmission	NOUN
ejpam-5396	102	6	rate	rate	NOUN
ejpam-5396	102	7	of	of	ADP
ejpam-5396	102	8	pneumonia	pneumonia	NOUN
ejpam-5396	102	9	,	,	PUNCT
ejpam-5396	102	10	denoting	denote	VERB
ejpam-5396	102	11	the	the	DET
ejpam-5396	102	12	efficiency	efficiency	NOUN
ejpam-5396	102	13	with	with	ADP
ejpam-5396	102	14	which	which	PRON
ejpam-5396	102	15	the	the	DET
ejpam-5396	102	16	disease	disease	NOUN
ejpam-5396	102	17	spreads	spread	VERB
ejpam-5396	102	18	from	from	ADP
ejpam-5396	102	19	infectious	infectious	ADJ
ejpam-5396	102	20	and	and	CCONJ
ejpam-5396	102	21	carrier	carrier	NOUN
ejpam-5396	102	22	individuals	individual	NOUN
ejpam-5396	102	23	to	to	PART
ejpam-5396	102	24	susceptible	susceptible	ADJ
ejpam-5396	102	25	individuals	individual	NOUN
ejpam-5396	102	26	.	.	PUNCT
ejpam-5396	103	1	ω	ω	NOUN
ejpam-5396	103	2	indicates	indicate	VERB
ejpam-5396	103	3	the	the	DET
ejpam-5396	103	4	rate	rate	NOUN
ejpam-5396	103	5	of	of	ADP
ejpam-5396	103	6	treated	treat	VERB
ejpam-5396	103	7	individuals	individual	NOUN
ejpam-5396	103	8	who	who	PRON
ejpam-5396	103	9	had	have	VERB
ejpam-5396	103	10	vaccinations	vaccination	NOUN
ejpam-5396	103	11	.	.	PUNCT
ejpam-5396	104	1	µ	µ	NOUN
ejpam-5396	104	2	stands	stand	VERB
ejpam-5396	104	3	for	for	ADP
ejpam-5396	104	4	the	the	DET
ejpam-5396	104	5	per	per	X
ejpam-5396	104	6	capita	capita	X
ejpam-5396	104	7	natural	natural	ADJ
ejpam-5396	104	8	death	death	NOUN
ejpam-5396	104	9	rate	rate	NOUN
ejpam-5396	104	10	of	of	ADP
ejpam-5396	104	11	individuals	individual	NOUN
ejpam-5396	104	12	due	due	ADJ
ejpam-5396	104	13	to	to	ADP
ejpam-5396	104	14	non	non	ADJ
ejpam-5396	104	15	-	-	ADJ
ejpam-5396	104	16	pneumonia	pneumonia	NOUN
ejpam-5396	104	17	-	-	PUNCT
ejpam-5396	104	18	related	relate	VERB
ejpam-5396	104	19	causes	cause	NOUN
ejpam-5396	104	20	.	.	PUNCT
ejpam-5396	105	1	η	η	PROPN
ejpam-5396	105	2	represents	represent	VERB
ejpam-5396	105	3	the	the	DET
ejpam-5396	105	4	rate	rate	NOUN
ejpam-5396	105	5	of	of	ADP
ejpam-5396	105	6	immunity	immunity	NOUN
ejpam-5396	105	7	loss	loss	NOUN
ejpam-5396	105	8	in	in	ADP
ejpam-5396	105	9	recovered	recovered	ADJ
ejpam-5396	105	10	individuals	individual	NOUN
ejpam-5396	105	11	,	,	PUNCT
ejpam-5396	105	12	leading	lead	VERB
ejpam-5396	105	13	to	to	ADP
ejpam-5396	105	14	their	their	PRON
ejpam-5396	105	15	return	return	NOUN
ejpam-5396	105	16	to	to	ADP
ejpam-5396	105	17	the	the	DET
ejpam-5396	105	18	susceptible	susceptible	ADJ
ejpam-5396	105	19	class	class	NOUN
ejpam-5396	105	20	and	and	CCONJ
ejpam-5396	105	21	accounting	accounting	NOUN
ejpam-5396	105	22	for	for	ADP
ejpam-5396	105	23	the	the	DET
ejpam-5396	105	24	potential	potential	NOUN
ejpam-5396	105	25	of	of	ADP
ejpam-5396	105	26	reinfection	reinfection	NOUN
ejpam-5396	105	27	.	.	PUNCT
ejpam-5396	106	1	z1	z1	NOUN
ejpam-5396	106	2	=	=	SYM
ejpam-5396	106	3	µ+β+π	µ+β+π	NOUN
ejpam-5396	106	4	is	be	AUX
ejpam-5396	106	5	a	a	DET
ejpam-5396	106	6	combined	combine	VERB
ejpam-5396	106	7	rate	rate	NOUN
ejpam-5396	106	8	representing	represent	VERB
ejpam-5396	106	9	the	the	DET
ejpam-5396	106	10	sum	sum	NOUN
ejpam-5396	106	11	of	of	ADP
ejpam-5396	106	12	(	(	PUNCT
ejpam-5396	106	13	µ	µ	NOUN
ejpam-5396	106	14	)	)	PUNCT
ejpam-5396	106	15	,	,	PUNCT
ejpam-5396	106	16	the	the	DET
ejpam-5396	106	17	per	per	ADP
ejpam-5396	106	18	capita	capita	NOUN
ejpam-5396	106	19	carriers	carrier	NOUN
ejpam-5396	106	20	recovery	recovery	NOUN
ejpam-5396	106	21	rate	rate	NOUN
ejpam-5396	106	22	(	(	PUNCT
ejpam-5396	106	23	β	β	NOUN
ejpam-5396	106	24	)	)	PUNCT
ejpam-5396	106	25	,	,	PUNCT
ejpam-5396	106	26	and	and	CCONJ
ejpam-5396	106	27	the	the	DET
ejpam-5396	106	28	rate	rate	NOUN
ejpam-5396	106	29	of	of	ADP
ejpam-5396	106	30	developing	develop	VERB
ejpam-5396	106	31	symptoms	symptom	NOUN
ejpam-5396	106	32	by	by	ADP
ejpam-5396	106	33	carriers	carrier	NOUN
ejpam-5396	106	34	(	(	PUNCT
ejpam-5396	106	35	π	π	NOUN
ejpam-5396	106	36	)	)	PUNCT
ejpam-5396	106	37	.	.	PUNCT
ejpam-5396	107	1	z2	z2	PROPN
ejpam-5396	107	2	=	=	SYM
ejpam-5396	108	1	τ	τ	PROPN
ejpam-5396	108	2	+	+	NUM
ejpam-5396	108	3	µ	µ	X
ejpam-5396	108	4	+	+	X
ejpam-5396	108	5	σ	σ	PROPN
ejpam-5396	108	6	is	be	AUX
ejpam-5396	108	7	a	a	DET
ejpam-5396	108	8	combined	combined	ADJ
ejpam-5396	108	9	rate	rate	NOUN
ejpam-5396	108	10	representing	represent	VERB
ejpam-5396	108	11	the	the	DET
ejpam-5396	108	12	sum	sum	NOUN
ejpam-5396	108	13	of	of	ADP
ejpam-5396	108	14	(	(	PUNCT
ejpam-5396	108	15	µ	µ	NOUN
ejpam-5396	108	16	)	)	PUNCT
ejpam-5396	108	17	,	,	PUNCT
ejpam-5396	108	18	the	the	DET
ejpam-5396	108	19	per	per	ADP
ejpam-5396	108	20	capita	capita	X
ejpam-5396	108	21	recovery	recovery	NOUN
ejpam-5396	108	22	rate	rate	NOUN
ejpam-5396	108	23	of	of	ADP
ejpam-5396	108	24	infected	infect	VERB
ejpam-5396	108	25	individuals	individual	NOUN
ejpam-5396	108	26	by	by	ADP
ejpam-5396	108	27	pneumonia	pneumonia	NOUN
ejpam-5396	108	28	(	(	PUNCT
ejpam-5396	108	29	τ	τ	PROPN
ejpam-5396	108	30	)	)	PUNCT
ejpam-5396	108	31	,	,	PUNCT
ejpam-5396	108	32	and	and	CCONJ
ejpam-5396	108	33	the	the	DET
ejpam-5396	108	34	disease	disease	NOUN
ejpam-5396	108	35	-	-	PUNCT
ejpam-5396	108	36	induced	induce	VERB
ejpam-5396	108	37	death	death	NOUN
ejpam-5396	108	38	rate	rate	NOUN
ejpam-5396	108	39	and	and	CCONJ
ejpam-5396	108	40	birth	birth	NOUN
ejpam-5396	108	41	rate	rate	NOUN
ejpam-5396	108	42	of	of	ADP
ejpam-5396	108	43	the	the	DET
ejpam-5396	108	44	human	human	ADJ
ejpam-5396	108	45	population	population	NOUN
ejpam-5396	108	46	per	per	ADP
ejpam-5396	108	47	capita	capita	X
ejpam-5396	108	48	(	(	PUNCT
ejpam-5396	108	49	σ	σ	NOUN
ejpam-5396	108	50	)	)	PUNCT
ejpam-5396	108	51	.	.	PUNCT
ejpam-5396	109	1	θ	θ	PROPN
ejpam-5396	109	2	is	be	AUX
ejpam-5396	109	3	the	the	DET
ejpam-5396	109	4	rate	rate	NOUN
ejpam-5396	109	5	of	of	ADP
ejpam-5396	109	6	susceptible	susceptible	ADJ
ejpam-5396	109	7	individuals	individual	NOUN
ejpam-5396	109	8	who	who	PRON
ejpam-5396	109	9	,	,	PUNCT
ejpam-5396	109	10	following	follow	VERB
ejpam-5396	109	11	infection	infection	NOUN
ejpam-5396	109	12	,	,	PUNCT
ejpam-5396	109	13	become	become	VERB
ejpam-5396	109	14	carriers	carrier	NOUN
ejpam-5396	109	15	instead	instead	ADV
ejpam-5396	109	16	of	of	ADP
ejpam-5396	109	17	manifesting	manifest	VERB
ejpam-5396	109	18	symptoms	symptom	NOUN
ejpam-5396	109	19	.	.	PUNCT
ejpam-5396	110	1	the	the	DET
ejpam-5396	110	2	total	total	ADJ
ejpam-5396	110	3	population	population	NOUN
ejpam-5396	110	4	size	size	NOUN
ejpam-5396	110	5	,	,	PUNCT
ejpam-5396	110	6	often	often	ADV
ejpam-5396	110	7	assumed	assume	VERB
ejpam-5396	110	8	to	to	PART
ejpam-5396	110	9	be	be	AUX
ejpam-5396	110	10	constant	constant	ADJ
ejpam-5396	110	11	,	,	PUNCT
ejpam-5396	110	12	is	be	AUX
ejpam-5396	110	13	denoted	denote	VERB
ejpam-5396	110	14	by	by	ADP
ejpam-5396	110	15	n	n	PROPN
ejpam-5396	110	16	,	,	PUNCT
ejpam-5396	110	17	where	where	SCONJ
ejpam-5396	110	18	n	n	X
ejpam-5396	110	19	=	=	SYM
ejpam-5396	110	20	s(t	s(t	PROPN
ejpam-5396	110	21	)	)	PUNCT
ejpam-5396	111	1	+	+	X
ejpam-5396	111	2	c(t	c(t	PROPN
ejpam-5396	111	3	)	)	PUNCT
ejpam-5396	112	1	+	+	NUM
ejpam-5396	112	2	i(t	i(t	NOUN
ejpam-5396	112	3	)	)	PUNCT
ejpam-5396	113	1	+	+	NOUN
ejpam-5396	113	2	r(t	r(t	NOUN
ejpam-5396	113	3	)	)	PUNCT
ejpam-5396	113	4	.	.	PUNCT
ejpam-5396	114	1	we	we	PRON
ejpam-5396	114	2	study	study	VERB
ejpam-5396	114	3	the	the	DET
ejpam-5396	114	4	local	local	ADJ
ejpam-5396	114	5	and	and	CCONJ
ejpam-5396	114	6	global	global	ADJ
ejpam-5396	114	7	stability	stability	NOUN
ejpam-5396	114	8	of	of	ADP
ejpam-5396	114	9	steady	steady	ADJ
ejpam-5396	114	10	states	state	NOUN
ejpam-5396	114	11	.	.	PUNCT
ejpam-5396	115	1	we	we	PRON
ejpam-5396	115	2	derive	derive	VERB
ejpam-5396	115	3	the	the	DET
ejpam-5396	115	4	fundamental	fundamental	ADJ
ejpam-5396	115	5	reproduction	reproduction	NOUN
ejpam-5396	115	6	threshold	threshold	NOUN
ejpam-5396	115	7	parameter	parameter	NOUN
ejpam-5396	115	8	to	to	PART
ejpam-5396	115	9	show	show	VERB
ejpam-5396	115	10	that	that	SCONJ
ejpam-5396	115	11	the	the	DET
ejpam-5396	115	12	disease	disease	NOUN
ejpam-5396	115	13	-	-	PUNCT
ejpam-5396	115	14	free	free	ADJ
ejpam-5396	115	15	steady	steady	ADJ
ejpam-5396	115	16	state	state	NOUN
ejpam-5396	115	17	is	be	AUX
ejpam-5396	115	18	locally	locally	ADV
ejpam-5396	115	19	and	and	CCONJ
ejpam-5396	115	20	globally	globally	ADV
ejpam-5396	115	21	asymptotically	asymptotically	ADV
ejpam-5396	115	22	stable	stable	ADJ
ejpam-5396	115	23	when	when	SCONJ
ejpam-5396	115	24	r0	r0	NOUN
ejpam-5396	115	25	<	<	X
ejpam-5396	115	26	1	1	NUM
ejpam-5396	115	27	.	.	PUNCT
ejpam-5396	116	1	however	however	ADV
ejpam-5396	116	2	,	,	PUNCT
ejpam-5396	116	3	a	a	DET
ejpam-5396	116	4	positive	positive	ADJ
ejpam-5396	116	5	(	(	PUNCT
ejpam-5396	116	6	endemic	endemic	ADJ
ejpam-5396	116	7	)	)	PUNCT
ejpam-5396	116	8	steady	steady	ADJ
ejpam-5396	116	9	state	state	NOUN
ejpam-5396	116	10	that	that	PRON
ejpam-5396	116	11	is	be	AUX
ejpam-5396	116	12	both	both	CCONJ
ejpam-5396	116	13	locally	locally	ADV
ejpam-5396	116	14	and	and	CCONJ
ejpam-5396	116	15	globally	globally	ADV
ejpam-5396	116	16	asymptotically	asymptotically	ADV
ejpam-5396	116	17	stable	stable	ADJ
ejpam-5396	116	18	exists	exist	VERB
ejpam-5396	116	19	when	when	SCONJ
ejpam-5396	116	20	r0	r0	NOUN
ejpam-5396	116	21	>	>	X
ejpam-5396	116	22	1	1	X
ejpam-5396	116	23	.	.	PUNCT
ejpam-5396	116	24	to	to	PART
ejpam-5396	116	25	obtain	obtain	VERB
ejpam-5396	116	26	the	the	DET
ejpam-5396	116	27	approximate	approximate	ADJ
ejpam-5396	116	28	solution	solution	NOUN
ejpam-5396	116	29	and	and	CCONJ
ejpam-5396	116	30	verify	verify	VERB
ejpam-5396	116	31	the	the	DET
ejpam-5396	116	32	theoretical	theoretical	ADJ
ejpam-5396	116	33	analysis	analysis	NOUN
ejpam-5396	116	34	of	of	ADP
ejpam-5396	116	35	the	the	DET
ejpam-5396	116	36	fractional	fractional	ADJ
ejpam-5396	116	37	-	-	PUNCT
ejpam-5396	116	38	order	order	NOUN
ejpam-5396	116	39	scir	scir	PROPN
ejpam-5396	116	40	model	model	NOUN
ejpam-5396	116	41	,	,	PUNCT
ejpam-5396	116	42	we	we	PRON
ejpam-5396	116	43	have	have	AUX
ejpam-5396	116	44	used	use	VERB
ejpam-5396	116	45	numerical	numerical	ADJ
ejpam-5396	116	46	methods	method	NOUN
ejpam-5396	116	47	including	include	VERB
ejpam-5396	116	48	the	the	DET
ejpam-5396	116	49	adams	adams	PROPN
ejpam-5396	116	50	-	-	PUNCT
ejpam-5396	116	51	bashforth	bashforth	PROPN
ejpam-5396	116	52	-	-	PUNCT
ejpam-5396	116	53	moulton	moulton	PROPN
ejpam-5396	116	54	method	method	NOUN
ejpam-5396	116	55	(	(	PUNCT
ejpam-5396	116	56	abmm	abmm	PROPN
ejpam-5396	116	57	)	)	PUNCT
ejpam-5396	116	58	,	,	PUNCT
ejpam-5396	116	59	the	the	DET
ejpam-5396	116	60	generalized	generalize	VERB
ejpam-5396	116	61	euler	euler	NOUN
ejpam-5396	116	62	method	method	NOUN
ejpam-5396	116	63	(	(	PUNCT
ejpam-5396	116	64	gem	gem	NOUN
ejpam-5396	116	65	)	)	PUNCT
ejpam-5396	116	66	,	,	PUNCT
ejpam-5396	116	67	the	the	DET
ejpam-5396	116	68	generalized	generalize	VERB
ejpam-5396	116	69	runge	runge	NOUN
ejpam-5396	116	70	-	-	PUNCT
ejpam-5396	116	71	kutta	kutta	NOUN
ejpam-5396	116	72	method	method	NOUN
ejpam-5396	116	73	(	(	PUNCT
ejpam-5396	116	74	grkm	grkm	NOUN
ejpam-5396	116	75	)	)	PUNCT
ejpam-5396	116	76	,	,	PUNCT
ejpam-5396	116	77	and	and	CCONJ
ejpam-5396	116	78	the	the	DET
ejpam-5396	116	79	multistep	multistep	ADJ
ejpam-5396	116	80	generalized	generalize	VERB
ejpam-5396	116	81	differential	differential	ADJ
ejpam-5396	116	82	transform	transform	NOUN
ejpam-5396	116	83	method	method	NOUN
ejpam-5396	116	84	(	(	PUNCT
ejpam-5396	116	85	msgdtm	msgdtm	NOUN
ejpam-5396	116	86	)	)	PUNCT
ejpam-5396	116	87	.	.	PUNCT
ejpam-5396	117	1	the	the	DET
ejpam-5396	117	2	paper	paper	NOUN
ejpam-5396	117	3	is	be	AUX
ejpam-5396	117	4	structured	structure	VERB
ejpam-5396	117	5	as	as	SCONJ
ejpam-5396	117	6	follows	follow	VERB
ejpam-5396	117	7	:	:	PUNCT
ejpam-5396	117	8	section	section	NOUN
ejpam-5396	117	9	2	2	NUM
ejpam-5396	117	10	discusses	discuss	VERB
ejpam-5396	117	11	the	the	DET
ejpam-5396	117	12	properties	property	NOUN
ejpam-5396	117	13	of	of	ADP
ejpam-5396	117	14	the	the	DET
ejpam-5396	117	15	model	model	NOUN
ejpam-5396	117	16	.	.	PUNCT
ejpam-5396	118	1	section	section	NOUN
ejpam-5396	118	2	3	3	NUM
ejpam-5396	118	3	investigates	investigate	VERB
ejpam-5396	118	4	the	the	DET
ejpam-5396	118	5	stability	stability	NOUN
ejpam-5396	118	6	analysis	analysis	NOUN
ejpam-5396	118	7	of	of	ADP
ejpam-5396	118	8	the	the	DET
ejpam-5396	118	9	model	model	NOUN
ejpam-5396	118	10	.	.	PUNCT
ejpam-5396	119	1	section	section	NOUN
ejpam-5396	119	2	4	4	NUM
ejpam-5396	119	3	explains	explain	VERB
ejpam-5396	119	4	the	the	DET
ejpam-5396	119	5	numerical	numerical	ADJ
ejpam-5396	119	6	computational	computational	ADJ
ejpam-5396	119	7	methods	method	NOUN
ejpam-5396	119	8	of	of	ADP
ejpam-5396	119	9	solution	solution	NOUN
ejpam-5396	119	10	.	.	PUNCT
ejpam-5396	120	1	sections	section	NOUN
ejpam-5396	120	2	5	5	NUM
ejpam-5396	120	3	,	,	PUNCT
ejpam-5396	120	4	6	6	NUM
ejpam-5396	120	5	,	,	PUNCT
ejpam-5396	120	6	and	and	CCONJ
ejpam-5396	120	7	7	7	NUM
ejpam-5396	120	8	present	present	VERB
ejpam-5396	120	9	the	the	DET
ejpam-5396	120	10	numerical	numerical	ADJ
ejpam-5396	120	11	simulations	simulation	NOUN
ejpam-5396	120	12	and	and	CCONJ
ejpam-5396	120	13	results	result	NOUN
ejpam-5396	120	14	,	,	PUNCT
ejpam-5396	120	15	discussion	discussion	NOUN
ejpam-5396	120	16	of	of	ADP
ejpam-5396	120	17	the	the	DET
ejpam-5396	120	18	results	result	NOUN
ejpam-5396	120	19	,	,	PUNCT
ejpam-5396	120	20	and	and	CCONJ
ejpam-5396	120	21	conclusion	conclusion	NOUN
ejpam-5396	120	22	.	.	PUNCT
ejpam-5396	121	1	2	2	X
ejpam-5396	121	2	.	.	X
ejpam-5396	121	3	properties	property	NOUN
ejpam-5396	121	4	of	of	ADP
ejpam-5396	121	5	the	the	DET
ejpam-5396	121	6	model	model	NOUN
ejpam-5396	121	7	let	let	VERB
ejpam-5396	121	8	r+	r+	NOUN
ejpam-5396	121	9	be	be	AUX
ejpam-5396	121	10	the	the	DET
ejpam-5396	121	11	set	set	NOUN
ejpam-5396	121	12	of	of	ADP
ejpam-5396	121	13	all	all	DET
ejpam-5396	121	14	nonnegative	nonnegative	ADJ
ejpam-5396	121	15	real	real	ADJ
ejpam-5396	121	16	numbers	number	NOUN
ejpam-5396	121	17	and	and	CCONJ
ejpam-5396	121	18	assume	assume	VERB
ejpam-5396	121	19	that	that	SCONJ
ejpam-5396	121	20	ω+	ω+	NUM
ejpam-5396	121	21	=	=	SYM
ejpam-5396	121	22	{	{	PUNCT
ejpam-5396	121	23	(	(	PUNCT
ejpam-5396	121	24	s	s	X
ejpam-5396	121	25	,	,	PUNCT
ejpam-5396	121	26	c	c	X
ejpam-5396	121	27	,	,	PUNCT
ejpam-5396	121	28	i	i	PRON
ejpam-5396	121	29	,	,	PUNCT
ejpam-5396	121	30	r	r	NOUN
ejpam-5396	121	31	)	)	PUNCT
ejpam-5396	121	32	∈	∈	NOUN
ejpam-5396	121	33	r4	r4	NOUN
ejpam-5396	121	34	+	+	CCONJ
ejpam-5396	121	35	:	:	PUNCT
ejpam-5396	121	36	s	s	X
ejpam-5396	121	37	≥	≥	NOUN
ejpam-5396	121	38	0	0	NUM
ejpam-5396	121	39	,	,	PUNCT
ejpam-5396	121	40	c	c	X
ejpam-5396	121	41	≥	≥	NUM
ejpam-5396	121	42	0	0	NUM
ejpam-5396	121	43	,	,	PUNCT
ejpam-5396	121	44	i	i	PRON
ejpam-5396	121	45	≥	≥	VERB
ejpam-5396	121	46	0	0	NUM
ejpam-5396	121	47	,	,	PUNCT
ejpam-5396	121	48	r	r	NOUN
ejpam-5396	121	49	≥	≥	NOUN
ejpam-5396	121	50	0	0	NUM
ejpam-5396	121	51	,	,	PUNCT
ejpam-5396	121	52	max	max	PROPN
ejpam-5396	121	53	(	(	PUNCT
ejpam-5396	121	54	|s|	|s|	PROPN
ejpam-5396	121	55	,	,	PUNCT
ejpam-5396	121	56	|c|	|c|	PROPN
ejpam-5396	121	57	,	,	PUNCT
ejpam-5396	121	58	|i|	|i|	PROPN
ejpam-5396	121	59	,	,	PUNCT
ejpam-5396	121	60	|r|	|r|	NOUN
ejpam-5396	121	61	)	)	PUNCT
ejpam-5396	121	62	≤	≤	NOUN
ejpam-5396	121	63	n	n	CCONJ
ejpam-5396	121	64	}	}	PUNCT
ejpam-5396	121	65	.	.	PUNCT
ejpam-5396	122	1	theorem	theorem	ADJ
ejpam-5396	122	2	1	1	NUM
ejpam-5396	122	3	(	(	PUNCT
ejpam-5396	122	4	[	[	X
ejpam-5396	122	5	13	13	NUM
ejpam-5396	122	6	]	]	NUM
ejpam-5396	122	7	)	)	PUNCT
ejpam-5396	122	8	.	.	PUNCT
ejpam-5396	123	1	if	if	SCONJ
ejpam-5396	123	2	the	the	DET
ejpam-5396	123	3	starting	start	VERB
ejpam-5396	123	4	condition	condition	NOUN
ejpam-5396	123	5	γ0	γ0	NOUN
ejpam-5396	123	6	=	=	SYM
ejpam-5396	123	7	(	(	PUNCT
ejpam-5396	123	8	s(0	s(0	PROPN
ejpam-5396	123	9	)	)	PUNCT
ejpam-5396	123	10	,	,	PUNCT
ejpam-5396	123	11	c(0	c(0	NOUN
ejpam-5396	123	12	)	)	PUNCT
ejpam-5396	123	13	,	,	PUNCT
ejpam-5396	123	14	i(0	i(0	PROPN
ejpam-5396	123	15	)	)	PUNCT
ejpam-5396	123	16	,	,	PUNCT
ejpam-5396	123	17	r(0	r(0	PROPN
ejpam-5396	123	18	)	)	PUNCT
ejpam-5396	123	19	)	)	PUNCT
ejpam-5396	124	1	∈	∈	PROPN
ejpam-5396	124	2	ω	ω	NOUN
ejpam-5396	124	3	is	be	AUX
ejpam-5396	124	4	satisfied	satisfied	ADJ
ejpam-5396	124	5	,	,	PUNCT
ejpam-5396	124	6	then	then	ADV
ejpam-5396	124	7	the	the	DET
ejpam-5396	124	8	solution	solution	NOUN
ejpam-5396	124	9	γ	γ	X
ejpam-5396	124	10	=	=	SYM
ejpam-5396	124	11	(	(	PUNCT
ejpam-5396	124	12	s(t	s(t	PROPN
ejpam-5396	124	13	)	)	PUNCT
ejpam-5396	124	14	,	,	PUNCT
ejpam-5396	124	15	c(t	c(t	PROPN
ejpam-5396	124	16	)	)	PUNCT
ejpam-5396	124	17	,	,	PUNCT
ejpam-5396	124	18	i(t	i(t	PROPN
ejpam-5396	124	19	)	)	PUNCT
ejpam-5396	124	20	,	,	PUNCT
ejpam-5396	124	21	r(t	r(t	NOUN
ejpam-5396	124	22	)	)	PUNCT
ejpam-5396	124	23	)	)	PUNCT
ejpam-5396	125	1	∈	∈	PROPN
ejpam-5396	125	2	ω	ω	NUM
ejpam-5396	125	3	to	to	ADP
ejpam-5396	125	4	the	the	DET
ejpam-5396	125	5	model	model	NOUN
ejpam-5396	125	6	(	(	PUNCT
ejpam-5396	125	7	1	1	X
ejpam-5396	125	8	)	)	PUNCT
ejpam-5396	125	9	is	be	AUX
ejpam-5396	125	10	the	the	DET
ejpam-5396	125	11	only	only	ADJ
ejpam-5396	125	12	one	one	NUM
ejpam-5396	125	13	that	that	PRON
ejpam-5396	125	14	can	can	AUX
ejpam-5396	125	15	exist	exist	VERB
ejpam-5396	125	16	for	for	ADP
ejpam-5396	125	17	t	t	PROPN
ejpam-5396	125	18	≥	≥	NOUN
ejpam-5396	125	19	0	0	NUM
ejpam-5396	125	20	.	.	PUNCT
ejpam-5396	125	21	a.	a.	PROPN
ejpam-5396	125	22	alalyani	alalyani	PROPN
ejpam-5396	125	23	/	/	SYM
ejpam-5396	125	24	eur	eur	PROPN
ejpam-5396	125	25	.	.	PUNCT
ejpam-5396	126	1	j.	j.	PROPN
ejpam-5396	126	2	pure	pure	PROPN
ejpam-5396	126	3	appl	appl	PROPN
ejpam-5396	126	4	.	.	PROPN
ejpam-5396	126	5	math	math	PROPN
ejpam-5396	126	6	,	,	PUNCT
ejpam-5396	126	7	17	17	NUM
ejpam-5396	126	8	(	(	PUNCT
ejpam-5396	126	9	4	4	NUM
ejpam-5396	126	10	)	)	PUNCT
ejpam-5396	126	11	(	(	PUNCT
ejpam-5396	126	12	2024	2024	NUM
ejpam-5396	126	13	)	)	PUNCT
ejpam-5396	126	14	,	,	PUNCT
ejpam-5396	126	15	2763	2763	NUM
ejpam-5396	126	16	-	-	SYM
ejpam-5396	126	17	2799	2799	NUM
ejpam-5396	126	18	2767	2767	NUM
ejpam-5396	126	19	proof	proof	NOUN
ejpam-5396	126	20	.	.	PUNCT
ejpam-5396	127	1	take	take	VERB
ejpam-5396	127	2	t1(γ	t1(γ	ADV
ejpam-5396	127	3	)	)	PUNCT
ejpam-5396	127	4	=	=	SYM
ejpam-5396	127	5	λ−	λ−	PROPN
ejpam-5396	127	6	δi(t)s(t	δi(t)s(t	PROPN
ejpam-5396	127	7	)	)	PUNCT
ejpam-5396	128	1	n	n	CCONJ
ejpam-5396	129	1	−	−	PROPN
ejpam-5396	129	2	δωc(t)s(t	δωc(t)s(t	PROPN
ejpam-5396	129	3	)	)	PUNCT
ejpam-5396	129	4	n	n	CCONJ
ejpam-5396	129	5	−	−	PROPN
ejpam-5396	129	6	µs(t	µs(t	PUNCT
ejpam-5396	129	7	)	)	PUNCT
ejpam-5396	129	8	+	+	CCONJ
ejpam-5396	129	9	δr(t	δr(t	NOUN
ejpam-5396	129	10	)	)	PUNCT
ejpam-5396	129	11	,	,	PUNCT
ejpam-5396	129	12	t2(γ	t2(γ	NUM
ejpam-5396	129	13	)	)	PUNCT
ejpam-5396	129	14	=	=	SYM
ejpam-5396	129	15	δθi(t)s(t	δθi(t)s(t	PROPN
ejpam-5396	129	16	)	)	PUNCT
ejpam-5396	129	17	n	n	NOUN
ejpam-5396	129	18	+	+	CCONJ
ejpam-5396	129	19	δωθc(t)s(t	δωθc(t)s(t	NOUN
ejpam-5396	129	20	)	)	PUNCT
ejpam-5396	129	21	n	n	CCONJ
ejpam-5396	129	22	−	−	PROPN
ejpam-5396	129	23	z1c(t	z1c(t	PROPN
ejpam-5396	129	24	)	)	PUNCT
ejpam-5396	129	25	,	,	PUNCT
ejpam-5396	129	26	t3(γ	t3(γ	X
ejpam-5396	129	27	)	)	PUNCT
ejpam-5396	129	28	=	=	SYM
ejpam-5396	129	29	δ(i(t	δ(i(t	PROPN
ejpam-5396	129	30	)	)	PUNCT
ejpam-5396	129	31	+	+	NUM
ejpam-5396	129	32	ωc(t	ωc(t	NOUN
ejpam-5396	129	33	)	)	PUNCT
ejpam-5396	129	34	)	)	PUNCT
ejpam-5396	130	1	n	n	CCONJ
ejpam-5396	130	2	(	(	PUNCT
ejpam-5396	130	3	1−	1−	NUM
ejpam-5396	130	4	θ)s(t	θ)s(t	NOUN
ejpam-5396	130	5	)	)	PUNCT
ejpam-5396	130	6	+	+	CCONJ
ejpam-5396	130	7	πc(t)−	πc(t)−	PROPN
ejpam-5396	130	8	z2i(t	z2i(t	PROPN
ejpam-5396	130	9	)	)	PUNCT
ejpam-5396	130	10	,	,	PUNCT
ejpam-5396	130	11	t4(γ	t4(γ	NUM
ejpam-5396	130	12	)	)	PUNCT
ejpam-5396	130	13	=	=	SYM
ejpam-5396	130	14	βc(t	βc(t	NOUN
ejpam-5396	130	15	)	)	PUNCT
ejpam-5396	131	1	+	+	CCONJ
ejpam-5396	131	2	τi(t)−	τi(t)−	PROPN
ejpam-5396	131	3	(	(	PUNCT
ejpam-5396	131	4	µ+	µ+	X
ejpam-5396	131	5	η)r(t	η)r(t	NOUN
ejpam-5396	131	6	)	)	PUNCT
ejpam-5396	131	7	.	.	PUNCT
ejpam-5396	132	1	inputting	inputte	VERB
ejpam-5396	132	2	the	the	DET
ejpam-5396	132	3	values	value	NOUN
ejpam-5396	132	4	γ	γ	X
ejpam-5396	132	5	,	,	PUNCT
ejpam-5396	132	6	γ	γ	PROPN
ejpam-5396	132	7	∈	∈	PROPN
ejpam-5396	132	8	ω	ω	PROPN
ejpam-5396	132	9	,	,	PUNCT
ejpam-5396	132	10	with	with	ADP
ejpam-5396	132	11	|	|	ADV
ejpam-5396	132	12	δ(i(t)+ωc(t	δ(i(t)+ωc(t	NOUN
ejpam-5396	132	13	)	)	PUNCT
ejpam-5396	132	14	)	)	PUNCT
ejpam-5396	133	1	n	n	CCONJ
ejpam-5396	133	2	|	|	ADV
ejpam-5396	133	3	≤	≤	PUNCT
ejpam-5396	133	4	k	k	NOUN
ejpam-5396	133	5	,	,	PUNCT
ejpam-5396	133	6	yields	yield	VERB
ejpam-5396	133	7	the	the	DET
ejpam-5396	133	8	following	following	NOUN
ejpam-5396	133	9	:	:	PUNCT
ejpam-5396	133	10	∥t(γ)−	∥t(γ)−	ADV
ejpam-5396	133	11	t(γ)∥	t(γ)∥	NOUN
ejpam-5396	133	12	=	=	PUNCT
ejpam-5396	133	13	|t1(γ)−	|t1(γ)−	PROPN
ejpam-5396	133	14	t1(γ)|+	t1(γ)|+	PROPN
ejpam-5396	133	15	|t2(γ)−	|t2(γ)−	PUNCT
ejpam-5396	134	1	t2(γ)|+	t2(γ)|+	PROPN
ejpam-5396	134	2	|t3(γ)−	|t3(γ)−	PROPN
ejpam-5396	135	1	t3(γ)|+	t3(γ)|+	PRON
ejpam-5396	135	2	|t4(x)−	|t4(x)−	NOUN
ejpam-5396	135	3	t4(x)|	t4(x)|	PROPN
ejpam-5396	135	4	≤	≤	PROPN
ejpam-5396	135	5	(	(	PUNCT
ejpam-5396	135	6	3k	3k	X
ejpam-5396	135	7	+	+	CCONJ
ejpam-5396	135	8	µ−kθ)|s	µ−kθ)|s	NUM
ejpam-5396	135	9	−	−	PROPN
ejpam-5396	136	1	s|+	s|+	NOUN
ejpam-5396	136	2	(	(	PUNCT
ejpam-5396	136	3	z1	z1	NOUN
ejpam-5396	136	4	+	+	NUM
ejpam-5396	136	5	β	β	X
ejpam-5396	136	6	+	+	CCONJ
ejpam-5396	136	7	π)|c	π)|c	PROPN
ejpam-5396	136	8	−	−	PROPN
ejpam-5396	136	9	c|	c|	PROPN
ejpam-5396	136	10	+	+	CCONJ
ejpam-5396	136	11	(	(	PUNCT
ejpam-5396	136	12	τ	τ	X
ejpam-5396	136	13	+	+	PROPN
ejpam-5396	136	14	z2)|i	z2)|i	NOUN
ejpam-5396	136	15	−	−	NOUN
ejpam-5396	136	16	i|+	i|+	PROPN
ejpam-5396	136	17	(	(	PUNCT
ejpam-5396	136	18	δ	δ	NOUN
ejpam-5396	136	19	+	+	CCONJ
ejpam-5396	136	20	µ+	µ+	PROPN
ejpam-5396	136	21	η)|r−r|	η)|r−r|	PROPN
ejpam-5396	136	22	≤	≤	NUM
ejpam-5396	136	23	γ|x	γ|x	X
ejpam-5396	137	1	−x|	−x|	NOUN
ejpam-5396	137	2	,	,	PUNCT
ejpam-5396	137	3	where	where	SCONJ
ejpam-5396	137	4	γ	γ	PROPN
ejpam-5396	137	5	=	=	SYM
ejpam-5396	137	6	max	max	PROPN
ejpam-5396	137	7	{	{	PUNCT
ejpam-5396	137	8	(	(	PUNCT
ejpam-5396	137	9	2δ(1	2δ(1	NUM
ejpam-5396	137	10	+	+	X
ejpam-5396	137	11	ω	ω	NUM
ejpam-5396	137	12	)	)	PUNCT
ejpam-5396	137	13	+	+	NUM
ejpam-5396	137	14	β	β	X
ejpam-5396	137	15	+	+	ADJ
ejpam-5396	137	16	z1	z1	NOUN
ejpam-5396	137	17	)	)	PUNCT
ejpam-5396	137	18	,	,	PUNCT
ejpam-5396	137	19	(	(	PUNCT
ejpam-5396	137	20	2δω	2δω	NOUN
ejpam-5396	137	21	+	+	X
ejpam-5396	137	22	π	π	PROPN
ejpam-5396	137	23	+	+	X
ejpam-5396	137	24	µ	µ	NOUN
ejpam-5396	137	25	)	)	PUNCT
ejpam-5396	137	26	,	,	PUNCT
ejpam-5396	137	27	(	(	PUNCT
ejpam-5396	137	28	2δ	2δ	NUM
ejpam-5396	137	29	+	+	CCONJ
ejpam-5396	137	30	τ	τ	PROPN
ejpam-5396	137	31	+	+	SYM
ejpam-5396	137	32	z2	z2	PROPN
ejpam-5396	137	33	)	)	PUNCT
ejpam-5396	137	34	,	,	PUNCT
ejpam-5396	137	35	(	(	PUNCT
ejpam-5396	137	36	δ	δ	PROPN
ejpam-5396	137	37	+	+	CCONJ
ejpam-5396	137	38	µ+	µ+	PROPN
ejpam-5396	137	39	η	η	NOUN
ejpam-5396	137	40	)	)	PUNCT
ejpam-5396	137	41	}	}	PUNCT
ejpam-5396	137	42	.	.	PUNCT
ejpam-5396	138	1	consequently	consequently	ADV
ejpam-5396	138	2	,	,	PUNCT
ejpam-5396	138	3	the	the	DET
ejpam-5396	138	4	solution	solution	NOUN
ejpam-5396	138	5	to	to	ADP
ejpam-5396	138	6	the	the	DET
ejpam-5396	138	7	model	model	NOUN
ejpam-5396	138	8	(	(	PUNCT
ejpam-5396	138	9	1	1	X
ejpam-5396	138	10	)	)	PUNCT
ejpam-5396	138	11	exists	exist	VERB
ejpam-5396	138	12	and	and	CCONJ
ejpam-5396	138	13	is	be	AUX
ejpam-5396	138	14	unique	unique	ADJ
ejpam-5396	138	15	iff	iff	PROPN
ejpam-5396	138	16	h(x	h(x	PROPN
ejpam-5396	138	17	)	)	PUNCT
ejpam-5396	138	18	satisfies	satisfy	VERB
ejpam-5396	138	19	the	the	DET
ejpam-5396	138	20	lipschitz	lipschitz	NOUN
ejpam-5396	138	21	condition	condition	NOUN
ejpam-5396	138	22	.	.	PUNCT
ejpam-5396	139	1	lemma	lemma	PROPN
ejpam-5396	139	2	1	1	NUM
ejpam-5396	139	3	(	(	PUNCT
ejpam-5396	139	4	[	[	X
ejpam-5396	139	5	31	31	NUM
ejpam-5396	139	6	]	]	PUNCT
ejpam-5396	139	7	,	,	PUNCT
ejpam-5396	139	8	lemma	lemma	PROPN
ejpam-5396	139	9	3	3	NUM
ejpam-5396	139	10	)	)	PUNCT
ejpam-5396	139	11	.	.	PUNCT
ejpam-5396	140	1	let	let	VERB
ejpam-5396	140	2	u(t	u(t	NOUN
ejpam-5396	140	3	)	)	PUNCT
ejpam-5396	140	4	be	be	AUX
ejpam-5396	140	5	a	a	DET
ejpam-5396	140	6	function	function	NOUN
ejpam-5396	140	7	meeting	meet	VERB
ejpam-5396	140	8	the	the	DET
ejpam-5396	140	9	conditions	condition	NOUN
ejpam-5396	140	10	that	that	PRON
ejpam-5396	140	11	dαu(t	dαu(t	PROPN
ejpam-5396	140	12	)	)	PUNCT
ejpam-5396	140	13	exists	exist	VERB
ejpam-5396	140	14	for	for	ADP
ejpam-5396	140	15	every	every	DET
ejpam-5396	140	16	t.	t.	NOUN
ejpam-5396	140	17	therefore	therefore	ADV
ejpam-5396	140	18	,	,	PUNCT
ejpam-5396	140	19	{	{	PUNCT
ejpam-5396	140	20	dαu(t	dαu(t	PROPN
ejpam-5396	140	21	)	)	PUNCT
ejpam-5396	140	22	≤	≤	NUM
ejpam-5396	140	23	−λu(t	−λu(t	NOUN
ejpam-5396	140	24	)	)	PUNCT
ejpam-5396	140	25	+	+	NUM
ejpam-5396	140	26	µ	µ	NOUN
ejpam-5396	140	27	,	,	PUNCT
ejpam-5396	140	28	u(t0	u(t0	NOUN
ejpam-5396	140	29	)	)	PUNCT
ejpam-5396	141	1	=	=	SYM
ejpam-5396	142	1	ut0	ut0	INTJ
ejpam-5396	142	2	,	,	PUNCT
ejpam-5396	142	3	where	where	SCONJ
ejpam-5396	142	4	0	0	X
ejpam-5396	142	5	<	<	X
ejpam-5396	142	6	α	α	X
ejpam-5396	142	7	<	<	X
ejpam-5396	142	8	1	1	NUM
ejpam-5396	142	9	,	,	PUNCT
ejpam-5396	142	10	(	(	PUNCT
ejpam-5396	142	11	λ	λ	PROPN
ejpam-5396	142	12	,	,	PUNCT
ejpam-5396	142	13	µ	µ	NOUN
ejpam-5396	142	14	)	)	PUNCT
ejpam-5396	142	15	∈	∈	NOUN
ejpam-5396	142	16	r2	r2	NOUN
ejpam-5396	142	17	,	,	PUNCT
ejpam-5396	142	18	λ	λ	X
ejpam-5396	142	19	̸=	̸=	PROPN
ejpam-5396	142	20	0	0	NUM
ejpam-5396	142	21	,	,	PUNCT
ejpam-5396	142	22	and	and	CCONJ
ejpam-5396	142	23	t0	t0	PRON
ejpam-5396	142	24	≥	≥	NUM
ejpam-5396	142	25	0	0	NUM
ejpam-5396	142	26	is	be	AUX
ejpam-5396	142	27	the	the	DET
ejpam-5396	142	28	initial	initial	ADJ
ejpam-5396	142	29	time	time	NOUN
ejpam-5396	142	30	.	.	PUNCT
ejpam-5396	143	1	then	then	ADV
ejpam-5396	143	2	,	,	PUNCT
ejpam-5396	143	3	u(t	u(t	PROPN
ejpam-5396	143	4	)	)	PUNCT
ejpam-5396	143	5	≤	≤	NOUN
ejpam-5396	143	6	(	(	PUNCT
ejpam-5396	143	7	u(t0)−	u(t0)−	PROPN
ejpam-5396	143	8	µ	µ	X
ejpam-5396	143	9	λ	λ	PROPN
ejpam-5396	143	10	)	)	PUNCT
ejpam-5396	143	11	eα,1	eα,1	PROPN
ejpam-5396	143	12	[	[	PUNCT
ejpam-5396	143	13	−	−	PROPN
ejpam-5396	143	14	λ(t−	λ(t−	PROPN
ejpam-5396	143	15	t0	t0	NOUN
ejpam-5396	143	16	)	)	PUNCT
ejpam-5396	143	17	α	α	NOUN
ejpam-5396	143	18	]	]	PUNCT
ejpam-5396	144	1	+	+	NUM
ejpam-5396	144	2	µ	µ	X
ejpam-5396	144	3	λ	λ	NOUN
ejpam-5396	144	4	,	,	PUNCT
ejpam-5396	144	5	where	where	SCONJ
ejpam-5396	144	6	eα,1(t	eα,1(t	ADJ
ejpam-5396	144	7	)	)	PUNCT
ejpam-5396	144	8	=	=	PUNCT
ejpam-5396	145	1	∞∑	∞∑	NUM
ejpam-5396	145	2	k=0	k=0	PROPN
ejpam-5396	145	3	tk	tk	PROPN
ejpam-5396	145	4	γ(kq	γ(kq	PROPN
ejpam-5396	145	5	+	+	CCONJ
ejpam-5396	145	6	1	1	X
ejpam-5396	145	7	)	)	PUNCT
ejpam-5396	145	8	>	>	X
ejpam-5396	145	9	0	0	PUNCT
ejpam-5396	145	10	is	be	AUX
ejpam-5396	145	11	the	the	DET
ejpam-5396	145	12	mittag	mittag	ADJ
ejpam-5396	145	13	leffler	leffl	ADJ
ejpam-5396	145	14	function	function	NOUN
ejpam-5396	145	15	.	.	PUNCT
ejpam-5396	146	1	theorem	theorem	ADJ
ejpam-5396	146	2	2	2	NUM
ejpam-5396	146	3	(	(	PUNCT
ejpam-5396	146	4	[	[	X
ejpam-5396	146	5	31	31	NUM
ejpam-5396	146	6	]	]	PUNCT
ejpam-5396	146	7	)	)	PUNCT
ejpam-5396	146	8	.	.	PUNCT
ejpam-5396	147	1	the	the	DET
ejpam-5396	147	2	model	model	NOUN
ejpam-5396	147	3	(	(	PUNCT
ejpam-5396	147	4	1	1	X
ejpam-5396	147	5	)	)	PUNCT
ejpam-5396	147	6	has	have	VERB
ejpam-5396	147	7	non	non	ADJ
ejpam-5396	147	8	-	-	ADJ
ejpam-5396	147	9	negative	negative	ADJ
ejpam-5396	147	10	solutions	solution	NOUN
ejpam-5396	147	11	if	if	SCONJ
ejpam-5396	147	12	and	and	CCONJ
ejpam-5396	147	13	only	only	ADV
ejpam-5396	147	14	if	if	SCONJ
ejpam-5396	147	15	θ	θ	PROPN
ejpam-5396	147	16	<	<	X
ejpam-5396	147	17	1	1	X
ejpam-5396	147	18	.	.	PUNCT
ejpam-5396	147	19	proof	proof	NOUN
ejpam-5396	147	20	.	.	PUNCT
ejpam-5396	148	1	we	we	PRON
ejpam-5396	148	2	have	have	VERB
ejpam-5396	148	3	dαs(t)|s=0	dαs(t)|s=0	NOUN
ejpam-5396	148	4	=	=	PUNCT
ejpam-5396	148	5	λ+	λ+	X
ejpam-5396	148	6	δr(t	δr(t	NOUN
ejpam-5396	148	7	)	)	PUNCT
ejpam-5396	148	8	>	>	X
ejpam-5396	148	9	0	0	NUM
ejpam-5396	148	10	,	,	PUNCT
ejpam-5396	148	11	dαc(t)|c=0	dαc(t)|c=0	NOUN
ejpam-5396	148	12	=	=	SYM
ejpam-5396	148	13	δθi(t)s(t	δθi(t)s(t	NUM
ejpam-5396	148	14	)	)	PUNCT
ejpam-5396	148	15	n	n	NOUN
ejpam-5396	148	16	+	+	CCONJ
ejpam-5396	148	17	δωθc(t)s(t	δωθc(t)s(t	NOUN
ejpam-5396	148	18	)	)	PUNCT
ejpam-5396	148	19	n	n	CCONJ
ejpam-5396	148	20	>	>	SYM
ejpam-5396	148	21	0	0	NUM
ejpam-5396	148	22	,	,	PUNCT
ejpam-5396	148	23	dαi(t)|i=0	dαi(t)|i=0	PROPN
ejpam-5396	148	24	=	=	SYM
ejpam-5396	148	25	δωc(t	δωc(t	NOUN
ejpam-5396	148	26	)	)	PUNCT
ejpam-5396	148	27	n	n	CCONJ
ejpam-5396	148	28	(	(	PUNCT
ejpam-5396	148	29	1−	1−	NUM
ejpam-5396	148	30	θ)s(t	θ)s(t	NOUN
ejpam-5396	148	31	)	)	PUNCT
ejpam-5396	148	32	+	+	NUM
ejpam-5396	148	33	πc(t	πc(t	NOUN
ejpam-5396	148	34	)	)	PUNCT
ejpam-5396	148	35	>	>	X
ejpam-5396	148	36	0	0	NUM
ejpam-5396	148	37	,	,	PUNCT
ejpam-5396	148	38	dαr(t)|r=0	dαr(t)|r=0	NOUN
ejpam-5396	148	39	=	=	SYM
ejpam-5396	148	40	βc(t	βc(t	NOUN
ejpam-5396	148	41	)	)	PUNCT
ejpam-5396	149	1	+	+	CCONJ
ejpam-5396	149	2	τi(t	τi(t	X
ejpam-5396	149	3	)	)	PUNCT
ejpam-5396	149	4	>	>	X
ejpam-5396	149	5	0	0	X
ejpam-5396	149	6	.	.	PUNCT
ejpam-5396	149	7	a.	a.	PROPN
ejpam-5396	149	8	alalyani	alalyani	PROPN
ejpam-5396	149	9	/	/	SYM
ejpam-5396	149	10	eur	eur	PROPN
ejpam-5396	149	11	.	.	PUNCT
ejpam-5396	150	1	j.	j.	PROPN
ejpam-5396	150	2	pure	pure	PROPN
ejpam-5396	150	3	appl	appl	PROPN
ejpam-5396	150	4	.	.	PROPN
ejpam-5396	150	5	math	math	PROPN
ejpam-5396	150	6	,	,	PUNCT
ejpam-5396	150	7	17	17	NUM
ejpam-5396	150	8	(	(	PUNCT
ejpam-5396	150	9	4	4	NUM
ejpam-5396	150	10	)	)	PUNCT
ejpam-5396	150	11	(	(	PUNCT
ejpam-5396	150	12	2024	2024	NUM
ejpam-5396	150	13	)	)	PUNCT
ejpam-5396	150	14	,	,	PUNCT
ejpam-5396	150	15	2763	2763	NUM
ejpam-5396	150	16	-	-	SYM
ejpam-5396	150	17	2799	2799	NUM
ejpam-5396	150	18	2768	2768	NUM
ejpam-5396	150	19	using	use	VERB
ejpam-5396	150	20	lemmas	lemmas	PROPN
ejpam-5396	150	21	5	5	NUM
ejpam-5396	150	22	and	and	CCONJ
ejpam-5396	150	23	6	6	NUM
ejpam-5396	150	24	from	from	ADP
ejpam-5396	150	25	[	[	X
ejpam-5396	150	26	15	15	NUM
ejpam-5396	150	27	]	]	PUNCT
ejpam-5396	150	28	,	,	PUNCT
ejpam-5396	150	29	we	we	PRON
ejpam-5396	150	30	see	see	VERB
ejpam-5396	150	31	that	that	SCONJ
ejpam-5396	150	32	the	the	DET
ejpam-5396	150	33	solutions	solution	NOUN
ejpam-5396	150	34	to	to	ADP
ejpam-5396	150	35	(	(	PUNCT
ejpam-5396	150	36	1	1	X
ejpam-5396	150	37	)	)	PUNCT
ejpam-5396	150	38	are	be	AUX
ejpam-5396	150	39	non	non	ADJ
ejpam-5396	150	40	-	-	ADJ
ejpam-5396	150	41	negative	negative	ADJ
ejpam-5396	150	42	.	.	PUNCT
ejpam-5396	151	1	theorem	theorem	ADJ
ejpam-5396	151	2	3	3	NUM
ejpam-5396	151	3	(	(	PUNCT
ejpam-5396	151	4	[	[	X
ejpam-5396	151	5	13	13	NUM
ejpam-5396	151	6	]	]	NUM
ejpam-5396	151	7	)	)	PUNCT
ejpam-5396	151	8	.	.	PUNCT
ejpam-5396	152	1	uniformly	uniformly	ADV
ejpam-5396	152	2	bounded	bound	VERB
ejpam-5396	152	3	solutions	solution	NOUN
ejpam-5396	152	4	for	for	ADP
ejpam-5396	152	5	the	the	DET
ejpam-5396	152	6	model	model	NOUN
ejpam-5396	152	7	(	(	PUNCT
ejpam-5396	152	8	1	1	X
ejpam-5396	152	9	)	)	PUNCT
ejpam-5396	152	10	begin	begin	VERB
ejpam-5396	152	11	in	in	ADP
ejpam-5396	152	12	ω	ω	PROPN
ejpam-5396	152	13	=	=	SYM
ejpam-5396	152	14	{	{	PUNCT
ejpam-5396	152	15	(	(	PUNCT
ejpam-5396	152	16	s	s	X
ejpam-5396	152	17	,	,	PUNCT
ejpam-5396	152	18	c	c	X
ejpam-5396	152	19	,	,	PUNCT
ejpam-5396	152	20	i	i	PRON
ejpam-5396	152	21	,	,	PUNCT
ejpam-5396	152	22	r	r	NOUN
ejpam-5396	152	23	)	)	PUNCT
ejpam-5396	152	24	∈	∈	NOUN
ejpam-5396	152	25	ω+	ω+	NUM
ejpam-5396	152	26	:	:	PUNCT
ejpam-5396	152	27	0	0	NUM
ejpam-5396	152	28	≤	≤	NUM
ejpam-5396	152	29	s	s	PART
ejpam-5396	152	30	+	+	X
ejpam-5396	152	31	c	c	NOUN
ejpam-5396	153	1	+	+	NOUN
ejpam-5396	153	2	i	i	PRON
ejpam-5396	154	1	+	+	NOUN
ejpam-5396	154	2	r	r	NOUN
ejpam-5396	154	3	≤	≤	NUM
ejpam-5396	154	4	λ	λ	PROPN
ejpam-5396	154	5	µ	µ	X
ejpam-5396	154	6	}	}	PUNCT
ejpam-5396	154	7	.	.	PUNCT
ejpam-5396	155	1	proof	proof	NOUN
ejpam-5396	155	2	.	.	PUNCT
ejpam-5396	156	1	let	let	VERB
ejpam-5396	156	2	n(t	n(t	PRON
ejpam-5396	156	3	)	)	PUNCT
ejpam-5396	156	4	=	=	SYM
ejpam-5396	156	5	s(t	s(t	PROPN
ejpam-5396	156	6	)	)	PUNCT
ejpam-5396	156	7	+	+	X
ejpam-5396	156	8	c(t	c(t	PROPN
ejpam-5396	156	9	)	)	PUNCT
ejpam-5396	157	1	+	+	NUM
ejpam-5396	157	2	i(t	i(t	NOUN
ejpam-5396	157	3	)	)	PUNCT
ejpam-5396	158	1	+	+	NOUN
ejpam-5396	158	2	r(t	r(t	NOUN
ejpam-5396	158	3	)	)	PUNCT
ejpam-5396	158	4	be	be	VERB
ejpam-5396	158	5	the	the	DET
ejpam-5396	158	6	total	total	ADJ
ejpam-5396	158	7	population	population	NOUN
ejpam-5396	158	8	at	at	ADP
ejpam-5396	158	9	time	time	NOUN
ejpam-5396	158	10	t.	t.	PROPN
ejpam-5396	158	11	thus	thus	ADV
ejpam-5396	158	12	,	,	PUNCT
ejpam-5396	158	13	we	we	PRON
ejpam-5396	158	14	have	have	VERB
ejpam-5396	158	15	dαn(t	dαn(t	PROPN
ejpam-5396	158	16	)	)	PUNCT
ejpam-5396	158	17	=	=	SYM
ejpam-5396	159	1	λ−	λ−	PROPN
ejpam-5396	159	2	µn(t)−	µn(t)−	PROPN
ejpam-5396	159	3	σi(t	σi(t	NOUN
ejpam-5396	159	4	)	)	PUNCT
ejpam-5396	159	5	≤	≤	NOUN
ejpam-5396	159	6	λ−	λ−	PROPN
ejpam-5396	159	7	µn(t	µn(t	NUM
ejpam-5396	159	8	)	)	PUNCT
ejpam-5396	159	9	.	.	PUNCT
ejpam-5396	160	1	thus	thus	ADV
ejpam-5396	160	2	,	,	PUNCT
ejpam-5396	160	3	dαn(t	dαn(t	PROPN
ejpam-5396	160	4	)	)	PUNCT
ejpam-5396	160	5	+	+	NUM
ejpam-5396	160	6	µn(t	µn(t	NOUN
ejpam-5396	160	7	)	)	PUNCT
ejpam-5396	160	8	≤	≤	NUM
ejpam-5396	161	1	λ	λ	NOUN
ejpam-5396	161	2	.	.	PUNCT
ejpam-5396	162	1	it	it	PRON
ejpam-5396	162	2	follows	follow	VERB
ejpam-5396	162	3	from	from	ADP
ejpam-5396	162	4	[	[	X
ejpam-5396	162	5	18	18	NUM
ejpam-5396	162	6	]	]	PUNCT
ejpam-5396	162	7	that	that	SCONJ
ejpam-5396	162	8	if	if	SCONJ
ejpam-5396	162	9	mα	mα	PROPN
ejpam-5396	162	10	is	be	AUX
ejpam-5396	162	11	the	the	DET
ejpam-5396	162	12	mittag	mittag	ADJ
ejpam-5396	162	13	-	-	PUNCT
ejpam-5396	162	14	leffler	leffler	NOUN
ejpam-5396	162	15	function	function	NOUN
ejpam-5396	162	16	,	,	PUNCT
ejpam-5396	162	17	we	we	PRON
ejpam-5396	162	18	have	have	VERB
ejpam-5396	162	19	0	0	NUM
ejpam-5396	162	20	≤	≤	NUM
ejpam-5396	162	21	n(t	n(t	PROPN
ejpam-5396	162	22	)	)	PUNCT
ejpam-5396	162	23	≤	≤	NUM
ejpam-5396	162	24	n(0)mα(−µtα	n(0)mα(−µtα	NOUN
ejpam-5396	162	25	)	)	PUNCT
ejpam-5396	163	1	+	+	NUM
ejpam-5396	163	2	tαmα	tαmα	NOUN
ejpam-5396	163	3	,	,	PUNCT
ejpam-5396	163	4	α+1(−µtα	α+1(−µtα	NUM
ejpam-5396	163	5	)	)	PUNCT
ejpam-5396	163	6	)	)	PUNCT
ejpam-5396	163	7	.	.	PUNCT
ejpam-5396	164	1	boukhouima	boukhouima	PROPN
ejpam-5396	164	2	et	et	PROPN
ejpam-5396	164	3	al	al	PROPN
ejpam-5396	164	4	.	.	PUNCT
ejpam-5396	165	1	[	[	X
ejpam-5396	165	2	15	15	NUM
ejpam-5396	165	3	]	]	X
ejpam-5396	165	4	yields	yield	NOUN
ejpam-5396	165	5	0	0	NUM
ejpam-5396	165	6	≤	≤	PROPN
ejpam-5396	165	7	n(t	n(t	NOUN
ejpam-5396	165	8	)	)	PUNCT
ejpam-5396	165	9	≤	≤	NUM
ejpam-5396	166	1	λ	λ	PROPN
ejpam-5396	166	2	µ	µ	X
ejpam-5396	166	3	,	,	PUNCT
ejpam-5396	166	4	t	t	PROPN
ejpam-5396	166	5	−→	−→	NOUN
ejpam-5396	166	6	∞.	∞.	PROPN
ejpam-5396	166	7	for	for	ADP
ejpam-5396	166	8	this	this	DET
ejpam-5396	166	9	reason	reason	NOUN
ejpam-5396	166	10	,	,	PUNCT
ejpam-5396	166	11	the	the	DET
ejpam-5396	166	12	solutions	solution	NOUN
ejpam-5396	166	13	of	of	ADP
ejpam-5396	166	14	(	(	PUNCT
ejpam-5396	166	15	1	1	X
ejpam-5396	166	16	)	)	PUNCT
ejpam-5396	166	17	are	be	AUX
ejpam-5396	166	18	uniformly	uniformly	ADV
ejpam-5396	166	19	limited	limit	VERB
ejpam-5396	166	20	in	in	ADP
ejpam-5396	166	21	the	the	DET
ejpam-5396	166	22	region	region	NOUN
ejpam-5396	166	23	ω	ω	PROPN
ejpam-5396	166	24	,	,	PUNCT
ejpam-5396	166	25	beginning	begin	VERB
ejpam-5396	166	26	with	with	ADP
ejpam-5396	166	27	ω+	ω+	NOUN
ejpam-5396	166	28	.	.	PUNCT
ejpam-5396	167	1	3	3	X
ejpam-5396	167	2	.	.	X
ejpam-5396	167	3	stability	stability	NOUN
ejpam-5396	167	4	analysis	analysis	NOUN
ejpam-5396	167	5	of	of	ADP
ejpam-5396	167	6	the	the	DET
ejpam-5396	167	7	model	model	NOUN
ejpam-5396	167	8	3.1	3.1	NUM
ejpam-5396	167	9	.	.	PUNCT
ejpam-5396	168	1	equilibria	equilibrium	NOUN
ejpam-5396	168	2	for	for	ADP
ejpam-5396	168	3	i	i	PRON
ejpam-5396	168	4	=	=	SYM
ejpam-5396	168	5	c	c	NOUN
ejpam-5396	168	6	=	=	SYM
ejpam-5396	168	7	0	0	PROPN
ejpam-5396	168	8	,	,	PUNCT
ejpam-5396	168	9	we	we	PRON
ejpam-5396	168	10	have	have	VERB
ejpam-5396	168	11	0	0	NUM
ejpam-5396	168	12	=	=	SYM
ejpam-5396	168	13	λ−	λ−	PROPN
ejpam-5396	168	14	µs(t	µs(t	PUNCT
ejpam-5396	168	15	)	)	PUNCT
ejpam-5396	169	1	+	+	NUM
ejpam-5396	169	2	ηr(t	ηr(t	NOUN
ejpam-5396	169	3	)	)	PUNCT
ejpam-5396	169	4	,	,	PUNCT
ejpam-5396	169	5	0	0	X
ejpam-5396	170	1	=	=	SYM
ejpam-5396	170	2	−(µ+	−(µ+	PROPN
ejpam-5396	170	3	η)r(t	η)r(t	NOUN
ejpam-5396	170	4	)	)	PUNCT
ejpam-5396	170	5	.	.	PUNCT
ejpam-5396	171	1	therefore	therefore	ADV
ejpam-5396	171	2	,	,	PUNCT
ejpam-5396	171	3	s0	s0	PROPN
ejpam-5396	171	4	=	=	SYM
ejpam-5396	171	5	λ	λ	PROPN
ejpam-5396	171	6	µ	µ	X
ejpam-5396	171	7	,	,	PUNCT
ejpam-5396	171	8	r0	r0	NOUN
ejpam-5396	171	9	=	=	NOUN
ejpam-5396	171	10	0	0	NUM
ejpam-5396	171	11	.	.	PUNCT
ejpam-5396	172	1	the	the	DET
ejpam-5396	172	2	disease	disease	NOUN
ejpam-5396	172	3	-	-	PUNCT
ejpam-5396	172	4	free	free	ADJ
ejpam-5396	172	5	equilibrium	equilibrium	NOUN
ejpam-5396	172	6	e1	e1	NOUN
ejpam-5396	172	7	=	=	SYM
ejpam-5396	172	8	(	(	PUNCT
ejpam-5396	172	9	λ	λ	X
ejpam-5396	172	10	µ	µ	X
ejpam-5396	172	11	,	,	PUNCT
ejpam-5396	172	12	0	0	NUM
ejpam-5396	172	13	,	,	PUNCT
ejpam-5396	172	14	0	0	NUM
ejpam-5396	172	15	,	,	PUNCT
ejpam-5396	172	16	0	0	NUM
ejpam-5396	172	17	)	)	PUNCT
ejpam-5396	172	18	is	be	AUX
ejpam-5396	172	19	easy	easy	ADJ
ejpam-5396	172	20	to	to	PART
ejpam-5396	172	21	obtain	obtain	VERB
ejpam-5396	172	22	.	.	PUNCT
ejpam-5396	173	1	the	the	DET
ejpam-5396	173	2	pneumonia	pneumonia	NOUN
ejpam-5396	173	3	endemic	endemic	ADJ
ejpam-5396	173	4	equilibrium	equilibrium	NOUN
ejpam-5396	173	5	is	be	AUX
ejpam-5396	173	6	represented	represent	VERB
ejpam-5396	173	7	by	by	ADP
ejpam-5396	173	8	e2	e2	PROPN
ejpam-5396	173	9	=	=	SYM
ejpam-5396	173	10	(	(	PUNCT
ejpam-5396	173	11	s∗	s∗	PROPN
ejpam-5396	173	12	,	,	PUNCT
ejpam-5396	173	13	c∗	c∗	NOUN
ejpam-5396	173	14	,	,	PUNCT
ejpam-5396	173	15	i∗	i∗	NOUN
ejpam-5396	173	16	,	,	PUNCT
ejpam-5396	173	17	r∗	r∗	PROPN
ejpam-5396	173	18	)	)	PUNCT
ejpam-5396	173	19	for	for	ADP
ejpam-5396	173	20	i∗	i∗	NOUN
ejpam-5396	173	21	>	>	X
ejpam-5396	173	22	0	0	NUM
ejpam-5396	173	23	,	,	PUNCT
ejpam-5396	173	24	and	and	CCONJ
ejpam-5396	173	25	can	can	AUX
ejpam-5396	173	26	be	be	AUX
ejpam-5396	173	27	derived	derive	VERB
ejpam-5396	173	28	by	by	ADP
ejpam-5396	173	29	solving	solve	VERB
ejpam-5396	173	30	the	the	DET
ejpam-5396	173	31	system	system	NOUN
ejpam-5396	173	32	of	of	ADP
ejpam-5396	173	33	equations	equation	NOUN
ejpam-5396	173	34	(	(	PUNCT
ejpam-5396	173	35	1	1	NUM
ejpam-5396	173	36	)	)	PUNCT
ejpam-5396	173	37	,	,	PUNCT
ejpam-5396	174	1	that	that	SCONJ
ejpam-5396	174	2	is,	is,	NOUN
ejpam-5396	174	3	dαs(t	dαs(t	PROPN
ejpam-5396	174	4	)	)	PUNCT
ejpam-5396	174	5	=	=	SYM
ejpam-5396	174	6	0	0	NUM
ejpam-5396	174	7	,	,	PUNCT
ejpam-5396	174	8	dαc(t	dαc(t	NOUN
ejpam-5396	174	9	)	)	PUNCT
ejpam-5396	174	10	=	=	SYM
ejpam-5396	174	11	0	0	NUM
ejpam-5396	174	12	,	,	PUNCT
ejpam-5396	174	13	dαi(t	dαi(t	NOUN
ejpam-5396	174	14	)	)	PUNCT
ejpam-5396	174	15	=	=	SYM
ejpam-5396	174	16	0	0	NUM
ejpam-5396	174	17	,	,	PUNCT
ejpam-5396	174	18	dαr(t	dαr(t	PROPN
ejpam-5396	174	19	)	)	PUNCT
ejpam-5396	174	20	=	=	SYM
ejpam-5396	174	21	0	0	X
ejpam-5396	174	22	.	.	PUNCT
ejpam-5396	174	23	a.	a.	NOUN
ejpam-5396	174	24	alalyani	alalyani	PROPN
ejpam-5396	174	25	/	/	SYM
ejpam-5396	174	26	eur	eur	PROPN
ejpam-5396	174	27	.	.	PUNCT
ejpam-5396	175	1	j.	j.	PROPN
ejpam-5396	175	2	pure	pure	PROPN
ejpam-5396	175	3	appl	appl	PROPN
ejpam-5396	175	4	.	.	PROPN
ejpam-5396	175	5	math	math	PROPN
ejpam-5396	175	6	,	,	PUNCT
ejpam-5396	175	7	17	17	NUM
ejpam-5396	175	8	(	(	PUNCT
ejpam-5396	175	9	4	4	NUM
ejpam-5396	175	10	)	)	PUNCT
ejpam-5396	175	11	(	(	PUNCT
ejpam-5396	175	12	2024	2024	NUM
ejpam-5396	175	13	)	)	PUNCT
ejpam-5396	175	14	,	,	PUNCT
ejpam-5396	175	15	2763	2763	NUM
ejpam-5396	175	16	-	-	SYM
ejpam-5396	175	17	2799	2799	NUM
ejpam-5396	175	18	2769	2769	NUM
ejpam-5396	175	19	by	by	ADP
ejpam-5396	175	20	taking	take	VERB
ejpam-5396	175	21	α1	α1	PROPN
ejpam-5396	175	22	=	=	SYM
ejpam-5396	175	23	θπ	θπ	PROPN
ejpam-5396	175	24	+	+	CCONJ
ejpam-5396	175	25	(	(	PUNCT
ejpam-5396	175	26	1−	1−	NUM
ejpam-5396	175	27	θ)z1	θ)z1	PROPN
ejpam-5396	175	28	z2	z2	PROPN
ejpam-5396	175	29	,	,	PUNCT
ejpam-5396	175	30	we	we	PRON
ejpam-5396	175	31	have	have	AUX
ejpam-5396	175	32	e∗	e∗	NOUN
ejpam-5396	175	33	=	=	SYM
ejpam-5396	175	34	(	(	PUNCT
ejpam-5396	175	35	s∗	s∗	PROPN
ejpam-5396	175	36	,	,	PUNCT
ejpam-5396	175	37	c∗	c∗	NOUN
ejpam-5396	175	38	,	,	PUNCT
ejpam-5396	175	39	i∗	i∗	NOUN
ejpam-5396	175	40	,	,	PUNCT
ejpam-5396	175	41	r∗	r∗	PROPN
ejpam-5396	175	42	)	)	PUNCT
ejpam-5396	175	43	,	,	PUNCT
ejpam-5396	175	44	where	where	SCONJ
ejpam-5396	175	45	s∗	s∗	PROPN
ejpam-5396	175	46	=	=	PUNCT
ejpam-5396	175	47	nz1	nz1	PROPN
ejpam-5396	175	48	α1	α1	PROPN
ejpam-5396	175	49	+	+	CCONJ
ejpam-5396	175	50	ω	ω	PROPN
ejpam-5396	175	51	,	,	PUNCT
ejpam-5396	175	52	c∗	c∗	PROPN
ejpam-5396	175	53	=	=	SYM
ejpam-5396	175	54	(	(	PUNCT
ejpam-5396	175	55	µ+	µ+	X
ejpam-5396	175	56	η)(λ(α1	η)(λ(α1	NOUN
ejpam-5396	175	57	+	+	CCONJ
ejpam-5396	175	58	ω)−	ω)−	PROPN
ejpam-5396	175	59	µnz1	µnz1	NOUN
ejpam-5396	175	60	)	)	PUNCT
ejpam-5396	175	61	(	(	PUNCT
ejpam-5396	175	62	α1	α1	PROPN
ejpam-5396	175	63	+	+	CCONJ
ejpam-5396	175	64	ω)(δz1(µ+	ω)(δz1(µ+	PROPN
ejpam-5396	175	65	η)−	η)−	PROPN
ejpam-5396	175	66	η(β	η(β	PROPN
ejpam-5396	175	67	+	+	CCONJ
ejpam-5396	175	68	τα1	τα1	NOUN
ejpam-5396	175	69	)	)	PUNCT
ejpam-5396	175	70	)	)	PUNCT
ejpam-5396	175	71	,	,	PUNCT
ejpam-5396	176	1	i∗	i∗	NOUN
ejpam-5396	176	2	=	=	PUNCT
ejpam-5396	177	1	α1(µ+	α1(µ+	NUM
ejpam-5396	177	2	η)(λ(α1	η)(λ(α1	NOUN
ejpam-5396	177	3	+	+	CCONJ
ejpam-5396	177	4	ω)−	ω)−	PROPN
ejpam-5396	177	5	µnz1	µnz1	NOUN
ejpam-5396	177	6	)	)	PUNCT
ejpam-5396	177	7	(	(	PUNCT
ejpam-5396	177	8	α1	α1	PROPN
ejpam-5396	177	9	+	+	CCONJ
ejpam-5396	177	10	ω)(δz1(µ+	ω)(δz1(µ+	PROPN
ejpam-5396	177	11	η)−	η)−	PROPN
ejpam-5396	177	12	η(β	η(β	PROPN
ejpam-5396	177	13	+	+	CCONJ
ejpam-5396	177	14	τα1	τα1	NOUN
ejpam-5396	177	15	)	)	PUNCT
ejpam-5396	177	16	)	)	PUNCT
ejpam-5396	177	17	,	,	PUNCT
ejpam-5396	177	18	r∗	r∗	PROPN
ejpam-5396	177	19	=	=	SYM
ejpam-5396	177	20	(	(	PUNCT
ejpam-5396	177	21	β	β	X
ejpam-5396	177	22	+	+	X
ejpam-5396	177	23	τα1)(λ(α1	τα1)(λ(α1	X
ejpam-5396	177	24	+	+	CCONJ
ejpam-5396	177	25	ω)−	ω)−	PROPN
ejpam-5396	177	26	µnz1	µnz1	NOUN
ejpam-5396	177	27	)	)	PUNCT
ejpam-5396	177	28	(	(	PUNCT
ejpam-5396	177	29	α1	α1	PROPN
ejpam-5396	177	30	+	+	CCONJ
ejpam-5396	177	31	ω)(δz1(µ+	ω)(δz1(µ+	PROPN
ejpam-5396	177	32	η)−	η)−	PROPN
ejpam-5396	177	33	η(β	η(β	PROPN
ejpam-5396	177	34	+	+	CCONJ
ejpam-5396	177	35	τα1	τα1	NOUN
ejpam-5396	177	36	)	)	PUNCT
ejpam-5396	177	37	)	)	PUNCT
ejpam-5396	177	38	.	.	PUNCT
ejpam-5396	178	1	3.2	3.2	NUM
ejpam-5396	178	2	.	.	PUNCT
ejpam-5396	179	1	the	the	DET
ejpam-5396	179	2	basic	basic	ADJ
ejpam-5396	179	3	reproductive	reproductive	ADJ
ejpam-5396	179	4	number	number	NOUN
ejpam-5396	179	5	r0	r0	NOUN
ejpam-5396	179	6	next	next	ADJ
ejpam-5396	179	7	-	-	PUNCT
ejpam-5396	179	8	generation	generation	NOUN
ejpam-5396	179	9	matrix	matrix	NOUN
ejpam-5396	179	10	theory	theory	NOUN
ejpam-5396	179	11	allows	allow	VERB
ejpam-5396	179	12	us	we	PRON
ejpam-5396	179	13	to	to	PART
ejpam-5396	179	14	deduce	deduce	VERB
ejpam-5396	179	15	that	that	SCONJ
ejpam-5396	179	16	we	we	PRON
ejpam-5396	179	17	obtain	obtain	VERB
ejpam-5396	179	18	dαy	dαy	NOUN
ejpam-5396	179	19	=	=	SYM
ejpam-5396	179	20	h(y)−	h(y)−	PROPN
ejpam-5396	179	21	h̄(y	h̄(y	PROPN
ejpam-5396	179	22	)	)	PUNCT
ejpam-5396	179	23	,	,	PUNCT
ejpam-5396	179	24	if	if	SCONJ
ejpam-5396	179	25	we	we	PRON
ejpam-5396	179	26	set	set	VERB
ejpam-5396	179	27	x	x	X
ejpam-5396	179	28	=	=	SYM
ejpam-5396	179	29	(	(	PUNCT
ejpam-5396	179	30	s	s	PROPN
ejpam-5396	179	31	,	,	PUNCT
ejpam-5396	179	32	r)t	r)t	ADJ
ejpam-5396	179	33	and	and	CCONJ
ejpam-5396	179	34	y	y	PROPN
ejpam-5396	179	35	=	=	SYM
ejpam-5396	179	36	(	(	PUNCT
ejpam-5396	179	37	c	c	X
ejpam-5396	179	38	,	,	PUNCT
ejpam-5396	179	39	i)t	i)t	NOUN
ejpam-5396	179	40	,	,	PUNCT
ejpam-5396	179	41	where	where	SCONJ
ejpam-5396	179	42	h(y	h(y	ADV
ejpam-5396	179	43	)	)	PUNCT
ejpam-5396	180	1	=	=	SYM
ejpam-5396	180	2	[	[	PUNCT
ejpam-5396	180	3	δθi(t)s(t	δθi(t)s(t	PROPN
ejpam-5396	180	4	)	)	PUNCT
ejpam-5396	180	5	n	n	NOUN
ejpam-5396	180	6	+	+	CCONJ
ejpam-5396	180	7	δωθc(t)s(t	δωθc(t)s(t	NOUN
ejpam-5396	180	8	)	)	PUNCT
ejpam-5396	180	9	n	n	PRON
ejpam-5396	180	10	δ(i(t)+ωc(t	δ(i(t)+ωc(t	NOUN
ejpam-5396	180	11	)	)	PUNCT
ejpam-5396	180	12	)	)	PUNCT
ejpam-5396	181	1	n	n	CCONJ
ejpam-5396	181	2	(	(	PUNCT
ejpam-5396	181	3	1−	1−	NUM
ejpam-5396	181	4	θ)s(t	θ)s(t	NOUN
ejpam-5396	181	5	)	)	PUNCT
ejpam-5396	181	6	]	]	PUNCT
ejpam-5396	181	7	,	,	PUNCT
ejpam-5396	181	8	h̄(y	h̄(y	PROPN
ejpam-5396	181	9	)	)	PUNCT
ejpam-5396	182	1	=	=	SYM
ejpam-5396	182	2	[	[	PUNCT
ejpam-5396	182	3	z1c(t	z1c(t	PROPN
ejpam-5396	182	4	)	)	PUNCT
ejpam-5396	182	5	−πc(t	−πc(t	NOUN
ejpam-5396	182	6	)	)	PUNCT
ejpam-5396	182	7	+	+	CCONJ
ejpam-5396	182	8	z2i(t	z2i(t	NOUN
ejpam-5396	182	9	)	)	PUNCT
ejpam-5396	182	10	]	]	PUNCT
ejpam-5396	182	11	.	.	PUNCT
ejpam-5396	183	1	at	at	ADP
ejpam-5396	183	2	e1	e1	NOUN
ejpam-5396	183	3	=	=	SYM
ejpam-5396	183	4	(	(	PUNCT
ejpam-5396	183	5	λ	λ	X
ejpam-5396	183	6	µ	µ	X
ejpam-5396	183	7	,	,	PUNCT
ejpam-5396	183	8	0	0	NUM
ejpam-5396	183	9	,	,	PUNCT
ejpam-5396	183	10	0	0	NUM
ejpam-5396	183	11	,	,	PUNCT
ejpam-5396	183	12	0	0	NUM
ejpam-5396	183	13	)	)	PUNCT
ejpam-5396	183	14	,	,	PUNCT
ejpam-5396	183	15	the	the	DET
ejpam-5396	183	16	jacobian	jacobian	ADJ
ejpam-5396	183	17	matrix	matrix	NOUN
ejpam-5396	183	18	of	of	ADP
ejpam-5396	183	19	h(y	h(y	PROPN
ejpam-5396	183	20	)	)	PUNCT
ejpam-5396	183	21	and	and	CCONJ
ejpam-5396	183	22	h̄(y	h̄(y	PROPN
ejpam-5396	183	23	)	)	PUNCT
ejpam-5396	183	24	w.r.t	w.r.t	NOUN
ejpam-5396	183	25	.	.	PUNCT
ejpam-5396	184	1	c	c	NOUN
ejpam-5396	185	1	and	and	CCONJ
ejpam-5396	185	2	i	i	PRON
ejpam-5396	185	3	may	may	AUX
ejpam-5396	185	4	be	be	AUX
ejpam-5396	185	5	obtained	obtain	VERB
ejpam-5396	185	6	as	as	ADP
ejpam-5396	185	7	follows	follow	VERB
ejpam-5396	185	8	:	:	PUNCT
ejpam-5396	185	9	h(y	h(y	ADV
ejpam-5396	185	10	)	)	PUNCT
ejpam-5396	186	1	=	=	PUNCT
ejpam-5396	186	2	[	[	PUNCT
ejpam-5396	186	3	h1	h1	PROPN
ejpam-5396	186	4	h2	h2	PROPN
ejpam-5396	186	5	]	]	PUNCT
ejpam-5396	186	6	,	,	PUNCT
ejpam-5396	186	7	h̄(y	h̄(y	PROPN
ejpam-5396	186	8	)	)	PUNCT
ejpam-5396	186	9	=	=	PUNCT
ejpam-5396	187	1	[	[	PUNCT
ejpam-5396	187	2	h̄1	h̄1	X
ejpam-5396	187	3	h̄2	h̄2	X
ejpam-5396	187	4	]	]	PUNCT
ejpam-5396	187	5	,	,	PUNCT
ejpam-5396	187	6	where	where	SCONJ
ejpam-5396	187	7	h1	h1	PROPN
ejpam-5396	187	8	=	=	SYM
ejpam-5396	187	9	δθi(t)s(t	δθi(t)s(t	PROPN
ejpam-5396	187	10	)	)	PUNCT
ejpam-5396	187	11	n	n	NOUN
ejpam-5396	187	12	+	+	CCONJ
ejpam-5396	187	13	δωθc(t)s(t	δωθc(t)s(t	NOUN
ejpam-5396	187	14	)	)	PUNCT
ejpam-5396	187	15	n	n	NOUN
ejpam-5396	187	16	,	,	PUNCT
ejpam-5396	187	17	h̄1	h̄1	PROPN
ejpam-5396	187	18	=	=	SYM
ejpam-5396	187	19	z1c(t	z1c(t	PROPN
ejpam-5396	187	20	)	)	PUNCT
ejpam-5396	187	21	,	,	PUNCT
ejpam-5396	187	22	h2	h2	NOUN
ejpam-5396	187	23	=	=	PUNCT
ejpam-5396	187	24	δ(i(t	δ(i(t	PROPN
ejpam-5396	187	25	)	)	PUNCT
ejpam-5396	187	26	+	+	NUM
ejpam-5396	187	27	ωc(t	ωc(t	NOUN
ejpam-5396	187	28	)	)	PUNCT
ejpam-5396	187	29	)	)	PUNCT
ejpam-5396	188	1	n	n	CCONJ
ejpam-5396	188	2	(	(	PUNCT
ejpam-5396	188	3	1−	1−	NUM
ejpam-5396	188	4	θ)s(t	θ)s(t	NOUN
ejpam-5396	188	5	)	)	PUNCT
ejpam-5396	188	6	,	,	PUNCT
ejpam-5396	188	7	h̄2	h̄2	X
ejpam-5396	188	8	=	=	SYM
ejpam-5396	188	9	−πc(t	−πc(t	NOUN
ejpam-5396	188	10	)	)	PUNCT
ejpam-5396	188	11	+	+	CCONJ
ejpam-5396	188	12	z2i(t	z2i(t	NOUN
ejpam-5396	188	13	)	)	PUNCT
ejpam-5396	188	14	.	.	PUNCT
ejpam-5396	189	1	hence	hence	ADV
ejpam-5396	189	2	,	,	PUNCT
ejpam-5396	189	3	at	at	ADP
ejpam-5396	189	4	e0	e0	PROPN
ejpam-5396	189	5	,	,	PUNCT
ejpam-5396	189	6	the	the	DET
ejpam-5396	189	7	jacobian	jacobian	ADJ
ejpam-5396	189	8	matrix	matrix	NOUN
ejpam-5396	189	9	of	of	ADP
ejpam-5396	189	10	h(y	h(y	PROPN
ejpam-5396	189	11	)	)	PUNCT
ejpam-5396	189	12	and	and	CCONJ
ejpam-5396	189	13	h̄(y	h̄(y	PROPN
ejpam-5396	189	14	)	)	PUNCT
ejpam-5396	189	15	is	be	AUX
ejpam-5396	189	16	derived	derive	VERB
ejpam-5396	189	17	by	by	ADP
ejpam-5396	189	18	f	f	PROPN
ejpam-5396	189	19	and	and	CCONJ
ejpam-5396	189	20	γ	γ	PROPN
ejpam-5396	189	21	,	,	PUNCT
ejpam-5396	189	22	respectively	respectively	ADV
ejpam-5396	189	23	,	,	PUNCT
ejpam-5396	189	24	f	f	PROPN
ejpam-5396	190	1	=	=	PUNCT
ejpam-5396	191	1	[	[	PUNCT
ejpam-5396	191	2	∂h1	∂h1	PROPN
ejpam-5396	191	3	∂c	∂c	PROPN
ejpam-5396	191	4	∂h1	∂h1	PROPN
ejpam-5396	191	5	∂i	∂i	PROPN
ejpam-5396	192	1	∂h2	∂h2	ADP
ejpam-5396	192	2	∂c	∂c	PUNCT
ejpam-5396	192	3	∂h2	∂h2	PROPN
ejpam-5396	192	4	∂i	∂i	PROPN
ejpam-5396	192	5	]	]	PUNCT
ejpam-5396	192	6	,	,	PUNCT
ejpam-5396	192	7	γ	γ	X
ejpam-5396	192	8	=	=	X
ejpam-5396	192	9	[	[	PUNCT
ejpam-5396	192	10	∂h̄1	∂h̄1	X
ejpam-5396	192	11	∂c	∂c	NOUN
ejpam-5396	192	12	∂h̄1	∂h̄1	PUNCT
ejpam-5396	192	13	∂i	∂i	PROPN
ejpam-5396	192	14	∂h̄2	∂h̄2	PROPN
ejpam-5396	192	15	∂c	∂c	PROPN
ejpam-5396	192	16	∂h̄2	∂h̄2	PROPN
ejpam-5396	192	17	∂i	∂i	X
ejpam-5396	192	18	]	]	PUNCT
ejpam-5396	192	19	.	.	PUNCT
ejpam-5396	193	1	then	then	ADV
ejpam-5396	193	2	,	,	PUNCT
ejpam-5396	193	3	∂h1	∂h1	PROPN
ejpam-5396	193	4	∂c	∂c	PUNCT
ejpam-5396	193	5	=	=	PUNCT
ejpam-5396	193	6	δωθ	δωθ	VERB
ejpam-5396	193	7	n	n	PRON
ejpam-5396	193	8	s(t	s(t	PROPN
ejpam-5396	193	9	)	)	PUNCT
ejpam-5396	193	10	,	,	PUNCT
ejpam-5396	193	11	∂h1	∂h1	PROPN
ejpam-5396	193	12	∂i	∂i	PROPN
ejpam-5396	193	13	=	=	PUNCT
ejpam-5396	193	14	δθ	δθ	PROPN
ejpam-5396	193	15	n	n	PROPN
ejpam-5396	193	16	s(t	s(t	PROPN
ejpam-5396	193	17	)	)	PUNCT
ejpam-5396	193	18	,	,	PUNCT
ejpam-5396	193	19	∂h2	∂h2	ADP
ejpam-5396	193	20	∂c	∂c	ADP
ejpam-5396	194	1	=	=	SYM
ejpam-5396	195	1	δω(1−	δω(1−	PROPN
ejpam-5396	195	2	θ	θ	PROPN
ejpam-5396	195	3	)	)	PUNCT
ejpam-5396	195	4	n	n	PRON
ejpam-5396	195	5	s(t	s(t	PROPN
ejpam-5396	195	6	)	)	PUNCT
ejpam-5396	195	7	,	,	PUNCT
ejpam-5396	195	8	∂h2	∂h2	ADP
ejpam-5396	195	9	∂i	∂i	PROPN
ejpam-5396	195	10	=	=	PUNCT
ejpam-5396	195	11	δ(1−	δ(1−	PROPN
ejpam-5396	195	12	θ	θ	PROPN
ejpam-5396	195	13	)	)	PUNCT
ejpam-5396	195	14	n	n	PRON
ejpam-5396	195	15	s(t	s(t	PROPN
ejpam-5396	195	16	)	)	PUNCT
ejpam-5396	195	17	.	.	PUNCT
ejpam-5396	196	1	a.	a.	NOUN
ejpam-5396	196	2	alalyani	alalyani	PROPN
ejpam-5396	196	3	/	/	SYM
ejpam-5396	196	4	eur	eur	PROPN
ejpam-5396	196	5	.	.	PUNCT
ejpam-5396	197	1	j.	j.	PROPN
ejpam-5396	197	2	pure	pure	PROPN
ejpam-5396	197	3	appl	appl	PROPN
ejpam-5396	197	4	.	.	PROPN
ejpam-5396	197	5	math	math	PROPN
ejpam-5396	197	6	,	,	PUNCT
ejpam-5396	197	7	17	17	NUM
ejpam-5396	197	8	(	(	PUNCT
ejpam-5396	197	9	4	4	NUM
ejpam-5396	197	10	)	)	PUNCT
ejpam-5396	197	11	(	(	PUNCT
ejpam-5396	197	12	2024	2024	NUM
ejpam-5396	197	13	)	)	PUNCT
ejpam-5396	197	14	,	,	PUNCT
ejpam-5396	197	15	2763	2763	NUM
ejpam-5396	197	16	-	-	SYM
ejpam-5396	197	17	2799	2799	NUM
ejpam-5396	197	18	2770	2770	NUM
ejpam-5396	197	19	similarly	similarly	ADV
ejpam-5396	197	20	,	,	PUNCT
ejpam-5396	197	21	we	we	PRON
ejpam-5396	197	22	may	may	AUX
ejpam-5396	197	23	obtain	obtain	VERB
ejpam-5396	197	24	the	the	DET
ejpam-5396	197	25	γ	γ	PROPN
ejpam-5396	197	26	entries	entry	NOUN
ejpam-5396	197	27	as	as	ADP
ejpam-5396	197	28	:	:	PUNCT
ejpam-5396	197	29	∂h̄1	∂h̄1	X
ejpam-5396	197	30	∂c	∂c	PUNCT
ejpam-5396	197	31	=	=	SYM
ejpam-5396	197	32	z1	z1	PROPN
ejpam-5396	197	33	,	,	PUNCT
ejpam-5396	197	34	∂h̄1	∂h̄1	X
ejpam-5396	197	35	∂i	∂i	PROPN
ejpam-5396	197	36	=	=	SYM
ejpam-5396	197	37	0	0	NUM
ejpam-5396	197	38	,	,	PUNCT
ejpam-5396	197	39	∂h̄2	∂h̄2	NOUN
ejpam-5396	197	40	∂c	∂c	PROPN
ejpam-5396	198	1	=	=	SYM
ejpam-5396	198	2	−π	−π	PROPN
ejpam-5396	198	3	,	,	PUNCT
ejpam-5396	198	4	∂h̄2	∂h̄2	NOUN
ejpam-5396	198	5	∂i	∂i	PROPN
ejpam-5396	198	6	=	=	SYM
ejpam-5396	198	7	z2	z2	PROPN
ejpam-5396	198	8	.	.	PUNCT
ejpam-5396	199	1	the	the	DET
ejpam-5396	199	2	entries	entry	NOUN
ejpam-5396	199	3	in	in	ADP
ejpam-5396	199	4	a	a	PRON
ejpam-5396	199	5	are	be	AUX
ejpam-5396	199	6	derived	derive	VERB
ejpam-5396	199	7	as	as	SCONJ
ejpam-5396	199	8	follows	follow	VERB
ejpam-5396	199	9	:	:	PUNCT
ejpam-5396	199	10	a	a	DET
ejpam-5396	199	11	=	=	X
ejpam-5396	199	12	[	[	PUNCT
ejpam-5396	199	13	δωθs0	δωθs0	NOUN
ejpam-5396	199	14	n	n	CCONJ
ejpam-5396	199	15	δθs0	δθs0	NOUN
ejpam-5396	199	16	n	n	ADP
ejpam-5396	199	17	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	199	18	n	n	PRON
ejpam-5396	199	19	δ(1−θ)s0	δ(1−θ)s0	PROPN
ejpam-5396	199	20	n	n	X
ejpam-5396	199	21	]	]	PUNCT
ejpam-5396	199	22	,	,	PUNCT
ejpam-5396	199	23	b	b	X
ejpam-5396	199	24	=	=	X
ejpam-5396	199	25	[	[	PUNCT
ejpam-5396	199	26	z1	z1	NOUN
ejpam-5396	199	27	0	0	NUM
ejpam-5396	199	28	−π	−π	PROPN
ejpam-5396	199	29	z2	z2	PROPN
ejpam-5396	199	30	]	]	PUNCT
ejpam-5396	199	31	.	.	PUNCT
ejpam-5396	200	1	thus	thus	ADV
ejpam-5396	200	2	,	,	PUNCT
ejpam-5396	200	3	b−1	b−1	PROPN
ejpam-5396	200	4	=	=	PUNCT
ejpam-5396	200	5	[	[	PUNCT
ejpam-5396	200	6	1	1	NUM
ejpam-5396	200	7	z1	z1	PROPN
ejpam-5396	200	8	π	π	PROPN
ejpam-5396	200	9	z1z2	z1z2	PROPN
ejpam-5396	200	10	0	0	NUM
ejpam-5396	200	11	1	1	NUM
ejpam-5396	200	12	z2	z2	PROPN
ejpam-5396	200	13	]	]	PUNCT
ejpam-5396	200	14	.	.	PUNCT
ejpam-5396	201	1	then	then	ADV
ejpam-5396	201	2	,	,	PUNCT
ejpam-5396	201	3	a.b−1	a.b−1	X
ejpam-5396	201	4	=	=	PUNCT
ejpam-5396	201	5	[	[	PUNCT
ejpam-5396	201	6	δωθs0	δωθs0	NOUN
ejpam-5396	201	7	n	n	CCONJ
ejpam-5396	201	8	δθs0	δθs0	NOUN
ejpam-5396	201	9	n	n	ADP
ejpam-5396	201	10	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	202	1	n	n	PRON
ejpam-5396	202	2	δ(1−θ)s0	δ(1−θ)s0	PROPN
ejpam-5396	202	3	n	n	X
ejpam-5396	202	4	]	]	PUNCT
ejpam-5396	202	5	.	.	PUNCT
ejpam-5396	203	1	[	[	PUNCT
ejpam-5396	203	2	1	1	NUM
ejpam-5396	203	3	z1	z1	PROPN
ejpam-5396	203	4	π	π	PROPN
ejpam-5396	203	5	z1z2	z1z2	PROPN
ejpam-5396	203	6	0	0	NUM
ejpam-5396	203	7	1	1	NUM
ejpam-5396	203	8	z2	z2	PROPN
ejpam-5396	203	9	]	]	PUNCT
ejpam-5396	203	10	.	.	PUNCT
ejpam-5396	203	11	a.b−1	a.b−1	X
ejpam-5396	204	1	=	=	PUNCT
ejpam-5396	204	2	[	[	PUNCT
ejpam-5396	204	3	ωθδs0	ωθδs0	X
ejpam-5396	204	4	nz1	nz1	NOUN
ejpam-5396	204	5	(	(	PUNCT
ejpam-5396	204	6	πω+z1)θδs0	πω+z1)θδs0	NUM
ejpam-5396	204	7	nz1z2	nz1z2	PROPN
ejpam-5396	204	8	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	204	9	nz1	nz1	NOUN
ejpam-5396	204	10	(	(	PUNCT
ejpam-5396	204	11	πω+z1)δ(1−θ)s0	πω+z1)δ(1−θ)s0	PROPN
ejpam-5396	204	12	nz1z2	nz1z2	PROPN
ejpam-5396	204	13	]	]	PUNCT
ejpam-5396	204	14	.	.	PUNCT
ejpam-5396	205	1	the	the	DET
ejpam-5396	205	2	eigenvalues	eigenvalues	PROPN
ejpam-5396	205	3	of	of	ADP
ejpam-5396	205	4	a.b−1	a.b−1	X
ejpam-5396	205	5	can	can	AUX
ejpam-5396	205	6	be	be	AUX
ejpam-5396	205	7	obtained	obtain	VERB
ejpam-5396	205	8	as:∣∣∣∣∣λ−	as:∣∣∣∣∣λ−	ADV
ejpam-5396	205	9	ωθδs0	ωθδs0	NOUN
ejpam-5396	206	1	nz1	nz1	NOUN
ejpam-5396	206	2	(	(	PUNCT
ejpam-5396	206	3	πω+z1)θδs0	πω+z1)θδs0	NUM
ejpam-5396	206	4	nz1z2	nz1z2	PROPN
ejpam-5396	206	5	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	206	6	nz1	nz1	NOUN
ejpam-5396	206	7	λ−	λ−	PROPN
ejpam-5396	206	8	(	(	PUNCT
ejpam-5396	206	9	πω+z1)δ(1−θ)s0	πω+z1)δ(1−θ)s0	PROPN
ejpam-5396	206	10	nz1z2	nz1z2	PROPN
ejpam-5396	206	11	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5396	206	12	=	=	SYM
ejpam-5396	206	13	0	0	X
ejpam-5396	206	14	.	.	PUNCT
ejpam-5396	207	1	as	as	ADP
ejpam-5396	207	2	a	a	DET
ejpam-5396	207	3	result	result	NOUN
ejpam-5396	207	4	,	,	PUNCT
ejpam-5396	207	5	the	the	DET
ejpam-5396	207	6	eigenvalues	eigenvalue	NOUN
ejpam-5396	207	7	are	be	AUX
ejpam-5396	207	8	:	:	PUNCT
ejpam-5396	207	9	λ1	λ1	ADJ
ejpam-5396	207	10	=	=	SYM
ejpam-5396	207	11	0	0	NUM
ejpam-5396	207	12	,	,	PUNCT
ejpam-5396	207	13	λ2	λ2	NOUN
ejpam-5396	207	14	=	=	SYM
ejpam-5396	207	15	(	(	PUNCT
ejpam-5396	207	16	ωθz2	ωθz2	NOUN
ejpam-5396	207	17	+	+	CCONJ
ejpam-5396	207	18	(	(	PUNCT
ejpam-5396	207	19	1−	1−	NUM
ejpam-5396	207	20	θ)(πω	θ)(πω	X
ejpam-5396	207	21	+	+	CCONJ
ejpam-5396	207	22	z1))δs0	z1))δs0	PROPN
ejpam-5396	207	23	nz1z2	nz1z2	PROPN
ejpam-5396	207	24	.	.	PUNCT
ejpam-5396	208	1	thus	thus	ADV
ejpam-5396	208	2	,	,	PUNCT
ejpam-5396	208	3	r0	r0	NOUN
ejpam-5396	208	4	=	=	SYM
ejpam-5396	208	5	(	(	PUNCT
ejpam-5396	208	6	ωθz2	ωθz2	NOUN
ejpam-5396	208	7	+	+	CCONJ
ejpam-5396	208	8	(	(	PUNCT
ejpam-5396	208	9	1−	1−	NUM
ejpam-5396	208	10	θ)(πω	θ)(πω	X
ejpam-5396	208	11	+	+	CCONJ
ejpam-5396	208	12	z1))δs0	z1))δs0	PROPN
ejpam-5396	208	13	nz1z2	nz1z2	PROPN
ejpam-5396	208	14	.	.	PUNCT
ejpam-5396	208	15	3.3	3.3	NUM
ejpam-5396	208	16	.	.	PUNCT
ejpam-5396	209	1	local	local	ADJ
ejpam-5396	209	2	stability	stability	NOUN
ejpam-5396	209	3	the	the	DET
ejpam-5396	209	4	jacobian	jacobian	ADJ
ejpam-5396	209	5	matrix	matrix	NOUN
ejpam-5396	209	6	of	of	ADP
ejpam-5396	209	7	the	the	DET
ejpam-5396	209	8	system	system	NOUN
ejpam-5396	209	9	(	(	PUNCT
ejpam-5396	209	10	1	1	NUM
ejpam-5396	209	11	)	)	PUNCT
ejpam-5396	209	12	along	along	ADP
ejpam-5396	209	13	with	with	ADP
ejpam-5396	209	14	its	its	PRON
ejpam-5396	209	15	elements	element	NOUN
ejpam-5396	209	16	is	be	AUX
ejpam-5396	209	17	presented	present	VERB
ejpam-5396	209	18	as	as	ADP
ejpam-5396	209	19	:	:	PUNCT
ejpam-5396	209	20	j(en	j(en	X
ejpam-5396	209	21	)	)	PUNCT
ejpam-5396	209	22	=	=	SYM
ejpam-5396	210	1			PROPN
ejpam-5396	210	2	j11	j11	NOUN
ejpam-5396	210	3	j12	j12	PROPN
ejpam-5396	210	4	j13	j13	PROPN
ejpam-5396	210	5	j14	j14	PROPN
ejpam-5396	210	6	j21	j21	PROPN
ejpam-5396	210	7	j22	j22	PROPN
ejpam-5396	210	8	j23	j23	PROPN
ejpam-5396	210	9	j24	j24	PROPN
ejpam-5396	210	10	j31	j31	PROPN
ejpam-5396	210	11	j32	j32	PROPN
ejpam-5396	210	12	j33	j33	PROPN
ejpam-5396	210	13	j34	j34	NOUN
ejpam-5396	210	14	j41	j41	VERB
ejpam-5396	210	15	j42	j42	PROPN
ejpam-5396	210	16	j43	j43	PROPN
ejpam-5396	210	17	j44	j44	NUM
ejpam-5396	210	18			NOUN
ejpam-5396	210	19	,	,	PUNCT
ejpam-5396	210	20	a.	a.	NOUN
ejpam-5396	210	21	alalyani	alalyani	PROPN
ejpam-5396	210	22	/	/	SYM
ejpam-5396	210	23	eur	eur	PROPN
ejpam-5396	210	24	.	.	PUNCT
ejpam-5396	211	1	j.	j.	PROPN
ejpam-5396	211	2	pure	pure	PROPN
ejpam-5396	211	3	appl	appl	PROPN
ejpam-5396	211	4	.	.	PROPN
ejpam-5396	211	5	math	math	PROPN
ejpam-5396	211	6	,	,	PUNCT
ejpam-5396	211	7	17	17	NUM
ejpam-5396	211	8	(	(	PUNCT
ejpam-5396	211	9	4	4	NUM
ejpam-5396	211	10	)	)	PUNCT
ejpam-5396	211	11	(	(	PUNCT
ejpam-5396	211	12	2024	2024	NUM
ejpam-5396	211	13	)	)	PUNCT
ejpam-5396	211	14	,	,	PUNCT
ejpam-5396	211	15	2763	2763	NUM
ejpam-5396	211	16	-	-	SYM
ejpam-5396	211	17	2799	2799	NUM
ejpam-5396	211	18	2771	2771	NUM
ejpam-5396	211	19	where	where	SCONJ
ejpam-5396	211	20	j11	j11	NOUN
ejpam-5396	211	21	=	=	SYM
ejpam-5396	211	22	−δi(t	−δi(t	PROPN
ejpam-5396	211	23	)	)	PUNCT
ejpam-5396	211	24	n	n	CCONJ
ejpam-5396	211	25	−	−	PROPN
ejpam-5396	211	26	δωc(t	δωc(t	PROPN
ejpam-5396	211	27	)	)	PUNCT
ejpam-5396	211	28	n	n	CCONJ
ejpam-5396	211	29	−	−	PROPN
ejpam-5396	211	30	µ	µ	PROPN
ejpam-5396	211	31	,	,	PUNCT
ejpam-5396	211	32	j12	j12	PROPN
ejpam-5396	211	33	=	=	PUNCT
ejpam-5396	211	34	−δωs(t	−δωs(t	PROPN
ejpam-5396	211	35	)	)	PUNCT
ejpam-5396	211	36	n	n	NOUN
ejpam-5396	211	37	,	,	PUNCT
ejpam-5396	211	38	j13	j13	NOUN
ejpam-5396	211	39	=	=	SYM
ejpam-5396	211	40	−δs(t	−δs(t	NOUN
ejpam-5396	211	41	)	)	PUNCT
ejpam-5396	211	42	n	n	PROPN
ejpam-5396	211	43	,	,	PUNCT
ejpam-5396	211	44	j14	j14	PROPN
ejpam-5396	211	45	=	=	SYM
ejpam-5396	211	46	η	η	PROPN
ejpam-5396	211	47	,	,	PUNCT
ejpam-5396	211	48	j21	j21	NOUN
ejpam-5396	211	49	=	=	SYM
ejpam-5396	211	50	δθi(t	δθi(t	PROPN
ejpam-5396	211	51	)	)	PUNCT
ejpam-5396	211	52	n	n	NOUN
ejpam-5396	211	53	+	+	NUM
ejpam-5396	211	54	δωθc(t	δωθc(t	NOUN
ejpam-5396	211	55	)	)	PUNCT
ejpam-5396	211	56	n	n	PROPN
ejpam-5396	211	57	,	,	PUNCT
ejpam-5396	211	58	j22	j22	PROPN
ejpam-5396	211	59	=	=	PUNCT
ejpam-5396	211	60	δωθs(t	δωθs(t	PROPN
ejpam-5396	211	61	)	)	PUNCT
ejpam-5396	211	62	n	n	CCONJ
ejpam-5396	211	63	−	−	PROPN
ejpam-5396	211	64	z1	z1	PROPN
ejpam-5396	211	65	,	,	PUNCT
ejpam-5396	211	66	j23	j23	NOUN
ejpam-5396	211	67	=	=	SYM
ejpam-5396	211	68	δθs(t	δθs(t	PROPN
ejpam-5396	211	69	)	)	PUNCT
ejpam-5396	211	70	n	n	PROPN
ejpam-5396	211	71	,	,	PUNCT
ejpam-5396	211	72	j24	j24	PROPN
ejpam-5396	211	73	=	=	SYM
ejpam-5396	211	74	0	0	PROPN
ejpam-5396	211	75	,	,	PUNCT
ejpam-5396	211	76	j31	j31	NOUN
ejpam-5396	211	77	=	=	SYM
ejpam-5396	211	78	δ(i(t	δ(i(t	PROPN
ejpam-5396	211	79	)	)	PUNCT
ejpam-5396	211	80	+	+	NUM
ejpam-5396	211	81	ωc(t	ωc(t	NOUN
ejpam-5396	211	82	)	)	PUNCT
ejpam-5396	211	83	)	)	PUNCT
ejpam-5396	212	1	n	n	CCONJ
ejpam-5396	212	2	(	(	PUNCT
ejpam-5396	212	3	1−	1−	NUM
ejpam-5396	212	4	θ	θ	NOUN
ejpam-5396	212	5	)	)	PUNCT
ejpam-5396	212	6	,	,	PUNCT
ejpam-5396	212	7	j32	j32	NOUN
ejpam-5396	212	8	=	=	SYM
ejpam-5396	212	9	δω	δω	PROPN
ejpam-5396	212	10	n	n	PROPN
ejpam-5396	212	11	(	(	PUNCT
ejpam-5396	212	12	1−	1−	NUM
ejpam-5396	212	13	θ)s(t	θ)s(t	NOUN
ejpam-5396	212	14	)	)	PUNCT
ejpam-5396	212	15	+	+	SYM
ejpam-5396	212	16	π	π	PROPN
ejpam-5396	212	17	,	,	PUNCT
ejpam-5396	212	18	j33	j33	NOUN
ejpam-5396	212	19	=	=	SYM
ejpam-5396	212	20	δ	δ	PROPN
ejpam-5396	212	21	n	n	CCONJ
ejpam-5396	212	22	(	(	PUNCT
ejpam-5396	212	23	1−	1−	NUM
ejpam-5396	212	24	θ)s(t)−	θ)s(t)−	PROPN
ejpam-5396	212	25	z2	z2	NOUN
ejpam-5396	212	26	,	,	PUNCT
ejpam-5396	212	27	j34	j34	NOUN
ejpam-5396	212	28	=	=	SYM
ejpam-5396	212	29	0	0	NUM
ejpam-5396	212	30	,	,	PUNCT
ejpam-5396	212	31	j41	j41	X
ejpam-5396	212	32	=	=	SYM
ejpam-5396	212	33	0	0	NUM
ejpam-5396	212	34	,	,	PUNCT
ejpam-5396	212	35	j42	j42	NOUN
ejpam-5396	212	36	=	=	SYM
ejpam-5396	212	37	β	β	X
ejpam-5396	212	38	,	,	PUNCT
ejpam-5396	212	39	j43	j43	PROPN
ejpam-5396	212	40	=	=	SYM
ejpam-5396	212	41	τ	τ	PROPN
ejpam-5396	212	42	,	,	PUNCT
ejpam-5396	212	43	j44	j44	PROPN
ejpam-5396	212	44	=	=	PROPN
ejpam-5396	212	45	−(µ+	−(µ+	PROPN
ejpam-5396	212	46	η	η	PROPN
ejpam-5396	212	47	)	)	PUNCT
ejpam-5396	212	48	.	.	PUNCT
ejpam-5396	213	1	lemma	lemma	PROPN
ejpam-5396	213	2	2	2	NUM
ejpam-5396	213	3	.	.	PUNCT
ejpam-5396	214	1	the	the	DET
ejpam-5396	214	2	trivial	trivial	ADJ
ejpam-5396	214	3	disease	disease	NOUN
ejpam-5396	214	4	equilibrium	equilibrium	NOUN
ejpam-5396	214	5	e0	e0	PROPN
ejpam-5396	214	6	=	=	PUNCT
ejpam-5396	214	7	(	(	PUNCT
ejpam-5396	214	8	0	0	NUM
ejpam-5396	214	9	,	,	PUNCT
ejpam-5396	214	10	0	0	NUM
ejpam-5396	214	11	,	,	PUNCT
ejpam-5396	214	12	0	0	NUM
ejpam-5396	214	13	,	,	PUNCT
ejpam-5396	214	14	0	0	NUM
ejpam-5396	214	15	)	)	PUNCT
ejpam-5396	214	16	is	be	AUX
ejpam-5396	214	17	locally	locally	ADV
ejpam-5396	214	18	asymptotically	asymptotically	ADV
ejpam-5396	214	19	stable	stable	ADJ
ejpam-5396	214	20	in	in	ADP
ejpam-5396	214	21	ω	ω	PROPN
ejpam-5396	214	22	.	.	PUNCT
ejpam-5396	215	1	proof	proof	NOUN
ejpam-5396	215	2	.	.	PUNCT
ejpam-5396	216	1	at	at	ADP
ejpam-5396	216	2	e0	e0	PROPN
ejpam-5396	216	3	=	=	PUNCT
ejpam-5396	216	4	(	(	PUNCT
ejpam-5396	216	5	0	0	NUM
ejpam-5396	216	6	,	,	PUNCT
ejpam-5396	216	7	0	0	NUM
ejpam-5396	216	8	,	,	PUNCT
ejpam-5396	216	9	0	0	NUM
ejpam-5396	216	10	,	,	PUNCT
ejpam-5396	216	11	0	0	NUM
ejpam-5396	216	12	)	)	PUNCT
ejpam-5396	216	13	,	,	PUNCT
ejpam-5396	216	14	the	the	DET
ejpam-5396	216	15	model	model	NOUN
ejpam-5396	216	16	(	(	PUNCT
ejpam-5396	216	17	1	1	X
ejpam-5396	216	18	)	)	PUNCT
ejpam-5396	216	19	has	have	VERB
ejpam-5396	216	20	the	the	DET
ejpam-5396	216	21	following	follow	VERB
ejpam-5396	216	22	jacobian	jacobian	ADJ
ejpam-5396	216	23	matrix	matrix	NOUN
ejpam-5396	216	24	j(e0	j(e0	NOUN
ejpam-5396	216	25	):	):	PUNCT
ejpam-5396	216	26	j(e0	j(e0	ADJ
ejpam-5396	216	27	)	)	PUNCT
ejpam-5396	216	28	=	=	SYM
ejpam-5396	217	1			PROPN
ejpam-5396	217	2	−µ	−µ	NOUN
ejpam-5396	217	3	0	0	NUM
ejpam-5396	217	4	0	0	NUM
ejpam-5396	217	5	η	η	PROPN
ejpam-5396	217	6	0	0	PROPN
ejpam-5396	217	7	−z1	−z1	VERB
ejpam-5396	217	8	0	0	NUM
ejpam-5396	217	9	0	0	NUM
ejpam-5396	217	10	0	0	NUM
ejpam-5396	218	1	π	π	X
ejpam-5396	218	2	−z2	−z2	PROPN
ejpam-5396	218	3	0	0	NUM
ejpam-5396	218	4	0	0	NUM
ejpam-5396	218	5	β	β	X
ejpam-5396	218	6	τ	τ	PROPN
ejpam-5396	218	7	−(µ+	−(µ+	PROPN
ejpam-5396	218	8	η	η	PROPN
ejpam-5396	218	9	)	)	PUNCT
ejpam-5396	218	10			NOUN
ejpam-5396	218	11	.	.	PUNCT
ejpam-5396	219	1	therefore	therefore	ADV
ejpam-5396	219	2	,	,	PUNCT
ejpam-5396	219	3	we	we	PRON
ejpam-5396	219	4	can	can	AUX
ejpam-5396	219	5	get	get	VERB
ejpam-5396	219	6	the	the	DET
ejpam-5396	219	7	eigenvalues	eigenvalue	NOUN
ejpam-5396	219	8	as	as	ADP
ejpam-5396	219	9	:	:	PUNCT
ejpam-5396	219	10	j(e0	j(e0	ADJ
ejpam-5396	219	11	)	)	PUNCT
ejpam-5396	219	12	=	=	PUNCT
ejpam-5396	220	1	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5396	220	2	λ+	λ+	PUNCT
ejpam-5396	220	3	µ	µ	X
ejpam-5396	220	4	0	0	NUM
ejpam-5396	220	5	0	0	NUM
ejpam-5396	220	6	η	η	PROPN
ejpam-5396	220	7	0	0	NUM
ejpam-5396	220	8	λ+	λ+	PUNCT
ejpam-5396	220	9	z1	z1	VERB
ejpam-5396	220	10	0	0	NUM
ejpam-5396	220	11	0	0	NUM
ejpam-5396	220	12	0	0	NUM
ejpam-5396	220	13	π	π	NOUN
ejpam-5396	220	14	λ+	λ+	PUNCT
ejpam-5396	220	15	z2	z2	PROPN
ejpam-5396	220	16	0	0	NUM
ejpam-5396	220	17	0	0	NUM
ejpam-5396	221	1	β	β	X
ejpam-5396	221	2	τ	τ	PROPN
ejpam-5396	221	3	λ+	λ+	PUNCT
ejpam-5396	221	4	(	(	PUNCT
ejpam-5396	221	5	µ+	µ+	X
ejpam-5396	221	6	η	η	NOUN
ejpam-5396	221	7	)	)	PUNCT
ejpam-5396	221	8	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-5396	222	1	=	=	SYM
ejpam-5396	222	2	0	0	X
ejpam-5396	222	3	.	.	PUNCT
ejpam-5396	223	1	then	then	ADV
ejpam-5396	223	2	,	,	PUNCT
ejpam-5396	223	3	(	(	PUNCT
ejpam-5396	223	4	λ+	λ+	NUM
ejpam-5396	223	5	µ)(λ+	µ)(λ+	X
ejpam-5396	223	6	µ+	µ+	X
ejpam-5396	223	7	η	η	NOUN
ejpam-5396	223	8	)	)	PUNCT
ejpam-5396	223	9	∣∣∣	∣∣∣	NOUN
ejpam-5396	223	10	λ+z1	λ+z1	PROPN
ejpam-5396	223	11	0	0	PUNCT
ejpam-5396	223	12	π	π	X
ejpam-5396	223	13	λ+z2	λ+z2	PROPN
ejpam-5396	223	14	∣∣∣	∣∣∣	NOUN
ejpam-5396	223	15	=	=	SYM
ejpam-5396	223	16	0	0	NUM
ejpam-5396	223	17	.	.	PUNCT
ejpam-5396	224	1	therefore	therefore	ADV
ejpam-5396	224	2	,	,	PUNCT
ejpam-5396	224	3	(	(	PUNCT
ejpam-5396	224	4	λ+	λ+	X
ejpam-5396	224	5	µ)(λ+	µ)(λ+	X
ejpam-5396	224	6	µ+	µ+	X
ejpam-5396	224	7	η)(λ+	η)(λ+	NOUN
ejpam-5396	224	8	z1)(λ+	z1)(λ+	NOUN
ejpam-5396	224	9	z2	z2	PROPN
ejpam-5396	224	10	)	)	PUNCT
ejpam-5396	224	11	=	=	SYM
ejpam-5396	225	1	0	0	X
ejpam-5396	225	2	.	.	PUNCT
ejpam-5396	226	1	(	(	PUNCT
ejpam-5396	226	2	2	2	NUM
ejpam-5396	226	3	)	)	PUNCT
ejpam-5396	226	4	from	from	ADP
ejpam-5396	226	5	equation	equation	NOUN
ejpam-5396	226	6	(	(	PUNCT
ejpam-5396	226	7	2	2	NUM
ejpam-5396	226	8	)	)	PUNCT
ejpam-5396	226	9	,	,	PUNCT
ejpam-5396	226	10	we	we	PRON
ejpam-5396	226	11	have	have	VERB
ejpam-5396	226	12	λ1	λ1	VERB
ejpam-5396	226	13	=	=	SYM
ejpam-5396	226	14	−(λ+	−(λ+	NUM
ejpam-5396	226	15	µ	µ	NUM
ejpam-5396	226	16	)	)	PUNCT
ejpam-5396	226	17	,	,	PUNCT
ejpam-5396	226	18	λ2	λ2	NOUN
ejpam-5396	226	19	=	=	PUNCT
ejpam-5396	226	20	−(λ+	−(λ+	PROPN
ejpam-5396	226	21	µ+	µ+	PROPN
ejpam-5396	226	22	η	η	PROPN
ejpam-5396	226	23	)	)	PUNCT
ejpam-5396	226	24	,	,	PUNCT
ejpam-5396	226	25	λ3	λ3	PROPN
ejpam-5396	226	26	=	=	SYM
ejpam-5396	226	27	−z1	−z1	PROPN
ejpam-5396	226	28	,	,	PUNCT
ejpam-5396	226	29	λ4	λ4	PROPN
ejpam-5396	226	30	=	=	PUNCT
ejpam-5396	226	31	−z2	−z2	PROPN
ejpam-5396	226	32	.	.	PUNCT
ejpam-5396	227	1	consequently	consequently	ADV
ejpam-5396	227	2	,	,	PUNCT
ejpam-5396	227	3	λ1	λ1	ADJ
ejpam-5396	227	4	,	,	PUNCT
ejpam-5396	227	5	λ2	λ2	PROPN
ejpam-5396	227	6	,	,	PUNCT
ejpam-5396	227	7	λ3	λ3	PROPN
ejpam-5396	227	8	,	,	PUNCT
ejpam-5396	227	9	λ4	λ4	PROPN
ejpam-5396	227	10	are	be	AUX
ejpam-5396	227	11	all	all	PRON
ejpam-5396	227	12	strictly	strictly	ADV
ejpam-5396	227	13	negative	negative	ADJ
ejpam-5396	227	14	roots	root	NOUN
ejpam-5396	227	15	of	of	ADP
ejpam-5396	227	16	eq	eq	NOUN
ejpam-5396	227	17	.	.	PUNCT
ejpam-5396	228	1	(	(	PUNCT
ejpam-5396	228	2	2	2	NUM
ejpam-5396	228	3	)	)	PUNCT
ejpam-5396	228	4	.	.	PUNCT
ejpam-5396	229	1	thus	thus	ADV
ejpam-5396	229	2	,	,	PUNCT
ejpam-5396	229	3	as	as	SCONJ
ejpam-5396	229	4	determined	determine	VERB
ejpam-5396	229	5	by	by	ADP
ejpam-5396	229	6	the	the	DET
ejpam-5396	229	7	routh	routh	PROPN
ejpam-5396	229	8	-	-	PUNCT
ejpam-5396	229	9	hurwitz	hurwitz	PROPN
ejpam-5396	229	10	criterion	criterion	NOUN
ejpam-5396	229	11	,	,	PUNCT
ejpam-5396	229	12	it	it	PRON
ejpam-5396	229	13	follows	follow	VERB
ejpam-5396	229	14	that	that	SCONJ
ejpam-5396	229	15	e0	e0	PROPN
ejpam-5396	229	16	=	=	PUNCT
ejpam-5396	229	17	(	(	PUNCT
ejpam-5396	229	18	0	0	NUM
ejpam-5396	229	19	,	,	PUNCT
ejpam-5396	229	20	0	0	NUM
ejpam-5396	229	21	,	,	PUNCT
ejpam-5396	229	22	0	0	NUM
ejpam-5396	229	23	,	,	PUNCT
ejpam-5396	229	24	0	0	NUM
ejpam-5396	229	25	)	)	PUNCT
ejpam-5396	229	26	is	be	AUX
ejpam-5396	229	27	locally	locally	ADV
ejpam-5396	229	28	asymptotically	asymptotically	ADV
ejpam-5396	229	29	stable	stable	ADJ
ejpam-5396	229	30	.	.	PUNCT
ejpam-5396	230	1	lemma	lemma	PROPN
ejpam-5396	230	2	3	3	X
ejpam-5396	230	3	.	.	PUNCT
ejpam-5396	231	1	the	the	DET
ejpam-5396	231	2	disease	disease	NOUN
ejpam-5396	231	3	-	-	PUNCT
ejpam-5396	231	4	free	free	ADJ
ejpam-5396	231	5	equilibrium	equilibrium	NOUN
ejpam-5396	231	6	e1	e1	NOUN
ejpam-5396	231	7	=	=	SYM
ejpam-5396	231	8	(	(	PUNCT
ejpam-5396	231	9	λ	λ	X
ejpam-5396	231	10	µ	µ	X
ejpam-5396	231	11	,	,	PUNCT
ejpam-5396	231	12	0	0	NUM
ejpam-5396	231	13	,	,	PUNCT
ejpam-5396	231	14	0	0	NUM
ejpam-5396	231	15	,	,	PUNCT
ejpam-5396	231	16	0	0	NUM
ejpam-5396	231	17	)	)	PUNCT
ejpam-5396	231	18	is	be	AUX
ejpam-5396	231	19	locally	locally	ADV
ejpam-5396	231	20	asymptotically	asymptotically	ADV
ejpam-5396	231	21	stable	stable	ADJ
ejpam-5396	231	22	in	in	ADP
ejpam-5396	231	23	ω	ω	NUM
ejpam-5396	231	24	if	if	SCONJ
ejpam-5396	231	25	r0	r0	NOUN
ejpam-5396	231	26	<	<	X
ejpam-5396	231	27	1	1	NUM
ejpam-5396	231	28	and	and	CCONJ
ejpam-5396	231	29	is	be	AUX
ejpam-5396	231	30	unstable	unstable	ADJ
ejpam-5396	231	31	if	if	SCONJ
ejpam-5396	231	32	r0	r0	NOUN
ejpam-5396	231	33	>	>	X
ejpam-5396	231	34	1	1	X
ejpam-5396	231	35	.	.	PUNCT
ejpam-5396	231	36	a.	a.	NOUN
ejpam-5396	231	37	alalyani	alalyani	PROPN
ejpam-5396	231	38	/	/	SYM
ejpam-5396	231	39	eur	eur	PROPN
ejpam-5396	231	40	.	.	PUNCT
ejpam-5396	232	1	j.	j.	PROPN
ejpam-5396	232	2	pure	pure	PROPN
ejpam-5396	232	3	appl	appl	PROPN
ejpam-5396	232	4	.	.	PROPN
ejpam-5396	232	5	math	math	PROPN
ejpam-5396	232	6	,	,	PUNCT
ejpam-5396	232	7	17	17	NUM
ejpam-5396	232	8	(	(	PUNCT
ejpam-5396	232	9	4	4	NUM
ejpam-5396	232	10	)	)	PUNCT
ejpam-5396	232	11	(	(	PUNCT
ejpam-5396	232	12	2024	2024	NUM
ejpam-5396	232	13	)	)	PUNCT
ejpam-5396	232	14	,	,	PUNCT
ejpam-5396	232	15	2763	2763	NUM
ejpam-5396	232	16	-	-	SYM
ejpam-5396	232	17	2799	2799	NUM
ejpam-5396	232	18	2772	2772	NUM
ejpam-5396	232	19	proof	proof	NOUN
ejpam-5396	232	20	.	.	PUNCT
ejpam-5396	233	1	at	at	ADP
ejpam-5396	233	2	e1	e1	NOUN
ejpam-5396	233	3	=	=	SYM
ejpam-5396	233	4	(	(	PUNCT
ejpam-5396	233	5	λ	λ	X
ejpam-5396	233	6	µ	µ	X
ejpam-5396	233	7	,	,	PUNCT
ejpam-5396	233	8	0	0	NUM
ejpam-5396	233	9	,	,	PUNCT
ejpam-5396	233	10	0	0	NUM
ejpam-5396	233	11	,	,	PUNCT
ejpam-5396	233	12	0	0	NUM
ejpam-5396	233	13	)	)	PUNCT
ejpam-5396	233	14	,	,	PUNCT
ejpam-5396	233	15	the	the	DET
ejpam-5396	233	16	model	model	NOUN
ejpam-5396	233	17	(	(	PUNCT
ejpam-5396	233	18	1	1	X
ejpam-5396	233	19	)	)	PUNCT
ejpam-5396	233	20	has	have	VERB
ejpam-5396	233	21	the	the	DET
ejpam-5396	233	22	following	follow	VERB
ejpam-5396	233	23	jacobian	jacobian	ADJ
ejpam-5396	233	24	matrix	matrix	NOUN
ejpam-5396	233	25	j(e1	j(e1	NOUN
ejpam-5396	233	26	):	):	PUNCT
ejpam-5396	233	27	j(e1	j(e1	NOUN
ejpam-5396	233	28	)	)	PUNCT
ejpam-5396	234	1	=	=	SYM
ejpam-5396	234	2	−µ	−µ	ADV
ejpam-5396	234	3	−	−	PROPN
ejpam-5396	234	4	δωs0	δωs0	PROPN
ejpam-5396	234	5	n	n	CCONJ
ejpam-5396	234	6	−	−	PROPN
ejpam-5396	234	7	δs0	δs0	NOUN
ejpam-5396	234	8	n	n	PROPN
ejpam-5396	234	9	η	η	PROPN
ejpam-5396	234	10	0	0	NUM
ejpam-5396	234	11	δωθs0	δωθs0	PROPN
ejpam-5396	234	12	n	n	CCONJ
ejpam-5396	234	13	−z1	−z1	VERB
ejpam-5396	234	14	δθs0	δθs0	NOUN
ejpam-5396	234	15	n	n	CCONJ
ejpam-5396	234	16	0	0	NUM
ejpam-5396	234	17	0	0	NUM
ejpam-5396	234	18	δω(1−θ)s0	δω(1−θ)s0	NOUN
ejpam-5396	234	19	n	n	PROPN
ejpam-5396	235	1	+	+	NOUN
ejpam-5396	235	2	π	π	PROPN
ejpam-5396	235	3	δ(1−θ)s0	δ(1−θ)s0	NOUN
ejpam-5396	235	4	n	n	CCONJ
ejpam-5396	235	5	−z2	−z2	PROPN
ejpam-5396	235	6	0	0	NUM
ejpam-5396	235	7	0	0	NUM
ejpam-5396	235	8	β	β	X
ejpam-5396	235	9	τ	τ	PROPN
ejpam-5396	235	10	−(µ+η	−(µ+η	PROPN
ejpam-5396	235	11	)	)	PUNCT
ejpam-5396	235	12			PROPN
ejpam-5396	235	13	.	.	PUNCT
ejpam-5396	236	1	therefore	therefore	ADV
ejpam-5396	236	2	,	,	PUNCT
ejpam-5396	236	3	we	we	PRON
ejpam-5396	236	4	can	can	AUX
ejpam-5396	236	5	get	get	VERB
ejpam-5396	236	6	the	the	DET
ejpam-5396	236	7	eigenvalues	eigenvalue	NOUN
ejpam-5396	236	8	as	as	ADP
ejpam-5396	236	9	:	:	PUNCT
ejpam-5396	236	10	j(e1	j(e1	NOUN
ejpam-5396	236	11	)	)	PUNCT
ejpam-5396	237	1	=	=	VERB
ejpam-5396	237	2	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	NOUN
ejpam-5396	237	3	λ+µ	λ+µ	DET
ejpam-5396	237	4	−	−	PROPN
ejpam-5396	237	5	δωs0	δωs0	PROPN
ejpam-5396	237	6	n	n	CCONJ
ejpam-5396	237	7	−	−	PROPN
ejpam-5396	237	8	δs0	δs0	NOUN
ejpam-5396	237	9	n	n	PROPN
ejpam-5396	237	10	η	η	PROPN
ejpam-5396	237	11	0	0	NUM
ejpam-5396	237	12	λ−	λ−	PROPN
ejpam-5396	237	13	δωθs0	δωθs0	PROPN
ejpam-5396	237	14	n	n	ADP
ejpam-5396	237	15	+	+	ADJ
ejpam-5396	237	16	z1	z1	ADJ
ejpam-5396	237	17	δθs0	δθs0	NOUN
ejpam-5396	237	18	n	n	CCONJ
ejpam-5396	237	19	0	0	NUM
ejpam-5396	237	20	0	0	NUM
ejpam-5396	237	21	δω(1−θ)s0	δω(1−θ)s0	NOUN
ejpam-5396	237	22	n	n	PROPN
ejpam-5396	237	23	+	+	ADP
ejpam-5396	237	24	π	π	PROPN
ejpam-5396	237	25	λ−	λ−	PROPN
ejpam-5396	237	26	δ(1−θ)s0	δ(1−θ)s0	PROPN
ejpam-5396	237	27	n	n	PROPN
ejpam-5396	237	28	+	+	PROPN
ejpam-5396	237	29	z2	z2	PROPN
ejpam-5396	237	30	0	0	NUM
ejpam-5396	237	31	0	0	NUM
ejpam-5396	237	32	β	β	X
ejpam-5396	237	33	τ	τ	PROPN
ejpam-5396	237	34	λ+(µ+η	λ+(µ+η	NOUN
ejpam-5396	237	35	)	)	PUNCT
ejpam-5396	237	36	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PUNCT
ejpam-5396	238	1	=	=	PUNCT
ejpam-5396	238	2	0	0	X
ejpam-5396	238	3	.	.	PUNCT
ejpam-5396	239	1	then	then	ADV
ejpam-5396	239	2	,	,	PUNCT
ejpam-5396	239	3	(	(	PUNCT
ejpam-5396	239	4	λ+	λ+	NUM
ejpam-5396	239	5	µ)(λ+	µ)(λ+	X
ejpam-5396	239	6	µ+	µ+	X
ejpam-5396	239	7	η	η	NOUN
ejpam-5396	239	8	)	)	PUNCT
ejpam-5396	239	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5396	239	10	λ−	λ−	PROPN
ejpam-5396	239	11	δωθs0	δωθs0	NOUN
ejpam-5396	239	12	n	n	ADP
ejpam-5396	239	13	+	+	ADJ
ejpam-5396	239	14	z1	z1	ADJ
ejpam-5396	239	15	δθs0	δθs0	NOUN
ejpam-5396	239	16	n	n	ADP
ejpam-5396	239	17	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	239	18	n	n	PROPN
ejpam-5396	240	1	+	+	ADP
ejpam-5396	240	2	π	π	PROPN
ejpam-5396	240	3	λ−	λ−	PROPN
ejpam-5396	240	4	δ(1−θ)s0	δ(1−θ)s0	PROPN
ejpam-5396	240	5	n	n	PROPN
ejpam-5396	240	6	+	+	ADJ
ejpam-5396	240	7	z2	z2	NOUN
ejpam-5396	240	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5396	240	9	=	=	SYM
ejpam-5396	240	10	0	0	X
ejpam-5396	240	11	.	.	PUNCT
ejpam-5396	240	12	therefore	therefore	ADV
ejpam-5396	240	13	,	,	PUNCT
ejpam-5396	240	14	(	(	PUNCT
ejpam-5396	240	15	λ+	λ+	NUM
ejpam-5396	240	16	µ)(λ+	µ)(λ+	X
ejpam-5396	240	17	µ+	µ+	X
ejpam-5396	240	18	η	η	PROPN
ejpam-5396	240	19	)	)	PUNCT
ejpam-5396	240	20	=	=	SYM
ejpam-5396	240	21	0	0	NUM
ejpam-5396	240	22	,	,	PUNCT
ejpam-5396	240	23	(	(	PUNCT
ejpam-5396	240	24	3	3	NUM
ejpam-5396	240	25	)	)	PUNCT
ejpam-5396	240	26	or	or	CCONJ
ejpam-5396	240	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5396	240	28	λ−	λ−	PROPN
ejpam-5396	240	29	δωθs0	δωθs0	NOUN
ejpam-5396	240	30	n	n	ADP
ejpam-5396	240	31	+	+	ADJ
ejpam-5396	240	32	z1	z1	ADJ
ejpam-5396	240	33	δθs0	δθs0	NOUN
ejpam-5396	240	34	n	n	ADP
ejpam-5396	240	35	δω(1−θ)s0	δω(1−θ)s0	PROPN
ejpam-5396	240	36	n	n	PROPN
ejpam-5396	241	1	+	+	ADP
ejpam-5396	241	2	π	π	PROPN
ejpam-5396	241	3	λ−	λ−	PROPN
ejpam-5396	241	4	δ(1−θ)s0	δ(1−θ)s0	PROPN
ejpam-5396	241	5	n	n	PROPN
ejpam-5396	241	6	+	+	ADJ
ejpam-5396	241	7	z2	z2	NOUN
ejpam-5396	241	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5396	241	9	=	=	NOUN
ejpam-5396	241	10	0	0	NUM
ejpam-5396	241	11	.	.	PUNCT
ejpam-5396	241	12	from	from	ADP
ejpam-5396	241	13	eq	eq	ADP
ejpam-5396	241	14	.	.	PUNCT
ejpam-5396	242	1	(	(	PUNCT
ejpam-5396	242	2	3	3	NUM
ejpam-5396	242	3	)	)	PUNCT
ejpam-5396	242	4	,	,	PUNCT
ejpam-5396	242	5	we	we	PRON
ejpam-5396	242	6	have	have	VERB
ejpam-5396	242	7	λ1	λ1	VERB
ejpam-5396	242	8	=	=	SYM
ejpam-5396	242	9	−(λ+	−(λ+	NUM
ejpam-5396	242	10	µ	µ	NUM
ejpam-5396	242	11	)	)	PUNCT
ejpam-5396	242	12	,	,	PUNCT
ejpam-5396	242	13	λ2	λ2	NOUN
ejpam-5396	242	14	=	=	PUNCT
ejpam-5396	242	15	−(λ+	−(λ+	PROPN
ejpam-5396	242	16	µ+	µ+	PROPN
ejpam-5396	242	17	η	η	PROPN
ejpam-5396	242	18	)	)	PUNCT
ejpam-5396	242	19	,	,	PUNCT
ejpam-5396	242	20	or	or	CCONJ
ejpam-5396	242	21	λ2	λ2	NOUN
ejpam-5396	242	22	+	+	CCONJ
ejpam-5396	242	23	c1λ+	c1λ+	PROPN
ejpam-5396	242	24	c2	c2	PROPN
ejpam-5396	242	25	=	=	SYM
ejpam-5396	242	26	0	0	PROPN
ejpam-5396	242	27	,	,	PUNCT
ejpam-5396	242	28	where	where	SCONJ
ejpam-5396	242	29	c1	c1	PROPN
ejpam-5396	242	30	=	=	PUNCT
ejpam-5396	242	31	−δωθs0	−δωθs0	PROPN
ejpam-5396	242	32	n	n	PROPN
ejpam-5396	242	33	+	+	CCONJ
ejpam-5396	242	34	z1	z1	PROPN
ejpam-5396	242	35	−	−	PROPN
ejpam-5396	242	36	δ(1−	δ(1−	ADJ
ejpam-5396	242	37	θ)s0	θ)s0	PROPN
ejpam-5396	242	38	n	n	PROPN
ejpam-5396	242	39	+	+	X
ejpam-5396	242	40	z2	z2	PROPN
ejpam-5396	242	41	,	,	PUNCT
ejpam-5396	242	42	c2	c2	PROPN
ejpam-5396	242	43	=	=	PUNCT
ejpam-5396	243	1	−πδθs0	−πδθs0	NOUN
ejpam-5396	243	2	n	n	CCONJ
ejpam-5396	243	3	−	−	PROPN
ejpam-5396	243	4	δωθz2s0	δωθz2s0	ADP
ejpam-5396	243	5	n	n	CCONJ
ejpam-5396	243	6	−	−	PROPN
ejpam-5396	243	7	δ(1−	δ(1−	ADJ
ejpam-5396	243	8	θ)z1s0	θ)z1s0	VERB
ejpam-5396	243	9	n	n	PROPN
ejpam-5396	243	10	+	+	CCONJ
ejpam-5396	243	11	z1z2	z1z2	PROPN
ejpam-5396	243	12	,	,	PUNCT
ejpam-5396	243	13	c2	c2	PROPN
ejpam-5396	243	14	=	=	PUNCT
ejpam-5396	244	1	−	−	PROPN
ejpam-5396	245	1	[	[	X
ejpam-5396	245	2	θπ	θπ	X
ejpam-5396	245	3	+	+	X
ejpam-5396	245	4	ωθz2	ωθz2	NOUN
ejpam-5396	245	5	+	+	CCONJ
ejpam-5396	245	6	(	(	PUNCT
ejpam-5396	245	7	1−	1−	NUM
ejpam-5396	245	8	θ)z1]δs0	θ)z1]δs0	NOUN
ejpam-5396	245	9	n	n	PROPN
ejpam-5396	245	10	+	+	CCONJ
ejpam-5396	245	11	z1z2	z1z2	NOUN
ejpam-5396	245	12	,	,	PUNCT
ejpam-5396	245	13	where	where	SCONJ
ejpam-5396	245	14	z1	z1	PROPN
ejpam-5396	245	15	=	=	PUNCT
ejpam-5396	245	16	µ+	µ+	X
ejpam-5396	245	17	β	β	X
ejpam-5396	245	18	+	+	SYM
ejpam-5396	245	19	π	π	PROPN
ejpam-5396	245	20	,	,	PUNCT
ejpam-5396	245	21	z2	z2	PROPN
ejpam-5396	245	22	=	=	SYM
ejpam-5396	245	23	τ	τ	PROPN
ejpam-5396	245	24	+	+	NUM
ejpam-5396	245	25	µ+	µ+	PROPN
ejpam-5396	245	26	σ	σ	PROPN
ejpam-5396	245	27	,	,	PUNCT
ejpam-5396	245	28	s0	s0	PROPN
ejpam-5396	245	29	=	=	SYM
ejpam-5396	245	30	λ	λ	PROPN
ejpam-5396	245	31	µ	µ	X
ejpam-5396	245	32	.	.	PUNCT
ejpam-5396	246	1	as	as	ADP
ejpam-5396	246	2	a	a	DET
ejpam-5396	246	3	result	result	NOUN
ejpam-5396	246	4	,	,	PUNCT
ejpam-5396	246	5	if	if	SCONJ
ejpam-5396	246	6	c1	c1	PROPN
ejpam-5396	246	7	>	>	X
ejpam-5396	246	8	0	0	PUNCT
ejpam-5396	246	9	and	and	CCONJ
ejpam-5396	246	10	c2	c2	PROPN
ejpam-5396	246	11	>	>	X
ejpam-5396	246	12	0	0	PROPN
ejpam-5396	246	13	,	,	PUNCT
ejpam-5396	246	14	the	the	DET
ejpam-5396	246	15	routh	routh	PROPN
ejpam-5396	246	16	-	-	PUNCT
ejpam-5396	246	17	hurwitz	hurwitz	PROPN
ejpam-5396	246	18	criteria	criterion	NOUN
ejpam-5396	246	19	states	state	VERB
ejpam-5396	246	20	that	that	SCONJ
ejpam-5396	246	21	e1	e1	NOUN
ejpam-5396	246	22	is	be	AUX
ejpam-5396	246	23	locally	locally	ADV
ejpam-5396	246	24	asymptotically	asymptotically	ADV
ejpam-5396	246	25	stable	stable	ADJ
ejpam-5396	246	26	when	when	SCONJ
ejpam-5396	246	27	r0	r0	NOUN
ejpam-5396	246	28	<	<	X
ejpam-5396	246	29	1	1	NUM
ejpam-5396	246	30	.	.	PUNCT
ejpam-5396	246	31	when	when	SCONJ
ejpam-5396	246	32	r0	r0	NOUN
ejpam-5396	246	33	<	<	X
ejpam-5396	246	34	1	1	NUM
ejpam-5396	246	35	holds	hold	NOUN
ejpam-5396	246	36	,	,	PUNCT
ejpam-5396	246	37	we	we	PRON
ejpam-5396	246	38	must	must	AUX
ejpam-5396	246	39	demonstrate	demonstrate	VERB
ejpam-5396	246	40	that	that	DET
ejpam-5396	246	41	c1	c1	PROPN
ejpam-5396	246	42	>	>	X
ejpam-5396	246	43	0	0	PUNCT
ejpam-5396	246	44	and	and	CCONJ
ejpam-5396	246	45	c2	c2	PROPN
ejpam-5396	246	46	>	>	X
ejpam-5396	246	47	0	0	X
ejpam-5396	246	48	.	.	PUNCT
ejpam-5396	247	1	r0	r0	NOUN
ejpam-5396	247	2	=	=	SYM
ejpam-5396	247	3	(	(	PUNCT
ejpam-5396	247	4	ωθz2	ωθz2	NOUN
ejpam-5396	247	5	+	+	CCONJ
ejpam-5396	247	6	(	(	PUNCT
ejpam-5396	247	7	1−	1−	NUM
ejpam-5396	247	8	θ)(πω	θ)(πω	X
ejpam-5396	247	9	+	+	CCONJ
ejpam-5396	247	10	z1))δs0	z1))δs0	PROPN
ejpam-5396	247	11	nz1z2	nz1z2	PROPN
ejpam-5396	247	12	.	.	PUNCT
ejpam-5396	247	13	a.	a.	PROPN
ejpam-5396	247	14	alalyani	alalyani	PROPN
ejpam-5396	247	15	/	/	SYM
ejpam-5396	247	16	eur	eur	PROPN
ejpam-5396	247	17	.	.	PUNCT
ejpam-5396	248	1	j.	j.	PROPN
ejpam-5396	248	2	pure	pure	PROPN
ejpam-5396	248	3	appl	appl	PROPN
ejpam-5396	248	4	.	.	PROPN
ejpam-5396	248	5	math	math	PROPN
ejpam-5396	248	6	,	,	PUNCT
ejpam-5396	248	7	17	17	NUM
ejpam-5396	248	8	(	(	PUNCT
ejpam-5396	248	9	4	4	NUM
ejpam-5396	248	10	)	)	PUNCT
ejpam-5396	248	11	(	(	PUNCT
ejpam-5396	248	12	2024	2024	NUM
ejpam-5396	248	13	)	)	PUNCT
ejpam-5396	248	14	,	,	PUNCT
ejpam-5396	248	15	2763	2763	NUM
ejpam-5396	248	16	-	-	SYM
ejpam-5396	248	17	2799	2799	NUM
ejpam-5396	248	18	2773	2773	NUM
ejpam-5396	248	19	if	if	SCONJ
ejpam-5396	248	20	r0	r0	NOUN
ejpam-5396	248	21	<	<	X
ejpam-5396	248	22	1	1	NUM
ejpam-5396	248	23	,	,	PUNCT
ejpam-5396	248	24	we	we	PRON
ejpam-5396	248	25	have	have	VERB
ejpam-5396	248	26	(	(	PUNCT
ejpam-5396	248	27	ωθz2	ωθz2	NOUN
ejpam-5396	248	28	+	+	CCONJ
ejpam-5396	248	29	z1(1−	z1(1−	X
ejpam-5396	248	30	θ))δs0	θ))δs0	PROPN
ejpam-5396	248	31	n	n	PROPN
ejpam-5396	248	32	<	<	X
ejpam-5396	248	33	z1z2	z1z2	PROPN
ejpam-5396	248	34	.	.	PUNCT
ejpam-5396	249	1	if	if	SCONJ
ejpam-5396	249	2	γ	γ	X
ejpam-5396	249	3	=	=	SYM
ejpam-5396	249	4	min{z2	min{z2	ADJ
ejpam-5396	249	5	,	,	PUNCT
ejpam-5396	249	6	z1	z1	NOUN
ejpam-5396	249	7	}	}	PUNCT
ejpam-5396	249	8	,	,	PUNCT
ejpam-5396	249	9	we	we	PRON
ejpam-5396	249	10	have	have	VERB
ejpam-5396	249	11	(	(	PUNCT
ejpam-5396	249	12	ωθ	ωθ	X
ejpam-5396	249	13	+	+	SYM
ejpam-5396	249	14	(	(	PUNCT
ejpam-5396	249	15	1−	1−	NUM
ejpam-5396	249	16	θ))δs0	θ))δs0	PROPN
ejpam-5396	249	17	n	n	PROPN
ejpam-5396	249	18	<	<	X
ejpam-5396	249	19	z1z2	z1z2	PROPN
ejpam-5396	249	20	γ	γ	X
ejpam-5396	249	21	.	.	PUNCT
ejpam-5396	250	1	thus	thus	ADV
ejpam-5396	250	2	,	,	PUNCT
ejpam-5396	250	3	(	(	PUNCT
ejpam-5396	250	4	ωθ	ωθ	X
ejpam-5396	250	5	+	+	SYM
ejpam-5396	250	6	(	(	PUNCT
ejpam-5396	250	7	1−	1−	NUM
ejpam-5396	250	8	θ))δs0	θ))δs0	PROPN
ejpam-5396	250	9	n	n	CCONJ
ejpam-5396	250	10	<	<	X
ejpam-5396	250	11	z1	z1	PROPN
ejpam-5396	250	12	+	+	CCONJ
ejpam-5396	250	13	z2	z2	PROPN
ejpam-5396	250	14	.	.	PUNCT
ejpam-5396	251	1	then	then	ADV
ejpam-5396	251	2	,	,	PUNCT
ejpam-5396	251	3	c1	c1	PROPN
ejpam-5396	251	4	=	=	PROPN
ejpam-5396	251	5	z1	z1	PROPN
ejpam-5396	251	6	+	+	CCONJ
ejpam-5396	251	7	z2	z2	PROPN
ejpam-5396	251	8	−	−	PROPN
ejpam-5396	251	9	(	(	PUNCT
ejpam-5396	251	10	ωθ	ωθ	NUM
ejpam-5396	251	11	+	+	SYM
ejpam-5396	251	12	(	(	PUNCT
ejpam-5396	251	13	1−	1−	NUM
ejpam-5396	251	14	θ))δs0	θ))δs0	PROPN
ejpam-5396	251	15	n	n	PROPN
ejpam-5396	251	16	>	>	X
ejpam-5396	251	17	0	0	X
ejpam-5396	251	18	.	.	PUNCT
ejpam-5396	252	1	if	if	SCONJ
ejpam-5396	252	2	r0	r0	NOUN
ejpam-5396	252	3	<	<	X
ejpam-5396	252	4	1	1	NUM
ejpam-5396	252	5	,	,	PUNCT
ejpam-5396	252	6	we	we	PRON
ejpam-5396	252	7	have	have	VERB
ejpam-5396	252	8	(	(	PUNCT
ejpam-5396	252	9	ωθz2	ωθz2	NOUN
ejpam-5396	252	10	+	+	CCONJ
ejpam-5396	252	11	(	(	PUNCT
ejpam-5396	252	12	πω	πω	ADP
ejpam-5396	252	13	+	+	CCONJ
ejpam-5396	252	14	z1)(1−	z1)(1−	PROPN
ejpam-5396	252	15	θ))δs0	θ))δs0	PROPN
ejpam-5396	252	16	nz1z2	nz1z2	PROPN
ejpam-5396	252	17	<	<	X
ejpam-5396	252	18	1	1	NUM
ejpam-5396	252	19	,	,	PUNCT
ejpam-5396	252	20	which	which	PRON
ejpam-5396	252	21	implies	imply	VERB
ejpam-5396	252	22	(	(	PUNCT
ejpam-5396	252	23	ωθz2	ωθz2	NOUN
ejpam-5396	252	24	+	+	CCONJ
ejpam-5396	252	25	(	(	PUNCT
ejpam-5396	252	26	πω	πω	ADP
ejpam-5396	252	27	+	+	CCONJ
ejpam-5396	252	28	z1)(1−	z1)(1−	PROPN
ejpam-5396	252	29	θ))δs0	θ))δs0	PROPN
ejpam-5396	252	30	<	<	X
ejpam-5396	252	31	nz1z2	nz1z2	PROPN
ejpam-5396	252	32	.	.	PROPN
ejpam-5396	252	33	that	that	PRON
ejpam-5396	252	34	is	be	AUX
ejpam-5396	252	35	,	,	PUNCT
ejpam-5396	252	36	nz1z2	nz1z2	PROPN
ejpam-5396	252	37	−	−	PROPN
ejpam-5396	253	1	[	[	X
ejpam-5396	253	2	ωθz2	ωθz2	NOUN
ejpam-5396	253	3	+	+	CCONJ
ejpam-5396	253	4	(	(	PUNCT
ejpam-5396	253	5	πω	πω	ADP
ejpam-5396	253	6	+	+	CCONJ
ejpam-5396	253	7	z1)(1−	z1)(1−	X
ejpam-5396	253	8	θ)]δs0	θ)]δs0	X
ejpam-5396	253	9	>	>	X
ejpam-5396	253	10	0	0	X
ejpam-5396	253	11	.	.	PUNCT
ejpam-5396	254	1	that	that	PRON
ejpam-5396	254	2	is	be	AUX
ejpam-5396	254	3	,	,	PUNCT
ejpam-5396	254	4	z1z2	z1z2	PROPN
ejpam-5396	254	5	−	−	PROPN
ejpam-5396	255	1	[	[	X
ejpam-5396	255	2	πω(1−	πω(1−	PROPN
ejpam-5396	255	3	θ	θ	NOUN
ejpam-5396	255	4	)	)	PUNCT
ejpam-5396	255	5	+	+	NUM
ejpam-5396	255	6	ωθz2	ωθz2	NOUN
ejpam-5396	255	7	+	+	CCONJ
ejpam-5396	255	8	z1(1−	z1(1−	X
ejpam-5396	255	9	θ)]δs0	θ)]δs0	X
ejpam-5396	255	10	n	n	CCONJ
ejpam-5396	255	11	>	>	X
ejpam-5396	255	12	0	0	PROPN
ejpam-5396	255	13	,	,	PUNCT
ejpam-5396	255	14	where	where	SCONJ
ejpam-5396	255	15	z1	z1	PROPN
ejpam-5396	255	16	=	=	PUNCT
ejpam-5396	255	17	µ+	µ+	X
ejpam-5396	255	18	β	β	X
ejpam-5396	255	19	+	+	SYM
ejpam-5396	255	20	π	π	PROPN
ejpam-5396	255	21	,	,	PUNCT
ejpam-5396	255	22	z2	z2	PROPN
ejpam-5396	255	23	=	=	SYM
ejpam-5396	255	24	τ	τ	PROPN
ejpam-5396	255	25	+	+	NUM
ejpam-5396	255	26	µ+	µ+	PROPN
ejpam-5396	255	27	σ	σ	PROPN
ejpam-5396	255	28	,	,	PUNCT
ejpam-5396	255	29	s0	s0	PROPN
ejpam-5396	255	30	=	=	SYM
ejpam-5396	255	31	λ	λ	PROPN
ejpam-5396	255	32	µ	µ	X
ejpam-5396	255	33	.	.	PUNCT
ejpam-5396	256	1	thus	thus	ADV
ejpam-5396	256	2	,	,	PUNCT
ejpam-5396	256	3	c2	c2	PROPN
ejpam-5396	256	4	>	>	X
ejpam-5396	256	5	0	0	PROPN
ejpam-5396	256	6	.	.	PUNCT
ejpam-5396	257	1	for	for	ADP
ejpam-5396	257	2	this	this	DET
ejpam-5396	257	3	reason	reason	NOUN
ejpam-5396	257	4	,	,	PUNCT
ejpam-5396	257	5	when	when	SCONJ
ejpam-5396	257	6	r0	r0	NOUN
ejpam-5396	257	7	<	<	X
ejpam-5396	257	8	1	1	NUM
ejpam-5396	257	9	,	,	PUNCT
ejpam-5396	257	10	e1	e1	NOUN
ejpam-5396	257	11	is	be	AUX
ejpam-5396	257	12	locally	locally	ADV
ejpam-5396	257	13	asymptotically	asymptotically	ADV
ejpam-5396	257	14	stable	stable	ADJ
ejpam-5396	257	15	and	and	CCONJ
ejpam-5396	257	16	unstable	unstable	ADJ
ejpam-5396	257	17	when	when	SCONJ
ejpam-5396	257	18	r0	r0	NOUN
ejpam-5396	257	19	>	>	X
ejpam-5396	257	20	1	1	X
ejpam-5396	257	21	.	.	PUNCT
ejpam-5396	258	1	lemma	lemma	PROPN
ejpam-5396	258	2	4	4	X
ejpam-5396	258	3	.	.	PUNCT
ejpam-5396	259	1	if	if	SCONJ
ejpam-5396	259	2	r0	r0	NOUN
ejpam-5396	259	3	>	>	X
ejpam-5396	259	4	1	1	NUM
ejpam-5396	259	5	,	,	PUNCT
ejpam-5396	259	6	the	the	DET
ejpam-5396	259	7	pneumonia	pneumonia	NOUN
ejpam-5396	259	8	endemic	endemic	ADJ
ejpam-5396	259	9	equilibrium	equilibrium	NOUN
ejpam-5396	259	10	e2	e2	PROPN
ejpam-5396	259	11	=	=	PUNCT
ejpam-5396	259	12	(	(	PUNCT
ejpam-5396	259	13	s∗	s∗	PROPN
ejpam-5396	259	14	,	,	PUNCT
ejpam-5396	259	15	c∗	c∗	NOUN
ejpam-5396	259	16	,	,	PUNCT
ejpam-5396	259	17	i∗	i∗	NOUN
ejpam-5396	259	18	,	,	PUNCT
ejpam-5396	259	19	r∗	r∗	PROPN
ejpam-5396	259	20	)	)	PUNCT
ejpam-5396	259	21	is	be	AUX
ejpam-5396	259	22	locally	locally	ADV
ejpam-5396	259	23	asymptotically	asymptotically	ADV
ejpam-5396	259	24	stable	stable	ADJ
ejpam-5396	259	25	in	in	ADP
ejpam-5396	259	26	ω	ω	PROPN
ejpam-5396	259	27	.	.	PUNCT
ejpam-5396	260	1	proof	proof	NOUN
ejpam-5396	260	2	.	.	PUNCT
ejpam-5396	261	1	at	at	ADP
ejpam-5396	261	2	e2	e2	PROPN
ejpam-5396	261	3	=	=	PUNCT
ejpam-5396	261	4	(	(	PUNCT
ejpam-5396	261	5	s∗	s∗	PROPN
ejpam-5396	261	6	,	,	PUNCT
ejpam-5396	261	7	c∗	c∗	NOUN
ejpam-5396	261	8	,	,	PUNCT
ejpam-5396	261	9	i∗	i∗	NOUN
ejpam-5396	261	10	,	,	PUNCT
ejpam-5396	261	11	r∗	r∗	PROPN
ejpam-5396	261	12	)	)	PUNCT
ejpam-5396	261	13	,	,	PUNCT
ejpam-5396	261	14	the	the	DET
ejpam-5396	261	15	model	model	NOUN
ejpam-5396	261	16	(	(	PUNCT
ejpam-5396	261	17	1	1	X
ejpam-5396	261	18	)	)	PUNCT
ejpam-5396	261	19	has	have	VERB
ejpam-5396	261	20	the	the	DET
ejpam-5396	261	21	following	follow	VERB
ejpam-5396	261	22	jacobian	jacobian	ADJ
ejpam-5396	261	23	matrix	matrix	NOUN
ejpam-5396	261	24	j(e2	j(e2	NOUN
ejpam-5396	261	25	):	):	PUNCT
ejpam-5396	261	26	j(e2	j(e2	NOUN
ejpam-5396	261	27	)	)	PUNCT
ejpam-5396	262	1	=	=	SYM
ejpam-5396	262	2			NOUN
ejpam-5396	262	3	−f1	−f1	PROPN
ejpam-5396	262	4	−	−	PROPN
ejpam-5396	262	5	µ	µ	PROPN
ejpam-5396	262	6	−f2	−f2	PROPN
ejpam-5396	262	7	−f3	−f3	PROPN
ejpam-5396	262	8	η	η	PROPN
ejpam-5396	262	9	f1θ	f1θ	NOUN
ejpam-5396	262	10	f2θ	f2θ	NOUN
ejpam-5396	262	11	−	−	PROPN
ejpam-5396	262	12	z1	z1	PROPN
ejpam-5396	262	13	f3θ	f3θ	PROPN
ejpam-5396	262	14	0	0	NUM
ejpam-5396	262	15	f1(1−	f1(1−	PROPN
ejpam-5396	262	16	θ	θ	PROPN
ejpam-5396	262	17	)	)	PUNCT
ejpam-5396	262	18	f2(1−	f2(1−	PROPN
ejpam-5396	262	19	θ	θ	NOUN
ejpam-5396	262	20	)	)	PUNCT
ejpam-5396	262	21	+	+	CCONJ
ejpam-5396	262	22	π	π	PROPN
ejpam-5396	262	23	f3(1−	f3(1−	PROPN
ejpam-5396	262	24	θ)−	θ)−	PROPN
ejpam-5396	262	25	z2	z2	PROPN
ejpam-5396	262	26	0	0	NUM
ejpam-5396	262	27	0	0	NUM
ejpam-5396	262	28	β	β	X
ejpam-5396	262	29	τ	τ	PROPN
ejpam-5396	262	30	−(µ+	−(µ+	PROPN
ejpam-5396	262	31	η	η	PROPN
ejpam-5396	262	32	)	)	PUNCT
ejpam-5396	262	33			PROPN
ejpam-5396	262	34	,	,	PUNCT
ejpam-5396	262	35	a.	a.	NOUN
ejpam-5396	262	36	alalyani	alalyani	PROPN
ejpam-5396	262	37	/	/	SYM
ejpam-5396	262	38	eur	eur	PROPN
ejpam-5396	262	39	.	.	PUNCT
ejpam-5396	263	1	j.	j.	PROPN
ejpam-5396	263	2	pure	pure	PROPN
ejpam-5396	263	3	appl	appl	PROPN
ejpam-5396	263	4	.	.	PROPN
ejpam-5396	263	5	math	math	PROPN
ejpam-5396	263	6	,	,	PUNCT
ejpam-5396	263	7	17	17	NUM
ejpam-5396	263	8	(	(	PUNCT
ejpam-5396	263	9	4	4	NUM
ejpam-5396	263	10	)	)	PUNCT
ejpam-5396	263	11	(	(	PUNCT
ejpam-5396	263	12	2024	2024	NUM
ejpam-5396	263	13	)	)	PUNCT
ejpam-5396	263	14	,	,	PUNCT
ejpam-5396	263	15	2763	2763	NUM
ejpam-5396	263	16	-	-	SYM
ejpam-5396	263	17	2799	2799	NUM
ejpam-5396	263	18	2774	2774	NUM
ejpam-5396	263	19	where	where	SCONJ
ejpam-5396	263	20	f1	f1	NOUN
ejpam-5396	263	21	=	=	SYM
ejpam-5396	263	22	δi∗	δi∗	NOUN
ejpam-5396	264	1	n	n	PROPN
ejpam-5396	264	2	+	+	CCONJ
ejpam-5396	264	3	δωc∗	δωc∗	NOUN
ejpam-5396	264	4	n	n	NOUN
ejpam-5396	264	5	,	,	PUNCT
ejpam-5396	264	6	f2	f2	PROPN
ejpam-5396	264	7	=	=	PUNCT
ejpam-5396	264	8	δωs∗	δωs∗	PROPN
ejpam-5396	264	9	n	n	NOUN
ejpam-5396	264	10	,	,	PUNCT
ejpam-5396	264	11	f3	f3	PROPN
ejpam-5396	264	12	=	=	SYM
ejpam-5396	264	13	δs∗	δs∗	NOUN
ejpam-5396	264	14	n	n	PRON
ejpam-5396	264	15	,	,	PUNCT
ejpam-5396	264	16	and	and	CCONJ
ejpam-5396	264	17	its	its	PRON
ejpam-5396	264	18	characteristic	characteristic	ADJ
ejpam-5396	264	19	equation	equation	NOUN
ejpam-5396	264	20	is	be	AUX
ejpam-5396	264	21	given	give	VERB
ejpam-5396	264	22	by	by	ADP
ejpam-5396	264	23	:	:	PUNCT
ejpam-5396	264	24	|j(e2)−	|j(e2)−	ADJ
ejpam-5396	264	25	λi|	λi|	X
ejpam-5396	264	26	=	=	SYM
ejpam-5396	264	27	0	0	NUM
ejpam-5396	264	28	.	.	PUNCT
ejpam-5396	265	1	that	that	PRON
ejpam-5396	265	2	is	be	AUX
ejpam-5396	265	3	,	,	PUNCT
ejpam-5396	265	4			PROPN
ejpam-5396	265	5	−f1	−f1	PROPN
ejpam-5396	265	6	−	−	PROPN
ejpam-5396	266	1	µ−	µ−	PROPN
ejpam-5396	266	2	λ	λ	PROPN
ejpam-5396	266	3	−f2	−f2	PROPN
ejpam-5396	266	4	−f3	−f3	PROPN
ejpam-5396	266	5	η	η	PROPN
ejpam-5396	266	6	f1θ	f1θ	NOUN
ejpam-5396	266	7	f2θ	f2θ	NOUN
ejpam-5396	266	8	−	−	PROPN
ejpam-5396	266	9	z1	z1	NOUN
ejpam-5396	266	10	−	−	PROPN
ejpam-5396	266	11	λ	λ	PROPN
ejpam-5396	266	12	f3θ	f3θ	PROPN
ejpam-5396	266	13	0	0	NUM
ejpam-5396	266	14	f1(1−	f1(1−	PROPN
ejpam-5396	266	15	θ	θ	PROPN
ejpam-5396	266	16	)	)	PUNCT
ejpam-5396	266	17	f2(1−	f2(1−	PROPN
ejpam-5396	266	18	θ	θ	NOUN
ejpam-5396	266	19	)	)	PUNCT
ejpam-5396	267	1	+	+	CCONJ
ejpam-5396	267	2	π	π	PROPN
ejpam-5396	267	3	f3(1−	f3(1−	PROPN
ejpam-5396	267	4	θ)−	θ)−	PROPN
ejpam-5396	267	5	z2	z2	PROPN
ejpam-5396	267	6	−	−	PROPN
ejpam-5396	267	7	λ	λ	NOUN
ejpam-5396	267	8	0	0	NUM
ejpam-5396	267	9	0	0	NUM
ejpam-5396	267	10	β	β	X
ejpam-5396	267	11	τ	τ	PROPN
ejpam-5396	267	12	−(µ+	−(µ+	PROPN
ejpam-5396	267	13	η)−	η)−	PROPN
ejpam-5396	267	14	λ	λ	PROPN
ejpam-5396	267	15			PROPN
ejpam-5396	267	16	=	=	SYM
ejpam-5396	267	17	η	η	PROPN
ejpam-5396	267	18			PROPN
ejpam-5396	267	19	f1θ	f1θ	NOUN
ejpam-5396	267	20	f2θ	f2θ	PUNCT
ejpam-5396	267	21	−	−	PROPN
ejpam-5396	267	22	z1	z1	NOUN
ejpam-5396	267	23	−	−	PROPN
ejpam-5396	267	24	λ	λ	PROPN
ejpam-5396	267	25	f3θ	f3θ	PROPN
ejpam-5396	267	26	f1(1−	f1(1−	PROPN
ejpam-5396	267	27	θ	θ	PROPN
ejpam-5396	267	28	)	)	PUNCT
ejpam-5396	267	29	f2(1−	f2(1−	PROPN
ejpam-5396	267	30	θ	θ	NOUN
ejpam-5396	267	31	)	)	PUNCT
ejpam-5396	268	1	+	+	CCONJ
ejpam-5396	268	2	π	π	PROPN
ejpam-5396	268	3	f3(1−	f3(1−	PROPN
ejpam-5396	268	4	θ)−	θ)−	PROPN
ejpam-5396	268	5	z2	z2	PROPN
ejpam-5396	268	6	−	−	PROPN
ejpam-5396	268	7	λ	λ	NOUN
ejpam-5396	268	8	0	0	NUM
ejpam-5396	268	9	β	β	X
ejpam-5396	268	10	τ	τ	PROPN
ejpam-5396	268	11			PROPN
ejpam-5396	268	12	−	−	PROPN
ejpam-5396	268	13	(	(	PUNCT
ejpam-5396	268	14	µ+	µ+	X
ejpam-5396	268	15	η	η	PROPN
ejpam-5396	268	16	+	+	PROPN
ejpam-5396	268	17	λ	λ	PROPN
ejpam-5396	268	18	)	)	PUNCT
ejpam-5396	268	19			PROPN
ejpam-5396	268	20	−f1	−f1	PROPN
ejpam-5396	268	21	−	−	PROPN
ejpam-5396	269	1	µ−	µ−	PROPN
ejpam-5396	269	2	λ	λ	PROPN
ejpam-5396	269	3	−f2	−f2	NOUN
ejpam-5396	269	4	−f3	−f3	NOUN
ejpam-5396	269	5	f1θ	f1θ	NOUN
ejpam-5396	269	6	f2θ	f2θ	PUNCT
ejpam-5396	269	7	−	−	PROPN
ejpam-5396	269	8	z1	z1	NOUN
ejpam-5396	269	9	−	−	PROPN
ejpam-5396	269	10	λ	λ	PROPN
ejpam-5396	269	11	f3θ	f3θ	PROPN
ejpam-5396	269	12	f1(1−	f1(1−	PROPN
ejpam-5396	269	13	θ	θ	PROPN
ejpam-5396	269	14	)	)	PUNCT
ejpam-5396	269	15	f2(1−	f2(1−	PROPN
ejpam-5396	269	16	θ	θ	NOUN
ejpam-5396	269	17	)	)	PUNCT
ejpam-5396	270	1	+	+	CCONJ
ejpam-5396	270	2	π	π	PROPN
ejpam-5396	270	3	f3(1−	f3(1−	PROPN
ejpam-5396	270	4	θ)−	θ)−	PROPN
ejpam-5396	270	5	z2	z2	PROPN
ejpam-5396	270	6	−	−	PROPN
ejpam-5396	270	7	λ	λ	PROPN
ejpam-5396	270	8			NOUN
ejpam-5396	270	9	=	=	SYM
ejpam-5396	270	10	0	0	NUM
ejpam-5396	270	11	.	.	PUNCT
ejpam-5396	271	1	thus	thus	ADV
ejpam-5396	271	2	,	,	PUNCT
ejpam-5396	271	3	the	the	DET
ejpam-5396	271	4	characteristic	characteristic	ADJ
ejpam-5396	271	5	values	value	NOUN
ejpam-5396	271	6	are	be	AUX
ejpam-5396	271	7	given	give	VERB
ejpam-5396	271	8	by	by	ADP
ejpam-5396	271	9	:	:	PUNCT
ejpam-5396	271	10	λ4	λ4	PROPN
ejpam-5396	271	11	+	+	CCONJ
ejpam-5396	271	12	ξ1λ	ξ1λ	ADJ
ejpam-5396	271	13	3	3	NUM
ejpam-5396	271	14	+	+	NUM
ejpam-5396	271	15	ξ2λ	ξ2λ	DET
ejpam-5396	271	16	2	2	NUM
ejpam-5396	271	17	+	+	CCONJ
ejpam-5396	271	18	ξ3λ+	ξ3λ+	PROPN
ejpam-5396	271	19	ξ4	ξ4	NOUN
ejpam-5396	271	20	=	=	SYM
ejpam-5396	271	21	0	0	PROPN
ejpam-5396	271	22	,	,	PUNCT
ejpam-5396	271	23	where	where	SCONJ
ejpam-5396	271	24	ξ1	ξ1	NOUN
ejpam-5396	271	25	=	=	SYM
ejpam-5396	271	26	z1	z1	PROPN
ejpam-5396	271	27	+	+	CCONJ
ejpam-5396	271	28	z2	z2	PROPN
ejpam-5396	271	29	−	−	NOUN
ejpam-5396	271	30	f2θ	f2θ	NOUN
ejpam-5396	271	31	−	−	PROPN
ejpam-5396	271	32	f3(1−	f3(1−	PROPN
ejpam-5396	271	33	θ	θ	PROPN
ejpam-5396	271	34	)	)	PUNCT
ejpam-5396	272	1	+	+	CCONJ
ejpam-5396	272	2	2µ+	2µ+	NUM
ejpam-5396	272	3	η	η	PROPN
ejpam-5396	272	4	+	+	PROPN
ejpam-5396	272	5	f1	f1	PROPN
ejpam-5396	272	6	,	,	PUNCT
ejpam-5396	272	7	ξ2	ξ2	NOUN
ejpam-5396	272	8	=	=	SYM
ejpam-5396	272	9	z1z2	z1z2	PROPN
ejpam-5396	272	10	−	−	NOUN
ejpam-5396	272	11	f2z2θ	f2z2θ	PUNCT
ejpam-5396	273	1	−	−	PROPN
ejpam-5396	273	2	f3z1(1−	f3z1(1−	PROPN
ejpam-5396	273	3	θ)−	θ)−	PROPN
ejpam-5396	273	4	f3πθ	f3πθ	PUNCT
ejpam-5396	274	1	+	+	CCONJ
ejpam-5396	274	2	(	(	PUNCT
ejpam-5396	274	3	f1	f1	NOUN
ejpam-5396	274	4	+	+	CCONJ
ejpam-5396	274	5	µ)(µ+	µ)(µ+	NOUN
ejpam-5396	274	6	η	η	PROPN
ejpam-5396	274	7	)	)	PUNCT
ejpam-5396	274	8	+	+	CCONJ
ejpam-5396	274	9	f1f2θ	f1f2θ	NUM
ejpam-5396	275	1	+	+	CCONJ
ejpam-5396	276	1	f1f3(1−	f1f3(1−	PROPN
ejpam-5396	276	2	θ	θ	PROPN
ejpam-5396	276	3	)	)	PUNCT
ejpam-5396	276	4	,	,	PUNCT
ejpam-5396	276	5	ξ3	ξ3	NOUN
ejpam-5396	276	6	=	=	SYM
ejpam-5396	276	7	(	(	PUNCT
ejpam-5396	276	8	2µ+	2µ+	NUM
ejpam-5396	276	9	η	η	PROPN
ejpam-5396	276	10	+	+	CCONJ
ejpam-5396	276	11	f1)(z1z2	f1)(z1z2	PROPN
ejpam-5396	276	12	−	−	NOUN
ejpam-5396	276	13	f2z2θ	f2z2θ	PUNCT
ejpam-5396	277	1	−	−	PROPN
ejpam-5396	277	2	f3z1(1−	f3z1(1−	PROPN
ejpam-5396	277	3	θ)−	θ)−	PROPN
ejpam-5396	277	4	f3πθ	f3πθ	PUNCT
ejpam-5396	277	5	)	)	PUNCT
ejpam-5396	278	1	+	+	CCONJ
ejpam-5396	278	2	(	(	PUNCT
ejpam-5396	278	3	µ+	µ+	X
ejpam-5396	278	4	f1)(µ+	f1)(µ+	PROPN
ejpam-5396	278	5	η)(z1	η)(z1	PROPN
ejpam-5396	278	6	+	+	CCONJ
ejpam-5396	278	7	z2	z2	PROPN
ejpam-5396	278	8	−	−	PROPN
ejpam-5396	278	9	f2θ	f2θ	NUM
ejpam-5396	278	10	)	)	PUNCT
ejpam-5396	278	11	+	+	CCONJ
ejpam-5396	278	12	(	(	PUNCT
ejpam-5396	278	13	µ+	µ+	X
ejpam-5396	278	14	η)f1f2θ	η)f1f2θ	NOUN
ejpam-5396	278	15	+	+	CCONJ
ejpam-5396	279	1	f1f2θz2	f1f2θz2	NUM
ejpam-5396	279	2	+	+	CCONJ
ejpam-5396	279	3	(	(	PUNCT
ejpam-5396	279	4	µ+	µ+	X
ejpam-5396	279	5	η)(f1f3(1−	η)(f1f3(1−	PROPN
ejpam-5396	279	6	θ	θ	PROPN
ejpam-5396	279	7	)	)	PUNCT
ejpam-5396	280	1	+	+	CCONJ
ejpam-5396	280	2	f1f3πθ	f1f3πθ	X
ejpam-5396	281	1	+	+	CCONJ
ejpam-5396	281	2	f1f3z1(1−	f1f3z1(1−	PROPN
ejpam-5396	281	3	θ	θ	PROPN
ejpam-5396	281	4	)	)	PUNCT
ejpam-5396	281	5	)	)	PUNCT
ejpam-5396	281	6	,	,	PUNCT
ejpam-5396	281	7	ξ4	ξ4	NOUN
ejpam-5396	281	8	=	=	SYM
ejpam-5396	281	9	(	(	PUNCT
ejpam-5396	281	10	µ+	µ+	X
ejpam-5396	281	11	f1)(µ+	f1)(µ+	X
ejpam-5396	281	12	η)(z1z2	η)(z1z2	PROPN
ejpam-5396	281	13	−	−	PROPN
ejpam-5396	281	14	f2z2θ	f2z2θ	PUNCT
ejpam-5396	281	15	−	−	PROPN
ejpam-5396	281	16	f3z1(1−	f3z1(1−	PROPN
ejpam-5396	281	17	θ)−	θ)−	PROPN
ejpam-5396	281	18	f3πθ	f3πθ	PUNCT
ejpam-5396	281	19	)	)	PUNCT
ejpam-5396	282	1	+	+	CCONJ
ejpam-5396	282	2	f1f2θ(µ+	f1f2θ(µ+	NOUN
ejpam-5396	282	3	η)z2	η)z2	NOUN
ejpam-5396	282	4	+	+	CCONJ
ejpam-5396	282	5	(	(	PUNCT
ejpam-5396	282	6	µ+	µ+	X
ejpam-5396	282	7	η)(f1f3πθ	η)(f1f3πθ	NOUN
ejpam-5396	282	8	+	+	CCONJ
ejpam-5396	282	9	f1f3z1(1−	f1f3z1(1−	PROPN
ejpam-5396	282	10	θ	θ	PROPN
ejpam-5396	282	11	)	)	PUNCT
ejpam-5396	282	12	)	)	PUNCT
ejpam-5396	282	13	.	.	PUNCT
ejpam-5396	283	1	according	accord	VERB
ejpam-5396	283	2	to	to	ADP
ejpam-5396	283	3	the	the	DET
ejpam-5396	283	4	routh	routh	PROPN
ejpam-5396	283	5	-	-	PUNCT
ejpam-5396	283	6	hurwitz	hurwitz	PROPN
ejpam-5396	283	7	criterion	criterion	NOUN
ejpam-5396	283	8	for	for	ADP
ejpam-5396	283	9	the	the	DET
ejpam-5396	283	10	fourth	fourth	ADJ
ejpam-5396	283	11	-	-	PUNCT
ejpam-5396	283	12	degree	degree	NOUN
ejpam-5396	283	13	polynomial	polynomial	NOUN
ejpam-5396	283	14	,	,	PUNCT
ejpam-5396	283	15	the	the	DET
ejpam-5396	283	16	provided	provide	VERB
ejpam-5396	283	17	constraint	constraint	NOUN
ejpam-5396	283	18	has	have	AUX
ejpam-5396	283	19	been	be	AUX
ejpam-5396	283	20	verified	verify	VERB
ejpam-5396	283	21	if	if	SCONJ
ejpam-5396	283	22	r0	r0	NOUN
ejpam-5396	283	23	>	>	X
ejpam-5396	283	24	1	1	NUM
ejpam-5396	283	25	.	.	X
ejpam-5396	283	26	3.4	3.4	NUM
ejpam-5396	283	27	.	.	PUNCT
ejpam-5396	284	1	global	global	ADJ
ejpam-5396	284	2	stability	stability	NOUN
ejpam-5396	284	3	theorem	theorem	VERB
ejpam-5396	284	4	4	4	NUM
ejpam-5396	284	5	.	.	PUNCT
ejpam-5396	285	1	the	the	DET
ejpam-5396	285	2	disease	disease	NOUN
ejpam-5396	285	3	-	-	PUNCT
ejpam-5396	285	4	free	free	ADJ
ejpam-5396	285	5	equilibrium	equilibrium	NOUN
ejpam-5396	285	6	e1	e1	NOUN
ejpam-5396	285	7	=	=	SYM
ejpam-5396	285	8	(	(	PUNCT
ejpam-5396	285	9	λ	λ	X
ejpam-5396	285	10	µ	µ	X
ejpam-5396	285	11	,	,	PUNCT
ejpam-5396	285	12	0	0	NUM
ejpam-5396	285	13	,	,	PUNCT
ejpam-5396	285	14	0	0	NUM
ejpam-5396	285	15	,	,	PUNCT
ejpam-5396	285	16	0	0	NUM
ejpam-5396	285	17	)	)	PUNCT
ejpam-5396	285	18	is	be	AUX
ejpam-5396	285	19	globally	globally	ADV
ejpam-5396	285	20	asymptotically	asymptotically	ADV
ejpam-5396	285	21	stable	stable	ADJ
ejpam-5396	285	22	in	in	ADP
ejpam-5396	285	23	ω	ω	PROPN
ejpam-5396	285	24	.	.	PUNCT
ejpam-5396	286	1	proof	proof	NOUN
ejpam-5396	286	2	.	.	PUNCT
ejpam-5396	287	1	take	take	VERB
ejpam-5396	287	2	the	the	DET
ejpam-5396	287	3	lyapunov	lyapunov	ADJ
ejpam-5396	287	4	function	function	NOUN
ejpam-5396	287	5	with	with	ADP
ejpam-5396	287	6	positive	positive	ADJ
ejpam-5396	287	7	definiteness	definiteness	NOUN
ejpam-5396	287	8	l2(s	l2(s	NOUN
ejpam-5396	287	9	,	,	PUNCT
ejpam-5396	287	10	c	c	X
ejpam-5396	287	11	,	,	PUNCT
ejpam-5396	287	12	i	i	PRON
ejpam-5396	287	13	,	,	PUNCT
ejpam-5396	287	14	r	r	NOUN
ejpam-5396	287	15	)	)	PUNCT
ejpam-5396	287	16	=	=	PUNCT
ejpam-5396	288	1	(	(	PUNCT
ejpam-5396	288	2	s	s	NOUN
ejpam-5396	288	3	−	−	PROPN
ejpam-5396	288	4	s0	s0	PROPN
ejpam-5396	288	5	−	−	PROPN
ejpam-5396	288	6	s0	s0	PROPN
ejpam-5396	288	7	ln	ln	PROPN
ejpam-5396	288	8	s	s	PROPN
ejpam-5396	288	9	s0	s0	PROPN
ejpam-5396	288	10	)	)	PUNCT
ejpam-5396	288	11	.	.	PUNCT
ejpam-5396	289	1	a.	a.	NOUN
ejpam-5396	289	2	alalyani	alalyani	PROPN
ejpam-5396	289	3	/	/	SYM
ejpam-5396	289	4	eur	eur	PROPN
ejpam-5396	289	5	.	.	PUNCT
ejpam-5396	290	1	j.	j.	PROPN
ejpam-5396	290	2	pure	pure	PROPN
ejpam-5396	290	3	appl	appl	PROPN
ejpam-5396	290	4	.	.	PROPN
ejpam-5396	290	5	math	math	PROPN
ejpam-5396	290	6	,	,	PUNCT
ejpam-5396	290	7	17	17	NUM
ejpam-5396	290	8	(	(	PUNCT
ejpam-5396	290	9	4	4	NUM
ejpam-5396	290	10	)	)	PUNCT
ejpam-5396	290	11	(	(	PUNCT
ejpam-5396	290	12	2024	2024	NUM
ejpam-5396	290	13	)	)	PUNCT
ejpam-5396	290	14	,	,	PUNCT
ejpam-5396	290	15	2763	2763	NUM
ejpam-5396	290	16	-	-	SYM
ejpam-5396	290	17	2799	2799	NUM
ejpam-5396	290	18	2775	2775	NUM
ejpam-5396	290	19	from	from	ADP
ejpam-5396	290	20	[	[	X
ejpam-5396	290	21	58	58	NUM
ejpam-5396	290	22	]	]	PUNCT
ejpam-5396	290	23	,	,	PUNCT
ejpam-5396	290	24	we	we	PRON
ejpam-5396	290	25	have	have	AUX
ejpam-5396	290	26	dαl2(s	dαl2(s	NUM
ejpam-5396	290	27	,	,	PUNCT
ejpam-5396	290	28	c	c	X
ejpam-5396	290	29	,	,	PUNCT
ejpam-5396	290	30	i	i	PRON
ejpam-5396	290	31	,	,	PUNCT
ejpam-5396	290	32	r	r	NOUN
ejpam-5396	290	33	)	)	PUNCT
ejpam-5396	290	34	≤	≤	NOUN
ejpam-5396	290	35	(	(	PUNCT
ejpam-5396	290	36	s	s	NOUN
ejpam-5396	290	37	−	−	PROPN
ejpam-5396	290	38	s0	s0	PROPN
ejpam-5396	290	39	s	s	PART
ejpam-5396	290	40	)	)	PUNCT
ejpam-5396	290	41	dαs	dαs	PROPN
ejpam-5396	290	42	=	=	PUNCT
ejpam-5396	291	1	(	(	PUNCT
ejpam-5396	291	2	s	s	AUX
ejpam-5396	291	3	−	−	PROPN
ejpam-5396	291	4	s0	s0	PROPN
ejpam-5396	291	5	s	s	PART
ejpam-5396	291	6	)	)	PUNCT
ejpam-5396	291	7	(	(	PUNCT
ejpam-5396	291	8	λ−	λ−	PROPN
ejpam-5396	291	9	δi(t)s(t	δi(t)s(t	PROPN
ejpam-5396	291	10	)	)	PUNCT
ejpam-5396	291	11	n	n	CCONJ
ejpam-5396	291	12	−	−	PROPN
ejpam-5396	292	1	δωc(t)s(t	δωc(t)s(t	PROPN
ejpam-5396	292	2	)	)	PUNCT
ejpam-5396	293	1	n	n	CCONJ
ejpam-5396	293	2	−	−	PROPN
ejpam-5396	293	3	µs(t	µs(t	PUNCT
ejpam-5396	293	4	)	)	PUNCT
ejpam-5396	293	5	+	+	NUM
ejpam-5396	293	6	ηr(t	ηr(t	NOUN
ejpam-5396	293	7	)	)	PUNCT
ejpam-5396	293	8	)	)	PUNCT
ejpam-5396	293	9	.	.	PUNCT
ejpam-5396	294	1	at	at	ADP
ejpam-5396	294	2	e1	e1	NOUN
ejpam-5396	294	3	=	=	SYM
ejpam-5396	294	4	(	(	PUNCT
ejpam-5396	294	5	λ	λ	X
ejpam-5396	294	6	µ	µ	X
ejpam-5396	294	7	,	,	PUNCT
ejpam-5396	294	8	0	0	NUM
ejpam-5396	294	9	,	,	PUNCT
ejpam-5396	294	10	0	0	NUM
ejpam-5396	294	11	,	,	PUNCT
ejpam-5396	294	12	0	0	NUM
ejpam-5396	294	13	)	)	PUNCT
ejpam-5396	294	14	,	,	PUNCT
ejpam-5396	294	15	we	we	PRON
ejpam-5396	294	16	have	have	VERB
ejpam-5396	294	17	dαl2(s	dαl2(s	NUM
ejpam-5396	294	18	,	,	PUNCT
ejpam-5396	294	19	v	v	NOUN
ejpam-5396	294	20	,	,	PUNCT
ejpam-5396	294	21	c	c	X
ejpam-5396	294	22	,	,	PUNCT
ejpam-5396	294	23	i	i	PRON
ejpam-5396	294	24	,	,	PUNCT
ejpam-5396	294	25	r	r	NOUN
ejpam-5396	294	26	)	)	PUNCT
ejpam-5396	294	27	≤	≤	NOUN
ejpam-5396	294	28	(	(	PUNCT
ejpam-5396	294	29	s	s	NOUN
ejpam-5396	294	30	−	−	PROPN
ejpam-5396	294	31	s0	s0	PROPN
ejpam-5396	294	32	s	s	PART
ejpam-5396	294	33	)	)	PUNCT
ejpam-5396	294	34	dαs	dαs	PROPN
ejpam-5396	295	1	=	=	PUNCT
ejpam-5396	295	2	(	(	PUNCT
ejpam-5396	295	3	s	s	NOUN
ejpam-5396	295	4	−	−	PROPN
ejpam-5396	295	5	s0	s0	PROPN
ejpam-5396	295	6	s	s	PART
ejpam-5396	295	7	)	)	PUNCT
ejpam-5396	295	8	(	(	PUNCT
ejpam-5396	295	9	λ−	λ−	PROPN
ejpam-5396	295	10	δ(i(t	δ(i(t	PROPN
ejpam-5396	295	11	)	)	PUNCT
ejpam-5396	295	12	+	+	NUM
ejpam-5396	295	13	ωc(t	ωc(t	NOUN
ejpam-5396	295	14	)	)	PUNCT
ejpam-5396	295	15	)	)	PUNCT
ejpam-5396	296	1	n	n	CCONJ
ejpam-5396	296	2	s(t)−	s(t)−	PROPN
ejpam-5396	296	3	µs(t	µs(t	PROPN
ejpam-5396	296	4	)	)	PUNCT
ejpam-5396	296	5	+	+	NUM
ejpam-5396	296	6	ηr(t	ηr(t	NOUN
ejpam-5396	296	7	)	)	PUNCT
ejpam-5396	296	8	)	)	PUNCT
ejpam-5396	297	1	=	=	PUNCT
ejpam-5396	297	2	(	(	PUNCT
ejpam-5396	297	3	s	s	NOUN
ejpam-5396	297	4	−	−	PROPN
ejpam-5396	297	5	s0	s0	NOUN
ejpam-5396	297	6	)	)	PUNCT
ejpam-5396	297	7	(	(	PUNCT
ejpam-5396	297	8	λ	λ	PROPN
ejpam-5396	297	9	s	s	PART
ejpam-5396	297	10	−	−	NOUN
ejpam-5396	297	11	δ(i(t	δ(i(t	PROPN
ejpam-5396	297	12	)	)	PUNCT
ejpam-5396	297	13	+	+	NUM
ejpam-5396	297	14	ωc(t	ωc(t	NOUN
ejpam-5396	297	15	)	)	PUNCT
ejpam-5396	297	16	)	)	PUNCT
ejpam-5396	298	1	n	n	CCONJ
ejpam-5396	298	2	−	−	PROPN
ejpam-5396	298	3	µ+	µ+	PUNCT
ejpam-5396	298	4	ηr(t	ηr(t	NOUN
ejpam-5396	298	5	)	)	PUNCT
ejpam-5396	298	6	s	s	PART
ejpam-5396	298	7	)	)	PUNCT
ejpam-5396	298	8	=	=	PUNCT
ejpam-5396	299	1	(	(	PUNCT
ejpam-5396	299	2	s	s	AUX
ejpam-5396	299	3	−	−	PROPN
ejpam-5396	299	4	s0	s0	NOUN
ejpam-5396	299	5	)	)	PUNCT
ejpam-5396	299	6	(	(	PUNCT
ejpam-5396	299	7	λ	λ	X
ejpam-5396	299	8	s	s	X
ejpam-5396	299	9	+	+	NUM
ejpam-5396	299	10	ηr(t	ηr(t	NOUN
ejpam-5396	299	11	)	)	PUNCT
ejpam-5396	299	12	s	s	PART
ejpam-5396	299	13	−	−	PROPN
ejpam-5396	299	14	λ	λ	PROPN
ejpam-5396	299	15	s0	s0	NOUN
ejpam-5396	299	16	−	−	PROPN
ejpam-5396	299	17	ηr(t	ηr(t	NOUN
ejpam-5396	299	18	)	)	PUNCT
ejpam-5396	299	19	s0	s0	NOUN
ejpam-5396	299	20	)	)	PUNCT
ejpam-5396	300	1	=	=	PUNCT
ejpam-5396	300	2	(	(	PUNCT
ejpam-5396	300	3	s	s	NOUN
ejpam-5396	300	4	−	−	PROPN
ejpam-5396	300	5	s0	s0	NOUN
ejpam-5396	300	6	)	)	PUNCT
ejpam-5396	300	7	(	(	PUNCT
ejpam-5396	300	8	−	−	PROPN
ejpam-5396	300	9	λ	λ	PROPN
ejpam-5396	300	10	ss0	ss0	PROPN
ejpam-5396	300	11	(	(	PUNCT
ejpam-5396	300	12	s	s	NOUN
ejpam-5396	300	13	−	−	PROPN
ejpam-5396	300	14	s0	s0	PROPN
ejpam-5396	300	15	)	)	PUNCT
ejpam-5396	300	16	−	−	PROPN
ejpam-5396	300	17	ηr(t	ηr(t	NOUN
ejpam-5396	300	18	)	)	PUNCT
ejpam-5396	300	19	ss0	ss0	NOUN
ejpam-5396	300	20	(	(	PUNCT
ejpam-5396	300	21	s	s	NOUN
ejpam-5396	300	22	−	−	PROPN
ejpam-5396	300	23	s0	s0	NOUN
ejpam-5396	300	24	)	)	PUNCT
ejpam-5396	300	25	)	)	PUNCT
ejpam-5396	301	1	=	=	PUNCT
ejpam-5396	302	1	−	−	PROPN
ejpam-5396	302	2	λ	λ	INTJ
ejpam-5396	302	3	ss0	ss0	PROPN
ejpam-5396	302	4	(	(	PUNCT
ejpam-5396	302	5	s	s	NOUN
ejpam-5396	302	6	−	−	PROPN
ejpam-5396	302	7	s0	s0	NOUN
ejpam-5396	302	8	)	)	PUNCT
ejpam-5396	302	9	2	2	NUM
ejpam-5396	302	10	−	−	PROPN
ejpam-5396	302	11	ηr	ηr	PROPN
ejpam-5396	302	12	ss0	ss0	PROPN
ejpam-5396	302	13	(	(	PUNCT
ejpam-5396	302	14	s	s	NOUN
ejpam-5396	302	15	−	−	PROPN
ejpam-5396	302	16	s0	s0	NOUN
ejpam-5396	302	17	)	)	PUNCT
ejpam-5396	302	18	2	2	NUM
ejpam-5396	302	19	.	.	PUNCT
ejpam-5396	303	1	thus	thus	ADV
ejpam-5396	303	2	,	,	PUNCT
ejpam-5396	303	3	for	for	ADP
ejpam-5396	303	4	all	all	DET
ejpam-5396	303	5	(	(	PUNCT
ejpam-5396	303	6	s	s	X
ejpam-5396	303	7	,	,	PUNCT
ejpam-5396	303	8	c	c	X
ejpam-5396	303	9	,	,	PUNCT
ejpam-5396	303	10	i	i	PRON
ejpam-5396	303	11	,	,	PUNCT
ejpam-5396	303	12	r	r	NOUN
ejpam-5396	303	13	)	)	PUNCT
ejpam-5396	303	14	∈	∈	PROPN
ejpam-5396	303	15	ω	ω	PROPN
ejpam-5396	303	16	,	,	PUNCT
ejpam-5396	303	17	dαl2(s	dαl2(s	NOUN
ejpam-5396	303	18	,	,	PUNCT
ejpam-5396	303	19	c	c	X
ejpam-5396	303	20	,	,	PUNCT
ejpam-5396	303	21	i	i	PRON
ejpam-5396	303	22	,	,	PUNCT
ejpam-5396	303	23	r	r	NOUN
ejpam-5396	303	24	)	)	PUNCT
ejpam-5396	303	25	<	<	X
ejpam-5396	303	26	0	0	X
ejpam-5396	303	27	.	.	PUNCT
ejpam-5396	303	28	therefore	therefore	ADV
ejpam-5396	303	29	,	,	PUNCT
ejpam-5396	303	30	it	it	PRON
ejpam-5396	303	31	follows	follow	VERB
ejpam-5396	303	32	from	from	ADP
ejpam-5396	303	33	[	[	X
ejpam-5396	303	34	30	30	NUM
ejpam-5396	303	35	]	]	PUNCT
ejpam-5396	303	36	that	that	PRON
ejpam-5396	303	37	e1	e1	PROPN
ejpam-5396	303	38	is	be	AUX
ejpam-5396	303	39	globally	globally	ADV
ejpam-5396	303	40	asymptotically	asymptotically	ADV
ejpam-5396	303	41	stable	stable	ADJ
ejpam-5396	303	42	in	in	ADP
ejpam-5396	303	43	ω	ω	PROPN
ejpam-5396	303	44	.	.	PUNCT
ejpam-5396	304	1	theorem	theorem	NOUN
ejpam-5396	304	2	5	5	NUM
ejpam-5396	304	3	.	.	PUNCT
ejpam-5396	305	1	the	the	DET
ejpam-5396	305	2	pneumonia	pneumonia	NOUN
ejpam-5396	305	3	endemic	endemic	ADJ
ejpam-5396	305	4	equilibrium	equilibrium	NOUN
ejpam-5396	305	5	e2	e2	PROPN
ejpam-5396	305	6	=	=	PUNCT
ejpam-5396	305	7	(	(	PUNCT
ejpam-5396	305	8	s∗	s∗	PROPN
ejpam-5396	305	9	,	,	PUNCT
ejpam-5396	305	10	c∗	c∗	NOUN
ejpam-5396	305	11	,	,	PUNCT
ejpam-5396	305	12	i∗	i∗	NOUN
ejpam-5396	305	13	,	,	PUNCT
ejpam-5396	305	14	r∗	r∗	PROPN
ejpam-5396	305	15	)	)	PUNCT
ejpam-5396	305	16	is	be	AUX
ejpam-5396	305	17	globally	globally	ADV
ejpam-5396	305	18	asymptotically	asymptotically	ADV
ejpam-5396	305	19	stable	stable	ADJ
ejpam-5396	305	20	in	in	ADP
ejpam-5396	305	21	ω	ω	PROPN
ejpam-5396	305	22	.	.	PUNCT
ejpam-5396	306	1	proof	proof	NOUN
ejpam-5396	306	2	.	.	PUNCT
ejpam-5396	307	1	take	take	VERB
ejpam-5396	307	2	the	the	DET
ejpam-5396	307	3	lyapunov	lyapunov	ADJ
ejpam-5396	307	4	function	function	NOUN
ejpam-5396	307	5	with	with	ADP
ejpam-5396	307	6	positive	positive	ADJ
ejpam-5396	307	7	definiteness	definiteness	NOUN
ejpam-5396	307	8	l2(s	l2(s	NOUN
ejpam-5396	307	9	,	,	PUNCT
ejpam-5396	307	10	c	c	X
ejpam-5396	307	11	,	,	PUNCT
ejpam-5396	307	12	i	i	PRON
ejpam-5396	307	13	,	,	PUNCT
ejpam-5396	307	14	r	r	NOUN
ejpam-5396	307	15	)	)	PUNCT
ejpam-5396	307	16	=	=	SYM
ejpam-5396	308	1	(	(	PUNCT
ejpam-5396	308	2	s	s	AUX
ejpam-5396	308	3	−	−	PROPN
ejpam-5396	308	4	s∗	s∗	PROPN
ejpam-5396	308	5	−	−	PROPN
ejpam-5396	308	6	s∗	s∗	PROPN
ejpam-5396	309	1	ln	ln	PROPN
ejpam-5396	309	2	s	s	PART
ejpam-5396	309	3	s∗	s∗	PROPN
ejpam-5396	309	4	)	)	PUNCT
ejpam-5396	310	1	+	+	CCONJ
ejpam-5396	310	2	(	(	PUNCT
ejpam-5396	310	3	c	c	NOUN
ejpam-5396	310	4	−	−	PROPN
ejpam-5396	310	5	c∗	c∗	PROPN
ejpam-5396	310	6	−	−	PROPN
ejpam-5396	310	7	c∗	c∗	PROPN
ejpam-5396	310	8	ln	ln	PROPN
ejpam-5396	310	9	c	c	PROPN
ejpam-5396	310	10	c∗	c∗	PROPN
ejpam-5396	310	11	)	)	PUNCT
ejpam-5396	311	1	+	+	CCONJ
ejpam-5396	311	2	(	(	PUNCT
ejpam-5396	311	3	i	i	PRON
ejpam-5396	311	4	−	−	VERB
ejpam-5396	311	5	i∗	i∗	NOUN
ejpam-5396	311	6	−	−	NOUN
ejpam-5396	311	7	i∗	i∗	NOUN
ejpam-5396	312	1	ln	ln	NOUN
ejpam-5396	312	2	i	i	PRON
ejpam-5396	312	3	i∗	i∗	NOUN
ejpam-5396	312	4	)	)	PUNCT
ejpam-5396	313	1	+	+	CCONJ
ejpam-5396	313	2	(	(	PUNCT
ejpam-5396	313	3	r−r∗	r−r∗	PROPN
ejpam-5396	313	4	−r∗	−r∗	PROPN
ejpam-5396	313	5	ln	ln	NOUN
ejpam-5396	313	6	r	r	NOUN
ejpam-5396	313	7	r∗	r∗	PROPN
ejpam-5396	313	8	)	)	PUNCT
ejpam-5396	313	9	.	.	PUNCT
ejpam-5396	314	1	from	from	ADP
ejpam-5396	314	2	[	[	X
ejpam-5396	314	3	58	58	NUM
ejpam-5396	314	4	]	]	PUNCT
ejpam-5396	314	5	,	,	PUNCT
ejpam-5396	314	6	we	we	PRON
ejpam-5396	314	7	have	have	VERB
ejpam-5396	314	8	dαl2(s	dαl2(s	NUM
ejpam-5396	314	9	,	,	PUNCT
ejpam-5396	314	10	v	v	NOUN
ejpam-5396	314	11	,	,	PUNCT
ejpam-5396	314	12	c	c	X
ejpam-5396	314	13	,	,	PUNCT
ejpam-5396	314	14	i	i	PRON
ejpam-5396	314	15	,	,	PUNCT
ejpam-5396	314	16	r	r	NOUN
ejpam-5396	314	17	)	)	PUNCT
ejpam-5396	314	18	≤	≤	NOUN
ejpam-5396	314	19	(	(	PUNCT
ejpam-5396	314	20	s	s	VERB
ejpam-5396	314	21	−	−	PROPN
ejpam-5396	314	22	s∗	s∗	PROPN
ejpam-5396	314	23	s	s	PART
ejpam-5396	314	24	)	)	PUNCT
ejpam-5396	314	25	dαs	dαs	PROPN
ejpam-5396	315	1	+	+	CCONJ
ejpam-5396	315	2	(	(	PUNCT
ejpam-5396	315	3	c	c	NOUN
ejpam-5396	315	4	−	−	PROPN
ejpam-5396	315	5	c∗	c∗	PROPN
ejpam-5396	315	6	c	c	PROPN
ejpam-5396	315	7	)	)	PUNCT
ejpam-5396	315	8	dαc	dαc	NOUN
ejpam-5396	316	1	+	+	CCONJ
ejpam-5396	316	2	(	(	PUNCT
ejpam-5396	316	3	i	i	PRON
ejpam-5396	316	4	−	−	VERB
ejpam-5396	316	5	i∗	i∗	NOUN
ejpam-5396	316	6	i	i	NOUN
ejpam-5396	316	7	)	)	PUNCT
ejpam-5396	316	8	dαi	dαi	NOUN
ejpam-5396	316	9	+	+	CCONJ
ejpam-5396	317	1	(	(	PUNCT
ejpam-5396	317	2	r−r∗	r−r∗	ADJ
ejpam-5396	317	3	r	r	NOUN
ejpam-5396	317	4	)	)	PUNCT
ejpam-5396	317	5	dαr	dαr	INTJ
ejpam-5396	317	6	=	=	PUNCT
ejpam-5396	318	1	(	(	PUNCT
ejpam-5396	318	2	s	s	AUX
ejpam-5396	318	3	−	−	PROPN
ejpam-5396	318	4	s∗	s∗	PROPN
ejpam-5396	318	5	s	s	PART
ejpam-5396	318	6	)	)	PUNCT
ejpam-5396	318	7	(	(	PUNCT
ejpam-5396	318	8	λ−	λ−	PROPN
ejpam-5396	318	9	δ(i	δ(i	PROPN
ejpam-5396	318	10	+	+	CCONJ
ejpam-5396	318	11	ωc	ωc	NOUN
ejpam-5396	318	12	)	)	PUNCT
ejpam-5396	318	13	n	n	PRON
ejpam-5396	318	14	s	s	NOUN
ejpam-5396	318	15	−	−	NOUN
ejpam-5396	318	16	µs	µs	X
ejpam-5396	318	17	+	+	CCONJ
ejpam-5396	318	18	ηr	ηr	X
ejpam-5396	318	19	)	)	PUNCT
ejpam-5396	319	1	+	+	CCONJ
ejpam-5396	319	2	(	(	PUNCT
ejpam-5396	319	3	c	c	NOUN
ejpam-5396	319	4	−	−	PROPN
ejpam-5396	319	5	c∗	c∗	PROPN
ejpam-5396	319	6	c	c	PROPN
ejpam-5396	319	7	)	)	PUNCT
ejpam-5396	319	8	(	(	PUNCT
ejpam-5396	319	9	δ(i(t	δ(i(t	PROPN
ejpam-5396	319	10	)	)	PUNCT
ejpam-5396	319	11	+	+	NUM
ejpam-5396	319	12	ωc	ωc	X
ejpam-5396	319	13	)	)	PUNCT
ejpam-5396	319	14	n	n	NOUN
ejpam-5396	319	15	θs	θs	NOUN
ejpam-5396	319	16	−	−	NOUN
ejpam-5396	319	17	z1c	z1c	NOUN
ejpam-5396	319	18	)	)	PUNCT
ejpam-5396	320	1	+	+	CCONJ
ejpam-5396	320	2	(	(	PUNCT
ejpam-5396	320	3	i	i	PRON
ejpam-5396	320	4	−	−	VERB
ejpam-5396	320	5	i∗	i∗	NOUN
ejpam-5396	320	6	i	i	NOUN
ejpam-5396	320	7	)	)	PUNCT
ejpam-5396	320	8	(	(	PUNCT
ejpam-5396	320	9	δ(i	δ(i	PROPN
ejpam-5396	320	10	+	+	CCONJ
ejpam-5396	320	11	ωc	ωc	NOUN
ejpam-5396	320	12	)	)	PUNCT
ejpam-5396	320	13	n	n	CCONJ
ejpam-5396	320	14	(	(	PUNCT
ejpam-5396	320	15	1−	1−	NUM
ejpam-5396	320	16	θ)s	θ)s	NOUN
ejpam-5396	320	17	+	+	CCONJ
ejpam-5396	320	18	πc	πc	VERB
ejpam-5396	320	19	−	−	PROPN
ejpam-5396	320	20	z2i	z2i	PROPN
ejpam-5396	320	21	)	)	PUNCT
ejpam-5396	321	1	+	+	CCONJ
ejpam-5396	321	2	(	(	PUNCT
ejpam-5396	321	3	r−r∗	r−r∗	ADJ
ejpam-5396	321	4	r	r	NOUN
ejpam-5396	321	5	)	)	PUNCT
ejpam-5396	321	6	(	(	PUNCT
ejpam-5396	321	7	βc	βc	INTJ
ejpam-5396	322	1	+	+	CCONJ
ejpam-5396	322	2	τi	τi	VERB
ejpam-5396	322	3	−	−	PROPN
ejpam-5396	322	4	(	(	PUNCT
ejpam-5396	322	5	µ+	µ+	X
ejpam-5396	322	6	η)r	η)r	NOUN
ejpam-5396	322	7	)	)	PUNCT
ejpam-5396	322	8	a.	a.	NOUN
ejpam-5396	322	9	alalyani	alalyani	PROPN
ejpam-5396	322	10	/	/	SYM
ejpam-5396	322	11	eur	eur	PROPN
ejpam-5396	322	12	.	.	PUNCT
ejpam-5396	323	1	j.	j.	PROPN
ejpam-5396	323	2	pure	pure	PROPN
ejpam-5396	323	3	appl	appl	PROPN
ejpam-5396	323	4	.	.	PROPN
ejpam-5396	323	5	math	math	PROPN
ejpam-5396	323	6	,	,	PUNCT
ejpam-5396	323	7	17	17	NUM
ejpam-5396	323	8	(	(	PUNCT
ejpam-5396	323	9	4	4	NUM
ejpam-5396	323	10	)	)	PUNCT
ejpam-5396	323	11	(	(	PUNCT
ejpam-5396	323	12	2024	2024	NUM
ejpam-5396	323	13	)	)	PUNCT
ejpam-5396	323	14	,	,	PUNCT
ejpam-5396	323	15	2763	2763	NUM
ejpam-5396	323	16	-	-	SYM
ejpam-5396	323	17	2799	2799	NUM
ejpam-5396	323	18	2776	2776	NUM
ejpam-5396	323	19	=	=	SYM
ejpam-5396	324	1	(	(	PUNCT
ejpam-5396	324	2	s	s	AUX
ejpam-5396	324	3	−	−	PROPN
ejpam-5396	324	4	s∗	s∗	PROPN
ejpam-5396	324	5	)	)	PUNCT
ejpam-5396	324	6	(	(	PUNCT
ejpam-5396	324	7	λ	λ	X
ejpam-5396	324	8	s	s	NOUN
ejpam-5396	324	9	−	−	PROPN
ejpam-5396	324	10	δ(i	δ(i	PROPN
ejpam-5396	324	11	+	+	CCONJ
ejpam-5396	324	12	ωc	ωc	NOUN
ejpam-5396	324	13	)	)	PUNCT
ejpam-5396	324	14	n	n	ADV
ejpam-5396	324	15	−	−	PROPN
ejpam-5396	324	16	µ+	µ+	PUNCT
ejpam-5396	324	17	ηr	ηr	PROPN
ejpam-5396	324	18	s	s	PART
ejpam-5396	324	19	)	)	PUNCT
ejpam-5396	325	1	+	+	CCONJ
ejpam-5396	325	2	(	(	PUNCT
ejpam-5396	325	3	c	c	NOUN
ejpam-5396	325	4	−	−	PROPN
ejpam-5396	325	5	c∗	c∗	NOUN
ejpam-5396	325	6	)	)	PUNCT
ejpam-5396	325	7	(	(	PUNCT
ejpam-5396	325	8	δ(is	δ(i	NOUN
ejpam-5396	325	9	)	)	PUNCT
ejpam-5396	325	10	nc	nc	PROPN
ejpam-5396	325	11	θ	θ	PROPN
ejpam-5396	325	12	+	+	CCONJ
ejpam-5396	325	13	δωs	δωs	VERB
ejpam-5396	325	14	n	n	PRON
ejpam-5396	325	15	θ	θ	NOUN
ejpam-5396	325	16	−	−	PROPN
ejpam-5396	325	17	z1	z1	PROPN
ejpam-5396	325	18	)	)	PUNCT
ejpam-5396	326	1	+	+	CCONJ
ejpam-5396	326	2	(	(	PUNCT
ejpam-5396	326	3	i	i	PRON
ejpam-5396	326	4	−	−	PROPN
ejpam-5396	326	5	i∗	i∗	NOUN
ejpam-5396	326	6	)	)	PUNCT
ejpam-5396	326	7	(	(	PUNCT
ejpam-5396	326	8	δs	δs	ADP
ejpam-5396	326	9	n	n	PROPN
ejpam-5396	326	10	(	(	PUNCT
ejpam-5396	326	11	1−	1−	NUM
ejpam-5396	326	12	θ	θ	NOUN
ejpam-5396	326	13	)	)	PUNCT
ejpam-5396	326	14	+	+	CCONJ
ejpam-5396	326	15	δωsc	δωsc	PROPN
ejpam-5396	326	16	ni	ni	PROPN
ejpam-5396	326	17	(	(	PUNCT
ejpam-5396	326	18	1−	1−	NUM
ejpam-5396	326	19	θ	θ	NOUN
ejpam-5396	326	20	)	)	PUNCT
ejpam-5396	327	1	+	+	CCONJ
ejpam-5396	327	2	πc	πc	VERB
ejpam-5396	327	3	i	i	PROPN
ejpam-5396	327	4	−	−	PROPN
ejpam-5396	327	5	z2	z2	PROPN
ejpam-5396	327	6	)	)	PUNCT
ejpam-5396	328	1	+	+	CCONJ
ejpam-5396	328	2	(	(	PUNCT
ejpam-5396	328	3	r−r∗	r−r∗	PROPN
ejpam-5396	328	4	)	)	PUNCT
ejpam-5396	328	5	(	(	PUNCT
ejpam-5396	328	6	βc	βc	INTJ
ejpam-5396	328	7	r	r	NOUN
ejpam-5396	328	8	+	+	CCONJ
ejpam-5396	328	9	τi(t	τi(t	X
ejpam-5396	328	10	)	)	PUNCT
ejpam-5396	328	11	r	r	NOUN
ejpam-5396	328	12	−	−	PROPN
ejpam-5396	328	13	(	(	PUNCT
ejpam-5396	328	14	µ+	µ+	X
ejpam-5396	328	15	η	η	NOUN
ejpam-5396	328	16	)	)	PUNCT
ejpam-5396	328	17	)	)	PUNCT
ejpam-5396	329	1	=	=	PUNCT
ejpam-5396	329	2	(	(	PUNCT
ejpam-5396	329	3	s	s	PROPN
ejpam-5396	329	4	−	−	PROPN
ejpam-5396	329	5	s∗	s∗	PROPN
ejpam-5396	329	6	)	)	PUNCT
ejpam-5396	329	7	(	(	PUNCT
ejpam-5396	329	8	λ	λ	X
ejpam-5396	329	9	ns	ns	X
ejpam-5396	329	10	+	+	X
ejpam-5396	329	11	ηr	ηr	NOUN
ejpam-5396	329	12	ns	ns	NUM
ejpam-5396	329	13	−	−	PROPN
ejpam-5396	329	14	λ	λ	PROPN
ejpam-5396	329	15	ns∗	ns∗	NOUN
ejpam-5396	329	16	−	−	PROPN
ejpam-5396	329	17	ηr	ηr	PROPN
ejpam-5396	329	18	ns∗	ns∗	PROPN
ejpam-5396	329	19	)	)	PUNCT
ejpam-5396	330	1	+	+	CCONJ
ejpam-5396	330	2	(	(	PUNCT
ejpam-5396	330	3	c	c	NOUN
ejpam-5396	330	4	−	−	PROPN
ejpam-5396	330	5	c∗	c∗	NOUN
ejpam-5396	330	6	)	)	PUNCT
ejpam-5396	330	7	(	(	PUNCT
ejpam-5396	330	8	δ(is	δ(i	NOUN
ejpam-5396	330	9	)	)	PUNCT
ejpam-5396	330	10	nc	nc	PROPN
ejpam-5396	330	11	θ	θ	PROPN
ejpam-5396	330	12	−	−	PROPN
ejpam-5396	330	13	δ(is	δ(i	NOUN
ejpam-5396	330	14	)	)	PUNCT
ejpam-5396	330	15	nc∗	nc∗	PROPN
ejpam-5396	330	16	θ	θ	PROPN
ejpam-5396	330	17	)	)	PUNCT
ejpam-5396	331	1	+	+	CCONJ
ejpam-5396	331	2	(	(	PUNCT
ejpam-5396	331	3	i	i	PRON
ejpam-5396	331	4	−	−	PROPN
ejpam-5396	331	5	i∗	i∗	NOUN
ejpam-5396	331	6	)	)	PUNCT
ejpam-5396	331	7	(	(	PUNCT
ejpam-5396	331	8	δωsc	δωsc	PROPN
ejpam-5396	331	9	ni	ni	PROPN
ejpam-5396	331	10	(	(	PUNCT
ejpam-5396	331	11	1−	1−	NUM
ejpam-5396	331	12	θ	θ	NOUN
ejpam-5396	331	13	)	)	PUNCT
ejpam-5396	332	1	+	+	CCONJ
ejpam-5396	332	2	πc	πc	VERB
ejpam-5396	332	3	i	i	PRON
ejpam-5396	332	4	−	−	PROPN
ejpam-5396	332	5	δωsc	δωsc	PROPN
ejpam-5396	332	6	ni∗	ni∗	PROPN
ejpam-5396	332	7	(	(	PUNCT
ejpam-5396	332	8	1−	1−	NUM
ejpam-5396	332	9	θ)−	θ)−	PROPN
ejpam-5396	332	10	πc	πc	VERB
ejpam-5396	332	11	i∗	i∗	NOUN
ejpam-5396	332	12	)	)	PUNCT
ejpam-5396	333	1	+	+	CCONJ
ejpam-5396	333	2	(	(	PUNCT
ejpam-5396	333	3	r−r∗	r−r∗	PROPN
ejpam-5396	333	4	)	)	PUNCT
ejpam-5396	333	5	(	(	PUNCT
ejpam-5396	333	6	βc	βc	INTJ
ejpam-5396	333	7	r	r	NOUN
ejpam-5396	334	1	+	+	CCONJ
ejpam-5396	334	2	τi	τi	AUX
ejpam-5396	334	3	r	r	NOUN
ejpam-5396	334	4	−	−	PROPN
ejpam-5396	334	5	βc	βc	INTJ
ejpam-5396	334	6	r∗	r∗	VERB
ejpam-5396	334	7	−	−	PROPN
ejpam-5396	334	8	τi	τi	ADV
ejpam-5396	334	9	r∗	r∗	PROPN
ejpam-5396	334	10	)	)	PUNCT
ejpam-5396	334	11	=	=	PUNCT
ejpam-5396	335	1	(	(	PUNCT
ejpam-5396	335	2	s	s	PROPN
ejpam-5396	335	3	−	−	PROPN
ejpam-5396	335	4	s∗	s∗	PROPN
ejpam-5396	335	5	)	)	PUNCT
ejpam-5396	335	6	(	(	PUNCT
ejpam-5396	335	7	−	−	PROPN
ejpam-5396	335	8	λ	λ	SYM
ejpam-5396	335	9	nss∗	nss∗	PROPN
ejpam-5396	336	1	(	(	PUNCT
ejpam-5396	336	2	s	s	PROPN
ejpam-5396	336	3	−	−	PROPN
ejpam-5396	336	4	s∗	s∗	PROPN
ejpam-5396	336	5	)	)	PUNCT
ejpam-5396	337	1	−	−	PROPN
ejpam-5396	337	2	ηr	ηr	PROPN
ejpam-5396	337	3	nss∗	nss∗	NOUN
ejpam-5396	337	4	(	(	PUNCT
ejpam-5396	337	5	s	s	PROPN
ejpam-5396	337	6	−	−	PROPN
ejpam-5396	337	7	s∗	s∗	PROPN
ejpam-5396	337	8	)	)	PUNCT
ejpam-5396	337	9	)	)	PUNCT
ejpam-5396	338	1	+	+	CCONJ
ejpam-5396	338	2	(	(	PUNCT
ejpam-5396	338	3	c	c	NOUN
ejpam-5396	338	4	−	−	PROPN
ejpam-5396	338	5	c∗	c∗	NOUN
ejpam-5396	338	6	)	)	PUNCT
ejpam-5396	338	7	(	(	PUNCT
ejpam-5396	338	8	−	−	PROPN
ejpam-5396	338	9	δ(isθ	δ(isθ	INTJ
ejpam-5396	338	10	)	)	PUNCT
ejpam-5396	338	11	ncc∗	ncc∗	NOUN
ejpam-5396	338	12	(	(	PUNCT
ejpam-5396	338	13	c	c	NOUN
ejpam-5396	338	14	−	−	PROPN
ejpam-5396	338	15	c∗	c∗	NOUN
ejpam-5396	338	16	)	)	PUNCT
ejpam-5396	338	17	)	)	PUNCT
ejpam-5396	339	1	+	+	CCONJ
ejpam-5396	339	2	(	(	PUNCT
ejpam-5396	339	3	i	i	PRON
ejpam-5396	339	4	−	−	PROPN
ejpam-5396	339	5	i∗	i∗	NOUN
ejpam-5396	339	6	)	)	PUNCT
ejpam-5396	339	7	(	(	PUNCT
ejpam-5396	339	8	−	−	PROPN
ejpam-5396	339	9	δω(1−	δω(1−	PROPN
ejpam-5396	339	10	θ)sc	θ)sc	PROPN
ejpam-5396	339	11	nii∗	nii∗	NOUN
ejpam-5396	339	12	(	(	PUNCT
ejpam-5396	339	13	i	i	PRON
ejpam-5396	339	14	−	−	PROPN
ejpam-5396	339	15	i∗	i∗	NOUN
ejpam-5396	339	16	)	)	PUNCT
ejpam-5396	339	17	−	−	PROPN
ejpam-5396	340	1	πc	πc	INTJ
ejpam-5396	340	2	ii∗	ii∗	PROPN
ejpam-5396	341	1	(	(	PUNCT
ejpam-5396	341	2	i	i	PRON
ejpam-5396	341	3	−	−	PROPN
ejpam-5396	341	4	i∗	i∗	NOUN
ejpam-5396	341	5	)	)	PUNCT
ejpam-5396	341	6	)	)	PUNCT
ejpam-5396	342	1	+	+	CCONJ
ejpam-5396	342	2	(	(	PUNCT
ejpam-5396	342	3	r−r∗	r−r∗	PROPN
ejpam-5396	342	4	)	)	PUNCT
ejpam-5396	342	5	(	(	PUNCT
ejpam-5396	342	6	−	−	NOUN
ejpam-5396	342	7	βc	βc	INTJ
ejpam-5396	342	8	nrr∗	nrr∗	ADJ
ejpam-5396	342	9	(	(	PUNCT
ejpam-5396	342	10	r−r∗	r−r∗	PROPN
ejpam-5396	342	11	)	)	PUNCT
ejpam-5396	342	12	−	−	PROPN
ejpam-5396	343	1	τi	τi	ADP
ejpam-5396	343	2	nrr∗	nrr∗	ADV
ejpam-5396	343	3	(	(	PUNCT
ejpam-5396	343	4	r−r∗	r−r∗	PROPN
ejpam-5396	343	5	)	)	PUNCT
ejpam-5396	343	6	)	)	PUNCT
ejpam-5396	344	1	=	=	PUNCT
ejpam-5396	345	1	−	−	PROPN
ejpam-5396	345	2	λ	λ	SYM
ejpam-5396	345	3	nss∗	nss∗	NOUN
ejpam-5396	345	4	(	(	PUNCT
ejpam-5396	345	5	s	s	AUX
ejpam-5396	345	6	−	−	PROPN
ejpam-5396	345	7	s∗	s∗	PROPN
ejpam-5396	345	8	)	)	PUNCT
ejpam-5396	345	9	2	2	NUM
ejpam-5396	345	10	−	−	NOUN
ejpam-5396	345	11	ηr	ηr	NOUN
ejpam-5396	345	12	nss∗	nss∗	NOUN
ejpam-5396	345	13	(	(	PUNCT
ejpam-5396	345	14	s	s	PROPN
ejpam-5396	345	15	−	−	PROPN
ejpam-5396	345	16	s∗	s∗	PROPN
ejpam-5396	345	17	)	)	PUNCT
ejpam-5396	345	18	2	2	NUM
ejpam-5396	345	19	−	−	NUM
ejpam-5396	345	20	δ(isθ	δ(isθ	PROPN
ejpam-5396	345	21	)	)	PUNCT
ejpam-5396	345	22	ncc∗	ncc∗	NOUN
ejpam-5396	345	23	(	(	PUNCT
ejpam-5396	345	24	c	c	NOUN
ejpam-5396	345	25	−	−	PROPN
ejpam-5396	345	26	c∗	c∗	NOUN
ejpam-5396	345	27	)	)	PUNCT
ejpam-5396	345	28	2	2	NUM
ejpam-5396	345	29	−	−	PROPN
ejpam-5396	345	30	δω(1−	δω(1−	PROPN
ejpam-5396	345	31	θ)sc	θ)sc	PROPN
ejpam-5396	345	32	nii∗	nii∗	NOUN
ejpam-5396	345	33	(	(	PUNCT
ejpam-5396	345	34	i	i	PRON
ejpam-5396	345	35	−	−	PROPN
ejpam-5396	345	36	i∗	i∗	NOUN
ejpam-5396	345	37	)	)	PUNCT
ejpam-5396	345	38	2	2	NUM
ejpam-5396	345	39	−	−	NOUN
ejpam-5396	345	40	πc	πc	NOUN
ejpam-5396	345	41	ii∗	ii∗	PROPN
ejpam-5396	345	42	(	(	PUNCT
ejpam-5396	345	43	i	i	PRON
ejpam-5396	345	44	−	−	PROPN
ejpam-5396	345	45	i∗	i∗	NOUN
ejpam-5396	345	46	)	)	PUNCT
ejpam-5396	345	47	2	2	NUM
ejpam-5396	345	48	−	−	NOUN
ejpam-5396	345	49	βc	βc	INTJ
ejpam-5396	345	50	rr∗	rr∗	ADV
ejpam-5396	345	51	(	(	PUNCT
ejpam-5396	345	52	r−r∗	r−r∗	PROPN
ejpam-5396	345	53	)	)	PUNCT
ejpam-5396	345	54	2	2	NUM
ejpam-5396	345	55	−	−	NOUN
ejpam-5396	345	56	τi	τi	NOUN
ejpam-5396	345	57	rr∗	rr∗	PROPN
ejpam-5396	345	58	(	(	PUNCT
ejpam-5396	345	59	r−r∗	r−r∗	PROPN
ejpam-5396	345	60	)	)	PUNCT
ejpam-5396	345	61	2	2	NUM
ejpam-5396	345	62	.	.	PUNCT
ejpam-5396	346	1	thus	thus	ADV
ejpam-5396	346	2	,	,	PUNCT
ejpam-5396	346	3	for	for	ADP
ejpam-5396	346	4	all	all	DET
ejpam-5396	346	5	(	(	PUNCT
ejpam-5396	346	6	s	s	X
ejpam-5396	346	7	,	,	PUNCT
ejpam-5396	346	8	c	c	X
ejpam-5396	346	9	,	,	PUNCT
ejpam-5396	346	10	i	i	PRON
ejpam-5396	346	11	,	,	PUNCT
ejpam-5396	346	12	r	r	NOUN
ejpam-5396	346	13	)	)	PUNCT
ejpam-5396	346	14	∈	∈	PROPN
ejpam-5396	346	15	ω	ω	PROPN
ejpam-5396	346	16	,	,	PUNCT
ejpam-5396	346	17	dαl2(s	dαl2(s	NOUN
ejpam-5396	346	18	,	,	PUNCT
ejpam-5396	346	19	c	c	X
ejpam-5396	346	20	,	,	PUNCT
ejpam-5396	346	21	i	i	PRON
ejpam-5396	346	22	,	,	PUNCT
ejpam-5396	346	23	r	r	NOUN
ejpam-5396	346	24	)	)	PUNCT
ejpam-5396	346	25	<	<	X
ejpam-5396	346	26	0	0	X
ejpam-5396	346	27	.	.	PUNCT
ejpam-5396	346	28	therefore	therefore	ADV
ejpam-5396	346	29	,	,	PUNCT
ejpam-5396	346	30	it	it	PRON
ejpam-5396	346	31	follows	follow	VERB
ejpam-5396	346	32	from	from	ADP
ejpam-5396	346	33	[	[	X
ejpam-5396	346	34	30	30	NUM
ejpam-5396	346	35	]	]	PUNCT
ejpam-5396	346	36	that	that	SCONJ
ejpam-5396	346	37	e2	e2	PROPN
ejpam-5396	346	38	is	be	AUX
ejpam-5396	346	39	globally	globally	ADV
ejpam-5396	346	40	asymptotically	asymptotically	ADV
ejpam-5396	346	41	stable	stable	ADJ
ejpam-5396	346	42	in	in	ADP
ejpam-5396	346	43	ω	ω	PROPN
ejpam-5396	346	44	.	.	PROPN
ejpam-5396	346	45	4	4	NUM
ejpam-5396	346	46	.	.	X
ejpam-5396	346	47	numerical	numerical	ADJ
ejpam-5396	346	48	computational	computational	ADJ
ejpam-5396	346	49	methods	method	NOUN
ejpam-5396	346	50	of	of	ADP
ejpam-5396	346	51	solution	solution	NOUN
ejpam-5396	346	52	in	in	ADP
ejpam-5396	346	53	this	this	DET
ejpam-5396	346	54	section	section	NOUN
ejpam-5396	346	55	,	,	PUNCT
ejpam-5396	346	56	we	we	PRON
ejpam-5396	346	57	describe	describe	VERB
ejpam-5396	346	58	an	an	DET
ejpam-5396	346	59	implementation	implementation	NOUN
ejpam-5396	346	60	of	of	ADP
ejpam-5396	346	61	the	the	DET
ejpam-5396	346	62	numerical	numerical	ADJ
ejpam-5396	346	63	methods	method	NOUN
ejpam-5396	346	64	we	we	PRON
ejpam-5396	346	65	will	will	AUX
ejpam-5396	346	66	apply	apply	VERB
ejpam-5396	346	67	for	for	ADP
ejpam-5396	346	68	solving	solve	VERB
ejpam-5396	346	69	the	the	DET
ejpam-5396	346	70	proposed	propose	VERB
ejpam-5396	346	71	model	model	NOUN
ejpam-5396	346	72	(	(	PUNCT
ejpam-5396	346	73	1	1	NUM
ejpam-5396	346	74	)	)	PUNCT
ejpam-5396	346	75	.	.	PUNCT
ejpam-5396	347	1	the	the	DET
ejpam-5396	347	2	fractional	fractional	ADJ
ejpam-5396	347	3	integral	integral	ADJ
ejpam-5396	347	4	jα	jα	NOUN
ejpam-5396	347	5	mf(t	mf(t	NOUN
ejpam-5396	347	6	)	)	PUNCT
ejpam-5396	347	7	of	of	ADP
ejpam-5396	347	8	the	the	DET
ejpam-5396	347	9	function	function	NOUN
ejpam-5396	347	10	f	f	NOUN
ejpam-5396	347	11	:	:	PUNCT
ejpam-5396	347	12	r+	r+	NOUN
ejpam-5396	347	13	−→	−→	NOUN
ejpam-5396	347	14	r	r	NOUN
ejpam-5396	347	15	is	be	AUX
ejpam-5396	347	16	defined	define	VERB
ejpam-5396	347	17	as	as	ADP
ejpam-5396	347	18	:	:	PUNCT
ejpam-5396	347	19	jα	jα	NOUN
ejpam-5396	347	20	mf(t	mf(t	NOUN
ejpam-5396	347	21	)	)	PUNCT
ejpam-5396	347	22	=	=	SYM
ejpam-5396	347	23	1	1	NUM
ejpam-5396	347	24	γ(α	γ(α	NOUN
ejpam-5396	347	25	)	)	PUNCT
ejpam-5396	348	1	∫	∫	PROPN
ejpam-5396	349	1	t	t	PROPN
ejpam-5396	349	2	m	m	PROPN
ejpam-5396	349	3	(	(	PUNCT
ejpam-5396	349	4	t−	t−	X
ejpam-5396	349	5	θ)α−1f(θ)dθ	θ)α−1f(θ)dθ	NOUN
ejpam-5396	349	6	,	,	PUNCT
ejpam-5396	349	7	t	t	PROPN
ejpam-5396	349	8	≥	≥	PROPN
ejpam-5396	349	9	m	m	PROPN
ejpam-5396	349	10	,	,	PUNCT
ejpam-5396	349	11	a.	a.	NOUN
ejpam-5396	349	12	alalyani	alalyani	PROPN
ejpam-5396	349	13	/	/	SYM
ejpam-5396	349	14	eur	eur	PROPN
ejpam-5396	349	15	.	.	PUNCT
ejpam-5396	350	1	j.	j.	PROPN
ejpam-5396	350	2	pure	pure	PROPN
ejpam-5396	350	3	appl	appl	PROPN
ejpam-5396	350	4	.	.	PROPN
ejpam-5396	350	5	math	math	PROPN
ejpam-5396	350	6	,	,	PUNCT
ejpam-5396	350	7	17	17	NUM
ejpam-5396	350	8	(	(	PUNCT
ejpam-5396	350	9	4	4	NUM
ejpam-5396	350	10	)	)	PUNCT
ejpam-5396	350	11	(	(	PUNCT
ejpam-5396	350	12	2024	2024	NUM
ejpam-5396	350	13	)	)	PUNCT
ejpam-5396	350	14	,	,	PUNCT
ejpam-5396	350	15	2763	2763	NUM
ejpam-5396	350	16	-	-	SYM
ejpam-5396	350	17	2799	2799	NUM
ejpam-5396	350	18	2777	2777	NUM
ejpam-5396	350	19	where	where	SCONJ
ejpam-5396	350	20	α	α	PROPN
ejpam-5396	350	21	∈	∈	PROPN
ejpam-5396	350	22	r+	r+	NOUN
ejpam-5396	350	23	is	be	AUX
ejpam-5396	350	24	a	a	DET
ejpam-5396	350	25	non	non	ADJ
ejpam-5396	350	26	-	-	ADJ
ejpam-5396	350	27	integer	integer	ADJ
ejpam-5396	350	28	order	order	NOUN
ejpam-5396	350	29	and	and	CCONJ
ejpam-5396	350	30	γ(z	γ(z	ADJ
ejpam-5396	350	31	)	)	PUNCT
ejpam-5396	350	32	=	=	SYM
ejpam-5396	351	1	∫	∫	PROPN
ejpam-5396	351	2	∞	∞	PROPN
ejpam-5396	351	3	0	0	NUM
ejpam-5396	352	1	e−ttz−1dt	e−ttz−1dt	PROPN
ejpam-5396	352	2	is	be	AUX
ejpam-5396	352	3	the	the	DET
ejpam-5396	352	4	euler	euler	PROPN
ejpam-5396	352	5	gamma	gamma	PROPN
ejpam-5396	352	6	function	function	PROPN
ejpam-5396	352	7	.	.	PUNCT
ejpam-5396	353	1	it	it	PRON
ejpam-5396	353	2	follows	follow	VERB
ejpam-5396	353	3	from	from	ADP
ejpam-5396	353	4	[	[	X
ejpam-5396	353	5	48	48	NUM
ejpam-5396	353	6	]	]	PUNCT
ejpam-5396	353	7	that	that	SCONJ
ejpam-5396	353	8	the	the	DET
ejpam-5396	353	9	caputo	caputo	PROPN
ejpam-5396	353	10	fractional	fractional	PROPN
ejpam-5396	353	11	derivative	derivative	ADJ
ejpam-5396	353	12	dαf(t	dαf(t	NOUN
ejpam-5396	353	13	)	)	PUNCT
ejpam-5396	353	14	of	of	ADP
ejpam-5396	353	15	order	order	NOUN
ejpam-5396	353	16	α	α	X
ejpam-5396	353	17	>	>	X
ejpam-5396	353	18	0	0	PROPN
ejpam-5396	353	19	,	,	PUNCT
ejpam-5396	353	20	n−	n−	NOUN
ejpam-5396	353	21	1	1	NUM
ejpam-5396	353	22	<	<	X
ejpam-5396	353	23	α	α	X
ejpam-5396	353	24	<	<	X
ejpam-5396	353	25	n	n	CCONJ
ejpam-5396	353	26	,	,	PUNCT
ejpam-5396	353	27	n	n	PRON
ejpam-5396	353	28	∈	∈	NOUN
ejpam-5396	353	29	n	n	VERB
ejpam-5396	353	30	is	be	AUX
ejpam-5396	353	31	defined	define	VERB
ejpam-5396	353	32	as	as	ADP
ejpam-5396	353	33	:	:	PUNCT
ejpam-5396	353	34	c	c	NOUN
ejpam-5396	353	35	mdαf(t	mdαf(t	NOUN
ejpam-5396	353	36	)	)	PUNCT
ejpam-5396	353	37	=	=	SYM
ejpam-5396	353	38	1	1	NUM
ejpam-5396	353	39	γ(n−	γ(n−	PROPN
ejpam-5396	353	40	α	α	NOUN
ejpam-5396	353	41	)	)	PUNCT
ejpam-5396	353	42	∫	∫	PROPN
ejpam-5396	354	1	t	t	PROPN
ejpam-5396	354	2	m	m	PROPN
ejpam-5396	354	3	f	f	PROPN
ejpam-5396	354	4	(	(	PUNCT
ejpam-5396	354	5	n)(θ	n)(θ	PROPN
ejpam-5396	354	6	)	)	PUNCT
ejpam-5396	354	7	(	(	PUNCT
ejpam-5396	354	8	t−	t−	PROPN
ejpam-5396	354	9	θ)α+1−n	θ)α+1−n	NOUN
ejpam-5396	354	10	dθ	dθ	PROPN
ejpam-5396	354	11	,	,	PUNCT
ejpam-5396	354	12	t	t	PROPN
ejpam-5396	354	13	≥	≥	PROPN
ejpam-5396	354	14	m.	m.	NOUN
ejpam-5396	354	15	4.1	4.1	NUM
ejpam-5396	354	16	.	.	PUNCT
ejpam-5396	355	1	the	the	DET
ejpam-5396	355	2	adams	adams	PROPN
ejpam-5396	355	3	-	-	PUNCT
ejpam-5396	355	4	bashforth	bashforth	PROPN
ejpam-5396	355	5	-	-	PUNCT
ejpam-5396	355	6	moulton	moulton	PROPN
ejpam-5396	355	7	method	method	NOUN
ejpam-5396	355	8	(	(	PUNCT
ejpam-5396	355	9	abmm	abmm	PROPN
ejpam-5396	355	10	)	)	PUNCT
ejpam-5396	355	11	we	we	PRON
ejpam-5396	355	12	consider	consider	VERB
ejpam-5396	355	13	the	the	DET
ejpam-5396	355	14	problem	problem	NOUN
ejpam-5396	355	15	,	,	PUNCT
ejpam-5396	355	16	dα	dα	DET
ejpam-5396	355	17	x(t	x(t	PROPN
ejpam-5396	355	18	)	)	PUNCT
ejpam-5396	355	19	=	=	PUNCT
ejpam-5396	355	20	f(t	f(t	NOUN
ejpam-5396	355	21	,	,	PUNCT
ejpam-5396	355	22	x(t	x(t	PROPN
ejpam-5396	355	23	)	)	PUNCT
ejpam-5396	355	24	)	)	PUNCT
ejpam-5396	355	25	,	,	PUNCT
ejpam-5396	355	26	t	t	PROPN
ejpam-5396	355	27	∈	∈	PROPN
ejpam-5396	356	1	[	[	X
ejpam-5396	356	2	0	0	NUM
ejpam-5396	356	3	,	,	PUNCT
ejpam-5396	356	4	t	t	X
ejpam-5396	356	5	]	]	PUNCT
ejpam-5396	356	6	,	,	PUNCT
ejpam-5396	356	7	0	0	PUNCT
ejpam-5396	356	8	<	<	X
ejpam-5396	356	9	α	α	PROPN
ejpam-5396	356	10	≤	≤	NUM
ejpam-5396	356	11	1	1	NUM
ejpam-5396	356	12	,	,	PUNCT
ejpam-5396	356	13	x(j)(0	x(j)(0	NUM
ejpam-5396	356	14	)	)	PUNCT
ejpam-5396	357	1	=	=	SYM
ejpam-5396	357	2	x	x	X
ejpam-5396	357	3	(	(	PUNCT
ejpam-5396	357	4	j	j	NOUN
ejpam-5396	357	5	)	)	PUNCT
ejpam-5396	357	6	0	0	NUM
ejpam-5396	357	7	,	,	PUNCT
ejpam-5396	357	8	j	j	PROPN
ejpam-5396	357	9	=	=	SYM
ejpam-5396	357	10	0	0	NUM
ejpam-5396	357	11	,	,	PUNCT
ejpam-5396	357	12	1	1	NUM
ejpam-5396	357	13	,	,	PUNCT
ejpam-5396	357	14	2	2	NUM
ejpam-5396	357	15	,	,	PUNCT
ejpam-5396	357	16	....	....	PUNCT
ejpam-5396	357	17	,	,	PUNCT
ejpam-5396	357	18	n−	n−	NOUN
ejpam-5396	357	19	1	1	NUM
ejpam-5396	357	20	.	.	PUNCT
ejpam-5396	358	1	(	(	PUNCT
ejpam-5396	358	2	4	4	X
ejpam-5396	358	3	)	)	PUNCT
ejpam-5396	358	4	let	let	VERB
ejpam-5396	358	5	h	h	NOUN
ejpam-5396	359	1	=	=	SYM
ejpam-5396	359	2	t	t	PROPN
ejpam-5396	359	3	k	k	AUX
ejpam-5396	359	4	be	be	AUX
ejpam-5396	359	5	the	the	DET
ejpam-5396	359	6	step	step	NOUN
ejpam-5396	359	7	size	size	NOUN
ejpam-5396	359	8	,	,	PUNCT
ejpam-5396	359	9	where	where	SCONJ
ejpam-5396	359	10	k	k	PROPN
ejpam-5396	359	11	is	be	AUX
ejpam-5396	359	12	a	a	DET
ejpam-5396	359	13	positive	positive	ADJ
ejpam-5396	359	14	integer	integer	NOUN
ejpam-5396	359	15	and	and	CCONJ
ejpam-5396	359	16	t	t	PROPN
ejpam-5396	359	17	>	>	X
ejpam-5396	359	18	0	0	NUM
ejpam-5396	359	19	,	,	PUNCT
ejpam-5396	359	20	and	and	CCONJ
ejpam-5396	359	21	xj	xj	PROPN
ejpam-5396	359	22	be	be	VERB
ejpam-5396	359	23	the	the	DET
ejpam-5396	359	24	approximate	approximate	ADJ
ejpam-5396	359	25	solution	solution	NOUN
ejpam-5396	359	26	of	of	ADP
ejpam-5396	359	27	x(tj	x(tj	NUM
ejpam-5396	359	28	)	)	PUNCT
ejpam-5396	359	29	at	at	ADP
ejpam-5396	359	30	t	t	NOUN
ejpam-5396	359	31	=	=	SYM
ejpam-5396	359	32	tj	tj	PROPN
ejpam-5396	359	33	,	,	PUNCT
ejpam-5396	359	34	where	where	SCONJ
ejpam-5396	359	35	tj	tj	PROPN
ejpam-5396	359	36	=	=	SYM
ejpam-5396	359	37	jh	jh	PROPN
ejpam-5396	359	38	,	,	PUNCT
ejpam-5396	359	39	j	j	PROPN
ejpam-5396	359	40	=	=	SYM
ejpam-5396	359	41	0	0	NUM
ejpam-5396	359	42	,	,	PUNCT
ejpam-5396	359	43	1	1	NUM
ejpam-5396	359	44	,	,	PUNCT
ejpam-5396	359	45	...	...	PUNCT
ejpam-5396	359	46	,	,	PUNCT
ejpam-5396	359	47	k.	k.	PROPN
ejpam-5396	359	48	take	take	VERB
ejpam-5396	359	49	into	into	ADP
ejpam-5396	359	50	consideration	consideration	NOUN
ejpam-5396	359	51	this	this	DET
ejpam-5396	359	52	integral	integral	ADJ
ejpam-5396	359	53	part	part	NOUN
ejpam-5396	359	54	,	,	PUNCT
ejpam-5396	359	55	in+1	in+1	NOUN
ejpam-5396	359	56	=	=	SYM
ejpam-5396	359	57	∫	∫	PROPN
ejpam-5396	359	58	tn+1	tn+1	PROPN
ejpam-5396	359	59	0	0	NUM
ejpam-5396	359	60	(	(	PUNCT
ejpam-5396	359	61	tn+1	tn+1	NOUN
ejpam-5396	359	62	−	−	NOUN
ejpam-5396	359	63	θ)α−1g(θ	θ)α−1g(θ	NOUN
ejpam-5396	359	64	)	)	PUNCT
ejpam-5396	359	65	dθ	dθ	PROPN
ejpam-5396	359	66	,	,	PUNCT
ejpam-5396	359	67	n	n	NOUN
ejpam-5396	359	68	=	=	SYM
ejpam-5396	359	69	0	0	NUM
ejpam-5396	359	70	,	,	PUNCT
ejpam-5396	359	71	1	1	NUM
ejpam-5396	359	72	,	,	PUNCT
ejpam-5396	359	73	2	2	NUM
ejpam-5396	359	74	,	,	PUNCT
ejpam-5396	359	75	...	...	PUNCT
ejpam-5396	359	76	,	,	PUNCT
ejpam-5396	359	77	k	k	PROPN
ejpam-5396	360	1	−	−	PROPN
ejpam-5396	360	2	1	1	X
ejpam-5396	360	3	.	.	PUNCT
ejpam-5396	361	1	this	this	PRON
ejpam-5396	361	2	can	can	AUX
ejpam-5396	361	3	be	be	AUX
ejpam-5396	361	4	approximately	approximately	ADV
ejpam-5396	361	5	estimated	estimate	VERB
ejpam-5396	361	6	using	use	VERB
ejpam-5396	361	7	the	the	DET
ejpam-5396	361	8	following	follow	VERB
ejpam-5396	361	9	method	method	NOUN
ejpam-5396	361	10	in+1	in+1	X
ejpam-5396	362	1	≈	≈	PROPN
ejpam-5396	362	2	∫	∫	PROPN
ejpam-5396	362	3	tn+1	tn+1	PROPN
ejpam-5396	362	4	0	0	NUM
ejpam-5396	362	5	(	(	PUNCT
ejpam-5396	362	6	tn+1	tn+1	NOUN
ejpam-5396	362	7	−	−	PROPN
ejpam-5396	362	8	θ)α−1g̃n+1(θ	θ)α−1g̃n+1(θ	PROPN
ejpam-5396	362	9	)	)	PUNCT
ejpam-5396	362	10	dθ	dθ	PROPN
ejpam-5396	362	11	,	,	PUNCT
ejpam-5396	362	12	n	n	NOUN
ejpam-5396	362	13	=	=	SYM
ejpam-5396	362	14	0	0	NUM
ejpam-5396	362	15	,	,	PUNCT
ejpam-5396	362	16	1	1	NUM
ejpam-5396	362	17	,	,	PUNCT
ejpam-5396	362	18	2	2	NUM
ejpam-5396	362	19	,	,	PUNCT
ejpam-5396	362	20	...	...	PUNCT
ejpam-5396	362	21	,	,	PUNCT
ejpam-5396	362	22	k	k	PROPN
ejpam-5396	363	1	−	−	PROPN
ejpam-5396	363	2	1	1	NUM
ejpam-5396	363	3	,	,	PUNCT
ejpam-5396	363	4	where	where	SCONJ
ejpam-5396	363	5	g̃n+1(θ	g̃n+1(θ	NOUN
ejpam-5396	363	6	)	)	PUNCT
ejpam-5396	363	7	is	be	AUX
ejpam-5396	363	8	the	the	DET
ejpam-5396	363	9	approximation	approximation	NOUN
ejpam-5396	363	10	of	of	ADP
ejpam-5396	363	11	g(θ	g(θ	NOUN
ejpam-5396	363	12	)	)	PUNCT
ejpam-5396	363	13	on	on	ADP
ejpam-5396	363	14	the	the	DET
ejpam-5396	363	15	interval	interval	NOUN
ejpam-5396	363	16	[	[	X
ejpam-5396	363	17	0	0	NUM
ejpam-5396	363	18	,	,	PUNCT
ejpam-5396	363	19	tn+1	tn+1	PROPN
ejpam-5396	363	20	]	]	PUNCT
ejpam-5396	363	21	.	.	PUNCT
ejpam-5396	364	1	diethelm	diethelm	PROPN
ejpam-5396	364	2	et	et	PROPN
ejpam-5396	364	3	al	al	PROPN
ejpam-5396	364	4	.	.	PUNCT
ejpam-5396	365	1	[	[	X
ejpam-5396	365	2	20	20	NUM
ejpam-5396	365	3	]	]	PUNCT
ejpam-5396	365	4	carried	carry	VERB
ejpam-5396	365	5	out	out	ADP
ejpam-5396	365	6	the	the	DET
ejpam-5396	365	7	preliminary	preliminary	ADJ
ejpam-5396	365	8	study	study	NOUN
ejpam-5396	365	9	on	on	ADP
ejpam-5396	365	10	the	the	DET
ejpam-5396	365	11	fractional	fractional	PROPN
ejpam-5396	365	12	adams	adams	PROPN
ejpam-5396	365	13	technique	technique	NOUN
ejpam-5396	365	14	for	for	ADP
ejpam-5396	365	15	(	(	PUNCT
ejpam-5396	365	16	1	1	NUM
ejpam-5396	365	17	)	)	PUNCT
ejpam-5396	365	18	,	,	PUNCT
ejpam-5396	365	19	which	which	PRON
ejpam-5396	365	20	may	may	AUX
ejpam-5396	365	21	be	be	AUX
ejpam-5396	365	22	formulated	formulate	VERB
ejpam-5396	365	23	in	in	ADP
ejpam-5396	365	24	the	the	DET
ejpam-5396	365	25	following	following	ADJ
ejpam-5396	365	26	way	way	NOUN
ejpam-5396	365	27	:	:	PUNCT
ejpam-5396	365	28	xpn+1	xpn+1	X
ejpam-5396	365	29	=	=	SYM
ejpam-5396	365	30	k−1∑	k−1∑	PROPN
ejpam-5396	365	31	j=0	j=0	PROPN
ejpam-5396	365	32	tjn+1	tjn+1	PROPN
ejpam-5396	365	33	j	j	PROPN
ejpam-5396	365	34	!	!	PUNCT
ejpam-5396	365	35	x	x	PROPN
ejpam-5396	365	36	(	(	PUNCT
ejpam-5396	365	37	j	j	NOUN
ejpam-5396	365	38	)	)	PUNCT
ejpam-5396	365	39	0	0	PUNCT
ejpam-5396	366	1	+	+	CCONJ
ejpam-5396	366	2	hα	hα	ADP
ejpam-5396	366	3	γ(α+	γ(α+	PRON
ejpam-5396	366	4	2	2	NUM
ejpam-5396	366	5	)	)	PUNCT
ejpam-5396	366	6	n∑	n∑	NOUN
ejpam-5396	366	7	j=0	j=0	PROPN
ejpam-5396	366	8	ℓj	ℓj	ADP
ejpam-5396	366	9	,	,	PUNCT
ejpam-5396	366	10	n+1f(tj	n+1f(tj	ADJ
ejpam-5396	366	11	,	,	PUNCT
ejpam-5396	366	12	xj	xj	PROPN
ejpam-5396	366	13	)	)	PUNCT
ejpam-5396	366	14	.	.	PUNCT
ejpam-5396	366	15	xn+1	xn+1	PUNCT
ejpam-5396	367	1	=	=	PRON
ejpam-5396	367	2	k−1∑	k−1∑	PROPN
ejpam-5396	367	3	j=0	j=0	PROPN
ejpam-5396	367	4	tjn+1	tjn+1	PROPN
ejpam-5396	367	5	j	j	PROPN
ejpam-5396	367	6	!	!	PUNCT
ejpam-5396	368	1	y	y	PROPN
ejpam-5396	368	2	(	(	PUNCT
ejpam-5396	368	3	j	j	PROPN
ejpam-5396	368	4	)	)	PUNCT
ejpam-5396	368	5	0	0	PUNCT
ejpam-5396	369	1	+	+	CCONJ
ejpam-5396	369	2	hα	hα	ADP
ejpam-5396	369	3	γ(α+	γ(α+	DET
ejpam-5396	369	4	2	2	NUM
ejpam-5396	369	5	)	)	PUNCT
ejpam-5396	369	6			PROPN
ejpam-5396	369	7	n∑	n∑	PROPN
ejpam-5396	369	8	j=0	j=0	PROPN
ejpam-5396	369	9	ℓj	ℓj	ADP
ejpam-5396	369	10	,	,	PUNCT
ejpam-5396	369	11	n+1f(tj	n+1f(tj	ADJ
ejpam-5396	369	12	,	,	PUNCT
ejpam-5396	369	13	xj	xj	PROPN
ejpam-5396	369	14	)	)	PUNCT
ejpam-5396	369	15	+	+	CCONJ
ejpam-5396	369	16	ℓn+1,n+1f(tn+1	ℓn+1,n+1f(tn+1	PROPN
ejpam-5396	369	17	,	,	PUNCT
ejpam-5396	369	18	x	x	PUNCT
ejpam-5396	369	19	p	p	NOUN
ejpam-5396	369	20	n+1	n+1	PROPN
ejpam-5396	369	21	)	)	PUNCT
ejpam-5396	369	22			PROPN
ejpam-5396	369	23	.	.	PUNCT
ejpam-5396	370	1	(	(	PUNCT
ejpam-5396	370	2	5	5	X
ejpam-5396	370	3	)	)	PUNCT
ejpam-5396	370	4	here	here	ADV
ejpam-5396	370	5	ℓj	ℓj	VERB
ejpam-5396	370	6	,	,	PUNCT
ejpam-5396	370	7	n+1	n+1	NUM
ejpam-5396	370	8	are	be	AUX
ejpam-5396	370	9	given	give	VERB
ejpam-5396	370	10	by	by	ADP
ejpam-5396	370	11	ℓj	ℓj	NOUN
ejpam-5396	370	12	,	,	PUNCT
ejpam-5396	370	13	n+1	n+1	X
ejpam-5396	371	1	=	=	PUNCT
ejpam-5396	372	1			PRON
ejpam-5396	372	2	nα+1	nα+1	VERB
ejpam-5396	372	3	−	−	PROPN
ejpam-5396	372	4	(	(	PUNCT
ejpam-5396	372	5	n−	n−	NOUN
ejpam-5396	372	6	α)(n+	α)(n+	NOUN
ejpam-5396	372	7	1)α	1)α	NUM
ejpam-5396	372	8	,	,	PUNCT
ejpam-5396	372	9	if	if	SCONJ
ejpam-5396	372	10	j	j	PROPN
ejpam-5396	372	11	=	=	SYM
ejpam-5396	372	12	0	0	PROPN
ejpam-5396	372	13	,	,	PUNCT
ejpam-5396	372	14	(	(	PUNCT
ejpam-5396	372	15	n−	n−	NOUN
ejpam-5396	372	16	j	j	NOUN
ejpam-5396	372	17	+	+	CCONJ
ejpam-5396	372	18	2)α+1	2)α+1	NUM
ejpam-5396	372	19	+	+	CCONJ
ejpam-5396	372	20	(	(	PUNCT
ejpam-5396	372	21	n−	n−	NOUN
ejpam-5396	372	22	j)α+1	j)α+1	VERB
ejpam-5396	372	23	−	−	PROPN
ejpam-5396	373	1	2(n−	2(n−	NUM
ejpam-5396	373	2	j	j	PROPN
ejpam-5396	373	3	+	+	CCONJ
ejpam-5396	373	4	1)α+1	1)α+1	NUM
ejpam-5396	373	5	,	,	PUNCT
ejpam-5396	373	6	if	if	SCONJ
ejpam-5396	373	7	1	1	NUM
ejpam-5396	373	8	≤	≤	NUM
ejpam-5396	373	9	j	j	PROPN
ejpam-5396	373	10	≤	≤	NUM
ejpam-5396	373	11	n	n	CCONJ
ejpam-5396	373	12	,	,	PUNCT
ejpam-5396	373	13	1	1	NUM
ejpam-5396	373	14	,	,	PUNCT
ejpam-5396	373	15	if	if	SCONJ
ejpam-5396	373	16	j	j	PROPN
ejpam-5396	373	17	=	=	SYM
ejpam-5396	373	18	n+	n+	PUNCT
ejpam-5396	373	19	1	1	NUM
ejpam-5396	373	20	.	.	PUNCT
ejpam-5396	373	21	a.	a.	NOUN
ejpam-5396	373	22	alalyani	alalyani	PROPN
ejpam-5396	373	23	/	/	SYM
ejpam-5396	373	24	eur	eur	PROPN
ejpam-5396	373	25	.	.	PUNCT
ejpam-5396	374	1	j.	j.	PROPN
ejpam-5396	374	2	pure	pure	PROPN
ejpam-5396	374	3	appl	appl	PROPN
ejpam-5396	374	4	.	.	PROPN
ejpam-5396	374	5	math	math	PROPN
ejpam-5396	374	6	,	,	PUNCT
ejpam-5396	374	7	17	17	NUM
ejpam-5396	374	8	(	(	PUNCT
ejpam-5396	374	9	4	4	NUM
ejpam-5396	374	10	)	)	PUNCT
ejpam-5396	374	11	(	(	PUNCT
ejpam-5396	374	12	2024	2024	NUM
ejpam-5396	374	13	)	)	PUNCT
ejpam-5396	374	14	,	,	PUNCT
ejpam-5396	374	15	2763	2763	NUM
ejpam-5396	374	16	-	-	SYM
ejpam-5396	374	17	2799	2799	NUM
ejpam-5396	374	18	2778	2778	NUM
ejpam-5396	374	19	by	by	ADP
ejpam-5396	374	20	taking	take	VERB
ejpam-5396	374	21	z1	z1	NOUN
ejpam-5396	374	22	=	=	SYM
ejpam-5396	374	23	µ+	µ+	X
ejpam-5396	374	24	β	β	NOUN
ejpam-5396	374	25	+	+	SYM
ejpam-5396	374	26	π	π	PROPN
ejpam-5396	374	27	,	,	PUNCT
ejpam-5396	374	28	z2	z2	PROPN
ejpam-5396	374	29	=	=	SYM
ejpam-5396	374	30	τ	τ	PROPN
ejpam-5396	374	31	+	+	NUM
ejpam-5396	374	32	µ+	µ+	PROPN
ejpam-5396	374	33	σ	σ	PROPN
ejpam-5396	374	34	,	,	PUNCT
ejpam-5396	374	35	(	(	PUNCT
ejpam-5396	374	36	6	6	NUM
ejpam-5396	374	37	)	)	PUNCT
ejpam-5396	374	38	the	the	DET
ejpam-5396	374	39	model	model	NOUN
ejpam-5396	374	40	(	(	PUNCT
ejpam-5396	374	41	1	1	X
ejpam-5396	374	42	)	)	PUNCT
ejpam-5396	374	43	may	may	AUX
ejpam-5396	374	44	be	be	AUX
ejpam-5396	374	45	reformulated	reformulate	VERB
ejpam-5396	374	46	in	in	ADP
ejpam-5396	374	47	the	the	DET
ejpam-5396	374	48	sense	sense	NOUN
ejpam-5396	374	49	of	of	ADP
ejpam-5396	374	50	the	the	DET
ejpam-5396	374	51	abmm	abmm	NOUN
ejpam-5396	374	52	,	,	PUNCT
ejpam-5396	374	53	according	accord	VERB
ejpam-5396	374	54	to	to	ADP
ejpam-5396	374	55	eq	eq	PROPN
ejpam-5396	374	56	.	.	PUNCT
ejpam-5396	375	1	(	(	PUNCT
ejpam-5396	375	2	5	5	NUM
ejpam-5396	375	3	)	)	PUNCT
ejpam-5396	375	4	,	,	PUNCT
ejpam-5396	375	5	as	as	SCONJ
ejpam-5396	375	6	follows	follow	VERB
ejpam-5396	375	7	:	:	PUNCT
ejpam-5396	375	8	sn+1	sn+1	X
ejpam-5396	375	9	=	=	SYM
ejpam-5396	375	10	s0	s0	PROPN
ejpam-5396	375	11	+	+	CCONJ
ejpam-5396	375	12	hα	hα	ADP
ejpam-5396	375	13	γ(α+	γ(α+	DET
ejpam-5396	375	14	2	2	NUM
ejpam-5396	375	15	)	)	PUNCT
ejpam-5396	375	16	(	(	PUNCT
ejpam-5396	375	17	λ−	λ−	PROPN
ejpam-5396	375	18	δ(ipn+1	δ(ipn+1	PROPN
ejpam-5396	375	19	+	+	CCONJ
ejpam-5396	375	20	ωcp	ωcp	PROPN
ejpam-5396	375	21	n+1	n+1	NOUN
ejpam-5396	375	22	)	)	PUNCT
ejpam-5396	375	23	n	n	PRON
ejpam-5396	375	24	sp	sp	ADP
ejpam-5396	375	25	n+1	n+1	PROPN
ejpam-5396	375	26	−	−	NOUN
ejpam-5396	375	27	µsp	µsp	PROPN
ejpam-5396	375	28	n+1	n+1	PROPN
ejpam-5396	375	29	+	+	NUM
ejpam-5396	375	30	ηrp	ηrp	PROPN
ejpam-5396	375	31	n+1	n+1	NUM
ejpam-5396	375	32	)	)	PUNCT
ejpam-5396	376	1	+	+	CCONJ
ejpam-5396	376	2	hα	hα	ADP
ejpam-5396	376	3	γ(α+	γ(α+	PRON
ejpam-5396	376	4	2	2	NUM
ejpam-5396	376	5	)	)	PUNCT
ejpam-5396	376	6	n∑	n∑	NOUN
ejpam-5396	376	7	j=0	j=0	PROPN
ejpam-5396	376	8	ψj	ψj	ADV
ejpam-5396	376	9	,	,	PUNCT
ejpam-5396	376	10	n+1	n+1	PROPN
ejpam-5396	376	11	(	(	PUNCT
ejpam-5396	376	12	λ−	λ−	PROPN
ejpam-5396	376	13	δ(i(tj	δ(i(tj	ADJ
ejpam-5396	376	14	)	)	PUNCT
ejpam-5396	376	15	+	+	CCONJ
ejpam-5396	376	16	ωc(tj	ωc(tj	NUM
ejpam-5396	376	17	)	)	PUNCT
ejpam-5396	376	18	)	)	PUNCT
ejpam-5396	376	19	n	n	ADP
ejpam-5396	376	20	s(tj)−	s(tj)−	NOUN
ejpam-5396	376	21	µs(tj	µs(tj	ADJ
ejpam-5396	376	22	)	)	PUNCT
ejpam-5396	376	23	+	+	CCONJ
ejpam-5396	376	24	ηr(tj	ηr(tj	ADJ
ejpam-5396	376	25	)	)	PUNCT
ejpam-5396	376	26	)	)	PUNCT
ejpam-5396	376	27	,	,	PUNCT
ejpam-5396	376	28	cn+1	cn+1	NOUN
ejpam-5396	376	29	=	=	SYM
ejpam-5396	376	30	c0	c0	NOUN
ejpam-5396	376	31	+	+	X
ejpam-5396	376	32	hα	hα	ADP
ejpam-5396	376	33	γ(α+	γ(α+	DET
ejpam-5396	376	34	2	2	NUM
ejpam-5396	376	35	)	)	PUNCT
ejpam-5396	376	36	(	(	PUNCT
ejpam-5396	376	37	δ(ipn+1	δ(ipn+1	VERB
ejpam-5396	376	38	+	+	CCONJ
ejpam-5396	376	39	ωcp	ωcp	NOUN
ejpam-5396	376	40	n+1	n+1	NOUN
ejpam-5396	376	41	)	)	PUNCT
ejpam-5396	376	42	n	n	CCONJ
ejpam-5396	376	43	θsp	θsp	VERB
ejpam-5396	376	44	n+1	n+1	NUM
ejpam-5396	376	45	−	−	PROPN
ejpam-5396	376	46	z1c	z1c	NOUN
ejpam-5396	376	47	p	p	X
ejpam-5396	376	48	n+1	n+1	PROPN
ejpam-5396	376	49	)	)	PUNCT
ejpam-5396	376	50	+	+	CCONJ
ejpam-5396	376	51	hα	hα	ADP
ejpam-5396	376	52	γ(α+	γ(α+	PRON
ejpam-5396	376	53	2	2	NUM
ejpam-5396	376	54	)	)	PUNCT
ejpam-5396	376	55	n∑	n∑	NOUN
ejpam-5396	376	56	j=0	j=0	PROPN
ejpam-5396	376	57	ψj	ψj	ADV
ejpam-5396	376	58	,	,	PUNCT
ejpam-5396	376	59	n+1	n+1	PROPN
ejpam-5396	376	60	(	(	PUNCT
ejpam-5396	376	61	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	376	62	)	)	PUNCT
ejpam-5396	376	63	+	+	CCONJ
ejpam-5396	376	64	ωc(tj	ωc(tj	NUM
ejpam-5396	376	65	)	)	PUNCT
ejpam-5396	376	66	)	)	PUNCT
ejpam-5396	376	67	n	n	CCONJ
ejpam-5396	376	68	θs(tj)−	θs(tj)−	ADP
ejpam-5396	376	69	z1c(tj	z1c(tj	NUM
ejpam-5396	376	70	)	)	PUNCT
ejpam-5396	376	71	)	)	PUNCT
ejpam-5396	376	72	,	,	PUNCT
ejpam-5396	376	73	in+1	in+1	X
ejpam-5396	376	74	=	=	SYM
ejpam-5396	376	75	i0	i0	PROPN
ejpam-5396	376	76	+	+	X
ejpam-5396	376	77	hα	hα	ADP
ejpam-5396	376	78	γ(α+	γ(α+	DET
ejpam-5396	376	79	2	2	NUM
ejpam-5396	376	80	)	)	PUNCT
ejpam-5396	376	81	(	(	PUNCT
ejpam-5396	376	82	δ(ipn+1	δ(ipn+1	VERB
ejpam-5396	376	83	+	+	CCONJ
ejpam-5396	376	84	ωcp	ωcp	NOUN
ejpam-5396	376	85	n+1	n+1	NOUN
ejpam-5396	376	86	)	)	PUNCT
ejpam-5396	376	87	n	n	CCONJ
ejpam-5396	376	88	(	(	PUNCT
ejpam-5396	376	89	1−	1−	NUM
ejpam-5396	376	90	θ)sp	θ)sp	PROPN
ejpam-5396	376	91	n+1	n+1	PROPN
ejpam-5396	377	1	+	+	CCONJ
ejpam-5396	377	2	πcp	πcp	VERB
ejpam-5396	377	3	n+1	n+1	NUM
ejpam-5396	377	4	−	−	PROPN
ejpam-5396	377	5	z2i	z2i	PROPN
ejpam-5396	377	6	p	p	NOUN
ejpam-5396	377	7	n+1	n+1	PROPN
ejpam-5396	377	8	)	)	PUNCT
ejpam-5396	378	1	+	+	CCONJ
ejpam-5396	378	2	hα	hα	ADP
ejpam-5396	378	3	γ(α+	γ(α+	PRON
ejpam-5396	378	4	2	2	NUM
ejpam-5396	378	5	)	)	PUNCT
ejpam-5396	378	6	n∑	n∑	NOUN
ejpam-5396	378	7	j=0	j=0	PROPN
ejpam-5396	378	8	ψj	ψj	ADV
ejpam-5396	378	9	,	,	PUNCT
ejpam-5396	378	10	n+1	n+1	PROPN
ejpam-5396	378	11	(	(	PUNCT
ejpam-5396	378	12	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	378	13	)	)	PUNCT
ejpam-5396	378	14	+	+	CCONJ
ejpam-5396	378	15	ωc(tj	ωc(tj	NUM
ejpam-5396	378	16	)	)	PUNCT
ejpam-5396	378	17	)	)	PUNCT
ejpam-5396	379	1	n	n	CCONJ
ejpam-5396	379	2	(	(	PUNCT
ejpam-5396	379	3	1−	1−	NUM
ejpam-5396	379	4	θ)s(tj	θ)s(tj	ADJ
ejpam-5396	379	5	)	)	PUNCT
ejpam-5396	380	1	+	+	CCONJ
ejpam-5396	380	2	πc(tj)−	πc(tj)−	X
ejpam-5396	380	3	z2i(tj	z2i(tj	NUM
ejpam-5396	380	4	)	)	PUNCT
ejpam-5396	380	5	)	)	PUNCT
ejpam-5396	380	6	,	,	PUNCT
ejpam-5396	380	7	rn+1	rn+1	X
ejpam-5396	380	8	=	=	SYM
ejpam-5396	380	9	r0	r0	NOUN
ejpam-5396	380	10	+	+	CCONJ
ejpam-5396	380	11	hα	hα	ADP
ejpam-5396	380	12	γ(α+	γ(α+	DET
ejpam-5396	380	13	2	2	NUM
ejpam-5396	380	14	)	)	PUNCT
ejpam-5396	380	15	(	(	PUNCT
ejpam-5396	380	16	βcp	βcp	NOUN
ejpam-5396	380	17	n+1	n+1	PUNCT
ejpam-5396	380	18	+	+	NUM
ejpam-5396	380	19	τipn+1	τipn+1	NOUN
ejpam-5396	380	20	−	−	NOUN
ejpam-5396	380	21	(	(	PUNCT
ejpam-5396	381	1	µ+	µ+	PROPN
ejpam-5396	381	2	η)rp	η)rp	PROPN
ejpam-5396	381	3	n+1	n+1	NUM
ejpam-5396	381	4	)	)	PUNCT
ejpam-5396	382	1	+	+	CCONJ
ejpam-5396	382	2	hα	hα	ADP
ejpam-5396	382	3	γ(α+	γ(α+	PRON
ejpam-5396	382	4	2	2	NUM
ejpam-5396	382	5	)	)	PUNCT
ejpam-5396	382	6	n∑	n∑	NOUN
ejpam-5396	382	7	j=0	j=0	PROPN
ejpam-5396	382	8	ψj	ψj	ADV
ejpam-5396	382	9	,	,	PUNCT
ejpam-5396	382	10	n+1	n+1	PROPN
ejpam-5396	382	11	(	(	PUNCT
ejpam-5396	382	12	βc(tj	βc(tj	PROPN
ejpam-5396	382	13	)	)	PUNCT
ejpam-5396	382	14	+	+	CCONJ
ejpam-5396	382	15	τi(tj)−	τi(tj)−	NOUN
ejpam-5396	382	16	(	(	PUNCT
ejpam-5396	382	17	µ+	µ+	X
ejpam-5396	382	18	η)r(tj	η)r(tj	NUM
ejpam-5396	382	19	)	)	PUNCT
ejpam-5396	382	20	)	)	PUNCT
ejpam-5396	382	21	,	,	PUNCT
ejpam-5396	382	22	where	where	SCONJ
ejpam-5396	382	23	sp	sp	ADP
ejpam-5396	382	24	n+1	n+1	PROPN
ejpam-5396	382	25	,	,	PUNCT
ejpam-5396	382	26	c	c	PROPN
ejpam-5396	382	27	p	p	PROPN
ejpam-5396	382	28	n+1	n+1	PROPN
ejpam-5396	382	29	,	,	PUNCT
ejpam-5396	382	30	i	i	PRON
ejpam-5396	382	31	p	p	NOUN
ejpam-5396	382	32	n+1	n+1	PROPN
ejpam-5396	382	33	,	,	PUNCT
ejpam-5396	382	34	and	and	CCONJ
ejpam-5396	382	35	rp	rp	NOUN
ejpam-5396	382	36	n+1	n+1	PROPN
ejpam-5396	382	37	are	be	AUX
ejpam-5396	382	38	given	give	VERB
ejpam-5396	382	39	below	below	ADV
ejpam-5396	382	40	:	:	PUNCT
ejpam-5396	382	41	sp	sp	ADP
ejpam-5396	382	42	n+1	n+1	PROPN
ejpam-5396	382	43	=	=	SYM
ejpam-5396	382	44	s0	s0	PROPN
ejpam-5396	382	45	+	+	CCONJ
ejpam-5396	382	46	hα	hα	ADP
ejpam-5396	382	47	γ(α+	γ(α+	DET
ejpam-5396	382	48	2	2	NUM
ejpam-5396	382	49	)	)	PUNCT
ejpam-5396	382	50	n∑	n∑	NOUN
ejpam-5396	382	51	j=0	j=0	PROPN
ejpam-5396	382	52	ψj	ψj	ADV
ejpam-5396	382	53	,	,	PUNCT
ejpam-5396	382	54	n+1	n+1	PROPN
ejpam-5396	382	55	(	(	PUNCT
ejpam-5396	382	56	λ−	λ−	PROPN
ejpam-5396	382	57	δ(i(tj	δ(i(tj	ADJ
ejpam-5396	382	58	)	)	PUNCT
ejpam-5396	382	59	+	+	CCONJ
ejpam-5396	382	60	ωc(tj	ωc(tj	NUM
ejpam-5396	382	61	)	)	PUNCT
ejpam-5396	382	62	)	)	PUNCT
ejpam-5396	382	63	n	n	ADP
ejpam-5396	382	64	s(tj)−	s(tj)−	NOUN
ejpam-5396	382	65	µs(tj	µs(tj	ADJ
ejpam-5396	382	66	)	)	PUNCT
ejpam-5396	382	67	+	+	CCONJ
ejpam-5396	382	68	ηr(tj	ηr(tj	ADJ
ejpam-5396	382	69	)	)	PUNCT
ejpam-5396	382	70	)	)	PUNCT
ejpam-5396	382	71	,	,	PUNCT
ejpam-5396	382	72	cp	cp	X
ejpam-5396	382	73	n+1	n+1	PROPN
ejpam-5396	382	74	=	=	SYM
ejpam-5396	382	75	c0	c0	PROPN
ejpam-5396	382	76	+	+	X
ejpam-5396	382	77	hα	hα	ADP
ejpam-5396	382	78	γ(α+	γ(α+	DET
ejpam-5396	382	79	2	2	NUM
ejpam-5396	382	80	)	)	PUNCT
ejpam-5396	382	81	n∑	n∑	NOUN
ejpam-5396	382	82	j=0	j=0	PROPN
ejpam-5396	382	83	ψj	ψj	ADV
ejpam-5396	382	84	,	,	PUNCT
ejpam-5396	382	85	n+1	n+1	PROPN
ejpam-5396	382	86	(	(	PUNCT
ejpam-5396	382	87	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	382	88	)	)	PUNCT
ejpam-5396	382	89	+	+	CCONJ
ejpam-5396	382	90	ωc(tj	ωc(tj	NUM
ejpam-5396	382	91	)	)	PUNCT
ejpam-5396	382	92	)	)	PUNCT
ejpam-5396	382	93	n	n	CCONJ
ejpam-5396	382	94	θs(tj)−	θs(tj)−	ADP
ejpam-5396	382	95	z1c(tj	z1c(tj	NUM
ejpam-5396	382	96	)	)	PUNCT
ejpam-5396	382	97	)	)	PUNCT
ejpam-5396	382	98	,	,	PUNCT
ejpam-5396	382	99	ipn+1	ipn+1	NOUN
ejpam-5396	382	100	=	=	SYM
ejpam-5396	382	101	i0	i0	PROPN
ejpam-5396	382	102	+	+	X
ejpam-5396	382	103	hα	hα	ADP
ejpam-5396	382	104	γ(α+	γ(α+	DET
ejpam-5396	382	105	2	2	NUM
ejpam-5396	382	106	)	)	PUNCT
ejpam-5396	382	107	n∑	n∑	NOUN
ejpam-5396	382	108	j=0	j=0	PROPN
ejpam-5396	382	109	ψj	ψj	ADV
ejpam-5396	382	110	,	,	PUNCT
ejpam-5396	382	111	n+1	n+1	PROPN
ejpam-5396	382	112	(	(	PUNCT
ejpam-5396	382	113	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	382	114	)	)	PUNCT
ejpam-5396	382	115	+	+	CCONJ
ejpam-5396	382	116	ωc(tj	ωc(tj	NUM
ejpam-5396	382	117	)	)	PUNCT
ejpam-5396	382	118	)	)	PUNCT
ejpam-5396	383	1	n	n	CCONJ
ejpam-5396	383	2	(	(	PUNCT
ejpam-5396	383	3	1−	1−	NUM
ejpam-5396	383	4	θ)s(tj	θ)s(tj	ADJ
ejpam-5396	383	5	)	)	PUNCT
ejpam-5396	384	1	+	+	CCONJ
ejpam-5396	384	2	πc(tj)−	πc(tj)−	X
ejpam-5396	384	3	z2i(tj	z2i(tj	NUM
ejpam-5396	384	4	)	)	PUNCT
ejpam-5396	384	5	)	)	PUNCT
ejpam-5396	384	6	,	,	PUNCT
ejpam-5396	384	7	rp	rp	NOUN
ejpam-5396	384	8	n+1	n+1	PROPN
ejpam-5396	384	9	=	=	SYM
ejpam-5396	384	10	r0	r0	NOUN
ejpam-5396	384	11	+	+	CCONJ
ejpam-5396	384	12	hα	hα	ADP
ejpam-5396	384	13	γ(α+	γ(α+	DET
ejpam-5396	384	14	2	2	NUM
ejpam-5396	384	15	)	)	PUNCT
ejpam-5396	384	16	n∑	n∑	NOUN
ejpam-5396	384	17	j=0	j=0	PROPN
ejpam-5396	384	18	ψj	ψj	ADV
ejpam-5396	384	19	,	,	PUNCT
ejpam-5396	384	20	n+1	n+1	PROPN
ejpam-5396	384	21	(	(	PUNCT
ejpam-5396	384	22	βc(tj	βc(tj	PROPN
ejpam-5396	384	23	)	)	PUNCT
ejpam-5396	384	24	+	+	CCONJ
ejpam-5396	384	25	τi(tj)−	τi(tj)−	NOUN
ejpam-5396	384	26	(	(	PUNCT
ejpam-5396	384	27	µ+	µ+	X
ejpam-5396	384	28	η)r(tj	η)r(tj	NUM
ejpam-5396	384	29	)	)	PUNCT
ejpam-5396	384	30	)	)	PUNCT
ejpam-5396	384	31	.	.	PUNCT
ejpam-5396	385	1	a.	a.	NOUN
ejpam-5396	385	2	alalyani	alalyani	PROPN
ejpam-5396	385	3	/	/	SYM
ejpam-5396	385	4	eur	eur	PROPN
ejpam-5396	385	5	.	.	PUNCT
ejpam-5396	386	1	j.	j.	PROPN
ejpam-5396	386	2	pure	pure	PROPN
ejpam-5396	386	3	appl	appl	PROPN
ejpam-5396	386	4	.	.	PROPN
ejpam-5396	386	5	math	math	PROPN
ejpam-5396	386	6	,	,	PUNCT
ejpam-5396	386	7	17	17	NUM
ejpam-5396	386	8	(	(	PUNCT
ejpam-5396	386	9	4	4	NUM
ejpam-5396	386	10	)	)	PUNCT
ejpam-5396	386	11	(	(	PUNCT
ejpam-5396	386	12	2024	2024	NUM
ejpam-5396	386	13	)	)	PUNCT
ejpam-5396	386	14	,	,	PUNCT
ejpam-5396	386	15	2763	2763	NUM
ejpam-5396	386	16	-	-	SYM
ejpam-5396	386	17	2799	2799	NUM
ejpam-5396	386	18	2779	2779	NUM
ejpam-5396	386	19	4.2	4.2	NUM
ejpam-5396	386	20	.	.	PUNCT
ejpam-5396	387	1	the	the	DET
ejpam-5396	387	2	generalized	generalize	VERB
ejpam-5396	387	3	euler	euler	NOUN
ejpam-5396	387	4	method	method	NOUN
ejpam-5396	387	5	(	(	PUNCT
ejpam-5396	387	6	gem	gem	NOUN
ejpam-5396	387	7	)	)	PUNCT
ejpam-5396	387	8	the	the	DET
ejpam-5396	387	9	extended	extend	VERB
ejpam-5396	387	10	euler	euler	NOUN
ejpam-5396	387	11	’s	’s	PART
ejpam-5396	387	12	method	method	NOUN
ejpam-5396	387	13	for	for	ADP
ejpam-5396	387	14	numerically	numerically	ADV
ejpam-5396	387	15	solving	solve	VERB
ejpam-5396	387	16	the	the	DET
ejpam-5396	387	17	initial	initial	ADJ
ejpam-5396	387	18	value	value	NOUN
ejpam-5396	387	19	problem	problem	NOUN
ejpam-5396	387	20	(	(	PUNCT
ejpam-5396	387	21	4	4	NUM
ejpam-5396	387	22	)	)	PUNCT
ejpam-5396	387	23	with	with	ADP
ejpam-5396	387	24	the	the	DET
ejpam-5396	387	25	caputo	caputo	PROPN
ejpam-5396	387	26	derivatives	derivative	NOUN
ejpam-5396	387	27	was	be	AUX
ejpam-5396	387	28	derived	derive	VERB
ejpam-5396	387	29	by	by	ADP
ejpam-5396	387	30	odibat	odibat	NOUN
ejpam-5396	387	31	and	and	CCONJ
ejpam-5396	387	32	momani	momani	X
ejpam-5396	387	33	[	[	X
ejpam-5396	387	34	43	43	NUM
ejpam-5396	387	35	]	]	PUNCT
ejpam-5396	387	36	.	.	PUNCT
ejpam-5396	388	1	first	first	ADV
ejpam-5396	388	2	,	,	PUNCT
ejpam-5396	388	3	let	let	VERB
ejpam-5396	388	4	’s	’s	PRON
ejpam-5396	388	5	look	look	VERB
ejpam-5396	388	6	at	at	ADP
ejpam-5396	388	7	the	the	DET
ejpam-5396	388	8	starting	starting	NOUN
ejpam-5396	388	9	value	value	NOUN
ejpam-5396	388	10	problem	problem	NOUN
ejpam-5396	388	11	.	.	PUNCT
ejpam-5396	389	1	if	if	SCONJ
ejpam-5396	389	2	x	x	X
ejpam-5396	389	3	,	,	PUNCT
ejpam-5396	389	4	dαx	dαx	NOUN
ejpam-5396	389	5	,	,	PUNCT
ejpam-5396	389	6	and	and	CCONJ
ejpam-5396	389	7	d2αx	d2αx	CCONJ
ejpam-5396	389	8	are	be	AUX
ejpam-5396	389	9	continuous	continuous	ADJ
ejpam-5396	389	10	on	on	ADP
ejpam-5396	389	11	[	[	X
ejpam-5396	389	12	0	0	NUM
ejpam-5396	389	13	,	,	PUNCT
ejpam-5396	389	14	b	b	NOUN
ejpam-5396	389	15	]	]	X
ejpam-5396	389	16	and	and	CCONJ
ejpam-5396	389	17	a1	a1	NOUN
ejpam-5396	389	18	,	,	PUNCT
ejpam-5396	389	19	.	.	PUNCT
ejpam-5396	389	20	.	.	PUNCT
ejpam-5396	390	1	.	.	PUNCT
ejpam-5396	391	1	,	,	PUNCT
ejpam-5396	391	2	an	an	PRON
ejpam-5396	391	3	are	be	AUX
ejpam-5396	391	4	positive	positive	ADJ
ejpam-5396	391	5	integer	integer	NOUN
ejpam-5396	391	6	constants	constant	NOUN
ejpam-5396	391	7	,	,	PUNCT
ejpam-5396	391	8	then	then	ADV
ejpam-5396	391	9	it	it	PRON
ejpam-5396	391	10	follows	follow	VERB
ejpam-5396	391	11	from	from	ADP
ejpam-5396	391	12	(	(	PUNCT
ejpam-5396	391	13	4	4	NUM
ejpam-5396	391	14	)	)	PUNCT
ejpam-5396	391	15	that	that	SCONJ
ejpam-5396	391	16	for	for	ADP
ejpam-5396	391	17	each	each	DET
ejpam-5396	391	18	value	value	NOUN
ejpam-5396	391	19	of	of	ADP
ejpam-5396	391	20	t	t	PROPN
ejpam-5396	391	21	,	,	PUNCT
ejpam-5396	391	22	there	there	PRON
ejpam-5396	391	23	is	be	VERB
ejpam-5396	391	24	a	a	DET
ejpam-5396	391	25	value	value	NOUN
ejpam-5396	391	26	a1	a1	NOUN
ejpam-5396	391	27	,	,	PUNCT
ejpam-5396	391	28	which	which	PRON
ejpam-5396	391	29	implies	imply	VERB
ejpam-5396	391	30	x(t	x(t	PROPN
ejpam-5396	391	31	)	)	PUNCT
ejpam-5396	391	32	=	=	SYM
ejpam-5396	391	33	x(t0	x(t0	PROPN
ejpam-5396	391	34	)	)	PUNCT
ejpam-5396	392	1	+	+	CCONJ
ejpam-5396	392	2	(	(	PUNCT
ejpam-5396	392	3	dα	dα	DET
ejpam-5396	392	4	x(t))(t0	x(t))(t0	PROPN
ejpam-5396	392	5	)	)	PUNCT
ejpam-5396	392	6	tα	tα	VERB
ejpam-5396	392	7	γ(α+	γ(α+	DET
ejpam-5396	392	8	1	1	NUM
ejpam-5396	392	9	)	)	PUNCT
ejpam-5396	393	1	+	+	CCONJ
ejpam-5396	393	2	(	(	PUNCT
ejpam-5396	393	3	d2α	d2α	NOUN
ejpam-5396	393	4	x(t))(a1	x(t))(a1	NOUN
ejpam-5396	393	5	)	)	PUNCT
ejpam-5396	393	6	t2α	t2α	ADP
ejpam-5396	393	7	γ(2α+	γ(2α+	PROPN
ejpam-5396	393	8	1	1	NUM
ejpam-5396	393	9	)	)	PUNCT
ejpam-5396	393	10	.	.	PUNCT
ejpam-5396	394	1	(	(	PUNCT
ejpam-5396	394	2	7	7	X
ejpam-5396	394	3	)	)	PUNCT
ejpam-5396	394	4	substituting	substituting	NOUN
ejpam-5396	394	5	(	(	PUNCT
ejpam-5396	394	6	dα	dα	PROPN
ejpam-5396	394	7	x(t))(t0	x(t))(t0	NOUN
ejpam-5396	394	8	)	)	PUNCT
ejpam-5396	394	9	=	=	SYM
ejpam-5396	394	10	f(t0	f(t0	NOUN
ejpam-5396	394	11	,	,	PUNCT
ejpam-5396	394	12	x(t0	x(t0	PROPN
ejpam-5396	394	13	)	)	PUNCT
ejpam-5396	394	14	)	)	PUNCT
ejpam-5396	395	1	and	and	CCONJ
ejpam-5396	395	2	h	h	NOUN
ejpam-5396	395	3	=	=	NOUN
ejpam-5396	396	1	t1	t1	NOUN
ejpam-5396	396	2	into	into	ADP
ejpam-5396	396	3	eq	eq	NOUN
ejpam-5396	396	4	.	.	PUNCT
ejpam-5396	397	1	(	(	PUNCT
ejpam-5396	397	2	7	7	X
ejpam-5396	397	3	)	)	PUNCT
ejpam-5396	397	4	yields	yield	VERB
ejpam-5396	397	5	an	an	DET
ejpam-5396	397	6	equation	equation	NOUN
ejpam-5396	397	7	for	for	ADP
ejpam-5396	397	8	x(t1	x(t1	PROPN
ejpam-5396	397	9	):	):	PUNCT
ejpam-5396	397	10	x(t1	x(t1	PROPN
ejpam-5396	397	11	)	)	PUNCT
ejpam-5396	398	1	=	=	SYM
ejpam-5396	398	2	x(t0	x(t0	PROPN
ejpam-5396	398	3	)	)	PUNCT
ejpam-5396	399	1	+	+	CCONJ
ejpam-5396	399	2	f(t0	f(t0	NOUN
ejpam-5396	399	3	,	,	PUNCT
ejpam-5396	399	4	x(t0	x(t0	PROPN
ejpam-5396	399	5	)	)	PUNCT
ejpam-5396	399	6	)	)	PUNCT
ejpam-5396	400	1	hα	hα	ADP
ejpam-5396	400	2	γ(α+	γ(α+	DET
ejpam-5396	400	3	1	1	NUM
ejpam-5396	400	4	)	)	PUNCT
ejpam-5396	400	5	+	+	CCONJ
ejpam-5396	400	6	(	(	PUNCT
ejpam-5396	400	7	d2α	d2α	NOUN
ejpam-5396	400	8	x(t))(a1	x(t))(a1	NOUN
ejpam-5396	400	9	)	)	PUNCT
ejpam-5396	400	10	h2α	h2α	VERB
ejpam-5396	400	11	γ(2α+	γ(2α+	PROPN
ejpam-5396	400	12	1	1	NUM
ejpam-5396	400	13	)	)	PUNCT
ejpam-5396	400	14	.	.	PUNCT
ejpam-5396	401	1	if	if	SCONJ
ejpam-5396	401	2	the	the	DET
ejpam-5396	401	3	step	step	NOUN
ejpam-5396	401	4	size	size	NOUN
ejpam-5396	401	5	h	h	NOUN
ejpam-5396	401	6	is	be	AUX
ejpam-5396	401	7	sufficiently	sufficiently	ADV
ejpam-5396	401	8	small	small	ADJ
ejpam-5396	401	9	,	,	PUNCT
ejpam-5396	401	10	the	the	DET
ejpam-5396	401	11	second	second	ADJ
ejpam-5396	401	12	-	-	PUNCT
ejpam-5396	401	13	order	order	NOUN
ejpam-5396	401	14	term	term	NOUN
ejpam-5396	401	15	(	(	PUNCT
ejpam-5396	401	16	involving	involve	VERB
ejpam-5396	401	17	h2α	h2α	NOUN
ejpam-5396	401	18	)	)	PUNCT
ejpam-5396	401	19	may	may	AUX
ejpam-5396	401	20	be	be	AUX
ejpam-5396	401	21	neglected	neglect	VERB
ejpam-5396	401	22	,	,	PUNCT
ejpam-5396	401	23	allowing	allow	VERB
ejpam-5396	401	24	us	we	PRON
ejpam-5396	401	25	to	to	PART
ejpam-5396	401	26	get	get	VERB
ejpam-5396	401	27	x(t1	x(t1	PRON
ejpam-5396	401	28	)	)	PUNCT
ejpam-5396	402	1	=	=	SYM
ejpam-5396	402	2	x(t0	x(t0	PROPN
ejpam-5396	402	3	)	)	PUNCT
ejpam-5396	403	1	+	+	CCONJ
ejpam-5396	403	2	hα	hα	ADP
ejpam-5396	403	3	γ(α+	γ(α+	PRON
ejpam-5396	403	4	1	1	NUM
ejpam-5396	403	5	)	)	PUNCT
ejpam-5396	403	6	f(t0	f(t0	NOUN
ejpam-5396	403	7	,	,	PUNCT
ejpam-5396	403	8	x(t0	x(t0	PROPN
ejpam-5396	403	9	)	)	PUNCT
ejpam-5396	403	10	)	)	PUNCT
ejpam-5396	403	11	.	.	PUNCT
ejpam-5396	404	1	repeating	repeat	VERB
ejpam-5396	404	2	this	this	DET
ejpam-5396	404	3	procedure	procedure	NOUN
ejpam-5396	404	4	yields	yield	VERB
ejpam-5396	404	5	a	a	DET
ejpam-5396	404	6	sequence	sequence	NOUN
ejpam-5396	404	7	of	of	ADP
ejpam-5396	404	8	points	point	NOUN
ejpam-5396	404	9	that	that	PRON
ejpam-5396	404	10	estimates	estimate	VERB
ejpam-5396	404	11	the	the	DET
ejpam-5396	404	12	solution	solution	NOUN
ejpam-5396	404	13	x(t	x(t	PROPN
ejpam-5396	404	14	)	)	PUNCT
ejpam-5396	404	15	.	.	PUNCT
ejpam-5396	405	1	this	this	DET
ejpam-5396	405	2	iterative	iterative	ADJ
ejpam-5396	405	3	general	general	ADJ
ejpam-5396	405	4	formula	formula	NOUN
ejpam-5396	405	5	for	for	ADP
ejpam-5396	405	6	the	the	DET
ejpam-5396	405	7	gem	gem	NOUN
ejpam-5396	405	8	when	when	SCONJ
ejpam-5396	405	9	tj+1	tj+1	ADJ
ejpam-5396	405	10	=	=	SYM
ejpam-5396	405	11	tj	tj	NOUN
ejpam-5396	406	1	+	+	NOUN
ejpam-5396	406	2	h	h	NOUN
ejpam-5396	406	3	is	be	AUX
ejpam-5396	406	4	x(tj+1	x(tj+1	NOUN
ejpam-5396	406	5	)	)	PUNCT
ejpam-5396	406	6	=	=	PUNCT
ejpam-5396	406	7	x(tj	x(tj	NUM
ejpam-5396	406	8	)	)	PUNCT
ejpam-5396	407	1	+	+	CCONJ
ejpam-5396	407	2	hα	hα	ADP
ejpam-5396	407	3	γ(α+	γ(α+	PRON
ejpam-5396	407	4	1	1	NUM
ejpam-5396	407	5	)	)	PUNCT
ejpam-5396	407	6	f(tj	f(tj	NOUN
ejpam-5396	407	7	,	,	PUNCT
ejpam-5396	407	8	x(tj	x(tj	NUM
ejpam-5396	407	9	)	)	PUNCT
ejpam-5396	407	10	)	)	PUNCT
ejpam-5396	407	11	,	,	PUNCT
ejpam-5396	407	12	(	(	PUNCT
ejpam-5396	407	13	8)	8)	NUM
ejpam-5396	407	14	for	for	ADP
ejpam-5396	407	15	j	j	PROPN
ejpam-5396	407	16	=	=	SYM
ejpam-5396	407	17	0	0	PROPN
ejpam-5396	407	18	,	,	PUNCT
ejpam-5396	407	19	1	1	NUM
ejpam-5396	407	20	,	,	PUNCT
ejpam-5396	407	21	...	...	PUNCT
ejpam-5396	407	22	,	,	PUNCT
ejpam-5396	407	23	k−	k−	PROPN
ejpam-5396	407	24	1	1	NUM
ejpam-5396	407	25	.	.	PUNCT
ejpam-5396	408	1	the	the	DET
ejpam-5396	408	2	model	model	NOUN
ejpam-5396	408	3	(	(	PUNCT
ejpam-5396	408	4	1	1	X
ejpam-5396	408	5	)	)	PUNCT
ejpam-5396	408	6	may	may	AUX
ejpam-5396	408	7	be	be	AUX
ejpam-5396	408	8	reformulated	reformulate	VERB
ejpam-5396	408	9	in	in	ADP
ejpam-5396	408	10	the	the	DET
ejpam-5396	408	11	sense	sense	NOUN
ejpam-5396	408	12	of	of	ADP
ejpam-5396	408	13	gem	gem	NOUN
ejpam-5396	408	14	,	,	PUNCT
ejpam-5396	408	15	according	accord	VERB
ejpam-5396	408	16	to	to	ADP
ejpam-5396	408	17	eq	eq	PROPN
ejpam-5396	408	18	.	.	PUNCT
ejpam-5396	409	1	(	(	PUNCT
ejpam-5396	409	2	8)	8)	NUM
ejpam-5396	409	3	,	,	PUNCT
ejpam-5396	409	4	as	as	SCONJ
ejpam-5396	409	5	follows	follow	VERB
ejpam-5396	409	6	:	:	PUNCT
ejpam-5396	409	7	s(tj+1	s(tj+1	ADJ
ejpam-5396	409	8	)	)	PUNCT
ejpam-5396	409	9	=	=	SYM
ejpam-5396	409	10	s(tj	s(tj	NUM
ejpam-5396	409	11	)	)	PUNCT
ejpam-5396	410	1	+	+	CCONJ
ejpam-5396	410	2	hα	hα	ADP
ejpam-5396	410	3	γ(α+	γ(α+	DET
ejpam-5396	410	4	1	1	NUM
ejpam-5396	410	5	)	)	PUNCT
ejpam-5396	410	6	(	(	PUNCT
ejpam-5396	410	7	λ−	λ−	PROPN
ejpam-5396	410	8	δ(i(tj	δ(i(tj	X
ejpam-5396	410	9	)	)	PUNCT
ejpam-5396	410	10	+	+	CCONJ
ejpam-5396	411	1	ωc(tj	ωc(tj	NUM
ejpam-5396	411	2	)	)	PUNCT
ejpam-5396	411	3	)	)	PUNCT
ejpam-5396	412	1	n	n	ADP
ejpam-5396	412	2	s(tj)−	s(tj)−	NOUN
ejpam-5396	412	3	µs(tj	µs(tj	ADJ
ejpam-5396	412	4	)	)	PUNCT
ejpam-5396	412	5	+	+	CCONJ
ejpam-5396	412	6	ηr(tj	ηr(tj	ADJ
ejpam-5396	412	7	)	)	PUNCT
ejpam-5396	412	8	)	)	PUNCT
ejpam-5396	412	9	,	,	PUNCT
ejpam-5396	412	10	c(tj+1	c(tj+1	X
ejpam-5396	412	11	)	)	PUNCT
ejpam-5396	412	12	=	=	SYM
ejpam-5396	412	13	c(tj	c(tj	NUM
ejpam-5396	412	14	)	)	PUNCT
ejpam-5396	412	15	+	+	X
ejpam-5396	412	16	hα	hα	ADP
ejpam-5396	412	17	γ(α+	γ(α+	DET
ejpam-5396	412	18	1	1	NUM
ejpam-5396	412	19	)	)	PUNCT
ejpam-5396	412	20	(	(	PUNCT
ejpam-5396	412	21	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	412	22	)	)	PUNCT
ejpam-5396	412	23	+	+	CCONJ
ejpam-5396	412	24	ωc(tj	ωc(tj	NUM
ejpam-5396	412	25	)	)	PUNCT
ejpam-5396	412	26	)	)	PUNCT
ejpam-5396	412	27	n	n	CCONJ
ejpam-5396	412	28	θs(tj)−	θs(tj)−	ADP
ejpam-5396	412	29	z1c(tj	z1c(tj	NUM
ejpam-5396	412	30	)	)	PUNCT
ejpam-5396	412	31	)	)	PUNCT
ejpam-5396	412	32	,	,	PUNCT
ejpam-5396	412	33	i(tj+1	i(tj+1	PROPN
ejpam-5396	412	34	)	)	PUNCT
ejpam-5396	412	35	=	=	SYM
ejpam-5396	412	36	i(tj	i(tj	NUM
ejpam-5396	412	37	)	)	PUNCT
ejpam-5396	412	38	+	+	CCONJ
ejpam-5396	412	39	hα	hα	ADP
ejpam-5396	412	40	γ(α+	γ(α+	DET
ejpam-5396	412	41	1	1	NUM
ejpam-5396	412	42	)	)	PUNCT
ejpam-5396	412	43	(	(	PUNCT
ejpam-5396	412	44	δ(i(tj	δ(i(tj	NOUN
ejpam-5396	412	45	)	)	PUNCT
ejpam-5396	412	46	+	+	CCONJ
ejpam-5396	412	47	ωc(tj	ωc(tj	NUM
ejpam-5396	412	48	)	)	PUNCT
ejpam-5396	412	49	)	)	PUNCT
ejpam-5396	412	50	n	n	CCONJ
ejpam-5396	412	51	(	(	PUNCT
ejpam-5396	412	52	1−	1−	NUM
ejpam-5396	412	53	θ)s(tj	θ)s(tj	ADJ
ejpam-5396	412	54	)	)	PUNCT
ejpam-5396	412	55	+	+	CCONJ
ejpam-5396	412	56	πc(tj)−	πc(tj)−	X
ejpam-5396	412	57	z2i(tj	z2i(tj	NUM
ejpam-5396	412	58	)	)	PUNCT
ejpam-5396	412	59	)	)	PUNCT
ejpam-5396	412	60	,	,	PUNCT
ejpam-5396	412	61	r(tj+1	r(tj+1	X
ejpam-5396	412	62	)	)	PUNCT
ejpam-5396	412	63	=	=	SYM
ejpam-5396	412	64	r(tj	r(tj	NUM
ejpam-5396	412	65	)	)	PUNCT
ejpam-5396	413	1	+	+	X
ejpam-5396	413	2	hα	hα	ADP
ejpam-5396	413	3	γ(α+	γ(α+	DET
ejpam-5396	413	4	1	1	NUM
ejpam-5396	413	5	)	)	PUNCT
ejpam-5396	413	6	(	(	PUNCT
ejpam-5396	413	7	βc(tj	βc(tj	PROPN
ejpam-5396	413	8	)	)	PUNCT
ejpam-5396	413	9	+	+	CCONJ
ejpam-5396	413	10	τi(tj)−	τi(tj)−	NOUN
ejpam-5396	413	11	(	(	PUNCT
ejpam-5396	413	12	µ+	µ+	X
ejpam-5396	413	13	η)r(tj	η)r(tj	NUM
ejpam-5396	413	14	)	)	PUNCT
ejpam-5396	413	15	)	)	PUNCT
ejpam-5396	413	16	.	.	PUNCT
ejpam-5396	414	1	through	through	ADP
ejpam-5396	414	2	this	this	PRON
ejpam-5396	414	3	,	,	PUNCT
ejpam-5396	414	4	we	we	PRON
ejpam-5396	414	5	have	have	VERB
ejpam-5396	414	6	sn+1	sn+1	NOUN
ejpam-5396	414	7	=	=	SYM
ejpam-5396	414	8	sn	sn	PROPN
ejpam-5396	415	1	+	+	X
ejpam-5396	415	2	hα	hα	VERB
ejpam-5396	415	3	γ(α+	γ(α+	DET
ejpam-5396	415	4	1	1	NUM
ejpam-5396	415	5	)	)	PUNCT
ejpam-5396	415	6	hα	hα	ADP
ejpam-5396	415	7	γ(α+	γ(α+	DET
ejpam-5396	415	8	1	1	NUM
ejpam-5396	415	9	)	)	PUNCT
ejpam-5396	415	10	(	(	PUNCT
ejpam-5396	415	11	λ−	λ−	PROPN
ejpam-5396	415	12	δ(in	δ(in	PROPN
ejpam-5396	415	13	+	+	CCONJ
ejpam-5396	415	14	ωcn	ωcn	NOUN
ejpam-5396	415	15	)	)	PUNCT
ejpam-5396	415	16	n	n	CCONJ
ejpam-5396	415	17	sn	sn	NOUN
ejpam-5396	415	18	−	−	PROPN
ejpam-5396	415	19	µsn	µsn	NOUN
ejpam-5396	415	20	+	+	CCONJ
ejpam-5396	415	21	ηrn	ηrn	NOUN
ejpam-5396	415	22	)	)	PUNCT
ejpam-5396	415	23	,	,	PUNCT
ejpam-5396	415	24	cn+1	cn+1	X
ejpam-5396	415	25	=	=	SYM
ejpam-5396	415	26	cn	cn	PROPN
ejpam-5396	415	27	+	+	CCONJ
ejpam-5396	415	28	hα	hα	ADP
ejpam-5396	415	29	γ(α+	γ(α+	DET
ejpam-5396	415	30	1	1	NUM
ejpam-5396	415	31	)	)	PUNCT
ejpam-5396	415	32	(	(	PUNCT
ejpam-5396	415	33	δ(in	δ(in	PROPN
ejpam-5396	415	34	+	+	CCONJ
ejpam-5396	415	35	ωcn	ωcn	NOUN
ejpam-5396	415	36	)	)	PUNCT
ejpam-5396	415	37	n	n	PRON
ejpam-5396	415	38	θsn	θsn	NOUN
ejpam-5396	415	39	−	−	NOUN
ejpam-5396	415	40	z1cn	z1cn	PROPN
ejpam-5396	415	41	)	)	PUNCT
ejpam-5396	415	42	,	,	PUNCT
ejpam-5396	415	43	in+1	in+1	NOUN
ejpam-5396	415	44	=	=	NOUN
ejpam-5396	415	45	in	in	ADP
ejpam-5396	415	46	+	+	CCONJ
ejpam-5396	415	47	hα	hα	ADP
ejpam-5396	415	48	γ(α+	γ(α+	DET
ejpam-5396	415	49	1	1	NUM
ejpam-5396	415	50	)	)	PUNCT
ejpam-5396	415	51	(	(	PUNCT
ejpam-5396	415	52	δ(in	δ(in	PROPN
ejpam-5396	415	53	+	+	CCONJ
ejpam-5396	415	54	ωcn	ωcn	NOUN
ejpam-5396	415	55	)	)	PUNCT
ejpam-5396	415	56	n	n	CCONJ
ejpam-5396	415	57	(	(	PUNCT
ejpam-5396	415	58	1−	1−	NUM
ejpam-5396	415	59	θ)sn	θ)sn	NOUN
ejpam-5396	415	60	+	+	NUM
ejpam-5396	415	61	πcn	πcn	NOUN
ejpam-5396	415	62	−	−	PROPN
ejpam-5396	415	63	z2	z2	PROPN
ejpam-5396	415	64	in	in	ADP
ejpam-5396	415	65	)	)	PUNCT
ejpam-5396	415	66	,	,	PUNCT
ejpam-5396	415	67	rn+1	rn+1	PROPN
ejpam-5396	415	68	=	=	SYM
ejpam-5396	415	69	rn	rn	PROPN
ejpam-5396	416	1	+	+	PROPN
ejpam-5396	416	2	hα	hα	ADP
ejpam-5396	416	3	γ(α+	γ(α+	DET
ejpam-5396	416	4	1	1	NUM
ejpam-5396	416	5	)	)	PUNCT
ejpam-5396	416	6	(	(	PUNCT
ejpam-5396	416	7	βcn	βcn	NOUN
ejpam-5396	416	8	+	+	CCONJ
ejpam-5396	416	9	τin	τin	NOUN
ejpam-5396	416	10	−	−	PROPN
ejpam-5396	416	11	(	(	PUNCT
ejpam-5396	416	12	µ+	µ+	PROPN
ejpam-5396	416	13	η)rn	η)rn	PROPN
ejpam-5396	416	14	)	)	PUNCT
ejpam-5396	416	15	,	,	PUNCT
ejpam-5396	416	16	a.	a.	NOUN
ejpam-5396	416	17	alalyani	alalyani	PROPN
ejpam-5396	416	18	/	/	SYM
ejpam-5396	416	19	eur	eur	PROPN
ejpam-5396	416	20	.	.	PUNCT
ejpam-5396	417	1	j.	j.	PROPN
ejpam-5396	417	2	pure	pure	PROPN
ejpam-5396	417	3	appl	appl	PROPN
ejpam-5396	417	4	.	.	PROPN
ejpam-5396	417	5	math	math	PROPN
ejpam-5396	417	6	,	,	PUNCT
ejpam-5396	417	7	17	17	NUM
ejpam-5396	417	8	(	(	PUNCT
ejpam-5396	417	9	4	4	NUM
ejpam-5396	417	10	)	)	PUNCT
ejpam-5396	417	11	(	(	PUNCT
ejpam-5396	417	12	2024	2024	NUM
ejpam-5396	417	13	)	)	PUNCT
ejpam-5396	417	14	,	,	PUNCT
ejpam-5396	417	15	2763	2763	NUM
ejpam-5396	417	16	-	-	SYM
ejpam-5396	417	17	2799	2799	NUM
ejpam-5396	417	18	2780	2780	NUM
ejpam-5396	417	19	where	where	SCONJ
ejpam-5396	417	20	0	0	X
ejpam-5396	417	21	<	<	X
ejpam-5396	417	22	hα	hα	ADP
ejpam-5396	417	23	γ(α+1	γ(α+1	NOUN
ejpam-5396	417	24	)	)	PUNCT
ejpam-5396	417	25	<	<	X
ejpam-5396	418	1	1	1	NUM
ejpam-5396	418	2	is	be	AUX
ejpam-5396	418	3	the	the	DET
ejpam-5396	418	4	step	step	NOUN
ejpam-5396	418	5	size	size	NOUN
ejpam-5396	418	6	and	and	CCONJ
ejpam-5396	418	7	subject	subject	NOUN
ejpam-5396	418	8	to	to	ADP
ejpam-5396	418	9	the	the	DET
ejpam-5396	418	10	initial	initial	ADJ
ejpam-5396	418	11	conditions	condition	NOUN
ejpam-5396	418	12	,	,	PUNCT
ejpam-5396	418	13	s(0	s(0	PROPN
ejpam-5396	418	14	)	)	PUNCT
ejpam-5396	418	15	=	=	SYM
ejpam-5396	418	16	s0	s0	PROPN
ejpam-5396	418	17	,	,	PUNCT
ejpam-5396	418	18	c(0	c(0	NOUN
ejpam-5396	418	19	)	)	PUNCT
ejpam-5396	418	20	=	=	SYM
ejpam-5396	418	21	c0	c0	NOUN
ejpam-5396	418	22	,	,	PUNCT
ejpam-5396	418	23	i(0	i(0	PROPN
ejpam-5396	418	24	)	)	PUNCT
ejpam-5396	418	25	=	=	SYM
ejpam-5396	418	26	i0	i0	PROPN
ejpam-5396	418	27	,	,	PUNCT
ejpam-5396	418	28	r(0	r(0	PROPN
ejpam-5396	418	29	)	)	PUNCT
ejpam-5396	418	30	=	=	SYM
ejpam-5396	418	31	r0	r0	NOUN
ejpam-5396	418	32	.	.	PUNCT
ejpam-5396	419	1	we	we	PRON
ejpam-5396	419	2	have	have	VERB
ejpam-5396	419	3	sn+1	sn+1	NOUN
ejpam-5396	420	1	=	=	SYM
ejpam-5396	420	2	sn	sn	PROPN
ejpam-5396	420	3	=	=	SYM
ejpam-5396	420	4	s	s	PROPN
ejpam-5396	420	5	,	,	PUNCT
ejpam-5396	420	6	cn+1	cn+1	X
ejpam-5396	420	7	=	=	SYM
ejpam-5396	420	8	cn	cn	NOUN
ejpam-5396	420	9	=	=	SYM
ejpam-5396	420	10	c	c	PROPN
ejpam-5396	420	11	,	,	PUNCT
ejpam-5396	420	12	in+1	in+1	NOUN
ejpam-5396	420	13	=	=	SYM
ejpam-5396	420	14	in	in	ADP
ejpam-5396	420	15	=	=	PROPN
ejpam-5396	420	16	i	i	PROPN
ejpam-5396	420	17	,	,	PUNCT
ejpam-5396	420	18	and	and	CCONJ
ejpam-5396	420	19	rn+1	rn+1	PROPN
ejpam-5396	420	20	=	=	SYM
ejpam-5396	420	21	rn	rn	PROPN
ejpam-5396	420	22	=	=	NOUN
ejpam-5396	420	23	r	r	NOUN
ejpam-5396	420	24	at	at	ADP
ejpam-5396	420	25	a	a	DET
ejpam-5396	420	26	fixed	fix	VERB
ejpam-5396	420	27	point	point	NOUN
ejpam-5396	420	28	.	.	PUNCT
ejpam-5396	421	1	4.3	4.3	NUM
ejpam-5396	421	2	.	.	PUNCT
ejpam-5396	422	1	the	the	DET
ejpam-5396	422	2	generalized	generalize	VERB
ejpam-5396	422	3	runge	runge	NOUN
ejpam-5396	422	4	-	-	PUNCT
ejpam-5396	422	5	kutta	kutta	NOUN
ejpam-5396	422	6	method	method	NOUN
ejpam-5396	422	7	(	(	PUNCT
ejpam-5396	422	8	grkm	grkm	NOUN
ejpam-5396	422	9	)	)	PUNCT
ejpam-5396	422	10	the	the	DET
ejpam-5396	422	11	numerical	numerical	ADJ
ejpam-5396	422	12	scheme	scheme	NOUN
ejpam-5396	422	13	of	of	ADP
ejpam-5396	422	14	equation	equation	NOUN
ejpam-5396	422	15	(	(	PUNCT
ejpam-5396	422	16	4	4	NUM
ejpam-5396	422	17	)	)	PUNCT
ejpam-5396	422	18	of	of	ADP
ejpam-5396	422	19	the	the	DET
ejpam-5396	422	20	grkm	grkm	NOUN
ejpam-5396	422	21	takes	take	VERB
ejpam-5396	422	22	the	the	DET
ejpam-5396	422	23	following	follow	VERB
ejpam-5396	422	24	form	form	NOUN
ejpam-5396	422	25	:	:	PUNCT
ejpam-5396	422	26	xn+1	xn+1	NUM
ejpam-5396	422	27	=	=	SYM
ejpam-5396	422	28	xn	xn	PUNCT
ejpam-5396	423	1	+	+	CCONJ
ejpam-5396	423	2	1	1	NUM
ejpam-5396	423	3	6	6	NUM
ejpam-5396	423	4	(	(	PUNCT
ejpam-5396	423	5	k1	k1	X
ejpam-5396	423	6	+	+	CCONJ
ejpam-5396	423	7	2k2	2k2	NUM
ejpam-5396	423	8	+	+	CCONJ
ejpam-5396	423	9	2k3	2k3	NUM
ejpam-5396	423	10	+	+	ADJ
ejpam-5396	423	11	k4	k4	NOUN
ejpam-5396	423	12	)	)	PUNCT
ejpam-5396	423	13	,	,	PUNCT
ejpam-5396	423	14	(	(	PUNCT
ejpam-5396	423	15	9	9	X
ejpam-5396	423	16	)	)	PUNCT
ejpam-5396	423	17	k1	k1	NOUN
ejpam-5396	423	18	=	=	SYM
ejpam-5396	423	19	ℏf(tn	ℏf(tn	PROPN
ejpam-5396	423	20	,	,	PUNCT
ejpam-5396	423	21	xn	xn	PROPN
ejpam-5396	423	22	)	)	PUNCT
ejpam-5396	423	23	,	,	PUNCT
ejpam-5396	423	24	k2	k2	NOUN
ejpam-5396	423	25	=	=	SYM
ejpam-5396	424	1	ℏf(tn	ℏf(tn	PROPN
ejpam-5396	424	2	+	+	CCONJ
ejpam-5396	424	3	1	1	NUM
ejpam-5396	424	4	2	2	NUM
ejpam-5396	424	5	ℏ	ℏ	NOUN
ejpam-5396	424	6	,	,	PUNCT
ejpam-5396	424	7	xn	xn	PUNCT
ejpam-5396	425	1	+	+	CCONJ
ejpam-5396	425	2	1	1	NUM
ejpam-5396	425	3	2	2	NUM
ejpam-5396	425	4	k1	k1	NOUN
ejpam-5396	425	5	)	)	PUNCT
ejpam-5396	425	6	,	,	PUNCT
ejpam-5396	425	7	k3	k3	VERB
ejpam-5396	425	8	=	=	PROPN
ejpam-5396	425	9	ℏf(tn	ℏf(tn	X
ejpam-5396	425	10	+	+	CCONJ
ejpam-5396	425	11	1	1	NUM
ejpam-5396	425	12	2	2	NUM
ejpam-5396	425	13	ℏ	ℏ	NOUN
ejpam-5396	425	14	,	,	PUNCT
ejpam-5396	425	15	xn	xn	PROPN
ejpam-5396	426	1	+	+	CCONJ
ejpam-5396	426	2	1	1	NUM
ejpam-5396	426	3	2	2	NUM
ejpam-5396	426	4	k2	k2	NOUN
ejpam-5396	426	5	)	)	PUNCT
ejpam-5396	426	6	,	,	PUNCT
ejpam-5396	426	7	k4	k4	NOUN
ejpam-5396	426	8	=	=	SYM
ejpam-5396	426	9	ℏf(tn	ℏf(tn	PROPN
ejpam-5396	427	1	+	+	NUM
ejpam-5396	427	2	ℏ	ℏ	PROPN
ejpam-5396	427	3	,	,	PUNCT
ejpam-5396	427	4	xn	xn	PUNCT
ejpam-5396	428	1	+	+	VERB
ejpam-5396	428	2	k3	k3	ADJ
ejpam-5396	428	3	)	)	PUNCT
ejpam-5396	428	4	,	,	PUNCT
ejpam-5396	428	5	where	where	SCONJ
ejpam-5396	428	6	h̄	h̄	NOUN
ejpam-5396	428	7	=	=	NOUN
ejpam-5396	428	8	hα	hα	X
ejpam-5396	428	9	γ(α+	γ(α+	DET
ejpam-5396	428	10	1	1	NUM
ejpam-5396	428	11	)	)	PUNCT
ejpam-5396	428	12	.	.	PUNCT
ejpam-5396	429	1	in	in	ADP
ejpam-5396	429	2	the	the	DET
ejpam-5396	429	3	sense	sense	NOUN
ejpam-5396	429	4	of	of	ADP
ejpam-5396	429	5	(	(	PUNCT
ejpam-5396	429	6	9	9	NUM
ejpam-5396	429	7	)	)	PUNCT
ejpam-5396	429	8	,	,	PUNCT
ejpam-5396	429	9	the	the	DET
ejpam-5396	429	10	numerical	numerical	ADJ
ejpam-5396	429	11	scheme	scheme	NOUN
ejpam-5396	429	12	of	of	ADP
ejpam-5396	429	13	(	(	PUNCT
ejpam-5396	429	14	1	1	NUM
ejpam-5396	429	15	)	)	PUNCT
ejpam-5396	429	16	of	of	ADP
ejpam-5396	429	17	the	the	DET
ejpam-5396	429	18	grkm	grkm	NOUN
ejpam-5396	429	19	takes	take	VERB
ejpam-5396	429	20	the	the	DET
ejpam-5396	429	21	following	follow	VERB
ejpam-5396	429	22	form	form	NOUN
ejpam-5396	429	23	:	:	PUNCT
ejpam-5396	429	24	sn+1	sn+1	X
ejpam-5396	429	25	=	=	SYM
ejpam-5396	429	26	sn	sn	PROPN
ejpam-5396	430	1	+	+	CCONJ
ejpam-5396	430	2	1	1	NUM
ejpam-5396	430	3	6	6	NUM
ejpam-5396	430	4	(	(	PUNCT
ejpam-5396	430	5	k1	k1	X
ejpam-5396	430	6	+	+	CCONJ
ejpam-5396	430	7	2k2	2k2	NUM
ejpam-5396	430	8	+	+	CCONJ
ejpam-5396	430	9	2k3	2k3	NUM
ejpam-5396	430	10	+	+	ADJ
ejpam-5396	430	11	k4	k4	NOUN
ejpam-5396	430	12	)	)	PUNCT
ejpam-5396	430	13	,	,	PUNCT
ejpam-5396	430	14	cn+1	cn+1	X
ejpam-5396	430	15	=	=	SYM
ejpam-5396	430	16	cn	cn	NOUN
ejpam-5396	431	1	+	+	NOUN
ejpam-5396	431	2	1	1	NUM
ejpam-5396	431	3	6	6	NUM
ejpam-5396	431	4	(	(	PUNCT
ejpam-5396	431	5	q1	q1	VERB
ejpam-5396	431	6	+	+	CCONJ
ejpam-5396	431	7	2q2	2q2	NUM
ejpam-5396	431	8	+	+	SYM
ejpam-5396	431	9	2q3	2q3	NUM
ejpam-5396	431	10	+	+	ADJ
ejpam-5396	431	11	q4	q4	PROPN
ejpam-5396	431	12	)	)	PUNCT
ejpam-5396	431	13	,	,	PUNCT
ejpam-5396	431	14	in+1	in+1	NOUN
ejpam-5396	431	15	=	=	NOUN
ejpam-5396	431	16	in	in	ADP
ejpam-5396	431	17	+	+	NUM
ejpam-5396	431	18	1	1	NUM
ejpam-5396	431	19	6	6	NUM
ejpam-5396	431	20	(	(	PUNCT
ejpam-5396	431	21	o1	o1	NOUN
ejpam-5396	431	22	+	+	CCONJ
ejpam-5396	431	23	2o2	2o2	NUM
ejpam-5396	431	24	+	+	NUM
ejpam-5396	431	25	2o3	2o3	NUM
ejpam-5396	432	1	+	+	ADJ
ejpam-5396	432	2	o4	o4	PROPN
ejpam-5396	432	3	)	)	PUNCT
ejpam-5396	432	4	,	,	PUNCT
ejpam-5396	432	5	rn+1	rn+1	PROPN
ejpam-5396	432	6	=	=	SYM
ejpam-5396	432	7	rn	rn	PROPN
ejpam-5396	432	8	+	+	NOUN
ejpam-5396	432	9	1	1	NUM
ejpam-5396	432	10	6	6	NUM
ejpam-5396	432	11	(	(	PUNCT
ejpam-5396	432	12	p1	p1	NOUN
ejpam-5396	432	13	+	+	CCONJ
ejpam-5396	432	14	2p2	2p2	NUM
ejpam-5396	432	15	+	+	CCONJ
ejpam-5396	432	16	2p3	2p3	NUM
ejpam-5396	432	17	+	+	CCONJ
ejpam-5396	432	18	p4	p4	ADJ
ejpam-5396	432	19	)	)	PUNCT
ejpam-5396	432	20	,	,	PUNCT
ejpam-5396	432	21	where	where	SCONJ
ejpam-5396	432	22	k1	k1	NOUN
ejpam-5396	432	23	,	,	PUNCT
ejpam-5396	432	24	q1	q1	NOUN
ejpam-5396	432	25	,	,	PUNCT
ejpam-5396	432	26	o1	o1	NOUN
ejpam-5396	432	27	,	,	PUNCT
ejpam-5396	432	28	p1,k2	p1,k2	PROPN
ejpam-5396	432	29	,	,	PUNCT
ejpam-5396	432	30	q2	q2	NOUN
ejpam-5396	432	31	,	,	PUNCT
ejpam-5396	432	32	o2	o2	PROPN
ejpam-5396	432	33	,	,	PUNCT
ejpam-5396	432	34	p2,k3	p2,k3	PROPN
ejpam-5396	432	35	,	,	PUNCT
ejpam-5396	432	36	q3	q3	PROPN
ejpam-5396	432	37	,	,	PUNCT
ejpam-5396	432	38	o3	o3	PROPN
ejpam-5396	432	39	,	,	PUNCT
ejpam-5396	432	40	p3,k4	p3,k4	PROPN
ejpam-5396	432	41	,	,	PUNCT
ejpam-5396	432	42	q4	q4	PROPN
ejpam-5396	432	43	,	,	PUNCT
ejpam-5396	432	44	o4	o4	PROPN
ejpam-5396	432	45	,	,	PUNCT
ejpam-5396	432	46	and	and	CCONJ
ejpam-5396	432	47	p4	p4	NOUN
ejpam-5396	432	48	are	be	AUX
ejpam-5396	432	49	given	give	VERB
ejpam-5396	432	50	below	below	ADP
ejpam-5396	432	51	:	:	PUNCT
ejpam-5396	432	52	k1	k1	NOUN
ejpam-5396	432	53	=	=	PUNCT
ejpam-5396	432	54	h̄f1(tn	h̄f1(tn	ADJ
ejpam-5396	432	55	,	,	PUNCT
ejpam-5396	432	56	sn	sn	X
ejpam-5396	432	57	,	,	PUNCT
ejpam-5396	432	58	cn	cn	PROPN
ejpam-5396	432	59	,	,	PUNCT
ejpam-5396	432	60	in	in	ADP
ejpam-5396	432	61	,	,	PUNCT
ejpam-5396	432	62	rn	rn	NOUN
ejpam-5396	432	63	)	)	PUNCT
ejpam-5396	432	64	=	=	PUNCT
ejpam-5396	433	1	h̄	h̄	NOUN
ejpam-5396	433	2	(	(	PUNCT
ejpam-5396	433	3	λ−	λ−	PROPN
ejpam-5396	433	4	δ(in	δ(in	PROPN
ejpam-5396	433	5	+	+	CCONJ
ejpam-5396	433	6	ωcn	ωcn	NOUN
ejpam-5396	433	7	)	)	PUNCT
ejpam-5396	433	8	n	n	CCONJ
ejpam-5396	433	9	sn	sn	NOUN
ejpam-5396	433	10	−	−	PROPN
ejpam-5396	433	11	µsn	µsn	NOUN
ejpam-5396	433	12	+	+	CCONJ
ejpam-5396	433	13	ηrn	ηrn	NOUN
ejpam-5396	433	14	)	)	PUNCT
ejpam-5396	433	15	,	,	PUNCT
ejpam-5396	433	16	q1	q1	PROPN
ejpam-5396	433	17	=	=	SYM
ejpam-5396	434	1	h̄f2(tn	h̄f2(tn	PROPN
ejpam-5396	434	2	,	,	PUNCT
ejpam-5396	434	3	sn	sn	PROPN
ejpam-5396	434	4	,	,	PUNCT
ejpam-5396	434	5	cn	cn	PROPN
ejpam-5396	434	6	,	,	PUNCT
ejpam-5396	434	7	in	in	ADP
ejpam-5396	434	8	,	,	PUNCT
ejpam-5396	434	9	rn	rn	NOUN
ejpam-5396	434	10	)	)	PUNCT
ejpam-5396	434	11	=	=	PRON
ejpam-5396	434	12	h̄	h̄	NOUN
ejpam-5396	434	13	(	(	PUNCT
ejpam-5396	434	14	δ(in	δ(in	PROPN
ejpam-5396	434	15	+	+	CCONJ
ejpam-5396	434	16	ωcn	ωcn	NOUN
ejpam-5396	434	17	)	)	PUNCT
ejpam-5396	434	18	n	n	PRON
ejpam-5396	434	19	θsn	θsn	NOUN
ejpam-5396	434	20	−	−	NOUN
ejpam-5396	434	21	z1cn	z1cn	NUM
ejpam-5396	434	22	)	)	PUNCT
ejpam-5396	434	23	,	,	PUNCT
ejpam-5396	434	24	o1	o1	NOUN
ejpam-5396	434	25	=	=	SYM
ejpam-5396	434	26	h̄f3(tn	h̄f3(tn	PROPN
ejpam-5396	434	27	,	,	PUNCT
ejpam-5396	434	28	sn	sn	PROPN
ejpam-5396	434	29	,	,	PUNCT
ejpam-5396	434	30	cn	cn	PROPN
ejpam-5396	434	31	,	,	PUNCT
ejpam-5396	434	32	in	in	ADP
ejpam-5396	434	33	,	,	PUNCT
ejpam-5396	434	34	rn	rn	NOUN
ejpam-5396	434	35	)	)	PUNCT
ejpam-5396	434	36	=	=	PRON
ejpam-5396	434	37	h̄	h̄	NOUN
ejpam-5396	434	38	(	(	PUNCT
ejpam-5396	434	39	δ(in	δ(in	PROPN
ejpam-5396	434	40	+	+	CCONJ
ejpam-5396	434	41	ωcn	ωcn	NOUN
ejpam-5396	434	42	)	)	PUNCT
ejpam-5396	434	43	n	n	CCONJ
ejpam-5396	434	44	(	(	PUNCT
ejpam-5396	434	45	1−	1−	NUM
ejpam-5396	434	46	θ)sn	θ)sn	NOUN
ejpam-5396	434	47	+	+	NUM
ejpam-5396	434	48	πcn	πcn	NOUN
ejpam-5396	434	49	−	−	PROPN
ejpam-5396	434	50	z2	z2	PROPN
ejpam-5396	434	51	in	in	ADP
ejpam-5396	434	52	)	)	PUNCT
ejpam-5396	434	53	,	,	PUNCT
ejpam-5396	434	54	p1	p1	NOUN
ejpam-5396	434	55	=	=	SYM
ejpam-5396	434	56	h̄f4(tn	h̄f4(tn	PROPN
ejpam-5396	434	57	,	,	PUNCT
ejpam-5396	434	58	sn	sn	PROPN
ejpam-5396	434	59	,	,	PUNCT
ejpam-5396	434	60	cn	cn	PROPN
ejpam-5396	434	61	,	,	PUNCT
ejpam-5396	434	62	in	in	ADP
ejpam-5396	434	63	,	,	PUNCT
ejpam-5396	434	64	rn	rn	NOUN
ejpam-5396	434	65	)	)	PUNCT
ejpam-5396	434	66	=	=	PUNCT
ejpam-5396	434	67	h̄	h̄	NOUN
ejpam-5396	434	68	(	(	PUNCT
ejpam-5396	434	69	βcn	βcn	NOUN
ejpam-5396	434	70	+	+	CCONJ
ejpam-5396	434	71	τin	τin	NOUN
ejpam-5396	434	72	−	−	PROPN
ejpam-5396	434	73	(	(	PUNCT
ejpam-5396	434	74	µ+	µ+	PROPN
ejpam-5396	434	75	η)rn	η)rn	PROPN
ejpam-5396	434	76	)	)	PUNCT
ejpam-5396	434	77	,	,	PUNCT
ejpam-5396	434	78	k2	k2	NOUN
ejpam-5396	434	79	=	=	SYM
ejpam-5396	434	80	h̄f1	h̄f1	X
ejpam-5396	434	81	(	(	PUNCT
ejpam-5396	434	82	tn	tn	NOUN
ejpam-5396	434	83	+	+	NOUN
ejpam-5396	434	84	1	1	NUM
ejpam-5396	434	85	2	2	NUM
ejpam-5396	434	86	h̄	h̄	NOUN
ejpam-5396	434	87	,	,	PUNCT
ejpam-5396	434	88	sn	sn	PROPN
ejpam-5396	434	89	+	+	CCONJ
ejpam-5396	434	90	1	1	NUM
ejpam-5396	434	91	2	2	NUM
ejpam-5396	434	92	k1	k1	NOUN
ejpam-5396	434	93	,	,	PUNCT
ejpam-5396	434	94	cn	cn	PROPN
ejpam-5396	434	95	+	+	CCONJ
ejpam-5396	434	96	1	1	NUM
ejpam-5396	434	97	2	2	NUM
ejpam-5396	434	98	q1	q1	NOUN
ejpam-5396	434	99	,	,	PUNCT
ejpam-5396	434	100	in	in	ADP
ejpam-5396	434	101	+	+	NOUN
ejpam-5396	434	102	1	1	NUM
ejpam-5396	434	103	2	2	NUM
ejpam-5396	434	104	o1	o1	NOUN
ejpam-5396	434	105	,	,	PUNCT
ejpam-5396	434	106	rn	rn	PROPN
ejpam-5396	434	107	+	+	NOUN
ejpam-5396	434	108	1	1	NUM
ejpam-5396	434	109	2	2	NUM
ejpam-5396	434	110	p1	p1	NOUN
ejpam-5396	434	111	)	)	PUNCT
ejpam-5396	434	112	,	,	PUNCT
ejpam-5396	434	113	q2	q2	NOUN
ejpam-5396	434	114	=	=	SYM
ejpam-5396	434	115	h̄f2	h̄f2	NOUN
ejpam-5396	434	116	(	(	PUNCT
ejpam-5396	434	117	tn	tn	NOUN
ejpam-5396	434	118	+	+	NOUN
ejpam-5396	434	119	1	1	NUM
ejpam-5396	434	120	2	2	NUM
ejpam-5396	434	121	h̄	h̄	NOUN
ejpam-5396	434	122	,	,	PUNCT
ejpam-5396	434	123	sn	sn	PROPN
ejpam-5396	434	124	+	+	CCONJ
ejpam-5396	434	125	1	1	NUM
ejpam-5396	434	126	2	2	NUM
ejpam-5396	434	127	k1	k1	NOUN
ejpam-5396	434	128	,	,	PUNCT
ejpam-5396	434	129	cn	cn	PROPN
ejpam-5396	435	1	+	+	CCONJ
ejpam-5396	435	2	1	1	NUM
ejpam-5396	435	3	2	2	NUM
ejpam-5396	435	4	q1	q1	NOUN
ejpam-5396	435	5	,	,	PUNCT
ejpam-5396	435	6	in	in	ADP
ejpam-5396	435	7	+	+	NOUN
ejpam-5396	435	8	1	1	NUM
ejpam-5396	435	9	2	2	NUM
ejpam-5396	435	10	o1	o1	NOUN
ejpam-5396	435	11	,	,	PUNCT
ejpam-5396	435	12	rn	rn	PROPN
ejpam-5396	435	13	+	+	NOUN
ejpam-5396	435	14	1	1	NUM
ejpam-5396	435	15	2	2	NUM
ejpam-5396	435	16	p1	p1	NOUN
ejpam-5396	435	17	)	)	PUNCT
ejpam-5396	435	18	,	,	PUNCT
ejpam-5396	435	19	o2	o2	PROPN
ejpam-5396	435	20	=	=	SYM
ejpam-5396	435	21	h̄f3	h̄f3	PROPN
ejpam-5396	435	22	(	(	PUNCT
ejpam-5396	435	23	tn	tn	NOUN
ejpam-5396	435	24	+	+	CCONJ
ejpam-5396	435	25	1	1	NUM
ejpam-5396	435	26	2	2	NUM
ejpam-5396	435	27	h̄	h̄	NOUN
ejpam-5396	435	28	,	,	PUNCT
ejpam-5396	435	29	sn	sn	PROPN
ejpam-5396	435	30	+	+	CCONJ
ejpam-5396	435	31	1	1	NUM
ejpam-5396	435	32	2	2	NUM
ejpam-5396	435	33	k1	k1	NOUN
ejpam-5396	435	34	,	,	PUNCT
ejpam-5396	435	35	cn	cn	PROPN
ejpam-5396	435	36	+	+	CCONJ
ejpam-5396	435	37	1	1	NUM
ejpam-5396	435	38	2	2	NUM
ejpam-5396	435	39	q1	q1	NOUN
ejpam-5396	435	40	,	,	PUNCT
ejpam-5396	435	41	in	in	ADP
ejpam-5396	435	42	+	+	NOUN
ejpam-5396	435	43	1	1	NUM
ejpam-5396	435	44	2	2	NUM
ejpam-5396	435	45	o1	o1	NOUN
ejpam-5396	435	46	,	,	PUNCT
ejpam-5396	435	47	rn	rn	PROPN
ejpam-5396	435	48	+	+	NOUN
ejpam-5396	435	49	1	1	NUM
ejpam-5396	435	50	2	2	NUM
ejpam-5396	435	51	p1	p1	NOUN
ejpam-5396	435	52	)	)	PUNCT
ejpam-5396	435	53	,	,	PUNCT
ejpam-5396	435	54	p2	p2	PROPN
ejpam-5396	435	55	=	=	SYM
ejpam-5396	435	56	h̄f4	h̄f4	NOUN
ejpam-5396	435	57	(	(	PUNCT
ejpam-5396	435	58	tn	tn	NOUN
ejpam-5396	435	59	+	+	NOUN
ejpam-5396	435	60	1	1	NUM
ejpam-5396	435	61	2	2	NUM
ejpam-5396	435	62	h̄	h̄	NOUN
ejpam-5396	435	63	,	,	PUNCT
ejpam-5396	435	64	sn	sn	PROPN
ejpam-5396	435	65	+	+	CCONJ
ejpam-5396	435	66	1	1	NUM
ejpam-5396	435	67	2	2	NUM
ejpam-5396	435	68	k1	k1	NOUN
ejpam-5396	435	69	,	,	PUNCT
ejpam-5396	435	70	cn	cn	PROPN
ejpam-5396	435	71	+	+	CCONJ
ejpam-5396	435	72	1	1	NUM
ejpam-5396	435	73	2	2	NUM
ejpam-5396	435	74	q1	q1	NOUN
ejpam-5396	435	75	,	,	PUNCT
ejpam-5396	435	76	in	in	ADP
ejpam-5396	435	77	+	+	NOUN
ejpam-5396	435	78	1	1	NUM
ejpam-5396	435	79	2	2	NUM
ejpam-5396	435	80	o1	o1	NOUN
ejpam-5396	435	81	,	,	PUNCT
ejpam-5396	435	82	rn	rn	PROPN
ejpam-5396	435	83	+	+	NOUN
ejpam-5396	435	84	1	1	NUM
ejpam-5396	435	85	2	2	NUM
ejpam-5396	435	86	p1	p1	NOUN
ejpam-5396	435	87	)	)	PUNCT
ejpam-5396	435	88	,	,	PUNCT
ejpam-5396	435	89	a.	a.	NOUN
ejpam-5396	435	90	alalyani	alalyani	PROPN
ejpam-5396	435	91	/	/	SYM
ejpam-5396	435	92	eur	eur	PROPN
ejpam-5396	435	93	.	.	PUNCT
ejpam-5396	436	1	j.	j.	PROPN
ejpam-5396	436	2	pure	pure	PROPN
ejpam-5396	436	3	appl	appl	PROPN
ejpam-5396	436	4	.	.	PROPN
ejpam-5396	436	5	math	math	PROPN
ejpam-5396	436	6	,	,	PUNCT
ejpam-5396	436	7	17	17	NUM
ejpam-5396	436	8	(	(	PUNCT
ejpam-5396	436	9	4	4	NUM
ejpam-5396	436	10	)	)	PUNCT
ejpam-5396	436	11	(	(	PUNCT
ejpam-5396	436	12	2024	2024	NUM
ejpam-5396	436	13	)	)	PUNCT
ejpam-5396	436	14	,	,	PUNCT
ejpam-5396	436	15	2763	2763	NUM
ejpam-5396	436	16	-	-	SYM
ejpam-5396	436	17	2799	2799	NUM
ejpam-5396	436	18	2781	2781	NUM
ejpam-5396	436	19	k3	k3	NOUN
ejpam-5396	436	20	=	=	X
ejpam-5396	436	21	h̄f1	h̄f1	X
ejpam-5396	436	22	(	(	PUNCT
ejpam-5396	436	23	tn	tn	NOUN
ejpam-5396	436	24	+	+	NOUN
ejpam-5396	436	25	1	1	NUM
ejpam-5396	436	26	2	2	NUM
ejpam-5396	436	27	h̄	h̄	NOUN
ejpam-5396	436	28	,	,	PUNCT
ejpam-5396	436	29	sn	sn	PROPN
ejpam-5396	436	30	+	+	CCONJ
ejpam-5396	436	31	1	1	NUM
ejpam-5396	436	32	2	2	NUM
ejpam-5396	436	33	k2	k2	NOUN
ejpam-5396	436	34	,	,	PUNCT
ejpam-5396	436	35	cn	cn	PROPN
ejpam-5396	436	36	+	+	CCONJ
ejpam-5396	436	37	1	1	NUM
ejpam-5396	436	38	2	2	NUM
ejpam-5396	436	39	q2	q2	NOUN
ejpam-5396	436	40	,	,	PUNCT
ejpam-5396	436	41	in	in	ADP
ejpam-5396	436	42	+	+	CCONJ
ejpam-5396	436	43	1	1	NUM
ejpam-5396	436	44	2	2	NUM
ejpam-5396	436	45	o2	o2	PROPN
ejpam-5396	436	46	,	,	PUNCT
ejpam-5396	436	47	rn	rn	PROPN
ejpam-5396	436	48	+	+	NOUN
ejpam-5396	436	49	1	1	NUM
ejpam-5396	436	50	2	2	NUM
ejpam-5396	436	51	p2	p2	NOUN
ejpam-5396	436	52	)	)	PUNCT
ejpam-5396	436	53	,	,	PUNCT
ejpam-5396	436	54	q3	q3	NOUN
ejpam-5396	436	55	=	=	NOUN
ejpam-5396	436	56	h̄f2	h̄f2	NOUN
ejpam-5396	436	57	(	(	PUNCT
ejpam-5396	436	58	tn	tn	NOUN
ejpam-5396	436	59	+	+	NOUN
ejpam-5396	436	60	1	1	NUM
ejpam-5396	436	61	2	2	NUM
ejpam-5396	436	62	h̄	h̄	NOUN
ejpam-5396	436	63	,	,	PUNCT
ejpam-5396	436	64	sn	sn	PROPN
ejpam-5396	436	65	+	+	CCONJ
ejpam-5396	436	66	1	1	NUM
ejpam-5396	436	67	2	2	NUM
ejpam-5396	436	68	k2	k2	NOUN
ejpam-5396	436	69	,	,	PUNCT
ejpam-5396	436	70	cn	cn	PROPN
ejpam-5396	436	71	+	+	CCONJ
ejpam-5396	436	72	1	1	NUM
ejpam-5396	436	73	2	2	NUM
ejpam-5396	436	74	q2	q2	NOUN
ejpam-5396	436	75	,	,	PUNCT
ejpam-5396	436	76	in	in	ADP
ejpam-5396	436	77	+	+	CCONJ
ejpam-5396	436	78	1	1	NUM
ejpam-5396	436	79	2	2	NUM
ejpam-5396	436	80	o2	o2	PROPN
ejpam-5396	436	81	,	,	PUNCT
ejpam-5396	436	82	rn	rn	PROPN
ejpam-5396	436	83	+	+	NOUN
ejpam-5396	436	84	1	1	NUM
ejpam-5396	436	85	2	2	NUM
ejpam-5396	436	86	p2	p2	NOUN
ejpam-5396	436	87	)	)	PUNCT
ejpam-5396	436	88	,	,	PUNCT
ejpam-5396	436	89	o3	o3	PROPN
ejpam-5396	436	90	=	=	SYM
ejpam-5396	436	91	h̄f3	h̄f3	PROPN
ejpam-5396	436	92	(	(	PUNCT
ejpam-5396	436	93	tn	tn	NOUN
ejpam-5396	437	1	+	+	CCONJ
ejpam-5396	437	2	1	1	NUM
ejpam-5396	437	3	2	2	NUM
ejpam-5396	437	4	h̄	h̄	NOUN
ejpam-5396	437	5	,	,	PUNCT
ejpam-5396	437	6	sn	sn	PROPN
ejpam-5396	437	7	+	+	CCONJ
ejpam-5396	437	8	1	1	NUM
ejpam-5396	437	9	2	2	NUM
ejpam-5396	437	10	k2	k2	NOUN
ejpam-5396	437	11	,	,	PUNCT
ejpam-5396	437	12	cn	cn	PROPN
ejpam-5396	437	13	+	+	CCONJ
ejpam-5396	437	14	1	1	NUM
ejpam-5396	437	15	2	2	NUM
ejpam-5396	437	16	q2	q2	NOUN
ejpam-5396	437	17	,	,	PUNCT
ejpam-5396	437	18	in	in	ADP
ejpam-5396	437	19	+	+	CCONJ
ejpam-5396	437	20	1	1	NUM
ejpam-5396	437	21	2	2	NUM
ejpam-5396	437	22	o2	o2	PROPN
ejpam-5396	437	23	,	,	PUNCT
ejpam-5396	437	24	rn	rn	PROPN
ejpam-5396	437	25	+	+	NOUN
ejpam-5396	437	26	1	1	NUM
ejpam-5396	437	27	2	2	NUM
ejpam-5396	437	28	p2	p2	NOUN
ejpam-5396	437	29	)	)	PUNCT
ejpam-5396	437	30	,	,	PUNCT
ejpam-5396	437	31	p3	p3	PROPN
ejpam-5396	437	32	=	=	SYM
ejpam-5396	437	33	h̄f4	h̄f4	NOUN
ejpam-5396	437	34	(	(	PUNCT
ejpam-5396	437	35	tn	tn	NOUN
ejpam-5396	437	36	+	+	NOUN
ejpam-5396	437	37	1	1	NUM
ejpam-5396	437	38	2	2	NUM
ejpam-5396	437	39	h̄	h̄	NOUN
ejpam-5396	437	40	,	,	PUNCT
ejpam-5396	437	41	sn	sn	PROPN
ejpam-5396	437	42	+	+	CCONJ
ejpam-5396	437	43	1	1	NUM
ejpam-5396	437	44	2	2	NUM
ejpam-5396	437	45	k2	k2	NOUN
ejpam-5396	437	46	,	,	PUNCT
ejpam-5396	437	47	cn	cn	PROPN
ejpam-5396	437	48	+	+	CCONJ
ejpam-5396	437	49	1	1	NUM
ejpam-5396	437	50	2	2	NUM
ejpam-5396	437	51	q2	q2	NOUN
ejpam-5396	437	52	,	,	PUNCT
ejpam-5396	437	53	in	in	ADP
ejpam-5396	437	54	+	+	CCONJ
ejpam-5396	437	55	1	1	NUM
ejpam-5396	437	56	2	2	NUM
ejpam-5396	437	57	o2	o2	PROPN
ejpam-5396	437	58	,	,	PUNCT
ejpam-5396	437	59	rn	rn	PROPN
ejpam-5396	437	60	+	+	NOUN
ejpam-5396	437	61	1	1	NUM
ejpam-5396	437	62	2	2	NUM
ejpam-5396	437	63	p2	p2	NOUN
ejpam-5396	437	64	)	)	PUNCT
ejpam-5396	437	65	,	,	PUNCT
ejpam-5396	437	66	k4	k4	NOUN
ejpam-5396	437	67	=	=	SYM
ejpam-5396	437	68	h̄f1(tn	h̄f1(tn	ADJ
ejpam-5396	437	69	+	+	CCONJ
ejpam-5396	437	70	h̄	h̄	NOUN
ejpam-5396	437	71	,	,	PUNCT
ejpam-5396	437	72	sn	sn	PROPN
ejpam-5396	438	1	+	+	X
ejpam-5396	438	2	k3	k3	ADJ
ejpam-5396	438	3	,	,	PUNCT
ejpam-5396	438	4	cn	cn	PROPN
ejpam-5396	438	5	+	+	NOUN
ejpam-5396	438	6	q3	q3	PROPN
ejpam-5396	438	7	,	,	PUNCT
ejpam-5396	438	8	in	in	ADP
ejpam-5396	438	9	+	+	PROPN
ejpam-5396	438	10	o3	o3	PROPN
ejpam-5396	438	11	,	,	PUNCT
ejpam-5396	438	12	rn	rn	PROPN
ejpam-5396	438	13	+	+	CCONJ
ejpam-5396	438	14	p3	p3	PROPN
ejpam-5396	438	15	)	)	PUNCT
ejpam-5396	438	16	,	,	PUNCT
ejpam-5396	438	17	q4	q4	PROPN
ejpam-5396	438	18	=	=	SYM
ejpam-5396	438	19	h̄f2(tn	h̄f2(tn	PROPN
ejpam-5396	438	20	+	+	NUM
ejpam-5396	438	21	h̄	h̄	NOUN
ejpam-5396	438	22	,	,	PUNCT
ejpam-5396	438	23	sn	sn	PROPN
ejpam-5396	439	1	+	+	X
ejpam-5396	439	2	k3	k3	ADJ
ejpam-5396	439	3	,	,	PUNCT
ejpam-5396	439	4	cn	cn	PROPN
ejpam-5396	439	5	+	+	NOUN
ejpam-5396	439	6	q3	q3	PROPN
ejpam-5396	439	7	,	,	PUNCT
ejpam-5396	439	8	in	in	ADP
ejpam-5396	439	9	+	+	PROPN
ejpam-5396	439	10	o3	o3	PROPN
ejpam-5396	439	11	,	,	PUNCT
ejpam-5396	439	12	rn	rn	PROPN
ejpam-5396	439	13	+	+	PROPN
ejpam-5396	439	14	p3	p3	PROPN
ejpam-5396	439	15	)	)	PUNCT
ejpam-5396	439	16	,	,	PUNCT
ejpam-5396	439	17	o4	o4	PROPN
ejpam-5396	439	18	=	=	PUNCT
ejpam-5396	439	19	h̄f3(tn	h̄f3(tn	NUM
ejpam-5396	439	20	+	+	NUM
ejpam-5396	439	21	h̄	h̄	NOUN
ejpam-5396	439	22	,	,	PUNCT
ejpam-5396	439	23	sn	sn	PROPN
ejpam-5396	440	1	+	+	X
ejpam-5396	440	2	k3	k3	ADJ
ejpam-5396	440	3	,	,	PUNCT
ejpam-5396	440	4	cn	cn	PROPN
ejpam-5396	440	5	+	+	NOUN
ejpam-5396	440	6	q3	q3	PROPN
ejpam-5396	440	7	,	,	PUNCT
ejpam-5396	440	8	in	in	ADP
ejpam-5396	440	9	+	+	PROPN
ejpam-5396	440	10	o3	o3	PROPN
ejpam-5396	440	11	,	,	PUNCT
ejpam-5396	440	12	rn	rn	PROPN
ejpam-5396	440	13	+	+	CCONJ
ejpam-5396	440	14	p3	p3	PROPN
ejpam-5396	440	15	)	)	PUNCT
ejpam-5396	440	16	,	,	PUNCT
ejpam-5396	440	17	p4	p4	NOUN
ejpam-5396	440	18	=	=	SYM
ejpam-5396	440	19	h̄f4(tn	h̄f4(tn	PROPN
ejpam-5396	440	20	+	+	NUM
ejpam-5396	440	21	h̄	h̄	NOUN
ejpam-5396	440	22	,	,	PUNCT
ejpam-5396	440	23	sn	sn	PROPN
ejpam-5396	441	1	+	+	X
ejpam-5396	441	2	k3	k3	ADJ
ejpam-5396	441	3	,	,	PUNCT
ejpam-5396	441	4	cn	cn	PROPN
ejpam-5396	441	5	+	+	NOUN
ejpam-5396	441	6	q3	q3	PROPN
ejpam-5396	441	7	,	,	PUNCT
ejpam-5396	441	8	in	in	ADP
ejpam-5396	441	9	+	+	PROPN
ejpam-5396	441	10	o3	o3	PROPN
ejpam-5396	441	11	,	,	PUNCT
ejpam-5396	441	12	rn	rn	PROPN
ejpam-5396	441	13	+	+	PROPN
ejpam-5396	441	14	p3	p3	PROPN
ejpam-5396	441	15	)	)	PUNCT
ejpam-5396	441	16	.	.	PUNCT
ejpam-5396	442	1	4.4	4.4	NUM
ejpam-5396	442	2	.	.	PUNCT
ejpam-5396	443	1	the	the	DET
ejpam-5396	443	2	multistep	multistep	ADJ
ejpam-5396	443	3	generalized	generalize	VERB
ejpam-5396	443	4	differential	differential	ADJ
ejpam-5396	443	5	transformmethod	transformmethod	NOUN
ejpam-5396	443	6	(	(	PUNCT
ejpam-5396	443	7	msgdtm	msgdtm	NOUN
ejpam-5396	443	8	)	)	PUNCT
ejpam-5396	443	9	to	to	PART
ejpam-5396	443	10	illustrate	illustrate	VERB
ejpam-5396	443	11	the	the	DET
ejpam-5396	443	12	msgdtm	msgdtm	NOUN
ejpam-5396	443	13	following	follow	VERB
ejpam-5396	443	14	(	(	PUNCT
ejpam-5396	443	15	[	[	X
ejpam-5396	443	16	42	42	NUM
ejpam-5396	443	17	]	]	PUNCT
ejpam-5396	443	18	,	,	PUNCT
ejpam-5396	443	19	[	[	X
ejpam-5396	443	20	24	24	NUM
ejpam-5396	443	21	]	]	PUNCT
ejpam-5396	443	22	,	,	PUNCT
ejpam-5396	443	23	[	[	X
ejpam-5396	443	24	22	22	NUM
ejpam-5396	443	25	]	]	PUNCT
ejpam-5396	443	26	,	,	PUNCT
ejpam-5396	443	27	[	[	X
ejpam-5396	443	28	25	25	NUM
ejpam-5396	443	29	]	]	PUNCT
ejpam-5396	443	30	)	)	PUNCT
ejpam-5396	443	31	,	,	PUNCT
ejpam-5396	443	32	we	we	PRON
ejpam-5396	443	33	consider	consider	VERB
ejpam-5396	443	34	the	the	DET
ejpam-5396	443	35	following	follow	VERB
ejpam-5396	443	36	initial	initial	ADJ
ejpam-5396	443	37	value	value	NOUN
ejpam-5396	443	38	problem	problem	NOUN
ejpam-5396	443	39	for	for	ADP
ejpam-5396	443	40	systems	system	NOUN
ejpam-5396	443	41	of	of	ADP
ejpam-5396	443	42	fractional	fractional	ADJ
ejpam-5396	443	43	differential	differential	ADJ
ejpam-5396	443	44	equations	equation	NOUN
ejpam-5396	443	45	:	:	PUNCT
ejpam-5396	443	46	dα	dα	ADP
ejpam-5396	443	47	1	1	NUM
ejpam-5396	443	48	x1(t	x1(t	PUNCT
ejpam-5396	443	49	)	)	PUNCT
ejpam-5396	443	50	=	=	SYM
ejpam-5396	443	51	f1(t	f1(t	PROPN
ejpam-5396	443	52	,	,	PUNCT
ejpam-5396	443	53	x1	x1	PROPN
ejpam-5396	443	54	,	,	PUNCT
ejpam-5396	443	55	x2	x2	PROPN
ejpam-5396	443	56	,	,	PUNCT
ejpam-5396	443	57	...	...	PUNCT
ejpam-5396	443	58	,	,	PUNCT
ejpam-5396	443	59	xn	xn	PROPN
ejpam-5396	443	60	)	)	PUNCT
ejpam-5396	443	61	,	,	PUNCT
ejpam-5396	443	62	dα	dα	VERB
ejpam-5396	443	63	2	2	NUM
ejpam-5396	443	64	x1(t	x1(t	PUNCT
ejpam-5396	443	65	)	)	PUNCT
ejpam-5396	443	66	=	=	SYM
ejpam-5396	443	67	f2(t	f2(t	PROPN
ejpam-5396	443	68	,	,	PUNCT
ejpam-5396	443	69	x1	x1	PROPN
ejpam-5396	443	70	,	,	PUNCT
ejpam-5396	443	71	x2	x2	PROPN
ejpam-5396	443	72	,	,	PUNCT
ejpam-5396	443	73	...	...	PUNCT
ejpam-5396	443	74	,	,	PUNCT
ejpam-5396	443	75	xn	xn	PROPN
ejpam-5396	443	76	)	)	PUNCT
ejpam-5396	443	77	,	,	PUNCT
ejpam-5396	443	78	...	...	PUNCT
ejpam-5396	444	1	dα	dα	ADP
ejpam-5396	444	2	n	n	PROPN
ejpam-5396	444	3	x1(t	x1(t	PROPN
ejpam-5396	444	4	)	)	PUNCT
ejpam-5396	444	5	=	=	SYM
ejpam-5396	445	1	fn(t	fn(t	NOUN
ejpam-5396	445	2	,	,	PUNCT
ejpam-5396	445	3	x1	x1	PROPN
ejpam-5396	445	4	,	,	PUNCT
ejpam-5396	445	5	x2	x2	PROPN
ejpam-5396	445	6	,	,	PUNCT
ejpam-5396	445	7	...	...	PUNCT
ejpam-5396	445	8	,	,	PUNCT
ejpam-5396	445	9	xn	xn	PROPN
ejpam-5396	445	10	)	)	PUNCT
ejpam-5396	445	11	,	,	PUNCT
ejpam-5396	445	12	(	(	PUNCT
ejpam-5396	445	13	10	10	NUM
ejpam-5396	445	14	)	)	PUNCT
ejpam-5396	445	15	subject	subject	NOUN
ejpam-5396	445	16	to	to	ADP
ejpam-5396	445	17	the	the	DET
ejpam-5396	445	18	initial	initial	ADJ
ejpam-5396	445	19	conditions	condition	NOUN
ejpam-5396	445	20	:	:	PUNCT
ejpam-5396	445	21	xi(t0	xi(t0	X
ejpam-5396	445	22	)	)	PUNCT
ejpam-5396	446	1	=	=	SYM
ejpam-5396	446	2	ci	ci	PROPN
ejpam-5396	446	3	,	,	PUNCT
ejpam-5396	446	4	i	i	NOUN
ejpam-5396	446	5	=	=	NOUN
ejpam-5396	446	6	1	1	NUM
ejpam-5396	446	7	,	,	PUNCT
ejpam-5396	446	8	2	2	NUM
ejpam-5396	446	9	,	,	PUNCT
ejpam-5396	446	10	...	...	PUNCT
ejpam-5396	446	11	,	,	PUNCT
ejpam-5396	446	12	n	n	CCONJ
ejpam-5396	446	13	,	,	PUNCT
ejpam-5396	446	14	(	(	PUNCT
ejpam-5396	446	15	11	11	NUM
ejpam-5396	446	16	)	)	PUNCT
ejpam-5396	446	17	where	where	SCONJ
ejpam-5396	446	18	dα	dα	PROPN
ejpam-5396	446	19	is	be	AUX
ejpam-5396	446	20	the	the	DET
ejpam-5396	446	21	caputo	caputo	PROPN
ejpam-5396	446	22	fractional	fractional	PROPN
ejpam-5396	446	23	derivative	derivative	NOUN
ejpam-5396	446	24	of	of	ADP
ejpam-5396	446	25	order	order	NOUN
ejpam-5396	446	26	αi	αi	VERB
ejpam-5396	446	27	,	,	PUNCT
ejpam-5396	446	28	i	i	PRON
ejpam-5396	446	29	=	=	NOUN
ejpam-5396	446	30	1	1	NUM
ejpam-5396	446	31	,	,	PUNCT
ejpam-5396	446	32	2	2	NUM
ejpam-5396	446	33	,	,	PUNCT
ejpam-5396	446	34	...	...	PUNCT
ejpam-5396	446	35	,	,	PUNCT
ejpam-5396	446	36	n.	n.	VERB
ejpam-5396	446	37	the	the	DET
ejpam-5396	446	38	initial	initial	ADJ
ejpam-5396	446	39	value	value	NOUN
ejpam-5396	446	40	problem	problem	NOUN
ejpam-5396	446	41	solution	solution	NOUN
ejpam-5396	446	42	(	(	PUNCT
ejpam-5396	446	43	10	10	NUM
ejpam-5396	446	44	)	)	PUNCT
ejpam-5396	446	45	,	,	PUNCT
ejpam-5396	446	46	(	(	PUNCT
ejpam-5396	446	47	11	11	NUM
ejpam-5396	446	48	)	)	PUNCT
ejpam-5396	446	49	is	be	AUX
ejpam-5396	446	50	looked	look	VERB
ejpam-5396	446	51	in	in	ADP
ejpam-5396	446	52	the	the	DET
ejpam-5396	446	53	range	range	NOUN
ejpam-5396	447	1	[	[	X
ejpam-5396	447	2	t0	t0	NOUN
ejpam-5396	447	3	,	,	PUNCT
ejpam-5396	447	4	t	t	X
ejpam-5396	447	5	]	]	PUNCT
ejpam-5396	447	6	.	.	PUNCT
ejpam-5396	448	1	in	in	ADP
ejpam-5396	448	2	real	real	ADJ
ejpam-5396	448	3	-	-	PUNCT
ejpam-5396	448	4	world	world	NOUN
ejpam-5396	448	5	applications	application	NOUN
ejpam-5396	448	6	of	of	ADP
ejpam-5396	448	7	the	the	DET
ejpam-5396	448	8	extended	extend	VERB
ejpam-5396	448	9	differential	differential	NOUN
ejpam-5396	448	10	transform	transform	NOUN
ejpam-5396	448	11	technique	technique	NOUN
ejpam-5396	448	12	,	,	PUNCT
ejpam-5396	448	13	the	the	DET
ejpam-5396	448	14	finite	finite	PROPN
ejpam-5396	448	15	series	series	PROPN
ejpam-5396	448	16	defines	define	VERB
ejpam-5396	448	17	the	the	DET
ejpam-5396	448	18	kth	kth	PROPN
ejpam-5396	448	19	order	order	NOUN
ejpam-5396	448	20	approximation	approximation	NOUN
ejpam-5396	448	21	solution	solution	NOUN
ejpam-5396	448	22	of	of	ADP
ejpam-5396	448	23	(	(	PUNCT
ejpam-5396	448	24	4	4	NUM
ejpam-5396	448	25	)	)	PUNCT
ejpam-5396	448	26	xi(t	xi(t	PUNCT
ejpam-5396	448	27	)	)	PUNCT
ejpam-5396	449	1	=	=	SYM
ejpam-5396	449	2	k∑	k∑	PROPN
ejpam-5396	449	3	i=0	i=0	PROPN
ejpam-5396	449	4	li(k)(t−	li(k)(t−	CCONJ
ejpam-5396	449	5	t0	t0	PROPN
ejpam-5396	449	6	)	)	PUNCT
ejpam-5396	449	7	kαi	kαi	NOUN
ejpam-5396	449	8	,	,	PUNCT
ejpam-5396	449	9	t	t	PROPN
ejpam-5396	449	10	∈	∈	PROPN
ejpam-5396	450	1	[	[	X
ejpam-5396	450	2	t0	t0	PROPN
ejpam-5396	450	3	,	,	PUNCT
ejpam-5396	450	4	t	t	X
ejpam-5396	450	5	]	]	PUNCT
ejpam-5396	450	6	,	,	PUNCT
ejpam-5396	450	7	where	where	SCONJ
ejpam-5396	450	8	li(k	li(k	NOUN
ejpam-5396	450	9	)	)	PUNCT
ejpam-5396	450	10	satisfied	satisfy	VERB
ejpam-5396	450	11	the	the	DET
ejpam-5396	450	12	(	(	PUNCT
ejpam-5396	450	13	recurrence	recurrence	NOUN
ejpam-5396	450	14	relation	relation	NOUN
ejpam-5396	450	15	):	):	PUNCT
ejpam-5396	450	16	γ((k	γ((k	PROPN
ejpam-5396	451	1	+	+	X
ejpam-5396	451	2	1)αi	1)αi	PROPN
ejpam-5396	451	3	+	+	CCONJ
ejpam-5396	451	4	1	1	X
ejpam-5396	451	5	)	)	PUNCT
ejpam-5396	451	6	γ(kαi	γ(kαi	NOUN
ejpam-5396	452	1	+	+	CCONJ
ejpam-5396	452	2	1	1	X
ejpam-5396	452	3	)	)	PUNCT
ejpam-5396	452	4	li(k	li(k	NOUN
ejpam-5396	453	1	+	+	NOUN
ejpam-5396	453	2	1	1	X
ejpam-5396	453	3	)	)	PUNCT
ejpam-5396	453	4	=	=	SYM
ejpam-5396	453	5	fi(k	fi(k	NOUN
ejpam-5396	453	6	,	,	PUNCT
ejpam-5396	453	7	l1,l2	l1,l2	PROPN
ejpam-5396	453	8	,	,	PUNCT
ejpam-5396	453	9	...	...	PUNCT
ejpam-5396	453	10	,	,	PUNCT
ejpam-5396	453	11	ln	ln	ADJ
ejpam-5396	453	12	)	)	PUNCT
ejpam-5396	453	13	,	,	PUNCT
ejpam-5396	453	14	li(0	li(0	PROPN
ejpam-5396	453	15	)	)	PUNCT
ejpam-5396	453	16	=	=	SYM
ejpam-5396	453	17	ci	ci	PROPN
ejpam-5396	453	18	,	,	PUNCT
ejpam-5396	453	19	and	and	CCONJ
ejpam-5396	453	20	fi(k	fi(k	NUM
ejpam-5396	453	21	,	,	PUNCT
ejpam-5396	453	22	l1,l2	l1,l2	PROPN
ejpam-5396	453	23	,	,	PUNCT
ejpam-5396	453	24	...	...	PUNCT
ejpam-5396	453	25	,	,	PUNCT
ejpam-5396	453	26	ln	ln	X
ejpam-5396	453	27	)	)	PUNCT
ejpam-5396	453	28	is	be	AUX
ejpam-5396	453	29	the	the	DET
ejpam-5396	453	30	differential	differential	ADJ
ejpam-5396	453	31	transform	transform	NOUN
ejpam-5396	453	32	of	of	ADP
ejpam-5396	453	33	function	function	NOUN
ejpam-5396	453	34	fit	fit	ADJ
ejpam-5396	453	35	,	,	PUNCT
ejpam-5396	453	36	fi(t	fi(t	NOUN
ejpam-5396	453	37	,	,	PUNCT
ejpam-5396	453	38	x1	x1	PROPN
ejpam-5396	453	39	,	,	PUNCT
ejpam-5396	453	40	x2	x2	PROPN
ejpam-5396	453	41	,	,	PUNCT
ejpam-5396	453	42	...	...	PUNCT
ejpam-5396	453	43	,	,	PUNCT
ejpam-5396	453	44	xn	xn	PROPN
ejpam-5396	453	45	)	)	PUNCT
ejpam-5396	453	46	for	for	ADP
ejpam-5396	453	47	i	i	PROPN
ejpam-5396	453	48	=	=	SYM
ejpam-5396	453	49	1	1	NUM
ejpam-5396	453	50	,	,	PUNCT
ejpam-5396	453	51	2	2	NUM
ejpam-5396	453	52	,	,	PUNCT
ejpam-5396	453	53	...	...	PUNCT
ejpam-5396	453	54	,	,	PUNCT
ejpam-5396	453	55	n.	n.	VERB
ejpam-5396	453	56	the	the	DET
ejpam-5396	453	57	basic	basic	ADJ
ejpam-5396	453	58	steps	step	NOUN
ejpam-5396	453	59	of	of	ADP
ejpam-5396	453	60	the	the	DET
ejpam-5396	453	61	gdtm	gdtm	NOUN
ejpam-5396	453	62	can	can	AUX
ejpam-5396	453	63	be	be	AUX
ejpam-5396	453	64	found	find	VERB
ejpam-5396	453	65	in	in	ADP
ejpam-5396	453	66	(	(	PUNCT
ejpam-5396	453	67	[	[	X
ejpam-5396	453	68	41	41	NUM
ejpam-5396	453	69	]	]	PUNCT
ejpam-5396	453	70	,	,	PUNCT
ejpam-5396	454	1	[	[	X
ejpam-5396	454	2	37	37	NUM
ejpam-5396	454	3	]	]	PUNCT
ejpam-5396	454	4	,	,	PUNCT
ejpam-5396	455	1	[	[	X
ejpam-5396	455	2	40	40	NUM
ejpam-5396	455	3	]	]	PUNCT
ejpam-5396	455	4	,	,	PUNCT
ejpam-5396	456	1	[	[	X
ejpam-5396	456	2	23	23	NUM
ejpam-5396	456	3	]	]	PUNCT
ejpam-5396	456	4	)	)	PUNCT
ejpam-5396	456	5	.	.	PUNCT
ejpam-5396	457	1	a.	a.	NOUN
ejpam-5396	457	2	alalyani	alalyani	PROPN
ejpam-5396	457	3	/	/	SYM
ejpam-5396	457	4	eur	eur	PROPN
ejpam-5396	457	5	.	.	PUNCT
ejpam-5396	458	1	j.	j.	PROPN
ejpam-5396	458	2	pure	pure	PROPN
ejpam-5396	458	3	appl	appl	PROPN
ejpam-5396	458	4	.	.	PROPN
ejpam-5396	458	5	math	math	PROPN
ejpam-5396	458	6	,	,	PUNCT
ejpam-5396	458	7	17	17	NUM
ejpam-5396	458	8	(	(	PUNCT
ejpam-5396	458	9	4	4	NUM
ejpam-5396	458	10	)	)	PUNCT
ejpam-5396	458	11	(	(	PUNCT
ejpam-5396	458	12	2024	2024	NUM
ejpam-5396	458	13	)	)	PUNCT
ejpam-5396	458	14	,	,	PUNCT
ejpam-5396	458	15	2763	2763	NUM
ejpam-5396	458	16	-	-	SYM
ejpam-5396	458	17	2799	2799	NUM
ejpam-5396	458	18	2782	2782	NUM
ejpam-5396	458	19	assume	assume	VERB
ejpam-5396	458	20	that	that	SCONJ
ejpam-5396	458	21	[	[	X
ejpam-5396	458	22	t0	t0	NOUN
ejpam-5396	458	23	,	,	PUNCT
ejpam-5396	458	24	t	t	PROPN
ejpam-5396	458	25	]	]	PUNCT
ejpam-5396	458	26	is	be	AUX
ejpam-5396	458	27	partitioned	partition	VERB
ejpam-5396	458	28	into	into	ADP
ejpam-5396	458	29	m	m	PROPN
ejpam-5396	458	30	subintervals	subinterval	NOUN
ejpam-5396	458	31	[	[	X
ejpam-5396	458	32	tm−1	tm−1	NOUN
ejpam-5396	458	33	,	,	PUNCT
ejpam-5396	458	34	tm	tm	NOUN
ejpam-5396	458	35	]	]	X
ejpam-5396	458	36	,	,	PUNCT
ejpam-5396	458	37	m	m	VERB
ejpam-5396	458	38	=	=	NOUN
ejpam-5396	458	39	1	1	NUM
ejpam-5396	458	40	,	,	PUNCT
ejpam-5396	458	41	2	2	NUM
ejpam-5396	458	42	,	,	PUNCT
ejpam-5396	458	43	...	...	PUNCT
ejpam-5396	458	44	,	,	PUNCT
ejpam-5396	458	45	m	m	VERB
ejpam-5396	458	46	,	,	PUNCT
ejpam-5396	458	47	with	with	ADP
ejpam-5396	458	48	steps	step	NOUN
ejpam-5396	458	49	h	h	NOUN
ejpam-5396	458	50	=	=	SYM
ejpam-5396	458	51	t	t	PROPN
ejpam-5396	458	52	−	−	PROPN
ejpam-5396	458	53	t0	t0	PROPN
ejpam-5396	458	54	m	m	AUX
ejpam-5396	458	55	using	use	VERB
ejpam-5396	458	56	the	the	DET
ejpam-5396	458	57	nodes	node	NOUN
ejpam-5396	458	58	tm	tm	NOUN
ejpam-5396	458	59	=	=	PROPN
ejpam-5396	458	60	t0	t0	PROPN
ejpam-5396	458	61	+	+	CCONJ
ejpam-5396	458	62	mh	mh	PROPN
ejpam-5396	458	63	.	.	PUNCT
ejpam-5396	459	1	the	the	DET
ejpam-5396	459	2	msgdtm	msgdtm	ADJ
ejpam-5396	459	3	principles	principle	NOUN
ejpam-5396	459	4	are	be	AUX
ejpam-5396	459	5	listed	list	VERB
ejpam-5396	459	6	below	below	ADV
ejpam-5396	459	7	.	.	PUNCT
ejpam-5396	460	1	first	first	ADV
ejpam-5396	460	2	,	,	PUNCT
ejpam-5396	460	3	the	the	DET
ejpam-5396	460	4	gdtm	gdtm	NOUN
ejpam-5396	460	5	solves	solve	NOUN
ejpam-5396	460	6	(	(	PUNCT
ejpam-5396	460	7	10	10	NUM
ejpam-5396	460	8	)	)	PUNCT
ejpam-5396	460	9	,	,	PUNCT
ejpam-5396	460	10	(	(	PUNCT
ejpam-5396	460	11	11	11	NUM
ejpam-5396	460	12	)	)	PUNCT
ejpam-5396	460	13	throughout	throughout	ADP
ejpam-5396	460	14	the	the	DET
ejpam-5396	460	15	interval	interval	NOUN
ejpam-5396	460	16	[	[	X
ejpam-5396	460	17	t0	t0	NOUN
ejpam-5396	460	18	,	,	PUNCT
ejpam-5396	460	19	t1	t1	PROPN
ejpam-5396	460	20	]	]	X
ejpam-5396	460	21	.	.	PUNCT
ejpam-5396	461	1	we	we	PRON
ejpam-5396	461	2	get	get	VERB
ejpam-5396	461	3	the	the	DET
ejpam-5396	461	4	approximate	approximate	ADJ
ejpam-5396	461	5	solution	solution	NOUN
ejpam-5396	461	6	by	by	ADP
ejpam-5396	461	7	beginning	begin	VERB
ejpam-5396	461	8	with	with	ADP
ejpam-5396	461	9	xi,1(t	xi,1(t	PROPN
ejpam-5396	461	10	)	)	PUNCT
ejpam-5396	461	11	,	,	PUNCT
ejpam-5396	461	12	t	t	PROPN
ejpam-5396	461	13	∈	∈	PROPN
ejpam-5396	461	14	[	[	X
ejpam-5396	461	15	t0	t0	NOUN
ejpam-5396	461	16	,	,	PUNCT
ejpam-5396	461	17	t1	t1	PROPN
ejpam-5396	461	18	]	]	X
ejpam-5396	461	19	,	,	PUNCT
ejpam-5396	461	20	for	for	ADP
ejpam-5396	461	21	i	i	PROPN
ejpam-5396	461	22	=	=	SYM
ejpam-5396	461	23	1	1	NUM
ejpam-5396	461	24	,	,	PUNCT
ejpam-5396	461	25	2	2	NUM
ejpam-5396	461	26	,	,	PUNCT
ejpam-5396	461	27	...	...	PUNCT
ejpam-5396	461	28	,	,	PUNCT
ejpam-5396	461	29	n.	n.	NOUN
ejpam-5396	461	30	for	for	ADP
ejpam-5396	461	31	m	m	PROPN
ejpam-5396	461	32	≥	≥	NOUN
ejpam-5396	461	33	2	2	NUM
ejpam-5396	461	34	,	,	PUNCT
ejpam-5396	461	35	applying	apply	VERB
ejpam-5396	461	36	the	the	DET
ejpam-5396	461	37	gdtm	gdtm	NOUN
ejpam-5396	461	38	to	to	ADP
ejpam-5396	461	39	(	(	PUNCT
ejpam-5396	461	40	10	10	NUM
ejpam-5396	461	41	)	)	PUNCT
ejpam-5396	461	42	,	,	PUNCT
ejpam-5396	461	43	(	(	PUNCT
ejpam-5396	461	44	11	11	NUM
ejpam-5396	461	45	)	)	PUNCT
ejpam-5396	461	46	across	across	ADP
ejpam-5396	461	47	the	the	DET
ejpam-5396	461	48	interval	interval	NOUN
ejpam-5396	461	49	[	[	X
ejpam-5396	461	50	tm−1	tm−1	NOUN
ejpam-5396	461	51	,	,	PUNCT
ejpam-5396	461	52	tm	tm	NOUN
ejpam-5396	461	53	]	]	PUNCT
ejpam-5396	461	54	will	will	AUX
ejpam-5396	461	55	employ	employ	VERB
ejpam-5396	461	56	the	the	DET
ejpam-5396	461	57	ic	ic	PROPN
ejpam-5396	461	58	xi	xi	PROPN
ejpam-5396	461	59	,	,	PUNCT
ejpam-5396	461	60	m(tm−1	m(tm−1	NOUN
ejpam-5396	461	61	)	)	PUNCT
ejpam-5396	461	62	=	=	SYM
ejpam-5396	461	63	xi	xi	PROPN
ejpam-5396	461	64	,	,	PUNCT
ejpam-5396	461	65	m−1(tm−1	m−1(tm−1	PROPN
ejpam-5396	461	66	)	)	PUNCT
ejpam-5396	461	67	.	.	PUNCT
ejpam-5396	462	1	repeating	repeat	VERB
ejpam-5396	462	2	the	the	DET
ejpam-5396	462	3	technique	technique	NOUN
ejpam-5396	462	4	yields	yield	NOUN
ejpam-5396	462	5	approximations	approximation	NOUN
ejpam-5396	462	6	for	for	ADP
ejpam-5396	462	7	xi	xi	PROPN
ejpam-5396	462	8	,	,	PUNCT
ejpam-5396	462	9	m(t	m(t	PROPN
ejpam-5396	462	10	)	)	PUNCT
ejpam-5396	462	11	,	,	PUNCT
ejpam-5396	462	12	m	m	AUX
ejpam-5396	462	13	=	=	NOUN
ejpam-5396	462	14	1	1	NUM
ejpam-5396	462	15	,	,	PUNCT
ejpam-5396	462	16	2	2	NUM
ejpam-5396	462	17	,	,	PUNCT
ejpam-5396	462	18	...	...	PUNCT
ejpam-5396	462	19	,	,	PUNCT
ejpam-5396	462	20	m	m	VERB
ejpam-5396	462	21	,	,	PUNCT
ejpam-5396	462	22	for	for	ADP
ejpam-5396	462	23	i	i	PROPN
ejpam-5396	462	24	=	=	SYM
ejpam-5396	462	25	1	1	NUM
ejpam-5396	462	26	,	,	PUNCT
ejpam-5396	462	27	2	2	NUM
ejpam-5396	462	28	,	,	PUNCT
ejpam-5396	462	29	...	...	PUNCT
ejpam-5396	462	30	,	,	PUNCT
ejpam-5396	462	31	n.	n.	PROPN
ejpam-5396	462	32	the	the	DET
ejpam-5396	462	33	msgdtm	msgdtm	NOUN
ejpam-5396	462	34	concludes	conclude	VERB
ejpam-5396	462	35	:	:	PUNCT
ejpam-5396	462	36	xi(t	xi(t	X
ejpam-5396	462	37	)	)	PUNCT
ejpam-5396	462	38	=	=	SYM
ejpam-5396	462	39			NOUN
ejpam-5396	462	40	xi,1(t	xi,1(t	ADJ
ejpam-5396	462	41	)	)	PUNCT
ejpam-5396	462	42	,	,	PUNCT
ejpam-5396	462	43	for	for	ADP
ejpam-5396	462	44	t	t	PROPN
ejpam-5396	462	45	∈	∈	PROPN
ejpam-5396	462	46	[	[	X
ejpam-5396	462	47	t0	t0	NOUN
ejpam-5396	462	48	,	,	PUNCT
ejpam-5396	462	49	t1	t1	PROPN
ejpam-5396	462	50	]	]	X
ejpam-5396	462	51	,	,	PUNCT
ejpam-5396	462	52	xi,2(t	xi,2(t	PROPN
ejpam-5396	462	53	)	)	PUNCT
ejpam-5396	462	54	,	,	PUNCT
ejpam-5396	462	55	for	for	ADP
ejpam-5396	462	56	t	t	PROPN
ejpam-5396	462	57	∈	∈	PROPN
ejpam-5396	463	1	[	[	X
ejpam-5396	463	2	t1	t1	NOUN
ejpam-5396	463	3	,	,	PUNCT
ejpam-5396	463	4	t2	t2	NOUN
ejpam-5396	463	5	]	]	PUNCT
ejpam-5396	463	6	,	,	PUNCT
ejpam-5396	463	7	...	...	PUNCT
ejpam-5396	463	8	xi	xi	X
ejpam-5396	463	9	,	,	PUNCT
ejpam-5396	463	10	m	m	PROPN
ejpam-5396	463	11	(	(	PUNCT
ejpam-5396	463	12	t	t	PROPN
ejpam-5396	463	13	)	)	PUNCT
ejpam-5396	463	14	,	,	PUNCT
ejpam-5396	463	15	for	for	ADP
ejpam-5396	463	16	t	t	PROPN
ejpam-5396	463	17	∈	∈	PROPN
ejpam-5396	463	18	[	[	AUX
ejpam-5396	463	19	tm−1	tm−1	NOUN
ejpam-5396	463	20	,	,	PUNCT
ejpam-5396	463	21	tm	tm	NOUN
ejpam-5396	463	22	]	]	X
ejpam-5396	463	23	.	.	PUNCT
ejpam-5396	464	1	the	the	DET
ejpam-5396	464	2	msgdtm	msgdtm	NOUN
ejpam-5396	464	3	is	be	AUX
ejpam-5396	464	4	efficient	efficient	ADJ
ejpam-5396	464	5	for	for	ADP
ejpam-5396	464	6	all	all	DET
ejpam-5396	464	7	values	value	NOUN
ejpam-5396	464	8	of	of	ADP
ejpam-5396	464	9	h.	h.	NOUN
ejpam-5396	464	10	the	the	DET
ejpam-5396	464	11	new	new	ADJ
ejpam-5396	464	12	algorithm	algorithm	NOUN
ejpam-5396	464	13	’s	’s	PART
ejpam-5396	464	14	key	key	ADJ
ejpam-5396	464	15	benefit	benefit	NOUN
ejpam-5396	464	16	is	be	AUX
ejpam-5396	464	17	that	that	SCONJ
ejpam-5396	464	18	the	the	DET
ejpam-5396	464	19	solution	solution	NOUN
ejpam-5396	464	20	converges	converge	VERB
ejpam-5396	464	21	over	over	ADP
ejpam-5396	464	22	vast	vast	ADJ
ejpam-5396	464	23	time	time	NOUN
ejpam-5396	464	24	periods	period	NOUN
ejpam-5396	464	25	,	,	PUNCT
ejpam-5396	464	26	as	as	SCONJ
ejpam-5396	464	27	we	we	PRON
ejpam-5396	464	28	shall	shall	AUX
ejpam-5396	464	29	show	show	VERB
ejpam-5396	464	30	in	in	ADP
ejpam-5396	464	31	the	the	DET
ejpam-5396	464	32	following	follow	VERB
ejpam-5396	464	33	section	section	NOUN
ejpam-5396	464	34	.	.	PUNCT
ejpam-5396	465	1	regarding	regard	VERB
ejpam-5396	465	2	(	(	PUNCT
ejpam-5396	465	3	1	1	NUM
ejpam-5396	465	4	)	)	PUNCT
ejpam-5396	465	5	,	,	PUNCT
ejpam-5396	465	6	the	the	DET
ejpam-5396	465	7	msgdtm	msgdtm	NOUN
ejpam-5396	465	8	algorithm	algorithm	NOUN
ejpam-5396	465	9	produces	produce	VERB
ejpam-5396	465	10	s(k	s(k	ADV
ejpam-5396	465	11	+	+	CCONJ
ejpam-5396	465	12	1	1	X
ejpam-5396	465	13	)	)	PUNCT
ejpam-5396	465	14	=	=	NOUN
ejpam-5396	465	15	γ(q1k	γ(q1k	NOUN
ejpam-5396	465	16	+	+	SYM
ejpam-5396	465	17	1	1	X
ejpam-5396	465	18	)	)	PUNCT
ejpam-5396	465	19	γ(q1(k	γ(q1(k	NOUN
ejpam-5396	465	20	+	+	CCONJ
ejpam-5396	465	21	1	1	NUM
ejpam-5396	465	22	)	)	PUNCT
ejpam-5396	465	23	+	+	CCONJ
ejpam-5396	465	24	1	1	X
ejpam-5396	465	25	)	)	PUNCT
ejpam-5396	465	26	(	(	PUNCT
ejpam-5396	465	27	λ−	λ−	PROPN
ejpam-5396	465	28	δ(i(k	δ(i(k	NOUN
ejpam-5396	465	29	)	)	PUNCT
ejpam-5396	465	30	+	+	NUM
ejpam-5396	465	31	ωc(k	ωc(k	NOUN
ejpam-5396	465	32	)	)	PUNCT
ejpam-5396	465	33	)	)	PUNCT
ejpam-5396	466	1	n	n	X
ejpam-5396	466	2	s(k)−	s(k)−	PROPN
ejpam-5396	466	3	µs(k	µs(k	PUNCT
ejpam-5396	466	4	)	)	PUNCT
ejpam-5396	467	1	+	+	CCONJ
ejpam-5396	467	2	ηr(k	ηr(k	NOUN
ejpam-5396	467	3	)	)	PUNCT
ejpam-5396	467	4	)	)	PUNCT
ejpam-5396	467	5	,	,	PUNCT
ejpam-5396	467	6	c(k	c(k	NOUN
ejpam-5396	467	7	+	+	CCONJ
ejpam-5396	467	8	1	1	X
ejpam-5396	467	9	)	)	PUNCT
ejpam-5396	467	10	=	=	NOUN
ejpam-5396	467	11	γ(q2k	γ(q2k	X
ejpam-5396	468	1	+	+	NOUN
ejpam-5396	468	2	1	1	X
ejpam-5396	468	3	)	)	PUNCT
ejpam-5396	468	4	γ(q2(k	γ(q2(k	PROPN
ejpam-5396	468	5	+	+	PROPN
ejpam-5396	468	6	1	1	NUM
ejpam-5396	468	7	)	)	PUNCT
ejpam-5396	468	8	+	+	CCONJ
ejpam-5396	468	9	1	1	X
ejpam-5396	468	10	)	)	PUNCT
ejpam-5396	468	11	(	(	PUNCT
ejpam-5396	468	12	δ(i(k	δ(i(k	NOUN
ejpam-5396	468	13	)	)	PUNCT
ejpam-5396	468	14	+	+	NUM
ejpam-5396	468	15	ωc(k	ωc(k	NOUN
ejpam-5396	468	16	)	)	PUNCT
ejpam-5396	468	17	)	)	PUNCT
ejpam-5396	469	1	n	n	CCONJ
ejpam-5396	469	2	θs(k)−	θs(k)−	VERB
ejpam-5396	469	3	z1c(k	z1c(k	PROPN
ejpam-5396	469	4	)	)	PUNCT
ejpam-5396	469	5	)	)	PUNCT
ejpam-5396	470	1	,	,	PUNCT
ejpam-5396	470	2	i(k	i(k	PROPN
ejpam-5396	470	3	+	+	NOUN
ejpam-5396	470	4	1	1	NUM
ejpam-5396	470	5	)	)	PUNCT
ejpam-5396	470	6	=	=	NOUN
ejpam-5396	470	7	γ(q3k	γ(q3k	X
ejpam-5396	470	8	+	+	CCONJ
ejpam-5396	470	9	1	1	X
ejpam-5396	470	10	)	)	PUNCT
ejpam-5396	470	11	γ(q3(k	γ(q3(k	NOUN
ejpam-5396	470	12	+	+	CCONJ
ejpam-5396	470	13	1	1	X
ejpam-5396	470	14	)	)	PUNCT
ejpam-5396	470	15	+	+	CCONJ
ejpam-5396	470	16	1	1	X
ejpam-5396	470	17	)	)	PUNCT
ejpam-5396	470	18	(	(	PUNCT
ejpam-5396	470	19	δ(i(k	δ(i(k	NOUN
ejpam-5396	470	20	)	)	PUNCT
ejpam-5396	470	21	+	+	NUM
ejpam-5396	470	22	ωc(k	ωc(k	NUM
ejpam-5396	470	23	)	)	PUNCT
ejpam-5396	470	24	)	)	PUNCT
ejpam-5396	471	1	n	n	CCONJ
ejpam-5396	471	2	(	(	PUNCT
ejpam-5396	471	3	1−	1−	NUM
ejpam-5396	471	4	θ)s(k	θ)s(k	NOUN
ejpam-5396	471	5	)	)	PUNCT
ejpam-5396	472	1	+	+	CCONJ
ejpam-5396	472	2	πc(k)−	πc(k)−	ADJ
ejpam-5396	472	3	z2i(k	z2i(k	NOUN
ejpam-5396	472	4	)	)	PUNCT
ejpam-5396	472	5	)	)	PUNCT
ejpam-5396	472	6	,	,	PUNCT
ejpam-5396	473	1	r(k	r(k	PROPN
ejpam-5396	473	2	+	+	NOUN
ejpam-5396	473	3	1	1	X
ejpam-5396	473	4	)	)	PUNCT
ejpam-5396	473	5	=	=	SYM
ejpam-5396	473	6	γ(q4k	γ(q4k	NOUN
ejpam-5396	473	7	+	+	NOUN
ejpam-5396	473	8	1	1	X
ejpam-5396	473	9	)	)	PUNCT
ejpam-5396	474	1	γ(q4(k	γ(q4(k	ADP
ejpam-5396	474	2	+	+	NOUN
ejpam-5396	474	3	1	1	NUM
ejpam-5396	474	4	)	)	PUNCT
ejpam-5396	474	5	+	+	CCONJ
ejpam-5396	474	6	1	1	X
ejpam-5396	474	7	)	)	PUNCT
ejpam-5396	474	8	(	(	PUNCT
ejpam-5396	474	9	βc(k	βc(k	PUNCT
ejpam-5396	474	10	)	)	PUNCT
ejpam-5396	474	11	+	+	CCONJ
ejpam-5396	474	12	τi(k)−	τi(k)−	NOUN
ejpam-5396	474	13	(	(	PUNCT
ejpam-5396	474	14	µ+	µ+	X
ejpam-5396	474	15	η)r(k	η)r(k	ADJ
ejpam-5396	474	16	)	)	PUNCT
ejpam-5396	474	17	)	)	PUNCT
ejpam-5396	474	18	,	,	PUNCT
ejpam-5396	474	19	where	where	SCONJ
ejpam-5396	474	20	s(k	s(k	ADV
ejpam-5396	474	21	)	)	PUNCT
ejpam-5396	474	22	,	,	PUNCT
ejpam-5396	474	23	c(k	c(k	NOUN
ejpam-5396	474	24	)	)	PUNCT
ejpam-5396	474	25	,	,	PUNCT
ejpam-5396	474	26	i(k	i(k	PROPN
ejpam-5396	474	27	)	)	PUNCT
ejpam-5396	474	28	,	,	PUNCT
ejpam-5396	474	29	and	and	CCONJ
ejpam-5396	474	30	r(k	r(k	PROPN
ejpam-5396	474	31	)	)	PUNCT
ejpam-5396	474	32	are	be	AUX
ejpam-5396	474	33	the	the	DET
ejpam-5396	474	34	differential	differential	ADJ
ejpam-5396	474	35	transformations	transformation	NOUN
ejpam-5396	474	36	of	of	ADP
ejpam-5396	474	37	s(k	s(k	NOUN
ejpam-5396	474	38	)	)	PUNCT
ejpam-5396	474	39	,	,	PUNCT
ejpam-5396	474	40	c(k	c(k	NOUN
ejpam-5396	474	41	)	)	PUNCT
ejpam-5396	474	42	,	,	PUNCT
ejpam-5396	474	43	i(k	i(k	PROPN
ejpam-5396	474	44	)	)	PUNCT
ejpam-5396	474	45	,	,	PUNCT
ejpam-5396	474	46	and	and	CCONJ
ejpam-5396	474	47	r(k	r(k	PROPN
ejpam-5396	474	48	)	)	PUNCT
ejpam-5396	474	49	,	,	PUNCT
ejpam-5396	474	50	respectively	respectively	ADV
ejpam-5396	474	51	.	.	PUNCT
ejpam-5396	475	1	the	the	DET
ejpam-5396	475	2	differential	differential	ADJ
ejpam-5396	475	3	transform	transform	NOUN
ejpam-5396	475	4	of	of	ADP
ejpam-5396	475	5	the	the	DET
ejpam-5396	475	6	starting	starting	NOUN
ejpam-5396	475	7	conditions	condition	NOUN
ejpam-5396	475	8	is	be	AUX
ejpam-5396	475	9	provided	provide	VERB
ejpam-5396	475	10	by	by	ADP
ejpam-5396	475	11	the	the	DET
ejpam-5396	475	12	formulas	formula	NOUN
ejpam-5396	475	13	s(0	s(0	PROPN
ejpam-5396	475	14	)	)	PUNCT
ejpam-5396	475	15	=	=	SYM
ejpam-5396	475	16	c1	c1	PROPN
ejpam-5396	475	17	,	,	PUNCT
ejpam-5396	475	18	c(0	c(0	PROPN
ejpam-5396	475	19	)	)	PUNCT
ejpam-5396	475	20	=	=	SYM
ejpam-5396	475	21	c2	c2	PROPN
ejpam-5396	475	22	,	,	PUNCT
ejpam-5396	475	23	i(0	i(0	PROPN
ejpam-5396	475	24	)	)	PUNCT
ejpam-5396	475	25	=	=	SYM
ejpam-5396	475	26	c3	c3	PROPN
ejpam-5396	475	27	,	,	PUNCT
ejpam-5396	475	28	and	and	CCONJ
ejpam-5396	475	29	r(0	r(0	PROPN
ejpam-5396	475	30	)	)	PUNCT
ejpam-5396	475	31	=	=	PROPN
ejpam-5396	475	32	c4	c4	NOUN
ejpam-5396	475	33	,	,	PUNCT
ejpam-5396	475	34	respectively	respectively	ADV
ejpam-5396	475	35	.	.	PUNCT
ejpam-5396	476	1	through	through	ADP
ejpam-5396	476	2	the	the	DET
ejpam-5396	476	3	differential	differential	ADJ
ejpam-5396	476	4	inverse	inverse	NOUN
ejpam-5396	476	5	transform	transform	NOUN
ejpam-5396	476	6	,	,	PUNCT
ejpam-5396	476	7	we	we	PRON
ejpam-5396	476	8	may	may	AUX
ejpam-5396	476	9	find	find	VERB
ejpam-5396	476	10	the	the	DET
ejpam-5396	476	11	differential	differential	ADJ
ejpam-5396	476	12	transform	transform	NOUN
ejpam-5396	476	13	series	series	NOUN
ejpam-5396	476	14	solution	solution	NOUN
ejpam-5396	476	15	for	for	ADP
ejpam-5396	476	16	the	the	DET
ejpam-5396	476	17	problem	problem	NOUN
ejpam-5396	476	18	(	(	PUNCT
ejpam-5396	476	19	1	1	NUM
ejpam-5396	476	20	):	):	PUNCT
ejpam-5396	476	21	s(t	s(t	PROPN
ejpam-5396	476	22	)	)	PUNCT
ejpam-5396	476	23	=	=	PRON
ejpam-5396	476	24	k∑	k∑	PROPN
ejpam-5396	476	25	n=0	n=0	NUM
ejpam-5396	476	26	s(n)tq1n	s(n)tq1n	PROPN
ejpam-5396	476	27	,	,	PUNCT
ejpam-5396	476	28	c(t	c(t	PROPN
ejpam-5396	476	29	)	)	PUNCT
ejpam-5396	476	30	=	=	PRON
ejpam-5396	476	31	k∑	k∑	PROPN
ejpam-5396	476	32	n=0	n=0	PROPN
ejpam-5396	477	1	c(n)tq2n	c(n)tq2n	PROPN
ejpam-5396	477	2	,	,	PUNCT
ejpam-5396	477	3	i(t	i(t	PROPN
ejpam-5396	477	4	)	)	PUNCT
ejpam-5396	477	5	=	=	PRON
ejpam-5396	478	1	k∑	k∑	PROPN
ejpam-5396	478	2	n=0	n=0	PUNCT
ejpam-5396	478	3	i(n)tq3n	i(n)tq3n	PROPN
ejpam-5396	478	4	,	,	PUNCT
ejpam-5396	478	5	r(t	r(t	NOUN
ejpam-5396	478	6	)	)	PUNCT
ejpam-5396	478	7	=	=	PUNCT
ejpam-5396	479	1	k∑	k∑	PROPN
ejpam-5396	479	2	n=0	n=0	NUM
ejpam-5396	479	3	r(n)tq4n	r(n)tq4n	NUM
ejpam-5396	479	4	.	.	PUNCT
ejpam-5396	479	5	a.	a.	NOUN
ejpam-5396	479	6	alalyani	alalyani	PROPN
ejpam-5396	479	7	/	/	SYM
ejpam-5396	479	8	eur	eur	PROPN
ejpam-5396	479	9	.	.	PUNCT
ejpam-5396	480	1	j.	j.	PROPN
ejpam-5396	480	2	pure	pure	PROPN
ejpam-5396	480	3	appl	appl	PROPN
ejpam-5396	480	4	.	.	PROPN
ejpam-5396	480	5	math	math	PROPN
ejpam-5396	480	6	,	,	PUNCT
ejpam-5396	480	7	17	17	NUM
ejpam-5396	480	8	(	(	PUNCT
ejpam-5396	480	9	4	4	NUM
ejpam-5396	480	10	)	)	PUNCT
ejpam-5396	480	11	(	(	PUNCT
ejpam-5396	480	12	2024	2024	NUM
ejpam-5396	480	13	)	)	PUNCT
ejpam-5396	480	14	,	,	PUNCT
ejpam-5396	480	15	2763	2763	NUM
ejpam-5396	480	16	-	-	SYM
ejpam-5396	480	17	2799	2799	NUM
ejpam-5396	480	18	2783	2783	NUM
ejpam-5396	480	19	for	for	ADP
ejpam-5396	480	20	the	the	DET
ejpam-5396	480	21	msgdtm	msgdtm	NOUN
ejpam-5396	480	22	,	,	PUNCT
ejpam-5396	480	23	the	the	DET
ejpam-5396	480	24	proposed	propose	VERB
ejpam-5396	480	25	series	series	NOUN
ejpam-5396	480	26	solution	solution	NOUN
ejpam-5396	480	27	of	of	ADP
ejpam-5396	480	28	(	(	PUNCT
ejpam-5396	480	29	1	1	NUM
ejpam-5396	480	30	)	)	PUNCT
ejpam-5396	480	31	is	be	AUX
ejpam-5396	480	32	:	:	PUNCT
ejpam-5396	480	33	s(t	s(t	NUM
ejpam-5396	480	34	)	)	PUNCT
ejpam-5396	480	35	=	=	PUNCT
ejpam-5396	481	1			PROPN
ejpam-5396	481	2	∑k	∑k	PROPN
ejpam-5396	481	3	n=0	n=0	NUM
ejpam-5396	481	4	s1(n)tq1n	s1(n)tq1n	NOUN
ejpam-5396	481	5	,	,	PUNCT
ejpam-5396	481	6	for	for	ADP
ejpam-5396	481	7	t	t	PROPN
ejpam-5396	481	8	∈	∈	PROPN
ejpam-5396	482	1	[	[	X
ejpam-5396	482	2	0	0	NUM
ejpam-5396	482	3	,	,	PUNCT
ejpam-5396	482	4	t1]∑k	t1]∑k	PROPN
ejpam-5396	482	5	n=0	n=0	PROPN
ejpam-5396	482	6	s2(n)(t−	s2(n)(t−	PROPN
ejpam-5396	482	7	t1	t1	NOUN
ejpam-5396	482	8	)	)	PUNCT
ejpam-5396	483	1	q1n	q1n	PROPN
ejpam-5396	483	2	,	,	PUNCT
ejpam-5396	483	3	for	for	ADP
ejpam-5396	483	4	t	t	PROPN
ejpam-5396	483	5	∈	∈	PROPN
ejpam-5396	484	1	[	[	X
ejpam-5396	484	2	t1	t1	NOUN
ejpam-5396	484	3	,	,	PUNCT
ejpam-5396	484	4	t2	t2	PROPN
ejpam-5396	484	5	]	]	PUNCT
ejpam-5396	484	6	...	...	PUNCT
ejpam-5396	485	1	∑k	∑k	PROPN
ejpam-5396	485	2	n=0	n=0	NUM
ejpam-5396	486	1	sm	sm	INTJ
ejpam-5396	486	2	(	(	PUNCT
ejpam-5396	486	3	n)(t−	n)(t−	PROPN
ejpam-5396	486	4	tm−1	tm−1	NOUN
ejpam-5396	486	5	)	)	PUNCT
ejpam-5396	486	6	q1n	q1n	PROPN
ejpam-5396	486	7	,	,	PUNCT
ejpam-5396	486	8	for	for	ADP
ejpam-5396	486	9	t	t	PROPN
ejpam-5396	486	10	∈	∈	PROPN
ejpam-5396	487	1	[	[	X
ejpam-5396	487	2	tm−1	tm−1	NOUN
ejpam-5396	487	3	,	,	PUNCT
ejpam-5396	487	4	tm	tm	NOUN
ejpam-5396	487	5	]	]	X
ejpam-5396	487	6	(	(	PUNCT
ejpam-5396	487	7	12	12	NUM
ejpam-5396	487	8	)	)	PUNCT
ejpam-5396	487	9	c(t	c(t	PROPN
ejpam-5396	487	10	)	)	PUNCT
ejpam-5396	487	11	=	=	PUNCT
ejpam-5396	488	1			PROPN
ejpam-5396	488	2	∑k	∑k	PROPN
ejpam-5396	489	1	n=0c1(n)t	n=0c1(n)t	PROPN
ejpam-5396	489	2	q2n	q2n	PROPN
ejpam-5396	489	3	,	,	PUNCT
ejpam-5396	489	4	for	for	ADP
ejpam-5396	489	5	t	t	PROPN
ejpam-5396	489	6	∈	∈	PROPN
ejpam-5396	490	1	[	[	X
ejpam-5396	490	2	0	0	NUM
ejpam-5396	490	3	,	,	PUNCT
ejpam-5396	490	4	t1]∑k	t1]∑k	PROPN
ejpam-5396	490	5	n=0c2(n)(t−	n=0c2(n)(t−	CCONJ
ejpam-5396	490	6	t1	t1	PROPN
ejpam-5396	490	7	)	)	PUNCT
ejpam-5396	491	1	q2n	q2n	CCONJ
ejpam-5396	491	2	,	,	PUNCT
ejpam-5396	491	3	for	for	ADP
ejpam-5396	491	4	t	t	PROPN
ejpam-5396	491	5	∈	∈	PROPN
ejpam-5396	492	1	[	[	X
ejpam-5396	492	2	t1	t1	NOUN
ejpam-5396	492	3	,	,	PUNCT
ejpam-5396	492	4	t2	t2	PROPN
ejpam-5396	492	5	]	]	PUNCT
ejpam-5396	492	6	...	...	PUNCT
ejpam-5396	493	1	∑k	∑k	PROPN
ejpam-5396	493	2	n=0	n=0	NUM
ejpam-5396	493	3	cm	cm	NOUN
ejpam-5396	493	4	(	(	PUNCT
ejpam-5396	493	5	n)(t−	n)(t−	PROPN
ejpam-5396	493	6	tm−1	tm−1	NOUN
ejpam-5396	493	7	)	)	PUNCT
ejpam-5396	493	8	q2n	q2n	CCONJ
ejpam-5396	493	9	,	,	PUNCT
ejpam-5396	493	10	for	for	ADP
ejpam-5396	493	11	t	t	PROPN
ejpam-5396	493	12	∈	∈	PROPN
ejpam-5396	493	13	[	[	X
ejpam-5396	493	14	tm−1	tm−1	NOUN
ejpam-5396	493	15	,	,	PUNCT
ejpam-5396	493	16	tm	tm	NOUN
ejpam-5396	493	17	]	]	X
ejpam-5396	493	18	(	(	PUNCT
ejpam-5396	493	19	13	13	NUM
ejpam-5396	493	20	)	)	PUNCT
ejpam-5396	493	21	i(t	i(t	NOUN
ejpam-5396	493	22	)	)	PUNCT
ejpam-5396	493	23	=	=	PUNCT
ejpam-5396	494	1			PROPN
ejpam-5396	494	2	∑k	∑k	PROPN
ejpam-5396	494	3	n=0	n=0	PROPN
ejpam-5396	494	4	i1(n)tq3n	i1(n)tq3n	PROPN
ejpam-5396	494	5	,	,	PUNCT
ejpam-5396	494	6	for	for	ADP
ejpam-5396	494	7	t	t	PROPN
ejpam-5396	494	8	∈	∈	PROPN
ejpam-5396	495	1	[	[	X
ejpam-5396	495	2	0	0	NUM
ejpam-5396	495	3	,	,	PUNCT
ejpam-5396	495	4	t1]∑k	t1]∑k	PROPN
ejpam-5396	495	5	n=0	n=0	PROPN
ejpam-5396	495	6	i2(n)(t−	i2(n)(t−	PROPN
ejpam-5396	495	7	t1	t1	NOUN
ejpam-5396	495	8	)	)	PUNCT
ejpam-5396	496	1	q3n	q3n	PROPN
ejpam-5396	496	2	,	,	PUNCT
ejpam-5396	496	3	for	for	ADP
ejpam-5396	496	4	t	t	PROPN
ejpam-5396	496	5	∈	∈	PROPN
ejpam-5396	497	1	[	[	X
ejpam-5396	497	2	t1	t1	NOUN
ejpam-5396	497	3	,	,	PUNCT
ejpam-5396	497	4	t2	t2	PROPN
ejpam-5396	497	5	]	]	PUNCT
ejpam-5396	497	6	...	...	PUNCT
ejpam-5396	498	1	∑k	∑k	PROPN
ejpam-5396	498	2	n=0	n=0	PRON
ejpam-5396	499	1	i	i	PRON
ejpam-5396	499	2	m	m	VERB
ejpam-5396	499	3	(	(	PUNCT
ejpam-5396	499	4	n)(t−	n)(t−	INTJ
ejpam-5396	499	5	tm−1	tm−1	NOUN
ejpam-5396	499	6	)	)	PUNCT
ejpam-5396	499	7	q3n	q3n	PROPN
ejpam-5396	499	8	,	,	PUNCT
ejpam-5396	499	9	for	for	ADP
ejpam-5396	499	10	t	t	PROPN
ejpam-5396	499	11	∈	∈	PROPN
ejpam-5396	500	1	[	[	X
ejpam-5396	500	2	tm−1	tm−1	NOUN
ejpam-5396	500	3	,	,	PUNCT
ejpam-5396	500	4	tm	tm	NOUN
ejpam-5396	500	5	]	]	X
ejpam-5396	500	6	(	(	PUNCT
ejpam-5396	500	7	14	14	NUM
ejpam-5396	500	8	)	)	PUNCT
ejpam-5396	500	9	r(t	r(t	NOUN
ejpam-5396	500	10	)	)	PUNCT
ejpam-5396	500	11	=	=	PUNCT
ejpam-5396	501	1			PROPN
ejpam-5396	501	2	∑k	∑k	PROPN
ejpam-5396	501	3	n=0r1(n)t	n=0r1(n)t	ADJ
ejpam-5396	501	4	q4n	q4n	NOUN
ejpam-5396	501	5	,	,	PUNCT
ejpam-5396	501	6	for	for	ADP
ejpam-5396	501	7	t	t	PROPN
ejpam-5396	501	8	∈	∈	PROPN
ejpam-5396	502	1	[	[	X
ejpam-5396	502	2	0	0	NUM
ejpam-5396	502	3	,	,	PUNCT
ejpam-5396	502	4	t1]∑k	t1]∑k	PROPN
ejpam-5396	502	5	n=0r2(n)(t−	n=0r2(n)(t−	NUM
ejpam-5396	502	6	t1	t1	NOUN
ejpam-5396	502	7	)	)	PUNCT
ejpam-5396	502	8	q4n	q4n	NOUN
ejpam-5396	502	9	,	,	PUNCT
ejpam-5396	502	10	for	for	ADP
ejpam-5396	502	11	t	t	PROPN
ejpam-5396	502	12	∈	∈	PROPN
ejpam-5396	502	13	[	[	X
ejpam-5396	502	14	t1	t1	NOUN
ejpam-5396	502	15	,	,	PUNCT
ejpam-5396	502	16	t2	t2	PROPN
ejpam-5396	502	17	]	]	PUNCT
ejpam-5396	502	18	...	...	PUNCT
ejpam-5396	502	19	∑k	∑k	PROPN
ejpam-5396	502	20	n=0rm	n=0rm	ADV
ejpam-5396	502	21	(	(	PUNCT
ejpam-5396	502	22	n)(t−	n)(t−	PROPN
ejpam-5396	502	23	tm−1	tm−1	NOUN
ejpam-5396	502	24	)	)	PUNCT
ejpam-5396	502	25	q4n	q4n	NOUN
ejpam-5396	502	26	,	,	PUNCT
ejpam-5396	502	27	for	for	ADP
ejpam-5396	502	28	t	t	PROPN
ejpam-5396	502	29	∈	∈	PROPN
ejpam-5396	503	1	[	[	X
ejpam-5396	503	2	tm−1	tm−1	NOUN
ejpam-5396	503	3	,	,	PUNCT
ejpam-5396	503	4	tm	tm	NOUN
ejpam-5396	503	5	]	]	X
ejpam-5396	503	6	,	,	PUNCT
ejpam-5396	503	7	(	(	PUNCT
ejpam-5396	503	8	15	15	NUM
ejpam-5396	503	9	)	)	PUNCT
ejpam-5396	504	1	where	where	SCONJ
ejpam-5396	504	2	si(n	si(n	NOUN
ejpam-5396	504	3	)	)	PUNCT
ejpam-5396	504	4	,	,	PUNCT
ejpam-5396	504	5	ci(n	ci(n	NOUN
ejpam-5396	504	6	)	)	PUNCT
ejpam-5396	504	7	,	,	PUNCT
ejpam-5396	504	8	ii(n	ii(n	NOUN
ejpam-5396	504	9	)	)	PUNCT
ejpam-5396	504	10	,	,	PUNCT
ejpam-5396	504	11	and	and	CCONJ
ejpam-5396	504	12	ri(n	ri(n	NOUN
ejpam-5396	504	13	)	)	PUNCT
ejpam-5396	504	14	for	for	ADP
ejpam-5396	504	15	i	i	PROPN
ejpam-5396	504	16	=	=	NOUN
ejpam-5396	504	17	1	1	NUM
ejpam-5396	504	18	,	,	PUNCT
ejpam-5396	504	19	2	2	NUM
ejpam-5396	504	20	,	,	PUNCT
ejpam-5396	504	21	...	...	PUNCT
ejpam-5396	504	22	,	,	PUNCT
ejpam-5396	504	23	m	m	VERB
ejpam-5396	504	24	satisfy	satisfy	VERB
ejpam-5396	504	25	the	the	DET
ejpam-5396	504	26	following	follow	VERB
ejpam-5396	504	27	(	(	PUNCT
ejpam-5396	504	28	recurrence	recurrence	NOUN
ejpam-5396	504	29	relations	relation	NOUN
ejpam-5396	504	30	):	):	PUNCT
ejpam-5396	504	31	si(k	si(k	NUM
ejpam-5396	505	1	+	+	SYM
ejpam-5396	505	2	1	1	X
ejpam-5396	505	3	)	)	PUNCT
ejpam-5396	505	4	=	=	NOUN
ejpam-5396	505	5	γ(q1k	γ(q1k	NOUN
ejpam-5396	505	6	+	+	SYM
ejpam-5396	505	7	1	1	X
ejpam-5396	505	8	)	)	PUNCT
ejpam-5396	505	9	γ(q1(k	γ(q1(k	NOUN
ejpam-5396	505	10	+	+	CCONJ
ejpam-5396	505	11	1	1	NUM
ejpam-5396	505	12	)	)	PUNCT
ejpam-5396	505	13	+	+	CCONJ
ejpam-5396	505	14	1	1	X
ejpam-5396	505	15	)	)	PUNCT
ejpam-5396	505	16	(	(	PUNCT
ejpam-5396	505	17	λ−	λ−	PROPN
ejpam-5396	505	18	δ(ii(k	δ(ii(k	NUM
ejpam-5396	505	19	)	)	PUNCT
ejpam-5396	505	20	+	+	CCONJ
ejpam-5396	505	21	ωci(k	ωci(k	NUM
ejpam-5396	505	22	)	)	PUNCT
ejpam-5396	505	23	)	)	PUNCT
ejpam-5396	506	1	n	n	X
ejpam-5396	506	2	si(k)−	si(k)−	NOUN
ejpam-5396	506	3	µsi(k	µsi(k	PROPN
ejpam-5396	506	4	)	)	PUNCT
ejpam-5396	506	5	+	+	SYM
ejpam-5396	506	6	ηri(k	ηri(k	NOUN
ejpam-5396	506	7	)	)	PUNCT
ejpam-5396	506	8	)	)	PUNCT
ejpam-5396	506	9	,	,	PUNCT
ejpam-5396	506	10	ci(k	ci(k	NOUN
ejpam-5396	507	1	+	+	CCONJ
ejpam-5396	507	2	1	1	X
ejpam-5396	507	3	)	)	PUNCT
ejpam-5396	507	4	=	=	NOUN
ejpam-5396	507	5	γ(q2k	γ(q2k	X
ejpam-5396	508	1	+	+	NOUN
ejpam-5396	508	2	1	1	X
ejpam-5396	508	3	)	)	PUNCT
ejpam-5396	508	4	γ(q2(k	γ(q2(k	PROPN
ejpam-5396	508	5	+	+	PROPN
ejpam-5396	508	6	1	1	NUM
ejpam-5396	508	7	)	)	PUNCT
ejpam-5396	508	8	+	+	CCONJ
ejpam-5396	508	9	1	1	X
ejpam-5396	508	10	)	)	PUNCT
ejpam-5396	508	11	(	(	PUNCT
ejpam-5396	508	12	δ(ii(k	δ(ii(k	NOUN
ejpam-5396	508	13	)	)	PUNCT
ejpam-5396	508	14	+	+	CCONJ
ejpam-5396	508	15	ωci(k	ωci(k	NUM
ejpam-5396	508	16	)	)	PUNCT
ejpam-5396	508	17	)	)	PUNCT
ejpam-5396	509	1	n	n	CCONJ
ejpam-5396	509	2	θsi(k)−	θsi(k)−	VERB
ejpam-5396	509	3	z1ci(k	z1ci(k	PROPN
ejpam-5396	509	4	)	)	PUNCT
ejpam-5396	509	5	)	)	PUNCT
ejpam-5396	509	6	,	,	PUNCT
ejpam-5396	509	7	ii(k	ii(k	NOUN
ejpam-5396	510	1	+	+	CCONJ
ejpam-5396	510	2	1	1	X
ejpam-5396	510	3	)	)	PUNCT
ejpam-5396	510	4	=	=	NOUN
ejpam-5396	510	5	γ(q3k	γ(q3k	X
ejpam-5396	510	6	+	+	CCONJ
ejpam-5396	510	7	1	1	X
ejpam-5396	510	8	)	)	PUNCT
ejpam-5396	510	9	γ(q3(k	γ(q3(k	NOUN
ejpam-5396	511	1	+	+	CCONJ
ejpam-5396	511	2	1	1	X
ejpam-5396	511	3	)	)	PUNCT
ejpam-5396	511	4	+	+	CCONJ
ejpam-5396	511	5	1	1	X
ejpam-5396	511	6	)	)	PUNCT
ejpam-5396	511	7	(	(	PUNCT
ejpam-5396	511	8	δ(ii(k	δ(ii(k	NOUN
ejpam-5396	511	9	)	)	PUNCT
ejpam-5396	511	10	+	+	CCONJ
ejpam-5396	512	1	ωci(k	ωci(k	NUM
ejpam-5396	512	2	)	)	PUNCT
ejpam-5396	512	3	)	)	PUNCT
ejpam-5396	513	1	n	n	CCONJ
ejpam-5396	513	2	(	(	PUNCT
ejpam-5396	513	3	1−	1−	NUM
ejpam-5396	513	4	θ)si(k	θ)si(k	NOUN
ejpam-5396	513	5	)	)	PUNCT
ejpam-5396	513	6	+	+	CCONJ
ejpam-5396	514	1	πci(k)−	πci(k)−	PROPN
ejpam-5396	514	2	z2ii(k	z2ii(k	PROPN
ejpam-5396	514	3	)	)	PUNCT
ejpam-5396	514	4	)	)	PUNCT
ejpam-5396	514	5	,	,	PUNCT
ejpam-5396	514	6	ri(k	ri(k	X
ejpam-5396	515	1	+	+	CCONJ
ejpam-5396	515	2	1	1	X
ejpam-5396	515	3	)	)	PUNCT
ejpam-5396	515	4	=	=	SYM
ejpam-5396	515	5	γ(q4k	γ(q4k	NOUN
ejpam-5396	515	6	+	+	NOUN
ejpam-5396	515	7	1	1	X
ejpam-5396	515	8	)	)	PUNCT
ejpam-5396	516	1	γ(q4(k	γ(q4(k	ADP
ejpam-5396	516	2	+	+	NOUN
ejpam-5396	516	3	1	1	NUM
ejpam-5396	516	4	)	)	PUNCT
ejpam-5396	516	5	+	+	CCONJ
ejpam-5396	516	6	1	1	X
ejpam-5396	516	7	)	)	PUNCT
ejpam-5396	516	8	(	(	PUNCT
ejpam-5396	516	9	βci(k	βci(k	X
ejpam-5396	516	10	)	)	PUNCT
ejpam-5396	517	1	+	+	CCONJ
ejpam-5396	517	2	τii(k)−	τii(k)−	PROPN
ejpam-5396	517	3	(	(	PUNCT
ejpam-5396	517	4	µ+	µ+	X
ejpam-5396	517	5	η)ri(k	η)ri(k	NOUN
ejpam-5396	517	6	)	)	PUNCT
ejpam-5396	517	7	)	)	PUNCT
ejpam-5396	517	8	,	,	PUNCT
ejpam-5396	517	9	(	(	PUNCT
ejpam-5396	517	10	16	16	NUM
ejpam-5396	517	11	)	)	PUNCT
ejpam-5396	517	12	with	with	ADP
ejpam-5396	517	13	si(0	si(0	PROPN
ejpam-5396	517	14	)	)	PUNCT
ejpam-5396	517	15	=	=	SYM
ejpam-5396	517	16	si(ti−1	si(ti−1	NUM
ejpam-5396	517	17	)	)	PUNCT
ejpam-5396	517	18	=	=	PUNCT
ejpam-5396	517	19	si−1(ti−1	si−1(ti−1	PROPN
ejpam-5396	517	20	)	)	PUNCT
ejpam-5396	517	21	,	,	PUNCT
ejpam-5396	517	22	ci(0	ci(0	PROPN
ejpam-5396	517	23	)	)	PUNCT
ejpam-5396	517	24	=	=	SYM
ejpam-5396	517	25	ci(ti−1	ci(ti−1	PROPN
ejpam-5396	517	26	)	)	PUNCT
ejpam-5396	517	27	=	=	SYM
ejpam-5396	517	28	ci−1(ti−1	ci−1(ti−1	PROPN
ejpam-5396	517	29	)	)	PUNCT
ejpam-5396	517	30	,	,	PUNCT
ejpam-5396	517	31	ii(0	ii(0	NOUN
ejpam-5396	517	32	)	)	PUNCT
ejpam-5396	517	33	=	=	SYM
ejpam-5396	517	34	ii(ti−1	ii(ti−1	PROPN
ejpam-5396	517	35	)	)	PUNCT
ejpam-5396	517	36	=	=	PUNCT
ejpam-5396	517	37	ii−1(ti−1	ii−1(ti−1	PROPN
ejpam-5396	517	38	)	)	PUNCT
ejpam-5396	517	39	,	,	PUNCT
ejpam-5396	517	40	and	and	CCONJ
ejpam-5396	517	41	ri(0	ri(0	NOUN
ejpam-5396	517	42	)	)	PUNCT
ejpam-5396	517	43	=	=	SYM
ejpam-5396	517	44	ri(ti−1	ri(ti−1	NOUN
ejpam-5396	517	45	)	)	PUNCT
ejpam-5396	517	46	=	=	SYM
ejpam-5396	517	47	ri−1(ti−1	ri−1(ti−1	PROPN
ejpam-5396	517	48	)	)	PUNCT
ejpam-5396	517	49	.	.	PUNCT
ejpam-5396	518	1	finally	finally	ADV
ejpam-5396	518	2	,	,	PUNCT
ejpam-5396	518	3	we	we	PRON
ejpam-5396	518	4	start	start	VERB
ejpam-5396	518	5	with	with	ADP
ejpam-5396	518	6	s0(0	s0(0	PROPN
ejpam-5396	518	7	)	)	PUNCT
ejpam-5396	519	1	=	=	SYM
ejpam-5396	519	2	c1	c1	PROPN
ejpam-5396	519	3	,	,	PUNCT
ejpam-5396	519	4	c0(0	c0(0	PROPN
ejpam-5396	519	5	)	)	PUNCT
ejpam-5396	519	6	=	=	SYM
ejpam-5396	519	7	c2	c2	PROPN
ejpam-5396	519	8	,	,	PUNCT
ejpam-5396	519	9	i0(0	i0(0	PROPN
ejpam-5396	519	10	)	)	PUNCT
ejpam-5396	519	11	=	=	SYM
ejpam-5396	519	12	c3	c3	PROPN
ejpam-5396	519	13	,	,	PUNCT
ejpam-5396	519	14	and	and	CCONJ
ejpam-5396	519	15	r0(0	r0(0	PROPN
ejpam-5396	519	16	)	)	PUNCT
ejpam-5396	519	17	=	=	SYM
ejpam-5396	519	18	c4	c4	NOUN
ejpam-5396	519	19	,	,	PUNCT
ejpam-5396	519	20	using	use	VERB
ejpam-5396	519	21	the	the	DET
ejpam-5396	519	22	(	(	PUNCT
ejpam-5396	519	23	recurrence	recurrence	NOUN
ejpam-5396	519	24	relations	relation	NOUN
ejpam-5396	519	25	)	)	PUNCT
ejpam-5396	519	26	(	(	PUNCT
ejpam-5396	519	27	16	16	NUM
ejpam-5396	519	28	)	)	PUNCT
ejpam-5396	519	29	,	,	PUNCT
ejpam-5396	519	30	then	then	ADV
ejpam-5396	519	31	we	we	PRON
ejpam-5396	519	32	can	can	AUX
ejpam-5396	519	33	get	get	VERB
ejpam-5396	519	34	the	the	DET
ejpam-5396	519	35	multistep	multistep	ADJ
ejpam-5396	519	36	solution	solution	NOUN
ejpam-5396	519	37	(	(	PUNCT
ejpam-5396	519	38	12)-(15	12)-(15	NUM
ejpam-5396	519	39	)	)	PUNCT
ejpam-5396	519	40	.	.	PUNCT
ejpam-5396	520	1	a.	a.	NOUN
ejpam-5396	520	2	alalyani	alalyani	PROPN
ejpam-5396	520	3	/	/	SYM
ejpam-5396	520	4	eur	eur	PROPN
ejpam-5396	520	5	.	.	PUNCT
ejpam-5396	521	1	j.	j.	PROPN
ejpam-5396	521	2	pure	pure	PROPN
ejpam-5396	521	3	appl	appl	PROPN
ejpam-5396	521	4	.	.	PROPN
ejpam-5396	521	5	math	math	PROPN
ejpam-5396	521	6	,	,	PUNCT
ejpam-5396	521	7	17	17	NUM
ejpam-5396	521	8	(	(	PUNCT
ejpam-5396	521	9	4	4	NUM
ejpam-5396	521	10	)	)	PUNCT
ejpam-5396	521	11	(	(	PUNCT
ejpam-5396	521	12	2024	2024	NUM
ejpam-5396	521	13	)	)	PUNCT
ejpam-5396	521	14	,	,	PUNCT
ejpam-5396	521	15	2763	2763	NUM
ejpam-5396	521	16	-	-	SYM
ejpam-5396	521	17	2799	2799	NUM
ejpam-5396	521	18	2784	2784	NUM
ejpam-5396	521	19	5	5	NUM
ejpam-5396	521	20	.	.	PUNCT
ejpam-5396	521	21	numerical	numerical	ADJ
ejpam-5396	521	22	simulations	simulation	NOUN
ejpam-5396	521	23	and	and	CCONJ
ejpam-5396	521	24	results	result	NOUN
ejpam-5396	521	25	using	use	VERB
ejpam-5396	521	26	the	the	DET
ejpam-5396	521	27	mathematical	mathematical	ADJ
ejpam-5396	521	28	software	software	NOUN
ejpam-5396	521	29	programs	program	NOUN
ejpam-5396	521	30	:	:	PUNCT
ejpam-5396	521	31	matlab	matlab	PROPN
ejpam-5396	521	32	and	and	CCONJ
ejpam-5396	521	33	mathematica	mathematica	PROPN
ejpam-5396	521	34	and	and	CCONJ
ejpam-5396	521	35	the	the	DET
ejpam-5396	521	36	parameter	parameter	NOUN
ejpam-5396	521	37	values	value	NOUN
ejpam-5396	521	38	listed	list	VERB
ejpam-5396	521	39	in	in	ADP
ejpam-5396	521	40	table	table	NOUN
ejpam-5396	521	41	1	1	NUM
ejpam-5396	521	42	,	,	PUNCT
ejpam-5396	521	43	which	which	PRON
ejpam-5396	521	44	are	be	AUX
ejpam-5396	521	45	taken	take	VERB
ejpam-5396	521	46	from	from	ADP
ejpam-5396	521	47	[	[	X
ejpam-5396	521	48	1	1	NUM
ejpam-5396	521	49	]	]	PUNCT
ejpam-5396	522	1	,	,	PUNCT
ejpam-5396	522	2	we	we	PRON
ejpam-5396	522	3	present	present	VERB
ejpam-5396	522	4	numerical	numerical	ADJ
ejpam-5396	522	5	simulations	simulation	NOUN
ejpam-5396	522	6	and	and	CCONJ
ejpam-5396	522	7	results	result	NOUN
ejpam-5396	522	8	in	in	ADP
ejpam-5396	522	9	this	this	DET
ejpam-5396	522	10	section	section	NOUN
ejpam-5396	522	11	.	.	PUNCT
ejpam-5396	523	1	table	table	NOUN
ejpam-5396	523	2	1	1	NUM
ejpam-5396	523	3	:	:	PUNCT
ejpam-5396	523	4	the	the	DET
ejpam-5396	523	5	parameter	parameter	NOUN
ejpam-5396	523	6	values	value	NOUN
ejpam-5396	523	7	parameter	parameter	NOUN
ejpam-5396	523	8	value	value	NOUN
ejpam-5396	523	9	/	/	SYM
ejpam-5396	523	10	source	source	NOUN
ejpam-5396	523	11	[	[	X
ejpam-5396	523	12	1	1	NUM
ejpam-5396	523	13	]	]	X
ejpam-5396	523	14	λ	λ	X
ejpam-5396	523	15	0.5	0.5	NUM
ejpam-5396	523	16	δ	δ	PROPN
ejpam-5396	523	17	2	2	NUM
ejpam-5396	523	18	(	(	PUNCT
ejpam-5396	523	19	dfe	dfe	PROPN
ejpam-5396	523	20	)	)	PUNCT
ejpam-5396	523	21	2.5	2.5	NUM
ejpam-5396	523	22	(	(	PUNCT
ejpam-5396	523	23	ee	ee	PROPN
ejpam-5396	523	24	)	)	PUNCT
ejpam-5396	523	25	ω	ω	NOUN
ejpam-5396	523	26	0.1124	0.1124	NUM
ejpam-5396	523	27	µ	µ	PROPN
ejpam-5396	523	28	0.5	0.5	NUM
ejpam-5396	523	29	η	η	PROPN
ejpam-5396	523	30	0.00641	0.00641	NUM
ejpam-5396	523	31	β	β	NOUN
ejpam-5396	523	32	0.515	0.515	NUM
ejpam-5396	523	33	π	π	NOUN
ejpam-5396	523	34	0.7096	0.7096	NUM
ejpam-5396	523	35	θ	θ	NOUN
ejpam-5396	523	36	0.563	0.563	NUM
ejpam-5396	523	37	τ	τ	NUM
ejpam-5396	523	38	0.641	0.641	NUM
ejpam-5396	523	39	σ	σ	NOUN
ejpam-5396	523	40	0.53	0.53	NUM
ejpam-5396	523	41	5.1	5.1	NUM
ejpam-5396	523	42	.	.	PUNCT
ejpam-5396	524	1	numerical	numerical	ADJ
ejpam-5396	524	2	simulations	simulation	NOUN
ejpam-5396	524	3	and	and	CCONJ
ejpam-5396	524	4	results	result	NOUN
ejpam-5396	524	5	of	of	ADP
ejpam-5396	524	6	the	the	DET
ejpam-5396	524	7	abmm	abmm	NOUN
ejpam-5396	524	8	method	method	NOUN
ejpam-5396	524	9	in	in	ADP
ejpam-5396	524	10	this	this	DET
ejpam-5396	524	11	subsection	subsection	NOUN
ejpam-5396	524	12	,	,	PUNCT
ejpam-5396	524	13	we	we	PRON
ejpam-5396	524	14	present	present	VERB
ejpam-5396	524	15	numerical	numerical	ADJ
ejpam-5396	524	16	simulations	simulation	NOUN
ejpam-5396	524	17	and	and	CCONJ
ejpam-5396	524	18	results	result	NOUN
ejpam-5396	524	19	for	for	ADP
ejpam-5396	524	20	the	the	DET
ejpam-5396	524	21	model	model	NOUN
ejpam-5396	524	22	(	(	PUNCT
ejpam-5396	524	23	1	1	NUM
ejpam-5396	524	24	)	)	PUNCT
ejpam-5396	524	25	solution	solution	NOUN
ejpam-5396	524	26	applying	apply	VERB
ejpam-5396	524	27	the	the	DET
ejpam-5396	524	28	abmm	abmm	NOUN
ejpam-5396	524	29	method	method	NOUN
ejpam-5396	524	30	.	.	PUNCT
ejpam-5396	525	1	the	the	DET
ejpam-5396	525	2	solution	solution	NOUN
ejpam-5396	525	3	to	to	ADP
ejpam-5396	525	4	the	the	DET
ejpam-5396	525	5	proposed	propose	VERB
ejpam-5396	525	6	model	model	NOUN
ejpam-5396	525	7	(	(	PUNCT
ejpam-5396	525	8	1	1	X
ejpam-5396	525	9	)	)	PUNCT
ejpam-5396	525	10	using	use	VERB
ejpam-5396	525	11	the	the	DET
ejpam-5396	525	12	adams	adams	PROPN
ejpam-5396	525	13	-	-	PUNCT
ejpam-5396	525	14	bashforth	bashforth	PROPN
ejpam-5396	525	15	-	-	PUNCT
ejpam-5396	525	16	moulton	moulton	PROPN
ejpam-5396	525	17	method	method	NOUN
ejpam-5396	525	18	appears	appear	VERB
ejpam-5396	525	19	in	in	ADP
ejpam-5396	525	20	figures	figure	NOUN
ejpam-5396	525	21	1(a	1(a	NUM
ejpam-5396	525	22	,	,	PUNCT
ejpam-5396	525	23	b	b	PROPN
ejpam-5396	525	24	,	,	PUNCT
ejpam-5396	525	25	c	c	NOUN
ejpam-5396	525	26	,	,	PUNCT
ejpam-5396	525	27	d	d	NOUN
ejpam-5396	525	28	)	)	PUNCT
ejpam-5396	525	29	and	and	CCONJ
ejpam-5396	525	30	figures	figure	NOUN
ejpam-5396	525	31	2(a	2(a	NUM
ejpam-5396	525	32	,	,	PUNCT
ejpam-5396	525	33	b	b	NOUN
ejpam-5396	525	34	,	,	PUNCT
ejpam-5396	525	35	c	c	NOUN
ejpam-5396	525	36	,	,	PUNCT
ejpam-5396	525	37	d	d	NOUN
ejpam-5396	525	38	,	,	PUNCT
ejpam-5396	525	39	e	e	NOUN
ejpam-5396	525	40	)	)	PUNCT
ejpam-5396	525	41	.	.	PUNCT
ejpam-5396	526	1	according	accord	VERB
ejpam-5396	526	2	to	to	ADP
ejpam-5396	526	3	these	these	DET
ejpam-5396	526	4	figures	figure	NOUN
ejpam-5396	526	5	,	,	PUNCT
ejpam-5396	526	6	we	we	PRON
ejpam-5396	526	7	observe	observe	VERB
ejpam-5396	526	8	that	that	SCONJ
ejpam-5396	526	9	s(t	s(t	PROPN
ejpam-5396	526	10	)	)	PUNCT
ejpam-5396	526	11	increases	increase	NOUN
ejpam-5396	526	12	at	at	ADP
ejpam-5396	526	13	α	α	NOUN
ejpam-5396	526	14	=	=	SYM
ejpam-5396	526	15	1	1	NUM
ejpam-5396	526	16	than	than	ADP
ejpam-5396	526	17	in	in	ADP
ejpam-5396	526	18	the	the	DET
ejpam-5396	526	19	case	case	NOUN
ejpam-5396	526	20	where	where	SCONJ
ejpam-5396	526	21	α	α	NOUN
ejpam-5396	526	22	is	be	AUX
ejpam-5396	526	23	a	a	DET
ejpam-5396	526	24	fractional	fractional	ADJ
ejpam-5396	526	25	variant	variant	NOUN
ejpam-5396	526	26	.	.	PUNCT
ejpam-5396	527	1	we	we	PRON
ejpam-5396	527	2	also	also	ADV
ejpam-5396	527	3	note	note	VERB
ejpam-5396	527	4	that	that	SCONJ
ejpam-5396	527	5	c(t	c(t	PROPN
ejpam-5396	527	6	)	)	PUNCT
ejpam-5396	527	7	,	,	PUNCT
ejpam-5396	527	8	i(t	i(t	PROPN
ejpam-5396	527	9	)	)	PUNCT
ejpam-5396	527	10	,	,	PUNCT
ejpam-5396	527	11	and	and	CCONJ
ejpam-5396	527	12	r(t	r(t	NOUN
ejpam-5396	527	13	)	)	PUNCT
ejpam-5396	527	14	decrease	decrease	NOUN
ejpam-5396	527	15	at	at	ADP
ejpam-5396	527	16	α	α	NOUN
ejpam-5396	527	17	=	=	SYM
ejpam-5396	527	18	1	1	NUM
ejpam-5396	527	19	than	than	ADP
ejpam-5396	527	20	in	in	ADP
ejpam-5396	527	21	the	the	DET
ejpam-5396	527	22	case	case	NOUN
ejpam-5396	527	23	where	where	SCONJ
ejpam-5396	527	24	α	α	NOUN
ejpam-5396	527	25	is	be	AUX
ejpam-5396	527	26	a	a	DET
ejpam-5396	527	27	fractional	fractional	ADJ
ejpam-5396	527	28	variant	variant	NOUN
ejpam-5396	527	29	.	.	PUNCT
ejpam-5396	528	1	a.	a.	NOUN
ejpam-5396	528	2	alalyani	alalyani	PROPN
ejpam-5396	528	3	/	/	SYM
ejpam-5396	528	4	eur	eur	PROPN
ejpam-5396	528	5	.	.	PUNCT
ejpam-5396	529	1	j.	j.	PROPN
ejpam-5396	529	2	pure	pure	PROPN
ejpam-5396	529	3	appl	appl	PROPN
ejpam-5396	529	4	.	.	PROPN
ejpam-5396	529	5	math	math	PROPN
ejpam-5396	529	6	,	,	PUNCT
ejpam-5396	529	7	17	17	NUM
ejpam-5396	529	8	(	(	PUNCT
ejpam-5396	529	9	4	4	NUM
ejpam-5396	529	10	)	)	PUNCT
ejpam-5396	529	11	(	(	PUNCT
ejpam-5396	529	12	2024	2024	NUM
ejpam-5396	529	13	)	)	PUNCT
ejpam-5396	529	14	,	,	PUNCT
ejpam-5396	529	15	2763	2763	NUM
ejpam-5396	529	16	-	-	SYM
ejpam-5396	529	17	2799	2799	NUM
ejpam-5396	529	18	2785	2785	NUM
ejpam-5396	529	19	0	0	NUM
ejpam-5396	529	20	10	10	NUM
ejpam-5396	529	21	20	20	NUM
ejpam-5396	529	22	30	30	NUM
ejpam-5396	529	23	40	40	NUM
ejpam-5396	529	24	50	50	NUM
ejpam-5396	529	25	60	60	NUM
ejpam-5396	529	26	70	70	NUM
ejpam-5396	529	27	80	80	NUM
ejpam-5396	529	28	90	90	NUM
ejpam-5396	529	29	100	100	NUM
ejpam-5396	529	30	time	time	NOUN
ejpam-5396	529	31	(	(	PUNCT
ejpam-5396	529	32	days	day	NOUN
ejpam-5396	529	33	)	)	PUNCT
ejpam-5396	529	34	0.9	0.9	NUM
ejpam-5396	529	35	0.91	0.91	NUM
ejpam-5396	529	36	0.92	0.92	NUM
ejpam-5396	529	37	0.93	0.93	NUM
ejpam-5396	529	38	0.94	0.94	NUM
ejpam-5396	529	39	0.95	0.95	NUM
ejpam-5396	529	40	0.96	0.96	NUM
ejpam-5396	529	41	0.97	0.97	NUM
ejpam-5396	529	42	0.98	0.98	NUM
ejpam-5396	529	43	0.99	0.99	NUM
ejpam-5396	529	44	1	1	NUM
ejpam-5396	529	45	s	s	PART
ejpam-5396	529	46	(	(	PUNCT
ejpam-5396	529	47	a	a	NOUN
ejpam-5396	529	48	)	)	PUNCT
ejpam-5396	529	49	0	0	NUM
ejpam-5396	530	1	10	10	NUM
ejpam-5396	530	2	20	20	NUM
ejpam-5396	530	3	30	30	NUM
ejpam-5396	530	4	40	40	NUM
ejpam-5396	530	5	50	50	NUM
ejpam-5396	530	6	60	60	NUM
ejpam-5396	530	7	70	70	NUM
ejpam-5396	530	8	80	80	NUM
ejpam-5396	530	9	90	90	NUM
ejpam-5396	530	10	100	100	NUM
ejpam-5396	530	11	time	time	NOUN
ejpam-5396	530	12	(	(	PUNCT
ejpam-5396	530	13	days	day	NOUN
ejpam-5396	530	14	)	)	PUNCT
ejpam-5396	530	15	-0.02	-0.02	NUM
ejpam-5396	530	16	0	0	NUM
ejpam-5396	530	17	0.02	0.02	NUM
ejpam-5396	530	18	0.04	0.04	NUM
ejpam-5396	530	19	0.06	0.06	NUM
ejpam-5396	530	20	0.08	0.08	NUM
ejpam-5396	530	21	0.1	0.1	NUM
ejpam-5396	530	22	c	c	NOUN
ejpam-5396	530	23	(	(	PUNCT
ejpam-5396	530	24	b	b	NOUN
ejpam-5396	530	25	)	)	PUNCT
ejpam-5396	530	26	0	0	NUM
ejpam-5396	530	27	10	10	NUM
ejpam-5396	530	28	20	20	NUM
ejpam-5396	530	29	30	30	NUM
ejpam-5396	530	30	40	40	NUM
ejpam-5396	530	31	50	50	NUM
ejpam-5396	530	32	60	60	NUM
ejpam-5396	530	33	70	70	NUM
ejpam-5396	530	34	80	80	NUM
ejpam-5396	530	35	90	90	NUM
ejpam-5396	530	36	100	100	NUM
ejpam-5396	530	37	time	time	NOUN
ejpam-5396	530	38	(	(	PUNCT
ejpam-5396	530	39	days	day	NOUN
ejpam-5396	530	40	)	)	PUNCT
ejpam-5396	530	41	-0.02	-0.02	NUM
ejpam-5396	530	42	0	0	NUM
ejpam-5396	530	43	0.02	0.02	NUM
ejpam-5396	530	44	0.04	0.04	NUM
ejpam-5396	530	45	0.06	0.06	NUM
ejpam-5396	530	46	0.08	0.08	NUM
ejpam-5396	530	47	0.1	0.1	NUM
ejpam-5396	530	48	i	i	NOUN
ejpam-5396	530	49	(	(	PUNCT
ejpam-5396	530	50	c	c	NOUN
ejpam-5396	530	51	)	)	PUNCT
ejpam-5396	530	52	0	0	NUM
ejpam-5396	530	53	10	10	NUM
ejpam-5396	530	54	20	20	NUM
ejpam-5396	530	55	30	30	NUM
ejpam-5396	530	56	40	40	NUM
ejpam-5396	530	57	50	50	NUM
ejpam-5396	530	58	60	60	NUM
ejpam-5396	530	59	70	70	NUM
ejpam-5396	530	60	80	80	NUM
ejpam-5396	530	61	90	90	NUM
ejpam-5396	530	62	100	100	NUM
ejpam-5396	530	63	time	time	NOUN
ejpam-5396	530	64	(	(	PUNCT
ejpam-5396	530	65	days	day	NOUN
ejpam-5396	530	66	)	)	PUNCT
ejpam-5396	530	67	-0.02	-0.02	NUM
ejpam-5396	530	68	0	0	NUM
ejpam-5396	530	69	0.02	0.02	NUM
ejpam-5396	530	70	0.04	0.04	NUM
ejpam-5396	530	71	0.06	0.06	NUM
ejpam-5396	530	72	0.08	0.08	NUM
ejpam-5396	530	73	0.1	0.1	NUM
ejpam-5396	530	74	0.12	0.12	NUM
ejpam-5396	530	75	r	r	NOUN
ejpam-5396	530	76	(	(	PUNCT
ejpam-5396	530	77	d	d	NOUN
ejpam-5396	530	78	)	)	PUNCT
ejpam-5396	530	79	figure	figure	NOUN
ejpam-5396	530	80	1	1	NUM
ejpam-5396	530	81	:	:	PUNCT
ejpam-5396	530	82	the	the	DET
ejpam-5396	530	83	abmm	abmm	NOUN
ejpam-5396	530	84	method	method	NOUN
ejpam-5396	530	85	for	for	ADP
ejpam-5396	530	86	the	the	DET
ejpam-5396	530	87	behavior	behavior	NOUN
ejpam-5396	530	88	of	of	ADP
ejpam-5396	530	89	s(t	s(t	PROPN
ejpam-5396	530	90	)	)	PUNCT
ejpam-5396	530	91	,	,	PUNCT
ejpam-5396	530	92	c(t	c(t	PROPN
ejpam-5396	530	93	)	)	PUNCT
ejpam-5396	530	94	,	,	PUNCT
ejpam-5396	530	95	i(t	i(t	PROPN
ejpam-5396	530	96	)	)	PUNCT
ejpam-5396	530	97	,	,	PUNCT
ejpam-5396	530	98	and	and	CCONJ
ejpam-5396	530	99	r(t	r(t	NOUN
ejpam-5396	530	100	)	)	PUNCT
ejpam-5396	530	101	at	at	ADP
ejpam-5396	530	102	various	various	ADJ
ejpam-5396	530	103	values	value	NOUN
ejpam-5396	530	104	of	of	ADP
ejpam-5396	530	105	α	α	NOUN
ejpam-5396	530	106	=	=	SYM
ejpam-5396	530	107	0.65	0.65	NUM
ejpam-5396	530	108	,	,	PUNCT
ejpam-5396	530	109	0.75	0.75	NUM
ejpam-5396	530	110	,	,	PUNCT
ejpam-5396	530	111	0.85	0.85	NUM
ejpam-5396	530	112	,	,	PUNCT
ejpam-5396	530	113	0.95	0.95	NUM
ejpam-5396	530	114	,	,	PUNCT
ejpam-5396	530	115	1	1	NUM
ejpam-5396	530	116	.	.	PUNCT
ejpam-5396	530	117	a.	a.	NOUN
ejpam-5396	530	118	alalyani	alalyani	PROPN
ejpam-5396	530	119	/	/	SYM
ejpam-5396	530	120	eur	eur	PROPN
ejpam-5396	530	121	.	.	PUNCT
ejpam-5396	531	1	j.	j.	PROPN
ejpam-5396	531	2	pure	pure	PROPN
ejpam-5396	531	3	appl	appl	PROPN
ejpam-5396	531	4	.	.	PROPN
ejpam-5396	531	5	math	math	PROPN
ejpam-5396	531	6	,	,	PUNCT
ejpam-5396	531	7	17	17	NUM
ejpam-5396	531	8	(	(	PUNCT
ejpam-5396	531	9	4	4	NUM
ejpam-5396	531	10	)	)	PUNCT
ejpam-5396	531	11	(	(	PUNCT
ejpam-5396	531	12	2024	2024	NUM
ejpam-5396	531	13	)	)	PUNCT
ejpam-5396	531	14	,	,	PUNCT
ejpam-5396	531	15	2763	2763	NUM
ejpam-5396	531	16	-	-	SYM
ejpam-5396	531	17	2799	2799	NUM
ejpam-5396	531	18	2786	2786	NUM
ejpam-5396	531	19	time	time	NOUN
ejpam-5396	531	20	,	,	PUNCT
ejpam-5396	531	21	α=0.65	α=0.65	ADV
ejpam-5396	531	22	0	0	NUM
ejpam-5396	531	23	10	10	NUM
ejpam-5396	531	24	20	20	NUM
ejpam-5396	531	25	30	30	NUM
ejpam-5396	531	26	40	40	NUM
ejpam-5396	531	27	50	50	NUM
ejpam-5396	531	28	60	60	NUM
ejpam-5396	531	29	s	s	NOUN
ejpam-5396	531	30	,	,	PUNCT
ejpam-5396	531	31	c	c	PROPN
ejpam-5396	531	32	,	,	PUNCT
ejpam-5396	531	33	i	i	PRON
ejpam-5396	531	34	,	,	PUNCT
ejpam-5396	531	35	r	r	NOUN
ejpam-5396	531	36	0	0	NUM
ejpam-5396	531	37	0.1	0.1	NUM
ejpam-5396	531	38	0.2	0.2	NUM
ejpam-5396	531	39	0.3	0.3	NUM
ejpam-5396	531	40	0.4	0.4	NUM
ejpam-5396	531	41	0.5	0.5	NUM
ejpam-5396	531	42	0.6	0.6	NUM
ejpam-5396	531	43	0.7	0.7	NUM
ejpam-5396	531	44	0.8	0.8	NUM
ejpam-5396	531	45	0.9	0.9	NUM
ejpam-5396	531	46	1	1	NUM
ejpam-5396	531	47	s	s	NOUN
ejpam-5396	531	48	c	c	NOUN
ejpam-5396	532	1	i	i	PRON
ejpam-5396	532	2	r	r	NOUN
ejpam-5396	532	3	(	(	PUNCT
ejpam-5396	532	4	a	a	NOUN
ejpam-5396	532	5	)	)	PUNCT
ejpam-5396	532	6	time	time	NOUN
ejpam-5396	532	7	,	,	PUNCT
ejpam-5396	532	8	α=0.75	α=0.75	ADJ
ejpam-5396	532	9	0	0	NUM
ejpam-5396	532	10	10	10	NUM
ejpam-5396	532	11	20	20	NUM
ejpam-5396	532	12	30	30	NUM
ejpam-5396	532	13	40	40	NUM
ejpam-5396	532	14	50	50	NUM
ejpam-5396	532	15	60	60	NUM
ejpam-5396	532	16	s	s	NOUN
ejpam-5396	532	17	,	,	PUNCT
ejpam-5396	532	18	c	c	PROPN
ejpam-5396	532	19	,	,	PUNCT
ejpam-5396	532	20	i	i	PRON
ejpam-5396	532	21	,	,	PUNCT
ejpam-5396	532	22	r	r	NOUN
ejpam-5396	532	23	0	0	NUM
ejpam-5396	532	24	0.1	0.1	NUM
ejpam-5396	532	25	0.2	0.2	NUM
ejpam-5396	532	26	0.3	0.3	NUM
ejpam-5396	532	27	0.4	0.4	NUM
ejpam-5396	532	28	0.5	0.5	NUM
ejpam-5396	532	29	0.6	0.6	NUM
ejpam-5396	532	30	0.7	0.7	NUM
ejpam-5396	532	31	0.8	0.8	NUM
ejpam-5396	532	32	0.9	0.9	NUM
ejpam-5396	532	33	1	1	NUM
ejpam-5396	532	34	s	s	NOUN
ejpam-5396	533	1	c	c	NOUN
ejpam-5396	534	1	i	i	PRON
ejpam-5396	534	2	r	r	NOUN
ejpam-5396	534	3	(	(	PUNCT
ejpam-5396	534	4	b	b	NOUN
ejpam-5396	534	5	)	)	PUNCT
ejpam-5396	534	6	time	time	NOUN
ejpam-5396	534	7	,	,	PUNCT
ejpam-5396	534	8	α=0.85	α=0.85	NOUN
ejpam-5396	534	9	0	0	NUM
ejpam-5396	534	10	10	10	NUM
ejpam-5396	534	11	20	20	NUM
ejpam-5396	534	12	30	30	NUM
ejpam-5396	534	13	40	40	NUM
ejpam-5396	534	14	50	50	NUM
ejpam-5396	534	15	60	60	NUM
ejpam-5396	534	16	s	s	NOUN
ejpam-5396	534	17	,	,	PUNCT
ejpam-5396	534	18	c	c	PROPN
ejpam-5396	534	19	,	,	PUNCT
ejpam-5396	534	20	i	i	PRON
ejpam-5396	534	21	,	,	PUNCT
ejpam-5396	534	22	r	r	NOUN
ejpam-5396	534	23	0	0	NUM
ejpam-5396	534	24	0.1	0.1	NUM
ejpam-5396	534	25	0.2	0.2	NUM
ejpam-5396	534	26	0.3	0.3	NUM
ejpam-5396	534	27	0.4	0.4	NUM
ejpam-5396	534	28	0.5	0.5	NUM
ejpam-5396	534	29	0.6	0.6	NUM
ejpam-5396	534	30	0.7	0.7	NUM
ejpam-5396	534	31	0.8	0.8	NUM
ejpam-5396	534	32	0.9	0.9	NUM
ejpam-5396	534	33	1	1	NUM
ejpam-5396	535	1	s	s	NOUN
ejpam-5396	535	2	c	c	NOUN
ejpam-5396	535	3	i	i	PRON
ejpam-5396	535	4	r	r	NOUN
ejpam-5396	535	5	(	(	PUNCT
ejpam-5396	535	6	c	c	NOUN
ejpam-5396	535	7	)	)	PUNCT
ejpam-5396	535	8	time	time	NOUN
ejpam-5396	535	9	,	,	PUNCT
ejpam-5396	535	10	α=0.95	α=0.95	NOUN
ejpam-5396	535	11	0	0	NUM
ejpam-5396	535	12	10	10	NUM
ejpam-5396	535	13	20	20	NUM
ejpam-5396	535	14	30	30	NUM
ejpam-5396	535	15	40	40	NUM
ejpam-5396	535	16	50	50	NUM
ejpam-5396	535	17	60	60	NUM
ejpam-5396	535	18	s	s	NOUN
ejpam-5396	535	19	,	,	PUNCT
ejpam-5396	535	20	c	c	PROPN
ejpam-5396	535	21	,	,	PUNCT
ejpam-5396	535	22	i	i	PRON
ejpam-5396	535	23	,	,	PUNCT
ejpam-5396	535	24	r	r	NOUN
ejpam-5396	535	25	0	0	NUM
ejpam-5396	535	26	0.1	0.1	NUM
ejpam-5396	535	27	0.2	0.2	NUM
ejpam-5396	535	28	0.3	0.3	NUM
ejpam-5396	535	29	0.4	0.4	NUM
ejpam-5396	535	30	0.5	0.5	NUM
ejpam-5396	535	31	0.6	0.6	NUM
ejpam-5396	535	32	0.7	0.7	NUM
ejpam-5396	535	33	0.8	0.8	NUM
ejpam-5396	535	34	0.9	0.9	NUM
ejpam-5396	535	35	1	1	NUM
ejpam-5396	535	36	s	s	NOUN
ejpam-5396	535	37	c	c	NOUN
ejpam-5396	535	38	i	i	PRON
ejpam-5396	535	39	r	r	NOUN
ejpam-5396	535	40	(	(	PUNCT
ejpam-5396	535	41	d	d	NOUN
ejpam-5396	535	42	)	)	PUNCT
ejpam-5396	535	43	time	time	NOUN
ejpam-5396	535	44	,	,	PUNCT
ejpam-5396	535	45	α=1	α=1	X
ejpam-5396	535	46	0	0	NUM
ejpam-5396	535	47	10	10	NUM
ejpam-5396	535	48	20	20	NUM
ejpam-5396	535	49	30	30	NUM
ejpam-5396	535	50	40	40	NUM
ejpam-5396	535	51	50	50	NUM
ejpam-5396	535	52	60	60	NUM
ejpam-5396	535	53	s	s	NOUN
ejpam-5396	535	54	,	,	PUNCT
ejpam-5396	535	55	c	c	PROPN
ejpam-5396	535	56	,	,	PUNCT
ejpam-5396	535	57	i	i	PRON
ejpam-5396	535	58	,	,	PUNCT
ejpam-5396	535	59	r	r	NOUN
ejpam-5396	535	60	-0.2	-0.2	PROPN
ejpam-5396	535	61	0	0	NUM
ejpam-5396	535	62	0.2	0.2	NUM
ejpam-5396	535	63	0.4	0.4	NUM
ejpam-5396	535	64	0.6	0.6	NUM
ejpam-5396	535	65	0.8	0.8	NUM
ejpam-5396	535	66	1	1	NUM
ejpam-5396	535	67	s	s	NOUN
ejpam-5396	535	68	c	c	NOUN
ejpam-5396	535	69	i	i	PRON
ejpam-5396	535	70	r	r	VERB
ejpam-5396	535	71	(	(	PUNCT
ejpam-5396	535	72	e	e	NOUN
ejpam-5396	535	73	)	)	PUNCT
ejpam-5396	535	74	figure	figure	NOUN
ejpam-5396	535	75	2	2	NUM
ejpam-5396	535	76	:	:	PUNCT
ejpam-5396	535	77	combined	combined	ADJ
ejpam-5396	535	78	graphical	graphical	ADJ
ejpam-5396	535	79	behaviors	behavior	NOUN
ejpam-5396	535	80	of	of	ADP
ejpam-5396	535	81	the	the	DET
ejpam-5396	535	82	abmm	abmm	NOUN
ejpam-5396	535	83	method	method	NOUN
ejpam-5396	535	84	for	for	ADP
ejpam-5396	535	85	s(t	s(t	PROPN
ejpam-5396	535	86	)	)	PUNCT
ejpam-5396	535	87	,	,	PUNCT
ejpam-5396	535	88	c(t	c(t	PROPN
ejpam-5396	535	89	)	)	PUNCT
ejpam-5396	535	90	,	,	PUNCT
ejpam-5396	535	91	i(t	i(t	PROPN
ejpam-5396	535	92	)	)	PUNCT
ejpam-5396	535	93	,	,	PUNCT
ejpam-5396	535	94	and	and	CCONJ
ejpam-5396	535	95	r(t	r(t	NOUN
ejpam-5396	535	96	)	)	PUNCT
ejpam-5396	535	97	at	at	ADP
ejpam-5396	535	98	various	various	ADJ
ejpam-5396	535	99	values	value	NOUN
ejpam-5396	535	100	of	of	ADP
ejpam-5396	535	101	α	α	NOUN
ejpam-5396	535	102	=	=	SYM
ejpam-5396	535	103	0.65	0.65	NUM
ejpam-5396	535	104	,	,	PUNCT
ejpam-5396	535	105	0.75	0.75	NUM
ejpam-5396	535	106	,	,	PUNCT
ejpam-5396	535	107	0.85	0.85	NUM
ejpam-5396	535	108	,	,	PUNCT
ejpam-5396	535	109	0.95	0.95	NUM
ejpam-5396	535	110	,	,	PUNCT
ejpam-5396	535	111	1	1	NUM
ejpam-5396	535	112	.	.	PUNCT
ejpam-5396	535	113	a.	a.	NOUN
ejpam-5396	535	114	alalyani	alalyani	PROPN
ejpam-5396	535	115	/	/	SYM
ejpam-5396	535	116	eur	eur	PROPN
ejpam-5396	535	117	.	.	PUNCT
ejpam-5396	536	1	j.	j.	PROPN
ejpam-5396	536	2	pure	pure	PROPN
ejpam-5396	536	3	appl	appl	PROPN
ejpam-5396	536	4	.	.	PROPN
ejpam-5396	536	5	math	math	PROPN
ejpam-5396	536	6	,	,	PUNCT
ejpam-5396	536	7	17	17	NUM
ejpam-5396	536	8	(	(	PUNCT
ejpam-5396	536	9	4	4	NUM
ejpam-5396	536	10	)	)	PUNCT
ejpam-5396	536	11	(	(	PUNCT
ejpam-5396	536	12	2024	2024	NUM
ejpam-5396	536	13	)	)	PUNCT
ejpam-5396	536	14	,	,	PUNCT
ejpam-5396	536	15	2763	2763	NUM
ejpam-5396	536	16	-	-	SYM
ejpam-5396	536	17	2799	2799	NUM
ejpam-5396	536	18	2787	2787	NUM
ejpam-5396	536	19	5.2	5.2	NUM
ejpam-5396	536	20	.	.	PUNCT
ejpam-5396	537	1	numerical	numerical	ADJ
ejpam-5396	537	2	simulations	simulation	NOUN
ejpam-5396	537	3	and	and	CCONJ
ejpam-5396	537	4	results	result	NOUN
ejpam-5396	537	5	of	of	ADP
ejpam-5396	537	6	the	the	DET
ejpam-5396	537	7	gem	gem	NOUN
ejpam-5396	537	8	method	method	NOUN
ejpam-5396	537	9	in	in	ADP
ejpam-5396	537	10	this	this	DET
ejpam-5396	537	11	subsection	subsection	NOUN
ejpam-5396	537	12	,	,	PUNCT
ejpam-5396	537	13	we	we	PRON
ejpam-5396	537	14	present	present	VERB
ejpam-5396	537	15	numerical	numerical	ADJ
ejpam-5396	537	16	simulations	simulation	NOUN
ejpam-5396	537	17	and	and	CCONJ
ejpam-5396	537	18	results	result	NOUN
ejpam-5396	537	19	for	for	ADP
ejpam-5396	537	20	the	the	DET
ejpam-5396	537	21	model	model	NOUN
ejpam-5396	537	22	(	(	PUNCT
ejpam-5396	537	23	1	1	NUM
ejpam-5396	537	24	)	)	PUNCT
ejpam-5396	537	25	solution	solution	NOUN
ejpam-5396	537	26	applying	apply	VERB
ejpam-5396	537	27	the	the	DET
ejpam-5396	537	28	gem	gem	NOUN
ejpam-5396	537	29	method	method	NOUN
ejpam-5396	537	30	.	.	PUNCT
ejpam-5396	538	1	the	the	DET
ejpam-5396	538	2	solution	solution	NOUN
ejpam-5396	538	3	to	to	ADP
ejpam-5396	538	4	the	the	DET
ejpam-5396	538	5	proposed	propose	VERB
ejpam-5396	538	6	model	model	NOUN
ejpam-5396	538	7	(	(	PUNCT
ejpam-5396	538	8	1	1	X
ejpam-5396	538	9	)	)	PUNCT
ejpam-5396	538	10	using	use	VERB
ejpam-5396	538	11	the	the	DET
ejpam-5396	538	12	generalized	generalize	VERB
ejpam-5396	538	13	euler	euler	NOUN
ejpam-5396	538	14	method	method	NOUN
ejpam-5396	538	15	appears	appear	VERB
ejpam-5396	538	16	in	in	ADP
ejpam-5396	538	17	figures	figure	NOUN
ejpam-5396	538	18	3(a	3(a	NUM
ejpam-5396	538	19	,	,	PUNCT
ejpam-5396	538	20	b	b	NOUN
ejpam-5396	538	21	,	,	PUNCT
ejpam-5396	538	22	c	c	NOUN
ejpam-5396	538	23	,	,	PUNCT
ejpam-5396	538	24	d	d	NOUN
ejpam-5396	538	25	)	)	PUNCT
ejpam-5396	538	26	and	and	CCONJ
ejpam-5396	538	27	figures	figure	NOUN
ejpam-5396	538	28	4(a	4(a	NUM
ejpam-5396	538	29	,	,	PUNCT
ejpam-5396	538	30	b	b	NOUN
ejpam-5396	538	31	,	,	PUNCT
ejpam-5396	538	32	c	c	NOUN
ejpam-5396	538	33	,	,	PUNCT
ejpam-5396	538	34	d	d	NOUN
ejpam-5396	538	35	,	,	PUNCT
ejpam-5396	538	36	e	e	NOUN
ejpam-5396	538	37	)	)	PUNCT
ejpam-5396	538	38	.	.	PUNCT
ejpam-5396	539	1	according	accord	VERB
ejpam-5396	539	2	to	to	ADP
ejpam-5396	539	3	these	these	DET
ejpam-5396	539	4	figures	figure	NOUN
ejpam-5396	539	5	,	,	PUNCT
ejpam-5396	539	6	we	we	PRON
ejpam-5396	539	7	observe	observe	VERB
ejpam-5396	539	8	that	that	SCONJ
ejpam-5396	539	9	s(t	s(t	PROPN
ejpam-5396	539	10	)	)	PUNCT
ejpam-5396	539	11	increases	increase	NOUN
ejpam-5396	539	12	at	at	ADP
ejpam-5396	539	13	α	α	NOUN
ejpam-5396	539	14	=	=	SYM
ejpam-5396	539	15	1	1	NUM
ejpam-5396	539	16	than	than	ADP
ejpam-5396	539	17	in	in	ADP
ejpam-5396	539	18	the	the	DET
ejpam-5396	539	19	case	case	NOUN
ejpam-5396	539	20	where	where	SCONJ
ejpam-5396	539	21	α	α	NOUN
ejpam-5396	539	22	is	be	AUX
ejpam-5396	539	23	a	a	DET
ejpam-5396	539	24	fractional	fractional	ADJ
ejpam-5396	539	25	variant	variant	NOUN
ejpam-5396	539	26	.	.	PUNCT
ejpam-5396	540	1	we	we	PRON
ejpam-5396	540	2	also	also	ADV
ejpam-5396	540	3	note	note	VERB
ejpam-5396	540	4	that	that	SCONJ
ejpam-5396	540	5	c(t	c(t	PROPN
ejpam-5396	540	6	)	)	PUNCT
ejpam-5396	540	7	and	and	CCONJ
ejpam-5396	540	8	i(t	i(t	NOUN
ejpam-5396	540	9	)	)	PUNCT
ejpam-5396	540	10	decrease	decrease	NOUN
ejpam-5396	540	11	at	at	ADP
ejpam-5396	540	12	α	α	NOUN
ejpam-5396	540	13	=	=	SYM
ejpam-5396	540	14	1	1	NUM
ejpam-5396	540	15	than	than	ADP
ejpam-5396	540	16	in	in	ADP
ejpam-5396	540	17	the	the	DET
ejpam-5396	540	18	case	case	NOUN
ejpam-5396	540	19	where	where	SCONJ
ejpam-5396	540	20	α	α	NOUN
ejpam-5396	540	21	is	be	AUX
ejpam-5396	540	22	a	a	DET
ejpam-5396	540	23	fractional	fractional	ADJ
ejpam-5396	540	24	variant	variant	NOUN
ejpam-5396	540	25	.	.	PUNCT
ejpam-5396	541	1	for	for	ADP
ejpam-5396	541	2	r(t	r(t	NOUN
ejpam-5396	541	3	)	)	PUNCT
ejpam-5396	541	4	,	,	PUNCT
ejpam-5396	541	5	the	the	DET
ejpam-5396	541	6	dynamical	dynamical	ADJ
ejpam-5396	541	7	behavior	behavior	NOUN
ejpam-5396	541	8	increases	increase	VERB
ejpam-5396	541	9	at	at	ADP
ejpam-5396	541	10	α	α	NOUN
ejpam-5396	541	11	=	=	NOUN
ejpam-5396	541	12	1	1	NUM
ejpam-5396	541	13	in	in	ADP
ejpam-5396	541	14	the	the	DET
ejpam-5396	541	15	first	first	ADJ
ejpam-5396	541	16	days	day	NOUN
ejpam-5396	541	17	and	and	CCONJ
ejpam-5396	541	18	then	then	ADV
ejpam-5396	541	19	gets	get	AUX
ejpam-5396	541	20	remarkably	remarkably	ADV
ejpam-5396	541	21	decreased	decrease	VERB
ejpam-5396	541	22	,	,	PUNCT
ejpam-5396	541	23	as	as	ADV
ejpam-5396	541	24	well	well	ADV
ejpam-5396	541	25	as	as	ADP
ejpam-5396	541	26	in	in	ADP
ejpam-5396	541	27	the	the	DET
ejpam-5396	541	28	case	case	NOUN
ejpam-5396	541	29	where	where	SCONJ
ejpam-5396	541	30	α	α	NOUN
ejpam-5396	541	31	is	be	AUX
ejpam-5396	541	32	a	a	DET
ejpam-5396	541	33	fractional	fractional	ADJ
ejpam-5396	541	34	variant	variant	NOUN
ejpam-5396	541	35	.	.	PUNCT
ejpam-5396	542	1	0	0	NUM
ejpam-5396	543	1	20	20	NUM
ejpam-5396	543	2	40	40	NUM
ejpam-5396	543	3	60	60	NUM
ejpam-5396	543	4	80	80	NUM
ejpam-5396	543	5	100	100	NUM
ejpam-5396	543	6	0.90	0.90	NUM
ejpam-5396	543	7	0.92	0.92	NUM
ejpam-5396	543	8	0.94	0.94	NUM
ejpam-5396	543	9	0.96	0.96	NUM
ejpam-5396	543	10	0.98	0.98	NUM
ejpam-5396	543	11	1.00	1.00	NUM
ejpam-5396	543	12	time	time	NOUN
ejpam-5396	543	13	(	(	PUNCT
ejpam-5396	543	14	days	day	NOUN
ejpam-5396	543	15	)	)	PUNCT
ejpam-5396	543	16	s	s	PART
ejpam-5396	543	17	�	�	NOUN
ejpam-5396	543	18	=	=	NOUN
ejpam-5396	543	19	0.65	0.65	NUM
ejpam-5396	543	20	�	�	NOUN
ejpam-5396	543	21	=	=	PRON
ejpam-5396	543	22	0.75	0.75	NUM
ejpam-5396	543	23	(	(	PUNCT
ejpam-5396	543	24	a	a	NOUN
ejpam-5396	543	25	)	)	PUNCT
ejpam-5396	543	26	0	0	NUM
ejpam-5396	543	27	20	20	NUM
ejpam-5396	543	28	40	40	NUM
ejpam-5396	543	29	60	60	NUM
ejpam-5396	543	30	80	80	NUM
ejpam-5396	543	31	100	100	NUM
ejpam-5396	543	32	0.00	0.00	NUM
ejpam-5396	543	33	0.02	0.02	NUM
ejpam-5396	543	34	0.04	0.04	NUM
ejpam-5396	543	35	0.06	0.06	NUM
ejpam-5396	543	36	0.08	0.08	NUM
ejpam-5396	543	37	0.10	0.10	NUM
ejpam-5396	543	38	time	time	NOUN
ejpam-5396	543	39	(	(	PUNCT
ejpam-5396	543	40	days	day	NOUN
ejpam-5396	543	41	)	)	PUNCT
ejpam-5396	543	42	c	c	NOUN
ejpam-5396	543	43	�	�	PROPN
ejpam-5396	543	44	=	=	NOUN
ejpam-5396	543	45	1	1	NUM
ejpam-5396	543	46	(	(	PUNCT
ejpam-5396	543	47	b	b	NOUN
ejpam-5396	543	48	)	)	PUNCT
ejpam-5396	543	49	0	0	NUM
ejpam-5396	543	50	20	20	NUM
ejpam-5396	543	51	40	40	NUM
ejpam-5396	543	52	60	60	NUM
ejpam-5396	543	53	80	80	NUM
ejpam-5396	543	54	100	100	NUM
ejpam-5396	543	55	0.00	0.00	NUM
ejpam-5396	543	56	0.02	0.02	NUM
ejpam-5396	543	57	0.04	0.04	NUM
ejpam-5396	543	58	0.06	0.06	NUM
ejpam-5396	543	59	0.08	0.08	NUM
ejpam-5396	543	60	0.10	0.10	NUM
ejpam-5396	543	61	time	time	NOUN
ejpam-5396	543	62	(	(	PUNCT
ejpam-5396	543	63	days	day	NOUN
ejpam-5396	543	64	)	)	PUNCT
ejpam-5396	543	65	i	i	PRON
ejpam-5396	543	66	�	�	X
ejpam-5396	543	67	=	=	ADJ
ejpam-5396	543	68	1	1	NUM
ejpam-5396	543	69	(	(	PUNCT
ejpam-5396	543	70	c	c	NOUN
ejpam-5396	543	71	)	)	PUNCT
ejpam-5396	543	72	0	0	NUM
ejpam-5396	543	73	20	20	NUM
ejpam-5396	543	74	40	40	NUM
ejpam-5396	543	75	60	60	NUM
ejpam-5396	543	76	80	80	NUM
ejpam-5396	543	77	100	100	NUM
ejpam-5396	543	78	0.00	0.00	NUM
ejpam-5396	543	79	0.02	0.02	NUM
ejpam-5396	543	80	0.04	0.04	NUM
ejpam-5396	543	81	0.06	0.06	NUM
ejpam-5396	543	82	0.08	0.08	NUM
ejpam-5396	543	83	0.10	0.10	NUM
ejpam-5396	543	84	0.12	0.12	NUM
ejpam-5396	543	85	time	time	NOUN
ejpam-5396	543	86	(	(	PUNCT
ejpam-5396	543	87	days	day	NOUN
ejpam-5396	543	88	)	)	PUNCT
ejpam-5396	543	89	r	r	NOUN
ejpam-5396	543	90	�	�	NOUN
ejpam-5396	543	91	=	=	SYM
ejpam-5396	543	92	0.65	0.65	NUM
ejpam-5396	543	93	�	�	NOUN
ejpam-5396	543	94	=	=	SYM
ejpam-5396	543	95	0.75	0.75	NUM
ejpam-5396	543	96	�	�	NOUN
ejpam-5396	543	97	=	=	SYM
ejpam-5396	543	98	0.85	0.85	NUM
ejpam-5396	543	99	�	�	NOUN
ejpam-5396	543	100	=	=	NOUN
ejpam-5396	543	101	0.95	0.95	NUM
ejpam-5396	543	102	�	�	NOUN
ejpam-5396	543	103	=	=	NOUN
ejpam-5396	543	104	1	1	NUM
ejpam-5396	543	105	(	(	PUNCT
ejpam-5396	543	106	d	d	NOUN
ejpam-5396	543	107	)	)	PUNCT
ejpam-5396	543	108	figure	figure	NOUN
ejpam-5396	543	109	3	3	NUM
ejpam-5396	543	110	:	:	PUNCT
ejpam-5396	543	111	the	the	DET
ejpam-5396	543	112	gem	gem	NOUN
ejpam-5396	543	113	method	method	NOUN
ejpam-5396	543	114	for	for	ADP
ejpam-5396	543	115	the	the	DET
ejpam-5396	543	116	behavior	behavior	NOUN
ejpam-5396	543	117	of	of	ADP
ejpam-5396	543	118	s(t	s(t	PROPN
ejpam-5396	543	119	)	)	PUNCT
ejpam-5396	543	120	,	,	PUNCT
ejpam-5396	543	121	c(t	c(t	PROPN
ejpam-5396	543	122	)	)	PUNCT
ejpam-5396	543	123	,	,	PUNCT
ejpam-5396	543	124	i(t	i(t	PROPN
ejpam-5396	543	125	)	)	PUNCT
ejpam-5396	543	126	,	,	PUNCT
ejpam-5396	543	127	and	and	CCONJ
ejpam-5396	543	128	r(t	r(t	NOUN
ejpam-5396	543	129	)	)	PUNCT
ejpam-5396	543	130	at	at	ADP
ejpam-5396	543	131	various	various	ADJ
ejpam-5396	543	132	values	value	NOUN
ejpam-5396	543	133	of	of	ADP
ejpam-5396	543	134	α	α	NOUN
ejpam-5396	543	135	=	=	SYM
ejpam-5396	543	136	0.65	0.65	NUM
ejpam-5396	543	137	,	,	PUNCT
ejpam-5396	543	138	0.75	0.75	NUM
ejpam-5396	543	139	,	,	PUNCT
ejpam-5396	543	140	0.85	0.85	NUM
ejpam-5396	543	141	,	,	PUNCT
ejpam-5396	543	142	0.95	0.95	NUM
ejpam-5396	543	143	,	,	PUNCT
ejpam-5396	543	144	1	1	NUM
ejpam-5396	543	145	.	.	PUNCT
ejpam-5396	543	146	a.	a.	NOUN
ejpam-5396	543	147	alalyani	alalyani	PROPN
ejpam-5396	543	148	/	/	SYM
ejpam-5396	543	149	eur	eur	PROPN
ejpam-5396	543	150	.	.	PUNCT
ejpam-5396	544	1	j.	j.	PROPN
ejpam-5396	544	2	pure	pure	PROPN
ejpam-5396	544	3	appl	appl	PROPN
ejpam-5396	544	4	.	.	PROPN
ejpam-5396	544	5	math	math	PROPN
ejpam-5396	544	6	,	,	PUNCT
ejpam-5396	544	7	17	17	NUM
ejpam-5396	544	8	(	(	PUNCT
ejpam-5396	544	9	4	4	NUM
ejpam-5396	544	10	)	)	PUNCT
ejpam-5396	544	11	(	(	PUNCT
ejpam-5396	544	12	2024	2024	NUM
ejpam-5396	544	13	)	)	PUNCT
ejpam-5396	544	14	,	,	PUNCT
ejpam-5396	544	15	2763	2763	NUM
ejpam-5396	544	16	-	-	SYM
ejpam-5396	544	17	2799	2799	NUM
ejpam-5396	544	18	2788	2788	NUM
ejpam-5396	544	19	0	0	NUM
ejpam-5396	544	20	20	20	NUM
ejpam-5396	544	21	40	40	NUM
ejpam-5396	544	22	60	60	NUM
ejpam-5396	544	23	80	80	NUM
ejpam-5396	544	24	100	100	NUM
ejpam-5396	544	25	0.0	0.0	NUM
ejpam-5396	544	26	0.2	0.2	NUM
ejpam-5396	544	27	0.4	0.4	NUM
ejpam-5396	544	28	0.6	0.6	NUM
ejpam-5396	544	29	0.8	0.8	NUM
ejpam-5396	544	30	1.0	1.0	NUM
ejpam-5396	544	31	time	time	NOUN
ejpam-5396	544	32	(	(	PUNCT
ejpam-5396	544	33	days),	days),	X
ejpam-5396	544	34	�	�	PROPN
ejpam-5396	544	35	=0.65	=0.65	PROPN
ejpam-5396	544	36	s	s	PART
ejpam-5396	544	37	,	,	PUNCT
ejpam-5396	544	38	c	c	PROPN
ejpam-5396	544	39	,	,	PUNCT
ejpam-5396	544	40	i	i	PRON
ejpam-5396	544	41	,	,	PUNCT
ejpam-5396	545	1	r	r	NOUN
ejpam-5396	545	2	r	r	NOUN
ejpam-5396	546	1	i	i	NOUN
ejpam-5396	546	2	c	c	NOUN
ejpam-5396	546	3	s	s	X
ejpam-5396	546	4	(	(	PUNCT
ejpam-5396	546	5	a	a	NOUN
ejpam-5396	546	6	)	)	PUNCT
ejpam-5396	546	7	0	0	NUM
ejpam-5396	546	8	20	20	NUM
ejpam-5396	546	9	40	40	NUM
ejpam-5396	546	10	60	60	NUM
ejpam-5396	546	11	80	80	NUM
ejpam-5396	546	12	100	100	NUM
ejpam-5396	546	13	0.0	0.0	NUM
ejpam-5396	546	14	0.2	0.2	NUM
ejpam-5396	546	15	0.4	0.4	NUM
ejpam-5396	546	16	0.6	0.6	NUM
ejpam-5396	546	17	0.8	0.8	NUM
ejpam-5396	546	18	1.0	1.0	NUM
ejpam-5396	546	19	time	time	NOUN
ejpam-5396	546	20	(	(	PUNCT
ejpam-5396	546	21	days),	days),	NUM
ejpam-5396	546	22	�	�	NOUN
ejpam-5396	546	23	=0.75	=0.75	PROPN
ejpam-5396	546	24	s	s	PART
ejpam-5396	546	25	,	,	PUNCT
ejpam-5396	546	26	c	c	PROPN
ejpam-5396	546	27	,	,	PUNCT
ejpam-5396	546	28	i	i	PRON
ejpam-5396	546	29	,	,	PUNCT
ejpam-5396	546	30	r	r	NOUN
ejpam-5396	546	31	r	r	NOUN
ejpam-5396	547	1	i	i	NOUN
ejpam-5396	547	2	c	c	NOUN
ejpam-5396	547	3	s	s	X
ejpam-5396	547	4	(	(	PUNCT
ejpam-5396	547	5	b	b	NOUN
ejpam-5396	547	6	)	)	PUNCT
ejpam-5396	547	7	0	0	NUM
ejpam-5396	547	8	20	20	NUM
ejpam-5396	547	9	40	40	NUM
ejpam-5396	547	10	60	60	NUM
ejpam-5396	547	11	80	80	NUM
ejpam-5396	547	12	100	100	NUM
ejpam-5396	547	13	0.0	0.0	NUM
ejpam-5396	547	14	0.2	0.2	NUM
ejpam-5396	547	15	0.4	0.4	NUM
ejpam-5396	547	16	0.6	0.6	NUM
ejpam-5396	547	17	0.8	0.8	NUM
ejpam-5396	547	18	1.0	1.0	NUM
ejpam-5396	547	19	time	time	NOUN
ejpam-5396	547	20	(	(	PUNCT
ejpam-5396	547	21	days),	days),	X
ejpam-5396	547	22	�	�	NOUN
ejpam-5396	547	23	=0.85	=0.85	PROPN
ejpam-5396	547	24	s	s	PART
ejpam-5396	547	25	,	,	PUNCT
ejpam-5396	547	26	c	c	PROPN
ejpam-5396	547	27	,	,	PUNCT
ejpam-5396	547	28	i	i	PRON
ejpam-5396	547	29	,	,	PUNCT
ejpam-5396	548	1	r	r	NOUN
ejpam-5396	548	2	r	r	NOUN
ejpam-5396	548	3	i	i	NOUN
ejpam-5396	548	4	c	c	NOUN
ejpam-5396	548	5	s	s	X
ejpam-5396	548	6	(	(	PUNCT
ejpam-5396	548	7	c	c	NOUN
ejpam-5396	548	8	)	)	PUNCT
ejpam-5396	548	9	0	0	NUM
ejpam-5396	548	10	20	20	NUM
ejpam-5396	548	11	40	40	NUM
ejpam-5396	548	12	60	60	NUM
ejpam-5396	548	13	80	80	NUM
ejpam-5396	548	14	100	100	NUM
ejpam-5396	548	15	0.0	0.0	NUM
ejpam-5396	548	16	0.2	0.2	NUM
ejpam-5396	548	17	0.4	0.4	NUM
ejpam-5396	548	18	0.6	0.6	NUM
ejpam-5396	548	19	0.8	0.8	NUM
ejpam-5396	548	20	time	time	NOUN
ejpam-5396	548	21	(	(	PUNCT
ejpam-5396	548	22	days),	days),	X
ejpam-5396	548	23	�	�	NOUN
ejpam-5396	548	24	=0.95	=0.95	NOUN
ejpam-5396	548	25	s	s	PART
ejpam-5396	548	26	,	,	PUNCT
ejpam-5396	548	27	c	c	NOUN
ejpam-5396	548	28	,	,	PUNCT
ejpam-5396	548	29	i	i	PRON
ejpam-5396	548	30	,	,	PUNCT
ejpam-5396	548	31	r	r	NOUN
ejpam-5396	548	32	r	r	NOUN
ejpam-5396	549	1	i	i	NOUN
ejpam-5396	549	2	c	c	NOUN
ejpam-5396	549	3	s	s	X
ejpam-5396	549	4	(	(	PUNCT
ejpam-5396	549	5	d	d	NOUN
ejpam-5396	549	6	)	)	PUNCT
ejpam-5396	549	7	0	0	NUM
ejpam-5396	549	8	20	20	NUM
ejpam-5396	549	9	40	40	NUM
ejpam-5396	549	10	60	60	NUM
ejpam-5396	549	11	80	80	NUM
ejpam-5396	549	12	100	100	NUM
ejpam-5396	549	13	0.0	0.0	NUM
ejpam-5396	549	14	0.2	0.2	NUM
ejpam-5396	549	15	0.4	0.4	NUM
ejpam-5396	549	16	0.6	0.6	NUM
ejpam-5396	549	17	0.8	0.8	NUM
ejpam-5396	549	18	time	time	NOUN
ejpam-5396	549	19	(	(	PUNCT
ejpam-5396	549	20	days),	days),	X
ejpam-5396	549	21	�	�	NOUN
ejpam-5396	549	22	=1	=1	NOUN
ejpam-5396	549	23	s	s	PART
ejpam-5396	549	24	,	,	PUNCT
ejpam-5396	549	25	c	c	PROPN
ejpam-5396	549	26	,	,	PUNCT
ejpam-5396	549	27	i	i	PRON
ejpam-5396	549	28	,	,	PUNCT
ejpam-5396	549	29	r	r	NOUN
ejpam-5396	549	30	r	r	NOUN
ejpam-5396	550	1	i	i	NOUN
ejpam-5396	550	2	c	c	NOUN
ejpam-5396	550	3	s	s	X
ejpam-5396	550	4	(	(	PUNCT
ejpam-5396	550	5	e	e	NOUN
ejpam-5396	550	6	)	)	PUNCT
ejpam-5396	550	7	figure	figure	NOUN
ejpam-5396	550	8	4	4	NUM
ejpam-5396	550	9	:	:	PUNCT
ejpam-5396	550	10	combined	combined	ADJ
ejpam-5396	550	11	graphical	graphical	ADJ
ejpam-5396	550	12	behaviors	behavior	NOUN
ejpam-5396	550	13	of	of	ADP
ejpam-5396	550	14	the	the	DET
ejpam-5396	550	15	gem	gem	NOUN
ejpam-5396	550	16	method	method	NOUN
ejpam-5396	550	17	for	for	ADP
ejpam-5396	550	18	s(t	s(t	PROPN
ejpam-5396	550	19	)	)	PUNCT
ejpam-5396	550	20	,	,	PUNCT
ejpam-5396	550	21	c(t	c(t	PROPN
ejpam-5396	550	22	)	)	PUNCT
ejpam-5396	550	23	,	,	PUNCT
ejpam-5396	550	24	i(t	i(t	PROPN
ejpam-5396	550	25	)	)	PUNCT
ejpam-5396	550	26	,	,	PUNCT
ejpam-5396	550	27	and	and	CCONJ
ejpam-5396	550	28	r(t	r(t	NOUN
ejpam-5396	550	29	)	)	PUNCT
ejpam-5396	550	30	at	at	ADP
ejpam-5396	550	31	various	various	ADJ
ejpam-5396	550	32	values	value	NOUN
ejpam-5396	550	33	of	of	ADP
ejpam-5396	550	34	α	α	NOUN
ejpam-5396	550	35	=	=	SYM
ejpam-5396	550	36	0.65	0.65	NUM
ejpam-5396	550	37	,	,	PUNCT
ejpam-5396	550	38	0.75	0.75	NUM
ejpam-5396	550	39	,	,	PUNCT
ejpam-5396	550	40	0.85	0.85	NUM
ejpam-5396	550	41	,	,	PUNCT
ejpam-5396	550	42	0.95	0.95	NUM
ejpam-5396	550	43	,	,	PUNCT
ejpam-5396	550	44	1	1	NUM
ejpam-5396	550	45	.	.	PUNCT
ejpam-5396	550	46	a.	a.	NOUN
ejpam-5396	550	47	alalyani	alalyani	PROPN
ejpam-5396	550	48	/	/	SYM
ejpam-5396	550	49	eur	eur	PROPN
ejpam-5396	550	50	.	.	PUNCT
ejpam-5396	551	1	j.	j.	PROPN
ejpam-5396	551	2	pure	pure	PROPN
ejpam-5396	551	3	appl	appl	PROPN
ejpam-5396	551	4	.	.	PROPN
ejpam-5396	551	5	math	math	PROPN
ejpam-5396	551	6	,	,	PUNCT
ejpam-5396	551	7	17	17	NUM
ejpam-5396	551	8	(	(	PUNCT
ejpam-5396	551	9	4	4	NUM
ejpam-5396	551	10	)	)	PUNCT
ejpam-5396	551	11	(	(	PUNCT
ejpam-5396	551	12	2024	2024	NUM
ejpam-5396	551	13	)	)	PUNCT
ejpam-5396	551	14	,	,	PUNCT
ejpam-5396	551	15	2763	2763	NUM
ejpam-5396	551	16	-	-	SYM
ejpam-5396	551	17	2799	2799	NUM
ejpam-5396	551	18	2789	2789	NUM
ejpam-5396	551	19	5.3	5.3	NUM
ejpam-5396	551	20	.	.	PUNCT
ejpam-5396	552	1	numerical	numerical	ADJ
ejpam-5396	552	2	simulations	simulation	NOUN
ejpam-5396	552	3	and	and	CCONJ
ejpam-5396	552	4	results	result	NOUN
ejpam-5396	552	5	of	of	ADP
ejpam-5396	552	6	the	the	DET
ejpam-5396	552	7	grkm	grkm	NOUN
ejpam-5396	552	8	method	method	NOUN
ejpam-5396	552	9	in	in	ADP
ejpam-5396	552	10	this	this	DET
ejpam-5396	552	11	subsection	subsection	NOUN
ejpam-5396	552	12	,	,	PUNCT
ejpam-5396	552	13	we	we	PRON
ejpam-5396	552	14	present	present	VERB
ejpam-5396	552	15	numerical	numerical	ADJ
ejpam-5396	552	16	simulations	simulation	NOUN
ejpam-5396	552	17	and	and	CCONJ
ejpam-5396	552	18	results	result	NOUN
ejpam-5396	552	19	for	for	ADP
ejpam-5396	552	20	the	the	DET
ejpam-5396	552	21	model	model	NOUN
ejpam-5396	552	22	(	(	PUNCT
ejpam-5396	552	23	1	1	NUM
ejpam-5396	552	24	)	)	PUNCT
ejpam-5396	552	25	solution	solution	NOUN
ejpam-5396	552	26	applying	apply	VERB
ejpam-5396	552	27	the	the	DET
ejpam-5396	552	28	grkm	grkm	NOUN
ejpam-5396	552	29	method	method	NOUN
ejpam-5396	552	30	.	.	PUNCT
ejpam-5396	553	1	in	in	ADP
ejpam-5396	553	2	figures	figure	NOUN
ejpam-5396	553	3	5(a	5(a	NUM
ejpam-5396	553	4	,	,	PUNCT
ejpam-5396	553	5	b	b	NOUN
ejpam-5396	553	6	,	,	PUNCT
ejpam-5396	553	7	c	c	NOUN
ejpam-5396	553	8	,	,	PUNCT
ejpam-5396	553	9	d	d	NOUN
ejpam-5396	553	10	)	)	PUNCT
ejpam-5396	554	1	and	and	CCONJ
ejpam-5396	554	2	figures	figure	NOUN
ejpam-5396	554	3	6(a	6(a	NUM
ejpam-5396	554	4	,	,	PUNCT
ejpam-5396	554	5	b	b	NOUN
ejpam-5396	554	6	,	,	PUNCT
ejpam-5396	554	7	c	c	NOUN
ejpam-5396	554	8	,	,	PUNCT
ejpam-5396	554	9	d	d	NOUN
ejpam-5396	554	10	,	,	PUNCT
ejpam-5396	554	11	e	e	NOUN
ejpam-5396	554	12	)	)	PUNCT
ejpam-5396	554	13	,	,	PUNCT
ejpam-5396	554	14	we	we	PRON
ejpam-5396	554	15	present	present	VERB
ejpam-5396	554	16	the	the	DET
ejpam-5396	554	17	solution	solution	NOUN
ejpam-5396	554	18	to	to	ADP
ejpam-5396	554	19	the	the	DET
ejpam-5396	554	20	proposed	propose	VERB
ejpam-5396	554	21	model	model	NOUN
ejpam-5396	554	22	(	(	PUNCT
ejpam-5396	554	23	1	1	X
ejpam-5396	554	24	)	)	PUNCT
ejpam-5396	554	25	using	use	VERB
ejpam-5396	554	26	the	the	DET
ejpam-5396	554	27	generalized	generalize	VERB
ejpam-5396	554	28	runge	runge	NOUN
ejpam-5396	554	29	-	-	PUNCT
ejpam-5396	554	30	kutta	kutta	NOUN
ejpam-5396	554	31	method	method	NOUN
ejpam-5396	554	32	.	.	PUNCT
ejpam-5396	555	1	according	accord	VERB
ejpam-5396	555	2	to	to	ADP
ejpam-5396	555	3	these	these	DET
ejpam-5396	555	4	figures	figure	NOUN
ejpam-5396	555	5	,	,	PUNCT
ejpam-5396	555	6	we	we	PRON
ejpam-5396	555	7	observe	observe	VERB
ejpam-5396	555	8	that	that	SCONJ
ejpam-5396	555	9	s(t	s(t	PROPN
ejpam-5396	555	10	)	)	PUNCT
ejpam-5396	555	11	increases	increase	VERB
ejpam-5396	555	12	more	more	ADJ
ejpam-5396	555	13	in	in	ADP
ejpam-5396	555	14	the	the	DET
ejpam-5396	555	15	case	case	NOUN
ejpam-5396	555	16	where	where	SCONJ
ejpam-5396	555	17	α	α	NOUN
ejpam-5396	555	18	is	be	AUX
ejpam-5396	555	19	a	a	DET
ejpam-5396	555	20	fractional	fractional	ADJ
ejpam-5396	555	21	variant	variant	NOUN
ejpam-5396	555	22	than	than	ADP
ejpam-5396	555	23	in	in	ADP
ejpam-5396	555	24	the	the	DET
ejpam-5396	555	25	case	case	NOUN
ejpam-5396	555	26	where	where	SCONJ
ejpam-5396	555	27	α	α	NOUN
ejpam-5396	555	28	=	=	NOUN
ejpam-5396	555	29	1	1	X
ejpam-5396	555	30	.	.	PUNCT
ejpam-5396	556	1	we	we	PRON
ejpam-5396	556	2	also	also	ADV
ejpam-5396	556	3	note	note	VERB
ejpam-5396	556	4	that	that	SCONJ
ejpam-5396	556	5	c(t	c(t	PROPN
ejpam-5396	556	6	)	)	PUNCT
ejpam-5396	556	7	,	,	PUNCT
ejpam-5396	556	8	i(t	i(t	PROPN
ejpam-5396	556	9	)	)	PUNCT
ejpam-5396	556	10	,	,	PUNCT
ejpam-5396	556	11	and	and	CCONJ
ejpam-5396	556	12	r(t	r(t	NOUN
ejpam-5396	556	13	)	)	PUNCT
ejpam-5396	556	14	decrease	decrease	VERB
ejpam-5396	556	15	more	more	ADJ
ejpam-5396	556	16	in	in	ADP
ejpam-5396	556	17	the	the	DET
ejpam-5396	556	18	case	case	NOUN
ejpam-5396	556	19	where	where	SCONJ
ejpam-5396	556	20	α	α	NOUN
ejpam-5396	556	21	is	be	AUX
ejpam-5396	556	22	a	a	DET
ejpam-5396	556	23	fractional	fractional	ADJ
ejpam-5396	556	24	variant	variant	NOUN
ejpam-5396	556	25	than	than	ADP
ejpam-5396	556	26	in	in	ADP
ejpam-5396	556	27	the	the	DET
ejpam-5396	556	28	case	case	NOUN
ejpam-5396	556	29	where	where	SCONJ
ejpam-5396	556	30	α	α	NOUN
ejpam-5396	556	31	=	=	NOUN
ejpam-5396	556	32	1	1	X
ejpam-5396	556	33	.	.	PUNCT
ejpam-5396	557	1	(	(	PUNCT
ejpam-5396	557	2	a	a	X
ejpam-5396	557	3	)	)	PUNCT
ejpam-5396	557	4	(	(	PUNCT
ejpam-5396	557	5	b	b	X
ejpam-5396	557	6	)	)	PUNCT
ejpam-5396	557	7	(	(	PUNCT
ejpam-5396	557	8	c	c	X
ejpam-5396	557	9	)	)	PUNCT
ejpam-5396	557	10	(	(	PUNCT
ejpam-5396	557	11	d	d	X
ejpam-5396	557	12	)	)	PUNCT
ejpam-5396	557	13	figure	figure	NOUN
ejpam-5396	557	14	5	5	NUM
ejpam-5396	557	15	:	:	PUNCT
ejpam-5396	557	16	the	the	DET
ejpam-5396	557	17	grkm	grkm	NOUN
ejpam-5396	557	18	method	method	NOUN
ejpam-5396	557	19	for	for	ADP
ejpam-5396	557	20	the	the	DET
ejpam-5396	557	21	behavior	behavior	NOUN
ejpam-5396	557	22	of	of	ADP
ejpam-5396	557	23	s(t	s(t	PROPN
ejpam-5396	557	24	)	)	PUNCT
ejpam-5396	557	25	,	,	PUNCT
ejpam-5396	557	26	c(t	c(t	PROPN
ejpam-5396	557	27	)	)	PUNCT
ejpam-5396	557	28	,	,	PUNCT
ejpam-5396	557	29	i(t	i(t	PROPN
ejpam-5396	557	30	)	)	PUNCT
ejpam-5396	557	31	,	,	PUNCT
ejpam-5396	557	32	and	and	CCONJ
ejpam-5396	557	33	r(t	r(t	NOUN
ejpam-5396	557	34	)	)	PUNCT
ejpam-5396	557	35	at	at	ADP
ejpam-5396	557	36	various	various	ADJ
ejpam-5396	557	37	values	value	NOUN
ejpam-5396	557	38	of	of	ADP
ejpam-5396	557	39	α	α	NOUN
ejpam-5396	557	40	=	=	SYM
ejpam-5396	557	41	0.65	0.65	NUM
ejpam-5396	557	42	,	,	PUNCT
ejpam-5396	557	43	0.75	0.75	NUM
ejpam-5396	557	44	,	,	PUNCT
ejpam-5396	557	45	0.85	0.85	NUM
ejpam-5396	557	46	,	,	PUNCT
ejpam-5396	557	47	0.95	0.95	NUM
ejpam-5396	557	48	,	,	PUNCT
ejpam-5396	557	49	1	1	NUM
ejpam-5396	557	50	.	.	PUNCT
ejpam-5396	557	51	a.	a.	NOUN
ejpam-5396	557	52	alalyani	alalyani	PROPN
ejpam-5396	557	53	/	/	SYM
ejpam-5396	557	54	eur	eur	PROPN
ejpam-5396	557	55	.	.	PUNCT
ejpam-5396	558	1	j.	j.	PROPN
ejpam-5396	558	2	pure	pure	PROPN
ejpam-5396	558	3	appl	appl	PROPN
ejpam-5396	558	4	.	.	PROPN
ejpam-5396	558	5	math	math	PROPN
ejpam-5396	558	6	,	,	PUNCT
ejpam-5396	558	7	17	17	NUM
ejpam-5396	558	8	(	(	PUNCT
ejpam-5396	558	9	4	4	NUM
ejpam-5396	558	10	)	)	PUNCT
ejpam-5396	558	11	(	(	PUNCT
ejpam-5396	558	12	2024	2024	NUM
ejpam-5396	558	13	)	)	PUNCT
ejpam-5396	558	14	,	,	PUNCT
ejpam-5396	558	15	2763	2763	NUM
ejpam-5396	558	16	-	-	SYM
ejpam-5396	558	17	2799	2799	NUM
ejpam-5396	558	18	2790	2790	NUM
ejpam-5396	558	19	(	(	PUNCT
ejpam-5396	558	20	a	a	NOUN
ejpam-5396	558	21	)	)	PUNCT
ejpam-5396	558	22	(	(	PUNCT
ejpam-5396	558	23	b	b	X
ejpam-5396	558	24	)	)	PUNCT
ejpam-5396	558	25	(	(	PUNCT
ejpam-5396	558	26	c	c	X
ejpam-5396	558	27	)	)	PUNCT
ejpam-5396	558	28	(	(	PUNCT
ejpam-5396	558	29	d	d	X
ejpam-5396	558	30	)	)	PUNCT
ejpam-5396	558	31	(	(	PUNCT
ejpam-5396	558	32	e	e	NOUN
ejpam-5396	558	33	)	)	PUNCT
ejpam-5396	558	34	figure	figure	NOUN
ejpam-5396	558	35	6	6	NUM
ejpam-5396	558	36	:	:	PUNCT
ejpam-5396	558	37	combined	combined	ADJ
ejpam-5396	558	38	graphical	graphical	ADJ
ejpam-5396	558	39	behaviors	behavior	NOUN
ejpam-5396	558	40	of	of	ADP
ejpam-5396	558	41	the	the	DET
ejpam-5396	558	42	grkm	grkm	NOUN
ejpam-5396	558	43	method	method	NOUN
ejpam-5396	558	44	for	for	ADP
ejpam-5396	558	45	s(t	s(t	PROPN
ejpam-5396	558	46	)	)	PUNCT
ejpam-5396	558	47	,	,	PUNCT
ejpam-5396	558	48	c(t	c(t	PROPN
ejpam-5396	558	49	)	)	PUNCT
ejpam-5396	558	50	,	,	PUNCT
ejpam-5396	558	51	i(t	i(t	PROPN
ejpam-5396	558	52	)	)	PUNCT
ejpam-5396	558	53	,	,	PUNCT
ejpam-5396	558	54	and	and	CCONJ
ejpam-5396	558	55	r(t	r(t	NOUN
ejpam-5396	558	56	)	)	PUNCT
ejpam-5396	558	57	at	at	ADP
ejpam-5396	558	58	various	various	ADJ
ejpam-5396	558	59	values	value	NOUN
ejpam-5396	558	60	of	of	ADP
ejpam-5396	558	61	α	α	NOUN
ejpam-5396	558	62	=	=	SYM
ejpam-5396	558	63	0.65	0.65	NUM
ejpam-5396	558	64	,	,	PUNCT
ejpam-5396	558	65	0.75	0.75	NUM
ejpam-5396	558	66	,	,	PUNCT
ejpam-5396	558	67	0.85	0.85	NUM
ejpam-5396	558	68	,	,	PUNCT
ejpam-5396	558	69	0.95	0.95	NUM
ejpam-5396	558	70	,	,	PUNCT
ejpam-5396	558	71	1	1	NUM
ejpam-5396	558	72	.	.	PUNCT
ejpam-5396	558	73	a.	a.	NOUN
ejpam-5396	558	74	alalyani	alalyani	PROPN
ejpam-5396	558	75	/	/	SYM
ejpam-5396	558	76	eur	eur	PROPN
ejpam-5396	558	77	.	.	PUNCT
ejpam-5396	559	1	j.	j.	PROPN
ejpam-5396	559	2	pure	pure	PROPN
ejpam-5396	559	3	appl	appl	PROPN
ejpam-5396	559	4	.	.	PROPN
ejpam-5396	559	5	math	math	PROPN
ejpam-5396	559	6	,	,	PUNCT
ejpam-5396	559	7	17	17	NUM
ejpam-5396	559	8	(	(	PUNCT
ejpam-5396	559	9	4	4	NUM
ejpam-5396	559	10	)	)	PUNCT
ejpam-5396	559	11	(	(	PUNCT
ejpam-5396	559	12	2024	2024	NUM
ejpam-5396	559	13	)	)	PUNCT
ejpam-5396	559	14	,	,	PUNCT
ejpam-5396	559	15	2763	2763	NUM
ejpam-5396	559	16	-	-	SYM
ejpam-5396	559	17	2799	2799	NUM
ejpam-5396	559	18	2791	2791	NUM
ejpam-5396	559	19	5.4	5.4	NUM
ejpam-5396	559	20	.	.	PUNCT
ejpam-5396	560	1	numerical	numerical	ADJ
ejpam-5396	560	2	simulations	simulation	NOUN
ejpam-5396	560	3	and	and	CCONJ
ejpam-5396	560	4	results	result	NOUN
ejpam-5396	560	5	of	of	ADP
ejpam-5396	560	6	the	the	DET
ejpam-5396	560	7	msgdtm	msgdtm	NOUN
ejpam-5396	560	8	method	method	NOUN
ejpam-5396	560	9	in	in	ADP
ejpam-5396	560	10	this	this	DET
ejpam-5396	560	11	subsection	subsection	NOUN
ejpam-5396	560	12	,	,	PUNCT
ejpam-5396	560	13	we	we	PRON
ejpam-5396	560	14	present	present	VERB
ejpam-5396	560	15	numerical	numerical	ADJ
ejpam-5396	560	16	simulations	simulation	NOUN
ejpam-5396	560	17	and	and	CCONJ
ejpam-5396	560	18	results	result	NOUN
ejpam-5396	560	19	for	for	ADP
ejpam-5396	560	20	the	the	DET
ejpam-5396	560	21	model	model	NOUN
ejpam-5396	560	22	(	(	PUNCT
ejpam-5396	560	23	1	1	NUM
ejpam-5396	560	24	)	)	PUNCT
ejpam-5396	560	25	solution	solution	NOUN
ejpam-5396	560	26	applying	apply	VERB
ejpam-5396	560	27	the	the	DET
ejpam-5396	560	28	msgdtm	msgdtm	NOUN
ejpam-5396	560	29	method	method	NOUN
ejpam-5396	560	30	.	.	PUNCT
ejpam-5396	561	1	the	the	DET
ejpam-5396	561	2	solution	solution	NOUN
ejpam-5396	561	3	to	to	ADP
ejpam-5396	561	4	the	the	DET
ejpam-5396	561	5	proposed	propose	VERB
ejpam-5396	561	6	model	model	NOUN
ejpam-5396	561	7	(	(	PUNCT
ejpam-5396	561	8	1	1	X
ejpam-5396	561	9	)	)	PUNCT
ejpam-5396	561	10	using	use	VERB
ejpam-5396	561	11	the	the	DET
ejpam-5396	561	12	multistep	multistep	ADJ
ejpam-5396	561	13	generalized	generalize	VERB
ejpam-5396	561	14	differential	differential	ADJ
ejpam-5396	561	15	transformmethod	transformmethod	NOUN
ejpam-5396	561	16	appears	appear	VERB
ejpam-5396	561	17	in	in	ADP
ejpam-5396	561	18	figures	figure	NOUN
ejpam-5396	561	19	7(a	7(a	NUM
ejpam-5396	561	20	,	,	PUNCT
ejpam-5396	561	21	b	b	NOUN
ejpam-5396	561	22	,	,	PUNCT
ejpam-5396	561	23	c	c	NOUN
ejpam-5396	561	24	,	,	PUNCT
ejpam-5396	561	25	d	d	NOUN
ejpam-5396	561	26	)	)	PUNCT
ejpam-5396	561	27	and	and	CCONJ
ejpam-5396	561	28	figures	figure	NOUN
ejpam-5396	561	29	8(a	8(a	NUM
ejpam-5396	561	30	,	,	PUNCT
ejpam-5396	561	31	b	b	NOUN
ejpam-5396	561	32	,	,	PUNCT
ejpam-5396	561	33	c	c	NOUN
ejpam-5396	561	34	,	,	PUNCT
ejpam-5396	561	35	d	d	NOUN
ejpam-5396	561	36	,	,	PUNCT
ejpam-5396	561	37	e	e	NOUN
ejpam-5396	561	38	)	)	PUNCT
ejpam-5396	561	39	.	.	PUNCT
ejpam-5396	562	1	according	accord	VERB
ejpam-5396	562	2	to	to	ADP
ejpam-5396	562	3	these	these	DET
ejpam-5396	562	4	figures	figure	NOUN
ejpam-5396	562	5	,	,	PUNCT
ejpam-5396	562	6	we	we	PRON
ejpam-5396	562	7	observe	observe	VERB
ejpam-5396	562	8	that	that	SCONJ
ejpam-5396	562	9	s(t	s(t	PROPN
ejpam-5396	562	10	)	)	PUNCT
ejpam-5396	562	11	remarkably	remarkably	ADV
ejpam-5396	562	12	increases	increase	VERB
ejpam-5396	562	13	in	in	ADP
ejpam-5396	562	14	the	the	DET
ejpam-5396	562	15	case	case	NOUN
ejpam-5396	562	16	where	where	SCONJ
ejpam-5396	562	17	α	α	NOUN
ejpam-5396	562	18	is	be	AUX
ejpam-5396	562	19	a	a	DET
ejpam-5396	562	20	fractional	fractional	ADJ
ejpam-5396	562	21	variant	variant	NOUN
ejpam-5396	562	22	than	than	ADP
ejpam-5396	562	23	in	in	ADP
ejpam-5396	562	24	the	the	DET
ejpam-5396	562	25	case	case	NOUN
ejpam-5396	562	26	where	where	SCONJ
ejpam-5396	562	27	α	α	NOUN
ejpam-5396	562	28	=	=	NOUN
ejpam-5396	562	29	1	1	X
ejpam-5396	562	30	.	.	PUNCT
ejpam-5396	563	1	we	we	PRON
ejpam-5396	563	2	also	also	ADV
ejpam-5396	563	3	note	note	VERB
ejpam-5396	563	4	that	that	SCONJ
ejpam-5396	563	5	c(t	c(t	PROPN
ejpam-5396	563	6	)	)	PUNCT
ejpam-5396	563	7	,	,	PUNCT
ejpam-5396	563	8	i(t	i(t	PROPN
ejpam-5396	563	9	)	)	PUNCT
ejpam-5396	563	10	,	,	PUNCT
ejpam-5396	563	11	and	and	CCONJ
ejpam-5396	563	12	r(t	r(t	NOUN
ejpam-5396	563	13	)	)	PUNCT
ejpam-5396	563	14	remarkably	remarkably	ADV
ejpam-5396	563	15	decrease	decrease	VERB
ejpam-5396	563	16	in	in	ADP
ejpam-5396	563	17	a	a	DET
ejpam-5396	563	18	similar	similar	ADJ
ejpam-5396	563	19	way	way	NOUN
ejpam-5396	563	20	for	for	ADP
ejpam-5396	563	21	both	both	DET
ejpam-5396	563	22	cases	case	NOUN
ejpam-5396	563	23	where	where	SCONJ
ejpam-5396	563	24	α	α	NOUN
ejpam-5396	563	25	is	be	AUX
ejpam-5396	563	26	a	a	DET
ejpam-5396	563	27	fractional	fractional	ADJ
ejpam-5396	563	28	variant	variant	NOUN
ejpam-5396	563	29	and	and	CCONJ
ejpam-5396	563	30	α	α	NOUN
ejpam-5396	563	31	=	=	SYM
ejpam-5396	563	32	1	1	X
ejpam-5396	563	33	.	.	PUNCT
ejpam-5396	564	1	(	(	PUNCT
ejpam-5396	564	2	a	a	X
ejpam-5396	564	3	)	)	PUNCT
ejpam-5396	564	4	(	(	PUNCT
ejpam-5396	564	5	b	b	X
ejpam-5396	564	6	)	)	PUNCT
ejpam-5396	564	7	(	(	PUNCT
ejpam-5396	564	8	c	c	X
ejpam-5396	564	9	)	)	PUNCT
ejpam-5396	564	10	(	(	PUNCT
ejpam-5396	564	11	d	d	X
ejpam-5396	564	12	)	)	PUNCT
ejpam-5396	564	13	figure	figure	NOUN
ejpam-5396	564	14	7	7	NUM
ejpam-5396	564	15	:	:	PUNCT
ejpam-5396	564	16	the	the	DET
ejpam-5396	564	17	msgdtm	msgdtm	NOUN
ejpam-5396	564	18	method	method	NOUN
ejpam-5396	564	19	for	for	ADP
ejpam-5396	564	20	the	the	DET
ejpam-5396	564	21	behavior	behavior	NOUN
ejpam-5396	564	22	of	of	ADP
ejpam-5396	564	23	s(t	s(t	PROPN
ejpam-5396	564	24	)	)	PUNCT
ejpam-5396	564	25	,	,	PUNCT
ejpam-5396	564	26	c(t	c(t	PROPN
ejpam-5396	564	27	)	)	PUNCT
ejpam-5396	564	28	,	,	PUNCT
ejpam-5396	564	29	i(t	i(t	PROPN
ejpam-5396	564	30	)	)	PUNCT
ejpam-5396	564	31	,	,	PUNCT
ejpam-5396	564	32	and	and	CCONJ
ejpam-5396	564	33	r(t	r(t	NOUN
ejpam-5396	564	34	)	)	PUNCT
ejpam-5396	564	35	at	at	ADP
ejpam-5396	564	36	various	various	ADJ
ejpam-5396	564	37	values	value	NOUN
ejpam-5396	564	38	of	of	ADP
ejpam-5396	564	39	α	α	NOUN
ejpam-5396	564	40	=	=	SYM
ejpam-5396	564	41	0.65	0.65	NUM
ejpam-5396	564	42	,	,	PUNCT
ejpam-5396	564	43	0.75	0.75	NUM
ejpam-5396	564	44	,	,	PUNCT
ejpam-5396	564	45	0.85	0.85	NUM
ejpam-5396	564	46	,	,	PUNCT
ejpam-5396	564	47	0.95	0.95	NUM
ejpam-5396	564	48	,	,	PUNCT
ejpam-5396	564	49	1	1	NUM
ejpam-5396	564	50	.	.	PUNCT
ejpam-5396	564	51	a.	a.	NOUN
ejpam-5396	564	52	alalyani	alalyani	PROPN
ejpam-5396	564	53	/	/	SYM
ejpam-5396	564	54	eur	eur	PROPN
ejpam-5396	564	55	.	.	PUNCT
ejpam-5396	565	1	j.	j.	PROPN
ejpam-5396	565	2	pure	pure	PROPN
ejpam-5396	565	3	appl	appl	PROPN
ejpam-5396	565	4	.	.	PROPN
ejpam-5396	565	5	math	math	PROPN
ejpam-5396	565	6	,	,	PUNCT
ejpam-5396	565	7	17	17	NUM
ejpam-5396	565	8	(	(	PUNCT
ejpam-5396	565	9	4	4	NUM
ejpam-5396	565	10	)	)	PUNCT
ejpam-5396	565	11	(	(	PUNCT
ejpam-5396	565	12	2024	2024	NUM
ejpam-5396	565	13	)	)	PUNCT
ejpam-5396	565	14	,	,	PUNCT
ejpam-5396	565	15	2763	2763	NUM
ejpam-5396	565	16	-	-	SYM
ejpam-5396	565	17	2799	2799	NUM
ejpam-5396	565	18	2792	2792	NUM
ejpam-5396	565	19	(	(	PUNCT
ejpam-5396	565	20	a	a	NOUN
ejpam-5396	565	21	)	)	PUNCT
ejpam-5396	565	22	(	(	PUNCT
ejpam-5396	565	23	b	b	X
ejpam-5396	565	24	)	)	PUNCT
ejpam-5396	565	25	(	(	PUNCT
ejpam-5396	565	26	c	c	X
ejpam-5396	565	27	)	)	PUNCT
ejpam-5396	565	28	(	(	PUNCT
ejpam-5396	565	29	d	d	X
ejpam-5396	565	30	)	)	PUNCT
ejpam-5396	565	31	(	(	PUNCT
ejpam-5396	565	32	e	e	NOUN
ejpam-5396	565	33	)	)	PUNCT
ejpam-5396	565	34	figure	figure	NOUN
ejpam-5396	565	35	8	8	NUM
ejpam-5396	565	36	:	:	PUNCT
ejpam-5396	565	37	combined	combined	ADJ
ejpam-5396	565	38	graphical	graphical	ADJ
ejpam-5396	565	39	behaviors	behavior	NOUN
ejpam-5396	565	40	of	of	ADP
ejpam-5396	565	41	the	the	DET
ejpam-5396	565	42	msgdtm	msgdtm	NOUN
ejpam-5396	565	43	method	method	NOUN
ejpam-5396	565	44	for	for	ADP
ejpam-5396	565	45	s(t	s(t	PROPN
ejpam-5396	565	46	)	)	PUNCT
ejpam-5396	565	47	,	,	PUNCT
ejpam-5396	565	48	c(t	c(t	PROPN
ejpam-5396	565	49	)	)	PUNCT
ejpam-5396	565	50	,	,	PUNCT
ejpam-5396	565	51	i(t	i(t	PROPN
ejpam-5396	565	52	)	)	PUNCT
ejpam-5396	565	53	,	,	PUNCT
ejpam-5396	565	54	and	and	CCONJ
ejpam-5396	565	55	r(t	r(t	NOUN
ejpam-5396	565	56	)	)	PUNCT
ejpam-5396	565	57	at	at	ADP
ejpam-5396	565	58	various	various	ADJ
ejpam-5396	565	59	values	value	NOUN
ejpam-5396	565	60	of	of	ADP
ejpam-5396	565	61	α	α	NOUN
ejpam-5396	565	62	=	=	SYM
ejpam-5396	565	63	0.65	0.65	NUM
ejpam-5396	565	64	,	,	PUNCT
ejpam-5396	565	65	0.75	0.75	NUM
ejpam-5396	565	66	,	,	PUNCT
ejpam-5396	565	67	0.85	0.85	NUM
ejpam-5396	565	68	,	,	PUNCT
ejpam-5396	565	69	0.95	0.95	NUM
ejpam-5396	565	70	,	,	PUNCT
ejpam-5396	565	71	1	1	NUM
ejpam-5396	565	72	.	.	PUNCT
ejpam-5396	565	73	a.	a.	NOUN
ejpam-5396	565	74	alalyani	alalyani	PROPN
ejpam-5396	565	75	/	/	SYM
ejpam-5396	565	76	eur	eur	PROPN
ejpam-5396	565	77	.	.	PUNCT
ejpam-5396	566	1	j.	j.	PROPN
ejpam-5396	566	2	pure	pure	PROPN
ejpam-5396	566	3	appl	appl	PROPN
ejpam-5396	566	4	.	.	PROPN
ejpam-5396	566	5	math	math	PROPN
ejpam-5396	566	6	,	,	PUNCT
ejpam-5396	566	7	17	17	NUM
ejpam-5396	566	8	(	(	PUNCT
ejpam-5396	566	9	4	4	NUM
ejpam-5396	566	10	)	)	PUNCT
ejpam-5396	566	11	(	(	PUNCT
ejpam-5396	566	12	2024	2024	NUM
ejpam-5396	566	13	)	)	PUNCT
ejpam-5396	566	14	,	,	PUNCT
ejpam-5396	566	15	2763	2763	NUM
ejpam-5396	566	16	-	-	SYM
ejpam-5396	566	17	2799	2799	NUM
ejpam-5396	566	18	2793	2793	NUM
ejpam-5396	566	19	6	6	NUM
ejpam-5396	566	20	.	.	PUNCT
ejpam-5396	567	1	discussion	discussion	NOUN
ejpam-5396	567	2	of	of	ADP
ejpam-5396	567	3	the	the	DET
ejpam-5396	567	4	results	result	NOUN
ejpam-5396	567	5	we	we	PRON
ejpam-5396	567	6	present	present	VERB
ejpam-5396	567	7	the	the	DET
ejpam-5396	567	8	solution	solution	NOUN
ejpam-5396	567	9	to	to	ADP
ejpam-5396	567	10	the	the	DET
ejpam-5396	567	11	proposed	propose	VERB
ejpam-5396	567	12	model	model	NOUN
ejpam-5396	567	13	(	(	PUNCT
ejpam-5396	567	14	1	1	X
ejpam-5396	567	15	)	)	PUNCT
ejpam-5396	567	16	using	use	VERB
ejpam-5396	567	17	four	four	NUM
ejpam-5396	567	18	different	different	ADJ
ejpam-5396	567	19	numerical	numerical	ADJ
ejpam-5396	567	20	methods	method	NOUN
ejpam-5396	567	21	.	.	PUNCT
ejpam-5396	568	1	from	from	ADP
ejpam-5396	568	2	the	the	DET
ejpam-5396	568	3	numerical	numerical	ADJ
ejpam-5396	568	4	simulations	simulation	NOUN
ejpam-5396	568	5	and	and	CCONJ
ejpam-5396	568	6	results	result	NOUN
ejpam-5396	568	7	in	in	ADP
ejpam-5396	568	8	section	section	NOUN
ejpam-5396	568	9	5	5	NUM
ejpam-5396	568	10	,	,	PUNCT
ejpam-5396	568	11	we	we	PRON
ejpam-5396	568	12	observe	observe	VERB
ejpam-5396	568	13	that	that	SCONJ
ejpam-5396	568	14	the	the	DET
ejpam-5396	568	15	solution	solution	NOUN
ejpam-5396	568	16	to	to	ADP
ejpam-5396	568	17	the	the	DET
ejpam-5396	568	18	proposed	propose	VERB
ejpam-5396	568	19	model	model	NOUN
ejpam-5396	568	20	(	(	PUNCT
ejpam-5396	568	21	1	1	X
ejpam-5396	568	22	)	)	PUNCT
ejpam-5396	568	23	gets	get	VERB
ejpam-5396	568	24	stable	stable	ADJ
ejpam-5396	568	25	faster	fast	ADV
ejpam-5396	568	26	using	use	VERB
ejpam-5396	568	27	the	the	DET
ejpam-5396	568	28	abmm	abmm	NOUN
ejpam-5396	568	29	and	and	CCONJ
ejpam-5396	568	30	the	the	DET
ejpam-5396	568	31	msgdtm	msgdtm	NOUN
ejpam-5396	568	32	methods	method	NOUN
ejpam-5396	568	33	than	than	ADP
ejpam-5396	568	34	using	use	VERB
ejpam-5396	568	35	the	the	DET
ejpam-5396	568	36	gem	gem	NOUN
ejpam-5396	568	37	and	and	CCONJ
ejpam-5396	568	38	the	the	DET
ejpam-5396	568	39	grkm	grkm	NOUN
ejpam-5396	568	40	methods	method	NOUN
ejpam-5396	568	41	.	.	PUNCT
ejpam-5396	569	1	the	the	DET
ejpam-5396	569	2	solution	solution	NOUN
ejpam-5396	569	3	to	to	ADP
ejpam-5396	569	4	the	the	DET
ejpam-5396	569	5	proposed	propose	VERB
ejpam-5396	569	6	model	model	NOUN
ejpam-5396	569	7	(	(	PUNCT
ejpam-5396	569	8	1	1	X
ejpam-5396	569	9	)	)	PUNCT
ejpam-5396	569	10	using	use	VERB
ejpam-5396	569	11	the	the	DET
ejpam-5396	569	12	abmm	abmm	NOUN
ejpam-5396	569	13	method	method	NOUN
ejpam-5396	569	14	gets	get	VERB
ejpam-5396	569	15	stable	stable	ADJ
ejpam-5396	569	16	faster	fast	ADV
ejpam-5396	569	17	in	in	ADP
ejpam-5396	569	18	the	the	DET
ejpam-5396	569	19	case	case	NOUN
ejpam-5396	569	20	where	where	SCONJ
ejpam-5396	569	21	α	α	NOUN
ejpam-5396	569	22	=	=	NOUN
ejpam-5396	569	23	1	1	NUM
ejpam-5396	569	24	than	than	ADP
ejpam-5396	569	25	in	in	ADP
ejpam-5396	569	26	the	the	DET
ejpam-5396	569	27	case	case	NOUN
ejpam-5396	569	28	where	where	SCONJ
ejpam-5396	569	29	α	α	NOUN
ejpam-5396	569	30	is	be	AUX
ejpam-5396	569	31	a	a	DET
ejpam-5396	569	32	fractional	fractional	ADJ
ejpam-5396	569	33	variant	variant	NOUN
ejpam-5396	569	34	.	.	PUNCT
ejpam-5396	570	1	on	on	ADP
ejpam-5396	570	2	the	the	DET
ejpam-5396	570	3	other	other	ADJ
ejpam-5396	570	4	hand	hand	NOUN
ejpam-5396	570	5	,	,	PUNCT
ejpam-5396	570	6	the	the	DET
ejpam-5396	570	7	solution	solution	NOUN
ejpam-5396	570	8	to	to	ADP
ejpam-5396	570	9	the	the	DET
ejpam-5396	570	10	proposed	propose	VERB
ejpam-5396	570	11	model	model	NOUN
ejpam-5396	570	12	(	(	PUNCT
ejpam-5396	570	13	1	1	X
ejpam-5396	570	14	)	)	PUNCT
ejpam-5396	570	15	using	use	VERB
ejpam-5396	570	16	the	the	DET
ejpam-5396	570	17	msgdtm	msgdtm	NOUN
ejpam-5396	570	18	method	method	NOUN
ejpam-5396	570	19	gets	get	VERB
ejpam-5396	570	20	stable	stable	ADJ
ejpam-5396	570	21	faster	fast	ADV
ejpam-5396	570	22	in	in	ADP
ejpam-5396	570	23	the	the	DET
ejpam-5396	570	24	case	case	NOUN
ejpam-5396	570	25	where	where	SCONJ
ejpam-5396	570	26	α	α	NOUN
ejpam-5396	570	27	is	be	AUX
ejpam-5396	570	28	a	a	DET
ejpam-5396	570	29	fractional	fractional	ADJ
ejpam-5396	570	30	variant	variant	NOUN
ejpam-5396	570	31	than	than	ADP
ejpam-5396	570	32	in	in	ADP
ejpam-5396	570	33	the	the	DET
ejpam-5396	570	34	case	case	NOUN
ejpam-5396	570	35	where	where	SCONJ
ejpam-5396	570	36	α	α	NOUN
ejpam-5396	570	37	=	=	NOUN
ejpam-5396	570	38	1	1	NUM
ejpam-5396	570	39	.	.	PUNCT
ejpam-5396	570	40	from	from	ADP
ejpam-5396	570	41	numerical	numerical	ADJ
ejpam-5396	570	42	simulations	simulation	NOUN
ejpam-5396	570	43	and	and	CCONJ
ejpam-5396	570	44	results	result	NOUN
ejpam-5396	570	45	,	,	PUNCT
ejpam-5396	570	46	we	we	PRON
ejpam-5396	570	47	can	can	AUX
ejpam-5396	570	48	say	say	VERB
ejpam-5396	570	49	that	that	SCONJ
ejpam-5396	570	50	the	the	DET
ejpam-5396	570	51	numerical	numerical	ADJ
ejpam-5396	570	52	methods	method	NOUN
ejpam-5396	570	53	we	we	PRON
ejpam-5396	570	54	used	use	VERB
ejpam-5396	570	55	are	be	AUX
ejpam-5396	570	56	efficient	efficient	ADJ
ejpam-5396	570	57	computational	computational	ADJ
ejpam-5396	570	58	methods	method	NOUN
ejpam-5396	570	59	.	.	PUNCT
ejpam-5396	571	1	the	the	DET
ejpam-5396	571	2	abmm	abmm	NOUN
ejpam-5396	571	3	,	,	PUNCT
ejpam-5396	571	4	the	the	DET
ejpam-5396	571	5	gem	gem	NOUN
ejpam-5396	571	6	,	,	PUNCT
ejpam-5396	571	7	the	the	DET
ejpam-5396	571	8	grkm	grkm	NOUN
ejpam-5396	571	9	,	,	PUNCT
ejpam-5396	571	10	and	and	CCONJ
ejpam-5396	571	11	the	the	DET
ejpam-5396	571	12	msgdtm	msgdtm	NOUN
ejpam-5396	571	13	exhibit	exhibit	VERB
ejpam-5396	571	14	greater	great	ADJ
ejpam-5396	571	15	flexibility	flexibility	NOUN
ejpam-5396	571	16	and	and	CCONJ
ejpam-5396	571	17	applicability	applicability	NOUN
ejpam-5396	571	18	across	across	ADP
ejpam-5396	571	19	a	a	DET
ejpam-5396	571	20	diverse	diverse	ADJ
ejpam-5396	571	21	spectrum	spectrum	NOUN
ejpam-5396	571	22	of	of	ADP
ejpam-5396	571	23	problems	problem	NOUN
ejpam-5396	571	24	,	,	PUNCT
ejpam-5396	571	25	with	with	ADP
ejpam-5396	571	26	a	a	DET
ejpam-5396	571	27	specific	specific	ADJ
ejpam-5396	571	28	emphasis	emphasis	NOUN
ejpam-5396	571	29	on	on	ADP
ejpam-5396	571	30	initial	initial	ADJ
ejpam-5396	571	31	value	value	NOUN
ejpam-5396	571	32	problems	problem	NOUN
ejpam-5396	571	33	and	and	CCONJ
ejpam-5396	571	34	systems	system	NOUN
ejpam-5396	571	35	of	of	ADP
ejpam-5396	571	36	ordinary	ordinary	ADJ
ejpam-5396	571	37	differential	differential	ADJ
ejpam-5396	571	38	equations	equation	NOUN
ejpam-5396	571	39	(	(	PUNCT
ejpam-5396	571	40	odes	ode	NOUN
ejpam-5396	571	41	)	)	PUNCT
ejpam-5396	571	42	.	.	PUNCT
ejpam-5396	572	1	the	the	DET
ejpam-5396	572	2	improved	improved	ADJ
ejpam-5396	572	3	shooting	shooting	NOUN
ejpam-5396	572	4	method	method	NOUN
ejpam-5396	572	5	,	,	PUNCT
ejpam-5396	572	6	specialized	specialize	VERB
ejpam-5396	572	7	for	for	ADP
ejpam-5396	572	8	boundary	boundary	ADJ
ejpam-5396	572	9	value	value	NOUN
ejpam-5396	572	10	problems	problem	NOUN
ejpam-5396	572	11	(	(	PUNCT
ejpam-5396	572	12	bvps	bvps	PROPN
ejpam-5396	572	13	)	)	PUNCT
ejpam-5396	572	14	,	,	PUNCT
ejpam-5396	572	15	exhibits	exhibit	VERB
ejpam-5396	572	16	high	high	ADJ
ejpam-5396	572	17	accuracy	accuracy	NOUN
ejpam-5396	572	18	,	,	PUNCT
ejpam-5396	572	19	stability	stability	NOUN
ejpam-5396	572	20	,	,	PUNCT
ejpam-5396	572	21	and	and	CCONJ
ejpam-5396	572	22	robustness	robustness	NOUN
ejpam-5396	572	23	when	when	SCONJ
ejpam-5396	572	24	applied	apply	VERB
ejpam-5396	572	25	to	to	ADP
ejpam-5396	572	26	coupled	couple	VERB
ejpam-5396	572	27	nonlinear	nonlinear	ADJ
ejpam-5396	572	28	higher	high	ADJ
ejpam-5396	572	29	-	-	PUNCT
ejpam-5396	572	30	order	order	NOUN
ejpam-5396	572	31	systems	system	NOUN
ejpam-5396	572	32	.	.	PUNCT
ejpam-5396	573	1	it	it	PRON
ejpam-5396	573	2	is	be	AUX
ejpam-5396	573	3	generally	generally	ADV
ejpam-5396	573	4	the	the	DET
ejpam-5396	573	5	preferred	preferred	ADJ
ejpam-5396	573	6	method	method	NOUN
ejpam-5396	573	7	for	for	ADP
ejpam-5396	573	8	dealing	deal	VERB
ejpam-5396	573	9	with	with	ADP
ejpam-5396	573	10	bvps	bvps	NOUN
ejpam-5396	573	11	,	,	PUNCT
ejpam-5396	573	12	particularly	particularly	ADV
ejpam-5396	573	13	in	in	ADP
ejpam-5396	573	14	complex	complex	ADJ
ejpam-5396	573	15	nonlinear	nonlinear	ADJ
ejpam-5396	573	16	intricate	intricate	ADJ
ejpam-5396	573	17	.	.	NOUN
ejpam-5396	574	1	7	7	X
ejpam-5396	574	2	.	.	X
ejpam-5396	574	3	conclusion	conclusion	NOUN
ejpam-5396	574	4	in	in	ADP
ejpam-5396	574	5	this	this	DET
ejpam-5396	574	6	work	work	NOUN
ejpam-5396	574	7	,	,	PUNCT
ejpam-5396	574	8	we	we	PRON
ejpam-5396	574	9	investigated	investigate	VERB
ejpam-5396	574	10	the	the	DET
ejpam-5396	574	11	solution	solution	NOUN
ejpam-5396	574	12	and	and	CCONJ
ejpam-5396	574	13	the	the	DET
ejpam-5396	574	14	dynamics	dynamic	NOUN
ejpam-5396	574	15	of	of	ADP
ejpam-5396	574	16	the	the	DET
ejpam-5396	574	17	pneumonia	pneumonia	NOUN
ejpam-5396	574	18	fractionalorder	fractionalorder	PROPN
ejpam-5396	574	19	mathematical	mathematical	PROPN
ejpam-5396	574	20	model	model	NOUN
ejpam-5396	574	21	(	(	PUNCT
ejpam-5396	574	22	1	1	X
ejpam-5396	574	23	)	)	PUNCT
ejpam-5396	574	24	using	use	VERB
ejpam-5396	574	25	numerical	numerical	ADJ
ejpam-5396	574	26	techniques	technique	NOUN
ejpam-5396	574	27	including	include	VERB
ejpam-5396	574	28	the	the	DET
ejpam-5396	574	29	adams	adam	NOUN
ejpam-5396	574	30	-	-	PUNCT
ejpam-5396	574	31	bashforthmoulton	bashforthmoulton	NOUN
ejpam-5396	574	32	method	method	NOUN
ejpam-5396	574	33	,	,	PUNCT
ejpam-5396	574	34	the	the	DET
ejpam-5396	574	35	generalized	generalize	VERB
ejpam-5396	574	36	euler	euler	NOUN
ejpam-5396	574	37	method	method	NOUN
ejpam-5396	574	38	,	,	PUNCT
ejpam-5396	574	39	the	the	DET
ejpam-5396	574	40	generalized	generalize	VERB
ejpam-5396	574	41	runge	runge	NOUN
ejpam-5396	574	42	-	-	PUNCT
ejpam-5396	574	43	kutta	kutta	NOUN
ejpam-5396	574	44	method	method	NOUN
ejpam-5396	574	45	,	,	PUNCT
ejpam-5396	574	46	and	and	CCONJ
ejpam-5396	574	47	the	the	DET
ejpam-5396	574	48	multistep	multistep	ADJ
ejpam-5396	574	49	generalized	generalize	VERB
ejpam-5396	574	50	differential	differential	NOUN
ejpam-5396	574	51	transform	transform	NOUN
ejpam-5396	574	52	method	method	NOUN
ejpam-5396	574	53	.	.	PUNCT
ejpam-5396	575	1	for	for	ADP
ejpam-5396	575	2	the	the	DET
ejpam-5396	575	3	sake	sake	NOUN
ejpam-5396	575	4	of	of	ADP
ejpam-5396	575	5	the	the	DET
ejpam-5396	575	6	analysis	analysis	NOUN
ejpam-5396	575	7	of	of	ADP
ejpam-5396	575	8	the	the	DET
ejpam-5396	575	9	proposed	propose	VERB
ejpam-5396	575	10	model	model	NOUN
ejpam-5396	575	11	(	(	PUNCT
ejpam-5396	575	12	1	1	NUM
ejpam-5396	575	13	)	)	PUNCT
ejpam-5396	575	14	,	,	PUNCT
ejpam-5396	575	15	we	we	PRON
ejpam-5396	575	16	discussed	discuss	VERB
ejpam-5396	575	17	positivity	positivity	NOUN
ejpam-5396	575	18	,	,	PUNCT
ejpam-5396	575	19	boundedness	boundedness	NOUN
ejpam-5396	575	20	,	,	PUNCT
ejpam-5396	575	21	equilibria	equilibrium	NOUN
ejpam-5396	575	22	,	,	PUNCT
ejpam-5396	575	23	local	local	ADJ
ejpam-5396	575	24	and	and	CCONJ
ejpam-5396	575	25	global	global	ADJ
ejpam-5396	575	26	stability	stability	NOUN
ejpam-5396	575	27	,	,	PUNCT
ejpam-5396	575	28	and	and	CCONJ
ejpam-5396	575	29	the	the	DET
ejpam-5396	575	30	basic	basic	ADJ
ejpam-5396	575	31	reproductive	reproductive	ADJ
ejpam-5396	575	32	number	number	NOUN
ejpam-5396	575	33	r0	r0	NOUN
ejpam-5396	575	34	.	.	PUNCT
ejpam-5396	576	1	based	base	VERB
ejpam-5396	576	2	on	on	ADP
ejpam-5396	576	3	the	the	DET
ejpam-5396	576	4	numerical	numerical	ADJ
ejpam-5396	576	5	simulations	simulation	NOUN
ejpam-5396	576	6	,	,	PUNCT
ejpam-5396	576	7	we	we	PRON
ejpam-5396	576	8	observed	observe	VERB
ejpam-5396	576	9	that	that	SCONJ
ejpam-5396	576	10	there	there	PRON
ejpam-5396	576	11	is	be	VERB
ejpam-5396	576	12	a	a	DET
ejpam-5396	576	13	convergence	convergence	NOUN
ejpam-5396	576	14	in	in	ADP
ejpam-5396	576	15	results	result	NOUN
ejpam-5396	576	16	between	between	ADP
ejpam-5396	576	17	the	the	DET
ejpam-5396	576	18	proposed	propose	VERB
ejpam-5396	576	19	fractional	fractional	ADJ
ejpam-5396	576	20	-	-	PUNCT
ejpam-5396	576	21	order	order	NOUN
ejpam-5396	576	22	mathematical	mathematical	ADJ
ejpam-5396	576	23	model	model	NOUN
ejpam-5396	576	24	(	(	PUNCT
ejpam-5396	576	25	1	1	NUM
ejpam-5396	576	26	)	)	PUNCT
ejpam-5396	576	27	and	and	CCONJ
ejpam-5396	576	28	its	its	PRON
ejpam-5396	576	29	integer	integer	NOUN
ejpam-5396	576	30	-	-	PUNCT
ejpam-5396	576	31	order	order	NOUN
ejpam-5396	576	32	form	form	NOUN
ejpam-5396	576	33	.	.	PUNCT
ejpam-5396	577	1	the	the	DET
ejpam-5396	577	2	aim	aim	NOUN
ejpam-5396	577	3	of	of	ADP
ejpam-5396	577	4	using	use	VERB
ejpam-5396	577	5	the	the	DET
ejpam-5396	577	6	fractional	fractional	ADJ
ejpam-5396	577	7	-	-	PUNCT
ejpam-5396	577	8	order	order	NOUN
ejpam-5396	577	9	mathematical	mathematical	ADJ
ejpam-5396	577	10	model	model	NOUN
ejpam-5396	577	11	(	(	PUNCT
ejpam-5396	577	12	1	1	NUM
ejpam-5396	577	13	)	)	PUNCT
ejpam-5396	577	14	is	be	AUX
ejpam-5396	577	15	to	to	PART
ejpam-5396	577	16	investigate	investigate	VERB
ejpam-5396	577	17	the	the	DET
ejpam-5396	577	18	memory	memory	NOUN
ejpam-5396	577	19	of	of	ADP
ejpam-5396	577	20	the	the	DET
ejpam-5396	577	21	model	model	NOUN
ejpam-5396	577	22	for	for	ADP
ejpam-5396	577	23	a	a	DET
ejpam-5396	577	24	long	long	ADJ
ejpam-5396	577	25	time	time	NOUN
ejpam-5396	577	26	period	period	NOUN
ejpam-5396	577	27	;	;	PUNCT
ejpam-5396	577	28	that	that	PRON
ejpam-5396	577	29	is	is	ADV
ejpam-5396	577	30	,	,	PUNCT
ejpam-5396	577	31	at	at	ADP
ejpam-5396	577	32	any	any	DET
ejpam-5396	577	33	time	time	NOUN
ejpam-5396	577	34	t	t	PROPN
ejpam-5396	577	35	,	,	PUNCT
ejpam-5396	577	36	the	the	DET
ejpam-5396	577	37	fractional	fractional	ADJ
ejpam-5396	577	38	-	-	PUNCT
ejpam-5396	577	39	order	order	NOUN
ejpam-5396	577	40	mathematical	mathematical	ADJ
ejpam-5396	577	41	model	model	NOUN
ejpam-5396	577	42	investigates	investigate	VERB
ejpam-5396	577	43	the	the	DET
ejpam-5396	577	44	behavior	behavior	NOUN
ejpam-5396	577	45	of	of	ADP
ejpam-5396	577	46	the	the	DET
ejpam-5396	577	47	variables	variable	NOUN
ejpam-5396	577	48	s(t	s(t	PROPN
ejpam-5396	577	49	)	)	PUNCT
ejpam-5396	577	50	,	,	PUNCT
ejpam-5396	577	51	c(t	c(t	PROPN
ejpam-5396	577	52	)	)	PUNCT
ejpam-5396	577	53	,	,	PUNCT
ejpam-5396	577	54	i(t	i(t	PROPN
ejpam-5396	577	55	)	)	PUNCT
ejpam-5396	577	56	,	,	PUNCT
ejpam-5396	577	57	and	and	CCONJ
ejpam-5396	577	58	r(t	r(t	NOUN
ejpam-5396	577	59	)	)	PUNCT
ejpam-5396	577	60	during	during	ADP
ejpam-5396	577	61	the	the	DET
ejpam-5396	577	62	period	period	NOUN
ejpam-5396	577	63	[	[	X
ejpam-5396	577	64	0	0	NUM
ejpam-5396	577	65	,	,	PUNCT
ejpam-5396	577	66	1	1	NUM
ejpam-5396	577	67	]	]	PUNCT
ejpam-5396	577	68	as	as	ADP
ejpam-5396	577	69	a	a	DET
ejpam-5396	577	70	result	result	NOUN
ejpam-5396	577	71	of	of	ADP
ejpam-5396	577	72	changing	change	VERB
ejpam-5396	577	73	the	the	DET
ejpam-5396	577	74	values	value	NOUN
ejpam-5396	577	75	of	of	ADP
ejpam-5396	577	76	α	α	NOUN
ejpam-5396	577	77	,	,	PUNCT
ejpam-5396	577	78	while	while	SCONJ
ejpam-5396	577	79	the	the	DET
ejpam-5396	577	80	integer	integer	NOUN
ejpam-5396	577	81	-	-	PUNCT
ejpam-5396	577	82	order	order	NOUN
ejpam-5396	577	83	form	form	NOUN
ejpam-5396	577	84	investigates	investigate	VERB
ejpam-5396	577	85	the	the	DET
ejpam-5396	577	86	behavior	behavior	NOUN
ejpam-5396	577	87	of	of	ADP
ejpam-5396	577	88	the	the	DET
ejpam-5396	577	89	variables	variable	NOUN
ejpam-5396	577	90	only	only	ADV
ejpam-5396	577	91	at	at	ADP
ejpam-5396	577	92	α	α	NOUN
ejpam-5396	577	93	=	=	SYM
ejpam-5396	577	94	1	1	X
ejpam-5396	577	95	.	.	PUNCT
ejpam-5396	578	1	this	this	PRON
ejpam-5396	578	2	was	be	AUX
ejpam-5396	578	3	useful	useful	ADJ
ejpam-5396	578	4	in	in	ADP
ejpam-5396	578	5	investigating	investigate	VERB
ejpam-5396	578	6	the	the	DET
ejpam-5396	578	7	stability	stability	NOUN
ejpam-5396	578	8	of	of	ADP
ejpam-5396	578	9	the	the	DET
ejpam-5396	578	10	model	model	NOUN
ejpam-5396	578	11	during	during	ADP
ejpam-5396	578	12	the	the	DET
ejpam-5396	578	13	period	period	NOUN
ejpam-5396	578	14	[	[	X
ejpam-5396	578	15	0	0	NUM
ejpam-5396	578	16	,	,	PUNCT
ejpam-5396	578	17	1	1	NUM
ejpam-5396	578	18	]	]	PUNCT
ejpam-5396	578	19	as	as	ADP
ejpam-5396	578	20	a	a	DET
ejpam-5396	578	21	result	result	NOUN
ejpam-5396	578	22	of	of	ADP
ejpam-5396	578	23	changing	change	VERB
ejpam-5396	578	24	the	the	DET
ejpam-5396	578	25	values	value	NOUN
ejpam-5396	578	26	of	of	ADP
ejpam-5396	578	27	α	α	NOUN
ejpam-5396	578	28	and	and	CCONJ
ejpam-5396	578	29	gaining	gain	VERB
ejpam-5396	578	30	a	a	DET
ejpam-5396	578	31	better	well	ADJ
ejpam-5396	578	32	understanding	understanding	NOUN
ejpam-5396	578	33	of	of	ADP
ejpam-5396	578	34	the	the	DET
ejpam-5396	578	35	disease	disease	NOUN
ejpam-5396	578	36	’s	’s	PART
ejpam-5396	578	37	dynamics	dynamic	NOUN
ejpam-5396	578	38	.	.	PUNCT
ejpam-5396	579	1	this	this	DET
ejpam-5396	579	2	work	work	NOUN
ejpam-5396	579	3	will	will	AUX
ejpam-5396	579	4	also	also	ADV
ejpam-5396	579	5	be	be	AUX
ejpam-5396	579	6	a	a	DET
ejpam-5396	579	7	valuable	valuable	ADJ
ejpam-5396	579	8	tool	tool	NOUN
ejpam-5396	579	9	for	for	ADP
ejpam-5396	579	10	different	different	ADJ
ejpam-5396	579	11	types	type	NOUN
ejpam-5396	579	12	of	of	ADP
ejpam-5396	579	13	disease	disease	NOUN
ejpam-5396	579	14	modeling	modeling	NOUN
ejpam-5396	579	15	.	.	PUNCT
ejpam-5396	580	1	the	the	DET
ejpam-5396	580	2	figures	figure	NOUN
ejpam-5396	580	3	presented	present	VERB
ejpam-5396	580	4	in	in	ADP
ejpam-5396	580	5	this	this	DET
ejpam-5396	580	6	paper	paper	NOUN
ejpam-5396	580	7	illustrate	illustrate	VERB
ejpam-5396	580	8	the	the	DET
ejpam-5396	580	9	dynamic	dynamic	ADJ
ejpam-5396	580	10	behavior	behavior	NOUN
ejpam-5396	580	11	of	of	ADP
ejpam-5396	580	12	the	the	DET
ejpam-5396	580	13	system	system	NOUN
ejpam-5396	580	14	variables	variable	NOUN
ejpam-5396	580	15	s(t	s(t	PROPN
ejpam-5396	580	16	)	)	PUNCT
ejpam-5396	580	17	,	,	PUNCT
ejpam-5396	580	18	c(t	c(t	PROPN
ejpam-5396	580	19	)	)	PUNCT
ejpam-5396	580	20	,	,	PUNCT
ejpam-5396	580	21	i(t	i(t	PROPN
ejpam-5396	580	22	)	)	PUNCT
ejpam-5396	580	23	,	,	PUNCT
ejpam-5396	580	24	and	and	CCONJ
ejpam-5396	580	25	r(t	r(t	NOUN
ejpam-5396	580	26	)	)	PUNCT
ejpam-5396	580	27	under	under	ADP
ejpam-5396	580	28	various	various	ADJ
ejpam-5396	580	29	fractional	fractional	ADJ
ejpam-5396	580	30	orders	order	NOUN
ejpam-5396	580	31	α	α	NOUN
ejpam-5396	580	32	using	use	VERB
ejpam-5396	580	33	four	four	NUM
ejpam-5396	580	34	different	different	ADJ
ejpam-5396	580	35	numerical	numerical	ADJ
ejpam-5396	580	36	methods	method	NOUN
ejpam-5396	580	37	:	:	PUNCT
ejpam-5396	580	38	the	the	DET
ejpam-5396	580	39	adams	adams	PROPN
ejpam-5396	580	40	-	-	PUNCT
ejpam-5396	580	41	bashforth	bashforth	PROPN
ejpam-5396	580	42	-	-	PUNCT
ejpam-5396	580	43	moulton	moulton	PROPN
ejpam-5396	580	44	method	method	NOUN
ejpam-5396	580	45	(	(	PUNCT
ejpam-5396	580	46	abmm	abmm	PROPN
ejpam-5396	580	47	)	)	PUNCT
ejpam-5396	580	48	,	,	PUNCT
ejpam-5396	580	49	the	the	DET
ejpam-5396	580	50	generalized	generalize	VERB
ejpam-5396	580	51	euler	euler	NOUN
ejpam-5396	580	52	method	method	NOUN
ejpam-5396	580	53	(	(	PUNCT
ejpam-5396	580	54	gem	gem	NOUN
ejpam-5396	580	55	)	)	PUNCT
ejpam-5396	580	56	,	,	PUNCT
ejpam-5396	580	57	the	the	DET
ejpam-5396	580	58	generalized	generalize	VERB
ejpam-5396	580	59	runge	runge	NOUN
ejpam-5396	580	60	-	-	PUNCT
ejpam-5396	580	61	kutta	kutta	NOUN
ejpam-5396	580	62	method	method	NOUN
ejpam-5396	580	63	(	(	PUNCT
ejpam-5396	580	64	grkm	grkm	NOUN
ejpam-5396	580	65	)	)	PUNCT
ejpam-5396	580	66	,	,	PUNCT
ejpam-5396	580	67	and	and	CCONJ
ejpam-5396	580	68	the	the	DET
ejpam-5396	580	69	multistep	multistep	ADJ
ejpam-5396	580	70	generalized	generalize	VERB
ejpam-5396	580	71	differential	differential	ADJ
ejpam-5396	580	72	transform	transform	NOUN
ejpam-5396	580	73	method	method	NOUN
ejpam-5396	580	74	(	(	PUNCT
ejpam-5396	580	75	msgdtm	msgdtm	NOUN
ejpam-5396	580	76	)	)	PUNCT
ejpam-5396	580	77	.	.	PUNCT
ejpam-5396	581	1	the	the	DET
ejpam-5396	581	2	main	main	ADJ
ejpam-5396	581	3	contribution	contribution	NOUN
ejpam-5396	581	4	of	of	ADP
ejpam-5396	581	5	these	these	DET
ejpam-5396	581	6	figures	figure	NOUN
ejpam-5396	581	7	lies	lie	VERB
ejpam-5396	581	8	in	in	ADP
ejpam-5396	581	9	conducting	conduct	VERB
ejpam-5396	581	10	a	a	DET
ejpam-5396	581	11	comparative	comparative	ADJ
ejpam-5396	581	12	analysis	analysis	NOUN
ejpam-5396	581	13	of	of	ADP
ejpam-5396	581	14	the	the	DET
ejpam-5396	581	15	four	four	NUM
ejpam-5396	581	16	different	different	ADJ
ejpam-5396	581	17	methods	method	NOUN
ejpam-5396	581	18	used	use	VERB
ejpam-5396	581	19	to	to	PART
ejpam-5396	581	20	approximate	approximate	VERB
ejpam-5396	581	21	solutions	solution	NOUN
ejpam-5396	581	22	for	for	ADP
ejpam-5396	581	23	the	the	DET
ejpam-5396	581	24	proposed	propose	VERB
ejpam-5396	581	25	fractional	fractional	ADJ
ejpam-5396	581	26	-	-	PUNCT
ejpam-5396	581	27	order	order	NOUN
ejpam-5396	581	28	mathematical	mathematical	ADJ
ejpam-5396	581	29	model	model	NOUN
ejpam-5396	581	30	.	.	PUNCT
ejpam-5396	582	1	specifically	specifically	ADV
ejpam-5396	582	2	,	,	PUNCT
ejpam-5396	582	3	figures	figure	NOUN
ejpam-5396	582	4	1	1	NUM
ejpam-5396	582	5	and	and	CCONJ
ejpam-5396	582	6	2	2	NUM
ejpam-5396	582	7	,	,	PUNCT
ejpam-5396	582	8	obtained	obtain	VERB
ejpam-5396	582	9	using	use	VERB
ejpam-5396	582	10	the	the	DET
ejpam-5396	582	11	abmm	abmm	NOUN
ejpam-5396	582	12	method	method	NOUN
ejpam-5396	582	13	,	,	PUNCT
ejpam-5396	582	14	references	reference	NOUN
ejpam-5396	582	15	2794	2794	NUM
ejpam-5396	582	16	and	and	CCONJ
ejpam-5396	582	17	figures	figure	NOUN
ejpam-5396	582	18	3	3	NUM
ejpam-5396	582	19	and	and	CCONJ
ejpam-5396	582	20	4	4	NUM
ejpam-5396	582	21	,	,	PUNCT
ejpam-5396	582	22	obtained	obtain	VERB
ejpam-5396	582	23	employing	employ	VERB
ejpam-5396	582	24	the	the	DET
ejpam-5396	582	25	gem	gem	NOUN
ejpam-5396	582	26	method	method	NOUN
ejpam-5396	582	27	,	,	PUNCT
ejpam-5396	582	28	illustrate	illustrate	VERB
ejpam-5396	582	29	that	that	SCONJ
ejpam-5396	582	30	s(t	s(t	PROPN
ejpam-5396	582	31	)	)	PUNCT
ejpam-5396	582	32	exhibits	exhibit	VERB
ejpam-5396	582	33	an	an	DET
ejpam-5396	582	34	increase	increase	NOUN
ejpam-5396	582	35	,	,	PUNCT
ejpam-5396	582	36	while	while	SCONJ
ejpam-5396	582	37	c(t	c(t	PROPN
ejpam-5396	582	38	)	)	PUNCT
ejpam-5396	582	39	,	,	PUNCT
ejpam-5396	582	40	i(t	i(t	PROPN
ejpam-5396	582	41	)	)	PUNCT
ejpam-5396	582	42	,	,	PUNCT
ejpam-5396	582	43	and	and	CCONJ
ejpam-5396	582	44	r(t	r(t	NOUN
ejpam-5396	582	45	)	)	PUNCT
ejpam-5396	583	1	all	all	PRON
ejpam-5396	583	2	decrease	decrease	VERB
ejpam-5396	583	3	as	as	ADP
ejpam-5396	583	4	the	the	DET
ejpam-5396	583	5	fractional	fractional	ADJ
ejpam-5396	583	6	order	order	NOUN
ejpam-5396	583	7	α	α	NOUN
ejpam-5396	583	8	approaches	approach	VERB
ejpam-5396	583	9	1	1	NUM
ejpam-5396	583	10	.	.	PUNCT
ejpam-5396	584	1	this	this	DET
ejpam-5396	584	2	observation	observation	NOUN
ejpam-5396	584	3	indicates	indicate	VERB
ejpam-5396	584	4	that	that	SCONJ
ejpam-5396	584	5	the	the	DET
ejpam-5396	584	6	behavior	behavior	NOUN
ejpam-5396	584	7	of	of	ADP
ejpam-5396	584	8	integer	integer	NOUN
ejpam-5396	584	9	-	-	PUNCT
ejpam-5396	584	10	order	order	NOUN
ejpam-5396	584	11	dynamics	dynamic	NOUN
ejpam-5396	584	12	diverges	diverge	VERB
ejpam-5396	584	13	notably	notably	ADV
ejpam-5396	584	14	from	from	ADP
ejpam-5396	584	15	that	that	PRON
ejpam-5396	584	16	of	of	ADP
ejpam-5396	584	17	fractional	fractional	ADJ
ejpam-5396	584	18	-	-	PUNCT
ejpam-5396	584	19	order	order	NOUN
ejpam-5396	584	20	dynamics	dynamic	NOUN
ejpam-5396	584	21	,	,	PUNCT
ejpam-5396	584	22	and	and	CCONJ
ejpam-5396	584	23	the	the	DET
ejpam-5396	584	24	depicted	depict	VERB
ejpam-5396	584	25	figures	figure	NOUN
ejpam-5396	584	26	highlight	highlight	VERB
ejpam-5396	584	27	the	the	DET
ejpam-5396	584	28	model	model	NOUN
ejpam-5396	584	29	’s	’s	PART
ejpam-5396	584	30	sensitivity	sensitivity	NOUN
ejpam-5396	584	31	to	to	ADP
ejpam-5396	584	32	fractional	fractional	ADJ
ejpam-5396	584	33	variations	variation	NOUN
ejpam-5396	584	34	.	.	PUNCT
ejpam-5396	585	1	figures	figure	NOUN
ejpam-5396	585	2	5	5	NUM
ejpam-5396	585	3	and	and	CCONJ
ejpam-5396	585	4	6	6	NUM
ejpam-5396	585	5	,	,	PUNCT
ejpam-5396	585	6	obtained	obtain	VERB
ejpam-5396	585	7	using	use	VERB
ejpam-5396	585	8	the	the	DET
ejpam-5396	585	9	grkm	grkm	NOUN
ejpam-5396	585	10	method	method	NOUN
ejpam-5396	585	11	,	,	PUNCT
ejpam-5396	585	12	illustrate	illustrate	VERB
ejpam-5396	585	13	a	a	DET
ejpam-5396	585	14	reverse	reverse	ADJ
ejpam-5396	585	15	trend	trend	NOUN
ejpam-5396	585	16	where	where	SCONJ
ejpam-5396	585	17	s(t	s(t	PROPN
ejpam-5396	585	18	)	)	PUNCT
ejpam-5396	585	19	increases	increase	VERB
ejpam-5396	585	20	more	more	ADJ
ejpam-5396	585	21	for	for	ADP
ejpam-5396	585	22	fractional	fractional	ADJ
ejpam-5396	585	23	values	value	NOUN
ejpam-5396	585	24	of	of	ADP
ejpam-5396	585	25	α	α	NOUN
ejpam-5396	585	26	compared	compare	VERB
ejpam-5396	585	27	to	to	ADP
ejpam-5396	585	28	α	α	NOUN
ejpam-5396	585	29	=	=	SYM
ejpam-5396	585	30	1	1	NUM
ejpam-5396	585	31	,	,	PUNCT
ejpam-5396	585	32	while	while	SCONJ
ejpam-5396	585	33	c(t	c(t	PROPN
ejpam-5396	585	34	)	)	PUNCT
ejpam-5396	585	35	,	,	PUNCT
ejpam-5396	585	36	i(t	i(t	PROPN
ejpam-5396	585	37	)	)	PUNCT
ejpam-5396	585	38	,	,	PUNCT
ejpam-5396	585	39	and	and	CCONJ
ejpam-5396	585	40	r(t	r(t	NOUN
ejpam-5396	585	41	)	)	PUNCT
ejpam-5396	585	42	decrease	decrease	NOUN
ejpam-5396	585	43	,	,	PUNCT
ejpam-5396	585	44	emphasizing	emphasize	VERB
ejpam-5396	585	45	the	the	DET
ejpam-5396	585	46	impact	impact	NOUN
ejpam-5396	585	47	of	of	ADP
ejpam-5396	585	48	employing	employ	VERB
ejpam-5396	585	49	a	a	DET
ejpam-5396	585	50	fractional	fractional	ADJ
ejpam-5396	585	51	order	order	NOUN
ejpam-5396	585	52	in	in	ADP
ejpam-5396	585	53	the	the	DET
ejpam-5396	585	54	model	model	NOUN
ejpam-5396	585	55	.	.	PUNCT
ejpam-5396	586	1	figures	figure	NOUN
ejpam-5396	586	2	7	7	NUM
ejpam-5396	586	3	and	and	CCONJ
ejpam-5396	586	4	8	8	NUM
ejpam-5396	586	5	,	,	PUNCT
ejpam-5396	586	6	obtained	obtain	VERB
ejpam-5396	586	7	using	use	VERB
ejpam-5396	586	8	the	the	DET
ejpam-5396	586	9	msgdtm	msgdtm	NOUN
ejpam-5396	586	10	method	method	NOUN
ejpam-5396	586	11	,	,	PUNCT
ejpam-5396	586	12	demonstrate	demonstrate	VERB
ejpam-5396	586	13	a	a	DET
ejpam-5396	586	14	remarkable	remarkable	ADJ
ejpam-5396	586	15	increase	increase	NOUN
ejpam-5396	586	16	in	in	ADP
ejpam-5396	586	17	s(t	s(t	PROPN
ejpam-5396	586	18	)	)	PUNCT
ejpam-5396	586	19	for	for	ADP
ejpam-5396	586	20	fractional	fractional	ADJ
ejpam-5396	586	21	values	value	NOUN
ejpam-5396	586	22	of	of	ADP
ejpam-5396	586	23	α	α	NOUN
ejpam-5396	586	24	compared	compare	VERB
ejpam-5396	586	25	to	to	ADP
ejpam-5396	586	26	α	α	NOUN
ejpam-5396	586	27	=	=	SYM
ejpam-5396	586	28	1	1	NUM
ejpam-5396	586	29	,	,	PUNCT
ejpam-5396	586	30	while	while	SCONJ
ejpam-5396	586	31	c(t	c(t	PROPN
ejpam-5396	586	32	)	)	PUNCT
ejpam-5396	586	33	,	,	PUNCT
ejpam-5396	586	34	i(t	i(t	PROPN
ejpam-5396	586	35	)	)	PUNCT
ejpam-5396	586	36	,	,	PUNCT
ejpam-5396	586	37	and	and	CCONJ
ejpam-5396	586	38	r(t	r(t	NOUN
ejpam-5396	586	39	)	)	PUNCT
ejpam-5396	586	40	consistently	consistently	ADV
ejpam-5396	586	41	decrease	decrease	VERB
ejpam-5396	586	42	,	,	PUNCT
ejpam-5396	586	43	reinforcing	reinforce	VERB
ejpam-5396	586	44	the	the	DET
ejpam-5396	586	45	consistent	consistent	ADJ
ejpam-5396	586	46	behavior	behavior	NOUN
ejpam-5396	586	47	observed	observe	VERB
ejpam-5396	586	48	across	across	ADP
ejpam-5396	586	49	various	various	ADJ
ejpam-5396	586	50	methods	method	NOUN
ejpam-5396	586	51	.	.	PUNCT
ejpam-5396	587	1	the	the	DET
ejpam-5396	587	2	collective	collective	ADJ
ejpam-5396	587	3	results	result	NOUN
ejpam-5396	587	4	indicate	indicate	VERB
ejpam-5396	587	5	that	that	SCONJ
ejpam-5396	587	6	fractional	fractional	ADJ
ejpam-5396	587	7	-	-	PUNCT
ejpam-5396	587	8	order	order	NOUN
ejpam-5396	587	9	models	model	NOUN
ejpam-5396	587	10	offer	offer	VERB
ejpam-5396	587	11	a	a	DET
ejpam-5396	587	12	more	more	ADV
ejpam-5396	587	13	nuanced	nuanced	ADJ
ejpam-5396	587	14	and	and	CCONJ
ejpam-5396	587	15	accurate	accurate	ADJ
ejpam-5396	587	16	representation	representation	NOUN
ejpam-5396	587	17	of	of	ADP
ejpam-5396	587	18	system	system	NOUN
ejpam-5396	587	19	dynamics	dynamic	NOUN
ejpam-5396	587	20	when	when	SCONJ
ejpam-5396	587	21	compared	compare	VERB
ejpam-5396	587	22	to	to	ADP
ejpam-5396	587	23	integer	integer	NOUN
ejpam-5396	587	24	-	-	PUNCT
ejpam-5396	587	25	order	order	NOUN
ejpam-5396	587	26	models	model	NOUN
ejpam-5396	587	27	.	.	PUNCT
ejpam-5396	588	1	additionally	additionally	ADV
ejpam-5396	588	2	,	,	PUNCT
ejpam-5396	588	3	the	the	DET
ejpam-5396	588	4	selection	selection	NOUN
ejpam-5396	588	5	of	of	ADP
ejpam-5396	588	6	a	a	DET
ejpam-5396	588	7	numerical	numerical	ADJ
ejpam-5396	588	8	method	method	NOUN
ejpam-5396	588	9	significantly	significantly	ADV
ejpam-5396	588	10	impacts	impact	VERB
ejpam-5396	588	11	the	the	DET
ejpam-5396	588	12	accuracy	accuracy	NOUN
ejpam-5396	588	13	and	and	CCONJ
ejpam-5396	588	14	stability	stability	NOUN
ejpam-5396	588	15	of	of	ADP
ejpam-5396	588	16	the	the	DET
ejpam-5396	588	17	solutions	solution	NOUN
ejpam-5396	588	18	.	.	PUNCT
ejpam-5396	589	1	the	the	DET
ejpam-5396	589	2	visual	visual	ADJ
ejpam-5396	589	3	comparisons	comparison	NOUN
ejpam-5396	589	4	presented	present	VERB
ejpam-5396	589	5	in	in	ADP
ejpam-5396	589	6	the	the	DET
ejpam-5396	589	7	figures	figure	NOUN
ejpam-5396	589	8	play	play	VERB
ejpam-5396	589	9	a	a	DET
ejpam-5396	589	10	pivotal	pivotal	ADJ
ejpam-5396	589	11	role	role	NOUN
ejpam-5396	589	12	in	in	ADP
ejpam-5396	589	13	comprehending	comprehending	ADJ
ejpam-5396	589	14	distinctions	distinction	NOUN
ejpam-5396	589	15	and	and	CCONJ
ejpam-5396	589	16	in	in	ADP
ejpam-5396	589	17	choosing	choose	VERB
ejpam-5396	589	18	suitable	suitable	ADJ
ejpam-5396	589	19	numerical	numerical	ADJ
ejpam-5396	589	20	techniques	technique	NOUN
ejpam-5396	589	21	for	for	ADP
ejpam-5396	589	22	fractionalorder	fractionalorder	ADJ
ejpam-5396	589	23	differential	differential	ADJ
ejpam-5396	589	24	equations	equation	NOUN
ejpam-5396	589	25	.	.	PUNCT
ejpam-5396	590	1	acknowledgements	acknowledgement	NOUN
ejpam-5396	590	2	the	the	DET
ejpam-5396	590	3	author	author	NOUN
ejpam-5396	590	4	expresses	express	VERB
ejpam-5396	590	5	gratitude	gratitude	NOUN
ejpam-5396	590	6	to	to	ADP
ejpam-5396	590	7	the	the	DET
ejpam-5396	590	8	editor	editor	NOUN
ejpam-5396	590	9	and	and	CCONJ
ejpam-5396	590	10	referees	referee	NOUN
ejpam-5396	590	11	for	for	ADP
ejpam-5396	590	12	their	their	PRON
ejpam-5396	590	13	time	time	NOUN
ejpam-5396	590	14	and	and	CCONJ
ejpam-5396	590	15	insightful	insightful	ADJ
ejpam-5396	590	16	comments	comment	NOUN
ejpam-5396	590	17	.	.	PUNCT
ejpam-5396	591	1	references	reference	NOUN
ejpam-5396	591	2	[	[	X
ejpam-5396	591	3	1	1	NUM
ejpam-5396	591	4	]	]	PUNCT
ejpam-5396	591	5	k.	k.	PROPN
ejpam-5396	591	6	abodayeh	abodayeh	PROPN
ejpam-5396	591	7	,	,	PUNCT
ejpam-5396	591	8	a.	a.	NOUN
ejpam-5396	591	9	raza	raza	PROPN
ejpam-5396	591	10	,	,	PUNCT
ejpam-5396	591	11	m.	m.	PROPN
ejpam-5396	591	12	rafiq	rafiq	PROPN
ejpam-5396	591	13	,	,	PUNCT
ejpam-5396	591	14	m.	m.	NOUN
ejpam-5396	591	15	shoaib	shoaib	PROPN
ejpam-5396	591	16	arif	arif	PROPN
ejpam-5396	591	17	,	,	PUNCT
ejpam-5396	591	18	m.	m.	PROPN
ejpam-5396	591	19	naveed	naveed	PROPN
ejpam-5396	591	20	,	,	PUNCT
ejpam-5396	591	21	et	et	PROPN
ejpam-5396	591	22	al	al	PROPN
ejpam-5396	591	23	.	.	PUNCT
ejpam-5396	592	1	analysis	analysis	NOUN
ejpam-5396	592	2	of	of	ADP
ejpam-5396	592	3	pneumonia	pneumonia	NOUN
ejpam-5396	592	4	model	model	NOUN
ejpam-5396	592	5	via	via	ADP
ejpam-5396	592	6	efficient	efficient	ADJ
ejpam-5396	592	7	computing	computing	NOUN
ejpam-5396	592	8	techniques	technique	NOUN
ejpam-5396	592	9	.	.	PUNCT
ejpam-5396	593	1	computers	computer	NOUN
ejpam-5396	593	2	,	,	PUNCT
ejpam-5396	593	3	materials	material	NOUN
ejpam-5396	593	4	&	&	CCONJ
ejpam-5396	593	5	continua	continua	PROPN
ejpam-5396	593	6	,	,	PUNCT
ejpam-5396	593	7	70(3):6073–6088	70(3):6073–6088	NUM
ejpam-5396	593	8	,	,	PUNCT
ejpam-5396	593	9	2022	2022	NUM
ejpam-5396	593	10	.	.	PUNCT
ejpam-5396	594	1	[	[	X
ejpam-5396	594	2	2	2	X
ejpam-5396	594	3	]	]	X
ejpam-5396	594	4	khalid	khalid	PROPN
ejpam-5396	594	5	ahmed	ahmed	PROPN
ejpam-5396	594	6	,	,	PUNCT
ejpam-5396	594	7	haroon	haroon	PROPN
ejpam-5396	594	8	adam	adam	PROPN
ejpam-5396	594	9	,	,	PUNCT
ejpam-5396	594	10	m.y	m.y	PROPN
ejpam-5396	594	11	.	.	PROPN
ejpam-5396	594	12	youssif	youssif	PROPN
ejpam-5396	594	13	,	,	PUNCT
ejpam-5396	594	14	and	and	CCONJ
ejpam-5396	594	15	sayed	say	VERB
ejpam-5396	594	16	saber	saber	PROPN
ejpam-5396	594	17	.	.	PUNCT
ejpam-5396	595	1	different	different	ADJ
ejpam-5396	595	2	strategies	strategy	NOUN
ejpam-5396	595	3	for	for	ADP
ejpam-5396	595	4	diabetes	diabetes	NOUN
ejpam-5396	595	5	by	by	ADP
ejpam-5396	595	6	mathematical	mathematical	ADJ
ejpam-5396	595	7	modeling	modeling	NOUN
ejpam-5396	595	8	:	:	PUNCT
ejpam-5396	595	9	applications	application	NOUN
ejpam-5396	595	10	of	of	ADP
ejpam-5396	595	11	fractal	fractal	ADJ
ejpam-5396	595	12	-	-	PUNCT
ejpam-5396	595	13	fractional	fractional	ADJ
ejpam-5396	595	14	derivatives	derivative	NOUN
ejpam-5396	595	15	in	in	ADP
ejpam-5396	595	16	the	the	DET
ejpam-5396	595	17	sense	sense	NOUN
ejpam-5396	595	18	of	of	ADP
ejpam-5396	595	19	atangana	atangana	PROPN
ejpam-5396	595	20	-	-	PUNCT
ejpam-5396	595	21	baleanu	baleanu	PROPN
ejpam-5396	595	22	.	.	PUNCT
ejpam-5396	596	1	results	result	NOUN
ejpam-5396	596	2	in	in	ADP
ejpam-5396	596	3	physics	physics	NOUN
ejpam-5396	596	4	,	,	PUNCT
ejpam-5396	596	5	52:106892	52:106892	NOUN
ejpam-5396	596	6	,	,	PUNCT
ejpam-5396	596	7	2023	2023	NUM
ejpam-5396	596	8	.	.	PUNCT
ejpam-5396	597	1	[	[	X
ejpam-5396	597	2	3	3	X
ejpam-5396	597	3	]	]	X
ejpam-5396	597	4	khalid	khalid	PROPN
ejpam-5396	597	5	ahmed	ahmed	PROPN
ejpam-5396	597	6	,	,	PUNCT
ejpam-5396	597	7	haroon	haroon	PROPN
ejpam-5396	597	8	adam	adam	PROPN
ejpam-5396	597	9	,	,	PUNCT
ejpam-5396	597	10	m.y	m.y	PROPN
ejpam-5396	597	11	.	.	PROPN
ejpam-5396	597	12	youssif	youssif	PROPN
ejpam-5396	597	13	,	,	PUNCT
ejpam-5396	597	14	and	and	CCONJ
ejpam-5396	597	15	sayed	say	VERB
ejpam-5396	597	16	saber	saber	PROPN
ejpam-5396	597	17	.	.	PUNCT
ejpam-5396	598	1	different	different	ADJ
ejpam-5396	598	2	strategies	strategy	NOUN
ejpam-5396	598	3	for	for	ADP
ejpam-5396	598	4	diabetes	diabetes	NOUN
ejpam-5396	598	5	by	by	ADP
ejpam-5396	598	6	mathematical	mathematical	ADJ
ejpam-5396	598	7	modeling	modeling	NOUN
ejpam-5396	598	8	:	:	PUNCT
ejpam-5396	598	9	modified	modify	VERB
ejpam-5396	598	10	minimal	minimal	ADJ
ejpam-5396	598	11	model	model	NOUN
ejpam-5396	598	12	.	.	PUNCT
ejpam-5396	599	1	alex	alex	PROPN
ejpam-5396	599	2	.	.	PUNCT
ejpam-5396	600	1	eng	eng	PROPN
ejpam-5396	600	2	.	.	PUNCT
ejpam-5396	601	1	j.	j.	PROPN
ejpam-5396	601	2	,	,	PUNCT
ejpam-5396	601	3	80:74–87	80:74–87	NUM
ejpam-5396	601	4	,	,	PUNCT
ejpam-5396	601	5	2023	2023	NUM
ejpam-5396	601	6	.	.	PUNCT
ejpam-5396	602	1	[	[	X
ejpam-5396	602	2	4	4	X
ejpam-5396	602	3	]	]	X
ejpam-5396	602	4	khalid	khalid	PROPN
ejpam-5396	602	5	i.a	i.a	PROPN
ejpam-5396	602	6	.	.	PROPN
ejpam-5396	602	7	ahmed	ahmed	PROPN
ejpam-5396	602	8	,	,	PUNCT
ejpam-5396	602	9	haroon	haroon	PROPN
ejpam-5396	602	10	d.s	d.s	PROPN
ejpam-5396	602	11	.	.	PROPN
ejpam-5396	602	12	adam	adam	PROPN
ejpam-5396	602	13	,	,	PUNCT
ejpam-5396	602	14	najat	najat	PROPN
ejpam-5396	602	15	almutairi	almutairi	NOUN
ejpam-5396	602	16	,	,	PUNCT
ejpam-5396	602	17	and	and	CCONJ
ejpam-5396	602	18	sayed	say	VERB
ejpam-5396	602	19	saber	saber	PROPN
ejpam-5396	602	20	.	.	PUNCT
ejpam-5396	603	1	analytical	analytical	ADJ
ejpam-5396	603	2	solutions	solution	NOUN
ejpam-5396	603	3	for	for	ADP
ejpam-5396	603	4	a	a	DET
ejpam-5396	603	5	class	class	NOUN
ejpam-5396	603	6	of	of	ADP
ejpam-5396	603	7	variable	variable	ADJ
ejpam-5396	603	8	-	-	PUNCT
ejpam-5396	603	9	order	order	NOUN
ejpam-5396	603	10	fractional	fractional	ADJ
ejpam-5396	603	11	liu	liu	PROPN
ejpam-5396	603	12	system	system	NOUN
ejpam-5396	603	13	under	under	ADP
ejpam-5396	603	14	time	time	NOUN
ejpam-5396	603	15	-	-	PUNCT
ejpam-5396	603	16	dependent	dependent	ADJ
ejpam-5396	603	17	variable	variable	ADJ
ejpam-5396	603	18	coefficients	coefficient	NOUN
ejpam-5396	603	19	.	.	PUNCT
ejpam-5396	604	1	results	result	NOUN
ejpam-5396	604	2	in	in	ADP
ejpam-5396	604	3	physics	physics	NOUN
ejpam-5396	604	4	,	,	PUNCT
ejpam-5396	604	5	56:107311	56:107311	NUM
ejpam-5396	604	6	,	,	PUNCT
ejpam-5396	604	7	2024	2024	NUM
ejpam-5396	604	8	.	.	PUNCT
ejpam-5396	605	1	[	[	X
ejpam-5396	605	2	5	5	X
ejpam-5396	605	3	]	]	PUNCT
ejpam-5396	605	4	s.	s.	PROPN
ejpam-5396	605	5	al	al	PROPN
ejpam-5396	605	6	-	-	PUNCT
ejpam-5396	605	7	zahrani	zahrani	PROPN
ejpam-5396	605	8	,	,	PUNCT
ejpam-5396	605	9	fathelrhman	fathelrhman	PROPN
ejpam-5396	605	10	guma	guma	PROPN
ejpam-5396	605	11	,	,	PUNCT
ejpam-5396	605	12	k.	k.	PROPN
ejpam-5396	605	13	al	al	PROPN
ejpam-5396	605	14	-	-	PUNCT
ejpam-5396	605	15	zahrani	zahrani	PROPN
ejpam-5396	605	16	,	,	PUNCT
ejpam-5396	605	17	and	and	CCONJ
ejpam-5396	605	18	sayed	say	VERB
ejpam-5396	605	19	saber	saber	PROPN
ejpam-5396	605	20	.	.	PUNCT
ejpam-5396	606	1	a	a	DET
ejpam-5396	606	2	fractional	fractional	ADJ
ejpam-5396	606	3	order	order	NOUN
ejpam-5396	606	4	sitr	sitr	NOUN
ejpam-5396	606	5	model	model	NOUN
ejpam-5396	606	6	for	for	ADP
ejpam-5396	606	7	forecasting	forecasting	NOUN
ejpam-5396	606	8	of	of	ADP
ejpam-5396	606	9	transmission	transmission	NOUN
ejpam-5396	606	10	of	of	ADP
ejpam-5396	606	11	covid-19	covid-19	PROPN
ejpam-5396	606	12	:	:	PUNCT
ejpam-5396	606	13	sensitivity	sensitivity	NOUN
ejpam-5396	606	14	statistical	statistical	ADJ
ejpam-5396	606	15	analysis	analysis	NOUN
ejpam-5396	606	16	.	.	PUNCT
ejpam-5396	607	1	malaysian	malaysian	ADJ
ejpam-5396	607	2	journal	journal	PROPN
ejpam-5396	607	3	of	of	ADP
ejpam-5396	607	4	mathematical	mathematical	ADJ
ejpam-5396	607	5	sciences	sciences	PROPN
ejpam-5396	607	6	,	,	PUNCT
ejpam-5396	607	7	16(3):517–536	16(3):517–536	PROPN
ejpam-5396	607	8	,	,	PUNCT
ejpam-5396	607	9	2022	2022	NUM
ejpam-5396	607	10	.	.	PUNCT
ejpam-5396	608	1	references	reference	NOUN
ejpam-5396	608	2	2795	2795	NUM
ejpam-5396	608	3	[	[	X
ejpam-5396	608	4	6	6	NUM
ejpam-5396	608	5	]	]	PUNCT
ejpam-5396	608	6	ahmad	ahmad	PROPN
ejpam-5396	608	7	alalyani	alalyani	PROPN
ejpam-5396	608	8	.	.	PUNCT
ejpam-5396	609	1	on	on	ADP
ejpam-5396	609	2	the	the	DET
ejpam-5396	609	3	solution	solution	NOUN
ejpam-5396	609	4	of	of	ADP
ejpam-5396	609	5	a	a	DET
ejpam-5396	609	6	nonlinear	nonlinear	ADJ
ejpam-5396	609	7	fractional	fractional	ADJ
ejpam-5396	609	8	-	-	PUNCT
ejpam-5396	609	9	order	order	NOUN
ejpam-5396	609	10	glucose	glucose	NOUN
ejpam-5396	609	11	-	-	PUNCT
ejpam-5396	609	12	insulin	insulin	NOUN
ejpam-5396	609	13	system	system	NOUN
ejpam-5396	609	14	incorporating	incorporate	VERB
ejpam-5396	609	15	β	β	NOUN
ejpam-5396	609	16	-	-	NOUN
ejpam-5396	609	17	cells	cell	NOUN
ejpam-5396	609	18	compartment	compartment	NOUN
ejpam-5396	609	19	.	.	PUNCT
ejpam-5396	610	1	malaysian	malaysian	ADJ
ejpam-5396	610	2	journal	journal	PROPN
ejpam-5396	610	3	of	of	ADP
ejpam-5396	610	4	mathematical	mathematical	ADJ
ejpam-5396	610	5	sciences	sciences	PROPN
ejpam-5396	610	6	,	,	PUNCT
ejpam-5396	610	7	17(1):1–12	17(1):1–12	NUM
ejpam-5396	610	8	,	,	PUNCT
ejpam-5396	610	9	2023	2023	NUM
ejpam-5396	610	10	.	.	PUNCT
ejpam-5396	611	1	[	[	X
ejpam-5396	611	2	7	7	X
ejpam-5396	611	3	]	]	X
ejpam-5396	611	4	ahmad	ahmad	PROPN
ejpam-5396	611	5	alalyani	alalyani	PROPN
ejpam-5396	611	6	and	and	CCONJ
ejpam-5396	611	7	sayed	say	VERB
ejpam-5396	611	8	saber	saber	PROPN
ejpam-5396	611	9	.	.	PUNCT
ejpam-5396	612	1	stability	stability	NOUN
ejpam-5396	612	2	analysis	analysis	NOUN
ejpam-5396	612	3	and	and	CCONJ
ejpam-5396	612	4	numerical	numerical	ADJ
ejpam-5396	612	5	simulations	simulation	NOUN
ejpam-5396	612	6	of	of	ADP
ejpam-5396	612	7	the	the	DET
ejpam-5396	612	8	fractional	fractional	ADJ
ejpam-5396	612	9	covid-19	covid-19	PROPN
ejpam-5396	612	10	pandemic	pandemic	ADJ
ejpam-5396	612	11	model	model	NOUN
ejpam-5396	612	12	.	.	PUNCT
ejpam-5396	613	1	int	int	NOUN
ejpam-5396	613	2	.	.	PUNCT
ejpam-5396	614	1	j.	j.	PROPN
ejpam-5396	614	2	nonlin	nonlin	PROPN
ejpam-5396	614	3	.	.	PUNCT
ejpam-5396	615	1	sci	sci	PROPN
ejpam-5396	615	2	.	.	PUNCT
ejpam-5396	616	1	num	num	PROPN
ejpam-5396	616	2	.	.	PROPN
ejpam-5396	616	3	,	,	PUNCT
ejpam-5396	616	4	24(3):989	24(3):989	NUM
ejpam-5396	616	5	–	–	PUNCT
ejpam-5396	616	6	1002	1002	NUM
ejpam-5396	616	7	,	,	PUNCT
ejpam-5396	616	8	2023	2023	NUM
ejpam-5396	616	9	.	.	PUNCT
ejpam-5396	617	1	[	[	X
ejpam-5396	617	2	8	8	NUM
ejpam-5396	617	3	]	]	X
ejpam-5396	617	4	n.	n.	NOUN
ejpam-5396	617	5	almutairi	almutairi	NOUN
ejpam-5396	617	6	and	and	CCONJ
ejpam-5396	617	7	s.	s.	PROPN
ejpam-5396	617	8	saber	saber	PROPN
ejpam-5396	617	9	.	.	PUNCT
ejpam-5396	618	1	on	on	ADP
ejpam-5396	618	2	chaos	chaos	NOUN
ejpam-5396	618	3	control	control	NOUN
ejpam-5396	618	4	of	of	ADP
ejpam-5396	618	5	nonlinear	nonlinear	PROPN
ejpam-5396	618	6	fractional	fractional	PROPN
ejpam-5396	618	7	newton	newton	PROPN
ejpam-5396	618	8	-	-	PUNCT
ejpam-5396	618	9	leipnik	leipnik	NOUN
ejpam-5396	618	10	system	system	NOUN
ejpam-5396	618	11	via	via	ADP
ejpam-5396	618	12	fractional	fractional	PROPN
ejpam-5396	618	13	caputo	caputo	PROPN
ejpam-5396	618	14	-	-	PUNCT
ejpam-5396	618	15	fabrizio	fabrizio	PROPN
ejpam-5396	618	16	derivatives	derivative	NOUN
ejpam-5396	618	17	.	.	PUNCT
ejpam-5396	619	1	scientific	scientific	ADJ
ejpam-5396	619	2	reports	report	NOUN
ejpam-5396	619	3	,	,	PUNCT
ejpam-5396	619	4	13:22726	13:22726	NOUN
ejpam-5396	619	5	,	,	PUNCT
ejpam-5396	619	6	2023	2023	NUM
ejpam-5396	619	7	.	.	PUNCT
ejpam-5396	620	1	[	[	X
ejpam-5396	620	2	9	9	NUM
ejpam-5396	620	3	]	]	X
ejpam-5396	620	4	najat	najat	ADJ
ejpam-5396	620	5	almutairi	almutairi	NOUN
ejpam-5396	620	6	and	and	CCONJ
ejpam-5396	620	7	sayed	sayed	PROPN
ejpam-5396	620	8	saber	saber	PROPN
ejpam-5396	620	9	.	.	PUNCT
ejpam-5396	621	1	chaos	chaos	NOUN
ejpam-5396	621	2	control	control	NOUN
ejpam-5396	621	3	and	and	CCONJ
ejpam-5396	621	4	numerical	numerical	ADJ
ejpam-5396	621	5	solution	solution	NOUN
ejpam-5396	621	6	of	of	ADP
ejpam-5396	621	7	timevarying	timevarye	VERB
ejpam-5396	621	8	fractional	fractional	PROPN
ejpam-5396	621	9	newton	newton	PROPN
ejpam-5396	621	10	-	-	PUNCT
ejpam-5396	621	11	leipnik	leipnik	NOUN
ejpam-5396	621	12	system	system	NOUN
ejpam-5396	621	13	using	use	VERB
ejpam-5396	621	14	fractional	fractional	ADJ
ejpam-5396	621	15	atangana	atangana	PROPN
ejpam-5396	621	16	-	-	PUNCT
ejpam-5396	621	17	baleanu	baleanu	ADJ
ejpam-5396	621	18	derivatives	derivative	NOUN
ejpam-5396	621	19	.	.	PUNCT
ejpam-5396	622	1	aims	aim	VERB
ejpam-5396	622	2	mathematics	mathematic	NOUN
ejpam-5396	622	3	,	,	PUNCT
ejpam-5396	622	4	8(11):25863–25887	8(11):25863–25887	NUM
ejpam-5396	622	5	,	,	PUNCT
ejpam-5396	622	6	2023	2023	NUM
ejpam-5396	622	7	.	.	PUNCT
ejpam-5396	623	1	[	[	X
ejpam-5396	623	2	10	10	NUM
ejpam-5396	623	3	]	]	X
ejpam-5396	623	4	najat	najat	ADJ
ejpam-5396	623	5	almutairi	almutairi	NOUN
ejpam-5396	623	6	and	and	CCONJ
ejpam-5396	623	7	sayed	sayed	PROPN
ejpam-5396	623	8	saber	saber	PROPN
ejpam-5396	623	9	.	.	PUNCT
ejpam-5396	624	1	application	application	NOUN
ejpam-5396	624	2	of	of	ADP
ejpam-5396	624	3	a	a	DET
ejpam-5396	624	4	time	time	NOUN
ejpam-5396	624	5	-	-	PUNCT
ejpam-5396	624	6	fractal	fractal	ADJ
ejpam-5396	624	7	fractional	fractional	ADJ
ejpam-5396	624	8	derivative	derivative	NOUN
ejpam-5396	624	9	with	with	ADP
ejpam-5396	624	10	a	a	DET
ejpam-5396	624	11	power	power	NOUN
ejpam-5396	624	12	-	-	PUNCT
ejpam-5396	624	13	law	law	NOUN
ejpam-5396	624	14	kernel	kernel	NOUN
ejpam-5396	624	15	to	to	ADP
ejpam-5396	624	16	the	the	DET
ejpam-5396	624	17	burke	burke	PROPN
ejpam-5396	624	18	-	-	PUNCT
ejpam-5396	624	19	shaw	shaw	PROPN
ejpam-5396	624	20	system	system	NOUN
ejpam-5396	624	21	based	base	VERB
ejpam-5396	624	22	on	on	ADP
ejpam-5396	624	23	newton	newton	PROPN
ejpam-5396	624	24	’s	’s	PART
ejpam-5396	624	25	interpolation	interpolation	NOUN
ejpam-5396	624	26	polynomials	polynomial	NOUN
ejpam-5396	624	27	.	.	PUNCT
ejpam-5396	625	1	methodsx	methodsx	PROPN
ejpam-5396	625	2	,	,	PUNCT
ejpam-5396	625	3	12:102510	12:102510	NUM
ejpam-5396	625	4	,	,	PUNCT
ejpam-5396	625	5	2024	2024	NUM
ejpam-5396	625	6	.	.	PUNCT
ejpam-5396	626	1	[	[	X
ejpam-5396	626	2	11	11	NUM
ejpam-5396	626	3	]	]	X
ejpam-5396	626	4	najat	najat	ADJ
ejpam-5396	626	5	almutairi	almutairi	NOUN
ejpam-5396	626	6	and	and	CCONJ
ejpam-5396	626	7	sayed	sayed	PROPN
ejpam-5396	626	8	saber	saber	PROPN
ejpam-5396	626	9	.	.	PUNCT
ejpam-5396	627	1	existence	existence	NOUN
ejpam-5396	627	2	of	of	ADP
ejpam-5396	627	3	chaos	chaos	NOUN
ejpam-5396	627	4	and	and	CCONJ
ejpam-5396	627	5	the	the	DET
ejpam-5396	627	6	approximate	approximate	ADJ
ejpam-5396	627	7	solution	solution	NOUN
ejpam-5396	627	8	of	of	ADP
ejpam-5396	627	9	the	the	DET
ejpam-5396	627	10	lorenz	lorenz	PROPN
ejpam-5396	627	11	–	–	PUNCT
ejpam-5396	627	12	lü–chen	lü–chen	NOUN
ejpam-5396	627	13	system	system	NOUN
ejpam-5396	627	14	with	with	ADP
ejpam-5396	627	15	the	the	DET
ejpam-5396	627	16	caputo	caputo	PROPN
ejpam-5396	627	17	fractional	fractional	PROPN
ejpam-5396	627	18	operator	operator	NOUN
ejpam-5396	627	19	.	.	PUNCT
ejpam-5396	628	1	aip	aip	PROPN
ejpam-5396	628	2	advances	advance	NOUN
ejpam-5396	628	3	,	,	PUNCT
ejpam-5396	628	4	14(1):015112	14(1):015112	NUM
ejpam-5396	628	5	,	,	PUNCT
ejpam-5396	628	6	2024	2024	NUM
ejpam-5396	628	7	.	.	PUNCT
ejpam-5396	629	1	[	[	X
ejpam-5396	629	2	12	12	NUM
ejpam-5396	629	3	]	]	X
ejpam-5396	629	4	najat	najat	PROPN
ejpam-5396	629	5	almutairi	almutairi	PROPN
ejpam-5396	629	6	,	,	PUNCT
ejpam-5396	629	7	sayed	sayed	PROPN
ejpam-5396	629	8	saber	saber	PROPN
ejpam-5396	629	9	,	,	PUNCT
ejpam-5396	629	10	and	and	CCONJ
ejpam-5396	629	11	hijaz	hijaz	PROPN
ejpam-5396	629	12	ahmad	ahmad	PROPN
ejpam-5396	629	13	.	.	PUNCT
ejpam-5396	630	1	the	the	DET
ejpam-5396	630	2	fractal	fractal	ADJ
ejpam-5396	630	3	-	-	PUNCT
ejpam-5396	630	4	fractional	fractional	ADJ
ejpam-5396	630	5	atanganabaleanu	atanganabaleanu	NOUN
ejpam-5396	630	6	operator	operator	NOUN
ejpam-5396	630	7	for	for	ADP
ejpam-5396	630	8	pneumonia	pneumonia	NOUN
ejpam-5396	630	9	disease	disease	NOUN
ejpam-5396	630	10	:	:	PUNCT
ejpam-5396	630	11	stability	stability	NOUN
ejpam-5396	630	12	,	,	PUNCT
ejpam-5396	630	13	statistical	statistical	ADJ
ejpam-5396	630	14	and	and	CCONJ
ejpam-5396	630	15	numerical	numerical	ADJ
ejpam-5396	630	16	analyses	analysis	NOUN
ejpam-5396	630	17	.	.	PUNCT
ejpam-5396	631	1	aims	aim	VERB
ejpam-5396	631	2	mathematics	mathematic	NOUN
ejpam-5396	631	3	,	,	PUNCT
ejpam-5396	631	4	8(12):29382–29410	8(12):29382–29410	NUM
ejpam-5396	631	5	,	,	PUNCT
ejpam-5396	631	6	2023	2023	NUM
ejpam-5396	631	7	.	.	PUNCT
ejpam-5396	632	1	[	[	X
ejpam-5396	632	2	13	13	NUM
ejpam-5396	632	3	]	]	PUNCT
ejpam-5396	632	4	m.	m.	NOUN
ejpam-5396	632	5	h.	h.	PROPN
ejpam-5396	632	6	alshehri	alshehri	PROPN
ejpam-5396	632	7	,	,	PUNCT
ejpam-5396	632	8	f.	f.	PROPN
ejpam-5396	632	9	z.	z.	PROPN
ejpam-5396	632	10	duraihem	duraihem	PROPN
ejpam-5396	632	11	,	,	PUNCT
ejpam-5396	632	12	a.	a.	NOUN
ejpam-5396	632	13	alalyani	alalyani	PROPN
ejpam-5396	632	14	,	,	PUNCT
ejpam-5396	632	15	and	and	CCONJ
ejpam-5396	632	16	s.	s.	PROPN
ejpam-5396	632	17	saber	saber	PROPN
ejpam-5396	632	18	.	.	PUNCT
ejpam-5396	633	1	a	a	DET
ejpam-5396	633	2	caputo	caputo	PROPN
ejpam-5396	633	3	(	(	PUNCT
ejpam-5396	633	4	discretization	discretization	NOUN
ejpam-5396	633	5	)	)	PUNCT
ejpam-5396	633	6	fractional	fractional	ADJ
ejpam-5396	633	7	-	-	PUNCT
ejpam-5396	633	8	order	order	NOUN
ejpam-5396	633	9	model	model	NOUN
ejpam-5396	633	10	of	of	ADP
ejpam-5396	633	11	glucose	glucose	NOUN
ejpam-5396	633	12	-	-	PUNCT
ejpam-5396	633	13	insulin	insulin	NOUN
ejpam-5396	633	14	interaction	interaction	NOUN
ejpam-5396	633	15	:	:	PUNCT
ejpam-5396	633	16	numerical	numerical	ADJ
ejpam-5396	633	17	solution	solution	NOUN
ejpam-5396	633	18	and	and	CCONJ
ejpam-5396	633	19	comparisons	comparison	NOUN
ejpam-5396	633	20	with	with	ADP
ejpam-5396	633	21	experimental	experimental	ADJ
ejpam-5396	633	22	data	datum	NOUN
ejpam-5396	633	23	.	.	PUNCT
ejpam-5396	634	1	j.	j.	PROPN
ejpam-5396	634	2	taibah	taibah	PROPN
ejpam-5396	634	3	univ	univ	PROPN
ejpam-5396	634	4	.	.	PUNCT
ejpam-5396	635	1	sci	sci	PROPN
ejpam-5396	635	2	.	.	PROPN
ejpam-5396	635	3	,	,	PUNCT
ejpam-5396	635	4	15(1):26–36	15(1):26–36	NUM
ejpam-5396	635	5	,	,	PUNCT
ejpam-5396	635	6	2021	2021	NUM
ejpam-5396	635	7	.	.	PUNCT
ejpam-5396	636	1	[	[	X
ejpam-5396	636	2	14	14	NUM
ejpam-5396	636	3	]	]	X
ejpam-5396	636	4	mansoor	mansoor	PROPN
ejpam-5396	636	5	h.	h.	PROPN
ejpam-5396	636	6	alshehri	alshehri	PROPN
ejpam-5396	636	7	,	,	PUNCT
ejpam-5396	636	8	sayed	say	VERB
ejpam-5396	636	9	saber	saber	PROPN
ejpam-5396	636	10	,	,	PUNCT
ejpam-5396	636	11	and	and	CCONJ
ejpam-5396	636	12	faisal	faisal	PROPN
ejpam-5396	636	13	z.	z.	PROPN
ejpam-5396	636	14	duraihem	duraihem	PROPN
ejpam-5396	636	15	.	.	PUNCT
ejpam-5396	637	1	dynamical	dynamical	ADJ
ejpam-5396	637	2	analysis	analysis	NOUN
ejpam-5396	637	3	of	of	ADP
ejpam-5396	637	4	fractional	fractional	ADJ
ejpam-5396	637	5	-	-	PUNCT
ejpam-5396	637	6	order	order	NOUN
ejpam-5396	637	7	of	of	ADP
ejpam-5396	637	8	ivgtt	ivgtt	ADJ
ejpam-5396	637	9	glucose	glucose	NOUN
ejpam-5396	637	10	–	–	PUNCT
ejpam-5396	637	11	insulin	insulin	NOUN
ejpam-5396	637	12	interaction	interaction	NOUN
ejpam-5396	637	13	.	.	PUNCT
ejpam-5396	638	1	int	int	NOUN
ejpam-5396	638	2	.	.	PUNCT
ejpam-5396	639	1	j.	j.	PROPN
ejpam-5396	639	2	nonlin	nonlin	PROPN
ejpam-5396	639	3	.	.	PUNCT
ejpam-5396	640	1	sci	sci	PROPN
ejpam-5396	640	2	.	.	PUNCT
ejpam-5396	641	1	num	num	PROPN
ejpam-5396	641	2	.	.	PROPN
ejpam-5396	641	3	,	,	PUNCT
ejpam-5396	641	4	24:1123–1140	24:1123–1140	NUM
ejpam-5396	641	5	,	,	PUNCT
ejpam-5396	641	6	2023	2023	NUM
ejpam-5396	641	7	.	.	PUNCT
ejpam-5396	642	1	[	[	X
ejpam-5396	642	2	15	15	NUM
ejpam-5396	642	3	]	]	X
ejpam-5396	642	4	a.	a.	NOUN
ejpam-5396	642	5	boukhouima	boukhouima	PROPN
ejpam-5396	642	6	,	,	PUNCT
ejpam-5396	642	7	k.	k.	PROPN
ejpam-5396	642	8	hattaf	hattaf	PROPN
ejpam-5396	642	9	,	,	PUNCT
ejpam-5396	642	10	and	and	CCONJ
ejpam-5396	642	11	n.	n.	PROPN
ejpam-5396	642	12	yousfi	yousfi	PROPN
ejpam-5396	642	13	.	.	PUNCT
ejpam-5396	643	1	dynamics	dynamic	NOUN
ejpam-5396	643	2	of	of	ADP
ejpam-5396	643	3	a	a	DET
ejpam-5396	643	4	fractional	fractional	ADJ
ejpam-5396	643	5	order	order	NOUN
ejpam-5396	643	6	hiv	hiv	PROPN
ejpam-5396	643	7	infection	infection	NOUN
ejpam-5396	643	8	model	model	NOUN
ejpam-5396	643	9	with	with	ADP
ejpam-5396	643	10	specific	specific	ADJ
ejpam-5396	643	11	functional	functional	ADJ
ejpam-5396	643	12	response	response	NOUN
ejpam-5396	643	13	and	and	CCONJ
ejpam-5396	643	14	cure	cure	NOUN
ejpam-5396	643	15	rate	rate	NOUN
ejpam-5396	643	16	.	.	PUNCT
ejpam-5396	644	1	int	int	NOUN
ejpam-5396	644	2	.	.	PUNCT
ejpam-5396	645	1	j.	j.	PROPN
ejpam-5396	645	2	differ	differ	VERB
ejpam-5396	645	3	.	.	PUNCT
ejpam-5396	646	1	equ	equ	PROPN
ejpam-5396	646	2	.	.	PROPN
ejpam-5396	646	3	,	,	PUNCT
ejpam-5396	646	4	2017	2017	NUM
ejpam-5396	646	5	:	:	PUNCT
ejpam-5396	646	6	article	article	NOUN
ejpam-5396	646	7	i	i	PROPN
ejpam-5396	646	8	d	d	PROPN
ejpam-5396	646	9	8372140	8372140	NUM
ejpam-5396	646	10	,	,	PUNCT
ejpam-5396	646	11	2017	2017	NUM
ejpam-5396	646	12	.	.	PUNCT
ejpam-5396	647	1	[	[	X
ejpam-5396	647	2	16	16	NUM
ejpam-5396	647	3	]	]	PUNCT
ejpam-5396	647	4	a.c.g	a.c.g	NOUN
ejpam-5396	647	5	.	.	PUNCT
ejpam-5396	647	6	cesar	cesar	PROPN
ejpam-5396	647	7	,	,	PUNCT
ejpam-5396	647	8	l.f.c	l.f.c	PROPN
ejpam-5396	647	9	.	.	PROPN
ejpam-5396	647	10	nascimento	nascimento	PROPN
ejpam-5396	647	11	,	,	PUNCT
ejpam-5396	647	12	k.c.c	k.c.c	PROPN
ejpam-5396	647	13	.	.	PUNCT
ejpam-5396	647	14	mantovani	mantovani	PROPN
ejpam-5396	647	15	,	,	PUNCT
ejpam-5396	647	16	and	and	CCONJ
ejpam-5396	647	17	l.c.p	l.c.p	NOUN
ejpam-5396	647	18	.	.	PUNCT
ejpam-5396	648	1	vieira	vieira	PROPN
ejpam-5396	648	2	.	.	PUNCT
ejpam-5396	649	1	fine	fine	ADJ
ejpam-5396	649	2	particulate	particulate	NOUN
ejpam-5396	649	3	matter	matter	NOUN
ejpam-5396	649	4	estimated	estimate	VERB
ejpam-5396	649	5	by	by	ADP
ejpam-5396	649	6	mathematical	mathematical	ADJ
ejpam-5396	649	7	model	model	NOUN
ejpam-5396	649	8	and	and	CCONJ
ejpam-5396	649	9	hospitalisations	hospitalisation	NOUN
ejpam-5396	649	10	for	for	ADP
ejpam-5396	649	11	pneumonia	pneumonia	NOUN
ejpam-5396	649	12	and	and	CCONJ
ejpam-5396	649	13	asthma	asthma	NOUN
ejpam-5396	649	14	in	in	ADP
ejpam-5396	649	15	children	child	NOUN
ejpam-5396	649	16	.	.	PUNCT
ejpam-5396	650	1	rev	rev	PROPN
ejpam-5396	650	2	.	.	PROPN
ejpam-5396	650	3	paul	paul	PROPN
ejpam-5396	650	4	.	.	PUNCT
ejpam-5396	651	1	pediatr	pediatr	PROPN
ejpam-5396	651	2	.	.	PUNCT
ejpam-5396	652	1	(	(	PUNCT
ejpam-5396	652	2	engl	engl	PROPN
ejpam-5396	652	3	.	.	PUNCT
ejpam-5396	653	1	ed	ed	NOUN
ejpam-5396	653	2	.	.	PUNCT
ejpam-5396	653	3	)	)	PUNCT
ejpam-5396	653	4	,	,	PUNCT
ejpam-5396	654	1	34(1):18–23	34(1):18–23	NUM
ejpam-5396	654	2	,	,	PUNCT
ejpam-5396	654	3	2016	2016	NUM
ejpam-5396	654	4	.	.	PUNCT
ejpam-5396	655	1	[	[	X
ejpam-5396	655	2	17	17	NUM
ejpam-5396	655	3	]	]	X
ejpam-5396	655	4	y.h	y.h	PROPN
ejpam-5396	655	5	.	.	PROPN
ejpam-5396	655	6	cheng	cheng	PROPN
ejpam-5396	655	7	,	,	PUNCT
ejpam-5396	655	8	s.h	s.h	PROPN
ejpam-5396	655	9	.	.	PUNCT
ejpam-5396	655	10	you	you	PRON
ejpam-5396	655	11	,	,	PUNCT
ejpam-5396	655	12	y.j	y.j	PROPN
ejpam-5396	655	13	.	.	PUNCT
ejpam-5396	655	14	lin	lin	PROPN
ejpam-5396	655	15	,	,	PUNCT
ejpam-5396	655	16	s.c	s.c	PROPN
ejpam-5396	655	17	.	.	PROPN
ejpam-5396	655	18	chen	chen	PROPN
ejpam-5396	655	19	,	,	PUNCT
ejpam-5396	656	1	w.y	w.y	PROPN
ejpam-5396	656	2	.	.	PUNCT
ejpam-5396	656	3	chen	chen	PROPN
ejpam-5396	656	4	,	,	PUNCT
ejpam-5396	656	5	w.c	w.c	PROPN
ejpam-5396	656	6	.	.	PROPN
ejpam-5396	656	7	chou	chou	PROPN
ejpam-5396	656	8	,	,	PUNCT
ejpam-5396	656	9	and	and	CCONJ
ejpam-5396	656	10	c.m	c.m	PROPN
ejpam-5396	656	11	.	.	PROPN
ejpam-5396	656	12	liao	liao	PROPN
ejpam-5396	656	13	.	.	PROPN
ejpam-5396	657	1	mathematical	mathematical	ADJ
ejpam-5396	657	2	modeling	modeling	NOUN
ejpam-5396	657	3	of	of	ADP
ejpam-5396	657	4	post	post	ADJ
ejpam-5396	657	5	coinfection	coinfection	NOUN
ejpam-5396	657	6	with	with	ADP
ejpam-5396	657	7	influenza	influenza	NOUN
ejpam-5396	657	8	a	a	DET
ejpam-5396	657	9	virus	virus	NOUN
ejpam-5396	657	10	and	and	CCONJ
ejpam-5396	657	11	streptococcus	streptococcus	VERB
ejpam-5396	657	12	pneumoniae	pneumoniae	NOUN
ejpam-5396	657	13	,	,	PUNCT
ejpam-5396	657	14	with	with	ADP
ejpam-5396	657	15	implications	implication	NOUN
ejpam-5396	657	16	for	for	ADP
ejpam-5396	657	17	pneumonia	pneumonia	NOUN
ejpam-5396	657	18	and	and	CCONJ
ejpam-5396	657	19	copd	copd	NOUN
ejpam-5396	657	20	-	-	PUNCT
ejpam-5396	657	21	risk	risk	NOUN
ejpam-5396	657	22	assessment	assessment	NOUN
ejpam-5396	657	23	.	.	PUNCT
ejpam-5396	658	1	int	int	NOUN
ejpam-5396	658	2	.	.	PUNCT
ejpam-5396	659	1	j.	j.	PROPN
ejpam-5396	659	2	chronic	chronic	PROPN
ejpam-5396	659	3	obstr	obstr	PROPN
ejpam-5396	659	4	.	.	PUNCT
ejpam-5396	660	1	pulm	pulm	NOUN
ejpam-5396	660	2	.	.	PUNCT
ejpam-5396	661	1	dis	dis	PROPN
ejpam-5396	661	2	.	.	PROPN
ejpam-5396	661	3	,	,	PUNCT
ejpam-5396	661	4	12:1973–1988	12:1973–1988	NUM
ejpam-5396	661	5	,	,	PUNCT
ejpam-5396	661	6	2017	2017	NUM
ejpam-5396	661	7	.	.	PUNCT
ejpam-5396	662	1	references	reference	NOUN
ejpam-5396	662	2	2796	2796	NUM
ejpam-5396	662	3	[	[	X
ejpam-5396	662	4	18	18	NUM
ejpam-5396	662	5	]	]	X
ejpam-5396	662	6	s.k	s.k	PROPN
ejpam-5396	662	7	.	.	PROPN
ejpam-5396	662	8	choi	choi	PROPN
ejpam-5396	662	9	,	,	PUNCT
ejpam-5396	662	10	b.	b.	PROPN
ejpam-5396	662	11	kang	kang	PROPN
ejpam-5396	662	12	,	,	PUNCT
ejpam-5396	662	13	and	and	CCONJ
ejpam-5396	662	14	n.	n.	PROPN
ejpam-5396	662	15	koo	koo	PROPN
ejpam-5396	662	16	.	.	PUNCT
ejpam-5396	662	17	stability	stability	NOUN
ejpam-5396	662	18	for	for	ADP
ejpam-5396	662	19	caputo	caputo	PROPN
ejpam-5396	662	20	fractional	fractional	PROPN
ejpam-5396	662	21	differential	differential	PROPN
ejpam-5396	662	22	systems	system	NOUN
ejpam-5396	662	23	.	.	PUNCT
ejpam-5396	663	1	abstr	abstr	PROPN
ejpam-5396	663	2	.	.	PUNCT
ejpam-5396	663	3	appl	appl	PROPN
ejpam-5396	663	4	.	.	PUNCT
ejpam-5396	664	1	anal	anal	PROPN
ejpam-5396	664	2	.	.	PROPN
ejpam-5396	664	3	,	,	PUNCT
ejpam-5396	664	4	2014	2014	NUM
ejpam-5396	664	5	:	:	PUNCT
ejpam-5396	664	6	article	article	NOUN
ejpam-5396	664	7	i	i	PROPN
ejpam-5396	664	8	d	d	PROPN
ejpam-5396	664	9	631419	631419	NUM
ejpam-5396	664	10	,	,	PUNCT
ejpam-5396	664	11	2014	2014	NUM
ejpam-5396	664	12	.	.	PUNCT
ejpam-5396	665	1	[	[	X
ejpam-5396	665	2	19	19	NUM
ejpam-5396	665	3	]	]	X
ejpam-5396	665	4	i.m	i.m	PROPN
ejpam-5396	665	5	.	.	PROPN
ejpam-5396	665	6	diah	diah	PROPN
ejpam-5396	665	7	and	and	CCONJ
ejpam-5396	665	8	n.	n.	PROPN
ejpam-5396	665	9	aziz	aziz	PROPN
ejpam-5396	665	10	.	.	PUNCT
ejpam-5396	666	1	stochastic	stochastic	ADJ
ejpam-5396	666	2	modelling	modelling	NOUN
ejpam-5396	666	3	for	for	ADP
ejpam-5396	666	4	pneumonia	pneumonia	NOUN
ejpam-5396	666	5	incidence	incidence	NOUN
ejpam-5396	666	6	:	:	PUNCT
ejpam-5396	666	7	a	a	DET
ejpam-5396	666	8	conceptual	conceptual	ADJ
ejpam-5396	666	9	framework	framework	NOUN
ejpam-5396	666	10	.	.	PUNCT
ejpam-5396	667	1	aip	aip	PROPN
ejpam-5396	667	2	conference	conference	NOUN
ejpam-5396	667	3	proceedings	proceeding	NOUN
ejpam-5396	667	4	new	new	PROPN
ejpam-5396	667	5	york	york	PROPN
ejpam-5396	667	6	,	,	PUNCT
ejpam-5396	667	7	1:1–3	1:1–3	NUM
ejpam-5396	667	8	,	,	PUNCT
ejpam-5396	667	9	2019	2019	NUM
ejpam-5396	667	10	.	.	PUNCT
ejpam-5396	668	1	[	[	X
ejpam-5396	668	2	20	20	NUM
ejpam-5396	668	3	]	]	PUNCT
ejpam-5396	668	4	k.	k.	PROPN
ejpam-5396	668	5	diethelm	diethelm	PROPN
ejpam-5396	668	6	and	and	CCONJ
ejpam-5396	668	7	a.	a.	PROPN
ejpam-5396	668	8	d.	d.	PROPN
ejpam-5396	668	9	freed	free	VERB
ejpam-5396	668	10	.	.	PUNCT
ejpam-5396	669	1	the	the	DET
ejpam-5396	669	2	fracpece	fracpece	NOUN
ejpam-5396	669	3	subroutine	subroutine	NOUN
ejpam-5396	669	4	for	for	ADP
ejpam-5396	669	5	the	the	DET
ejpam-5396	669	6	numerical	numerical	ADJ
ejpam-5396	669	7	solution	solution	NOUN
ejpam-5396	669	8	of	of	ADP
ejpam-5396	669	9	differential	differential	ADJ
ejpam-5396	669	10	equations	equation	NOUN
ejpam-5396	669	11	of	of	ADP
ejpam-5396	669	12	fractional	fractional	ADJ
ejpam-5396	669	13	order	order	NOUN
ejpam-5396	669	14	.	.	PUNCT
ejpam-5396	670	1	forschung	forschung	PROPN
ejpam-5396	670	2	und	und	PROPN
ejpam-5396	670	3	wissenschaftliches	wissenschaftliche	NOUN
ejpam-5396	670	4	rechnen	rechnen	PROPN
ejpam-5396	670	5	,	,	PUNCT
ejpam-5396	670	6	1999:57–71	1999:57–71	PROPN
ejpam-5396	670	7	,	,	PUNCT
ejpam-5396	670	8	2002	2002	NUM
ejpam-5396	670	9	.	.	PUNCT
ejpam-5396	671	1	[	[	X
ejpam-5396	671	2	21	21	NUM
ejpam-5396	671	3	]	]	X
ejpam-5396	671	4	g.l	g.l	PROPN
ejpam-5396	671	5	.	.	PROPN
ejpam-5396	671	6	drusano	drusano	PROPN
ejpam-5396	671	7	,	,	PUNCT
ejpam-5396	671	8	w.	w.	PROPN
ejpam-5396	671	9	liu	liu	PROPN
ejpam-5396	671	10	,	,	PUNCT
ejpam-5396	671	11	s.	s.	PROPN
ejpam-5396	671	12	fikes	fikes	PROPN
ejpam-5396	671	13	,	,	PUNCT
ejpam-5396	671	14	r.	r.	PROPN
ejpam-5396	671	15	cirz	cirz	PROPN
ejpam-5396	671	16	,	,	PUNCT
ejpam-5396	671	17	n.	n.	NOUN
ejpam-5396	671	18	robbins	robbins	PROPN
ejpam-5396	671	19	,	,	PUNCT
ejpam-5396	671	20	s.	s.	PROPN
ejpam-5396	671	21	kurhanewicz	kurhanewicz	PROPN
ejpam-5396	671	22	,	,	PUNCT
ejpam-5396	671	23	and	and	CCONJ
ejpam-5396	671	24	a.	a.	PROPN
ejpam-5396	671	25	louie	louie	PROPN
ejpam-5396	671	26	.	.	PUNCT
ejpam-5396	672	1	interaction	interaction	NOUN
ejpam-5396	672	2	of	of	ADP
ejpam-5396	672	3	drug	drug	NOUN
ejpam-5396	672	4	-	-	PUNCT
ejpam-5396	672	5	and	and	CCONJ
ejpam-5396	672	6	granulocyte	granulocyte	ADJ
ejpam-5396	672	7	-	-	PUNCT
ejpam-5396	672	8	mediated	mediate	VERB
ejpam-5396	672	9	killing	killing	NOUN
ejpam-5396	672	10	of	of	ADP
ejpam-5396	672	11	pseudomonas	pseudomona	NOUN
ejpam-5396	672	12	aeruginosa	aeruginosa	NOUN
ejpam-5396	672	13	in	in	ADP
ejpam-5396	672	14	a	a	DET
ejpam-5396	672	15	murine	murine	ADJ
ejpam-5396	672	16	pneumonia	pneumonia	NOUN
ejpam-5396	672	17	model	model	NOUN
ejpam-5396	672	18	.	.	PUNCT
ejpam-5396	673	1	j.	j.	PROPN
ejpam-5396	673	2	infect	infect	PROPN
ejpam-5396	673	3	.	.	PUNCT
ejpam-5396	674	1	dis	dis	PROPN
ejpam-5396	674	2	.	.	PROPN
ejpam-5396	674	3	,	,	PUNCT
ejpam-5396	674	4	210(8):1319–1324	210(8):1319–1324	NUM
ejpam-5396	674	5	,	,	PUNCT
ejpam-5396	674	6	2014	2014	NUM
ejpam-5396	674	7	.	.	PUNCT
ejpam-5396	675	1	[	[	X
ejpam-5396	675	2	22	22	NUM
ejpam-5396	675	3	]	]	PUNCT
ejpam-5396	675	4	v.	v.	PROPN
ejpam-5396	675	5	erturk	erturk	PROPN
ejpam-5396	675	6	,	,	PUNCT
ejpam-5396	675	7	g.	g.	PROPN
ejpam-5396	675	8	zaman	zaman	PROPN
ejpam-5396	675	9	,	,	PUNCT
ejpam-5396	675	10	and	and	CCONJ
ejpam-5396	675	11	s.	s.	PROPN
ejpam-5396	675	12	momani	momani	PROPN
ejpam-5396	675	13	.	.	PUNCT
ejpam-5396	676	1	a	a	DET
ejpam-5396	676	2	numeric	numeric	ADJ
ejpam-5396	676	3	-	-	PUNCT
ejpam-5396	676	4	analytic	analytic	ADJ
ejpam-5396	676	5	method	method	NOUN
ejpam-5396	676	6	for	for	ADP
ejpam-5396	676	7	approximating	approximate	VERB
ejpam-5396	676	8	a	a	DET
ejpam-5396	676	9	giving	giving	NOUN
ejpam-5396	676	10	up	up	ADP
ejpam-5396	676	11	smoking	smoking	NOUN
ejpam-5396	676	12	model	model	NOUN
ejpam-5396	676	13	containing	contain	VERB
ejpam-5396	676	14	fractional	fractional	ADJ
ejpam-5396	676	15	derivatives	derivative	NOUN
ejpam-5396	676	16	.	.	PUNCT
ejpam-5396	677	1	computers	computer	NOUN
ejpam-5396	677	2	&	&	CCONJ
ejpam-5396	677	3	mathematics	mathematics	PROPN
ejpam-5396	677	4	with	with	ADP
ejpam-5396	677	5	applications	application	NOUN
ejpam-5396	677	6	,	,	PUNCT
ejpam-5396	677	7	64(10):3065–3074	64(10):3065–3074	PROPN
ejpam-5396	677	8	,	,	PUNCT
ejpam-5396	677	9	2012	2012	NUM
ejpam-5396	677	10	.	.	PUNCT
ejpam-5396	678	1	[	[	X
ejpam-5396	678	2	23	23	NUM
ejpam-5396	678	3	]	]	X
ejpam-5396	678	4	v.	v.	CCONJ
ejpam-5396	678	5	s.	s.	PROPN
ejpam-5396	678	6	erturk	erturk	PROPN
ejpam-5396	678	7	,	,	PUNCT
ejpam-5396	678	8	s.	s.	PROPN
ejpam-5396	678	9	momani	momani	PROPN
ejpam-5396	678	10	,	,	PUNCT
ejpam-5396	678	11	and	and	CCONJ
ejpam-5396	678	12	z.	z.	PROPN
ejpam-5396	678	13	odibat	odibat	PROPN
ejpam-5396	678	14	.	.	PUNCT
ejpam-5396	679	1	application	application	NOUN
ejpam-5396	679	2	of	of	ADP
ejpam-5396	679	3	generalized	generalized	ADJ
ejpam-5396	679	4	differential	differential	ADJ
ejpam-5396	679	5	transform	transform	NOUN
ejpam-5396	679	6	method	method	NOUN
ejpam-5396	679	7	to	to	PART
ejpam-5396	679	8	multi	multi	ADJ
ejpam-5396	679	9	-	-	ADJ
ejpam-5396	679	10	order	order	ADJ
ejpam-5396	679	11	fractional	fractional	ADJ
ejpam-5396	679	12	differential	differential	ADJ
ejpam-5396	679	13	equations	equation	NOUN
ejpam-5396	679	14	.	.	PUNCT
ejpam-5396	680	1	communications	communication	NOUN
ejpam-5396	680	2	in	in	ADP
ejpam-5396	680	3	nonlinear	nonlinear	ADJ
ejpam-5396	680	4	science	science	NOUN
ejpam-5396	680	5	and	and	CCONJ
ejpam-5396	680	6	numerical	numerical	PROPN
ejpam-5396	680	7	simulation	simulation	PROPN
ejpam-5396	680	8	,	,	PUNCT
ejpam-5396	680	9	13(8):1642–1654	13(8):1642–1654	NUM
ejpam-5396	680	10	,	,	PUNCT
ejpam-5396	680	11	2008	2008	NUM
ejpam-5396	680	12	.	.	PUNCT
ejpam-5396	681	1	[	[	X
ejpam-5396	681	2	24	24	NUM
ejpam-5396	681	3	]	]	PUNCT
ejpam-5396	681	4	v.	v.	CCONJ
ejpam-5396	681	5	s.	s.	PROPN
ejpam-5396	681	6	erturk	erturk	PROPN
ejpam-5396	681	7	,	,	PUNCT
ejpam-5396	681	8	z.	z.	PROPN
ejpam-5396	681	9	m.	m.	PROPN
ejpam-5396	681	10	odibat	odibat	PROPN
ejpam-5396	681	11	,	,	PUNCT
ejpam-5396	681	12	and	and	CCONJ
ejpam-5396	681	13	s.	s.	PROPN
ejpam-5396	681	14	momani	momani	PROPN
ejpam-5396	681	15	.	.	PUNCT
ejpam-5396	682	1	an	an	DET
ejpam-5396	682	2	approximate	approximate	ADJ
ejpam-5396	682	3	solution	solution	NOUN
ejpam-5396	682	4	of	of	ADP
ejpam-5396	682	5	a	a	DET
ejpam-5396	682	6	fractional	fractional	ADJ
ejpam-5396	682	7	order	order	NOUN
ejpam-5396	682	8	differential	differential	NOUN
ejpam-5396	682	9	equation	equation	NOUN
ejpam-5396	682	10	model	model	NOUN
ejpam-5396	682	11	of	of	ADP
ejpam-5396	682	12	human	human	PROPN
ejpam-5396	682	13	t	t	PROPN
ejpam-5396	682	14	-	-	PUNCT
ejpam-5396	682	15	cell	cell	NOUN
ejpam-5396	682	16	lymphotropic	lymphotropic	NOUN
ejpam-5396	682	17	virus	virus	NOUN
ejpam-5396	682	18	i	i	PRON
ejpam-5396	682	19	(	(	PUNCT
ejpam-5396	682	20	htlv	htlv	PROPN
ejpam-5396	682	21	-	-	PUNCT
ejpam-5396	682	22	i	i	PROPN
ejpam-5396	682	23	)	)	PUNCT
ejpam-5396	682	24	infection	infection	NOUN
ejpam-5396	682	25	of	of	ADP
ejpam-5396	682	26	cd4	cd4	PROPN
ejpam-5396	682	27	t	t	PROPN
ejpam-5396	682	28	-	-	PUNCT
ejpam-5396	682	29	cells	cell	NOUN
ejpam-5396	682	30	.	.	PUNCT
ejpam-5396	683	1	computers	computer	NOUN
ejpam-5396	683	2	&	&	CCONJ
ejpam-5396	683	3	mathematics	mathematics	PROPN
ejpam-5396	683	4	with	with	ADP
ejpam-5396	683	5	applications	application	NOUN
ejpam-5396	683	6	,	,	PUNCT
ejpam-5396	683	7	62(3):996	62(3):996	NOUN
ejpam-5396	683	8	–	–	PUNCT
ejpam-5396	683	9	1002	1002	NUM
ejpam-5396	683	10	,	,	PUNCT
ejpam-5396	683	11	2011	2011	NUM
ejpam-5396	683	12	.	.	PUNCT
ejpam-5396	684	1	[	[	X
ejpam-5396	684	2	25	25	NUM
ejpam-5396	684	3	]	]	X
ejpam-5396	684	4	asad	asad	PROPN
ejpam-5396	684	5	freihat	freihat	PROPN
ejpam-5396	684	6	and	and	CCONJ
ejpam-5396	684	7	shaher	shaher	ADJ
ejpam-5396	684	8	momani	momani	PROPN
ejpam-5396	684	9	.	.	PUNCT
ejpam-5396	685	1	application	application	NOUN
ejpam-5396	685	2	of	of	ADP
ejpam-5396	685	3	multistep	multistep	ADJ
ejpam-5396	685	4	generalized	generalize	VERB
ejpam-5396	685	5	differential	differential	ADJ
ejpam-5396	685	6	transform	transform	NOUN
ejpam-5396	685	7	method	method	NOUN
ejpam-5396	685	8	for	for	ADP
ejpam-5396	685	9	the	the	DET
ejpam-5396	685	10	solutions	solution	NOUN
ejpam-5396	685	11	of	of	ADP
ejpam-5396	685	12	the	the	DET
ejpam-5396	685	13	fractional	fractional	ADJ
ejpam-5396	685	14	-	-	PUNCT
ejpam-5396	685	15	order	order	NOUN
ejpam-5396	685	16	chua	chua	PROPN
ejpam-5396	685	17	’s	’s	PART
ejpam-5396	685	18	system	system	NOUN
ejpam-5396	685	19	.	.	PUNCT
ejpam-5396	686	1	discrete	discrete	ADJ
ejpam-5396	686	2	dynamics	dynamic	NOUN
ejpam-5396	686	3	in	in	ADP
ejpam-5396	686	4	nature	nature	NOUN
ejpam-5396	686	5	and	and	CCONJ
ejpam-5396	686	6	society	society	NOUN
ejpam-5396	686	7	,	,	PUNCT
ejpam-5396	686	8	2012	2012	NUM
ejpam-5396	686	9	:	:	PUNCT
ejpam-5396	686	10	article	article	NOUN
ejpam-5396	686	11	i	i	PROPN
ejpam-5396	686	12	d	d	PROPN
ejpam-5396	686	13	427393	427393	NUM
ejpam-5396	686	14	,	,	PUNCT
ejpam-5396	686	15	2012	2012	NUM
ejpam-5396	686	16	.	.	PUNCT
ejpam-5396	687	1	[	[	X
ejpam-5396	687	2	26	26	NUM
ejpam-5396	687	3	]	]	X
ejpam-5396	687	4	s.m	s.m	PROPN
ejpam-5396	687	5	.	.	PROPN
ejpam-5396	687	6	jung	jung	PROPN
ejpam-5396	687	7	,	,	PUNCT
ejpam-5396	687	8	r.	r.	PROPN
ejpam-5396	687	9	kinoshita	kinoshita	PROPN
ejpam-5396	687	10	,	,	PUNCT
ejpam-5396	687	11	r.n	r.n	PROPN
ejpam-5396	687	12	.	.	PROPN
ejpam-5396	687	13	thompson	thompson	PROPN
ejpam-5396	687	14	,	,	PUNCT
ejpam-5396	687	15	n.m	n.m	PROPN
ejpam-5396	687	16	.	.	PROPN
ejpam-5396	687	17	linton	linton	PROPN
ejpam-5396	687	18	,	,	PUNCT
ejpam-5396	687	19	y.	y.	PROPN
ejpam-5396	687	20	yang	yang	PROPN
ejpam-5396	687	21	,	,	PUNCT
ejpam-5396	687	22	a.r	a.r	PROPN
ejpam-5396	687	23	.	.	PROPN
ejpam-5396	687	24	akhmetzhanov	akhmetzhanov	PROPN
ejpam-5396	687	25	,	,	PUNCT
ejpam-5396	687	26	and	and	CCONJ
ejpam-5396	687	27	h.	h.	PROPN
ejpam-5396	687	28	nishiura	nishiura	PROPN
ejpam-5396	687	29	.	.	PUNCT
ejpam-5396	688	1	epidemiological	epidemiological	ADJ
ejpam-5396	688	2	identification	identification	NOUN
ejpam-5396	688	3	of	of	ADP
ejpam-5396	688	4	a	a	DET
ejpam-5396	688	5	novel	novel	ADJ
ejpam-5396	688	6	pathogen	pathogen	NOUN
ejpam-5396	688	7	in	in	ADP
ejpam-5396	688	8	realtime	realtime	NOUN
ejpam-5396	688	9	:	:	PUNCT
ejpam-5396	688	10	analysis	analysis	NOUN
ejpam-5396	688	11	of	of	ADP
ejpam-5396	688	12	the	the	DET
ejpam-5396	688	13	atypical	atypical	ADJ
ejpam-5396	688	14	pneumonia	pneumonia	NOUN
ejpam-5396	688	15	outbreak	outbreak	NOUN
ejpam-5396	688	16	in	in	ADP
ejpam-5396	688	17	wuhan	wuhan	PROPN
ejpam-5396	688	18	,	,	PUNCT
ejpam-5396	688	19	china	china	PROPN
ejpam-5396	688	20	,	,	PUNCT
ejpam-5396	688	21	2019	2019	NUM
ejpam-5396	688	22	-	-	SYM
ejpam-5396	688	23	2020	2020	NUM
ejpam-5396	688	24	.	.	PUNCT
ejpam-5396	689	1	j.	j.	PROPN
ejpam-5396	689	2	clin	clin	PROPN
ejpam-5396	689	3	.	.	PUNCT
ejpam-5396	690	1	med	med	PROPN
ejpam-5396	690	2	.	.	PROPN
ejpam-5396	690	3	,	,	PUNCT
ejpam-5396	690	4	9(3):1–18	9(3):1–18	NUM
ejpam-5396	690	5	,	,	PUNCT
ejpam-5396	690	6	2020	2020	NUM
ejpam-5396	690	7	.	.	PUNCT
ejpam-5396	691	1	[	[	X
ejpam-5396	691	2	27	27	NUM
ejpam-5396	691	3	]	]	PUNCT
ejpam-5396	691	4	m.	m.	NOUN
ejpam-5396	691	5	kizito	kizito	PROPN
ejpam-5396	691	6	and	and	CCONJ
ejpam-5396	691	7	j.	j.	PROPN
ejpam-5396	691	8	tumwiine	tumwiine	PROPN
ejpam-5396	691	9	.	.	PUNCT
ejpam-5396	692	1	a	a	DET
ejpam-5396	692	2	mathematical	mathematical	ADJ
ejpam-5396	692	3	model	model	NOUN
ejpam-5396	692	4	of	of	ADP
ejpam-5396	692	5	treatment	treatment	NOUN
ejpam-5396	692	6	and	and	CCONJ
ejpam-5396	692	7	vaccination	vaccination	NOUN
ejpam-5396	692	8	interventions	intervention	NOUN
ejpam-5396	692	9	of	of	ADP
ejpam-5396	692	10	pneumococcal	pneumococcal	ADJ
ejpam-5396	692	11	pneumonia	pneumonia	NOUN
ejpam-5396	692	12	infection	infection	NOUN
ejpam-5396	692	13	dynamics	dynamic	NOUN
ejpam-5396	692	14	.	.	PUNCT
ejpam-5396	693	1	j.	j.	PROPN
ejpam-5396	693	2	appl	appl	PROPN
ejpam-5396	693	3	.	.	PROPN
ejpam-5396	693	4	math	math	PROPN
ejpam-5396	693	5	.	.	PUNCT
ejpam-5396	693	6	,	,	PUNCT
ejpam-5396	693	7	2018	2018	NUM
ejpam-5396	693	8	:	:	PUNCT
ejpam-5396	693	9	article	article	NOUN
ejpam-5396	693	10	i	i	PROPN
ejpam-5396	693	11	d	d	PROPN
ejpam-5396	693	12	2539465	2539465	NUM
ejpam-5396	693	13	,	,	PUNCT
ejpam-5396	693	14	2018	2018	NUM
ejpam-5396	693	15	.	.	PUNCT
ejpam-5396	694	1	[	[	X
ejpam-5396	694	2	28	28	NUM
ejpam-5396	694	3	]	]	PUNCT
ejpam-5396	694	4	k.	k.	PROPN
ejpam-5396	694	5	kosasih	kosasih	PROPN
ejpam-5396	694	6	and	and	CCONJ
ejpam-5396	694	7	u.	u.	PROPN
ejpam-5396	694	8	abeyratne	abeyratne	PROPN
ejpam-5396	694	9	.	.	PUNCT
ejpam-5396	695	1	exhaustive	exhaustive	ADJ
ejpam-5396	695	2	mathematical	mathematical	ADJ
ejpam-5396	695	3	analysis	analysis	NOUN
ejpam-5396	695	4	of	of	ADP
ejpam-5396	695	5	simple	simple	ADJ
ejpam-5396	695	6	clinical	clinical	ADJ
ejpam-5396	695	7	measurements	measurement	NOUN
ejpam-5396	695	8	for	for	ADP
ejpam-5396	695	9	childhood	childhood	ADJ
ejpam-5396	695	10	pneumonia	pneumonia	NOUN
ejpam-5396	695	11	diagnosis	diagnosis	NOUN
ejpam-5396	695	12	.	.	PUNCT
ejpam-5396	696	1	world	world	NOUN
ejpam-5396	696	2	j.	j.	PROPN
ejpam-5396	696	3	pediatr	pediatr	PROPN
ejpam-5396	696	4	.	.	PROPN
ejpam-5396	696	5	,	,	PUNCT
ejpam-5396	696	6	13(5):446–456	13(5):446–456	PROPN
ejpam-5396	696	7	,	,	PUNCT
ejpam-5396	696	8	2017	2017	NUM
ejpam-5396	696	9	.	.	PUNCT
ejpam-5396	697	1	[	[	X
ejpam-5396	697	2	29	29	NUM
ejpam-5396	697	3	]	]	PUNCT
ejpam-5396	697	4	k.	k.	PROPN
ejpam-5396	697	5	kosasih	kosasih	PROPN
ejpam-5396	697	6	,	,	PUNCT
ejpam-5396	697	7	u.r	u.r	PROPN
ejpam-5396	697	8	.	.	PROPN
ejpam-5396	697	9	abeyratne	abeyratne	PROPN
ejpam-5396	697	10	,	,	PUNCT
ejpam-5396	697	11	v.	v.	CCONJ
ejpam-5396	697	12	swarnkar	swarnkar	NOUN
ejpam-5396	697	13	,	,	PUNCT
ejpam-5396	697	14	and	and	CCONJ
ejpam-5396	697	15	r.	r.	PROPN
ejpam-5396	697	16	triasih	triasih	PROPN
ejpam-5396	697	17	.	.	PUNCT
ejpam-5396	698	1	wavelet	wavelet	PROPN
ejpam-5396	698	2	augmented	augment	VERB
ejpam-5396	698	3	cough	cough	NOUN
ejpam-5396	698	4	analysis	analysis	NOUN
ejpam-5396	698	5	for	for	ADP
ejpam-5396	698	6	rapid	rapid	ADJ
ejpam-5396	698	7	childhood	childhood	NOUN
ejpam-5396	698	8	pneumonia	pneumonia	NOUN
ejpam-5396	698	9	diagnosis	diagnosis	NOUN
ejpam-5396	698	10	.	.	PUNCT
ejpam-5396	699	1	ieee	ieee	PROPN
ejpam-5396	699	2	trans	trans	PROPN
ejpam-5396	699	3	.	.	PROPN
ejpam-5396	699	4	biomed	biome	VERB
ejpam-5396	699	5	.	.	PUNCT
ejpam-5396	700	1	eng	eng	PROPN
ejpam-5396	700	2	.	.	PROPN
ejpam-5396	700	3	,	,	PUNCT
ejpam-5396	700	4	62(4):1185–1194	62(4):1185–1194	NUM
ejpam-5396	700	5	,	,	PUNCT
ejpam-5396	700	6	2015	2015	NUM
ejpam-5396	700	7	.	.	PUNCT
ejpam-5396	701	1	references	reference	NOUN
ejpam-5396	701	2	2797	2797	NUM
ejpam-5396	701	3	[	[	X
ejpam-5396	701	4	30	30	NUM
ejpam-5396	701	5	]	]	X
ejpam-5396	701	6	j.p	j.p	PROPN
ejpam-5396	701	7	.	.	PROPN
ejpam-5396	701	8	lasalle	lasalle	PROPN
ejpam-5396	701	9	.	.	PUNCT
ejpam-5396	702	1	the	the	DET
ejpam-5396	702	2	stability	stability	NOUN
ejpam-5396	702	3	of	of	ADP
ejpam-5396	702	4	dynamical	dynamical	ADJ
ejpam-5396	702	5	systems	system	NOUN
ejpam-5396	702	6	.	.	PUNCT
ejpam-5396	703	1	siam	siam	PROPN
ejpam-5396	703	2	,	,	PUNCT
ejpam-5396	703	3	philadelphia	philadelphia	PROPN
ejpam-5396	703	4	,	,	PUNCT
ejpam-5396	703	5	1976	1976	NUM
ejpam-5396	703	6	.	.	PUNCT
ejpam-5396	704	1	[	[	X
ejpam-5396	704	2	31	31	NUM
ejpam-5396	704	3	]	]	X
ejpam-5396	704	4	h.l	h.l	PROPN
ejpam-5396	704	5	.	.	PROPN
ejpam-5396	704	6	li	li	PROPN
ejpam-5396	704	7	,	,	PUNCT
ejpam-5396	704	8	l.	l.	PROPN
ejpam-5396	704	9	zhang	zhang	PROPN
ejpam-5396	704	10	,	,	PUNCT
ejpam-5396	704	11	c.	c.	PROPN
ejpam-5396	704	12	hu	hu	PROPN
ejpam-5396	704	13	,	,	PUNCT
ejpam-5396	704	14	et	et	PROPN
ejpam-5396	704	15	al	al	PROPN
ejpam-5396	704	16	.	.	PUNCT
ejpam-5396	705	1	dynamical	dynamical	ADJ
ejpam-5396	705	2	analysis	analysis	NOUN
ejpam-5396	705	3	of	of	ADP
ejpam-5396	705	4	a	a	DET
ejpam-5396	705	5	fractional	fractional	ADJ
ejpam-5396	705	6	-	-	PUNCT
ejpam-5396	705	7	order	order	NOUN
ejpam-5396	705	8	predatorprey	predatorprey	NOUN
ejpam-5396	705	9	model	model	NOUN
ejpam-5396	705	10	incorporating	incorporate	VERB
ejpam-5396	705	11	a	a	DET
ejpam-5396	705	12	prey	prey	NOUN
ejpam-5396	705	13	refuge	refuge	NOUN
ejpam-5396	705	14	.	.	PUNCT
ejpam-5396	706	1	j.	j.	PROPN
ejpam-5396	706	2	appl	appl	PROPN
ejpam-5396	706	3	.	.	PROPN
ejpam-5396	706	4	math	math	PROPN
ejpam-5396	706	5	.	.	PUNCT
ejpam-5396	707	1	comput	comput	NOUN
ejpam-5396	707	2	.	.	PUNCT
ejpam-5396	707	3	,	,	PUNCT
ejpam-5396	707	4	54(1	54(1	PROPN
ejpam-5396	707	5	-	-	SYM
ejpam-5396	707	6	2):435–449	2):435–449	NUM
ejpam-5396	707	7	,	,	PUNCT
ejpam-5396	707	8	2017	2017	NUM
ejpam-5396	707	9	.	.	PUNCT
ejpam-5396	708	1	[	[	X
ejpam-5396	708	2	32	32	NUM
ejpam-5396	708	3	]	]	PUNCT
ejpam-5396	708	4	c.	c.	PROPN
ejpam-5396	708	5	marchello	marchello	PROPN
ejpam-5396	708	6	,	,	PUNCT
ejpam-5396	708	7	a.p	a.p	PROPN
ejpam-5396	708	8	.	.	PROPN
ejpam-5396	708	9	dale	dale	PROPN
ejpam-5396	708	10	,	,	PUNCT
ejpam-5396	708	11	t.n	t.n	PROPN
ejpam-5396	708	12	.	.	PROPN
ejpam-5396	708	13	thai	thai	PROPN
ejpam-5396	708	14	,	,	PUNCT
ejpam-5396	708	15	d.s	d.s	PROPN
ejpam-5396	708	16	.	.	PROPN
ejpam-5396	708	17	han	han	PROPN
ejpam-5396	708	18	,	,	PUNCT
ejpam-5396	708	19	and	and	CCONJ
ejpam-5396	708	20	m.h	m.h	PROPN
ejpam-5396	708	21	.	.	PROPN
ejpam-5396	708	22	ebell	ebell	NOUN
ejpam-5396	708	23	.	.	PUNCT
ejpam-5396	709	1	prevalence	prevalence	NOUN
ejpam-5396	709	2	of	of	ADP
ejpam-5396	709	3	atypical	atypical	ADJ
ejpam-5396	709	4	pathogens	pathogen	NOUN
ejpam-5396	709	5	in	in	ADP
ejpam-5396	709	6	patients	patient	NOUN
ejpam-5396	709	7	with	with	ADP
ejpam-5396	709	8	cough	cough	NOUN
ejpam-5396	709	9	and	and	CCONJ
ejpam-5396	709	10	community	community	NOUN
ejpam-5396	709	11	-	-	PUNCT
ejpam-5396	709	12	acquired	acquire	VERB
ejpam-5396	709	13	pneumonia	pneumonia	NOUN
ejpam-5396	709	14	:	:	PUNCT
ejpam-5396	709	15	a	a	DET
ejpam-5396	709	16	metaanalysis	metaanalysis	NOUN
ejpam-5396	709	17	.	.	PUNCT
ejpam-5396	710	1	ann	ann	PROPN
ejpam-5396	710	2	.	.	PUNCT
ejpam-5396	710	3	fam	fam	PROPN
ejpam-5396	710	4	.	.	PUNCT
ejpam-5396	710	5	med	med	PROPN
ejpam-5396	710	6	.	.	PROPN
ejpam-5396	710	7	,	,	PUNCT
ejpam-5396	710	8	14(6):552–566	14(6):552–566	PROPN
ejpam-5396	710	9	,	,	PUNCT
ejpam-5396	710	10	2016	2016	NUM
ejpam-5396	710	11	.	.	PUNCT
ejpam-5396	711	1	[	[	X
ejpam-5396	711	2	33	33	NUM
ejpam-5396	711	3	]	]	X
ejpam-5396	711	4	f.k	f.k	PROPN
ejpam-5396	711	5	.	.	PROPN
ejpam-5396	711	6	mbabazi	mbabazi	PROPN
ejpam-5396	711	7	,	,	PUNCT
ejpam-5396	711	8	j.y.t	j.y.t	PROPN
ejpam-5396	711	9	.	.	PUNCT
ejpam-5396	711	10	mugisha	mugisha	PROPN
ejpam-5396	711	11	,	,	PUNCT
ejpam-5396	711	12	and	and	CCONJ
ejpam-5396	711	13	m.	m.	NOUN
ejpam-5396	711	14	kimathi	kimathi	PROPN
ejpam-5396	711	15	.	.	PUNCT
ejpam-5396	712	1	modeling	model	VERB
ejpam-5396	712	2	the	the	DET
ejpam-5396	712	3	within	within	ADP
ejpam-5396	712	4	-	-	PUNCT
ejpam-5396	712	5	host	host	NOUN
ejpam-5396	712	6	coinfection	coinfection	NOUN
ejpam-5396	712	7	of	of	ADP
ejpam-5396	712	8	influenza	influenza	NOUN
ejpam-5396	712	9	a	a	DET
ejpam-5396	712	10	virus	virus	NOUN
ejpam-5396	712	11	and	and	CCONJ
ejpam-5396	712	12	pneumococcus	pneumococcus	NOUN
ejpam-5396	712	13	.	.	PUNCT
ejpam-5396	713	1	appl	appl	PROPN
ejpam-5396	713	2	.	.	PROPN
ejpam-5396	713	3	math	math	PROPN
ejpam-5396	713	4	.	.	PUNCT
ejpam-5396	714	1	comput	comput	NOUN
ejpam-5396	714	2	.	.	PUNCT
ejpam-5396	714	3	,	,	PUNCT
ejpam-5396	714	4	339:488–506	339:488–506	NUM
ejpam-5396	714	5	,	,	PUNCT
ejpam-5396	714	6	2018	2018	NUM
ejpam-5396	714	7	.	.	PUNCT
ejpam-5396	715	1	[	[	X
ejpam-5396	715	2	34	34	NUM
ejpam-5396	715	3	]	]	X
ejpam-5396	715	4	johns	johns	PROPN
ejpam-5396	715	5	hopkins	hopkins	PROPN
ejpam-5396	715	6	medicine	medicine	PROPN
ejpam-5396	715	7	.	.	PUNCT
ejpam-5396	716	1	johns	johns	PROPN
ejpam-5396	716	2	hopkins	hopkins	PROPN
ejpam-5396	716	3	medicine	medicine	NOUN
ejpam-5396	716	4	:	:	PUNCT
ejpam-5396	716	5	pneumonia	pneumonia	NOUN
ejpam-5396	716	6	.	.	PUNCT
ejpam-5396	717	1	report	report	VERB
ejpam-5396	717	2	n.d	n.d	PROPN
ejpam-5396	717	3	.	.	PROPN
ejpam-5396	717	4	,	,	PUNCT
ejpam-5396	717	5	johns	johns	PROPN
ejpam-5396	717	6	hopkins	hopkins	PROPN
ejpam-5396	717	7	medicine	medicine	PROPN
ejpam-5396	717	8	,	,	PUNCT
ejpam-5396	717	9	n.d	n.d	PROPN
ejpam-5396	717	10	.	.	PUNCT
ejpam-5396	718	1	[	[	X
ejpam-5396	718	2	35	35	NUM
ejpam-5396	718	3	]	]	SYM
ejpam-5396	718	4	w.k	w.k	PROPN
ejpam-5396	718	5	.	.	PROPN
ejpam-5396	718	6	ming	ming	PROPN
ejpam-5396	718	7	,	,	PUNCT
ejpam-5396	718	8	j.	j.	PROPN
ejpam-5396	718	9	huang	huang	PROPN
ejpam-5396	718	10	,	,	PUNCT
ejpam-5396	718	11	and	and	CCONJ
ejpam-5396	718	12	c.j	c.j	PROPN
ejpam-5396	718	13	.	.	PROPN
ejpam-5396	718	14	zhang	zhang	PROPN
ejpam-5396	718	15	.	.	PUNCT
ejpam-5396	719	1	breaking	break	VERB
ejpam-5396	719	2	down	down	ADP
ejpam-5396	719	3	of	of	ADP
ejpam-5396	719	4	healthcare	healthcare	NOUN
ejpam-5396	719	5	system	system	NOUN
ejpam-5396	719	6	:	:	PUNCT
ejpam-5396	719	7	mathematical	mathematical	ADJ
ejpam-5396	719	8	modelling	modelling	NOUN
ejpam-5396	719	9	for	for	ADP
ejpam-5396	719	10	controlling	control	VERB
ejpam-5396	719	11	the	the	DET
ejpam-5396	719	12	novel	novel	ADJ
ejpam-5396	719	13	coronavirus	coronavirus	NOUN
ejpam-5396	719	14	(	(	PUNCT
ejpam-5396	719	15	2019	2019	NUM
ejpam-5396	719	16	-	-	PUNCT
ejpam-5396	719	17	ncov	ncov	NOUN
ejpam-5396	719	18	)	)	PUNCT
ejpam-5396	719	19	outbreak	outbreak	NOUN
ejpam-5396	719	20	in	in	ADP
ejpam-5396	719	21	wuhan	wuhan	PROPN
ejpam-5396	719	22	,	,	PUNCT
ejpam-5396	719	23	china	china	PROPN
ejpam-5396	719	24	.	.	PUNCT
ejpam-5396	720	1	biorxiv	biorxiv	PROPN
ejpam-5396	720	2	,	,	PUNCT
ejpam-5396	720	3	1:1–18	1:1–18	NUM
ejpam-5396	720	4	,	,	PUNCT
ejpam-5396	720	5	2020	2020	NUM
ejpam-5396	720	6	.	.	PUNCT
ejpam-5396	721	1	[	[	X
ejpam-5396	721	2	36	36	NUM
ejpam-5396	721	3	]	]	X
ejpam-5396	721	4	e.	e.	PROPN
ejpam-5396	721	5	mochan	mochan	PROPN
ejpam-5396	721	6	,	,	PUNCT
ejpam-5396	721	7	d.	d.	PROPN
ejpam-5396	721	8	swigon	swigon	PROPN
ejpam-5396	721	9	,	,	PUNCT
ejpam-5396	721	10	g.	g.	PROPN
ejpam-5396	721	11	ermentrout	ermentrout	PROPN
ejpam-5396	721	12	,	,	PUNCT
ejpam-5396	721	13	s.	s.	PROPN
ejpam-5396	721	14	luken	luken	VERB
ejpam-5396	721	15	,	,	PUNCT
ejpam-5396	721	16	and	and	CCONJ
ejpam-5396	721	17	g.a	g.a	PROPN
ejpam-5396	721	18	.	.	PROPN
ejpam-5396	721	19	clermont	clermont	PROPN
ejpam-5396	721	20	.	.	PUNCT
ejpam-5396	722	1	mathematical	mathematical	ADJ
ejpam-5396	722	2	model	model	NOUN
ejpam-5396	722	3	of	of	ADP
ejpam-5396	722	4	intrahost	intrahost	ADJ
ejpam-5396	722	5	pneumococcal	pneumococcal	ADJ
ejpam-5396	722	6	pneumonia	pneumonia	NOUN
ejpam-5396	722	7	infection	infection	NOUN
ejpam-5396	722	8	dynamics	dynamic	NOUN
ejpam-5396	722	9	in	in	ADP
ejpam-5396	722	10	murine	murine	ADJ
ejpam-5396	722	11	strains	strain	NOUN
ejpam-5396	722	12	.	.	PUNCT
ejpam-5396	723	1	j.	j.	PROPN
ejpam-5396	723	2	theor	theor	PROPN
ejpam-5396	723	3	.	.	PUNCT
ejpam-5396	724	1	biol	biol	PROPN
ejpam-5396	724	2	.	.	PUNCT
ejpam-5396	724	3	,	,	PUNCT
ejpam-5396	724	4	353:44–54	353:44–54	NUM
ejpam-5396	724	5	,	,	PUNCT
ejpam-5396	724	6	2014	2014	NUM
ejpam-5396	724	7	.	.	PUNCT
ejpam-5396	725	1	[	[	X
ejpam-5396	725	2	37	37	NUM
ejpam-5396	725	3	]	]	PUNCT
ejpam-5396	725	4	s.	s.	PROPN
ejpam-5396	725	5	momani	momani	PROPN
ejpam-5396	725	6	and	and	CCONJ
ejpam-5396	725	7	z.	z.	PROPN
ejpam-5396	725	8	odibat	odibat	PROPN
ejpam-5396	725	9	.	.	PUNCT
ejpam-5396	726	1	a	a	DET
ejpam-5396	726	2	novel	novel	ADJ
ejpam-5396	726	3	method	method	NOUN
ejpam-5396	726	4	for	for	ADP
ejpam-5396	726	5	nonlinear	nonlinear	ADJ
ejpam-5396	726	6	fractional	fractional	ADJ
ejpam-5396	726	7	partial	partial	ADJ
ejpam-5396	726	8	differential	differential	NOUN
ejpam-5396	726	9	equations	equation	NOUN
ejpam-5396	726	10	:	:	PUNCT
ejpam-5396	726	11	combination	combination	NOUN
ejpam-5396	726	12	of	of	ADP
ejpam-5396	726	13	dtm	dtm	PROPN
ejpam-5396	726	14	and	and	CCONJ
ejpam-5396	726	15	generalized	generalize	VERB
ejpam-5396	726	16	taylor	taylor	PROPN
ejpam-5396	726	17	’s	’s	PART
ejpam-5396	726	18	formula	formula	NOUN
ejpam-5396	726	19	.	.	PUNCT
ejpam-5396	727	1	journal	journal	NOUN
ejpam-5396	727	2	of	of	ADP
ejpam-5396	727	3	computational	computational	ADJ
ejpam-5396	727	4	and	and	CCONJ
ejpam-5396	727	5	applied	applied	ADJ
ejpam-5396	727	6	mathematics	mathematic	NOUN
ejpam-5396	727	7	,	,	PUNCT
ejpam-5396	727	8	220(1	220(1	NUM
ejpam-5396	727	9	-	-	SYM
ejpam-5396	727	10	2):85–95	2):85–95	NUM
ejpam-5396	727	11	,	,	PUNCT
ejpam-5396	727	12	2008	2008	NUM
ejpam-5396	727	13	.	.	PUNCT
ejpam-5396	728	1	[	[	X
ejpam-5396	728	2	38	38	NUM
ejpam-5396	728	3	]	]	PUNCT
ejpam-5396	728	4	m.	m.	NOUN
ejpam-5396	728	5	naveed	naveed	PROPN
ejpam-5396	728	6	,	,	PUNCT
ejpam-5396	728	7	d.	d.	PROPN
ejpam-5396	728	8	baleanu	baleanu	PROPN
ejpam-5396	728	9	,	,	PUNCT
ejpam-5396	728	10	a.	a.	NOUN
ejpam-5396	728	11	raza	raza	PROPN
ejpam-5396	728	12	,	,	PUNCT
ejpam-5396	728	13	et	et	PROPN
ejpam-5396	728	14	al	al	PROPN
ejpam-5396	728	15	.	.	PUNCT
ejpam-5396	729	1	modeling	model	VERB
ejpam-5396	729	2	the	the	DET
ejpam-5396	729	3	transmission	transmission	NOUN
ejpam-5396	729	4	dynamics	dynamic	NOUN
ejpam-5396	729	5	of	of	ADP
ejpam-5396	729	6	delayed	delay	VERB
ejpam-5396	729	7	pneumonia	pneumonia	NOUN
ejpam-5396	729	8	-	-	PUNCT
ejpam-5396	729	9	like	like	ADJ
ejpam-5396	729	10	diseases	disease	NOUN
ejpam-5396	729	11	with	with	ADP
ejpam-5396	729	12	a	a	DET
ejpam-5396	729	13	sensitivity	sensitivity	NOUN
ejpam-5396	729	14	of	of	ADP
ejpam-5396	729	15	parameters	parameter	NOUN
ejpam-5396	729	16	.	.	PUNCT
ejpam-5396	730	1	adv	adv	PROPN
ejpam-5396	730	2	.	.	PROPN
ejpam-5396	730	3	differ	differ	VERB
ejpam-5396	730	4	.	.	PUNCT
ejpam-5396	731	1	equ	equ	PROPN
ejpam-5396	731	2	.	.	PROPN
ejpam-5396	731	3	,	,	PUNCT
ejpam-5396	731	4	2021:468	2021:468	NOUN
ejpam-5396	731	5	,	,	PUNCT
ejpam-5396	731	6	2021	2021	NUM
ejpam-5396	731	7	.	.	PUNCT
ejpam-5396	732	1	[	[	X
ejpam-5396	732	2	39	39	NUM
ejpam-5396	732	3	]	]	SYM
ejpam-5396	732	4	e.j	e.j	PROPN
ejpam-5396	732	5	.	.	PROPN
ejpam-5396	732	6	ndelwa	ndelwa	PROPN
ejpam-5396	732	7	,	,	PUNCT
ejpam-5396	732	8	m.	m.	NOUN
ejpam-5396	732	9	kgosimore	kgosimore	PROPN
ejpam-5396	732	10	,	,	PUNCT
ejpam-5396	732	11	e.s	e.s	PROPN
ejpam-5396	732	12	.	.	PROPN
ejpam-5396	732	13	massawe	massawe	PROPN
ejpam-5396	732	14	,	,	PUNCT
ejpam-5396	732	15	and	and	CCONJ
ejpam-5396	732	16	l.	l.	PROPN
ejpam-5396	732	17	namkinga	namkinga	PROPN
ejpam-5396	732	18	.	.	PUNCT
ejpam-5396	733	1	mathematical	mathematical	ADJ
ejpam-5396	733	2	modelling	modelling	NOUN
ejpam-5396	733	3	and	and	CCONJ
ejpam-5396	733	4	analysis	analysis	NOUN
ejpam-5396	733	5	of	of	ADP
ejpam-5396	733	6	treatment	treatment	NOUN
ejpam-5396	733	7	and	and	CCONJ
ejpam-5396	733	8	screening	screening	NOUN
ejpam-5396	733	9	of	of	ADP
ejpam-5396	733	10	pneumonia	pneumonia	NOUN
ejpam-5396	733	11	.	.	PUNCT
ejpam-5396	734	1	math	math	NOUN
ejpam-5396	734	2	.	.	PUNCT
ejpam-5396	735	1	theory	theory	NOUN
ejpam-5396	735	2	model	model	PROPN
ejpam-5396	735	3	.	.	PUNCT
ejpam-5396	735	4	,	,	PUNCT
ejpam-5396	735	5	5(10):21–39	5(10):21–39	NUM
ejpam-5396	735	6	,	,	PUNCT
ejpam-5396	735	7	2015	2015	NUM
ejpam-5396	735	8	.	.	PUNCT
ejpam-5396	736	1	[	[	X
ejpam-5396	736	2	40	40	NUM
ejpam-5396	736	3	]	]	PUNCT
ejpam-5396	736	4	z.	z.	PROPN
ejpam-5396	736	5	odibat	odibat	PROPN
ejpam-5396	736	6	and	and	CCONJ
ejpam-5396	736	7	s.	s.	PROPN
ejpam-5396	736	8	momani	momani	PROPN
ejpam-5396	736	9	.	.	PUNCT
ejpam-5396	737	1	a	a	DET
ejpam-5396	737	2	generalized	generalize	VERB
ejpam-5396	737	3	differential	differential	NOUN
ejpam-5396	737	4	transform	transform	NOUN
ejpam-5396	737	5	method	method	NOUN
ejpam-5396	737	6	for	for	ADP
ejpam-5396	737	7	linear	linear	ADJ
ejpam-5396	737	8	partial	partial	ADJ
ejpam-5396	737	9	differential	differential	ADJ
ejpam-5396	737	10	equations	equation	NOUN
ejpam-5396	737	11	of	of	ADP
ejpam-5396	737	12	fractional	fractional	ADJ
ejpam-5396	737	13	order	order	NOUN
ejpam-5396	737	14	.	.	PUNCT
ejpam-5396	738	1	applied	apply	VERB
ejpam-5396	738	2	mathematics	mathematics	NOUN
ejpam-5396	738	3	letters	letter	NOUN
ejpam-5396	738	4	,	,	PUNCT
ejpam-5396	738	5	21(2):194	21(2):194	NUM
ejpam-5396	738	6	–	–	PUNCT
ejpam-5396	738	7	199	199	NUM
ejpam-5396	738	8	,	,	PUNCT
ejpam-5396	738	9	2008	2008	NUM
ejpam-5396	738	10	.	.	PUNCT
ejpam-5396	739	1	[	[	X
ejpam-5396	739	2	41	41	NUM
ejpam-5396	739	3	]	]	PUNCT
ejpam-5396	739	4	z.	z.	PROPN
ejpam-5396	739	5	odibat	odibat	PROPN
ejpam-5396	739	6	,	,	PUNCT
ejpam-5396	739	7	s.	s.	PROPN
ejpam-5396	739	8	momani	momani	PROPN
ejpam-5396	739	9	,	,	PUNCT
ejpam-5396	739	10	and	and	CCONJ
ejpam-5396	739	11	v.	v.	PROPN
ejpam-5396	739	12	s.	s.	PROPN
ejpam-5396	739	13	erturk	erturk	PROPN
ejpam-5396	739	14	.	.	PUNCT
ejpam-5396	740	1	generalized	generalized	ADJ
ejpam-5396	740	2	differential	differential	ADJ
ejpam-5396	740	3	transform	transform	NOUN
ejpam-5396	740	4	method	method	NOUN
ejpam-5396	740	5	:	:	PUNCT
ejpam-5396	740	6	application	application	NOUN
ejpam-5396	740	7	to	to	PART
ejpam-5396	740	8	differential	differential	ADJ
ejpam-5396	740	9	equations	equation	NOUN
ejpam-5396	740	10	of	of	ADP
ejpam-5396	740	11	fractional	fractional	ADJ
ejpam-5396	740	12	order	order	NOUN
ejpam-5396	740	13	.	.	PUNCT
ejpam-5396	741	1	applied	apply	VERB
ejpam-5396	741	2	mathematics	mathematic	NOUN
ejpam-5396	741	3	and	and	CCONJ
ejpam-5396	741	4	computation	computation	NOUN
ejpam-5396	741	5	,	,	PUNCT
ejpam-5396	741	6	197(2):467–477	197(2):467–477	NUM
ejpam-5396	741	7	,	,	PUNCT
ejpam-5396	741	8	2008	2008	NUM
ejpam-5396	741	9	.	.	PUNCT
ejpam-5396	742	1	[	[	X
ejpam-5396	742	2	42	42	NUM
ejpam-5396	742	3	]	]	PUNCT
ejpam-5396	742	4	z.	z.	PROPN
ejpam-5396	742	5	m.	m.	PROPN
ejpam-5396	742	6	odibat	odibat	PROPN
ejpam-5396	742	7	,	,	PUNCT
ejpam-5396	742	8	c.	c.	PROPN
ejpam-5396	742	9	bertelle	bertelle	PROPN
ejpam-5396	742	10	,	,	PUNCT
ejpam-5396	742	11	m.	m.	PROPN
ejpam-5396	742	12	a.	a.	PROPN
ejpam-5396	742	13	aziz	aziz	PROPN
ejpam-5396	742	14	-	-	PUNCT
ejpam-5396	742	15	alaoui	alaoui	PROPN
ejpam-5396	742	16	,	,	PUNCT
ejpam-5396	742	17	and	and	CCONJ
ejpam-5396	742	18	g.	g.	PROPN
ejpam-5396	742	19	h.	h.	PROPN
ejpam-5396	742	20	e.	e.	PROPN
ejpam-5396	742	21	duchamp	duchamp	PROPN
ejpam-5396	742	22	.	.	PUNCT
ejpam-5396	743	1	a	a	DET
ejpam-5396	743	2	multistep	multistep	ADJ
ejpam-5396	743	3	differential	differential	NOUN
ejpam-5396	743	4	transform	transform	NOUN
ejpam-5396	743	5	method	method	NOUN
ejpam-5396	743	6	and	and	CCONJ
ejpam-5396	743	7	application	application	NOUN
ejpam-5396	743	8	to	to	ADP
ejpam-5396	743	9	non	non	ADJ
ejpam-5396	743	10	-	-	ADJ
ejpam-5396	743	11	chaotic	chaotic	ADJ
ejpam-5396	743	12	or	or	CCONJ
ejpam-5396	743	13	chaotic	chaotic	ADJ
ejpam-5396	743	14	systems	system	NOUN
ejpam-5396	743	15	.	.	PUNCT
ejpam-5396	744	1	computers	computer	NOUN
ejpam-5396	744	2	&	&	CCONJ
ejpam-5396	744	3	mathematics	mathematics	PROPN
ejpam-5396	744	4	with	with	ADP
ejpam-5396	744	5	applications	application	NOUN
ejpam-5396	744	6	,	,	PUNCT
ejpam-5396	744	7	59(4):1462–1472	59(4):1462–1472	NUM
ejpam-5396	744	8	,	,	PUNCT
ejpam-5396	744	9	2010	2010	NUM
ejpam-5396	744	10	.	.	PUNCT
ejpam-5396	745	1	references	reference	NOUN
ejpam-5396	745	2	2798	2798	NUM
ejpam-5396	746	1	[	[	X
ejpam-5396	746	2	43	43	NUM
ejpam-5396	746	3	]	]	X
ejpam-5396	746	4	z.m	z.m	PROPN
ejpam-5396	746	5	.	.	PROPN
ejpam-5396	746	6	odibat	odibat	PROPN
ejpam-5396	746	7	and	and	CCONJ
ejpam-5396	746	8	s.	s.	PROPN
ejpam-5396	746	9	momani	momani	PROPN
ejpam-5396	746	10	.	.	PUNCT
ejpam-5396	747	1	an	an	DET
ejpam-5396	747	2	algorithm	algorithm	NOUN
ejpam-5396	747	3	for	for	ADP
ejpam-5396	747	4	the	the	DET
ejpam-5396	747	5	numerical	numerical	ADJ
ejpam-5396	747	6	solution	solution	NOUN
ejpam-5396	747	7	of	of	ADP
ejpam-5396	747	8	differential	differential	ADJ
ejpam-5396	747	9	equations	equation	NOUN
ejpam-5396	747	10	of	of	ADP
ejpam-5396	747	11	fractional	fractional	ADJ
ejpam-5396	747	12	order	order	NOUN
ejpam-5396	747	13	.	.	PUNCT
ejpam-5396	748	1	j.	j.	PROPN
ejpam-5396	748	2	appl	appl	PROPN
ejpam-5396	748	3	.	.	PROPN
ejpam-5396	748	4	math	math	PROPN
ejpam-5396	748	5	.	.	PUNCT
ejpam-5396	749	1	inform	inform	NOUN
ejpam-5396	749	2	.	.	PUNCT
ejpam-5396	749	3	,	,	PUNCT
ejpam-5396	749	4	26(1	26(1	NUM
ejpam-5396	749	5	-	-	PUNCT
ejpam-5396	749	6	2):15–27	2):15–27	NUM
ejpam-5396	749	7	,	,	PUNCT
ejpam-5396	749	8	2008	2008	NUM
ejpam-5396	749	9	.	.	PUNCT
ejpam-5396	750	1	[	[	X
ejpam-5396	750	2	44	44	NUM
ejpam-5396	750	3	]	]	X
ejpam-5396	750	4	j.p	j.p	PROPN
ejpam-5396	750	5	.	.	PROPN
ejpam-5396	750	6	olumuyiwa	olumuyiwa	PROPN
ejpam-5396	750	7	,	,	PUNCT
ejpam-5396	750	8	a.	a.	PROPN
ejpam-5396	750	9	yusuf	yusuf	PROPN
ejpam-5396	750	10	,	,	PUNCT
ejpam-5396	750	11	k.	k.	PROPN
ejpam-5396	750	12	oshinubi	oshinubi	PROPN
ejpam-5396	750	13	,	,	PUNCT
ejpam-5396	750	14	f.a	f.a	PROPN
ejpam-5396	750	15	.	.	PROPN
ejpam-5396	750	16	oguntolu	oguntolu	PROPN
ejpam-5396	750	17	,	,	PUNCT
ejpam-5396	750	18	j.o	j.o	PROPN
ejpam-5396	750	19	.	.	PROPN
ejpam-5396	750	20	lawal	lawal	PROPN
ejpam-5396	750	21	,	,	PUNCT
ejpam-5396	750	22	a.i	a.i	PROPN
ejpam-5396	750	23	.	.	PROPN
ejpam-5396	750	24	abioye	abioye	PROPN
ejpam-5396	750	25	,	,	PUNCT
ejpam-5396	750	26	and	and	CCONJ
ejpam-5396	750	27	t.a	t.a	PROPN
ejpam-5396	750	28	.	.	PROPN
ejpam-5396	750	29	ayoola	ayoola	PROPN
ejpam-5396	750	30	.	.	PUNCT
ejpam-5396	751	1	fractional	fractional	ADJ
ejpam-5396	751	2	order	order	NOUN
ejpam-5396	751	3	of	of	ADP
ejpam-5396	751	4	pneumococcal	pneumococcal	ADJ
ejpam-5396	751	5	pneumonia	pneumonia	NOUN
ejpam-5396	751	6	infection	infection	NOUN
ejpam-5396	751	7	model	model	NOUN
ejpam-5396	751	8	with	with	ADP
ejpam-5396	751	9	caputo	caputo	PROPN
ejpam-5396	751	10	fabrizio	fabrizio	PROPN
ejpam-5396	751	11	operator	operator	NOUN
ejpam-5396	751	12	.	.	PUNCT
ejpam-5396	752	1	results	result	NOUN
ejpam-5396	752	2	in	in	ADP
ejpam-5396	752	3	physics	physics	NOUN
ejpam-5396	752	4	,	,	PUNCT
ejpam-5396	752	5	29:104–581	29:104–581	PROPN
ejpam-5396	752	6	,	,	PUNCT
ejpam-5396	752	7	2021	2021	NUM
ejpam-5396	752	8	.	.	PUNCT
ejpam-5396	753	1	[	[	X
ejpam-5396	753	2	45	45	NUM
ejpam-5396	753	3	]	]	X
ejpam-5396	753	4	k.i	k.i	PROPN
ejpam-5396	753	5	.	.	PROPN
ejpam-5396	753	6	oluwatobi	oluwatobi	PROPN
ejpam-5396	753	7	and	and	CCONJ
ejpam-5396	753	8	l.m	l.m	PROPN
ejpam-5396	753	9	.	.	PROPN
ejpam-5396	753	10	erinle	erinle	PROPN
ejpam-5396	753	11	-	-	PUNCT
ejpam-5396	753	12	ibrahim	ibrahim	PROPN
ejpam-5396	753	13	.	.	PUNCT
ejpam-5396	754	1	mathematical	mathematical	ADJ
ejpam-5396	754	2	modeling	modeling	NOUN
ejpam-5396	754	3	of	of	ADP
ejpam-5396	754	4	pneumonia	pneumonia	NOUN
ejpam-5396	754	5	dynamics	dynamic	NOUN
ejpam-5396	754	6	of	of	ADP
ejpam-5396	754	7	children	child	NOUN
ejpam-5396	754	8	under	under	ADP
ejpam-5396	754	9	the	the	DET
ejpam-5396	754	10	age	age	NOUN
ejpam-5396	754	11	of	of	ADP
ejpam-5396	754	12	five	five	NUM
ejpam-5396	754	13	.	.	PUNCT
ejpam-5396	755	1	res	re	NOUN
ejpam-5396	755	2	.	.	PUNCT
ejpam-5396	756	1	square	square	PROPN
ejpam-5396	756	2	,	,	PUNCT
ejpam-5396	756	3	1:1–16	1:1–16	NUM
ejpam-5396	756	4	,	,	PUNCT
ejpam-5396	756	5	2021	2021	NUM
ejpam-5396	756	6	.	.	PUNCT
ejpam-5396	757	1	[	[	X
ejpam-5396	757	2	46	46	NUM
ejpam-5396	757	3	]	]	X
ejpam-5396	757	4	j.	j.	PROPN
ejpam-5396	757	5	ong’ala	ong’ala	PROPN
ejpam-5396	757	6	,	,	PUNCT
ejpam-5396	757	7	p.	p.	NOUN
ejpam-5396	757	8	oleche	oleche	NOUN
ejpam-5396	757	9	,	,	PUNCT
ejpam-5396	757	10	and	and	CCONJ
ejpam-5396	757	11	j.y.t	j.y.t	PROPN
ejpam-5396	757	12	.	.	PUNCT
ejpam-5396	757	13	mugisha	mugisha	PROPN
ejpam-5396	757	14	.	.	PUNCT
ejpam-5396	758	1	mathematical	mathematical	ADJ
ejpam-5396	758	2	model	model	NOUN
ejpam-5396	758	3	for	for	ADP
ejpam-5396	758	4	pneumonia	pneumonia	NOUN
ejpam-5396	758	5	dynamics	dynamic	NOUN
ejpam-5396	758	6	with	with	ADP
ejpam-5396	758	7	carriers	carrier	NOUN
ejpam-5396	758	8	.	.	PUNCT
ejpam-5396	759	1	int	int	NOUN
ejpam-5396	759	2	.	.	PUNCT
ejpam-5396	760	1	j.	j.	PROPN
ejpam-5396	760	2	math	math	PROPN
ejpam-5396	760	3	.	.	PUNCT
ejpam-5396	761	1	anal	anal	PROPN
ejpam-5396	761	2	.	.	PROPN
ejpam-5396	761	3	,	,	PUNCT
ejpam-5396	761	4	7(50):2457–2473	7(50):2457–2473	NUM
ejpam-5396	761	5	,	,	PUNCT
ejpam-5396	761	6	2013	2013	NUM
ejpam-5396	761	7	.	.	PUNCT
ejpam-5396	762	1	[	[	X
ejpam-5396	762	2	47	47	NUM
ejpam-5396	762	3	]	]	X
ejpam-5396	762	4	d.	d.	PROPN
ejpam-5396	762	5	otoo	otoo	PROPN
ejpam-5396	762	6	,	,	PUNCT
ejpam-5396	762	7	p.	p.	PROPN
ejpam-5396	762	8	opoku	opoku	PROPN
ejpam-5396	762	9	,	,	PUNCT
ejpam-5396	762	10	s.	s.	PROPN
ejpam-5396	762	11	charles	charles	PROPN
ejpam-5396	762	12	,	,	PUNCT
ejpam-5396	762	13	and	and	CCONJ
ejpam-5396	762	14	a.p	a.p	PROPN
ejpam-5396	762	15	.	.	PROPN
ejpam-5396	762	16	kingsley	kingsley	PROPN
ejpam-5396	762	17	.	.	PUNCT
ejpam-5396	763	1	deterministic	deterministic	ADJ
ejpam-5396	763	2	epidemic	epidemic	NOUN
ejpam-5396	763	3	model	model	NOUN
ejpam-5396	763	4	for	for	ADP
ejpam-5396	763	5	(	(	PUNCT
ejpam-5396	763	6	svcsycasyir	svcsycasyir	NOUN
ejpam-5396	763	7	)	)	PUNCT
ejpam-5396	763	8	pneumonia	pneumonia	NOUN
ejpam-5396	763	9	dynamics	dynamic	NOUN
ejpam-5396	763	10	,	,	PUNCT
ejpam-5396	763	11	with	with	ADP
ejpam-5396	763	12	vaccination	vaccination	NOUN
ejpam-5396	763	13	and	and	CCONJ
ejpam-5396	763	14	temporal	temporal	ADJ
ejpam-5396	763	15	immunity	immunity	NOUN
ejpam-5396	763	16	.	.	PUNCT
ejpam-5396	764	1	infect	infect	VERB
ejpam-5396	764	2	.	.	PUNCT
ejpam-5396	765	1	dis	dis	PROPN
ejpam-5396	765	2	.	.	PUNCT
ejpam-5396	765	3	model	model	PROPN
ejpam-5396	765	4	.	.	PROPN
ejpam-5396	765	5	,	,	PUNCT
ejpam-5396	765	6	5:42–60	5:42–60	NUM
ejpam-5396	765	7	,	,	PUNCT
ejpam-5396	765	8	2020	2020	NUM
ejpam-5396	765	9	.	.	PUNCT
ejpam-5396	766	1	[	[	X
ejpam-5396	766	2	48	48	NUM
ejpam-5396	766	3	]	]	PUNCT
ejpam-5396	766	4	i.	i.	NOUN
ejpam-5396	766	5	podlubny	podlubny	PROPN
ejpam-5396	766	6	.	.	PUNCT
ejpam-5396	767	1	fractional	fractional	ADJ
ejpam-5396	767	2	differential	differential	ADJ
ejpam-5396	767	3	equations	equation	NOUN
ejpam-5396	767	4	.	.	PUNCT
ejpam-5396	768	1	academic	academic	ADJ
ejpam-5396	768	2	press	press	NOUN
ejpam-5396	768	3	,	,	PUNCT
ejpam-5396	768	4	new	new	PROPN
ejpam-5396	768	5	york	york	PROPN
ejpam-5396	768	6	,	,	PUNCT
ejpam-5396	768	7	ny	ny	PROPN
ejpam-5396	768	8	,	,	PUNCT
ejpam-5396	768	9	usa	usa	PROPN
ejpam-5396	768	10	,	,	PUNCT
ejpam-5396	768	11	1999	1999	NUM
ejpam-5396	768	12	.	.	PUNCT
ejpam-5396	769	1	[	[	X
ejpam-5396	769	2	49	49	NUM
ejpam-5396	769	3	]	]	PUNCT
ejpam-5396	769	4	m.	m.	NOUN
ejpam-5396	769	5	raj	raj	PROPN
ejpam-5396	769	6	,	,	PUNCT
ejpam-5396	769	7	m.	m.	PROPN
ejpam-5396	769	8	reddy	reddy	PROPN
ejpam-5396	769	9	,	,	PUNCT
ejpam-5396	769	10	m.	m.	NOUN
ejpam-5396	769	11	mufeed	mufeed	PROPN
ejpam-5396	769	12	,	,	PUNCT
ejpam-5396	769	13	and	and	CCONJ
ejpam-5396	769	14	s.	s.	PROPN
ejpam-5396	769	15	karthika	karthika	PROPN
ejpam-5396	769	16	.	.	PUNCT
ejpam-5396	770	1	hmm	hmm	PROPN
ejpam-5396	770	2	based	base	VERB
ejpam-5396	770	3	cough	cough	NOUN
ejpam-5396	770	4	sound	sound	NOUN
ejpam-5396	770	5	analysis	analysis	NOUN
ejpam-5396	770	6	for	for	ADP
ejpam-5396	770	7	classifying	classify	VERB
ejpam-5396	770	8	asthma	asthma	NOUN
ejpam-5396	770	9	and	and	CCONJ
ejpam-5396	770	10	pneumonia	pneumonia	NOUN
ejpam-5396	770	11	in	in	ADP
ejpam-5396	770	12	paediatric	paediatric	ADJ
ejpam-5396	770	13	population	population	NOUN
ejpam-5396	770	14	.	.	PUNCT
ejpam-5396	771	1	int	int	NOUN
ejpam-5396	771	2	.	.	PUNCT
ejpam-5396	772	1	j.	j.	PROPN
ejpam-5396	772	2	pure	pure	PROPN
ejpam-5396	772	3	appl	appl	PROPN
ejpam-5396	772	4	.	.	PUNCT
ejpam-5396	772	5	math	math	PROPN
ejpam-5396	772	6	.	.	PUNCT
ejpam-5396	772	7	,	,	PUNCT
ejpam-5396	772	8	118(18):609–616	118(18):609–616	NUM
ejpam-5396	772	9	,	,	PUNCT
ejpam-5396	772	10	2018	2018	NUM
ejpam-5396	772	11	.	.	PUNCT
ejpam-5396	773	1	[	[	X
ejpam-5396	773	2	50	50	NUM
ejpam-5396	773	3	]	]	PUNCT
ejpam-5396	773	4	s.	s.	PROPN
ejpam-5396	773	5	saber	saber	PROPN
ejpam-5396	773	6	and	and	CCONJ
ejpam-5396	773	7	a.	a.	NOUN
ejpam-5396	773	8	alalyani	alalyani	PROPN
ejpam-5396	773	9	.	.	PUNCT
ejpam-5396	774	1	stability	stability	NOUN
ejpam-5396	774	2	analysis	analysis	NOUN
ejpam-5396	774	3	and	and	CCONJ
ejpam-5396	774	4	numerical	numerical	ADJ
ejpam-5396	774	5	simulations	simulation	NOUN
ejpam-5396	774	6	of	of	ADP
ejpam-5396	774	7	ivgtt	ivgtt	PROPN
ejpam-5396	774	8	glucoseinsulin	glucoseinsulin	PROPN
ejpam-5396	774	9	interaction	interaction	NOUN
ejpam-5396	774	10	models	model	NOUN
ejpam-5396	774	11	with	with	ADP
ejpam-5396	774	12	two	two	NUM
ejpam-5396	774	13	time	time	NOUN
ejpam-5396	774	14	delays	delay	NOUN
ejpam-5396	774	15	.	.	PUNCT
ejpam-5396	775	1	math	math	NOUN
ejpam-5396	775	2	.	.	PUNCT
ejpam-5396	776	1	model	model	PROPN
ejpam-5396	776	2	.	.	PUNCT
ejpam-5396	777	1	anal	anal	PROPN
ejpam-5396	777	2	.	.	PUNCT
ejpam-5396	777	3	,	,	PUNCT
ejpam-5396	777	4	27:383–407	27:383–407	PROPN
ejpam-5396	777	5	,	,	PUNCT
ejpam-5396	777	6	2022	2022	NUM
ejpam-5396	777	7	.	.	PUNCT
ejpam-5396	778	1	[	[	X
ejpam-5396	778	2	51	51	NUM
ejpam-5396	778	3	]	]	PUNCT
ejpam-5396	778	4	sayed	say	VERB
ejpam-5396	778	5	saber	saber	PROPN
ejpam-5396	778	6	.	.	PUNCT
ejpam-5396	779	1	control	control	NOUN
ejpam-5396	779	2	of	of	ADP
ejpam-5396	779	3	chaos	chaos	NOUN
ejpam-5396	779	4	in	in	ADP
ejpam-5396	779	5	the	the	DET
ejpam-5396	779	6	burke	burke	PROPN
ejpam-5396	779	7	-	-	PUNCT
ejpam-5396	779	8	shaw	shaw	PROPN
ejpam-5396	779	9	system	system	NOUN
ejpam-5396	779	10	of	of	ADP
ejpam-5396	779	11	fractal	fractal	ADJ
ejpam-5396	779	12	-	-	PUNCT
ejpam-5396	779	13	fractional	fractional	ADJ
ejpam-5396	779	14	order	order	NOUN
ejpam-5396	779	15	in	in	ADP
ejpam-5396	779	16	the	the	DET
ejpam-5396	779	17	sense	sense	NOUN
ejpam-5396	779	18	of	of	ADP
ejpam-5396	779	19	caputo	caputo	PROPN
ejpam-5396	779	20	-	-	PUNCT
ejpam-5396	779	21	fabrizio	fabrizio	PROPN
ejpam-5396	779	22	.	.	PUNCT
ejpam-5396	780	1	journal	journal	PROPN
ejpam-5396	780	2	of	of	ADP
ejpam-5396	780	3	applied	apply	VERB
ejpam-5396	780	4	mathematics	mathematic	NOUN
ejpam-5396	780	5	and	and	CCONJ
ejpam-5396	780	6	computational	computational	ADJ
ejpam-5396	780	7	mechanics	mechanic	NOUN
ejpam-5396	780	8	,	,	PUNCT
ejpam-5396	780	9	23(1):83–96	23(1):83–96	NUM
ejpam-5396	780	10	,	,	PUNCT
ejpam-5396	780	11	2024	2024	NUM
ejpam-5396	780	12	.	.	PUNCT
ejpam-5396	781	1	[	[	X
ejpam-5396	781	2	52	52	NUM
ejpam-5396	781	3	]	]	PUNCT
ejpam-5396	781	4	sayed	say	VERB
ejpam-5396	781	5	saber	saber	PROPN
ejpam-5396	781	6	,	,	PUNCT
ejpam-5396	781	7	azza	azza	PROPN
ejpam-5396	781	8	m.	m.	PROPN
ejpam-5396	781	9	alghamdi	alghamdi	PROPN
ejpam-5396	781	10	,	,	PUNCT
ejpam-5396	781	11	ghada	ghada	PROPN
ejpam-5396	781	12	a.	a.	PROPN
ejpam-5396	781	13	ahmed	ahmed	PROPN
ejpam-5396	781	14	,	,	PUNCT
ejpam-5396	781	15	and	and	CCONJ
ejpam-5396	781	16	khulud	khulud	PROPN
ejpam-5396	781	17	m.	m.	PROPN
ejpam-5396	781	18	alshehri	alshehri	PROPN
ejpam-5396	781	19	.	.	PUNCT
ejpam-5396	782	1	mathematical	mathematical	ADJ
ejpam-5396	782	2	modelling	modelling	NOUN
ejpam-5396	782	3	and	and	CCONJ
ejpam-5396	782	4	optimal	optimal	ADJ
ejpam-5396	782	5	control	control	NOUN
ejpam-5396	782	6	of	of	ADP
ejpam-5396	782	7	pneumonia	pneumonia	NOUN
ejpam-5396	782	8	disease	disease	NOUN
ejpam-5396	782	9	in	in	ADP
ejpam-5396	782	10	sheep	sheep	NOUN
ejpam-5396	782	11	and	and	CCONJ
ejpam-5396	782	12	goats	goat	NOUN
ejpam-5396	782	13	in	in	ADP
ejpam-5396	782	14	al	al	PROPN
ejpam-5396	782	15	-	-	PUNCT
ejpam-5396	782	16	baha	baha	PROPN
ejpam-5396	782	17	region	region	NOUN
ejpam-5396	782	18	with	with	ADP
ejpam-5396	782	19	cost	cost	NOUN
ejpam-5396	782	20	-	-	PUNCT
ejpam-5396	782	21	effective	effective	ADJ
ejpam-5396	782	22	strategies	strategy	NOUN
ejpam-5396	782	23	.	.	PUNCT
ejpam-5396	783	1	aims	aim	VERB
ejpam-5396	783	2	mathematics	mathematic	NOUN
ejpam-5396	783	3	,	,	PUNCT
ejpam-5396	783	4	7(7):12011–12049	7(7):12011–12049	PROPN
ejpam-5396	783	5	,	,	PUNCT
ejpam-5396	783	6	2022	2022	NUM
ejpam-5396	783	7	.	.	PUNCT
ejpam-5396	784	1	[	[	X
ejpam-5396	784	2	53	53	NUM
ejpam-5396	784	3	]	]	X
ejpam-5396	784	4	g.t	g.t	PROPN
ejpam-5396	784	5	.	.	PROPN
ejpam-5396	784	6	tilahun	tilahun	PROPN
ejpam-5396	784	7	.	.	PUNCT
ejpam-5396	785	1	modeling	model	VERB
ejpam-5396	785	2	co	co	NOUN
ejpam-5396	785	3	-	-	NOUN
ejpam-5396	785	4	dynamics	dynamic	NOUN
ejpam-5396	785	5	of	of	ADP
ejpam-5396	785	6	pneumonia	pneumonia	NOUN
ejpam-5396	785	7	and	and	CCONJ
ejpam-5396	785	8	meningitis	meningitis	NOUN
ejpam-5396	785	9	diseases	disease	NOUN
ejpam-5396	785	10	.	.	PUNCT
ejpam-5396	786	1	adv	adv	PROPN
ejpam-5396	786	2	.	.	PROPN
ejpam-5396	786	3	differ	differ	VERB
ejpam-5396	786	4	.	.	PUNCT
ejpam-5396	787	1	equ	equ	PROPN
ejpam-5396	787	2	.	.	PROPN
ejpam-5396	787	3	,	,	PUNCT
ejpam-5396	787	4	2019(1):1	2019(1):1	PROPN
ejpam-5396	787	5	,	,	PUNCT
ejpam-5396	787	6	2019	2019	NUM
ejpam-5396	787	7	.	.	PUNCT
ejpam-5396	788	1	[	[	X
ejpam-5396	788	2	54	54	NUM
ejpam-5396	788	3	]	]	X
ejpam-5396	788	4	g.t	g.t	PROPN
ejpam-5396	788	5	.	.	PROPN
ejpam-5396	788	6	tilahun	tilahun	PROPN
ejpam-5396	788	7	.	.	PUNCT
ejpam-5396	789	1	optimal	optimal	ADJ
ejpam-5396	789	2	control	control	NOUN
ejpam-5396	789	3	analysis	analysis	NOUN
ejpam-5396	789	4	of	of	ADP
ejpam-5396	789	5	pneumonia	pneumonia	NOUN
ejpam-5396	789	6	and	and	CCONJ
ejpam-5396	789	7	meningitis	meningitis	NOUN
ejpam-5396	789	8	coinfection	coinfection	NOUN
ejpam-5396	789	9	.	.	PUNCT
ejpam-5396	790	1	comput	comput	NOUN
ejpam-5396	790	2	.	.	PUNCT
ejpam-5396	791	1	math	math	NOUN
ejpam-5396	791	2	.	.	PUNCT
ejpam-5396	792	1	methods	method	NOUN
ejpam-5396	792	2	med	me	VERB
ejpam-5396	792	3	.	.	PROPN
ejpam-5396	792	4	,	,	PUNCT
ejpam-5396	792	5	2019:1–15	2019:1–15	NUM
ejpam-5396	792	6	,	,	PUNCT
ejpam-5396	792	7	2019	2019	NUM
ejpam-5396	792	8	.	.	PUNCT
ejpam-5396	793	1	[	[	X
ejpam-5396	793	2	55	55	NUM
ejpam-5396	793	3	]	]	X
ejpam-5396	793	4	g.t	g.t	PROPN
ejpam-5396	793	5	.	.	PROPN
ejpam-5396	793	6	tilahun	tilahun	PROPN
ejpam-5396	793	7	,	,	PUNCT
ejpam-5396	793	8	o.d	o.d	PROPN
ejpam-5396	793	9	.	.	PROPN
ejpam-5396	793	10	makinde	makinde	PROPN
ejpam-5396	793	11	,	,	PUNCT
ejpam-5396	793	12	and	and	CCONJ
ejpam-5396	793	13	d.	d.	PROPN
ejpam-5396	793	14	malonza	malonza	PROPN
ejpam-5396	793	15	.	.	PUNCT
ejpam-5396	794	1	modelling	modelling	NOUN
ejpam-5396	794	2	and	and	CCONJ
ejpam-5396	794	3	optimal	optimal	ADJ
ejpam-5396	794	4	control	control	NOUN
ejpam-5396	794	5	of	of	ADP
ejpam-5396	794	6	pneumonia	pneumonia	NOUN
ejpam-5396	794	7	disease	disease	NOUN
ejpam-5396	794	8	with	with	ADP
ejpam-5396	794	9	cost	cost	NOUN
ejpam-5396	794	10	-	-	PUNCT
ejpam-5396	794	11	effective	effective	ADJ
ejpam-5396	794	12	strategies	strategy	NOUN
ejpam-5396	794	13	.	.	PUNCT
ejpam-5396	795	1	j.	j.	PROPN
ejpam-5396	795	2	biol	biol	PROPN
ejpam-5396	795	3	.	.	PUNCT
ejpam-5396	796	1	dyn	dyn	PROPN
ejpam-5396	796	2	.	.	PUNCT
ejpam-5396	796	3	,	,	PUNCT
ejpam-5396	796	4	11(2):400–426	11(2):400–426	NUM
ejpam-5396	796	5	,	,	PUNCT
ejpam-5396	796	6	2017	2017	NUM
ejpam-5396	796	7	.	.	PUNCT
ejpam-5396	797	1	references	reference	NOUN
ejpam-5396	797	2	2799	2799	NUM
ejpam-5396	798	1	[	[	X
ejpam-5396	798	2	56	56	NUM
ejpam-5396	798	3	]	]	X
ejpam-5396	798	4	g.t	g.t	PROPN
ejpam-5396	798	5	.	.	PROPN
ejpam-5396	798	6	tilahun	tilahun	PROPN
ejpam-5396	798	7	,	,	PUNCT
ejpam-5396	798	8	o.d	o.d	PROPN
ejpam-5396	798	9	.	.	PROPN
ejpam-5396	798	10	makinde	makinde	PROPN
ejpam-5396	798	11	,	,	PUNCT
ejpam-5396	798	12	and	and	CCONJ
ejpam-5396	798	13	d.	d.	PROPN
ejpam-5396	798	14	malonza	malonza	PROPN
ejpam-5396	798	15	.	.	PUNCT
ejpam-5396	799	1	co	co	NOUN
ejpam-5396	800	1	-	-	NOUN
ejpam-5396	800	2	dynamics	dynamic	NOUN
ejpam-5396	800	3	of	of	ADP
ejpam-5396	800	4	pneumonia	pneumonia	NOUN
ejpam-5396	800	5	and	and	CCONJ
ejpam-5396	800	6	typhoid	typhoid	NOUN
ejpam-5396	800	7	fever	fever	NOUN
ejpam-5396	800	8	diseases	disease	NOUN
ejpam-5396	800	9	with	with	ADP
ejpam-5396	800	10	cost	cost	NOUN
ejpam-5396	800	11	-	-	PUNCT
ejpam-5396	800	12	effective	effective	ADJ
ejpam-5396	800	13	optimal	optimal	ADJ
ejpam-5396	800	14	control	control	NOUN
ejpam-5396	800	15	analysis	analysis	NOUN
ejpam-5396	800	16	.	.	PUNCT
ejpam-5396	801	1	appl	appl	PROPN
ejpam-5396	801	2	.	.	PROPN
ejpam-5396	801	3	math	math	PROPN
ejpam-5396	801	4	.	.	PUNCT
ejpam-5396	802	1	comput	comput	NOUN
ejpam-5396	802	2	.	.	PUNCT
ejpam-5396	802	3	,	,	PUNCT
ejpam-5396	802	4	316:438–459	316:438–459	PROPN
ejpam-5396	802	5	,	,	PUNCT
ejpam-5396	802	6	2018	2018	NUM
ejpam-5396	802	7	.	.	PUNCT
ejpam-5396	803	1	[	[	X
ejpam-5396	803	2	57	57	NUM
ejpam-5396	803	3	]	]	PUNCT
ejpam-5396	803	4	r.	r.	PROPN
ejpam-5396	803	5	ullah	ullah	PROPN
ejpam-5396	803	6	,	,	PUNCT
ejpam-5396	803	7	r.	r.	PROPN
ejpam-5396	803	8	ellahi	ellahi	PROPN
ejpam-5396	803	9	,	,	PUNCT
ejpam-5396	803	10	s.	s.	PROPN
ejpam-5396	803	11	m.	m.	PROPN
ejpam-5396	803	12	sait	sait	PROPN
ejpam-5396	803	13	,	,	PUNCT
ejpam-5396	803	14	and	and	CCONJ
ejpam-5396	803	15	s.	s.	PROPN
ejpam-5396	803	16	t.	t.	PROPN
ejpam-5396	803	17	mohyud	mohyud	PROPN
ejpam-5396	803	18	-	-	PUNCT
ejpam-5396	803	19	din	din	NOUN
ejpam-5396	803	20	.	.	PROPN
ejpam-5396	803	21	on	on	ADP
ejpam-5396	803	22	the	the	DET
ejpam-5396	803	23	fractional	fractional	ADJ
ejpam-5396	803	24	order	order	NOUN
ejpam-5396	803	25	model	model	NOUN
ejpam-5396	803	26	of	of	ADP
ejpam-5396	803	27	hiv-1	hiv-1	ADJ
ejpam-5396	803	28	infection	infection	NOUN
ejpam-5396	803	29	of	of	ADP
ejpam-5396	803	30	cd4	cd4	PROPN
ejpam-5396	803	31	+	+	PROPN
ejpam-5396	803	32	t	t	PROPN
ejpam-5396	803	33	-	-	PUNCT
ejpam-5396	803	34	cells	cell	NOUN
ejpam-5396	803	35	under	under	ADP
ejpam-5396	803	36	the	the	DET
ejpam-5396	803	37	influence	influence	NOUN
ejpam-5396	803	38	of	of	ADP
ejpam-5396	803	39	antiviral	antiviral	ADJ
ejpam-5396	803	40	drug	drug	NOUN
ejpam-5396	803	41	treatment	treatment	NOUN
ejpam-5396	803	42	.	.	PUNCT
ejpam-5396	804	1	j.	j.	PROPN
ejpam-5396	804	2	taibah	taibah	PROPN
ejpam-5396	804	3	.	.	PUNCT
ejpam-5396	805	1	univ	univ	PROPN
ejpam-5396	805	2	.	.	PUNCT
ejpam-5396	806	1	sci	sci	PROPN
ejpam-5396	806	2	.	.	PROPN
ejpam-5396	806	3	,	,	PUNCT
ejpam-5396	806	4	14(1):50–59	14(1):50–59	NUM
ejpam-5396	806	5	,	,	PUNCT
ejpam-5396	806	6	2020	2020	NUM
ejpam-5396	806	7	.	.	PUNCT
ejpam-5396	807	1	[	[	X
ejpam-5396	807	2	58	58	NUM
ejpam-5396	807	3	]	]	X
ejpam-5396	807	4	c.	c.	PROPN
ejpam-5396	807	5	vargas	vargas	PROPN
ejpam-5396	807	6	-	-	PUNCT
ejpam-5396	807	7	de	de	NOUN
ejpam-5396	807	8	-	-	NOUN
ejpam-5396	807	9	león	león	PROPN
ejpam-5396	807	10	.	.	PUNCT
ejpam-5396	807	11	volterra	volterra	NOUN
ejpam-5396	807	12	-	-	PUNCT
ejpam-5396	807	13	type	type	NOUN
ejpam-5396	807	14	lyapunov	lyapunov	NOUN
ejpam-5396	807	15	functions	function	NOUN
ejpam-5396	807	16	for	for	ADP
ejpam-5396	807	17	fractional	fractional	ADJ
ejpam-5396	807	18	-	-	PUNCT
ejpam-5396	807	19	order	order	NOUN
ejpam-5396	807	20	epidemic	epidemic	NOUN
ejpam-5396	807	21	systems	system	NOUN
ejpam-5396	807	22	.	.	PUNCT
ejpam-5396	808	1	commun	commun	PROPN
ejpam-5396	808	2	.	.	PUNCT
ejpam-5396	809	1	nonlinear	nonlinear	PROPN
ejpam-5396	809	2	sci	sci	PROPN
ejpam-5396	809	3	.	.	PUNCT
ejpam-5396	809	4	numer	numer	PROPN
ejpam-5396	809	5	.	.	PUNCT
ejpam-5396	810	1	simul	simul	PROPN
ejpam-5396	810	2	.	.	PROPN
ejpam-5396	810	3	,	,	PUNCT
ejpam-5396	810	4	24:75–85	24:75–85	NUM
ejpam-5396	810	5	,	,	PUNCT
ejpam-5396	810	6	2015	2015	NUM
ejpam-5396	810	7	.	.	PUNCT
ejpam-5396	811	1	[	[	X
ejpam-5396	811	2	59	59	NUM
ejpam-5396	811	3	]	]	SYM
ejpam-5396	811	4	n.m	n.m	PROPN
ejpam-5396	811	5	.	.	PROPN
ejpam-5396	811	6	wafula	wafula	PROPN
ejpam-5396	811	7	,	,	PUNCT
ejpam-5396	811	8	b.o	b.o	PROPN
ejpam-5396	811	9	.	.	PROPN
ejpam-5396	811	10	kwach	kwach	PROPN
ejpam-5396	811	11	,	,	PUNCT
ejpam-5396	811	12	and	and	CCONJ
ejpam-5396	811	13	v.n	v.n	PROPN
ejpam-5396	811	14	.	.	PROPN
ejpam-5396	811	15	marani	marani	PROPN
ejpam-5396	811	16	.	.	PUNCT
ejpam-5396	811	17	mathematical	mathematical	ADJ
ejpam-5396	811	18	modeling	modeling	NOUN
ejpam-5396	811	19	and	and	CCONJ
ejpam-5396	811	20	optimal	optimal	ADJ
ejpam-5396	811	21	control	control	NOUN
ejpam-5396	811	22	for	for	ADP
ejpam-5396	811	23	controlling	control	VERB
ejpam-5396	811	24	pneumoniahiv	pneumoniahiv	PROPN
ejpam-5396	811	25	coinfection	coinfection	NOUN
ejpam-5396	811	26	.	.	PUNCT
ejpam-5396	812	1	int	int	NOUN
ejpam-5396	812	2	.	.	PUNCT
ejpam-5396	813	1	j.	j.	PROPN
ejpam-5396	813	2	innov	innov	PROPN
ejpam-5396	813	3	.	.	PUNCT
ejpam-5396	814	1	res	res	PROPN
ejpam-5396	814	2	.	.	PUNCT
ejpam-5396	815	1	dev	dev	PROPN
ejpam-5396	815	2	.	.	PROPN
ejpam-5396	815	3	,	,	PUNCT
ejpam-5396	815	4	10(1):138–144	10(1):138–144	NUM
ejpam-5396	815	5	,	,	PUNCT
ejpam-5396	815	6	2021	2021	NUM
ejpam-5396	815	7	.	.	PUNCT
ejpam-5396	816	1	[	[	X
ejpam-5396	816	2	60	60	NUM
ejpam-5396	816	3	]	]	X
ejpam-5396	816	4	o.c	o.c	PROPN
ejpam-5396	816	5	.	.	PROPN
ejpam-5396	816	6	zephaniah	zephaniah	PROPN
ejpam-5396	816	7	,	,	PUNCT
ejpam-5396	816	8	u.i.r	u.i.r	NOUN
ejpam-5396	816	9	.	.	PUNCT
ejpam-5396	816	10	nwaugonma	nwaugonma	PROPN
ejpam-5396	816	11	,	,	PUNCT
ejpam-5396	816	12	i.s	i.s	PROPN
ejpam-5396	816	13	.	.	PROPN
ejpam-5396	816	14	chioma	chioma	PROPN
ejpam-5396	816	15	,	,	PUNCT
ejpam-5396	816	16	and	and	CCONJ
ejpam-5396	816	17	o.	o.	PROPN
ejpam-5396	816	18	adrew	adrew	PROPN
ejpam-5396	816	19	.	.	PUNCT
ejpam-5396	817	1	a	a	DET
ejpam-5396	817	2	mathematical	mathematical	ADJ
ejpam-5396	817	3	model	model	NOUN
ejpam-5396	817	4	and	and	CCONJ
ejpam-5396	817	5	analysis	analysis	NOUN
ejpam-5396	817	6	of	of	ADP
ejpam-5396	817	7	an	an	DET
ejpam-5396	817	8	sveir	sveir	ADJ
ejpam-5396	817	9	model	model	NOUN
ejpam-5396	817	10	for	for	ADP
ejpam-5396	817	11	streptococcus	streptococcus	ADJ
ejpam-5396	817	12	pneumonia	pneumonia	NOUN
ejpam-5396	817	13	with	with	ADP
ejpam-5396	817	14	saturated	saturate	VERB
ejpam-5396	817	15	incidence	incidence	NOUN
ejpam-5396	817	16	force	force	NOUN
ejpam-5396	817	17	of	of	ADP
ejpam-5396	817	18	infection	infection	NOUN
ejpam-5396	817	19	.	.	PUNCT
ejpam-5396	818	1	math	math	NOUN
ejpam-5396	818	2	.	.	PUNCT
ejpam-5396	819	1	model	model	PROPN
ejpam-5396	819	2	.	.	PUNCT
ejpam-5396	820	1	appl	appl	PROPN
ejpam-5396	820	2	.	.	PROPN
ejpam-5396	820	3	,	,	PUNCT
ejpam-5396	820	4	5(1):16	5(1):16	NUM
ejpam-5396	820	5	,	,	PUNCT
ejpam-5396	820	6	2020	2020	NUM
ejpam-5396	820	7	.	.	PUNCT