id	sid	tid	token	lemma	pos
ejpam-5861	1	1	european	european	PROPN
ejpam-5861	1	2	journal	journal	PROPN
ejpam-5861	1	3	of	of	ADP
ejpam-5861	1	4	pure	pure	ADJ
ejpam-5861	1	5	and	and	CCONJ
ejpam-5861	1	6	applied	applied	ADJ
ejpam-5861	1	7	mathematics	mathematic	NOUN
ejpam-5861	1	8	2025	2025	NUM
ejpam-5861	1	9	,	,	PUNCT
ejpam-5861	1	10	vol	vol	NOUN
ejpam-5861	1	11	.	.	PROPN
ejpam-5861	1	12	18	18	NUM
ejpam-5861	1	13	,	,	PUNCT
ejpam-5861	1	14	issue	issue	NOUN
ejpam-5861	1	15	2	2	NUM
ejpam-5861	1	16	,	,	PUNCT
ejpam-5861	1	17	article	article	NOUN
ejpam-5861	1	18	number	number	NOUN
ejpam-5861	1	19	5861	5861	NUM
ejpam-5861	1	20	issn	issn	VERB
ejpam-5861	1	21	1307	1307	NUM
ejpam-5861	1	22	-	-	SYM
ejpam-5861	1	23	5543	5543	NUM
ejpam-5861	1	24	–	–	PUNCT
ejpam-5861	1	25	ejpam.com	ejpam.com	X
ejpam-5861	1	26	published	publish	VERB
ejpam-5861	1	27	by	by	ADP
ejpam-5861	1	28	new	new	PROPN
ejpam-5861	1	29	york	york	PROPN
ejpam-5861	1	30	business	business	PROPN
ejpam-5861	1	31	global	global	PROPN
ejpam-5861	1	32	a	a	DET
ejpam-5861	1	33	mathematical	mathematical	ADJ
ejpam-5861	1	34	model	model	NOUN
ejpam-5861	1	35	of	of	ADP
ejpam-5861	1	36	covid-19	covid-19	PROPN
ejpam-5861	1	37	using	use	VERB
ejpam-5861	1	38	piecewise	piecewise	NOUN
ejpam-5861	1	39	derivative	derivative	NOUN
ejpam-5861	1	40	of	of	ADP
ejpam-5861	1	41	fractional	fractional	ADJ
ejpam-5861	1	42	order	order	NOUN
ejpam-5861	1	43	shabana	shabana	PROPN
ejpam-5861	1	44	naz1	naz1	PROPN
ejpam-5861	1	45	,	,	PUNCT
ejpam-5861	1	46	muhammad	muhammad	PROPN
ejpam-5861	1	47	sarwar1,2	sarwar1,2	PROPN
ejpam-5861	1	48	,	,	PUNCT
ejpam-5861	1	49	kamal	kamal	PROPN
ejpam-5861	1	50	shah1,2	shah1,2	PROPN
ejpam-5861	1	51	,	,	PUNCT
ejpam-5861	1	52	nahid	nahid	PROPN
ejpam-5861	1	53	fatima2	fatima2	PROPN
ejpam-5861	1	54	,	,	PUNCT
ejpam-5861	1	55	thabet	thabet	PROPN
ejpam-5861	1	56	abdeljawad3,2,4,∗	abdeljawad3,2,4,∗	PROPN
ejpam-5861	1	57	1	1	NUM
ejpam-5861	1	58	department	department	NOUN
ejpam-5861	1	59	of	of	ADP
ejpam-5861	1	60	mathematics	mathematic	NOUN
ejpam-5861	1	61	,	,	PUNCT
ejpam-5861	1	62	university	university	NOUN
ejpam-5861	1	63	of	of	ADP
ejpam-5861	1	64	malakand	malakand	PROPN
ejpam-5861	1	65	,	,	PUNCT
ejpam-5861	1	66	chakdara	chakdara	NOUN
ejpam-5861	1	67	dir(l	dir(l	PROPN
ejpam-5861	1	68	)	)	PUNCT
ejpam-5861	1	69	,	,	PUNCT
ejpam-5861	1	70	18000	18000	NUM
ejpam-5861	1	71	,	,	PUNCT
ejpam-5861	1	72	khyber	khyber	PROPN
ejpam-5861	1	73	pakhtunkhwa	pakhtunkhwa	PROPN
ejpam-5861	1	74	,	,	PUNCT
ejpam-5861	1	75	pakistan	pakistan	PROPN
ejpam-5861	1	76	2	2	NUM
ejpam-5861	1	77	department	department	NOUN
ejpam-5861	1	78	of	of	ADP
ejpam-5861	1	79	mathematics	mathematic	NOUN
ejpam-5861	1	80	and	and	CCONJ
ejpam-5861	1	81	sciences	science	NOUN
ejpam-5861	1	82	,	,	PUNCT
ejpam-5861	1	83	prince	prince	PROPN
ejpam-5861	1	84	sultan	sultan	PROPN
ejpam-5861	1	85	university	university	PROPN
ejpam-5861	1	86	,	,	PUNCT
ejpam-5861	1	87	riyadh	riyadh	NOUN
ejpam-5861	1	88	,	,	PUNCT
ejpam-5861	1	89	11586	11586	NUM
ejpam-5861	1	90	,	,	PUNCT
ejpam-5861	1	91	saudi	saudi	PROPN
ejpam-5861	1	92	arabia	arabia	PROPN
ejpam-5861	1	93	3	3	NUM
ejpam-5861	1	94	department	department	NOUN
ejpam-5861	1	95	of	of	ADP
ejpam-5861	1	96	mathematics	mathematic	NOUN
ejpam-5861	1	97	,	,	PUNCT
ejpam-5861	1	98	saveetha	saveetha	PROPN
ejpam-5861	1	99	school	school	PROPN
ejpam-5861	1	100	of	of	ADP
ejpam-5861	1	101	engineering	engineering	PROPN
ejpam-5861	1	102	,	,	PUNCT
ejpam-5861	1	103	saveetha	saveetha	PROPN
ejpam-5861	1	104	institute	institute	PROPN
ejpam-5861	1	105	of	of	ADP
ejpam-5861	1	106	medical	medical	ADJ
ejpam-5861	1	107	and	and	CCONJ
ejpam-5861	1	108	technical	technical	ADJ
ejpam-5861	1	109	sciences	science	NOUN
ejpam-5861	1	110	,	,	PUNCT
ejpam-5861	1	111	saveetha	saveetha	PROPN
ejpam-5861	1	112	university	university	PROPN
ejpam-5861	1	113	,	,	PUNCT
ejpam-5861	1	114	chennai	chennai	NOUN
ejpam-5861	1	115	602105	602105	NUM
ejpam-5861	1	116	,	,	PUNCT
ejpam-5861	1	117	tamil	tamil	PROPN
ejpam-5861	1	118	nadu	nadu	PROPN
ejpam-5861	1	119	,	,	PUNCT
ejpam-5861	1	120	india	india	PROPN
ejpam-5861	1	121	4	4	NUM
ejpam-5861	1	122	department	department	NOUN
ejpam-5861	1	123	of	of	ADP
ejpam-5861	1	124	mathematics	mathematic	NOUN
ejpam-5861	1	125	and	and	CCONJ
ejpam-5861	1	126	applied	apply	VERB
ejpam-5861	1	127	mathematics	mathematic	NOUN
ejpam-5861	1	128	,	,	PUNCT
ejpam-5861	1	129	school	school	NOUN
ejpam-5861	1	130	of	of	ADP
ejpam-5861	1	131	science	science	NOUN
ejpam-5861	1	132	and	and	CCONJ
ejpam-5861	1	133	technology	technology	NOUN
ejpam-5861	1	134	,	,	PUNCT
ejpam-5861	1	135	sefako	sefako	VERB
ejpam-5861	1	136	makgatho	makgatho	PROPN
ejpam-5861	1	137	health	health	PROPN
ejpam-5861	1	138	sciences	sciences	PROPN
ejpam-5861	1	139	university	university	PROPN
ejpam-5861	1	140	,	,	PUNCT
ejpam-5861	1	141	ga	ga	PROPN
ejpam-5861	1	142	-	-	NOUN
ejpam-5861	1	143	rankuwa	rankuwa	PROPN
ejpam-5861	1	144	,	,	PUNCT
ejpam-5861	1	145	south	south	PROPN
ejpam-5861	1	146	africa	africa	PROPN
ejpam-5861	1	147	abstract	abstract	PROPN
ejpam-5861	1	148	.	.	PUNCT
ejpam-5861	2	1	currently	currently	ADV
ejpam-5861	2	2	the	the	DET
ejpam-5861	2	3	dynamical	dynamical	ADJ
ejpam-5861	2	4	systems	system	NOUN
ejpam-5861	2	5	of	of	ADP
ejpam-5861	2	6	infectious	infectious	ADJ
ejpam-5861	2	7	disease	disease	NOUN
ejpam-5861	2	8	were	be	AUX
ejpam-5861	2	9	studied	study	VERB
ejpam-5861	2	10	by	by	ADP
ejpam-5861	2	11	using	use	VERB
ejpam-5861	2	12	various	various	ADJ
ejpam-5861	2	13	definitions	definition	NOUN
ejpam-5861	2	14	of	of	ADP
ejpam-5861	2	15	fractional	fractional	ADJ
ejpam-5861	2	16	calculus	calculus	NOUN
ejpam-5861	2	17	.	.	PUNCT
ejpam-5861	3	1	because	because	SCONJ
ejpam-5861	3	2	the	the	DET
ejpam-5861	3	3	mentioned	mention	VERB
ejpam-5861	3	4	area	area	NOUN
ejpam-5861	3	5	has	have	VERB
ejpam-5861	3	6	the	the	DET
ejpam-5861	3	7	ability	ability	NOUN
ejpam-5861	3	8	to	to	PART
ejpam-5861	3	9	demonstrate	demonstrate	VERB
ejpam-5861	3	10	the	the	DET
ejpam-5861	3	11	short	short	ADJ
ejpam-5861	3	12	and	and	CCONJ
ejpam-5861	3	13	long	long	ADJ
ejpam-5861	3	14	memory	memory	NOUN
ejpam-5861	3	15	terms	term	NOUN
ejpam-5861	3	16	involved	involve	VERB
ejpam-5861	3	17	in	in	ADP
ejpam-5861	3	18	the	the	DET
ejpam-5861	3	19	physical	physical	ADJ
ejpam-5861	3	20	dynamics	dynamic	NOUN
ejpam-5861	3	21	of	of	ADP
ejpam-5861	3	22	numerous	numerous	ADJ
ejpam-5861	3	23	real	real	ADJ
ejpam-5861	3	24	world	world	NOUN
ejpam-5861	3	25	problems	problem	NOUN
ejpam-5861	3	26	.	.	PUNCT
ejpam-5861	4	1	in	in	ADP
ejpam-5861	4	2	this	this	DET
ejpam-5861	4	3	work	work	NOUN
ejpam-5861	4	4	,	,	PUNCT
ejpam-5861	4	5	we	we	PRON
ejpam-5861	4	6	consider	consider	VERB
ejpam-5861	4	7	a	a	DET
ejpam-5861	4	8	seven	seven	NUM
ejpam-5861	4	9	compartmental	compartmental	ADJ
ejpam-5861	4	10	model	model	NOUN
ejpam-5861	4	11	for	for	ADP
ejpam-5861	4	12	the	the	DET
ejpam-5861	4	13	transmission	transmission	NOUN
ejpam-5861	4	14	dynamics	dynamic	NOUN
ejpam-5861	4	15	of	of	ADP
ejpam-5861	4	16	covid-19	covid-19	PROPN
ejpam-5861	4	17	including	include	VERB
ejpam-5861	4	18	susceptible	susceptible	ADJ
ejpam-5861	4	19	(	(	PUNCT
ejpam-5861	4	20	s	s	NOUN
ejpam-5861	4	21	)	)	PUNCT
ejpam-5861	4	22	,	,	PUNCT
ejpam-5861	4	23	vaccinated	vaccinate	VERB
ejpam-5861	4	24	(	(	PUNCT
ejpam-5861	4	25	v	v	NOUN
ejpam-5861	4	26	)	)	PUNCT
ejpam-5861	4	27	,	,	PUNCT
ejpam-5861	4	28	exposed	expose	VERB
ejpam-5861	4	29	(	(	PUNCT
ejpam-5861	4	30	e	e	NOUN
ejpam-5861	4	31	)	)	PUNCT
ejpam-5861	4	32	,	,	PUNCT
ejpam-5861	4	33	infected	infect	VERB
ejpam-5861	4	34	(	(	PUNCT
ejpam-5861	4	35	i	i	NOUN
ejpam-5861	4	36	)	)	PUNCT
ejpam-5861	4	37	,	,	PUNCT
ejpam-5861	4	38	quarantined	quarantine	VERB
ejpam-5861	4	39	(	(	PUNCT
ejpam-5861	4	40	q	q	NOUN
ejpam-5861	4	41	)	)	PUNCT
ejpam-5861	4	42	,	,	PUNCT
ejpam-5861	4	43	recovered	recover	VERB
ejpam-5861	4	44	(	(	PUNCT
ejpam-5861	4	45	r	r	NOUN
ejpam-5861	4	46	)	)	PUNCT
ejpam-5861	4	47	,	,	PUNCT
ejpam-5861	4	48	and	and	CCONJ
ejpam-5861	4	49	death	death	NOUN
ejpam-5861	4	50	(	(	PUNCT
ejpam-5861	4	51	d	d	NOUN
ejpam-5861	4	52	)	)	PUNCT
ejpam-5861	4	53	classes	class	NOUN
ejpam-5861	4	54	.	.	PUNCT
ejpam-5861	5	1	we	we	PRON
ejpam-5861	5	2	first	first	ADV
ejpam-5861	5	3	revisit	revisit	VERB
ejpam-5861	5	4	the	the	DET
ejpam-5861	5	5	fundamental	fundamental	ADJ
ejpam-5861	5	6	outcomes	outcome	NOUN
ejpam-5861	5	7	related	relate	VERB
ejpam-5861	5	8	to	to	ADP
ejpam-5861	5	9	equilibrium	equilibrium	NOUN
ejpam-5861	5	10	points	point	NOUN
ejpam-5861	5	11	,	,	PUNCT
ejpam-5861	5	12	basic	basic	ADJ
ejpam-5861	5	13	reproduction	reproduction	NOUN
ejpam-5861	5	14	numbers	number	NOUN
ejpam-5861	5	15	,	,	PUNCT
ejpam-5861	5	16	sensitivity	sensitivity	NOUN
ejpam-5861	5	17	analysis	analysis	NOUN
ejpam-5861	5	18	,	,	PUNCT
ejpam-5861	5	19	and	and	CCONJ
ejpam-5861	5	20	equilibrium	equilibrium	NOUN
ejpam-5861	5	21	points	point	NOUN
ejpam-5861	5	22	including	include	VERB
ejpam-5861	5	23	disease	disease	NOUN
ejpam-5861	5	24	free	free	ADJ
ejpam-5861	5	25	(	(	PUNCT
ejpam-5861	5	26	df	df	NOUN
ejpam-5861	5	27	)	)	PUNCT
ejpam-5861	5	28	and	and	CCONJ
ejpam-5861	5	29	endemic	endemic	ADJ
ejpam-5861	5	30	equilibrium	equilibrium	NOUN
ejpam-5861	5	31	(	(	PUNCT
ejpam-5861	5	32	ee	ee	NOUN
ejpam-5861	5	33	)	)	PUNCT
ejpam-5861	5	34	points	point	NOUN
ejpam-5861	5	35	.	.	PUNCT
ejpam-5861	6	1	in	in	ADP
ejpam-5861	6	2	addition	addition	NOUN
ejpam-5861	6	3	,	,	PUNCT
ejpam-5861	6	4	our	our	PRON
ejpam-5861	6	5	main	main	ADJ
ejpam-5861	6	6	goal	goal	NOUN
ejpam-5861	6	7	is	be	AUX
ejpam-5861	6	8	to	to	PART
ejpam-5861	6	9	investigate	investigate	VERB
ejpam-5861	6	10	the	the	DET
ejpam-5861	6	11	considered	consider	VERB
ejpam-5861	6	12	model	model	NOUN
ejpam-5861	6	13	under	under	ADP
ejpam-5861	6	14	the	the	DET
ejpam-5861	6	15	new	new	ADJ
ejpam-5861	6	16	aspect	aspect	NOUN
ejpam-5861	6	17	of	of	ADP
ejpam-5861	6	18	fractional	fractional	ADJ
ejpam-5861	6	19	calculus	calculus	NOUN
ejpam-5861	6	20	known	know	VERB
ejpam-5861	6	21	as	as	ADP
ejpam-5861	6	22	piecewise	piecewise	NOUN
ejpam-5861	6	23	fractional	fractional	ADJ
ejpam-5861	6	24	order	order	NOUN
ejpam-5861	6	25	operators	operator	NOUN
ejpam-5861	6	26	.	.	PUNCT
ejpam-5861	7	1	the	the	DET
ejpam-5861	7	2	mentioned	mention	VERB
ejpam-5861	7	3	operators	operator	NOUN
ejpam-5861	7	4	have	have	VERB
ejpam-5861	7	5	the	the	DET
ejpam-5861	7	6	ability	ability	NOUN
ejpam-5861	7	7	to	to	PART
ejpam-5861	7	8	demonstrate	demonstrate	VERB
ejpam-5861	7	9	the	the	DET
ejpam-5861	7	10	multi	multi	ADJ
ejpam-5861	7	11	phase	phase	NOUN
ejpam-5861	7	12	behaviours	behaviour	NOUN
ejpam-5861	7	13	of	of	ADP
ejpam-5861	7	14	the	the	DET
ejpam-5861	7	15	dynamical	dynamical	ADJ
ejpam-5861	7	16	problems	problem	NOUN
ejpam-5861	7	17	.	.	PUNCT
ejpam-5861	8	1	the	the	DET
ejpam-5861	8	2	said	say	VERB
ejpam-5861	8	3	characteristics	characteristic	NOUN
ejpam-5861	8	4	can	can	AUX
ejpam-5861	8	5	not	not	PART
ejpam-5861	8	6	be	be	AUX
ejpam-5861	8	7	described	describe	VERB
ejpam-5861	8	8	by	by	ADP
ejpam-5861	8	9	using	use	VERB
ejpam-5861	8	10	the	the	DET
ejpam-5861	8	11	traditional	traditional	ADJ
ejpam-5861	8	12	operators	operator	NOUN
ejpam-5861	8	13	.	.	PUNCT
ejpam-5861	9	1	we	we	PRON
ejpam-5861	9	2	apply	apply	VERB
ejpam-5861	9	3	the	the	DET
ejpam-5861	9	4	tools	tool	NOUN
ejpam-5861	9	5	of	of	ADP
ejpam-5861	9	6	nonlinear	nonlinear	ADJ
ejpam-5861	9	7	analysis	analysis	NOUN
ejpam-5861	9	8	to	to	PART
ejpam-5861	9	9	deduce	deduce	VERB
ejpam-5861	9	10	sufficient	sufficient	ADJ
ejpam-5861	9	11	conditions	condition	NOUN
ejpam-5861	9	12	for	for	ADP
ejpam-5861	9	13	the	the	DET
ejpam-5861	9	14	existence	existence	NOUN
ejpam-5861	9	15	of	of	ADP
ejpam-5861	9	16	at	at	ADV
ejpam-5861	9	17	least	least	ADV
ejpam-5861	9	18	one	one	NUM
ejpam-5861	9	19	solution	solution	NOUN
ejpam-5861	9	20	and	and	CCONJ
ejpam-5861	9	21	its	its	PRON
ejpam-5861	9	22	uniqueness	uniqueness	NOUN
ejpam-5861	9	23	.	.	PUNCT
ejpam-5861	10	1	additionally	additionally	ADV
ejpam-5861	10	2	,	,	PUNCT
ejpam-5861	10	3	we	we	PRON
ejpam-5861	10	4	also	also	ADV
ejpam-5861	10	5	investigate	investigate	VERB
ejpam-5861	10	6	the	the	DET
ejpam-5861	10	7	results	result	NOUN
ejpam-5861	10	8	related	relate	VERB
ejpam-5861	10	9	to	to	ADP
ejpam-5861	10	10	stability	stability	VERB
ejpam-5861	10	11	analysis	analysis	NOUN
ejpam-5861	10	12	of	of	ADP
ejpam-5861	10	13	ulam	ulam	NOUN
ejpam-5861	10	14	-	-	PUNCT
ejpam-5861	10	15	hyers	hyer	NOUN
ejpam-5861	10	16	(	(	PUNCT
ejpam-5861	10	17	uh	uh	INTJ
ejpam-5861	10	18	)	)	PUNCT
ejpam-5861	10	19	type	type	NOUN
ejpam-5861	10	20	.	.	PUNCT
ejpam-5861	11	1	finally	finally	ADV
ejpam-5861	11	2	,	,	PUNCT
ejpam-5861	11	3	we	we	PRON
ejpam-5861	11	4	extend	extend	VERB
ejpam-5861	11	5	the	the	DET
ejpam-5861	11	6	concepts	concept	NOUN
ejpam-5861	11	7	of	of	ADP
ejpam-5861	11	8	rk2	rk2	PROPN
ejpam-5861	11	9	method	method	NOUN
ejpam-5861	11	10	to	to	PART
ejpam-5861	11	11	form	form	VERB
ejpam-5861	11	12	a	a	DET
ejpam-5861	11	13	sophisticated	sophisticated	ADJ
ejpam-5861	11	14	algorithm	algorithm	NOUN
ejpam-5861	11	15	to	to	PART
ejpam-5861	11	16	simulate	simulate	VERB
ejpam-5861	11	17	the	the	DET
ejpam-5861	11	18	results	result	NOUN
ejpam-5861	11	19	graphically	graphically	ADV
ejpam-5861	11	20	.	.	PUNCT
ejpam-5861	12	1	we	we	PRON
ejpam-5861	12	2	present	present	VERB
ejpam-5861	12	3	the	the	DET
ejpam-5861	12	4	numerical	numerical	ADJ
ejpam-5861	12	5	results	result	NOUN
ejpam-5861	12	6	for	for	ADP
ejpam-5861	12	7	various	various	ADJ
ejpam-5861	12	8	fractional	fractional	ADJ
ejpam-5861	12	9	orders	order	NOUN
ejpam-5861	12	10	.	.	PUNCT
ejpam-5861	13	1	2020	2020	NUM
ejpam-5861	13	2	mathematics	mathematic	NOUN
ejpam-5861	13	3	subject	subject	NOUN
ejpam-5861	13	4	classifications	classification	NOUN
ejpam-5861	13	5	:	:	PUNCT
ejpam-5861	13	6	26a33	26a33	NUM
ejpam-5861	13	7	,	,	PUNCT
ejpam-5861	13	8	34a08	34a08	NUM
ejpam-5861	13	9	,	,	PUNCT
ejpam-5861	13	10	03c65	03c65	X
ejpam-5861	13	11	key	key	ADJ
ejpam-5861	13	12	words	word	NOUN
ejpam-5861	13	13	and	and	CCONJ
ejpam-5861	13	14	phrases	phrase	NOUN
ejpam-5861	13	15	:	:	PUNCT
ejpam-5861	13	16	crossover	crossover	ADP
ejpam-5861	13	17	effect	effect	NOUN
ejpam-5861	13	18	,	,	PUNCT
ejpam-5861	13	19	fractional	fractional	ADJ
ejpam-5861	13	20	calculus	calculus	NOUN
ejpam-5861	13	21	,	,	PUNCT
ejpam-5861	13	22	stability	stability	NOUN
ejpam-5861	13	23	,	,	PUNCT
ejpam-5861	13	24	numerical	numerical	ADJ
ejpam-5861	13	25	results	result	NOUN
ejpam-5861	13	26	,	,	PUNCT
ejpam-5861	13	27	sensitivity	sensitivity	NOUN
ejpam-5861	13	28	∗corresponding	∗corresponde	VERB
ejpam-5861	13	29	author	author	NOUN
ejpam-5861	13	30	.	.	PUNCT
ejpam-5861	14	1	doi	doi	NOUN
ejpam-5861	14	2	:	:	PUNCT
ejpam-5861	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5861	https://doi.org/10.29020/nybg.ejpam.v18i2.5861	PROPN
ejpam-5861	14	4	email	email	NOUN
ejpam-5861	14	5	addresses	address	VERB
ejpam-5861	14	6	:	:	PUNCT
ejpam-5861	14	7	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-5861	14	8	(	(	PUNCT
ejpam-5861	14	9	m.sarwar	m.sarwar	NOUN
ejpam-5861	14	10	)	)	PUNCT
ejpam-5861	14	11	,	,	PUNCT
ejpam-5861	15	1	kamalshah408@gmail.com	kamalshah408@gmail.com	X
ejpam-5861	15	2	kshah@psu.edu.sa	kshah@psu.edu.sa	PROPN
ejpam-5861	15	3	(	(	PUNCT
ejpam-5861	15	4	k.	k.	NOUN
ejpam-5861	15	5	shah	shah	PROPN
ejpam-5861	15	6	)	)	PUNCT
ejpam-5861	15	7	,	,	PUNCT
ejpam-5861	15	8	nfatima@psu.edu.sa	nfatima@psu.edu.sa	PROPN
ejpam-5861	15	9	(	(	PUNCT
ejpam-5861	15	10	n.	n.	NOUN
ejpam-5861	15	11	fatima),tabdeljawad@psu.edu.sa	fatima),tabdeljawad@psu.edu.sa	PROPN
ejpam-5861	15	12	(	(	PUNCT
ejpam-5861	15	13	t.	t.	NOUN
ejpam-5861	15	14	abdeljawad	abdeljawad	PROPN
ejpam-5861	15	15	)	)	PUNCT
ejpam-5861	15	16	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5861	15	17	1	1	NUM
ejpam-5861	15	18	copyright	copyright	NOUN
ejpam-5861	15	19	:	:	PUNCT
ejpam-5861	15	20	©	©	PROPN
ejpam-5861	15	21	2025	2025	NUM
ejpam-5861	15	22	the	the	DET
ejpam-5861	15	23	author(s	author(s	NOUN
ejpam-5861	15	24	)	)	PUNCT
ejpam-5861	15	25	.	.	PUNCT
ejpam-5861	16	1	(	(	PUNCT
ejpam-5861	16	2	cc	cc	NOUN
ejpam-5861	16	3	by	by	ADP
ejpam-5861	16	4	-	-	PUNCT
ejpam-5861	16	5	nc	nc	PROPN
ejpam-5861	16	6	4.0	4.0	NUM
ejpam-5861	16	7	)	)	PUNCT
ejpam-5861	16	8	s.	s.	PROPN
ejpam-5861	16	9	naz	naz	PROPN
ejpam-5861	16	10	et	et	PROPN
ejpam-5861	16	11	al	al	PROPN
ejpam-5861	16	12	.	.	PUNCT
ejpam-5861	16	13	/	/	SYM
ejpam-5861	16	14	eur	eur	PROPN
ejpam-5861	16	15	.	.	PUNCT
ejpam-5861	17	1	j.	j.	PROPN
ejpam-5861	17	2	pure	pure	PROPN
ejpam-5861	17	3	appl	appl	PROPN
ejpam-5861	17	4	.	.	PROPN
ejpam-5861	17	5	math	math	PROPN
ejpam-5861	17	6	,	,	PUNCT
ejpam-5861	17	7	18	18	NUM
ejpam-5861	17	8	(	(	PUNCT
ejpam-5861	17	9	2	2	NUM
ejpam-5861	17	10	)	)	PUNCT
ejpam-5861	17	11	(	(	PUNCT
ejpam-5861	17	12	2025	2025	NUM
ejpam-5861	17	13	)	)	PUNCT
ejpam-5861	17	14	,	,	PUNCT
ejpam-5861	17	15	5861	5861	NUM
ejpam-5861	17	16	2	2	NUM
ejpam-5861	17	17	of	of	ADP
ejpam-5861	17	18	33	33	NUM
ejpam-5861	17	19	1	1	NUM
ejpam-5861	17	20	.	.	PUNCT
ejpam-5861	18	1	introduction	introduction	NOUN
ejpam-5861	18	2	mathematical	mathematical	ADJ
ejpam-5861	18	3	models	model	NOUN
ejpam-5861	18	4	constitutes	constitute	VERB
ejpam-5861	18	5	an	an	DET
ejpam-5861	18	6	interesting	interesting	ADJ
ejpam-5861	18	7	and	and	CCONJ
ejpam-5861	18	8	applicable	applicable	ADJ
ejpam-5861	18	9	area	area	NOUN
ejpam-5861	18	10	of	of	ADP
ejpam-5861	18	11	research	research	NOUN
ejpam-5861	18	12	to	to	PART
ejpam-5861	18	13	describe	describe	VERB
ejpam-5861	18	14	various	various	ADJ
ejpam-5861	18	15	real	real	ADJ
ejpam-5861	18	16	world	world	NOUN
ejpam-5861	18	17	problems	problem	NOUN
ejpam-5861	18	18	.	.	PUNCT
ejpam-5861	19	1	the	the	DET
ejpam-5861	19	2	said	say	VERB
ejpam-5861	19	3	concept	concept	NOUN
ejpam-5861	19	4	was	be	AUX
ejpam-5861	19	5	initiated	initiate	VERB
ejpam-5861	19	6	bernoulli	bernoulli	PROPN
ejpam-5861	19	7	in	in	ADP
ejpam-5861	19	8	1776	1776	NUM
ejpam-5861	19	9	.	.	PUNCT
ejpam-5861	20	1	later	later	ADV
ejpam-5861	20	2	on	on	ADP
ejpam-5861	20	3	the	the	DET
ejpam-5861	20	4	idea	idea	NOUN
ejpam-5861	20	5	was	be	AUX
ejpam-5861	20	6	formally	formally	ADV
ejpam-5861	20	7	presented	present	VERB
ejpam-5861	20	8	by	by	ADP
ejpam-5861	20	9	karmark	karmark	NOUN
ejpam-5861	20	10	and	and	CCONJ
ejpam-5861	20	11	his	his	PRON
ejpam-5861	20	12	co	co	NOUN
ejpam-5861	20	13	-	-	NOUN
ejpam-5861	20	14	authors	author	NOUN
ejpam-5861	20	15	in	in	ADP
ejpam-5861	20	16	1927	1927	NUM
ejpam-5861	20	17	who	who	PRON
ejpam-5861	20	18	established	establish	VERB
ejpam-5861	20	19	a	a	DET
ejpam-5861	20	20	simple	simple	ADJ
ejpam-5861	20	21	susceptible	susceptible	ADJ
ejpam-5861	20	22	infected	infect	VERB
ejpam-5861	20	23	and	and	CCONJ
ejpam-5861	20	24	recovered	recover	VERB
ejpam-5861	20	25	(	(	PUNCT
ejpam-5861	20	26	sir	sir	NOUN
ejpam-5861	20	27	)	)	PUNCT
ejpam-5861	20	28	type	type	NOUN
ejpam-5861	20	29	model	model	NOUN
ejpam-5861	20	30	[	[	X
ejpam-5861	20	31	13	13	NUM
ejpam-5861	20	32	]	]	PUNCT
ejpam-5861	20	33	.	.	PUNCT
ejpam-5861	21	1	in	in	ADP
ejpam-5861	21	2	subsequent	subsequent	ADJ
ejpam-5861	21	3	years	year	NOUN
ejpam-5861	21	4	the	the	DET
ejpam-5861	21	5	mentioned	mention	VERB
ejpam-5861	21	6	area	area	NOUN
ejpam-5861	21	7	was	be	AUX
ejpam-5861	21	8	increasingly	increasingly	ADV
ejpam-5861	21	9	extended	extend	VERB
ejpam-5861	21	10	to	to	PART
ejpam-5861	21	11	model	model	VERB
ejpam-5861	21	12	various	various	ADJ
ejpam-5861	21	13	real	real	ADJ
ejpam-5861	21	14	world	world	NOUN
ejpam-5861	21	15	problems	problem	NOUN
ejpam-5861	21	16	mathematically	mathematically	ADV
ejpam-5861	21	17	[	[	X
ejpam-5861	21	18	10	10	NUM
ejpam-5861	21	19	]	]	PUNCT
ejpam-5861	21	20	.	.	PUNCT
ejpam-5861	22	1	it	it	PRON
ejpam-5861	22	2	is	be	AUX
ejpam-5861	22	3	authenticating	authenticate	VERB
ejpam-5861	22	4	that	that	DET
ejpam-5861	22	5	epidemiology	epidemiology	NOUN
ejpam-5861	22	6	is	be	AUX
ejpam-5861	22	7	the	the	DET
ejpam-5861	22	8	important	important	ADJ
ejpam-5861	22	9	area	area	NOUN
ejpam-5861	22	10	of	of	ADP
ejpam-5861	22	11	medical	medical	ADJ
ejpam-5861	22	12	field	field	NOUN
ejpam-5861	22	13	.	.	PUNCT
ejpam-5861	23	1	therefore	therefore	ADV
ejpam-5861	23	2	,	,	PUNCT
ejpam-5861	23	3	researchers	researcher	NOUN
ejpam-5861	23	4	have	have	AUX
ejpam-5861	23	5	increasingly	increasingly	ADV
ejpam-5861	23	6	used	use	VERB
ejpam-5861	23	7	mathematical	mathematical	ADJ
ejpam-5861	23	8	models	model	NOUN
ejpam-5861	23	9	of	of	ADP
ejpam-5861	23	10	classical	classical	ADJ
ejpam-5861	23	11	,	,	PUNCT
ejpam-5861	23	12	or	or	CCONJ
ejpam-5861	23	13	difference	difference	NOUN
ejpam-5861	23	14	type	type	NOUN
ejpam-5861	23	15	differential	differential	ADJ
ejpam-5861	23	16	equations	equation	NOUN
ejpam-5861	23	17	for	for	ADP
ejpam-5861	23	18	mathematical	mathematical	ADJ
ejpam-5861	23	19	models	model	NOUN
ejpam-5861	23	20	of	of	ADP
ejpam-5861	23	21	various	various	ADJ
ejpam-5861	23	22	infectious	infectious	ADJ
ejpam-5861	23	23	diseases	disease	NOUN
ejpam-5861	23	24	[	[	X
ejpam-5861	23	25	11	11	NUM
ejpam-5861	23	26	,	,	PUNCT
ejpam-5861	23	27	16	16	NUM
ejpam-5861	23	28	]	]	PUNCT
ejpam-5861	23	29	.	.	PUNCT
ejpam-5861	24	1	since	since	SCONJ
ejpam-5861	24	2	infectious	infectious	ADJ
ejpam-5861	24	3	diseases	disease	NOUN
ejpam-5861	24	4	have	have	AUX
ejpam-5861	24	5	been	be	AUX
ejpam-5861	24	6	investigated	investigate	VERB
ejpam-5861	24	7	by	by	ADP
ejpam-5861	24	8	using	use	VERB
ejpam-5861	24	9	the	the	DET
ejpam-5861	24	10	idea	idea	NOUN
ejpam-5861	24	11	of	of	ADP
ejpam-5861	24	12	mathematical	mathematical	ADJ
ejpam-5861	24	13	models	model	NOUN
ejpam-5861	24	14	.	.	PUNCT
ejpam-5861	25	1	researchers	researcher	NOUN
ejpam-5861	25	2	in	in	ADP
ejpam-5861	25	3	majority	majority	NOUN
ejpam-5861	25	4	of	of	ADP
ejpam-5861	25	5	published	publish	VERB
ejpam-5861	25	6	work	work	NOUN
ejpam-5861	25	7	have	have	AUX
ejpam-5861	25	8	used	use	VERB
ejpam-5861	25	9	ordinary	ordinary	ADJ
ejpam-5861	25	10	derivatives	derivative	NOUN
ejpam-5861	25	11	or	or	CCONJ
ejpam-5861	25	12	simple	simple	ADJ
ejpam-5861	25	13	algebraic	algebraic	ADJ
ejpam-5861	25	14	type	type	NOUN
ejpam-5861	25	15	equations	equation	NOUN
ejpam-5861	25	16	[	[	X
ejpam-5861	25	17	19	19	NUM
ejpam-5861	25	18	]	]	PUNCT
ejpam-5861	25	19	to	to	PART
ejpam-5861	25	20	study	study	VERB
ejpam-5861	25	21	the	the	DET
ejpam-5861	25	22	mentioned	mention	VERB
ejpam-5861	25	23	area	area	NOUN
ejpam-5861	25	24	.	.	PUNCT
ejpam-5861	26	1	one	one	NUM
ejpam-5861	26	2	of	of	ADP
ejpam-5861	26	3	the	the	DET
ejpam-5861	26	4	major	major	ADJ
ejpam-5861	26	5	infectious	infectious	ADJ
ejpam-5861	26	6	diseases	disease	NOUN
ejpam-5861	26	7	is	be	AUX
ejpam-5861	26	8	caused	cause	VERB
ejpam-5861	26	9	by	by	ADP
ejpam-5861	26	10	coronavirus	coronaviru	NOUN
ejpam-5861	26	11	known	know	VERB
ejpam-5861	26	12	as	as	ADP
ejpam-5861	26	13	severe	severe	ADJ
ejpam-5861	26	14	acute	acute	ADJ
ejpam-5861	26	15	respiratory	respiratory	ADJ
ejpam-5861	26	16	syndrome	syndrome	NOUN
ejpam-5861	26	17	coronavirus	coronavirus	NOUN
ejpam-5861	26	18	2	2	NUM
ejpam-5861	26	19	(	(	PUNCT
ejpam-5861	26	20	sars	sar	NOUN
ejpam-5861	26	21	-	-	PUNCT
ejpam-5861	26	22	cov-2	cov-2	NOUN
ejpam-5861	26	23	)	)	PUNCT
ejpam-5861	26	24	.	.	PUNCT
ejpam-5861	27	1	recently	recently	ADV
ejpam-5861	27	2	the	the	DET
ejpam-5861	27	3	said	say	VERB
ejpam-5861	27	4	infectious	infectious	ADJ
ejpam-5861	27	5	disease	disease	NOUN
ejpam-5861	27	6	gave	give	VERB
ejpam-5861	27	7	birth	birth	NOUN
ejpam-5861	27	8	a	a	DET
ejpam-5861	27	9	world	world	NOUN
ejpam-5861	27	10	wide	wide	ADJ
ejpam-5861	27	11	pandemic	pandemic	ADJ
ejpam-5861	27	12	in	in	ADP
ejpam-5861	27	13	which	which	PRON
ejpam-5861	27	14	more	more	ADJ
ejpam-5861	27	15	than	than	ADP
ejpam-5861	27	16	6	6	NUM
ejpam-5861	27	17	millions	million	NOUN
ejpam-5861	27	18	people	people	NOUN
ejpam-5861	27	19	have	have	AUX
ejpam-5861	27	20	died	die	VERB
ejpam-5861	27	21	.	.	PUNCT
ejpam-5861	28	1	also	also	ADV
ejpam-5861	28	2	more	more	ADJ
ejpam-5861	28	3	than	than	ADP
ejpam-5861	28	4	60	60	NUM
ejpam-5861	28	5	millions	million	NOUN
ejpam-5861	28	6	have	have	AUX
ejpam-5861	28	7	infected	infect	VERB
ejpam-5861	28	8	.	.	PUNCT
ejpam-5861	29	1	still	still	ADV
ejpam-5861	29	2	the	the	DET
ejpam-5861	29	3	disease	disease	NOUN
ejpam-5861	29	4	is	be	AUX
ejpam-5861	29	5	in	in	ADP
ejpam-5861	29	6	progress	progress	NOUN
ejpam-5861	29	7	around	around	ADP
ejpam-5861	29	8	the	the	DET
ejpam-5861	29	9	globe	globe	NOUN
ejpam-5861	29	10	[	[	X
ejpam-5861	29	11	44	44	NUM
ejpam-5861	29	12	]	]	PUNCT
ejpam-5861	29	13	.	.	PUNCT
ejpam-5861	30	1	in	in	ADP
ejpam-5861	30	2	the	the	DET
ejpam-5861	30	3	end	end	NOUN
ejpam-5861	30	4	of	of	ADP
ejpam-5861	30	5	2019	2019	NUM
ejpam-5861	30	6	,	,	PUNCT
ejpam-5861	30	7	the	the	DET
ejpam-5861	30	8	first	first	ADJ
ejpam-5861	30	9	patient	patient	NOUN
ejpam-5861	30	10	was	be	AUX
ejpam-5861	30	11	reported	report	VERB
ejpam-5861	30	12	in	in	ADP
ejpam-5861	30	13	wuhan	wuhan	PROPN
ejpam-5861	30	14	china	china	PROPN
ejpam-5861	30	15	.	.	PUNCT
ejpam-5861	31	1	then	then	ADV
ejpam-5861	31	2	many	many	ADJ
ejpam-5861	31	3	cases	case	NOUN
ejpam-5861	31	4	were	be	AUX
ejpam-5861	31	5	reported	report	VERB
ejpam-5861	31	6	in	in	ADP
ejpam-5861	31	7	the	the	DET
ejpam-5861	31	8	coming	come	VERB
ejpam-5861	31	9	few	few	ADJ
ejpam-5861	31	10	months	month	NOUN
ejpam-5861	31	11	.	.	PUNCT
ejpam-5861	32	1	at	at	ADP
ejpam-5861	32	2	the	the	DET
ejpam-5861	32	3	end	end	NOUN
ejpam-5861	32	4	of	of	ADP
ejpam-5861	32	5	march	march	NOUN
ejpam-5861	32	6	there	there	PRON
ejpam-5861	32	7	were	be	VERB
ejpam-5861	32	8	11	11	NUM
ejpam-5861	32	9	millions	million	NOUN
ejpam-5861	32	10	people	people	NOUN
ejpam-5861	32	11	been	be	AUX
ejpam-5861	32	12	infected	infect	VERB
ejpam-5861	32	13	in	in	ADP
ejpam-5861	32	14	the	the	DET
ejpam-5861	32	15	wuhan	wuhan	PROPN
ejpam-5861	32	16	city	city	PROPN
ejpam-5861	32	17	in	in	ADP
ejpam-5861	32	18	which	which	PRON
ejpam-5861	32	19	nearly	nearly	ADV
ejpam-5861	32	20	4	4	NUM
ejpam-5861	32	21	thousands	thousand	NOUN
ejpam-5861	32	22	were	be	AUX
ejpam-5861	32	23	died	die	VERB
ejpam-5861	32	24	.	.	PUNCT
ejpam-5861	33	1	in	in	ADP
ejpam-5861	33	2	april	april	PROPN
ejpam-5861	33	3	2020	2020	NUM
ejpam-5861	33	4	the	the	DET
ejpam-5861	33	5	said	say	VERB
ejpam-5861	33	6	diseases	disease	NOUN
ejpam-5861	33	7	were	be	AUX
ejpam-5861	33	8	spread	spread	VERB
ejpam-5861	33	9	in	in	ADP
ejpam-5861	33	10	many	many	ADJ
ejpam-5861	33	11	countries	country	NOUN
ejpam-5861	33	12	of	of	ADP
ejpam-5861	33	13	the	the	DET
ejpam-5861	33	14	world	world	NOUN
ejpam-5861	33	15	and	and	CCONJ
ejpam-5861	33	16	hence	hence	ADV
ejpam-5861	33	17	who	who	PRON
ejpam-5861	33	18	announced	announce	VERB
ejpam-5861	33	19	it	it	PRON
ejpam-5861	33	20	a	a	DET
ejpam-5861	33	21	global	global	ADJ
ejpam-5861	33	22	outbreak	outbreak	NOUN
ejpam-5861	34	1	[	[	X
ejpam-5861	34	2	47	47	NUM
ejpam-5861	34	3	]	]	PUNCT
ejpam-5861	34	4	.	.	PUNCT
ejpam-5861	35	1	many	many	ADJ
ejpam-5861	35	2	countries	country	NOUN
ejpam-5861	35	3	of	of	ADP
ejpam-5861	35	4	the	the	DET
ejpam-5861	35	5	globe	globe	NOUN
ejpam-5861	35	6	implemented	implement	VERB
ejpam-5861	35	7	lockdown	lockdown	NOUN
ejpam-5861	35	8	and	and	CCONJ
ejpam-5861	35	9	imposed	impose	VERB
ejpam-5861	35	10	strict	strict	ADJ
ejpam-5861	35	11	precautionary	precautionary	ADJ
ejpam-5861	35	12	measures	measure	NOUN
ejpam-5861	35	13	to	to	PART
ejpam-5861	35	14	control	control	VERB
ejpam-5861	35	15	the	the	DET
ejpam-5861	35	16	disease	disease	NOUN
ejpam-5861	35	17	from	from	ADP
ejpam-5861	35	18	further	further	ADJ
ejpam-5861	35	19	spreading	spread	VERB
ejpam-5861	35	20	.	.	PUNCT
ejpam-5861	36	1	in	in	ADP
ejpam-5861	36	2	the	the	DET
ejpam-5861	36	3	mean	mean	ADJ
ejpam-5861	36	4	time	time	NOUN
ejpam-5861	36	5	,	,	PUNCT
ejpam-5861	36	6	researchers	researcher	NOUN
ejpam-5861	36	7	of	of	ADP
ejpam-5861	36	8	medical	medical	ADJ
ejpam-5861	36	9	and	and	CCONJ
ejpam-5861	36	10	bio	bio	ADJ
ejpam-5861	36	11	-	-	ADJ
ejpam-5861	36	12	engineering	engineering	ADJ
ejpam-5861	36	13	fields	field	NOUN
ejpam-5861	36	14	focused	focus	VERB
ejpam-5861	36	15	on	on	ADP
ejpam-5861	36	16	investigating	investigate	VERB
ejpam-5861	36	17	the	the	DET
ejpam-5861	36	18	cure	cure	NOUN
ejpam-5861	36	19	or	or	CCONJ
ejpam-5861	36	20	proper	proper	ADJ
ejpam-5861	36	21	medicine	medicine	NOUN
ejpam-5861	36	22	for	for	ADP
ejpam-5861	36	23	the	the	DET
ejpam-5861	36	24	diseases	disease	NOUN
ejpam-5861	36	25	[	[	X
ejpam-5861	36	26	6	6	NUM
ejpam-5861	36	27	]	]	PUNCT
ejpam-5861	36	28	.	.	PUNCT
ejpam-5861	37	1	here	here	ADV
ejpam-5861	37	2	,	,	PUNCT
ejpam-5861	37	3	we	we	PRON
ejpam-5861	37	4	remark	remark	VERB
ejpam-5861	37	5	that	that	SCONJ
ejpam-5861	37	6	researchers	researcher	NOUN
ejpam-5861	37	7	of	of	ADP
ejpam-5861	37	8	bio	bio	NOUN
ejpam-5861	37	9	-	-	ADJ
ejpam-5861	37	10	engineering	engineering	ADJ
ejpam-5861	37	11	and	and	CCONJ
ejpam-5861	37	12	applied	apply	VERB
ejpam-5861	37	13	sciences	science	NOUN
ejpam-5861	37	14	developed	develop	VERB
ejpam-5861	37	15	various	various	ADJ
ejpam-5861	37	16	mathematical	mathematical	ADJ
ejpam-5861	37	17	models	model	NOUN
ejpam-5861	37	18	to	to	PART
ejpam-5861	37	19	investigate	investigate	VERB
ejpam-5861	37	20	the	the	DET
ejpam-5861	37	21	transmission	transmission	NOUN
ejpam-5861	37	22	dynamics	dynamic	NOUN
ejpam-5861	37	23	of	of	ADP
ejpam-5861	37	24	the	the	DET
ejpam-5861	37	25	mentioned	mention	VERB
ejpam-5861	37	26	diseases	disease	NOUN
ejpam-5861	37	27	[	[	X
ejpam-5861	37	28	18	18	NUM
ejpam-5861	37	29	]	]	PUNCT
ejpam-5861	37	30	.	.	PUNCT
ejpam-5861	38	1	researchers	researcher	NOUN
ejpam-5861	38	2	used	use	VERB
ejpam-5861	38	3	classical	classical	ADJ
ejpam-5861	38	4	calculus	calculus	NOUN
ejpam-5861	38	5	and	and	CCONJ
ejpam-5861	38	6	algebraic	algebraic	ADJ
ejpam-5861	38	7	tools	tool	NOUN
ejpam-5861	38	8	to	to	PART
ejpam-5861	38	9	investigate	investigate	VERB
ejpam-5861	38	10	the	the	DET
ejpam-5861	38	11	said	say	VERB
ejpam-5861	38	12	infectious	infectious	ADJ
ejpam-5861	38	13	disease	disease	NOUN
ejpam-5861	38	14	.	.	PUNCT
ejpam-5861	39	1	they	they	PRON
ejpam-5861	39	2	used	use	VERB
ejpam-5861	39	3	traditional	traditional	ADJ
ejpam-5861	39	4	tools	tool	NOUN
ejpam-5861	39	5	for	for	ADP
ejpam-5861	39	6	numerical	numerical	ADJ
ejpam-5861	39	7	simulations	simulation	NOUN
ejpam-5861	39	8	in	in	ADP
ejpam-5861	39	9	their	their	PRON
ejpam-5861	39	10	models	model	NOUN
ejpam-5861	39	11	.	.	PUNCT
ejpam-5861	40	1	for	for	ADP
ejpam-5861	40	2	instance	instance	NOUN
ejpam-5861	40	3	authors	author	NOUN
ejpam-5861	40	4	[	[	X
ejpam-5861	40	5	29	29	NUM
ejpam-5861	40	6	]	]	PUNCT
ejpam-5861	40	7	studied	study	VERB
ejpam-5861	40	8	the	the	DET
ejpam-5861	40	9	following	following	ADJ
ejpam-5861	40	10	compartmental	compartmental	ADJ
ejpam-5861	40	11	model	model	NOUN
ejpam-5861	40	12	of	of	ADP
ejpam-5861	40	13	sars	sars	PROPN
ejpam-5861	40	14	-	-	PUNCT
ejpam-5861	40	15	cov-2	cov-2	NUM
ejpam-5861	40	16	s.	s.	PROPN
ejpam-5861	40	17	naz	naz	PROPN
ejpam-5861	40	18	et	et	PROPN
ejpam-5861	40	19	al	al	PROPN
ejpam-5861	40	20	.	.	PUNCT
ejpam-5861	40	21	/	/	SYM
ejpam-5861	40	22	eur	eur	PROPN
ejpam-5861	40	23	.	.	PUNCT
ejpam-5861	41	1	j.	j.	PROPN
ejpam-5861	41	2	pure	pure	PROPN
ejpam-5861	41	3	appl	appl	PROPN
ejpam-5861	41	4	.	.	PROPN
ejpam-5861	41	5	math	math	PROPN
ejpam-5861	41	6	,	,	PUNCT
ejpam-5861	41	7	18	18	NUM
ejpam-5861	41	8	(	(	PUNCT
ejpam-5861	41	9	2	2	NUM
ejpam-5861	41	10	)	)	PUNCT
ejpam-5861	41	11	(	(	PUNCT
ejpam-5861	41	12	2025	2025	NUM
ejpam-5861	41	13	)	)	PUNCT
ejpam-5861	41	14	,	,	PUNCT
ejpam-5861	41	15	5861	5861	NUM
ejpam-5861	41	16	3	3	NUM
ejpam-5861	41	17	of	of	ADP
ejpam-5861	41	18	33	33	NUM
ejpam-5861	41	19	using	use	VERB
ejpam-5861	41	20	integer	integer	NOUN
ejpam-5861	41	21	order	order	NOUN
ejpam-5861	41	22	derivative	derivative	NOUN
ejpam-5861	41	23	as	as	ADP
ejpam-5861	41	24	follows:	follows:	PROPN
ejpam-5861	41	25	d	d	PROPN
ejpam-5861	41	26	dt	dt	X
ejpam-5861	42	1	[	[	X
ejpam-5861	42	2	s(t	s(t	X
ejpam-5861	42	3	)	)	PUNCT
ejpam-5861	42	4	]	]	PUNCT
ejpam-5861	43	1	=	=	PUNCT
ejpam-5861	43	2	λ−	λ−	PROPN
ejpam-5861	43	3	[	[	PUNCT
ejpam-5861	43	4	b(1−	b(1−	NOUN
ejpam-5861	43	5	pξ)i(t	pξ)i(t	NOUN
ejpam-5861	43	6	)	)	PUNCT
ejpam-5861	44	1	+	+	CCONJ
ejpam-5861	44	2	(	(	PUNCT
ejpam-5861	44	3	η	η	X
ejpam-5861	44	4	+	+	PROPN
ejpam-5861	44	5	d	d	PROPN
ejpam-5861	44	6	)	)	PUNCT
ejpam-5861	44	7	]	]	PUNCT
ejpam-5861	45	1	s(t	s(t	PROPN
ejpam-5861	45	2	)	)	PUNCT
ejpam-5861	45	3	,	,	PUNCT
ejpam-5861	46	1	d	d	X
ejpam-5861	46	2	dt	dt	X
ejpam-5861	47	1	[	[	X
ejpam-5861	47	2	v	v	X
ejpam-5861	47	3	(	(	PUNCT
ejpam-5861	47	4	t	t	PROPN
ejpam-5861	47	5	)	)	PUNCT
ejpam-5861	47	6	]	]	PUNCT
ejpam-5861	48	1	=	=	PUNCT
ejpam-5861	48	2	ηs(t)−	ηs(t)−	PROPN
ejpam-5861	48	3	[	[	PUNCT
ejpam-5861	48	4	wbi(t	wbi(t	PROPN
ejpam-5861	48	5	)	)	PUNCT
ejpam-5861	48	6	+	+	SYM
ejpam-5861	48	7	d	d	X
ejpam-5861	48	8	]	]	X
ejpam-5861	48	9	v	v	PROPN
ejpam-5861	48	10	(	(	PUNCT
ejpam-5861	48	11	t	t	PROPN
ejpam-5861	48	12	)	)	PUNCT
ejpam-5861	48	13	,	,	PUNCT
ejpam-5861	49	1	d	d	X
ejpam-5861	49	2	dt	dt	X
ejpam-5861	50	1	[	[	X
ejpam-5861	50	2	e(t	e(t	NOUN
ejpam-5861	50	3	)	)	PUNCT
ejpam-5861	50	4	]	]	PUNCT
ejpam-5861	51	1	=	=	PUNCT
ejpam-5861	51	2	wbv	wbv	INTJ
ejpam-5861	51	3	(	(	PUNCT
ejpam-5861	51	4	t)i(t	t)i(t	NOUN
ejpam-5861	51	5	)	)	PUNCT
ejpam-5861	51	6	+	+	CCONJ
ejpam-5861	51	7	b(1−	b(1−	PROPN
ejpam-5861	51	8	pξ)s(t)i(t)−	pξ)s(t)i(t)−	PROPN
ejpam-5861	51	9	(	(	PUNCT
ejpam-5861	51	10	τ	τ	X
ejpam-5861	51	11	+	+	PROPN
ejpam-5861	51	12	d)e(t	d)e(t	PROPN
ejpam-5861	51	13	)	)	PUNCT
ejpam-5861	51	14	,	,	PUNCT
ejpam-5861	52	1	d	d	X
ejpam-5861	52	2	dt	dt	X
ejpam-5861	53	1	[	[	X
ejpam-5861	53	2	i(t	i(t	NOUN
ejpam-5861	53	3	)	)	PUNCT
ejpam-5861	53	4	]	]	PUNCT
ejpam-5861	54	1	=	=	SYM
ejpam-5861	54	2	τe(t)−	τe(t)−	PROPN
ejpam-5861	54	3	(	(	PUNCT
ejpam-5861	54	4	αi	αi	VERB
ejpam-5861	54	5	+	+	CCONJ
ejpam-5861	54	6	δi	δi	PRON
ejpam-5861	54	7	+	+	CCONJ
ejpam-5861	54	8	σi	σi	X
ejpam-5861	54	9	+	+	CCONJ
ejpam-5861	54	10	d)i(t	d)i(t	NOUN
ejpam-5861	54	11	)	)	PUNCT
ejpam-5861	54	12	,	,	PUNCT
ejpam-5861	55	1	d	d	X
ejpam-5861	55	2	dt	dt	X
ejpam-5861	56	1	[	[	X
ejpam-5861	56	2	q(t	q(t	X
ejpam-5861	56	3	)	)	PUNCT
ejpam-5861	56	4	]	]	PUNCT
ejpam-5861	57	1	=	=	PUNCT
ejpam-5861	57	2	αii(t)−	αii(t)−	PROPN
ejpam-5861	58	1	[	[	X
ejpam-5861	58	2	σq	σq	X
ejpam-5861	58	3	+	+	NOUN
ejpam-5861	58	4	δq	δq	X
ejpam-5861	58	5	+	+	CCONJ
ejpam-5861	58	6	d]q(t	d]q(t	PROPN
ejpam-5861	58	7	)	)	PUNCT
ejpam-5861	58	8	,	,	PUNCT
ejpam-5861	59	1	d	d	X
ejpam-5861	59	2	dt	dt	X
ejpam-5861	60	1	[	[	X
ejpam-5861	60	2	r(t	r(t	NOUN
ejpam-5861	60	3	)	)	PUNCT
ejpam-5861	60	4	]	]	PUNCT
ejpam-5861	61	1	=	=	PUNCT
ejpam-5861	61	2	σii(t	σii(t	PROPN
ejpam-5861	61	3	)	)	PUNCT
ejpam-5861	62	1	+	+	CCONJ
ejpam-5861	62	2	σqq(t)−	σqq(t)−	PROPN
ejpam-5861	62	3	dr(t	dr(t	PUNCT
ejpam-5861	62	4	)	)	PUNCT
ejpam-5861	62	5	,	,	PUNCT
ejpam-5861	63	1	d	d	X
ejpam-5861	63	2	dt	dt	X
ejpam-5861	64	1	[	[	X
ejpam-5861	64	2	d(t	d(t	PROPN
ejpam-5861	64	3	)	)	PUNCT
ejpam-5861	64	4	]	]	PUNCT
ejpam-5861	64	5	=	=	PUNCT
ejpam-5861	64	6	δii(t	δii(t	PROPN
ejpam-5861	64	7	)	)	PUNCT
ejpam-5861	64	8	+	+	CCONJ
ejpam-5861	64	9	δqq(t	δqq(t	PROPN
ejpam-5861	64	10	)	)	PUNCT
ejpam-5861	64	11	,	,	PUNCT
ejpam-5861	64	12	s(0	s(0	PROPN
ejpam-5861	64	13	)	)	PUNCT
ejpam-5861	64	14	=	=	SYM
ejpam-5861	64	15	s0	s0	PROPN
ejpam-5861	64	16	,	,	PUNCT
ejpam-5861	64	17	v	v	NOUN
ejpam-5861	64	18	(	(	PUNCT
ejpam-5861	64	19	0	0	NUM
ejpam-5861	64	20	)	)	PUNCT
ejpam-5861	64	21	=	=	SYM
ejpam-5861	64	22	v0	v0	NOUN
ejpam-5861	64	23	,	,	PUNCT
ejpam-5861	64	24	e(0	e(0	NOUN
ejpam-5861	64	25	)	)	PUNCT
ejpam-5861	64	26	=	=	SYM
ejpam-5861	64	27	e0	e0	PROPN
ejpam-5861	64	28	,	,	PUNCT
ejpam-5861	64	29	i(0	i(0	PROPN
ejpam-5861	64	30	)	)	PUNCT
ejpam-5861	64	31	=	=	SYM
ejpam-5861	64	32	i0	i0	PROPN
ejpam-5861	64	33	,	,	PUNCT
ejpam-5861	64	34	q(0	q(0	PROPN
ejpam-5861	64	35	)	)	PUNCT
ejpam-5861	64	36	=	=	SYM
ejpam-5861	65	1	q0	q0	PROPN
ejpam-5861	65	2	,	,	PUNCT
ejpam-5861	65	3	r(0	r(0	PROPN
ejpam-5861	65	4	)	)	PUNCT
ejpam-5861	65	5	=	=	SYM
ejpam-5861	65	6	r0	r0	NOUN
ejpam-5861	65	7	,	,	PUNCT
ejpam-5861	65	8	d(0	d(0	NOUN
ejpam-5861	65	9	)	)	PUNCT
ejpam-5861	65	10	=	=	SYM
ejpam-5861	65	11	d0	d0	NOUN
ejpam-5861	65	12	.	.	PUNCT
ejpam-5861	66	1	(	(	PUNCT
ejpam-5861	66	2	1	1	X
ejpam-5861	66	3	)	)	PUNCT
ejpam-5861	66	4	the	the	DET
ejpam-5861	66	5	nomenclatures	nomenclature	NOUN
ejpam-5861	66	6	are	be	AUX
ejpam-5861	66	7	described	describe	VERB
ejpam-5861	66	8	as	as	ADP
ejpam-5861	66	9	:	:	PUNCT
ejpam-5861	66	10	λ	λ	NOUN
ejpam-5861	66	11	is	be	AUX
ejpam-5861	66	12	denoted	denote	VERB
ejpam-5861	66	13	birth	birth	NOUN
ejpam-5861	66	14	or	or	CCONJ
ejpam-5861	66	15	recruitment	recruitment	NOUN
ejpam-5861	66	16	rate	rate	NOUN
ejpam-5861	66	17	,	,	PUNCT
ejpam-5861	66	18	b	b	NOUN
ejpam-5861	66	19	stands	stand	VERB
ejpam-5861	66	20	for	for	ADP
ejpam-5861	66	21	transmission	transmission	NOUN
ejpam-5861	66	22	rate	rate	NOUN
ejpam-5861	66	23	of	of	ADP
ejpam-5861	66	24	infection	infection	NOUN
ejpam-5861	66	25	,	,	PUNCT
ejpam-5861	66	26	p	p	NOUN
ejpam-5861	66	27	for	for	ADP
ejpam-5861	66	28	rate	rate	NOUN
ejpam-5861	66	29	of	of	ADP
ejpam-5861	66	30	individuals	individual	NOUN
ejpam-5861	66	31	who	who	PRON
ejpam-5861	66	32	wear	wear	VERB
ejpam-5861	66	33	face	face	NOUN
ejpam-5861	66	34	masks	mask	NOUN
ejpam-5861	66	35	,	,	PUNCT
ejpam-5861	66	36	ξ	ξ	PROPN
ejpam-5861	66	37	is	be	AUX
ejpam-5861	66	38	used	use	VERB
ejpam-5861	66	39	for	for	ADP
ejpam-5861	66	40	the	the	DET
ejpam-5861	66	41	rate	rate	NOUN
ejpam-5861	66	42	of	of	ADP
ejpam-5861	66	43	effectiveness	effectiveness	NOUN
ejpam-5861	66	44	of	of	ADP
ejpam-5861	66	45	face	face	NOUN
ejpam-5861	66	46	masks	mask	NOUN
ejpam-5861	66	47	,	,	PUNCT
ejpam-5861	66	48	αi	αi	ADV
ejpam-5861	66	49	stands	stand	VERB
ejpam-5861	66	50	for	for	ADP
ejpam-5861	66	51	the	the	DET
ejpam-5861	66	52	rate	rate	NOUN
ejpam-5861	66	53	of	of	ADP
ejpam-5861	66	54	isolation	isolation	NOUN
ejpam-5861	66	55	of	of	ADP
ejpam-5861	66	56	infected	infected	ADJ
ejpam-5861	66	57	people	people	NOUN
ejpam-5861	66	58	.	.	PUNCT
ejpam-5861	67	1	in	in	ADP
ejpam-5861	67	2	addition	addition	NOUN
ejpam-5861	67	3	,	,	PUNCT
ejpam-5861	67	4	σi	σi	PRON
ejpam-5861	67	5	denoted	denote	VERB
ejpam-5861	67	6	recovered	recover	VERB
ejpam-5861	67	7	people	people	NOUN
ejpam-5861	67	8	rate	rate	NOUN
ejpam-5861	67	9	,	,	PUNCT
ejpam-5861	67	10	δi	δi	PROPN
ejpam-5861	67	11	denotes	denote	VERB
ejpam-5861	67	12	mortality	mortality	NOUN
ejpam-5861	67	13	rate	rate	NOUN
ejpam-5861	67	14	of	of	ADP
ejpam-5861	67	15	infection	infection	NOUN
ejpam-5861	67	16	,	,	PUNCT
ejpam-5861	67	17	σq	σq	PROPN
ejpam-5861	67	18	denotes	denote	NOUN
ejpam-5861	67	19	recovered	recover	VERB
ejpam-5861	67	20	people	people	NOUN
ejpam-5861	67	21	during	during	ADP
ejpam-5861	67	22	isolation	isolation	NOUN
ejpam-5861	67	23	,	,	PUNCT
ejpam-5861	67	24	δq	δq	PRON
ejpam-5861	67	25	represents	represent	VERB
ejpam-5861	67	26	death	death	NOUN
ejpam-5861	67	27	rate	rate	NOUN
ejpam-5861	67	28	of	of	ADP
ejpam-5861	67	29	quarantined	quarantine	VERB
ejpam-5861	67	30	people	people	NOUN
ejpam-5861	67	31	due	due	ADJ
ejpam-5861	67	32	to	to	ADP
ejpam-5861	67	33	infection	infection	NOUN
ejpam-5861	67	34	.	.	PUNCT
ejpam-5861	68	1	further	far	ADV
ejpam-5861	68	2	,	,	PUNCT
ejpam-5861	68	3	d	d	PROPN
ejpam-5861	68	4	stands	stand	VERB
ejpam-5861	68	5	for	for	ADP
ejpam-5861	68	6	natural	natural	ADJ
ejpam-5861	68	7	death	death	NOUN
ejpam-5861	68	8	rate	rate	NOUN
ejpam-5861	68	9	,	,	PUNCT
ejpam-5861	68	10	and	and	CCONJ
ejpam-5861	68	11	w	w	NOUN
ejpam-5861	68	12	stands	stand	VERB
ejpam-5861	68	13	for	for	ADP
ejpam-5861	68	14	the	the	DET
ejpam-5861	68	15	rate	rate	NOUN
ejpam-5861	68	16	of	of	ADP
ejpam-5861	68	17	reduction	reduction	NOUN
ejpam-5861	68	18	due	due	ADP
ejpam-5861	68	19	to	to	ADP
ejpam-5861	68	20	vaccination	vaccination	NOUN
ejpam-5861	68	21	process	process	NOUN
ejpam-5861	68	22	,	,	PUNCT
ejpam-5861	68	23	η	η	PROPN
ejpam-5861	68	24	denotes	denotes	PROPN
ejpam-5861	68	25	rate	rate	NOUN
ejpam-5861	68	26	of	of	ADP
ejpam-5861	68	27	vaccination	vaccination	NOUN
ejpam-5861	68	28	,	,	PUNCT
ejpam-5861	68	29	and	and	CCONJ
ejpam-5861	68	30	τ	τ	PROPN
ejpam-5861	68	31	stands	stand	VERB
ejpam-5861	68	32	for	for	ADP
ejpam-5861	68	33	incubation	incubation	NOUN
ejpam-5861	68	34	period	period	NOUN
ejpam-5861	68	35	.	.	PUNCT
ejpam-5861	69	1	on	on	ADP
ejpam-5861	69	2	the	the	DET
ejpam-5861	69	3	other	other	ADJ
ejpam-5861	69	4	hand	hand	NOUN
ejpam-5861	69	5	due	due	ADP
ejpam-5861	69	6	to	to	ADP
ejpam-5861	69	7	the	the	DET
ejpam-5861	69	8	significant	significant	ADJ
ejpam-5861	69	9	use	use	NOUN
ejpam-5861	69	10	of	of	ADP
ejpam-5861	69	11	fractional	fractional	ADJ
ejpam-5861	69	12	calculus	calculus	NOUN
ejpam-5861	69	13	in	in	ADP
ejpam-5861	69	14	mathematical	mathematical	ADJ
ejpam-5861	69	15	models	model	NOUN
ejpam-5861	69	16	of	of	ADP
ejpam-5861	69	17	real	real	ADJ
ejpam-5861	69	18	world	world	NOUN
ejpam-5861	69	19	problems	problem	NOUN
ejpam-5861	69	20	,	,	PUNCT
ejpam-5861	69	21	researchers	researcher	NOUN
ejpam-5861	69	22	have	have	AUX
ejpam-5861	69	23	introduced	introduce	VERB
ejpam-5861	69	24	many	many	ADJ
ejpam-5861	69	25	operators	operator	NOUN
ejpam-5861	69	26	for	for	ADP
ejpam-5861	69	27	integrations	integration	NOUN
ejpam-5861	69	28	and	and	CCONJ
ejpam-5861	69	29	differentiations	differentiation	NOUN
ejpam-5861	69	30	with	with	ADP
ejpam-5861	69	31	real	real	ADJ
ejpam-5861	69	32	and	and	CCONJ
ejpam-5861	69	33	complex	complex	ADJ
ejpam-5861	69	34	orders	order	NOUN
ejpam-5861	69	35	.	.	PUNCT
ejpam-5861	70	1	since	since	SCONJ
ejpam-5861	70	2	traditional	traditional	ADJ
ejpam-5861	70	3	tools	tool	NOUN
ejpam-5861	70	4	of	of	ADP
ejpam-5861	70	5	calculus	calculus	NOUN
ejpam-5861	70	6	can	can	AUX
ejpam-5861	70	7	not	not	PART
ejpam-5861	70	8	describe	describe	VERB
ejpam-5861	70	9	the	the	DET
ejpam-5861	70	10	past	past	ADJ
ejpam-5861	70	11	history	history	NOUN
ejpam-5861	70	12	and	and	CCONJ
ejpam-5861	70	13	memory	memory	NOUN
ejpam-5861	70	14	terms	term	NOUN
ejpam-5861	70	15	involved	involve	VERB
ejpam-5861	70	16	in	in	ADP
ejpam-5861	70	17	the	the	DET
ejpam-5861	70	18	mathematical	mathematical	ADJ
ejpam-5861	70	19	models	model	NOUN
ejpam-5861	70	20	of	of	ADP
ejpam-5861	70	21	real	real	ADJ
ejpam-5861	70	22	world	world	NOUN
ejpam-5861	70	23	problems	problem	NOUN
ejpam-5861	70	24	.	.	PUNCT
ejpam-5861	71	1	also	also	ADV
ejpam-5861	71	2	,	,	PUNCT
ejpam-5861	71	3	most	most	ADJ
ejpam-5861	71	4	of	of	ADP
ejpam-5861	71	5	the	the	DET
ejpam-5861	71	6	biological	biological	ADJ
ejpam-5861	71	7	populations	population	NOUN
ejpam-5861	71	8	dynamical	dynamical	ADJ
ejpam-5861	71	9	systems	system	NOUN
ejpam-5861	71	10	consist	consist	VERB
ejpam-5861	71	11	of	of	ADP
ejpam-5861	71	12	discrete	discrete	ADJ
ejpam-5861	71	13	type	type	NOUN
ejpam-5861	71	14	quantities	quantity	NOUN
ejpam-5861	71	15	which	which	PRON
ejpam-5861	71	16	can	can	AUX
ejpam-5861	71	17	not	not	PART
ejpam-5861	71	18	be	be	AUX
ejpam-5861	71	19	understood	understand	VERB
ejpam-5861	71	20	using	use	VERB
ejpam-5861	71	21	ordinary	ordinary	ADJ
ejpam-5861	71	22	derivatives	derivative	NOUN
ejpam-5861	71	23	and	and	CCONJ
ejpam-5861	71	24	integrals	integral	NOUN
ejpam-5861	71	25	.	.	PUNCT
ejpam-5861	72	1	therefore	therefore	ADV
ejpam-5861	72	2	,	,	PUNCT
ejpam-5861	72	3	researchers	researcher	NOUN
ejpam-5861	72	4	recommend	recommend	VERB
ejpam-5861	72	5	for	for	ADP
ejpam-5861	72	6	better	well	ADJ
ejpam-5861	72	7	understanding	understand	VERB
ejpam-5861	72	8	the	the	DET
ejpam-5861	72	9	dynamical	dynamical	ADJ
ejpam-5861	72	10	behavior	behavior	NOUN
ejpam-5861	72	11	of	of	ADP
ejpam-5861	72	12	real	real	ADJ
ejpam-5861	72	13	world	world	NOUN
ejpam-5861	72	14	problems	problem	NOUN
ejpam-5861	72	15	by	by	ADP
ejpam-5861	72	16	using	use	VERB
ejpam-5861	72	17	the	the	DET
ejpam-5861	72	18	techniques	technique	NOUN
ejpam-5861	72	19	of	of	ADP
ejpam-5861	72	20	fractional	fractional	ADJ
ejpam-5861	72	21	calculus	calculus	NOUN
ejpam-5861	72	22	[	[	X
ejpam-5861	72	23	15	15	NUM
ejpam-5861	72	24	]	]	PUNCT
ejpam-5861	72	25	.	.	PUNCT
ejpam-5861	73	1	some	some	DET
ejpam-5861	73	2	valuable	valuable	ADJ
ejpam-5861	73	3	work	work	NOUN
ejpam-5861	73	4	recently	recently	ADV
ejpam-5861	73	5	conducted	conduct	VERB
ejpam-5861	73	6	on	on	ADP
ejpam-5861	73	7	the	the	DET
ejpam-5861	73	8	aforementioned	aforementioned	ADJ
ejpam-5861	73	9	area	area	NOUN
ejpam-5861	73	10	,	,	PUNCT
ejpam-5861	73	11	we	we	PRON
ejpam-5861	73	12	refer	refer	VERB
ejpam-5861	73	13	to	to	ADP
ejpam-5861	73	14	[	[	X
ejpam-5861	73	15	5	5	NUM
ejpam-5861	73	16	,	,	PUNCT
ejpam-5861	73	17	25	25	NUM
ejpam-5861	73	18	,	,	PUNCT
ejpam-5861	73	19	26	26	NUM
ejpam-5861	73	20	,	,	PUNCT
ejpam-5861	73	21	32	32	NUM
ejpam-5861	73	22	,	,	PUNCT
ejpam-5861	73	23	37	37	NUM
ejpam-5861	73	24	]	]	PUNCT
ejpam-5861	73	25	.	.	PUNCT
ejpam-5861	74	1	for	for	ADP
ejpam-5861	74	2	the	the	DET
ejpam-5861	74	3	importance	importance	NOUN
ejpam-5861	74	4	of	of	ADP
ejpam-5861	74	5	mathematical	mathematical	ADJ
ejpam-5861	74	6	models	model	NOUN
ejpam-5861	74	7	,	,	PUNCT
ejpam-5861	74	8	we	we	PRON
ejpam-5861	74	9	refer	refer	VERB
ejpam-5861	74	10	to	to	ADP
ejpam-5861	74	11	[	[	X
ejpam-5861	74	12	28	28	NUM
ejpam-5861	74	13	]	]	PUNCT
ejpam-5861	74	14	.	.	PUNCT
ejpam-5861	75	1	after	after	ADP
ejpam-5861	75	2	looking	look	VERB
ejpam-5861	75	3	at	at	ADP
ejpam-5861	75	4	the	the	DET
ejpam-5861	75	5	existing	exist	VERB
ejpam-5861	75	6	literature	literature	NOUN
ejpam-5861	75	7	,	,	PUNCT
ejpam-5861	75	8	we	we	PRON
ejpam-5861	75	9	found	find	VERB
ejpam-5861	75	10	that	that	SCONJ
ejpam-5861	75	11	numerous	numerous	ADJ
ejpam-5861	75	12	mathematical	mathematical	ADJ
ejpam-5861	75	13	models	model	NOUN
ejpam-5861	75	14	have	have	AUX
ejpam-5861	75	15	been	be	AUX
ejpam-5861	75	16	developed	develop	VERB
ejpam-5861	75	17	to	to	PART
ejpam-5861	75	18	examine	examine	VERB
ejpam-5861	75	19	the	the	DET
ejpam-5861	75	20	illness	illness	NOUN
ejpam-5861	75	21	of	of	ADP
ejpam-5861	75	22	sars	sar	NOUN
ejpam-5861	75	23	-	-	PUNCT
ejpam-5861	75	24	cov-2	cov-2	PART
ejpam-5861	75	25	using	use	VERB
ejpam-5861	75	26	different	different	ADJ
ejpam-5861	75	27	concepts	concept	NOUN
ejpam-5861	75	28	of	of	ADP
ejpam-5861	75	29	fractional	fractional	ADJ
ejpam-5861	75	30	orders	order	NOUN
ejpam-5861	75	31	derivatives	derivative	NOUN
ejpam-5861	75	32	.	.	PUNCT
ejpam-5861	76	1	as	as	ADP
ejpam-5861	76	2	a	a	DET
ejpam-5861	76	3	result	result	NOUN
ejpam-5861	76	4	,	,	PUNCT
ejpam-5861	76	5	a	a	DET
ejpam-5861	76	6	great	great	ADJ
ejpam-5861	76	7	deal	deal	NOUN
ejpam-5861	76	8	of	of	ADP
ejpam-5861	76	9	research	research	NOUN
ejpam-5861	76	10	has	have	AUX
ejpam-5861	76	11	been	be	AUX
ejpam-5861	76	12	done	do	VERB
ejpam-5861	76	13	on	on	ADP
ejpam-5861	76	14	these	these	DET
ejpam-5861	76	15	pandemic	pandemic	ADJ
ejpam-5861	76	16	using	use	VERB
ejpam-5861	76	17	compartmental	compartmental	ADJ
ejpam-5861	76	18	models	model	NOUN
ejpam-5861	76	19	with	with	ADP
ejpam-5861	76	20	vaccinated	vaccinated	ADJ
ejpam-5861	76	21	class	class	NOUN
ejpam-5861	76	22	.	.	PUNCT
ejpam-5861	77	1	however	however	ADV
ejpam-5861	77	2	,	,	PUNCT
ejpam-5861	77	3	after	after	ADP
ejpam-5861	77	4	a	a	DET
ejpam-5861	77	5	careful	careful	ADJ
ejpam-5861	77	6	examination	examination	NOUN
ejpam-5861	77	7	,	,	PUNCT
ejpam-5861	77	8	we	we	PRON
ejpam-5861	77	9	noted	note	VERB
ejpam-5861	77	10	that	that	SCONJ
ejpam-5861	77	11	the	the	DET
ejpam-5861	77	12	mathematical	mathematical	ADJ
ejpam-5861	77	13	models	model	NOUN
ejpam-5861	77	14	of	of	ADP
ejpam-5861	77	15	the	the	DET
ejpam-5861	77	16	said	say	VERB
ejpam-5861	77	17	disease	disease	NOUN
ejpam-5861	77	18	with	with	ADP
ejpam-5861	77	19	seven	seven	NUM
ejpam-5861	77	20	compartments	compartment	NOUN
ejpam-5861	77	21	have	have	AUX
ejpam-5861	77	22	not	not	PART
ejpam-5861	77	23	been	be	AUX
ejpam-5861	77	24	adequately	adequately	ADV
ejpam-5861	77	25	examined	examine	VERB
ejpam-5861	77	26	in	in	ADP
ejpam-5861	77	27	relation	relation	NOUN
ejpam-5861	77	28	to	to	ADP
ejpam-5861	77	29	the	the	DET
ejpam-5861	77	30	piecewise	piecewise	NOUN
ejpam-5861	77	31	derivatives	derivative	NOUN
ejpam-5861	77	32	to	to	ADP
ejpam-5861	77	33	s.	s.	PROPN
ejpam-5861	77	34	naz	naz	PROPN
ejpam-5861	77	35	et	et	PROPN
ejpam-5861	77	36	al	al	PROPN
ejpam-5861	77	37	.	.	PUNCT
ejpam-5861	77	38	/	/	SYM
ejpam-5861	77	39	eur	eur	PROPN
ejpam-5861	77	40	.	.	PUNCT
ejpam-5861	78	1	j.	j.	PROPN
ejpam-5861	78	2	pure	pure	PROPN
ejpam-5861	78	3	appl	appl	PROPN
ejpam-5861	78	4	.	.	PROPN
ejpam-5861	78	5	math	math	PROPN
ejpam-5861	78	6	,	,	PUNCT
ejpam-5861	78	7	18	18	NUM
ejpam-5861	78	8	(	(	PUNCT
ejpam-5861	78	9	2	2	NUM
ejpam-5861	78	10	)	)	PUNCT
ejpam-5861	78	11	(	(	PUNCT
ejpam-5861	78	12	2025	2025	NUM
ejpam-5861	78	13	)	)	PUNCT
ejpam-5861	78	14	,	,	PUNCT
ejpam-5861	78	15	5861	5861	NUM
ejpam-5861	78	16	4	4	NUM
ejpam-5861	78	17	of	of	ADP
ejpam-5861	78	18	33	33	NUM
ejpam-5861	78	19	investigate	investigate	VERB
ejpam-5861	78	20	the	the	DET
ejpam-5861	78	21	multi	multi	ADJ
ejpam-5861	78	22	-	-	ADJ
ejpam-5861	78	23	phase	phase	NOUN
ejpam-5861	78	24	dynamics	dynamic	NOUN
ejpam-5861	78	25	.	.	PUNCT
ejpam-5861	79	1	therefore	therefore	ADV
ejpam-5861	79	2	,	,	PUNCT
ejpam-5861	79	3	in	in	ADP
ejpam-5861	79	4	this	this	DET
ejpam-5861	79	5	regard	regard	NOUN
ejpam-5861	79	6	,	,	PUNCT
ejpam-5861	79	7	we	we	PRON
ejpam-5861	79	8	need	need	VERB
ejpam-5861	79	9	further	further	ADJ
ejpam-5861	79	10	investigation	investigation	NOUN
ejpam-5861	79	11	of	of	ADP
ejpam-5861	79	12	such	such	ADJ
ejpam-5861	79	13	models	model	NOUN
ejpam-5861	79	14	to	to	PART
ejpam-5861	79	15	develop	develop	VERB
ejpam-5861	79	16	the	the	DET
ejpam-5861	79	17	computational	computational	ADJ
ejpam-5861	79	18	as	as	ADV
ejpam-5861	79	19	well	well	ADV
ejpam-5861	79	20	as	as	ADP
ejpam-5861	79	21	theoretical	theoretical	ADJ
ejpam-5861	79	22	results	result	NOUN
ejpam-5861	79	23	for	for	ADP
ejpam-5861	79	24	better	well	ADJ
ejpam-5861	79	25	understanding	understanding	NOUN
ejpam-5861	79	26	.	.	PUNCT
ejpam-5861	80	1	as	as	ADP
ejpam-5861	80	2	of	of	ADP
ejpam-5861	80	3	october	october	PROPN
ejpam-5861	80	4	10	10	NUM
ejpam-5861	80	5	,	,	PUNCT
ejpam-5861	80	6	2020	2020	NUM
ejpam-5861	80	7	,	,	PUNCT
ejpam-5861	80	8	the	the	DET
ejpam-5861	80	9	novel	novel	ADJ
ejpam-5861	80	10	coronavirus	coronavirus	NOUN
ejpam-5861	80	11	,	,	PUNCT
ejpam-5861	80	12	known	know	VERB
ejpam-5861	80	13	as	as	ADP
ejpam-5861	80	14	covid-19	covid-19	PROPN
ejpam-5861	80	15	,	,	PUNCT
ejpam-5861	80	16	had	have	AUX
ejpam-5861	80	17	spread	spread	VERB
ejpam-5861	80	18	to	to	ADP
ejpam-5861	80	19	more	more	ADJ
ejpam-5861	80	20	than	than	ADP
ejpam-5861	80	21	200	200	NUM
ejpam-5861	80	22	nations	nation	NOUN
ejpam-5861	80	23	globally	globally	ADV
ejpam-5861	80	24	and	and	CCONJ
ejpam-5861	80	25	resulted	result	VERB
ejpam-5861	80	26	in	in	ADP
ejpam-5861	80	27	over	over	ADP
ejpam-5861	80	28	36	36	NUM
ejpam-5861	80	29	million	million	NUM
ejpam-5861	80	30	confirmed	confirm	VERB
ejpam-5861	80	31	cases	case	NOUN
ejpam-5861	80	32	.	.	PUNCT
ejpam-5861	81	1	as	as	ADP
ejpam-5861	81	2	a	a	DET
ejpam-5861	81	3	result	result	NOUN
ejpam-5861	81	4	,	,	PUNCT
ejpam-5861	81	5	a	a	DET
ejpam-5861	81	6	number	number	NOUN
ejpam-5861	81	7	of	of	ADP
ejpam-5861	81	8	machine	machine	NOUN
ejpam-5861	81	9	learning	learning	NOUN
ejpam-5861	81	10	models	model	NOUN
ejpam-5861	81	11	that	that	PRON
ejpam-5861	81	12	can	can	AUX
ejpam-5861	81	13	predict	predict	VERB
ejpam-5861	81	14	the	the	DET
ejpam-5861	81	15	outbreak	outbreak	NOUN
ejpam-5861	81	16	worldwide	worldwide	ADV
ejpam-5861	81	17	have	have	AUX
ejpam-5861	81	18	been	be	AUX
ejpam-5861	81	19	made	make	VERB
ejpam-5861	81	20	public	public	ADJ
ejpam-5861	81	21	.	.	PUNCT
ejpam-5861	82	1	researchers	researcher	NOUN
ejpam-5861	82	2	have	have	AUX
ejpam-5861	82	3	developed	develop	VERB
ejpam-5861	82	4	huge	huge	ADJ
ejpam-5861	82	5	amount	amount	NOUN
ejpam-5861	82	6	of	of	ADP
ejpam-5861	82	7	research	research	NOUN
ejpam-5861	82	8	work	work	NOUN
ejpam-5861	82	9	about	about	ADP
ejpam-5861	82	10	the	the	DET
ejpam-5861	82	11	said	say	VERB
ejpam-5861	82	12	diseases	disease	NOUN
ejpam-5861	82	13	by	by	ADP
ejpam-5861	82	14	using	use	VERB
ejpam-5861	82	15	the	the	DET
ejpam-5861	82	16	concepts	concept	NOUN
ejpam-5861	82	17	of	of	ADP
ejpam-5861	82	18	mathematical	mathematical	ADJ
ejpam-5861	82	19	models	model	NOUN
ejpam-5861	82	20	.	.	PUNCT
ejpam-5861	83	1	compartmental	compartmental	ADJ
ejpam-5861	83	2	models	model	NOUN
ejpam-5861	83	3	have	have	AUX
ejpam-5861	83	4	played	play	VERB
ejpam-5861	83	5	great	great	ADJ
ejpam-5861	83	6	roles	role	NOUN
ejpam-5861	83	7	in	in	ADP
ejpam-5861	83	8	predicting	predict	VERB
ejpam-5861	83	9	the	the	DET
ejpam-5861	83	10	future	future	ADJ
ejpam-5861	83	11	dynamics	dynamic	NOUN
ejpam-5861	83	12	of	of	ADP
ejpam-5861	83	13	such	such	ADJ
ejpam-5861	83	14	infectious	infectious	ADJ
ejpam-5861	83	15	diseases	disease	NOUN
ejpam-5861	83	16	.	.	PUNCT
ejpam-5861	84	1	infectious	infectious	ADJ
ejpam-5861	84	2	diseases	disease	NOUN
ejpam-5861	84	3	were	be	AUX
ejpam-5861	84	4	regularly	regularly	ADV
ejpam-5861	84	5	investigated	investigate	VERB
ejpam-5861	84	6	by	by	ADP
ejpam-5861	84	7	researchers	researcher	NOUN
ejpam-5861	84	8	by	by	ADP
ejpam-5861	84	9	using	use	VERB
ejpam-5861	84	10	various	various	ADJ
ejpam-5861	84	11	tools	tool	NOUN
ejpam-5861	84	12	of	of	ADP
ejpam-5861	84	13	mathematics	mathematic	NOUN
ejpam-5861	84	14	.	.	PUNCT
ejpam-5861	85	1	we	we	PRON
ejpam-5861	85	2	refer	refer	VERB
ejpam-5861	85	3	some	some	DET
ejpam-5861	85	4	remarkable	remarkable	ADJ
ejpam-5861	85	5	work	work	NOUN
ejpam-5861	85	6	as	as	ADP
ejpam-5861	85	7	[	[	X
ejpam-5861	85	8	22	22	NUM
ejpam-5861	85	9	,	,	PUNCT
ejpam-5861	85	10	31	31	NUM
ejpam-5861	85	11	,	,	PUNCT
ejpam-5861	85	12	35	35	NUM
ejpam-5861	85	13	,	,	PUNCT
ejpam-5861	85	14	41	41	NUM
ejpam-5861	85	15	,	,	PUNCT
ejpam-5861	85	16	48	48	NUM
ejpam-5861	85	17	]	]	PUNCT
ejpam-5861	85	18	.	.	PUNCT
ejpam-5861	86	1	the	the	DET
ejpam-5861	86	2	mentioned	mention	VERB
ejpam-5861	86	3	area	area	NOUN
ejpam-5861	86	4	has	have	AUX
ejpam-5861	86	5	been	be	AUX
ejpam-5861	86	6	greatly	greatly	ADV
ejpam-5861	86	7	applied	apply	VERB
ejpam-5861	86	8	in	in	ADP
ejpam-5861	86	9	various	various	ADJ
ejpam-5861	86	10	disciplines	discipline	NOUN
ejpam-5861	86	11	to	to	PART
ejpam-5861	86	12	study	study	VERB
ejpam-5861	86	13	various	various	ADJ
ejpam-5861	86	14	real	real	ADJ
ejpam-5861	86	15	world	world	NOUN
ejpam-5861	86	16	problems	problem	NOUN
ejpam-5861	86	17	.	.	PUNCT
ejpam-5861	87	1	because	because	SCONJ
ejpam-5861	87	2	it	it	PRON
ejpam-5861	87	3	has	have	VERB
ejpam-5861	87	4	many	many	ADJ
ejpam-5861	87	5	important	important	ADJ
ejpam-5861	87	6	applications	application	NOUN
ejpam-5861	87	7	.	.	PUNCT
ejpam-5861	88	1	we	we	PRON
ejpam-5861	88	2	refer	refer	VERB
ejpam-5861	88	3	to	to	ADP
ejpam-5861	88	4	some	some	PRON
ejpam-5861	88	5	[	[	X
ejpam-5861	88	6	23	23	NUM
ejpam-5861	88	7	,	,	PUNCT
ejpam-5861	88	8	27	27	NUM
ejpam-5861	88	9	,	,	PUNCT
ejpam-5861	88	10	42	42	NUM
ejpam-5861	88	11	,	,	PUNCT
ejpam-5861	88	12	48	48	NUM
ejpam-5861	88	13	]	]	PUNCT
ejpam-5861	88	14	.	.	PUNCT
ejpam-5861	89	1	but	but	CCONJ
ejpam-5861	89	2	fractional	fractional	ADJ
ejpam-5861	89	3	derivatives	derivative	NOUN
ejpam-5861	89	4	have	have	AUX
ejpam-5861	89	5	not	not	PART
ejpam-5861	89	6	been	be	AUX
ejpam-5861	89	7	uniquely	uniquely	ADV
ejpam-5861	89	8	defined	define	VERB
ejpam-5861	89	9	yet	yet	ADV
ejpam-5861	89	10	.	.	PUNCT
ejpam-5861	90	1	there	there	PRON
ejpam-5861	90	2	are	be	VERB
ejpam-5861	90	3	several	several	ADJ
ejpam-5861	90	4	approaches	approach	NOUN
ejpam-5861	90	5	which	which	PRON
ejpam-5861	90	6	are	be	AUX
ejpam-5861	90	7	used	use	VERB
ejpam-5861	90	8	by	by	ADP
ejpam-5861	90	9	researchers	researcher	NOUN
ejpam-5861	90	10	.	.	PUNCT
ejpam-5861	91	1	recently	recently	ADV
ejpam-5861	91	2	,	,	PUNCT
ejpam-5861	91	3	researchers	researcher	NOUN
ejpam-5861	91	4	found	find	VERB
ejpam-5861	91	5	that	that	SCONJ
ejpam-5861	91	6	some	some	DET
ejpam-5861	91	7	evolution	evolution	NOUN
ejpam-5861	91	8	processes	process	NOUN
ejpam-5861	91	9	suffer	suffer	VERB
ejpam-5861	91	10	from	from	ADP
ejpam-5861	91	11	abrupt	abrupt	ADJ
ejpam-5861	91	12	changes	change	NOUN
ejpam-5861	91	13	in	in	ADP
ejpam-5861	91	14	their	their	PRON
ejpam-5861	91	15	state	state	NOUN
ejpam-5861	91	16	of	of	ADP
ejpam-5861	91	17	dynamics	dynamic	NOUN
ejpam-5861	91	18	.	.	PUNCT
ejpam-5861	92	1	in	in	ADP
ejpam-5861	92	2	such	such	ADJ
ejpam-5861	92	3	effect	effect	NOUN
ejpam-5861	92	4	the	the	DET
ejpam-5861	92	5	process	process	NOUN
ejpam-5861	92	6	starts	start	VERB
ejpam-5861	92	7	to	to	PART
ejpam-5861	92	8	show	show	VERB
ejpam-5861	92	9	multi	multi	ADJ
ejpam-5861	92	10	phase	phase	NOUN
ejpam-5861	92	11	behaviours	behaviour	NOUN
ejpam-5861	92	12	which	which	PRON
ejpam-5861	92	13	can	can	AUX
ejpam-5861	92	14	not	not	PART
ejpam-5861	92	15	be	be	AUX
ejpam-5861	92	16	explained	explain	VERB
ejpam-5861	92	17	by	by	ADP
ejpam-5861	92	18	traditional	traditional	ADJ
ejpam-5861	92	19	calculus	calculus	NOUN
ejpam-5861	92	20	or	or	CCONJ
ejpam-5861	92	21	fractional	fractional	ADJ
ejpam-5861	92	22	calculus	calculus	NOUN
ejpam-5861	92	23	concepts	concept	NOUN
ejpam-5861	92	24	.	.	PUNCT
ejpam-5861	93	1	therefore	therefore	ADV
ejpam-5861	93	2	,	,	PUNCT
ejpam-5861	93	3	atangana	atangana	PROPN
ejpam-5861	93	4	and	and	CCONJ
ejpam-5861	93	5	his	his	PRON
ejpam-5861	93	6	co	co	NOUN
ejpam-5861	93	7	-	-	NOUN
ejpam-5861	93	8	author	author	NOUN
ejpam-5861	93	9	[	[	X
ejpam-5861	93	10	8	8	NUM
ejpam-5861	93	11	]	]	PUNCT
ejpam-5861	93	12	used	use	VERB
ejpam-5861	93	13	piecewise	piecewise	NOUN
ejpam-5861	93	14	concepts	concept	NOUN
ejpam-5861	93	15	and	and	CCONJ
ejpam-5861	93	16	brilliantly	brilliantly	ADV
ejpam-5861	93	17	deduced	deduce	VERB
ejpam-5861	93	18	some	some	DET
ejpam-5861	93	19	remarkable	remarkable	ADJ
ejpam-5861	93	20	results	result	NOUN
ejpam-5861	93	21	for	for	ADP
ejpam-5861	93	22	various	various	ADJ
ejpam-5861	93	23	dynamical	dynamical	ADJ
ejpam-5861	93	24	problems	problem	NOUN
ejpam-5861	93	25	.	.	PUNCT
ejpam-5861	94	1	some	some	DET
ejpam-5861	94	2	contribution	contribution	NOUN
ejpam-5861	94	3	of	of	ADP
ejpam-5861	94	4	piecewise	piecewise	NOUN
ejpam-5861	94	5	derivatives	derivative	NOUN
ejpam-5861	94	6	,	,	PUNCT
ejpam-5861	94	7	we	we	PRON
ejpam-5861	94	8	offer	offer	VERB
ejpam-5861	94	9	here	here	ADV
ejpam-5861	94	10	as	as	ADP
ejpam-5861	94	11	[	[	X
ejpam-5861	94	12	20	20	NUM
ejpam-5861	94	13	,	,	PUNCT
ejpam-5861	94	14	21	21	NUM
ejpam-5861	94	15	,	,	PUNCT
ejpam-5861	94	16	45	45	NUM
ejpam-5861	94	17	]	]	PUNCT
ejpam-5861	94	18	.	.	PUNCT
ejpam-5861	95	1	many	many	ADJ
ejpam-5861	95	2	real	real	ADJ
ejpam-5861	95	3	world	world	NOUN
ejpam-5861	95	4	problems	problem	NOUN
ejpam-5861	95	5	exhibit	exhibit	VERB
ejpam-5861	95	6	abrupt	abrupt	ADJ
ejpam-5861	95	7	changes	change	NOUN
ejpam-5861	95	8	in	in	ADP
ejpam-5861	95	9	their	their	PRON
ejpam-5861	95	10	state	state	NOUN
ejpam-5861	95	11	of	of	ADP
ejpam-5861	95	12	dynamics	dynamic	NOUN
ejpam-5861	95	13	.	.	PUNCT
ejpam-5861	96	1	for	for	ADP
ejpam-5861	96	2	example	example	NOUN
ejpam-5861	96	3	earth	earth	NOUN
ejpam-5861	96	4	quake	quake	NOUN
ejpam-5861	96	5	,	,	PUNCT
ejpam-5861	96	6	fluctuation	fluctuation	NOUN
ejpam-5861	96	7	in	in	ADP
ejpam-5861	96	8	economy	economy	NOUN
ejpam-5861	96	9	of	of	ADP
ejpam-5861	96	10	less	less	ADV
ejpam-5861	96	11	developed	developed	ADJ
ejpam-5861	96	12	countries	country	NOUN
ejpam-5861	96	13	,	,	PUNCT
ejpam-5861	96	14	and	and	CCONJ
ejpam-5861	96	15	propagations	propagation	NOUN
ejpam-5861	96	16	of	of	ADP
ejpam-5861	96	17	infections	infection	NOUN
ejpam-5861	96	18	in	in	ADP
ejpam-5861	96	19	society	society	NOUN
ejpam-5861	96	20	[	[	X
ejpam-5861	96	21	46	46	NUM
ejpam-5861	96	22	]	]	PUNCT
ejpam-5861	96	23	.	.	PUNCT
ejpam-5861	97	1	the	the	PRON
ejpam-5861	97	2	mentioned	mention	VERB
ejpam-5861	97	3	sudden	sudden	ADJ
ejpam-5861	97	4	or	or	CCONJ
ejpam-5861	97	5	abrupt	abrupt	ADJ
ejpam-5861	97	6	changes	change	NOUN
ejpam-5861	97	7	in	in	ADP
ejpam-5861	97	8	the	the	DET
ejpam-5861	97	9	dynamics	dynamic	NOUN
ejpam-5861	97	10	of	of	ADP
ejpam-5861	97	11	real	real	ADJ
ejpam-5861	97	12	world	world	NOUN
ejpam-5861	97	13	problems	problem	NOUN
ejpam-5861	97	14	can	can	AUX
ejpam-5861	97	15	not	not	PART
ejpam-5861	97	16	be	be	AUX
ejpam-5861	97	17	accommodate	accommodate	ADJ
ejpam-5861	97	18	by	by	ADP
ejpam-5861	97	19	using	use	VERB
ejpam-5861	97	20	the	the	DET
ejpam-5861	97	21	classical	classical	ADJ
ejpam-5861	97	22	tools	tool	NOUN
ejpam-5861	97	23	of	of	ADP
ejpam-5861	97	24	calculus	calculus	NOUN
ejpam-5861	97	25	.	.	PUNCT
ejpam-5861	98	1	for	for	ADP
ejpam-5861	98	2	these	these	DET
ejpam-5861	98	3	purposes	purpose	NOUN
ejpam-5861	98	4	recently	recently	ADV
ejpam-5861	98	5	researchers	researcher	NOUN
ejpam-5861	98	6	[	[	X
ejpam-5861	98	7	7	7	X
ejpam-5861	98	8	]	]	PUNCT
ejpam-5861	98	9	introduced	introduce	VERB
ejpam-5861	98	10	the	the	DET
ejpam-5861	98	11	concept	concept	NOUN
ejpam-5861	98	12	of	of	ADP
ejpam-5861	98	13	piecewise	piecewise	NOUN
ejpam-5861	98	14	derivatives	derivative	NOUN
ejpam-5861	98	15	of	of	ADP
ejpam-5861	98	16	fractional	fractional	ADJ
ejpam-5861	98	17	orders	order	NOUN
ejpam-5861	98	18	.	.	PUNCT
ejpam-5861	99	1	the	the	DET
ejpam-5861	99	2	mentioned	mention	VERB
ejpam-5861	99	3	concepts	concept	NOUN
ejpam-5861	99	4	were	be	AUX
ejpam-5861	99	5	applied	apply	VERB
ejpam-5861	99	6	in	in	ADP
ejpam-5861	99	7	many	many	ADJ
ejpam-5861	99	8	real	real	ADJ
ejpam-5861	99	9	world	world	NOUN
ejpam-5861	99	10	problems	problem	NOUN
ejpam-5861	99	11	investigations	investigation	NOUN
ejpam-5861	99	12	using	use	VERB
ejpam-5861	99	13	mathematical	mathematical	ADJ
ejpam-5861	99	14	models	model	NOUN
ejpam-5861	99	15	.	.	PUNCT
ejpam-5861	100	1	researchers	researcher	NOUN
ejpam-5861	100	2	found	find	VERB
ejpam-5861	100	3	that	that	SCONJ
ejpam-5861	100	4	the	the	DET
ejpam-5861	100	5	said	say	VERB
ejpam-5861	100	6	area	area	NOUN
ejpam-5861	100	7	excellently	excellently	ADV
ejpam-5861	100	8	accommodate	accommodate	VERB
ejpam-5861	100	9	the	the	DET
ejpam-5861	100	10	concerned	concerned	ADJ
ejpam-5861	100	11	gap	gap	NOUN
ejpam-5861	100	12	and	and	CCONJ
ejpam-5861	100	13	comprehensively	comprehensively	ADV
ejpam-5861	100	14	explain	explain	VERB
ejpam-5861	100	15	the	the	DET
ejpam-5861	100	16	dynamics	dynamic	NOUN
ejpam-5861	100	17	of	of	ADP
ejpam-5861	100	18	those	those	DET
ejpam-5861	100	19	evolution	evolution	NOUN
ejpam-5861	100	20	processes	process	NOUN
ejpam-5861	100	21	preserving	preserve	VERB
ejpam-5861	100	22	the	the	DET
ejpam-5861	100	23	crossover	crossover	NOUN
ejpam-5861	100	24	or	or	CCONJ
ejpam-5861	100	25	multi	multi	ADJ
ejpam-5861	100	26	-	-	ADJ
ejpam-5861	100	27	phase	phase	NOUN
ejpam-5861	100	28	dynamics	dynamic	NOUN
ejpam-5861	100	29	[	[	X
ejpam-5861	100	30	36	36	NUM
ejpam-5861	100	31	]	]	PUNCT
ejpam-5861	100	32	.	.	PUNCT
ejpam-5861	101	1	the	the	DET
ejpam-5861	101	2	mentioned	mention	VERB
ejpam-5861	101	3	tools	tool	NOUN
ejpam-5861	101	4	have	have	AUX
ejpam-5861	101	5	not	not	PART
ejpam-5861	101	6	been	be	AUX
ejpam-5861	101	7	yet	yet	ADV
ejpam-5861	101	8	applied	apply	VERB
ejpam-5861	101	9	in	in	ADP
ejpam-5861	101	10	the	the	DET
ejpam-5861	101	11	mathematical	mathematical	ADJ
ejpam-5861	101	12	model	model	NOUN
ejpam-5861	101	13	of	of	ADP
ejpam-5861	101	14	sars	sar	NOUN
ejpam-5861	101	15	-	-	PUNCT
ejpam-5861	101	16	cov-2	cov-2	PART
ejpam-5861	101	17	given	give	VERB
ejpam-5861	101	18	in	in	ADP
ejpam-5861	101	19	(	(	PUNCT
ejpam-5861	101	20	1	1	NUM
ejpam-5861	101	21	)	)	PUNCT
ejpam-5861	101	22	to	to	PART
ejpam-5861	101	23	investigate	investigate	VERB
ejpam-5861	101	24	the	the	DET
ejpam-5861	101	25	crossover	crossover	NOUN
ejpam-5861	101	26	dynamics	dynamic	NOUN
ejpam-5861	101	27	.	.	PUNCT
ejpam-5861	102	1	to	to	PART
ejpam-5861	102	2	fill	fill	VERB
ejpam-5861	102	3	this	this	DET
ejpam-5861	102	4	gap	gap	NOUN
ejpam-5861	102	5	and	and	CCONJ
ejpam-5861	102	6	to	to	PART
ejpam-5861	102	7	investigate	investigate	VERB
ejpam-5861	102	8	the	the	DET
ejpam-5861	102	9	crossover	crossover	NOUN
ejpam-5861	102	10	dynamics	dynamic	NOUN
ejpam-5861	102	11	of	of	ADP
ejpam-5861	102	12	the	the	DET
ejpam-5861	102	13	model	model	NOUN
ejpam-5861	102	14	under	under	ADP
ejpam-5861	102	15	the	the	DET
ejpam-5861	102	16	piecewise	piecewise	NOUN
ejpam-5861	102	17	derivative	derivative	ADJ
ejpam-5861	102	18	concepts	concept	NOUN
ejpam-5861	102	19	,	,	PUNCT
ejpam-5861	102	20	we	we	PRON
ejpam-5861	102	21	will	will	AUX
ejpam-5861	102	22	follow	follow	VERB
ejpam-5861	102	23	the	the	DET
ejpam-5861	102	24	theory	theory	NOUN
ejpam-5861	102	25	given	give	VERB
ejpam-5861	102	26	in	in	ADP
ejpam-5861	102	27	[	[	X
ejpam-5861	102	28	40	40	NUM
ejpam-5861	102	29	]	]	PUNCT
ejpam-5861	102	30	and	and	CCONJ
ejpam-5861	102	31	numerical	numerical	ADJ
ejpam-5861	102	32	procedures	procedure	NOUN
ejpam-5861	102	33	to	to	PART
ejpam-5861	102	34	achieve	achieve	VERB
ejpam-5861	102	35	our	our	PRON
ejpam-5861	102	36	study	study	NOUN
ejpam-5861	102	37	.	.	PUNCT
ejpam-5861	103	1	also	also	ADV
ejpam-5861	103	2	,	,	PUNCT
ejpam-5861	103	3	for	for	ADP
ejpam-5861	103	4	numerical	numerical	ADJ
ejpam-5861	103	5	tools	tool	NOUN
ejpam-5861	103	6	and	and	CCONJ
ejpam-5861	103	7	qualitative	qualitative	ADJ
ejpam-5861	103	8	analysis	analysis	NOUN
ejpam-5861	103	9	we	we	PRON
ejpam-5861	103	10	utilized	utilize	VERB
ejpam-5861	103	11	the	the	DET
ejpam-5861	103	12	procedures	procedure	NOUN
ejpam-5861	103	13	given	give	VERB
ejpam-5861	103	14	in	in	ADP
ejpam-5861	103	15	[	[	NOUN
ejpam-5861	103	16	9	9	NUM
ejpam-5861	103	17	,	,	PUNCT
ejpam-5861	103	18	30	30	NUM
ejpam-5861	103	19	,	,	PUNCT
ejpam-5861	103	20	38	38	NUM
ejpam-5861	103	21	]	]	PUNCT
ejpam-5861	103	22	.	.	PUNCT
ejpam-5861	104	1	hence	hence	ADV
ejpam-5861	104	2	inspired	inspire	VERB
ejpam-5861	104	3	from	from	ADP
ejpam-5861	104	4	the	the	DET
ejpam-5861	104	5	useful	useful	ADJ
ejpam-5861	104	6	applications	application	NOUN
ejpam-5861	104	7	of	of	ADP
ejpam-5861	104	8	piecewise	piecewise	NOUN
ejpam-5861	104	9	derivatives	derivative	NOUN
ejpam-5861	104	10	of	of	ADP
ejpam-5861	104	11	fractional	fractional	ADJ
ejpam-5861	104	12	order	order	NOUN
ejpam-5861	104	13	,	,	PUNCT
ejpam-5861	104	14	we	we	PRON
ejpam-5861	104	15	will	will	AUX
ejpam-5861	104	16	extend	extend	VERB
ejpam-5861	104	17	the	the	DET
ejpam-5861	104	18	seven	seven	NUM
ejpam-5861	104	19	compartmental	compartmental	ADJ
ejpam-5861	104	20	model	model	NOUN
ejpam-5861	104	21	given	give	VERB
ejpam-5861	104	22	in	in	ADP
ejpam-5861	104	23	(	(	PUNCT
ejpam-5861	104	24	1	1	NUM
ejpam-5861	104	25	)	)	PUNCT
ejpam-5861	104	26	under	under	ADP
ejpam-5861	104	27	the	the	DET
ejpam-5861	104	28	piecewise	piecewise	NOUN
ejpam-5861	104	29	derivative	derivative	NOUN
ejpam-5861	104	30	of	of	ADP
ejpam-5861	104	31	fractional	fractional	ADJ
ejpam-5861	104	32	order	order	NOUN
ejpam-5861	104	33	for	for	ADP
ejpam-5861	104	34	further	further	ADJ
ejpam-5861	104	35	study	study	NOUN
ejpam-5861	104	36	in	in	ADP
ejpam-5861	104	37	this	this	DET
ejpam-5861	104	38	project	project	NOUN
ejpam-5861	104	39	.	.	PUNCT
ejpam-5861	105	1	we	we	PRON
ejpam-5861	105	2	will	will	AUX
ejpam-5861	105	3	establish	establish	VERB
ejpam-5861	105	4	the	the	DET
ejpam-5861	105	5	qualitative	qualitative	ADJ
ejpam-5861	105	6	theory	theory	NOUN
ejpam-5861	105	7	of	of	ADP
ejpam-5861	105	8	existence	existence	NOUN
ejpam-5861	105	9	of	of	ADP
ejpam-5861	105	10	solution	solution	NOUN
ejpam-5861	105	11	by	by	ADP
ejpam-5861	105	12	using	use	VERB
ejpam-5861	105	13	fixed	fix	VERB
ejpam-5861	105	14	point	point	NOUN
ejpam-5861	105	15	theory	theory	NOUN
ejpam-5861	105	16	of	of	ADP
ejpam-5861	105	17	banach	banach	NOUN
ejpam-5861	105	18	and	and	CCONJ
ejpam-5861	105	19	schauder	schauder	NOUN
ejpam-5861	105	20	type	type	NOUN
ejpam-5861	105	21	.	.	PUNCT
ejpam-5861	106	1	additionally	additionally	ADV
ejpam-5861	106	2	,	,	PUNCT
ejpam-5861	106	3	we	we	PRON
ejpam-5861	106	4	will	will	AUX
ejpam-5861	106	5	study	study	VERB
ejpam-5861	106	6	the	the	DET
ejpam-5861	106	7	global	global	ADJ
ejpam-5861	106	8	stability	stability	NOUN
ejpam-5861	106	9	under	under	ADP
ejpam-5861	106	10	the	the	DET
ejpam-5861	106	11	mentioned	mention	VERB
ejpam-5861	106	12	piecewise	piecewise	NOUN
ejpam-5861	106	13	derivative	derivative	NOUN
ejpam-5861	106	14	by	by	ADP
ejpam-5861	106	15	using	use	VERB
ejpam-5861	106	16	volterra	volterra	NOUN
ejpam-5861	106	17	-	-	PUNCT
ejpam-5861	106	18	laypunov	laypunov	NOUN
ejpam-5861	106	19	method	method	NOUN
ejpam-5861	106	20	.	.	PUNCT
ejpam-5861	107	1	we	we	PRON
ejpam-5861	107	2	also	also	ADV
ejpam-5861	107	3	establish	establish	VERB
ejpam-5861	107	4	a	a	DET
ejpam-5861	107	5	numerical	numerical	ADJ
ejpam-5861	107	6	scheme	scheme	NOUN
ejpam-5861	107	7	based	base	VERB
ejpam-5861	107	8	on	on	ADP
ejpam-5861	107	9	the	the	DET
ejpam-5861	107	10	modified	modify	VERB
ejpam-5861	107	11	euler	euler	NOUN
ejpam-5861	107	12	method	method	NOUN
ejpam-5861	107	13	to	to	PART
ejpam-5861	107	14	simulate	simulate	VERB
ejpam-5861	107	15	our	our	PRON
ejpam-5861	107	16	theoretical	theoretical	ADJ
ejpam-5861	107	17	results	result	NOUN
ejpam-5861	107	18	graphically	graphically	ADV
ejpam-5861	107	19	.	.	PUNCT
ejpam-5861	108	1	here	here	ADV
ejpam-5861	108	2	,	,	PUNCT
ejpam-5861	108	3	we	we	PRON
ejpam-5861	108	4	state	state	VERB
ejpam-5861	108	5	that	that	SCONJ
ejpam-5861	108	6	the	the	DET
ejpam-5861	108	7	local	local	ADJ
ejpam-5861	108	8	stability	stability	NOUN
ejpam-5861	108	9	around	around	ADP
ejpam-5861	108	10	the	the	DET
ejpam-5861	108	11	best	good	ADJ
ejpam-5861	108	12	numerical	numerical	ADJ
ejpam-5861	108	13	solution	solution	NOUN
ejpam-5861	108	14	for	for	ADP
ejpam-5861	108	15	any	any	DET
ejpam-5861	108	16	solution	solution	NOUN
ejpam-5861	108	17	of	of	ADP
ejpam-5861	108	18	the	the	DET
ejpam-5861	108	19	considered	consider	VERB
ejpam-5861	108	20	model	model	NOUN
ejpam-5861	108	21	(	(	PUNCT
ejpam-5861	108	22	1	1	X
ejpam-5861	108	23	)	)	PUNCT
ejpam-5861	108	24	will	will	AUX
ejpam-5861	108	25	be	be	AUX
ejpam-5861	108	26	studied	study	VERB
ejpam-5861	108	27	by	by	ADP
ejpam-5861	108	28	using	use	VERB
ejpam-5861	108	29	uh	uh	INTJ
ejpam-5861	108	30	concept	concept	NOUN
ejpam-5861	108	31	.	.	PUNCT
ejpam-5861	109	1	to	to	PART
ejpam-5861	109	2	achieve	achieve	VERB
ejpam-5861	109	3	the	the	DET
ejpam-5861	109	4	above	above	ADJ
ejpam-5861	109	5	statements	statement	NOUN
ejpam-5861	109	6	,	,	PUNCT
ejpam-5861	110	1	our	our	PRON
ejpam-5861	110	2	s.	s.	PROPN
ejpam-5861	110	3	naz	naz	PROPN
ejpam-5861	110	4	et	et	PROPN
ejpam-5861	110	5	al	al	PROPN
ejpam-5861	110	6	.	.	PUNCT
ejpam-5861	110	7	/	/	SYM
ejpam-5861	110	8	eur	eur	PROPN
ejpam-5861	110	9	.	.	PUNCT
ejpam-5861	111	1	j.	j.	PROPN
ejpam-5861	111	2	pure	pure	PROPN
ejpam-5861	111	3	appl	appl	PROPN
ejpam-5861	111	4	.	.	PROPN
ejpam-5861	111	5	math	math	PROPN
ejpam-5861	111	6	,	,	PUNCT
ejpam-5861	111	7	18	18	NUM
ejpam-5861	111	8	(	(	PUNCT
ejpam-5861	111	9	2	2	NUM
ejpam-5861	111	10	)	)	PUNCT
ejpam-5861	111	11	(	(	PUNCT
ejpam-5861	111	12	2025	2025	NUM
ejpam-5861	111	13	)	)	PUNCT
ejpam-5861	111	14	,	,	PUNCT
ejpam-5861	111	15	5861	5861	NUM
ejpam-5861	111	16	5	5	NUM
ejpam-5861	111	17	of	of	ADP
ejpam-5861	111	18	33	33	NUM
ejpam-5861	111	19	proposed	propose	VERB
ejpam-5861	111	20	model	model	NOUN
ejpam-5861	111	21	will	will	AUX
ejpam-5861	111	22	be	be	AUX
ejpam-5861	111	23	described	describe	VERB
ejpam-5861	111	24	as	as	ADP
ejpam-5861	111	25	follows:	follows:	NUM
ejpam-5861	111	26	pc	pc	NOUN
ejpam-5861	111	27	0	0	NUM
ejpam-5861	111	28	dε	dε	VERB
ejpam-5861	111	29	t	t	NOUN
ejpam-5861	111	30	[	[	X
ejpam-5861	111	31	s(t	s(t	PROPN
ejpam-5861	111	32	)	)	PUNCT
ejpam-5861	111	33	]	]	PUNCT
ejpam-5861	112	1	=	=	PUNCT
ejpam-5861	112	2	λ−	λ−	PROPN
ejpam-5861	112	3	[	[	PUNCT
ejpam-5861	112	4	b(1−	b(1−	NOUN
ejpam-5861	112	5	pξ)i(t	pξ)i(t	NOUN
ejpam-5861	112	6	)	)	PUNCT
ejpam-5861	113	1	+	+	CCONJ
ejpam-5861	113	2	(	(	PUNCT
ejpam-5861	113	3	η	η	X
ejpam-5861	113	4	+	+	PROPN
ejpam-5861	113	5	d	d	PROPN
ejpam-5861	113	6	)	)	PUNCT
ejpam-5861	113	7	]	]	PUNCT
ejpam-5861	114	1	s(t	s(t	PROPN
ejpam-5861	114	2	)	)	PUNCT
ejpam-5861	114	3	,	,	PUNCT
ejpam-5861	114	4	pc	pc	NOUN
ejpam-5861	114	5	0	0	NUM
ejpam-5861	114	6	dε	dε	VERB
ejpam-5861	114	7	t	t	NOUN
ejpam-5861	114	8	[	[	X
ejpam-5861	114	9	v	v	X
ejpam-5861	114	10	(	(	PUNCT
ejpam-5861	114	11	t	t	PROPN
ejpam-5861	114	12	)	)	PUNCT
ejpam-5861	114	13	]	]	PUNCT
ejpam-5861	115	1	=	=	PUNCT
ejpam-5861	115	2	ηs(t)−	ηs(t)−	PROPN
ejpam-5861	115	3	[	[	PUNCT
ejpam-5861	115	4	wbi(t	wbi(t	PROPN
ejpam-5861	115	5	)	)	PUNCT
ejpam-5861	115	6	+	+	SYM
ejpam-5861	115	7	d	d	X
ejpam-5861	115	8	]	]	X
ejpam-5861	115	9	v	v	PROPN
ejpam-5861	115	10	(	(	PUNCT
ejpam-5861	115	11	t	t	PROPN
ejpam-5861	115	12	)	)	PUNCT
ejpam-5861	115	13	,	,	PUNCT
ejpam-5861	115	14	pc	pc	NOUN
ejpam-5861	115	15	0	0	NUM
ejpam-5861	115	16	dε	dε	VERB
ejpam-5861	115	17	t	t	NOUN
ejpam-5861	115	18	[	[	X
ejpam-5861	115	19	e(t	e(t	NOUN
ejpam-5861	115	20	)	)	PUNCT
ejpam-5861	115	21	]	]	PUNCT
ejpam-5861	116	1	=	=	PUNCT
ejpam-5861	116	2	wbv	wbv	INTJ
ejpam-5861	116	3	(	(	PUNCT
ejpam-5861	116	4	t)i(t	t)i(t	NOUN
ejpam-5861	116	5	)	)	PUNCT
ejpam-5861	116	6	+	+	CCONJ
ejpam-5861	116	7	b(1−	b(1−	PROPN
ejpam-5861	116	8	pξ)s(t)i(t)−	pξ)s(t)i(t)−	PROPN
ejpam-5861	116	9	(	(	PUNCT
ejpam-5861	116	10	τ	τ	X
ejpam-5861	116	11	+	+	X
ejpam-5861	116	12	d)e(t	d)e(t	PROPN
ejpam-5861	116	13	)	)	PUNCT
ejpam-5861	116	14	,	,	PUNCT
ejpam-5861	116	15	pc	pc	NOUN
ejpam-5861	116	16	0	0	NUM
ejpam-5861	116	17	dε	dε	VERB
ejpam-5861	116	18	t	t	NOUN
ejpam-5861	116	19	[	[	X
ejpam-5861	116	20	i(t	i(t	NOUN
ejpam-5861	116	21	)	)	PUNCT
ejpam-5861	116	22	]	]	PUNCT
ejpam-5861	117	1	=	=	SYM
ejpam-5861	117	2	τe(t)−	τe(t)−	PROPN
ejpam-5861	117	3	(	(	PUNCT
ejpam-5861	117	4	αi	αi	VERB
ejpam-5861	117	5	+	+	CCONJ
ejpam-5861	117	6	δi	δi	PRON
ejpam-5861	117	7	+	+	CCONJ
ejpam-5861	117	8	σi	σi	X
ejpam-5861	117	9	+	+	CCONJ
ejpam-5861	117	10	d)i(t	d)i(t	NOUN
ejpam-5861	117	11	)	)	PUNCT
ejpam-5861	117	12	,	,	PUNCT
ejpam-5861	117	13	pc	pc	NOUN
ejpam-5861	117	14	0	0	NUM
ejpam-5861	117	15	dε	dε	VERB
ejpam-5861	117	16	t	t	NOUN
ejpam-5861	117	17	[	[	X
ejpam-5861	117	18	q(t	q(t	X
ejpam-5861	117	19	)	)	PUNCT
ejpam-5861	117	20	]	]	PUNCT
ejpam-5861	118	1	=	=	PUNCT
ejpam-5861	118	2	αii(t)−	αii(t)−	PROPN
ejpam-5861	119	1	[	[	X
ejpam-5861	119	2	σq	σq	X
ejpam-5861	119	3	+	+	NOUN
ejpam-5861	119	4	δq	δq	X
ejpam-5861	119	5	+	+	CCONJ
ejpam-5861	119	6	d]q(t	d]q(t	PROPN
ejpam-5861	119	7	)	)	PUNCT
ejpam-5861	119	8	,	,	PUNCT
ejpam-5861	119	9	pc	pc	NOUN
ejpam-5861	119	10	0	0	NUM
ejpam-5861	119	11	dε	dε	VERB
ejpam-5861	119	12	t	t	NOUN
ejpam-5861	119	13	[	[	X
ejpam-5861	119	14	r(t	r(t	NOUN
ejpam-5861	119	15	)	)	PUNCT
ejpam-5861	119	16	]	]	PUNCT
ejpam-5861	119	17	=	=	PUNCT
ejpam-5861	119	18	σii(t	σii(t	PROPN
ejpam-5861	119	19	)	)	PUNCT
ejpam-5861	120	1	+	+	CCONJ
ejpam-5861	120	2	σqq(t)−	σqq(t)−	PROPN
ejpam-5861	120	3	dr(t	dr(t	PRON
ejpam-5861	120	4	)	)	PUNCT
ejpam-5861	120	5	,	,	PUNCT
ejpam-5861	120	6	pc	pc	NOUN
ejpam-5861	120	7	0	0	NUM
ejpam-5861	120	8	dε	dε	VERB
ejpam-5861	120	9	t	t	X
ejpam-5861	120	10	[	[	X
ejpam-5861	120	11	d(t	d(t	PROPN
ejpam-5861	120	12	)	)	PUNCT
ejpam-5861	120	13	]	]	PUNCT
ejpam-5861	121	1	=	=	PUNCT
ejpam-5861	121	2	δii(t	δii(t	PROPN
ejpam-5861	121	3	)	)	PUNCT
ejpam-5861	121	4	+	+	CCONJ
ejpam-5861	121	5	δqq(t	δqq(t	PROPN
ejpam-5861	121	6	)	)	PUNCT
ejpam-5861	121	7	,	,	PUNCT
ejpam-5861	121	8	(	(	PUNCT
ejpam-5861	121	9	2	2	X
ejpam-5861	121	10	)	)	PUNCT
ejpam-5861	121	11	where	where	SCONJ
ejpam-5861	121	12	pc	pc	NOUN
ejpam-5861	121	13	0	0	NUM
ejpam-5861	121	14	dε	dε	NOUN
ejpam-5861	121	15	t	t	NOUN
ejpam-5861	121	16	denotes	denote	NOUN
ejpam-5861	121	17	piecewise	piecewise	VERB
ejpam-5861	121	18	derivative	derivative	NOUN
ejpam-5861	121	19	with	with	ADP
ejpam-5861	121	20	fractional	fractional	ADJ
ejpam-5861	121	21	order	order	NOUN
ejpam-5861	121	22	ε	ε	PROPN
ejpam-5861	121	23	∈	∈	PROPN
ejpam-5861	121	24	(	(	PUNCT
ejpam-5861	121	25	0	0	NUM
ejpam-5861	121	26	,	,	PUNCT
ejpam-5861	121	27	1	1	NUM
ejpam-5861	121	28	]	]	PUNCT
ejpam-5861	121	29	.	.	PUNCT
ejpam-5861	122	1	here	here	ADV
ejpam-5861	122	2	,	,	PUNCT
ejpam-5861	122	3	we	we	PRON
ejpam-5861	122	4	investigate	investigate	VERB
ejpam-5861	122	5	the	the	DET
ejpam-5861	122	6	model	model	NOUN
ejpam-5861	122	7	over	over	ADP
ejpam-5861	122	8	[	[	X
ejpam-5861	122	9	0,t	0,t	X
ejpam-5861	122	10	]	]	PUNCT
ejpam-5861	122	11	which	which	PRON
ejpam-5861	122	12	can	can	AUX
ejpam-5861	122	13	be	be	AUX
ejpam-5861	122	14	expressed	express	VERB
ejpam-5861	122	15	in	in	ADP
ejpam-5861	122	16	sub	sub	NOUN
ejpam-5861	122	17	intervals	interval	NOUN
ejpam-5861	122	18	described	describe	VERB
ejpam-5861	122	19	by	by	ADP
ejpam-5861	122	20	∇1	∇1	PROPN
ejpam-5861	122	21	=	=	PUNCT
ejpam-5861	123	1	[	[	X
ejpam-5861	123	2	0	0	NUM
ejpam-5861	123	3	,	,	PUNCT
ejpam-5861	123	4	t1	t1	NOUN
ejpam-5861	123	5	]	]	X
ejpam-5861	123	6	,	,	PUNCT
ejpam-5861	123	7	∇2	∇2	PROPN
ejpam-5861	123	8	=	=	SYM
ejpam-5861	123	9	(	(	PUNCT
ejpam-5861	123	10	t1,t	t1,t	PROPN
ejpam-5861	123	11	]	]	PUNCT
ejpam-5861	123	12	.	.	PUNCT
ejpam-5861	124	1	the	the	DET
ejpam-5861	124	2	flow	flow	NOUN
ejpam-5861	124	3	chart	chart	NOUN
ejpam-5861	124	4	of	of	ADP
ejpam-5861	124	5	the	the	DET
ejpam-5861	124	6	model	model	NOUN
ejpam-5861	124	7	is	be	AUX
ejpam-5861	124	8	given	give	VERB
ejpam-5861	124	9	in	in	ADP
ejpam-5861	124	10	figure	figure	NOUN
ejpam-5861	124	11	1	1	NUM
ejpam-5861	124	12	.	.	PUNCT
ejpam-5861	124	13	figure	figure	NOUN
ejpam-5861	124	14	1	1	NUM
ejpam-5861	124	15	:	:	PUNCT
ejpam-5861	124	16	flow	flow	VERB
ejpam-5861	124	17	chart	chart	NOUN
ejpam-5861	124	18	of	of	ADP
ejpam-5861	124	19	model	model	NOUN
ejpam-5861	124	20	(	(	PUNCT
ejpam-5861	124	21	2	2	NUM
ejpam-5861	124	22	)	)	PUNCT
ejpam-5861	124	23	.	.	PUNCT
ejpam-5861	125	1	in	in	ADP
ejpam-5861	125	2	addition	addition	NOUN
ejpam-5861	125	3	,	,	PUNCT
ejpam-5861	125	4	the	the	DET
ejpam-5861	125	5	involve	involve	NOUN
ejpam-5861	125	6	parameters	parameter	NOUN
ejpam-5861	125	7	have	have	AUX
ejpam-5861	125	8	been	be	AUX
ejpam-5861	125	9	described	describe	VERB
ejpam-5861	125	10	with	with	ADP
ejpam-5861	125	11	their	their	PRON
ejpam-5861	125	12	numerical	numerical	ADJ
ejpam-5861	125	13	values	value	NOUN
ejpam-5861	125	14	as	as	ADP
ejpam-5861	125	15	in	in	ADP
ejpam-5861	125	16	table	table	NOUN
ejpam-5861	126	1	1	1	NUM
ejpam-5861	126	2	s.	s.	PROPN
ejpam-5861	126	3	naz	naz	PROPN
ejpam-5861	126	4	et	et	PROPN
ejpam-5861	126	5	al	al	PROPN
ejpam-5861	126	6	.	.	PUNCT
ejpam-5861	126	7	/	/	SYM
ejpam-5861	126	8	eur	eur	PROPN
ejpam-5861	126	9	.	.	PUNCT
ejpam-5861	127	1	j.	j.	PROPN
ejpam-5861	127	2	pure	pure	PROPN
ejpam-5861	127	3	appl	appl	PROPN
ejpam-5861	127	4	.	.	PROPN
ejpam-5861	127	5	math	math	PROPN
ejpam-5861	127	6	,	,	PUNCT
ejpam-5861	127	7	18	18	NUM
ejpam-5861	127	8	(	(	PUNCT
ejpam-5861	127	9	2	2	NUM
ejpam-5861	127	10	)	)	PUNCT
ejpam-5861	127	11	(	(	PUNCT
ejpam-5861	127	12	2025	2025	NUM
ejpam-5861	127	13	)	)	PUNCT
ejpam-5861	127	14	,	,	PUNCT
ejpam-5861	127	15	5861	5861	NUM
ejpam-5861	127	16	6	6	NUM
ejpam-5861	127	17	of	of	ADP
ejpam-5861	127	18	33	33	NUM
ejpam-5861	127	19	nomenclatures	nomenclature	NOUN
ejpam-5861	127	20	description	description	NOUN
ejpam-5861	127	21	values	value	NOUN
ejpam-5861	127	22	λ	λ	X
ejpam-5861	127	23	natural	natural	ADJ
ejpam-5861	127	24	birth	birth	NOUN
ejpam-5861	127	25	rate	rate	NOUN
ejpam-5861	127	26	0.0020	0.0020	NUM
ejpam-5861	127	27	b	b	NOUN
ejpam-5861	127	28	infection	infection	NOUN
ejpam-5861	127	29	transmission	transmission	NOUN
ejpam-5861	127	30	rate	rate	NOUN
ejpam-5861	127	31	0.00005	0.00005	NUM
ejpam-5861	127	32	p	p	NOUN
ejpam-5861	127	33	the	the	DET
ejpam-5861	127	34	proportional	proportional	NOUN
ejpam-5861	127	35	of	of	ADP
ejpam-5861	127	36	facing	face	VERB
ejpam-5861	127	37	mask	mask	NOUN
ejpam-5861	127	38	0.01	0.01	NUM
ejpam-5861	127	39	ξ	ξ	PUNCT
ejpam-5861	128	1	the	the	DET
ejpam-5861	128	2	rate	rate	NOUN
ejpam-5861	128	3	of	of	ADP
ejpam-5861	128	4	efficacy	efficacy	NOUN
ejpam-5861	128	5	of	of	ADP
ejpam-5861	128	6	face	face	NOUN
ejpam-5861	128	7	masks	mask	NOUN
ejpam-5861	128	8	0.01	0.01	NUM
ejpam-5861	128	9	η	η	NOUN
ejpam-5861	128	10	rate	rate	NOUN
ejpam-5861	128	11	of	of	ADP
ejpam-5861	128	12	vaccination	vaccination	NOUN
ejpam-5861	128	13	0.02202643	0.02202643	NUM
ejpam-5861	128	14	τ	τ	X
ejpam-5861	128	15	period	period	NOUN
ejpam-5861	128	16	of	of	ADP
ejpam-5861	128	17	incubation	incubation	NOUN
ejpam-5861	128	18	0.05	0.05	NUM
ejpam-5861	128	19	d	d	NOUN
ejpam-5861	128	20	natural	natural	ADJ
ejpam-5861	128	21	martially	martially	NOUN
ejpam-5861	128	22	rate	rate	NOUN
ejpam-5861	128	23	0.019	0.019	NUM
ejpam-5861	128	24	ω	ω	NOUN
ejpam-5861	128	25	recovery	recovery	NOUN
ejpam-5861	128	26	rate	rate	NOUN
ejpam-5861	128	27	0.0099259	0.0099259	NUM
ejpam-5861	128	28	αi	αi	NOUN
ejpam-5861	128	29	isolation	isolation	NOUN
ejpam-5861	128	30	rate	rate	NOUN
ejpam-5861	128	31	of	of	ADP
ejpam-5861	128	32	infected	infected	ADJ
ejpam-5861	128	33	people	people	NOUN
ejpam-5861	128	34	0.020	0.020	NUM
ejpam-5861	128	35	δi	δi	ADP
ejpam-5861	128	36	the	the	DET
ejpam-5861	128	37	rate	rate	NOUN
ejpam-5861	128	38	at	at	ADP
ejpam-5861	128	39	which	which	PRON
ejpam-5861	128	40	infected	infect	VERB
ejpam-5861	128	41	die	die	VERB
ejpam-5861	128	42	0.010	0.010	NUM
ejpam-5861	128	43	σi	σi	NOUN
ejpam-5861	128	44	the	the	DET
ejpam-5861	128	45	rate	rate	NOUN
ejpam-5861	128	46	at	at	ADP
ejpam-5861	128	47	which	which	PRON
ejpam-5861	128	48	infected	infect	VERB
ejpam-5861	128	49	recovered	recover	VERB
ejpam-5861	128	50	0.10	0.10	NUM
ejpam-5861	128	51	σq	σq	NOUN
ejpam-5861	128	52	the	the	DET
ejpam-5861	128	53	rate	rate	NOUN
ejpam-5861	128	54	at	at	ADP
ejpam-5861	128	55	which	which	PRON
ejpam-5861	128	56	quarantine	quarantine	NOUN
ejpam-5861	128	57	recovered	recover	VERB
ejpam-5861	128	58	0.013978	0.013978	NUM
ejpam-5861	128	59	δq	δq	ADP
ejpam-5861	128	60	the	the	DET
ejpam-5861	128	61	rate	rate	NOUN
ejpam-5861	128	62	at	at	ADP
ejpam-5861	128	63	which	which	PRON
ejpam-5861	128	64	quarantine	quarantine	NOUN
ejpam-5861	128	65	die	die	VERB
ejpam-5861	128	66	0.015	0.015	NUM
ejpam-5861	128	67	table	table	NOUN
ejpam-5861	128	68	1	1	NUM
ejpam-5861	128	69	:	:	PUNCT
ejpam-5861	128	70	nomenclature	nomenclature	NOUN
ejpam-5861	128	71	,	,	PUNCT
ejpam-5861	128	72	description	description	NOUN
ejpam-5861	128	73	and	and	CCONJ
ejpam-5861	128	74	values	value	NOUN
ejpam-5861	128	75	.	.	PUNCT
ejpam-5861	129	1	in	in	ADP
ejpam-5861	129	2	our	our	PRON
ejpam-5861	129	3	study	study	NOUN
ejpam-5861	129	4	,	,	PUNCT
ejpam-5861	129	5	we	we	PRON
ejpam-5861	129	6	also	also	ADV
ejpam-5861	129	7	compute	compute	VERB
ejpam-5861	129	8	the	the	DET
ejpam-5861	129	9	feasible	feasible	ADJ
ejpam-5861	129	10	region	region	NOUN
ejpam-5861	129	11	,	,	PUNCT
ejpam-5861	129	12	positivity	positivity	NOUN
ejpam-5861	129	13	and	and	CCONJ
ejpam-5861	129	14	boundedness	boundedness	NOUN
ejpam-5861	129	15	of	of	ADP
ejpam-5861	129	16	solution	solution	NOUN
ejpam-5861	129	17	under	under	ADP
ejpam-5861	129	18	the	the	DET
ejpam-5861	129	19	mentioned	mention	VERB
ejpam-5861	129	20	derivative	derivative	ADJ
ejpam-5861	129	21	and	and	CCONJ
ejpam-5861	129	22	equilibrium	equilibrium	NOUN
ejpam-5861	129	23	points	point	NOUN
ejpam-5861	129	24	.	.	PUNCT
ejpam-5861	130	1	also	also	ADV
ejpam-5861	130	2	,	,	PUNCT
ejpam-5861	130	3	the	the	DET
ejpam-5861	130	4	basic	basic	ADJ
ejpam-5861	130	5	reproductive	reproductive	ADJ
ejpam-5861	130	6	numbers	number	NOUN
ejpam-5861	130	7	together	together	ADV
ejpam-5861	130	8	with	with	ADP
ejpam-5861	130	9	the	the	DET
ejpam-5861	130	10	equilibrium	equilibrium	NOUN
ejpam-5861	130	11	points	point	NOUN
ejpam-5861	130	12	will	will	AUX
ejpam-5861	130	13	be	be	AUX
ejpam-5861	130	14	deduced	deduce	VERB
ejpam-5861	130	15	for	for	ADP
ejpam-5861	130	16	the	the	DET
ejpam-5861	130	17	model	model	NOUN
ejpam-5861	130	18	(	(	PUNCT
ejpam-5861	130	19	2	2	NUM
ejpam-5861	130	20	)	)	PUNCT
ejpam-5861	130	21	.	.	PUNCT
ejpam-5861	131	1	also	also	ADV
ejpam-5861	131	2	an	an	DET
ejpam-5861	131	3	attempt	attempt	NOUN
ejpam-5861	131	4	will	will	AUX
ejpam-5861	131	5	be	be	AUX
ejpam-5861	131	6	done	do	VERB
ejpam-5861	131	7	to	to	PART
ejpam-5861	131	8	investigate	investigate	VERB
ejpam-5861	131	9	the	the	DET
ejpam-5861	131	10	sensitivity	sensitivity	NOUN
ejpam-5861	131	11	analysis	analysis	NOUN
ejpam-5861	131	12	of	of	ADP
ejpam-5861	131	13	the	the	DET
ejpam-5861	131	14	basic	basic	ADJ
ejpam-5861	131	15	reproduction	reproduction	NOUN
ejpam-5861	131	16	number	number	NOUN
ejpam-5861	131	17	by	by	ADP
ejpam-5861	131	18	following	follow	VERB
ejpam-5861	131	19	[	[	X
ejpam-5861	131	20	34	34	NUM
ejpam-5861	131	21	]	]	PUNCT
ejpam-5861	131	22	.	.	PUNCT
ejpam-5861	132	1	results	result	NOUN
ejpam-5861	132	2	related	relate	VERB
ejpam-5861	132	3	to	to	ADP
ejpam-5861	132	4	global	global	ADJ
ejpam-5861	132	5	stability	stability	NOUN
ejpam-5861	132	6	of	of	ADP
ejpam-5861	132	7	endemic	endemic	ADJ
ejpam-5861	132	8	equilibrium	equilibrium	NOUN
ejpam-5861	132	9	have	have	AUX
ejpam-5861	132	10	been	be	AUX
ejpam-5861	132	11	studied	study	VERB
ejpam-5861	132	12	by	by	ADP
ejpam-5861	132	13	using	use	VERB
ejpam-5861	132	14	volterra	volterra	PROPN
ejpam-5861	132	15	-	-	PUNCT
ejpam-5861	132	16	lyapunov	lyapunov	ADJ
ejpam-5861	132	17	method	method	NOUN
ejpam-5861	133	1	[	[	X
ejpam-5861	133	2	43	43	NUM
ejpam-5861	133	3	]	]	PUNCT
ejpam-5861	133	4	.	.	PUNCT
ejpam-5861	134	1	some	some	DET
ejpam-5861	134	2	results	result	NOUN
ejpam-5861	134	3	devoted	devote	VERB
ejpam-5861	134	4	to	to	ADP
ejpam-5861	134	5	existence	existence	NOUN
ejpam-5861	134	6	theory	theory	NOUN
ejpam-5861	134	7	and	and	CCONJ
ejpam-5861	134	8	ulam	ulam	PROPN
ejpam-5861	134	9	stability	stability	PROPN
ejpam-5861	134	10	have	have	AUX
ejpam-5861	134	11	been	be	AUX
ejpam-5861	134	12	investigated	investigate	VERB
ejpam-5861	134	13	by	by	ADP
ejpam-5861	134	14	using	use	VERB
ejpam-5861	134	15	tools	tool	NOUN
ejpam-5861	134	16	used	use	VERB
ejpam-5861	134	17	in	in	ADP
ejpam-5861	134	18	[	[	X
ejpam-5861	134	19	1	1	NUM
ejpam-5861	134	20	,	,	PUNCT
ejpam-5861	134	21	14	14	NUM
ejpam-5861	134	22	,	,	PUNCT
ejpam-5861	134	23	17	17	NUM
ejpam-5861	134	24	]	]	PUNCT
ejpam-5861	134	25	and	and	CCONJ
ejpam-5861	134	26	[	[	X
ejpam-5861	134	27	12	12	NUM
ejpam-5861	134	28	,	,	PUNCT
ejpam-5861	134	29	33	33	NUM
ejpam-5861	134	30	,	,	PUNCT
ejpam-5861	134	31	39	39	NUM
ejpam-5861	134	32	]	]	PUNCT
ejpam-5861	134	33	.	.	PUNCT
ejpam-5861	135	1	the	the	DET
ejpam-5861	135	2	numerical	numerical	ADJ
ejpam-5861	135	3	investigations	investigation	NOUN
ejpam-5861	135	4	are	be	AUX
ejpam-5861	135	5	investigated	investigate	VERB
ejpam-5861	135	6	by	by	ADP
ejpam-5861	135	7	establishing	establish	VERB
ejpam-5861	135	8	a	a	DET
ejpam-5861	135	9	numerical	numerical	ADJ
ejpam-5861	135	10	scheme	scheme	NOUN
ejpam-5861	135	11	based	base	VERB
ejpam-5861	135	12	on	on	ADP
ejpam-5861	135	13	the	the	DET
ejpam-5861	135	14	procedure	procedure	NOUN
ejpam-5861	135	15	given	give	VERB
ejpam-5861	135	16	in	in	ADP
ejpam-5861	135	17	[	[	X
ejpam-5861	135	18	24	24	NUM
ejpam-5861	135	19	]	]	PUNCT
ejpam-5861	135	20	.	.	PUNCT
ejpam-5861	136	1	finally	finally	ADV
ejpam-5861	136	2	the	the	DET
ejpam-5861	136	3	results	result	NOUN
ejpam-5861	136	4	for	for	ADP
ejpam-5861	136	5	various	various	ADJ
ejpam-5861	136	6	fractional	fractional	ADJ
ejpam-5861	136	7	orders	order	NOUN
ejpam-5861	136	8	will	will	AUX
ejpam-5861	136	9	be	be	AUX
ejpam-5861	136	10	presented	present	VERB
ejpam-5861	136	11	graphically	graphically	ADV
ejpam-5861	136	12	.	.	PUNCT
ejpam-5861	137	1	various	various	ADJ
ejpam-5861	137	2	models	model	NOUN
ejpam-5861	137	3	of	of	ADP
ejpam-5861	137	4	dynamical	dynamical	ADJ
ejpam-5861	137	5	systems	system	NOUN
ejpam-5861	137	6	like	like	ADP
ejpam-5861	137	7	studied	study	VERB
ejpam-5861	137	8	in	in	ADP
ejpam-5861	137	9	[	[	X
ejpam-5861	137	10	2–4	2–4	NUM
ejpam-5861	137	11	]	]	X
ejpam-5861	137	12	,	,	PUNCT
ejpam-5861	137	13	researchers	researcher	NOUN
ejpam-5861	137	14	have	have	AUX
ejpam-5861	137	15	used	use	VERB
ejpam-5861	137	16	fractional	fractional	ADJ
ejpam-5861	137	17	derivatives	derivative	NOUN
ejpam-5861	137	18	with	with	ADP
ejpam-5861	137	19	power	power	NOUN
ejpam-5861	137	20	law	law	NOUN
ejpam-5861	137	21	type	type	NOUN
ejpam-5861	137	22	kernels	kernel	NOUN
ejpam-5861	137	23	to	to	PART
ejpam-5861	137	24	investigate	investigate	VERB
ejpam-5861	137	25	the	the	DET
ejpam-5861	137	26	numerical	numerical	ADJ
ejpam-5861	137	27	solutions	solution	NOUN
ejpam-5861	137	28	.	.	PUNCT
ejpam-5861	138	1	our	our	PRON
ejpam-5861	138	2	study	study	NOUN
ejpam-5861	138	3	uses	use	VERB
ejpam-5861	138	4	piecewise	piecewise	NOUN
ejpam-5861	138	5	version	version	NOUN
ejpam-5861	138	6	of	of	ADP
ejpam-5861	138	7	fractional	fractional	ADJ
ejpam-5861	138	8	derivative	derivative	NOUN
ejpam-5861	138	9	to	to	PART
ejpam-5861	138	10	investigate	investigate	VERB
ejpam-5861	138	11	the	the	DET
ejpam-5861	138	12	existence	existence	NOUN
ejpam-5861	138	13	and	and	CCONJ
ejpam-5861	138	14	numerical	numerical	ADJ
ejpam-5861	138	15	solution	solution	NOUN
ejpam-5861	138	16	for	for	ADP
ejpam-5861	138	17	seven	seven	NUM
ejpam-5861	138	18	compartmental	compartmental	ADJ
ejpam-5861	138	19	models	model	NOUN
ejpam-5861	138	20	.	.	PUNCT
ejpam-5861	139	1	2	2	X
ejpam-5861	139	2	.	.	X
ejpam-5861	139	3	fundamental	fundamental	ADJ
ejpam-5861	139	4	results	result	NOUN
ejpam-5861	139	5	here	here	ADV
ejpam-5861	139	6	,	,	PUNCT
ejpam-5861	139	7	we	we	PRON
ejpam-5861	139	8	recall	recall	VERB
ejpam-5861	139	9	some	some	DET
ejpam-5861	139	10	basic	basic	ADJ
ejpam-5861	139	11	definitions	definition	NOUN
ejpam-5861	139	12	from	from	ADP
ejpam-5861	139	13	fractional	fractional	ADJ
ejpam-5861	139	14	calculus	calculus	NOUN
ejpam-5861	139	15	.	.	PUNCT
ejpam-5861	140	1	for	for	ADP
ejpam-5861	140	2	the	the	DET
ejpam-5861	140	3	given	give	VERB
ejpam-5861	140	4	definitions	definition	NOUN
ejpam-5861	140	5	we	we	PRON
ejpam-5861	140	6	have	have	AUX
ejpam-5861	140	7	used	use	VERB
ejpam-5861	140	8	[	[	PUNCT
ejpam-5861	140	9	32	32	NUM
ejpam-5861	140	10	]	]	PUNCT
ejpam-5861	140	11	.	.	PUNCT
ejpam-5861	141	1	definition	definition	NOUN
ejpam-5861	141	2	1	1	NUM
ejpam-5861	141	3	.	.	PUNCT
ejpam-5861	142	1	the	the	DET
ejpam-5861	142	2	ml	ml	PROPN
ejpam-5861	142	3	function	function	NOUN
ejpam-5861	142	4	is	be	AUX
ejpam-5861	142	5	a	a	DET
ejpam-5861	142	6	recognisee	recognisee	ADJ
ejpam-5861	142	7	generalization	generalization	NOUN
ejpam-5861	142	8	of	of	ADP
ejpam-5861	142	9	the	the	DET
ejpam-5861	142	10	exponential	exponential	NOUN
ejpam-5861	142	11	.	.	PUNCT
ejpam-5861	143	1	the	the	DET
ejpam-5861	143	2	ml	ml	PROPN
ejpam-5861	143	3	function	function	NOUN
ejpam-5861	143	4	with	with	ADP
ejpam-5861	143	5	one	one	NUM
ejpam-5861	143	6	argument	argument	NOUN
ejpam-5861	143	7	is	be	AUX
ejpam-5861	143	8	defined	define	VERB
ejpam-5861	143	9	as	as	ADP
ejpam-5861	143	10	follows	follow	VERB
ejpam-5861	143	11	:	:	PUNCT
ejpam-5861	143	12	eε(t	eε(t	NUM
ejpam-5861	143	13	)	)	PUNCT
ejpam-5861	143	14	=	=	PUNCT
ejpam-5861	144	1	∞∑	∞∑	NUM
ejpam-5861	144	2	k=0	k=0	PUNCT
ejpam-5861	144	3	tk	tk	PROPN
ejpam-5861	144	4	γ(kε+	γ(kε+	NOUN
ejpam-5861	144	5	1	1	NUM
ejpam-5861	144	6	)	)	PUNCT
ejpam-5861	144	7	,	,	PUNCT
ejpam-5861	144	8	s.	s.	PROPN
ejpam-5861	144	9	naz	naz	PROPN
ejpam-5861	144	10	et	et	PROPN
ejpam-5861	144	11	al	al	PROPN
ejpam-5861	144	12	.	.	PUNCT
ejpam-5861	144	13	/	/	SYM
ejpam-5861	144	14	eur	eur	PROPN
ejpam-5861	144	15	.	.	PUNCT
ejpam-5861	145	1	j.	j.	PROPN
ejpam-5861	145	2	pure	pure	PROPN
ejpam-5861	145	3	appl	appl	PROPN
ejpam-5861	145	4	.	.	PROPN
ejpam-5861	145	5	math	math	PROPN
ejpam-5861	145	6	,	,	PUNCT
ejpam-5861	145	7	18	18	NUM
ejpam-5861	145	8	(	(	PUNCT
ejpam-5861	145	9	2	2	NUM
ejpam-5861	145	10	)	)	PUNCT
ejpam-5861	145	11	(	(	PUNCT
ejpam-5861	145	12	2025	2025	NUM
ejpam-5861	145	13	)	)	PUNCT
ejpam-5861	145	14	,	,	PUNCT
ejpam-5861	145	15	5861	5861	NUM
ejpam-5861	145	16	7	7	NUM
ejpam-5861	145	17	of	of	ADP
ejpam-5861	145	18	33	33	NUM
ejpam-5861	145	19	while	while	NOUN
ejpam-5861	145	20	for	for	ADP
ejpam-5861	145	21	double	double	ADJ
ejpam-5861	145	22	parameters	parameter	NOUN
ejpam-5861	145	23	it	it	PRON
ejpam-5861	145	24	is	be	AUX
ejpam-5861	145	25	defined	define	VERB
ejpam-5861	145	26	as	as	SCONJ
ejpam-5861	145	27	described	describe	VERB
ejpam-5861	145	28	by	by	ADP
ejpam-5861	145	29	:	:	PUNCT
ejpam-5861	145	30	ep	ep	PROPN
ejpam-5861	145	31	,	,	PUNCT
ejpam-5861	145	32	q(t	q(t	PROPN
ejpam-5861	145	33	)	)	PUNCT
ejpam-5861	145	34	=	=	NOUN
ejpam-5861	146	1	∞∑	∞∑	NUM
ejpam-5861	146	2	k=0	k=0	PROPN
ejpam-5861	146	3	tk	tk	X
ejpam-5861	146	4	γ(kp+	γ(kp+	PROPN
ejpam-5861	146	5	q	q	NOUN
ejpam-5861	146	6	)	)	PUNCT
ejpam-5861	146	7	.	.	PUNCT
ejpam-5861	147	1	definition	definition	NOUN
ejpam-5861	147	2	2	2	NUM
ejpam-5861	147	3	.	.	PUNCT
ejpam-5861	148	1	[	[	X
ejpam-5861	148	2	5	5	X
ejpam-5861	148	3	]	]	PUNCT
ejpam-5861	148	4	the	the	DET
ejpam-5861	148	5	riemann	riemann	PROPN
ejpam-5861	148	6	-	-	PUNCT
ejpam-5861	148	7	liouville	liouville	PROPN
ejpam-5861	148	8	(	(	PUNCT
ejpam-5861	148	9	rl	rl	NOUN
ejpam-5861	148	10	)	)	PUNCT
ejpam-5861	148	11	fractional	fractional	ADJ
ejpam-5861	148	12	integral	integral	ADJ
ejpam-5861	148	13	with	with	ADP
ejpam-5861	148	14	fractional	fractional	ADJ
ejpam-5861	148	15	order	order	NOUN
ejpam-5861	148	16	ε	ε	X
ejpam-5861	148	17	>	>	X
ejpam-5861	148	18	0	0	NUM
ejpam-5861	149	1	for	for	ADP
ejpam-5861	149	2	a	a	DET
ejpam-5861	149	3	continuous	continuous	ADJ
ejpam-5861	149	4	function	function	NOUN
ejpam-5861	149	5	ϕ	ϕ	NOUN
ejpam-5861	149	6	on	on	ADP
ejpam-5861	149	7	[	[	X
ejpam-5861	149	8	0,t	0,t	X
ejpam-5861	149	9	]	]	X
ejpam-5861	149	10	is	be	AUX
ejpam-5861	149	11	defined	define	VERB
ejpam-5861	149	12	by	by	ADP
ejpam-5861	149	13	iε0+ϕ(t	iε0+ϕ(t	NOUN
ejpam-5861	149	14	)	)	PUNCT
ejpam-5861	149	15	=	=	SYM
ejpam-5861	149	16	1	1	NUM
ejpam-5861	149	17	γ(ε	γ(ε	PROPN
ejpam-5861	149	18	)	)	PUNCT
ejpam-5861	150	1	∫	∫	PROPN
ejpam-5861	150	2	t	t	PROPN
ejpam-5861	150	3	0	0	NUM
ejpam-5861	151	1	(	(	PUNCT
ejpam-5861	151	2	t−	t−	PROPN
ejpam-5861	151	3	φ)ε−1ϕ(φ)dφ	φ)ε−1ϕ(φ)dφ	NOUN
ejpam-5861	151	4	,	,	PUNCT
ejpam-5861	151	5	(	(	PUNCT
ejpam-5861	151	6	3	3	X
ejpam-5861	151	7	)	)	PUNCT
ejpam-5861	151	8	such	such	ADJ
ejpam-5861	151	9	that	that	DET
ejpam-5861	151	10	integral	integral	ADJ
ejpam-5861	151	11	exists	exist	NOUN
ejpam-5861	151	12	on	on	ADP
ejpam-5861	151	13	right	right	ADJ
ejpam-5861	151	14	side	side	NOUN
ejpam-5861	151	15	.	.	PUNCT
ejpam-5861	152	1	definition	definition	NOUN
ejpam-5861	152	2	3	3	NUM
ejpam-5861	152	3	.	.	PUNCT
ejpam-5861	153	1	[	[	X
ejpam-5861	153	2	5	5	X
ejpam-5861	153	3	]	]	PUNCT
ejpam-5861	153	4	the	the	DET
ejpam-5861	153	5	rl	rl	PROPN
ejpam-5861	153	6	differentiation	differentiation	NOUN
ejpam-5861	153	7	with	with	ADP
ejpam-5861	153	8	non	non	ADJ
ejpam-5861	153	9	-	-	ADJ
ejpam-5861	153	10	integer	integer	ADJ
ejpam-5861	153	11	order	order	NOUN
ejpam-5861	153	12	n	n	CCONJ
ejpam-5861	153	13	−	−	PROPN
ejpam-5861	153	14	1	1	NUM
ejpam-5861	153	15	<	<	X
ejpam-5861	153	16	ε	ε	X
ejpam-5861	153	17	<	<	X
ejpam-5861	153	18	n	n	PROPN
ejpam-5861	153	19	of	of	ADP
ejpam-5861	153	20	a	a	DET
ejpam-5861	153	21	function	function	NOUN
ejpam-5861	153	22	ϕ	ϕ	NOUN
ejpam-5861	153	23	which	which	PRON
ejpam-5861	153	24	has	have	VERB
ejpam-5861	153	25	absolutely	absolutely	ADV
ejpam-5861	153	26	continuous	continuous	ADJ
ejpam-5861	153	27	derivative	derivative	NOUN
ejpam-5861	153	28	up	up	ADP
ejpam-5861	153	29	(	(	PUNCT
ejpam-5861	153	30	n−	n−	NOUN
ejpam-5861	153	31	1	1	NUM
ejpam-5861	153	32	)	)	PUNCT
ejpam-5861	153	33	is	be	AUX
ejpam-5861	153	34	defined	define	VERB
ejpam-5861	153	35	by	by	ADP
ejpam-5861	153	36	dε	dε	ADP
ejpam-5861	153	37	0+ϕ(t	0+ϕ(t	ADJ
ejpam-5861	153	38	)	)	PUNCT
ejpam-5861	153	39	=	=	SYM
ejpam-5861	153	40	1	1	NUM
ejpam-5861	153	41	γ(n−	γ(n−	PROPN
ejpam-5861	153	42	ε	ε	PROPN
ejpam-5861	153	43	)	)	PUNCT
ejpam-5861	153	44	(	(	PUNCT
ejpam-5861	153	45	d	d	X
ejpam-5861	153	46	dt	dt	NOUN
ejpam-5861	153	47	)	)	PUNCT
ejpam-5861	153	48	n	n	CCONJ
ejpam-5861	153	49	∫	∫	PROPN
ejpam-5861	153	50	t	t	PROPN
ejpam-5861	153	51	0	0	NUM
ejpam-5861	153	52	(	(	PUNCT
ejpam-5861	153	53	t−	t−	DET
ejpam-5861	153	54	φ)n−ε−1ϕ(φ)dφ	φ)n−ε−1ϕ(φ)dφ	NOUN
ejpam-5861	153	55	,	,	PUNCT
ejpam-5861	153	56	where	where	SCONJ
ejpam-5861	153	57	n	n	ADV
ejpam-5861	153	58	=	=	SYM
ejpam-5861	154	1	[	[	X
ejpam-5861	154	2	ε	ε	X
ejpam-5861	154	3	]	]	X
ejpam-5861	154	4	+	+	NOUN
ejpam-5861	154	5	1	1	X
ejpam-5861	154	6	.	.	X
ejpam-5861	154	7	definition	definition	NOUN
ejpam-5861	154	8	4	4	NUM
ejpam-5861	154	9	.	.	PUNCT
ejpam-5861	155	1	[	[	X
ejpam-5861	155	2	26	26	NUM
ejpam-5861	155	3	]	]	PUNCT
ejpam-5861	155	4	the	the	DET
ejpam-5861	155	5	caputo	caputo	PROPN
ejpam-5861	155	6	fractional	fractional	PROPN
ejpam-5861	155	7	order	order	NOUN
ejpam-5861	155	8	derivative	derivative	NOUN
ejpam-5861	155	9	of	of	ADP
ejpam-5861	155	10	order	order	NOUN
ejpam-5861	155	11	n	n	CCONJ
ejpam-5861	155	12	−	−	PROPN
ejpam-5861	155	13	1	1	NUM
ejpam-5861	155	14	<	<	X
ejpam-5861	155	15	ε	ε	X
ejpam-5861	155	16	<	<	X
ejpam-5861	155	17	n	n	PROPN
ejpam-5861	155	18	of	of	ADP
ejpam-5861	155	19	a	a	DET
ejpam-5861	155	20	differentiable	differentiable	ADJ
ejpam-5861	155	21	function	function	NOUN
ejpam-5861	155	22	ϕ	ϕ	PROPN
ejpam-5861	155	23	∈	∈	PROPN
ejpam-5861	155	24	cn[0,t	cn[0,t	NOUN
ejpam-5861	155	25	]	]	PUNCT
ejpam-5861	155	26	is	be	AUX
ejpam-5861	155	27	defined	define	VERB
ejpam-5861	155	28	by	by	ADP
ejpam-5861	155	29	cdε	cdε	NOUN
ejpam-5861	155	30	0+ϕ(t	0+ϕ(t	PROPN
ejpam-5861	155	31	)	)	PUNCT
ejpam-5861	155	32	=	=	SYM
ejpam-5861	156	1	1	1	NUM
ejpam-5861	156	2	γ(n−	γ(n−	PROPN
ejpam-5861	156	3	ε	ε	PROPN
ejpam-5861	156	4	)	)	PUNCT
ejpam-5861	156	5	∫	∫	PROPN
ejpam-5861	156	6	t	t	PROPN
ejpam-5861	156	7	0	0	NUM
ejpam-5861	156	8	(	(	PUNCT
ejpam-5861	156	9	t−	t−	PROPN
ejpam-5861	156	10	φ)n−ε−1ϕ(n)(φ)dφ	φ)n−ε−1ϕ(n)(φ)dφ	PROPN
ejpam-5861	156	11	,	,	PUNCT
ejpam-5861	156	12	where	where	SCONJ
ejpam-5861	156	13	n	n	ADV
ejpam-5861	156	14	=	=	SYM
ejpam-5861	157	1	[	[	X
ejpam-5861	157	2	ε	ε	X
ejpam-5861	157	3	]	]	X
ejpam-5861	157	4	+	+	NOUN
ejpam-5861	157	5	1	1	X
ejpam-5861	157	6	.	.	X
ejpam-5861	157	7	lemma	lemma	PROPN
ejpam-5861	157	8	1	1	NUM
ejpam-5861	157	9	.	.	PUNCT
ejpam-5861	158	1	[	[	X
ejpam-5861	158	2	26]the	26]the	DET
ejpam-5861	158	3	given	give	VERB
ejpam-5861	158	4	equation	equation	NOUN
ejpam-5861	158	5	cdε	cdε	NOUN
ejpam-5861	158	6	0+ϕ(t	0+ϕ(t	ADJ
ejpam-5861	158	7	)	)	PUNCT
ejpam-5861	158	8	=	=	SYM
ejpam-5861	158	9	χ(t	χ(t	NOUN
ejpam-5861	158	10	)	)	PUNCT
ejpam-5861	158	11	,	,	PUNCT
ejpam-5861	158	12	ϕ(0	ϕ(0	PROPN
ejpam-5861	158	13	)	)	PUNCT
ejpam-5861	158	14	=	=	SYM
ejpam-5861	158	15	ϕ0	ϕ0	NOUN
ejpam-5861	158	16	(	(	PUNCT
ejpam-5861	158	17	4	4	NUM
ejpam-5861	158	18	)	)	PUNCT
ejpam-5861	158	19	has	have	VERB
ejpam-5861	158	20	a	a	DET
ejpam-5861	158	21	solution	solution	NOUN
ejpam-5861	158	22	of	of	ADP
ejpam-5861	158	23	the	the	DET
ejpam-5861	158	24	form	form	NOUN
ejpam-5861	158	25	ϕ(t	ϕ(t	NUM
ejpam-5861	158	26	)	)	PUNCT
ejpam-5861	159	1	=	=	SYM
ejpam-5861	159	2	ϕ0	ϕ0	NOUN
ejpam-5861	159	3	+	+	CCONJ
ejpam-5861	159	4	1	1	NUM
ejpam-5861	159	5	γ(ε	γ(ε	PROPN
ejpam-5861	159	6	)	)	PUNCT
ejpam-5861	160	1	∫	∫	PROPN
ejpam-5861	160	2	t	t	PROPN
ejpam-5861	160	3	0	0	NUM
ejpam-5861	161	1	(	(	PUNCT
ejpam-5861	161	2	t−	t−	PROPN
ejpam-5861	161	3	φ)ε−1χ(φ)dφ	φ)ε−1χ(φ)dφ	ADJ
ejpam-5861	161	4	.	.	PUNCT
ejpam-5861	162	1	(	(	PUNCT
ejpam-5861	162	2	5	5	X
ejpam-5861	162	3	)	)	PUNCT
ejpam-5861	162	4	definition	definition	NOUN
ejpam-5861	162	5	5	5	NUM
ejpam-5861	162	6	.	.	PUNCT
ejpam-5861	163	1	the	the	DET
ejpam-5861	163	2	piecewise	piecewise	NOUN
ejpam-5861	163	3	integration	integration	NOUN
ejpam-5861	163	4	of	of	ADP
ejpam-5861	163	5	a	a	DET
ejpam-5861	163	6	continuous	continuous	ADJ
ejpam-5861	163	7	function	function	NOUN
ejpam-5861	163	8	ϕ	ϕ	NOUN
ejpam-5861	163	9	such	such	ADJ
ejpam-5861	163	10	that	that	SCONJ
ejpam-5861	163	11	0	0	NUM
ejpam-5861	163	12	<	<	X
ejpam-5861	163	13	t1	t1	NOUN
ejpam-5861	163	14	<	<	X
ejpam-5861	163	15	t2	t2	PROPN
ejpam-5861	163	16	<	<	X
ejpam-5861	163	17	t3	t3	PROPN
ejpam-5861	163	18	<	<	X
ejpam-5861	163	19	t	t	PROPN
ejpam-5861	163	20	is	be	AUX
ejpam-5861	163	21	defined	define	VERB
ejpam-5861	163	22	by	by	ADP
ejpam-5861	163	23	∫	∫	PROPN
ejpam-5861	163	24	t3	t3	PROPN
ejpam-5861	163	25	t1	t1	PROPN
ejpam-5861	163	26	ϕ(t)dt	ϕ(t)dt	NOUN
ejpam-5861	164	1	=	=	SYM
ejpam-5861	164	2	∫	∫	PROPN
ejpam-5861	164	3	t2	t2	PROPN
ejpam-5861	164	4	t1	t1	PROPN
ejpam-5861	164	5	ϕ(t)dt+	ϕ(t)dt+	PROPN
ejpam-5861	165	1	∫	∫	PROPN
ejpam-5861	165	2	t3	t3	PROPN
ejpam-5861	165	3	t2	t2	PROPN
ejpam-5861	165	4	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-5861	165	5	.	.	PUNCT
ejpam-5861	166	1	definition	definition	NOUN
ejpam-5861	166	2	6	6	NUM
ejpam-5861	166	3	.	.	PUNCT
ejpam-5861	167	1	[	[	X
ejpam-5861	167	2	37	37	NUM
ejpam-5861	167	3	]	]	PUNCT
ejpam-5861	167	4	the	the	DET
ejpam-5861	167	5	piecewise	piecewise	NOUN
ejpam-5861	167	6	rl	rl	VERB
ejpam-5861	167	7	fractional	fractional	ADJ
ejpam-5861	167	8	integral	integral	ADJ
ejpam-5861	167	9	of	of	ADP
ejpam-5861	167	10	order	order	NOUN
ejpam-5861	167	11	ε	ε	PROPN
ejpam-5861	167	12	∈	∈	PROPN
ejpam-5861	167	13	(	(	PUNCT
ejpam-5861	167	14	0	0	NUM
ejpam-5861	167	15	,	,	PUNCT
ejpam-5861	167	16	1	1	NUM
ejpam-5861	167	17	]	]	PUNCT
ejpam-5861	167	18	of	of	ADP
ejpam-5861	167	19	a	a	DET
ejpam-5861	167	20	continuous	continuous	ADJ
ejpam-5861	167	21	function	function	NOUN
ejpam-5861	167	22	ϕ	ϕ	NOUN
ejpam-5861	167	23	is	be	AUX
ejpam-5861	167	24	described	describe	VERB
ejpam-5861	167	25	as	as	ADP
ejpam-5861	167	26	prliε0+ϕ(t	prliε0+ϕ(t	NOUN
ejpam-5861	167	27	)	)	PUNCT
ejpam-5861	167	28	=	=	PUNCT
ejpam-5861	168	1			PROPN
ejpam-5861	168	2	∫	∫	PROPN
ejpam-5861	168	3	t1	t1	NOUN
ejpam-5861	168	4	0	0	NUM
ejpam-5861	169	1	ϕ(t)dt	ϕ(t)dt	PROPN
ejpam-5861	169	2	,	,	PUNCT
ejpam-5861	169	3	with	with	ADP
ejpam-5861	169	4	t	t	PROPN
ejpam-5861	169	5	∈	∈	PROPN
ejpam-5861	169	6	∇1	∇1	PROPN
ejpam-5861	169	7	,	,	PUNCT
ejpam-5861	169	8	1	1	NUM
ejpam-5861	169	9	γ(ε	γ(ε	PROPN
ejpam-5861	169	10	)	)	PUNCT
ejpam-5861	170	1	∫	∫	PROPN
ejpam-5861	170	2	t	t	PROPN
ejpam-5861	170	3	t1	t1	PROPN
ejpam-5861	170	4	(	(	PUNCT
ejpam-5861	170	5	t−	t−	PROPN
ejpam-5861	170	6	φ)ε−1ϕ(φ)dφ	φ)ε−1ϕ(φ)dφ	NOUN
ejpam-5861	170	7	,	,	PUNCT
ejpam-5861	170	8	with	with	ADP
ejpam-5861	170	9	t	t	PROPN
ejpam-5861	170	10	∈	∈	PROPN
ejpam-5861	170	11	∇2	∇2	PROPN
ejpam-5861	170	12	.	.	PUNCT
ejpam-5861	171	1	s.	s.	PROPN
ejpam-5861	171	2	naz	naz	PROPN
ejpam-5861	171	3	et	et	PROPN
ejpam-5861	171	4	al	al	PROPN
ejpam-5861	171	5	.	.	PUNCT
ejpam-5861	171	6	/	/	SYM
ejpam-5861	171	7	eur	eur	PROPN
ejpam-5861	171	8	.	.	PUNCT
ejpam-5861	172	1	j.	j.	PROPN
ejpam-5861	172	2	pure	pure	PROPN
ejpam-5861	172	3	appl	appl	PROPN
ejpam-5861	172	4	.	.	PROPN
ejpam-5861	172	5	math	math	PROPN
ejpam-5861	172	6	,	,	PUNCT
ejpam-5861	172	7	18	18	NUM
ejpam-5861	172	8	(	(	PUNCT
ejpam-5861	172	9	2	2	NUM
ejpam-5861	172	10	)	)	PUNCT
ejpam-5861	172	11	(	(	PUNCT
ejpam-5861	172	12	2025	2025	NUM
ejpam-5861	172	13	)	)	PUNCT
ejpam-5861	172	14	,	,	PUNCT
ejpam-5861	172	15	5861	5861	NUM
ejpam-5861	172	16	8	8	NUM
ejpam-5861	172	17	of	of	ADP
ejpam-5861	172	18	33	33	NUM
ejpam-5861	172	19	definition	definition	NOUN
ejpam-5861	172	20	7	7	NUM
ejpam-5861	172	21	.	.	PUNCT
ejpam-5861	173	1	[	[	X
ejpam-5861	173	2	37	37	NUM
ejpam-5861	173	3	]	]	PUNCT
ejpam-5861	173	4	the	the	DET
ejpam-5861	173	5	piece	piece	NOUN
ejpam-5861	173	6	-	-	PUNCT
ejpam-5861	173	7	wise	wise	ADJ
ejpam-5861	173	8	derivative	derivative	NOUN
ejpam-5861	173	9	of	of	ADP
ejpam-5861	173	10	order	order	NOUN
ejpam-5861	173	11	ε	ε	PROPN
ejpam-5861	173	12	∈	∈	PROPN
ejpam-5861	173	13	(	(	PUNCT
ejpam-5861	173	14	0	0	NUM
ejpam-5861	173	15	,	,	PUNCT
ejpam-5861	173	16	1	1	NUM
ejpam-5861	173	17	]	]	PUNCT
ejpam-5861	173	18	in	in	ADP
ejpam-5861	173	19	the	the	DET
ejpam-5861	173	20	caputo	caputo	PROPN
ejpam-5861	173	21	sense	sense	NOUN
ejpam-5861	173	22	of	of	ADP
ejpam-5861	173	23	a	a	DET
ejpam-5861	173	24	differentiable	differentiable	ADJ
ejpam-5861	173	25	function	function	NOUN
ejpam-5861	173	26	ϕ	ϕ	PROPN
ejpam-5861	173	27	∈	∈	PROPN
ejpam-5861	173	28	c[0	c[0	PROPN
ejpam-5861	173	29	,	,	PUNCT
ejpam-5861	173	30	t	t	PROPN
ejpam-5861	173	31	]	]	PUNCT
ejpam-5861	173	32	is	be	AUX
ejpam-5861	173	33	defined	define	VERB
ejpam-5861	173	34	by	by	ADP
ejpam-5861	173	35	pc	pc	NOUN
ejpam-5861	173	36	0	0	NUM
ejpam-5861	173	37	dε	dε	NOUN
ejpam-5861	173	38	tϕ(t	tϕ(t	NOUN
ejpam-5861	173	39	)	)	PUNCT
ejpam-5861	173	40	=	=	PUNCT
ejpam-5861	173	41			X
ejpam-5861	173	42	dϕ(t	dϕ(t	NUM
ejpam-5861	173	43	)	)	PUNCT
ejpam-5861	173	44	dt	dt	NOUN
ejpam-5861	173	45	,	,	PUNCT
ejpam-5861	173	46	with	with	ADP
ejpam-5861	173	47	t	t	PROPN
ejpam-5861	173	48	∈	∈	PROPN
ejpam-5861	173	49	∇1	∇1	PROPN
ejpam-5861	173	50	,	,	PUNCT
ejpam-5861	173	51	cdε	cdε	NOUN
ejpam-5861	173	52	0+ϕ(t	0+ϕ(t	NUM
ejpam-5861	173	53	)	)	PUNCT
ejpam-5861	173	54	,	,	PUNCT
ejpam-5861	173	55	with	with	ADP
ejpam-5861	173	56	t	t	PROPN
ejpam-5861	173	57	∈	∈	PROPN
ejpam-5861	173	58	∇2	∇2	PROPN
ejpam-5861	173	59	,	,	PUNCT
ejpam-5861	173	60	such	such	ADJ
ejpam-5861	173	61	that	that	DET
ejpam-5861	173	62	pcdε	pcdε	NOUN
ejpam-5861	173	63	0	0	PUNCT
ejpam-5861	173	64	+	+	NUM
ejpam-5861	173	65	represents	represent	VERB
ejpam-5861	173	66	ordinary	ordinary	ADJ
ejpam-5861	173	67	differentiation	differentiation	NOUN
ejpam-5861	173	68	in	in	ADP
ejpam-5861	173	69	∇1	∇1	PROPN
ejpam-5861	173	70	and	and	CCONJ
ejpam-5861	173	71	the	the	DET
ejpam-5861	173	72	caputo	caputo	PROPN
ejpam-5861	173	73	differentiation	differentiation	NOUN
ejpam-5861	173	74	on	on	ADP
ejpam-5861	173	75	∇2	∇2	PROPN
ejpam-5861	173	76	.	.	PUNCT
ejpam-5861	174	1	lemma	lemma	PROPN
ejpam-5861	174	2	2	2	NUM
ejpam-5861	174	3	.	.	PUNCT
ejpam-5861	175	1	[	[	X
ejpam-5861	175	2	25	25	NUM
ejpam-5861	175	3	]	]	PUNCT
ejpam-5861	175	4	the	the	DET
ejpam-5861	175	5	solution	solution	NOUN
ejpam-5861	175	6	of	of	ADP
ejpam-5861	175	7	the	the	DET
ejpam-5861	175	8	problem	problem	NOUN
ejpam-5861	175	9	pc	pc	NOUN
ejpam-5861	175	10	0	0	NUM
ejpam-5861	175	11	dε	dε	NOUN
ejpam-5861	175	12	tϕ(t	tϕ(t	NOUN
ejpam-5861	175	13	)	)	PUNCT
ejpam-5861	175	14	=	=	SYM
ejpam-5861	175	15	χ(t	χ(t	NOUN
ejpam-5861	175	16	)	)	PUNCT
ejpam-5861	175	17	,	,	PUNCT
ejpam-5861	175	18	ϕ(0	ϕ(0	PROPN
ejpam-5861	175	19	)	)	PUNCT
ejpam-5861	175	20	=	=	SYM
ejpam-5861	175	21	ϕ0	ϕ0	NOUN
ejpam-5861	175	22	,	,	PUNCT
ejpam-5861	175	23	is	be	AUX
ejpam-5861	175	24	given	give	VERB
ejpam-5861	175	25	by	by	ADP
ejpam-5861	175	26	ϕ(t	ϕ(t	NUM
ejpam-5861	175	27	)	)	PUNCT
ejpam-5861	176	1	=	=	PUNCT
ejpam-5861	177	1			PROPN
ejpam-5861	177	2	ϕ0	ϕ0	NOUN
ejpam-5861	177	3	+	+	CCONJ
ejpam-5861	177	4	∫	∫	PROPN
ejpam-5861	177	5	t1	t1	NOUN
ejpam-5861	177	6	0	0	NUM
ejpam-5861	178	1	χ(φ)dφ	χ(φ)dφ	PROPN
ejpam-5861	178	2	,	,	PUNCT
ejpam-5861	178	3	with	with	ADP
ejpam-5861	178	4	t	t	PROPN
ejpam-5861	178	5	∈	∈	PROPN
ejpam-5861	178	6	∇1	∇1	PROPN
ejpam-5861	178	7	,	,	PUNCT
ejpam-5861	178	8	ϕ(t1	ϕ(t1	ADP
ejpam-5861	178	9	)	)	PUNCT
ejpam-5861	179	1	+	+	CCONJ
ejpam-5861	179	2	1	1	NUM
ejpam-5861	179	3	γ(ε	γ(ε	PROPN
ejpam-5861	179	4	)	)	PUNCT
ejpam-5861	180	1	∫	∫	PROPN
ejpam-5861	180	2	t	t	PROPN
ejpam-5861	180	3	t1	t1	PROPN
ejpam-5861	180	4	(	(	PUNCT
ejpam-5861	180	5	t−	t−	PROPN
ejpam-5861	180	6	φ)ε−1χ(φ)dφ	φ)ε−1χ(φ)dφ	ADJ
ejpam-5861	180	7	,	,	PUNCT
ejpam-5861	180	8	with	with	ADP
ejpam-5861	180	9	t	t	PROPN
ejpam-5861	180	10	∈	∈	PROPN
ejpam-5861	180	11	∇2	∇2	PROPN
ejpam-5861	180	12	.	.	PUNCT
ejpam-5861	180	13	theorem	theorem	NOUN
ejpam-5861	180	14	1	1	NUM
ejpam-5861	180	15	.	.	PUNCT
ejpam-5861	181	1	[	[	X
ejpam-5861	181	2	14]let	14]let	NUM
ejpam-5861	181	3	d	d	PUNCT
ejpam-5861	181	4	⊂	⊂	PROPN
ejpam-5861	181	5	b	b	AUX
ejpam-5861	181	6	be	be	AUX
ejpam-5861	181	7	closed	close	VERB
ejpam-5861	181	8	convex	convex	NOUN
ejpam-5861	181	9	bounded	bound	VERB
ejpam-5861	181	10	set	set	VERB
ejpam-5861	181	11	such	such	ADJ
ejpam-5861	181	12	that	that	SCONJ
ejpam-5861	181	13	d	d	NOUN
ejpam-5861	181	14	=	=	PRON
ejpam-5861	181	15	{	{	PUNCT
ejpam-5861	181	16	z	z	PROPN
ejpam-5861	181	17	∈	∈	PROPN
ejpam-5861	181	18	b	b	PROPN
ejpam-5861	181	19	z	z	NOUN
ejpam-5861	181	20	=	=	SYM
ejpam-5861	181	21	λnz	λnz	NOUN
ejpam-5861	181	22	,	,	PUNCT
ejpam-5861	181	23	λ	λ	X
ejpam-5861	181	24	∈	∈	PROPN
ejpam-5861	182	1	[	[	X
ejpam-5861	182	2	0	0	NUM
ejpam-5861	182	3	,	,	PUNCT
ejpam-5861	182	4	1	1	NUM
ejpam-5861	182	5	]	]	PUNCT
ejpam-5861	182	6	}	}	PUNCT
ejpam-5861	182	7	,	,	PUNCT
ejpam-5861	182	8	,	,	PUNCT
ejpam-5861	182	9	then	then	ADV
ejpam-5861	182	10	n	n	CCONJ
ejpam-5861	182	11	:	:	PUNCT
ejpam-5861	182	12	d	d	X
ejpam-5861	182	13	→	→	SYM
ejpam-5861	182	14	b	b	PROPN
ejpam-5861	182	15	is	be	AUX
ejpam-5861	182	16	completely	completely	ADV
ejpam-5861	182	17	continuous	continuous	ADJ
ejpam-5861	182	18	operator	operator	NOUN
ejpam-5861	182	19	has	have	VERB
ejpam-5861	182	20	at	at	ADV
ejpam-5861	182	21	least	least	ADV
ejpam-5861	182	22	one	one	NUM
ejpam-5861	182	23	fixed	fix	VERB
ejpam-5861	182	24	point	point	NOUN
ejpam-5861	182	25	.	.	PUNCT
ejpam-5861	183	1	definition	definition	NOUN
ejpam-5861	183	2	8	8	NUM
ejpam-5861	183	3	.	.	PUNCT
ejpam-5861	184	1	according	accord	VERB
ejpam-5861	184	2	to	to	ADP
ejpam-5861	184	3	ulam	ulam	PROPN
ejpam-5861	184	4	[	[	X
ejpam-5861	184	5	12	12	NUM
ejpam-5861	184	6	,	,	PUNCT
ejpam-5861	184	7	33	33	NUM
ejpam-5861	184	8	,	,	PUNCT
ejpam-5861	184	9	39	39	NUM
ejpam-5861	184	10	]	]	PUNCT
ejpam-5861	184	11	”	"	PUNCT
ejpam-5861	184	12	near	near	ADP
ejpam-5861	184	13	every	every	DET
ejpam-5861	184	14	exact	exact	ADJ
ejpam-5861	184	15	function	function	NOUN
ejpam-5861	184	16	there	there	PRON
ejpam-5861	184	17	are	be	VERB
ejpam-5861	184	18	many	many	ADJ
ejpam-5861	184	19	approximation	approximation	NOUN
ejpam-5861	184	20	of	of	ADP
ejpam-5861	184	21	it	it	PRON
ejpam-5861	184	22	”	"	PUNCT
ejpam-5861	184	23	.	.	PUNCT
ejpam-5861	185	1	according	accord	VERB
ejpam-5861	185	2	to	to	ADP
ejpam-5861	185	3	their	their	PRON
ejpam-5861	185	4	definition	definition	NOUN
ejpam-5861	185	5	consider	consider	VERB
ejpam-5861	185	6	a	a	DET
ejpam-5861	185	7	functional	functional	ADJ
ejpam-5861	185	8	equation	equation	NOUN
ejpam-5861	185	9	given	give	VERB
ejpam-5861	185	10	by	by	ADP
ejpam-5861	185	11	nz	nz	NOUN
ejpam-5861	185	12	=	=	SYM
ejpam-5861	185	13	z	z	NOUN
ejpam-5861	185	14	is	be	AUX
ejpam-5861	185	15	uh	uh	INTJ
ejpam-5861	185	16	stable	stable	ADJ
ejpam-5861	185	17	if	if	SCONJ
ejpam-5861	185	18	for	for	ADP
ejpam-5861	185	19	any	any	DET
ejpam-5861	185	20	ε	ε	PROPN
ejpam-5861	185	21	>	>	X
ejpam-5861	185	22	0	0	PROPN
ejpam-5861	185	23	,	,	PUNCT
ejpam-5861	185	24	for	for	ADP
ejpam-5861	185	25	the	the	DET
ejpam-5861	185	26	inequality	inequality	NOUN
ejpam-5861	186	1	|z	|z	PROPN
ejpam-5861	186	2	−nz|	−nz|	PROPN
ejpam-5861	186	3	≤	≤	PROPN
ejpam-5861	186	4	ε	ε	PROPN
ejpam-5861	186	5	,	,	PUNCT
ejpam-5861	186	6	z	z	PROPN
ejpam-5861	186	7	∈	∈	PROPN
ejpam-5861	186	8	b	b	PROPN
ejpam-5861	186	9	,	,	PUNCT
ejpam-5861	186	10	and	and	CCONJ
ejpam-5861	186	11	constant	constant	ADJ
ejpam-5861	187	1	ln	ln	ADV
ejpam-5861	187	2	>	>	SYM
ejpam-5861	187	3	0	0	PUNCT
ejpam-5861	187	4	one	one	NUM
ejpam-5861	187	5	has	have	VERB
ejpam-5861	187	6	|z	|z	PROPN
ejpam-5861	187	7	−	−	PROPN
ejpam-5861	187	8	z∗|	z∗|	PROPN
ejpam-5861	187	9	≤	≤	NUM
ejpam-5861	187	10	lnε	lnε	NOUN
ejpam-5861	187	11	,	,	PUNCT
ejpam-5861	187	12	where	where	SCONJ
ejpam-5861	187	13	z∗	z∗	NOUN
ejpam-5861	187	14	is	be	AUX
ejpam-5861	187	15	the	the	DET
ejpam-5861	187	16	best	good	ADJ
ejpam-5861	187	17	approximate	approximate	ADJ
ejpam-5861	187	18	or	or	CCONJ
ejpam-5861	187	19	exact	exact	ADJ
ejpam-5861	187	20	solution	solution	NOUN
ejpam-5861	187	21	.	.	PUNCT
ejpam-5861	188	1	definition	definition	NOUN
ejpam-5861	188	2	9	9	NUM
ejpam-5861	188	3	.	.	PUNCT
ejpam-5861	188	4	sensitivity	sensitivity	NOUN
ejpam-5861	188	5	index[34	index[34	PROPN
ejpam-5861	188	6	]	]	X
ejpam-5861	188	7	it	it	PRON
ejpam-5861	188	8	is	be	AUX
ejpam-5861	188	9	an	an	DET
ejpam-5861	188	10	important	important	ADJ
ejpam-5861	188	11	threshold	threshold	NOUN
ejpam-5861	188	12	value	value	NOUN
ejpam-5861	188	13	calculated	calculate	VERB
ejpam-5861	188	14	by	by	ADP
ejpam-5861	188	15	the	the	DET
ejpam-5861	188	16	formula	formula	NOUN
ejpam-5861	188	17	given	give	VERB
ejpam-5861	188	18	by	by	ADP
ejpam-5861	188	19	sr0	sr0	NOUN
ejpam-5861	188	20	p	p	NOUN
ejpam-5861	188	21	=	=	PUNCT
ejpam-5861	188	22	p	p	NOUN
ejpam-5861	188	23	r0	r0	NOUN
ejpam-5861	188	24	∂r0	∂r0	ADP
ejpam-5861	188	25	∂p	∂p	PROPN
ejpam-5861	188	26	,	,	PUNCT
ejpam-5861	188	27	(	(	PUNCT
ejpam-5861	188	28	6	6	NUM
ejpam-5861	188	29	)	)	PUNCT
ejpam-5861	188	30	were	be	AUX
ejpam-5861	188	31	p	p	NOUN
ejpam-5861	188	32	is	be	AUX
ejpam-5861	188	33	the	the	DET
ejpam-5861	188	34	parameter	parameter	NOUN
ejpam-5861	188	35	describing	describe	VERB
ejpam-5861	188	36	the	the	DET
ejpam-5861	188	37	relation	relation	NOUN
ejpam-5861	188	38	of	of	ADP
ejpam-5861	188	39	r0	r0	NOUN
ejpam-5861	188	40	.	.	PUNCT
ejpam-5861	189	1	sensitivity	sensitivity	NOUN
ejpam-5861	189	2	index	index	NOUN
ejpam-5861	189	3	tells	tell	VERB
ejpam-5861	189	4	us	we	PRON
ejpam-5861	189	5	how	how	SCONJ
ejpam-5861	189	6	much	much	ADJ
ejpam-5861	189	7	be	be	VERB
ejpam-5861	189	8	the	the	DET
ejpam-5861	189	9	dynamic	dynamic	ADJ
ejpam-5861	189	10	effected	effect	VERB
ejpam-5861	189	11	by	by	ADP
ejpam-5861	189	12	increasing	increase	VERB
ejpam-5861	189	13	or	or	CCONJ
ejpam-5861	189	14	decreasing	decrease	VERB
ejpam-5861	189	15	the	the	DET
ejpam-5861	189	16	values	value	NOUN
ejpam-5861	189	17	of	of	ADP
ejpam-5861	189	18	parameters	parameter	NOUN
ejpam-5861	189	19	.	.	PUNCT
ejpam-5861	190	1	s.	s.	PROPN
ejpam-5861	190	2	naz	naz	PROPN
ejpam-5861	190	3	et	et	PROPN
ejpam-5861	190	4	al	al	PROPN
ejpam-5861	190	5	.	.	PUNCT
ejpam-5861	190	6	/	/	SYM
ejpam-5861	190	7	eur	eur	PROPN
ejpam-5861	190	8	.	.	PUNCT
ejpam-5861	191	1	j.	j.	PROPN
ejpam-5861	191	2	pure	pure	PROPN
ejpam-5861	191	3	appl	appl	PROPN
ejpam-5861	191	4	.	.	PROPN
ejpam-5861	191	5	math	math	PROPN
ejpam-5861	191	6	,	,	PUNCT
ejpam-5861	191	7	18	18	NUM
ejpam-5861	191	8	(	(	PUNCT
ejpam-5861	191	9	2	2	NUM
ejpam-5861	191	10	)	)	PUNCT
ejpam-5861	191	11	(	(	PUNCT
ejpam-5861	191	12	2025	2025	NUM
ejpam-5861	191	13	)	)	PUNCT
ejpam-5861	191	14	,	,	PUNCT
ejpam-5861	191	15	5861	5861	NUM
ejpam-5861	191	16	9	9	NUM
ejpam-5861	191	17	of	of	ADP
ejpam-5861	191	18	33	33	NUM
ejpam-5861	191	19	3	3	NUM
ejpam-5861	191	20	.	.	PUNCT
ejpam-5861	192	1	fundamental	fundamental	ADJ
ejpam-5861	192	2	results	result	NOUN
ejpam-5861	192	3	of	of	ADP
ejpam-5861	192	4	model	model	NOUN
ejpam-5861	192	5	(	(	PUNCT
ejpam-5861	192	6	2	2	NUM
ejpam-5861	192	7	)	)	PUNCT
ejpam-5861	192	8	here	here	ADV
ejpam-5861	192	9	we	we	PRON
ejpam-5861	192	10	provide	provide	VERB
ejpam-5861	192	11	the	the	DET
ejpam-5861	192	12	positivity	positivity	NOUN
ejpam-5861	192	13	,	,	PUNCT
ejpam-5861	192	14	boundedness	boundedness	NOUN
ejpam-5861	192	15	,	,	PUNCT
ejpam-5861	192	16	df	df	PROPN
ejpam-5861	192	17	and	and	CCONJ
ejpam-5861	192	18	ee	ee	PROPN
ejpam-5861	192	19	points	point	NOUN
ejpam-5861	192	20	.	.	PUNCT
ejpam-5861	193	1	also	also	ADV
ejpam-5861	193	2	we	we	PRON
ejpam-5861	193	3	compute	compute	VERB
ejpam-5861	193	4	the	the	DET
ejpam-5861	193	5	basic	basic	ADJ
ejpam-5861	193	6	reproductive	reproductive	ADJ
ejpam-5861	193	7	number	number	NOUN
ejpam-5861	193	8	and	and	CCONJ
ejpam-5861	193	9	presents	present	VERB
ejpam-5861	193	10	its	its	PRON
ejpam-5861	193	11	3d	3d	NUM
ejpam-5861	193	12	profile	profile	NOUN
ejpam-5861	193	13	.	.	PUNCT
ejpam-5861	194	1	sensitivity	sensitivity	NOUN
ejpam-5861	194	2	is	be	AUX
ejpam-5861	194	3	also	also	ADV
ejpam-5861	194	4	discussed	discuss	VERB
ejpam-5861	194	5	here	here	ADV
ejpam-5861	194	6	.	.	PUNCT
ejpam-5861	195	1	theorem	theorem	VERB
ejpam-5861	195	2	2	2	NUM
ejpam-5861	195	3	.	.	PUNCT
ejpam-5861	196	1	all	all	DET
ejpam-5861	196	2	solutions	solution	NOUN
ejpam-5861	196	3	of	of	ADP
ejpam-5861	196	4	model	model	NOUN
ejpam-5861	196	5	(	(	PUNCT
ejpam-5861	196	6	2	2	NUM
ejpam-5861	196	7	)	)	PUNCT
ejpam-5861	196	8	are	be	AUX
ejpam-5861	196	9	bounded	bound	VERB
ejpam-5861	196	10	and	and	CCONJ
ejpam-5861	196	11	inclined	incline	VERB
ejpam-5861	196	12	to	to	ADP
ejpam-5861	196	13	a	a	DET
ejpam-5861	196	14	feasible	feasible	ADJ
ejpam-5861	196	15	region	region	NOUN
ejpam-5861	196	16	described	describe	VERB
ejpam-5861	196	17	by	by	ADP
ejpam-5861	196	18	ω	ω	PROPN
ejpam-5861	196	19	=	=	SYM
ejpam-5861	196	20	{	{	PUNCT
ejpam-5861	196	21	(	(	PUNCT
ejpam-5861	196	22	s	s	X
ejpam-5861	196	23	,	,	PUNCT
ejpam-5861	196	24	v	v	NOUN
ejpam-5861	196	25	,	,	PUNCT
ejpam-5861	196	26	e	e	NOUN
ejpam-5861	196	27	,	,	PUNCT
ejpam-5861	196	28	i	i	PRON
ejpam-5861	196	29	,	,	PUNCT
ejpam-5861	196	30	q	q	NOUN
ejpam-5861	196	31	,	,	PUNCT
ejpam-5861	196	32	r	r	NOUN
ejpam-5861	196	33	)	)	PUNCT
ejpam-5861	196	34	∈	∈	NOUN
ejpam-5861	196	35	r6	r6	NOUN
ejpam-5861	197	1	+	+	PROPN
ejpam-5861	197	2	s	s	NOUN
ejpam-5861	197	3	+	+	X
ejpam-5861	197	4	v	v	NOUN
ejpam-5861	197	5	+	+	CCONJ
ejpam-5861	197	6	e	e	NOUN
ejpam-5861	198	1	+	+	CCONJ
ejpam-5861	198	2	i	i	PRON
ejpam-5861	198	3	+	+	VERB
ejpam-5861	198	4	q+r	q+r	VERB
ejpam-5861	198	5	≤	≤	NUM
ejpam-5861	198	6	λ	λ	X
ejpam-5861	198	7	d	d	NOUN
ejpam-5861	198	8	}	}	PUNCT
ejpam-5861	198	9	.	.	PUNCT
ejpam-5861	199	1	proof	proof	NOUN
ejpam-5861	199	2	.	.	PUNCT
ejpam-5861	200	1	let	let	VERB
ejpam-5861	200	2	m	m	PRON
ejpam-5861	200	3	be	be	AUX
ejpam-5861	200	4	the	the	DET
ejpam-5861	200	5	total	total	ADJ
ejpam-5861	200	6	pollution	pollution	NOUN
ejpam-5861	200	7	at	at	ADP
ejpam-5861	200	8	time	time	NOUN
ejpam-5861	200	9	t	t	PROPN
ejpam-5861	200	10	>	>	X
ejpam-5861	200	11	0	0	PROPN
ejpam-5861	200	12	,	,	PUNCT
ejpam-5861	200	13	such	such	ADJ
ejpam-5861	200	14	that	that	SCONJ
ejpam-5861	200	15	m(t	m(t	NOUN
ejpam-5861	200	16	)	)	PUNCT
ejpam-5861	200	17	=	=	SYM
ejpam-5861	200	18	s(t	s(t	PROPN
ejpam-5861	200	19	)	)	PUNCT
ejpam-5861	200	20	+	+	X
ejpam-5861	200	21	v	v	X
ejpam-5861	200	22	(	(	PUNCT
ejpam-5861	200	23	t	t	PROPN
ejpam-5861	200	24	)	)	PUNCT
ejpam-5861	200	25	+	+	NOUN
ejpam-5861	200	26	e(t	e(t	NOUN
ejpam-5861	200	27	)	)	PUNCT
ejpam-5861	200	28	+	+	CCONJ
ejpam-5861	200	29	i(t	i(t	NOUN
ejpam-5861	200	30	)	)	PUNCT
ejpam-5861	201	1	+	+	NOUN
ejpam-5861	201	2	q(t	q(t	ADJ
ejpam-5861	201	3	)	)	PUNCT
ejpam-5861	201	4	+	+	NOUN
ejpam-5861	201	5	r(t	r(t	NOUN
ejpam-5861	201	6	)	)	PUNCT
ejpam-5861	201	7	.	.	PUNCT
ejpam-5861	202	1	(	(	PUNCT
ejpam-5861	202	2	7	7	X
ejpam-5861	202	3	)	)	PUNCT
ejpam-5861	202	4	applying	apply	VERB
ejpam-5861	202	5	pc	pc	NOUN
ejpam-5861	202	6	0	0	NUM
ejpam-5861	202	7	dε	dε	VERB
ejpam-5861	202	8	t	t	NOUN
ejpam-5861	202	9	to	to	ADP
ejpam-5861	202	10	both	both	DET
ejpam-5861	202	11	sides	side	NOUN
ejpam-5861	202	12	of	of	ADP
ejpam-5861	202	13	(	(	PUNCT
ejpam-5861	202	14	7	7	X
ejpam-5861	202	15	)	)	PUNCT
ejpam-5861	202	16	gives	give	VERB
ejpam-5861	202	17	pc	pc	NOUN
ejpam-5861	202	18	0	0	NUM
ejpam-5861	202	19	dε	dε	VERB
ejpam-5861	202	20	t	t	NOUN
ejpam-5861	202	21	[	[	X
ejpam-5861	202	22	m(t	m(t	NOUN
ejpam-5861	202	23	)	)	PUNCT
ejpam-5861	202	24	]	]	PUNCT
ejpam-5861	203	1	=	=	PUNCT
ejpam-5861	203	2	pc	pc	NOUN
ejpam-5861	203	3	0	0	NUM
ejpam-5861	203	4	dε	dε	VERB
ejpam-5861	203	5	t	t	NOUN
ejpam-5861	203	6	[	[	X
ejpam-5861	203	7	s(t	s(t	PROPN
ejpam-5861	203	8	)	)	PUNCT
ejpam-5861	203	9	]	]	PUNCT
ejpam-5861	204	1	+	+	CCONJ
ejpam-5861	204	2	pc	pc	NOUN
ejpam-5861	204	3	0	0	NUM
ejpam-5861	204	4	dε	dε	VERB
ejpam-5861	204	5	t	t	NOUN
ejpam-5861	205	1	[	[	X
ejpam-5861	205	2	v	v	X
ejpam-5861	205	3	(	(	PUNCT
ejpam-5861	205	4	t	t	PROPN
ejpam-5861	205	5	)	)	PUNCT
ejpam-5861	205	6	]	]	PUNCT
ejpam-5861	206	1	+	+	PUNCT
ejpam-5861	206	2	pc	pc	NOUN
ejpam-5861	206	3	0	0	NUM
ejpam-5861	206	4	dε	dε	VERB
ejpam-5861	206	5	t	t	NOUN
ejpam-5861	206	6	[	[	X
ejpam-5861	206	7	e(t	e(t	NOUN
ejpam-5861	206	8	)	)	PUNCT
ejpam-5861	206	9	]	]	PUNCT
ejpam-5861	207	1	+	+	PUNCT
ejpam-5861	207	2	pc	pc	NOUN
ejpam-5861	207	3	0	0	NUM
ejpam-5861	207	4	dε	dε	VERB
ejpam-5861	207	5	t	t	NOUN
ejpam-5861	207	6	[	[	X
ejpam-5861	207	7	i(t	i(t	NOUN
ejpam-5861	207	8	)	)	PUNCT
ejpam-5861	207	9	]	]	PUNCT
ejpam-5861	208	1	(	(	PUNCT
ejpam-5861	208	2	8)	8)	NUM
ejpam-5861	208	3	+	+	CCONJ
ejpam-5861	208	4	pc	pc	NOUN
ejpam-5861	208	5	0	0	NUM
ejpam-5861	208	6	dε	dε	VERB
ejpam-5861	208	7	t	t	NOUN
ejpam-5861	209	1	[	[	X
ejpam-5861	209	2	q(t	q(t	X
ejpam-5861	209	3	)	)	PUNCT
ejpam-5861	209	4	]	]	PUNCT
ejpam-5861	210	1	+	+	PUNCT
ejpam-5861	210	2	pc	pc	NOUN
ejpam-5861	210	3	0	0	NUM
ejpam-5861	210	4	dε	dε	VERB
ejpam-5861	210	5	t	t	NOUN
ejpam-5861	210	6	[	[	X
ejpam-5861	210	7	r(t	r(t	NOUN
ejpam-5861	210	8	)	)	PUNCT
ejpam-5861	210	9	]	]	PUNCT
ejpam-5861	210	10	.	.	PUNCT
ejpam-5861	211	1	using	use	VERB
ejpam-5861	211	2	the	the	DET
ejpam-5861	211	3	corresponding	correspond	VERB
ejpam-5861	211	4	values	value	NOUN
ejpam-5861	211	5	from	from	ADP
ejpam-5861	211	6	(	(	PUNCT
ejpam-5861	211	7	2	2	NUM
ejpam-5861	211	8	)	)	PUNCT
ejpam-5861	211	9	in	in	ADP
ejpam-5861	211	10	(	(	PUNCT
ejpam-5861	211	11	7	7	NUM
ejpam-5861	211	12	)	)	PUNCT
ejpam-5861	211	13	and	and	CCONJ
ejpam-5861	211	14	simplifying	simplify	VERB
ejpam-5861	211	15	,	,	PUNCT
ejpam-5861	211	16	we	we	PRON
ejpam-5861	211	17	get	get	VERB
ejpam-5861	211	18	pc	pc	NOUN
ejpam-5861	211	19	0	0	NUM
ejpam-5861	211	20	dε	dε	VERB
ejpam-5861	211	21	t	t	NOUN
ejpam-5861	211	22	[	[	X
ejpam-5861	211	23	m(t	m(t	NOUN
ejpam-5861	211	24	)	)	PUNCT
ejpam-5861	211	25	]	]	PUNCT
ejpam-5861	212	1	=	=	PUNCT
ejpam-5861	212	2	λ−	λ−	PROPN
ejpam-5861	212	3	d(s	d(s	PROPN
ejpam-5861	212	4	+	+	CCONJ
ejpam-5861	212	5	e	e	X
ejpam-5861	212	6	+	+	NOUN
ejpam-5861	212	7	v	v	X
ejpam-5861	212	8	+	+	CCONJ
ejpam-5861	212	9	i	i	PRON
ejpam-5861	212	10	+	+	NOUN
ejpam-5861	212	11	q+r	q+r	NUM
ejpam-5861	212	12	)	)	PUNCT
ejpam-5861	213	1	=	=	SYM
ejpam-5861	214	1	λ−	λ−	PROPN
ejpam-5861	214	2	dm	dm	X
ejpam-5861	214	3	.	.	PUNCT
ejpam-5861	215	1	(	(	PUNCT
ejpam-5861	215	2	9	9	X
ejpam-5861	215	3	)	)	PUNCT
ejpam-5861	215	4	we	we	PRON
ejpam-5861	215	5	can	can	AUX
ejpam-5861	215	6	write	write	VERB
ejpam-5861	215	7	(	(	PUNCT
ejpam-5861	215	8	9	9	NUM
ejpam-5861	215	9	)	)	PUNCT
ejpam-5861	215	10	pc	pc	NOUN
ejpam-5861	215	11	0	0	NUM
ejpam-5861	215	12	dε	dε	VERB
ejpam-5861	215	13	t	t	NOUN
ejpam-5861	215	14	[	[	X
ejpam-5861	215	15	m(t	m(t	NOUN
ejpam-5861	215	16	)	)	PUNCT
ejpam-5861	215	17	]	]	PUNCT
ejpam-5861	216	1	=	=	PUNCT
ejpam-5861	216	2	dm	dm	X
ejpam-5861	216	3	dt	dt	NOUN
ejpam-5861	216	4	=	=	SYM
ejpam-5861	216	5	λ−	λ−	PROPN
ejpam-5861	216	6	dm	dm	PROPN
ejpam-5861	216	7	,	,	PUNCT
ejpam-5861	216	8	t	t	PROPN
ejpam-5861	216	9	∈	∈	PROPN
ejpam-5861	216	10	∇1	∇1	PROPN
ejpam-5861	216	11	,	,	PUNCT
ejpam-5861	216	12	c	c	NOUN
ejpam-5861	216	13	0d	0d	X
ejpam-5861	216	14	ε	ε	PROPN
ejpam-5861	216	15	t	t	PROPN
ejpam-5861	217	1	[	[	X
ejpam-5861	217	2	m(t	m(t	NOUN
ejpam-5861	217	3	)	)	PUNCT
ejpam-5861	217	4	]	]	PUNCT
ejpam-5861	218	1	=	=	PUNCT
ejpam-5861	218	2	λ−	λ−	PROPN
ejpam-5861	218	3	dm	dm	PROPN
ejpam-5861	218	4	,	,	PUNCT
ejpam-5861	218	5	t	t	PROPN
ejpam-5861	218	6	∈	∈	PROPN
ejpam-5861	218	7	∇2	∇2	PROPN
ejpam-5861	218	8	.	.	PUNCT
ejpam-5861	219	1	(	(	PUNCT
ejpam-5861	219	2	10	10	NUM
ejpam-5861	219	3	)	)	PUNCT
ejpam-5861	219	4	applying	apply	VERB
ejpam-5861	219	5	laplace	laplace	NOUN
ejpam-5861	219	6	transform	transform	NOUN
ejpam-5861	219	7	in	in	ADP
ejpam-5861	219	8	(	(	PUNCT
ejpam-5861	219	9	15	15	NUM
ejpam-5861	219	10	)	)	PUNCT
ejpam-5861	219	11	yields	yield	NOUN
ejpam-5861	219	12	that	that	SCONJ
ejpam-5861	219	13	m(t	m(t	NOUN
ejpam-5861	219	14	)	)	PUNCT
ejpam-5861	220	1	=	=	PUNCT
ejpam-5861	220	2	λ	λ	X
ejpam-5861	220	3	d	d	X
ejpam-5861	220	4	−m0	−m0	PROPN
ejpam-5861	220	5	exp(−dt	exp(−dt	PROPN
ejpam-5861	220	6	)	)	PUNCT
ejpam-5861	220	7	,	,	PUNCT
ejpam-5861	220	8	t	t	PROPN
ejpam-5861	220	9	∈	∈	PROPN
ejpam-5861	220	10	∇1	∇1	PROPN
ejpam-5861	220	11	,	,	PUNCT
ejpam-5861	220	12	λ	λ	X
ejpam-5861	220	13	d	d	X
ejpam-5861	220	14	(	(	PUNCT
ejpam-5861	220	15	1−eε(−dtε	1−eε(−dtε	NUM
ejpam-5861	220	16	)	)	PUNCT
ejpam-5861	220	17	)	)	PUNCT
ejpam-5861	221	1	+	+	VERB
ejpam-5861	221	2	eε(−dtε	eε(−dtε	NOUN
ejpam-5861	221	3	)	)	PUNCT
ejpam-5861	221	4	,	,	PUNCT
ejpam-5861	221	5	t	t	PROPN
ejpam-5861	221	6	∈	∈	PROPN
ejpam-5861	221	7	∇2	∇2	PROPN
ejpam-5861	221	8	.	.	PUNCT
ejpam-5861	222	1	(	(	PUNCT
ejpam-5861	222	2	11	11	NUM
ejpam-5861	222	3	)	)	PUNCT
ejpam-5861	222	4	hence	hence	ADV
ejpam-5861	222	5	at	at	ADP
ejpam-5861	222	6	t	t	PROPN
ejpam-5861	222	7	→	→	SYM
ejpam-5861	222	8	∞	∞	PROPN
ejpam-5861	222	9	,	,	PUNCT
ejpam-5861	222	10	we	we	PRON
ejpam-5861	222	11	get	get	VERB
ejpam-5861	222	12	from	from	ADP
ejpam-5861	222	13	(	(	PUNCT
ejpam-5861	222	14	11	11	NUM
ejpam-5861	222	15	)	)	PUNCT
ejpam-5861	222	16	m(t	m(t	NOUN
ejpam-5861	222	17	)	)	PUNCT
ejpam-5861	222	18	≤	≤	PUNCT
ejpam-5861	223	1	λ	λ	PROPN
ejpam-5861	223	2	d	d	PROPN
ejpam-5861	223	3	.	.	PUNCT
ejpam-5861	224	1	theorem	theorem	NOUN
ejpam-5861	224	2	3	3	NUM
ejpam-5861	224	3	.	.	PUNCT
ejpam-5861	225	1	all	all	DET
ejpam-5861	225	2	the	the	DET
ejpam-5861	225	3	solutions	solution	NOUN
ejpam-5861	225	4	(	(	PUNCT
ejpam-5861	225	5	s	s	X
ejpam-5861	225	6	,	,	PUNCT
ejpam-5861	225	7	v	v	NOUN
ejpam-5861	225	8	,	,	PUNCT
ejpam-5861	225	9	e	e	NOUN
ejpam-5861	225	10	,	,	PUNCT
ejpam-5861	225	11	i	i	PRON
ejpam-5861	225	12	,	,	PUNCT
ejpam-5861	225	13	q	q	NOUN
ejpam-5861	225	14	,	,	PUNCT
ejpam-5861	225	15	r	r	NOUN
ejpam-5861	225	16	,	,	PUNCT
ejpam-5861	225	17	d	d	NOUN
ejpam-5861	225	18	)	)	PUNCT
ejpam-5861	225	19	of	of	ADP
ejpam-5861	225	20	model	model	NOUN
ejpam-5861	225	21	(	(	PUNCT
ejpam-5861	225	22	2	2	NUM
ejpam-5861	225	23	)	)	PUNCT
ejpam-5861	225	24	are	be	AUX
ejpam-5861	225	25	non	non	ADJ
ejpam-5861	225	26	-	-	ADJ
ejpam-5861	225	27	negative	negative	ADJ
ejpam-5861	225	28	for	for	ADP
ejpam-5861	225	29	t	t	PROPN
ejpam-5861	225	30	>	>	X
ejpam-5861	225	31	0	0	PUNCT
ejpam-5861	225	32	with	with	ADP
ejpam-5861	225	33	positive	positive	ADJ
ejpam-5861	225	34	initial	initial	ADJ
ejpam-5861	225	35	condition	condition	NOUN
ejpam-5861	225	36	(	(	PUNCT
ejpam-5861	225	37	s0	s0	PROPN
ejpam-5861	225	38	,	,	PUNCT
ejpam-5861	225	39	v0	v0	PROPN
ejpam-5861	225	40	,	,	PUNCT
ejpam-5861	225	41	e0	e0	PROPN
ejpam-5861	225	42	,	,	PUNCT
ejpam-5861	225	43	i0	i0	PROPN
ejpam-5861	225	44	,	,	PUNCT
ejpam-5861	225	45	q0	q0	PROPN
ejpam-5861	225	46	,	,	PUNCT
ejpam-5861	225	47	r0	r0	NOUN
ejpam-5861	225	48	,	,	PUNCT
ejpam-5861	225	49	d0	d0	NOUN
ejpam-5861	225	50	)	)	PUNCT
ejpam-5861	225	51	>	>	X
ejpam-5861	225	52	0	0	X
ejpam-5861	225	53	.	.	PUNCT
ejpam-5861	226	1	s.	s.	PROPN
ejpam-5861	226	2	naz	naz	PROPN
ejpam-5861	226	3	et	et	PROPN
ejpam-5861	226	4	al	al	PROPN
ejpam-5861	226	5	.	.	PUNCT
ejpam-5861	226	6	/	/	SYM
ejpam-5861	226	7	eur	eur	PROPN
ejpam-5861	226	8	.	.	PUNCT
ejpam-5861	227	1	j.	j.	PROPN
ejpam-5861	227	2	pure	pure	PROPN
ejpam-5861	227	3	appl	appl	PROPN
ejpam-5861	227	4	.	.	PROPN
ejpam-5861	227	5	math	math	PROPN
ejpam-5861	227	6	,	,	PUNCT
ejpam-5861	227	7	18	18	NUM
ejpam-5861	227	8	(	(	PUNCT
ejpam-5861	227	9	2	2	NUM
ejpam-5861	227	10	)	)	PUNCT
ejpam-5861	227	11	(	(	PUNCT
ejpam-5861	227	12	2025	2025	NUM
ejpam-5861	227	13	)	)	PUNCT
ejpam-5861	227	14	,	,	PUNCT
ejpam-5861	227	15	5861	5861	NUM
ejpam-5861	227	16	10	10	NUM
ejpam-5861	227	17	of	of	ADP
ejpam-5861	227	18	33	33	NUM
ejpam-5861	227	19	proof	proof	NOUN
ejpam-5861	227	20	.	.	PUNCT
ejpam-5861	228	1	from	from	ADP
ejpam-5861	228	2	model	model	NOUN
ejpam-5861	228	3	(	(	PUNCT
ejpam-5861	228	4	2	2	NUM
ejpam-5861	228	5	)	)	PUNCT
ejpam-5861	228	6	,	,	PUNCT
ejpam-5861	228	7	we	we	PRON
ejpam-5861	228	8	have	have	VERB
ejpam-5861	228	9	pc	pc	NOUN
ejpam-5861	228	10	0	0	NUM
ejpam-5861	228	11	dε	dε	VERB
ejpam-5861	228	12	t	t	NOUN
ejpam-5861	228	13	[	[	X
ejpam-5861	228	14	s(t	s(t	PROPN
ejpam-5861	228	15	)	)	PUNCT
ejpam-5861	228	16	]	]	PUNCT
ejpam-5861	229	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	229	2	s=0	s=0	NOUN
ejpam-5861	229	3	=	=	PUNCT
ejpam-5861	229	4	λ	λ	X
ejpam-5861	229	5	>	>	X
ejpam-5861	229	6	0	0	NUM
ejpam-5861	229	7	,	,	PUNCT
ejpam-5861	229	8	pc	pc	NOUN
ejpam-5861	229	9	0	0	NUM
ejpam-5861	229	10	dε	dε	VERB
ejpam-5861	229	11	t	t	NOUN
ejpam-5861	229	12	[	[	X
ejpam-5861	229	13	v	v	X
ejpam-5861	229	14	(	(	PUNCT
ejpam-5861	229	15	t	t	PROPN
ejpam-5861	229	16	)	)	PUNCT
ejpam-5861	229	17	]	]	PUNCT
ejpam-5861	229	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	229	19	v=0	v=0	PUNCT
ejpam-5861	229	20	=	=	SYM
ejpam-5861	229	21	0	0	NUM
ejpam-5861	229	22	,	,	PUNCT
ejpam-5861	229	23	pc	pc	NOUN
ejpam-5861	229	24	0	0	NUM
ejpam-5861	229	25	dε	dε	VERB
ejpam-5861	229	26	t	t	NOUN
ejpam-5861	230	1	[	[	X
ejpam-5861	230	2	e(t	e(t	NOUN
ejpam-5861	230	3	)	)	PUNCT
ejpam-5861	230	4	]	]	PUNCT
ejpam-5861	231	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	231	2	e=0	e=0	PROPN
ejpam-5861	231	3	=	=	SYM
ejpam-5861	231	4	0	0	NUM
ejpam-5861	231	5	,	,	PUNCT
ejpam-5861	231	6	pc	pc	NOUN
ejpam-5861	231	7	0	0	NUM
ejpam-5861	231	8	dε	dε	VERB
ejpam-5861	231	9	t	t	NOUN
ejpam-5861	231	10	[	[	X
ejpam-5861	231	11	i(t	i(t	NOUN
ejpam-5861	231	12	)	)	PUNCT
ejpam-5861	231	13	]	]	PUNCT
ejpam-5861	231	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	231	15	i=0	i=0	PROPN
ejpam-5861	231	16	=	=	SYM
ejpam-5861	231	17	0	0	NUM
ejpam-5861	231	18	,	,	PUNCT
ejpam-5861	231	19	pc	pc	NOUN
ejpam-5861	231	20	0	0	NUM
ejpam-5861	231	21	dε	dε	VERB
ejpam-5861	231	22	t	t	NOUN
ejpam-5861	232	1	[	[	X
ejpam-5861	232	2	q(t	q(t	X
ejpam-5861	232	3	)	)	PUNCT
ejpam-5861	232	4	]	]	PUNCT
ejpam-5861	232	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	232	6	q=0	q=0	NOUN
ejpam-5861	233	1	=	=	NOUN
ejpam-5861	233	2	0	0	NUM
ejpam-5861	233	3	,	,	PUNCT
ejpam-5861	233	4	pc	pc	NOUN
ejpam-5861	233	5	0	0	NUM
ejpam-5861	233	6	dε	dε	VERB
ejpam-5861	233	7	t	t	NOUN
ejpam-5861	233	8	[	[	X
ejpam-5861	233	9	r(t	r(t	NOUN
ejpam-5861	233	10	)	)	PUNCT
ejpam-5861	233	11	]	]	PUNCT
ejpam-5861	234	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	234	2	r=0	r=0	PROPN
ejpam-5861	234	3	=	=	SYM
ejpam-5861	234	4	0	0	NUM
ejpam-5861	234	5	,	,	PUNCT
ejpam-5861	234	6	pc	pc	NOUN
ejpam-5861	234	7	0	0	NUM
ejpam-5861	234	8	dε	dε	VERB
ejpam-5861	234	9	t	t	X
ejpam-5861	234	10	[	[	X
ejpam-5861	234	11	d(t	d(t	PROPN
ejpam-5861	234	12	)	)	PUNCT
ejpam-5861	234	13	]	]	PUNCT
ejpam-5861	235	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	235	2	d=0	d=0	PROPN
ejpam-5861	235	3	=	=	PROPN
ejpam-5861	235	4	0	0	NUM
ejpam-5861	235	5	,	,	PUNCT
ejpam-5861	235	6	from	from	ADP
ejpam-5861	235	7	(	(	PUNCT
ejpam-5861	235	8	12	12	NUM
ejpam-5861	235	9	)	)	PUNCT
ejpam-5861	235	10	,	,	PUNCT
ejpam-5861	235	11	one	one	PRON
ejpam-5861	235	12	see	see	VERB
ejpam-5861	235	13	that	that	DET
ejpam-5861	235	14	pc	pc	NOUN
ejpam-5861	235	15	0	0	NUM
ejpam-5861	235	16	dε	dε	VERB
ejpam-5861	235	17	t	t	NOUN
ejpam-5861	235	18	[	[	X
ejpam-5861	235	19	s(t	s(t	PROPN
ejpam-5861	235	20	)	)	PUNCT
ejpam-5861	235	21	]	]	PUNCT
ejpam-5861	235	22	>	>	X
ejpam-5861	235	23	0	0	NUM
ejpam-5861	235	24	which	which	PRON
ejpam-5861	235	25	yields	yield	VERB
ejpam-5861	235	26	that	that	SCONJ
ejpam-5861	235	27	s(t	s(t	PROPN
ejpam-5861	235	28	)	)	PUNCT
ejpam-5861	235	29	>	>	X
ejpam-5861	235	30	0	0	NUM
ejpam-5861	235	31	,	,	PUNCT
ejpam-5861	235	32	at	at	ADP
ejpam-5861	235	33	t	t	PROPN
ejpam-5861	235	34	>	>	X
ejpam-5861	235	35	0	0	PROPN
ejpam-5861	235	36	,	,	PUNCT
ejpam-5861	235	37	hence	hence	ADV
ejpam-5861	235	38	we	we	PRON
ejpam-5861	235	39	conclude	conclude	VERB
ejpam-5861	235	40	that	that	SCONJ
ejpam-5861	235	41	(	(	PUNCT
ejpam-5861	235	42	s	s	X
ejpam-5861	235	43	,	,	PUNCT
ejpam-5861	235	44	v	v	NOUN
ejpam-5861	235	45	,	,	PUNCT
ejpam-5861	235	46	e	e	NOUN
ejpam-5861	235	47	,	,	PUNCT
ejpam-5861	235	48	i	i	PRON
ejpam-5861	235	49	,	,	PUNCT
ejpam-5861	235	50	q	q	NOUN
ejpam-5861	235	51	,	,	PUNCT
ejpam-5861	235	52	r	r	NOUN
ejpam-5861	235	53	,	,	PUNCT
ejpam-5861	235	54	d	d	NOUN
ejpam-5861	235	55	)	)	PUNCT
ejpam-5861	235	56	>	>	X
ejpam-5861	235	57	0	0	PUNCT
ejpam-5861	236	1	at	at	ADP
ejpam-5861	236	2	t	t	PROPN
ejpam-5861	236	3	>	>	X
ejpam-5861	236	4	0	0	X
ejpam-5861	236	5	.	.	PUNCT
ejpam-5861	237	1	hence	hence	ADV
ejpam-5861	237	2	positivity	positivity	NOUN
ejpam-5861	237	3	condition	condition	NOUN
ejpam-5861	237	4	derived	derive	VERB
ejpam-5861	237	5	.	.	PUNCT
ejpam-5861	238	1	further	far	ADV
ejpam-5861	238	2	,	,	PUNCT
ejpam-5861	238	3	the	the	DET
ejpam-5861	238	4	dfe	dfe	PROPN
ejpam-5861	238	5	and	and	CCONJ
ejpam-5861	238	6	endemic	endemic	ADJ
ejpam-5861	238	7	equilibrium	equilibrium	NOUN
ejpam-5861	238	8	points	point	NOUN
ejpam-5861	238	9	can	can	AUX
ejpam-5861	238	10	be	be	AUX
ejpam-5861	238	11	computed	compute	VERB
ejpam-5861	238	12	by	by	ADP
ejpam-5861	238	13	using	use	VERB
ejpam-5861	238	14	the	the	DET
ejpam-5861	238	15	results	result	NOUN
ejpam-5861	238	16	of	of	ADP
ejpam-5861	238	17	[	[	X
ejpam-5861	238	18	29	29	NUM
ejpam-5861	238	19	]	]	PUNCT
ejpam-5861	238	20	as	as	SCONJ
ejpam-5861	238	21	follows	follow	VERB
ejpam-5861	238	22	:	:	PUNCT
ejpam-5861	238	23	dfe	dfe	PROPN
ejpam-5861	238	24	from	from	ADP
ejpam-5861	238	25	(	(	PUNCT
ejpam-5861	238	26	2	2	X
ejpam-5861	238	27	)	)	PUNCT
ejpam-5861	238	28	putting	put	VERB
ejpam-5861	238	29	left	left	ADJ
ejpam-5861	238	30	sides	side	NOUN
ejpam-5861	238	31	equal	equal	ADJ
ejpam-5861	238	32	to	to	ADP
ejpam-5861	238	33	zeros	zero	NOUN
ejpam-5861	238	34	,	,	PUNCT
ejpam-5861	238	35	that	that	PRON
ejpam-5861	238	36	is	be	AUX
ejpam-5861	238	37	λ−	λ−	PROPN
ejpam-5861	238	38	[	[	PUNCT
ejpam-5861	238	39	b(1−	b(1−	NOUN
ejpam-5861	238	40	pξ)i(t	pξ)i(t	NOUN
ejpam-5861	238	41	)	)	PUNCT
ejpam-5861	239	1	+	+	CCONJ
ejpam-5861	239	2	(	(	PUNCT
ejpam-5861	239	3	η	η	X
ejpam-5861	239	4	+	+	PROPN
ejpam-5861	239	5	d	d	PROPN
ejpam-5861	239	6	)	)	PUNCT
ejpam-5861	240	1	]	]	PUNCT
ejpam-5861	240	2	s(t	s(t	PROPN
ejpam-5861	240	3	)	)	PUNCT
ejpam-5861	240	4	=	=	SYM
ejpam-5861	240	5	0	0	NUM
ejpam-5861	240	6	,	,	PUNCT
ejpam-5861	240	7	ηs(t)−	ηs(t)−	PROPN
ejpam-5861	240	8	[	[	PUNCT
ejpam-5861	240	9	wbi(t	wbi(t	PROPN
ejpam-5861	240	10	)	)	PUNCT
ejpam-5861	240	11	+	+	SYM
ejpam-5861	240	12	d	d	X
ejpam-5861	240	13	]	]	X
ejpam-5861	240	14	v	v	PROPN
ejpam-5861	240	15	(	(	PUNCT
ejpam-5861	240	16	t	t	NOUN
ejpam-5861	240	17	)	)	PUNCT
ejpam-5861	240	18	=	=	SYM
ejpam-5861	240	19	0	0	NUM
ejpam-5861	240	20	,	,	PUNCT
ejpam-5861	240	21	wbv	wbv	INTJ
ejpam-5861	240	22	(	(	PUNCT
ejpam-5861	240	23	t)i(t	t)i(t	NOUN
ejpam-5861	240	24	)	)	PUNCT
ejpam-5861	240	25	+	+	CCONJ
ejpam-5861	240	26	b(1−	b(1−	PROPN
ejpam-5861	240	27	pξ)s(t)i(t)−	pξ)s(t)i(t)−	PROPN
ejpam-5861	240	28	(	(	PUNCT
ejpam-5861	240	29	τ	τ	PROPN
ejpam-5861	240	30	+	+	SYM
ejpam-5861	240	31	d)e(t	d)e(t	PROPN
ejpam-5861	240	32	)	)	PUNCT
ejpam-5861	240	33	=	=	SYM
ejpam-5861	240	34	0	0	NUM
ejpam-5861	240	35	,	,	PUNCT
ejpam-5861	240	36	τe(t)−	τe(t)−	PROPN
ejpam-5861	240	37	(	(	PUNCT
ejpam-5861	240	38	αi	αi	VERB
ejpam-5861	240	39	+	+	CCONJ
ejpam-5861	240	40	δi	δi	PRON
ejpam-5861	241	1	+	+	CCONJ
ejpam-5861	241	2	σi	σi	X
ejpam-5861	241	3	+	+	CCONJ
ejpam-5861	241	4	d)i(t	d)i(t	NOUN
ejpam-5861	241	5	)	)	PUNCT
ejpam-5861	241	6	=	=	SYM
ejpam-5861	241	7	0	0	NUM
ejpam-5861	241	8	,	,	PUNCT
ejpam-5861	241	9	αii(t)−	αii(t)−	PROPN
ejpam-5861	242	1	[	[	X
ejpam-5861	242	2	σq	σq	X
ejpam-5861	242	3	+	+	CCONJ
ejpam-5861	242	4	δq	δq	ADP
ejpam-5861	242	5	+	+	CCONJ
ejpam-5861	242	6	d]q(t	d]q(t	NOUN
ejpam-5861	242	7	)	)	PUNCT
ejpam-5861	242	8	=	=	SYM
ejpam-5861	242	9	0	0	NUM
ejpam-5861	242	10	,	,	PUNCT
ejpam-5861	242	11	σii(t	σii(t	PROPN
ejpam-5861	242	12	)	)	PUNCT
ejpam-5861	243	1	+	+	CCONJ
ejpam-5861	243	2	σqq(t)−	σqq(t)−	PROPN
ejpam-5861	243	3	dr(t	dr(t	PUNCT
ejpam-5861	243	4	)	)	PUNCT
ejpam-5861	244	1	=	=	SYM
ejpam-5861	244	2	0	0	NUM
ejpam-5861	244	3	,	,	PUNCT
ejpam-5861	244	4	δii(t	δii(t	PROPN
ejpam-5861	244	5	)	)	PUNCT
ejpam-5861	244	6	+	+	CCONJ
ejpam-5861	244	7	δqq(t	δqq(t	ADJ
ejpam-5861	244	8	)	)	PUNCT
ejpam-5861	244	9	=	=	SYM
ejpam-5861	244	10	0	0	X
ejpam-5861	244	11	.	.	X
ejpam-5861	244	12			NOUN
ejpam-5861	244	13	now	now	ADV
ejpam-5861	244	14	i	i	PRON
ejpam-5861	244	15	=	=	NOUN
ejpam-5861	244	16	0	0	NUM
ejpam-5861	244	17	,	,	PUNCT
ejpam-5861	244	18	e	e	X
ejpam-5861	244	19	=	=	SYM
ejpam-5861	244	20	0	0	NUM
ejpam-5861	244	21	,	,	PUNCT
ejpam-5861	244	22	q	q	NOUN
ejpam-5861	244	23	=	=	SYM
ejpam-5861	244	24	0	0	NUM
ejpam-5861	244	25	,	,	PUNCT
ejpam-5861	244	26	r	r	NOUN
ejpam-5861	244	27	=	=	SYM
ejpam-5861	244	28	0	0	NUM
ejpam-5861	244	29	,	,	PUNCT
ejpam-5861	244	30	d	d	NOUN
ejpam-5861	244	31	=	=	SYM
ejpam-5861	244	32	0	0	NUM
ejpam-5861	245	1	due	due	ADP
ejpam-5861	245	2	to	to	ADP
ejpam-5861	245	3	absence	absence	NOUN
ejpam-5861	245	4	of	of	ADP
ejpam-5861	245	5	infection	infection	NOUN
ejpam-5861	245	6	,	,	PUNCT
ejpam-5861	245	7	and	and	CCONJ
ejpam-5861	245	8	s	s	NOUN
ejpam-5861	245	9	=	=	PROPN
ejpam-5861	245	10	s0	s0	PROPN
ejpam-5861	245	11	,	,	PUNCT
ejpam-5861	245	12	v	v	NOUN
ejpam-5861	245	13	=	=	SYM
ejpam-5861	245	14	v	v	NOUN
ejpam-5861	245	15	0	0	NUM
ejpam-5861	245	16	,	,	PUNCT
ejpam-5861	245	17	and	and	CCONJ
ejpam-5861	245	18	solving	solve	VERB
ejpam-5861	245	19	system	system	NOUN
ejpam-5861	245	20	(	(	PUNCT
ejpam-5861	245	21	12	12	NUM
ejpam-5861	245	22	)	)	PUNCT
ejpam-5861	245	23	,	,	PUNCT
ejpam-5861	245	24	we	we	PRON
ejpam-5861	245	25	have	have	VERB
ejpam-5861	245	26	e0	e0	PROPN
ejpam-5861	245	27	=	=	PUNCT
ejpam-5861	245	28	(	(	PUNCT
ejpam-5861	245	29	λ	λ	X
ejpam-5861	245	30	η	η	PROPN
ejpam-5861	245	31	+	+	PROPN
ejpam-5861	245	32	d	d	PROPN
ejpam-5861	245	33	,	,	PUNCT
ejpam-5861	245	34	λ	λ	X
ejpam-5861	245	35	d(η	d(η	NOUN
ejpam-5861	245	36	+	+	CCONJ
ejpam-5861	245	37	d	d	NOUN
ejpam-5861	245	38	)	)	PUNCT
ejpam-5861	245	39	,	,	PUNCT
ejpam-5861	245	40	0	0	NUM
ejpam-5861	245	41	,	,	PUNCT
ejpam-5861	245	42	0	0	NUM
ejpam-5861	245	43	,	,	PUNCT
ejpam-5861	245	44	0	0	NUM
ejpam-5861	245	45	,	,	PUNCT
ejpam-5861	245	46	0	0	NUM
ejpam-5861	245	47	,	,	PUNCT
ejpam-5861	245	48	0	0	NUM
ejpam-5861	245	49	)	)	PUNCT
ejpam-5861	245	50	.	.	PUNCT
ejpam-5861	246	1	endemic	endemic	ADJ
ejpam-5861	246	2	equilibrium	equilibrium	NOUN
ejpam-5861	246	3	point	point	NOUN
ejpam-5861	246	4	in	in	ADP
ejpam-5861	246	5	the	the	DET
ejpam-5861	246	6	same	same	ADJ
ejpam-5861	246	7	way	way	NOUN
ejpam-5861	246	8	,	,	PUNCT
ejpam-5861	246	9	we	we	PRON
ejpam-5861	246	10	can	can	AUX
ejpam-5861	246	11	compute	compute	VERB
ejpam-5861	246	12	endemic	endemic	ADJ
ejpam-5861	246	13	equilibrium	equilibrium	NOUN
ejpam-5861	246	14	point	point	NOUN
ejpam-5861	246	15	e∗	e∗	NOUN
ejpam-5861	246	16	=	=	SYM
ejpam-5861	246	17	(	(	PUNCT
ejpam-5861	246	18	s̃	s̃	PROPN
ejpam-5861	246	19	,	,	PUNCT
ejpam-5861	246	20	ṽ	ṽ	PROPN
ejpam-5861	246	21	,	,	PUNCT
ejpam-5861	246	22	ẽ	ẽ	PROPN
ejpam-5861	246	23	,	,	PUNCT
ejpam-5861	246	24	ĩ	ĩ	PROPN
ejpam-5861	246	25	,	,	PUNCT
ejpam-5861	246	26	q̃	q̃	PROPN
ejpam-5861	246	27	,	,	PUNCT
ejpam-5861	246	28	r̃	r̃	PROPN
ejpam-5861	246	29	,	,	PUNCT
ejpam-5861	246	30	d̃	d̃	PROPN
ejpam-5861	246	31	)	)	PUNCT
ejpam-5861	246	32	,	,	PUNCT
ejpam-5861	247	1	s.	s.	PROPN
ejpam-5861	247	2	naz	naz	PROPN
ejpam-5861	247	3	et	et	PROPN
ejpam-5861	247	4	al	al	PROPN
ejpam-5861	247	5	.	.	PUNCT
ejpam-5861	247	6	/	/	SYM
ejpam-5861	247	7	eur	eur	PROPN
ejpam-5861	247	8	.	.	PUNCT
ejpam-5861	248	1	j.	j.	PROPN
ejpam-5861	248	2	pure	pure	PROPN
ejpam-5861	248	3	appl	appl	PROPN
ejpam-5861	248	4	.	.	PROPN
ejpam-5861	248	5	math	math	PROPN
ejpam-5861	248	6	,	,	PUNCT
ejpam-5861	248	7	18	18	NUM
ejpam-5861	248	8	(	(	PUNCT
ejpam-5861	248	9	2	2	NUM
ejpam-5861	248	10	)	)	PUNCT
ejpam-5861	248	11	(	(	PUNCT
ejpam-5861	248	12	2025	2025	NUM
ejpam-5861	248	13	)	)	PUNCT
ejpam-5861	248	14	,	,	PUNCT
ejpam-5861	248	15	5861	5861	NUM
ejpam-5861	248	16	11	11	NUM
ejpam-5861	248	17	of	of	ADP
ejpam-5861	248	18	33	33	NUM
ejpam-5861	248	19	again	again	ADV
ejpam-5861	248	20	from	from	ADP
ejpam-5861	248	21	equating	equate	VERB
ejpam-5861	248	22	right	right	ADJ
ejpam-5861	248	23	sides	side	NOUN
ejpam-5861	248	24	of	of	ADP
ejpam-5861	248	25	model	model	NOUN
ejpam-5861	248	26	(	(	PUNCT
ejpam-5861	248	27	2	2	NUM
ejpam-5861	248	28	)	)	PUNCT
ejpam-5861	248	29	equal	equal	ADJ
ejpam-5861	248	30	to	to	ADP
ejpam-5861	248	31	zero	zero	NUM
ejpam-5861	248	32	as	as	SCONJ
ejpam-5861	248	33	follows	follow	VERB
ejpam-5861	248	34	:	:	PUNCT
ejpam-5861	248	35	λ−	λ−	PROPN
ejpam-5861	248	36	[	[	PUNCT
ejpam-5861	248	37	b(1−	b(1−	PROPN
ejpam-5861	248	38	pξ)ĩ(t	pξ)ĩ(t	NOUN
ejpam-5861	248	39	)	)	PUNCT
ejpam-5861	249	1	+	+	CCONJ
ejpam-5861	249	2	(	(	PUNCT
ejpam-5861	249	3	η	η	X
ejpam-5861	249	4	+	+	PROPN
ejpam-5861	249	5	d	d	PROPN
ejpam-5861	249	6	)	)	PUNCT
ejpam-5861	249	7	]	]	PUNCT
ejpam-5861	250	1	s̃(t	s̃(t	PROPN
ejpam-5861	250	2	)	)	PUNCT
ejpam-5861	250	3	=	=	SYM
ejpam-5861	250	4	0	0	NUM
ejpam-5861	250	5	,	,	PUNCT
ejpam-5861	250	6	ηs̃(t)−	ηs̃(t)−	PROPN
ejpam-5861	250	7	[	[	PUNCT
ejpam-5861	250	8	wbĩ(t	wbĩ(t	PROPN
ejpam-5861	250	9	)	)	PUNCT
ejpam-5861	250	10	+	+	PROPN
ejpam-5861	250	11	d	d	X
ejpam-5861	250	12	]	]	X
ejpam-5861	250	13	ṽ	ṽ	PROPN
ejpam-5861	250	14	(	(	PUNCT
ejpam-5861	250	15	t	t	PROPN
ejpam-5861	250	16	)	)	PUNCT
ejpam-5861	250	17	=	=	SYM
ejpam-5861	250	18	0	0	NUM
ejpam-5861	250	19	,	,	PUNCT
ejpam-5861	250	20	wbṽ	wbṽ	X
ejpam-5861	250	21	(	(	PUNCT
ejpam-5861	250	22	t)ĩ(t	t)ĩ(t	PROPN
ejpam-5861	250	23	)	)	PUNCT
ejpam-5861	250	24	+	+	SYM
ejpam-5861	250	25	b(1−	b(1−	PROPN
ejpam-5861	250	26	pξ)s̃(t)ĩ(t)−	pξ)s̃(t)ĩ(t)−	PROPN
ejpam-5861	250	27	(	(	PUNCT
ejpam-5861	250	28	τ	τ	PROPN
ejpam-5861	250	29	+	+	X
ejpam-5861	250	30	d)ẽ(t	d)ẽ(t	PROPN
ejpam-5861	250	31	)	)	PUNCT
ejpam-5861	250	32	=	=	SYM
ejpam-5861	250	33	0	0	NUM
ejpam-5861	250	34	,	,	PUNCT
ejpam-5861	250	35	τ	τ	PROPN
ejpam-5861	250	36	ẽ(t)−	ẽ(t)−	PROPN
ejpam-5861	250	37	(	(	PUNCT
ejpam-5861	250	38	αi	αi	VERB
ejpam-5861	250	39	+	+	CCONJ
ejpam-5861	250	40	δi	δi	PRON
ejpam-5861	250	41	+	+	CCONJ
ejpam-5861	250	42	σi	σi	X
ejpam-5861	250	43	+	+	CCONJ
ejpam-5861	250	44	d)ĩ(t	d)ĩ(t	PROPN
ejpam-5861	250	45	)	)	PUNCT
ejpam-5861	250	46	=	=	SYM
ejpam-5861	250	47	0	0	NUM
ejpam-5861	250	48	,	,	PUNCT
ejpam-5861	250	49	αi	αi	PRON
ejpam-5861	250	50	ĩ(t)−	ĩ(t)−	PROPN
ejpam-5861	251	1	[	[	X
ejpam-5861	251	2	σq	σq	X
ejpam-5861	251	3	+	+	NOUN
ejpam-5861	251	4	δq	δq	X
ejpam-5861	251	5	+	+	NUM
ejpam-5861	251	6	d]q̃(t	d]q̃(t	NOUN
ejpam-5861	251	7	)	)	PUNCT
ejpam-5861	251	8	=	=	SYM
ejpam-5861	252	1	0	0	NUM
ejpam-5861	252	2	,	,	PUNCT
ejpam-5861	252	3	σi	σi	PRON
ejpam-5861	252	4	ĩ(t	ĩ(t	PROPN
ejpam-5861	252	5	)	)	PUNCT
ejpam-5861	253	1	+	+	CCONJ
ejpam-5861	253	2	σqq̃(t)−	σqq̃(t)−	X
ejpam-5861	253	3	dr̃(t	dr̃(t	X
ejpam-5861	253	4	)	)	PUNCT
ejpam-5861	253	5	=	=	SYM
ejpam-5861	253	6	0	0	NUM
ejpam-5861	253	7	,	,	PUNCT
ejpam-5861	253	8	δi	δi	ADP
ejpam-5861	253	9	ĩ(t	ĩ(t	PROPN
ejpam-5861	253	10	)	)	PUNCT
ejpam-5861	254	1	+	+	CCONJ
ejpam-5861	255	1	δqq̃(t	δqq̃(t	PROPN
ejpam-5861	255	2	)	)	PUNCT
ejpam-5861	255	3	=	=	SYM
ejpam-5861	255	4	0	0	X
ejpam-5861	255	5	.	.	X
ejpam-5861	255	6			NOUN
ejpam-5861	255	7	on	on	ADP
ejpam-5861	255	8	solving	solve	VERB
ejpam-5861	255	9	(	(	PUNCT
ejpam-5861	255	10	12	12	NUM
ejpam-5861	255	11	)	)	PUNCT
ejpam-5861	255	12	,	,	PUNCT
ejpam-5861	255	13	we	we	PRON
ejpam-5861	255	14	get	get	VERB
ejpam-5861	255	15	s̃	s̃	PROPN
ejpam-5861	255	16	=	=	PUNCT
ejpam-5861	255	17	λ	λ	PROPN
ejpam-5861	255	18	b(1−	b(1−	NOUN
ejpam-5861	255	19	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	255	20	+	+	CCONJ
ejpam-5861	255	21	η	η	PROPN
ejpam-5861	255	22	+	+	PROPN
ejpam-5861	255	23	d	d	PROPN
ejpam-5861	255	24	,	,	PUNCT
ejpam-5861	255	25	ṽ	ṽ	PROPN
ejpam-5861	255	26	=	=	SYM
ejpam-5861	255	27	η	η	PROPN
ejpam-5861	255	28	wbĩ	wbĩ	NOUN
ejpam-5861	256	1	+	+	X
ejpam-5861	256	2	d	d	X
ejpam-5861	256	3	[	[	PUNCT
ejpam-5861	256	4	λ	λ	X
ejpam-5861	256	5	b(1−	b(1−	NOUN
ejpam-5861	256	6	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	256	7	+	+	CCONJ
ejpam-5861	256	8	η	η	PROPN
ejpam-5861	256	9	+	+	PROPN
ejpam-5861	256	10	d	d	X
ejpam-5861	256	11	]	]	X
ejpam-5861	256	12	,	,	PUNCT
ejpam-5861	256	13	ẽ	ẽ	PROPN
ejpam-5861	256	14	=	=	SYM
ejpam-5861	256	15	1	1	NUM
ejpam-5861	256	16	θ	θ	NOUN
ejpam-5861	257	1	+	+	CCONJ
ejpam-5861	257	2	d	d	X
ejpam-5861	257	3	[	[	PUNCT
ejpam-5861	257	4	λb(1−	λb(1−	ADJ
ejpam-5861	257	5	pξ	pξ	NOUN
ejpam-5861	257	6	)	)	PUNCT
ejpam-5861	257	7	b(1−	b(1−	NOUN
ejpam-5861	257	8	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	257	9	+	+	CCONJ
ejpam-5861	257	10	η	η	PROPN
ejpam-5861	257	11	+	+	PROPN
ejpam-5861	257	12	d	d	PROPN
ejpam-5861	257	13	+	+	NUM
ejpam-5861	257	14	wbηλ	wbηλ	NOUN
ejpam-5861	257	15	b(1−	b(1−	NOUN
ejpam-5861	257	16	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	257	17	+	+	CCONJ
ejpam-5861	257	18	η	η	PROPN
ejpam-5861	257	19	+	+	PROPN
ejpam-5861	257	20	d	d	X
ejpam-5861	257	21	]	]	X
ejpam-5861	257	22	ĩ	ĩ	PROPN
ejpam-5861	257	23	,	,	PUNCT
ejpam-5861	257	24	ĩ	ĩ	PROPN
ejpam-5861	257	25	=	=	SYM
ejpam-5861	257	26	θ	θ	PROPN
ejpam-5861	257	27	(	(	PUNCT
ejpam-5861	257	28	αi	αi	VERB
ejpam-5861	258	1	+	+	CCONJ
ejpam-5861	258	2	δi	δi	PRON
ejpam-5861	259	1	+	+	CCONJ
ejpam-5861	259	2	σi	σi	X
ejpam-5861	260	1	+	+	CCONJ
ejpam-5861	261	1	d	d	X
ejpam-5861	261	2	)	)	PUNCT
ejpam-5861	261	3	[	[	PUNCT
ejpam-5861	261	4	1	1	NUM
ejpam-5861	261	5	θ	θ	NOUN
ejpam-5861	261	6	+	+	CCONJ
ejpam-5861	262	1	d	d	X
ejpam-5861	262	2	[	[	PUNCT
ejpam-5861	262	3	λb(1−	λb(1−	ADJ
ejpam-5861	262	4	pξ	pξ	NOUN
ejpam-5861	262	5	)	)	PUNCT
ejpam-5861	262	6	b(1−	b(1−	NOUN
ejpam-5861	262	7	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	262	8	+	+	CCONJ
ejpam-5861	262	9	η	η	PROPN
ejpam-5861	262	10	+	+	PROPN
ejpam-5861	262	11	d	d	PROPN
ejpam-5861	262	12	+	+	NUM
ejpam-5861	262	13	wbηλ	wbηλ	NOUN
ejpam-5861	262	14	b(1−	b(1−	NOUN
ejpam-5861	262	15	pξ)ĩ	pξ)ĩ	NOUN
ejpam-5861	262	16	+	+	CCONJ
ejpam-5861	262	17	η	η	PROPN
ejpam-5861	262	18	+	+	PROPN
ejpam-5861	262	19	d	d	X
ejpam-5861	262	20	]	]	X
ejpam-5861	262	21	ĩ	ĩ	PROPN
ejpam-5861	262	22	]	]	PUNCT
ejpam-5861	262	23	,	,	PUNCT
ejpam-5861	262	24	q̃	q̃	PROPN
ejpam-5861	262	25	=	=	SYM
ejpam-5861	262	26	αi	αi	VERB
ejpam-5861	262	27	ĩ	ĩ	NOUN
ejpam-5861	262	28	σq	σq	VERB
ejpam-5861	262	29	+	+	NOUN
ejpam-5861	262	30	δq	δq	ADP
ejpam-5861	263	1	+	+	CCONJ
ejpam-5861	263	2	d	d	NOUN
ejpam-5861	263	3	,	,	PUNCT
ejpam-5861	263	4	r̃	r̃	NOUN
ejpam-5861	263	5	=	=	PUNCT
ejpam-5861	263	6	σi	σi	NOUN
ejpam-5861	263	7	d	d	PROPN
ejpam-5861	263	8	ĩ	ĩ	PROPN
ejpam-5861	264	1	+	+	CCONJ
ejpam-5861	264	2	σq	σq	NOUN
ejpam-5861	265	1	d	d	NOUN
ejpam-5861	265	2	αi	αi	VERB
ejpam-5861	265	3	ĩ	ĩ	NOUN
ejpam-5861	265	4	σq	σq	VERB
ejpam-5861	265	5	+	+	NOUN
ejpam-5861	265	6	δq	δq	X
ejpam-5861	266	1	+	+	CCONJ
ejpam-5861	266	2	d	d	NOUN
ejpam-5861	266	3	,	,	PUNCT
ejpam-5861	266	4	q̃	q̃	PROPN
ejpam-5861	266	5	=	=	SYM
ejpam-5861	266	6	0	0	PROPN
ejpam-5861	266	7	.	.	PUNCT
ejpam-5861	267	1	the	the	DET
ejpam-5861	267	2	basic	basic	ADJ
ejpam-5861	267	3	reproductive	reproductive	ADJ
ejpam-5861	267	4	number	number	NOUN
ejpam-5861	267	5	r0	r0	NOUN
ejpam-5861	267	6	has	have	AUX
ejpam-5861	267	7	been	be	AUX
ejpam-5861	267	8	computed	compute	VERB
ejpam-5861	267	9	for	for	ADP
ejpam-5861	267	10	integer	integer	NOUN
ejpam-5861	267	11	order	order	NOUN
ejpam-5861	267	12	model	model	NOUN
ejpam-5861	267	13	in	in	ADP
ejpam-5861	267	14	[	[	X
ejpam-5861	267	15	29	29	NUM
ejpam-5861	267	16	]	]	PUNCT
ejpam-5861	267	17	,	,	PUNCT
ejpam-5861	267	18	we	we	PRON
ejpam-5861	267	19	recall	recall	VERB
ejpam-5861	267	20	it	it	PRON
ejpam-5861	267	21	as	as	SCONJ
ejpam-5861	267	22	follows	follow	VERB
ejpam-5861	267	23	:	:	PUNCT
ejpam-5861	267	24	rvac	rvac	PROPN
ejpam-5861	267	25	=	=	SYM
ejpam-5861	268	1	τb(1−	τb(1−	ADP
ejpam-5861	268	2	pξ)λ	pξ)λ	NOUN
ejpam-5861	268	3	(	(	PUNCT
ejpam-5861	268	4	τ	τ	X
ejpam-5861	268	5	+	+	CCONJ
ejpam-5861	268	6	d)(αi	d)(αi	VERB
ejpam-5861	268	7	+	+	CCONJ
ejpam-5861	268	8	δi	δi	PRON
ejpam-5861	268	9	+	+	CCONJ
ejpam-5861	268	10	σi	σi	X
ejpam-5861	268	11	+	+	CCONJ
ejpam-5861	268	12	d	d	X
ejpam-5861	268	13	)	)	PUNCT
ejpam-5861	268	14	[	[	PUNCT
ejpam-5861	268	15	d+	d+	X
ejpam-5861	268	16	ω	ω	NUM
ejpam-5861	268	17	d(η	d(η	NOUN
ejpam-5861	268	18	+	+	NUM
ejpam-5861	268	19	d	d	NOUN
ejpam-5861	268	20	)	)	PUNCT
ejpam-5861	268	21	]	]	PUNCT
ejpam-5861	268	22	,	,	PUNCT
ejpam-5861	268	23	(	(	PUNCT
ejpam-5861	268	24	12	12	NUM
ejpam-5861	268	25	)	)	PUNCT
ejpam-5861	268	26	but	but	CCONJ
ejpam-5861	268	27	if	if	SCONJ
ejpam-5861	268	28	no	no	DET
ejpam-5861	268	29	vaccination	vaccination	NOUN
ejpam-5861	268	30	,	,	PUNCT
ejpam-5861	268	31	then	then	ADV
ejpam-5861	268	32	ω	ω	X
ejpam-5861	268	33	=	=	SYM
ejpam-5861	268	34	0	0	PROPN
ejpam-5861	268	35	,	,	PUNCT
ejpam-5861	268	36	we	we	PRON
ejpam-5861	268	37	get	get	VERB
ejpam-5861	268	38	the	the	DET
ejpam-5861	268	39	fundamental	fundamental	ADJ
ejpam-5861	268	40	reproductive	reproductive	ADJ
ejpam-5861	268	41	number	number	NOUN
ejpam-5861	268	42	as	as	SCONJ
ejpam-5861	268	43	follows	follow	VERB
ejpam-5861	268	44	:	:	PUNCT
ejpam-5861	268	45	r0	r0	NOUN
ejpam-5861	268	46	=	=	PUNCT
ejpam-5861	268	47	τb(1−	τb(1−	ADP
ejpam-5861	268	48	pξ)λ	pξ)λ	DET
ejpam-5861	268	49	d(τ	d(τ	PROPN
ejpam-5861	268	50	+	+	CCONJ
ejpam-5861	268	51	d)(αi	d)(αi	VERB
ejpam-5861	268	52	+	+	CCONJ
ejpam-5861	268	53	δi	δi	PRON
ejpam-5861	269	1	+	+	CCONJ
ejpam-5861	269	2	σi	σi	X
ejpam-5861	269	3	+	+	CCONJ
ejpam-5861	269	4	d	d	NOUN
ejpam-5861	269	5	)	)	PUNCT
ejpam-5861	269	6	.	.	PUNCT
ejpam-5861	270	1	(	(	PUNCT
ejpam-5861	270	2	13	13	NUM
ejpam-5861	270	3	)	)	PUNCT
ejpam-5861	270	4	in	in	ADP
ejpam-5861	270	5	figure	figure	NOUN
ejpam-5861	270	6	2	2	NUM
ejpam-5861	270	7	,	,	PUNCT
ejpam-5861	270	8	we	we	PRON
ejpam-5861	270	9	describe	describe	VERB
ejpam-5861	270	10	surface	surface	NOUN
ejpam-5861	270	11	plot	plot	NOUN
ejpam-5861	270	12	of	of	ADP
ejpam-5861	270	13	the	the	DET
ejpam-5861	270	14	reproductive	reproductive	ADJ
ejpam-5861	270	15	numbers	number	NOUN
ejpam-5861	270	16	to	to	PART
ejpam-5861	270	17	see	see	VERB
ejpam-5861	270	18	the	the	DET
ejpam-5861	270	19	behaviour	behaviour	NOUN
ejpam-5861	270	20	on	on	ADP
ejpam-5861	270	21	decreasing	decrease	VERB
ejpam-5861	270	22	or	or	CCONJ
ejpam-5861	270	23	increasing	increase	VERB
ejpam-5861	270	24	the	the	DET
ejpam-5861	270	25	parameters	parameter	NOUN
ejpam-5861	270	26	values	value	NOUN
ejpam-5861	270	27	.	.	PUNCT
ejpam-5861	271	1	s.	s.	PROPN
ejpam-5861	271	2	naz	naz	PROPN
ejpam-5861	271	3	et	et	PROPN
ejpam-5861	271	4	al	al	PROPN
ejpam-5861	271	5	.	.	PUNCT
ejpam-5861	271	6	/	/	SYM
ejpam-5861	271	7	eur	eur	PROPN
ejpam-5861	271	8	.	.	PUNCT
ejpam-5861	272	1	j.	j.	PROPN
ejpam-5861	272	2	pure	pure	PROPN
ejpam-5861	272	3	appl	appl	PROPN
ejpam-5861	272	4	.	.	PROPN
ejpam-5861	272	5	math	math	PROPN
ejpam-5861	272	6	,	,	PUNCT
ejpam-5861	272	7	18	18	NUM
ejpam-5861	272	8	(	(	PUNCT
ejpam-5861	272	9	2	2	NUM
ejpam-5861	272	10	)	)	PUNCT
ejpam-5861	272	11	(	(	PUNCT
ejpam-5861	272	12	2025	2025	NUM
ejpam-5861	272	13	)	)	PUNCT
ejpam-5861	272	14	,	,	PUNCT
ejpam-5861	272	15	5861	5861	NUM
ejpam-5861	272	16	12	12	NUM
ejpam-5861	272	17	of	of	ADP
ejpam-5861	272	18	33	33	NUM
ejpam-5861	272	19	10.80.6	10.80.6	NUM
ejpam-5861	273	1	λ	λ	NOUN
ejpam-5861	273	2	0.40.200	0.40.200	NOUN
ejpam-5861	273	3	0.2	0.2	NUM
ejpam-5861	273	4	0.4	0.4	NUM
ejpam-5861	274	1	ξ	ξ	X
ejpam-5861	274	2	0.6	0.6	NUM
ejpam-5861	274	3	0.8	0.8	NUM
ejpam-5861	274	4	0	0	NUM
ejpam-5861	274	5	0.02	0.02	NUM
ejpam-5861	274	6	0.01	0.01	NUM
ejpam-5861	274	7	0.03	0.03	NUM
ejpam-5861	274	8	1	1	NUM
ejpam-5861	274	9	r	r	NOUN
ejpam-5861	274	10	0	0	NUM
ejpam-5861	274	11	1	1	NUM
ejpam-5861	274	12	0.8	0.8	NUM
ejpam-5861	274	13	0.6	0.6	NUM
ejpam-5861	274	14	d	d	NOUN
ejpam-5861	274	15	0.4	0.4	NUM
ejpam-5861	274	16	0.2	0.2	NUM
ejpam-5861	274	17	00	00	NUM
ejpam-5861	274	18	0.5	0.5	NUM
ejpam-5861	274	19	ξ	ξ	SYM
ejpam-5861	274	20	0	0	NUM
ejpam-5861	274	21	1	1	NUM
ejpam-5861	274	22	0.5	0.5	NUM
ejpam-5861	274	23	1	1	NUM
ejpam-5861	274	24	×10	×10	NOUN
ejpam-5861	274	25	-	-	SYM
ejpam-5861	274	26	5	5	NUM
ejpam-5861	274	27	r	r	NOUN
ejpam-5861	274	28	0	0	NUM
ejpam-5861	274	29	1	1	NUM
ejpam-5861	274	30	0.8	0.8	NUM
ejpam-5861	274	31	0.6	0.6	NUM
ejpam-5861	274	32	λ	λ	NOUN
ejpam-5861	274	33	0.4	0.4	NUM
ejpam-5861	274	34	0.2	0.2	NUM
ejpam-5861	274	35	00	00	NUM
ejpam-5861	274	36	0.2	0.2	NUM
ejpam-5861	274	37	0.4	0.4	NUM
ejpam-5861	274	38	τ	τ	PROPN
ejpam-5861	274	39	0.6	0.6	NUM
ejpam-5861	274	40	0.8	0.8	NUM
ejpam-5861	274	41	0	0	NUM
ejpam-5861	274	42	0.01	0.01	NUM
ejpam-5861	274	43	0.02	0.02	NUM
ejpam-5861	274	44	0.03	0.03	NUM
ejpam-5861	274	45	0.04	0.04	NUM
ejpam-5861	274	46	1	1	NUM
ejpam-5861	274	47	r	r	NOUN
ejpam-5861	274	48	0	0	NUM
ejpam-5861	274	49	10.80.6	10.80.6	NUM
ejpam-5861	274	50	p	p	NOUN
ejpam-5861	274	51	0.40.200	0.40.200	PROPN
ejpam-5861	274	52	0.5	0.5	NUM
ejpam-5861	274	53	τ	τ	PROPN
ejpam-5861	274	54	8	8	NUM
ejpam-5861	274	55	7	7	NUM
ejpam-5861	274	56	5	5	NUM
ejpam-5861	274	57	6	6	NUM
ejpam-5861	274	58	1	1	NUM
ejpam-5861	274	59	×10	×10	NOUN
ejpam-5861	274	60	-	-	SYM
ejpam-5861	274	61	5	5	NUM
ejpam-5861	274	62	r	r	NOUN
ejpam-5861	274	63	0	0	NUM
ejpam-5861	274	64	figure	figure	NOUN
ejpam-5861	274	65	2	2	NUM
ejpam-5861	274	66	:	:	PUNCT
ejpam-5861	274	67	surface	surface	NOUN
ejpam-5861	274	68	plots	plot	NOUN
ejpam-5861	274	69	of	of	ADP
ejpam-5861	274	70	r0	r0	NOUN
ejpam-5861	274	71	.	.	PUNCT
ejpam-5861	275	1	we	we	PRON
ejpam-5861	275	2	see	see	VERB
ejpam-5861	275	3	that	that	SCONJ
ejpam-5861	275	4	as	as	SCONJ
ejpam-5861	275	5	the	the	DET
ejpam-5861	275	6	values	value	NOUN
ejpam-5861	275	7	of	of	ADP
ejpam-5861	275	8	the	the	DET
ejpam-5861	275	9	given	give	VERB
ejpam-5861	275	10	parameters	parameter	NOUN
ejpam-5861	275	11	are	be	AUX
ejpam-5861	275	12	decreasing	decrease	VERB
ejpam-5861	275	13	,	,	PUNCT
ejpam-5861	275	14	the	the	DET
ejpam-5861	275	15	value	value	NOUN
ejpam-5861	275	16	of	of	ADP
ejpam-5861	275	17	r0	r0	NOUN
ejpam-5861	275	18	is	be	AUX
ejpam-5861	275	19	also	also	ADV
ejpam-5861	275	20	increasing	increase	VERB
ejpam-5861	275	21	but	but	CCONJ
ejpam-5861	275	22	never	never	ADV
ejpam-5861	275	23	exceeds	exceed	VERB
ejpam-5861	275	24	1	1	NUM
ejpam-5861	275	25	.	.	SYM
ejpam-5861	275	26	3.1	3.1	NUM
ejpam-5861	275	27	.	.	PUNCT
ejpam-5861	276	1	sensitivity	sensitivity	NOUN
ejpam-5861	276	2	analysis	analysis	NOUN
ejpam-5861	276	3	next	next	ADV
ejpam-5861	276	4	,	,	PUNCT
ejpam-5861	276	5	we	we	PRON
ejpam-5861	276	6	apply	apply	VERB
ejpam-5861	276	7	the	the	DET
ejpam-5861	276	8	formula	formula	NOUN
ejpam-5861	276	9	to	to	PART
ejpam-5861	276	10	get	get	VERB
ejpam-5861	276	11	the	the	DET
ejpam-5861	276	12	sensitivity	sensitivity	NOUN
ejpam-5861	276	13	of	of	ADP
ejpam-5861	276	14	the	the	DET
ejpam-5861	276	15	fundamental	fundamental	ADJ
ejpam-5861	276	16	reproduction	reproduction	NOUN
ejpam-5861	276	17	number	number	NOUN
ejpam-5861	276	18	.	.	PUNCT
ejpam-5861	277	1	sr0	sr0	NOUN
ejpam-5861	277	2	q	q	NOUN
ejpam-5861	277	3	=	=	PUNCT
ejpam-5861	277	4	q	q	NOUN
ejpam-5861	277	5	r0	r0	NOUN
ejpam-5861	277	6	∂r0	∂r0	PROPN
ejpam-5861	277	7	∂q	∂q	PROPN
ejpam-5861	277	8	,	,	PUNCT
ejpam-5861	277	9	(	(	PUNCT
ejpam-5861	277	10	14	14	NUM
ejpam-5861	277	11	)	)	PUNCT
ejpam-5861	277	12	where	where	SCONJ
ejpam-5861	277	13	q	q	NOUN
ejpam-5861	277	14	represents	represent	VERB
ejpam-5861	277	15	parameter	parameter	NOUN
ejpam-5861	277	16	involve	involve	NOUN
ejpam-5861	277	17	in	in	ADP
ejpam-5861	277	18	the	the	DET
ejpam-5861	277	19	r0	r0	NOUN
ejpam-5861	277	20	.	.	PUNCT
ejpam-5861	278	1	according	accord	VERB
ejpam-5861	278	2	to	to	ADP
ejpam-5861	278	3	(	(	PUNCT
ejpam-5861	278	4	14	14	NUM
ejpam-5861	278	5	)	)	PUNCT
ejpam-5861	278	6	,	,	PUNCT
ejpam-5861	278	7	we	we	PRON
ejpam-5861	278	8	compute	compute	VERB
ejpam-5861	278	9	sensitivity	sensitivity	NOUN
ejpam-5861	278	10	indices	indice	VERB
ejpam-5861	278	11	2	2	NUM
ejpam-5861	278	12	.	.	X
ejpam-5861	278	13	sensitivity	sensitivity	NOUN
ejpam-5861	278	14	index	index	NOUN
ejpam-5861	278	15	value	value	NOUN
ejpam-5861	278	16	sensitivity	sensitivity	NOUN
ejpam-5861	278	17	index	index	NOUN
ejpam-5861	278	18	value	value	NOUN
ejpam-5861	278	19	sr0	sr0	NOUN
ejpam-5861	278	20	b	b	PROPN
ejpam-5861	278	21	1.0	1.0	NUM
ejpam-5861	278	22	sr0	sr0	NOUN
ejpam-5861	278	23	τ	τ	X
ejpam-5861	278	24	1.0	1.0	NUM
ejpam-5861	278	25	sr0	sr0	NOUN
ejpam-5861	278	26	ξ	ξ	SYM
ejpam-5861	278	27	0.637	0.637	NUM
ejpam-5861	278	28	sr0	sr0	NOUN
ejpam-5861	278	29	d	d	NOUN
ejpam-5861	278	30	-0.4567	-0.4567	NOUN
ejpam-5861	278	31	sr0	sr0	NOUN
ejpam-5861	278	32	p	p	NOUN
ejpam-5861	278	33	-0.776	-0.776	NOUN
ejpam-5861	278	34	sr0	sr0	NOUN
ejpam-5861	278	35	αi	αi	NOUN
ejpam-5861	278	36	-0.7675	-0.7675	PUNCT
ejpam-5861	279	1	sr0	sr0	NOUN
ejpam-5861	279	2	λ	λ	PROPN
ejpam-5861	279	3	1.0	1.0	NUM
ejpam-5861	279	4	sr0	sr0	NOUN
ejpam-5861	279	5	δi	δi	NOUN
ejpam-5861	279	6	-0.9986	-0.9986	PROPN
ejpam-5861	279	7	sr0	sr0	NOUN
ejpam-5861	280	1	σi	σi	X
ejpam-5861	280	2	-0.895	-0.895	NOUN
ejpam-5861	280	3	table	table	NOUN
ejpam-5861	280	4	2	2	NUM
ejpam-5861	280	5	:	:	PUNCT
ejpam-5861	280	6	sensitivity	sensitivity	NOUN
ejpam-5861	280	7	indices	index	NOUN
ejpam-5861	280	8	of	of	ADP
ejpam-5861	280	9	basic	basic	ADJ
ejpam-5861	280	10	reproduction	reproduction	NOUN
ejpam-5861	280	11	number	number	NOUN
ejpam-5861	280	12	.	.	PUNCT
ejpam-5861	281	1	from	from	ADP
ejpam-5861	281	2	sensitivity	sensitivity	NOUN
ejpam-5861	281	3	indices	index	NOUN
ejpam-5861	281	4	table	table	NOUN
ejpam-5861	281	5	2	2	NUM
ejpam-5861	281	6	,	,	PUNCT
ejpam-5861	281	7	we	we	PRON
ejpam-5861	281	8	see	see	VERB
ejpam-5861	281	9	that	that	DET
ejpam-5861	281	10	increase	increase	NOUN
ejpam-5861	281	11	of	of	ADP
ejpam-5861	281	12	specific	specific	ADJ
ejpam-5861	281	13	percentage	percentage	NOUN
ejpam-5861	281	14	of	of	ADP
ejpam-5861	281	15	values	value	NOUN
ejpam-5861	281	16	means	mean	VERB
ejpam-5861	281	17	that	that	SCONJ
ejpam-5861	281	18	percentage	percentage	NOUN
ejpam-5861	281	19	increase	increase	NOUN
ejpam-5861	281	20	or	or	CCONJ
ejpam-5861	281	21	decrease	decrease	NOUN
ejpam-5861	281	22	in	in	ADP
ejpam-5861	281	23	the	the	DET
ejpam-5861	281	24	index	index	NOUN
ejpam-5861	281	25	which	which	PRON
ejpam-5861	281	26	implies	imply	VERB
ejpam-5861	281	27	the	the	DET
ejpam-5861	281	28	impact	impact	NOUN
ejpam-5861	281	29	of	of	ADP
ejpam-5861	281	30	parameters	parameter	NOUN
ejpam-5861	281	31	values	value	NOUN
ejpam-5861	281	32	for	for	ADP
ejpam-5861	281	33	simulations	simulation	NOUN
ejpam-5861	281	34	in	in	ADP
ejpam-5861	281	35	the	the	DET
ejpam-5861	281	36	current	current	ADJ
ejpam-5861	281	37	studies	study	NOUN
ejpam-5861	281	38	.	.	PUNCT
ejpam-5861	282	1	here	here	ADV
ejpam-5861	282	2	,	,	PUNCT
ejpam-5861	282	3	in	in	ADP
ejpam-5861	282	4	figure	figure	NOUN
ejpam-5861	282	5	3	3	NUM
ejpam-5861	282	6	,	,	PUNCT
ejpam-5861	282	7	we	we	PRON
ejpam-5861	282	8	present	present	VERB
ejpam-5861	282	9	the	the	DET
ejpam-5861	282	10	pi	pi	PROPN
ejpam-5861	282	11	chart	chart	NOUN
ejpam-5861	282	12	of	of	ADP
ejpam-5861	282	13	sensitivity	sensitivity	NOUN
ejpam-5861	282	14	indices	index	NOUN
ejpam-5861	282	15	which	which	PRON
ejpam-5861	282	16	describe	describe	VERB
ejpam-5861	282	17	the	the	DET
ejpam-5861	282	18	percentage	percentage	NOUN
ejpam-5861	282	19	impact	impact	NOUN
ejpam-5861	282	20	of	of	ADP
ejpam-5861	282	21	variable	variable	NOUN
ejpam-5861	282	22	on	on	ADP
ejpam-5861	282	23	the	the	DET
ejpam-5861	282	24	reproductive	reproductive	ADJ
ejpam-5861	282	25	number	number	NOUN
ejpam-5861	282	26	.	.	PUNCT
ejpam-5861	283	1	s.	s.	PROPN
ejpam-5861	283	2	naz	naz	PROPN
ejpam-5861	283	3	et	et	PROPN
ejpam-5861	283	4	al	al	PROPN
ejpam-5861	283	5	.	.	PUNCT
ejpam-5861	283	6	/	/	SYM
ejpam-5861	283	7	eur	eur	PROPN
ejpam-5861	283	8	.	.	PUNCT
ejpam-5861	284	1	j.	j.	PROPN
ejpam-5861	284	2	pure	pure	PROPN
ejpam-5861	284	3	appl	appl	PROPN
ejpam-5861	284	4	.	.	PROPN
ejpam-5861	284	5	math	math	PROPN
ejpam-5861	284	6	,	,	PUNCT
ejpam-5861	284	7	18	18	NUM
ejpam-5861	284	8	(	(	PUNCT
ejpam-5861	284	9	2	2	NUM
ejpam-5861	284	10	)	)	PUNCT
ejpam-5861	284	11	(	(	PUNCT
ejpam-5861	284	12	2025	2025	NUM
ejpam-5861	284	13	)	)	PUNCT
ejpam-5861	284	14	,	,	PUNCT
ejpam-5861	284	15	5861	5861	NUM
ejpam-5861	284	16	13	13	NUM
ejpam-5861	284	17	of	of	ADP
ejpam-5861	284	18	33	33	NUM
ejpam-5861	284	19	figure	figure	NOUN
ejpam-5861	284	20	3	3	NUM
ejpam-5861	284	21	:	:	PUNCT
ejpam-5861	284	22	plot	plot	NOUN
ejpam-5861	284	23	of	of	ADP
ejpam-5861	284	24	sensitivity	sensitivity	NOUN
ejpam-5861	284	25	index	index	NOUN
ejpam-5861	284	26	.	.	PUNCT
ejpam-5861	285	1	4	4	X
ejpam-5861	285	2	.	.	X
ejpam-5861	285	3	existence	existence	NOUN
ejpam-5861	285	4	theory	theory	NOUN
ejpam-5861	285	5	let	let	VERB
ejpam-5861	285	6	j	j	PROPN
ejpam-5861	285	7	=	=	PUNCT
ejpam-5861	286	1	[	[	X
ejpam-5861	286	2	0,t	0,t	X
ejpam-5861	286	3	]	]	X
ejpam-5861	286	4	,	,	PUNCT
ejpam-5861	286	5	0	0	NUM
ejpam-5861	286	6	≤	≤	NUM
ejpam-5861	286	7	t	t	PROPN
ejpam-5861	286	8	≤	≤	PROPN
ejpam-5861	286	9	t	t	PROPN
ejpam-5861	286	10	<	<	X
ejpam-5861	286	11	∞	∞	PROPN
ejpam-5861	286	12	,	,	PUNCT
ejpam-5861	286	13	and	and	CCONJ
ejpam-5861	286	14	ϕ	ϕ	X
ejpam-5861	286	15	=	=	SYM
ejpam-5861	286	16	(	(	PUNCT
ejpam-5861	286	17	s	s	PROPN
ejpam-5861	286	18	,	,	PUNCT
ejpam-5861	286	19	v	v	NOUN
ejpam-5861	286	20	,	,	PUNCT
ejpam-5861	286	21	e	e	NOUN
ejpam-5861	286	22	,	,	PUNCT
ejpam-5861	286	23	i	i	PRON
ejpam-5861	286	24	,	,	PUNCT
ejpam-5861	286	25	q	q	NOUN
ejpam-5861	286	26	,	,	PUNCT
ejpam-5861	286	27	r	r	NOUN
ejpam-5861	286	28	,	,	PUNCT
ejpam-5861	286	29	d	d	NOUN
ejpam-5861	286	30	)	)	PUNCT
ejpam-5861	286	31	,	,	PUNCT
ejpam-5861	286	32	then	then	ADV
ejpam-5861	286	33	the	the	DET
ejpam-5861	286	34	right	right	ADJ
ejpam-5861	286	35	sides	side	NOUN
ejpam-5861	286	36	of	of	ADP
ejpam-5861	286	37	(	(	PUNCT
ejpam-5861	286	38	2	2	NUM
ejpam-5861	286	39	)	)	PUNCT
ejpam-5861	286	40	,	,	PUNCT
ejpam-5861	286	41	we	we	PRON
ejpam-5861	286	42	can	can	AUX
ejpam-5861	286	43	express	express	VERB
ejpam-5861	286	44	as	as	PUNCT
ejpam-5861	286	45	l1(t	l1(t	PROPN
ejpam-5861	286	46	,	,	PUNCT
ejpam-5861	286	47	ϕ(t	ϕ(t	NUM
ejpam-5861	286	48	)	)	PUNCT
ejpam-5861	286	49	)	)	PUNCT
ejpam-5861	287	1	=	=	SYM
ejpam-5861	288	1	λ−	λ−	PROPN
ejpam-5861	288	2	[	[	PUNCT
ejpam-5861	288	3	b(1−	b(1−	NOUN
ejpam-5861	288	4	pξ)i(t	pξ)i(t	NOUN
ejpam-5861	288	5	)	)	PUNCT
ejpam-5861	289	1	+	+	CCONJ
ejpam-5861	289	2	(	(	PUNCT
ejpam-5861	289	3	η	η	X
ejpam-5861	289	4	+	+	PROPN
ejpam-5861	289	5	d	d	PROPN
ejpam-5861	289	6	)	)	PUNCT
ejpam-5861	289	7	]	]	PUNCT
ejpam-5861	290	1	s(t	s(t	PROPN
ejpam-5861	290	2	)	)	PUNCT
ejpam-5861	290	3	,	,	PUNCT
ejpam-5861	290	4	l2(t	l2(t	PROPN
ejpam-5861	290	5	,	,	PUNCT
ejpam-5861	290	6	ϕ(t	ϕ(t	NUM
ejpam-5861	290	7	)	)	PUNCT
ejpam-5861	290	8	)	)	PUNCT
ejpam-5861	291	1	=	=	SYM
ejpam-5861	291	2	ηs(t)−	ηs(t)−	PROPN
ejpam-5861	291	3	[	[	PUNCT
ejpam-5861	291	4	wbi(t	wbi(t	PROPN
ejpam-5861	291	5	)	)	PUNCT
ejpam-5861	292	1	+	+	SYM
ejpam-5861	292	2	d	d	X
ejpam-5861	292	3	]	]	X
ejpam-5861	292	4	v	v	PROPN
ejpam-5861	292	5	(	(	PUNCT
ejpam-5861	292	6	t	t	PROPN
ejpam-5861	292	7	)	)	PUNCT
ejpam-5861	292	8	,	,	PUNCT
ejpam-5861	292	9	l3(t	l3(t	PRON
ejpam-5861	292	10	,	,	PUNCT
ejpam-5861	292	11	ϕ(t	ϕ(t	NUM
ejpam-5861	292	12	)	)	PUNCT
ejpam-5861	292	13	)	)	PUNCT
ejpam-5861	293	1	=	=	PUNCT
ejpam-5861	293	2	wbv	wbv	INTJ
ejpam-5861	293	3	(	(	PUNCT
ejpam-5861	293	4	t)i(t	t)i(t	NOUN
ejpam-5861	293	5	)	)	PUNCT
ejpam-5861	293	6	+	+	CCONJ
ejpam-5861	293	7	b(1−	b(1−	PROPN
ejpam-5861	293	8	pξ)s(t)i(t)−	pξ)s(t)i(t)−	PROPN
ejpam-5861	293	9	(	(	PUNCT
ejpam-5861	293	10	τ	τ	X
ejpam-5861	293	11	+	+	PROPN
ejpam-5861	293	12	d)e(t	d)e(t	PROPN
ejpam-5861	293	13	)	)	PUNCT
ejpam-5861	293	14	,	,	PUNCT
ejpam-5861	293	15	l4(t	l4(t	PROPN
ejpam-5861	293	16	,	,	PUNCT
ejpam-5861	293	17	ϕ(t	ϕ(t	NUM
ejpam-5861	293	18	)	)	PUNCT
ejpam-5861	293	19	)	)	PUNCT
ejpam-5861	294	1	=	=	SYM
ejpam-5861	294	2	τe(t)−	τe(t)−	PROPN
ejpam-5861	294	3	(	(	PUNCT
ejpam-5861	294	4	εi	εi	VERB
ejpam-5861	294	5	+	+	X
ejpam-5861	294	6	δi	δi	PRON
ejpam-5861	294	7	+	+	CCONJ
ejpam-5861	294	8	σi	σi	X
ejpam-5861	294	9	+	+	CCONJ
ejpam-5861	294	10	d)i(t	d)i(t	NOUN
ejpam-5861	294	11	)	)	PUNCT
ejpam-5861	294	12	,	,	PUNCT
ejpam-5861	294	13	l5(t	l5(t	NOUN
ejpam-5861	294	14	,	,	PUNCT
ejpam-5861	294	15	ϕ(t	ϕ(t	NUM
ejpam-5861	294	16	)	)	PUNCT
ejpam-5861	294	17	)	)	PUNCT
ejpam-5861	295	1	=	=	PUNCT
ejpam-5861	296	1	εii(t)−	εii(t)−	PROPN
ejpam-5861	297	1	[	[	X
ejpam-5861	297	2	σq	σq	X
ejpam-5861	297	3	+	+	NOUN
ejpam-5861	297	4	δq	δq	X
ejpam-5861	297	5	+	+	CCONJ
ejpam-5861	297	6	d]q(t	d]q(t	PROPN
ejpam-5861	297	7	)	)	PUNCT
ejpam-5861	297	8	,	,	PUNCT
ejpam-5861	297	9	l6(t	l6(t	PROPN
ejpam-5861	297	10	,	,	PUNCT
ejpam-5861	297	11	ϕ(t	ϕ(t	NUM
ejpam-5861	297	12	)	)	PUNCT
ejpam-5861	297	13	)	)	PUNCT
ejpam-5861	298	1	=	=	PUNCT
ejpam-5861	298	2	σii(t	σii(t	PROPN
ejpam-5861	298	3	)	)	PUNCT
ejpam-5861	299	1	+	+	CCONJ
ejpam-5861	299	2	σqq(t)−	σqq(t)−	PROPN
ejpam-5861	299	3	dr(t	dr(t	NUM
ejpam-5861	299	4	)	)	PUNCT
ejpam-5861	299	5	,	,	PUNCT
ejpam-5861	299	6	l7(t	l7(t	PROPN
ejpam-5861	299	7	,	,	PUNCT
ejpam-5861	299	8	ϕ(t	ϕ(t	NUM
ejpam-5861	299	9	)	)	PUNCT
ejpam-5861	299	10	)	)	PUNCT
ejpam-5861	300	1	=	=	PUNCT
ejpam-5861	300	2	δii(t	δii(t	PROPN
ejpam-5861	300	3	)	)	PUNCT
ejpam-5861	300	4	+	+	CCONJ
ejpam-5861	300	5	δqq(t	δqq(t	PROPN
ejpam-5861	300	6	)	)	PUNCT
ejpam-5861	300	7	.	.	PUNCT
ejpam-5861	301	1	(	(	PUNCT
ejpam-5861	301	2	15	15	X
ejpam-5861	301	3	)	)	PUNCT
ejpam-5861	301	4	utilizing	utilizing	NOUN
ejpam-5861	301	5	(	(	PUNCT
ejpam-5861	301	6	15	15	NUM
ejpam-5861	301	7	)	)	PUNCT
ejpam-5861	301	8	,	,	PUNCT
ejpam-5861	301	9	model	model	NOUN
ejpam-5861	301	10	(	(	PUNCT
ejpam-5861	301	11	2	2	NUM
ejpam-5861	301	12	)	)	PUNCT
ejpam-5861	301	13	,	,	PUNCT
ejpam-5861	301	14	with	with	ADP
ejpam-5861	301	15	ε	ε	PROPN
ejpam-5861	301	16	∈	∈	PROPN
ejpam-5861	301	17	(	(	PUNCT
ejpam-5861	301	18	0	0	NUM
ejpam-5861	301	19	,	,	PUNCT
ejpam-5861	301	20	1	1	NUM
ejpam-5861	301	21	]	]	PUNCT
ejpam-5861	301	22	may	may	AUX
ejpam-5861	301	23	be	be	AUX
ejpam-5861	301	24	express	express	ADJ
ejpam-5861	301	25	as	as	ADP
ejpam-5861	301	26	:	:	PUNCT
ejpam-5861	301	27	{	{	PUNCT
ejpam-5861	301	28	pc	pc	NOUN
ejpam-5861	301	29	0	0	NUM
ejpam-5861	301	30	dε	dε	NOUN
ejpam-5861	301	31	tϕ(t	tϕ(t	NOUN
ejpam-5861	301	32	)	)	PUNCT
ejpam-5861	302	1	=	=	SYM
ejpam-5861	302	2	g(t	g(t	PROPN
ejpam-5861	302	3	,	,	PUNCT
ejpam-5861	302	4	ϕ(t	ϕ(t	NUM
ejpam-5861	302	5	)	)	PUNCT
ejpam-5861	302	6	)	)	PUNCT
ejpam-5861	302	7	,	,	PUNCT
ejpam-5861	302	8	t	t	PROPN
ejpam-5861	302	9	∈	∈	PROPN
ejpam-5861	302	10	j	j	PROPN
ejpam-5861	302	11	,	,	PUNCT
ejpam-5861	302	12	ϕ(0	ϕ(0	PROPN
ejpam-5861	302	13	)	)	PUNCT
ejpam-5861	303	1	=	=	SYM
ejpam-5861	303	2	ϕ0	ϕ0	NOUN
ejpam-5861	303	3	,	,	PUNCT
ejpam-5861	303	4	(	(	PUNCT
ejpam-5861	303	5	16	16	NUM
ejpam-5861	303	6	)	)	PUNCT
ejpam-5861	303	7	where	where	SCONJ
ejpam-5861	303	8	ϕ(t	ϕ(t	NUM
ejpam-5861	303	9	)	)	PUNCT
ejpam-5861	304	1	=	=	SYM
ejpam-5861	304	2			PROPN
ejpam-5861	304	3	s(t	s(t	PROPN
ejpam-5861	304	4	)	)	PUNCT
ejpam-5861	304	5	,	,	PUNCT
ejpam-5861	304	6	v	v	X
ejpam-5861	304	7	(	(	PUNCT
ejpam-5861	304	8	t	t	PROPN
ejpam-5861	304	9	)	)	PUNCT
ejpam-5861	304	10	,	,	PUNCT
ejpam-5861	304	11	e(t	e(t	NOUN
ejpam-5861	304	12	)	)	PUNCT
ejpam-5861	304	13	,	,	PUNCT
ejpam-5861	304	14	i(t	i(t	PROPN
ejpam-5861	304	15	)	)	PUNCT
ejpam-5861	304	16	,	,	PUNCT
ejpam-5861	304	17	q(t	q(t	PROPN
ejpam-5861	304	18	)	)	PUNCT
ejpam-5861	304	19	,	,	PUNCT
ejpam-5861	304	20	r(t	r(t	NOUN
ejpam-5861	304	21	)	)	PUNCT
ejpam-5861	304	22	,	,	PUNCT
ejpam-5861	304	23	d(t	d(t	PROPN
ejpam-5861	304	24	)	)	PUNCT
ejpam-5861	304	25	.	.	PUNCT
ejpam-5861	305	1	,	,	PUNCT
ejpam-5861	305	2	ϕ0(t	ϕ0(t	X
ejpam-5861	305	3	)	)	PUNCT
ejpam-5861	305	4	=	=	SYM
ejpam-5861	305	5			NUM
ejpam-5861	305	6	s0	s0	PROPN
ejpam-5861	305	7	,	,	PUNCT
ejpam-5861	305	8	v0	v0	PROPN
ejpam-5861	305	9	,	,	PUNCT
ejpam-5861	305	10	e0	e0	PROPN
ejpam-5861	305	11	,	,	PUNCT
ejpam-5861	305	12	i0	i0	PROPN
ejpam-5861	305	13	,	,	PUNCT
ejpam-5861	305	14	q0	q0	PROPN
ejpam-5861	305	15	,	,	PUNCT
ejpam-5861	305	16	r0	r0	NOUN
ejpam-5861	305	17	,	,	PUNCT
ejpam-5861	305	18	d0	d0	NOUN
ejpam-5861	305	19	.	.	PUNCT
ejpam-5861	306	1	g(t	g(t	PROPN
ejpam-5861	306	2	,	,	PUNCT
ejpam-5861	306	3	ϕ(t	ϕ(t	NUM
ejpam-5861	306	4	)	)	PUNCT
ejpam-5861	306	5	)	)	PUNCT
ejpam-5861	307	1	=	=	PUNCT
ejpam-5861	307	2			NUM
ejpam-5861	307	3	l1(t	l1(t	PROPN
ejpam-5861	307	4	,	,	PUNCT
ejpam-5861	307	5	ϕ(t	ϕ(t	NUM
ejpam-5861	307	6	)	)	PUNCT
ejpam-5861	307	7	)	)	PUNCT
ejpam-5861	307	8	,	,	PUNCT
ejpam-5861	307	9	l2(t	l2(t	PROPN
ejpam-5861	307	10	,	,	PUNCT
ejpam-5861	307	11	ϕ(t	ϕ(t	NUM
ejpam-5861	307	12	)	)	PUNCT
ejpam-5861	307	13	)	)	PUNCT
ejpam-5861	307	14	,	,	PUNCT
ejpam-5861	307	15	l3(t	l3(t	PRON
ejpam-5861	307	16	,	,	PUNCT
ejpam-5861	307	17	ϕ(t	ϕ(t	NUM
ejpam-5861	307	18	)	)	PUNCT
ejpam-5861	307	19	)	)	PUNCT
ejpam-5861	307	20	,	,	PUNCT
ejpam-5861	308	1	l4(t	l4(t	PROPN
ejpam-5861	308	2	,	,	PUNCT
ejpam-5861	308	3	ϕ(t	ϕ(t	NUM
ejpam-5861	308	4	)	)	PUNCT
ejpam-5861	308	5	)	)	PUNCT
ejpam-5861	308	6	,	,	PUNCT
ejpam-5861	308	7	l5(t	l5(t	NOUN
ejpam-5861	308	8	,	,	PUNCT
ejpam-5861	308	9	ϕ(t	ϕ(t	NUM
ejpam-5861	308	10	)	)	PUNCT
ejpam-5861	308	11	)	)	PUNCT
ejpam-5861	308	12	,	,	PUNCT
ejpam-5861	308	13	l6(t	l6(t	PROPN
ejpam-5861	308	14	,	,	PUNCT
ejpam-5861	308	15	ϕ(t	ϕ(t	NUM
ejpam-5861	308	16	)	)	PUNCT
ejpam-5861	308	17	)	)	PUNCT
ejpam-5861	308	18	.	.	PUNCT
ejpam-5861	309	1	(	(	PUNCT
ejpam-5861	309	2	17	17	NUM
ejpam-5861	309	3	)	)	PUNCT
ejpam-5861	309	4	s.	s.	PROPN
ejpam-5861	309	5	naz	naz	PROPN
ejpam-5861	309	6	et	et	PROPN
ejpam-5861	309	7	al	al	PROPN
ejpam-5861	309	8	.	.	PUNCT
ejpam-5861	309	9	/	/	SYM
ejpam-5861	309	10	eur	eur	PROPN
ejpam-5861	309	11	.	.	PUNCT
ejpam-5861	310	1	j.	j.	PROPN
ejpam-5861	310	2	pure	pure	PROPN
ejpam-5861	310	3	appl	appl	PROPN
ejpam-5861	310	4	.	.	PROPN
ejpam-5861	310	5	math	math	PROPN
ejpam-5861	310	6	,	,	PUNCT
ejpam-5861	310	7	18	18	NUM
ejpam-5861	310	8	(	(	PUNCT
ejpam-5861	310	9	2	2	NUM
ejpam-5861	310	10	)	)	PUNCT
ejpam-5861	310	11	(	(	PUNCT
ejpam-5861	310	12	2025	2025	NUM
ejpam-5861	310	13	)	)	PUNCT
ejpam-5861	310	14	,	,	PUNCT
ejpam-5861	310	15	5861	5861	NUM
ejpam-5861	310	16	14	14	NUM
ejpam-5861	310	17	of	of	ADP
ejpam-5861	310	18	33	33	NUM
ejpam-5861	310	19	lemma	lemma	PROPN
ejpam-5861	310	20	3	3	NUM
ejpam-5861	310	21	.	.	PUNCT
ejpam-5861	311	1	for	for	ADP
ejpam-5861	311	2	the	the	DET
ejpam-5861	311	3	function	function	NOUN
ejpam-5861	311	4	g	g	NOUN
ejpam-5861	311	5	:	:	PUNCT
ejpam-5861	311	6	[	[	X
ejpam-5861	311	7	0,t×r	0,t×r	NUM
ejpam-5861	311	8	→	→	SYM
ejpam-5861	311	9	r	r	NOUN
ejpam-5861	311	10	,	,	PUNCT
ejpam-5861	311	11	the	the	DET
ejpam-5861	311	12	given	give	VERB
ejpam-5861	311	13	problem	problem	NOUN
ejpam-5861	311	14	pc	pc	NOUN
ejpam-5861	311	15	0	0	NUM
ejpam-5861	311	16	dε	dε	NOUN
ejpam-5861	311	17	tϕ(t	tϕ(t	NOUN
ejpam-5861	311	18	)	)	PUNCT
ejpam-5861	311	19	=	=	SYM
ejpam-5861	312	1	g(t	g(t	PROPN
ejpam-5861	312	2	,	,	PUNCT
ejpam-5861	312	3	ϕ(t	ϕ(t	NUM
ejpam-5861	312	4	)	)	PUNCT
ejpam-5861	312	5	)	)	PUNCT
ejpam-5861	312	6	,	,	PUNCT
ejpam-5861	312	7	0	0	NUM
ejpam-5861	312	8	<	<	X
ejpam-5861	312	9	ε	ε	PROPN
ejpam-5861	312	10	≤	≤	PROPN
ejpam-5861	312	11	1	1	NUM
ejpam-5861	312	12	,	,	PUNCT
ejpam-5861	312	13	(	(	PUNCT
ejpam-5861	312	14	18	18	NUM
ejpam-5861	312	15	)	)	PUNCT
ejpam-5861	312	16	ϕ(0	ϕ(0	PROPN
ejpam-5861	312	17	)	)	PUNCT
ejpam-5861	313	1	=	=	SYM
ejpam-5861	313	2	ϕ0	ϕ0	NOUN
ejpam-5861	313	3	is	be	AUX
ejpam-5861	313	4	equivalent	equivalent	ADJ
ejpam-5861	313	5	to	to	ADP
ejpam-5861	313	6	the	the	DET
ejpam-5861	313	7	integral	integral	ADJ
ejpam-5861	313	8	equation	equation	NOUN
ejpam-5861	313	9	described	describe	VERB
ejpam-5861	313	10	by	by	ADP
ejpam-5861	313	11	ϕ(t	ϕ(t	PROPN
ejpam-5861	313	12	)	)	PUNCT
ejpam-5861	314	1	=	=	PUNCT
ejpam-5861	315	1			PROPN
ejpam-5861	315	2	ϕ0	ϕ0	NOUN
ejpam-5861	315	3	+	+	CCONJ
ejpam-5861	315	4	∫	∫	PROPN
ejpam-5861	315	5	t	t	NOUN
ejpam-5861	315	6	0	0	NUM
ejpam-5861	316	1	g(u	g(u	PROPN
ejpam-5861	316	2	,	,	PUNCT
ejpam-5861	316	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	316	4	,	,	PUNCT
ejpam-5861	316	5	t	t	PROPN
ejpam-5861	316	6	∈	∈	PROPN
ejpam-5861	316	7	∇1	∇1	PROPN
ejpam-5861	316	8	,	,	PUNCT
ejpam-5861	316	9	ϕ(t1	ϕ(t1	NUM
ejpam-5861	316	10	)	)	PUNCT
ejpam-5861	317	1	+	+	CCONJ
ejpam-5861	317	2	∫	∫	PROPN
ejpam-5861	317	3	t	t	PROPN
ejpam-5861	317	4	t1	t1	PROPN
ejpam-5861	317	5	(	(	PUNCT
ejpam-5861	317	6	t−	t−	PROPN
ejpam-5861	317	7	u)ε−1	u)ε−1	PROPN
ejpam-5861	317	8	γ(ε	γ(ε	PROPN
ejpam-5861	317	9	)	)	PUNCT
ejpam-5861	318	1	g(u	g(u	PROPN
ejpam-5861	318	2	,	,	PUNCT
ejpam-5861	318	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	318	4	,	,	PUNCT
ejpam-5861	318	5	t1	t1	NOUN
ejpam-5861	318	6	<	<	X
ejpam-5861	318	7	t	t	PROPN
ejpam-5861	318	8	≤	≤	PROPN
ejpam-5861	318	9	t	t	PROPN
ejpam-5861	318	10	,	,	PUNCT
ejpam-5861	318	11	(	(	PUNCT
ejpam-5861	318	12	19	19	NUM
ejpam-5861	318	13	)	)	PUNCT
ejpam-5861	318	14	proof	proof	NOUN
ejpam-5861	318	15	.	.	PUNCT
ejpam-5861	319	1	following	follow	VERB
ejpam-5861	319	2	the	the	DET
ejpam-5861	319	3	fashion	fashion	NOUN
ejpam-5861	319	4	of	of	ADP
ejpam-5861	319	5	lemma	lemma	PROPN
ejpam-5861	319	6	2	2	NUM
ejpam-5861	319	7	,	,	PUNCT
ejpam-5861	319	8	we	we	PRON
ejpam-5861	319	9	can	can	AUX
ejpam-5861	319	10	easily	easily	ADV
ejpam-5861	319	11	obtain	obtain	VERB
ejpam-5861	319	12	the	the	DET
ejpam-5861	319	13	solution	solution	NOUN
ejpam-5861	319	14	above	above	ADV
ejpam-5861	319	15	.	.	PUNCT
ejpam-5861	320	1	the	the	DET
ejpam-5861	320	2	hypothesis	hypothesis	NOUN
ejpam-5861	320	3	given	give	VERB
ejpam-5861	320	4	hold	hold	NOUN
ejpam-5861	320	5	:	:	PUNCT
ejpam-5861	320	6	(	(	PUNCT
ejpam-5861	320	7	h1	h1	PROPN
ejpam-5861	320	8	)	)	PUNCT
ejpam-5861	320	9	let	let	VERB
ejpam-5861	320	10	lg	lg	NOUN
ejpam-5861	320	11	>	>	X
ejpam-5861	320	12	0	0	PUNCT
ejpam-5861	320	13	is	be	AUX
ejpam-5861	320	14	real	real	ADJ
ejpam-5861	320	15	number	number	NOUN
ejpam-5861	320	16	and	and	CCONJ
ejpam-5861	320	17	ϕ	ϕ	NOUN
ejpam-5861	320	18	,	,	PUNCT
ejpam-5861	320	19	ϕ̄	ϕ̄	PROPN
ejpam-5861	320	20	∈	∈	PROPN
ejpam-5861	320	21	b	b	PROPN
ejpam-5861	320	22	,	,	PUNCT
ejpam-5861	320	23	then	then	ADV
ejpam-5861	320	24	|g(t	|g(t	PROPN
ejpam-5861	320	25	,	,	PUNCT
ejpam-5861	320	26	ϕ)−	ϕ)−	PROPN
ejpam-5861	320	27	g(t	g(t	PROPN
ejpam-5861	320	28	,	,	PUNCT
ejpam-5861	320	29	ϕ̄)|	ϕ̄)|	ADP
ejpam-5861	320	30	≤	≤	PROPN
ejpam-5861	320	31	lg|ϕ−	lg|ϕ−	PUNCT
ejpam-5861	320	32	ϕ̄|	ϕ̄|	NOUN
ejpam-5861	320	33	.	.	PUNCT
ejpam-5861	321	1	(	(	PUNCT
ejpam-5861	321	2	h2	h2	NOUN
ejpam-5861	321	3	)	)	PUNCT
ejpam-5861	321	4	let	let	VERB
ejpam-5861	321	5	cg	cg	NOUN
ejpam-5861	321	6	>	>	X
ejpam-5861	321	7	0	0	PUNCT
ejpam-5861	321	8	and	and	CCONJ
ejpam-5861	321	9	mg	mg	PROPN
ejpam-5861	321	10	>	>	X
ejpam-5861	321	11	0	0	NUM
ejpam-5861	321	12	,	,	PUNCT
ejpam-5861	321	13	then	then	ADV
ejpam-5861	321	14	|g(t	|g(t	PROPN
ejpam-5861	321	15	,	,	PUNCT
ejpam-5861	321	16	ϕ(t))|	ϕ(t))|	PROPN
ejpam-5861	321	17	≤	≤	PROPN
ejpam-5861	321	18	cg|ϕ|+mg	cg|ϕ|+mg	VERB
ejpam-5861	321	19	.	.	PUNCT
ejpam-5861	322	1	theorem	theorem	VERB
ejpam-5861	322	2	4	4	NUM
ejpam-5861	322	3	.	.	PUNCT
ejpam-5861	323	1	at	at	ADV
ejpam-5861	323	2	least	least	ADV
ejpam-5861	323	3	one	one	NUM
ejpam-5861	323	4	solution	solution	NOUN
ejpam-5861	323	5	exists	exist	VERB
ejpam-5861	323	6	for	for	ADP
ejpam-5861	323	7	the	the	DET
ejpam-5861	323	8	problem	problem	NOUN
ejpam-5861	323	9	(	(	PUNCT
ejpam-5861	323	10	18	18	NUM
ejpam-5861	323	11	)	)	PUNCT
ejpam-5861	323	12	under	under	ADP
ejpam-5861	323	13	the	the	DET
ejpam-5861	323	14	hypotheses	hypothesis	NOUN
ejpam-5861	323	15	(	(	PUNCT
ejpam-5861	323	16	h1	h1	PROPN
ejpam-5861	323	17	)	)	PUNCT
ejpam-5861	323	18	,	,	PUNCT
ejpam-5861	323	19	(	(	PUNCT
ejpam-5861	323	20	h2	h2	NOUN
ejpam-5861	323	21	)	)	PUNCT
ejpam-5861	323	22	.	.	PUNCT
ejpam-5861	324	1	proof	proof	NOUN
ejpam-5861	324	2	.	.	PUNCT
ejpam-5861	325	1	let	let	VERB
ejpam-5861	325	2	define	define	VERB
ejpam-5861	325	3	a	a	DET
ejpam-5861	325	4	closed	closed	ADJ
ejpam-5861	325	5	and	and	CCONJ
ejpam-5861	325	6	convex	convex	NOUN
ejpam-5861	325	7	subset	subset	VERB
ejpam-5861	326	1	d	d	X
ejpam-5861	326	2	⊂	⊂	PROPN
ejpam-5861	326	3	b	b	PROPN
ejpam-5861	326	4	as	as	ADP
ejpam-5861	326	5	d	d	PROPN
ejpam-5861	326	6	=	=	PUNCT
ejpam-5861	326	7	{	{	PUNCT
ejpam-5861	326	8	ϕ	ϕ	NOUN
ejpam-5861	326	9	∈	∈	PROPN
ejpam-5861	326	10	b	b	PROPN
ejpam-5861	326	11	:	:	PUNCT
ejpam-5861	326	12	∥ϕ∥	∥ϕ∥	PROPN
ejpam-5861	326	13	≤	≤	PROPN
ejpam-5861	326	14	r1,2	r1,2	PROPN
ejpam-5861	326	15	,	,	PUNCT
ejpam-5861	326	16	r1,2	r1,2	PROPN
ejpam-5861	326	17	>	>	X
ejpam-5861	326	18	0	0	NUM
ejpam-5861	326	19	}	}	PUNCT
ejpam-5861	326	20	.	.	PUNCT
ejpam-5861	327	1	let	let	VERB
ejpam-5861	327	2	n	n	PRON
ejpam-5861	327	3	:	:	PUNCT
ejpam-5861	327	4	d	d	X
ejpam-5861	327	5	→	→	SYM
ejpam-5861	327	6	d	d	X
ejpam-5861	327	7	using	use	VERB
ejpam-5861	327	8	(	(	PUNCT
ejpam-5861	327	9	35	35	NUM
ejpam-5861	327	10	)	)	PUNCT
ejpam-5861	327	11	,	,	PUNCT
ejpam-5861	327	12	then	then	ADV
ejpam-5861	327	13	n(ϕ	n(ϕ	NOUN
ejpam-5861	327	14	)	)	PUNCT
ejpam-5861	327	15	=	=	PUNCT
ejpam-5861	328	1			PROPN
ejpam-5861	328	2	ϕ0	ϕ0	NOUN
ejpam-5861	328	3	+	+	CCONJ
ejpam-5861	328	4	∫	∫	PROPN
ejpam-5861	328	5	t	t	NOUN
ejpam-5861	328	6	0	0	NUM
ejpam-5861	329	1	g(u	g(u	PROPN
ejpam-5861	329	2	,	,	PUNCT
ejpam-5861	329	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	329	4	,	,	PUNCT
ejpam-5861	329	5	t	t	PROPN
ejpam-5861	329	6	∈	∈	PROPN
ejpam-5861	329	7	∇1	∇1	PROPN
ejpam-5861	329	8	,	,	PUNCT
ejpam-5861	329	9	ϕ(t1	ϕ(t1	NUM
ejpam-5861	329	10	)	)	PUNCT
ejpam-5861	330	1	+	+	CCONJ
ejpam-5861	330	2	∫	∫	PROPN
ejpam-5861	330	3	t	t	PROPN
ejpam-5861	330	4	t1	t1	PROPN
ejpam-5861	330	5	(	(	PUNCT
ejpam-5861	330	6	t−	t−	PROPN
ejpam-5861	330	7	u)ε−1	u)ε−1	PROPN
ejpam-5861	330	8	γ(ε	γ(ε	PROPN
ejpam-5861	330	9	)	)	PUNCT
ejpam-5861	331	1	g(u	g(u	PROPN
ejpam-5861	331	2	,	,	PUNCT
ejpam-5861	331	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	331	4	,	,	PUNCT
ejpam-5861	331	5	t1	t1	NOUN
ejpam-5861	331	6	<	<	X
ejpam-5861	331	7	t	t	X
ejpam-5861	331	8	≤	≤	ADJ
ejpam-5861	331	9	t.	t.	NOUN
ejpam-5861	331	10	(	(	PUNCT
ejpam-5861	331	11	20	20	NUM
ejpam-5861	331	12	)	)	PUNCT
ejpam-5861	331	13	for	for	ADP
ejpam-5861	331	14	ϕ	ϕ	PROPN
ejpam-5861	331	15	∈	∈	PROPN
ejpam-5861	331	16	d	d	X
ejpam-5861	331	17	,	,	PUNCT
ejpam-5861	331	18	it	it	PRON
ejpam-5861	331	19	follows	follow	VERB
ejpam-5861	331	20	that	that	SCONJ
ejpam-5861	331	21	|n(ϕ)(t)|	|n(ϕ)(t)|	NOUN
ejpam-5861	331	22	≤	≤	NOUN
ejpam-5861	331	23			PROPN
ejpam-5861	331	24	|ϕ0|+	|ϕ0|+	NOUN
ejpam-5861	331	25	∫	∫	PROPN
ejpam-5861	331	26	t1	t1	NOUN
ejpam-5861	331	27	0	0	NUM
ejpam-5861	332	1	|g(u	|g(u	PROPN
ejpam-5861	332	2	,	,	PUNCT
ejpam-5861	332	3	ϕ(u))|du	ϕ(u))|du	PRON
ejpam-5861	332	4	,	,	PUNCT
ejpam-5861	332	5	|ϕ(t1)|+	|ϕ(t1)|+	PROPN
ejpam-5861	332	6	∫	∫	PROPN
ejpam-5861	332	7	t	t	PROPN
ejpam-5861	332	8	t1	t1	PROPN
ejpam-5861	332	9	(	(	PUNCT
ejpam-5861	332	10	t−	t−	PROPN
ejpam-5861	332	11	u)ε−1	u)ε−1	PROPN
ejpam-5861	332	12	γ(ε	γ(ε	PROPN
ejpam-5861	332	13	)	)	PUNCT
ejpam-5861	332	14	|g(u	|g(u	PROPN
ejpam-5861	332	15	,	,	PUNCT
ejpam-5861	332	16	ϕ(u))|	ϕ(u))|	X
ejpam-5861	332	17	du	du	PROPN
ejpam-5861	332	18	s.	s.	PROPN
ejpam-5861	332	19	naz	naz	PROPN
ejpam-5861	332	20	et	et	PROPN
ejpam-5861	332	21	al	al	PROPN
ejpam-5861	332	22	.	.	PUNCT
ejpam-5861	332	23	/	/	SYM
ejpam-5861	332	24	eur	eur	PROPN
ejpam-5861	332	25	.	.	PUNCT
ejpam-5861	333	1	j.	j.	PROPN
ejpam-5861	333	2	pure	pure	PROPN
ejpam-5861	333	3	appl	appl	PROPN
ejpam-5861	333	4	.	.	PROPN
ejpam-5861	333	5	math	math	PROPN
ejpam-5861	333	6	,	,	PUNCT
ejpam-5861	333	7	18	18	NUM
ejpam-5861	333	8	(	(	PUNCT
ejpam-5861	333	9	2	2	NUM
ejpam-5861	333	10	)	)	PUNCT
ejpam-5861	333	11	(	(	PUNCT
ejpam-5861	333	12	2025	2025	NUM
ejpam-5861	333	13	)	)	PUNCT
ejpam-5861	333	14	,	,	PUNCT
ejpam-5861	333	15	5861	5861	NUM
ejpam-5861	333	16	15	15	NUM
ejpam-5861	333	17	of	of	ADP
ejpam-5861	333	18	33	33	NUM
ejpam-5861	333	19	≤	≤	NUM
ejpam-5861	333	20			PROPN
ejpam-5861	333	21	|ϕ0|+	|ϕ0|+	NOUN
ejpam-5861	333	22	∫	∫	PROPN
ejpam-5861	333	23	t1	t1	NOUN
ejpam-5861	333	24	0	0	PUNCT
ejpam-5861	334	1	[	[	X
ejpam-5861	334	2	cg∥ϕ∥+mg	cg∥ϕ∥+mg	X
ejpam-5861	334	3	]	]	X
ejpam-5861	334	4	du	du	X
ejpam-5861	334	5	,	,	PUNCT
ejpam-5861	334	6	|ϕ(t1)|+	|ϕ(t1)|+	PROPN
ejpam-5861	334	7	∫	∫	PROPN
ejpam-5861	334	8	t	t	PROPN
ejpam-5861	334	9	t1	t1	PROPN
ejpam-5861	334	10	(	(	PUNCT
ejpam-5861	334	11	t−	t−	PROPN
ejpam-5861	334	12	u)ε−1	u)ε−1	PROPN
ejpam-5861	334	13	γ(ε	γ(ε	PROPN
ejpam-5861	334	14	)	)	PUNCT
ejpam-5861	335	1	[	[	X
ejpam-5861	335	2	cg∥ϕ∥+mg	cg∥ϕ∥+mg	X
ejpam-5861	335	3	]	]	X
ejpam-5861	335	4	du	du	X
ejpam-5861	335	5	,	,	PUNCT
ejpam-5861	335	6	≤	≤	NUM
ejpam-5861	335	7			PUNCT
ejpam-5861	335	8	|ϕ0|+	|ϕ0|+	X
ejpam-5861	335	9	t1	t1	NOUN
ejpam-5861	335	10	[	[	X
ejpam-5861	336	1	cgr1,2	cgr1,2	PROPN
ejpam-5861	336	2	+	+	NOUN
ejpam-5861	336	3	mg	mg	PROPN
ejpam-5861	336	4	]	]	X
ejpam-5861	336	5	≤	≤	PROPN
ejpam-5861	336	6	r1,2	r1,2	PROPN
ejpam-5861	336	7	,	,	PUNCT
ejpam-5861	336	8	t	t	PROPN
ejpam-5861	336	9	∈	∈	PROPN
ejpam-5861	336	10	∇1	∇1	PROPN
ejpam-5861	336	11	,	,	PUNCT
ejpam-5861	336	12	|ϕ(t1)|+	|ϕ(t1)|+	PROPN
ejpam-5861	336	13	tε	tε	ADP
ejpam-5861	336	14	γ(ε+	γ(ε+	NOUN
ejpam-5861	336	15	1	1	NUM
ejpam-5861	336	16	)	)	PUNCT
ejpam-5861	337	1	[	[	X
ejpam-5861	337	2	cgr1,2	cgr1,2	NOUN
ejpam-5861	337	3	+	+	NOUN
ejpam-5861	337	4	mg	mg	PROPN
ejpam-5861	337	5	]	]	X
ejpam-5861	337	6	≤	≤	PROPN
ejpam-5861	337	7	r1,2	r1,2	PROPN
ejpam-5861	337	8	,	,	PUNCT
ejpam-5861	337	9	t1	t1	NOUN
ejpam-5861	337	10	<	<	X
ejpam-5861	337	11	t	t	PROPN
ejpam-5861	337	12	≤	≤	X
ejpam-5861	337	13	t	t	PROPN
ejpam-5861	337	14	,	,	PUNCT
ejpam-5861	337	15	for	for	ADP
ejpam-5861	337	16	t1	t1	NOUN
ejpam-5861	337	17	<	<	X
ejpam-5861	337	18	t	t	PROPN
ejpam-5861	337	19	≤	≤	PROPN
ejpam-5861	337	20	t	t	PROPN
ejpam-5861	337	21	,	,	PUNCT
ejpam-5861	337	22	use	use	NOUN
ejpam-5861	337	23	|(t1	|(t1	NOUN
ejpam-5861	337	24	−	−	PROPN
ejpam-5861	337	25	u)ε	u)ε	SYM
ejpam-5861	337	26	−	−	PROPN
ejpam-5861	338	1	(	(	PUNCT
ejpam-5861	338	2	t−	t−	PROPN
ejpam-5861	338	3	u)ε|	u)ε|	NOUN
ejpam-5861	338	4	≤	≤	NUM
ejpam-5861	338	5	tε	tε	NOUN
ejpam-5861	338	6	,	,	PUNCT
ejpam-5861	338	7	one	one	PRON
ejpam-5861	338	8	has	have	VERB
ejpam-5861	338	9	r1,2	r1,2	PROPN
ejpam-5861	338	10	≥	≥	NUM
ejpam-5861	338	11	max	max	PROPN
ejpam-5861	338	12			PROPN
ejpam-5861	338	13	|ϕ0|+	|ϕ0|+	X
ejpam-5861	338	14	t1	t1	NOUN
ejpam-5861	338	15	mg	mg	PROPN
ejpam-5861	338	16	1−	1−	NUM
ejpam-5861	338	17	t1cg	t1cg	NUM
ejpam-5861	338	18	,	,	PUNCT
ejpam-5861	338	19	t	t	PROPN
ejpam-5861	338	20	∈	∈	PROPN
ejpam-5861	338	21	∇1	∇1	PROPN
ejpam-5861	338	22	,	,	PUNCT
ejpam-5861	338	23	|ϕ(t1)|γ(ε+	|ϕ(t1)|γ(ε+	NOUN
ejpam-5861	338	24	1	1	NUM
ejpam-5861	338	25	)	)	PUNCT
ejpam-5861	338	26	+	+	CCONJ
ejpam-5861	338	27	tεmg	tεmg	ADJ
ejpam-5861	338	28	(	(	PUNCT
ejpam-5861	338	29	γ(ε+	γ(ε+	PROPN
ejpam-5861	338	30	1)−	1)−	PROPN
ejpam-5861	338	31	tεcg	tεcg	NOUN
ejpam-5861	338	32	,	,	PUNCT
ejpam-5861	338	33	t1	t1	NOUN
ejpam-5861	338	34	<	<	X
ejpam-5861	338	35	t	t	X
ejpam-5861	338	36	≤	≤	NOUN
ejpam-5861	338	37	t.	t.	NOUN
ejpam-5861	338	38	thus	thus	ADV
ejpam-5861	338	39	proved	prove	VERB
ejpam-5861	338	40	that	that	SCONJ
ejpam-5861	338	41	∥n(ϕ)∥	∥n(ϕ)∥	PROPN
ejpam-5861	338	42	≤	≤	PROPN
ejpam-5861	338	43	r1,2	r1,2	PROPN
ejpam-5861	338	44	,	,	PUNCT
ejpam-5861	338	45	implies	imply	VERB
ejpam-5861	338	46	that	that	SCONJ
ejpam-5861	338	47	n(d	n(d	PROPN
ejpam-5861	338	48	)	)	PUNCT
ejpam-5861	338	49	⊂	⊂	PROPN
ejpam-5861	338	50	d.	d.	PROPN
ejpam-5861	338	51	thus	thus	ADV
ejpam-5861	338	52	,	,	PUNCT
ejpam-5861	338	53	bounded	bound	VERB
ejpam-5861	338	54	set	set	VERB
ejpam-5861	338	55	to	to	PART
ejpam-5861	338	56	bounded	bounded	ADJ
ejpam-5861	338	57	set	set	PROPN
ejpam-5861	338	58	is	be	AUX
ejpam-5861	338	59	mapped	map	VERB
ejpam-5861	338	60	by	by	ADP
ejpam-5861	338	61	n.	n.	PROPN
ejpam-5861	338	62	hence	hence	ADV
ejpam-5861	338	63	,	,	PUNCT
ejpam-5861	338	64	n	n	PRON
ejpam-5861	338	65	is	be	AUX
ejpam-5861	338	66	bounded	bound	VERB
ejpam-5861	338	67	.	.	PUNCT
ejpam-5861	339	1	take	take	VERB
ejpam-5861	339	2	tm	tm	NOUN
ejpam-5861	339	3	<	<	X
ejpam-5861	339	4	tn	tn	PROPN
ejpam-5861	339	5	∈	∈	PROPN
ejpam-5861	340	1	[	[	X
ejpam-5861	340	2	0	0	NUM
ejpam-5861	340	3	,	,	PUNCT
ejpam-5861	340	4	t1	t1	NOUN
ejpam-5861	340	5	]	]	X
ejpam-5861	340	6	,	,	PUNCT
ejpam-5861	340	7	we	we	PRON
ejpam-5861	340	8	have	have	VERB
ejpam-5861	340	9	|n(ϕ)(tn)−n(ϕ)(tm)|	|n(ϕ)(tn)−n(ϕ)(tm)|	NUM
ejpam-5861	340	10	=	=	SYM
ejpam-5861	340	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	340	12	∫	∫	PROPN
ejpam-5861	340	13	tn	tn	PROPN
ejpam-5861	340	14	0	0	NUM
ejpam-5861	341	1	g(u	g(u	PROPN
ejpam-5861	341	2	,	,	PUNCT
ejpam-5861	341	3	ϕ(u))du−	ϕ(u))du−	PROPN
ejpam-5861	341	4	∫	∫	PROPN
ejpam-5861	341	5	tm	tm	NOUN
ejpam-5861	341	6	0	0	PROPN
ejpam-5861	341	7	g(u	g(u	PROPN
ejpam-5861	341	8	,	,	PUNCT
ejpam-5861	341	9	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	341	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	341	11	≤	≤	NUM
ejpam-5861	341	12	∫	∫	PROPN
ejpam-5861	341	13	tn	tn	PROPN
ejpam-5861	341	14	tm	tm	PROPN
ejpam-5861	341	15	|g(u	|g(u	PROPN
ejpam-5861	341	16	,	,	PUNCT
ejpam-5861	341	17	ϕ(u))|du	ϕ(u))|du	ADJ
ejpam-5861	341	18	≤	≤	NUM
ejpam-5861	341	19	∫	∫	PROPN
ejpam-5861	341	20	tn	tn	PROPN
ejpam-5861	341	21	tm	tm	PROPN
ejpam-5861	341	22	[	[	X
ejpam-5861	341	23	cg∥ϕ∥+mg	cg∥ϕ∥+mg	X
ejpam-5861	341	24	]	]	X
ejpam-5861	341	25	du	du	X
ejpam-5861	341	26	≤	≤	X
ejpam-5861	341	27	(	(	PUNCT
ejpam-5861	341	28	cgr1,2	cgr1,2	ADJ
ejpam-5861	341	29	+	+	NOUN
ejpam-5861	341	30	mg)[tn	mg)[tn	NOUN
ejpam-5861	341	31	−	−	PROPN
ejpam-5861	341	32	tm	tm	NOUN
ejpam-5861	341	33	]	]	X
ejpam-5861	341	34	.	.	PUNCT
ejpam-5861	342	1	(	(	PUNCT
ejpam-5861	342	2	21	21	NUM
ejpam-5861	342	3	)	)	PUNCT
ejpam-5861	342	4	the	the	DET
ejpam-5861	342	5	(	(	PUNCT
ejpam-5861	342	6	21	21	NUM
ejpam-5861	342	7	)	)	PUNCT
ejpam-5861	342	8	tells	tell	VERB
ejpam-5861	342	9	us	we	PRON
ejpam-5861	342	10	that	that	SCONJ
ejpam-5861	342	11	tm	tm	PROPN
ejpam-5861	342	12	→	→	SYM
ejpam-5861	342	13	tn	tn	PROPN
ejpam-5861	342	14	,	,	PUNCT
ejpam-5861	342	15	implies	imply	VERB
ejpam-5861	342	16	that	that	SCONJ
ejpam-5861	342	17	|n(ϕ)(tn)−n(ϕ)(tm)|	|n(ϕ)(tn)−n(ϕ)(tm)|	NUM
ejpam-5861	342	18	→	→	SYM
ejpam-5861	342	19	0	0	NUM
ejpam-5861	342	20	.	.	PUNCT
ejpam-5861	343	1	the	the	DET
ejpam-5861	343	2	uniform	uniform	ADJ
ejpam-5861	343	3	continuity	continuity	NOUN
ejpam-5861	343	4	of	of	ADP
ejpam-5861	343	5	n	n	PROPN
ejpam-5861	343	6	implies	imply	VERB
ejpam-5861	343	7	that	that	SCONJ
ejpam-5861	343	8	∥n(ϕ)(tn)−n(ϕ)(tm)∥	∥n(ϕ)(tn)−n(ϕ)(tm)∥	NOUN
ejpam-5861	343	9	→	→	SYM
ejpam-5861	343	10	0	0	NUM
ejpam-5861	343	11	,	,	PUNCT
ejpam-5861	343	12	as	as	ADP
ejpam-5861	343	13	tn	tn	PROPN
ejpam-5861	343	14	→	→	SYM
ejpam-5861	343	15	tm	tm	PROPN
ejpam-5861	343	16	.	.	PUNCT
ejpam-5861	344	1	it	it	PRON
ejpam-5861	344	2	follows	follow	VERB
ejpam-5861	344	3	that	that	SCONJ
ejpam-5861	344	4	n	n	PRON
ejpam-5861	344	5	is	be	AUX
ejpam-5861	344	6	equi	equi	NOUN
ejpam-5861	344	7	-	-	PUNCT
ejpam-5861	344	8	continuous	continuous	ADJ
ejpam-5861	344	9	in	in	ADP
ejpam-5861	344	10	this	this	DET
ejpam-5861	344	11	case	case	NOUN
ejpam-5861	344	12	.	.	PUNCT
ejpam-5861	345	1	next	next	ADV
ejpam-5861	345	2	,	,	PUNCT
ejpam-5861	345	3	we	we	PRON
ejpam-5861	345	4	take	take	VERB
ejpam-5861	345	5	the	the	DET
ejpam-5861	345	6	other	other	ADJ
ejpam-5861	345	7	interval	interval	NOUN
ejpam-5861	345	8	tm	tm	ADP
ejpam-5861	345	9	<	<	X
ejpam-5861	345	10	tn	tn	PROPN
ejpam-5861	345	11	∈	∈	PROPN
ejpam-5861	345	12	(	(	PUNCT
ejpam-5861	345	13	t1,t	t1,t	PROPN
ejpam-5861	345	14	]	]	PUNCT
ejpam-5861	345	15	as	as	ADP
ejpam-5861	345	16	|n(ϕ)(tn)−n(ϕ)(tm)|	|n(ϕ)(tn)−n(ϕ)(tm)|	NUM
ejpam-5861	345	17	=	=	SYM
ejpam-5861	345	18	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	345	19	∫	∫	PROPN
ejpam-5861	345	20	tn	tn	PROPN
ejpam-5861	345	21	0	0	NUM
ejpam-5861	345	22	(	(	PUNCT
ejpam-5861	345	23	tn	tn	NOUN
ejpam-5861	345	24	−	−	PROPN
ejpam-5861	345	25	u)ε−1	u)ε−1	PROPN
ejpam-5861	345	26	γ(ε	γ(ε	PROPN
ejpam-5861	345	27	)	)	PUNCT
ejpam-5861	345	28	g(u	g(u	PROPN
ejpam-5861	345	29	,	,	PUNCT
ejpam-5861	345	30	g(u))du−	g(u))du−	PROPN
ejpam-5861	345	31	∫	∫	PROPN
ejpam-5861	345	32	tm	tm	PROPN
ejpam-5861	345	33	0	0	PROPN
ejpam-5861	346	1	(	(	PUNCT
ejpam-5861	346	2	tm	tm	NOUN
ejpam-5861	346	3	−	−	PROPN
ejpam-5861	346	4	τ)ε−1	τ)ε−1	PROPN
ejpam-5861	346	5	γ(ε	γ(ε	PROPN
ejpam-5861	346	6	)	)	PUNCT
ejpam-5861	347	1	g(u	g(u	PROPN
ejpam-5861	347	2	,	,	PUNCT
ejpam-5861	347	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	347	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	347	5	≤	≤	NUM
ejpam-5861	347	6	∫	∫	PROPN
ejpam-5861	347	7	tm	tm	NOUN
ejpam-5861	347	8	0	0	PUNCT
ejpam-5861	348	1	[	[	X
ejpam-5861	348	2	(	(	PUNCT
ejpam-5861	348	3	tm	tm	PROPN
ejpam-5861	348	4	−	−	PROPN
ejpam-5861	348	5	u)ε−1	u)ε−1	PROPN
ejpam-5861	348	6	−	−	PROPN
ejpam-5861	348	7	(	(	PUNCT
ejpam-5861	348	8	tn	tn	NOUN
ejpam-5861	348	9	−	−	PROPN
ejpam-5861	348	10	u)ε−1	u)ε−1	SYM
ejpam-5861	348	11	]	]	PUNCT
ejpam-5861	348	12	γ(ε	γ(ε	PROPN
ejpam-5861	348	13	)	)	PUNCT
ejpam-5861	348	14	|g(u	|g(u	PROPN
ejpam-5861	348	15	,	,	PUNCT
ejpam-5861	348	16	ϕ(u))|du	ϕ(u))|du	PRON
ejpam-5861	348	17	+	+	NUM
ejpam-5861	348	18	∫	∫	PROPN
ejpam-5861	348	19	tn	tn	PROPN
ejpam-5861	348	20	tm	tm	PROPN
ejpam-5861	348	21	(	(	PUNCT
ejpam-5861	348	22	tn	tn	PROPN
ejpam-5861	348	23	−	−	PROPN
ejpam-5861	348	24	u)ε−1	u)ε−1	PROPN
ejpam-5861	348	25	γ(ε	γ(ε	PROPN
ejpam-5861	348	26	)	)	PUNCT
ejpam-5861	348	27	|g(u	|g(u	PROPN
ejpam-5861	348	28	,	,	PUNCT
ejpam-5861	348	29	ϕ(u))|du	ϕ(u))|du	ADJ
ejpam-5861	348	30	s.	s.	PROPN
ejpam-5861	348	31	naz	naz	PROPN
ejpam-5861	348	32	et	et	PROPN
ejpam-5861	348	33	al	al	PROPN
ejpam-5861	348	34	.	.	PUNCT
ejpam-5861	348	35	/	/	SYM
ejpam-5861	348	36	eur	eur	PROPN
ejpam-5861	348	37	.	.	PUNCT
ejpam-5861	349	1	j.	j.	PROPN
ejpam-5861	349	2	pure	pure	PROPN
ejpam-5861	349	3	appl	appl	PROPN
ejpam-5861	349	4	.	.	PROPN
ejpam-5861	349	5	math	math	PROPN
ejpam-5861	349	6	,	,	PUNCT
ejpam-5861	349	7	18	18	NUM
ejpam-5861	349	8	(	(	PUNCT
ejpam-5861	349	9	2	2	NUM
ejpam-5861	349	10	)	)	PUNCT
ejpam-5861	349	11	(	(	PUNCT
ejpam-5861	349	12	2025	2025	NUM
ejpam-5861	349	13	)	)	PUNCT
ejpam-5861	349	14	,	,	PUNCT
ejpam-5861	349	15	5861	5861	NUM
ejpam-5861	349	16	16	16	NUM
ejpam-5861	349	17	of	of	ADP
ejpam-5861	349	18	33	33	NUM
ejpam-5861	349	19	≤	≤	NOUN
ejpam-5861	349	20	[	[	PUNCT
ejpam-5861	349	21	∫	∫	NOUN
ejpam-5861	349	22	tm	tm	NOUN
ejpam-5861	349	23	0	0	PUNCT
ejpam-5861	350	1	[	[	X
ejpam-5861	350	2	(	(	PUNCT
ejpam-5861	350	3	tm	tm	PROPN
ejpam-5861	350	4	−	−	PROPN
ejpam-5861	350	5	u)ε−1	u)ε−1	PROPN
ejpam-5861	350	6	−	−	PROPN
ejpam-5861	350	7	(	(	PUNCT
ejpam-5861	350	8	tn	tn	NOUN
ejpam-5861	350	9	−	−	PROPN
ejpam-5861	350	10	u)ε−1	u)ε−1	NOUN
ejpam-5861	350	11	]	]	PUNCT
ejpam-5861	350	12	γ(ε	γ(ε	PROPN
ejpam-5861	350	13	)	)	PUNCT
ejpam-5861	350	14	du	du	PROPN
ejpam-5861	351	1	+	+	CCONJ
ejpam-5861	351	2	∫	∫	PROPN
ejpam-5861	351	3	tn	tn	PROPN
ejpam-5861	351	4	tm	tm	PROPN
ejpam-5861	351	5	(	(	PUNCT
ejpam-5861	351	6	tn	tn	PROPN
ejpam-5861	351	7	−	−	PROPN
ejpam-5861	351	8	u)ε−1	u)ε−1	PROPN
ejpam-5861	351	9	γ(ε	γ(ε	PROPN
ejpam-5861	351	10	)	)	PUNCT
ejpam-5861	351	11	du	du	X
ejpam-5861	351	12	]	]	PUNCT
ejpam-5861	351	13	(	(	PUNCT
ejpam-5861	351	14	cg∥ϕ∥+mg	cg∥ϕ∥+mg	X
ejpam-5861	351	15	)	)	PUNCT
ejpam-5861	351	16	≤	≤	NOUN
ejpam-5861	351	17	(	(	PUNCT
ejpam-5861	351	18	cgr1,2	cgr1,2	NOUN
ejpam-5861	351	19	+	+	NOUN
ejpam-5861	351	20	mg	mg	PROPN
ejpam-5861	351	21	)	)	PUNCT
ejpam-5861	351	22	γ(ε+	γ(ε+	NOUN
ejpam-5861	351	23	1	1	NUM
ejpam-5861	351	24	)	)	PUNCT
ejpam-5861	352	1	[	[	X
ejpam-5861	352	2	tεn	tεn	NOUN
ejpam-5861	352	3	−	−	VERB
ejpam-5861	352	4	tεm	tεm	NOUN
ejpam-5861	352	5	+	+	CCONJ
ejpam-5861	352	6	2(tn	2(tn	NUM
ejpam-5861	352	7	−	−	NOUN
ejpam-5861	352	8	tm	tm	NOUN
ejpam-5861	352	9	)	)	PUNCT
ejpam-5861	352	10	ε	ε	PROPN
ejpam-5861	352	11	]	]	PUNCT
ejpam-5861	352	12	.	.	PUNCT
ejpam-5861	353	1	(	(	PUNCT
ejpam-5861	353	2	22	22	X
ejpam-5861	353	3	)	)	PUNCT
ejpam-5861	353	4	we	we	PRON
ejpam-5861	353	5	see	see	VERB
ejpam-5861	353	6	from	from	ADP
ejpam-5861	353	7	(	(	PUNCT
ejpam-5861	353	8	22	22	NUM
ejpam-5861	353	9	)	)	PUNCT
ejpam-5861	353	10	,	,	PUNCT
ejpam-5861	353	11	that	that	SCONJ
ejpam-5861	353	12	|n(ϕ)(tn)−n(ϕ)(tm)|	|n(ϕ)(tn)−n(ϕ)(tm)|	PRON
ejpam-5861	353	13	→	→	SYM
ejpam-5861	353	14	0	0	NUM
ejpam-5861	353	15	,	,	PUNCT
ejpam-5861	353	16	as	as	ADP
ejpam-5861	353	17	tm	tm	PROPN
ejpam-5861	353	18	→	→	SYM
ejpam-5861	353	19	tn	tn	PROPN
ejpam-5861	353	20	.	.	PUNCT
ejpam-5861	354	1	as	as	SCONJ
ejpam-5861	354	2	n	n	PROPN
ejpam-5861	354	3	is	be	AUX
ejpam-5861	354	4	bounded	bound	VERB
ejpam-5861	354	5	over	over	ADP
ejpam-5861	354	6	[	[	X
ejpam-5861	354	7	t1,t	t1,t	X
ejpam-5861	354	8	]	]	PUNCT
ejpam-5861	354	9	and	and	CCONJ
ejpam-5861	354	10	also	also	ADV
ejpam-5861	354	11	uniformly	uniformly	ADV
ejpam-5861	354	12	continuous	continuous	ADJ
ejpam-5861	354	13	.	.	PUNCT
ejpam-5861	355	1	thus	thus	ADV
ejpam-5861	355	2	∥n(ϕ)(tn)−n(ϕ)(tm)∥	∥n(ϕ)(tn)−n(ϕ)(tm)∥	NOUN
ejpam-5861	355	3	→	→	SYM
ejpam-5861	355	4	0	0	NUM
ejpam-5861	355	5	,	,	PUNCT
ejpam-5861	355	6	as	as	ADP
ejpam-5861	355	7	tm	tm	PROPN
ejpam-5861	355	8	→	→	SYM
ejpam-5861	355	9	tn	tn	PROPN
ejpam-5861	355	10	.	.	PUNCT
ejpam-5861	356	1	hence	hence	ADV
ejpam-5861	356	2	,	,	PUNCT
ejpam-5861	356	3	n	n	PRON
ejpam-5861	356	4	is	be	AUX
ejpam-5861	356	5	equi	equi	NOUN
ejpam-5861	356	6	-	-	PUNCT
ejpam-5861	356	7	continuous	continuous	ADJ
ejpam-5861	356	8	over	over	ADP
ejpam-5861	356	9	(	(	PUNCT
ejpam-5861	356	10	t1,t	t1,t	PROPN
ejpam-5861	356	11	]	]	PUNCT
ejpam-5861	356	12	.	.	PUNCT
ejpam-5861	357	1	therefore	therefore	ADV
ejpam-5861	357	2	,	,	PUNCT
ejpam-5861	357	3	n	n	PRON
ejpam-5861	357	4	is	be	AUX
ejpam-5861	357	5	equicontinuous	equicontinuous	ADJ
ejpam-5861	357	6	mapping	mapping	NOUN
ejpam-5861	357	7	over	over	ADP
ejpam-5861	357	8	[	[	X
ejpam-5861	357	9	0	0	NUM
ejpam-5861	357	10	,	,	PUNCT
ejpam-5861	357	11	t1]∪(t1,t	t1]∪(t1,t	ADP
ejpam-5861	357	12	]	]	PUNCT
ejpam-5861	357	13	.	.	PUNCT
ejpam-5861	358	1	by	by	ADP
ejpam-5861	358	2	arzelá-ascoli	arzelá-ascoli	NOUN
ejpam-5861	358	3	theorem	theorem	VERB
ejpam-5861	358	4	,	,	PUNCT
ejpam-5861	358	5	n	n	PRON
ejpam-5861	358	6	is	be	AUX
ejpam-5861	358	7	completely	completely	ADV
ejpam-5861	358	8	continuous	continuous	ADJ
ejpam-5861	358	9	.	.	PUNCT
ejpam-5861	359	1	thus	thus	ADV
ejpam-5861	359	2	in	in	ADP
ejpam-5861	359	3	view	view	NOUN
ejpam-5861	359	4	of	of	ADP
ejpam-5861	359	5	theorem	theorem	NOUN
ejpam-5861	359	6	1	1	NUM
ejpam-5861	359	7	,	,	PUNCT
ejpam-5861	359	8	the	the	DET
ejpam-5861	359	9	problem	problem	NOUN
ejpam-5861	359	10	(	(	PUNCT
ejpam-5861	359	11	18	18	NUM
ejpam-5861	359	12	)	)	PUNCT
ejpam-5861	359	13	has	have	VERB
ejpam-5861	359	14	at	at	ADV
ejpam-5861	359	15	least	least	ADJ
ejpam-5861	359	16	one	one	NUM
ejpam-5861	359	17	solution	solution	NOUN
ejpam-5861	359	18	.	.	PUNCT
ejpam-5861	360	1	theorem	theorem	NOUN
ejpam-5861	360	2	5	5	NUM
ejpam-5861	360	3	.	.	PUNCT
ejpam-5861	361	1	under	under	ADP
ejpam-5861	361	2	the	the	DET
ejpam-5861	361	3	hypothesis	hypothesis	NOUN
ejpam-5861	361	4	(	(	PUNCT
ejpam-5861	361	5	h1	h1	PROPN
ejpam-5861	361	6	)	)	PUNCT
ejpam-5861	361	7	,	,	PUNCT
ejpam-5861	361	8	the	the	DET
ejpam-5861	361	9	problem	problem	NOUN
ejpam-5861	361	10	(	(	PUNCT
ejpam-5861	361	11	18	18	NUM
ejpam-5861	361	12	)	)	PUNCT
ejpam-5861	361	13	has	have	VERB
ejpam-5861	361	14	a	a	DET
ejpam-5861	361	15	unique	unique	ADJ
ejpam-5861	361	16	solution	solution	NOUN
ejpam-5861	361	17	with	with	ADP
ejpam-5861	361	18	max	max	PROPN
ejpam-5861	361	19	{	{	PUNCT
ejpam-5861	361	20	t1lg	t1lg	PROPN
ejpam-5861	361	21	,	,	PUNCT
ejpam-5861	361	22	tε	tε	ADP
ejpam-5861	361	23	γ(ε+	γ(ε+	NOUN
ejpam-5861	361	24	1	1	NUM
ejpam-5861	361	25	)	)	PUNCT
ejpam-5861	361	26	lg	lg	NOUN
ejpam-5861	361	27	}	}	PUNCT
ejpam-5861	361	28	=	=	PUNCT
ejpam-5861	361	29	∆	∆	X
ejpam-5861	361	30	<	<	X
ejpam-5861	361	31	1	1	NUM
ejpam-5861	361	32	holds	hold	NOUN
ejpam-5861	361	33	.	.	PUNCT
ejpam-5861	362	1	proof	proof	NOUN
ejpam-5861	362	2	.	.	PUNCT
ejpam-5861	363	1	let	let	VERB
ejpam-5861	363	2	n	n	PRON
ejpam-5861	363	3	:	:	PUNCT
ejpam-5861	363	4	b	b	X
ejpam-5861	363	5	→	→	SYM
ejpam-5861	363	6	b	b	X
ejpam-5861	363	7	be	be	AUX
ejpam-5861	363	8	the	the	DET
ejpam-5861	363	9	mapping	mapping	NOUN
ejpam-5861	363	10	,	,	PUNCT
ejpam-5861	363	11	then	then	ADV
ejpam-5861	363	12	for	for	ADP
ejpam-5861	363	13	ϕ	ϕ	NOUN
ejpam-5861	363	14	,	,	PUNCT
ejpam-5861	363	15	ϕ̄	ϕ̄	PROPN
ejpam-5861	363	16	∈	∈	PROPN
ejpam-5861	363	17	b	b	PROPN
ejpam-5861	363	18	,	,	PUNCT
ejpam-5861	363	19	we	we	PRON
ejpam-5861	363	20	consider	consider	VERB
ejpam-5861	363	21	for	for	ADP
ejpam-5861	363	22	[	[	X
ejpam-5861	363	23	0	0	NUM
ejpam-5861	363	24	,	,	PUNCT
ejpam-5861	363	25	t1	t1	NOUN
ejpam-5861	363	26	]	]	PUNCT
ejpam-5861	363	27	as	as	ADP
ejpam-5861	363	28	∥n(ϕ)−n(ϕ̄)∥	∥n(ϕ)−n(ϕ̄)∥	PROPN
ejpam-5861	363	29	=	=	SYM
ejpam-5861	363	30	max	max	PROPN
ejpam-5861	363	31	t∈[0,t1	t∈[0,t1	PROPN
ejpam-5861	363	32	]	]	PUNCT
ejpam-5861	363	33	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	363	34	∫	∫	PROPN
ejpam-5861	363	35	t1	t1	NOUN
ejpam-5861	363	36	0	0	PUNCT
ejpam-5861	364	1	g(u	g(u	X
ejpam-5861	364	2	,	,	PUNCT
ejpam-5861	364	3	ϕ(u))du−	ϕ(u))du−	PROPN
ejpam-5861	364	4	∫	∫	PROPN
ejpam-5861	364	5	t1	t1	NOUN
ejpam-5861	364	6	0	0	PUNCT
ejpam-5861	365	1	g(u	g(u	X
ejpam-5861	365	2	,	,	PUNCT
ejpam-5861	365	3	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	365	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	365	5	≤	≤	NUM
ejpam-5861	365	6	t1lg∥ϕ−	t1lg∥ϕ−	PUNCT
ejpam-5861	365	7	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	365	8	(	(	PUNCT
ejpam-5861	365	9	23	23	NUM
ejpam-5861	365	10	)	)	PUNCT
ejpam-5861	365	11	hence	hence	ADV
ejpam-5861	365	12	,	,	PUNCT
ejpam-5861	365	13	we	we	PRON
ejpam-5861	365	14	have	have	VERB
ejpam-5861	365	15	from	from	ADP
ejpam-5861	365	16	(	(	PUNCT
ejpam-5861	365	17	23	23	NUM
ejpam-5861	365	18	)	)	PUNCT
ejpam-5861	365	19	∥n(ϕ)−n(ϕ̄)∥	∥n(ϕ)−n(ϕ̄)∥	NOUN
ejpam-5861	365	20	≤	≤	NOUN
ejpam-5861	365	21	t1lg∥ϕ−	t1lg∥ϕ−	PUNCT
ejpam-5861	365	22	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	365	23	(	(	PUNCT
ejpam-5861	365	24	24	24	NUM
ejpam-5861	365	25	)	)	PUNCT
ejpam-5861	365	26	if	if	SCONJ
ejpam-5861	365	27	t1	t1	PROPN
ejpam-5861	365	28	≤	≤	X
ejpam-5861	365	29	t	t	PROPN
ejpam-5861	365	30	≤	≤	PROPN
ejpam-5861	365	31	t	t	PROPN
ejpam-5861	365	32	,	,	PUNCT
ejpam-5861	365	33	one	one	NUM
ejpam-5861	365	34	has	have	VERB
ejpam-5861	365	35	∥n(ϕ)−n(ϕ̄)∥	∥n(ϕ)−n(ϕ̄)∥	NOUN
ejpam-5861	365	36	=	=	SYM
ejpam-5861	365	37	max	max	PROPN
ejpam-5861	365	38	t∈(t1,t	t∈(t1,t	X
ejpam-5861	365	39	]	]	PUNCT
ejpam-5861	365	40	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	365	41	∫	∫	PROPN
ejpam-5861	365	42	t	t	PROPN
ejpam-5861	365	43	t1	t1	PROPN
ejpam-5861	365	44	(	(	PUNCT
ejpam-5861	365	45	t−	t−	PROPN
ejpam-5861	365	46	u)ε−1	u)ε−1	PROPN
ejpam-5861	365	47	γ(ε	γ(ε	PROPN
ejpam-5861	365	48	)	)	PUNCT
ejpam-5861	365	49	g(u	g(u	PROPN
ejpam-5861	365	50	,	,	PUNCT
ejpam-5861	365	51	ϕ(u))du−	ϕ(u))du−	PROPN
ejpam-5861	365	52	∫	∫	PROPN
ejpam-5861	365	53	t	t	PROPN
ejpam-5861	365	54	t1	t1	PROPN
ejpam-5861	365	55	(	(	PUNCT
ejpam-5861	365	56	t−	t−	PROPN
ejpam-5861	365	57	u)ε−1	u)ε−1	PROPN
ejpam-5861	365	58	γ(ε	γ(ε	PROPN
ejpam-5861	365	59	)	)	PUNCT
ejpam-5861	365	60	g(u	g(u	PROPN
ejpam-5861	365	61	,	,	PUNCT
ejpam-5861	365	62	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	365	63	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	365	64	≤	≤	NUM
ejpam-5861	365	65	tεlg	tεlg	NOUN
ejpam-5861	365	66	γ(ε+	γ(ε+	NOUN
ejpam-5861	365	67	1	1	NUM
ejpam-5861	365	68	)	)	PUNCT
ejpam-5861	365	69	∥ϕ−	∥ϕ−	NUM
ejpam-5861	365	70	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	365	71	(	(	PUNCT
ejpam-5861	365	72	25	25	NUM
ejpam-5861	365	73	)	)	PUNCT
ejpam-5861	365	74	let	let	VERB
ejpam-5861	365	75	max	max	PROPN
ejpam-5861	365	76	{	{	PUNCT
ejpam-5861	365	77	tlg	tlg	PROPN
ejpam-5861	365	78	,	,	PUNCT
ejpam-5861	365	79	tεlg	tεlg	PROPN
ejpam-5861	365	80	γ(ε+1	γ(ε+1	NOUN
ejpam-5861	365	81	)	)	PUNCT
ejpam-5861	365	82	}	}	PUNCT
ejpam-5861	366	1	=	=	PUNCT
ejpam-5861	366	2	∆.	∆.	X
ejpam-5861	366	3	then	then	ADV
ejpam-5861	366	4	,	,	PUNCT
ejpam-5861	366	5	from	from	ADP
ejpam-5861	366	6	(	(	PUNCT
ejpam-5861	366	7	24	24	NUM
ejpam-5861	366	8	)	)	PUNCT
ejpam-5861	366	9	and	and	CCONJ
ejpam-5861	366	10	(	(	PUNCT
ejpam-5861	366	11	25	25	NUM
ejpam-5861	366	12	)	)	PUNCT
ejpam-5861	366	13	)	)	PUNCT
ejpam-5861	366	14	,	,	PUNCT
ejpam-5861	366	15	we	we	PRON
ejpam-5861	366	16	have	have	VERB
ejpam-5861	366	17	∥n(ϕ)−n(ϕ̄)∥	∥n(ϕ)−n(ϕ̄)∥	NOUN
ejpam-5861	366	18	≤	≤	NOUN
ejpam-5861	366	19	∆∥ϕ−	∆∥ϕ−	ADJ
ejpam-5861	366	20	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	366	21	(	(	PUNCT
ejpam-5861	366	22	26	26	NUM
ejpam-5861	366	23	)	)	PUNCT
ejpam-5861	366	24	as	as	ADP
ejpam-5861	366	25	a	a	DET
ejpam-5861	366	26	result	result	NOUN
ejpam-5861	366	27	,	,	PUNCT
ejpam-5861	366	28	an	an	DET
ejpam-5861	366	29	operator	operator	NOUN
ejpam-5861	366	30	of	of	ADP
ejpam-5861	366	31	contraction	contraction	NOUN
ejpam-5861	366	32	is	be	AUX
ejpam-5861	366	33	n.	n.	ADJ
ejpam-5861	366	34	as	as	ADP
ejpam-5861	366	35	a	a	DET
ejpam-5861	366	36	result	result	NOUN
ejpam-5861	366	37	,	,	PUNCT
ejpam-5861	366	38	there	there	PRON
ejpam-5861	366	39	is	be	VERB
ejpam-5861	366	40	only	only	ADV
ejpam-5861	366	41	one	one	NUM
ejpam-5861	366	42	solution	solution	NOUN
ejpam-5861	366	43	to	to	ADP
ejpam-5861	366	44	the	the	DET
ejpam-5861	366	45	problem	problem	NOUN
ejpam-5861	366	46	(	(	PUNCT
ejpam-5861	366	47	18	18	NUM
ejpam-5861	366	48	)	)	PUNCT
ejpam-5861	366	49	.	.	PUNCT
ejpam-5861	367	1	s.	s.	PROPN
ejpam-5861	367	2	naz	naz	PROPN
ejpam-5861	367	3	et	et	PROPN
ejpam-5861	367	4	al	al	PROPN
ejpam-5861	367	5	.	.	PUNCT
ejpam-5861	367	6	/	/	SYM
ejpam-5861	367	7	eur	eur	PROPN
ejpam-5861	367	8	.	.	PUNCT
ejpam-5861	368	1	j.	j.	PROPN
ejpam-5861	368	2	pure	pure	PROPN
ejpam-5861	368	3	appl	appl	PROPN
ejpam-5861	368	4	.	.	PROPN
ejpam-5861	368	5	math	math	PROPN
ejpam-5861	368	6	,	,	PUNCT
ejpam-5861	368	7	18	18	NUM
ejpam-5861	368	8	(	(	PUNCT
ejpam-5861	368	9	2	2	NUM
ejpam-5861	368	10	)	)	PUNCT
ejpam-5861	368	11	(	(	PUNCT
ejpam-5861	368	12	2025	2025	NUM
ejpam-5861	368	13	)	)	PUNCT
ejpam-5861	368	14	,	,	PUNCT
ejpam-5861	368	15	5861	5861	NUM
ejpam-5861	368	16	17	17	NUM
ejpam-5861	368	17	of	of	ADP
ejpam-5861	368	18	33	33	NUM
ejpam-5861	368	19	5	5	NUM
ejpam-5861	368	20	.	.	PUNCT
ejpam-5861	369	1	stability	stability	NOUN
ejpam-5861	369	2	theory	theory	NOUN
ejpam-5861	369	3	here	here	ADV
ejpam-5861	369	4	we	we	PRON
ejpam-5861	369	5	discuss	discuss	VERB
ejpam-5861	369	6	the	the	DET
ejpam-5861	369	7	stability	stability	NOUN
ejpam-5861	369	8	results	result	NOUN
ejpam-5861	369	9	for	for	ADP
ejpam-5861	369	10	local	local	ADJ
ejpam-5861	369	11	and	and	CCONJ
ejpam-5861	369	12	global	global	ADJ
ejpam-5861	369	13	stability	stability	NOUN
ejpam-5861	369	14	as	as	ADV
ejpam-5861	369	15	well	well	ADV
ejpam-5861	369	16	as	as	ADP
ejpam-5861	369	17	uh	uh	INTJ
ejpam-5861	369	18	stability	stability	NOUN
ejpam-5861	369	19	.	.	PUNCT
ejpam-5861	370	1	5.1	5.1	NUM
ejpam-5861	370	2	.	.	PUNCT
ejpam-5861	371	1	stability	stability	NOUN
ejpam-5861	371	2	results	result	NOUN
ejpam-5861	371	3	we	we	PRON
ejpam-5861	371	4	use	use	VERB
ejpam-5861	371	5	the	the	DET
ejpam-5861	371	6	jacobian	jacobian	ADJ
ejpam-5861	371	7	matrix	matrix	NOUN
ejpam-5861	371	8	method	method	NOUN
ejpam-5861	371	9	and	and	CCONJ
ejpam-5861	371	10	lyapunovvolterra	lyapunovvolterra	NOUN
ejpam-5861	371	11	method	method	NOUN
ejpam-5861	371	12	to	to	PART
ejpam-5861	371	13	prove	prove	VERB
ejpam-5861	371	14	some	some	DET
ejpam-5861	371	15	results	result	NOUN
ejpam-5861	371	16	for	for	ADP
ejpam-5861	371	17	las	las	NOUN
ejpam-5861	371	18	and	and	CCONJ
ejpam-5861	371	19	gas	gas	NOUN
ejpam-5861	371	20	of	of	ADP
ejpam-5861	371	21	dfe	dfe	PROPN
ejpam-5861	371	22	and	and	CCONJ
ejpam-5861	371	23	endemic	endemic	ADJ
ejpam-5861	371	24	equilibrium	equilibrium	NOUN
ejpam-5861	371	25	points	point	NOUN
ejpam-5861	371	26	.	.	PUNCT
ejpam-5861	372	1	theorem	theorem	VERB
ejpam-5861	372	2	6	6	NUM
ejpam-5861	372	3	.	.	PUNCT
ejpam-5861	373	1	the	the	DET
ejpam-5861	373	2	dfe	dfe	PROPN
ejpam-5861	373	3	point	point	NOUN
ejpam-5861	373	4	is	be	AUX
ejpam-5861	373	5	las	las	PROPN
ejpam-5861	373	6	if	if	SCONJ
ejpam-5861	373	7	r0	r0	NOUN
ejpam-5861	373	8	<	<	X
ejpam-5861	373	9	1	1	NUM
ejpam-5861	373	10	,	,	PUNCT
ejpam-5861	373	11	otherwise	otherwise	ADV
ejpam-5861	373	12	unstable	unstable	ADJ
ejpam-5861	373	13	.	.	PUNCT
ejpam-5861	374	1	proof	proof	NOUN
ejpam-5861	374	2	.	.	PUNCT
ejpam-5861	375	1	the	the	DET
ejpam-5861	375	2	jacobian	jacobian	ADJ
ejpam-5861	375	3	matrix	matrix	NOUN
ejpam-5861	375	4	say	say	VERB
ejpam-5861	375	5	j	j	PROPN
ejpam-5861	375	6	at	at	ADP
ejpam-5861	375	7	dfe	dfe	PROPN
ejpam-5861	375	8	(	(	PUNCT
ejpam-5861	375	9	λ	λ	X
ejpam-5861	375	10	η+d	η+d	PROPN
ejpam-5861	375	11	,	,	PUNCT
ejpam-5861	375	12	λ	λ	PROPN
ejpam-5861	375	13	d(η+d	d(η+d	PROPN
ejpam-5861	375	14	)	)	PUNCT
ejpam-5861	375	15	,	,	PUNCT
ejpam-5861	375	16	0	0	NUM
ejpam-5861	375	17	,	,	PUNCT
ejpam-5861	375	18	0	0	NUM
ejpam-5861	375	19	,	,	PUNCT
ejpam-5861	375	20	0	0	NUM
ejpam-5861	375	21	,	,	PUNCT
ejpam-5861	375	22	0	0	NUM
ejpam-5861	375	23	,	,	PUNCT
ejpam-5861	375	24	0	0	NUM
ejpam-5861	375	25	)	)	PUNCT
ejpam-5861	375	26	of	of	ADP
ejpam-5861	375	27	model	model	NOUN
ejpam-5861	375	28	(	(	PUNCT
ejpam-5861	375	29	2	2	NUM
ejpam-5861	375	30	)	)	PUNCT
ejpam-5861	375	31	is	be	AUX
ejpam-5861	375	32	given	give	VERB
ejpam-5861	375	33	by	by	ADP
ejpam-5861	375	34	j	j	PROPN
ejpam-5861	375	35	=	=	SYM
ejpam-5861	375	36			NOUN
ejpam-5861	376	1	−(η	−(η	NOUN
ejpam-5861	376	2	+	+	CCONJ
ejpam-5861	376	3	d	d	NOUN
ejpam-5861	376	4	)	)	PUNCT
ejpam-5861	376	5	0	0	NUM
ejpam-5861	376	6	0	0	NUM
ejpam-5861	376	7	−b(1−	−b(1−	NOUN
ejpam-5861	376	8	pξ	pξ	NOUN
ejpam-5861	376	9	)	)	PUNCT
ejpam-5861	376	10	λ	λ	PROPN
ejpam-5861	376	11	η+d	η+d	PROPN
ejpam-5861	376	12	0	0	NUM
ejpam-5861	376	13	0	0	NUM
ejpam-5861	376	14	η	η	PROPN
ejpam-5861	376	15	−d	−d	PROPN
ejpam-5861	376	16	0	0	PUNCT
ejpam-5861	376	17	−wbλ	−wbλ	PROPN
ejpam-5861	376	18	d(d+η	d(d+η	NOUN
ejpam-5861	376	19	)	)	PUNCT
ejpam-5861	376	20	0	0	NUM
ejpam-5861	376	21	0	0	NUM
ejpam-5861	376	22	0	0	NUM
ejpam-5861	376	23	0	0	NUM
ejpam-5861	377	1	−(τ	−(τ	NOUN
ejpam-5861	377	2	+	+	CCONJ
ejpam-5861	377	3	d	d	NOUN
ejpam-5861	377	4	)	)	PUNCT
ejpam-5861	377	5	wbλ	wbλ	PROPN
ejpam-5861	377	6	d(d+η	d(d+η	NOUN
ejpam-5861	377	7	)	)	PUNCT
ejpam-5861	378	1	+	+	CCONJ
ejpam-5861	378	2	b(1−pξ)λ	b(1−pξ)λ	PROPN
ejpam-5861	378	3	η+d	η+d	PROPN
ejpam-5861	378	4	0	0	NUM
ejpam-5861	378	5	0	0	NUM
ejpam-5861	378	6	0	0	NUM
ejpam-5861	378	7	0	0	NUM
ejpam-5861	379	1	τ	τ	X
ejpam-5861	380	1	−(αi	−(αi	PROPN
ejpam-5861	381	1	+	+	NUM
ejpam-5861	381	2	σi	σi	X
ejpam-5861	381	3	+	+	CCONJ
ejpam-5861	381	4	d	d	NOUN
ejpam-5861	381	5	)	)	PUNCT
ejpam-5861	381	6	0	0	NUM
ejpam-5861	381	7	0	0	NUM
ejpam-5861	381	8	0	0	NUM
ejpam-5861	381	9	0	0	NUM
ejpam-5861	381	10	0	0	NUM
ejpam-5861	381	11	σi	σi	NOUN
ejpam-5861	381	12	−(σq	−(σq	PROPN
ejpam-5861	382	1	+	+	CCONJ
ejpam-5861	382	2	δq	δq	PART
ejpam-5861	382	3	+	+	CCONJ
ejpam-5861	382	4	d	d	NOUN
ejpam-5861	382	5	)	)	PUNCT
ejpam-5861	382	6	0	0	NUM
ejpam-5861	382	7	0	0	NUM
ejpam-5861	382	8	0	0	NUM
ejpam-5861	382	9	0	0	NUM
ejpam-5861	383	1	σi	σi	PRON
ejpam-5861	383	2	σq	σq	NOUN
ejpam-5861	383	3	−d	−d	ADJ
ejpam-5861	383	4			PROPN
ejpam-5861	383	5	(	(	PUNCT
ejpam-5861	383	6	27	27	NUM
ejpam-5861	383	7	)	)	PUNCT
ejpam-5861	383	8	computing	compute	VERB
ejpam-5861	383	9	the	the	DET
ejpam-5861	383	10	eigenvalues	eigenvalue	NOUN
ejpam-5861	383	11	of	of	ADP
ejpam-5861	383	12	(	(	PUNCT
ejpam-5861	383	13	27	27	NUM
ejpam-5861	383	14	)	)	PUNCT
ejpam-5861	383	15	,	,	PUNCT
ejpam-5861	383	16	we	we	PRON
ejpam-5861	383	17	have	have	AUX
ejpam-5861	383	18	(	(	PUNCT
ejpam-5861	383	19	λ+	λ+	PUNCT
ejpam-5861	383	20	(	(	PUNCT
ejpam-5861	383	21	η	η	NOUN
ejpam-5861	383	22	+	+	NOUN
ejpam-5861	383	23	d))(λ+	d))(λ+	VERB
ejpam-5861	383	24	µ)(λ4	µ)(λ4	ADJ
ejpam-5861	383	25	+	+	CCONJ
ejpam-5861	383	26	a1λ	a1λ	PROPN
ejpam-5861	383	27	3	3	NUM
ejpam-5861	383	28	+	+	NUM
ejpam-5861	383	29	a2λ	a2λ	NOUN
ejpam-5861	383	30	2	2	NUM
ejpam-5861	383	31	+	+	CCONJ
ejpam-5861	383	32	a3λ+	a3λ+	NOUN
ejpam-5861	383	33	a4	a4	ADV
ejpam-5861	383	34	)	)	PUNCT
ejpam-5861	383	35	=	=	SYM
ejpam-5861	383	36	0	0	NUM
ejpam-5861	383	37	,	,	PUNCT
ejpam-5861	383	38	(	(	PUNCT
ejpam-5861	383	39	28	28	NUM
ejpam-5861	383	40	)	)	PUNCT
ejpam-5861	384	1	where	where	SCONJ
ejpam-5861	384	2	a1	a1	NOUN
ejpam-5861	384	3	=	=	SYM
ejpam-5861	384	4	k	k	PROPN
ejpam-5861	384	5	+	+	NUM
ejpam-5861	384	6	l	l	NOUN
ejpam-5861	385	1	+	+	X
ejpam-5861	385	2	τ	τ	PROPN
ejpam-5861	385	3	+	+	SYM
ejpam-5861	385	4	d	d	PROPN
ejpam-5861	385	5	,	,	PUNCT
ejpam-5861	385	6	a2	a2	PROPN
ejpam-5861	385	7	=	=	SYM
ejpam-5861	385	8	kl	kl	PROPN
ejpam-5861	386	1	+	+	PROPN
ejpam-5861	386	2	m+	m+	NUM
ejpam-5861	386	3	n+	n+	X
ejpam-5861	386	4	(	(	PUNCT
ejpam-5861	386	5	k	k	X
ejpam-5861	386	6	+	+	CCONJ
ejpam-5861	386	7	l)(τ	l)(τ	VERB
ejpam-5861	387	1	+	+	CCONJ
ejpam-5861	387	2	d	d	X
ejpam-5861	387	3	)	)	PUNCT
ejpam-5861	387	4	,	,	PUNCT
ejpam-5861	387	5	a3	a3	NOUN
ejpam-5861	387	6	=	=	SYM
ejpam-5861	387	7	km+	km+	NOUN
ejpam-5861	387	8	(	(	PUNCT
ejpam-5861	387	9	τ	τ	PROPN
ejpam-5861	387	10	+	+	NUM
ejpam-5861	387	11	d)(kl	d)(kl	PROPN
ejpam-5861	387	12	+	+	PROPN
ejpam-5861	387	13	m	m	NOUN
ejpam-5861	387	14	)	)	PUNCT
ejpam-5861	387	15	+	+	CCONJ
ejpam-5861	387	16	nl	nl	PROPN
ejpam-5861	387	17	,	,	PUNCT
ejpam-5861	387	18	a4	a4	NOUN
ejpam-5861	387	19	=	=	SYM
ejpam-5861	387	20	km(τ	km(τ	X
ejpam-5861	387	21	+	+	CCONJ
ejpam-5861	387	22	d	d	X
ejpam-5861	387	23	)	)	PUNCT
ejpam-5861	387	24	+	+	CCONJ
ejpam-5861	387	25	nm	nm	ADJ
ejpam-5861	387	26	,	,	PUNCT
ejpam-5861	387	27	such	such	ADJ
ejpam-5861	387	28	that	that	SCONJ
ejpam-5861	387	29	k	k	PROPN
ejpam-5861	387	30	=	=	PUNCT
ejpam-5861	387	31	σi	σi	PROPN
ejpam-5861	388	1	+	+	CCONJ
ejpam-5861	388	2	αi	αi	VERB
ejpam-5861	389	1	+	+	CCONJ
ejpam-5861	390	1	d	d	X
ejpam-5861	390	2	,	,	PUNCT
ejpam-5861	390	3	l	l	NOUN
ejpam-5861	390	4	=	=	PUNCT
ejpam-5861	390	5	σq	σq	PROPN
ejpam-5861	390	6	+	+	NOUN
ejpam-5861	390	7	δq	δq	ADP
ejpam-5861	390	8	+	+	CCONJ
ejpam-5861	390	9	2d	2d	NOUN
ejpam-5861	390	10	,	,	PUNCT
ejpam-5861	390	11	m	m	VERB
ejpam-5861	390	12	=	=	ADJ
ejpam-5861	390	13	d(σq	d(σq	PROPN
ejpam-5861	390	14	+	+	CCONJ
ejpam-5861	390	15	δq	δq	ADP
ejpam-5861	390	16	+	+	CCONJ
ejpam-5861	390	17	d	d	NOUN
ejpam-5861	390	18	)	)	PUNCT
ejpam-5861	390	19	,	,	PUNCT
ejpam-5861	390	20	n	n	NOUN
ejpam-5861	390	21	=	=	SYM
ejpam-5861	390	22	(	(	PUNCT
ejpam-5861	390	23	τb(w	τb(w	X
ejpam-5861	390	24	+	+	NUM
ejpam-5861	390	25	a(1−	a(1−	ADJ
ejpam-5861	390	26	pξ))λ	pξ))λ	PROPN
ejpam-5861	390	27	d(η	d(η	NOUN
ejpam-5861	390	28	+	+	CCONJ
ejpam-5861	390	29	d	d	X
ejpam-5861	390	30	)	)	PUNCT
ejpam-5861	390	31	.	.	PUNCT
ejpam-5861	391	1	we	we	PRON
ejpam-5861	391	2	see	see	VERB
ejpam-5861	391	3	from	from	ADP
ejpam-5861	391	4	(	(	PUNCT
ejpam-5861	391	5	28	28	NUM
ejpam-5861	391	6	)	)	PUNCT
ejpam-5861	391	7	that	that	ADV
ejpam-5861	391	8	λ1	λ1	ADJ
ejpam-5861	391	9	=	=	SYM
ejpam-5861	391	10	−(η	−(η	NOUN
ejpam-5861	391	11	+	+	CCONJ
ejpam-5861	391	12	d	d	X
ejpam-5861	391	13	)	)	PUNCT
ejpam-5861	391	14	<	<	X
ejpam-5861	391	15	0	0	NUM
ejpam-5861	391	16	,	,	PUNCT
ejpam-5861	391	17	λ2	λ2	NOUN
ejpam-5861	391	18	=	=	SYM
ejpam-5861	391	19	−µ	−µ	ADJ
ejpam-5861	391	20	<	<	X
ejpam-5861	391	21	0	0	NUM
ejpam-5861	391	22	,	,	PUNCT
ejpam-5861	391	23	which	which	PRON
ejpam-5861	391	24	implies	imply	VERB
ejpam-5861	391	25	that	that	SCONJ
ejpam-5861	391	26	real	real	ADJ
ejpam-5861	391	27	parts	part	NOUN
ejpam-5861	391	28	of	of	ADP
ejpam-5861	391	29	eigenvalues	eigenvalue	NOUN
ejpam-5861	391	30	are	be	AUX
ejpam-5861	391	31	negative	negative	ADJ
ejpam-5861	391	32	.	.	PUNCT
ejpam-5861	392	1	it	it	PRON
ejpam-5861	392	2	is	be	AUX
ejpam-5861	392	3	possible	possible	ADJ
ejpam-5861	392	4	to	to	PART
ejpam-5861	392	5	demonstrate	demonstrate	VERB
ejpam-5861	392	6	that	that	SCONJ
ejpam-5861	392	7	the	the	DET
ejpam-5861	392	8	eigenvalues	eigenvalue	NOUN
ejpam-5861	392	9	have	have	VERB
ejpam-5861	392	10	negative	negative	ADJ
ejpam-5861	392	11	real	real	ADJ
ejpam-5861	392	12	parts	part	NOUN
ejpam-5861	392	13	by	by	ADP
ejpam-5861	392	14	applying	apply	VERB
ejpam-5861	392	15	the	the	DET
ejpam-5861	392	16	routh	routh	PROPN
ejpam-5861	392	17	-	-	PUNCT
ejpam-5861	392	18	hurwitz	hurwitz	PROPN
ejpam-5861	392	19	criterion	criterion	NOUN
ejpam-5861	392	20	.	.	PUNCT
ejpam-5861	393	1	hence	hence	ADV
ejpam-5861	393	2	,	,	PUNCT
ejpam-5861	393	3	we	we	PRON
ejpam-5861	393	4	get	get	VERB
ejpam-5861	393	5	from	from	ADP
ejpam-5861	393	6	λ4	λ4	PROPN
ejpam-5861	393	7	+	+	CCONJ
ejpam-5861	393	8	a1λ	a1λ	PROPN
ejpam-5861	393	9	3	3	NUM
ejpam-5861	393	10	+	+	NUM
ejpam-5861	393	11	a2λ	a2λ	NOUN
ejpam-5861	393	12	2	2	NUM
ejpam-5861	393	13	+	+	CCONJ
ejpam-5861	393	14	a3λ+	a3λ+	NOUN
ejpam-5861	393	15	a4	a4	NOUN
ejpam-5861	393	16	=	=	SYM
ejpam-5861	393	17	0	0	NUM
ejpam-5861	393	18	,	,	PUNCT
ejpam-5861	393	19	from	from	ADP
ejpam-5861	393	20	which	which	PRON
ejpam-5861	393	21	we	we	PRON
ejpam-5861	393	22	see	see	VERB
ejpam-5861	393	23	that	that	SCONJ
ejpam-5861	393	24	λ4	λ4	PROPN
ejpam-5861	393	25	:	:	PUNCT
ejpam-5861	393	26	a0	a0	PROPN
ejpam-5861	393	27	a2	a2	PROPN
ejpam-5861	393	28	a4	a4	PROPN
ejpam-5861	394	1	λ3	λ3	PROPN
ejpam-5861	394	2	:	:	PUNCT
ejpam-5861	394	3	b1	b1	PROPN
ejpam-5861	394	4	b3	b3	PROPN
ejpam-5861	394	5	b5	b5	PROPN
ejpam-5861	394	6	λ2	λ2	PROPN
ejpam-5861	394	7	:	:	PUNCT
ejpam-5861	395	1	c1	c1	PROPN
ejpam-5861	395	2	c3	c3	PROPN
ejpam-5861	395	3	c5	c5	PROPN
ejpam-5861	395	4	s.	s.	PROPN
ejpam-5861	395	5	naz	naz	PROPN
ejpam-5861	395	6	et	et	PROPN
ejpam-5861	395	7	al	al	PROPN
ejpam-5861	395	8	.	.	PUNCT
ejpam-5861	395	9	/	/	SYM
ejpam-5861	395	10	eur	eur	PROPN
ejpam-5861	395	11	.	.	PUNCT
ejpam-5861	396	1	j.	j.	PROPN
ejpam-5861	396	2	pure	pure	PROPN
ejpam-5861	396	3	appl	appl	PROPN
ejpam-5861	396	4	.	.	PROPN
ejpam-5861	396	5	math	math	PROPN
ejpam-5861	396	6	,	,	PUNCT
ejpam-5861	396	7	18	18	NUM
ejpam-5861	396	8	(	(	PUNCT
ejpam-5861	396	9	2	2	NUM
ejpam-5861	396	10	)	)	PUNCT
ejpam-5861	396	11	(	(	PUNCT
ejpam-5861	396	12	2025	2025	NUM
ejpam-5861	396	13	)	)	PUNCT
ejpam-5861	396	14	,	,	PUNCT
ejpam-5861	396	15	5861	5861	NUM
ejpam-5861	396	16	18	18	NUM
ejpam-5861	396	17	of	of	ADP
ejpam-5861	396	18	33	33	NUM
ejpam-5861	396	19	λ1	λ1	ADJ
ejpam-5861	396	20	:	:	PUNCT
ejpam-5861	396	21	d1	d1	PROPN
ejpam-5861	396	22	d3	d3	PROPN
ejpam-5861	396	23	d5	d5	NOUN
ejpam-5861	396	24	λ0	λ0	NOUN
ejpam-5861	396	25	:	:	PUNCT
ejpam-5861	396	26	e1	e1	VERB
ejpam-5861	396	27	e3	e3	NOUN
ejpam-5861	396	28	e5	e5	NOUN
ejpam-5861	396	29	,	,	PUNCT
ejpam-5861	396	30	where	where	SCONJ
ejpam-5861	396	31	b1	b1	NOUN
ejpam-5861	396	32	=	=	SYM
ejpam-5861	396	33	−1	−1	NOUN
ejpam-5861	396	34	a1	a1	NOUN
ejpam-5861	396	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	396	36	a0	a0	PROPN
ejpam-5861	396	37	a2	a2	PROPN
ejpam-5861	396	38	a1	a1	PROPN
ejpam-5861	396	39	a3	a3	NOUN
ejpam-5861	396	40	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	396	41	=	=	PROPN
ejpam-5861	396	42	−(a3	−(a3	X
ejpam-5861	396	43	−	−	PROPN
ejpam-5861	396	44	a1a2	a1a2	NOUN
ejpam-5861	396	45	)	)	PUNCT
ejpam-5861	396	46	a1	a1	NOUN
ejpam-5861	396	47	,	,	PUNCT
ejpam-5861	396	48	b3	b3	NOUN
ejpam-5861	396	49	=	=	SYM
ejpam-5861	396	50	−1	−1	NOUN
ejpam-5861	396	51	a1	a1	NOUN
ejpam-5861	396	52	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	396	53	a0	a0	PROPN
ejpam-5861	396	54	a4	a4	PROPN
ejpam-5861	396	55	a1	a1	NOUN
ejpam-5861	396	56	a5	a5	PROPN
ejpam-5861	396	57	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	396	58	=	=	SYM
ejpam-5861	396	59	−(a0a5	−(a0a5	PUNCT
ejpam-5861	396	60	−	−	PROPN
ejpam-5861	396	61	a1a4	a1a4	NOUN
ejpam-5861	396	62	)	)	PUNCT
ejpam-5861	396	63	a1	a1	NOUN
ejpam-5861	396	64	,	,	PUNCT
ejpam-5861	396	65	c1	c1	NOUN
ejpam-5861	396	66	=	=	SYM
ejpam-5861	396	67	−1	−1	NOUN
ejpam-5861	396	68	b1	b1	NOUN
ejpam-5861	396	69	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	396	70	a1	a1	NOUN
ejpam-5861	396	71	a3	a3	NOUN
ejpam-5861	396	72	b1	b1	PROPN
ejpam-5861	396	73	b3	b3	PROPN
ejpam-5861	396	74	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	396	75	=	=	SYM
ejpam-5861	396	76	−(a1b3	−(a1b3	X
ejpam-5861	397	1	−	−	PROPN
ejpam-5861	397	2	a3b1	a3b1	NOUN
ejpam-5861	397	3	)	)	PUNCT
ejpam-5861	397	4	b1	b1	NOUN
ejpam-5861	397	5	,	,	PUNCT
ejpam-5861	397	6	c3	c3	PROPN
ejpam-5861	397	7	=	=	SYM
ejpam-5861	397	8	−1	−1	NOUN
ejpam-5861	397	9	b1	b1	NOUN
ejpam-5861	397	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	397	11	a1	a1	NOUN
ejpam-5861	397	12	a5	a5	PROPN
ejpam-5861	397	13	b1	b1	NOUN
ejpam-5861	397	14	b5	b5	PROPN
ejpam-5861	397	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	16	=	=	SYM
ejpam-5861	397	17	−(a1b5	−(a1b5	PUNCT
ejpam-5861	397	18	−	−	X
ejpam-5861	397	19	a5b1	a5b1	ADJ
ejpam-5861	397	20	)	)	PUNCT
ejpam-5861	397	21	b1	b1	NOUN
ejpam-5861	397	22	,	,	PUNCT
ejpam-5861	397	23	d1	d1	PROPN
ejpam-5861	397	24	=	=	SYM
ejpam-5861	397	25	−1	−1	NOUN
ejpam-5861	397	26	c1	c1	PROPN
ejpam-5861	397	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	28	a1	a1	PROPN
ejpam-5861	397	29	a3	a3	NOUN
ejpam-5861	397	30	c1	c1	PROPN
ejpam-5861	397	31	c3	c3	PROPN
ejpam-5861	397	32	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	33	=	=	X
ejpam-5861	397	34	−(a1c3	−(a1c3	NUM
ejpam-5861	397	35	−	−	PRON
ejpam-5861	397	36	a3c1	a3c1	ADJ
ejpam-5861	397	37	)	)	PUNCT
ejpam-5861	397	38	c1	c1	NOUN
ejpam-5861	397	39	,	,	PUNCT
ejpam-5861	397	40	d3	d3	PROPN
ejpam-5861	397	41	=	=	SYM
ejpam-5861	397	42	−1	−1	NOUN
ejpam-5861	397	43	c1	c1	PROPN
ejpam-5861	397	44	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	45	a1	a1	PROPN
ejpam-5861	397	46	a5	a5	PROPN
ejpam-5861	397	47	c1	c1	PROPN
ejpam-5861	397	48	c5	c5	PROPN
ejpam-5861	397	49	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	50	=	=	X
ejpam-5861	397	51	−(a1c5	−(a1c5	NUM
ejpam-5861	397	52	−	−	PROPN
ejpam-5861	397	53	a5c1	a5c1	NOUN
ejpam-5861	397	54	)	)	PUNCT
ejpam-5861	397	55	c1	c1	NOUN
ejpam-5861	397	56	,	,	PUNCT
ejpam-5861	397	57	e1	e1	PROPN
ejpam-5861	397	58	=	=	SYM
ejpam-5861	397	59	−1	−1	NOUN
ejpam-5861	397	60	d1	d1	PROPN
ejpam-5861	397	61	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	397	62	a1	a1	NOUN
ejpam-5861	397	63	a3	a3	NOUN
ejpam-5861	397	64	d1	d1	PROPN
ejpam-5861	397	65	d3	d3	PROPN
ejpam-5861	397	66	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	67	=	=	SYM
ejpam-5861	397	68	−(a1d3	−(a1d3	NUM
ejpam-5861	397	69	−	−	PROPN
ejpam-5861	397	70	a3d1	a3d1	NOUN
ejpam-5861	397	71	)	)	PUNCT
ejpam-5861	397	72	d1	d1	PROPN
ejpam-5861	397	73	,	,	PUNCT
ejpam-5861	397	74	e3	e3	NOUN
ejpam-5861	397	75	=	=	SYM
ejpam-5861	397	76	−1	−1	NOUN
ejpam-5861	397	77	d1	d1	PROPN
ejpam-5861	397	78	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	397	79	a1	a1	NOUN
ejpam-5861	397	80	a5	a5	PROPN
ejpam-5861	397	81	d1	d1	PROPN
ejpam-5861	397	82	d5	d5	PROPN
ejpam-5861	397	83	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	397	84	=	=	PUNCT
ejpam-5861	397	85	−(a1d5	−(a1d5	NUM
ejpam-5861	397	86	−	−	PUNCT
ejpam-5861	397	87	a5d1	a5d1	X
ejpam-5861	397	88	)	)	PUNCT
ejpam-5861	397	89	d1	d1	NOUN
ejpam-5861	397	90	.	.	PUNCT
ejpam-5861	398	1	by	by	ADP
ejpam-5861	398	2	computing	compute	VERB
ejpam-5861	398	3	the	the	DET
ejpam-5861	398	4	above	above	ADJ
ejpam-5861	398	5	determinants	determinant	NOUN
ejpam-5861	398	6	,	,	PUNCT
ejpam-5861	398	7	we	we	PRON
ejpam-5861	398	8	can	can	AUX
ejpam-5861	398	9	see	see	VERB
ejpam-5861	398	10	that	that	SCONJ
ejpam-5861	398	11	the	the	DET
ejpam-5861	398	12	coefficients	coefficient	NOUN
ejpam-5861	398	13	in	in	ADP
ejpam-5861	398	14	the	the	DET
ejpam-5861	398	15	first	first	ADJ
ejpam-5861	398	16	column	column	NOUN
ejpam-5861	398	17	are	be	AUX
ejpam-5861	398	18	of	of	ADP
ejpam-5861	398	19	same	same	ADJ
ejpam-5861	398	20	positive	positive	ADJ
ejpam-5861	398	21	sign	sign	NOUN
ejpam-5861	398	22	.	.	PUNCT
ejpam-5861	399	1	hence	hence	ADV
ejpam-5861	399	2	,	,	PUNCT
ejpam-5861	399	3	all	all	DET
ejpam-5861	399	4	the	the	DET
ejpam-5861	399	5	roots	root	NOUN
ejpam-5861	399	6	have	have	VERB
ejpam-5861	399	7	negative	negative	ADJ
ejpam-5861	399	8	real	real	ADJ
ejpam-5861	399	9	parts	part	NOUN
ejpam-5861	399	10	.	.	PUNCT
ejpam-5861	400	1	thus	thus	ADV
ejpam-5861	400	2	the	the	DET
ejpam-5861	400	3	dfe	dfe	PROPN
ejpam-5861	400	4	is	be	AUX
ejpam-5861	400	5	locally	locally	ADV
ejpam-5861	400	6	asymptotically	asymptotically	ADV
ejpam-5861	400	7	stable	stable	ADJ
ejpam-5861	400	8	.	.	PUNCT
ejpam-5861	401	1	theorem	theorem	VERB
ejpam-5861	401	2	7	7	NUM
ejpam-5861	401	3	.	.	PUNCT
ejpam-5861	402	1	the	the	DET
ejpam-5861	402	2	ee	ee	PROPN
ejpam-5861	402	3	point	point	PROPN
ejpam-5861	402	4	e∗	e∗	PROPN
ejpam-5861	402	5	of	of	ADP
ejpam-5861	402	6	the	the	DET
ejpam-5861	402	7	proposed	propose	VERB
ejpam-5861	402	8	model	model	NOUN
ejpam-5861	402	9	(	(	PUNCT
ejpam-5861	402	10	2	2	X
ejpam-5861	402	11	)	)	PUNCT
ejpam-5861	402	12	is	be	AUX
ejpam-5861	402	13	gas	gas	NOUN
ejpam-5861	402	14	in	in	ADP
ejpam-5861	402	15	the	the	DET
ejpam-5861	402	16	given	give	VERB
ejpam-5861	402	17	feasible	feasible	ADJ
ejpam-5861	402	18	region	region	NOUN
ejpam-5861	402	19	ω	ω	NOUN
ejpam-5861	402	20	.	.	PUNCT
ejpam-5861	403	1	proof	proof	NOUN
ejpam-5861	403	2	.	.	PUNCT
ejpam-5861	404	1	let	let	VERB
ejpam-5861	404	2	us	we	PRON
ejpam-5861	404	3	define	define	VERB
ejpam-5861	404	4	a	a	DET
ejpam-5861	404	5	lyapunov	lyapunov	ADJ
ejpam-5861	404	6	function	function	NOUN
ejpam-5861	404	7	f	f	PROPN
ejpam-5861	404	8	:	:	PUNCT
ejpam-5861	404	9	ω	ω	X
ejpam-5861	404	10	→	→	SYM
ejpam-5861	404	11	r	r	NOUN
ejpam-5861	404	12	by	by	ADP
ejpam-5861	404	13	f	f	PROPN
ejpam-5861	404	14	(	(	PUNCT
ejpam-5861	404	15	t	t	PROPN
ejpam-5861	404	16	)	)	PUNCT
ejpam-5861	404	17	=	=	PROPN
ejpam-5861	404	18	q1	q1	PROPN
ejpam-5861	404	19	(	(	PUNCT
ejpam-5861	404	20	s	s	PROPN
ejpam-5861	404	21	−	−	PROPN
ejpam-5861	404	22	s∗	s∗	PROPN
ejpam-5861	404	23	−	−	PROPN
ejpam-5861	404	24	s∗	s∗	PROPN
ejpam-5861	405	1	ln	ln	ADV
ejpam-5861	405	2	[	[	PUNCT
ejpam-5861	405	3	s	s	X
ejpam-5861	405	4	s∗	s∗	PROPN
ejpam-5861	405	5	]	]	PUNCT
ejpam-5861	405	6	)	)	PUNCT
ejpam-5861	406	1	+	+	CCONJ
ejpam-5861	406	2	q2	q2	NOUN
ejpam-5861	406	3	(	(	PUNCT
ejpam-5861	406	4	v	v	ADP
ejpam-5861	406	5	−	−	NOUN
ejpam-5861	406	6	v	v	NOUN
ejpam-5861	406	7	∗	∗	NOUN
ejpam-5861	406	8	−	−	NOUN
ejpam-5861	406	9	v	v	ADP
ejpam-5861	406	10	∗	∗	NOUN
ejpam-5861	406	11	ln	ln	NOUN
ejpam-5861	406	12	[	[	PUNCT
ejpam-5861	406	13	v	v	NOUN
ejpam-5861	406	14	v	v	ADP
ejpam-5861	406	15	∗	∗	NOUN
ejpam-5861	406	16	]	]	PUNCT
ejpam-5861	406	17	)	)	PUNCT
ejpam-5861	407	1	+	+	CCONJ
ejpam-5861	407	2	q3	q3	PROPN
ejpam-5861	407	3	(	(	PUNCT
ejpam-5861	407	4	e	e	NOUN
ejpam-5861	407	5	−	−	PROPN
ejpam-5861	407	6	e∗	e∗	PROPN
ejpam-5861	407	7	−	−	PROPN
ejpam-5861	407	8	e∗	e∗	PROPN
ejpam-5861	407	9	ln	ln	ADP
ejpam-5861	407	10	[	[	PUNCT
ejpam-5861	407	11	e	e	X
ejpam-5861	407	12	e∗	e∗	PROPN
ejpam-5861	407	13	]	]	PUNCT
ejpam-5861	407	14	)	)	PUNCT
ejpam-5861	407	15	=	=	SYM
ejpam-5861	407	16	q4	q4	PROPN
ejpam-5861	407	17	(	(	PUNCT
ejpam-5861	407	18	i	i	PRON
ejpam-5861	407	19	−	−	PROPN
ejpam-5861	407	20	i∗	i∗	NOUN
ejpam-5861	407	21	−	−	NOUN
ejpam-5861	407	22	i∗	i∗	NOUN
ejpam-5861	407	23	ln	ln	NOUN
ejpam-5861	407	24	[	[	PUNCT
ejpam-5861	407	25	i	i	PRON
ejpam-5861	407	26	i∗	i∗	VERB
ejpam-5861	407	27	]	]	PUNCT
ejpam-5861	407	28	)	)	PUNCT
ejpam-5861	408	1	+	+	CCONJ
ejpam-5861	408	2	q5	q5	PROPN
ejpam-5861	408	3	(	(	PUNCT
ejpam-5861	408	4	q−q∗	q−q∗	PROPN
ejpam-5861	408	5	−q∗	−q∗	PROPN
ejpam-5861	408	6	ln	ln	NOUN
ejpam-5861	408	7	[	[	PUNCT
ejpam-5861	408	8	q	q	NOUN
ejpam-5861	408	9	q∗	q∗	NOUN
ejpam-5861	408	10	]	]	PUNCT
ejpam-5861	408	11	)	)	PUNCT
ejpam-5861	408	12	(	(	PUNCT
ejpam-5861	408	13	29	29	NUM
ejpam-5861	408	14	)	)	PUNCT
ejpam-5861	408	15	+	+	NUM
ejpam-5861	408	16	q6	q6	NOUN
ejpam-5861	408	17	(	(	PUNCT
ejpam-5861	408	18	r−r∗	r−r∗	PROPN
ejpam-5861	408	19	−r∗	−r∗	NOUN
ejpam-5861	408	20	ln	ln	NOUN
ejpam-5861	408	21	[	[	PUNCT
ejpam-5861	408	22	r	r	NOUN
ejpam-5861	408	23	r∗	r∗	PROPN
ejpam-5861	408	24	]	]	PUNCT
ejpam-5861	408	25	)	)	PUNCT
ejpam-5861	409	1	+	+	CCONJ
ejpam-5861	409	2	q7	q7	PROPN
ejpam-5861	409	3	(	(	PUNCT
ejpam-5861	409	4	d	d	X
ejpam-5861	409	5	−d∗	−d∗	X
ejpam-5861	409	6	−d∗	−d∗	NOUN
ejpam-5861	409	7	ln	ln	NOUN
ejpam-5861	409	8	[	[	PUNCT
ejpam-5861	409	9	d	d	X
ejpam-5861	409	10	d∗	d∗	PROPN
ejpam-5861	409	11	]	]	PUNCT
ejpam-5861	409	12	)	)	PUNCT
ejpam-5861	409	13	,	,	PUNCT
ejpam-5861	409	14	where	where	SCONJ
ejpam-5861	409	15	qi	qi	PROPN
ejpam-5861	409	16	,	,	PUNCT
ejpam-5861	409	17	i	i	NOUN
ejpam-5861	409	18	=	=	NOUN
ejpam-5861	409	19	1	1	NUM
ejpam-5861	409	20	,	,	PUNCT
ejpam-5861	409	21	2	2	NUM
ejpam-5861	409	22	,	,	PUNCT
ejpam-5861	409	23	...	...	PUNCT
ejpam-5861	409	24	,	,	PUNCT
ejpam-5861	409	25	7	7	NUM
ejpam-5861	409	26	are	be	AUX
ejpam-5861	409	27	positive	positive	ADJ
ejpam-5861	409	28	constants	constant	NOUN
ejpam-5861	409	29	and	and	CCONJ
ejpam-5861	409	30	will	will	AUX
ejpam-5861	409	31	be	be	AUX
ejpam-5861	409	32	specified	specify	VERB
ejpam-5861	409	33	latter	latter	ADJ
ejpam-5861	409	34	.	.	PUNCT
ejpam-5861	410	1	upon	upon	SCONJ
ejpam-5861	410	2	application	application	NOUN
ejpam-5861	410	3	of	of	ADP
ejpam-5861	410	4	pc	pc	NOUN
ejpam-5861	410	5	0	0	NUM
ejpam-5861	410	6	dε	dε	ADP
ejpam-5861	410	7	t	t	NOUN
ejpam-5861	410	8	on	on	ADP
ejpam-5861	410	9	both	both	DET
ejpam-5861	410	10	sides	side	NOUN
ejpam-5861	410	11	of	of	ADP
ejpam-5861	410	12	(	(	PUNCT
ejpam-5861	410	13	29	29	NUM
ejpam-5861	410	14	)	)	PUNCT
ejpam-5861	410	15	,	,	PUNCT
ejpam-5861	410	16	and	and	CCONJ
ejpam-5861	410	17	replacing	replace	VERB
ejpam-5861	410	18	s	s	PROPN
ejpam-5861	410	19	,	,	PUNCT
ejpam-5861	410	20	v	v	NOUN
ejpam-5861	410	21	,	,	PUNCT
ejpam-5861	410	22	e	e	NOUN
ejpam-5861	410	23	,	,	PUNCT
ejpam-5861	410	24	i	i	PRON
ejpam-5861	410	25	,	,	PUNCT
ejpam-5861	410	26	q	q	NOUN
ejpam-5861	410	27	,	,	PUNCT
ejpam-5861	410	28	r	r	NOUN
ejpam-5861	410	29	,	,	PUNCT
ejpam-5861	410	30	d	d	NOUN
ejpam-5861	410	31	by	by	ADP
ejpam-5861	410	32	s	s	PRON
ejpam-5861	410	33	−	−	PROPN
ejpam-5861	410	34	s∗	s∗	PROPN
ejpam-5861	410	35	,	,	PUNCT
ejpam-5861	410	36	v	v	ADP
ejpam-5861	410	37	−	−	PROPN
ejpam-5861	410	38	v	v	ADP
ejpam-5861	410	39	∗	∗	NOUN
ejpam-5861	410	40	,	,	PUNCT
ejpam-5861	410	41	e	e	NOUN
ejpam-5861	410	42	−	−	PROPN
ejpam-5861	410	43	e∗	e∗	PROPN
ejpam-5861	410	44	,	,	PUNCT
ejpam-5861	410	45	i	i	PRON
ejpam-5861	410	46	−	−	VERB
ejpam-5861	410	47	i∗	i∗	NOUN
ejpam-5861	410	48	,	,	PUNCT
ejpam-5861	410	49	q−q∗	q−q∗	PROPN
ejpam-5861	410	50	,	,	PUNCT
ejpam-5861	410	51	r−r∗	r−r∗	PROPN
ejpam-5861	410	52	,	,	PUNCT
ejpam-5861	410	53	d	d	X
ejpam-5861	410	54	−d8	−d8	PROPN
ejpam-5861	410	55	,	,	PUNCT
ejpam-5861	410	56	respectively	respectively	ADV
ejpam-5861	410	57	,	,	PUNCT
ejpam-5861	410	58	we	we	PRON
ejpam-5861	410	59	have	have	VERB
ejpam-5861	410	60	pc	pc	NOUN
ejpam-5861	410	61	0	0	NUM
ejpam-5861	410	62	dε	dε	VERB
ejpam-5861	410	63	t	t	NOUN
ejpam-5861	411	1	[	[	X
ejpam-5861	411	2	f	f	X
ejpam-5861	411	3	(	(	PUNCT
ejpam-5861	411	4	t	t	PROPN
ejpam-5861	411	5	)	)	PUNCT
ejpam-5861	411	6	]	]	PUNCT
ejpam-5861	412	1	=	=	PUNCT
ejpam-5861	412	2	q1	q1	PROPN
ejpam-5861	412	3	[	[	PUNCT
ejpam-5861	412	4	s	s	NOUN
ejpam-5861	412	5	−	−	NOUN
ejpam-5861	412	6	s∗	s∗	PROPN
ejpam-5861	412	7	s	s	X
ejpam-5861	412	8	]	]	X
ejpam-5861	412	9	pc	pc	NOUN
ejpam-5861	412	10	0	0	NUM
ejpam-5861	412	11	dε	dε	NOUN
ejpam-5861	412	12	ts(t	ts(t	NUM
ejpam-5861	412	13	)	)	PUNCT
ejpam-5861	413	1	+	+	NUM
ejpam-5861	413	2	q2	q2	X
ejpam-5861	413	3	[	[	PUNCT
ejpam-5861	413	4	v	v	NOUN
ejpam-5861	413	5	−	−	PROPN
ejpam-5861	413	6	v	v	NOUN
ejpam-5861	413	7	∗	∗	NOUN
ejpam-5861	413	8	v	v	NOUN
ejpam-5861	413	9	]	]	X
ejpam-5861	413	10	pc	pc	NOUN
ejpam-5861	413	11	0	0	NUM
ejpam-5861	413	12	dε	dε	VERB
ejpam-5861	413	13	tv	tv	NOUN
ejpam-5861	413	14	(	(	PUNCT
ejpam-5861	413	15	t	t	PROPN
ejpam-5861	413	16	)	)	PUNCT
ejpam-5861	413	17	s.	s.	PROPN
ejpam-5861	413	18	naz	naz	PROPN
ejpam-5861	413	19	et	et	PROPN
ejpam-5861	413	20	al	al	PROPN
ejpam-5861	413	21	.	.	PUNCT
ejpam-5861	413	22	/	/	SYM
ejpam-5861	413	23	eur	eur	PROPN
ejpam-5861	413	24	.	.	PUNCT
ejpam-5861	414	1	j.	j.	PROPN
ejpam-5861	414	2	pure	pure	PROPN
ejpam-5861	414	3	appl	appl	PROPN
ejpam-5861	414	4	.	.	PROPN
ejpam-5861	414	5	math	math	PROPN
ejpam-5861	414	6	,	,	PUNCT
ejpam-5861	414	7	18	18	NUM
ejpam-5861	414	8	(	(	PUNCT
ejpam-5861	414	9	2	2	NUM
ejpam-5861	414	10	)	)	PUNCT
ejpam-5861	414	11	(	(	PUNCT
ejpam-5861	414	12	2025	2025	NUM
ejpam-5861	414	13	)	)	PUNCT
ejpam-5861	414	14	,	,	PUNCT
ejpam-5861	414	15	5861	5861	NUM
ejpam-5861	414	16	19	19	NUM
ejpam-5861	414	17	of	of	ADP
ejpam-5861	414	18	33	33	NUM
ejpam-5861	414	19	+	+	NUM
ejpam-5861	414	20	q3	q3	NOUN
ejpam-5861	414	21	[	[	PUNCT
ejpam-5861	414	22	e	e	NOUN
ejpam-5861	414	23	−	−	PROPN
ejpam-5861	414	24	e∗	e∗	PROPN
ejpam-5861	414	25	e	e	X
ejpam-5861	414	26	]	]	X
ejpam-5861	414	27	pc	pc	NOUN
ejpam-5861	414	28	0	0	NUM
ejpam-5861	414	29	dε	dε	NOUN
ejpam-5861	414	30	te(t	te(t	NUM
ejpam-5861	414	31	)	)	PUNCT
ejpam-5861	415	1	+	+	CCONJ
ejpam-5861	415	2	q4	q4	PROPN
ejpam-5861	415	3	[	[	PUNCT
ejpam-5861	415	4	i	i	PRON
ejpam-5861	415	5	−	−	PROPN
ejpam-5861	415	6	i∗	i∗	NOUN
ejpam-5861	416	1	i	i	PRON
ejpam-5861	416	2	]	]	X
ejpam-5861	416	3	pc	pc	NOUN
ejpam-5861	416	4	0	0	NUM
ejpam-5861	416	5	dε	dε	NOUN
ejpam-5861	416	6	ti(t	ti(t	NOUN
ejpam-5861	416	7	)	)	PUNCT
ejpam-5861	417	1	+	+	CCONJ
ejpam-5861	417	2	q5	q5	PROPN
ejpam-5861	417	3	[	[	PUNCT
ejpam-5861	417	4	q−q∗	q−q∗	PROPN
ejpam-5861	417	5	q	q	PROPN
ejpam-5861	417	6	]	]	PUNCT
ejpam-5861	417	7	pc	pc	NOUN
ejpam-5861	417	8	0	0	NUM
ejpam-5861	417	9	dε	dε	NOUN
ejpam-5861	417	10	tq(t	tq(t	X
ejpam-5861	417	11	)	)	PUNCT
ejpam-5861	418	1	+	+	NUM
ejpam-5861	418	2	q6	q6	NOUN
ejpam-5861	418	3	[	[	PUNCT
ejpam-5861	418	4	r−r∗	r−r∗	NOUN
ejpam-5861	418	5	r	r	NOUN
ejpam-5861	418	6	]	]	PUNCT
ejpam-5861	418	7	pc	pc	NOUN
ejpam-5861	418	8	0	0	NUM
ejpam-5861	418	9	dε	dε	PROPN
ejpam-5861	418	10	tr(t	tr(t	NOUN
ejpam-5861	418	11	)	)	PUNCT
ejpam-5861	419	1	+	+	CCONJ
ejpam-5861	419	2	q7	q7	PROPN
ejpam-5861	419	3	[	[	PUNCT
ejpam-5861	419	4	d	d	X
ejpam-5861	419	5	−d∗	−d∗	X
ejpam-5861	419	6	d	d	NOUN
ejpam-5861	419	7	]	]	X
ejpam-5861	419	8	pc	pc	NOUN
ejpam-5861	419	9	0	0	NUM
ejpam-5861	419	10	dε	dε	PROPN
ejpam-5861	419	11	td(t	td(t	NOUN
ejpam-5861	419	12	)	)	PUNCT
ejpam-5861	419	13	.	.	PUNCT
ejpam-5861	420	1	(	(	PUNCT
ejpam-5861	420	2	30	30	NUM
ejpam-5861	420	3	)	)	PUNCT
ejpam-5861	420	4	by	by	ADP
ejpam-5861	420	5	choosing	choose	VERB
ejpam-5861	420	6	qi	qi	PROPN
ejpam-5861	420	7	=	=	SYM
ejpam-5861	420	8	1	1	NUM
ejpam-5861	420	9	,	,	PUNCT
ejpam-5861	420	10	for	for	ADP
ejpam-5861	420	11	i	i	PROPN
ejpam-5861	420	12	=	=	SYM
ejpam-5861	420	13	1	1	NUM
ejpam-5861	420	14	,	,	PUNCT
ejpam-5861	420	15	2	2	NUM
ejpam-5861	420	16	,	,	PUNCT
ejpam-5861	420	17	...	...	PUNCT
ejpam-5861	420	18	,	,	PUNCT
ejpam-5861	420	19	7	7	NUM
ejpam-5861	420	20	,	,	PUNCT
ejpam-5861	420	21	and	and	CCONJ
ejpam-5861	420	22	plugging	plug	VERB
ejpam-5861	420	23	values	value	NOUN
ejpam-5861	420	24	from	from	ADP
ejpam-5861	420	25	(	(	PUNCT
ejpam-5861	420	26	2	2	NUM
ejpam-5861	420	27	)	)	PUNCT
ejpam-5861	420	28	in	in	ADP
ejpam-5861	420	29	(	(	PUNCT
ejpam-5861	420	30	30	30	NUM
ejpam-5861	420	31	)	)	PUNCT
ejpam-5861	420	32	,	,	PUNCT
ejpam-5861	420	33	and	and	CCONJ
ejpam-5861	420	34	separating	separate	VERB
ejpam-5861	420	35	positive	positive	ADJ
ejpam-5861	420	36	and	and	CCONJ
ejpam-5861	420	37	negative	negative	ADJ
ejpam-5861	420	38	parts	part	NOUN
ejpam-5861	420	39	,	,	PUNCT
ejpam-5861	420	40	such	such	ADJ
ejpam-5861	420	41	that	that	SCONJ
ejpam-5861	420	42	θ1	θ1	NOUN
ejpam-5861	420	43	=	=	SYM
ejpam-5861	420	44	λ	λ	X
ejpam-5861	420	45	s	s	PART
ejpam-5861	420	46	−	−	NOUN
ejpam-5861	420	47	s∗	s∗	PROPN
ejpam-5861	420	48	s	s	PART
ejpam-5861	420	49	+	+	PROPN
ejpam-5861	420	50	η	η	PROPN
ejpam-5861	420	51	(	(	PUNCT
ejpam-5861	420	52	v	v	ADP
ejpam-5861	420	53	−	−	PROPN
ejpam-5861	420	54	v	v	NOUN
ejpam-5861	420	55	∗)(s	∗)(s	PROPN
ejpam-5861	420	56	−	−	PROPN
ejpam-5861	420	57	s∗	s∗	PROPN
ejpam-5861	420	58	)	)	PUNCT
ejpam-5861	420	59	v	v	ADP
ejpam-5861	420	60	+	+	CCONJ
ejpam-5861	420	61	wb	wb	PROPN
ejpam-5861	420	62	(	(	PUNCT
ejpam-5861	420	63	e	e	NOUN
ejpam-5861	420	64	−	−	PROPN
ejpam-5861	420	65	e∗)(v	e∗)(v	NOUN
ejpam-5861	420	66	−	−	PROPN
ejpam-5861	420	67	v	v	ADP
ejpam-5861	420	68	∗)(i	∗)(i	NUM
ejpam-5861	420	69	−	−	PROPN
ejpam-5861	420	70	i∗	i∗	NOUN
ejpam-5861	420	71	)	)	PUNCT
ejpam-5861	420	72	e	e	NOUN
ejpam-5861	421	1	+	+	CCONJ
ejpam-5861	421	2	b(1−	b(1−	NOUN
ejpam-5861	421	3	pξ	pξ	NOUN
ejpam-5861	421	4	)	)	PUNCT
ejpam-5861	421	5	(	(	PUNCT
ejpam-5861	421	6	s	s	NOUN
ejpam-5861	421	7	−	−	PROPN
ejpam-5861	421	8	s∗)(i	s∗)(i	NOUN
ejpam-5861	421	9	−	−	PROPN
ejpam-5861	421	10	i∗)(e	i∗)(e	ADJ
ejpam-5861	421	11	−	−	PROPN
ejpam-5861	421	12	e∗	e∗	PROPN
ejpam-5861	421	13	)	)	PUNCT
ejpam-5861	422	1	e	e	PROPN
ejpam-5861	423	1	+	+	CCONJ
ejpam-5861	423	2	τ	τ	PROPN
ejpam-5861	423	3	(	(	PUNCT
ejpam-5861	423	4	e	e	PROPN
ejpam-5861	423	5	−	−	PROPN
ejpam-5861	423	6	e∗)(i	e∗)(i	NOUN
ejpam-5861	423	7	−	−	PROPN
ejpam-5861	423	8	i∗	i∗	NOUN
ejpam-5861	423	9	)	)	PUNCT
ejpam-5861	424	1	i	i	PRON
ejpam-5861	424	2	+	+	NUM
ejpam-5861	425	1	αi	αi	VERB
ejpam-5861	425	2	(	(	PUNCT
ejpam-5861	425	3	q−q∗)(i	q−q∗)(i	PROPN
ejpam-5861	425	4	−	−	PROPN
ejpam-5861	425	5	i∗	i∗	NOUN
ejpam-5861	425	6	)	)	PUNCT
ejpam-5861	425	7	q	q	NOUN
ejpam-5861	426	1	(	(	PUNCT
ejpam-5861	426	2	31	31	NUM
ejpam-5861	426	3	)	)	PUNCT
ejpam-5861	426	4	+	+	SYM
ejpam-5861	426	5	σi(r−r∗	σi(r−r∗	NOUN
ejpam-5861	426	6	)	)	PUNCT
ejpam-5861	426	7	(	(	PUNCT
ejpam-5861	427	1	i	i	PRON
ejpam-5861	427	2	−	−	PROPN
ejpam-5861	427	3	i∗	i∗	NOUN
ejpam-5861	427	4	)	)	PUNCT
ejpam-5861	427	5	r	r	NOUN
ejpam-5861	428	1	+	+	NUM
ejpam-5861	428	2	σq	σq	PROPN
ejpam-5861	428	3	(	(	PUNCT
ejpam-5861	428	4	q−q∗)(r−r∗	q−q∗)(r−r∗	NOUN
ejpam-5861	428	5	)	)	PUNCT
ejpam-5861	428	6	r	r	NOUN
ejpam-5861	428	7	+	+	CCONJ
ejpam-5861	428	8	δi	δi	PROPN
ejpam-5861	428	9	(	(	PUNCT
ejpam-5861	428	10	d	d	PROPN
ejpam-5861	428	11	−d∗)(i	−d∗)(i	PROPN
ejpam-5861	428	12	−	−	PROPN
ejpam-5861	428	13	i∗	i∗	NOUN
ejpam-5861	428	14	)	)	PUNCT
ejpam-5861	429	1	d	d	NOUN
ejpam-5861	430	1	+	+	CCONJ
ejpam-5861	430	2	δq	δq	PROPN
ejpam-5861	430	3	(	(	PUNCT
ejpam-5861	430	4	q−q∗)(d	q−q∗)(d	NOUN
ejpam-5861	430	5	−d∗	−d∗	NOUN
ejpam-5861	430	6	)	)	PUNCT
ejpam-5861	430	7	d	d	NOUN
ejpam-5861	430	8	,	,	PUNCT
ejpam-5861	430	9	and	and	CCONJ
ejpam-5861	430	10	θ2	θ2	PROPN
ejpam-5861	430	11	=	=	SYM
ejpam-5861	430	12	b(1−	b(1−	PROPN
ejpam-5861	430	13	pξ	pξ	NOUN
ejpam-5861	430	14	)	)	PUNCT
ejpam-5861	430	15	(	(	PUNCT
ejpam-5861	430	16	s	s	NOUN
ejpam-5861	430	17	−	−	PROPN
ejpam-5861	430	18	s∗)2(i	s∗)2(i	NOUN
ejpam-5861	430	19	−	−	PROPN
ejpam-5861	430	20	i∗	i∗	NOUN
ejpam-5861	430	21	)	)	PUNCT
ejpam-5861	430	22	s	s	PART
ejpam-5861	431	1	+	+	CCONJ
ejpam-5861	431	2	(	(	PUNCT
ejpam-5861	431	3	η	η	PROPN
ejpam-5861	431	4	+	+	PROPN
ejpam-5861	431	5	d	d	PROPN
ejpam-5861	431	6	)	)	PUNCT
ejpam-5861	431	7	(	(	PUNCT
ejpam-5861	431	8	s	s	VERB
ejpam-5861	431	9	−	−	PROPN
ejpam-5861	431	10	s∗)2	s∗)2	NOUN
ejpam-5861	431	11	s	s	PART
ejpam-5861	431	12	+	+	X
ejpam-5861	431	13	wb	wb	PROPN
ejpam-5861	431	14	(	(	PUNCT
ejpam-5861	431	15	e	e	NOUN
ejpam-5861	431	16	−	−	PROPN
ejpam-5861	431	17	e∗)(v	e∗)(v	NOUN
ejpam-5861	431	18	−	−	PROPN
ejpam-5861	431	19	v	v	NOUN
ejpam-5861	431	20	∗)2(i	∗)2(i	NOUN
ejpam-5861	431	21	−	−	NOUN
ejpam-5861	431	22	i∗	i∗	NOUN
ejpam-5861	431	23	)	)	PUNCT
ejpam-5861	431	24	v	v	NOUN
ejpam-5861	432	1	+	+	CCONJ
ejpam-5861	432	2	d(v	d(v	ADJ
ejpam-5861	432	3	−	−	PROPN
ejpam-5861	432	4	v∗)2	v∗)2	NUM
ejpam-5861	432	5	v	v	NOUN
ejpam-5861	432	6	+	+	CCONJ
ejpam-5861	432	7	(	(	PUNCT
ejpam-5861	432	8	τ	τ	PROPN
ejpam-5861	432	9	+	+	CCONJ
ejpam-5861	432	10	d	d	NOUN
ejpam-5861	432	11	)	)	PUNCT
ejpam-5861	432	12	(	(	PUNCT
ejpam-5861	432	13	e	e	NOUN
ejpam-5861	432	14	−	−	PROPN
ejpam-5861	432	15	e∗)2	e∗)2	ADJ
ejpam-5861	432	16	e	e	NOUN
ejpam-5861	433	1	+	+	CCONJ
ejpam-5861	433	2	(	(	PUNCT
ejpam-5861	433	3	αi	αi	VERB
ejpam-5861	433	4	+	+	CCONJ
ejpam-5861	433	5	δi	δi	PRON
ejpam-5861	434	1	+	+	CCONJ
ejpam-5861	434	2	σi	σi	X
ejpam-5861	435	1	+	+	CCONJ
ejpam-5861	436	1	d	d	X
ejpam-5861	436	2	)	)	PUNCT
ejpam-5861	436	3	(	(	PUNCT
ejpam-5861	436	4	i	i	PRON
ejpam-5861	436	5	−	−	VERB
ejpam-5861	436	6	i∗)2	i∗)2	NOUN
ejpam-5861	436	7	i	i	PRON
ejpam-5861	436	8	(	(	PUNCT
ejpam-5861	436	9	32	32	NUM
ejpam-5861	436	10	)	)	PUNCT
ejpam-5861	437	1	+	+	CCONJ
ejpam-5861	437	2	(	(	PUNCT
ejpam-5861	437	3	σq	σq	X
ejpam-5861	437	4	+	+	NOUN
ejpam-5861	437	5	δq	δq	X
ejpam-5861	437	6	+	+	CCONJ
ejpam-5861	437	7	d	d	X
ejpam-5861	437	8	)	)	PUNCT
ejpam-5861	437	9	(	(	PUNCT
ejpam-5861	437	10	q−q∗)2	q−q∗)2	ADV
ejpam-5861	437	11	q	q	X
ejpam-5861	438	1	+	+	NUM
ejpam-5861	438	2	d	d	NOUN
ejpam-5861	438	3	(	(	PUNCT
ejpam-5861	438	4	r−r∗)2	r−r∗)2	NOUN
ejpam-5861	438	5	r	r	NOUN
ejpam-5861	438	6	.	.	PUNCT
ejpam-5861	439	1	using	use	VERB
ejpam-5861	439	2	(	(	PUNCT
ejpam-5861	439	3	31	31	NUM
ejpam-5861	439	4	)	)	PUNCT
ejpam-5861	439	5	,	,	PUNCT
ejpam-5861	439	6	and	and	CCONJ
ejpam-5861	439	7	(	(	PUNCT
ejpam-5861	439	8	32	32	NUM
ejpam-5861	439	9	)	)	PUNCT
ejpam-5861	439	10	in	in	ADP
ejpam-5861	439	11	(	(	PUNCT
ejpam-5861	439	12	30	30	NUM
ejpam-5861	439	13	)	)	PUNCT
ejpam-5861	439	14	,	,	PUNCT
ejpam-5861	439	15	we	we	PRON
ejpam-5861	439	16	have	have	VERB
ejpam-5861	439	17	pc	pc	NOUN
ejpam-5861	439	18	0	0	NUM
ejpam-5861	439	19	dε	dε	VERB
ejpam-5861	439	20	t	t	NOUN
ejpam-5861	440	1	[	[	X
ejpam-5861	440	2	f	f	X
ejpam-5861	440	3	(	(	PUNCT
ejpam-5861	440	4	t	t	PROPN
ejpam-5861	440	5	)	)	PUNCT
ejpam-5861	440	6	]	]	PUNCT
ejpam-5861	440	7	=	=	SYM
ejpam-5861	440	8	θ1	θ1	PROPN
ejpam-5861	440	9	−θ2	−θ2	PROPN
ejpam-5861	440	10	.	.	PUNCT
ejpam-5861	441	1	(	(	PUNCT
ejpam-5861	441	2	33	33	NUM
ejpam-5861	441	3	)	)	PUNCT
ejpam-5861	441	4	we	we	PRON
ejpam-5861	441	5	see	see	VERB
ejpam-5861	441	6	that	that	SCONJ
ejpam-5861	441	7	in	in	ADP
ejpam-5861	441	8	(	(	PUNCT
ejpam-5861	441	9	33	33	NUM
ejpam-5861	441	10	)	)	PUNCT
ejpam-5861	441	11	if	if	SCONJ
ejpam-5861	441	12	θ1	θ1	PROPN
ejpam-5861	441	13	<	<	X
ejpam-5861	441	14	θ2	θ2	PROPN
ejpam-5861	441	15	,	,	PUNCT
ejpam-5861	441	16	then	then	ADV
ejpam-5861	441	17	pc	pc	VERB
ejpam-5861	441	18	0	0	NUM
ejpam-5861	441	19	dε	dε	VERB
ejpam-5861	441	20	t	t	NOUN
ejpam-5861	442	1	[	[	X
ejpam-5861	442	2	f	f	X
ejpam-5861	442	3	(	(	PUNCT
ejpam-5861	442	4	t	t	PROPN
ejpam-5861	442	5	)	)	PUNCT
ejpam-5861	442	6	]	]	PUNCT
ejpam-5861	442	7	≤	≤	NUM
ejpam-5861	442	8	0	0	NUM
ejpam-5861	442	9	,	,	PUNCT
ejpam-5861	442	10	hence	hence	ADV
ejpam-5861	442	11	the	the	DET
ejpam-5861	442	12	lyapunovvolterra	lyapunovvolterra	NOUN
ejpam-5861	442	13	function	function	NOUN
ejpam-5861	442	14	f	f	PROPN
ejpam-5861	442	15	is	be	AUX
ejpam-5861	442	16	negative	negative	ADJ
ejpam-5861	442	17	under	under	ADP
ejpam-5861	442	18	the	the	DET
ejpam-5861	442	19	derivative	derivative	NOUN
ejpam-5861	442	20	of	of	ADP
ejpam-5861	442	21	piecewise	piecewise	NOUN
ejpam-5861	442	22	.	.	PUNCT
ejpam-5861	443	1	but	but	CCONJ
ejpam-5861	443	2	f	f	PROPN
ejpam-5861	443	3	>	>	X
ejpam-5861	443	4	0	0	PROPN
ejpam-5861	443	5	,	,	PUNCT
ejpam-5861	443	6	therefore	therefore	ADV
ejpam-5861	443	7	f	f	PROPN
ejpam-5861	443	8	is	be	AUX
ejpam-5861	443	9	positive	positive	ADJ
ejpam-5861	443	10	definite	definite	ADJ
ejpam-5861	443	11	function	function	NOUN
ejpam-5861	443	12	,	,	PUNCT
ejpam-5861	443	13	therefore	therefore	ADV
ejpam-5861	443	14	,	,	PUNCT
ejpam-5861	443	15	the	the	DET
ejpam-5861	443	16	endemic	endemic	ADJ
ejpam-5861	443	17	equilibrium	equilibrium	NOUN
ejpam-5861	443	18	point	point	NOUN
ejpam-5861	443	19	e∗	e∗	PROPN
ejpam-5861	443	20	is	be	AUX
ejpam-5861	443	21	gas	gas	NOUN
ejpam-5861	443	22	.	.	PUNCT
ejpam-5861	444	1	5.2	5.2	NUM
ejpam-5861	444	2	.	.	PUNCT
ejpam-5861	444	3	uh	uh	INTJ
ejpam-5861	444	4	stability	stability	NOUN
ejpam-5861	444	5	the	the	DET
ejpam-5861	444	6	uh	uh	INTJ
ejpam-5861	444	7	stability	stability	NOUN
ejpam-5861	444	8	results	result	NOUN
ejpam-5861	444	9	are	be	AUX
ejpam-5861	444	10	derived	derive	VERB
ejpam-5861	444	11	in	in	ADP
ejpam-5861	444	12	this	this	DET
ejpam-5861	444	13	portion	portion	NOUN
ejpam-5861	444	14	.	.	PUNCT
ejpam-5861	445	1	remark	remark	PROPN
ejpam-5861	445	2	1	1	NUM
ejpam-5861	445	3	.	.	PUNCT
ejpam-5861	446	1	if	if	SCONJ
ejpam-5861	446	2	h	h	NOUN
ejpam-5861	446	3	is	be	AUX
ejpam-5861	446	4	a	a	DET
ejpam-5861	446	5	function	function	NOUN
ejpam-5861	446	6	that	that	PRON
ejpam-5861	446	7	is	be	AUX
ejpam-5861	446	8	independent	independent	ADJ
ejpam-5861	446	9	of	of	ADP
ejpam-5861	446	10	ϕ	ϕ	NOUN
ejpam-5861	446	11	,	,	PUNCT
ejpam-5861	446	12	then	then	ADV
ejpam-5861	446	13	h	h	NOUN
ejpam-5861	446	14	:	:	PUNCT
ejpam-5861	446	15	j	j	PROPN
ejpam-5861	446	16	→	→	PUNCT
ejpam-5861	446	17	(	(	PUNCT
ejpam-5861	446	18	0,∞	0,∞	NUM
ejpam-5861	446	19	)	)	PUNCT
ejpam-5861	446	20	,	,	PUNCT
ejpam-5861	446	21	∋	∋	NOUN
ejpam-5861	446	22	h(0	h(0	PROPN
ejpam-5861	446	23	)	)	PUNCT
ejpam-5861	446	24	=	=	SYM
ejpam-5861	446	25	h(t1	h(t1	X
ejpam-5861	446	26	)	)	PUNCT
ejpam-5861	446	27	=	=	SYM
ejpam-5861	446	28	0	0	PUNCT
ejpam-5861	446	29	and	and	CCONJ
ejpam-5861	446	30	|h(t)|	|h(t)|	NOUN
ejpam-5861	446	31	≤	≤	NUM
ejpam-5861	446	32	ϵ	ϵ	ADP
ejpam-5861	446	33	,	,	PUNCT
ejpam-5861	446	34	for	for	ADP
ejpam-5861	446	35	every	every	DET
ejpam-5861	446	36	t	t	PROPN
ejpam-5861	446	37	∈	∈	PROPN
ejpam-5861	446	38	j	j	PROPN
ejpam-5861	446	39	.	.	PUNCT
ejpam-5861	447	1	s.	s.	PROPN
ejpam-5861	447	2	naz	naz	PROPN
ejpam-5861	447	3	et	et	PROPN
ejpam-5861	447	4	al	al	PROPN
ejpam-5861	447	5	.	.	PUNCT
ejpam-5861	447	6	/	/	SYM
ejpam-5861	447	7	eur	eur	PROPN
ejpam-5861	447	8	.	.	PUNCT
ejpam-5861	448	1	j.	j.	PROPN
ejpam-5861	448	2	pure	pure	PROPN
ejpam-5861	448	3	appl	appl	PROPN
ejpam-5861	448	4	.	.	PROPN
ejpam-5861	448	5	math	math	PROPN
ejpam-5861	448	6	,	,	PUNCT
ejpam-5861	448	7	18	18	NUM
ejpam-5861	448	8	(	(	PUNCT
ejpam-5861	448	9	2	2	NUM
ejpam-5861	448	10	)	)	PUNCT
ejpam-5861	448	11	(	(	PUNCT
ejpam-5861	448	12	2025	2025	NUM
ejpam-5861	448	13	)	)	PUNCT
ejpam-5861	448	14	,	,	PUNCT
ejpam-5861	448	15	5861	5861	NUM
ejpam-5861	448	16	20	20	NUM
ejpam-5861	448	17	of	of	ADP
ejpam-5861	448	18	33	33	NUM
ejpam-5861	448	19	lemma	lemma	PROPN
ejpam-5861	448	20	4	4	NUM
ejpam-5861	448	21	.	.	PUNCT
ejpam-5861	449	1	the	the	DET
ejpam-5861	449	2	pc	pc	NOUN
ejpam-5861	449	3	0	0	NUM
ejpam-5861	449	4	dε	dε	NOUN
ejpam-5861	449	5	tϕ(t	tϕ(t	NOUN
ejpam-5861	449	6	)	)	PUNCT
ejpam-5861	449	7	=	=	SYM
ejpam-5861	449	8	g(t	g(t	PROPN
ejpam-5861	449	9	,	,	PUNCT
ejpam-5861	449	10	ϕ(t	ϕ(t	NUM
ejpam-5861	449	11	)	)	PUNCT
ejpam-5861	449	12	)	)	PUNCT
ejpam-5861	450	1	+	+	CCONJ
ejpam-5861	450	2	h(t	h(t	PROPN
ejpam-5861	450	3	)	)	PUNCT
ejpam-5861	450	4	,	,	PUNCT
ejpam-5861	450	5	0	0	NUM
ejpam-5861	450	6	<	<	X
ejpam-5861	450	7	ε	ε	PROPN
ejpam-5861	450	8	≤	≤	PROPN
ejpam-5861	450	9	1	1	NUM
ejpam-5861	450	10	,	,	PUNCT
ejpam-5861	450	11	ϕ(0	ϕ(0	PROPN
ejpam-5861	450	12	)	)	PUNCT
ejpam-5861	450	13	=	=	SYM
ejpam-5861	450	14	ϕ0	ϕ0	NOUN
ejpam-5861	450	15	yield	yield	VERB
ejpam-5861	450	16	a	a	DET
ejpam-5861	450	17	result	result	NOUN
ejpam-5861	450	18	of	of	ADP
ejpam-5861	450	19	the	the	DET
ejpam-5861	450	20	form	form	NOUN
ejpam-5861	450	21	ϕ(t	ϕ(t	NUM
ejpam-5861	450	22	)	)	PUNCT
ejpam-5861	451	1	=	=	PUNCT
ejpam-5861	452	1			PROPN
ejpam-5861	452	2	ϕ0	ϕ0	NOUN
ejpam-5861	452	3	+	+	CCONJ
ejpam-5861	452	4	∫	∫	PROPN
ejpam-5861	452	5	t	t	PROPN
ejpam-5861	452	6	0	0	NUM
ejpam-5861	453	1	g(u	g(u	PROPN
ejpam-5861	453	2	,	,	PUNCT
ejpam-5861	453	3	ϕ(u))du+	ϕ(u))du+	PROPN
ejpam-5861	453	4	∫	∫	PROPN
ejpam-5861	453	5	t	t	PROPN
ejpam-5861	453	6	0	0	NUM
ejpam-5861	453	7	h(u)du	h(u)du	PROPN
ejpam-5861	453	8	,	,	PUNCT
ejpam-5861	453	9	t	t	PROPN
ejpam-5861	453	10	∈	∈	PROPN
ejpam-5861	453	11	∇1	∇1	PROPN
ejpam-5861	453	12	,	,	PUNCT
ejpam-5861	453	13	ϕ(t1	ϕ(t1	NUM
ejpam-5861	453	14	)	)	PUNCT
ejpam-5861	454	1	+	+	CCONJ
ejpam-5861	454	2	∫	∫	PROPN
ejpam-5861	454	3	t	t	PROPN
ejpam-5861	454	4	t1	t1	PROPN
ejpam-5861	454	5	(	(	PUNCT
ejpam-5861	454	6	t−	t−	PROPN
ejpam-5861	454	7	u)ε−1	u)ε−1	PROPN
ejpam-5861	454	8	γ(ε	γ(ε	PROPN
ejpam-5861	454	9	)	)	PUNCT
ejpam-5861	455	1	g(u	g(u	PROPN
ejpam-5861	455	2	,	,	PUNCT
ejpam-5861	455	3	ϕ(u))d(u	ϕ(u))d(u	ADJ
ejpam-5861	455	4	)	)	PUNCT
ejpam-5861	456	1	+	+	CCONJ
ejpam-5861	456	2	∫	∫	PROPN
ejpam-5861	456	3	t	t	PROPN
ejpam-5861	456	4	t1	t1	PROPN
ejpam-5861	456	5	(	(	PUNCT
ejpam-5861	456	6	t−	t−	PROPN
ejpam-5861	456	7	u)ε−1	u)ε−1	PROPN
ejpam-5861	456	8	γ(ε	γ(ε	PROPN
ejpam-5861	456	9	)	)	PUNCT
ejpam-5861	456	10	h(u)du	h(u)du	PROPN
ejpam-5861	456	11	,	,	PUNCT
ejpam-5861	456	12	t	t	PROPN
ejpam-5861	456	13	∈	∈	PROPN
ejpam-5861	456	14	∇2	∇2	PROPN
ejpam-5861	456	15	.	.	PUNCT
ejpam-5861	457	1	(	(	PUNCT
ejpam-5861	457	2	34	34	NUM
ejpam-5861	457	3	)	)	PUNCT
ejpam-5861	457	4	moreover	moreover	ADV
ejpam-5861	457	5	,	,	PUNCT
ejpam-5861	457	6	the	the	DET
ejpam-5861	457	7	solution	solution	NOUN
ejpam-5861	457	8	(	(	PUNCT
ejpam-5861	457	9	34	34	NUM
ejpam-5861	457	10	)	)	PUNCT
ejpam-5861	457	11	satisfies	satisfy	VERB
ejpam-5861	457	12	the	the	DET
ejpam-5861	457	13	following	follow	VERB
ejpam-5861	457	14	relation	relation	NOUN
ejpam-5861	457	15	in	in	ADP
ejpam-5861	457	16	view	view	NOUN
ejpam-5861	457	17	of	of	ADP
ejpam-5861	457	18	remark	remark	NOUN
ejpam-5861	457	19	1	1	NUM
ejpam-5861	457	20	and	and	CCONJ
ejpam-5861	457	21	using	use	VERB
ejpam-5861	457	22	|t−	|t−	PROPN
ejpam-5861	457	23	t1|	t1|	PROPN
ejpam-5861	457	24	≤	≤	PROPN
ejpam-5861	457	25	t	t	PROPN
ejpam-5861	457	26	as	as	ADP
ejpam-5861	457	27	∣∣∣∣ϕ(t)−	∣∣∣∣ϕ(t)−	PRON
ejpam-5861	457	28	ϕ0	ϕ0	PROPN
ejpam-5861	457	29	−	−	PROPN
ejpam-5861	457	30	∫	∫	PROPN
ejpam-5861	457	31	t	t	NOUN
ejpam-5861	457	32	0	0	NUM
ejpam-5861	458	1	g(u	g(u	PROPN
ejpam-5861	458	2	,	,	PUNCT
ejpam-5861	458	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	458	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	458	5	≤	≤	NOUN
ejpam-5861	458	6	t1ϵ	t1ϵ	NOUN
ejpam-5861	458	7	,	,	PUNCT
ejpam-5861	458	8	t	t	PROPN
ejpam-5861	458	9	∈	∈	PROPN
ejpam-5861	458	10	∇1,∣∣∣∣ϕ(t)−	∇1,∣∣∣∣ϕ(t)−	PROPN
ejpam-5861	459	1	ϕ(t1)−	ϕ(t1)−	PROPN
ejpam-5861	459	2	∫	∫	PROPN
ejpam-5861	459	3	t	t	PROPN
ejpam-5861	459	4	t1	t1	PROPN
ejpam-5861	459	5	(	(	PUNCT
ejpam-5861	459	6	t−	t−	PROPN
ejpam-5861	459	7	u)ε−1	u)ε−1	PROPN
ejpam-5861	459	8	γ(ε	γ(ε	PROPN
ejpam-5861	459	9	)	)	PUNCT
ejpam-5861	459	10	g(u	g(u	PROPN
ejpam-5861	459	11	,	,	PUNCT
ejpam-5861	459	12	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	459	13	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	459	14	≤	≤	PROPN
ejpam-5861	459	15	tεϵ	tεϵ	PROPN
ejpam-5861	459	16	γ(ε+	γ(ε+	PROPN
ejpam-5861	459	17	1	1	NUM
ejpam-5861	459	18	)	)	PUNCT
ejpam-5861	459	19	,	,	PUNCT
ejpam-5861	459	20	t	t	PROPN
ejpam-5861	459	21	∈	∈	PROPN
ejpam-5861	459	22	∇2	∇2	PROPN
ejpam-5861	459	23	.	.	PUNCT
ejpam-5861	460	1	proof	proof	NOUN
ejpam-5861	460	2	.	.	PUNCT
ejpam-5861	461	1	the	the	DET
ejpam-5861	461	2	proof	proof	NOUN
ejpam-5861	461	3	of	of	ADP
ejpam-5861	461	4	the	the	DET
ejpam-5861	461	5	lemma	lemma	PROPN
ejpam-5861	461	6	4	4	NUM
ejpam-5861	461	7	is	be	AUX
ejpam-5861	461	8	easy	easy	ADJ
ejpam-5861	461	9	to	to	PART
ejpam-5861	461	10	derive	derive	VERB
ejpam-5861	461	11	.	.	PUNCT
ejpam-5861	462	1	theorem	theorem	ADJ
ejpam-5861	462	2	8	8	NUM
ejpam-5861	462	3	.	.	PUNCT
ejpam-5861	463	1	we	we	PRON
ejpam-5861	463	2	get	get	VERB
ejpam-5861	463	3	uh	uh	INTJ
ejpam-5861	463	4	and	and	CCONJ
ejpam-5861	463	5	generalized	generalize	VERB
ejpam-5861	463	6	uh	uh	INTJ
ejpam-5861	463	7	stable	stable	ADJ
ejpam-5861	463	8	if	if	SCONJ
ejpam-5861	463	9	the	the	DET
ejpam-5861	463	10	condition	condition	NOUN
ejpam-5861	463	11	max	max	PROPN
ejpam-5861	463	12	{	{	PUNCT
ejpam-5861	463	13	1	1	NUM
ejpam-5861	463	14	−	−	NOUN
ejpam-5861	463	15	t1lg	t1lg	PUNCT
ejpam-5861	463	16	,	,	PUNCT
ejpam-5861	463	17	1	1	NUM
ejpam-5861	463	18	−	−	PROPN
ejpam-5861	463	19	∆̄	∆̄	NOUN
ejpam-5861	463	20	}	}	PUNCT
ejpam-5861	463	21	<	<	X
ejpam-5861	463	22	1	1	NUM
ejpam-5861	463	23	,	,	PUNCT
ejpam-5861	463	24	where	where	SCONJ
ejpam-5861	463	25	∆̄	∆̄	NOUN
ejpam-5861	463	26	=	=	PROPN
ejpam-5861	463	27	tεlg	tεlg	PROPN
ejpam-5861	463	28	γ(ε+1	γ(ε+1	NOUN
ejpam-5861	463	29	)	)	PUNCT
ejpam-5861	463	30	holds	hold	VERB
ejpam-5861	463	31	corresponding	correspond	VERB
ejpam-5861	463	32	to	to	ADP
ejpam-5861	463	33	the	the	DET
ejpam-5861	463	34	solution	solution	NOUN
ejpam-5861	463	35	of	of	ADP
ejpam-5861	463	36	problem	problem	NOUN
ejpam-5861	463	37	(	(	PUNCT
ejpam-5861	463	38	18	18	NUM
ejpam-5861	463	39	)	)	PUNCT
ejpam-5861	463	40	.	.	PUNCT
ejpam-5861	464	1	proof	proof	NOUN
ejpam-5861	464	2	.	.	PUNCT
ejpam-5861	465	1	we	we	PRON
ejpam-5861	465	2	derive	derive	VERB
ejpam-5861	465	3	proof	proof	NOUN
ejpam-5861	465	4	in	in	ADP
ejpam-5861	465	5	two	two	NUM
ejpam-5861	465	6	steps	step	NOUN
ejpam-5861	465	7	:	:	PUNCT
ejpam-5861	465	8	step	step	NOUN
ejpam-5861	465	9	i	i	PRON
ejpam-5861	465	10	:	:	PUNCT
ejpam-5861	465	11	t	t	PROPN
ejpam-5861	465	12	∈	∈	PROPN
ejpam-5861	466	1	[	[	X
ejpam-5861	466	2	0	0	NUM
ejpam-5861	466	3	,	,	PUNCT
ejpam-5861	466	4	t1	t1	NOUN
ejpam-5861	466	5	]	]	X
ejpam-5861	466	6	,	,	PUNCT
ejpam-5861	466	7	then	then	ADV
ejpam-5861	466	8	∥∥ϕ−	∥∥ϕ−	PROPN
ejpam-5861	466	9	ϕ̄	ϕ̄	INTJ
ejpam-5861	466	10	∥∥	∥∥	X
ejpam-5861	466	11	=	=	SYM
ejpam-5861	466	12	max	max	PROPN
ejpam-5861	466	13	t∈j	t∈j	PROPN
ejpam-5861	466	14	∣∣∣∣ϕ(t)−	∣∣∣∣ϕ(t)−	PROPN
ejpam-5861	466	15	ϕ0	ϕ0	PROPN
ejpam-5861	466	16	−	−	PROPN
ejpam-5861	466	17	∫	∫	PROPN
ejpam-5861	466	18	t	t	NOUN
ejpam-5861	466	19	0	0	NUM
ejpam-5861	467	1	g(u	g(u	PROPN
ejpam-5861	467	2	,	,	PUNCT
ejpam-5861	467	3	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	467	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	467	5	≤	≤	NUM
ejpam-5861	467	6	max	max	PROPN
ejpam-5861	467	7	t∈j	t∈j	PROPN
ejpam-5861	467	8	∣∣∣∣ϕ(t)−	∣∣∣∣ϕ(t)−	PROPN
ejpam-5861	467	9	ϕ0	ϕ0	PROPN
ejpam-5861	468	1	−	−	PROPN
ejpam-5861	468	2	∫	∫	PROPN
ejpam-5861	468	3	t	t	NOUN
ejpam-5861	468	4	0	0	NUM
ejpam-5861	469	1	g(u	g(u	PROPN
ejpam-5861	469	2	,	,	PUNCT
ejpam-5861	469	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	469	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	469	5	+	+	CCONJ
ejpam-5861	469	6	max	max	PROPN
ejpam-5861	469	7	t∈j	t∈j	NOUN
ejpam-5861	469	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	469	9	∫	∫	PROPN
ejpam-5861	469	10	t	t	PROPN
ejpam-5861	469	11	0	0	NUM
ejpam-5861	469	12	g(u	g(u	PROPN
ejpam-5861	469	13	,	,	PUNCT
ejpam-5861	469	14	ϕ(u))du−	ϕ(u))du−	PROPN
ejpam-5861	469	15	∫	∫	PROPN
ejpam-5861	469	16	t	t	PROPN
ejpam-5861	469	17	0	0	NUM
ejpam-5861	470	1	g(u	g(u	PROPN
ejpam-5861	470	2	,	,	PUNCT
ejpam-5861	470	3	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	470	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5861	470	5	≤	≤	NUM
ejpam-5861	470	6	ϵt1	ϵt1	NOUN
ejpam-5861	471	1	+	+	CCONJ
ejpam-5861	471	2	lgt1∥ϕ−	lgt1∥ϕ−	PROPN
ejpam-5861	471	3	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	471	4	(	(	PUNCT
ejpam-5861	471	5	35	35	NUM
ejpam-5861	471	6	)	)	PUNCT
ejpam-5861	471	7	hence	hence	ADV
ejpam-5861	471	8	from	from	ADP
ejpam-5861	471	9	(	(	PUNCT
ejpam-5861	471	10	35	35	NUM
ejpam-5861	471	11	)	)	PUNCT
ejpam-5861	471	12	,	,	PUNCT
ejpam-5861	471	13	we	we	PRON
ejpam-5861	471	14	get	get	VERB
ejpam-5861	471	15	∥∥ϕ−	∥∥ϕ−	PROPN
ejpam-5861	472	1	ϕ̄	ϕ̄	PROPN
ejpam-5861	473	1	∥∥	∥∥	PUNCT
ejpam-5861	473	2	≤	≤	NUM
ejpam-5861	473	3	ϵt1	ϵt1	NOUN
ejpam-5861	473	4	1−	1−	NUM
ejpam-5861	473	5	t1lg	t1lg	NUM
ejpam-5861	473	6	.	.	PUNCT
ejpam-5861	474	1	(	(	PUNCT
ejpam-5861	474	2	36	36	NUM
ejpam-5861	474	3	)	)	PUNCT
ejpam-5861	474	4	s.	s.	PROPN
ejpam-5861	474	5	naz	naz	PROPN
ejpam-5861	474	6	et	et	PROPN
ejpam-5861	474	7	al	al	PROPN
ejpam-5861	474	8	.	.	PUNCT
ejpam-5861	474	9	/	/	SYM
ejpam-5861	474	10	eur	eur	PROPN
ejpam-5861	474	11	.	.	PUNCT
ejpam-5861	475	1	j.	j.	PROPN
ejpam-5861	475	2	pure	pure	PROPN
ejpam-5861	475	3	appl	appl	PROPN
ejpam-5861	475	4	.	.	PROPN
ejpam-5861	475	5	math	math	PROPN
ejpam-5861	475	6	,	,	PUNCT
ejpam-5861	475	7	18	18	NUM
ejpam-5861	475	8	(	(	PUNCT
ejpam-5861	475	9	2	2	NUM
ejpam-5861	475	10	)	)	PUNCT
ejpam-5861	475	11	(	(	PUNCT
ejpam-5861	475	12	2025	2025	NUM
ejpam-5861	475	13	)	)	PUNCT
ejpam-5861	475	14	,	,	PUNCT
ejpam-5861	475	15	5861	5861	NUM
ejpam-5861	475	16	21	21	NUM
ejpam-5861	475	17	of	of	ADP
ejpam-5861	475	18	33	33	NUM
ejpam-5861	475	19	step	step	NOUN
ejpam-5861	475	20	ii	ii	NOUN
ejpam-5861	475	21	:	:	PUNCT
ejpam-5861	475	22	if	if	SCONJ
ejpam-5861	475	23	t	t	PROPN
ejpam-5861	475	24	∈	∈	PROPN
ejpam-5861	476	1	[	[	X
ejpam-5861	476	2	t1,t	t1,t	PROPN
ejpam-5861	476	3	]	]	PUNCT
ejpam-5861	476	4	,	,	PUNCT
ejpam-5861	476	5	then	then	ADV
ejpam-5861	476	6	we	we	PRON
ejpam-5861	476	7	have	have	VERB
ejpam-5861	476	8	∥∥ϕ−	∥∥ϕ−	PROPN
ejpam-5861	476	9	ϕ̄	ϕ̄	INTJ
ejpam-5861	476	10	∥∥	∥∥	X
ejpam-5861	477	1	=	=	SYM
ejpam-5861	477	2	max	max	PROPN
ejpam-5861	477	3	t∈j	t∈j	PROPN
ejpam-5861	477	4	∣∣∣∣ϕ(t)−	∣∣∣∣ϕ(t)−	PROPN
ejpam-5861	477	5	ϕ(t1)−	ϕ(t1)−	PROPN
ejpam-5861	478	1	∫	∫	PROPN
ejpam-5861	478	2	t	t	PROPN
ejpam-5861	478	3	t1	t1	PROPN
ejpam-5861	478	4	(	(	PUNCT
ejpam-5861	478	5	t−	t−	PROPN
ejpam-5861	478	6	u)ε−1	u)ε−1	PROPN
ejpam-5861	478	7	γ(ε	γ(ε	PROPN
ejpam-5861	478	8	)	)	PUNCT
ejpam-5861	478	9	g(u	g(u	PROPN
ejpam-5861	478	10	,	,	PUNCT
ejpam-5861	478	11	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	478	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	478	13	≤	≤	NUM
ejpam-5861	478	14	max	max	PROPN
ejpam-5861	478	15	t∈j	t∈j	PROPN
ejpam-5861	478	16	∣∣∣∣ϕ(t)−	∣∣∣∣ϕ(t)−	PROPN
ejpam-5861	478	17	ϕ(t1)−	ϕ(t1)−	PROPN
ejpam-5861	478	18	∫	∫	PROPN
ejpam-5861	478	19	t	t	PROPN
ejpam-5861	478	20	t1	t1	PROPN
ejpam-5861	478	21	(	(	PUNCT
ejpam-5861	478	22	t−	t−	PROPN
ejpam-5861	478	23	u)ε−1	u)ε−1	PROPN
ejpam-5861	478	24	γ(ε	γ(ε	PROPN
ejpam-5861	478	25	)	)	PUNCT
ejpam-5861	479	1	g(u	g(u	PROPN
ejpam-5861	479	2	,	,	PUNCT
ejpam-5861	479	3	ϕ(u))du	ϕ(u))du	PROPN
ejpam-5861	479	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	479	5	+	+	CCONJ
ejpam-5861	479	6	max	max	PROPN
ejpam-5861	479	7	t∈j	t∈j	NOUN
ejpam-5861	479	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	479	9	∫	∫	PROPN
ejpam-5861	479	10	t	t	PROPN
ejpam-5861	479	11	t1	t1	PROPN
ejpam-5861	479	12	(	(	PUNCT
ejpam-5861	479	13	t−	t−	PROPN
ejpam-5861	479	14	u)ε−1	u)ε−1	PROPN
ejpam-5861	479	15	γ(ε	γ(ε	PROPN
ejpam-5861	479	16	)	)	PUNCT
ejpam-5861	480	1	g(u	g(u	PROPN
ejpam-5861	480	2	,	,	PUNCT
ejpam-5861	480	3	ϕ(u))du−	ϕ(u))du−	PROPN
ejpam-5861	480	4	∫	∫	PROPN
ejpam-5861	480	5	t	t	PROPN
ejpam-5861	480	6	t1	t1	PROPN
ejpam-5861	480	7	(	(	PUNCT
ejpam-5861	480	8	t−	t−	PROPN
ejpam-5861	480	9	u)ε−1	u)ε−1	PROPN
ejpam-5861	480	10	γ(ε	γ(ε	PROPN
ejpam-5861	480	11	)	)	PUNCT
ejpam-5861	481	1	g(u	g(u	PROPN
ejpam-5861	481	2	,	,	PUNCT
ejpam-5861	481	3	ϕ̄(u))du	ϕ̄(u))du	PRON
ejpam-5861	481	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5861	481	5	≤	≤	NUM
ejpam-5861	481	6	tεϵ	tεϵ	NOUN
ejpam-5861	481	7	γ(ε+	γ(ε+	PROPN
ejpam-5861	481	8	1	1	NUM
ejpam-5861	481	9	)	)	PUNCT
ejpam-5861	481	10	+	+	NUM
ejpam-5861	481	11	tεlg	tεlg	NOUN
ejpam-5861	481	12	γ(ε+	γ(ε+	NOUN
ejpam-5861	481	13	1	1	NUM
ejpam-5861	481	14	)	)	PUNCT
ejpam-5861	481	15	∥ϕ−	∥ϕ−	NUM
ejpam-5861	481	16	ϕ̄∥.	ϕ̄∥.	X
ejpam-5861	481	17	(	(	PUNCT
ejpam-5861	481	18	37	37	NUM
ejpam-5861	481	19	)	)	PUNCT
ejpam-5861	481	20	from	from	ADP
ejpam-5861	481	21	(	(	PUNCT
ejpam-5861	481	22	37	37	NUM
ejpam-5861	481	23	)	)	PUNCT
ejpam-5861	481	24	,	,	PUNCT
ejpam-5861	481	25	∥∥ϕ−	∥∥ϕ−	PROPN
ejpam-5861	481	26	ϕ̄	ϕ̄	PROPN
ejpam-5861	481	27	∥∥	∥∥	X
ejpam-5861	481	28	≤	≤	X
ejpam-5861	481	29	[	[	PUNCT
ejpam-5861	481	30	tε	tε	X
ejpam-5861	481	31	(	(	PUNCT
ejpam-5861	481	32	1−	1−	NUM
ejpam-5861	481	33	∆̄)γ(ε+	∆̄)γ(ε+	PROPN
ejpam-5861	481	34	1	1	NUM
ejpam-5861	481	35	)	)	PUNCT
ejpam-5861	481	36	]	]	PUNCT
ejpam-5861	482	1	ϵ.	ϵ.	NOUN
ejpam-5861	482	2	(	(	PUNCT
ejpam-5861	482	3	38	38	NUM
ejpam-5861	482	4	)	)	PUNCT
ejpam-5861	482	5	we	we	PRON
ejpam-5861	482	6	can	can	AUX
ejpam-5861	482	7	now	now	ADV
ejpam-5861	482	8	see	see	VERB
ejpam-5861	482	9	that	that	SCONJ
ejpam-5861	482	10	the	the	DET
ejpam-5861	482	11	solution	solution	NOUN
ejpam-5861	482	12	to	to	PART
ejpam-5861	482	13	issue	issue	NOUN
ejpam-5861	482	14	(	(	PUNCT
ejpam-5861	482	15	18	18	NUM
ejpam-5861	482	16	)	)	PUNCT
ejpam-5861	482	17	is	be	AUX
ejpam-5861	482	18	uh	uh	INTJ
ejpam-5861	482	19	stable	stable	ADJ
ejpam-5861	482	20	based	base	VERB
ejpam-5861	482	21	on	on	ADP
ejpam-5861	482	22	(	(	PUNCT
ejpam-5861	482	23	36	36	NUM
ejpam-5861	482	24	)	)	PUNCT
ejpam-5861	482	25	and	and	CCONJ
ejpam-5861	482	26	(	(	PUNCT
ejpam-5861	482	27	38	38	NUM
ejpam-5861	482	28	)	)	PUNCT
ejpam-5861	482	29	.	.	PUNCT
ejpam-5861	483	1	moreover	moreover	ADV
ejpam-5861	483	2	,	,	PUNCT
ejpam-5861	483	3	the	the	DET
ejpam-5861	483	4	solution	solution	NOUN
ejpam-5861	483	5	is	be	AUX
ejpam-5861	483	6	unquestionably	unquestionably	ADV
ejpam-5861	483	7	generalized	generalize	VERB
ejpam-5861	483	8	uh	uh	INTJ
ejpam-5861	483	9	stable	stable	ADJ
ejpam-5861	483	10	if	if	SCONJ
ejpam-5861	483	11	there	there	PRON
ejpam-5861	483	12	is	be	VERB
ejpam-5861	483	13	a	a	DET
ejpam-5861	483	14	non	non	ADJ
ejpam-5861	483	15	-	-	ADJ
ejpam-5861	483	16	decreasing	decrease	VERB
ejpam-5861	483	17	function	function	NOUN
ejpam-5861	483	18	φ	φ	NOUN
ejpam-5861	483	19	:	:	PUNCT
ejpam-5861	484	1	j	j	PROPN
ejpam-5861	484	2	→	→	PUNCT
ejpam-5861	484	3	[	[	X
ejpam-5861	484	4	0,∞	0,∞	NUM
ejpam-5861	484	5	)	)	PUNCT
ejpam-5861	484	6	such	such	ADJ
ejpam-5861	484	7	that	that	SCONJ
ejpam-5861	484	8	φ(ϵ	φ(ϵ	NOUN
ejpam-5861	484	9	)	)	PUNCT
ejpam-5861	484	10	=	=	PUNCT
ejpam-5861	484	11	ϵ.	ϵ.	NOUN
ejpam-5861	484	12	6	6	NUM
ejpam-5861	484	13	.	.	PUNCT
ejpam-5861	484	14	numerical	numerical	ADJ
ejpam-5861	484	15	scheme	scheme	PROPN
ejpam-5861	484	16	here	here	ADV
ejpam-5861	484	17	,	,	PUNCT
ejpam-5861	484	18	we	we	PRON
ejpam-5861	484	19	expand	expand	VERB
ejpam-5861	484	20	the	the	DET
ejpam-5861	484	21	approach	approach	NOUN
ejpam-5861	484	22	from	from	ADP
ejpam-5861	484	23	[	[	X
ejpam-5861	484	24	24	24	NUM
ejpam-5861	484	25	]	]	PUNCT
ejpam-5861	484	26	to	to	PART
ejpam-5861	484	27	build	build	VERB
ejpam-5861	484	28	the	the	DET
ejpam-5861	484	29	numerical	numerical	ADJ
ejpam-5861	484	30	scheme	scheme	NOUN
ejpam-5861	484	31	based	base	VERB
ejpam-5861	484	32	on	on	ADP
ejpam-5861	484	33	the	the	DET
ejpam-5861	484	34	rkm	rkm	PROPN
ejpam-5861	484	35	method	method	NOUN
ejpam-5861	484	36	of	of	ADP
ejpam-5861	484	37	order	order	NOUN
ejpam-5861	484	38	four	four	NUM
ejpam-5861	484	39	.	.	PUNCT
ejpam-5861	485	1	for	for	ADP
ejpam-5861	485	2	computation	computation	NOUN
ejpam-5861	485	3	purposes	purpose	NOUN
ejpam-5861	485	4	,	,	PUNCT
ejpam-5861	485	5	where	where	SCONJ
ejpam-5861	485	6	small	small	ADJ
ejpam-5861	485	7	steps	step	NOUN
ejpam-5861	485	8	are	be	AUX
ejpam-5861	485	9	to	to	PART
ejpam-5861	485	10	be	be	AUX
ejpam-5861	485	11	computed	compute	VERB
ejpam-5861	485	12	the	the	DET
ejpam-5861	485	13	euler	euler	NOUN
ejpam-5861	485	14	method	method	NOUN
ejpam-5861	485	15	is	be	AUX
ejpam-5861	485	16	good	good	ADJ
ejpam-5861	485	17	.	.	PUNCT
ejpam-5861	486	1	however	however	ADV
ejpam-5861	486	2	,	,	PUNCT
ejpam-5861	486	3	for	for	ADP
ejpam-5861	486	4	evaluations	evaluation	NOUN
ejpam-5861	486	5	of	of	ADP
ejpam-5861	486	6	largen	largen	NOUN
ejpam-5861	486	7	numbers	number	NOUN
ejpam-5861	486	8	of	of	ADP
ejpam-5861	486	9	steps	step	NOUN
ejpam-5861	486	10	,	,	PUNCT
ejpam-5861	486	11	the	the	DET
ejpam-5861	486	12	rkm	rkm	PROPN
ejpam-5861	486	13	method	method	NOUN
ejpam-5861	486	14	is	be	AUX
ejpam-5861	486	15	given	give	VERB
ejpam-5861	486	16	preferred	prefer	VERB
ejpam-5861	486	17	because	because	SCONJ
ejpam-5861	486	18	in	in	ADP
ejpam-5861	486	19	such	such	DET
ejpam-5861	486	20	a	a	DET
ejpam-5861	486	21	situation	situation	NOUN
ejpam-5861	486	22	it	it	PRON
ejpam-5861	486	23	gives	give	VERB
ejpam-5861	486	24	efficient	efficient	ADJ
ejpam-5861	486	25	and	and	CCONJ
ejpam-5861	486	26	accurate	accurate	ADJ
ejpam-5861	486	27	solution	solution	NOUN
ejpam-5861	486	28	.	.	PUNCT
ejpam-5861	487	1	in	in	ADP
ejpam-5861	487	2	light	light	NOUN
ejpam-5861	487	3	of	of	ADP
ejpam-5861	487	4	this	this	DET
ejpam-5861	487	5	need	need	NOUN
ejpam-5861	487	6	,	,	PUNCT
ejpam-5861	487	7	we	we	PRON
ejpam-5861	487	8	view	view	VERB
ejpam-5861	487	9	the	the	DET
ejpam-5861	487	10	fractional	fractional	ADJ
ejpam-5861	487	11	order	order	NOUN
ejpam-5861	487	12	problem	problem	NOUN
ejpam-5861	487	13	as	as	ADP
ejpam-5861	487	14	pc	pc	NOUN
ejpam-5861	487	15	0	0	NUM
ejpam-5861	487	16	dε	dε	NOUN
ejpam-5861	487	17	tϕ(t	tϕ(t	NOUN
ejpam-5861	487	18	)	)	PUNCT
ejpam-5861	487	19	=	=	SYM
ejpam-5861	487	20	gj(t	gj(t	PROPN
ejpam-5861	487	21	,	,	PUNCT
ejpam-5861	487	22	ϕ(t	ϕ(t	NUM
ejpam-5861	487	23	)	)	PUNCT
ejpam-5861	487	24	)	)	PUNCT
ejpam-5861	487	25	,	,	PUNCT
ejpam-5861	487	26	j	j	PROPN
ejpam-5861	487	27	=	=	SYM
ejpam-5861	487	28	1	1	NUM
ejpam-5861	487	29	,	,	PUNCT
ejpam-5861	487	30	2	2	NUM
ejpam-5861	487	31	,	,	PUNCT
ejpam-5861	487	32	...	...	PUNCT
ejpam-5861	487	33	,	,	PUNCT
ejpam-5861	487	34	7	7	NUM
ejpam-5861	487	35	ϕ(0	ϕ(0	NOUN
ejpam-5861	487	36	)	)	PUNCT
ejpam-5861	488	1	=	=	SYM
ejpam-5861	488	2	ϕ0	ϕ0	NOUN
ejpam-5861	488	3	.	.	PUNCT
ejpam-5861	489	1	(	(	PUNCT
ejpam-5861	489	2	39	39	NUM
ejpam-5861	489	3	)	)	PUNCT
ejpam-5861	489	4	where	where	SCONJ
ejpam-5861	489	5	gj	gj	NOUN
ejpam-5861	489	6	:	:	PUNCT
ejpam-5861	489	7	j	j	PROPN
ejpam-5861	489	8	×	×	PROPN
ejpam-5861	489	9	r	r	PROPN
ejpam-5861	489	10	→	→	SYM
ejpam-5861	489	11	r.	r.	NOUN
ejpam-5861	489	12	we	we	PRON
ejpam-5861	489	13	may	may	AUX
ejpam-5861	489	14	express	express	VERB
ejpam-5861	489	15	taylor	taylor	PROPN
ejpam-5861	489	16	series	series	PROPN
ejpam-5861	489	17	in	in	ADP
ejpam-5861	489	18	general	general	ADJ
ejpam-5861	489	19	form	form	NOUN
ejpam-5861	489	20	as	as	ADP
ejpam-5861	489	21	ϕ(t+	ϕ(t+	PROPN
ejpam-5861	489	22	h	h	NOUN
ejpam-5861	489	23	)	)	PUNCT
ejpam-5861	489	24	=	=	SYM
ejpam-5861	489	25	ϕ(t	ϕ(t	NUM
ejpam-5861	489	26	)	)	PUNCT
ejpam-5861	490	1	+	+	CCONJ
ejpam-5861	490	2	hε	hε	ADP
ejpam-5861	490	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	490	4	1	1	NUM
ejpam-5861	490	5	)	)	PUNCT
ejpam-5861	490	6	dt	dt	NOUN
ejpam-5861	490	7	εϕ(t	εϕ(t	NUM
ejpam-5861	490	8	)	)	PUNCT
ejpam-5861	490	9	+	+	CCONJ
ejpam-5861	490	10	h2ε	h2ε	PROPN
ejpam-5861	490	11	γ(2ε+	γ(2ε+	NOUN
ejpam-5861	490	12	1	1	NUM
ejpam-5861	490	13	)	)	PUNCT
ejpam-5861	490	14	d2ε	d2ε	PROPN
ejpam-5861	490	15	t	t	PROPN
ejpam-5861	490	16	x(t	x(t	PROPN
ejpam-5861	490	17	)	)	PUNCT
ejpam-5861	491	1	+	+	CCONJ
ejpam-5861	491	2	...	...	PUNCT
ejpam-5861	491	3	(	(	PUNCT
ejpam-5861	491	4	40	40	NUM
ejpam-5861	491	5	)	)	PUNCT
ejpam-5861	491	6	on	on	ADP
ejpam-5861	491	7	applying	apply	VERB
ejpam-5861	491	8	dt	dt	NOUN
ejpam-5861	491	9	2εϕ	2εϕ	NOUN
ejpam-5861	491	10	=	=	SYM
ejpam-5861	491	11	dtgj(t	dtgj(t	PROPN
ejpam-5861	491	12	,	,	PUNCT
ejpam-5861	491	13	ϕ(t	ϕ(t	NUM
ejpam-5861	491	14	)	)	PUNCT
ejpam-5861	491	15	)	)	PUNCT
ejpam-5861	492	1	+	+	CCONJ
ejpam-5861	492	2	gj(t	gj(t	PROPN
ejpam-5861	492	3	,	,	PUNCT
ejpam-5861	492	4	ϕ(t))dϕ	ϕ(t))dϕ	PROPN
ejpam-5861	492	5	εg(t	εg(t	ADV
ejpam-5861	492	6	,	,	PUNCT
ejpam-5861	492	7	ϕ(t	ϕ(t	NUM
ejpam-5861	492	8	)	)	PUNCT
ejpam-5861	492	9	)	)	PUNCT
ejpam-5861	492	10	in	in	ADP
ejpam-5861	492	11	(	(	PUNCT
ejpam-5861	492	12	40	40	NUM
ejpam-5861	492	13	)	)	PUNCT
ejpam-5861	492	14	implies	imply	VERB
ejpam-5861	492	15	the	the	DET
ejpam-5861	492	16	following	follow	VERB
ejpam-5861	492	17	results	result	NOUN
ejpam-5861	492	18	:	:	PUNCT
ejpam-5861	492	19	ϕi+1	ϕi+1	X
ejpam-5861	492	20	=	=	SYM
ejpam-5861	493	1	ϕi	ϕi	ADP
ejpam-5861	493	2	+	+	CCONJ
ejpam-5861	493	3	hε	hε	PRON
ejpam-5861	493	4	γ(ε+	γ(ε+	NOUN
ejpam-5861	493	5	1	1	NUM
ejpam-5861	493	6	)	)	PUNCT
ejpam-5861	493	7	gj(ti	gj(ti	NOUN
ejpam-5861	493	8	,	,	PUNCT
ejpam-5861	493	9	ϕ(ti	ϕ(ti	PROPN
ejpam-5861	493	10	)	)	PUNCT
ejpam-5861	493	11	)	)	PUNCT
ejpam-5861	494	1	+	+	CCONJ
ejpam-5861	494	2	hε	hε	ADP
ejpam-5861	494	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	494	4	1	1	NUM
ejpam-5861	494	5	)	)	PUNCT
ejpam-5861	494	6	[	[	PUNCT
ejpam-5861	494	7	k1	k1	NOUN
ejpam-5861	494	8	+	+	X
ejpam-5861	494	9	k2	k2	NOUN
ejpam-5861	494	10	]	]	PUNCT
ejpam-5861	494	11	,	,	PUNCT
ejpam-5861	494	12	(	(	PUNCT
ejpam-5861	494	13	41	41	NUM
ejpam-5861	494	14	)	)	PUNCT
ejpam-5861	495	1	where	where	SCONJ
ejpam-5861	495	2	k1	k1	NOUN
ejpam-5861	495	3	=	=	SYM
ejpam-5861	495	4	gj(ti	gj(ti	PROPN
ejpam-5861	495	5	,	,	PUNCT
ejpam-5861	495	6	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	495	7	)	)	PUNCT
ejpam-5861	495	8	)	)	PUNCT
ejpam-5861	495	9	,	,	PUNCT
ejpam-5861	495	10	k2	k2	PROPN
ejpam-5861	495	11	=	=	SYM
ejpam-5861	495	12	gj	gj	PROPN
ejpam-5861	495	13	(	(	PUNCT
ejpam-5861	495	14	ti	ti	PROPN
ejpam-5861	495	15	+	+	CCONJ
ejpam-5861	495	16	2hεγ(ε+	2hεγ(ε+	PROPN
ejpam-5861	495	17	1	1	NUM
ejpam-5861	495	18	)	)	PUNCT
ejpam-5861	495	19	γ(2ε+	γ(2ε+	NOUN
ejpam-5861	495	20	1	1	NUM
ejpam-5861	495	21	)	)	PUNCT
ejpam-5861	495	22	,	,	PUNCT
ejpam-5861	495	23	ϕ(ti	ϕ(ti	PROPN
ejpam-5861	495	24	)	)	PUNCT
ejpam-5861	496	1	+	+	CCONJ
ejpam-5861	496	2	2hεγ(ε+	2hεγ(ε+	NUM
ejpam-5861	496	3	1	1	NUM
ejpam-5861	496	4	)	)	PUNCT
ejpam-5861	496	5	γ(2ε+	γ(2ε+	NOUN
ejpam-5861	496	6	1	1	NUM
ejpam-5861	496	7	)	)	PUNCT
ejpam-5861	496	8	gj(ti	gj(ti	NOUN
ejpam-5861	496	9	,	,	PUNCT
ejpam-5861	496	10	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	496	11	)	)	PUNCT
ejpam-5861	496	12	)	)	PUNCT
ejpam-5861	496	13	)	)	PUNCT
ejpam-5861	496	14	.	.	PUNCT
ejpam-5861	497	1	(	(	PUNCT
ejpam-5861	497	2	42	42	NUM
ejpam-5861	497	3	)	)	PUNCT
ejpam-5861	497	4	s.	s.	PROPN
ejpam-5861	497	5	naz	naz	PROPN
ejpam-5861	497	6	et	et	PROPN
ejpam-5861	497	7	al	al	PROPN
ejpam-5861	497	8	.	.	PUNCT
ejpam-5861	497	9	/	/	SYM
ejpam-5861	497	10	eur	eur	PROPN
ejpam-5861	497	11	.	.	PUNCT
ejpam-5861	498	1	j.	j.	PROPN
ejpam-5861	498	2	pure	pure	PROPN
ejpam-5861	498	3	appl	appl	PROPN
ejpam-5861	498	4	.	.	PROPN
ejpam-5861	498	5	math	math	PROPN
ejpam-5861	498	6	,	,	PUNCT
ejpam-5861	498	7	18	18	NUM
ejpam-5861	498	8	(	(	PUNCT
ejpam-5861	498	9	2	2	NUM
ejpam-5861	498	10	)	)	PUNCT
ejpam-5861	498	11	(	(	PUNCT
ejpam-5861	498	12	2025	2025	NUM
ejpam-5861	498	13	)	)	PUNCT
ejpam-5861	498	14	,	,	PUNCT
ejpam-5861	498	15	5861	5861	NUM
ejpam-5861	498	16	22	22	NUM
ejpam-5861	498	17	of	of	ADP
ejpam-5861	498	18	33	33	NUM
ejpam-5861	498	19	on	on	ADP
ejpam-5861	498	20	using	use	VERB
ejpam-5861	498	21	ε	ε	PROPN
ejpam-5861	498	22	=	=	SYM
ejpam-5861	498	23	1	1	NUM
ejpam-5861	498	24	,	,	PUNCT
ejpam-5861	498	25	gives	give	VERB
ejpam-5861	498	26	ordinary	ordinary	ADJ
ejpam-5861	498	27	numerical	numerical	ADJ
ejpam-5861	498	28	method	method	NOUN
ejpam-5861	498	29	.	.	PUNCT
ejpam-5861	499	1	to	to	PART
ejpam-5861	499	2	illustrate	illustrate	VERB
ejpam-5861	499	3	the	the	DET
ejpam-5861	499	4	compartmental	compartmental	ADJ
ejpam-5861	499	5	solutions	solution	NOUN
ejpam-5861	499	6	graphically	graphically	ADV
ejpam-5861	499	7	,	,	PUNCT
ejpam-5861	499	8	we	we	PRON
ejpam-5861	499	9	derive	derive	VERB
ejpam-5861	499	10	numerical	numerical	ADJ
ejpam-5861	499	11	scheme	scheme	NOUN
ejpam-5861	499	12	as	as	ADP
ejpam-5861	499	13	:	:	PUNCT
ejpam-5861	499	14	s(ti+1	s(ti+1	NOUN
ejpam-5861	499	15	)	)	PUNCT
ejpam-5861	499	16	)	)	PUNCT
ejpam-5861	500	1	=	=	SYM
ejpam-5861	500	2			PUNCT
ejpam-5861	500	3	si−1(ti−1	si−1(ti−1	PROPN
ejpam-5861	500	4	)	)	PUNCT
ejpam-5861	501	1	+	+	CCONJ
ejpam-5861	501	2	h	h	NOUN
ejpam-5861	501	3	2	2	NUM
ejpam-5861	501	4	g1	g1	NOUN
ejpam-5861	501	5	[	[	PUNCT
ejpam-5861	501	6	ti−1	ti−1	NOUN
ejpam-5861	501	7	+	+	CCONJ
ejpam-5861	501	8	h	h	NOUN
ejpam-5861	501	9	2	2	NUM
ejpam-5861	501	10	,	,	PUNCT
ejpam-5861	501	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	501	12	)	)	PUNCT
ejpam-5861	502	1	+	+	NUM
ejpam-5861	502	2	k1	k1	NOUN
ejpam-5861	502	3	2	2	NUM
ejpam-5861	502	4	]	]	PUNCT
ejpam-5861	502	5	,	,	PUNCT
ejpam-5861	502	6	t	t	PROPN
ejpam-5861	502	7	∈	∈	PROPN
ejpam-5861	502	8	∇1	∇1	PROPN
ejpam-5861	502	9	si(ti	si(ti	PROPN
ejpam-5861	502	10	)	)	PUNCT
ejpam-5861	503	1	+	+	CCONJ
ejpam-5861	503	2	hφ	hφ	PROPN
ejpam-5861	503	3	γ(ε+	γ(ε+	PROPN
ejpam-5861	503	4	1	1	NUM
ejpam-5861	503	5	)	)	PUNCT
ejpam-5861	503	6	g1(ti	g1(ti	PROPN
ejpam-5861	503	7	,	,	PUNCT
ejpam-5861	503	8	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	503	9	)	)	PUNCT
ejpam-5861	503	10	)	)	PUNCT
ejpam-5861	504	1	+	+	CCONJ
ejpam-5861	504	2	hε	hε	ADP
ejpam-5861	504	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	504	4	1	1	NUM
ejpam-5861	504	5	)	)	PUNCT
ejpam-5861	504	6	[	[	PUNCT
ejpam-5861	504	7	k2	k2	PROPN
ejpam-5861	504	8	+	+	X
ejpam-5861	504	9	k3	k3	X
ejpam-5861	504	10	]	]	PUNCT
ejpam-5861	504	11	,	,	PUNCT
ejpam-5861	504	12	t	t	PROPN
ejpam-5861	504	13	∈	∈	PROPN
ejpam-5861	504	14	∇2	∇2	PROPN
ejpam-5861	504	15	,	,	PUNCT
ejpam-5861	504	16	(	(	PUNCT
ejpam-5861	504	17	43	43	NUM
ejpam-5861	504	18	)	)	PUNCT
ejpam-5861	505	1	where	where	SCONJ
ejpam-5861	505	2	h	h	NOUN
ejpam-5861	505	3	=	=	NOUN
ejpam-5861	505	4	ti+1	ti+1	NOUN
ejpam-5861	505	5	−	−	ADP
ejpam-5861	505	6	ti	ti	NOUN
ejpam-5861	505	7	and	and	CCONJ
ejpam-5861	505	8	k1	k1	NOUN
ejpam-5861	505	9	=	=	SYM
ejpam-5861	505	10	g1(ti−1	g1(ti−1	PROPN
ejpam-5861	505	11	,	,	PUNCT
ejpam-5861	505	12	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	505	13	)	)	PUNCT
ejpam-5861	505	14	)	)	PUNCT
ejpam-5861	505	15	,	,	PUNCT
ejpam-5861	505	16	k2	k2	PROPN
ejpam-5861	505	17	=	=	SYM
ejpam-5861	505	18	g1(ti	g1(ti	PROPN
ejpam-5861	505	19	,	,	PUNCT
ejpam-5861	505	20	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	505	21	)	)	PUNCT
ejpam-5861	505	22	)	)	PUNCT
ejpam-5861	506	1	,	,	PUNCT
ejpam-5861	506	2	k3	k3	PROPN
ejpam-5861	506	3	=	=	PROPN
ejpam-5861	506	4	g1	g1	PROPN
ejpam-5861	506	5	(	(	PUNCT
ejpam-5861	506	6	ti	ti	X
ejpam-5861	506	7	+	+	CCONJ
ejpam-5861	506	8	2hεγ(ε+	2hεγ(ε+	PROPN
ejpam-5861	506	9	1	1	NUM
ejpam-5861	506	10	)	)	PUNCT
ejpam-5861	506	11	γ(2ε+	γ(2ε+	NOUN
ejpam-5861	506	12	1	1	NUM
ejpam-5861	506	13	)	)	PUNCT
ejpam-5861	506	14	,	,	PUNCT
ejpam-5861	506	15	ϕ(ti	ϕ(ti	PROPN
ejpam-5861	506	16	)	)	PUNCT
ejpam-5861	507	1	+	+	CCONJ
ejpam-5861	507	2	2hεγ(ε+	2hεγ(ε+	NUM
ejpam-5861	507	3	1	1	NUM
ejpam-5861	507	4	)	)	PUNCT
ejpam-5861	507	5	γ(2ε+	γ(2ε+	NOUN
ejpam-5861	507	6	1	1	NUM
ejpam-5861	507	7	)	)	PUNCT
ejpam-5861	507	8	g1(ti	g1(ti	PROPN
ejpam-5861	507	9	,	,	PUNCT
ejpam-5861	507	10	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	507	11	)	)	PUNCT
ejpam-5861	507	12	)	)	PUNCT
ejpam-5861	507	13	)	)	PUNCT
ejpam-5861	507	14	.	.	PUNCT
ejpam-5861	508	1	(	(	PUNCT
ejpam-5861	508	2	44	44	NUM
ejpam-5861	508	3	)	)	PUNCT
ejpam-5861	508	4	with	with	ADP
ejpam-5861	508	5	the	the	DET
ejpam-5861	508	6	same	same	ADJ
ejpam-5861	508	7	patron	patron	NOUN
ejpam-5861	508	8	v(ti+1	v(ti+1	NOUN
ejpam-5861	508	9	)	)	PUNCT
ejpam-5861	508	10	)	)	PUNCT
ejpam-5861	509	1	=	=	SYM
ejpam-5861	509	2			PUNCT
ejpam-5861	509	3	vi−1(ti−1	vi−1(ti−1	PROPN
ejpam-5861	509	4	)	)	PUNCT
ejpam-5861	510	1	+	+	NUM
ejpam-5861	510	2	h	h	NOUN
ejpam-5861	510	3	2	2	NUM
ejpam-5861	510	4	g2	g2	PROPN
ejpam-5861	510	5	[	[	PUNCT
ejpam-5861	510	6	ti−1	ti−1	NOUN
ejpam-5861	510	7	+	+	CCONJ
ejpam-5861	510	8	h	h	NOUN
ejpam-5861	510	9	2	2	NUM
ejpam-5861	510	10	,	,	PUNCT
ejpam-5861	510	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	510	12	)	)	PUNCT
ejpam-5861	511	1	+	+	NUM
ejpam-5861	511	2	k1	k1	NOUN
ejpam-5861	511	3	2	2	NUM
ejpam-5861	511	4	]	]	PUNCT
ejpam-5861	511	5	,	,	PUNCT
ejpam-5861	511	6	t	t	PROPN
ejpam-5861	511	7	∈	∈	PROPN
ejpam-5861	511	8	∇1	∇1	PROPN
ejpam-5861	511	9	vi(ti	vi(ti	PROPN
ejpam-5861	511	10	)	)	PUNCT
ejpam-5861	512	1	+	+	CCONJ
ejpam-5861	512	2	hε	hε	PRON
ejpam-5861	512	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	512	4	1	1	NUM
ejpam-5861	512	5	)	)	PUNCT
ejpam-5861	512	6	g2(ti	g2(ti	PROPN
ejpam-5861	512	7	,	,	PUNCT
ejpam-5861	512	8	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	512	9	)	)	PUNCT
ejpam-5861	512	10	)	)	PUNCT
ejpam-5861	513	1	+	+	CCONJ
ejpam-5861	513	2	hε	hε	ADP
ejpam-5861	513	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	513	4	1	1	NUM
ejpam-5861	513	5	)	)	PUNCT
ejpam-5861	513	6	[	[	PUNCT
ejpam-5861	513	7	k2	k2	PROPN
ejpam-5861	513	8	+	+	X
ejpam-5861	513	9	k3	k3	X
ejpam-5861	513	10	]	]	PUNCT
ejpam-5861	513	11	,	,	PUNCT
ejpam-5861	513	12	t	t	PROPN
ejpam-5861	513	13	∈	∈	PROPN
ejpam-5861	513	14	∇2	∇2	PROPN
ejpam-5861	513	15	,	,	PUNCT
ejpam-5861	513	16	(	(	PUNCT
ejpam-5861	513	17	45	45	NUM
ejpam-5861	513	18	)	)	PUNCT
ejpam-5861	513	19	e(ti+1	e(ti+1	NOUN
ejpam-5861	513	20	)	)	PUNCT
ejpam-5861	513	21	)	)	PUNCT
ejpam-5861	513	22	=	=	SYM
ejpam-5861	513	23			PUNCT
ejpam-5861	513	24	ei−1(ti−1	ei−1(ti−1	PROPN
ejpam-5861	513	25	)	)	PUNCT
ejpam-5861	514	1	+	+	CCONJ
ejpam-5861	514	2	h	h	NOUN
ejpam-5861	514	3	2	2	NUM
ejpam-5861	514	4	g3	g3	NOUN
ejpam-5861	514	5	[	[	PUNCT
ejpam-5861	514	6	ti−1	ti−1	NOUN
ejpam-5861	514	7	+	+	CCONJ
ejpam-5861	514	8	h	h	NOUN
ejpam-5861	514	9	2	2	NUM
ejpam-5861	514	10	,	,	PUNCT
ejpam-5861	514	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	514	12	)	)	PUNCT
ejpam-5861	515	1	+	+	NUM
ejpam-5861	515	2	k1	k1	NOUN
ejpam-5861	515	3	2	2	NUM
ejpam-5861	515	4	]	]	PUNCT
ejpam-5861	515	5	,	,	PUNCT
ejpam-5861	515	6	t	t	PROPN
ejpam-5861	515	7	∈	∈	PROPN
ejpam-5861	515	8	∇1	∇1	PROPN
ejpam-5861	515	9	ei(ti	ei(ti	PROPN
ejpam-5861	515	10	)	)	PUNCT
ejpam-5861	516	1	+	+	CCONJ
ejpam-5861	516	2	hε	hε	PRON
ejpam-5861	516	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	516	4	1	1	NUM
ejpam-5861	516	5	)	)	PUNCT
ejpam-5861	516	6	g3(ti	g3(ti	PROPN
ejpam-5861	516	7	,	,	PUNCT
ejpam-5861	516	8	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	516	9	)	)	PUNCT
ejpam-5861	516	10	)	)	PUNCT
ejpam-5861	517	1	+	+	CCONJ
ejpam-5861	517	2	hε	hε	ADP
ejpam-5861	517	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	517	4	1	1	NUM
ejpam-5861	517	5	)	)	PUNCT
ejpam-5861	517	6	[	[	PUNCT
ejpam-5861	517	7	k2	k2	PROPN
ejpam-5861	517	8	+	+	X
ejpam-5861	517	9	k3	k3	X
ejpam-5861	517	10	]	]	PUNCT
ejpam-5861	517	11	,	,	PUNCT
ejpam-5861	517	12	t	t	PROPN
ejpam-5861	517	13	∈	∈	PROPN
ejpam-5861	517	14	∇2	∇2	PROPN
ejpam-5861	517	15	,	,	PUNCT
ejpam-5861	517	16	(	(	PUNCT
ejpam-5861	517	17	46	46	NUM
ejpam-5861	517	18	)	)	PUNCT
ejpam-5861	517	19	i(ti+1	i(ti+1	NOUN
ejpam-5861	517	20	)	)	PUNCT
ejpam-5861	517	21	)	)	PUNCT
ejpam-5861	518	1	=	=	SYM
ejpam-5861	518	2			NUM
ejpam-5861	518	3	ii−1(ti−1	ii−1(ti−1	PROPN
ejpam-5861	518	4	)	)	PUNCT
ejpam-5861	519	1	+	+	NUM
ejpam-5861	519	2	h	h	NOUN
ejpam-5861	519	3	2	2	NUM
ejpam-5861	519	4	g4	g4	NOUN
ejpam-5861	519	5	[	[	PUNCT
ejpam-5861	519	6	ti−1	ti−1	NOUN
ejpam-5861	519	7	+	+	CCONJ
ejpam-5861	519	8	h	h	NOUN
ejpam-5861	519	9	2	2	NUM
ejpam-5861	519	10	,	,	PUNCT
ejpam-5861	519	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	519	12	)	)	PUNCT
ejpam-5861	520	1	+	+	NUM
ejpam-5861	520	2	k1	k1	NOUN
ejpam-5861	520	3	2	2	NUM
ejpam-5861	520	4	]	]	PUNCT
ejpam-5861	520	5	,	,	PUNCT
ejpam-5861	520	6	t	t	PROPN
ejpam-5861	520	7	∈	∈	PROPN
ejpam-5861	520	8	∇1	∇1	PROPN
ejpam-5861	520	9	ii(ti	ii(ti	PROPN
ejpam-5861	520	10	)	)	PUNCT
ejpam-5861	521	1	+	+	CCONJ
ejpam-5861	521	2	hε	hε	PRON
ejpam-5861	521	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	521	4	1	1	NUM
ejpam-5861	521	5	)	)	PUNCT
ejpam-5861	521	6	g4(ti	g4(ti	PROPN
ejpam-5861	521	7	,	,	PUNCT
ejpam-5861	521	8	ϕi(ti	ϕi(ti	PROPN
ejpam-5861	521	9	)	)	PUNCT
ejpam-5861	521	10	)	)	PUNCT
ejpam-5861	522	1	+	+	CCONJ
ejpam-5861	522	2	hε	hε	ADP
ejpam-5861	522	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	522	4	1	1	NUM
ejpam-5861	522	5	)	)	PUNCT
ejpam-5861	522	6	[	[	PUNCT
ejpam-5861	522	7	k2	k2	PROPN
ejpam-5861	522	8	+	+	X
ejpam-5861	522	9	k3	k3	X
ejpam-5861	522	10	]	]	PUNCT
ejpam-5861	522	11	,	,	PUNCT
ejpam-5861	522	12	t	t	PROPN
ejpam-5861	522	13	∈	∈	PROPN
ejpam-5861	522	14	∇2	∇2	PROPN
ejpam-5861	522	15	,	,	PUNCT
ejpam-5861	522	16	(	(	PUNCT
ejpam-5861	522	17	47	47	NUM
ejpam-5861	522	18	)	)	PUNCT
ejpam-5861	522	19	q(ti+1	q(ti+1	ADJ
ejpam-5861	522	20	)	)	PUNCT
ejpam-5861	522	21	)	)	PUNCT
ejpam-5861	523	1	=	=	SYM
ejpam-5861	523	2			NUM
ejpam-5861	523	3	qi−1(ti−1	qi−1(ti−1	PROPN
ejpam-5861	523	4	)	)	PUNCT
ejpam-5861	524	1	+	+	CCONJ
ejpam-5861	524	2	h	h	NOUN
ejpam-5861	524	3	2	2	NUM
ejpam-5861	524	4	g5	g5	NOUN
ejpam-5861	524	5	[	[	PUNCT
ejpam-5861	524	6	ti−1	ti−1	NOUN
ejpam-5861	524	7	+	+	CCONJ
ejpam-5861	524	8	h	h	NOUN
ejpam-5861	524	9	2	2	NUM
ejpam-5861	524	10	,	,	PUNCT
ejpam-5861	524	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	524	12	)	)	PUNCT
ejpam-5861	525	1	+	+	NUM
ejpam-5861	525	2	k1	k1	NOUN
ejpam-5861	525	3	2	2	NUM
ejpam-5861	525	4	]	]	PUNCT
ejpam-5861	525	5	,	,	PUNCT
ejpam-5861	525	6	t	t	PROPN
ejpam-5861	525	7	∈	∈	PROPN
ejpam-5861	525	8	∇1	∇1	PROPN
ejpam-5861	525	9	ri(ti	ri(ti	NOUN
ejpam-5861	525	10	)	)	PUNCT
ejpam-5861	526	1	+	+	CCONJ
ejpam-5861	526	2	hε	hε	ADP
ejpam-5861	526	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	526	4	1	1	NUM
ejpam-5861	526	5	)	)	PUNCT
ejpam-5861	526	6	g5(ti	g5(ti	PROPN
ejpam-5861	526	7	,	,	PUNCT
ejpam-5861	526	8	ϕi(ti	ϕi(ti	NOUN
ejpam-5861	526	9	)	)	PUNCT
ejpam-5861	526	10	)	)	PUNCT
ejpam-5861	527	1	+	+	CCONJ
ejpam-5861	527	2	hε	hε	ADP
ejpam-5861	527	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	527	4	1	1	NUM
ejpam-5861	527	5	)	)	PUNCT
ejpam-5861	527	6	[	[	PUNCT
ejpam-5861	527	7	k2	k2	PROPN
ejpam-5861	527	8	+	+	X
ejpam-5861	527	9	k3	k3	X
ejpam-5861	527	10	]	]	PUNCT
ejpam-5861	527	11	,	,	PUNCT
ejpam-5861	527	12	t	t	PROPN
ejpam-5861	527	13	∈	∈	PROPN
ejpam-5861	527	14	∇2	∇2	PROPN
ejpam-5861	527	15	,	,	PUNCT
ejpam-5861	527	16	(	(	PUNCT
ejpam-5861	527	17	48	48	NUM
ejpam-5861	527	18	)	)	PUNCT
ejpam-5861	527	19	r(ti+1	r(ti+1	ADV
ejpam-5861	527	20	)	)	PUNCT
ejpam-5861	527	21	)	)	PUNCT
ejpam-5861	528	1	=	=	SYM
ejpam-5861	528	2			NUM
ejpam-5861	528	3	ri−1(ti−1	ri−1(ti−1	PROPN
ejpam-5861	528	4	)	)	PUNCT
ejpam-5861	529	1	+	+	NUM
ejpam-5861	529	2	h	h	NOUN
ejpam-5861	529	3	2	2	NUM
ejpam-5861	529	4	g6	g6	ADJ
ejpam-5861	529	5	[	[	PUNCT
ejpam-5861	529	6	ti−1	ti−1	NOUN
ejpam-5861	529	7	+	+	CCONJ
ejpam-5861	529	8	h	h	NOUN
ejpam-5861	529	9	2	2	NUM
ejpam-5861	529	10	,	,	PUNCT
ejpam-5861	529	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	529	12	)	)	PUNCT
ejpam-5861	530	1	+	+	NUM
ejpam-5861	530	2	k1	k1	NOUN
ejpam-5861	530	3	2	2	NUM
ejpam-5861	530	4	]	]	PUNCT
ejpam-5861	530	5	,	,	PUNCT
ejpam-5861	530	6	t	t	PROPN
ejpam-5861	530	7	∈	∈	PROPN
ejpam-5861	530	8	∇1	∇1	PROPN
ejpam-5861	530	9	ri(ti	ri(ti	NOUN
ejpam-5861	530	10	)	)	PUNCT
ejpam-5861	531	1	+	+	CCONJ
ejpam-5861	531	2	hε	hε	ADP
ejpam-5861	531	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	531	4	1	1	NUM
ejpam-5861	531	5	)	)	PUNCT
ejpam-5861	531	6	g6(ti	g6(ti	PROPN
ejpam-5861	531	7	,	,	PUNCT
ejpam-5861	531	8	ϕi(ti	ϕi(ti	NOUN
ejpam-5861	531	9	)	)	PUNCT
ejpam-5861	531	10	)	)	PUNCT
ejpam-5861	532	1	+	+	CCONJ
ejpam-5861	532	2	hε	hε	ADP
ejpam-5861	532	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	532	4	1	1	NUM
ejpam-5861	532	5	)	)	PUNCT
ejpam-5861	532	6	[	[	PUNCT
ejpam-5861	532	7	k2	k2	PROPN
ejpam-5861	532	8	+	+	X
ejpam-5861	532	9	k3	k3	X
ejpam-5861	532	10	]	]	PUNCT
ejpam-5861	532	11	,	,	PUNCT
ejpam-5861	532	12	t	t	PROPN
ejpam-5861	532	13	∈	∈	PROPN
ejpam-5861	532	14	∇2	∇2	PROPN
ejpam-5861	532	15	,	,	PUNCT
ejpam-5861	532	16	(	(	PUNCT
ejpam-5861	532	17	49	49	NUM
ejpam-5861	532	18	)	)	PUNCT
ejpam-5861	532	19	and	and	CCONJ
ejpam-5861	532	20	d(ti+1	d(ti+1	NOUN
ejpam-5861	532	21	)	)	PUNCT
ejpam-5861	532	22	)	)	PUNCT
ejpam-5861	532	23	=	=	SYM
ejpam-5861	532	24			NUM
ejpam-5861	532	25	di−1(ti−1	di−1(ti−1	PROPN
ejpam-5861	532	26	)	)	PUNCT
ejpam-5861	533	1	+	+	CCONJ
ejpam-5861	533	2	h	h	NOUN
ejpam-5861	533	3	2	2	NUM
ejpam-5861	533	4	g7	g7	PROPN
ejpam-5861	533	5	[	[	PUNCT
ejpam-5861	533	6	ti−1	ti−1	NOUN
ejpam-5861	533	7	+	+	CCONJ
ejpam-5861	533	8	h	h	NOUN
ejpam-5861	533	9	2	2	NUM
ejpam-5861	533	10	,	,	PUNCT
ejpam-5861	533	11	ϕi−1(ti−1	ϕi−1(ti−1	PROPN
ejpam-5861	533	12	)	)	PUNCT
ejpam-5861	534	1	+	+	NUM
ejpam-5861	534	2	k1	k1	NOUN
ejpam-5861	534	3	2	2	NUM
ejpam-5861	534	4	]	]	PUNCT
ejpam-5861	534	5	,	,	PUNCT
ejpam-5861	534	6	t	t	PROPN
ejpam-5861	534	7	∈	∈	PROPN
ejpam-5861	534	8	∇1	∇1	PROPN
ejpam-5861	534	9	di(ti	di(ti	PROPN
ejpam-5861	534	10	)	)	PUNCT
ejpam-5861	535	1	+	+	CCONJ
ejpam-5861	535	2	hε	hε	ADP
ejpam-5861	535	3	γ(ε+	γ(ε+	NOUN
ejpam-5861	535	4	1	1	NUM
ejpam-5861	535	5	)	)	PUNCT
ejpam-5861	535	6	g7(ti	g7(ti	PROPN
ejpam-5861	535	7	,	,	PUNCT
ejpam-5861	535	8	ϕi(ti	ϕi(ti	NOUN
ejpam-5861	535	9	)	)	PUNCT
ejpam-5861	535	10	)	)	PUNCT
ejpam-5861	536	1	+	+	CCONJ
ejpam-5861	536	2	hε	hε	ADP
ejpam-5861	536	3	2γ(ε+	2γ(ε+	NUM
ejpam-5861	536	4	1	1	NUM
ejpam-5861	536	5	)	)	PUNCT
ejpam-5861	536	6	[	[	PUNCT
ejpam-5861	536	7	k2	k2	PROPN
ejpam-5861	536	8	+	+	X
ejpam-5861	536	9	k3	k3	X
ejpam-5861	536	10	]	]	PUNCT
ejpam-5861	536	11	,	,	PUNCT
ejpam-5861	536	12	t	t	PROPN
ejpam-5861	536	13	∈	∈	PROPN
ejpam-5861	536	14	∇2	∇2	PROPN
ejpam-5861	536	15	.	.	PUNCT
ejpam-5861	537	1	(	(	PUNCT
ejpam-5861	537	2	50	50	NUM
ejpam-5861	537	3	)	)	PUNCT
ejpam-5861	537	4	s.	s.	PROPN
ejpam-5861	537	5	naz	naz	PROPN
ejpam-5861	537	6	et	et	PROPN
ejpam-5861	537	7	al	al	PROPN
ejpam-5861	537	8	.	.	PUNCT
ejpam-5861	537	9	/	/	SYM
ejpam-5861	537	10	eur	eur	PROPN
ejpam-5861	537	11	.	.	PUNCT
ejpam-5861	538	1	j.	j.	PROPN
ejpam-5861	538	2	pure	pure	PROPN
ejpam-5861	538	3	appl	appl	PROPN
ejpam-5861	538	4	.	.	PROPN
ejpam-5861	538	5	math	math	PROPN
ejpam-5861	538	6	,	,	PUNCT
ejpam-5861	538	7	18	18	NUM
ejpam-5861	538	8	(	(	PUNCT
ejpam-5861	538	9	2	2	NUM
ejpam-5861	538	10	)	)	PUNCT
ejpam-5861	538	11	(	(	PUNCT
ejpam-5861	538	12	2025	2025	NUM
ejpam-5861	538	13	)	)	PUNCT
ejpam-5861	538	14	,	,	PUNCT
ejpam-5861	538	15	5861	5861	NUM
ejpam-5861	538	16	23	23	NUM
ejpam-5861	538	17	of	of	ADP
ejpam-5861	538	18	33	33	NUM
ejpam-5861	538	19	7	7	NUM
ejpam-5861	538	20	.	.	PUNCT
ejpam-5861	538	21	graphical	graphical	ADJ
ejpam-5861	538	22	illustrations	illustration	NOUN
ejpam-5861	538	23	and	and	CCONJ
ejpam-5861	538	24	explanations	explanation	NOUN
ejpam-5861	538	25	to	to	PART
ejpam-5861	538	26	simulate	simulate	VERB
ejpam-5861	538	27	our	our	PRON
ejpam-5861	538	28	results	result	NOUN
ejpam-5861	538	29	graphically	graphically	ADV
ejpam-5861	538	30	,	,	PUNCT
ejpam-5861	538	31	we	we	PRON
ejpam-5861	538	32	use	use	VERB
ejpam-5861	538	33	the	the	DET
ejpam-5861	538	34	numerical	numerical	ADJ
ejpam-5861	538	35	values	value	NOUN
ejpam-5861	538	36	of	of	ADP
ejpam-5861	538	37	table	table	NOUN
ejpam-5861	538	38	1	1	NUM
ejpam-5861	538	39	and	and	CCONJ
ejpam-5861	538	40	taking	take	VERB
ejpam-5861	538	41	the	the	DET
ejpam-5861	538	42	initial	initial	ADJ
ejpam-5861	538	43	data	datum	NOUN
ejpam-5861	538	44	as	as	SCONJ
ejpam-5861	538	45	given	give	VERB
ejpam-5861	538	46	by	by	ADP
ejpam-5861	538	47	s(0	s(0	PROPN
ejpam-5861	538	48	)	)	PUNCT
ejpam-5861	538	49	=	=	SYM
ejpam-5861	538	50	97.00000	97.00000	NUM
ejpam-5861	538	51	;	;	PUNCT
ejpam-5861	538	52	v	v	NUM
ejpam-5861	538	53	(	(	PUNCT
ejpam-5861	538	54	0	0	NUM
ejpam-5861	538	55	)	)	PUNCT
ejpam-5861	538	56	=	=	SYM
ejpam-5861	538	57	50.00000	50.00000	NUM
ejpam-5861	538	58	;	;	PUNCT
ejpam-5861	538	59	e(0	e(0	NOUN
ejpam-5861	538	60	)	)	PUNCT
ejpam-5861	538	61	=	=	SYM
ejpam-5861	538	62	70.00000	70.00000	NUM
ejpam-5861	538	63	;	;	PUNCT
ejpam-5861	538	64	i(0	i(0	PROPN
ejpam-5861	538	65	)	)	PUNCT
ejpam-5861	539	1	=	=	SYM
ejpam-5861	539	2	1.581936	1.581936	NUM
ejpam-5861	539	3	;	;	PUNCT
ejpam-5861	539	4	q(0	q(0	PROPN
ejpam-5861	539	5	)	)	PUNCT
ejpam-5861	539	6	=	=	NOUN
ejpam-5861	540	1	1.581936	1.581936	NUM
ejpam-5861	540	2	;	;	PUNCT
ejpam-5861	540	3	r(0	r(0	PROPN
ejpam-5861	540	4	)	)	PUNCT
ejpam-5861	540	5	=	=	PROPN
ejpam-5861	540	6	1.538689	1.538689	NUM
ejpam-5861	540	7	;	;	PUNCT
ejpam-5861	540	8	d(0	d(0	NOUN
ejpam-5861	540	9	)	)	PUNCT
ejpam-5861	540	10	=	=	PUNCT
ejpam-5861	541	1	0.030664	0.030664	NUM
ejpam-5861	541	2	.	.	PUNCT
ejpam-5861	542	1	7.1	7.1	NUM
ejpam-5861	542	2	.	.	PUNCT
ejpam-5861	543	1	case	case	NOUN
ejpam-5861	543	2	-	-	PUNCT
ejpam-5861	543	3	i	i	PRON
ejpam-5861	543	4	we	we	PRON
ejpam-5861	543	5	take	take	VERB
ejpam-5861	543	6	the	the	DET
ejpam-5861	543	7	first	first	ADJ
ejpam-5861	543	8	set	set	NOUN
ejpam-5861	543	9	of	of	ADP
ejpam-5861	543	10	fractional	fractional	ADJ
ejpam-5861	543	11	order	order	NOUN
ejpam-5861	543	12	values	value	NOUN
ejpam-5861	543	13	in	in	ADP
ejpam-5861	543	14	(	(	PUNCT
ejpam-5861	543	15	0.60	0.60	NUM
ejpam-5861	543	16	,	,	PUNCT
ejpam-5861	543	17	0.80	0.80	NUM
ejpam-5861	543	18	]	]	PUNCT
ejpam-5861	543	19	and	and	CCONJ
ejpam-5861	543	20	presented	present	VERB
ejpam-5861	543	21	solutions	solution	NOUN
ejpam-5861	543	22	graphically	graphically	ADV
ejpam-5861	543	23	in	in	ADP
ejpam-5861	543	24	figures	figure	NOUN
ejpam-5861	543	25	4	4	NUM
ejpam-5861	543	26	,	,	PUNCT
ejpam-5861	543	27	5	5	NUM
ejpam-5861	543	28	,	,	PUNCT
ejpam-5861	543	29	6	6	NUM
ejpam-5861	543	30	,	,	PUNCT
ejpam-5861	543	31	7	7	NUM
ejpam-5861	543	32	,	,	PUNCT
ejpam-5861	543	33	8	8	NUM
ejpam-5861	543	34	,	,	PUNCT
ejpam-5861	543	35	9	9	NUM
ejpam-5861	543	36	,	,	PUNCT
ejpam-5861	543	37	10	10	NUM
ejpam-5861	543	38	respectively	respectively	ADV
ejpam-5861	543	39	.	.	PUNCT
ejpam-5861	544	1	t	t	NOUN
ejpam-5861	544	2	0	0	NUM
ejpam-5861	544	3	50	50	NUM
ejpam-5861	544	4	100	100	NUM
ejpam-5861	544	5	150	150	NUM
ejpam-5861	544	6	200	200	NUM
ejpam-5861	544	7	250	250	NUM
ejpam-5861	544	8	300	300	NUM
ejpam-5861	544	9	s	s	PART
ejpam-5861	544	10	us	us	PROPN
ejpam-5861	544	11	ce	ce	PROPN
ejpam-5861	544	12	pt	pt	X
ejpam-5861	544	13	ib	ib	X
ejpam-5861	544	14	le	le	PROPN
ejpam-5861	544	15	c	c	PROPN
ejpam-5861	544	16	la	la	INTJ
ejpam-5861	544	17	ss	ss	NOUN
ejpam-5861	544	18	0	0	NUM
ejpam-5861	544	19	20	20	NUM
ejpam-5861	544	20	40	40	NUM
ejpam-5861	544	21	60	60	NUM
ejpam-5861	544	22	80	80	NUM
ejpam-5861	544	23	100	100	NUM
ejpam-5861	544	24	0.65	0.65	NUM
ejpam-5861	544	25	0.70	0.70	NUM
ejpam-5861	544	26	0.75	0.75	NUM
ejpam-5861	544	27	0.80	0.80	NUM
ejpam-5861	544	28	figure	figure	NOUN
ejpam-5861	544	29	4	4	NUM
ejpam-5861	544	30	:	:	PUNCT
ejpam-5861	544	31	solution	solution	NOUN
ejpam-5861	544	32	illustration	illustration	NOUN
ejpam-5861	544	33	of	of	ADP
ejpam-5861	544	34	susceptible	susceptible	ADJ
ejpam-5861	544	35	class	class	NOUN
ejpam-5861	544	36	for	for	ADP
ejpam-5861	544	37	ε	ε	PROPN
ejpam-5861	544	38	∈	∈	PROPN
ejpam-5861	544	39	(	(	PUNCT
ejpam-5861	544	40	0.60	0.60	NUM
ejpam-5861	544	41	,	,	PUNCT
ejpam-5861	544	42	0.80	0.80	NUM
ejpam-5861	544	43	]	]	PUNCT
ejpam-5861	544	44	.	.	PUNCT
ejpam-5861	545	1	t	t	NOUN
ejpam-5861	545	2	0	0	NUM
ejpam-5861	545	3	50	50	NUM
ejpam-5861	545	4	100	100	NUM
ejpam-5861	545	5	150	150	NUM
ejpam-5861	545	6	200	200	NUM
ejpam-5861	545	7	250	250	NUM
ejpam-5861	545	8	300	300	NUM
ejpam-5861	545	9	v	v	NUM
ejpam-5861	545	10	ac	ac	PROPN
ejpam-5861	545	11	ci	ci	PROPN
ejpam-5861	545	12	na	na	X
ejpam-5861	545	13	te	te	PROPN
ejpam-5861	545	14	d	d	X
ejpam-5861	545	15	cl	cl	NOUN
ejpam-5861	545	16	as	as	ADP
ejpam-5861	545	17	s	s	NOUN
ejpam-5861	545	18	50	50	NUM
ejpam-5861	545	19	60	60	NUM
ejpam-5861	545	20	70	70	NUM
ejpam-5861	545	21	80	80	NUM
ejpam-5861	545	22	90	90	NUM
ejpam-5861	545	23	0.65	0.65	NUM
ejpam-5861	545	24	0.70	0.70	NUM
ejpam-5861	545	25	0.75	0.75	NUM
ejpam-5861	545	26	0.80	0.80	NUM
ejpam-5861	545	27	figure	figure	NOUN
ejpam-5861	545	28	5	5	NUM
ejpam-5861	545	29	:	:	PUNCT
ejpam-5861	545	30	solution	solution	NOUN
ejpam-5861	545	31	illustration	illustration	NOUN
ejpam-5861	545	32	of	of	ADP
ejpam-5861	545	33	vaccinated	vaccinated	ADJ
ejpam-5861	545	34	class	class	NOUN
ejpam-5861	545	35	for	for	ADP
ejpam-5861	545	36	ε	ε	PROPN
ejpam-5861	545	37	∈	∈	PROPN
ejpam-5861	545	38	(	(	PUNCT
ejpam-5861	545	39	0.60	0.60	NUM
ejpam-5861	545	40	,	,	PUNCT
ejpam-5861	545	41	0.80	0.80	NUM
ejpam-5861	545	42	]	]	PUNCT
ejpam-5861	545	43	.	.	PUNCT
ejpam-5861	546	1	s.	s.	PROPN
ejpam-5861	546	2	naz	naz	PROPN
ejpam-5861	546	3	et	et	PROPN
ejpam-5861	546	4	al	al	PROPN
ejpam-5861	546	5	.	.	PUNCT
ejpam-5861	546	6	/	/	SYM
ejpam-5861	546	7	eur	eur	PROPN
ejpam-5861	546	8	.	.	PUNCT
ejpam-5861	547	1	j.	j.	PROPN
ejpam-5861	547	2	pure	pure	PROPN
ejpam-5861	547	3	appl	appl	PROPN
ejpam-5861	547	4	.	.	PROPN
ejpam-5861	547	5	math	math	PROPN
ejpam-5861	547	6	,	,	PUNCT
ejpam-5861	547	7	18	18	NUM
ejpam-5861	547	8	(	(	PUNCT
ejpam-5861	547	9	2	2	NUM
ejpam-5861	547	10	)	)	PUNCT
ejpam-5861	547	11	(	(	PUNCT
ejpam-5861	547	12	2025	2025	NUM
ejpam-5861	547	13	)	)	PUNCT
ejpam-5861	547	14	,	,	PUNCT
ejpam-5861	547	15	5861	5861	NUM
ejpam-5861	547	16	24	24	NUM
ejpam-5861	547	17	of	of	ADP
ejpam-5861	547	18	33	33	NUM
ejpam-5861	547	19	t	t	NOUN
ejpam-5861	547	20	0	0	NUM
ejpam-5861	547	21	50	50	NUM
ejpam-5861	547	22	100	100	NUM
ejpam-5861	547	23	150	150	NUM
ejpam-5861	547	24	200	200	NUM
ejpam-5861	547	25	250	250	NUM
ejpam-5861	547	26	300	300	NUM
ejpam-5861	547	27	e	e	NOUN
ejpam-5861	547	28	xp	xp	ADV
ejpam-5861	547	29	os	os	INTJ
ejpam-5861	548	1	ed	ed	NOUN
ejpam-5861	548	2	c	c	PROPN
ejpam-5861	548	3	la	la	INTJ
ejpam-5861	548	4	ss	ss	NOUN
ejpam-5861	548	5	0	0	NUM
ejpam-5861	548	6	20	20	NUM
ejpam-5861	548	7	40	40	NUM
ejpam-5861	548	8	60	60	NUM
ejpam-5861	548	9	80	80	NUM
ejpam-5861	548	10	0.65	0.65	NUM
ejpam-5861	548	11	0.70	0.70	NUM
ejpam-5861	548	12	0.75	0.75	NUM
ejpam-5861	548	13	0.80	0.80	NUM
ejpam-5861	548	14	figure	figure	NOUN
ejpam-5861	548	15	6	6	NUM
ejpam-5861	548	16	:	:	PUNCT
ejpam-5861	548	17	solution	solution	NOUN
ejpam-5861	548	18	illustration	illustration	NOUN
ejpam-5861	548	19	of	of	ADP
ejpam-5861	548	20	exposed	expose	VERB
ejpam-5861	548	21	class	class	NOUN
ejpam-5861	548	22	for	for	ADP
ejpam-5861	548	23	ε	ε	PROPN
ejpam-5861	548	24	∈	∈	PROPN
ejpam-5861	548	25	(	(	PUNCT
ejpam-5861	548	26	0.60	0.60	NUM
ejpam-5861	548	27	,	,	PUNCT
ejpam-5861	548	28	0.80	0.80	NUM
ejpam-5861	548	29	]	]	PUNCT
ejpam-5861	548	30	.	.	PUNCT
ejpam-5861	549	1	t	t	NOUN
ejpam-5861	549	2	0	0	NUM
ejpam-5861	549	3	50	50	NUM
ejpam-5861	549	4	100	100	NUM
ejpam-5861	549	5	150	150	NUM
ejpam-5861	549	6	200	200	NUM
ejpam-5861	549	7	250	250	NUM
ejpam-5861	549	8	300	300	NUM
ejpam-5861	549	9	in	in	ADP
ejpam-5861	549	10	fe	fe	X
ejpam-5861	549	11	ct	ct	NUM
ejpam-5861	549	12	ed	ed	PROPN
ejpam-5861	549	13	c	c	PROPN
ejpam-5861	549	14	la	la	NOUN
ejpam-5861	549	15	ss	ss	NOUN
ejpam-5861	549	16	0	0	NUM
ejpam-5861	549	17	5	5	NUM
ejpam-5861	549	18	10	10	NUM
ejpam-5861	549	19	15	15	NUM
ejpam-5861	549	20	20	20	NUM
ejpam-5861	549	21	25	25	NUM
ejpam-5861	549	22	0.65	0.65	NUM
ejpam-5861	549	23	0.70	0.70	NUM
ejpam-5861	549	24	0.75	0.75	NUM
ejpam-5861	549	25	0.80	0.80	NUM
ejpam-5861	549	26	figure	figure	NOUN
ejpam-5861	549	27	7	7	NUM
ejpam-5861	549	28	:	:	PUNCT
ejpam-5861	549	29	solution	solution	NOUN
ejpam-5861	549	30	illustration	illustration	NOUN
ejpam-5861	549	31	of	of	ADP
ejpam-5861	549	32	infected	infected	ADJ
ejpam-5861	549	33	class	class	NOUN
ejpam-5861	549	34	for	for	ADP
ejpam-5861	549	35	ε	ε	PROPN
ejpam-5861	549	36	∈	∈	PROPN
ejpam-5861	549	37	(	(	PUNCT
ejpam-5861	549	38	0.60	0.60	NUM
ejpam-5861	549	39	,	,	PUNCT
ejpam-5861	549	40	0.80	0.80	NUM
ejpam-5861	549	41	]	]	PUNCT
ejpam-5861	549	42	.	.	PUNCT
ejpam-5861	550	1	s.	s.	PROPN
ejpam-5861	550	2	naz	naz	PROPN
ejpam-5861	550	3	et	et	PROPN
ejpam-5861	550	4	al	al	PROPN
ejpam-5861	550	5	.	.	PUNCT
ejpam-5861	550	6	/	/	SYM
ejpam-5861	550	7	eur	eur	PROPN
ejpam-5861	550	8	.	.	PUNCT
ejpam-5861	551	1	j.	j.	PROPN
ejpam-5861	551	2	pure	pure	PROPN
ejpam-5861	551	3	appl	appl	PROPN
ejpam-5861	551	4	.	.	PROPN
ejpam-5861	551	5	math	math	PROPN
ejpam-5861	551	6	,	,	PUNCT
ejpam-5861	551	7	18	18	NUM
ejpam-5861	551	8	(	(	PUNCT
ejpam-5861	551	9	2	2	NUM
ejpam-5861	551	10	)	)	PUNCT
ejpam-5861	551	11	(	(	PUNCT
ejpam-5861	551	12	2025	2025	NUM
ejpam-5861	551	13	)	)	PUNCT
ejpam-5861	551	14	,	,	PUNCT
ejpam-5861	551	15	5861	5861	NUM
ejpam-5861	551	16	25	25	NUM
ejpam-5861	551	17	of	of	ADP
ejpam-5861	551	18	33	33	NUM
ejpam-5861	551	19	0	0	NUM
ejpam-5861	551	20	50	50	NUM
ejpam-5861	551	21	100	100	NUM
ejpam-5861	551	22	150	150	NUM
ejpam-5861	551	23	200	200	NUM
ejpam-5861	551	24	250	250	NUM
ejpam-5861	551	25	300	300	NUM
ejpam-5861	551	26	t	t	NOUN
ejpam-5861	551	27	0	0	NUM
ejpam-5861	551	28	1	1	NUM
ejpam-5861	551	29	2	2	NUM
ejpam-5861	551	30	3	3	NUM
ejpam-5861	551	31	4	4	NUM
ejpam-5861	551	32	5	5	NUM
ejpam-5861	551	33	6	6	NUM
ejpam-5861	551	34	q	q	PROPN
ejpam-5861	551	35	ua	ua	PROPN
ejpam-5861	551	36	ra	ra	PROPN
ejpam-5861	551	37	nt	not	PART
ejpam-5861	551	38	in	in	ADP
ejpam-5861	551	39	ed	ed	PROPN
ejpam-5861	551	40	c	c	PROPN
ejpam-5861	551	41	la	la	NOUN
ejpam-5861	551	42	ss	ss	NOUN
ejpam-5861	551	43	0.65	0.65	NUM
ejpam-5861	551	44	0.70	0.70	NUM
ejpam-5861	551	45	0.75	0.75	NUM
ejpam-5861	551	46	0.80	0.80	NUM
ejpam-5861	551	47	figure	figure	NOUN
ejpam-5861	551	48	8	8	NUM
ejpam-5861	551	49	:	:	PUNCT
ejpam-5861	551	50	solution	solution	NOUN
ejpam-5861	551	51	illustration	illustration	NOUN
ejpam-5861	551	52	of	of	ADP
ejpam-5861	551	53	quarantined	quarantined	ADJ
ejpam-5861	551	54	class	class	NOUN
ejpam-5861	551	55	for	for	ADP
ejpam-5861	551	56	ε	ε	PROPN
ejpam-5861	551	57	∈	∈	PROPN
ejpam-5861	551	58	(	(	PUNCT
ejpam-5861	551	59	0.60	0.60	NUM
ejpam-5861	551	60	,	,	PUNCT
ejpam-5861	551	61	0.80	0.80	NUM
ejpam-5861	551	62	]	]	PUNCT
ejpam-5861	551	63	.	.	PUNCT
ejpam-5861	552	1	t	t	NOUN
ejpam-5861	552	2	0	0	NUM
ejpam-5861	552	3	50	50	NUM
ejpam-5861	552	4	100	100	NUM
ejpam-5861	552	5	150	150	NUM
ejpam-5861	552	6	200	200	NUM
ejpam-5861	552	7	250	250	NUM
ejpam-5861	552	8	300	300	NUM
ejpam-5861	552	9	r	r	NOUN
ejpam-5861	552	10	ec	ec	X
ejpam-5861	552	11	ov	ov	INTJ
ejpam-5861	552	12	er	er	INTJ
ejpam-5861	552	13	ed	ed	NOUN
ejpam-5861	552	14	c	c	PROPN
ejpam-5861	552	15	la	la	NOUN
ejpam-5861	553	1	ss	ss	NOUN
ejpam-5861	554	1	0	0	NUM
ejpam-5861	554	2	2	2	NUM
ejpam-5861	554	3	4	4	NUM
ejpam-5861	554	4	6	6	NUM
ejpam-5861	554	5	8	8	NUM
ejpam-5861	554	6	0.65	0.65	NUM
ejpam-5861	554	7	0.70	0.70	NUM
ejpam-5861	554	8	0.75	0.75	NUM
ejpam-5861	554	9	0.80	0.80	NUM
ejpam-5861	554	10	figure	figure	NOUN
ejpam-5861	554	11	9	9	NUM
ejpam-5861	554	12	:	:	PUNCT
ejpam-5861	554	13	solution	solution	NOUN
ejpam-5861	554	14	illustration	illustration	NOUN
ejpam-5861	554	15	of	of	ADP
ejpam-5861	554	16	recovered	recovered	ADJ
ejpam-5861	554	17	class	class	NOUN
ejpam-5861	554	18	for	for	ADP
ejpam-5861	554	19	ε	ε	PROPN
ejpam-5861	554	20	∈	∈	PROPN
ejpam-5861	554	21	(	(	PUNCT
ejpam-5861	554	22	0.60	0.60	NUM
ejpam-5861	554	23	,	,	PUNCT
ejpam-5861	554	24	0.80	0.80	NUM
ejpam-5861	554	25	]	]	PUNCT
ejpam-5861	554	26	.	.	PUNCT
ejpam-5861	555	1	s.	s.	PROPN
ejpam-5861	555	2	naz	naz	PROPN
ejpam-5861	555	3	et	et	PROPN
ejpam-5861	555	4	al	al	PROPN
ejpam-5861	555	5	.	.	PUNCT
ejpam-5861	555	6	/	/	SYM
ejpam-5861	555	7	eur	eur	PROPN
ejpam-5861	555	8	.	.	PUNCT
ejpam-5861	556	1	j.	j.	PROPN
ejpam-5861	556	2	pure	pure	PROPN
ejpam-5861	556	3	appl	appl	PROPN
ejpam-5861	556	4	.	.	PROPN
ejpam-5861	556	5	math	math	PROPN
ejpam-5861	556	6	,	,	PUNCT
ejpam-5861	556	7	18	18	NUM
ejpam-5861	556	8	(	(	PUNCT
ejpam-5861	556	9	2	2	NUM
ejpam-5861	556	10	)	)	PUNCT
ejpam-5861	556	11	(	(	PUNCT
ejpam-5861	556	12	2025	2025	NUM
ejpam-5861	556	13	)	)	PUNCT
ejpam-5861	556	14	,	,	PUNCT
ejpam-5861	556	15	5861	5861	NUM
ejpam-5861	556	16	26	26	NUM
ejpam-5861	556	17	of	of	ADP
ejpam-5861	556	18	33	33	NUM
ejpam-5861	556	19	t	t	NOUN
ejpam-5861	556	20	0	0	NUM
ejpam-5861	556	21	50	50	NUM
ejpam-5861	556	22	100	100	NUM
ejpam-5861	556	23	150	150	NUM
ejpam-5861	556	24	200	200	NUM
ejpam-5861	556	25	250	250	NUM
ejpam-5861	556	26	300	300	NUM
ejpam-5861	556	27	d	d	NOUN
ejpam-5861	556	28	ea	ea	X
ejpam-5861	556	29	th	th	X
ejpam-5861	556	30	c	c	NOUN
ejpam-5861	556	31	la	la	INTJ
ejpam-5861	556	32	ss	ss	NOUN
ejpam-5861	556	33	0	0	NUM
ejpam-5861	556	34	5	5	NUM
ejpam-5861	556	35	10	10	NUM
ejpam-5861	556	36	15	15	NUM
ejpam-5861	556	37	20	20	NUM
ejpam-5861	556	38	25	25	NUM
ejpam-5861	556	39	0.65	0.65	NUM
ejpam-5861	556	40	0.70	0.70	NUM
ejpam-5861	556	41	0.75	0.75	NUM
ejpam-5861	556	42	0.80	0.80	NUM
ejpam-5861	556	43	figure	figure	NOUN
ejpam-5861	556	44	10	10	NUM
ejpam-5861	556	45	:	:	PUNCT
ejpam-5861	556	46	solution	solution	NOUN
ejpam-5861	556	47	illustration	illustration	NOUN
ejpam-5861	556	48	of	of	ADP
ejpam-5861	556	49	death	death	NOUN
ejpam-5861	556	50	class	class	NOUN
ejpam-5861	556	51	for	for	ADP
ejpam-5861	556	52	ε	ε	PROPN
ejpam-5861	556	53	∈	∈	PROPN
ejpam-5861	556	54	(	(	PUNCT
ejpam-5861	556	55	0.60	0.60	NUM
ejpam-5861	556	56	,	,	PUNCT
ejpam-5861	556	57	0.80	0.80	NUM
ejpam-5861	556	58	]	]	PUNCT
ejpam-5861	556	59	.	.	PUNCT
ejpam-5861	557	1	in	in	ADP
ejpam-5861	557	2	the	the	DET
ejpam-5861	557	3	above	above	ADJ
ejpam-5861	557	4	graphical	graphical	ADJ
ejpam-5861	557	5	presentations	presentation	NOUN
ejpam-5861	557	6	,	,	PUNCT
ejpam-5861	557	7	we	we	PRON
ejpam-5861	557	8	have	have	AUX
ejpam-5861	557	9	taken	take	VERB
ejpam-5861	557	10	t1	t1	NOUN
ejpam-5861	557	11	<	<	X
ejpam-5861	557	12	50	50	NUM
ejpam-5861	557	13	,	,	PUNCT
ejpam-5861	557	14	and	and	CCONJ
ejpam-5861	557	15	t	t	X
ejpam-5861	557	16	=	=	SYM
ejpam-5861	557	17	300	300	NUM
ejpam-5861	557	18	,	,	PUNCT
ejpam-5861	557	19	the	the	DET
ejpam-5861	557	20	corresponding	correspond	VERB
ejpam-5861	557	21	crossover	crossover	NOUN
ejpam-5861	557	22	effect	effect	NOUN
ejpam-5861	557	23	can	can	AUX
ejpam-5861	557	24	be	be	AUX
ejpam-5861	557	25	observed	observe	VERB
ejpam-5861	557	26	near	near	ADP
ejpam-5861	557	27	the	the	DET
ejpam-5861	557	28	point	point	NOUN
ejpam-5861	557	29	t1	t1	NOUN
ejpam-5861	557	30	<	<	X
ejpam-5861	557	31	50	50	NUM
ejpam-5861	557	32	in	in	ADP
ejpam-5861	557	33	all	all	DET
ejpam-5861	557	34	compartments	compartment	NOUN
ejpam-5861	557	35	.	.	PUNCT
ejpam-5861	558	1	the	the	DET
ejpam-5861	558	2	susceptible	susceptible	ADJ
ejpam-5861	558	3	population	population	NOUN
ejpam-5861	558	4	is	be	AUX
ejpam-5861	558	5	decreasing	decrease	VERB
ejpam-5861	558	6	,	,	PUNCT
ejpam-5861	558	7	in	in	SCONJ
ejpam-5861	558	8	the	the	DET
ejpam-5861	558	9	same	same	ADJ
ejpam-5861	558	10	vaccinated	vaccinated	ADJ
ejpam-5861	558	11	classes	class	NOUN
ejpam-5861	558	12	has	have	AUX
ejpam-5861	558	13	raised	raise	VERB
ejpam-5861	558	14	.	.	PUNCT
ejpam-5861	559	1	on	on	ADP
ejpam-5861	559	2	the	the	DET
ejpam-5861	559	3	other	other	ADJ
ejpam-5861	559	4	hand	hand	NOUN
ejpam-5861	559	5	exposed	expose	VERB
ejpam-5861	559	6	class	class	NOUN
ejpam-5861	559	7	was	be	AUX
ejpam-5861	559	8	reducing	reduce	VERB
ejpam-5861	559	9	as	as	SCONJ
ejpam-5861	559	10	infection	infection	NOUN
ejpam-5861	559	11	was	be	AUX
ejpam-5861	559	12	spreading	spread	VERB
ejpam-5861	559	13	in	in	ADP
ejpam-5861	559	14	the	the	DET
ejpam-5861	559	15	society	society	NOUN
ejpam-5861	559	16	.	.	PUNCT
ejpam-5861	560	1	in	in	ADP
ejpam-5861	560	2	the	the	DET
ejpam-5861	560	3	mean	mean	ADJ
ejpam-5861	560	4	time	time	NOUN
ejpam-5861	560	5	quarantined	quarantine	VERB
ejpam-5861	560	6	initially	initially	ADV
ejpam-5861	560	7	risen	rise	VERB
ejpam-5861	560	8	and	and	CCONJ
ejpam-5861	560	9	then	then	ADV
ejpam-5861	560	10	went	go	VERB
ejpam-5861	560	11	on	on	ADP
ejpam-5861	560	12	on	on	ADP
ejpam-5861	560	13	decreasing	decrease	VERB
ejpam-5861	560	14	.	.	PUNCT
ejpam-5861	561	1	the	the	DET
ejpam-5861	561	2	recovered	recover	VERB
ejpam-5861	561	3	individuals	individual	NOUN
ejpam-5861	561	4	were	be	AUX
ejpam-5861	561	5	increasing	increase	VERB
ejpam-5861	561	6	with	with	ADP
ejpam-5861	561	7	the	the	DET
ejpam-5861	561	8	passage	passage	NOUN
ejpam-5861	561	9	of	of	ADP
ejpam-5861	561	10	time	time	NOUN
ejpam-5861	561	11	and	and	CCONJ
ejpam-5861	561	12	also	also	ADV
ejpam-5861	561	13	the	the	DET
ejpam-5861	561	14	death	death	NOUN
ejpam-5861	561	15	class	class	NOUN
ejpam-5861	561	16	has	have	AUX
ejpam-5861	561	17	grown	grow	VERB
ejpam-5861	561	18	.	.	PUNCT
ejpam-5861	562	1	in	in	ADP
ejpam-5861	562	2	all	all	DET
ejpam-5861	562	3	compartment	compartment	NOUN
ejpam-5861	562	4	stability	stability	NOUN
ejpam-5861	562	5	after	after	SCONJ
ejpam-5861	562	6	some	some	DET
ejpam-5861	562	7	time	time	NOUN
ejpam-5861	562	8	occurred	occur	VERB
ejpam-5861	562	9	.	.	PUNCT
ejpam-5861	563	1	7.2	7.2	NUM
ejpam-5861	563	2	.	.	PUNCT
ejpam-5861	563	3	case	case	NOUN
ejpam-5861	563	4	-	-	PUNCT
ejpam-5861	563	5	ii	ii	NOUN
ejpam-5861	563	6	we	we	PRON
ejpam-5861	563	7	take	take	VERB
ejpam-5861	563	8	the	the	DET
ejpam-5861	563	9	first	first	ADJ
ejpam-5861	563	10	set	set	NOUN
ejpam-5861	563	11	of	of	ADP
ejpam-5861	563	12	fractional	fractional	ADJ
ejpam-5861	563	13	order	order	NOUN
ejpam-5861	563	14	values	value	NOUN
ejpam-5861	563	15	in	in	ADP
ejpam-5861	563	16	(	(	PUNCT
ejpam-5861	563	17	0.80	0.80	NUM
ejpam-5861	563	18	,	,	PUNCT
ejpam-5861	563	19	1.00	1.00	NUM
ejpam-5861	563	20	]	]	PUNCT
ejpam-5861	563	21	and	and	CCONJ
ejpam-5861	563	22	presented	present	VERB
ejpam-5861	563	23	solutions	solution	NOUN
ejpam-5861	563	24	graphically	graphically	ADV
ejpam-5861	563	25	in	in	ADP
ejpam-5861	563	26	figures	figure	NOUN
ejpam-5861	563	27	11	11	NUM
ejpam-5861	563	28	,	,	PUNCT
ejpam-5861	563	29	12	12	NUM
ejpam-5861	563	30	,	,	PUNCT
ejpam-5861	563	31	13	13	NUM
ejpam-5861	563	32	,	,	PUNCT
ejpam-5861	563	33	14	14	NUM
ejpam-5861	563	34	,	,	PUNCT
ejpam-5861	563	35	15	15	NUM
ejpam-5861	563	36	,	,	PUNCT
ejpam-5861	563	37	16	16	NUM
ejpam-5861	563	38	,	,	PUNCT
ejpam-5861	563	39	17	17	NUM
ejpam-5861	563	40	respectively	respectively	ADV
ejpam-5861	563	41	.	.	PUNCT
ejpam-5861	564	1	t	t	NOUN
ejpam-5861	564	2	0	0	NUM
ejpam-5861	564	3	50	50	NUM
ejpam-5861	564	4	100	100	NUM
ejpam-5861	564	5	150	150	NUM
ejpam-5861	564	6	200	200	NUM
ejpam-5861	564	7	250	250	NUM
ejpam-5861	564	8	300	300	NUM
ejpam-5861	564	9	s	s	PART
ejpam-5861	564	10	us	us	PROPN
ejpam-5861	564	11	ce	ce	PROPN
ejpam-5861	564	12	pt	pt	X
ejpam-5861	564	13	ib	ib	X
ejpam-5861	564	14	le	le	PROPN
ejpam-5861	564	15	c	c	PROPN
ejpam-5861	564	16	la	la	INTJ
ejpam-5861	564	17	ss	ss	NOUN
ejpam-5861	564	18	0	0	NUM
ejpam-5861	564	19	20	20	NUM
ejpam-5861	564	20	40	40	NUM
ejpam-5861	564	21	60	60	NUM
ejpam-5861	564	22	80	80	NUM
ejpam-5861	564	23	100	100	NUM
ejpam-5861	564	24	0.85	0.85	NUM
ejpam-5861	564	25	0.90	0.90	NUM
ejpam-5861	564	26	0.95	0.95	NUM
ejpam-5861	564	27	1.00	1.00	NUM
ejpam-5861	564	28	figure	figure	NOUN
ejpam-5861	564	29	11	11	NUM
ejpam-5861	564	30	:	:	PUNCT
ejpam-5861	564	31	solution	solution	NOUN
ejpam-5861	564	32	illustration	illustration	NOUN
ejpam-5861	564	33	of	of	ADP
ejpam-5861	564	34	susceptible	susceptible	ADJ
ejpam-5861	564	35	class	class	NOUN
ejpam-5861	564	36	for	for	ADP
ejpam-5861	564	37	ε	ε	PROPN
ejpam-5861	564	38	∈	∈	PROPN
ejpam-5861	564	39	(	(	PUNCT
ejpam-5861	564	40	0.80	0.80	NUM
ejpam-5861	564	41	,	,	PUNCT
ejpam-5861	564	42	1.00	1.00	NUM
ejpam-5861	564	43	]	]	PUNCT
ejpam-5861	564	44	.	.	PUNCT
ejpam-5861	565	1	s.	s.	PROPN
ejpam-5861	565	2	naz	naz	PROPN
ejpam-5861	565	3	et	et	PROPN
ejpam-5861	565	4	al	al	PROPN
ejpam-5861	565	5	.	.	PUNCT
ejpam-5861	565	6	/	/	SYM
ejpam-5861	565	7	eur	eur	PROPN
ejpam-5861	565	8	.	.	PUNCT
ejpam-5861	566	1	j.	j.	PROPN
ejpam-5861	566	2	pure	pure	PROPN
ejpam-5861	566	3	appl	appl	PROPN
ejpam-5861	566	4	.	.	PROPN
ejpam-5861	566	5	math	math	PROPN
ejpam-5861	566	6	,	,	PUNCT
ejpam-5861	566	7	18	18	NUM
ejpam-5861	566	8	(	(	PUNCT
ejpam-5861	566	9	2	2	NUM
ejpam-5861	566	10	)	)	PUNCT
ejpam-5861	566	11	(	(	PUNCT
ejpam-5861	566	12	2025	2025	NUM
ejpam-5861	566	13	)	)	PUNCT
ejpam-5861	566	14	,	,	PUNCT
ejpam-5861	566	15	5861	5861	NUM
ejpam-5861	566	16	27	27	NUM
ejpam-5861	566	17	of	of	ADP
ejpam-5861	566	18	33	33	NUM
ejpam-5861	566	19	t	t	NOUN
ejpam-5861	566	20	0	0	NUM
ejpam-5861	566	21	50	50	NUM
ejpam-5861	566	22	100	100	NUM
ejpam-5861	566	23	150	150	NUM
ejpam-5861	566	24	200	200	NUM
ejpam-5861	566	25	250	250	NUM
ejpam-5861	566	26	300	300	NUM
ejpam-5861	566	27	v	v	NUM
ejpam-5861	566	28	ac	ac	PROPN
ejpam-5861	566	29	ci	ci	PROPN
ejpam-5861	566	30	na	na	X
ejpam-5861	566	31	te	te	PROPN
ejpam-5861	566	32	d	d	X
ejpam-5861	566	33	cl	cl	NOUN
ejpam-5861	566	34	as	as	ADP
ejpam-5861	566	35	s	s	NOUN
ejpam-5861	566	36	50	50	NUM
ejpam-5861	566	37	60	60	NUM
ejpam-5861	566	38	70	70	NUM
ejpam-5861	566	39	80	80	NUM
ejpam-5861	566	40	90	90	NUM
ejpam-5861	566	41	0.85	0.85	NUM
ejpam-5861	566	42	0.90	0.90	NUM
ejpam-5861	566	43	0.95	0.95	NUM
ejpam-5861	566	44	1.00	1.00	NUM
ejpam-5861	566	45	figure	figure	NOUN
ejpam-5861	566	46	12	12	NUM
ejpam-5861	566	47	:	:	PUNCT
ejpam-5861	566	48	solution	solution	NOUN
ejpam-5861	566	49	illustration	illustration	NOUN
ejpam-5861	566	50	of	of	ADP
ejpam-5861	566	51	vaccinated	vaccinated	ADJ
ejpam-5861	566	52	class	class	NOUN
ejpam-5861	566	53	for	for	ADP
ejpam-5861	566	54	ε	ε	PROPN
ejpam-5861	566	55	∈	∈	PROPN
ejpam-5861	566	56	(	(	PUNCT
ejpam-5861	566	57	0.80	0.80	NUM
ejpam-5861	566	58	,	,	PUNCT
ejpam-5861	566	59	1.00	1.00	NUM
ejpam-5861	566	60	]	]	PUNCT
ejpam-5861	566	61	.	.	PUNCT
ejpam-5861	567	1	t	t	NOUN
ejpam-5861	567	2	0	0	NUM
ejpam-5861	567	3	50	50	NUM
ejpam-5861	567	4	100	100	NUM
ejpam-5861	567	5	150	150	NUM
ejpam-5861	567	6	200	200	NUM
ejpam-5861	567	7	250	250	NUM
ejpam-5861	567	8	300	300	NUM
ejpam-5861	567	9	e	e	NOUN
ejpam-5861	567	10	xp	xp	ADV
ejpam-5861	567	11	os	os	INTJ
ejpam-5861	567	12	ed	ed	NOUN
ejpam-5861	567	13	c	c	PROPN
ejpam-5861	567	14	la	la	INTJ
ejpam-5861	567	15	ss	ss	NOUN
ejpam-5861	567	16	0	0	NUM
ejpam-5861	567	17	20	20	NUM
ejpam-5861	567	18	40	40	NUM
ejpam-5861	567	19	60	60	NUM
ejpam-5861	567	20	80	80	NUM
ejpam-5861	567	21	0.85	0.85	NUM
ejpam-5861	567	22	0.90	0.90	NUM
ejpam-5861	567	23	0.95	0.95	NUM
ejpam-5861	567	24	1.00	1.00	NUM
ejpam-5861	567	25	figure	figure	NOUN
ejpam-5861	567	26	13	13	NUM
ejpam-5861	567	27	:	:	PUNCT
ejpam-5861	567	28	solution	solution	NOUN
ejpam-5861	567	29	illustration	illustration	NOUN
ejpam-5861	567	30	of	of	ADP
ejpam-5861	567	31	exposed	expose	VERB
ejpam-5861	567	32	class	class	NOUN
ejpam-5861	567	33	for	for	ADP
ejpam-5861	567	34	ε	ε	PROPN
ejpam-5861	567	35	∈	∈	PROPN
ejpam-5861	567	36	(	(	PUNCT
ejpam-5861	567	37	0.80	0.80	NUM
ejpam-5861	567	38	,	,	PUNCT
ejpam-5861	567	39	1.00	1.00	NUM
ejpam-5861	567	40	]	]	PUNCT
ejpam-5861	567	41	.	.	PUNCT
ejpam-5861	568	1	s.	s.	PROPN
ejpam-5861	568	2	naz	naz	PROPN
ejpam-5861	568	3	et	et	PROPN
ejpam-5861	568	4	al	al	PROPN
ejpam-5861	568	5	.	.	PUNCT
ejpam-5861	568	6	/	/	SYM
ejpam-5861	568	7	eur	eur	PROPN
ejpam-5861	568	8	.	.	PUNCT
ejpam-5861	569	1	j.	j.	PROPN
ejpam-5861	569	2	pure	pure	PROPN
ejpam-5861	569	3	appl	appl	PROPN
ejpam-5861	569	4	.	.	PROPN
ejpam-5861	569	5	math	math	PROPN
ejpam-5861	569	6	,	,	PUNCT
ejpam-5861	569	7	18	18	NUM
ejpam-5861	569	8	(	(	PUNCT
ejpam-5861	569	9	2	2	NUM
ejpam-5861	569	10	)	)	PUNCT
ejpam-5861	569	11	(	(	PUNCT
ejpam-5861	569	12	2025	2025	NUM
ejpam-5861	569	13	)	)	PUNCT
ejpam-5861	569	14	,	,	PUNCT
ejpam-5861	569	15	5861	5861	NUM
ejpam-5861	569	16	28	28	NUM
ejpam-5861	569	17	of	of	ADP
ejpam-5861	569	18	33	33	NUM
ejpam-5861	569	19	t	t	NOUN
ejpam-5861	569	20	0	0	NUM
ejpam-5861	569	21	50	50	NUM
ejpam-5861	569	22	100	100	NUM
ejpam-5861	569	23	150	150	NUM
ejpam-5861	569	24	200	200	NUM
ejpam-5861	569	25	250	250	NUM
ejpam-5861	569	26	300	300	NUM
ejpam-5861	569	27	in	in	ADP
ejpam-5861	569	28	fe	fe	X
ejpam-5861	569	29	ct	ct	NUM
ejpam-5861	569	30	ed	ed	PROPN
ejpam-5861	569	31	c	c	PROPN
ejpam-5861	569	32	la	la	NOUN
ejpam-5861	569	33	ss	ss	NOUN
ejpam-5861	569	34	0	0	NUM
ejpam-5861	569	35	5	5	NUM
ejpam-5861	569	36	10	10	NUM
ejpam-5861	569	37	15	15	NUM
ejpam-5861	569	38	20	20	NUM
ejpam-5861	569	39	25	25	NUM
ejpam-5861	569	40	0.85	0.85	NUM
ejpam-5861	569	41	0.90	0.90	NUM
ejpam-5861	569	42	0.95	0.95	NUM
ejpam-5861	569	43	1.00	1.00	NUM
ejpam-5861	569	44	figure	figure	NOUN
ejpam-5861	569	45	14	14	NUM
ejpam-5861	569	46	:	:	PUNCT
ejpam-5861	569	47	solution	solution	NOUN
ejpam-5861	569	48	illustration	illustration	NOUN
ejpam-5861	569	49	of	of	ADP
ejpam-5861	569	50	infected	infected	ADJ
ejpam-5861	569	51	class	class	NOUN
ejpam-5861	569	52	for	for	ADP
ejpam-5861	569	53	ε	ε	PROPN
ejpam-5861	569	54	∈	∈	PROPN
ejpam-5861	569	55	(	(	PUNCT
ejpam-5861	569	56	0.80	0.80	NUM
ejpam-5861	569	57	,	,	PUNCT
ejpam-5861	569	58	1.00	1.00	NUM
ejpam-5861	569	59	]	]	PUNCT
ejpam-5861	569	60	.	.	PUNCT
ejpam-5861	570	1	0	0	NUM
ejpam-5861	570	2	50	50	NUM
ejpam-5861	570	3	100	100	NUM
ejpam-5861	570	4	150	150	NUM
ejpam-5861	570	5	200	200	NUM
ejpam-5861	570	6	250	250	NUM
ejpam-5861	570	7	300	300	NUM
ejpam-5861	570	8	t	t	NOUN
ejpam-5861	570	9	0	0	NUM
ejpam-5861	570	10	1	1	NUM
ejpam-5861	570	11	2	2	NUM
ejpam-5861	570	12	3	3	NUM
ejpam-5861	570	13	4	4	NUM
ejpam-5861	570	14	5	5	NUM
ejpam-5861	570	15	6	6	NUM
ejpam-5861	570	16	q	q	PROPN
ejpam-5861	570	17	ua	ua	PROPN
ejpam-5861	570	18	ra	ra	PROPN
ejpam-5861	570	19	nt	not	PART
ejpam-5861	570	20	in	in	ADP
ejpam-5861	570	21	ed	ed	PROPN
ejpam-5861	570	22	c	c	PROPN
ejpam-5861	570	23	la	la	NOUN
ejpam-5861	570	24	ss	ss	NOUN
ejpam-5861	570	25	0.85	0.85	NUM
ejpam-5861	570	26	0.90	0.90	NUM
ejpam-5861	570	27	0.95	0.95	NUM
ejpam-5861	570	28	1.00	1.00	NUM
ejpam-5861	570	29	figure	figure	NOUN
ejpam-5861	570	30	15	15	NUM
ejpam-5861	570	31	:	:	PUNCT
ejpam-5861	570	32	solution	solution	NOUN
ejpam-5861	570	33	illustration	illustration	NOUN
ejpam-5861	570	34	of	of	ADP
ejpam-5861	570	35	quarantined	quarantined	ADJ
ejpam-5861	570	36	class	class	NOUN
ejpam-5861	570	37	for	for	ADP
ejpam-5861	570	38	ε	ε	PROPN
ejpam-5861	570	39	∈	∈	PROPN
ejpam-5861	570	40	(	(	PUNCT
ejpam-5861	570	41	0.80	0.80	NUM
ejpam-5861	570	42	,	,	PUNCT
ejpam-5861	570	43	1.00	1.00	NUM
ejpam-5861	570	44	]	]	PUNCT
ejpam-5861	570	45	.	.	PUNCT
ejpam-5861	571	1	s.	s.	PROPN
ejpam-5861	571	2	naz	naz	PROPN
ejpam-5861	571	3	et	et	PROPN
ejpam-5861	571	4	al	al	PROPN
ejpam-5861	571	5	.	.	PUNCT
ejpam-5861	571	6	/	/	SYM
ejpam-5861	571	7	eur	eur	PROPN
ejpam-5861	571	8	.	.	PUNCT
ejpam-5861	572	1	j.	j.	PROPN
ejpam-5861	572	2	pure	pure	PROPN
ejpam-5861	572	3	appl	appl	PROPN
ejpam-5861	572	4	.	.	PROPN
ejpam-5861	572	5	math	math	PROPN
ejpam-5861	572	6	,	,	PUNCT
ejpam-5861	572	7	18	18	NUM
ejpam-5861	572	8	(	(	PUNCT
ejpam-5861	572	9	2	2	NUM
ejpam-5861	572	10	)	)	PUNCT
ejpam-5861	572	11	(	(	PUNCT
ejpam-5861	572	12	2025	2025	NUM
ejpam-5861	572	13	)	)	PUNCT
ejpam-5861	572	14	,	,	PUNCT
ejpam-5861	572	15	5861	5861	NUM
ejpam-5861	572	16	29	29	NUM
ejpam-5861	572	17	of	of	ADP
ejpam-5861	572	18	33	33	NUM
ejpam-5861	572	19	t	t	NOUN
ejpam-5861	572	20	0	0	NUM
ejpam-5861	572	21	50	50	NUM
ejpam-5861	572	22	100	100	NUM
ejpam-5861	572	23	150	150	NUM
ejpam-5861	572	24	200	200	NUM
ejpam-5861	572	25	250	250	NUM
ejpam-5861	572	26	300	300	NUM
ejpam-5861	572	27	r	r	NOUN
ejpam-5861	572	28	ec	ec	X
ejpam-5861	572	29	ov	ov	INTJ
ejpam-5861	572	30	er	er	INTJ
ejpam-5861	572	31	ed	ed	NOUN
ejpam-5861	572	32	c	c	PROPN
ejpam-5861	572	33	la	la	NOUN
ejpam-5861	573	1	ss	ss	NOUN
ejpam-5861	574	1	0	0	NUM
ejpam-5861	574	2	2	2	NUM
ejpam-5861	574	3	4	4	NUM
ejpam-5861	574	4	6	6	NUM
ejpam-5861	574	5	8	8	NUM
ejpam-5861	574	6	0.85	0.85	NUM
ejpam-5861	574	7	0.90	0.90	NUM
ejpam-5861	574	8	0.95	0.95	NUM
ejpam-5861	574	9	1.00	1.00	NUM
ejpam-5861	574	10	figure	figure	NOUN
ejpam-5861	574	11	16	16	NUM
ejpam-5861	574	12	:	:	PUNCT
ejpam-5861	574	13	solution	solution	NOUN
ejpam-5861	574	14	illustration	illustration	NOUN
ejpam-5861	574	15	of	of	ADP
ejpam-5861	574	16	recovered	recovered	ADJ
ejpam-5861	574	17	class	class	NOUN
ejpam-5861	574	18	for	for	ADP
ejpam-5861	574	19	ε	ε	PROPN
ejpam-5861	574	20	∈	∈	PROPN
ejpam-5861	574	21	(	(	PUNCT
ejpam-5861	574	22	0.80	0.80	NUM
ejpam-5861	574	23	,	,	PUNCT
ejpam-5861	574	24	1.00	1.00	NUM
ejpam-5861	574	25	]	]	PUNCT
ejpam-5861	574	26	.	.	PUNCT
ejpam-5861	575	1	t	t	NOUN
ejpam-5861	575	2	0	0	NUM
ejpam-5861	575	3	50	50	NUM
ejpam-5861	575	4	100	100	NUM
ejpam-5861	575	5	150	150	NUM
ejpam-5861	575	6	200	200	NUM
ejpam-5861	575	7	250	250	NUM
ejpam-5861	575	8	300	300	NUM
ejpam-5861	575	9	d	d	NOUN
ejpam-5861	575	10	ea	ea	X
ejpam-5861	575	11	th	th	X
ejpam-5861	575	12	c	c	NOUN
ejpam-5861	575	13	la	la	INTJ
ejpam-5861	575	14	ss	ss	NOUN
ejpam-5861	575	15	0	0	NUM
ejpam-5861	575	16	5	5	NUM
ejpam-5861	575	17	10	10	NUM
ejpam-5861	575	18	15	15	NUM
ejpam-5861	575	19	20	20	NUM
ejpam-5861	575	20	25	25	NUM
ejpam-5861	575	21	0.85	0.85	NUM
ejpam-5861	575	22	0.90	0.90	NUM
ejpam-5861	575	23	0.95	0.95	NUM
ejpam-5861	575	24	1.00	1.00	NUM
ejpam-5861	575	25	figure	figure	NOUN
ejpam-5861	575	26	17	17	NUM
ejpam-5861	575	27	:	:	PUNCT
ejpam-5861	575	28	solution	solution	NOUN
ejpam-5861	575	29	illustration	illustration	NOUN
ejpam-5861	575	30	of	of	ADP
ejpam-5861	575	31	death	death	NOUN
ejpam-5861	575	32	class	class	NOUN
ejpam-5861	575	33	for	for	ADP
ejpam-5861	575	34	ε	ε	PROPN
ejpam-5861	575	35	∈	∈	PROPN
ejpam-5861	575	36	(	(	PUNCT
ejpam-5861	575	37	0.80	0.80	NUM
ejpam-5861	575	38	,	,	PUNCT
ejpam-5861	575	39	1.00	1.00	NUM
ejpam-5861	575	40	]	]	PUNCT
ejpam-5861	575	41	.	.	PUNCT
ejpam-5861	576	1	given	give	VERB
ejpam-5861	576	2	t1	t1	PROPN
ejpam-5861	576	3	<	<	X
ejpam-5861	576	4	50	50	NUM
ejpam-5861	576	5	and	and	CCONJ
ejpam-5861	576	6	t	t	NOUN
ejpam-5861	576	7	=	=	SYM
ejpam-5861	576	8	300	300	NUM
ejpam-5861	576	9	in	in	ADP
ejpam-5861	576	10	the	the	DET
ejpam-5861	576	11	graphical	graphical	ADJ
ejpam-5861	576	12	displays	display	NOUN
ejpam-5861	576	13	above	above	ADV
ejpam-5861	576	14	,	,	PUNCT
ejpam-5861	576	15	the	the	DET
ejpam-5861	576	16	relevant	relevant	ADJ
ejpam-5861	576	17	crossover	crossover	NOUN
ejpam-5861	576	18	effect	effect	NOUN
ejpam-5861	576	19	is	be	AUX
ejpam-5861	576	20	visible	visible	ADJ
ejpam-5861	576	21	in	in	ADP
ejpam-5861	576	22	all	all	DET
ejpam-5861	576	23	compartments	compartment	NOUN
ejpam-5861	576	24	close	close	ADV
ejpam-5861	576	25	to	to	PART
ejpam-5861	576	26	t1	t1	VERB
ejpam-5861	576	27	<	<	X
ejpam-5861	576	28	50	50	NUM
ejpam-5861	576	29	.	.	PUNCT
ejpam-5861	577	1	in	in	ADP
ejpam-5861	577	2	the	the	DET
ejpam-5861	577	3	same	same	ADJ
ejpam-5861	577	4	classes	class	NOUN
ejpam-5861	577	5	that	that	PRON
ejpam-5861	577	6	have	have	AUX
ejpam-5861	577	7	increased	increase	VERB
ejpam-5861	577	8	in	in	ADP
ejpam-5861	577	9	vaccinations	vaccination	NOUN
ejpam-5861	577	10	,	,	PUNCT
ejpam-5861	577	11	the	the	DET
ejpam-5861	577	12	vulnerable	vulnerable	ADJ
ejpam-5861	577	13	population	population	NOUN
ejpam-5861	577	14	is	be	AUX
ejpam-5861	577	15	declining	decline	VERB
ejpam-5861	577	16	.	.	PUNCT
ejpam-5861	578	1	on	on	ADP
ejpam-5861	578	2	the	the	DET
ejpam-5861	578	3	other	other	ADJ
ejpam-5861	578	4	hand	hand	NOUN
ejpam-5861	578	5	,	,	PUNCT
ejpam-5861	578	6	as	as	SCONJ
ejpam-5861	578	7	infection	infection	NOUN
ejpam-5861	578	8	increased	increase	VERB
ejpam-5861	578	9	throughout	throughout	ADP
ejpam-5861	578	10	society	society	NOUN
ejpam-5861	578	11	,	,	PUNCT
ejpam-5861	578	12	the	the	DET
ejpam-5861	578	13	exposed	expose	VERB
ejpam-5861	578	14	class	class	NOUN
ejpam-5861	578	15	shrank	shrank	NOUN
ejpam-5861	578	16	.	.	PUNCT
ejpam-5861	579	1	quarantined	quarantine	VERB
ejpam-5861	579	2	cases	case	NOUN
ejpam-5861	579	3	increased	increase	VERB
ejpam-5861	579	4	in	in	ADP
ejpam-5861	579	5	the	the	DET
ejpam-5861	579	6	interim	interim	NOUN
ejpam-5861	579	7	before	before	ADP
ejpam-5861	579	8	continuing	continue	VERB
ejpam-5861	579	9	to	to	PART
ejpam-5861	579	10	decline	decline	VERB
ejpam-5861	579	11	.	.	PUNCT
ejpam-5861	580	1	over	over	ADP
ejpam-5861	580	2	time	time	NOUN
ejpam-5861	580	3	,	,	PUNCT
ejpam-5861	580	4	both	both	CCONJ
ejpam-5861	580	5	the	the	DET
ejpam-5861	580	6	number	number	NOUN
ejpam-5861	580	7	of	of	ADP
ejpam-5861	580	8	recovered	recover	VERB
ejpam-5861	580	9	individuals	individual	NOUN
ejpam-5861	580	10	and	and	CCONJ
ejpam-5861	580	11	the	the	DET
ejpam-5861	580	12	number	number	NOUN
ejpam-5861	580	13	of	of	ADP
ejpam-5861	580	14	deaths	death	NOUN
ejpam-5861	580	15	have	have	AUX
ejpam-5861	580	16	increased	increase	VERB
ejpam-5861	580	17	.	.	PUNCT
ejpam-5861	581	1	after	after	ADP
ejpam-5861	581	2	a	a	DET
ejpam-5861	581	3	while	while	NOUN
ejpam-5861	581	4	,	,	PUNCT
ejpam-5861	581	5	stability	stability	NOUN
ejpam-5861	581	6	happened	happen	VERB
ejpam-5861	581	7	in	in	ADP
ejpam-5861	581	8	every	every	DET
ejpam-5861	581	9	compartment	compartment	NOUN
ejpam-5861	581	10	.	.	PUNCT
ejpam-5861	582	1	from	from	ADP
ejpam-5861	582	2	the	the	DET
ejpam-5861	582	3	figures	figure	NOUN
ejpam-5861	582	4	given	give	VERB
ejpam-5861	582	5	above	above	ADV
ejpam-5861	582	6	,	,	PUNCT
ejpam-5861	582	7	we	we	PRON
ejpam-5861	582	8	see	see	VERB
ejpam-5861	582	9	that	that	SCONJ
ejpam-5861	582	10	the	the	DET
ejpam-5861	582	11	decay	decay	NOUN
ejpam-5861	582	12	dynamics	dynamic	NOUN
ejpam-5861	582	13	is	be	AUX
ejpam-5861	582	14	faster	fast	ADJ
ejpam-5861	582	15	at	at	ADP
ejpam-5861	582	16	lower	low	ADJ
ejpam-5861	582	17	values	value	NOUN
ejpam-5861	582	18	of	of	ADP
ejpam-5861	582	19	fractional	fractional	ADJ
ejpam-5861	582	20	orders	order	NOUN
ejpam-5861	582	21	while	while	SCONJ
ejpam-5861	582	22	in	in	ADP
ejpam-5861	582	23	case	case	NOUN
ejpam-5861	582	24	of	of	ADP
ejpam-5861	582	25	growth	growth	NOUN
ejpam-5861	582	26	,	,	PUNCT
ejpam-5861	582	27	the	the	DET
ejpam-5861	582	28	dynamic	dynamic	NOUN
ejpam-5861	582	29	is	be	AUX
ejpam-5861	582	30	rapidly	rapidly	ADV
ejpam-5861	582	31	increasing	increase	VERB
ejpam-5861	582	32	under	under	ADP
ejpam-5861	582	33	the	the	DET
ejpam-5861	582	34	larger	large	ADJ
ejpam-5861	582	35	values	value	NOUN
ejpam-5861	582	36	of	of	ADP
ejpam-5861	582	37	fractional	fractional	ADJ
ejpam-5861	582	38	orders	order	NOUN
ejpam-5861	582	39	.	.	PUNCT
ejpam-5861	583	1	in	in	ADP
ejpam-5861	583	2	the	the	DET
ejpam-5861	583	3	same	same	ADJ
ejpam-5861	583	4	way	way	NOUN
ejpam-5861	583	5	,	,	PUNCT
ejpam-5861	583	6	the	the	DET
ejpam-5861	583	7	growth	growth	NOUN
ejpam-5861	583	8	in	in	ADP
ejpam-5861	583	9	dynamics	dynamic	NOUN
ejpam-5861	583	10	is	be	AUX
ejpam-5861	583	11	slower	slow	ADJ
ejpam-5861	583	12	at	at	ADP
ejpam-5861	583	13	small	small	ADJ
ejpam-5861	583	14	fractional	fractional	ADJ
ejpam-5861	583	15	orders	order	NOUN
ejpam-5861	583	16	and	and	CCONJ
ejpam-5861	583	17	faster	fast	ADV
ejpam-5861	583	18	at	at	ADP
ejpam-5861	583	19	higher	high	ADJ
ejpam-5861	583	20	values	value	NOUN
ejpam-5861	583	21	.	.	PUNCT
ejpam-5861	584	1	this	this	DET
ejpam-5861	584	2	chastities	chastity	NOUN
ejpam-5861	584	3	demonstrate	demonstrate	VERB
ejpam-5861	584	4	the	the	DET
ejpam-5861	584	5	influence	influence	NOUN
ejpam-5861	584	6	of	of	ADP
ejpam-5861	584	7	fractional	fractional	ADJ
ejpam-5861	584	8	orders	order	NOUN
ejpam-5861	584	9	on	on	ADP
ejpam-5861	584	10	the	the	DET
ejpam-5861	584	11	dynamical	dynamical	ADJ
ejpam-5861	584	12	behaviours	behaviour	NOUN
ejpam-5861	584	13	of	of	ADP
ejpam-5861	584	14	various	various	ADJ
ejpam-5861	584	15	classes	class	NOUN
ejpam-5861	584	16	.	.	PUNCT
ejpam-5861	585	1	s.	s.	PROPN
ejpam-5861	585	2	naz	naz	PROPN
ejpam-5861	585	3	et	et	PROPN
ejpam-5861	585	4	al	al	PROPN
ejpam-5861	585	5	.	.	PUNCT
ejpam-5861	585	6	/	/	SYM
ejpam-5861	585	7	eur	eur	PROPN
ejpam-5861	585	8	.	.	PUNCT
ejpam-5861	586	1	j.	j.	PROPN
ejpam-5861	586	2	pure	pure	PROPN
ejpam-5861	586	3	appl	appl	PROPN
ejpam-5861	586	4	.	.	PROPN
ejpam-5861	586	5	math	math	PROPN
ejpam-5861	586	6	,	,	PUNCT
ejpam-5861	586	7	18	18	NUM
ejpam-5861	586	8	(	(	PUNCT
ejpam-5861	586	9	2	2	NUM
ejpam-5861	586	10	)	)	PUNCT
ejpam-5861	586	11	(	(	PUNCT
ejpam-5861	586	12	2025	2025	NUM
ejpam-5861	586	13	)	)	PUNCT
ejpam-5861	586	14	,	,	PUNCT
ejpam-5861	586	15	5861	5861	NUM
ejpam-5861	586	16	30	30	NUM
ejpam-5861	586	17	of	of	ADP
ejpam-5861	586	18	33	33	NUM
ejpam-5861	586	19	8	8	NUM
ejpam-5861	586	20	.	.	PUNCT
ejpam-5861	587	1	conclusion	conclusion	NOUN
ejpam-5861	587	2	with	with	ADP
ejpam-5861	587	3	the	the	DET
ejpam-5861	587	4	help	help	NOUN
ejpam-5861	587	5	of	of	ADP
ejpam-5861	587	6	new	new	ADJ
ejpam-5861	587	7	recently	recently	ADV
ejpam-5861	587	8	introduced	introduce	VERB
ejpam-5861	587	9	concepts	concept	NOUN
ejpam-5861	587	10	of	of	ADP
ejpam-5861	587	11	fractional	fractional	ADJ
ejpam-5861	587	12	calculus	calculus	NOUN
ejpam-5861	587	13	,	,	PUNCT
ejpam-5861	587	14	we	we	PRON
ejpam-5861	587	15	have	have	AUX
ejpam-5861	587	16	investigated	investigate	VERB
ejpam-5861	587	17	a	a	DET
ejpam-5861	587	18	determinacy	determinacy	NOUN
ejpam-5861	587	19	mathematical	mathematical	ADJ
ejpam-5861	587	20	model	model	NOUN
ejpam-5861	587	21	of	of	ADP
ejpam-5861	587	22	covid-19	covid-19	PROPN
ejpam-5861	587	23	.	.	PUNCT
ejpam-5861	588	1	because	because	SCONJ
ejpam-5861	588	2	such	such	ADJ
ejpam-5861	588	3	modeling	modeling	NOUN
ejpam-5861	588	4	is	be	AUX
ejpam-5861	588	5	very	very	ADV
ejpam-5861	588	6	effective	effective	ADJ
ejpam-5861	588	7	if	if	SCONJ
ejpam-5861	588	8	the	the	PRON
ejpam-5861	588	9	involve	involve	VERB
ejpam-5861	588	10	parameters	parameter	NOUN
ejpam-5861	588	11	and	and	CCONJ
ejpam-5861	588	12	functions	function	NOUN
ejpam-5861	588	13	are	be	AUX
ejpam-5861	588	14	suitably	suitably	ADV
ejpam-5861	588	15	defined	define	VERB
ejpam-5861	588	16	.	.	PUNCT
ejpam-5861	589	1	additionally	additionally	ADV
ejpam-5861	589	2	,	,	PUNCT
ejpam-5861	589	3	if	if	SCONJ
ejpam-5861	589	4	the	the	DET
ejpam-5861	589	5	parameters	parameter	NOUN
ejpam-5861	589	6	can	can	AUX
ejpam-5861	589	7	be	be	AUX
ejpam-5861	589	8	accurately	accurately	ADV
ejpam-5861	589	9	approximated	approximate	VERB
ejpam-5861	589	10	,	,	PUNCT
ejpam-5861	589	11	epidemic	epidemic	NOUN
ejpam-5861	589	12	modeling	modeling	NOUN
ejpam-5861	589	13	is	be	AUX
ejpam-5861	589	14	a	a	DET
ejpam-5861	589	15	very	very	ADV
ejpam-5861	589	16	useful	useful	ADJ
ejpam-5861	589	17	method	method	NOUN
ejpam-5861	589	18	for	for	ADP
ejpam-5861	589	19	estimating	estimate	VERB
ejpam-5861	589	20	the	the	DET
ejpam-5861	589	21	state	state	NOUN
ejpam-5861	589	22	of	of	ADP
ejpam-5861	589	23	the	the	DET
ejpam-5861	589	24	covid-19	covid-19	PROPN
ejpam-5861	589	25	worldwide	worldwide	ADV
ejpam-5861	589	26	pandemic	pandemic	ADJ
ejpam-5861	589	27	.	.	PUNCT
ejpam-5861	590	1	keeping	keep	VERB
ejpam-5861	590	2	these	these	DET
ejpam-5861	590	3	things	thing	NOUN
ejpam-5861	590	4	in	in	ADP
ejpam-5861	590	5	mind	mind	NOUN
ejpam-5861	590	6	,	,	PUNCT
ejpam-5861	590	7	we	we	PRON
ejpam-5861	590	8	have	have	AUX
ejpam-5861	590	9	revisited	revisit	VERB
ejpam-5861	590	10	a	a	DET
ejpam-5861	590	11	mathematical	mathematical	ADJ
ejpam-5861	590	12	model	model	NOUN
ejpam-5861	590	13	[	[	X
ejpam-5861	590	14	29	29	NUM
ejpam-5861	590	15	]	]	PUNCT
ejpam-5861	590	16	under	under	ADP
ejpam-5861	590	17	the	the	DET
ejpam-5861	590	18	piecewise	piecewise	NOUN
ejpam-5861	590	19	fractional	fractional	ADJ
ejpam-5861	590	20	order	order	NOUN
ejpam-5861	590	21	derivative	derivative	NOUN
ejpam-5861	590	22	.	.	PUNCT
ejpam-5861	591	1	fundamental	fundamental	ADJ
ejpam-5861	591	2	results	result	NOUN
ejpam-5861	591	3	including	include	VERB
ejpam-5861	591	4	positivity	positivity	NOUN
ejpam-5861	591	5	,	,	PUNCT
ejpam-5861	591	6	boundedness	boundedness	NOUN
ejpam-5861	591	7	and	and	CCONJ
ejpam-5861	591	8	equilibrium	equilibrium	NOUN
ejpam-5861	591	9	points	point	NOUN
ejpam-5861	591	10	were	be	AUX
ejpam-5861	591	11	deduced	deduce	VERB
ejpam-5861	591	12	.	.	PUNCT
ejpam-5861	592	1	also	also	ADV
ejpam-5861	592	2	reproductive	reproductive	ADJ
ejpam-5861	592	3	numbers	number	NOUN
ejpam-5861	592	4	was	be	AUX
ejpam-5861	592	5	calculated	calculate	VERB
ejpam-5861	592	6	.	.	PUNCT
ejpam-5861	593	1	here	here	ADV
ejpam-5861	593	2	,	,	PUNCT
ejpam-5861	593	3	we	we	PRON
ejpam-5861	593	4	have	have	AUX
ejpam-5861	593	5	investigated	investigate	VERB
ejpam-5861	593	6	sensitivity	sensitivity	NOUN
ejpam-5861	593	7	analysis	analysis	NOUN
ejpam-5861	593	8	of	of	ADP
ejpam-5861	593	9	the	the	DET
ejpam-5861	593	10	model	model	NOUN
ejpam-5861	593	11	via	via	ADP
ejpam-5861	593	12	reproductive	reproductive	ADJ
ejpam-5861	593	13	number	number	NOUN
ejpam-5861	593	14	analysis	analysis	NOUN
ejpam-5861	593	15	.	.	PUNCT
ejpam-5861	594	1	we	we	PRON
ejpam-5861	594	2	observe	observe	VERB
ejpam-5861	594	3	that	that	PRON
ejpam-5861	594	4	increase	increase	NOUN
ejpam-5861	594	5	the	the	DET
ejpam-5861	594	6	value	value	NOUN
ejpam-5861	594	7	value	value	NOUN
ejpam-5861	594	8	of	of	ADP
ejpam-5861	594	9	percentage	percentage	NOUN
ejpam-5861	594	10	upto	upto	NOUN
ejpam-5861	594	11	some	some	DET
ejpam-5861	594	12	extent	extent	NOUN
ejpam-5861	594	13	can	can	AUX
ejpam-5861	594	14	increase	increase	VERB
ejpam-5861	594	15	or	or	CCONJ
ejpam-5861	594	16	decrease	decrease	VERB
ejpam-5861	594	17	the	the	DET
ejpam-5861	594	18	sensitivity	sensitivity	NOUN
ejpam-5861	594	19	index	index	NOUN
ejpam-5861	594	20	by	by	ADP
ejpam-5861	594	21	that	that	DET
ejpam-5861	594	22	percent	percent	NOUN
ejpam-5861	594	23	.	.	PUNCT
ejpam-5861	595	1	the	the	DET
ejpam-5861	595	2	existence	existence	NOUN
ejpam-5861	595	3	theory	theory	NOUN
ejpam-5861	595	4	is	be	AUX
ejpam-5861	595	5	an	an	DET
ejpam-5861	595	6	important	important	ADJ
ejpam-5861	595	7	tool	tool	NOUN
ejpam-5861	595	8	to	to	PART
ejpam-5861	595	9	be	be	AUX
ejpam-5861	595	10	investigated	investigate	VERB
ejpam-5861	595	11	for	for	ADP
ejpam-5861	595	12	dynamical	dynamical	ADJ
ejpam-5861	595	13	problem	problem	NOUN
ejpam-5861	595	14	.	.	PUNCT
ejpam-5861	596	1	here	here	ADV
ejpam-5861	596	2	,	,	PUNCT
ejpam-5861	596	3	we	we	PRON
ejpam-5861	596	4	have	have	AUX
ejpam-5861	596	5	used	use	VERB
ejpam-5861	596	6	schauder	schauder	NOUN
ejpam-5861	596	7	’s	’s	PART
ejpam-5861	596	8	and	and	CCONJ
ejpam-5861	596	9	banach	banach	ADV
ejpam-5861	596	10	fixed	fix	VERB
ejpam-5861	596	11	point	point	NOUN
ejpam-5861	596	12	theorems	theorem	NOUN
ejpam-5861	596	13	to	to	PART
ejpam-5861	596	14	establish	establish	VERB
ejpam-5861	596	15	a	a	DET
ejpam-5861	596	16	detailed	detailed	ADJ
ejpam-5861	596	17	analysis	analysis	NOUN
ejpam-5861	596	18	for	for	ADP
ejpam-5861	596	19	existence	existence	NOUN
ejpam-5861	596	20	theory	theory	NOUN
ejpam-5861	596	21	of	of	ADP
ejpam-5861	596	22	solution	solution	NOUN
ejpam-5861	596	23	to	to	ADP
ejpam-5861	596	24	the	the	DET
ejpam-5861	596	25	proposed	propose	VERB
ejpam-5861	596	26	model	model	NOUN
ejpam-5861	596	27	.	.	PUNCT
ejpam-5861	597	1	additional	additional	ADJ
ejpam-5861	597	2	stability	stability	NOUN
ejpam-5861	597	3	is	be	AUX
ejpam-5861	597	4	important	important	ADJ
ejpam-5861	597	5	consequence	consequence	NOUN
ejpam-5861	597	6	and	and	CCONJ
ejpam-5861	597	7	for	for	ADP
ejpam-5861	597	8	dynamical	dynamical	ADJ
ejpam-5861	597	9	systems	system	NOUN
ejpam-5861	597	10	two	two	NUM
ejpam-5861	597	11	kinds	kind	NOUN
ejpam-5861	597	12	of	of	ADP
ejpam-5861	597	13	stability	stability	NOUN
ejpam-5861	597	14	be	be	AUX
ejpam-5861	597	15	studied	study	VERB
ejpam-5861	597	16	.	.	PUNCT
ejpam-5861	598	1	one	one	NUM
ejpam-5861	598	2	is	be	AUX
ejpam-5861	598	3	devoted	devote	VERB
ejpam-5861	598	4	to	to	ADP
ejpam-5861	598	5	stability	stability	NOUN
ejpam-5861	598	6	of	of	ADP
ejpam-5861	598	7	equilibrium	equilibrium	NOUN
ejpam-5861	598	8	points	point	NOUN
ejpam-5861	598	9	which	which	PRON
ejpam-5861	598	10	is	be	AUX
ejpam-5861	598	11	global	global	ADJ
ejpam-5861	598	12	or	or	CCONJ
ejpam-5861	598	13	local	local	ADJ
ejpam-5861	598	14	in	in	ADP
ejpam-5861	598	15	nature	nature	NOUN
ejpam-5861	598	16	.	.	PUNCT
ejpam-5861	599	1	therefore	therefore	ADV
ejpam-5861	599	2	,	,	PUNCT
ejpam-5861	599	3	we	we	PRON
ejpam-5861	599	4	have	have	AUX
ejpam-5861	599	5	attempted	attempt	VERB
ejpam-5861	599	6	to	to	PART
ejpam-5861	599	7	deduce	deduce	VERB
ejpam-5861	599	8	some	some	DET
ejpam-5861	599	9	results	result	NOUN
ejpam-5861	599	10	related	relate	VERB
ejpam-5861	599	11	to	to	ADP
ejpam-5861	599	12	local	local	ADJ
ejpam-5861	599	13	asymptotically	asymptotically	ADV
ejpam-5861	599	14	stability	stability	NOUN
ejpam-5861	599	15	of	of	ADP
ejpam-5861	599	16	dfe	dfe	PROPN
ejpam-5861	599	17	point	point	NOUN
ejpam-5861	599	18	.	.	PUNCT
ejpam-5861	600	1	it	it	PRON
ejpam-5861	600	2	was	be	AUX
ejpam-5861	600	3	deduced	deduce	VERB
ejpam-5861	600	4	that	that	SCONJ
ejpam-5861	600	5	dfe	dfe	PROPN
ejpam-5861	600	6	point	point	NOUN
ejpam-5861	600	7	is	be	AUX
ejpam-5861	600	8	asymptotically	asymptotically	ADV
ejpam-5861	600	9	stable	stable	ADJ
ejpam-5861	600	10	if	if	SCONJ
ejpam-5861	600	11	r0	r0	NOUN
ejpam-5861	600	12	<	<	X
ejpam-5861	600	13	1	1	NUM
ejpam-5861	600	14	.	.	PUNCT
ejpam-5861	601	1	on	on	ADP
ejpam-5861	601	2	the	the	DET
ejpam-5861	601	3	other	other	ADJ
ejpam-5861	601	4	hand	hand	NOUN
ejpam-5861	601	5	laypunov	laypunov	NOUN
ejpam-5861	601	6	-	-	PUNCT
ejpam-5861	601	7	volterra	volterra	NOUN
ejpam-5861	601	8	theory	theory	NOUN
ejpam-5861	601	9	was	be	AUX
ejpam-5861	601	10	used	use	VERB
ejpam-5861	601	11	to	to	PART
ejpam-5861	601	12	show	show	VERB
ejpam-5861	601	13	some	some	DET
ejpam-5861	601	14	results	result	NOUN
ejpam-5861	601	15	for	for	ADP
ejpam-5861	601	16	global	global	ADJ
ejpam-5861	601	17	stability	stability	NOUN
ejpam-5861	601	18	of	of	ADP
ejpam-5861	601	19	endemic	endemic	ADJ
ejpam-5861	601	20	equilibrium	equilibrium	NOUN
ejpam-5861	601	21	point	point	NOUN
ejpam-5861	601	22	.	.	PUNCT
ejpam-5861	602	1	the	the	DET
ejpam-5861	602	2	second	second	ADJ
ejpam-5861	602	3	stability	stability	NOUN
ejpam-5861	602	4	results	result	NOUN
ejpam-5861	602	5	were	be	AUX
ejpam-5861	602	6	devoted	devote	VERB
ejpam-5861	602	7	to	to	ADP
ejpam-5861	602	8	numerical	numerical	ADJ
ejpam-5861	602	9	type	type	NOUN
ejpam-5861	602	10	.	.	PUNCT
ejpam-5861	603	1	hence	hence	ADV
ejpam-5861	603	2	,	,	PUNCT
ejpam-5861	603	3	we	we	PRON
ejpam-5861	603	4	have	have	AUX
ejpam-5861	603	5	used	use	VERB
ejpam-5861	603	6	uh	uh	INTJ
ejpam-5861	603	7	concepts	concept	NOUN
ejpam-5861	603	8	to	to	PART
ejpam-5861	603	9	deduce	deduce	VERB
ejpam-5861	603	10	such	such	ADJ
ejpam-5861	603	11	results	result	NOUN
ejpam-5861	603	12	.	.	PUNCT
ejpam-5861	604	1	finally	finally	ADV
ejpam-5861	604	2	,	,	PUNCT
ejpam-5861	604	3	a	a	DET
ejpam-5861	604	4	sophisticated	sophisticated	ADJ
ejpam-5861	604	5	numerical	numerical	ADJ
ejpam-5861	604	6	algorithm	algorithm	NOUN
ejpam-5861	604	7	was	be	AUX
ejpam-5861	604	8	derived	derive	VERB
ejpam-5861	604	9	by	by	ADP
ejpam-5861	604	10	using	use	VERB
ejpam-5861	604	11	the	the	DET
ejpam-5861	604	12	rk2	rk2	NOUN
ejpam-5861	604	13	method	method	NOUN
ejpam-5861	604	14	.	.	PUNCT
ejpam-5861	605	1	we	we	PRON
ejpam-5861	605	2	have	have	AUX
ejpam-5861	605	3	used	use	VERB
ejpam-5861	605	4	this	this	DET
ejpam-5861	605	5	scheme	scheme	NOUN
ejpam-5861	605	6	to	to	PART
ejpam-5861	605	7	simulate	simulate	VERB
ejpam-5861	605	8	our	our	PRON
ejpam-5861	605	9	results	result	NOUN
ejpam-5861	605	10	graphically	graphically	ADV
ejpam-5861	605	11	.	.	PUNCT
ejpam-5861	606	1	we	we	PRON
ejpam-5861	606	2	see	see	VERB
ejpam-5861	606	3	that	that	PRON
ejpam-5861	606	4	crossover	crossover	NOUN
ejpam-5861	606	5	behaviors	behavior	NOUN
ejpam-5861	606	6	can	can	AUX
ejpam-5861	606	7	seen	see	VERB
ejpam-5861	606	8	in	in	ADP
ejpam-5861	606	9	each	each	DET
ejpam-5861	606	10	compartment	compartment	NOUN
ejpam-5861	606	11	after	after	ADP
ejpam-5861	606	12	t1	t1	NOUN
ejpam-5861	606	13	in	in	ADP
ejpam-5861	606	14	their	their	PRON
ejpam-5861	606	15	graphical	graphical	ADJ
ejpam-5861	606	16	presentation	presentation	NOUN
ejpam-5861	606	17	.	.	PUNCT
ejpam-5861	607	1	in	in	ADP
ejpam-5861	607	2	the	the	DET
ejpam-5861	607	3	future	future	NOUN
ejpam-5861	607	4	,	,	PUNCT
ejpam-5861	607	5	we	we	PRON
ejpam-5861	607	6	can	can	AUX
ejpam-5861	607	7	investigate	investigate	VERB
ejpam-5861	607	8	the	the	DET
ejpam-5861	607	9	mentioned	mention	VERB
ejpam-5861	607	10	models	model	NOUN
ejpam-5861	607	11	from	from	ADP
ejpam-5861	607	12	different	different	ADJ
ejpam-5861	607	13	perspectives	perspective	NOUN
ejpam-5861	607	14	like	like	ADP
ejpam-5861	607	15	:	:	PUNCT
ejpam-5861	607	16	•	•	NUM
ejpam-5861	607	17	by	by	ADP
ejpam-5861	607	18	using	use	VERB
ejpam-5861	607	19	fractals	fractal	NOUN
ejpam-5861	607	20	fractional	fractional	ADJ
ejpam-5861	607	21	calculus	calculus	NOUN
ejpam-5861	607	22	the	the	DET
ejpam-5861	607	23	considered	consider	VERB
ejpam-5861	607	24	model	model	NOUN
ejpam-5861	607	25	has	have	AUX
ejpam-5861	607	26	not	not	PART
ejpam-5861	607	27	studied	study	VERB
ejpam-5861	607	28	.	.	PUNCT
ejpam-5861	608	1	•	•	NUM
ejpam-5861	608	2	on	on	ADP
ejpam-5861	608	3	applying	apply	VERB
ejpam-5861	608	4	the	the	DET
ejpam-5861	608	5	traditional	traditional	ADJ
ejpam-5861	608	6	tools	tool	NOUN
ejpam-5861	608	7	of	of	ADP
ejpam-5861	608	8	fractional	fractional	ADJ
ejpam-5861	608	9	calculus	calculus	NOUN
ejpam-5861	608	10	in	in	ADP
ejpam-5861	608	11	terms	term	NOUN
ejpam-5861	608	12	of	of	ADP
ejpam-5861	608	13	conformable	conformable	NOUN
ejpam-5861	608	14	can	can	AUX
ejpam-5861	608	15	be	be	AUX
ejpam-5861	608	16	investigated	investigate	VERB
ejpam-5861	608	17	.	.	PUNCT
ejpam-5861	609	1	•	•	INTJ
ejpam-5861	609	2	we	we	PRON
ejpam-5861	609	3	can	can	AUX
ejpam-5861	609	4	investigate	investigate	VERB
ejpam-5861	609	5	the	the	DET
ejpam-5861	609	6	model	model	NOUN
ejpam-5861	609	7	by	by	ADP
ejpam-5861	609	8	using	use	VERB
ejpam-5861	609	9	non	non	ADJ
ejpam-5861	609	10	-	-	ADJ
ejpam-5861	609	11	singular	singular	ADJ
ejpam-5861	609	12	type	type	NOUN
ejpam-5861	609	13	derivatives	derivative	NOUN
ejpam-5861	609	14	.	.	PUNCT
ejpam-5861	610	1	•	•	NUM
ejpam-5861	610	2	stochastic	stochastic	ADJ
ejpam-5861	610	3	form	form	NOUN
ejpam-5861	610	4	of	of	ADP
ejpam-5861	610	5	this	this	DET
ejpam-5861	610	6	model	model	NOUN
ejpam-5861	610	7	has	have	AUX
ejpam-5861	610	8	not	not	PART
ejpam-5861	610	9	yet	yet	ADV
ejpam-5861	610	10	studied	study	VERB
ejpam-5861	610	11	.	.	PUNCT
ejpam-5861	611	1	•	•	NUM
ejpam-5861	611	2	in	in	ADP
ejpam-5861	611	3	the	the	DET
ejpam-5861	611	4	future	future	NOUN
ejpam-5861	611	5	,	,	PUNCT
ejpam-5861	611	6	if	if	SCONJ
ejpam-5861	611	7	we	we	PRON
ejpam-5861	611	8	include	include	VERB
ejpam-5861	611	9	the	the	DET
ejpam-5861	611	10	harmonic	harmonic	ADJ
ejpam-5861	611	11	mean	mean	NOUN
ejpam-5861	611	12	type	type	NOUN
ejpam-5861	611	13	nonlinear	nonlinear	ADJ
ejpam-5861	611	14	incidence	incidence	NOUN
ejpam-5861	611	15	rate	rate	NOUN
ejpam-5861	611	16	to	to	PART
ejpam-5861	611	17	properly	properly	ADV
ejpam-5861	611	18	investigate	investigate	VERB
ejpam-5861	611	19	the	the	DET
ejpam-5861	611	20	disease	disease	NOUN
ejpam-5861	611	21	dynamics	dynamic	NOUN
ejpam-5861	611	22	.	.	PUNCT
ejpam-5861	612	1	in	in	ADP
ejpam-5861	612	2	the	the	DET
ejpam-5861	612	3	future	future	NOUN
ejpam-5861	612	4	,	,	PUNCT
ejpam-5861	612	5	we	we	PRON
ejpam-5861	612	6	will	will	AUX
ejpam-5861	612	7	extend	extend	VERB
ejpam-5861	612	8	the	the	DET
ejpam-5861	612	9	numerical	numerical	ADJ
ejpam-5861	612	10	schemes	scheme	NOUN
ejpam-5861	612	11	introduced	introduce	VERB
ejpam-5861	612	12	in	in	ADP
ejpam-5861	612	13	[	[	X
ejpam-5861	612	14	2–4	2–4	X
ejpam-5861	612	15	]	]	X
ejpam-5861	612	16	for	for	ADP
ejpam-5861	612	17	piecewise	piecewise	NOUN
ejpam-5861	612	18	derivatives	derivative	NOUN
ejpam-5861	612	19	of	of	ADP
ejpam-5861	612	20	fractional	fractional	ADJ
ejpam-5861	612	21	orders	order	NOUN
ejpam-5861	612	22	using	use	VERB
ejpam-5861	612	23	different	different	ADJ
ejpam-5861	612	24	kinds	kind	NOUN
ejpam-5861	612	25	of	of	ADP
ejpam-5861	612	26	definitions	definition	NOUN
ejpam-5861	612	27	.	.	PUNCT
ejpam-5861	613	1	acknowledgements	acknowledgement	NOUN
ejpam-5861	613	2	we	we	PRON
ejpam-5861	613	3	are	be	AUX
ejpam-5861	613	4	thankful	thankful	ADJ
ejpam-5861	613	5	to	to	ADP
ejpam-5861	613	6	prince	prince	PROPN
ejpam-5861	613	7	sultan	sultan	PROPN
ejpam-5861	613	8	university	university	PROPN
ejpam-5861	613	9	for	for	ADP
ejpam-5861	613	10	support	support	NOUN
ejpam-5861	613	11	through	through	ADP
ejpam-5861	613	12	tas	ta	NOUN
ejpam-5861	613	13	research	research	NOUN
ejpam-5861	613	14	lab	lab	NOUN
ejpam-5861	613	15	.	.	PUNCT
ejpam-5861	614	1	s.	s.	PROPN
ejpam-5861	614	2	naz	naz	PROPN
ejpam-5861	614	3	et	et	PROPN
ejpam-5861	614	4	al	al	PROPN
ejpam-5861	614	5	.	.	PUNCT
ejpam-5861	614	6	/	/	SYM
ejpam-5861	614	7	eur	eur	PROPN
ejpam-5861	614	8	.	.	PUNCT
ejpam-5861	615	1	j.	j.	PROPN
ejpam-5861	615	2	pure	pure	PROPN
ejpam-5861	615	3	appl	appl	PROPN
ejpam-5861	615	4	.	.	PROPN
ejpam-5861	615	5	math	math	PROPN
ejpam-5861	615	6	,	,	PUNCT
ejpam-5861	615	7	18	18	NUM
ejpam-5861	615	8	(	(	PUNCT
ejpam-5861	615	9	2	2	NUM
ejpam-5861	615	10	)	)	PUNCT
ejpam-5861	615	11	(	(	PUNCT
ejpam-5861	615	12	2025	2025	NUM
ejpam-5861	615	13	)	)	PUNCT
ejpam-5861	615	14	,	,	PUNCT
ejpam-5861	615	15	5861	5861	NUM
ejpam-5861	615	16	31	31	NUM
ejpam-5861	615	17	of	of	ADP
ejpam-5861	615	18	33	33	NUM
ejpam-5861	615	19	references	reference	NOUN
ejpam-5861	615	20	[	[	X
ejpam-5861	615	21	1	1	NUM
ejpam-5861	615	22	]	]	PUNCT
ejpam-5861	615	23	r.	r.	PROPN
ejpam-5861	615	24	p.	p.	PROPN
ejpam-5861	615	25	agarwal	agarwal	PROPN
ejpam-5861	615	26	.	.	PUNCT
ejpam-5861	616	1	fixed	fix	VERB
ejpam-5861	616	2	point	point	NOUN
ejpam-5861	616	3	theory	theory	NOUN
ejpam-5861	616	4	and	and	CCONJ
ejpam-5861	616	5	applications	application	NOUN
ejpam-5861	616	6	.	.	PUNCT
ejpam-5861	617	1	cambridge	cambridge	PROPN
ejpam-5861	617	2	university	university	PROPN
ejpam-5861	617	3	press	press	NOUN
ejpam-5861	617	4	,	,	PUNCT
ejpam-5861	617	5	2001	2001	NUM
ejpam-5861	617	6	.	.	PUNCT
ejpam-5861	618	1	[	[	X
ejpam-5861	618	2	2	2	NUM
ejpam-5861	618	3	]	]	X
ejpam-5861	618	4	n.	n.	NOUN
ejpam-5861	618	5	almutairi	almutairi	PROPN
ejpam-5861	618	6	and	and	CCONJ
ejpam-5861	618	7	s.	s.	PROPN
ejpam-5861	618	8	saber	saber	PROPN
ejpam-5861	618	9	.	.	PUNCT
ejpam-5861	619	1	chaos	chaos	NOUN
ejpam-5861	619	2	control	control	NOUN
ejpam-5861	619	3	and	and	CCONJ
ejpam-5861	619	4	numerical	numerical	ADJ
ejpam-5861	619	5	solution	solution	NOUN
ejpam-5861	619	6	of	of	ADP
ejpam-5861	619	7	time	time	NOUN
ejpam-5861	619	8	-	-	PUNCT
ejpam-5861	619	9	varying	vary	VERB
ejpam-5861	619	10	fractional	fractional	ADJ
ejpam-5861	619	11	newton	newton	PROPN
ejpam-5861	619	12	-	-	PUNCT
ejpam-5861	619	13	leipnik	leipnik	NOUN
ejpam-5861	619	14	system	system	NOUN
ejpam-5861	619	15	using	use	VERB
ejpam-5861	619	16	fractional	fractional	ADJ
ejpam-5861	619	17	atangana	atangana	PROPN
ejpam-5861	619	18	-	-	PUNCT
ejpam-5861	619	19	baleanu	baleanu	ADJ
ejpam-5861	619	20	derivatives	derivative	NOUN
ejpam-5861	619	21	.	.	PUNCT
ejpam-5861	620	1	aims	aim	VERB
ejpam-5861	620	2	mathematics	mathematic	NOUN
ejpam-5861	620	3	,	,	PUNCT
ejpam-5861	620	4	8(11):25863–25887	8(11):25863–25887	NUM
ejpam-5861	620	5	,	,	PUNCT
ejpam-5861	620	6	2023	2023	NUM
ejpam-5861	620	7	.	.	PUNCT
ejpam-5861	621	1	[	[	X
ejpam-5861	621	2	3	3	NUM
ejpam-5861	621	3	]	]	X
ejpam-5861	621	4	n.	n.	NOUN
ejpam-5861	621	5	almutairi	almutairi	PROPN
ejpam-5861	621	6	and	and	CCONJ
ejpam-5861	621	7	s.	s.	PROPN
ejpam-5861	621	8	saber	saber	PROPN
ejpam-5861	621	9	.	.	PUNCT
ejpam-5861	622	1	on	on	ADP
ejpam-5861	622	2	chaos	chaos	NOUN
ejpam-5861	622	3	control	control	NOUN
ejpam-5861	622	4	of	of	ADP
ejpam-5861	622	5	nonlinear	nonlinear	PROPN
ejpam-5861	622	6	fractional	fractional	PROPN
ejpam-5861	622	7	newton	newton	PROPN
ejpam-5861	622	8	-	-	PUNCT
ejpam-5861	622	9	leipnik	leipnik	NOUN
ejpam-5861	622	10	system	system	NOUN
ejpam-5861	622	11	via	via	ADP
ejpam-5861	622	12	fractional	fractional	PROPN
ejpam-5861	622	13	caputo	caputo	PROPN
ejpam-5861	622	14	-	-	PUNCT
ejpam-5861	622	15	fabrizio	fabrizio	PROPN
ejpam-5861	622	16	derivatives	derivative	NOUN
ejpam-5861	622	17	.	.	PUNCT
ejpam-5861	623	1	scientific	scientific	ADJ
ejpam-5861	623	2	reports	report	NOUN
ejpam-5861	623	3	,	,	PUNCT
ejpam-5861	623	4	13(1):22726	13(1):22726	NUM
ejpam-5861	623	5	,	,	PUNCT
ejpam-5861	623	6	2023	2023	NUM
ejpam-5861	623	7	.	.	PUNCT
ejpam-5861	624	1	[	[	X
ejpam-5861	624	2	4	4	NUM
ejpam-5861	624	3	]	]	X
ejpam-5861	624	4	n.	n.	NOUN
ejpam-5861	624	5	almutairi	almutairi	PROPN
ejpam-5861	624	6	and	and	CCONJ
ejpam-5861	624	7	s.	s.	PROPN
ejpam-5861	624	8	saber	saber	PROPN
ejpam-5861	624	9	.	.	PUNCT
ejpam-5861	625	1	application	application	NOUN
ejpam-5861	625	2	of	of	ADP
ejpam-5861	625	3	a	a	DET
ejpam-5861	625	4	time	time	NOUN
ejpam-5861	625	5	-	-	PUNCT
ejpam-5861	625	6	fractal	fractal	ADJ
ejpam-5861	625	7	fractional	fractional	ADJ
ejpam-5861	625	8	derivative	derivative	NOUN
ejpam-5861	625	9	with	with	ADP
ejpam-5861	625	10	a	a	DET
ejpam-5861	625	11	power	power	NOUN
ejpam-5861	625	12	-	-	PUNCT
ejpam-5861	625	13	law	law	NOUN
ejpam-5861	625	14	kernel	kernel	NOUN
ejpam-5861	625	15	to	to	ADP
ejpam-5861	625	16	the	the	DET
ejpam-5861	625	17	burke	burke	PROPN
ejpam-5861	625	18	-	-	PUNCT
ejpam-5861	625	19	shaw	shaw	PROPN
ejpam-5861	625	20	system	system	NOUN
ejpam-5861	625	21	based	base	VERB
ejpam-5861	625	22	on	on	ADP
ejpam-5861	625	23	newton	newton	PROPN
ejpam-5861	625	24	’s	’s	PART
ejpam-5861	625	25	interpolation	interpolation	NOUN
ejpam-5861	625	26	polynomials	polynomial	NOUN
ejpam-5861	625	27	.	.	PUNCT
ejpam-5861	626	1	methodsx	methodsx	PROPN
ejpam-5861	626	2	,	,	PUNCT
ejpam-5861	626	3	12:102510	12:102510	NUM
ejpam-5861	626	4	,	,	PUNCT
ejpam-5861	626	5	2024	2024	NUM
ejpam-5861	626	6	.	.	PUNCT
ejpam-5861	627	1	[	[	X
ejpam-5861	627	2	5	5	NUM
ejpam-5861	627	3	]	]	PUNCT
ejpam-5861	627	4	m.	m.	NOUN
ejpam-5861	627	5	h.	h.	PROPN
ejpam-5861	627	6	aqlan	aqlan	PROPN
ejpam-5861	627	7	,	,	PUNCT
ejpam-5861	627	8	a.	a.	NOUN
ejpam-5861	627	9	alsaedi	alsaedi	PROPN
ejpam-5861	627	10	,	,	PUNCT
ejpam-5861	627	11	b.	b.	PROPN
ejpam-5861	627	12	ahmad	ahmad	PROPN
ejpam-5861	627	13	,	,	PUNCT
ejpam-5861	627	14	and	and	CCONJ
ejpam-5861	627	15	j.	j.	PROPN
ejpam-5861	627	16	j.	j.	PROPN
ejpam-5861	627	17	nieto	nieto	PROPN
ejpam-5861	627	18	.	.	PUNCT
ejpam-5861	628	1	mathematical	mathematical	ADJ
ejpam-5861	628	2	modeling	modeling	NOUN
ejpam-5861	628	3	and	and	CCONJ
ejpam-5861	628	4	prediction	prediction	NOUN
ejpam-5861	628	5	in	in	ADP
ejpam-5861	628	6	infectious	infectious	ADJ
ejpam-5861	628	7	disease	disease	NOUN
ejpam-5861	628	8	epidemiology	epidemiology	NOUN
ejpam-5861	628	9	.	.	PUNCT
ejpam-5861	629	1	open	open	ADJ
ejpam-5861	629	2	mathematics	mathematic	NOUN
ejpam-5861	629	3	,	,	PUNCT
ejpam-5861	629	4	14(1):723–735	14(1):723–735	NUM
ejpam-5861	629	5	,	,	PUNCT
ejpam-5861	629	6	2016	2016	NUM
ejpam-5861	629	7	.	.	PUNCT
ejpam-5861	630	1	[	[	X
ejpam-5861	630	2	6	6	NUM
ejpam-5861	630	3	]	]	PUNCT
ejpam-5861	630	4	a.	a.	NOUN
ejpam-5861	630	5	atangana	atangana	PROPN
ejpam-5861	630	6	.	.	PUNCT
ejpam-5861	631	1	modelling	model	VERB
ejpam-5861	631	2	the	the	DET
ejpam-5861	631	3	spread	spread	NOUN
ejpam-5861	631	4	of	of	ADP
ejpam-5861	631	5	covid-19	covid-19	PROPN
ejpam-5861	631	6	with	with	ADP
ejpam-5861	631	7	new	new	ADJ
ejpam-5861	631	8	fractal	fractal	ADJ
ejpam-5861	631	9	-	-	PUNCT
ejpam-5861	631	10	fractional	fractional	ADJ
ejpam-5861	631	11	operators	operator	NOUN
ejpam-5861	631	12	:	:	PUNCT
ejpam-5861	631	13	can	can	AUX
ejpam-5861	631	14	the	the	DET
ejpam-5861	631	15	lockdown	lockdown	NOUN
ejpam-5861	631	16	save	save	VERB
ejpam-5861	631	17	mankind	mankind	NOUN
ejpam-5861	631	18	before	before	ADP
ejpam-5861	631	19	vaccination	vaccination	NOUN
ejpam-5861	631	20	?	?	PUNCT
ejpam-5861	632	1	chaos	chaos	NOUN
ejpam-5861	632	2	,	,	PUNCT
ejpam-5861	632	3	solitons	soliton	NOUN
ejpam-5861	632	4	fractals	fractal	NOUN
ejpam-5861	632	5	,	,	PUNCT
ejpam-5861	632	6	136:109860	136:109860	NUM
ejpam-5861	632	7	,	,	PUNCT
ejpam-5861	632	8	2020	2020	NUM
ejpam-5861	632	9	.	.	PUNCT
ejpam-5861	633	1	[	[	X
ejpam-5861	633	2	7	7	X
ejpam-5861	633	3	]	]	PUNCT
ejpam-5861	633	4	a.	a.	NOUN
ejpam-5861	633	5	atangana	atangana	PROPN
ejpam-5861	633	6	and	and	CCONJ
ejpam-5861	633	7	s.	s.	PROPN
ejpam-5861	633	8	i.	i.	PROPN
ejpam-5861	633	9	araz	araz	PROPN
ejpam-5861	633	10	.	.	PUNCT
ejpam-5861	634	1	new	new	ADJ
ejpam-5861	634	2	concept	concept	NOUN
ejpam-5861	634	3	in	in	ADP
ejpam-5861	634	4	calculus	calculus	NOUN
ejpam-5861	634	5	:	:	PUNCT
ejpam-5861	634	6	piecewise	piecewise	NOUN
ejpam-5861	634	7	differential	differential	NOUN
ejpam-5861	634	8	and	and	CCONJ
ejpam-5861	634	9	integral	integral	ADJ
ejpam-5861	634	10	operators	operator	NOUN
ejpam-5861	634	11	.	.	PUNCT
ejpam-5861	635	1	chaos	chaos	NOUN
ejpam-5861	635	2	,	,	PUNCT
ejpam-5861	635	3	solitons	soliton	NOUN
ejpam-5861	635	4	fractals	fractal	NOUN
ejpam-5861	635	5	,	,	PUNCT
ejpam-5861	635	6	145:110638	145:110638	NUM
ejpam-5861	635	7	,	,	PUNCT
ejpam-5861	635	8	2021	2021	NUM
ejpam-5861	635	9	.	.	PUNCT
ejpam-5861	636	1	[	[	X
ejpam-5861	636	2	8	8	NUM
ejpam-5861	636	3	]	]	PUNCT
ejpam-5861	636	4	a.	a.	NOUN
ejpam-5861	636	5	atangana	atangana	PROPN
ejpam-5861	636	6	and	and	CCONJ
ejpam-5861	636	7	s.	s.	PROPN
ejpam-5861	636	8	i.	i.	PROPN
ejpam-5861	636	9	araz	araz	PROPN
ejpam-5861	636	10	.	.	PUNCT
ejpam-5861	637	1	rhythmic	rhythmic	ADJ
ejpam-5861	637	2	behaviors	behavior	NOUN
ejpam-5861	637	3	of	of	ADP
ejpam-5861	637	4	the	the	DET
ejpam-5861	637	5	human	human	ADJ
ejpam-5861	637	6	heart	heart	NOUN
ejpam-5861	637	7	with	with	ADP
ejpam-5861	637	8	piecewise	piecewise	NOUN
ejpam-5861	637	9	derivative	derivative	NOUN
ejpam-5861	637	10	.	.	PUNCT
ejpam-5861	638	1	mathematical	mathematical	ADJ
ejpam-5861	638	2	biosciences	bioscience	NOUN
ejpam-5861	638	3	and	and	CCONJ
ejpam-5861	638	4	engineering	engineering	NOUN
ejpam-5861	638	5	,	,	PUNCT
ejpam-5861	638	6	19:3091–3109	19:3091–3109	NUM
ejpam-5861	638	7	,	,	PUNCT
ejpam-5861	638	8	2022	2022	NUM
ejpam-5861	638	9	.	.	PUNCT
ejpam-5861	639	1	[	[	X
ejpam-5861	639	2	9	9	NUM
ejpam-5861	639	3	]	]	PUNCT
ejpam-5861	639	4	a.	a.	NOUN
ejpam-5861	639	5	atangana	atangana	PROPN
ejpam-5861	639	6	and	and	CCONJ
ejpam-5861	639	7	s.	s.	PROPN
ejpam-5861	639	8	i.	i.	PROPN
ejpam-5861	639	9	araz	araz	PROPN
ejpam-5861	639	10	.	.	PUNCT
ejpam-5861	640	1	piecewise	piecewise	NOUN
ejpam-5861	640	2	differential	differential	ADJ
ejpam-5861	640	3	equations	equation	NOUN
ejpam-5861	640	4	:	:	PUNCT
ejpam-5861	641	1	theory	theory	NOUN
ejpam-5861	641	2	,	,	PUNCT
ejpam-5861	641	3	methods	method	NOUN
ejpam-5861	641	4	and	and	CCONJ
ejpam-5861	641	5	applications	application	NOUN
ejpam-5861	641	6	.	.	PUNCT
ejpam-5861	642	1	aims	aim	VERB
ejpam-5861	642	2	mathematics	mathematic	NOUN
ejpam-5861	642	3	,	,	PUNCT
ejpam-5861	642	4	8(7):15352–15382	8(7):15352–15382	NUM
ejpam-5861	642	5	,	,	PUNCT
ejpam-5861	642	6	2023	2023	NUM
ejpam-5861	642	7	.	.	PUNCT
ejpam-5861	643	1	[	[	X
ejpam-5861	643	2	10	10	NUM
ejpam-5861	643	3	]	]	X
ejpam-5861	643	4	n.	n.	PROPN
ejpam-5861	643	5	bacaer	bacaer	PROPN
ejpam-5861	643	6	.	.	PUNCT
ejpam-5861	644	1	a	a	DET
ejpam-5861	644	2	short	short	ADJ
ejpam-5861	644	3	history	history	NOUN
ejpam-5861	644	4	of	of	ADP
ejpam-5861	644	5	mathematical	mathematical	ADJ
ejpam-5861	644	6	population	population	NOUN
ejpam-5861	644	7	dynamics	dynamic	NOUN
ejpam-5861	644	8	.	.	PUNCT
ejpam-5861	645	1	springer	springer	PROPN
ejpam-5861	645	2	,	,	PUNCT
ejpam-5861	645	3	london	london	PROPN
ejpam-5861	645	4	,	,	PUNCT
ejpam-5861	645	5	2011	2011	NUM
ejpam-5861	645	6	.	.	PUNCT
ejpam-5861	646	1	[	[	X
ejpam-5861	646	2	11	11	NUM
ejpam-5861	646	3	]	]	X
ejpam-5861	646	4	f.	f.	PROPN
ejpam-5861	646	5	brauer	brauer	PROPN
ejpam-5861	646	6	,	,	PUNCT
ejpam-5861	646	7	c.	c.	PROPN
ejpam-5861	646	8	castillo	castillo	PROPN
ejpam-5861	646	9	-	-	PUNCT
ejpam-5861	646	10	chavez	chavez	PROPN
ejpam-5861	646	11	,	,	PUNCT
ejpam-5861	646	12	and	and	CCONJ
ejpam-5861	646	13	z.	z.	PROPN
ejpam-5861	646	14	feng	feng	PROPN
ejpam-5861	646	15	.	.	PUNCT
ejpam-5861	647	1	mathematical	mathematical	ADJ
ejpam-5861	647	2	models	model	NOUN
ejpam-5861	647	3	in	in	ADP
ejpam-5861	647	4	epidemiology	epidemiology	NOUN
ejpam-5861	647	5	.	.	PUNCT
ejpam-5861	648	1	springer	springer	NOUN
ejpam-5861	648	2	,	,	PUNCT
ejpam-5861	648	3	new	new	PROPN
ejpam-5861	648	4	york	york	PROPN
ejpam-5861	648	5	,	,	PUNCT
ejpam-5861	648	6	2019	2019	NUM
ejpam-5861	648	7	.	.	PUNCT
ejpam-5861	649	1	[	[	X
ejpam-5861	649	2	12	12	NUM
ejpam-5861	649	3	]	]	X
ejpam-5861	649	4	c.	c.	PROPN
ejpam-5861	649	5	chen	chen	PROPN
ejpam-5861	649	6	,	,	PUNCT
ejpam-5861	649	7	m.	m.	NOUN
ejpam-5861	649	8	bohner	bohner	NOUN
ejpam-5861	649	9	,	,	PUNCT
ejpam-5861	649	10	and	and	CCONJ
ejpam-5861	649	11	b.	b.	PROPN
ejpam-5861	649	12	jia	jia	PROPN
ejpam-5861	649	13	.	.	PUNCT
ejpam-5861	649	14	ulam	ulam	PROPN
ejpam-5861	649	15	-	-	PUNCT
ejpam-5861	649	16	hyers	hyer	NOUN
ejpam-5861	649	17	stability	stability	NOUN
ejpam-5861	649	18	of	of	ADP
ejpam-5861	649	19	caputo	caputo	PROPN
ejpam-5861	649	20	fractional	fractional	PROPN
ejpam-5861	649	21	difference	difference	NOUN
ejpam-5861	649	22	equations	equation	NOUN
ejpam-5861	649	23	.	.	PUNCT
ejpam-5861	650	1	mathematical	mathematical	ADJ
ejpam-5861	650	2	methods	method	NOUN
ejpam-5861	650	3	in	in	ADP
ejpam-5861	650	4	the	the	DET
ejpam-5861	650	5	applied	apply	VERB
ejpam-5861	650	6	sciences	science	NOUN
ejpam-5861	650	7	,	,	PUNCT
ejpam-5861	650	8	42(18):7461–7470	42(18):7461–7470	NUM
ejpam-5861	650	9	,	,	PUNCT
ejpam-5861	650	10	2019	2019	NUM
ejpam-5861	650	11	.	.	PUNCT
ejpam-5861	651	1	[	[	X
ejpam-5861	651	2	13	13	NUM
ejpam-5861	651	3	]	]	PUNCT
ejpam-5861	651	4	a.	a.	NOUN
ejpam-5861	651	5	k.	k.	PROPN
ejpam-5861	651	6	cheng	cheng	PROPN
ejpam-5861	651	7	.	.	PUNCT
ejpam-5861	652	1	mathematical	mathematical	ADJ
ejpam-5861	652	2	modelling	modelling	NOUN
ejpam-5861	652	3	and	and	CCONJ
ejpam-5861	652	4	real	real	ADJ
ejpam-5861	652	5	life	life	NOUN
ejpam-5861	652	6	problem	problem	NOUN
ejpam-5861	652	7	solving	solving	NOUN
ejpam-5861	652	8	.	.	PUNCT
ejpam-5861	653	1	association	association	NOUN
ejpam-5861	653	2	of	of	ADP
ejpam-5861	653	3	mathematics	mathematics	PROPN
ejpam-5861	653	4	educators	educator	NOUN
ejpam-5861	653	5	,	,	PUNCT
ejpam-5861	653	6	2009	2009	NUM
ejpam-5861	653	7	.	.	PUNCT
ejpam-5861	654	1	[	[	X
ejpam-5861	654	2	14	14	NUM
ejpam-5861	654	3	]	]	X
ejpam-5861	654	4	y.	y.	PROPN
ejpam-5861	654	5	j.	j.	PROPN
ejpam-5861	654	6	cho	cho	PROPN
ejpam-5861	654	7	.	.	PUNCT
ejpam-5861	655	1	survey	survey	NOUN
ejpam-5861	655	2	on	on	ADP
ejpam-5861	655	3	metric	metric	ADJ
ejpam-5861	655	4	fixed	fix	VERB
ejpam-5861	655	5	point	point	NOUN
ejpam-5861	655	6	theory	theory	NOUN
ejpam-5861	655	7	and	and	CCONJ
ejpam-5861	655	8	applications	application	NOUN
ejpam-5861	655	9	.	.	PUNCT
ejpam-5861	656	1	advances	advance	NOUN
ejpam-5861	656	2	in	in	ADP
ejpam-5861	656	3	real	real	ADJ
ejpam-5861	656	4	and	and	CCONJ
ejpam-5861	656	5	complex	complex	ADJ
ejpam-5861	656	6	analysis	analysis	NOUN
ejpam-5861	656	7	with	with	ADP
ejpam-5861	656	8	applications	application	NOUN
ejpam-5861	656	9	,	,	PUNCT
ejpam-5861	656	10	pages	page	NOUN
ejpam-5861	656	11	183–241	183–241	NUM
ejpam-5861	656	12	,	,	PUNCT
ejpam-5861	656	13	2017	2017	NUM
ejpam-5861	656	14	.	.	PUNCT
ejpam-5861	657	1	[	[	X
ejpam-5861	657	2	15	15	NUM
ejpam-5861	657	3	]	]	X
ejpam-5861	657	4	m.	m.	NOUN
ejpam-5861	657	5	dalir	dalir	NOUN
ejpam-5861	657	6	and	and	CCONJ
ejpam-5861	657	7	m.	m.	NOUN
ejpam-5861	657	8	bashour	bashour	PROPN
ejpam-5861	657	9	.	.	PUNCT
ejpam-5861	658	1	applications	application	NOUN
ejpam-5861	658	2	of	of	ADP
ejpam-5861	658	3	fractional	fractional	ADJ
ejpam-5861	658	4	calculus	calculus	NOUN
ejpam-5861	658	5	.	.	PUNCT
ejpam-5861	659	1	applied	apply	VERB
ejpam-5861	659	2	mathematical	mathematical	ADJ
ejpam-5861	659	3	sciences	sciences	PROPN
ejpam-5861	659	4	,	,	PUNCT
ejpam-5861	659	5	4(21):1021–1032	4(21):1021–1032	NUM
ejpam-5861	659	6	,	,	PUNCT
ejpam-5861	659	7	2011	2011	NUM
ejpam-5861	659	8	.	.	PUNCT
ejpam-5861	660	1	[	[	X
ejpam-5861	660	2	16	16	NUM
ejpam-5861	660	3	]	]	PUNCT
ejpam-5861	660	4	l.	l.	PROPN
ejpam-5861	660	5	edelstein	edelstein	PROPN
ejpam-5861	660	6	-	-	PUNCT
ejpam-5861	660	7	keshet	keshet	PROPN
ejpam-5861	660	8	.	.	PUNCT
ejpam-5861	661	1	mathematical	mathematical	ADJ
ejpam-5861	661	2	models	model	NOUN
ejpam-5861	661	3	in	in	ADP
ejpam-5861	661	4	biology	biology	NOUN
ejpam-5861	661	5	.	.	PUNCT
ejpam-5861	662	1	siam	siam	PROPN
ejpam-5861	662	2	,	,	PUNCT
ejpam-5861	662	3	2004	2004	NUM
ejpam-5861	662	4	.	.	PUNCT
ejpam-5861	663	1	[	[	X
ejpam-5861	663	2	17	17	NUM
ejpam-5861	663	3	]	]	PUNCT
ejpam-5861	663	4	a.	a.	NOUN
ejpam-5861	663	5	granas	grana	NOUN
ejpam-5861	663	6	and	and	CCONJ
ejpam-5861	663	7	j.	j.	PROPN
ejpam-5861	663	8	dugundji	dugundji	PROPN
ejpam-5861	663	9	.	.	PUNCT
ejpam-5861	664	1	fixed	fix	VERB
ejpam-5861	664	2	point	point	NOUN
ejpam-5861	664	3	theory	theory	NOUN
ejpam-5861	664	4	,	,	PUNCT
ejpam-5861	664	5	volume	volume	NOUN
ejpam-5861	664	6	14	14	NUM
ejpam-5861	664	7	.	.	PUNCT
ejpam-5861	665	1	springer	springer	NOUN
ejpam-5861	665	2	,	,	PUNCT
ejpam-5861	665	3	new	new	PROPN
ejpam-5861	665	4	york	york	PROPN
ejpam-5861	665	5	,	,	PUNCT
ejpam-5861	665	6	2003	2003	NUM
ejpam-5861	665	7	.	.	PUNCT
ejpam-5861	666	1	[	[	X
ejpam-5861	666	2	18	18	NUM
ejpam-5861	666	3	]	]	PUNCT
ejpam-5861	666	4	a.	a.	PROPN
ejpam-5861	666	5	b.	b.	PROPN
ejpam-5861	666	6	gumel	gumel	PROPN
ejpam-5861	666	7	,	,	PUNCT
ejpam-5861	666	8	s.	s.	PROPN
ejpam-5861	666	9	ruan	ruan	PROPN
ejpam-5861	666	10	,	,	PUNCT
ejpam-5861	666	11	t.	t.	PROPN
ejpam-5861	666	12	day	day	PROPN
ejpam-5861	666	13	,	,	PUNCT
ejpam-5861	666	14	j.	j.	PROPN
ejpam-5861	666	15	watmough	watmough	PROPN
ejpam-5861	666	16	,	,	PUNCT
ejpam-5861	666	17	f.	f.	PROPN
ejpam-5861	666	18	brauer	brauer	PROPN
ejpam-5861	666	19	,	,	PUNCT
ejpam-5861	666	20	p.	p.	PROPN
ejpam-5861	666	21	van	van	PROPN
ejpam-5861	666	22	den	den	PROPN
ejpam-5861	666	23	driessche	driessche	PROPN
ejpam-5861	666	24	,	,	PUNCT
ejpam-5861	666	25	d.	d.	PROPN
ejpam-5861	666	26	gabrielson	gabrielson	PROPN
ejpam-5861	666	27	,	,	PUNCT
ejpam-5861	666	28	c.	c.	PROPN
ejpam-5861	666	29	bowman	bowman	PROPN
ejpam-5861	666	30	,	,	PUNCT
ejpam-5861	666	31	m.	m.	PROPN
ejpam-5861	666	32	e.	e.	PROPN
ejpam-5861	666	33	alexander	alexander	PROPN
ejpam-5861	666	34	,	,	PUNCT
ejpam-5861	666	35	s.	s.	PROPN
ejpam-5861	666	36	ardal	ardal	PROPN
ejpam-5861	666	37	,	,	PUNCT
ejpam-5861	666	38	and	and	CCONJ
ejpam-5861	666	39	j.	j.	PROPN
ejpam-5861	666	40	wu	wu	PROPN
ejpam-5861	666	41	.	.	PUNCT
ejpam-5861	667	1	modelling	model	VERB
ejpam-5861	667	2	strategies	strategy	NOUN
ejpam-5861	667	3	for	for	ADP
ejpam-5861	667	4	controlling	control	VERB
ejpam-5861	667	5	sars	sar	NOUN
ejpam-5861	667	6	outbreaks	outbreak	NOUN
ejpam-5861	667	7	.	.	PUNCT
ejpam-5861	668	1	proceedings	proceeding	NOUN
ejpam-5861	668	2	of	of	ADP
ejpam-5861	668	3	the	the	DET
ejpam-5861	668	4	royal	royal	ADJ
ejpam-5861	668	5	society	society	NOUN
ejpam-5861	668	6	of	of	ADP
ejpam-5861	668	7	london	london	PROPN
ejpam-5861	668	8	.	.	PUNCT
ejpam-5861	669	1	series	series	PROPN
ejpam-5861	669	2	b	b	PROPN
ejpam-5861	669	3	:	:	PUNCT
ejpam-5861	669	4	biological	biological	ADJ
ejpam-5861	669	5	sciences	science	NOUN
ejpam-5861	669	6	,	,	PUNCT
ejpam-5861	669	7	1554:2223–2232	1554:2223–2232	NOUN
ejpam-5861	669	8	,	,	PUNCT
ejpam-5861	669	9	2004	2004	NUM
ejpam-5861	669	10	.	.	PUNCT
ejpam-5861	670	1	s.	s.	PROPN
ejpam-5861	670	2	naz	naz	PROPN
ejpam-5861	670	3	et	et	PROPN
ejpam-5861	670	4	al	al	PROPN
ejpam-5861	670	5	.	.	PUNCT
ejpam-5861	670	6	/	/	SYM
ejpam-5861	670	7	eur	eur	PROPN
ejpam-5861	670	8	.	.	PUNCT
ejpam-5861	671	1	j.	j.	PROPN
ejpam-5861	671	2	pure	pure	PROPN
ejpam-5861	671	3	appl	appl	PROPN
ejpam-5861	671	4	.	.	PROPN
ejpam-5861	671	5	math	math	PROPN
ejpam-5861	671	6	,	,	PUNCT
ejpam-5861	671	7	18	18	NUM
ejpam-5861	671	8	(	(	PUNCT
ejpam-5861	671	9	2	2	NUM
ejpam-5861	671	10	)	)	PUNCT
ejpam-5861	671	11	(	(	PUNCT
ejpam-5861	671	12	2025	2025	NUM
ejpam-5861	671	13	)	)	PUNCT
ejpam-5861	671	14	,	,	PUNCT
ejpam-5861	671	15	5861	5861	NUM
ejpam-5861	671	16	32	32	NUM
ejpam-5861	671	17	of	of	ADP
ejpam-5861	671	18	33	33	NUM
ejpam-5861	671	19	[	[	SYM
ejpam-5861	671	20	19	19	NUM
ejpam-5861	671	21	]	]	PUNCT
ejpam-5861	671	22	a.	a.	NOUN
ejpam-5861	671	23	huppert	huppert	PROPN
ejpam-5861	671	24	and	and	CCONJ
ejpam-5861	671	25	g.	g.	PROPN
ejpam-5861	671	26	katriel	katriel	PROPN
ejpam-5861	671	27	.	.	PUNCT
ejpam-5861	672	1	mathematical	mathematical	ADJ
ejpam-5861	672	2	modeling	modeling	NOUN
ejpam-5861	672	3	and	and	CCONJ
ejpam-5861	672	4	prediction	prediction	NOUN
ejpam-5861	672	5	in	in	ADP
ejpam-5861	672	6	infectious	infectious	ADJ
ejpam-5861	672	7	disease	disease	NOUN
ejpam-5861	672	8	epidemiology	epidemiology	NOUN
ejpam-5861	672	9	.	.	PUNCT
ejpam-5861	673	1	clinical	clinical	ADJ
ejpam-5861	673	2	microbiology	microbiology	NOUN
ejpam-5861	673	3	and	and	CCONJ
ejpam-5861	673	4	infection	infection	NOUN
ejpam-5861	673	5	,	,	PUNCT
ejpam-5861	673	6	19(11):999–1005	19(11):999–1005	NUM
ejpam-5861	673	7	,	,	PUNCT
ejpam-5861	673	8	2013	2013	NUM
ejpam-5861	673	9	.	.	PUNCT
ejpam-5861	674	1	[	[	X
ejpam-5861	674	2	20	20	NUM
ejpam-5861	674	3	]	]	X
ejpam-5861	674	4	r.	r.	PROPN
ejpam-5861	674	5	m.	m.	PROPN
ejpam-5861	674	6	jena	jena	PROPN
ejpam-5861	674	7	.	.	PUNCT
ejpam-5861	675	1	piecewise	piecewise	NOUN
ejpam-5861	675	2	concept	concept	NOUN
ejpam-5861	675	3	in	in	ADP
ejpam-5861	675	4	fractional	fractional	ADJ
ejpam-5861	675	5	models	model	NOUN
ejpam-5861	675	6	.	.	PUNCT
ejpam-5861	676	1	academic	academic	ADJ
ejpam-5861	676	2	press	press	NOUN
ejpam-5861	676	3	,	,	PUNCT
ejpam-5861	676	4	new	new	PROPN
ejpam-5861	676	5	york	york	PROPN
ejpam-5861	676	6	,	,	PUNCT
ejpam-5861	676	7	2024	2024	NUM
ejpam-5861	676	8	.	.	PUNCT
ejpam-5861	677	1	[	[	X
ejpam-5861	677	2	21	21	NUM
ejpam-5861	677	3	]	]	X
ejpam-5861	677	4	h.	h.	PROPN
ejpam-5861	677	5	khan	khan	PROPN
ejpam-5861	677	6	,	,	PUNCT
ejpam-5861	677	7	s.	s.	PROPN
ejpam-5861	677	8	ahmad	ahmad	PROPN
ejpam-5861	677	9	,	,	PUNCT
ejpam-5861	677	10	j.	j.	PROPN
ejpam-5861	677	11	alzabut	alzabut	PROPN
ejpam-5861	677	12	,	,	PUNCT
ejpam-5861	677	13	and	and	CCONJ
ejpam-5861	677	14	a.	a.	NOUN
ejpam-5861	677	15	t.	t.	PROPN
ejpam-5861	677	16	azar	azar	PROPN
ejpam-5861	677	17	.	.	PUNCT
ejpam-5861	678	1	a	a	DET
ejpam-5861	678	2	generalized	generalize	VERB
ejpam-5861	678	3	coupled	couple	VERB
ejpam-5861	678	4	system	system	NOUN
ejpam-5861	678	5	of	of	ADP
ejpam-5861	678	6	fractional	fractional	ADJ
ejpam-5861	678	7	differential	differential	ADJ
ejpam-5861	678	8	equations	equation	NOUN
ejpam-5861	678	9	with	with	ADP
ejpam-5861	678	10	application	application	NOUN
ejpam-5861	678	11	to	to	PART
ejpam-5861	678	12	finite	finite	VERB
ejpam-5861	678	13	time	time	NOUN
ejpam-5861	678	14	sliding	slide	VERB
ejpam-5861	678	15	mode	mode	NOUN
ejpam-5861	678	16	control	control	NOUN
ejpam-5861	678	17	for	for	ADP
ejpam-5861	678	18	leukemia	leukemia	NOUN
ejpam-5861	678	19	therapy	therapy	NOUN
ejpam-5861	678	20	.	.	PUNCT
ejpam-5861	679	1	chaos	chaos	NOUN
ejpam-5861	679	2	,	,	PUNCT
ejpam-5861	679	3	solitons	soliton	NOUN
ejpam-5861	679	4	fractals	fractal	NOUN
ejpam-5861	679	5	,	,	PUNCT
ejpam-5861	679	6	174:113901	174:113901	NUM
ejpam-5861	679	7	,	,	PUNCT
ejpam-5861	679	8	2023	2023	NUM
ejpam-5861	679	9	.	.	PUNCT
ejpam-5861	680	1	[	[	X
ejpam-5861	680	2	22	22	NUM
ejpam-5861	680	3	]	]	X
ejpam-5861	680	4	h.	h.	PROPN
ejpam-5861	680	5	khan	khan	PROPN
ejpam-5861	680	6	,	,	PUNCT
ejpam-5861	680	7	j.	j.	PROPN
ejpam-5861	680	8	alzabut	alzabut	PROPN
ejpam-5861	680	9	,	,	PUNCT
ejpam-5861	680	10	w.	w.	PROPN
ejpam-5861	680	11	f.	f.	PROPN
ejpam-5861	680	12	alfwzan	alfwzan	PROPN
ejpam-5861	680	13	,	,	PUNCT
ejpam-5861	680	14	and	and	CCONJ
ejpam-5861	680	15	h.	h.	PROPN
ejpam-5861	680	16	gulzar	gulzar	PROPN
ejpam-5861	680	17	.	.	PUNCT
ejpam-5861	681	1	nonlinear	nonlinear	ADJ
ejpam-5861	681	2	dynamics	dynamic	NOUN
ejpam-5861	681	3	of	of	ADP
ejpam-5861	681	4	a	a	DET
ejpam-5861	681	5	piecewise	piecewise	NOUN
ejpam-5861	681	6	modified	modify	VERB
ejpam-5861	681	7	abc	abc	PROPN
ejpam-5861	681	8	fractional	fractional	ADJ
ejpam-5861	681	9	-	-	PUNCT
ejpam-5861	681	10	order	order	NOUN
ejpam-5861	681	11	leukemia	leukemia	NOUN
ejpam-5861	681	12	model	model	NOUN
ejpam-5861	681	13	with	with	ADP
ejpam-5861	681	14	symmetric	symmetric	ADJ
ejpam-5861	681	15	numerical	numerical	ADJ
ejpam-5861	681	16	simulations	simulation	NOUN
ejpam-5861	681	17	.	.	PUNCT
ejpam-5861	682	1	symmetry	symmetry	NOUN
ejpam-5861	682	2	,	,	PUNCT
ejpam-5861	682	3	15(7):1338	15(7):1338	NUM
ejpam-5861	682	4	,	,	PUNCT
ejpam-5861	682	5	2023	2023	NUM
ejpam-5861	682	6	.	.	PUNCT
ejpam-5861	683	1	[	[	X
ejpam-5861	683	2	23	23	NUM
ejpam-5861	683	3	]	]	X
ejpam-5861	683	4	h.	h.	PROPN
ejpam-5861	683	5	khan	khan	PROPN
ejpam-5861	683	6	,	,	PUNCT
ejpam-5861	683	7	j.	j.	PROPN
ejpam-5861	683	8	alzabut	alzabut	PROPN
ejpam-5861	683	9	,	,	PUNCT
ejpam-5861	683	10	j.	j.	PROPN
ejpam-5861	683	11	f.	f.	PROPN
ejpam-5861	683	12	gomez	gomez	PROPN
ejpam-5861	683	13	-	-	PUNCT
ejpam-5861	683	14	aguilar	aguilar	PROPN
ejpam-5861	683	15	,	,	PUNCT
ejpam-5861	683	16	and	and	CCONJ
ejpam-5861	683	17	r.	r.	PROPN
ejpam-5861	683	18	p.	p.	PROPN
ejpam-5861	683	19	agarwal	agarwal	PROPN
ejpam-5861	683	20	.	.	PUNCT
ejpam-5861	684	1	piecewise	piecewise	PROPN
ejpam-5861	684	2	mabc	mabc	VERB
ejpam-5861	684	3	fractional	fractional	ADJ
ejpam-5861	684	4	derivative	derivative	NOUN
ejpam-5861	684	5	with	with	ADP
ejpam-5861	684	6	an	an	DET
ejpam-5861	684	7	application	application	NOUN
ejpam-5861	684	8	.	.	PUNCT
ejpam-5861	685	1	aims	aim	VERB
ejpam-5861	685	2	mathematics	mathematic	NOUN
ejpam-5861	685	3	,	,	PUNCT
ejpam-5861	685	4	8(10):24345–24366	8(10):24345–24366	NUM
ejpam-5861	685	5	,	,	PUNCT
ejpam-5861	685	6	2023	2023	NUM
ejpam-5861	685	7	.	.	PUNCT
ejpam-5861	686	1	[	[	X
ejpam-5861	686	2	24	24	NUM
ejpam-5861	686	3	]	]	X
ejpam-5861	686	4	s.	s.	PROPN
ejpam-5861	686	5	khan	khan	PROPN
ejpam-5861	686	6	,	,	PUNCT
ejpam-5861	686	7	z.	z.	PROPN
ejpam-5861	686	8	a.	a.	PROPN
ejpam-5861	686	9	khan	khan	PROPN
ejpam-5861	686	10	,	,	PUNCT
ejpam-5861	686	11	h.	h.	PROPN
ejpam-5861	686	12	alrabaiah	alrabaiah	PROPN
ejpam-5861	686	13	,	,	PUNCT
ejpam-5861	686	14	and	and	CCONJ
ejpam-5861	686	15	s.	s.	PROPN
ejpam-5861	686	16	zeb	zeb	PROPN
ejpam-5861	686	17	.	.	PUNCT
ejpam-5861	687	1	on	on	ADP
ejpam-5861	687	2	using	use	VERB
ejpam-5861	687	3	piecewise	piecewise	NOUN
ejpam-5861	687	4	fractional	fractional	ADJ
ejpam-5861	687	5	differential	differential	NOUN
ejpam-5861	687	6	operator	operator	NOUN
ejpam-5861	687	7	to	to	PART
ejpam-5861	687	8	study	study	VERB
ejpam-5861	687	9	a	a	DET
ejpam-5861	687	10	dynamical	dynamical	ADJ
ejpam-5861	687	11	system	system	NOUN
ejpam-5861	687	12	.	.	PUNCT
ejpam-5861	688	1	axioms	axiom	NOUN
ejpam-5861	688	2	,	,	PUNCT
ejpam-5861	688	3	12(3):292	12(3):292	NUM
ejpam-5861	688	4	,	,	PUNCT
ejpam-5861	688	5	2023	2023	NUM
ejpam-5861	688	6	.	.	PUNCT
ejpam-5861	689	1	[	[	X
ejpam-5861	689	2	25	25	NUM
ejpam-5861	689	3	]	]	X
ejpam-5861	689	4	s.	s.	PROPN
ejpam-5861	689	5	khan	khan	PROPN
ejpam-5861	689	6	,	,	PUNCT
ejpam-5861	689	7	k.	k.	PROPN
ejpam-5861	689	8	shah	shah	PROPN
ejpam-5861	689	9	,	,	PUNCT
ejpam-5861	689	10	a.	a.	NOUN
ejpam-5861	689	11	debbouche	debbouche	PROPN
ejpam-5861	689	12	,	,	PUNCT
ejpam-5861	689	13	s.	s.	PROPN
ejpam-5861	689	14	zeb	zeb	PROPN
ejpam-5861	689	15	,	,	PUNCT
ejpam-5861	689	16	and	and	CCONJ
ejpam-5861	689	17	v.	v.	ADP
ejpam-5861	689	18	antonov	antonov	PROPN
ejpam-5861	689	19	.	.	PUNCT
ejpam-5861	689	20	solvability	solvability	NOUN
ejpam-5861	689	21	and	and	CCONJ
ejpam-5861	689	22	ulam	ulam	NOUN
ejpam-5861	689	23	-	-	PUNCT
ejpam-5861	689	24	hyers	hyer	NOUN
ejpam-5861	689	25	stability	stability	NOUN
ejpam-5861	689	26	analysis	analysis	NOUN
ejpam-5861	689	27	for	for	ADP
ejpam-5861	689	28	nonlinear	nonlinear	ADJ
ejpam-5861	689	29	piecewise	piecewise	NOUN
ejpam-5861	689	30	fractional	fractional	ADJ
ejpam-5861	689	31	cancer	cancer	NOUN
ejpam-5861	689	32	dynamic	dynamic	ADJ
ejpam-5861	689	33	systems	system	NOUN
ejpam-5861	689	34	.	.	PUNCT
ejpam-5861	690	1	physica	physica	PROPN
ejpam-5861	690	2	scripta	scripta	PROPN
ejpam-5861	690	3	,	,	PUNCT
ejpam-5861	690	4	99(2):025225	99(2):025225	PROPN
ejpam-5861	690	5	,	,	PUNCT
ejpam-5861	690	6	2024	2024	NUM
ejpam-5861	690	7	.	.	PUNCT
ejpam-5861	691	1	[	[	X
ejpam-5861	691	2	26	26	NUM
ejpam-5861	691	3	]	]	PUNCT
ejpam-5861	691	4	v.	v.	CCONJ
ejpam-5861	691	5	kiryakova	kiryakova	PROPN
ejpam-5861	691	6	.	.	PUNCT
ejpam-5861	692	1	the	the	DET
ejpam-5861	692	2	special	special	ADJ
ejpam-5861	692	3	functions	function	NOUN
ejpam-5861	692	4	of	of	ADP
ejpam-5861	692	5	fractional	fractional	ADJ
ejpam-5861	692	6	calculus	calculus	NOUN
ejpam-5861	692	7	as	as	ADP
ejpam-5861	692	8	generalized	generalized	ADJ
ejpam-5861	692	9	fractional	fractional	ADJ
ejpam-5861	692	10	calculus	calculus	NOUN
ejpam-5861	692	11	operators	operator	NOUN
ejpam-5861	692	12	of	of	ADP
ejpam-5861	692	13	some	some	DET
ejpam-5861	692	14	basic	basic	ADJ
ejpam-5861	692	15	functions	function	NOUN
ejpam-5861	692	16	.	.	PUNCT
ejpam-5861	693	1	computers	computer	NOUN
ejpam-5861	693	2	mathematics	mathematic	NOUN
ejpam-5861	693	3	with	with	ADP
ejpam-5861	693	4	applications	application	NOUN
ejpam-5861	693	5	,	,	PUNCT
ejpam-5861	693	6	59(3):1128–1141	59(3):1128–1141	NUM
ejpam-5861	693	7	,	,	PUNCT
ejpam-5861	693	8	2020	2020	NUM
ejpam-5861	693	9	.	.	PUNCT
ejpam-5861	694	1	[	[	X
ejpam-5861	694	2	27	27	NUM
ejpam-5861	694	3	]	]	X
ejpam-5861	694	4	r.	r.	PROPN
ejpam-5861	694	5	l.	l.	PROPN
ejpam-5861	694	6	magin	magin	PROPN
ejpam-5861	694	7	.	.	PUNCT
ejpam-5861	695	1	fractional	fractional	ADJ
ejpam-5861	695	2	calculus	calculus	NOUN
ejpam-5861	695	3	in	in	ADP
ejpam-5861	695	4	bioengineering	bioengineering	NOUN
ejpam-5861	695	5	:	:	PUNCT
ejpam-5861	695	6	a	a	DET
ejpam-5861	695	7	tool	tool	NOUN
ejpam-5861	695	8	to	to	PART
ejpam-5861	695	9	model	model	VERB
ejpam-5861	695	10	complex	complex	ADJ
ejpam-5861	695	11	dynamics	dynamic	NOUN
ejpam-5861	695	12	.	.	PUNCT
ejpam-5861	696	1	in	in	ADP
ejpam-5861	696	2	proceedings	proceeding	NOUN
ejpam-5861	696	3	of	of	ADP
ejpam-5861	696	4	the	the	DET
ejpam-5861	696	5	13th	13th	ADJ
ejpam-5861	696	6	international	international	ADJ
ejpam-5861	696	7	carpathian	carpathian	PROPN
ejpam-5861	696	8	control	control	PROPN
ejpam-5861	696	9	conference	conference	PROPN
ejpam-5861	696	10	(	(	PUNCT
ejpam-5861	696	11	iccc	iccc	PROPN
ejpam-5861	696	12	)	)	PUNCT
ejpam-5861	696	13	,	,	PUNCT
ejpam-5861	696	14	pages	page	VERB
ejpam-5861	696	15	464–469	464–469	NUM
ejpam-5861	696	16	.	.	PUNCT
ejpam-5861	696	17	ieee	ieee	PROPN
ejpam-5861	696	18	,	,	PUNCT
ejpam-5861	696	19	2012	2012	NUM
ejpam-5861	696	20	.	.	PUNCT
ejpam-5861	697	1	[	[	X
ejpam-5861	697	2	28	28	NUM
ejpam-5861	697	3	]	]	X
ejpam-5861	697	4	m.	m.	NOUN
ejpam-5861	697	5	meerschaert	meerschaert	NOUN
ejpam-5861	697	6	.	.	PUNCT
ejpam-5861	698	1	mathematical	mathematical	ADJ
ejpam-5861	698	2	modeling	modeling	NOUN
ejpam-5861	698	3	.	.	PUNCT
ejpam-5861	699	1	academic	academic	ADJ
ejpam-5861	699	2	press	press	NOUN
ejpam-5861	699	3	,	,	PUNCT
ejpam-5861	699	4	new	new	PROPN
ejpam-5861	699	5	york	york	PROPN
ejpam-5861	699	6	,	,	PUNCT
ejpam-5861	699	7	2013	2013	NUM
ejpam-5861	699	8	.	.	PUNCT
ejpam-5861	700	1	[	[	X
ejpam-5861	700	2	29	29	NUM
ejpam-5861	700	3	]	]	X
ejpam-5861	700	4	c.	c.	PROPN
ejpam-5861	700	5	photphanloet	photphanloet	PROPN
ejpam-5861	700	6	,	,	PUNCT
ejpam-5861	700	7	s.	s.	PROPN
ejpam-5861	700	8	ritraksa	ritraksa	PROPN
ejpam-5861	700	9	,	,	PUNCT
ejpam-5861	700	10	s.	s.	PROPN
ejpam-5861	700	11	e.	e.	PROPN
ejpam-5861	700	12	shuaib	shuaib	PROPN
ejpam-5861	700	13	,	,	PUNCT
ejpam-5861	700	14	a.	a.	NOUN
ejpam-5861	700	15	intarasit	intarasit	NOUN
ejpam-5861	700	16	,	,	PUNCT
ejpam-5861	700	17	and	and	CCONJ
ejpam-5861	700	18	p.	p.	PROPN
ejpam-5861	700	19	riyapan	riyapan	PROPN
ejpam-5861	700	20	.	.	PUNCT
ejpam-5861	701	1	a	a	DET
ejpam-5861	701	2	compartmental	compartmental	ADJ
ejpam-5861	701	3	model	model	NOUN
ejpam-5861	701	4	for	for	ADP
ejpam-5861	701	5	assessing	assess	VERB
ejpam-5861	701	6	effects	effect	NOUN
ejpam-5861	701	7	of	of	ADP
ejpam-5861	701	8	covid-19	covid-19	PROPN
ejpam-5861	701	9	vaccination	vaccination	NOUN
ejpam-5861	701	10	in	in	ADP
ejpam-5861	701	11	thailand	thailand	PROPN
ejpam-5861	701	12	.	.	PUNCT
ejpam-5861	702	1	universal	universal	ADJ
ejpam-5861	702	2	journal	journal	PROPN
ejpam-5861	702	3	of	of	ADP
ejpam-5861	702	4	public	public	ADJ
ejpam-5861	702	5	health	health	NOUN
ejpam-5861	702	6	,	,	PUNCT
ejpam-5861	702	7	10(6):596–605	10(6):596–605	PROPN
ejpam-5861	702	8	,	,	PUNCT
ejpam-5861	702	9	2022	2022	NUM
ejpam-5861	702	10	.	.	PUNCT
ejpam-5861	703	1	[	[	X
ejpam-5861	703	2	30	30	NUM
ejpam-5861	703	3	]	]	PUNCT
ejpam-5861	703	4	s.	s.	PROPN
ejpam-5861	703	5	s.	s.	PROPN
ejpam-5861	703	6	redhwan	redhwan	PROPN
ejpam-5861	703	7	,	,	PUNCT
ejpam-5861	703	8	m.	m.	PROPN
ejpam-5861	703	9	han	han	PROPN
ejpam-5861	703	10	,	,	PUNCT
ejpam-5861	703	11	m.	m.	NOUN
ejpam-5861	703	12	a.	a.	NOUN
ejpam-5861	703	13	almalahi	almalahi	PROPN
ejpam-5861	703	14	,	,	PUNCT
ejpam-5861	703	15	m.	m.	NOUN
ejpam-5861	703	16	a.	a.	NOUN
ejpam-5861	703	17	alyami	alyami	PROPN
ejpam-5861	703	18	,	,	PUNCT
ejpam-5861	703	19	m.	m.	NOUN
ejpam-5861	703	20	alsulami	alsulami	NOUN
ejpam-5861	703	21	,	,	PUNCT
ejpam-5861	703	22	and	and	CCONJ
ejpam-5861	703	23	n.	n.	NOUN
ejpam-5861	703	24	alghamdi	alghamdi	NOUN
ejpam-5861	703	25	.	.	PUNCT
ejpam-5861	704	1	piecewise	piecewise	NOUN
ejpam-5861	704	2	implicit	implicit	ADJ
ejpam-5861	704	3	coupled	couple	VERB
ejpam-5861	704	4	system	system	NOUN
ejpam-5861	704	5	under	under	ADP
ejpam-5861	704	6	abc	abc	PROPN
ejpam-5861	704	7	fractional	fractional	PROPN
ejpam-5861	704	8	differential	differential	NOUN
ejpam-5861	704	9	equations	equation	NOUN
ejpam-5861	704	10	with	with	ADP
ejpam-5861	704	11	variable	variable	ADJ
ejpam-5861	704	12	order	order	NOUN
ejpam-5861	704	13	.	.	PUNCT
ejpam-5861	705	1	aims	aim	VERB
ejpam-5861	705	2	mathematics	mathematic	NOUN
ejpam-5861	705	3	,	,	PUNCT
ejpam-5861	705	4	9(6):15303–15324	9(6):15303–15324	NUM
ejpam-5861	705	5	,	,	PUNCT
ejpam-5861	705	6	2024	2024	NUM
ejpam-5861	705	7	.	.	PUNCT
ejpam-5861	706	1	[	[	X
ejpam-5861	706	2	31	31	NUM
ejpam-5861	706	3	]	]	PUNCT
ejpam-5861	706	4	m.	m.	NOUN
ejpam-5861	706	5	roccetti	roccetti	NOUN
ejpam-5861	706	6	.	.	PUNCT
ejpam-5861	707	1	drawing	draw	VERB
ejpam-5861	707	2	a	a	DET
ejpam-5861	707	3	parallel	parallel	NOUN
ejpam-5861	707	4	between	between	ADP
ejpam-5861	707	5	the	the	DET
ejpam-5861	707	6	trend	trend	NOUN
ejpam-5861	707	7	of	of	ADP
ejpam-5861	707	8	confirmed	confirm	VERB
ejpam-5861	707	9	covid-19	covid-19	PROPN
ejpam-5861	707	10	deaths	death	NOUN
ejpam-5861	707	11	in	in	ADP
ejpam-5861	707	12	the	the	DET
ejpam-5861	707	13	winters	winter	NOUN
ejpam-5861	707	14	of	of	ADP
ejpam-5861	707	15	2022/2023	2022/2023	NUM
ejpam-5861	707	16	and	and	CCONJ
ejpam-5861	707	17	2023/2024	2023/2024	NUM
ejpam-5861	707	18	in	in	ADP
ejpam-5861	707	19	italy	italy	PROPN
ejpam-5861	707	20	,	,	PUNCT
ejpam-5861	707	21	with	with	ADP
ejpam-5861	707	22	a	a	DET
ejpam-5861	707	23	prediction	prediction	NOUN
ejpam-5861	707	24	.	.	PUNCT
ejpam-5861	708	1	mathematical	mathematical	ADJ
ejpam-5861	708	2	biosciences	bioscience	NOUN
ejpam-5861	708	3	and	and	CCONJ
ejpam-5861	708	4	engineering	engineering	NOUN
ejpam-5861	708	5	,	,	PUNCT
ejpam-5861	708	6	21(3):3742–3754	21(3):3742–3754	NUM
ejpam-5861	708	7	,	,	PUNCT
ejpam-5861	708	8	2024	2024	NUM
ejpam-5861	708	9	.	.	PUNCT
ejpam-5861	709	1	[	[	X
ejpam-5861	709	2	32	32	NUM
ejpam-5861	709	3	]	]	PUNCT
ejpam-5861	709	4	b.	b.	PROPN
ejpam-5861	709	5	ross	ross	PROPN
ejpam-5861	709	6	.	.	PUNCT
ejpam-5861	710	1	a	a	DET
ejpam-5861	710	2	brief	brief	ADJ
ejpam-5861	710	3	history	history	NOUN
ejpam-5861	710	4	and	and	CCONJ
ejpam-5861	710	5	exposition	exposition	NOUN
ejpam-5861	710	6	of	of	ADP
ejpam-5861	710	7	the	the	DET
ejpam-5861	710	8	fundamental	fundamental	ADJ
ejpam-5861	710	9	theory	theory	NOUN
ejpam-5861	710	10	of	of	ADP
ejpam-5861	710	11	fractional	fractional	ADJ
ejpam-5861	710	12	calculus	calculus	NOUN
ejpam-5861	710	13	.	.	PUNCT
ejpam-5861	711	1	in	in	ADP
ejpam-5861	711	2	fractional	fractional	ADJ
ejpam-5861	711	3	calculus	calculus	NOUN
ejpam-5861	711	4	and	and	CCONJ
ejpam-5861	711	5	its	its	PRON
ejpam-5861	711	6	applications	application	NOUN
ejpam-5861	711	7	.	.	PUNCT
ejpam-5861	712	1	springer	springer	NOUN
ejpam-5861	712	2	,	,	PUNCT
ejpam-5861	712	3	berlin	berlin	PROPN
ejpam-5861	712	4	,	,	PUNCT
ejpam-5861	712	5	1975	1975	NUM
ejpam-5861	712	6	.	.	PUNCT
ejpam-5861	713	1	[	[	X
ejpam-5861	713	2	33	33	NUM
ejpam-5861	713	3	]	]	PUNCT
ejpam-5861	713	4	i.	i.	PROPN
ejpam-5861	713	5	a.	a.	PROPN
ejpam-5861	713	6	rus	rus	PROPN
ejpam-5861	713	7	.	.	PUNCT
ejpam-5861	714	1	ulam	ulam	PROPN
ejpam-5861	714	2	stability	stability	NOUN
ejpam-5861	714	3	of	of	ADP
ejpam-5861	714	4	the	the	DET
ejpam-5861	714	5	operatorial	operatorial	ADJ
ejpam-5861	714	6	equations	equation	NOUN
ejpam-5861	714	7	.	.	PUNCT
ejpam-5861	715	1	springer	springer	NOUN
ejpam-5861	715	2	,	,	PUNCT
ejpam-5861	715	3	new	new	PROPN
ejpam-5861	715	4	york	york	PROPN
ejpam-5861	715	5	,	,	PUNCT
ejpam-5861	715	6	2011	2011	NUM
ejpam-5861	715	7	.	.	PUNCT
ejpam-5861	716	1	[	[	X
ejpam-5861	716	2	34	34	NUM
ejpam-5861	716	3	]	]	X
ejpam-5861	716	4	m.	m.	NOUN
ejpam-5861	716	5	a.	a.	PROPN
ejpam-5861	716	6	sanchez	sanchez	PROPN
ejpam-5861	716	7	and	and	CCONJ
ejpam-5861	716	8	s.	s.	PROPN
ejpam-5861	716	9	m.	m.	PROPN
ejpam-5861	716	10	blower	blower	NOUN
ejpam-5861	716	11	.	.	PUNCT
ejpam-5861	717	1	uncertainty	uncertainty	NOUN
ejpam-5861	717	2	and	and	CCONJ
ejpam-5861	717	3	sensitivity	sensitivity	NOUN
ejpam-5861	717	4	analysis	analysis	NOUN
ejpam-5861	717	5	of	of	ADP
ejpam-5861	717	6	the	the	DET
ejpam-5861	717	7	basic	basic	ADJ
ejpam-5861	717	8	reproductive	reproductive	ADJ
ejpam-5861	717	9	rate	rate	NOUN
ejpam-5861	717	10	:	:	PUNCT
ejpam-5861	717	11	tuberculosis	tuberculosis	NOUN
ejpam-5861	717	12	as	as	ADP
ejpam-5861	717	13	an	an	DET
ejpam-5861	717	14	example	example	NOUN
ejpam-5861	717	15	.	.	PUNCT
ejpam-5861	718	1	american	american	ADJ
ejpam-5861	718	2	journal	journal	PROPN
ejpam-5861	718	3	of	of	ADP
ejpam-5861	718	4	epidemiology	epidemiology	NOUN
ejpam-5861	718	5	,	,	PUNCT
ejpam-5861	718	6	145(12):1127–1137	145(12):1127–1137	NUM
ejpam-5861	718	7	,	,	PUNCT
ejpam-5861	718	8	1997	1997	NUM
ejpam-5861	718	9	.	.	PUNCT
ejpam-5861	719	1	[	[	X
ejpam-5861	719	2	35	35	NUM
ejpam-5861	719	3	]	]	X
ejpam-5861	719	4	f.	f.	PROPN
ejpam-5861	719	5	schaffner	schaffner	PROPN
ejpam-5861	719	6	and	and	CCONJ
ejpam-5861	719	7	a.	a.	PROPN
ejpam-5861	719	8	mathis	mathis	PROPN
ejpam-5861	719	9	.	.	PUNCT
ejpam-5861	720	1	dengue	dengue	PROPN
ejpam-5861	720	2	and	and	CCONJ
ejpam-5861	720	3	dengue	dengue	NOUN
ejpam-5861	720	4	vectors	vector	NOUN
ejpam-5861	720	5	in	in	ADP
ejpam-5861	720	6	the	the	DET
ejpam-5861	720	7	who	who	PRON
ejpam-5861	720	8	european	european	PROPN
ejpam-5861	720	9	region	region	NOUN
ejpam-5861	720	10	:	:	PUNCT
ejpam-5861	720	11	past	past	ADJ
ejpam-5861	720	12	,	,	PUNCT
ejpam-5861	720	13	present	present	ADJ
ejpam-5861	720	14	,	,	PUNCT
ejpam-5861	720	15	and	and	CCONJ
ejpam-5861	720	16	scenarios	scenario	NOUN
ejpam-5861	720	17	for	for	ADP
ejpam-5861	720	18	the	the	DET
ejpam-5861	720	19	future	future	NOUN
ejpam-5861	720	20	.	.	PUNCT
ejpam-5861	721	1	the	the	DET
ejpam-5861	721	2	lancet	lancet	ADJ
ejpam-5861	721	3	infectious	infectious	ADJ
ejpam-5861	721	4	diseases	disease	NOUN
ejpam-5861	721	5	,	,	PUNCT
ejpam-5861	721	6	14(12):1271–1280	14(12):1271–1280	NUM
ejpam-5861	721	7	,	,	PUNCT
ejpam-5861	721	8	2014	2014	NUM
ejpam-5861	721	9	.	.	PUNCT
ejpam-5861	722	1	[	[	X
ejpam-5861	722	2	36	36	NUM
ejpam-5861	722	3	]	]	PUNCT
ejpam-5861	722	4	k.	k.	PROPN
ejpam-5861	722	5	shah	shah	PROPN
ejpam-5861	722	6	,	,	PUNCT
ejpam-5861	722	7	t.	t.	NOUN
ejpam-5861	722	8	abdeljawad	abdeljawad	NOUN
ejpam-5861	722	9	,	,	PUNCT
ejpam-5861	722	10	and	and	CCONJ
ejpam-5861	722	11	a.	a.	PROPN
ejpam-5861	722	12	ali	ali	PROPN
ejpam-5861	722	13	.	.	PROPN
ejpam-5861	723	1	mathematical	mathematical	ADJ
ejpam-5861	723	2	analysis	analysis	NOUN
ejpam-5861	723	3	of	of	ADP
ejpam-5861	723	4	the	the	DET
ejpam-5861	723	5	cauchy	cauchy	ADJ
ejpam-5861	723	6	type	type	NOUN
ejpam-5861	723	7	s.	s.	PROPN
ejpam-5861	723	8	naz	naz	PROPN
ejpam-5861	723	9	et	et	PROPN
ejpam-5861	723	10	al	al	PROPN
ejpam-5861	723	11	.	.	PUNCT
ejpam-5861	723	12	/	/	SYM
ejpam-5861	723	13	eur	eur	PROPN
ejpam-5861	723	14	.	.	PUNCT
ejpam-5861	724	1	j.	j.	PROPN
ejpam-5861	724	2	pure	pure	PROPN
ejpam-5861	724	3	appl	appl	PROPN
ejpam-5861	724	4	.	.	PROPN
ejpam-5861	724	5	math	math	PROPN
ejpam-5861	724	6	,	,	PUNCT
ejpam-5861	724	7	18	18	NUM
ejpam-5861	724	8	(	(	PUNCT
ejpam-5861	724	9	2	2	NUM
ejpam-5861	724	10	)	)	PUNCT
ejpam-5861	724	11	(	(	PUNCT
ejpam-5861	724	12	2025	2025	NUM
ejpam-5861	724	13	)	)	PUNCT
ejpam-5861	724	14	,	,	PUNCT
ejpam-5861	724	15	5861	5861	NUM
ejpam-5861	724	16	33	33	NUM
ejpam-5861	724	17	of	of	ADP
ejpam-5861	724	18	33	33	NUM
ejpam-5861	724	19	dynamical	dynamical	ADJ
ejpam-5861	724	20	system	system	NOUN
ejpam-5861	724	21	under	under	ADP
ejpam-5861	724	22	piecewise	piecewise	NOUN
ejpam-5861	724	23	equations	equation	NOUN
ejpam-5861	724	24	with	with	ADP
ejpam-5861	724	25	caputo	caputo	PROPN
ejpam-5861	724	26	fractional	fractional	PROPN
ejpam-5861	724	27	derivative	derivative	PROPN
ejpam-5861	724	28	.	.	PUNCT
ejpam-5861	725	1	chaos	chaos	NOUN
ejpam-5861	725	2	,	,	PUNCT
ejpam-5861	725	3	solitons	soliton	NOUN
ejpam-5861	725	4	fractals	fractal	NOUN
ejpam-5861	725	5	,	,	PUNCT
ejpam-5861	725	6	161:112356	161:112356	NUM
ejpam-5861	725	7	,	,	PUNCT
ejpam-5861	725	8	2022	2022	NUM
ejpam-5861	725	9	.	.	PUNCT
ejpam-5861	726	1	[	[	X
ejpam-5861	726	2	37	37	NUM
ejpam-5861	726	3	]	]	PUNCT
ejpam-5861	726	4	k.	k.	PROPN
ejpam-5861	726	5	shah	shah	PROPN
ejpam-5861	726	6	,	,	PUNCT
ejpam-5861	726	7	a.	a.	PROPN
ejpam-5861	726	8	khan	khan	PROPN
ejpam-5861	726	9	,	,	PUNCT
ejpam-5861	726	10	b.	b.	PROPN
ejpam-5861	726	11	abdalla	abdalla	PROPN
ejpam-5861	726	12	,	,	PUNCT
ejpam-5861	726	13	t.	t.	NOUN
ejpam-5861	726	14	abdeljawad	abdeljawad	NOUN
ejpam-5861	726	15	,	,	PUNCT
ejpam-5861	726	16	and	and	CCONJ
ejpam-5861	726	17	k.	k.	PROPN
ejpam-5861	726	18	a.	a.	PROPN
ejpam-5861	726	19	khan	khan	PROPN
ejpam-5861	726	20	.	.	PUNCT
ejpam-5861	727	1	a	a	DET
ejpam-5861	727	2	mathematical	mathematical	ADJ
ejpam-5861	727	3	model	model	NOUN
ejpam-5861	727	4	for	for	ADP
ejpam-5861	727	5	nipah	nipah	NOUN
ejpam-5861	727	6	virus	virus	NOUN
ejpam-5861	727	7	disease	disease	NOUN
ejpam-5861	727	8	by	by	ADP
ejpam-5861	727	9	using	use	VERB
ejpam-5861	727	10	piecewise	piecewise	NOUN
ejpam-5861	727	11	fractional	fractional	ADJ
ejpam-5861	727	12	order	order	NOUN
ejpam-5861	727	13	caputo	caputo	PROPN
ejpam-5861	727	14	derivative	derivative	PROPN
ejpam-5861	727	15	.	.	PUNCT
ejpam-5861	728	1	fractals	fractal	NOUN
ejpam-5861	728	2	,	,	PUNCT
ejpam-5861	728	3	32(02):2440013	32(02):2440013	NUM
ejpam-5861	728	4	,	,	PUNCT
ejpam-5861	728	5	2024	2024	NUM
ejpam-5861	728	6	.	.	PUNCT
ejpam-5861	729	1	[	[	X
ejpam-5861	729	2	38	38	NUM
ejpam-5861	729	3	]	]	PUNCT
ejpam-5861	729	4	k.	k.	PROPN
ejpam-5861	729	5	shah	shah	PROPN
ejpam-5861	729	6	,	,	PUNCT
ejpam-5861	729	7	a.	a.	PROPN
ejpam-5861	729	8	khan	khan	PROPN
ejpam-5861	729	9	,	,	PUNCT
ejpam-5861	729	10	b.	b.	PROPN
ejpam-5861	729	11	abdalla	abdalla	PROPN
ejpam-5861	729	12	,	,	PUNCT
ejpam-5861	729	13	t.	t.	NOUN
ejpam-5861	729	14	abdeljawad	abdeljawad	NOUN
ejpam-5861	729	15	,	,	PUNCT
ejpam-5861	729	16	and	and	CCONJ
ejpam-5861	729	17	k.	k.	PROPN
ejpam-5861	729	18	a.	a.	PROPN
ejpam-5861	729	19	khan	khan	PROPN
ejpam-5861	729	20	.	.	PUNCT
ejpam-5861	730	1	a	a	DET
ejpam-5861	730	2	mathematical	mathematical	ADJ
ejpam-5861	730	3	model	model	NOUN
ejpam-5861	730	4	for	for	ADP
ejpam-5861	730	5	nipah	nipah	NOUN
ejpam-5861	730	6	virus	virus	NOUN
ejpam-5861	730	7	disease	disease	NOUN
ejpam-5861	730	8	by	by	ADP
ejpam-5861	730	9	using	use	VERB
ejpam-5861	730	10	piecewise	piecewise	NOUN
ejpam-5861	730	11	fractional	fractional	ADJ
ejpam-5861	730	12	order	order	NOUN
ejpam-5861	730	13	caputo	caputo	PROPN
ejpam-5861	730	14	derivative	derivative	PROPN
ejpam-5861	730	15	.	.	PUNCT
ejpam-5861	731	1	fractals	fractal	NOUN
ejpam-5861	731	2	,	,	PUNCT
ejpam-5861	731	3	32(2):2440013	32(2):2440013	NUM
ejpam-5861	731	4	,	,	PUNCT
ejpam-5861	731	5	2024	2024	NUM
ejpam-5861	731	6	.	.	PUNCT
ejpam-5861	732	1	[	[	X
ejpam-5861	732	2	39	39	NUM
ejpam-5861	732	3	]	]	PUNCT
ejpam-5861	732	4	k.	k.	PROPN
ejpam-5861	732	5	shah	shah	PROPN
ejpam-5861	732	6	,	,	PUNCT
ejpam-5861	732	7	p.	p.	PROPN
ejpam-5861	732	8	kumam	kumam	PROPN
ejpam-5861	732	9	,	,	PUNCT
ejpam-5861	732	10	and	and	CCONJ
ejpam-5861	732	11	i.	i.	PROPN
ejpam-5861	732	12	ullah	ullah	PROPN
ejpam-5861	732	13	.	.	PUNCT
ejpam-5861	733	1	on	on	ADP
ejpam-5861	733	2	ulam	ulam	PROPN
ejpam-5861	733	3	stability	stability	PROPN
ejpam-5861	733	4	and	and	CCONJ
ejpam-5861	733	5	multiplicity	multiplicity	NOUN
ejpam-5861	733	6	results	result	NOUN
ejpam-5861	733	7	to	to	ADP
ejpam-5861	733	8	a	a	DET
ejpam-5861	733	9	nonlinear	nonlinear	ADJ
ejpam-5861	733	10	coupled	couple	VERB
ejpam-5861	733	11	system	system	NOUN
ejpam-5861	733	12	with	with	ADP
ejpam-5861	733	13	integral	integral	ADJ
ejpam-5861	733	14	boundary	boundary	ADJ
ejpam-5861	733	15	conditions	condition	NOUN
ejpam-5861	733	16	.	.	PUNCT
ejpam-5861	734	1	mathematics	mathematic	NOUN
ejpam-5861	734	2	,	,	PUNCT
ejpam-5861	734	3	7(3):223	7(3):223	NUM
ejpam-5861	734	4	,	,	PUNCT
ejpam-5861	734	5	2019	2019	NUM
ejpam-5861	734	6	.	.	PUNCT
ejpam-5861	735	1	[	[	X
ejpam-5861	735	2	40	40	NUM
ejpam-5861	735	3	]	]	PUNCT
ejpam-5861	735	4	k.	k.	PROPN
ejpam-5861	735	5	shah	shah	PROPN
ejpam-5861	735	6	,	,	PUNCT
ejpam-5861	735	7	h.	h.	PROPN
ejpam-5861	735	8	naz	naz	PROPN
ejpam-5861	735	9	,	,	PUNCT
ejpam-5861	735	10	t.	t.	NOUN
ejpam-5861	735	11	abdeljawad	abdeljawad	NOUN
ejpam-5861	735	12	,	,	PUNCT
ejpam-5861	735	13	and	and	CCONJ
ejpam-5861	735	14	b.	b.	PROPN
ejpam-5861	735	15	abdalla	abdalla	PROPN
ejpam-5861	735	16	.	.	PUNCT
ejpam-5861	736	1	study	study	NOUN
ejpam-5861	736	2	of	of	ADP
ejpam-5861	736	3	fractional	fractional	ADJ
ejpam-5861	736	4	order	order	NOUN
ejpam-5861	736	5	dynamical	dynamical	ADJ
ejpam-5861	736	6	system	system	NOUN
ejpam-5861	736	7	of	of	ADP
ejpam-5861	736	8	viral	viral	ADJ
ejpam-5861	736	9	infection	infection	NOUN
ejpam-5861	736	10	disease	disease	NOUN
ejpam-5861	736	11	under	under	ADP
ejpam-5861	736	12	piecewise	piecewise	NOUN
ejpam-5861	736	13	derivative	derivative	NOUN
ejpam-5861	736	14	.	.	PUNCT
ejpam-5861	737	1	cmes	cmes	PROPN
ejpam-5861	737	2	-	-	PUNCT
ejpam-5861	737	3	computer	computer	NOUN
ejpam-5861	737	4	modeling	modeling	NOUN
ejpam-5861	737	5	in	in	ADP
ejpam-5861	737	6	engineering	engineering	NOUN
ejpam-5861	737	7	sciences	science	NOUN
ejpam-5861	737	8	,	,	PUNCT
ejpam-5861	737	9	136(1):921–941	136(1):921–941	NUM
ejpam-5861	737	10	,	,	PUNCT
ejpam-5861	737	11	2023	2023	NUM
ejpam-5861	737	12	.	.	PUNCT
ejpam-5861	738	1	[	[	X
ejpam-5861	738	2	41	41	NUM
ejpam-5861	738	3	]	]	X
ejpam-5861	738	4	n.	n.	PROPN
ejpam-5861	738	5	h.	h.	PROPN
ejpam-5861	738	6	tuan	tuan	PROPN
ejpam-5861	738	7	,	,	PUNCT
ejpam-5861	738	8	h.	h.	PROPN
ejpam-5861	738	9	mohammadi	mohammadi	PROPN
ejpam-5861	738	10	,	,	PUNCT
ejpam-5861	738	11	and	and	CCONJ
ejpam-5861	738	12	s.	s.	PROPN
ejpam-5861	738	13	rezapour	rezapour	PROPN
ejpam-5861	738	14	.	.	PUNCT
ejpam-5861	739	1	a	a	DET
ejpam-5861	739	2	mathematical	mathematical	ADJ
ejpam-5861	739	3	model	model	NOUN
ejpam-5861	739	4	for	for	ADP
ejpam-5861	739	5	covid-19	covid-19	PROPN
ejpam-5861	739	6	transmission	transmission	NOUN
ejpam-5861	739	7	by	by	ADP
ejpam-5861	739	8	using	use	VERB
ejpam-5861	739	9	the	the	DET
ejpam-5861	739	10	caputo	caputo	PROPN
ejpam-5861	739	11	fractional	fractional	PROPN
ejpam-5861	739	12	derivative	derivative	PROPN
ejpam-5861	739	13	.	.	PUNCT
ejpam-5861	740	1	chaos	chaos	NOUN
ejpam-5861	740	2	,	,	PUNCT
ejpam-5861	740	3	solitons	soliton	NOUN
ejpam-5861	740	4	fractals	fractal	NOUN
ejpam-5861	740	5	,	,	PUNCT
ejpam-5861	740	6	140:110107	140:110107	NUM
ejpam-5861	740	7	,	,	PUNCT
ejpam-5861	740	8	2020	2020	NUM
ejpam-5861	740	9	.	.	PUNCT
ejpam-5861	741	1	[	[	X
ejpam-5861	741	2	42	42	NUM
ejpam-5861	741	3	]	]	X
ejpam-5861	741	4	v.	v.	PROPN
ejpam-5861	741	5	v.	v.	ADP
ejpam-5861	741	6	uchaikin	uchaikin	PROPN
ejpam-5861	741	7	.	.	PUNCT
ejpam-5861	742	1	fractional	fractional	ADJ
ejpam-5861	742	2	derivatives	derivative	NOUN
ejpam-5861	742	3	for	for	ADP
ejpam-5861	742	4	physicists	physicist	NOUN
ejpam-5861	742	5	and	and	CCONJ
ejpam-5861	742	6	engineers	engineer	NOUN
ejpam-5861	742	7	,	,	PUNCT
ejpam-5861	742	8	volume	volume	NOUN
ejpam-5861	742	9	2	2	NUM
ejpam-5861	742	10	.	.	PUNCT
ejpam-5861	742	11	springer	springer	NOUN
ejpam-5861	742	12	,	,	PUNCT
ejpam-5861	742	13	berlin	berlin	PROPN
ejpam-5861	742	14	,	,	PUNCT
ejpam-5861	742	15	2013	2013	NUM
ejpam-5861	742	16	.	.	PUNCT
ejpam-5861	743	1	[	[	X
ejpam-5861	743	2	43	43	NUM
ejpam-5861	743	3	]	]	X
ejpam-5861	743	4	c.	c.	PROPN
ejpam-5861	743	5	vargas	vargas	PROPN
ejpam-5861	743	6	-	-	PUNCT
ejpam-5861	743	7	de	de	NOUN
ejpam-5861	743	8	-	-	NOUN
ejpam-5861	743	9	león	león	PROPN
ejpam-5861	743	10	.	.	PUNCT
ejpam-5861	743	11	volterra	volterra	NOUN
ejpam-5861	743	12	-	-	PUNCT
ejpam-5861	743	13	type	type	NOUN
ejpam-5861	743	14	lyapunov	lyapunov	NOUN
ejpam-5861	743	15	functions	function	NOUN
ejpam-5861	743	16	for	for	ADP
ejpam-5861	743	17	fractional	fractional	ADJ
ejpam-5861	743	18	-	-	PUNCT
ejpam-5861	743	19	order	order	NOUN
ejpam-5861	743	20	epidemic	epidemic	NOUN
ejpam-5861	743	21	systems	system	NOUN
ejpam-5861	743	22	.	.	PUNCT
ejpam-5861	744	1	communications	communication	NOUN
ejpam-5861	744	2	in	in	ADP
ejpam-5861	744	3	nonlinear	nonlinear	ADJ
ejpam-5861	744	4	science	science	NOUN
ejpam-5861	744	5	and	and	CCONJ
ejpam-5861	744	6	numerical	numerical	PROPN
ejpam-5861	744	7	simulation	simulation	PROPN
ejpam-5861	744	8	,	,	PUNCT
ejpam-5861	744	9	24(13):75–85	24(13):75–85	NUM
ejpam-5861	744	10	,	,	PUNCT
ejpam-5861	744	11	2015	2015	NUM
ejpam-5861	744	12	.	.	PUNCT
ejpam-5861	745	1	[	[	X
ejpam-5861	745	2	44	44	NUM
ejpam-5861	745	3	]	]	PUNCT
ejpam-5861	745	4	j.	j.	PROPN
ejpam-5861	745	5	t.	t.	PROPN
ejpam-5861	745	6	wu	wu	PROPN
ejpam-5861	745	7	,	,	PUNCT
ejpam-5861	745	8	k.	k.	PROPN
ejpam-5861	745	9	leung	leung	PROPN
ejpam-5861	745	10	,	,	PUNCT
ejpam-5861	745	11	and	and	CCONJ
ejpam-5861	745	12	g.	g.	PROPN
ejpam-5861	745	13	m.	m.	PROPN
ejpam-5861	745	14	leung	leung	PROPN
ejpam-5861	745	15	.	.	PUNCT
ejpam-5861	746	1	nowcasting	nowcaste	VERB
ejpam-5861	746	2	and	and	CCONJ
ejpam-5861	746	3	forecasting	forecast	VERB
ejpam-5861	746	4	the	the	DET
ejpam-5861	746	5	potential	potential	ADJ
ejpam-5861	746	6	domestic	domestic	ADJ
ejpam-5861	746	7	and	and	CCONJ
ejpam-5861	746	8	international	international	ADJ
ejpam-5861	746	9	spread	spread	NOUN
ejpam-5861	746	10	of	of	ADP
ejpam-5861	746	11	the	the	DET
ejpam-5861	746	12	2019	2019	NUM
ejpam-5861	746	13	-	-	PUNCT
ejpam-5861	746	14	ncov	ncov	NOUN
ejpam-5861	746	15	outbreak	outbreak	NOUN
ejpam-5861	746	16	originating	originate	VERB
ejpam-5861	746	17	in	in	ADP
ejpam-5861	746	18	wuhan	wuhan	PROPN
ejpam-5861	746	19	,	,	PUNCT
ejpam-5861	746	20	china	china	PROPN
ejpam-5861	746	21	:	:	PUNCT
ejpam-5861	746	22	a	a	DET
ejpam-5861	746	23	modelling	model	VERB
ejpam-5861	746	24	study	study	NOUN
ejpam-5861	746	25	.	.	PUNCT
ejpam-5861	747	1	the	the	DET
ejpam-5861	747	2	lancet	lancet	NOUN
ejpam-5861	747	3	,	,	PUNCT
ejpam-5861	747	4	395(10225):689–697	395(10225):689–697	NUM
ejpam-5861	747	5	,	,	PUNCT
ejpam-5861	747	6	2020	2020	NUM
ejpam-5861	747	7	.	.	PUNCT
ejpam-5861	748	1	[	[	X
ejpam-5861	748	2	45	45	NUM
ejpam-5861	748	3	]	]	PUNCT
ejpam-5861	748	4	a.	a.	NOUN
ejpam-5861	748	5	zeb	zeb	PROPN
ejpam-5861	748	6	,	,	PUNCT
ejpam-5861	748	7	a.	a.	PROPN
ejpam-5861	748	8	atangana	atangana	PROPN
ejpam-5861	748	9	,	,	PUNCT
ejpam-5861	748	10	z.	z.	PROPN
ejpam-5861	748	11	a.	a.	PROPN
ejpam-5861	748	12	khan	khan	PROPN
ejpam-5861	748	13	,	,	PUNCT
ejpam-5861	748	14	and	and	CCONJ
ejpam-5861	748	15	s.	s.	PROPN
ejpam-5861	748	16	djillali	djillali	PROPN
ejpam-5861	748	17	.	.	PUNCT
ejpam-5861	749	1	a	a	DET
ejpam-5861	749	2	robust	robust	ADJ
ejpam-5861	749	3	study	study	NOUN
ejpam-5861	749	4	of	of	ADP
ejpam-5861	749	5	a	a	DET
ejpam-5861	749	6	piecewise	piecewise	NOUN
ejpam-5861	749	7	fractional	fractional	ADJ
ejpam-5861	749	8	order	order	NOUN
ejpam-5861	749	9	covid-19	covid-19	PROPN
ejpam-5861	749	10	mathematical	mathematical	ADJ
ejpam-5861	749	11	model	model	NOUN
ejpam-5861	749	12	.	.	PUNCT
ejpam-5861	750	1	alexandria	alexandria	PROPN
ejpam-5861	750	2	engineering	engineering	PROPN
ejpam-5861	750	3	journal	journal	PROPN
ejpam-5861	750	4	,	,	PUNCT
ejpam-5861	750	5	61(7):5649–5665	61(7):5649–5665	NUM
ejpam-5861	750	6	,	,	PUNCT
ejpam-5861	750	7	2022	2022	NUM
ejpam-5861	750	8	.	.	PUNCT
ejpam-5861	751	1	[	[	X
ejpam-5861	751	2	46	46	NUM
ejpam-5861	751	3	]	]	X
ejpam-5861	751	4	y.	y.	PROPN
ejpam-5861	751	5	zhang	zhang	PROPN
ejpam-5861	751	6	,	,	PUNCT
ejpam-5861	751	7	x.	x.	PROPN
ejpam-5861	751	8	yu	yu	PROPN
ejpam-5861	751	9	,	,	PUNCT
ejpam-5861	751	10	h.	h.	PROPN
ejpam-5861	751	11	sun	sun	PROPN
ejpam-5861	751	12	,	,	PUNCT
ejpam-5861	751	13	g.	g.	PROPN
ejpam-5861	751	14	r.	r.	PROPN
ejpam-5861	751	15	tick	tick	PROPN
ejpam-5861	751	16	,	,	PUNCT
ejpam-5861	751	17	w.	w.	PROPN
ejpam-5861	751	18	wei	wei	PROPN
ejpam-5861	751	19	,	,	PUNCT
ejpam-5861	751	20	and	and	CCONJ
ejpam-5861	751	21	b.	b.	PROPN
ejpam-5861	751	22	jin	jin	PROPN
ejpam-5861	751	23	.	.	PUNCT
ejpam-5861	752	1	applicability	applicability	NOUN
ejpam-5861	752	2	of	of	ADP
ejpam-5861	752	3	time	time	NOUN
ejpam-5861	752	4	fractional	fractional	ADJ
ejpam-5861	752	5	derivative	derivative	ADJ
ejpam-5861	752	6	models	model	NOUN
ejpam-5861	752	7	for	for	ADP
ejpam-5861	752	8	simulating	simulate	VERB
ejpam-5861	752	9	the	the	DET
ejpam-5861	752	10	dynamics	dynamic	NOUN
ejpam-5861	752	11	and	and	CCONJ
ejpam-5861	752	12	mitigation	mitigation	NOUN
ejpam-5861	752	13	scenarios	scenario	NOUN
ejpam-5861	752	14	of	of	ADP
ejpam-5861	752	15	covid-19	covid-19	PROPN
ejpam-5861	752	16	.	.	PUNCT
ejpam-5861	752	17	chaos	chaos	NOUN
ejpam-5861	752	18	,	,	PUNCT
ejpam-5861	752	19	solitons	soliton	NOUN
ejpam-5861	752	20	fractals	fractal	NOUN
ejpam-5861	752	21	,	,	PUNCT
ejpam-5861	752	22	138:109959	138:109959	NUM
ejpam-5861	752	23	,	,	PUNCT
ejpam-5861	752	24	2020	2020	NUM
ejpam-5861	752	25	.	.	PUNCT
ejpam-5861	753	1	[	[	X
ejpam-5861	753	2	47	47	NUM
ejpam-5861	753	3	]	]	PUNCT
ejpam-5861	753	4	s.	s.	PROPN
ejpam-5861	753	5	zhao	zhao	PROPN
ejpam-5861	753	6	,	,	PUNCT
ejpam-5861	753	7	q.	q.	PROPN
ejpam-5861	753	8	lin	lin	PROPN
ejpam-5861	753	9	,	,	PUNCT
ejpam-5861	753	10	j.	j.	PROPN
ejpam-5861	753	11	ran	run	VERB
ejpam-5861	753	12	,	,	PUNCT
ejpam-5861	753	13	s.	s.	PROPN
ejpam-5861	753	14	s.	s.	PROPN
ejpam-5861	753	15	musa	musa	PROPN
ejpam-5861	753	16	,	,	PUNCT
ejpam-5861	753	17	g.	g.	PROPN
ejpam-5861	753	18	yang	yang	PROPN
ejpam-5861	753	19	,	,	PUNCT
ejpam-5861	753	20	w.	w.	PROPN
ejpam-5861	753	21	wang	wang	PROPN
ejpam-5861	753	22	,	,	PUNCT
ejpam-5861	753	23	y.	y.	PROPN
ejpam-5861	753	24	lou	lou	PROPN
ejpam-5861	753	25	,	,	PUNCT
ejpam-5861	753	26	d.	d.	PROPN
ejpam-5861	753	27	gao	gao	PROPN
ejpam-5861	753	28	,	,	PUNCT
ejpam-5861	753	29	l.	l.	PROPN
ejpam-5861	753	30	yang	yang	PROPN
ejpam-5861	753	31	,	,	PUNCT
ejpam-5861	753	32	d.	d.	PROPN
ejpam-5861	753	33	he	he	PRON
ejpam-5861	753	34	,	,	PUNCT
ejpam-5861	753	35	and	and	CCONJ
ejpam-5861	753	36	m.	m.	PROPN
ejpam-5861	753	37	h.	h.	PROPN
ejpam-5861	753	38	wang	wang	PROPN
ejpam-5861	753	39	.	.	PUNCT
ejpam-5861	754	1	preliminary	preliminary	ADJ
ejpam-5861	754	2	estimation	estimation	NOUN
ejpam-5861	754	3	of	of	ADP
ejpam-5861	754	4	the	the	DET
ejpam-5861	754	5	basic	basic	ADJ
ejpam-5861	754	6	reproduction	reproduction	NOUN
ejpam-5861	754	7	number	number	NOUN
ejpam-5861	754	8	of	of	ADP
ejpam-5861	754	9	novel	novel	ADJ
ejpam-5861	754	10	coronavirus	coronavirus	NOUN
ejpam-5861	754	11	(	(	PUNCT
ejpam-5861	754	12	2019	2019	NUM
ejpam-5861	754	13	-	-	PUNCT
ejpam-5861	754	14	ncov	ncov	NOUN
ejpam-5861	754	15	)	)	PUNCT
ejpam-5861	754	16	in	in	ADP
ejpam-5861	754	17	china	china	PROPN
ejpam-5861	754	18	,	,	PUNCT
ejpam-5861	754	19	from	from	ADP
ejpam-5861	754	20	2019	2019	NUM
ejpam-5861	754	21	to	to	ADP
ejpam-5861	754	22	2020	2020	NUM
ejpam-5861	754	23	:	:	PUNCT
ejpam-5861	754	24	a	a	DET
ejpam-5861	754	25	data	data	NOUN
ejpam-5861	754	26	-	-	PUNCT
ejpam-5861	754	27	driven	drive	VERB
ejpam-5861	754	28	analysis	analysis	NOUN
ejpam-5861	754	29	in	in	ADP
ejpam-5861	754	30	the	the	DET
ejpam-5861	754	31	early	early	ADJ
ejpam-5861	754	32	phase	phase	NOUN
ejpam-5861	754	33	of	of	ADP
ejpam-5861	754	34	the	the	DET
ejpam-5861	754	35	outbreak	outbreak	NOUN
ejpam-5861	754	36	.	.	PUNCT
ejpam-5861	755	1	international	international	ADJ
ejpam-5861	755	2	journal	journal	NOUN
ejpam-5861	755	3	of	of	ADP
ejpam-5861	755	4	infectious	infectious	ADJ
ejpam-5861	755	5	diseases	disease	NOUN
ejpam-5861	755	6	,	,	PUNCT
ejpam-5861	755	7	92:214–217	92:214–217	NUM
ejpam-5861	755	8	,	,	PUNCT
ejpam-5861	755	9	2020	2020	NUM
ejpam-5861	755	10	.	.	PUNCT
ejpam-5861	756	1	[	[	X
ejpam-5861	756	2	48	48	NUM
ejpam-5861	756	3	]	]	PUNCT
ejpam-5861	756	4	y.	y.	PROPN
ejpam-5861	756	5	zhou	zhou	PROPN
ejpam-5861	756	6	.	.	PUNCT
ejpam-5861	757	1	basic	basic	ADJ
ejpam-5861	757	2	theory	theory	NOUN
ejpam-5861	757	3	of	of	ADP
ejpam-5861	757	4	fractional	fractional	ADJ
ejpam-5861	757	5	differential	differential	ADJ
ejpam-5861	757	6	equations	equation	NOUN
ejpam-5861	757	7	.	.	PUNCT
ejpam-5861	758	1	world	world	PROPN
ejpam-5861	758	2	scientific	scientific	PROPN
ejpam-5861	758	3	,	,	PUNCT
ejpam-5861	758	4	singapore	singapore	PROPN
ejpam-5861	758	5	,	,	PUNCT
ejpam-5861	758	6	2010	2010	NUM
ejpam-5861	758	7	.	.	PUNCT